LMFDB - Embedded newform 19.7.f.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,7,Mod(2,19)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.37102758878$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	19.3
Dual form			19.7.f.a.13.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.32193 - 8.72593i) q^{2} +(-9.97412 - 27.4037i) q^{3} +(-11.4178 - 64.7536i) q^{4} +(-5.58040 + 31.6480i) q^{5} +(-312.152 - 113.614i) q^{6} +(-45.3132 - 78.4847i) q^{7} +(-17.2882 - 9.98136i) q^{8} +(-93.0319 + 78.0631i) q^{9} +O(q^{10})$	\(q+(7.32193 - 8.72593i) q^{2} +(-9.97412 - 27.4037i) q^{3} +(-11.4178 - 64.7536i) q^{4} +(-5.58040 + 31.6480i) q^{5} +(-312.152 - 113.614i) q^{6} +(-45.3132 - 78.4847i) q^{7} +(-17.2882 - 9.98136i) q^{8} +(-93.0319 + 78.0631i) q^{9} +(235.299 + 280.419i) q^{10} +(124.307 - 215.306i) q^{11} +(-1660.60 + 958.750i) q^{12} +(873.915 - 2401.06i) q^{13} +(-1016.63 - 179.260i) q^{14} +(922.932 - 162.738i) q^{15} +(3740.70 - 1361.50i) q^{16} +(2991.23 + 2509.94i) q^{17} +1383.36i q^{18} +(-812.577 + 6810.70i) q^{19} +2113.04 q^{20} +(-1698.81 + 2024.56i) q^{21} +(-968.579 - 2661.15i) q^{22} +(2402.77 + 13626.8i) q^{23} +(-101.091 + 573.316i) q^{24} +(13712.2 + 4990.85i) q^{25} +(-14552.8 - 25206.1i) q^{26} +(-15344.0 - 8858.88i) q^{27} +(-4564.79 + 3830.31i) q^{28} +(-18852.1 - 22467.1i) q^{29} +(5337.60 - 9245.00i) q^{30} +(-27056.5 + 15621.1i) q^{31} +(15945.7 - 43810.5i) q^{32} +(-7140.03 - 1258.98i) q^{33} +(43803.2 - 7723.68i) q^{34} +(2736.75 - 996.096i) q^{35} +(6117.08 + 5132.84i) q^{36} +44085.6i q^{37} +(53480.1 + 56957.9i) q^{38} -74514.5 q^{39} +(412.366 - 491.438i) q^{40} +(35.5838 + 97.7657i) q^{41} +(5227.64 + 29647.4i) q^{42} +(-20232.0 + 114742. i) q^{43} +(-15361.2 - 5591.00i) q^{44} +(-1951.39 - 3379.90i) q^{45} +(136499. + 78807.8i) q^{46} +(48012.0 - 40286.9i) q^{47} +(-74620.4 - 88929.1i) q^{48} +(54717.9 - 94774.2i) q^{49} +(143950. - 83109.5i) q^{50} +(38946.7 - 107005. i) q^{51} +(-165456. - 29174.3i) q^{52} +(58714.0 - 10352.9i) q^{53} +(-189650. + 69026.9i) q^{54} +(6120.33 + 5135.57i) q^{55} +1809.15i q^{56} +(194743. - 45663.1i) q^{57} -334080. q^{58} +(-130219. + 155189. i) q^{59} +(-21075.7 - 57905.0i) q^{60} +(13673.9 + 77548.4i) q^{61} +(-61797.3 + 350470. i) q^{62} +(10342.3 + 3764.30i) q^{63} +(-138149. - 239282. i) q^{64} +(71112.1 + 41056.6i) q^{65} +(-63264.6 + 53085.3i) q^{66} +(-165255. - 196943. i) q^{67} +(128374. - 222351. i) q^{68} +(349458. - 201760. i) q^{69} +(11346.4 - 31174.1i) q^{70} +(447787. + 78956.9i) q^{71} +(2387.53 - 420.986i) q^{72} +(-331555. + 120676. i) q^{73} +(384688. + 322791. i) q^{74} -425545. i q^{75} +(450295. - 25145.9i) q^{76} -22531.0 q^{77} +(-545590. + 650208. i) q^{78} +(-273242. - 750725. i) q^{79} +(22214.3 + 125983. i) q^{80} +(-105096. + 596031. i) q^{81} +(1113.64 + 405.332i) q^{82} +(-110677. - 191698. i) q^{83} +(150494. + 86888.0i) q^{84} +(-96127.0 + 80660.2i) q^{85} +(853090. + 1.01667e6i) q^{86} +(-427647. + 740707. i) q^{87} +(-4298.09 + 2481.51i) q^{88} +(436029. - 1.19798e6i) q^{89} +(-43780.7 - 7719.72i) q^{90} +(-228047. + 40210.8i) q^{91} +(854948. - 311176. i) q^{92} +(697941. + 585642. i) q^{93} -713928. i q^{94} +(-211011. - 63722.9i) q^{95} -1.35961e6 q^{96} +(-1.00116e6 + 1.19313e6i) q^{97} +(-426353. - 1.17140e6i) q^{98} +(5242.93 + 29734.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9}+O(q^{10}) $ 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} - 1689 q^{10} + 1677 q^{11} - 9 q^{12} - 10506 q^{13} + 6105 q^{14} + 24138 q^{15} + 23760 q^{16} - 3438 q^{17} - 30918 q^{19} - 76650 q^{20} - 59055 q^{21} + 20490 q^{22} + 42498 q^{23} + 31848 q^{24} + 7914 q^{25} + 109989 q^{26} + 124821 q^{27} - 109476 q^{28} - 27726 q^{29} - 153516 q^{30} - 30789 q^{31} - 114375 q^{32} + 126039 q^{33} + 359796 q^{34} + 160161 q^{35} + 184995 q^{36} - 245244 q^{38} - 390564 q^{39} - 372678 q^{40} - 24708 q^{41} - 244893 q^{42} - 30726 q^{43} - 301419 q^{44} + 293037 q^{45} + 69246 q^{46} - 71454 q^{47} + 1024041 q^{48} - 350346 q^{49} - 104148 q^{50} - 180672 q^{51} + 921801 q^{52} + 822558 q^{53} + 308469 q^{54} + 623517 q^{55} - 17862 q^{57} - 1150644 q^{58} - 463812 q^{59} - 908130 q^{60} - 583698 q^{61} - 429732 q^{62} - 2576043 q^{63} - 328293 q^{64} - 1056789 q^{65} - 1038756 q^{66} + 1120464 q^{67} + 717270 q^{68} + 3771567 q^{69} + 4845345 q^{70} + 94494 q^{71} + 2351634 q^{72} + 950850 q^{73} + 55149 q^{74} - 218814 q^{76} - 343086 q^{77} + 1833471 q^{78} - 4936494 q^{79} - 9642039 q^{80} - 769551 q^{81} - 8627793 q^{82} - 412131 q^{83} - 3125205 q^{84} - 896910 q^{85} + 8878236 q^{86} + 610737 q^{87} + 13604751 q^{88} + 6653022 q^{89} + 3142734 q^{90} + 3409821 q^{91} - 3043740 q^{92} - 816393 q^{93} + 4839186 q^{95} - 5667138 q^{96} - 853656 q^{97} - 17679315 q^{98} - 13991937 q^{99}+O(q^{100}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9 - 1689 * q^10 + 1677 * q^11 - 9 * q^12 - 10506 * q^13 + 6105 * q^14 + 24138 * q^15 + 23760 * q^16 - 3438 * q^17 - 30918 * q^19 - 76650 * q^20 - 59055 * q^21 + 20490 * q^22 + 42498 * q^23 + 31848 * q^24 + 7914 * q^25 + 109989 * q^26 + 124821 * q^27 - 109476 * q^28 - 27726 * q^29 - 153516 * q^30 - 30789 * q^31 - 114375 * q^32 + 126039 * q^33 + 359796 * q^34 + 160161 * q^35 + 184995 * q^36 - 245244 * q^38 - 390564 * q^39 - 372678 * q^40 - 24708 * q^41 - 244893 * q^42 - 30726 * q^43 - 301419 * q^44 + 293037 * q^45 + 69246 * q^46 - 71454 * q^47 + 1024041 * q^48 - 350346 * q^49 - 104148 * q^50 - 180672 * q^51 + 921801 * q^52 + 822558 * q^53 + 308469 * q^54 + 623517 * q^55 - 17862 * q^57 - 1150644 * q^58 - 463812 * q^59 - 908130 * q^60 - 583698 * q^61 - 429732 * q^62 - 2576043 * q^63 - 328293 * q^64 - 1056789 * q^65 - 1038756 * q^66 + 1120464 * q^67 + 717270 * q^68 + 3771567 * q^69 + 4845345 * q^70 + 94494 * q^71 + 2351634 * q^72 + 950850 * q^73 + 55149 * q^74 - 218814 * q^76 - 343086 * q^77 + 1833471 * q^78 - 4936494 * q^79 - 9642039 * q^80 - 769551 * q^81 - 8627793 * q^82 - 412131 * q^83 - 3125205 * q^84 - 896910 * q^85 + 8878236 * q^86 + 610737 * q^87 + 13604751 * q^88 + 6653022 * q^89 + 3142734 * q^90 + 3409821 * q^91 - 3043740 * q^92 - 816393 * q^93 + 4839186 * q^95 - 5667138 * q^96 - 853656 * q^97 - 17679315 * q^98 - 13991937 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	7.32193	−	8.72593i	0.915241	−	1.09074i	−0.0803338	−	0.996768i	$-0.525599\pi$
$2$	7.32193	−	8.72593i	0.915241	−	1.09074i	0.995575	−	0.0939736i	$-0.0299569\pi$
$3$	−9.97412	−	27.4037i	−0.369412	−	1.01495i	−0.975586	−	0.219619i	$-0.929519\pi$
$3$	−9.97412	−	27.4037i	−0.369412	−	1.01495i	0.606174	−	0.795332i	$-0.292704\pi$
$4$	−11.4178	−	64.7536i	−0.178403	−	1.01177i
$5$	−5.58040	+	31.6480i	−0.0446432	+	0.253184i	−0.998959	−	0.0456154i	$-0.985475\pi$
$5$	−5.58040	+	31.6480i	−0.0446432	+	0.253184i	0.954316	+	0.298800i	$0.0965862\pi$
$6$	−312.152	−	113.614i	−1.44515	−	0.525992i
$7$	−45.3132	−	78.4847i	−0.132108	−	0.228818i	0.792381	−	0.610027i	$-0.208841\pi$
$7$	−45.3132	−	78.4847i	−0.132108	−	0.228818i	−0.924489	+	0.381208i	$0.875508\pi$
$8$	−17.2882	−	9.98136i	−0.0337661	−	0.0194948i
$9$	−93.0319	+	78.0631i	−0.127616	+	0.107082i
$10$	235.299	+	280.419i	0.235299	+	0.280419i
$11$	124.307	−	215.306i	0.0933937	−	0.161763i	−0.815543	−	0.578696i	$-0.803562\pi$
$11$	124.307	−	215.306i	0.0933937	−	0.161763i	0.908937	+	0.416933i	$0.136895\pi$
$12$	−1660.60	+	958.750i	−0.960998	+	0.554832i
$13$	873.915	−	2401.06i	0.397777	−	1.09288i	−0.565588	−	0.824688i	$-0.691351\pi$
$13$	873.915	−	2401.06i	0.397777	−	1.09288i	0.963365	−	0.268194i	$-0.0864270\pi$
$14$	−1016.63	−	179.260i	−0.370493	−	0.0653279i
$15$	922.932	−	162.738i	0.273461	−	0.0482186i
$16$	3740.70	−	1361.50i	0.913256	−	0.332398i
$17$	2991.23	+	2509.94i	0.608841	+	0.510878i	0.894274	−	0.447521i	$-0.147693\pi$
$17$	2991.23	+	2509.94i	0.608841	+	0.510878i	−0.285433	+	0.958399i	$0.592137\pi$
$18$			1383.36i			0.237202i
$19$	−812.577	+	6810.70i	−0.118469	+	0.992958i
$19$	−812.577	+	6810.70i	−0.118469	+	0.992958i
$20$	2113.04			0.264130
$21$	−1698.81	+	2024.56i	−0.183437	+	0.218612i
$22$	−968.579	−	2661.15i	−0.0909635	−	0.249920i
$23$	2402.77	+	13626.8i	0.197482	+	1.11998i	0.908839	+	0.417147i	$0.136970\pi$
$23$	2402.77	+	13626.8i	0.197482	+	1.11998i	−0.711357	+	0.702831i	$0.751919\pi$
$24$	−101.091	+	573.316i	−0.00731272	+	0.0414725i
$25$	13712.2	+	4990.85i	0.877583	+	0.319414i
$26$	−14552.8	−	25206.1i	−0.827991	−	1.43412i
$27$	−15344.0	−	8858.88i	−0.779558	−	0.450078i
$28$	−4564.79	+	3830.31i	−0.207944	+	0.174486i
$29$	−18852.1	−	22467.1i	−0.772977	−	0.921198i	0.225617	−	0.974216i	$-0.427560\pi$
$29$	−18852.1	−	22467.1i	−0.772977	−	0.921198i	−0.998594	+	0.0530185i	$0.983116\pi$
$30$	5337.60	−	9245.00i	0.197689	−	0.342407i
$31$	−27056.5	+	15621.1i	−0.908211	+	0.524356i	−0.879855	−	0.475242i	$-0.842361\pi$
$31$	−27056.5	+	15621.1i	−0.908211	+	0.524356i	−0.0283562	+	0.999598i	$0.509027\pi$
$32$	15945.7	−	43810.5i	0.486624	−	1.33699i
$33$	−7140.03	−	1258.98i	−0.198682	−	0.0350330i
$34$	43803.2	−	7723.68i	1.11447	−	0.196511i
$35$	2736.75	−	996.096i	0.0638310	−	0.0232326i
$36$	6117.08	+	5132.84i	0.131110	+	0.110015i
$37$			44085.6i			0.870345i	0.900347	+	0.435172i	$0.143313\pi$
$37$			44085.6i			0.870345i	−0.900347	+	0.435172i	$0.856687\pi$
$38$	53480.1	+	56957.9i	0.974633	+	1.03801i
$39$	−74514.5			−1.25617
$40$	412.366	−	491.438i	0.00644321	−	0.00767872i
$41$	35.5838	+	97.7657i	0.000516299	+	0.00141852i	0.939951	−	0.341311i	$-0.110871\pi$
$41$	35.5838	+	97.7657i	0.000516299	+	0.00141852i	−0.939434	+	0.342729i	$0.888649\pi$
$42$	5227.64	+	29647.4i	0.0705599	+	0.400165i
$43$	−20232.0	+	114742.i	−0.254469	+	1.44316i	0.542964	+	0.839756i	$0.317302\pi$
$43$	−20232.0	+	114742.i	−0.254469	+	1.44316i	−0.797433	+	0.603408i	$0.793809\pi$
$44$	−15361.2	−	5591.00i	−0.180329	−	0.0656344i
$45$	−1951.39	−	3379.90i	−0.0214144	−	0.0370908i
$46$	136499.	+	78807.8i	1.40235	+	0.809647i
$47$	48012.0	−	40286.9i	0.462441	−	0.388034i	−0.381587	−	0.924333i	$-0.624622\pi$
$47$	48012.0	−	40286.9i	0.462441	−	0.388034i	0.844028	+	0.536299i	$0.180178\pi$
$48$	−74620.4	−	88929.1i	−0.674736	−	0.804119i
$49$	54717.9	−	94774.2i	0.465095	−	0.805568i
$50$	143950.	−	83109.5i	1.15160	−	0.664876i
$51$	38946.7	−	107005.i	0.293603	−	0.806668i
$52$	−165456.	−	29174.3i	−1.17672	−	0.207487i
$53$	58714.0	−	10352.9i	0.394379	−	0.0695397i	0.0270579	−	0.999634i	$-0.491386\pi$
$53$	58714.0	−	10352.9i	0.394379	−	0.0695397i	0.367321	+	0.930094i	$0.380275\pi$
$54$	−189650.	+	69026.9i	−1.20440	+	0.438366i
$55$	6120.33	+	5135.57i	0.0367863	+	0.0308674i
$56$			1809.15i			0.0103017i
$57$	194743.	−	45663.1i	1.05157	−	0.246571i
$58$	−334080.			−1.71225
$59$	−130219.	+	155189.i	−0.634043	+	0.755623i	−0.983417	−	0.181361i	$-0.941950\pi$
$59$	−130219.	+	155189.i	−0.634043	+	0.755623i	0.349374	+	0.936983i	$0.386394\pi$
$60$	−21075.7	−	57905.0i	−0.0975727	−	0.268079i
$61$	13673.9	+	77548.4i	0.0602424	+	0.341651i	1.00000		0.000190118i	$-6.05164e-5\pi$
$61$	13673.9	+	77548.4i	0.0602424	+	0.341651i	−0.939758	+	0.341841i	$0.888949\pi$
$62$	−61797.3	+	350470.i	−0.259295	+	1.47054i
$63$	10342.3	+	3764.30i	0.0413615	+	0.0150544i
$64$	−138149.	−	239282.i	−0.526998	−	0.912787i
$65$	71112.1	+	41056.6i	0.258943	+	0.149501i
$66$	−63264.6	+	53085.3i	−0.220054	+	0.184647i
$67$	−165255.	−	196943.i	−0.549451	−	0.654810i	0.417828	−	0.908526i	$-0.362792\pi$
$67$	−165255.	−	196943.i	−0.549451	−	0.654810i	−0.967279	+	0.253716i	$0.918347\pi$
$68$	128374.	−	222351.i	0.408274	−	0.707152i
$69$	349458.	−	201760.i	1.06377	−	0.614168i
$70$	11346.4	−	31174.1i	0.0330800	−	0.0908865i
$71$	447787.	+	78956.9i	1.25111	+	0.220605i	0.759672	−	0.650306i	$-0.225359\pi$
$71$	447787.	+	78956.9i	1.25111	+	0.220605i	0.491441	+	0.870911i	$0.336470\pi$
$72$	2387.53	−	420.986i	0.00639664	−	0.00112790i
$73$	−331555.	+	120676.i	−0.852290	+	0.310208i	−0.730974	−	0.682406i	$-0.760934\pi$
$73$	−331555.	+	120676.i	−0.852290	+	0.310208i	−0.121316	+	0.992614i	$0.538712\pi$
$74$	384688.	+	322791.i	0.949321	+	0.796575i
$75$		−	425545.i		−	1.00870i
$76$	450295.	−	25145.9i	1.02578	−	0.0572832i
$77$	−22531.0			−0.0493524
$78$	−545590.	+	650208.i	−1.14969	+	1.37015i
$79$	−273242.	−	750725.i	−0.554199	−	1.52265i	−0.827924	−	0.560841i	$-0.810478\pi$
$79$	−273242.	−	750725.i	−0.554199	−	1.52265i	0.273725	−	0.961808i	$-0.411744\pi$
$80$	22214.3	+	125983.i	0.0433873	+	0.246061i
$81$	−105096.	+	596031.i	−0.197757	+	1.12154i
$82$	1113.64	+	405.332i	0.00201978	+	0.000735138i
$83$	−110677.	−	191698.i	−0.193563	−	0.335261i	0.752865	−	0.658175i	$-0.228671\pi$
$83$	−110677.	−	191698.i	−0.193563	−	0.335261i	−0.946429	+	0.322913i	$0.895338\pi$
$84$	150494.	+	86888.0i	0.253912	+	0.146596i
$85$	−96127.0	+	80660.2i	−0.156527	+	0.131342i
$86$	853090.	+	1.01667e6i	1.34122	+	1.59840i
$87$	−427647.	+	740707.i	−0.649424	+	1.12483i
$88$	−4298.09	+	2481.51i	−0.00630707	+	0.00364139i
$89$	436029.	−	1.19798e6i	0.618508	−	1.69934i	−0.0921016	−	0.995750i	$-0.529358\pi$
$89$	436029.	−	1.19798e6i	0.618508	−	1.69934i	0.710609	−	0.703587i	$-0.248419\pi$
$90$	−43780.7	−	7719.72i	−0.0600558	−	0.0105895i
$91$	−228047.	+	40210.8i	−0.302621	+	0.0533603i
$92$	854948.	−	311176.i	1.09793	−	0.399615i
$93$	697941.	+	585642.i	0.867700	+	0.728087i
$94$		−	713928.i		−	0.859549i
$95$	−211011.	−	63722.9i	−0.246112	−	0.0743232i
$96$	−1.35961e6			−1.53674
$97$	−1.00116e6	+	1.19313e6i	−1.09695	+	1.30729i	−0.149013	+	0.988835i	$0.547610\pi$
$97$	−1.00116e6	+	1.19313e6i	−1.09695	+	1.30729i	−0.947937	+	0.318459i	$0.896835\pi$
$98$	−426353.	−	1.17140e6i	−0.452993	−	1.24459i
$99$	5242.93	+	29734.1i	0.00540342	+	0.0306443i
$100$	166612.	−	944901.i	0.166612	−	0.944901i
$101$	−225523.	−	82083.7i	−0.218891	−	0.0796697i	0.230247	−	0.973132i	$-0.426047\pi$
$101$	−225523.	−	82083.7i	−0.218891	−	0.0796697i	−0.449138	+	0.893463i	$0.648269\pi$
$102$	−648556.	−	1.12333e6i	−0.611149	−	1.05854i
$103$	−602565.	−	347891.i	−0.551432	−	0.318370i	0.198267	−	0.980148i	$-0.436469\pi$
$103$	−602565.	−	347891.i	−0.551432	−	0.318370i	−0.749699	+	0.661778i	$0.769802\pi$
$104$	−39074.3	+	32787.2i	−0.0347369	+	0.0291477i
$105$	−54593.4	−	65061.9i	−0.0471598	−	0.0562029i
$106$	339561.	−	588137.i	0.285102	−	0.493811i
$107$	−80637.3	+	46556.0i	−0.0658240	+	0.0380035i	−0.532551	−	0.846398i	$-0.678766\pi$
$107$	−80637.3	+	46556.0i	−0.0658240	+	0.0380035i	0.466727	+	0.884402i	$0.345433\pi$
$108$	−398449.	+	1.09473e6i	−0.316302	+	0.869032i
$109$	1.32388e6	+	233436.i	1.02228	+	0.180255i	0.659567	−	0.751646i	$-0.270740\pi$
$109$	1.32388e6	+	233436.i	1.02228	+	0.180255i	0.362712	+	0.931901i	$0.381851\pi$
$110$	89625.2	−	15803.3i	0.0673367	−	0.0118733i
$111$	1.20811e6	−	439715.i	0.883357	−	0.321516i
$112$	−276360.	−	231894.i	−0.196708	−	0.165057i
$113$			637105.i			0.441546i	0.975325	+	0.220773i	$0.0708580\pi$
$113$			637105.i			0.441546i	−0.975325	+	0.220773i	$0.929142\pi$
$114$	1.02744e6	−	2.03366e6i	0.693493	−	1.37266i
$115$	−444669.			−0.292377
$116$	−1.23957e6	+	1.47727e6i	−0.794143	+	0.946423i
$117$	106132.	+	291596.i	0.0662659	+	0.182064i
$118$	400715.	+	2.27257e6i	0.243887	+	1.38315i
$119$	61449.9	−	348500.i	0.0364653	−	0.206805i
$120$	−17580.2	−	6398.67i	−0.0101737	−	0.00370293i
$121$	854876.	+	1.48069e6i	0.482555	+	0.835810i
$122$	776801.	+	448486.i	0.427790	+	0.246984i
$123$	2324.22	−	1950.25i	0.00124900	−	0.00104804i
$124$	1.32045e6	+	1.57365e6i	0.692558	+	0.825359i
$125$	−485535.	+	840971.i	−0.248594	+	0.430577i
$126$	108573.	−	62684.6i	0.0542762	−	0.0313364i
$127$	−794711.	+	2.18345e6i	−0.387970	+	1.06594i	0.579944	+	0.814656i	$0.303074\pi$
$127$	−794711.	+	2.18345e6i	−0.387970	+	1.06594i	−0.967914	+	0.251282i	$0.919148\pi$
$128$	−160990.	−	28386.8i	−0.0767659	−	0.0135359i
$129$	3.34614e6	−	590015.i	1.55874	−	0.274849i
$130$	878935.	−	319906.i	0.400061	−	0.145610i
$131$	−2.98775e6	−	2.50702e6i	−1.32902	−	1.11518i	−0.984306	−	0.176471i	$-0.943532\pi$
$131$	−2.98775e6	−	2.50702e6i	−1.32902	−	1.11518i	−0.344713	−	0.938708i	$-0.612024\pi$
$132$			476717.i			0.207271i
$133$	571356.	−	244839.i	0.242858	−	0.104070i
$134$	−2.92849e6			−1.21711
$135$	365992.	−	436172.i	0.148755	−	0.177279i
$136$	−26660.5	−	73249.0i	−0.0105987	−	0.0291196i
$137$	95273.1	+	540320.i	0.0370517	+	0.210131i	0.997713	−	0.0675917i	$-0.0215315\pi$
$137$	95273.1	+	540320.i	0.0370517	+	0.210131i	−0.960661	+	0.277723i	$0.910420\pi$
$138$	798165.	−	4.52662e6i	0.303707	−	1.72241i
$139$	−2.15114e6	−	782950.i	−0.800984	−	0.291534i	−0.0910898	−	0.995843i	$-0.529035\pi$
$139$	−2.15114e6	−	782950.i	−0.800984	−	0.291534i	−0.709894	+	0.704308i	$0.751257\pi$
$140$	−95748.5	−	165841.i	−0.0348938	−	0.0604378i
$141$	−1.58289e6	−	913880.i	−0.564667	−	0.326011i
$142$	3.96764e6	−	3.32924e6i	1.38569	−	1.16273i
$143$	−408330.	−	486628.i	−0.139638	−	0.166414i
$144$	−241721.	+	418674.i	−0.0809520	+	0.140213i
$145$	816241.	−	471257.i	0.267741	−	0.154580i
$146$	−1.37461e6	+	3.77671e6i	−0.441694	+	1.21354i
$147$	−3.14293e6	−	554183.i	−0.989423	−	0.174462i
$148$	2.85470e6	−	503360.i	0.880593	−	0.155272i
$149$	2.42353e6	−	882094.i	0.732639	−	0.266659i	0.0513577	−	0.998680i	$-0.483645\pi$
$149$	2.42353e6	−	882094.i	0.732639	−	0.266659i	0.681282	+	0.732021i	$0.261423\pi$
$150$	−3.71328e6	−	3.11581e6i	−1.10023	−	0.923203i
$151$			5.96088e6i			1.73133i	0.500626	+	0.865664i	$0.333103\pi$
$151$			5.96088e6i			1.73133i	−0.500626	+	0.865664i	$0.666897\pi$
$152$	82028.0	−	109634.i	0.0233578	−	0.0312187i
$153$	−474214.			−0.132404
$154$	−164970.	+	196604.i	−0.0451693	+	0.0538307i
$155$	−343391.	−	943458.i	−0.0922132	−	0.253354i
$156$	850792.	+	4.82508e6i	0.224104	+	1.27096i
$157$	265002.	−	1.50290e6i	0.0684780	−	0.388358i	−0.931235	−	0.364418i	$-0.881268\pi$
$157$	265002.	−	1.50290e6i	0.0684780	−	0.388358i	0.999713	−	0.0239397i	$-0.00762097\pi$
$158$	−8.55143e6	−	3.11247e6i	−2.16804	−	0.789103i
$159$	−869327.	−	1.50572e6i	−0.216268	−	0.374587i
$160$	1.29753e6	+	749130.i	0.316780	+	0.182893i
$161$	960616.	−	806053.i	0.230183	−	0.193146i
$162$	4.43142e6	+	5.28116e6i	1.04231	+	1.24218i
$163$	−1.39572e6	+	2.41745e6i	−0.322281	+	0.558207i	−0.980958	−	0.194219i	$-0.937783\pi$
$163$	−1.39572e6	+	2.41745e6i	−0.322281	+	0.558207i	0.658677	+	0.752426i	$0.271116\pi$
$164$	5924.39	−	3420.45i	0.00134311	−	0.000775446i
$165$	79688.5	−	218942.i	0.0177396	−	0.0487391i
$166$	−2.48311e6	−	437840.i	−0.542840	−	0.0957174i
$167$	3.64099e6	−	642005.i	0.781754	−	0.137844i	0.231492	−	0.972837i	$-0.425639\pi$
$167$	3.64099e6	−	642005.i	0.781754	−	0.137844i	0.550261	+	0.834992i	$0.314528\pi$
$168$	49577.3	−	18044.7i	0.0104557	−	0.00380558i
$169$	−1.30382e6	−	1.09404e6i	−0.270121	−	0.226659i
$170$			1.42939e6i			0.290939i
$171$	−456068.	−	697045.i	−0.0912098	−	0.139403i
$172$	7.66094e6			1.50555
$173$	1.94415e6	−	2.31695e6i	0.375485	−	0.447485i	−0.544899	−	0.838502i	$-0.683432\pi$
$173$	1.94415e6	−	2.31695e6i	0.375485	−	0.447485i	0.920384	+	0.391017i	$0.127876\pi$
$174$	3.33216e6	+	9.15503e6i	0.632525	+	1.73785i
$175$	−229640.	−	1.30235e6i	−0.0428483	−	0.243005i
$176$	171855.	−	974639.i	0.0315228	−	0.178775i
$177$	5.55157e6	+	2.02061e6i	1.00114	+	0.364386i
$178$	−7.26092e6	−	1.25763e7i	−1.28745	−	2.22993i
$179$	−7.32338e6	−	4.22815e6i	−1.27689	−	0.737211i	−0.300612	−	0.953747i	$-0.597191\pi$
$179$	−7.32338e6	−	4.22815e6i	−1.27689	−	0.737211i	−0.976275	+	0.216536i	$0.930524\pi$
$180$	−196580.	+	164950.i	−0.0337072	+	0.0282837i
$181$	5.50309e6	+	6.55832e6i	0.928048	+	1.10600i	0.994130	+	0.108191i	$0.0345057\pi$
$181$	5.50309e6	+	6.55832e6i	0.928048	+	1.10600i	−0.0660820	+	0.997814i	$0.521050\pi$
$182$	−1.31886e6	+	2.28434e6i	−0.218769	+	0.378919i
$183$	1.98873e6	−	1.14819e6i	0.324505	−	0.187353i
$184$	94474.1	−	259566.i	0.0151656	−	0.0416671i
$185$	−1.39522e6	−	246015.i	−0.220358	−	0.0388550i
$186$	1.02205e7	−	1.80216e6i	1.58831	−	0.280062i
$187$	912237.	−	332027.i	0.139503	−	0.0507749i
$188$	−3.15691e6	−	2.64896e6i	−0.475104	−	0.398660i
$189$			1.60570e6i			0.237836i
$190$	−2.10105e6	+	1.37469e6i	−0.306320	+	0.200421i
$191$	1.17957e7			1.69287			0.846437	−	0.532489i	$-0.178743\pi$
$191$	1.17957e7			1.69287			0.846437	+	0.532489i	$0.178743\pi$
$192$	−5.17928e6	+	6.17242e6i	−0.731755	+	0.872071i
$193$	−2.97498e6	−	8.17370e6i	−0.413821	−	1.13696i	−0.955142	−	0.296148i	$-0.904298\pi$
$193$	−2.97498e6	−	8.17370e6i	−0.413821	−	1.13696i	0.541321	−	0.840816i	$-0.317924\pi$
$194$	3.08079e6	+	1.74721e7i	0.421947	+	2.39298i
$195$	415821.	−	2.35824e6i	0.0560793	−	0.318041i
$196$	−6.76173e6	−	2.46107e6i	−0.898028	−	0.326855i
$197$	−2.01424e6	−	3.48876e6i	−0.263458	−	0.456323i	0.703700	−	0.710497i	$-0.251530\pi$
$197$	−2.01424e6	−	3.48876e6i	−0.263458	−	0.456323i	−0.967159	+	0.254174i	$0.918196\pi$
$198$	297846.	+	171962.i	0.0383704	+	0.0221532i
$199$	−5.20023e6	+	4.36351e6i	−0.659878	+	0.553703i	−0.910050	−	0.414498i	$-0.863957\pi$
$199$	−5.20023e6	+	4.36351e6i	−0.659878	+	0.553703i	0.250172	+	0.968201i	$0.419513\pi$
$200$	−187245.	−	223150.i	−0.0234056	−	0.0278937i
$201$	−3.74869e6	+	6.49291e6i	−0.461627	+	0.799561i
$202$	−2.36752e6	+	1.36689e6i	−0.287237	+	0.165836i
$203$	−909073.	+	2.49766e6i	−0.108670	+	0.298569i
$204$	−7.37366e6	−	1.30018e6i	−0.868546	−	0.153148i
$205$	−3292.66	+	580.586i	−0.000382196	+	6.73914e-5i
$206$	−7.44761e6	+	2.71071e6i	−0.851952	+	0.310085i
$207$	−1.28728e6	−	1.08016e6i	−0.145132	−	0.121780i
$208$		−	1.01715e7i		−	1.13030i
$209$	1.36538e6	+	1.02157e6i	0.149559	+	0.111900i
$210$	−967454.			−0.104465
$211$	6.78025e6	−	8.08039e6i	0.721770	−	0.860172i	−0.273032	−	0.962005i	$-0.588026\pi$
$211$	6.78025e6	−	8.08039e6i	0.721770	−	0.860172i	0.994801	+	0.101833i	$0.0324709\pi$
$212$	−1.34077e6	−	3.68373e6i	−0.140717	−	0.386617i
$213$	−2.30257e6	−	1.30585e7i	−0.238273	−	1.35131i
$214$	−184176.	+	1.04451e6i	−0.0187928	+	0.106579i
$215$	−3.51844e6	−	1.28061e6i	−0.354026	−	0.128855i
$216$	176847.	+	306309.i	0.0175484	+	0.0303947i
$217$	2.45203e6	+	1.41568e6i	0.239965	+	0.138544i
$218$	1.17303e7	−	9.84289e6i	1.13224	−	0.950064i
$219$	6.61395e6	+	7.88219e6i	0.629692	+	0.750438i
$220$	262666.	−	454950.i	0.0246681	−	0.0427263i
$221$	8.64062e6	−	4.98866e6i	0.800512	−	0.462176i
$222$	5.00875e6	−	1.37614e7i	0.457794	−	1.25778i
$223$	784167.	+	138270.i	0.0707121	+	0.0124685i	0.208892	−	0.977939i	$-0.433014\pi$
$223$	784167.	+	138270.i	0.0707121	+	0.0124685i	−0.138180	+	0.990407i	$0.544125\pi$
$224$	−4.16100e6	+	733697.i	−0.370215	+	0.0652789i
$225$	−1.66528e6	+	606111.i	−0.146197	+	0.0532114i
$226$	5.55934e6	+	4.66484e6i	0.481613	+	0.404121i
$227$			4.06849e6i			0.347821i	0.984762	+	0.173910i	$0.0556403\pi$
$227$			4.06849e6i			0.347821i	−0.984762	+	0.173910i	$0.944360\pi$
$228$	−5.18039e6	−	1.20889e7i	−0.437077	−	1.01996i
$229$	−1.69119e7			−1.40827			−0.704137	−	0.710064i	$-0.748666\pi$
$229$	−1.69119e7			−1.40827			−0.704137	+	0.710064i	$0.748666\pi$
$230$	−3.25583e6	+	3.88015e6i	−0.267595	+	0.318908i
$231$	224727.	+	617432.i	0.0182314	+	0.0500902i
$232$	101668.	+	576586.i	0.00814177	+	0.0461743i
$233$	−2.98555e6	+	1.69319e7i	−0.236024	+	1.33856i	0.604421	+	0.796665i	$0.293405\pi$
$233$	−2.98555e6	+	1.69319e7i	−0.236024	+	1.33856i	−0.840445	+	0.541896i	$0.817707\pi$
$234$	3.32154e6	+	1.20894e6i	0.259234	+	0.0943535i
$235$	1.00707e6	+	1.74430e6i	0.0775993	+	0.134406i
$236$	1.15359e7	+	6.66023e6i	0.877635	+	0.506703i
$237$	−1.78473e7	+	1.49757e7i	−1.34069	+	1.12497i
$238$	−2.59105e6	−	3.08790e6i	−0.192196	−	0.229051i
$239$	−2.96315e6	+	5.13232e6i	−0.217050	+	0.375941i	−0.953905	−	0.300110i	$-0.902977\pi$
$239$	−2.96315e6	+	5.13232e6i	−0.217050	+	0.375941i	0.736855	+	0.676051i	$0.236310\pi$
$240$	3.23084e6	−	1.86533e6i	0.233712	−	0.134934i
$241$	−6.89097e6	+	1.89328e7i	−0.492300	+	1.35258i	0.406271	+	0.913753i	$0.366829\pi$
$241$	−6.89097e6	+	1.89328e7i	−0.492300	+	1.35258i	−0.898570	+	0.438829i	$0.855393\pi$
$242$	1.91797e7	+	3.38190e6i	1.35331	+	0.238625i
$243$	4.66165e6	−	821975.i	0.324878	−	0.0572848i
$244$	4.86541e6	−	1.77086e6i	0.334927	−	0.121903i
$245$	2.69407e6	+	2.26059e6i	0.183194	+	0.153718i
$246$		−	34560.6i		−	0.00232154i
$247$	1.56428e7	+	7.90302e6i	1.03806	+	0.524448i
$248$	623679.			0.0408890
$249$	−4.14933e6	+	4.94497e6i	−0.268769	+	0.320307i
$250$	3.78320e6	+	1.03943e7i	0.242125	+	0.665233i
$251$	−1.87130e6	−	1.06127e7i	−0.118338	−	0.671126i	−0.985043	−	0.172306i	$-0.944878\pi$
$251$	−1.87130e6	−	1.06127e7i	−0.118338	−	0.671126i	0.866706	−	0.498820i	$-0.166233\pi$
$252$	125665.	−	712683.i	0.00785260	−	0.0445343i
$253$	3.23261e6	+	1.17657e6i	0.199614	+	0.0726536i
$254$	1.32338e7	+	2.29217e7i	0.807578	+	1.39877i
$255$	3.16917e6	+	1.82972e6i	0.191128	+	0.110348i
$256$	1.21196e7	−	1.01695e7i	0.722384	−	0.606152i
$257$	−2.07487e7	−	2.47273e7i	−1.22234	−	1.45673i	−0.848470	−	0.529244i	$-0.822476\pi$
$257$	−2.07487e7	−	2.47273e7i	−1.22234	−	1.45673i	−0.373868	−	0.927482i	$-0.621969\pi$
$258$	1.93518e7	−	3.35182e7i	1.12684	−	1.95174i
$259$	3.46004e6	−	1.99766e6i	0.199151	−	0.114980i
$260$	1.84662e6	−	5.07354e6i	0.105065	−	0.288663i
$261$	3.50770e6	+	618502.i	0.197288	+	0.0347872i
$262$	−4.37522e7	+	7.71470e6i	−2.43274	+	0.428958i
$263$	1.14792e7	−	4.17809e6i	0.631023	−	0.229673i	−0.00665370	−	0.999978i	$-0.502118\pi$
$263$	1.14792e7	−	4.17809e6i	0.631023	−	0.229673i	0.637676	+	0.770304i	$0.279896\pi$
$264$	110872.	+	93032.8i	0.00602574	+	0.00505620i
$265$			1.91595e6i			0.102955i
$266$	2.04698e6	−	6.77831e6i	0.108760	−	0.360144i
$267$	−3.71780e7			−1.95323
$268$	−1.08659e7	+	1.29495e7i	−0.564497	+	0.672741i
$269$	−1.12677e7	−	3.09578e7i	−0.578868	−	1.59043i	−0.790092	−	0.612988i	$-0.789967\pi$
$269$	−1.12677e7	−	3.09578e7i	−0.578868	−	1.59043i	0.211224	−	0.977438i	$-0.432255\pi$
$270$	−1.12624e6	−	6.38724e6i	−0.0572191	−	0.324506i
$271$	45213.0	−	256415.i	0.00227172	−	0.0128836i	−0.983651	−	0.180086i	$-0.942362\pi$
$271$	45213.0	−	256415.i	0.00227172	−	0.0128836i	0.985923	+	0.167203i	$0.0534734\pi$
$272$	1.46066e7	+	5.31637e6i	0.725842	+	0.264185i
$273$	3.37649e6	+	5.84825e6i	0.165950	+	0.287434i
$274$	5.41238e6	+	3.12484e6i	0.263110	+	0.151906i
$275$	2.77909e6	−	2.33193e6i	0.133630	−	0.112129i
$276$	−1.70547e7	−	2.03250e7i	−0.811180	−	0.966727i
$277$	3.81330e6	−	6.60483e6i	0.179416	−	0.310758i	−0.762265	−	0.647266i	$-0.775912\pi$
$277$	3.81330e6	−	6.60483e6i	0.179416	−	0.310758i	0.941681	+	0.336508i	$0.109246\pi$
$278$	−2.25824e7	+	1.30380e7i	−1.05108	+	0.606842i
$279$	1.29769e6	−	3.56538e6i	0.0597529	−	0.164170i
$280$	−57256.0	−	10095.8i	−0.00260823	−	0.000459902i
$281$	5.44191e6	−	959555.i	0.245263	−	0.0432465i	−0.0496651	−	0.998766i	$-0.515815\pi$
$281$	5.44191e6	−	959555.i	0.245263	−	0.0432465i	0.294928	+	0.955519i	$0.404704\pi$
$282$	−1.95642e7	+	7.12080e6i	−0.872400	+	0.317528i
$283$	1.26104e7	+	1.05814e7i	0.556377	+	0.466856i	0.877094	−	0.480319i	$-0.159479\pi$
$283$	1.26104e7	+	1.05814e7i	0.556377	+	0.466856i	−0.320716	+	0.947175i	$0.603924\pi$
$284$		−	2.98973e7i		−	1.30520i
$285$	358405.	+	6.41805e6i	0.0154824	+	0.277248i
$286$	−7.23604e6			−0.309316
$287$	6060.70	−	7222.86i	0.000256376	−	0.000305537i
$288$	1.93652e6	+	5.32054e6i	0.0810671	+	0.222730i
$289$	−1.54378e6	−	8.75521e6i	−0.0639576	−	0.362721i
$290$	1.86430e6	−	1.05730e7i	0.0764403	−	0.433514i
$291$	4.26819e7	+	1.55349e7i	1.73207	+	0.630420i
$292$	1.15999e7	+	2.00915e7i	0.465912	+	0.806983i
$293$	−1.97966e7	−	1.14296e7i	−0.787023	−	0.454388i	0.0518905	−	0.998653i	$-0.483475\pi$
$293$	−1.97966e7	−	1.14296e7i	−0.787023	−	0.454388i	−0.838913	+	0.544265i	$0.816809\pi$
$294$	−2.78480e7	+	2.33673e7i	−1.09585	+	0.919530i
$295$	−4.18475e6	−	4.98719e6i	−0.163006	−	0.194263i
$296$	440034.	−	762161.i	0.0169672	−	0.0293881i
$297$	−3.81474e6	+	2.20244e6i	−0.145612	+	0.0840689i
$298$	1.00478e7	−	2.76062e7i	0.379685	−	1.04318i
$299$	3.48185e7	+	6.13945e6i	1.30256	+	0.229676i
$300$	−2.75556e7	+	4.85879e6i	−1.02058	+	0.179955i
$301$	9.92224e6	−	3.61140e6i	0.363840	−	0.132427i
$302$	5.20142e7	+	4.36451e7i	1.88843	+	1.58458i
$303$			6.99888e6i			0.251594i
$304$	6.23318e6	+	2.65831e7i	0.221865	+	0.946204i
$305$	−2.53056e6			−0.0891901
$306$	−3.47216e6	+	4.13796e6i	−0.121181	+	0.144418i
$307$	−357689.	−	982741.i	−0.0123620	−	0.0339644i	0.933358	−	0.358946i	$-0.116864\pi$
$307$	−357689.	−	982741.i	−0.0123620	−	0.0339644i	−0.945720	+	0.324982i	$0.894642\pi$
$308$	257254.	+	1.45896e6i	0.00880462	+	0.0499335i
$309$	−3.52344e6	+	1.99824e7i	−0.119424	+	0.677286i
$310$	−1.07468e7	−	3.91153e6i	−0.360741	−	0.131299i
$311$	7.63569e6	+	1.32254e7i	0.253844	+	0.439671i	0.964581	−	0.263787i	$-0.0849716\pi$
$311$	7.63569e6	+	1.32254e7i	0.253844	+	0.439671i	−0.710737	+	0.703458i	$0.751638\pi$
$312$	1.28822e6	+	743756.i	0.0424158	+	0.0244887i
$313$	1.65990e7	−	1.39282e7i	0.541313	−	0.454216i	−0.330674	−	0.943745i	$-0.607276\pi$
$313$	1.65990e7	−	1.39282e7i	0.541313	−	0.454216i	0.871987	+	0.489530i	$0.162831\pi$
$314$	−1.11739e7	−	1.33165e7i	−0.360924	−	0.430133i
$315$	−176847.	+	306308.i	−0.00565804	+	0.00980002i
$316$	−4.54923e7	+	2.62650e7i	−1.44171	+	0.832370i
$317$	1.77981e7	−	4.89000e7i	0.558724	−	1.53508i	−0.262768	−	0.964859i	$-0.584635\pi$
$317$	1.77981e7	−	4.89000e7i	0.558724	−	1.53508i	0.821491	−	0.570221i	$-0.193142\pi$
$318$	−1.95039e7	−	3.43907e6i	−0.606514	−	0.106945i
$319$	−7.18075e6	+	1.26616e6i	−0.221207	+	0.0390047i
$320$	8.34372e6	−	3.03687e6i	0.254630	−	0.0926778i
$321$	2.08009e6	+	1.74540e6i	0.0628879	+	0.0527692i
$322$		−	1.42841e7i		−	0.427845i
$323$	−1.95251e7	+	1.83329e7i	−0.579409	+	0.544030i
$324$	3.97951e7			1.17002
$325$	2.39667e7	−	2.85624e7i	0.698164	−	0.832040i
$326$	1.08752e7	+	2.98794e7i	0.313895	+	0.862419i
$327$	−6.80754e6	−	3.86075e7i	−0.194692	−	1.10415i
$328$	360.654	−	2045.37i	1.02204e−5	−	5.79630e-5i
$329$	−5.33748e6	−	1.94269e6i	−0.149882	−	0.0545525i
$330$	−1.32700e6	−	2.29844e6i	−0.0369258	−	0.0639574i
$331$	7.57941e6	+	4.37597e6i	0.209002	+	0.120668i	0.600848	−	0.799364i	$-0.294830\pi$
$331$	7.57941e6	+	4.37597e6i	0.209002	+	0.120668i	−0.391845	+	0.920031i	$0.628163\pi$
$332$	−1.11494e7	+	9.35550e6i	−0.304677	+	0.255654i
$333$	−3.44146e6	−	4.10137e6i	−0.0931986	−	0.111070i
$334$	2.10570e7	−	3.64717e7i	0.565140	−	0.978852i
$335$	7.15503e6	−	4.13096e6i	0.190317	−	0.109880i
$336$	−3.59829e6	+	9.88622e6i	−0.0948589	+	0.260623i
$337$	2.85464e7	+	5.03350e6i	0.745867	+	0.131517i	0.533649	−	0.845706i	$-0.320820\pi$
$337$	2.85464e7	+	5.03350e6i	0.745867	+	0.131517i	0.212218	+	0.977222i	$0.431931\pi$
$338$	−1.90930e7	+	3.36661e6i	−0.494452	+	0.0871852i
$339$	1.74590e7	−	6.35457e6i	0.448148	−	0.163112i
$340$	6.32059e6	+	5.30361e6i	0.160813	+	0.134938i
$341$			7.76725e6i			0.195886i
$342$	−9.42166e6	−	1.12409e6i	−0.235532	−	0.0281010i
$343$	−2.05799e7			−0.509988
$344$	1.49505e6	−	1.78174e6i	0.0367267	−	0.0437691i
$345$	4.43518e6	+	1.21856e7i	0.108008	+	0.296748i
$346$	−5.98262e6	−	3.39291e7i	−0.144432	−	0.819113i
$347$	−1.04524e7	+	5.92783e7i	−0.250165	+	1.41875i	0.558021	+	0.829827i	$0.311561\pi$
$347$	−1.04524e7	+	5.92783e7i	−0.250165	+	1.41875i	−0.808186	+	0.588928i	$0.799550\pi$
$348$	5.28462e7	+	1.92345e7i	1.25394	+	0.456396i
$349$	−2.50693e7	−	4.34214e7i	−0.589748	−	1.02147i	−0.994265	−	0.106943i	$-0.965894\pi$
$349$	−2.50693e7	−	4.34214e7i	−0.589748	−	1.02147i	0.404517	−	0.914530i	$-0.367440\pi$
$350$	−1.30456e7	−	7.53191e6i	−0.304272	−	0.175671i
$351$	−3.46801e7	+	2.91001e7i	−0.801972	+	0.672934i
$352$	−7.45050e6	−	8.87916e6i	−0.170827	−	0.203584i
$353$	−3.87723e7	+	6.71556e7i	−0.881450	+	1.52672i	−0.0317205	+	0.999497i	$0.510099\pi$
$353$	−3.87723e7	+	6.71556e7i	−0.881450	+	1.52672i	−0.849729	+	0.527219i	$0.823235\pi$
$354$	5.82799e7	−	3.36479e7i	1.31374	−	0.758487i
$355$	−4.99766e6	+	1.37310e7i	−0.111707	+	0.306914i
$356$	−8.25520e7	−	1.45561e7i	−1.82969	−	0.322624i
$357$	−1.01631e7	+	1.79203e6i	−0.223368	+	0.0393858i
$358$	−9.05158e7	+	3.29451e7i	−1.97276	+	0.718028i
$359$	−5.29748e7	−	4.44512e7i	−1.14495	−	0.960727i	−0.145360	−	0.989379i	$-0.546434\pi$
$359$	−5.29748e7	−	4.44512e7i	−1.14495	−	0.960727i	−0.999589	+	0.0286523i	$0.990878\pi$
$360$			77910.0i			0.00166988i
$361$	−4.57253e7	−	1.10684e7i	−0.971930	−	0.235269i
$362$	9.75207e7			2.05575
$363$	3.20497e7	−	3.81953e7i	0.670045	−	0.798528i
$364$	5.20758e6	+	1.43077e7i	0.107977	+	0.296665i
$365$	−1.96895e6	−	1.11665e7i	−0.0404909	−	0.229635i
$366$	4.54226e6	−	2.57605e7i	0.0926465	−	0.525424i
$367$	1.70153e7	+	6.19308e6i	0.344225	+	0.125288i	0.508347	−	0.861152i	$-0.330257\pi$
$367$	1.70153e7	+	6.19308e6i	0.344225	+	0.125288i	−0.164122	+	0.986440i	$0.552479\pi$
$368$	2.75409e7	+	4.77023e7i	0.552631	+	0.957184i
$369$	−10942.3	−	6317.56i	−0.000217786	−	0.000125739i
$370$	−1.23624e7	+	1.03733e7i	−0.244061	+	0.204791i
$371$	−3.47306e6	−	4.13903e6i	−0.0680127	−	0.0810544i
$372$	2.99534e7	−	5.18809e7i	0.581859	−	1.00781i
$373$	−3.79918e6	+	2.19346e6i	−0.0732089	+	0.0422672i	−0.536158	−	0.844118i	$-0.680125\pi$
$373$	−3.79918e6	+	2.19346e6i	−0.0732089	+	0.0422672i	0.462949	+	0.886385i	$0.346791\pi$
$374$	3.78209e6	−	1.03912e7i	0.0722964	−	0.198633i
$375$	2.78885e7	+	4.91749e6i	0.528848	+	0.0932502i
$376$	−1.23216e6	+	217263.i	−0.0231795	+	0.00408717i
$377$	−7.04200e7	+	2.56308e7i	−1.31423	+	0.478342i
$378$	1.40112e7	+	1.17568e7i	0.259418	+	0.217677i
$379$		−	4.32482e7i		−	0.794421i	−0.917728	−	0.397211i	$-0.869978\pi$
$379$		−	4.32482e7i		−	0.794421i	0.917728	−	0.397211i	$-0.130022\pi$
$380$	−1.71701e6	+	1.43913e7i	−0.0312911	+	0.262270i
$381$	6.77611e7			1.22520
$382$	8.63675e7	−	1.02929e8i	1.54939	−	1.84649i
$383$	−5.09521e6	−	1.39990e7i	−0.0906913	−	0.249172i	0.886051	−	0.463587i	$-0.153438\pi$
$383$	−5.09521e6	−	1.39990e7i	−0.0906913	−	0.249172i	−0.976743	+	0.214415i	$0.931216\pi$
$384$	827828.	+	4.69485e6i	0.0146200	+	0.0829139i
$385$	125732.	−	713061.i	0.00220325	−	0.0124952i
$386$	−9.31058e7	−	3.38877e7i	−1.61888	−	0.589224i
$387$	−7.07486e6	−	1.22540e7i	−0.122063	−	0.211420i
$388$	8.86906e7	+	5.12055e7i	1.51839	+	0.876641i
$389$	5.19804e7	−	4.36167e7i	0.883061	−	0.740976i	−0.0837452	−	0.996487i	$-0.526688\pi$
$389$	5.19804e7	−	4.36167e7i	0.883061	−	0.740976i	0.966806	+	0.255511i	$0.0822437\pi$
$390$	−1.75332e7	−	2.08953e7i	−0.295575	−	0.352252i
$391$	−2.70152e7	+	4.67917e7i	−0.451937	+	0.782777i
$392$	−1.89195e6	+	1.09232e6i	−0.0314088	+	0.0181339i
$393$	−3.89014e7	+	1.06881e8i	−0.640897	+	1.76085i
$394$	−4.51908e7	−	7.96835e6i	−0.738858	−	0.130281i
$395$	2.52838e7	−	4.45821e6i	0.410252	−	0.0723385i
$396$	1.86553e6	−	678997.i	0.0300411	−	0.0109341i
$397$	−1.64243e7	−	1.37816e7i	−0.262491	−	0.220256i	0.502038	−	0.864846i	$-0.332584\pi$
$397$	−1.64243e7	−	1.37816e7i	−0.262491	−	0.220256i	−0.764529	+	0.644589i	$0.777028\pi$
$398$			7.73262e7i			1.22653i
$399$	−1.24083e7	−	1.32152e7i	−0.195341	−	0.208044i
$400$	5.80884e7			0.907631
$401$	4.60015e7	−	5.48225e7i	0.713409	−	0.850208i	−0.280563	−	0.959836i	$-0.590521\pi$
$401$	4.60015e7	−	5.48225e7i	0.713409	−	0.850208i	0.993973	+	0.109627i	$0.0349657\pi$
$402$	2.92091e7	+	8.02514e7i	0.449615	+	1.23531i
$403$	1.38621e7	+	7.86159e7i	0.211794	+	1.20114i
$404$	−2.74024e6	+	1.55407e7i	−0.0415570	+	0.235681i
$405$	−1.82767e7	−	6.65218e6i	−0.275127	−	0.100138i
$406$	1.51382e7	+	2.62202e7i	0.226202	+	0.391794i
$407$	9.49189e6	+	5.48015e6i	0.140789	+	0.0812847i
$408$	−1.74138e6	+	1.46119e6i	−0.0256397	+	0.0215142i
$409$	4.73854e7	+	5.64717e7i	0.692587	+	0.825393i	0.991666	−	0.128835i	$-0.0411238\pi$
$409$	4.73854e7	+	5.64717e7i	0.692587	+	0.825393i	−0.299079	+	0.954228i	$0.596679\pi$
$410$	−19042.5	+	32982.6i	−0.000276295	+	0.000478556i
$411$	1.38565e7	−	8.00005e6i	0.199585	−	0.115230i
$412$	−1.56472e7	+	4.29904e7i	−0.223741	+	0.614723i
$413$	1.80806e7	+	3.18810e6i	0.256663	+	0.0452566i
$414$	−1.88508e7	+	3.32390e6i	−0.265661	+	0.0468432i
$415$	6.68449e6	−	2.43295e6i	0.0935241	−	0.0340400i
$416$	−9.12565e7	−	7.65733e7i	−1.26760	−	1.06365i
$417$			6.67583e7i			0.920656i
$418$	1.89113e7	−	4.43431e6i	0.258937	−	0.0607152i
$419$	−3.52714e7			−0.479491			−0.239746	−	0.970836i	$-0.577064\pi$
$419$	−3.52714e7			−0.479491			−0.239746	+	0.970836i	$0.577064\pi$
$420$	−3.58965e6	+	4.27798e6i	−0.0484512	+	0.0577419i
$421$	1.95145e7	+	5.36155e7i	0.261523	+	0.718529i	0.999065	+	0.0432278i	$0.0137641\pi$
$421$	1.95145e7	+	5.36155e7i	0.261523	+	0.718529i	−0.737542	+	0.675301i	$0.764014\pi$
$422$	−2.08644e7	−	1.18328e8i	−0.277632	−	1.57453i
$423$	−1.32174e6	+	7.49594e6i	−0.0174632	+	0.0990387i
$424$	−1.11840e6	−	407063.i	−0.0146723	−	0.00534028i
$425$	2.84898e7	+	4.93457e7i	0.371127	+	0.642810i
$426$	−1.30807e8	−	7.55216e7i	−1.69201	−	0.976882i
$427$	5.46676e6	−	4.58715e6i	0.0702176	−	0.0589196i
$428$	3.93537e6	+	4.68999e6i	0.0501942	+	0.0598191i
$429$	−9.26267e6	+	1.60434e7i	−0.117318	+	0.203201i
$430$	−3.69363e7	+	2.13252e7i	−0.464566	+	0.268218i
$431$	2.59150e7	−	7.12008e7i	0.323682	−	0.889310i	−0.665990	−	0.745961i	$-0.731991\pi$
$431$	2.59150e7	−	7.12008e7i	0.323682	−	0.889310i	0.989672	−	0.143349i	$-0.0457872\pi$
$432$	−6.94588e7	−	1.22475e7i	−0.861541	−	0.151913i
$433$	4.53791e7	−	8.00157e6i	0.558975	−	0.0985624i	0.112979	−	0.993597i	$-0.463961\pi$
$433$	4.53791e7	−	8.00157e6i	0.558975	−	0.0985624i	0.445996	+	0.895035i	$0.352850\pi$
$434$	3.03068e7	−	1.10308e7i	0.370741	−	0.134939i
$435$	−2.10555e7	−	1.76676e7i	−0.255798	−	0.214640i
$436$		−	8.83913e7i		−	1.06647i
$437$	−9.47603e7	+	5.29172e6i	−1.13549	+	0.0634093i
$438$	1.17206e8			1.39485
$439$	4.03140e7	−	4.80443e7i	0.476499	−	0.567870i	−0.473231	−	0.880938i	$-0.656913\pi$
$439$	4.03140e7	−	4.80443e7i	0.476499	−	0.567870i	0.949731	+	0.313069i	$0.101357\pi$
$440$	−54549.7	−	149874.i	−0.000640375	−	0.00175942i
$441$	2.30785e6	+	1.30885e7i	0.0269087	+	0.152607i
$442$	1.97352e7	−	1.11924e8i	0.228547	−	1.29615i
$443$	−2.31738e7	−	8.43458e6i	−0.266555	−	0.0970180i	0.205285	−	0.978702i	$-0.434188\pi$
$443$	−2.31738e7	−	8.43458e6i	−0.266555	−	0.0970180i	−0.471840	+	0.881684i	$0.656410\pi$
$444$	−4.22670e7	−	7.32087e7i	−0.482895	−	0.836399i
$445$	3.54805e7	+	2.04847e7i	0.402633	+	0.232460i
$446$	6.94815e6	−	5.83019e6i	0.0783185	−	0.0657170i
$447$	−4.83452e7	−	5.76156e7i	−0.541291	−	0.645086i
$448$	−1.25200e7	+	2.16852e7i	−0.139242	+	0.241174i
$449$	−4.64537e7	+	2.68201e7i	−0.513194	+	0.296292i	−0.734145	−	0.678992i	$-0.762417\pi$
$449$	−4.64537e7	+	2.68201e7i	−0.513194	+	0.296292i	0.220952	+	0.975285i	$0.429084\pi$
$450$	−6.90415e6	+	1.89690e7i	−0.0757657	+	0.208165i
$451$	25472.9	+	4491.56i	0.000277682	+	4.89629e-5i
$452$	4.12549e7	−	7.27435e6i	0.446745	−	0.0787732i
$453$	1.63350e8	−	5.94545e7i	1.75721	−	0.639573i
$454$	3.55013e7	+	2.97892e7i	0.379382	+	0.318340i
$455$		−	7.44162e6i		−	0.0790011i
$456$	−3.82254e6	−	1.15436e6i	−0.0403141	−	0.0121744i
$457$	−1.03671e8			−1.08620			−0.543100	−	0.839668i	$-0.682750\pi$
$457$	−1.03671e8			−1.08620			−0.543100	+	0.839668i	$0.682750\pi$
$458$	−1.23828e8	+	1.47572e8i	−1.28891	+	1.53606i
$459$	−2.36623e7	−	6.50116e7i	−0.244692	−	0.672284i
$460$	5.07714e6	+	2.87939e7i	0.0521610	+	0.295820i
$461$	1.95577e7	−	1.10917e8i	0.199625	−	1.13213i	−0.706053	−	0.708159i	$-0.749526\pi$
$461$	1.95577e7	−	1.10917e8i	0.199625	−	1.13213i	0.905677	−	0.423968i	$-0.139363\pi$
$462$	7.03310e6	+	2.55984e6i	0.0713216	+	0.0259589i
$463$	−6.09641e7	−	1.05593e8i	−0.614230	−	1.06388i	−0.990519	−	0.137375i	$-0.956133\pi$
$463$	−6.09641e7	−	1.05593e8i	−0.614230	−	1.06388i	0.376289	−	0.926502i	$-0.377200\pi$
$464$	−1.01109e8	−	5.83754e7i	−1.01213	−	0.584354i
$465$	−2.24292e7	+	1.88203e7i	−0.223077	+	0.187184i
$466$	1.25887e8	+	1.50026e8i	1.24401	+	1.48255i
$467$	3.97262e6	−	6.88077e6i	0.0390055	−	0.0675595i	−0.845864	−	0.533399i	$-0.820914\pi$
$467$	3.97262e6	−	6.88077e6i	0.0390055	−	0.0675595i	0.884869	+	0.465840i	$0.154248\pi$
$468$	1.76701e7	−	1.02018e7i	0.172386	−	0.0995269i
$469$	−7.96878e6	+	2.18941e7i	−0.0772456	+	0.212230i
$470$	2.25944e7	+	3.98400e6i	0.217624	+	0.0383730i
$471$	−4.38282e7	+	7.72810e6i	−0.419461	+	0.0739622i
$472$	3.80025e6	−	1.38318e6i	0.0361399	−	0.0131538i
$473$	2.21896e7	+	1.86193e7i	0.209684	+	0.175946i
$474$			2.65385e8i			2.49196i
$475$	−4.51334e7	+	8.93345e7i	−0.421131	+	0.833563i
$476$	−2.32682e7			−0.215746
$477$	−4.65410e6	+	5.54654e6i	−0.0428825	+	0.0511054i
$478$	2.30883e7	+	6.34347e7i	0.211402	+	0.580822i
$479$	2.04920e7	+	1.16216e8i	0.186457	+	1.05745i	0.924069	+	0.382225i	$0.124842\pi$
$479$	2.04920e7	+	1.16216e8i	0.186457	+	1.05745i	−0.737612	+	0.675224i	$0.764047\pi$
$480$	7.58718e6	−	4.30290e7i	0.0686052	−	0.389079i
$481$	1.05852e8	+	3.85271e7i	0.951184	+	0.346203i
$482$	1.14751e8	+	1.98755e8i	1.02474	+	1.77491i
$483$	−3.16701e7	−	1.82848e7i	−0.281066	−	0.162274i
$484$	8.61191e7	−	7.22625e7i	0.759562	−	0.637348i
$485$	−3.21734e7	−	3.83428e7i	−0.282015	−	0.336092i
$486$	2.69598e7	−	4.66957e7i	0.234859	−	0.406788i
$487$	−1.45462e8	+	8.39825e7i	−1.25940	+	0.727113i	−0.972957	−	0.230985i	$-0.925805\pi$
$487$	−1.45462e8	+	8.39825e7i	−1.25940	+	0.727113i	−0.286440	+	0.958098i	$0.592472\pi$
$488$	537641.	−	1.47716e6i	0.00462629	−	0.0127106i
$489$	8.01682e7	+	1.41358e7i	0.685607	+	0.120891i
$490$	3.94516e7	−	6.95637e6i	0.335333	−	0.0591282i
$491$	7.82706e7	−	2.84882e7i	0.661232	−	0.240669i	0.0104639	−	0.999945i	$-0.496669\pi$
$491$	7.82706e7	−	2.84882e7i	0.661232	−	0.240669i	0.650768	+	0.759276i	$0.274447\pi$
$492$	−152824.	−	128234.i	−0.00128320	−	0.00107673i
$493$		−	1.14522e8i		−	0.955759i
$494$	1.83497e8	−	7.86326e7i	1.52211	−	0.652261i
$495$	−970284.			−0.00799988
$496$	−7.99421e7	+	9.52713e7i	−0.655135	+	0.780759i
$497$	−1.40937e7	−	3.87222e7i	−0.114804	−	0.315421i
$498$	1.27684e7	+	7.24135e7i	0.103383	+	0.586315i
$499$	1.96954e7	−	1.11698e8i	0.158512	−	0.898968i	−0.796992	−	0.603990i	$-0.793577\pi$
$499$	1.96954e7	−	1.11698e8i	0.158512	−	0.898968i	0.955504	−	0.294978i	$-0.0953123\pi$
$500$	5.99996e7	+	2.18381e7i	0.479997	+	0.174705i
$501$	−5.39090e7	−	9.33731e7i	−0.428694	−	0.742520i
$502$	−1.06307e8	−	6.13764e7i	−0.840332	−	0.485166i
$503$	−9.05306e7	+	7.59642e7i	−0.711363	+	0.596904i	−0.924981	−	0.380013i	$-0.875920\pi$
$503$	−9.05306e7	+	7.59642e7i	−0.711363	+	0.596904i	0.213618	+	0.976917i	$0.431475\pi$
$504$	−141228.	−	168309.i	−0.00110313	−	0.00131466i
$505$	3.85630e6	−	6.67930e6i	0.0299431	−	0.0518629i
$506$	3.39356e7	−	1.95927e7i	0.261941	−	0.151232i
$507$	−1.69762e7	+	4.66416e7i	−0.130261	+	0.357890i
$508$	1.50460e8	+	2.65302e7i	1.14770	+	0.202371i
$509$	1.48184e8	−	2.61288e7i	1.12369	−	0.198137i	0.419231	−	0.907879i	$-0.362300\pi$
$509$	1.48184e8	−	2.61288e7i	1.12369	−	0.198137i	0.704462	+	0.709742i	$0.251188\pi$
$510$	3.91704e7	−	1.42569e7i	0.295289	−	0.107477i
$511$	2.44951e7	+	2.05538e7i	0.183576	+	0.154039i
$512$		−	1.90678e8i		−	1.42066i
$513$	7.28034e7	−	9.73050e7i	0.539261	−	0.720748i
$514$	−3.67689e8			−2.70764
$515$	1.43726e7	−	1.71286e7i	0.105224	−	0.125401i
$516$	−7.64111e7	−	2.09938e8i	−0.556170	−	1.52806i
$517$	−2.70578e6	−	1.53452e7i	−0.0195804	−	0.111046i
$518$	7.90276e6	−	4.48188e7i	0.0568578	−	0.322456i
$519$	−8.28842e7	−	3.01674e7i	−0.592884	−	0.215792i
$520$	−819601.	−	1.41959e6i	−0.00582898	−	0.0100961i
$521$	2.23504e8	+	1.29040e8i	1.58042	+	0.912456i	0.994797	+	0.101873i	$0.0324836\pi$
$521$	2.23504e8	+	1.29040e8i	1.58042	+	0.912456i	0.585624	+	0.810583i	$0.300850\pi$
$522$	3.10801e7	−	2.60793e7i	0.218510	−	0.183352i
$523$	6.13200e7	+	7.30783e7i	0.428644	+	0.510838i	0.936531	−	0.350586i	$-0.114017\pi$
$523$	6.13200e7	+	7.30783e7i	0.428644	+	0.510838i	−0.507886	+	0.861424i	$0.669573\pi$
$524$	−1.28225e8	+	2.22093e8i	−0.891209	+	1.54362i
$525$	−3.33988e7	+	1.92828e7i	−0.230809	+	0.133258i
$526$	4.75922e7	−	1.30759e8i	0.327023	−	0.898489i
$527$	−1.20140e8	−	2.11840e7i	−0.820838	−	0.144736i
$528$	−2.84228e7	+	5.01171e6i	−0.193092	+	0.0340474i
$529$	−4.08074e7	+	1.48527e7i	−0.275659	+	0.100332i
$530$	1.67185e7	+	1.40285e7i	0.112297	+	0.0942286i
$531$		−	2.46028e7i		−	0.164324i
$532$	−2.23779e7	−	3.42018e7i	−0.148622	−	0.227151i
$533$	265839.			0.00175565
$534$	−2.72215e8	+	3.24413e8i	−1.78767	+	2.13047i
$535$	−1.02342e6	−	2.81181e6i	−0.00668330	−	0.0183622i
$536$	891201.	+	5.05425e6i	0.00578737	+	0.0328218i
$537$	−4.28227e7	+	2.42860e8i	−0.276536	+	1.56831i
$538$	−3.52637e8	−	1.28349e8i	−2.26455	−	0.824228i
$539$	−1.36036e7	−	2.35622e7i	−0.0868738	−	0.150470i
$540$	−3.24225e7	−	1.87192e7i	−0.205904	−	0.118879i
$541$	1.05759e8	−	8.87425e7i	0.667923	−	0.560454i	−0.244527	−	0.969643i	$-0.578633\pi$
$541$	1.05759e8	−	8.87425e7i	0.667923	−	0.560454i	0.912450	+	0.409188i	$0.134188\pi$
$542$	−1.90642e6	−	2.27198e6i	−0.0119735	−	0.0142694i
$543$	1.24834e8	−	2.16218e8i	0.779709	−	1.35049i
$544$	1.57659e8	−	9.10245e7i	0.979315	−	0.565408i
$545$	−1.47756e7	+	4.05955e7i	−0.0912756	+	0.250778i
$546$	7.57538e7	+	1.33574e7i	0.465400	+	0.0820626i
$547$	−2.46926e8	+	4.35398e7i	−1.50871	+	0.266026i	−0.865984	−	0.500071i	$-0.833307\pi$
$547$	−2.46926e8	+	4.35398e7i	−1.50871	+	0.266026i	−0.642725	+	0.766097i	$0.722196\pi$
$548$	3.38999e7	−	1.23385e7i	0.205995	−	0.0749760i
$549$	−7.32577e6	−	6.14705e6i	−0.0442727	−	0.0371492i
$550$		−	4.13244e7i		−	0.248381i
$551$	1.68335e8	−	1.10140e8i	1.00628	−	0.658400i
$552$	−8.05535e6			−0.0478924
$553$	−4.65390e7	+	5.54630e7i	−0.275196	+	0.327966i
$554$	−2.97126e7	−	8.16347e7i	−0.174748	−	0.480115i
$555$	7.17439e6	+	4.06880e7i	0.0419668	+	0.238006i
$556$	−2.61376e7	+	1.48233e8i	−0.152069	+	0.862426i
$557$	1.52907e8	+	5.56536e7i	0.884835	+	0.322053i	0.744159	−	0.668002i	$-0.232850\pi$
$557$	1.52907e8	+	5.56536e7i	0.884835	+	0.322053i	0.140675	+	0.990056i	$0.455073\pi$
$558$	−2.16096e7	−	3.74290e7i	−0.124378	−	0.215430i
$559$	2.57821e8	+	1.48853e8i	1.47599	+	0.852161i
$560$	8.88118e6	−	7.45219e6i	0.0505716	−	0.0424346i
$561$	−1.81975e7	−	2.16870e7i	−0.103068	−	0.122832i
$562$	3.14722e7	−	5.45115e7i	0.177304	−	0.307100i
$563$	2.05673e8	−	1.18745e8i	1.15253	−	0.665413i	0.203027	−	0.979173i	$-0.434922\pi$
$563$	2.05673e8	−	1.18745e8i	1.15253	−	0.665413i	0.949502	+	0.313760i	$0.101589\pi$
$564$	−4.11039e7	+	1.12932e8i	−0.229111	+	0.629477i
$565$	−2.01631e7	−	3.55530e6i	−0.111792	−	0.0197120i
$566$	1.84665e8	−	3.25614e7i	1.01844	−	0.179578i
$567$	5.15415e7	−	1.87596e7i	0.282754	−	0.102914i
$568$	−6.95334e6	−	5.83455e6i	−0.0379445	−	0.0318392i
$569$			9.94382e7i			0.539779i	0.962891	+	0.269890i	$0.0869872\pi$
$569$			9.94382e7i			0.539779i	−0.962891	+	0.269890i	$0.913013\pi$
$570$	5.86277e7	+	4.38651e7i	0.316576	+	0.236861i
$571$	−3.43503e8			−1.84511			−0.922554	−	0.385868i	$-0.873902\pi$
$571$	−3.43503e8			−1.84511			−0.922554	+	0.385868i	$0.873902\pi$
$572$	−2.68487e7	+	3.19970e7i	−0.143461	+	0.170971i
$573$	−1.17652e8	−	3.23246e8i	−0.625368	−	1.71818i
$574$	−18650.2	−	105771.i	−9.86161e−5	−	0.000559280i
$575$	−3.50618e7	+	1.98845e8i	−0.184430	+	1.04595i
$576$	3.15314e7	+	1.14765e7i	0.164997	+	0.0600539i
$577$	−5.62150e7	−	9.73672e7i	−0.292634	−	0.506857i	0.681798	−	0.731541i	$-0.261198\pi$
$577$	−5.62150e7	−	9.73672e7i	−0.292634	−	0.506857i	−0.974432	+	0.224684i	$0.927865\pi$
$578$	−8.77008e7	−	5.06341e7i	−0.454172	−	0.262216i
$579$	−1.94317e8	+	1.63051e8i	−1.00109	+	0.840016i
$580$	−3.98353e7	−	4.74738e7i	−0.204166	−	0.243316i
$581$	−1.00302e7	+	1.73729e7i	−0.0511426	+	0.0885816i
$582$	4.48070e8	−	2.58693e8i	2.27288	−	1.31225i
$583$	5.06953e6	−	1.39284e7i	0.0255836	−	0.0702904i
$584$	6.93651e6	+	1.22309e6i	0.0348259	+	0.00614075i
$585$	−9.82070e6	+	1.73165e6i	−0.0490540	+	0.00864955i
$586$	−2.44683e8	+	8.90572e7i	−1.21594	+	0.442564i
$587$	1.24250e7	+	1.04258e7i	0.0614303	+	0.0515462i	0.672986	−	0.739655i	$-0.265011\pi$
$587$	1.24250e7	+	1.04258e7i	0.0614303	+	0.0515462i	−0.611556	+	0.791202i	$0.709456\pi$
$588$			2.09843e8i			1.03220i
$589$	−8.44050e7	−	1.96967e8i	−0.413069	−	0.963935i
$590$	−7.41584e7			−0.361081
$591$	−7.55146e7	+	8.99948e7i	−0.365821	+	0.435968i
$592$	6.00226e7	+	1.64911e8i	0.289301	+	0.794848i
$593$	2.47707e7	+	1.40481e8i	0.118788	+	0.673682i	0.984805	+	0.173666i	$0.0555614\pi$
$593$	2.47707e7	+	1.40481e8i	0.118788	+	0.673682i	−0.866016	+	0.500016i	$0.833327\pi$
$594$	−8.71290e6	+	4.94133e7i	−0.0415722	+	0.235768i
$595$	1.06864e7	+	3.88954e6i	0.0507319	+	0.0184649i
$596$	−8.47902e7	−	1.46861e8i	−0.400504	−	0.693693i
$597$	1.71444e8	+	9.89833e7i	0.805748	+	0.465199i
$598$	3.08511e8	−	2.58872e8i	1.44267	−	1.21055i
$599$	1.72934e8	+	2.06095e8i	0.804638	+	0.958931i	0.999761	−	0.0218481i	$-0.00695502\pi$
$599$	1.72934e8	+	2.06095e8i	0.804638	+	0.958931i	−0.195123	+	0.980779i	$0.562511\pi$
$600$	−4.24752e6	+	7.35692e6i	−0.0196644	+	0.0340598i
$601$	−1.40948e8	+	8.13766e7i	−0.649287	+	0.374866i	−0.788183	−	0.615441i	$-0.788978\pi$
$601$	−1.40948e8	+	8.13766e7i	−0.649287	+	0.374866i	0.138896	+	0.990307i	$0.455645\pi$
$602$	4.11371e7	−	1.13023e8i	0.188558	−	0.518058i
$603$	3.07479e7	+	5.42169e6i	0.140237	+	0.0247276i
$604$	3.85988e8	−	6.80601e7i	1.75171	−	0.308874i
$605$	−5.16314e7	+	1.87923e7i	−0.233157	+	0.0848621i
$606$	6.10717e7	+	5.12453e7i	0.274424	+	0.230269i
$607$		−	2.82405e8i		−	1.26272i	−0.775490	−	0.631359i	$-0.782497\pi$
$607$		−	2.82405e8i		−	1.26272i	0.775490	−	0.631359i	$-0.217503\pi$
$608$	2.85423e8	+	1.44201e8i	1.26992	+	0.641589i
$609$	7.75122e7			0.343177
$610$	−1.85286e7	+	2.20815e7i	−0.0816305	+	0.0972834i
$611$	−5.47729e7	−	1.50487e8i	−0.240128	−	0.659745i
$612$	5.41448e6	+	3.07071e7i	0.0236212	+	0.133963i
$613$	−2.79189e7	+	1.58336e8i	−0.121204	+	0.687381i	0.862286	+	0.506421i	$0.169032\pi$
$613$	−2.79189e7	+	1.58336e8i	−0.121204	+	0.687381i	−0.983490	+	0.180961i	$0.942079\pi$
$614$	−1.11943e7	−	4.07439e6i	−0.0483606	−	0.0176018i
$615$	48751.6	+	84440.3i	0.000209587	+	0.000363015i
$616$	389521.	+	224890.i	0.00166643	+	0.000962117i
$617$	−2.68006e8	+	2.24884e8i	−1.14101	+	0.957419i	−0.999471	−	0.0325138i	$-0.989649\pi$
$617$	−2.68006e8	+	2.24884e8i	−1.14101	+	0.957419i	−0.141537	+	0.989933i	$0.545204\pi$
$618$	1.48567e8	+	1.77055e8i	0.629443	+	0.750141i
$619$	−5.61877e7	+	9.73200e7i	−0.236902	+	0.410327i	−0.959824	−	0.280603i	$-0.909466\pi$
$619$	−5.61877e7	+	9.73200e7i	−0.236902	+	0.410327i	0.722921	+	0.690930i	$0.242799\pi$
$620$	−5.71715e7	+	3.30080e7i	−0.239886	+	0.138498i
$621$	8.38498e7	−	2.30375e8i	0.350128	−	0.961970i
$622$	1.71312e8	+	3.02069e7i	0.711896	+	0.125526i
$623$	−1.13781e8	+	2.00626e7i	−0.470550	+	0.0829706i
$624$	−2.78736e8	+	1.01452e8i	−1.14720	+	0.417547i
$625$	1.50756e8	+	1.26499e8i	0.617495	+	0.518140i
$626$		−	2.46823e8i		−	1.00615i
$627$	1.43764e7	−	4.76056e7i	0.0583239	−	0.193132i
$628$	−1.00344e8			−0.405147
$629$	−1.10652e8	+	1.31870e8i	−0.444640	+	0.529901i
$630$	1.37796e6	+	3.78592e6i	0.00551081	+	0.0151408i
$631$	7.81845e7	+	4.43406e8i	0.311195	+	1.76487i	0.592806	+	0.805345i	$0.298020\pi$
$631$	7.81845e7	+	4.43406e8i	0.311195	+	1.76487i	−0.281611	+	0.959529i	$0.590869\pi$
$632$	−2.76940e6	+	1.57060e7i	−0.0109707	+	0.0622179i
$633$	−2.89060e8	−	1.05209e8i	−1.13966	−	0.414803i
$634$	−2.96381e8	−	5.13348e8i	−1.16301	−	2.01439i
$635$	−6.46671e7	−	3.73356e7i	−0.252559	−	0.145815i
$636$	−8.75748e7	+	7.34840e7i	−0.340414	+	0.285642i
$637$	−1.79740e8	−	2.14206e8i	−0.695387	−	0.828730i
$638$	−4.15285e7	+	7.19295e7i	−0.159913	+	0.276978i
$639$	−4.78221e7	+	2.76101e7i	−0.183285	+	0.105819i
$640$	1.79677e6	−	4.93660e6i	0.00685415	−	0.0188316i
$641$	−5.03235e8	−	8.87340e7i	−1.91072	−	0.336912i	−0.913214	−	0.407481i	$-0.866407\pi$
$641$	−5.03235e8	−	8.87340e7i	−1.91072	−	0.336912i	−0.997507	+	0.0705695i	$0.977518\pi$
$642$	3.04605e7	−	5.37101e6i	0.115115	−	0.0202979i
$643$	1.82655e8	−	6.64809e7i	0.687065	−	0.250071i	0.0251871	−	0.999683i	$-0.491982\pi$
$643$	1.82655e8	−	6.64809e7i	0.687065	−	0.250071i	0.661878	+	0.749611i	$0.269760\pi$
$644$	−6.31629e7	−	5.30000e7i	−0.236486	−	0.198435i
$645$			1.09191e8i			0.406919i
$646$	1.70102e7	+	3.04606e8i	0.0630975	+	1.12990i
$647$	4.86247e8			1.79533			0.897664	−	0.440681i	$-0.145263\pi$
$647$	4.86247e8			1.79533			0.897664	+	0.440681i	$0.145263\pi$
$648$	7.76612e6	−	9.25531e6i	0.0285417	−	0.0340146i
$649$	1.72260e7	+	4.73280e7i	0.0630159	+	0.173135i
$650$	−7.37511e7	−	4.18263e8i	−0.268552	−	1.52303i
$651$	1.43380e7	−	8.13149e7i	0.0519692	−	0.294732i
$652$	1.72475e8	+	6.27757e7i	0.622276	+	0.226490i
$653$	−4.85494e7	−	8.40900e7i	−0.174359	−	0.301998i	0.765580	−	0.643340i	$-0.222452\pi$
$653$	−4.85494e7	−	8.40900e7i	−0.174359	−	0.301998i	−0.939939	+	0.341342i	$0.889119\pi$
$654$	−3.86731e8	−	2.23279e8i	−1.38253	−	0.798206i
$655$	9.60152e7	−	8.05663e7i	0.341677	−	0.286701i
$656$	266217.	+	317265.i	0.000943026	+	0.00112385i
$657$	2.14249e7	−	3.71090e7i	0.0755479	−	0.130853i
$658$	−5.60324e7	+	3.23503e7i	−0.196681	+	0.113554i
$659$	3.72714e7	−	1.02402e8i	0.130233	−	0.357811i	−0.857388	−	0.514670i	$-0.827915\pi$
$659$	3.72714e7	−	1.02402e8i	0.130233	−	0.357811i	0.987621	+	0.156859i	$0.0501367\pi$
$660$	−1.50872e7	−	2.66027e6i	−0.0524778	−	0.00925326i
$661$	2.18889e8	−	3.85961e7i	0.757915	−	0.133641i	0.218680	−	0.975797i	$-0.429825\pi$
$661$	2.18889e8	−	3.85961e7i	0.757915	−	0.133641i	0.539234	+	0.842156i	$0.318714\pi$
$662$	9.36803e7	−	3.40968e7i	0.322905	−	0.117528i
$663$	−2.22890e8	−	1.87027e8i	−0.764804	−	0.641747i
$664$			4.41882e6i			0.0150939i
$665$	4.56029e6	+	1.94486e7i	0.0155070	+	0.0661338i
$666$	−6.09863e7			−0.206448
$667$	2.60857e8	−	3.10877e8i	0.879072	−	1.04764i
$668$	−8.31442e7	−	2.28437e8i	−0.278935	−	0.766367i
$669$	−4.03228e6	−	2.28682e7i	−0.0134670	−	0.0763754i
$670$	1.63422e7	−	9.26809e7i	0.0543356	−	0.308153i
$671$	1.83964e7	+	6.69574e6i	0.0608927	+	0.0221631i
$672$	6.16083e7	+	1.06709e8i	0.203017	+	0.351635i
$673$	1.88919e8	+	1.09073e8i	0.619771	+	0.357825i	0.776780	−	0.629772i	$-0.216852\pi$
$673$	1.88919e8	+	1.09073e8i	0.619771	+	0.357825i	−0.157009	+	0.987597i	$0.550185\pi$
$674$	2.52937e8	−	2.12239e8i	0.826099	−	0.693179i
$675$	−1.66188e8	−	1.98055e8i	−0.540366	−	0.643983i
$676$	−5.59561e7	+	9.69187e7i	−0.181137	+	0.313738i
$677$	−3.61663e8	+	2.08806e8i	−1.16557	+	0.672942i	−0.952633	−	0.304124i	$-0.901636\pi$
$677$	−3.61663e8	+	2.08806e8i	−1.16557	+	0.672942i	−0.212937	+	0.977066i	$0.568303\pi$
$678$	7.23842e7	−	1.98874e8i	0.232250	−	0.638100i
$679$	1.39008e8	+	2.45109e7i	0.444049	+	0.0782979i
$680$	2.46696e6	−	434992.i	0.00784578	−	0.00138342i
$681$	1.11491e8	−	4.05796e7i	0.353021	−	0.128489i
$682$	6.77765e7	+	5.68712e7i	0.213661	+	0.179283i
$683$			2.79371e8i			0.876837i	0.898771	+	0.438418i	$0.144461\pi$
$683$			2.79371e8i			0.876837i	−0.898771	+	0.438418i	$0.855539\pi$
$684$	−3.99288e7	+	3.74908e7i	−0.124772	+	0.117154i
$685$	−1.76317e7			−0.0548559
$686$	−1.50684e8	+	1.79579e8i	−0.466762	+	0.556266i
$687$	1.68682e8	+	4.63449e8i	0.520233	+	1.42933i
$688$	8.05391e7	+	4.56760e8i	0.247310	+	1.40256i
$689$	2.64532e7	−	1.50023e8i	0.0808761	−	0.458671i
$690$	1.38804e8	+	5.05207e7i	0.422529	+	0.153788i
$691$	1.29786e8	+	2.24796e8i	0.393363	+	0.681324i	0.992891	−	0.119030i	$-0.0379784\pi$
$691$	1.29786e8	+	2.24796e8i	0.393363	+	0.681324i	−0.599528	+	0.800354i	$0.704645\pi$
$692$	−1.72229e8	−	9.94364e7i	−0.519742	−	0.300073i
$693$	2.09610e6	−	1.75884e6i	0.00629814	−	0.00528477i
$694$	4.40727e8	+	5.25238e8i	1.31853	+	1.57137i
$695$	3.67830e7	−	6.37101e7i	0.109570	−	0.189781i
$696$	1.47865e7	−	8.53701e6i	0.0438570	−	0.0253208i
$697$	−138947.	+	381754.i	−0.000410346	+	0.00112742i
$698$	−5.62448e8	−	9.91747e7i	−1.65393	−	0.291632i
$699$	4.93775e8	−	8.70658e7i	1.44576	−	0.254927i
$700$	−8.17100e7	+	2.97400e7i	−0.238222	+	0.0867056i
$701$	3.93585e7	+	3.30257e7i	0.114257	+	0.0958733i	0.698126	−	0.715975i	$-0.254017\pi$
$701$	3.93585e7	+	3.30257e7i	0.114257	+	0.0958733i	−0.583869	+	0.811848i	$0.698462\pi$
$702$			5.15685e8i			1.49064i
$703$	−3.00253e8	−	3.58229e7i	−0.864216	−	0.103109i
$704$	−6.86917e7			−0.196873
$705$	3.77556e7	−	4.49954e7i	0.107749	−	0.128411i
$706$	3.02107e8	+	8.30033e8i	0.858514	+	2.35875i
$707$	3.77685e6	+	2.14196e7i	0.0106874	+	0.0606112i
$708$	6.74548e7	−	3.82555e8i	0.190070	−	1.07794i
$709$	−1.21658e8	−	4.42799e7i	−0.341352	−	0.124242i	0.165656	−	0.986184i	$-0.447026\pi$
$709$	−1.21658e8	−	4.42799e7i	−0.341352	−	0.124242i	−0.507007	+	0.861942i	$0.669248\pi$
$710$	8.32230e7	+	1.44146e8i	0.232524	+	0.402744i
$711$	8.40241e7	+	4.85113e7i	0.233773	+	0.134969i
$712$	−1.94956e7	+	1.63588e7i	−0.0540129	+	0.0453222i
$713$	−2.77876e8	−	3.31159e8i	−0.766623	−	0.913626i
$714$	−5.87762e7	+	1.01803e8i	−0.161476	+	0.279684i
$715$	1.76795e7	−	1.02072e7i	0.0483672	−	0.0279248i
$716$	−1.90171e8	+	5.22491e8i	−0.518091	+	1.42344i
$717$	1.70199e8	+	3.00107e7i	0.461743	+	0.0814177i
$718$	−7.75756e8	+	1.36787e8i	−2.09581	+	0.369548i
$719$	5.96507e8	−	2.17111e8i	1.60483	−	0.584110i	0.624421	−	0.781088i	$-0.285335\pi$
$719$	5.96507e8	−	2.17111e8i	1.60483	−	0.584110i	0.980408	+	0.196978i	$0.0631128\pi$
$720$	−1.19013e7	−	9.98637e6i	−0.0318857	−	0.0267553i
$721$			6.30562e7i			0.168237i
$722$	−4.31380e8	+	3.17954e8i	−1.14617	+	0.844797i
$723$	5.87560e8			1.55467
$724$	3.61842e8	−	4.31226e8i	0.953461	−	1.13629i
$725$	−1.46375e8	−	4.02162e8i	−0.384108	−	1.05533i
$726$	−9.86244e7	−	5.59327e8i	−0.257736	−	1.46169i
$727$	6.11374e7	−	3.46727e8i	0.159112	−	0.902370i	−0.795817	−	0.605537i	$-0.792958\pi$
$727$	6.11374e7	−	3.46727e8i	0.159112	−	0.902370i	0.954929	−	0.296833i	$-0.0959305\pi$
$728$	4.34388e6	+	1.58104e6i	0.0112586	+	0.00409779i
$729$	1.51584e8	+	2.62551e8i	0.391264	+	0.677689i
$730$	−1.11855e8	−	6.45793e7i	−0.287531	−	0.166006i
$731$	−3.48514e8	+	2.92438e8i	−0.892211	+	0.748654i
$732$	−9.70564e7	−	1.15667e8i	−0.247452	−	0.294902i
$733$	2.63026e8	−	4.55574e8i	0.667861	−	1.15677i	−0.310640	−	0.950528i	$-0.600543\pi$
$733$	2.63026e8	−	4.55574e8i	0.667861	−	1.15677i	0.978501	−	0.206242i	$-0.0661233\pi$
$734$	1.78626e8	−	1.03130e8i	0.451705	−	0.260792i
$735$	3.50776e7	−	9.63748e7i	0.0883421	−	0.242718i
$736$	6.35309e8	+	1.12022e8i	1.59350	+	0.280977i
$737$	−6.29453e7	+	1.10989e7i	−0.157239	+	0.0277255i
$738$	−135245.	+	49225.3i	−0.000336476	+	0.000122467i
$739$	−4.58575e8	−	3.84790e8i	−1.13626	−	0.953433i	−0.136947	−	0.990578i	$-0.543729\pi$
$739$	−4.58575e8	−	3.84790e8i	−1.13626	−	0.953433i	−0.999310	+	0.0371454i	$0.988174\pi$
$740$			9.31545e7i			0.229884i
$741$	6.05487e7	−	5.07496e8i	0.148816	−	1.24732i
$742$	−6.15464e7			−0.150657
$743$	9.76755e7	−	1.16405e8i	0.238133	−	0.283796i	−0.633721	−	0.773562i	$-0.718473\pi$
$743$	9.76755e7	−	1.16405e8i	0.238133	−	0.283796i	0.871854	+	0.489766i	$0.162918\pi$
$744$	−6.22065e6	−	1.70911e7i	−0.0151049	−	0.0415003i
$745$	1.43922e7	+	8.16225e7i	0.0348065	+	0.197397i
$746$	−8.67736e6	+	4.92118e7i	−0.0209012	+	0.118537i
$747$	2.52610e7	+	9.19426e6i	0.0606023	+	0.0220574i
$748$	−3.19157e7	−	5.52796e7i	−0.0762605	−	0.132087i
$749$	7.30786e6	+	4.21920e6i	0.0173918	+	0.0100412i
$750$	2.47107e8	−	2.07347e8i	0.585735	−	0.491490i
$751$	−5.81056e7	−	6.92475e7i	−0.137182	−	0.163487i	0.693079	−	0.720861i	$-0.256253\pi$
$751$	−5.81056e7	−	6.92475e7i	−0.137182	−	0.163487i	−0.830262	+	0.557374i	$0.811809\pi$
$752$	1.24748e8	−	2.16070e8i	0.293346	−	0.508089i
$753$	−2.72162e8	+	1.57133e8i	−0.637445	+	0.368029i
$754$	−2.91958e8	+	8.02147e8i	−0.681092	+	1.87129i
$755$	−1.88650e8	−	3.32641e7i	−0.438345	−	0.0772920i
$756$	1.03975e8	−	1.83335e7i	0.240637	−	0.0424307i
$757$	−4.82747e8	+	1.75706e8i	−1.11284	+	0.405040i	−0.832034	−	0.554725i	$-0.812824\pi$
$757$	−4.82747e8	+	1.75706e8i	−1.11284	+	0.405040i	−0.280805	+	0.959765i	$0.590601\pi$
$758$	−3.77381e8	−	3.16660e8i	−0.866508	−	0.727087i
$759$		−	1.00321e8i		−	0.229438i
$760$	3.01196e6	+	3.20783e6i	0.00686133	+	0.00730753i
$761$	8.89026e7			0.201725			0.100863	−	0.994900i	$-0.467840\pi$
$761$	8.89026e7			0.201725			0.100863	+	0.994900i	$0.467840\pi$
$762$	4.96142e8	−	5.91279e8i	1.12135	−	1.33637i
$763$	−4.16681e7	−	1.14482e8i	−0.0938058	−	0.257729i
$764$	−1.34681e8	−	7.63816e8i	−0.302014	−	1.71281i
$765$	2.64631e6	−	1.50079e7i	0.00591093	−	0.0335225i
$766$	−1.59461e8	−	5.80390e7i	−0.354787	−	0.129132i
$767$	2.58818e8	+	4.48286e8i	0.573599	+	0.993503i
$768$	−3.99565e8	−	2.30689e8i	−0.882072	−	0.509265i
$769$	5.18020e8	−	4.34671e8i	1.13912	−	0.955832i	0.139706	−	0.990193i	$-0.455384\pi$
$769$	5.18020e8	−	4.34671e8i	1.13912	−	0.955832i	0.999409	+	0.0343614i	$0.0109397\pi$
$770$	−5.30152e6	−	6.31811e6i	−0.0116126	−	0.0138393i
$771$	−4.70670e8	+	8.15224e8i	−1.02696	+	1.77874i
$772$	−4.95309e8	+	2.85967e8i	−1.07652	+	0.621532i
$773$	−3.07528e8	+	8.44927e8i	−0.665804	+	1.82928i	−0.117369	+	0.993088i	$0.537446\pi$
$773$	−3.07528e8	+	8.44927e8i	−0.665804	+	1.82928i	−0.548435	+	0.836193i	$0.684776\pi$
$774$	−1.58729e8	−	2.79882e7i	−0.342321	−	0.0603605i
$775$	−4.48968e8	+	7.91652e7i	−0.964518	+	0.170071i
$776$	2.92173e7	−	1.06342e7i	0.0625252	−	0.0227573i
$777$	−8.92540e7	−	7.48930e7i	−0.190268	−	0.159653i
$778$		−	7.72936e8i		−	1.64136i
$779$	−694767.	+	162908.i	−0.00146969	+	0.000344613i
$780$	−1.57452e8			−0.331791
$781$	7.26630e7	−	8.65964e7i	0.152532	−	0.181780i
$782$	2.10498e8	+	5.78338e8i	0.440177	+	1.20938i
$783$	9.02344e7	+	5.11745e8i	0.187969	+	1.06603i
$784$	7.56479e7	−	4.29020e8i	0.156982	−	0.890286i
$785$	4.60851e7	+	1.67736e7i	0.0952690	+	0.0346751i
$786$	6.47801e8	+	1.12202e9i	1.33406	+	2.31065i
$787$	1.36141e8	+	7.86012e7i	0.279296	+	0.161252i	0.633105	−	0.774066i	$-0.281780\pi$
$787$	1.36141e8	+	7.86012e7i	0.279296	+	0.161252i	−0.353808	+	0.935318i	$0.615114\pi$
$788$	−2.02912e8	+	1.70263e8i	−0.414694	+	0.347970i
$789$	−2.28990e8	−	2.72900e8i	−0.466215	−	0.555613i
$790$	1.46224e8	−	2.53267e8i	0.296577	−	0.513686i
$791$	5.00030e7	−	2.88693e7i	0.101034	−	0.0583319i
$792$	206146.	−	566382.i	0.000414954	−	0.00114008i
$793$	1.98148e8	+	3.49389e7i	0.397348	+	0.0700631i
$794$	−2.40515e8	+	4.24093e7i	−0.480486	+	0.0847226i
$795$	5.25042e7	−	1.91100e7i	0.104494	−	0.0380328i
$796$	3.41928e8	+	2.86912e8i	0.677947	+	0.568865i
$797$			4.01317e8i			0.792707i	0.918098	+	0.396353i	$0.129724\pi$
$797$			4.01317e8i			0.792707i	−0.918098	+	0.396353i	$0.870276\pi$
$798$	−2.06167e8	+	1.15131e7i	−0.405706	+	0.0226560i
$799$	2.44733e8			0.479791
$800$	4.37303e8	−	5.21157e8i	0.854107	−	1.01788i
$801$	5.29533e7	+	1.45488e8i	0.103038	+	0.283094i
$802$	−1.41557e8	−	8.02812e8i	−0.274416	−	1.55629i
$803$	−1.52323e7	+	8.63868e7i	−0.0294184	+	0.166840i
$804$	4.63241e8	+	1.68606e8i	0.891331	+	0.324418i
$805$	2.01494e7	+	3.48997e7i	0.0386254	+	0.0669012i
$806$	7.87495e8	+	4.54660e8i	1.50398	+	0.868324i
$807$	−7.35972e8	+	6.17554e8i	−1.40036	+	1.17504i
$808$	3.07959e6	+	3.67011e6i	0.00583793	+	0.00695737i
$809$	−1.51891e8	+	2.63084e8i	−0.286872	+	0.496876i	−0.973061	−	0.230546i	$-0.925949\pi$
$809$	−1.51891e8	+	2.63084e8i	−0.286872	+	0.496876i	0.686190	+	0.727423i	$0.259282\pi$
$810$	−1.91867e8	+	1.10775e8i	−0.361032	+	0.208442i
$811$	2.26037e8	−	6.21030e8i	0.423756	−	1.16426i	−0.525785	−	0.850618i	$-0.676228\pi$
$811$	2.26037e8	−	6.21030e8i	0.423756	−	1.16426i	0.949541	−	0.313643i	$-0.101550\pi$
$812$	1.72112e8	+	3.03480e7i	0.321472	+	0.0566842i
$813$	−7.47769e6	+	1.31852e6i	−0.0139154	+	0.00245366i
$814$	1.17318e8	−	4.27004e7i	0.217517	−	0.0791696i
$815$	−6.87190e7	−	5.76621e7i	−0.126942	−	0.106517i
$816$		−	4.53301e8i		−	0.834288i
$817$	−7.65030e8	−	2.31031e8i	−1.40285	−	0.423646i
$818$	8.39720e8			1.53417
$819$	1.80766e7	−	2.15429e7i	0.0329053	−	0.0392150i
$820$	75190.0	+	206583.i	0.000136370	+	0.000374673i
$821$	−5.38802e7	−	3.05570e8i	−0.0973643	−	0.552181i	−0.993997	−	0.109406i	$-0.965105\pi$
$821$	−5.38802e7	−	3.05570e8i	−0.0973643	−	0.552181i	0.896633	−	0.442775i	$-0.146006\pi$
$822$	3.16483e7	−	1.79487e8i	0.0569817	−	0.323159i
$823$	−2.38627e8	−	8.68532e7i	−0.428076	−	0.155807i	0.118992	−	0.992895i	$-0.462034\pi$
$823$	−2.38627e8	−	8.68532e7i	−0.428076	−	0.155807i	−0.547068	+	0.837088i	$0.684256\pi$
$824$	6.94485e6	+	1.20288e7i	0.0124131	+	0.0215002i
$825$	−9.16224e7	−	5.28982e7i	−0.163170	−	0.0942062i
$826$	1.60204e8	−	1.34427e8i	0.284271	−	0.238532i
$827$	2.89563e8	+	3.45088e8i	0.511949	+	0.610117i	0.958657	−	0.284563i	$-0.0918484\pi$
$827$	2.89563e8	+	3.45088e8i	0.511949	+	0.610117i	−0.446709	+	0.894679i	$0.647404\pi$
$828$	−5.52462e7	+	9.56892e7i	−0.0973220	+	0.168567i
$829$	4.19752e8	−	2.42344e8i	0.736766	−	0.425372i	−0.0841263	−	0.996455i	$-0.526810\pi$
$829$	4.19752e8	−	2.42344e8i	0.736766	−	0.425372i	0.820892	+	0.571083i	$0.193477\pi$
$830$	2.77135e7	−	7.61423e7i	0.0484683	−	0.133165i
$831$	−2.19031e8	−	3.86211e7i	−0.381683	−	0.0673009i
$832$	−6.95261e8	+	1.22593e8i	−1.20720	+	0.212861i
$833$	4.01552e8	−	1.46153e8i	0.694715	−	0.252856i
$834$	5.82529e8	+	4.88800e8i	1.00420	+	0.842622i
$835$			1.18813e8i			0.204082i
$836$	5.05607e7	−	1.00077e8i	0.0865356	−	0.171284i
$837$	5.53542e8			0.944004
$838$	−2.58255e8	+	3.07776e8i	−0.438850	+	0.523001i
$839$	−1.76158e8	−	4.83990e8i	−0.298275	−	0.819503i	−0.994789	−	0.101960i	$-0.967489\pi$
$839$	−1.76158e8	−	4.83990e8i	−0.298275	−	0.819503i	0.696514	−	0.717544i	$-0.254734\pi$
$840$	294417.	+	1.66972e6i	0.000496735	+	0.00281712i
$841$	−4.60774e7	+	2.61318e8i	−0.0774641	+	0.439321i
$842$	6.10729e8	+	2.22287e8i	1.02309	+	0.372373i
$843$	−8.05736e7	−	1.39558e8i	−0.134496	−	0.232954i
$844$	−6.00650e8	−	3.46785e8i	−0.999066	−	0.576811i
$845$	4.19000e7	−	3.51583e7i	0.0694454	−	0.0582716i
$846$	5.57314e7	+	6.64181e7i	0.0920426	+	0.109692i
$847$	7.74743e7	−	1.34189e8i	0.127499	−	0.220835i
$848$	2.05536e8	−	1.18666e8i	0.337054	−	0.194598i
$849$	1.64191e8	−	4.51111e8i	0.268304	−	0.737158i
$850$	6.39188e8	+	1.12706e8i	1.04081	+	0.183523i
$851$	−6.00744e8	+	1.05927e8i	−0.974767	+	0.171878i
$852$	−8.19297e8	+	2.98200e8i	−1.32472	+	0.482157i
$853$	6.09237e8	+	5.11211e8i	0.981611	+	0.823669i	0.984332	−	0.176327i	$-0.0564216\pi$
$853$	6.09237e8	+	5.11211e8i	0.981611	+	0.823669i	−0.00272066	+	0.999996i	$0.500866\pi$
$854$		−	8.12893e7i		−	0.130515i
$855$	2.46051e7	−	1.05439e7i	0.0393666	−	0.0168695i
$856$	1.85877e6			0.00296349
$857$	−3.03913e8	+	3.62189e8i	−0.482843	+	0.575430i	−0.951382	−	0.308012i	$-0.900336\pi$
$857$	−3.03913e8	+	3.62189e8i	−0.482843	+	0.575430i	0.468539	+	0.883443i	$0.344781\pi$
$858$	7.21732e7	+	1.98294e8i	0.114265	+	0.313941i
$859$	4.81234e7	+	2.72921e8i	0.0759236	+	0.430584i	0.998949	+	0.0458441i	$0.0145978\pi$
$859$	4.81234e7	+	2.72921e8i	0.0759236	+	0.430584i	−0.923025	+	0.384740i	$0.874291\pi$
$860$	−4.27511e7	+	2.42453e8i	−0.0672128	+	0.381183i
$861$	−258383.	−	94043.8i	−0.000404813	−	0.000147340i
$862$	−4.31546e8	−	7.47459e8i	−0.673760	−	1.16699i
$863$	−5.53002e7	−	3.19276e7i	−0.0860387	−	0.0496745i	0.456363	−	0.889794i	$-0.349152\pi$
$863$	−5.53002e7	−	3.19276e7i	−0.0860387	−	0.0496745i	−0.542402	+	0.840119i	$0.682485\pi$
$864$	−6.32783e8	+	5.30968e8i	−0.981101	+	0.823241i
$865$	6.24778e7	+	7.44581e7i	0.0965333	+	0.115044i
$866$	2.62442e8	−	4.54562e8i	0.404091	−	0.699906i
$867$	−2.24527e8	+	1.29631e8i	−0.344518	+	0.198907i
$868$	6.36737e7	−	1.74942e8i	0.0973645	−	0.267507i
$869$	−1.95602e8	−	3.44898e7i	−0.298066	−	0.0525571i
$870$	−3.08333e8	+	5.43675e7i	−0.468234	+	0.0825622i
$871$	−6.17290e8	+	2.24675e8i	−0.934189	+	0.340017i
$872$	−2.05575e7	−	1.72498e7i	−0.0310043	−	0.0260157i
$873$		−	1.89153e8i		−	0.284295i
$874$	−6.47652e8	+	8.65617e8i	−0.970080	+	1.29656i
$875$	8.80045e7			0.131365
$876$	4.34884e8	−	5.18274e8i	0.646935	−	0.770987i
$877$	6.09099e7	+	1.67349e8i	0.0903004	+	0.248098i	0.976619	−	0.214978i	$-0.0689679\pi$
$877$	6.09099e7	+	1.67349e8i	0.0903004	+	0.248098i	−0.886319	+	0.463076i	$0.846746\pi$
$878$	−1.24056e8	−	7.03554e8i	−0.183287	−	1.03947i
$879$	−1.15758e8	+	6.56499e8i	−0.170446	+	0.966646i
$880$	2.98864e7	+	1.08778e7i	0.0438556	+	0.0159621i
$881$	6.29536e7	+	1.09039e8i	0.0920647	+	0.159461i	0.908380	−	0.418146i	$-0.137320\pi$
$881$	6.29536e7	+	1.09039e8i	0.0920647	+	0.159461i	−0.816315	+	0.577607i	$0.803987\pi$
$882$	1.31107e8	+	7.56947e7i	0.191082	+	0.110321i
$883$	−7.32058e7	+	6.14270e7i	−0.106332	+	0.0892230i	−0.694404	−	0.719586i	$-0.744332\pi$
$883$	−7.32058e7	+	6.14270e7i	−0.106332	+	0.0892230i	0.588072	+	0.808809i	$0.299887\pi$
$884$	−4.21691e8	−	5.02551e8i	−0.610432	−	0.727484i
$885$	−9.49282e7	+	1.64420e8i	−0.136951	+	0.237206i
$886$	−2.43277e8	+	1.40456e8i	−0.349783	+	0.201948i
$887$	2.15606e8	−	5.92372e8i	0.308951	−	0.848836i	−0.683911	−	0.729565i	$-0.739722\pi$
$887$	2.15606e8	−	5.92372e8i	0.308951	−	0.848836i	0.992862	−	0.119270i	$-0.0380554\pi$
$888$	−2.52750e7	−	4.45666e6i	−0.0360954	−	0.00636459i
$889$	2.07378e8	−	3.65664e7i	0.295160	−	0.0520448i
$890$	4.38533e8	−	1.59613e8i	0.622060	−	0.226411i
$891$	1.15265e8	+	9.67186e7i	0.162953	+	0.136734i
$892$		−	5.23564e7i		−	0.0737692i
$893$	2.35368e8	+	3.59732e8i	0.330517	+	0.505155i
$894$	−8.56730e8			−1.19903
$895$	1.74680e8	−	2.08176e8i	0.243654	−	0.290376i
$896$	5.06702e6	+	1.39215e7i	0.00704416	+	0.0193537i
$897$	−1.79041e8	−	1.01539e9i	−0.248070	−	1.40688i
$898$	−1.06101e8	+	6.01726e8i	−0.146517	+	0.830941i
$899$	8.61034e8	+	3.13391e8i	1.18506	+	0.431327i
$900$	5.82617e7	+	1.00912e8i	0.0799200	+	0.138426i
$901$	2.01612e8	+	1.16401e8i	0.275640	+	0.159141i
$902$	225704.	−	189388.i	0.000307552	−	0.000258067i
$903$	−1.97931e8	−	2.35885e8i	−0.268814	−	0.320360i
$904$	6.35918e6	−	1.10144e7i	0.00860787	−	0.0149093i
$905$	−2.38267e8	+	1.37564e8i	−0.321454	+	0.185592i
$906$	6.77240e8	−	1.86070e9i	0.910664	−	2.50203i
$907$	4.26771e8	+	7.52513e7i	0.571970	+	0.100854i	0.452150	−	0.891942i	$-0.350657\pi$
$907$	4.26771e8	+	7.52513e7i	0.571970	+	0.100854i	0.119820	+	0.992796i	$0.461768\pi$
$908$	2.63449e8	−	4.64532e7i	0.351916	−	0.0620523i
$909$	2.73886e7	−	9.96862e6i	0.0364651	−	0.0132722i
$910$	−6.49350e7	−	5.44870e7i	−0.0861698	−	0.0723050i
$911$		−	1.40619e9i		−	1.85990i	−0.367686	−	0.929950i	$-0.619850\pi$
$911$		−	1.40619e9i		−	1.85990i	0.367686	−	0.929950i	$-0.380150\pi$
$912$	6.66304e8	−	4.35955e8i	0.878391	−	0.574721i
$913$	−5.50317e7			−0.0723103
$914$	−7.59074e8	+	9.04629e8i	−0.994135	+	1.18476i
$915$	2.52401e7	+	6.93466e7i	0.0329479	+	0.0905236i
$916$	1.93097e8	+	1.09511e9i	0.251241	+	1.42486i
$917$	−6.13784e7	+	3.48094e8i	−0.0795990	+	0.451428i
$918$	−7.40541e8	−	2.69535e8i	−0.957240	−	0.348407i
$919$	−3.93534e8	−	6.81621e8i	−0.507033	−	0.878206i	−0.999967	−	0.00813973i	$-0.997409\pi$
$919$	−3.93534e8	−	6.81621e8i	−0.507033	−	0.878206i	0.492934	−	0.870067i	$-0.335924\pi$
$920$	7.68753e6	+	4.43840e6i	0.00987242	+	0.00569984i
$921$	−2.33631e7	+	1.96040e7i	−0.0299055	+	0.0250937i
$922$	−8.24654e8	−	9.82785e8i	−1.05215	−	1.25391i
$923$	5.80909e8	−	1.00616e9i	0.738759	−	1.27957i
$924$	3.74150e7	−	2.16016e7i	0.0474275	−	0.0273823i
$925$	−2.20024e8	+	6.04512e8i	−0.278000	+	0.763800i
$926$	−1.36777e9	−	2.41175e8i	−1.72258	−	0.303738i
$927$	8.32152e7	−	1.46731e7i	0.104463	−	0.0184197i
$928$	−1.28490e9	+	4.67667e8i	−1.60778	+	0.585184i
$929$	2.61959e8	+	2.19810e8i	0.326728	+	0.274157i	0.791365	−	0.611344i	$-0.209371\pi$
$929$	2.61959e8	+	2.19810e8i	0.326728	+	0.274157i	−0.464637	+	0.885501i	$0.653815\pi$
$930$			3.33517e8i			0.414638i
$931$	6.01016e8	+	4.49679e8i	0.744796	+	0.557254i
$932$	1.13049e9			1.39643
$933$	2.86265e8	−	3.41158e8i	0.352471	−	0.420059i
$934$	−3.09540e7	−	8.50453e7i	−0.0379906	−	0.104378i
$935$	5.41736e6	+	3.07234e7i	0.00662754	+	0.0375867i
$936$	1.07569e6	−	6.10052e6i	0.00131177	−	0.00743943i
$937$	1.02659e9	+	3.73649e8i	1.24790	+	0.454198i	0.879691	−	0.475546i	$-0.157750\pi$
$937$	1.02659e9	+	3.73649e8i	1.24790	+	0.454198i	0.368207	+	0.929744i	$0.379972\pi$
$938$	1.32699e8	+	2.29842e8i	0.160790	+	0.278497i
$939$	−5.47244e8	−	3.15952e8i	−0.660974	−	0.381614i
$940$	1.01451e8	−	8.51278e7i	0.122145	−	0.102491i
$941$	8.12363e7	+	9.68137e7i	0.0974948	+	0.116190i	0.812586	−	0.582842i	$-0.198059\pi$
$941$	8.12363e7	+	9.68137e7i	0.0974948	+	0.116190i	−0.715091	+	0.699031i	$0.753615\pi$
$942$	−2.53472e8	+	4.39027e8i	−0.303234	+	0.525216i
$943$	−1.24673e6	+	719801.i	−0.00148675	+	0.000858376i
$944$	−2.75820e8	+	7.57809e8i	−0.327876	+	0.900832i
$945$	−5.08171e7	−	8.96043e6i	−0.0602164	−	0.0106178i
$946$	3.24941e8	−	5.72959e7i	0.383823	−	0.0676784i
$947$	2.11155e8	−	7.68540e7i	0.248628	−	0.0904933i	−0.214700	−	0.976680i	$-0.568877\pi$
$947$	2.11155e8	−	7.68540e7i	0.248628	−	0.0904933i	0.463328	+	0.886187i	$0.346655\pi$
$948$	1.17350e9	+	9.84687e8i	1.37740	+	1.15577i
$949$			9.01546e8i			1.05485i
$950$	4.49063e8	+	1.04793e9i	0.523765	+	1.22226i
$951$	−1.51756e9			−1.76443
$952$	−4.54086e6	+	5.41159e6i	−0.00526293	+	0.00627211i
$953$	−2.87351e8	−	7.89491e8i	−0.331997	−	0.912154i	−0.987592	−	0.157042i	$-0.949804\pi$
$953$	−2.87351e8	−	7.89491e8i	−0.331997	−	0.912154i	0.655595	−	0.755113i	$-0.272418\pi$
$954$	1.43218e7	+	8.12227e7i	0.0164950	+	0.0935475i
$955$	−6.58249e7	+	3.73311e8i	−0.0755753	+	0.428609i
$956$	3.66169e8	+	1.33274e8i	0.419090	+	0.152536i
$957$	1.06319e8	+	1.84150e8i	0.121304	+	0.210105i
$958$	1.16413e9	+	6.72114e8i	1.32406	+	0.764445i
$959$	3.80898e7	−	3.19611e7i	0.0431869	−	0.0362382i
$960$	−1.66443e8	−	1.98359e8i	−0.188127	−	0.224201i
$961$	4.42853e7	−	7.67044e7i	0.0498987	−	0.0864271i
$962$	1.11123e9	−	6.41567e8i	1.24818	−	0.720637i
$963$	3.86754e6	−	1.06260e7i	0.00433068	−	0.0118984i
$964$	1.30465e9	+	2.30044e8i	1.45634	+	0.256791i
$965$	2.75283e8	−	4.85398e7i	0.306336	−	0.0540153i
$966$	−3.91438e8	+	1.42472e8i	−0.434242	+	0.158051i
$967$	2.31425e8	+	1.94189e8i	0.255936	+	0.214756i	0.761723	−	0.647902i	$-0.224354\pi$
$967$	2.31425e8	+	1.94189e8i	0.255936	+	0.214756i	−0.505787	+	0.862658i	$0.668798\pi$
$968$		−	3.41313e7i		−	0.0376294i
$969$	6.97133e8	+	3.52204e8i	0.766204	+	0.387100i
$970$	−5.70148e8			−0.624701
$971$	2.49294e7	−	2.97097e7i	0.0272304	−	0.0324519i	−0.752257	−	0.658869i	$-0.771035\pi$
$971$	2.49294e7	−	2.97097e7i	0.0272304	−	0.0324519i	0.779488	+	0.626417i	$0.215479\pi$
$972$	−1.06452e8	−	2.92473e8i	−0.115919	−	0.318484i
$973$	3.60253e7	+	2.04309e8i	0.0391083	+	0.221794i
$974$	−3.32236e8	+	1.88421e9i	−0.359559	+	2.03916i
$975$	−1.02176e9	−	3.71890e8i	−1.10239	−	0.401237i
$976$	1.56732e8	+	2.71468e8i	0.168581	+	0.291991i
$977$	3.78306e8	+	2.18415e8i	0.405657	+	0.234206i	0.688922	−	0.724835i	$-0.258084\pi$
$977$	3.78306e8	+	2.18415e8i	0.405657	+	0.234206i	−0.283265	+	0.959042i	$0.591418\pi$
$978$	7.10334e8	−	5.96041e8i	0.759357	−	0.637176i
$979$	−2.03731e8	−	2.42797e8i	−0.217124	−	0.258759i
$980$	1.15621e8	−	2.00262e8i	0.122845	−	0.212775i
$981$	−1.41386e8	+	8.16292e7i	−0.149761	+	0.0864646i
$982$	3.24506e8	−	8.91572e8i	0.342679	−	0.941503i
$983$	1.55762e7	+	2.74651e6i	0.0163984	+	0.00289148i	0.181841	−	0.983328i	$-0.441794\pi$
$983$	1.55762e7	+	2.74651e6i	0.0163984	+	0.00289148i	−0.165443	+	0.986219i	$0.552905\pi$
$984$	−59647.9	+	10517.5i	−6.26051e−5	+	1.10390e-5i
$985$	1.21653e8	−	4.42779e7i	0.127295	−	0.0463317i
$986$	−9.99312e8	−	8.38522e8i	−1.04249	−	0.874750i
$987$			1.65643e8i			0.172275i
$988$	3.33143e8	−	1.10316e9i	0.345429	−	1.14385i
$989$	−1.61217e9			−1.66656
$990$	−7.10435e6	+	8.46663e6i	−0.00732182	+	0.00872580i
$991$	1.06714e8	+	2.93195e8i	0.109648	+	0.301256i	0.982366	−	0.186970i	$-0.0598666\pi$
$991$	1.06714e8	+	2.93195e8i	0.109648	+	0.301256i	−0.872717	+	0.488226i	$0.837644\pi$
$992$	2.52932e8	+	1.43445e9i	0.259101	+	1.46943i
$993$	4.43198e7	−	2.51350e8i	0.0452637	−	0.256703i
$994$	−4.41081e8	−	1.60540e8i	−0.449117	−	0.163465i
$995$	−1.09077e8	−	1.88927e8i	−0.110730	−	0.191790i
$996$	3.67581e8	+	2.12223e8i	0.372027	+	0.214790i
$997$	1.11892e8	−	9.38883e7i	0.112905	−	0.0947384i	−0.584587	−	0.811331i	$-0.698744\pi$
$997$	1.11892e8	−	9.38883e7i	0.112905	−	0.0947384i	0.697492	+	0.716592i	$0.254299\pi$
$998$	−8.30462e8	−	9.89706e8i	−0.835465	−	0.995668i
$999$	3.90549e8	−	6.76450e8i	0.391723	−	0.678484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.7.f.a.3.8	✓	54
19.13	odd	18	inner	19.7.f.a.13.8	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.7.f.a.3.8	✓	54	1.1	even	1	trivial
19.7.f.a.13.8	yes	54	19.13	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.32193 - 8.72593i) q^{2} +(-9.97412 - 27.4037i) q^{3} +(-11.4178 - 64.7536i) q^{4} +(-5.58040 + 31.6480i) q^{5} +(-312.152 - 113.614i) q^{6} +(-45.3132 - 78.4847i) q^{7} +(-17.2882 - 9.98136i) q^{8} +(-93.0319 + 78.0631i) q^{9} +O(q^{10})\)	\(q+(7.32193 - 8.72593i) q^{2} +(-9.97412 - 27.4037i) q^{3} +(-11.4178 - 64.7536i) q^{4} +(-5.58040 + 31.6480i) q^{5} +(-312.152 - 113.614i) q^{6} +(-45.3132 - 78.4847i) q^{7} +(-17.2882 - 9.98136i) q^{8} +(-93.0319 + 78.0631i) q^{9} +(235.299 + 280.419i) q^{10} +(124.307 - 215.306i) q^{11} +(-1660.60 + 958.750i) q^{12} +(873.915 - 2401.06i) q^{13} +(-1016.63 - 179.260i) q^{14} +(922.932 - 162.738i) q^{15} +(3740.70 - 1361.50i) q^{16} +(2991.23 + 2509.94i) q^{17} +1383.36i q^{18} +(-812.577 + 6810.70i) q^{19} +2113.04 q^{20} +(-1698.81 + 2024.56i) q^{21} +(-968.579 - 2661.15i) q^{22} +(2402.77 + 13626.8i) q^{23} +(-101.091 + 573.316i) q^{24} +(13712.2 + 4990.85i) q^{25} +(-14552.8 - 25206.1i) q^{26} +(-15344.0 - 8858.88i) q^{27} +(-4564.79 + 3830.31i) q^{28} +(-18852.1 - 22467.1i) q^{29} +(5337.60 - 9245.00i) q^{30} +(-27056.5 + 15621.1i) q^{31} +(15945.7 - 43810.5i) q^{32} +(-7140.03 - 1258.98i) q^{33} +(43803.2 - 7723.68i) q^{34} +(2736.75 - 996.096i) q^{35} +(6117.08 + 5132.84i) q^{36} +44085.6i q^{37} +(53480.1 + 56957.9i) q^{38} -74514.5 q^{39} +(412.366 - 491.438i) q^{40} +(35.5838 + 97.7657i) q^{41} +(5227.64 + 29647.4i) q^{42} +(-20232.0 + 114742. i) q^{43} +(-15361.2 - 5591.00i) q^{44} +(-1951.39 - 3379.90i) q^{45} +(136499. + 78807.8i) q^{46} +(48012.0 - 40286.9i) q^{47} +(-74620.4 - 88929.1i) q^{48} +(54717.9 - 94774.2i) q^{49} +(143950. - 83109.5i) q^{50} +(38946.7 - 107005. i) q^{51} +(-165456. - 29174.3i) q^{52} +(58714.0 - 10352.9i) q^{53} +(-189650. + 69026.9i) q^{54} +(6120.33 + 5135.57i) q^{55} +1809.15i q^{56} +(194743. - 45663.1i) q^{57} -334080. q^{58} +(-130219. + 155189. i) q^{59} +(-21075.7 - 57905.0i) q^{60} +(13673.9 + 77548.4i) q^{61} +(-61797.3 + 350470. i) q^{62} +(10342.3 + 3764.30i) q^{63} +(-138149. - 239282. i) q^{64} +(71112.1 + 41056.6i) q^{65} +(-63264.6 + 53085.3i) q^{66} +(-165255. - 196943. i) q^{67} +(128374. - 222351. i) q^{68} +(349458. - 201760. i) q^{69} +(11346.4 - 31174.1i) q^{70} +(447787. + 78956.9i) q^{71} +(2387.53 - 420.986i) q^{72} +(-331555. + 120676. i) q^{73} +(384688. + 322791. i) q^{74} -425545. i q^{75} +(450295. - 25145.9i) q^{76} -22531.0 q^{77} +(-545590. + 650208. i) q^{78} +(-273242. - 750725. i) q^{79} +(22214.3 + 125983. i) q^{80} +(-105096. + 596031. i) q^{81} +(1113.64 + 405.332i) q^{82} +(-110677. - 191698. i) q^{83} +(150494. + 86888.0i) q^{84} +(-96127.0 + 80660.2i) q^{85} +(853090. + 1.01667e6i) q^{86} +(-427647. + 740707. i) q^{87} +(-4298.09 + 2481.51i) q^{88} +(436029. - 1.19798e6i) q^{89} +(-43780.7 - 7719.72i) q^{90} +(-228047. + 40210.8i) q^{91} +(854948. - 311176. i) q^{92} +(697941. + 585642. i) q^{93} -713928. i q^{94} +(-211011. - 63722.9i) q^{95} -1.35961e6 q^{96} +(-1.00116e6 + 1.19313e6i) q^{97} +(-426353. - 1.17140e6i) q^{98} +(5242.93 + 29734.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9}+O(q^{10}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} - 1689 q^{10} + 1677 q^{11} - 9 q^{12} - 10506 q^{13} + 6105 q^{14} + 24138 q^{15} + 23760 q^{16} - 3438 q^{17} - 30918 q^{19} - 76650 q^{20} - 59055 q^{21} + 20490 q^{22} + 42498 q^{23} + 31848 q^{24} + 7914 q^{25} + 109989 q^{26} + 124821 q^{27} - 109476 q^{28} - 27726 q^{29} - 153516 q^{30} - 30789 q^{31} - 114375 q^{32} + 126039 q^{33} + 359796 q^{34} + 160161 q^{35} + 184995 q^{36} - 245244 q^{38} - 390564 q^{39} - 372678 q^{40} - 24708 q^{41} - 244893 q^{42} - 30726 q^{43} - 301419 q^{44} + 293037 q^{45} + 69246 q^{46} - 71454 q^{47} + 1024041 q^{48} - 350346 q^{49} - 104148 q^{50} - 180672 q^{51} + 921801 q^{52} + 822558 q^{53} + 308469 q^{54} + 623517 q^{55} - 17862 q^{57} - 1150644 q^{58} - 463812 q^{59} - 908130 q^{60} - 583698 q^{61} - 429732 q^{62} - 2576043 q^{63} - 328293 q^{64} - 1056789 q^{65} - 1038756 q^{66} + 1120464 q^{67} + 717270 q^{68} + 3771567 q^{69} + 4845345 q^{70} + 94494 q^{71} + 2351634 q^{72} + 950850 q^{73} + 55149 q^{74} - 218814 q^{76} - 343086 q^{77} + 1833471 q^{78} - 4936494 q^{79} - 9642039 q^{80} - 769551 q^{81} - 8627793 q^{82} - 412131 q^{83} - 3125205 q^{84} - 896910 q^{85} + 8878236 q^{86} + 610737 q^{87} + 13604751 q^{88} + 6653022 q^{89} + 3142734 q^{90} + 3409821 q^{91} - 3043740 q^{92} - 816393 q^{93} + 4839186 q^{95} - 5667138 q^{96} - 853656 q^{97} - 17679315 q^{98} - 13991937 q^{99}+O(q^{100}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9 - 1689 * q^10 + 1677 * q^11 - 9 * q^12 - 10506 * q^13 + 6105 * q^14 + 24138 * q^15 + 23760 * q^16 - 3438 * q^17 - 30918 * q^19 - 76650 * q^20 - 59055 * q^21 + 20490 * q^22 + 42498 * q^23 + 31848 * q^24 + 7914 * q^25 + 109989 * q^26 + 124821 * q^27 - 109476 * q^28 - 27726 * q^29 - 153516 * q^30 - 30789 * q^31 - 114375 * q^32 + 126039 * q^33 + 359796 * q^34 + 160161 * q^35 + 184995 * q^36 - 245244 * q^38 - 390564 * q^39 - 372678 * q^40 - 24708 * q^41 - 244893 * q^42 - 30726 * q^43 - 301419 * q^44 + 293037 * q^45 + 69246 * q^46 - 71454 * q^47 + 1024041 * q^48 - 350346 * q^49 - 104148 * q^50 - 180672 * q^51 + 921801 * q^52 + 822558 * q^53 + 308469 * q^54 + 623517 * q^55 - 17862 * q^57 - 1150644 * q^58 - 463812 * q^59 - 908130 * q^60 - 583698 * q^61 - 429732 * q^62 - 2576043 * q^63 - 328293 * q^64 - 1056789 * q^65 - 1038756 * q^66 + 1120464 * q^67 + 717270 * q^68 + 3771567 * q^69 + 4845345 * q^70 + 94494 * q^71 + 2351634 * q^72 + 950850 * q^73 + 55149 * q^74 - 218814 * q^76 - 343086 * q^77 + 1833471 * q^78 - 4936494 * q^79 - 9642039 * q^80 - 769551 * q^81 - 8627793 * q^82 - 412131 * q^83 - 3125205 * q^84 - 896910 * q^85 + 8878236 * q^86 + 610737 * q^87 + 13604751 * q^88 + 6653022 * q^89 + 3142734 * q^90 + 3409821 * q^91 - 3043740 * q^92 - 816393 * q^93 + 4839186 * q^95 - 5667138 * q^96 - 853656 * q^97 - 17679315 * q^98 - 13991937 * q^99

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