LMFDB - Embedded newform 62.8.g.b.9.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,144] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.5
Character	$\chi$	$=$	62.9
Dual form			62.8.g.b.7.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.47214 + 7.60845i) q^{2} +(-20.1699 - 4.28724i) q^{3} +(-51.7771 - 37.6183i) q^{4} +(104.818 + 181.551i) q^{5} +(82.4820 - 142.863i) q^{6} +(-243.185 + 108.273i) q^{7} +(414.217 - 300.946i) q^{8} +(-1609.48 - 716.587i) q^{9} +(-1640.45 + 348.687i) q^{10} +(-321.232 + 3056.32i) q^{11} +(883.060 + 980.737i) q^{12} +(-1391.34 + 1545.24i) q^{13} +(-222.603 - 2117.92i) q^{14} +(-1335.82 - 4111.24i) q^{15} +(1265.73 + 3895.53i) q^{16} +(-1261.74 - 12004.7i) q^{17} +(9430.97 - 10474.1i) q^{18} +(-21164.7 - 23505.8i) q^{19} +(1402.43 - 13343.3i) q^{20} +(5369.20 - 1141.26i) q^{21} +(-22459.7 - 9999.71i) q^{22} +(54649.6 - 39705.3i) q^{23} +(-9644.94 + 4294.20i) q^{24} +(17088.7 - 29598.5i) q^{25} +(-8317.32 - 14406.0i) q^{26} +(65875.1 + 47861.1i) q^{27} +(16664.4 + 3542.13i) q^{28} +(32511.4 - 100060. i) q^{29} +34582.5 q^{30} +(157890. - 50827.8i) q^{31} -32768.0 q^{32} +(19582.4 - 60268.4i) q^{33} +(94456.1 + 20077.3i) q^{34} +(-45147.2 - 32801.4i) q^{35} +(56377.4 + 97648.6i) q^{36} +(-22493.7 + 38960.2i) q^{37} +(231165. - 102921. i) q^{38} +(34688.1 - 25202.4i) q^{39} +(98054.5 + 43656.7i) q^{40} +(463200. - 98456.2i) q^{41} +(-4590.18 + 43672.6i) q^{42} +(-482522. - 535895. i) q^{43} +(131606. - 146163. i) q^{44} +(-38606.2 - 367314. i) q^{45} +(166994. + 513956. i) q^{46} +(-351018. - 1.08032e6i) q^{47} +(-8828.64 - 83998.9i) q^{48} +(-503642. + 559351. i) q^{49} +(182953. + 203190. i) q^{50} +(-26017.7 + 247542. i) q^{51} +(130169. - 27668.3i) q^{52} +(35331.6 + 15730.6i) q^{53} +(-527001. + 382889. i) q^{54} +(-588548. + 262038. i) q^{55} +(-68146.9 + 118034. i) q^{56} +(326115. + 564849. i) q^{57} +(680928. + 494723. i) q^{58} +(-1.65292e6 - 351339. i) q^{59} +(-85492.7 + 263119. i) q^{60} -362507. q^{61} +(-3603.80 + 1.32695e6i) q^{62} +468988. q^{63} +(81007.0 - 249314. i) q^{64} +(-426379. - 90629.6i) q^{65} +(410139. + 297984. i) q^{66} +(-576167. - 997950. i) q^{67} +(-386265. + 669031. i) q^{68} +(-1.27250e6 + 566555. i) q^{69} +(361178. - 262411. i) q^{70} +(-1.58243e6 - 704542. i) q^{71} +(-882327. + 187544. i) q^{72} +(-265047. + 2.52175e6i) q^{73} +(-240819. - 267457. i) q^{74} +(-471574. + 523736. i) q^{75} +(211601. + 2.01324e6i) q^{76} +(-252797. - 778030. i) q^{77} +(105997. + 326226. i) q^{78} +(219395. + 2.08741e6i) q^{79} +(-574564. + 638118. i) q^{80} +(1.45469e6 + 1.61559e6i) q^{81} +(-395994. + 3.76763e6i) q^{82} +(1.14313e6 - 242980. i) q^{83} +(-320934. - 142889. i) q^{84} +(2.04720e6 - 1.48738e6i) q^{85} +(5.27019e6 - 2.34644e6i) q^{86} +(-1.08473e6 + 1.87881e6i) q^{87} +(786727. + 1.36265e6i) q^{88} +(145033. + 105373. i) q^{89} +(2.89013e6 + 614316. i) q^{90} +(171046. - 526424. i) q^{91} -4.32324e6 q^{92} +(-3.40253e6 + 348280. i) q^{93} +9.08734e6 q^{94} +(2.04905e6 - 6.30632e6i) q^{95} +(660927. + 140484. i) q^{96} +(-2.90851e6 - 2.11315e6i) q^{97} +(-3.01072e6 - 5.21473e6i) q^{98} +(2.70713e6 - 4.68889e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) $ 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−2.47214	+	7.60845i	−0.218508	+	0.672499i
$2$	−2.47214	+	7.60845i	−0.218508	+	0.672499i
$3$	−20.1699	−	4.28724i	−0.431300	−	0.0916756i	−0.0128540	−	0.999917i	$-0.504092\pi$
$3$	−20.1699	−	4.28724i	−0.431300	−	0.0916756i	−0.418446	+	0.908242i	$0.637425\pi$
$4$	−51.7771	−	37.6183i	−0.404508	−	0.293893i
$5$	104.818	+	181.551i	0.375010	+	0.649536i	0.990328	−	0.138743i	$-0.0443061\pi$
$5$	104.818	+	181.551i	0.375010	+	0.649536i	−0.615319	+	0.788278i	$0.710973\pi$
$6$	82.4820	−	142.863i	0.155894	−	0.270017i
$7$	−243.185	+	108.273i	−0.267974	+	0.119310i	−0.536325	−	0.844011i	$-0.680188\pi$
$7$	−243.185	+	108.273i	−0.267974	+	0.119310i	0.268351	+	0.963321i	$0.413521\pi$
$8$	414.217	−	300.946i	0.286031	−	0.207813i
$9$	−1609.48	−	716.587i	−0.735930	−	0.327657i
$10$	−1640.45	+	348.687i	−0.518754	+	0.110265i
$11$	−321.232	+	3056.32i	−0.0727687	+	0.692348i	0.895945	+	0.444166i	$0.146500\pi$
$11$	−321.232	+	3056.32i	−0.0727687	+	0.692348i	−0.968713	+	0.248182i	$0.920167\pi$
$12$	883.060	+	980.737i	0.147522	+	0.163839i
$13$	−1391.34	+	1545.24i	−0.175644	+	0.195072i	−0.824538	−	0.565806i	$-0.808565\pi$
$13$	−1391.34	+	1545.24i	−0.175644	+	0.195072i	0.648894	+	0.760878i	$0.275232\pi$
$14$	−222.603	−	2117.92i	−0.0216812	−	0.206282i
$15$	−1335.82	−	4111.24i	−0.102195	−	0.314524i
$16$	1265.73	+	3895.53i	0.0772542	+	0.237764i
$17$	−1261.74	−	12004.7i	−0.0622872	−	0.592623i	−0.980498	−	0.196530i	$-0.937033\pi$
$17$	−1261.74	−	12004.7i	−0.0622872	−	0.592623i	0.918211	−	0.396093i	$-0.129634\pi$
$18$	9430.97	−	10474.1i	0.381156	−	0.423316i
$19$	−21164.7	−	23505.8i	−0.707906	−	0.786209i	0.276708	−	0.960954i	$-0.410757\pi$
$19$	−21164.7	−	23505.8i	−0.707906	−	0.786209i	−0.984614	+	0.174745i	$0.944090\pi$
$20$	1402.43	−	13343.3i	0.0391992	−	0.372955i
$21$	5369.20	−	1141.26i	0.126515	−	0.0268916i
$22$	−22459.7	−	9999.71i	−0.449702	−	0.200220i
$23$	54649.6	−	39705.3i	0.936568	−	0.680457i	−0.0110238	−	0.999939i	$-0.503509\pi$
$23$	54649.6	−	39705.3i	0.936568	−	0.680457i	0.947592	+	0.319482i	$0.103509\pi$
$24$	−9644.94	+	4294.20i	−0.142416	+	0.0634079i
$25$	17088.7	−	29598.5i	0.218736	−	0.378861i
$26$	−8317.32	−	14406.0i	−0.0928062	−	0.160745i
$27$	65875.1	+	47861.1i	0.644093	+	0.467961i
$28$	16664.4	+	3542.13i	0.143462	+	0.0304938i
$29$	32511.4	−	100060.i	0.247539	−	0.761846i	−0.747670	−	0.664071i	$-0.768827\pi$
$29$	32511.4	−	100060.i	0.247539	−	0.761846i	0.995209	−	0.0977752i	$-0.0311726\pi$
$30$	34582.5			0.233847
$31$	157890.	−	50827.8i	0.951892	−	0.306433i
$31$	157890.	−	50827.8i	0.951892	−	0.306433i
$32$	−32768.0			−0.176777
$33$	19582.4	−	60268.4i	0.0948565	−	0.291938i
$34$	94456.1	+	20077.3i	0.412148	+	0.0876049i
$35$	−45147.2	−	32801.4i	−0.177989	−	0.129316i
$36$	56377.4	+	97648.6i	0.201394	+	0.348825i
$37$	−22493.7	+	38960.2i	−0.0730053	+	0.126449i	−0.900217	−	0.435441i	$-0.856592\pi$
$37$	−22493.7	+	38960.2i	−0.0730053	+	0.126449i	0.827212	+	0.561890i	$0.189926\pi$
$38$	231165.	−	102921.i	0.683407	−	0.304273i
$39$	34688.1	−	25202.4i	0.0936385	−	0.0680323i
$40$	98054.5	+	43656.7i	0.242247	+	0.107855i
$41$	463200.	−	98456.2i	1.04960	−	0.223100i	0.349348	−	0.936993i	$-0.386403\pi$
$41$	463200.	−	98456.2i	1.04960	−	0.223100i	0.700255	+	0.713893i	$0.253070\pi$
$42$	−4590.18	+	43672.6i	−0.00955999	+	0.0909572i
$43$	−482522.	−	535895.i	−0.925503	−	1.02788i	−0.999531	−	0.0306190i	$-0.990252\pi$
$43$	−482522.	−	535895.i	−0.925503	−	1.02788i	0.0740282	−	0.997256i	$-0.476415\pi$
$44$	131606.	−	146163.i	0.232911	−	0.258674i
$45$	−38606.2	−	367314.i	−0.0631558	−	0.600888i
$46$	166994.	+	513956.i	0.252958	+	0.778526i
$47$	−351018.	−	1.08032e6i	−0.493159	−	1.51779i	−0.819807	−	0.572640i	$-0.805919\pi$
$47$	−351018.	−	1.08032e6i	−0.493159	−	1.51779i	0.326648	−	0.945146i	$-0.394081\pi$
$48$	−8828.64	−	83998.9i	−0.0115226	−	0.109630i
$49$	−503642.	+	559351.i	−0.611555	+	0.679201i
$50$	182953.	+	203190.i	0.206988	+	0.229883i
$51$	−26017.7	+	247542.i	−0.0274646	+	0.261308i
$52$	130169.	−	27668.3i	0.128380	−	0.0272879i
$53$	35331.6	+	15730.6i	0.0325985	+	0.0145138i	0.422971	−	0.906143i	$-0.360987\pi$
$53$	35331.6	+	15730.6i	0.0325985	+	0.0145138i	−0.390373	+	0.920657i	$0.627654\pi$
$54$	−527001.	+	382889.i	−0.455442	+	0.330898i
$55$	−588548.	+	262038.i	−0.476994	+	0.212371i
$56$	−68146.9	+	118034.i	−0.0518547	+	0.0898149i
$57$	326115.	+	564849.i	0.233243	+	0.403989i
$58$	680928.	+	494723.i	0.458251	+	0.332939i
$59$	−1.65292e6	−	351339.i	−1.04778	−	0.222712i	−0.348313	−	0.937378i	$-0.613245\pi$
$59$	−1.65292e6	−	351339.i	−1.04778	−	0.222712i	−0.699466	+	0.714666i	$0.746579\pi$
$60$	−85492.7	+	263119.i	−0.0510975	+	0.157262i
$61$	−362507.			−0.204485			−0.102243	−	0.994759i	$-0.532602\pi$
$61$	−362507.			−0.204485			−0.102243	+	0.994759i	$0.532602\pi$
$62$	−3603.80	+	1.32695e6i	−0.00192039	+	0.707104i
$63$	468988.			0.236303
$64$	81007.0	−	249314.i	0.0386271	−	0.118882i
$65$	−426379.	−	90629.6i	−0.192574	−	0.0409330i
$66$	410139.	+	297984.i	0.175601	+	0.127582i
$67$	−576167.	−	997950.i	−0.234038	−	0.405366i	0.724955	−	0.688797i	$-0.241861\pi$
$67$	−576167.	−	997950.i	−0.234038	−	0.405366i	−0.958993	+	0.283431i	$0.908527\pi$
$68$	−386265.	+	669031.i	−0.148972	+	0.258027i
$69$	−1.27250e6	+	566555.i	−0.466323	+	0.207620i
$70$	361178.	−	262411.i	0.125857	−	0.0914406i
$71$	−1.58243e6	−	704542.i	−0.524710	−	0.233616i	0.127248	−	0.991871i	$-0.459386\pi$
$71$	−1.58243e6	−	704542.i	−0.524710	−	0.233616i	−0.651958	+	0.758255i	$0.726052\pi$
$72$	−882327.	+	187544.i	−0.278590	+	0.0592162i
$73$	−265047.	+	2.52175e6i	−0.0797430	+	0.758704i	0.879458	+	0.475977i	$0.157906\pi$
$73$	−265047.	+	2.52175e6i	−0.0797430	+	0.758704i	−0.959201	+	0.282726i	$0.908761\pi$
$74$	−240819.	−	267457.i	−0.0690845	−	0.0767261i
$75$	−471574.	+	523736.i	−0.129073	+	0.143350i
$76$	211601.	+	2.01324e6i	0.0552929	+	0.526077i
$77$	−252797.	−	778030.i	−0.0631037	−	0.194213i
$78$	105997.	+	326226.i	0.0252909	+	0.0778373i
$79$	219395.	+	2.08741e6i	0.0500648	+	0.476335i	0.990615	+	0.136681i	$0.0436434\pi$
$79$	219395.	+	2.08741e6i	0.0500648	+	0.476335i	−0.940550	+	0.339654i	$0.889690\pi$
$80$	−574564.	+	638118.i	−0.125465	+	0.139343i
$81$	1.45469e6	+	1.61559e6i	0.304139	+	0.337781i
$82$	−395994.	+	3.76763e6i	−0.0793122	+	0.754605i
$83$	1.14313e6	−	242980.i	0.219444	−	0.0466442i	−0.0968776	−	0.995296i	$-0.530886\pi$
$83$	1.14313e6	−	242980.i	0.219444	−	0.0466442i	0.316321	+	0.948652i	$0.397552\pi$
$84$	−320934.	−	142889.i	−0.0590796	−	0.0263040i
$85$	2.04720e6	−	1.48738e6i	0.361572	−	0.262697i
$86$	5.27019e6	−	2.34644e6i	0.893474	−	0.397800i
$87$	−1.08473e6	+	1.87881e6i	−0.176606	+	0.305891i
$88$	786727.	+	1.36265e6i	0.123065	+	0.213155i
$89$	145033.	+	105373.i	0.0218073	+	0.0158439i	0.598636	−	0.801022i	$-0.295710\pi$
$89$	145033.	+	105373.i	0.0218073	+	0.0158439i	−0.576828	+	0.816865i	$0.695710\pi$
$90$	2.89013e6	+	614316.i	0.417896	+	0.0888266i
$91$	171046.	−	526424.i	0.0237940	−	0.0732303i
$92$	−4.32324e6			−0.578831
$93$	−3.40253e6	+	348280.i	−0.438643	+	0.0448992i
$94$	9.08734e6			1.12847
$95$	2.04905e6	−	6.30632e6i	0.245199	−	0.754646i
$96$	660927.	+	140484.i	0.0762438	+	0.0162061i
$97$	−2.90851e6	−	2.11315e6i	−0.323571	−	0.235088i	0.414127	−	0.910219i	$-0.364087\pi$
$97$	−2.90851e6	−	2.11315e6i	−0.323571	−	0.235088i	−0.737698	+	0.675131i	$0.764087\pi$
$98$	−3.01072e6	−	5.21473e6i	−0.323132	−	0.559681i
$99$	2.70713e6	−	4.68889e6i	0.280405	−	0.485676i
$100$	−1.99825e6	+	889677.i	−0.199825	+	0.0889677i
$101$	−3.43370e6	+	2.49473e6i	−0.331617	+	0.240934i	−0.741117	−	0.671376i	$-0.765703\pi$
$101$	−3.43370e6	+	2.49473e6i	−0.331617	+	0.240934i	0.409499	+	0.912310i	$0.365703\pi$
$102$	−1.81909e6	−	809912.i	−0.169728	−	0.0755679i
$103$	4.32115e6	−	918489.i	0.389645	−	0.0828216i	−0.00892351	−	0.999960i	$-0.502840\pi$
$103$	4.32115e6	−	918489.i	0.389645	−	0.0828216i	0.398568	+	0.917139i	$0.369507\pi$
$104$	−111283.	+	1.05879e6i	−0.00970089	+	0.0922978i
$105$	769987.	+	855158.i	0.0649114	+	0.0720914i
$106$	−207030.	+	229931.i	−0.0168835	+	0.0187511i
$107$	−1.23111e6	−	1.17132e7i	−0.0971521	−	0.924341i	−0.929185	−	0.369615i	$-0.879490\pi$
$107$	−1.23111e6	−	1.17132e7i	−0.0971521	−	0.924341i	0.832033	−	0.554726i	$-0.187177\pi$
$108$	−1.61037e6	−	4.95621e6i	−0.123011	−	0.378588i
$109$	−5.73000e6	−	1.76351e7i	−0.423801	−	1.30433i	−0.904138	−	0.427241i	$-0.859485\pi$
$109$	−5.73000e6	−	1.76351e7i	−0.423801	−	1.30433i	0.480337	−	0.877084i	$-0.340515\pi$
$110$	−538736.	−	5.12573e6i	−0.0385924	−	0.367182i
$111$	620727.	−	689387.i	0.0430795	−	0.0478446i
$112$	−729586.	−	810288.i	−0.0490697	−	0.0544975i
$113$	−246298.	+	2.34337e6i	−0.0160578	+	0.152780i	−0.999613	−	0.0278297i	$-0.991140\pi$
$113$	−246298.	+	2.34337e6i	−0.0160578	+	0.152780i	0.983555	+	0.180610i	$0.0578071\pi$
$114$	−5.10383e6	+	1.08485e6i	−0.322648	+	0.0685809i
$115$	1.29368e7	+	5.75983e6i	0.793203	+	0.353157i
$116$	−5.44743e6	+	3.95779e6i	−0.324032	+	0.235423i
$117$	3.34664e6	−	1.49002e6i	0.193178	−	0.0860086i
$118$	6.75939e6	−	1.17076e7i	0.378722	−	0.655966i
$119$	1.60661e6	+	2.78274e6i	0.0873971	+	0.151376i
$120$	−1.79058e6	−	1.30093e6i	−0.0945932	−	0.0687260i
$121$	9.82344e6	+	2.08804e6i	0.504098	+	0.107149i
$122$	896167.	−	2.75812e6i	0.0446817	−	0.137516i
$123$	−9.76480e6			−0.473146
$124$	−1.00871e7	−	3.30782e6i	−0.475107	−	0.155799i
$125$	2.35427e7			1.07813
$126$	−1.15940e6	+	3.56827e6i	−0.0516341	+	0.158913i
$127$	1.19967e7	+	2.54997e6i	0.519693	+	0.110464i	0.460288	−	0.887770i	$-0.347746\pi$
$127$	1.19967e7	+	2.54997e6i	0.519693	+	0.110464i	0.0594055	+	0.998234i	$0.481080\pi$
$128$	1.69663e6	+	1.23268e6i	0.0715077	+	0.0519534i
$129$	7.43491e6	+	1.28776e7i	0.304938	+	0.528168i
$130$	1.74362e6	−	3.02003e6i	0.0696064	−	0.120562i
$131$	−3.07641e6	+	1.36971e6i	−0.119563	+	0.0532327i	−0.465646	−	0.884971i	$-0.654178\pi$
$131$	−3.07641e6	+	1.36971e6i	−0.119563	+	0.0532327i	0.346084	+	0.938204i	$0.387511\pi$
$132$	−3.28111e6	+	2.38387e6i	−0.124169	+	0.0902139i
$133$	7.69198e6	+	3.42469e6i	0.283503	+	0.126224i
$134$	9.01722e6	−	1.91667e6i	0.323747	−	0.0688146i
$135$	−1.78429e6	+	1.69764e7i	−0.0624163	+	0.593851i
$136$	−4.13539e6	−	4.59281e6i	−0.140971	−	0.156564i
$137$	−3.55902e7	+	3.95269e7i	−1.18252	+	1.31332i	−0.243319	+	0.969946i	$0.578236\pi$
$137$	−3.55902e7	+	3.95269e7i	−1.18252	+	1.31332i	−0.939199	+	0.343373i	$0.888430\pi$
$138$	−1.16480e6	−	1.10824e7i	−0.0377291	−	0.358968i
$139$	−1.13784e7	−	3.50192e7i	−0.359360	−	1.10600i	−0.953438	−	0.301590i	$-0.902483\pi$
$139$	−1.13784e7	−	3.50192e7i	−0.359360	−	1.10600i	0.594077	−	0.804408i	$-0.297517\pi$
$140$	1.10366e6	+	3.39672e6i	0.0339929	+	0.104619i
$141$	2.44839e6	+	2.32949e7i	0.0735552	+	0.699831i
$142$	9.27244e6	−	1.02981e7i	0.271760	−	0.301820i
$143$	−4.27581e6	−	4.74877e6i	−0.122276	−	0.135802i
$144$	754310.	−	7.17678e6i	0.0210514	−	0.200291i
$145$	2.15738e7	−	4.58564e6i	0.587676	−	0.124914i
$146$	−1.85314e7	−	8.25071e6i	−0.492803	−	0.219410i
$147$	1.25565e7	−	9.12282e6i	0.326030	−	0.236875i
$148$	2.63027e6	−	1.17107e6i	0.0666937	−	0.0296939i
$149$	8.03950e6	−	1.39248e7i	0.199103	−	0.344856i	−0.749135	−	0.662417i	$-0.769531\pi$
$149$	8.03950e6	−	1.39248e7i	0.199103	−	0.344856i	0.948238	+	0.317561i	$0.102864\pi$
$150$	−2.81902e6	−	4.88269e6i	−0.0681992	−	0.118124i
$151$	2.34754e7	+	1.70559e7i	0.554873	+	0.403139i	0.829579	−	0.558389i	$-0.188580\pi$
$151$	2.34754e7	+	1.70559e7i	0.554873	+	0.403139i	−0.274706	+	0.961528i	$0.588580\pi$
$152$	−1.58408e7	−	3.36706e6i	−0.365868	−	0.0777676i
$153$	−6.57163e6	+	2.02254e7i	−0.148338	+	0.456538i
$154$	6.54456e6			0.144397
$155$	2.57776e7	+	2.33373e7i	0.556008	+	0.503373i
$156$	−2.74412e6			−0.0578718
$157$	−1.21361e7	+	3.73510e7i	−0.250282	+	0.770288i	0.744441	+	0.667688i	$0.232716\pi$
$157$	−1.21361e7	+	3.73510e7i	−0.250282	+	0.770288i	−0.994723	+	0.102600i	$0.967284\pi$
$158$	−1.64243e7	−	3.49110e6i	−0.331274	−	0.0704145i
$159$	−645194.	−	468761.i	−0.0127292	−	0.00924829i
$160$	−3.43469e6	−	5.94906e6i	−0.0662930	−	0.114823i
$161$	−8.99094e6	+	1.55728e7i	−0.169791	+	0.294087i
$162$	−1.58884e7	+	7.07396e6i	−0.293614	+	0.130725i
$163$	−1.53728e7	+	1.11690e7i	−0.278034	+	0.202003i	−0.718059	−	0.695982i	$-0.754969\pi$
$163$	−1.53728e7	+	1.11690e7i	−0.278034	+	0.202003i	0.440026	+	0.897985i	$0.354969\pi$
$164$	−2.76869e7	−	1.23270e7i	−0.490141	−	0.218225i
$165$	1.29944e7	−	2.76204e6i	0.225196	−	0.0478670i
$166$	−977275.	+	9.29815e6i	−0.0165821	+	0.157768i
$167$	−5.80145e7	−	6.44316e7i	−0.963893	−	1.07051i	−0.997471	−	0.0710753i	$-0.977357\pi$
$167$	−5.80145e7	−	6.44316e7i	−0.963893	−	1.07051i	0.0335781	−	0.999436i	$-0.489310\pi$
$168$	1.88056e6	−	2.08857e6i	0.0305987	−	0.0339833i
$169$	6.10707e6	+	5.81048e7i	0.0973260	+	0.925995i
$170$	6.25569e6	+	1.92530e7i	0.0976572	+	0.300558i
$171$	1.72203e7	+	5.29985e7i	0.263362	+	0.810546i
$172$	4.82415e6	+	4.58987e7i	0.0722889	+	0.687783i
$173$	−6.23446e7	+	6.92407e7i	−0.915457	+	1.01672i	0.0843376	+	0.996437i	$0.473123\pi$
$173$	−6.23446e7	+	6.92407e7i	−0.915457	+	1.01672i	−0.999794	+	0.0202804i	$0.993544\pi$
$174$	−1.16133e7	−	1.28978e7i	−0.167121	−	0.185607i
$175$	−950998.	+	9.04815e6i	−0.0134136	+	0.127622i
$176$	−1.23126e7	+	2.61712e6i	−0.170237	+	0.0361850i
$177$	3.18329e7	+	1.41729e7i	0.431490	+	0.192112i
$178$	−1.16026e6	+	842982.i	−0.0154201	+	0.0112034i
$179$	−6.97607e7	+	3.10595e7i	−0.909128	+	0.404770i	−0.807374	−	0.590040i	$-0.799112\pi$
$179$	−6.97607e7	+	3.10595e7i	−0.909128	+	0.404770i	−0.101754	+	0.994810i	$0.532445\pi$
$180$	−1.18188e7	+	2.04707e7i	−0.151049	+	0.261625i
$181$	−5.65058e7	−	9.78709e7i	−0.708301	−	1.22681i	−0.965487	−	0.260451i	$-0.916129\pi$
$181$	−5.65058e7	−	9.78709e7i	−0.708301	−	1.22681i	0.257186	−	0.966362i	$-0.417205\pi$
$182$	3.58243e6	+	2.60278e6i	0.0440481	+	0.0320028i
$183$	7.31173e6	+	1.55416e6i	0.0881945	+	0.0187463i
$184$	1.06876e7	−	3.28932e7i	0.126479	−	0.389263i
$185$	−9.43101e6			−0.109511
$186$	5.76164e6	−	2.67490e7i	0.0656525	−	0.304798i
$187$	3.70954e7			0.414834
$188$	−2.24651e7	+	6.91406e7i	−0.246579	+	0.758893i
$189$	−2.12019e7	−	4.50660e6i	−0.228432	−	0.0485548i
$190$	4.29158e7	+	3.11802e7i	0.453920	+	0.329792i
$191$	−8.28423e7	−	1.43487e8i	−0.860272	−	1.49003i	−0.871667	−	0.490099i	$-0.836961\pi$
$191$	−8.28423e7	−	1.43487e8i	−0.860272	−	1.49003i	0.0113953	−	0.999935i	$-0.496373\pi$
$192$	−2.70277e6	+	4.68134e6i	−0.0275585	+	0.0477326i
$193$	4.79065e7	−	2.13293e7i	0.479671	−	0.213563i	−0.152634	−	0.988283i	$-0.548776\pi$
$193$	4.79065e7	−	2.13293e7i	0.479671	−	0.213563i	0.632305	+	0.774719i	$0.282109\pi$
$194$	2.32681e7	−	1.69052e7i	0.228799	−	0.166232i
$195$	8.21146e6	+	3.65598e6i	0.0793048	+	0.0353088i
$196$	4.71189e7	−	1.00154e7i	0.446991	−	0.0950110i
$197$	1.34392e7	−	1.27866e8i	0.125240	−	1.19158i	−0.733690	−	0.679485i	$-0.762203\pi$
$197$	1.34392e7	−	1.27866e8i	0.125240	−	1.19158i	0.858930	−	0.512094i	$-0.171130\pi$
$198$	2.89828e7	+	3.21887e7i	0.265346	+	0.294696i
$199$	2.83979e7	−	3.15391e7i	0.255447	−	0.283703i	−0.601757	−	0.798679i	$-0.705533\pi$
$199$	2.83979e7	−	3.15391e7i	0.255447	−	0.283703i	0.857205	+	0.514976i	$0.172199\pi$
$200$	−1.82913e6	−	1.74030e7i	−0.0161674	−	0.153822i
$201$	7.34277e6	+	2.25987e7i	0.0637784	+	0.196290i
$202$	−1.04924e7	−	3.22924e7i	−0.0895668	−	0.275658i
$203$	2.92748e6	+	2.78531e7i	0.0245617	+	0.233689i
$204$	1.06592e7	−	1.18383e7i	0.0879063	−	0.0976298i
$205$	6.64267e7	+	7.37743e7i	0.538523	+	0.598090i
$206$	−3.69419e6	+	3.51479e7i	−0.0294431	+	0.280133i
$207$	−1.16410e8	+	2.47436e7i	−0.912206	+	0.193895i
$208$	−7.78061e6	−	3.46415e6i	−0.0599504	−	0.0266916i
$209$	7.86401e7	−	5.71354e7i	0.595843	−	0.432906i
$210$	−8.40994e6	+	3.74435e6i	−0.0626650	+	0.0279003i
$211$	8.60845e7	−	1.49103e8i	0.630865	−	1.09269i	−0.356510	−	0.934291i	$-0.616034\pi$
$211$	8.60845e7	−	1.49103e8i	0.630865	−	1.09269i	0.987375	−	0.158399i	$-0.0506331\pi$
$212$	−1.23761e6	−	2.14360e6i	−0.00892088	−	0.0154514i
$213$	2.88968e7	+	2.09948e7i	0.204890	+	0.148862i
$214$	9.21627e7	+	1.95898e7i	0.642846	+	0.136641i
$215$	4.67150e7	−	1.43774e8i	0.320569	−	0.986610i
$216$	4.16902e7			0.281479
$217$	−3.28931e7	+	2.94557e7i	−0.218522	+	0.195686i
$218$	1.48341e8			0.969761
$219$	1.61573e7	−	4.97271e7i	0.103948	−	0.319918i
$220$	4.03307e7	+	8.57256e6i	0.255362	+	0.0542789i
$221$	2.03056e7	+	1.47529e7i	0.126545	+	0.0919401i
$222$	3.71065e6	+	6.42703e6i	0.0227622	+	0.0394253i
$223$	6.48492e7	−	1.12322e8i	0.391596	−	0.678264i	−0.601065	−	0.799201i	$-0.705257\pi$
$223$	6.48492e7	−	1.12322e8i	0.391596	−	0.678264i	0.992660	+	0.120937i	$0.0385899\pi$
$224$	7.96867e6	−	3.54788e6i	0.0473716	−	0.0210912i
$225$	−4.87138e7	+	3.53927e7i	−0.285111	+	0.207145i
$226$	−1.72205e7	−	7.66708e6i	−0.0992356	−	0.0441825i
$227$	−6.16845e7	+	1.31114e7i	−0.350014	+	0.0743977i	−0.379564	−	0.925166i	$-0.623926\pi$
$227$	−6.16845e7	+	1.31114e7i	−0.350014	+	0.0743977i	0.0295500	+	0.999563i	$0.490593\pi$
$228$	4.36331e6	−	4.15141e7i	0.0243806	−	0.231966i
$229$	−892641.	−	991378.i	−0.00491193	−	0.00545526i	0.740684	−	0.671854i	$-0.234502\pi$
$229$	−892641.	−	991378.i	−0.00491193	−	0.00545526i	−0.745596	+	0.666398i	$0.767835\pi$
$230$	−7.58050e7	+	8.41899e7i	−0.410819	+	0.456260i
$231$	1.76329e6	+	1.67766e7i	0.00941200	+	0.0895492i
$232$	−1.66459e7	−	5.12307e7i	−0.0875182	−	0.269353i
$233$	3.80934e7	+	1.17239e8i	0.197290	+	0.607195i	0.999942	+	0.0107482i	$0.00342132\pi$
$233$	3.80934e7	+	1.17239e8i	0.197290	+	0.607195i	−0.802653	+	0.596447i	$0.796579\pi$
$234$	3.06340e6	+	2.91463e7i	0.0156296	+	0.148706i
$235$	1.59340e8	−	1.76965e8i	0.800917	−	0.889509i
$236$	7.23666e7	+	8.03713e7i	0.358382	+	0.398024i
$237$	4.52404e6	−	4.30434e7i	0.0220753	−	0.210033i
$238$	−2.51441e7	+	5.34454e6i	−0.120897	+	0.0256975i
$239$	7.09802e7	+	3.16024e7i	0.336314	+	0.149736i	0.567944	−	0.823067i	$-0.307739\pi$
$239$	7.09802e7	+	3.16024e7i	0.336314	+	0.149736i	−0.231630	+	0.972804i	$0.574406\pi$
$240$	1.43247e7	−	1.04075e7i	0.0668875	−	0.0485966i
$241$	−3.75641e7	+	1.67246e7i	−0.172868	+	0.0769656i	−0.491346	−	0.870965i	$-0.663495\pi$
$241$	−3.75641e7	+	1.67246e7i	−0.172868	+	0.0769656i	0.318478	+	0.947930i	$0.396828\pi$
$242$	−4.01716e7	+	6.95792e7i	−0.182207	+	0.315592i
$243$	−1.11454e8	−	1.93044e8i	−0.498280	−	0.863046i
$244$	1.87696e7	+	1.36369e7i	0.0827161	+	0.0600967i
$245$	−1.54342e8	−	3.28063e7i	−0.670504	−	0.142520i
$246$	2.41399e7	−	7.42950e7i	0.103386	−	0.318190i
$247$	6.57697e7			0.277707
$248$	5.01041e7	−	6.85700e7i	0.208590	−	0.285465i
$249$	−2.40986e7			−0.0989222
$250$	−5.82008e7	+	1.79124e8i	−0.235580	+	0.725042i
$251$	−1.54311e8	−	3.27998e7i	−0.615940	−	0.130922i	−0.110633	−	0.993861i	$-0.535288\pi$
$251$	−1.54311e8	−	3.27998e7i	−0.615940	−	0.130922i	−0.505308	+	0.862939i	$0.668621\pi$
$252$	−2.42828e7	−	1.76425e7i	−0.0955866	−	0.0694477i
$253$	1.03797e8	+	1.79781e8i	0.402960	+	0.697947i
$254$	−4.90587e7	+	8.49721e7i	−0.187844	+	0.325356i
$255$	−4.76686e7	+	2.12234e7i	−0.180029	+	0.0801539i
$256$	−1.35731e7	+	9.86140e6i	−0.0505636	+	0.0367366i
$257$	−4.22707e7	−	1.88201e7i	−0.155336	−	0.0691602i	0.327596	−	0.944818i	$-0.393762\pi$
$257$	−4.22707e7	−	1.88201e7i	−0.155336	−	0.0691602i	−0.482932	+	0.875658i	$0.660428\pi$
$258$	−1.16359e8	+	2.47329e7i	−0.421824	+	0.0896614i
$259$	1.25179e6	−	1.19100e7i	0.00447695	−	0.0425953i
$260$	1.86673e7	+	2.07322e7i	0.0658681	+	0.0731539i
$261$	−1.24028e8	+	1.37747e8i	−0.431796	+	0.479558i
$262$	−2.81604e6	−	2.67928e7i	−0.00967352	−	0.0920374i
$263$	−1.11407e7	−	3.42876e7i	−0.0377632	−	0.116223i	0.930398	−	0.366551i	$-0.119462\pi$
$263$	−1.11407e7	−	3.42876e7i	−0.0377632	−	0.116223i	−0.968161	+	0.250328i	$0.919462\pi$
$264$	−1.00262e7	−	3.08574e7i	−0.0335368	−	0.103216i
$265$	847491.	+	8.06334e6i	0.00279753	+	0.0266167i
$266$	−4.50722e7	+	5.00578e7i	−0.146833	+	0.163074i
$267$	−2.47354e6	−	2.74715e6i	−0.00795299	−	0.00883269i
$268$	−7.70891e6	+	7.33453e7i	−0.0244636	+	0.232756i
$269$	−3.54241e8	+	7.52963e7i	−1.10960	+	0.235853i	−0.726033	−	0.687660i	$-0.758638\pi$
$269$	−3.54241e8	+	7.52963e7i	−1.10960	+	0.235853i	−0.383567	+	0.923513i	$0.625305\pi$
$270$	−1.24753e8	−	5.55437e7i	−0.385725	−	0.171736i
$271$	3.49339e8	−	2.53809e8i	1.06624	−	0.774667i	0.0910057	−	0.995850i	$-0.470992\pi$
$271$	3.49339e8	−	2.53809e8i	1.06624	−	0.774667i	0.975232	+	0.221183i	$0.0709918\pi$
$272$	4.51675e7	−	2.01098e7i	0.136093	−	0.0605923i
$273$	−5.70688e6	+	9.88461e6i	−0.0169758	+	0.0294029i
$274$	−2.12755e8	−	3.68502e8i	−0.624816	−	1.08221i
$275$	8.49731e7	+	6.17365e7i	0.246386	+	0.179010i
$276$	8.71993e7	+	1.85348e7i	0.249650	+	0.0530647i
$277$	−9.14740e7	+	2.81528e8i	−0.258594	+	0.795871i	0.734506	+	0.678602i	$0.237414\pi$
$277$	−9.14740e7	+	2.81528e8i	−0.258594	+	0.795871i	−0.993100	+	0.117269i	$0.962586\pi$
$278$	2.94571e8			0.822305
$279$	−2.90543e8	−	3.13353e7i	−0.800931	−	0.0863812i
$280$	−2.85722e7			−0.0777840
$281$	−1.32399e8	+	4.07483e8i	−0.355970	+	1.09556i	0.599475	+	0.800393i	$0.295376\pi$
$281$	−1.32399e8	+	4.07483e8i	−0.355970	+	1.09556i	−0.955445	+	0.295169i	$0.904624\pi$
$282$	−1.83291e8	−	3.89596e7i	−0.486708	−	0.103453i
$283$	−1.26080e8	−	9.16028e7i	−0.330670	−	0.240246i	0.410045	−	0.912065i	$-0.365513\pi$
$283$	−1.26080e8	−	9.16028e7i	−0.330670	−	0.240246i	−0.740715	+	0.671819i	$0.765513\pi$
$284$	5.54298e7	+	9.60072e7i	0.143592	+	0.248708i
$285$	−6.83658e7	+	1.18413e8i	−0.174937	+	0.303000i
$286$	4.67012e7	−	2.07927e7i	0.118045	−	0.0525569i
$287$	−1.01983e8	+	7.40950e7i	−0.254648	+	0.185013i
$288$	5.27394e7	+	2.34811e7i	0.130095	+	0.0579222i
$289$	2.58852e8	−	5.50207e7i	0.630825	−	0.134086i
$290$	−1.84436e7	+	1.75479e8i	−0.0444071	+	0.422506i
$291$	4.96047e7	+	5.50916e7i	0.118004	+	0.131057i
$292$	1.08587e8	−	1.20598e8i	0.255234	−	0.283466i
$293$	5.05248e7	+	4.80712e8i	0.117346	+	1.11647i	0.881744	+	0.471728i	$0.156370\pi$
$293$	5.05248e7	+	4.80712e8i	0.117346	+	1.11647i	−0.764398	+	0.644744i	$0.776964\pi$
$294$	3.83692e7	+	1.18088e8i	0.0880576	+	0.271014i
$295$	−1.09471e8	−	3.36916e8i	−0.248268	−	0.764089i
$296$	2.40766e6	+	2.29074e7i	0.00539603	+	0.0513398i
$297$	−1.67440e8	+	1.85961e8i	−0.370861	+	0.411883i
$298$	8.60716e7	+	9.55922e7i	0.188410	+	0.209250i
$299$	−1.46821e7	+	1.39691e8i	−0.0317642	+	0.302216i
$300$	4.41187e7	−	9.37772e6i	0.0943406	−	0.0200527i
$301$	1.75365e8	+	7.80775e7i	0.370646	+	0.165022i
$302$	−1.87803e8	+	1.36447e8i	−0.392355	+	0.285062i
$303$	7.99528e7	−	3.55973e7i	0.165114	−	0.0735136i
$304$	6.47787e7	−	1.12200e8i	0.132244	−	0.229053i
$305$	−3.79974e7	−	6.58135e7i	−0.0766840	−	0.132821i
$306$	−1.37638e8	−	9.99999e7i	−0.274608	−	0.199515i
$307$	−6.61792e8	−	1.40668e8i	−1.30538	−	0.277467i	−0.497835	−	0.867272i	$-0.665872\pi$
$307$	−6.61792e8	−	1.40668e8i	−1.30538	−	0.277467i	−0.807546	+	0.589804i	$0.799205\pi$
$308$	−1.61790e7	+	4.97939e7i	−0.0315519	+	0.0971067i
$309$	−9.10949e7			−0.175646
$310$	−2.41286e8	+	1.38434e8i	−0.460010	+	0.263924i
$311$	3.74468e8			0.705916			0.352958	−	0.935639i	$-0.385176\pi$
$311$	3.74468e8			0.705916			0.352958	+	0.935639i	$0.385176\pi$
$312$	6.78383e6	−	2.08785e7i	0.0126454	−	0.0389187i
$313$	8.12366e8	+	1.72674e8i	1.49743	+	0.318288i	0.882507	−	0.470299i	$-0.155854\pi$
$313$	8.12366e8	+	1.72674e8i	1.49743	+	0.318288i	0.614922	+	0.788588i	$0.289187\pi$
$314$	−2.54181e8	−	1.84673e8i	−0.463329	−	0.336628i
$315$	4.91585e7	+	8.51450e7i	0.0886159	+	0.153487i
$316$	6.71650e7	−	1.16333e8i	0.119740	−	0.207395i
$317$	2.51170e8	−	1.11828e8i	0.442853	−	0.197171i	−0.173182	−	0.984890i	$-0.555405\pi$
$317$	2.51170e8	−	1.11828e8i	0.442853	−	0.197171i	0.616035	+	0.787719i	$0.288738\pi$
$318$	5.16155e6	−	3.75009e6i	0.00900089	−	0.00653953i
$319$	2.95371e8	+	1.31508e8i	0.509449	+	0.226821i
$320$	5.37541e7	−	1.14258e7i	0.0917037	−	0.0194922i
$321$	−2.53860e7	+	2.41532e8i	−0.0428378	+	0.407574i
$322$	−9.62578e7	−	1.06905e8i	−0.160672	−	0.178444i
$323$	−2.55475e8	+	2.83734e8i	−0.421832	+	0.468492i
$324$	−1.45437e7	−	1.38374e8i	−0.0237556	−	0.226019i
$325$	2.19607e7	+	6.75879e7i	0.0354857	+	0.109214i
$326$	−4.69752e7	−	1.44575e8i	−0.0750944	−	0.231117i
$327$	3.99674e7	+	3.80265e8i	0.0632105	+	0.601408i
$328$	1.62235e8	−	1.80180e8i	0.253855	−	0.281935i
$329$	2.02332e8	+	2.24712e8i	0.313241	+	0.347889i
$330$	−1.11090e7	+	1.05695e8i	−0.0170168	+	0.161904i
$331$	4.45469e8	−	9.46873e7i	0.675180	−	0.143514i	0.142453	−	0.989802i	$-0.454501\pi$
$331$	4.45469e8	−	9.46873e7i	0.675180	−	0.143514i	0.532726	+	0.846288i	$0.321168\pi$
$332$	−6.83286e7	−	3.04218e7i	−0.102475	−	0.0456249i
$333$	6.41215e7	−	4.65870e7i	0.0951588	−	0.0691369i
$334$	6.33644e8	−	2.82117e8i	0.930536	−	0.414301i
$335$	1.20786e8	−	2.09207e8i	0.175533	−	0.304032i
$336$	1.12418e7	+	1.94713e7i	0.0161677	+	0.0280032i
$337$	4.87316e7	+	3.54056e7i	0.0693595	+	0.0503926i	0.621925	−	0.783077i	$-0.286351\pi$
$337$	4.87316e7	+	3.54056e7i	0.0693595	+	0.0503926i	−0.552565	+	0.833470i	$0.686351\pi$
$338$	−4.57185e8	−	9.71778e7i	−0.643997	−	0.136886i
$339$	1.50144e7	−	4.62096e7i	0.0209319	−	0.0644219i
$340$	−1.61951e8			−0.223464
$341$	1.04627e8	+	4.98889e8i	0.142890	+	0.681339i
$342$	−4.45808e8			−0.602637
$343$	1.29660e8	−	3.99053e8i	0.173491	−	0.533950i
$344$	−3.61144e8	−	7.67636e7i	−0.478329	−	0.101672i
$345$	−2.36240e8	−	1.71638e8i	−0.309733	−	0.225034i
$346$	−3.72690e8	−	6.45519e8i	−0.483706	−	0.837804i
$347$	1.61176e7	−	2.79164e7i	0.0207084	−	0.0358680i	−0.855486	−	0.517827i	$-0.826741\pi$
$347$	1.61176e7	−	2.79164e7i	0.0207084	−	0.0358680i	0.876194	+	0.481959i	$0.160075\pi$
$348$	1.26842e8	−	5.64737e7i	0.161338	−	0.0718322i
$349$	9.28370e8	−	6.74500e8i	1.16905	−	0.849363i	0.178153	−	0.984003i	$-0.442988\pi$
$349$	9.28370e8	−	6.74500e8i	1.16905	−	0.849363i	0.990895	+	0.134640i	$0.0429878\pi$
$350$	−6.64914e7	−	2.96039e7i	−0.0828948	−	0.0369071i
$351$	−1.65612e8	+	3.52019e7i	−0.204417	+	0.0434502i
$352$	1.05261e7	−	1.00149e8i	0.0128638	−	0.122391i
$353$	−1.45020e8	−	1.61061e8i	−0.175476	−	0.194885i	0.648991	−	0.760796i	$-0.275191\pi$
$353$	−1.45020e8	−	1.61061e8i	−0.175476	−	0.194885i	−0.824466	+	0.565911i	$0.808525\pi$
$354$	−1.86530e8	+	2.07162e8i	−0.223479	+	0.248198i
$355$	−3.79573e7	−	3.61140e8i	−0.0450294	−	0.428426i
$356$	−3.54545e6	−	1.09118e7i	−0.00416483	−	0.0128180i
$357$	−2.04750e7	−	6.30154e7i	−0.0238168	−	0.0733007i
$358$	−6.38565e7	−	6.07554e8i	−0.0735554	−	0.699833i
$359$	1.10670e9	−	1.22912e9i	1.26241	−	1.40205i	0.384565	−	0.923098i	$-0.374352\pi$
$359$	1.10670e9	−	1.22912e9i	1.26241	−	1.40205i	0.877843	−	0.478948i	$-0.158982\pi$
$360$	−1.26533e8	−	1.40529e8i	−0.142937	−	0.158748i
$361$	−1.11426e7	+	1.06015e8i	−0.0124656	+	0.118602i
$362$	8.84336e8	−	1.87971e8i	0.979800	−	0.208263i
$363$	−1.89186e8	−	8.42309e7i	−0.207594	−	0.0924269i
$364$	−2.86594e7	+	2.08223e7i	−0.0311467	+	0.0226294i
$365$	−4.85608e8	+	2.16206e8i	−0.522710	+	0.232725i
$366$	−2.99003e7	+	5.17889e7i	−0.0318781	+	0.0552144i
$367$	−2.42168e8	−	4.19448e8i	−0.255733	−	0.442942i	0.709362	−	0.704845i	$-0.248983\pi$
$367$	−2.42168e8	−	4.19448e8i	−0.255733	−	0.442942i	−0.965094	+	0.261903i	$0.915650\pi$
$368$	2.23845e8	+	1.62633e8i	0.234142	+	0.170114i
$369$	−8.16063e8	−	1.73460e8i	−0.845535	−	0.179724i
$370$	2.33147e7	−	7.17554e7i	0.0239290	−	0.0736459i
$371$	−1.02953e7			−0.0104672
$372$	1.89275e8	+	1.09964e8i	0.190631	+	0.110752i
$373$	1.05790e9			1.05552			0.527759	−	0.849394i	$-0.323032\pi$
$373$	1.05790e9			1.05552			0.527759	+	0.849394i	$0.323032\pi$
$374$	−9.17048e7	+	2.82238e8i	−0.0906445	+	0.278975i
$375$	−4.74854e8	−	1.00933e8i	−0.464998	−	0.0988383i
$376$	−4.70516e8	−	3.41850e8i	−0.456475	−	0.331648i
$377$	1.09382e8	+	1.89456e8i	0.105136	+	0.182101i
$378$	8.67021e7	−	1.50172e8i	0.0825674	−	0.143011i
$379$	−3.38815e8	+	1.50850e8i	−0.319687	+	0.142334i	−0.560306	−	0.828286i	$-0.689316\pi$
$379$	−3.38815e8	+	1.50850e8i	−0.319687	+	0.142334i	0.240619	+	0.970620i	$0.422650\pi$
$380$	−3.43326e8	+	2.49441e8i	−0.320970	+	0.233198i
$381$	−2.31039e8	−	1.02865e8i	−0.214017	−	0.0952864i
$382$	1.29651e9	−	2.75582e8i	1.19002	−	0.252947i
$383$	7.71344e7	−	7.33885e8i	0.0701540	−	0.667471i	−0.901777	−	0.432203i	$-0.857737\pi$
$383$	7.71344e7	−	7.33885e8i	0.0701540	−	0.667471i	0.971931	−	0.235268i	$-0.0755968\pi$
$384$	−2.89361e7	−	3.21368e7i	−0.0260784	−	0.0289630i
$385$	1.14754e8	−	1.27447e8i	0.102484	−	0.113820i
$386$	4.38519e7	+	4.17223e8i	0.0388091	+	0.369244i
$387$	3.92594e8	+	1.20828e9i	0.344315	+	1.05969i
$388$	7.11008e7	+	2.18826e8i	0.0617965	+	0.190190i
$389$	−6.80125e7	−	6.47096e8i	−0.0585821	−	0.557372i	−0.983968	−	0.178345i	$-0.942926\pi$
$389$	−6.80125e7	−	6.47096e8i	−0.0585821	−	0.557372i	0.925386	−	0.379026i	$-0.123741\pi$
$390$	−4.81162e7	+	5.34384e7i	−0.0410738	+	0.0456171i
$391$	−5.45602e8	−	6.05952e8i	−0.461591	−	0.512648i
$392$	−4.02824e7	+	3.83262e8i	−0.0337765	+	0.321362i
$393$	6.79232e7	−	1.44375e7i	0.0564474	−	0.0119983i
$394$	9.39637e8	+	4.18354e8i	0.773969	+	0.344593i
$395$	−3.55974e8	+	2.58630e8i	−0.290622	+	0.211149i
$396$	−3.16555e8	+	1.40940e8i	−0.256163	+	0.114051i
$397$	−1.14715e9	+	1.98692e9i	−0.920137	+	1.59372i	−0.120937	+	0.992660i	$0.538590\pi$
$397$	−1.14715e9	+	1.98692e9i	−0.920137	+	1.59372i	−0.799200	+	0.601065i	$0.794743\pi$
$398$	1.69760e8	+	2.94033e8i	0.134973	+	0.233779i
$399$	−1.40464e8	−	1.02053e8i	−0.110703	−	0.0804305i
$400$	1.36932e8	+	2.91057e7i	0.106978	+	0.0227388i
$401$	−1.65819e8	+	5.10338e8i	−0.128419	+	0.395232i	−0.994508	−	0.104656i	$-0.966626\pi$
$401$	−1.65819e8	+	5.10338e8i	−0.128419	+	0.395232i	0.866090	+	0.499889i	$0.166626\pi$
$402$	−1.90094e8			−0.145941
$403$	−1.41137e8	+	3.14697e8i	−0.107417	+	0.239511i
$404$	2.71634e8			0.204951
$405$	−1.40834e8	+	4.33444e8i	−0.105346	+	0.324220i
$406$	−2.19156e8	−	4.65831e7i	−0.162522	−	0.0345452i
$407$	−1.11849e8	−	8.12631e7i	−0.0822341	−	0.0597466i
$408$	6.37198e7	+	1.10366e8i	0.0464477	+	0.0804498i
$409$	8.93857e8	−	1.54820e9i	0.646006	−	1.11891i	−0.338063	−	0.941124i	$-0.609772\pi$
$409$	8.93857e8	−	1.54820e9i	0.646006	−	1.11891i	0.984068	−	0.177791i	$-0.0568950\pi$
$410$	−7.25524e8	+	3.23024e8i	−0.519886	+	0.231468i
$411$	8.87311e8	−	6.44669e8i	0.630419	−	0.458026i
$412$	−2.58288e8	−	1.14997e8i	−0.181955	−	0.0810117i
$413$	4.40005e8	−	9.35260e7i	0.307350	−	0.0653292i
$414$	9.95197e7	−	9.46867e8i	0.0689299	−	0.655825i
$415$	1.63935e8	+	1.82068e8i	0.112591	+	0.125045i
$416$	4.55916e7	−	5.06345e7i	0.0310497	−	0.0344842i
$417$	7.93658e7	+	7.55115e8i	0.0535991	+	0.509961i
$418$	2.40303e8	+	7.39576e8i	0.160932	+	0.495297i
$419$	−1.99227e8	−	6.13158e8i	−0.132312	−	0.407215i	0.862850	−	0.505460i	$-0.168677\pi$
$419$	−1.99227e8	−	6.13158e8i	−0.132312	−	0.407215i	−0.995162	+	0.0982450i	$0.968677\pi$
$420$	−7.69816e6	−	7.32431e7i	−0.00507008	−	0.0482386i
$421$	8.97123e8	−	9.96357e8i	0.585956	−	0.650770i	−0.375145	−	0.926966i	$-0.622407\pi$
$421$	8.97123e8	−	9.96357e8i	0.585956	−	0.650770i	0.961101	+	0.276196i	$0.0890739\pi$
$422$	9.21628e8	+	1.02357e9i	0.596983	+	0.663017i
$423$	−2.09188e8	+	1.99029e9i	−0.134383	+	1.27857i
$424$	1.93690e7	−	4.11701e6i	0.0123403	−	0.00262302i
$425$	−3.76882e8	−	1.67799e8i	−0.238146	−	0.106030i
$426$	−2.31175e8	+	1.67958e8i	−0.144879	+	0.105261i
$427$	8.81562e7	−	3.92497e7i	0.0547968	−	0.0243971i
$428$	−3.76887e8	+	6.52787e8i	−0.232358	+	0.402456i
$429$	6.58836e7	+	1.14114e8i	0.0402881	+	0.0697810i
$430$	9.78412e8	+	7.10858e8i	0.593447	+	0.431165i
$431$	−2.04343e9	−	4.34345e8i	−1.22939	−	0.261315i	−0.452968	−	0.891527i	$-0.649635\pi$
$431$	−2.04343e9	−	4.34345e8i	−1.22939	−	0.261315i	−0.776423	+	0.630212i	$0.782968\pi$
$432$	−1.03064e8	+	3.17198e8i	−0.0615054	+	0.189294i
$433$	−1.32686e9			−0.785448			−0.392724	−	0.919656i	$-0.628467\pi$
$433$	−1.32686e9			−0.785448			−0.392724	+	0.919656i	$0.628467\pi$
$434$	−1.42796e8	−	3.23084e8i	−0.0838498	−	0.189715i
$435$	−4.54800e8			−0.264916
$436$	−3.66720e8	+	1.12865e9i	−0.211901	+	0.652163i
$437$	−2.08995e9	−	4.44233e8i	−1.19798	−	0.254639i
$438$	3.38403e8	+	2.45864e8i	0.192431	+	0.139809i
$439$	1.04012e9	+	1.80154e9i	0.586757	+	1.01629i	0.994654	+	0.103265i	$0.0329291\pi$
$439$	1.04012e9	+	1.80154e9i	0.586757	+	1.01629i	−0.407896	+	0.913028i	$0.633738\pi$
$440$	−1.64927e8	+	2.85662e8i	−0.0923012	+	0.159870i
$441$	1.21143e9	−	5.39361e8i	0.672607	−	0.299464i
$442$	−1.62445e8	+	1.18023e8i	−0.0894806	+	0.0650114i
$443$	1.34428e9	+	5.98510e8i	0.734641	+	0.327083i	0.739730	−	0.672904i	$-0.234953\pi$
$443$	1.34428e9	+	5.98510e8i	0.734641	+	0.327083i	−0.00508901	+	0.999987i	$0.501620\pi$
$444$	−5.80730e7	+	1.23438e7i	−0.0314872	+	0.00669281i
$445$	−3.92836e6	+	3.73759e7i	−0.00211325	+	0.0201063i
$446$	6.94282e8	+	7.71078e8i	0.370564	+	0.411554i
$447$	−2.21855e8	+	2.46395e8i	−0.117488	+	0.130483i
$448$	7.29425e6	+	6.94001e7i	0.00383272	+	0.0364659i
$449$	−1.10074e9	−	3.38774e9i	−0.573884	−	1.76623i	−0.639947	−	0.768419i	$-0.721044\pi$
$449$	−1.10074e9	−	3.38774e9i	−0.573884	−	1.76623i	0.0660628	−	0.997815i	$-0.478956\pi$
$450$	−1.48856e8	−	4.58132e8i	−0.0770058	−	0.236999i
$451$	1.52119e8	+	1.44731e9i	0.0780845	+	0.742925i
$452$	1.00906e8	−	1.12068e8i	0.0513964	−	0.0570815i
$453$	−4.00374e8	−	4.44660e8i	−0.202359	−	0.224742i
$454$	5.27346e7	−	5.01736e8i	0.0264485	−	0.251640i
$455$	1.13501e8	−	2.41255e7i	0.0564887	−	0.0120070i
$456$	3.05071e8	+	1.35827e8i	0.150669	+	0.0670823i
$457$	−1.83112e9	+	1.33039e9i	−0.897450	+	0.652036i	−0.937810	−	0.347150i	$-0.887150\pi$
$457$	−1.83112e9	+	1.33039e9i	−0.897450	+	0.652036i	0.0403598	+	0.999185i	$0.487150\pi$
$458$	9.74958e6	−	4.34079e6i	0.00474195	−	0.00211125i
$459$	4.91439e8	−	8.51197e8i	0.237206	−	0.410852i
$460$	−4.53155e8	−	7.84887e8i	−0.217067	−	0.375972i
$461$	−1.92801e9	−	1.40078e9i	−0.916549	−	0.665912i	0.0261134	−	0.999659i	$-0.491687\pi$
$461$	−1.92801e9	−	1.40078e9i	−0.916549	−	0.665912i	−0.942663	+	0.333747i	$0.891687\pi$
$462$	−1.32003e8	−	2.80581e7i	−0.0622783	−	0.0132377i
$463$	−6.28538e8	+	1.93444e9i	−0.294305	+	0.905778i	0.689149	+	0.724620i	$0.257985\pi$
$463$	−6.28538e8	+	1.93444e9i	−0.294305	+	0.905778i	−0.983454	+	0.181158i	$0.942015\pi$
$464$	4.30937e8			0.200263
$465$	−4.19878e8	−	5.81226e8i	−0.193659	−	0.268077i
$466$	−9.86183e8			−0.451447
$467$	−4.42044e8	+	1.36047e9i	−0.200843	+	0.618131i	0.799016	+	0.601310i	$0.205354\pi$
$467$	−4.42044e8	+	1.36047e9i	−0.200843	+	0.618131i	−0.999859	+	0.0168207i	$0.994646\pi$
$468$	−2.29331e8	−	4.87459e7i	−0.103420	−	0.0219825i
$469$	2.48166e8	+	1.80303e8i	0.111080	+	0.0807045i
$470$	9.52520e8	+	1.64981e9i	0.423186	+	0.732980i
$471$	4.04916e8	−	7.01335e8i	0.178563	−	0.309280i
$472$	−7.90401e8	+	3.51909e8i	−0.345980	+	0.154040i
$473$	1.79287e9	−	1.30260e9i	0.778995	−	0.565973i
$474$	3.16310e8	+	1.40830e8i	0.136423	+	0.0607395i
$475$	−1.05742e9	+	2.24761e8i	−0.452708	+	0.0962261i
$476$	2.14959e7	−	2.04520e8i	0.00913549	−	0.0869183i
$477$	−4.55931e7	−	5.06363e7i	−0.0192347	−	0.0213623i
$478$	−4.15918e8	+	4.61924e8i	−0.174185	+	0.193452i
$479$	2.32325e8	+	2.21042e9i	0.0965875	+	0.918968i	0.930307	+	0.366781i	$0.119540\pi$
$479$	2.32325e8	+	2.21042e9i	0.0965875	+	0.918968i	−0.833720	+	0.552188i	$0.813793\pi$
$480$	4.37723e7	+	1.34717e8i	0.0180657	+	0.0556005i
$481$	−2.89066e7	−	8.89653e7i	−0.0118437	−	0.0364513i
$482$	−3.43849e7	−	3.27151e8i	−0.0139863	−	0.133071i
$483$	2.48111e8	−	2.75555e8i	0.100191	−	0.111274i
$484$	−4.30081e8	−	4.77653e8i	−0.172421	−	0.191493i
$485$	7.87797e7	−	7.49539e8i	0.0313558	−	0.298331i
$486$	1.74429e9	−	3.70761e8i	0.689276	−	0.146510i
$487$	8.27156e7	+	3.68274e7i	0.0324516	+	0.0144484i	0.422898	−	0.906177i	$-0.361013\pi$
$487$	8.27156e7	+	3.68274e7i	0.0324516	+	0.0144484i	−0.390447	+	0.920626i	$0.627679\pi$
$488$	−1.50157e8	+	1.09095e8i	−0.0584891	+	0.0424948i
$489$	3.57953e8	−	1.59371e8i	0.138435	−	0.0616351i
$490$	6.31159e8	−	1.09320e9i	0.242355	−	0.419771i
$491$	−4.00302e7	−	6.93343e7i	−0.0152617	−	0.0264340i	0.858294	−	0.513159i	$-0.171525\pi$
$491$	−4.00302e7	−	6.93343e7i	−0.0152617	−	0.0264340i	−0.873555	+	0.486725i	$0.838191\pi$
$492$	5.05593e8	+	3.67335e8i	0.191392	+	0.139054i
$493$	−1.24221e9	−	2.64039e8i	−0.466906	−	0.0992439i
$494$	−1.62592e8	+	5.00405e8i	−0.0606811	+	0.186757i
$495$	1.13503e9			0.420619
$496$	3.97847e8	+	5.50729e8i	0.146396	+	0.202653i
$497$	4.61104e8			0.168481
$498$	5.95750e7	−	1.83353e8i	0.0216153	−	0.0665250i
$499$	−3.63308e9	−	7.72235e8i	−1.30895	−	0.278226i	−0.499960	−	0.866048i	$-0.666652\pi$
$499$	−3.63308e9	−	7.72235e8i	−1.30895	−	0.278226i	−0.808990	+	0.587823i	$0.799985\pi$
$500$	−1.21897e9	−	8.85636e8i	−0.436113	−	0.316855i
$501$	8.93912e8	+	1.54830e9i	0.317587	+	0.550077i
$502$	6.31033e8	−	1.09298e9i	0.222633	−	0.385611i
$503$	4.46646e8	−	1.98860e8i	0.156486	−	0.0696721i	−0.326999	−	0.945025i	$-0.606037\pi$
$503$	4.46646e8	−	1.98860e8i	0.156486	−	0.0696721i	0.483485	+	0.875353i	$0.339371\pi$
$504$	1.94262e8	−	1.41140e8i	0.0675899	−	0.0491070i
$505$	−8.12835e8	−	3.61897e8i	−0.280855	−	0.125045i
$506$	−1.62446e9	+	3.45289e8i	−0.557418	+	0.118483i
$507$	1.25931e8	−	1.19815e9i	0.0429145	−	0.408304i
$508$	−5.25227e8	−	5.83323e8i	−0.177756	−	0.197418i
$509$	1.66368e8	−	1.84770e8i	0.0559187	−	0.0621040i	−0.714536	−	0.699598i	$-0.753362\pi$
$509$	1.66368e8	−	1.84770e8i	0.0559187	−	0.0621040i	0.770455	+	0.637494i	$0.220029\pi$
$510$	−4.36342e7	−	4.15151e8i	−0.0145657	−	0.138583i
$511$	−2.08582e8	−	6.41948e8i	−0.0691517	−	0.212827i
$512$	−4.14756e7	−	1.27649e8i	−0.0136568	−	0.0420312i
$513$	−2.69216e8	−	2.56142e9i	−0.0880420	−	0.837663i
$514$	2.47691e8	−	2.75088e8i	0.0804524	−	0.0893514i
$515$	6.19688e8	+	6.88234e8i	0.199916	+	0.222029i
$516$	9.94765e7	−	9.46455e8i	0.0318747	−	0.303268i
$517$	3.41457e9	−	7.25788e8i	1.08672	−	0.230990i
$518$	8.75219e7	+	3.89673e7i	0.0276670	+	0.0123182i
$519$	1.55434e9	−	1.12929e9i	0.488044	−	0.354585i
$520$	−2.03888e8	+	9.07767e7i	−0.0635886	+	0.0283115i
$521$	1.71023e9	−	2.96221e9i	0.529813	−	0.917663i	−0.469582	−	0.882889i	$-0.655595\pi$
$521$	1.71023e9	−	2.96221e9i	0.529813	−	0.917663i	0.999395	−	0.0347743i	$-0.0110712\pi$
$522$	−7.41428e8	−	1.28419e9i	−0.228151	−	0.395169i
$523$	2.63217e9	+	1.91238e9i	0.804558	+	0.584546i	0.912248	−	0.409639i	$-0.134345\pi$
$523$	2.63217e9	+	1.91238e9i	0.804558	+	0.584546i	−0.107690	+	0.994185i	$0.534345\pi$
$524$	2.10814e8	+	4.48098e7i	0.0640087	+	0.0136055i
$525$	5.79731e7	−	1.78423e8i	0.0174851	−	0.0538138i
$526$	2.88417e8			0.0864114
$527$	−8.09386e8	−	1.83128e9i	−0.240890	−	0.545027i
$528$	2.59563e8			0.0767405
$529$	3.57922e8	−	1.10157e9i	0.105122	−	0.323532i
$530$	−6.34447e7	−	1.34856e7i	−0.0185110	−	0.00393463i
$531$	2.40858e9	+	1.74993e9i	0.698119	+	0.507213i
$532$	−2.69438e8	−	4.66679e8i	−0.0775831	−	0.134378i
$533$	−4.92331e8	+	8.52743e8i	−0.140836	+	0.243934i
$534$	2.70165e7	−	1.20285e7i	0.00767776	−	0.00341836i
$535$	1.99750e9	−	1.45127e9i	0.563959	−	0.409740i
$536$	−5.38987e8	−	2.39973e8i	−0.151183	−	0.0673108i
$537$	1.54023e9	−	3.27385e8i	0.429214	−	0.0912323i
$538$	3.02844e8	−	2.88137e9i	0.0838458	−	0.797740i
$539$	−1.54777e9	−	1.71897e9i	−0.425741	−	0.472833i
$540$	7.31008e8	−	8.11867e8i	0.199776	−	0.221874i
$541$	4.62459e8	+	4.40000e9i	0.125569	+	1.19471i	0.857920	+	0.513783i	$0.171756\pi$
$541$	4.62459e8	+	4.40000e9i	0.125569	+	1.19471i	−0.732351	+	0.680927i	$0.761577\pi$
$542$	1.06748e9	+	3.28538e9i	0.287981	+	0.886315i
$543$	7.20119e8	+	2.21630e9i	0.193021	+	0.594058i
$544$	4.13447e7	+	3.93369e8i	0.0110109	+	0.104762i
$545$	2.60106e9	−	2.88877e9i	0.688277	−	0.764409i
$546$	−6.10984e7	−	6.78566e7i	−0.0160641	−	0.0178409i
$547$	−4.47722e8	+	4.25979e9i	−0.116964	+	1.11284i	0.765818	+	0.643057i	$0.222334\pi$
$547$	−4.47722e8	+	4.25979e9i	−0.116964	+	1.11284i	−0.882782	+	0.469782i	$0.844333\pi$
$548$	3.32969e9	−	7.07747e8i	0.864314	−	0.183716i
$549$	5.83448e8	+	2.59768e8i	0.150487	+	0.0670011i
$550$	−6.79784e8	+	4.93892e8i	−0.174222	+	0.126579i
$551$	−3.04009e9	+	1.35353e9i	−0.774204	+	0.344698i
$552$	−3.56589e8	+	6.17631e8i	−0.0902364	+	0.156294i
$553$	−2.79363e8	−	4.83871e8i	−0.0702475	−	0.121672i
$554$	−1.91586e9	−	1.39195e9i	−0.478717	−	0.347808i
$555$	1.90222e8	+	4.04330e7i	0.0472320	+	0.0100395i
$556$	−7.28219e8	+	2.24123e9i	−0.179680	+	0.552999i
$557$	1.42480e9			0.349350			0.174675	−	0.984626i	$-0.444112\pi$
$557$	1.42480e9			0.349350			0.174675	+	0.984626i	$0.444112\pi$
$558$	9.56674e8	−	2.13312e9i	0.233101	−	0.519750i
$559$	1.49944e9			0.363069
$560$	7.06343e7	−	2.17390e8i	0.0169964	−	0.0523096i
$561$	−7.48210e8	−	1.59037e8i	−0.178918	−	0.0380301i
$562$	−2.77300e9	−	2.01471e9i	−0.658982	−	0.478778i
$563$	2.50415e9	+	4.33732e9i	0.591400	+	1.02434i	0.994044	+	0.108978i	$0.0347579\pi$
$563$	2.50415e9	+	4.33732e9i	0.591400	+	1.02434i	−0.402644	+	0.915357i	$0.631909\pi$
$564$	7.49542e8	−	1.29824e9i	0.175922	−	0.304705i
$565$	−4.51257e8	+	2.00913e8i	−0.105258	+	0.0468638i
$566$	1.00864e9	−	7.32823e8i	0.233819	−	0.169880i
$567$	−5.28683e8	−	2.35385e8i	−0.121802	−	0.0542297i
$568$	−8.67497e8	+	1.84392e8i	−0.198632	+	0.0422205i
$569$	5.11064e8	−	4.86245e9i	0.116301	−	1.10653i	−0.768272	−	0.640124i	$-0.778883\pi$
$569$	5.11064e8	−	4.86245e9i	0.116301	−	1.10653i	0.884572	−	0.466403i	$-0.154450\pi$
$570$	−7.31930e8	−	8.12891e8i	−0.165542	−	0.183853i
$571$	1.49291e9	−	1.65804e9i	0.335588	−	0.372708i	−0.551606	−	0.834105i	$-0.685985\pi$
$571$	1.49291e9	−	1.65804e9i	0.335588	−	0.372708i	0.887194	+	0.461397i	$0.152652\pi$
$572$	4.27486e7	+	4.06726e8i	0.00955072	+	0.0908691i
$573$	1.05576e9	+	3.24929e9i	0.234435	+	0.721517i
$574$	−3.11632e8	−	9.59105e8i	−0.0687782	−	0.211677i
$575$	−2.41325e8	−	2.29606e9i	−0.0529378	−	0.503669i
$576$	−3.09034e8	+	3.43217e8i	−0.0673794	+	0.0748325i
$577$	4.04422e9	+	4.49156e9i	0.876434	+	0.973378i	0.999820	−	0.0189806i	$-0.00604208\pi$
$577$	4.04422e9	+	4.49156e9i	0.876434	+	0.973378i	−0.123386	+	0.992359i	$0.539375\pi$
$578$	−2.21295e8	+	2.10548e9i	−0.0476677	+	0.453528i
$579$	−1.05771e9	+	2.24824e8i	−0.226461	+	0.0481357i
$580$	−1.28953e9	−	5.74136e8i	−0.274431	−	0.122185i
$581$	−2.51684e8	+	1.82859e8i	−0.0532402	+	0.0386812i
$582$	−5.41791e8	+	2.41221e8i	−0.113920	+	0.0507206i
$583$	−5.94275e7	+	1.02931e8i	−0.0124207	+	0.0215134i
$584$	6.49124e8	+	1.12432e9i	0.134860	+	0.233584i
$585$	6.21304e8	+	4.51404e8i	0.128309	+	0.0932222i
$586$	−3.78238e9	−	8.03969e8i	−0.776467	−	0.165043i
$587$	1.86414e9	−	5.73724e9i	0.380404	−	1.17076i	−0.559355	−	0.828928i	$-0.688951\pi$
$587$	1.86414e9	−	5.73724e9i	0.380404	−	1.17076i	0.939760	−	0.341836i	$-0.111049\pi$
$588$	−9.93323e8			−0.201498
$589$	−4.53644e9	−	2.63557e9i	−0.914770	−	0.531461i
$590$	2.83403e9			0.568097
$591$	−8.19260e8	+	2.52142e9i	−0.163255	+	0.502446i
$592$	−1.80242e8	−	3.83115e7i	−0.0357050	−	0.00758933i
$593$	−3.38023e9	−	2.45588e9i	−0.665663	−	0.483632i	0.202908	−	0.979198i	$-0.434961\pi$
$593$	−3.38023e9	−	2.45588e9i	−0.665663	−	0.483632i	−0.868571	+	0.495566i	$0.834961\pi$
$594$	−1.00094e9	−	1.73368e9i	−0.195955	−	0.339403i
$595$	−3.36805e8	+	5.83364e8i	−0.0655495	+	0.113535i
$596$	−9.40089e8	+	4.18555e8i	−0.181889	+	0.0809824i
$597$	−7.08000e8	+	5.14392e8i	−0.136183	+	0.0989427i
$598$	−1.02653e9	−	4.57042e8i	−0.196299	−	0.0873981i
$599$	−4.45150e9	+	9.46196e8i	−0.846277	+	0.179882i	−0.610590	−	0.791947i	$-0.709068\pi$
$599$	−4.45150e9	+	9.46196e8i	−0.846277	+	0.179882i	−0.235688	+	0.971829i	$0.575734\pi$
$600$	−3.77175e7	+	3.58858e8i	−0.00712876	+	0.0678256i
$601$	3.39612e9	+	3.77178e9i	0.638150	+	0.708737i	0.972288	−	0.233787i	$-0.0751118\pi$
$601$	3.39612e9	+	3.77178e9i	0.638150	+	0.708737i	−0.334138	+	0.942524i	$0.608445\pi$
$602$	−1.02757e9	+	1.14124e9i	−0.191967	+	0.213200i
$603$	2.12211e8	+	2.01905e9i	0.0394146	+	0.375005i
$604$	−5.73875e8	−	1.76621e9i	−0.105971	−	0.326146i
$605$	6.50592e8	+	2.00232e9i	0.119444	+	0.367611i
$606$	7.31861e7	+	6.96319e8i	0.0133590	+	0.127102i
$607$	−3.98245e9	+	4.42296e9i	−0.722754	+	0.802700i	−0.986823	−	0.161804i	$-0.948269\pi$
$607$	−3.98245e9	+	4.42296e9i	−0.722754	+	0.802700i	0.264069	+	0.964504i	$0.414935\pi$
$608$	6.93526e8	+	7.70239e8i	0.125141	+	0.138983i
$609$	6.03662e7	−	5.74346e8i	0.0108301	−	0.103042i
$610$	5.94673e8	−	1.26402e8i	0.106078	−	0.0225475i
$611$	2.15775e9	+	9.60691e8i	0.382698	+	0.170388i
$612$	1.10110e9	−	7.99999e8i	0.194177	−	0.141078i
$613$	−8.91737e9	+	3.97027e9i	−1.56360	+	0.696159i	−0.992216	−	0.124526i	$-0.960259\pi$
$613$	−8.91737e9	+	3.97027e9i	−1.56360	+	0.696159i	−0.571382	+	0.820685i	$0.693592\pi$
$614$	2.70631e9	−	4.68746e9i	0.471833	−	0.817238i
$615$	−1.02353e9	−	1.77281e9i	−0.177434	−	0.307325i
$616$	−3.38858e8	−	2.46195e8i	−0.0584097	−	0.0424372i
$617$	−9.81760e9	−	2.08680e9i	−1.68270	−	0.357669i	−0.735307	−	0.677734i	$-0.762962\pi$
$617$	−9.81760e9	−	2.08680e9i	−1.68270	−	0.357669i	−0.947396	+	0.320065i	$0.896295\pi$
$618$	2.25199e8	−	6.93091e8i	0.0383802	−	0.118122i
$619$	−9.02568e9			−1.52955			−0.764773	−	0.644300i	$-0.777149\pi$
$619$	−9.02568e9			−1.52955			−0.764773	+	0.644300i	$0.777149\pi$
$620$	−4.56779e8	−	2.17804e9i	−0.0769724	−	0.367025i
$621$	5.50039e9			0.921664
$622$	−9.25735e8	+	2.84912e9i	−0.154248	+	0.474727i
$623$	−4.66788e7	−	9.92189e6i	−0.00773413	−	0.00164394i
$624$	1.42082e8	+	1.03229e8i	0.0234096	+	0.0170081i
$625$	1.13265e9	+	1.96181e9i	0.185574	+	0.321424i
$626$	−3.32206e9	+	5.75397e9i	−0.541249	+	0.937470i
$627$	−1.83112e9	+	8.15265e8i	−0.296674	+	0.132088i
$628$	2.03345e9	−	1.47739e9i	0.327623	−	0.238032i
$629$	4.96085e8	+	2.20871e8i	0.0794839	+	0.0353885i
$630$	−7.69349e8	+	1.63530e8i	−0.122583	+	0.0260559i
$631$	−1.24202e9	+	1.18170e10i	−0.196800	+	1.87243i	0.237123	+	0.971480i	$0.423796\pi$
$631$	−1.24202e9	+	1.18170e10i	−0.196800	+	1.87243i	−0.433923	+	0.900950i	$0.642871\pi$
$632$	7.19074e8	+	7.98613e8i	0.113309	+	0.125842i
$633$	−2.37556e9	+	2.63832e9i	−0.372265	+	0.413442i
$634$	2.29912e8	+	2.18747e9i	0.0358302	+	0.340902i
$635$	7.94522e8	+	2.44529e9i	0.123140	+	0.378985i
$636$	1.57723e7	+	4.85421e7i	0.00243106	+	0.00748202i
$637$	−1.63595e8	−	1.55650e9i	−0.0250773	−	0.238595i
$638$	−1.73077e9	+	1.92221e9i	−0.263856	+	0.293042i
$639$	2.04202e9	+	2.26789e9i	0.309604	+	0.343850i
$640$	−4.59549e7	+	4.37232e8i	−0.00692950	+	0.0659298i
$641$	1.18161e10	−	2.51160e9i	1.77204	−	0.376658i	0.797931	−	0.602749i	$-0.205928\pi$
$641$	1.18161e10	−	2.51160e9i	1.77204	−	0.376658i	0.974106	+	0.226091i	$0.0725947\pi$
$642$	−1.77493e9	−	7.90248e8i	−0.264733	−	0.117867i
$643$	−2.16711e9	+	1.57449e9i	−0.321471	+	0.233562i	−0.736803	−	0.676108i	$-0.763665\pi$
$643$	−2.16711e9	+	1.57449e9i	−0.321471	+	0.233562i	0.415332	+	0.909670i	$0.363665\pi$
$644$	1.05135e9	−	4.68089e8i	0.155112	−	0.0690602i
$645$	−1.55863e9	+	2.69963e9i	−0.228710	+	0.396137i
$646$	−1.52721e9	−	2.64520e9i	−0.222887	−	0.386051i
$647$	5.47313e9	+	3.97646e9i	0.794457	+	0.577207i	0.909283	−	0.416179i	$-0.136631\pi$
$647$	5.47313e9	+	3.97646e9i	0.794457	+	0.577207i	−0.114826	+	0.993386i	$0.536631\pi$
$648$	1.08876e9	+	2.31424e8i	0.157189	+	0.0334115i
$649$	1.60477e9	−	4.93899e9i	0.230440	−	0.709221i
$650$	−5.68529e8			−0.0812000
$651$	7.89734e8	−	4.53098e8i	0.112188	−	0.0643663i
$652$	1.21612e9			0.171834
$653$	1.10428e9	−	3.39863e9i	0.155197	−	0.477648i	−0.842984	−	0.537939i	$-0.819203\pi$
$653$	1.10428e9	−	3.39863e9i	0.155197	−	0.477648i	0.998181	+	0.0602914i	$0.0192030\pi$
$654$	−2.99203e9	−	6.35976e8i	−0.418258	−	0.0889034i
$655$	−5.71136e8	−	4.14955e8i	−0.0794136	−	0.0576974i
$656$	9.69826e8	+	1.67979e9i	0.134131	+	0.232322i
$657$	2.23364e9	−	3.86878e9i	0.307280	−	0.532225i
$658$	−2.20990e9	+	9.83911e8i	−0.302400	+	0.134637i
$659$	−7.28477e8	+	5.29270e8i	−0.0991555	+	0.0720407i	−0.636258	−	0.771476i	$-0.719519\pi$
$659$	−7.28477e8	+	5.29270e8i	−0.0991555	+	0.0720407i	0.537103	+	0.843517i	$0.319519\pi$
$660$	−7.76714e8	−	3.45815e8i	−0.105162	−	0.0468210i
$661$	4.77044e9	−	1.01399e9i	0.642471	−	0.136561i	0.124856	−	0.992175i	$-0.460153\pi$
$661$	4.77044e9	−	1.01399e9i	0.642471	−	0.136561i	0.517615	+	0.855613i	$0.326820\pi$
$662$	−3.80835e8	+	3.62341e9i	−0.0510193	+	0.485416i
$663$	−3.46313e8	−	3.84620e8i	−0.0461500	−	0.0512548i
$664$	4.00381e8	−	4.44668e8i	0.0530744	−	0.0589451i
$665$	1.84506e8	+	1.75546e9i	0.0243296	+	0.231480i
$666$	1.95938e8	+	6.03035e8i	0.0257015	+	0.0791011i
$667$	−2.19617e9	−	6.75911e9i	−0.286566	−	0.881960i
$668$	5.80016e8	+	5.51848e9i	0.0752874	+	0.716312i
$669$	−1.78956e9	+	1.98750e9i	−0.231075	+	0.256635i
$670$	1.29314e9	+	1.43618e9i	0.166106	+	0.184479i
$671$	1.16449e8	−	1.10794e9i	0.0148801	−	0.141575i
$672$	−1.75938e8	+	3.73968e7i	−0.0223649	+	0.00475381i
$673$	6.94482e8	+	3.09203e8i	0.0878230	+	0.0391013i	0.450178	−	0.892939i	$-0.351361\pi$
$673$	6.94482e8	+	3.09203e8i	0.0878230	+	0.0391013i	−0.362355	+	0.932040i	$0.618027\pi$
$674$	−3.89853e8	+	2.83245e8i	−0.0490446	+	0.0356330i
$675$	2.54234e9	−	1.13192e9i	0.318178	−	0.141662i
$676$	1.86960e9	−	3.23824e9i	0.232774	−	0.403176i
$677$	−3.14980e9	−	5.45561e9i	−0.390141	−	0.675745i	0.602327	−	0.798250i	$-0.294241\pi$
$677$	−3.14980e9	−	5.45561e9i	−0.390141	−	0.675745i	−0.992468	+	0.122505i	$0.960907\pi$
$678$	3.14466e8	+	2.28473e8i	0.0387498	+	0.0281534i
$679$	9.36101e8	+	1.98974e8i	0.114757	+	0.0243923i
$680$	4.00364e8	−	1.23219e9i	0.0488286	−	0.150279i
$681$	1.30038e9			0.157781
$682$	−4.05442e9	−	4.37273e8i	−0.489422	−	0.0527846i
$683$	1.06259e10			1.27612			0.638062	−	0.769985i	$-0.279736\pi$
$683$	1.06259e10			1.27612			0.638062	+	0.769985i	$0.279736\pi$
$684$	1.10210e9	−	3.39191e9i	0.131681	−	0.405273i
$685$	−1.09066e10	−	2.31828e9i	−1.29650	−	0.275580i
$686$	2.71564e9	+	1.97303e9i	0.321172	+	0.233345i
$687$	1.37542e7	+	2.38230e7i	0.00161840	+	0.00280316i
$688$	1.47685e9	−	2.55798e9i	0.172893	−	0.299459i
$689$	−7.34661e7	+	3.27092e7i	−0.00855696	+	0.00380981i
$690$	1.88992e9	−	1.37311e9i	0.219014	−	0.159123i
$691$	3.28270e9	+	1.46155e9i	0.378494	+	0.168516i	0.587160	−	0.809471i	$-0.300246\pi$
$691$	3.28270e9	+	1.46155e9i	0.378494	+	0.168516i	−0.208667	+	0.977987i	$0.566912\pi$
$692$	5.83274e9	−	1.23979e9i	0.669116	−	0.142225i
$693$	−1.50654e8	+	1.43338e9i	−0.0171955	+	0.163604i
$694$	1.72556e8	+	1.91643e8i	0.0195962	+	0.0217638i
$695$	5.16509e9	−	5.73642e9i	0.583621	−	0.648177i
$696$	1.16107e8	+	1.10468e9i	0.0130534	+	0.124195i
$697$	−1.76637e9	−	5.43633e9i	−0.197591	−	0.608123i
$698$	2.83685e9	+	8.73092e9i	0.315749	+	0.971775i
$699$	−2.65706e8	−	2.52802e9i	−0.0294260	−	0.279970i
$700$	3.89615e8	−	4.32712e8i	0.0429332	−	0.0476821i
$701$	−6.09481e9	−	6.76897e9i	−0.668263	−	0.742181i	0.309729	−	0.950825i	$-0.399762\pi$
$701$	−6.09481e9	−	6.76897e9i	−0.668263	−	0.742181i	−0.977992	+	0.208644i	$0.933095\pi$
$702$	1.41583e8	−	1.34707e9i	0.0154466	−	0.146964i
$703$	1.39187e9	−	2.95850e8i	0.151096	−	0.0321165i
$704$	7.35960e8	+	3.27671e8i	0.0794969	+	0.0353943i
$705$	−3.97257e9	+	2.88624e9i	−0.426982	+	0.310220i
$706$	1.58394e9	−	7.05213e8i	0.169403	−	0.0754231i
$707$	5.64912e8	−	9.78456e8i	0.0601191	−	0.104129i
$708$	−1.11506e9	−	1.93133e9i	−0.118081	−	0.204522i
$709$	−8.21001e9	−	5.96492e9i	−0.865131	−	0.628554i	0.0641453	−	0.997941i	$-0.479568\pi$
$709$	−8.21001e9	−	5.96492e9i	−0.865131	−	0.628554i	−0.929276	+	0.369386i	$0.879568\pi$
$710$	2.84155e9	+	6.03990e8i	0.297955	+	0.0633323i
$711$	1.14270e9	−	3.51686e9i	0.119230	−	0.366953i
$712$	9.17866e7			0.00953015
$713$	6.61048e9	−	9.04677e9i	0.682998	−	0.934717i
$714$	5.30067e8			0.0544988
$715$	4.13959e8	−	1.27404e9i	0.0423532	−	0.130350i
$716$	4.78041e9	+	1.01611e9i	0.486709	+	0.103453i
$717$	−1.29618e9	−	9.41727e8i	−0.131325	−	0.0954131i
$718$	6.61576e9	+	1.14588e10i	0.667028	+	1.15533i
$719$	8.14063e9	−	1.41000e10i	0.816784	−	1.41471i	−0.0912565	−	0.995827i	$-0.529088\pi$
$719$	8.14063e9	−	1.41000e10i	0.816784	−	1.41471i	0.908040	−	0.418883i	$-0.137578\pi$
$720$	1.38202e9	−	6.15313e8i	0.137990	−	0.0614373i
$721$	−9.51390e8	+	6.91225e8i	−0.0945333	+	0.0686825i
$722$	−7.79063e8	−	3.46861e8i	−0.0770358	−	0.0342985i
$723$	8.29367e8	−	1.76287e8i	0.0816137	−	0.0173475i
$724$	−7.56027e8	+	7.19312e9i	−0.0740376	+	0.704421i
$725$	−2.40605e9	−	2.67219e9i	−0.234488	−	0.260426i
$726$	1.10856e9	−	1.23118e9i	0.107518	−	0.119411i
$727$	1.27586e9	+	1.21390e10i	0.123150	+	1.17169i	0.865228	+	0.501378i	$0.167174\pi$
$727$	1.27586e9	+	1.21390e10i	0.123150	+	1.17169i	−0.742078	+	0.670313i	$0.766160\pi$
$728$	−8.75753e7	−	2.69529e8i	−0.00841244	−	0.0258908i
$729$	−4.88431e7	−	1.50324e8i	−0.00466935	−	0.0143708i
$730$	−4.44508e8	−	4.22921e9i	−0.0422912	−	0.402374i
$731$	−5.82442e9	+	6.46868e9i	−0.551496	+	0.612498i
$732$	−3.20116e8	−	3.55524e8i	−0.0301660	−	0.0335028i
$733$	−1.10589e9	+	1.05218e10i	−0.103716	+	0.986796i	0.811642	+	0.584155i	$0.198574\pi$
$733$	−1.10589e9	+	1.05218e10i	−0.103716	+	0.986796i	−0.915358	+	0.402640i	$0.868093\pi$
$734$	3.79002e9	−	8.05594e8i	0.353757	−	0.0751935i
$735$	2.97241e9	+	1.32340e9i	0.276123	+	0.122938i
$736$	−1.79076e9	+	1.30106e9i	−0.165563	+	0.120289i
$737$	3.23514e9	−	1.44038e9i	0.297685	−	0.132538i
$738$	3.33718e9	−	5.78016e9i	0.305620	−	0.529350i
$739$	−9.97731e9	−	1.72812e10i	−0.909406	−	1.57514i	−0.814891	−	0.579614i	$-0.803203\pi$
$739$	−9.97731e9	−	1.72812e10i	−0.909406	−	1.57514i	−0.0945145	−	0.995523i	$-0.530130\pi$
$740$	4.88310e8	+	3.54778e8i	0.0442981	+	0.0321844i
$741$	−1.32657e9	−	2.81971e8i	−0.119775	−	0.0254589i
$742$	2.54514e7	−	7.83313e7i	0.00228717	−	0.00703918i
$743$	−1.42814e10			−1.27735			−0.638676	−	0.769476i	$-0.720518\pi$
$743$	−1.42814e10			−1.27735			−0.638676	+	0.769476i	$0.720518\pi$
$744$	−1.30457e9	+	1.16824e9i	−0.116135	+	0.103999i
$745$	3.37075e9			0.298662
$746$	−2.61528e9	+	8.04902e9i	−0.230639	+	0.709834i
$747$	−2.01397e9	−	4.28082e8i	−0.176779	−	0.0375755i
$748$	−1.92069e9	−	1.39546e9i	−0.167804	−	0.121917i
$749$	1.56761e9	+	2.71517e9i	0.136317	+	0.236108i
$750$	1.94185e9	−	3.36338e9i	0.168074	−	0.291113i
$751$	−3.86488e9	+	1.72076e9i	−0.332963	+	0.148245i	−0.566407	−	0.824125i	$-0.691667\pi$
$751$	−3.86488e9	+	1.72076e9i	−0.332963	+	0.148245i	0.233444	+	0.972370i	$0.425000\pi$
$752$	3.76413e9	−	2.73480e9i	0.322776	−	0.234511i
$753$	2.97181e9	+	1.32314e9i	0.253653	+	0.112933i
$754$	−1.71187e9	+	3.63870e8i	−0.145436	+	0.0309134i
$755$	−6.35854e8	+	6.04975e9i	−0.0537704	+	0.511591i
$756$	9.28241e8	+	1.03092e9i	0.0781330	+	0.0867755i
$757$	4.99158e9	−	5.54371e9i	0.418217	−	0.464477i	−0.496816	−	0.867856i	$-0.665498\pi$
$757$	4.99158e9	−	5.54371e9i	0.418217	−	0.464477i	0.915033	+	0.403379i	$0.132164\pi$
$758$	−3.10139e8	−	2.95078e9i	−0.0258651	−	0.246090i
$759$	−1.32280e9	−	4.07117e9i	−0.109812	−	0.337966i
$760$	−1.04911e9	−	3.22884e9i	−0.0866911	−	0.266808i
$761$	7.12357e8	+	6.77763e9i	0.0585938	+	0.557483i	0.983958	+	0.178402i	$0.0570929\pi$
$761$	7.12357e8	+	6.77763e9i	0.0585938	+	0.557483i	−0.925364	+	0.379080i	$0.876240\pi$
$762$	1.35380e9	−	1.50355e9i	0.110844	−	0.123105i
$763$	3.30285e9	+	3.66819e9i	0.269187	+	0.298962i
$764$	−1.10840e9	+	1.05457e10i	−0.0899229	+	0.855559i
$765$	−4.36077e9	+	9.26909e8i	−0.352166	+	0.0748552i
$766$	5.39304e9	+	2.40114e9i	0.433544	+	0.193026i
$767$	2.84268e9	−	2.06533e9i	0.227481	−	0.165275i
$768$	3.16045e8	−	1.40712e8i	0.0251759	−	0.0112090i
$769$	8.31593e9	−	1.44036e10i	0.659430	−	1.14217i	−0.321334	−	0.946966i	$-0.604131\pi$
$769$	8.31593e9	−	1.44036e10i	0.659430	−	1.14217i	0.980763	−	0.195200i	$-0.0625356\pi$
$770$	6.85990e8	+	1.18817e9i	0.0541502	+	0.0937909i
$771$	7.71909e8	+	5.60824e8i	0.0606562	+	0.0440693i
$772$	−3.28283e9	−	6.97787e8i	−0.256796	−	0.0545836i
$773$	4.70379e8	−	1.44768e9i	0.0366285	−	0.112731i	−0.931070	−	0.364839i	$-0.881124\pi$
$773$	4.70379e8	−	1.44768e9i	0.0366285	−	0.112731i	0.967699	+	0.252108i	$0.0811239\pi$
$774$	−1.01637e10			−0.787877
$775$	1.19370e9	−	5.54188e9i	0.0921171	−	0.427663i
$776$	−1.84070e9			−0.141406
$777$	−7.63094e7	+	2.34856e8i	−0.00583586	+	0.0179609i
$778$	5.09153e9	+	1.08224e9i	0.387632	+	0.0823938i
$779$	−1.21178e10	−	8.80410e9i	−0.918423	−	0.667273i
$780$	−2.87634e8	−	4.98197e8i	−0.0217025	−	0.0375898i
$781$	2.66163e9	−	4.61008e9i	0.199926	−	0.346282i
$782$	5.95916e9	−	2.65319e9i	0.445617	−	0.198401i
$783$	6.93067e9	−	5.03543e9i	0.515952	−	0.374861i
$784$	−2.81644e9	−	1.25396e9i	−0.208735	−	0.0929347i
$785$	−8.05318e9	+	1.71176e9i	−0.594188	+	0.126299i
$786$	−5.80682e7	+	5.52482e8i	−0.00426540	+	0.0405825i
$787$	1.56496e8	+	1.73806e8i	0.0114443	+	0.0127102i	0.748840	−	0.662751i	$-0.230611\pi$
$787$	1.56496e8	+	1.73806e8i	0.0114443	+	0.0127102i	−0.737395	+	0.675461i	$0.763945\pi$
$788$	−5.50593e9	+	6.11496e9i	−0.400857	+	0.445197i
$789$	7.77079e7	+	7.39341e8i	0.00563243	+	0.0535890i
$790$	−1.08776e9	−	3.34778e9i	−0.0784943	−	0.241581i
$791$	−1.93827e8	−	5.96539e8i	−0.0139251	−	0.0428570i
$792$	−2.89764e8	−	2.75692e9i	−0.0207255	−	0.197190i
$793$	5.04372e8	−	5.60162e8i	0.0359166	−	0.0398894i
$794$	−1.22815e10	−	1.36400e10i	−0.870720	−	0.967033i
$795$	1.74757e7	−	1.66270e8i	0.00123353	−	0.0117363i
$796$	−2.65681e9	+	5.64722e8i	−0.186709	+	0.0396862i
$797$	1.93137e10	+	8.59902e9i	1.35133	+	0.601652i	0.949415	−	0.314025i	$-0.101677\pi$
$797$	1.93137e10	+	8.59902e9i	1.35133	+	0.601652i	0.401917	+	0.915676i	$0.368344\pi$
$798$	1.12371e9	−	8.16425e8i	0.0782789	−	0.0568730i
$799$	−1.25260e10	+	5.57693e9i	−0.868758	+	0.386796i
$800$	−5.59963e8	+	9.69884e8i	−0.0386673	+	0.0669738i
$801$	−1.57919e8	−	2.73524e8i	−0.0108573	−	0.0188054i
$802$	−3.47295e9	−	2.52325e9i	−0.237733	−	0.172723i
$803$	−7.62213e9	−	1.62013e9i	−0.519484	−	0.110420i
$804$	4.69937e8	−	1.44632e9i	0.0318892	−	0.0981449i
$805$	−3.76966e9			−0.254693
$806$	−2.04545e9	−	1.85181e9i	−0.137599	−	0.124573i
$807$	7.46783e9			0.500192
$808$	−6.71517e8	+	2.06672e9i	−0.0447834	+	0.137829i
$809$	−7.29852e8	−	1.55135e8i	−0.0484635	−	0.0103012i	0.183616	−	0.982998i	$-0.441220\pi$
$809$	−7.29852e8	−	1.55135e8i	−0.0484635	−	0.0103012i	−0.232080	+	0.972697i	$0.574553\pi$
$810$	−2.94967e9	−	2.14306e9i	−0.195019	−	0.141689i
$811$	−1.83999e9	−	3.18696e9i	−0.121127	−	0.209799i	0.799085	−	0.601218i	$-0.205318\pi$
$811$	−1.83999e9	−	3.18696e9i	−0.121127	−	0.209799i	−0.920213	+	0.391419i	$0.871984\pi$
$812$	8.96210e8	−	1.55228e9i	0.0587440	−	0.101748i
$813$	−8.13427e9	+	3.62161e9i	−0.530886	+	0.236366i
$814$	8.94793e8	−	6.50105e8i	0.0581483	−	0.0422472i
$815$	−3.63910e9	−	1.62023e9i	−0.235474	−	0.104840i
$816$	−9.97239e8	+	2.11970e8i	−0.0642515	+	0.0136571i
$817$	−2.38420e9	+	2.26842e10i	−0.152956	+	1.45528i
$818$	9.56971e9	+	1.06282e10i	0.611311	+	0.678930i
$819$	−6.52523e8	+	7.24700e8i	−0.0415052	+	0.0460961i
$820$	−6.64119e8	−	6.31867e9i	−0.0420627	−	0.400200i
$821$	7.39463e9	+	2.27583e10i	0.466353	+	1.43529i	0.857272	+	0.514863i	$0.172157\pi$
$821$	7.39463e9	+	2.27583e10i	0.466353	+	1.43529i	−0.390919	+	0.920425i	$0.627843\pi$
$822$	2.71138e9	+	8.34477e9i	0.170270	+	0.524038i
$823$	1.58573e9	+	1.50873e10i	0.0991588	+	0.943433i	0.925112	+	0.379694i	$0.123971\pi$
$823$	1.58573e9	+	1.50873e10i	0.0991588	+	0.943433i	−0.825953	+	0.563739i	$0.809363\pi$
$824$	1.51348e9	−	1.68089e9i	0.0942390	−	0.104663i
$825$	−1.44922e9	−	1.60952e9i	−0.0898556	−	0.0997947i
$826$	−3.76165e8	+	3.57897e9i	−0.0232246	+	0.220967i
$827$	2.34749e10	−	4.98973e9i	1.44322	−	0.306767i	0.581252	−	0.813724i	$-0.302563\pi$
$827$	2.34749e10	−	4.98973e9i	1.44322	−	0.306767i	0.861971	+	0.506957i	$0.169230\pi$
$828$	6.95817e9	+	3.09797e9i	0.425979	+	0.189658i
$829$	−1.38432e10	+	1.00577e10i	−0.843908	+	0.613135i	−0.923460	−	0.383696i	$-0.874651\pi$
$829$	−1.38432e10	+	1.00577e10i	−0.843908	+	0.613135i	0.0795518	+	0.996831i	$0.474651\pi$
$830$	−1.79052e9	+	7.97192e8i	−0.108694	+	0.0483938i
$831$	3.05200e9	−	5.28622e9i	0.184493	−	0.319552i
$832$	2.72542e8	+	4.72057e8i	0.0164060	+	0.0284160i
$833$	7.35029e9	+	5.34030e9i	0.440602	+	0.320116i
$834$	−5.94146e9	−	1.26290e9i	−0.354660	−	0.0753853i
$835$	5.61662e9	−	1.72862e10i	0.333866	−	1.02753i
$836$	−6.22109e9			−0.368251
$837$	1.28337e10	+	4.20848e9i	0.756505	+	0.248077i
$838$	5.15770e9			0.302763
$839$	−6.39606e9	+	1.96851e10i	−0.373892	+	1.15072i	0.570331	+	0.821415i	$0.306815\pi$
$839$	−6.39606e9	+	1.96851e10i	−0.373892	+	1.15072i	−0.944223	+	0.329306i	$0.893185\pi$
$840$	5.76298e8	+	1.22496e8i	0.0335482	+	0.00713089i
$841$	5.00045e9	+	3.63304e9i	0.289883	+	0.210612i
$842$	5.36292e9	+	9.28885e9i	0.309606	+	0.536253i
$843$	4.41746e9	−	7.65126e9i	0.253966	−	0.439882i
$844$	−1.00662e10	+	4.48176e9i	−0.576324	+	0.256596i
$845$	−9.90885e9	+	7.19920e9i	−0.564969	+	0.410474i
$846$	−1.46259e10	−	6.51186e9i	−0.830474	−	0.369751i
$847$	−2.61499e9	+	5.55832e8i	−0.147869	+	0.0314305i
$848$	−1.65588e7	+	1.57546e8i	−0.000932486	+	0.00887201i
$849$	2.15031e9	+	2.38816e9i	0.120593	+	0.133933i
$850$	2.20839e9	−	2.45267e9i	0.123342	−	0.136985i
$851$	3.17654e8	+	3.02228e9i	0.0176686	+	0.168105i
$852$	−7.06407e8	−	2.17410e9i	−0.0391306	−	0.120432i
$853$	1.01662e10	+	3.12885e10i	0.560840	+	1.72609i	0.680001	+	0.733212i	$0.261980\pi$
$853$	1.01662e10	+	3.12885e10i	0.560840	+	1.72609i	−0.119161	+	0.992875i	$0.538020\pi$
$854$	8.06951e7	+	7.67763e8i	0.00443348	+	0.0421817i
$855$	−7.81692e9	+	8.68157e9i	−0.427715	+	0.475026i
$856$	−4.03498e9	−	4.48130e9i	−0.219879	−	0.244200i
$857$	−1.03169e9	+	9.81589e9i	−0.0559909	+	0.532717i	0.930194	+	0.367068i	$0.119639\pi$
$857$	−1.03169e9	+	9.81589e9i	−0.0559909	+	0.532717i	−0.986185	+	0.165649i	$0.947028\pi$
$858$	−1.03110e9	+	2.19167e8i	−0.0557309	+	0.0118460i
$859$	2.04536e10	+	9.10653e9i	1.10102	+	0.490204i	0.875100	−	0.483943i	$-0.160796\pi$
$859$	2.04536e10	+	9.10653e9i	1.10102	+	0.490204i	0.225917	+	0.974147i	$0.427462\pi$
$860$	−7.82729e9	+	5.68686e9i	−0.419630	+	0.304879i
$861$	2.37465e9	−	1.05726e9i	0.126791	−	0.0564510i
$862$	8.35634e9	−	1.44736e10i	0.444366	−	0.769664i
$863$	−1.21061e9	−	2.09685e9i	−0.0641163	−	0.111053i	0.832185	−	0.554498i	$-0.187090\pi$
$863$	−1.21061e9	−	2.09685e9i	−0.0641163	−	0.111053i	−0.896302	+	0.443445i	$0.853756\pi$
$864$	−2.15860e9	−	1.56831e9i	−0.113861	−	0.0827245i
$865$	−1.91056e10	−	4.06102e9i	−1.00370	−	0.213343i
$866$	3.28018e9	−	1.00954e10i	0.171627	−	0.528213i
$867$	−5.45690e9			−0.284367
$868$	2.81118e9	−	2.87750e8i	0.145905	−	0.0149347i
$869$	−6.45026e9			−0.333433
$870$	1.12433e9	−	3.46032e9i	0.0578863	−	0.178156i
$871$	2.34372e9	+	4.98174e8i	0.120183	+	0.0255457i
$872$	−7.68069e9	−	5.58035e9i	−0.392277	−	0.285006i
$873$	3.16692e9	+	5.48527e9i	0.161097	+	0.279028i
$874$	8.54656e9	−	1.48031e10i	0.433013	−	0.750001i
$875$	−5.72523e9	+	2.54904e9i	−0.288911	+	0.128632i
$876$	−2.70723e9	+	1.96692e9i	−0.136069	+	0.0988602i
$877$	−3.09035e10	−	1.37591e10i	−1.54707	−	0.688799i	−0.557146	−	0.830415i	$-0.688104\pi$
$877$	−3.09035e10	−	1.37591e10i	−1.54707	−	0.688799i	−0.989922	+	0.141616i	$0.954770\pi$
$878$	−1.62783e10	+	3.46006e9i	−0.811667	+	0.172525i
$879$	1.04185e9	−	9.91252e9i	0.0517420	−	0.492292i
$880$	−1.76572e9	−	1.96103e9i	−0.0873440	−	0.0970054i
$881$	2.05614e10	−	2.28358e10i	1.01306	−	1.12512i	0.0209514	−	0.999780i	$-0.493330\pi$
$881$	2.05614e10	−	2.28358e10i	1.01306	−	1.12512i	0.992114	−	0.125342i	$-0.0400029\pi$
$882$	1.10890e9	+	1.05504e10i	0.0544190	+	0.517763i
$883$	1.08600e10	+	3.34237e10i	0.530846	+	1.63378i	0.752457	+	0.658641i	$0.228868\pi$
$883$	1.08600e10	+	3.34237e10i	0.530846	+	1.63378i	−0.221611	+	0.975135i	$0.571132\pi$
$884$	−4.96388e8	−	1.52773e9i	−0.0241679	−	0.0743811i
$885$	7.63570e8	+	7.26488e9i	0.0370295	+	0.352312i
$886$	−7.87696e9	+	8.74826e9i	−0.380488	+	0.422575i
$887$	−5.29729e9	−	5.88323e9i	−0.254871	−	0.283063i	0.602107	−	0.798415i	$-0.294328\pi$
$887$	−5.29729e9	−	5.88323e9i	−0.254871	−	0.283063i	−0.856979	+	0.515352i	$0.827661\pi$
$888$	4.96472e7	−	4.72361e8i	0.00237930	−	0.0226375i
$889$	−3.19349e9	+	6.78798e8i	−0.152444	+	0.0324029i
$890$	−2.74661e8	−	1.22287e8i	−0.0130597	−	0.00581454i
$891$	−5.40507e9	+	3.92701e9i	−0.255994	+	0.185990i
$892$	−7.58307e9	+	3.37620e9i	−0.357740	+	0.159276i
$893$	−1.79647e10	+	3.11157e10i	−0.844187	+	1.46218i
$894$	−1.32623e9	−	2.29709e9i	−0.0620779	−	0.107522i
$895$	−1.29511e10	−	9.40950e9i	−0.603844	−	0.438719i
$896$	−5.46060e8	−	1.16069e8i	−0.0253608	−	0.00539060i
$897$	8.95023e8	−	2.75460e9i	0.0414058	−	0.127434i
$898$	2.84967e10			1.31319
$899$	4.73942e7	−	1.74509e10i	0.00217553	−	0.801049i
$900$	3.85367e9			0.176208
$901$	1.44262e8	−	4.43992e8i	0.00657074	−	0.0202227i
$902$	−1.13879e10	−	2.42057e9i	−0.516678	−	0.109823i
$903$	−3.20235e9	−	2.32665e9i	−0.144731	−	0.105153i
$904$	6.03207e8	+	1.04479e9i	0.0271567	+	0.0470368i
$905$	1.18457e10	−	2.05173e10i	0.531239	−	0.920134i
$906$	4.37295e9	−	1.94696e9i	0.195356	−	0.0869780i
$907$	4.37665e9	−	3.17982e9i	0.194767	−	0.141507i	−0.486128	−	0.873888i	$-0.661591\pi$
$907$	4.37665e9	−	3.17982e9i	0.194767	−	0.141507i	0.680895	+	0.732381i	$0.261591\pi$
$908$	3.68707e9	+	1.64159e9i	0.163449	+	0.0727720i
$909$	7.31416e9	−	1.55467e9i	0.322991	−	0.0686539i
$910$	−9.70335e7	+	9.23212e8i	−0.00426851	+	0.0406122i
$911$	−2.41546e10	−	2.68264e10i	−1.05849	−	1.17557i	−0.983967	−	0.178349i	$-0.942924\pi$
$911$	−2.41546e10	−	2.68264e10i	−1.05849	−	1.17557i	−0.0745195	−	0.997220i	$-0.523742\pi$
$912$	−1.78761e9	+	1.98534e9i	−0.0780352	+	0.0866668i
$913$	3.75415e8	+	3.57183e9i	0.0163254	+	0.155326i
$914$	−5.59541e9	−	1.72209e10i	−0.242393	−	0.746009i
$915$	4.84246e8	+	1.49035e9i	0.0208974	+	0.0643155i
$916$	8.92443e6	+	8.49103e7i	0.000383660	+	0.00365028i
$917$	5.99834e8	−	6.66183e8i	0.0256885	−	0.0285300i
$918$	5.26139e9	+	5.84336e9i	0.224466	+	0.249295i
$919$	2.05265e9	−	1.95297e10i	0.0872391	−	0.830025i	−0.860172	−	0.510005i	$-0.829644\pi$
$919$	2.05265e9	−	1.95297e10i	0.0872391	−	0.830025i	0.947411	−	0.320020i	$-0.103690\pi$
$920$	7.09204e9	−	1.50746e9i	0.300271	−	0.0638246i
$921$	1.27452e10	+	5.67453e9i	0.537574	+	0.239343i
$922$	1.54241e10	−	1.12062e10i	0.648098	−	0.470871i
$923$	3.29039e9	−	1.46498e9i	0.137734	−	0.0613231i
$924$	5.39808e8	−	9.34975e8i	0.0225106	−	0.0389895i
$925$	7.68776e8	+	1.33156e9i	0.0319377	+	0.0553177i
$926$	−1.31643e10	−	9.56440e9i	−0.544826	−	0.395840i
$927$	−7.61298e9	−	1.61819e9i	−0.313889	−	0.0667191i
$928$	−1.06533e9	+	3.27876e9i	−0.0437591	+	0.134677i
$929$	2.45205e10			1.00340			0.501701	−	0.865041i	$-0.332708\pi$
$929$	2.45205e10			1.00340			0.501701	+	0.865041i	$0.332708\pi$
$930$	5.46022e9	−	1.75775e9i	0.222597	−	0.0716585i
$931$	2.38075e10			0.966917
$932$	2.43798e9	−	7.50333e9i	0.0986448	−	0.303597i
$933$	−7.55297e9	−	1.60543e9i	−0.304461	−	0.0647153i
$934$	−9.25829e9	−	6.72654e9i	−0.371806	−	0.270133i
$935$	3.88828e9	+	6.73469e9i	0.155567	+	0.269449i
$936$	9.37819e8	−	1.62435e9i	0.0373812	−	0.0647462i
$937$	4.22616e10	−	1.88161e10i	1.67825	−	0.747207i	0.678332	−	0.734755i	$-0.262703\pi$
$937$	4.22616e10	−	1.88161e10i	1.67825	−	0.747207i	0.999922	−	0.0124517i	$-0.00396359\pi$
$938$	−1.98533e9	+	1.44242e9i	−0.0785456	+	0.0570667i
$939$	−1.56450e10	−	6.96562e9i	−0.616662	−	0.274555i
$940$	−1.49073e10	+	3.16864e9i	−0.585398	+	0.124430i
$941$	−4.88328e9	+	4.64613e10i	−0.191051	+	1.81772i	0.308261	+	0.951302i	$0.400253\pi$
$941$	−4.88328e9	+	4.64613e10i	−0.191051	+	1.81772i	−0.499311	+	0.866423i	$0.666414\pi$
$942$	4.33507e9	+	4.81458e9i	0.168973	+	0.187664i
$943$	2.14045e10	−	2.37721e10i	0.831215	−	0.923158i
$944$	−7.23506e8	−	6.88370e9i	−0.0279924	−	0.266330i
$945$	−1.40417e9	−	4.32159e9i	−0.0541263	−	0.166584i
$946$	5.47852e9	+	1.68611e10i	0.210399	+	0.647542i
$947$	−4.21606e9	−	4.01131e10i	−0.161318	−	1.53483i	−0.713229	−	0.700931i	$-0.752768\pi$
$947$	−4.21606e9	−	4.01131e10i	−0.161318	−	1.53483i	0.551911	−	0.833903i	$-0.313899\pi$
$948$	−1.85346e9	+	2.05848e9i	−0.0706568	+	0.0784723i
$949$	−3.52795e9	−	3.91818e9i	−0.133996	−	0.148817i
$950$	9.03995e8	−	8.60094e9i	0.0342085	−	0.325472i
$951$	−5.54550e9	+	1.17873e9i	−0.209078	+	0.0444410i
$952$	1.50294e9	+	6.69152e8i	0.0564563	+	0.0251360i
$953$	−4.19516e10	+	3.04796e10i	−1.57009	+	1.14073i	−0.643011	+	0.765857i	$0.722315\pi$
$953$	−4.19516e10	+	3.04796e10i	−1.57009	+	1.14073i	−0.927075	+	0.374877i	$0.877685\pi$
$954$	4.97976e8	−	2.21713e8i	0.0185690	−	0.00826747i
$955$	1.73668e10	−	3.00802e10i	0.645220	−	1.11755i
$956$	−2.48632e9	−	4.30643e9i	−0.0920353	−	0.159410i
$957$	−5.39380e9	−	3.91883e9i	−0.198931	−	0.144532i
$958$	−1.73922e10	−	3.69683e9i	−0.639110	−	0.135847i
$959$	4.37529e9	−	1.34658e10i	0.160192	−	0.493022i
$960$	−1.13320e9			−0.0413387
$961$	2.23457e10	−	1.60504e10i	0.812198	−	0.583382i
$962$	7.48349e8			0.0271014
$963$	−6.41208e9	+	1.97343e10i	−0.231370	+	0.712083i
$964$	2.57411e9	+	5.47145e8i	0.0925461	+	0.0196713i
$965$	8.89384e9	+	6.46175e9i	0.318598	+	0.231475i
$966$	1.48318e9	+	2.56895e9i	0.0529389	+	0.0916928i
$967$	9.67347e9	−	1.67549e10i	0.344025	−	0.595868i	−0.641151	−	0.767414i	$-0.721543\pi$
$967$	9.67347e9	−	1.67549e10i	0.344025	−	0.595868i	0.985176	+	0.171546i	$0.0548763\pi$
$968$	4.69742e9	−	2.09142e9i	0.166454	−	0.0741103i
$969$	6.36934e9	−	4.62760e9i	0.224885	−	0.163389i
$970$	5.50808e9	+	2.45235e9i	0.193776	+	0.0862744i
$971$	−3.06983e10	+	6.52513e9i	−1.07609	+	0.228729i	−0.711675	−	0.702509i	$-0.752063\pi$
$971$	−3.06983e10	+	6.52513e9i	−1.07609	+	0.228729i	−0.364412	+	0.931238i	$0.618730\pi$
$972$	−1.49121e9	+	1.41880e10i	−0.0520844	+	0.495550i
$973$	6.55868e9	+	7.28415e9i	0.228256	+	0.253504i
$974$	−4.84684e8	+	5.38296e8i	−0.0168075	+	0.0186666i
$975$	−1.53178e8	−	1.45739e9i	−0.00529274	−	0.0503571i
$976$	−4.58838e8	−	1.41216e9i	−0.0157974	−	0.0486193i
$977$	−4.23592e9	−	1.30368e10i	−0.145317	−	0.447240i	0.851734	−	0.523974i	$-0.175551\pi$
$977$	−4.23592e9	−	1.30368e10i	−0.145317	−	0.447240i	−0.997052	+	0.0767333i	$0.975551\pi$
$978$	3.27658e8	+	3.11746e9i	0.0112004	+	0.106565i
$979$	−3.68642e8	+	4.09418e8i	−0.0125564	+	0.0139453i
$980$	6.75724e9	+	7.50468e9i	0.229339	+	0.254707i
$981$	−3.41478e9	+	3.24894e10i	−0.115484	+	1.09875i
$982$	6.26487e8	−	1.33164e8i	0.0211116	−	0.00448742i
$983$	3.61192e10	+	1.60813e10i	1.21283	+	0.539988i	0.910617	−	0.413252i	$-0.135607\pi$
$983$	3.61192e10	+	1.60813e10i	1.21283	+	0.539988i	0.302215	+	0.953240i	$0.402274\pi$
$984$	−4.04474e9	+	2.93868e9i	−0.135334	+	0.0983262i
$985$	2.46228e10	−	1.09628e10i	0.820939	−	0.365506i
$986$	5.07983e9	−	8.79853e9i	0.168764	−	0.292308i
$987$	−3.11761e9	−	5.39986e9i	−0.103208	−	0.178761i
$988$	−3.40536e9	−	2.47414e9i	−0.112335	−	0.0816160i
$989$	−4.76475e10	−	1.01278e10i	−1.56622	−	0.332911i
$990$	−2.80595e9	+	8.63582e9i	−0.0919086	+	0.282866i
$991$	4.11353e10			1.34263			0.671316	−	0.741171i	$-0.265729\pi$
$991$	4.11353e10			1.34263			0.671316	+	0.741171i	$0.265729\pi$
$992$	−5.17373e9	+	1.66553e9i	−0.168272	+	0.0541702i
$993$	−9.39101e9			−0.304362
$994$	−1.13991e9	+	3.50829e9i	−0.0368145	+	0.113303i
$995$	8.70258e9	+	1.84979e9i	0.280070	+	0.0595308i
$996$	1.24775e9	+	9.06547e8i	0.0400149	+	0.0290725i
$997$	2.77540e10	+	4.80714e10i	0.886938	+	1.53622i	0.843477	+	0.537166i	$0.180505\pi$
$997$	2.77540e10	+	4.80714e10i	0.886938	+	1.53622i	0.0434610	+	0.999055i	$0.486162\pi$
$998$	1.48570e10	−	2.57330e10i	0.473123	−	0.819472i
$999$	−3.34645e9	+	1.48994e9i	−0.106195	+	0.0472812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.g.b.9.5	yes	72
31.7	even	15	inner	62.8.g.b.7.5	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.g.b.7.5	✓	72	31.7	even	15	inner
62.8.g.b.9.5	yes	72	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47214 + 7.60845i) q^{2} +(-20.1699 - 4.28724i) q^{3} +(-51.7771 - 37.6183i) q^{4} +(104.818 + 181.551i) q^{5} +(82.4820 - 142.863i) q^{6} +(-243.185 + 108.273i) q^{7} +(414.217 - 300.946i) q^{8} +(-1609.48 - 716.587i) q^{9} +(-1640.45 + 348.687i) q^{10} +(-321.232 + 3056.32i) q^{11} +(883.060 + 980.737i) q^{12} +(-1391.34 + 1545.24i) q^{13} +(-222.603 - 2117.92i) q^{14} +(-1335.82 - 4111.24i) q^{15} +(1265.73 + 3895.53i) q^{16} +(-1261.74 - 12004.7i) q^{17} +(9430.97 - 10474.1i) q^{18} +(-21164.7 - 23505.8i) q^{19} +(1402.43 - 13343.3i) q^{20} +(5369.20 - 1141.26i) q^{21} +(-22459.7 - 9999.71i) q^{22} +(54649.6 - 39705.3i) q^{23} +(-9644.94 + 4294.20i) q^{24} +(17088.7 - 29598.5i) q^{25} +(-8317.32 - 14406.0i) q^{26} +(65875.1 + 47861.1i) q^{27} +(16664.4 + 3542.13i) q^{28} +(32511.4 - 100060. i) q^{29} +34582.5 q^{30} +(157890. - 50827.8i) q^{31} -32768.0 q^{32} +(19582.4 - 60268.4i) q^{33} +(94456.1 + 20077.3i) q^{34} +(-45147.2 - 32801.4i) q^{35} +(56377.4 + 97648.6i) q^{36} +(-22493.7 + 38960.2i) q^{37} +(231165. - 102921. i) q^{38} +(34688.1 - 25202.4i) q^{39} +(98054.5 + 43656.7i) q^{40} +(463200. - 98456.2i) q^{41} +(-4590.18 + 43672.6i) q^{42} +(-482522. - 535895. i) q^{43} +(131606. - 146163. i) q^{44} +(-38606.2 - 367314. i) q^{45} +(166994. + 513956. i) q^{46} +(-351018. - 1.08032e6i) q^{47} +(-8828.64 - 83998.9i) q^{48} +(-503642. + 559351. i) q^{49} +(182953. + 203190. i) q^{50} +(-26017.7 + 247542. i) q^{51} +(130169. - 27668.3i) q^{52} +(35331.6 + 15730.6i) q^{53} +(-527001. + 382889. i) q^{54} +(-588548. + 262038. i) q^{55} +(-68146.9 + 118034. i) q^{56} +(326115. + 564849. i) q^{57} +(680928. + 494723. i) q^{58} +(-1.65292e6 - 351339. i) q^{59} +(-85492.7 + 263119. i) q^{60} -362507. q^{61} +(-3603.80 + 1.32695e6i) q^{62} +468988. q^{63} +(81007.0 - 249314. i) q^{64} +(-426379. - 90629.6i) q^{65} +(410139. + 297984. i) q^{66} +(-576167. - 997950. i) q^{67} +(-386265. + 669031. i) q^{68} +(-1.27250e6 + 566555. i) q^{69} +(361178. - 262411. i) q^{70} +(-1.58243e6 - 704542. i) q^{71} +(-882327. + 187544. i) q^{72} +(-265047. + 2.52175e6i) q^{73} +(-240819. - 267457. i) q^{74} +(-471574. + 523736. i) q^{75} +(211601. + 2.01324e6i) q^{76} +(-252797. - 778030. i) q^{77} +(105997. + 326226. i) q^{78} +(219395. + 2.08741e6i) q^{79} +(-574564. + 638118. i) q^{80} +(1.45469e6 + 1.61559e6i) q^{81} +(-395994. + 3.76763e6i) q^{82} +(1.14313e6 - 242980. i) q^{83} +(-320934. - 142889. i) q^{84} +(2.04720e6 - 1.48738e6i) q^{85} +(5.27019e6 - 2.34644e6i) q^{86} +(-1.08473e6 + 1.87881e6i) q^{87} +(786727. + 1.36265e6i) q^{88} +(145033. + 105373. i) q^{89} +(2.89013e6 + 614316. i) q^{90} +(171046. - 526424. i) q^{91} -4.32324e6 q^{92} +(-3.40253e6 + 348280. i) q^{93} +9.08734e6 q^{94} +(2.04905e6 - 6.30632e6i) q^{95} +(660927. + 140484. i) q^{96} +(-2.90851e6 - 2.11315e6i) q^{97} +(-3.01072e6 - 5.21473e6i) q^{98} +(2.70713e6 - 4.68889e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) \) 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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