LMFDB - Embedded newform 27.7.f.a.2.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, 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("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.15
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.6192 + 2.04878i) q^{2} +(14.4502 + 22.8077i) q^{3} +(70.6679 + 25.7210i) q^{4} +(2.84045 + 3.38512i) q^{5} +(121.171 + 294.613i) q^{6} +(129.733 - 47.2189i) q^{7} +(114.471 + 66.0899i) q^{8} +(-311.386 + 659.151i) q^{9} +O(q^{10})$	\(q+(11.6192 + 2.04878i) q^{2} +(14.4502 + 22.8077i) q^{3} +(70.6679 + 25.7210i) q^{4} +(2.84045 + 3.38512i) q^{5} +(121.171 + 294.613i) q^{6} +(129.733 - 47.2189i) q^{7} +(114.471 + 66.0899i) q^{8} +(-311.386 + 659.151i) q^{9} +(26.0684 + 45.1518i) q^{10} +(294.101 - 350.496i) q^{11} +(434.524 + 1983.45i) q^{12} +(-280.466 - 1590.60i) q^{13} +(1604.13 - 282.852i) q^{14} +(-36.1619 + 113.700i) q^{15} +(-2492.32 - 2091.30i) q^{16} +(5244.19 - 3027.73i) q^{17} +(-4968.51 + 7020.84i) q^{18} +(-2355.94 + 4080.61i) q^{19} +(113.660 + 312.278i) q^{20} +(2951.62 + 2276.59i) q^{21} +(4135.30 - 3469.93i) q^{22} +(340.377 - 935.179i) q^{23} +(146.764 + 3565.83i) q^{24} +(2709.86 - 15368.4i) q^{25} -19056.1i q^{26} +(-19533.3 + 2422.83i) q^{27} +10382.5 q^{28} +(-45792.4 - 8074.43i) q^{29} +(-653.117 + 1247.01i) q^{30} +(5662.75 + 2061.07i) q^{31} +(-30111.8 - 35885.8i) q^{32} +(12243.8 + 1643.06i) q^{33} +(67136.4 - 24435.6i) q^{34} +(528.341 + 305.038i) q^{35} +(-38959.0 + 38571.6i) q^{36} +(43820.6 + 75899.5i) q^{37} +(-35734.4 + 42586.6i) q^{38} +(32225.2 - 29381.2i) q^{39} +(101.427 + 575.223i) q^{40} +(-36649.8 + 6462.35i) q^{41} +(29631.2 + 32499.4i) q^{42} +(83844.2 + 70353.6i) q^{43} +(29798.6 - 17204.2i) q^{44} +(-3115.78 + 818.208i) q^{45} +(5870.88 - 10168.7i) q^{46} +(55157.8 + 151545. i) q^{47} +(11683.5 - 87063.7i) q^{48} +(-75523.4 + 63371.6i) q^{49} +(62972.8 - 173016. i) q^{50} +(144835. + 75856.8i) q^{51} +(21091.9 - 119618. i) q^{52} +27392.1i q^{53} +(-231925. - 11868.1i) q^{54} +2021.85 q^{55} +(17971.3 + 3168.83i) q^{56} +(-127113. + 5231.78i) q^{57} +(-515528. - 187637. i) q^{58} +(-178059. - 212202. i) q^{59} +(-5479.95 + 7104.79i) q^{60} +(202270. - 73620.2i) q^{61} +(61573.9 + 35549.7i) q^{62} +(-9272.58 + 100217. i) q^{63} +(-172241. - 298330. i) q^{64} +(4587.72 - 5467.43i) q^{65} +(138897. + 44175.9i) q^{66} +(28548.0 + 161904. i) q^{67} +(448472. - 79077.7i) q^{68} +(26247.8 - 5750.25i) q^{69} +(5513.94 + 4626.75i) q^{70} +(102242. - 59029.3i) q^{71} +(-79207.9 + 54874.2i) q^{72} +(-72494.1 + 125563. i) q^{73} +(353659. + 971670. i) q^{74} +(389676. - 160270. i) q^{75} +(-271447. + 227771. i) q^{76} +(21604.5 - 59357.9i) q^{77} +(434626. - 275364. i) q^{78} +(-34101.7 + 193401. i) q^{79} -14377.0i q^{80} +(-337519. - 410500. i) q^{81} -439081. q^{82} +(-588323. - 103737. i) q^{83} +(150028. + 236800. i) q^{84} +(25145.1 + 9152.06i) q^{85} +(830063. + 989230. i) q^{86} +(-477548. - 1.16110e6i) q^{87} +(56830.3 - 20684.5i) q^{88} +(-760977. - 439350. i) q^{89} +(-37879.2 + 3123.38i) q^{90} +(-111492. - 193110. i) q^{91} +(48107.5 - 57332.2i) q^{92} +(34819.2 + 158937. i) q^{93} +(330408. + 1.87383e6i) q^{94} +(-20505.3 + 3615.63i) q^{95} +(383354. - 1.20534e6i) q^{96} +(526763. + 442007. i) q^{97} +(-1.00736e6 + 581597. i) q^{98} +(139451. + 302996. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	11.6192	+	2.04878i	1.45240	+	0.256097i	0.843491	−	0.537143i	$-0.180497\pi$
$2$	11.6192	+	2.04878i	1.45240	+	0.256097i	0.608908	+	0.793241i	$0.291608\pi$
$3$	14.4502	+	22.8077i	0.535191	+	0.844731i
$3$	14.4502	+	22.8077i	0.535191	+	0.844731i
$4$	70.6679	+	25.7210i	1.10419	+	0.401891i
$5$	2.84045	+	3.38512i	0.0227236	+	0.0270809i	0.777287	−	0.629147i	$-0.216596\pi$
$5$	2.84045	+	3.38512i	0.0227236	+	0.0270809i	−0.754563	+	0.656228i	$0.772151\pi$
$6$	121.171	+	294.613i	0.560978	+	1.36395i
$7$	129.733	−	47.2189i	0.378230	−	0.137664i	−0.145907	−	0.989298i	$-0.546610\pi$
$7$	129.733	−	47.2189i	0.378230	−	0.137664i	0.524137	+	0.851634i	$0.324388\pi$
$8$	114.471	+	66.0899i	0.223576	+	0.129082i
$9$	−311.386	+	659.151i	−0.427141	+	0.904185i
$10$	26.0684	+	45.1518i	0.0260684	+	0.0451518i
$11$	294.101	−	350.496i	0.220962	−	0.263333i	−0.644163	−	0.764888i	$-0.722794\pi$
$11$	294.101	−	350.496i	0.220962	−	0.263333i	0.865126	+	0.501555i	$0.167239\pi$
$12$	434.524	+	1983.45i	0.251461	+	1.14783i
$13$	−280.466	−	1590.60i	−0.127658	−	0.723987i	−0.979693	−	0.200502i	$-0.935743\pi$
$13$	−280.466	−	1590.60i	−0.127658	−	0.723987i	0.852035	−	0.523485i	$-0.175368\pi$
$14$	1604.13	−	282.852i	0.584596	−	0.103080i
$15$	−36.1619	+	113.700i	−0.0107146	+	0.0336888i
$16$	−2492.32	−	2091.30i	−0.608476	−	0.510572i
$17$	5244.19	−	3027.73i	1.06741	−	0.616270i	0.139938	−	0.990160i	$-0.455310\pi$
$17$	5244.19	−	3027.73i	1.06741	−	0.616270i	0.927473	+	0.373890i	$0.121976\pi$
$18$	−4968.51	+	7020.84i	−0.851938	+	1.20385i
$19$	−2355.94	+	4080.61i	−0.343482	+	0.594928i	−0.985077	−	0.172116i	$-0.944940\pi$
$19$	−2355.94	+	4080.61i	−0.343482	+	0.594928i	0.641595	+	0.767044i	$0.278273\pi$
$20$	113.660	+	312.278i	0.0142075	+	0.0390348i
$21$	2951.62	+	2276.59i	0.318715	+	0.245826i
$22$	4135.30	−	3469.93i	0.388364	−	0.325876i
$23$	340.377	−	935.179i	0.0279754	−	0.0768619i	−0.924919	−	0.380165i	$-0.875867\pi$
$23$	340.377	−	935.179i	0.0279754	−	0.0768619i	0.952894	+	0.303303i	$0.0980894\pi$
$24$	146.764	+	3565.83i	0.0106166	+	0.257945i
$25$	2709.86	−	15368.4i	0.173431	−	0.983577i
$26$		−	19056.1i		−	1.08421i
$27$	−19533.3	+	2422.83i	−0.992395	+	0.123093i
$28$	10382.5			0.472962
$29$	−45792.4	−	8074.43i	−1.87758	−	0.331068i	−0.886331	−	0.463052i	$-0.846754\pi$
$29$	−45792.4	−	8074.43i	−1.87758	−	0.331068i	−0.991252	+	0.131984i	$0.957865\pi$
$30$	−653.117	+	1247.01i	−0.0241895	+	0.0461856i
$31$	5662.75	+	2061.07i	0.190082	+	0.0691844i	0.435308	−	0.900282i	$-0.356640\pi$
$31$	5662.75	+	2061.07i	0.190082	+	0.0691844i	−0.245225	+	0.969466i	$0.578862\pi$
$32$	−30111.8	−	35885.8i	−0.918938	−	1.09515i
$33$	12243.8	+	1643.06i	0.340702	+	0.0457205i
$34$	67136.4	−	24435.6i	1.70813	−	0.621709i
$35$	528.341	+	305.038i	0.0123228	+	0.00711458i
$36$	−38959.0	+	38571.6i	−0.835026	+	0.826724i
$37$	43820.6	+	75899.5i	0.865113	+	1.49842i	0.866935	+	0.498422i	$0.166087\pi$
$37$	43820.6	+	75899.5i	0.865113	+	1.49842i	−0.00182112	+	0.999998i	$0.500580\pi$
$38$	−35734.4	+	42586.6i	−0.651232	+	0.776108i
$39$	32225.2	−	29381.2i	0.543253	−	0.495309i
$40$	101.427	+	575.223i	0.00158480	+	0.00898786i
$41$	−36649.8	+	6462.35i	−0.531766	+	0.0937646i	−0.433083	−	0.901354i	$-0.642574\pi$
$41$	−36649.8	+	6462.35i	−0.531766	+	0.0937646i	−0.0986831	+	0.995119i	$0.531463\pi$
$42$	29631.2	+	32499.4i	0.399946	+	0.438659i
$43$	83844.2	+	70353.6i	1.05455	+	0.884873i	0.993565	−	0.113266i	$-0.0361311\pi$
$43$	83844.2	+	70353.6i	1.05455	+	0.884873i	0.0609859	+	0.998139i	$0.480576\pi$
$44$	29798.6	−	17204.2i	0.349814	−	0.201965i
$45$	−3115.78	+	818.208i	−0.0341924	+	0.00897896i
$46$	5870.88	−	10168.7i	0.0603156	−	0.104470i
$47$	55157.8	+	151545.i	0.531268	+	1.45965i	0.857564	+	0.514378i	$0.171977\pi$
$47$	55157.8	+	151545.i	0.531268	+	1.45965i	−0.326296	+	0.945268i	$0.605801\pi$
$48$	11683.5	−	87063.7i	0.105645	−	0.787252i
$49$	−75523.4	+	63371.6i	−0.641938	+	0.538650i
$50$	62972.8	−	173016.i	0.503783	−	1.38413i
$51$	144835.	+	75856.8i	1.09185	+	0.571853i
$52$	21091.9	−	119618.i	0.150005	−	0.850721i
$53$			27392.1i			0.183991i	0.995759	+	0.0919957i	$0.0293246\pi$
$53$			27392.1i			0.183991i	−0.995759	+	0.0919957i	$0.970675\pi$
$54$	−231925.	−	11868.1i	−1.47288	−	0.0753701i
$55$	2021.85			0.0121524
$56$	17971.3	+	3168.83i	0.102333	+	0.0180441i
$57$	−127113.	+	5231.78i	−0.686383	+	0.0282504i
$58$	−515528.	−	187637.i	−2.64221	−	0.961687i
$59$	−178059.	−	212202.i	−0.866976	−	1.03322i	−0.999118	−	0.0419905i	$-0.986630\pi$
$59$	−178059.	−	212202.i	−0.866976	−	1.03322i	0.132142	−	0.991231i	$-0.457814\pi$
$60$	−5479.95	+	7104.79i	−0.0253702	+	0.0328926i
$61$	202270.	−	73620.2i	0.891131	−	0.324345i	0.144438	−	0.989514i	$-0.453863\pi$
$61$	202270.	−	73620.2i	0.891131	−	0.324345i	0.746693	+	0.665168i	$0.231640\pi$
$62$	61573.9	+	35549.7i	0.258358	+	0.149163i
$63$	−9272.58	+	100217.i	−0.0370834	+	0.400792i
$64$	−172241.	−	298330.i	−0.657046	−	1.13804i
$65$	4587.72	−	5467.43i	0.0167054	−	0.0199087i
$66$	138897.	+	44175.9i	0.483127	+	0.153657i
$67$	28548.0	+	161904.i	0.0949185	+	0.538310i	0.994772	+	0.102118i	$0.0325619\pi$
$67$	28548.0	+	161904.i	0.0949185	+	0.538310i	−0.899854	+	0.436192i	$0.856327\pi$
$68$	448472.	−	79077.7i	1.42629	−	0.251494i
$69$	26247.8	−	5750.25i	0.0798998	−	0.0175041i
$70$	5513.94	+	4626.75i	0.0160756	+	0.0134891i
$71$	102242.	−	59029.3i	0.285662	−	0.164927i	−0.350322	−	0.936629i	$-0.613928\pi$
$71$	102242.	−	59029.3i	0.285662	−	0.164927i	0.635984	+	0.771702i	$0.280594\pi$
$72$	−79207.9	+	54874.2i	−0.212212	+	0.147018i
$73$	−72494.1	+	125563.i	−0.186352	+	0.322771i	−0.944031	−	0.329856i	$-0.893000\pi$
$73$	−72494.1	+	125563.i	−0.186352	+	0.322771i	0.757679	+	0.652627i	$0.226333\pi$
$74$	353659.	+	971670.i	0.872749	+	2.39786i
$75$	389676.	−	160270.i	0.923677	−	0.379899i
$76$	−271447.	+	227771.i	−0.618363	+	0.518869i
$77$	21604.5	−	59357.9i	0.0473230	−	0.130019i
$78$	434626.	−	275364.i	0.915867	−	0.580260i
$79$	−34101.7	+	193401.i	−0.0691664	+	0.392262i	0.930497	+	0.366301i	$0.119376\pi$
$79$	−34101.7	+	193401.i	−0.0691664	+	0.392262i	−0.999663	+	0.0259615i	$0.991735\pi$
$80$		−	14377.0i		−	0.0280801i
$81$	−337519.	−	410500.i	−0.635101	−	0.772429i
$82$	−439081.			−0.796349
$83$	−588323.	−	103737.i	−1.02892	−	0.181426i	−0.366389	−	0.930462i	$-0.619406\pi$
$83$	−588323.	−	103737.i	−1.02892	−	0.181426i	−0.662530	+	0.749036i	$0.730517\pi$
$84$	150028.	+	236800.i	0.253125	+	0.399525i
$85$	25145.1	+	9152.06i	0.0409446	+	0.0149026i
$86$	830063.	+	989230.i	1.30502	+	1.55526i
$87$	−477548.	−	1.16110e6i	−0.725202	−	1.76324i
$88$	56830.3	−	20684.5i	0.0833934	−	0.0303527i
$89$	−760977.	−	439350.i	−1.07945	−	0.623219i	−0.148700	−	0.988882i	$-0.547509\pi$
$89$	−760977.	−	439350.i	−1.07945	−	0.623219i	−0.930747	+	0.365663i	$0.880842\pi$
$90$	−37879.2	+	3123.38i	−0.0519604	+	0.00428447i
$91$	−111492.	−	193110.i	−0.147951	−	0.256259i
$92$	48107.5	−	57332.2i	0.0617801	−	0.0736267i
$93$	34819.2	+	158937.i	0.0432883	+	0.197595i
$94$	330408.	+	1.87383e6i	0.397801	+	2.25604i
$95$	−20505.3	+	3615.63i	−0.0239163	+	0.00421710i
$96$	383354.	−	1.20534e6i	0.433298	−	1.36237i
$97$	526763.	+	442007.i	0.577165	+	0.484299i	0.884015	−	0.467459i	$-0.154830\pi$
$97$	526763.	+	442007.i	0.577165	+	0.484299i	−0.306850	+	0.951758i	$0.599275\pi$
$98$	−1.00736e6	+	581597.i	−1.07030	+	0.617936i
$99$	139451.	+	302996.i	0.143719	+	0.312271i
$100$	586790.	−	1.01635e6i	0.586790	−	1.01635i
$101$	−18798.8	−	51649.2i	−0.0182459	−	0.0501302i	0.930235	−	0.366964i	$-0.119603\pi$
$101$	−18798.8	−	51649.2i	−0.0182459	−	0.0501302i	−0.948481	+	0.316833i	$0.897380\pi$
$102$	1.52745e6	+	1.17813e6i	1.43935	+	1.11018i
$103$	1.39122e6	−	1.16738e6i	1.27317	−	1.06831i	0.279020	−	0.960285i	$-0.409991\pi$
$103$	1.39122e6	−	1.16738e6i	1.27317	−	1.06831i	0.994148	−	0.108029i	$-0.0344539\pi$
$104$	73017.4	−	200614.i	0.0649122	−	0.178345i
$105$	677.389	+	16458.1i	0.000585154	+	0.0142171i
$106$	−56120.3	+	318274.i	−0.0471197	+	0.267229i
$107$		−	994546.i		−	0.811846i	−0.913907	−	0.405923i	$-0.866950\pi$
$107$		−	994546.i		−	0.811846i	0.913907	−	0.405923i	$-0.133050\pi$
$108$	−1.44270e6	−	331200.i	−1.14526	−	0.262917i
$109$	−199021.			−0.153681			−0.0768405	−	0.997043i	$-0.524483\pi$
$109$	−199021.			−0.153681			−0.0768405	+	0.997043i	$0.524483\pi$
$110$	23492.3	+	4142.32i	0.0176501	+	0.00311218i
$111$	−1.09788e6	+	2.09621e6i	−0.802761	+	1.53273i
$112$	−422084.	−	153626.i	−0.300431	−	0.109348i
$113$	3822.10	+	4555.00i	0.00264891	+	0.00315685i	0.767367	−	0.641208i	$-0.221566\pi$
$113$	3822.10	+	4555.00i	0.00264891	+	0.00315685i	−0.764718	+	0.644365i	$0.777122\pi$
$114$	−1.48767e6	−	199638.i	−1.00414	−	0.134750i
$115$	4132.51	−	1504.11i	0.00271719	−	0.000988978i
$116$	−3.02837e6	−	1.74843e6i	−1.94015	−	1.12014i
$117$	1.13578e6	+	310421.i	0.709146	+	0.193818i
$118$	−1.63414e6	−	2.83042e6i	−0.994590	−	1.72268i
$119$	537377.	−	640421.i	0.318888	−	0.380036i
$120$	−11653.9	+	10625.4i	−0.00674415	+	0.00614895i
$121$	271276.	+	1.53848e6i	0.153128	+	0.868434i
$122$	2.50104e6	−	441002.i	1.37734	−	0.242863i
$123$	−676987.	−	742518.i	−0.363802	−	0.399017i
$124$	347161.	+	291303.i	0.182082	+	0.152785i
$125$	119517.	−	69003.0i	0.0611926	−	0.0353296i
$126$	−313062.	+	1.14544e6i	−0.156501	+	0.572613i
$127$	1.08566e6	−	1.88042e6i	0.530010	−	0.918004i	−0.469377	−	0.882998i	$-0.655522\pi$
$127$	1.08566e6	−	1.88042e6i	0.530010	−	0.918004i	0.999387	−	0.0350061i	$-0.0111451\pi$
$128$	−364671.	−	1.00193e6i	−0.173889	−	0.477755i
$129$	−393045.	+	2.92892e6i	−0.183094	+	1.36439i
$130$	64507.1	−	54127.9i	0.0293615	−	0.0246372i
$131$	615794.	−	1.69188e6i	0.273919	−	0.752585i	−0.724102	−	0.689693i	$-0.757745\pi$
$131$	615794.	−	1.69188e6i	0.273919	−	0.752585i	0.998020	−	0.0628921i	$-0.0200324\pi$
$132$	822984.	+	431035.i	0.357824	+	0.187409i
$133$	−112961.	+	640634.i	−0.0480147	+	0.272305i
$134$			1.93968e6i			0.806149i
$135$	−63685.0	−	59240.6i	−0.0258843	−	0.0240779i
$136$	800410.			0.318197
$137$	3.92552e6	+	692176.i	1.52664	+	0.269187i	0.873037	−	0.487653i	$-0.162147\pi$
$137$	3.92552e6	+	692176.i	1.52664	+	0.269187i	0.653600	+	0.756840i	$0.273258\pi$
$138$	316759.	−	13037.3i	0.120529	−	0.00496079i
$139$	−3.20759e6	−	1.16747e6i	−1.19436	−	0.434710i	−0.333105	−	0.942890i	$-0.608096\pi$
$139$	−3.20759e6	−	1.16747e6i	−1.19436	−	0.434710i	−0.861251	+	0.508180i	$0.830319\pi$
$140$	29490.8	+	35145.8i	0.0107474	+	0.0128082i
$141$	−2.65935e6	+	3.44787e6i	−0.948678	+	1.22997i
$142$	1.30890e6	−	476402.i	0.457133	−	0.166383i
$143$	−639984.	−	369495.i	−0.218857	−	0.126357i
$144$	2.15455e6	−	991611.i	0.721556	−	0.332088i
$145$	−102738.	−	177947.i	−0.0336998	−	0.0583698i
$146$	−1.09957e6	+	1.31042e6i	−0.353318	+	0.421068i
$147$	−2.53669e6	−	806787.i	−0.798574	−	0.253984i
$148$	1.14450e6	+	6.49076e6i	0.353044	+	2.00221i
$149$	−1.30017e6	+	229255.i	−0.393044	+	0.0693042i	−0.366677	−	0.930348i	$-0.619505\pi$
$149$	−1.30017e6	+	229255.i	−0.393044	+	0.0693042i	−0.0263662	+	0.999652i	$0.508394\pi$
$150$	4.85608e6	−	1.06385e6i	1.43884	−	0.315214i
$151$	3.06600e6	+	2.57268e6i	0.890515	+	0.747231i	0.968313	−	0.249738i	$-0.0803446\pi$
$151$	3.06600e6	+	2.57268e6i	0.890515	+	0.747231i	−0.0777984	+	0.996969i	$0.524789\pi$
$152$	−539374.	+	311408.i	−0.153589	+	0.0886745i
$153$	362768.	+	4.39950e6i	0.101287	+	1.22837i
$154$	372638.	−	645428.i	0.102029	−	0.176720i
$155$	9107.78	+	25023.4i	0.00244578	+	0.00671973i
$156$	3.03300e6	−	1.24744e6i	0.798911	−	0.328584i
$157$	4.89279e6	−	4.10554e6i	1.26432	−	1.06089i	0.269115	−	0.963108i	$-0.413269\pi$
$157$	4.89279e6	−	4.10554e6i	1.26432	−	1.06089i	0.995208	−	0.0977843i	$-0.0311755\pi$
$158$	−792469.	+	2.17729e6i	−0.200914	+	0.552008i
$159$	−624752.	+	395820.i	−0.155423	+	0.0984706i
$160$	35946.7	−	203864.i	0.00877604	−	0.0497714i
$161$		−	137396.i		−	0.0329227i
$162$	−3.08067e6	−	5.46118e6i	−0.724604	−	1.28452i
$163$	−1.05910e6			−0.244554			−0.122277	−	0.992496i	$-0.539020\pi$
$163$	−1.05910e6			−0.244554			−0.122277	+	0.992496i	$0.539020\pi$
$164$	−2.75618e6	−	485989.i	−0.624851	−	0.110178i
$165$	29216.0	+	46113.8i	0.00650383	+	0.0102655i
$166$	−6.62330e6	−	2.41068e6i	−1.44794	−	0.527007i
$167$	−3.86848e6	−	4.61028e6i	−0.830599	−	0.989869i	−0.999991	−	0.00432036i	$-0.998625\pi$
$167$	−3.86848e6	−	4.61028e6i	−0.830599	−	0.989869i	0.169392	−	0.985549i	$-0.445820\pi$
$168$	187415.	+	455676.i	0.0395254	+	0.0961010i
$169$	2.08437e6	−	758649.i	0.431832	−	0.157174i
$170$	273415.	+	157856.i	0.0556514	+	0.0321303i
$171$	−1.95613e6	−	2.82357e6i	−0.391210	−	0.564689i
$172$	4.11552e6	+	7.12829e6i	0.808797	+	1.40088i
$173$	−5.54238e6	+	6.60515e6i	−1.07043	+	1.27569i	−0.110975	+	0.993823i	$0.535397\pi$
$173$	−5.54238e6	+	6.60515e6i	−1.07043	+	1.27569i	−0.959454	+	0.281865i	$0.909047\pi$
$174$	−3.16989e6	−	1.44694e7i	−0.601722	−	2.74665i
$175$	−374120.	−	2.12174e6i	−0.0698067	−	0.395893i
$176$	−1.46599e6	+	258493.i	−0.268900	+	0.0474144i
$177$	2.26687e6	−	7.12746e6i	0.408796	−	1.28533i
$178$	−7.94181e6	−	6.66397e6i	−1.40818	−	1.18161i
$179$	8.81467e6	−	5.08915e6i	1.53690	−	0.887332i	0.537887	−	0.843017i	$-0.319223\pi$
$179$	8.81467e6	−	5.08915e6i	1.53690	−	0.887332i	0.999018	−	0.0443155i	$-0.0141107\pi$
$180$	−241230.	−	22319.9i	−0.0413633	−	0.00382715i
$181$	−5.65375e6	+	9.79258e6i	−0.953456	+	1.65143i	−0.215593	+	0.976483i	$0.569169\pi$
$181$	−5.65375e6	+	9.79258e6i	−0.953456	+	1.65143i	−0.737863	+	0.674951i	$0.764165\pi$
$182$	−899808.	−	2.47220e6i	−0.149257	−	0.410081i
$183$	4.60194e6	+	3.54950e6i	0.750910	+	0.579180i
$184$	100769.	−	84555.4i	0.0161761	−	0.0135734i
$185$	−132458.	+	363926.i	−0.0209201	+	0.0574776i
$186$	78944.3	+	1.91806e6i	0.0122682	+	0.298073i
$187$	481113.	−	2.72853e6i	0.0735736	−	0.417257i
$188$			1.21281e7i			1.82523i
$189$	−2.41971e6	+	1.23666e6i	−0.358408	+	0.183175i
$190$	−245662.			−0.0358161
$191$	3.38847e6	+	597479.i	0.486299	+	0.0857476i	0.411422	−	0.911445i	$-0.365032\pi$
$191$	3.38847e6	+	597479.i	0.486299	+	0.0857476i	0.0748773	+	0.997193i	$0.476143\pi$
$192$	4.31532e6	−	8.23933e6i	0.609690	−	1.16409i
$193$	−6.08790e6	−	2.21582e6i	−0.846829	−	0.308221i	−0.118082	−	0.993004i	$-0.537675\pi$
$193$	−6.08790e6	−	2.21582e6i	−0.846829	−	0.308221i	−0.728747	+	0.684783i	$0.759897\pi$
$194$	5.21499e6	+	6.21498e6i	0.714247	+	0.851206i
$195$	190993.	+	25630.2i	0.0257581	+	0.00345660i
$196$	−6.96706e6	+	2.53580e6i	−0.925297	+	0.336781i
$197$	8.92926e6	+	5.15531e6i	1.16793	+	0.674305i	0.953192	−	0.302366i	$-0.0977766\pi$
$197$	8.92926e6	+	5.15531e6i	1.16793	+	0.674305i	0.214739	+	0.976672i	$0.431110\pi$
$198$	999534.	+	3.80628e6i	0.128766	+	0.490348i
$199$	2.98414e6	+	5.16868e6i	0.378669	+	0.655874i	0.990869	−	0.134829i	$-0.0430485\pi$
$199$	2.98414e6	+	5.16868e6i	0.378669	+	0.655874i	−0.612200	+	0.790703i	$0.709715\pi$
$200$	1.32590e6	−	1.58014e6i	0.165737	−	0.197518i
$201$	−3.28013e6	+	2.99065e6i	−0.403927	+	0.368279i
$202$	−112609.	−	638637.i	−0.0136621	−	0.0774818i
$203$	−6.32204e6	+	1.11475e6i	−0.755734	+	0.133256i
$204$	8.28407e6	+	9.08594e6i	0.975783	+	1.07024i
$205$	−125978.	−	105708.i	−0.0146229	−	0.0122700i
$206$	1.85566e7	−	1.07137e7i	2.12274	−	1.22556i
$207$	510435.	+	515561.i	0.0575479	+	0.0581259i
$208$	−2.62741e6	+	4.55081e6i	−0.291970	+	0.505707i
$209$	737353.	+	2.02586e6i	0.0807675	+	0.221907i
$210$	−25848.3	+	192618.i	−0.00279109	+	0.0207988i
$211$	6.10945e6	−	5.12644e6i	0.650361	−	0.545718i	−0.256819	−	0.966459i	$-0.582674\pi$
$211$	6.10945e6	−	5.12644e6i	0.650361	−	0.545718i	0.907181	+	0.420741i	$0.138230\pi$
$212$	−704552.	+	1.93574e6i	−0.0739444	+	0.203161i
$213$	2.82373e6	+	1.47892e6i	0.292203	+	0.153040i
$214$	2.03760e6	−	1.15558e7i	0.207911	−	1.17912i
$215$			483658.i			0.0486657i
$216$	−2.39612e6	−	1.01361e6i	−0.237765	−	0.100580i
$217$	831966.			0.0814191
$218$	−2.31247e6	−	407750.i	−0.223206	−	0.0393573i
$219$	−3.91137e6	+	160986.i	−0.372389	+	0.0153269i
$220$	142880.	+	52004.0i	0.0134185	+	0.00488392i
$221$	−6.28673e6	−	7.49223e6i	−0.582435	−	0.694119i
$222$	−1.70512e7	+	2.21069e7i	−1.55846	+	2.02055i
$223$	−2.40994e6	+	877147.i	−0.217316	+	0.0790966i	−0.448384	−	0.893841i	$-0.648000\pi$
$223$	−2.40994e6	+	877147.i	−0.217316	+	0.0790966i	0.231068	+	0.972938i	$0.425778\pi$
$224$	−5.60097e6	−	3.23372e6i	−0.498332	−	0.287712i
$225$	9.28628e6	+	6.57171e6i	0.815256	+	0.576940i
$226$	35077.6	+	60756.1i	0.00303881	+	0.00526338i
$227$	2.71352e6	−	3.23384e6i	0.231982	−	0.276466i	−0.637478	−	0.770469i	$-0.720022\pi$
$227$	2.71352e6	−	3.23384e6i	0.231982	−	0.276466i	0.869460	+	0.494003i	$0.164467\pi$
$228$	−9.11739e6	−	2.89976e6i	−0.769247	−	0.244657i
$229$	−1.56873e6	−	8.89671e6i	−0.130630	−	0.740837i	−0.977804	−	0.209522i	$-0.932809\pi$
$229$	−1.56873e6	−	8.89671e6i	−0.130630	−	0.740837i	0.847174	−	0.531315i	$-0.178302\pi$
$230$	51098.1	−	9009.97i	0.00419973	−	0.000740525i
$231$	1.66601e6	−	364981.i	0.135158	−	0.0296098i
$232$	−4.70826e6	−	3.95070e6i	−0.377048	−	0.316381i
$233$	−3.23447e6	+	1.86742e6i	−0.255702	+	0.147630i	−0.622373	−	0.782721i	$-0.713831\pi$
$233$	−3.23447e6	+	1.86742e6i	−0.255702	+	0.147630i	0.366670	+	0.930351i	$0.380498\pi$
$234$	1.25608e7	+	5.93380e6i	0.980328	+	0.463111i
$235$	−356324.	+	617171.i	−0.0274563	+	0.0475556i
$236$	−7.12497e6	−	1.95757e7i	−0.542060	−	1.48930i
$237$	−4.90380e6	+	2.01689e6i	−0.368373	+	0.151508i
$238$	7.55597e6	−	6.34021e6i	0.560479	−	0.470298i
$239$	−651370.	+	1.78962e6i	−0.0477127	+	0.131090i	−0.961260	−	0.275642i	$-0.911109\pi$
$239$	−651370.	+	1.78962e6i	−0.0477127	+	0.131090i	0.913548	+	0.406732i	$0.133332\pi$
$240$	327907.	−	207750.i	0.0237201	−	0.0150282i
$241$	−2.97380e6	+	1.68653e7i	−0.212452	+	1.20488i	0.672821	+	0.739805i	$0.265082\pi$
$241$	−2.97380e6	+	1.68653e7i	−0.212452	+	1.20488i	−0.885273	+	0.465071i	$0.846029\pi$
$242$			1.84317e7i			1.30053i
$243$	4.48539e6	−	1.36298e7i	0.312594	−	0.949887i
$244$	1.61876e7			1.11433
$245$	−429041.	−	75651.5i	−0.0291743	−	0.00514421i
$246$	−6.34480e6	−	1.00145e7i	−0.426199	−	0.672701i
$247$	7.15138e6	+	2.60289e6i	0.474569	+	0.172729i
$248$	512005.	+	610183.i	0.0335675	+	0.0400042i
$249$	−6.13535e6	−	1.49173e7i	−0.397412	−	0.966258i
$250$	1.53006e6	−	556896.i	0.0979239	−	0.0356414i
$251$	−1.60071e7	−	9.24173e6i	−1.01226	−	0.584429i	−0.100408	−	0.994946i	$-0.532015\pi$
$251$	−1.60071e7	−	9.24173e6i	−1.01226	−	0.584429i	−0.911853	+	0.410517i	$0.865348\pi$
$252$	−3.23295e6	+	6.84360e6i	−0.202021	+	0.427645i
$253$	−227671.	−	394338.i	−0.0140587	−	0.0243504i
$254$	1.64671e7	−	1.96247e7i	1.00488	−	1.19757i
$255$	154613.	+	705751.i	0.00932448	+	0.0425629i
$256$	1.64393e6	+	9.32318e6i	0.0979857	+	0.555705i
$257$	−2.24944e7	+	3.96637e6i	−1.32518	+	0.233665i	−0.791057	−	0.611742i	$-0.790469\pi$
$257$	−2.24944e7	+	3.96637e6i	−1.32518	+	0.233665i	−0.534122	+	0.845407i	$0.679358\pi$
$258$	−1.05676e7	+	3.32264e7i	−0.615341	+	1.93475i
$259$	9.26886e6	+	7.77749e6i	0.533491	+	0.447652i
$260$	464832.	−	268371.i	0.0264470	−	0.0152692i
$261$	1.95814e7	−	2.76698e7i	1.10134	−	1.55627i
$262$	1.06213e7	−	1.83967e7i	0.590574	−	1.02290i
$263$	2.18030e6	+	5.99032e6i	0.119853	+	0.329293i	0.985082	−	0.172083i	$-0.0550497\pi$
$263$	2.18030e6	+	5.99032e6i	0.119853	+	0.329293i	−0.865230	+	0.501376i	$0.832827\pi$
$264$	1.29297e6	+	997275.i	0.0702713	+	0.0542005i
$265$	−92725.4	+	77805.9i	−0.00498266	+	0.00418095i
$266$	−2.62503e6	+	7.21222e6i	−0.139473	+	0.383199i
$267$	−975653.	−	2.37048e7i	−0.0512580	−	1.24538i
$268$	−2.14690e6	+	1.21757e7i	−0.111534	+	0.632540i
$269$			1.66769e7i			0.856758i	0.903599	+	0.428379i	$0.140915\pi$
$269$			1.66769e7i			0.856758i	−0.903599	+	0.428379i	$0.859085\pi$
$270$	−618597.	−	818805.i	−0.0314280	−	0.0415996i
$271$	−1.49281e6			−0.0750061			−0.0375030	−	0.999297i	$-0.511940\pi$
$271$	−1.49281e6			−0.0750061			−0.0375030	+	0.999297i	$0.511940\pi$
$272$	−1.94021e7	−	3.42111e6i	−0.964143	−	0.170004i
$273$	2.79332e6	−	5.33334e6i	0.137288	−	0.262127i
$274$	4.41933e7	+	1.60850e7i	2.14835	+	0.781935i
$275$	−4.58958e6	−	5.46965e6i	−0.220686	−	0.263004i
$276$	2.00278e6	+	268762.i	0.0952590	+	0.0127832i
$277$	−2.07795e7	+	7.56311e6i	−0.977677	+	0.355845i	−0.780937	−	0.624610i	$-0.785258\pi$
$277$	−2.07795e7	+	7.56311e6i	−0.977677	+	0.355845i	−0.196741	+	0.980456i	$0.563036\pi$
$278$	−3.48777e7	−	2.01366e7i	−1.62335	−	0.937244i
$279$	−3.12186e6	+	3.09082e6i	−0.143747	+	0.142318i
$280$	40319.8	+	69836.0i	0.00183673	+	0.00318130i
$281$	1.67865e7	−	2.00054e7i	0.756556	−	0.901628i	−0.241069	−	0.970508i	$-0.577498\pi$
$281$	1.67865e7	−	2.00054e7i	0.756556	−	0.901628i	0.997625	+	0.0688796i	$0.0219424\pi$
$282$	−3.79635e7	+	3.46131e7i	−1.69285	+	1.54345i
$283$	−3.95232e6	−	2.24147e7i	−0.174379	−	0.988950i	−0.938859	−	0.344303i	$-0.888115\pi$
$283$	−3.95232e6	−	2.24147e7i	−0.174379	−	0.988950i	0.764480	−	0.644647i	$-0.222996\pi$
$284$	8.74349e6	−	1.54171e6i	0.381707	−	0.0673052i
$285$	−378769.	−	415433.i	−0.0163621	−	0.0179459i
$286$	−6.67908e6	−	5.60442e6i	−0.285508	−	0.239570i
$287$	−4.44954e6	+	2.56894e6i	−0.188222	+	0.108670i
$288$	3.30305e7	−	8.67386e6i	1.38273	−	0.363107i
$289$	6.26556e6	−	1.08523e7i	0.259577	−	0.449600i
$290$	−829158.	−	2.27809e6i	−0.0339972	−	0.0934066i
$291$	−2.46936e6	+	1.84013e7i	−0.100209	+	0.746742i
$292$	−8.35262e6	+	7.00868e6i	−0.335486	+	0.281506i
$293$	−3.39276e6	+	9.32154e6i	−0.134881	+	0.370582i	−0.988684	−	0.150014i	$-0.952068\pi$
$293$	−3.39276e6	+	9.32154e6i	−0.134881	+	0.370582i	0.853803	+	0.520596i	$0.174290\pi$
$294$	−2.78214e7	−	1.45713e7i	−1.09480	−	0.573399i
$295$	212562.	−	1.20550e6i	0.00827979	−	0.0469570i
$296$			1.15844e7i			0.446682i
$297$	−4.89557e6	+	7.55890e6i	−0.186868	+	0.288529i
$298$	−1.55766e7			−0.588605
$299$	−1.58296e6	−	279118.i	−0.0592183	−	0.0104418i
$300$	3.16599e7	−	1.30307e6i	1.17259	−	0.0482618i
$301$	1.41994e7	+	5.16814e6i	0.520678	+	0.189511i
$302$	3.03536e7	+	3.61740e7i	1.10202	+	1.31334i
$303$	906356.	−	1.17510e6i	0.0325815	−	0.0422421i
$304$	1.44055e7	−	5.24319e6i	0.512754	−	0.186627i
$305$	823751.	+	475593.i	0.0290333	+	0.0167624i
$306$	−4.79854e6	+	5.18619e7i	−0.167473	+	1.81002i
$307$	2.01632e6	+	3.49237e6i	0.0696858	+	0.120699i	0.898763	−	0.438435i	$-0.144467\pi$
$307$	2.01632e6	+	3.49237e6i	0.0696858	+	0.120699i	−0.829077	+	0.559134i	$0.811134\pi$
$308$	3.05349e6	−	3.63901e6i	0.104507	−	0.124546i
$309$	4.67286e7	+	1.48619e7i	1.58383	+	0.503732i
$310$	54557.7	+	309412.i	0.00183135	+	0.0103861i
$311$	3.19304e7	−	5.63020e6i	1.06151	−	0.187173i	0.384483	−	0.923132i	$-0.374380\pi$
$311$	3.19304e7	−	5.63020e6i	1.06151	−	0.187173i	0.677026	+	0.735959i	$0.263268\pi$
$312$	5.63065e6	−	1.23354e6i	0.185394	−	0.0406152i
$313$	−1.53523e7	−	1.28821e7i	−0.500658	−	0.420102i	0.357170	−	0.934040i	$-0.383742\pi$
$313$	−1.53523e7	−	1.28821e7i	−0.500658	−	0.420102i	−0.857827	+	0.513938i	$0.828186\pi$
$314$	6.52616e7	−	3.76788e7i	2.10799	−	1.21705i
$315$	−365584.	+	253272.i	−0.0116965	+	0.00810318i
$316$	−7.38435e6	+	1.27901e7i	−0.234019	+	0.405333i
$317$	1.36242e7	+	3.74323e7i	0.427695	+	1.17508i	0.947208	+	0.320620i	$0.103891\pi$
$317$	1.36242e7	+	3.74323e7i	0.427695	+	1.17508i	−0.519513	+	0.854463i	$0.673886\pi$
$318$	−8.07006e6	+	3.31913e6i	−0.250955	+	0.103215i
$319$	−1.62976e7	+	1.36753e7i	−0.502056	+	0.421275i
$320$	520640.	−	1.43045e6i	0.0158887	−	0.0436537i
$321$	2.26833e7	−	1.43713e7i	0.685791	−	0.434493i
$322$	281493.	−	1.59643e6i	0.00843141	−	0.0478169i
$323$			2.85327e7i			0.846710i
$324$	−1.32932e7	−	3.76905e7i	−0.390837	−	1.10815i
$325$	−2.52050e7			−0.734237
$326$	−1.23059e7	−	2.16986e6i	−0.355189	−	0.0626295i
$327$	−2.87589e6	−	4.53923e6i	−0.0822487	−	0.129819i
$328$	−4.62244e6	−	1.68243e6i	−0.130993	−	0.0476777i
$329$	1.43115e7	+	1.70558e7i	0.401882	+	0.478945i
$330$	244990.	+	595662.i	0.00681720	+	0.0165752i
$331$	−5.38220e7	+	1.95896e7i	−1.48414	+	0.540184i	−0.951901	−	0.306407i	$-0.900873\pi$
$331$	−5.38220e7	+	1.95896e7i	−1.48414	+	0.540184i	−0.532244	+	0.846591i	$0.678651\pi$
$332$	−3.89073e7	−	2.24631e7i	−1.06320	−	0.613841i
$333$	−6.36743e7	+	5.25036e6i	−1.72437	+	0.142186i
$334$	−3.55032e7	−	6.14934e7i	−0.952858	−	1.65040i
$335$	−466974.	+	556517.i	−0.0124210	+	0.0148028i
$336$	−2.59532e6	−	1.18467e7i	−0.0684184	−	0.312305i
$337$	−8.68875e6	−	4.92764e7i	−0.227022	−	1.28751i	−0.858782	−	0.512341i	$-0.828778\pi$
$337$	−8.68875e6	−	4.92764e7i	−0.227022	−	1.28751i	0.631760	−	0.775164i	$-0.282333\pi$
$338$	2.57730e7	−	4.54448e6i	0.667444	−	0.117688i
$339$	−48659.4	+	152994.i	−0.00124901	+	0.00392713i
$340$	1.54155e6	+	1.29351e6i	0.0392212	+	0.0329105i
$341$	2.38782e6	−	1.37861e6i	0.0602196	−	0.0347678i
$342$	−1.69438e7	−	3.68152e7i	−0.423578	−	0.920342i
$343$	−1.49268e7	+	2.58539e7i	−0.369899	+	0.640684i
$344$	4.94807e6	+	1.35947e7i	0.121551	+	0.333960i
$345$	94020.9	+	72518.6i	0.00228964	+	0.00176601i
$346$	−7.79305e7	+	6.53914e7i	−1.88139	+	1.57867i
$347$	3.16090e6	−	8.68449e6i	0.0756522	−	0.207853i	−0.896102	−	0.443848i	$-0.853613\pi$
$347$	3.16090e6	−	8.68449e6i	0.0756522	−	0.207853i	0.971754	+	0.235996i	$0.0758351\pi$
$348$	−3.88269e6	−	9.43352e7i	−0.0921286	−	2.23839i
$349$	6.82227e6	−	3.86910e7i	0.160492	−	0.910194i	−0.793100	−	0.609092i	$-0.791534\pi$
$349$	6.82227e6	−	3.86910e7i	0.160492	−	0.910194i	0.953592	−	0.301103i	$-0.0973547\pi$
$350$		−	2.54194e7i		−	0.592873i
$351$	9.33218e6	+	3.03902e7i	0.215805	+	0.702768i
$352$	−2.14337e7			−0.491439
$353$	4.43743e7	+	7.82438e6i	1.00880	+	0.177880i	0.653545	−	0.756888i	$-0.273281\pi$
$353$	4.43743e7	+	7.82438e6i	1.00880	+	0.177880i	0.355260	+	0.934767i	$0.384392\pi$
$354$	4.09418e7	−	7.81711e7i	0.922905	−	1.76212i
$355$	490233.	+	178430.i	0.0109577	+	0.00398826i
$356$	−4.24761e7	−	5.06210e7i	−0.941444	−	1.12197i
$357$	2.23717e7	+	3.00217e6i	0.491694	+	0.0659828i
$358$	1.12846e8	−	4.10725e7i	2.45944	−	0.895164i
$359$	1.63887e7	+	9.46199e6i	0.354209	+	0.204503i	0.666538	−	0.745471i	$-0.267776\pi$
$359$	1.63887e7	+	9.46199e6i	0.354209	+	0.204503i	−0.312328	+	0.949974i	$0.601109\pi$
$360$	−410742.	−	112260.i	−0.00880362	−	0.00240613i
$361$	1.24220e7	+	2.15156e7i	0.264040	+	0.457331i
$362$	−8.57548e7	+	1.02199e8i	−1.80773	+	2.15436i
$363$	−3.11694e7	+	2.84185e7i	−0.651641	+	0.594131i
$364$	−2.91192e6	−	1.65143e7i	−0.0603776	−	0.342418i
$365$	−630963.	+	111256.i	−0.0129755	+	0.00228794i
$366$	4.61987e7	+	5.06706e7i	0.942295	+	1.03351i
$367$	3.72889e7	+	3.12891e7i	0.754365	+	0.632987i	0.936653	−	0.350258i	$-0.113906\pi$
$367$	3.72889e7	+	3.12891e7i	0.754365	+	0.632987i	−0.182288	+	0.983245i	$0.558350\pi$
$368$	−2.80407e6	+	1.61893e6i	−0.0562659	+	0.0324851i
$369$	7.15257e6	−	2.61700e7i	0.142358	−	0.520865i
$370$	−2.28466e6	+	3.95715e6i	−0.0451042	+	0.0781228i
$371$	1.29342e6	+	3.55365e6i	0.0253291	+	0.0695910i
$372$	−1.62742e6	+	1.21273e7i	−0.0316135	+	0.235579i
$373$	−4.82410e7	+	4.04790e7i	−0.929586	+	0.780016i	−0.975743	−	0.218919i	$-0.929747\pi$
$373$	−4.82410e7	+	4.04790e7i	−0.929586	+	0.780016i	0.0461566	+	0.998934i	$0.485303\pi$
$374$	1.11803e7	−	3.07176e7i	0.213716	−	0.587181i
$375$	3.30084e6	+	1.72880e6i	0.0625937	+	0.0327832i
$376$	−3.70161e6	+	2.09929e7i	−0.0696349	+	0.394919i
$377$			7.51019e7i			1.40161i
$378$	−3.06487e7	+	9.41157e6i	−0.567462	+	0.174256i
$379$	1.05216e8			1.93270			0.966348	−	0.257239i	$-0.0828126\pi$
$379$	1.05216e8			1.93270			0.966348	+	0.257239i	$0.0828126\pi$
$380$	−1.54206e6	−	271907.i	−0.0281029	−	0.00495530i
$381$	5.85762e7	−	2.41090e6i	1.05912	−	0.0435918i
$382$	3.81472e7	+	1.38844e7i	0.684341	+	0.249080i
$383$	−3.65204e7	−	4.35233e7i	−0.650038	−	0.774685i	0.335882	−	0.941904i	$-0.390966\pi$
$383$	−3.65204e7	−	4.35233e7i	−0.650038	−	0.774685i	−0.985920	+	0.167219i	$0.946521\pi$
$384$	1.75821e7	−	2.27953e7i	0.310511	−	0.402580i
$385$	262300.	−	95469.4i	0.00459638	−	0.00167295i
$386$	−6.61968e7	−	3.82187e7i	−1.15100	−	0.664530i
$387$	−7.24815e7	+	3.33588e7i	−1.25053	+	0.575543i
$388$	2.58564e7	+	4.47845e7i	0.442662	+	0.766713i
$389$	−1.44070e7	+	1.71696e7i	−0.244751	+	0.291683i	−0.874409	−	0.485190i	$-0.838751\pi$
$389$	−1.44070e7	+	1.71696e7i	−0.244751	+	0.291683i	0.629658	+	0.776872i	$0.283195\pi$
$390$	2.16667e6	+	689105.i	0.0365258	+	0.0116169i
$391$	−1.04647e6	−	5.93483e6i	−0.0175064	−	0.0992836i
$392$	−1.28335e7	+	2.26289e6i	−0.213052	+	0.0375668i
$393$	4.74863e7	−	1.04031e7i	0.782331	−	0.171389i
$394$	9.31888e7	+	7.81947e7i	1.52361	+	1.27846i
$395$	−751548.	+	433906.i	−0.0121945	+	0.00704052i
$396$	2.06132e6	+	2.49989e7i	0.0331941	+	0.402565i
$397$	4.18592e7	−	7.25022e7i	0.668989	−	1.15872i	−0.309198	−	0.950998i	$-0.600061\pi$
$397$	4.18592e7	−	7.25022e7i	0.668989	−	1.15872i	0.978187	−	0.207725i	$-0.0666060\pi$
$398$	2.40838e7	+	6.61698e7i	0.382011	+	1.04957i
$399$	−1.62437e7	+	6.68088e6i	−0.255721	+	0.105176i
$400$	−3.88938e7	+	3.26357e7i	−0.607715	+	0.509934i
$401$	2.45570e7	−	6.74698e7i	0.380839	−	1.04635i	−0.590164	−	0.807283i	$-0.700937\pi$
$401$	2.45570e7	−	6.74698e7i	0.380839	−	1.04635i	0.971004	−	0.239065i	$-0.0768408\pi$
$402$	−4.42397e7	+	2.80287e7i	−0.680979	+	0.431444i
$403$	1.69013e6	−	9.58522e6i	0.0258230	−	0.146449i
$404$		−	4.13346e6i		−	0.0626859i
$405$	430886.	−	2.30855e6i	0.00648631	−	0.0347515i
$406$	−7.57408e7			−1.13175
$407$	3.94901e7	+	6.96318e6i	0.585741	+	0.103282i
$408$	1.15661e7	+	1.82555e7i	0.170296	+	0.268791i
$409$	−8.15337e7	−	2.96758e7i	−1.19170	−	0.433744i	−0.331381	−	0.943497i	$-0.607514\pi$
$409$	−8.15337e7	−	2.96758e7i	−1.19170	−	0.433744i	−0.860321	+	0.509753i	$0.829737\pi$
$410$	−1.24719e6	−	1.48634e6i	−0.0180959	−	0.0215659i
$411$	4.09375e7	+	9.95343e7i	0.589652	+	1.43366i
$412$	1.28341e8	−	4.67123e7i	1.83516	−	0.667943i
$413$	−3.31200e7	−	1.91218e7i	−0.470154	−	0.271443i
$414$	4.87458e6	+	7.03618e6i	0.0686967	+	0.0991598i
$415$	−1.31994e6	−	2.28620e6i	−0.0184676	−	0.0319867i
$416$	−4.86346e7	+	5.79605e7i	−0.675562	+	0.805104i
$417$	−1.97229e7	−	9.00278e7i	−0.271996	−	1.24156i
$418$	4.41691e6	+	2.50495e7i	0.0604769	+	0.342982i
$419$	6.04853e6	−	1.06652e6i	0.0822258	−	0.0144986i	−0.132384	−	0.991199i	$-0.542263\pi$
$419$	6.04853e6	−	1.06652e6i	0.0822258	−	0.0144986i	0.214610	+	0.976700i	$0.431152\pi$
$420$	−375449.	+	1.18048e6i	−0.00506761	+	0.0159335i
$421$	−5.58883e7	−	4.68959e7i	−0.748988	−	0.628476i	0.186247	−	0.982503i	$-0.440368\pi$
$421$	−5.58883e7	−	4.68959e7i	−0.748988	−	0.628476i	−0.935235	+	0.354027i	$0.884812\pi$
$422$	8.14898e7	−	4.70482e7i	1.08434	−	0.626045i
$423$	−1.17066e8	−	1.08316e7i	−1.54672	−	0.143110i
$424$	−1.81034e6	+	3.13560e6i	−0.0237499	+	0.0411361i
$425$	−3.23204e7	−	8.87995e7i	−0.421027	−	1.15676i
$426$	2.97795e7	+	2.29691e7i	0.385202	+	0.297108i
$427$	2.27648e7	−	1.91019e7i	0.292402	−	0.245354i
$428$	2.55807e7	−	7.02824e7i	0.326273	−	0.896428i
$429$	−820527.	−	1.99358e7i	−0.0103925	−	0.252501i
$430$	−990908.	+	5.61972e6i	−0.0124632	+	0.0706820i
$431$		−	7.69500e6i		−	0.0961119i	−0.998845	−	0.0480559i	$-0.984697\pi$
$431$		−	7.69500e6i		−	0.0961119i	0.998845	−	0.0480559i	$-0.0153026\pi$
$432$	5.37501e7	+	3.48116e7i	0.666696	+	0.431790i
$433$	−8.62065e6			−0.106188			−0.0530941	−	0.998590i	$-0.516908\pi$
$433$	−8.62065e6			−0.106188			−0.0530941	+	0.998590i	$0.516908\pi$
$434$	9.66677e6	+	1.70451e6i	0.118253	+	0.0208512i
$435$	2.57400e6	−	4.91459e6i	0.0312709	−	0.0597062i
$436$	−1.40644e7	−	5.11903e6i	−0.169692	−	0.0617629i
$437$	3.01419e6	+	3.59217e6i	0.0361182	+	0.0430440i
$438$	−4.57768e7	−	6.14300e6i	−0.544782	−	0.0731069i
$439$	−4.04087e7	+	1.47076e7i	−0.477619	+	0.173839i	−0.569601	−	0.821922i	$-0.692902\pi$
$439$	−4.04087e7	+	1.47076e7i	−0.477619	+	0.173839i	0.0919816	+	0.995761i	$0.470680\pi$
$440$	231443.	+	133624.i	0.00271698	+	0.00156865i
$441$	−1.82546e7	−	6.95143e7i	−0.212841	−	0.810510i
$442$	−5.76968e7	−	9.99338e7i	−0.668167	−	1.15730i
$443$	6.51701e7	−	7.76666e7i	0.749613	−	0.893354i	−0.247531	−	0.968880i	$-0.579619\pi$
$443$	6.51701e7	−	7.76666e7i	0.749613	−	0.893354i	0.997144	+	0.0755264i	$0.0240637\pi$
$444$	−1.31501e8	+	1.19896e8i	−1.50239	+	1.36979i
$445$	−674265.	−	3.82395e6i	−0.00765157	−	0.0433942i
$446$	−2.97986e7	+	5.25431e6i	−0.335886	+	0.0592258i
$447$	−2.40164e7	−	2.63411e7i	−0.268897	−	0.294925i
$448$	−3.64321e7	−	3.05701e7i	−0.405182	−	0.339988i
$449$	−5.58515e7	+	3.22459e7i	−0.617015	+	0.356234i	−0.775706	−	0.631094i	$-0.782606\pi$
$449$	−5.58515e7	+	3.22459e7i	−0.617015	+	0.356234i	0.158691	+	0.987328i	$0.449273\pi$
$450$	9.44351e7	+	9.53834e7i	1.03632	+	1.04673i
$451$	−8.51372e6	+	1.47462e7i	−0.0928089	+	0.160750i
$452$	152941.	+	420201.i	0.00165618	+	0.00455031i
$453$	−1.43728e7	+	1.07104e8i	−0.154613	+	1.15216i
$454$	3.81543e7	−	3.20153e7i	0.407733	−	0.342129i
$455$	337012.	−	925932.i	0.00357775	−	0.00982980i
$456$	−1.48966e7	−	7.80201e6i	−0.157105	−	0.0822834i
$457$	1.72398e7	−	9.77717e7i	0.180627	−	1.02439i	−0.750819	−	0.660508i	$-0.770341\pi$
$457$	1.72398e7	−	9.77717e7i	0.180627	−	1.02439i	0.931446	−	0.363880i	$-0.118548\pi$
$458$		−	1.06587e8i		−	1.10945i
$459$	−9.51007e7	+	7.18475e7i	−0.983435	+	0.742973i
$460$	330723.			0.00339775
$461$	−3.74768e7	−	6.60816e6i	−0.382525	−	0.0674494i	−0.0209204	−	0.999781i	$-0.506660\pi$
$461$	−3.74768e7	−	6.60816e6i	−0.382525	−	0.0674494i	−0.361604	+	0.932332i	$0.617771\pi$
$462$	2.01054e7	−	827508.i	0.203886	−	0.00839163i
$463$	1.09033e8	+	3.96848e7i	1.09854	+	0.399836i	0.826778	−	0.562529i	$-0.190172\pi$
$463$	1.09033e8	+	3.96848e7i	1.09854	+	0.399836i	0.271762	+	0.962365i	$0.412394\pi$
$464$	9.72430e7	+	1.15890e8i	0.973429	+	1.16009i
$465$	−439119.	+	569320.i	−0.00436740	+	0.00566237i
$466$	−4.14078e7	+	1.50712e7i	−0.409190	+	0.148933i
$467$	−4.85000e7	−	2.80015e7i	−0.476202	−	0.274935i	0.242631	−	0.970119i	$-0.421990\pi$
$467$	−4.85000e7	−	2.80015e7i	−0.476202	−	0.274935i	−0.718832	+	0.695184i	$0.755323\pi$
$468$	7.22787e7	+	5.11501e7i	0.705136	+	0.499010i
$469$	1.13485e7	+	1.96562e7i	0.110007	+	0.190538i
$470$	−5.40464e6	+	6.44100e6i	−0.0520563	+	0.0620383i
$471$	1.64340e8	+	5.22678e7i	1.57282	+	0.500232i
$472$	−6.35815e6	−	3.60588e7i	−0.0604651	−	0.342914i
$473$	4.93173e7	−	8.69597e6i	0.466032	−	0.0821740i
$474$	−6.11104e7	+	1.33878e7i	−0.573826	+	0.125711i
$475$	5.63281e7	+	4.72649e7i	0.525587	+	0.441020i
$476$	5.44475e7	−	3.14353e7i	0.504844	−	0.291472i
$477$	−1.80555e7	−	8.52951e6i	−0.166362	−	0.0785903i
$478$	−1.12349e7	+	1.94595e7i	−0.102870	+	0.178175i
$479$	−4.98611e7	−	1.36992e8i	−0.453686	−	1.24649i	−0.930112	−	0.367277i	$-0.880290\pi$
$479$	−4.98611e7	−	1.36992e8i	−0.453686	−	1.24649i	0.476426	−	0.879215i	$-0.341932\pi$
$480$	5.16910e6	−	2.12600e6i	0.0467403	−	0.0192238i
$481$	1.08436e8	−	9.09882e7i	0.974398	−	0.817617i
$482$	−6.91064e7	+	1.89868e8i	−0.617131	+	1.69555i
$483$	3.13368e6	−	1.98539e6i	0.0278108	−	0.0176199i
$484$	−2.04008e7	+	1.15699e8i	−0.179933	+	1.02045i
$485$			3.03865e6i			0.0266352i
$486$	8.00411e7	−	1.49178e8i	0.697275	−	1.29956i
$487$	1.46723e8			1.27031			0.635155	−	0.772384i	$-0.280936\pi$
$487$	1.46723e8			1.27031			0.635155	+	0.772384i	$0.280936\pi$
$488$	2.80196e7	+	4.94061e6i	0.241103	+	0.0425129i
$489$	−1.53042e7	−	2.41557e7i	−0.130883	−	0.206582i
$490$	−4.83012e6	−	1.75802e6i	−0.0410553	−	0.0149429i
$491$	−4.37293e7	−	5.21145e7i	−0.369426	−	0.440265i	0.549021	−	0.835809i	$-0.315001\pi$
$491$	−4.37293e7	−	5.21145e7i	−0.369426	−	0.440265i	−0.918447	+	0.395543i	$0.870556\pi$
$492$	−2.87430e7	−	6.98849e7i	−0.241344	−	0.586797i
$493$	−2.64591e8	+	9.63033e7i	−2.20818	+	0.803712i
$494$	7.77605e7	+	4.48951e7i	0.645028	+	0.372407i
$495$	−629575.	+	1.33270e6i	−0.00519077	+	0.0109880i
$496$	−9.80303e6	−	1.69794e7i	−0.0803370	−	0.139148i
$497$	1.04768e7	−	1.24858e7i	0.0853414	−	0.101706i
$498$	−4.07255e7	−	1.85897e8i	−0.329745	−	1.50517i
$499$	3.71753e7	+	2.10832e8i	0.299194	+	1.69682i	0.649648	+	0.760235i	$0.274916\pi$
$499$	3.71753e7	+	2.10832e8i	0.299194	+	1.69682i	−0.350454	+	0.936580i	$0.613973\pi$
$500$	1.02208e7	−	1.80221e6i	0.0817666	−	0.0144177i
$501$	4.92498e7	−	1.54851e8i	0.391644	−	1.23140i
$502$	−1.67056e8	−	1.40177e8i	−1.32054	−	1.10806i
$503$	−1.62811e8	+	9.39991e7i	−1.27932	+	0.738618i	−0.976724	−	0.214500i	$-0.931188\pi$
$503$	−1.62811e8	+	9.39991e7i	−1.27932	+	0.738618i	−0.302599	+	0.953118i	$0.597854\pi$
$504$	−7.68476e6	+	1.08591e7i	−0.0600259	+	0.0848207i
$505$	121442.	−	210343.i	0.000942960	−	0.00163325i
$506$	−1.83744e6	−	5.04834e6i	−0.0141828	−	0.0389670i
$507$	4.74225e7	+	3.65772e7i	0.363882	+	0.280664i
$508$	1.25088e8	−	1.04961e8i	0.954166	−	0.800640i
$509$	−6.67068e7	+	1.83275e8i	−0.505844	+	1.38979i	0.379644	+	0.925133i	$0.376046\pi$
$509$	−6.67068e7	+	1.83275e8i	−0.505844	+	1.38979i	−0.885488	+	0.464662i	$0.846176\pi$
$510$	350547.	+	8.51703e6i	0.00264263	+	0.0642063i
$511$	−3.47590e6	+	1.97128e7i	−0.0260498	+	0.147736i
$512$			1.79934e8i			1.34062i
$513$	3.61327e7	−	8.54159e7i	0.267639	−	0.632684i
$514$	−2.69493e8			−1.98453
$515$	7.90341e6	+	1.39358e6i	0.0578619	+	0.0102026i
$516$	−1.03110e8	+	1.96871e8i	−0.750504	+	1.43295i
$517$	6.93378e7	+	2.52369e7i	0.501763	+	0.182627i
$518$	9.17623e7	+	1.09358e8i	0.660199	+	0.786795i
$519$	−2.30737e8	−	3.09637e7i	−1.65050	−	0.221488i
$520$	886502.	−	322660.i	0.00630478	−	0.00229475i
$521$	9.17933e6	+	5.29969e6i	0.0649079	+	0.0374746i	0.532103	−	0.846680i	$-0.321402\pi$
$521$	9.17933e6	+	5.29969e6i	0.0649079	+	0.0374746i	−0.467195	+	0.884154i	$0.654735\pi$
$522$	2.84209e8	−	2.81383e8i	1.99814	−	1.97827i
$523$	1.12236e8	+	1.94399e8i	0.784565	+	1.35891i	0.929259	+	0.369429i	$0.120447\pi$
$523$	1.12236e8	+	1.94399e8i	0.784565	+	1.35891i	−0.144694	+	0.989476i	$0.546220\pi$
$524$	8.70337e7	−	1.03723e8i	0.604914	−	0.720908i
$525$	4.29860e7	−	3.91923e7i	0.297063	−	0.270846i
$526$	1.30605e7	+	7.40696e7i	0.0897432	+	0.508959i
$527$	3.59369e7	−	6.33664e6i	0.245532	−	0.0432940i
$528$	−2.70794e7	−	2.97005e7i	−0.183966	−	0.201773i
$529$	1.12643e8	+	9.45190e7i	0.760919	+	0.638487i
$530$	−1.23680e6	+	714068.i	−0.00830754	+	0.00479636i
$531$	1.95318e8	−	5.12908e7i	1.30454	−	0.342575i
$532$	−2.44605e7	+	4.23668e7i	−0.162454	+	0.281378i
$533$	2.05580e7	+	5.64827e7i	0.135769	+	0.373022i
$534$	3.72296e7	−	2.77430e8i	0.244492	−	1.82192i
$535$	3.36665e6	−	2.82496e6i	0.0219855	−	0.0184481i
$536$	−7.43228e6	+	2.04200e7i	−0.0482645	+	0.132606i
$537$	2.43445e8	+	1.27504e8i	1.57209	+	0.823379i
$538$	−3.41673e7	+	1.93772e8i	−0.219413	+	1.24436i
$539$			4.51083e7i			0.288065i
$540$	−2.97675e6	−	5.82445e6i	−0.0189043	−	0.0369891i
$541$	1.00721e8			0.636104			0.318052	−	0.948073i	$-0.396971\pi$
$541$	1.00721e8			0.636104			0.318052	+	0.948073i	$0.396971\pi$
$542$	−1.73452e7	−	3.05843e6i	−0.108939	−	0.0192088i
$543$	−3.05044e8	+	1.25551e7i	−1.90530	+	0.0784190i
$544$	−2.66564e8	−	9.70215e7i	−1.65579	−	0.602658i
$545$	−565310.	−	673710.i	−0.00349219	−	0.00416182i
$546$	4.33829e7	−	5.62463e7i	0.266527	−	0.345554i
$547$	−3.48327e7	+	1.26781e7i	−0.212826	+	0.0774625i	−0.446233	−	0.894917i	$-0.647235\pi$
$547$	−3.48327e7	+	1.26781e7i	−0.212826	+	0.0774625i	0.233407	+	0.972379i	$0.425013\pi$
$548$	2.59605e8	+	1.49883e8i	1.57751	+	0.910774i
$549$	−1.44571e7	+	1.56251e8i	−0.0873706	+	0.944289i
$550$	−4.21212e7	−	7.29560e7i	−0.253170	−	0.438503i
$551$	1.40833e8	−	1.67838e8i	0.841877	−	1.00331i
$552$	3.38465e6	+	1.07648e6i	0.0201232	+	0.00640012i
$553$	4.70804e6	+	2.67006e7i	0.0278397	+	0.157887i
$554$	−2.56936e8	+	4.53048e7i	−1.51111	+	0.266449i
$555$	−1.02144e7	+	2.23772e6i	−0.0597494	+	0.0130896i
$556$	−1.96645e8	−	1.65005e8i	−1.14408	−	0.960001i
$557$	−9.64666e7	+	5.56950e7i	−0.558228	+	0.322293i	−0.752434	−	0.658668i	$-0.771120\pi$
$557$	−9.64666e7	+	5.56950e7i	−0.558228	+	0.322293i	0.194206	+	0.980961i	$0.437787\pi$
$558$	−4.26058e7	+	2.95168e7i	−0.245226	+	0.169890i
$559$	8.83890e7	−	1.53094e8i	0.506014	−	0.876443i
$560$	−678867.	−	1.86517e6i	−0.00386563	−	0.0106207i
$561$	6.91837e7	−	2.84545e7i	0.391846	−	0.161162i
$562$	2.36032e8	−	1.98054e8i	1.32973	−	1.11577i
$563$	4.42274e7	−	1.21514e8i	0.247837	−	0.680927i	−0.751928	−	0.659245i	$-0.770876\pi$
$563$	4.42274e7	−	1.21514e8i	0.247837	−	0.680927i	0.999765	−	0.0216814i	$-0.00690193\pi$
$564$	−2.76614e8	+	1.75252e8i	−1.54183	+	0.976847i
$565$	−4562.73	+	25876.5i	−2.52976e−5	+	0.000143470i
$566$		−	2.68539e8i		−	1.48101i
$567$	−6.31706e7	−	3.73181e7i	−0.346550	−	0.204725i
$568$	1.56049e7			0.0851564
$569$	−4.56414e7	−	8.04781e6i	−0.247755	−	0.0436859i	0.0483914	−	0.998828i	$-0.484591\pi$
$569$	−4.56414e7	−	8.04781e6i	−0.247755	−	0.0436859i	−0.296146	+	0.955143i	$0.595702\pi$
$570$	−3.54986e6	−	5.60300e6i	−0.0191684	−	0.0302549i
$571$	−1.80686e8	−	6.57644e7i	−0.970547	−	0.353250i	−0.192389	−	0.981319i	$-0.561623\pi$
$571$	−1.80686e8	−	6.57644e7i	−0.970547	−	0.353250i	−0.778158	+	0.628069i	$0.783846\pi$
$572$	−3.57225e7	−	4.25724e7i	−0.190877	−	0.227479i
$573$	3.53368e7	+	8.59170e7i	0.187829	+	0.456683i
$574$	−5.69633e7	+	2.07329e7i	−0.301203	+	0.109629i
$575$	−1.34498e7	−	7.76526e6i	−0.0707478	−	0.0408463i
$576$	2.50278e8	−	2.06370e7i	1.30965	−	0.107989i
$577$	−1.05498e8	−	1.82728e8i	−0.549182	−	0.951212i	−0.998331	−	0.0577545i	$-0.981606\pi$
$577$	−1.05498e8	−	1.82728e8i	−0.549182	−	0.951212i	0.449149	−	0.893457i	$-0.351727\pi$
$578$	9.50346e7	−	1.13258e8i	0.492151	−	0.586522i
$579$	−3.74334e7	−	1.70870e8i	−0.192852	−	0.880300i
$580$	−2.68329e6	−	1.52177e7i	−0.0137526	−	0.0779946i
$581$	−8.12231e7	+	1.43218e7i	−0.414144	+	0.0730247i
$582$	−6.63923e7	+	2.08750e8i	−0.336782	+	1.05890i
$583$	9.60081e6	+	8.05604e6i	0.0484510	+	0.0406552i
$584$	−1.65970e7	+	9.58225e6i	−0.0833278	+	0.0481093i
$585$	2.17531e6	+	4.72648e6i	0.0108656	+	0.0236086i
$586$	−5.85189e7	+	1.01358e8i	−0.290806	+	0.503691i
$587$	7.65643e6	+	2.10359e7i	0.0378540	+	0.104003i	0.957180	−	0.289495i	$-0.0934872\pi$
$587$	7.65643e6	+	2.10359e7i	0.0378540	+	0.104003i	−0.919326	+	0.393498i	$0.871265\pi$
$588$	−1.58511e8	−	1.22260e8i	−0.779700	−	0.601385i
$589$	−2.17515e7	+	1.82517e7i	−0.106450	+	0.0893218i
$590$	4.93959e6	−	1.35714e7i	0.0240511	−	0.0660799i
$591$	1.14483e7	+	2.78151e8i	0.0554597	+	1.34747i
$592$	4.95139e7	−	2.80808e8i	0.238651	−	1.35345i
$593$			1.59096e7i			0.0762950i	0.999272	+	0.0381475i	$0.0121457\pi$
$593$			1.59096e7i			0.0762950i	−0.999272	+	0.0381475i	$0.987854\pi$
$594$	−7.23691e7	+	7.77984e7i	−0.345298	+	0.371203i
$595$	3.69429e6			0.0175380
$596$	−9.77767e7	−	1.72407e7i	−0.461846	−	0.0814358i
$597$	−7.47647e7	+	1.42750e8i	−0.351377	+	0.670892i
$598$	−1.78209e7	−	6.48626e6i	−0.0833346	−	0.0303313i
$599$	−1.36753e8	−	1.62976e8i	−0.636290	−	0.758301i	0.347489	−	0.937684i	$-0.387034\pi$
$599$	−1.36753e8	−	1.62976e8i	−0.636290	−	0.758301i	−0.983779	+	0.179383i	$0.942590\pi$
$600$	5.51989e7	+	7.40739e6i	0.255550	+	0.0342935i
$601$	−4.83089e7	+	1.75830e7i	−0.222538	+	0.0809970i	−0.450883	−	0.892583i	$-0.648891\pi$
$601$	−4.83089e7	+	1.75830e7i	−0.222538	+	0.0809970i	0.228345	+	0.973580i	$0.426669\pi$
$602$	1.54397e8	+	8.91410e7i	0.707699	+	0.408590i
$603$	−1.15608e8	−	3.15971e7i	−0.527275	−	0.144110i
$604$	1.50496e8	+	2.60666e8i	0.682988	+	1.18297i
$605$	−4.43740e6	+	5.28829e6i	−0.0200384	+	0.0238808i
$606$	1.29386e7	−	1.17968e7i	0.0581394	−	0.0530084i
$607$	−3.92737e7	−	2.22732e8i	−0.175605	−	0.995904i	−0.937444	−	0.348137i	$-0.886814\pi$
$607$	−3.92737e7	−	2.22732e8i	−0.175605	−	0.995904i	0.761839	−	0.647767i	$-0.224297\pi$
$608$	2.17378e8	−	3.83295e7i	0.967172	−	0.170539i
$609$	−1.16779e8	−	1.28083e8i	−0.517028	−	0.567074i
$610$	8.59693e6	+	7.21368e6i	0.0378751	+	0.0317810i
$611$	2.25577e8	−	1.30237e8i	0.988944	−	0.570967i
$612$	−8.75236e7	+	3.20234e8i	−0.381831	+	1.39706i
$613$	−1.75123e8	+	3.03323e8i	−0.760261	+	1.31681i	0.182455	+	0.983214i	$0.441596\pi$
$613$	−1.75123e8	+	3.03323e8i	−0.760261	+	1.31681i	−0.942716	+	0.333596i	$0.891738\pi$
$614$	1.62729e7	+	4.47095e7i	0.0703009	+	0.193150i
$615$	590559.	−	4.40077e6i	0.00253886	−	0.0189192i
$616$	6.39605e6	−	5.36692e6i	0.0273634	−	0.0229606i
$617$	−2.51467e6	+	6.90900e6i	−0.0107060	+	0.0294144i	−0.944931	−	0.327271i	$-0.893871\pi$
$617$	−2.51467e6	+	6.90900e6i	−0.0107060	+	0.0294144i	0.934225	+	0.356685i	$0.116093\pi$
$618$	5.12500e8	+	2.68420e8i	2.17134	+	1.13723i
$619$	2.53069e7	−	1.43523e8i	0.106701	−	0.605130i	−0.883827	−	0.467815i	$-0.845041\pi$
$619$	2.53069e7	−	1.43523e8i	0.106701	−	0.605130i	0.990527	−	0.137316i	$-0.0438474\pi$
$620$			2.00261e6i			0.00840276i
$621$	−4.38292e6	+	1.90918e7i	−0.0183016	+	0.0797210i
$622$	3.82541e8			1.58967
$623$	−1.19469e8	−	2.10657e7i	−0.494074	−	0.0871186i
$624$	−1.41760e8	+	5.83463e6i	−0.583446	+	0.0240137i
$625$	−2.28557e8	−	8.31881e7i	−0.936171	−	0.340738i
$626$	−1.51989e8	−	1.81133e8i	−0.619568	−	0.738373i
$627$	−3.55504e7	+	4.60913e7i	−0.144225	+	0.186989i
$628$	4.51362e8	−	1.64282e8i	1.82241	−	0.663303i
$629$	4.59607e8	+	2.65354e8i	1.84686	+	1.06629i
$630$	−4.76669e6	+	2.19382e6i	−0.0190632	+	0.00877362i
$631$	1.05328e8	+	1.82434e8i	0.419234	+	0.726135i	0.995863	−	0.0908717i	$-0.0289653\pi$
$631$	1.05328e8	+	1.82434e8i	0.419234	+	0.726135i	−0.576629	+	0.817006i	$0.695632\pi$
$632$	−1.66855e7	+	1.98850e7i	−0.0660979	+	0.0787724i
$633$	2.05205e8	+	6.52649e7i	0.809053	+	0.257317i
$634$	8.16122e7	+	4.62846e8i	0.320249	+	1.81622i
$635$	9.44922e6	−	1.66615e6i	0.0369041	−	0.00650719i
$636$	−5.43307e7	+	1.19025e7i	−0.211190	+	0.0462666i
$637$	1.21981e8	+	1.02354e8i	0.471925	+	0.395992i
$638$	−2.17383e8	+	1.25506e8i	−0.837074	+	0.483285i
$639$	7.07259e6	+	8.57736e7i	0.0271066	+	0.328739i
$640$	2.35580e6	−	4.08037e6i	0.00898668	−	0.0155654i
$641$	1.10031e8	+	3.02307e8i	0.417773	+	1.14782i	0.952962	+	0.303089i	$0.0980181\pi$
$641$	1.10031e8	+	3.02307e8i	0.417773	+	1.14782i	−0.535189	+	0.844732i	$0.679760\pi$
$642$	2.93006e8	−	1.20510e8i	1.10732	−	0.455428i
$643$	3.39360e8	−	2.84757e8i	1.27652	−	1.07113i	0.282805	−	0.959177i	$-0.408735\pi$
$643$	3.39360e8	−	2.84757e8i	1.27652	−	1.07113i	0.993714	−	0.111949i	$-0.0357094\pi$
$644$	3.53395e6	−	9.70945e6i	0.0132313	−	0.0363527i
$645$	−1.10311e7	+	6.98894e6i	−0.0411094	+	0.0260455i
$646$	−5.84571e7	+	3.31526e8i	−0.216840	+	1.22976i
$647$		−	3.38740e8i		−	1.25070i	−0.780344	−	0.625351i	$-0.784956\pi$
$647$		−	3.38740e8i		−	1.25070i	0.780344	−	0.625351i	$-0.215044\pi$
$648$	−1.15062e7	−	6.92970e7i	−0.0422870	−	0.254677i
$649$	−1.26743e8			−0.463650
$650$	−2.92862e8	−	5.16394e7i	−1.06641	−	0.188036i
$651$	1.20220e7	+	1.89753e7i	0.0435748	+	0.0687772i
$652$	−7.48443e7	−	2.72411e7i	−0.270032	−	0.0982838i
$653$	2.77043e7	+	3.30167e7i	0.0994964	+	0.118575i	0.813495	−	0.581572i	$-0.197562\pi$
$653$	2.77043e7	+	3.30167e7i	0.0994964	+	0.118575i	−0.713999	+	0.700147i	$0.753118\pi$
$654$	−2.41157e7	−	5.86342e7i	−0.0862116	−	0.209613i
$655$	7.47634e6	−	2.72117e6i	0.0266051	−	0.00968348i
$656$	1.04858e8	+	6.05396e7i	0.371440	+	0.214451i
$657$	−6.01916e7	−	8.68832e7i	−0.212246	−	0.306366i
$658$	1.31345e8	+	2.27496e8i	0.461037	+	0.798540i
$659$	−2.48435e8	+	2.96073e8i	−0.868073	+	1.03453i	0.130996	+	0.991383i	$0.458183\pi$
$659$	−2.48435e8	+	2.96073e8i	−0.868073	+	1.03453i	−0.999069	+	0.0431461i	$0.986262\pi$
$660$	878542.	+	4.01023e6i	0.00305584	+	0.0139488i
$661$	1.14889e7	+	6.51570e7i	0.0397810	+	0.225609i	0.998216	−	0.0597006i	$-0.0190146\pi$
$661$	1.14889e7	+	6.51570e7i	0.0397810	+	0.225609i	−0.958435	+	0.285310i	$0.907903\pi$
$662$	−6.65503e8	+	1.17346e8i	−2.29391	+	0.404478i
$663$	8.00366e7	−	2.51650e8i	0.274630	−	0.863488i
$664$	−6.04899e7	−	5.07571e7i	−0.206623	−	0.173377i
$665$	−2.48948e6	+	1.43730e6i	−0.00846533	+	0.00488746i
$666$	−7.50601e8	−	6.94496e7i	−2.54089	−	0.235097i
$667$	−2.31377e7	+	4.00757e7i	−0.0779728	+	0.135053i
$668$	−1.54796e8	−	4.25300e8i	−0.519316	−	1.42681i
$669$	−5.48298e7	−	4.22904e7i	−0.183121	−	0.141242i
$670$	−6.56604e6	+	5.50956e6i	−0.0218313	+	0.0183186i
$671$	3.36842e7	−	9.25466e7i	0.111496	−	0.306332i
$672$	−7.18104e6	−	1.74473e8i	−0.0236635	−	0.574938i
$673$	8.73394e7	−	4.95326e8i	0.286527	−	1.62497i	−0.413254	−	0.910616i	$-0.635608\pi$
$673$	8.73394e7	−	4.95326e8i	0.286527	−	1.62497i	0.699781	−	0.714358i	$-0.253281\pi$
$674$		−	5.90353e8i		−	1.92811i
$675$	−1.56976e7	+	3.06761e8i	−0.0510413	+	0.997445i
$676$	1.66811e8			0.539989
$677$	6.32693e7	+	1.11561e7i	0.203905	+	0.0359539i	0.274667	−	0.961539i	$-0.411432\pi$
$677$	6.32693e7	+	1.11561e7i	0.203905	+	0.0359539i	−0.0707628	+	0.997493i	$0.522543\pi$
$678$	−878833.	+	1.67798e6i	−0.00281979	+	0.00538389i
$679$	8.92095e7	+	3.24696e7i	0.284972	+	0.103721i
$680$	2.27353e6	+	2.70948e6i	0.00723058	+	0.00861707i
$681$	1.12967e8	+	1.51596e7i	0.357694	+	0.0480006i
$682$	3.05690e7	−	1.11262e7i	0.0963668	−	0.0350747i
$683$	−2.49294e8	−	1.43930e8i	−0.782439	−	0.451741i	0.0548549	−	0.998494i	$-0.482530\pi$
$683$	−2.49294e8	−	1.43930e8i	−0.782439	−	0.451741i	−0.837294	+	0.546753i	$0.815864\pi$
$684$	−6.56107e7	−	2.49849e8i	−0.205025	−	0.780745i
$685$	8.80716e6	+	1.52544e7i	0.0274008	+	0.0474597i
$686$	−2.26406e8	+	2.69820e8i	−0.701318	+	0.835799i
$687$	1.80245e8	−	1.64338e8i	0.555896	−	0.506836i
$688$	−6.18355e7	−	3.50687e8i	−0.189877	−	1.07685i
$689$	4.35698e7	−	7.68254e6i	0.133207	−	0.0234881i
$690$	943872.	+	1.03524e6i	0.00287320	+	0.00315132i
$691$	8.20462e7	+	6.88449e7i	0.248670	+	0.208659i	0.758600	−	0.651557i	$-0.225884\pi$
$691$	8.20462e7	+	6.88449e7i	0.248670	+	0.208659i	−0.509929	+	0.860216i	$0.670328\pi$
$692$	−5.61559e8	+	3.24216e8i	−1.69464	+	0.978400i
$693$	3.23985e7	+	3.27239e7i	0.0973476	+	0.0983252i
$694$	5.45197e7	−	9.44308e7i	0.163108	−	0.282511i
$695$	−5.15898e6	−	1.41742e7i	−0.0153677	−	0.0422224i
$696$	2.20714e7	−	1.64473e8i	0.0654640	−	0.487828i
$697$	−1.72632e8	+	1.44856e8i	−0.509828	+	0.427797i
$698$	1.58539e8	−	4.35581e8i	0.466196	−	1.28086i
$699$	−8.93302e7	−	4.67863e7i	−0.261557	−	0.136990i
$700$	2.81350e7	−	1.59562e8i	0.0820263	−	0.465194i
$701$			9.65458e7i			0.280272i	0.990132	+	0.140136i	$0.0447540\pi$
$701$			9.65458e7i			0.280272i	−0.990132	+	0.140136i	$0.955246\pi$
$702$	4.61697e7	+	3.72229e8i	0.133458	+	1.07597i
$703$	−4.12955e8			−1.18860
$704$	−1.55220e8	−	2.73694e7i	−0.444865	−	0.0784417i
$705$	−1.92252e7	+	791279.i	−0.0548660	+	0.00225820i
$706$	4.99563e8	+	1.81826e8i	1.41963	+	0.516704i
$707$	−4.87763e6	−	5.81294e6i	−0.0138023	−	0.0164489i
$708$	3.43520e8	−	4.45376e8i	0.967950	−	1.25495i
$709$	−1.61527e6	+	587910.i	−0.00453217	+	0.00164957i	−0.344285	−	0.938865i	$-0.611879\pi$
$709$	−1.61527e6	+	587910.i	−0.00453217	+	0.00164957i	0.339753	+	0.940515i	$0.389656\pi$
$710$	5.33055e6	+	3.07760e6i	0.0148935	+	0.00859877i
$711$	−1.16861e8	−	8.27004e7i	−0.325134	−	0.230090i
$712$	−5.80732e7	−	1.00586e8i	−0.160892	−	0.278674i
$713$	3.85494e6	−	4.59414e6i	0.0106353	−	0.0126746i
$714$	2.53791e8	+	8.07175e7i	0.697238	+	0.221755i
$715$	−567059.	−	3.21595e6i	−0.00155135	−	0.00879815i
$716$	7.53812e8	−	1.32917e8i	2.05364	−	0.362112i
$717$	−5.02297e7	+	1.10041e7i	−0.136271	+	0.0298536i
$718$	1.71037e8	+	1.43517e8i	0.462081	+	0.387732i
$719$	4.70282e8	−	2.71517e8i	1.26524	−	0.730484i	0.291153	−	0.956676i	$-0.405961\pi$
$719$	4.70282e8	−	2.71517e8i	1.26524	−	0.730484i	0.974083	+	0.226192i	$0.0726277\pi$
$720$	9.47662e6	+	4.47680e6i	0.0253896	+	0.0119942i
$721$	1.25365e8	−	2.17139e8i	0.334481	−	0.579338i
$722$	1.00253e8	+	2.75443e8i	0.266371	+	0.731848i
$723$	−4.27631e8	+	1.75880e8i	−1.13150	+	0.465374i
$724$	−6.51413e8	+	5.46600e8i	−1.71649	+	1.44030i
$725$	−2.48182e8	+	6.81874e8i	−0.651263	+	1.78933i
$726$	−4.20386e8	+	2.66342e8i	−1.09860	+	0.696032i
$727$	−2.97880e7	+	1.68936e8i	−0.0775243	+	0.439662i	0.921196	+	0.389098i	$0.127213\pi$
$727$	−2.97880e7	+	1.68936e8i	−0.0775243	+	0.439662i	−0.998721	+	0.0505645i	$0.983898\pi$
$728$		−	2.94740e7i		−	0.0763914i
$729$	3.75680e8	−	9.46518e7i	0.969696	−	0.244313i
$730$	−7.55922e6			−0.0194316
$731$	6.52707e8	+	1.15090e8i	1.67096	+	0.294635i
$732$	2.33913e8	+	3.69202e8i	0.596377	+	0.941305i
$733$	−3.30558e8	−	1.20313e8i	−0.839337	−	0.305494i	−0.113652	−	0.993521i	$-0.536255\pi$
$733$	−3.30558e8	−	1.20313e8i	−0.839337	−	0.305494i	−0.725685	+	0.688027i	$0.758477\pi$
$734$	3.69163e8	+	4.39951e8i	0.933533	+	1.11254i
$735$	−4.47427e6	−	1.08786e7i	−0.0112683	−	0.0273976i
$736$	−4.38090e7	+	1.59452e7i	−0.109883	+	0.0399941i
$737$	6.51425e7	+	3.76101e7i	0.162728	+	0.0939511i
$738$	1.36724e8	−	2.89421e8i	0.340153	−	0.720047i
$739$	−3.60899e8	−	6.25096e8i	−0.894237	−	1.54886i	−0.834746	−	0.550635i	$-0.814386\pi$
$739$	−3.60899e8	−	6.25096e8i	−0.894237	−	1.54886i	−0.0594907	−	0.998229i	$-0.518948\pi$
$740$	−1.87211e7	+	2.23109e7i	−0.0461994	+	0.0550583i
$741$	4.39726e7	+	2.00719e8i	0.108075	+	0.493326i
$742$	7.74790e6	+	4.39405e7i	0.0189658	+	0.107561i
$743$	3.80648e8	−	6.71185e7i	0.928020	−	0.163635i	0.310845	−	0.950461i	$-0.399388\pi$
$743$	3.80648e8	−	6.71185e7i	0.928020	−	0.163635i	0.617175	+	0.786826i	$0.288277\pi$
$744$	−6.51835e6	+	2.04949e7i	−0.0158277	+	0.0497654i
$745$	−4.46912e6	−	3.75003e6i	−0.0108082	−	0.00906914i
$746$	−6.43454e8	+	3.71498e8i	−1.54989	+	0.894830i
$747$	2.51574e8	−	3.55491e8i	0.603536	−	0.852839i
$748$	1.04180e8	−	1.80444e8i	0.248930	−	0.431160i
$749$	−4.69613e7	−	1.29025e8i	−0.111762	−	0.307064i
$750$	3.48112e7	+	2.68500e7i	0.0825154	+	0.0636444i
$751$	−2.74462e8	+	2.30301e8i	−0.647981	+	0.543721i	−0.906458	−	0.422297i	$-0.861224\pi$
$751$	−2.74462e8	+	2.30301e8i	−0.647981	+	0.543721i	0.258476	+	0.966018i	$0.416780\pi$
$752$	1.79455e8	−	4.93049e8i	0.421990	−	1.15941i
$753$	−2.05229e7	−	4.98631e8i	−0.0480677	−	1.16787i
$754$	−1.53867e8	+	8.72624e8i	−0.358948	+	2.03570i
$755$			1.76863e7i			0.0410957i
$756$	−2.02804e8	+	2.51549e7i	−0.469365	+	0.0582181i
$757$	−7.79205e8			−1.79624			−0.898120	−	0.439751i	$-0.855067\pi$
$757$	−7.79205e8			−1.79624			−0.898120	+	0.439751i	$0.855067\pi$
$758$	1.22252e9	+	2.15564e8i	2.80705	+	0.494958i
$759$	5.70407e6	−	1.08909e7i	0.0130455	−	0

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(11.6192 + 2.04878i) q^{2} +(14.4502 + 22.8077i) q^{3} +(70.6679 + 25.7210i) q^{4} +(2.84045 + 3.38512i) q^{5} +(121.171 + 294.613i) q^{6} +(129.733 - 47.2189i) q^{7} +(114.471 + 66.0899i) q^{8} +(-311.386 + 659.151i) q^{9} +O(q^{10})\)	\(q+(11.6192 + 2.04878i) q^{2} +(14.4502 + 22.8077i) q^{3} +(70.6679 + 25.7210i) q^{4} +(2.84045 + 3.38512i) q^{5} +(121.171 + 294.613i) q^{6} +(129.733 - 47.2189i) q^{7} +(114.471 + 66.0899i) q^{8} +(-311.386 + 659.151i) q^{9} +(26.0684 + 45.1518i) q^{10} +(294.101 - 350.496i) q^{11} +(434.524 + 1983.45i) q^{12} +(-280.466 - 1590.60i) q^{13} +(1604.13 - 282.852i) q^{14} +(-36.1619 + 113.700i) q^{15} +(-2492.32 - 2091.30i) q^{16} +(5244.19 - 3027.73i) q^{17} +(-4968.51 + 7020.84i) q^{18} +(-2355.94 + 4080.61i) q^{19} +(113.660 + 312.278i) q^{20} +(2951.62 + 2276.59i) q^{21} +(4135.30 - 3469.93i) q^{22} +(340.377 - 935.179i) q^{23} +(146.764 + 3565.83i) q^{24} +(2709.86 - 15368.4i) q^{25} -19056.1i q^{26} +(-19533.3 + 2422.83i) q^{27} +10382.5 q^{28} +(-45792.4 - 8074.43i) q^{29} +(-653.117 + 1247.01i) q^{30} +(5662.75 + 2061.07i) q^{31} +(-30111.8 - 35885.8i) q^{32} +(12243.8 + 1643.06i) q^{33} +(67136.4 - 24435.6i) q^{34} +(528.341 + 305.038i) q^{35} +(-38959.0 + 38571.6i) q^{36} +(43820.6 + 75899.5i) q^{37} +(-35734.4 + 42586.6i) q^{38} +(32225.2 - 29381.2i) q^{39} +(101.427 + 575.223i) q^{40} +(-36649.8 + 6462.35i) q^{41} +(29631.2 + 32499.4i) q^{42} +(83844.2 + 70353.6i) q^{43} +(29798.6 - 17204.2i) q^{44} +(-3115.78 + 818.208i) q^{45} +(5870.88 - 10168.7i) q^{46} +(55157.8 + 151545. i) q^{47} +(11683.5 - 87063.7i) q^{48} +(-75523.4 + 63371.6i) q^{49} +(62972.8 - 173016. i) q^{50} +(144835. + 75856.8i) q^{51} +(21091.9 - 119618. i) q^{52} +27392.1i q^{53} +(-231925. - 11868.1i) q^{54} +2021.85 q^{55} +(17971.3 + 3168.83i) q^{56} +(-127113. + 5231.78i) q^{57} +(-515528. - 187637. i) q^{58} +(-178059. - 212202. i) q^{59} +(-5479.95 + 7104.79i) q^{60} +(202270. - 73620.2i) q^{61} +(61573.9 + 35549.7i) q^{62} +(-9272.58 + 100217. i) q^{63} +(-172241. - 298330. i) q^{64} +(4587.72 - 5467.43i) q^{65} +(138897. + 44175.9i) q^{66} +(28548.0 + 161904. i) q^{67} +(448472. - 79077.7i) q^{68} +(26247.8 - 5750.25i) q^{69} +(5513.94 + 4626.75i) q^{70} +(102242. - 59029.3i) q^{71} +(-79207.9 + 54874.2i) q^{72} +(-72494.1 + 125563. i) q^{73} +(353659. + 971670. i) q^{74} +(389676. - 160270. i) q^{75} +(-271447. + 227771. i) q^{76} +(21604.5 - 59357.9i) q^{77} +(434626. - 275364. i) q^{78} +(-34101.7 + 193401. i) q^{79} -14377.0i q^{80} +(-337519. - 410500. i) q^{81} -439081. q^{82} +(-588323. - 103737. i) q^{83} +(150028. + 236800. i) q^{84} +(25145.1 + 9152.06i) q^{85} +(830063. + 989230. i) q^{86} +(-477548. - 1.16110e6i) q^{87} +(56830.3 - 20684.5i) q^{88} +(-760977. - 439350. i) q^{89} +(-37879.2 + 3123.38i) q^{90} +(-111492. - 193110. i) q^{91} +(48107.5 - 57332.2i) q^{92} +(34819.2 + 158937. i) q^{93} +(330408. + 1.87383e6i) q^{94} +(-20505.3 + 3615.63i) q^{95} +(383354. - 1.20534e6i) q^{96} +(526763. + 442007. i) q^{97} +(-1.00736e6 + 581597. i) q^{98} +(139451. + 302996. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

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