LMFDB - Embedded newform 630.2.bk.b.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bk (of order $6$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.b.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.72522 - 0.153652i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.153652 - 1.72522i) q^{6} +(0.145275 + 2.64176i) q^{7} -1.00000i q^{8} +(2.95278 + 0.530167i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.72522 - 0.153652i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.153652 - 1.72522i) q^{6} +(0.145275 + 2.64176i) q^{7} -1.00000i q^{8} +(2.95278 + 0.530167i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-2.74924 + 1.58727i) q^{11} +(1.72522 + 0.153652i) q^{12} +(1.82400 - 1.05309i) q^{13} +(-2.64176 + 0.145275i) q^{14} +(0.995677 - 1.41726i) q^{15} +1.00000 q^{16} +(0.0900212 - 0.155921i) q^{17} +(-0.530167 + 2.95278i) q^{18} +(-5.17571 + 2.98820i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.155279 - 4.57994i) q^{21} +(-1.58727 - 2.74924i) q^{22} +(-0.683360 - 0.394538i) q^{23} +(-0.153652 + 1.72522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.05309 + 1.82400i) q^{26} +(-5.01274 - 1.36835i) q^{27} +(-0.145275 - 2.64176i) q^{28} +(-6.84694 - 3.95308i) q^{29} +(1.41726 + 0.995677i) q^{30} -9.70317i q^{31} +1.00000i q^{32} +(4.98693 - 2.31597i) q^{33} +(0.155921 + 0.0900212i) q^{34} +(-2.36047 - 1.19507i) q^{35} +(-2.95278 - 0.530167i) q^{36} +(4.27097 + 7.39754i) q^{37} +(-2.98820 - 5.17571i) q^{38} +(-3.30862 + 1.53655i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-5.85731 - 10.1452i) q^{41} +(4.57994 + 0.155279i) q^{42} +(-1.84922 + 3.20294i) q^{43} +(2.74924 - 1.58727i) q^{44} +(-1.93553 + 2.29210i) q^{45} +(0.394538 - 0.683360i) q^{46} -2.08361 q^{47} +(-1.72522 - 0.153652i) q^{48} +(-6.95779 + 0.767563i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-0.179264 + 0.255167i) q^{51} +(-1.82400 + 1.05309i) q^{52} +(-0.613086 - 0.353965i) q^{53} +(1.36835 - 5.01274i) q^{54} -3.17454i q^{55} +(2.64176 - 0.145275i) q^{56} +(9.38840 - 4.36005i) q^{57} +(3.95308 - 6.84694i) q^{58} -11.7733 q^{59} +(-0.995677 + 1.41726i) q^{60} -2.89604i q^{61} +9.70317 q^{62} +(-0.971608 + 7.87756i) q^{63} -1.00000 q^{64} +2.10618i q^{65} +(2.31597 + 4.98693i) q^{66} +9.95697 q^{67} +(-0.0900212 + 0.155921i) q^{68} +(1.11833 + 0.785665i) q^{69} +(1.19507 - 2.36047i) q^{70} +10.1885i q^{71} +(0.530167 - 2.95278i) q^{72} +(-5.09156 - 2.93961i) q^{73} +(-7.39754 + 4.27097i) q^{74} +(0.729545 + 1.57091i) q^{75} +(5.17571 - 2.98820i) q^{76} +(-4.59259 - 7.03223i) q^{77} +(-1.53655 - 3.30862i) q^{78} +11.0054 q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.43785 + 3.13093i) q^{81} +(10.1452 - 5.85731i) q^{82} +(-4.41475 + 7.64657i) q^{83} +(-0.155279 + 4.57994i) q^{84} +(0.0900212 + 0.155921i) q^{85} +(-3.20294 - 1.84922i) q^{86} +(11.2051 + 7.87199i) q^{87} +(1.58727 + 2.74924i) q^{88} +(-2.91136 - 5.04262i) q^{89} +(-2.29210 - 1.93553i) q^{90} +(3.04699 + 4.66559i) q^{91} +(0.683360 + 0.394538i) q^{92} +(-1.49091 + 16.7401i) q^{93} -2.08361i q^{94} -5.97640i q^{95} +(0.153652 - 1.72522i) q^{96} +(3.79334 + 2.19008i) q^{97} +(-0.767563 - 6.95779i) q^{98} +(-8.95941 + 3.22932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.72522	−	0.153652i	−0.996057	−	0.0887108i
$3$	−1.72522	−	0.153652i	−0.996057	−	0.0887108i
$4$	−1.00000			−0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.153652	−	1.72522i	0.0627280	−	0.704319i
$7$	0.145275	+	2.64176i	0.0549087	+	0.998491i
$7$	0.145275	+	2.64176i	0.0549087	+	0.998491i
$8$		−	1.00000i		−	0.353553i
$9$	2.95278	+	0.530167i	0.984261	+	0.176722i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−2.74924	+	1.58727i	−0.828926	+	0.478581i	−0.853485	−	0.521118i	$-0.825515\pi$
$11$	−2.74924	+	1.58727i	−0.828926	+	0.478581i	0.0245589	+	0.999698i	$0.492182\pi$
$12$	1.72522	+	0.153652i	0.498029	+	0.0443554i
$13$	1.82400	−	1.05309i	0.505887	−	0.292074i	−0.225254	−	0.974300i	$-0.572321\pi$
$13$	1.82400	−	1.05309i	0.505887	−	0.292074i	0.731141	+	0.682226i	$0.238988\pi$
$14$	−2.64176	+	0.145275i	−0.706040	+	0.0388263i
$15$	0.995677	−	1.41726i	0.257083	−	0.365935i
$16$	1.00000			0.250000
$17$	0.0900212	−	0.155921i	0.0218333	−	0.0378165i	−0.854902	−	0.518789i	$-0.826383\pi$
$17$	0.0900212	−	0.155921i	0.0218333	−	0.0378165i	0.876736	+	0.480973i	$0.159716\pi$
$18$	−0.530167	+	2.95278i	−0.124961	+	0.695977i
$19$	−5.17571	+	2.98820i	−1.18739	+	0.685540i	−0.957713	−	0.287727i	$-0.907101\pi$
$19$	−5.17571	+	2.98820i	−1.18739	+	0.685540i	−0.229678	+	0.973267i	$0.573767\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	0.155279	−	4.57994i	0.0338847	−	0.999426i
$22$	−1.58727	−	2.74924i	−0.338408	−	0.586139i
$23$	−0.683360	−	0.394538i	−0.142490	−	0.0822669i	0.427060	−	0.904223i	$-0.359549\pi$
$23$	−0.683360	−	0.394538i	−0.142490	−	0.0822669i	−0.569550	+	0.821956i	$0.692883\pi$
$24$	−0.153652	+	1.72522i	−0.0313640	+	0.352159i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.05309	+	1.82400i	0.206528	+	0.357716i
$27$	−5.01274	−	1.36835i	−0.964703	−	0.263340i
$28$	−0.145275	−	2.64176i	−0.0274544	−	0.499246i
$29$	−6.84694	−	3.95308i	−1.27144	−	0.734069i	−0.296185	−	0.955131i	$-0.595714\pi$
$29$	−6.84694	−	3.95308i	−1.27144	−	0.734069i	−0.975260	+	0.221062i	$0.929048\pi$
$30$	1.41726	+	0.995677i	0.258755	+	0.181785i
$31$		−	9.70317i		−	1.74274i	−0.490626	−	0.871370i	$-0.663232\pi$
$31$		−	9.70317i		−	1.74274i	0.490626	−	0.871370i	$-0.336768\pi$
$32$			1.00000i			0.176777i
$33$	4.98693	−	2.31597i	0.868113	−	0.403159i
$34$	0.155921	+	0.0900212i	0.0267403	+	0.0154385i
$35$	−2.36047	−	1.19507i	−0.398992	−	0.202003i
$36$	−2.95278	−	0.530167i	−0.492130	−	0.0883611i
$37$	4.27097	+	7.39754i	0.702143	+	1.21615i	0.967713	+	0.252056i	$0.0811068\pi$
$37$	4.27097	+	7.39754i	0.702143	+	1.21615i	−0.265569	+	0.964092i	$0.585560\pi$
$38$	−2.98820	−	5.17571i	−0.484750	−	0.839612i
$39$	−3.30862	+	1.53655i	−0.529803	+	0.246045i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−5.85731	−	10.1452i	−0.914758	−	1.58441i	−0.807256	−	0.590202i	$-0.799048\pi$
$41$	−5.85731	−	10.1452i	−0.914758	−	1.58441i	−0.107502	−	0.994205i	$-0.534285\pi$
$42$	4.57994	+	0.155279i	0.706701	+	0.0239601i
$43$	−1.84922	+	3.20294i	−0.282003	+	0.488443i	−0.971878	−	0.235485i	$-0.924332\pi$
$43$	−1.84922	+	3.20294i	−0.282003	+	0.488443i	0.689875	+	0.723929i	$0.257665\pi$
$44$	2.74924	−	1.58727i	0.414463	−	0.239290i
$45$	−1.93553	+	2.29210i	−0.288532	+	0.341686i
$46$	0.394538	−	0.683360i	0.0581715	−	0.100756i
$47$	−2.08361			−0.303926			−0.151963	−	0.988386i	$-0.548559\pi$
$47$	−2.08361			−0.303926			−0.151963	+	0.988386i	$0.548559\pi$
$48$	−1.72522	−	0.153652i	−0.249014	−	0.0221777i
$49$	−6.95779	+	0.767563i	−0.993970	+	0.109652i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−0.179264	+	0.255167i	−0.0251020	+	0.0357305i
$52$	−1.82400	+	1.05309i	−0.252944	+	0.146037i
$53$	−0.613086	−	0.353965i	−0.0842138	−	0.0486209i	0.457302	−	0.889312i	$-0.348816\pi$
$53$	−0.613086	−	0.353965i	−0.0842138	−	0.0486209i	−0.541516	+	0.840691i	$0.682149\pi$
$54$	1.36835	−	5.01274i	0.186210	−	0.682148i
$55$		−	3.17454i		−	0.428055i
$56$	2.64176	−	0.145275i	0.353020	−	0.0194132i
$57$	9.38840	−	4.36005i	1.24352	−	0.577503i
$58$	3.95308	−	6.84694i	0.519065	−	0.899047i
$59$	−11.7733			−1.53275			−0.766377	−	0.642391i	$-0.777943\pi$
$59$	−11.7733			−1.53275			−0.766377	+	0.642391i	$0.777943\pi$
$60$	−0.995677	+	1.41726i	−0.128541	+	0.182968i
$61$		−	2.89604i		−	0.370800i	−0.982663	−	0.185400i	$-0.940642\pi$
$61$		−	2.89604i		−	0.370800i	0.982663	−	0.185400i	$-0.0593581\pi$
$62$	9.70317			1.23230
$63$	−0.971608	+	7.87756i	−0.122411	+	0.992479i
$64$	−1.00000			−0.125000
$65$			2.10618i			0.261239i
$66$	2.31597	+	4.98693i	0.285076	+	0.613849i
$67$	9.95697			1.21644			0.608219	−	0.793770i	$-0.291884\pi$
$67$	9.95697			1.21644			0.608219	+	0.793770i	$0.291884\pi$
$68$	−0.0900212	+	0.155921i	−0.0109167	+	0.0189082i
$69$	1.11833	+	0.785665i	0.134631	+	0.0945830i
$70$	1.19507	−	2.36047i	0.142838	−	0.282130i
$71$			10.1885i			1.20915i	0.796549	+	0.604574i	$0.206656\pi$
$71$			10.1885i			1.20915i	−0.796549	+	0.604574i	$0.793344\pi$
$72$	0.530167	−	2.95278i	0.0624807	−	0.347989i
$73$	−5.09156	−	2.93961i	−0.595921	−	0.344055i	0.171514	−	0.985182i	$-0.445134\pi$
$73$	−5.09156	−	2.93961i	−0.595921	−	0.344055i	−0.767435	+	0.641126i	$0.778467\pi$
$74$	−7.39754	+	4.27097i	−0.859947	+	0.496490i
$75$	0.729545	+	1.57091i	0.0842406	+	0.181393i
$76$	5.17571	−	2.98820i	0.593695	−	0.342770i
$77$	−4.59259	−	7.03223i	−0.523374	−	0.801397i
$78$	−1.53655	−	3.30862i	−0.173980	−	0.374627i
$79$	11.0054			1.23820			0.619099	−	0.785313i	$-0.287498\pi$
$79$	11.0054			1.23820			0.619099	+	0.785313i	$0.287498\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	8.43785	+	3.13093i	0.937539	+	0.347881i
$82$	10.1452	−	5.85731i	1.12034	−	0.646831i
$83$	−4.41475	+	7.64657i	−0.484582	+	0.839320i	−0.999843	−	0.0177130i	$-0.994361\pi$
$83$	−4.41475	+	7.64657i	−0.484582	+	0.839320i	0.515261	+	0.857033i	$0.327695\pi$
$84$	−0.155279	+	4.57994i	−0.0169424	+	0.499713i
$85$	0.0900212	+	0.155921i	0.00976417	+	0.0169120i
$86$	−3.20294	−	1.84922i	−0.345382	−	0.199406i
$87$	11.2051	+	7.87199i	1.20131	+	0.843966i
$88$	1.58727	+	2.74924i	0.169204	+	0.293070i
$89$	−2.91136	−	5.04262i	−0.308603	−	0.534516i	0.669454	−	0.742854i	$-0.266528\pi$
$89$	−2.91136	−	5.04262i	−0.308603	−	0.534516i	−0.978057	+	0.208337i	$0.933195\pi$
$90$	−2.29210	−	1.93553i	−0.241609	−	0.204023i
$91$	3.04699	+	4.66559i	0.319411	+	0.489087i
$92$	0.683360	+	0.394538i	0.0712452	+	0.0411335i
$93$	−1.49091	+	16.7401i	−0.154600	+	1.73587i
$94$		−	2.08361i		−	0.214908i
$95$		−	5.97640i		−	0.613166i
$96$	0.153652	−	1.72522i	0.0156820	−	0.176080i
$97$	3.79334	+	2.19008i	0.385155	+	0.222369i	0.680059	−	0.733158i	$-0.261954\pi$
$97$	3.79334	+	2.19008i	0.385155	+	0.222369i	−0.294904	+	0.955527i	$0.595288\pi$
$98$	−0.767563	−	6.95779i	−0.0775355	−	0.702843i
$99$	−8.95941	+	3.22932i	−0.900455	+	0.324558i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	8.45957	+	14.6524i	0.841759	+	1.45797i	0.888407	+	0.459057i	$0.151813\pi$
$101$	8.45957	+	14.6524i	0.841759	+	1.45797i	−0.0466478	+	0.998911i	$0.514854\pi$
$102$	−0.255167	−	0.179264i	−0.0252653	−	0.0177498i
$103$	4.59953	+	2.65554i	0.453205	+	0.261658i	0.709183	−	0.705025i	$-0.249064\pi$
$103$	4.59953	+	2.65554i	0.453205	+	0.261658i	−0.255978	+	0.966683i	$0.582397\pi$
$104$	−1.05309	−	1.82400i	−0.103264	−	0.178858i
$105$	3.88871	+	2.42445i	0.379499	+	0.236602i
$106$	0.353965	−	0.613086i	0.0343801	−	0.0595482i
$107$	−7.07344	+	4.08385i	−0.683816	+	0.394801i	−0.801291	−	0.598275i	$-0.795853\pi$
$107$	−7.07344	+	4.08385i	−0.683816	+	0.394801i	0.117476	+	0.993076i	$0.462520\pi$
$108$	5.01274	+	1.36835i	0.482352	+	0.131670i
$109$	−0.606828	+	1.05106i	−0.0581235	+	0.100673i	−0.893623	−	0.448818i	$-0.851845\pi$
$109$	−0.606828	+	1.05106i	−0.0581235	+	0.100673i	0.835500	+	0.549491i	$0.185178\pi$
$110$	3.17454			0.302681
$111$	−6.23173	−	13.4186i	−0.591490	−	1.27364i
$112$	0.145275	+	2.64176i	0.0137272	+	0.249623i
$113$	−1.23720	+	0.714296i	−0.116386	+	0.0671953i	−0.557063	−	0.830470i	$-0.688072\pi$
$113$	−1.23720	+	0.714296i	−0.116386	+	0.0671953i	0.440677	+	0.897666i	$0.354738\pi$
$114$	4.36005	+	9.38840i	0.408356	+	0.879304i
$115$	0.683360	−	0.394538i	0.0637237	−	0.0367909i
$116$	6.84694	+	3.95308i	0.635722	+	0.367034i
$117$	5.94419	−	2.14252i	0.549541	−	0.198076i
$118$		−	11.7733i		−	1.08382i
$119$	0.424984	+	0.215163i	0.0389583	+	0.0197240i
$120$	−1.41726	−	0.995677i	−0.129378	−	0.0908925i
$121$	−0.461135	+	0.798709i	−0.0419214	+	0.0726099i
$122$	2.89604			0.262195
$123$	8.54634	+	18.4026i	0.770597	+	1.65931i
$124$			9.70317i			0.871370i
$125$	1.00000			0.0894427
$126$	−7.87756	−	0.971608i	−0.701789	−	0.0865577i
$127$	−15.1021			−1.34010			−0.670048	−	0.742318i	$-0.733726\pi$
$127$	−15.1021			−1.34010			−0.670048	+	0.742318i	$0.733726\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.68245	−	5.24164i	0.324221	−	0.461501i
$130$	−2.10618			−0.184724
$131$	−4.19019	+	7.25762i	−0.366099	+	0.634101i	−0.988952	−	0.148237i	$-0.952640\pi$
$131$	−4.19019	+	7.25762i	−0.366099	+	0.634101i	0.622853	+	0.782339i	$0.285973\pi$
$132$	−4.98693	+	2.31597i	−0.434056	+	0.201579i
$133$	−8.64601	−	13.2389i	−0.749704	−	1.14796i
$134$			9.95697i			0.860151i
$135$	3.69140	−	3.65699i	0.317705	−	0.314743i
$136$	−0.155921	−	0.0900212i	−0.0133701	−	0.00771925i
$137$	7.58919	−	4.38162i	0.648388	−	0.374347i	−0.139450	−	0.990229i	$-0.544534\pi$
$137$	7.58919	−	4.38162i	0.648388	−	0.374347i	0.787838	+	0.615882i	$0.211200\pi$
$138$	−0.785665	+	1.11833i	−0.0668803	+	0.0951983i
$139$	−2.76711	+	1.59759i	−0.234704	+	0.135506i	−0.612740	−	0.790285i	$-0.709933\pi$
$139$	−2.76711	+	1.59759i	−0.234704	+	0.135506i	0.378036	+	0.925791i	$0.376599\pi$
$140$	2.36047	+	1.19507i	0.199496	+	0.101002i
$141$	3.59469	+	0.320150i	0.302728	+	0.0269615i
$142$	−10.1885			−0.854996
$143$	−3.34308	+	5.79038i	−0.279562	+	0.484216i
$144$	2.95278	+	0.530167i	0.246065	+	0.0441805i
$145$	6.84694	−	3.95308i	0.568607	−	0.328286i
$146$	2.93961	−	5.09156i	0.243284	−	0.421380i
$147$	12.1217	−	0.255140i	0.999779	−	0.0210436i
$148$	−4.27097	−	7.39754i	−0.351072	−	0.608074i
$149$	5.37389	+	3.10262i	0.440246	+	0.254176i	0.703702	−	0.710495i	$-0.251529\pi$
$149$	5.37389	+	3.10262i	0.440246	+	0.254176i	−0.263456	+	0.964671i	$0.584862\pi$
$150$	−1.57091	+	0.729545i	−0.128264	+	0.0595671i
$151$	−5.33037	−	9.23247i	−0.433779	−	0.751328i	0.563416	−	0.826174i	$-0.309487\pi$
$151$	−5.33037	−	9.23247i	−0.433779	−	0.751328i	−0.997195	+	0.0748455i	$0.976154\pi$
$152$	2.98820	+	5.17571i	0.242375	+	0.419806i
$153$	0.348477	−	0.412675i	0.0281727	−	0.0333628i
$154$	7.03223	−	4.59259i	0.566673	−	0.370081i
$155$	8.40319	+	4.85159i	0.674961	+	0.389689i
$156$	3.30862	−	1.53655i	0.264901	−	0.123022i
$157$		−	4.39858i		−	0.351045i	−0.984475	−	0.175523i	$-0.943839\pi$
$157$		−	4.39858i		−	0.351045i	0.984475	−	0.175523i	$-0.0561615\pi$
$158$			11.0054i			0.875539i
$159$	1.00332	+	0.704870i	0.0795686	+	0.0558999i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	0.943000	−	1.86259i	0.0743188	−	0.146793i
$162$	−3.13093	+	8.43785i	−0.245989	+	0.662940i
$163$	9.94559	+	17.2263i	0.778999	+	1.34927i	0.932519	+	0.361120i	$0.117606\pi$
$163$	9.94559	+	17.2263i	0.778999	+	1.34927i	−0.153520	+	0.988146i	$0.549061\pi$
$164$	5.85731	+	10.1452i	0.457379	+	0.792203i
$165$	−0.487774	+	5.47679i	−0.0379732	+	0.426368i
$166$	−7.64657	−	4.41475i	−0.593489	−	0.342651i
$167$	−7.13831	−	12.3639i	−0.552379	−	0.956749i	−0.998102	−	0.0615778i	$-0.980387\pi$
$167$	−7.13831	−	12.3639i	−0.552379	−	0.956749i	0.445723	−	0.895171i	$-0.352947\pi$
$168$	−4.57994	−	0.155279i	−0.353350	−	0.0119801i
$169$	−4.28201	+	7.41666i	−0.329385	+	0.570512i
$170$	−0.155921	+	0.0900212i	−0.0119586	+	0.00690431i
$171$	−16.8670	+	6.07951i	−1.28985	+	0.464912i
$172$	1.84922	−	3.20294i	0.141001	−	0.244222i
$173$	−13.2286			−1.00575			−0.502876	−	0.864359i	$-0.667725\pi$
$173$	−13.2286			−1.00575			−0.502876	+	0.864359i	$0.667725\pi$
$174$	−7.87199	+	11.2051i	−0.596774	+	0.849456i
$175$	2.21519	−	1.44669i	0.167453	−	0.109360i
$176$	−2.74924	+	1.58727i	−0.207231	+	0.119645i
$177$	20.3116	+	1.80899i	1.52671	+	0.135972i
$178$	5.04262	−	2.91136i	0.377960	−	0.218215i
$179$	−3.52462	−	2.03494i	−0.263442	−	0.152098i	0.362462	−	0.931999i	$-0.381936\pi$
$179$	−3.52462	−	2.03494i	−0.263442	−	0.152098i	−0.625904	+	0.779900i	$0.715270\pi$
$180$	1.93553	−	2.29210i	0.144266	−	0.170843i
$181$			21.7339i			1.61547i	0.589546	+	0.807735i	$0.299307\pi$
$181$			21.7339i			1.61547i	−0.589546	+	0.807735i	$0.700693\pi$
$182$	−4.66559	+	3.04699i	−0.345837	+	0.225858i
$183$	−0.444982	+	4.99632i	−0.0328940	+	0.369338i
$184$	−0.394538	+	0.683360i	−0.0290857	+	0.0503780i
$185$	−8.54194			−0.628016
$186$	−16.7401	−	1.49091i	−1.22745	−	0.109319i
$187$			0.571552i			0.0417961i
$188$	2.08361			0.151963
$189$	2.88664	−	13.4413i	0.209972	−	0.977707i
$190$	5.97640			0.433574
$191$			7.77914i			0.562878i	0.959579	+	0.281439i	$0.0908118\pi$
$191$			7.77914i			0.562878i	−0.959579	+	0.281439i	$0.909188\pi$
$192$	1.72522	+	0.153652i	0.124507	+	0.0110889i
$193$	8.29363			0.596988			0.298494	−	0.954411i	$-0.403516\pi$
$193$	8.29363			0.596988			0.298494	+	0.954411i	$0.403516\pi$
$194$	−2.19008	+	3.79334i	−0.157239	+	0.272346i
$195$	0.323618	−	3.63362i	0.0231747	−	0.260209i
$196$	6.95779	−	0.767563i	0.496985	−	0.0548259i
$197$		−	13.3008i		−	0.947643i	−0.880621	−	0.473822i	$-0.842874\pi$
$197$		−	13.3008i		−	0.947643i	0.880621	−	0.473822i	$-0.157126\pi$
$198$	−3.22932	−	8.95941i	−0.229497	−	0.636718i
$199$	−16.1833	−	9.34343i	−1.14720	−	0.662338i	−0.198999	−	0.980000i	$-0.563769\pi$
$199$	−16.1833	−	9.34343i	−1.14720	−	0.662338i	−0.948204	+	0.317661i	$0.897102\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−17.1780	−	1.52990i	−1.21164	−	0.107911i
$202$	−14.6524	+	8.45957i	−1.03094	+	0.595213i
$203$	9.44841	−	18.6623i	0.663148	−	1.30983i
$204$	0.179264	−	0.255167i	0.0125510	−	0.0178653i
$205$	11.7146			0.818184
$206$	−2.65554	+	4.59953i	−0.185020	+	0.320464i
$207$	−1.80864	−	1.52728i	−0.125709	−	0.106153i
$208$	1.82400	−	1.05309i	0.126472	−	0.0730185i
$209$	9.48617	−	16.4305i	0.656172	−	1.13652i
$210$	−2.42445	+	3.88871i	−0.167303	+	0.268346i
$211$	−12.1577	−	21.0578i	−0.836971	−	1.44968i	−0.892416	−	0.451214i	$-0.850991\pi$
$211$	−12.1577	−	21.0578i	−0.836971	−	1.44968i	0.0554450	−	0.998462i	$-0.482342\pi$
$212$	0.613086	+	0.353965i	0.0421069	+	0.0243104i
$213$	1.56547	−	17.5773i	0.107264	−	1.20438i
$214$	−4.08385	−	7.07344i	−0.279167	−	0.483531i
$215$	−1.84922	−	3.20294i	−0.126116	−	0.218439i
$216$	−1.36835	+	5.01274i	−0.0931048	+	0.341074i
$217$	25.6334	−	1.40963i	1.74011	−	0.0956917i
$218$	−1.05106	−	0.606828i	−0.0711865	−	0.0410996i
$219$	8.33239	+	5.85381i	0.563051	+	0.395564i
$220$			3.17454i			0.214028i
$221$		−	0.379201i		−	0.0255078i
$222$	13.4186	−	6.23173i	0.900600	−	0.418246i
$223$	14.5348	+	8.39165i	0.973320	+	0.561946i	0.900247	−	0.435380i	$-0.143386\pi$
$223$	14.5348	+	8.39165i	0.973320	+	0.561946i	0.0730731	+	0.997327i	$0.476719\pi$
$224$	−2.64176	+	0.145275i	−0.176510	+	0.00970659i
$225$	−1.01725	−	2.82227i	−0.0678169	−	0.188151i
$226$	−0.714296	−	1.23720i	−0.0475143	−	0.0822971i
$227$	8.39567	+	14.5417i	0.557240	+	0.965168i	0.997725	+	0.0674083i	$0.0214730\pi$
$227$	8.39567	+	14.5417i	0.557240	+	0.965168i	−0.440485	+	0.897760i	$0.645194\pi$
$228$	−9.38840	+	4.36005i	−0.621762	+	0.288751i
$229$	−5.74293	−	3.31568i	−0.379503	−	0.219106i	0.298099	−	0.954535i	$-0.403648\pi$
$229$	−5.74293	−	3.31568i	−0.379503	−	0.219106i	−0.677602	+	0.735429i	$0.736981\pi$
$230$	0.394538	+	0.683360i	0.0260151	+	0.0450594i
$231$	6.84272	+	12.8378i	0.450218	+	0.844666i
$232$	−3.95308	+	6.84694i	−0.259533	+	0.449524i
$233$	−6.79700	+	3.92425i	−0.445286	+	0.257086i	−0.705837	−	0.708374i	$-0.749429\pi$
$233$	−6.79700	+	3.92425i	−0.445286	+	0.257086i	0.260551	+	0.965460i	$0.416096\pi$
$234$	2.14252	+	5.94419i	0.140061	+	0.388584i
$235$	1.04181	−	1.80446i	0.0679599	−	0.117710i
$236$	11.7733			0.766377
$237$	−18.9867	−	1.69099i	−1.23332	−	0.109842i
$238$	−0.215163	+	0.424984i	−0.0139469	+	0.0275476i
$239$	−14.3341	+	8.27578i	−0.927195	+	0.535316i	−0.885923	−	0.463832i	$-0.846474\pi$
$239$	−14.3341	+	8.27578i	−0.927195	+	0.535316i	−0.0412714	+	0.999148i	$0.513141\pi$
$240$	0.995677	−	1.41726i	0.0642707	−	0.0914838i
$241$	16.6800	−	9.63020i	1.07445	−	0.620336i	0.145058	−	0.989423i	$-0.453663\pi$
$241$	16.6800	−	9.63020i	1.07445	−	0.620336i	0.929395	+	0.369087i	$0.120330\pi$
$242$	−0.798709	−	0.461135i	−0.0513430	−	0.0296429i
$243$	−14.0761	−	6.69804i	−0.902981	−	0.429680i
$244$			2.89604i			0.185400i
$245$	2.81417	−	6.40940i	0.179791	−	0.409482i
$246$	−18.4026	+	8.54634i	−1.17331	+	0.544895i
$247$	−6.29368	+	10.9010i	−0.400457	+	0.693612i
$248$	−9.70317			−0.616152
$249$	8.79133	−	12.5137i	0.557128	−	0.793023i
$250$			1.00000i			0.0632456i
$251$	22.0186			1.38980			0.694901	−	0.719105i	$-0.255448\pi$
$251$	22.0186			1.38980			0.694901	+	0.719105i	$0.255448\pi$
$252$	0.971608	−	7.87756i	0.0612055	−	0.496240i
$253$	2.50496			0.157485
$254$		−	15.1021i		−	0.947590i
$255$	−0.131349	−	0.282831i	−0.00822539	−	0.0177115i
$256$	1.00000			0.0625000
$257$	−10.4221	+	18.0516i	−0.650112	+	1.12603i	0.332984	+	0.942933i	$0.391945\pi$
$257$	−10.4221	+	18.0516i	−0.650112	+	1.12603i	−0.983095	+	0.183094i	$0.941389\pi$
$258$	5.24164	+	3.68245i	0.326331	+	0.229259i
$259$	−18.9221	+	12.3576i	−1.17576	+	0.767861i
$260$		−	2.10618i		−	0.130620i
$261$	−18.1217	−	15.3026i	−1.12171	−	0.947208i
$262$	−7.25762	−	4.19019i	−0.448377	−	0.258871i
$263$	−19.5177	+	11.2685i	−1.20351	+	0.694847i	−0.961334	−	0.275385i	$-0.911195\pi$
$263$	−19.5177	+	11.2685i	−1.20351	+	0.694847i	−0.242177	+	0.970232i	$0.577861\pi$
$264$	−2.31597	−	4.98693i	−0.142538	−	0.306924i
$265$	0.613086	−	0.353965i	0.0376616	−	0.0217439i
$266$	13.2389	−	8.64601i	0.811728	−	0.530121i
$267$	4.24793	+	9.14697i	0.259969	+	0.559785i
$268$	−9.95697			−0.608219
$269$	11.8691	−	20.5578i	0.723670	−	1.25343i	−0.235849	−	0.971790i	$-0.575787\pi$
$269$	11.8691	−	20.5578i	0.723670	−	1.25343i	0.959519	−	0.281643i	$-0.0908794\pi$
$270$	3.65699	+	3.69140i	0.222557	+	0.224652i
$271$	−10.2170	+	5.89877i	−0.620636	+	0.358325i	−0.777117	−	0.629356i	$-0.783319\pi$
$271$	−10.2170	+	5.89877i	−0.620636	+	0.358325i	0.156480	+	0.987681i	$0.449985\pi$
$272$	0.0900212	−	0.155921i	0.00545834	−	0.00945412i
$273$	−4.53986	−	8.51735i	−0.274765	−	0.515494i
$274$	4.38162	+	7.58919i	0.264703	+	0.458480i
$275$	2.74924	+	1.58727i	0.165785	+	0.0957161i
$276$	−1.11833	−	0.785665i	−0.0673154	−	0.0472915i
$277$	9.15321	+	15.8538i	0.549963	+	0.952564i	0.998276	+	0.0586874i	$0.0186915\pi$
$277$	9.15321	+	15.8538i	0.549963	+	0.952564i	−0.448313	+	0.893876i	$0.647975\pi$
$278$	−1.59759	−	2.76711i	−0.0958173	−	0.165960i
$279$	5.14430	−	28.6514i	0.307981	−	1.71531i
$280$	−1.19507	+	2.36047i	−0.0714190	+	0.141065i
$281$	18.8875	+	10.9047i	1.12674	+	0.650521i	0.943112	−	0.332475i	$-0.107884\pi$
$281$	18.8875	+	10.9047i	1.12674	+	0.650521i	0.183624	+	0.982997i	$0.441217\pi$
$282$	−0.320150	+	3.59469i	−0.0190647	+	0.214061i
$283$			1.51803i			0.0902374i	0.998982	+	0.0451187i	$0.0143666\pi$
$283$			1.51803i			0.0902374i	−0.998982	+	0.0451187i	$0.985633\pi$
$284$		−	10.1885i		−	0.604574i
$285$	−0.918284	+	10.3106i	−0.0543944	+	0.610748i
$286$	−5.79038	−	3.34308i	−0.342392	−	0.197680i
$287$	25.9501	−	16.9474i	1.53179	−	1.00038i
$288$	−0.530167	+	2.95278i	−0.0312404	+	0.173994i
$289$	8.48379	+	14.6944i	0.499047	+	0.864374i
$290$	3.95308	+	6.84694i	0.232133	+	0.402066i
$291$	−6.20784	−	4.36123i	−0.363910	−	0.255660i
$292$	5.09156	+	2.93961i	0.297961	+	0.172028i
$293$	−2.79327	−	4.83808i	−0.163184	−	0.282643i	0.772825	−	0.634620i	$-0.218843\pi$
$293$	−2.79327	−	4.83808i	−0.163184	−	0.282643i	−0.936009	+	0.351976i	$0.885510\pi$
$294$	0.255140	+	12.1217i	0.0148801	+	0.706950i
$295$	5.88665	−	10.1960i	0.342734	−	0.593633i
$296$	7.39754	−	4.27097i	0.429973	−	0.248245i
$297$	15.9532	−	4.19466i	0.925697	−	0.243399i
$298$	−3.10262	+	5.37389i	−0.179730	+	0.311301i
$299$	−1.66193			−0.0961121
$300$	−0.729545	−	1.57091i	−0.0421203	−	0.0906966i
$301$	−8.73004	−	4.41988i	−0.503191	−	0.254758i
$302$	9.23247	−	5.33037i	0.531269	−	0.306728i
$303$	−12.3433	−	26.5785i	−0.709102	−	1.52689i
$304$	−5.17571	+	2.98820i	−0.296848	+	0.171385i
$305$	2.50805	+	1.44802i	0.143610	+	0.0829134i
$306$	0.412675	+	0.348477i	0.0235911	+	0.0199211i
$307$		−	22.8941i		−	1.30663i	−0.757085	−	0.653316i	$-0.773377\pi$
$307$		−	22.8941i		−	1.30663i	0.757085	−	0.653316i	$-0.226623\pi$
$308$	4.59259	+	7.03223i	0.261687	+	0.400698i
$309$	−7.52718	−	5.28812i	−0.428206	−	0.300831i
$310$	−4.85159	+	8.40319i	−0.275552	+	0.477269i
$311$	21.7317			1.23229			0.616146	−	0.787632i	$-0.288693\pi$
$311$	21.7317			1.23229			0.616146	+	0.787632i	$0.288693\pi$
$312$	1.53655	+	3.30862i	0.0869900	+	0.187314i
$313$			3.13232i			0.177049i	0.996074	+	0.0885247i	$0.0282152\pi$
$313$			3.13232i			0.177049i	−0.996074	+	0.0885247i	$0.971785\pi$
$314$	4.39858			0.248226
$315$	−6.33636	−	4.78022i	−0.357014	−	0.269335i
$316$	−11.0054			−0.619099
$317$		−	28.6867i		−	1.61120i	−0.592457	−	0.805602i	$-0.701842\pi$
$317$		−	28.6867i		−	1.61120i	0.592457	−	0.805602i	$-0.298158\pi$
$318$	−0.704870	+	1.00332i	−0.0395272	+	0.0562635i
$319$	25.0985			1.40524
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	12.8308	−	5.95871i	0.716143	−	0.332583i
$322$	1.86259	+	0.943000i	0.103798	+	0.0525513i
$323$			1.07601i			0.0598705i
$324$	−8.43785	−	3.13093i	−0.468769	−	0.173941i
$325$	−1.82400	−	1.05309i	−0.101177	−	0.0584148i
$326$	−17.2263	+	9.94559i	−0.954075	+	0.550836i
$327$	1.20841	−	1.72007i	0.0668252	−	0.0951198i
$328$	−10.1452	+	5.85731i	−0.560172	+	0.323416i
$329$	−0.302696	−	5.50440i	−0.0166882	−	0.303467i
$330$	−5.47679	−	0.487774i	−0.301488	−	0.0268511i
$331$	−5.70943			−0.313819			−0.156909	−	0.987613i	$-0.550153\pi$
$331$	−5.70943			−0.313819			−0.156909	+	0.987613i	$0.550153\pi$
$332$	4.41475	−	7.64657i	0.242291	−	0.419660i
$333$	8.68932	+	24.1077i	0.476172	+	1.32109i
$334$	12.3639	−	7.13831i	0.676523	−	0.390591i
$335$	−4.97848	+	8.62299i	−0.272004	+	0.471124i
$336$	0.155279	−	4.57994i	0.00847119	−	0.249856i
$337$	5.41618	+	9.38110i	0.295038	+	0.511021i	0.974994	−	0.222232i	$-0.0713343\pi$
$337$	5.41618	+	9.38110i	0.295038	+	0.511021i	−0.679956	+	0.733253i	$0.738001\pi$
$338$	−7.41666	−	4.28201i	−0.403413	−	0.232911i
$339$	2.24419	−	1.04222i	0.121888	−	0.0566057i
$340$	−0.0900212	−	0.155921i	−0.00488208	−	0.00845602i
$341$	15.4016	+	26.6763i	0.834042	+	1.44460i
$342$	−6.07951	−	16.8670i	−0.328742	−	0.912063i
$343$	−3.03851	−	18.2693i	−0.164064	−	0.986450i
$344$	3.20294	+	1.84922i	0.172691	+	0.0997031i
$345$	−1.23957	+	0.575667i	−0.0667362	+	0.0309928i
$346$		−	13.2286i		−	0.711174i
$347$		−	19.3689i		−	1.03978i	−0.854234	−	0.519889i	$-0.825973\pi$
$347$		−	19.3689i		−	1.03978i	0.854234	−	0.519889i	$-0.174027\pi$
$348$	−11.2051	−	7.87199i	−0.600656	−	0.421983i
$349$	−17.1942	−	9.92710i	−0.920387	−	0.531385i	−0.0366282	−	0.999329i	$-0.511662\pi$
$349$	−17.1942	−	9.92710i	−0.920387	−	0.531385i	−0.883758	+	0.467944i	$0.844995\pi$
$350$	1.44669	+	2.21519i	0.0773289	+	0.118407i
$351$	−10.5843	+	2.78298i	−0.564946	+	0.148544i
$352$	−1.58727	−	2.74924i	−0.0846019	−	0.146535i
$353$	5.74699	+	9.95408i	0.305881	+	0.529802i	0.977457	−	0.211134i	$-0.0677155\pi$
$353$	5.74699	+	9.95408i	0.305881	+	0.529802i	−0.671576	+	0.740936i	$0.734382\pi$
$354$	−1.80899	+	20.3116i	−0.0961466	+	1.07955i
$355$	−8.82346	−	5.09423i	−0.468301	−	0.270374i
$356$	2.91136	+	5.04262i	0.154302	+	0.267258i
$357$	−0.700132	−	0.436503i	−0.0370549	−	0.0231022i
$358$	2.03494	−	3.52462i	0.107550	−	0.186282i
$359$	19.1794	−	11.0732i	1.01225	−	0.584422i	0.100400	−	0.994947i	$-0.467988\pi$
$359$	19.1794	−	11.0732i	1.01225	−	0.584422i	0.911849	+	0.410525i	$0.134654\pi$
$360$	2.29210	+	1.93553i	0.120804	+	0.102011i
$361$	8.35868	−	14.4777i	0.439930	−	0.761982i
$362$	−21.7339			−1.14231
$363$	0.918283	−	1.30710i	0.0481974	−	0.0686048i
$364$	−3.04699	−	4.66559i	−0.159706	−	0.244543i
$365$	5.09156	−	2.93961i	0.266504	−	0.153866i
$366$	−4.99632	−	0.444982i	−0.261162	−	0.0232596i
$367$	−17.4441	+	10.0714i	−0.910577	+	0.525722i	−0.880617	−	0.473829i	$-0.842871\pi$
$367$	−17.4441	+	10.0714i	−0.910577	+	0.525722i	−0.0299604	+	0.999551i	$0.509538\pi$
$368$	−0.683360	−	0.394538i	−0.0356226	−	0.0205667i
$369$	−11.9167	−	33.0618i	−0.620360	−	1.72113i
$370$		−	8.54194i		−	0.444074i
$371$	0.846025	−	1.67105i	0.0439234	−	0.0867565i
$372$	1.49091	−	16.7401i	0.0773000	−	0.867935i
$373$	−13.6455	+	23.6347i	−0.706538	+	1.22376i	0.259596	+	0.965717i	$0.416411\pi$
$373$	−13.6455	+	23.6347i	−0.706538	+	1.22376i	−0.966134	+	0.258042i	$0.916923\pi$
$374$	−0.571552			−0.0295543
$375$	−1.72522	−	0.153652i	−0.0890901	−	0.00793454i
$376$			2.08361i			0.107454i
$377$	−16.6518			−0.857610
$378$	13.4413	+	2.88664i	0.691344	+	0.148473i
$379$	−19.6022			−1.00690			−0.503448	−	0.864026i	$-0.667935\pi$
$379$	−19.6022			−1.00690			−0.503448	+	0.864026i	$0.667935\pi$
$380$			5.97640i			0.306583i
$381$	26.0545	+	2.32046i	1.33481	+	0.118881i
$382$	−7.77914			−0.398015
$383$	−1.98579	+	3.43949i	−0.101469	+	0.175750i	−0.912290	−	0.409544i	$-0.865688\pi$
$383$	−1.98579	+	3.43949i	−0.101469	+	0.175750i	0.810821	+	0.585294i	$0.199021\pi$
$384$	−0.153652	+	1.72522i	−0.00784100	+	0.0880399i
$385$	8.38638	−	0.461181i	0.427410	−	0.0235040i
$386$			8.29363i			0.422134i
$387$	−7.15843	+	8.47719i	−0.363883	+	0.430920i
$388$	−3.79334	−	2.19008i	−0.192577	−	0.111185i
$389$	−16.3614	+	9.44628i	−0.829558	+	0.478945i	−0.853701	−	0.520763i	$-0.825647\pi$
$389$	−16.3614	+	9.44628i	−0.829558	+	0.478945i	0.0241434	+	0.999709i	$0.492314\pi$
$390$	3.63362	+	0.323618i	0.183996	+	0.0163870i
$391$	−0.123034	+	0.0710336i	−0.00622209	+	0.00359232i
$392$	0.767563	+	6.95779i	0.0387678	+	0.351421i
$393$	8.34415	−	11.8772i	0.420907	−	0.599124i
$394$	13.3008			0.670085
$395$	−5.50268	+	9.53091i	−0.276870	+	0.479552i
$396$	8.95941	−	3.22932i	0.450227	−	0.162279i
$397$	−30.5990	+	17.6664i	−1.53572	+	0.886649i	−0.536640	+	0.843812i	$0.680307\pi$
$397$	−30.5990	+	17.6664i	−1.53572	+	0.886649i	−0.999082	+	0.0428377i	$0.986360\pi$
$398$	9.34343	−	16.1833i	0.468344	−	0.811195i
$399$	12.8821	+	24.1685i	0.644912	+	1.20994i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	0.539822	+	0.311666i	0.0269574	+	0.0155639i	0.513418	−	0.858139i	$-0.328379\pi$
$401$	0.539822	+	0.311666i	0.0269574	+	0.0155639i	−0.486461	+	0.873702i	$0.661712\pi$
$402$	1.52990	−	17.1780i	0.0763047	−	0.856760i
$403$	−10.2183	−	17.6986i	−0.509010	−	0.881630i
$404$	−8.45957	−	14.6524i	−0.420879	−	0.728984i
$405$	−6.93039	+	5.74192i	−0.344374	+	0.285318i
$406$	18.6623	+	9.44841i	0.926192	+	0.468916i
$407$	−23.4838	−	13.5584i	−1.16405	−	0.672064i
$408$	0.255167	+	0.179264i	0.0126326	+	0.00887490i
$409$			1.39035i			0.0687483i	0.999409	+	0.0343741i	$0.0109438\pi$
$409$			1.39035i			0.0687483i	−0.999409	+	0.0343741i	$0.989056\pi$
$410$			11.7146i			0.578544i
$411$	−13.7663	+	6.39318i	−0.679040	+	0.315352i
$412$	−4.59953	−	2.65554i	−0.226603	−	0.130829i
$413$	−1.71037	−	31.1023i	−0.0841616	−	1.53044i
$414$	1.52728	−	1.80864i	0.0750617	−	0.0888900i
$415$	−4.41475	−	7.64657i	−0.216711	−	0.375355i
$416$	1.05309	+	1.82400i	0.0516319	+	0.0894291i
$417$	5.01936	−	2.33103i	0.245799	−	0.114151i
$418$	16.4305	+	9.48617i	0.803644	+	0.463984i
$419$	13.7784	+	23.8650i	0.673121	+	1.16588i	0.977014	+	0.213174i	$0.0683800\pi$
$419$	13.7784	+	23.8650i	0.673121	+	1.16588i	−0.303893	+	0.952706i	$0.598287\pi$
$420$	−3.88871	−	2.42445i	−0.189750	−	0.118301i
$421$	−17.1806	+	29.7576i	−0.837331	+	1.45030i	0.0547882	+	0.998498i	$0.482552\pi$
$421$	−17.1806	+	29.7576i	−0.837331	+	1.45030i	−0.892119	+	0.451801i	$0.850782\pi$
$422$	21.0578	−	12.1577i	1.02508	−	0.591828i
$423$	−6.15245	−	1.10466i	−0.299142	−	0.0537104i
$424$	−0.353965	+	0.613086i	−0.0171901	+	0.0297741i
$425$	−0.180042			−0.00873334
$426$	17.5773	+	1.56547i	0.851625	+	0.0758474i
$427$	7.65065	−	0.420722i	0.370241	−	0.0203602i
$428$	7.07344	−	4.08385i	0.341908	−	0.197401i
$429$	6.65725	−	9.47602i	0.321415	−	0.457506i
$430$	3.20294	−	1.84922i	0.154459	−	0.0891772i
$431$	−24.3620	−	14.0654i	−1.17348	−	0.677508i	−0.218981	−	0.975729i	$-0.570273\pi$
$431$	−24.3620	−	14.0654i	−1.17348	−	0.677508i	−0.954497	+	0.298221i	$0.903607\pi$
$432$	−5.01274	−	1.36835i	−0.241176	−	0.0658350i
$433$			11.9782i			0.575635i	0.957685	+	0.287817i	$0.0929296\pi$
$433$			11.9782i			0.575635i	−0.957685	+	0.287817i	$0.907070\pi$
$434$	1.40963	+	25.6334i	0.0676643	+	1.23044i
$435$	−12.4199	+	5.76790i	−0.595488	+	0.276550i
$436$	0.606828	−	1.05106i	0.0290618	−	0.0503365i
$437$	4.71584			0.225589
$438$	−5.85381	+	8.33239i	−0.279706	+	0.398137i
$439$		−	10.8588i		−	0.518264i	−0.965842	−	0.259132i	$-0.916564\pi$
$439$		−	10.8588i		−	0.518264i	0.965842	−	0.259132i	$-0.0834364\pi$
$440$	−3.17454			−0.151340
$441$	−20.9518	−	1.42234i	−0.997704	−	0.0677306i
$442$	0.379201			0.0180368
$443$			2.11680i			0.100572i	0.998735	+	0.0502862i	$0.0160134\pi$
$443$			2.11680i			0.100572i	−0.998735	+	0.0502862i	$0.983987\pi$
$444$	6.23173	+	13.4186i	0.295745	+	0.636821i
$445$	5.82271			0.276023
$446$	−8.39165	+	14.5348i	−0.397356	+	0.688241i
$447$	−8.79443	−	6.17841i	−0.415962	−	0.292229i
$448$	−0.145275	−	2.64176i	−0.00686359	−	0.124811i
$449$		−	12.2537i		−	0.578290i	−0.957285	−	0.289145i	$-0.906629\pi$
$449$		−	12.2537i		−	0.578290i	0.957285	−	0.289145i	$-0.0933710\pi$
$450$	2.82227	−	1.01725i	0.133043	−	0.0479538i
$451$	32.2062	+	18.5943i	1.51653	+	0.875571i
$452$	1.23720	−	0.714296i	0.0581928	−	0.0335976i
$453$	7.77749	+	16.7471i	0.365418	+	0.786847i
$454$	−14.5417	+	8.39567i	−0.682477	+	0.394028i
$455$	−5.56401	+	0.305975i	−0.260845	+	0.0143443i
$456$	−4.36005	−	9.38840i	−0.204178	−	0.439652i
$457$	−33.1134			−1.54898			−0.774490	−	0.632586i	$-0.781994\pi$
$457$	−33.1134			−1.54898			−0.774490	+	0.632586i	$0.781994\pi$
$458$	3.31568	−	5.74293i	0.154932	−	0.268349i
$459$	−0.664609	+	0.658412i	−0.0310213	+	0.0307321i
$460$	−0.683360	+	0.394538i	−0.0318618	+	0.0183954i
$461$	−14.1222	+	24.4604i	−0.657737	+	1.13923i	0.323463	+	0.946241i	$0.395153\pi$
$461$	−14.1222	+	24.4604i	−0.657737	+	1.13923i	−0.981200	+	0.192994i	$0.938180\pi$
$462$	−12.8378	+	6.84272i	−0.597269	+	0.318352i
$463$	20.1122	+	34.8353i	0.934692	+	1.61893i	0.775181	+	0.631739i	$0.217658\pi$
$463$	20.1122	+	34.8353i	0.934692	+	1.61893i	0.159511	+	0.987196i	$0.449008\pi$
$464$	−6.84694	−	3.95308i	−0.317861	−	0.183517i
$465$	−13.7519	−	9.66123i	−0.637730	−	0.448029i
$466$	−3.92425	−	6.79700i	−0.181787	−	0.314865i
$467$	0.824539	+	1.42814i	0.0381551	+	0.0660866i	0.884472	−	0.466593i	$-0.154519\pi$
$467$	0.824539	+	1.42814i	0.0381551	+	0.0660866i	−0.846317	+	0.532679i	$0.821185\pi$
$468$	−5.94419	+	2.14252i	−0.274770	+	0.0990378i
$469$	1.44650	+	26.3039i	0.0667930	+	1.21460i
$470$	1.80446	+	1.04181i	0.0832335	+	0.0480549i
$471$	−0.675850	+	7.58853i	−0.0311415	+	0.349661i
$472$			11.7733i			0.541910i
$473$		−	11.7408i		−	0.539845i
$474$	1.69099	−	18.9867i	0.0776698	−	0.872087i
$475$	5.17571	+	2.98820i	0.237478	+	0.137108i
$476$	−0.424984	−	0.215163i	−0.0194791	−	0.00986198i
$477$	−1.62265	−	1.37022i	−0.0742960	−	0.0627381i
$478$	−8.27578	−	14.3341i	−0.378526	−	0.655626i
$479$	14.1267	+	24.4682i	0.645467	+	1.11798i	0.984193	+	0.177097i	$0.0566707\pi$
$479$	14.1267	+	24.4682i	0.645467	+	1.11798i	−0.338726	+	0.940885i	$0.609996\pi$
$480$	1.41726	+	0.995677i	0.0646888	+	0.0454462i
$481$	15.5805	+	8.99542i	0.710411	+	0.410156i
$482$	9.63020	+	16.6800i	0.438644	+	0.759753i
$483$	−1.91307	+	3.06849i	−0.0870479	+	0.139621i
$484$	0.461135	−	0.798709i	0.0209607	−	0.0363050i
$485$	−3.79334	+	2.19008i	−0.172246	+	0.0994465i
$486$	6.69804	−	14.0761i	0.303829	−	0.638504i
$487$	−3.70797	+	6.42239i	−0.168024	+	0.291026i	−0.937725	−	0.347378i	$-0.887072\pi$
$487$	−3.70797	+	6.42239i	−0.168024	+	0.291026i	0.769701	+	0.638405i	$0.220405\pi$
$488$	−2.89604			−0.131098
$489$	−14.5115	−	31.2473i	−0.656233	−	1.41305i
$490$	6.40940	+	2.81417i	0.289547	+	0.127131i
$491$	20.6718	−	11.9348i	0.932904	−	0.538612i	0.0451748	−	0.998979i	$-0.485616\pi$
$491$	20.6718	−	11.9348i	0.932904	−	0.538612i	0.887729	+	0.460367i	$0.152282\pi$
$492$	−8.54634	−	18.4026i	−0.385299	−	0.829655i
$493$	−1.23274	+	0.711722i	−0.0555198	+	0.0320544i
$494$	−10.9010	−	6.29368i	−0.490458	−	0.283166i
$495$	1.68304	−	9.37374i	0.0756469	−	0.421318i
$496$		−	9.70317i		−	0.435685i
$497$	−26.9155	+	1.48013i	−1.20732	+	0.0663927i
$498$	12.5137	+	8.79133i	0.560752	+	0.393949i
$499$	3.98294	−	6.89865i	0.178301	−	0.308826i	−0.762998	−	0.646401i	$-0.776273\pi$
$499$	3.98294	−	6.89865i	0.178301	−	0.308826i	0.941299	+	0.337575i	$0.109607\pi$
$500$	−1.00000			−0.0447214
$501$	10.4154	+	22.4273i	0.465327	+	1.00198i
$502$			22.0186i			0.982738i
$503$	39.3978			1.75666			0.878332	−	0.478052i	$-0.158657\pi$
$503$	39.3978			1.75666			0.878332	+	0.478052i	$0.158657\pi$
$504$	7.87756	+	0.971608i	0.350894	+	0.0432788i
$505$	−16.9191			−0.752892
$506$			2.50496i			0.111359i
$507$	8.52700	−	12.1374i	0.378697	−	0.539043i
$508$	15.1021			0.670048
$509$	1.13505	−	1.96596i	0.0503102	−	0.0871399i	−0.839774	−	0.542937i	$-0.817312\pi$
$509$	1.13505	−	1.96596i	0.0503102	−	0.0871399i	0.890084	+	0.455797i	$0.150646\pi$
$510$	0.282831	−	0.131349i	0.0125240	−	0.00581623i
$511$	7.02607	−	13.8777i	0.310815	−	0.613914i
$512$			1.00000i			0.0441942i
$513$	30.0334	−	7.89687i	1.32601	−	0.348655i
$514$	−18.0516	−	10.4221i	−0.796221	−	0.459698i
$515$	−4.59953	+	2.65554i	−0.202679	+	0.117017i
$516$	−3.68245	+	5.24164i	−0.162111	+	0.230751i
$517$	5.72834	−	3.30726i	0.251932	−	0.145453i
$518$	−12.3576	−	18.9221i	−0.542960	−	0.831388i
$519$	22.8223	+	2.03260i	1.00179	+	0.0892211i
$520$	2.10618			0.0923620
$521$	−9.24087	+	16.0057i	−0.404850	+	0.701221i	−0.994304	−	0.106581i	$-0.966010\pi$
$521$	−9.24087	+	16.0057i	−0.404850	+	0.701221i	0.589454	+	0.807802i	$0.299343\pi$
$522$	15.3026	−	18.1217i	0.669777	−	0.793167i
$523$	−30.9554	+	17.8721i	−1.35359	+	0.781493i	−0.988750	−	0.149578i	$-0.952208\pi$
$523$	−30.9554	+	17.8721i	−1.35359	+	0.781493i	−0.364836	+	0.931072i	$0.618875\pi$
$524$	4.19019	−	7.25762i	0.183049	−	0.317051i
$525$	−4.04399	+	2.15550i	−0.176494	+	0.0940736i
$526$	−11.2685	−	19.5177i	−0.491331	−	0.851011i
$527$	−1.51293	−	0.873491i	−0.0659043	−	0.0380499i
$528$	4.98693	−	2.31597i	0.217028	−	0.100790i
$529$	−11.1887	−	19.3794i	−0.486464	−	0.842581i
$530$	0.353965	+	0.613086i	0.0153753	+	0.0266307i
$531$	−34.7640	−	6.24181i	−1.50863	−	0.270872i
$532$	8.64601	+	13.2389i	0.374852	+	0.573978i
$533$	−21.3675	−	12.3365i	−0.925529	−	0.534354i
$534$	−9.14697	+	4.24793i	−0.395828	+	0.183826i
$535$		−	8.16771i		−	0.353121i
$536$		−	9.95697i		−	0.430075i
$537$	5.76808	+	4.05229i	0.248911	+	0.174869i
$538$	20.5578	+	11.8691i	0.886311	+	0.511712i
$539$	17.9103	−	13.1541i	0.771450	−	0.566588i
$540$	−3.69140	+	3.65699i	−0.158853	+	0.157372i
$541$	5.94967	+	10.3051i	0.255796	+	0.443052i	0.965111	−	0.261839i	$-0.0843291\pi$
$541$	5.94967	+	10.3051i	0.255796	+	0.443052i	−0.709315	+	0.704891i	$0.750996\pi$
$542$	−5.89877	−	10.2170i	−0.253374	−	0.438856i
$543$	3.33945	−	37.4958i	0.143310	−	1.60910i
$544$	0.155921	+	0.0900212i	0.00668507	+	0.00385963i
$545$	−0.606828	−	1.05106i	−0.0259936	−	0.0450223i
$546$	8.51735	−	4.53986i	0.364509	−	0.194288i
$547$	7.70794	−	13.3505i	0.329568	−	0.570828i	−0.652858	−	0.757480i	$-0.726430\pi$
$547$	7.70794	−	13.3505i	0.329568	−	0.570828i	0.982426	+	0.186652i	$0.0597637\pi$
$548$	−7.58919	+	4.38162i	−0.324194	+	0.187174i
$549$	1.53538	−	8.55138i	0.0655286	−	0.364964i
$550$	−1.58727	+	2.74924i	−0.0676815	+	0.117228i
$551$	47.2504			2.01293
$552$	0.785665	−	1.11833i	0.0334401	−	0.0475991i
$553$	1.59880	+	29.0735i	0.0679879	+	1.23633i
$554$	−15.8538	+	9.15321i	−0.673564	+	0.388883i
$555$	14.7367	+	1.31248i	0.625540	+	0.0557118i
$556$	2.76711	−	1.59759i	0.117352	−	0.0677531i
$557$	−14.4583	−	8.34752i	−0.612619	−	0.353696i	0.161371	−	0.986894i	$-0.448408\pi$
$557$	−14.4583	−	8.34752i	−0.612619	−	0.353696i	−0.773990	+	0.633198i	$0.781742\pi$
$558$	28.6514	+	5.14430i	1.21291	+	0.217775i
$559$			7.78956i			0.329463i
$560$	−2.36047	−	1.19507i	−0.0997480	−	0.0505008i
$561$	0.0878200	−	0.986055i	0.00370776	−	0.0416313i
$562$	−10.9047	+	18.8875i	−0.459988	+	0.796723i
$563$	29.4425			1.24085			0.620427	−	0.784265i	$-0.286959\pi$
$563$	29.4425			1.24085			0.620427	+	0.784265i	$0.286959\pi$
$564$	−3.59469	−	0.320150i	−0.151364	−	0.0134808i
$565$		−	1.42859i		−	0.0601013i
$566$	−1.51803			−0.0638075
$567$	−7.04537	+	22.7456i	−0.295878	+	0.955226i
$568$	10.1885			0.427498
$569$			5.69471i			0.238735i	0.992850	+	0.119367i	$0.0380866\pi$
$569$			5.69471i			0.238735i	−0.992850	+	0.119367i	$0.961913\pi$
$570$	−10.3106	−	0.918284i	−0.431864	−	0.0384627i
$571$	−3.56033			−0.148995			−0.0744976	−	0.997221i	$-0.523735\pi$
$571$	−3.56033			−0.148995			−0.0744976	+	0.997221i	$0.523735\pi$
$572$	3.34308	−	5.79038i	0.139781	−	0.242108i
$573$	1.19528	−	13.4207i	0.0499334	−	0.560659i
$574$	16.9474	+	25.9501i	0.707372	+	1.08314i
$575$			0.789076i			0.0329068i
$576$	−2.95278	−	0.530167i	−0.123033	−	0.0220903i
$577$	−5.31447	−	3.06831i	−0.221244	−	0.127735i	0.385282	−	0.922799i	$-0.374104\pi$
$577$	−5.31447	−	3.06831i	−0.221244	−	0.127735i	−0.606526	+	0.795064i	$0.707437\pi$
$578$	−14.6944	+	8.48379i	−0.611205	+	0.352879i
$579$	−14.3083	−	1.27433i	−0.594635	−	0.0529593i
$580$	−6.84694	+	3.95308i	−0.284304	+	0.164143i
$581$	−20.8418	−	10.5519i	−0.864662	−	0.437765i
$582$	4.36123	−	6.20784i	0.180779	−	0.257323i
$583$	2.24736			0.0930760
$584$	−2.93961	+	5.09156i	−0.121642	+	0.210690i
$585$	−1.11662	+	6.21908i	−0.0461667	+	0.257127i
$586$	4.83808	−	2.79327i	0.199859	−	0.115389i
$587$	1.76206	−	3.05198i	0.0727279	−	0.125969i	−0.827368	−	0.561660i	$-0.810163\pi$
$587$	1.76206	−	3.05198i	0.0727279	−	0.125969i	0.900096	+	0.435692i	$0.143496\pi$
$588$	−12.1217	+	0.255140i	−0.499889	+	0.0105218i
$589$	28.9950	+	50.2208i	1.19472	+	2.06931i
$590$	10.1960	+	5.88665i	0.419762	+	0.242350i
$591$	−2.04369	+	22.9468i	−0.0840662	+	0.943907i
$592$	4.27097	+	7.39754i	0.175536	+	0.304037i
$593$	20.0316	+	34.6957i	0.822598	+	1.42478i	0.903741	+	0.428079i	$0.140810\pi$
$593$	20.0316	+	34.6957i	0.822598	+	1.42478i	−0.0811430	+	0.996702i	$0.525857\pi$
$594$	4.19466	+	15.9532i	0.172109	+	0.654566i
$595$	−0.398829	+	0.260466i	−0.0163504	+	0.0106781i
$596$	−5.37389	−	3.10262i	−0.220123	−	0.127088i
$597$	26.4841	+	18.6061i	1.08392	+	0.761496i
$598$		−	1.66193i		−	0.0679616i
$599$		−	1.82047i		−	0.0743825i	−0.999308	−	0.0371913i	$-0.988159\pi$
$599$		−	1.82047i		−	0.0743825i	0.999308	−	0.0371913i	$-0.0118411\pi$
$600$	1.57091	−	0.729545i	0.0641322	−	0.0297835i
$601$	15.9038	+	9.18204i	0.648728	+	0.374543i	0.787969	−	0.615715i	$-0.211133\pi$
$601$	15.9038	+	9.18204i	0.648728	+	0.374543i	−0.139241	+	0.990259i	$0.544466\pi$
$602$	4.41988	−	8.73004i	0.180141	−	0.355810i
$603$	29.4008	+	5.27885i	1.19729	+	0.214971i
$604$	5.33037	+	9.23247i	0.216890	+	0.375664i
$605$	−0.461135	−	0.798709i	−0.0187478	−	0.0324721i
$606$	26.5785	−	12.3433i	1.07968	−	0.501411i
$607$	25.0342	+	14.4535i	1.01611	+	0.586649i	0.912973	−	0.408019i	$-0.133780\pi$
$607$	25.0342	+	14.4535i	1.01611	+	0.586649i	0.103132	+	0.994668i	$0.467114\pi$
$608$	−2.98820	−	5.17571i	−0.121188	−	0.209903i
$609$	−19.1681	+	30.7448i	−0.776730	+	1.24584i
$610$	−1.44802	+	2.50805i	−0.0586287	+	0.101548i
$611$	−3.80051	+	2.19423i	−0.153752	+	0.0887689i
$612$	−0.348477	+	0.412675i	−0.0140864	+	0.0166814i
$613$	20.0655	−	34.7545i	0.810439	−	1.40372i	−0.102119	−	0.994772i	$-0.532562\pi$
$613$	20.0655	−	34.7545i	0.810439	−	1.40372i	0.912557	−	0.408949i	$-0.134104\pi$
$614$	22.8941			0.923929
$615$	−20.2103	−	1.79997i	−0.814958	−	0.0725818i
$616$	−7.03223	+	4.59259i	−0.283337	+	0.185041i
$617$	−4.18249	+	2.41476i	−0.168381	+	0.0972146i	−0.581822	−	0.813316i	$-0.697660\pi$
$617$	−4.18249	+	2.41476i	−0.168381	+	0.0972146i	0.413441	+	0.910531i	$0.364327\pi$
$618$	5.28812	−	7.52718i	0.212719	−	0.302788i
$619$	−15.5286	+	8.96546i	−0.624149	+	0.360352i	−0.778482	−	0.627666i	$-0.784010\pi$
$619$	−15.5286	+	8.96546i	−0.624149	+	0.360352i	0.154334	+	0.988019i	$0.450677\pi$
$620$	−8.40319	−	4.85159i	−0.337480	−	0.194844i
$621$	2.88564	+	2.91280i	0.115797	+	0.116887i
$622$			21.7317i			0.871362i
$623$	12.8984	−	8.42367i	0.516765	−	0.337487i
$624$	−3.30862	+	1.53655i	−0.132451	+	0.0615112i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.13232			−0.125193
$627$	−18.8903	+	26.8888i	−0.754407	+	1.07383i
$628$			4.39858i			0.175523i
$629$	1.53791			0.0613206
$630$	4.78022	−	6.33636i	0.190448	−	0.252447i
$631$	15.6119			0.621502			0.310751	−	0.950491i	$-0.399420\pi$
$631$	15.6119			0.621502			0.310751	+	0.950491i	$0.399420\pi$
$632$		−	11.0054i		−	0.437769i
$633$	17.7392	+	38.1974i	0.705069	+	1.51821i
$634$	28.6867			1.13929
$635$	7.55105	−	13.0788i	0.299654	−	0.519017i
$636$	−1.00332	−	0.704870i	−0.0397843	−	0.0279499i
$637$	−11.8827	+	8.72720i	−0.470810	+	0.345784i
$638$			25.0985i			0.993658i
$639$	−5.40158	+	30.0843i	−0.213683	+	1.19012i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	13.2778	−	7.66593i	0.524441	−	0.302786i	−0.214309	−	0.976766i	$-0.568750\pi$
$641$	13.2778	−	7.66593i	0.524441	−	0.302786i	0.738750	+	0.673980i	$0.235417\pi$
$642$	5.95871	+	12.8308i	0.235172	+	0.506389i
$643$	−26.2575	+	15.1598i	−1.03550	+	0.597844i	−0.918554	−	0.395295i	$-0.870642\pi$
$643$	−26.2575	+	15.1598i	−1.03550	+	0.597844i	−0.116941	+	0.993139i	$0.537309\pi$
$644$	−0.943000	+	1.86259i	−0.0371594	+	0.0733963i
$645$	2.69817	+	5.80991i	0.106240	+	0.228765i
$646$	−1.07601			−0.0423349
$647$	−14.5503	+	25.2018i	−0.572030	+	0.990785i	0.424327	+	0.905509i	$0.360511\pi$
$647$	−14.5503	+	25.2018i	−0.572030	+	0.990785i	−0.996357	+	0.0852761i	$0.972823\pi$
$648$	3.13093	−	8.43785i	0.122995	−	0.331470i
$649$	32.3676	−	18.6874i	1.27054	−	0.733546i
$650$	1.05309	−	1.82400i	0.0413055	−	0.0715433i
$651$	−44.4400	−	1.50670i	−1.74174	−	0.0590523i
$652$	−9.94559	−	17.2263i	−0.389500	−	0.674633i
$653$	2.85434	+	1.64796i	0.111699	+	0.0644895i	0.554809	−	0.831978i	$-0.312791\pi$
$653$	2.85434	+	1.64796i	0.111699	+	0.0644895i	−0.443110	+	0.896467i	$0.646125\pi$
$654$	1.72007	+	1.20841i	0.0672599	+	0.0472525i
$655$	−4.19019	−	7.25762i	−0.163724	−	0.283579i
$656$	−5.85731	−	10.1452i	−0.228689	−	0.396102i
$657$	−13.4758	−	11.3794i	−0.525740	−	0.443953i
$658$	5.50440	−	0.302696i	0.214584	−	0.0118003i
$659$	5.58702	+	3.22567i	0.217639	+	0.125654i	0.604857	−	0.796334i	$-0.293230\pi$
$659$	5.58702	+	3.22567i	0.217639	+	0.125654i	−0.387217	+	0.921988i	$0.626564\pi$
$660$	0.487774	−	5.47679i	0.0189866	−	0.213184i
$661$		−	37.6383i		−	1.46396i	−0.681327	−	0.731979i	$-0.738597\pi$
$661$		−	37.6383i		−	1.46396i	0.681327	−	0.731979i	$-0.261403\pi$
$662$		−	5.70943i		−	0.221903i
$663$	−0.0582649	+	0.654206i	−0.00226282	+	0.0254073i
$664$	7.64657	+	4.41475i	0.296744	+	0.171325i
$665$	15.7882	−	0.868221i	0.612241	−	0.0336682i
$666$	−24.1077	+	8.68932i	−0.934153	+	0.336704i
$667$	3.11928	+	5.40276i	0.120779	+	0.209196i
$668$	7.13831	+	12.3639i	0.276190	+	0.478374i
$669$	−23.7863	−	16.7108i	−0.919632	−	0.646075i
$670$	−8.62299	−	4.97848i	−0.333135	−	0.192336i
$671$	4.59681	+	7.96190i	0.177458	+	0.307366i
$672$	4.57994	+	0.155279i	0.176675	+	0.00599003i
$673$	24.8051	−	42.9637i	0.956166	−	1.65613i	0.224490	−	0.974476i	$-0.427928\pi$
$673$	24.8051	−	42.9637i	0.956166	−	1.65613i	0.731676	−	0.681652i	$-0.238738\pi$
$674$	−9.38110	+	5.41618i	−0.361347	+	0.208624i
$675$	1.32134	+	5.02534i	0.0508585	+	0.193425i
$676$	4.28201	−	7.41666i	0.164693	−	0.285256i
$677$	7.27326			0.279534			0.139767	−	0.990184i	$-0.455365\pi$
$677$	7.27326			0.279534			0.139767	+	0.990184i	$0.455365\pi$
$678$	1.04222	+	2.24419i	0.0400263	+	0.0861877i
$679$	−5.23460	+	10.3392i	−0.200885	+	0.396784i
$680$	0.155921	−	0.0900212i	0.00597931	−	0.00345215i
$681$	−12.2500	−	26.3777i	−0.469422	−	1.01080i
$682$	−26.6763	+	15.4016i	−1.02149	+	0.589757i
$683$	14.4216	+	8.32633i	0.551828	+	0.318598i	0.749859	−	0.661598i	$-0.230121\pi$
$683$	14.4216	+	8.32633i	0.551828	+	0.318598i	−0.198031	+	0.980196i	$0.563455\pi$
$684$	16.8670	−	6.07951i	0.644926	−	0.232456i
$685$			8.76324i			0.334826i
$686$	18.2693	−	3.03851i	0.697525	−	0.116011i
$687$	9.39837	+	6.60270i	0.358570	+	0.251909i
$688$	−1.84922	+	3.20294i	−0.0705007	+	0.122111i
$689$	−1.49103			−0.0568036
$690$	−0.575667	−	1.23957i	−0.0219153	−	0.0471896i
$691$		−	39.1077i		−	1.48773i	−0.668332	−	0.743863i	$-0.732992\pi$
$691$		−	39.1077i		−	1.48773i	0.668332	−	0.743863i	$-0.267008\pi$
$692$	13.2286			0.502876
$693$	−9.83266	−	23.1995i	−0.373512	−	0.881275i
$694$	19.3689			0.735234
$695$		−	3.19519i		−	0.121200i
$696$	7.87199	−	11.2051i	0.298387	−	0.424728i
$697$	−2.10913			−0.0798889
$698$	9.92710	−	17.1942i	0.375746	−	0.650812i
$699$	12.3293	−	5.72583i	0.466337	−	0.216571i
$700$	−2.21519	+	1.44669i	−0.0837265	+	0.0546798i
$701$			38.2997i			1.44656i	0.690555	+	0.723280i	$0.257366\pi$
$701$			38.2997i			1.44656i	−0.690555	+	0.723280i	$0.742634\pi$
$702$	−2.78298	−	10.5843i	−0.105037	−	0.399477i
$703$	−44.2107	−	25.5250i	−1.66744	−	0.962695i
$704$	2.74924	−	1.58727i	0.103616	−	0.0598226i
$705$	−2.07460	+	2.95302i	−0.0781341	+	0.111217i
$706$	−9.95408	+	5.74699i	−0.374627	+	0.216291i
$707$	−37.4792	+	24.4768i	−1.40955	+	0.920544i
$708$	−20.3116	−	1.80899i	−0.763356	−	0.0679859i
$709$	−9.17097			−0.344423			−0.172211	−	0.985060i	$-0.555091\pi$
$709$	−9.17097			−0.344423			−0.172211	+	0.985060i	$0.555091\pi$
$710$	5.09423	−	8.82346i	0.191183	−	0.331139i
$711$	32.4964	+	5.83467i	1.21871	+	0.218817i
$712$	−5.04262	+	2.91136i	−0.188980	+	0.109108i
$713$	−3.82827	+	6.63076i	−0.143370	+	0.248324i
$714$	0.436503	−	0.700132i	0.0163357	−	0.0262018i
$715$	−3.34308	−	5.79038i	−0.125024	−	0.216548i
$716$	3.52462	+	2.03494i	0.131721	+	0.0760492i
$717$	26.0011	−	12.0751i	0.971027	−	0.450953i
$718$	11.0732	+	19.1794i	0.413249	+	0.715768i
$719$	−16.5618	−	28.6858i	−0.617650	−	1.06980i	−0.989913	−	0.141674i	$-0.954752\pi$
$719$	−16.5618	−	28.6858i	−0.617650	−	1.06980i	0.372263	−	0.928127i	$-0.378582\pi$
$720$	−1.93553	+	2.29210i	−0.0721329	+	0.0854216i
$721$	−6.34710	+	12.5366i	−0.236378	+	0.466889i
$722$	14.4777	+	8.35868i	0.538802	+	0.311078i
$723$	−30.2564	+	14.0513i	−1.12525	+	0.522574i
$724$		−	21.7339i		−	0.807735i
$725$			7.90616i			0.293628i
$726$	1.30710	+	0.918283i	0.0485109	+	0.0340807i
$727$	21.5870	+	12.4633i	0.800617	+	0.462236i	0.843687	−	0.536836i	$-0.180380\pi$
$727$	21.5870	+	12.4633i	0.800617	+	0.462236i	−0.0430699	+	0.999072i	$0.513714\pi$
$728$	4.66559	−	3.04699i	0.172918	−	0.112929i
$729$	23.2552	+	13.7184i	0.861304	+	0.508090i
$730$	2.93961	+	5.09156i	0.108800	+	0.188447i
$731$	0.332937	+	0.576665i	0.0123141	+	0.0213287i
$732$	0.444982	−	4.99632i	0.0164470	−	0.184669i
$733$	−12.7522	−	7.36247i	−0.471012	−	0.271939i	0.245651	−	0.969358i	$-0.420998\pi$
$733$	−12.7522	−	7.36247i	−0.471012	−	0.271939i	−0.716663	+	0.697419i	$0.754332\pi$
$734$	−10.0714	−	17.4441i	−0.371742	−	0.643875i
$735$	−5.83988	+	10.6252i	−0.215407	+	0.391918i
$736$	0.394538	−	0.683360i	0.0145429	−	0.0251890i
$737$	−27.3740	+	15.8044i	−1.00834	+	0.582163i
$738$	33.0618	−	11.9167i	1.21702	−	0.438661i
$739$	13.3365	−	23.0995i	0.490590	−	0.849727i	−0.509351	−	0.860559i	$-0.670115\pi$
$739$	13.3365	−	23.0995i	0.490590	−	0.849727i	0.999941	+	0.0108315i	$0.00344786\pi$
$740$	8.54194			0.314008
$741$	12.5329	−	17.8396i	0.460409	−	0.655353i
$742$	1.67105	+	0.846025i	0.0613461	+	0.0310586i
$743$	4.24232	−	2.44930i	0.155636	−	0.0898562i	−0.420160	−	0.907450i	$-0.638026\pi$
$743$	4.24232	−	2.44930i	0.155636	−	0.0898562i	0.575795	+	0.817594i	$0.304693\pi$
$744$	16.7401	+	1.49091i	0.613723	+	0.0546594i
$745$	−5.37389	+	3.10262i	−0.196884	+	0.113671i
$746$	−23.6347	−	13.6455i	−0.865329	−	0.499598i
$747$	−17.0897	+	20.2381i	−0.625281	+	0.740473i
$748$		−	0.571552i		−	0.0208980i
$749$	−11.8162	−	18.0931i	−0.431753	−	0.661106i
$750$	0.153652	−	1.72522i	0.00561057	−	0.0629962i
$751$	7.96028	−	13.7876i	0.290475	−	0.503117i	−0.683447	−	0.730000i	$-0.739520\pi$
$751$	7.96028	−	13.7876i	0.290475	−	0.503117i	0.973922	+	0.226883i	$0.0728535\pi$
$752$	−2.08361			−0.0759815
$753$	−37.9870	−	3.38320i	−1.38432	−	0.123291i
$754$		−	16.6518i		−	0.606422i
$755$	10.6607			0.387984
$756$	−2.88664	+	13.4413i	−0.104986	+	0.488854i
$757$	−27.4236			−0.996729			−0.498365	−	0.866968i	$-0.666066\pi$
$757$	−27.4236			−0.996729			−0.498365	+	0.866968i	$0.666066\pi$
$758$		−	19.6022i		−	0.711983i
$759$	−4.32161	−	0.384891i	−0.156864	−	0.0139707i
$760$	−5.97640			−0.216787
$761$	−0.773619	+	1.33995i	−0.0280437	+	0.0485731i	−0.879707	−	0.475517i	$-0.842261\pi$
$761$	−0.773619	+	1.33995i	−0.0280437	+	0.0485731i	0.851663	+	0.524090i	$0.175594\pi$
$762$	−2.32046	+	26.0545i	−0.0840615	+	0.943854i
$763$	−2.86480	−	1.45040i	−0.103713	−	0.0525080i
$764$		−	7.77914i		−	0.281439i
$765$	0.183149	+	0.508128i	0.00662176	+	0.0183714i
$766$	−3.43949	−	1.98579i	−0.124274	−	0.0717495i
$767$	−21.4745	+	12.3983i	−0.775401	+	0.447678i
$768$	−1.72522	−	0.153652i	−0.0622536	−	0.00554443i
$769$	−2.38768	+	1.37853i	−0.0861019	+	0.0497110i	−0.542433	−	0.840099i	$-0.682497\pi$
$769$	−2.38768	+	1.37853i	−0.0861019	+	0.0497110i	0.456331	+	0.889810i	$0.349163\pi$
$770$	0.461181	+	8.38638i	0.0166198	+	0.302224i
$771$	20.7541	−	29.5416i	0.747439	−	1.06392i
$772$	−8.29363			−0.298494
$773$	−0.745114	+	1.29057i	−0.0267999	+	0.0464187i	−0.879114	−	0.476611i	$-0.841865\pi$
$773$	−0.745114	+	1.29057i	−0.0267999	+	0.0464187i	0.852314	+	0.523030i	$0.175198\pi$
$774$	−8.47719	−	7.15843i	−0.304706	−	0.257304i
$775$	−8.40319	+	4.85159i	−0.301852	+	0.174274i
$776$	2.19008	−	3.79334i	0.0786194	−	0.136173i
$777$	34.5435	−	18.4121i	1.23924	−	0.660531i
$778$	−9.44628	−	16.3614i	−0.338666	−	0.586586i
$779$	60.6315	+	35.0056i	2.17235	+	1.25421i
$780$	−0.323618	+	3.63362i	−0.0115874	+	0.130105i
$781$	−16.1718	−	28.0105i	−0.578674	−	1.00229i
$782$	−0.0710336	−	0.123034i	−0.00254016	−	0.00439968i
$783$	28.9127	+	29.1848i	1.03326	+	1.04298i
$784$	−6.95779	+	0.767563i	−0.248493	+	0.0274130i
$785$	3.80928	+	2.19929i	0.135959	+	0.0784961i
$786$	11.8772	+	8.34415i	0.423645	+	0.297626i
$787$		−	22.4371i		−	0.799796i	−0.916560	−	0.399898i	$-0.869046\pi$
$787$		−	22.4371i		−	0.799796i	0.916560	−	0.399898i	$-0.130954\pi$
$788$			13.3008i			0.473822i
$789$	35.4037	−	16.4418i	1.26041	−	0.585343i
$790$	−9.53091	−	5.50268i	−0.339095	−	0.195776i
$791$	−2.06673	−	3.16461i	−0.0734845	−	0.112520i
$792$	3.22932	+	8.95941i	0.114749	+	0.318359i
$793$	−3.04979	−	5.28239i	−0.108301	−	0.187583i
$794$	−17.6664	−	30.5990i	−0.626956	−	1.08592i
$795$	−1.11210	+	0.516467i	−0.0394420	+	0.0183172i
$796$	16.1833	+	9.34343i	0.573602	+	0.331169i
$797$	16.4080	+	28.4195i	0.581202	+	1.00667i	0.995337	+	0.0964565i	$0.0307509\pi$
$797$	16.4080	+	28.4195i	0.581202	+	1.00667i	−0.414135	+	0.910216i	$0.635916\pi$
$798$	−24.1685	+	12.8821i	−0.855555	+	0.456022i
$799$	−0.187569	+	0.324879i	−0.00663572	+	0.0114934i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−5.92317	−	16.4332i	−0.209285	−	0.580640i
$802$	−0.311666	+	0.539822i	−0.0110053	+	0.0190618i
$803$	18.6638			0.658633
$804$	17.1780	+	1.52990i	0.605821	+	0.0539556i
$805$	1.14155	+	1.74796i	0.0402344	+	0.0616074i
$806$	17.6986	−	10.2183i	0.623407	−	0.359924i
$807$	−23.6355	+	33.6431i	−0.832010	+	1.18429i
$808$	14.6524	−	8.45957i	0.515470	−	0.297607i
$809$	9.17296	+	5.29601i	0.322504	+	0.186198i	0.652508	−	0.757782i	$-0.273717\pi$
$809$	9.17296	+	5.29601i	0.322504	+	0.186198i	−0.330004	+	0.943980i	$0.607050\pi$
$810$	−5.74192	−	6.93039i	−0.201751	−	0.243509i
$811$		−	23.0365i		−	0.808921i	−0.914555	−	0.404461i	$-0.867459\pi$
$811$		−	23.0365i		−	0.808921i	0.914555	−	0.404461i	$-0.132541\pi$
$812$	−9.44841	+	18.6623i	−0.331574	+	0.654917i
$813$	18.5329	−	8.60683i	0.649977	−	0.301855i
$814$	13.5584	−	23.4838i	0.475221	−	0.823107i
$815$	−19.8912			−0.696758
$816$	−0.179264	+	0.255167i	−0.00627550	+	0.00893263i
$817$		−	22.1033i		−	0.773297i
$818$	−1.39035			−0.0486124
$819$	6.52355	+	15.3919i	0.227951	+	0.537836i
$820$	−11.7146			−0.409092
$821$		−	2.69452i		−	0.0940392i	−0.998894	−	0.0470196i	$-0.985028\pi$
$821$		−	2.69452i		−	0.0940392i	0.998894	−	0.0470196i	$-0.0149723\pi$
$822$	−6.39318	−	13.7663i	−0.222988	−	0.480154i
$823$	−2.08107			−0.0725417			−0.0362708	−	0.999342i	$-0.511548\pi$
$823$	−2.08107			−0.0725417			−0.0362708	+	0.999342i	$0.511548\pi$
$824$	2.65554	−	4.59953i	0.0925101	−	0.160232i
$825$	−4.49916	−	3.16082i	−0.156640	−	0.110046i
$826$	31.1023	−	1.71037i	1.08219	−	0.0595112i
$827$		−	37.0830i		−	1.28950i	−0.764393	−	0.644751i	$-0.776961\pi$
$827$		−	37.0830i		−	1.28950i	0.764393	−	0.644751i	$-0.223039\pi$
$828$	1.80864	+	1.52728i	0.0628547	+	0.0530767i
$829$	−13.9461	−	8.05176i	−0.484367	−	0.279649i	0.237868	−	0.971298i	$-0.423551\pi$
$829$	−13.9461	−	8.05176i	−0.484367	−	0.279649i	−0.722234	+	0.691648i	$0.756885\pi$
$830$	7.64657	−	4.41475i	0.265416	−	0.153238i
$831$	−13.3553	−	28.7578i	−0.463292	−	0.997596i
$832$	−1.82400	+	1.05309i	−0.0632359	+	0.0365093i
$833$	−0.506669	+	1.15396i	−0.0175550	+	0.0399825i
$834$	2.33103	+	5.01936i	0.0807171	+	0.173806i
$835$	14.2766			0.494063
$836$	−9.48617	+	16.4305i	−0.328086	+	0.568262i
$837$	−13.2774	+	48.6395i	−0.458933	+	1.68123i
$838$	−23.8650	+	13.7784i	−0.824402	+	0.475968i
$839$	9.48006	−	16.4199i	0.327288	−	0.566879i	−0.654685	−	0.755902i	$-0.727199\pi$
$839$	9.48006	−	16.4199i	0.327288	−	0.566879i	0.981973	+	0.189023i	$0.0605319\pi$
$840$	2.42445	−	3.88871i	0.0836514	−	0.134173i
$841$	16.7537	+	29.0183i	0.577714	+	1.00063i
$842$	−29.7576	−	17.1806i	−1.02552	−	0.592082i
$843$	−30.9097	−	21.7152i	−1.06459	−	0.747910i
$844$	12.1577	+	21.0578i	0.418485	+	0.724838i
$845$	−4.28201	−	7.41666i	−0.147306	−	0.255141i
$846$	1.10466	−	6.15245i	0.0379790	−	0.211526i
$847$	−2.17699	−	1.10218i	−0.0748022	−	0.0378712i
$848$	−0.613086	−	0.353965i	−0.0210535	−	0.0121552i
$849$	0.233248	−	2.61893i	0.00800503	−	0.0898816i
$850$		−	0.180042i		−	0.00617540i
$851$		−	6.74025i		−	0.231053i
$852$	−1.56547	+	17.5773i	−0.0536322	+	0.602190i
$853$	19.4322	+	11.2192i	0.665347	+	0.384138i	0.794311	−	0.607511i	$-0.207832\pi$
$853$	19.4322	+	11.2192i	0.665347	+	0.384138i	−0.128964	+	0.991649i	$0.541165\pi$
$854$	0.420722	+	7.65065i	0.0143968	+	0.261800i
$855$	3.16849	−	17.6470i	0.108360	−	0.603515i
$856$	4.08385	+	7.07344i	0.139583	+	0.241765i
$857$	−17.5728	−	30.4371i	−0.600277	−	1.03971i	−0.992779	−	0.119959i	$-0.961724\pi$
$857$	−17.5728	−	30.4371i	−0.600277	−	1.03971i	0.392502	−	0.919751i	$-0.371610\pi$
$858$	9.47602	+	6.65725i	0.323506	+	0.227275i
$859$	−28.1881	−	16.2744i	−0.961764	−	0.555275i	−0.0650488	−	0.997882i	$-0.520720\pi$
$859$	−28.1881	−	16.2744i	−0.961764	−	0.555275i	−0.896716	+	0.442607i	$0.854054\pi$
$860$	1.84922	+	3.20294i	0.0630578	+	0.109219i
$861$	−47.3738	+	25.2508i	−1.61449	+	0.860545i
$862$	14.0654	−	24.3620i	0.479070	−	0.829774i
$863$	−10.9055	+	6.29628i	−0.371227	+	0.214328i	−0.673994	−	0.738737i	$-0.735423\pi$
$863$	−10.9055	+	6.29628i	−0.371227	+	0.214328i	0.302768	+	0.953064i	$0.402089\pi$
$864$	1.36835	−	5.01274i	0.0465524	−	0.170537i
$865$	6.61430	−	11.4563i	0.224893	−	0.389526i
$866$	−11.9782			−0.407035
$867$	−12.3786	−	26.6546i	−0.420400	−	0.905237i
$868$	−25.6334	+	1.40963i	−0.870056	+	0.0478459i
$869$	−30.2563	+	17.4685i	−1.02637	+	0.592578i
$870$	−5.76790	−	12.4199i	−0.195550	−	0.421074i
$871$	18.1615	−	10.4856i	0.615380	−	0.355290i
$872$	1.05106	+	0.606828i	0.0355933	+	0.0205498i
$873$	10.0398	+	8.47794i	0.339795	+	0.286935i
$874$			4.71584i			0.159516i
$875$	0.145275	+	2.64176i	0.00491119	+	0.0893078i
$876$	−8.33239	−	5.85381i	−0.281525	−	0.197782i
$877$	13.6134	−	23.5791i	0.459691	−	0.796209i	−0.539253	−	0.842144i	$-0.681293\pi$
$877$	13.6134	−	23.5791i	0.459691	−	0.796209i	0.998944	+	0.0459350i	$0.0146267\pi$
$878$	10.8588			0.366468
$879$	4.07562	+	8.77595i	0.137467	+	0.296005i
$880$		−	3.17454i		−	0.107014i
$881$	8.99478			0.303042			0.151521	−	0.988454i	$-0.451583\pi$
$881$	8.99478			0.303042			0.151521	+	0.988454i	$0.451583\pi$
$882$	1.42234	−	20.9518i	0.0478928	−	0.705483i
$883$	−15.9491			−0.536730			−0.268365	−	0.963317i	$-0.586483\pi$
$883$	−15.9491			−0.536730			−0.268365	+	0.963317i	$0.586483\pi$
$884$			0.379201i			0.0127539i
$885$	−11.7224	+	16.6858i	−0.394045	+	0.560888i
$886$	−2.11680			−0.0711154
$887$	−14.3532	+	24.8605i	−0.481934	+	0.834734i	−0.999785	−	0.0207370i	$-0.993399\pi$
$887$	−14.3532	+	24.8605i	−0.481934	+	0.834734i	0.517851	+	0.855471i	$0.326732\pi$
$888$	−13.4186	+	6.23173i	−0.450300	+	0.209123i
$889$	−2.19396	−	39.8961i	−0.0735829	−	1.33807i
$890$			5.82271i			0.195178i
$891$	−28.1673	+	4.78549i	−0.943639	+	0.160320i
$892$	−14.5348	−	8.39165i	−0.486660	−	0.280973i
$893$	10.7842	−	6.22624i	0.360879	−	0.208353i
$894$	6.17841	−	8.79443i	0.206637	−	0.294130i
$895$	3.52462	−	2.03494i	0.117815	−	0.0680205i
$896$	2.64176	−	0.145275i	0.0882550	−	0.00485329i
$897$	2.86721	+	0.255359i	0.0957332	+	0.00852619i
$898$	12.2537			0.408913
$899$	−38.3574	+	66.4370i	−1.27929	+	2.21580i
$900$	1.01725	+	2.82227i	0.0339084	+	0.0940756i
$901$	−0.110381	+	0.0637287i	−0.00367734	+	0.00212311i
$902$	−18.5943	+	32.2062i	−0.619122	+	1.07235i
$903$	14.3821	+	8.96666i	0.478607	+	0.298392i
$904$	0.714296	+	1.23720i	0.0237571	+	0.0411485i
$905$	−18.8221	−	10.8670i	−0.625669	−	0.361230i
$906$	−16.7471	+	7.77749i	−0.556385	+	0.258390i
$907$	10.4645	+	18.1251i	0.347469	+	0.601834i	0.985799	−	0.167929i	$-0.0537079\pi$
$907$	10.4645	+	18.1251i	0.347469	+	0.601834i	−0.638330	+	0.769763i	$0.720375\pi$
$908$	−8.39567	−	14.5417i	−0.278620	−	0.482584i
$909$	17.2111	+	47.7503i	0.570855	+	1.58378i
$910$	−0.305975	−	5.56401i	−0.0101430	−	0.184445i
$911$	−48.9296	−	28.2495i	−1.62111	−	0.935949i	−0.986623	−	0.163017i	$-0.947878\pi$
$911$	−48.9296	−	28.2495i	−1.62111	−	0.935949i	−0.634488	−	0.772933i	$-0.718789\pi$
$912$	9.38840	−	4.36005i	0.310881	−	0.144376i
$913$		−	28.0296i		−	0.927645i
$914$		−	33.1134i		−	1.09529i
$915$	−4.10445	−	2.88352i	−0.135689	−	0.0953263i
$916$	5.74293	+	3.31568i	0.189752	+	0.109553i
$917$	−19.7816	−	10.0151i	−0.653247	−	0.330729i
$918$	−0.658412	−	0.664609i	−0.0217308	−	0.0219354i
$919$	−7.93346	−	13.7412i	−0.261701	−	0.453279i	0.704993	−	0.709214i	$-0.250950\pi$
$919$	−7.93346	−	13.7412i	−0.261701	−	0.453279i	−0.966694	+	0.255935i	$0.917617\pi$
$920$	−0.394538	−	0.683360i	−0.0130075	−	0.0225297i
$921$	−3.51771	+	39.4973i	−0.115912	+	1.30148i
$922$	−24.4604	−	14.1222i	−0.805560	−	0.465091i
$923$	10.7293	+	18.5838i	0.353161	+	0.611692i
$924$	−6.84272	−	12.8378i	−0.225109	−	0.422333i
$925$	4.27097	−	7.39754i	0.140429	−	0.243230i
$926$	−34.8353	+	20.1122i	−1.14476	+	0.660927i
$927$	12.1735	+	10.2797i	0.399831	+	0.337631i
$928$	3.95308	−	6.84694i	0.129766	−	0.224762i
$929$	48.0576			1.57672			0.788359	−	0.615216i	$-0.210931\pi$
$929$	48.0576			1.57672			0.788359	+	0.615216i	$0.210931\pi$
$930$	9.66123	−	13.7519i	0.316804	−	0.450943i
$931$	33.7179	−	24.7640i	1.10506	−	0.811606i
$932$	6.79700	−	3.92425i	0.222643	−	0.128543i
$933$	−37.4920	−	3.33911i	−1.22743	−	0.109318i
$934$	−1.42814	+	0.824539i	−0.0467303	+	0.0269797i
$935$	−0.494979	−	0.285776i	−0.0161875	−	0.00934588i
$936$	−2.14252	−	5.94419i	−0.0700303	−	0.194292i
$937$			8.04349i			0.262769i	0.991331	+	0.131385i	$0.0419423\pi$
$937$			8.04349i			0.262769i	−0.991331	+	0.131385i	$0.958058\pi$
$938$	−26.3039	+	1.44650i	−0.858853	+	0.0472298i
$939$	0.481287	−	5.40395i	0.0157062	−	0.176351i
$940$	−1.04181	+	1.80446i	−0.0339799	+	0.0588550i
$941$	−33.2880			−1.08516			−0.542579	−	0.840004i	$-0.682552\pi$
$941$	−33.2880			−1.08516			−0.542579	+	0.840004i	$0.682552\pi$
$942$	−7.58853	−	0.675850i	−0.247248	−	0.0220204i
$943$			9.24373i			0.301017i
$944$	−11.7733			−0.383189
$945$	10.1971	+	9.22053i	0.331713	+	0.299944i
$946$	11.7408			0.381728
$947$		−	31.2034i		−	1.01397i	−0.861954	−	0.506987i	$-0.830759\pi$
$947$		−	31.2034i		−	1.01397i	0.861954	−	0.506987i	$-0.169241\pi$
$948$	18.9867	+	1.69099i	0.616659	+	0.0549208i
$949$	−12.3827			−0.401959
$950$	−2.98820	+	5.17571i	−0.0969500	+	0.167922i
$951$	−4.40776	+	49.4909i	−0.142931	+	1.60485i
$952$	0.215163	−	0.424984i	0.00697347	−	0.0137738i
$953$			10.1723i			0.329512i	0.986334	+	0.164756i	$0.0526837\pi$
$953$			10.1723i			0.329512i	−0.986334	+	0.164756i	$0.947316\pi$
$954$	1.37022	−	1.62265i	0.0443625	−	0.0525352i
$955$	−6.73693	−	3.88957i	−0.218002	−	0.125863i
$956$	14.3341	−	8.27578i	0.463597	−	0.267658i
$957$	−43.3004	−	3.85642i	−1.39970	−	0.124660i
$958$	−24.4682	+	14.1267i	−0.790533	+	0.456414i
$959$	12.6777	+	19.4123i	0.409384	+	0.626855i
$960$	−0.995677	+	1.41726i	−0.0321353	+	0.0457419i
$961$	−63.1515			−2.03715
$962$	−8.99542	+	15.5805i	−0.290024	+	0.502336i
$963$	−23.0515	+	8.30863i	−0.742823	+	0.267742i
$964$	−16.6800	+	9.63020i	−0.537227	+	0.310168i
$965$	−4.14681	+	7.18249i	−0.133491	+	0.231213i
$966$	−3.06849	−	1.91307i	−0.0987270	−	0.0615522i
$967$	−26.3617	−	45.6599i	−0.847737	−	1.46832i	−0.883223	−	0.468953i	$-0.844631\pi$
$967$	−26.3617	−	45.6599i	−0.847737	−	1.46832i	0.0354867	−	0.999370i	$-0.488702\pi$
$968$	0.798709	+	0.461135i	0.0256715	+	0.0148214i
$969$	0.165330	−	1.85635i	0.00531116	−	0.0596345i
$970$	−2.19008	−	3.79334i	−0.0703193	−	0.121797i
$971$	−4.76329	−	8.25026i	−0.152861	−	0.264763i	0.779417	−	0.626506i	$-0.215515\pi$
$971$	−4.76329	−	8.25026i	−0.152861	−	0.264763i	−0.932278	+	0.361742i	$0.882182\pi$
$972$	14.0761	+	6.69804i	0.451491	+	0.214840i
$973$	−4.62245	−	7.07796i	−0.148189	−	0.226909i
$974$	−6.42239	−	3.70797i	−0.205787	−	0.118811i
$975$	2.98500	+	2.09707i	0.0955965	+	0.0671601i
$976$		−	2.89604i		−	0.0927001i
$977$		−	30.7329i		−	0.983231i	−0.870812	−	0.491616i	$-0.836407\pi$
$977$		−	30.7329i		−	0.983231i	0.870812	−	0.491616i	$-0.163593\pi$
$978$	31.2473	−	14.5115i	0.999179	−	0.464027i
$979$	16.0080	+	9.24223i	0.511618	+	0.295383i
$980$	−2.81417	+	6.40940i	−0.0898953	+	0.204741i
$981$	−2.34906	+	2.78182i	−0.0749999	+	0.0888167i
$982$	11.9348	+	20.6718i	0.380856	+	0.659662i
$983$	5.17474	+	8.96291i	0.165049	+	0.285872i	0.936673	−	0.350206i	$-0.113889\pi$
$983$	5.17474	+	8.96291i	0.165049	+	0.285872i	−0.771624	+	0.636079i	$0.780555\pi$
$984$	18.4026	−	8.54634i	0.586654	−	0.272447i
$985$	11.5188	+	6.65040i	0.367021	+	0.211899i
$986$	−0.711722	−	1.23274i	−0.0226659	−	0.0392584i
$987$	−0.323542	+	9.54282i	−0.0102984	+	0.303751i
$988$	6.29368	−	10.9010i	0.200229	−	0.346806i
$989$	2.52736	−	1.45917i	0.0803655	−	0.0463990i
$990$	9.37374	+	1.68304i	0.297917	+	0.0534904i
$991$	−0.948097	+	1.64215i	−0.0301173	+	0.0521647i	−0.880691	−	0.473691i	$-0.842921\pi$
$991$	−0.948097	+	1.64215i	−0.0301173	+	0.0521647i	0.850574	+	0.525856i	$0.176255\pi$
$992$	9.70317			0.308076
$993$	9.85004	+	0.877264i	0.312581	+	0.0278391i
$994$	−1.48013	−	26.9155i	−0.0469468	−	0.853706i
$995$	16.1833	−	9.34343i	0.513045	−	0.296207i
$996$	−8.79133	+	12.5137i	−0.278564	+	0.396512i
$997$	−24.8252	+	14.3329i	−0.786223	+	0.453926i	−0.838631	−	0.544700i	$-0.816644\pi$
$997$	−24.8252	+	14.3329i	−0.786223	+	0.453926i	0.0524080	+	0.998626i	$0.483310\pi$
$998$	6.89865	+	3.98294i	0.218373	+	0.126078i
$999$	−11.2868	−	42.9262i	−0.357099	−	1.35812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.101.8	yes	28
3.2	odd	2		1890.2.bk.b.521.4		28
7.5	odd	6		630.2.t.b.551.11	yes	28
9.4	even	3		1890.2.t.b.1151.2		28
9.5	odd	6		630.2.t.b.311.11	✓	28
21.5	even	6		1890.2.t.b.1601.2		28
63.5	even	6	inner	630.2.bk.b.131.1	yes	28
63.40	odd	6		1890.2.bk.b.341.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.11	✓	28	9.5	odd	6
630.2.t.b.551.11	yes	28	7.5	odd	6
630.2.bk.b.101.8	yes	28	1.1	even	1	trivial
630.2.bk.b.131.1	yes	28	63.5	even	6	inner
1890.2.t.b.1151.2		28	9.4	even	3
1890.2.t.b.1601.2		28	21.5	even	6
1890.2.bk.b.341.4		28	63.40	odd	6
1890.2.bk.b.521.4		28	3.2	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.72522 - 0.153652i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.153652 - 1.72522i) q^{6} +(0.145275 + 2.64176i) q^{7} -1.00000i q^{8} +(2.95278 + 0.530167i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.72522 - 0.153652i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.153652 - 1.72522i) q^{6} +(0.145275 + 2.64176i) q^{7} -1.00000i q^{8} +(2.95278 + 0.530167i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-2.74924 + 1.58727i) q^{11} +(1.72522 + 0.153652i) q^{12} +(1.82400 - 1.05309i) q^{13} +(-2.64176 + 0.145275i) q^{14} +(0.995677 - 1.41726i) q^{15} +1.00000 q^{16} +(0.0900212 - 0.155921i) q^{17} +(-0.530167 + 2.95278i) q^{18} +(-5.17571 + 2.98820i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.155279 - 4.57994i) q^{21} +(-1.58727 - 2.74924i) q^{22} +(-0.683360 - 0.394538i) q^{23} +(-0.153652 + 1.72522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.05309 + 1.82400i) q^{26} +(-5.01274 - 1.36835i) q^{27} +(-0.145275 - 2.64176i) q^{28} +(-6.84694 - 3.95308i) q^{29} +(1.41726 + 0.995677i) q^{30} -9.70317i q^{31} +1.00000i q^{32} +(4.98693 - 2.31597i) q^{33} +(0.155921 + 0.0900212i) q^{34} +(-2.36047 - 1.19507i) q^{35} +(-2.95278 - 0.530167i) q^{36} +(4.27097 + 7.39754i) q^{37} +(-2.98820 - 5.17571i) q^{38} +(-3.30862 + 1.53655i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-5.85731 - 10.1452i) q^{41} +(4.57994 + 0.155279i) q^{42} +(-1.84922 + 3.20294i) q^{43} +(2.74924 - 1.58727i) q^{44} +(-1.93553 + 2.29210i) q^{45} +(0.394538 - 0.683360i) q^{46} -2.08361 q^{47} +(-1.72522 - 0.153652i) q^{48} +(-6.95779 + 0.767563i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-0.179264 + 0.255167i) q^{51} +(-1.82400 + 1.05309i) q^{52} +(-0.613086 - 0.353965i) q^{53} +(1.36835 - 5.01274i) q^{54} -3.17454i q^{55} +(2.64176 - 0.145275i) q^{56} +(9.38840 - 4.36005i) q^{57} +(3.95308 - 6.84694i) q^{58} -11.7733 q^{59} +(-0.995677 + 1.41726i) q^{60} -2.89604i q^{61} +9.70317 q^{62} +(-0.971608 + 7.87756i) q^{63} -1.00000 q^{64} +2.10618i q^{65} +(2.31597 + 4.98693i) q^{66} +9.95697 q^{67} +(-0.0900212 + 0.155921i) q^{68} +(1.11833 + 0.785665i) q^{69} +(1.19507 - 2.36047i) q^{70} +10.1885i q^{71} +(0.530167 - 2.95278i) q^{72} +(-5.09156 - 2.93961i) q^{73} +(-7.39754 + 4.27097i) q^{74} +(0.729545 + 1.57091i) q^{75} +(5.17571 - 2.98820i) q^{76} +(-4.59259 - 7.03223i) q^{77} +(-1.53655 - 3.30862i) q^{78} +11.0054 q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.43785 + 3.13093i) q^{81} +(10.1452 - 5.85731i) q^{82} +(-4.41475 + 7.64657i) q^{83} +(-0.155279 + 4.57994i) q^{84} +(0.0900212 + 0.155921i) q^{85} +(-3.20294 - 1.84922i) q^{86} +(11.2051 + 7.87199i) q^{87} +(1.58727 + 2.74924i) q^{88} +(-2.91136 - 5.04262i) q^{89} +(-2.29210 - 1.93553i) q^{90} +(3.04699 + 4.66559i) q^{91} +(0.683360 + 0.394538i) q^{92} +(-1.49091 + 16.7401i) q^{93} -2.08361i q^{94} -5.97640i q^{95} +(0.153652 - 1.72522i) q^{96} +(3.79334 + 2.19008i) q^{97} +(-0.767563 - 6.95779i) q^{98} +(-8.95941 + 3.22932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more