LMFDB - Embedded newform 370.2.n.f.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.2
Root			$-1.16746 - 0.312819i$ of defining polynomial
Character	$\chi$	$=$	370.269
Dual form			370.2.n.f.359.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.41240 + 0.815449i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 + 1.55199i) q^{5} +1.63090 q^{6} +(0.466951 - 0.269594i) q^{7} -1.00000i q^{8} +(-0.170086 + 0.294598i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.41240 + 0.815449i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 + 1.55199i) q^{5} +1.63090 q^{6} +(0.466951 - 0.269594i) q^{7} -1.00000i q^{8} +(-0.170086 + 0.294598i) q^{9} +(2.17009 - 0.539189i) q^{10} -0.829914 q^{11} +(-1.41240 - 0.815449i) q^{12} +(0.945448 - 0.545854i) q^{13} -0.539189 q^{14} +(1.00804 - 3.50471i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.01332 - 0.585043i) q^{17} +(0.294598 - 0.170086i) q^{18} +(-3.87936 - 6.71925i) q^{19} +(-2.14894 - 0.618092i) q^{20} +(-0.439681 + 0.761550i) q^{21} +(0.718726 + 0.414957i) q^{22} +0.539189i q^{23} +(0.815449 + 1.41240i) q^{24} +(0.182626 - 4.99666i) q^{25} -1.09171 q^{26} -5.44748i q^{27} +(0.466951 + 0.269594i) q^{28} -9.57531 q^{29} +(-2.62535 + 2.53114i) q^{30} +3.09171 q^{31} +(0.866025 - 0.500000i) q^{32} +(1.17217 - 0.676752i) q^{33} +(0.585043 + 1.01332i) q^{34} +(-0.333268 + 1.15869i) q^{35} -0.340173 q^{36} +(-4.29353 - 4.30878i) q^{37} +7.75872i q^{38} +(-0.890233 + 1.54193i) q^{39} +(1.55199 + 1.60976i) q^{40} +(-0.960811 - 1.66417i) q^{41} +(0.761550 - 0.439681i) q^{42} -1.29072i q^{43} +(-0.414957 - 0.718726i) q^{44} +(-0.183417 - 0.738205i) q^{45} +(0.269594 - 0.466951i) q^{46} +5.80098i q^{47} -1.63090i q^{48} +(-3.35464 + 5.81040i) q^{49} +(-2.65649 + 4.23592i) q^{50} +1.90829 q^{51} +(0.945448 + 0.545854i) q^{52} +(-3.06503 - 1.76959i) q^{53} +(-2.72374 + 4.71766i) q^{54} +(1.33596 - 1.28802i) q^{55} +(-0.269594 - 0.466951i) q^{56} +(10.9584 + 6.32684i) q^{57} +(8.29246 + 4.78765i) q^{58} +(1.95415 - 3.38468i) q^{59} +(3.53919 - 0.879362i) q^{60} +(0.908291 + 1.57321i) q^{61} +(-2.67750 - 1.54585i) q^{62} +0.183417i q^{63} -1.00000 q^{64} +(-0.674776 + 2.34602i) q^{65} -1.35350 q^{66} +(11.0744 - 6.39383i) q^{67} -1.17009i q^{68} +(-0.439681 - 0.761550i) q^{69} +(0.867962 - 0.836818i) q^{70} +(-0.290725 - 0.503550i) q^{71} +(0.294598 + 0.170086i) q^{72} +5.75154i q^{73} +(1.56391 + 5.87828i) q^{74} +(3.81658 + 7.20620i) q^{75} +(3.87936 - 6.71925i) q^{76} +(-0.387529 + 0.223740i) q^{77} +(1.54193 - 0.890233i) q^{78} +(-4.65562 - 8.06377i) q^{79} +(-0.539189 - 2.17009i) q^{80} +(3.93188 + 6.81022i) q^{81} +1.92162i q^{82} +(-1.86781 - 1.07838i) q^{83} -0.879362 q^{84} +(2.53919 - 0.630898i) q^{85} +(-0.645362 + 1.11780i) q^{86} +(13.5242 - 7.80817i) q^{87} +0.829914i q^{88} +(-5.39383 + 9.34238i) q^{89} +(-0.210258 + 0.731013i) q^{90} +(0.294319 - 0.509775i) q^{91} +(-0.466951 + 0.269594i) q^{92} +(-4.36673 + 2.52113i) q^{93} +(2.90049 - 5.02380i) q^{94} +(16.6731 + 4.79560i) q^{95} +(-0.815449 + 1.41240i) q^{96} +9.17727i q^{97} +(5.81040 - 3.35464i) q^{98} +(0.141157 - 0.244491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9	$ 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9} + 4 q^{10} - 32 q^{11} + 18 q^{15} - 6 q^{16} + 4 q^{19} + 20 q^{21} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 32 q^{29} - 20 q^{30} + 28 q^{31} - 4 q^{34} + 4 q^{35} + 40 q^{36} - 58 q^{39} + 2 q^{40} - 18 q^{41} - 16 q^{44} + 16 q^{45} - 26 q^{49} - 8 q^{50} + 32 q^{51} - 34 q^{54} - 4 q^{55} + 28 q^{59} + 36 q^{60} + 20 q^{61} - 12 q^{64} - 22 q^{65} + 24 q^{66} + 20 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{74} + 64 q^{75} - 4 q^{76} - 4 q^{79} - 6 q^{81} + 40 q^{84} + 24 q^{85} - 22 q^{86} - 44 q^{89} - 20 q^{90} - 36 q^{91} + 16 q^{94} + 16 q^{95} - 2 q^{96} - 80 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9 + 4 * q^10 - 32 * q^11 + 18 * q^15 - 6 * q^16 + 4 * q^19 + 20 * q^21 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 32 * q^29 - 20 * q^30 + 28 * q^31 - 4 * q^34 + 4 * q^35 + 40 * q^36 - 58 * q^39 + 2 * q^40 - 18 * q^41 - 16 * q^44 + 16 * q^45 - 26 * q^49 - 8 * q^50 + 32 * q^51 - 34 * q^54 - 4 * q^55 + 28 * q^59 + 36 * q^60 + 20 * q^61 - 12 * q^64 - 22 * q^65 + 24 * q^66 + 20 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^74 + 64 * q^75 - 4 * q^76 - 4 * q^79 - 6 * q^81 + 40 * q^84 + 24 * q^85 - 22 * q^86 - 44 * q^89 - 20 * q^90 - 36 * q^91 + 16 * q^94 + 16 * q^95 - 2 * q^96 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.41240	+	0.815449i	−0.815449	+	0.470800i	−0.848844	−	0.528643i	$-0.822701\pi$
$3$	−1.41240	+	0.815449i	−0.815449	+	0.470800i	0.0333957	+	0.999442i	$0.489368\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.60976	+	1.55199i	−0.719905	+	0.694073i
$5$	−1.60976	+	1.55199i	−0.719905	+	0.694073i
$6$	1.63090			0.665811
$7$	0.466951	−	0.269594i	0.176491	−	0.101897i	−0.409152	−	0.912466i	$-0.634175\pi$
$7$	0.466951	−	0.269594i	0.176491	−	0.101897i	0.585643	+	0.810569i	$0.300842\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.170086	+	0.294598i	−0.0566955	+	0.0981995i
$10$	2.17009	−	0.539189i	0.686242	−	0.170506i
$11$	−0.829914			−0.250228			−0.125114	−	0.992142i	$-0.539930\pi$
$11$	−0.829914			−0.250228			−0.125114	+	0.992142i	$0.539930\pi$
$12$	−1.41240	−	0.815449i	−0.407724	−	0.235400i
$13$	0.945448	−	0.545854i	0.262220	−	0.151393i	−0.363127	−	0.931740i	$-0.618291\pi$
$13$	0.945448	−	0.545854i	0.262220	−	0.151393i	0.625347	+	0.780347i	$0.284958\pi$
$14$	−0.539189			−0.144104
$15$	1.00804	−	3.50471i	0.260276	−	0.904912i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.01332	−	0.585043i	−0.245767	−	0.141894i	0.372057	−	0.928210i	$-0.378652\pi$
$17$	−1.01332	−	0.585043i	−0.245767	−	0.141894i	−0.617825	+	0.786316i	$0.711986\pi$
$18$	0.294598	−	0.170086i	0.0694375	−	0.0400898i
$19$	−3.87936	−	6.71925i	−0.889987	−	1.54150i	−0.839889	−	0.542758i	$-0.817380\pi$
$19$	−3.87936	−	6.71925i	−0.889987	−	1.54150i	−0.0500974	−	0.998744i	$-0.515953\pi$
$20$	−2.14894	−	0.618092i	−0.480519	−	0.138210i
$21$	−0.439681	+	0.761550i	−0.0959462	+	0.166184i
$22$	0.718726	+	0.414957i	0.153233	+	0.0884691i
$23$			0.539189i			0.112429i	0.998419	+	0.0562143i	$0.0179030\pi$
$23$			0.539189i			0.112429i	−0.998419	+	0.0562143i	$0.982097\pi$
$24$	0.815449	+	1.41240i	0.166453	+	0.288305i
$25$	0.182626	−	4.99666i	0.0365252	−	0.999333i
$26$	−1.09171			−0.214102
$27$		−	5.44748i		−	1.04837i
$28$	0.466951	+	0.269594i	0.0882455	+	0.0509486i
$29$	−9.57531			−1.77809			−0.889045	−	0.457820i	$-0.848630\pi$
$29$	−9.57531			−1.77809			−0.889045	+	0.457820i	$0.848630\pi$
$30$	−2.62535	+	2.53114i	−0.479321	+	0.462122i
$31$	3.09171			0.555287			0.277644	−	0.960684i	$-0.410447\pi$
$31$	3.09171			0.555287			0.277644	+	0.960684i	$0.410447\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.17217	−	0.676752i	0.204048	−	0.117807i
$34$	0.585043	+	1.01332i	0.100334	+	0.173784i
$35$	−0.333268	+	1.15869i	−0.0563326	+	0.195854i
$36$	−0.340173			−0.0566955
$37$	−4.29353	−	4.30878i	−0.705852	−	0.708360i
$37$	−4.29353	−	4.30878i	−0.705852	−	0.708360i
$38$			7.75872i			1.25863i
$39$	−0.890233	+	1.54193i	−0.142551	+	0.246906i
$40$	1.55199	+	1.60976i	0.245392	+	0.254525i
$41$	−0.960811	−	1.66417i	−0.150053	−	0.259900i	0.781193	−	0.624289i	$-0.214611\pi$
$41$	−0.960811	−	1.66417i	−0.150053	−	0.259900i	−0.931247	+	0.364389i	$0.881278\pi$
$42$	0.761550	−	0.439681i	0.117510	−	0.0678442i
$43$		−	1.29072i		−	0.196834i	−0.995145	−	0.0984168i	$-0.968622\pi$
$43$		−	1.29072i		−	0.196834i	0.995145	−	0.0984168i	$-0.0313778\pi$
$44$	−0.414957	−	0.718726i	−0.0625571	−	0.108352i
$45$	−0.183417	−	0.738205i	−0.0273423	−	0.110045i
$46$	0.269594	−	0.466951i	0.0397495	−	0.0688482i
$47$			5.80098i			0.846160i	0.906092	+	0.423080i	$0.139051\pi$
$47$			5.80098i			0.846160i	−0.906092	+	0.423080i	$0.860949\pi$
$48$		−	1.63090i		−	0.235400i
$49$	−3.35464	+	5.81040i	−0.479234	+	0.830058i
$50$	−2.65649	+	4.23592i	−0.375685	+	0.599050i
$51$	1.90829			0.267214
$52$	0.945448	+	0.545854i	0.131110	+	0.0756964i
$53$	−3.06503	−	1.76959i	−0.421014	−	0.243072i	0.274497	−	0.961588i	$-0.411489\pi$
$53$	−3.06503	−	1.76959i	−0.421014	−	0.243072i	−0.695511	+	0.718515i	$0.744822\pi$
$54$	−2.72374	+	4.71766i	−0.370654	+	0.641992i
$55$	1.33596	−	1.28802i	0.180141	−	0.173677i
$56$	−0.269594	−	0.466951i	−0.0360261	−	0.0623990i
$57$	10.9584	+	6.32684i	1.45148	+	0.838011i
$58$	8.29246	+	4.78765i	1.08885	+	0.628650i
$59$	1.95415	−	3.38468i	0.254408	−	0.440648i	−0.710326	−	0.703872i	$-0.751453\pi$
$59$	1.95415	−	3.38468i	0.254408	−	0.440648i	0.964735	+	0.263225i	$0.0847860\pi$
$60$	3.53919	−	0.879362i	0.456907	−	0.113525i
$61$	0.908291	+	1.57321i	0.116295	+	0.201428i	0.918297	−	0.395893i	$-0.129565\pi$
$61$	0.908291	+	1.57321i	0.116295	+	0.201428i	−0.802002	+	0.597322i	$0.796232\pi$
$62$	−2.67750	−	1.54585i	−0.340043	−	0.196324i
$63$			0.183417i			0.0231084i
$64$	−1.00000			−0.125000
$65$	−0.674776	+	2.34602i	−0.0836957	+	0.290988i
$66$	−1.35350			−0.166605
$67$	11.0744	−	6.39383i	1.35296	−	0.781130i	0.364295	−	0.931284i	$-0.381310\pi$
$67$	11.0744	−	6.39383i	1.35296	−	0.781130i	0.988663	+	0.150154i	$0.0479768\pi$
$68$		−	1.17009i		−	0.141894i
$69$	−0.439681	−	0.761550i	−0.0529314	−	0.0916798i
$70$	0.867962	−	0.836818i	0.103741	−	0.100019i
$71$	−0.290725	−	0.503550i	−0.0345027	−	0.0597604i	0.848258	−	0.529582i	$-0.177651\pi$
$71$	−0.290725	−	0.503550i	−0.0345027	−	0.0597604i	−0.882761	+	0.469822i	$0.844318\pi$
$72$	0.294598	+	0.170086i	0.0347188	+	0.0200449i
$73$			5.75154i			0.673166i	0.941654	+	0.336583i	$0.109271\pi$
$73$			5.75154i			0.673166i	−0.941654	+	0.336583i	$0.890729\pi$
$74$	1.56391	+	5.87828i	0.181801	+	0.683336i
$75$	3.81658	+	7.20620i	0.440701	+	0.832101i
$76$	3.87936	−	6.71925i	0.444993	−	0.770751i
$77$	−0.387529	+	0.223740i	−0.0441630	+	0.0254975i
$78$	1.54193	−	0.890233i	0.174589	−	0.100799i
$79$	−4.65562	−	8.06377i	−0.523798	−	0.907245i	−0.999616	−	0.0277016i	$-0.991181\pi$
$79$	−4.65562	−	8.06377i	−0.523798	−	0.907245i	0.475818	−	0.879544i	$-0.342152\pi$
$80$	−0.539189	−	2.17009i	−0.0602831	−	0.242623i
$81$	3.93188	+	6.81022i	0.436876	+	0.756691i
$82$			1.92162i			0.212208i
$83$	−1.86781	−	1.07838i	−0.205018	−	0.118367i	0.393976	−	0.919121i	$-0.371099\pi$
$83$	−1.86781	−	1.07838i	−0.205018	−	0.118367i	−0.598994	+	0.800753i	$0.704433\pi$
$84$	−0.879362			−0.0959462
$85$	2.53919	−	0.630898i	0.275414	−	0.0684305i
$86$	−0.645362	+	1.11780i	−0.0695912	+	0.120536i
$87$	13.5242	−	7.80817i	1.44994	−	0.837124i
$88$			0.829914i			0.0884691i
$89$	−5.39383	+	9.34238i	−0.571744	+	0.990290i	0.424643	+	0.905361i	$0.360400\pi$
$89$	−5.39383	+	9.34238i	−0.571744	+	0.990290i	−0.996387	+	0.0849294i	$0.972934\pi$
$90$	−0.210258	+	0.731013i	−0.0221632	+	0.0770555i
$91$	0.294319	−	0.509775i	0.0308530	−	0.0534389i
$92$	−0.466951	+	0.269594i	−0.0486830	+	0.0281072i
$93$	−4.36673	+	2.52113i	−0.452808	+	0.261429i
$94$	2.90049	−	5.02380i	0.299163	−	0.518165i
$95$	16.6731	+	4.79560i	1.71062	+	0.492019i
$96$	−0.815449	+	1.41240i	−0.0832264	+	0.144152i
$97$			9.17727i			0.931811i	0.884834	+	0.465906i	$0.154271\pi$
$97$			9.17727i			0.931811i	−0.884834	+	0.465906i	$0.845729\pi$
$98$	5.81040	−	3.35464i	0.586939	−	0.338870i
$99$	0.141157	−	0.244491i	0.0141868	−	0.0245723i
$100$	4.41855	−	2.34017i	0.441855	−	0.234017i
$101$	11.8999			1.18408			0.592041	−	0.805908i	$-0.298322\pi$
$101$	11.8999			1.18408			0.592041	+	0.805908i	$0.298322\pi$
$102$	−1.65263	−	0.954146i	−0.163635	−	0.0944745i
$103$		−	3.21953i		−	0.317230i	−0.987340	−	0.158615i	$-0.949297\pi$
$103$		−	3.21953i		−	0.317230i	0.987340	−	0.158615i	$-0.0507029\pi$
$104$	−0.545854	−	0.945448i	−0.0535254	−	0.0927088i
$105$	−0.474142	−	1.90829i	−0.0462715	−	0.186230i
$106$	1.76959	+	3.06503i	0.171878	+	0.297702i
$107$	−12.3207	+	7.11336i	−1.19109	+	0.687675i	−0.958553	−	0.284914i	$-0.908035\pi$
$107$	−12.3207	+	7.11336i	−1.19109	+	0.687675i	−0.232534	+	0.972588i	$0.574702\pi$
$108$	4.71766	−	2.72374i	0.453957	−	0.262092i
$109$	−4.68035	+	8.10660i	−0.448296	+	0.776471i	−0.998275	−	0.0587070i	$-0.981302\pi$
$109$	−4.68035	+	8.10660i	−0.448296	+	0.776471i	0.549979	+	0.835178i	$0.314636\pi$
$110$	−1.80098	+	0.447480i	−0.171717	+	0.0426656i
$111$	9.57777	+	2.58457i	0.909081	+	0.245316i
$112$			0.539189i			0.0509486i
$113$	−11.4119	−	6.58864i	−1.07354	−	0.619807i	−0.144391	−	0.989521i	$-0.546122\pi$
$113$	−11.4119	−	6.58864i	−1.07354	−	0.619807i	−0.929146	+	0.369714i	$0.879456\pi$
$114$	−6.32684	−	10.9584i	−0.592563	−	1.02635i
$115$	−0.836818	−	0.867962i	−0.0780337	−	0.0809379i
$116$	−4.78765	−	8.29246i	−0.444522	−	0.769935i
$117$			0.371370i			0.0343332i
$118$	−3.38468	+	1.95415i	−0.311585	+	0.179894i
$119$	−0.630898			−0.0578343
$120$	−3.50471	−	1.00804i	−0.319935	−	0.0920215i
$121$	−10.3112			−0.937386
$122$		−	1.81658i		−	0.164466i
$123$	2.71410	+	1.56698i	0.244722	+	0.141290i
$124$	1.54585	+	2.67750i	0.138822	+	0.240446i
$125$	7.46081	+	8.32684i	0.667315	+	0.744775i
$126$	0.0917087	−	0.158844i	0.00817006	−	0.0141510i
$127$	2.73915	+	1.58145i	0.243060	+	0.140331i	0.616582	−	0.787290i	$-0.288517\pi$
$127$	2.73915	+	1.58145i	0.243060	+	0.140331i	−0.373522	+	0.927621i	$0.621850\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.05252	+	1.82302i	0.0926692	+	0.160508i
$130$	1.75738	−	1.69433i	0.154133	−	0.148602i
$131$	2.92162	−	5.06040i	0.255263	−	0.442129i	−0.709704	−	0.704500i	$-0.751171\pi$
$131$	2.92162	−	5.06040i	0.255263	−	0.442129i	0.964967	+	0.262371i	$0.0845045\pi$
$132$	1.17217	+	0.676752i	0.102024	+	0.0589037i
$133$	−3.62295	−	2.09171i	−0.314149	−	0.181374i
$134$	−12.7877			−1.10468
$135$	8.45446	+	8.76911i	0.727644	+	0.754725i
$136$	−0.585043	+	1.01332i	−0.0501670	+	0.0868919i
$137$			10.9288i			0.933711i	0.884334	+	0.466856i	$0.154613\pi$
$137$			10.9288i			0.933711i	−0.884334	+	0.466856i	$0.845387\pi$
$138$			0.879362i			0.0748563i
$139$	0.124232	−	0.215176i	0.0105372	−	0.0182510i	−0.860709	−	0.509098i	$-0.829979\pi$
$139$	0.124232	−	0.215176i	0.0105372	−	0.0182510i	0.871246	+	0.490847i	$0.163312\pi$
$140$	−1.17009	+	0.290725i	−0.0988904	+	0.0245707i
$141$	−4.73041	−	8.19330i	−0.398372	−	0.690001i
$142$			0.581449i			0.0487941i
$143$	−0.784640	+	0.453012i	−0.0656149	+	0.0378828i
$144$	−0.170086	−	0.294598i	−0.0141739	−	0.0245499i
$145$	15.4139	−	14.8608i	1.28005	−	1.23412i
$146$	2.87577	−	4.98098i	0.238000	−	0.412229i
$147$		−	10.9421i		−	0.902493i
$148$	1.58475	−	5.87270i	0.130266	−	0.482733i
$149$	−8.99386			−0.736805			−0.368403	−	0.929666i	$-0.620095\pi$
$149$	−8.99386			−0.736805			−0.368403	+	0.929666i	$0.620095\pi$
$150$	0.297844	−	8.14905i	0.0243189	−	0.665367i
$151$	−3.49220	−	6.04867i	−0.284191	−	0.492234i	0.688221	−	0.725501i	$-0.258392\pi$
$151$	−3.49220	−	6.04867i	−0.284191	−	0.492234i	−0.972413	+	0.233267i	$0.925058\pi$
$152$	−6.71925	+	3.87936i	−0.545003	+	0.314658i
$153$	0.344706	−	0.199016i	0.0278678	−	0.0160895i
$154$	0.447480			0.0360590
$155$	−4.97690	+	4.79831i	−0.399754	+	0.385410i
$156$	−1.78047			−0.142551
$157$	−7.03268	−	4.06032i	−0.561269	−	0.324049i	0.192386	−	0.981319i	$-0.438378\pi$
$157$	−7.03268	−	4.06032i	−0.561269	−	0.324049i	−0.753655	+	0.657271i	$0.771711\pi$
$158$			9.31124i			0.740763i
$159$	5.77205			0.457754
$160$	−0.618092	+	2.14894i	−0.0488645	+	0.169889i
$161$	0.145362	+	0.251775i	0.0114562	+	0.0198426i
$162$		−	7.86376i		−	0.617836i
$163$	−13.1690	−	7.60310i	−1.03147	−	0.595521i	−0.114066	−	0.993473i	$-0.536388\pi$
$163$	−13.1690	−	7.60310i	−1.03147	−	0.595521i	−0.917406	+	0.397952i	$0.869721\pi$
$164$	0.960811	−	1.66417i	0.0750267	−	0.129950i
$165$	−0.836590	+	2.90860i	−0.0651284	+	0.226435i
$166$	1.07838	+	1.86781i	0.0836983	+	0.144970i
$167$	−16.8170	+	9.70928i	−1.30134	+	0.751326i	−0.980633	−	0.195854i	$-0.937252\pi$
$167$	−16.8170	+	9.70928i	−1.30134	+	0.751326i	−0.320702	+	0.947180i	$0.603919\pi$
$168$	0.761550	+	0.439681i	0.0587548	+	0.0339221i
$169$	−5.90409	+	10.2262i	−0.454160	+	0.786629i
$170$	−2.51445	−	0.723221i	−0.192850	−	0.0554685i
$171$	2.63931			0.201833
$172$	1.11780	−	0.645362i	0.0852315	−	0.0492084i
$173$	−20.0293	−	11.5639i	−1.52280	−	0.879188i	−0.999637	−	0.0269546i	$-0.991419\pi$
$173$	−20.0293	−	11.5639i	−1.52280	−	0.879188i	−0.523162	−	0.852233i	$-0.675248\pi$
$174$	−15.6163			−1.18387
$175$	−1.26180	−	2.38243i	−0.0953828	−	0.180095i
$176$	0.414957	−	0.718726i	0.0312785	−	0.0541760i
$177$			6.37402i			0.479101i
$178$	9.34238	−	5.39383i	0.700241	−	0.404284i
$179$	−11.5174			−0.860854			−0.430427	−	0.902625i	$-0.641637\pi$
$179$	−11.5174			−0.860854			−0.430427	+	0.902625i	$0.641637\pi$
$180$	0.547595	−	0.527947i	0.0408153	−	0.0393508i
$181$	6.56032	+	11.3628i	0.487625	+	0.844591i	0.999899	−	0.0142313i	$-0.00453012\pi$
$181$	6.56032	+	11.3628i	0.487625	+	0.844591i	−0.512274	+	0.858822i	$0.671197\pi$
$182$	−0.509775	+	0.294319i	−0.0377870	+	0.0218163i
$183$	−2.56574	−	1.48133i	−0.189665	−	0.109503i
$184$	0.539189			0.0397495
$185$	13.5987	+	0.272555i	0.999799	+	0.0200387i
$186$	5.04226			0.369716
$187$	0.840972	+	0.485535i	0.0614979	+	0.0355059i
$188$	−5.02380	+	2.90049i	−0.366398	+	0.211540i
$189$	−1.46861	−	2.54371i	−0.106826	−	0.185028i
$190$	−12.0415	−	12.4896i	−0.873582	−	0.906094i
$191$	17.2979			1.25163			0.625817	−	0.779970i	$-0.284766\pi$
$191$	17.2979			1.25163			0.625817	+	0.779970i	$0.284766\pi$
$192$	1.41240	−	0.815449i	0.101931	−	0.0588499i
$193$		−	16.6153i		−	1.19600i	−0.801498	−	0.597998i	$-0.795963\pi$
$193$		−	16.6153i		−	1.19600i	0.801498	−	0.597998i	$-0.204037\pi$
$194$	4.58864	−	7.94775i	0.329445	−	0.570615i
$195$	−0.960007	−	3.86376i	−0.0687475	−	0.276690i
$196$	−6.70928			−0.479234
$197$	−10.4236	−	6.01806i	−0.742650	−	0.428769i	0.0803823	−	0.996764i	$-0.474386\pi$
$197$	−10.4236	−	6.01806i	−0.742650	−	0.428769i	−0.823032	+	0.567995i	$0.807719\pi$
$198$	−0.244491	+	0.141157i	−0.0173752	+	0.0100316i
$199$	18.2195			1.29155			0.645774	−	0.763528i	$-0.276535\pi$
$199$	18.2195			1.29155			0.645774	+	0.763528i	$0.276535\pi$
$200$	−4.99666	−	0.182626i	−0.353317	−	0.0129136i
$201$	−10.4277	+	18.0613i	−0.735512	+	1.27394i
$202$	−10.3056	−	5.94994i	−0.725099	−	0.418636i
$203$	−4.47120	+	2.58145i	−0.313817	+	0.181182i
$204$	0.954146	+	1.65263i	0.0668036	+	0.115707i
$205$	4.12946	+	1.18774i	0.288414	+	0.0829553i
$206$	−1.60977	+	2.78820i	−0.112158	+	0.194263i
$207$	−0.158844	−	0.0917087i	−0.0110404	−	0.00637420i
$208$			1.09171i			0.0756964i
$209$	3.21953	+	5.57640i	0.222700	+	0.385728i
$210$	−0.543527	+	1.88970i	−0.0375069	+	0.130402i
$211$	−10.0722			−0.693401			−0.346701	−	0.937976i	$-0.612698\pi$
$211$	−10.0722			−0.693401			−0.346701	+	0.937976i	$0.612698\pi$
$212$		−	3.53919i		−	0.243072i
$213$	0.821238	+	0.474142i	0.0562703	+	0.0324877i
$214$	14.2267			0.972519
$215$	2.00320	+	2.07775i	0.136617	+	0.141701i
$216$	−5.44748			−0.370654
$217$	1.44368	−	0.833507i	0.0980032	−	0.0565822i
$218$	8.10660	−	4.68035i	0.549048	−	0.316993i
$219$	−4.69008	−	8.12346i	−0.316926	−	0.548933i
$220$	1.78344	+	0.512963i	0.120239	+	0.0345840i
$221$	−1.27739			−0.0859268
$222$	−7.00231	−	7.02718i	−0.469964	−	0.471634i
$223$			23.5597i			1.57767i	0.614602	+	0.788837i	$0.289317\pi$
$223$			23.5597i			1.57767i	−0.614602	+	0.788837i	$0.710683\pi$
$224$	0.269594	−	0.466951i	0.0180130	−	0.0311995i
$225$	1.44095	+	0.903666i	0.0960631	+	0.0602444i
$226$	6.58864	+	11.4119i	0.438270	+	0.759105i
$227$	−8.40652	+	4.85350i	−0.557960	+	0.322138i	−0.752326	−	0.658791i	$-0.771068\pi$
$227$	−8.40652	+	4.85350i	−0.557960	+	0.322138i	0.194366	+	0.980929i	$0.437735\pi$
$228$			12.6537i			0.838011i
$229$	9.62310	+	16.6677i	0.635912	+	1.10143i	0.986321	+	0.164835i	$0.0527093\pi$
$229$	9.62310	+	16.6677i	0.635912	+	1.10143i	−0.350409	+	0.936597i	$0.613957\pi$
$230$	0.290725	+	1.17009i	0.0191698	+	0.0771532i
$231$	0.364897	−	0.632020i	0.0240085	−	0.0415839i
$232$			9.57531i			0.628650i
$233$		−	5.14342i		−	0.336957i	−0.985705	−	0.168478i	$-0.946115\pi$
$233$		−	5.14342i		−	0.336957i	0.985705	−	0.168478i	$-0.0538854\pi$
$234$	0.185685	−	0.321616i	0.0121386	−	0.0210247i
$235$	−9.00310	−	9.33817i	−0.587297	−	0.609155i
$236$	3.90829			0.254408
$237$	13.1512	+	7.59284i	0.854262	+	0.493208i
$238$	0.546373	+	0.315449i	0.0354161	+	0.0204475i
$239$	15.1526	−	26.2450i	0.980137	−	1.69765i	0.318317	−	0.947984i	$-0.396882\pi$
$239$	15.1526	−	26.2450i	0.980137	−	1.69765i	0.661820	−	0.749663i	$-0.269784\pi$
$240$	2.53114	+	2.62535i	0.163385	+	0.169465i
$241$	−4.95774	−	8.58706i	−0.319356	−	0.553141i	0.660998	−	0.750388i	$-0.270133\pi$
$241$	−4.95774	−	8.58706i	−0.319356	−	0.553141i	−0.980354	+	0.197247i	$0.936800\pi$
$242$	8.92980	+	5.15562i	0.574029	+	0.331416i
$243$	3.04620	+	1.75872i	0.195414	+	0.112822i
$244$	−0.908291	+	1.57321i	−0.0581474	+	0.100714i
$245$	−3.61757	−	14.5597i	−0.231118	−	0.930186i
$246$	−1.56698	−	2.71410i	−0.0999073	−	0.173044i
$247$	−7.33547	−	4.23513i	−0.466745	−	0.269475i
$248$		−	3.09171i		−	0.196324i
$249$	3.51745			0.222909
$250$	−2.29783	−	10.9417i	−0.145328	−	0.692011i
$251$	−23.0472			−1.45473			−0.727363	−	0.686253i	$-0.759254\pi$
$251$	−23.0472			−1.45473			−0.727363	+	0.686253i	$0.759254\pi$
$252$	−0.158844	+	0.0917087i	−0.0100062	+	0.00577711i
$253$		−	0.447480i		−	0.0281328i
$254$	−1.58145	−	2.73915i	−0.0992290	−	0.171870i
$255$	−3.07188	+	2.96166i	−0.192369	+	0.185466i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.93797	+	3.42829i	0.370400	+	0.213851i	0.673633	−	0.739066i	$-0.264733\pi$
$257$	5.93797	+	3.42829i	0.370400	+	0.213851i	−0.303233	+	0.952916i	$0.598066\pi$
$258$		−	2.10504i		−	0.131054i
$259$	−3.16649	−	0.854480i	−0.196756	−	0.0530948i
$260$	−2.36910	+	0.588637i	−0.146925	+	0.0365057i
$261$	1.62863	−	2.82087i	0.100810	−	0.174607i
$262$	−5.06040	+	2.92162i	−0.312632	+	0.180498i
$263$	2.99715	−	1.73041i	0.184812	−	0.106701i	−0.404739	−	0.914432i	$-0.632638\pi$
$263$	2.99715	−	1.73041i	0.184812	−	0.106701i	0.589552	+	0.807731i	$0.299304\pi$
$264$	−0.676752	−	1.17217i	−0.0416512	−	0.0721420i
$265$	7.68035	−	1.90829i	0.471800	−	0.117225i
$266$	2.09171	+	3.62295i	0.128251	+	0.222137i
$267$		−	17.5936i		−	1.07671i
$268$	11.0744	+	6.39383i	0.676479	+	0.390565i
$269$	26.6381			1.62415			0.812076	−	0.583551i	$-0.198337\pi$
$269$	26.6381			1.62415			0.812076	+	0.583551i	$0.198337\pi$
$270$	−2.93722	−	11.8215i	−0.178754	−	0.719434i
$271$	−5.84377	+	10.1217i	−0.354984	+	0.614850i	−0.987115	−	0.160011i	$-0.948847\pi$
$271$	−5.84377	+	10.1217i	−0.354984	+	0.614850i	0.632132	+	0.774861i	$0.282180\pi$
$272$	1.01332	−	0.585043i	0.0614418	−	0.0354735i
$273$			0.960007i			0.0581023i
$274$	5.46441	−	9.46463i	0.330117	−	0.571779i
$275$	−0.151564	+	4.14680i	−0.00913965	+	0.250061i
$276$	0.439681	−	0.761550i	0.0264657	−	0.0458399i
$277$	−6.06840	+	3.50359i	−0.364615	+	0.210511i	−0.671103	−	0.741364i	$-0.734179\pi$
$277$	−6.06840	+	3.50359i	−0.364615	+	0.210511i	0.306488	+	0.951874i	$0.400846\pi$
$278$	−0.215176	+	0.124232i	−0.0129054	+	0.00745095i
$279$	−0.525858	+	0.910813i	−0.0314823	+	0.0545289i
$280$	1.15869	+	0.333268i	0.0692448	+	0.0199166i
$281$	11.4535	−	19.8381i	0.683261	−	1.18344i	−0.290719	−	0.956808i	$-0.593895\pi$
$281$	11.4535	−	19.8381i	0.683261	−	1.18344i	0.973980	−	0.226634i	$-0.0727720\pi$
$282$			9.46081i			0.563383i
$283$	13.9401	−	8.04831i	0.828652	−	0.478423i	−0.0247387	−	0.999694i	$-0.507875\pi$
$283$	13.9401	−	8.04831i	0.828652	−	0.478423i	0.853391	+	0.521271i	$0.174542\pi$
$284$	0.290725	−	0.503550i	0.0172513	−	0.0298802i
$285$	−27.4596	+	6.82273i	−1.62657	+	0.404143i
$286$	0.906024			0.0535743
$287$	−0.897304	−	0.518059i	−0.0529662	−	0.0305800i
$288$			0.340173i			0.0200449i
$289$	−7.81545	−	13.5368i	−0.459732	−	0.796280i
$290$	−20.7792	+	5.16290i	−1.22020	+	0.303176i
$291$	−7.48360	−	12.9620i	−0.438696	−	0.759844i
$292$	−4.98098	+	2.87577i	−0.291490	+	0.168292i
$293$	21.4248	−	12.3696i	1.25165	−	0.722641i	0.280214	−	0.959938i	$-0.409595\pi$
$293$	21.4248	−	12.3696i	1.25165	−	0.722641i	0.971437	+	0.237296i	$0.0762612\pi$
$294$	−5.47107	+	9.47617i	−0.319079	+	0.552662i
$295$	2.10731	+	8.48133i	0.122692	+	0.493802i
$296$	−4.30878	+	4.29353i	−0.250443	+	0.249556i
$297$			4.52094i			0.262331i
$298$	7.78891	+	4.49693i	0.451199	+	0.260500i
$299$	0.294319	+	0.509775i	0.0170209	+	0.0294810i
$300$	−4.33246	+	6.90836i	−0.250135	+	0.398854i
$301$	−0.347972	−	0.602705i	−0.0200568	−	0.0347394i
$302$			6.98440i			0.401907i
$303$	−16.8074	+	9.70374i	−0.965559	+	0.557466i
$304$	7.75872			0.444993
$305$	−3.90373	−	1.12282i	−0.223527	−	0.0642922i
$306$	−0.398032			−0.0227540
$307$			4.56690i			0.260647i	0.991472	+	0.130323i	$0.0416015\pi$
$307$			4.56690i			0.260647i	−0.991472	+	0.130323i	$0.958398\pi$
$308$	−0.387529	−	0.223740i	−0.0220815	−	0.0127488i
$309$	2.62537	+	4.54727i	0.149352	+	0.258685i
$310$	6.70928	−	1.66701i	0.381061	−	0.0946801i
$311$	5.08084	−	8.80027i	0.288108	−	0.499018i	−0.685250	−	0.728308i	$-0.740307\pi$
$311$	5.08084	−	8.80027i	0.288108	−	0.499018i	0.973358	+	0.229290i	$0.0736405\pi$
$312$	1.54193	+	0.890233i	0.0872945	+	0.0503995i
$313$	11.0671	+	6.38962i	0.625552	+	0.361163i	0.779028	−	0.626990i	$-0.215713\pi$
$313$	11.0671	+	6.38962i	0.625552	+	0.361163i	−0.153475	+	0.988152i	$0.549047\pi$
$314$	4.06032	+	7.03268i	0.229137	+	0.396877i
$315$	−0.284663	−	0.295257i	−0.0160389	−	0.0166359i
$316$	4.65562	−	8.06377i	0.261899	−	0.453623i
$317$	9.83439	+	5.67789i	0.552354	+	0.318902i	0.750071	−	0.661357i	$-0.230019\pi$
$317$	9.83439	+	5.67789i	0.552354	+	0.318902i	−0.197717	+	0.980259i	$0.563353\pi$
$318$	−4.99875	−	2.88603i	−0.280316	−	0.161840i
$319$	7.94668			0.444928
$320$	1.60976	−	1.55199i	0.0899881	−	0.0867591i
$321$	11.6012	−	20.0938i	0.647514	−	1.12153i
$322$		−	0.290725i		−	0.0162015i
$323$			9.07838i			0.505134i
$324$	−3.93188	+	6.81022i	−0.218438	+	0.378345i
$325$	−2.55479	−	4.82377i	−0.141714	−	0.267575i
$326$	7.60310	+	13.1690i	0.421097	+	0.729361i
$327$		−	15.2663i		−	0.844230i
$328$	−1.66417	+	0.960811i	−0.0918886	+	0.0530519i
$329$	1.56391	+	2.70878i	0.0862213	+	0.149340i
$330$	2.17881	−	2.10063i	0.119940	−	0.115636i
$331$	−13.8540	+	23.9959i	−0.761486	+	1.31893i	0.180598	+	0.983557i	$0.442197\pi$
$331$	−13.8540	+	23.9959i	−0.761486	+	1.31893i	−0.942084	+	0.335376i	$0.891137\pi$
$332$		−	2.15676i		−	0.118367i
$333$	1.99963	−	0.532001i	0.109579	−	0.0291535i
$334$	19.4186			1.06254
$335$	−7.90395	+	27.4800i	−0.431839	+	1.50139i
$336$	−0.439681	−	0.761550i	−0.0239866	−	0.0415459i
$337$	22.1844	−	12.8082i	1.20846	−	0.697706i	0.246038	−	0.969260i	$-0.420871\pi$
$337$	22.1844	−	12.8082i	1.20846	−	0.697706i	0.962423	+	0.271554i	$0.0875377\pi$
$338$	10.2262	−	5.90409i	0.556231	−	0.321140i
$339$	21.4908			1.16722
$340$	1.81597	+	1.88355i	0.0984847	+	0.102150i
$341$	−2.56585			−0.138949
$342$	−2.28571	−	1.31965i	−0.123597	−	0.0713587i
$343$			7.39189i			0.399124i
$344$	−1.29072			−0.0695912
$345$	1.88970	+	0.543527i	0.101738	+	0.0292625i
$346$	11.5639	+	20.0293i	0.621680	+	1.07678i
$347$			18.5464i			0.995622i	0.867286	+	0.497811i	$0.165863\pi$
$347$			18.5464i			0.995622i	−0.867286	+	0.497811i	$0.834137\pi$
$348$	13.5242	+	7.80817i	0.724971	+	0.418562i
$349$	−4.23513	+	7.33547i	−0.226701	+	0.392658i	−0.956829	−	0.290653i	$-0.906128\pi$
$349$	−4.23513	+	7.33547i	−0.226701	+	0.392658i	0.730127	+	0.683311i	$0.239461\pi$
$350$	−0.0984700	+	2.69415i	−0.00526344	+	0.144008i
$351$	−2.97353	−	5.15031i	−0.158715	−	0.274903i
$352$	−0.718726	+	0.414957i	−0.0383082	+	0.0221173i
$353$	18.5051	+	10.6839i	0.984929	+	0.568649i	0.903754	−	0.428051i	$-0.140800\pi$
$353$	18.5051	+	10.6839i	0.984929	+	0.568649i	0.0811740	+	0.996700i	$0.474133\pi$
$354$	3.18701	−	5.52007i	0.169388	−	0.293388i
$355$	1.24950	+	0.359389i	0.0663167	+	0.0190744i
$356$	−10.7877			−0.571744
$357$	0.891079	−	0.514465i	0.0471609	−	0.0272284i
$358$	9.97440	+	5.75872i	0.527164	+	0.304358i
$359$	18.6319			0.983356			0.491678	−	0.870777i	$-0.336384\pi$
$359$	18.6319			0.983356			0.491678	+	0.870777i	$0.336384\pi$
$360$	−0.738205	+	0.183417i	−0.0389068	+	0.00966695i
$361$	−20.5989	+	35.6783i	−1.08415	+	1.87781i
$362$		−	13.1206i		−	0.689605i
$363$	14.5636	−	8.40829i	0.764390	−	0.441321i
$364$	0.588637			0.0308530
$365$	−8.92635	−	9.25857i	−0.467227	−	0.484616i
$366$	1.48133	+	2.56574i	0.0774304	+	0.134113i
$367$	21.5721	−	12.4547i	1.12606	−	0.650128i	0.183116	−	0.983091i	$-0.441382\pi$
$367$	21.5721	−	12.4547i	1.12606	−	0.650128i	0.942940	+	0.332963i	$0.108048\pi$
$368$	−0.466951	−	0.269594i	−0.0243415	−	0.0140536i
$369$	0.653684			0.0340294
$370$	−11.6406	−	7.03541i	−0.605165	−	0.365754i
$371$	−1.90829			−0.0990735
$372$	−4.36673	−	2.52113i	−0.226404	−	0.130715i
$373$	−8.36992	+	4.83237i	−0.433378	+	0.250211i	−0.700785	−	0.713373i	$-0.747167\pi$
$373$	−8.36992	+	4.83237i	−0.433378	+	0.250211i	0.267407	+	0.963584i	$0.413833\pi$
$374$	−0.485535	−	0.840972i	−0.0251064	−	0.0434856i
$375$	−17.3278	−	5.67691i	−0.894801	−	0.293154i
$376$	5.80098			0.299163
$377$	−9.05295	+	5.22672i	−0.466251	+	0.269190i
$378$			2.93722i			0.151074i
$379$	−6.09530	+	10.5574i	−0.313095	+	0.542296i	−0.979031	−	0.203713i	$-0.934699\pi$
$379$	−6.09530	+	10.5574i	−0.313095	+	0.542296i	0.665936	+	0.746009i	$0.268032\pi$
$380$	4.18342	+	16.8371i	0.214605	+	0.863725i
$381$	−5.15836			−0.264271
$382$	−14.9804	−	8.64896i	−0.766466	−	0.442519i
$383$	4.52025	−	2.60977i	0.230974	−	0.133353i	−0.380047	−	0.924967i	$-0.624092\pi$
$383$	4.52025	−	2.60977i	0.230974	−	0.133353i	0.611021	+	0.791614i	$0.290759\pi$
$384$	−1.63090			−0.0832264
$385$	0.276584	−	0.961610i	0.0140960	−	0.0490082i
$386$	−8.30765	+	14.3893i	−0.422848	+	0.732395i
$387$	0.380245	+	0.219535i	0.0193290	+	0.0111596i
$388$	−7.94775	+	4.58864i	−0.403486	+	0.232953i
$389$	−6.37629	−	11.0441i	−0.323291	−	0.559956i	0.657874	−	0.753128i	$-0.271456\pi$
$389$	−6.37629	−	11.0441i	−0.323291	−	0.559956i	−0.981165	+	0.193172i	$0.938123\pi$
$390$	−1.10049	+	3.82612i	−0.0557255	+	0.193743i
$391$	0.315449	−	0.546373i	0.0159529	−	0.0276313i
$392$	5.81040	+	3.35464i	0.293470	+	0.169435i
$393$			9.52973i			0.480711i
$394$	6.01806	+	10.4236i	0.303185	+	0.525133i
$395$	20.0093	+	5.75520i	1.00678	+	0.289576i
$396$	0.282314			0.0141868
$397$			25.2895i			1.26924i	0.772823	+	0.634622i	$0.218844\pi$
$397$			25.2895i			1.26924i	−0.772823	+	0.634622i	$0.781156\pi$
$398$	−15.7786	−	9.10977i	−0.790909	−	0.456631i
$399$	6.82273			0.341564
$400$	4.23592	+	2.65649i	0.211796	+	0.132825i
$401$	−13.7237			−0.685326			−0.342663	−	0.939458i	$-0.611329\pi$
$401$	−13.7237			−0.685326			−0.342663	+	0.939458i	$0.611329\pi$
$402$	18.0613	−	10.4277i	0.900814	−	0.520085i
$403$	2.92305	−	1.68762i	0.145607	−	0.0840665i
$404$	5.94994	+	10.3056i	0.296021	+	0.512723i
$405$	−16.8988	−	4.86053i	−0.839708	−	0.241522i
$406$	5.16290			0.256230
$407$	3.56326	+	3.57592i	0.176624	+	0.177252i
$408$		−	1.90829i		−	0.0944745i
$409$	6.02586	−	10.4371i	0.297959	−	0.516081i	−0.677709	−	0.735330i	$-0.737027\pi$
$409$	6.02586	−	10.4371i	0.297959	−	0.516081i	0.975669	+	0.219249i	$0.0703606\pi$
$410$	−2.98235	−	3.09334i	−0.147288	−	0.152769i
$411$	−8.91189	−	15.4358i	−0.439591	−	0.761394i
$412$	2.78820	−	1.60977i	0.137365	−	0.0793075i
$413$		−	2.10731i		−	0.103694i
$414$	0.0917087	+	0.158844i	0.00450724	+	0.00780677i
$415$	4.68035	−	1.16290i	0.229749	−	0.0570844i
$416$	0.545854	−	0.945448i	0.0267627	−	0.0463544i
$417$			0.405220i			0.0198437i
$418$		−	6.43907i		−	0.314945i
$419$	−8.75513	+	15.1643i	−0.427716	+	0.740826i	−0.996670	−	0.0815436i	$-0.974015\pi$
$419$	−8.75513	+	15.1643i	−0.427716	+	0.740826i	0.568954	+	0.822370i	$0.307348\pi$
$420$	1.41556	−	1.36476i	0.0690721	−	0.0665937i
$421$	−1.70209			−0.0829547			−0.0414773	−	0.999139i	$-0.513206\pi$
$421$	−1.70209			−0.0829547			−0.0414773	+	0.999139i	$0.513206\pi$
$422$	8.72281	+	5.03612i	0.424620	+	0.245154i
$423$	−1.70896	−	0.986669i	−0.0830925	−	0.0479735i
$424$	−1.76959	+	3.06503i	−0.0859391	+	0.148851i
$425$	−3.10832	+	4.95640i	−0.150776	+	0.240421i
$426$	−0.474142	−	0.821238i	−0.0229723	−	0.0397891i
$427$	0.848255	+	0.489741i	0.0410500	+	0.0237002i
$428$	−12.3207	−	7.11336i	−0.595544	−	0.343837i
$429$	0.738816	−	1.27967i	0.0356704	−	0.0617829i
$430$	−0.695944	−	2.80098i	−0.0335614	−	0.135075i
$431$	−10.8902	−	18.8624i	−0.524564	−	0.908572i	−0.999591	−	0.0286003i	$-0.990895\pi$
$431$	−10.8902	−	18.8624i	−0.524564	−	0.908572i	0.475027	−	0.879971i	$-0.342438\pi$
$432$	4.71766	+	2.72374i	0.226978	+	0.131046i
$433$		−	10.6803i		−	0.513265i	−0.966509	−	0.256632i	$-0.917387\pi$
$433$		−	10.6803i		−	0.513265i	0.966509	−	0.256632i	$-0.0826129\pi$
$434$	−1.66701			−0.0800193
$435$	−9.65234	+	33.5587i	−0.462794	+	1.60901i
$436$	−9.36069			−0.448296
$437$	3.62295	−	2.09171i	0.173309	−	0.100060i
$438$			9.38017i			0.448202i
$439$	−15.4613	−	26.7798i	−0.737929	−	1.27813i	−0.953426	−	0.301626i	$-0.902470\pi$
$439$	−15.4613	−	26.7798i	−0.737929	−	1.27813i	0.215497	−	0.976504i	$-0.430863\pi$
$440$	−1.28802	−	1.33596i	−0.0614040	−	0.0636893i
$441$	−1.14116	−	1.97654i	−0.0543408	−	0.0941210i
$442$	1.10626	+	0.638697i	0.0526192	+	0.0303797i
$443$		−	4.78539i		−	0.227361i	−0.993517	−	0.113680i	$-0.963736\pi$
$443$		−	4.78539i		−	0.227361i	0.993517	−	0.113680i	$-0.0362639\pi$
$444$	2.55058	+	9.58687i	0.121045	+	0.454973i
$445$	−5.81658	−	23.4101i	−0.275732	−	1.10975i
$446$	11.7799	−	20.4033i	0.557792	−	0.966125i
$447$	12.7029	−	7.33403i	0.600827	−	0.346888i
$448$	−0.466951	+	0.269594i	−0.0220614	+	0.0127371i
$449$	−9.04831	−	15.6721i	−0.427016	−	0.739614i	0.569590	−	0.821929i	$-0.307102\pi$
$449$	−9.04831	−	15.6721i	−0.427016	−	0.739614i	−0.996606	+	0.0823149i	$0.973769\pi$
$450$	−0.796064	−	1.50307i	−0.0375268	−	0.0708555i
$451$	0.797390	+	1.38112i	0.0375476	+	0.0650344i
$452$		−	13.1773i		−	0.619807i
$453$	9.86476	+	5.69542i	0.463487	+	0.267594i
$454$	9.70701			0.455572
$455$	0.317387	+	1.27739i	0.0148793	+	0.0598851i
$456$	6.32684	−	10.9584i	0.296282	−	0.513175i
$457$	−33.6965	+	19.4547i	−1.57625	+	0.910051i	−0.580879	+	0.813990i	$0.697291\pi$
$457$	−33.6965	+	19.4547i	−1.57625	+	0.910051i	−0.995375	+	0.0960611i	$0.969376\pi$
$458$		−	19.2462i		−	0.899316i
$459$	−3.18701	+	5.52007i	−0.148757	+	0.257655i
$460$	0.333268	−	1.15869i	0.0155387	−	0.0540241i
$461$	11.4319	−	19.8006i	0.532436	−	0.922206i	−0.466847	−	0.884338i	$-0.654610\pi$
$461$	11.4319	−	19.8006i	0.532436	−	0.922206i	0.999283	−	0.0378677i	$-0.0120566\pi$
$462$	−0.632020	+	0.364897i	−0.0294042	+	0.0169766i
$463$	−23.7807	+	13.7298i	−1.10518	+	0.638078i	−0.937577	−	0.347777i	$-0.886937\pi$
$463$	−23.7807	+	13.7298i	−1.10518	+	0.638078i	−0.167605	+	0.985854i	$0.553603\pi$
$464$	4.78765	−	8.29246i	0.222261	−	0.384968i
$465$	3.11658	−	10.8355i	0.144528	−	0.502486i
$466$	−2.57171	+	4.45434i	−0.119132	+	0.206343i
$467$		−	29.3896i		−	1.35999i	−0.733217	−	0.679995i	$-0.761982\pi$
$467$		−	29.3896i		−	1.35999i	0.733217	−	0.679995i	$-0.238018\pi$
$468$	−0.321616	+	0.185685i	−0.0148667	+	0.00858329i
$469$	3.44748	−	5.97121i	0.159190	−	0.275725i
$470$	3.12783	+	12.5886i	0.144276	+	0.580671i
$471$	13.2439			0.610248
$472$	−3.38468	−	1.95415i	−0.155793	−	0.0899468i
$473$			1.07119i			0.0492534i
$474$	−7.59284	−	13.1512i	−0.348751	−	0.604054i
$475$	−34.2823	+	18.1568i	−1.57298	+	0.833089i
$476$	−0.315449	−	0.546373i	−0.0144586	−	0.0250430i
$477$	1.04264	−	0.601968i	0.0477392	−	0.0275622i
$478$	−26.2450	+	15.1526i	−1.20042	+	0.693062i
$479$	−15.5706	+	26.9690i	−0.711438	+	1.23225i	0.252880	+	0.967498i	$0.418622\pi$
$479$	−15.5706	+	26.9690i	−0.711438	+	1.23225i	−0.964317	+	0.264749i	$0.914711\pi$
$480$	−0.879362	−	3.53919i	−0.0401372	−	0.161541i
$481$	−6.41127	−	1.73009i	−0.292329	−	0.0788852i
$482$			9.91548i			0.451638i
$483$	−0.410619	−	0.237071i	−0.0186838	−	0.0107871i
$484$	−5.15562	−	8.92980i	−0.234346	−	0.405900i
$485$	−14.2431	−	14.7732i	−0.646745	−	0.670815i
$486$	−1.75872	−	3.04620i	−0.0797773	−	0.138178i
$487$		−	39.1194i		−	1.77267i	−0.463045	−	0.886335i	$-0.653243\pi$
$487$		−	39.1194i		−	1.77267i	0.463045	−	0.886335i	$-0.346757\pi$
$488$	1.57321	−	0.908291i	0.0712157	−	0.0411164i
$489$	24.7998			1.12148
$490$	−4.14695	+	14.4179i	−0.187340	+	0.651333i
$491$	5.88163			0.265434			0.132717	−	0.991154i	$-0.457630\pi$
$491$	5.88163			0.265434			0.132717	+	0.991154i	$0.457630\pi$
$492$			3.13397i			0.141290i
$493$	9.70289	+	5.60197i	0.436996	+	0.252300i
$494$	4.23513	+	7.33547i	0.190548	+	0.330038i
$495$	0.152221	+	0.612646i	0.00684181	+	0.0275364i
$496$	−1.54585	+	2.67750i	−0.0694109	+	0.120223i
$497$	−0.271508	−	0.156755i	−0.0121788	−	0.00703144i
$498$	−3.04620	−	1.75872i	−0.136503	−	0.0788103i
$499$	−10.3691	−	17.9598i	−0.464185	−	0.803992i	0.534980	−	0.844865i	$-0.320319\pi$
$499$	−10.3691	−	17.9598i	−0.464185	−	0.803992i	−0.999164	+	0.0408734i	$0.986986\pi$
$500$	−3.48085	+	10.6247i	−0.155668	+	0.475150i
$501$	15.8348	−	27.4267i	0.707448	−	1.22534i
$502$	19.9594	+	11.5236i	0.890834	+	0.514323i
$503$	−14.2502	−	8.22733i	−0.635383	−	0.366839i	0.147451	−	0.989069i	$-0.452893\pi$
$503$	−14.2502	−	8.22733i	−0.635383	−	0.366839i	−0.782834	+	0.622231i	$0.786227\pi$
$504$	0.183417			0.00817006
$505$	−19.1559	+	18.4685i	−0.852426	+	0.821840i
$506$	−0.223740	+	0.387529i	−0.00994646	+	0.0172278i
$507$		−	19.2579i		−	0.855274i
$508$			3.16290i			0.140331i
$509$	−2.80878	+	4.86496i	−0.124497	+	0.215635i	−0.921536	−	0.388292i	$-0.873065\pi$
$509$	−2.80878	+	4.86496i	−0.124497	+	0.215635i	0.797039	+	0.603928i	$0.206398\pi$
$510$	4.14116	−	1.02893i	0.183374	−	0.0455618i
$511$	1.55058	+	2.68569i	0.0685937	+	0.118808i
$512$			1.00000i			0.0441942i
$513$	−36.6030	+	21.1327i	−1.61606	+	0.933034i
$514$	−3.42829	−	5.93797i	−0.151215	−	0.261913i
$515$	4.99670	+	5.18266i	0.220181	+	0.228375i
$516$	−1.05252	+	1.82302i	−0.0463346	+	0.0802539i
$517$		−	4.81432i		−	0.211733i
$518$	2.31502	+	2.32325i	0.101716	+	0.102078i
$519$	37.7191			1.65569
$520$	2.34602	+	0.674776i	0.102880	+	0.0295909i
$521$	−10.9433	−	18.9543i	−0.479434	−	0.830403i	0.520288	−	0.853991i	$-0.325825\pi$
$521$	−10.9433	−	18.9543i	−0.479434	−	0.830403i	−0.999722	+	0.0235874i	$0.992491\pi$
$522$	−2.82087	+	1.62863i	−0.123466	+	0.0712832i
$523$	26.5021	−	15.3010i	1.15886	−	0.669065i	0.207826	−	0.978166i	$-0.433361\pi$
$523$	26.5021	−	15.3010i	1.15886	−	0.669065i	0.951029	+	0.309101i	$0.100028\pi$
$524$	5.84324			0.255263
$525$	3.72491	+	2.33602i	0.162568	+	0.101952i
$526$	−3.46081			−0.150899
$527$	−3.13290	−	1.80878i	−0.136471	−	0.0787918i
$528$			1.35350i			0.0589037i
$529$	22.7093			0.987360
$530$	−7.60552	−	2.18754i	−0.330363	−	0.0950209i
$531$	0.664748	+	1.15138i	0.0288476	+	0.0499655i
$532$		−	4.18342i		−	0.181374i
$533$	−1.81679	−	1.04893i	−0.0786940	−	0.0454340i
$534$	−8.79678	+	15.2365i	−0.380674	+	0.659346i
$535$	8.79342	−	30.5724i	0.380173	−	1.32176i
$536$	−6.39383	−	11.0744i	−0.276171	−	0.478343i
$537$	16.2672	−	9.39189i	0.701983	−	0.405290i
$538$	−23.0693	−	13.3190i	−0.994586	−	0.574225i
$539$	2.78406	−	4.82213i	0.119918	−	0.207704i
$540$	−3.36704	+	11.7063i	−0.144894	+	0.503760i
$541$	1.38735			0.0596470			0.0298235	−	0.999555i	$-0.490505\pi$
$541$	1.38735			0.0596470			0.0298235	+	0.999555i	$0.490505\pi$
$542$	10.1217	−	5.84377i	0.434764	−	0.251011i
$543$	−18.5316	−	10.6992i	−0.795266	−	0.459147i
$544$	−1.17009			−0.0501670
$545$	−5.04718	−	20.3135i	−0.216197	−	0.870135i
$546$	0.480004	−	0.831390i	0.0205423	−	0.0355802i
$547$		−	4.81658i		−	0.205942i	−0.994684	−	0.102971i	$-0.967165\pi$
$547$		−	4.81658i		−	0.205942i	0.994684	−	0.102971i	$-0.0328349\pi$
$548$	−9.46463	+	5.46441i	−0.404309	+	0.233428i
$549$	−0.617952			−0.0263736
$550$	2.20466	−	3.51545i	0.0940069	−	0.149899i
$551$	37.1461	+	64.3389i	1.58248	+	2.74093i
$552$	−0.761550	+	0.439681i	−0.0324137	+	0.0187141i
$553$	−4.34790	−	2.51026i	−0.184891	−	0.106747i
$554$	7.00719			0.297707
$555$	−19.4291	+	10.7041i	−0.824719	+	0.454365i
$556$	0.248464			0.0105372
$557$	24.3887	+	14.0808i	1.03338	+	0.596624i	0.917952	−	0.396691i	$-0.129842\pi$
$557$	24.3887	+	14.0808i	1.03338	+	0.596624i	0.115431	+	0.993315i	$0.463175\pi$
$558$	0.910813	−	0.525858i	0.0385578	−	0.0222613i
$559$	−0.704548	−	1.22031i	−0.0297992	−	0.0516137i
$560$	−0.836818	−	0.867962i	−0.0353620	−	0.0366781i
$561$	−1.58372			−0.0668646
$562$	−19.8381	+	11.4535i	−0.836820	+	0.483138i
$563$		−	12.0228i		−	0.506700i	−0.967375	−	0.253350i	$-0.918468\pi$
$563$		−	12.0228i		−	0.506700i	0.967375	−	0.253350i	$-0.0815324\pi$
$564$	4.73041	−	8.19330i	0.199186	−	0.345000i
$565$	28.5958	−	7.10504i	1.20304	−	0.298911i
$566$	−16.0966			−0.676592
$567$	3.67199	+	2.12003i	0.154209	+	0.0890328i
$568$	−0.503550	+	0.290725i	−0.0211285	+	0.0121985i
$569$	30.7009			1.28705			0.643524	−	0.765426i	$-0.277472\pi$
$569$	30.7009			1.28705			0.643524	+	0.765426i	$0.277472\pi$
$570$	27.1921	+	7.82114i	1.13895	+	0.327592i
$571$	−23.1617	+	40.1172i	−0.969286	+	1.67885i	−0.271656	+	0.962394i	$0.587571\pi$
$571$	−23.1617	+	40.1172i	−0.969286	+	1.67885i	−0.697630	+	0.716458i	$0.745762\pi$
$572$	−0.784640	−	0.453012i	−0.0328074	−	0.0189414i
$573$	−24.4316	+	14.1056i	−1.02064	+	0.589268i
$574$	0.518059	+	0.897304i	0.0216234	+	0.0374527i
$575$	2.69415	+	0.0984700i	0.112354	+	0.00410648i
$576$	0.170086	−	0.294598i	0.00708694	−	0.0122749i
$577$	−15.5677	−	8.98800i	−0.648090	−	0.374175i	0.139634	−	0.990203i	$-0.455407\pi$
$577$	−15.5677	−	8.98800i	−0.648090	−	0.374175i	−0.787724	+	0.616028i	$0.788741\pi$
$578$			15.6309i			0.650160i
$579$	13.5489	+	23.4674i	0.563074	+	0.975273i
$580$	20.5768	+	5.91842i	0.854405	+	0.245749i
$581$	−1.16290			−0.0482452
$582$			14.9672i			0.620410i
$583$	2.54371	+	1.46861i	0.105350	+	0.0608236i
$584$	5.75154			0.238000
$585$	−0.576364	−	0.597815i	−0.0238297	−	0.0247166i
$586$	−24.7392			−1.02197
$587$	−18.8489	+	10.8824i	−0.777978	+	0.449166i	−0.835713	−	0.549166i	$-0.814946\pi$
$587$	−18.8489	+	10.8824i	−0.777978	+	0.449166i	0.0577349	+	0.998332i	$0.481612\pi$
$588$	9.47617	−	5.47107i	0.390791	−	0.225623i
$589$	−11.9939	−	20.7740i	−0.494198	−	0.855977i
$590$	2.41568	−	8.39870i	0.0994521	−	0.345769i
$591$	19.6297			0.807457
$592$	5.87828	−	1.56391i	0.241596	−	0.0642764i
$593$		−	31.7803i		−	1.30506i	−0.757763	−	0.652530i	$-0.773708\pi$
$593$		−	31.7803i		−	1.30506i	0.757763	−	0.652530i	$-0.226292\pi$
$594$	2.26047	−	3.91525i	0.0927482	−	0.160645i
$595$	1.01559	−	0.979150i	0.0416352	−	0.0401412i
$596$	−4.49693	−	7.78891i	−0.184201	−	0.319046i
$597$	−25.7332	+	14.8571i	−1.05319	+	0.608061i
$598$		−	0.588637i		−	0.0240712i
$599$	13.6603	+	23.6604i	0.558147	+	0.966739i	0.997651	+	0.0684981i	$0.0218207\pi$
$599$	13.6603	+	23.6604i	0.558147	+	0.966739i	−0.439504	+	0.898240i	$0.644846\pi$
$600$	7.20620	−	3.81658i	0.294192	−	0.155811i
$601$	−10.7176	+	18.5634i	−0.437180	+	0.757218i	−0.997471	−	0.0710781i	$-0.977356\pi$
$601$	−10.7176	+	18.5634i	−0.437180	+	0.757218i	0.560291	+	0.828296i	$0.310689\pi$
$602$			0.695944i			0.0283646i
$603$			4.35001i			0.177146i
$604$	3.49220	−	6.04867i	0.142096	−	0.246117i
$605$	16.5986	−	16.0030i	0.674828	−	0.650614i
$606$	19.4075			0.788375
$607$	0.993591	+	0.573650i	0.0403286	+	0.0232837i	0.520029	−	0.854149i	$-0.325921\pi$
$607$	0.993591	+	0.573650i	0.0403286	+	0.0232837i	−0.479700	+	0.877432i	$0.659255\pi$
$608$	−6.71925	−	3.87936i	−0.272502	−	0.157329i
$609$	4.21008	−	7.29207i	0.170601	−	0.295490i
$610$	2.81933	+	2.92425i	0.114151	+	0.118400i
$611$	3.16649	+	5.48453i	0.128103	+	0.221880i
$612$	0.344706	+	0.199016i	0.0139339	+	0.00804474i
$613$	−14.9115	−	8.60916i	−0.602270	−	0.347721i	0.167664	−	0.985844i	$-0.446378\pi$
$613$	−14.9115	−	8.60916i	−0.602270	−	0.347721i	−0.769934	+	0.638124i	$0.779711\pi$
$614$	2.28345	−	3.95505i	0.0921525	−	0.159613i
$615$	−6.80098	+	1.68980i	−0.274242	+	0.0681394i
$616$	0.223740	+	0.387529i	0.00901474	+	0.0156140i
$617$	8.90867	+	5.14342i	0.358650	+	0.207066i	0.668488	−	0.743723i	$-0.266942\pi$
$617$	8.90867	+	5.14342i	0.358650	+	0.207066i	−0.309839	+	0.950789i	$0.600275\pi$
$618$		−	5.25073i		−	0.211215i
$619$	−32.8371			−1.31983			−0.659917	−	0.751338i	$-0.729409\pi$
$619$	−32.8371			−1.31983			−0.659917	+	0.751338i	$0.729409\pi$
$620$	−6.64391	−	1.91096i	−0.266826	−	0.0767460i
$621$	2.93722			0.117867
$622$	−8.80027	+	5.08084i	−0.352859	+	0.203723i
$623$			5.81658i			0.233036i
$624$	−0.890233	−	1.54193i	−0.0356378	−	0.0617265i
$625$	−24.9333	−	1.82504i	−0.997332	−	0.0730017i
$626$	−6.38962	−	11.0671i	−0.255381	−	0.442332i
$627$	−9.09453	−	5.25073i	−0.363201	−	0.209694i
$628$		−	8.12064i		−	0.324049i
$629$	1.82991	+	6.87810i	0.0729634	+	0.274248i
$630$	0.0988967	+	0.398032i	0.00394014	+	0.0158580i
$631$	13.0405	−	22.5868i	0.519135	−	0.899168i	−0.480618	−	0.876930i	$-0.659588\pi$
$631$	13.0405	−	22.5868i	0.519135	−	0.899168i	0.999753	−	0.0222376i	$-0.00707905\pi$
$632$	−8.06377	+	4.65562i	−0.320760	+	0.185191i
$633$	14.2260	−	8.21339i	0.565433	−	0.326453i
$634$	−5.67789	−	9.83439i	−0.225498	−	0.390573i
$635$	−6.86376	+	1.70540i	−0.272380	+	0.0676767i
$636$	2.88603	+	4.99875i	0.114438	+	0.198213i
$637$			7.32457i			0.290210i
$638$	−6.88202	−	3.97334i	−0.272462	−	0.157306i
$639$	0.197793			0.00782458
$640$	−2.17009	+	0.539189i	−0.0857802	+	0.0213133i
$641$	0.461945	−	0.800112i	0.0182457	−	0.0316025i	−0.856758	−	0.515718i	$-0.827525\pi$
$641$	0.461945	−	0.800112i	0.0182457	−	0.0316025i	0.875004	+	0.484116i	$0.160859\pi$
$642$	−20.0938	+	11.6012i	−0.793039	+	0.457861i
$643$		−	9.24128i		−	0.364440i	−0.983258	−	0.182220i	$-0.941672\pi$
$643$		−	9.24128i		−	0.364440i	0.983258	−	0.182220i	$-0.0583284\pi$
$644$	−0.145362	+	0.251775i	−0.00572808	+	0.00992132i
$645$	−4.52361	−	1.30111i	−0.178117	−	0.0512311i
$646$	4.53919	−	7.86211i	0.178592	−	0.309330i
$647$	38.7299	−	22.3607i	1.52263	−	0.879090i	0.522985	−	0.852342i	$-0.324818\pi$
$647$	38.7299	−	22.3607i	1.52263	−	0.879090i	0.999642	−	0.0267479i	$-0.00851514\pi$
$648$	6.81022	−	3.93188i	0.267531	−	0.154459i
$649$	−1.62177	+	2.80899i	−0.0636601	+	0.110263i
$650$	−0.199375	+	5.45490i	−0.00782011	+	0.213959i
$651$	−1.35937	+	2.35449i	−0.0532777	+	0.0922797i
$652$		−	15.2062i		−	0.595521i
$653$	−5.01848	+	2.89742i	−0.196388	+	0.113385i	−0.594970	−	0.803748i	$-0.702836\pi$
$653$	−5.01848	+	2.89742i	−0.196388	+	0.113385i	0.398581	+	0.917133i	$0.369503\pi$
$654$	−7.63317	+	13.2210i	−0.298480	+	0.516983i
$655$	3.15061	+	12.6803i	0.123105	+	0.495462i
$656$	1.92162			0.0750267
$657$	−1.69439	−	0.978259i	−0.0661046	−	0.0381655i
$658$		−	3.12783i		−	0.121935i
$659$	−3.66701	−	6.35146i	−0.142847	−	0.247418i	0.785721	−	0.618581i	$-0.212292\pi$
$659$	−3.66701	−	6.35146i	−0.142847	−	0.247418i	−0.928567	+	0.371164i	$0.878959\pi$
$660$	−2.93722	+	0.729794i	−0.114331	+	0.0284072i
$661$	20.7870	+	36.0042i	0.808522	+	1.40040i	0.913887	+	0.405968i	$0.133066\pi$
$661$	20.7870	+	36.0042i	0.808522	+	1.40040i	−0.105365	+	0.994434i	$0.533601\pi$
$662$	23.9959	−	13.8540i	0.932626	−	0.538452i
$663$	1.80419	−	1.04165i	0.0700689	−	0.0404543i
$664$	−1.07838	+	1.86781i	−0.0418492	+	0.0724849i
$665$	9.07838	−	2.25565i	0.352044	−	0.0874704i
$666$	−1.99773	−	0.539090i	−0.0774106	−	0.0208893i
$667$		−	5.16290i		−	0.199908i
$668$	−16.8170	−	9.70928i	−0.650668	−	0.375663i
$669$	−19.2117	−	33.2757i	−0.742769	−	1.28651i
$670$	20.5850	−	19.8464i	0.795268	−	0.766732i
$671$	−0.753803	−	1.30563i	−0.0291002	−	0.0504031i
$672$			0.879362i			0.0339221i
$673$	−27.2780	+	15.7490i	−1.05149	+	0.607079i	−0.923066	−	0.384640i	$-0.874325\pi$
$673$	−27.2780	+	15.7490i	−1.05149	+	0.607079i	−0.128425	+	0.991719i	$0.540992\pi$
$674$	−25.6163			−0.986705
$675$	−27.2192	−	0.994852i	−1.04767	−	0.0382919i
$676$	−11.8082			−0.454160
$677$			21.2351i			0.816132i	0.912952	+	0.408066i	$0.133797\pi$
$677$			21.2351i			0.816132i	−0.912952	+	0.408066i	$0.866203\pi$
$678$	−18.6116	−	10.7454i	−0.714773	−	0.412674i
$679$	2.47414	+	4.28534i	0.0949489	+	0.164456i
$680$	−0.630898	−	2.53919i	−0.0241938	−	0.0973734i
$681$	7.91557	−	13.7102i	0.303325	−	0.525375i
$682$	2.22209	+	1.28293i	0.0850883	+	0.0491258i
$683$	37.1124	+	21.4269i	1.42007	+	0.819876i	0.996304	−	0.0858963i	$-0.0273754\pi$
$683$	37.1124	+	21.4269i	1.42007	+	0.819876i	0.423764	+	0.905773i	$0.360709\pi$
$684$	1.31965	+	2.28571i	0.0504582	+	0.0873962i
$685$	−16.9615	−	17.5927i	−0.648064	−	0.672183i
$686$	3.69594	−	6.40156i	0.141112	−	0.244413i
$687$	−27.1833	−	15.6943i	−1.03711	−	0.598774i
$688$	1.11780	+	0.645362i	0.0426157	+	0.0246042i
$689$	−3.86376			−0.147198
$690$	−1.36476	−	1.41556i	−0.0519557	−	0.0538894i
$691$	−15.9480	+	27.6228i	−0.606691	+	1.05082i	0.385091	+	0.922879i	$0.374170\pi$
$691$	−15.9480	+	27.6228i	−0.606691	+	1.05082i	−0.991782	+	0.127940i	$0.959163\pi$
$692$		−	23.1278i		−	0.879188i
$693$		−	0.152221i		−	0.00578238i
$694$	9.27319	−	16.0616i	0.352005	−	0.609691i
$695$	0.133969	+	0.539189i	0.00508174	+	0.0204526i
$696$	−7.80817	−	13.5242i	−0.295968	−	0.512632i
$697$			2.24846i			0.0851667i
$698$	7.33547	−	4.23513i	0.277651	−	0.160302i
$699$	4.19420	+	7.26457i	0.158639	+	0.274771i
$700$	1.43235	−	2.28396i	0.0541377	−	0.0863257i
$701$	9.63809	−	16.6937i	0.364025	−	0.630511i	−0.624594	−	0.780950i	$-0.714735\pi$
$701$	9.63809	−	16.6937i	0.364025	−	0.630511i	0.988619	+	0.150439i	$0.0480688\pi$
$702$			5.94706i			0.224457i
$703$	−12.2956	+	45.5646i	−0.463739	+	1.71850i
$704$	0.829914			0.0312785
$705$	20.3308	+	5.84765i	0.765701	+	0.220235i
$706$	−10.6839	−	18.5051i	−0.402095	−	0.696450i
$707$	5.55666	−	3.20814i	0.208980	−	0.120655i
$708$	−5.52007	+	3.18701i	−0.207457	+	0.119775i
$709$	31.4740			1.18203			0.591015	−	0.806661i	$-0.298727\pi$
$709$	31.4740			1.18203			0.591015	+	0.806661i	$0.298727\pi$
$710$	−0.902406	−	0.935991i	−0.0338667	−	0.0351271i
$711$	3.16743			0.118788
$712$	9.34238	+	5.39383i	0.350121	+	0.202142i
$713$			1.66701i			0.0624302i
$714$	−1.02893			−0.0385067
$715$	0.560006	−	1.94699i	0.0209430	−	0.0728135i
$716$	−5.75872	−	9.97440i	−0.215214	−	0.372761i
$717$			49.4245i			1.84579i
$718$	−16.1357	−	9.31597i	−0.602180	−	0.347669i
$719$	−9.23041	+	15.9875i	−0.344236	+	0.596234i	−0.985215	−	0.171324i	$-0.945195\pi$
$719$	−9.23041	+	15.9875i	−0.344236	+	0.596234i	0.640979	+	0.767559i	$0.278529\pi$
$720$	0.731013	+	0.210258i	0.0272432	+	0.00783586i
$721$	−0.867969	−	1.50337i	−0.0323248	−	0.0559883i
$722$	35.6783	−	20.5989i	1.32781	−	0.766612i
$723$	14.0046	+	8.08557i	0.520837	+	0.300705i
$724$	−6.56032	+	11.3628i	−0.243812	+	0.422295i
$725$	−1.74870	+	47.8446i	−0.0649451	+	1.77690i
$726$	−16.8166			−0.624122
$727$	−37.0479	+	21.3896i	−1.37403	+	0.793297i	−0.991433	−	0.130618i	$-0.958304\pi$
$727$	−37.0479	+	21.3896i	−1.37403	+	0.793297i	−0.382598	+	0.923915i	$0.624971\pi$
$728$	−0.509775	−	0.294319i	−0.0188935	−	0.0109082i
$729$	−29.3279			−1.08622
$730$	3.10116	+	12.4813i	0.114779	+	0.461955i
$731$	−0.755130	+	1.30792i	−0.0279295	+	0.0483753i
$732$		−	2.96266i		−	0.109503i
$733$	28.3770	−	16.3835i	1.04813	−	0.605138i	0.126004	−	0.992030i	$-0.459785\pi$
$733$	28.3770	−	16.3835i	1.04813	−	0.605138i	0.922125	+	0.386892i	$0.126451\pi$
$734$	−24.9093			−0.919420
$735$	16.9821	+	17.6142i	0.626396	+	0.649709i
$736$	0.269594	+	0.466951i	0.00993738	+	0.0172121i
$737$	−9.19082	+	5.30632i	−0.338548	+	0.195461i
$738$	−0.566107	−	0.326842i	−0.0208387	−	0.0120312i
$739$	−32.9965			−1.21380			−0.606898	−	0.794780i	$-0.707586\pi$
$739$	−32.9965			−1.21380			−0.606898	+	0.794780i	$0.707586\pi$
$740$	6.56333	+	11.9131i	0.241273	+	0.437935i
$741$	13.8141			0.507475
$742$	1.65263	+	0.954146i	0.0606699	+	0.0350278i
$743$	34.2722	−	19.7870i	1.25732	−	0.725916i	0.284770	−	0.958596i	$-0.408083\pi$
$743$	34.2722	−	19.7870i	1.25732	−	0.725916i	0.972553	+	0.232680i	$0.0747494\pi$
$744$	2.52113	+	4.36673i	0.0924291	+	0.160092i
$745$	14.4779	−	13.9584i	0.530430	−	0.511397i
$746$	9.66475			0.353852
$747$	0.635377	−	0.366835i	0.0232472	−	0.0134218i
$748$			0.971071i			0.0355059i
$749$	−3.83545	+	6.64319i	−0.140144	+	0.242737i
$750$	12.1678	+	13.5802i	0.444306	+	0.495880i
$751$	−47.1699			−1.72125			−0.860627	−	0.509236i	$-0.829928\pi$
$751$	−47.1699			−1.72125			−0.860627	+	0.509236i	$0.829928\pi$
$752$	−5.02380	−	2.90049i	−0.183199	−	0.105770i
$753$	32.5518	−	18.7938i	1.18625	−	0.684884i
$754$	10.4534			0.380692
$755$	15.0091	+	4.31700i	0.546237	+	0.157112i
$756$	1.46861	−	2.54371i	0.0534128	−	0.0925138i
$757$	42.0005	+	24.2490i	1.52653	+	0.881344i	0.999504	+	0.0314974i	$0.0100276\pi$
$757$	42.0005	+	24.2490i	1.52653	+	0.881344i	0.527029	+	0.849847i	$0.323306\pi$
$758$	10.5574	−	6.09530i	0.383461	−	0.221391i
$759$	0.364897	+	0.632020i	0.0132449	+	0.0229409i
$760$	4.79560	−	16.6731i	0.173955	−	0.604796i
$761$	−13.7607	+	23.8342i	−0.498824	+	0.863988i	−0.999999	−	0.00135787i	$-0.999568\pi$
$761$	−13.7607	+	23.8342i	−0.498824	+	0.863988i	0.501175	+	0.865346i	$0.332901\pi$
$762$	4.46727	+	2.57918i	0.161832	+	0.0934339i
$763$			5.04718i			0.182720i
$764$	8.64896	+	14.9804i	0.312908	+	0.541973i
$765$	−0.246020	+	0.855348i	−0.00889488	+	0.0309252i
$766$	−5.21953			−0.188589
$767$		−	4.26672i		−	0.154062i
$768$	1.41240	+	0.815449i	0.0509656	+	0.0294250i
$769$	−5.24354			−0.189087			−0.0945435	−	0.995521i	$-0.530139\pi$
$769$	−5.24354			−0.189087			−0.0945435	+	0.995521i	$0.530139\pi$
$770$	−0.720334	+	0.694487i	−0.0259590	+	0.0250276i
$771$	−11.1824			−0.402723
$772$	14.3893	−	8.30765i	0.517881	−	0.298999i
$773$	20.6604	−	11.9283i	0.743103	−	0.429031i	−0.0800935	−	0.996787i	$-0.525522\pi$
$773$	20.6604	−	11.9283i	0.743103	−	0.429031i	0.823196	+	0.567757i	$0.192189\pi$
$774$	−0.219535	−	0.380245i	−0.00789102	−	0.0136676i
$775$	0.564627	−	15.4482i	0.0202820	−	0.554917i
$776$	9.17727			0.329445
$777$	5.16914	−	1.37525i	0.185442	−	0.0493367i
$778$			12.7526i			0.457202i
$779$	−7.45467	+	12.9119i	−0.267091	+	0.462616i
$780$	2.86611	−	2.76327i	0.102623	−	0.0989410i
$781$	0.241276	+	0.417903i	0.00863355	+	0.0149537i
$782$	−0.546373	+	0.315449i	−0.0195383	+	0.0112804i
$783$			52.1613i			1.86409i
$784$	−3.35464	−	5.81040i	−0.119808	−	0.207514i
$785$	17.6225	−	4.37856i	0.628974	−	0.156277i
$786$	4.76487	−	8.25299i	0.169957	−	0.294374i
$787$		−	29.1894i		−	1.04049i	−0.854017	−	0.520245i	$-0.825841\pi$
$787$		−	29.1894i		−	1.04049i	0.854017	−	0.520245i	$-0.174159\pi$
$788$		−	12.0361i		−	0.428769i
$789$	−2.82211	+	4.88805i	−0.100470	+	0.174019i
$790$	−14.4510	−	14.9888i	−0.514143	−	0.533279i
$791$	−7.10504			−0.252626
$792$	−0.244491	−	0.141157i	−0.00868762	−	0.00501580i
$793$	1.71748	+	0.991590i	0.0609896	+	0.0352124i
$794$	12.6448	−	21.9014i	0.448745	−	0.777250i
$795$	−9.29160	+	8.95820i	−0.329539	+	0.317715i
$796$	9.10977	+	15.7786i	0.322887	+	0.559257i
$797$	−7.49857	−	4.32930i	−0.265613	−	0.153352i	0.361279	−	0.932458i	$-0.382340\pi$
$797$	−7.49857	−	4.32930i	−0.265613	−	0.153352i	−0.626892	+	0.779106i	$0.715673\pi$
$798$	−5.90865	−	3.41136i	−0.209164	−	0.120761i
$799$	3.39383	−	5.87828i	0.120065	−	0.207959i
$800$	−2.34017	−	4.41855i	−0.0827376	−	0.156219i
$801$	−1.83483	−	3.17803i	−0.0648307	−	0.112290i
$802$	11.8850	+	6.86183i	0.419675	+	0.242299i
$803$		−	4.77328i		−	0.168445i
$804$	−20.8554			−0.735512
$805$	−0.624751	−	0.179695i	−0.0220196	−	0.00633340i
$806$	−3.37525			−0.118888
$807$	−37.6236	+	21.7220i	−1.32441	+	0.764650i
$808$		−	11.8999i		−	0.418636i
$809$	−18.9885	−	32.8891i	−0.667601	−	1.15632i	−0.978573	−	0.205899i	$-0.933988\pi$
$809$	−18.9885	−	32.8891i	−0.667601	−	1.15632i	0.310972	−	0.950419i	$-0.399345\pi$
$810$	12.2045	+	12.6587i	0.428823	+	0.444783i
$811$	−3.39576	−	5.88164i	−0.119241	−	0.206532i	0.800226	−	0.599699i	$-0.204713\pi$
$811$	−3.39576	−	5.88164i	−0.119241	−	0.206532i	−0.919467	+	0.393167i	$0.871380\pi$
$812$	−4.47120	−	2.58145i	−0.156908	−	0.0905911i
$813$		−	19.0612i		−	0.668504i
$814$	−1.29791	−	4.87846i	−0.0454918	−	0.170990i
$815$	32.9988	−	8.19902i	1.15590	−	0.287199i
$816$	−0.954146	+	1.65263i	−0.0334018	+	0.0578536i
$817$	−8.67270	+	5.00719i	−0.303420	+	0.175179i
$818$	−10.4371	+	6.02586i	−0.364924	+	0.210689i
$819$	0.100119	+	0.173412i	0.00349845	+	0.00605949i
$820$	1.03612	+	4.17009i	0.0361828	+	0.145626i
$821$	24.3545	+	42.1833i	0.849980	+	1.47221i	0.881225	+	0.472696i	$0.156719\pi$
$821$	24.3545	+	42.1833i	0.849980	+	1.47221i	−0.0312459	+	0.999512i	$0.509947\pi$
$822$			17.8238i			0.621675i
$823$	22.4300	+	12.9499i	0.781859	+	0.451407i	0.837089	−	0.547067i	$-0.184256\pi$
$823$	22.4300	+	12.9499i	0.781859	+	0.451407i	−0.0552297	+	0.998474i	$0.517589\pi$
$824$	−3.21953			−0.112158
$825$	−3.16743	−	5.98053i	−0.110276	−	0.208215i
$826$	−1.05365	+	1.82498i	−0.0366613	+	0.0634992i
$827$	−7.49767	+	4.32878i	−0.260719	+	0.150526i	−0.624663	−	0.780895i	$-0.714764\pi$
$827$	−7.49767	+	4.32878i	−0.260719	+	0.150526i	0.363943	+	0.931421i	$0.381430\pi$
$828$		−	0.183417i		−	0.00637420i
$829$	−4.23348	+	7.33260i	−0.147035	+	0.254672i	−0.930130	−	0.367230i	$-0.880306\pi$
$829$	−4.23348	+	7.33260i	−0.147035	+	0.254672i	0.783095	+	0.621901i	$0.213640\pi$
$830$	−4.63475	−	1.33307i	−0.160874	−	0.0462716i
$831$	5.71400	−	9.89694i	0.198217	−	0.343321i
$832$	−0.945448	+	0.545854i	−0.0327775	+	0.0189241i
$833$	6.79867	−	3.92522i	0.235560	−	0.136001i
$834$	0.202610	−	0.350931i	0.00701581	−	0.0121517i
$835$	12.0025	−	41.7294i	0.415362	−	1.44410i
$836$	−3.21953	+	5.57640i	−0.111350	+	0.192864i
$837$		−	16.8420i		−	0.582145i
$838$	15.1643	−	8.75513i	0.523843	−	0.302441i
$839$	−7.72313	+	13.3769i	−0.266632	+	0.461820i	−0.967990	−	0.250989i	$-0.919244\pi$
$839$	−7.72313	+	13.3769i	−0.266632	+	0.461820i	0.701358	+	0.712809i	$0.252578\pi$
$840$	−1.90829	+	0.474142i	−0.0658423	+	0.0163595i
$841$	62.6865			2.16160
$842$	1.47405	+	0.851044i	0.0507992	+	0.0293289i
$843$			37.3591i			1.28672i
$844$	−5.03612	−	8.72281i	−0.173350	−	0.300252i
$845$	−6.36683	−	25.6248i	−0.219026	−	0.881518i
$846$	0.986669	+	1.70896i	0.0339224	+	0.0587553i
$847$	−4.81485	+	2.77985i	−0.165440	+	0.0955169i
$848$	3.06503	−	1.76959i	0.105253	−	0.0607681i
$849$	−13.1260	+	22.7349i	−0.450482	+	0.780258i
$850$	5.17009	−	2.73820i	0.177333	−	0.0939196i
$851$	2.32325	−	2.31502i	0.0796399	−	0.0793580i
$852$			0.948284i			0.0324877i
$853$	41.9200	+	24.2025i	1.43531	+	0.828679i	0.997519	−	0.0703967i	$-0.0224265\pi$
$853$	41.9200	+	24.2025i	1.43531	+	0.828679i	0.437794	+	0.899075i	$0.355760\pi$
$854$	−0.489741	−	0.848255i	−0.0167586	−	0.0290267i
$855$	−4.24864	+	4.09619i	−0.145300	+	0.140087i
$856$	7.11336	+	12.3207i	0.243130	+	0.421113i
$857$		−	12.9821i		−	0.443461i	−0.975108	−	0.221731i	$-0.928829\pi$
$857$		−	12.9821i		−	0.443461i	0.975108	−	0.221731i	$-0.0711706\pi$
$858$	−1.27967	+	0.738816i	−0.0436871	+	0.0252228i
$859$	15.0061			0.512003			0.256001	−	0.966676i	$-0.417595\pi$
$859$	15.0061			0.512003			0.256001	+	0.966676i	$0.417595\pi$
$860$	−0.797787	+	2.77370i	−0.0272043	+	0.0945822i
$861$	1.68980			0.0575883
$862$			21.7805i			0.741846i
$863$	2.27114	+	1.31124i	0.0773105	+	0.0446352i	0.538157	−	0.842845i	$-0.319121\pi$
$863$	2.27114	+	1.31124i	0.0773105	+	0.0446352i	−0.460846	+	0.887480i	$0.652454\pi$
$864$	−2.72374	−	4.71766i	−0.0926635	−	0.160498i
$865$	50.1894	−	12.4703i	1.70649	−	0.424002i
$866$	−5.34017	+	9.24945i	−0.181466	+	0.314309i
$867$	22.0771	+	12.7462i	0.749776	+	0.432884i
$868$	1.44368	+	0.833507i	0.0490016	+	0.0282911i
$869$	3.86376	+	6.69223i	0.131069	+	0.227019i
$870$	25.1385	−	24.2365i	0.852275	−	0.821694i
$871$	6.98020	−	12.0901i	0.236515	−	0.409656i
$872$	8.10660	+	4.68035i	0.274524	+	0.158497i
$873$	−2.70361	−	1.56093i	−0.0915034	−	0.0528295i
$874$	−4.18342			−0.141506
$875$	5.72871	+	1.87684i	0.193666	+	0.0634486i
$876$	4.69008	−	8.12346i	0.158463	−	0.274466i
$877$		−	5.18673i		−	0.175143i	−0.996158	−	0.0875717i	$-0.972089\pi$
$877$		−	5.18673i		−	0.175143i	0.996158	−	0.0875717i	$-0.0279107\pi$
$878$			30.9227i			1.04359i
$879$	−20.1736	+	34.9417i	−0.680438	+	1.17855i
$880$	0.447480	+	1.80098i	0.0150846	+	0.0607112i
$881$	−13.9402	−	24.1451i	−0.469657	−	0.813470i	0.529741	−	0.848160i	$-0.322289\pi$
$881$	−13.9402	−	24.1451i	−0.469657	−	0.813470i	−0.999398	+	0.0346892i	$0.988956\pi$
$882$			2.28231i			0.0768495i
$883$	4.30311	−	2.48440i	0.144811	−	0.0836068i	−0.425844	−	0.904797i	$-0.640023\pi$
$883$	4.30311	−	2.48440i	0.144811	−	0.0836068i	0.570655	+	0.821190i	$0.306689\pi$
$884$	−0.638697	−	1.10626i	−0.0214817	−	0.0372074i
$885$	−9.89245	−	10.2606i	−0.332531	−	0.344907i
$886$	−2.39269	+	4.14427i	−0.0803841	+	0.139229i
$887$		−	18.4969i		−	0.621066i	−0.950563	−	0.310533i	$-0.899492\pi$
$887$		−	18.4969i		−	0.621066i	0.950563	−	0.310533i	$-0.100508\pi$
$888$	2.58457	−	9.57777i	0.0867324	−	0.321409i
$889$	1.70540			0.0571973
$890$	−6.66776	+	23.1821i	−0.223504	+	0.777065i
$891$	−3.26312	−	5.65189i	−0.109319	−	0.189346i
$892$	−20.4033	+	11.7799i	−0.683153	+	0.394419i
$893$	38.9783	−	22.5041i	1.30436	−	0.753072i
$894$	−14.6681			−0.490573
$895$	18.5403	−	17.8750i	0.619733	−	0.597496i
$896$	0.539189			0.0180130
$897$	−0.831390	−	0.480004i	−0.0277593	−	0.0160269i
$898$			18.0966i			0.603892i
$899$	−29.6041			−0.987351
$900$	−0.0621245	+	1.69973i	−0.00207082	+	0.0566577i
$901$	2.07058	+	3.58635i	0.0689810	+	0.119479i
$902$		−	1.59478i		−	0.0531004i
$903$	0.982951	+	0.567507i	0.0327106	+	0.0188855i
$904$	−6.58864	+	11.4119i	−0.219135	+	0.379553i
$905$	−28.1955	−	8.10976i	−0.937251	−	0.269578i
$906$	−5.69542	−	9.86476i	−0.189218	−	0.327735i
$907$	−22.9898	+	13.2732i	−0.763365	+	0.440729i	−0.830503	−	0.557015i	$-0.811947\pi$
$907$	−22.9898	+	13.2732i	−0.763365	+	0.440729i	0.0671376	+	0.997744i	$0.478613\pi$
$908$	−8.40652	−	4.85350i	−0.278980	−	0.161069i
$909$	−2.02401	+	3.50569i	−0.0671321	+	0.116276i
$910$	0.363832	−	1.26495i	0.0120609	−	0.0419326i
$911$	33.2095			1.10028			0.550140	−	0.835072i	$-0.314574\pi$
$911$	33.2095			1.10028			0.550140	+	0.835072i	$0.314574\pi$
$912$	−10.9584	+	6.32684i	−0.362869	+	0.209503i
$913$	1.55012	+	0.894960i	0.0513014	+	0.0296189i
$914$	38.9093			1.28701
$915$	6.42923	−	1.59743i	0.212544	−	0.0528095i
$916$	−9.62310	+	16.6677i	−0.317956	+	0.550716i
$917$		−	3.15061i		−	0.104042i
$918$	5.52007	−	3.18701i	0.182189	−	0.105187i
$919$	−2.65368			−0.0875370			−0.0437685	−	0.999042i	$-0.513936\pi$
$919$	−2.65368			−0.0875370			−0.0437685	+	0.999042i	$0.513936\pi$
$920$	−0.867962	+	0.836818i	−0.0286159	+	0.0275891i
$921$	−3.72407	−	6.45028i	−0.122712	−	0.212544i
$922$	−19.8006	+	11.4319i	−0.652098	+	0.376489i
$923$	−0.549730	−	0.317387i	−0.0180946	−	0.0104469i
$924$	0.729794			0.0240085
$925$	−22.3137	+	20.6664i	−0.733668	+	0.679508i
$926$	27.4596			0.902378
$927$	0.948470	+	0.547599i	0.0311518	+	0.0179855i
$928$	−8.29246	+	4.78765i	−0.272213	+	0.157162i
$929$	−26.9101	−	46.6097i	−0.882893	−	1.52922i	−0.848110	−	0.529821i	$-0.822259\pi$
$929$	−26.9101	−	46.6097i	−0.882893	−	1.52922i	−0.0347834	−	0.999395i	$-0.511074\pi$
$930$	−8.11681	+	7.82556i	−0.266161	+	0.256610i
$931$	52.0554			1.70605
$932$	4.45434	−	2.57171i	0.145907	−	0.0842392i
$933$			16.5727i			0.542564i
$934$	−14.6948	+	25.4522i	−0.480829	+	0.832820i
$935$	−2.10731	+	0.523590i	−0.0689163	+	0.0171232i
$936$	0.371370			0.0121386
$937$	23.2416	+	13.4186i	0.759270	+	0.438365i	0.829034	−	0.559199i	$-0.188891\pi$
$937$	23.2416	+	13.4186i	0.759270	+	0.438365i	−0.0697634	+	0.997564i	$0.522224\pi$
$938$	−5.97121	+	3.44748i	−0.194967	+	0.112564i
$939$	−20.8416			−0.680141
$940$	3.58554	−	12.4660i	0.116947	−	0.406596i
$941$	−6.66536	+	11.5447i	−0.217284	+	0.376348i	−0.953977	−	0.299880i	$-0.903053\pi$
$941$	−6.66536	+	11.5447i	−0.217284	+	0.376348i	0.736692	+	0.676228i	$0.236387\pi$
$942$	−11.4696	−	6.62196i	−0.373699	−	0.215755i
$943$	0.897304	−	0.518059i	0.0292202	−	0.0168703i
$944$	1.95415	+	3.38468i	0.0636020	+	0.110162i
$945$	6.31192	+	1.81547i	0.205327	+	0.0590573i
$946$	0.535595	−	0.927678i	0.0174137	−	0.0301614i
$947$	−44.4671	−	25.6731i	−1.44499	−	0.834263i	−0.446809	−	0.894629i	$-0.647440\pi$
$947$	−44.4671	−	25.6731i	−1.44499	−	0.834263i	−0.998176	+	0.0603667i	$0.980773\pi$
$948$			15.1857i			0.493208i
$949$	3.13950	+	5.43778i	0.101913	+	0.176518i
$950$	38.7677	+	1.41695i	1.25779	+	0.0459718i
$951$	−18.5201			−0.600555
$952$			0.630898i			0.0204475i
$953$	38.3288	+	22.1292i	1.24159	+	0.716834i	0.969418	−	0.245415i	$-0.0789241\pi$
$953$	38.3288	+	22.1292i	1.24159	+	0.716834i	0.272174	+	0.962248i	$0.412257\pi$
$954$	−1.20394			−0.0389789
$955$	−27.8454	+	26.8463i	−0.901056	+	0.868725i
$956$	30.3051			0.980137
$957$	−11.2239	+	6.48011i	−0.362816	+	0.209472i
$958$	26.9690	−	15.5706i	0.871330	−	0.503063i
$959$	2.94635	+	5.10322i	0.0951425	+	0.164792i
$960$	−1.00804	+	3.50471i	−0.0325345	+	0.113114i
$961$	−21.4413			−0.691656
$962$	4.68728	+	4.70394i	0.151124	+	0.151661i
$963$		−	4.83955i		−	0.155952i
$964$	4.95774	−	8.58706i	0.159678	−	0.276570i
$965$	25.7869	+	26.7466i	0.830108	+	0.861003i
$966$	0.237071	+	0.410619i	0.00762764	+	0.0132115i
$967$	20.4062	−	11.7815i	0.656218	−	0.378868i	−0.134616	−	0.990898i	$-0.542980\pi$
$967$	20.4062	−	11.7815i	0.656218	−	0.378868i	0.790835	+	0.612030i	$0.209647\pi$
$968$			10.3112i			0.331416i
$969$	−7.40295	−	12.8223i	−0.237817	−	0.411911i
$970$	4.94828	+	19.9155i	0.158880	+	0.639447i
$971$	30.2147	−	52.3334i	0.969636	−	1.67946i	0.273031	−	0.962005i	$-0.411974\pi$
$971$	30.2147	−	52.3334i	0.969636	−	1.67946i	0.696606	−	0.717454i	$-0.254693\pi$
$972$			3.51745i			0.112822i
$973$		−	0.133969i		−	0.00429485i
$974$	−19.5597	+	33.8784i	−0.626733	+	1.08553i
$975$	7.54192	+	4.72979i	0.241535	+	0.151474i
$976$	−1.81658			−0.0581474
$977$	−22.3347	−	12.8950i	−0.714551	−	0.412546i	0.0981927	−	0.995167i	$-0.468694\pi$
$977$	−22.3347	−	12.8950i	−0.714551	−	0.412546i	−0.812744	+	0.582621i	$0.802027\pi$
$978$	−21.4772	−	12.3999i	−0.686766	−	0.396504i
$979$	4.47641	−	7.75337i	0.143067	−	0.247799i
$980$	10.8003	−	10.4128i	0.345003	−	0.332623i
$981$	−1.59213	−	2.75765i	−0.0508327	−	0.0880448i
$982$	−5.09364	−	2.94081i	−0.162545	−	0.0938452i
$983$	−28.0700	−	16.2062i	−0.895293	−	0.516898i	−0.0196229	−	0.999807i	$-0.506247\pi$
$983$	−28.0700	−	16.2062i	−0.895293	−	0.516898i	−0.875670	+	0.482910i	$0.839580\pi$
$984$	1.56698	−	2.71410i	0.0499536	−	0.0865222i
$985$	26.1194	−	6.48974i	0.832234	−	0.206780i
$986$	−5.60197	−	9.70289i	−0.178403	−	0.309003i
$987$	−4.41774	−	2.55058i	−0.140618	−	0.0811859i
$988$		−	8.47027i		−	0.269475i
$989$	0.695944			0.0221297
$990$	0.174496	−	0.606677i	0.00554585	−	0.0192815i
$991$	−3.46308			−0.110008			−0.0550042	−	0.998486i	$-0.517517\pi$
$991$	−3.46308			−0.110008			−0.0550042	+	0.998486i	$0.517517\pi$
$992$	2.67750	−	1.54585i	0.0850107	−	0.0490809i
$993$		−	45.1890i		−	1.43403i
$994$	0.156755	+	0.271508i	0.00497198	+	0.00861173i
$995$	−29.3290	+	28.2766i	−0.929792	+	0.896429i
$996$	1.75872	+	3.04620i	0.0557273	+	0.0965225i
$997$	4.96837	+	2.86849i	0.157350	+	0.0908460i	0.576607	−	0.817021i	$-0.304376\pi$
$997$	4.96837	+	2.86849i	0.157350	+	0.0908460i	−0.419258	+	0.907867i	$0.637710\pi$
$998$			20.7382i			0.656456i
$999$	−23.4720	+	23.3889i	−0.742622	+	0.739992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.f.269.2	✓	12
5.4	even	2	inner	370.2.n.f.269.5	yes	12
37.26	even	3	inner	370.2.n.f.359.5	yes	12
185.174	even	6	inner	370.2.n.f.359.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.f.269.2	✓	12	1.1	even	1	trivial
370.2.n.f.269.5	yes	12	5.4	even	2	inner
370.2.n.f.359.2	yes	12	185.174	even	6	inner
370.2.n.f.359.5	yes	12	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.41240 + 0.815449i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 + 1.55199i) q^{5} +1.63090 q^{6} +(0.466951 - 0.269594i) q^{7} -1.00000i q^{8} +(-0.170086 + 0.294598i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.41240 + 0.815449i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 + 1.55199i) q^{5} +1.63090 q^{6} +(0.466951 - 0.269594i) q^{7} -1.00000i q^{8} +(-0.170086 + 0.294598i) q^{9} +(2.17009 - 0.539189i) q^{10} -0.829914 q^{11} +(-1.41240 - 0.815449i) q^{12} +(0.945448 - 0.545854i) q^{13} -0.539189 q^{14} +(1.00804 - 3.50471i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.01332 - 0.585043i) q^{17} +(0.294598 - 0.170086i) q^{18} +(-3.87936 - 6.71925i) q^{19} +(-2.14894 - 0.618092i) q^{20} +(-0.439681 + 0.761550i) q^{21} +(0.718726 + 0.414957i) q^{22} +0.539189i q^{23} +(0.815449 + 1.41240i) q^{24} +(0.182626 - 4.99666i) q^{25} -1.09171 q^{26} -5.44748i q^{27} +(0.466951 + 0.269594i) q^{28} -9.57531 q^{29} +(-2.62535 + 2.53114i) q^{30} +3.09171 q^{31} +(0.866025 - 0.500000i) q^{32} +(1.17217 - 0.676752i) q^{33} +(0.585043 + 1.01332i) q^{34} +(-0.333268 + 1.15869i) q^{35} -0.340173 q^{36} +(-4.29353 - 4.30878i) q^{37} +7.75872i q^{38} +(-0.890233 + 1.54193i) q^{39} +(1.55199 + 1.60976i) q^{40} +(-0.960811 - 1.66417i) q^{41} +(0.761550 - 0.439681i) q^{42} -1.29072i q^{43} +(-0.414957 - 0.718726i) q^{44} +(-0.183417 - 0.738205i) q^{45} +(0.269594 - 0.466951i) q^{46} +5.80098i q^{47} -1.63090i q^{48} +(-3.35464 + 5.81040i) q^{49} +(-2.65649 + 4.23592i) q^{50} +1.90829 q^{51} +(0.945448 + 0.545854i) q^{52} +(-3.06503 - 1.76959i) q^{53} +(-2.72374 + 4.71766i) q^{54} +(1.33596 - 1.28802i) q^{55} +(-0.269594 - 0.466951i) q^{56} +(10.9584 + 6.32684i) q^{57} +(8.29246 + 4.78765i) q^{58} +(1.95415 - 3.38468i) q^{59} +(3.53919 - 0.879362i) q^{60} +(0.908291 + 1.57321i) q^{61} +(-2.67750 - 1.54585i) q^{62} +0.183417i q^{63} -1.00000 q^{64} +(-0.674776 + 2.34602i) q^{65} -1.35350 q^{66} +(11.0744 - 6.39383i) q^{67} -1.17009i q^{68} +(-0.439681 - 0.761550i) q^{69} +(0.867962 - 0.836818i) q^{70} +(-0.290725 - 0.503550i) q^{71} +(0.294598 + 0.170086i) q^{72} +5.75154i q^{73} +(1.56391 + 5.87828i) q^{74} +(3.81658 + 7.20620i) q^{75} +(3.87936 - 6.71925i) q^{76} +(-0.387529 + 0.223740i) q^{77} +(1.54193 - 0.890233i) q^{78} +(-4.65562 - 8.06377i) q^{79} +(-0.539189 - 2.17009i) q^{80} +(3.93188 + 6.81022i) q^{81} +1.92162i q^{82} +(-1.86781 - 1.07838i) q^{83} -0.879362 q^{84} +(2.53919 - 0.630898i) q^{85} +(-0.645362 + 1.11780i) q^{86} +(13.5242 - 7.80817i) q^{87} +0.829914i q^{88} +(-5.39383 + 9.34238i) q^{89} +(-0.210258 + 0.731013i) q^{90} +(0.294319 - 0.509775i) q^{91} +(-0.466951 + 0.269594i) q^{92} +(-4.36673 + 2.52113i) q^{93} +(2.90049 - 5.02380i) q^{94} +(16.6731 + 4.79560i) q^{95} +(-0.815449 + 1.41240i) q^{96} +9.17727i q^{97} +(5.81040 - 3.35464i) q^{98} +(0.141157 - 0.244491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9	\( 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9} + 4 q^{10} - 32 q^{11} + 18 q^{15} - 6 q^{16} + 4 q^{19} + 20 q^{21} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 32 q^{29} - 20 q^{30} + 28 q^{31} - 4 q^{34} + 4 q^{35} + 40 q^{36} - 58 q^{39} + 2 q^{40} - 18 q^{41} - 16 q^{44} + 16 q^{45} - 26 q^{49} - 8 q^{50} + 32 q^{51} - 34 q^{54} - 4 q^{55} + 28 q^{59} + 36 q^{60} + 20 q^{61} - 12 q^{64} - 22 q^{65} + 24 q^{66} + 20 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{74} + 64 q^{75} - 4 q^{76} - 4 q^{79} - 6 q^{81} + 40 q^{84} + 24 q^{85} - 22 q^{86} - 44 q^{89} - 20 q^{90} - 36 q^{91} + 16 q^{94} + 16 q^{95} - 2 q^{96} - 80 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9 + 4 * q^10 - 32 * q^11 + 18 * q^15 - 6 * q^16 + 4 * q^19 + 20 * q^21 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 32 * q^29 - 20 * q^30 + 28 * q^31 - 4 * q^34 + 4 * q^35 + 40 * q^36 - 58 * q^39 + 2 * q^40 - 18 * q^41 - 16 * q^44 + 16 * q^45 - 26 * q^49 - 8 * q^50 + 32 * q^51 - 34 * q^54 - 4 * q^55 + 28 * q^59 + 36 * q^60 + 20 * q^61 - 12 * q^64 - 22 * q^65 + 24 * q^66 + 20 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^74 + 64 * q^75 - 4 * q^76 - 4 * q^79 - 6 * q^81 + 40 * q^84 + 24 * q^85 - 22 * q^86 - 44 * q^89 - 20 * q^90 - 36 * q^91 + 16 * q^94 + 16 * q^95 - 2 * q^96 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more