LMFDB - Embedded newform 546.2.z.a.131.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.3
Character	$\chi$	$=$	546.131
Dual form			546.2.z.a.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.631675 - 1.61276i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.49759 + 2.59391i) q^{5} +(-0.259332 + 1.71253i) q^{6} +(-0.0366585 - 2.64550i) q^{7} -1.00000i q^{8} +(-2.20197 + 2.03748i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.631675 - 1.61276i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.49759 + 2.59391i) q^{5} +(-0.259332 + 1.71253i) q^{6} +(-0.0366585 - 2.64550i) q^{7} -1.00000i q^{8} +(-2.20197 + 2.03748i) q^{9} +(2.59391 - 1.49759i) q^{10} +(-1.10550 + 0.638259i) q^{11} +(1.08085 - 1.35343i) q^{12} +1.00000i q^{13} +(-1.29100 + 2.30940i) q^{14} +(5.12934 + 0.776747i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.544273 - 0.942709i) q^{17} +(2.92570 - 0.663521i) q^{18} +(6.52489 + 3.76715i) q^{19} -2.99519 q^{20} +(-4.24339 + 1.73022i) q^{21} +1.27652 q^{22} +(5.47232 + 3.15945i) q^{23} +(-1.61276 + 0.631675i) q^{24} +(-1.98557 - 3.43911i) q^{25} +(0.500000 - 0.866025i) q^{26} +(4.67689 + 2.26422i) q^{27} +(2.27274 - 1.35450i) q^{28} +3.01992i q^{29} +(-4.05376 - 3.23735i) q^{30} +(-7.20189 + 4.15801i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.72767 + 1.37973i) q^{33} +1.08855i q^{34} +(6.91708 + 3.86679i) q^{35} +(-2.86549 - 0.888225i) q^{36} +(0.363608 - 0.629787i) q^{37} +(-3.76715 - 6.52489i) q^{38} +(1.61276 - 0.631675i) q^{39} +(2.59391 + 1.49759i) q^{40} +9.09924 q^{41} +(4.53999 + 0.623283i) q^{42} +8.73475 q^{43} +(-1.10550 - 0.638259i) q^{44} +(-1.98737 - 8.76303i) q^{45} +(-3.15945 - 5.47232i) q^{46} +(-0.962355 + 1.66685i) q^{47} +(1.71253 + 0.259332i) q^{48} +(-6.99731 + 0.193960i) q^{49} +3.97115i q^{50} +(-1.17656 + 1.47327i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(8.80968 - 5.08627i) q^{53} +(-2.91819 - 4.29932i) q^{54} -3.82341i q^{55} +(-2.64550 + 0.0366585i) q^{56} +(1.95388 - 12.9027i) q^{57} +(1.50996 - 2.61533i) q^{58} +(1.18064 + 2.04493i) q^{59} +(1.89199 + 4.83051i) q^{60} +(-5.29992 - 3.05991i) q^{61} +8.31602 q^{62} +(5.47086 + 5.75062i) q^{63} -1.00000 q^{64} +(-2.59391 - 1.49759i) q^{65} +(-0.806345 - 2.05871i) q^{66} +(5.68742 + 9.85089i) q^{67} +(0.544273 - 0.942709i) q^{68} +(1.63869 - 10.8213i) q^{69} +(-4.05697 - 6.80728i) q^{70} +3.18659i q^{71} +(2.03748 + 2.20197i) q^{72} +(-9.69406 + 5.59687i) q^{73} +(-0.629787 + 0.363608i) q^{74} +(-4.29222 + 5.37465i) q^{75} +7.53429i q^{76} +(1.72904 + 2.90119i) q^{77} +(-1.71253 - 0.259332i) q^{78} +(6.66108 - 11.5373i) q^{79} +(-1.49759 - 2.59391i) q^{80} +(0.697366 - 8.97294i) q^{81} +(-7.88017 - 4.54962i) q^{82} -8.63079 q^{83} +(-3.62011 - 2.80977i) q^{84} +3.26040 q^{85} +(-7.56452 - 4.36738i) q^{86} +(4.87040 - 1.90761i) q^{87} +(0.638259 + 1.10550i) q^{88} +(-6.56159 + 11.3650i) q^{89} +(-2.66040 + 8.58269i) q^{90} +(2.64550 - 0.0366585i) q^{91} +6.31889i q^{92} +(11.2551 + 8.98838i) q^{93} +(1.66685 - 0.962355i) q^{94} +(-19.5433 + 11.2833i) q^{95} +(-1.35343 - 1.08085i) q^{96} +16.3693i q^{97} +(6.15683 + 3.33068i) q^{98} +(1.13383 - 3.65785i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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
$3$	−0.631675	−	1.61276i	−0.364698	−	0.931126i
$3$	−0.631675	−	1.61276i	−0.364698	−	0.931126i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.49759	+	2.59391i	−0.669744	+	1.16003i	0.308231	+	0.951311i	$0.400263\pi$
$5$	−1.49759	+	2.59391i	−0.669744	+	1.16003i	−0.977976	+	0.208720i	$0.933070\pi$
$6$	−0.259332	+	1.71253i	−0.105872	+	0.699136i
$7$	−0.0366585	−	2.64550i	−0.0138556	−	0.999904i
$7$	−0.0366585	−	2.64550i	−0.0138556	−	0.999904i
$8$		−	1.00000i		−	0.353553i
$9$	−2.20197	+	2.03748i	−0.733991	+	0.679159i
$10$	2.59391	−	1.49759i	0.820266	−	0.473581i
$11$	−1.10550	+	0.638259i	−0.333320	+	0.192442i	−0.657314	−	0.753617i	$-0.728307\pi$
$11$	−1.10550	+	0.638259i	−0.333320	+	0.192442i	0.323994	+	0.946059i	$0.394974\pi$
$12$	1.08085	−	1.35343i	0.312015	−	0.390700i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−1.29100	+	2.30940i	−0.345035	+	0.617212i
$15$	5.12934	+	0.776747i	1.32439	+	0.200555i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.544273	−	0.942709i	−0.132006	−	0.228640i	0.792444	−	0.609945i	$-0.208808\pi$
$17$	−0.544273	−	0.942709i	−0.132006	−	0.228640i	−0.924450	+	0.381304i	$0.875475\pi$
$18$	2.92570	−	0.663521i	0.689595	−	0.156394i
$19$	6.52489	+	3.76715i	1.49691	+	0.864243i	0.999994	−	0.00355473i	$-0.00113151\pi$
$19$	6.52489	+	3.76715i	1.49691	+	0.864243i	0.496918	+	0.867797i	$0.334465\pi$
$20$	−2.99519			−0.669744
$21$	−4.24339	+	1.73022i	−0.925983	+	0.377564i
$22$	1.27652			0.272154
$23$	5.47232	+	3.15945i	1.14106	+	0.658790i	0.946692	−	0.322139i	$-0.104402\pi$
$23$	5.47232	+	3.15945i	1.14106	+	0.658790i	0.194366	+	0.980929i	$0.437735\pi$
$24$	−1.61276	+	0.631675i	−0.329203	+	0.128940i
$25$	−1.98557	−	3.43911i	−0.397115	−	0.687823i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	4.67689	+	2.26422i	0.900068	+	0.435750i
$28$	2.27274	−	1.35450i	0.429507	−	0.255976i
$29$			3.01992i			0.560785i	0.959885	+	0.280393i	$0.0904647\pi$
$29$			3.01992i			0.560785i	−0.959885	+	0.280393i	$0.909535\pi$
$30$	−4.05376	−	3.23735i	−0.740112	−	0.591057i
$31$	−7.20189	+	4.15801i	−1.29350	+	0.746801i	−0.979272	−	0.202548i	$-0.935078\pi$
$31$	−7.20189	+	4.15801i	−1.29350	+	0.746801i	−0.314224	+	0.949349i	$0.601744\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.72767	+	1.37973i	0.300749	+	0.240179i
$34$			1.08855i			0.186684i
$35$	6.91708	+	3.86679i	1.16920	+	0.653607i
$36$	−2.86549	−	0.888225i	−0.477582	−	0.148038i
$37$	0.363608	−	0.629787i	0.0597767	−	0.103536i	−0.834588	−	0.550874i	$-0.814294\pi$
$37$	0.363608	−	0.629787i	0.0597767	−	0.103536i	0.894365	+	0.447338i	$0.147628\pi$
$38$	−3.76715	−	6.52489i	−0.611112	−	1.05848i
$39$	1.61276	−	0.631675i	0.258248	−	0.101149i
$40$	2.59391	+	1.49759i	0.410133	+	0.236790i
$41$	9.09924			1.42106			0.710531	−	0.703666i	$-0.248455\pi$
$41$	9.09924			1.42106			0.710531	+	0.703666i	$0.248455\pi$
$42$	4.53999	+	0.623283i	0.700536	+	0.0961746i
$43$	8.73475			1.33204			0.666019	−	0.745935i	$-0.267997\pi$
$43$	8.73475			1.33204			0.666019	+	0.745935i	$0.267997\pi$
$44$	−1.10550	−	0.638259i	−0.166660	−	0.0962211i
$45$	−1.98737	−	8.76303i	−0.296260	−	1.30632i
$46$	−3.15945	−	5.47232i	−0.465835	−	0.806850i
$47$	−0.962355	+	1.66685i	−0.140374	+	0.243135i	−0.927637	−	0.373482i	$-0.878164\pi$
$47$	−0.962355	+	1.66685i	−0.140374	+	0.243135i	0.787264	+	0.616617i	$0.211497\pi$
$48$	1.71253	+	0.259332i	0.247182	+	0.0374313i
$49$	−6.99731	+	0.193960i	−0.999616	+	0.0277086i
$50$			3.97115i			0.561605i
$51$	−1.17656	+	1.47327i	−0.164751	+	0.206299i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	8.80968	−	5.08627i	1.21010	−	0.698653i	0.247321	−	0.968934i	$-0.420450\pi$
$53$	8.80968	−	5.08627i	1.21010	−	0.698653i	0.962782	+	0.270281i	$0.0871165\pi$
$54$	−2.91819	−	4.29932i	−0.397116	−	0.585063i
$55$		−	3.82341i		−	0.515548i
$56$	−2.64550	+	0.0366585i	−0.353519	+	0.00489870i
$57$	1.95388	−	12.9027i	0.258798	−	1.70900i
$58$	1.50996	−	2.61533i	0.198268	−	0.343409i
$59$	1.18064	+	2.04493i	0.153706	+	0.266227i	0.932587	−	0.360945i	$-0.117546\pi$
$59$	1.18064	+	2.04493i	0.153706	+	0.266227i	−0.778881	+	0.627172i	$0.784212\pi$
$60$	1.89199	+	4.83051i	0.244254	+	0.623616i
$61$	−5.29992	−	3.05991i	−0.678585	−	0.391782i	0.120736	−	0.992685i	$-0.461474\pi$
$61$	−5.29992	−	3.05991i	−0.678585	−	0.391782i	−0.799322	+	0.600903i	$0.794808\pi$
$62$	8.31602			1.05614
$63$	5.47086	+	5.75062i	0.689264	+	0.724510i
$64$	−1.00000			−0.125000
$65$	−2.59391	−	1.49759i	−0.321735	−	0.185754i
$66$	−0.806345	−	2.05871i	−0.0992542	−	0.253410i
$67$	5.68742	+	9.85089i	0.694828	+	1.20348i	0.970239	+	0.242151i	$0.0778530\pi$
$67$	5.68742	+	9.85089i	0.694828	+	1.20348i	−0.275410	+	0.961327i	$0.588814\pi$
$68$	0.544273	−	0.942709i	0.0660028	−	0.114320i
$69$	1.63869	−	10.8213i	0.197275	−	1.30273i
$70$	−4.05697	−	6.80728i	−0.484901	−	0.813625i
$71$			3.18659i			0.378179i	0.981960	+	0.189089i	$0.0605536\pi$
$71$			3.18659i			0.378179i	−0.981960	+	0.189089i	$0.939446\pi$
$72$	2.03748	+	2.20197i	0.240119	+	0.259505i
$73$	−9.69406	+	5.59687i	−1.13460	+	0.655064i	−0.945089	−	0.326814i	$-0.894025\pi$
$73$	−9.69406	+	5.59687i	−1.13460	+	0.655064i	−0.189515	+	0.981878i	$0.560692\pi$
$74$	−0.629787	+	0.363608i	−0.0732112	+	0.0422685i
$75$	−4.29222	+	5.37465i	−0.495623	+	0.620611i
$76$			7.53429i			0.864243i
$77$	1.72904	+	2.90119i	0.197042	+	0.330621i
$78$	−1.71253	−	0.259332i	−0.193905	−	0.0293635i
$79$	6.66108	−	11.5373i	0.749430	−	1.29805i	−0.198667	−	0.980067i	$-0.563661\pi$
$79$	6.66108	−	11.5373i	0.749430	−	1.29805i	0.948096	−	0.317983i	$-0.103006\pi$
$80$	−1.49759	−	2.59391i	−0.167436	−	0.290008i
$81$	0.697366	−	8.97294i	0.0774851	−	0.996994i
$82$	−7.88017	−	4.54962i	−0.870219	−	0.502421i
$83$	−8.63079			−0.947352			−0.473676	−	0.880699i	$-0.657073\pi$
$83$	−8.63079			−0.947352			−0.473676	+	0.880699i	$0.657073\pi$
$84$	−3.62011	−	2.80977i	−0.394986	−	0.306572i
$85$	3.26040			0.353640
$86$	−7.56452	−	4.36738i	−0.815703	−	0.470946i
$87$	4.87040	−	1.90761i	0.522162	−	0.204517i
$88$	0.638259	+	1.10550i	0.0680386	+	0.117846i
$89$	−6.56159	+	11.3650i	−0.695527	+	1.20469i	0.274476	+	0.961594i	$0.411496\pi$
$89$	−6.56159	+	11.3650i	−0.695527	+	1.20469i	−0.970003	+	0.243094i	$0.921838\pi$
$90$	−2.66040	+	8.58269i	−0.280431	+	0.904695i
$91$	2.64550	−	0.0366585i	0.277323	−	0.00384286i
$92$			6.31889i			0.658790i
$93$	11.2551	+	8.98838i	1.16710	+	0.932052i
$94$	1.66685	−	0.962355i	0.171922	−	0.0992593i
$95$	−19.5433	+	11.2833i	−2.00510	+	1.15764i
$96$	−1.35343	−	1.08085i	−0.138133	−	0.110314i
$97$			16.3693i			1.66205i	0.556235	+	0.831025i	$0.312245\pi$
$97$			16.3693i			1.66205i	−0.556235	+	0.831025i	$0.687755\pi$
$98$	6.15683	+	3.33068i	0.621934	+	0.336450i
$99$	1.13383	−	3.65785i	0.113955	−	0.367628i
$100$	1.98557	−	3.43911i	0.198557	−	0.343911i
$101$	6.40881	+	11.1004i	0.637701	+	1.10453i	0.985936	+	0.167123i	$0.0534477\pi$
$101$	6.40881	+	11.1004i	0.637701	+	1.10453i	−0.348235	+	0.937407i	$0.613219\pi$
$102$	1.75556	−	0.687608i	0.173826	−	0.0680833i
$103$	−10.4732	−	6.04671i	−1.03196	−	0.595800i	−0.114412	−	0.993433i	$-0.536498\pi$
$103$	−10.4732	−	6.04671i	−1.03196	−	0.595800i	−0.917545	+	0.397633i	$0.869832\pi$
$104$	1.00000			0.0980581
$105$	1.86685	−	13.5981i	0.182186	−	1.32704i
$106$	−10.1725			−0.988044
$107$	−2.15383	−	1.24351i	−0.208218	−	0.120215i	0.392265	−	0.919852i	$-0.371692\pi$
$107$	−2.15383	−	1.24351i	−0.208218	−	0.120215i	−0.600483	+	0.799637i	$0.705025\pi$
$108$	0.377570	+	5.18242i	0.0363317	+	0.498678i
$109$	−0.731469	−	1.26694i	−0.0700620	−	0.121351i	0.828866	−	0.559447i	$-0.188986\pi$
$109$	−0.731469	−	1.26694i	−0.0700620	−	0.121351i	−0.898928	+	0.438096i	$0.855653\pi$
$110$	−1.91170	+	3.31117i	−0.182274	+	0.315708i
$111$	−1.24538	−	0.188590i	−0.118206	−	0.0179002i
$112$	2.30940	+	1.29100i	0.218218	+	0.121988i
$113$			1.22611i			0.115342i	0.998336	+	0.0576712i	$0.0183675\pi$
$113$			1.22611i			0.115342i	−0.998336	+	0.0576712i	$0.981633\pi$
$114$	−8.14345	+	10.1971i	−0.762704	+	0.955046i
$115$	−16.3906	+	9.46313i	−1.52843	+	0.882442i
$116$	−2.61533	+	1.50996i	−0.242827	+	0.140196i
$117$	−2.03748	−	2.20197i	−0.188365	−	0.203572i
$118$		−	2.36128i		−	0.217373i
$119$	−2.47398	+	1.47443i	−0.226789	+	0.135161i
$120$	0.776747	−	5.12934i	0.0709070	−	0.468242i
$121$	−4.68525	+	8.11509i	−0.425932	+	0.737736i
$122$	3.05991	+	5.29992i	0.277031	+	0.479832i
$123$	−5.74776	−	14.6749i	−0.518258	−	1.32319i
$124$	−7.20189	−	4.15801i	−0.646748	−	0.373400i
$125$	−3.08161			−0.275627
$126$	−1.86260	−	7.71562i	−0.165933	−	0.687362i
$127$	7.00839			0.621894			0.310947	−	0.950427i	$-0.399354\pi$
$127$	7.00839			0.621894			0.310947	+	0.950427i	$0.399354\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−5.51753	−	14.0870i	−0.485791	−	1.24029i
$130$	1.49759	+	2.59391i	0.131348	+	0.227501i
$131$	−0.171196	+	0.296521i	−0.0149575	+	0.0259071i	−0.873407	−	0.486991i	$-0.838095\pi$
$131$	−0.171196	+	0.296521i	−0.0149575	+	0.0259071i	0.858450	+	0.512898i	$0.171428\pi$
$132$	−0.331042	+	2.18607i	−0.0288135	+	0.190273i
$133$	9.72678	−	17.3997i	0.843419	−	1.50874i
$134$		−	11.3748i		−	0.982636i
$135$	−12.8773	+	8.74054i	−1.10830	+	0.752266i
$136$	−0.942709	+	0.544273i	−0.0808366	+	0.0466710i
$137$	−7.14446	+	4.12486i	−0.610393	+	0.352410i	−0.773119	−	0.634261i	$-0.781305\pi$
$137$	−7.14446	+	4.12486i	−0.610393	+	0.352410i	0.162726	+	0.986671i	$0.447971\pi$
$138$	−6.82978	+	8.55215i	−0.581390	+	0.728007i
$139$			14.6821i			1.24532i	0.782493	+	0.622660i	$0.213948\pi$
$139$			14.6821i			1.24532i	−0.782493	+	0.622660i	$0.786052\pi$
$140$	0.109799	+	7.92376i	0.00927972	+	0.669680i
$141$	3.29612	+	0.499138i	0.277583	+	0.0420350i
$142$	1.59330	−	2.75967i	0.133706	−	0.231586i
$143$	−0.638259	−	1.10550i	−0.0533739	−	0.0924463i
$144$	−0.663521	−	2.92570i	−0.0552935	−	0.243809i
$145$	−7.83340	−	4.52261i	−0.650528	−	0.375583i
$146$	11.1937			0.926400
$147$	4.73284	+	11.1624i	0.390358	+	0.920663i
$148$	0.727215			0.0597767
$149$	−7.66677	−	4.42641i	−0.628086	−	0.362626i	0.151924	−	0.988392i	$-0.451453\pi$
$149$	−7.66677	−	4.42641i	−0.628086	−	0.362626i	−0.780011	+	0.625766i	$0.784786\pi$
$150$	6.40450	−	2.50848i	0.522925	−	0.204816i
$151$	−3.09389	−	5.35878i	−0.251778	−	0.436091i	0.712238	−	0.701938i	$-0.247682\pi$
$151$	−3.09389	−	5.35878i	−0.251778	−	0.436091i	−0.964015	+	0.265847i	$0.914348\pi$
$152$	3.76715	−	6.52489i	0.305556	−	0.529238i
$153$	3.11922	+	0.966874i	0.252174	+	0.0781671i
$154$	−0.0467952	−	3.37702i	−0.00377087	−	0.272128i
$155$		−	24.9080i		−	2.00066i
$156$	1.35343	+	1.08085i	0.108361	+	0.0865374i
$157$	2.35077	−	1.35722i	0.187612	−	0.108318i	−0.403252	−	0.915089i	$-0.632120\pi$
$157$	2.35077	−	1.35722i	0.187612	−	0.108318i	0.590864	+	0.806771i	$0.298787\pi$
$158$	−11.5373	+	6.66108i	−0.917860	+	0.529927i
$159$	−13.7678	−	10.9950i	−1.09186	−	0.871960i
$160$			2.99519i			0.236790i
$161$	8.15770	−	14.5928i	0.642917	−	1.15008i
$162$	−5.09041	+	7.42211i	−0.399940	+	0.583136i
$163$	10.0460	−	17.4001i	0.786862	−	1.36288i	−0.141019	−	0.990007i	$-0.545038\pi$
$163$	10.0460	−	17.4001i	0.786862	−	1.36288i	0.927880	−	0.372878i	$-0.121629\pi$
$164$	4.54962	+	7.88017i	0.355266	+	0.615338i
$165$	−6.16623	+	2.41515i	−0.480040	+	0.188019i
$166$	7.47449	+	4.31540i	0.580133	+	0.334940i
$167$	13.7060			1.06060			0.530301	−	0.847809i	$-0.322079\pi$
$167$	13.7060			1.06060			0.530301	+	0.847809i	$0.322079\pi$
$168$	1.73022	+	4.24339i	0.133489	+	0.327385i
$169$	−1.00000			−0.0769231
$170$	−2.82359	−	1.63020i	−0.216559	−	0.125031i
$171$	−22.0431	+	4.99916i	−1.68568	+	0.382296i
$172$	4.36738	+	7.56452i	0.333009	+	0.576789i
$173$	12.7091	−	22.0128i	0.966256	−	1.67361i	0.260055	−	0.965594i	$-0.416259\pi$
$173$	12.7091	−	22.0128i	0.966256	−	1.67361i	0.706201	−	0.708011i	$-0.250408\pi$
$174$	−5.17170	−	0.783162i	−0.392065	−	0.0593713i
$175$	−9.02538	+	5.37890i	−0.682255	+	0.406607i
$176$		−	1.27652i		−	0.0962211i
$177$	2.55219	−	3.19581i	0.191834	−	0.240212i
$178$	11.3650	−	6.56159i	0.851843	−	0.491812i
$179$	−11.7441	+	6.78045i	−0.877794	+	0.506795i	−0.869931	−	0.493174i	$-0.835836\pi$
$179$	−11.7441	+	6.78045i	−0.877794	+	0.506795i	−0.00786381	+	0.999969i	$0.502503\pi$
$180$	6.59532	−	6.10263i	0.491586	−	0.454863i
$181$		−	0.213431i		−	0.0158642i	−0.999969	−	0.00793209i	$-0.997475\pi$
$181$		−	0.213431i		−	0.0158642i	0.999969	−	0.00793209i	$-0.00252489\pi$
$182$	−2.30940	−	1.29100i	−0.171184	−	0.0956954i
$183$	−1.58706	+	10.4804i	−0.117319	+	0.774730i
$184$	3.15945	−	5.47232i	0.232917	−	0.403425i
$185$	1.08907	+	1.88633i	0.0800702	+	0.138686i
$186$	−5.25303	−	13.4117i	−0.385170	−	0.983395i
$187$	1.20338	+	0.694774i	0.0880002	+	0.0508069i
$188$	−1.92471			−0.140374
$189$	5.81855	−	12.4557i	0.423237	−	0.906019i
$190$	22.5666			1.63715
$191$	−5.73987	−	3.31392i	−0.415323	−	0.239787i	0.277752	−	0.960653i	$-0.410411\pi$
$191$	−5.73987	−	3.31392i	−0.415323	−	0.239787i	−0.693074	+	0.720866i	$0.743744\pi$
$192$	0.631675	+	1.61276i	0.0455872	+	0.116391i
$193$	−3.47303	−	6.01546i	−0.249994	−	0.433002i	0.713530	−	0.700625i	$-0.247095\pi$
$193$	−3.47303	−	6.01546i	−0.249994	−	0.433002i	−0.963524	+	0.267623i	$0.913762\pi$
$194$	8.18465	−	14.1762i	0.587623	−	1.01779i
$195$	−0.776747	+	5.12934i	−0.0556240	+	0.367319i
$196$	−3.66663	−	5.96287i	−0.261902	−	0.425919i
$197$		−	2.71345i		−	0.193325i	−0.995317	−	0.0966625i	$-0.969183\pi$
$197$		−	2.71345i		−	0.193325i	0.995317	−	0.0966625i	$-0.0308167\pi$
$198$	−2.81086	+	2.60088i	−0.199759	+	0.184836i
$199$	−2.50961	+	1.44892i	−0.177901	+	0.102711i	−0.586306	−	0.810090i	$-0.699418\pi$
$199$	−2.50961	+	1.44892i	−0.177901	+	0.102711i	0.408405	+	0.912801i	$0.366085\pi$
$200$	−3.43911	+	1.98557i	−0.243182	+	0.140401i
$201$	12.2945	−	15.3950i	0.867187	−	1.08588i
$202$		−	12.8176i		−	0.901845i
$203$	7.98919	−	0.110706i	0.560731	−	0.00777002i
$204$	−1.86416	−	0.282295i	−0.130518	−	0.0197646i
$205$	−13.6270	+	23.6026i	−0.951748	+	1.64848i
$206$	6.04671	+	10.4732i	0.421295	+	0.729704i
$207$	−18.4872	+	4.19272i	−1.28495	+	0.291414i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	−9.61765			−0.665267
$210$	−8.41580	+	10.8429i	−0.580745	+	0.748231i
$211$	17.2082			1.18466			0.592332	−	0.805694i	$-0.298207\pi$
$211$	17.2082			1.18466			0.592332	+	0.805694i	$0.298207\pi$
$212$	8.80968	+	5.08627i	0.605051	+	0.349326i
$213$	5.13920	−	2.01289i	0.352132	−	0.137921i
$214$	1.24351	+	2.15383i	0.0850047	+	0.147232i
$215$	−13.0811	+	22.6572i	−0.892124	+	1.54520i
$216$	2.26422	−	4.67689i	0.154061	−	0.318222i
$217$	11.2640	+	18.9001i	0.764651	+	1.28303i
$218$			1.46294i			0.0990826i
$219$	15.1499	+	12.0988i	1.02373	+	0.817559i
$220$	3.31117	−	1.91170i	0.223239	−	0.128887i
$221$	0.942709	−	0.544273i	0.0634135	−	0.0366118i
$222$	0.984232	+	0.786012i	0.0660573	+	0.0527536i
$223$			22.4594i			1.50399i	0.659169	+	0.751995i	$0.270908\pi$
$223$			22.4594i			1.50399i	−0.659169	+	0.751995i	$0.729092\pi$
$224$	−1.35450	−	2.27274i	−0.0905011	−	0.151854i
$225$	11.3793	+	3.52727i	0.758620	+	0.235152i
$226$	0.613053	−	1.06184i	0.0407797	−	0.0706325i
$227$	8.45721	+	14.6483i	0.561325	+	0.972243i	0.997381	+	0.0723240i	$0.0230416\pi$
$227$	8.45721	+	14.6483i	0.561325	+	0.972243i	−0.436056	+	0.899919i	$0.643625\pi$
$228$	12.1510	−	4.75923i	0.804719	−	0.315187i
$229$	−4.53055	−	2.61571i	−0.299387	−	0.172851i	0.342781	−	0.939416i	$-0.388631\pi$
$229$	−4.53055	−	2.61571i	−0.299387	−	0.172851i	−0.642167	+	0.766564i	$0.721965\pi$
$230$	18.9263			1.24796
$231$	3.58673	−	4.62113i	0.235989	−	0.304048i
$232$	3.01992			0.198268
$233$	18.1176	+	10.4602i	1.18692	+	0.685269i	0.957606	−	0.288083i	$-0.0930178\pi$
$233$	18.1176	+	10.4602i	1.18692	+	0.685269i	0.229316	+	0.973352i	$0.426351\pi$
$234$	0.663521	+	2.92570i	0.0433758	+	0.191259i
$235$	−2.88243	−	4.99252i	−0.188029	−	0.325676i
$236$	−1.18064	+	2.04493i	−0.0768530	+	0.133113i
$237$	−22.8145	−	3.45486i	−1.48196	−	0.224417i
$238$	2.87975	−	0.0399045i	0.186666	−	0.00258662i
$239$			1.05708i			0.0683770i	0.999415	+	0.0341885i	$0.0108847\pi$
$239$			1.05708i			0.0683770i	−0.999415	+	0.0341885i	$0.989115\pi$
$240$	−3.23735	+	4.05376i	−0.208970	+	0.261669i
$241$	16.1264	−	9.31056i	1.03879	−	0.599746i	0.119300	−	0.992858i	$-0.461935\pi$
$241$	16.1264	−	9.31056i	1.03879	−	0.599746i	0.919490	+	0.393112i	$0.128602\pi$
$242$	8.11509	−	4.68525i	0.521658	−	0.301179i
$243$	−14.9117	+	4.54330i	−0.956585	+	0.291453i
$244$		−	6.11982i		−	0.391782i
$245$	9.97602	−	18.4409i	0.637344	−	1.17814i
$246$	−2.35972	+	15.5827i	−0.150450	+	0.993516i
$247$	−3.76715	+	6.52489i	−0.239698	+	0.415169i
$248$	4.15801	+	7.20189i	0.264034	+	0.457320i
$249$	5.45186	+	13.9194i	0.345497	+	0.882104i
$250$	2.66875	+	1.54080i	0.168787	+	0.0974490i
$251$	−3.48190			−0.219776			−0.109888	−	0.993944i	$-0.535049\pi$
$251$	−3.48190			−0.219776			−0.109888	+	0.993944i	$0.535049\pi$
$252$	−2.24475	+	7.61322i	−0.141406	+	0.479588i
$253$	−8.06618			−0.507116
$254$	−6.06945	−	3.50420i	−0.380831	−	0.219873i
$255$	−2.05951	−	5.25823i	−0.128972	−	0.329283i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.29114	−	5.70042i	0.205296	−	0.355582i	−0.744931	−	0.667141i	$-0.767518\pi$
$257$	3.29114	−	5.70042i	0.205296	−	0.355582i	0.950227	+	0.311559i	$0.100851\pi$
$258$	−2.26520	+	14.9585i	−0.141025	+	0.931275i
$259$	−1.67943	−	0.938836i	−0.104355	−	0.0583364i
$260$		−	2.99519i		−	0.185754i
$261$	−6.15302	−	6.64978i	−0.380863	−	0.411611i
$262$	0.296521	−	0.171196i	0.0183191	−	0.0105765i
$263$	−10.7444	+	6.20331i	−0.662531	+	0.382513i	−0.793241	−	0.608908i	$-0.791608\pi$
$263$	−10.7444	+	6.20331i	−0.662531	+	0.382513i	0.130710	+	0.991421i	$0.458274\pi$
$264$	1.37973	−	1.72767i	0.0849162	−	0.106331i
$265$			30.4687i			1.87167i
$266$	−17.1235	+	10.2052i	−1.04991	+	0.625719i
$267$	22.4738	+	3.40326i	1.37537	+	0.208276i
$268$	−5.68742	+	9.85089i	−0.347414	+	0.601739i
$269$	−6.81196	−	11.7987i	−0.415332	−	0.719377i	0.580131	−	0.814523i	$-0.303001\pi$
$269$	−6.81196	−	11.7987i	−0.415332	−	0.719377i	−0.995463	+	0.0951463i	$0.969668\pi$
$270$	15.5223	−	1.13089i	0.944658	−	0.0688240i
$271$	7.15279	+	4.12966i	0.434501	+	0.250859i	0.701262	−	0.712903i	$-0.252620\pi$
$271$	7.15279	+	4.12966i	0.434501	+	0.250859i	−0.266761	+	0.963763i	$0.585954\pi$
$272$	1.08855			0.0660028
$273$	−1.73022	−	4.24339i	−0.104717	−	0.256822i
$274$	8.24972			0.498384
$275$	4.39009	+	2.53462i	0.264732	+	0.152843i
$276$	10.1908	−	3.99149i	0.613416	−	0.240259i
$277$	2.10791	+	3.65102i	0.126652	+	0.219368i	0.922378	−	0.386289i	$-0.126243\pi$
$277$	2.10791	+	3.65102i	0.126652	+	0.219368i	−0.795725	+	0.605658i	$0.792910\pi$
$278$	7.34105	−	12.7151i	0.440287	−	0.762599i
$279$	7.38650	−	23.8295i	0.442218	−	1.42664i
$280$	3.86679	−	6.91708i	0.231085	−	0.413374i
$281$		−	7.04869i		−	0.420490i	−0.977649	−	0.210245i	$-0.932574\pi$
$281$		−	7.04869i		−	0.420490i	0.977649	−	0.210245i	$-0.0674261\pi$
$282$	−2.60495	−	2.08032i	−0.155123	−	0.123882i
$283$	12.9685	−	7.48735i	0.770896	−	0.445077i	−0.0622983	−	0.998058i	$-0.519843\pi$
$283$	12.9685	−	7.48735i	0.770896	−	0.445077i	0.833194	+	0.552981i	$0.186510\pi$
$284$	−2.75967	+	1.59330i	−0.163756	+	0.0945447i
$285$	30.5422	+	24.3912i	1.80917	+	1.44481i
$286$			1.27652i			0.0754821i
$287$	−0.333565	−	24.0720i	−0.0196897	−	1.42093i
$288$	−0.888225	+	2.86549i	−0.0523392	+	0.168851i
$289$	7.90753	−	13.6962i	0.465149	−	0.805662i
$290$	4.52261	+	7.83340i	0.265577	+	0.459993i
$291$	26.3997	−	10.3401i	1.54758	−	0.606146i
$292$	−9.69406	−	5.59687i	−0.567302	−	0.327532i
$293$	−21.3317			−1.24621			−0.623106	−	0.782138i	$-0.714129\pi$
$293$	−21.3317			−1.24621			−0.623106	+	0.782138i	$0.714129\pi$
$294$	1.48246	−	12.0334i	0.0864591	−	0.701801i
$295$	−7.07246			−0.411775
$296$	−0.629787	−	0.363608i	−0.0366056	−	0.0211343i
$297$	−6.61544	+	0.481975i	−0.383867	+	0.0279670i
$298$	4.42641	+	7.66677i	0.256415	+	0.444124i
$299$	−3.15945	+	5.47232i	−0.182715	+	0.316473i
$300$	−6.80069	−	1.02984i	−0.392638	−	0.0594581i
$301$	−0.320203	−	23.1078i	−0.0184562	−	1.33191i
$302$			6.18779i			0.356067i
$303$	13.8539	−	17.3477i	0.795889	−	0.996600i
$304$	−6.52489	+	3.76715i	−0.374228	+	0.216061i
$305$	15.8743	−	9.16501i	0.908957	−	0.524787i
$306$	−2.21789	−	2.39695i	−0.126788	−	0.137024i
$307$			9.13303i			0.521250i	0.965440	+	0.260625i	$0.0839286\pi$
$307$			9.13303i			0.521250i	−0.965440	+	0.260625i	$0.916071\pi$
$308$	−1.64799	+	2.94799i	−0.0939027	+	0.167977i
$309$	−3.13621	+	20.7103i	−0.178413	+	1.17817i
$310$	−12.4540	+	21.5710i	−0.707341	+	1.22515i
$311$	−12.3535	−	21.3968i	−0.700500	−	1.21330i	−0.968291	−	0.249825i	$-0.919627\pi$
$311$	−12.3535	−	21.3968i	−0.700500	−	1.21330i	0.267791	−	0.963477i	$-0.413706\pi$
$312$	−0.631675	−	1.61276i	−0.0357616	−	0.0913044i
$313$	−8.98647	−	5.18834i	−0.507945	−	0.293262i	0.224043	−	0.974579i	$-0.428074\pi$
$313$	−8.98647	−	5.18834i	−0.507945	−	0.293262i	−0.731989	+	0.681317i	$0.761408\pi$
$314$	−2.71444			−0.153185
$315$	−23.1097	+	5.57882i	−1.30208	+	0.314331i
$316$	13.3222			0.749430
$317$	1.95071	+	1.12624i	0.109563	+	0.0632560i	0.553780	−	0.832663i	$-0.313185\pi$
$317$	1.95071	+	1.12624i	0.109563	+	0.0632560i	−0.444217	+	0.895919i	$0.646518\pi$
$318$	6.42574	+	16.4058i	0.360338	+	0.919994i
$319$	−1.92749	−	3.33851i	−0.107919	−	0.186921i
$320$	1.49759	−	2.59391i	0.0837180	−	0.145004i
$321$	−0.644964	+	4.25909i	−0.0359984	+	0.237719i
$322$	−14.3612	+	8.55891i	−0.800318	+	0.476970i
$323$		−	8.20143i		−	0.456340i
$324$	8.11948	−	3.88253i	0.451082	−	0.215696i
$325$	3.43911	−	1.98557i	0.190768	−	0.110140i
$326$	−17.4001	+	10.0460i	−0.963705	+	0.556395i
$327$	−1.58122	+	1.97998i	−0.0874416	+	0.109493i
$328$		−	9.09924i		−	0.502421i
$329$	4.44492	+	2.48480i	0.245056	+	0.136992i
$330$	6.54769	+	0.991531i	0.360438	+	0.0545820i
$331$	10.4267	−	18.0595i	0.573102	−	0.992642i	−0.423143	−	0.906063i	$-0.639073\pi$
$331$	10.4267	−	18.0595i	0.573102	−	0.992642i	0.996245	−	0.0865788i	$-0.0275934\pi$
$332$	−4.31540	−	7.47449i	−0.236838	−	0.410216i
$333$	0.482523	+	2.12762i	0.0264421	+	0.116593i
$334$	−11.8697	−	6.85300i	−0.649484	−	0.374980i
$335$	−34.0698			−1.86143
$336$	0.623283	−	4.53999i	0.0340029	−	0.247677i
$337$	−11.1350			−0.606564			−0.303282	−	0.952901i	$-0.598082\pi$
$337$	−11.1350			−0.606564			−0.303282	+	0.952901i	$0.598082\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$	1.97741	−	0.774501i	0.107398	−	0.0420651i
$340$	1.63020	+	2.82359i	0.0884100	+	0.153131i
$341$	5.30777	−	9.19333i	0.287432	−	0.497847i
$342$	21.5895	+	6.69215i	1.16742	+	0.361870i
$343$	0.769632	+	18.5043i	0.0415562	+	0.999136i
$344$		−	8.73475i		−	0.470946i
$345$	25.6153	+	20.4565i	1.37908	+	1.10134i
$346$	−22.0128	+	12.7091i	−1.18342	+	0.683246i
$347$	27.6683	−	15.9743i	1.48531	−	0.857545i	0.485452	−	0.874263i	$-0.338655\pi$
$347$	27.6683	−	15.9743i	1.48531	−	0.857545i	0.999860	+	0.0167179i	$0.00532172\pi$
$348$	4.08724	+	3.26409i	0.219099	+	0.174973i
$349$			7.76692i			0.415754i	0.978155	+	0.207877i	$0.0666553\pi$
$349$			7.76692i			0.415754i	−0.978155	+	0.207877i	$0.933345\pi$
$350$	10.5057	−	0.145576i	0.561551	−	0.00778138i
$351$	−2.26422	+	4.67689i	−0.120855	+	0.249634i
$352$	−0.638259	+	1.10550i	−0.0340193	+	0.0589232i
$353$	−16.9957	−	29.4374i	−0.904589	−	1.56679i	−0.821467	−	0.570256i	$-0.806844\pi$
$353$	−16.9957	−	29.4374i	−0.904589	−	1.56679i	−0.0831221	−	0.996539i	$-0.526489\pi$
$354$	−3.80817	+	1.49156i	−0.202402	+	0.0792755i
$355$	−8.26572	−	4.77222i	−0.438699	−	0.253283i
$356$	−13.1232			−0.695527
$357$	3.94065	+	3.05857i	0.208561	+	0.161877i
$358$	13.5609			0.716716
$359$	30.3728	+	17.5357i	1.60301	+	0.925500i	0.990880	+	0.134744i	$0.0430213\pi$
$359$	30.3728	+	17.5357i	1.60301	+	0.925500i	0.612132	+	0.790755i	$0.290312\pi$
$360$	−8.76303	+	1.98737i	−0.461852	+	0.104744i
$361$	18.8828	+	32.7059i	0.993830	+	1.72136i
$362$	−0.106715	+	0.184836i	−0.00560883	+	0.00971479i
$363$	16.0472	+	2.43007i	0.842261	+	0.127546i
$364$	1.35450	+	2.27274i	0.0709949	+	0.119124i
$365$		−	33.5273i		−	1.75490i
$366$	6.61462	−	8.28272i	0.345752	−	0.432945i
$367$	6.09340	−	3.51803i	0.318073	−	0.183639i	−0.332460	−	0.943117i	$-0.607879\pi$
$367$	6.09340	−	3.51803i	0.318073	−	0.183639i	0.650533	+	0.759478i	$0.274545\pi$
$368$	−5.47232	+	3.15945i	−0.285264	+	0.164698i
$369$	−20.0363	+	18.5395i	−1.04305	+	0.965128i
$370$		−	2.17815i		−	0.113236i
$371$	−13.7787	−	23.1195i	−0.715352	−	1.20031i
$372$	−2.15661	+	14.2414i	−0.111815	+	0.738382i
$373$	6.25175	−	10.8283i	0.323703	−	0.560670i	−0.657546	−	0.753414i	$-0.728405\pi$
$373$	6.25175	−	10.8283i	0.323703	−	0.560670i	0.981249	+	0.192744i	$0.0617388\pi$
$374$	−0.694774	−	1.20338i	−0.0359259	−	0.0622255i
$375$	1.94658	+	4.96989i	0.100521	+	0.256644i
$376$	1.66685	+	0.962355i	0.0859611	+	0.0496297i
$377$	−3.01992			−0.155534
$378$	−11.2669	+	7.87768i	−0.579505	+	0.405184i
$379$	25.1675			1.29277			0.646384	−	0.763012i	$-0.276280\pi$
$379$	25.1675			1.29277			0.646384	+	0.763012i	$0.276280\pi$
$380$	−19.5433	−	11.2833i	−1.00255	−	0.578821i
$381$	−4.42703	−	11.3028i	−0.226804	−	0.579062i
$382$	3.31392	+	5.73987i	0.169555	+	0.293677i
$383$	2.97615	−	5.15484i	0.152074	−	0.263400i	−0.779916	−	0.625884i	$-0.784738\pi$
$383$	2.97615	−	5.15484i	0.152074	−	0.263400i	0.931990	+	0.362485i	$0.118071\pi$
$384$	0.259332	−	1.71253i	0.0132340	−	0.0873920i
$385$	−10.1148	+	0.140160i	−0.515499	+	0.00714324i
$386$			6.94606i			0.353545i
$387$	−19.2337	+	17.7969i	−0.977703	+	0.904666i
$388$	−14.1762	+	8.18465i	−0.719689	+	0.415512i
$389$	−8.59892	+	4.96459i	−0.435983	+	0.251715i	−0.701892	−	0.712283i	$-0.747661\pi$
$389$	−8.59892	+	4.96459i	−0.435983	+	0.251715i	0.265909	+	0.963998i	$0.414328\pi$
$390$	3.23735	−	4.05376i	0.163930	−	0.205270i
$391$		−	6.87841i		−	0.347856i
$392$	0.193960	+	6.99731i	0.00979646	+	0.353418i
$393$	0.586356	+	0.0887932i	0.0295777	+	0.00447903i
$394$	−1.35672	+	2.34991i	−0.0683507	+	0.118387i
$395$	19.9512	+	34.5564i	1.00385	+	1.73872i
$396$	3.73471	−	0.846997i	0.187676	−	0.0425632i
$397$	−12.7492	−	7.36074i	−0.639863	−	0.369425i	0.144699	−	0.989476i	$-0.453779\pi$
$397$	−12.7492	−	7.36074i	−0.639863	−	0.369425i	−0.784562	+	0.620051i	$0.787112\pi$
$398$	2.89784			0.145256
$399$	−34.2056	−	4.69600i	−1.71242	−	0.235094i
$400$	3.97115			0.198557
$401$	−11.9346	−	6.89042i	−0.595984	−	0.344091i	0.171476	−	0.985188i	$-0.445146\pi$
$401$	−11.9346	−	6.89042i	−0.595984	−	0.344091i	−0.767460	+	0.641097i	$0.778480\pi$
$402$	−18.3448	+	7.18520i	−0.914958	+	0.358365i
$403$	−4.15801	−	7.20189i	−0.207125	−	0.358751i
$404$	−6.40881	+	11.1004i	−0.318850	+	0.552265i
$405$	22.2306	+	15.2467i	1.10465	+	0.757616i
$406$	−6.97420	−	3.89872i	−0.346124	−	0.193490i
$407$			0.928303i			0.0460143i
$408$	1.47327	+	1.17656i	0.0729376	+	0.0582482i
$409$	−0.704883	+	0.406964i	−0.0348542	+	0.0201231i	−0.517326	−	0.855788i	$-0.673072\pi$
$409$	−0.704883	+	0.406964i	−0.0348542	+	0.0201231i	0.482472	+	0.875912i	$0.339739\pi$
$410$	23.6026	−	13.6270i	1.16565	−	0.672988i
$411$	11.1654	+	8.91672i	0.550747	+	0.439829i
$412$		−	12.0934i		−	0.595800i
$413$	5.36656	−	3.19834i	0.264071	−	0.157380i
$414$	18.1067	+	5.61260i	0.889898	+	0.275844i
$415$	12.9254	−	22.3875i	0.634484	−	1.09896i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	23.6787	−	9.27432i	1.15955	−	0.454165i
$418$	8.32913	+	4.80883i	0.407391	+	0.235207i
$419$	30.2778			1.47917			0.739583	−	0.673065i	$-0.235023\pi$
$419$	30.2778			1.47917			0.739583	+	0.673065i	$0.235023\pi$
$420$	12.7097	−	5.18232i	0.620172	−	0.252871i
$421$	−7.43240			−0.362233			−0.181117	−	0.983462i	$-0.557971\pi$
$421$	−7.43240			−0.362233			−0.181117	+	0.983462i	$0.557971\pi$
$422$	−14.9028	−	8.60412i	−0.725455	−	0.418842i
$423$	−1.27709	−	5.63113i	−0.0620941	−	0.273795i
$424$	−5.08627	−	8.80968i	−0.247011	−	0.427836i
$425$	−2.16139	+	3.74363i	−0.104843	+	0.181593i
$426$	−5.45712	−	0.826384i	−0.264398	−	0.0400384i
$427$	−7.90070	+	14.1331i	−0.382342	+	0.683949i
$428$		−	2.48702i		−	0.120215i
$429$	−1.37973	+	1.72767i	−0.0666138	+	0.0834128i
$430$	22.6572	−	13.0811i	1.09262	−	0.630827i
$431$	−20.9668	+	12.1052i	−1.00993	+	0.583085i	−0.911172	−	0.412026i	$-0.864821\pi$
$431$	−20.9668	+	12.1052i	−1.00993	+	0.583085i	−0.0987614	+	0.995111i	$0.531488\pi$
$432$	−4.29932	+	2.91819i	−0.206851	+	0.140402i
$433$		−	26.2104i		−	1.25959i	−0.776761	−	0.629796i	$-0.783138\pi$
$433$		−	26.2104i		−	1.25959i	0.776761	−	0.629796i	$-0.216862\pi$
$434$	−0.304853	−	22.0000i	−0.0146334	−	1.05603i
$435$	−2.34572	+	15.4902i	−0.112468	+	0.742698i
$436$	0.731469	−	1.26694i	0.0350310	−	0.0606755i
$437$	23.8042	+	41.2301i	1.13871	+	1.97230i
$438$	−7.07081	−	18.0528i	−0.337856	−	0.862595i
$439$	−17.6766	−	10.2056i	−0.843656	−	0.487085i	0.0148490	−	0.999890i	$-0.495273\pi$
$439$	−17.6766	−	10.2056i	−0.843656	−	0.487085i	−0.858505	+	0.512805i	$0.828607\pi$
$440$	−3.82341			−0.182274
$441$	15.0127	−	14.6840i	0.714890	−	0.699236i
$442$	−1.08855			−0.0517769
$443$	−1.82693	−	1.05478i	−0.0868002	−	0.0501141i	0.455972	−	0.889994i	$-0.349292\pi$
$443$	−1.82693	−	1.05478i	−0.0868002	−	0.0501141i	−0.542772	+	0.839880i	$0.682625\pi$
$444$	−0.459364	−	1.17282i	−0.0218005	−	0.0556597i
$445$	−19.6532	−	34.0403i	−0.931650	−	1.61367i
$446$	11.2297	−	19.4504i	0.531741	−	0.921002i
$447$	−2.29582	+	15.1607i	−0.108589	+	0.717076i
$448$	0.0366585	+	2.64550i	0.00173195	+	0.124988i
$449$			26.0621i			1.22995i	0.788548	+	0.614974i	$0.210833\pi$
$449$			26.0621i			1.22995i	−0.788548	+	0.614974i	$0.789167\pi$
$450$	−8.09112	−	8.74436i	−0.381419	−	0.412213i
$451$	−10.0592	+	5.80767i	−0.473668	+	0.273472i
$452$	−1.06184	+	0.613053i	−0.0499447	+	0.0288356i
$453$	−6.68808	+	8.37471i	−0.314233	+	0.393478i
$454$		−	16.9144i		−	0.793833i
$455$	−3.86679	+	6.91708i	−0.181278	+	0.324278i
$456$	−12.9027	−	1.95388i	−0.604223	−	0.0914989i
$457$	−12.8815	+	22.3115i	−0.602573	+	1.04369i	0.389857	+	0.920875i	$0.372524\pi$
$457$	−12.8815	+	22.3115i	−0.602573	+	1.04369i	−0.992430	+	0.122812i	$0.960809\pi$
$458$	2.61571	+	4.53055i	0.122224	+	0.211699i
$459$	−0.411003	−	5.64130i	−0.0191840	−	0.263313i
$460$	−16.3906	−	9.46313i	−0.764217	−	0.441221i
$461$	−4.63148			−0.215709			−0.107855	−	0.994167i	$-0.534398\pi$
$461$	−4.63148			−0.215709			−0.107855	+	0.994167i	$0.534398\pi$
$462$	−5.41676	+	2.20865i	−0.252010	+	0.102756i
$463$	2.39668			0.111383			0.0556916	−	0.998448i	$-0.482264\pi$
$463$	2.39668			0.111383			0.0556916	+	0.998448i	$0.482264\pi$
$464$	−2.61533	−	1.50996i	−0.121414	−	0.0700982i
$465$	−40.1706	+	15.7338i	−1.86287	+	0.729637i
$466$	−10.4602	−	18.1176i	−0.484559	−	0.839280i
$467$	−21.3514	+	36.9817i	−0.988024	+	1.71131i	−0.360384	+	0.932804i	$0.617354\pi$
$467$	−21.3514	+	36.9817i	−0.988024	+	1.71131i	−0.627640	+	0.778504i	$0.715979\pi$
$468$	0.888225	−	2.86549i	0.0410582	−	0.132458i
$469$	25.8520	−	15.4072i	1.19374	−	0.711437i
$470$			5.76487i			0.265913i
$471$	−3.67379	−	2.93390i	−0.169279	−	0.135187i
$472$	2.04493	−	1.18064i	0.0941253	−	0.0543433i
$473$	−9.65624	+	5.57503i	−0.443994	+	0.256340i
$474$	18.0305	+	14.3993i	0.828170	+	0.661380i
$475$		−	29.9198i		−	1.37281i
$476$	−2.51389	−	1.40531i	−0.115224	−	0.0644125i
$477$	−9.03550	+	29.1494i	−0.413707	+	1.33466i
$478$	0.528541	−	0.915460i	0.0241749	−	0.0418722i
$479$	−13.0998	−	22.6895i	−0.598545	−	1.03671i	−0.993036	−	0.117810i	$-0.962413\pi$
$479$	−13.0998	−	22.6895i	−0.598545	−	1.03671i	0.394491	−	0.918900i	$-0.370921\pi$
$480$	4.83051	−	1.89199i	0.220482	−	0.0863569i
$481$	0.629787	+	0.363608i	0.0287158	+	0.0165791i
$482$	−18.6211			−0.848169
$483$	−28.6877	−	3.93846i	−1.30534	−	0.179206i
$484$	−9.37050			−0.425932
$485$	−42.4604	−	24.5145i	−1.92803	−	1.11315i
$486$	15.1856	+	3.52123i	0.688831	+	0.159726i
$487$	12.1330	+	21.0150i	0.549798	+	0.952279i	0.998288	+	0.0584906i	$0.0186288\pi$
$487$	12.1330	+	21.0150i	0.549798	+	0.952279i	−0.448490	+	0.893788i	$0.648038\pi$
$488$	−3.05991	+	5.29992i	−0.138516	+	0.239916i
$489$	−34.4080	−	5.21048i	−1.55598	−	0.235626i
$490$	−17.8599	+	10.9822i	−0.806829	+	0.496127i
$491$		−	14.5899i		−	0.658434i	−0.944254	−	0.329217i	$-0.893215\pi$
$491$		−	14.5899i		−	0.658434i	0.944254	−	0.329217i	$-0.106785\pi$
$492$	9.83492	−	12.3151i	0.443393	−	0.555210i
$493$	2.84691	−	1.64366i	0.128218	−	0.0740268i
$494$	6.52489	−	3.76715i	0.293569	−	0.169492i
$495$	7.79011	+	8.41904i	0.350139	+	0.378408i
$496$		−	8.31602i		−	0.373400i
$497$	8.43012	−	0.116816i	0.378142	−	0.00523990i
$498$	2.23824	−	14.7805i	0.100298	−	0.662328i
$499$	13.6722	−	23.6809i	0.612050	−	1.06010i	−0.378844	−	0.925460i	$-0.623678\pi$
$499$	13.6722	−	23.6809i	0.612050	−	1.06010i	0.990894	−	0.134642i	$-0.0429883\pi$
$500$	−1.54080	−	2.66875i	−0.0689068	−	0.119350i
$501$	−8.65774	−	22.1045i	−0.386799	−	0.987554i
$502$	3.01542	+	1.74095i	0.134585	+	0.0777025i
$503$	−14.2379			−0.634839			−0.317419	−	0.948285i	$-0.602816\pi$
$503$	−14.2379			−0.634839			−0.317419	+	0.948285i	$0.602816\pi$
$504$	5.75062	−	5.47086i	0.256153	−	0.243692i
$505$	−38.3912			−1.70839
$506$	6.98551	+	4.03309i	0.310544	+	0.179293i
$507$	0.631675	+	1.61276i	0.0280537	+	0.0716251i
$508$	3.50420	+	6.06945i	0.155474	+	0.269288i
$509$	11.6247	−	20.1346i	0.515257	−	0.892452i	−0.484586	−	0.874744i	$-0.661030\pi$
$509$	11.6247	−	20.1346i	0.515257	−	0.892452i	0.999843	−	0.0177081i	$-0.00563697\pi$
$510$	−0.845525	+	5.58352i	−0.0374405	+	0.247242i
$511$	15.1619	+	25.4404i	0.670722	+	1.12542i
$512$			1.00000i			0.0441942i
$513$	21.9865	+	32.3923i	0.970729	+	1.43016i
$514$	−5.70042	+	3.29114i	−0.251435	+	0.145166i
$515$	31.3692	−	18.1110i	1.38229	−	0.798068i
$516$	9.44097	−	11.8218i	0.415615	−	0.520427i
$517$		−	2.45693i		−	0.108055i
$518$	0.985010	+	1.65277i	0.0432789	+	0.0726186i
$519$	−43.5294	−	6.59176i	−1.91073	−	0.289346i
$520$	−1.49759	+	2.59391i	−0.0656738	+	0.113750i
$521$	19.2555	+	33.3515i	0.843598	+	1.46115i	0.886833	+	0.462090i	$0.152900\pi$
$521$	19.2555	+	33.3515i	0.843598	+	1.46115i	−0.0432351	+	0.999065i	$0.513766\pi$
$522$	2.00378	+	8.83539i	0.0877032	+	0.386715i
$523$	15.2132	+	8.78337i	0.665229	+	0.384070i	0.794266	−	0.607570i	$-0.207856\pi$
$523$	15.2132	+	8.78337i	0.665229	+	0.384070i	−0.129038	+	0.991640i	$0.541189\pi$
$524$	−0.342392			−0.0149575
$525$	14.3760	+	11.1580i	0.627419	+	0.486976i
$526$	12.4066			0.540954
$527$	7.83959	+	4.52619i	0.341498	+	0.197164i
$528$	−2.05871	+	0.806345i	−0.0895940	+	0.0350916i
$529$	8.46420	+	14.6604i	0.368009	+	0.637410i
$530$	15.2343	−	26.3866i	0.661737	−	1.14616i
$531$	−6.76622	−	2.09735i	−0.293629	−	0.0910170i
$532$	19.9319	−	0.276196i	0.864160	−	0.0119746i
$533$			9.09924i			0.394132i
$534$	−17.7612	−	14.1842i	−0.768604	−	0.613810i
$535$	6.45111	−	3.72455i	0.278906	−	0.161026i
$536$	9.85089	−	5.68742i	0.425494	−	0.245659i
$537$	18.3537	+	14.6573i	0.792020	+	0.632510i
$538$			13.6239i			0.587369i
$539$	7.61171	−	4.68052i	0.327859	−	0.201604i
$540$	−14.0082	−	6.78177i	−0.602815	−	0.291841i
$541$	−15.2218	+	26.3650i	−0.654438	+	1.13352i	0.327596	+	0.944818i	$0.393761\pi$
$541$	−15.2218	+	26.3650i	−0.654438	+	1.13352i	−0.982034	+	0.188702i	$0.939572\pi$
$542$	−4.12966	−	7.15279i	−0.177384	−	0.307238i
$543$	−0.344212	+	0.134819i	−0.0147715	+	0.00578563i
$544$	−0.942709	−	0.544273i	−0.0404183	−	0.0233355i
$545$	4.38177			0.187695
$546$	−0.623283	+	4.53999i	−0.0266740	+	0.194294i
$547$	−30.5580			−1.30657			−0.653283	−	0.757114i	$-0.726609\pi$
$547$	−30.5580			−1.30657			−0.653283	+	0.757114i	$0.726609\pi$
$548$	−7.14446	−	4.12486i	−0.305196	−	0.176205i
$549$	17.9048	−	4.06063i	0.764158	−	0.173304i
$550$	−2.53462	−	4.39009i	−0.108077	−	0.187194i
$551$	−11.3765	+	19.7046i	−0.484655	+	0.839446i
$552$	−10.8213	−	1.63869i	−0.460584	−	0.0697473i
$553$	−30.7661	−	17.1989i	−1.30831	−	0.731372i
$554$		−	4.21583i		−	0.179113i
$555$	2.35425	−	2.94796i	0.0999324	−	0.125134i
$556$	−12.7151	+	7.34105i	−0.539239	+	0.311330i
$557$	16.1902	−	9.34739i	0.685999	−	0.396062i	−0.116112	−	0.993236i	$-0.537043\pi$
$557$	16.1902	−	9.34739i	0.685999	−	0.396062i	0.802112	+	0.597174i	$0.203710\pi$
$558$	−18.3116	+	16.9437i	−0.775194	+	0.717284i
$559$			8.73475i			0.369441i
$560$	−6.80728	+	4.05697i	−0.287660	+	0.171438i
$561$	0.360354	−	2.37964i	0.0152142	−	0.100468i
$562$	−3.52434	+	6.10434i	−0.148666	+	0.257496i
$563$	16.4320	+	28.4610i	0.692525	+	1.19949i	0.971008	+	0.239048i	$0.0768353\pi$
$563$	16.4320	+	28.4610i	0.692525	+	1.19949i	−0.278482	+	0.960441i	$0.589831\pi$
$564$	1.21579	+	3.10409i	0.0511941	+	0.130706i
$565$	−3.18041	−	1.83621i	−0.133801	−	0.0772499i
$566$	−14.9747			−0.629434
$567$	−23.7635	−	1.51595i	−0.997971	−	0.0636637i
$568$	3.18659			0.133706
$569$	−2.78940	−	1.61046i	−0.116938	−	0.0675141i	0.440390	−	0.897806i	$-0.354840\pi$
$569$	−2.78940	−	1.61046i	−0.116938	−	0.0675141i	−0.557328	+	0.830292i	$0.688173\pi$
$570$	−14.2548	−	36.3945i	−0.597067	−	1.52440i
$571$	−3.67031	−	6.35717i	−0.153598	−	0.266039i	0.778950	−	0.627086i	$-0.215753\pi$
$571$	−3.67031	−	6.35717i	−0.153598	−	0.266039i	−0.932548	+	0.361047i	$0.882419\pi$
$572$	0.638259	−	1.10550i	0.0266869	−	0.0462231i
$573$	−1.71881	+	11.3503i	−0.0718042	+	0.474167i
$574$	−11.7471	+	21.0138i	−0.490316	+	0.877097i
$575$		−	25.0932i		−	1.04646i
$576$	2.20197	−	2.03748i	0.0917489	−	0.0848949i
$577$	15.4343	−	8.91102i	0.642540	−	0.370971i	−0.143052	−	0.989715i	$-0.545692\pi$
$577$	15.4343	−	8.91102i	0.642540	−	0.370971i	0.785592	+	0.618744i	$0.212358\pi$
$578$	−13.6962	+	7.90753i	−0.569689	+	0.328910i
$579$	−7.50765	+	9.40097i	−0.312007	+	0.390691i
$580$		−	9.04523i		−	0.375583i
$581$	0.316392	+	22.8327i	0.0131262	+	0.947262i
$582$	−28.0328	−	4.24508i	−1.16200	−	0.175964i
$583$	−6.49271	+	11.2457i	−0.268901	+	0.465750i
$584$	5.59687	+	9.69406i	0.231600	+	0.401143i
$585$	8.76303	−	1.98737i	0.362307	−	0.0821677i
$586$	18.4738	+	10.6659i	0.763146	+	0.440602i
$587$	27.8171			1.14813			0.574067	−	0.818808i	$-0.305365\pi$
$587$	27.8171			1.14813			0.574067	+	0.818808i	$0.305365\pi$
$588$	−7.30054	+	9.67998i	−0.301069	+	0.399196i
$589$	−62.6553			−2.58167
$590$	6.12493	+	3.53623i	0.252160	+	0.145584i
$591$	−4.37613	+	1.71402i	−0.180010	+	0.0705052i
$592$	0.363608	+	0.629787i	0.0149442	+	0.0258841i
$593$	12.3538	−	21.3973i	0.507308	−	0.878683i	−0.492656	−	0.870224i	$-0.663974\pi$
$593$	12.3538	−	21.3973i	0.507308	−	0.878683i	0.999964	−	0.00845898i	$-0.00269261\pi$
$594$	5.97013	+	2.89032i	0.244957	+	0.118591i
$595$	−0.119521	−	8.62538i	−0.00489990	−	0.353606i
$596$		−	8.85283i		−	0.362626i
$597$	3.92201	+	3.13214i	0.160517	+	0.128190i
$598$	5.47232	−	3.15945i	0.223780	−	0.129199i
$599$	−9.38101	+	5.41613i	−0.383297	+	0.221297i	−0.679252	−	0.733905i	$-0.737696\pi$
$599$	−9.38101	+	5.41613i	−0.383297	+	0.221297i	0.295954	+	0.955202i	$0.404362\pi$
$600$	5.37465	+	4.29222i	0.219419	+	0.175229i
$601$			11.4087i			0.465369i	0.972552	+	0.232684i	$0.0747509\pi$
$601$			11.4087i			0.465369i	−0.972552	+	0.232684i	$0.925249\pi$
$602$	−11.2766	+	20.1720i	−0.459599	+	0.822150i
$603$	−32.5945	−	10.1034i	−1.32735	−	0.411443i
$604$	3.09389	−	5.35878i	0.125889	−	0.218046i
$605$	−14.0332	−	24.3062i	−0.570531	−	0.988189i
$606$	−20.6717	+	8.09658i	−0.839731	+	0.328901i
$607$	−1.41237	−	0.815433i	−0.0573264	−	0.0330974i	0.471063	−	0.882100i	$-0.343870\pi$
$607$	−1.41237	−	0.815433i	−0.0573264	−	0.0330974i	−0.528389	+	0.849002i	$0.677204\pi$
$608$	7.53429			0.305556
$609$	−5.22512	−	12.8147i	−0.211732	−	0.519278i
$610$	−18.3300			−0.742161
$611$	−1.66685	−	0.962355i	−0.0674334	−	0.0389327i
$612$	0.722274	+	3.18476i	0.0291962	+	0.128736i
$613$	−10.9776	−	19.0137i	−0.443381	−	0.767958i	0.554557	−	0.832146i	$-0.312888\pi$
$613$	−10.9776	−	19.0137i	−0.443381	−	0.767958i	−0.997938	+	0.0641876i	$0.979554\pi$
$614$	4.56652	−	7.90944i	0.184290	−	0.319199i
$615$	46.6731	+	7.06781i	1.88204	+	0.285002i
$616$	2.90119	−	1.72904i	0.116892	−	0.0696649i
$617$			11.6678i			0.469727i	0.972028	+	0.234863i	$0.0754643\pi$
$617$			11.6678i			0.469727i	−0.972028	+	0.234863i	$0.924536\pi$
$618$	13.0712	−	16.3676i	0.525801	−	0.658400i
$619$	42.6836	−	24.6434i	1.71560	−	0.990501i	0.789045	−	0.614336i	$-0.210576\pi$
$619$	42.6836	−	24.6434i	1.71560	−	0.990501i	0.926553	−	0.376165i	$-0.122757\pi$
$620$	21.5710	−	12.4540i	0.866312	−	0.500165i
$621$	18.4398	+	27.1669i	0.739962	+	1.09017i
$622$			24.7069i			0.990657i
$623$	30.3066	+	16.9420i	1.21421	+	0.678768i
$624$	−0.259332	+	1.71253i	−0.0103816	+	0.0685559i
$625$	14.5429	−	25.1890i	0.581715	−	1.00756i
$626$	5.18834	+	8.98647i	0.207368	+	0.359172i
$627$	6.07524	+	15.5109i	0.242622	+	0.619447i
$628$	2.35077	+	1.35722i	0.0938060	+	0.0541589i
$629$	−0.791608			−0.0315635
$630$	22.8030	+	6.72345i	0.908494	+	0.267869i
$631$	18.9327			0.753698			0.376849	−	0.926275i	$-0.377007\pi$
$631$	18.9327			0.753698			0.376849	+	0.926275i	$0.377007\pi$
$632$	−11.5373	−	6.66108i	−0.458930	−	0.264963i
$633$	−10.8700	−	27.7527i	−0.432044	−	1.10307i
$634$	−1.12624	−	1.95071i	−0.0447287	−	0.0774725i
$635$	−10.4957	+	18.1791i	−0.416510	+	0.721417i
$636$	2.63806	−	17.4207i	0.104606	−	0.690777i
$637$	−0.193960	−	6.99731i	−0.00768497	−	0.277244i
$638$			3.85498i			0.152620i
$639$	−6.49261	−	7.01678i	−0.256844	−	0.277580i
$640$	−2.59391	+	1.49759i	−0.102533	+	0.0591976i
$641$	−41.0435	+	23.6965i	−1.62112	+	0.935955i	−0.634501	+	0.772922i	$0.718795\pi$
$641$	−41.0435	+	23.6965i	−1.62112	+	0.935955i	−0.986621	+	0.163033i	$0.947872\pi$
$642$	2.68810	−	3.36600i	0.106091	−	0.132845i
$643$		−	48.5956i		−	1.91642i	−0.286062	−	0.958211i	$-0.592346\pi$
$643$		−	48.5956i		−	1.91642i	0.286062	−	0.958211i	$-0.407654\pi$
$644$	16.7166	−	0.231641i	0.658727	−	0.00912794i
$645$	44.8035	+	6.78470i	1.76414	+	0.267147i
$646$	−4.10071	+	7.10264i	−0.161340	+	0.279450i
$647$	−1.17998	−	2.04378i	−0.0463898	−	0.0803495i	0.841898	−	0.539636i	$-0.181438\pi$
$647$	−1.17998	−	2.04378i	−0.0463898	−	0.0803495i	−0.888288	+	0.459287i	$0.848105\pi$
$648$	−8.97294	−	0.697366i	−0.352490	−	0.0273951i
$649$	−2.61038	−	1.50711i	−0.102466	−	0.0591591i
$650$	−3.97115			−0.155761
$651$	23.3661	−	30.1049i	0.915791	−	1.17990i
$652$	20.0920			0.786862
$653$	19.9844	+	11.5380i	0.782049	+	0.451516i	0.837156	−	0.546964i	$-0.184217\pi$
$653$	19.9844	+	11.5380i	0.782049	+	0.451516i	−0.0551066	+	0.998480i	$0.517550\pi$
$654$	2.35936	−	0.924102i	0.0922584	−	0.0361352i
$655$	−0.512765	−	0.888134i	−0.0200354	−	0.0347023i
$656$	−4.54962	+	7.88017i	−0.177633	+	0.307669i
$657$	9.94256	−	32.0756i	0.387896	−	1.25139i
$658$	−2.60701	−	4.37436i	−0.101632	−	0.170530i
$659$		−	4.95281i		−	0.192934i	−0.995336	−	0.0964670i	$-0.969246\pi$
$659$		−	4.95281i		−	0.192934i	0.995336	−	0.0964670i	$-0.0307542\pi$
$660$	−5.17470	−	4.13254i	−0.201425	−	0.160859i
$661$	−4.81837	+	2.78189i	−0.187413	+	0.108203i	−0.590771	−	0.806839i	$-0.701176\pi$
$661$	−4.81837	+	2.78189i	−0.187413	+	0.108203i	0.403358	+	0.915042i	$0.367843\pi$
$662$	−18.0595	+	10.4267i	−0.701904	+	0.405244i
$663$	−1.47327	−	1.17656i	−0.0572169	−	0.0456937i
$664$			8.63079i			0.334940i
$665$	30.5664	+	51.2880i	1.18531	+	1.98886i
$666$	0.645931	−	2.08383i	0.0250293	−	0.0807468i
$667$	−9.54128	+	16.5260i	−0.369440	+	0.639888i
$668$	6.85300	+	11.8697i	0.265151	+	0.459254i
$669$	36.2215	−	14.1870i	1.40040	−	0.548502i
$670$	29.5053	+	17.0349i	1.13989	+	0.658115i
$671$	7.81206			0.301581
$672$	−2.80977	+	3.62011i	−0.108389	+	0.139649i
$673$	7.25823			0.279784			0.139892	−	0.990167i	$-0.455324\pi$
$673$	7.25823			0.279784			0.139892	+	0.990167i	$0.455324\pi$
$674$	9.64322	+	5.56751i	0.371443	+	0.214453i
$675$	−1.49939	−	20.5801i	−0.0577114	−	0.792130i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	13.7881	−	23.8817i	0.529919	−	0.917847i	−0.469472	−	0.882947i	$-0.655556\pi$
$677$	13.7881	−	23.8817i	0.529919	−	0.917847i	0.999391	−	0.0348992i	$-0.0111110\pi$
$678$	−2.09974	−	0.317968i	−0.0806400	−	0.0122115i
$679$	43.3049	−	0.600074i	1.66189	−	0.0230287i
$680$		−	3.26040i		−	0.125031i
$681$	18.2820	−	22.8924i	0.700567	−	0.877239i
$682$	−9.19333	+	5.30777i	−0.352031	+	0.203245i
$683$	−10.8942	+	6.28974i	−0.416853	+	0.240670i	−0.693730	−	0.720235i	$-0.744034\pi$
$683$	−10.8942	+	6.28974i	−0.416853	+	0.240670i	0.276877	+	0.960905i	$0.410701\pi$
$684$	−15.3510	−	16.5903i	−0.586958	−	0.634346i
$685$		−	24.7094i		−	0.944099i
$686$	8.58561	−	16.4100i	0.327800	−	0.626536i
$687$	−1.35667	+	8.95895i	−0.0517604	+	0.341805i
$688$	−4.36738	+	7.56452i	−0.166505	+	0.288395i
$689$	5.08627	+	8.80968i	0.193771	+	0.335622i
$690$	−11.9553	−	30.5235i	−0.455129	−	1.16201i
$691$	−14.1462	−	8.16730i	−0.538146	−	0.310699i	0.206181	−	0.978514i	$-0.433896\pi$
$691$	−14.1462	−	8.16730i	−0.538146	−	0.310699i	−0.744327	+	0.667815i	$0.767230\pi$
$692$	25.4182			0.966256
$693$	−9.71841	−	2.86547i	−0.369172	−	0.108850i
$694$	−31.9486			−1.21275
$695$	−38.0840	−	21.9878i	−1.44461	−	0.834046i
$696$	−1.90761	−	4.87040i	−0.0723078	−	0.184612i
$697$	−4.95247	−	8.57793i	−0.187588	−	0.324912i
$698$	3.88346	−	6.72635i	0.146991	−	0.254596i
$699$	5.42532	−	35.8267i	0.205204	−	1.35509i
$700$	−9.17096	−	5.12676i	−0.346630	−	0.193773i
$701$			28.2379i			1.06653i	0.845948	+	0.533265i	$0.179035\pi$
$701$			28.2379i			1.06653i	−0.845948	+	0.533265i	$0.820965\pi$
$702$	4.29932	−	2.91819i	0.162267	−	0.110140i
$703$	4.74500	−	2.73953i	0.178961	−	0.103323i
$704$	1.10550	−	0.638259i	0.0416650	−	0.0240553i
$705$	−6.23096	+	7.80232i	−0.234672	+	0.293852i
$706$			33.9914i			1.27928i
$707$	29.1311	−	17.3614i	1.09559	−	0.652944i
$708$	4.04375	+	0.612354i	0.151973	+	0.0230137i
$709$	−8.92677	+	15.4616i	−0.335252	+	0.580674i	−0.983533	−	0.180727i	$-0.942155\pi$
$709$	−8.92677	+	15.4616i	−0.335252	+	0.580674i	0.648281	+	0.761401i	$0.275488\pi$
$710$	4.77222	+	8.26572i	0.179098	+	0.310207i
$711$	8.83953	+	38.9767i	0.331508	+	1.46174i
$712$	11.3650	+	6.56159i	0.425921	+	0.245906i
$713$	−52.5480			−1.96794
$714$	−1.88342	−	4.61913i	−0.0704853	−	0.172866i
$715$	3.82341			0.142987
$716$	−11.7441	−	6.78045i	−0.438897	−	0.253397i
$717$	1.70482	−	0.667733i	0.0636676	−	0.0249369i
$718$	−17.5357	−	30.3728i	−0.654427	−	1.13350i
$719$	−12.4077	+	21.4907i	−0.462728	+	0.801468i	−0.999096	−	0.0425160i	$-0.986463\pi$
$719$	−12.4077	+	21.4907i	−0.462728	+	0.801468i	0.536368	+	0.843984i	$0.319796\pi$
$720$	8.58269	+	2.66040i	0.319858	+	0.0991473i
$721$	−15.6126	+	27.9285i	−0.581445	+	1.04011i
$722$		−	37.7656i		−	1.40549i
$723$	−25.2023	−	20.1267i	−0.937283	−	0.748518i
$724$	0.184836	−	0.106715i	0.00686939	−	0.00396604i
$725$	10.3859	−	5.99628i	0.385721	−	0.222696i
$726$	−12.6823	−	10.1281i	−0.470684	−	0.375890i
$727$			49.0657i			1.81975i	0.414887	+	0.909873i	$0.363821\pi$
$727$			49.0657i			1.81975i	−0.414887	+	0.909873i	$0.636179\pi$
$728$	−0.0366585	−	2.64550i	−0.00135865	−	0.0980487i
$729$	16.7466	+	21.1790i	0.620244	+	0.784409i
$730$	−16.7637	+	29.0355i	−0.620451	+	1.07465i
$731$	−4.75409	−	8.23433i	−0.175836	−	0.304558i
$732$	−9.86979	+	3.86574i	−0.364798	+	0.142882i
$733$	28.5935	+	16.5084i	1.05612	+	0.609753i	0.924357	−	0.381528i	$-0.124602\pi$
$733$	28.5935	+	16.5084i	1.05612	+	0.609753i	0.131766	+	0.991281i	$0.457935\pi$
$734$	−7.03605			−0.259705
$735$	−36.0422	−	4.44026i	−1.32944	−	0.163781i
$736$	6.31889			0.232917
$737$	−12.5748	−	7.26009i	−0.463200	−	0.267429i
$738$	26.6217	−	6.03754i	0.979957	−	0.222245i
$739$	14.1975	+	24.5908i	0.522265	+	0.904589i	0.999664	+	0.0259028i	$0.00824604\pi$
$739$	14.1975	+	24.5908i	0.522265	+	0.904589i	−0.477400	+	0.878686i	$0.658421\pi$
$740$	−1.08907	+	1.88633i	−0.0400351	+	0.0693429i
$741$	12.9027	+	1.95388i	0.473992	+	0.0717776i
$742$	0.372910	+	26.9114i	0.0136900	+	0.987949i
$743$		−	44.3420i		−	1.62675i	−0.581739	−	0.813376i	$-0.697627\pi$
$743$		−	44.3420i		−	1.62675i	0.581739	−	0.813376i	$-0.302373\pi$
$744$	8.98838	−	11.2551i	0.329530	−	0.412633i
$745$	22.9634	−	13.2579i	0.841315	−	0.485733i
$746$	−10.8283	+	6.25175i	−0.396454	+	0.228893i
$747$	19.0048	−	17.5850i	0.695348	−	0.643403i
$748$			1.38955i			0.0508069i
$749$	−3.21075	+	5.74353i	−0.117318	+	0.209864i
$750$	0.799159	−	5.27733i	0.0291812	−	0.192701i
$751$	12.9925	−	22.5037i	0.474104	−	0.821171i	−0.525457	−	0.850820i	$-0.676106\pi$
$751$	12.9925	−	22.5037i	0.474104	−	0.821171i	0.999560	+	0.0296488i	$0.00943890\pi$
$752$	−0.962355	−	1.66685i	−0.0350935	−	0.0607837i
$753$	2.19943	+	5.61546i	0.0801518	+	0.204639i
$754$	2.61533	+	1.50996i	0.0952446	+	0.0549895i
$755$	18.5336			0.674506
$756$	13.6962	−	1.18884i	0.498127	−	0.0432377i
$757$	12.5789			0.457188			0.228594	−	0.973522i	$-0.426587\pi$
$757$	12.5789			0.457188			0.228594	+	0.973522i	$0.426587\pi$
$758$	−21.7957	−	12.5838i	−0.791656	−	0.457063i
$759$	5.09520	+	13.0088i	0.184944	+	0.472189i
$760$	11.2833	+	19.5433i	0.409289	+	0.708909i
$761$	−13.5716	+	23.5066i	−0.491969	+	0.852115i	−0.999957	−	0.00924880i	$-0.997056\pi$
$761$	−13.5716	+	23.5066i	−0.491969	+	0.852115i	0.507988	+	0.861364i	$0.330389\pi$
$762$	−1.81750	+	12.0021i	−0.0658411	+	0.434789i
$763$	−3.32488	+	1.98154i	−0.120369	+	0.0717367i
$764$		−	6.62783i		−	0.239787i
$765$	−7.17931	+	6.64299i	−0.259569	+	0.240178i
$766$	−5.15484	+	2.97615i	−0.186252	+	0.107533i
$767$	−2.04493	+	1.18064i	−0.0738380	+	0.0426304i
$768$	−1.08085	+	1.35343i	−0.0390019	+	0.0488375i
$769$		−	36.6833i		−	1.32283i	−0.750019	−	0.661416i	$-0.769956\pi$
$769$		−	36.6833i		−	1.32283i	0.750019	−	0.661416i	$-0.230044\pi$
$770$	8.82977	+	4.93603i	0.318203	+	0.177882i
$771$	−11.2723	−	1.70699i	−0.405963	−	0.0614759i
$772$	3.47303	−	6.01546i	0.124997	−	0.216501i
$773$	−9.06676	−	15.7041i	−0.326109	−	0.564837i	0.655627	−	0.755085i	$-0.272404\pi$
$773$	−9.06676	−	15.7041i	−0.326109	−	0.564837i	−0.981736	+	0.190248i	$0.939071\pi$
$774$	25.5553	−	5.79570i	0.918566	−	0.208322i
$775$	28.5997	+	16.5121i	1.02733	+	0.593131i
$776$	16.3693			0.587623
$777$	−0.453261	+	3.30155i	−0.0162606	+	0.118442i
$778$	9.92918			0.355978
$779$	59.3715	+	34.2782i	2.12721	+	1.22814i
$780$	−4.83051	+	1.89199i	−0.172960	+	0.0677440i
$781$	−2.03387	−	3.52276i	−0.0727776	−	0.126054i
$782$	−3.43920	+	5.95687i	−0.122986	+	0.213017i
$783$	−6.83777	+	14.1238i	−0.244362	+	0.504745i
$784$	3.33068	−	6.15683i	0.118953	−	0.219887i
$785$			8.13025i			0.290181i
$786$	−0.463403	−	0.370075i	−0.0165290	−	0.0132001i
$787$	−15.8903	+	9.17428i	−0.566429	+	0.327028i	−0.755722	−	0.654893i	$-0.772714\pi$
$787$	−15.8903	+	9.17428i	−0.566429	+	0.327028i	0.189293	+	0.981921i	$0.439380\pi$
$788$	2.34991	−	1.35672i	0.0837122	−	0.0483312i
$789$	16.7914	+	13.4097i	0.597791	+	0.477398i
$790$		−	39.9023i		−	1.41966i
$791$	3.24366	−	0.0449472i	0.115331	−	0.00159814i
$792$	−3.65785	−	1.13383i	−0.129976	−	0.0402891i
$793$	3.05991	−	5.29992i	0.108661	−	0.188206i
$794$	7.36074	+	12.7492i	0.261223	+	0.452451i
$795$	49.1386	−	19.2463i	1.74276	−	0.682596i
$796$	−2.50961	−	1.44892i	−0.0889506	−	0.0513557i
$797$	−46.3708			−1.64254			−0.821270	−	0.570540i	$-0.806734\pi$
$797$	−46.3708			−1.64254			−0.821270	+	0.570540i	$0.806734\pi$
$798$	27.2749	+	21.1697i	0.965522	+	0.749398i
$799$	2.09514			0.0741206
$800$	−3.43911	−	1.98557i	−0.121591	−	0.0702006i
$801$	−8.70751	−	38.3945i	−0.307665	−	1.35660i
$802$	6.89042	+	11.9346i	0.243309	+	0.421424i
$803$	7.14450	−	12.3746i	0.252124	−	0.436691i
$804$	19.4797	+	2.94986i	0.686996	+	0.104033i
$805$	25.6355	+	43.0145i	0.903534	+	1.51606i
$806$			8.31602i			0.292919i
$807$	−14.7254	+	18.4390i	−0.518360	+	0.649082i
$808$	11.1004	−	6.40881i	0.390510	−	0.225461i
$809$	−32.6066	+	18.8255i	−1.14639	+	0.661868i	−0.948005	−	0.318257i	$-0.896903\pi$
$809$	−32.6066	+	18.8255i	−1.14639	+	0.661868i	−0.198384	+	0.980124i	$0.563569\pi$
$810$	−11.6289	−	24.3194i	−0.408598	−	0.854495i
$811$			28.0019i			0.983281i	0.870798	+	0.491640i	$0.163603\pi$
$811$			28.0019i			0.983281i	−0.870798	+	0.491640i	$0.836397\pi$
$812$	4.09047	+	6.86349i	0.143547	+	0.240861i
$813$	2.14191	−	14.1443i	0.0751199	−	0.496063i
$814$	0.464152	−	0.803934i	0.0162685	−	0.0281779i
$815$	30.0896	+	52.1167i	1.05399	+	1.82557i
$816$	−0.687608	−	1.75556i	−0.0240711	−	0.0614569i
$817$	56.9933	+	32.9051i	1.99394	+	1.15120i
$818$	0.813929			0.0284583
$819$	−5.75062	+	5.47086i	−0.200943	+	0.191167i
$820$	−27.2539			−0.951748
$821$	−2.21352	−	1.27797i	−0.0772523	−	0.0446016i	0.460876	−	0.887464i	$-0.347535\pi$
$821$	−2.21352	−	1.27797i	−0.0772523	−	0.0446016i	−0.538129	+	0.842863i	$0.680869\pi$
$822$	−5.21114	−	13.3048i	−0.181759	−	0.464058i
$823$	−12.8472	−	22.2520i	−0.447825	−	0.775656i	0.550419	−	0.834888i	$-0.314468\pi$
$823$	−12.8472	−	22.2520i	−0.447825	−	0.775656i	−0.998244	+	0.0592327i	$0.981135\pi$
$824$	−6.04671	+	10.4732i	−0.210647	+	0.364852i
$825$	1.31461	−	8.68120i	0.0457690	−	0.302241i
$826$	−6.24675	+	0.0865609i	−0.217352	+	0.00301184i
$827$		−	31.8041i		−	1.10594i	−0.833202	−	0.552969i	$-0.813495\pi$
$827$		−	31.8041i		−	1.10594i	0.833202	−	0.552969i	$-0.186505\pi$
$828$	−12.8746	−	13.9140i	−0.447423	−	0.483546i
$829$	−21.7833	+	12.5766i	−0.756564	+	0.436802i	−0.828061	−	0.560639i	$-0.810556\pi$
$829$	−21.7833	+	12.5766i	−0.756564	+	0.436802i	0.0714969	+	0.997441i	$0.477222\pi$
$830$	−22.3875	+	12.9254i	−0.777081	+	0.448648i
$831$	4.55668	−	5.70581i	0.158070	−	0.197932i
$832$		−	1.00000i		−	0.0346688i
$833$	3.99130	+	6.49086i	0.138290	+	0.224895i
$834$	−25.1435	−	3.80754i	−0.870648	−	0.131844i
$835$	−20.5260	+	35.5521i	−0.710332	+	1.23033i
$836$	−4.80883	−	8.32913i	−0.166317	−	0.288069i
$837$	−43.0971	+	3.13988i	−1.48965	+	0.108530i
$838$	−26.2213	−	15.1389i	−0.905801	−	0.522964i
$839$	−54.8773			−1.89458			−0.947288	−	0.320384i	$-0.896188\pi$
$839$	−54.8773			−1.89458			−0.947288	+	0.320384i	$0.896188\pi$
$840$	−13.5981	−	1.86685i	−0.469180	−	0.0644124i
$841$	19.8801			0.685520
$842$	6.43665	+	3.71620i	0.221822	+	0.128069i
$843$	−11.3678	+	4.45248i	−0.391529	+	0.153352i
$844$	8.60412	+	14.9028i	0.296166	+	0.512974i
$845$	1.49759	−	2.59391i	0.0515188	−	0.0892332i
$846$	−1.70958	+	5.51524i	−0.0587764	+	0.189618i
$847$	21.6402	+	12.0973i	0.743567	+	0.415669i
$848$			10.1725i			0.349326i
$849$	−20.2671	−	16.1854i	−0.695567	−	0.555482i
$850$	3.74363	−	2.16139i	0.128406	−	0.0741350i
$851$	3.97956	−	2.29760i	0.136417	−	0.0787606i
$852$	4.31281	+	3.44423i	0.147755	+	0.117997i
$853$		−	29.7854i		−	1.01983i	−0.860224	−	0.509916i	$-0.829677\pi$
$853$		−	29.7854i		−	1.01983i	0.860224	−	0.509916i	$-0.170323\pi$
$854$	13.9088	−	8.28927i	0.475948	−	0.283653i
$855$	20.0442	−	64.6645i	0.685498	−	2.21148i
$856$	−1.24351	+	2.15383i	−0.0425024	+	0.0736162i
$857$	−8.26123	−	14.3089i	−0.282198	−	0.488781i	0.689728	−	0.724069i	$-0.257730\pi$
$857$	−8.26123	−	14.3089i	−0.282198	−	0.488781i	−0.971926	+	0.235287i	$0.924397\pi$
$858$	2.05871	−	0.806345i	0.0702833	−	0.0275281i
$859$	−21.8847	−	12.6351i	−0.746695	−	0.431105i	0.0778035	−	0.996969i	$-0.475209\pi$
$859$	−21.8847	−	12.6351i	−0.746695	−	0.431105i	−0.824498	+	0.565864i	$0.808543\pi$
$860$	−26.1622			−0.892124
$861$	−38.6116	+	15.7437i	−1.31588	+	0.536542i
$862$	24.2103			0.824607
$863$	−28.7785	−	16.6153i	−0.979631	−	0.565590i	−0.0774721	−	0.996995i	$-0.524685\pi$
$863$	−28.7785	−	16.6153i	−0.979631	−	0.565590i	−0.902159	+	0.431404i	$0.858018\pi$
$864$	5.18242	−	0.377570i	0.176309	−	0.0128452i
$865$	38.0662	+	65.9326i	1.29429	+	2.24177i
$866$	−13.1052	+	22.6989i	−0.445333	+	0.771340i
$867$	−27.0837	−	4.10135i	−0.919811	−	0.139289i
$868$	−10.7360	+	19.2050i	−0.364403	+	0.651860i
$869$			17.0060i			0.576888i
$870$	9.77655	−	12.2420i	0.331456	−	0.415044i
$871$	−9.85089	+	5.68742i	−0.333785	+	0.192711i
$872$	−1.26694	+	0.731469i	−0.0429040	+	0.0247707i
$873$	−33.3521	−	36.0447i	−1.12880	−	1.21993i
$874$		−	47.6084i		−	1.61038i
$875$	0.112967	+	8.15239i	0.00381899	+	0.275601i
$876$	−2.90289	+	19.1696i	−0.0980796	+	0.647680i
$877$	−9.64315	+	16.7024i	−0.325626	+	0.564001i	−0.981639	−	0.190749i	$-0.938908\pi$
$877$	−9.64315	+	16.7024i	−0.325626	+	0.564001i	0.656013	+	0.754750i	$0.272242\pi$
$878$	10.2056	+	17.6766i	0.344421	+	0.596555i
$879$	13.4747	+	34.4029i	0.454491	+	1.16038i
$880$	3.31117	+	1.91170i	0.111619	+	0.0644435i
$881$	37.3741			1.25917			0.629583	−	0.776934i	$-0.283226\pi$
$881$	37.3741			1.25917			0.629583	+	0.776934i	$0.283226\pi$
$882$	−20.3434	+	5.21034i	−0.684997	+	0.175441i
$883$	3.49194			0.117513			0.0587565	−	0.998272i	$-0.481286\pi$
$883$	3.49194			0.117513			0.0587565	+	0.998272i	$0.481286\pi$
$884$	0.942709	+	0.544273i	0.0317067	+	0.0183059i
$885$	4.46750	+	11.4062i	0.150173	+	0.383414i
$886$	1.05478	+	1.82693i	0.0354360	+	0.0613770i
$887$	23.4235	−	40.5707i	0.786484	−	1.36223i	−0.141624	−	0.989920i	$-0.545233\pi$
$887$	23.4235	−	40.5707i	0.786484	−	1.36223i	0.928108	−	0.372310i	$-0.121434\pi$
$888$	−0.188590	+	1.24538i	−0.00632867	+	0.0417921i
$889$	−0.256917	−	18.5407i	−0.00861673	−	0.621835i
$890$			39.3064i			1.31755i
$891$	4.95612	+	10.3647i	0.166036	+	0.347229i
$892$	−19.4504	+	11.2297i	−0.651247	+	0.375997i
$893$	−12.5585	+	7.25066i	−0.420255	+	0.242634i
$894$	9.56859	−	11.9816i	0.320021	−	0.400726i
$895$		−	40.6174i		−	1.35769i
$896$	1.29100	−	2.30940i	0.0431293	−	0.0771515i
$897$	10.8213	+	1.63869i	0.361312	+	0.0547143i
$898$	13.0311	−	22.5705i	0.434852	−	0.753186i
$899$	−12.5569	−	21.7491i	−0.418795	−	0.725374i
$900$	2.63494	+	11.6184i	0.0878314	+	0.387280i
$901$	−9.58974	−	5.53664i	−0.319481	−	0.184452i
$902$	11.6153			0.386748
$903$	−37.0650	+	15.1130i	−1.23344	+	0.502930i
$904$	1.22611			0.0407797
$905$	0.553620	+	0.319632i	0.0184029	+	0.0106249i
$906$	9.97940	−	3.90867i	0.331543	−	0.129857i
$907$	5.81159	+	10.0660i	0.192971	+	0.334235i	0.946233	−	0.323485i	$-0.104854\pi$
$907$	5.81159	+	10.0660i	0.192971	+	0.334235i	−0.753263	+	0.657720i	$0.771521\pi$
$908$	−8.45721	+	14.6483i	−0.280662	+	0.486122i
$909$	−36.7288	−	11.3849i	−1.21822	−	0.377615i
$910$	6.80728	−	4.05697i	0.225659	−	0.134487i
$911$			2.14217i			0.0709734i	0.999370	+	0.0354867i	$0.0112981\pi$
$911$			2.14217i			0.0709734i	−0.999370	+	0.0354867i	$0.988702\pi$
$912$	10.1971	+	8.14345i	0.337660	+	0.269657i
$913$	9.54131	−	5.50868i	0.315771	−	0.182311i
$914$	22.3115	−	12.8815i	0.737998	−	0.426083i
$915$	−24.8083	−	19.8120i	−0.820137	−	0.654965i
$916$		−	5.23142i		−	0.172851i
$917$	0.790720	+	0.442029i	0.0261119	+	0.0145971i
$918$	−2.46471	+	5.09101i	−0.0813476	+	0.168028i
$919$	24.8523	−	43.0455i	0.819803	−	1.41994i	−0.0860236	−	0.996293i	$-0.527416\pi$
$919$	24.8523	−	43.0455i	0.819803	−	1.41994i	0.905827	−	0.423648i	$-0.139251\pi$
$920$	9.46313	+	16.3906i	0.311990	+	0.540383i
$921$	14.7294	−	5.76911i	0.485349	−	0.190099i
$922$	4.01098	+	2.31574i	0.132095	+	0.0762648i
$923$	−3.18659			−0.104888
$924$	5.79538	+	0.795631i	0.190654	+	0.0261744i
$925$	−2.88788			−0.0949529
$926$	−2.07559	−	1.19834i	−0.0682080	−	0.0393799i
$927$	35.3818	−	8.02425i	1.16209	−	0.263551i
$928$	1.50996	+	2.61533i	0.0495669	+	0.0858524i
$929$	−2.31897	+	4.01657i	−0.0760828	+	0.131779i	−0.901557	−	0.432661i	$-0.857575\pi$
$929$	−2.31897	+	4.01657i	−0.0760828	+	0.131779i	0.825474	+	0.564440i	$0.190908\pi$
$930$	42.6557	+	6.45945i	1.39873	+	0.211814i
$931$	−46.3874	−	25.0943i	−1.52028	−	0.822433i
$932$			20.9204i			0.685269i
$933$	−26.7045	+	33.4390i	−0.874266	+	1.09474i
$934$	36.9817	−	21.3514i	1.21008	−	0.698638i
$935$	−3.60436	+	2.08098i	−0.117875	+	0.0680553i
$936$	−2.20197	+	2.03748i	−0.0719737	+	0.0665971i
$937$			1.95544i			0.0638814i	0.999490	+	0.0319407i	$0.0101688\pi$
$937$			1.95544i			0.0638814i	−0.999490	+	0.0319407i	$0.989831\pi$
$938$	−30.0921	+	0.416984i	−0.982541	+	0.0136150i
$939$	−2.69100	+	17.7703i	−0.0878176	+	0.579913i
$940$	2.88243	−	4.99252i	0.0940146	−	0.162838i
$941$	−7.82917	−	13.5605i	−0.255224	−	0.442061i	0.709732	−	0.704471i	$-0.248816\pi$
$941$	−7.82917	−	13.5605i	−0.255224	−	0.442061i	−0.964956	+	0.262411i	$0.915482\pi$
$942$	1.71464	+	4.37773i	0.0558661	+	0.142634i
$943$	49.7940	+	28.7486i	1.62151	+	0.936182i
$944$	−2.36128			−0.0768530
$945$	23.5951	+	33.7464i	0.767550	+	1.09777i
$946$	11.1501			0.362520
$947$	33.6143	+	19.4072i	1.09232	+	0.630650i	0.934192	−	0.356769i	$-0.116122\pi$
$947$	33.6143	+	19.4072i	1.09232	+	0.630650i	0.158125	+	0.987419i	$0.449455\pi$
$948$	−8.41527	−	21.4854i	−0.273315	−	0.697813i
$949$	−5.59687	−	9.69406i	−0.181682	−	0.314683i
$950$	−14.9599	+	25.9113i	−0.485363	+	0.840673i
$951$	0.584140	−	3.85744i	0.0189420	−	0.125086i
$952$	1.47443	+	2.47398i	0.0477866	+	0.0801822i
$953$			9.43984i			0.305786i	0.988243	+	0.152893i	$0.0488591\pi$
$953$			9.43984i			0.305786i	−0.988243	+	0.152893i	$0.951141\pi$
$954$	22.3997	−	20.7263i	0.725216	−	0.671040i
$955$	17.1920	−	9.92580i	0.556320	−	0.321191i
$956$	−0.915460	+	0.528541i	−0.0296081	+	0.0170942i
$957$	−4.16666	+	5.21743i	−0.134689	+	0.168656i
$958$			26.1996i			0.846470i
$959$	11.1742	+	18.7494i	0.360834	+	0.605451i
$960$	−5.12934	−	0.776747i	−0.165549	−	0.0250694i
$961$	19.0781	−	33.0442i	0.615423	−	1.06594i
$962$	−0.363608	−	0.629787i	−0.0117232	−	0.0203051i
$963$	7.27629	−	1.65019i	0.234475	−	0.0531767i
$964$	16.1264	+	9.31056i	0.519395	+	0.299873i
$965$	20.8047			0.669728
$966$	22.8751	+	17.7547i	0.735993	+	0.571247i
$967$	−31.8551			−1.02439			−0.512196	−	0.858868i	$-0.671168\pi$
$967$	−31.8551			−1.02439			−0.512196	+	0.858868i	$0.671168\pi$
$968$	8.11509	+	4.68525i	0.260829	+	0.150590i
$969$	−13.2269	+	5.18064i	−0.424910	+	0.166426i
$970$	24.5145	+	42.4604i	0.787115	+	1.36332i
$971$	15.3430	−	26.5748i	0.492380	−	0.852826i	−0.507582	−	0.861604i	$-0.669461\pi$
$971$	15.3430	−	26.5748i	0.492380	−	0.852826i	0.999961	+	0.00877706i	$0.00279386\pi$
$972$	−11.3905	−	10.6422i	−0.365349	−	0.341350i
$973$	38.8415	−	0.538224i	1.24520	−	0.0172547i
$974$		−	24.2660i		−	0.777532i
$975$	−5.37465	−	4.29222i	−0.172127	−	0.137461i
$976$	5.29992	−	3.05991i	0.169646	−	0.0979454i
$977$	−43.9167	+	25.3553i	−1.40502	+	0.811189i	−0.994902	−	0.100844i	$-0.967846\pi$
$977$	−43.9167	+	25.3553i	−1.40502	+	0.811189i	−0.410118	+	0.912033i	$0.634512\pi$
$978$	27.1930	+	21.7164i	0.869535	+	0.694414i
$979$		−	16.7520i		−	0.535395i
$980$	20.9583	−	0.580946i	0.669487	−	0.0185577i
$981$	4.19204	+	1.29942i	0.133842	+	0.0414872i
$982$	−7.29496	+	12.6352i	−0.232792	+	0.403207i
$983$	−7.11198	−	12.3183i	−0.226837	−	0.392893i	0.730032	−	0.683413i	$-0.239505\pi$
$983$	−7.11198	−	12.3183i	−0.226837	−	0.392893i	−0.956869	+	0.290520i	$0.906172\pi$
$984$	−14.6749	+	5.74776i	−0.467818	+	0.183232i
$985$	7.03843	+	4.06364i	0.224263	+	0.129478i
$986$	−3.28732			−0.104690
$987$	1.19964	−	8.73817i	0.0381849	−	0.278139i
$988$	−7.53429			−0.239698
$989$	47.7994	+	27.5970i	1.51993	+	0.877533i
$990$	−2.53691	−	11.1862i	−0.0806284	−	0.355519i
$991$	8.62638	+	14.9413i	0.274026	+	0.474627i	0.969889	−	0.243548i	$-0.0783112\pi$
$991$	8.62638	+	14.9413i	0.274026	+	0.474627i	−0.695863	+	0.718175i	$0.744978\pi$
$992$	−4.15801	+	7.20189i	−0.132017	+	0.228660i
$993$	−35.7119	−	5.40794i	−1.13328	−	0.171616i
$994$	−7.35910	−	4.11389i	−0.233417	−	0.130485i
$995$		−	8.67958i		−	0.275161i
$996$	−9.32860	+	11.6811i	−0.295588	+	0.370131i
$997$	1.93422	−	1.11672i	0.0612574	−	0.0353670i	−0.469058	−	0.883167i	$-0.655407\pi$
$997$	1.93422	−	1.11672i	0.0612574	−	0.0353670i	0.530316	+	0.847800i	$0.322073\pi$
$998$	−23.6809	+	13.6722i	−0.749605	+	0.432785i
$999$	3.12653	−	2.12216i	0.0989191	−	0.0671420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.131.3	✓	32
3.2	odd	2		546.2.z.b.131.14	yes	32
7.3	odd	6		546.2.z.b.521.14	yes	32
21.17	even	6	inner	546.2.z.a.521.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.3	✓	32	1.1	even	1	trivial
546.2.z.a.521.3	yes	32	21.17	even	6	inner
546.2.z.b.131.14	yes	32	3.2	odd	2
546.2.z.b.521.14	yes	32	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.631675 - 1.61276i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.49759 + 2.59391i) q^{5} +(-0.259332 + 1.71253i) q^{6} +(-0.0366585 - 2.64550i) q^{7} -1.00000i q^{8} +(-2.20197 + 2.03748i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.631675 - 1.61276i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.49759 + 2.59391i) q^{5} +(-0.259332 + 1.71253i) q^{6} +(-0.0366585 - 2.64550i) q^{7} -1.00000i q^{8} +(-2.20197 + 2.03748i) q^{9} +(2.59391 - 1.49759i) q^{10} +(-1.10550 + 0.638259i) q^{11} +(1.08085 - 1.35343i) q^{12} +1.00000i q^{13} +(-1.29100 + 2.30940i) q^{14} +(5.12934 + 0.776747i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.544273 - 0.942709i) q^{17} +(2.92570 - 0.663521i) q^{18} +(6.52489 + 3.76715i) q^{19} -2.99519 q^{20} +(-4.24339 + 1.73022i) q^{21} +1.27652 q^{22} +(5.47232 + 3.15945i) q^{23} +(-1.61276 + 0.631675i) q^{24} +(-1.98557 - 3.43911i) q^{25} +(0.500000 - 0.866025i) q^{26} +(4.67689 + 2.26422i) q^{27} +(2.27274 - 1.35450i) q^{28} +3.01992i q^{29} +(-4.05376 - 3.23735i) q^{30} +(-7.20189 + 4.15801i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.72767 + 1.37973i) q^{33} +1.08855i q^{34} +(6.91708 + 3.86679i) q^{35} +(-2.86549 - 0.888225i) q^{36} +(0.363608 - 0.629787i) q^{37} +(-3.76715 - 6.52489i) q^{38} +(1.61276 - 0.631675i) q^{39} +(2.59391 + 1.49759i) q^{40} +9.09924 q^{41} +(4.53999 + 0.623283i) q^{42} +8.73475 q^{43} +(-1.10550 - 0.638259i) q^{44} +(-1.98737 - 8.76303i) q^{45} +(-3.15945 - 5.47232i) q^{46} +(-0.962355 + 1.66685i) q^{47} +(1.71253 + 0.259332i) q^{48} +(-6.99731 + 0.193960i) q^{49} +3.97115i q^{50} +(-1.17656 + 1.47327i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(8.80968 - 5.08627i) q^{53} +(-2.91819 - 4.29932i) q^{54} -3.82341i q^{55} +(-2.64550 + 0.0366585i) q^{56} +(1.95388 - 12.9027i) q^{57} +(1.50996 - 2.61533i) q^{58} +(1.18064 + 2.04493i) q^{59} +(1.89199 + 4.83051i) q^{60} +(-5.29992 - 3.05991i) q^{61} +8.31602 q^{62} +(5.47086 + 5.75062i) q^{63} -1.00000 q^{64} +(-2.59391 - 1.49759i) q^{65} +(-0.806345 - 2.05871i) q^{66} +(5.68742 + 9.85089i) q^{67} +(0.544273 - 0.942709i) q^{68} +(1.63869 - 10.8213i) q^{69} +(-4.05697 - 6.80728i) q^{70} +3.18659i q^{71} +(2.03748 + 2.20197i) q^{72} +(-9.69406 + 5.59687i) q^{73} +(-0.629787 + 0.363608i) q^{74} +(-4.29222 + 5.37465i) q^{75} +7.53429i q^{76} +(1.72904 + 2.90119i) q^{77} +(-1.71253 - 0.259332i) q^{78} +(6.66108 - 11.5373i) q^{79} +(-1.49759 - 2.59391i) q^{80} +(0.697366 - 8.97294i) q^{81} +(-7.88017 - 4.54962i) q^{82} -8.63079 q^{83} +(-3.62011 - 2.80977i) q^{84} +3.26040 q^{85} +(-7.56452 - 4.36738i) q^{86} +(4.87040 - 1.90761i) q^{87} +(0.638259 + 1.10550i) q^{88} +(-6.56159 + 11.3650i) q^{89} +(-2.66040 + 8.58269i) q^{90} +(2.64550 - 0.0366585i) q^{91} +6.31889i q^{92} +(11.2551 + 8.98838i) q^{93} +(1.66685 - 0.962355i) q^{94} +(-19.5433 + 11.2833i) q^{95} +(-1.35343 - 1.08085i) q^{96} +16.3693i q^{97} +(6.15683 + 3.33068i) q^{98} +(1.13383 - 3.65785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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