LMFDB - Embedded newform 546.2.z.b.131.14

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			131.14
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.08085 + 1.35343i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.49759 - 2.59391i) q^{5} +(0.259332 + 1.71253i) q^{6} +(-0.0366585 - 2.64550i) q^{7} +1.00000i q^{8} +(-0.663521 + 2.92570i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.08085 + 1.35343i) 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} +(-0.663521 + 2.92570i) q^{9} +(2.59391 - 1.49759i) q^{10} +(1.10550 - 0.638259i) q^{11} +(-0.631675 + 1.61276i) 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} +(-2.03748 + 2.20197i) q^{18} +(6.52489 + 3.76715i) q^{19} +2.99519 q^{20} +(3.54086 - 2.90900i) q^{21} +1.27652 q^{22} +(-5.47232 - 3.15945i) q^{23} +(-1.35343 + 1.08085i) 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} +(4.83051 + 1.89199i) q^{30} +(-7.20189 + 4.15801i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.05871 + 0.806345i) 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} +(-1.35343 + 1.08085i) q^{39} +(2.59391 + 1.49759i) q^{40} -9.09924 q^{41} +(4.52098 - 0.748840i) q^{42} +8.73475 q^{43} +(1.10550 + 0.638259i) q^{44} +(6.59532 + 6.10263i) 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} +(-0.687608 + 1.75556i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(-8.80968 + 5.08627i) q^{53} +(-5.18242 - 0.377570i) 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} +(3.23735 + 4.05376i) q^{60} +(-5.29992 - 3.05991i) q^{61} -8.31602 q^{62} +(7.76426 + 1.64809i) q^{63} -1.00000 q^{64} +(2.59391 + 1.49759i) q^{65} +(1.37973 + 1.72767i) 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} +(-2.92570 - 0.663521i) q^{72} +(-9.69406 + 5.59687i) q^{73} +(0.629787 - 0.363608i) q^{74} +(2.50848 - 6.40450i) 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} +(-8.11948 - 3.88253i) q^{81} +(-7.88017 - 4.54962i) q^{82} +8.63079 q^{83} +(4.28970 + 1.61197i) q^{84} +3.26040 q^{85} +(7.56452 + 4.36738i) q^{86} +(4.08724 - 3.26409i) 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} +(-13.4117 - 5.25303i) q^{93} +(1.66685 - 0.962355i) q^{94} +(19.5433 - 11.2833i) q^{95} +(-1.61276 - 0.631675i) 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} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 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} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 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} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 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 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * 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 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * 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 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * 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
$3$	1.08085	+	1.35343i	0.624030	+	0.781401i
$3$	1.08085	+	1.35343i	0.624030	+	0.781401i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.49759	−	2.59391i	0.669744	−	1.16003i	−0.308231	−	0.951311i	$-0.599737\pi$
$5$	1.49759	−	2.59391i	0.669744	−	1.16003i	0.977976	−	0.208720i	$-0.0669296\pi$
$6$	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
$9$	−0.663521	+	2.92570i	−0.221174	+	0.975234i
$10$	2.59391	−	1.49759i	0.820266	−	0.473581i
$11$	1.10550	−	0.638259i	0.333320	−	0.192442i	−0.323994	−	0.946059i	$-0.605026\pi$
$11$	1.10550	−	0.638259i	0.333320	−	0.192442i	0.657314	+	0.753617i	$0.271693\pi$
$12$	−0.631675	+	1.61276i	−0.182349	+	0.465563i
$13$			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	0.924450	−	0.381304i	$-0.124525\pi$
$17$	0.544273	+	0.942709i	0.132006	+	0.228640i	−0.792444	+	0.609945i	$0.791192\pi$
$18$	−2.03748	+	2.20197i	−0.480238	+	0.519010i
$19$	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
$21$	3.54086	−	2.90900i	0.772679	−	0.634797i
$22$	1.27652			0.272154
$23$	−5.47232	−	3.15945i	−1.14106	−	0.658790i	−0.194366	−	0.980929i	$-0.562265\pi$
$23$	−5.47232	−	3.15945i	−1.14106	−	0.658790i	−0.946692	+	0.322139i	$0.895598\pi$
$24$	−1.35343	+	1.08085i	−0.276267	+	0.220628i
$25$	−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	$-0.909535\pi$
$29$		−	3.01992i		−	0.560785i	0.959885	−	0.280393i	$-0.0904647\pi$
$30$	4.83051	+	1.89199i	0.881926	+	0.345428i
$31$	−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
$33$	2.05871	+	0.806345i	0.358376	+	0.140367i
$34$			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
$39$	−1.35343	+	1.08085i	−0.216722	+	0.173075i
$40$	2.59391	+	1.49759i	0.410133	+	0.236790i
$41$	−9.09924			−1.42106			−0.710531	−	0.703666i	$-0.751545\pi$
$41$	−9.09924			−1.42106			−0.710531	+	0.703666i	$0.751545\pi$
$42$	4.52098	−	0.748840i	0.697602	−	0.115549i
$43$	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
$45$	6.59532	+	6.10263i	0.983172	+	0.909726i
$46$	−3.15945	−	5.47232i	−0.465835	−	0.806850i
$47$	0.962355	−	1.66685i	0.140374	−	0.243135i	−0.787264	−	0.616617i	$-0.788503\pi$
$47$	0.962355	−	1.66685i	0.140374	−	0.243135i	0.927637	+	0.373482i	$0.121836\pi$
$48$	−1.71253	+	0.259332i	−0.247182	+	0.0374313i
$49$	−6.99731	+	0.193960i	−0.999616	+	0.0277086i
$50$		−	3.97115i		−	0.561605i
$51$	−0.687608	+	1.75556i	−0.0962844	+	0.245828i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	−8.80968	+	5.08627i	−1.21010	+	0.698653i	−0.962782	−	0.270281i	$-0.912883\pi$
$53$	−8.80968	+	5.08627i	−1.21010	+	0.698653i	−0.247321	+	0.968934i	$0.579550\pi$
$54$	−5.18242	−	0.377570i	−0.705238	−	0.0513808i
$55$		−	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	0.778881	−	0.627172i	$-0.215788\pi$
$59$	−1.18064	−	2.04493i	−0.153706	−	0.266227i	−0.932587	+	0.360945i	$0.882454\pi$
$60$	3.23735	+	4.05376i	0.417940	+	0.523339i
$61$	−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
$63$	7.76426	+	1.64809i	0.978205	+	0.207640i
$64$	−1.00000			−0.125000
$65$	2.59391	+	1.49759i	0.321735	+	0.185754i
$66$	1.37973	+	1.72767i	0.169832	+	0.212662i
$67$	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	$-0.939446\pi$
$71$		−	3.18659i		−	0.378179i	0.981960	−	0.189089i	$-0.0605536\pi$
$72$	−2.92570	−	0.663521i	−0.344797	−	0.0781968i
$73$	−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
$75$	2.50848	−	6.40450i	0.289654	−	0.739528i
$76$			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
$81$	−8.11948	−	3.88253i	−0.902164	−	0.431393i
$82$	−7.88017	−	4.54962i	−0.870219	−	0.502421i
$83$	8.63079			0.947352			0.473676	−	0.880699i	$-0.342927\pi$
$83$	8.63079			0.947352			0.473676	+	0.880699i	$0.342927\pi$
$84$	4.28970	+	1.61197i	0.468045	+	0.175881i
$85$	3.26040			0.353640
$86$	7.56452	+	4.36738i	0.815703	+	0.470946i
$87$	4.08724	−	3.26409i	0.438198	−	0.349947i
$88$	0.638259	+	1.10550i	0.0680386	+	0.117846i
$89$	6.56159	−	11.3650i	0.695527	−	1.20469i	−0.274476	−	0.961594i	$-0.588504\pi$
$89$	6.56159	−	11.3650i	0.695527	−	1.20469i	0.970003	−	0.243094i	$-0.0781623\pi$
$90$	2.66040	+	8.58269i	0.280431	+	0.904695i
$91$	2.64550	−	0.0366585i	0.277323	−	0.00384286i
$92$		−	6.31889i		−	0.658790i
$93$	−13.4117	−	5.25303i	−1.39073	−	0.544713i
$94$	1.66685	−	0.962355i	0.171922	−	0.0992593i
$95$	19.5433	−	11.2833i	2.00510	−	1.15764i
$96$	−1.61276	−	0.631675i	−0.164601	−	0.0644701i
$97$			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	$-0.946552\pi$
$101$	−6.40881	−	11.1004i	−0.637701	−	1.10453i	0.348235	−	0.937407i	$-0.386781\pi$
$102$	−1.47327	+	1.17656i	−0.145875	+	0.116496i
$103$	−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
$105$	−2.24292	−	13.5412i	−0.218886	−	1.32148i
$106$	−10.1725			−0.988044
$107$	2.15383	+	1.24351i	0.208218	+	0.120215i	0.600483	−	0.799637i	$-0.294975\pi$
$107$	2.15383	+	1.24351i	0.208218	+	0.120215i	−0.392265	+	0.919852i	$0.628308\pi$
$108$	−4.29932	−	2.91819i	−0.413702	−	0.280803i
$109$	−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	$-0.981633\pi$
$113$		−	1.22611i		−	0.115342i	0.998336	−	0.0576712i	$-0.0183675\pi$
$114$	−4.75923	+	12.1510i	−0.445742	+	1.13804i
$115$	−16.3906	+	9.46313i	−1.52843	+	0.882442i
$116$	2.61533	−	1.50996i	0.242827	−	0.140196i
$117$	−2.92570	−	0.663521i	−0.270481	−	0.0613426i
$118$		−	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
$123$	−9.83492	−	12.3151i	−0.886785	−	1.11042i
$124$	−7.20189	−	4.15801i	−0.646748	−	0.373400i
$125$	3.08161			0.275627
$126$	5.90000	+	5.30942i	0.525614	+	0.473001i
$127$	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
$129$	9.44097	+	11.8218i	0.831231	+	1.04085i
$130$	1.49759	+	2.59391i	0.131348	+	0.227501i
$131$	0.171196	−	0.296521i	0.0149575	−	0.0259071i	−0.858450	−	0.512898i	$-0.828572\pi$
$131$	0.171196	−	0.296521i	0.0149575	−	0.0259071i	0.873407	+	0.486991i	$0.161905\pi$
$132$	0.331042	+	2.18607i	0.0288135	+	0.190273i
$133$	9.72678	−	17.3997i	0.843419	−	1.50874i
$134$			11.3748i			0.982636i
$135$	−1.13089	+	15.5223i	−0.0973318	+	1.33595i
$136$	−0.942709	+	0.544273i	−0.0808366	+	0.0466710i
$137$	7.14446	−	4.12486i	0.610393	−	0.352410i	−0.162726	−	0.986671i	$-0.552029\pi$
$137$	7.14446	−	4.12486i	0.610393	−	0.352410i	0.773119	+	0.634261i	$0.218695\pi$
$138$	3.99149	−	10.1908i	0.339778	−	0.867502i
$139$			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
$144$	−2.20197	−	2.03748i	−0.183498	−	0.169790i
$145$	−7.83340	−	4.52261i	−0.650528	−	0.375583i
$146$	−11.1937			−0.926400
$147$	−7.82556	−	9.26070i	−0.645442	−	0.763810i
$148$	0.727215			0.0597767
$149$	7.66677	+	4.42641i	0.628086	+	0.362626i	0.780011	−	0.625766i	$-0.215214\pi$
$149$	7.66677	+	4.42641i	0.628086	+	0.362626i	−0.151924	+	0.988392i	$0.548547\pi$
$150$	5.37465	−	4.29222i	0.438838	−	0.350458i
$151$	−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
$156$	−1.61276	−	0.631675i	−0.129124	−	0.0505745i
$157$	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
$159$	−16.4058	−	6.42574i	−1.30107	−	0.509594i
$160$			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
$165$	5.17470	−	4.13254i	0.402850	−	0.321717i
$166$	7.47449	+	4.31540i	0.580133	+	0.334940i
$167$	−13.7060			−1.06060			−0.530301	−	0.847809i	$-0.677921\pi$
$167$	−13.7060			−1.06060			−0.530301	+	0.847809i	$0.677921\pi$
$168$	2.90900	+	3.54086i	0.224434	+	0.273183i
$169$	−1.00000			−0.0769231
$170$	2.82359	+	1.63020i	0.216559	+	0.125031i
$171$	−15.3510	+	16.5903i	−1.17392	+	1.26869i
$172$	4.36738	+	7.56452i	0.333009	+	0.576789i
$173$	−12.7091	+	22.0128i	−0.966256	+	1.67361i	−0.260055	+	0.965594i	$0.583741\pi$
$173$	−12.7091	+	22.0128i	−0.966256	+	1.67361i	−0.706201	+	0.708011i	$0.749592\pi$
$174$	5.17170	−	0.783162i	0.392065	−	0.0593713i
$175$	−9.02538	+	5.37890i	−0.682255	+	0.406607i
$176$			1.27652i			0.0962211i
$177$	1.49156	−	3.80817i	0.112113	−	0.286239i
$178$	11.3650	−	6.56159i	0.851843	−	0.491812i
$179$	11.7441	−	6.78045i	0.877794	−	0.506795i	0.00786381	−	0.999969i	$-0.497497\pi$
$179$	11.7441	−	6.78045i	0.877794	−	0.506795i	0.869931	+	0.493174i	$0.164164\pi$
$180$	−1.98737	+	8.76303i	−0.148130	+	0.653158i
$181$		−	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
$186$	−8.98838	−	11.2551i	−0.659060	−	0.825265i
$187$	1.20338	+	0.694774i	0.0880002	+	0.0508069i
$188$	1.92471			0.140374
$189$	6.16144	+	12.2897i	0.448179	+	0.893944i
$190$	22.5666			1.63715
$191$	5.73987	+	3.31392i	0.415323	+	0.239787i	0.693074	−	0.720866i	$-0.256256\pi$
$191$	5.73987	+	3.31392i	0.415323	+	0.239787i	−0.277752	+	0.960653i	$0.589589\pi$
$192$	−1.08085	−	1.35343i	−0.0780037	−	0.0976751i
$193$	−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	$0.0308167\pi$
$197$			2.71345i			0.193325i	−0.995317	+	0.0966625i	$0.969183\pi$
$198$	−0.846997	+	3.73471i	−0.0601934	+	0.265414i
$199$	−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
$201$	−7.18520	+	18.3448i	−0.506805	+	1.29395i
$202$		−	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
$207$	12.8746	−	13.9140i	0.894847	−	0.967092i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	9.61765			0.665267
$210$	4.82816	−	12.8485i	0.333175	−	0.886628i
$211$	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
$213$	4.31281	−	3.44423i	0.295509	−	0.235995i
$214$	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
$219$	−18.0528	−	7.07081i	−1.21989	−	0.477801i
$220$	3.31117	−	1.91170i	0.223239	−	0.128887i
$221$	−0.942709	+	0.544273i	−0.0634135	+	0.0366118i
$222$	1.17282	+	0.459364i	0.0787147	+	0.0308305i
$223$			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	$-0.976958\pi$
$227$	−8.45721	−	14.6483i	−0.561325	−	0.972243i	0.436056	−	0.899919i	$-0.356375\pi$
$228$	−10.1971	+	8.14345i	−0.675320	+	0.539313i
$229$	−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
$231$	2.05771	−	5.47588i	0.135388	−	0.360286i
$232$	3.01992			0.198268
$233$	−18.1176	−	10.4602i	−1.18692	−	0.685269i	−0.229316	−	0.973352i	$-0.573649\pi$
$233$	−18.1176	−	10.4602i	−1.18692	−	0.685269i	−0.957606	+	0.288083i	$0.906982\pi$
$234$	−2.20197	−	2.03748i	−0.143947	−	0.133194i
$235$	−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	$-0.989115\pi$
$239$		−	1.05708i		−	0.0683770i	0.999415	−	0.0341885i	$-0.0108847\pi$
$240$	−1.89199	+	4.83051i	−0.122127	+	0.311808i
$241$	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
$243$	−3.52123	−	15.1856i	−0.225887	−	0.974154i
$244$		−	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
$249$	9.32860	+	11.6811i	0.591176	+	0.740262i
$250$	2.66875	+	1.54080i	0.168787	+	0.0974490i
$251$	3.48190			0.219776			0.109888	−	0.993944i	$-0.464951\pi$
$251$	3.48190			0.219776			0.109888	+	0.993944i	$0.464951\pi$
$252$	2.45484	+	7.54810i	0.154641	+	0.475485i
$253$	−8.06618			−0.507116
$254$	6.06945	+	3.50420i	0.380831	+	0.219873i
$255$	3.52401	+	4.41271i	0.220682	+	0.276335i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.29114	+	5.70042i	−0.205296	+	0.355582i	−0.950227	−	0.311559i	$-0.899149\pi$
$257$	−3.29114	+	5.70042i	−0.205296	+	0.355582i	0.744931	+	0.667141i	$0.232482\pi$
$258$	2.26520	+	14.9585i	0.141025	+	0.931275i
$259$	−1.67943	−	0.938836i	−0.104355	−	0.0583364i
$260$			2.99519i			0.185754i
$261$	8.83539	+	2.00378i	0.546897	+	0.124031i
$262$	0.296521	−	0.171196i	0.0183191	−	0.0105765i
$263$	10.7444	−	6.20331i	0.662531	−	0.382513i	−0.130710	−	0.991421i	$-0.541726\pi$
$263$	10.7444	−	6.20331i	0.662531	−	0.382513i	0.793241	+	0.608908i	$0.208392\pi$
$264$	−0.806345	+	2.05871i	−0.0496271	+	0.126705i
$265$			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	0.995463	−	0.0951463i	$-0.0303319\pi$
$269$	6.81196	+	11.7987i	0.415332	+	0.719377i	−0.580131	+	0.814523i	$0.696999\pi$
$270$	−8.74054	+	12.8773i	−0.531932	+	0.783685i
$271$	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
$273$	2.90900	+	3.54086i	0.176061	+	0.214303i
$274$	8.24972			0.498384
$275$	−4.39009	−	2.53462i	−0.264732	−	0.152843i
$276$	8.55215	−	6.82978i	0.514779	−	0.411105i
$277$	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	$0.0674261\pi$
$281$			7.04869i			0.420490i	−0.977649	+	0.210245i	$0.932574\pi$
$282$	3.10409	+	1.21579i	0.184846	+	0.0723993i
$283$	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
$285$	36.3945	+	14.2548i	2.15582	+	0.844380i
$286$			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
$291$	−22.1546	+	17.6928i	−1.29873	+	1.03717i
$292$	−9.69406	−	5.59687i	−0.567302	−	0.327532i
$293$	21.3317			1.24621			0.623106	−	0.782138i	$-0.285871\pi$
$293$	21.3317			1.24621			0.623106	+	0.782138i	$0.285871\pi$
$294$	−2.14679	−	11.9328i	−0.125203	−	0.695934i
$295$	−7.07246			−0.411775
$296$	0.629787	+	0.363608i	0.0366056	+	0.0211343i
$297$	−3.72512	+	5.48816i	−0.216154	+	0.318455i
$298$	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
$303$	8.09658	−	20.6717i	0.465136	−	1.18756i
$304$	−6.52489	+	3.76715i	−0.374228	+	0.216061i
$305$	−15.8743	+	9.16501i	−0.908957	+	0.524787i
$306$	−3.18476	−	0.722274i	−0.182061	−	0.0412896i
$307$			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	$0.0803731\pi$
$311$	12.3535	+	21.3968i	0.700500	+	1.21330i	−0.267791	+	0.963477i	$0.586294\pi$
$312$	−1.08085	−	1.35343i	−0.0611911	−	0.0766226i
$313$	−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
$315$	15.9027	−	17.6716i	0.896016	−	0.995683i
$316$	13.3222			0.749430
$317$	−1.95071	−	1.12624i	−0.109563	−	0.0632560i	0.444217	−	0.895919i	$-0.353482\pi$
$317$	−1.95071	−	1.12624i	−0.109563	−	0.0632560i	−0.553780	+	0.832663i	$0.686815\pi$
$318$	−10.9950	−	13.7678i	−0.616569	−	0.772058i
$319$	−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
$324$	−0.697366	−	8.97294i	−0.0387426	−	0.498497i
$325$	3.43911	−	1.98557i	0.190768	−	0.110140i
$326$	17.4001	−	10.0460i	0.963705	−	0.556395i
$327$	0.924102	−	2.35936i	0.0511029	−	0.130473i
$328$		−	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
$333$	1.60131	+	1.48169i	0.0877512	+	0.0811959i
$334$	−11.8697	−	6.85300i	−0.649484	−	0.374980i
$335$	34.0698			1.86143
$336$	0.748840	+	4.52098i	0.0408526	+	0.246640i
$337$	−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
$339$	1.65944	−	1.32524i	0.0901286	−	0.0719771i
$340$	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
$345$	−30.5235	−	11.9553i	−1.64333	−	0.643649i
$346$	−22.0128	+	12.7091i	−1.18342	+	0.683246i
$347$	−27.6683	+	15.9743i	−1.48531	+	0.857545i	−0.999860	−	0.0167179i	$-0.994678\pi$
$347$	−27.6683	+	15.9743i	−1.48531	+	0.857545i	−0.485452	+	0.874263i	$0.661345\pi$
$348$	4.87040	+	1.90761i	0.261081	+	0.102259i
$349$			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	$0.193156\pi$
$353$	16.9957	+	29.4374i	0.904589	+	1.56679i	0.0831221	+	0.996539i	$0.473511\pi$
$354$	3.19581	−	2.55219i	0.169855	−	0.135647i
$355$	−8.26572	−	4.77222i	−0.438699	−	0.253283i
$356$	13.1232			0.695527
$357$	4.66954	+	1.75471i	0.247138	+	0.0928690i
$358$	13.5609			0.716716
$359$	−30.3728	−	17.5357i	−1.60301	−	0.925500i	−0.990880	−	0.134744i	$-0.956979\pi$
$359$	−30.3728	−	17.5357i	−1.60301	−	0.925500i	−0.612132	−	0.790755i	$-0.709688\pi$
$360$	−6.10263	+	6.59532i	−0.321637	+	0.347604i
$361$	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
$366$	3.86574	−	9.86979i	0.202066	−	0.515902i
$367$	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
$369$	6.03754	−	26.6217i	0.314302	−	1.38587i
$370$		−	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
$375$	3.33076	+	4.17073i	0.172000	+	0.215375i
$376$	1.66685	+	0.962355i	0.0859611	+	0.0496297i
$377$	3.01992			0.155534
$378$	−0.808881	+	13.7239i	−0.0416044	+	0.705882i
$379$	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
$381$	7.57503	+	9.48534i	0.388081	+	0.485949i
$382$	3.31392	+	5.73987i	0.169555	+	0.293677i
$383$	−2.97615	+	5.15484i	−0.152074	+	0.263400i	−0.931990	−	0.362485i	$-0.881929\pi$
$383$	−2.97615	+	5.15484i	−0.152074	+	0.263400i	0.779916	+	0.625884i	$0.215262\pi$
$384$	−0.259332	−	1.71253i	−0.0132340	−	0.0873920i
$385$	−10.1148	+	0.140160i	−0.515499	+	0.00714324i
$386$		−	6.94606i		−	0.353545i
$387$	−5.79570	+	25.5553i	−0.294612	+	1.29905i
$388$	−14.1762	+	8.18465i	−0.719689	+	0.415512i
$389$	8.59892	−	4.96459i	0.435983	−	0.251715i	−0.265909	−	0.963998i	$-0.585672\pi$
$389$	8.59892	−	4.96459i	0.435983	−	0.251715i	0.701892	+	0.712283i	$0.252339\pi$
$390$	−1.89199	+	4.83051i	−0.0958044	+	0.244602i
$391$		−	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
$396$	−2.60088	+	2.81086i	−0.130699	+	0.141251i
$397$	−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
$399$	34.0624	−	5.64198i	1.70525	−	0.282452i
$400$	3.97115			0.198557
$401$	11.9346	+	6.89042i	0.595984	+	0.344091i	0.767460	−	0.641097i	$-0.221520\pi$
$401$	11.9346	+	6.89042i	0.595984	+	0.344091i	−0.171476	+	0.985188i	$0.554854\pi$
$402$	−15.3950	+	12.2945i	−0.767832	+	0.613194i
$403$	−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
$408$	−1.75556	−	0.687608i	−0.0869132	−	0.0340417i
$409$	−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
$411$	13.3048	+	5.21114i	0.656277	+	0.257047i
$412$		−	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
$417$	−19.8711	+	15.8692i	−0.973094	+	0.777116i
$418$	8.32913	+	4.80883i	0.407391	+	0.235207i
$419$	−30.2778			−1.47917			−0.739583	−	0.673065i	$-0.764977\pi$
$419$	−30.2778			−1.47917			−0.739583	+	0.673065i	$0.764977\pi$
$420$	10.6055	−	8.71301i	0.517498	−	0.425151i
$421$	−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
$423$	4.23816	+	3.92155i	0.206066	+	0.190672i
$424$	−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
$429$	−0.806345	+	2.05871i	−0.0389307	+	0.0993956i
$430$	22.6572	−	13.0811i	1.09262	−	0.630827i
$431$	20.9668	−	12.1052i	1.00993	−	0.583085i	0.0987614	−	0.995111i	$-0.468512\pi$
$431$	20.9668	−	12.1052i	1.00993	−	0.583085i	0.911172	+	0.412026i	$0.135179\pi$
$432$	0.377570	−	5.18242i	0.0181659	−	0.249339i
$433$		−	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
$438$	−12.0988	−	15.1499i	−0.578101	−	0.723890i
$439$	−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
$441$	4.07540	−	20.6008i	0.194067	−	0.980988i
$442$	−1.08855			−0.0517769
$443$	1.82693	+	1.05478i	0.0868002	+	0.0501141i	0.542772	−	0.839880i	$-0.317375\pi$
$443$	1.82693	+	1.05478i	0.0868002	+	0.0501141i	−0.455972	+	0.889994i	$0.650708\pi$
$444$	0.786012	+	0.984232i	0.0373025	+	0.0467096i
$445$	−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	$-0.789167\pi$
$449$		−	26.0621i		−	1.22995i	0.788548	−	0.614974i	$-0.210833\pi$
$450$	11.6184	+	2.63494i	0.547696	+	0.124212i
$451$	−10.0592	+	5.80767i	−0.473668	+	0.273472i
$452$	1.06184	−	0.613053i	0.0499447	−	0.0288356i
$453$	3.90867	−	9.97940i	0.183645	−	0.468873i
$454$		−	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
$459$	−4.68001	−	3.17659i	−0.218444	−	0.148270i
$460$	−16.3906	−	9.46313i	−0.764217	−	0.441221i
$461$	4.63148			0.215709			0.107855	−	0.994167i	$-0.465602\pi$
$461$	4.63148			0.215709			0.107855	+	0.994167i	$0.465602\pi$
$462$	4.51997	−	3.71339i	0.210288	−	0.172763i
$463$	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
$465$	−33.7112	+	26.9219i	−1.56332	+	1.24847i
$466$	−10.4602	−	18.1176i	−0.484559	−	0.839280i
$467$	21.3514	−	36.9817i	0.988024	−	1.71131i	0.360384	−	0.932804i	$-0.382646\pi$
$467$	21.3514	−	36.9817i	0.988024	−	1.71131i	0.627640	−	0.778504i	$-0.284021\pi$
$468$	−0.888225	−	2.86549i	−0.0410582	−	0.132458i
$469$	25.8520	−	15.4072i	1.19374	−	0.711437i
$470$		−	5.76487i		−	0.265913i
$471$	4.37773	+	1.71464i	0.201715	+	0.0790066i
$472$	2.04493	−	1.18064i	0.0941253	−	0.0543433i
$473$	9.65624	−	5.57503i	0.443994	−	0.256340i
$474$	21.4854	+	8.41527i	0.986857	+	0.386526i
$475$		−	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	$0.0375874\pi$
$479$	13.0998	+	22.6895i	0.598545	+	1.03671i	−0.394491	+	0.918900i	$0.629079\pi$
$480$	−4.05376	+	3.23735i	−0.185028	+	0.147764i
$481$	0.629787	+	0.363608i	0.0287158	+	0.0165791i
$482$	18.6211			0.848169
$483$	−28.5676	+	4.73184i	−1.29987	+	0.215306i
$484$	−9.37050			−0.425932
$485$	42.4604	+	24.5145i	1.92803	+	1.11315i
$486$	4.54330	−	14.9117i	0.206088	−	0.676408i
$487$	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	$0.106785\pi$
$491$			14.5899i			0.658434i	−0.944254	+	0.329217i	$0.893215\pi$
$492$	5.74776	−	14.6749i	0.259129	−	0.661594i
$493$	2.84691	−	1.64366i	0.128218	−	0.0740268i
$494$	−6.52489	+	3.76715i	−0.293569	+	0.169492i
$495$	11.1862	+	2.53691i	0.502780	+	0.114026i
$496$		−	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
$501$	−14.8142	−	18.5501i	−0.661847	−	0.828755i
$502$	3.01542	+	1.74095i	0.134585	+	0.0777025i
$503$	14.2379			0.634839			0.317419	−	0.948285i	$-0.397184\pi$
$503$	14.2379			0.634839			0.317419	+	0.948285i	$0.397184\pi$
$504$	−1.64809	+	7.76426i	−0.0734119	+	0.345848i
$505$	−38.3912			−1.70839
$506$	−6.98551	−	4.03309i	−0.310544	−	0.179293i
$507$	−1.08085	−	1.35343i	−0.0480023	−	0.0601077i
$508$	3.50420	+	6.06945i	0.155474	+	0.269288i
$509$	−11.6247	+	20.1346i	−0.515257	+	0.892452i	0.484586	+	0.874744i	$0.338970\pi$
$509$	−11.6247	+	20.1346i	−0.515257	+	0.892452i	−0.999843	+	0.0177081i	$0.994363\pi$
$510$	0.845525	+	5.58352i	0.0374405	+	0.247242i
$511$	15.1619	+	25.4404i	0.670722	+	1.12542i
$512$		−	1.00000i		−	0.0441942i
$513$	−39.0458	−	2.84472i	−1.72392	−	0.125598i
$514$	−5.70042	+	3.29114i	−0.251435	+	0.145166i
$515$	−31.3692	+	18.1110i	−1.38229	+	0.798068i
$516$	−5.51753	+	14.0870i	−0.242896	+	0.620147i
$517$		−	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	$-0.847100\pi$
$521$	−19.2555	−	33.3515i	−0.843598	−	1.46115i	0.0432351	−	0.999065i	$-0.486234\pi$
$522$	6.64978	+	6.15302i	0.291053	+	0.269311i
$523$	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
$525$	−17.0350	−	6.40139i	−0.743470	−	0.279379i
$526$	12.4066			0.540954
$527$	−7.83959	−	4.52619i	−0.341498	−	0.197164i
$528$	−1.72767	+	1.37973i	−0.0751872	+	0.0600448i
$529$	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
$534$	21.1645	+	8.28959i	0.915877	+	0.358725i
$535$	6.45111	−	3.72455i	0.278906	−	0.161026i
$536$	−9.85089	+	5.68742i	−0.425494	+	0.245659i
$537$	21.8704	+	8.56609i	0.943780	+	0.369654i
$538$			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
$543$	0.288863	−	0.230687i	0.0123963	−	0.00989972i
$544$	−0.942709	−	0.544273i	−0.0404183	−	0.0233355i
$545$	−4.38177			−0.187695
$546$	0.748840	+	4.52098i	0.0320474	+	0.193480i
$547$	−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
$549$	12.4690	−	13.4757i	0.532164	−	0.575128i
$550$	−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
$555$	1.37588	−	3.51282i	0.0584029	−	0.149111i
$556$	−12.7151	+	7.34105i	−0.539239	+	0.311330i
$557$	−16.1902	+	9.34739i	−0.685999	+	0.396062i	−0.802112	−	0.597174i	$-0.796290\pi$
$557$	−16.1902	+	9.34739i	−0.685999	+	0.396062i	0.116112	+	0.993236i	$0.462957\pi$
$558$	5.51786	−	24.3302i	0.233590	−	1.02998i
$559$			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	$-0.923165\pi$
$563$	−16.4320	−	28.4610i	−0.692525	−	1.19949i	0.278482	−	0.960441i	$-0.410169\pi$
$564$	2.08032	+	2.60495i	0.0875975	+	0.109688i
$565$	−3.18041	−	1.83621i	−0.133801	−	0.0772499i
$566$	14.9747			0.629434
$567$	−9.97359	+	21.6224i	−0.418851	+	0.908055i
$568$	3.18659			0.133706
$569$	2.78940	+	1.61046i	0.116938	+	0.0675141i	0.557328	−	0.830292i	$-0.311827\pi$
$569$	2.78940	+	1.61046i	0.116938	+	0.0675141i	−0.440390	+	0.897806i	$0.645160\pi$
$570$	24.3912	+	30.5422i	1.02163	+	1.27927i
$571$	−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
$576$	0.663521	−	2.92570i	0.0276467	−	0.121904i
$577$	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
$579$	4.38765	−	11.2023i	0.182345	−	0.465552i
$580$		−	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
$585$	−6.10263	+	6.59532i	−0.252313	+	0.272683i
$586$	18.4738	+	10.6659i	0.763146	+	0.440602i
$587$	−27.8171			−1.14813			−0.574067	−	0.818808i	$-0.694635\pi$
$587$	−27.8171			−1.14813			−0.574067	+	0.818808i	$0.694635\pi$
$588$	4.10722	−	11.4075i	0.169379	−	0.470437i
$589$	−62.6553			−2.58167
$590$	−6.12493	−	3.53623i	−0.252160	−	0.145584i
$591$	−3.67245	+	2.93283i	−0.151064	+	0.120641i
$592$	0.363608	+	0.629787i	0.0149442	+	0.0258841i
$593$	−12.3538	+	21.3973i	−0.507308	+	0.878683i	0.492656	+	0.870224i	$0.336026\pi$
$593$	−12.3538	+	21.3973i	−0.507308	+	0.878683i	−0.999964	+	0.00845898i	$0.997307\pi$
$594$	−5.97013	+	2.89032i	−0.244957	+	0.118591i
$595$	−0.119521	−	8.62538i	−0.00489990	−	0.353606i
$596$			8.85283i			0.362626i
$597$	−4.67352	−	1.83050i	−0.191274	−	0.0749172i
$598$	5.47232	−	3.15945i	0.223780	−	0.129199i
$599$	9.38101	−	5.41613i	0.383297	−	0.221297i	−0.295954	−	0.955202i	$-0.595638\pi$
$599$	9.38101	−	5.41613i	0.383297	−	0.221297i	0.679252	+	0.733905i	$0.262304\pi$
$600$	6.40450	+	2.50848i	0.261462	+	0.102408i
$601$			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
$606$	17.3477	−	13.8539i	0.704702	−	0.562778i
$607$	−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
$609$	−8.78496	−	10.6931i	−0.355985	−	0.433307i
$610$	−18.3300			−0.742161
$611$	1.66685	+	0.962355i	0.0674334	+	0.0389327i
$612$	−2.39695	−	2.21789i	−0.0968909	−	0.0896529i
$613$	−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	$-0.924536\pi$
$617$		−	11.6678i		−	0.469727i	0.972028	−	0.234863i	$-0.0754643\pi$
$618$	7.63912	−	19.5038i	0.307290	−	0.784556i
$619$	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
$621$	32.7471	+	2.38583i	1.31410	+	0.0957399i
$622$			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
$627$	10.3953	+	13.0168i	0.415146	+	0.519840i
$628$	2.35077	+	1.35722i	0.0938060	+	0.0541589i
$629$	0.791608			0.0315635
$630$	22.6080	−	7.35271i	0.900723	−	0.292939i
$631$	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
$633$	18.5995	+	23.2901i	0.739265	+	0.925697i
$634$	−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
$639$	9.32302	+	2.11437i	0.368813	+	0.0836432i
$640$	−2.59391	+	1.49759i	−0.102533	+	0.0591976i
$641$	41.0435	−	23.6965i	1.62112	−	0.935955i	0.634501	−	0.772922i	$-0.281205\pi$
$641$	41.0435	−	23.6965i	1.62112	−	0.935955i	0.986621	−	0.163033i	$-0.0521278\pi$
$642$	−1.57099	+	4.01097i	−0.0620021	+	0.158300i
$643$		−	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	0.888288	−	0.459287i	$-0.151895\pi$
$647$	1.17998	+	2.04378i	0.0463898	+	0.0803495i	−0.841898	+	0.539636i	$0.818562\pi$
$648$	3.88253	−	8.11948i	0.152520	−	0.318963i
$649$	−2.61038	−	1.50711i	−0.102466	−	0.0591591i
$650$	3.97115			0.155761
$651$	−13.4052	+	35.6732i	−0.525392	+	1.39814i
$652$	20.0920			0.786862
$653$	−19.9844	−	11.5380i	−0.782049	−	0.451516i	0.0551066	−	0.998480i	$-0.482450\pi$
$653$	−19.9844	−	11.5380i	−0.782049	−	0.451516i	−0.837156	+	0.546964i	$0.815783\pi$
$654$	1.97998	−	1.58122i	0.0774232	−	0.0618305i
$655$	−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	$0.0307542\pi$
$659$			4.95281i			0.192934i	−0.995336	+	0.0964670i	$0.969246\pi$
$660$	6.16623	+	2.41515i	0.240020	+	0.0940097i
$661$	−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
$663$	−1.75556	−	0.687608i	−0.0681803	−	0.0267045i
$664$			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
$669$	−30.3971	+	24.2752i	−1.17522	+	0.938534i
$670$	29.5053	+	17.0349i	1.13989	+	0.658115i
$671$	−7.81206			−0.301581
$672$	−1.61197	+	4.28970i	−0.0621833	+	0.165479i
$673$	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
$675$	17.0732	+	11.5886i	0.657149	+	0.446044i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−13.7881	+	23.8817i	−0.529919	+	0.917847i	0.469472	+	0.882947i	$0.344444\pi$
$677$	−13.7881	+	23.8817i	−0.529919	+	0.917847i	−0.999391	+	0.0348992i	$0.988889\pi$
$678$	2.09974	−	0.317968i	0.0806400	−	0.0122115i
$679$	43.3049	−	0.600074i	1.66189	−	0.0230287i
$680$			3.26040i			0.125031i
$681$	10.6844	−	27.2789i	0.409428	−	1.04533i
$682$	−9.19333	+	5.30777i	−0.352031	+	0.203245i
$683$	10.8942	−	6.28974i	0.416853	−	0.240670i	−0.276877	−	0.960905i	$-0.589299\pi$
$683$	10.8942	−	6.28974i	0.416853	−	0.240670i	0.693730	+	0.720235i	$0.255966\pi$
$684$	−22.0431	−	4.99916i	−0.842839	−	0.191148i
$685$		−	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
$690$	−20.4565	−	25.6153i	−0.778765	−	0.975157i
$691$	−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
$693$	9.63528	−	3.13365i	0.366014	−	0.119037i
$694$	−31.9486			−1.21275
$695$	38.0840	+	21.9878i	1.44461	+	0.834046i
$696$	3.26409	+	4.08724i	0.123725	+	0.154926i
$697$	−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	$-0.820965\pi$
$701$		−	28.2379i		−	1.06653i	0.845948	−	0.533265i	$-0.179035\pi$
$702$	0.377570	−	5.18242i	0.0142505	−	0.195598i
$703$	4.74500	−	2.73953i	0.178961	−	0.103323i
$704$	−1.10550	+	0.638259i	−0.0416650	+	0.0240553i
$705$	3.64152	−	9.29733i	0.137148	−	0.350158i
$706$			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
$711$	29.3350	+	27.1436i	1.10015	+	1.01796i
$712$	11.3650	+	6.56159i	0.425921	+	0.245906i
$713$	52.5480			1.96794
$714$	3.16658	+	3.85439i	0.118506	+	0.144247i
$715$	3.82341			0.142987
$716$	11.7441	+	6.78045i	0.438897	+	0.253397i
$717$	1.43068	−	1.14255i	0.0534298	−	0.0426693i
$718$	−17.5357	−	30.3728i	−0.654427	−	1.13350i
$719$	12.4077	−	21.4907i	0.462728	−	0.801468i	−0.536368	−	0.843984i	$-0.680204\pi$
$719$	12.4077	−	21.4907i	0.462728	−	0.801468i	0.999096	+	0.0425160i	$0.0135373\pi$
$720$	−8.58269	+	2.66040i	−0.319858	+	0.0991473i
$721$	−15.6126	+	27.9285i	−0.581445	+	1.04011i
$722$			37.7656i			1.40549i
$723$	30.0313	+	11.7625i	1.11688	+	0.437452i
$724$	0.184836	−	0.106715i	0.00686939	−	0.00396604i
$725$	−10.3859	+	5.99628i	−0.385721	+	0.222696i
$726$	−15.1123	−	5.91912i	−0.560872	−	0.219679i
$727$			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
$732$	8.28272	−	6.61462i	0.306138	−	0.244483i
$733$	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
$735$	−35.7409	+	6.43003i	−1.31832	+	0.237175i
$736$	6.31889			0.232917
$737$	12.5748	+	7.26009i	0.463200	+	0.267429i
$738$	18.5395	−	20.0363i	0.682448	−	0.737545i
$739$	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	$0.302373\pi$
$743$			44.3420i			1.62675i	−0.581739	+	0.813376i	$0.697627\pi$
$744$	5.25303	−	13.4117i	0.192585	−	0.491698i
$745$	22.9634	−	13.2579i	0.841315	−	0.485733i
$746$	10.8283	−	6.25175i	0.396454	−	0.228893i
$747$	−5.72672	+	25.2511i	−0.209530	+	0.923891i
$748$			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
$753$	3.76342	+	4.71250i	0.137147	+	0.171733i
$754$	2.61533	+	1.50996i	0.0952446	+	0.0549895i
$755$	−18.5336			−0.674506
$756$	−7.56247	+	11.4808i	−0.275044	+	0.417553i
$757$	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
$759$	−8.71834	−	10.9170i	−0.316456	−	0.396261i
$760$	11.2833	+	19.5433i	0.409289	+	0.708909i
$761$	13.5716	−	23.5066i	0.491969	−	0.852115i	−0.507988	−	0.861364i	$-0.669611\pi$
$761$	13.5716	−	23.5066i	0.491969	−	0.852115i	0.999957	+	0.00924880i	$0.00294403\pi$
$762$	1.81750	+	12.0021i	0.0658411	+	0.434789i
$763$	−3.32488	+	1.98154i	−0.120369	+	0.0717367i
$764$			6.62783i			0.239787i
$765$	−2.16335	+	9.53896i	−0.0782159	+	0.344882i
$766$	−5.15484	+	2.97615i	−0.186252	+	0.107533i
$767$	2.04493	−	1.18064i	0.0738380	−	0.0426304i
$768$	0.631675	−	1.61276i	0.0227936	−	0.0581954i
$769$		−	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	0.981736	−	0.190248i	$-0.0609291\pi$
$773$	9.06676	+	15.7041i	0.326109	+	0.564837i	−0.655627	+	0.755085i	$0.727596\pi$
$774$	−17.7969	+	19.2337i	−0.639695	+	0.691341i
$775$	28.5997	+	16.5121i	1.02733	+	0.593131i
$776$	−16.3693			−0.587623
$777$	−0.544568	−	3.28772i	−0.0195363	−	0.117946i
$778$	9.92918			0.355978
$779$	−59.3715	−	34.2782i	−2.12721	−	1.22814i
$780$	−4.05376	+	3.23735i	−0.145148	+	0.115916i
$781$	−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
$786$	0.552196	+	0.216281i	0.0196962	+	0.00771448i
$787$	−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
$789$	20.0089	+	7.83696i	0.712335	+	0.279003i
$790$		−	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
$795$	−41.2371	+	32.9321i	−1.46253	+	1.16798i
$796$	−2.50961	−	1.44892i	−0.0889506	−	0.0513557i
$797$	46.3708			1.64254			0.821270	−	0.570540i	$-0.193266\pi$
$797$	46.3708			1.64254			0.821270	+	0.570540i	$0.193266\pi$
$798$	32.3199	+	12.1451i	1.14411	+	0.429931i
$799$	2.09514			0.0741206
$800$	3.43911	+	1.98557i	0.121591	+	0.0702006i
$801$	28.8969	+	26.7382i	1.02102	+	0.944747i
$802$	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
$807$	−8.60589	+	21.9721i	−0.302942	+	0.773454i
$808$	11.1004	−	6.40881i	0.390510	−	0.225461i
$809$	32.6066	−	18.8255i	1.14639	−	0.661868i	0.198384	−	0.980124i	$-0.436431\pi$
$809$	32.6066	−	18.8255i	1.14639	−	0.661868i	0.948005	+	0.318257i	$0.103097\pi$
$810$	−26.8756	+	2.08874i	−0.944314	+	0.0733909i
$811$			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
$816$	−1.17656	−	1.47327i	−0.0411877	−	0.0515746i
$817$	56.9933	+	32.9051i	1.99394	+	1.15120i
$818$	−0.813929			−0.0284583
$819$	−1.64809	+	7.76426i	−0.0575890	+	0.271305i
$820$	−27.2539			−0.951748
$821$	2.21352	+	1.27797i	0.0772523	+	0.0446016i	0.538129	−	0.842863i	$-0.319131\pi$
$821$	2.21352	+	1.27797i	0.0772523	+	0.0446016i	−0.460876	+	0.887464i	$0.652465\pi$
$822$	8.91672	+	11.1654i	0.311006	+	0.389437i
$823$	−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	$0.186505\pi$
$827$			31.8041i			1.10594i	−0.833202	+	0.552969i	$0.813495\pi$
$828$	18.4872	+	4.19272i	0.642475	+	0.145707i
$829$	−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
$831$	−2.66304	+	6.79911i	−0.0923797	+	0.235858i
$832$		−	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
$837$	24.2678	−	35.7532i	0.838816	−	1.23581i
$838$	−26.2213	−	15.1389i	−0.905801	−	0.522964i
$839$	54.8773			1.89458			0.947288	−	0.320384i	$-0.103812\pi$
$839$	54.8773			1.89458			0.947288	+	0.320384i	$0.103812\pi$
$840$	13.5412	−	2.24292i	0.467215	−	0.0773880i
$841$	19.8801			0.685520
$842$	−6.43665	−	3.71620i	−0.221822	−	0.128069i
$843$	−9.53988	+	7.61858i	−0.328571	+	0.262398i
$844$	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
$849$	24.1506	+	9.45915i	0.828845	+	0.324637i
$850$	3.74363	−	2.16139i	0.128406	−	0.0741350i
$851$	−3.97956	+	2.29760i	−0.136417	+	0.0787606i
$852$	5.13920	+	2.01289i	0.176066	+	0.0689605i
$853$		−	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	0.971926	−	0.235287i	$-0.0756031\pi$
$857$	8.26123	+	14.3089i	0.282198	+	0.488781i	−0.689728	+	0.724069i	$0.742270\pi$
$858$	−1.72767	+	1.37973i	−0.0589817	+	0.0471030i
$859$	−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
$861$	−32.2191	+	26.4697i	−1.09803	+	0.902086i
$862$	24.2103			0.824607
$863$	28.7785	+	16.6153i	0.979631	+	0.565590i	0.902159	−	0.431404i	$-0.141982\pi$
$863$	28.7785	+	16.6153i	0.979631	+	0.565590i	0.0774721	+	0.996995i	$0.475315\pi$
$864$	2.91819	−	4.29932i	0.0992790	−	0.146266i
$865$	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
$870$	5.71365	−	14.5878i	0.193711	−	0.494571i
$871$	−9.85089	+	5.68742i	−0.333785	+	0.192711i
$872$	1.26694	−	0.731469i	0.0429040	−	0.0247707i
$873$	−47.8917	−	10.8614i	−1.62089	−	0.367602i
$874$		−	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
$879$	23.0564	+	28.8709i	0.777673	+	0.973791i
$880$	3.31117	+	1.91170i	0.111619	+	0.0644435i
$881$	−37.3741			−1.25917			−0.629583	−	0.776934i	$-0.716774\pi$
$881$	−37.3741			−1.25917			−0.629583	+	0.776934i	$0.716774\pi$
$882$	13.8298	−	15.8031i	0.465673	−	0.532117i
$883$	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
$885$	−7.64428	−	9.57205i	−0.256960	−	0.321761i
$886$	1.05478	+	1.82693i	0.0354360	+	0.0613770i
$887$	−23.4235	+	40.5707i	−0.786484	+	1.36223i	0.141624	+	0.989920i	$0.454767\pi$
$887$	−23.4235	+	40.5707i	−0.786484	+	1.36223i	−0.928108	+	0.372310i	$0.878566\pi$
$888$	0.188590	+	1.24538i	0.00632867	+	0.0417921i
$889$	−0.256917	−	18.5407i	−0.00861673	−	0.621835i
$890$		−	39.3064i		−	1.31755i
$891$	−11.4541	+	0.890200i	−0.383727	+	0.0298228i
$892$	−19.4504	+	11.2297i	−0.651247	+	0.375997i
$893$	12.5585	−	7.25066i	0.420255	−	0.242634i
$894$	−5.59211	+	14.2775i	−0.187028	+	0.477510i
$895$		−	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
$900$	8.74436	+	8.09112i	0.291479	+	0.269704i
$901$	−9.58974	−	5.53664i	−0.319481	−	0.184452i
$902$	−11.6153			−0.386748
$903$	30.9286	−	25.4094i	1.02924	−	0.845573i
$904$	1.22611			0.0407797
$905$	−0.553620	−	0.319632i	−0.0184029	−	0.0106249i
$906$	8.37471	−	6.68808i	0.278231	−	0.222196i
$907$	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	$-0.988702\pi$
$911$		−	2.14217i		−	0.0709734i	0.999370	−	0.0354867i	$-0.0112981\pi$
$912$	−12.1510	−	4.75923i	−0.402359	−	0.157594i
$913$	9.54131	−	5.50868i	0.315771	−	0.182311i
$914$	−22.3115	+	12.8815i	−0.737998	+	0.426083i
$915$	−29.5619	−	11.5786i	−0.977285	−	0.382777i
$916$		−	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
$921$	−12.3609	+	9.87145i	−0.407305	+	0.325275i
$922$	4.01098	+	2.31574i	0.132095	+	0.0762648i
$923$	3.18659			0.104888
$924$	5.77111	−	0.955908i	0.189855	−	0.0314471i
$925$	−2.88788			−0.0949529
$926$	2.07559	+	1.19834i	0.0682080	+	0.0393799i
$927$	24.6401	−	26.6294i	0.809287	−	0.874624i
$928$	1.50996	+	2.61533i	0.0495669	+	0.0858524i
$929$	2.31897	−	4.01657i	0.0760828	−	0.131779i	−0.825474	−	0.564440i	$-0.809092\pi$
$929$	2.31897	−	4.01657i	0.0760828	−	0.131779i	0.901557	+	0.432661i	$0.142425\pi$
$930$	−42.6557	+	6.45945i	−1.39873	+	0.211814i
$931$	−46.3874	−	25.0943i	−1.52028	−	0.822433i
$932$		−	20.9204i		−	0.685269i
$933$	−15.6067	+	39.8463i	−0.510942	+	1.30451i
$934$	36.9817	−	21.3514i	1.21008	−	0.698638i
$935$	3.60436	−	2.08098i	0.117875	−	0.0680553i
$936$	0.663521	−	2.92570i	0.0216879	−	0.0956296i
$937$			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	0.964956	−	0.262411i	$-0.0845175\pi$
$941$	7.82917	+	13.5605i	0.255224	+	0.442061i	−0.709732	+	0.704471i	$0.751184\pi$
$942$	2.93390	+	3.67379i	0.0955917	+	0.119699i
$943$	49.7940	+	28.7486i	1.62151	+	0.936182i
$944$	2.36128			0.0768530
$945$	41.1057	+	2.42275i	1.33717	+	0.0788121i
$946$	11.1501			0.362520
$947$	−33.6143	−	19.4072i	−1.09232	−	0.630650i	−0.158125	−	0.987419i	$-0.550545\pi$
$947$	−33.6143	−	19.4072i	−1.09232	−	0.630650i	−0.934192	+	0.356769i	$0.883878\pi$
$948$	14.3993	+	18.0305i	0.467666	+	0.585605i
$949$	−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	$-0.951141\pi$
$953$		−	9.43984i		−	0.305786i	0.988243	−	0.152893i	$-0.0488591\pi$
$954$	6.74970	−	29.7618i	0.218530	−	0.963575i
$955$	17.1920	−	9.92580i	0.556320	−	0.321191i
$956$	0.915460	−	0.528541i	0.0296081	−	0.0170942i
$957$	2.43510	−	6.21715i	0.0787155	−	0.200972i
$958$			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
$963$	−5.06726	+	5.47636i	−0.163290	+	0.176473i
$964$	16.1264	+	9.31056i	0.519395	+	0.299873i
$965$	−20.8047			−0.669728
$966$	−27.1062	−	10.1859i	−0.872126	−	0.327726i
$967$	−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
$969$	−11.1000	+	8.86452i	−0.356584	+	0.284769i
$970$	24.5145	+	42.4604i	0.787115	+	1.36332i
$971$	−15.3430	+	26.5748i	−0.492380	+	0.852826i	−0.999961	−	0.00877706i	$-0.997206\pi$
$971$	−15.3430	+	26.5748i	−0.492380	+	0.852826i	0.507582	+	0.861604i	$0.330539\pi$
$972$	11.3905	−	10.6422i	0.365349	−	0.341350i
$973$	38.8415	−	0.538224i	1.24520	−	0.0172547i
$974$			24.2660i			0.777532i
$975$	6.40450	+	2.50848i	0.205108	+	0.0803355i
$976$	5.29992	−	3.05991i	0.169646	−	0.0979454i
$977$	43.9167	−	25.3553i	1.40502	−	0.811189i	0.410118	−	0.912033i	$-0.365488\pi$
$977$	43.9167	−	25.3553i	1.40502	−	0.811189i	0.994902	+	0.100844i	$0.0321542\pi$
$978$	32.4035	+	12.6916i	1.03615	+	0.405832i
$979$		−	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	0.956869	−	0.290520i	$-0.0938282\pi$
$983$	7.11198	+	12.3183i	0.226837	+	0.392893i	−0.730032	+	0.683413i	$0.760495\pi$
$984$	12.3151	−	9.83492i	0.392592	−	0.313526i
$985$	7.03843	+	4.06364i	0.224263	+	0.129478i
$986$	3.28732			0.104690
$987$	−1.44130	−	8.70157i	−0.0458771	−	0.276974i
$988$	−7.53429			−0.239698
$989$	−47.7994	−	27.5970i	−1.51993	−	0.877533i
$990$	8.41904	+	7.79011i	0.267575	+	0.247586i
$991$	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
$996$	−5.45186	+	13.9194i	−0.172749	+	0.441052i
$997$	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
$999$	−0.274575	+	3.76873i	−0.00868717	+	0.119237i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.3	✓	32	3.2	odd	2
546.2.z.a.521.3	yes	32	7.3	odd	6
546.2.z.b.131.14	yes	32	1.1	even	1	trivial
546.2.z.b.521.14	yes	32	21.17	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.08085 + 1.35343i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.49759 - 2.59391i) q^{5} +(0.259332 + 1.71253i) q^{6} +(-0.0366585 - 2.64550i) q^{7} +1.00000i q^{8} +(-0.663521 + 2.92570i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.08085 + 1.35343i) 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} +(-0.663521 + 2.92570i) q^{9} +(2.59391 - 1.49759i) q^{10} +(1.10550 - 0.638259i) q^{11} +(-0.631675 + 1.61276i) 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} +(-2.03748 + 2.20197i) q^{18} +(6.52489 + 3.76715i) q^{19} +2.99519 q^{20} +(3.54086 - 2.90900i) q^{21} +1.27652 q^{22} +(-5.47232 - 3.15945i) q^{23} +(-1.35343 + 1.08085i) 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} +(4.83051 + 1.89199i) q^{30} +(-7.20189 + 4.15801i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.05871 + 0.806345i) 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} +(-1.35343 + 1.08085i) q^{39} +(2.59391 + 1.49759i) q^{40} -9.09924 q^{41} +(4.52098 - 0.748840i) q^{42} +8.73475 q^{43} +(1.10550 + 0.638259i) q^{44} +(6.59532 + 6.10263i) 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} +(-0.687608 + 1.75556i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(-8.80968 + 5.08627i) q^{53} +(-5.18242 - 0.377570i) 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} +(3.23735 + 4.05376i) q^{60} +(-5.29992 - 3.05991i) q^{61} -8.31602 q^{62} +(7.76426 + 1.64809i) q^{63} -1.00000 q^{64} +(2.59391 + 1.49759i) q^{65} +(1.37973 + 1.72767i) 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} +(-2.92570 - 0.663521i) q^{72} +(-9.69406 + 5.59687i) q^{73} +(0.629787 - 0.363608i) q^{74} +(2.50848 - 6.40450i) 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} +(-8.11948 - 3.88253i) q^{81} +(-7.88017 - 4.54962i) q^{82} +8.63079 q^{83} +(4.28970 + 1.61197i) q^{84} +3.26040 q^{85} +(7.56452 + 4.36738i) q^{86} +(4.08724 - 3.26409i) 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} +(-13.4117 - 5.25303i) q^{93} +(1.66685 - 0.962355i) q^{94} +(19.5433 - 11.2833i) q^{95} +(-1.61276 - 0.631675i) 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	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 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 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * 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 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * 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 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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