LMFDB - Embedded newform 930.2.be.b.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.604368 + 2.15284i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.350136 + 1.30673i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.604368 + 2.15284i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.350136 + 1.30673i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.94964 + 1.09494i) q^{10} +(-2.25869 - 1.30405i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-3.15790 + 0.846157i) q^{13} +(-1.17158 + 0.676411i) q^{14} +(-1.92307 - 1.14097i) q^{15} -1.00000 q^{16} +(-4.80046 - 1.28628i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(4.49113 - 2.59295i) q^{19} +(-2.15284 - 0.604368i) q^{20} +(-1.17158 - 0.676411i) q^{21} +(-0.675028 - 2.51924i) q^{22} +(2.27397 + 2.27397i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.26948 - 2.60222i) q^{25} +(-2.83130 - 1.63465i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.30673 - 0.350136i) q^{28} +4.75729 q^{29} +(-0.553024 - 2.16660i) q^{30} +(3.09599 + 4.62762i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.84421 - 1.84421i) q^{33} +(-2.48490 - 4.30397i) q^{34} +(-2.60157 - 1.54353i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.0928042 + 0.0248668i) q^{37} +(5.00920 + 1.34221i) q^{38} -3.26930i q^{39} +(-1.09494 - 1.94964i) q^{40} +(-2.50363 + 4.33641i) q^{41} +(-0.350136 - 1.30673i) q^{42} +(-1.90246 + 7.10006i) q^{43} +(1.30405 - 2.25869i) q^{44} +(1.59982 - 1.56223i) q^{45} +3.21588i q^{46} +(-8.61365 - 8.61365i) q^{47} +(0.258819 - 0.965926i) q^{48} +(4.47724 + 2.58494i) q^{49} +(-1.17893 - 4.85903i) q^{50} +(2.48490 - 4.30397i) q^{51} +(-0.846157 - 3.15790i) q^{52} +(-0.514660 + 0.137903i) q^{53} +1.00000 q^{54} +(4.17250 - 4.07448i) q^{55} +(-0.676411 - 1.17158i) q^{56} +(1.34221 + 5.00920i) q^{57} +(3.36391 + 3.36391i) q^{58} +(-7.50275 + 4.33171i) q^{59} +(1.14097 - 1.92307i) q^{60} -6.95735i q^{61} +(-1.08302 + 5.46142i) q^{62} +(0.956590 - 0.956590i) q^{63} -1.00000i q^{64} +(0.0868898 - 7.30986i) q^{65} +2.60811 q^{66} +(-15.2555 + 4.08769i) q^{67} +(1.28628 - 4.80046i) q^{68} +(-2.78504 + 1.60794i) q^{69} +(-0.748143 - 2.93103i) q^{70} +(-3.50746 + 6.07509i) q^{71} +(0.965926 - 0.258819i) q^{72} +(9.90670 - 2.65449i) q^{73} +(0.0480390 + 0.0832060i) q^{74} +(3.61857 - 3.45050i) q^{75} +(2.59295 + 4.49113i) q^{76} +(2.49489 - 2.49489i) q^{77} +(2.31175 - 2.31175i) q^{78} +(3.21866 + 5.57488i) q^{79} +(0.604368 - 2.15284i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-4.83664 + 1.29597i) q^{82} +(-9.97352 + 2.67240i) q^{83} +(0.676411 - 1.17158i) q^{84} +(5.67040 - 9.55725i) q^{85} +(-6.36574 + 3.67526i) q^{86} +(-1.23128 + 4.59519i) q^{87} +(2.51924 - 0.675028i) q^{88} -8.83632 q^{89} +(2.23591 + 0.0265775i) q^{90} -4.42278i q^{91} +(-2.27397 + 2.27397i) q^{92} +(-5.27124 + 1.79278i) q^{93} -12.1815i q^{94} +(2.86793 + 11.2358i) q^{95} +(0.866025 - 0.500000i) q^{96} +(6.18084 + 6.18084i) q^{97} +(1.33806 + 4.99371i) q^{98} +(1.30405 + 2.25869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	−0.604368	+	2.15284i	−0.270282	+	0.962781i
$5$	−0.604368	+	2.15284i	−0.270282	+	0.962781i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.350136	+	1.30673i	−0.132339	+	0.493896i	−0.999995	−	0.00326969i	$-0.998959\pi$
$7$	−0.350136	+	1.30673i	−0.132339	+	0.493896i	0.867656	+	0.497166i	$0.165626\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.94964	+	1.09494i	−0.616531	+	0.346250i
$11$	−2.25869	−	1.30405i	−0.681020	−	0.393187i	0.119219	−	0.992868i	$-0.461961\pi$
$11$	−2.25869	−	1.30405i	−0.681020	−	0.393187i	−0.800239	+	0.599681i	$0.795294\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−3.15790	+	0.846157i	−0.875845	+	0.234682i	−0.668613	−	0.743610i	$-0.733112\pi$
$13$	−3.15790	+	0.846157i	−0.875845	+	0.234682i	−0.207231	+	0.978292i	$0.566445\pi$
$14$	−1.17158	+	0.676411i	−0.313118	+	0.180778i
$15$	−1.92307	−	1.14097i	−0.496534	−	0.294598i
$16$	−1.00000			−0.250000
$17$	−4.80046	−	1.28628i	−1.16428	−	0.311968i	−0.375607	−	0.926779i	$-0.622566\pi$
$17$	−4.80046	−	1.28628i	−1.16428	−	0.311968i	−0.788675	+	0.614810i	$0.789233\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	4.49113	−	2.59295i	1.03034	−	0.594864i	0.113255	−	0.993566i	$-0.463872\pi$
$19$	4.49113	−	2.59295i	1.03034	−	0.594864i	0.917081	+	0.398702i	$0.130539\pi$
$20$	−2.15284	−	0.604368i	−0.481391	−	0.135141i
$21$	−1.17158	−	0.676411i	−0.255659	−	0.147605i
$22$	−0.675028	−	2.51924i	−0.143916	−	0.537104i
$23$	2.27397	+	2.27397i	0.474156	+	0.474156i	0.903257	−	0.429101i	$-0.141169\pi$
$23$	2.27397	+	2.27397i	0.474156	+	0.474156i	−0.429101	+	0.903257i	$0.641169\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.26948	−	2.60222i	−0.853896	−	0.520444i
$26$	−2.83130	−	1.63465i	−0.555263	−	0.320581i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.30673	−	0.350136i	−0.246948	−	0.0661695i
$29$	4.75729			0.883407			0.441703	−	0.897161i	$-0.354374\pi$
$29$	4.75729			0.883407			0.441703	+	0.897161i	$0.354374\pi$
$30$	−0.553024	−	2.16660i	−0.100968	−	0.395566i
$31$	3.09599	+	4.62762i	0.556057	+	0.831144i
$31$	3.09599	+	4.62762i	0.556057	+	0.831144i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.84421	−	1.84421i	0.321036	−	0.321036i
$34$	−2.48490	−	4.30397i	−0.426157	−	0.738125i
$35$	−2.60157	−	1.54353i	−0.439745	−	0.260905i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	0.0928042	+	0.0248668i	0.0152569	+	0.00408808i	0.266439	−	0.963852i	$-0.414153\pi$
$37$	0.0928042	+	0.0248668i	0.0152569	+	0.00408808i	−0.251183	+	0.967940i	$0.580819\pi$
$38$	5.00920	+	1.34221i	0.812600	+	0.217735i
$39$		−	3.26930i		−	0.523507i
$40$	−1.09494	−	1.94964i	−0.173125	−	0.308266i
$41$	−2.50363	+	4.33641i	−0.391001	+	0.677234i	−0.992582	−	0.121578i	$-0.961205\pi$
$41$	−2.50363	+	4.33641i	−0.391001	+	0.677234i	0.601581	+	0.798812i	$0.294538\pi$
$42$	−0.350136	−	1.30673i	−0.0540272	−	0.201632i
$43$	−1.90246	+	7.10006i	−0.290122	+	1.08275i	0.654893	+	0.755722i	$0.272714\pi$
$43$	−1.90246	+	7.10006i	−0.290122	+	1.08275i	−0.945015	+	0.327028i	$0.893953\pi$
$44$	1.30405	−	2.25869i	0.196594	−	0.340510i
$45$	1.59982	−	1.56223i	0.238487	−	0.232884i
$46$			3.21588i			0.474156i
$47$	−8.61365	−	8.61365i	−1.25643	−	1.25643i	−0.952785	−	0.303645i	$-0.901796\pi$
$47$	−8.61365	−	8.61365i	−1.25643	−	1.25643i	−0.303645	−	0.952785i	$-0.598204\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	4.47724	+	2.58494i	0.639606	+	0.369277i
$50$	−1.17893	−	4.85903i	−0.166726	−	0.687170i
$51$	2.48490	−	4.30397i	0.347956	−	0.602677i
$52$	−0.846157	−	3.15790i	−0.117341	−	0.437922i
$53$	−0.514660	+	0.137903i	−0.0706939	+	0.0189424i	−0.293993	−	0.955808i	$-0.594984\pi$
$53$	−0.514660	+	0.137903i	−0.0706939	+	0.0189424i	0.223299	+	0.974750i	$0.428317\pi$
$54$	1.00000			0.136083
$55$	4.17250	−	4.07448i	0.562620	−	0.549402i
$56$	−0.676411	−	1.17158i	−0.0903892	−	0.156559i
$57$	1.34221	+	5.00920i	0.177780	+	0.663485i
$58$	3.36391	+	3.36391i	0.441703	+	0.441703i
$59$	−7.50275	+	4.33171i	−0.976774	+	0.563941i	−0.901295	−	0.433206i	$-0.857382\pi$
$59$	−7.50275	+	4.33171i	−0.976774	+	0.563941i	−0.0754797	+	0.997147i	$0.524049\pi$
$60$	1.14097	−	1.92307i	0.147299	−	0.248267i
$61$		−	6.95735i		−	0.890798i	−0.895332	−	0.445399i	$-0.853062\pi$
$61$		−	6.95735i		−	0.890798i	0.895332	−	0.445399i	$-0.146938\pi$
$62$	−1.08302	+	5.46142i	−0.137544	+	0.693601i
$63$	0.956590	−	0.956590i	0.120519	−	0.120519i
$64$		−	1.00000i		−	0.125000i
$65$	0.0868898	−	7.30986i	0.0107774	−	0.906677i
$66$	2.60811			0.321036
$67$	−15.2555	+	4.08769i	−1.86375	+	0.499391i	−0.999990	−	0.00450782i	$-0.998565\pi$
$67$	−15.2555	+	4.08769i	−1.86375	+	0.499391i	−0.863763	+	0.503899i	$0.831898\pi$
$68$	1.28628	−	4.80046i	0.155984	−	0.582141i
$69$	−2.78504	+	1.60794i	−0.335279	+	0.193573i
$70$	−0.748143	−	2.93103i	−0.0894202	−	0.350325i
$71$	−3.50746	+	6.07509i	−0.416258	+	0.720981i	−0.995560	−	0.0941327i	$-0.969992\pi$
$71$	−3.50746	+	6.07509i	−0.416258	+	0.720981i	0.579301	+	0.815114i	$0.303326\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	9.90670	−	2.65449i	1.15949	−	0.310685i	0.372729	−	0.927940i	$-0.378422\pi$
$73$	9.90670	−	2.65449i	1.15949	−	0.310685i	0.786763	+	0.617256i	$0.211756\pi$
$74$	0.0480390	+	0.0832060i	0.00558442	+	0.00967250i
$75$	3.61857	−	3.45050i	0.417837	−	0.398429i
$76$	2.59295	+	4.49113i	0.297432	+	0.515168i
$77$	2.49489	−	2.49489i	0.284319	−	0.284319i
$78$	2.31175	−	2.31175i	0.261754	−	0.261754i
$79$	3.21866	+	5.57488i	0.362127	+	0.627223i	0.988311	−	0.152453i	$-0.0487172\pi$
$79$	3.21866	+	5.57488i	0.362127	+	0.627223i	−0.626183	+	0.779676i	$0.715384\pi$
$80$	0.604368	−	2.15284i	0.0675704	−	0.240695i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−4.83664	+	1.29597i	−0.534118	+	0.143116i
$83$	−9.97352	+	2.67240i	−1.09474	+	0.293334i	−0.760619	−	0.649198i	$-0.775105\pi$
$83$	−9.97352	+	2.67240i	−1.09474	+	0.293334i	−0.334117	+	0.942532i	$0.608438\pi$
$84$	0.676411	−	1.17158i	0.0738025	−	0.127830i
$85$	5.67040	−	9.55725i	0.615041	−	1.03663i
$86$	−6.36574	+	3.67526i	−0.686435	+	0.396314i
$87$	−1.23128	+	4.59519i	−0.132007	+	0.492656i
$88$	2.51924	−	0.675028i	0.268552	−	0.0719582i
$89$	−8.83632			−0.936648			−0.468324	−	0.883557i	$-0.655142\pi$
$89$	−8.83632			−0.936648			−0.468324	+	0.883557i	$0.655142\pi$
$90$	2.23591	+	0.0265775i	0.235686	+	0.00280151i
$91$		−	4.42278i		−	0.463634i
$92$	−2.27397	+	2.27397i	−0.237078	+	0.237078i
$93$	−5.27124	+	1.79278i	−0.546602	+	0.185903i
$94$		−	12.1815i		−	1.25643i
$95$	2.86793	+	11.2358i	0.294244	+	1.15277i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	6.18084	+	6.18084i	0.627569	+	0.627569i	0.947456	−	0.319887i	$-0.103645\pi$
$97$	6.18084	+	6.18084i	0.627569	+	0.627569i	−0.319887	+	0.947456i	$0.603645\pi$
$98$	1.33806	+	4.99371i	0.135165	+	0.504441i
$99$	1.30405	+	2.25869i	0.131062	+	0.227007i
$100$	2.60222	−	4.26948i	0.260222	−	0.426948i
$101$	10.3765			1.03250			0.516248	−	0.856439i	$-0.327328\pi$
$101$	10.3765			1.03250			0.516248	+	0.856439i	$0.327328\pi$
$102$	4.80046	−	1.28628i	0.475316	−	0.127361i
$103$	0.248586	+	0.927737i	0.0244939	+	0.0914127i	0.977091	−	0.212823i	$-0.0682657\pi$
$103$	0.248586	+	0.927737i	0.0244939	+	0.0914127i	−0.952597	+	0.304235i	$0.901599\pi$
$104$	1.63465	−	2.83130i	0.160291	−	0.277632i
$105$	2.16427	−	2.11343i	0.211211	−	0.206249i
$106$	−0.461431	−	0.266407i	−0.0448182	−	0.0258758i
$107$	−0.931731	+	3.47727i	−0.0900738	+	0.336160i	−0.996227	−	0.0867904i	$-0.972339\pi$
$107$	−0.931731	+	3.47727i	−0.0900738	+	0.336160i	0.906153	+	0.422951i	$0.139006\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			18.5710i			1.77878i	0.457147	+	0.889391i	$0.348871\pi$
$109$			18.5710i			1.77878i	−0.457147	+	0.889391i	$0.651129\pi$
$110$	5.83150	+	0.0693170i	0.556011	+	0.00660912i
$111$	−0.0480390	+	0.0832060i	−0.00455966	+	0.00789756i
$112$	0.350136	−	1.30673i	0.0330848	−	0.123474i
$113$	4.74718	+	17.7167i	0.446577	+	1.66665i	0.711740	+	0.702443i	$0.247908\pi$
$113$	4.74718	+	17.7167i	0.446577	+	1.66665i	−0.265163	+	0.964204i	$0.585426\pi$
$114$	−2.59295	+	4.49113i	−0.242852	+	0.420633i
$115$	−6.26983	+	3.52119i	−0.584664	+	0.328353i
$116$			4.75729i			0.441703i
$117$	3.15790	+	0.846157i	0.291948	+	0.0782273i
$118$	−8.36823	−	2.24226i	−0.770358	−	0.206417i
$119$	3.36163	−	5.82251i	0.308160	−	0.533749i
$120$	2.16660	−	0.553024i	0.197783	−	0.0504840i
$121$	−2.09889	−	3.63538i	−0.190808	−	0.330489i
$122$	4.91959	−	4.91959i	0.445399	−	0.445399i
$123$	−3.54067	−	3.54067i	−0.319251	−	0.319251i
$124$	−4.62762	+	3.09599i	−0.415572	+	0.278028i
$125$	8.18251	−	7.61882i	0.731866	−	0.681448i
$126$	1.35282			0.120519
$127$	0.100069	+	0.0268135i	0.00887973	+	0.00237932i	0.263256	−	0.964726i	$-0.415204\pi$
$127$	0.100069	+	0.0268135i	0.00887973	+	0.00237932i	−0.254376	+	0.967105i	$0.581870\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−6.36574	−	3.67526i	−0.560472	−	0.323589i
$130$	5.23029	−	5.10741i	0.458727	−	0.447950i
$131$	−3.81069	−	6.60032i	−0.332942	−	0.576672i	0.650145	−	0.759810i	$-0.274708\pi$
$131$	−3.81069	−	6.60032i	−0.332942	−	0.576672i	−0.983087	+	0.183138i	$0.941375\pi$
$132$	1.84421	+	1.84421i	0.160518	+	0.160518i
$133$	1.81577	+	6.77656i	0.157448	+	0.587602i
$134$	−13.6777	−	7.89681i	−1.18157	−	0.682181i
$135$	1.09494	+	1.94964i	0.0942373	+	0.167799i
$136$	4.30397	−	2.48490i	0.369063	−	0.213078i
$137$	0.754710	+	2.81662i	0.0644792	+	0.240640i	0.990642	−	0.136483i	$-0.0435800\pi$
$137$	0.754710	+	2.81662i	0.0644792	+	0.240640i	−0.926163	+	0.377123i	$0.876913\pi$
$138$	−3.10631	−	0.832332i	−0.264426	−	0.0708528i
$139$	14.3372			1.21607			0.608033	−	0.793912i	$-0.291959\pi$
$139$	14.3372			1.21607			0.608033	+	0.793912i	$0.291959\pi$
$140$	1.54353	−	2.60157i	0.130452	−	0.219873i
$141$	10.5495	−	6.09077i	0.888430	−	0.512935i
$142$	−6.77589	+	1.81559i	−0.568620	+	0.152361i
$143$	8.23615	+	2.20687i	0.688742	+	0.184548i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−2.87515	+	10.2417i	−0.238769	+	0.850528i
$146$	8.88210	+	5.12808i	0.735088	+	0.424403i
$147$	−3.65565	+	3.65565i	−0.301513	+	0.301513i
$148$	−0.0248668	+	0.0928042i	−0.00204404	+	0.00762846i
$149$	−4.24239	+	2.44934i	−0.347550	+	0.200658i	−0.663606	−	0.748083i	$-0.730975\pi$
$149$	−4.24239	+	2.44934i	−0.347550	+	0.200658i	0.316056	+	0.948741i	$0.397641\pi$
$150$	4.99859	+	0.118850i	0.408133	+	0.00970404i
$151$		−	23.7140i		−	1.92982i	−0.262590	−	0.964908i	$-0.584577\pi$
$151$		−	23.7140i		−	1.92982i	0.262590	−	0.964908i	$-0.415423\pi$
$152$	−1.34221	+	5.00920i	−0.108868	+	0.406300i
$153$	3.51418	+	3.51418i	0.284105	+	0.284105i
$154$	3.52831			0.284319
$155$	−11.8337	+	3.86841i	−0.950502	+	0.310718i
$156$	3.26930			0.261754
$157$	8.73159	+	8.73159i	0.696857	+	0.696857i	0.963731	−	0.266875i	$-0.0859909\pi$
$157$	8.73159	+	8.73159i	0.696857	+	0.696857i	−0.266875	+	0.963731i	$0.585991\pi$
$158$	−1.66610	+	6.21797i	−0.132548	+	0.494675i
$159$		−	0.532815i		−	0.0422550i
$160$	1.94964	−	1.09494i	0.154133	−	0.0865625i
$161$	−3.76766	+	2.17526i	−0.296933	+	0.171434i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−0.427317	+	0.427317i	−0.0334701	+	0.0334701i	−0.723644	−	0.690174i	$-0.757534\pi$
$163$	−0.427317	+	0.427317i	−0.0334701	+	0.0334701i	0.690174	+	0.723644i	$0.257534\pi$
$164$	−4.33641	−	2.50363i	−0.338617	−	0.195501i
$165$	2.85572	+	5.08488i	0.222317	+	0.395857i
$166$	−8.94201	−	5.16267i	−0.694035	−	0.400701i
$167$	−5.90454	−	1.58212i	−0.456907	−	0.122428i	0.0230225	−	0.999735i	$-0.492671\pi$
$167$	−5.90454	−	1.58212i	−0.456907	−	0.122428i	−0.479929	+	0.877307i	$0.659338\pi$
$168$	1.30673	−	0.350136i	0.100816	−	0.0270136i
$169$	−2.00196	+	1.15583i	−0.153997	+	0.0889103i
$170$	10.7676	−	2.74842i	0.825836	−	0.210794i
$171$	−5.18591			−0.396576
$172$	−7.10006	−	1.90246i	−0.541375	−	0.145061i
$173$	2.06992	+	7.72506i	0.157373	+	0.587325i	0.998890	+	0.0470948i	$0.0149963\pi$
$173$	2.06992	+	7.72506i	0.157373	+	0.587325i	−0.841517	+	0.540231i	$0.818337\pi$
$174$	−4.11994	+	2.37865i	−0.312331	+	0.180325i
$175$	4.89529	−	4.66791i	0.370049	−	0.352861i
$176$	2.25869	+	1.30405i	0.170255	+	0.0982968i
$177$	−2.24226	−	8.36823i	−0.168539	−	0.628994i
$178$	−6.24822	−	6.24822i	−0.468324	−	0.468324i
$179$	9.27604	+	16.0666i	0.693324	+	1.20087i	0.970743	+	0.240123i	$0.0771877\pi$
$179$	9.27604	+	16.0666i	0.693324	+	1.20087i	−0.277419	+	0.960749i	$0.589479\pi$
$180$	1.56223	+	1.59982i	0.116442	+	0.119244i
$181$	8.68725	+	5.01559i	0.645718	+	0.372806i	0.786814	−	0.617190i	$-0.211729\pi$
$181$	8.68725	+	5.01559i	0.645718	+	0.372806i	−0.141096	+	0.989996i	$0.545062\pi$
$182$	3.12738	−	3.12738i	0.231817	−	0.231817i
$183$	6.72028	+	1.80069i	0.496778	+	0.133111i
$184$	−3.21588			−0.237078
$185$	−0.109622	+	0.184764i	−0.00805959	+	0.0135841i
$186$	−4.99502	−	2.45964i	−0.366252	−	0.180349i
$187$	9.16536	+	9.16536i	0.670238	+	0.670238i
$188$	8.61365	−	8.61365i	0.628215	−	0.628215i
$189$	0.676411	+	1.17158i	0.0492017	+	0.0852198i
$190$	−5.91697	+	9.97284i	−0.429262	+	0.723506i
$191$	−3.82470	+	6.62457i	−0.276745	+	0.479337i	−0.970574	−	0.240803i	$-0.922589\pi$
$191$	−3.82470	+	6.62457i	−0.276745	+	0.479337i	0.693829	+	0.720140i	$0.255922\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	15.5384	+	4.16351i	1.11848	+	0.299696i	0.770269	−	0.637719i	$-0.220122\pi$
$193$	15.5384	+	4.16351i	1.11848	+	0.299696i	0.348213	+	0.937416i	$0.386789\pi$
$194$			8.74102i			0.627569i
$195$	7.03830	+	1.97586i	0.504023	+	0.141494i
$196$	−2.58494	+	4.47724i	−0.184638	+	0.319803i
$197$	−1.87426	−	6.99485i	−0.133536	−	0.498363i	0.866464	−	0.499240i	$-0.166387\pi$
$197$	−1.87426	−	6.99485i	−0.133536	−	0.498363i	−1.00000		0.000877420i	$0.999721\pi$
$198$	−0.675028	+	2.51924i	−0.0479722	+	0.179035i
$199$	11.4936	−	19.9075i	0.814758	−	1.41120i	−0.0947429	−	0.995502i	$-0.530203\pi$
$199$	11.4936	−	19.9075i	0.814758	−	1.41120i	0.909501	−	0.415701i	$-0.136464\pi$
$200$	4.85903	−	1.17893i	0.343585	−	0.0833629i
$201$		−	15.7936i		−	1.11400i
$202$	7.33726	+	7.33726i	0.516248	+	0.516248i
$203$	−1.66570	+	6.21648i	−0.116909	+	0.436311i
$204$	4.30397	+	2.48490i	0.301338	+	0.173978i
$205$	−7.82251	−	8.01072i	−0.546348	−	0.559493i
$206$	−0.480232	+	0.831786i	−0.0334594	+	0.0579533i
$207$	−0.832332	−	3.10631i	−0.0578511	−	0.215903i
$208$	3.15790	−	0.846157i	0.218961	−	0.0586705i
$209$	−13.5254			−0.935572
$210$	3.02479	+	0.0359546i	0.208730	+	0.00248111i
$211$	4.47977	+	7.75920i	0.308400	+	0.534165i	0.978013	−	0.208546i	$-0.0668730\pi$
$211$	4.47977	+	7.75920i	0.308400	+	0.534165i	−0.669612	+	0.742711i	$0.733540\pi$
$212$	−0.137903	−	0.514660i	−0.00947119	−	0.0353470i
$213$	−4.96029	−	4.96029i	−0.339874	−	0.339874i
$214$	−3.11763	+	1.79997i	−0.213117	+	0.123043i
$215$	−14.1355	−	8.38674i	−0.964036	−	0.571971i
$216$			1.00000i			0.0680414i
$217$	−7.13104	+	2.42532i	−0.484087	+	0.164641i
$218$	−13.1317	+	13.1317i	−0.889391	+	0.889391i
$219$			10.2562i			0.693048i
$220$	4.07448	+	4.17250i	0.274701	+	0.281310i
$221$	16.2478			1.09294
$222$	−0.0928042	+	0.0248668i	−0.00622861	+	0.00166895i
$223$	−0.678799	+	2.53331i	−0.0454558	+	0.169643i	−0.984922	−	0.172998i	$-0.944655\pi$
$223$	−0.678799	+	2.53331i	−0.0454558	+	0.169643i	0.939466	+	0.342641i	$0.111321\pi$
$224$	1.17158	−	0.676411i	0.0782794	−	0.0451946i
$225$	2.39637	+	4.38833i	0.159758	+	0.292555i
$226$	−9.17084	+	15.8844i	−0.610035	+	1.05661i
$227$	−24.0294	+	6.43867i	−1.59489	+	0.427350i	−0.943494	−	0.331389i	$-0.892483\pi$
$227$	−24.0294	+	6.43867i	−1.59489	+	0.427350i	−0.651396	+	0.758738i	$0.725816\pi$
$228$	−5.00920	+	1.34221i	−0.331743	+	0.0888901i
$229$	−3.35813	−	5.81646i	−0.221912	−	0.384362i	0.733477	−	0.679715i	$-0.237896\pi$
$229$	−3.35813	−	5.81646i	−0.221912	−	0.384362i	−0.955388	+	0.295352i	$0.904563\pi$
$230$	−6.92330	−	1.94358i	−0.456509	−	0.128156i
$231$	1.76415	+	3.05560i	0.116073	+	0.201044i
$232$	−3.36391	+	3.36391i	−0.220852	+	0.220852i
$233$	−0.830572	+	0.830572i	−0.0544126	+	0.0544126i	−0.733789	−	0.679377i	$-0.762250\pi$
$233$	−0.830572	+	0.830572i	−0.0544126	+	0.0544126i	0.679377	+	0.733789i	$0.262250\pi$
$234$	1.63465	+	2.83130i	0.106860	+	0.185088i
$235$	23.7497	−	13.3380i	1.54926	−	0.870078i
$236$	−4.33171	−	7.50275i	−0.281970	−	0.488387i
$237$	−6.21797	+	1.66610i	−0.403901	+	0.108225i
$238$	6.49417	−	1.74011i	0.420954	−	0.112794i
$239$	1.83003	−	3.16971i	0.118375	−	0.205032i	−0.800749	−	0.599000i	$-0.795565\pi$
$239$	1.83003	−	3.16971i	0.118375	−	0.205032i	0.919124	+	0.393969i	$0.128898\pi$
$240$	1.92307	+	1.14097i	0.124133	+	0.0736494i
$241$	26.6239	−	15.3713i	1.71499	−	0.990152i	0.787500	−	0.616314i	$-0.211375\pi$
$241$	26.6239	−	15.3713i	1.71499	−	0.990152i	0.927494	−	0.373838i	$-0.121958\pi$
$242$	1.08646	−	4.05474i	0.0698405	−	0.260648i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	6.95735			0.445399
$245$	−8.27087	+	8.07655i	−0.528406	+	0.515992i
$246$		−	5.00726i		−	0.319251i
$247$	−11.9885	+	11.9885i	−0.762810	+	0.762810i
$248$	−5.46142	−	1.08302i	−0.346800	−	0.0687719i
$249$		−	10.3253i		−	0.654342i
$250$	11.1732	+	0.398587i	0.706657	+	0.0252089i
$251$	−13.9303	+	8.04264i	−0.879271	+	0.507647i	−0.870418	−	0.492314i	$-0.836151\pi$
$251$	−13.9303	+	8.04264i	−0.879271	+	0.507647i	−0.00885276	+	0.999961i	$0.502818\pi$
$252$	0.956590	+	0.956590i	0.0602595	+	0.0602595i
$253$	−2.17081	−	8.10158i	−0.136478	−	0.509342i
$254$	0.0517998	+	0.0897198i	0.00325021	+	0.00562952i
$255$	7.76399	+	7.95079i	0.486200	+	0.497898i
$256$	1.00000			0.0625000
$257$	19.3815	−	5.19327i	1.20899	−	0.323947i	0.402623	−	0.915366i	$-0.368099\pi$
$257$	19.3815	−	5.19327i	1.20899	−	0.323947i	0.806364	+	0.591419i	$0.201432\pi$
$258$	−1.90246	−	7.10006i	−0.118442	−	0.442030i
$259$	−0.0649882	+	0.112563i	−0.00403817	+	0.00699432i
$260$	7.30986	+	0.0868898i	0.453338	+	0.00538868i
$261$	−4.11994	−	2.37865i	−0.255018	−	0.147234i
$262$	1.97256	−	7.36170i	0.121865	−	0.454807i
$263$	9.60944	+	9.60944i	0.592543	+	0.592543i	0.938318	−	0.345774i	$-0.112384\pi$
$263$	9.60944	+	9.60944i	0.592543	+	0.592543i	−0.345774	+	0.938318i	$0.612384\pi$
$264$			2.60811i			0.160518i
$265$	0.0141609	−	1.19133i	0.000869896	−	0.0731826i
$266$	−3.50781	+	6.07570i	−0.215077	+	0.372525i
$267$	2.28701	−	8.53523i	0.139963	−	0.522348i
$268$	−4.08769	−	15.2555i	−0.249695	−	0.931876i
$269$	−6.89329	+	11.9395i	−0.420291	+	0.727966i	−0.995968	−	0.0897118i	$-0.971405\pi$
$269$	−6.89329	+	11.9395i	−0.420291	+	0.727966i	0.575677	+	0.817677i	$0.304739\pi$
$270$	−0.604368	+	2.15284i	−0.0367807	+	0.131018i
$271$		−	17.5212i		−	1.06434i	−0.846638	−	0.532170i	$-0.821377\pi$
$271$		−	17.5212i		−	1.06434i	0.846638	−	0.532170i	$-0.178623\pi$
$272$	4.80046	+	1.28628i	0.291071	+	0.0779921i
$273$	4.27208	+	1.14470i	0.258558	+	0.0692804i
$274$	−1.45799	+	2.52531i	−0.0880803	+	0.152560i
$275$	6.24998	+	11.4452i	0.376888	+	0.690174i
$276$	−1.60794	−	2.78504i	−0.0967867	−	0.167640i
$277$	−17.8491	+	17.8491i	−1.07245	+	1.07245i	−0.0752867	+	0.997162i	$0.523987\pi$
$277$	−17.8491	+	17.8491i	−1.07245	+	1.07245i	−0.997162	+	0.0752867i	$0.976013\pi$
$278$	10.1379	+	10.1379i	0.608033	+	0.608033i
$279$	−0.367401	−	5.55563i	−0.0219957	−	0.332607i
$280$	2.93103	−	0.748143i	0.175162	−	0.0447101i
$281$	20.8580			1.24428			0.622142	−	0.782904i	$-0.286262\pi$
$281$	20.8580			1.24428			0.622142	+	0.782904i	$0.286262\pi$
$282$	11.7665	+	3.15282i	0.700683	+	0.187747i
$283$	1.93612	−	1.93612i	0.115091	−	0.115091i	−0.647216	−	0.762307i	$-0.724067\pi$
$283$	1.93612	−	1.93612i	0.115091	−	0.115091i	0.762307	+	0.647216i	$0.224067\pi$
$284$	−6.07509	−	3.50746i	−0.360490	−	0.208129i
$285$	−11.5952	−	0.137828i	−0.686842	−	0.00816425i
$286$	4.26335	+	7.38433i	0.252097	+	0.436645i
$287$	−4.78989	−	4.78989i	−0.282738	−	0.282738i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	6.66746	+	3.84946i	0.392203	+	0.226439i
$290$	−9.27502	+	5.20894i	−0.544648	+	0.305879i
$291$	−7.56995	+	4.37051i	−0.443758	+	0.256204i
$292$	2.65449	+	9.90670i	0.155342	+	0.579746i
$293$	17.7399	+	4.75340i	1.03638	+	0.277697i	0.736612	−	0.676316i	$-0.236425\pi$
$293$	17.7399	+	4.75340i	1.03638	+	0.277697i	0.299766	+	0.954013i	$0.403091\pi$
$294$	−5.16987			−0.301513
$295$	−4.79108	−	18.7702i	−0.278948	−	1.09284i
$296$	−0.0832060	+	0.0480390i	−0.00483625	+	0.00279221i
$297$	−2.51924	+	0.675028i	−0.146181	+	0.0391691i
$298$	−4.73177	−	1.26787i	−0.274104	−	0.0734460i
$299$	−9.10513	−	5.25685i	−0.526563	−	0.304011i
$300$	3.45050	+	3.61857i	0.199214	+	0.208918i
$301$	−8.61172	−	4.97198i	−0.496371	−	0.286580i
$302$	16.7683	−	16.7683i	0.964908	−	0.964908i
$303$	−2.68562	+	10.0229i	−0.154285	+	0.575800i
$304$	−4.49113	+	2.59295i	−0.257584	+	0.148716i
$305$	14.9781	+	4.20480i	0.857643	+	0.240766i
$306$			4.96980i			0.284105i
$307$	−4.38125	+	16.3511i	−0.250051	+	0.933204i	0.720726	+	0.693220i	$0.243809\pi$
$307$	−4.38125	+	16.3511i	−0.250051	+	0.933204i	−0.970777	+	0.239984i	$0.922858\pi$
$308$	2.49489	+	2.49489i	0.142160	+	0.142160i
$309$	−0.960464			−0.0546389
$310$	−11.1030	−	5.63228i	−0.630610	−	0.319892i
$311$	−19.7529			−1.12008			−0.560042	−	0.828464i	$-0.689215\pi$
$311$	−19.7529			−1.12008			−0.560042	+	0.828464i	$0.689215\pi$
$312$	2.31175	+	2.31175i	0.130877	+	0.130877i
$313$	0.691255	−	2.57980i	0.0390720	−	0.145819i	−0.943634	−	0.330990i	$-0.892617\pi$
$313$	0.691255	−	2.57980i	0.0390720	−	0.145819i	0.982706	+	0.185171i	$0.0592840\pi$
$314$			12.3483i			0.696857i
$315$	1.48126	+	2.63752i	0.0834594	+	0.148607i
$316$	−5.57488	+	3.21866i	−0.313611	+	0.181064i
$317$	2.43805	−	9.09894i	0.136935	−	0.511047i	−0.863048	−	0.505122i	$-0.831447\pi$
$317$	2.43805	−	9.09894i	0.136935	−	0.511047i	0.999982	−	0.00592490i	$-0.00188596\pi$
$318$	0.376757	−	0.376757i	0.0211275	−	0.0211275i
$319$	−10.7452	−	6.20377i	−0.601618	−	0.347344i
$320$	2.15284	+	0.604368i	0.120348	+	0.0337852i
$321$	−3.11763	−	1.79997i	−0.174009	−	0.100464i
$322$	−4.20228	−	1.12600i	−0.234184	−	0.0627494i
$323$	−24.8947	+	6.67052i	−1.38518	+	0.371158i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	15.6845	+	4.60491i	0.870019	+	0.255434i
$326$	−0.604318			−0.0334701
$327$	−17.9382	−	4.80654i	−0.991987	−	0.265802i
$328$	−1.29597	−	4.83664i	−0.0715582	−	0.267059i
$329$	14.2716	−	8.23973i	0.786821	−	0.454271i
$330$	−1.57626	+	5.61485i	−0.0867701	+	0.309087i
$331$	11.7026	+	6.75651i	0.643234	+	0.371371i	0.785859	−	0.618405i	$-0.212221\pi$
$331$	11.7026	+	6.75651i	0.643234	+	0.371371i	−0.142625	+	0.989777i	$0.545554\pi$
$332$	−2.67240	−	9.97352i	−0.146667	−	0.547368i
$333$	−0.0679374	−	0.0679374i	−0.00372295	−	0.00372295i
$334$	−3.05641	−	5.29386i	−0.167240	−	0.289667i
$335$	0.419755	−	35.3131i	0.0229337	−	1.92936i
$336$	1.17158	+	0.676411i	0.0639148	+	0.0369013i
$337$	−5.86106	+	5.86106i	−0.319272	+	0.319272i	−0.848488	−	0.529215i	$-0.822486\pi$
$337$	−5.86106	+	5.86106i	−0.319272	+	0.319272i	0.529215	+	0.848488i	$0.322486\pi$
$338$	−2.23290	−	0.598304i	−0.121454	−	0.0325434i
$339$	−18.3417			−0.996183
$340$	9.55725	+	5.67040i	0.518315	+	0.307521i
$341$	−0.958222	−	14.4897i	−0.0518906	−	0.784660i
$342$	−3.66699	−	3.66699i	−0.198288	−	0.198288i
$343$	−11.6416	+	11.6416i	−0.628586	+	0.628586i
$344$	−3.67526	−	6.36574i	−0.198157	−	0.343218i
$345$	−1.77846	−	6.96754i	−0.0957492	−	0.375120i
$346$	−3.99878	+	6.92610i	−0.214976	+	0.372349i
$347$	10.0245	+	2.68604i	0.538141	+	0.144194i	0.517645	−	0.855596i	$-0.326809\pi$
$347$	10.0245	+	2.68604i	0.538141	+	0.144194i	0.0204958	+	0.999790i	$0.493476\pi$
$348$	−4.59519	−	1.23128i	−0.246328	−	0.0660034i
$349$		−	4.17104i		−	0.223271i	−0.993749	−	0.111635i	$-0.964391\pi$
$349$		−	4.17104i		−	0.223271i	0.993749	−	0.111635i	$-0.0356089\pi$
$350$	6.76220	+	0.160783i	0.361455	+	0.00859419i
$351$	−1.63465	+	2.83130i	−0.0872512	+	0.151124i
$352$	0.675028	+	2.51924i	0.0359791	+	0.134276i
$353$	5.91165	−	22.0626i	0.314645	−	1.17427i	−0.609674	−	0.792652i	$-0.708700\pi$
$353$	5.91165	−	22.0626i	0.314645	−	1.17427i	0.924319	−	0.381620i	$-0.124634\pi$
$354$	4.33171	−	7.50275i	0.230228	−	0.398766i
$355$	−10.9589	−	11.2226i	−0.581640	−	0.595634i
$356$		−	8.83632i		−	0.468324i
$357$	4.75406	+	4.75406i	0.251612	+	0.251612i
$358$	−4.80163	+	17.9199i	−0.253774	+	0.947098i
$359$	3.55662	+	2.05341i	0.187711	+	0.108375i	0.590911	−	0.806737i	$-0.298769\pi$
$359$	3.55662	+	2.05341i	0.187711	+	0.108375i	−0.403199	+	0.915112i	$0.632102\pi$
$360$	−0.0265775	+	2.23591i	−0.00140076	+	0.117843i
$361$	3.94682	−	6.83609i	0.207727	−	0.359794i
$362$	2.59626	+	9.68937i	0.136456	+	0.509262i
$363$	4.05474	−	1.08646i	0.212818	−	0.0570245i
$364$	4.42278			0.231817
$365$	−0.272583	+	22.9319i	−0.0142677	+	1.20031i
$366$	3.47868	+	6.02524i	0.181833	+	0.314944i
$367$	−2.99970	−	11.1950i	−0.156583	−	0.584376i	−0.998965	−	0.0454943i	$-0.985514\pi$
$367$	−2.99970	−	11.1950i	−0.156583	−	0.584376i	0.842382	−	0.538881i	$-0.181153\pi$
$368$	−2.27397	−	2.27397i	−0.118539	−	0.118539i
$369$	4.33641	−	2.50363i	0.225745	−	0.130334i
$370$	−0.208163	+	0.0531335i	−0.0108219	+	0.00276228i
$371$		−	0.720804i		−	0.0374223i
$372$	−1.79278	−	5.27124i	−0.0929516	−	0.273301i
$373$	6.85892	−	6.85892i	0.355141	−	0.355141i	−0.506877	−	0.862018i	$-0.669200\pi$
$373$	6.85892	−	6.85892i	0.355141	−	0.355141i	0.862018	+	0.506877i	$0.169200\pi$
$374$			12.9618i			0.670238i
$375$	5.24143	+	9.87560i	0.270666	+	0.509974i
$376$	12.1815			0.628215
$377$	−15.0231	+	4.02542i	−0.773727	+	0.207320i
$378$	−0.350136	+	1.30673i	−0.0180091	+	0.0672107i
$379$	15.4432	−	8.91613i	0.793264	−	0.457991i	−0.0478465	−	0.998855i	$-0.515236\pi$
$379$	15.4432	−	8.91613i	0.793264	−	0.457991i	0.841110	+	0.540864i	$0.181903\pi$
$380$	−11.2358	+	2.86793i	−0.576384	+	0.147122i
$381$	−0.0517998	+	0.0897198i	−0.00265378	+	0.00459649i
$382$	−7.38874	+	1.97981i	−0.378041	+	0.101296i
$383$	12.1075	−	3.24420i	0.618665	−	0.165771i	0.0641444	−	0.997941i	$-0.479568\pi$
$383$	12.1075	−	3.24420i	0.618665	−	0.165771i	0.554521	+	0.832170i	$0.312902\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	3.86328	+	6.87894i	0.196891	+	0.350583i
$386$	8.04329	+	13.9314i	0.409393	+	0.709089i
$387$	5.19761	−	5.19761i	0.264209	−	0.264209i
$388$	−6.18084	+	6.18084i	−0.313784	+	0.313784i
$389$	−14.3267	−	24.8145i	−0.726390	−	1.25814i	−0.958399	−	0.285431i	$-0.907863\pi$
$389$	−14.3267	−	24.8145i	−0.726390	−	1.25814i	0.232009	−	0.972714i	$-0.425470\pi$
$390$	3.57968	+	6.37397i	0.181264	+	0.322759i
$391$	−7.99115	−	13.8411i	−0.404130	−	0.699973i
$392$	−4.99371	+	1.33806i	−0.252221	+	0.0675823i
$393$	7.36170	−	1.97256i	0.371348	−	0.0995025i
$394$	3.62080	−	6.27141i	0.182413	−	0.315949i
$395$	−13.9471	+	3.55999i	−0.701755	+	0.179123i
$396$	−2.25869	+	1.30405i	−0.113503	+	0.0655312i
$397$	2.45205	−	9.15117i	0.123065	−	0.459284i	−0.876699	−	0.481040i	$-0.840259\pi$
$397$	2.45205	−	9.15117i	0.123065	−	0.459284i	0.999763	+	0.0217562i	$0.00692577\pi$
$398$	22.2039	−	5.94952i	1.11298	−	0.298222i
$399$	−7.01561			−0.351220
$400$	4.26948	+	2.60222i	0.213474	+	0.130111i
$401$		−	21.3860i		−	1.06796i	−0.845496	−	0.533982i	$-0.820695\pi$
$401$		−	21.3860i		−	1.06796i	0.845496	−	0.533982i	$-0.179305\pi$
$402$	11.1678	−	11.1678i	0.556998	−	0.556998i
$403$	−13.6925	−	11.9939i	−0.682074	−	0.597457i
$404$			10.3765i			0.516248i
$405$	−2.16660	+	0.553024i	−0.107659	+	0.0274800i
$406$	−5.57354	+	3.21788i	−0.276610	+	0.159701i
$407$	−0.177188	−	0.177188i	−0.00878289	−	0.00878289i
$408$	1.28628	+	4.80046i	0.0636803	+	0.237658i
$409$	5.36866	+	9.29879i	0.265463	+	0.459796i	0.967685	−	0.252163i	$-0.0811418\pi$
$409$	5.36866	+	9.29879i	0.265463	+	0.459796i	−0.702222	+	0.711958i	$0.747808\pi$
$410$	0.133080	−	11.1958i	0.00657237	−	0.552920i
$411$	−2.91598			−0.143834
$412$	−0.927737	+	0.248586i	−0.0457063	+	0.0122470i
$413$	−3.03338	−	11.3207i	−0.149263	−	0.557056i
$414$	1.60794	−	2.78504i	0.0790260	−	0.136877i
$415$	0.274422	−	23.0866i	0.0134708	−	1.13327i
$416$	2.83130	+	1.63465i	0.138816	+	0.0801453i
$417$	−3.71074	+	13.8487i	−0.181716	+	0.678173i
$418$	−9.56391	−	9.56391i	−0.467786	−	0.467786i
$419$		−	20.6605i		−	1.00933i	−0.863315	−	0.504665i	$-0.831616\pi$
$419$		−	20.6605i		−	1.00933i	0.863315	−	0.504665i	$-0.168384\pi$
$420$	2.11343	+	2.16427i	0.103125	+	0.105606i
$421$	−16.5096	+	28.5956i	−0.804631	+	1.39366i	0.111909	+	0.993718i	$0.464304\pi$
$421$	−16.5096	+	28.5956i	−0.804631	+	1.39366i	−0.916540	+	0.399943i	$0.869030\pi$
$422$	−2.31890	+	8.65426i	−0.112882	+	0.421283i
$423$	3.15282	+	11.7665i	0.153295	+	0.572105i
$424$	0.266407	−	0.461431i	0.0129379	−	0.0224091i
$425$	17.1483	+	17.9836i	0.831813	+	0.872332i
$426$		−	7.01491i		−	0.339874i
$427$	9.09135	+	2.43602i	0.439961	+	0.117887i
$428$	−3.47727	−	0.931731i	−0.168080	−	0.0450369i
$429$	−4.26335	+	7.38433i	−0.205836	+	0.356519i
$430$	−4.06502	−	15.9257i	−0.196033	−	0.768004i
$431$	7.00684	+	12.1362i	0.337507	+	0.584580i	0.983963	−	0.178371i	$-0.0570829\pi$
$431$	7.00684	+	12.1362i	0.337507	+	0.584580i	−0.646456	+	0.762951i	$0.723750\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	7.83830	+	7.83830i	0.376685	+	0.376685i	0.869905	−	0.493220i	$-0.164180\pi$
$433$	7.83830	+	7.83830i	0.376685	+	0.376685i	−0.493220	+	0.869905i	$0.664180\pi$
$434$	−6.75737	−	3.32745i	−0.324364	−	0.159723i
$435$	−9.14859	−	5.42794i	−0.438641	−	0.260250i
$436$	−18.5710			−0.889391
$437$	16.1090	+	4.31640i	0.770599	+	0.206481i
$438$	−7.25221	+	7.25221i	−0.346524	+	0.346524i
$439$	−22.7975	−	13.1621i	−1.08806	−	0.628194i	−0.155003	−	0.987914i	$-0.549539\pi$
$439$	−22.7975	−	13.1621i	−1.08806	−	0.628194i	−0.933060	+	0.359720i	$0.882872\pi$
$440$	−0.0693170	+	5.83150i	−0.00330456	+	0.278006i
$441$	−2.58494	−	4.47724i	−0.123092	−	0.213202i
$442$	11.4889	+	11.4889i	0.546472	+	0.546472i
$443$	2.87359	+	10.7244i	0.136528	+	0.509531i	0.999987	+	0.00511119i	$0.00162695\pi$
$443$	2.87359	+	10.7244i	0.136528	+	0.509531i	−0.863458	+	0.504420i	$0.831706\pi$
$444$	−0.0832060	−	0.0480390i	−0.00394878	−	0.00227983i
$445$	5.34039	−	19.0232i	0.253159	−	0.901787i
$446$	−2.27131	+	1.31134i	−0.107549	+	0.0620937i
$447$	−1.26787	−	4.73177i	−0.0599684	−	0.223805i
$448$	1.30673	+	0.350136i	0.0617370	+	0.0165424i
$449$	−25.0119			−1.18038			−0.590192	−	0.807263i	$-0.700948\pi$
$449$	−25.0119			−1.18038			−0.590192	+	0.807263i	$0.700948\pi$
$450$	−1.40853	+	4.79750i	−0.0663987	+	0.226157i
$451$	11.3098	−	6.52974i	0.532559	−	0.307473i
$452$	−17.7167	+	4.74718i	−0.833323	+	0.223288i
$453$	22.9059	+	6.13763i	1.07621	+	0.288371i
$454$	−21.5442	−	12.4386i	−1.01112	−	0.583770i
$455$	9.52157	+	2.67299i	0.446378	+	0.125312i
$456$	−4.49113	−	2.59295i	−0.210316	−	0.121426i
$457$	19.2857	−	19.2857i	0.902145	−	0.902145i	−0.0934762	−	0.995622i	$-0.529798\pi$
$457$	19.2857	−	19.2857i	0.902145	−	0.902145i	0.995622	+	0.0934762i	$0.0297979\pi$
$458$	1.73830	−	6.48742i	0.0812253	−	0.303137i
$459$	−4.30397	+	2.48490i	−0.200892	+	0.115985i
$460$	−3.52119	−	6.26983i	−0.164177	−	0.292332i
$461$		−	14.5911i		−	0.679576i	−0.940502	−	0.339788i	$-0.889645\pi$
$461$		−	14.5911i		−	0.679576i	0.940502	−	0.339788i	$-0.110355\pi$
$462$	−0.913193	+	3.40808i	−0.0424856	+	0.158558i
$463$	21.4207	+	21.4207i	0.995504	+	0.995504i	0.999990	−	0.00448620i	$-0.00142801\pi$
$463$	21.4207	+	21.4207i	0.995504	+	0.995504i	−0.00448620	+	0.999990i	$0.501428\pi$
$464$	−4.75729			−0.220852
$465$	−0.673821	−	12.4317i	−0.0312477	−	0.576504i
$466$	−1.17461			−0.0544126
$467$	17.8217	+	17.8217i	0.824692	+	0.824692i	0.986777	−	0.162085i	$-0.0518218\pi$
$467$	17.8217	+	17.8217i	0.824692	+	0.824692i	−0.162085	+	0.986777i	$0.551822\pi$
$468$	−0.846157	+	3.15790i	−0.0391136	+	0.145974i
$469$		−	21.3660i		−	0.986589i
$470$	26.2250	+	7.36213i	1.20967	+	0.339590i
$471$	−10.6940	+	6.17417i	−0.492752	+	0.284491i
$472$	2.24226	−	8.36823i	0.103208	−	0.385179i
$473$	13.5559	−	13.5559i	0.623302	−	0.623302i
$474$	−5.57488	−	3.21866i	−0.256063	−	0.147838i
$475$	−25.9222	−	0.616344i	−1.18939	−	0.0282798i
$476$	5.82251	+	3.36163i	0.266874	+	0.154080i
$477$	0.514660	+	0.137903i	0.0235646	+	0.00631413i
$478$	3.53535	−	0.947295i	0.161703	−	0.0433283i
$479$	−1.96810	+	1.13628i	−0.0899247	+	0.0519180i	−0.544288	−	0.838898i	$-0.683200\pi$
$479$	−1.96810	+	1.13628i	−0.0899247	+	0.0519180i	0.454363	+	0.890816i	$0.349867\pi$
$480$	0.553024	+	2.16660i	0.0252420	+	0.0988914i
$481$	−0.314108			−0.0143221
$482$	29.6951	+	7.95677i	1.35257	+	0.362421i
$483$	−1.12600	−	4.20228i	−0.0512347	−	0.191210i
$484$	3.63538	−	2.09889i	0.165244	−	0.0954039i
$485$	−17.0419	+	9.57088i	−0.773832	+	0.434591i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−6.29628	−	23.4980i	−0.285312	−	1.06480i	−0.948611	−	0.316444i	$-0.897511\pi$
$487$	−6.29628	−	23.4980i	−0.285312	−	1.06480i	0.663300	−	0.748354i	$-0.269156\pi$
$488$	4.91959	+	4.91959i	0.222699	+	0.222699i
$489$	−0.302159	−	0.523355i	−0.0136641	−	0.0236669i
$490$	−11.5594	−	0.137402i	−0.522199	−	0.00620720i
$491$	−29.7940	−	17.2016i	−1.34458	−	0.776296i	−0.357107	−	0.934063i	$-0.616237\pi$
$491$	−29.7940	−	17.2016i	−1.34458	−	0.776296i	−0.987476	+	0.157768i	$0.949570\pi$
$492$	3.54067	−	3.54067i	0.159626	−	0.159626i
$493$	−22.8372	−	6.11920i	−1.02853	−	0.275595i
$494$	−16.9543			−0.762810
$495$	−5.65073	+	1.44235i	−0.253982	+	0.0648287i
$496$	−3.09599	−	4.62762i	−0.139014	−	0.207786i
$497$	−6.71039	−	6.71039i	−0.301002	−	0.301002i
$498$	7.30112	−	7.30112i	0.327171	−	0.327171i
$499$	19.4720	+	33.7266i	0.871688	+	1.50981i	0.860249	+	0.509874i	$0.170308\pi$
$499$	19.4720	+	33.7266i	0.871688	+	1.50981i	0.0114392	+	0.999935i	$0.496359\pi$
$500$	7.61882	+	8.18251i	0.340724	+	0.365933i
$501$	3.05641	−	5.29386i	0.136551	−	0.236512i
$502$	−15.5372	−	4.16318i	−0.693459	−	0.185812i
$503$	10.8328	+	2.90265i	0.483012	+	0.129423i	0.492105	−	0.870536i	$-0.336228\pi$
$503$	10.8328	+	2.90265i	0.483012	+	0.129423i	−0.00909303	+	0.999959i	$0.502894\pi$
$504$			1.35282i			0.0602595i
$505$	−6.27120	+	22.3389i	−0.279065	+	0.994068i
$506$	4.19369	−	7.26368i	0.186432	−	0.322910i
$507$	−0.598304	−	2.23290i	−0.0265716	−	0.0991666i
$508$	−0.0268135	+	0.100069i	−0.00118966	+	0.00443986i
$509$	9.16488	−	15.8740i	0.406226	−	0.703604i	−0.588237	−	0.808688i	$-0.700178\pi$
$509$	9.16488	−	15.8740i	0.406226	−	0.703604i	0.994463	+	0.105084i	$0.0335112\pi$
$510$	−0.132085	+	11.1120i	−0.00584882	+	0.492049i
$511$			13.8748i			0.613784i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.34221	−	5.00920i	0.0592601	−	0.221162i
$514$	17.3770	+	10.0326i	0.766467	+	0.442520i
$515$	−2.14751	−	0.0255267i	−0.0946307	−	0.00112484i
$516$	3.67526	−	6.36574i	0.161794	−	0.280236i
$517$	8.22288	+	30.6882i	0.361642	+	1.34967i
$518$	−0.125548	+	0.0336404i	−0.00551625	+	0.00147807i
$519$	−7.99757			−0.351054
$520$	5.10741	+	5.23029i	0.223975	+	0.229364i
$521$	0.693498	+	1.20117i	0.0303827	+	0.0526243i	0.880817	−	0.473457i	$-0.156994\pi$
$521$	0.693498	+	1.20117i	0.0303827	+	0.0526243i	−0.850434	+	0.526081i	$0.823661\pi$
$522$	−1.23128	−	4.59519i	−0.0538916	−	0.201126i
$523$	−8.06243	−	8.06243i	−0.352546	−	0.352546i	0.508510	−	0.861056i	$-0.330196\pi$
$523$	−8.06243	−	8.06243i	−0.352546	−	0.352546i	−0.861056	+	0.508510i	$0.830196\pi$
$524$	6.60032	−	3.81069i	0.288336	−	0.166471i
$525$	3.24186	+	5.93663i	0.141486	+	0.259096i
$526$			13.5898i			0.592543i
$527$	−8.90978	−	26.1970i	−0.388116	−	1.14116i
$528$	−1.84421	+	1.84421i	−0.0802590	+	0.0802590i
$529$		−	12.6581i		−	0.550352i
$530$	0.852408	−	0.832382i	0.0370262	−	0.0361563i
$531$	8.66343			0.375961
$532$	−6.77656	+	1.81577i	−0.293801	+	0.0787238i
$533$	4.23693	−	15.8124i	0.183522	−	0.684913i
$534$	7.65248	−	4.41816i	0.331155	−	0.191192i
$535$	−6.92291	−	4.10742i	−0.299303	−	0.177579i
$536$	7.89681	−	13.6777i	0.341090	−	0.590786i
$537$	−17.9199	+	4.80163i	−0.773302	+	0.207206i
$538$	−13.3168	+	3.56823i	−0.574128	+	0.153837i
$539$	−6.74179	−	11.6771i	−0.290390	−	0.502969i
$540$	−1.94964	+	1.09494i	−0.0838993	+	0.0471186i
$541$	12.2689	+	21.2503i	0.527481	+	0.913624i	0.999487	+	0.0320285i	$0.0101967\pi$
$541$	12.2689	+	21.2503i	0.527481	+	0.913624i	−0.472006	+	0.881595i	$0.656470\pi$
$542$	12.3894	−	12.3894i	0.532170	−	0.532170i
$543$	−7.09311	+	7.09311i	−0.304395	+	0.304395i
$544$	2.48490	+	4.30397i	0.106539	+	0.184531i
$545$	−39.9805	−	11.2237i	−1.71258	−	0.480772i
$546$	2.21139	+	3.83024i	0.0946388	+	0.163919i
$547$	−29.1907	+	7.82162i	−1.24810	+	0.334428i	−0.821604	−	0.570059i	$-0.806920\pi$
$547$	−29.1907	+	7.82162i	−1.24810	+	0.334428i	−0.426500	+	0.904487i	$0.640254\pi$
$548$	−2.81662	+	0.754710i	−0.120320	+	0.0322396i
$549$	−3.47868	+	6.02524i	−0.148466	+	0.257151i
$550$	−3.67360	+	12.5124i	−0.156643	+	0.533531i
$551$	21.3656	−	12.3354i	0.910205	−	0.525507i
$552$	0.832332	−	3.10631i	0.0354264	−	0.132213i
$553$	−8.41181	+	2.25394i	−0.357706	+	0.0958472i
$554$	−25.2424			−1.07245
$555$	−0.150096	−	0.153708i	−0.00637124	−	0.00652452i
$556$			14.3372i			0.608033i
$557$	15.4697	−	15.4697i	0.655472	−	0.655472i	−0.298833	−	0.954305i	$-0.596598\pi$
$557$	15.4697	−	15.4697i	0.655472	−	0.655472i	0.954305	+	0.298833i	$0.0965975\pi$
$558$	3.66863	−	4.18822i	0.155306	−	0.177301i
$559$		−	24.0311i		−	1.01641i
$560$	2.60157	+	1.54353i	0.109936	+	0.0652261i
$561$	−11.2252	+	6.48089i	−0.473929	+	0.273623i
$562$	14.7488	+	14.7488i	0.622142	+	0.622142i
$563$	4.11193	+	15.3459i	0.173297	+	0.646754i	0.996835	+	0.0794932i	$0.0253302\pi$
$563$	4.11193	+	15.3459i	0.173297	+	0.646754i	−0.823538	+	0.567261i	$0.808003\pi$
$564$	6.09077	+	10.5495i	0.256468	+	0.444215i
$565$	−41.0103	−	0.487476i	−1.72532	−	0.0205083i
$566$	2.73809			0.115091
$567$	−1.30673	+	0.350136i	−0.0548773	+	0.0147043i
$568$	−1.81559	−	6.77589i	−0.0761806	−	0.284310i
$569$	−10.3330	+	17.8973i	−0.433182	+	0.750294i	−0.997145	−	0.0755063i	$-0.975943\pi$
$569$	−10.3330	+	17.8973i	−0.433182	+	0.750294i	0.563963	+	0.825800i	$0.309276\pi$
$570$	−8.10160	−	8.29652i	−0.339339	−	0.347503i
$571$	−25.5899	−	14.7743i	−1.07091	−	0.618287i	−0.142476	−	0.989798i	$-0.545507\pi$
$571$	−25.5899	−	14.7743i	−1.07091	−	0.618287i	−0.928429	+	0.371511i	$0.878840\pi$
$572$	−2.20687	+	8.23615i	−0.0922739	+	0.344371i
$573$	−5.40894	−	5.40894i	−0.225962	−	0.225962i
$574$		−	6.77393i		−	0.282738i
$575$	−3.79130	−	15.6261i	−0.158108	−	0.651652i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	11.9674	−	44.6629i	0.498209	−	1.85934i	−0.0130511	−	0.999915i	$-0.504154\pi$
$577$	11.9674	−	44.6629i	0.498209	−	1.85934i	0.511260	−	0.859426i	$-0.329179\pi$
$578$	1.99263	+	7.43658i	0.0828823	+	0.309321i
$579$	−8.04329	+	13.9314i	−0.334268	+	0.578969i
$580$	−10.2417	−	2.87515i	−0.425264	−	0.119384i
$581$		−	13.9684i		−	0.579505i
$582$	−8.44318	−	2.26234i	−0.349981	−	0.0937771i
$583$	1.34229	+	0.359665i	0.0555919	+	0.0148958i
$584$	−5.12808	+	8.88210i	−0.212202	+	0.367544i
$585$	−3.73018	+	6.28708i	−0.154224	+	0.259939i
$586$	9.18286	+	15.9052i	0.379341	+	0.657037i
$587$	23.9869	−	23.9869i	0.990045	−	0.990045i	−0.00990560	−	0.999951i	$-0.503153\pi$
$587$	23.9869	−	23.9869i	0.990045	−	0.990045i	0.999951	+	0.00990560i	$0.00315310\pi$
$588$	−3.65565	−	3.65565i	−0.150757	−	0.150757i
$589$	25.9037	+	12.7554i	1.06734	+	0.525579i
$590$	9.88472	−	16.6603i	0.406948	−	0.685895i
$591$	7.24160			0.297880
$592$	−0.0928042	−	0.0248668i	−0.00381423	−	0.00102202i
$593$	−10.6593	+	10.6593i	−0.437727	+	0.437727i	−0.891246	−	0.453520i	$-0.850168\pi$
$593$	−10.6593	+	10.6593i	−0.437727	+	0.437727i	0.453520	+	0.891246i	$0.350168\pi$
$594$	−2.25869	−	1.30405i	−0.0926751	−	0.0535060i
$595$	10.5033	+	10.7560i	0.430593	+	0.440953i
$596$	−2.44934	−	4.24239i	−0.100329	−	0.173775i
$597$	16.2544	+	16.2544i	0.665247	+	0.665247i
$598$	−2.72114	−	10.1554i	−0.111276	−	0.415287i
$599$	34.0792	+	19.6757i	1.39244	+	0.803926i	0.993585	−	0.113088i	$-0.0360743\pi$
$599$	34.0792	+	19.6757i	1.39244	+	0.803926i	0.398855	+	0.917014i	$0.369408\pi$
$600$	−0.118850	+	4.99859i	−0.00485202	+	0.204066i
$601$	−18.5869	+	10.7312i	−0.758176	+	0.437733i	−0.828641	−	0.559781i	$-0.810885\pi$
$601$	−18.5869	+	10.7312i	−0.758176	+	0.437733i	0.0704644	+	0.997514i	$0.477552\pi$
$602$	−2.57368	−	9.60512i	−0.104896	−	0.391475i
$603$	15.2555	+	4.08769i	0.621251	+	0.166464i
$604$	23.7140			0.964908
$605$	9.09490	−	2.32147i	0.369760	−	0.0943812i
$606$	−8.98628	+	5.18823i	−0.365042	+	0.210757i
$607$	−35.7346	+	9.57505i	−1.45042	+	0.388639i	−0.896171	−	0.443710i	$-0.853662\pi$
$607$	−35.7346	+	9.57505i	−1.45042	+	0.388639i	−0.554252	+	0.832349i	$0.686995\pi$
$608$	−5.00920	−	1.34221i	−0.203150	−	0.0544339i
$609$	−5.57354	−	3.21788i	−0.225851	−	0.130395i
$610$	7.61787	+	13.5644i	0.308439	+	0.549205i
$611$	34.4896	+	19.9126i	1.39530	+	0.805576i
$612$	−3.51418	+	3.51418i	−0.142052	+	0.142052i
$613$	−5.89122	+	21.9863i	−0.237944	+	0.888020i	0.738855	+	0.673864i	$0.235367\pi$
$613$	−5.89122	+	21.9863i	−0.237944	+	0.888020i	−0.976799	+	0.214156i	$0.931300\pi$
$614$	−14.6600	+	8.46393i	−0.591628	+	0.341576i
$615$	9.76237	−	5.48264i	0.393657	−	0.221081i
$616$			3.52831i			0.142160i
$617$	9.86808	−	36.8282i	0.397274	−	1.48265i	−0.420598	−	0.907247i	$-0.638180\pi$
$617$	9.86808	−	36.8282i	0.397274	−	1.48265i	0.817872	−	0.575400i	$-0.195153\pi$
$618$	−0.679151	−	0.679151i	−0.0273194	−	0.0273194i
$619$	−24.8598			−0.999201			−0.499601	−	0.866256i	$-0.666520\pi$
$619$	−24.8598			−0.999201			−0.499601	+	0.866256i	$0.666520\pi$
$620$	−3.86841	−	11.8337i	−0.155359	−	0.475251i
$621$	3.21588			0.129049
$622$	−13.9674	−	13.9674i	−0.560042	−	0.560042i
$623$	3.09392	−	11.5466i	0.123955	−	0.462607i
$624$			3.26930i			0.130877i
$625$	11.4569	+	22.2203i	0.458276	+	0.888810i
$626$	2.31298	−	1.33540i	0.0924454	−	0.0533734i
$627$	3.50063	−	13.0645i	0.139802	−	0.521748i
$628$	−8.73159	+	8.73159i	−0.348428	+	0.348428i
$629$	−0.413517	−	0.238744i	−0.0164880	−	0.00951936i
$630$	−0.817602	+	2.91242i	−0.0325741	+	0.116033i
$631$	2.74810	+	1.58662i	0.109400	+	0.0631622i	0.553702	−	0.832715i	$-0.313215\pi$
$631$	2.74810	+	1.58662i	0.109400	+	0.0631622i	−0.444302	+	0.895877i	$0.646548\pi$
$632$	−6.21797	−	1.66610i	−0.247338	−	0.0662739i
$633$	−8.65426	+	2.31890i	−0.343976	+	0.0921681i
$634$	8.15788	−	4.70996i	0.323991	−	0.187056i
$635$	−0.118204	+	0.199229i	−0.00469079	+	0.00790615i
$636$	0.532815			0.0211275
$637$	−16.3260	−	4.37453i	−0.646858	−	0.173325i
$638$	−3.21131	−	11.9848i	−0.127137	−	0.474481i
$639$	6.07509	−	3.50746i	0.240327	−	0.138753i
$640$	1.09494	+	1.94964i	0.0432812	+	0.0770664i
$641$	0.631014	+	0.364316i	0.0249236	+	0.0143896i	0.512410	−	0.858741i	$-0.328753\pi$
$641$	0.631014	+	0.364316i	0.0249236	+	0.0143896i	−0.487486	+	0.873131i	$0.662086\pi$
$642$	−0.931731	−	3.47727i	−0.0367725	−	0.137237i
$643$	−9.47401	−	9.47401i	−0.373619	−	0.373619i	0.495175	−	0.868793i	$-0.335104\pi$
$643$	−9.47401	−	9.47401i	−0.373619	−	0.373619i	−0.868793	+	0.495175i	$0.835104\pi$
$644$	−2.17526	−	3.76766i	−0.0857172	−	0.148467i
$645$	11.7595	−	11.4832i	0.463031	−	0.452152i
$646$	−22.3200	−	12.8865i	−0.878169	−	0.507011i
$647$	−10.0649	+	10.0649i	−0.395690	+	0.395690i	−0.876710	−	0.481020i	$-0.840267\pi$
$647$	−10.0649	+	10.0649i	−0.395690	+	0.395690i	0.481020	+	0.876710i	$0.340267\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	22.5952			0.886937
$650$	7.83444	+	14.3468i	0.307292	+	0.562727i
$651$	−0.497029	−	7.51578i	−0.0194801	−	0.294567i
$652$	−0.427317	−	0.427317i	−0.0167350	−	0.0167350i
$653$	15.1427	−	15.1427i	0.592581	−	0.592581i	−0.345747	−	0.938328i	$-0.612374\pi$
$653$	15.1427	−	15.1427i	0.592581	−	0.592581i	0.938328	+	0.345747i	$0.112374\pi$
$654$	−9.28552	−	16.0830i	−0.363092	−	0.628895i
$655$	16.5125	−	4.21481i	0.645197	−	0.164686i
$656$	2.50363	−	4.33641i	0.0977503	−	0.169309i
$657$	−9.90670	−	2.65449i	−0.386497	−	0.103562i
$658$	15.9179	+	4.26520i	0.620546	+	0.166275i
$659$			8.33732i			0.324776i	0.986727	+	0.162388i	$0.0519196\pi$
$659$			8.33732i			0.324776i	−0.986727	+	0.162388i	$0.948080\pi$
$660$	−5.08488	+	2.85572i	−0.197929	+	0.111159i
$661$	−20.7925	+	36.0137i	−0.808735	+	1.40077i	0.105006	+	0.994472i	$0.466514\pi$
$661$	−20.7925	+	36.0137i	−0.808735	+	1.40077i	−0.913741	+	0.406298i	$0.866820\pi$
$662$	3.49743	+	13.0526i	0.135931	+	0.507303i
$663$	−4.20523	+	15.6941i	−0.163318	+	0.609510i
$664$	5.16267	−	8.94201i	0.200351	−	0.347017i
$665$	−15.6863	−	0.186457i	−0.608288	−	0.00723051i
$666$		−	0.0960780i		−	0.00372295i
$667$	10.8180	+	10.8180i	0.418873	+	0.418873i
$668$	1.58212	−	5.90454i	0.0612139	−	0.228453i
$669$	−2.27131	−	1.31134i	−0.0878138	−	0.0506993i
$670$	25.2670	−	24.6733i	0.976148	−	0.953214i
$671$	−9.07276	+	15.7145i	−0.350250	+	0.606651i
$672$	0.350136	+	1.30673i	0.0135068	+	0.0504080i
$673$	−24.2814	+	6.50617i	−0.935978	+	0.250794i	−0.694402	−	0.719587i	$-0.744331\pi$
$673$	−24.2814	+	6.50617i	−0.935978	+	0.250794i	−0.241576	+	0.970382i	$0.577664\pi$
$674$	−8.28879			−0.319272
$675$	−4.85903	+	1.17893i	−0.187024	+	0.0453770i
$676$	−1.15583	−	2.00196i	−0.0444552	−	0.0769986i
$677$	−8.94245	−	33.3737i	−0.343686	−	1.28265i	−0.894139	−	0.447789i	$-0.852212\pi$
$677$	−8.94245	−	33.3737i	−0.343686	−	1.28265i	0.550453	−	0.834866i	$-0.314455\pi$
$678$	−12.9695	−	12.9695i	−0.498092	−	0.498092i
$679$	−10.2408	+	5.91252i	−0.393006	+	0.226902i
$680$	2.74842	+	10.7676i	0.105397	+	0.412918i
$681$		−	24.8771i		−	0.953293i
$682$	9.56819	−	10.9233i	0.366385	−	0.418275i
$683$	−0.761394	+	0.761394i	−0.0291339	+	0.0291339i	−0.721524	−	0.692390i	$-0.756558\pi$
$683$	−0.761394	+	0.761394i	−0.0291339	+	0.0291339i	0.692390	+	0.721524i	$0.256558\pi$
$684$		−	5.18591i		−	0.198288i
$685$	−6.51986	−	0.0774993i	−0.249111	−	0.00296110i
$686$	−16.4637			−0.628586
$687$	6.48742	−	1.73830i	0.247510	−	0.0663202i
$688$	1.90246	−	7.10006i	0.0725304	−	0.270687i
$689$	1.50856	−	0.870966i	0.0574715	−	0.0331812i
$690$	3.66923	−	6.18436i	0.139685	−	0.235434i
$691$	−15.8716	+	27.4904i	−0.603785	+	1.04579i	0.388458	+	0.921467i	$0.373008\pi$
$691$	−15.8716	+	27.4904i	−0.603785	+	1.04579i	−0.992242	+	0.124319i	$0.960325\pi$
$692$	−7.72506	+	2.06992i	−0.293663	+	0.0786867i
$693$	−3.40808	+	0.913193i	−0.129462	+	0.0346893i
$694$	5.18904	+	8.98768i	0.196973	+	0.341168i
$695$	−8.66495	+	30.8658i	−0.328680	+	1.17081i
$696$	−2.37865	−	4.11994i	−0.0901623	−	0.156166i
$697$	17.5964	−	17.5964i	0.666511	−	0.666511i
$698$	2.94937	−	2.94937i	0.111635	−	0.111635i
$699$	−0.587303	−	1.01724i	−0.0222138	−	0.0384755i
$700$	4.66791	+	4.89529i	0.176430	+	0.185025i
$701$	−13.7934	−	23.8908i	−0.520969	−	0.902344i	−0.999703	−	0.0243841i	$-0.992238\pi$
$701$	−13.7934	−	23.8908i	−0.520969	−	0.902344i	0.478734	−	0.877960i	$-0.341096\pi$
$702$	−3.15790	+	0.846157i	−0.119187	+	0.0319362i
$703$	0.481274	−	0.128957i	0.0181516	−	0.00486371i
$704$	−1.30405	+	2.25869i	−0.0491484	+	0.0851275i
$705$	6.73669	+	26.3926i	0.253718	+	0.994001i
$706$	19.7808	−	11.4204i	0.744459	−	0.429814i
$707$	−3.63317	+	13.5592i	−0.136640	+	0.509946i
$708$	8.36823	−	2.24226i	0.314497	−	0.0842693i
$709$	−6.20165			−0.232908			−0.116454	−	0.993196i	$-0.537153\pi$
$709$	−6.20165			−0.232908			−0.116454	+	0.993196i	$0.537153\pi$
$710$	0.186439	−	15.6847i	0.00699692	−	0.588637i
$711$		−	6.43732i		−	0.241418i
$712$	6.24822	−	6.24822i	0.234162	−	0.234162i
$713$	−3.48287	+	17.5633i	−0.130434	+	0.657750i
$714$			6.72326i			0.251612i
$715$	−9.72871	+	16.3974i	−0.363833	+	0.613228i
$716$	−16.0666	+	9.27604i	−0.600436	+	0.346662i
$717$	2.58806	+	2.58806i	0.0966528	+	0.0966528i
$718$	1.06293	+	3.96689i	0.0396680	+	0.148043i
$719$	−14.9452	−	25.8859i	−0.557363	−	0.965381i	−0.997715	−	0.0675560i	$-0.978480\pi$
$719$	−14.9452	−	25.8859i	−0.557363	−	0.965381i	0.440353	−	0.897825i	$-0.354853\pi$
$720$	−1.59982	+	1.56223i	−0.0596218	+	0.0582210i
$721$	−1.29934			−0.0483898
$722$	7.62467	−	2.04302i	0.283761	−	0.0760335i
$723$	7.95677	+	29.6951i	0.295915	+	1.10437i
$724$	−5.01559	+	8.68725i	−0.186403	+	0.322859i
$725$	−20.3112	−	12.3795i	−0.754337	−	0.459764i
$726$	3.63538	+	2.09889i	0.134921	+	0.0778970i
$727$	−10.2847	+	38.3832i	−0.381440	+	1.42355i	0.462262	+	0.886743i	$0.347038\pi$
$727$	−10.2847	+	38.3832i	−0.381440	+	1.42355i	−0.843703	+	0.536811i	$0.819629\pi$
$728$	3.12738	+	3.12738i	0.115908	+	0.115908i
$729$		−	1.00000i		−	0.0370370i
$730$	−16.4080	+	16.0225i	−0.607288	+	0.593021i
$731$	18.2653	−	31.6365i	0.675567	−	1.17012i
$732$	−1.80069	+	6.72028i	−0.0665556	+	0.248389i
$733$	3.46713	+	12.9395i	0.128061	+	0.477932i	0.999930	−	0.0118076i	$-0.00375857\pi$
$733$	3.46713	+	12.9395i	0.128061	+	0.477932i	−0.871869	+	0.489739i	$0.837092\pi$
$734$	5.79497	−	10.0372i	0.213896	−	0.370479i
$735$	−5.66069	−	10.0794i	−0.208798	−	0.371785i
$736$		−	3.21588i		−	0.118539i
$737$	39.7879	+	10.6611i	1.46561	+	0.392708i
$738$	4.83664	+	1.29597i	0.178039	+	0.0477055i
$739$	7.40071	−	12.8184i	0.272239	−	0.471533i	−0.697195	−	0.716881i	$-0.745569\pi$
$739$	7.40071	−	12.8184i	0.272239	−	0.471533i	0.969435	+	0.245348i	$0.0789024\pi$
$740$	−0.184764	−	0.109622i	−0.00679207	−	0.00402980i
$741$	−8.47715	−	14.6829i	−0.311416	−	0.539388i
$742$	0.509685	−	0.509685i	0.0187111	−	0.0187111i
$743$	−7.64036	−	7.64036i	−0.280298	−	0.280298i	0.552930	−	0.833228i	$-0.313510\pi$
$743$	−7.64036	−	7.64036i	−0.280298	−	0.280298i	−0.833228	+	0.552930i	$0.813510\pi$
$744$	2.45964	−	4.99502i	0.0901746	−	0.183126i
$745$	−2.70909	−	10.6135i	−0.0992535	−	0.388849i
$746$	9.69997			0.355141
$747$	9.97352	+	2.67240i	0.364912	+	0.0977779i
$748$	−9.16536	+	9.16536i	−0.335119	+	0.335119i
$749$	−4.21760	−	2.43503i	−0.154108	−	0.0889742i
$750$	−3.27685	+	10.6894i	−0.119654	+	0.390320i
$751$	6.12064	+	10.6013i	0.223345	+	0.386846i	0.955822	−	0.293947i	$-0.0949689\pi$
$751$	6.12064	+	10.6013i	0.223345	+	0.386846i	−0.732476	+	0.680793i	$0.761636\pi$
$752$	8.61365	+	8.61365i	0.314108	+	0.314108i
$753$	−4.16318	−	15.5372i	−0.151715	−	0.566207i
$754$	−13.4693	−	7.77651i	−0.490523	−	0.283204i
$755$	51.0525	+	14.3320i	1.85799	+	0.521594i
$756$	−1.17158	+	0.676411i	−0.0426099	+	0.0246008i
$757$	7.23148	+	26.9883i	0.262833	+	0.980905i	0.963564	+	0.267479i	$0.0861907\pi$
$757$	7.23148	+	26.9883i	0.262833	+	0.980905i	−0.700731	+	0.713426i	$0.747143\pi$
$758$	17.2246	+	4.61533i	0.625627	+	0.167636i
$759$	8.38737			0.304442
$760$	−9.97284	−	5.91697i	−0.361753	−	0.214631i
$761$	31.6256	−	18.2590i	1.14643	−	0.661890i	0.198413	−	0.980118i	$-0.436421\pi$
$761$	31.6256	−	18.2590i	1.14643	−	0.661890i	0.948014	+	0.318229i	$0.103088\pi$
$762$	−0.100069	+	0.0268135i	−0.00362513	+	0.000971352i
$763$	−24.2673	−	6.50239i	−0.878533	−	0.235402i
$764$	−6.62457	−	3.82470i	−0.239668	−	0.138373i
$765$	−9.68934	+	5.44162i	−0.350319	+	0.196742i
$766$	10.8553	+	6.26731i	0.392218	+	0.226447i
$767$	20.0276	−	20.0276i	0.723156	−	0.723156i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	43.7445	−	25.2559i	1.57747	−	0.910750i	0.582254	−	0.813007i	$-0.302171\pi$
$769$	43.7445	−	25.2559i	1.57747	−	0.910750i	0.995212	−	0.0977432i	$-0.0311624\pi$
$770$	−2.13240	+	7.59590i	−0.0768462	+	0.273737i
$771$			20.0652i			0.722632i
$772$	−4.16351	+	15.5384i	−0.149848	+	0.559241i
$773$	2.14840	+	2.14840i	0.0772727	+	0.0772727i	0.744687	−	0.667414i	$-0.232599\pi$
$773$	2.14840	+	2.14840i	0.0772727	+	0.0772727i	−0.667414	+	0.744687i	$0.732599\pi$
$774$	7.35052			0.264209
$775$	−1.17620	−	27.8140i	−0.0422504	−	0.999107i
$776$	−8.74102			−0.313784
$777$	−0.0919073	−	0.0919073i	−0.00329715	−	0.00329715i
$778$	7.41602	−	27.6770i	0.265877	−	0.992267i
$779$			25.9672i			0.930371i
$780$	−1.97586	+	7.03830i	−0.0707472	+	0.252011i
$781$	15.8445	−	9.14783i	0.566961	−	0.327335i
$782$	4.13652	−	15.4377i	0.147922	−	0.552052i
$783$	3.36391	−	3.36391i	0.120216	−	0.120216i
$784$	−4.47724	−	2.58494i	−0.159901	−	0.0923191i
$785$	−24.0748	+	13.5207i	−0.859268	+	0.482573i
$786$	6.60032	+	3.81069i	0.235425	+	0.135923i
$787$	13.4817	+	3.61240i	0.480569	+	0.128768i	0.490968	−	0.871178i	$-0.336643\pi$
$787$	13.4817	+	3.61240i	0.480569	+	0.128768i	−0.0103986	+	0.999946i	$0.503310\pi$
$788$	6.99485	−	1.87426i	0.249181	−	0.0667679i
$789$	−11.7691	+	6.79490i	−0.418991	+	0.241905i
$790$	−12.3794	−	7.34480i	−0.440439	−	0.261316i
$791$	−24.8130			−0.882250
$792$	−2.51924	−	0.675028i	−0.0895173	−	0.0239861i
$793$	5.88701	+	21.9706i	0.209054	+	0.780200i
$794$	8.20471	−	4.73699i	0.291174	−	0.168110i
$795$	1.14707	+	0.322016i	0.0406823	+	0.0114207i
$796$	19.9075	+	11.4936i	0.705601	+	0.407379i
$797$	−2.26425	−	8.45030i	−0.0802039	−	0.299325i	0.914159	−	0.405356i	$-0.132852\pi$
$797$	−2.26425	−	8.45030i	−0.0802039	−	0.299325i	−0.994363	+	0.106031i	$0.966186\pi$
$798$	−4.96079	−	4.96079i	−0.175610	−	0.175610i
$799$	30.2699	+	52.4290i	1.07087	+	1.85481i
$800$	1.17893	+	4.85903i	0.0416815	+	0.171792i
$801$	7.65248	+	4.41816i	0.270387	+	0.156108i
$802$	15.1222	−	15.1222i	0.533982	−	0.533982i
$803$	−25.8377	−	6.92320i	−0.911794	−	0.244314i
$804$	15.7936			0.556998
$805$	−2.40594	−	9.42584i	−0.0847983	−	0.332217i
$806$	−1.20115	−	18.1630i	−0.0423085	−	0.639765i
$807$	−9.74858	−	9.74858i	−0.343166	−	0.343166i
$808$	−7.33726	+	7.33726i	−0.258124	+	0.258124i
$809$	18.8071	+	32.5749i	0.661224	+	1.14527i	0.980294	+	0.197543i	$0.0632961\pi$
$809$	18.8071	+	32.5749i	0.661224	+	1.14527i	−0.319070	+	0.947731i	$0.603371\pi$
$810$	−1.92307	−	1.14097i	−0.0675697	−	0.0400897i
$811$	−8.41842	+	14.5811i	−0.295611	+	0.512013i	−0.975127	−	0.221648i	$-0.928856\pi$
$811$	−8.41842	+	14.5811i	−0.295611	+	0.512013i	0.679516	+	0.733661i	$0.262190\pi$
$812$	−6.21648	−	1.66570i	−0.218156	−	0.0584546i
$813$	16.9242	+	4.53483i	0.593558	+	0.159043i
$814$		−	0.250582i		−	0.00878289i
$815$	−0.661691	−	1.17821i	−0.0231780	−	0.0412707i
$816$	−2.48490	+	4.30397i	−0.0869889	+	0.150669i
$817$	9.86596	+	36.8203i	0.345166	+	1.28818i
$818$	−2.77902	+	10.3715i	−0.0971663	+	0.362629i
$819$	−2.21139	+	3.83024i	−0.0772723	+	0.133840i
$820$	8.01072	−	7.82251i	0.279746	−	0.273174i
$821$			10.0582i			0.351033i	0.984476	+	0.175517i	$0.0561596\pi$
$821$			10.0582i			0.351033i	−0.984476	+	0.175517i	$0.943840\pi$
$822$	−2.06191	−	2.06191i	−0.0719172	−	0.0719172i
$823$	10.0708	−	37.5846i	0.351045	−	1.31012i	−0.534344	−	0.845267i	$-0.679441\pi$
$823$	10.0708	−	37.5846i	0.351045	−	1.31012i	0.885389	−	0.464850i	$-0.153892\pi$
$824$	−0.831786	−	0.480232i	−0.0289766	−	0.0167297i
$825$	−12.6729	+	3.07478i	−0.441212	+	0.107050i
$826$	5.86004	−	10.1499i	0.203897	−	0.353160i
$827$	6.65550	+	24.8387i	0.231434	+	0.863725i	0.979724	+	0.200353i	$0.0642088\pi$
$827$	6.65550	+	24.8387i	0.231434	+	0.863725i	−0.748289	+	0.663372i	$0.769125\pi$
$828$	3.10631	−	0.832332i	0.107952	−	0.0289255i
$829$	27.2935			0.947944			0.473972	−	0.880540i	$-0.342820\pi$
$829$	27.2935			0.947944			0.473972	+	0.880540i	$0.342820\pi$
$830$	16.5187	−	16.1306i	0.573373	−	0.559902i
$831$	−12.6212	−	21.8606i	−0.437825	−	0.758336i
$832$	0.846157	+	3.15790i	0.0293352	+	0.109481i
$833$	−18.1679	−	18.1679i	−0.629479	−	0.629479i
$834$	−12.4164	+	7.16860i	−0.429944	+	0.248228i
$835$	6.97456	−	11.7554i	0.241365	−	0.406811i
$836$		−	13.5254i		−	0.467786i
$837$	5.46142	+	1.08302i	0.188774	+	0.0374347i
$838$	14.6092	−	14.6092i	0.504665	−	0.504665i
$839$			21.9096i			0.756402i	0.925724	+	0.378201i	$0.123457\pi$
$839$			21.9096i			0.756402i	−0.925724	+	0.378201i	$0.876543\pi$
$840$	−0.0359546	+	3.02479i	−0.00124055	+	0.104365i
$841$	−6.36818			−0.219592
$842$	−31.8942	+	8.54602i	−1.09915	+	0.294515i
$843$	−5.39845	+	20.1473i	−0.185933	+	0.693910i
$844$	−7.75920	+	4.47977i	−0.267083	+	0.154200i
$845$	−1.27841	−	5.00847i	−0.0439786	−	0.172296i
$846$	−6.09077	+	10.5495i	−0.209405	+	0.362700i
$847$	5.48534	−	1.46979i	0.188478	−	0.0505026i
$848$	0.514660	−	0.137903i	0.0176735	−	0.00473560i
$849$	1.36905	+	2.37126i	0.0469855	+	0.0813813i
$850$	−0.590660	+	24.8420i	−0.0202595	+	0.852073i
$851$	0.154488	+	0.267581i	0.00529578	+	0.00917255i
$852$	4.96029	−	4.96029i	0.169937	−	0.169937i
$853$	−16.0586	+	16.0586i	−0.549836	+	0.549836i	−0.926393	−	0.376557i	$-0.877108\pi$
$853$	−16.0586	+	16.0586i	−0.549836	+	0.549836i	0.376557	+	0.926393i	$0.377108\pi$
$854$	4.70603	+	8.15108i	0.161037	+	0.278924i
$855$	3.13420	−	11.1645i	0.107187	−	0.381816i
$856$	−1.79997	−	3.11763i	−0.0615216	−	0.106559i
$857$	43.5776	−	11.6766i	1.48858	−	0.398865i	0.579325	−	0.815096i	$-0.303316\pi$
$857$	43.5776	−	11.6766i	1.48858	−	0.398865i	0.909259	+	0.416232i	$0.136649\pi$
$858$	−8.23615	+	2.20687i	−0.281178	+	0.0753413i
$859$	4.76273	−	8.24930i	0.162502	−	0.281462i	−0.773263	−	0.634085i	$-0.781377\pi$
$859$	4.76273	−	8.24930i	0.162502	−	0.281462i	0.935766	+	0.352623i	$0.114710\pi$
$860$	8.38674	−	14.1355i	0.285985	−	0.482018i
$861$	5.86640	−	3.38697i	0.199926	−	0.115427i
$862$	−3.62701	+	13.5362i	−0.123536	+	0.461044i
$863$	−4.61075	+	1.23545i	−0.156952	+	0.0420551i	−0.336439	−	0.941705i	$-0.609223\pi$
$863$	−4.61075	+	1.23545i	−0.156952	+	0.0420551i	0.179488	+	0.983760i	$0.442556\pi$
$864$	−1.00000			−0.0340207
$865$	−17.8818	−	0.212555i	−0.608001	−	0.00722710i
$866$			11.0850i			0.376685i
$867$	−5.44395	+	5.44395i	−0.184886	+	0.184886i
$868$	−2.42532	−	7.13104i	−0.0823207	−	0.242043i
$869$		−	16.7892i		−	0.569535i
$870$	−2.63090	−	10.3072i	−0.0891958	−	0.349445i
$871$	44.7165	−	25.8171i	1.51516	−	0.874778i
$872$	−13.1317	−	13.1317i	−0.444696	−	0.444696i
$873$	−2.26234	−	8.44318i	−0.0765687	−	0.285758i
$874$	8.33864	+	14.4429i	0.282059	+	0.488540i
$875$	7.09072	+	13.3599i	0.239710	+	0.451648i
$876$	−10.2562			−0.346524
$877$	−15.4857	+	4.14939i	−0.522916	+	0.140115i	−0.510615	−	0.859809i	$-0.670582\pi$
$877$	−15.4857	+	4.14939i	−0.522916	+	0.140115i	−0.0123009	+	0.999924i	$0.503916\pi$
$878$	−6.81321	−	25.4273i	−0.229935	−	0.858128i
$879$	−9.18286	+	15.9052i	−0.309730	+	0.536469i
$880$	−4.17250	+	4.07448i	−0.140655	+	0.137351i
$881$	42.0344	+	24.2686i	1.41617	+	0.817629i	0.995960	−	0.0897965i	$-0.0286217\pi$
$881$	42.0344	+	24.2686i	1.41617	+	0.817629i	0.420214	+	0.907425i	$0.361955\pi$
$882$	1.33806	−	4.99371i	0.0450549	−	0.168147i
$883$	19.9330	+	19.9330i	0.670800	+	0.670800i	0.957900	−	0.287101i	$-0.0926915\pi$
$883$	19.9330	+	19.9330i	0.670800	+	0.670800i	−0.287101	+	0.957900i	$0.592691\pi$
$884$			16.2478i			0.546472i
$885$	19.3706	+	0.230252i	0.651137	+	0.00773984i
$886$	−5.55135	+	9.61522i	−0.186501	+	0.323030i
$887$	−4.38445	+	16.3630i	−0.147215	+	0.549415i	0.852431	+	0.522839i	$0.175127\pi$
$887$	−4.38445	+	16.3630i	−0.147215	+	0.549415i	−0.999647	+	0.0265762i	$0.991540\pi$
$888$	−0.0248668	−	0.0928042i	−0.000834476	−	0.00311431i
$889$	−0.0700759	+	0.121375i	−0.00235027	+	0.00407079i
$890$	17.2277	−	9.67522i	0.577473	−	0.324314i
$891$		−	2.60811i		−	0.0873749i
$892$	−2.53331	−	0.678799i	−0.0848216	−	0.0227279i
$893$	−61.0198	−	16.3502i	−2.04195	−	0.547139i
$894$	2.44934	−	4.24239i	0.0819183	−	0.141887i
$895$	−40.1950	+	10.2597i	−1.34357	+	0.342946i
$896$	0.676411	+	1.17158i	0.0225973	+	0.0391397i
$897$	7.43430	−	7.43430i	0.248224	−	0.248224i
$898$	−17.6861	−	17.6861i	−0.590192	−	0.590192i
$899$	14.7285	+	22.0149i	0.491224	+	0.734239i
$900$	−4.38833	+	2.39637i	−0.146278	+	0.0798789i
$901$	2.64798			0.0882171
$902$	12.6145	+	3.38004i	0.420016	+	0.112543i
$903$	7.03144	−	7.03144i	0.233992	−	0.233992i
$904$	−15.8844	−	9.17084i	−0.528306	−	0.305018i
$905$	−16.0481	+	15.6710i	−0.533456	+	0.520923i
$906$	11.8570	+	20.5369i	0.393922	+	0.682293i
$907$	4.57398	+	4.57398i	0.151877	+	0.151877i	0.778956	−	0.627079i	$-0.215750\pi$
$907$	4.57398	+	4.57398i	0.151877	+	0.151877i	−0.627079	+	0.778956i	$0.715750\pi$
$908$	−6.43867	−	24.0294i	−0.213675	−	0.797445i
$909$	−8.98628	−	5.18823i	−0.298056	−	0.172083i
$910$	4.84267	+	8.62285i	0.160533	+	0.285845i
$911$	28.3053	−	16.3421i	0.937795	−	0.541436i	0.0485268	−	0.998822i	$-0.484547\pi$
$911$	28.3053	−	16.3421i	0.937795	−	0.541436i	0.889269	+	0.457386i	$0.151214\pi$
$912$	−1.34221	−	5.00920i	−0.0444451	−	0.165871i
$913$	26.0120	+	6.96990i	0.860872	+	0.230670i
$914$	27.2740			0.902145
$915$	−7.93814	+	13.3794i	−0.262427	+	0.442311i
$916$	5.81646	−	3.35813i	0.192181	−	0.110956i
$917$	9.95907	−	2.66852i	0.328877	−	0.0881224i
$918$	−4.80046	−	1.28628i	−0.158439	−	0.0424535i
$919$	35.4878	+	20.4889i	1.17063	+	0.675866i	0.953829	−	0.300349i	$-0.0971031\pi$
$919$	35.4878	+	20.4889i	1.17063	+	0.675866i	0.216805	+	0.976215i	$0.430436\pi$
$920$	1.94358	−	6.92330i	0.0640778	−	0.228254i
$921$	−14.6600	−	8.46393i	−0.483062	−	0.278896i
$922$	10.3175	−	10.3175i	0.339788	−	0.339788i
$923$	5.93572	−	22.1524i	0.195377	−	0.729155i
$924$	−3.05560	+	1.76415i	−0.100522	+	0.0580364i
$925$	−0.331517	−	0.347665i	−0.0109002	−	0.0114312i
$926$			30.2934i			0.995504i
$927$	0.248586	−	0.927737i	0.00816465	−	0.0304709i
$928$	−3.36391	−	3.36391i	−0.110426	−	0.110426i
$929$	−9.88224			−0.324226			−0.162113	−	0.986772i	$-0.551831\pi$
$929$	−9.88224			−0.324226			−0.162113	+	0.986772i	$0.551831\pi$
$930$	8.31404	−	9.26697i	0.272628	−	0.303876i
$931$	26.8105			0.878678
$932$	−0.830572	−	0.830572i	−0.0272063	−	0.0272063i
$933$	5.11243	−	19.0798i	0.167373	−	0.624646i
$934$			25.2038i			0.824692i
$935$	−25.2708	+	14.1923i	−0.826445	+	0.464139i
$936$	−2.83130	+	1.63465i	−0.0925439	+	0.0534302i
$937$	−12.0945	+	45.1372i	−0.395109	+	1.47457i	0.426485	+	0.904495i	$0.359752\pi$
$937$	−12.0945	+	45.1372i	−0.395109	+	1.47457i	−0.821594	+	0.570073i	$0.806915\pi$
$938$	15.1080	−	15.1080i	0.493294	−	0.493294i
$939$	2.31298	+	1.33540i	0.0754814	+	0.0435792i
$940$	13.3380	+	23.7497i	0.435039	+	0.774629i
$941$	18.4421	+	10.6475i	0.601195	+	0.347100i	0.769511	−	0.638633i	$-0.220500\pi$
$941$	18.4421	+	10.6475i	0.601195	+	0.347100i	−0.168317	+	0.985733i	$0.553833\pi$
$942$	−11.9276	−	3.19598i	−0.388621	−	0.104131i
$943$	−15.5541	+	4.16770i	−0.506510	+	0.135719i
$944$	7.50275	−	4.33171i	0.244194	−	0.140985i
$945$	−2.93103	+	0.748143i	−0.0953463	+	0.0243371i
$946$	19.1710			0.623302
$947$	22.5299	+	6.03687i	0.732124	+	0.196172i	0.605575	−	0.795788i	$-0.292943\pi$
$947$	22.5299	+	6.03687i	0.732124	+	0.196172i	0.126549	+	0.991960i	$0.459610\pi$
$948$	−1.66610	−	6.21797i	−0.0541124	−	0.201950i
$949$	−29.0383	+	16.7653i	−0.942622	+	0.544223i
$950$	−17.8940	−	18.7656i	−0.580556	−	0.608836i
$951$	8.15788	+	4.70996i	0.264538	+	0.152731i
$952$	1.74011	+	6.49417i	0.0563972	+	0.210477i
$953$	16.7755	+	16.7755i	0.543412	+	0.543412i	0.924527	−	0.381116i	$-0.124460\pi$
$953$	16.7755	+	16.7755i	0.543412	+	0.543412i	−0.381116	+	0.924527i	$0.624460\pi$
$954$	0.266407	+	0.461431i	0.00862526	+	0.0149394i
$955$	−11.9501	−	12.2376i	−0.386697	−	0.396001i
$956$	3.16971	+	1.83003i	0.102516	+	0.0591875i
$957$	8.77345	−	8.77345i	0.283605	−	0.283605i
$958$	−2.19513	−	0.588183i	−0.0709214	−	0.0190033i
$959$	−3.94480			−0.127384
$960$	−1.14097	+	1.92307i	−0.0368247	+	0.0620667i
$961$	−11.8296	+	28.6541i	−0.381602	+	0.924327i
$962$	−0.222108	−	0.222108i	−0.00716105	−	0.00716105i
$963$	2.54554	−	2.54554i	0.0820288	−	0.0820288i
$964$	15.3713	+	26.6239i	0.495076	+	0.857497i
$965$	−18.3543	+	30.9355i	−0.590847	+	0.995851i
$966$	2.17526	−	3.76766i	0.0699878	−	0.121222i
$967$	−6.42694	−	1.72209i	−0.206677	−	0.0553788i	0.153995	−	0.988072i	$-0.450786\pi$
$967$	−6.42694	−	1.72209i	−0.206677	−	0.0553788i	−0.360672	+	0.932693i	$0.617453\pi$
$968$	4.05474	+	1.08646i	0.130324	+	0.0349203i
$969$		−	25.7729i		−	0.827946i
$970$	−18.8181	−	5.28279i	−0.604211	−	0.169620i
$971$	2.09147	−	3.62253i	0.0671184	−	0.116253i	−0.830513	−	0.556999i	$-0.811953\pi$
$971$	2.09147	−	3.62253i	0.0671184	−	0.116253i	0.897632	+	0.440746i	$0.145286\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−5.01997	+	18.7348i	−0.160933	+	0.600610i
$974$	12.1635	−	21.0678i	0.389743	−	0.675055i
$975$	−8.50744	+	13.9582i	−0.272456	+	0.447021i
$976$			6.95735i			0.222699i
$977$	32.2616	+	32.2616i	1.03214	+	1.03214i	0.999466	+	0.0326744i	$0.0104024\pi$
$977$	32.2616	+	32.2616i	1.03214	+	1.03214i	0.0326744	+	0.999466i	$0.489598\pi$
$978$	0.156409	−	0.583727i	0.00500141	−	0.0186655i
$979$	19.9585	+	11.5230i	0.637876	+	0.368278i
$980$	−8.07655	−	8.27087i	−0.257996	−	0.264203i
$981$	9.28552	−	16.0830i	0.296464	−	0.513490i
$982$	−8.90418	−	33.2309i	−0.284144	−	1.06044i
$983$	−13.6562	+	3.65917i	−0.435566	+	0.116710i	−0.469938	−	0.882700i	$-0.655724\pi$
$983$	−13.6562	+	3.65917i	−0.435566	+	0.116710i	0.0343718	+	0.999409i	$0.489057\pi$
$984$	5.00726			0.159626
$985$	16.1916	+	0.192464i	0.515906	+	0.00613240i
$986$	−11.8214	−	20.4753i	−0.376470	−	0.652065i
$987$	4.26520	+	15.9179i	0.135763	+	0.506674i
$988$	−11.9885	−	11.9885i	−0.381405	−	0.381405i
$989$	−20.4715	+	11.8192i	−0.650955	+	0.375829i
$990$	−5.01556	−	2.97578i	−0.159405	−	0.0945764i
$991$			46.1993i			1.46757i	0.679382	+	0.733785i	$0.262248\pi$
$991$			46.1993i			1.46757i	−0.679382	+	0.733785i	$0.737752\pi$
$992$	1.08302	−	5.46142i	0.0343859	−	0.173400i
$993$	−9.55515	+	9.55515i	−0.303223	+	0.303223i
$994$		−	9.48993i		−	0.301002i
$995$	35.9113	+	36.7753i	1.13847	+	1.16586i
$996$	10.3253			0.327171
$997$	−13.3893	+	3.58765i	−0.424043	+	0.113622i	−0.464529	−	0.885558i	$-0.653776\pi$
$997$	−13.3893	+	3.58765i	−0.424043	+	0.113622i	0.0404855	+	0.999180i	$0.487110\pi$
$998$	−10.0795	+	37.6171i	−0.319060	+	1.19075i
$999$	0.0832060	−	0.0480390i	0.00263252	−	0.00151989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.11	yes	64
5.3	odd	4		930.2.be.a.223.10	✓	64
31.26	odd	6		930.2.be.a.367.10	yes	64
155.88	even	12	inner	930.2.be.b.553.11	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.10	✓	64	5.3	odd	4
930.2.be.a.367.10	yes	64	31.26	odd	6
930.2.be.b.37.11	yes	64	1.1	even	1	trivial
930.2.be.b.553.11	yes	64	155.88	even	12	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.604368 + 2.15284i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.350136 + 1.30673i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-0.604368 + 2.15284i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.350136 + 1.30673i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.94964 + 1.09494i) q^{10} +(-2.25869 - 1.30405i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-3.15790 + 0.846157i) q^{13} +(-1.17158 + 0.676411i) q^{14} +(-1.92307 - 1.14097i) q^{15} -1.00000 q^{16} +(-4.80046 - 1.28628i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(4.49113 - 2.59295i) q^{19} +(-2.15284 - 0.604368i) q^{20} +(-1.17158 - 0.676411i) q^{21} +(-0.675028 - 2.51924i) q^{22} +(2.27397 + 2.27397i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.26948 - 2.60222i) q^{25} +(-2.83130 - 1.63465i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.30673 - 0.350136i) q^{28} +4.75729 q^{29} +(-0.553024 - 2.16660i) q^{30} +(3.09599 + 4.62762i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.84421 - 1.84421i) q^{33} +(-2.48490 - 4.30397i) q^{34} +(-2.60157 - 1.54353i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.0928042 + 0.0248668i) q^{37} +(5.00920 + 1.34221i) q^{38} -3.26930i q^{39} +(-1.09494 - 1.94964i) q^{40} +(-2.50363 + 4.33641i) q^{41} +(-0.350136 - 1.30673i) q^{42} +(-1.90246 + 7.10006i) q^{43} +(1.30405 - 2.25869i) q^{44} +(1.59982 - 1.56223i) q^{45} +3.21588i q^{46} +(-8.61365 - 8.61365i) q^{47} +(0.258819 - 0.965926i) q^{48} +(4.47724 + 2.58494i) q^{49} +(-1.17893 - 4.85903i) q^{50} +(2.48490 - 4.30397i) q^{51} +(-0.846157 - 3.15790i) q^{52} +(-0.514660 + 0.137903i) q^{53} +1.00000 q^{54} +(4.17250 - 4.07448i) q^{55} +(-0.676411 - 1.17158i) q^{56} +(1.34221 + 5.00920i) q^{57} +(3.36391 + 3.36391i) q^{58} +(-7.50275 + 4.33171i) q^{59} +(1.14097 - 1.92307i) q^{60} -6.95735i q^{61} +(-1.08302 + 5.46142i) q^{62} +(0.956590 - 0.956590i) q^{63} -1.00000i q^{64} +(0.0868898 - 7.30986i) q^{65} +2.60811 q^{66} +(-15.2555 + 4.08769i) q^{67} +(1.28628 - 4.80046i) q^{68} +(-2.78504 + 1.60794i) q^{69} +(-0.748143 - 2.93103i) q^{70} +(-3.50746 + 6.07509i) q^{71} +(0.965926 - 0.258819i) q^{72} +(9.90670 - 2.65449i) q^{73} +(0.0480390 + 0.0832060i) q^{74} +(3.61857 - 3.45050i) q^{75} +(2.59295 + 4.49113i) q^{76} +(2.49489 - 2.49489i) q^{77} +(2.31175 - 2.31175i) q^{78} +(3.21866 + 5.57488i) q^{79} +(0.604368 - 2.15284i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-4.83664 + 1.29597i) q^{82} +(-9.97352 + 2.67240i) q^{83} +(0.676411 - 1.17158i) q^{84} +(5.67040 - 9.55725i) q^{85} +(-6.36574 + 3.67526i) q^{86} +(-1.23128 + 4.59519i) q^{87} +(2.51924 - 0.675028i) q^{88} -8.83632 q^{89} +(2.23591 + 0.0265775i) q^{90} -4.42278i q^{91} +(-2.27397 + 2.27397i) q^{92} +(-5.27124 + 1.79278i) q^{93} -12.1815i q^{94} +(2.86793 + 11.2358i) q^{95} +(0.866025 - 0.500000i) q^{96} +(6.18084 + 6.18084i) q^{97} +(1.33806 + 4.99371i) q^{98} +(1.30405 + 2.25869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

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