LMFDB - Embedded newform 784.2.x.o.557.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.2
Character	$\chi$	$=$	784.557
Dual form			784.2.x.o.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36184 + 0.381311i) q^{2} +(1.60845 - 0.430984i) q^{3} +(1.70920 - 1.03857i) q^{4} +(-1.94900 - 0.522232i) q^{5} +(-2.02612 + 1.20025i) q^{6} +(-1.93164 + 2.06610i) q^{8} +(-0.196696 + 0.113563i) q^{9} +(2.85335 - 0.0319777i) q^{10} +(1.63411 + 6.09856i) q^{11} +(2.30157 - 2.40713i) q^{12} +(-1.13388 - 1.13388i) q^{13} -3.35995 q^{15} +(1.84276 - 3.55024i) q^{16} +(0.960789 - 1.66414i) q^{17} +(0.224566 - 0.229656i) q^{18} +(-1.63324 + 6.09532i) q^{19} +(-3.87361 + 1.13156i) q^{20} +(-4.55083 - 7.68215i) q^{22} +(-0.924606 + 0.533821i) q^{23} +(-2.21651 + 4.15573i) q^{24} +(-0.804265 - 0.464342i) q^{25} +(1.97651 + 1.11180i) q^{26} +(-3.79985 + 3.79985i) q^{27} +(5.08936 + 5.08936i) q^{29} +(4.57570 - 1.28118i) q^{30} +(0.198293 - 0.343454i) q^{31} +(-1.15579 + 5.53752i) q^{32} +(5.25677 + 9.10499i) q^{33} +(-0.673887 + 2.63264i) q^{34} +(-0.218252 + 0.398384i) q^{36} +(0.327303 + 0.0877006i) q^{37} +(-0.100007 - 8.92360i) q^{38} +(-2.31247 - 1.33510i) q^{39} +(4.84375 - 3.01805i) q^{40} +7.26189i q^{41} +(1.75565 - 1.75565i) q^{43} +(9.12678 + 8.72657i) q^{44} +(0.442666 - 0.118612i) q^{45} +(1.05561 - 1.07954i) q^{46} +(1.08118 + 1.87265i) q^{47} +(1.43390 - 6.50461i) q^{48} +(1.27234 + 0.325684i) q^{50} +(0.828170 - 3.09077i) q^{51} +(-3.11563 - 0.760420i) q^{52} +(0.111394 + 0.415727i) q^{53} +(3.72585 - 6.62369i) q^{54} -12.7395i q^{55} +10.5079i q^{57} +(-8.87151 - 4.99025i) q^{58} +(2.32453 + 8.67527i) q^{59} +(-5.74284 + 3.48953i) q^{60} +(2.72673 - 10.1763i) q^{61} +(-0.139080 + 0.543339i) q^{62} +(-0.537512 - 7.98192i) q^{64} +(1.61777 + 2.80206i) q^{65} +(-10.6307 - 10.3951i) q^{66} +(7.87441 - 2.10994i) q^{67} +(-0.0861303 - 3.84219i) q^{68} +(-1.25712 + 1.25712i) q^{69} +2.78982i q^{71} +(0.145316 - 0.625756i) q^{72} +(-2.05730 - 1.18779i) q^{73} +(-0.479175 + 0.00537015i) q^{74} +(-1.49375 - 0.400248i) q^{75} +(3.53886 + 12.1144i) q^{76} +(3.65830 + 0.936427i) q^{78} +(5.10829 + 8.84782i) q^{79} +(-5.44558 + 5.95707i) q^{80} +(-4.13352 + 7.15947i) q^{81} +(-2.76904 - 9.88952i) q^{82} +(-1.17951 - 1.17951i) q^{83} +(-2.74164 + 2.74164i) q^{85} +(-1.72147 + 3.06036i) q^{86} +(10.3794 + 5.99257i) q^{87} +(-15.7567 - 8.40403i) q^{88} +(-11.0470 + 6.37800i) q^{89} +(-0.557612 + 0.330324i) q^{90} +(-1.02593 + 1.87267i) q^{92} +(0.170922 - 0.637891i) q^{93} +(-2.18645 - 2.13799i) q^{94} +(6.36634 - 11.0268i) q^{95} +(0.527542 + 9.40498i) q^{96} +2.21148 q^{97} +(-1.01399 - 1.01399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.36184	+	0.381311i	−0.962965	+	0.269627i
$2$	−1.36184	+	0.381311i	−0.962965	+	0.269627i
$3$	1.60845	−	0.430984i	0.928642	−	0.248829i	0.237366	−	0.971420i	$-0.423716\pi$
$3$	1.60845	−	0.430984i	0.928642	−	0.248829i	0.691275	+	0.722591i	$0.257049\pi$
$4$	1.70920	−	1.03857i	0.854602	−	0.519283i
$5$	−1.94900	−	0.522232i	−0.871618	−	0.233549i	−0.204831	−	0.978797i	$-0.565664\pi$
$5$	−1.94900	−	0.522232i	−0.871618	−	0.233549i	−0.666787	+	0.745248i	$0.732331\pi$
$6$	−2.02612	+	1.20025i	−0.827158	+	0.490001i
$7$		0			0
$7$		0			0
$8$	−1.93164	+	2.06610i	−0.682939	+	0.730476i
$9$	−0.196696	+	0.113563i	−0.0655654	+	0.0378542i
$10$	2.85335	−	0.0319777i	0.902309	−	0.0101122i
$11$	1.63411	+	6.09856i	0.492701	+	1.83879i	0.542542	+	0.840029i	$0.317462\pi$
$11$	1.63411	+	6.09856i	0.492701	+	1.83879i	−0.0498403	+	0.998757i	$0.515871\pi$
$12$	2.30157	−	2.40713i	0.664407	−	0.694878i
$13$	−1.13388	−	1.13388i	−0.314480	−	0.314480i	0.532162	−	0.846642i	$-0.321380\pi$
$13$	−1.13388	−	1.13388i	−0.314480	−	0.314480i	−0.846642	+	0.532162i	$0.821380\pi$
$14$		0			0
$15$	−3.35995			−0.867535
$16$	1.84276	−	3.55024i	0.460690	−	0.887561i
$17$	0.960789	−	1.66414i	0.233026	−	0.403612i	−0.725671	−	0.688041i	$-0.758471\pi$
$17$	0.960789	−	1.66414i	0.233026	−	0.403612i	0.958697	+	0.284429i	$0.0918041\pi$
$18$	0.224566	−	0.229656i	0.0529307	−	0.0541305i
$19$	−1.63324	+	6.09532i	−0.374690	+	1.39836i	0.479107	+	0.877756i	$0.340960\pi$
$19$	−1.63324	+	6.09532i	−0.374690	+	1.39836i	−0.853797	+	0.520605i	$0.825706\pi$
$20$	−3.87361	+	1.13156i	−0.866165	+	0.253025i
$21$		0			0
$22$	−4.55083	−	7.68215i	−0.970241	−	1.63784i
$23$	−0.924606	+	0.533821i	−0.192794	+	0.111309i	−0.593290	−	0.804989i	$-0.702171\pi$
$23$	−0.924606	+	0.533821i	−0.192794	+	0.111309i	0.400496	+	0.916298i	$0.368838\pi$
$24$	−2.21651	+	4.15573i	−0.452442	+	0.848285i
$25$	−0.804265	−	0.464342i	−0.160853	−	0.0928685i
$26$	1.97651	+	1.11180i	0.387626	+	0.218041i
$27$	−3.79985	+	3.79985i	−0.731281	+	0.731281i
$28$		0			0
$29$	5.08936	+	5.08936i	0.945070	+	0.945070i	0.998568	−	0.0534979i	$-0.0170370\pi$
$29$	5.08936	+	5.08936i	0.945070	+	0.945070i	−0.0534979	+	0.998568i	$0.517037\pi$
$30$	4.57570	−	1.28118i	0.835405	−	0.233911i
$31$	0.198293	−	0.343454i	0.0356145	−	0.0616861i	−0.847669	−	0.530526i	$-0.821994\pi$
$31$	0.198293	−	0.343454i	0.0356145	−	0.0616861i	0.883283	+	0.468840i	$0.155328\pi$
$32$	−1.15579	+	5.53752i	−0.204317	+	0.978905i
$33$	5.25677	+	9.10499i	0.915086	+	1.58498i
$34$	−0.673887	+	2.63264i	−0.115571	+	0.451494i
$35$		0			0
$36$	−0.218252	+	0.398384i	−0.0363753	+	0.0663973i
$37$	0.327303	+	0.0877006i	0.0538083	+	0.0144179i	0.285623	−	0.958342i	$-0.407800\pi$
$37$	0.327303	+	0.0877006i	0.0538083	+	0.0144179i	−0.231814	+	0.972760i	$0.574466\pi$
$38$	−0.100007	−	8.92360i	−0.0162234	−	1.44760i
$39$	−2.31247	−	1.33510i	−0.370291	−	0.213788i
$40$	4.84375	−	3.01805i	0.765864	−	0.477196i
$41$			7.26189i			1.13412i	0.823678	+	0.567058i	$0.191919\pi$
$41$			7.26189i			1.13412i	−0.823678	+	0.567058i	$0.808081\pi$
$42$		0			0
$43$	1.75565	−	1.75565i	0.267734	−	0.267734i	−0.560452	−	0.828187i	$-0.689373\pi$
$43$	1.75565	−	1.75565i	0.267734	−	0.267734i	0.828187	+	0.560452i	$0.189373\pi$
$44$	9.12678	+	8.72657i	1.37591	+	1.31558i
$45$	0.442666	−	0.118612i	0.0659888	−	0.0176816i
$46$	1.05561	−	1.07954i	0.155641	−	0.159170i
$47$	1.08118	+	1.87265i	0.157706	+	0.273155i	0.934041	−	0.357166i	$-0.116257\pi$
$47$	1.08118	+	1.87265i	0.157706	+	0.273155i	−0.776335	+	0.630320i	$0.782924\pi$
$48$	1.43390	−	6.50461i	0.206965	−	0.938859i
$49$		0			0
$50$	1.27234	+	0.325684i	0.179936	+	0.0460587i
$51$	0.828170	−	3.09077i	0.115967	−	0.432795i
$52$	−3.11563	−	0.760420i	−0.432060	−	0.105451i
$53$	0.111394	+	0.415727i	0.0153011	+	0.0571045i	0.973154	−	0.230154i	$-0.0739229\pi$
$53$	0.111394	+	0.415727i	0.0153011	+	0.0571045i	−0.957853	+	0.287258i	$0.907256\pi$
$54$	3.72585	−	6.62369i	0.507024	−	0.901371i
$55$		−	12.7395i		−	1.71779i
$56$		0			0
$57$			10.5079i			1.39181i
$58$	−8.87151	−	4.99025i	−1.16489	−	0.655252i
$59$	2.32453	+	8.67527i	0.302628	+	1.12942i	0.934968	+	0.354732i	$0.115428\pi$
$59$	2.32453	+	8.67527i	0.302628	+	1.12942i	−0.632340	+	0.774691i	$0.717905\pi$
$60$	−5.74284	+	3.48953i	−0.741397	+	0.450496i
$61$	2.72673	−	10.1763i	0.349122	−	1.30294i	−0.538601	−	0.842561i	$-0.681047\pi$
$61$	2.72673	−	10.1763i	0.349122	−	1.30294i	0.887722	−	0.460379i	$-0.152287\pi$
$62$	−0.139080	+	0.543339i	−0.0176632	+	0.0690042i
$63$		0			0
$64$	−0.537512	−	7.98192i	−0.0671890	−	0.997740i
$65$	1.61777	+	2.80206i	0.200660	+	0.347553i
$66$	−10.6307	−	10.3951i	−1.30855	−	1.27954i
$67$	7.87441	−	2.10994i	0.962012	−	0.257770i	0.256560	−	0.966528i	$-0.417411\pi$
$67$	7.87441	−	2.10994i	0.962012	−	0.257770i	0.705452	+	0.708758i	$0.250744\pi$
$68$	−0.0861303	−	3.84219i	−0.0104448	−	0.465934i
$69$	−1.25712	+	1.25712i	−0.151339	+	0.151339i
$70$		0			0
$71$			2.78982i			0.331090i	0.986202	+	0.165545i	$0.0529384\pi$
$71$			2.78982i			0.331090i	−0.986202	+	0.165545i	$0.947062\pi$
$72$	0.145316	−	0.625756i	0.0171256	−	0.0737460i
$73$	−2.05730	−	1.18779i	−0.240789	−	0.139020i	0.374750	−	0.927126i	$-0.377728\pi$
$73$	−2.05730	−	1.18779i	−0.240789	−	0.139020i	−0.615539	+	0.788106i	$0.711062\pi$
$74$	−0.479175	+	0.00537015i	−0.0557030	+	0.000624267i
$75$	−1.49375	−	0.400248i	−0.172483	−	0.0462167i
$76$	3.53886	+	12.1144i	0.405935	+	1.38961i
$77$		0			0
$78$	3.65830	+	0.936427i	0.414221	+	0.106029i
$79$	5.10829	+	8.84782i	0.574727	+	0.995457i	0.996071	+	0.0885562i	$0.0282253\pi$
$79$	5.10829	+	8.84782i	0.574727	+	0.995457i	−0.421344	+	0.906901i	$0.638441\pi$
$80$	−5.44558	+	5.95707i	−0.608835	+	0.666020i
$81$	−4.13352	+	7.15947i	−0.459280	+	0.795496i
$82$	−2.76904	−	9.88952i	−0.305789	−	1.09211i
$83$	−1.17951	−	1.17951i	−0.129468	−	0.129468i	0.639404	−	0.768871i	$-0.279181\pi$
$83$	−1.17951	−	1.17951i	−0.129468	−	0.129468i	−0.768871	+	0.639404i	$0.779181\pi$
$84$		0			0
$85$	−2.74164	+	2.74164i	−0.297373	+	0.297373i
$86$	−1.72147	+	3.06036i	−0.185630	+	0.330007i
$87$	10.3794	+	5.99257i	1.11279	+	0.642471i
$88$	−15.7567	−	8.40403i	−1.67967	−	0.895872i
$89$	−11.0470	+	6.37800i	−1.17098	+	0.676066i	−0.953911	−	0.300089i	$-0.902983\pi$
$89$	−11.0470	+	6.37800i	−1.17098	+	0.676066i	−0.217070	+	0.976156i	$0.569650\pi$
$90$	−0.557612	+	0.330324i	−0.0587774	+	0.0348192i
$91$		0			0
$92$	−1.02593	+	1.87267i	−0.106961	+	0.195240i
$93$	0.170922	−	0.637891i	0.0177238	−	0.0661462i
$94$	−2.18645	−	2.13799i	−0.225515	−	0.220517i
$95$	6.36634	−	11.0268i	0.653173	−	1.13133i
$96$	0.527542	+	9.40498i	0.0538420	+	0.959892i
$97$	2.21148			0.224542			0.112271	−	0.993678i	$-0.464187\pi$
$97$	2.21148			0.224542			0.112271	+	0.993678i	$0.464187\pi$
$98$		0			0
$99$	−1.01399	−	1.01399i	−0.101910	−	0.101910i
$100$	−1.85690	+	0.0416261i	−0.185690	+	0.00416261i
$101$	−1.86231	−	6.95024i	−0.185307	−	0.691575i	−0.994565	−	0.104121i	$-0.966797\pi$
$101$	−1.86231	−	6.95024i	−0.185307	−	0.691575i	0.809258	−	0.587454i	$-0.199870\pi$
$102$	0.0507111	+	4.52492i	0.00502115	+	0.448034i
$103$	−15.1457	+	8.74438i	−1.49235	+	0.861609i	−0.999962	−	0.00876536i	$-0.997210\pi$
$103$	−15.1457	+	8.74438i	−1.49235	+	0.861609i	−0.492390	+	0.870375i	$0.663877\pi$
$104$	4.53294	−	0.152454i	0.444491	−	0.0149493i
$105$		0			0
$106$	−0.310221	−	0.523677i	−0.0301314	−	0.0508640i
$107$	2.90855	+	0.779344i	0.281180	+	0.0753420i	0.396653	−	0.917969i	$-0.370172\pi$
$107$	2.90855	+	0.779344i	0.281180	+	0.0753420i	−0.115473	+	0.993311i	$0.536838\pi$
$108$	−2.54832	+	10.4411i	−0.245212	+	1.00470i
$109$	6.86536	−	1.83957i	0.657583	−	0.176199i	0.0854277	−	0.996344i	$-0.472774\pi$
$109$	6.86536	−	1.83957i	0.657583	−	0.176199i	0.572155	+	0.820146i	$0.306108\pi$
$110$	4.85769	+	17.3491i	0.463163	+	1.65417i
$111$	0.564250			0.0535562
$112$		0			0
$113$	−5.96535			−0.561173			−0.280586	−	0.959829i	$-0.590529\pi$
$113$	−5.96535			−0.561173			−0.280586	+	0.959829i	$0.590529\pi$
$114$	−4.00679	−	14.3101i	−0.375270	−	1.34026i
$115$	2.08083	−	0.557557i	0.194039	−	0.0519925i
$116$	13.9844	+	3.41312i	1.29842	+	0.316900i
$117$	0.351795	+	0.0942631i	0.0325234	+	0.00871463i
$118$	−6.47360	−	10.9279i	−0.595944	−	1.00600i
$119$		0			0
$120$	6.49022	−	6.94198i	0.592473	−	0.633713i
$121$	−24.9959	+	14.4314i	−2.27235	+	1.31194i
$122$	0.166965	+	14.8982i	0.0151163	+	1.34882i
$123$	3.12976	+	11.6804i	0.282201	+	1.05319i
$124$	−0.0177760	−	0.792973i	−0.00159634	−	0.0712111i
$125$	8.45884	+	8.45884i	0.756582	+	0.756582i
$126$		0			0
$127$	6.41296			0.569058			0.284529	−	0.958667i	$-0.408163\pi$
$127$	6.41296			0.569058			0.284529	+	0.958667i	$0.408163\pi$
$128$	3.77560	+	10.6651i	0.333719	+	0.942673i
$129$	2.06723	−	3.58055i	0.182009	−	0.315250i
$130$	−3.27160	−	3.19908i	−0.286938	−	0.280578i
$131$	3.87298	−	14.4542i	0.338384	−	1.26287i	−0.561769	−	0.827294i	$-0.689879\pi$
$131$	3.87298	−	14.4542i	0.338384	−	1.26287i	0.900154	−	0.435573i	$-0.143454\pi$
$132$	18.4410	+	10.1028i	1.60509	+	0.879335i
$133$		0			0
$134$	−9.91913	+	5.87600i	−0.856882	+	0.507609i
$135$	9.39029	−	5.42149i	0.808187	−	0.466607i
$136$	1.58236	+	5.19960i	0.135687	+	0.445862i
$137$	1.50928	+	0.871382i	0.128946	+	0.0744472i	0.563086	−	0.826399i	$-0.309614\pi$
$137$	1.50928	+	0.871382i	0.128946	+	0.0744472i	−0.434139	+	0.900846i	$0.642947\pi$
$138$	1.23264	−	2.19134i	0.104929	−	0.186540i
$139$	−2.84436	+	2.84436i	−0.241256	+	0.241256i	−0.817370	−	0.576114i	$-0.804569\pi$
$139$	−2.84436	+	2.84436i	−0.241256	+	0.241256i	0.576114	+	0.817370i	$0.304569\pi$
$140$		0			0
$141$	2.54611	+	2.54611i	0.214421	+	0.214421i
$142$	−1.06379	−	3.79928i	−0.0892710	−	0.318828i
$143$	5.06214	−	8.76788i	0.423317	−	0.733207i
$144$	0.0407112	+	0.907588i	0.00339260	+	0.0756324i
$145$	−7.26132	−	12.5770i	−0.603020	−	1.04446i
$146$	3.25463	+	0.833099i	0.269355	+	0.0689478i
$147$		0			0
$148$	0.650511	−	0.190028i	0.0534717	−	0.0156202i
$149$	−17.7848	−	4.76543i	−1.45699	−	0.390399i	−0.558541	−	0.829477i	$-0.688639\pi$
$149$	−17.7848	−	4.76543i	−1.45699	−	0.390399i	−0.898449	+	0.439077i	$0.855305\pi$
$150$	2.18686	−	0.0245083i	0.178556	−	0.00200110i
$151$	−5.52437	−	3.18949i	−0.449567	−	0.259557i	0.258081	−	0.966123i	$-0.416910\pi$
$151$	−5.52437	−	3.18949i	−0.449567	−	0.259557i	−0.707647	+	0.706566i	$0.750243\pi$
$152$	−9.43869	−	15.1484i	−0.765579	−	1.22870i
$153$			0.436439i			0.0352840i
$154$		0			0
$155$	−0.565835	+	0.565835i	−0.0454490	+	0.0454490i
$156$	−5.33908	+	0.119686i	−0.427468	+	0.00958254i
$157$	−17.6177	+	4.72065i	−1.40605	+	0.376749i	−0.880512	−	0.474024i	$-0.842801\pi$
$157$	−17.6177	+	4.72065i	−1.40605	+	0.376749i	−0.525534	+	0.850773i	$0.676134\pi$
$158$	−10.3304	−	10.1014i	−0.821845	−	0.803628i
$159$	0.358344	+	0.620669i	0.0284185	+	0.0492223i
$160$	5.14451	−	10.1890i	0.406709	−	0.805513i
$161$		0			0
$162$	2.89920	−	11.3262i	0.227783	−	0.889869i
$163$	2.97338	−	11.0968i	0.232893	−	0.869170i	−0.746194	−	0.665729i	$-0.768121\pi$
$163$	2.97338	−	11.0968i	0.232893	−	0.869170i	0.979087	−	0.203441i	$-0.0652125\pi$
$164$	7.54196	+	12.4121i	0.588928	+	0.969219i
$165$	−5.49051	−	20.4909i	−0.427435	−	1.59521i
$166$	2.05605	+	1.15654i	0.159581	+	0.0897647i
$167$		−	21.6693i		−	1.67682i	−0.545040	−	0.838410i	$-0.683486\pi$
$167$		−	21.6693i		−	1.67682i	0.545040	−	0.838410i	$-0.316514\pi$
$168$		0			0
$169$		−	10.4287i		−	0.802204i
$170$	2.68825	−	4.77909i	0.206180	−	0.366539i
$171$	−0.370949	−	1.38440i	−0.0283672	−	0.105868i
$172$	1.17741	−	4.82413i	0.0897765	−	0.367837i
$173$	−3.31175	+	12.3596i	−0.251788	+	0.939684i	0.718062	+	0.695979i	$0.245030\pi$
$173$	−3.31175	+	12.3596i	−0.251788	+	0.939684i	−0.969849	+	0.243705i	$0.921637\pi$
$174$	−16.4201	−	4.20312i	−1.24481	−	0.318638i
$175$		0			0
$176$	24.6627	+	5.43671i	1.85902	+	0.409808i
$177$	7.47780	+	12.9519i	0.562066	+	0.973527i
$178$	12.6122	−	12.8981i	0.945328	−	0.966757i
$179$	3.05939	−	0.819762i	0.228670	−	0.0612719i	−0.142665	−	0.989771i	$-0.545567\pi$
$179$	3.05939	−	0.819762i	0.228670	−	0.0612719i	0.371334	+	0.928499i	$0.378900\pi$
$180$	0.633421	−	0.662471i	0.0472124	−	0.0493777i
$181$	14.3765	−	14.3765i	1.06860	−	1.06860i	0.0711279	−	0.997467i	$-0.477340\pi$
$181$	14.3765	−	14.3765i	1.06860	−	1.06860i	0.997467	−	0.0711279i	$-0.0226598\pi$
$182$		0			0
$183$		−	17.5433i		−	1.29684i
$184$	0.683082	−	2.94148i	0.0503574	−	0.216849i
$185$	−0.592113	−	0.341857i	−0.0435330	−	0.0251338i
$186$	0.0104660	+	0.933878i	0.000767408	+	0.0684753i
$187$	11.7189	+	3.14006i	0.856969	+	0.229624i
$188$	3.79283	+	2.07787i	0.276620	+	0.151545i
$189$		0			0
$190$	−4.46528	+	17.4443i	−0.323945	+	1.26554i
$191$	−6.12089	−	10.6017i	−0.442892	−	0.767111i	0.555011	−	0.831843i	$-0.312714\pi$
$191$	−6.12089	−	10.6017i	−0.442892	−	0.767111i	−0.997903	+	0.0647319i	$0.979381\pi$
$192$	−4.30465	−	12.6069i	−0.310661	−	0.909825i
$193$	1.08900	−	1.88620i	0.0783877	−	0.135771i	−0.824167	−	0.566347i	$-0.808356\pi$
$193$	1.08900	−	1.88620i	0.0783877	−	0.135771i	0.902554	+	0.430576i	$0.141689\pi$
$194$	−3.01168	+	0.843263i	−0.216226	+	0.0605427i
$195$	3.80976	+	3.80976i	0.272823	+	0.272823i
$196$		0			0
$197$	9.97878	−	9.97878i	0.710959	−	0.710959i	−0.255777	−	0.966736i	$-0.582331\pi$
$197$	9.97878	−	9.97878i	0.710959	−	0.710959i	0.966736	+	0.255777i	$0.0823313\pi$
$198$	1.76754	+	0.994246i	0.125613	+	0.0706580i
$199$	9.14271	+	5.27854i	0.648109	+	0.374186i	0.787731	−	0.616019i	$-0.211255\pi$
$199$	9.14271	+	5.27854i	0.648109	+	0.374186i	−0.139622	+	0.990205i	$0.544589\pi$
$200$	2.51293	−	0.764745i	0.177691	−	0.0540756i
$201$	11.7563	−	6.78749i	0.829224	−	0.478753i
$202$	5.18637	+	8.75499i	0.364912	+	0.615999i
$203$		0			0
$204$	−1.79446	−	6.14287i	−0.125637	−	0.430087i
$205$	3.79239	−	14.1534i	0.264872	−	0.988516i
$206$	17.2917	−	17.6836i	1.20477	−	1.23208i
$207$	0.121244	−	0.210001i	0.00842706	−	0.0145961i
$208$	−6.11499	+	1.93607i	−0.423998	+	0.134243i
$209$	−39.8416			−2.75590
$210$		0			0
$211$	5.20378	+	5.20378i	0.358243	+	0.358243i	0.863165	−	0.504922i	$-0.168479\pi$
$211$	5.20378	+	5.20378i	0.358243	+	0.358243i	−0.504922	+	0.863165i	$0.668479\pi$
$212$	0.622155	+	0.594873i	0.0427298	+	0.0408560i
$213$	1.20237	+	4.48730i	0.0823849	+	0.307464i
$214$	−4.25815	+	0.0477214i	−0.291081	+	0.00326217i
$215$	−4.33862	+	2.50490i	−0.295891	+	0.170833i
$216$	−0.510904	−	15.1908i	−0.0347626	−	1.03360i
$217$		0			0
$218$	−8.64806	+	5.12303i	−0.585721	+	0.346975i
$219$	−3.82100	−	1.02383i	−0.258199	−	0.0691843i
$220$	−13.2308	−	21.7743i	−0.892019	−	1.46803i
$221$	−2.97634	+	0.797507i	−0.200210	+	0.0536461i
$222$	−0.768417	+	0.215155i	−0.0515728	+	0.0144402i
$223$	22.3888			1.49926			0.749632	−	0.661855i	$-0.230230\pi$
$223$	22.3888			1.49926			0.749632	+	0.661855i	$0.230230\pi$
$224$		0			0
$225$	0.210928			0.0140619
$226$	8.12384	−	2.27465i	0.540390	−	0.151307i
$227$	17.9753	−	4.81647i	1.19306	−	0.319680i	0.392967	−	0.919552i	$-0.371448\pi$
$227$	17.9753	−	4.81647i	1.19306	−	0.319680i	0.800096	+	0.599872i	$0.204782\pi$
$228$	10.9132	+	17.9602i	0.722744	+	1.18944i
$229$	−8.12426	−	2.17689i	−0.536866	−	0.143853i	−0.0198093	−	0.999804i	$-0.506306\pi$
$229$	−8.12426	−	2.17689i	−0.536866	−	0.143853i	−0.517057	+	0.855951i	$0.672973\pi$
$230$	−2.62115	+	1.55275i	−0.172834	+	0.102385i
$231$		0			0
$232$	−20.3459	+	0.684284i	−1.33578	+	0.0449255i
$233$	14.9278	−	8.61859i	0.977955	−	0.564623i	0.0763032	−	0.997085i	$-0.475688\pi$
$233$	14.9278	−	8.61859i	0.977955	−	0.564623i	0.901652	+	0.432462i	$0.142355\pi$
$234$	−0.515031	+	0.00577199i	−0.0336686	+	0.000377327i
$235$	−1.12925	−	4.21442i	−0.0736642	−	0.274919i
$236$	12.9829	+	12.4136i	0.845117	+	0.808058i
$237$	12.0297	+	12.0297i	0.781414	+	0.781414i
$238$		0			0
$239$	−0.572679			−0.0370435			−0.0185218	−	0.999828i	$-0.505896\pi$
$239$	−0.572679			−0.0370435			−0.0185218	+	0.999828i	$0.505896\pi$
$240$	−6.19158	+	11.9286i	−0.399664	+	0.769990i
$241$	−5.89318	+	10.2073i	−0.379613	+	0.657510i	−0.991006	−	0.133818i	$-0.957276\pi$
$241$	−5.89318	+	10.2073i	−0.379613	+	0.657510i	0.611393	+	0.791327i	$0.290610\pi$
$242$	28.5375	−	29.1844i	1.83446	−	1.87605i
$243$	0.609557	−	2.27490i	0.0391031	−	0.145935i
$244$	−5.90822	−	20.2252i	−0.378235	−	1.29479i
$245$		0			0
$246$	−8.71610	−	14.7134i	−0.555718	−	0.938094i
$247$	8.76321	−	5.05944i	0.557590	−	0.321925i
$248$	0.326577	+	1.07312i	0.0207377	+	0.0681433i
$249$	−2.40553	−	1.38883i	−0.152444	−	0.0880137i
$250$	−14.7450	−	8.29412i	−0.932556	−	0.524566i
$251$	5.57539	−	5.57539i	0.351916	−	0.351916i	−0.508906	−	0.860822i	$-0.669950\pi$
$251$	5.57539	−	5.57539i	0.351916	−	0.351916i	0.860822	+	0.508906i	$0.169950\pi$
$252$		0			0
$253$	−4.76645	−	4.76645i	−0.299664	−	0.299664i
$254$	−8.73341	+	2.44533i	−0.547983	+	0.153434i
$255$	−3.22820	+	5.59141i	−0.202158	+	0.350148i
$256$	−9.20847	−	13.0845i	−0.575530	−	0.817781i
$257$	14.5328	+	25.1715i	0.906528	+	1.57015i	0.818853	+	0.574004i	$0.194610\pi$
$257$	14.5328	+	25.1715i	0.906528	+	1.57015i	0.0876753	+	0.996149i	$0.472056\pi$
$258$	−1.44993	+	5.66438i	−0.0902688	+	0.352649i
$259$		0			0
$260$	5.67523	+	3.10914i	0.351963	+	0.192820i
$261$	−1.57902	−	0.423097i	−0.0977388	−	0.0261890i
$262$	0.237153	+	21.1610i	0.0146514	+	1.30733i
$263$	−15.3142	−	8.84163i	−0.944311	−	0.545198i	−0.0530021	−	0.998594i	$-0.516879\pi$
$263$	−15.3142	−	8.84163i	−0.944311	−	0.545198i	−0.891309	+	0.453396i	$0.850212\pi$
$264$	−28.9660	−	6.72660i	−1.78273	−	0.413993i
$265$		−	0.868424i		−	0.0533469i
$266$		0			0
$267$	−15.0198	+	15.0198i	−0.919198	+	0.919198i
$268$	11.2677	−	11.7844i	0.688282	−	0.719848i
$269$	−14.4268	+	3.86566i	−0.879620	+	0.235693i	−0.670243	−	0.742142i	$-0.733810\pi$
$269$	−14.4268	+	3.86566i	−0.879620	+	0.235693i	−0.209377	+	0.977835i	$0.567144\pi$
$270$	−10.7208	+	10.9638i	−0.652446	+	0.667236i
$271$	−6.93172	−	12.0061i	−0.421072	−	0.729319i	0.574972	−	0.818173i	$-0.305013\pi$
$271$	−6.93172	−	12.0061i	−0.421072	−	0.729319i	−0.996045	+	0.0888543i	$0.971679\pi$
$272$	−4.13759	−	6.47764i	−0.250878	−	0.392765i
$273$		0			0
$274$	−2.38766	−	0.611177i	−0.144244	−	0.0369226i
$275$	1.51757	−	5.66364i	0.0915128	−	0.341531i
$276$	−0.843071	+	3.45427i	−0.0507469	+	0.207923i
$277$	−0.597472	−	2.22980i	−0.0358986	−	0.133975i	0.945651	−	0.325184i	$-0.105426\pi$
$277$	−0.597472	−	2.22980i	−0.0358986	−	0.133975i	−0.981550	+	0.191208i	$0.938759\pi$
$278$	2.78898	−	4.95815i	0.167272	−	0.297370i
$279$			0.0900747i			0.00539263i
$280$		0			0
$281$			0.680351i			0.0405863i	0.999794	+	0.0202932i	$0.00645996\pi$
$281$			0.680351i			0.0405863i	−0.999794	+	0.0202932i	$0.993540\pi$
$282$	−4.43825	−	2.49653i	−0.264294	−	0.148666i
$283$	−0.0985120	−	0.367652i	−0.00585593	−	0.0218546i	0.962936	−	0.269730i	$-0.0869344\pi$
$283$	−0.0985120	−	0.367652i	−0.00585593	−	0.0218546i	−0.968792	+	0.247875i	$0.920268\pi$
$284$	2.89741	+	4.76837i	0.171930	+	0.282951i
$285$	5.48759	−	20.4799i	0.325056	−	1.21313i
$286$	−3.55053	+	13.8707i	−0.209947	+	0.820190i
$287$		0			0
$288$	−0.401515	−	1.22046i	−0.0236595	−	0.0719166i
$289$	6.65377	+	11.5247i	0.391398	+	0.677921i
$290$	14.6845	+	14.3590i	0.862302	+	0.843188i
$291$	3.55707	−	0.953115i	0.208519	−	0.0558726i
$292$	−4.74995	+	0.106479i	−0.277970	+	0.00623124i
$293$	−7.49220	+	7.49220i	−0.437699	+	0.437699i	−0.891237	−	0.453538i	$-0.850162\pi$
$293$	−7.49220	+	7.49220i	−0.437699	+	0.437699i	0.453538	+	0.891237i	$0.350162\pi$
$294$		0			0
$295$		−	18.1220i		−	1.05510i
$296$	−0.813431	+	0.506834i	−0.0472797	+	0.0294591i
$297$	−29.3829	−	16.9643i	−1.70497	−	0.984366i
$298$	26.0372	−	0.291801i	1.50829	−	0.0169036i
$299$	1.65367	+	0.443101i	0.0956345	+	0.0256252i
$300$	−2.96880	+	0.867250i	−0.171404	+	0.0500707i
$301$		0			0
$302$	8.73948	+	2.23707i	0.502901	+	0.128729i
$303$	−5.99089	−	10.3765i	−0.344168	−	0.596116i
$304$	18.6302	+	17.0306i	1.06852	+	0.976771i
$305$	−10.6288	+	18.4096i	−0.608602	+	1.05413i
$306$	−0.166419	−	0.594359i	−0.00951353	−	0.0339773i
$307$	6.27988	+	6.27988i	0.358412	+	0.358412i	0.863227	−	0.504816i	$-0.168439\pi$
$307$	6.27988	+	6.27988i	0.358412	+	0.358412i	−0.504816	+	0.863227i	$0.668439\pi$
$308$		0			0
$309$	−20.5925	+	20.5925i	−1.17147	+	1.17147i
$310$	0.554817	−	0.986334i	0.0315115	−	0.0560200i
$311$	−8.55685	−	4.94030i	−0.485215	−	0.280139i	0.237372	−	0.971419i	$-0.423714\pi$
$311$	−8.55685	−	4.94030i	−0.485215	−	0.280139i	−0.722587	+	0.691280i	$0.757047\pi$
$312$	7.22532	−	2.19884i	0.409053	−	0.124485i
$313$	14.8734	−	8.58714i	0.840692	−	0.485374i	−0.0168075	−	0.999859i	$-0.505350\pi$
$313$	14.8734	−	8.58714i	0.840692	−	0.485374i	0.857499	+	0.514485i	$0.172017\pi$
$314$	22.1924	−	13.1466i	1.25239	−	0.741904i
$315$		0			0
$316$	17.9202	+	9.81743i	1.00809	+	0.552274i
$317$	−5.49870	+	20.5214i	−0.308838	+	1.15260i	0.620754	+	0.784006i	$0.286827\pi$
$317$	−5.49870	+	20.5214i	−0.308838	+	1.15260i	−0.929591	+	0.368592i	$0.879840\pi$
$318$	−0.724674	−	0.708611i	−0.0406377	−	0.0397369i
$319$	−22.7212	+	39.3543i	−1.27214	+	2.20342i
$320$	−3.12081	+	15.8374i	−0.174458	+	0.885340i
$321$	5.01416			0.279863
$322$		0			0
$323$	8.57424	+	8.57424i	0.477084	+	0.477084i
$324$	0.370551	+	16.5299i	0.0205862	+	0.918329i
$325$	0.385429	+	1.43844i	0.0213798	+	0.0797904i
$326$	0.182068	+	16.2458i	0.0100838	+	0.899774i
$327$	10.2498	−	5.91773i	0.566815	−	0.327251i
$328$	−15.0038	−	14.0274i	−0.828445	−	0.774532i
$329$		0			0
$330$	15.2906	+	25.8116i	0.841718	+	1.42088i
$331$	23.3748	+	6.26326i	1.28479	+	0.344260i	0.835681	−	0.549215i	$-0.185073\pi$
$331$	23.3748	+	6.26326i	1.28479	+	0.344260i	0.449113	+	0.893475i	$0.351740\pi$
$332$	−3.24101	−	0.791021i	−0.177874	−	0.0434129i
$333$	−0.0743388	+	0.0199190i	−0.00407374	+	0.00109156i
$334$	8.26273	+	29.5101i	0.452116	+	1.61472i
$335$	−16.4491			−0.898709
$336$		0			0
$337$	−4.26739			−0.232460			−0.116230	−	0.993222i	$-0.537081\pi$
$337$	−4.26739			−0.232460			−0.116230	+	0.993222i	$0.537081\pi$
$338$	3.97656	+	14.2021i	0.216296	+	0.772494i
$339$	−9.59499	+	2.57097i	−0.521128	+	0.139636i
$340$	−1.83865	+	7.53340i	−0.0997147	+	0.408556i
$341$	2.41861	+	0.648063i	0.130975	+	0.0350946i
$342$	1.03306	+	1.74388i	0.0558614	+	0.0942983i
$343$		0			0
$344$	0.236054	+	7.01864i	0.0127272	+	0.378420i
$345$	3.10663	−	1.79361i	0.167255	−	0.0965648i
$346$	−0.202788	−	18.0946i	−0.0109019	−	0.972772i
$347$	−0.0139833	−	0.0521865i	−0.000750664	−	0.00280152i	0.965549	−	0.260220i	$-0.0837949\pi$
$347$	−0.0139833	−	0.0521865i	−0.000750664	−	0.00280152i	−0.966300	+	0.257418i	$0.917128\pi$
$348$	23.9643	−	0.537206i	1.28462	−	0.0287973i
$349$	15.4928	+	15.4928i	0.829309	+	0.829309i	0.987421	−	0.158112i	$-0.0505407\pi$
$349$	15.4928	+	15.4928i	0.829309	+	0.829309i	−0.158112	+	0.987421i	$0.550541\pi$
$350$		0			0
$351$	8.61710			0.459947
$352$	−35.6596	+	2.00021i	−1.90066	+	0.106612i
$353$	8.38161	−	14.5174i	0.446108	−	0.772682i	−0.552020	−	0.833831i	$-0.686143\pi$
$353$	8.38161	−	14.5174i	0.446108	−	0.772682i	0.998129	+	0.0611484i	$0.0194763\pi$
$354$	−15.1223	−	14.7871i	−0.803740	−	0.785924i
$355$	1.45693	−	5.43735i	0.0773259	−	0.288584i
$356$	−12.2576	+	22.3744i	−0.649653	+	1.18584i
$357$		0			0
$358$	−3.85381	+	2.28296i	−0.203680	+	0.120658i
$359$	−29.8777	+	17.2499i	−1.57689	+	0.910415i	−0.581595	+	0.813479i	$0.697571\pi$
$359$	−29.8777	+	17.2499i	−1.57689	+	0.910415i	−0.995291	+	0.0969365i	$0.969096\pi$
$360$	−0.610009	+	1.14371i	−0.0321503	+	0.0602787i
$361$	−18.0310	−	10.4102i	−0.948998	−	0.547904i
$362$	−14.0965	+	25.0603i	−0.740897	+	1.31714i
$363$	−33.9851	+	33.9851i	−1.78375	+	1.78375i
$364$		0			0
$365$	3.38938	+	3.38938i	0.177408	+	0.177408i
$366$	6.68944	+	23.8911i	0.349663	+	1.24881i
$367$	−10.2644	+	17.7785i	−0.535799	+	0.928032i	0.463325	+	0.886189i	$0.346656\pi$
$367$	−10.2644	+	17.7785i	−0.535799	+	0.928032i	−0.999124	+	0.0418433i	$0.986677\pi$
$368$	0.191370	+	4.26628i	0.00997587	+	0.222395i
$369$	−0.824679	−	1.42839i	−0.0429311	−	0.0743588i
$370$	0.936715	+	0.239774i	0.0486975	+	0.0124653i
$371$		0			0
$372$	−0.370351	−	1.26780i	−0.0192018	−	0.0657324i
$373$	15.2773	+	4.09353i	0.791027	+	0.211955i	0.631641	−	0.775261i	$-0.282382\pi$
$373$	15.2773	+	4.09353i	0.791027	+	0.211955i	0.159386	+	0.987216i	$0.449049\pi$
$374$	−17.1565	+	0.192275i	−0.887144	+	0.00994228i
$375$	17.2513	+	9.96003i	0.890853	+	0.514334i
$376$	−5.95753	−	1.38348i	−0.307236	−	0.0713476i
$377$		−	11.5414i		−	0.594412i
$378$		0			0
$379$	11.2717	−	11.2717i	0.578987	−	0.578987i	−0.355637	−	0.934624i	$-0.615736\pi$
$379$	11.2717	−	11.2717i	0.578987	−	0.578987i	0.934624	+	0.355637i	$0.115736\pi$
$380$	−0.570713	−	25.4590i	−0.0292770	−	1.30602i
$381$	10.3150	−	2.76388i	0.528451	−	0.141598i
$382$	12.3782	+	12.1038i	0.633323	+	0.619285i
$383$	5.14594	+	8.91303i	0.262945	+	0.455434i	0.967023	−	0.254688i	$-0.0819728\pi$
$383$	5.14594	+	8.91303i	0.262945	+	0.455434i	−0.704078	+	0.710123i	$0.748640\pi$
$384$	10.6694	+	15.5272i	0.544469	+	0.792367i
$385$		0			0
$386$	−0.763809	+	2.98394i	−0.0388769	+	0.151879i
$387$	−0.145954	+	0.544707i	−0.00741925	+	0.0276890i
$388$	3.77988	−	2.29677i	0.191894	−	0.116601i
$389$	5.30513	+	19.7990i	0.268981	+	1.00385i	0.959769	+	0.280792i	$0.0905972\pi$
$389$	5.30513	+	19.7990i	0.268981	+	1.00385i	−0.690788	+	0.723058i	$0.742736\pi$
$390$	−6.64098	−	3.73557i	−0.336279	−	0.189158i
$391$			2.05156i			0.103752i
$392$		0			0
$393$		−	24.9181i		−	1.25695i
$394$	−9.78447	+	17.3945i	−0.492934	+	0.876322i
$395$	−5.33543	−	19.9121i	−0.268454	−	1.00189i
$396$	−2.78622	−	0.680021i	−0.140013	−	0.0341723i
$397$	2.02632	−	7.56231i	0.101698	−	0.379542i	−0.896252	−	0.443546i	$-0.853720\pi$
$397$	2.02632	−	7.56231i	0.101698	−	0.379542i	0.997950	+	0.0640041i	$0.0203871\pi$
$398$	−14.4636	−	3.70231i	−0.724997	−	0.185580i
$399$		0			0
$400$	−3.13060	+	1.99966i	−0.156530	+	0.0999832i
$401$	−7.09985	−	12.2973i	−0.354549	−	0.614098i	0.632491	−	0.774567i	$-0.282032\pi$
$401$	−7.09985	−	12.2973i	−0.354549	−	0.614098i	−0.987041	+	0.160470i	$0.948699\pi$
$402$	−13.4220	+	13.7263i	−0.669429	+	0.684604i
$403$	−0.614273	+	0.164594i	−0.0305991	+	0.00819901i
$404$	−10.4014	−	9.94525i	−0.517487	−	0.494795i
$405$	11.7951	−	11.7951i	0.586104	−	0.586104i
$406$		0			0
$407$			2.13939i			0.106046i
$408$	4.78611	+	7.68135i	0.236948	+	0.380283i
$409$	22.8759	+	13.2074i	1.13114	+	0.653065i	0.944222	−	0.329310i	$-0.106816\pi$
$409$	22.8759	+	13.2074i	1.13114	+	0.653065i	0.186920	+	0.982375i	$0.440149\pi$
$410$	0.232219	+	20.7207i	0.0114685	+	1.02332i
$411$	2.80316	+	0.751104i	0.138270	+	0.0370492i
$412$	−16.8055	+	30.6758i	−0.827947	+	1.51129i
$413$		0			0
$414$	−0.0850394	+	0.332220i	−0.00417946	+	0.0163277i
$415$	1.68288	+	2.91483i	0.0826092	+	0.143083i
$416$	7.58938	−	4.96833i	0.372100	−	0.243592i
$417$	−3.34915	+	5.80091i	−0.164009	+	0.284072i
$418$	54.2577	−	15.1920i	2.65383	−	0.743065i
$419$	15.6893	+	15.6893i	0.766471	+	0.766471i	0.977483	−	0.211012i	$-0.0676759\pi$
$419$	15.6893	+	15.6893i	0.766471	+	0.766471i	−0.211012	+	0.977483i	$0.567676\pi$
$420$		0			0
$421$	25.7068	−	25.7068i	1.25287	−	1.25287i	0.298444	−	0.954427i	$-0.403532\pi$
$421$	25.7068	−	25.7068i	1.25287	−	1.25287i	0.954427	−	0.298444i	$-0.0964675\pi$
$422$	−9.07096	−	5.10245i	−0.441568	−	0.248383i
$423$	−0.425327	−	0.245563i	−0.0206801	−	0.0119397i
$424$	−1.07411	−	0.572886i	−0.0521632	−	0.0278218i
$425$	−1.54546	+	0.892270i	−0.0749657	+	0.0432815i
$426$	−3.34848	−	5.65249i	−0.162235	−	0.273864i
$427$		0			0
$428$	5.78071	−	1.68867i	0.279421	−	0.0816247i
$429$	4.36340	−	16.2844i	0.210667	−	0.786220i
$430$	4.95335	−	5.06563i	0.238872	−	0.244287i
$431$	12.3981	−	21.4741i	0.597194	−	1.03437i	−0.396039	−	0.918234i	$-0.629616\pi$
$431$	12.3981	−	21.4741i	0.597194	−	1.03437i	0.993233	−	0.116137i	$-0.0370510\pi$
$432$	6.48818	+	20.4926i	0.312163	+	0.985950i
$433$	−5.22863			−0.251272			−0.125636	−	0.992076i	$-0.540097\pi$
$433$	−5.22863			−0.251272			−0.125636	+	0.992076i	$0.540097\pi$
$434$		0			0
$435$	−17.1000	−	17.1000i	−0.819881	−	0.819881i
$436$	9.82380	−	10.2743i	0.470474	−	0.492051i
$437$	−1.74371	−	6.50762i	−0.0834131	−	0.311302i
$438$	5.59398	−	0.0626921i	0.267291	−	0.00299555i
$439$	19.1771	−	11.0719i	0.915273	−	0.528433i	0.0331491	−	0.999450i	$-0.489446\pi$
$439$	19.1771	−	11.0719i	0.915273	−	0.528433i	0.882124	+	0.471017i	$0.156113\pi$
$440$	26.3210	+	24.6081i	1.25480	+	1.17314i
$441$		0			0
$442$	3.74919	−	2.22098i	0.178331	−	0.105641i
$443$	21.8067	+	5.84309i	1.03607	+	0.277614i	0.736483	−	0.676456i	$-0.236485\pi$
$443$	21.8067	+	5.84309i	1.03607	+	0.277614i	0.299585	+	0.954070i	$0.403152\pi$
$444$	0.964419	−	0.586011i	0.0457693	−	0.0278109i
$445$	24.8614	−	6.66159i	1.17854	−	0.315790i
$446$	−30.4899	+	8.53708i	−1.44374	+	0.404243i
$447$	−30.6599			−1.45017
$448$		0			0
$449$	−36.3678			−1.71630			−0.858152	−	0.513396i	$-0.828387\pi$
$449$	−36.3678			−1.71630			−0.858152	+	0.513396i	$0.828387\pi$
$450$	−0.287249	+	0.0804290i	−0.0135411	+	0.00379146i
$451$	−44.2871	+	11.8667i	−2.08540	+	0.558781i
$452$	−10.1960	+	6.19541i	−0.479579	+	0.291408i
$453$	−10.2603	−	2.74924i	−0.482072	−	0.129171i
$454$	−22.6429	+	13.4134i	−1.06268	+	0.629523i
$455$		0			0
$456$	−21.7104	−	20.2976i	−1.01668	−	0.950522i
$457$	21.5807	−	12.4596i	1.00950	−	0.582837i	0.0984570	−	0.995141i	$-0.468609\pi$
$457$	21.5807	−	12.4596i	1.00950	−	0.582837i	0.911046	+	0.412304i	$0.135276\pi$
$458$	11.8940	−	0.133297i	0.555770	−	0.00622856i
$459$	2.67261	+	9.97431i	0.124747	+	0.465561i
$460$	2.97751	−	3.11406i	0.138827	−	0.145194i
$461$	1.60588	+	1.60588i	0.0747933	+	0.0747933i	0.743514	−	0.668721i	$-0.233158\pi$
$461$	1.60588	+	1.60588i	0.0747933	+	0.0747933i	−0.668721	+	0.743514i	$0.733158\pi$
$462$		0			0
$463$	−14.8176			−0.688634			−0.344317	−	0.938853i	$-0.611890\pi$
$463$	−14.8176			−0.688634			−0.344317	+	0.938853i	$0.611890\pi$
$464$	27.4469	−	8.69000i	1.27419	−	0.403423i
$465$	−0.666254	+	1.15399i	−0.0308968	+	0.0535148i
$466$	−17.0429	+	17.4293i	−0.789499	+	0.807395i
$467$	3.21315	−	11.9916i	0.148687	−	0.554907i	−0.850877	−	0.525365i	$-0.823929\pi$
$467$	3.21315	−	11.9916i	0.148687	−	0.554907i	0.999564	−	0.0295414i	$-0.00940469\pi$
$468$	0.699188	−	0.204247i	0.0323200	−	0.00944133i
$469$		0			0
$470$	3.14486	+	5.30876i	0.145062	+	0.244875i
$471$	−26.3028	+	15.1859i	−1.21197	+	0.699730i
$472$	−22.4141	−	11.9548i	−1.03169	−	0.550265i
$473$	13.5759	+	7.83804i	0.624220	+	0.360393i
$474$	−20.9696	−	11.7955i	−0.963165	−	0.541784i
$475$	4.14387	−	4.14387i	0.190134	−	0.190134i
$476$		0			0
$477$	−0.0691218	−	0.0691218i	−0.00316487	−	0.00316487i
$478$	0.779896	−	0.218369i	0.0356716	−	0.00998795i
$479$	−1.02709	+	1.77897i	−0.0469288	+	0.0812831i	−0.888536	−	0.458808i	$-0.848277\pi$
$479$	−1.02709	+	1.77897i	−0.0469288	+	0.0812831i	0.841607	+	0.540091i	$0.181610\pi$
$480$	3.88341	−	18.6058i	0.177252	−	0.849234i
$481$	−0.271679	−	0.470563i	−0.0123875	−	0.0214558i
$482$	4.13341	−	16.1478i	0.188272	−	0.735513i
$483$		0			0
$484$	−27.7351	+	50.6261i	−1.26069	+	2.30119i
$485$	−4.31018	−	1.15491i	−0.195715	−	0.0524417i
$486$	0.0373249	+	3.33047i	0.00169309	+	0.151073i
$487$	−35.4045	−	20.4408i	−1.60433	−	0.926261i	−0.990607	−	0.136740i	$-0.956338\pi$
$487$	−35.4045	−	20.4408i	−1.60433	−	0.926261i	−0.613724	−	0.789521i	$-0.710329\pi$
$488$	15.7581	+	25.2906i	0.713337	+	1.14485i
$489$		−	19.1302i		−	0.865098i
$490$		0			0
$491$	−0.278015	+	0.278015i	−0.0125466	+	0.0125466i	−0.713352	−	0.700806i	$-0.752824\pi$
$491$	−0.278015	+	0.278015i	−0.0125466	+	0.0125466i	0.700806	+	0.713352i	$0.252824\pi$
$492$	17.4803	+	16.7138i	0.788073	+	0.753515i
$493$	13.3592	−	3.57958i	0.601667	−	0.161216i
$494$	−10.0049	+	10.2316i	−0.450140	+	0.460344i
$495$	1.44673	+	2.50580i	0.0650255	+	0.112628i
$496$	−0.853938	−	1.33689i	−0.0383429	−	0.0600282i
$497$		0			0
$498$	3.80552	+	0.974112i	0.170529	+	0.0436510i
$499$	−3.19039	+	11.9067i	−0.142822	+	0.533018i	0.857021	+	0.515281i	$0.172313\pi$
$499$	−3.19039	+	11.9067i	−0.142822	+	0.533018i	−0.999843	+	0.0177363i	$0.994354\pi$
$500$	23.2429	+	5.67282i	1.03946	+	0.253696i
$501$	−9.33912	−	34.8541i	−0.417241	−	1.55717i
$502$	−5.46682	+	9.71874i	−0.243996	+	0.433768i
$503$		−	0.367839i		−	0.0164011i	−0.999966	−	0.00820057i	$-0.997390\pi$
$503$		−	0.367839i		−	0.0164011i	0.999966	−	0.00820057i	$-0.00261035\pi$
$504$		0			0
$505$			14.5186i			0.646068i
$506$	8.30862	+	4.67363i	0.369363	+	0.207768i
$507$	−4.49459	−	16.7740i	−0.199612	−	0.744960i
$508$	10.9611	−	6.66028i	0.486318	−	0.295502i
$509$	2.09820	−	7.83060i	0.0930012	−	0.347085i	−0.903708	−	0.428150i	$-0.859165\pi$
$509$	2.09820	−	7.83060i	0.0930012	−	0.347085i	0.996709	+	0.0810649i	$0.0258321\pi$
$510$	2.26422	−	8.84554i	0.100262	−	0.391687i
$511$		0			0
$512$	17.5297	+	14.3077i	0.774711	+	0.632316i
$513$	−16.9552	−	29.3673i	−0.748591	−	1.29660i
$514$	−29.3894	−	28.7380i	−1.29631	−	1.26758i
$515$	34.0855	−	9.13319i	1.50199	−	0.402457i
$516$	−0.185317	−	8.26684i	−0.00815815	−	0.363927i
$517$	−9.65374	+	9.65374i	−0.424571	+	0.424571i
$518$		0			0
$519$			21.3072i			0.935282i
$520$	−8.91430	−	2.07011i	−0.390918	−	0.0907805i
$521$	11.5215	+	6.65193i	0.504766	+	0.291427i	0.730679	−	0.682721i	$-0.239203\pi$
$521$	11.5215	+	6.65193i	0.504766	+	0.291427i	−0.225914	+	0.974147i	$0.572537\pi$
$522$	2.31170	−	0.0259074i	0.101180	−	0.00113394i
$523$	27.4536	+	7.35616i	1.20046	+	0.321663i	0.803013	−	0.595962i	$-0.203229\pi$
$523$	27.4536	+	7.35616i	1.20046	+	0.321663i	0.397448	+	0.917625i	$0.369896\pi$
$524$	−8.39189	−	28.7275i	−0.366602	−	1.25497i
$525$		0			0
$526$	24.2268	+	6.20142i	1.05634	+	0.270395i
$527$	−0.381036	−	0.659973i	−0.0165982	−	0.0287489i
$528$	42.0119	−	1.88451i	1.82833	−	0.0820126i
$529$	−10.9301	+	18.9314i	−0.475220	+	0.823106i
$530$	0.331139	+	1.18265i	0.0143838	+	0.0513712i
$531$	−1.44241	−	1.44241i	−0.0625954	−	0.0625954i
$532$		0			0
$533$	8.23408	−	8.23408i	0.356657	−	0.356657i
$534$	14.7273	−	26.1818i	0.637314	−	1.13300i
$535$	−5.26176	−	3.03788i	−0.227486	−	0.131339i
$536$	−10.8512	+	20.3449i	−0.468701	+	0.878768i
$537$	4.56759	−	2.63710i	0.197106	−	0.113799i
$538$	18.1730	−	10.7655i	0.783494	−	0.464134i
$539$		0			0
$540$	10.4194	−	19.0189i	0.448377	−	0.818442i
$541$	−4.75802	+	17.7572i	−0.204563	+	0.763441i	0.785019	+	0.619472i	$0.212653\pi$
$541$	−4.75802	+	17.7572i	−0.204563	+	0.763441i	−0.989582	+	0.143969i	$0.954013\pi$
$542$	14.0179	+	13.7072i	0.602122	+	0.588775i
$543$	16.9279	−	29.3199i	0.726445	−	1.25824i
$544$	8.10471	+	7.24379i	0.347487	+	0.310575i
$545$	−14.3413			−0.614312
$546$		0			0
$547$	−22.9801	−	22.9801i	−0.982558	−	0.982558i	0.0172930	−	0.999850i	$-0.494495\pi$
$547$	−22.9801	−	22.9801i	−0.982558	−	0.982558i	−0.999850	+	0.0172930i	$0.994495\pi$
$548$	3.48465	−	0.0781153i	0.148857	−	0.00333692i
$549$	0.619309	+	2.31129i	0.0264315	+	0.0986436i
$550$	0.0929249	+	8.29163i	0.00396233	+	0.353556i
$551$	−39.3334	+	22.7091i	−1.67566	+	0.967442i
$552$	−0.169024	−	5.02563i	−0.00719416	−	0.213905i
$553$		0			0
$554$	1.66390	+	2.80880i	0.0706925	+	0.119334i
$555$	−1.09972	−	0.294670i	−0.0466806	−	0.0125080i
$556$	−1.90754	+	7.81566i	−0.0808976	+	0.331458i
$557$	4.50327	−	1.20665i	0.190810	−	0.0511273i	−0.162149	−	0.986766i	$-0.551842\pi$
$557$	4.50327	−	1.20665i	0.190810	−	0.0511273i	0.352958	+	0.935639i	$0.385176\pi$
$558$	−0.0343464	−	0.122667i	−0.00145400	−	0.00519291i
$559$	−3.98138			−0.168394
$560$		0			0
$561$	20.2026			0.852954
$562$	−0.259425	−	0.926527i	−0.0109432	−	0.0390832i
$563$	4.04301	−	1.08332i	0.170393	−	0.0456566i	−0.172614	−	0.984990i	$-0.555221\pi$
$563$	4.04301	−	1.08332i	0.170393	−	0.0456566i	0.343007	+	0.939333i	$0.388555\pi$
$564$	6.99613	+	1.70752i	0.294590	+	0.0718995i
$565$	11.6264	+	3.11530i	0.489128	+	0.131061i
$566$	0.274347	+	0.463118i	0.0115317	+	0.0194663i
$567$		0			0
$568$	−5.76403	−	5.38893i	−0.241853	−	0.226115i
$569$	3.88173	−	2.24111i	0.162730	−	0.0939524i	−0.416423	−	0.909171i	$-0.636717\pi$
$569$	3.88173	−	2.24111i	0.162730	−	0.0939524i	0.579154	+	0.815218i	$0.303383\pi$
$570$	0.336020	+	29.9828i	0.0140743	+	1.25584i
$571$	−0.126176	−	0.470896i	−0.00528031	−	0.0197064i	0.963235	−	0.268659i	$-0.0865804\pi$
$571$	−0.126176	−	0.470896i	−0.00528031	−	0.0197064i	−0.968516	+	0.248952i	$0.919914\pi$
$572$	−0.453797	−	20.2435i	−0.0189742	−	0.846422i
$573$	−14.4143	−	14.4143i	−0.602167	−	0.602167i
$574$		0			0
$575$	0.991504			0.0413486
$576$	1.01217	+	1.50897i	0.0421739	+	0.0628739i
$577$	−5.31982	+	9.21420i	−0.221467	+	0.383592i	−0.955254	−	0.295788i	$-0.904418\pi$
$577$	−5.31982	+	9.21420i	−0.221467	+	0.383592i	0.733787	+	0.679380i	$0.237751\pi$
$578$	−13.4558	−	13.1576i	−0.559689	−	0.547283i
$579$	0.938680	−	3.50320i	0.0390102	−	0.145588i
$580$	−25.4731	−	13.9553i	−1.05771	−	0.579460i
$581$		0			0
$582$	−4.48072	+	2.65434i	−0.185732	+	0.110026i
$583$	−2.35331	+	1.35868i	−0.0974641	+	0.0562709i
$584$	6.42806	−	1.95621i	0.265995	−	0.0809487i
$585$	−0.636420	−	0.367437i	−0.0263127	−	0.0151917i
$586$	7.34631	−	13.0600i	0.303473	−	0.539505i
$587$	13.2861	−	13.2861i	0.548376	−	0.548376i	−0.377595	−	0.925971i	$-0.623249\pi$
$587$	13.2861	−	13.2861i	0.548376	−	0.548376i	0.925971	+	0.377595i	$0.123249\pi$
$588$		0			0
$589$	1.76960	+	1.76960i	0.0729151	+	0.0729151i
$590$	6.91011	+	24.6792i	0.284485	+	1.01603i
$591$	11.7497	−	20.3511i	0.483319	−	0.837133i
$592$	0.914500	−	1.00040i	0.0375857	−	0.0411160i
$593$	−0.198497	−	0.343806i	−0.00815128	−	0.0141184i	0.861921	−	0.507043i	$-0.169261\pi$
$593$	−0.198497	−	0.343806i	−0.00815128	−	0.0141184i	−0.870072	+	0.492924i	$0.835928\pi$
$594$	46.4835	+	11.8985i	1.90724	+	0.488203i
$595$		0			0
$596$	−35.3471	+	10.3256i	−1.44788	+	0.422954i
$597$	16.9806	+	4.54994i	0.694970	+	0.186217i
$598$	−2.42100	+	0.0271323i	−0.0990019	+	0.00110952i
$599$	11.9718	+	6.91190i	0.489153	+	0.282412i	0.724223	−	0.689566i	$-0.242199\pi$
$599$	11.9718	+	6.91190i	0.489153	+	0.282412i	−0.235070	+	0.971978i	$0.575532\pi$
$600$	3.71234	−	2.31309i	0.151556	−	0.0944315i
$601$			8.73396i			0.356266i	0.984006	+	0.178133i	$0.0570057\pi$
$601$			8.73396i			0.356266i	−0.984006	+	0.178133i	$0.942994\pi$
$602$		0			0
$603$	−1.30926	+	1.30926i	−0.0533170	+	0.0533170i
$604$	−12.7548	+	0.285923i	−0.518984	+	0.0116341i
$605$	56.2535	−	15.0731i	2.28703	−	0.612807i
$606$	12.1153	+	11.8468i	0.492150	+	0.481242i
$607$	−14.3937	−	24.9305i	−0.584220	−	1.01190i	−0.994972	−	0.100152i	$-0.968067\pi$
$607$	−14.3937	−	24.9305i	−0.584220	−	1.01190i	0.410752	−	0.911747i	$-0.365266\pi$
$608$	−31.8653	−	16.0890i	−1.29231	−	0.652495i
$609$		0			0
$610$	7.45490	−	29.1237i	0.301840	−	1.17918i
$611$	0.897436	−	3.34928i	0.0363064	−	0.135497i
$612$	0.453271	+	0.745964i	0.0183224	+	0.0301538i
$613$	9.13486	+	34.0918i	0.368954	+	1.37695i	0.861981	+	0.506940i	$0.169223\pi$
$613$	9.13486	+	34.0918i	0.368954	+	1.37695i	−0.493028	+	0.870014i	$0.664110\pi$
$614$	−10.9468	−	6.15759i	−0.441775	−	0.248500i
$615$		−	24.3996i		−	0.983886i
$616$		0			0
$617$			33.4612i			1.34710i	0.739143	+	0.673548i	$0.235231\pi$
$617$			33.4612i			1.34710i	−0.739143	+	0.673548i	$0.764769\pi$
$618$	20.1915	−	35.8958i	0.812222	−	1.44394i
$619$	2.41362	+	9.00777i	0.0970118	+	0.362053i	0.997317	−	0.0732067i	$-0.0233233\pi$
$619$	2.41362	+	9.00777i	0.0970118	+	0.362053i	−0.900305	+	0.435260i	$0.856657\pi$
$620$	−0.379470	+	1.55478i	−0.0152399	+	0.0624417i
$621$	1.48492	−	5.54180i	0.0595878	−	0.222385i
$622$	13.5368	+	3.46507i	0.542778	+	0.138937i
$623$		0			0
$624$	−9.00127	+	5.74955i	−0.360339	+	0.230166i
$625$	−9.74706	−	16.8824i	−0.389882	−	0.675296i
$626$	−16.9807	+	17.3657i	−0.678687	+	0.694071i
$627$	−64.0834	+	17.1711i	−2.55924	+	0.685747i
$628$	−25.2096	+	26.3657i	−1.00597	+	1.05211i
$629$	0.460415	−	0.460415i	0.0183580	−	0.0183580i
$630$		0			0
$631$			22.2587i			0.886105i	0.896496	+	0.443053i	$0.146104\pi$
$631$			22.2587i			0.886105i	−0.896496	+	0.443053i	$0.853896\pi$
$632$	−28.1478	−	6.53660i	−1.11966	−	0.260012i
$633$	10.6128	+	6.12730i	0.421821	+	0.243538i
$634$	−0.336700	−	30.0436i	−0.0133721	−	1.19318i
$635$	−12.4988	−	3.34905i	−0.496001	−	0.132903i
$636$	1.25709	+	0.688687i	0.0498468	+	0.0273082i
$637$		0			0
$638$	15.9364	−	62.2580i	0.630928	−	2.46482i
$639$	−0.316819	−	0.548747i	−0.0125332	−	0.0217081i
$640$	−1.78895	−	22.7580i	−0.0707146	−	0.899590i
$641$	4.13758	−	7.16649i	0.163424	−	0.283059i	−0.772670	−	0.634808i	$-0.781079\pi$
$641$	4.13758	−	7.16649i	0.163424	−	0.283059i	0.936095	+	0.351748i	$0.114413\pi$
$642$	−6.82847	+	1.91195i	−0.269498	+	0.0754587i
$643$	−4.19175	−	4.19175i	−0.165307	−	0.165307i	0.619606	−	0.784913i	$-0.287292\pi$
$643$	−4.19175	−	4.19175i	−0.165307	−	0.165307i	−0.784913	+	0.619606i	$0.787292\pi$
$644$		0			0
$645$	−5.89890	+	5.89890i	−0.232269	+	0.232269i
$646$	−14.9462	−	8.40728i	−0.588049	−	0.330780i
$647$	−18.2428	−	10.5325i	−0.717199	−	0.414075i	0.0965221	−	0.995331i	$-0.469228\pi$
$647$	−18.2428	−	10.5325i	−0.717199	−	0.414075i	−0.813721	+	0.581256i	$0.802561\pi$
$648$	−6.80767	−	22.3698i	−0.267430	−	0.878768i
$649$	−49.1081	+	28.3526i	−1.92766	+	1.11294i
$650$	−1.07339	−	1.81196i	−0.0421016	−	0.0710708i
$651$		0			0
$652$	−6.44266	−	22.0548i	−0.252314	−	0.863732i
$653$	4.43173	−	16.5394i	0.173427	−	0.647239i	−0.823387	−	0.567480i	$-0.807918\pi$
$653$	4.43173	−	16.5394i	0.173427	−	0.647239i	0.996814	−	0.0797585i	$-0.0254149\pi$
$654$	−11.7021	+	11.9673i	−0.457587	+	0.467960i
$655$	−15.0969	+	26.1485i	−0.589883	+	1.02171i
$656$	25.7815	+	13.3819i	1.00660	+	0.522476i
$657$	0.539552			0.0210499
$658$		0			0
$659$	19.9513	+	19.9513i	0.777192	+	0.777192i	0.979352	−	0.202161i	$-0.0647964\pi$
$659$	19.9513	+	19.9513i	0.777192	+	0.777192i	−0.202161	+	0.979352i	$0.564796\pi$
$660$	−30.6655	−	29.3208i	−1.19365	−	1.14131i
$661$	5.55822	+	20.7436i	0.216190	+	0.806831i	0.985744	+	0.168250i	$0.0538117\pi$
$661$	5.55822	+	20.7436i	0.216190	+	0.806831i	−0.769555	+	0.638581i	$0.779522\pi$
$662$	−34.2209	+	0.383516i	−1.33003	+	0.0149058i
$663$	−4.44359	+	2.56551i	−0.172575	+	0.0996361i
$664$	4.71536	−	0.158589i	0.182991	−	0.00615445i
$665$		0			0
$666$	0.0936421	−	0.0554727i	0.00362856	−	0.00214952i
$667$	−7.42246	−	1.98884i	−0.287399	−	0.0770083i
$668$	−22.5050	−	37.0372i	−0.870744	−	1.43301i
$669$	36.0114	−	9.64922i	1.39228	−	0.373060i
$670$	22.4010	−	6.27221i	0.865425	−	0.242317i
$671$	66.5165			2.56784
$672$		0			0
$673$	21.0339			0.810796			0.405398	−	0.914140i	$-0.367133\pi$
$673$	21.0339			0.810796			0.405398	+	0.914140i	$0.367133\pi$
$674$	5.81150	−	1.62720i	0.223851	−	0.0626775i
$675$	4.82051	−	1.29165i	0.185542	−	0.0497157i
$676$	−10.8309	−	17.8247i	−0.416571	−	0.685566i
$677$	−6.02033	−	1.61314i	−0.231380	−	0.0619982i	0.141266	−	0.989972i	$-0.454883\pi$
$677$	−6.02033	−	1.61314i	−0.231380	−	0.0619982i	−0.372646	+	0.927974i	$0.621549\pi$
$678$	12.0865	−	7.15992i	0.464179	−	0.274975i
$679$		0			0
$680$	−0.368624	−	10.9604i	−0.0141361	−	0.420311i
$681$	26.8367	−	15.4942i	1.02838	−	0.593737i
$682$	−3.54086	+	0.0396827i	−0.135587	+	0.00151953i
$683$	−5.78001	−	21.5713i	−0.221166	−	0.825402i	−0.983904	−	0.178695i	$-0.942812\pi$
$683$	−5.78001	−	21.5713i	−0.221166	−	0.825402i	0.762739	−	0.646707i	$-0.223854\pi$
$684$	−2.07182	−	1.98097i	−0.0792180	−	0.0757442i
$685$	−2.48651	−	2.48651i	−0.0950048	−	0.0950048i
$686$		0			0
$687$	−14.0057			−0.534351
$688$	−2.99775	−	9.46824i	−0.114288	−	0.360973i
$689$	0.345076	−	0.597689i	0.0131463	−	0.0227701i
$690$	−3.54680	+	3.62720i	−0.135024	+	0.138085i
$691$	−9.94413	+	37.1120i	−0.378292	+	1.41181i	0.470182	+	0.882570i	$0.344188\pi$
$691$	−9.94413	+	37.1120i	−0.378292	+	1.41181i	−0.848474	+	0.529237i	$0.822478\pi$
$692$	7.17583	+	24.5646i	0.272784	+	0.933805i
$693$		0			0
$694$	0.0389423	+	0.0657375i	0.00147823	+	0.00249536i
$695$	7.02907	−	4.05824i	0.266628	−	0.153938i
$696$	−32.4306	+	9.86941i	−1.22928	+	0.374099i
$697$	12.0848	+	6.97715i	0.457743	+	0.264278i
$698$	−27.0062	−	15.1911i	−1.02220	−	0.574991i
$699$	20.2963	−	20.2963i	0.767676	−	0.767676i
$700$		0			0
$701$	1.40129	+	1.40129i	0.0529259	+	0.0529259i	0.733074	−	0.680148i	$-0.238085\pi$
$701$	1.40129	+	1.40129i	0.0529259	+	0.0529259i	−0.680148	+	0.733074i	$0.738085\pi$
$702$	−11.7351	+	3.28579i	−0.442913	+	0.124014i
$703$	−1.06913	+	1.85178i	−0.0403229	+	0.0698413i
$704$	47.7999	−	16.3214i	1.80153	−	0.615134i
$705$	−3.63270	−	6.29202i	−0.136815	−	0.236971i
$706$	−5.87877	+	22.9663i	−0.221250	+	0.864349i
$707$		0			0
$708$	26.2325	+	14.3713i	0.985879	+	0.540107i
$709$	−8.42034	−	2.25622i	−0.316232	−	0.0847342i	0.0972117	−	0.995264i	$-0.469008\pi$
$709$	−8.42034	−	2.25622i	−0.316232	−	0.0847342i	−0.413444	+	0.910530i	$0.635674\pi$
$710$	0.0892120	+	7.96033i	0.00334807	+	0.298746i
$711$	−2.00956	−	1.16022i	−0.0753645	−	0.0435117i
$712$	8.16133	−	35.1442i	0.305859	−	1.31709i
$713$			0.423412i			0.0158569i
$714$		0			0
$715$	−14.4450	+	14.4450i	−0.540211	+	0.540211i
$716$	4.37775	−	4.57852i	0.163604	−	0.171107i
$717$	−0.921129	+	0.246816i	−0.0344002	+	0.00921750i
$718$	34.1110	−	34.8843i	1.27301	−	1.30187i
$719$	13.3330	+	23.0934i	0.497236	+	0.861239i	0.999995	−	0.00318810i	$-0.00101481\pi$
$719$	13.3330	+	23.0934i	0.497236	+	0.861239i	−0.502758	+	0.864427i	$0.667681\pi$
$720$	0.394626	−	1.79015i	0.0147068	−	0.0667149i
$721$		0			0
$722$	28.5247	+	7.30158i	1.06158	+	0.271737i
$723$	−5.07974	+	18.9578i	−0.188917	+	0.705050i
$724$	9.64141	−	39.5033i	0.358320	−	1.46813i
$725$	−1.72999	−	6.45640i	−0.0642501	−	0.239785i
$726$	33.3233	−	59.2410i	1.23674	−	2.19864i
$727$			37.7224i			1.39905i	0.714610	+	0.699523i	$0.246604\pi$
$727$			37.7224i			1.39905i	−0.714610	+	0.699523i	$0.753396\pi$
$728$		0			0
$729$		−	28.7229i		−	1.06381i
$730$	−5.90819	−	3.32338i	−0.218672	−	0.123004i
$731$	−1.23483	−	4.60846i	−0.0456719	−	0.170450i
$732$	−18.2199	−	29.9851i	−0.673425	−	1.10828i
$733$	−5.88050	+	21.9463i	−0.217201	+	0.810606i	0.768179	+	0.640235i	$0.221163\pi$
$733$	−5.88050	+	21.9463i	−0.217201	+	0.810606i	−0.985380	+	0.170371i	$0.945504\pi$
$734$	7.19936	−	28.1254i	0.265733	−	1.03813i
$735$		0			0
$736$	−1.88739	−	5.73701i	−0.0695703	−	0.211469i
$737$	25.7352	+	44.5747i	0.947969	+	1.64193i
$738$	1.66774	+	1.63077i	0.0613903	+	0.0600295i
$739$	25.3304	−	6.78727i	0.931795	−	0.249674i	0.239175	−	0.970977i	$-0.423123\pi$
$739$	25.3304	−	6.78727i	0.931795	−	0.249674i	0.692620	+	0.721303i	$0.256456\pi$
$740$	−1.36708	+	0.0306458i	−0.0502550	+	0.00112656i
$741$	11.9147	−	11.9147i	0.437697	−	0.437697i
$742$		0			0
$743$		−	20.7110i		−	0.759812i	−0.925025	−	0.379906i	$-0.875956\pi$
$743$		−	20.7110i		−	0.759812i	0.925025	−	0.379906i	$-0.124044\pi$
$744$	0.987783	+	1.58532i	0.0362139	+	0.0581206i
$745$	32.1739	+	18.5756i	1.17876	+	0.680558i
$746$	−22.3661	+	0.250658i	−0.818880	+	0.00917724i
$747$	0.365952	+	0.0980566i	0.0133895	+	0.00358770i
$748$	23.2911	−	6.80382i	0.851607	−	0.248772i
$749$		0			0
$750$	−27.2913	−	6.98585i	−0.996538	−	0.255087i
$751$	7.73865	+	13.4037i	0.282387	+	0.489109i	0.971972	−	0.235096i	$-0.0755403\pi$
$751$	7.73865	+	13.4037i	0.282387	+	0.489109i	−0.689585	+	0.724205i	$0.742207\pi$
$752$	8.64073	−	0.387593i	0.315095	−	0.0141341i
$753$	6.56486	−	11.3707i	0.239237	−	0.414370i
$754$	4.40086	+	15.7175i	0.160270	+	0.572398i
$755$	9.10132	+	9.10132i	0.331231	+	0.331231i
$756$		0			0
$757$	18.4631	−	18.4631i	0.671051	−	0.671051i	−0.286907	−	0.957958i	$-0.592627\pi$
$757$	18.4631	−	18.4631i	0.671051	−	0.671051i	0.957958	+	0.286907i	$0.0926272\pi$
$758$	−11.0522	+	19.6482i	−0.401434	+	0.713655i
$759$	−9.72088	−	5.61235i	−0.352846	−	0.203715i
$760$	10.4850	+	34.4534i	0.380331	+	1.24976i
$761$	11.1420	−	6.43283i	0.403897	−	0.233190i	−0.284267	−	0.958745i	$-0.591750\pi$
$761$	11.1420	−	6.43283i	0.403897	−	0.233190i	0.688164	+	0.725555i	$0.258417\pi$
$762$	−12.9934	+	7.69716i	−0.470701	+	0.278839i
$763$		0			0
$764$	−21.4724	−	11.7635i	−0.776844	−	0.425589i
$765$	0.227923	−	0.850618i	0.00824056	−	0.0307542i
$766$	−10.4066	−	10.1759i	−0.376004	−	0.367670i
$767$	7.20094	−	12.4724i	0.260011	−	0.450352i
$768$	−20.4506	−	17.0771i	−0.737948	−	0.616217i
$769$	16.5676			0.597443			0.298722	−	0.954340i	$-0.403440\pi$
$769$	16.5676			0.597443			0.298722	+	0.954340i	$0.403440\pi$
$770$		0			0
$771$	34.2238	+	34.2238i	1.23254	+	1.23254i
$772$	−0.0976234	−	4.35489i	−0.00351354	−	0.156736i
$773$	12.6807	+	47.3250i	0.456093	+	1.70216i	0.684856	+	0.728679i	$0.259865\pi$
$773$	12.6807	+	47.3250i	0.456093	+	1.70216i	−0.228763	+	0.973482i	$0.573468\pi$
$774$	−0.00893715	−	0.797456i	−0.000321239	−	0.0286640i
$775$	−0.318960	+	0.184152i	−0.0114574	+	0.00661492i
$776$	−4.27180	+	4.56914i	−0.153349	+	0.164023i
$777$		0			0
$778$	−14.7743	−	24.9401i	−0.529684	−	0.894147i
$779$	−44.2635	−	11.8604i	−1.58591	−	0.424942i
$780$	10.4683	+	2.55497i	0.374827	+	0.0914826i
$781$	−17.0139	+	4.55886i	−0.608805	+	0.163129i
$782$	−0.782282	−	2.79389i	−0.0279743	−	0.0999094i
$783$	−38.6776			−1.38222
$784$		0			0
$785$	36.8021			1.31352
$786$	9.50153	+	33.9344i	0.338908	+	1.21040i
$787$	5.05999	−	1.35582i	0.180369	−	0.0483298i	−0.167504	−	0.985871i	$-0.553571\pi$
$787$	5.05999	−	1.35582i	0.180369	−	0.0483298i	0.347873	+	0.937542i	$0.386904\pi$
$788$	6.69215	−	27.4194i	0.238398	−	0.976776i
$789$	−28.4427	−	7.62121i	−1.01259	−	0.271322i
$790$	14.8587	+	25.0826i	0.528648	+	0.892398i
$791$		0			0
$792$	4.05367	−	0.136335i	0.144041	−	0.00484446i
$793$	−14.6304	+	8.44687i	−0.519541	+	0.299957i
$794$	0.124077	+	11.0713i	0.00440332	+	0.392906i
$795$	−0.374277	−	1.39682i	−0.0132742	−	0.0495401i
$796$	21.1089	−	0.473197i	0.748184	−	0.0167720i
$797$	−20.4204	−	20.4204i	−0.723329	−	0.723329i	0.245953	−	0.969282i	$-0.420899\pi$
$797$	−20.4204	−	20.4204i	−0.723329	−	0.723329i	−0.969282	+	0.245953i	$0.920899\pi$
$798$		0			0
$799$	4.15514			0.146998
$800$	3.50087	−	3.91695i	0.123774	−	0.138485i
$801$	1.44860	−	2.50906i	0.0511839	−	0.0886532i
$802$	14.3579	+	14.0397i	0.506996	+	0.495758i
$803$	3.88193	−	14.4876i	0.136990	−	0.511255i
$804$	13.0446	−	23.8109i	0.460049	−	0.839746i
$805$		0			0
$806$	0.773779	−	0.458379i	0.0272552	−	0.0161457i
$807$	−21.5389	+	12.4355i	−0.758205	+	0.437750i
$808$	17.9572	+	9.57767i	0.631732	+	0.336941i
$809$	−33.6734	−	19.4413i	−1.18389	−	0.683521i	−0.226981	−	0.973899i	$-0.572886\pi$
$809$	−33.6734	−	19.4413i	−1.18389	−	0.683521i	−0.956912	+	0.290378i	$0.906219\pi$
$810$	−11.5654	+	20.5606i	−0.406368	+	0.722427i
$811$	−12.4718	+	12.4718i	−0.437945	+	0.437945i	−0.891320	−	0.453375i	$-0.850220\pi$
$811$	−12.4718	+	12.4718i	−0.437945	+	0.437945i	0.453375	+	0.891320i	$0.350220\pi$
$812$		0			0
$813$	−16.3238	−	16.3238i	−0.572501	−	0.572501i
$814$	−0.815773	−	2.91350i	−0.0285928	−	0.102118i
$815$	−11.5902	+	20.0749i	−0.405988	+	0.703192i
$816$	−9.44688	−	8.63576i	−0.330707	−	0.302312i
$817$	7.83387	+	13.5687i	0.274072	+	0.474707i
$818$	−36.1894	−	9.26354i	−1.26533	−	0.323892i
$819$		0			0
$820$	−8.21727	−	28.1297i	−0.286960	−	0.982332i
$821$	−18.4979	−	4.95650i	−0.645581	−	0.172983i	−0.0788511	−	0.996886i	$-0.525125\pi$
$821$	−18.4979	−	4.95650i	−0.645581	−	0.172983i	−0.566730	+	0.823903i	$0.691792\pi$
$822$	−4.10385	+	0.0459921i	−0.143138	+	0.00160416i
$823$	8.96748	+	5.17738i	0.312587	+	0.180472i	0.648083	−	0.761569i	$-0.275571\pi$
$823$	8.96748	+	5.17738i	0.312587	+	0.180472i	−0.335497	+	0.942041i	$0.608904\pi$
$824$	11.1894	−	48.1835i	0.389800	−	1.67855i
$825$		−	9.76376i		−	0.339931i
$826$		0			0
$827$	−9.65786	+	9.65786i	−0.335837	+	0.335837i	−0.854798	−	0.518961i	$-0.826319\pi$
$827$	−9.65786	+	9.65786i	−0.335837	+	0.335837i	0.518961	+	0.854798i	$0.326319\pi$
$828$	−0.0108690	−	0.484856i	−0.000377723	−	0.0168499i
$829$	−25.6983	+	6.88583i	−0.892538	+	0.239155i	−0.675809	−	0.737077i	$-0.736205\pi$
$829$	−25.6983	+	6.88583i	−0.892538	+	0.239155i	−0.216729	+	0.976232i	$0.569539\pi$
$830$	−3.40326	−	3.32783i	−0.118129	−	0.115511i
$831$	−1.92201	−	3.32902i	−0.0666739	−	0.115483i
$832$	−8.44103	+	9.65997i	−0.292640	+	0.334899i
$833$		0			0
$834$	2.34906	−	9.17696i	0.0813412	−	0.317772i
$835$	−11.3164	+	42.2334i	−0.391620	+	1.46155i
$836$	−68.0974	+	41.3781i	−2.35520	+	1.43109i
$837$	0.551588	+	2.05855i	0.0190657	+	0.0711540i
$838$	−27.3487	−	15.3838i	−0.944747	−	0.531423i
$839$			46.4429i			1.60339i	0.597736	+	0.801693i	$0.296067\pi$
$839$			46.4429i			1.60339i	−0.597736	+	0.801693i	$0.703933\pi$
$840$		0			0
$841$			22.8031i			0.786315i
$842$	−25.2062	+	44.8107i	−0.868662	+	1.54428i
$843$	0.293220	+	1.09431i	0.0100990	+	0.0376902i
$844$	14.2988	+	3.48985i	0.492185	+	0.120126i
$845$	−5.44618	+	20.3254i	−0.187354	+	0.699216i
$846$	0.672862	+	0.172235i	0.0231335	+	0.00592156i
$847$		0			0
$848$	1.68120	+	0.370610i	0.0577328	+	0.0127268i
$849$	−0.316904	−	0.548894i	−0.0108761	−	0.0188380i
$850$	1.76443	−	1.80443i	0.0605195	−	0.0618913i
$851$	−0.349443	+	0.0936330i	−0.0119788	+	0.00320970i
$852$	6.71545	+	6.42097i	0.230067	+	0.219979i
$853$	31.3013	−	31.3013i	1.07174	−	1.07174i	0.0745177	−	0.997220i	$-0.476258\pi$
$853$	31.3013	−	31.3013i	1.07174	−	1.07174i	0.997220	−	0.0745177i	$-0.0237417\pi$
$854$		0			0
$855$			2.89191i			0.0989014i
$856$	−7.22848	+	4.50393i	−0.247064	+	0.153941i
$857$	−22.8393	−	13.1863i	−0.780175	−	0.450434i	0.0563171	−	0.998413i	$-0.482064\pi$
$857$	−22.8393	−	13.1863i	−0.780175	−	0.450434i	−0.836492	+	0.547979i	$0.815398\pi$
$858$	0.267183	+	23.8406i	0.00912148	+	0.813904i
$859$	2.91867	+	0.782055i	0.0995837	+	0.0266834i	0.308267	−	0.951300i	$-0.400251\pi$
$859$	2.91867	+	0.782055i	0.0995837	+	0.0266834i	−0.208683	+	0.977983i	$0.566918\pi$
$860$	−4.81408	+	8.78734i	−0.164159	+	0.299646i
$861$		0			0
$862$	−8.69586	+	33.9717i	−0.296182	+	1.15708i
$863$	−3.50456	−	6.07008i	−0.119297	−	0.206628i	0.800192	−	0.599743i	$-0.204731\pi$
$863$	−3.50456	−	6.07008i	−0.119297	−	0.206628i	−0.919489	+	0.393115i	$0.871397\pi$
$864$	−16.6499	−	25.4336i	−0.566441	−	0.865267i
$865$	12.9092	−	22.3594i	0.438925	−	0.760241i
$866$	7.12055	−	1.99373i	0.241966	−	0.0677498i
$867$	15.6692	+	15.6692i	0.532155	+	0.532155i
$868$		0			0
$869$	−45.6115	+	45.6115i	−1.54726	+	1.54726i
$870$	29.8078	+	16.7670i	1.01058	+	0.568454i
$871$	−11.3210	−	6.53619i	−0.383598	−	0.221470i
$872$	−9.46070	+	17.7379i	−0.320380	+	0.600681i
$873$	−0.434991	+	0.251142i	−0.0147222	+	0.00849987i
$874$	4.85608	+	8.19743i	0.164259	+	0.277282i
$875$		0			0
$876$	−7.59419	+	2.21842i	−0.256584	+	0.0749535i
$877$	10.6267	−	39.6594i	0.358838	−	1.33920i	−0.516748	−	0.856138i	$-0.672857\pi$
$877$	10.6267	−	39.6594i	0.358838	−	1.33920i	0.875585	−	0.483063i	$-0.160476\pi$
$878$	−21.8943	+	22.3906i	−0.738896	+	0.755645i
$879$	−8.82185	+	15.2799i	−0.297554	+	0.515378i
$880$	−45.2282	−	23.4758i	−1.52464	−	0.791368i
$881$	13.6166			0.458755			0.229377	−	0.973338i	$-0.426331\pi$
$881$	13.6166			0.458755			0.229377	+	0.973338i	$0.426331\pi$
$882$		0			0
$883$	35.2238	+	35.2238i	1.18537	+	1.18537i	0.978332	+	0.207042i	$0.0663836\pi$
$883$	35.2238	+	35.2238i	1.18537	+	1.18537i	0.207042	+	0.978332i	$0.433616\pi$
$884$	−4.25890	+	4.45423i	−0.143242	+	0.149812i
$885$	−7.81030	−	29.1484i	−0.262540	−	0.979814i
$886$	−31.9252	+	0.357789i	−1.07255	+	0.0120201i
$887$	5.44911	−	3.14604i	0.182963	−	0.105634i	−0.405721	−	0.913997i	$-0.632980\pi$
$887$	5.44911	−	3.14604i	0.182963	−	0.105634i	0.588684	+	0.808363i	$0.299646\pi$
$888$	−1.08993	+	1.16580i	−0.0365756	+	0.0391215i
$889$		0			0
$890$	−31.3171	+	18.5519i	−1.04975	+	0.621862i
$891$	−50.4171	−	13.5092i	−1.68904	−	0.452576i
$892$	38.2670	−	23.2522i	1.28127	−	0.778543i
$893$	−13.1802	+	3.53163i	−0.441060	+	0.118182i
$894$	41.7539	−	11.6910i	1.39646	−	0.391004i
$895$	−6.39085			−0.213623
$896$		0			0
$897$	2.85083			0.0951864
$898$	49.5271	−	13.8674i	1.65274	−	0.462762i
$899$	2.75714	−	0.738774i	0.0919559	−	0.0246395i
$900$	0.360519	−	0.219062i	0.0120173	−	0.00730208i
$901$	0.798852	+	0.214052i	0.0266136	+	0.00713110i
$902$	55.7870	−	33.0477i	1.85750	−	1.10037i
$903$		0			0
$904$	11.5229	−	12.3250i	0.383247	−	0.409923i
$905$	−35.5276	+	20.5118i	−1.18098	+	0.681837i
$906$	15.0212	−	0.168344i	0.499046	−	0.00559285i
$907$	11.6035	+	43.3049i	0.385289	+	1.43792i	0.837711	+	0.546113i	$0.183893\pi$
$907$	11.6035	+	43.3049i	0.385289	+	1.43792i	−0.452423	+	0.891804i	$0.649440\pi$
$908$	25.7213	−	26.9009i	0.853590	−	0.892737i
$909$	1.15560	+	1.15560i	0.0383288	+	0.0383288i
$910$		0			0
$911$	42.8973			1.42125			0.710625	−	0.703571i	$-0.248412\pi$
$911$	42.8973			1.42125			0.710625	+	0.703571i	$0.248412\pi$
$912$	37.3058	+	19.3636i	1.23532	+	0.641193i
$913$	5.26585	−	9.12073i	0.174274	−	0.301852i
$914$	−24.6384	+	25.1970i	−0.814967	+	0.833441i
$915$	−9.16166	+	34.1918i	−0.302875	+	1.13035i
$916$	−16.1469	+	4.71684i	−0.533508	+	0.155849i
$917$		0			0
$918$	−7.44297	−	12.5643i	−0.245655	−	0.414684i
$919$	26.2242	−	15.1405i	0.865056	−	0.499440i	−0.000646343	−	1.00000i	$-0.500206\pi$
$919$	26.2242	−	15.1405i	0.865056	−	0.499440i	0.865702	+	0.500560i	$0.166872\pi$
$920$	−2.86746	+	5.37620i	−0.0945373	+	0.177248i
$921$	12.8074	+	7.39438i	0.422019	+	0.243653i
$922$	−2.79929	−	1.57461i	−0.0921896	−	0.0518570i
$923$	3.16330	−	3.16330i	0.104121	−	0.104121i
$924$		0			0
$925$	−0.222515	−	0.222515i	−0.00731626	−	0.00731626i
$926$	20.1792	−	5.65012i	0.663130	−	0.185675i
$927$	1.98607	−	3.43997i	0.0652311	−	0.112984i
$928$	−34.0647	+	22.3002i	−1.11823	+	0.732039i
$929$	−6.93334	−	12.0089i	−0.227475	−	0.393999i	0.729584	−	0.683891i	$-0.239714\pi$
$929$	−6.93334	−	12.0089i	−0.227475	−	0.393999i	−0.957059	+	0.289892i	$0.906380\pi$
$930$	0.467303	−	1.82559i	0.0153235	−	0.0598635i
$931$		0			0
$932$	16.5638	−	30.2345i	0.542564	−	0.990364i
$933$	−15.8925	−	4.25838i	−0.520297	−	0.139413i
$934$	0.196750	+	17.5559i	0.00643786	+	0.574446i
$935$	−21.2002	−	12.2399i	−0.693321	−	0.400289i
$936$	−0.874299	+	0.544759i	−0.0285773	+	0.0178060i
$937$		−	46.7544i		−	1.52740i	−0.645572	−	0.763699i	$-0.723381\pi$
$937$		−	46.7544i		−	1.52740i	0.645572	−	0.763699i	$-0.276619\pi$
$938$		0			0
$939$	20.2222	−	20.2222i	0.659927	−	0.659927i
$940$	−6.30708	−	6.03051i	−0.205714	−	0.196693i
$941$	−8.04407	+	2.15540i	−0.262229	+	0.0702641i	−0.387538	−	0.921854i	$-0.626674\pi$
$941$	−8.04407	+	2.15540i	−0.262229	+	0.0702641i	0.125309	+	0.992118i	$0.460008\pi$
$942$	30.0295	−	30.7103i	0.978416	−	1.00059i
$943$	−3.87655	−	6.71439i	−0.126238	−	0.218651i
$944$	35.0829	+	7.73378i	1.14185	+	0.251713i
$945$		0			0
$946$	−21.4769	−	5.49751i	−0.698273	−	0.178739i
$947$	1.89988	−	7.09044i	0.0617378	−	0.230408i	−0.928162	−	0.372176i	$-0.878612\pi$
$947$	1.89988	−	7.09044i	0.0617378	−	0.230408i	0.989900	+	0.141767i	$0.0452785\pi$
$948$	33.0549	+	8.06759i	1.07357	+	0.262023i
$949$	0.985926	+	3.67953i	0.0320045	+	0.119442i
$950$	−4.06317	+	7.22338i	−0.131827	+	0.234357i
$951$			35.3776i			1.14720i
$952$		0			0
$953$		−	41.3553i		−	1.33963i	−0.742528	−	0.669815i	$-0.766373\pi$
$953$		−	41.3553i		−	1.33963i	0.742528	−	0.669815i	$-0.233627\pi$
$954$	0.120490	+	0.0677758i	0.00390099	+	0.00219432i
$955$	6.39305	+	23.8592i	0.206874	+	0.772065i
$956$	−0.978826	+	0.594765i	−0.0316575	+	0.0192361i
$957$	−19.5850	+	73.0921i	−0.633093	+	2.36273i
$958$	0.720387	−	2.81430i	0.0232746	−	0.0909260i
$959$		0			0
$960$	1.80601	+	26.8188i	0.0582888	+	0.865574i
$961$	15.4214	+	26.7106i	0.497463	+	0.861632i
$962$	0.549414	+	0.537236i	0.0177138	+	0.0173212i
$963$	−0.660606	+	0.177009i	−0.0212877	+	0.00570403i
$964$	0.528296	+	23.5668i	0.0170153	+	0.759036i
$965$	−3.10748	+	3.10748i	−0.100033	+	0.100033i
$966$		0			0
$967$			40.5984i			1.30556i	0.757549	+	0.652778i	$0.226397\pi$
$967$			40.5984i			1.30556i	−0.757549	+	0.652778i	$0.773603\pi$
$968$	18.4665	−	79.5202i	0.593536	−	2.55588i
$969$	17.4866	+	10.0959i	0.561752	+	0.324328i
$970$	6.31014	−	0.0707182i	0.202606	−	0.00227062i
$971$	−31.4132	−	8.41714i	−1.00810	−	0.270119i	−0.283263	−	0.959042i	$-0.591417\pi$
$971$	−31.4132	−	8.41714i	−1.00810	−	0.270119i	−0.724834	+	0.688924i	$0.758084\pi$
$972$	−1.32077	−	4.52133i	−0.0423639	−	0.145022i
$973$		0			0
$974$	56.0095	+	14.3369i	1.79466	+	0.459385i
$975$	1.23989	+	2.14755i	0.0397083	+	0.0687768i
$976$	−31.1036	−	28.4330i	−0.995602	−	0.910118i
$977$	8.34286	−	14.4503i	0.266912	−	0.462305i	−0.701151	−	0.713013i	$-0.747330\pi$
$977$	8.34286	−	14.4503i	0.266912	−	0.462305i	0.968063	+	0.250708i	$0.0806635\pi$
$978$	7.29455	+	26.0522i	0.233254	+	0.833059i
$979$	−56.9486	−	56.9486i	−1.82009	−	1.82009i
$980$		0			0
$981$	−1.14148	+	1.14148i	−0.0364448	+	0.0364448i
$982$	0.272601	−	0.484621i	0.00869904	−	0.0154649i
$983$	10.1999	+	5.88892i	0.325326	+	0.187827i	0.653764	−	0.756698i	$-0.273189\pi$
$983$	10.1999	+	5.88892i	0.325326	+	0.187827i	−0.328438	+	0.944526i	$0.606522\pi$
$984$	−30.1785	−	16.0960i	−0.962054	−	0.513122i
$985$	−24.6599	+	14.2374i	−0.785728	+	0.453640i
$986$	−16.8281	+	9.96881i	−0.535916	+	0.317472i
$987$		0			0
$988$	9.72355	−	17.7488i	0.309347	−	0.564665i
$989$	−0.686082	+	2.56049i	−0.0218161	+	0.0814189i
$990$	−2.92570	−	2.86085i	−0.0929848	−	0.0909237i
$991$	15.8872	−	27.5175i	0.504675	−	0.874122i	−0.495311	−	0.868716i	$-0.664946\pi$
$991$	15.8872	−	27.5175i	0.504675	−	0.874122i	0.999985	−	0.00540613i	$-0.00172083\pi$
$992$	1.67270	+	1.49501i	0.0531081	+	0.0474667i
$993$	40.2967			1.27878
$994$		0			0
$995$	−15.0625	−	15.0625i	−0.477513	−	0.477513i
$996$	−5.55394	+	0.124502i	−0.175983	+	0.00394501i
$997$	0.309461	+	1.15492i	0.00980073	+	0.0365768i	0.970653	−	0.240484i	$-0.0773062\pi$
$997$	0.309461	+	1.15492i	0.00980073	+	0.0365768i	−0.960852	+	0.277061i	$0.910640\pi$
$998$	−0.195357	−	17.4315i	−0.00618391	−	0.551786i
$999$	−1.57695	+	0.910453i	−0.0498925	+	0.0288055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.557.2		48
7.2	even	3	inner	784.2.x.o.765.10		48
7.3	odd	6		784.2.m.j.589.6		24
7.4	even	3		784.2.m.k.589.6		24
7.5	odd	6		112.2.w.c.93.10	yes	48
7.6	odd	2		112.2.w.c.109.2	yes	48
16.5	even	4	inner	784.2.x.o.165.10		48
28.19	even	6		448.2.ba.c.401.4		48
28.27	even	2		448.2.ba.c.81.9		48
56.5	odd	6		896.2.ba.f.289.4		48
56.13	odd	2		896.2.ba.f.417.9		48
56.19	even	6		896.2.ba.e.289.9		48
56.27	even	2		896.2.ba.e.417.4		48
112.5	odd	12		112.2.w.c.37.2	✓	48
112.13	odd	4		896.2.ba.f.865.4		48
112.19	even	12		896.2.ba.e.737.4		48
112.27	even	4		448.2.ba.c.305.4		48
112.37	even	12	inner	784.2.x.o.373.2		48
112.53	even	12		784.2.m.k.197.6		24
112.61	odd	12		896.2.ba.f.737.9		48
112.69	odd	4		112.2.w.c.53.10	yes	48
112.75	even	12		448.2.ba.c.177.9		48
112.83	even	4		896.2.ba.e.865.9		48
112.101	odd	12		784.2.m.j.197.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.2	✓	48	112.5	odd	12
112.2.w.c.53.10	yes	48	112.69	odd	4
112.2.w.c.93.10	yes	48	7.5	odd	6
112.2.w.c.109.2	yes	48	7.6	odd	2
448.2.ba.c.81.9		48	28.27	even	2
448.2.ba.c.177.9		48	112.75	even	12
448.2.ba.c.305.4		48	112.27	even	4
448.2.ba.c.401.4		48	28.19	even	6
784.2.m.j.197.6		24	112.101	odd	12
784.2.m.j.589.6		24	7.3	odd	6
784.2.m.k.197.6		24	112.53	even	12
784.2.m.k.589.6		24	7.4	even	3
784.2.x.o.165.10		48	16.5	even	4	inner
784.2.x.o.373.2		48	112.37	even	12	inner
784.2.x.o.557.2		48	1.1	even	1	trivial
784.2.x.o.765.10		48	7.2	even	3	inner
896.2.ba.e.289.9		48	56.19	even	6
896.2.ba.e.417.4		48	56.27	even	2
896.2.ba.e.737.4		48	112.19	even	12
896.2.ba.e.865.9		48	112.83	even	4
896.2.ba.f.289.4		48	56.5	odd	6
896.2.ba.f.417.9		48	56.13	odd	2
896.2.ba.f.737.9		48	112.61	odd	12
896.2.ba.f.865.4		48	112.13	odd	4

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36184 + 0.381311i) q^{2} +(1.60845 - 0.430984i) q^{3} +(1.70920 - 1.03857i) q^{4} +(-1.94900 - 0.522232i) q^{5} +(-2.02612 + 1.20025i) q^{6} +(-1.93164 + 2.06610i) q^{8} +(-0.196696 + 0.113563i) q^{9} +(2.85335 - 0.0319777i) q^{10} +(1.63411 + 6.09856i) q^{11} +(2.30157 - 2.40713i) q^{12} +(-1.13388 - 1.13388i) q^{13} -3.35995 q^{15} +(1.84276 - 3.55024i) q^{16} +(0.960789 - 1.66414i) q^{17} +(0.224566 - 0.229656i) q^{18} +(-1.63324 + 6.09532i) q^{19} +(-3.87361 + 1.13156i) q^{20} +(-4.55083 - 7.68215i) q^{22} +(-0.924606 + 0.533821i) q^{23} +(-2.21651 + 4.15573i) q^{24} +(-0.804265 - 0.464342i) q^{25} +(1.97651 + 1.11180i) q^{26} +(-3.79985 + 3.79985i) q^{27} +(5.08936 + 5.08936i) q^{29} +(4.57570 - 1.28118i) q^{30} +(0.198293 - 0.343454i) q^{31} +(-1.15579 + 5.53752i) q^{32} +(5.25677 + 9.10499i) q^{33} +(-0.673887 + 2.63264i) q^{34} +(-0.218252 + 0.398384i) q^{36} +(0.327303 + 0.0877006i) q^{37} +(-0.100007 - 8.92360i) q^{38} +(-2.31247 - 1.33510i) q^{39} +(4.84375 - 3.01805i) q^{40} +7.26189i q^{41} +(1.75565 - 1.75565i) q^{43} +(9.12678 + 8.72657i) q^{44} +(0.442666 - 0.118612i) q^{45} +(1.05561 - 1.07954i) q^{46} +(1.08118 + 1.87265i) q^{47} +(1.43390 - 6.50461i) q^{48} +(1.27234 + 0.325684i) q^{50} +(0.828170 - 3.09077i) q^{51} +(-3.11563 - 0.760420i) q^{52} +(0.111394 + 0.415727i) q^{53} +(3.72585 - 6.62369i) q^{54} -12.7395i q^{55} +10.5079i q^{57} +(-8.87151 - 4.99025i) q^{58} +(2.32453 + 8.67527i) q^{59} +(-5.74284 + 3.48953i) q^{60} +(2.72673 - 10.1763i) q^{61} +(-0.139080 + 0.543339i) q^{62} +(-0.537512 - 7.98192i) q^{64} +(1.61777 + 2.80206i) q^{65} +(-10.6307 - 10.3951i) q^{66} +(7.87441 - 2.10994i) q^{67} +(-0.0861303 - 3.84219i) q^{68} +(-1.25712 + 1.25712i) q^{69} +2.78982i q^{71} +(0.145316 - 0.625756i) q^{72} +(-2.05730 - 1.18779i) q^{73} +(-0.479175 + 0.00537015i) q^{74} +(-1.49375 - 0.400248i) q^{75} +(3.53886 + 12.1144i) q^{76} +(3.65830 + 0.936427i) q^{78} +(5.10829 + 8.84782i) q^{79} +(-5.44558 + 5.95707i) q^{80} +(-4.13352 + 7.15947i) q^{81} +(-2.76904 - 9.88952i) q^{82} +(-1.17951 - 1.17951i) q^{83} +(-2.74164 + 2.74164i) q^{85} +(-1.72147 + 3.06036i) q^{86} +(10.3794 + 5.99257i) q^{87} +(-15.7567 - 8.40403i) q^{88} +(-11.0470 + 6.37800i) q^{89} +(-0.557612 + 0.330324i) q^{90} +(-1.02593 + 1.87267i) q^{92} +(0.170922 - 0.637891i) q^{93} +(-2.18645 - 2.13799i) q^{94} +(6.36634 - 11.0268i) q^{95} +(0.527542 + 9.40498i) q^{96} +2.21148 q^{97} +(-1.01399 - 1.01399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more