LMFDB - Embedded newform 578.2.d.i.423.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,2,Mod(155,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.155"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.d (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			423.6
Character	$\chi$	$=$	578.423
Dual form			578.2.d.i.399.6

$q$-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} +(1.10189 + 2.66021i) q^{3} +1.00000i q^{4} +(1.52690 - 0.632462i) q^{5} +(1.10189 - 2.66021i) q^{6} +(-2.22791 - 0.922831i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.74120 + 3.74120i) q^{9} +(-1.52690 - 0.632462i) q^{10} +(-0.179062 + 0.432294i) q^{11} +(-2.66021 + 1.10189i) q^{12} +6.22668i q^{13} +(0.922831 + 2.22791i) q^{14} +(3.36496 + 3.36496i) q^{15} -1.00000 q^{16} +5.29086 q^{18} +(4.17311 + 4.17311i) q^{19} +(0.632462 + 1.52690i) q^{20} -6.94356i q^{21} +(0.432294 - 0.179062i) q^{22} +(0.735240 - 1.77503i) q^{23} +(2.66021 + 1.10189i) q^{24} +(-1.60412 + 1.60412i) q^{25} +(4.40293 - 4.40293i) q^{26} +(-6.09416 - 2.52428i) q^{27} +(0.922831 - 2.22791i) q^{28} +(-4.52856 + 1.87579i) q^{29} -4.75877i q^{30} +(-0.320496 - 0.773746i) q^{31} +(0.707107 + 0.707107i) q^{32} -1.34730 q^{33} -3.98545 q^{35} +(-3.74120 - 3.74120i) q^{36} +(0.444871 + 1.07401i) q^{37} -5.90167i q^{38} +(-16.5643 + 6.86114i) q^{39} +(0.632462 - 1.52690i) q^{40} +(3.73422 + 1.54676i) q^{41} +(-4.90984 + 4.90984i) q^{42} +(1.87574 - 1.87574i) q^{43} +(-0.432294 - 0.179062i) q^{44} +(-3.34627 + 8.07861i) q^{45} +(-1.77503 + 0.735240i) q^{46} +3.98545i q^{47} +(-1.10189 - 2.66021i) q^{48} +(-0.837775 - 0.837775i) q^{49} +2.26857 q^{50} -6.22668 q^{52} +(-1.05373 - 1.05373i) q^{53} +(2.52428 + 6.09416i) q^{54} +0.773318i q^{55} +(-2.22791 + 0.922831i) q^{56} +(-6.50301 + 15.6997i) q^{57} +(4.52856 + 1.87579i) q^{58} +(9.76401 - 9.76401i) q^{59} +(-3.36496 + 3.36496i) q^{60} +(-4.07567 - 1.68820i) q^{61} +(-0.320496 + 0.773746i) q^{62} +(11.7876 - 4.88257i) q^{63} -1.00000i q^{64} +(3.93814 + 9.50751i) q^{65} +(0.952682 + 0.952682i) q^{66} -2.10607 q^{67} +5.53209 q^{69} +(2.81814 + 2.81814i) q^{70} +(-4.69498 - 11.3347i) q^{71} +5.29086i q^{72} +(12.0563 - 4.99388i) q^{73} +(0.444871 - 1.07401i) q^{74} +(-6.03486 - 2.49972i) q^{75} +(-4.17311 + 4.17311i) q^{76} +(0.797868 - 0.797868i) q^{77} +(16.5643 + 6.86114i) q^{78} +(3.37640 - 8.15134i) q^{79} +(-1.52690 + 0.632462i) q^{80} -3.12061i q^{81} +(-1.54676 - 3.73422i) q^{82} +(6.28415 + 6.28415i) q^{83} +6.94356 q^{84} -2.65270 q^{86} +(-9.97997 - 9.97997i) q^{87} +(0.179062 + 0.432294i) q^{88} +14.3628i q^{89} +(8.07861 - 3.34627i) q^{90} +(5.74618 - 13.8725i) q^{91} +(1.77503 + 0.735240i) q^{92} +(1.70517 - 1.70517i) q^{93} +(2.81814 - 2.81814i) q^{94} +(9.01126 + 3.73259i) q^{95} +(-1.10189 + 2.66021i) q^{96} +(-12.0104 + 4.97488i) q^{97} +1.18479i q^{98} +(-0.947391 - 2.28720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{16} - 24 q^{33} + 48 q^{35} - 24 q^{50} - 96 q^{52} + 48 q^{67} + 96 q^{69} + 48 q^{84} - 72 q^{86}+O(q^{100}) $ 24 * q - 24 * q^16 - 24 * q^33 + 48 * q^35 - 24 * q^50 - 96 * q^52 + 48 * q^67 + 96 * q^69 + 48 * q^84 - 72 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

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
$3$	1.10189	+	2.66021i	0.636178	+	1.53587i	0.831732	+	0.555177i	$0.187350\pi$
$3$	1.10189	+	2.66021i	0.636178	+	1.53587i	−0.195554	+	0.980693i	$0.562650\pi$
$4$			1.00000i			0.500000i
$5$	1.52690	−	0.632462i	0.682850	−	0.282846i	−0.0141677	−	0.999900i	$-0.504510\pi$
$5$	1.52690	−	0.632462i	0.682850	−	0.282846i	0.697018	+	0.717054i	$0.254510\pi$
$6$	1.10189	−	2.66021i	0.449846	−	1.08602i
$7$	−2.22791	−	0.922831i	−0.842071	−	0.348797i	−0.0804015	−	0.996763i	$-0.525620\pi$
$7$	−2.22791	−	0.922831i	−0.842071	−	0.348797i	−0.761670	+	0.647965i	$0.775620\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−3.74120	+	3.74120i	−1.24707	+	1.24707i
$10$	−1.52690	−	0.632462i	−0.482848	−	0.200002i
$11$	−0.179062	+	0.432294i	−0.0539892	+	0.130341i	−0.948573	−	0.316559i	$-0.897472\pi$
$11$	−0.179062	+	0.432294i	−0.0539892	+	0.130341i	0.894584	+	0.446901i	$0.147472\pi$
$12$	−2.66021	+	1.10189i	−0.767935	+	0.318089i
$13$			6.22668i			1.72697i	0.504374	+	0.863485i	$0.331723\pi$
$13$			6.22668i			1.72697i	−0.504374	+	0.863485i	$0.668277\pi$
$14$	0.922831	+	2.22791i	0.246637	+	0.595434i
$15$	3.36496	+	3.36496i	0.868829	+	0.868829i
$16$	−1.00000			−0.250000
$17$		0			0
$17$		0			0
$18$	5.29086			1.24707
$19$	4.17311	+	4.17311i	0.957378	+	0.957378i	0.999128	−	0.0417501i	$-0.0132933\pi$
$19$	4.17311	+	4.17311i	0.957378	+	0.957378i	−0.0417501	+	0.999128i	$0.513293\pi$
$20$	0.632462	+	1.52690i	0.141423	+	0.341425i
$21$		−	6.94356i		−	1.51521i
$22$	0.432294	−	0.179062i	0.0921653	−	0.0381761i
$23$	0.735240	−	1.77503i	0.153308	−	0.370119i	−0.828501	−	0.559987i	$-0.810806\pi$
$23$	0.735240	−	1.77503i	0.153308	−	0.370119i	0.981810	+	0.189868i	$0.0608061\pi$
$24$	2.66021	+	1.10189i	0.543012	+	0.224923i
$25$	−1.60412	+	1.60412i	−0.320824	+	0.320824i
$26$	4.40293	−	4.40293i	0.863485	−	0.863485i
$27$	−6.09416	−	2.52428i	−1.17282	−	0.485798i
$28$	0.922831	−	2.22791i	0.174399	−	0.421036i
$29$	−4.52856	+	1.87579i	−0.840932	+	0.348325i	−0.761221	−	0.648493i	$-0.775400\pi$
$29$	−4.52856	+	1.87579i	−0.840932	+	0.348325i	−0.0797109	+	0.996818i	$0.525400\pi$
$30$		−	4.75877i		−	0.868829i
$31$	−0.320496	−	0.773746i	−0.0575628	−	0.138969i	0.892482	−	0.451084i	$-0.148963\pi$
$31$	−0.320496	−	0.773746i	−0.0575628	−	0.138969i	−0.950044	+	0.312115i	$0.898963\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.34730			−0.234534
$34$		0			0
$35$	−3.98545			−0.673664
$36$	−3.74120	−	3.74120i	−0.623534	−	0.623534i
$37$	0.444871	+	1.07401i	0.0731363	+	0.176567i	0.956220	−	0.292649i	$-0.0945367\pi$
$37$	0.444871	+	1.07401i	0.0731363	+	0.176567i	−0.883084	+	0.469216i	$0.844537\pi$
$38$		−	5.90167i		−	0.957378i
$39$	−16.5643	+	6.86114i	−2.65240	+	1.09866i
$40$	0.632462	−	1.52690i	0.100001	−	0.241424i
$41$	3.73422	+	1.54676i	0.583187	+	0.241564i	0.654716	−	0.755875i	$-0.272788\pi$
$41$	3.73422	+	1.54676i	0.583187	+	0.241564i	−0.0715295	+	0.997438i	$0.522788\pi$
$42$	−4.90984	+	4.90984i	−0.757605	+	0.757605i
$43$	1.87574	−	1.87574i	0.286048	−	0.286048i	−0.549467	−	0.835515i	$-0.685169\pi$
$43$	1.87574	−	1.87574i	0.286048	−	0.286048i	0.835515	+	0.549467i	$0.185169\pi$
$44$	−0.432294	−	0.179062i	−0.0651707	−	0.0269946i
$45$	−3.34627	+	8.07861i	−0.498832	+	1.20429i
$46$	−1.77503	+	0.735240i	−0.261713	+	0.108405i
$47$			3.98545i			0.581338i	0.956824	+	0.290669i	$0.0938778\pi$
$47$			3.98545i			0.581338i	−0.956824	+	0.290669i	$0.906122\pi$
$48$	−1.10189	−	2.66021i	−0.159045	−	0.383968i
$49$	−0.837775	−	0.837775i	−0.119682	−	0.119682i
$50$	2.26857			0.320824
$51$		0			0
$52$	−6.22668			−0.863485
$53$	−1.05373	−	1.05373i	−0.144741	−	0.144741i	0.631023	−	0.775764i	$-0.282635\pi$
$53$	−1.05373	−	1.05373i	−0.144741	−	0.144741i	−0.775764	+	0.631023i	$0.782635\pi$
$54$	2.52428	+	6.09416i	0.343511	+	0.829310i
$55$			0.773318i			0.104274i
$56$	−2.22791	+	0.922831i	−0.297717	+	0.123319i
$57$	−6.50301	+	15.6997i	−0.861345	+	2.07947i
$58$	4.52856	+	1.87579i	0.594629	+	0.246303i
$59$	9.76401	−	9.76401i	1.27117	−	1.27117i	0.325690	−	0.945477i	$-0.394404\pi$
$59$	9.76401	−	9.76401i	1.27117	−	1.27117i	0.945477	−	0.325690i	$-0.105596\pi$
$60$	−3.36496	+	3.36496i	−0.434414	+	0.434414i
$61$	−4.07567	−	1.68820i	−0.521836	−	0.216152i	0.106187	−	0.994346i	$-0.466136\pi$
$61$	−4.07567	−	1.68820i	−0.521836	−	0.216152i	−0.628023	+	0.778195i	$0.716136\pi$
$62$	−0.320496	+	0.773746i	−0.0407030	+	0.0982658i
$63$	11.7876	−	4.88257i	1.48509	−	0.615146i
$64$		−	1.00000i		−	0.125000i
$65$	3.93814	+	9.50751i	0.488466	+	1.17926i
$66$	0.952682	+	0.952682i	0.117267	+	0.117267i
$67$	−2.10607			−0.257297			−0.128649	−	0.991690i	$-0.541064\pi$
$67$	−2.10607			−0.257297			−0.128649	+	0.991690i	$0.541064\pi$
$68$		0			0
$69$	5.53209			0.665985
$70$	2.81814	+	2.81814i	0.336832	+	0.336832i
$71$	−4.69498	−	11.3347i	−0.557191	−	1.34518i	−0.911981	−	0.410233i	$-0.865447\pi$
$71$	−4.69498	−	11.3347i	−0.557191	−	1.34518i	0.354789	−	0.934946i	$-0.384553\pi$
$72$			5.29086i			0.623534i
$73$	12.0563	−	4.99388i	1.41108	−	0.584489i	0.458479	−	0.888705i	$-0.348395\pi$
$73$	12.0563	−	4.99388i	1.41108	−	0.584489i	0.952603	+	0.304216i	$0.0983946\pi$
$74$	0.444871	−	1.07401i	0.0517152	−	0.124852i
$75$	−6.03486	−	2.49972i	−0.696846	−	0.288643i
$76$	−4.17311	+	4.17311i	−0.478689	+	0.478689i
$77$	0.797868	−	0.797868i	0.0909255	−	0.0909255i
$78$	16.5643	+	6.86114i	1.87553	+	0.776871i
$79$	3.37640	−	8.15134i	0.379874	−	0.917098i	−0.612114	−	0.790769i	$-0.709681\pi$
$79$	3.37640	−	8.15134i	0.379874	−	0.917098i	0.991988	−	0.126328i	$-0.0403193\pi$
$80$	−1.52690	+	0.632462i	−0.170713	+	0.0707114i
$81$		−	3.12061i		−	0.346735i
$82$	−1.54676	−	3.73422i	−0.170812	−	0.412375i
$83$	6.28415	+	6.28415i	0.689775	+	0.689775i	0.962182	−	0.272407i	$-0.0878198\pi$
$83$	6.28415	+	6.28415i	0.689775	+	0.689775i	−0.272407	+	0.962182i	$0.587820\pi$
$84$	6.94356			0.757605
$85$		0			0
$86$	−2.65270			−0.286048
$87$	−9.97997	−	9.97997i	−1.06996	−	1.06996i
$88$	0.179062	+	0.432294i	0.0190881	+	0.0460826i
$89$			14.3628i			1.52245i	0.648487	+	0.761226i	$0.275402\pi$
$89$			14.3628i			1.52245i	−0.648487	+	0.761226i	$0.724598\pi$
$90$	8.07861	−	3.34627i	0.851560	−	0.352728i
$91$	5.74618	−	13.8725i	0.602363	−	1.45423i
$92$	1.77503	+	0.735240i	0.185059	+	0.0766541i
$93$	1.70517	−	1.70517i	0.176818	−	0.176818i
$94$	2.81814	−	2.81814i	0.290669	−	0.290669i
$95$	9.01126	+	3.73259i	0.924536	+	0.382955i
$96$	−1.10189	+	2.66021i	−0.112461	+	0.271506i
$97$	−12.0104	+	4.97488i	−1.21947	+	0.505123i	−0.897243	−	0.441538i	$-0.854433\pi$
$97$	−12.0104	+	4.97488i	−1.21947	+	0.505123i	−0.322232	+	0.946661i	$0.604433\pi$
$98$			1.18479i			0.119682i
$99$	−0.947391	−	2.28720i	−0.0952164	−	0.229873i
$100$	−1.60412	−	1.60412i	−0.160412	−	0.160412i
$101$	15.3550			1.52788			0.763942	−	0.645285i	$-0.223262\pi$
$101$	15.3550			1.52788			0.763942	+	0.645285i	$0.223262\pi$
$102$		0			0
$103$	4.49525			0.442930			0.221465	−	0.975168i	$-0.428916\pi$
$103$	4.49525			0.442930			0.221465	+	0.975168i	$0.428916\pi$
$104$	4.40293	+	4.40293i	0.431743	+	0.431743i
$105$	−4.39154	−	10.6021i	−0.428571	−	1.03466i
$106$			1.49020i			0.144741i
$107$	17.5340	−	7.26281i	1.69507	−	0.702123i	0.695213	−	0.718804i	$-0.255310\pi$
$107$	17.5340	−	7.26281i	1.69507	−	0.702123i	0.999861	+	0.0166810i	$0.00530999\pi$
$108$	2.52428	−	6.09416i	0.242899	−	0.586410i
$109$	−11.1711	−	4.62722i	−1.07000	−	0.443208i	−0.223008	−	0.974817i	$-0.571588\pi$
$109$	−11.1711	−	4.62722i	−1.07000	−	0.443208i	−0.846990	+	0.531609i	$0.821588\pi$
$110$	0.546819	−	0.546819i	0.0521371	−	0.0521371i
$111$	−2.36690	+	2.36690i	−0.224656	+	0.224656i
$112$	2.22791	+	0.922831i	0.210518	+	0.0871994i
$113$	−0.486490	+	1.17449i	−0.0457651	+	0.110487i	−0.945109	−	0.326755i	$-0.894045\pi$
$113$	−0.486490	+	1.17449i	−0.0457651	+	0.110487i	0.899344	+	0.437242i	$0.144045\pi$
$114$	15.6997	−	6.50301i	1.47041	−	0.609063i
$115$		−	3.17530i		−	0.296098i
$116$	−1.87579	−	4.52856i	−0.174163	−	0.420466i
$117$	−23.2953	−	23.2953i	−2.15365	−	2.15365i
$118$	−13.8084			−1.27117
$119$		0			0
$120$	4.75877			0.434414
$121$	7.62336	+	7.62336i	0.693033	+	0.693033i
$122$	1.68820	+	4.07567i	0.152842	+	0.368994i
$123$			11.6382i			1.04938i
$124$	0.773746	−	0.320496i	0.0694844	−	0.0287814i
$125$	−4.59710	+	11.0984i	−0.411177	+	0.992669i
$126$	−11.7876	−	4.88257i	−1.05012	−	0.434974i
$127$	−3.00448	+	3.00448i	−0.266604	+	0.266604i	−0.827730	−	0.561126i	$-0.810368\pi$
$127$	−3.00448	+	3.00448i	−0.266604	+	0.266604i	0.561126	+	0.827730i	$0.310368\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	7.05674	+	2.92300i	0.621311	+	0.257355i
$130$	3.93814	−	9.50751i	0.345398	−	0.833864i
$131$	17.0377	−	7.05726i	1.48859	−	0.616595i	0.517583	−	0.855633i	$-0.326832\pi$
$131$	17.0377	−	7.05726i	1.48859	−	0.616595i	0.971010	+	0.239038i	$0.0768319\pi$
$132$		−	1.34730i		−	0.117267i
$133$	−5.44625	−	13.1484i	−0.472250	−	1.14011i
$134$	1.48921	+	1.48921i	0.128649	+	0.128649i
$135$	−10.9017			−0.938267
$136$		0			0
$137$	−4.79561			−0.409716			−0.204858	−	0.978792i	$-0.565673\pi$
$137$	−4.79561			−0.409716			−0.204858	+	0.978792i	$0.565673\pi$
$138$	−3.91178	−	3.91178i	−0.332993	−	0.332993i
$139$	−1.72685	−	4.16900i	−0.146470	−	0.353610i	0.833569	−	0.552415i	$-0.186294\pi$
$139$	−1.72685	−	4.16900i	−0.146470	−	0.353610i	−0.980039	+	0.198806i	$0.936294\pi$
$140$		−	3.98545i		−	0.336832i
$141$	−10.6021	+	4.39154i	−0.892860	+	0.369835i
$142$	−4.69498	+	11.3347i	−0.393994	+	0.951185i
$143$	−2.69175	−	1.11496i	−0.225096	−	0.0932377i
$144$	3.74120	−	3.74120i	0.311767	−	0.311767i
$145$	−5.72828	+	5.72828i	−0.475708	+	0.475708i
$146$	−12.0563	−	4.99388i	−0.997785	−	0.413296i
$147$	1.30551	−	3.15179i	0.107677	−	0.259955i
$148$	−1.07401	+	0.444871i	−0.0882834	+	0.0365682i
$149$		−	11.3696i		−	0.931433i	−0.884934	−	0.465716i	$-0.845797\pi$
$149$		−	11.3696i		−	0.931433i	0.884934	−	0.465716i	$-0.154203\pi$
$150$	2.49972	+	6.03486i	0.204101	+	0.492745i
$151$	−4.60670	−	4.60670i	−0.374888	−	0.374888i	0.494366	−	0.869254i	$-0.335400\pi$
$151$	−4.60670	−	4.60670i	−0.374888	−	0.374888i	−0.869254	+	0.494366i	$0.835400\pi$
$152$	5.90167			0.478689
$153$		0			0
$154$	−1.12836			−0.0909255
$155$	−0.978730	−	0.978730i	−0.0786135	−	0.0786135i
$156$	−6.86114	−	16.5643i	−0.549331	−	1.32620i
$157$		−	9.55169i		−	0.762308i	−0.924512	−	0.381154i	$-0.875527\pi$
$157$		−	9.55169i		−	0.762308i	0.924512	−	0.381154i	$-0.124473\pi$
$158$	−8.15134	+	3.37640i	−0.648486	+	0.268612i
$159$	1.64204	−	3.96424i	0.130222	−	0.314384i
$160$	1.52690	+	0.632462i	0.120712	+	0.0500005i
$161$	−3.27610	+	3.27610i	−0.258193	+	0.258193i
$162$	−2.20661	+	2.20661i	−0.173367	+	0.173367i
$163$	−10.7136	−	4.43770i	−0.839150	−	0.347587i	−0.0786318	−	0.996904i	$-0.525055\pi$
$163$	−10.7136	−	4.43770i	−0.839150	−	0.347587i	−0.760518	+	0.649316i	$0.775055\pi$
$164$	−1.54676	+	3.73422i	−0.120782	+	0.291593i
$165$	−2.05719	+	0.852114i	−0.160152	+	0.0663370i
$166$		−	8.88713i		−	0.689775i
$167$	0.336526	+	0.812446i	0.0260412	+	0.0628690i	0.936365	−	0.351027i	$-0.114168\pi$
$167$	0.336526	+	0.812446i	0.0260412	+	0.0628690i	−0.910324	+	0.413896i	$0.864168\pi$
$168$	−4.90984	−	4.90984i	−0.378802	−	0.378802i
$169$	−25.7716			−1.98243
$170$		0			0
$171$	−31.2249			−2.38783
$172$	1.87574	+	1.87574i	0.143024	+	0.143024i
$173$	6.54917	+	15.8111i	0.497924	+	1.20210i	0.950600	+	0.310420i	$0.100470\pi$
$173$	6.54917	+	15.8111i	0.497924	+	1.20210i	−0.452675	+	0.891675i	$0.649530\pi$
$174$			14.1138i			1.06996i
$175$	5.05417	−	2.09351i	0.382060	−	0.158254i
$176$	0.179062	−	0.432294i	0.0134973	−	0.0325853i
$177$	36.7332	+	15.2154i	2.76103	+	1.14366i
$178$	10.1560	−	10.1560i	0.761226	−	0.761226i
$179$	10.0810	−	10.0810i	0.753491	−	0.753491i	−0.221638	−	0.975129i	$-0.571140\pi$
$179$	10.0810	−	10.0810i	0.753491	−	0.753491i	0.975129	+	0.221638i	$0.0711404\pi$
$180$	−8.07861	−	3.34627i	−0.602144	−	0.249416i
$181$	4.13063	−	9.97222i	0.307027	−	0.741229i	−0.692771	−	0.721157i	$-0.743610\pi$
$181$	4.13063	−	9.97222i	0.307027	−	0.741229i	0.999799	−	0.0200719i	$-0.00638952\pi$
$182$	−13.8725	+	5.74618i	−1.02830	+	0.425935i
$183$		−	12.7023i		−	0.938984i
$184$	−0.735240	−	1.77503i	−0.0542026	−	0.130857i
$185$	1.35855	+	1.35855i	0.0998823	+	0.0998823i
$186$	−2.41147			−0.176818
$187$		0			0
$188$	−3.98545			−0.290669
$189$	11.2478	+	11.2478i	0.818154	+	0.818154i
$190$	−3.73259	−	9.01126i	−0.270790	−	0.653746i
$191$		−	9.09926i		−	0.658399i	−0.944260	−	0.329200i	$-0.893221\pi$
$191$		−	9.09926i		−	0.658399i	0.944260	−	0.329200i	$-0.106779\pi$
$192$	2.66021	−	1.10189i	0.191984	−	0.0795223i
$193$	3.05590	−	7.37760i	0.219969	−	0.531051i	−0.774917	−	0.632063i	$-0.782208\pi$
$193$	3.05590	−	7.37760i	0.219969	−	0.531051i	0.994885	+	0.101012i	$0.0322082\pi$
$194$	12.0104	+	4.97488i	0.862299	+	0.357176i
$195$	−20.9525	+	20.9525i	−1.50044	+	1.50044i
$196$	0.837775	−	0.837775i	0.0598411	−	0.0598411i
$197$	17.5340	+	7.26281i	1.24924	+	0.517454i	0.906592	−	0.422008i	$-0.138675\pi$
$197$	17.5340	+	7.26281i	1.24924	+	0.517454i	0.342652	+	0.939462i	$0.388675\pi$
$198$	−0.947391	+	2.28720i	−0.0673281	+	0.162545i
$199$	1.26533	−	0.524118i	0.0896970	−	0.0371537i	−0.337384	−	0.941367i	$-0.609542\pi$
$199$	1.26533	−	0.524118i	0.0896970	−	0.0371537i	0.427081	+	0.904213i	$0.359542\pi$
$200$			2.26857i			0.160412i
$201$	−2.32066	−	5.60257i	−0.163687	−	0.395175i
$202$	−10.8577	−	10.8577i	−0.763942	−	0.763942i
$203$	11.8203			0.829620
$204$		0			0
$205$	6.68004			0.466555
$206$	−3.17862	−	3.17862i	−0.221465	−	0.221465i
$207$	3.89005	+	9.39141i	0.270377	+	0.652748i
$208$		−	6.22668i		−	0.431743i
$209$	−2.55126	+	1.05676i	−0.176474	+	0.0730979i
$210$	−4.39154	+	10.6021i	−0.303045	+	0.731616i
$211$	−11.4873	−	4.75820i	−0.790818	−	0.327568i	−0.0495458	−	0.998772i	$-0.515777\pi$
$211$	−11.4873	−	4.75820i	−0.790818	−	0.327568i	−0.741273	+	0.671204i	$0.765777\pi$
$212$	1.05373	−	1.05373i	0.0723705	−	0.0723705i
$213$	24.9792	−	24.9792i	1.71155	−	1.71155i
$214$	−17.5340	−	7.26281i	−1.19860	−	0.496476i
$215$	1.67774	−	4.05041i	0.114421	−	0.276236i
$216$	−6.09416	+	2.52428i	−0.414655	+	0.171756i
$217$			2.01960i			0.137099i
$218$	4.62722	+	11.1711i	0.313395	+	0.756603i
$219$	26.5695	+	26.5695i	1.79540	+	1.79540i
$220$	−0.773318			−0.0521371
$221$		0			0
$222$	3.34730			0.224656
$223$	3.80234	+	3.80234i	0.254624	+	0.254624i	0.822863	−	0.568239i	$-0.192375\pi$
$223$	3.80234	+	3.80234i	0.254624	+	0.254624i	−0.568239	+	0.822863i	$0.692375\pi$
$224$	−0.922831	−	2.22791i	−0.0616593	−	0.148859i
$225$		−	12.0027i		−	0.800179i
$226$	1.17449	−	0.486490i	0.0781259	−	0.0323608i
$227$	−4.23147	+	10.2157i	−0.280853	+	0.678038i	−0.999856	−	0.0169682i	$-0.994599\pi$
$227$	−4.23147	+	10.2157i	−0.280853	+	0.678038i	0.719003	+	0.695007i	$0.244599\pi$
$228$	−15.6997	−	6.50301i	−1.03974	−	0.430673i
$229$	16.9464	−	16.9464i	1.11985	−	1.11985i	0.128088	−	0.991763i	$-0.459116\pi$
$229$	16.9464	−	16.9464i	1.11985	−	1.11985i	0.991763	−	0.128088i	$-0.0408840\pi$
$230$	−2.24527	+	2.24527i	−0.148049	+	0.148049i
$231$	3.00166	+	1.24333i	0.197495	+	0.0818049i
$232$	−1.87579	+	4.52856i	−0.123152	+	0.297314i
$233$	9.65765	−	4.00033i	0.632694	−	0.262070i	−0.0432035	−	0.999066i	$-0.513756\pi$
$233$	9.65765	−	4.00033i	0.632694	−	0.262070i	0.675897	+	0.736996i	$0.263756\pi$
$234$			32.9445i			2.15365i
$235$	2.52065	+	6.08538i	0.164429	+	0.396967i
$236$	9.76401	+	9.76401i	0.635583	+	0.635583i
$237$	25.4047			1.65021
$238$		0			0
$239$	1.86484			0.120626			0.0603131	−	0.998180i	$-0.480790\pi$
$239$	1.86484			0.120626			0.0603131	+	0.998180i	$0.480790\pi$
$240$	−3.36496	−	3.36496i	−0.217207	−	0.217207i
$241$	7.02974	+	16.9713i	0.452825	+	1.09322i	0.971243	+	0.238089i	$0.0765211\pi$
$241$	7.02974	+	16.9713i	0.452825	+	1.09322i	−0.518418	+	0.855127i	$0.673479\pi$
$242$		−	10.7811i		−	0.693033i
$243$	−9.98099	+	4.13426i	−0.640281	+	0.265213i
$244$	1.68820	−	4.07567i	0.108076	−	0.260918i
$245$	−1.80906	−	0.749337i	−0.115577	−	0.0478734i
$246$	8.22942	−	8.22942i	0.524689	−	0.524689i
$247$	−25.9847	+	25.9847i	−1.65336	+	1.65336i
$248$	−0.773746	−	0.320496i	−0.0491329	−	0.0203515i
$249$	−9.79266	+	23.6416i	−0.620585	+	1.49822i
$250$	11.0984	−	4.59710i	0.701923	−	0.290746i
$251$			1.30810i			0.0825663i	0.999147	+	0.0412831i	$0.0131446\pi$
$251$			1.30810i			0.0825663i	−0.999147	+	0.0412831i	$0.986855\pi$
$252$	4.88257	+	11.7876i	0.307573	+	0.742547i
$253$	0.635679	+	0.635679i	0.0399648	+	0.0399648i
$254$	4.24897			0.266604
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.46661	−	8.46661i	−0.528133	−	0.528133i	0.391883	−	0.920015i	$-0.371824\pi$
$257$	−8.46661	−	8.46661i	−0.528133	−	0.528133i	−0.920015	+	0.391883i	$0.871824\pi$
$258$	−2.92300	−	7.05674i	−0.181978	−	0.439333i
$259$		−	2.80335i		−	0.174192i
$260$	−9.50751	+	3.93814i	−0.589631	+	0.244233i
$261$	9.92454	−	23.9600i	0.614313	−	1.48308i
$262$	−17.0377	−	7.05726i	−1.05259	−	0.435999i
$263$	−10.2709	+	10.2709i	−0.633332	+	0.633332i	−0.948902	−	0.315570i	$-0.897804\pi$
$263$	−10.2709	+	10.2709i	−0.633332	+	0.633332i	0.315570	+	0.948902i	$0.397804\pi$
$264$	−0.952682	+	0.952682i	−0.0586335	+	0.0586335i
$265$	−2.27538	−	0.942495i	−0.139776	−	0.0578970i
$266$	−5.44625	+	13.1484i	−0.333931	+	0.806181i
$267$	−38.2079	+	15.8262i	−2.33829	+	0.968550i
$268$		−	2.10607i		−	0.128649i
$269$	−10.7070	−	25.8489i	−0.652815	−	1.57604i	−0.808675	−	0.588256i	$-0.799815\pi$
$269$	−10.7070	−	25.8489i	−0.652815	−	1.57604i	0.155860	−	0.987779i	$-0.450185\pi$
$270$	7.70865	+	7.70865i	0.469133	+	0.469133i
$271$	13.3678			0.812038			0.406019	−	0.913865i	$-0.366917\pi$
$271$	13.3678			0.812038			0.406019	+	0.913865i	$0.366917\pi$
$272$		0			0
$273$	43.2354			2.61672
$274$	3.39101	+	3.39101i	0.204858	+	0.204858i
$275$	−0.406214	−	0.980688i	−0.0244957	−	0.0591377i
$276$			5.53209i			0.332993i
$277$	0.550016	−	0.227824i	0.0330473	−	0.0136886i	−0.366099	−	0.930576i	$-0.619307\pi$
$277$	0.550016	−	0.227824i	0.0330473	−	0.0136886i	0.399146	+	0.916887i	$0.369307\pi$
$278$	−1.72685	+	4.16900i	−0.103570	+	0.250040i
$279$	4.09378	+	1.69570i	0.245088	+	0.101519i
$280$	−2.81814	+	2.81814i	−0.168416	+	0.168416i
$281$	−12.6572	+	12.6572i	−0.755063	+	0.755063i	−0.975419	−	0.220357i	$-0.929278\pi$
$281$	−12.6572	+	12.6572i	−0.755063	+	0.755063i	0.220357	+	0.975419i	$0.429278\pi$
$282$	10.6021	+	4.39154i	0.631347	+	0.261513i
$283$	1.51210	−	3.65053i	0.0898849	−	0.217001i	−0.872544	−	0.488536i	$-0.837531\pi$
$283$	1.51210	−	3.65053i	0.0898849	−	0.217001i	0.962429	+	0.271535i	$0.0875311\pi$
$284$	11.3347	−	4.69498i	0.672590	−	0.278596i
$285$			28.0847i			1.66359i
$286$	1.11496	+	2.69175i	0.0659290	+	0.159167i
$287$	−6.89211	−	6.89211i	−0.406828	−	0.406828i
$288$	−5.29086			−0.311767
$289$		0			0
$290$	8.10101			0.475708
$291$	−26.4684	−	26.4684i	−1.55161	−	1.55161i
$292$	4.99388	+	12.0563i	0.292245	+	0.705541i
$293$			28.0479i			1.63857i	0.573383	+	0.819287i	$0.305631\pi$
$293$			28.0479i			1.63857i	−0.573383	+	0.819287i	$0.694369\pi$
$294$	−3.15179	+	1.30551i	−0.183816	+	0.0761392i
$295$	8.73329	−	21.0840i	0.508472	−	1.22756i
$296$	1.07401	+	0.444871i	0.0624258	+	0.0258576i
$297$	2.18246	−	2.18246i	0.126639	−	0.126639i
$298$	−8.03951	+	8.03951i	−0.465716	+	0.465716i
$299$	11.0525	+	4.57810i	0.639184	+	0.264759i
$300$	2.49972	−	6.03486i	0.144322	−	0.348423i
$301$	−5.90999	+	2.44800i	−0.340646	+	0.141100i
$302$			6.51485i			0.374888i
$303$	16.9196	+	40.8475i	0.972006	+	2.34663i
$304$	−4.17311	−	4.17311i	−0.239344	−	0.239344i
$305$	−7.29086			−0.417473
$306$		0			0
$307$	21.5202			1.22822			0.614112	−	0.789219i	$-0.289514\pi$
$307$	21.5202			1.22822			0.614112	+	0.789219i	$0.289514\pi$
$308$	0.797868	+	0.797868i	0.0454627	+	0.0454627i
$309$	4.95329	+	11.9583i	0.281783	+	0.680284i
$310$			1.38413i			0.0786135i
$311$	−4.36879	+	1.80961i	−0.247731	+	0.102614i	−0.503094	−	0.864232i	$-0.667805\pi$
$311$	−4.36879	+	1.80961i	−0.247731	+	0.102614i	0.255363	+	0.966845i	$0.417805\pi$
$312$	−6.86114	+	16.5643i	−0.388435	+	0.937766i
$313$	16.2909	+	6.74790i	0.920814	+	0.381414i	0.792186	−	0.610279i	$-0.208943\pi$
$313$	16.2909	+	6.74790i	0.920814	+	0.381414i	0.128628	+	0.991693i	$0.458943\pi$
$314$	−6.75406	+	6.75406i	−0.381154	+	0.381154i
$315$	14.9104	−	14.9104i	0.840105	−	0.840105i
$316$	8.15134	+	3.37640i	0.458549	+	0.189937i
$317$	−6.80941	+	16.4394i	−0.382455	+	0.923327i	0.609035	+	0.793143i	$0.291557\pi$
$317$	−6.80941	+	16.4394i	−0.382455	+	0.923327i	−0.991490	+	0.130184i	$0.958443\pi$
$318$	−3.96424	+	1.64204i	−0.222303	+	0.0920811i
$319$		−	2.29355i		−	0.128414i
$320$	−0.632462	−	1.52690i	−0.0353557	−	0.0853563i
$321$	38.6411	+	38.6411i	2.15674	+	2.15674i
$322$	4.63310			0.258193
$323$		0			0
$324$	3.12061			0.173367
$325$	−9.98836	−	9.98836i	−0.554054	−	0.554054i
$326$	4.43770	+	10.7136i	0.245781	+	0.593369i
$327$		−	34.8161i		−	1.92534i
$328$	3.73422	−	1.54676i	0.206188	−	0.0854058i
$329$	3.67790	−	8.87923i	0.202769	−	0.489528i
$330$	2.05719	+	0.852114i	0.113244	+	0.0469073i
$331$	−24.7198	+	24.7198i	−1.35872	+	1.35872i	−0.483226	+	0.875495i	$0.660535\pi$
$331$	−24.7198	+	24.7198i	−1.35872	+	1.35872i	−0.875495	+	0.483226i	$0.839465\pi$
$332$	−6.28415	+	6.28415i	−0.344887	+	0.344887i
$333$	−5.68245	−	2.35375i	−0.311397	−	0.128985i
$334$	0.336526	−	0.812446i	0.0184139	−	0.0444551i
$335$	−3.21575	+	1.33201i	−0.175695	+	0.0727754i
$336$			6.94356i			0.378802i
$337$	5.99402	+	14.4708i	0.326515	+	0.788277i	0.998846	+	0.0480266i	$0.0152932\pi$
$337$	5.99402	+	14.4708i	0.326515	+	0.788277i	−0.672331	+	0.740251i	$0.734707\pi$
$338$	18.2232	+	18.2232i	0.991214	+	0.991214i
$339$	−3.66044			−0.198808
$340$		0			0
$341$	0.391874			0.0212212
$342$	22.0794	+	22.0794i	1.19391	+	1.19391i
$343$	7.55318	+	18.2350i	0.407833	+	0.984597i
$344$		−	2.65270i		−	0.143024i
$345$	8.44694	−	3.49884i	0.454768	−	0.188371i
$346$	6.54917	−	15.8111i	0.352086	−	0.850010i
$347$	−9.65136	−	3.99772i	−0.518112	−	0.214609i	0.108275	−	0.994121i	$-0.465467\pi$
$347$	−9.65136	−	3.99772i	−0.518112	−	0.214609i	−0.626387	+	0.779512i	$0.715467\pi$
$348$	9.97997	−	9.97997i	0.534982	−	0.534982i
$349$	5.88857	−	5.88857i	0.315208	−	0.315208i	−0.531715	−	0.846923i	$-0.678452\pi$
$349$	5.88857	−	5.88857i	0.315208	−	0.315208i	0.846923	+	0.531715i	$0.178452\pi$
$350$	−5.05417	−	2.09351i	−0.270157	−	0.111903i
$351$	15.7179	−	37.9464i	0.838959	−	2.02543i
$352$	−0.432294	+	0.179062i	−0.0230413	+	0.00954403i
$353$		−	7.20439i		−	0.383451i	−0.981449	−	0.191726i	$-0.938592\pi$
$353$		−	7.20439i		−	0.383451i	0.981449	−	0.191726i	$-0.0614084\pi$
$354$	−15.2154	−	36.7332i	−0.808688	−	1.95235i
$355$	−14.3375	−	14.3375i	−0.760956	−	0.760956i
$356$	−14.3628			−0.761226
$357$		0			0
$358$	−14.2567			−0.753491
$359$	−8.59538	−	8.59538i	−0.453647	−	0.453647i	0.442916	−	0.896563i	$-0.353944\pi$
$359$	−8.59538	−	8.59538i	−0.453647	−	0.453647i	−0.896563	+	0.442916i	$0.853944\pi$
$360$	3.34627	+	8.07861i	0.176364	+	0.425780i
$361$			15.8298i			0.833145i
$362$	−9.97222	+	4.13063i	−0.524128	+	0.217101i
$363$	−11.8796	+	28.6798i	−0.623516	+	1.50530i
$364$	13.8725	+	5.74618i	0.727116	+	0.301181i
$365$	15.2503	−	15.2503i	0.798237	−	0.798237i
$366$	−8.98191	+	8.98191i	−0.469492	+	0.469492i
$367$	−33.4169	−	13.8418i	−1.74435	−	0.722534i	−0.998401	−	0.0565314i	$-0.981996\pi$
$367$	−33.4169	−	13.8418i	−1.74435	−	0.722534i	−0.745950	−	0.666002i	$-0.768004\pi$
$368$	−0.735240	+	1.77503i	−0.0383270	+	0.0925296i
$369$	−19.7572	+	8.18371i	−1.02852	+	0.426027i
$370$		−	1.92127i		−	0.0998823i
$371$	1.37520	+	3.32003i	0.0713970	+	0.172368i
$372$	1.70517	+	1.70517i	0.0884089	+	0.0884089i
$373$	−28.0077			−1.45019			−0.725093	−	0.688651i	$-0.758203\pi$
$373$	−28.0077			−1.45019			−0.725093	+	0.688651i	$0.758203\pi$
$374$		0			0
$375$	−34.5895			−1.78619
$376$	2.81814	+	2.81814i	0.145334	+	0.145334i
$377$	−11.6799	−	28.1979i	−0.601548	−	1.45226i
$378$		−	15.9067i		−	0.818154i
$379$	0.0655815	−	0.0271647i	0.00336870	−	0.00139536i	−0.380998	−	0.924576i	$-0.624420\pi$
$379$	0.0655815	−	0.0271647i	0.00336870	−	0.00139536i	0.384367	+	0.923180i	$0.374420\pi$
$380$	−3.73259	+	9.01126i	−0.191478	+	0.462268i
$381$	−11.3031	−	4.68191i	−0.579077	−	0.239862i
$382$	−6.43415	+	6.43415i	−0.329200	+	0.329200i
$383$	11.9742	−	11.9742i	0.611853	−	0.611853i	−0.331576	−	0.943429i	$-0.607580\pi$
$383$	11.9742	−	11.9742i	0.611853	−	0.611853i	0.943429	+	0.331576i	$0.107580\pi$
$384$	−2.66021	−	1.10189i	−0.135753	−	0.0562307i
$385$	0.713642	−	1.72289i	0.0363706	−	0.0878064i
$386$	−7.37760	+	3.05590i	−0.375510	+	0.155541i
$387$			14.0351i			0.713443i
$388$	−4.97488	−	12.0104i	−0.252562	−	0.609737i
$389$	−21.6632	−	21.6632i	−1.09837	−	1.09837i	−0.994602	−	0.103767i	$-0.966911\pi$
$389$	−21.6632	−	21.6632i	−1.09837	−	1.09837i	−0.103767	−	0.994602i	$-0.533089\pi$
$390$	29.6313			1.50044
$391$		0			0
$392$	−1.18479			−0.0598411
$393$	37.5475	+	37.5475i	1.89402	+	1.89402i
$394$	−7.26281	−	17.5340i	−0.365895	−	0.883349i
$395$		−	14.5817i		−	0.733686i
$396$	2.28720	−	0.947391i	0.114936	−	0.0476082i
$397$	0.260913	−	0.629901i	0.0130949	−	0.0316138i	−0.917197	−	0.398434i	$-0.869554\pi$
$397$	0.260913	−	0.629901i	0.0130949	−	0.0316138i	0.930292	+	0.366821i	$0.119554\pi$
$398$	−1.26533	−	0.524118i	−0.0634253	−	0.0262716i
$399$	28.9763	−	28.9763i	1.45063	−	1.45063i
$400$	1.60412	−	1.60412i	0.0802061	−	0.0802061i
$401$	−15.1329	−	6.26824i	−0.755699	−	0.313021i	−0.0286345	−	0.999590i	$-0.509116\pi$
$401$	−15.1329	−	6.26824i	−0.755699	−	0.313021i	−0.727064	+	0.686569i	$0.759116\pi$
$402$	−2.32066	+	5.60257i	−0.115744	+	0.279431i
$403$	4.81787	−	1.99563i	0.239995	−	0.0994092i
$404$			15.3550i			0.763942i
$405$	−1.97367	−	4.76486i	−0.0980725	−	0.236768i
$406$	−8.35819	−	8.35819i	−0.414810	−	0.414810i
$407$	−0.543948			−0.0269625
$408$		0			0
$409$	−1.64084			−0.0811345			−0.0405673	−	0.999177i	$-0.512917\pi$
$409$	−1.64084			−0.0811345			−0.0405673	+	0.999177i	$0.512917\pi$
$410$	−4.72350	−	4.72350i	−0.233277	−	0.233277i
$411$	−5.28425	−	12.7573i	−0.260653	−	0.629271i
$412$			4.49525i			0.221465i
$413$	−30.7639	+	12.7428i	−1.51379	+	0.627033i
$414$	3.89005	−	9.39141i	0.191186	−	0.461563i
$415$	13.5697	+	5.62077i	0.666113	+	0.275913i
$416$	−4.40293	+	4.40293i	−0.215871	+	0.215871i
$417$	9.18757	−	9.18757i	0.449917	−	0.449917i
$418$	2.55126	+	1.05676i	0.124786	+	0.0516880i
$419$	−11.2838	+	27.2416i	−0.551251	+	1.33084i	0.365288	+	0.930895i	$0.380970\pi$
$419$	−11.2838	+	27.2416i	−0.551251	+	1.33084i	−0.916540	+	0.399944i	$0.869030\pi$
$420$	10.6021	−	4.39154i	0.517330	−	0.214285i
$421$		−	20.2550i		−	0.987166i	−0.869699	−	0.493583i	$-0.835687\pi$
$421$		−	20.2550i		−	0.987166i	0.869699	−	0.493583i	$-0.164313\pi$
$422$	4.75820	+	11.4873i	0.231625	+	0.559193i
$423$	−14.9104	−	14.9104i	−0.724968	−	0.724968i
$424$	−1.49020			−0.0723705
$425$		0			0
$426$	−35.3259			−1.71155
$427$	7.52231	+	7.52231i	0.364030	+	0.364030i
$428$	7.26281	+	17.5340i	0.351061	+	0.847537i
$429$		−	8.38919i		−	0.405034i
$430$	−4.05041	+	1.67774i	−0.195328	+	0.0809076i
$431$	1.21912	−	2.94323i	0.0587232	−	0.141770i	−0.891795	−	0.452441i	$-0.850553\pi$
$431$	1.21912	−	2.94323i	0.0587232	−	0.141770i	0.950518	+	0.310670i	$0.100553\pi$
$432$	6.09416	+	2.52428i	0.293205	+	0.121450i
$433$	−3.83006	+	3.83006i	−0.184061	+	0.184061i	−0.793123	−	0.609062i	$-0.791546\pi$
$433$	−3.83006	+	3.83006i	−0.184061	+	0.184061i	0.609062	+	0.793123i	$0.291546\pi$
$434$	1.42807	−	1.42807i	0.0685497	−	0.0685497i
$435$	−21.5504	−	8.92645i	−1.03326	−	0.427991i
$436$	4.62722	−	11.1711i	0.221604	−	0.534999i
$437$	10.4756	−	4.33915i	0.501117	−	0.207569i
$438$		−	37.5749i		−	1.79540i
$439$	−0.767300	−	1.85243i	−0.0366212	−	0.0884115i	0.904511	−	0.426451i	$-0.140236\pi$
$439$	−0.767300	−	1.85243i	−0.0366212	−	0.0884115i	−0.941132	+	0.338039i	$0.890236\pi$
$440$	0.546819	+	0.546819i	0.0260686	+	0.0260686i
$441$	6.26857			0.298503
$442$		0			0
$443$	0.0760373			0.00361264			0.00180632	−	0.999998i	$-0.499425\pi$
$443$	0.0760373			0.00361264			0.00180632	+	0.999998i	$0.499425\pi$
$444$	−2.36690	−	2.36690i	−0.112328	−	0.112328i
$445$	9.08392	+	21.9305i	0.430619	+	1.03961i
$446$		−	5.37733i		−	0.254624i
$447$	30.2454	−	12.5281i	1.43056	−	0.592557i
$448$	−0.922831	+	2.22791i	−0.0435997	+	0.105259i
$449$	11.2241	+	4.64918i	0.529699	+	0.219408i	0.631471	−	0.775399i	$-0.282451\pi$
$449$	11.2241	+	4.64918i	0.529699	+	0.219408i	−0.101773	+	0.994808i	$0.532451\pi$
$450$	−8.48718	+	8.48718i	−0.400090	+	0.400090i
$451$	−1.33731	+	1.33731i	−0.0629716	+	0.0629716i
$452$	−1.17449	−	0.486490i	−0.0552434	−	0.0228826i
$453$	7.17867	−	17.3308i	0.337283	−	0.814274i
$454$	10.2157	−	4.23147i	0.479446	−	0.198593i
$455$		−	24.8161i		−	1.16340i
$456$	6.50301	+	15.6997i	0.304532	+	0.735204i
$457$	−6.72635	−	6.72635i	−0.314645	−	0.314645i	0.532061	−	0.846706i	$-0.321418\pi$
$457$	−6.72635	−	6.72635i	−0.314645	−	0.314645i	−0.846706	+	0.532061i	$0.821418\pi$
$458$	−23.9659			−1.11985
$459$		0			0
$460$	3.17530			0.148049
$461$	−7.52779	−	7.52779i	−0.350604	−	0.350604i	0.509730	−	0.860334i	$-0.329745\pi$
$461$	−7.52779	−	7.52779i	−0.350604	−	0.350604i	−0.860334	+	0.509730i	$0.829745\pi$
$462$	−1.24333	−	3.00166i	−0.0578448	−	0.139650i
$463$		−	20.2172i		−	0.939572i	−0.882780	−	0.469786i	$-0.844331\pi$
$463$		−	20.2172i		−	0.939572i	0.882780	−	0.469786i	$-0.155669\pi$
$464$	4.52856	−	1.87579i	0.210233	−	0.0870813i
$465$	1.52517	−	3.68208i	0.0707279	−	0.170752i
$466$	−9.65765	−	4.00033i	−0.447382	−	0.185312i
$467$	−13.1476	+	13.1476i	−0.608400	+	0.608400i	−0.942528	−	0.334127i	$-0.891558\pi$
$467$	−13.1476	+	13.1476i	−0.608400	+	0.608400i	0.334127	+	0.942528i	$0.391558\pi$
$468$	23.2953	−	23.2953i	1.07682	−	1.07682i
$469$	4.69213	+	1.94354i	0.216662	+	0.0897445i
$470$	2.52065	−	6.08538i	0.116269	−	0.280698i
$471$	25.4095	−	10.5249i	1.17081	−	0.484964i
$472$		−	13.8084i		−	0.635583i
$473$	0.474998	+	1.14675i	0.0218404	+	0.0527275i
$474$	−17.9638	−	17.9638i	−0.825105	−	0.825105i
$475$	−13.3884			−0.614300
$476$		0			0
$477$	7.88444			0.361004
$478$	−1.31864	−	1.31864i	−0.0603131	−	0.0603131i
$479$	−9.61621	−	23.2156i	−0.439376	−	1.06075i	−0.976165	−	0.217030i	$-0.930363\pi$
$479$	−9.61621	−	23.2156i	−0.439376	−	1.06075i	0.536789	−	0.843716i	$-0.319637\pi$
$480$			4.75877i			0.217207i
$481$	−6.68754	+	2.77007i	−0.304926	+	0.126304i
$482$	7.02974	−	16.9713i	0.320196	−	0.773021i
$483$	−12.3250	−	5.10518i	−0.560807	−	0.232294i
$484$	−7.62336	+	7.62336i	−0.346516	+	0.346516i
$485$	−15.1923	+	15.1923i	−0.689847	+	0.689847i
$486$	9.98099	+	4.13426i	0.452747	+	0.187534i
$487$	−10.2159	+	24.6635i	−0.462928	+	1.11761i	0.504261	+	0.863551i	$0.331765\pi$
$487$	−10.2159	+	24.6635i	−0.462928	+	1.11761i	−0.967189	+	0.254056i	$0.918235\pi$
$488$	−4.07567	+	1.68820i	−0.184497	+	0.0764211i
$489$		−	33.3901i		−	1.50995i
$490$	0.749337	+	1.80906i	0.0338516	+	0.0817249i
$491$	−3.39268	−	3.39268i	−0.153109	−	0.153109i	0.626396	−	0.779505i	$-0.284529\pi$
$491$	−3.39268	−	3.39268i	−0.153109	−	0.153109i	−0.779505	+	0.626396i	$0.784529\pi$
$492$	−11.6382			−0.524689
$493$		0			0
$494$	36.7478			1.65336
$495$	−2.89314	−	2.89314i	−0.130037	−	0.130037i
$496$	0.320496	+	0.773746i	0.0143907	+	0.0347422i
$497$			29.5853i			1.32708i
$498$	23.6416	−	9.79266i	1.05940	−	0.438820i
$499$	−2.68925	+	6.49242i	−0.120387	+	0.290640i	−0.972573	−	0.232600i	$-0.925277\pi$
$499$	−2.68925	+	6.49242i	−0.120387	+	0.290640i	0.852185	+	0.523240i	$0.175277\pi$
$500$	−11.0984	−	4.59710i	−0.496334	−	0.205588i
$501$	−1.79046	+	1.79046i	−0.0799917	+	0.0799917i
$502$	0.924963	−	0.924963i	0.0412831	−	0.0412831i
$503$	30.5520	+	12.6550i	1.36225	+	0.564261i	0.939675	−	0.342069i	$-0.111128\pi$
$503$	30.5520	+	12.6550i	1.36225	+	0.564261i	0.422571	+	0.906330i	$0.361128\pi$
$504$	4.88257	−	11.7876i	0.217487	−	0.525060i
$505$	23.4456	−	9.71148i	1.04332	−	0.432155i
$506$		−	0.898986i		−	0.0399648i
$507$	−28.3975	−	68.5576i	−1.26118	−	3.04475i
$508$	−3.00448	−	3.00448i	−0.133302	−	0.133302i
$509$	−0.182104			−0.00807163			−0.00403581	−	0.999992i	$-0.501285\pi$
$509$	−0.182104			−0.00807163			−0.00403581	+	0.999992i	$0.501285\pi$
$510$		0			0
$511$	−31.4688			−1.39210
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−14.8975	−	35.9657i	−0.657740	−	1.58793i
$514$			11.9736i			0.528133i
$515$	6.86380	−	2.84308i	0.302455	−	0.125281i
$516$	−2.92300	+	7.05674i	−0.128678	+	0.310655i
$517$	−1.72289	−	0.713642i	−0.0757724	−	0.0313860i
$518$	−1.98227	+	1.98227i	−0.0870958	+	0.0870958i
$519$	−34.8443	+	34.8443i	−1.52949	+	1.52949i
$520$	9.50751	+	3.93814i	0.416932	+	0.172699i
$521$	12.5893	−	30.3934i	0.551549	−	1.33156i	−0.364765	−	0.931099i	$-0.618851\pi$
$521$	12.5893	−	30.3934i	0.551549	−	1.33156i	0.916315	−	0.400459i	$-0.131149\pi$
$522$	−23.9600	+	9.92454i	−1.04870	+	0.434385i
$523$			27.3756i			1.19705i	0.801104	+	0.598525i	$0.204246\pi$
$523$			27.3756i			1.19705i	−0.801104	+	0.598525i	$0.795754\pi$
$524$	7.05726	+	17.0377i	0.308298	+	0.744297i
$525$	11.1383	+	11.1383i	0.486116	+	0.486116i
$526$	14.5253			0.633332
$527$		0			0
$528$	1.34730			0.0586335
$529$	13.6533	+	13.6533i	0.593622	+	0.593622i
$530$	0.942495	+	2.27538i	0.0409394	+	0.0988364i
$531$			73.0583i			3.17046i
$532$	13.1484	−	5.44625i	0.570056	−	0.236125i
$533$	−9.63121	+	23.2518i	−0.417174	+	1.00715i
$534$	38.2079	+	15.8262i	1.65342	+	0.684869i
$535$	22.1792	−	22.1792i	0.958889	−	0.958889i
$536$	−1.48921	+	1.48921i	−0.0643243	+	0.0643243i
$537$	37.9258	+	15.7094i	1.63662	+	0.677909i
$538$	−10.7070	+	25.8489i	−0.461610	+	1.11443i
$539$	0.512178	−	0.212151i	0.0220611	−	0.00913800i
$540$		−	10.9017i		−	0.469133i
$541$	4.74011	+	11.4436i	0.203793	+	0.492000i	0.992423	−	0.122868i	$-0.0392092\pi$
$541$	4.74011	+	11.4436i	0.203793	+	0.492000i	−0.788630	+	0.614868i	$0.789209\pi$
$542$	−9.45248	−	9.45248i	−0.406019	−	0.406019i
$543$	31.0797			1.33376
$544$		0			0
$545$	−19.9837			−0.856008
$546$	−30.5720	−	30.5720i	−1.30836	−	1.30836i
$547$	−0.239673	−	0.578622i	−0.0102477	−	0.0247401i	0.918673	−	0.395019i	$-0.129262\pi$
$547$	−0.239673	−	0.578622i	−0.0102477	−	0.0247401i	−0.928921	+	0.370279i	$0.879262\pi$
$548$		−	4.79561i		−	0.204858i
$549$	21.5638	−	8.93202i	0.920321	−	0.381209i
$550$	−0.406214	+	0.980688i	−0.0173210	+	0.0418167i
$551$	−26.7261	−	11.0703i	−1.13857	−	0.471611i
$552$	3.91178	−	3.91178i	0.166496	−	0.166496i
$553$	−15.0446	+	15.0446i	−0.639762	+	0.639762i
$554$	−0.550016	−	0.227824i	−0.0233679	−	0.00967932i
$555$	−2.11704	+	5.11098i	−0.0898633	+	0.216949i
$556$	4.16900	−	1.72685i	0.176805	−	0.0732349i
$557$			31.1516i			1.31993i	0.751294	+	0.659967i	$0.229430\pi$
$557$			31.1516i			1.31993i	−0.751294	+	0.659967i	$0.770570\pi$
$558$	−1.69570	−	4.09378i	−0.0717847	−	0.173303i
$559$	11.6797	+	11.6797i	0.493997	+	0.493997i
$560$	3.98545			0.168416
$561$		0			0
$562$	17.8999			0.755063
$563$	7.18473	+	7.18473i	0.302800	+	0.302800i	0.842109	−	0.539308i	$-0.181314\pi$
$563$	7.18473	+	7.18473i	0.302800	+	0.302800i	−0.539308	+	0.842109i	$0.681314\pi$
$564$	−4.39154	−	10.6021i	−0.184917	−	0.446430i
$565$			2.10101i			0.0883903i
$566$	−3.65053	+	1.51210i	−0.153443	+	0.0635582i
$567$	−2.87980	+	6.95245i	−0.120940	+	0.291976i
$568$	−11.3347	−	4.69498i	−0.475593	−	0.196997i
$569$	−9.44534	+	9.44534i	−0.395969	+	0.395969i	−0.876809	−	0.480839i	$-0.840332\pi$
$569$	−9.44534	+	9.44534i	−0.395969	+	0.395969i	0.480839	+	0.876809i	$0.340332\pi$
$570$	19.8589	−	19.8589i	0.831797	−	0.831797i
$571$	4.75771	+	1.97071i	0.199104	+	0.0824716i	0.480007	−	0.877264i	$-0.340634\pi$
$571$	4.75771	+	1.97071i	0.199104	+	0.0824716i	−0.280903	+	0.959736i	$0.590634\pi$
$572$	1.11496	−	2.69175i	0.0466189	−	0.112548i
$573$	24.2059	−	10.0264i	1.01122	−	0.418859i
$574$			9.74691i			0.406828i
$575$	1.66794	+	4.02677i	0.0695581	+	0.167928i
$576$	3.74120	+	3.74120i	0.155883	+	0.155883i
$577$	6.24628			0.260036			0.130018	−	0.991512i	$-0.458496\pi$
$577$	6.24628			0.260036			0.130018	+	0.991512i	$0.458496\pi$
$578$		0			0
$579$	22.9932			0.955564
$580$	−5.72828	−	5.72828i	−0.237854	−	0.237854i
$581$	−8.20132	−	19.7997i	−0.340248	−	0.821431i
$582$			37.4320i			1.55161i
$583$	0.644204	−	0.266838i	0.0266802	−	0.0110513i
$584$	4.99388	−	12.0563i	0.206648	−	0.498893i
$585$	−50.3029	−	20.8362i	−2.07977	−	0.861469i
$586$	19.8328	−	19.8328i	0.819287	−	0.819287i
$587$	21.5908	−	21.5908i	0.891146	−	0.891146i	−0.103485	−	0.994631i	$-0.532999\pi$
$587$	21.5908	−	21.5908i	0.891146	−	0.891146i	0.994631	+	0.103485i	$0.0329993\pi$
$588$	3.15179	+	1.30551i	0.129978	+	0.0538385i
$589$	1.89146	−	4.56639i	0.0779363	−	0.188155i
$590$	−21.0840	+	8.73329i	−0.868016	+	0.359544i
$591$			54.6468i			2.24787i
$592$	−0.444871	−	1.07401i	−0.0182841	−	0.0441417i
$593$	−16.7801	−	16.7801i	−0.689075	−	0.689075i	0.272952	−	0.962028i	$-0.412000\pi$
$593$	−16.7801	−	16.7801i	−0.689075	−	0.689075i	−0.962028	+	0.272952i	$0.912000\pi$
$594$	−3.08647			−0.126639
$595$		0			0
$596$	11.3696			0.465716
$597$	2.78852	+	2.78852i	0.114127	+	0.114127i
$598$	−4.57810	−	11.0525i	−0.187213	−	0.451971i
$599$			8.16344i			0.333549i	0.985995	+	0.166775i	$0.0533352\pi$
$599$			8.16344i			0.333549i	−0.985995	+	0.166775i	$0.946665\pi$
$600$	−6.03486	+	2.49972i	−0.246372	+	0.102051i
$601$	−11.8926	+	28.7114i	−0.485111	+	1.17116i	0.472041	+	0.881576i	$0.343517\pi$
$601$	−11.8926	+	28.7114i	−0.485111	+	1.17116i	−0.957152	+	0.289585i	$0.906483\pi$
$602$	5.90999	+	2.44800i	0.240873	+	0.0997729i
$603$	7.87922	−	7.87922i	0.320867	−	0.320867i
$604$	4.60670	−	4.60670i	0.187444	−	0.187444i
$605$	16.4616	+	6.81861i	0.669259	+	0.277216i
$606$	16.9196	−	40.8475i	0.687312	−	1.65932i
$607$	5.30200	−	2.19616i	0.215202	−	0.0891394i	−0.272478	−	0.962162i	$-0.587843\pi$
$607$	5.30200	−	2.19616i	0.215202	−	0.0891394i	0.487680	+	0.873022i	$0.337843\pi$
$608$			5.90167i			0.239344i
$609$	13.0247	+	31.4443i	0.527786	+	1.27419i
$610$	5.15542	+	5.15542i	0.208737	+	0.208737i
$611$	−24.8161			−1.00395
$612$		0			0
$613$	−33.1762			−1.33998			−0.669988	−	0.742372i	$-0.733701\pi$
$613$	−33.1762			−1.33998			−0.669988	+	0.742372i	$0.733701\pi$
$614$	−15.2171	−	15.2171i	−0.614112	−	0.614112i
$615$	7.36069	+	17.7703i	0.296812	+	0.716567i
$616$		−	1.12836i		−	0.0454627i
$617$	13.8338	−	5.73015i	0.556928	−	0.230687i	−0.0864231	−	0.996259i	$-0.527544\pi$
$617$	13.8338	−	5.73015i	0.556928	−	0.230687i	0.643351	+	0.765572i	$0.277544\pi$
$618$	4.95329	−	11.9583i	0.199250	−	0.481033i
$619$	−18.6610	−	7.72964i	−0.750049	−	0.310680i	−0.0252873	−	0.999680i	$-0.508050\pi$
$619$	−18.6610	−	7.72964i	−0.750049	−	0.310680i	−0.724762	+	0.689000i	$0.758050\pi$
$620$	0.978730	−	0.978730i	0.0393067	−	0.0393067i
$621$	−8.96133	+	8.96133i	−0.359606	+	0.359606i
$622$	4.36879	+	1.80961i	0.175172	+	0.0725588i
$623$	13.2544	−	31.9990i	0.531027	−	1.28201i
$624$	16.5643	−	6.86114i	0.663101	−	0.274665i
$625$			8.51073i			0.340429i
$626$	−6.74790	−	16.2909i	−0.269700	−	0.651114i
$627$	−5.62242	−	5.62242i	−0.224538	−	0.224538i
$628$	9.55169			0.381154
$629$		0			0
$630$	−21.0865			−0.840105
$631$	−2.86899	−	2.86899i	−0.114213	−	0.114213i	0.647691	−	0.761903i	$-0.275735\pi$
$631$	−2.86899	−	2.86899i	−0.114213	−	0.114213i	−0.761903	+	0.647691i	$0.775735\pi$
$632$	−3.37640	−	8.15134i	−0.134306	−	0.324243i
$633$		−	35.8016i		−	1.42299i
$634$	16.4394	−	6.80941i	0.652891	−	0.270436i
$635$	−2.68731	+	6.48775i	−0.106643	+	0.257458i
$636$	3.96424	+	1.64204i	0.157192	+	0.0651112i
$637$	5.21656	−	5.21656i	0.206688	−	0.206688i
$638$	−1.62178	+	1.62178i	−0.0642070	+	0.0642070i
$639$	59.9702	+	24.8405i	2.37238	+	0.982674i
$640$	−0.632462	+	1.52690i	−0.0250003	+	0.0603560i
$641$	9.97384	−	4.13130i	0.393943	−	0.163177i	−0.176913	−	0.984226i	$-0.556611\pi$
$641$	9.97384	−	4.13130i	0.393943	−	0.163177i	0.570856	+	0.821050i	$0.306611\pi$
$642$		−	54.6468i		−	2.15674i
$643$	−6.32759	−	15.2761i	−0.249536	−	0.602432i	0.748629	−	0.662989i	$-0.230712\pi$
$643$	−6.32759	−	15.2761i	−0.249536	−	0.602432i	−0.998165	+	0.0605567i	$0.980712\pi$
$644$	−3.27610	−	3.27610i	−0.129096	−	0.129096i
$645$	12.6236			0.497054
$646$		0			0
$647$	49.4397			1.94368			0.971839	−	0.235648i	$-0.0757211\pi$
$647$	49.4397			1.94368			0.971839	+	0.235648i	$0.0757211\pi$
$648$	−2.20661	−	2.20661i	−0.0866837	−	0.0866837i
$649$	2.47256	+	5.96928i	0.0970564	+	0.234315i
$650$			14.1257i			0.554054i
$651$	−5.37255	+	2.22538i	−0.210567	+	0.0872197i
$652$	4.43770	−	10.7136i	0.173794	−	0.419575i
$653$	28.6845	+	11.8815i	1.12251	+	0.464959i	0.865229	−	0.501377i	$-0.167173\pi$
$653$	28.6845	+	11.8815i	1.12251	+	0.464959i	0.257282	+	0.966336i	$0.417173\pi$
$654$	−24.6187	+	24.6187i	−0.962669	+	0.962669i
$655$	21.5514	−	21.5514i	0.842084	−	0.842084i
$656$	−3.73422	−	1.54676i	−0.145797	−	0.0603910i
$657$	−26.4219	+	63.7881i	−1.03082	+	2.48861i
$658$	−8.87923	+	3.67790i	−0.346149	+	0.143379i
$659$		−	45.3783i		−	1.76769i	−0.467784	−	0.883843i	$-0.654947\pi$
$659$		−	45.3783i		−	1.76769i	0.467784	−	0.883843i	$-0.345053\pi$
$660$	−0.852114	−	2.05719i	−0.0331685	−	0.0800758i
$661$	17.1927	+	17.1927i	0.668717	+	0.668717i	0.957419	−	0.288702i	$-0.0932238\pi$
$661$	17.1927	+	17.1927i	0.668717	+	0.668717i	−0.288702	+	0.957419i	$0.593224\pi$
$662$	34.9590			1.35872
$663$		0			0
$664$	8.88713			0.344887
$665$	−16.6317	−	16.6317i	−0.644951	−	0.644951i
$666$	2.35375	+	5.68245i	0.0912059	+	0.220191i
$667$			9.41746i			0.364646i
$668$	−0.812446	+	0.336526i	−0.0314345	+	0.0130206i
$669$	−5.92524	+	14.3048i	−0.229083	+	0.553055i
$670$	3.21575	+	1.33201i	0.124235	+	0.0514600i
$671$	1.45959	−	1.45959i	0.0563470	−	0.0563470i
$672$	4.90984	−	4.90984i	0.189401	−	0.189401i
$673$	−15.5819	−	6.45425i	−0.600640	−	0.248793i	0.0615809	−	0.998102i	$-0.480386\pi$
$673$	−15.5819	−	6.45425i	−0.600640	−	0.248793i	−0.662221	+	0.749309i	$0.730386\pi$
$674$	5.99402	−	14.4708i	0.230881	−	0.557396i
$675$	13.8250	−	5.72651i	0.532125	−	0.220414i
$676$		−	25.7716i		−	0.991214i
$677$	−7.95746	−	19.2110i	−0.305830	−	0.738339i	−0.999831	−	0.0183654i	$-0.994154\pi$
$677$	−7.95746	−	19.2110i	−0.305830	−	0.738339i	0.694001	−	0.719974i	$-0.255846\pi$
$678$	2.58833	+	2.58833i	0.0994040	+	0.0994040i
$679$	31.3492			1.20307
$680$		0			0
$681$	−31.8384			−1.22005
$682$	−0.277097	−	0.277097i	−0.0106106	−	0.0106106i
$683$	−1.60544	−	3.87588i	−0.0614305	−	0.148306i	0.890184	−	0.455602i	$-0.150576\pi$
$683$	−1.60544	−	3.87588i	−0.0614305	−	0.148306i	−0.951614	+	0.307296i	$0.900576\pi$
$684$		−	31.2249i		−	1.19391i
$685$	−7.32241	+	3.03304i	−0.279775	+	0.115887i
$686$	7.55318	−	18.2350i	0.288382	−	0.696215i
$687$	63.7541	+	26.4078i	2.43237	+	1.00752i
$688$	−1.87574	+	1.87574i	−0.0715121	+	0.0715121i
$689$	6.56124	−	6.56124i	0.249963	−	0.249963i
$690$	−8.44694	−	3.49884i	−0.321570	−	0.133198i
$691$	−15.2765	+	36.8808i	−0.581147	+	1.40301i	0.310627	+	0.950532i	$0.399461\pi$
$691$	−15.2765	+	36.8808i	−0.581147	+	1.40301i	−0.891774	+	0.452481i	$0.850539\pi$
$692$	−15.8111	+	6.54917i	−0.601048	+	0.248962i
$693$			5.96997i			0.226780i
$694$	3.99772	+	9.65136i	0.151752	+	0.366361i
$695$	−5.27347	−	5.27347i	−0.200034	−	0.200034i
$696$	−14.1138			−0.534982
$697$		0			0
$698$	−8.32770			−0.315208
$699$	21.2834	+	21.2834i	0.805012	+	0.805012i
$700$	2.09351	+	5.05417i	0.0791272	+	0.191030i
$701$		−	33.6100i		−	1.26943i	−0.772746	−	0.634716i	$-0.781117\pi$
$701$		−	33.6100i		−	1.26943i	0.772746	−	0.634716i	$-0.218883\pi$
$702$	−37.9464	+	15.7179i	−1.43219	+	0.593234i
$703$	−2.62548	+	6.33848i	−0.0990220	+	0.239060i
$704$	0.432294	+	0.179062i	0.0162927	+	0.00674865i
$705$	−13.4109	+	13.4109i	−0.505083	+	0.505083i
$706$	−5.09428	+	5.09428i	−0.191726	+	0.191726i
$707$	−34.2097	−	14.1701i	−1.28659	−	0.532922i
$708$	−15.2154	+	36.7332i	−0.571829	+	1.38052i
$709$	−40.3244	+	16.7029i	−1.51442	+	0.627291i	−0.976463	−	0.215684i	$-0.930802\pi$
$709$	−40.3244	+	16.7029i	−1.51442	+	0.627291i	−0.537952	+	0.842976i	$0.680802\pi$
$710$			20.2763i			0.760956i
$711$	17.8640	+	43.1276i	0.669954	+	1.61741i
$712$	10.1560	+	10.1560i	0.380613	+	0.380613i
$713$	−1.60906			−0.0602598
$714$		0			0
$715$	−4.81521			−0.180079
$716$	10.0810	+	10.0810i	0.376745	+	0.376745i
$717$	2.05485	+	4.96085i	0.0767398	+	0.185266i
$718$			12.1557i			0.453647i
$719$	−40.2311	+	16.6643i	−1.50037	+	0.621472i	−0.973543	−	0.228503i	$-0.926617\pi$
$719$	−40.2311	+	16.6643i	−1.50037	+	0.621472i	−0.526823	+	0.849975i	$0.676617\pi$
$720$	3.34627	−	8.07861i	0.124708	−	0.301072i
$721$	−10.0150	−	4.14836i	−0.372979	−	0.154493i
$722$	11.1933	−	11.1933i	0.416573	−	0.416573i
$723$	−37.4011	+	37.4011i	−1.39096	+	1.39096i
$724$	9.97222	+	4.13063i	0.370615	+	0.153514i
$725$	4.25536	−	10.2733i	0.158040	−	0.381543i
$726$	28.6798	−	11.8796i	1.06441	−	0.440892i
$727$		−	18.3473i		−	0.680464i	−0.940342	−	0.340232i	$-0.889494\pi$
$727$		−	18.3473i		−	0.680464i	0.940342	−	0.340232i	$-0.110506\pi$
$728$	−5.74618	−	13.8725i	−0.212967	−	0.514149i
$729$	−28.6158	−	28.6158i	−1.05984	−	1.05984i
$730$	−21.5672			−0.798237
$731$		0			0
$732$	12.7023			0.469492
$733$	−24.7131	−	24.7131i	−0.912798	−	0.912798i	0.0836937	−	0.996492i	$-0.473328\pi$
$733$	−24.7131	−	24.7131i	−0.912798	−	0.912798i	−0.996492	+	0.0836937i	$0.973328\pi$
$734$	13.8418	+	33.4169i	0.510908	+	1.23344i
$735$		−	5.63816i		−	0.207967i
$736$	1.77503	−	0.735240i	0.0654283	−	0.0271013i
$737$	0.377116	−	0.910439i	0.0138913	−	0.0335365i
$738$	19.7572	+	8.18371i	0.727274	+	0.301247i
$739$	−4.65565	+	4.65565i	−0.171261	+	0.171261i	−0.787533	−	0.616272i	$-0.788642\pi$
$739$	−4.65565	+	4.65565i	−0.171261	+	0.171261i	0.616272	+	0.787533i	$0.288642\pi$
$740$	−1.35855	+	1.35855i	−0.0499411	+	0.0499411i
$741$	−97.7568	−	40.4922i	−3.59119	−	1.48752i
$742$	1.37520	−	3.32003i	0.0504853	−	0.121882i
$743$	7.68882	−	3.18481i	0.282075	−	0.116839i	−0.237160	−	0.971471i	$-0.576217\pi$
$743$	7.68882	−	3.18481i	0.282075	−	0.116839i	0.519236	+	0.854631i	$0.326217\pi$
$744$		−	2.41147i		−	0.0884089i
$745$	−7.19083	−	17.3602i	−0.263452	−	0.636029i
$746$	19.8045	+	19.8045i	0.725093	+	0.725093i
$747$	−47.0205			−1.72039
$748$		0			0
$749$	−45.7665			−1.67227
$750$	24.4584	+	24.4584i	0.893096	+	0.893096i
$751$	−19.6952	−	47.5485i	−0.718690	−	1.73507i	−0.677049	−	0.735938i	$-0.736742\pi$
$751$	−19.6952	−	47.5485i	−0.718690	−	1.73507i	−0.0416406	−	0.999133i	$-0.513258\pi$
$752$		−	3.98545i		−	0.145334i
$753$	−3.47980	+	1.44138i	−0.126811	+	0.0525269i
$754$	−11.6799	+	28.1979i	−0.425358	+	1.02691i
$755$	−9.94752	−	4.12040i	−0.362027	−	0.149957i
$756$	−11.2478	+	11.2478i	−0.409077	+	0.409077i
$757$	15.9362	−	15.9362i	0.579210	−	0.579210i	−0.355476	−	0.934686i	$-0.615681\pi$
$757$	15.9362	−	15.9362i	0.579210	−	0.579210i	0.934686	+	0.355476i	$0.115681\pi$
$758$	−0.0655815	−	0.0271647i	−0.00238203	−	0.000986668i
$759$	−0.990586	+	2.39149i	−0.0359560	+	0.0868054i
$760$	9.01126	−	3.73259i	0.326873	−	0.135395i
$761$			8.39599i			0.304354i	0.988353	+	0.152177i	$0.0486285\pi$
$761$			8.39599i			0.304354i	−0.988353	+	0.152177i	$0.951372\pi$
$762$	4.68191	+	11.3031i	0.169608	+	0.409469i
$763$	20.6181	+	20.6181i	0.746425	+	0.746425i
$764$	9.09926			0.329200
$765$		0			0
$766$	−16.9341			−0.611853
$767$	60.7974	+	60.7974i	2.19527	+	2.19527i
$768$	1.10189	+	2.66021i	0.0397611	+	0.0959919i
$769$		−	32.0063i		−	1.15418i	−0.816682	−	0.577089i	$-0.804189\pi$
$769$		−	32.0063i		−	1.15418i	0.816682	−	0.577089i	$-0.195811\pi$
$770$	−1.72289	+	0.713642i	−0.0620885	+	0.0257179i
$771$	13.1936	−	31.8522i	0.475157	−	1.14713i
$772$	7.37760	+	3.05590i	0.265525	+	0.109984i
$773$	−15.8509	+	15.8509i	−0.570116	+	0.570116i	−0.932161	−	0.362044i	$-0.882079\pi$
$773$	−15.8509	+	15.8509i	−0.570116	+	0.570116i	0.362044	+	0.932161i	$0.382079\pi$
$774$	9.92430	−	9.92430i	0.356722	−	0.356722i
$775$	1.75530	+	0.727068i	0.0630521	+	0.0261170i
$776$	−4.97488	+	12.0104i	−0.178588	+	0.431149i
$777$	7.45748	−	3.08899i	0.267536	−	0.110817i
$778$			30.6364i			1.09837i
$779$	9.12850	+	22.0381i	0.327062	+	0.789598i
$780$	−20.9525	−	20.9525i	−0.750221	−	0.750221i
$781$	5.74060			0.205415
$782$		0			0
$783$	32.3327			1.15548
$784$	0.837775	+	0.837775i	0.0299205	+	0.0299205i
$785$	−6.04108	−	14.5845i	−0.215616	−	0.520542i
$786$		−	53.1002i		−	1.89402i
$787$	−30.8699	+	12.7867i	−1.10039	+	0.455798i	−0.857619	−	0.514285i	$-0.828057\pi$
$787$	−30.8699	+	12.7867i	−1.10039	+	0.455798i	−0.242774	+	0.970083i	$0.578057\pi$
$788$	−7.26281	+	17.5340i	−0.258727	+	0.624622i
$789$	−38.6402	−	16.0053i	−1.37563	−	0.569804i
$790$	−10.3108	+	10.3108i	−0.366843	+	0.366843i
$791$	2.16771	−	2.16771i	0.0770750	−	0.0770750i
$792$	−2.28720	−	0.947391i	−0.0812723	−	0.0336641i
$793$	10.5119	−	25.3779i	0.373288	−	0.901196i
$794$	−0.629901	+	0.260913i	−0.0223543	+	0.00925947i
$795$		−	7.09152i		−	0.251510i
$796$	0.524118	+	1.26533i	0.0185769	+	0.0448485i
$797$	17.1418	+	17.1418i	0.607194	+	0.607194i	0.942212	−	0.335018i	$-0.108742\pi$
$797$	17.1418	+	17.1418i	0.607194	+	0.607194i	−0.335018	+	0.942212i	$0.608742\pi$
$798$	−40.9786			−1.45063
$799$		0			0
$800$	−2.26857			−0.0802061
$801$	−53.7341	−	53.7341i	−1.89860	−	1.89860i
$802$	6.26824	+	15.1329i	0.221339	+	0.534360i
$803$			6.10607i			0.215478i
$804$	5.60257	−	2.32066i	0.197587	−	0.0818434i
$805$	−2.93026	+	7.07428i	−0.103278	+	0.249336i
$806$	−4.81787	−	1.99563i	−0.169702	−	0.0702929i
$807$	56.9654	−	56.9654i	2.00528	−	2.00528i
$808$	10.8577	−	10.8577i	0.381971	−	0.381971i
$809$	−41.6641	−	17.2578i	−1.46483	−	0.606753i	−0.499158	−	0.866511i	$-0.666357\pi$
$809$	−41.6641	−	17.2578i	−1.46483	−	0.606753i	−0.965674	+	0.259758i	$0.916357\pi$
$810$	−1.97367	+	4.76486i	−0.0693477	+	0.167420i
$811$	−35.2496	+	14.6009i	−1.23778	+	0.512706i	−0.903021	−	0.429597i	$-0.858656\pi$
$811$	−35.2496	+	14.6009i	−1.23778	+	0.512706i	−0.334762	+	0.942303i	$0.608656\pi$
$812$			11.8203i			0.414810i
$813$	14.7299	+	35.5612i	0.516601	+	1.24718i
$814$	0.384630	+	0.384630i	0.0134813	+	0.0134813i
$815$	−19.1652			−0.671327
$816$		0			0
$817$	15.6554			0.547713
$818$	1.16025	+	1.16025i	0.0405673	+	0.0405673i
$819$	30.4022	+	73.3974i	1.06234	+	2.56471i
$820$			6.68004i			0.233277i
$821$	28.1680	−	11.6675i	0.983068	−	0.407200i	0.167507	−	0.985871i	$-0.446428\pi$
$821$	28.1680	−	11.6675i	0.983068	−	0.407200i	0.815561	+	0.578671i	$0.196428\pi$
$822$	−5.28425	+	12.7573i	−0.184309	+	0.444962i
$823$	39.3821	+	16.3126i	1.37277	+	0.568622i	0.942539	−	0.334095i	$-0.108431\pi$
$823$	39.3821	+	16.3126i	1.37277	+	0.568622i	0.430235	+	0.902717i	$0.358431\pi$
$824$	3.17862	−	3.17862i	0.110733	−	0.110733i
$825$	2.16123	−	2.16123i	0.0752443	−	0.0752443i
$826$	30.7639	+	12.7428i	1.07041	+	0.443380i
$827$	5.07380	−	12.2492i	0.176433	−	0.425947i	−0.810780	−	0.585350i	$-0.800957\pi$
$827$	5.07380	−	12.2492i	0.176433	−	0.425947i	0.987214	+	0.159403i	$0.0509570\pi$
$828$	−9.39141	+	3.89005i	−0.326374	+	0.135189i
$829$			6.68779i			0.232276i	0.993233	+	0.116138i	$0.0370515\pi$
$829$			6.68779i			0.232276i	−0.993233	+	0.116138i	$0.962948\pi$
$830$	−5.62077	−	13.5697i	−0.195100	−	0.471013i
$831$	1.21212	+	1.21212i	0.0420479	+	0.0420479i
$832$	6.22668			0.215871
$833$		0			0
$834$	−12.9932			−0.449917
$835$	1.02768	+	1.02768i	0.0355644	+	0.0355644i
$836$	−1.05676	−	2.55126i	−0.0365490	−	0.0882370i
$837$			5.52435i			0.190949i
$838$	27.2416	−	11.2838i	0.941045	−	0.389794i
$839$	−3.79307	+	9.15729i	−0.130951	+	0.316145i	−0.975732	−	0.218968i	$-0.929731\pi$
$839$	−3.79307	+	9.15729i	−0.130951	+	0.316145i	0.844781	+	0.535113i	$0.179731\pi$
$840$	−10.6021	−	4.39154i	−0.365808	−	0.151523i
$841$	−3.51686	+	3.51686i	−0.121271	+	0.121271i
$842$	−14.3224	+	14.3224i	−0.493583	+	0.493583i
$843$	−47.6175	−	19.7238i	−1.64003	−	0.679324i
$844$	4.75820	−	11.4873i	0.163784	−	0.395409i
$845$	−39.3506	+	16.2995i	−1.35370	+	0.560721i
$846$			21.0865i			0.724968i
$847$	−9.94910	−	24.0192i	−0.341855	−	0.825311i
$848$	1.05373	+	1.05373i	0.0361853	+	0.0361853i
$849$	11.3773			0.390469
$850$		0			0
$851$	2.23349			0.0765630
$852$	24.9792	+	24.9792i	0.855774	+	0.855774i
$853$	2.13271	+	5.14882i	0.0730227	+	0.176292i	0.956176	−	0.292792i	$-0.0945842\pi$
$853$	2.13271	+	5.14882i	0.0730227	+	0.176292i	−0.883154	+	0.469084i	$0.844584\pi$
$854$		−	10.6382i		−	0.364030i
$855$	−47.6773	+	19.7486i	−1.63053	+	0.675387i
$856$	7.26281	−	17.5340i	0.248238	−	0.599299i
$857$	12.8838	+	5.33664i	0.440102	+	0.182296i	0.591721	−	0.806143i	$-0.298449\pi$
$857$	12.8838	+	5.33664i	0.440102	+	0.182296i	−0.151619	+	0.988439i	$0.548449\pi$
$858$	−5.93205	+	5.93205i	−0.202517	+	0.202517i
$859$	25.4842	−	25.4842i	0.869510	−	0.869510i	−0.122908	−	0.992418i	$-0.539222\pi$
$859$	25.4842	−	25.4842i	0.869510	−	0.869510i	0.992418	+	0.122908i	$0.0392219\pi$
$860$	4.05041	+	1.67774i	0.138118	+	0.0572103i
$861$	10.7401	−	25.9288i	0.366020	−	0.883651i
$862$	−2.94323	+	1.21912i	−0.100247	+	0.0415235i
$863$			23.4088i			0.796844i	0.917202	+	0.398422i	$0.130442\pi$
$863$			23.4088i			0.796844i	−0.917202	+	0.398422i	$0.869558\pi$
$864$	−2.52428	−	6.09416i	−0.0858778	−	0.207327i
$865$	19.9998	+	19.9998i	0.680015	+	0.680015i
$866$	5.41653			0.184061
$867$		0			0
$868$	−2.01960			−0.0685497
$869$	2.91919	+	2.91919i	0.0990267	+	0.0990267i
$870$	8.92645	+	21.5504i	0.302635	+	0.730626i
$871$		−	13.1138i		−	0.444344i
$872$	−11.1711	+	4.62722i	−0.378301	+	0.156698i
$873$	26.3214	−	63.5455i	0.890845	−	2.15069i
$874$	−10.4756	−	4.33915i	−0.354343	−	0.146774i
$875$	20.4839	−	20.4839i	0.692481	−	0.692481i
$876$	−26.5695	+	26.5695i	−0.897699	+	0.897699i
$877$	42.8669	+	17.7560i	1.44751	+	0.599579i	0.961606	−	0.274432i	$-0.0884898\pi$
$877$	42.8669	+	17.7560i	1.44751	+	0.599579i	0.485906	+	0.874011i	$0.338490\pi$
$878$	−0.767300	+	1.85243i	−0.0258951	+	0.0625164i
$879$	−74.6131	+	30.9058i	−2.51664	+	1.04243i
$880$		−	0.773318i		−	0.0260686i
$881$	−12.9400	−	31.2399i	−0.435959	−	1.05250i	−0.977331	−	0.211715i	$-0.932095\pi$
$881$	−12.9400	−	31.2399i	−0.435959	−	1.05250i	0.541373	−	0.840783i	$-0.317905\pi$
$882$	−4.43255	−	4.43255i	−0.149252	−	0.149252i
$883$	37.5776			1.26459			0.632293	−	0.774729i	$-0.282114\pi$
$883$	37.5776			1.26459			0.632293	+	0.774729i	$0.282114\pi$
$884$		0			0
$885$	65.7110			2.20885
$886$	−0.0537665	−	0.0537665i	−0.00180632	−	0.00180632i
$887$	5.13168	+	12.3890i	0.172305	+	0.415981i	0.986315	−	0.164869i	$-0.0527202\pi$
$887$	5.13168	+	12.3890i	0.172305	+	0.415981i	−0.814011	+	0.580850i	$0.802720\pi$
$888$			3.34730i			0.112328i
$889$	9.46633	−	3.92108i	0.317491	−	0.131509i
$890$	9.08392	−	21.9305i	0.304494	−	0.735112i
$891$	1.34902	+	0.558783i	0.0451939	+	0.0187199i
$892$	−3.80234	+	3.80234i	−0.127312	+	0.127312i
$893$	−16.6317	+	16.6317i	−0.556560	+	0.556560i
$894$	−30.2454	−	12.5281i	−1.01156	−	0.419001i
$895$	9.01683	−	21.7686i	0.301399	−	0.727643i
$896$	2.22791	−	0.922831i	0.0744293	−	0.0308296i
$897$			34.4466i			1.15014i
$898$	−4.64918	−	11.2241i	−0.155145	−	0.374553i
$899$	2.90277	+	2.90277i	0.0968127	+	0.0968127i
$900$	12.0027			0.400090
$901$		0			0
$902$	1.89124			0.0629716
$903$	−13.0244	−	13.0244i	−0.433423	−	0.433423i
$904$	0.486490	+	1.17449i	0.0161804	+	0.0390630i
$905$		−	17.8390i		−	0.592990i
$906$	−17.3308	+	7.17867i	−0.575779	+	0.238495i
$907$	10.7508	−	25.9548i	0.356975	−	0.861815i	−0.638747	−	0.769417i	$-0.720547\pi$
$907$	10.7508	−	25.9548i	0.356975	−	0.861815i	0.995722	−	0.0923979i	$-0.0294532\pi$
$908$	−10.2157	−	4.23147i	−0.339019	−	0.140426i
$909$	−57.4463	+	57.4463i	−1.90537	+	1.90537i
$910$	−17.5477	+	17.5477i	−0.581699	+	0.581699i
$911$	20.7497	+	8.59482i	0.687469	+	0.284759i	0.698945	−	0.715175i	$-0.253653\pi$
$911$	20.7497	+	8.59482i	0.687469	+	0.284759i	−0.0114761	+	0.999934i	$0.503653\pi$
$912$	6.50301	−	15.6997i	0.215336	−	0.519868i
$913$	−3.84185	+	1.59135i	−0.127147	+	0.0526658i
$914$			9.51249i			0.314645i
$915$	−8.03375	−	19.3952i	−0.265587	−	0.641185i
$916$	16.9464	+	16.9464i	0.559925	+	0.559925i
$917$	−44.4712			−1.46857
$918$		0			0
$919$	51.0215			1.68304			0.841521	−	0.540224i	$-0.181660\pi$
$919$	51.0215			1.68304			0.841521	+	0.540224i	$0.181660\pi$
$920$	−2.24527	−	2.24527i	−0.0740245	−	0.0740245i
$921$	23.7130	+	57.2482i	0.781370	+	1.88639i
$922$			10.6459i			0.350604i
$923$	70.5775	−	29.2341i	2.32309	−	0.962253i
$924$	−1.24333	+	3.00166i	−0.0409025	+	0.0987473i
$925$	−2.43648	−	1.00922i	−0.0801108	−	0.0331830i
$926$	−14.2957	+	14.2957i	−0.469786	+	0.469786i
$927$	−16.8176	+	16.8176i	−0.552364	+	0.552364i
$928$	−4.52856	−	1.87579i	−0.148657	−	0.0615758i
$929$	14.2985	−	34.5196i	0.469118	−	1.13255i	−0.495431	−	0.868647i	$-0.664990\pi$
$929$	14.2985	−	34.5196i	0.469118	−	1.13255i	0.964549	−	0.263903i	$-0.0850100\pi$
$930$	−3.68208	+	1.52517i	−0.120740	+	0.0500122i
$931$		−	6.99226i		−	0.229162i
$932$	4.00033	+	9.65765i	0.131035	+	0.316347i
$933$	−9.62787	−	9.62787i	−0.315202	−	0.315202i
$934$	18.5936			0.608400
$935$		0			0
$936$	−32.9445			−1.07682
$937$	−12.8325	−	12.8325i	−0.419221	−	0.419221i	0.465714	−	0.884935i	$-0.345797\pi$
$937$	−12.8325	−	12.8325i	−0.419221	−	0.419221i	−0.884935	+	0.465714i	$0.845797\pi$
$938$	−1.94354	−	4.69213i	−0.0634590	−	0.153203i
$939$			50.7725i			1.65690i
$940$	−6.08538	+	2.52065i	−0.198483	+	0.0822145i
$941$	10.3854	−	25.0727i	0.338556	−	0.817346i	−0.659299	−	0.751881i	$-0.729147\pi$
$941$	10.3854	−	25.0727i	0.338556	−	0.817346i	0.997855	−	0.0654650i	$-0.0208531\pi$
$942$	−25.4095	−	10.5249i	−0.827885	−	0.342921i
$943$	5.49109	−	5.49109i	0.178815	−	0.178815i
$944$	−9.76401	+	9.76401i	−0.317792	+	0.317792i
$945$	24.2880	+	10.0604i	0.790088	+	0.327265i
$946$	0.474998	−	1.14675i	0.0154435	−	0.0372839i
$947$	49.0519	−	20.3180i	1.59397	−	0.660245i	0.603425	−	0.797419i	$-0.293802\pi$
$947$	49.0519	−	20.3180i	1.59397	−	0.660245i	0.990547	+	0.137174i	$0.0438021\pi$
$948$			25.4047i			0.825105i
$949$	31.0953	+	75.0707i	1.00940	+	2.43690i
$950$	9.46700	+	9.46700i	0.307150	+	0.307150i
$951$	−51.2354			−1.66142
$952$		0			0
$953$	5.62454			0.182197			0.0910984	−	0.995842i	$-0.470962\pi$
$953$	5.62454			0.182197			0.0910984	+	0.995842i	$0.470962\pi$
$954$	−5.57514	−	5.57514i	−0.180502	−	0.180502i
$955$	−5.75494	−	13.8937i	−0.186225	−	0.449588i
$956$			1.86484i			0.0603131i
$957$	6.10131	−	2.52724i	0.197227	−	0.0816942i
$958$	−9.61621	+	23.2156i	−0.310685	+	0.750061i
$959$	10.6842	+	4.42554i	0.345010	+	0.142908i
$960$	3.36496	−	3.36496i	0.108604	−	0.108604i
$961$	21.4243	−	21.4243i	0.691108	−	0.691108i
$962$	6.68754	+	2.77007i	0.215615	+	0.0893106i
$963$	−38.4265	+	92.7698i	−1.23828	+	2.98947i
$964$	−16.9713	+	7.02974i	−0.546608	+	0.226413i
$965$		−	13.1976i		−	0.424845i
$966$	5.10518	+	12.3250i	0.164257	+	0.396551i
$967$	4.75961	+	4.75961i	0.153059	+	0.153059i	0.779483	−	0.626424i	$-0.215482\pi$
$967$	4.75961	+	4.75961i	0.153059	+	0.153059i	−0.626424	+	0.779483i	$0.715482\pi$
$968$	10.7811			0.346516
$969$		0			0
$970$	21.4851			0.689847
$971$	14.9529	+	14.9529i	0.479860	+	0.479860i	0.905087	−	0.425227i	$-0.139806\pi$
$971$	14.9529	+	14.9529i	0.479860	+	0.479860i	−0.425227	+	0.905087i	$0.639806\pi$
$972$	−4.13426	−	9.98099i	−0.132607	−	0.320140i
$973$			10.8817i			0.348853i
$974$	24.6635	−	10.2159i	0.790268	−	0.327340i
$975$	15.5650	−	37.5772i	0.498478	−	1.20343i
$976$	4.07567	+	1.68820i	0.130459	+	0.0540379i
$977$	29.9277	−	29.9277i	0.957473	−	0.957473i	−0.0416593	−	0.999132i	$-0.513264\pi$
$977$	29.9277	−	29.9277i	0.957473	−	0.957473i	0.999132	+	0.0416593i	$0.0132644\pi$
$978$	−23.6104	+	23.6104i	−0.754977	+	0.754977i
$979$	−6.20894	−	2.57183i	−0.198438	−	0.0821959i
$980$	0.749337	−	1.80906i	0.0239367	−	0.0577883i
$981$	59.1048	−	24.4820i	1.88707	−	0.781650i
$982$			4.79797i			0.153109i
$983$	2.99214	+	7.22366i	0.0954343	+	0.230399i	0.964386	−	0.264497i	$-0.0852061\pi$
$983$	2.99214	+	7.22366i	0.0954343	+	0.230399i	−0.868952	+	0.494896i	$0.835206\pi$
$984$	8.22942	+	8.22942i	0.262344	+	0.262344i
$985$	31.3661			0.999406
$986$		0			0
$987$	27.6732			0.880849
$988$	−25.9847	−	25.9847i	−0.826682	−	0.826682i
$989$	−1.95037	−	4.70862i	−0.0620183	−	0.149725i
$990$			4.09152i			0.130037i
$991$	−4.89937	+	2.02939i	−0.155634	+	0.0644656i	−0.459140	−	0.888364i	$-0.651843\pi$
$991$	−4.89937	+	2.02939i	−0.155634	+	0.0644656i	0.303507	+	0.952829i	$0.401843\pi$
$992$	0.320496	−	0.773746i	0.0101758	−	0.0245664i
$993$	−92.9982	−	38.5211i	−2.95121	−	1.22243i
$994$	20.9200	−	20.9200i	0.663542	−	0.663542i
$995$	1.60055	−	1.60055i	0.0507408	−	0.0507408i
$996$	−23.6416	−	9.79266i	−0.749112	−	0.310292i
$997$	−12.5883	+	30.3909i	−0.398676	+	0.962489i	0.589304	+	0.807911i	$0.299402\pi$
$997$	−12.5883	+	30.3909i	−0.398676	+	0.962489i	−0.987981	+	0.154578i	$0.950598\pi$
$998$	6.49242	−	2.68925i	0.205514	−	0.0851266i
$999$		−	7.66819i		−	0.242611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.d.i.423.6		24
17.2	even	8	inner	578.2.d.i.179.6		24
17.3	odd	16		578.2.b.e.577.6		6
17.4	even	4	inner	578.2.d.i.155.6		24
17.5	odd	16		578.2.a.g.1.1	✓	3
17.6	odd	16		578.2.c.h.251.6		12
17.7	odd	16		578.2.c.h.327.6		12
17.8	even	8	inner	578.2.d.i.399.6		24
17.9	even	8	inner	578.2.d.i.399.1		24
17.10	odd	16		578.2.c.h.327.1		12
17.11	odd	16		578.2.c.h.251.1		12
17.12	odd	16		578.2.a.h.1.3	yes	3
17.13	even	4	inner	578.2.d.i.155.1		24
17.14	odd	16		578.2.b.e.577.1		6
17.15	even	8	inner	578.2.d.i.179.1		24
17.16	even	2	inner	578.2.d.i.423.1		24
51.5	even	16		5202.2.a.bi.1.2		3
51.29	even	16		5202.2.a.bg.1.2		3
68.39	even	16		4624.2.a.bh.1.3		3
68.63	even	16		4624.2.a.bc.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
578.2.a.g.1.1	✓	3	17.5	odd	16
578.2.a.h.1.3	yes	3	17.12	odd	16
578.2.b.e.577.1		6	17.14	odd	16
578.2.b.e.577.6		6	17.3	odd	16
578.2.c.h.251.1		12	17.11	odd	16
578.2.c.h.251.6		12	17.6	odd	16
578.2.c.h.327.1		12	17.10	odd	16
578.2.c.h.327.6		12	17.7	odd	16
578.2.d.i.155.1		24	17.13	even	4	inner
578.2.d.i.155.6		24	17.4	even	4	inner
578.2.d.i.179.1		24	17.15	even	8	inner
578.2.d.i.179.6		24	17.2	even	8	inner
578.2.d.i.399.1		24	17.9	even	8	inner
578.2.d.i.399.6		24	17.8	even	8	inner
578.2.d.i.423.1		24	17.16	even	2	inner
578.2.d.i.423.6		24	1.1	even	1	trivial
4624.2.a.bc.1.1		3	68.63	even	16
4624.2.a.bh.1.3		3	68.39	even	16
5202.2.a.bg.1.2		3	51.29	even	16
5202.2.a.bi.1.2		3	51.5	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.10189 + 2.66021i) q^{3} +1.00000i q^{4} +(1.52690 - 0.632462i) q^{5} +(1.10189 - 2.66021i) q^{6} +(-2.22791 - 0.922831i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.74120 + 3.74120i) q^{9} +(-1.52690 - 0.632462i) q^{10} +(-0.179062 + 0.432294i) q^{11} +(-2.66021 + 1.10189i) q^{12} +6.22668i q^{13} +(0.922831 + 2.22791i) q^{14} +(3.36496 + 3.36496i) q^{15} -1.00000 q^{16} +5.29086 q^{18} +(4.17311 + 4.17311i) q^{19} +(0.632462 + 1.52690i) q^{20} -6.94356i q^{21} +(0.432294 - 0.179062i) q^{22} +(0.735240 - 1.77503i) q^{23} +(2.66021 + 1.10189i) q^{24} +(-1.60412 + 1.60412i) q^{25} +(4.40293 - 4.40293i) q^{26} +(-6.09416 - 2.52428i) q^{27} +(0.922831 - 2.22791i) q^{28} +(-4.52856 + 1.87579i) q^{29} -4.75877i q^{30} +(-0.320496 - 0.773746i) q^{31} +(0.707107 + 0.707107i) q^{32} -1.34730 q^{33} -3.98545 q^{35} +(-3.74120 - 3.74120i) q^{36} +(0.444871 + 1.07401i) q^{37} -5.90167i q^{38} +(-16.5643 + 6.86114i) q^{39} +(0.632462 - 1.52690i) q^{40} +(3.73422 + 1.54676i) q^{41} +(-4.90984 + 4.90984i) q^{42} +(1.87574 - 1.87574i) q^{43} +(-0.432294 - 0.179062i) q^{44} +(-3.34627 + 8.07861i) q^{45} +(-1.77503 + 0.735240i) q^{46} +3.98545i q^{47} +(-1.10189 - 2.66021i) q^{48} +(-0.837775 - 0.837775i) q^{49} +2.26857 q^{50} -6.22668 q^{52} +(-1.05373 - 1.05373i) q^{53} +(2.52428 + 6.09416i) q^{54} +0.773318i q^{55} +(-2.22791 + 0.922831i) q^{56} +(-6.50301 + 15.6997i) q^{57} +(4.52856 + 1.87579i) q^{58} +(9.76401 - 9.76401i) q^{59} +(-3.36496 + 3.36496i) q^{60} +(-4.07567 - 1.68820i) q^{61} +(-0.320496 + 0.773746i) q^{62} +(11.7876 - 4.88257i) q^{63} -1.00000i q^{64} +(3.93814 + 9.50751i) q^{65} +(0.952682 + 0.952682i) q^{66} -2.10607 q^{67} +5.53209 q^{69} +(2.81814 + 2.81814i) q^{70} +(-4.69498 - 11.3347i) q^{71} +5.29086i q^{72} +(12.0563 - 4.99388i) q^{73} +(0.444871 - 1.07401i) q^{74} +(-6.03486 - 2.49972i) q^{75} +(-4.17311 + 4.17311i) q^{76} +(0.797868 - 0.797868i) q^{77} +(16.5643 + 6.86114i) q^{78} +(3.37640 - 8.15134i) q^{79} +(-1.52690 + 0.632462i) q^{80} -3.12061i q^{81} +(-1.54676 - 3.73422i) q^{82} +(6.28415 + 6.28415i) q^{83} +6.94356 q^{84} -2.65270 q^{86} +(-9.97997 - 9.97997i) q^{87} +(0.179062 + 0.432294i) q^{88} +14.3628i q^{89} +(8.07861 - 3.34627i) q^{90} +(5.74618 - 13.8725i) q^{91} +(1.77503 + 0.735240i) q^{92} +(1.70517 - 1.70517i) q^{93} +(2.81814 - 2.81814i) q^{94} +(9.01126 + 3.73259i) q^{95} +(-1.10189 + 2.66021i) q^{96} +(-12.0104 + 4.97488i) q^{97} +1.18479i q^{98} +(-0.947391 - 2.28720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{16} - 24 q^{33} + 48 q^{35} - 24 q^{50} - 96 q^{52} + 48 q^{67} + 96 q^{69} + 48 q^{84} - 72 q^{86}+O(q^{100}) \) 24 * q - 24 * q^16 - 24 * q^33 + 48 * q^35 - 24 * q^50 - 96 * q^52 + 48 * q^67 + 96 * q^69 + 48 * q^84 - 72 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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