LMFDB - Embedded newform 768.2.n.b.673.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.n (of order $8$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			673.7
Character	$\chi$	$=$	768.673
Dual form			768.2.n.b.97.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 + 0.382683i) q^{3} +(0.155637 + 0.375742i) q^{5} +(-0.709092 + 0.709092i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.923880 + 0.382683i) q^{3} +(0.155637 + 0.375742i) q^{5} +(-0.709092 + 0.709092i) q^{7} +(0.707107 + 0.707107i) q^{9} +(-2.79128 + 1.15619i) q^{11} +(-2.58738 + 6.24650i) q^{13} +0.406700i q^{15} +1.05927i q^{17} +(-1.48755 + 3.59125i) q^{19} +(-0.926474 + 0.383758i) q^{21} +(-0.922176 - 0.922176i) q^{23} +(3.41858 - 3.41858i) q^{25} +(0.382683 + 0.923880i) q^{27} +(7.64351 + 3.16605i) q^{29} +1.88437 q^{31} -3.02126 q^{33} +(-0.376797 - 0.156074i) q^{35} +(-1.24806 - 3.01308i) q^{37} +(-4.78086 + 4.78086i) q^{39} +(5.11980 + 5.11980i) q^{41} +(-10.9474 + 4.53458i) q^{43} +(-0.155637 + 0.375742i) q^{45} -7.47912i q^{47} +5.99438i q^{49} +(-0.405364 + 0.978635i) q^{51} +(7.58131 - 3.14028i) q^{53} +(-0.868855 - 0.868855i) q^{55} +(-2.74863 + 2.74863i) q^{57} +(-4.13463 - 9.98188i) q^{59} +(-1.35860 - 0.562751i) q^{61} -1.00281 q^{63} -2.74976 q^{65} +(10.8701 + 4.50256i) q^{67} +(-0.499078 - 1.20488i) q^{69} +(-9.35165 + 9.35165i) q^{71} +(0.367639 + 0.367639i) q^{73} +(4.46658 - 1.85012i) q^{75} +(1.15943 - 2.79912i) q^{77} +5.87774i q^{79} +1.00000i q^{81} +(1.62041 - 3.91201i) q^{83} +(-0.398011 + 0.164861i) q^{85} +(5.85009 + 5.85009i) q^{87} +(8.33036 - 8.33036i) q^{89} +(-2.59465 - 6.26404i) q^{91} +(1.74093 + 0.721116i) q^{93} -1.58090 q^{95} -7.97088 q^{97} +(-2.79128 - 1.15619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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			0
$2$		0			0
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$		0			0
$5$	0.155637	+	0.375742i	0.0696031	+	0.168037i	0.954853	−	0.297079i	$-0.0960126\pi$
$5$	0.155637	+	0.375742i	0.0696031	+	0.168037i	−0.885250	+	0.465116i	$0.846013\pi$
$6$		0			0
$7$	−0.709092	+	0.709092i	−0.268012	+	0.268012i	−0.828299	−	0.560287i	$-0.810691\pi$
$7$	−0.709092	+	0.709092i	−0.268012	+	0.268012i	0.560287	+	0.828299i	$0.310691\pi$
$8$		0			0
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	−2.79128	+	1.15619i	−0.841603	+	0.348603i	−0.761485	−	0.648182i	$-0.775530\pi$
$11$	−2.79128	+	1.15619i	−0.841603	+	0.348603i	−0.0801174	+	0.996785i	$0.525530\pi$
$12$		0			0
$13$	−2.58738	+	6.24650i	−0.717611	+	1.73247i	−0.0375686	+	0.999294i	$0.511961\pi$
$13$	−2.58738	+	6.24650i	−0.717611	+	1.73247i	−0.680043	+	0.733173i	$0.738039\pi$
$14$		0			0
$15$			0.406700i			0.105009i
$16$		0			0
$17$			1.05927i			0.256910i	0.991715	+	0.128455i	$0.0410018\pi$
$17$			1.05927i			0.256910i	−0.991715	+	0.128455i	$0.958998\pi$
$18$		0			0
$19$	−1.48755	+	3.59125i	−0.341266	+	0.823890i	0.656322	+	0.754481i	$0.272111\pi$
$19$	−1.48755	+	3.59125i	−0.341266	+	0.823890i	−0.997588	+	0.0694090i	$0.977889\pi$
$20$		0			0
$21$	−0.926474	+	0.383758i	−0.202173	+	0.0837429i
$22$		0			0
$23$	−0.922176	−	0.922176i	−0.192287	−	0.192287i	0.604397	−	0.796684i	$-0.293414\pi$
$23$	−0.922176	−	0.922176i	−0.192287	−	0.192287i	−0.796684	+	0.604397i	$0.793414\pi$
$24$		0			0
$25$	3.41858	−	3.41858i	0.683715	−	0.683715i
$26$		0			0
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$		0			0
$29$	7.64351	+	3.16605i	1.41936	+	0.587920i	0.954701	−	0.297567i	$-0.0961753\pi$
$29$	7.64351	+	3.16605i	1.41936	+	0.587920i	0.464664	+	0.885487i	$0.346175\pi$
$30$		0			0
$31$	1.88437			0.338442			0.169221	−	0.985578i	$-0.445875\pi$
$31$	1.88437			0.338442			0.169221	+	0.985578i	$0.445875\pi$
$32$		0			0
$33$	−3.02126			−0.525934
$34$		0			0
$35$	−0.376797	−	0.156074i	−0.0636903	−	0.0263814i
$36$		0			0
$37$	−1.24806	−	3.01308i	−0.205179	−	0.495347i	0.787473	−	0.616349i	$-0.211389\pi$
$37$	−1.24806	−	3.01308i	−0.205179	−	0.495347i	−0.992652	+	0.121003i	$0.961389\pi$
$38$		0			0
$39$	−4.78086	+	4.78086i	−0.765551	+	0.765551i
$40$		0			0
$41$	5.11980	+	5.11980i	0.799579	+	0.799579i	0.983029	−	0.183450i	$-0.0587266\pi$
$41$	5.11980	+	5.11980i	0.799579	+	0.799579i	−0.183450	+	0.983029i	$0.558727\pi$
$42$		0			0
$43$	−10.9474	+	4.53458i	−1.66947	+	0.691517i	−0.998740	−	0.0501855i	$-0.984019\pi$
$43$	−10.9474	+	4.53458i	−1.66947	+	0.691517i	−0.670729	+	0.741702i	$0.734019\pi$
$44$		0			0
$45$	−0.155637	+	0.375742i	−0.0232010	+	0.0560123i
$46$		0			0
$47$		−	7.47912i		−	1.09094i	−0.838130	−	0.545471i	$-0.816351\pi$
$47$		−	7.47912i		−	1.09094i	0.838130	−	0.545471i	$-0.183649\pi$
$48$		0			0
$49$			5.99438i			0.856339i
$50$		0			0
$51$	−0.405364	+	0.978635i	−0.0567623	+	0.137036i
$52$		0			0
$53$	7.58131	−	3.14028i	1.04137	−	0.431351i	0.204569	−	0.978852i	$-0.434421\pi$
$53$	7.58131	−	3.14028i	1.04137	−	0.431351i	0.836805	+	0.547501i	$0.184421\pi$
$54$		0			0
$55$	−0.868855	−	0.868855i	−0.117156	−	0.117156i
$56$		0			0
$57$	−2.74863	+	2.74863i	−0.364064	+	0.364064i
$58$		0			0
$59$	−4.13463	−	9.98188i	−0.538283	−	1.29953i	−0.925921	−	0.377718i	$-0.876709\pi$
$59$	−4.13463	−	9.98188i	−0.538283	−	1.29953i	0.387637	−	0.921812i	$-0.373291\pi$
$60$		0			0
$61$	−1.35860	−	0.562751i	−0.173951	−	0.0720529i	0.294008	−	0.955803i	$-0.405011\pi$
$61$	−1.35860	−	0.562751i	−0.173951	−	0.0720529i	−0.467959	+	0.883750i	$0.655011\pi$
$62$		0			0
$63$	−1.00281			−0.126342
$64$		0			0
$65$	−2.74976			−0.341066
$66$		0			0
$67$	10.8701	+	4.50256i	1.32800	+	0.550075i	0.930084	−	0.367347i	$-0.119734\pi$
$67$	10.8701	+	4.50256i	1.32800	+	0.550075i	0.397915	+	0.917422i	$0.369734\pi$
$68$		0			0
$69$	−0.499078	−	1.20488i	−0.0600820	−	0.145051i
$70$		0			0
$71$	−9.35165	+	9.35165i	−1.10984	+	1.10984i	−0.116666	+	0.993171i	$0.537221\pi$
$71$	−9.35165	+	9.35165i	−1.10984	+	1.10984i	−0.993171	+	0.116666i	$0.962779\pi$
$72$		0			0
$73$	0.367639	+	0.367639i	0.0430289	+	0.0430289i	0.728294	−	0.685265i	$-0.240314\pi$
$73$	0.367639	+	0.367639i	0.0430289	+	0.0430289i	−0.685265	+	0.728294i	$0.740314\pi$
$74$		0			0
$75$	4.46658	−	1.85012i	0.515757	−	0.213633i
$76$		0			0
$77$	1.15943	−	2.79912i	0.132130	−	0.318989i
$78$		0			0
$79$			5.87774i			0.661297i	0.943754	+	0.330649i	$0.107267\pi$
$79$			5.87774i			0.661297i	−0.943754	+	0.330649i	$0.892733\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	1.62041	−	3.91201i	0.177863	−	0.429398i	−0.809655	−	0.586906i	$-0.800346\pi$
$83$	1.62041	−	3.91201i	0.177863	−	0.429398i	0.987518	+	0.157507i	$0.0503458\pi$
$84$		0			0
$85$	−0.398011	+	0.164861i	−0.0431703	+	0.0178817i
$86$		0			0
$87$	5.85009	+	5.85009i	0.627195	+	0.627195i
$88$		0			0
$89$	8.33036	−	8.33036i	0.883016	−	0.883016i	−0.110824	−	0.993840i	$-0.535349\pi$
$89$	8.33036	−	8.33036i	0.883016	−	0.883016i	0.993840	+	0.110824i	$0.0353489\pi$
$90$		0			0
$91$	−2.59465	−	6.26404i	−0.271993	−	0.656650i
$92$		0			0
$93$	1.74093	+	0.721116i	0.180526	+	0.0747762i
$94$		0			0
$95$	−1.58090			−0.162197
$96$		0			0
$97$	−7.97088			−0.809320			−0.404660	−	0.914467i	$-0.632610\pi$
$97$	−7.97088			−0.809320			−0.404660	+	0.914467i	$0.632610\pi$
$98$		0			0
$99$	−2.79128	−	1.15619i	−0.280534	−	0.116201i
$100$		0			0
$101$	−3.63502	−	8.77571i	−0.361698	−	0.873216i	−0.995052	−	0.0993539i	$-0.968322\pi$
$101$	−3.63502	−	8.77571i	−0.361698	−	0.873216i	0.633354	−	0.773862i	$-0.281678\pi$
$102$		0			0
$103$	2.44527	−	2.44527i	0.240940	−	0.240940i	−0.576299	−	0.817239i	$-0.695504\pi$
$103$	2.44527	−	2.44527i	0.240940	−	0.240940i	0.817239	+	0.576299i	$0.195504\pi$
$104$		0			0
$105$	−0.288388	−	0.288388i	−0.0281438	−	0.0281438i
$106$		0			0
$107$	14.7198	−	6.09714i	1.42302	−	0.589433i	0.467401	−	0.884045i	$-0.345190\pi$
$107$	14.7198	−	6.09714i	1.42302	−	0.589433i	0.955617	+	0.294612i	$0.0951905\pi$
$108$		0			0
$109$	−3.64422	+	8.79792i	−0.349053	+	0.842688i	0.647679	+	0.761913i	$0.275740\pi$
$109$	−3.64422	+	8.79792i	−0.349053	+	0.842688i	−0.996732	+	0.0807753i	$0.974260\pi$
$110$		0			0
$111$		−	3.26133i		−	0.309552i
$112$		0			0
$113$		−	6.79924i		−	0.639619i	−0.947482	−	0.319810i	$-0.896381\pi$
$113$		−	6.79924i		−	0.639619i	0.947482	−	0.319810i	$-0.103619\pi$
$114$		0			0
$115$	0.202975	−	0.490025i	0.0189275	−	0.0456951i
$116$		0			0
$117$	−6.24650	+	2.58738i	−0.577489	+	0.239204i
$118$		0			0
$119$	−0.751118	−	0.751118i	−0.0688549	−	0.0688549i
$120$		0			0
$121$	−1.32369	+	1.32369i	−0.120336	+	0.120336i
$122$		0			0
$123$	2.77082	+	6.68934i	0.249836	+	0.603158i
$124$		0			0
$125$	3.69527	+	1.53063i	0.330515	+	0.136904i
$126$		0			0
$127$	5.17506			0.459212			0.229606	−	0.973284i	$-0.426256\pi$
$127$	5.17506			0.459212			0.229606	+	0.973284i	$0.426256\pi$
$128$		0			0
$129$	−11.8494			−1.04328
$130$		0			0
$131$	0.0139993	+	0.00579870i	0.00122313	+	0.000506635i	0.383295	−	0.923626i	$-0.374789\pi$
$131$	0.0139993	+	0.00579870i	0.00122313	+	0.000506635i	−0.382072	+	0.924133i	$0.624789\pi$
$132$		0			0
$133$	−1.49172	−	3.60134i	−0.129349	−	0.312276i
$134$		0			0
$135$	−0.287580	+	0.287580i	−0.0247510	+	0.0247510i
$136$		0			0
$137$	8.75347	+	8.75347i	0.747859	+	0.747859i	0.974077	−	0.226217i	$-0.0726360\pi$
$137$	8.75347	+	8.75347i	0.747859	+	0.747859i	−0.226217	+	0.974077i	$0.572636\pi$
$138$		0			0
$139$	−0.340231	+	0.140928i	−0.0288581	+	0.0119534i	−0.397066	−	0.917790i	$-0.629972\pi$
$139$	−0.340231	+	0.140928i	−0.0288581	+	0.0119534i	0.368208	+	0.929744i	$0.379972\pi$
$140$		0			0
$141$	2.86213	−	6.90980i	0.241035	−	0.581910i
$142$		0			0
$143$		−	20.4272i		−	1.70821i
$144$		0			0
$145$			3.36474i			0.279426i
$146$		0			0
$147$	−2.29395	+	5.53808i	−0.189202	+	0.456773i
$148$		0			0
$149$	−11.5258	+	4.77413i	−0.944228	+	0.391112i	−0.801059	−	0.598586i	$-0.795729\pi$
$149$	−11.5258	+	4.77413i	−0.944228	+	0.391112i	−0.143170	+	0.989698i	$0.545729\pi$
$150$		0			0
$151$	5.63305	+	5.63305i	0.458411	+	0.458411i	0.898134	−	0.439723i	$-0.144923\pi$
$151$	5.63305	+	5.63305i	0.458411	+	0.458411i	−0.439723	+	0.898134i	$0.644923\pi$
$152$		0			0
$153$	−0.749015	+	0.749015i	−0.0605542	+	0.0605542i
$154$		0			0
$155$	0.293278	+	0.708035i	0.0235566	+	0.0568707i
$156$		0			0
$157$	−15.1312	−	6.26756i	−1.20760	−	0.500206i	−0.314155	−	0.949372i	$-0.601721\pi$
$157$	−15.1312	−	6.26756i	−1.20760	−	0.500206i	−0.893448	+	0.449166i	$0.851721\pi$
$158$		0			0
$159$	8.20595			0.650775
$160$		0			0
$161$	1.30782			0.103070
$162$		0			0
$163$	12.4717	+	5.16594i	0.976858	+	0.404628i	0.813261	−	0.581899i	$-0.197690\pi$
$163$	12.4717	+	5.16594i	0.976858	+	0.404628i	0.163597	+	0.986527i	$0.447690\pi$
$164$		0			0
$165$	−0.470221	−	1.13521i	−0.0366066	−	0.0883762i
$166$		0			0
$167$	13.0928	−	13.0928i	1.01315	−	1.01315i	0.0132424	−	0.999912i	$-0.495785\pi$
$167$	13.0928	−	13.0928i	1.01315	−	1.01315i	0.999912	−	0.0132424i	$-0.00421531\pi$
$168$		0			0
$169$	−23.1318	−	23.1318i	−1.77937	−	1.77937i
$170$		0			0
$171$	−3.59125	+	1.48755i	−0.274630	+	0.113755i
$172$		0			0
$173$	3.08646	−	7.45138i	0.234659	−	0.566518i	−0.762055	−	0.647512i	$-0.775809\pi$
$173$	3.08646	−	7.45138i	0.234659	−	0.566518i	0.996715	+	0.0809941i	$0.0258095\pi$
$174$		0			0
$175$			4.84817i			0.366487i
$176$		0			0
$177$		−	10.8043i		−	0.812102i
$178$		0			0
$179$	3.47037	−	8.37820i	0.259387	−	0.626216i	−0.739511	−	0.673145i	$-0.764943\pi$
$179$	3.47037	−	8.37820i	0.259387	−	0.626216i	0.998898	+	0.0469281i	$0.0149432\pi$
$180$		0			0
$181$	20.8285	−	8.62745i	1.54817	−	0.641274i	0.565187	−	0.824963i	$-0.308804\pi$
$181$	20.8285	−	8.62745i	1.54817	−	0.641274i	0.982984	+	0.183689i	$0.0588040\pi$
$182$		0			0
$183$	−1.03983	−	1.03983i	−0.0768663	−	0.0768663i
$184$		0			0
$185$	0.937894	−	0.937894i	0.0689553	−	0.0689553i
$186$		0			0
$187$	−1.22471	−	2.95671i	−0.0895596	−	0.216216i
$188$		0			0
$189$	−0.926474	−	0.383758i	−0.0673911	−	0.0279143i
$190$		0			0
$191$	10.0099			0.724293			0.362147	−	0.932121i	$-0.382044\pi$
$191$	10.0099			0.724293			0.362147	+	0.932121i	$0.382044\pi$
$192$		0			0
$193$	9.51081			0.684603			0.342301	−	0.939590i	$-0.388794\pi$
$193$	9.51081			0.684603			0.342301	+	0.939590i	$0.388794\pi$
$194$		0			0
$195$	−2.54045	−	1.05229i	−0.181925	−	0.0753559i
$196$		0			0
$197$	5.27324	+	12.7307i	0.375703	+	0.907028i	0.992761	+	0.120110i	$0.0383246\pi$
$197$	5.27324	+	12.7307i	0.375703	+	0.907028i	−0.617058	+	0.786918i	$0.711675\pi$
$198$		0			0
$199$	9.74284	−	9.74284i	0.690652	−	0.690652i	−0.271724	−	0.962375i	$-0.587594\pi$
$199$	9.74284	−	9.74284i	0.690652	−	0.690652i	0.962375	+	0.271724i	$0.0875937\pi$
$200$		0			0
$201$	8.31964	+	8.31964i	0.586822	+	0.586822i
$202$		0			0
$203$	−7.66497	+	3.17494i	−0.537976	+	0.222837i
$204$		0			0
$205$	−1.12689	+	2.72055i	−0.0787055	+	0.190012i
$206$		0			0
$207$		−	1.30415i		−	0.0906450i
$208$		0			0
$209$		−	11.7441i		−	0.812355i
$210$		0			0
$211$	2.30086	−	5.55477i	0.158398	−	0.382406i	−0.824679	−	0.565601i	$-0.808644\pi$
$211$	2.30086	−	5.55477i	0.158398	−	0.382406i	0.983077	+	0.183195i	$0.0586441\pi$
$212$		0			0
$213$	−12.2185	+	5.06108i	−0.837199	+	0.346779i
$214$		0			0
$215$	−3.40766	−	3.40766i	−0.232400	−	0.232400i
$216$		0			0
$217$	−1.33619	+	1.33619i	−0.0907065	+	0.0907065i
$218$		0			0
$219$	0.198965	+	0.480344i	0.0134448	+	0.0324586i
$220$		0			0
$221$	−6.61671	−	2.74073i	−0.445088	−	0.184361i
$222$		0			0
$223$	−8.30716			−0.556288			−0.278144	−	0.960539i	$-0.589719\pi$
$223$	−8.30716			−0.556288			−0.278144	+	0.960539i	$0.589719\pi$
$224$		0			0
$225$	4.83460			0.322306
$226$		0			0
$227$	−21.6055	−	8.94931i	−1.43401	−	0.593987i	−0.475672	−	0.879623i	$-0.657795\pi$
$227$	−21.6055	−	8.94931i	−1.43401	−	0.593987i	−0.958338	+	0.285636i	$0.907795\pi$
$228$		0			0
$229$	−4.89379	−	11.8147i	−0.323391	−	0.780734i	−0.999052	−	0.0435225i	$-0.986142\pi$
$229$	−4.89379	−	11.8147i	−0.323391	−	0.780734i	0.675662	−	0.737212i	$-0.263858\pi$
$230$		0			0
$231$	2.14235	−	2.14235i	0.140956	−	0.140956i
$232$		0			0
$233$	−14.3237	−	14.3237i	−0.938376	−	0.938376i	0.0598327	−	0.998208i	$-0.480943\pi$
$233$	−14.3237	−	14.3237i	−0.938376	−	0.938376i	−0.998208	+	0.0598327i	$0.980943\pi$
$234$		0			0
$235$	2.81021	−	1.16403i	0.183318	−	0.0759329i
$236$		0			0
$237$	−2.24931	+	5.43032i	−0.146109	+	0.352737i
$238$		0			0
$239$			11.8083i			0.763816i	0.924200	+	0.381908i	$0.124733\pi$
$239$			11.8083i			0.763816i	−0.924200	+	0.381908i	$0.875267\pi$
$240$		0			0
$241$			8.34145i			0.537320i	0.963235	+	0.268660i	$0.0865808\pi$
$241$			8.34145i			0.537320i	−0.963235	+	0.268660i	$0.913419\pi$
$242$		0			0
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$		0			0
$245$	−2.25234	+	0.932948i	−0.143896	+	0.0596039i
$246$		0			0
$247$	−18.5839	−	18.5839i	−1.18247	−	1.18247i
$248$		0			0
$249$	2.99412	−	2.99412i	0.189745	−	0.189745i
$250$		0			0
$251$	8.31548	+	20.0753i	0.524868	+	1.26714i	0.934848	+	0.355049i	$0.115536\pi$
$251$	8.31548	+	20.0753i	0.524868	+	1.26714i	−0.409979	+	0.912095i	$0.634464\pi$
$252$		0			0
$253$	3.64026	+	1.50785i	0.228861	+	0.0947974i
$254$		0			0
$255$	−0.430804			−0.0269780
$256$		0			0
$257$	10.8777			0.678532			0.339266	−	0.940690i	$-0.389821\pi$
$257$	10.8777			0.678532			0.339266	+	0.940690i	$0.389821\pi$
$258$		0			0
$259$	3.02154	+	1.25156i	0.187749	+	0.0777683i
$260$		0			0
$261$	3.16605	+	7.64351i	0.195973	+	0.473121i
$262$		0			0
$263$	2.59878	−	2.59878i	0.160248	−	0.160248i	−0.622429	−	0.782676i	$-0.713854\pi$
$263$	2.59878	−	2.59878i	0.160248	−	0.160248i	0.782676	+	0.622429i	$0.213854\pi$
$264$		0			0
$265$	2.35987	+	2.35987i	0.144966	+	0.144966i
$266$		0			0
$267$	10.8841	−	4.50836i	0.666098	−	0.275907i
$268$		0			0
$269$	2.53422	−	6.11815i	0.154514	−	0.373030i	−0.827600	−	0.561319i	$-0.810294\pi$
$269$	2.53422	−	6.11815i	0.154514	−	0.373030i	0.982114	+	0.188289i	$0.0602941\pi$
$270$		0			0
$271$			25.4870i			1.54823i	0.633046	+	0.774114i	$0.281804\pi$
$271$			25.4870i			1.54823i	−0.633046	+	0.774114i	$0.718196\pi$
$272$		0			0
$273$		−	6.78015i		−	0.410353i
$274$		0			0
$275$	−5.58969	+	13.4947i	−0.337071	+	0.813762i
$276$		0			0
$277$	−1.45033	+	0.600745i	−0.0871416	+	0.0360952i	−0.425828	−	0.904804i	$-0.640017\pi$
$277$	−1.45033	+	0.600745i	−0.0871416	+	0.0360952i	0.338687	+	0.940899i	$0.390017\pi$
$278$		0			0
$279$	1.33245	+	1.33245i	0.0797716	+	0.0797716i
$280$		0			0
$281$	−3.62873	+	3.62873i	−0.216472	+	0.216472i	−0.807010	−	0.590538i	$-0.798916\pi$
$281$	−3.62873	+	3.62873i	−0.216472	+	0.216472i	0.590538	+	0.807010i	$0.298916\pi$
$282$		0			0
$283$	2.49752	+	6.02955i	0.148462	+	0.358419i	0.980563	−	0.196205i	$-0.0628619\pi$
$283$	2.49752	+	6.02955i	0.148462	+	0.358419i	−0.832101	+	0.554625i	$0.812862\pi$
$284$		0			0
$285$	−1.46056	−	0.604985i	−0.0865162	−	0.0358362i
$286$		0			0
$287$	−7.26082			−0.428593
$288$		0			0
$289$	15.8780			0.933997
$290$		0			0
$291$	−7.36413	−	3.05032i	−0.431693	−	0.178813i
$292$		0			0
$293$	0.743879	+	1.79588i	0.0434579	+	0.104917i	0.944118	−	0.329608i	$-0.106916\pi$
$293$	0.743879	+	1.79588i	0.0434579	+	0.104917i	−0.900660	+	0.434524i	$0.856916\pi$
$294$		0			0
$295$	3.10711	−	3.10711i	0.180903	−	0.180903i
$296$		0			0
$297$	−2.13635	−	2.13635i	−0.123964	−	0.123964i
$298$		0			0
$299$	8.14640	−	3.37435i	0.471118	−	0.195144i
$300$		0			0
$301$	4.54731	−	10.9782i	0.262103	−	0.632772i
$302$		0			0
$303$		−	9.49876i		−	0.545690i
$304$		0			0
$305$		−	0.598068i		−	0.0342453i
$306$		0			0
$307$	8.42212	−	20.3328i	0.480676	−	1.16045i	−0.478613	−	0.878026i	$-0.658860\pi$
$307$	8.42212	−	20.3328i	0.480676	−	1.16045i	0.959289	−	0.282428i	$-0.0911397\pi$
$308$		0			0
$309$	3.19490	−	1.32337i	0.181752	−	0.0752840i
$310$		0			0
$311$	13.1751	+	13.1751i	0.747092	+	0.747092i	0.973932	−	0.226840i	$-0.0728394\pi$
$311$	13.1751	+	13.1751i	0.747092	+	0.747092i	−0.226840	+	0.973932i	$0.572839\pi$
$312$		0			0
$313$	−17.0669	+	17.0669i	−0.964680	+	0.964680i	−0.999397	−	0.0347173i	$-0.988947\pi$
$313$	−17.0669	+	17.0669i	−0.964680	+	0.964680i	0.0347173	+	0.999397i	$0.488947\pi$
$314$		0			0
$315$	−0.156074	−	0.376797i	−0.00879379	−	0.0212301i
$316$		0			0
$317$	−2.20756	−	0.914403i	−0.123989	−	0.0513580i	0.319826	−	0.947476i	$-0.396375\pi$
$317$	−2.20756	−	0.914403i	−0.123989	−	0.0513580i	−0.443815	+	0.896118i	$0.646375\pi$
$318$		0			0
$319$	−24.9957			−1.39949
$320$		0			0
$321$	15.9326			0.889271
$322$		0			0
$323$	−3.80409	−	1.57571i	−0.211666	−	0.0876747i
$324$		0			0
$325$	12.5090	+	30.1993i	0.693872	+	1.67516i
$326$		0			0
$327$	−6.73364	+	6.73364i	−0.372371	+	0.372371i
$328$		0			0
$329$	5.30338	+	5.30338i	0.292385	+	0.292385i
$330$		0			0
$331$	−5.52800	+	2.28977i	−0.303846	+	0.125857i	−0.529397	−	0.848374i	$-0.677582\pi$
$331$	−5.52800	+	2.28977i	−0.303846	+	0.125857i	0.225551	+	0.974231i	$0.427582\pi$
$332$		0			0
$333$	1.24806	−	3.01308i	0.0683931	−	0.165116i
$334$		0			0
$335$			4.78513i			0.261440i
$336$		0			0
$337$			12.4013i			0.675540i	0.941229	+	0.337770i	$0.109673\pi$
$337$			12.4013i			0.675540i	−0.941229	+	0.337770i	$0.890327\pi$
$338$		0			0
$339$	2.60196	−	6.28168i	0.141319	−	0.341174i
$340$		0			0
$341$	−5.25979	+	2.17868i	−0.284834	+	0.117982i
$342$		0			0
$343$	−9.21421	−	9.21421i	−0.497521	−	0.497521i
$344$		0			0
$345$	0.375049	−	0.375049i	0.0201920	−	0.0201920i
$346$		0			0
$347$	−1.93560	−	4.67295i	−0.103908	−	0.250857i	0.863371	−	0.504569i	$-0.168349\pi$
$347$	−1.93560	−	4.67295i	−0.103908	−	0.250857i	−0.967280	+	0.253712i	$0.918349\pi$
$348$		0			0
$349$	−2.69921	−	1.11805i	−0.144485	−	0.0598478i	0.309269	−	0.950975i	$-0.399916\pi$
$349$	−2.69921	−	1.11805i	−0.144485	−	0.0598478i	−0.453754	+	0.891127i	$0.649916\pi$
$350$		0			0
$351$	−6.76116			−0.360884
$352$		0			0
$353$	3.35055			0.178332			0.0891658	−	0.996017i	$-0.471580\pi$
$353$	3.35055			0.178332			0.0891658	+	0.996017i	$0.471580\pi$
$354$		0			0
$355$	−4.96927	−	2.05834i	−0.263741	−	0.109245i
$356$		0			0
$357$	−0.406502	−	0.981383i	−0.0215144	−	0.0519403i
$358$		0			0
$359$	−11.9270	+	11.9270i	−0.629483	+	0.629483i	−0.947938	−	0.318455i	$-0.896836\pi$
$359$	−11.9270	+	11.9270i	−0.629483	+	0.629483i	0.318455	+	0.947938i	$0.396836\pi$
$360$		0			0
$361$	2.75072	+	2.75072i	0.144775	+	0.144775i
$362$		0			0
$363$	−1.72949	+	0.716378i	−0.0907747	+	0.0376001i
$364$		0			0
$365$	−0.0809190	+	0.195356i	−0.00423549	+	0.0102254i
$366$		0			0
$367$			28.5325i			1.48939i	0.667407	+	0.744693i	$0.267404\pi$
$367$			28.5325i			1.48939i	−0.667407	+	0.744693i	$0.732596\pi$
$368$		0			0
$369$			7.24049i			0.376925i
$370$		0			0
$371$	−3.14910	+	7.60260i	−0.163493	+	0.394707i
$372$		0			0
$373$	16.9506	−	7.02116i	0.877668	−	0.363542i	0.102076	−	0.994777i	$-0.467452\pi$
$373$	16.9506	−	7.02116i	0.877668	−	0.363542i	0.775592	+	0.631235i	$0.217452\pi$
$374$		0			0
$375$	2.82823	+	2.82823i	0.146049	+	0.146049i
$376$		0			0
$377$	−39.5534	+	39.5534i	−2.03710	+	2.03710i
$378$		0			0
$379$	−4.48842	−	10.8360i	−0.230555	−	0.556608i	0.765688	−	0.643212i	$-0.222399\pi$
$379$	−4.48842	−	10.8360i	−0.230555	−	0.556608i	−0.996243	+	0.0866037i	$0.972399\pi$
$380$		0			0
$381$	4.78113	+	1.98041i	0.244945	+	0.101459i
$382$		0			0
$383$	3.94835			0.201751			0.100876	−	0.994899i	$-0.467836\pi$
$383$	3.94835			0.201751			0.100876	+	0.994899i	$0.467836\pi$
$384$		0			0
$385$	1.23220			0.0627985
$386$		0			0
$387$	−10.9474	−	4.53458i	−0.556490	−	0.230506i
$388$		0			0
$389$	6.63971	+	16.0297i	0.336647	+	0.812737i	0.998033	+	0.0626914i	$0.0199684\pi$
$389$	6.63971	+	16.0297i	0.336647	+	0.812737i	−0.661386	+	0.750045i	$0.730032\pi$
$390$		0			0
$391$	0.976831	−	0.976831i	0.0494005	−	0.0494005i
$392$		0			0
$393$	0.0107146	+	0.0107146i	0.000540480	+	0.000540480i
$394$		0			0
$395$	−2.20851	+	0.914795i	−0.111122	+	0.0460283i
$396$		0			0
$397$	1.83049	−	4.41918i	0.0918695	−	0.221792i	−0.871265	−	0.490813i	$-0.836700\pi$
$397$	1.83049	−	4.41918i	0.0918695	−	0.221792i	0.963134	+	0.269020i	$0.0866999\pi$
$398$		0			0
$399$		−	3.89806i		−	0.195147i
$400$		0			0
$401$			23.8940i			1.19321i	0.802536	+	0.596604i	$0.203484\pi$
$401$			23.8940i			1.19321i	−0.802536	+	0.596604i	$0.796516\pi$
$402$		0			0
$403$	−4.87558	+	11.7707i	−0.242870	+	0.586340i
$404$		0			0
$405$	−0.375742	+	0.155637i	−0.0186708	+	0.00773368i
$406$		0			0
$407$	6.96736	+	6.96736i	0.345359	+	0.345359i
$408$		0			0
$409$	13.8337	−	13.8337i	0.684032	−	0.684032i	−0.276874	−	0.960906i	$-0.589299\pi$
$409$	13.8337	−	13.8337i	0.684032	−	0.684032i	0.960906	+	0.276874i	$0.0892985\pi$
$410$		0			0
$411$	4.73734	+	11.4370i	0.233676	+	0.564144i
$412$		0			0
$413$	10.0099	+	4.14624i	0.492556	+	0.204023i
$414$		0			0
$415$	1.72210			0.0845345
$416$		0			0
$417$	−0.368264			−0.0180340
$418$		0			0
$419$	0.473345	+	0.196066i	0.0231244	+	0.00957845i	0.394216	−	0.919018i	$-0.371016\pi$
$419$	0.473345	+	0.196066i	0.0231244	+	0.00957845i	−0.371091	+	0.928596i	$0.621016\pi$
$420$		0			0
$421$	−1.25389	−	3.02716i	−0.0611109	−	0.147535i	0.890374	−	0.455229i	$-0.150443\pi$
$421$	−1.25389	−	3.02716i	−0.0611109	−	0.147535i	−0.951485	+	0.307694i	$0.900443\pi$
$422$		0			0
$423$	5.28853	−	5.28853i	0.257137	−	0.257137i
$424$		0			0
$425$	3.62118	+	3.62118i	0.175653	+	0.175653i
$426$		0			0
$427$	1.36242	−	0.564331i	0.0659319	−	0.0273099i
$428$		0			0
$429$	7.81716	−	18.8723i	0.377416	−	0.911163i
$430$		0			0
$431$			29.1399i			1.40362i	0.712365	+	0.701810i	$0.247624\pi$
$431$			29.1399i			1.40362i	−0.712365	+	0.701810i	$0.752376\pi$
$432$		0			0
$433$			5.66352i			0.272172i	0.990697	+	0.136086i	$0.0434523\pi$
$433$			5.66352i			0.272172i	−0.990697	+	0.136086i	$0.956548\pi$
$434$		0			0
$435$	−1.28763	+	3.10861i	−0.0617371	+	0.149047i
$436$		0			0
$437$	4.68355	−	1.93999i	0.224045	−	0.0928023i
$438$		0			0
$439$	10.7013	+	10.7013i	0.510743	+	0.510743i	0.914754	−	0.404011i	$-0.132384\pi$
$439$	10.7013	+	10.7013i	0.510743	+	0.510743i	−0.404011	+	0.914754i	$0.632384\pi$
$440$		0			0
$441$	−4.23866	+	4.23866i	−0.201841	+	0.201841i
$442$		0			0
$443$	14.3853	+	34.7291i	0.683464	+	1.65003i	0.757551	+	0.652776i	$0.226396\pi$
$443$	14.3853	+	34.7291i	0.683464	+	1.65003i	−0.0740866	+	0.997252i	$0.523604\pi$
$444$		0			0
$445$	4.42658	+	1.83355i	0.209840	+	0.0869185i
$446$		0			0
$447$	−12.4754			−0.590067
$448$		0			0
$449$	−26.7000			−1.26005			−0.630025	−	0.776575i	$-0.716956\pi$
$449$	−26.7000			−1.26005			−0.630025	+	0.776575i	$0.716956\pi$
$450$		0			0
$451$	−20.2102	−	8.37136i	−0.951663	−	0.394192i
$452$		0			0
$453$	3.04858	+	7.35993i	0.143235	+	0.345800i
$454$		0			0
$455$	1.94984	−	1.94984i	0.0914097	−	0.0914097i
$456$		0			0
$457$	1.66332	+	1.66332i	0.0778069	+	0.0778069i	0.744939	−	0.667132i	$-0.232478\pi$
$457$	1.66332	+	1.66332i	0.0778069	+	0.0778069i	−0.667132	+	0.744939i	$0.732478\pi$
$458$		0			0
$459$	−0.978635	+	0.405364i	−0.0456788	+	0.0189208i
$460$		0			0
$461$	−3.49519	+	8.43813i	−0.162787	+	0.393003i	−0.984134	−	0.177426i	$-0.943223\pi$
$461$	−3.49519	+	8.43813i	−0.162787	+	0.393003i	0.821347	+	0.570429i	$0.193223\pi$
$462$		0			0
$463$		−	12.1833i		−	0.566204i	−0.959090	−	0.283102i	$-0.908636\pi$
$463$		−	12.1833i		−	0.566204i	0.959090	−	0.283102i	$-0.0913635\pi$
$464$		0			0
$465$			0.766371i			0.0355396i
$466$		0			0
$467$	−4.89494	+	11.8174i	−0.226511	+	0.546846i	−0.995748	−	0.0921176i	$-0.970636\pi$
$467$	−4.89494	+	11.8174i	−0.226511	+	0.546846i	0.769237	+	0.638963i	$0.220636\pi$
$468$		0			0
$469$	−10.9007	+	4.51520i	−0.503346	+	0.208493i
$470$		0			0
$471$	−11.5809	−	11.5809i	−0.533621	−	0.533621i
$472$		0			0
$473$	25.3146	−	25.3146i	1.16396	−	1.16396i
$474$		0			0
$475$	7.19168	+	17.3623i	0.329977	+	0.796635i
$476$		0			0
$477$	7.58131	+	3.14028i	0.347125	+	0.143784i
$478$		0			0
$479$	−19.9031			−0.909396			−0.454698	−	0.890646i	$-0.650253\pi$
$479$	−19.9031			−0.909396			−0.454698	+	0.890646i	$0.650253\pi$
$480$		0			0
$481$	22.0504			1.00541
$482$		0			0
$483$	1.20826	+	0.500480i	0.0549780	+	0.0227726i
$484$		0			0
$485$	−1.24057	−	2.99499i	−0.0563312	−	0.135995i
$486$		0			0
$487$	16.3518	−	16.3518i	0.740969	−	0.740969i	−0.231795	−	0.972765i	$-0.574460\pi$
$487$	16.3518	−	16.3518i	0.740969	−	0.740969i	0.972765	+	0.231795i	$0.0744599\pi$
$488$		0			0
$489$	9.54542	+	9.54542i	0.431659	+	0.431659i
$490$		0			0
$491$	−7.50463	+	3.10852i	−0.338679	+	0.140286i	−0.545540	−	0.838085i	$-0.683675\pi$
$491$	−7.50463	+	3.10852i	−0.338679	+	0.140286i	0.206861	+	0.978370i	$0.433675\pi$
$492$		0			0
$493$	−3.35369	+	8.09652i	−0.151042	+	0.364649i
$494$		0			0
$495$		−	1.22875i		−	0.0552280i
$496$		0			0
$497$		−	13.2624i		−	0.594899i
$498$		0			0
$499$	−4.17340	+	10.0755i	−0.186827	+	0.451041i	−0.989345	−	0.145587i	$-0.953493\pi$
$499$	−4.17340	+	10.0755i	−0.186827	+	0.451041i	0.802518	+	0.596627i	$0.203493\pi$
$500$		0			0
$501$	17.1066	−	7.08580i	0.764268	−	0.316570i
$502$		0			0
$503$	−18.7140	−	18.7140i	−0.834416	−	0.834416i	0.153701	−	0.988117i	$-0.450881\pi$
$503$	−18.7140	−	18.7140i	−0.834416	−	0.834416i	−0.988117	+	0.153701i	$0.950881\pi$
$504$		0			0
$505$	2.73166	−	2.73166i	0.121557	−	0.121557i
$506$		0			0
$507$	−12.5188	−	30.2231i	−0.555981	−	1.34226i
$508$		0			0
$509$	−37.2151	−	15.4150i	−1.64953	−	0.683258i	−0.652324	−	0.757940i	$-0.726206\pi$
$509$	−37.2151	−	15.4150i	−1.64953	−	0.683258i	−0.997207	+	0.0746822i	$0.976206\pi$
$510$		0			0
$511$	−0.521380			−0.0230645
$512$		0			0
$513$	−3.88714			−0.171622
$514$		0			0
$515$	1.29937	+	0.538215i	0.0572569	+	0.0237166i
$516$		0			0
$517$	8.64725	+	20.8763i	0.380306	+	0.918139i
$518$		0			0
$519$	5.70304	−	5.70304i	0.250336	−	0.250336i
$520$		0			0
$521$	9.78297	+	9.78297i	0.428600	+	0.428600i	0.888151	−	0.459551i	$-0.151990\pi$
$521$	9.78297	+	9.78297i	0.428600	+	0.428600i	−0.459551	+	0.888151i	$0.651990\pi$
$522$		0			0
$523$	9.08765	−	3.76423i	0.397375	−	0.164598i	−0.175042	−	0.984561i	$-0.556006\pi$
$523$	9.08765	−	3.76423i	0.397375	−	0.164598i	0.572417	+	0.819963i	$0.306006\pi$
$524$		0			0
$525$	−1.85531	+	4.47913i	−0.0809726	+	0.195485i
$526$		0			0
$527$			1.99605i			0.0869491i
$528$		0			0
$529$		−	21.2992i		−	0.926051i
$530$		0			0
$531$	4.13463	−	9.98188i	0.179428	−	0.433177i
$532$		0			0
$533$	−45.2277	+	18.7339i	−1.95903	+	0.811457i
$534$		0			0
$535$	4.58190	+	4.58190i	0.198093	+	0.198093i
$536$		0			0
$537$	6.41240	−	6.41240i	0.276715	−	0.276715i
$538$		0			0
$539$	−6.93062	−	16.7320i	−0.298523	−	0.720698i
$540$		0			0
$541$	20.5649	+	8.51826i	0.884154	+	0.366229i	0.778106	−	0.628132i	$-0.216180\pi$
$541$	20.5649	+	8.51826i	0.884154	+	0.366229i	0.106048	+	0.994361i	$0.466180\pi$
$542$		0			0
$543$	22.5446			0.967482
$544$		0			0
$545$	−3.87292			−0.165898
$546$		0			0
$547$	−18.2473	−	7.55828i	−0.780198	−	0.323169i	−0.0432027	−	0.999066i	$-0.513756\pi$
$547$	−18.2473	−	7.55828i	−0.780198	−	0.323169i	−0.736996	+	0.675898i	$0.763756\pi$
$548$		0			0
$549$	−0.562751	−	1.35860i	−0.0240176	−	0.0579837i
$550$		0			0
$551$	−22.7401	+	22.7401i	−0.968763	+	0.968763i
$552$		0			0
$553$	−4.16786	−	4.16786i	−0.177235	−	0.177235i
$554$		0			0
$555$	1.22542	−	0.507585i	0.0520161	−	0.0215458i
$556$		0			0
$557$	2.57380	−	6.21371i	0.109056	−	0.263283i	−0.859925	−	0.510420i	$-0.829490\pi$
$557$	2.57380	−	6.21371i	0.109056	−	0.263283i	0.968981	+	0.247137i	$0.0794898\pi$
$558$		0			0
$559$		−	80.1159i		−	3.38854i
$560$		0			0
$561$		−	3.20032i		−	0.135118i
$562$		0			0
$563$	−3.34911	+	8.08547i	−0.141148	+	0.340762i	−0.978607	−	0.205738i	$-0.934040\pi$
$563$	−3.34911	+	8.08547i	−0.141148	+	0.340762i	0.837459	+	0.546501i	$0.184040\pi$
$564$		0			0
$565$	2.55476	−	1.05822i	0.107480	−	0.0445195i
$566$		0			0
$567$	−0.709092	−	0.709092i	−0.0297791	−	0.0297791i
$568$		0			0
$569$	−5.86928	+	5.86928i	−0.246053	+	0.246053i	−0.819349	−	0.573296i	$-0.805665\pi$
$569$	−5.86928	+	5.86928i	−0.246053	+	0.246053i	0.573296	+	0.819349i	$0.305665\pi$
$570$		0			0
$571$	−4.92409	−	11.8878i	−0.206067	−	0.497489i	0.786730	−	0.617297i	$-0.211772\pi$
$571$	−4.92409	−	11.8878i	−0.206067	−	0.497489i	−0.992797	+	0.119808i	$0.961772\pi$
$572$		0			0
$573$	9.24797	+	3.83064i	0.386340	+	0.160027i
$574$		0			0
$575$	−6.30506			−0.262939
$576$		0			0
$577$	12.4165			0.516905			0.258453	−	0.966024i	$-0.416787\pi$
$577$	12.4165			0.516905			0.258453	+	0.966024i	$0.416787\pi$
$578$		0			0
$579$	8.78684	+	3.63963i	0.365169	+	0.151258i
$580$		0			0
$581$	1.62496	+	3.92299i	0.0674145	+	0.162753i
$582$		0			0
$583$	−17.5308	+	17.5308i	−0.726052	+	0.726052i
$584$		0			0
$585$	−1.94438	−	1.94438i	−0.0803900	−	0.0803900i
$586$		0			0
$587$	11.0333	−	4.57014i	0.455392	−	0.188630i	−0.143183	−	0.989696i	$-0.545734\pi$
$587$	11.0333	−	4.57014i	0.455392	−	0.188630i	0.598575	+	0.801067i	$0.295734\pi$
$588$		0			0
$589$	−2.80308	+	6.76724i	−0.115499	+	0.278839i
$590$		0			0
$591$			13.7797i			0.566819i
$592$		0			0
$593$		−	24.1273i		−	0.990791i	−0.868668	−	0.495395i	$-0.835023\pi$
$593$		−	24.1273i		−	0.990791i	0.868668	−	0.495395i	$-0.164977\pi$
$594$		0			0
$595$	0.165324	−	0.399128i	0.00677764	−	0.0163627i
$596$		0			0
$597$	12.7296	−	5.27279i	0.520989	−	0.215801i
$598$		0			0
$599$	22.1187	+	22.1187i	0.903747	+	0.903747i	0.995758	−	0.0920113i	$-0.0293296\pi$
$599$	22.1187	+	22.1187i	0.903747	+	0.903747i	−0.0920113	+	0.995758i	$0.529330\pi$
$600$		0			0
$601$	20.4369	−	20.4369i	0.833637	−	0.833637i	−0.154375	−	0.988012i	$-0.549336\pi$
$601$	20.4369	−	20.4369i	0.833637	−	0.833637i	0.988012	+	0.154375i	$0.0493365\pi$
$602$		0			0
$603$	4.50256	+	10.8701i	0.183358	+	0.442666i
$604$		0			0
$605$	−0.703383	−	0.291351i	−0.0285966	−	0.0118451i
$606$		0			0
$607$	38.6180			1.56745			0.783727	−	0.621105i	$-0.213316\pi$
$607$	38.6180			1.56745			0.783727	+	0.621105i	$0.213316\pi$
$608$		0			0
$609$	−8.29651			−0.336191
$610$		0			0
$611$	46.7183	+	19.3513i	1.89002	+	0.782872i
$612$		0			0
$613$	−10.6069	−	25.6072i	−0.428407	−	1.03427i	−0.979793	−	0.200016i	$-0.935901\pi$
$613$	−10.6069	−	25.6072i	−0.428407	−	1.03427i	0.551385	−	0.834251i	$-0.314099\pi$
$614$		0			0
$615$	−2.08222	+	2.08222i	−0.0839633	+	0.0839633i
$616$		0			0
$617$	−31.9989	−	31.9989i	−1.28823	−	1.28823i	−0.935863	−	0.352364i	$-0.885378\pi$
$617$	−31.9989	−	31.9989i	−1.28823	−	1.28823i	−0.352364	−	0.935863i	$-0.614622\pi$
$618$		0			0
$619$	−29.4178	+	12.1852i	−1.18240	+	0.489766i	−0.885273	−	0.465072i	$-0.846029\pi$
$619$	−29.4178	+	12.1852i	−1.18240	+	0.489766i	−0.297127	+	0.954838i	$0.596029\pi$
$620$		0			0
$621$	0.499078	−	1.20488i	0.0200273	−	0.0483502i
$622$		0			0
$623$			11.8140i			0.473317i
$624$		0			0
$625$		−	22.5463i		−	0.901852i
$626$		0			0
$627$	4.49426	−	10.8501i	0.179484	−	0.433312i
$628$		0			0
$629$	3.19165	−	1.32203i	0.127260	−	0.0527126i
$630$		0			0
$631$	8.23619	+	8.23619i	0.327878	+	0.327878i	0.851779	−	0.523901i	$-0.175524\pi$
$631$	8.23619	+	8.23619i	0.327878	+	0.327878i	−0.523901	+	0.851779i	$0.675524\pi$
$632$		0			0
$633$	4.25143	−	4.25143i	0.168979	−	0.168979i
$634$		0			0
$635$	0.805431	+	1.94448i	0.0319626	+	0.0771645i
$636$		0			0
$637$	−37.4439	−	15.5098i	−1.48358	−	0.614519i
$638$		0			0
$639$	−13.2252			−0.523182
$640$		0			0
$641$	8.56808			0.338419			0.169209	−	0.985580i	$-0.445879\pi$
$641$	8.56808			0.338419			0.169209	+	0.985580i	$0.445879\pi$
$642$		0			0
$643$	3.61947	+	1.49923i	0.142738	+	0.0591240i	0.452909	−	0.891557i	$-0.350386\pi$
$643$	3.61947	+	1.49923i	0.142738	+	0.0591240i	−0.310171	+	0.950681i	$0.600386\pi$
$644$		0			0
$645$	−1.84421	−	4.45232i	−0.0726158	−	0.175310i
$646$		0			0
$647$	23.7346	−	23.7346i	0.933105	−	0.933105i	−0.0647935	−	0.997899i	$-0.520639\pi$
$647$	23.7346	−	23.7346i	0.933105	−	0.933105i	0.997899	+	0.0647935i	$0.0206389\pi$
$648$		0			0
$649$	23.0818	+	23.0818i	0.906041	+	0.906041i
$650$		0			0
$651$	−1.74582	+	0.723141i	−0.0684239	+	0.0283421i
$652$		0			0
$653$	−9.65936	+	23.3198i	−0.378000	+	0.912573i	0.614341	+	0.789041i	$0.289422\pi$
$653$	−9.65936	+	23.3198i	−0.378000	+	0.912573i	−0.992341	+	0.123532i	$0.960578\pi$
$654$		0			0
$655$			0.00616262i			0.000240793i
$656$		0			0
$657$			0.519920i			0.0202840i
$658$		0			0
$659$	14.0711	−	33.9708i	0.548134	−	1.32331i	−0.370731	−	0.928740i	$-0.620893\pi$
$659$	14.0711	−	33.9708i	0.548134	−	1.32331i	0.918865	−	0.394572i	$-0.129107\pi$
$660$		0			0
$661$	−20.5485	+	8.51149i	−0.799246	+	0.331058i	−0.744654	−	0.667450i	$-0.767386\pi$
$661$	−20.5485	+	8.51149i	−0.799246	+	0.331058i	−0.0545915	+	0.998509i	$0.517386\pi$
$662$		0			0
$663$	−5.06421	−	5.06421i	−0.196678	−	0.196678i
$664$		0			0
$665$	1.12100	−	1.12100i	0.0434707	−	0.0434707i
$666$		0			0
$667$	−4.12901	−	9.96832i	−0.159876	−	0.385975i
$668$		0			0
$669$	−7.67481	−	3.17901i	−0.296725	−	0.122908i
$670$		0			0
$671$	4.44288			0.171516
$672$		0			0
$673$	−32.6628			−1.25906			−0.629529	−	0.776977i	$-0.716752\pi$
$673$	−32.6628			−1.25906			−0.629529	+	0.776977i	$0.716752\pi$
$674$		0			0
$675$	4.46658	+	1.85012i	0.171919	+	0.0712111i
$676$		0			0
$677$	−18.6093	−	44.9269i	−0.715215	−	1.72668i	−0.686539	−	0.727093i	$-0.740871\pi$
$677$	−18.6093	−	44.9269i	−0.715215	−	1.72668i	−0.0286762	−	0.999589i	$-0.509129\pi$
$678$		0			0
$679$	5.65209	−	5.65209i	0.216907	−	0.216907i
$680$		0			0
$681$	−16.5362	−	16.5362i	−0.633667	−	0.633667i
$682$		0			0
$683$	7.54722	−	3.12616i	0.288786	−	0.119619i	−0.233588	−	0.972336i	$-0.575047\pi$
$683$	7.54722	−	3.12616i	0.288786	−	0.119619i	0.522374	+	0.852717i	$0.325047\pi$
$684$		0			0
$685$	−1.92668	+	4.65141i	−0.0736145	+	0.177721i
$686$		0			0
$687$		−	12.7881i		−	0.487896i
$688$		0			0
$689$			55.4818i			2.11369i
$690$		0			0
$691$	−11.8386	+	28.5808i	−0.450360	+	1.08727i	0.521825	+	0.853053i	$0.325251\pi$
$691$	−11.8386	+	28.5808i	−0.450360	+	1.08727i	−0.972185	+	0.234213i	$0.924749\pi$
$692$		0			0
$693$	2.79912	−	1.15943i	0.106330	−	0.0440432i
$694$		0			0
$695$	−0.105905	−	0.105905i	−0.00401722	−	0.00401722i
$696$		0			0
$697$	−5.42324	+	5.42324i	−0.205420	+	0.205420i
$698$		0			0
$699$	−7.75192	−	18.7148i	−0.293205	−	0.707859i
$700$		0			0
$701$	39.3636	+	16.3049i	1.48674	+	0.615829i	0.970606	−	0.240676i	$-0.0773691\pi$
$701$	39.3636	+	16.3049i	1.48674	+	0.615829i	0.516138	+	0.856505i	$0.327369\pi$
$702$		0			0
$703$	12.6773			0.478132
$704$		0			0
$705$	3.04175			0.114559
$706$		0			0
$707$	8.80035	+	3.64523i	0.330971	+	0.137093i
$708$		0			0
$709$	−9.95013	−	24.0218i	−0.373685	−	0.902156i	−0.993119	−	0.117107i	$-0.962638\pi$
$709$	−9.95013	−	24.0218i	−0.373685	−	0.902156i	0.619434	−	0.785049i	$-0.287362\pi$
$710$		0			0
$711$	−4.15619	+	4.15619i	−0.155869	+	0.155869i
$712$		0			0
$713$	−1.73772	−	1.73772i	−0.0650781	−	0.0650781i
$714$		0			0
$715$	7.67536	−	3.17924i	0.287042	−	0.118897i
$716$		0			0
$717$	−4.51884	+	10.9095i	−0.168759	+	0.407421i
$718$		0			0
$719$		−	21.4598i		−	0.800314i	−0.916447	−	0.400157i	$-0.868956\pi$
$719$		−	21.4598i		−	0.800314i	0.916447	−	0.400157i	$-0.131044\pi$
$720$		0			0
$721$			3.46785i			0.129149i
$722$		0			0
$723$	−3.19213	+	7.70649i	−0.118717	+	0.286608i
$724$		0			0
$725$	36.9533	−	15.3066i	1.37241	−	0.568471i
$726$		0			0
$727$	−29.1500	−	29.1500i	−1.08111	−	1.08111i	−0.996406	−	0.0847075i	$-0.973004\pi$
$727$	−29.1500	−	29.1500i	−1.08111	−	1.08111i	−0.0847075	−	0.996406i	$-0.526996\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$	−4.80333	−	11.5963i	−0.177658	−	0.428903i
$732$		0			0
$733$	24.5981	+	10.1889i	0.908551	+	0.376334i	0.787502	−	0.616312i	$-0.211374\pi$
$733$	24.5981	+	10.1889i	0.908551	+	0.376334i	0.121049	+	0.992646i	$0.461374\pi$
$734$		0			0
$735$	−2.43791			−0.0899237
$736$		0			0
$737$	−35.5474			−1.30941
$738$		0			0
$739$	32.6336	+	13.5173i	1.20044	+	0.497240i	0.891143	−	0.453723i	$-0.149905\pi$
$739$	32.6336	+	13.5173i	1.20044	+	0.497240i	0.309302	+	0.950964i	$0.399905\pi$
$740$		0			0
$741$	−10.0575	−	24.2810i	−0.369473	−	0.891986i
$742$		0			0
$743$	1.74184	−	1.74184i	0.0639017	−	0.0639017i	−0.674434	−	0.738335i	$-0.735612\pi$
$743$	1.74184	−	1.74184i	0.0639017	−	0.0639017i	0.738335	+	0.674434i	$0.235612\pi$
$744$		0			0
$745$	−3.58768	−	3.58768i	−0.131442	−	0.131442i
$746$		0			0
$747$	3.91201	−	1.62041i	0.143133	−	0.0592876i
$748$		0			0
$749$	−6.11427	+	14.7611i	−0.223410	+	0.539360i
$750$		0			0
$751$		−	2.87921i		−	0.105064i	−0.998619	−	0.0525319i	$-0.983271\pi$
$751$		−	2.87921i		−	0.105064i	0.998619	−	0.0525319i	$-0.0167291\pi$
$752$		0			0
$753$			21.7294i			0.791863i
$754$		0			0
$755$	−1.23986	+	2.99328i	−0.0451231	+	0.108937i
$756$		0			0
$757$	−5.34241	+	2.21290i	−0.194173	+	0.0804292i	−0.477651	−	0.878550i	$-0.658512\pi$
$757$	−5.34241	+	2.21290i	−0.194173	+	0.0804292i	0.283478	+	0.958979i	$0.408512\pi$
$758$		0			0
$759$	2.78614	+	2.78614i	0.101130	+	0.101130i
$760$		0			0
$761$	10.3052	−	10.3052i	0.373565	−	0.373565i	−0.495209	−	0.868774i	$-0.664908\pi$
$761$	10.3052	−	10.3052i	0.373565	−	0.373565i	0.868774	+	0.495209i	$0.164908\pi$
$762$		0			0
$763$	−3.65445	−	8.82263i	−0.132300	−	0.319401i
$764$		0			0
$765$	−0.398011	−	0.164861i	−0.0143901	−	0.00596058i
$766$		0			0
$767$	73.0497			2.63767
$768$		0			0
$769$	−45.8055			−1.65179			−0.825894	−	0.563826i	$-0.809329\pi$
$769$	−45.8055			−1.65179			−0.825894	+	0.563826i	$0.809329\pi$
$770$		0			0
$771$	10.0497	+	4.16272i	0.361931	+	0.149917i
$772$		0			0
$773$	−5.47235	−	13.2114i	−0.196827	−	0.475182i	0.794393	−	0.607404i	$-0.207789\pi$
$773$	−5.47235	−	13.2114i	−0.196827	−	0.475182i	−0.991220	+	0.132222i	$0.957789\pi$
$774$		0			0
$775$	6.44185	−	6.44185i	0.231398	−	0.231398i
$776$		0			0
$777$	2.31258	+	2.31258i	0.0829635	+	0.0829635i
$778$		0			0
$779$	−26.0024	+	10.7706i	−0.931634	+	0.385896i
$780$		0			0
$781$	15.2908	−	36.9153i	0.547149	−	1.32093i
$782$		0			0
$783$			8.27328i			0.295663i
$784$		0			0
$785$		−	6.66090i		−	0.237738i
$786$		0			0
$787$	15.7659	−	38.0621i	0.561992	−	1.35677i	−0.346179	−	0.938169i	$-0.612521\pi$
$787$	15.7659	−	38.0621i	0.561992	−	1.35677i	0.908171	−	0.418600i	$-0.137479\pi$
$788$		0			0
$789$	3.39547	−	1.40645i	0.120882	−	0.0500709i
$790$		0			0
$791$	4.82129	+	4.82129i	0.171425	+	0.171425i
$792$		0			0
$793$	7.03044	−	7.03044i	0.249658	−	0.249658i
$794$		0			0
$795$	1.27715	+	3.08332i	0.0452959	+	0.109354i
$796$		0			0
$797$	−48.3932	−	20.0451i	−1.71418	−	0.710035i	−0.999949	−	0.0101198i	$-0.996779\pi$
$797$	−48.3932	−	20.0451i	−1.71418	−	0.710035i	−0.714226	−	0.699915i	$-0.753221\pi$
$798$		0			0
$799$	7.92238			0.280274
$800$		0			0
$801$	11.7809			0.416258
$802$		0			0
$803$	−1.45124	−	0.601125i	−0.0512133	−	0.0212132i
$804$		0			0
$805$	0.203545	+	0.491401i	0.00717402	+	0.0173196i
$806$		0			0
$807$	4.68263	−	4.68263i	0.164836	−	0.164836i
$808$		0			0
$809$	−8.44314	−	8.44314i	−0.296845	−	0.296845i	0.542932	−	0.839777i	$-0.317314\pi$
$809$	−8.44314	−	8.44314i	−0.296845	−	0.296845i	−0.839777	+	0.542932i	$0.817314\pi$
$810$		0			0
$811$	23.8583	−	9.88243i	0.837778	−	0.347019i	0.0778011	−	0.996969i	$-0.475210\pi$
$811$	23.8583	−	9.88243i	0.837778	−	0.347019i	0.759977	+	0.649950i	$0.225210\pi$
$812$		0			0
$813$	−9.75347	+	23.5470i	−0.342069	+	0.825828i
$814$		0			0
$815$			5.49015i			0.192311i
$816$		0			0
$817$		−	46.0604i		−	1.61145i
$818$		0			0
$819$	2.59465	−	6.26404i	0.0906644	−	0.218883i
$820$		0			0
$821$	32.6979	−	13.5439i	1.14117	−	0.472686i	0.269604	−	0.962971i	$-0.413107\pi$
$821$	32.6979	−	13.5439i	1.14117	−	0.472686i	0.871562	+	0.490285i	$0.163107\pi$
$822$		0			0
$823$	36.5949	+	36.5949i	1.27562	+	1.27562i	0.943095	+	0.332524i	$0.107900\pi$
$823$	36.5949	+	36.5949i	1.27562	+	1.27562i	0.332524	+	0.943095i	$0.392100\pi$
$824$		0			0
$825$	−10.3284	+	10.3284i	−0.359589	+	0.359589i
$826$		0			0
$827$	3.44587	+	8.31906i	0.119824	+	0.289282i	0.972399	−	0.233323i	$-0.0749601\pi$
$827$	3.44587	+	8.31906i	0.119824	+	0.289282i	−0.852575	+	0.522605i	$0.824960\pi$
$828$		0			0
$829$	31.0049	+	12.8427i	1.07685	+	0.446044i	0.849402	−	0.527747i	$-0.176963\pi$
$829$	31.0049	+	12.8427i	1.07685	+	0.446044i	0.227444	+	0.973791i	$0.426963\pi$
$830$		0			0
$831$	−1.56982			−0.0544565
$832$		0			0
$833$	−6.34964			−0.220002
$834$		0			0
$835$	6.95726	+	2.88179i	0.240766	+	0.0997285i
$836$		0			0
$837$	0.721116	+	1.74093i	0.0249254	+	0.0601753i
$838$		0			0
$839$	−24.3721	+	24.3721i	−0.841418	+	0.841418i	−0.989043	−	0.147625i	$-0.952837\pi$
$839$	−24.3721	+	24.3721i	−0.841418	+	0.841418i	0.147625	+	0.989043i	$0.452837\pi$
$840$		0			0
$841$	27.8933	+	27.8933i	0.961838	+	0.961838i
$842$		0			0
$843$	−4.74116	+	1.96385i	−0.163294	+	0.0676387i
$844$		0			0
$845$	5.09141	−	12.2917i	0.175150	−	0.422849i
$846$		0			0
$847$		−	1.87724i		−	0.0645028i
$848$		0			0
$849$			6.52633i			0.223983i
$850$		0			0
$851$	−1.62766	+	3.92952i	−0.0557955	+	0.134702i
$852$		0			0
$853$	−33.3194	+	13.8013i	−1.14083	+	0.472548i	−0.871450	−	0.490485i	$-0.836820\pi$
$853$	−33.3194	+	13.8013i	−1.14083	+	0.472548i	−0.269383	+	0.963033i	$0.586820\pi$
$854$		0			0
$855$	−1.11787	−	1.11787i	−0.0382302	−	0.0382302i
$856$		0			0
$857$	−18.3586	+	18.3586i	−0.627119	+	0.627119i	−0.947342	−	0.320223i	$-0.896242\pi$
$857$	−18.3586	+	18.3586i	−0.627119	+	0.627119i	0.320223	+	0.947342i	$0.396242\pi$
$858$		0			0
$859$	3.92601	+	9.47823i	0.133954	+	0.323393i	0.976596	−	0.215080i	$-0.0690013\pi$
$859$	3.92601	+	9.47823i	0.133954	+	0.323393i	−0.842643	+	0.538473i	$0.819001\pi$
$860$		0			0
$861$	−6.70813	−	2.77860i	−0.228612	−	0.0946943i
$862$		0			0
$863$	−31.1176			−1.05925			−0.529627	−	0.848231i	$-0.677668\pi$
$863$	−31.1176			−1.05925			−0.529627	+	0.848231i	$0.677668\pi$
$864$		0			0
$865$	3.28016			0.111529
$866$		0			0
$867$	14.6693	+	6.07623i	0.498196	+	0.206360i
$868$		0			0
$869$	−6.79576	−	16.4064i	−0.230530	−	0.556550i
$870$		0			0
$871$	−56.2504	+	56.2504i	−1.90597	+	1.90597i
$872$		0			0
$873$	−5.63626	−	5.63626i	−0.190759	−	0.190759i
$874$		0			0
$875$	−3.70564	+	1.53493i	−0.125274	+	0.0518900i
$876$		0			0
$877$	−1.50097	+	3.62367i	−0.0506843	+	0.122363i	−0.947194	−	0.320662i	$-0.896095\pi$
$877$	−1.50097	+	3.62367i	−0.0506843	+	0.122363i	0.896509	+	0.443025i	$0.146095\pi$
$878$		0			0
$879$			1.94385i			0.0655644i
$880$		0			0
$881$		−	5.19539i		−	0.175037i	−0.996163	−	0.0875186i	$-0.972106\pi$
$881$		−	5.19539i		−	0.175037i	0.996163	−	0.0875186i	$-0.0278937\pi$
$882$		0			0
$883$	16.3773	−	39.5382i	0.551139	−	1.33057i	−0.365486	−	0.930817i	$-0.619097\pi$
$883$	16.3773	−	39.5382i	0.551139	−	1.33057i	0.916624	−	0.399750i	$-0.130903\pi$
$884$		0			0
$885$	4.05963	−	1.68155i	0.136463	−	0.0565248i
$886$		0			0
$887$	−16.0073	−	16.0073i	−0.537473	−	0.537473i	0.385313	−	0.922786i	$-0.374093\pi$
$887$	−16.0073	−	16.0073i	−0.537473	−	0.537473i	−0.922786	+	0.385313i	$0.874093\pi$
$888$		0			0
$889$	−3.66959	+	3.66959i	−0.123074	+	0.123074i
$890$		0			0
$891$	−1.15619	−	2.79128i	−0.0387337	−	0.0935114i
$892$		0			0
$893$	26.8594	+	11.1255i	0.898815	+	0.372302i
$894$		0			0
$895$	3.68816			0.123282
$896$		0			0
$897$	8.81760			0.294411
$898$		0			0
$899$	14.4032	+	5.96599i	0.480373	+	0.198977i
$900$		0			0
$901$	3.32640	+	8.03063i	0.110818	+	0.267539i
$902$		0			0
$903$	8.40234	−	8.40234i	0.279612	−	0.279612i
$904$		0			0
$905$	6.48339	+	6.48339i	0.215515	+	0.215515i
$906$		0			0
$907$	27.8131	−	11.5206i	0.923519	−	0.382534i	0.130303	−	0.991474i	$-0.458405\pi$
$907$	27.8131	−	11.5206i	0.923519	−	0.382534i	0.793216	+	0.608940i	$0.208405\pi$
$908$		0			0
$909$	3.63502	−	8.77571i	0.120566	−	0.291072i
$910$		0			0
$911$		−	39.3207i		−	1.30275i	−0.758755	−	0.651376i	$-0.774192\pi$
$911$		−	39.3207i		−	1.30275i	0.758755	−	0.651376i	$-0.225808\pi$
$912$		0			0
$913$			12.7930i			0.423386i
$914$		0			0
$915$	0.228871	−	0.552543i	0.00756623	−	0.0182665i
$916$		0			0
$917$	−0.0140386	+	0.00581499i	−0.000463596	+	0.000192028i
$918$		0			0
$919$	11.6061	+	11.6061i	0.382849	+	0.382849i	0.872128	−	0.489279i	$-0.162740\pi$
$919$	11.6061	+	11.6061i	0.382849	+	0.382849i	−0.489279	+	0.872128i	$0.662740\pi$
$920$		0			0
$921$	15.5620	−	15.5620i	0.512787	−	0.512787i
$922$		0			0
$923$	−34.2188	−	82.6114i	−1.12632	−	2.71919i
$924$		0			0
$925$	−14.5670	−	6.03385i	−0.478960	−	0.198392i
$926$		0			0
$927$	3.45814			0.113580
$928$		0			0
$929$	0.158082			0.00518650			0.00259325	−	0.999997i	$-0.499175\pi$
$929$	0.158082			0.00518650			0.00259325	+	0.999997i	$0.499175\pi$
$930$		0			0
$931$	−21.5273	−	8.91691i	−0.705529	−	0.292240i
$932$		0			0
$933$	7.13032	+	17.2141i	0.233436	+	0.563565i
$934$		0			0
$935$	0.920349	−	0.920349i	0.0300986	−	0.0300986i
$936$		0			0
$937$	4.69489	+	4.69489i	0.153376	+	0.153376i	0.779624	−	0.626248i	$-0.215410\pi$
$937$	4.69489	+	4.69489i	0.153376	+	0.153376i	−0.626248	+	0.779624i	$0.715410\pi$
$938$		0			0
$939$	−22.2990	+	9.23656i	−0.727701	+	0.301424i
$940$		0			0
$941$	−10.6171	+	25.6321i	−0.346109	+	0.835581i	0.650963	+	0.759110i	$0.274365\pi$
$941$	−10.6171	+	25.6321i	−0.346109	+	0.835581i	−0.997072	+	0.0764715i	$0.975635\pi$
$942$		0			0
$943$		−	9.44272i		−	0.307497i
$944$		0			0
$945$		−	0.407842i		−	0.0132671i
$946$		0			0
$947$	−3.51311	+	8.48139i	−0.114161	+	0.275608i	−0.970625	−	0.240598i	$-0.922656\pi$
$947$	−3.51311	+	8.48139i	−0.114161	+	0.275608i	0.856464	+	0.516207i	$0.172656\pi$
$948$		0			0
$949$	−3.24768	+	1.34523i	−0.105424	+	0.0436681i
$950$		0			0
$951$	−1.68960	−	1.68960i	−0.0547889	−	0.0547889i
$952$		0			0
$953$	26.3477	−	26.3477i	0.853487	−	0.853487i	−0.137074	−	0.990561i	$-0.543770\pi$
$953$	26.3477	−	26.3477i	0.853487	−	0.853487i	0.990561	+	0.137074i	$0.0437697\pi$
$954$		0			0
$955$	1.55792	+	3.76115i	0.0504131	+	0.121708i
$956$		0			0
$957$	−23.0930	−	9.56545i	−0.746492	−	0.309207i
$958$		0			0
$959$	−12.4140			−0.400870
$960$		0			0
$961$	−27.4492			−0.885457
$962$		0			0
$963$	14.7198	+	6.09714i	0.474339	+	0.196478i
$964$		0			0
$965$	1.48024	+	3.57361i	0.0476505	+	0.115038i
$966$		0			0
$967$	−18.1509	+	18.1509i	−0.583694	+	0.583694i	−0.935916	−	0.352222i	$-0.885426\pi$
$967$	−18.1509	+	18.1509i	−0.583694	+	0.583694i	0.352222	+	0.935916i	$0.385426\pi$
$968$		0			0
$969$	−2.91153	−	2.91153i	−0.0935318	−	0.0935318i
$970$		0			0
$971$	−38.1928	+	15.8200i	−1.22566	+	0.507687i	−0.899206	−	0.437525i	$-0.855855\pi$
$971$	−38.1928	+	15.8200i	−1.22566	+	0.507687i	−0.326458	+	0.945212i	$0.605855\pi$
$972$		0			0
$973$	0.141324	−	0.341187i	0.00453065	−	0.0109379i
$974$		0			0
$975$			32.6875i			1.04684i
$976$		0			0
$977$			18.3863i			0.588229i	0.955770	+	0.294114i	$0.0950246\pi$
$977$			18.3863i			0.588229i	−0.955770	+	0.294114i	$0.904975\pi$
$978$		0			0
$979$	−13.6209	+	32.8838i	−0.435327	+	1.05097i
$980$		0			0
$981$	−8.79792	+	3.64422i	−0.280896	+	0.116351i
$982$		0			0
$983$	−29.1468	−	29.1468i	−0.929639	−	0.929639i	0.0680436	−	0.997682i	$-0.478324\pi$
$983$	−29.1468	−	29.1468i	−0.929639	−	0.929639i	−0.997682	+	0.0680436i	$0.978324\pi$
$984$		0			0
$985$	−3.96275	+	3.96275i	−0.126264	+	0.126264i
$986$		0			0
$987$	2.87017	+	6.92920i	0.0913585	+	0.220559i
$988$		0			0
$989$	14.2772	+	5.91379i	0.453987	+	0.188048i
$990$		0			0
$991$	−29.7473			−0.944954			−0.472477	−	0.881343i	$-0.656640\pi$
$991$	−29.7473			−0.944954			−0.472477	+	0.881343i	$0.656640\pi$
$992$		0			0
$993$	−5.98346			−0.189879
$994$		0			0
$995$	5.17714	+	2.14444i	0.164126	+	0.0679834i
$996$		0			0
$997$	−13.8686	−	33.4817i	−0.439223	−	1.06038i	−0.976218	−	0.216792i	$-0.930441\pi$
$997$	−13.8686	−	33.4817i	−0.439223	−	1.06038i	0.536995	−	0.843585i	$-0.319559\pi$
$998$		0			0
$999$	2.30611	−	2.30611i	0.0729621	−	0.0729621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.673.7		32
4.3	odd	2		768.2.n.a.673.3		32
8.3	odd	2		96.2.n.a.61.6	✓	32
8.5	even	2		384.2.n.a.337.2		32
24.5	odd	2		1152.2.v.c.721.6		32
24.11	even	2		288.2.v.d.253.3		32
32.5	even	8		384.2.n.a.49.2		32
32.11	odd	8		768.2.n.a.97.3		32
32.21	even	8	inner	768.2.n.b.97.7		32
32.27	odd	8		96.2.n.a.85.6	yes	32
96.5	odd	8		1152.2.v.c.433.6		32
96.59	even	8		288.2.v.d.181.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.6	✓	32	8.3	odd	2
96.2.n.a.85.6	yes	32	32.27	odd	8
288.2.v.d.181.3		32	96.59	even	8
288.2.v.d.253.3		32	24.11	even	2
384.2.n.a.49.2		32	32.5	even	8
384.2.n.a.337.2		32	8.5	even	2
768.2.n.a.97.3		32	32.11	odd	8
768.2.n.a.673.3		32	4.3	odd	2
768.2.n.b.97.7		32	32.21	even	8	inner
768.2.n.b.673.7		32	1.1	even	1	trivial
1152.2.v.c.433.6		32	96.5	odd	8
1152.2.v.c.721.6		32	24.5	odd	2

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{3} +(0.155637 + 0.375742i) q^{5} +(-0.709092 + 0.709092i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.923880 + 0.382683i) q^{3} +(0.155637 + 0.375742i) q^{5} +(-0.709092 + 0.709092i) q^{7} +(0.707107 + 0.707107i) q^{9} +(-2.79128 + 1.15619i) q^{11} +(-2.58738 + 6.24650i) q^{13} +0.406700i q^{15} +1.05927i q^{17} +(-1.48755 + 3.59125i) q^{19} +(-0.926474 + 0.383758i) q^{21} +(-0.922176 - 0.922176i) q^{23} +(3.41858 - 3.41858i) q^{25} +(0.382683 + 0.923880i) q^{27} +(7.64351 + 3.16605i) q^{29} +1.88437 q^{31} -3.02126 q^{33} +(-0.376797 - 0.156074i) q^{35} +(-1.24806 - 3.01308i) q^{37} +(-4.78086 + 4.78086i) q^{39} +(5.11980 + 5.11980i) q^{41} +(-10.9474 + 4.53458i) q^{43} +(-0.155637 + 0.375742i) q^{45} -7.47912i q^{47} +5.99438i q^{49} +(-0.405364 + 0.978635i) q^{51} +(7.58131 - 3.14028i) q^{53} +(-0.868855 - 0.868855i) q^{55} +(-2.74863 + 2.74863i) q^{57} +(-4.13463 - 9.98188i) q^{59} +(-1.35860 - 0.562751i) q^{61} -1.00281 q^{63} -2.74976 q^{65} +(10.8701 + 4.50256i) q^{67} +(-0.499078 - 1.20488i) q^{69} +(-9.35165 + 9.35165i) q^{71} +(0.367639 + 0.367639i) q^{73} +(4.46658 - 1.85012i) q^{75} +(1.15943 - 2.79912i) q^{77} +5.87774i q^{79} +1.00000i q^{81} +(1.62041 - 3.91201i) q^{83} +(-0.398011 + 0.164861i) q^{85} +(5.85009 + 5.85009i) q^{87} +(8.33036 - 8.33036i) q^{89} +(-2.59465 - 6.26404i) q^{91} +(1.74093 + 0.721116i) q^{93} -1.58090 q^{95} -7.97088 q^{97} +(-2.79128 - 1.15619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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