LMFDB - Embedded newform 384.2.n.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(49,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, 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("384.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.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:	$3.06625543762$
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			49.2
Character	$\chi$	$=$	384.49
Dual form			384.2.n.a.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 + 0.382683i) q^{3} +(-0.155637 + 0.375742i) q^{5} +(-0.709092 - 0.709092i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.923880 + 0.382683i) q^{3} +(-0.155637 + 0.375742i) q^{5} +(-0.709092 - 0.709092i) q^{7} +(0.707107 - 0.707107i) q^{9} +(2.79128 + 1.15619i) q^{11} +(2.58738 + 6.24650i) q^{13} -0.406700i q^{15} -1.05927i q^{17} +(1.48755 + 3.59125i) q^{19} +(0.926474 + 0.383758i) q^{21} +(-0.922176 + 0.922176i) q^{23} +(3.41858 + 3.41858i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(-7.64351 + 3.16605i) q^{29} +1.88437 q^{31} -3.02126 q^{33} +(0.376797 - 0.156074i) q^{35} +(1.24806 - 3.01308i) q^{37} +(-4.78086 - 4.78086i) q^{39} +(5.11980 - 5.11980i) q^{41} +(10.9474 + 4.53458i) q^{43} +(0.155637 + 0.375742i) q^{45} +7.47912i q^{47} -5.99438i q^{49} +(0.405364 + 0.978635i) q^{51} +(-7.58131 - 3.14028i) q^{53} +(-0.868855 + 0.868855i) q^{55} +(-2.74863 - 2.74863i) q^{57} +(4.13463 - 9.98188i) q^{59} +(1.35860 - 0.562751i) q^{61} -1.00281 q^{63} -2.74976 q^{65} +(-10.8701 + 4.50256i) q^{67} +(0.499078 - 1.20488i) q^{69} +(-9.35165 - 9.35165i) q^{71} +(0.367639 - 0.367639i) q^{73} +(-4.46658 - 1.85012i) q^{75} +(-1.15943 - 2.79912i) q^{77} -5.87774i q^{79} -1.00000i q^{81} +(-1.62041 - 3.91201i) q^{83} +(0.398011 + 0.164861i) q^{85} +(5.85009 - 5.85009i) q^{87} +(8.33036 + 8.33036i) q^{89} +(2.59465 - 6.26404i) q^{91} +(-1.74093 + 0.721116i) q^{93} -1.58090 q^{95} -7.97088 q^{97} +(2.79128 - 1.15619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			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	$-0.903987\pi$
$5$	−0.155637	+	0.375742i	−0.0696031	+	0.168037i	0.885250	+	0.465116i	$0.153987\pi$
$6$		0			0
$7$	−0.709092	−	0.709092i	−0.268012	−	0.268012i	0.560287	−	0.828299i	$-0.310691\pi$
$7$	−0.709092	−	0.709092i	−0.268012	−	0.268012i	−0.828299	+	0.560287i	$0.810691\pi$
$8$		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	$-0.224470\pi$
$11$	2.79128	+	1.15619i	0.841603	+	0.348603i	0.0801174	+	0.996785i	$0.474470\pi$
$12$		0			0
$13$	2.58738	+	6.24650i	0.717611	+	1.73247i	0.680043	+	0.733173i	$0.261961\pi$
$13$	2.58738	+	6.24650i	0.717611	+	1.73247i	0.0375686	+	0.999294i	$0.488039\pi$
$14$		0			0
$15$		−	0.406700i		−	0.105009i
$16$		0			0
$17$		−	1.05927i		−	0.256910i	−0.991715	−	0.128455i	$-0.958998\pi$
$17$		−	1.05927i		−	0.256910i	0.991715	−	0.128455i	$-0.0410018\pi$
$18$		0			0
$19$	1.48755	+	3.59125i	0.341266	+	0.823890i	0.997588	+	0.0694090i	$0.0221113\pi$
$19$	1.48755	+	3.59125i	0.341266	+	0.823890i	−0.656322	+	0.754481i	$0.727889\pi$
$20$		0			0
$21$	0.926474	+	0.383758i	0.202173	+	0.0837429i
$22$		0			0
$23$	−0.922176	+	0.922176i	−0.192287	+	0.192287i	−0.796684	−	0.604397i	$-0.793414\pi$
$23$	−0.922176	+	0.922176i	−0.192287	+	0.192287i	0.604397	+	0.796684i	$0.293414\pi$
$24$		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	$-0.903825\pi$
$29$	−7.64351	+	3.16605i	−1.41936	+	0.587920i	−0.464664	+	0.885487i	$0.653825\pi$
$30$		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	$-0.788611\pi$
$37$	1.24806	−	3.01308i	0.205179	−	0.495347i	0.992652	+	0.121003i	$0.0386109\pi$
$38$		0			0
$39$	−4.78086	−	4.78086i	−0.765551	−	0.765551i
$40$		0			0
$41$	5.11980	−	5.11980i	0.799579	−	0.799579i	−0.183450	−	0.983029i	$-0.558727\pi$
$41$	5.11980	−	5.11980i	0.799579	−	0.799579i	0.983029	+	0.183450i	$0.0587266\pi$
$42$		0			0
$43$	10.9474	+	4.53458i	1.66947	+	0.691517i	0.998740	−	0.0501855i	$-0.0159812\pi$
$43$	10.9474	+	4.53458i	1.66947	+	0.691517i	0.670729	+	0.741702i	$0.265981\pi$
$44$		0			0
$45$	0.155637	+	0.375742i	0.0232010	+	0.0560123i
$46$		0			0
$47$			7.47912i			1.09094i	0.838130	+	0.545471i	$0.183649\pi$
$47$			7.47912i			1.09094i	−0.838130	+	0.545471i	$0.816351\pi$
$48$		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	$-0.565579\pi$
$53$	−7.58131	−	3.14028i	−1.04137	−	0.431351i	−0.836805	+	0.547501i	$0.815579\pi$
$54$		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	−0.387637	−	0.921812i	$-0.626709\pi$
$59$	4.13463	−	9.98188i	0.538283	−	1.29953i	0.925921	−	0.377718i	$-0.123291\pi$
$60$		0			0
$61$	1.35860	−	0.562751i	0.173951	−	0.0720529i	−0.294008	−	0.955803i	$-0.594989\pi$
$61$	1.35860	−	0.562751i	0.173951	−	0.0720529i	0.467959	+	0.883750i	$0.344989\pi$
$62$		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	$-0.880266\pi$
$67$	−10.8701	+	4.50256i	−1.32800	+	0.550075i	−0.397915	+	0.917422i	$0.630266\pi$
$68$		0			0
$69$	0.499078	−	1.20488i	0.0600820	−	0.145051i
$70$		0			0
$71$	−9.35165	−	9.35165i	−1.10984	−	1.10984i	−0.993171	−	0.116666i	$-0.962779\pi$
$71$	−9.35165	−	9.35165i	−1.10984	−	1.10984i	−0.116666	−	0.993171i	$-0.537221\pi$
$72$		0			0
$73$	0.367639	−	0.367639i	0.0430289	−	0.0430289i	−0.685265	−	0.728294i	$-0.740314\pi$
$73$	0.367639	−	0.367639i	0.0430289	−	0.0430289i	0.728294	+	0.685265i	$0.240314\pi$
$74$		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	$-0.892733\pi$
$79$		−	5.87774i		−	0.661297i	0.943754	−	0.330649i	$-0.107267\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−1.62041	−	3.91201i	−0.177863	−	0.429398i	0.809655	−	0.586906i	$-0.199654\pi$
$83$	−1.62041	−	3.91201i	−0.177863	−	0.429398i	−0.987518	+	0.157507i	$0.949654\pi$
$84$		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	0.993840	−	0.110824i	$-0.0353489\pi$
$89$	8.33036	+	8.33036i	0.883016	+	0.883016i	−0.110824	+	0.993840i	$0.535349\pi$
$90$		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	−0.633354	−	0.773862i	$-0.718322\pi$
$101$	3.63502	−	8.77571i	0.361698	−	0.873216i	0.995052	−	0.0993539i	$-0.0316776\pi$
$102$		0			0
$103$	2.44527	+	2.44527i	0.240940	+	0.240940i	0.817239	−	0.576299i	$-0.195504\pi$
$103$	2.44527	+	2.44527i	0.240940	+	0.240940i	−0.576299	+	0.817239i	$0.695504\pi$
$104$		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	$-0.654810\pi$
$107$	−14.7198	−	6.09714i	−1.42302	−	0.589433i	−0.955617	+	0.294612i	$0.904810\pi$
$108$		0			0
$109$	3.64422	+	8.79792i	0.349053	+	0.842688i	0.996732	+	0.0807753i	$0.0257396\pi$
$109$	3.64422	+	8.79792i	0.349053	+	0.842688i	−0.647679	+	0.761913i	$0.724260\pi$
$110$		0			0
$111$			3.26133i			0.309552i
$112$		0			0
$113$			6.79924i			0.639619i	0.947482	+	0.319810i	$0.103619\pi$
$113$			6.79924i			0.639619i	−0.947482	+	0.319810i	$0.896381\pi$
$114$		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	$-0.625211\pi$
$131$	−0.0139993	+	0.00579870i	−0.00122313	+	0.000506635i	0.382072	+	0.924133i	$0.375211\pi$
$132$		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	−0.226217	−	0.974077i	$-0.572636\pi$
$137$	8.75347	−	8.75347i	0.747859	−	0.747859i	0.974077	+	0.226217i	$0.0726360\pi$
$138$		0			0
$139$	0.340231	+	0.140928i	0.0288581	+	0.0119534i	0.397066	−	0.917790i	$-0.370028\pi$
$139$	0.340231	+	0.140928i	0.0288581	+	0.0119534i	−0.368208	+	0.929744i	$0.620028\pi$
$140$		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	$-0.204271\pi$
$149$	11.5258	+	4.77413i	0.944228	+	0.391112i	0.143170	+	0.989698i	$0.454271\pi$
$150$		0			0
$151$	5.63305	−	5.63305i	0.458411	−	0.458411i	−0.439723	−	0.898134i	$-0.644923\pi$
$151$	5.63305	−	5.63305i	0.458411	−	0.458411i	0.898134	+	0.439723i	$0.144923\pi$
$152$		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	$-0.398279\pi$
$157$	15.1312	−	6.26756i	1.20760	−	0.500206i	0.893448	+	0.449166i	$0.148279\pi$
$158$		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	$-0.802310\pi$
$163$	−12.4717	+	5.16594i	−0.976858	+	0.404628i	−0.163597	+	0.986527i	$0.552310\pi$
$164$		0			0
$165$	0.470221	−	1.13521i	0.0366066	−	0.0883762i
$166$		0			0
$167$	13.0928	+	13.0928i	1.01315	+	1.01315i	0.999912	+	0.0132424i	$0.00421531\pi$
$167$	13.0928	+	13.0928i	1.01315	+	1.01315i	0.0132424	+	0.999912i	$0.495785\pi$
$168$		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	$-0.224191\pi$
$173$	−3.08646	−	7.45138i	−0.234659	−	0.566518i	−0.996715	+	0.0809941i	$0.974191\pi$
$174$		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	$-0.235057\pi$
$179$	−3.47037	−	8.37820i	−0.259387	−	0.626216i	−0.998898	+	0.0469281i	$0.985057\pi$
$180$		0			0
$181$	−20.8285	−	8.62745i	−1.54817	−	0.641274i	−0.565187	−	0.824963i	$-0.691196\pi$
$181$	−20.8285	−	8.62745i	−1.54817	−	0.641274i	−0.982984	+	0.183689i	$0.941196\pi$
$182$		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	0.617058	+	0.786918i	$0.288325\pi$
$197$	−5.27324	+	12.7307i	−0.375703	+	0.907028i	−0.992761	+	0.120110i	$0.961675\pi$
$198$		0			0
$199$	9.74284	+	9.74284i	0.690652	+	0.690652i	0.962375	−	0.271724i	$-0.0875937\pi$
$199$	9.74284	+	9.74284i	0.690652	+	0.690652i	−0.271724	+	0.962375i	$0.587594\pi$
$200$		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	$-0.191356\pi$
$211$	−2.30086	−	5.55477i	−0.158398	−	0.382406i	−0.983077	+	0.183195i	$0.941356\pi$
$212$		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	$-0.342205\pi$
$227$	21.6055	−	8.94931i	1.43401	−	0.593987i	0.958338	+	0.285636i	$0.0922049\pi$
$228$		0			0
$229$	4.89379	−	11.8147i	0.323391	−	0.780734i	−0.675662	−	0.737212i	$-0.736142\pi$
$229$	4.89379	−	11.8147i	0.323391	−	0.780734i	0.999052	−	0.0435225i	$-0.0138580\pi$
$230$		0			0
$231$	2.14235	+	2.14235i	0.140956	+	0.140956i
$232$		0			0
$233$	−14.3237	+	14.3237i	−0.938376	+	0.938376i	−0.998208	−	0.0598327i	$-0.980943\pi$
$233$	−14.3237	+	14.3237i	−0.938376	+	0.938376i	0.0598327	+	0.998208i	$0.480943\pi$
$234$		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	$-0.875267\pi$
$239$		−	11.8083i		−	0.763816i	0.924200	−	0.381908i	$-0.124733\pi$
$240$		0			0
$241$		−	8.34145i		−	0.537320i	−0.963235	−	0.268660i	$-0.913419\pi$
$241$		−	8.34145i		−	0.537320i	0.963235	−	0.268660i	$-0.0865808\pi$
$242$		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	0.409979	+	0.912095i	$0.365536\pi$
$251$	−8.31548	+	20.0753i	−0.524868	+	1.26714i	−0.934848	+	0.355049i	$0.884464\pi$
$252$		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	0.782676	−	0.622429i	$-0.213854\pi$
$263$	2.59878	+	2.59878i	0.160248	+	0.160248i	−0.622429	+	0.782676i	$0.713854\pi$
$264$		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	$-0.189706\pi$
$269$	−2.53422	−	6.11815i	−0.154514	−	0.373030i	−0.982114	+	0.188289i	$0.939706\pi$
$270$		0			0
$271$		−	25.4870i		−	1.54823i	−0.633046	−	0.774114i	$-0.718196\pi$
$271$		−	25.4870i		−	1.54823i	0.633046	−	0.774114i	$-0.281804\pi$
$272$		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	$-0.359983\pi$
$277$	1.45033	+	0.600745i	0.0871416	+	0.0360952i	−0.338687	+	0.940899i	$0.609983\pi$
$278$		0			0
$279$	1.33245	−	1.33245i	0.0797716	−	0.0797716i
$280$		0			0
$281$	−3.62873	−	3.62873i	−0.216472	−	0.216472i	0.590538	−	0.807010i	$-0.298916\pi$
$281$	−3.62873	−	3.62873i	−0.216472	−	0.216472i	−0.807010	+	0.590538i	$0.798916\pi$
$282$		0			0
$283$	−2.49752	+	6.02955i	−0.148462	+	0.358419i	−0.980563	−	0.196205i	$-0.937138\pi$
$283$	−2.49752	+	6.02955i	−0.148462	+	0.358419i	0.832101	+	0.554625i	$0.187138\pi$
$284$		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	$-0.893084\pi$
$293$	−0.743879	+	1.79588i	−0.0434579	+	0.104917i	0.900660	+	0.434524i	$0.143084\pi$
$294$		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	−0.959289	−	0.282428i	$-0.908860\pi$
$307$	−8.42212	−	20.3328i	−0.480676	−	1.16045i	0.478613	−	0.878026i	$-0.341140\pi$
$308$		0			0
$309$	−3.19490	−	1.32337i	−0.181752	−	0.0752840i
$310$		0			0
$311$	13.1751	−	13.1751i	0.747092	−	0.747092i	−0.226840	−	0.973932i	$-0.572839\pi$
$311$	13.1751	−	13.1751i	0.747092	−	0.747092i	0.973932	+	0.226840i	$0.0728394\pi$
$312$		0			0
$313$	−17.0669	−	17.0669i	−0.964680	−	0.964680i	0.0347173	−	0.999397i	$-0.488947\pi$
$313$	−17.0669	−	17.0669i	−0.964680	−	0.964680i	−0.999397	+	0.0347173i	$0.988947\pi$
$314$		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	$-0.603625\pi$
$317$	2.20756	−	0.914403i	0.123989	−	0.0513580i	0.443815	+	0.896118i	$0.353625\pi$
$318$		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	$-0.322418\pi$
$331$	5.52800	+	2.28977i	0.303846	+	0.125857i	−0.225551	+	0.974231i	$0.572418\pi$
$332$		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	$-0.890327\pi$
$337$		−	12.4013i		−	0.675540i	0.941229	−	0.337770i	$-0.109673\pi$
$338$		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	$-0.831651\pi$
$347$	1.93560	−	4.67295i	0.103908	−	0.250857i	0.967280	+	0.253712i	$0.0816514\pi$
$348$		0			0
$349$	2.69921	−	1.11805i	0.144485	−	0.0598478i	−0.309269	−	0.950975i	$-0.600084\pi$
$349$	2.69921	−	1.11805i	0.144485	−	0.0598478i	0.453754	+	0.891127i	$0.350084\pi$
$350$		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	0.318455	−	0.947938i	$-0.396836\pi$
$359$	−11.9270	−	11.9270i	−0.629483	−	0.629483i	−0.947938	+	0.318455i	$0.896836\pi$
$360$		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	$-0.732596\pi$
$367$		−	28.5325i		−	1.48939i	0.667407	−	0.744693i	$-0.267404\pi$
$368$		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	$-0.532548\pi$
$373$	−16.9506	−	7.02116i	−0.877668	−	0.363542i	−0.775592	+	0.631235i	$0.782548\pi$
$374$		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	$-0.777601\pi$
$379$	4.48842	−	10.8360i	0.230555	−	0.556608i	0.996243	+	0.0866037i	$0.0276014\pi$
$380$		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	0.661386	+	0.750045i	$0.269968\pi$
$389$	−6.63971	+	16.0297i	−0.336647	+	0.812737i	−0.998033	+	0.0626914i	$0.980032\pi$
$390$		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	$-0.163300\pi$
$397$	−1.83049	−	4.41918i	−0.0918695	−	0.221792i	−0.963134	+	0.269020i	$0.913300\pi$
$398$		0			0
$399$			3.89806i			0.195147i
$400$		0			0
$401$		−	23.8940i		−	1.19321i	−0.802536	−	0.596604i	$-0.796516\pi$
$401$		−	23.8940i		−	1.19321i	0.802536	−	0.596604i	$-0.203484\pi$
$402$		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	0.960906	−	0.276874i	$-0.0892985\pi$
$409$	13.8337	+	13.8337i	0.684032	+	0.684032i	−0.276874	+	0.960906i	$0.589299\pi$
$410$		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	$-0.628984\pi$
$419$	−0.473345	+	0.196066i	−0.0231244	+	0.00957845i	0.371091	+	0.928596i	$0.378984\pi$
$420$		0			0
$421$	1.25389	−	3.02716i	0.0611109	−	0.147535i	−0.890374	−	0.455229i	$-0.849557\pi$
$421$	1.25389	−	3.02716i	0.0611109	−	0.147535i	0.951485	+	0.307694i	$0.0995574\pi$
$422$		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	$-0.752376\pi$
$431$		−	29.1399i		−	1.40362i	0.712365	−	0.701810i	$-0.247624\pi$
$432$		0			0
$433$		−	5.66352i		−	0.272172i	−0.990697	−	0.136086i	$-0.956548\pi$
$433$		−	5.66352i		−	0.272172i	0.990697	−	0.136086i	$-0.0434523\pi$
$434$		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	−0.404011	−	0.914754i	$-0.632384\pi$
$439$	10.7013	−	10.7013i	0.510743	−	0.510743i	0.914754	+	0.404011i	$0.132384\pi$
$440$		0			0
$441$	−4.23866	−	4.23866i	−0.201841	−	0.201841i
$442$		0			0
$443$	−14.3853	+	34.7291i	−0.683464	+	1.65003i	0.0740866	+	0.997252i	$0.476396\pi$
$443$	−14.3853	+	34.7291i	−0.683464	+	1.65003i	−0.757551	+	0.652776i	$0.773604\pi$
$444$		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	−0.667132	−	0.744939i	$-0.732478\pi$
$457$	1.66332	−	1.66332i	0.0778069	−	0.0778069i	0.744939	+	0.667132i	$0.232478\pi$
$458$		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	$-0.0567770\pi$
$461$	3.49519	+	8.43813i	0.162787	+	0.393003i	−0.821347	+	0.570429i	$0.806777\pi$
$462$		0			0
$463$			12.1833i			0.566204i	0.959090	+	0.283102i	$0.0913635\pi$
$463$			12.1833i			0.566204i	−0.959090	+	0.283102i	$0.908636\pi$
$464$		0			0
$465$		−	0.766371i		−	0.0355396i
$466$		0			0
$467$	4.89494	+	11.8174i	0.226511	+	0.546846i	0.995748	−	0.0921176i	$-0.0293636\pi$
$467$	4.89494	+	11.8174i	0.226511	+	0.546846i	−0.769237	+	0.638963i	$0.779364\pi$
$468$		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	0.972765	−	0.231795i	$-0.0744599\pi$
$487$	16.3518	+	16.3518i	0.740969	+	0.740969i	−0.231795	+	0.972765i	$0.574460\pi$
$488$		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	$-0.316325\pi$
$491$	7.50463	+	3.10852i	0.338679	+	0.140286i	−0.206861	+	0.978370i	$0.566325\pi$
$492$		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	$-0.0465070\pi$
$499$	4.17340	+	10.0755i	0.186827	+	0.451041i	−0.802518	+	0.596627i	$0.796507\pi$
$500$		0			0
$501$	−17.1066	−	7.08580i	−0.764268	−	0.316570i
$502$		0			0
$503$	−18.7140	+	18.7140i	−0.834416	+	0.834416i	−0.988117	−	0.153701i	$-0.950881\pi$
$503$	−18.7140	+	18.7140i	−0.834416	+	0.834416i	0.153701	+	0.988117i	$0.450881\pi$
$504$		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	$-0.273794\pi$
$509$	37.2151	−	15.4150i	1.64953	−	0.683258i	0.997207	+	0.0746822i	$0.0237942\pi$
$510$		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	−0.459551	−	0.888151i	$-0.651990\pi$
$521$	9.78297	−	9.78297i	0.428600	−	0.428600i	0.888151	+	0.459551i	$0.151990\pi$
$522$		0			0
$523$	−9.08765	−	3.76423i	−0.397375	−	0.164598i	0.175042	−	0.984561i	$-0.443994\pi$
$523$	−9.08765	−	3.76423i	−0.397375	−	0.164598i	−0.572417	+	0.819963i	$0.693994\pi$
$524$		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	$-0.783820\pi$
$541$	−20.5649	+	8.51826i	−0.884154	+	0.366229i	−0.106048	+	0.994361i	$0.533820\pi$
$542$		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	$-0.486244\pi$
$547$	18.2473	−	7.55828i	0.780198	−	0.323169i	0.736996	+	0.675898i	$0.236244\pi$
$548$		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	$-0.170510\pi$
$557$	−2.57380	−	6.21371i	−0.109056	−	0.263283i	−0.968981	+	0.247137i	$0.920510\pi$
$558$		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	$-0.0659596\pi$
$563$	3.34911	+	8.08547i	0.141148	+	0.340762i	−0.837459	+	0.546501i	$0.815960\pi$
$564$		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	0.573296	−	0.819349i	$-0.305665\pi$
$569$	−5.86928	−	5.86928i	−0.246053	−	0.246053i	−0.819349	+	0.573296i	$0.805665\pi$
$570$		0			0
$571$	4.92409	−	11.8878i	0.206067	−	0.497489i	−0.786730	−	0.617297i	$-0.788228\pi$
$571$	4.92409	−	11.8878i	0.206067	−	0.497489i	0.992797	+	0.119808i	$0.0382277\pi$
$572$		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	$-0.454266\pi$
$587$	−11.0333	−	4.57014i	−0.455392	−	0.188630i	−0.598575	+	0.801067i	$0.704266\pi$
$588$		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	$0.164977\pi$
$593$			24.1273i			0.990791i	−0.868668	+	0.495395i	$0.835023\pi$
$594$		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	−0.0920113	−	0.995758i	$-0.529330\pi$
$599$	22.1187	−	22.1187i	0.903747	−	0.903747i	0.995758	+	0.0920113i	$0.0293296\pi$
$600$		0			0
$601$	20.4369	+	20.4369i	0.833637	+	0.833637i	0.988012	−	0.154375i	$-0.0493365\pi$
$601$	20.4369	+	20.4369i	0.833637	+	0.833637i	−0.154375	+	0.988012i	$0.549336\pi$
$602$		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	−0.551385	−	0.834251i	$-0.685901\pi$
$613$	10.6069	−	25.6072i	0.428407	−	1.03427i	0.979793	−	0.200016i	$-0.0640994\pi$
$614$		0			0
$615$	−2.08222	−	2.08222i	−0.0839633	−	0.0839633i
$616$		0			0
$617$	−31.9989	+	31.9989i	−1.28823	+	1.28823i	−0.352364	+	0.935863i	$0.614622\pi$
$617$	−31.9989	+	31.9989i	−1.28823	+	1.28823i	−0.935863	+	0.352364i	$0.885378\pi$
$618$		0			0
$619$	29.4178	+	12.1852i	1.18240	+	0.489766i	0.885273	−	0.465072i	$-0.153971\pi$
$619$	29.4178	+	12.1852i	1.18240	+	0.489766i	0.297127	+	0.954838i	$0.403971\pi$
$620$		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	−0.523901	−	0.851779i	$-0.675524\pi$
$631$	8.23619	−	8.23619i	0.327878	−	0.327878i	0.851779	+	0.523901i	$0.175524\pi$
$632$		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	$-0.649614\pi$
$643$	−3.61947	+	1.49923i	−0.142738	+	0.0591240i	0.310171	+	0.950681i	$0.399614\pi$
$644$		0			0
$645$	1.84421	−	4.45232i	0.0726158	−	0.175310i
$646$		0			0
$647$	23.7346	+	23.7346i	0.933105	+	0.933105i	0.997899	−	0.0647935i	$-0.0206389\pi$
$647$	23.7346	+	23.7346i	0.933105	+	0.933105i	−0.0647935	+	0.997899i	$0.520639\pi$
$648$		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	0.992341	+	0.123532i	$0.0394221\pi$
$653$	9.65936	+	23.3198i	0.378000	+	0.912573i	−0.614341	+	0.789041i	$0.710578\pi$
$654$		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	−0.918865	−	0.394572i	$-0.870893\pi$
$659$	−14.0711	−	33.9708i	−0.548134	−	1.32331i	0.370731	−	0.928740i	$-0.379107\pi$
$660$		0			0
$661$	20.5485	+	8.51149i	0.799246	+	0.331058i	0.744654	−	0.667450i	$-0.232614\pi$
$661$	20.5485	+	8.51149i	0.799246	+	0.331058i	0.0545915	+	0.998509i	$0.482614\pi$
$662$		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	0.0286762	−	0.999589i	$-0.490871\pi$
$677$	18.6093	−	44.9269i	0.715215	−	1.72668i	0.686539	−	0.727093i	$-0.259129\pi$
$678$		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	$-0.424953\pi$
$683$	−7.54722	−	3.12616i	−0.288786	−	0.119619i	−0.522374	+	0.852717i	$0.674953\pi$
$684$		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	0.972185	+	0.234213i	$0.0752514\pi$
$691$	11.8386	+	28.5808i	0.450360	+	1.08727i	−0.521825	+	0.853053i	$0.674749\pi$
$692$		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	$-0.922631\pi$
$701$	−39.3636	+	16.3049i	−1.48674	+	0.615829i	−0.516138	+	0.856505i	$0.672631\pi$
$702$		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	−0.619434	−	0.785049i	$-0.712638\pi$
$709$	9.95013	−	24.0218i	0.373685	−	0.902156i	0.993119	−	0.117107i	$-0.0373621\pi$
$710$		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	$0.131044\pi$
$719$			21.4598i			0.800314i	−0.916447	+	0.400157i	$0.868956\pi$
$720$		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	−0.0847075	+	0.996406i	$0.526996\pi$
$727$	−29.1500	+	29.1500i	−1.08111	+	1.08111i	−0.996406	+	0.0847075i	$0.973004\pi$
$728$		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	$-0.788626\pi$
$733$	−24.5981	+	10.1889i	−0.908551	+	0.376334i	−0.121049	+	0.992646i	$0.538626\pi$
$734$		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	$-0.850095\pi$
$739$	−32.6336	+	13.5173i	−1.20044	+	0.497240i	−0.309302	+	0.950964i	$0.600095\pi$
$740$		0			0
$741$	10.0575	−	24.2810i	0.369473	−	0.891986i
$742$		0			0
$743$	1.74184	+	1.74184i	0.0639017	+	0.0639017i	0.738335	−	0.674434i	$-0.235612\pi$
$743$	1.74184	+	1.74184i	0.0639017	+	0.0639017i	−0.674434	+	0.738335i	$0.735612\pi$
$744$		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	$0.0167291\pi$
$751$			2.87921i			0.105064i	−0.998619	+	0.0525319i	$0.983271\pi$
$752$		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	$-0.341488\pi$
$757$	5.34241	+	2.21290i	0.194173	+	0.0804292i	−0.283478	+	0.958979i	$0.591488\pi$
$758$		0			0
$759$	2.78614	−	2.78614i	0.101130	−	0.101130i
$760$		0			0
$761$	10.3052	+	10.3052i	0.373565	+	0.373565i	0.868774	−	0.495209i	$-0.164908\pi$
$761$	10.3052	+	10.3052i	0.373565	+	0.373565i	−0.495209	+	0.868774i	$0.664908\pi$
$762$		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	$-0.792211\pi$
$773$	5.47235	−	13.2114i	0.196827	−	0.475182i	0.991220	+	0.132222i	$0.0422111\pi$
$774$		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	−0.908171	−	0.418600i	$-0.862521\pi$
$787$	−15.7659	−	38.0621i	−0.561992	−	1.35677i	0.346179	−	0.938169i	$-0.387479\pi$
$788$		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	0.714226	−	0.699915i	$-0.246779\pi$
$797$	48.3932	−	20.0451i	1.71418	−	0.710035i	0.999949	−	0.0101198i	$-0.00322128\pi$
$798$		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	−0.839777	−	0.542932i	$-0.817314\pi$
$809$	−8.44314	+	8.44314i	−0.296845	+	0.296845i	0.542932	+	0.839777i	$0.317314\pi$
$810$		0			0
$811$	−23.8583	−	9.88243i	−0.837778	−	0.347019i	−0.0778011	−	0.996969i	$-0.524790\pi$
$811$	−23.8583	−	9.88243i	−0.837778	−	0.347019i	−0.759977	+	0.649950i	$0.774790\pi$
$812$		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	$-0.586893\pi$
$821$	−32.6979	−	13.5439i	−1.14117	−	0.472686i	−0.871562	+	0.490285i	$0.836893\pi$
$822$		0			0
$823$	36.5949	−	36.5949i	1.27562	−	1.27562i	0.332524	−	0.943095i	$-0.392100\pi$
$823$	36.5949	−	36.5949i	1.27562	−	1.27562i	0.943095	−	0.332524i	$-0.107900\pi$
$824$		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	$-0.925040\pi$
$827$	−3.44587	+	8.31906i	−0.119824	+	0.289282i	0.852575	+	0.522605i	$0.175040\pi$
$828$		0			0
$829$	−31.0049	+	12.8427i	−1.07685	+	0.446044i	−0.849402	−	0.527747i	$-0.823037\pi$
$829$	−31.0049	+	12.8427i	−1.07685	+	0.446044i	−0.227444	+	0.973791i	$0.573037\pi$
$830$		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	0.147625	−	0.989043i	$-0.452837\pi$
$839$	−24.3721	−	24.3721i	−0.841418	−	0.841418i	−0.989043	+	0.147625i	$0.952837\pi$
$840$		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	$-0.163180\pi$
$853$	33.3194	+	13.8013i	1.14083	+	0.472548i	0.269383	+	0.963033i	$0.413180\pi$
$854$		0			0
$855$	−1.11787	+	1.11787i	−0.0382302	+	0.0382302i
$856$		0			0
$857$	−18.3586	−	18.3586i	−0.627119	−	0.627119i	0.320223	−	0.947342i	$-0.396242\pi$
$857$	−18.3586	−	18.3586i	−0.627119	−	0.627119i	−0.947342	+	0.320223i	$0.896242\pi$
$858$		0			0
$859$	−3.92601	+	9.47823i	−0.133954	+	0.323393i	−0.976596	−	0.215080i	$-0.930999\pi$
$859$	−3.92601	+	9.47823i	−0.133954	+	0.323393i	0.842643	+	0.538473i	$0.180999\pi$
$860$		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	$-0.103905\pi$
$877$	1.50097	+	3.62367i	0.0506843	+	0.122363i	−0.896509	+	0.443025i	$0.853905\pi$
$878$		0			0
$879$		−	1.94385i		−	0.0655644i
$880$		0			0
$881$			5.19539i			0.175037i	0.996163	+	0.0875186i	$0.0278937\pi$
$881$			5.19539i			0.175037i	−0.996163	+	0.0875186i	$0.972106\pi$
$882$		0			0
$883$	−16.3773	−	39.5382i	−0.551139	−	1.33057i	−0.916624	−	0.399750i	$-0.869097\pi$
$883$	−16.3773	−	39.5382i	−0.551139	−	1.33057i	0.365486	−	0.930817i	$-0.380903\pi$
$884$		0			0
$885$	−4.05963	−	1.68155i	−0.136463	−	0.0565248i
$886$		0			0
$887$	−16.0073	+	16.0073i	−0.537473	+	0.537473i	−0.922786	−	0.385313i	$-0.874093\pi$
$887$	−16.0073	+	16.0073i	−0.537473	+	0.537473i	0.385313	+	0.922786i	$0.374093\pi$
$888$		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	$-0.541595\pi$
$907$	−27.8131	−	11.5206i	−0.923519	−	0.382534i	−0.793216	+	0.608940i	$0.791595\pi$
$908$		0			0
$909$	−3.63502	−	8.77571i	−0.120566	−	0.291072i
$910$		0			0
$911$			39.3207i			1.30275i	0.758755	+	0.651376i	$0.225808\pi$
$911$			39.3207i			1.30275i	−0.758755	+	0.651376i	$0.774192\pi$
$912$		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	−0.489279	−	0.872128i	$-0.662740\pi$
$919$	11.6061	−	11.6061i	0.382849	−	0.382849i	0.872128	+	0.489279i	$0.162740\pi$
$920$		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	−0.626248	−	0.779624i	$-0.715410\pi$
$937$	4.69489	−	4.69489i	0.153376	−	0.153376i	0.779624	+	0.626248i	$0.215410\pi$
$938$		0			0
$939$	22.2990	+	9.23656i	0.727701	+	0.301424i
$940$		0			0
$941$	10.6171	+	25.6321i	0.346109	+	0.835581i	0.997072	+	0.0764715i	$0.0243654\pi$
$941$	10.6171	+	25.6321i	0.346109	+	0.835581i	−0.650963	+	0.759110i	$0.725635\pi$
$942$		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	$-0.0773437\pi$
$947$	3.51311	+	8.48139i	0.114161	+	0.275608i	−0.856464	+	0.516207i	$0.827344\pi$
$948$		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	0.990561	−	0.137074i	$-0.0437697\pi$
$953$	26.3477	+	26.3477i	0.853487	+	0.853487i	−0.137074	+	0.990561i	$0.543770\pi$
$954$		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	0.352222	−	0.935916i	$-0.385426\pi$
$967$	−18.1509	−	18.1509i	−0.583694	−	0.583694i	−0.935916	+	0.352222i	$0.885426\pi$
$968$		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	$-0.144145\pi$
$971$	38.1928	+	15.8200i	1.22566	+	0.507687i	0.326458	+	0.945212i	$0.394145\pi$
$972$		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	$-0.904975\pi$
$977$		−	18.3863i		−	0.588229i	0.955770	−	0.294114i	$-0.0950246\pi$
$978$		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	−0.997682	−	0.0680436i	$-0.978324\pi$
$983$	−29.1468	+	29.1468i	−0.929639	+	0.929639i	0.0680436	+	0.997682i	$0.478324\pi$
$984$		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	−0.536995	−	0.843585i	$-0.680441\pi$
$997$	13.8686	−	33.4817i	0.439223	−	1.06038i	0.976218	−	0.216792i	$-0.0695594\pi$
$998$		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	384.2.n.a.49.2		32
3.2	odd	2		1152.2.v.c.433.6		32
4.3	odd	2		96.2.n.a.85.6	yes	32
8.3	odd	2		768.2.n.a.97.3		32
8.5	even	2		768.2.n.b.97.7		32
12.11	even	2		288.2.v.d.181.3		32
32.3	odd	8		96.2.n.a.61.6	✓	32
32.13	even	8		768.2.n.b.673.7		32
32.19	odd	8		768.2.n.a.673.3		32
32.29	even	8	inner	384.2.n.a.337.2		32
96.29	odd	8		1152.2.v.c.721.6		32
96.35	even	8		288.2.v.d.253.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.6	✓	32	32.3	odd	8
96.2.n.a.85.6	yes	32	4.3	odd	2
288.2.v.d.181.3		32	12.11	even	2
288.2.v.d.253.3		32	96.35	even	8
384.2.n.a.49.2		32	1.1	even	1	trivial
384.2.n.a.337.2		32	32.29	even	8	inner
768.2.n.a.97.3		32	8.3	odd	2
768.2.n.a.673.3		32	32.19	odd	8
768.2.n.b.97.7		32	8.5	even	2
768.2.n.b.673.7		32	32.13	even	8
1152.2.v.c.433.6		32	3.2	odd	2
1152.2.v.c.721.6		32	96.29	odd	8

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.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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