LMFDB - Embedded newform 702.2.bb.a.71.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.11
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.653109 + 0.175000i) q^{5} +(-3.90017 + 1.04505i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.585562 - 0.338074i) q^{10} +(0.502310 - 0.502310i) q^{11} +(-2.29871 + 2.77775i) q^{13} +(-3.49679 - 2.01888i) q^{14} -1.00000 q^{16} +(-3.24443 - 5.61952i) q^{17} +(-0.253608 - 0.0679541i) q^{19} +(-0.175000 - 0.653109i) q^{20} +0.710373 q^{22} +(-0.860504 - 1.49044i) q^{23} +(-3.93420 + 2.27141i) q^{25} +(-3.58960 + 0.338733i) q^{26} +(-1.04505 - 3.90017i) q^{28} -1.28654i q^{29} +(1.04468 + 3.89881i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.67944 - 6.26776i) q^{34} +(2.36435 - 1.36506i) q^{35} +(-7.96159 + 2.13330i) q^{37} +(-0.131277 - 0.227379i) q^{38} +(0.338074 - 0.585562i) q^{40} +(-2.39802 + 8.94954i) q^{41} +(-5.67915 - 3.27886i) q^{43} +(0.502310 + 0.502310i) q^{44} +(0.445430 - 1.66237i) q^{46} +(9.07214 + 2.43087i) q^{47} +(8.05701 - 4.65172i) q^{49} +(-4.38803 - 1.17577i) q^{50} +(-2.77775 - 2.29871i) q^{52} +6.34328i q^{53} +(-0.240159 + 0.415967i) q^{55} +(2.01888 - 3.49679i) q^{56} +(0.909720 - 0.909720i) q^{58} +(3.52351 - 3.52351i) q^{59} +(-1.64932 + 2.85670i) q^{61} +(-2.01817 + 3.49557i) q^{62} -1.00000i q^{64} +(1.01520 - 2.21645i) q^{65} +(10.0909 + 2.70385i) q^{67} +(5.61952 - 3.24443i) q^{68} +(2.63709 + 0.706607i) q^{70} +(2.09577 - 7.82153i) q^{71} +(-1.40415 - 1.40415i) q^{73} +(-7.13817 - 4.12122i) q^{74} +(0.0679541 - 0.253608i) q^{76} +(-1.43416 + 2.48403i) q^{77} +(7.29283 + 12.6316i) q^{79} +(0.653109 - 0.175000i) q^{80} +(-8.02394 + 4.63262i) q^{82} +(-1.04760 + 3.90968i) q^{83} +(3.10238 + 3.10238i) q^{85} +(-1.69726 - 6.33427i) q^{86} +0.710373i q^{88} +(2.64065 + 9.85503i) q^{89} +(6.06248 - 13.2360i) q^{91} +(1.49044 - 0.860504i) q^{92} +(4.69609 + 8.13386i) q^{94} +0.177526 q^{95} +(0.520942 + 1.94418i) q^{97} +(8.98642 + 2.40791i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.653109	+	0.175000i	−0.292079	+	0.0782624i	−0.401883	−	0.915691i	$-0.631644\pi$
$5$	−0.653109	+	0.175000i	−0.292079	+	0.0782624i	0.109804	+	0.993953i	$0.464978\pi$
$6$		0			0
$7$	−3.90017	+	1.04505i	−1.47412	+	0.394991i	−0.904343	−	0.426806i	$-0.859639\pi$
$7$	−3.90017	+	1.04505i	−1.47412	+	0.394991i	−0.569781	+	0.821796i	$0.692972\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−0.585562	−	0.338074i	−0.185171	−	0.106908i
$11$	0.502310	−	0.502310i	0.151452	−	0.151452i	−0.627314	−	0.778766i	$-0.715846\pi$
$11$	0.502310	−	0.502310i	0.151452	−	0.151452i	0.778766	+	0.627314i	$0.215846\pi$
$12$		0			0
$13$	−2.29871	+	2.77775i	−0.637548	+	0.770410i
$13$	−2.29871	+	2.77775i	−0.637548	+	0.770410i
$14$	−3.49679	−	2.01888i	−0.934558	−	0.539567i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.24443	−	5.61952i	−0.786890	−	1.36293i	−0.927863	−	0.372920i	$-0.878356\pi$
$17$	−3.24443	−	5.61952i	−0.786890	−	1.36293i	0.140973	−	0.990013i	$-0.454977\pi$
$18$		0			0
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	0.229611	−	0.973283i	$-0.426255\pi$
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	−0.287792	+	0.957693i	$0.592921\pi$
$20$	−0.175000	−	0.653109i	−0.0391312	−	0.146040i
$21$		0			0
$22$	0.710373			0.151452
$23$	−0.860504	−	1.49044i	−0.179427	−	0.310777i	0.762257	−	0.647274i	$-0.224091\pi$
$23$	−0.860504	−	1.49044i	−0.179427	−	0.310777i	−0.941685	+	0.336497i	$0.890758\pi$
$24$		0			0
$25$	−3.93420	+	2.27141i	−0.786840	+	0.454282i
$26$	−3.58960	+	0.338733i	−0.703979	+	0.0664310i
$27$		0			0
$28$	−1.04505	−	3.90017i	−0.197495	−	0.737062i
$29$		−	1.28654i		−	0.238904i	−0.992840	−	0.119452i	$-0.961886\pi$
$29$		−	1.28654i		−	0.238904i	0.992840	−	0.119452i	$-0.0381138\pi$
$30$		0			0
$31$	1.04468	+	3.89881i	0.187630	+	0.700246i	0.994052	+	0.108905i	$0.0347346\pi$
$31$	1.04468	+	3.89881i	0.187630	+	0.700246i	−0.806422	+	0.591341i	$0.798599\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	1.67944	−	6.26776i	0.288022	−	1.07491i
$35$	2.36435	−	1.36506i	0.399648	−	0.230737i
$36$		0			0
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.844800	−	0.535082i	$-0.820281\pi$
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.464077	+	0.885795i	$0.653614\pi$
$38$	−0.131277	−	0.227379i	−0.0212960	−	0.0368857i
$39$		0			0
$40$	0.338074	−	0.585562i	0.0534542	−	0.0925854i
$41$	−2.39802	+	8.94954i	−0.374508	+	1.39768i	0.479554	+	0.877512i	$0.340798\pi$
$41$	−2.39802	+	8.94954i	−0.374508	+	1.39768i	−0.854062	+	0.520171i	$0.825868\pi$
$42$		0			0
$43$	−5.67915	−	3.27886i	−0.866062	−	0.500021i	−2.44809e−5	−	1.00000i	$-0.500008\pi$
$43$	−5.67915	−	3.27886i	−0.866062	−	0.500021i	−0.866038	+	0.499979i	$0.833341\pi$
$44$	0.502310	+	0.502310i	0.0757261	+	0.0757261i
$45$		0			0
$46$	0.445430	−	1.66237i	0.0656750	−	0.245102i
$47$	9.07214	+	2.43087i	1.32331	+	0.354579i	0.850216	−	0.526434i	$-0.176471\pi$
$47$	9.07214	+	2.43087i	1.32331	+	0.354579i	0.473092	+	0.881013i	$0.343138\pi$
$48$		0			0
$49$	8.05701	−	4.65172i	1.15100	−	0.664531i
$50$	−4.38803	−	1.17577i	−0.620561	−	0.166279i
$51$		0			0
$52$	−2.77775	−	2.29871i	−0.385205	−	0.318774i
$53$			6.34328i			0.871317i	0.900112	+	0.435658i	$0.143484\pi$
$53$			6.34328i			0.871317i	−0.900112	+	0.435658i	$0.856516\pi$
$54$		0			0
$55$	−0.240159	+	0.415967i	−0.0323830	+	0.0560890i
$56$	2.01888	−	3.49679i	0.269784	−	0.467279i
$57$		0			0
$58$	0.909720	−	0.909720i	0.119452	−	0.119452i
$59$	3.52351	−	3.52351i	0.458722	−	0.458722i	−0.439514	−	0.898236i	$-0.644849\pi$
$59$	3.52351	−	3.52351i	0.458722	−	0.458722i	0.898236	+	0.439514i	$0.144849\pi$
$60$		0			0
$61$	−1.64932	+	2.85670i	−0.211173	+	0.365763i	−0.952082	−	0.305843i	$-0.901062\pi$
$61$	−1.64932	+	2.85670i	−0.211173	+	0.365763i	0.740909	+	0.671606i	$0.234395\pi$
$62$	−2.01817	+	3.49557i	−0.256308	+	0.443938i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	1.01520	−	2.21645i	0.125921	−	0.274917i
$66$		0			0
$67$	10.0909	+	2.70385i	1.23280	+	0.330327i	0.815669	−	0.578520i	$-0.196369\pi$
$67$	10.0909	+	2.70385i	1.23280	+	0.330327i	0.417130	+	0.908847i	$0.363036\pi$
$68$	5.61952	−	3.24443i	0.681467	−	0.393445i
$69$		0			0
$70$	2.63709	+	0.706607i	0.315193	+	0.0844556i
$71$	2.09577	−	7.82153i	0.248722	−	0.928245i	−0.722753	−	0.691106i	$-0.757124\pi$
$71$	2.09577	−	7.82153i	0.248722	−	0.928245i	0.971476	−	0.237139i	$-0.0762096\pi$
$72$		0			0
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	0.620145	−	0.784488i	$-0.287074\pi$
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	−0.784488	+	0.620145i	$0.787074\pi$
$74$	−7.13817	−	4.12122i	−0.829795	−	0.479082i
$75$		0			0
$76$	0.0679541	−	0.253608i	0.00779487	−	0.0290909i
$77$	−1.43416	+	2.48403i	−0.163437	+	0.283081i
$78$		0			0
$79$	7.29283	+	12.6316i	0.820507	+	1.42116i	0.905305	+	0.424762i	$0.139642\pi$
$79$	7.29283	+	12.6316i	0.820507	+	1.42116i	−0.0847976	+	0.996398i	$0.527024\pi$
$80$	0.653109	−	0.175000i	0.0730198	−	0.0195656i
$81$		0			0
$82$	−8.02394	+	4.63262i	−0.886096	+	0.511588i
$83$	−1.04760	+	3.90968i	−0.114989	+	0.429144i	−0.999286	−	0.0377806i	$-0.987971\pi$
$83$	−1.04760	+	3.90968i	−0.114989	+	0.429144i	0.884297	+	0.466924i	$0.154638\pi$
$84$		0			0
$85$	3.10238	+	3.10238i	0.336501	+	0.336501i
$86$	−1.69726	−	6.33427i	−0.183020	−	0.683042i
$87$		0			0
$88$			0.710373i			0.0757261i
$89$	2.64065	+	9.85503i	0.279908	+	1.04463i	0.952481	+	0.304600i	$0.0985226\pi$
$89$	2.64065	+	9.85503i	0.279908	+	1.04463i	−0.672573	+	0.740031i	$0.734811\pi$
$90$		0			0
$91$	6.06248	−	13.2360i	0.635521	−	1.38751i
$92$	1.49044	−	0.860504i	0.155389	−	0.0897137i
$93$		0			0
$94$	4.69609	+	8.13386i	0.484364	+	0.838944i
$95$	0.177526			0.0182138
$96$		0			0
$97$	0.520942	+	1.94418i	0.0528937	+	0.197402i	0.987317	−	0.158763i	$-0.0507507\pi$
$97$	0.520942	+	1.94418i	0.0528937	+	0.197402i	−0.934423	+	0.356165i	$0.884084\pi$
$98$	8.98642	+	2.40791i	0.907766	+	0.243235i
$99$		0			0
$100$	−2.27141	−	3.93420i	−0.227141	−	0.393420i
$101$	−14.5201			−1.44481			−0.722404	−	0.691472i	$-0.756963\pi$
$101$	−14.5201			−1.44481			−0.722404	+	0.691472i	$0.756963\pi$
$102$		0			0
$103$	−16.7121	−	9.64874i	−1.64669	−	0.950719i	−0.978374	−	0.206844i	$-0.933681\pi$
$103$	−16.7121	−	9.64874i	−1.64669	−	0.950719i	−0.668319	−	0.743874i	$-0.732986\pi$
$104$	−0.338733	−	3.58960i	−0.0332155	−	0.351990i
$105$		0			0
$106$	−4.48538	+	4.48538i	−0.435658	+	0.435658i
$107$	−11.5211	−	6.65169i	−1.11378	−	0.643043i	−0.173977	−	0.984750i	$-0.555662\pi$
$107$	−11.5211	−	6.65169i	−1.11378	−	0.643043i	−0.939807	+	0.341706i	$0.888995\pi$
$108$		0			0
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	−0.239488	−	0.970899i	$-0.576979\pi$
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	0.970899	+	0.239488i	$0.0769794\pi$
$110$	−0.463951	+	0.124315i	−0.0442360	+	0.0118530i
$111$		0			0
$112$	3.90017	−	1.04505i	0.368531	−	0.0987476i
$113$		−	15.2122i		−	1.43105i	−0.698588	−	0.715524i	$-0.746188\pi$
$113$		−	15.2122i		−	1.43105i	0.698588	−	0.715524i	$-0.253812\pi$
$114$		0			0
$115$	0.822829	+	0.822829i	0.0767292	+	0.0767292i
$116$	1.28654			0.119452
$117$		0			0
$118$	4.98300			0.458722
$119$	18.5265	+	18.5265i	1.69832	+	1.69832i
$120$		0			0
$121$			10.4954i			0.954125i
$122$	−3.18623	+	0.853749i	−0.288468	+	0.0772948i
$123$		0			0
$124$	−3.89881	+	1.04468i	−0.350123	+	0.0938152i
$125$	4.56251	−	4.56251i	0.408083	−	0.408083i
$126$		0			0
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.999999	−	0.00111133i	$-0.000353747\pi$
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.499037	+	0.866581i	$0.333687\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	2.28513	−	0.849411i	0.200419	−	0.0744982i
$131$	4.87564	+	2.81495i	0.425986	+	0.245943i	0.697635	−	0.716453i	$-0.254236\pi$
$131$	4.87564	+	2.81495i	0.425986	+	0.245943i	−0.271649	+	0.962396i	$0.587569\pi$
$132$		0			0
$133$	1.06013			0.0919249
$134$	5.22343	+	9.04724i	0.451236	+	0.781563i
$135$		0			0
$136$	6.26776	+	1.67944i	0.537456	+	0.144011i
$137$	−3.04445	−	11.3621i	−0.260105	−	0.970726i	−0.965179	−	0.261592i	$-0.915753\pi$
$137$	−3.04445	−	11.3621i	−0.260105	−	0.970726i	0.705073	−	0.709134i	$-0.250914\pi$
$138$		0			0
$139$	2.96212			0.251244			0.125622	−	0.992078i	$-0.459907\pi$
$139$	2.96212			0.251244			0.125622	+	0.992078i	$0.459907\pi$
$140$	1.36506	+	2.36435i	0.115369	+	0.199824i
$141$		0			0
$142$	7.01259	−	4.04872i	0.588484	−	0.339761i
$143$	0.240627	+	2.54996i	0.0201222	+	0.213238i
$144$		0			0
$145$	0.225144	+	0.840250i	0.0186972	+	0.0697790i
$146$		−	1.98576i		−	0.164343i
$147$		0			0
$148$	−2.13330	−	7.96159i	−0.175356	−	0.654439i
$149$	16.4140	+	16.4140i	1.34469	+	1.34469i	0.891329	+	0.453358i	$0.149774\pi$
$149$	16.4140	+	16.4140i	1.34469	+	1.34469i	0.453358	+	0.891329i	$0.350226\pi$
$150$		0			0
$151$	−1.78383	+	6.65733i	−0.145166	+	0.541766i	0.854582	+	0.519316i	$0.173813\pi$
$151$	−1.78383	+	6.65733i	−0.145166	+	0.541766i	−0.999748	+	0.0224496i	$0.992853\pi$
$152$	0.227379	−	0.131277i	0.0184429	−	0.0106480i
$153$		0			0
$154$	−2.77058	+	0.742373i	−0.223259	+	0.0598222i
$155$	−1.36458	−	2.36353i	−0.109606	−	0.189843i
$156$		0			0
$157$	−5.48299	+	9.49681i	−0.437590	+	0.757928i	−0.997503	−	0.0706232i	$-0.977501\pi$
$157$	−5.48299	+	9.49681i	−0.437590	+	0.757928i	0.559913	+	0.828551i	$0.310835\pi$
$158$	−3.77505	+	14.0887i	−0.300327	+	1.12083i
$159$		0			0
$160$	0.585562	+	0.338074i	0.0462927	+	0.0267271i
$161$	4.91369	+	4.91369i	0.387253	+	0.387253i
$162$		0			0
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	−0.706096	−	0.708116i	$-0.749545\pi$
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	0.965555	−	0.260198i	$-0.0837880\pi$
$164$	−8.94954	−	2.39802i	−0.698842	−	0.187254i
$165$		0			0
$166$	−3.50533	+	2.02380i	−0.272066	+	0.157077i
$167$	0.811408	+	0.217416i	0.0627886	+	0.0168242i	0.290077	−	0.957003i	$-0.406319\pi$
$167$	0.811408	+	0.217416i	0.0627886	+	0.0168242i	−0.227288	+	0.973828i	$0.572986\pi$
$168$		0			0
$169$	−2.43183	−	12.7705i	−0.187064	−	0.982348i
$170$			4.38743i			0.336501i
$171$		0			0
$172$	3.27886	−	5.67915i	0.250011	−	0.433031i
$173$	−10.6585	+	18.4610i	−0.810349	+	1.40356i	0.102272	+	0.994757i	$0.467389\pi$
$173$	−10.6585	+	18.4610i	−0.810349	+	1.40356i	−0.912620	+	0.408808i	$0.865944\pi$
$174$		0			0
$175$	12.9703	−	12.9703i	0.980463	−	0.980463i
$176$	−0.502310	+	0.502310i	−0.0378630	+	0.0378630i
$177$		0			0
$178$	−5.10134	+	8.83578i	−0.382361	+	0.662269i
$179$	−0.120767	+	0.209175i	−0.00902656	+	0.0156345i	−0.870503	−	0.492162i	$-0.836207\pi$
$179$	−0.120767	+	0.209175i	−0.00902656	+	0.0156345i	0.861477	+	0.507797i	$0.169540\pi$
$180$		0			0
$181$			1.73952i			0.129298i	0.997908	+	0.0646488i	$0.0205927\pi$
$181$			1.73952i			0.129298i	−0.997908	+	0.0646488i	$0.979407\pi$
$182$	13.6461	−	5.07242i	1.01151	−	0.375993i
$183$		0			0
$184$	1.66237	+	0.445430i	0.122551	+	0.0328375i
$185$	4.82646	−	2.78656i	0.354848	−	0.204872i
$186$		0			0
$187$	−4.45245	−	1.19303i	−0.325595	−	0.0872430i
$188$	−2.43087	+	9.07214i	−0.177290	+	0.661654i
$189$		0			0
$190$	0.125530	+	0.125530i	0.00910688	+	0.00910688i
$191$	−7.31652	−	4.22419i	−0.529404	−	0.305652i	0.211369	−	0.977406i	$-0.432208\pi$
$191$	−7.31652	−	4.22419i	−0.529404	−	0.305652i	−0.740774	+	0.671754i	$0.765541\pi$
$192$		0			0
$193$	0.0138895	−	0.0518362i	0.000999786	−	0.00373125i	−0.965424	−	0.260684i	$-0.916052\pi$
$193$	0.0138895	−	0.0518362i	0.000999786	−	0.00373125i	0.966424	+	0.256953i	$0.0827185\pi$
$194$	−1.00638	+	1.74311i	−0.0722541	+	0.125148i
$195$		0			0
$196$	4.65172	+	8.05701i	0.332265	+	0.575501i
$197$	−2.56942	+	0.688475i	−0.183064	+	0.0490518i	−0.349186	−	0.937053i	$-0.613542\pi$
$197$	−2.56942	+	0.688475i	−0.183064	+	0.0490518i	0.166122	+	0.986105i	$0.446875\pi$
$198$		0			0
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	−0.552595	−	0.833450i	$-0.686362\pi$
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	0.445492	+	0.895286i	$0.353029\pi$
$200$	1.17577	−	4.38803i	0.0831394	−	0.310281i
$201$		0			0
$202$	−10.2673	−	10.2673i	−0.722404	−	0.722404i
$203$	1.34449	+	5.01771i	0.0943649	+	0.352175i
$204$		0			0
$205$		−	6.26468i		−	0.437544i
$206$	−4.99456	−	18.6399i	−0.347987	−	1.29871i
$207$		0			0
$208$	2.29871	−	2.77775i	0.159387	−	0.192603i
$209$	−0.161524	+	0.0932559i	−0.0111728	+	0.00645064i
$210$		0			0
$211$	0.651117	+	1.12777i	0.0448248	+	0.0776388i	0.887567	−	0.460678i	$-0.152394\pi$
$211$	0.651117	+	1.12777i	0.0448248	+	0.0776388i	−0.842743	+	0.538317i	$0.819060\pi$
$212$	−6.34328			−0.435658
$213$		0			0
$214$	−3.44317	−	12.8501i	−0.235370	−	0.878414i
$215$	4.28290	+	1.14760i	0.292092	+	0.0782657i
$216$		0			0
$217$	−8.14887	−	14.1143i	−0.553181	−	0.958138i
$218$	10.7992			0.731412
$219$		0			0
$220$	−0.415967	−	0.240159i	−0.0280445	−	0.0161915i
$221$	23.0677	+	3.90543i	1.55170	+	0.262708i
$222$		0			0
$223$	−13.4964	+	13.4964i	−0.903785	+	0.903785i	−0.995761	−	0.0919766i	$-0.970682\pi$
$223$	−13.4964	+	13.4964i	−0.903785	+	0.903785i	0.0919766	+	0.995761i	$0.470682\pi$
$224$	3.49679	+	2.01888i	0.233639	+	0.134892i
$225$		0			0
$226$	10.7567	−	10.7567i	0.715524	−	0.715524i
$227$	−15.8751	+	4.25372i	−1.05367	+	0.282329i	−0.743766	−	0.668440i	$-0.766963\pi$
$227$	−15.8751	+	4.25372i	−1.05367	+	0.282329i	−0.309901	+	0.950769i	$0.600296\pi$
$228$		0			0
$229$	−13.1402	+	3.52092i	−0.868332	+	0.232669i	−0.665366	−	0.746517i	$-0.731725\pi$
$229$	−13.1402	+	3.52092i	−0.868332	+	0.232669i	−0.202965	+	0.979186i	$0.565058\pi$
$230$			1.16366i			0.0767292i
$231$		0			0
$232$	0.909720	+	0.909720i	0.0597260	+	0.0597260i
$233$	−3.89618			−0.255247			−0.127623	−	0.991823i	$-0.540735\pi$
$233$	−3.89618			−0.255247			−0.127623	+	0.991823i	$0.540735\pi$
$234$		0			0
$235$	−6.35050			−0.414261
$236$	3.52351	+	3.52351i	0.229361	+	0.229361i
$237$		0			0
$238$			26.2004i			1.69832i
$239$	−1.52259	+	0.407977i	−0.0984882	+	0.0263898i	−0.307727	−	0.951475i	$-0.599568\pi$
$239$	−1.52259	+	0.407977i	−0.0984882	+	0.0263898i	0.209238	+	0.977865i	$0.432902\pi$
$240$		0			0
$241$	−4.98879	+	1.33674i	−0.321356	+	0.0861071i	−0.415891	−	0.909414i	$-0.636530\pi$
$241$	−4.98879	+	1.33674i	−0.321356	+	0.0861071i	0.0945350	+	0.995522i	$0.469864\pi$
$242$	−7.42135	+	7.42135i	−0.477062	+	0.477062i
$243$		0			0
$244$	−2.85670	−	1.64932i	−0.182881	−	0.105587i
$245$	−4.44806	+	4.44806i	−0.284176	+	0.284176i
$246$		0			0
$247$	0.771732	−	0.548254i	0.0491042	−	0.0348846i
$248$	−3.49557	−	2.01817i	−0.221969	−	0.128154i
$249$		0			0
$250$	6.45236			0.408083
$251$	−3.50515	−	6.07109i	−0.221243	−	0.383204i	0.733943	−	0.679211i	$-0.237678\pi$
$251$	−3.50515	−	6.07109i	−0.221243	−	0.383204i	−0.955186	+	0.296007i	$0.904345\pi$
$252$		0			0
$253$	−1.18090	−	0.316421i	−0.0742426	−	0.0198932i
$254$	5.04870	+	18.8420i	0.316784	+	1.18225i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.89609	−	3.28412i	−0.118275	−	0.204858i	0.800809	−	0.598919i	$-0.204403\pi$
$257$	−1.89609	−	3.28412i	−0.118275	−	0.204858i	−0.919084	+	0.394062i	$0.871070\pi$
$258$		0			0
$259$	28.8221	−	16.6405i	1.79092	−	1.03399i
$260$	2.21645	+	1.01520i	0.137458	+	0.0629603i
$261$		0			0
$262$	1.45713	+	5.43807i	0.0900215	+	0.335965i
$263$		−	8.35425i		−	0.515145i	−0.966259	−	0.257573i	$-0.917077\pi$
$263$		−	8.35425i		−	0.515145i	0.966259	−	0.257573i	$-0.0829226\pi$
$264$		0			0
$265$	−1.11007	−	4.14286i	−0.0681914	−	0.254494i
$266$	0.749625	+	0.749625i	0.0459625	+	0.0459625i
$267$		0			0
$268$	−2.70385	+	10.0909i	−0.165164	+	0.616399i
$269$	−3.60032	+	2.07864i	−0.219515	+	0.126737i	−0.605726	−	0.795674i	$-0.707117\pi$
$269$	−3.60032	+	2.07864i	−0.219515	+	0.126737i	0.386211	+	0.922411i	$0.373784\pi$
$270$		0			0
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.813368	−	0.581749i	$-0.802369\pi$
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.413523	+	0.910494i	$0.635702\pi$
$272$	3.24443	+	5.61952i	0.196723	+	0.340733i
$273$		0			0
$274$	5.88143	−	10.1869i	0.355310	−	0.615416i
$275$	−0.835235	+	3.11714i	−0.0503666	+	0.187971i
$276$		0			0
$277$	13.1496	+	7.59192i	0.790082	+	0.456154i	0.839991	−	0.542600i	$-0.182560\pi$
$277$	13.1496	+	7.59192i	0.790082	+	0.456154i	−0.0499093	+	0.998754i	$0.515893\pi$
$278$	2.09454	+	2.09454i	0.125622	+	0.125622i
$279$		0			0
$280$	−0.706607	+	2.63709i	−0.0422278	+	0.157596i
$281$	−29.2088	−	7.82648i	−1.74245	−	0.466889i	−0.759463	−	0.650550i	$-0.774538\pi$
$281$	−29.2088	−	7.82648i	−1.74245	−	0.466889i	−0.982990	+	0.183662i	$0.941205\pi$
$282$		0			0
$283$	17.0472	−	9.84221i	1.01335	−	0.585059i	0.101180	−	0.994868i	$-0.467738\pi$
$283$	17.0472	−	9.84221i	1.01335	−	0.585059i	0.912171	+	0.409810i	$0.134405\pi$
$284$	7.82153	+	2.09577i	0.464122	+	0.124361i
$285$		0			0
$286$	−1.63294	+	1.97324i	−0.0965580	+	0.116680i
$287$		−	37.4107i		−	2.20829i
$288$		0			0
$289$	−12.5527	+	21.7419i	−0.738393	+	1.27893i
$290$	−0.434945	+	0.753347i	−0.0255409	+	0.0442381i
$291$		0			0
$292$	1.40415	−	1.40415i	0.0821715	−	0.0821715i
$293$	−7.02611	+	7.02611i	−0.410470	+	0.410470i	−0.881902	−	0.471433i	$-0.843737\pi$
$293$	−7.02611	+	7.02611i	−0.410470	+	0.410470i	0.471433	+	0.881902i	$0.343737\pi$
$294$		0			0
$295$	−1.68462	+	2.91785i	−0.0980825	+	0.169884i
$296$	4.12122	−	7.13817i	0.239541	−	0.414897i
$297$		0			0
$298$			23.2129i			1.34469i
$299$	6.11812	+	1.03582i	0.353820	+	0.0599029i
$300$		0			0
$301$	25.5762	+	6.85312i	1.47419	+	0.395007i
$302$	−5.96880	+	3.44609i	−0.343466	+	0.198300i
$303$		0			0
$304$	0.253608	+	0.0679541i	0.0145454	+	0.00389744i
$305$	0.577261	−	2.15437i	0.0330539	−	0.123359i
$306$		0			0
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	0.987039	−	0.160479i	$-0.0513040\pi$
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	−0.160479	+	0.987039i	$0.551304\pi$
$308$	−2.48403	−	1.43416i	−0.141541	−	0.0817186i
$309$		0			0
$310$	0.706360	−	2.63617i	0.0401186	−	0.149724i
$311$	11.3091	−	19.5879i	0.641281	−	1.11073i	−0.343866	−	0.939019i	$-0.611737\pi$
$311$	11.3091	−	19.5879i	0.641281	−	1.11073i	0.985147	−	0.171712i	$-0.0549299\pi$
$312$		0			0
$313$	−9.43419	−	16.3405i	−0.533252	−	0.923619i	−0.999246	−	0.0388313i	$-0.987636\pi$
$313$	−9.43419	−	16.3405i	−0.533252	−	0.923619i	0.465994	−	0.884788i	$-0.345697\pi$
$314$	−10.5923	+	2.83820i	−0.597759	+	0.160169i
$315$		0			0
$316$	−12.6316	+	7.29283i	−0.710580	+	0.410254i
$317$	4.92071	−	18.3643i	0.276375	−	1.03144i	−0.678540	−	0.734563i	$-0.737387\pi$
$317$	4.92071	−	18.3643i	0.276375	−	1.03144i	0.954915	−	0.296881i	$-0.0959463\pi$
$318$		0			0
$319$	−0.646241	−	0.646241i	−0.0361825	−	0.0361825i
$320$	0.175000	+	0.653109i	0.00978280	+	0.0365099i
$321$		0			0
$322$			6.94900i			0.387253i
$323$	0.440945	+	1.64563i	0.0245348	+	0.0915652i
$324$		0			0
$325$	2.73418	−	16.1496i	0.151665	−	0.895817i
$326$	11.0840	−	6.39936i	0.613887	−	0.354428i
$327$		0			0
$328$	−4.63262	−	8.02394i	−0.255794	−	0.443048i
$329$	−37.9233			−2.09078
$330$		0			0
$331$	−6.85161	−	25.5705i	−0.376598	−	1.40548i	−0.850995	−	0.525173i	$-0.824001\pi$
$331$	−6.85161	−	25.5705i	−0.376598	−	1.40548i	0.474397	−	0.880311i	$-0.342666\pi$
$332$	−3.90968	−	1.04760i	−0.214572	−	0.0574943i
$333$		0			0
$334$	0.420016	+	0.727488i	0.0229822	+	0.0398064i
$335$	−7.06363			−0.385927
$336$		0			0
$337$	−19.6500	−	11.3449i	−1.07040	−	0.617996i	−0.142110	−	0.989851i	$-0.545389\pi$
$337$	−19.6500	−	11.3449i	−1.07040	−	0.617996i	−0.928291	+	0.371854i	$0.878722\pi$
$338$	7.31055	−	10.7497i	0.397642	−	0.584706i
$339$		0			0
$340$	−3.10238	+	3.10238i	−0.168250	+	0.168250i
$341$	2.48316	+	1.43365i	0.134471	+	0.0776368i
$342$		0			0
$343$	−6.57658	+	6.57658i	−0.355102	+	0.355102i
$344$	6.33427	−	1.69726i	0.341521	−	0.0915102i
$345$		0			0
$346$	−20.5906	+	5.51723i	−1.10696	+	0.296608i
$347$		−	16.6116i		−	0.891759i	−0.895093	−	0.445879i	$-0.852891\pi$
$347$		−	16.6116i		−	0.891759i	0.895093	−	0.445879i	$-0.147109\pi$
$348$		0			0
$349$	−1.58754	−	1.58754i	−0.0849789	−	0.0849789i	0.663340	−	0.748318i	$-0.269139\pi$
$349$	−1.58754	−	1.58754i	−0.0849789	−	0.0849789i	−0.748318	+	0.663340i	$0.769139\pi$
$350$	18.3428			0.980463
$351$		0			0
$352$	−0.710373			−0.0378630
$353$	6.34497	+	6.34497i	0.337709	+	0.337709i	0.855504	−	0.517796i	$-0.173247\pi$
$353$	6.34497	+	6.34497i	0.337709	+	0.337709i	−0.517796	+	0.855504i	$0.673247\pi$
$354$		0			0
$355$			5.47507i			0.290587i
$356$	−9.85503	+	2.64065i	−0.522315	+	0.139954i
$357$		0			0
$358$	−0.233304	+	0.0625136i	−0.0123305	+	0.00330395i
$359$	25.1620	−	25.1620i	1.32800	−	1.32800i	0.420885	−	0.907114i	$-0.361720\pi$
$359$	25.1620	−	25.1620i	1.32800	−	1.32800i	0.907114	−	0.420885i	$-0.138280\pi$
$360$		0			0
$361$	−16.3948	−	9.46553i	−0.862883	−	0.498186i
$362$	−1.23003	+	1.23003i	−0.0646488	+	0.0646488i
$363$		0			0
$364$	13.2360	+	6.06248i	0.693753	+	0.317761i
$365$	1.16279	+	0.671335i	0.0608631	+	0.0351393i
$366$		0			0
$367$	23.1998			1.21102			0.605509	−	0.795839i	$-0.292970\pi$
$367$	23.1998			1.21102			0.605509	+	0.795839i	$0.292970\pi$
$368$	0.860504	+	1.49044i	0.0448569	+	0.0776944i
$369$		0			0
$370$	5.38322	+	1.44243i	0.279860	+	0.0749883i
$371$	−6.62903	−	24.7399i	−0.344162	−	1.28443i
$372$		0			0
$373$	−30.0462			−1.55573			−0.777866	−	0.628430i	$-0.783698\pi$
$373$	−30.0462			−1.55573			−0.777866	+	0.628430i	$0.783698\pi$
$374$	−2.30476	−	3.99196i	−0.119176	−	0.206419i
$375$		0			0
$376$	−8.13386	+	4.69609i	−0.419472	+	0.242182i
$377$	3.57369	+	2.95738i	0.184054	+	0.152313i
$378$		0			0
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	0.849739	+	0.527203i	$0.176759\pi$
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	−0.472294	+	0.881441i	$0.656574\pi$
$380$			0.177526i			0.00910688i
$381$		0			0
$382$	−2.18660	−	8.16051i	−0.111876	−	0.417528i
$383$	2.62509	+	2.62509i	0.134136	+	0.134136i	0.770987	−	0.636851i	$-0.219763\pi$
$383$	2.62509	+	2.62509i	0.134136	+	0.134136i	−0.636851	+	0.770987i	$0.719763\pi$
$384$		0			0
$385$	0.501955	−	1.87332i	0.0255820	−	0.0954732i
$386$	0.0464751	−	0.0268324i	0.00236552	−	0.00136573i
$387$		0			0
$388$	−1.94418	+	0.520942i	−0.0987009	+	0.0264468i
$389$	−1.01593	−	1.75965i	−0.0515099	−	0.0892178i	0.839121	−	0.543945i	$-0.183070\pi$
$389$	−1.01593	−	1.75965i	−0.0515099	−	0.0892178i	−0.890631	+	0.454727i	$0.849737\pi$
$390$		0			0
$391$	−5.58369	+	9.67124i	−0.282379	+	0.489096i
$392$	−2.40791	+	8.98642i	−0.121618	+	0.453883i
$393$		0			0
$394$	−2.30368	−	1.33003i	−0.116058	−	0.0670060i
$395$	−6.97354	−	6.97354i	−0.350877	−	0.350877i
$396$		0			0
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	−0.999073	−	0.0430503i	$-0.986292\pi$
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	0.886748	+	0.462254i	$0.152959\pi$
$398$	−1.68516	−	0.451537i	−0.0844694	−	0.0226335i
$399$		0			0
$400$	3.93420	−	2.27141i	0.196710	−	0.113571i
$401$	−37.9864	−	10.1784i	−1.89695	−	0.508286i	−0.997450	−	0.0713636i	$-0.977265\pi$
$401$	−37.9864	−	10.1784i	−1.89695	−	0.508286i	−0.899499	−	0.436923i	$-0.856068\pi$
$402$		0			0
$403$	−13.2313	−	6.06037i	−0.659100	−	0.301888i
$404$		−	14.5201i		−	0.722404i
$405$		0			0
$406$	−2.59736	+	4.49876i	−0.128905	+	0.223270i
$407$	−2.92761	+	5.07076i	−0.145116	+	0.251348i
$408$		0			0
$409$	−21.0344	+	21.0344i	−1.04008	+	1.04008i	−0.0409222	+	0.999162i	$0.513030\pi$
$409$	−21.0344	+	21.0344i	−1.04008	+	1.04008i	−0.999162	+	0.0409222i	$0.986970\pi$
$410$	4.42980	−	4.42980i	0.218772	−	0.218772i
$411$		0			0
$412$	9.64874	−	16.7121i	0.475359	−	0.823347i
$413$	−10.0600	+	17.4245i	−0.495023	+	0.857404i
$414$		0			0
$415$		−	2.73678i		−	0.134343i
$416$	3.58960	−	0.338733i	0.175995	−	0.0166077i
$417$		0			0
$418$	−0.180157	−	0.0482728i	−0.00881174	−	0.00236110i
$419$	12.1901	−	7.03797i	0.595527	−	0.343827i	−0.171753	−	0.985140i	$-0.554943\pi$
$419$	12.1901	−	7.03797i	0.595527	−	0.343827i	0.767280	+	0.641313i	$0.221610\pi$
$420$		0			0
$421$	4.66713	+	1.25055i	0.227462	+	0.0609482i	0.370750	−	0.928733i	$-0.379101\pi$
$421$	4.66713	+	1.25055i	0.227462	+	0.0609482i	−0.143288	+	0.989681i	$0.545767\pi$
$422$	−0.337043	+	1.25786i	−0.0164070	+	0.0612318i
$423$		0			0
$424$	−4.48538	−	4.48538i	−0.217829	−	0.217829i
$425$	25.5285	+	14.7389i	1.23831	+	0.714941i
$426$		0			0
$427$	3.44722	−	12.8652i	0.166823	−	0.622591i
$428$	6.65169	−	11.5211i	0.321522	−	0.556892i
$429$		0			0
$430$	2.21699	+	3.83995i	0.106913	+	0.185179i
$431$	−16.0936	+	4.31228i	−0.775203	+	0.207715i	−0.624669	−	0.780890i	$-0.714766\pi$
$431$	−16.0936	+	4.31228i	−0.775203	+	0.207715i	−0.150534	+	0.988605i	$0.548099\pi$
$432$		0			0
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	−0.361142	−	0.932511i	$-0.617613\pi$
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	0.627007	+	0.779014i	$0.284280\pi$
$434$	4.21817	−	15.7424i	0.202478	−	0.755660i
$435$		0			0
$436$	7.63616	+	7.63616i	0.365706	+	0.365706i
$437$	0.116950	+	0.436462i	0.00559446	+	0.0208788i
$438$		0			0
$439$		−	13.2838i		−	0.633999i	−0.948426	−	0.317000i	$-0.897325\pi$
$439$		−	13.2838i		−	0.633999i	0.948426	−	0.317000i	$-0.102675\pi$
$440$	−0.124315	−	0.463951i	−0.00592650	−	0.0221180i
$441$		0			0
$442$	13.5497	+	19.0729i	0.644496	+	0.907203i
$443$	−19.0340	+	10.9893i	−0.904332	+	0.522117i	−0.878603	−	0.477552i	$-0.841524\pi$
$443$	−19.0340	+	10.9893i	−0.904332	+	0.522117i	−0.0257292	+	0.999669i	$0.508191\pi$
$444$		0			0
$445$	−3.44926	−	5.97429i	−0.163511	−	0.283209i
$446$	−19.0868			−0.903785
$447$		0			0
$448$	1.04505	+	3.90017i	0.0493738	+	0.184266i
$449$	−8.04520	−	2.15570i	−0.379676	−	0.101734i	0.0639330	−	0.997954i	$-0.479636\pi$
$449$	−8.04520	−	2.15570i	−0.379676	−	0.101734i	−0.443609	+	0.896220i	$0.646302\pi$
$450$		0			0
$451$	3.29089	+	5.69999i	0.154962	+	0.268402i
$452$	15.2122			0.715524
$453$		0			0
$454$	−14.2332	−	8.21756i	−0.667998	−	0.385669i
$455$	−1.64317	+	9.70547i	−0.0770329	+	0.454999i
$456$		0			0
$457$	9.62978	−	9.62978i	0.450462	−	0.450462i	−0.445046	−	0.895508i	$-0.646813\pi$
$457$	9.62978	−	9.62978i	0.450462	−	0.450462i	0.895508	+	0.445046i	$0.146813\pi$
$458$	−11.7812	−	6.80189i	−0.550500	−	0.317831i
$459$		0			0
$460$	−0.822829	+	0.822829i	−0.0383646	+	0.0383646i
$461$	34.5408	−	9.25517i	1.60872	−	0.431056i	0.661062	−	0.750331i	$-0.270106\pi$
$461$	34.5408	−	9.25517i	1.60872	−	0.431056i	0.947662	+	0.319275i	$0.103439\pi$
$462$		0			0
$463$	12.0689	−	3.23386i	0.560891	−	0.150290i	0.0327754	−	0.999463i	$-0.489565\pi$
$463$	12.0689	−	3.23386i	0.560891	−	0.150290i	0.528116	+	0.849172i	$0.322899\pi$
$464$			1.28654i			0.0597260i
$465$		0			0
$466$	−2.75501	−	2.75501i	−0.127623	−	0.127623i
$467$	−11.9847			−0.554587			−0.277293	−	0.960785i	$-0.589437\pi$
$467$	−11.9847			−0.554587			−0.277293	+	0.960785i	$0.589437\pi$
$468$		0			0
$469$	−42.1818			−1.94777
$470$	−4.49048	−	4.49048i	−0.207131	−	0.207131i
$471$		0			0
$472$			4.98300i			0.229361i
$473$	−4.49970	+	1.20569i	−0.206896	+	0.0554377i
$474$		0			0
$475$	1.15210	−	0.308704i	0.0528618	−	0.0141643i
$476$	−18.5265	+	18.5265i	−0.849160	+	0.849160i
$477$		0			0
$478$	−1.36512	−	0.788151i	−0.0624390	−	0.0360492i
$479$	−10.1637	+	10.1637i	−0.464393	+	0.464393i	−0.900092	−	0.435699i	$-0.856501\pi$
$479$	−10.1637	+	10.1637i	−0.464393	+	0.464393i	0.435699	+	0.900092i	$0.356501\pi$
$480$		0			0
$481$	12.3756	−	27.0192i	0.564280	−	1.23197i
$482$	−4.47282	−	2.58239i	−0.203732	−	0.117624i
$483$		0			0
$484$	−10.4954			−0.477062
$485$	−0.680464	−	1.17860i	−0.0308983	−	0.0535174i
$486$		0			0
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.714748	−	0.699382i	$-0.246541\pi$
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.269299	+	0.963057i	$0.413208\pi$
$488$	−0.853749	−	3.18623i	−0.0386474	−	0.144234i
$489$		0			0
$490$	−6.29050			−0.284176
$491$	21.6874	+	37.5637i	0.978738	+	1.69522i	0.667003	+	0.745055i	$0.267577\pi$
$491$	21.6874	+	37.5637i	0.978738	+	1.69522i	0.311735	+	0.950169i	$0.399090\pi$
$492$		0			0
$493$	−7.22973	+	4.17409i	−0.325611	+	0.187991i
$494$	0.933371	+	0.158023i	0.0419944	+	0.00710979i
$495$		0			0
$496$	−1.04468	−	3.89881i	−0.0469076	−	0.175062i
$497$			32.6955i			1.46659i
$498$		0			0
$499$	7.45370	+	27.8176i	0.333673	+	1.24529i	0.905300	+	0.424772i	$0.139646\pi$
$499$	7.45370	+	27.8176i	0.333673	+	1.24529i	−0.571627	+	0.820514i	$0.693687\pi$
$500$	4.56251	+	4.56251i	0.204042	+	0.204042i
$501$		0			0
$502$	1.81440	−	6.77143i	0.0809805	−	0.302224i
$503$	−13.3453	+	7.70492i	−0.595038	+	0.343545i	−0.767087	−	0.641543i	$-0.778295\pi$
$503$	−13.3453	+	7.70492i	−0.595038	+	0.343545i	0.172049	+	0.985088i	$0.444961\pi$
$504$		0			0
$505$	9.48323	−	2.54102i	0.421998	−	0.113074i
$506$	−0.611279	−	1.05877i	−0.0271747	−	0.0470679i
$507$		0			0
$508$	−9.75334	+	16.8933i	−0.432735	+	0.749518i
$509$	−1.81959	+	6.79081i	−0.0806519	+	0.300997i	−0.994455	−	0.105160i	$-0.966465\pi$
$509$	−1.81959	+	6.79081i	−0.0806519	+	0.300997i	0.913803	+	0.406157i	$0.133131\pi$
$510$		0			0
$511$	6.94381	+	4.00901i	0.307176	+	0.177348i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	0.981486	−	3.66296i	0.0432915	−	0.161566i
$515$	12.6034	+	3.37706i	0.555371	+	0.148811i
$516$		0			0
$517$	5.77808	−	3.33598i	0.254120	−	0.146716i
$518$	32.1469	+	8.61374i	1.41245	+	0.378466i
$519$		0			0
$520$	0.849411	+	2.28513i	0.0372491	+	0.100209i
$521$			42.4222i			1.85855i	0.369391	+	0.929274i	$0.379566\pi$
$521$			42.4222i			1.85855i	−0.369391	+	0.929274i	$0.620434\pi$
$522$		0			0
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	−0.829345	−	0.558737i	$-0.811286\pi$
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	0.898553	+	0.438866i	$0.144620\pi$
$524$	−2.81495	+	4.87564i	−0.122972	+	0.212993i
$525$		0			0
$526$	5.90735	−	5.90735i	0.257573	−	0.257573i
$527$	18.5200	−	18.5200i	0.806745	−	0.806745i
$528$		0			0
$529$	10.0191	−	17.3535i	0.435612	−	0.754501i
$530$	2.14450	−	3.71438i	0.0931511	−	0.161342i
$531$		0			0
$532$			1.06013i			0.0459625i
$533$	−19.3473	−	27.2335i	−0.838023	−	1.17962i
$534$		0			0
$535$	8.68856	+	2.32809i	0.375639	+	0.100652i
$536$	−9.04724	+	5.22343i	−0.390781	+	0.225618i
$537$		0			0
$538$	−4.01563	−	1.07599i	−0.173126	−	0.0463890i
$539$	1.71051	−	6.38372i	0.0736770	−	0.274966i
$540$		0			0
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	0.568321	−	0.822807i	$-0.307593\pi$
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	−0.822807	+	0.568321i	$0.807593\pi$
$542$	−18.1083	−	10.4548i	−0.777818	−	0.449074i
$543$		0			0
$544$	−1.67944	+	6.26776i	−0.0720055	+	0.268728i
$545$	−3.65092	+	6.32358i	−0.156388	+	0.270872i
$546$		0			0
$547$	16.9449	+	29.3493i	0.724510	+	1.25489i	0.959176	+	0.282811i	$0.0912670\pi$
$547$	16.9449	+	29.3493i	0.724510	+	1.25489i	−0.234666	+	0.972076i	$0.575400\pi$
$548$	11.3621	−	3.04445i	0.485363	−	0.130053i
$549$		0			0
$550$	−2.79475	+	1.61355i	−0.119169	+	0.0688020i
$551$	−0.0874256	+	0.326277i	−0.00372445	+	0.0138999i
$552$		0			0
$553$	−41.6438	−	41.6438i	−1.77088	−	1.77088i
$554$	3.92987	+	14.6665i	0.166964	+	0.623118i
$555$		0			0
$556$			2.96212i			0.125622i
$557$	2.17805	+	8.12858i	0.0922868	+	0.344419i	0.996594	−	0.0824630i	$-0.0262786\pi$
$557$	2.17805	+	8.12858i	0.0922868	+	0.344419i	−0.904307	+	0.426882i	$0.859612\pi$
$558$		0			0
$559$	22.1626	−	8.23812i	0.937378	−	0.348436i
$560$	−2.36435	+	1.36506i	−0.0999121	+	0.0576843i
$561$		0			0
$562$	−15.1196	−	26.1879i	−0.637782	−	1.10467i
$563$	−31.8876			−1.34390			−0.671951	−	0.740596i	$-0.734543\pi$
$563$	−31.8876			−1.34390			−0.671951	+	0.740596i	$0.734543\pi$
$564$		0			0
$565$	2.66214	+	9.93526i	0.111997	+	0.417979i
$566$	19.0137	+	5.09470i	0.799205	+	0.214146i
$567$		0			0
$568$	4.04872	+	7.01259i	0.169881	+	0.294242i
$569$	32.4802			1.36164			0.680821	−	0.732450i	$-0.261623\pi$
$569$	32.4802			1.36164			0.680821	+	0.732450i	$0.261623\pi$
$570$		0			0
$571$	−27.2576	−	15.7372i	−1.14070	−	0.658582i	−0.194094	−	0.980983i	$-0.562177\pi$
$571$	−27.2576	−	15.7372i	−1.14070	−	0.658582i	−0.946603	+	0.322401i	$0.895510\pi$
$572$	−2.54996	+	0.240627i	−0.106619	+	0.0100611i
$573$		0			0
$574$	26.4534	−	26.4534i	1.10414	−	1.10414i
$575$	6.77079	+	3.90912i	0.282361	+	0.163021i
$576$		0			0
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	−0.623966	−	0.781451i	$-0.714480\pi$
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	0.781451	+	0.623966i	$0.214480\pi$
$578$	−24.2499	+	6.49774i	−1.00866	+	0.270270i
$579$		0			0
$580$	−0.840250	+	0.225144i	−0.0348895	+	0.00934861i
$581$		−	16.3432i		−	0.678031i
$582$		0			0
$583$	3.18629	+	3.18629i	0.131963	+	0.131963i
$584$	1.98576			0.0821715
$585$		0			0
$586$	−9.93642			−0.410470
$587$	30.8578	+	30.8578i	1.27364	+	1.27364i	0.944165	+	0.329474i	$0.106871\pi$
$587$	30.8578	+	30.8578i	1.27364	+	1.27364i	0.329474	+	0.944165i	$0.393129\pi$
$588$		0			0
$589$		−	1.05976i		−	0.0436666i
$590$	−3.25444	+	0.872025i	−0.133983	+	0.0359007i
$591$		0			0
$592$	7.96159	−	2.13330i	0.327219	−	0.0876781i
$593$	3.43157	−	3.43157i	0.140918	−	0.140918i	−0.633129	−	0.774047i	$-0.718230\pi$
$593$	3.43157	−	3.43157i	0.140918	−	0.140918i	0.774047	+	0.633129i	$0.218230\pi$
$594$		0			0
$595$	−15.3420	−	8.85768i	−0.628959	−	0.363130i
$596$	−16.4140	+	16.4140i	−0.672343	+	0.672343i
$597$		0			0
$598$	3.59373	+	5.05860i	0.146958	+	0.206861i
$599$	−6.49912	−	3.75227i	−0.265547	−	0.153313i	0.361315	−	0.932444i	$-0.382328\pi$
$599$	−6.49912	−	3.75227i	−0.265547	−	0.153313i	−0.626862	+	0.779130i	$0.715661\pi$
$600$		0			0
$601$	17.4262			0.710831			0.355416	−	0.934708i	$-0.384339\pi$
$601$	17.4262			0.710831			0.355416	+	0.934708i	$0.384339\pi$
$602$	13.2392	+	22.9310i	0.539590	+	0.934597i
$603$		0			0
$604$	−6.65733	−	1.78383i	−0.270883	−	0.0725828i
$605$	−1.83669	−	6.85462i	−0.0746721	−	0.278680i
$606$		0			0
$607$	−30.9125			−1.25470			−0.627350	−	0.778737i	$-0.715861\pi$
$607$	−30.9125			−1.25470			−0.627350	+	0.778737i	$0.715861\pi$
$608$	0.131277	+	0.227379i	0.00532400	+	0.00922143i
$609$		0			0
$610$	1.93155	−	1.11518i	0.0782063	−	0.0451524i
$611$	−27.6066	+	19.6123i	−1.11684	+	0.793429i
$612$		0			0
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	0.701113	+	0.713050i	$0.252687\pi$
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	−0.250657	+	0.968076i	$0.580646\pi$
$614$			20.4813i			0.826560i
$615$		0			0
$616$	−0.742373	−	2.77058i	−0.0299111	−	0.111630i
$617$	8.95150	+	8.95150i	0.360374	+	0.360374i	0.863950	−	0.503577i	$-0.167983\pi$
$617$	8.95150	+	8.95150i	0.360374	+	0.360374i	−0.503577	+	0.863950i	$0.667983\pi$
$618$		0			0
$619$	0.291078	−	1.08632i	0.0116994	−	0.0436628i	−0.959829	−	0.280584i	$-0.909472\pi$
$619$	0.291078	−	1.08632i	0.0116994	−	0.0436628i	0.971529	+	0.236922i	$0.0761384\pi$
$620$	2.36353	−	1.36458i	0.0949215	−	0.0548030i
$621$		0			0
$622$	21.8475	−	5.85403i	0.876006	−	0.234725i
$623$	−20.5979	−	35.6767i	−0.825239	−	1.42936i
$624$		0			0
$625$	9.17568	−	15.8927i	0.367027	−	0.635710i
$626$	4.88349	−	18.2255i	0.195184	−	0.728436i
$627$		0			0
$628$	−9.49681	−	5.48299i	−0.378964	−	0.218795i
$629$	37.8190	+	37.8190i	1.50794	+	1.50794i
$630$		0			0
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	0.860197	+	0.509962i	$0.170341\pi$
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	−0.999933	+	0.0115421i	$0.996326\pi$
$632$	−14.0887	−	3.77505i	−0.560417	−	0.150163i
$633$		0			0
$634$	16.4650	−	9.50608i	0.653909	−	0.377535i
$635$	−12.7400	−	3.41367i	−0.505571	−	0.135467i
$636$		0			0
$637$	−5.59943	+	33.0733i	−0.221857	+	1.31041i
$638$		−	0.913923i		−	0.0361825i
$639$		0			0
$640$	−0.338074	+	0.585562i	−0.0133636	+	0.0231464i
$641$	23.6580	−	40.9769i	0.934436	−	1.61849i	0.158801	−	0.987311i	$-0.449237\pi$
$641$	23.6580	−	40.9769i	0.934436	−	1.61849i	0.775636	−	0.631181i	$-0.217429\pi$
$642$		0			0
$643$	6.73860	−	6.73860i	0.265745	−	0.265745i	−0.561638	−	0.827383i	$-0.689829\pi$
$643$	6.73860	−	6.73860i	0.265745	−	0.265745i	0.827383	+	0.561638i	$0.189829\pi$
$644$	−4.91369	+	4.91369i	−0.193626	+	0.193626i
$645$		0			0
$646$	−0.851840	+	1.47543i	−0.0335152	+	0.0580500i
$647$	8.42061	−	14.5849i	0.331048	−	0.573392i	−0.651669	−	0.758503i	$-0.725931\pi$
$647$	8.42061	−	14.5849i	0.331048	−	0.573392i	0.982718	+	0.185111i	$0.0592644\pi$
$648$		0			0
$649$		−	3.53979i		−	0.138949i
$650$	13.3528	−	9.48611i	0.523741	−	0.372076i
$651$		0			0
$652$	12.3626	+	3.31255i	0.484157	+	0.129730i
$653$	25.2989	−	14.6063i	0.990022	−	0.571589i	0.0847408	−	0.996403i	$-0.472994\pi$
$653$	25.2989	−	14.6063i	0.990022	−	0.571589i	0.905281	+	0.424814i	$0.139660\pi$
$654$		0			0
$655$	−3.67694	−	0.985233i	−0.143670	−	0.0384962i
$656$	2.39802	−	8.94954i	0.0936270	−	0.349421i
$657$		0			0
$658$	−26.8158	−	26.8158i	−1.04539	−	1.04539i
$659$	12.4412	+	7.18293i	0.484641	+	0.279807i	0.722348	−	0.691529i	$-0.243063\pi$
$659$	12.4412	+	7.18293i	0.484641	+	0.279807i	−0.237708	+	0.971337i	$0.576396\pi$
$660$		0			0
$661$	−10.7255	+	40.0282i	−0.417174	+	1.55692i	0.363267	+	0.931685i	$0.381661\pi$
$661$	−10.7255	+	40.0282i	−0.417174	+	1.55692i	−0.780441	+	0.625230i	$0.785005\pi$
$662$	13.2363	−	22.9259i	0.514443	−	0.891041i
$663$		0			0
$664$	−2.02380	−	3.50533i	−0.0785387	−	0.136033i
$665$	−0.692380	+	0.185523i	−0.0268494	+	0.00719426i
$666$		0			0
$667$	−1.91750	+	1.10707i	−0.0742460	+	0.0428660i
$668$	−0.217416	+	0.811408i	−0.00841208	+	0.0313943i
$669$		0			0
$670$	−4.99474	−	4.99474i	−0.192964	−	0.192964i
$671$	0.606480	+	2.26342i	0.0234129	+	0.0873782i
$672$		0			0
$673$			39.4913i			1.52228i	0.648588	+	0.761140i	$0.275360\pi$
$673$			39.4913i			1.52228i	−0.648588	+	0.761140i	$0.724640\pi$
$674$	−5.87256	−	21.9167i	−0.226202	−	0.844199i
$675$		0			0
$676$	12.7705	−	2.43183i	0.491174	−	0.0935321i
$677$	−14.7062	+	8.49064i	−0.565206	+	0.326322i	−0.755232	−	0.655457i	$-0.772476\pi$
$677$	−14.7062	+	8.49064i	−0.565206	+	0.326322i	0.190026	+	0.981779i	$0.439143\pi$
$678$		0			0
$679$	−4.06352	−	7.03823i	−0.155944	−	0.270103i
$680$	−4.38743			−0.168250
$681$		0			0
$682$	0.742114	+	2.76961i	0.0284170	+	0.106054i
$683$	1.34228	+	0.359662i	0.0513607	+	0.0137621i	0.284408	−	0.958703i	$-0.408203\pi$
$683$	1.34228	+	0.359662i	0.0513607	+	0.0137621i	−0.233047	+	0.972465i	$0.574870\pi$
$684$		0			0
$685$	3.97672	+	6.88788i	0.151943	+	0.263173i
$686$	−9.30068			−0.355102
$687$		0			0
$688$	5.67915	+	3.27886i	0.216516	+	0.125005i
$689$	−17.6201	−	14.5814i	−0.671272	−	0.555507i
$690$		0			0
$691$	−7.28822	+	7.28822i	−0.277257	+	0.277257i	−0.832013	−	0.554756i	$-0.812812\pi$
$691$	−7.28822	+	7.28822i	−0.277257	+	0.277257i	0.554756	+	0.832013i	$0.312812\pi$
$692$	−18.4610	−	10.6585i	−0.701782	−	0.405174i
$693$		0			0
$694$	11.7462	−	11.7462i	0.445879	−	0.445879i
$695$	−1.93459	+	0.518372i	−0.0733832	+	0.0196630i
$696$		0			0
$697$	58.0723	−	15.5604i	2.19965	−	0.589393i
$698$		−	2.24512i		−	0.0849789i
$699$		0			0
$700$	12.9703	+	12.9703i	0.490232	+	0.490232i
$701$	26.3023			0.993423			0.496712	−	0.867916i	$-0.334541\pi$
$701$	26.3023			0.993423			0.496712	+	0.867916i	$0.334541\pi$
$702$		0			0
$703$	2.16409			0.0816202
$704$	−0.502310	−	0.502310i	−0.0189315	−	0.0189315i
$705$		0			0
$706$			8.97314i			0.337709i
$707$	56.6310	−	15.1742i	2.12983	−	0.570685i
$708$		0			0
$709$	31.3179	−	8.39161i	1.17617	−	0.315154i	0.382763	−	0.923846i	$-0.374972\pi$
$709$	31.3179	−	8.39161i	1.17617	−	0.315154i	0.793406	+	0.608693i	$0.208306\pi$
$710$	−3.87146	+	3.87146i	−0.145293	+	0.145293i
$711$		0			0
$712$	−8.83578	−	5.10134i	−0.331135	−	0.191181i
$713$	4.91197	−	4.91197i	0.183955	−	0.183955i
$714$		0			0
$715$	−0.603399	−	1.62329i	−0.0225658	−	0.0607077i
$716$	−0.209175	−	0.120767i	−0.00781723	−	0.00451328i
$717$		0			0
$718$	35.5844			1.32800
$719$	−8.65353	−	14.9884i	−0.322722	−	0.558971i	0.658326	−	0.752733i	$-0.271265\pi$
$719$	−8.65353	−	14.9884i	−0.322722	−	0.558971i	−0.981049	+	0.193761i	$0.937931\pi$
$720$		0			0
$721$	75.2634	+	20.1668i	2.80296	+	0.751050i
$722$	−4.89972	−	18.2860i	−0.182349	−	0.680535i
$723$		0			0
$724$	−1.73952			−0.0646488
$725$	2.92226	+	5.06150i	0.108530	+	0.187979i
$726$		0			0
$727$	8.04825	−	4.64666i	0.298493	−	0.172335i	−0.343273	−	0.939236i	$-0.611536\pi$
$727$	8.04825	−	4.64666i	0.298493	−	0.172335i	0.641766	+	0.766901i	$0.278202\pi$
$728$	5.07242	+	13.6461i	0.187996	+	0.505757i
$729$		0			0
$730$	0.347509	+	1.29692i	0.0128619	+	0.0480012i
$731$			42.5521i			1.57385i
$732$		0			0
$733$	9.12426	+	34.0522i	0.337012	+	1.25775i	0.901671	+	0.432422i	$0.142341\pi$
$733$	9.12426	+	34.0522i	0.337012	+	1.25775i	−0.564659	+	0.825324i	$0.690992\pi$
$734$	16.4047	+	16.4047i	0.605509	+	0.605509i
$735$		0			0
$736$	−0.445430	+	1.66237i	−0.0164188	+	0.0612756i
$737$	6.42692	−	3.71058i	0.236739	−	0.136681i
$738$		0			0
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.399795	−	0.916604i	$-0.369081\pi$
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.804535	+	0.593905i	$0.202415\pi$
$740$	2.78656	+	4.82646i	0.102436	+	0.177424i
$741$		0			0
$742$	12.8063	−	22.1812i	0.470134	−	0.814296i
$743$	2.77031	−	10.3389i	0.101633	−	0.379299i	−0.896309	−	0.443431i	$-0.853761\pi$
$743$	2.77031	−	10.3389i	0.101633	−	0.379299i	0.997941	+	0.0641321i	$0.0204279\pi$
$744$		0			0
$745$	−13.5926	−	7.84768i	−0.497993	−	0.287517i
$746$	−21.2459	−	21.2459i	−0.777866	−	0.777866i
$747$		0			0
$748$	1.19303	−	4.45245i	0.0436215	−	0.162798i
$749$	51.8854	+	13.9027i	1.89585	+	0.507992i
$750$		0			0
$751$	−12.1245	+	7.00006i	−0.442428	+	0.255436i	−0.704627	−	0.709578i	$-0.748886\pi$
$751$	−12.1245	+	7.00006i	−0.442428	+	0.255436i	0.262199	+	0.965014i	$0.415552\pi$
$752$	−9.07214	−	2.43087i	−0.330827	−	0.0886448i
$753$		0			0
$754$	0.435793	+	4.61816i	0.0158706	+	0.168184i
$755$		−	4.66013i		−	0.169600i
$756$		0			0
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	−0.932237	−	0.361848i	$-0.882146\pi$
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	0.779488	+	0.626417i	$0.215479\pi$
$758$	−14.1954	+	24.5871i	−0.515600	+	0.893045i
$759$		0			0
$760$	−0.125530	+	0.125530i	−0.00455344	+	0.00455344i
$761$	−20.7884	+	20.7884i	−0.753578	+	0.753578i	−0.975145	−	0.221567i	$-0.928883\pi$
$761$	−20.7884	+	20.7884i	−0.753578	+	0.753578i	0.221567	+	0.975145i	$0.428883\pi$
$762$		0			0
$763$	−21.8022	+	37.7625i	−0.789292	+	1.36709i
$764$	4.22419	−	7.31652i	0.152826	−	0.264702i
$765$		0			0
$766$			3.71244i			0.134136i
$767$	1.68790	+	17.8870i	0.0609467	+	0.645862i
$768$		0			0
$769$	35.1291	+	9.41282i	1.26679	+	0.339435i	0.828800	−	0.559545i	$-0.189024\pi$
$769$	35.1291	+	9.41282i	1.26679	+	0.339435i	0.437989	+	0.898980i	$0.355691\pi$
$770$	1.67957	−	0.969702i	0.0605276	−	0.0349456i
$771$		0			0
$772$	0.0518362	+	0.0138895i	0.00186563	+	0.000499893i
$773$	1.91671	−	7.15325i	0.0689391	−	0.257284i	−0.922852	−	0.385156i	$-0.874148\pi$
$773$	1.91671	−	7.15325i	0.0689391	−	0.257284i	0.991791	+	0.127871i	$0.0408144\pi$
$774$		0			0
$775$	−12.9658	−	12.9658i	−0.465745	−	0.465745i
$776$	−1.74311	−	1.00638i	−0.0625739	−	0.0361271i
$777$		0			0
$778$	0.525886	−	1.96263i	0.0188539	−	0.0703638i
$779$	1.21632	−	2.10672i	0.0435790	−	0.0754811i
$780$		0			0
$781$	−2.87610	−	4.98156i	−0.102915	−	0.178254i
$782$	−10.7869	+	2.89033i	−0.385738	+	0.103358i
$783$		0			0
$784$	−8.05701	+	4.65172i	−0.287750	+	0.166133i
$785$	1.91905	−	7.16198i	0.0684937	−	0.255622i
$786$		0			0
$787$	−8.59029	−	8.59029i	−0.306211	−	0.306211i	0.537227	−	0.843438i	$-0.319472\pi$
$787$	−8.59029	−	8.59029i	−0.306211	−	0.306211i	−0.843438	+	0.537227i	$0.819472\pi$
$788$	−0.688475	−	2.56942i	−0.0245259	−	0.0915319i
$789$		0			0
$790$		−	9.86207i		−	0.350877i
$791$	15.8975	+	59.3303i	0.565250	+	2.10954i
$792$		0			0
$793$	−4.14390	−	11.1481i	−0.147154	−	0.395881i
$794$	−7.48871	+	4.32361i	−0.265764	+	0.153439i
$795$		0			0
$796$	−0.872302	−	1.51087i	−0.0309179	−	0.0535514i
$797$	32.4028			1.14777			0.573883	−	0.818937i	$-0.305436\pi$
$797$	32.4028			1.14777			0.573883	+	0.818937i	$0.305436\pi$
$798$		0			0
$799$	−15.7736	−	58.8679i	−0.558030	−	2.08260i
$800$	4.38803	+	1.17577i	0.155140	+	0.0415697i
$801$		0			0
$802$	−19.6632	−	34.0577i	−0.694332	−	1.20262i
$803$	−1.41063			−0.0497802
$804$		0			0
$805$	−4.06907	−	2.34928i	−0.143416	−	0.0828012i
$806$	−5.07065	−	13.6413i	−0.178606	−	0.480494i
$807$		0			0
$808$	10.2673	−	10.2673i	0.361202	−	0.361202i
$809$	16.9078	+	9.76174i	0.594448	+	0.343205i	0.766854	−	0.641821i	$-0.221821\pi$
$809$	16.9078	+	9.76174i	0.594448	+	0.343205i	−0.172406	+	0.985026i	$0.555154\pi$
$810$		0			0
$811$	−22.8460	+	22.8460i	−0.802232	+	0.802232i	−0.983444	−	0.181212i	$-0.941998\pi$
$811$	−22.8460	+	22.8460i	−0.802232	+	0.802232i	0.181212	+	0.983444i	$0.441998\pi$
$812$	−5.01771	+	1.34449i	−0.176087	+	0.0471824i
$813$		0			0
$814$	−5.65570	+	1.51544i	−0.198232	+	0.0531162i
$815$			8.65383i			0.303131i
$816$		0			0
$817$	1.21747	+	1.21747i	0.0425938	+	0.0425938i
$818$	−29.7471			−1.04008
$819$		0			0
$820$	6.26468			0.218772
$821$	−26.9448	−	26.9448i	−0.940379	−	0.940379i	0.0579409	−	0.998320i	$-0.481547\pi$
$821$	−26.9448	−	26.9448i	−0.940379	−	0.940379i	−0.998320	+	0.0579409i	$0.981547\pi$
$822$		0			0
$823$			7.48458i			0.260896i	0.991455	+	0.130448i	$0.0416416\pi$
$823$			7.48458i			0.260896i	−0.991455	+	0.130448i	$0.958358\pi$
$824$	18.6399	−	4.99456i	0.649353	−	0.173994i
$825$		0			0
$826$	−19.4345	+	5.20746i	−0.676214	+	0.181191i
$827$	7.82102	−	7.82102i	0.271963	−	0.271963i	−0.557927	−	0.829890i	$-0.688403\pi$
$827$	7.82102	−	7.82102i	0.271963	−	0.271963i	0.829890	+	0.557927i	$0.188403\pi$
$828$		0			0
$829$	−8.88429	−	5.12935i	−0.308564	−	0.178150i	0.337720	−	0.941247i	$-0.390344\pi$
$829$	−8.88429	−	5.12935i	−0.308564	−	0.178150i	−0.646284	+	0.763097i	$0.723678\pi$
$830$	1.93520	−	1.93520i	0.0671716	−	0.0671716i
$831$		0			0
$832$	2.77775	+	2.29871i	0.0963013	+	0.0796935i
$833$	−52.2808	−	30.1843i	−1.81142	−	1.04583i
$834$		0			0
$835$	−0.567986			−0.0196560
$836$	−0.0932559	−	0.161524i	−0.00322532	−	0.00558642i
$837$		0			0
$838$	13.5963	+	3.64312i	0.469677	+	0.125850i
$839$	−3.05007	−	11.3830i	−0.105300	−	0.392985i	0.893079	−	0.449900i	$-0.148540\pi$
$839$	−3.05007	−	11.3830i	−0.105300	−	0.392985i	−0.998379	+	0.0569146i	$0.981874\pi$
$840$		0			0
$841$	27.3448			0.942925
$842$	2.41588	+	4.18443i	0.0832568	+	0.144205i
$843$		0			0
$844$	−1.12777	+	0.651117i	−0.0388194	+	0.0224124i
$845$	3.82310	+	7.91497i	0.131518	+	0.272283i
$846$		0			0
$847$	−10.9682	−	40.9337i	−0.376870	−	1.40650i
$848$		−	6.34328i		−	0.217829i
$849$		0			0
$850$	7.62941	+	28.4733i	0.261686	+	0.976627i
$851$	10.0305	+	10.0305i	0.343842	+	0.343842i
$852$		0			0
$853$	−6.39301	+	23.8590i	−0.218892	+	0.816918i	0.765868	+	0.642998i	$0.222310\pi$
$853$	−6.39301	+	23.8590i	−0.218892	+	0.816918i	−0.984760	+	0.173919i	$0.944357\pi$
$854$	11.5346	−	6.65953i	0.394707	−	0.227884i
$855$		0			0
$856$	12.8501	−	3.44317i	0.439207	−	0.117685i
$857$	−24.8560	−	43.0518i	−0.849063	−	1.47062i	−0.882045	−	0.471165i	$-0.843834\pi$
$857$	−24.8560	−	43.0518i	−0.849063	−	1.47062i	0.0329818	−	0.999456i	$-0.489500\pi$
$858$		0			0
$859$	−11.5341	+	19.9776i	−0.393538	+	0.681628i	−0.992913	−	0.118840i	$-0.962082\pi$
$859$	−11.5341	+	19.9776i	−0.393538	+	0.681628i	0.599375	+	0.800468i	$0.295416\pi$
$860$	−1.14760	+	4.28290i	−0.0391329	+	0.146046i
$861$		0			0
$862$	−14.4292	−	8.33068i	−0.491459	−	0.283744i
$863$	4.06937	+	4.06937i	0.138523	+	0.138523i	0.772968	−	0.634445i	$-0.218771\pi$
$863$	4.06937	+	4.06937i	0.138523	+	0.138523i	−0.634445	+	0.772968i	$0.718771\pi$
$864$		0			0
$865$	3.73047	−	13.9223i	0.126840	−	0.473372i
$866$	6.17046	+	1.65337i	0.209681	+	0.0561838i
$867$		0			0
$868$	14.1143	−	8.14887i	0.479069	−	0.276591i
$869$	10.0082	+	2.68169i	0.339505	+	0.0909702i
$870$		0			0
$871$	−30.7067	+	21.8146i	−1.04046	+	0.739161i
$872$			10.7992i			0.365706i
$873$		0			0
$874$	−0.225929	+	0.391321i	−0.00764217	+	0.0132366i
$875$	−13.0265	+	22.5626i	−0.440377	+	0.762755i
$876$		0			0
$877$	−25.0480	+	25.0480i	−0.845812	+	0.845812i	−0.989607	−	0.143796i	$-0.954069\pi$
$877$	−25.0480	+	25.0480i	−0.845812	+	0.845812i	0.143796	+	0.989607i	$0.454069\pi$
$878$	9.39304	−	9.39304i	0.317000	−	0.317000i
$879$		0			0
$880$	0.240159	−	0.415967i	0.00809575	−	0.0140223i
$881$	9.78090	−	16.9410i	0.329527	−	0.570757i	−0.652891	−	0.757452i	$-0.726444\pi$
$881$	9.78090	−	16.9410i	0.329527	−	0.570757i	0.982418	+	0.186695i	$0.0597775\pi$
$882$		0			0
$883$			7.96488i			0.268040i	0.990979	+	0.134020i	$0.0427886\pi$
$883$			7.96488i			0.268040i	−0.990979	+	0.134020i	$0.957211\pi$
$884$	−3.90543	+	23.0677i	−0.131354	+	0.775849i
$885$		0			0
$886$	−21.2297	−	5.68847i	−0.713225	−	0.191108i
$887$	−44.3470	+	25.6038i	−1.48903	+	0.859690i	−0.999921	−	0.0125348i	$-0.996010\pi$
$887$	−44.3470	+	25.6038i	−1.48903	+	0.859690i	−0.489105	+	0.872225i	$0.662677\pi$
$888$		0			0
$889$	−76.0793	−	20.3854i	−2.55162	−	0.683704i
$890$	1.78547	−	6.66346i	0.0598490	−	0.223360i
$891$		0			0
$892$	−13.4964	−	13.4964i	−0.451892	−	0.451892i
$893$	−2.13558	−	1.23298i	−0.0714645	−	0.0412601i
$894$		0			0
$895$	0.0422685	−	0.157748i	0.00141288	−	0.00527294i
$896$	−2.01888	+	3.49679i	−0.0674459	+	0.116820i
$897$		0			0
$898$	−4.16450	−	7.21313i	−0.138971	−	0.240705i
$899$	5.01596	−	1.34402i	0.167292	−	0.0448257i
$900$		0			0
$901$	35.6462	−	20.5803i	1.18755	−	0.685631i
$902$	−1.70349	+	6.35751i	−0.0567200	+	0.211682i
$903$		0			0
$904$	10.7567	+	10.7567i	0.357762	+	0.357762i
$905$	−0.304416	−	1.13610i	−0.0101191	−	0.0377652i
$906$		0			0
$907$			12.9015i			0.428388i	0.976791	+	0.214194i	$0.0687125\pi$
$907$			12.9015i			0.428388i	−0.976791	+	0.214194i	$0.931288\pi$
$908$	−4.25372	−	15.8751i	−0.141165	−	0.526834i
$909$		0			0
$910$	−8.02470	+	5.70091i	−0.266016	+	0.188983i
$911$	6.52125	−	3.76504i	0.216059	−	0.124741i	−0.388065	−	0.921632i	$-0.626857\pi$
$911$	6.52125	−	3.76504i	0.216059	−	0.124741i	0.604124	+	0.796890i	$0.293523\pi$
$912$		0			0
$913$	1.43765	+	2.49009i	0.0475794	+	0.0824100i
$914$	13.6186			0.450462
$915$		0			0
$916$	−3.52092	−	13.1402i	−0.116334	−	0.434166i
$917$	−21.9576	−	5.88351i	−0.725103	−	0.194291i
$918$		0			0
$919$	−9.25517	−	16.0304i	−0.305300	−	0.528795i	0.672028	−	0.740526i	$-0.265423\pi$
$919$	−9.25517	−	16.0304i	−0.305300	−	0.528795i	−0.977328	+	0.211731i	$0.932090\pi$
$920$	−1.16366			−0.0383646
$921$		0			0
$922$	30.9684	+	17.8796i	1.01989	+	0.588834i
$923$	16.9087	+	23.8010i	0.556557	+	0.783419i
$924$		0			0
$925$	26.4769	−	26.4769i	0.870555	−	0.870555i
$926$	10.8207	+	6.24734i	0.355591	+	0.205300i
$927$		0			0
$928$	−0.909720	+	0.909720i	−0.0298630	+	0.0298630i
$929$	−1.65623	+	0.443784i	−0.0543390	+	0.0145601i	−0.285886	−	0.958264i	$-0.592288\pi$
$929$	−1.65623	+	0.443784i	−0.0543390	+	0.0145601i	0.231547	+	0.972824i	$0.425621\pi$
$930$		0			0
$931$	−2.35943	+	0.632206i	−0.0773271	+	0.0207197i
$932$		−	3.89618i		−	0.127623i
$933$		0			0
$934$	−8.47448	−	8.47448i	−0.277293	−	0.277293i
$935$	3.11672			0.101928
$936$		0			0
$937$	−25.3011			−0.826552			−0.413276	−	0.910606i	$-0.635616\pi$
$937$	−25.3011			−0.826552			−0.413276	+	0.910606i	$0.635616\pi$
$938$	−29.8270	−	29.8270i	−0.973887	−	0.973887i
$939$		0			0
$940$		−	6.35050i		−	0.207131i
$941$	−45.8826	+	12.2942i	−1.49573	+	0.400779i	−0.911667	−	0.410929i	$-0.865204\pi$
$941$	−45.8826	+	12.2942i	−1.49573	+	0.400779i	−0.584062	+	0.811709i	$0.698538\pi$
$942$		0			0
$943$	15.4022	−	4.12701i	0.501565	−	0.134394i
$944$	−3.52351	+	3.52351i	−0.114681	+	0.114681i
$945$		0			0
$946$	−4.03432	−	2.32921i	−0.131167	−	0.0757293i
$947$	29.0592	−	29.0592i	0.944299	−	0.944299i	−0.0542299	−	0.998528i	$-0.517270\pi$
$947$	29.0592	−	29.0592i	0.944299	−	0.944299i	0.998528	+	0.0542299i	$0.0172704\pi$
$948$		0			0
$949$	7.12811	−	0.672644i	0.231388	−	0.0218349i
$950$	1.03294	+	0.596369i	0.0335131	+	0.0193488i
$951$		0			0
$952$	−26.2004			−0.849160
$953$	−18.5200	−	32.0775i	−0.599921	−	1.03909i	−0.992832	−	0.119517i	$-0.961865\pi$
$953$	−18.5200	−	32.0775i	−0.599921	−	1.03909i	0.392911	−	0.919576i	$-0.371468\pi$
$954$		0			0
$955$	5.51772	+	1.47847i	0.178549	+	0.0478421i
$956$	−0.407977	−	1.52259i	−0.0131949	−	0.0492441i
$957$		0			0
$958$	−14.3737			−0.464393
$959$	23.7478	+	41.1323i	0.766855	+	1.32823i
$960$		0			0
$961$	12.7375	−	7.35397i	0.410886	−	0.237225i
$962$	27.8563	−	10.3546i	0.898124	−	0.333844i
$963$		0			0
$964$	−1.33674	−	4.98879i	−0.0430536	−	0.160678i
$965$			0.0362854i			0.00116807i
$966$		0			0
$967$	1.54647	+	5.77149i	0.0497310	+	0.185599i	0.986323	−	0.164822i	$-0.0527051\pi$
$967$	1.54647	+	5.77149i	0.0497310	+	0.185599i	−0.936592	+	0.350421i	$0.886038\pi$
$968$	−7.42135	−	7.42135i	−0.238531	−	0.238531i
$969$		0			0
$970$	0.352234	−	1.31456i	0.0113096	−	0.0422079i
$971$	−1.66482	+	0.961183i	−0.0534266	+	0.0308458i	−0.526475	−	0.850190i	$-0.676487\pi$
$971$	−1.66482	+	0.961183i	−0.0534266	+	0.0308458i	0.473049	+	0.881036i	$0.343153\pi$
$972$		0			0
$973$	−11.5528	+	3.09556i	−0.370365	+	0.0992390i
$974$	11.2410	+	19.4701i	0.360186	+	0.623861i
$975$		0			0
$976$	1.64932	−	2.85670i	0.0527933	−	0.0914407i
$977$	−1.06347	+	3.96893i	−0.0340235	+	0.126977i	−0.980849	−	0.194771i	$-0.937604\pi$
$977$	−1.06347	+	3.96893i	−0.0340235	+	0.126977i	0.946825	+	0.321748i	$0.104270\pi$
$978$		0			0
$979$	6.27670	+	3.62385i	0.200604	+	0.115819i
$980$	−4.44806	−	4.44806i	−0.142088	−	0.142088i
$981$		0			0
$982$	−11.2262	+	41.8968i	−0.358243	+	1.33698i
$983$	−14.8251	−	3.97238i	−0.472848	−	0.126699i	0.0145225	−	0.999895i	$-0.495377\pi$
$983$	−14.8251	−	3.97238i	−0.472848	−	0.126699i	−0.487370	+	0.873195i	$0.662044\pi$
$984$		0			0
$985$	1.55763	−	0.899299i	0.0496302	−	0.0286540i
$986$	−8.06371	−	2.16067i	−0.256801	−	0.0688096i
$987$		0			0
$988$	0.548254	+	0.771732i	0.0174423	+	0.0245521i
$989$			11.2859i			0.358870i
$990$		0			0
$991$	−2.52005	+	4.36486i	−0.0800521	+	0.138654i	−0.903272	−	0.429068i	$-0.858842\pi$
$991$	−2.52005	+	4.36486i	−0.0800521	+	0.138654i	0.823220	+	0.567722i	$0.192175\pi$
$992$	2.01817	−	3.49557i	0.0640770	−	0.110985i
$993$		0			0
$994$	−23.1192	+	23.1192i	−0.733296	+	0.733296i
$995$	0.834111	−	0.834111i	0.0264431	−	0.0264431i
$996$		0			0
$997$	5.85786	−	10.1461i	0.185520	−	0.321331i	−0.758231	−	0.651986i	$-0.773936\pi$
$997$	5.85786	−	10.1461i	0.185520	−	0.321331i	0.943752	+	0.330655i	$0.107270\pi$
$998$	−14.3994	+	24.9406i	−0.455806	+	0.789480i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.71.11		56
3.2	odd	2		234.2.y.a.149.2	yes	56
9.2	odd	6		702.2.bc.a.305.4		56
9.7	even	3		234.2.z.a.227.13	yes	56
13.11	odd	12		702.2.bc.a.557.4		56
39.11	even	12		234.2.z.a.167.13	yes	56
117.11	even	12	inner	702.2.bb.a.89.11		56
117.115	odd	12		234.2.y.a.11.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.2	✓	56	117.115	odd	12
234.2.y.a.149.2	yes	56	3.2	odd	2
234.2.z.a.167.13	yes	56	39.11	even	12
234.2.z.a.227.13	yes	56	9.7	even	3
702.2.bb.a.71.11		56	1.1	even	1	trivial
702.2.bb.a.89.11		56	117.11	even	12	inner
702.2.bc.a.305.4		56	9.2	odd	6
702.2.bc.a.557.4		56	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.653109 + 0.175000i) q^{5} +(-3.90017 + 1.04505i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.585562 - 0.338074i) q^{10} +(0.502310 - 0.502310i) q^{11} +(-2.29871 + 2.77775i) q^{13} +(-3.49679 - 2.01888i) q^{14} -1.00000 q^{16} +(-3.24443 - 5.61952i) q^{17} +(-0.253608 - 0.0679541i) q^{19} +(-0.175000 - 0.653109i) q^{20} +0.710373 q^{22} +(-0.860504 - 1.49044i) q^{23} +(-3.93420 + 2.27141i) q^{25} +(-3.58960 + 0.338733i) q^{26} +(-1.04505 - 3.90017i) q^{28} -1.28654i q^{29} +(1.04468 + 3.89881i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.67944 - 6.26776i) q^{34} +(2.36435 - 1.36506i) q^{35} +(-7.96159 + 2.13330i) q^{37} +(-0.131277 - 0.227379i) q^{38} +(0.338074 - 0.585562i) q^{40} +(-2.39802 + 8.94954i) q^{41} +(-5.67915 - 3.27886i) q^{43} +(0.502310 + 0.502310i) q^{44} +(0.445430 - 1.66237i) q^{46} +(9.07214 + 2.43087i) q^{47} +(8.05701 - 4.65172i) q^{49} +(-4.38803 - 1.17577i) q^{50} +(-2.77775 - 2.29871i) q^{52} +6.34328i q^{53} +(-0.240159 + 0.415967i) q^{55} +(2.01888 - 3.49679i) q^{56} +(0.909720 - 0.909720i) q^{58} +(3.52351 - 3.52351i) q^{59} +(-1.64932 + 2.85670i) q^{61} +(-2.01817 + 3.49557i) q^{62} -1.00000i q^{64} +(1.01520 - 2.21645i) q^{65} +(10.0909 + 2.70385i) q^{67} +(5.61952 - 3.24443i) q^{68} +(2.63709 + 0.706607i) q^{70} +(2.09577 - 7.82153i) q^{71} +(-1.40415 - 1.40415i) q^{73} +(-7.13817 - 4.12122i) q^{74} +(0.0679541 - 0.253608i) q^{76} +(-1.43416 + 2.48403i) q^{77} +(7.29283 + 12.6316i) q^{79} +(0.653109 - 0.175000i) q^{80} +(-8.02394 + 4.63262i) q^{82} +(-1.04760 + 3.90968i) q^{83} +(3.10238 + 3.10238i) q^{85} +(-1.69726 - 6.33427i) q^{86} +0.710373i q^{88} +(2.64065 + 9.85503i) q^{89} +(6.06248 - 13.2360i) q^{91} +(1.49044 - 0.860504i) q^{92} +(4.69609 + 8.13386i) q^{94} +0.177526 q^{95} +(0.520942 + 1.94418i) q^{97} +(8.98642 + 2.40791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Introduction

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