LMFDB - Embedded newform 702.2.g.d.451.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(451,702)] 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("702.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [12,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.157365759791601.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{10} + 11x^{8} - 6x^{7} - 17x^{6} - 12x^{5} + 44x^{4} + 16x^{2} - 96x + 64 $ x^12 - 3x^11 + x^10 + 11x^8 - 6x^7 - 17x^6 - 12x^5 + 44x^4 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.4
Root			$1.25202 - 0.657613i$ of defining polynomial
Character	$\chi$	$=$	702.451
Dual form			702.2.g.d.523.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.635090 - 1.10001i) q^{5} -1.83842 q^{7} -1.00000 q^{8} +(0.635090 - 1.10001i) q^{10} +(-2.49362 - 4.31907i) q^{11} +(3.10824 - 1.82725i) q^{13} +(-0.919212 - 1.59212i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.76636 - 3.05943i) q^{17} +(0.245787 + 0.425715i) q^{19} +1.27018 q^{20} +(2.49362 - 4.31907i) q^{22} -0.105878 q^{23} +(1.69332 - 2.93292i) q^{25} +(3.13656 + 1.77819i) q^{26} +(0.919212 - 1.59212i) q^{28} +(-4.15087 - 7.18951i) q^{29} +(2.94508 + 5.10103i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.76636 - 3.05943i) q^{34} +(1.16756 + 2.02228i) q^{35} +(0.354597 - 0.614179i) q^{37} +(-0.245787 + 0.425715i) q^{38} +(0.635090 + 1.10001i) q^{40} +4.72491 q^{41} -8.11941 q^{43} +4.98723 q^{44} +(-0.0529389 - 0.0916929i) q^{46} +(4.67263 - 8.09324i) q^{47} -3.62020 q^{49} +3.38664 q^{50} +(0.0283227 + 3.60544i) q^{52} -4.00295 q^{53} +(-3.16734 + 5.48600i) q^{55} +1.83842 q^{56} +(4.15087 - 7.18951i) q^{58} +(-4.77135 + 8.26423i) q^{59} -6.35471 q^{61} +(-2.94508 + 5.10103i) q^{62} +1.00000 q^{64} +(-3.98400 - 2.25862i) q^{65} +6.00235 q^{67} +3.53272 q^{68} +(-1.16756 + 2.02228i) q^{70} +(-0.142948 - 0.247594i) q^{71} +10.7906 q^{73} +0.709193 q^{74} -0.491573 q^{76} +(4.58432 + 7.94028i) q^{77} +(4.96331 - 8.59671i) q^{79} +(-0.635090 + 1.10001i) q^{80} +(2.36245 + 4.09189i) q^{82} +(-6.39507 + 11.0766i) q^{83} +(-2.24360 + 3.88603i) q^{85} +(-4.05970 - 7.03161i) q^{86} +(2.49362 + 4.31907i) q^{88} +(6.30723 - 10.9244i) q^{89} +(-5.71426 + 3.35926i) q^{91} +(0.0529389 - 0.0916929i) q^{92} +9.34527 q^{94} +(0.312193 - 0.540735i) q^{95} -6.74408 q^{97} +(-1.81010 - 3.13519i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - q^{5} + 10 q^{7} - 12 q^{8} + q^{10} - 8 q^{11} + 8 q^{13} + 5 q^{14} - 6 q^{16} - 3 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} + 2 q^{23} - 13 q^{25} + q^{26} - 5 q^{28} - q^{29}+ \cdots + 3 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - q^5 + 10 * q^7 - 12 * q^8 + q^10 - 8 * q^11 + 8 * q^13 + 5 * q^14 - 6 * q^16 - 3 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 + 2 * q^23 - 13 * q^25 + q^26 - 5 * q^28 - q^29 - 14 * q^31 + 6 * q^32 + 3 * q^34 + 5 * q^35 - 7 * q^37 + 7 * q^38 + q^40 + 18 * q^41 + 16 * q^43 + 16 * q^44 + q^46 + 13 * q^47 + 6 * q^49 - 26 * q^50 - 7 * q^52 + 12 * q^53 - 20 * q^55 - 10 * q^56 + q^58 - 4 * q^59 - 56 * q^61 + 14 * q^62 + 12 * q^64 + 7 * q^65 - 8 * q^67 + 6 * q^68 - 5 * q^70 + 13 * q^71 + 54 * q^73 - 14 * q^74 + 14 * q^76 + 4 * q^77 - 6 * q^79 - q^80 + 9 * q^82 - 30 * q^83 - 9 * q^85 + 8 * q^86 + 8 * q^88 - 3 * q^89 - 12 * q^91 - q^92 + 26 * q^94 + 21 * q^95 + 48 * q^97 + 3 * q^98

Character values

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

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.635090	−	1.10001i	−0.284021	−	0.491939i	0.688350	−	0.725378i	$-0.258335\pi$
$5$	−0.635090	−	1.10001i	−0.284021	−	0.491939i	−0.972371	+	0.233440i	$0.925002\pi$
$6$		0			0
$7$	−1.83842			−0.694859			−0.347429	−	0.937706i	$-0.612945\pi$
$7$	−1.83842			−0.694859			−0.347429	+	0.937706i	$0.612945\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.635090	−	1.10001i	0.200833	−	0.347853i
$11$	−2.49362	−	4.31907i	−0.751853	−	1.30225i	−0.946923	−	0.321459i	$-0.895827\pi$
$11$	−2.49362	−	4.31907i	−0.751853	−	1.30225i	0.195070	−	0.980789i	$-0.437507\pi$
$12$		0			0
$13$	3.10824	−	1.82725i	0.862071	−	0.506787i
$13$	3.10824	−	1.82725i	0.862071	−	0.506787i
$14$	−0.919212	−	1.59212i	−0.245670	−	0.425512i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.76636	−	3.05943i	−0.428406	−	0.742021i	0.568326	−	0.822804i	$-0.307591\pi$
$17$	−1.76636	−	3.05943i	−0.428406	−	0.742021i	−0.996732	+	0.0807829i	$0.974258\pi$
$18$		0			0
$19$	0.245787	+	0.425715i	0.0563873	+	0.0976657i	0.892841	−	0.450372i	$-0.148708\pi$
$19$	0.245787	+	0.425715i	0.0563873	+	0.0976657i	−0.836454	+	0.548037i	$0.815375\pi$
$20$	1.27018			0.284021
$21$		0			0
$22$	2.49362	−	4.31907i	0.531641	−	0.920829i
$23$	−0.105878			−0.0220771			−0.0110385	−	0.999939i	$-0.503514\pi$
$23$	−0.105878			−0.0220771			−0.0110385	+	0.999939i	$0.503514\pi$
$24$		0			0
$25$	1.69332	−	2.93292i	0.338664	−	0.586584i
$26$	3.13656	+	1.77819i	0.615131	+	0.348732i
$27$		0			0
$28$	0.919212	−	1.59212i	0.173715	−	0.300883i
$29$	−4.15087	−	7.18951i	−0.770797	−	1.33506i	−0.937127	−	0.348989i	$-0.886525\pi$
$29$	−4.15087	−	7.18951i	−0.770797	−	1.33506i	0.166330	−	0.986070i	$-0.446808\pi$
$30$		0			0
$31$	2.94508	+	5.10103i	0.528952	+	0.916171i	0.999430	+	0.0337598i	$0.0107481\pi$
$31$	2.94508	+	5.10103i	0.528952	+	0.916171i	−0.470478	+	0.882412i	$0.655919\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	1.76636	−	3.05943i	0.302929	−	0.524688i
$35$	1.16756	+	2.02228i	0.197354	+	0.341828i
$36$		0			0
$37$	0.354597	−	0.614179i	0.0582953	−	0.100970i	−0.835405	−	0.549635i	$-0.814767\pi$
$37$	0.354597	−	0.614179i	0.0582953	−	0.100970i	0.893700	+	0.448664i	$0.148100\pi$
$38$	−0.245787	+	0.425715i	−0.0398719	+	0.0690601i
$39$		0			0
$40$	0.635090	+	1.10001i	0.100417	+	0.173927i
$41$	4.72491			0.737907			0.368953	−	0.929448i	$-0.379716\pi$
$41$	4.72491			0.737907			0.368953	+	0.929448i	$0.379716\pi$
$42$		0			0
$43$	−8.11941			−1.23820			−0.619099	−	0.785313i	$-0.712502\pi$
$43$	−8.11941			−1.23820			−0.619099	+	0.785313i	$0.712502\pi$
$44$	4.98723			0.751853
$45$		0			0
$46$	−0.0529389	−	0.0916929i	−0.00780542	−	0.0135194i
$47$	4.67263	−	8.09324i	0.681574	−	1.18052i	−0.292927	−	0.956135i	$-0.594629\pi$
$47$	4.67263	−	8.09324i	0.681574	−	1.18052i	0.974500	−	0.224385i	$-0.0720374\pi$
$48$		0			0
$49$	−3.62020			−0.517172
$50$	3.38664			0.478943
$51$		0			0
$52$	0.0283227	+	3.60544i	0.00392765	+	0.499985i
$53$	−4.00295			−0.549847			−0.274924	−	0.961466i	$-0.588653\pi$
$53$	−4.00295			−0.549847			−0.274924	+	0.961466i	$0.588653\pi$
$54$		0			0
$55$	−3.16734	+	5.48600i	−0.427084	+	0.739732i
$56$	1.83842			0.245670
$57$		0			0
$58$	4.15087	−	7.18951i	0.545036	−	0.944029i
$59$	−4.77135	+	8.26423i	−0.621177	+	1.07591i	0.368090	+	0.929790i	$0.380012\pi$
$59$	−4.77135	+	8.26423i	−0.621177	+	1.07591i	−0.989267	+	0.146120i	$0.953321\pi$
$60$		0			0
$61$	−6.35471			−0.813637			−0.406818	−	0.913509i	$-0.633362\pi$
$61$	−6.35471			−0.813637			−0.406818	+	0.913509i	$0.633362\pi$
$62$	−2.94508	+	5.10103i	−0.374025	+	0.647831i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.98400	−	2.25862i	−0.494155	−	0.280148i
$66$		0			0
$67$	6.00235			0.733303			0.366652	−	0.930358i	$-0.380504\pi$
$67$	6.00235			0.733303			0.366652	+	0.930358i	$0.380504\pi$
$68$	3.53272			0.428406
$69$		0			0
$70$	−1.16756	+	2.02228i	−0.139551	+	0.241709i
$71$	−0.142948	−	0.247594i	−0.0169648	−	0.0293839i	0.857418	−	0.514620i	$-0.172067\pi$
$71$	−0.142948	−	0.247594i	−0.0169648	−	0.0293839i	−0.874383	+	0.485236i	$0.838734\pi$
$72$		0			0
$73$	10.7906			1.26294			0.631471	−	0.775399i	$-0.282451\pi$
$73$	10.7906			1.26294			0.631471	+	0.775399i	$0.282451\pi$
$74$	0.709193			0.0824420
$75$		0			0
$76$	−0.491573			−0.0563873
$77$	4.58432	+	7.94028i	0.522432	+	0.904878i
$78$		0			0
$79$	4.96331	−	8.59671i	0.558416	−	0.967205i	−0.439213	−	0.898383i	$-0.644743\pi$
$79$	4.96331	−	8.59671i	0.558416	−	0.967205i	0.997629	−	0.0688221i	$-0.0219241\pi$
$80$	−0.635090	+	1.10001i	−0.0710052	+	0.122985i
$81$		0			0
$82$	2.36245	+	4.09189i	0.260889	+	0.451874i
$83$	−6.39507	+	11.0766i	−0.701950	+	1.21581i	0.265831	+	0.964020i	$0.414354\pi$
$83$	−6.39507	+	11.0766i	−0.701950	+	1.21581i	−0.967781	+	0.251793i	$0.918980\pi$
$84$		0			0
$85$	−2.24360	+	3.88603i	−0.243352	+	0.421499i
$86$	−4.05970	−	7.03161i	−0.437769	−	0.758238i
$87$		0			0
$88$	2.49362	+	4.31907i	0.265820	+	0.460414i
$89$	6.30723	−	10.9244i	0.668565	−	1.15799i	−0.309740	−	0.950821i	$-0.600242\pi$
$89$	6.30723	−	10.9244i	0.668565	−	1.15799i	0.978305	−	0.207168i	$-0.0664246\pi$
$90$		0			0
$91$	−5.71426	+	3.35926i	−0.599017	+	0.352146i
$92$	0.0529389	−	0.0916929i	0.00551927	−	0.00955965i
$93$		0			0
$94$	9.34527			0.963891
$95$	0.312193	−	0.540735i	0.0320304	−	0.0554782i
$96$		0			0
$97$	−6.74408			−0.684757			−0.342379	−	0.939562i	$-0.611233\pi$
$97$	−6.74408			−0.684757			−0.342379	+	0.939562i	$0.611233\pi$
$98$	−1.81010	−	3.13519i	−0.182848	−	0.316702i
$99$		0			0
$100$	1.69332	+	2.93292i	0.169332	+	0.293292i
$101$	7.05673	+	12.2226i	0.702170	+	1.21619i	0.967703	+	0.252093i	$0.0811189\pi$
$101$	7.05673	+	12.2226i	0.702170	+	1.21619i	−0.265533	+	0.964102i	$0.585548\pi$
$102$		0			0
$103$	−6.75482	−	11.6997i	−0.665572	−	1.15280i	−0.979130	−	0.203235i	$-0.934854\pi$
$103$	−6.75482	−	11.6997i	−0.665572	−	1.15280i	0.313558	−	0.949569i	$-0.398479\pi$
$104$	−3.10824	+	1.82725i	−0.304788	+	0.179176i
$105$		0			0
$106$	−2.00147	−	3.46665i	−0.194400	−	0.336711i
$107$	−5.22920	+	9.05724i	−0.505526	+	0.875597i	0.494454	+	0.869204i	$0.335368\pi$
$107$	−5.22920	+	9.05724i	−0.505526	+	0.875597i	−0.999980	+	0.00639253i	$0.997965\pi$
$108$		0			0
$109$	14.9071			1.42784			0.713918	−	0.700229i	$-0.246919\pi$
$109$	14.9071			1.42784			0.713918	+	0.700229i	$0.246919\pi$
$110$	−6.33468			−0.603988
$111$		0			0
$112$	0.919212	+	1.59212i	0.0868573	+	0.150441i
$113$	−5.02912	+	8.71069i	−0.473100	+	0.819432i	−0.999526	−	0.0307883i	$-0.990198\pi$
$113$	−5.02912	+	8.71069i	−0.473100	+	0.819432i	0.526426	+	0.850221i	$0.323532\pi$
$114$		0			0
$115$	0.0672420	+	0.116467i	0.00627035	+	0.0108606i
$116$	8.30173			0.770797
$117$		0			0
$118$	−9.54271			−0.878477
$119$	3.24732	+	5.62453i	0.297681	+	0.515599i
$120$		0			0
$121$	−6.93624	+	12.0139i	−0.630567	+	1.09217i
$122$	−3.17735	−	5.50334i	−0.287664	−	0.498249i
$123$		0			0
$124$	−5.89016			−0.528952
$125$	−10.6525			−0.952793
$126$		0			0
$127$	−7.53526	+	13.0515i	−0.668646	+	1.15813i	0.309637	+	0.950855i	$0.399793\pi$
$127$	−7.53526	+	13.0515i	−0.668646	+	1.15813i	−0.978283	+	0.207274i	$0.933541\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.0359749	−	4.57956i	−0.00315521	−	0.401654i
$131$	−4.24537	−	7.35320i	−0.370920	−	0.642452i	0.618787	−	0.785559i	$-0.287624\pi$
$131$	−4.24537	−	7.35320i	−0.370920	−	0.642452i	−0.989707	+	0.143106i	$0.954291\pi$
$132$		0			0
$133$	−0.451860	−	0.782644i	−0.0391812	−	0.0678639i
$134$	3.00117	+	5.19818i	0.259262	+	0.449055i
$135$		0			0
$136$	1.76636	+	3.05943i	0.151464	+	0.262344i
$137$	3.86219			0.329969			0.164984	−	0.986296i	$-0.447243\pi$
$137$	3.86219			0.329969			0.164984	+	0.986296i	$0.447243\pi$
$138$		0			0
$139$	9.44950	−	16.3670i	0.801496	−	1.38823i	−0.117135	−	0.993116i	$-0.537371\pi$
$139$	9.44950	−	16.3670i	0.801496	−	1.38823i	0.918631	−	0.395116i	$-0.129296\pi$
$140$	−2.33513			−0.197354
$141$		0			0
$142$	0.142948	−	0.247594i	0.0119959	−	0.0207776i
$143$	−15.6428	−	8.86825i	−1.30811	−	0.741601i
$144$		0			0
$145$	−5.27235	+	9.13198i	−0.437845	+	0.758369i
$146$	5.39529	+	9.34492i	0.446517	+	0.773391i
$147$		0			0
$148$	0.354597	+	0.614179i	0.0291477	+	0.0504852i
$149$	4.79370	−	8.30294i	0.392716	−	0.680203i	−0.600091	−	0.799932i	$-0.704869\pi$
$149$	4.79370	−	8.30294i	0.392716	−	0.680203i	0.992807	+	0.119728i	$0.0382024\pi$
$150$		0			0
$151$	−10.0516	+	17.4100i	−0.817991	+	1.41680i	0.0891694	+	0.996016i	$0.471579\pi$
$151$	−10.0516	+	17.4100i	−0.817991	+	1.41680i	−0.907160	+	0.420785i	$0.861755\pi$
$152$	−0.245787	−	0.425715i	−0.0199359	−	0.0345300i
$153$		0			0
$154$	−4.58432	+	7.94028i	−0.369415	+	0.639846i
$155$	3.74078	−	6.47922i	0.300467	−	0.520424i
$156$		0			0
$157$	−8.89279	−	15.4028i	−0.709722	−	1.22927i	−0.964960	−	0.262396i	$-0.915487\pi$
$157$	−8.89279	−	15.4028i	−0.709722	−	1.22927i	0.255238	−	0.966878i	$-0.417846\pi$
$158$	9.92662			0.789720
$159$		0			0
$160$	−1.27018			−0.100417
$161$	0.194648			0.0153404
$162$		0			0
$163$	4.58291	+	7.93783i	0.358961	+	0.621739i	0.987788	−	0.155807i	$-0.0497977\pi$
$163$	4.58291	+	7.93783i	0.358961	+	0.621739i	−0.628826	+	0.777546i	$0.716464\pi$
$164$	−2.36245	+	4.09189i	−0.184477	+	0.319523i
$165$		0			0
$166$	−12.7901			−0.992707
$167$	13.2064			1.02194			0.510972	−	0.859597i	$-0.329286\pi$
$167$	13.2064			1.02194			0.510972	+	0.859597i	$0.329286\pi$
$168$		0			0
$169$	6.32233	−	11.3591i	0.486333	−	0.873774i
$170$	−4.48720			−0.344152
$171$		0			0
$172$	4.05970	−	7.03161i	0.309550	−	0.536156i
$173$	6.11874			0.465199			0.232600	−	0.972573i	$-0.425277\pi$
$173$	6.11874			0.465199			0.232600	+	0.972573i	$0.425277\pi$
$174$		0			0
$175$	−3.11304	+	5.39194i	−0.235324	+	0.407593i
$176$	−2.49362	+	4.31907i	−0.187963	+	0.325562i
$177$		0			0
$178$	12.6145			0.945494
$179$	−6.30514	+	10.9208i	−0.471268	+	0.816261i	−0.999460	−	0.0328647i	$-0.989537\pi$
$179$	−6.30514	+	10.9208i	−0.471268	+	0.816261i	0.528192	+	0.849125i	$0.322870\pi$
$180$		0			0
$181$	−13.8293			−1.02793			−0.513963	−	0.857812i	$-0.671823\pi$
$181$	−13.8293			−1.02793			−0.513963	+	0.857812i	$0.671823\pi$
$182$	−5.76633	−	3.26907i	−0.427429	−	0.242320i
$183$		0			0
$184$	0.105878			0.00780542
$185$	−0.900803			−0.0662284
$186$		0			0
$187$	−8.80926	+	15.2581i	−0.644197	+	1.11578i
$188$	4.67263	+	8.09324i	0.340787	+	0.590260i
$189$		0			0
$190$	0.624387			0.0452978
$191$	5.68784			0.411557			0.205779	−	0.978599i	$-0.434027\pi$
$191$	5.68784			0.411557			0.205779	+	0.978599i	$0.434027\pi$
$192$		0			0
$193$	9.90974			0.713318			0.356659	−	0.934235i	$-0.383916\pi$
$193$	9.90974			0.713318			0.356659	+	0.934235i	$0.383916\pi$
$194$	−3.37204	−	5.84054i	−0.242098	−	0.419326i
$195$		0			0
$196$	1.81010	−	3.13519i	0.129293	−	0.223942i
$197$	3.36448	−	5.82745i	0.239709	−	0.415189i	−0.720922	−	0.693017i	$-0.756281\pi$
$197$	3.36448	−	5.82745i	0.239709	−	0.415189i	0.960631	+	0.277828i	$0.0896145\pi$
$198$		0			0
$199$	−2.10185	−	3.64052i	−0.148996	−	0.258069i	0.781860	−	0.623454i	$-0.214271\pi$
$199$	−2.10185	−	3.64052i	−0.148996	−	0.258069i	−0.930857	+	0.365384i	$0.880938\pi$
$200$	−1.69332	+	2.93292i	−0.119736	+	0.207389i
$201$		0			0
$202$	−7.05673	+	12.2226i	−0.496509	+	0.859980i
$203$	7.63105	+	13.2174i	0.535595	+	0.927677i
$204$		0			0
$205$	−3.00074	−	5.19744i	−0.209581	−	0.363005i
$206$	6.75482	−	11.6997i	0.470630	−	0.815156i
$207$		0			0
$208$	−3.13656	−	1.77819i	−0.217482	−	0.123295i
$209$	1.22580	−	2.12314i	0.0847900	−	0.146861i
$210$		0			0
$211$	16.3392			1.12484			0.562419	−	0.826852i	$-0.309871\pi$
$211$	16.3392			1.12484			0.562419	+	0.826852i	$0.309871\pi$
$212$	2.00147	−	3.46665i	0.137462	−	0.238091i
$213$		0			0
$214$	−10.4584			−0.714922
$215$	5.15656	+	8.93142i	0.351674	+	0.609118i
$216$		0			0
$217$	−5.41430	−	9.37784i	−0.367547	−	0.636610i
$218$	7.45353	+	12.9099i	0.504816	+	0.874368i
$219$		0			0
$220$	−3.16734	−	5.48600i	−0.213542	−	0.369866i
$221$	−11.0806	−	6.28186i	−0.745363	−	0.422564i
$222$		0			0
$223$	6.36839	+	11.0304i	0.426459	+	0.738649i	0.996555	−	0.0829291i	$-0.0264275\pi$
$223$	6.36839	+	11.0304i	0.426459	+	0.738649i	−0.570096	+	0.821578i	$0.693094\pi$
$224$	−0.919212	+	1.59212i	−0.0614174	+	0.106378i
$225$		0			0
$226$	−10.0582			−0.669064
$227$	−2.88018			−0.191164			−0.0955821	−	0.995422i	$-0.530471\pi$
$227$	−2.88018			−0.191164			−0.0955821	+	0.995422i	$0.530471\pi$
$228$		0			0
$229$	−9.51562	−	16.4815i	−0.628810	−	1.08913i	−0.987791	−	0.155785i	$-0.950209\pi$
$229$	−9.51562	−	16.4815i	−0.628810	−	1.08913i	0.358981	−	0.933345i	$-0.383124\pi$
$230$	−0.0672420	+	0.116467i	−0.00443381	+	0.00767958i
$231$		0			0
$232$	4.15087	+	7.18951i	0.272518	+	0.472015i
$233$	24.8771			1.62975			0.814876	−	0.579635i	$-0.196805\pi$
$233$	24.8771			1.62975			0.814876	+	0.579635i	$0.196805\pi$
$234$		0			0
$235$	−11.8702			−0.774325
$236$	−4.77135	−	8.26423i	−0.310589	−	0.537955i
$237$		0			0
$238$	−3.24732	+	5.62453i	−0.210493	+	0.364584i
$239$	−7.81360	−	13.5336i	−0.505420	−	0.875413i	−0.999980	−	0.00626958i	$-0.998004\pi$
$239$	−7.81360	−	13.5336i	−0.505420	−	0.875413i	0.494561	−	0.869143i	$-0.335329\pi$
$240$		0			0
$241$	7.05329			0.454342			0.227171	−	0.973855i	$-0.427052\pi$
$241$	7.05329			0.454342			0.227171	+	0.973855i	$0.427052\pi$
$242$	−13.8725			−0.891757
$243$		0			0
$244$	3.17735	−	5.50334i	0.203409	−	0.352315i
$245$	2.29915	+	3.98225i	0.146888	+	0.254417i
$246$		0			0
$247$	1.54185	+	0.874112i	0.0981057	+	0.0556184i
$248$	−2.94508	−	5.10103i	−0.187013	−	0.323916i
$249$		0			0
$250$	−5.32627	−	9.22538i	−0.336863	−	0.583464i
$251$	7.65918	+	13.2661i	0.483443	+	0.837348i	0.999819	−	0.0190137i	$-0.00605260\pi$
$251$	7.65918	+	13.2661i	0.483443	+	0.837348i	−0.516376	+	0.856362i	$0.672719\pi$
$252$		0			0
$253$	0.264019	+	0.457294i	0.0165987	+	0.0287498i
$254$	−15.0705			−0.945609
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.0929			0.754336			0.377168	−	0.926145i	$-0.376898\pi$
$257$	12.0929			0.754336			0.377168	+	0.926145i	$0.376898\pi$
$258$		0			0
$259$	−0.651899	+	1.12912i	−0.0405070	+	0.0701602i
$260$	3.94803	−	2.32093i	0.244846	−	0.143938i
$261$		0			0
$262$	4.24537	−	7.35320i	0.262280	−	0.454282i
$263$	2.34113	+	4.05495i	0.144360	+	0.250039i	0.929134	−	0.369743i	$-0.120554\pi$
$263$	2.34113	+	4.05495i	0.144360	+	0.250039i	−0.784774	+	0.619782i	$0.787221\pi$
$264$		0			0
$265$	2.54223	+	4.40328i	0.156168	+	0.270491i
$266$	0.451860	−	0.782644i	0.0277053	−	0.0479870i
$267$		0			0
$268$	−3.00117	+	5.19818i	−0.183326	+	0.317530i
$269$	−7.84132	−	13.5816i	−0.478094	−	0.828083i	0.521591	−	0.853196i	$-0.325339\pi$
$269$	−7.84132	−	13.5816i	−0.478094	−	0.828083i	−0.999685	+	0.0251131i	$0.992005\pi$
$270$		0			0
$271$	5.71509	−	9.89882i	0.347167	−	0.601311i	−0.638578	−	0.769557i	$-0.720477\pi$
$271$	5.71509	−	9.89882i	0.347167	−	0.601311i	0.985745	+	0.168246i	$0.0538104\pi$
$272$	−1.76636	+	3.05943i	−0.107101	+	0.185505i
$273$		0			0
$274$	1.93109	+	3.34475i	0.116662	+	0.202064i
$275$	−16.8900			−1.01850
$276$		0			0
$277$	−3.75151			−0.225407			−0.112703	−	0.993629i	$-0.535951\pi$
$277$	−3.75151			−0.225407			−0.112703	+	0.993629i	$0.535951\pi$
$278$	18.8990			1.13349
$279$		0			0
$280$	−1.16756	−	2.02228i	−0.0697753	−	0.120854i
$281$	7.15098	−	12.3859i	0.426592	−	0.738878i	−0.569976	−	0.821661i	$-0.693048\pi$
$281$	7.15098	−	12.3859i	0.426592	−	0.738878i	0.996568	+	0.0827830i	$0.0263808\pi$
$282$		0			0
$283$	1.21112			0.0719936			0.0359968	−	0.999352i	$-0.488539\pi$
$283$	1.21112			0.0719936			0.0359968	+	0.999352i	$0.488539\pi$
$284$	0.285896			0.0169648
$285$		0			0
$286$	−0.141252	−	17.9812i	−0.00835239	−	1.06325i
$287$	−8.68638			−0.512741
$288$		0			0
$289$	2.25993	−	3.91431i	0.132937	−	0.230253i
$290$	−10.5447			−0.619206
$291$		0			0
$292$	−5.39529	+	9.34492i	−0.315736	+	0.546870i
$293$	−13.8829	+	24.0459i	−0.811048	+	1.40478i	0.101083	+	0.994878i	$0.467769\pi$
$293$	−13.8829	+	24.0459i	−0.811048	+	1.40478i	−0.912131	+	0.409898i	$0.865564\pi$
$294$		0			0
$295$	12.1210			0.705709
$296$	−0.354597	+	0.614179i	−0.0206105	+	0.0356985i
$297$		0			0
$298$	9.58741			0.555384
$299$	−0.329094	+	0.193465i	−0.0190320	+	0.0111884i
$300$		0			0
$301$	14.9269			0.860373
$302$	−20.1033			−1.15681
$303$		0			0
$304$	0.245787	−	0.425715i	0.0140968	−	0.0244164i
$305$	4.03581	+	6.99023i	0.231090	+	0.400260i
$306$		0			0
$307$	7.77480			0.443731			0.221866	−	0.975077i	$-0.428785\pi$
$307$	7.77480			0.443731			0.221866	+	0.975077i	$0.428785\pi$
$308$	−9.16864			−0.522432
$309$		0			0
$310$	7.48156			0.424924
$311$	6.18439	+	10.7117i	0.350684	+	0.607403i	0.986370	−	0.164545i	$-0.0526157\pi$
$311$	6.18439	+	10.7117i	0.350684	+	0.607403i	−0.635685	+	0.771948i	$0.719282\pi$
$312$		0			0
$313$	15.7073	−	27.2058i	0.887828	−	1.53776i	0.0453912	−	0.998969i	$-0.485547\pi$
$313$	15.7073	−	27.2058i	0.887828	−	1.53776i	0.842437	−	0.538795i	$-0.181120\pi$
$314$	8.89279	−	15.4028i	0.501849	−	0.869228i
$315$		0			0
$316$	4.96331	+	8.59671i	0.279208	+	0.483603i
$317$	2.86459	−	4.96162i	0.160892	−	0.278672i	−0.774297	−	0.632822i	$-0.781896\pi$
$317$	2.86459	−	4.96162i	0.160892	−	0.278672i	0.935189	+	0.354150i	$0.115230\pi$
$318$		0			0
$319$	−20.7013	+	35.8558i	−1.15905	+	2.00754i
$320$	−0.635090	−	1.10001i	−0.0355026	−	0.0614923i
$321$		0			0
$322$	0.0973242	+	0.168570i	0.00542366	+	0.00939406i
$323$	0.868297	−	1.50393i	0.0483133	−	0.0836811i
$324$		0			0
$325$	−0.0959188	−	12.2103i	−0.00532062	−	0.677307i
$326$	−4.58291	+	7.93783i	−0.253824	+	0.439636i
$327$		0			0
$328$	−4.72491			−0.260889
$329$	−8.59028	+	14.8788i	−0.473597	+	0.820295i
$330$		0			0
$331$	30.0179			1.64993			0.824967	−	0.565181i	$-0.191194\pi$
$331$	30.0179			1.64993			0.824967	+	0.565181i	$0.191194\pi$
$332$	−6.39507	−	11.0766i	−0.350975	−	0.607906i
$333$		0			0
$334$	6.60322	+	11.4371i	0.361312	+	0.625811i
$335$	−3.81203	−	6.60263i	−0.208273	−	0.360740i
$336$		0			0
$337$	14.8547	+	25.7291i	0.809187	+	1.40155i	0.913428	+	0.407000i	$0.133425\pi$
$337$	14.8547	+	25.7291i	0.809187	+	1.40155i	−0.104241	+	0.994552i	$0.533241\pi$
$338$	12.9984	−	0.204232i	0.707020	−	0.0111087i
$339$		0			0
$340$	−2.24360	−	3.88603i	−0.121676	−	0.210749i
$341$	14.6878	−	25.4400i	0.795388	−	1.37765i
$342$		0			0
$343$	19.5244			1.05422
$344$	8.11941			0.437769
$345$		0			0
$346$	3.05937	+	5.29899i	0.164473	+	0.284875i
$347$	13.4221	−	23.2478i	0.720537	−	1.24801i	−0.240247	−	0.970712i	$-0.577229\pi$
$347$	13.4221	−	23.2478i	0.720537	−	1.24801i	0.960785	−	0.277296i	$-0.0894381\pi$
$348$		0			0
$349$	−6.32664	−	10.9581i	−0.338657	−	0.586571i	0.645523	−	0.763741i	$-0.276639\pi$
$349$	−6.32664	−	10.9581i	−0.338657	−	0.586571i	−0.984180	+	0.177169i	$0.943306\pi$
$350$	−6.22608			−0.332798
$351$		0			0
$352$	−4.98723			−0.265820
$353$	4.22646	+	7.32045i	0.224952	+	0.389628i	0.956305	−	0.292371i	$-0.0944442\pi$
$353$	4.22646	+	7.32045i	0.224952	+	0.389628i	−0.731353	+	0.681999i	$0.761111\pi$
$354$		0			0
$355$	−0.181570	+	0.314488i	−0.00963673	+	0.0166913i
$356$	6.30723	+	10.9244i	0.334283	+	0.578995i
$357$		0			0
$358$	−12.6103			−0.666474
$359$	−0.450985			−0.0238021			−0.0119010	−	0.999929i	$-0.503788\pi$
$359$	−0.450985			−0.0238021			−0.0119010	+	0.999929i	$0.503788\pi$
$360$		0			0
$361$	9.37918	−	16.2452i	0.493641	−	0.855011i
$362$	−6.91466	−	11.9765i	−0.363427	−	0.629473i
$363$		0			0
$364$	−0.0520691	−	6.62832i	−0.00272916	−	0.347419i
$365$	−6.85299	−	11.8697i	−0.358702	−	0.621290i
$366$		0			0
$367$	4.68103	+	8.10778i	0.244348	+	0.423223i	0.961948	−	0.273232i	$-0.0880928\pi$
$367$	4.68103	+	8.10778i	0.244348	+	0.423223i	−0.717600	+	0.696455i	$0.754759\pi$
$368$	0.0529389	+	0.0916929i	0.00275963	+	0.00477982i
$369$		0			0
$370$	−0.450402	−	0.780119i	−0.0234153	−	0.0405564i
$371$	7.35911			0.382066
$372$		0			0
$373$	5.10507	−	8.84224i	0.264330	−	0.457834i	−0.703058	−	0.711133i	$-0.748182\pi$
$373$	5.10507	−	8.84224i	0.264330	−	0.457834i	0.967388	+	0.253299i	$0.0815157\pi$
$374$	−17.6185			−0.911032
$375$		0			0
$376$	−4.67263	+	8.09324i	−0.240973	+	0.417377i
$377$	−26.0389	−	14.7621i	−1.34107	−	0.760286i
$378$		0			0
$379$	10.3917	−	17.9990i	0.533787	−	0.924547i	−0.465434	−	0.885083i	$-0.654102\pi$
$379$	10.3917	−	17.9990i	0.533787	−	0.924547i	0.999221	−	0.0394638i	$-0.0125650\pi$
$380$	0.312193	+	0.540735i	0.0160152	+	0.0277391i
$381$		0			0
$382$	2.84392	+	4.92581i	0.145507	+	0.252026i
$383$	4.50114	−	7.79620i	0.229998	−	0.398367i	−0.727810	−	0.685779i	$-0.759462\pi$
$383$	4.50114	−	7.79620i	0.229998	−	0.398367i	0.957807	+	0.287412i	$0.0927949\pi$
$384$		0			0
$385$	5.82291	−	10.0856i	0.296763	−	0.514009i
$386$	4.95487	+	8.58208i	0.252196	+	0.436817i
$387$		0			0
$388$	3.37204	−	5.84054i	0.171189	−	0.296509i
$389$	16.0084	−	27.7273i	0.811657	−	1.40583i	−0.100046	−	0.994983i	$-0.531899\pi$
$389$	16.0084	−	27.7273i	0.811657	−	1.40583i	0.911704	−	0.410849i	$-0.134768\pi$
$390$		0			0
$391$	0.187019	+	0.323926i	0.00945794	+	0.0163816i
$392$	3.62020			0.182848
$393$		0			0
$394$	6.72896			0.339000
$395$	−12.6086			−0.634408
$396$		0			0
$397$	−17.0464	−	29.5252i	−0.855532	−	1.48183i	−0.876150	−	0.482038i	$-0.839897\pi$
$397$	−17.0464	−	29.5252i	−0.855532	−	1.48183i	0.0206177	−	0.999787i	$-0.493437\pi$
$398$	2.10185	−	3.64052i	0.105356	−	0.182483i
$399$		0			0
$400$	−3.38664			−0.169332
$401$	21.0324			1.05031			0.525154	−	0.851007i	$-0.324008\pi$
$401$	21.0324			1.05031			0.525154	+	0.851007i	$0.324008\pi$
$402$		0			0
$403$	18.4749	+	10.4738i	0.920298	+	0.521739i
$404$	−14.1135			−0.702170
$405$		0			0
$406$	−7.63105	+	13.2174i	−0.378723	+	0.655967i
$407$	−3.53691			−0.175318
$408$		0			0
$409$	3.86593	−	6.69600i	0.191158	−	0.331096i	−0.754476	−	0.656327i	$-0.772109\pi$
$409$	3.86593	−	6.69600i	0.191158	−	0.331096i	0.945634	+	0.325232i	$0.105442\pi$
$410$	3.00074	−	5.19744i	0.148196	−	0.256683i
$411$		0			0
$412$	13.5096			0.665572
$413$	8.77177	−	15.1931i	0.431630	−	0.747606i
$414$		0			0
$415$	16.2458			0.797474
$416$	−0.0283227	−	3.60544i	−0.00138863	−	0.176771i
$417$		0			0
$418$	2.45159			0.119911
$419$	1.95363			0.0954409			0.0477204	−	0.998861i	$-0.484804\pi$
$419$	1.95363			0.0954409			0.0477204	+	0.998861i	$0.484804\pi$
$420$		0			0
$421$	−5.83294	+	10.1030i	−0.284280	+	0.492388i	−0.972434	−	0.233177i	$-0.925088\pi$
$421$	−5.83294	+	10.1030i	−0.284280	+	0.492388i	0.688154	+	0.725564i	$0.258421\pi$
$422$	8.16961	+	14.1502i	0.397690	+	0.688820i
$423$		0			0
$424$	4.00295			0.194400
$425$	−11.9641			−0.580343
$426$		0			0
$427$	11.6826			0.565363
$428$	−5.22920	−	9.05724i	−0.252763	−	0.437798i
$429$		0			0
$430$	−5.15656	+	8.93142i	−0.248671	+	0.430711i
$431$	−17.8063	+	30.8415i	−0.857701	+	1.48558i	0.0164145	+	0.999865i	$0.494775\pi$
$431$	−17.8063	+	30.8415i	−0.857701	+	1.48558i	−0.874116	+	0.485717i	$0.838558\pi$
$432$		0			0
$433$	13.0186	+	22.5488i	0.625632	+	1.08363i	0.988418	+	0.151754i	$0.0484922\pi$
$433$	13.0186	+	22.5488i	0.625632	+	1.08363i	−0.362786	+	0.931872i	$0.618174\pi$
$434$	5.41430	−	9.37784i	0.259895	−	0.450151i
$435$		0			0
$436$	−7.45353	+	12.9099i	−0.356959	+	0.618271i
$437$	−0.0260234	−	0.0450738i	−0.00124487	−	0.00215617i
$438$		0			0
$439$	−9.85356	−	17.0669i	−0.470285	−	0.814557i	0.529138	−	0.848536i	$-0.322515\pi$
$439$	−9.85356	−	17.0669i	−0.470285	−	0.814557i	−0.999423	+	0.0339788i	$0.989182\pi$
$440$	3.16734	−	5.48600i	0.150997	−	0.261535i
$441$		0			0
$442$	−0.100056	−	12.7370i	−0.00475919	−	0.605839i
$443$	−13.8611	+	24.0081i	−0.658559	+	1.14066i	0.322430	+	0.946593i	$0.395500\pi$
$443$	−13.8611	+	24.0081i	−0.658559	+	1.14066i	−0.980989	+	0.194064i	$0.937833\pi$
$444$		0			0
$445$	−16.0226			−0.759546
$446$	−6.36839	+	11.0304i	−0.301552	+	0.522304i
$447$		0			0
$448$	−1.83842			−0.0868573
$449$	16.5142	+	28.6035i	0.779354	+	1.34988i	0.932314	+	0.361649i	$0.117786\pi$
$449$	16.5142	+	28.6035i	0.779354	+	1.34988i	−0.152960	+	0.988232i	$0.548881\pi$
$450$		0			0
$451$	−11.7821	−	20.4072i	−0.554798	−	0.960938i
$452$	−5.02912	−	8.71069i	−0.236550	−	0.409716i
$453$		0			0
$454$	−1.44009	−	2.49431i	−0.0675867	−	0.117064i
$455$	7.32428	+	4.15231i	0.343368	+	0.194663i
$456$		0			0
$457$	12.2986	+	21.3018i	0.575303	+	0.996455i	0.996009	+	0.0892574i	$0.0284494\pi$
$457$	12.2986	+	21.3018i	0.575303	+	0.996455i	−0.420705	+	0.907197i	$0.638217\pi$
$458$	9.51562	−	16.4815i	0.444635	−	0.770131i
$459$		0			0
$460$	−0.134484			−0.00627035
$461$	13.6445			0.635488			0.317744	−	0.948177i	$-0.397075\pi$
$461$	13.6445			0.635488			0.317744	+	0.948177i	$0.397075\pi$
$462$		0			0
$463$	−14.8595	−	25.7374i	−0.690579	−	1.19612i	−0.971648	−	0.236431i	$-0.924022\pi$
$463$	−14.8595	−	25.7374i	−0.690579	−	1.19612i	0.281069	−	0.959688i	$-0.409311\pi$
$464$	−4.15087	+	7.18951i	−0.192699	+	0.333765i
$465$		0			0
$466$	12.4385	+	21.5442i	0.576205	+	0.998016i
$467$	7.00001			0.323922			0.161961	−	0.986797i	$-0.448218\pi$
$467$	7.00001			0.323922			0.161961	+	0.986797i	$0.448218\pi$
$468$		0			0
$469$	−11.0348			−0.509542
$470$	−5.93509	−	10.2799i	−0.273765	−	0.474175i
$471$		0			0
$472$	4.77135	−	8.26423i	0.219619	−	0.380392i
$473$	20.2467	+	35.0683i	0.930944	+	1.61244i
$474$		0			0
$475$	1.66478			0.0763855
$476$	−6.49464			−0.297681
$477$		0			0
$478$	7.81360	−	13.5336i	0.357386	−	0.619010i
$479$	−18.8400	−	32.6319i	−0.860823	−	1.49099i	−0.871136	−	0.491042i	$-0.836616\pi$
$479$	−18.8400	−	32.6319i	−0.860823	−	1.49099i	0.0103133	−	0.999947i	$-0.496717\pi$
$480$		0			0
$481$	−0.0200863	−	2.55695i	−0.000915855	−	0.116587i
$482$	3.52665	+	6.10833i	0.160634	+	0.278227i
$483$		0			0
$484$	−6.93624	−	12.0139i	−0.315284	−	0.546087i
$485$	4.28310	+	7.41854i	0.194485	+	0.336859i
$486$		0			0
$487$	−11.0287	−	19.1023i	−0.499758	−	0.865607i	0.500242	−	0.865886i	$-0.333245\pi$
$487$	−11.0287	−	19.1023i	−0.499758	−	0.865607i	−1.00000		0.000279059i	$0.999911\pi$
$488$	6.35471			0.287664
$489$		0			0
$490$	−2.29915	+	3.98225i	−0.103865	+	0.179900i
$491$	−43.5898			−1.96718			−0.983590	−	0.180419i	$-0.942255\pi$
$491$	−43.5898			−1.96718			−0.983590	+	0.180419i	$0.942255\pi$
$492$		0			0
$493$	−14.6639	+	25.3986i	−0.660428	+	1.14389i
$494$	0.0139227	+	1.77234i	0.000626411	+	0.0797413i
$495$		0			0
$496$	2.94508	−	5.10103i	0.132238	−	0.229043i
$497$	0.262799	+	0.455182i	0.0117882	+	0.0204177i
$498$		0			0
$499$	−1.25644	−	2.17622i	−0.0562461	−	0.0974211i	0.836531	−	0.547919i	$-0.184580\pi$
$499$	−1.25644	−	2.17622i	−0.0562461	−	0.0974211i	−0.892777	+	0.450498i	$0.851246\pi$
$500$	5.32627	−	9.22538i	0.238198	−	0.412571i
$501$		0			0
$502$	−7.65918	+	13.2661i	−0.341846	+	0.592095i
$503$	−5.78135	−	10.0136i	−0.257778	−	0.446484i	0.707869	−	0.706344i	$-0.249657\pi$
$503$	−5.78135	−	10.0136i	−0.257778	−	0.446484i	−0.965646	+	0.259860i	$0.916324\pi$
$504$		0			0
$505$	8.96331	−	15.5249i	0.398862	−	0.690850i
$506$	−0.264019	+	0.457294i	−0.0117371	+	0.0203292i
$507$		0			0
$508$	−7.53526	−	13.0515i	−0.334323	−	0.579065i
$509$	6.39064			0.283260			0.141630	−	0.989920i	$-0.454766\pi$
$509$	6.39064			0.283260			0.141630	+	0.989920i	$0.454766\pi$
$510$		0			0
$511$	−19.8377			−0.877566
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.04646	+	10.4728i	0.266698	+	0.461935i
$515$	−8.57984	+	14.8607i	−0.378073	+	0.654841i
$516$		0			0
$517$	−46.6070			−2.04977
$518$	−1.30380			−0.0572856
$519$		0			0
$520$	3.98400	+	2.25862i	0.174710	+	0.0990472i
$521$	9.47288			0.415014			0.207507	−	0.978234i	$-0.433465\pi$
$521$	9.47288			0.415014			0.207507	+	0.978234i	$0.433465\pi$
$522$		0			0
$523$	−18.4125	+	31.8914i	−0.805122	+	1.39451i	0.111087	+	0.993811i	$0.464567\pi$
$523$	−18.4125	+	31.8914i	−0.805122	+	1.39451i	−0.916209	+	0.400702i	$0.868766\pi$
$524$	8.49075			0.370920
$525$		0			0
$526$	−2.34113	+	4.05495i	−0.102078	+	0.176804i
$527$	10.4042	−	18.0205i	0.453212	−	0.784986i
$528$		0			0
$529$	−22.9888			−0.999513
$530$	−2.54223	+	4.40328i	−0.110428	+	0.191266i
$531$		0			0
$532$	0.903720			0.0391812
$533$	14.6862	−	8.63358i	0.636128	−	0.373962i
$534$		0			0
$535$	13.2841			0.574320
$536$	−6.00235			−0.259262
$537$		0			0
$538$	7.84132	−	13.5816i	0.338063	−	0.585543i
$539$	9.02739	+	15.6359i	0.388837	+	0.673486i
$540$		0			0
$541$	−11.5112			−0.494903			−0.247452	−	0.968900i	$-0.579593\pi$
$541$	−11.5112			−0.494903			−0.247452	+	0.968900i	$0.579593\pi$
$542$	11.4302			0.490968
$543$		0			0
$544$	−3.53272			−0.151464
$545$	−9.46732	−	16.3979i	−0.405536	−	0.702408i
$546$		0			0
$547$	12.1922	−	21.1175i	0.521300	−	0.902917i	−0.478394	−	0.878146i	$-0.658781\pi$
$547$	12.1922	−	21.1175i	0.521300	−	0.902917i	0.999693	−	0.0247717i	$-0.00788589\pi$
$548$	−1.93109	+	3.34475i	−0.0824922	+	0.142881i
$549$		0			0
$550$	−8.44498	−	14.6271i	−0.360095	−	0.623703i
$551$	2.04046	−	3.53417i	0.0869263	−	0.150561i
$552$		0			0
$553$	−9.12467	+	15.8044i	−0.388020	+	0.672071i
$554$	−1.87576	−	3.24891i	−0.0796933	−	0.138033i
$555$		0			0
$556$	9.44950	+	16.3670i	0.400748	+	0.694116i
$557$	3.91467	−	6.78040i	0.165870	−	0.287295i	−0.771094	−	0.636721i	$-0.780290\pi$
$557$	3.91467	−	6.78040i	0.165870	−	0.287295i	0.936964	+	0.349426i	$0.113624\pi$
$558$		0			0
$559$	−25.2371	+	14.8362i	−1.06741	+	0.627503i
$560$	1.16756	−	2.02228i	0.0493386	−	0.0854570i
$561$		0			0
$562$	14.3020			0.603292
$563$	6.94941	−	12.0367i	0.292883	−	0.507287i	−0.681608	−	0.731718i	$-0.738719\pi$
$563$	6.94941	−	12.0367i	0.292883	−	0.507287i	0.974490	+	0.224430i	$0.0720522\pi$
$564$		0			0
$565$	12.7758			0.537481
$566$	0.605560	+	1.04886i	0.0254536	+	0.0440869i
$567$		0			0
$568$	0.142948	+	0.247594i	0.00599797	+	0.0103888i
$569$	17.7140	+	30.6815i	0.742609	+	1.28624i	0.951303	+	0.308256i	$0.0997453\pi$
$569$	17.7140	+	30.6815i	0.742609	+	1.28624i	−0.208694	+	0.977981i	$0.566921\pi$
$570$		0			0
$571$	−4.61965	−	8.00146i	−0.193326	−	0.334851i	0.753024	−	0.657993i	$-0.228594\pi$
$571$	−4.61965	−	8.00146i	−0.193326	−	0.334851i	−0.946351	+	0.323142i	$0.895261\pi$
$572$	15.5015	−	9.11291i	0.648151	−	0.381030i
$573$		0			0
$574$	−4.34319	−	7.52263i	−0.181281	−	0.313988i
$575$	−0.179285	+	0.310531i	−0.00747671	+	0.0129500i
$576$		0			0
$577$	−22.1603			−0.922547			−0.461273	−	0.887258i	$-0.652607\pi$
$577$	−22.1603			−0.922547			−0.461273	+	0.887258i	$0.652607\pi$
$578$	4.51986			0.188001
$579$		0			0
$580$	−5.27235	−	9.13198i	−0.218922	−	0.379185i
$581$	11.7568	−	20.3634i	0.487756	−	0.844818i
$582$		0			0
$583$	9.98181	+	17.2890i	0.413404	+	0.716038i
$584$	−10.7906			−0.446517
$585$		0			0
$586$	−27.7658			−1.14699
$587$	−10.3280	−	17.8886i	−0.426281	−	0.738340i	0.570258	−	0.821466i	$-0.306843\pi$
$587$	−10.3280	−	17.8886i	−0.426281	−	0.738340i	−0.996539	+	0.0831252i	$0.973510\pi$
$588$		0			0
$589$	−1.44772	+	2.50753i	−0.0596524	+	0.103321i
$590$	6.06048	+	10.4971i	0.249506	+	0.432157i
$591$		0			0
$592$	−0.709193			−0.0291477
$593$	−18.5090			−0.760072			−0.380036	−	0.924972i	$-0.624088\pi$
$593$	−18.5090			−0.760072			−0.380036	+	0.924972i	$0.624088\pi$
$594$		0			0
$595$	4.12468	−	7.14416i	0.169096	−	0.292882i
$596$	4.79370	+	8.30294i	0.196358	+	0.340102i
$597$		0			0
$598$	−0.332093	−	0.188271i	−0.0135803	−	0.00769898i
$599$	−11.4353	−	19.8065i	−0.467233	−	0.809272i	0.532066	−	0.846703i	$-0.321416\pi$
$599$	−11.4353	−	19.8065i	−0.467233	−	0.809272i	−0.999299	+	0.0374312i	$0.988083\pi$
$600$		0			0
$601$	−11.5959	−	20.0847i	−0.473006	−	0.819271i	0.526516	−	0.850165i	$-0.323498\pi$
$601$	−11.5959	−	20.0847i	−0.473006	−	0.819271i	−0.999523	+	0.0308942i	$0.990165\pi$
$602$	7.46345	+	12.9271i	0.304188	+	0.526869i
$603$		0			0
$604$	−10.0516	−	17.4100i	−0.408995	−	0.708401i
$605$	17.6206			0.716377
$606$		0			0
$607$	−17.4519	+	30.2276i	−0.708352	+	1.22690i	0.257116	+	0.966381i	$0.417228\pi$
$607$	−17.4519	+	30.2276i	−0.708352	+	1.22690i	−0.965468	+	0.260522i	$0.916105\pi$
$608$	0.491573			0.0199359
$609$		0			0
$610$	−4.03581	+	6.99023i	−0.163405	+	0.283026i
$611$	−0.264683	−	33.6938i	−0.0107079	−	1.36311i
$612$		0			0
$613$	−16.5093	+	28.5949i	−0.666803	+	1.15494i	0.311990	+	0.950085i	$0.399005\pi$
$613$	−16.5093	+	28.5949i	−0.666803	+	1.15494i	−0.978793	+	0.204852i	$0.934329\pi$
$614$	3.88740	+	6.73318i	0.156883	+	0.271729i
$615$		0			0
$616$	−4.58432	−	7.94028i	−0.184708	−	0.319923i
$617$	−17.7708	+	30.7799i	−0.715426	+	1.23915i	0.247369	+	0.968921i	$0.420434\pi$
$617$	−17.7708	+	30.7799i	−0.715426	+	1.23915i	−0.962795	+	0.270233i	$0.912899\pi$
$618$		0			0
$619$	16.0147	−	27.7383i	0.643685	−	1.11490i	−0.340919	−	0.940093i	$-0.610738\pi$
$619$	16.0147	−	27.7383i	0.643685	−	1.11490i	0.984604	−	0.174802i	$-0.0559286\pi$
$620$	3.74078	+	6.47922i	0.150233	+	0.260212i
$621$		0			0
$622$	−6.18439	+	10.7117i	−0.247971	+	0.429499i
$623$	−11.5954	+	20.0838i	−0.464558	+	0.804639i
$624$		0			0
$625$	−1.70128	−	2.94670i	−0.0680510	−	0.117868i
$626$	31.4146			1.25558
$627$		0			0
$628$	17.7856			0.709722
$629$	−2.50538			−0.0998962
$630$		0			0
$631$	6.46046	+	11.1898i	0.257187	+	0.445461i	0.965487	−	0.260451i	$-0.0838711\pi$
$631$	6.46046	+	11.1898i	0.257187	+	0.445461i	−0.708300	+	0.705911i	$0.750538\pi$
$632$	−4.96331	+	8.59671i	−0.197430	+	0.341959i
$633$		0			0
$634$	5.72918			0.227535
$635$	19.1423			0.759638
$636$		0			0
$637$	−11.2525	+	6.61501i	−0.445839	+	0.262096i
$638$	−41.4027			−1.63915
$639$		0			0
$640$	0.635090	−	1.10001i	0.0251041	−	0.0434817i
$641$	−31.8124			−1.25651			−0.628257	−	0.778006i	$-0.716231\pi$
$641$	−31.8124			−1.25651			−0.628257	+	0.778006i	$0.716231\pi$
$642$		0			0
$643$	−19.1721	+	33.2071i	−0.756075	+	1.30956i	0.188763	+	0.982023i	$0.439552\pi$
$643$	−19.1721	+	33.2071i	−0.756075	+	1.30956i	−0.944838	+	0.327538i	$0.893781\pi$
$644$	−0.0973242	+	0.168570i	−0.00383511	+	0.00664260i
$645$		0			0
$646$	1.73659			0.0683254
$647$	−12.2147	+	21.1565i	−0.480210	+	0.831749i	−0.999742	−	0.0227022i	$-0.992773\pi$
$647$	−12.2147	+	21.1565i	−0.480210	+	0.831749i	0.519532	+	0.854451i	$0.326106\pi$
$648$		0			0
$649$	47.5917			1.86814
$650$	10.5265	−	6.18824i	0.412883	−	0.242723i
$651$		0			0
$652$	−9.16582			−0.358961
$653$	13.2244			0.517512			0.258756	−	0.965943i	$-0.416687\pi$
$653$	13.2244			0.517512			0.258756	+	0.965943i	$0.416687\pi$
$654$		0			0
$655$	−5.39239	+	9.33989i	−0.210698	+	0.364940i
$656$	−2.36245	−	4.09189i	−0.0922384	−	0.159762i
$657$		0			0
$658$	−17.1806			−0.669768
$659$	−24.7130			−0.962682			−0.481341	−	0.876534i	$-0.659850\pi$
$659$	−24.7130			−0.962682			−0.481341	+	0.876534i	$0.659850\pi$
$660$		0			0
$661$	49.8661			1.93957			0.969784	−	0.243965i	$-0.0784482\pi$
$661$	49.8661			1.93957			0.969784	+	0.243965i	$0.0784482\pi$
$662$	15.0090	+	25.9963i	0.583340	+	1.01037i
$663$		0			0
$664$	6.39507	−	11.0766i	0.248177	−	0.429855i
$665$	−0.573944	+	0.994099i	−0.0222566	+	0.0385495i
$666$		0			0
$667$	0.439485	+	0.761210i	0.0170169	+	0.0294742i
$668$	−6.60322	+	11.4371i	−0.255486	+	0.442515i
$669$		0			0
$670$	3.81203	−	6.60263i	0.147272	−	0.255082i
$671$	15.8462	+	27.4464i	0.611736	+	1.05956i
$672$		0			0
$673$	15.7069	+	27.2052i	0.605457	+	1.04868i	0.991979	+	0.126402i	$0.0403429\pi$
$673$	15.7069	+	27.2052i	0.605457	+	1.04868i	−0.386522	+	0.922280i	$0.626324\pi$
$674$	−14.8547	+	25.7291i	−0.572181	+	0.991047i
$675$		0			0
$676$	6.67607	+	11.1548i	0.256772	+	0.429032i
$677$	−10.3977	+	18.0094i	−0.399617	+	0.692157i	−0.993679	−	0.112262i	$-0.964190\pi$
$677$	−10.3977	+	18.0094i	−0.399617	+	0.692157i	0.594061	+	0.804420i	$0.297524\pi$
$678$		0			0
$679$	12.3985			0.475809
$680$	2.24360	−	3.88603i	0.0860381	−	0.149022i
$681$		0			0
$682$	29.3756			1.12485
$683$	13.7499	+	23.8155i	0.526125	+	0.911275i	0.999537	+	0.0304336i	$0.00968882\pi$
$683$	13.7499	+	23.8155i	0.526125	+	0.911275i	−0.473412	+	0.880841i	$0.656978\pi$
$684$		0			0
$685$	−2.45284	−	4.24844i	−0.0937181	−	0.162325i
$686$	9.76221	+	16.9086i	0.372723	+	0.645575i
$687$		0			0
$688$	4.05970	+	7.03161i	0.154775	+	0.268078i
$689$	−12.4421	+	7.31438i	−0.474007	+	0.278656i
$690$		0			0
$691$	8.16734	+	14.1463i	0.310700	+	0.538149i	0.978514	−	0.206180i	$-0.0661031\pi$
$691$	8.16734	+	14.1463i	0.310700	+	0.538149i	−0.667814	+	0.744328i	$0.732770\pi$
$692$	−3.05937	+	5.29899i	−0.116300	+	0.201437i
$693$		0			0
$694$	26.8442			1.01899
$695$	−24.0051			−0.910567
$696$		0			0
$697$	−8.34590	−	14.4555i	−0.316124	−	0.547542i
$698$	6.32664	−	10.9581i	0.239467	−	0.414769i
$699$		0			0
$700$	−3.11304	−	5.39194i	−0.117662	−	0.203796i
$701$	−31.5990			−1.19348			−0.596740	−	0.802435i	$-0.703537\pi$
$701$	−31.5990			−1.19348			−0.596740	+	0.802435i	$0.703537\pi$
$702$		0			0
$703$	0.348621			0.0131485
$704$	−2.49362	−	4.31907i	−0.0939817	−	0.162781i
$705$		0			0
$706$	−4.22646	+	7.32045i	−0.159065	+	0.275509i
$707$	−12.9732	−	22.4703i	−0.487909	−	0.845083i
$708$		0			0
$709$	40.2134			1.51025			0.755124	−	0.655582i	$-0.227577\pi$
$709$	40.2134			1.51025			0.755124	+	0.655582i	$0.227577\pi$
$710$	−0.363140			−0.0136284
$711$		0			0
$712$	−6.30723	+	10.9244i	−0.236374	+	0.409411i
$713$	−0.311819	−	0.540086i	−0.0116777	−	0.0202264i
$714$		0			0
$715$	0.179415	+	22.8393i	0.00670975	+	0.854142i
$716$	−6.30514	−	10.9208i	−0.235634	−	0.408130i
$717$		0			0
$718$	−0.225492	−	0.390564i	−0.00841530	−	0.0145757i
$719$	15.0346	+	26.0407i	0.560696	+	0.971154i	0.997436	+	0.0715659i	$0.0227996\pi$
$719$	15.0346	+	26.0407i	0.560696	+	0.971154i	−0.436740	+	0.899588i	$0.643867\pi$
$720$		0			0
$721$	12.4182	+	21.5090i	0.462478	+	0.801036i
$722$	18.7584			0.698114
$723$		0			0
$724$	6.91466	−	11.9765i	0.256981	−	0.445105i
$725$	−28.1150			−1.04416
$726$		0			0
$727$	−1.50339	+	2.60394i	−0.0557575	+	0.0965748i	−0.892557	−	0.450935i	$-0.851091\pi$
$727$	−1.50339	+	2.60394i	−0.0557575	+	0.0965748i	0.836799	+	0.547510i	$0.184424\pi$
$728$	5.71426	−	3.35926i	0.211785	−	0.124502i
$729$		0			0
$730$	6.85299	−	11.8697i	0.253641	−	0.439318i
$731$	14.3418	+	24.8408i	0.530451	+	0.918769i
$732$		0			0
$733$	−8.43374	−	14.6077i	−0.311507	−	0.539547i	0.667181	−	0.744895i	$-0.267501\pi$
$733$	−8.43374	−	14.6077i	−0.311507	−	0.539547i	−0.978689	+	0.205349i	$0.934167\pi$
$734$	−4.68103	+	8.10778i	−0.172780	+	0.299264i
$735$		0			0
$736$	−0.0529389	+	0.0916929i	−0.00195136	+	0.00337985i
$737$	−14.9675	−	25.9245i	−0.551337	−	0.954943i
$738$		0			0
$739$	−4.30617	+	7.45851i	−0.158405	+	0.274366i	−0.934294	−	0.356504i	$-0.883969\pi$
$739$	−4.30617	+	7.45851i	−0.158405	+	0.274366i	0.775889	+	0.630870i	$0.217302\pi$
$740$	0.450402	−	0.780119i	0.0165571	−	0.0286777i
$741$		0			0
$742$	3.67956	+	6.37318i	0.135081	+	0.233967i
$743$	30.2390			1.10936			0.554681	−	0.832063i	$-0.312840\pi$
$743$	30.2390			1.10936			0.554681	+	0.832063i	$0.312840\pi$
$744$		0			0
$745$	−12.1777			−0.446158
$746$	10.2101			0.373820
$747$		0			0
$748$	−8.80926	−	15.2581i	−0.322098	−	0.557891i
$749$	9.61348	−	16.6510i	0.351269	−	0.608416i
$750$		0			0
$751$	−6.67209			−0.243468			−0.121734	−	0.992563i	$-0.538845\pi$
$751$	−6.67209			−0.243468			−0.121734	+	0.992563i	$0.538845\pi$
$752$	−9.34527			−0.340787
$753$		0			0
$754$	−0.235127	−	29.9314i	−0.00856284	−	1.09004i
$755$	25.5348			0.929306
$756$		0			0
$757$	−19.1595	+	33.1853i	−0.696366	+	1.20614i	0.273353	+	0.961914i	$0.411867\pi$
$757$	−19.1595	+	33.1853i	−0.696366	+	1.20614i	−0.969718	+	0.244227i	$0.921466\pi$
$758$	20.7835			0.754889
$759$		0			0
$760$	−0.312193	+	0.540735i	−0.0113244	+	0.0196145i
$761$	−2.23239	+	3.86661i	−0.0809239	+	0.140164i	−0.903647	−	0.428278i	$-0.859120\pi$
$761$	−2.23239	+	3.86661i	−0.0809239	+	0.140164i	0.822723	+	0.568442i	$0.192454\pi$
$762$		0			0
$763$	−27.4055			−0.992144
$764$	−2.84392	+	4.92581i	−0.102889	+	0.178210i
$765$		0			0
$766$	9.00228			0.325266
$767$	0.270275	+	34.4057i	0.00975907	+	1.24232i
$768$		0			0
$769$	−36.4406			−1.31408			−0.657041	−	0.753855i	$-0.728192\pi$
$769$	−36.4406			−1.31408			−0.657041	+	0.753855i	$0.728192\pi$
$770$	11.6458			0.419687
$771$		0			0
$772$	−4.95487	+	8.58208i	−0.178330	+	0.308876i
$773$	−14.1884	−	24.5750i	−0.510321	−	0.883902i	−0.999928	−	0.0119589i	$-0.996193\pi$
$773$	−14.1884	−	24.5750i	−0.510321	−	0.883902i	0.489607	−	0.871943i	$-0.337140\pi$
$774$		0			0
$775$	19.9479			0.716548
$776$	6.74408			0.242098
$777$		0			0
$778$	32.0168			1.14786
$779$	1.16132	+	2.01146i	0.0416086	+	0.0720682i
$780$		0			0
$781$	−0.712916	+	1.23481i	−0.0255101	+	0.0441848i
$782$	−0.187019	+	0.323926i	−0.00668778	+	0.0115836i
$783$		0			0
$784$	1.81010	+	3.13519i	0.0646464	+	0.111971i
$785$	−11.2954	+	19.5643i	−0.403152	+	0.698279i
$786$		0			0
$787$	−3.40942	+	5.90529i	−0.121533	+	0.210501i	−0.920372	−	0.391043i	$-0.872114\pi$
$787$	−3.40942	+	5.90529i	−0.121533	+	0.210501i	0.798840	+	0.601544i	$0.205448\pi$
$788$	3.36448	+	5.82745i	0.119855	+	0.207594i
$789$		0			0
$790$	−6.30430	−	10.9194i	−0.224297	−	0.388494i
$791$	9.24564	−	16.0139i	0.328737	−	0.569390i
$792$		0			0
$793$	−19.7520	+	11.6116i	−0.701413	+	0.412341i
$794$	17.0464	−	29.5252i	0.604953	−	1.04781i
$795$		0			0
$796$	4.20371			0.148996
$797$	2.36638	−	4.09869i	0.0838216	−	0.145183i	−0.821067	−	0.570832i	$-0.806621\pi$
$797$	2.36638	−	4.09869i	0.0838216	−	0.145183i	0.904888	+	0.425649i	$0.139954\pi$
$798$		0			0
$799$	−33.0143			−1.16796
$800$	−1.69332	−	2.93292i	−0.0598679	−	0.103694i
$801$		0			0
$802$	10.5162	+	18.2146i	0.371340	+	0.643180i
$803$	−26.9076	−	46.6053i	−0.949547	−	1.64466i
$804$		0			0
$805$	−0.123619	−	0.214115i	−0.00435701	−	0.00754656i
$806$	0.166825	+	21.2366i	0.00587616	+	0.748028i
$807$		0			0
$808$	−7.05673	−	12.2226i	−0.248255	−	0.429990i
$809$	−18.2483	+	31.6070i	−0.641577	+	1.11124i	0.343504	+	0.939151i	$0.388386\pi$
$809$	−18.2483	+	31.6070i	−0.641577	+	1.11124i	−0.985081	+	0.172093i	$0.944947\pi$
$810$		0			0
$811$	−22.6866			−0.796634			−0.398317	−	0.917248i	$-0.630406\pi$
$811$	−22.6866			−0.796634			−0.398317	+	0.917248i	$0.630406\pi$
$812$	−15.2621			−0.535595
$813$		0			0
$814$	−1.76846	−	3.06305i	−0.0619843	−	0.107360i
$815$	5.82112	−	10.0825i	0.203905	−	0.353174i
$816$		0			0
$817$	−1.99564	−	3.45655i	−0.0698187	−	0.120930i
$818$	7.73187			0.270338
$819$		0			0
$820$	6.00149			0.209581
$821$	−0.299576	−	0.518880i	−0.0104553	−	0.0181090i	0.860750	−	0.509027i	$-0.169995\pi$
$821$	−0.299576	−	0.518880i	−0.0104553	−	0.0181090i	−0.871206	+	0.490918i	$0.836661\pi$
$822$		0			0
$823$	12.5927	−	21.8111i	0.438953	−	0.760289i	−0.558656	−	0.829399i	$-0.688683\pi$
$823$	12.5927	−	21.8111i	0.438953	−	0.760289i	0.997609	+	0.0691107i	$0.0220162\pi$
$824$	6.75482	+	11.6997i	0.235315	+	0.407578i
$825$		0			0
$826$	17.5435			0.610417
$827$	28.9952			1.00826			0.504131	−	0.863627i	$-0.331813\pi$
$827$	28.9952			1.00826			0.504131	+	0.863627i	$0.331813\pi$
$828$		0			0
$829$	18.1438	−	31.4260i	0.630161	−	1.09147i	−0.357357	−	0.933968i	$-0.616322\pi$
$829$	18.1438	−	31.4260i	0.630161	−	1.09147i	0.987518	−	0.157504i	$-0.0503446\pi$
$830$	8.12289	+	14.0693i	0.281950	+	0.488351i
$831$		0			0
$832$	3.10824	−	1.82725i	0.107759	−	0.0633484i
$833$	6.39459	+	11.0757i	0.221559	+	0.383752i
$834$		0			0
$835$	−8.38728	−	14.5272i	−0.290254	−	0.502734i
$836$	1.22580	+	2.12314i	0.0423950	+	0.0734303i
$837$		0			0
$838$	0.976813	+	1.69189i	0.0337434	+	0.0584453i
$839$	−7.31785			−0.252640			−0.126320	−	0.991990i	$-0.540317\pi$
$839$	−7.31785			−0.252640			−0.126320	+	0.991990i	$0.540317\pi$
$840$		0			0
$841$	−19.9594	+	34.5707i	−0.688255	+	1.19209i
$842$	−11.6659			−0.402033
$843$		0			0
$844$	−8.16961	+	14.1502i	−0.281209	+	0.487069i
$845$	−16.5103	+	0.259411i	−0.567972	+	0.00892401i
$846$		0			0
$847$	12.7517	−	22.0867i	0.438155	−	0.758907i
$848$	2.00147	+	3.46665i	0.0687309	+	0.119045i
$849$		0			0
$850$	−5.98204	−	10.3612i	−0.205182	−	0.355386i
$851$	−0.0375439	+	0.0650280i	−0.00128699	+	0.00222913i
$852$		0			0
$853$	−18.7768	+	32.5223i	−0.642905	+	1.11354i	0.341876	+	0.939745i	$0.388938\pi$
$853$	−18.7768	+	32.5223i	−0.642905	+	1.11354i	−0.984781	+	0.173799i	$0.944396\pi$
$854$	5.84132	+	10.1175i	0.199886	+	0.346212i
$855$		0			0
$856$	5.22920	−	9.05724i	0.178730	−	0.309570i
$857$	−8.11144	+	14.0494i	−0.277081	+	0.479919i	−0.970658	−	0.240464i	$-0.922701\pi$
$857$	−8.11144	+	14.0494i	−0.277081	+	0.479919i	0.693577	+	0.720383i	$0.256034\pi$
$858$		0			0
$859$	−23.8618	−	41.3298i	−0.814154	−	1.41016i	−0.909934	−	0.414753i	$-0.863868\pi$
$859$	−23.8618	−	41.3298i	−0.814154	−	1.41016i	0.0957804	−	0.995402i	$-0.469465\pi$
$860$	−10.3131			−0.351674
$861$		0			0
$862$	−35.6127			−1.21297
$863$	22.3184			0.759728			0.379864	−	0.925042i	$-0.375971\pi$
$863$	22.3184			0.759728			0.379864	+	0.925042i	$0.375971\pi$
$864$		0			0
$865$	−3.88595	−	6.73067i	−0.132126	−	0.228850i
$866$	−13.0186	+	22.5488i	−0.442389	+	0.766240i
$867$		0			0
$868$	10.8286			0.367547
$869$	−49.5064			−1.67939
$870$		0			0
$871$	18.6567	−	10.9678i	0.632159	−	0.371629i
$872$	−14.9071			−0.504816
$873$		0			0
$874$	0.0260234	−	0.0450738i	0.000880254	−	0.00152464i
$875$	19.5839			0.662056
$876$		0			0
$877$	−14.1662	+	24.5365i	−0.478357	+	0.828539i	−0.999692	−	0.0248134i	$-0.992101\pi$
$877$	−14.1662	+	24.5365i	−0.478357	+	0.828539i	0.521335	+	0.853352i	$0.325434\pi$
$878$	9.85356	−	17.0669i	0.332542	−	0.575979i
$879$		0			0
$880$	6.33468			0.213542
$881$	20.4409	−	35.4048i	0.688673	−	1.19282i	−0.283594	−	0.958944i	$-0.591527\pi$
$881$	20.4409	−	35.4048i	0.688673	−	1.19282i	0.972267	−	0.233872i	$-0.0751398\pi$
$882$		0			0
$883$	0.138458			0.00465950			0.00232975	−	0.999997i	$-0.499258\pi$
$883$	0.138458			0.00465950			0.00232975	+	0.999997i	$0.499258\pi$
$884$	10.9806	−	6.45517i	0.369316	−	0.217111i
$885$		0			0
$886$	−27.7221			−0.931343
$887$	4.03333			0.135426			0.0677130	−	0.997705i	$-0.478430\pi$
$887$	4.03333			0.135426			0.0677130	+	0.997705i	$0.478430\pi$
$888$		0			0
$889$	13.8530	−	23.9941i	0.464615	−	0.804736i
$890$	−8.01132	−	13.8760i	−0.268540	−	0.465125i
$891$		0			0
$892$	−12.7368			−0.426459
$893$	4.59388			0.153728
$894$		0			0
$895$	16.0173			0.535400
$896$	−0.919212	−	1.59212i	−0.0307087	−	0.0531890i
$897$		0			0
$898$	−16.5142	+	28.6035i	−0.551087	+	0.954510i
$899$	24.4493	−	42.3474i	0.815429	−	1.41236i
$900$		0			0
$901$	7.07066	+	12.2467i	0.235558	+	0.407998i
$902$	11.7821	−	20.4072i	0.392301	−	0.679486i
$903$		0			0
$904$	5.02912	−	8.71069i	0.167266	−	0.289713i
$905$	8.78287	+	15.2124i	0.291952	+	0.505677i
$906$		0			0
$907$	−4.67472	−	8.09685i	−0.155221	−	0.268851i	0.777918	−	0.628366i	$-0.216276\pi$
$907$	−4.67472	−	8.09685i	−0.155221	−	0.268851i	−0.933140	+	0.359514i	$0.882942\pi$
$908$	1.44009	−	2.49431i	0.0477910	−	0.0827765i
$909$		0			0
$910$	0.0661371	+	8.41917i	0.00219242	+	0.279093i
$911$	7.27132	−	12.5943i	0.240910	−	0.417268i	−0.720064	−	0.693908i	$-0.755888\pi$
$911$	7.27132	−	12.5943i	0.240910	−	0.417268i	0.960974	+	0.276640i	$0.0892210\pi$
$912$		0			0
$913$	63.7874			2.11105
$914$	−12.2986	+	21.3018i	−0.406801	+	0.704600i
$915$		0			0
$916$	19.0312			0.628810
$917$	7.80479	+	13.5183i	0.257737	+	0.446414i
$918$		0			0
$919$	−2.10280	−	3.64216i	−0.0693650	−	0.120144i	0.829257	−	0.558868i	$-0.188764\pi$
$919$	−2.10280	−	3.64216i	−0.0693650	−	0.120144i	−0.898622	+	0.438724i	$0.855431\pi$
$920$	−0.0672420	−	0.116467i	−0.00221690	−	0.00383979i
$921$		0			0
$922$	6.82225	+	11.8165i	0.224679	+	0.389155i
$923$	−0.896732	−	0.508379i	−0.0295163	−	0.0167335i
$924$		0			0
$925$	−1.20089	−	2.08001i	−0.0394851	−	0.0683902i
$926$	14.8595	−	25.7374i	0.488313	−	0.845783i
$927$		0			0
$928$	−8.30173			−0.272518
$929$	−23.6796			−0.776903			−0.388452	−	0.921469i	$-0.626990\pi$
$929$	−23.6796			−0.776903			−0.388452	+	0.921469i	$0.626990\pi$
$930$		0			0
$931$	−0.889797	−	1.54117i	−0.0291619	−	0.0505099i
$932$	−12.4385	+	21.5442i	−0.407438	+	0.705704i
$933$		0			0
$934$	3.50000	+	6.06218i	0.114524	+	0.198361i
$935$	22.3787			0.731862
$936$		0			0
$937$	33.5310			1.09541			0.547705	−	0.836672i	$-0.315502\pi$
$937$	33.5310			1.09541			0.547705	+	0.836672i	$0.315502\pi$
$938$	−5.51742	−	9.55646i	−0.180150	−	0.312029i
$939$		0			0
$940$	5.93509	−	10.2799i	0.193581	−	0.335292i
$941$	−14.9802	−	25.9464i	−0.488339	−	0.845828i	0.511571	−	0.859241i	$-0.329064\pi$
$941$	−14.9802	−	25.9464i	−0.488339	−	0.845828i	−0.999910	+	0.0134128i	$0.995730\pi$
$942$		0			0
$943$	−0.500263			−0.0162908
$944$	9.54271			0.310589
$945$		0			0
$946$	−20.2467	+	35.0683i	−0.658277	+	1.14017i
$947$	2.99443	+	5.18650i	0.0973059	+	0.168539i	0.910569	−	0.413358i	$-0.135644\pi$
$947$	2.99443	+	5.18650i	0.0973059	+	0.168539i	−0.813263	+	0.581897i	$0.802311\pi$
$948$		0			0
$949$	33.5397	−	19.7171i	1.08875	−	0.640043i
$950$	0.832391	+	1.44174i	0.0270063	+	0.0467764i
$951$		0			0
$952$	−3.24732	−	5.62453i	−0.105246	−	0.182292i
$953$	2.59657	+	4.49740i	0.0841113	+	0.145685i	0.905012	−	0.425386i	$-0.139862\pi$
$953$	2.59657	+	4.49740i	0.0841113	+	0.145685i	−0.820901	+	0.571071i	$0.806528\pi$
$954$		0			0
$955$	−3.61229	−	6.25667i	−0.116891	−	0.202461i
$956$	15.6272			0.505420
$957$		0			0
$958$	18.8400	−	32.6319i	0.608694	−	1.05429i
$959$	−7.10034			−0.229282
$960$		0			0
$961$	−1.84698	+	3.19906i	−0.0595800	+	0.103196i
$962$	2.20434	−	1.29587i	0.0710709	−	0.0417806i
$963$		0			0
$964$	−3.52665	+	6.10833i	−0.113586	+	0.196736i
$965$	−6.29358	−	10.9008i	−0.202597	−	0.350909i
$966$		0			0
$967$	−7.70982	−	13.3538i	−0.247931	−	0.429429i	0.715020	−	0.699103i	$-0.246417\pi$
$967$	−7.70982	−	13.3538i	−0.247931	−	0.429429i	−0.962952	+	0.269674i	$0.913084\pi$
$968$	6.93624	−	12.0139i	0.222939	−	0.386142i
$969$		0			0
$970$	−4.28310	+	7.41854i	−0.137522	+	0.238195i
$971$	−3.66024	−	6.33973i	−0.117463	−	0.203451i	0.801299	−	0.598264i	$-0.204143\pi$
$971$	−3.66024	−	6.33973i	−0.117463	−	0.203451i	−0.918762	+	0.394813i	$0.870809\pi$
$972$		0			0
$973$	−17.3722	+	30.0895i	−0.556927	+	0.964625i
$974$	11.0287	−	19.1023i	0.353382	−	0.612076i
$975$		0			0
$976$	3.17735	+	5.50334i	0.101705	+	0.176158i
$977$	−48.3507			−1.54687			−0.773437	−	0.633873i	$-0.781464\pi$
$977$	−48.3507			−1.54687			−0.773437	+	0.633873i	$0.781464\pi$
$978$		0			0
$979$	−62.9113			−2.01065
$980$	−4.59831			−0.146888
$981$		0			0
$982$	−21.7949	−	37.7499i	−0.695503	−	1.20465i
$983$	14.6591	−	25.3902i	0.467551	−	0.809822i	−0.531761	−	0.846894i	$-0.678470\pi$
$983$	14.6591	−	25.3902i	0.467551	−	0.809822i	0.999313	+	0.0370718i	$0.0118030\pi$
$984$		0			0
$985$	−8.54699			−0.272330
$986$	−29.3277			−0.933986
$987$		0			0
$988$	−1.52793	+	0.898227i	−0.0486099	+	0.0285764i
$989$	0.859666			0.0273358
$990$		0			0
$991$	10.6409	−	18.4305i	0.338018	−	0.585465i	−0.646042	−	0.763302i	$-0.723577\pi$
$991$	10.6409	−	18.4305i	0.338018	−	0.585465i	0.984060	+	0.177837i	$0.0569101\pi$
$992$	5.89016			0.187013
$993$		0			0
$994$	−0.262799	+	0.455182i	−0.00833549	+	0.0144375i
$995$	−2.66973	+	4.62411i	−0.0846362	+	0.146594i
$996$		0			0
$997$	6.92733			0.219391			0.109695	−	0.993965i	$-0.465012\pi$
$997$	6.92733			0.219391			0.109695	+	0.993965i	$0.465012\pi$
$998$	1.25644	−	2.17622i	0.0397720	−	0.0688871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.g.d.451.4		12
3.2	odd	2		234.2.g.c.61.1	yes	12
9.4	even	3		702.2.f.c.685.4		12
9.5	odd	6		234.2.f.d.139.4	yes	12
13.3	even	3		702.2.f.c.289.4		12
39.29	odd	6		234.2.f.d.133.4	✓	12
117.68	odd	6		234.2.g.c.211.1	yes	12
117.94	even	3	inner	702.2.g.d.523.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.f.d.133.4	✓	12	39.29	odd	6
234.2.f.d.139.4	yes	12	9.5	odd	6
234.2.g.c.61.1	yes	12	3.2	odd	2
234.2.g.c.211.1	yes	12	117.68	odd	6
702.2.f.c.289.4		12	13.3	even	3
702.2.f.c.685.4		12	9.4	even	3
702.2.g.d.451.4		12	1.1	even	1	trivial
702.2.g.d.523.4		12	117.94	even	3	inner

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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.635090 - 1.10001i) q^{5} -1.83842 q^{7} -1.00000 q^{8} +(0.635090 - 1.10001i) q^{10} +(-2.49362 - 4.31907i) q^{11} +(3.10824 - 1.82725i) q^{13} +(-0.919212 - 1.59212i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.76636 - 3.05943i) q^{17} +(0.245787 + 0.425715i) q^{19} +1.27018 q^{20} +(2.49362 - 4.31907i) q^{22} -0.105878 q^{23} +(1.69332 - 2.93292i) q^{25} +(3.13656 + 1.77819i) q^{26} +(0.919212 - 1.59212i) q^{28} +(-4.15087 - 7.18951i) q^{29} +(2.94508 + 5.10103i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.76636 - 3.05943i) q^{34} +(1.16756 + 2.02228i) q^{35} +(0.354597 - 0.614179i) q^{37} +(-0.245787 + 0.425715i) q^{38} +(0.635090 + 1.10001i) q^{40} +4.72491 q^{41} -8.11941 q^{43} +4.98723 q^{44} +(-0.0529389 - 0.0916929i) q^{46} +(4.67263 - 8.09324i) q^{47} -3.62020 q^{49} +3.38664 q^{50} +(0.0283227 + 3.60544i) q^{52} -4.00295 q^{53} +(-3.16734 + 5.48600i) q^{55} +1.83842 q^{56} +(4.15087 - 7.18951i) q^{58} +(-4.77135 + 8.26423i) q^{59} -6.35471 q^{61} +(-2.94508 + 5.10103i) q^{62} +1.00000 q^{64} +(-3.98400 - 2.25862i) q^{65} +6.00235 q^{67} +3.53272 q^{68} +(-1.16756 + 2.02228i) q^{70} +(-0.142948 - 0.247594i) q^{71} +10.7906 q^{73} +0.709193 q^{74} -0.491573 q^{76} +(4.58432 + 7.94028i) q^{77} +(4.96331 - 8.59671i) q^{79} +(-0.635090 + 1.10001i) q^{80} +(2.36245 + 4.09189i) q^{82} +(-6.39507 + 11.0766i) q^{83} +(-2.24360 + 3.88603i) q^{85} +(-4.05970 - 7.03161i) q^{86} +(2.49362 + 4.31907i) q^{88} +(6.30723 - 10.9244i) q^{89} +(-5.71426 + 3.35926i) q^{91} +(0.0529389 - 0.0916929i) q^{92} +9.34527 q^{94} +(0.312193 - 0.540735i) q^{95} -6.74408 q^{97} +(-1.81010 - 3.13519i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - q^{5} + 10 q^{7} - 12 q^{8} + q^{10} - 8 q^{11} + 8 q^{13} + 5 q^{14} - 6 q^{16} - 3 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} + 2 q^{23} - 13 q^{25} + q^{26} - 5 q^{28} - q^{29}+ \cdots + 3 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - q^5 + 10 * q^7 - 12 * q^8 + q^10 - 8 * q^11 + 8 * q^13 + 5 * q^14 - 6 * q^16 - 3 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 + 2 * q^23 - 13 * q^25 + q^26 - 5 * q^28 - q^29 - 14 * q^31 + 6 * q^32 + 3 * q^34 + 5 * q^35 - 7 * q^37 + 7 * q^38 + q^40 + 18 * q^41 + 16 * q^43 + 16 * q^44 + q^46 + 13 * q^47 + 6 * q^49 - 26 * q^50 - 7 * q^52 + 12 * q^53 - 20 * q^55 - 10 * q^56 + q^58 - 4 * q^59 - 56 * q^61 + 14 * q^62 + 12 * q^64 + 7 * q^65 - 8 * q^67 + 6 * q^68 - 5 * q^70 + 13 * q^71 + 54 * q^73 - 14 * q^74 + 14 * q^76 + 4 * q^77 - 6 * q^79 - q^80 + 9 * q^82 - 30 * q^83 - 9 * q^85 + 8 * q^86 + 8 * q^88 - 3 * q^89 - 12 * q^91 - q^92 + 26 * q^94 + 21 * q^95 + 48 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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