LMFDB - Embedded newform 700.2.p.e.451.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(451,700)] 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("700.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.14
Character	$\chi$	$=$	700.451
Dual form			700.2.p.e.551.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24320 + 0.674125i) q^{2} +(0.366453 - 0.634715i) q^{3} +(1.09111 + 1.67615i) q^{4} +(0.883452 - 0.542044i) q^{6} +(-0.664037 + 2.56107i) q^{7} +(0.226536 + 2.81934i) q^{8} +(1.23142 + 2.13289i) q^{9} +(-2.33007 - 1.34527i) q^{11} +(1.46372 - 0.0783137i) q^{12} +3.95118i q^{13} +(-2.55201 + 2.73628i) q^{14} +(-1.61896 + 3.65773i) q^{16} +(-1.22891 - 0.709509i) q^{17} +(0.0930760 + 3.48175i) q^{18} +(-1.61265 - 2.79319i) q^{19} +(1.38221 + 1.35998i) q^{21} +(-1.98987 - 3.24320i) q^{22} +(4.25426 - 2.45620i) q^{23} +(1.87249 + 0.889369i) q^{24} +(-2.66359 + 4.91212i) q^{26} +4.00375 q^{27} +(-5.01727 + 1.68138i) q^{28} +5.17926 q^{29} +(3.81745 - 6.61201i) q^{31} +(-4.47846 + 3.45592i) q^{32} +(-1.70772 + 0.985953i) q^{33} +(-1.04948 - 1.71050i) q^{34} +(-2.23142 + 4.39127i) q^{36} +(2.23990 + 3.87963i) q^{37} +(-0.121890 - 4.55962i) q^{38} +(2.50787 + 1.44792i) q^{39} -0.325509i q^{41} +(0.801566 + 2.62252i) q^{42} +9.28165i q^{43} +(-0.287494 - 5.37338i) q^{44} +(6.94469 - 0.185649i) q^{46} +(-3.28287 - 5.68610i) q^{47} +(1.72834 + 2.36796i) q^{48} +(-6.11811 - 3.40128i) q^{49} +(-0.900672 + 0.520003i) q^{51} +(-6.62277 + 4.31117i) q^{52} +(-0.807955 + 1.39942i) q^{53} +(4.97748 + 2.69903i) q^{54} +(-7.37094 - 1.29197i) q^{56} -2.36383 q^{57} +(6.43888 + 3.49147i) q^{58} +(3.81745 - 6.61201i) q^{59} +(12.3842 - 7.15003i) q^{61} +(9.20319 - 5.64664i) q^{62} +(-6.28018 + 1.73744i) q^{63} +(-7.89736 + 1.27737i) q^{64} +(-2.78770 + 0.0745223i) q^{66} +(2.62109 + 1.51329i) q^{67} +(-0.151627 - 2.83398i) q^{68} -3.60032i q^{69} -15.4089i q^{71} +(-5.73438 + 3.95498i) q^{72} +(-1.22891 - 0.709509i) q^{73} +(0.169301 + 6.33314i) q^{74} +(2.92222 - 5.75071i) q^{76} +(4.99257 - 5.07415i) q^{77} +(2.14171 + 3.49068i) q^{78} +(-10.5765 + 6.10637i) q^{79} +(-2.22709 + 3.85743i) q^{81} +(0.219434 - 0.404674i) q^{82} +5.26172 q^{83} +(-0.771396 + 3.80068i) q^{84} +(-6.25699 + 11.5390i) q^{86} +(1.89795 - 3.28735i) q^{87} +(3.26492 - 6.87401i) q^{88} +(-4.10930 + 2.37250i) q^{89} +(-10.1192 - 2.62373i) q^{91} +(8.75882 + 4.45079i) q^{92} +(-2.79783 - 4.84598i) q^{93} +(-0.248133 - 9.28205i) q^{94} +(0.552378 + 4.10898i) q^{96} +8.35134i q^{97} +(-5.31316 - 8.35286i) q^{98} -6.62638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) $ 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.24320	+	0.674125i	0.879078	+	0.476679i
$2$	1.24320	+	0.674125i	0.879078	+	0.476679i
$3$	0.366453	−	0.634715i	0.211572	−	0.366453i	−0.740635	−	0.671908i	$-0.765475\pi$
$3$	0.366453	−	0.634715i	0.211572	−	0.366453i	0.952207	+	0.305455i	$0.0988085\pi$
$4$	1.09111	+	1.67615i	0.545555	+	0.838075i
$5$		0			0
$5$		0			0
$6$	0.883452	−	0.542044i	0.360668	−	0.221289i
$7$	−0.664037	+	2.56107i	−0.250982	+	0.967992i
$7$	−0.664037	+	2.56107i	−0.250982	+	0.967992i
$8$	0.226536	+	2.81934i	0.0800926	+	0.996787i
$9$	1.23142	+	2.13289i	0.410475	+	0.710964i
$10$		0			0
$11$	−2.33007	−	1.34527i	−0.702542	−	0.405613i	0.105751	−	0.994393i	$-0.466275\pi$
$11$	−2.33007	−	1.34527i	−0.702542	−	0.405613i	−0.808294	+	0.588780i	$0.799609\pi$
$12$	1.46372	−	0.0783137i	0.422539	−	0.0226072i
$13$			3.95118i			1.09586i	0.836524	+	0.547930i	$0.184584\pi$
$13$			3.95118i			1.09586i	−0.836524	+	0.547930i	$0.815416\pi$
$14$	−2.55201	+	2.73628i	−0.682054	+	0.731302i
$15$		0			0
$16$	−1.61896	+	3.65773i	−0.404740	+	0.914432i
$17$	−1.22891	−	0.709509i	−0.298053	−	0.172081i	0.343515	−	0.939147i	$-0.388382\pi$
$17$	−1.22891	−	0.709509i	−0.298053	−	0.172081i	−0.641568	+	0.767066i	$0.721716\pi$
$18$	0.0930760	+	3.48175i	0.0219382	+	0.820657i
$19$	−1.61265	−	2.79319i	−0.369966	−	0.640801i	0.619593	−	0.784923i	$-0.287297\pi$
$19$	−1.61265	−	2.79319i	−0.369966	−	0.640801i	−0.989560	+	0.144122i	$0.953964\pi$
$20$		0			0
$21$	1.38221	+	1.35998i	0.301622	+	0.296773i
$22$	−1.98987	−	3.24320i	−0.424242	−	0.691452i
$23$	4.25426	−	2.45620i	0.887074	−	0.512152i	0.0140897	−	0.999901i	$-0.495515\pi$
$23$	4.25426	−	2.45620i	0.887074	−	0.512152i	0.872984	+	0.487748i	$0.162182\pi$
$24$	1.87249	+	0.889369i	0.382221	+	0.181542i
$25$		0			0
$26$	−2.66359	+	4.91212i	−0.522373	+	0.963345i
$27$	4.00375			0.770522
$28$	−5.01727	+	1.68138i	−0.948174	+	0.317751i
$29$	5.17926			0.961765			0.480882	−	0.876785i	$-0.340316\pi$
$29$	5.17926			0.961765			0.480882	+	0.876785i	$0.340316\pi$
$30$		0			0
$31$	3.81745	−	6.61201i	0.685634	−	1.18755i	−0.287603	−	0.957750i	$-0.592858\pi$
$31$	3.81745	−	6.61201i	0.685634	−	1.18755i	0.973237	−	0.229803i	$-0.0738082\pi$
$32$	−4.47846	+	3.45592i	−0.791688	+	0.610926i
$33$	−1.70772	+	0.985953i	−0.297276	+	0.171632i
$34$	−1.04948	−	1.71050i	−0.179985	−	0.293349i
$35$		0			0
$36$	−2.23142	+	4.39127i	−0.371904	+	0.731878i
$37$	2.23990	+	3.87963i	0.368238	+	0.637806i	0.989290	−	0.145963i	$-0.0466279\pi$
$37$	2.23990	+	3.87963i	0.368238	+	0.637806i	−0.621052	+	0.783769i	$0.713295\pi$
$38$	−0.121890	−	4.55962i	−0.0197732	−	0.739669i
$39$	2.50787	+	1.44792i	0.401581	+	0.231853i
$40$		0			0
$41$		−	0.325509i		−	0.0508359i	−0.999677	−	0.0254180i	$-0.991908\pi$
$41$		−	0.325509i		−	0.0508359i	0.999677	−	0.0254180i	$-0.00809166\pi$
$42$	0.801566	+	2.62252i	0.123684	+	0.404663i
$43$			9.28165i			1.41544i	0.706494	+	0.707719i	$0.250276\pi$
$43$			9.28165i			1.41544i	−0.706494	+	0.707719i	$0.749724\pi$
$44$	−0.287494	−	5.37338i	−0.0433413	−	0.810067i
$45$		0			0
$46$	6.94469	−	0.185649i	1.02394	−	0.0273725i
$47$	−3.28287	−	5.68610i	−0.478856	−	0.829403i	0.520850	−	0.853648i	$-0.325615\pi$
$47$	−3.28287	−	5.68610i	−0.478856	−	0.829403i	−0.999706	+	0.0242453i	$0.992282\pi$
$48$	1.72834	+	2.36796i	0.249465	+	0.341786i
$49$	−6.11811	−	3.40128i	−0.874016	−	0.485898i
$50$		0			0
$51$	−0.900672	+	0.520003i	−0.126119	+	0.0728150i
$52$	−6.62277	+	4.31117i	−0.918412	+	0.597851i
$53$	−0.807955	+	1.39942i	−0.110981	+	0.192225i	−0.916166	−	0.400799i	$-0.868733\pi$
$53$	−0.807955	+	1.39942i	−0.110981	+	0.192225i	0.805185	+	0.593024i	$0.202066\pi$
$54$	4.97748	+	2.69903i	0.677349	+	0.367292i
$55$		0			0
$56$	−7.37094	−	1.29197i	−0.984984	−	0.172647i
$57$	−2.36383			−0.313097
$58$	6.43888	+	3.49147i	0.845466	+	0.458453i
$59$	3.81745	−	6.61201i	0.496989	−	0.860811i	−0.503005	−	0.864284i	$-0.667772\pi$
$59$	3.81745	−	6.61201i	0.496989	−	0.860811i	0.999994	+	0.00347297i	$0.00110548\pi$
$60$		0			0
$61$	12.3842	−	7.15003i	1.58564	−	0.915467i	0.591622	−	0.806215i	$-0.298488\pi$
$61$	12.3842	−	7.15003i	1.58564	−	0.915467i	0.994014	−	0.109252i	$-0.0348455\pi$
$62$	9.20319	−	5.64664i	1.16881	−	0.717124i
$63$	−6.28018	+	1.73744i	−0.791229	+	0.218897i
$64$	−7.89736	+	1.27737i	−0.987170	+	0.159671i
$65$		0			0
$66$	−2.78770	+	0.0745223i	−0.343142	+	0.00917306i
$67$	2.62109	+	1.51329i	0.320218	+	0.184878i	0.651490	−	0.758658i	$-0.274144\pi$
$67$	2.62109	+	1.51329i	0.320218	+	0.184878i	−0.331272	+	0.943535i	$0.607478\pi$
$68$	−0.151627	−	2.83398i	−0.0183875	−	0.343671i
$69$		−	3.60032i		−	0.433427i
$70$		0			0
$71$		−	15.4089i		−	1.82870i	−0.404922	−	0.914351i	$-0.632701\pi$
$71$		−	15.4089i		−	1.82870i	0.404922	−	0.914351i	$-0.367299\pi$
$72$	−5.73438	+	3.95498i	−0.675803	+	0.466099i
$73$	−1.22891	−	0.709509i	−0.143833	−	0.0830418i	0.426357	−	0.904555i	$-0.359797\pi$
$73$	−1.22891	−	0.709509i	−0.143833	−	0.0830418i	−0.570189	+	0.821513i	$0.693130\pi$
$74$	0.169301	+	6.33314i	0.0196808	+	0.736212i
$75$		0			0
$76$	2.92222	−	5.75071i	0.335202	−	0.659652i
$77$	4.99257	−	5.07415i	0.568956	−	0.578253i
$78$	2.14171	+	3.49068i	0.242501	+	0.395241i
$79$	−10.5765	+	6.10637i	−1.18995	+	0.687021i	−0.958296	−	0.285776i	$-0.907749\pi$
$79$	−10.5765	+	6.10637i	−1.18995	+	0.687021i	−0.231659	+	0.972797i	$0.574415\pi$
$80$		0			0
$81$	−2.22709	+	3.85743i	−0.247454	+	0.428604i
$82$	0.219434	−	0.404674i	0.0242324	−	0.0446887i
$83$	5.26172			0.577549			0.288774	−	0.957397i	$-0.406752\pi$
$83$	5.26172			0.577549			0.288774	+	0.957397i	$0.406752\pi$
$84$	−0.771396	+	3.80068i	−0.0841662	+	0.414688i
$85$		0			0
$86$	−6.25699	+	11.5390i	−0.674709	+	1.24428i
$87$	1.89795	−	3.28735i	0.203482	−	0.352441i
$88$	3.26492	−	6.87401i	0.348041	−	0.732772i
$89$	−4.10930	+	2.37250i	−0.435585	+	0.251485i	−0.701723	−	0.712450i	$-0.747586\pi$
$89$	−4.10930	+	2.37250i	−0.435585	+	0.251485i	0.266138	+	0.963935i	$0.414252\pi$
$90$		0			0
$91$	−10.1192	−	2.62373i	−1.06078	−	0.275041i
$92$	8.75882	+	4.45079i	0.913170	+	0.464027i
$93$	−2.79783	−	4.84598i	−0.290121	−	0.502505i
$94$	−0.248133	−	9.28205i	−0.0255929	−	0.957370i
$95$		0			0
$96$	0.552378	+	4.10898i	0.0563768	+	0.419371i
$97$			8.35134i			0.847950i	0.905674	+	0.423975i	$0.139366\pi$
$97$			8.35134i			0.847950i	−0.905674	+	0.423975i	$0.860634\pi$
$98$	−5.31316	−	8.35286i	−0.536711	−	0.843766i
$99$		−	6.62638i		−	0.665976i
$100$		0			0
$101$	−0.241927	−	0.139677i	−0.0240727	−	0.0138984i	0.487915	−	0.872891i	$-0.337757\pi$
$101$	−0.241927	−	0.139677i	−0.0240727	−	0.0138984i	−0.511988	+	0.858993i	$0.671091\pi$
$102$	−1.47027	+	0.0393039i	−0.145578	+	0.00389167i
$103$	−6.70030	−	11.6053i	−0.660200	−	1.14350i	−0.980563	−	0.196206i	$-0.937138\pi$
$103$	−6.70030	−	11.6053i	−0.660200	−	1.14350i	0.320362	−	0.947295i	$-0.396195\pi$
$104$	−11.1397	+	0.895084i	−1.09234	+	0.0877703i
$105$		0			0
$106$	−1.94784	+	1.19510i	−0.189191	+	0.116078i
$107$	−4.70160	+	2.71447i	−0.454521	+	0.262418i	−0.709738	−	0.704466i	$-0.751187\pi$
$107$	−4.70160	+	2.71447i	−0.454521	+	0.262418i	0.255217	+	0.966884i	$0.417853\pi$
$108$	4.36853	+	6.71089i	0.420362	+	0.645756i
$109$	4.45851	−	7.72237i	0.427048	−	0.739669i	−0.569561	−	0.821949i	$-0.692887\pi$
$109$	4.45851	−	7.72237i	0.427048	−	0.739669i	0.996609	+	0.0822798i	$0.0262201\pi$
$110$		0			0
$111$	3.28327			0.311634
$112$	−8.29263	−	6.57512i	−0.783580	−	0.621291i
$113$	1.05161			0.0989268			0.0494634	−	0.998776i	$-0.484249\pi$
$113$	1.05161			0.0989268			0.0494634	+	0.998776i	$0.484249\pi$
$114$	−2.93873	−	1.59352i	−0.275237	−	0.149247i
$115$		0			0
$116$	5.65114	+	8.68122i	0.524695	+	0.806031i
$117$	−8.42743	+	4.86558i	−0.779116	+	0.449823i
$118$	9.20319	−	5.64664i	0.847222	−	0.519815i
$119$	2.63314	−	2.67617i	0.241379	−	0.245324i
$120$		0			0
$121$	−1.88052	−	3.25715i	−0.170956	−	0.296105i
$122$	20.2161	−	0.540428i	1.83028	−	0.0489280i
$123$	−0.206605	−	0.119284i	−0.0186290	−	0.0107554i
$124$	15.2480	−	0.815817i	1.36931	−	0.0732626i
$125$		0			0
$126$	−8.97880	−	2.07364i	−0.799895	−	0.184734i
$127$			1.71773i			0.152424i	0.997092	+	0.0762121i	$0.0242826\pi$
$127$			1.71773i			0.152424i	−0.997092	+	0.0762121i	$0.975717\pi$
$128$	−10.6791	−	3.73579i	−0.943911	−	0.330200i
$129$	5.89120	+	3.40128i	0.518691	+	0.299466i
$130$		0			0
$131$	7.07173	+	12.2486i	0.617860	+	1.07016i	0.989876	+	0.141938i	$0.0453335\pi$
$131$	7.07173	+	12.2486i	0.617860	+	1.07016i	−0.372016	+	0.928226i	$0.621333\pi$
$132$	−3.51591	−	1.78661i	−0.306021	−	0.155505i
$133$	8.22439	−	2.27531i	0.713145	−	0.197295i
$134$	2.23841	+	3.64827i	0.193369	+	0.315163i
$135$		0			0
$136$	1.72196	−	3.62543i	0.147657	−	0.310878i
$137$	7.43551	−	12.8787i	0.635259	−	1.10030i	−0.351202	−	0.936300i	$-0.614227\pi$
$137$	7.43551	−	12.8787i	0.635259	−	1.10030i	0.986460	−	0.164000i	$-0.0524398\pi$
$138$	2.42707	−	4.47593i	0.206606	−	0.381016i
$139$	7.06762			0.599468			0.299734	−	0.954023i	$-0.403102\pi$
$139$	7.06762			0.599468			0.299734	+	0.954023i	$0.403102\pi$
$140$		0			0
$141$	−4.81207			−0.405249
$142$	10.3875	−	19.1564i	0.871703	−	1.60757i
$143$	5.31538	−	9.20652i	0.444495	−	0.769888i
$144$	−9.79516	+	1.05116i	−0.816263	+	0.0875963i
$145$		0			0
$146$	−1.04948	−	1.71050i	−0.0868557	−	0.141562i
$147$	−4.40084	+	2.63684i	−0.362975	+	0.217483i
$148$	−4.05885	+	7.98751i	−0.333636	+	0.656569i
$149$	4.39289	+	7.60870i	0.359879	+	0.623329i	0.987940	−	0.154835i	$-0.0494846\pi$
$149$	4.39289	+	7.60870i	0.359879	+	0.623329i	−0.628061	+	0.778164i	$0.716151\pi$
$150$		0			0
$151$	0.260095	+	0.150166i	0.0211663	+	0.0122204i	0.510546	−	0.859851i	$-0.329443\pi$
$151$	0.260095	+	0.150166i	0.0211663	+	0.0122204i	−0.489380	+	0.872071i	$0.662777\pi$
$152$	7.50962	−	5.17936i	0.609110	−	0.420101i
$153$		−	3.49483i		−	0.282540i
$154$	9.62739	−	2.94259i	0.775797	−	0.237121i
$155$		0			0
$156$	0.309431	+	5.78341i	0.0247743	+	0.463043i
$157$	−16.6579	−	9.61742i	−1.32944	−	0.767553i	−0.344228	−	0.938886i	$-0.611859\pi$
$157$	−16.6579	−	9.61742i	−1.32944	−	0.767553i	−0.985213	+	0.171333i	$0.945193\pi$
$158$	−17.2653	+	0.461544i	−1.37355	+	0.0367185i
$159$	0.592155	+	1.02564i	0.0469609	+	0.0813387i
$160$		0			0
$161$	3.46550	+	12.5264i	0.273119	+	0.987221i
$162$	−5.36912	+	3.29424i	−0.421838	+	0.258820i
$163$	−9.28306	+	5.35958i	−0.727105	+	0.419795i	−0.817362	−	0.576124i	$-0.804565\pi$
$163$	−9.28306	+	5.35958i	−0.727105	+	0.419795i	0.0902569	+	0.995919i	$0.471231\pi$
$164$	0.545602	−	0.355166i	0.0426043	−	0.0277338i
$165$		0			0
$166$	6.54139	+	3.54706i	0.507710	+	0.275305i
$167$	−13.2256			−1.02343			−0.511715	−	0.859155i	$-0.670990\pi$
$167$	−13.2256			−1.02343			−0.511715	+	0.859155i	$0.670990\pi$
$168$	−3.52114	+	4.20500i	−0.271661	+	0.324423i
$169$	−2.61180			−0.200908
$170$		0			0
$171$	3.97171	−	6.87920i	0.303724	−	0.526065i
$172$	−15.5574	+	10.1273i	−1.18624	+	0.772199i
$173$	9.74632	−	5.62704i	0.740999	−	0.427816i	−0.0814335	−	0.996679i	$-0.525950\pi$
$173$	9.74632	−	5.62704i	0.740999	−	0.427816i	0.822432	+	0.568863i	$0.192616\pi$
$174$	4.57563	−	2.80739i	0.346878	−	0.212828i
$175$		0			0
$176$	8.69290	−	6.34483i	0.655252	−	0.478259i
$177$	−2.79783	−	4.84598i	−0.210298	−	0.364246i
$178$	−6.70806	+	0.179323i	−0.502790	+	0.0134409i
$179$	0.697992	+	0.402986i	0.0521703	+	0.0301206i	0.525858	−	0.850572i	$-0.323744\pi$
$179$	0.697992	+	0.402986i	0.0521703	+	0.0301206i	−0.473688	+	0.880693i	$0.657078\pi$
$180$		0			0
$181$			0.0667108i			0.00495857i	0.999997	+	0.00247929i	$0.000789182\pi$
$181$			0.0667108i			0.00495857i	−0.999997	+	0.00247929i	$0.999211\pi$
$182$	−10.8115	−	10.0835i	−0.801404	−	0.747435i
$183$		−	10.4806i		−	0.774747i
$184$	7.88860	+	11.4378i	0.581555	+	0.843205i
$185$		0			0
$186$	−0.211471	−	7.91062i	−0.0155058	−	0.580035i
$187$	1.90896	+	3.30641i	0.139597	+	0.241789i
$188$	5.94878	−	11.7067i	0.433860	−	0.853802i
$189$	−2.65864	+	10.2539i	−0.193388	+	0.745859i
$190$		0			0
$191$	−15.1210	+	8.73010i	−1.09412	+	0.631688i	−0.934669	−	0.355519i	$-0.884304\pi$
$191$	−15.1210	+	8.73010i	−1.09412	+	0.631688i	−0.159446	+	0.987207i	$0.550971\pi$
$192$	−2.08325	+	5.48067i	−0.150345	+	0.395533i
$193$	8.59835	−	14.8928i	0.618923	−	1.07201i	−0.370760	−	0.928729i	$-0.620903\pi$
$193$	8.59835	−	14.8928i	0.618923	−	1.07201i	0.989683	−	0.143277i	$-0.0457639\pi$
$194$	−5.62985	+	10.3824i	−0.404200	+	0.745414i
$195$		0			0
$196$	−0.974468	−	13.9660i	−0.0696049	−	0.997575i
$197$	11.9392			0.850635			0.425318	−	0.905044i	$-0.360162\pi$
$197$	11.9392			0.850635			0.425318	+	0.905044i	$0.360162\pi$
$198$	4.46701	−	8.23793i	0.317457	−	0.585445i
$199$	−7.76016	+	13.4410i	−0.550103	+	0.952807i	0.448163	+	0.893952i	$0.352078\pi$
$199$	−7.76016	+	13.4410i	−0.550103	+	0.952807i	−0.998267	+	0.0588552i	$0.981255\pi$
$200$		0			0
$201$	1.92101	−	1.10910i	0.135498	−	0.0782297i
$202$	−0.206605	−	0.336736i	−0.0145367	−	0.0236927i
$203$	−3.43922	+	13.2644i	−0.241386	+	0.930980i
$204$	−1.85433	−	0.942281i	−0.129829	−	0.0659728i
$205$		0			0
$206$	−0.506436	−	18.9445i	−0.0352850	−	1.31993i
$207$	10.4776	+	6.04924i	0.728243	+	0.420452i
$208$	−14.4523	−	6.39679i	−1.00209	−	0.443538i
$209$			8.67775i			0.600253i
$210$		0			0
$211$			14.1636i			0.975063i	0.873105	+	0.487531i	$0.162103\pi$
$211$			14.1636i			0.975063i	−0.873105	+	0.487531i	$0.837897\pi$
$212$	−3.22720	+	0.172666i	−0.221645	+	0.0118588i
$213$	−9.78027	−	5.64664i	−0.670133	−	0.386901i
$214$	−7.67494	+	0.205171i	−0.524648	+	0.0140252i
$215$		0			0
$216$	0.906994	+	11.2879i	0.0617132	+	0.768047i
$217$	14.3989	+	14.1674i	0.977459	+	0.961742i
$218$	10.7487	−	6.59488i	0.727993	−	0.446662i
$219$	−0.900672	+	0.520003i	−0.0608618	+	0.0351385i
$220$		0			0
$221$	2.80340	−	4.85563i	0.188577	−	0.326625i
$222$	4.08178	+	2.21334i	0.273951	+	0.148550i
$223$	3.03443			0.203201			0.101600	−	0.994825i	$-0.467604\pi$
$223$	3.03443			0.203201			0.101600	+	0.994825i	$0.467604\pi$
$224$	−5.87697	−	13.7645i	−0.392672	−	0.919679i
$225$		0			0
$226$	1.30736	+	0.708914i	0.0869643	+	0.0471563i
$227$	7.38839	−	12.7971i	0.490385	−	0.849371i	−0.509554	−	0.860439i	$-0.670190\pi$
$227$	7.38839	−	12.7971i	0.490385	−	0.849371i	0.999939	+	0.0110676i	$0.00352299\pi$
$228$	−2.57920	−	3.96214i	−0.170812	−	0.262399i
$229$	5.56933	−	3.21545i	0.368031	−	0.212483i	−0.304567	−	0.952491i	$-0.598512\pi$
$229$	5.56933	−	3.21545i	0.368031	−	0.212483i	0.672598	+	0.740008i	$0.265178\pi$
$230$		0			0
$231$	−1.39110	−	5.02829i	−0.0915277	−	0.330837i
$232$	1.17329	+	14.6021i	0.0770303	+	0.958675i
$233$	8.73532	+	15.1300i	0.572270	+	0.991201i	0.996332	+	0.0855677i	$0.0272704\pi$
$233$	8.73532	+	15.1300i	0.572270	+	0.991201i	−0.424062	+	0.905633i	$0.639396\pi$
$234$	−13.7570	+	0.367760i	−0.899324	+	0.0240412i
$235$		0			0
$236$	15.2480	−	0.815817i	0.992559	−	0.0531052i
$237$			8.95079i			0.581416i
$238$	5.07760	−	1.55196i	0.329132	−	0.100598i
$239$		−	3.22490i		−	0.208601i	−0.994546	−	0.104301i	$-0.966740\pi$
$239$		−	3.22490i		−	0.208601i	0.994546	−	0.104301i	$-0.0332604\pi$
$240$		0			0
$241$	−17.7424	−	10.2436i	−1.14289	−	0.659848i	−0.195745	−	0.980655i	$-0.562713\pi$
$241$	−17.7424	−	10.2436i	−1.14289	−	0.659848i	−0.947145	+	0.320807i	$0.896046\pi$
$242$	−0.142137	−	5.31701i	−0.00913692	−	0.341790i
$243$	7.63787	+	13.2292i	0.489970	+	0.848653i
$244$	25.4971	+	12.9563i	1.63228	+	0.829444i
$245$		0			0
$246$	−0.176440	−	0.287572i	−0.0112494	−	0.0183349i
$247$	11.0364	−	6.37185i	0.702227	−	0.405431i
$248$	19.5063	+	9.26482i	1.23865	+	0.588317i
$249$	1.92817	−	3.33969i	0.122193	−	0.211644i
$250$		0			0
$251$	15.1647			0.957189			0.478594	−	0.878036i	$-0.341146\pi$
$251$	15.1647			0.957189			0.478594	+	0.878036i	$0.341146\pi$
$252$	−9.76458	−	8.63079i	−0.615111	−	0.543689i
$253$	−13.2170			−0.830943
$254$	−1.15797	+	2.13549i	−0.0726574	+	0.133993i
$255$		0			0
$256$	−10.7579	−	11.8434i	−0.672372	−	0.740214i
$257$	4.09764	−	2.36577i	0.255604	−	0.147573i	−0.366724	−	0.930330i	$-0.619521\pi$
$257$	4.09764	−	2.36577i	0.255604	−	0.147573i	0.622327	+	0.782757i	$0.286187\pi$
$258$	5.03106	+	8.19989i	0.313220	+	0.510503i
$259$	−11.4234	+	3.16032i	−0.709813	+	0.196373i
$260$		0			0
$261$	6.37787	+	11.0468i	0.394780	+	0.683780i
$262$	0.534510	+	19.9947i	0.0330221	+	1.23528i
$263$	−4.07068	−	2.35021i	−0.251009	−	0.144920i	0.369217	−	0.929343i	$-0.379626\pi$
$263$	−4.07068	−	2.35021i	−0.251009	−	0.144920i	−0.620226	+	0.784423i	$0.712959\pi$
$264$	−3.16660	−	4.59129i	−0.194891	−	0.282574i
$265$		0			0
$266$	11.7584	+	2.71559i	0.720956	+	0.166503i
$267$			3.47764i			0.212828i
$268$	0.323401	+	6.04451i	0.0197549	+	0.369227i
$269$	−21.2532	−	12.2706i	−1.29583	−	0.748149i	−0.316151	−	0.948709i	$-0.602391\pi$
$269$	−21.2532	−	12.2706i	−1.29583	−	0.748149i	−0.979682	+	0.200559i	$0.935724\pi$
$270$		0			0
$271$	13.1957	+	22.8556i	0.801582	+	1.38838i	0.918574	+	0.395248i	$0.129341\pi$
$271$	13.1957	+	22.8556i	0.801582	+	1.38838i	−0.116993	+	0.993133i	$0.537325\pi$
$272$	4.58474	−	3.34634i	0.277991	−	0.202902i
$273$	−5.37353	+	5.46135i	−0.325221	+	0.330536i
$274$	17.9257	−	10.9984i	1.08293	−	0.664435i
$275$		0			0
$276$	6.03468	−	3.92834i	0.363245	−	0.236458i
$277$	12.0350	−	20.8453i	0.723115	−	1.25247i	−0.236630	−	0.971600i	$-0.576043\pi$
$277$	12.0350	−	20.8453i	0.723115	−	1.25247i	0.959745	−	0.280872i	$-0.0906238\pi$
$278$	8.78649	+	4.76446i	0.526979	+	0.285753i
$279$	18.8036			1.12574
$280$		0			0
$281$	−7.78577			−0.464460			−0.232230	−	0.972661i	$-0.574602\pi$
$281$	−7.78577			−0.464460			−0.232230	+	0.972661i	$0.574602\pi$
$282$	−5.98238	−	3.24394i	−0.356245	−	0.193174i
$283$	−3.97529	+	6.88540i	−0.236306	+	0.409294i	−0.959651	−	0.281192i	$-0.909270\pi$
$283$	−3.97529	+	6.88540i	−0.236306	+	0.409294i	0.723345	+	0.690487i	$0.242604\pi$
$284$	25.8277	−	16.8128i	1.53259	−	0.997657i
$285$		0			0
$286$	12.8145	−	7.86234i	0.757734	−	0.464910i
$287$	0.833649	+	0.216150i	0.0492088	+	0.0127589i
$288$	−12.8860	−	5.29637i	−0.759314	−	0.312091i
$289$	−7.49319	−	12.9786i	−0.440776	−	0.763447i
$290$		0			0
$291$	5.30071	+	3.06037i	0.310733	+	0.179402i
$292$	−0.151627	−	2.83398i	−0.00887333	−	0.165846i
$293$			2.11501i			0.123560i	0.998090	+	0.0617801i	$0.0196777\pi$
$293$			2.11501i			0.123560i	−0.998090	+	0.0617801i	$0.980322\pi$
$294$	−7.24871	+	0.311415i	−0.422753	+	0.0181621i
$295$		0			0
$296$	−10.4306	+	7.19392i	−0.606264	+	0.418138i
$297$	−9.32902	−	5.38611i	−0.541325	−	0.312534i
$298$	0.332032	+	12.4205i	0.0192341	+	0.719501i
$299$	9.70487	+	16.8093i	0.561247	+	0.972108i
$300$		0			0
$301$	−23.7709	−	6.16335i	−1.37013	−	0.355250i
$302$	0.222121	+	0.362024i	0.0127816	+	0.0208321i
$303$	−0.177310	+	0.102370i	−0.0101862	+	0.00588100i
$304$	12.8275	−	1.37657i	0.735709	−	0.0789517i
$305$		0			0
$306$	2.35595	−	4.34478i	0.134681	−	0.248375i
$307$	−18.6560			−1.06475			−0.532376	−	0.846508i	$-0.678701\pi$
$307$	−18.6560			−1.06475			−0.532376	+	0.846508i	$0.678701\pi$
$308$	13.9525	+	2.83183i	0.795016	+	0.161359i
$309$	−9.82137			−0.558718
$310$		0			0
$311$	−4.09153	+	7.08673i	−0.232009	+	0.401852i	−0.958399	−	0.285431i	$-0.907863\pi$
$311$	−4.09153	+	7.08673i	−0.232009	+	0.401852i	0.726390	+	0.687283i	$0.241197\pi$
$312$	−3.51405	+	7.39855i	−0.198944	+	0.418860i
$313$	−20.2427	+	11.6871i	−1.14419	+	0.660597i	−0.947464	−	0.319863i	$-0.896363\pi$
$313$	−20.2427	+	11.6871i	−1.14419	+	0.660597i	−0.196723	+	0.980459i	$0.563030\pi$
$314$	−14.2258	−	23.1859i	−0.802806	−	1.30846i
$315$		0			0
$316$	−21.7754	−	11.0652i	−1.22496	−	0.622464i
$317$	13.1039	+	22.6966i	0.735988	+	1.27477i	0.954288	+	0.298887i	$0.0966154\pi$
$317$	13.1039	+	22.6966i	0.735988	+	1.27477i	−0.218300	+	0.975882i	$0.570051\pi$
$318$	0.0447574	+	1.67427i	0.00250987	+	0.0938883i
$319$	−12.0680	−	6.96749i	−0.675680	−	0.390104i
$320$		0			0
$321$			3.97890i			0.222081i
$322$	−4.13607	+	17.9091i	−0.230494	+	0.998034i
$323$			4.57675i			0.254657i
$324$	−8.89563	+	0.475946i	−0.494202	+	0.0264414i
$325$		0			0
$326$	−15.1538	+	0.405098i	−0.839289	+	0.0224363i
$327$	−3.26767	−	5.65977i	−0.180702	−	0.312986i
$328$	0.917720	−	0.0737395i	0.0506726	−	0.00407158i
$329$	16.7424	−	4.63187i	0.923039	−	0.255363i
$330$		0			0
$331$	−16.9060	+	9.76067i	−0.929237	+	0.536495i	−0.886570	−	0.462594i	$-0.846919\pi$
$331$	−16.9060	+	9.76067i	−0.929237	+	0.536495i	−0.0426665	+	0.999089i	$0.513585\pi$
$332$	5.74111	+	8.81943i	0.315085	+	0.484029i
$333$	−5.51654	+	9.55493i	−0.302305	+	0.523607i
$334$	−16.4422	−	8.91574i	−0.899675	−	0.487848i
$335$		0			0
$336$	−7.21218	+	2.85398i	−0.393457	+	0.155697i
$337$	−31.7520			−1.72964			−0.864820	−	0.502082i	$-0.832567\pi$
$337$	−31.7520			−1.72964			−0.864820	+	0.502082i	$0.832567\pi$
$338$	−3.24700	−	1.76068i	−0.176614	−	0.0957684i
$339$	0.385364	−	0.667470i	0.0209301	−	0.0362520i
$340$		0			0
$341$	−17.7898	+	10.2710i	−0.963373	+	0.556204i
$342$	9.57508	−	5.87481i	0.517761	−	0.317674i
$343$	12.7736	−	13.4103i	0.689707	−	0.724088i
$344$	−26.1681	+	2.10263i	−1.41089	+	0.113366i
$345$		0			0
$346$	15.9100	−	0.425314i	0.855326	−	0.0228650i
$347$	15.9212	+	9.19210i	0.854694	+	0.493458i	0.862232	−	0.506514i	$-0.169066\pi$
$347$	15.9212	+	9.19210i	0.854694	+	0.493458i	−0.00753782	+	0.999972i	$0.502399\pi$
$348$	7.58097	−	0.405607i	0.406383	−	0.0217428i
$349$		−	2.37390i		−	0.127072i	−0.997980	−	0.0635360i	$-0.979762\pi$
$349$		−	2.37390i		−	0.127072i	0.997980	−	0.0635360i	$-0.0202378\pi$
$350$		0			0
$351$			15.8195i			0.844384i
$352$	15.0843	−	2.02781i	0.803994	−	0.108082i
$353$	−1.86560	−	1.07710i	−0.0992958	−	0.0573284i	0.449530	−	0.893265i	$-0.351592\pi$
$353$	−1.86560	−	1.07710i	−0.0992958	−	0.0573284i	−0.548826	+	0.835937i	$0.684925\pi$
$354$	−0.211471	−	7.91062i	−0.0112396	−	0.420445i
$355$		0			0
$356$	−8.46037	−	4.29914i	−0.448399	−	0.227854i
$357$	−0.733682	−	2.65198i	−0.0388306	−	0.140358i
$358$	0.596083	+	0.971527i	0.0315039	+	0.0513468i
$359$	4.40004	−	2.54037i	0.232225	−	0.134075i	−0.379373	−	0.925244i	$-0.623860\pi$
$359$	4.40004	−	2.54037i	0.232225	−	0.134075i	0.611598	+	0.791168i	$0.290527\pi$
$360$		0			0
$361$	4.29874	−	7.44564i	0.226250	−	0.391876i
$362$	−0.0449714	+	0.0829350i	−0.00236364	+	0.00435897i
$363$	−2.75648			−0.144678
$364$	−6.64342	−	19.8241i	−0.348210	−	1.03907i
$365$		0			0
$366$	7.06523	−	13.0295i	0.369306	−	0.681063i
$367$	6.77267	−	11.7306i	0.353530	−	0.612333i	−0.633335	−	0.773878i	$-0.718314\pi$
$367$	6.77267	−	11.7306i	0.353530	−	0.612333i	0.986865	+	0.161545i	$0.0516478\pi$
$368$	2.09663	+	19.5374i	0.109295	+	1.01846i
$369$	0.694275	−	0.400840i	0.0361425	−	0.0208669i
$370$		0			0
$371$	−3.04749	−	2.99849i	−0.158218	−	0.155674i
$372$	5.06985	−	9.97707i	0.262860	−	0.517287i
$373$	3.56700	+	6.17822i	0.184692	+	0.319896i	0.943473	−	0.331450i	$-0.107538\pi$
$373$	3.56700	+	6.17822i	0.184692	+	0.319896i	−0.758781	+	0.651346i	$0.774205\pi$
$374$	0.144287	+	5.39742i	0.00746089	+	0.279094i
$375$		0			0
$376$	15.2874	−	10.5436i	0.788386	−	0.543747i
$377$			20.4642i			1.05396i
$378$	−10.2176	+	10.9554i	−0.525538	+	0.563484i
$379$			16.2436i			0.834379i	0.908820	+	0.417189i	$0.136985\pi$
$379$			16.2436i			0.834379i	−0.908820	+	0.417189i	$0.863015\pi$
$380$		0			0
$381$	1.09027	+	0.629468i	0.0558562	+	0.0322486i
$382$	−24.6836	+	0.659856i	−1.26292	+	0.0337612i
$383$	−4.94358	−	8.56254i	−0.252605	−	0.437525i	0.711637	−	0.702547i	$-0.247954\pi$
$383$	−4.94358	−	8.56254i	−0.252605	−	0.437525i	−0.964242	+	0.265022i	$0.914621\pi$
$384$	−6.28456	+	5.40921i	−0.320707	+	0.276038i
$385$		0			0
$386$	20.7291	−	12.7184i	1.05508	−	0.647349i
$387$	−19.7967	+	11.4296i	−1.00632	+	0.581002i
$388$	−13.9981	+	9.11222i	−0.710645	+	0.462603i
$389$	−15.9811	+	27.6802i	−0.810276	+	1.40344i	0.102395	+	0.994744i	$0.467350\pi$
$389$	−15.9811	+	27.6802i	−0.810276	+	1.40344i	−0.912671	+	0.408696i	$0.865984\pi$
$390$		0			0
$391$	−6.97078			−0.352527
$392$	8.20340	−	18.0195i	0.414334	−	0.910125i
$393$	10.3658			0.522886
$394$	14.8429	+	8.04854i	0.747774	+	0.405480i
$395$		0			0
$396$	11.1068	−	7.23011i	0.558138	−	0.363326i
$397$	−15.1344	+	8.73784i	−0.759573	+	0.438539i	−0.829142	−	0.559038i	$-0.811171\pi$
$397$	−15.1344	+	8.73784i	−0.759573	+	0.438539i	0.0695697	+	0.997577i	$0.477837\pi$
$398$	−18.7084	+	11.4786i	−0.937766	+	0.575369i
$399$	1.56967	−	6.05393i	0.0785819	−	0.303076i
$400$		0			0
$401$	8.67926	+	15.0329i	0.433422	+	0.750708i	0.997165	−	0.0752415i	$-0.0239728\pi$
$401$	8.67926	+	15.0329i	0.433422	+	0.750708i	−0.563744	+	0.825950i	$0.690639\pi$
$402$	3.13588	−	0.0838301i	0.156404	−	0.00418106i
$403$	26.1252	+	15.0834i	1.30139	+	0.751358i
$404$	−0.0298500	−	0.557909i	−0.00148509	−	0.0277570i
$405$		0			0
$406$	−13.2175	+	14.1719i	−0.655975	+	0.703340i
$407$		−	12.0531i		−	0.597448i
$408$	−1.67010	−	2.42150i	−0.0826823	−	0.119882i
$409$	−6.32187	−	3.64993i	−0.312596	−	0.180478i	0.335491	−	0.942043i	$-0.391098\pi$
$409$	−6.32187	−	3.64993i	−0.312596	−	0.180478i	−0.648088	+	0.761566i	$0.724431\pi$
$410$		0			0
$411$	−5.44952	−	9.43885i	−0.268805	−	0.465584i
$412$	12.1414	−	23.8933i	0.598164	−	1.17714i
$413$	14.3989	+	14.1674i	0.708522	+	0.697130i
$414$	8.94784	+	14.5837i	0.439762	+	0.716748i
$415$		0			0
$416$	−13.6549	−	17.6952i	−0.669489	−	0.867578i
$417$	2.58995	−	4.48592i	0.126830	−	0.219677i
$418$	−5.84989	+	10.7882i	−0.286128	+	0.527669i
$419$	−17.9278			−0.875831			−0.437915	−	0.899016i	$-0.644283\pi$
$419$	−17.9278			−0.875831			−0.437915	+	0.899016i	$0.644283\pi$
$420$		0			0
$421$	12.6334			0.615716			0.307858	−	0.951432i	$-0.400388\pi$
$421$	12.6334			0.615716			0.307858	+	0.951432i	$0.400388\pi$
$422$	−9.54805	+	17.6082i	−0.464792	+	0.857156i
$423$	8.08522	−	14.0040i	0.393117	−	0.680898i
$424$	−4.12847	−	1.96088i	−0.200496	−	0.0952288i
$425$		0			0
$426$	−8.35232	−	13.6130i	−0.404671	−	0.659554i
$427$	10.0881	+	36.4647i	0.488198	+	1.76465i
$428$	−9.67983	−	4.91881i	−0.467892	−	0.237759i
$429$	−3.89567	−	6.74750i	−0.188085	−	0.325773i
$430$		0			0
$431$	28.2962	+	16.3368i	1.36298	+	0.786918i	0.990020	−	0.140929i	$-0.0450090\pi$
$431$	28.2962	+	16.3368i	1.36298	+	0.786918i	0.372962	+	0.927847i	$0.378342\pi$
$432$	−6.48191	+	14.6446i	−0.311861	+	0.704590i
$433$			23.5884i			1.13359i	0.823860	+	0.566794i	$0.191816\pi$
$433$			23.5884i			1.13359i	−0.823860	+	0.566794i	$0.808184\pi$
$434$	8.35015	+	27.3195i	0.400820	+	1.31138i
$435$		0			0
$436$	17.8086	−	0.952818i	0.852877	−	0.0456317i
$437$	−13.7212	−	7.92195i	−0.656375	−	0.378958i
$438$	−1.47027	+	0.0393039i	−0.0702520	+	0.00187801i
$439$	9.19501	+	15.9262i	0.438854	+	0.760117i	0.997601	−	0.0692207i	$-0.0220513\pi$
$439$	9.19501	+	15.9262i	0.438854	+	0.760117i	−0.558748	+	0.829338i	$0.688718\pi$
$440$		0			0
$441$	−0.279428	−	17.2377i	−0.0133061	−	0.820842i
$442$	6.75849	−	4.14669i	0.321469	−	0.197238i
$443$	2.93092	−	1.69217i	0.139252	−	0.0803973i	−0.428755	−	0.903421i	$-0.641048\pi$
$443$	2.93092	−	1.69217i	0.139252	−	0.0803973i	0.568008	+	0.823023i	$0.307714\pi$
$444$	3.58241	+	5.50326i	0.170014	+	0.261173i
$445$		0			0
$446$	3.77242	+	2.04559i	0.178629	+	0.0968614i
$447$	6.43914			0.304561
$448$	1.97272	−	21.0739i	0.0932025	−	0.995647i
$449$	11.9013			0.561658			0.280829	−	0.959758i	$-0.409391\pi$
$449$	11.9013			0.561658			0.280829	+	0.959758i	$0.409391\pi$
$450$		0			0
$451$	−0.437896	+	0.758458i	−0.0206197	+	0.0357144i
$452$	1.14742	+	1.76265i	0.0539700	+	0.0829081i
$453$	0.190625	−	0.110058i	0.00895636	−	0.00517096i
$454$	17.8121	−	10.9287i	0.835963	−	0.512907i
$455$		0			0
$456$	−0.535494	−	6.66445i	−0.0250768	−	0.312092i
$457$	−10.5352	−	18.2475i	−0.492816	−	0.853582i	0.507150	−	0.861858i	$-0.330699\pi$
$457$	−10.5352	−	18.2475i	−0.492816	−	0.853582i	−0.999966	+	0.00827601i	$0.997366\pi$
$458$	9.09142	−	0.243037i	0.424814	−	0.0113564i
$459$	−4.92023	−	2.84070i	−0.229657	−	0.132592i
$460$		0			0
$461$		−	29.6708i		−	1.38191i	−0.722899	−	0.690954i	$-0.757191\pi$
$461$		−	29.6708i		−	1.38191i	0.722899	−	0.690954i	$-0.242809\pi$
$462$	1.66028	−	7.18897i	0.0772432	−	0.334461i
$463$		−	15.0481i		−	0.699342i	−0.936873	−	0.349671i	$-0.886293\pi$
$463$		−	15.0481i		−	0.699342i	0.936873	−	0.349671i	$-0.113707\pi$
$464$	−8.38501	+	18.9443i	−0.389264	+	0.879468i
$465$		0			0
$466$	0.660251	+	24.6984i	0.0305855	+	1.14413i
$467$	−2.57299	−	4.45656i	−0.119064	−	0.206225i	0.800333	−	0.599556i	$-0.204656\pi$
$467$	−2.57299	−	4.45656i	−0.119064	−	0.206225i	−0.919397	+	0.393331i	$0.871323\pi$
$468$	−17.3507	−	8.81676i	−0.802036	−	0.407555i
$469$	−5.61614	+	5.70791i	−0.259329	+	0.263567i
$470$		0			0
$471$	−12.2086	+	7.04865i	−0.562544	+	0.324785i
$472$	19.5063	+	9.26482i	0.897850	+	0.426448i
$473$	12.4863	−	21.6269i	0.574120	−	0.994405i
$474$	−6.03395	+	11.1277i	−0.277149	+	0.511110i
$475$		0			0
$476$	7.35870	+	1.49354i	0.337286	+	0.0684564i
$477$	−3.97974			−0.182220
$478$	2.17399	−	4.00921i	0.0994358	−	0.183377i
$479$	19.9783	−	34.6035i	0.912834	−	1.58107i	0.102792	−	0.994703i	$-0.467222\pi$
$479$	19.9783	−	34.6035i	0.912834	−	1.58107i	0.810042	−	0.586372i	$-0.199444\pi$
$480$		0			0
$481$	−15.3291	+	8.85025i	−0.698946	+	0.403537i
$482$	−15.1520	−	24.6955i	−0.690153	−	1.12485i
$483$	9.22065	+	2.39074i	0.419554	+	0.108783i
$484$	3.40763	−	6.70594i	0.154892	−	0.304816i
$485$		0			0
$486$	0.577301	+	21.5955i	0.0261869	+	0.979590i
$487$	−10.5871	−	6.11246i	−0.479747	−	0.276982i	0.240564	−	0.970633i	$-0.422668\pi$
$487$	−10.5871	−	6.11246i	−0.479747	−	0.276982i	−0.720311	+	0.693651i	$0.756001\pi$
$488$	22.9638	+	33.2956i	1.03952	+	1.50722i
$489$			7.85613i			0.355266i
$490$		0			0
$491$		−	22.9515i		−	1.03579i	−0.855445	−	0.517894i	$-0.826716\pi$
$491$		−	22.9515i		−	1.03579i	0.855445	−	0.517894i	$-0.173284\pi$
$492$	−0.0254918	−	0.476453i	−0.00114926	−	0.0214802i
$493$	−6.36483	−	3.67473i	−0.286657	−	0.165502i
$494$	18.0159	−	0.481610i	0.810573	−	0.0216687i
$495$		0			0
$496$	18.0047	+	24.6678i	0.808433	+	1.10762i
$497$	39.4632	+	10.2321i	1.77017	+	0.458972i
$498$	4.64848	−	2.85209i	0.208303	−	0.127805i
$499$	−3.64376	+	2.10372i	−0.163117	+	0.0941756i	−0.579336	−	0.815089i	$-0.696688\pi$
$499$	−3.64376	+	2.10372i	−0.163117	+	0.0941756i	0.416219	+	0.909264i	$0.363355\pi$
$500$		0			0
$501$	−4.84657	+	8.39451i	−0.216529	+	0.375039i
$502$	18.8528	+	10.2229i	0.841443	+	0.456272i
$503$	−43.1904			−1.92576			−0.962882	−	0.269924i	$-0.913001\pi$
$503$	−43.1904			−1.92576			−0.962882	+	0.269924i	$0.913001\pi$
$504$	−6.32113	−	17.3124i	−0.281565	−	0.771155i
$505$		0			0
$506$	−16.4314	−	8.90988i	−0.730463	−	0.396093i
$507$	−0.957101	+	1.65775i	−0.0425064	+	0.0736232i
$508$	−2.87918	+	1.87424i	−0.127743	+	0.0831558i
$509$	32.3532	−	18.6791i	1.43403	−	0.827937i	0.436604	−	0.899654i	$-0.356181\pi$
$509$	32.3532	−	18.6791i	1.43403	−	0.827937i	0.997425	+	0.0717169i	$0.0228478\pi$
$510$		0			0
$511$	2.63314	−	2.67617i	0.116483	−	0.118387i
$512$	−5.39037	−	21.9760i	−0.238223	−	0.971211i
$513$	−6.45664	−	11.1832i	−0.285067	−	0.493751i
$514$	6.68903	−	0.178815i	0.295040	−	0.00788717i
$515$		0			0
$516$	0.726880	+	13.5857i	0.0319991	+	0.598077i
$517$			17.6653i			0.776921i
$518$	−16.3320	−	3.77185i	−0.717587	−	0.165725i
$519$		−	8.24817i		−	0.362055i
$520$		0			0
$521$	13.9610	+	8.06040i	0.611643	+	0.353132i	0.773608	−	0.633664i	$-0.218450\pi$
$521$	13.9610	+	8.06040i	0.611643	+	0.353132i	−0.161965	+	0.986796i	$0.551783\pi$
$522$	0.482065	+	18.0329i	0.0210994	+	0.789279i
$523$	7.98356	+	13.8279i	0.349097	+	0.604653i	0.986089	−	0.166217i	$-0.0531552\pi$
$523$	7.98356	+	13.8279i	0.349097	+	0.604653i	−0.636993	+	0.770870i	$0.719822\pi$
$524$	−12.8145	+	25.2178i	−0.559802	+	1.10165i
$525$		0			0
$526$	−3.47635	−	5.66594i	−0.151576	−	0.247047i
$527$	−9.38257	+	5.41703i	−0.408711	+	0.235969i
$528$	−0.841618	−	7.84259i	−0.0366267	−	0.341305i
$529$	0.565805	−	0.980002i	0.0246002	−	0.0426088i
$530$		0			0
$531$	18.8036			0.816007
$532$	12.7875	+	11.3027i	0.554407	+	0.490034i
$533$	1.28614			0.0557090
$534$	−2.34437	+	4.32342i	−0.101451	+	0.187092i
$535$		0			0
$536$	−3.67271	+	7.73257i	−0.158637	+	0.333996i
$537$	0.511562	−	0.295350i	0.0220755	−	0.0127453i
$538$	−18.1502	−	29.5822i	−0.782511	−	1.27538i
$539$	9.67999	+	16.1557i	0.416947	+	0.695876i
$540$		0			0
$541$	7.31686	+	12.6732i	0.314576	+	0.544862i	0.979347	−	0.202185i	$-0.0648042\pi$
$541$	7.31686	+	12.6732i	0.314576	+	0.544862i	−0.664771	+	0.747047i	$0.731471\pi$
$542$	0.997384	+	37.3098i	0.0428413	+	1.60259i
$543$	0.0423423	+	0.0244463i	0.00181708	+	0.00104909i
$544$	7.95562	−	1.06949i	0.341094	−	0.0458540i
$545$		0			0
$546$	−10.3620	+	3.16713i	−0.443454	+	0.135541i
$547$		−	16.5936i		−	0.709493i	−0.934963	−	0.354747i	$-0.884567\pi$
$547$		−	16.5936i		−	0.709493i	0.934963	−	0.354747i	$-0.115433\pi$
$548$	29.6996	−	1.58902i	1.26870	−	0.0678798i
$549$	30.5005	+	17.6094i	1.30173	+	0.751553i
$550$		0			0
$551$	−8.35232	−	14.4666i	−0.355821	−	0.616300i
$552$	10.1505	−	0.815602i	0.432035	−	0.0347143i
$553$	−8.61560	−	31.1421i	−0.366373	−	1.32430i
$554$	29.0143	−	17.8018i	1.23270	−	0.756327i
$555$		0			0
$556$	7.71155	+	11.8464i	0.327043	+	0.502399i
$557$	12.3878	−	21.4562i	0.524886	−	0.909129i	−0.474694	−	0.880151i	$-0.657441\pi$
$557$	12.3878	−	21.4562i	0.524886	−	0.909129i	0.999580	−	0.0289782i	$-0.00922532\pi$
$558$	23.3767	+	12.6760i	0.989615	+	0.536617i
$559$	−36.6734			−1.55112
$560$		0			0
$561$	2.79817			0.118139
$562$	−9.67930	−	5.24859i	−0.408296	−	0.221398i
$563$	−11.9762	+	20.7434i	−0.504737	+	0.874230i	0.495248	+	0.868751i	$0.335077\pi$
$563$	−11.9762	+	20.7434i	−0.504737	+	0.874230i	−0.999985	+	0.00547814i	$0.998256\pi$
$564$	−5.25049	−	8.06575i	−0.221086	−	0.339629i
$565$		0			0
$566$	−9.58371	+	5.88011i	−0.402833	+	0.247159i
$567$	−8.40027	−	8.26520i	−0.352778	−	0.347106i
$568$	43.4430	−	3.49068i	1.82283	−	0.146466i
$569$	4.58078	+	7.93415i	0.192036	+	0.332617i	0.945925	−	0.324385i	$-0.105157\pi$
$569$	4.58078	+	7.93415i	0.192036	+	0.332617i	−0.753889	+	0.657002i	$0.771824\pi$
$570$		0			0
$571$	−21.4132	−	12.3629i	−0.896114	−	0.517372i	−0.0201768	−	0.999796i	$-0.506423\pi$
$571$	−21.4132	−	12.3629i	−0.896114	−	0.517372i	−0.875938	+	0.482425i	$0.839756\pi$
$572$	21.2312	−	1.13594i	0.887720	−	0.0474959i
$573$			12.7967i			0.534589i
$574$	0.890684	+	0.830703i	0.0371764	+	0.0346729i
$575$		0			0
$576$	−12.4495	−	15.2712i	−0.518729	−	0.636301i
$577$	−8.23042	−	4.75184i	−0.342637	−	0.197822i	0.318801	−	0.947822i	$-0.396720\pi$
$577$	−8.23042	−	4.75184i	−0.342637	−	0.197822i	−0.661438	+	0.750000i	$0.730053\pi$
$578$	−0.566366	−	21.1864i	−0.0235577	−	0.881237i
$579$	−6.30178	−	10.9150i	−0.261893	−	0.453612i
$580$		0			0
$581$	−3.49398	+	13.4756i	−0.144955	+	0.559062i
$582$	4.52679	+	7.37801i	0.187642	+	0.305828i
$583$	3.76518	−	2.17383i	0.155938	−	0.0900308i
$584$	1.72196	−	3.62543i	0.0712551	−	0.150022i
$585$		0			0
$586$	−1.42578	+	2.62939i	−0.0588985	+	0.108619i
$587$	14.2100			0.586508			0.293254	−	0.956035i	$-0.405262\pi$
$587$	14.2100			0.586508			0.293254	+	0.956035i	$0.405262\pi$
$588$	−9.22155	−	4.49938i	−0.380290	−	0.185552i
$589$	−24.6248			−1.01465
$590$		0			0
$591$	4.37516	−	7.57801i	0.179970	−	0.311717i
$592$	−17.8169	+	1.91200i	−0.732271	+	0.0785828i
$593$	−15.3781	+	8.87854i	−0.631502	+	0.364598i	−0.781334	−	0.624114i	$-0.785460\pi$
$593$	−15.3781	+	8.87854i	−0.631502	+	0.364598i	0.149831	+	0.988712i	$0.452127\pi$
$594$	−7.96695	−	12.9850i	−0.326888	−	0.532779i
$595$		0			0
$596$	−7.96020	+	15.6651i	−0.326063	+	0.641666i
$597$	5.68746	+	9.85098i	0.232772	+	0.403174i
$598$	0.733533	+	27.4397i	0.0299964	+	1.12209i
$599$	18.1537	+	10.4811i	0.741741	+	0.428244i	0.822702	−	0.568473i	$-0.192466\pi$
$599$	18.1537	+	10.4811i	0.741741	+	0.428244i	−0.0809612	+	0.996717i	$0.525799\pi$
$600$		0			0
$601$			20.7196i			0.845169i	0.906324	+	0.422585i	$0.138877\pi$
$601$			20.7196i			0.845169i	−0.906324	+	0.422585i	$0.861123\pi$
$602$	−25.3972	−	23.6869i	−1.03511	−	0.965405i
$603$			7.45401i			0.303551i
$604$	0.0320917	+	0.599807i	0.00130579	+	0.0244058i
$605$		0			0
$606$	−0.289442	+	0.00773753i	−0.0117578	+	0.000314316i
$607$	−1.60263	−	2.77584i	−0.0650487	−	0.112668i	0.831667	−	0.555275i	$-0.187387\pi$
$607$	−1.60263	−	2.77584i	−0.0650487	−	0.112668i	−0.896716	+	0.442607i	$0.854054\pi$
$608$	16.8752	+	6.93600i	0.684380	+	0.281292i
$609$	7.15881	+	7.04371i	0.290090	+	0.285425i
$610$		0			0
$611$	22.4668	−	12.9712i	0.908909	−	0.524759i
$612$	5.85786	−	3.81324i	0.236790	−	0.154141i
$613$	2.39778	−	4.15308i	0.0968454	−	0.167741i	−0.813532	−	0.581520i	$-0.802458\pi$
$613$	2.39778	−	4.15308i	0.0968454	−	0.167741i	0.910377	+	0.413779i	$0.135791\pi$
$614$	−23.1932	−	12.5765i	−0.936000	−	0.507545i
$615$		0			0
$616$	15.4368	+	12.9263i	0.621965	+	0.520814i
$617$	8.95961			0.360700			0.180350	−	0.983602i	$-0.442277\pi$
$617$	8.95961			0.360700			0.180350	+	0.983602i	$0.442277\pi$
$618$	−12.2100	−	6.62084i	−0.491157	−	0.266329i
$619$	−12.8347	+	22.2303i	−0.515868	+	0.893510i	0.483962	+	0.875089i	$0.339197\pi$
$619$	−12.8347	+	22.2303i	−0.515868	+	0.893510i	−0.999830	+	0.0184212i	$0.994136\pi$
$620$		0			0
$621$	17.0330	−	9.83400i	0.683510	−	0.394625i
$622$	−9.86394	+	6.05205i	−0.395508	+	0.242665i
$623$	−3.34741	−	12.0996i	−0.134111	−	0.484761i
$624$	−9.35623	+	6.82898i	−0.374549	+	0.273378i
$625$		0			0
$626$	−33.0444	+	0.883361i	−1.32072	+	0.0353062i
$627$	5.50790	+	3.17999i	0.219964	+	0.126996i
$628$	−2.05531	−	38.4147i	−0.0820160	−	1.53291i
$629$		−	6.35693i		−	0.253467i
$630$		0			0
$631$			1.75095i			0.0697043i	0.999392	+	0.0348521i	$0.0110960\pi$
$631$			1.75095i			0.0697043i	−0.999392	+	0.0348521i	$0.988904\pi$
$632$	−19.6119	−	28.4356i	−0.780120	−	1.13111i
$633$	8.98985	+	5.19029i	0.357314	+	0.206296i
$634$	0.990445	+	37.0502i	0.0393356	+	1.47145i
$635$		0			0
$636$	−1.07302	+	2.11163i	−0.0425482	+	0.0837315i
$637$	13.4391	−	24.1737i	0.532475	−	0.957798i
$638$	−10.3061	−	16.7974i	−0.408021	−	0.665014i
$639$	32.8655	−	18.9749i	1.30014	−	0.750636i
$640$		0			0
$641$	20.3887	−	35.3143i	0.805306	−	1.39483i	−0.110778	−	0.993845i	$-0.535334\pi$
$641$	20.3887	−	35.3143i	0.805306	−	1.39483i	0.916084	−	0.400986i	$-0.131332\pi$
$642$	−2.68228	+	4.94658i	−0.105861	+	0.195226i
$643$	−35.0077			−1.38057			−0.690285	−	0.723538i	$-0.742515\pi$
$643$	−35.0077			−1.38057			−0.690285	+	0.723538i	$0.742515\pi$
$644$	−17.2150	+	19.4764i	−0.678364	+	0.767478i
$645$		0			0
$646$	−3.08530	+	5.68983i	−0.121390	+	0.223863i
$647$	12.1215	−	20.9951i	0.476547	−	0.825404i	−0.523092	−	0.852276i	$-0.675221\pi$
$647$	12.1215	−	20.9951i	0.476547	−	0.825404i	0.999639	+	0.0268724i	$0.00855480\pi$
$648$	−11.3799	−	5.40508i	−0.447046	−	0.212331i
$649$	−17.7898	+	10.2710i	−0.698312	+	0.403171i
$650$		0			0
$651$	14.2687	−	3.94751i	0.559236	−	0.154715i
$652$	−19.1123	−	9.71192i	−0.748495	−	0.380348i
$653$	−21.5956	−	37.4046i	−0.845100	−	1.46376i	−0.885534	−	0.464574i	$-0.846208\pi$
$653$	−21.5956	−	37.4046i	−0.845100	−	1.46376i	0.0404346	−	0.999182i	$-0.487126\pi$
$654$	−0.246984	−	9.23906i	−0.00965782	−	0.361276i
$655$		0			0
$656$	1.19062	+	0.526985i	0.0464860	+	0.0205753i
$657$		−	3.49483i		−	0.136346i
$658$	23.9367	+	5.52814i	0.933150	+	0.215509i
$659$		−	11.6398i		−	0.453422i	−0.973962	−	0.226711i	$-0.927203\pi$
$659$		−	11.6398i		−	0.453422i	0.973962	−	0.226711i	$-0.0727973\pi$
$660$		0			0
$661$	14.8021	+	8.54599i	0.575735	+	0.332400i	0.759436	−	0.650582i	$-0.225475\pi$
$661$	14.8021	+	8.54599i	0.575735	+	0.332400i	−0.183702	+	0.982982i	$0.558808\pi$
$662$	−27.5975	+	0.737751i	−1.07261	+	0.0286735i
$663$	−2.05462	−	3.55871i	−0.0797950	−	0.138209i
$664$	1.19197	+	14.8346i	0.0462574	+	0.575693i
$665$		0			0
$666$	−13.2994	+	8.15989i	−0.515342	+	0.316189i
$667$	22.0339	−	12.7213i	0.853157	−	0.492570i
$668$	−14.4306	−	22.1682i	−0.558338	−	0.857712i
$669$	1.11198	−	1.92600i	0.0429915	−	0.0744634i
$670$		0			0
$671$	−38.4748			−1.48530
$672$	−10.8902	−	1.31384i	−0.420097	−	0.0506823i
$673$	3.77972			0.145697			0.0728487	−	0.997343i	$-0.476791\pi$
$673$	3.77972			0.145697			0.0728487	+	0.997343i	$0.476791\pi$
$674$	−39.4742	−	21.4048i	−1.52049	−	0.824482i
$675$		0			0
$676$	−2.84976	−	4.37777i	−0.109606	−	0.168376i
$677$	−24.0534	+	13.8872i	−0.924446	+	0.533729i	−0.885051	−	0.465494i	$-0.845877\pi$
$677$	−24.0534	+	13.8872i	−0.924446	+	0.533729i	−0.0393956	+	0.999224i	$0.512543\pi$
$678$	0.929044	−	0.570017i	0.0356797	−	0.0218914i
$679$	−21.3883	−	5.54559i	−0.820808	−	0.212820i
$680$		0			0
$681$	−5.41499	−	9.37904i	−0.207503	−	0.359405i
$682$	−29.0403	+	0.776321i	−1.11201	+	0.0297269i
$683$	9.67614	+	5.58652i	0.370247	+	0.213762i	0.673567	−	0.739127i	$-0.264761\pi$
$683$	9.67614	+	5.58652i	0.370247	+	0.213762i	−0.303319	+	0.952889i	$0.598095\pi$
$684$	15.8641	−	0.848783i	0.606580	−	0.0324540i
$685$		0			0
$686$	24.9204	−	8.06075i	0.951464	−	0.307761i
$687$		−	4.71324i		−	0.179821i
$688$	−33.9497	−	15.0266i	−1.29432	−	0.572884i
$689$	−5.52935	−	3.19237i	−0.210652	−	0.121620i
$690$		0			0
$691$	−17.7057	−	30.6672i	−0.673556	−	1.16663i	−0.976889	−	0.213749i	$-0.931433\pi$
$691$	−17.7057	−	30.6672i	−0.673556	−	1.16663i	0.303332	−	0.952885i	$-0.401901\pi$
$692$	20.0661	+	10.1966i	0.762797	+	0.387616i
$693$	16.9706	+	4.40016i	0.644659	+	0.167148i
$694$	13.5966	+	22.1605i	0.516122	+	0.841202i
$695$		0			0
$696$	9.69812	+	4.60627i	0.367606	+	0.174600i
$697$	−0.230952	+	0.400020i	−0.00874791	+	0.0151518i
$698$	1.60031	−	2.95124i	0.0605725	−	0.111706i
$699$	12.8043			0.484304
$700$		0			0
$701$	2.24955			0.0849643			0.0424821	−	0.999097i	$-0.486473\pi$
$701$	2.24955			0.0849643			0.0424821	+	0.999097i	$0.486473\pi$
$702$	−10.6643	+	19.6669i	−0.402500	+	0.742279i
$703$	7.22434	−	12.5129i	0.272471	−	0.471934i
$704$	20.1198	+	7.64771i	0.758293	+	0.288234i
$705$		0			0
$706$	−1.59321	−	2.59671i	−0.0599614	−	0.0977283i
$707$	0.518370	−	0.526841i	0.0194953	−	0.0198139i
$708$	5.06985	−	9.97707i	0.190537	−	0.374961i
$709$	−7.94601	−	13.7629i	−0.298418	−	0.516876i	0.677356	−	0.735656i	$-0.263126\pi$
$709$	−7.94601	−	13.7629i	−0.298418	−	0.516876i	−0.975774	+	0.218780i	$0.929792\pi$
$710$		0			0
$711$	−26.0485	−	15.0391i	−0.976893	−	0.564010i
$712$	−7.61980	−	11.0480i	−0.285564	−	0.414043i
$713$		−	37.5056i		−	1.40460i
$714$	0.875651	−	3.79154i	0.0327704	−	0.141895i
$715$		0			0
$716$	0.0861211	+	1.60964i	0.00321850	+	0.0601551i
$717$	−2.04689	−	1.18177i	−0.0764425	−	0.0441341i
$718$	7.18267	−	0.192011i	0.268055	−	0.00716579i
$719$	−18.0142	−	31.2015i	−0.671817	−	1.16362i	−0.977388	−	0.211452i	$-0.932181\pi$
$719$	−18.0142	−	31.2015i	−0.671817	−	1.16362i	0.305572	−	0.952169i	$-0.401152\pi$
$720$		0			0
$721$	34.1711	−	9.45359i	1.27260	−	0.352070i
$722$	10.3635	−	6.35856i	0.385690	−	0.236641i
$723$	−13.0035	+	7.50758i	−0.483606	+	0.279210i
$724$	−0.111817	+	0.0727888i	−0.00415565	+	0.00270517i
$725$		0			0
$726$	−3.42687	−	1.85822i	−0.127183	−	0.0689648i
$727$	−51.4779			−1.90921			−0.954604	−	0.297878i	$-0.903721\pi$
$727$	−51.4779			−1.90921			−0.954604	+	0.297878i	$0.903721\pi$
$728$	5.10481	−	29.1239i	0.189197	−	1.07940i
$729$	−2.16686			−0.0802541
$730$		0			0
$731$	6.58541	−	11.4063i	0.243570	−	0.421876i
$732$	17.5670	−	11.4355i	0.649296	−	0.422667i
$733$	31.1280	−	17.9717i	1.14974	−	0.663801i	0.200914	−	0.979609i	$-0.435609\pi$
$733$	31.1280	−	17.9717i	1.14974	−	0.663801i	0.948823	+	0.315807i	$0.102275\pi$
$734$	16.3277	−	10.0179i	0.602667	−	0.369768i
$735$		0			0
$736$	−10.5641	+	25.7024i	−0.389398	+	0.947401i
$737$	−4.07155	−	7.05214i	−0.149978	−	0.259769i
$738$	1.13334	−	0.0302971i	0.0417189	−	0.00111525i
$739$	15.7903	+	9.11653i	0.580855	+	0.335357i	0.761473	−	0.648196i	$-0.224476\pi$
$739$	15.7903	+	9.11653i	0.580855	+	0.335357i	−0.180618	+	0.983553i	$0.557810\pi$
$740$		0			0
$741$		−	9.33993i		−	0.343111i
$742$	−1.76729	−	5.78213i	−0.0648794	−	0.212269i
$743$		−	29.1171i		−	1.06820i	−0.845420	−	0.534102i	$-0.820650\pi$
$743$		−	29.1171i		−	1.06820i	0.845420	−	0.534102i	$-0.179350\pi$
$744$	13.0287	−	8.98582i	0.477654	−	0.329436i
$745$		0			0
$746$	0.269608	+	10.0854i	0.00987105	+	0.369252i
$747$	6.47941	+	11.2227i	0.237069	+	0.410616i
$748$	−3.45916	+	6.80736i	−0.126479	+	0.248902i
$749$	−3.82990	−	13.8436i	−0.139942	−	0.505835i
$750$		0			0
$751$	37.2703	−	21.5180i	1.36001	−	0.785203i	0.370386	−	0.928878i	$-0.379225\pi$
$751$	37.2703	−	21.5180i	1.36001	−	0.785203i	0.989625	+	0.143675i	$0.0458921\pi$
$752$	26.1130	−	2.80229i	0.952245	−	0.102189i
$753$	5.55715	−	9.62527i	0.202514	−	0.350764i
$754$	−13.7954	+	25.4411i	−0.502400	+	0.926512i
$755$		0			0
$756$	−20.0879	+	6.73182i	−0.730590	+	0.244834i
$757$	10.6531			0.387193			0.193597	−	0.981081i	$-0.437985\pi$
$757$	10.6531			0.387193			0.193597	+	0.981081i	$0.437985\pi$
$758$	−10.9502	+	20.1941i	−0.397730	+	0.733484i
$759$	−4.84339	+	8.38899i	−0.175804	+	0.304501i
$760$		0			0
$761$	12.3298	−	7.11864i	0.446956	−	0.258050i	−0.259588	−	0.965720i	$-0.583587\pi$
$761$	12.3298	−	7.11864i	0.446956	−	0.258050i	0.706544	+	0.707669i	$0.250253\pi$
$762$	0.931088	+	1.51754i	0.0337297	+	0.0549745i
$763$	16.8169	+	16.5465i	0.608812	+	0.599023i
$764$	−31.1316	−	15.8195i	−1.12630	−	0.572331i
$765$		0			0
$766$	−0.373656	−	13.9776i	−0.0135007	−	0.505030i
$767$	26.1252	+	15.0834i	0.943327	+	0.544630i
$768$	−11.4595	+	2.48817i	−0.413508	+	0.0897842i
$769$		−	35.5770i		−	1.28294i	−0.767149	−	0.641469i	$-0.778325\pi$
$769$		−	35.5770i		−	1.28294i	0.767149	−	0.641469i	$-0.221675\pi$
$770$		0			0
$771$		−	3.46777i		−	0.124889i
$772$	34.3443	−	1.83753i	1.23608	−	0.0661342i
$773$	−10.2930	−	5.94268i	−0.370214	−	0.213743i	0.303338	−	0.952883i	$-0.401899\pi$
$773$	−10.2930	−	5.94268i	−0.370214	−	0.213743i	−0.673552	+	0.739140i	$0.735232\pi$
$774$	−32.3164	+	0.863899i	−1.16159	+	0.0310522i
$775$		0			0
$776$	−23.5453	+	1.89188i	−0.845226	+	0.0679145i
$777$	−2.18021	+	8.40868i	−0.0782148	+	0.301660i
$778$	−38.5277	+	23.6388i	−1.38129	+	0.847491i
$779$	−0.909207	+	0.524931i	−0.0325757	+	0.0188076i
$780$		0			0
$781$	−20.7291	+	35.9038i	−0.741745	+	1.28474i
$782$	−8.66609	−	4.69918i	−0.309899	−	0.168042i
$783$	20.7365			0.741061
$784$	22.3459	−	16.8718i	0.798069	−	0.602566i
$785$		0			0
$786$	12.8868	+	6.98786i	0.459658	+	0.249249i
$787$	−23.1890	+	40.1645i	−0.826597	+	1.43171i	0.0740951	+	0.997251i	$0.476393\pi$
$787$	−23.1890	+	40.1645i	−0.826597	+	1.43171i	−0.900692	+	0.434457i	$0.856940\pi$
$788$	13.0270	+	20.0119i	0.464068	+	0.712896i
$789$	−2.98342	+	1.72248i	−0.106213	+	0.0613219i
$790$		0			0
$791$	−0.698305	+	2.69323i	−0.0248289	+	0.0957603i
$792$	18.6820	−	1.50111i	0.663836	−	0.0533398i
$793$	28.2510	+	48.9322i	1.00322	+	1.73763i
$794$	−24.7055	+	0.660441i	−0.876766	+	0.0234382i
$795$		0			0
$796$	−30.9963	+	1.65841i	−1.09864	+	0.0587806i
$797$		−	9.09251i		−	0.322073i	−0.986948	−	0.161037i	$-0.948516\pi$
$797$		−	9.09251i		−	0.322073i	0.986948	−	0.161037i	$-0.0514837\pi$
$798$	6.03253	−	6.46811i	0.213549	−	0.228969i
$799$			9.31691i			0.329609i
$800$		0			0
$801$	−10.1206	−	5.84312i	−0.357593	−	0.206457i
$802$	0.656013	+	24.5399i	0.0231646	+	0.866534i
$803$	1.90896	+	3.30641i	0.0673656	+	0.116681i
$804$	3.95505	+	2.00976i	0.139484	+	0.0708788i
$805$		0			0
$806$	22.3109	+	36.3634i	0.785867	+	1.28085i
$807$	−15.5766	+	8.99316i	−0.548323	+	0.316574i
$808$	0.338991	−	0.713717i	0.0119257	−	0.0251085i
$809$	8.66128	−	15.0018i	0.304515	−	0.527435i	−0.672639	−	0.739971i	$-0.734839\pi$
$809$	8.66128	−	15.0018i	0.304515	−	0.527435i	0.977153	+	0.212536i	$0.0681724\pi$
$810$		0			0
$811$	−16.4459			−0.577493			−0.288746	−	0.957406i	$-0.593238\pi$
$811$	−16.4459			−0.577493			−0.288746	+	0.957406i	$0.593238\pi$
$812$	−25.9857	+	8.70830i	−0.911921	+	0.305601i
$813$	19.3424			0.678368
$814$	8.12527	−	14.9844i	0.284791	−	0.525203i
$815$		0			0
$816$	−0.443879	−	4.13628i	−0.0155389	−	0.144799i
$817$	25.9254	−	14.9680i	0.907013	−	0.523664i
$818$	−5.39886	−	8.79934i	−0.188767	−	0.307662i
$819$	−6.86494	−	24.8141i	−0.239880	−	0.867075i
$820$		0			0
$821$	−22.4527	−	38.8892i	−0.783603	−	1.35724i	−0.929830	−	0.367990i	$-0.880046\pi$
$821$	−22.4527	−	38.8892i	−0.783603	−	1.35724i	0.146226	−	0.989251i	$-0.453287\pi$
$822$	−0.411897	−	15.4081i	−0.0143666	−	0.537418i
$823$	−20.5328	−	11.8546i	−0.715729	−	0.413226i	0.0974497	−	0.995240i	$-0.468931\pi$
$823$	−20.5328	−	11.8546i	−0.715729	−	0.413226i	−0.813179	+	0.582014i	$0.802265\pi$
$824$	31.2013	−	21.5194i	1.08695	−	0.749665i
$825$		0			0
$826$	8.35015	+	27.3195i	0.290539	+	0.950569i
$827$			8.20536i			0.285328i	0.989771	+	0.142664i	$0.0455669\pi$
$827$			8.20536i			0.285328i	−0.989771	+	0.142664i	$0.954433\pi$
$828$	1.29277	+	24.1624i	0.0449268	+	0.839702i
$829$	19.1548	+	11.0590i	0.665272	+	0.384095i	0.794283	−	0.607548i	$-0.207847\pi$
$829$	19.1548	+	11.0590i	0.665272	+	0.384095i	−0.129011	+	0.991643i	$0.541180\pi$
$830$		0			0
$831$	−8.82054	−	15.2776i	−0.305981	−	0.529975i
$832$	−5.04710	−	31.2039i	−0.174977	−	1.08180i
$833$	5.10534	+	8.52071i	0.176890	+	0.295225i
$834$	6.24391	−	3.83096i	0.216209	−	0.132655i
$835$		0			0
$836$	−14.5452	+	9.46838i	−0.503057	+	0.327471i
$837$	15.2841	−	26.4729i	0.528296	−	0.915036i
$838$	−22.2879	−	12.0856i	−0.769923	−	0.417490i
$839$	−3.64977			−0.126004			−0.0630020	−	0.998013i	$-0.520067\pi$
$839$	−3.64977			−0.126004			−0.0630020	+	0.998013i	$0.520067\pi$
$840$		0			0
$841$	−2.17525			−0.0750086
$842$	15.7059	+	8.51652i	0.541262	+	0.293499i
$843$	−2.85312	+	4.94174i	−0.0982665	+	0.170203i
$844$	−23.7403	+	15.4541i	−0.817176	+	0.531950i
$845$		0			0
$846$	19.4920	−	11.9594i	0.670150	−	0.411172i
$847$	9.59051	−	2.65326i	0.329534	−	0.0911671i
$848$	−3.81065	−	5.22088i	−0.130858	−	0.179286i
$849$	2.91351	+	5.04634i	0.0999913	+	0.173190i
$850$		0			0
$851$	19.0582	+	11.0033i	0.653308	+	0.377188i
$852$	−1.20673	−	22.5543i	−0.0413419	−	0.772697i
$853$		−	1.03474i		−	0.0354290i	−0.999843	−	0.0177145i	$-0.994361\pi$
$853$		−	1.03474i		−	0.0354290i	0.999843	−	0.0177145i	$-0.00563899\pi$
$854$	−12.0402	+	52.1337i	−0.412006	+	1.78398i
$855$		0			0
$856$	−8.71810	−	12.6405i	−0.297979	−	0.432043i
$857$	−42.0132	−	24.2563i	−1.43514	−	0.828581i	−0.437637	−	0.899152i	$-0.644185\pi$
$857$	−42.0132	−	24.2563i	−1.43514	−	0.828581i	−0.997507	+	0.0705709i	$0.977518\pi$
$858$	−0.294451	−	11.0147i	−0.0100524	−	0.376035i
$859$	−12.4674	−	21.5941i	−0.425382	−	0.736783i	0.571074	−	0.820898i	$-0.306527\pi$
$859$	−12.4674	−	21.5941i	−0.425382	−	0.736783i	−0.996456	+	0.0841157i	$0.973193\pi$
$860$		0			0
$861$	0.442687	−	0.449921i	0.0150867	−	0.0153333i
$862$	24.1649	+	39.3852i	0.823060	+	1.34147i
$863$	5.16765	−	2.98354i	0.175909	−	0.101561i	−0.409460	−	0.912328i	$-0.634283\pi$
$863$	5.16765	−	2.98354i	0.175909	−	0.101561i	0.585369	+	0.810767i	$0.300950\pi$
$864$	−17.9307	+	13.8366i	−0.610013	+	0.470732i
$865$		0			0
$866$	−15.9016	+	29.3252i	−0.540357	+	0.996511i
$867$	−10.9836			−0.373023
$868$	−8.03586	+	39.5928i	−0.272755	+	1.34387i
$869$	32.8588			1.11466
$870$		0			0
$871$	−5.97927	+	10.3564i	−0.202600	+	0.350913i
$872$	22.7820	+	10.8207i	0.771496	+	0.366434i
$873$	−17.8125	+	10.2840i	−0.602861	+	0.348062i
$874$	−11.7179	−	19.0984i	−0.396363	−	0.646014i
$875$		0			0
$876$	−1.85433	−	0.942281i	−0.0626522	−	0.0318367i
$877$	16.9149	+	29.2974i	0.571175	+	0.989304i	0.996446	+	0.0842381i	$0.0268456\pi$
$877$	16.9149	+	29.2974i	0.571175	+	0.989304i	−0.425270	+	0.905066i	$0.639821\pi$
$878$	0.694996	+	25.9981i	0.0234550	+	0.877394i
$879$	1.34243	+	0.775051i	0.0452789	+	0.0261418i
$880$		0			0
$881$			20.9239i			0.704944i	0.935822	+	0.352472i	$0.114659\pi$
$881$			20.9239i			0.704944i	−0.935822	+	0.352472i	$0.885341\pi$
$882$	11.2730	−	21.6183i	0.379581	−	0.727927i
$883$		−	14.7876i		−	0.497642i	−0.968549	−	0.248821i	$-0.919957\pi$
$883$		−	14.7876i		−	0.497642i	0.968549	−	0.248821i	$-0.0800432\pi$
$884$	11.1976	−	0.599107i	0.376615	−	0.0201501i
$885$		0			0
$886$	4.78446	−	0.127901i	0.160737	−	0.00429691i
$887$	3.69958	+	6.40786i	0.124220	+	0.215155i	0.921428	−	0.388550i	$-0.127024\pi$
$887$	3.69958	+	6.40786i	0.124220	+	0.215155i	−0.797208	+	0.603705i	$0.793691\pi$
$888$	0.743780	+	9.25667i	0.0249596	+	0.310633i
$889$	−4.39923	−	1.14064i	−0.147545	−	0.0382558i
$890$		0			0
$891$	10.3785	−	5.99206i	0.347694	−	0.200741i
$892$	3.31090	+	5.08617i	0.110857	+	0.170297i
$893$	−10.5882	+	18.3393i	−0.354321	+	0.613702i
$894$	8.00516	+	4.34079i	0.267733	+	0.145178i
$895$		0			0
$896$	16.6589	−	24.8693i	0.556536	−	0.830824i
$897$	14.2255			0.474976
$898$	14.7958	+	8.02298i	0.493741	+	0.267730i
$899$	19.7716	−	34.2453i	0.659418	−	1.14215i
$900$		0			0
$901$	1.98580	−	1.14650i	0.0661566	−	0.0381956i
$902$	−1.05569	+	0.647721i	−0.0351506	+	0.0215668i
$903$	−12.6229	+	12.8292i	−0.420063	+	0.426928i
$904$	0.238227	+	2.96484i	0.00792331	+	0.0986090i
$905$		0			0
$906$	0.311179	−	0.00831860i	0.0103382	−	0.000276367i
$907$	16.0320	+	9.25608i	0.532334	+	0.307343i	0.741966	−	0.670437i	$-0.233893\pi$
$907$	16.0320	+	9.25608i	0.532334	+	0.307343i	−0.209632	+	0.977780i	$0.567227\pi$
$908$	29.5113	−	1.57895i	0.979368	−	0.0523994i
$909$		−	0.688006i		−	0.0228197i
$910$		0			0
$911$		−	10.8437i		−	0.359267i	−0.983734	−	0.179634i	$-0.942509\pi$
$911$		−	10.8437i		−	0.359267i	0.983734	−	0.179634i	$-0.0574912\pi$
$912$	3.82695	−	8.64626i	0.126723	−	0.286306i
$913$	−12.2602	−	7.07841i	−0.405752	−	0.234261i
$914$	−0.796292	−	29.7874i	−0.0263390	−	0.985279i
$915$		0			0
$916$	11.4663	+	5.82661i	0.378858	+	0.192517i
$917$	−36.0653	+	9.97764i	−1.19098	+	0.329491i
$918$	−4.20187	−	6.84842i	−0.138682	−	0.226032i
$919$	−13.9555	+	8.05723i	−0.460351	+	0.265784i	−0.712192	−	0.701985i	$-0.752297\pi$
$919$	−13.9555	+	8.05723i	−0.460351	+	0.265784i	0.251841	+	0.967769i	$0.418964\pi$
$920$		0			0
$921$	−6.83653	+	11.8412i	−0.225271	+	0.390181i
$922$	20.0019	−	36.8869i	0.658726	−	1.21480i
$923$	60.8834			2.00400
$924$	6.91033	−	7.81811i	0.227333	−	0.257197i
$925$		0			0
$926$	10.1443	−	18.7078i	0.333362	−	0.614776i
$927$	16.5018	−	28.5820i	0.541991	−	0.938757i
$928$	−23.1951	+	17.8991i	−0.761417	+	0.587567i
$929$	−42.7419	+	24.6770i	−1.40232	+	0.809627i	−0.994630	−	0.103495i	$-0.966998\pi$
$929$	−42.7419	+	24.6770i	−1.40232	+	0.809627i	−0.407686	+	0.913122i	$0.633664\pi$
$930$		0			0
$931$	0.365932	+	22.5741i	0.0119930	+	0.739836i
$932$	−15.8290	+	31.1502i	−0.518496	+	1.02036i
$933$	2.99870	+	5.19390i	0.0981731	+	0.170041i
$934$	−0.194477	−	7.27493i	−0.00636349	−	0.238043i
$935$		0			0
$936$	−15.6268	−	22.6576i	−0.510779	−	0.740586i
$937$			31.3085i			1.02280i	0.859342	+	0.511402i	$0.170874\pi$
$937$			31.3085i			1.02280i	−0.859342	+	0.511402i	$0.829126\pi$
$938$	−10.8298	+	3.31012i	−0.353607	+	0.108079i
$939$			17.1311i			0.559054i
$940$		0			0
$941$	37.9492	+	21.9100i	1.23711	+	0.714245i	0.968502	−	0.249005i	$-0.0801035\pi$
$941$	37.9492	+	21.9100i	1.23711	+	0.714245i	0.268606	+	0.963250i	$0.413437\pi$
$942$	−19.9295	+	0.532766i	−0.649338	+	0.0173584i
$943$	−0.799514	−	1.38480i	−0.0260358	−	0.0450952i
$944$	18.0047	+	24.6678i	0.586002	+	0.802867i
$945$		0			0
$946$	30.1022	−	18.4693i	0.978708	−	0.600488i
$947$	−12.6739	+	7.31729i	−0.411847	+	0.237780i	−0.691583	−	0.722297i	$-0.743086\pi$
$947$	−12.6739	+	7.31729i	−0.411847	+	0.237780i	0.279736	+	0.960077i	$0.409753\pi$
$948$	−15.0029	+	9.76629i	−0.487270	+	0.317194i
$949$	2.80340	−	4.85563i	0.0910021	−	0.157620i
$950$		0			0
$951$	19.2078			0.622857
$952$	8.14153	+	6.81746i	0.263869	+	0.220955i
$953$	−28.2044			−0.913630			−0.456815	−	0.889562i	$-0.651010\pi$
$953$	−28.2044			−0.913630			−0.456815	+	0.889562i	$0.651010\pi$
$954$	−4.94763	−	2.68285i	−0.160186	−	0.0868604i
$955$		0			0
$956$	5.40542	−	3.51872i	0.174824	−	0.113804i
$957$	−8.84473	+	5.10651i	−0.285909	+	0.165070i
$958$	48.1643	−	29.5513i	1.55612	−	0.954759i
$959$	28.0457	+	27.5947i	0.905643	+	0.891081i
$960$		0			0
$961$	−13.6458	−	23.6352i	−0.440187	−	0.762427i
$962$	−25.0234	+	0.668938i	−0.806785	+	0.0215674i
$963$	−11.5793	−	6.68534i	−0.373139	−	0.215432i
$964$	−2.18913	−	40.9158i	−0.0705072	−	1.31781i
$965$		0			0
$966$	9.85149	+	9.18806i	0.316966	+	0.295621i
$967$			8.88824i			0.285827i	0.989735	+	0.142913i	$0.0456470\pi$
$967$			8.88824i			0.285827i	−0.989735	+	0.142913i	$0.954353\pi$
$968$	8.75702	−	6.03968i	0.281461	−	0.194123i
$969$	2.90493	+	1.67716i	0.0933198	+	0.0538782i
$970$		0			0
$971$	4.37105	+	7.57089i	0.140274	+	0.242961i	0.927600	−	0.373576i	$-0.121868\pi$
$971$	4.37105	+	7.57089i	0.140274	+	0.242961i	−0.787326	+	0.616537i	$0.788535\pi$
$972$	−13.8403	+	27.2367i	−0.443929	+	0.873618i
$973$	−4.69316	+	18.1006i	−0.150456	+	0.580280i
$974$	−9.04134	−	14.7360i	−0.289703	−	0.472173i
$975$		0			0
$976$	6.10333	+	56.8737i	0.195363	+	1.82048i
$977$	−20.9907	+	36.3569i	−0.671551	+	1.16316i	0.305914	+	0.952059i	$0.401038\pi$
$977$	−20.9907	+	36.3569i	−0.671551	+	1.16316i	−0.977464	+	0.211100i	$0.932295\pi$
$978$	−5.29601	+	9.76676i	−0.169348	+	0.312307i
$979$	12.7666			0.408022
$980$		0			0
$981$	21.9613			0.701170
$982$	15.4722	−	28.5334i	0.493738	−	0.910539i
$983$	5.50236	−	9.53036i	0.175498	−	0.303971i	−0.764836	−	0.644226i	$-0.777180\pi$
$983$	5.50236	−	9.53036i	0.175498	−	0.303971i	0.940333	+	0.340254i	$0.110513\pi$
$984$	0.289497	−	0.609513i	0.00922884	−	0.0194306i
$985$		0			0
$986$	−5.43554	−	8.85913i	−0.173103	−	0.282132i
$987$	3.19539	−	12.3240i	0.101710	−	0.392278i
$988$	22.7221	+	11.5462i	0.722885	+	0.367334i
$989$	22.7975	+	39.4865i	0.724920	+	1.25560i
$990$		0			0
$991$	−31.6799	−	18.2904i	−1.00634	−	0.581013i	−0.0962255	−	0.995360i	$-0.530677\pi$
$991$	−31.6799	−	18.2904i	−1.00634	−	0.581013i	−0.910119	+	0.414346i	$0.864010\pi$
$992$	5.75429	+	42.8044i	0.182699	+	1.35904i
$993$			14.3073i			0.454028i
$994$	42.1631	+	39.3237i	1.33733	+	1.24727i
$995$		0			0
$996$	7.70167	−	0.412065i	0.244037	−	0.0130568i
$997$	12.5263	+	7.23204i	0.396711	+	0.229041i	0.685064	−	0.728483i	$-0.259774\pi$
$997$	12.5263	+	7.23204i	0.396711	+	0.229041i	−0.288353	+	0.957524i	$0.593108\pi$
$998$	−5.94811	+	0.159008i	−0.188284	+	0.00503331i
$999$	8.96801	+	15.5331i	0.283735	+	0.491444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.e.451.14		32
4.3	odd	2	inner	700.2.p.e.451.8		32
5.2	odd	4		140.2.s.b.59.6	yes	32
5.3	odd	4		140.2.s.b.59.11	yes	32
5.4	even	2	inner	700.2.p.e.451.3		32
7.5	odd	6	inner	700.2.p.e.551.8		32
20.3	even	4		140.2.s.b.59.16	yes	32
20.7	even	4		140.2.s.b.59.1	yes	32
20.19	odd	2	inner	700.2.p.e.451.9		32
28.19	even	6	inner	700.2.p.e.551.14		32
35.2	odd	12		980.2.s.e.19.16		32
35.3	even	12		980.2.c.d.979.24		32
35.12	even	12		140.2.s.b.19.16	yes	32
35.13	even	4		980.2.s.e.619.11		32
35.17	even	12		980.2.c.d.979.9		32
35.18	odd	12		980.2.c.d.979.23		32
35.19	odd	6	inner	700.2.p.e.551.9		32
35.23	odd	12		980.2.s.e.19.1		32
35.27	even	4		980.2.s.e.619.6		32
35.32	odd	12		980.2.c.d.979.10		32
35.33	even	12		140.2.s.b.19.1	✓	32
140.3	odd	12		980.2.c.d.979.11		32
140.19	even	6	inner	700.2.p.e.551.3		32
140.23	even	12		980.2.s.e.19.6		32
140.27	odd	4		980.2.s.e.619.1		32
140.47	odd	12		140.2.s.b.19.11	yes	32
140.67	even	12		980.2.c.d.979.21		32
140.83	odd	4		980.2.s.e.619.16		32
140.87	odd	12		980.2.c.d.979.22		32
140.103	odd	12		140.2.s.b.19.6	yes	32
140.107	even	12		980.2.s.e.19.11		32
140.123	even	12		980.2.c.d.979.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.1	✓	32	35.33	even	12
140.2.s.b.19.6	yes	32	140.103	odd	12
140.2.s.b.19.11	yes	32	140.47	odd	12
140.2.s.b.19.16	yes	32	35.12	even	12
140.2.s.b.59.1	yes	32	20.7	even	4
140.2.s.b.59.6	yes	32	5.2	odd	4
140.2.s.b.59.11	yes	32	5.3	odd	4
140.2.s.b.59.16	yes	32	20.3	even	4
700.2.p.e.451.3		32	5.4	even	2	inner
700.2.p.e.451.8		32	4.3	odd	2	inner
700.2.p.e.451.9		32	20.19	odd	2	inner
700.2.p.e.451.14		32	1.1	even	1	trivial
700.2.p.e.551.3		32	140.19	even	6	inner
700.2.p.e.551.8		32	7.5	odd	6	inner
700.2.p.e.551.9		32	35.19	odd	6	inner
700.2.p.e.551.14		32	28.19	even	6	inner
980.2.c.d.979.9		32	35.17	even	12
980.2.c.d.979.10		32	35.32	odd	12
980.2.c.d.979.11		32	140.3	odd	12
980.2.c.d.979.12		32	140.123	even	12
980.2.c.d.979.21		32	140.67	even	12
980.2.c.d.979.22		32	140.87	odd	12
980.2.c.d.979.23		32	35.18	odd	12
980.2.c.d.979.24		32	35.3	even	12
980.2.s.e.19.1		32	35.23	odd	12
980.2.s.e.19.6		32	140.23	even	12
980.2.s.e.19.11		32	140.107	even	12
980.2.s.e.19.16		32	35.2	odd	12
980.2.s.e.619.1		32	140.27	odd	4
980.2.s.e.619.6		32	35.27	even	4
980.2.s.e.619.11		32	35.13	even	4
980.2.s.e.619.16		32	140.83	odd	4

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24320 + 0.674125i) q^{2} +(0.366453 - 0.634715i) q^{3} +(1.09111 + 1.67615i) q^{4} +(0.883452 - 0.542044i) q^{6} +(-0.664037 + 2.56107i) q^{7} +(0.226536 + 2.81934i) q^{8} +(1.23142 + 2.13289i) q^{9} +(-2.33007 - 1.34527i) q^{11} +(1.46372 - 0.0783137i) q^{12} +3.95118i q^{13} +(-2.55201 + 2.73628i) q^{14} +(-1.61896 + 3.65773i) q^{16} +(-1.22891 - 0.709509i) q^{17} +(0.0930760 + 3.48175i) q^{18} +(-1.61265 - 2.79319i) q^{19} +(1.38221 + 1.35998i) q^{21} +(-1.98987 - 3.24320i) q^{22} +(4.25426 - 2.45620i) q^{23} +(1.87249 + 0.889369i) q^{24} +(-2.66359 + 4.91212i) q^{26} +4.00375 q^{27} +(-5.01727 + 1.68138i) q^{28} +5.17926 q^{29} +(3.81745 - 6.61201i) q^{31} +(-4.47846 + 3.45592i) q^{32} +(-1.70772 + 0.985953i) q^{33} +(-1.04948 - 1.71050i) q^{34} +(-2.23142 + 4.39127i) q^{36} +(2.23990 + 3.87963i) q^{37} +(-0.121890 - 4.55962i) q^{38} +(2.50787 + 1.44792i) q^{39} -0.325509i q^{41} +(0.801566 + 2.62252i) q^{42} +9.28165i q^{43} +(-0.287494 - 5.37338i) q^{44} +(6.94469 - 0.185649i) q^{46} +(-3.28287 - 5.68610i) q^{47} +(1.72834 + 2.36796i) q^{48} +(-6.11811 - 3.40128i) q^{49} +(-0.900672 + 0.520003i) q^{51} +(-6.62277 + 4.31117i) q^{52} +(-0.807955 + 1.39942i) q^{53} +(4.97748 + 2.69903i) q^{54} +(-7.37094 - 1.29197i) q^{56} -2.36383 q^{57} +(6.43888 + 3.49147i) q^{58} +(3.81745 - 6.61201i) q^{59} +(12.3842 - 7.15003i) q^{61} +(9.20319 - 5.64664i) q^{62} +(-6.28018 + 1.73744i) q^{63} +(-7.89736 + 1.27737i) q^{64} +(-2.78770 + 0.0745223i) q^{66} +(2.62109 + 1.51329i) q^{67} +(-0.151627 - 2.83398i) q^{68} -3.60032i q^{69} -15.4089i q^{71} +(-5.73438 + 3.95498i) q^{72} +(-1.22891 - 0.709509i) q^{73} +(0.169301 + 6.33314i) q^{74} +(2.92222 - 5.75071i) q^{76} +(4.99257 - 5.07415i) q^{77} +(2.14171 + 3.49068i) q^{78} +(-10.5765 + 6.10637i) q^{79} +(-2.22709 + 3.85743i) q^{81} +(0.219434 - 0.404674i) q^{82} +5.26172 q^{83} +(-0.771396 + 3.80068i) q^{84} +(-6.25699 + 11.5390i) q^{86} +(1.89795 - 3.28735i) q^{87} +(3.26492 - 6.87401i) q^{88} +(-4.10930 + 2.37250i) q^{89} +(-10.1192 - 2.62373i) q^{91} +(8.75882 + 4.45079i) q^{92} +(-2.79783 - 4.84598i) q^{93} +(-0.248133 - 9.28205i) q^{94} +(0.552378 + 4.10898i) q^{96} +8.35134i q^{97} +(-5.31316 - 8.35286i) q^{98} -6.62638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{4} - 4 q^{9} - 22 q^{14} + 18 q^{16} - 52 q^{21} + 48 q^{24} - 18 q^{26} - 28 q^{36} + 26 q^{44} - 22 q^{46} - 48 q^{54} - 16 q^{56} + 36 q^{61} - 36 q^{64} - 24 q^{66} - 14 q^{74} + 72 q^{81}+ \cdots + 60 q^{96}+O(q^{100}) \) 32 * q - 6 * q^4 - 4 * q^9 - 22 * q^14 + 18 * q^16 - 52 * q^21 + 48 * q^24 - 18 * q^26 - 28 * q^36 + 26 * q^44 - 22 * q^46 - 48 * q^54 - 16 * q^56 + 36 * q^61 - 36 * q^64 - 24 * q^66 - 14 * q^74 + 72 * q^81 - 56 * q^84 + 8 * q^86 + 108 * q^89 - 30 * q^94 + 60 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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