LMFDB - Embedded newform 700.2.p.e.551.9

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)

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")

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);

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			551.9
Character	$\chi$	$=$	700.551
Dual form			700.2.p.e.451.9

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0377920 + 1.41371i) q^{2} +(0.366453 + 0.634715i) q^{3} +(-1.99714 + 0.106854i) 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} +(-0.799680 - 1.22846i) q^{12} +3.95118i q^{13} +(3.59550 - 1.03554i) q^{14} +(3.97716 - 0.426805i) q^{16} +(1.22891 - 0.709509i) q^{17} +(3.06182 + 1.66027i) 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} +(1.70646 - 1.17694i) q^{24} +(-5.58581 + 0.149323i) q^{26} +4.00375 q^{27} +(1.59984 + 5.04386i) q^{28} +5.17926 q^{29} +(-3.81745 - 6.61201i) q^{31} +(0.753682 + 5.60642i) 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} +(4.00970 + 2.17425i) q^{38} +(-2.50787 + 1.44792i) q^{39} +0.325509i q^{41} +(1.97486 + 1.90264i) q^{42} -9.28165i q^{43} +(-4.50974 + 2.93567i) q^{44} +(-3.31157 + 6.10710i) 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} +(-0.422198 - 7.89107i) q^{52} +(0.807955 + 1.39942i) q^{53} +(0.151310 + 5.66014i) q^{54} +(-7.07009 + 2.45232i) q^{56} +2.36383 q^{57} +(0.195735 + 7.32197i) 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} +(-1.32931 + 2.45148i) q^{66} +(2.62109 - 1.51329i) q^{67} +(-2.37849 + 1.54830i) q^{68} +3.60032i q^{69} -15.4089i q^{71} +(-6.29231 - 2.98863i) q^{72} +(1.22891 - 0.709509i) q^{73} +(-5.56931 - 3.01995i) 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} +(-0.460175 + 0.0123016i) q^{82} +5.26172 q^{83} +(-2.61515 + 2.86378i) q^{84} +(13.1215 - 0.350772i) q^{86} +(1.89795 + 3.28735i) q^{87} +(-4.32061 - 6.26451i) 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} +(-8.16255 - 4.42613i) q^{94} +(-3.28229 + 2.53286i) q^{96} +8.35134i q^{97} +(-5.03964 - 8.52068i) 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$ .

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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

)

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

$2$	0.0377920	+	1.41371i	0.0267230	+	0.999643i
$2$	0.0377920	+	1.41371i	0.0267230	+	0.999643i
$3$	0.366453	+	0.634715i	0.211572	+	0.366453i	0.952207	−	0.305455i	$-0.0988085\pi$
$3$	0.366453	+	0.634715i	0.211572	+	0.366453i	−0.740635	+	0.671908i	$0.765475\pi$
$4$	−1.99714	+	0.106854i	−0.998572	+	0.0534269i
$5$		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	$-0.533725\pi$
$11$	2.33007	−	1.34527i	0.702542	−	0.405613i	0.808294	+	0.588780i	$0.200391\pi$
$12$	−0.799680	−	1.22846i	−0.230848	−	0.354626i
$13$			3.95118i			1.09586i	0.836524	+	0.547930i	$0.184584\pi$
$13$			3.95118i			1.09586i	−0.836524	+	0.547930i	$0.815416\pi$
$14$	3.59550	−	1.03554i	0.960939	−	0.276760i
$15$		0			0
$16$	3.97716	−	0.426805i	0.994291	−	0.106701i
$17$	1.22891	−	0.709509i	0.298053	−	0.172081i	−0.343515	−	0.939147i	$-0.611618\pi$
$17$	1.22891	−	0.709509i	0.298053	−	0.172081i	0.641568	+	0.767066i	$0.278284\pi$
$18$	3.06182	+	1.66027i	0.721679	+	0.391329i
$19$	1.61265	−	2.79319i	0.369966	−	0.640801i	−0.619593	−	0.784923i	$-0.712703\pi$
$19$	1.61265	−	2.79319i	0.369966	−	0.640801i	0.989560	+	0.144122i	$0.0460358\pi$
$20$		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	0.872984	−	0.487748i	$-0.162182\pi$
$23$	4.25426	+	2.45620i	0.887074	+	0.512152i	0.0140897	+	0.999901i	$0.495515\pi$
$24$	1.70646	−	1.17694i	0.348330	−	0.240242i
$25$		0			0
$26$	−5.58581	+	0.149323i	−1.09547	+	0.0292846i
$27$	4.00375			0.770522
$28$	1.59984	+	5.04386i	0.302341	+	0.953200i
$29$	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	−0.973237	−	0.229803i	$-0.926192\pi$
$31$	−3.81745	−	6.61201i	−0.685634	−	1.18755i	0.287603	−	0.957750i	$-0.407142\pi$
$32$	0.753682	+	5.60642i	0.133233	+	0.991085i
$33$	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	$-0.953372\pi$
$37$	−2.23990	+	3.87963i	−0.368238	+	0.637806i	0.621052	+	0.783769i	$0.286705\pi$
$38$	4.00970	+	2.17425i	0.650458	+	0.352710i
$39$	−2.50787	+	1.44792i	−0.401581	+	0.231853i
$40$		0			0
$41$			0.325509i			0.0508359i	0.999677	+	0.0254180i	$0.00809166\pi$
$41$			0.325509i			0.0508359i	−0.999677	+	0.0254180i	$0.991908\pi$
$42$	1.97486	+	1.90264i	0.304727	+	0.293584i
$43$		−	9.28165i		−	1.41544i	−0.706494	−	0.707719i	$-0.749724\pi$
$43$		−	9.28165i		−	1.41544i	0.706494	−	0.707719i	$-0.250276\pi$
$44$	−4.50974	+	2.93567i	−0.679868	+	0.442568i
$45$		0			0
$46$	−3.31157	+	6.10710i	−0.488264	+	0.900443i
$47$	−3.28287	+	5.68610i	−0.478856	+	0.829403i	−0.999706	−	0.0242453i	$-0.992282\pi$
$47$	−3.28287	+	5.68610i	−0.478856	+	0.829403i	0.520850	+	0.853648i	$0.325615\pi$
$48$	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
$52$	−0.422198	−	7.89107i	−0.0585484	−	1.09429i
$53$	0.807955	+	1.39942i	0.110981	+	0.192225i	0.916166	−	0.400799i	$-0.131267\pi$
$53$	0.807955	+	1.39942i	0.110981	+	0.192225i	−0.805185	+	0.593024i	$0.797934\pi$
$54$	0.151310	+	5.66014i	0.0205907	+	0.770247i
$55$		0			0
$56$	−7.07009	+	2.45232i	−0.944780	+	0.327705i
$57$	2.36383			0.313097
$58$	0.195735	+	7.32197i	0.0257012	+	0.961421i
$59$	−3.81745	−	6.61201i	−0.496989	−	0.860811i	0.503005	−	0.864284i	$-0.332228\pi$
$59$	−3.81745	−	6.61201i	−0.496989	−	0.860811i	−0.999994	+	0.00347297i	$0.998895\pi$
$60$		0			0
$61$	12.3842	+	7.15003i	1.58564	+	0.915467i	0.994014	+	0.109252i	$0.0348455\pi$
$61$	12.3842	+	7.15003i	1.58564	+	0.915467i	0.591622	+	0.806215i	$0.298488\pi$
$62$	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
$66$	−1.32931	+	2.45148i	−0.163627	+	0.301756i
$67$	2.62109	−	1.51329i	0.320218	−	0.184878i	−0.331272	−	0.943535i	$-0.607478\pi$
$67$	2.62109	−	1.51329i	0.320218	−	0.184878i	0.651490	+	0.758658i	$0.274144\pi$
$68$	−2.37849	+	1.54830i	−0.288434	+	0.187760i
$69$			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	$-0.367299\pi$
$72$	−6.29231	−	2.98863i	−0.741556	−	0.352213i
$73$	1.22891	−	0.709509i	0.143833	−	0.0830418i	−0.426357	−	0.904555i	$-0.640203\pi$
$73$	1.22891	−	0.709509i	0.143833	−	0.0830418i	0.570189	+	0.821513i	$0.306870\pi$
$74$	−5.56931	−	3.01995i	−0.647419	−	0.351062i
$75$		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	$-0.0922515\pi$
$79$	10.5765	+	6.10637i	1.18995	+	0.687021i	0.231659	+	0.972797i	$0.425585\pi$
$80$		0			0
$81$	−2.22709	−	3.85743i	−0.247454	−	0.428604i
$82$	−0.460175	+	0.0123016i	−0.0508178	+	0.00135849i
$83$	5.26172			0.577549			0.288774	−	0.957397i	$-0.406752\pi$
$83$	5.26172			0.577549			0.288774	+	0.957397i	$0.406752\pi$
$84$	−2.61515	+	2.86378i	−0.285336	+	0.312464i
$85$		0			0
$86$	13.1215	−	0.350772i	1.41493	−	0.0378247i
$87$	1.89795	+	3.28735i	0.203482	+	0.352441i
$88$	−4.32061	−	6.26451i	−0.460578	−	0.667799i
$89$	−4.10930	−	2.37250i	−0.435585	−	0.251485i	0.266138	−	0.963935i	$-0.414252\pi$
$89$	−4.10930	−	2.37250i	−0.435585	−	0.251485i	−0.701723	+	0.712450i	$0.747586\pi$
$90$		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
$94$	−8.16255	−	4.42613i	−0.841903	−	0.456521i
$95$		0			0
$96$	−3.28229	+	2.53286i	−0.334997	+	0.258509i
$97$			8.35134i			0.847950i	0.905674	+	0.423975i	$0.139366\pi$
$97$			8.35134i			0.847950i	−0.905674	+	0.423975i	$0.860634\pi$
$98$	−5.03964	−	8.52068i	−0.509080	−	0.860719i
$99$		−	6.62638i		−	0.665976i
$100$		0			0
$101$	−0.241927	+	0.139677i	−0.0240727	+	0.0138984i	−0.511988	−	0.858993i	$-0.671091\pi$
$101$	−0.241927	+	0.139677i	−0.0240727	+	0.0138984i	0.487915	+	0.872891i	$0.337757\pi$
$102$	−0.701095	+	1.29294i	−0.0694187	+	0.128020i
$103$	−6.70030	+	11.6053i	−0.660200	+	1.14350i	0.320362	+	0.947295i	$0.396195\pi$
$103$	−6.70030	+	11.6053i	−0.660200	+	1.14350i	−0.980563	+	0.196206i	$0.937138\pi$
$104$	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	0.255217	−	0.966884i	$-0.417853\pi$
$107$	−4.70160	−	2.71447i	−0.454521	−	0.262418i	−0.709738	+	0.704466i	$0.751187\pi$
$108$	−7.99607	+	0.427816i	−0.769422	+	0.0411666i
$109$	4.45851	+	7.72237i	0.427048	+	0.739669i	0.996609	−	0.0822798i	$-0.0262201\pi$
$109$	4.45851	+	7.72237i	0.427048	+	0.739669i	−0.569561	+	0.821949i	$0.692887\pi$
$110$		0			0
$111$	−3.28327			−0.311634
$112$	−3.73406	−	9.90236i	−0.352835	−	0.935685i
$113$	−1.05161			−0.0989268			−0.0494634	−	0.998776i	$-0.515751\pi$
$113$	−1.05161			−0.0989268			−0.0494634	+	0.998776i	$0.515751\pi$
$114$	0.0893340	+	3.34177i	0.00836690	+	0.312986i
$115$		0			0
$116$	−10.3437	+	0.553424i	−0.960391	+	0.0513841i
$117$	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
$122$	−9.64003	+	17.7779i	−0.872768	+	1.60953i
$123$	−0.206605	+	0.119284i	−0.0186290	+	0.0107554i
$124$	8.33051	+	12.7972i	0.748102	+	1.14923i
$125$		0			0
$126$	2.21890	−	8.94401i	0.197675	−	0.796796i
$127$		−	1.71773i		−	0.152424i	−0.997092	−	0.0762121i	$-0.975717\pi$
$127$		−	1.71773i		−	0.152424i	0.997092	−	0.0762121i	$-0.0242826\pi$
$128$	−2.10428	−	11.1163i	−0.185994	−	0.982551i
$129$	5.89120	−	3.40128i	0.518691	−	0.299466i
$130$		0			0
$131$	−7.07173	+	12.2486i	−0.617860	+	1.07016i	0.372016	+	0.928226i	$0.378667\pi$
$131$	−7.07173	+	12.2486i	−0.617860	+	1.07016i	−0.989876	+	0.141938i	$0.954667\pi$
$132$	−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
$136$	−2.27874	−	3.30397i	−0.195400	−	0.283314i
$137$	−7.43551	−	12.8787i	−0.635259	−	1.10030i	−0.986460	−	0.164000i	$-0.947560\pi$
$137$	−7.43551	−	12.8787i	−0.635259	−	1.10030i	0.351202	−	0.936300i	$-0.385773\pi$
$138$	−5.08980	+	0.136063i	−0.433273	+	0.0115825i
$139$	−7.06762			−0.599468			−0.299734	−	0.954023i	$-0.596898\pi$
$139$	−7.06762			−0.599468			−0.299734	+	0.954023i	$0.596898\pi$
$140$		0			0
$141$	−4.81207			−0.405249
$142$	21.7837	−	0.582334i	1.82805	−	0.0488684i
$143$	5.31538	+	9.20652i	0.444495	+	0.769888i
$144$	3.98725	−	9.00843i	0.332271	−	0.750703i
$145$		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	−0.628061	−	0.778164i	$-0.716151\pi$
$149$	4.39289	−	7.60870i	0.359879	−	0.623329i	0.987940	+	0.154835i	$0.0494846\pi$
$150$		0			0
$151$	−0.260095	+	0.150166i	−0.0211663	+	0.0122204i	−0.510546	−	0.859851i	$-0.670557\pi$
$151$	−0.260095	+	0.150166i	−0.0211663	+	0.0122204i	0.489380	+	0.872071i	$0.337223\pi$
$152$	−8.24026	−	3.91384i	−0.668374	−	0.317454i
$153$		−	3.49483i		−	0.282540i
$154$	6.98469	−	7.24980i	0.562843	−	0.584205i
$155$		0			0
$156$	4.85386	−	3.15968i	0.388620	−	0.252977i
$157$	16.6579	−	9.61742i	1.32944	−	0.767553i	0.344228	−	0.938886i	$-0.388141\pi$
$157$	16.6579	−	9.61742i	1.32944	−	0.767553i	0.985213	+	0.171333i	$0.0548073\pi$
$158$	−8.23292	+	15.1829i	−0.654976	+	1.20789i
$159$	−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	0.0902569	−	0.995919i	$-0.471231\pi$
$163$	−9.28306	−	5.35958i	−0.727105	−	0.419795i	−0.817362	+	0.576124i	$0.804565\pi$
$164$	−0.0347818	−	0.650088i	−0.00271601	−	0.0507633i
$165$		0			0
$166$	0.198851	+	7.43854i	0.0154338	+	0.577342i
$167$	−13.2256			−1.02343			−0.511715	−	0.859155i	$-0.670990\pi$
$167$	−13.2256			−1.02343			−0.511715	+	0.859155i	$0.670990\pi$
$168$	−4.14738	−	3.58883i	−0.319977	−	0.276884i
$169$	−2.61180			−0.200908
$170$		0			0
$171$	−3.97171	−	6.87920i	−0.303724	−	0.526065i
$172$	0.991779	+	18.5368i	0.0756224	+	1.41342i
$173$	−9.74632	−	5.62704i	−0.740999	−	0.427816i	0.0814335	−	0.996679i	$-0.474050\pi$
$173$	−9.74632	−	5.62704i	−0.740999	−	0.427816i	−0.822432	+	0.568863i	$0.807384\pi$
$174$	−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
$178$	3.19873	−	5.89901i	0.239755	−	0.442149i
$179$	−0.697992	+	0.402986i	−0.0521703	+	0.0301206i	−0.525858	−	0.850572i	$-0.676256\pi$
$179$	−0.697992	+	0.402986i	−0.0521703	+	0.0301206i	0.473688	+	0.880693i	$0.342922\pi$
$180$		0			0
$181$		−	0.0667108i		−	0.00495857i	−0.999997	−	0.00247929i	$-0.999211\pi$
$181$		−	0.0667108i		−	0.00495857i	0.999997	−	0.00247929i	$-0.000789182\pi$
$182$	4.09161	+	14.2065i	0.303290	+	1.05305i
$183$			10.4806i			0.774747i
$184$	5.96111	−	12.5506i	0.439459	−	0.925244i
$185$		0			0
$186$	6.95654	+	3.77217i	0.510078	+	0.276589i
$187$	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	$-0.115696\pi$
$191$	15.1210	+	8.73010i	1.09412	+	0.631688i	0.159446	+	0.987207i	$0.449029\pi$
$192$	−3.70477	−	4.54448i	−0.267369	−	0.327969i
$193$	−8.59835	−	14.8928i	−0.618923	−	1.07201i	−0.989683	−	0.143277i	$-0.954236\pi$
$193$	−8.59835	−	14.8928i	−0.618923	−	1.07201i	0.370760	−	0.928729i	$-0.379097\pi$
$194$	−11.8064	+	0.315614i	−0.847647	+	0.0226597i
$195$		0			0
$196$	11.8553	−	7.44659i	0.846807	−	0.531900i
$197$	−11.9392			−0.850635			−0.425318	−	0.905044i	$-0.639838\pi$
$197$	−11.9392			−0.850635			−0.425318	+	0.905044i	$0.639838\pi$
$198$	9.36777	−	0.250424i	0.665738	−	0.0177969i
$199$	7.76016	+	13.4410i	0.550103	+	0.952807i	0.998267	+	0.0588552i	$0.0187450\pi$
$199$	7.76016	+	13.4410i	0.550103	+	0.952807i	−0.448163	+	0.893952i	$0.647922\pi$
$200$		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
$206$	−16.6597	−	9.03369i	−1.16073	−	0.629407i
$207$	10.4776	−	6.04924i	0.728243	−	0.420452i
$208$	1.68638	+	15.7145i	0.116929	+	1.08960i
$209$		−	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	$0.837897\pi$
$212$	−1.76314	−	2.70851i	−0.121093	−	0.186021i
$213$	9.78027	−	5.64664i	0.670133	−	0.386901i
$214$	3.65979	−	6.74928i	0.250178	−	0.461371i
$215$		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
$222$	−0.124081	−	4.64159i	−0.00832780	−	0.311523i
$223$	3.03443			0.203201			0.101600	−	0.994825i	$-0.467604\pi$
$223$	3.03443			0.203201			0.101600	+	0.994825i	$0.467604\pi$
$224$	13.8579	−	5.65310i	0.925922	−	0.377714i
$225$		0			0
$226$	−0.0397423	−	1.48666i	−0.00264362	−	0.0988914i
$227$	7.38839	+	12.7971i	0.490385	+	0.849371i	0.999939	−	0.0110676i	$-0.00352299\pi$
$227$	7.38839	+	12.7971i	0.490385	+	0.849371i	−0.509554	+	0.860439i	$0.670190\pi$
$228$	−4.72092	+	0.252585i	−0.312650	+	0.0167278i
$229$	5.56933	+	3.21545i	0.368031	+	0.212483i	0.672598	−	0.740008i	$-0.265178\pi$
$229$	5.56933	+	3.21545i	0.368031	+	0.212483i	−0.304567	+	0.952491i	$0.598512\pi$
$230$		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	0.424062	+	0.905633i	$0.360604\pi$
$233$	−8.73532	+	15.1300i	−0.572270	+	0.991201i	−0.996332	+	0.0855677i	$0.972730\pi$
$234$	−6.56002	+	12.0978i	−0.428842	+	0.790858i
$235$		0			0
$236$	8.33051	+	12.7972i	0.542270	+	0.833029i
$237$			8.95079i			0.581416i
$238$	3.68381	−	3.82363i	0.238786	−	0.247849i
$239$		−	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	−0.947145	−	0.320807i	$-0.896046\pi$
$241$	−17.7424	+	10.2436i	−1.14289	+	0.659848i	−0.195745	+	0.980655i	$0.562713\pi$
$242$	−4.67573	−	2.53541i	−0.300568	−	0.162982i
$243$	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
$248$	−17.7767	+	12.2605i	−1.12882	+	0.778545i
$249$	1.92817	+	3.33969i	0.122193	+	0.211644i
$250$		0			0
$251$	−15.1647			−0.957189			−0.478594	−	0.878036i	$-0.658854\pi$
$251$	−15.1647			−0.957189			−0.478594	+	0.878036i	$0.658854\pi$
$252$	12.7281	+	2.79886i	0.801794	+	0.176312i
$253$	13.2170			0.830943
$254$	2.42837	−	0.0649166i	0.152370	−	0.00407323i
$255$		0			0
$256$	15.6357	−	3.39494i	0.977230	−	0.212184i
$257$	−4.09764	−	2.36577i	−0.255604	−	0.147573i	0.366724	−	0.930330i	$-0.380479\pi$
$257$	−4.09764	−	2.36577i	−0.255604	−	0.147573i	−0.622327	+	0.782757i	$0.713813\pi$
$258$	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
$262$	−17.5832	−	9.53447i	−1.08629	−	0.589041i
$263$	−4.07068	+	2.35021i	−0.251009	+	0.144920i	−0.620226	−	0.784423i	$-0.712959\pi$
$263$	−4.07068	+	2.35021i	−0.251009	+	0.144920i	0.369217	+	0.929343i	$0.379626\pi$
$264$	2.39288	−	5.03800i	0.147271	−	0.310067i
$265$		0			0
$266$	2.90582	−	11.7129i	0.178167	−	0.718162i
$267$		−	3.47764i		−	0.212828i
$268$	−5.07300	+	3.30233i	−0.309883	+	0.201722i
$269$	−21.2532	+	12.2706i	−1.29583	+	0.748149i	−0.979682	−	0.200559i	$-0.935724\pi$
$269$	−21.2532	+	12.2706i	−1.29583	+	0.748149i	−0.316151	+	0.948709i	$0.602391\pi$
$270$		0			0
$271$	−13.1957	+	22.8556i	−0.801582	+	1.38838i	0.116993	+	0.993133i	$0.462675\pi$
$271$	−13.1957	+	22.8556i	−0.801582	+	1.38838i	−0.918574	+	0.395248i	$0.870659\pi$
$272$	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
$276$	−0.384708	−	7.19035i	−0.0231567	−	0.432808i
$277$	−12.0350	−	20.8453i	−0.723115	−	1.25247i	−0.959745	−	0.280872i	$-0.909376\pi$
$277$	−12.0350	−	20.8453i	−0.723115	−	1.25247i	0.236630	−	0.971600i	$-0.423957\pi$
$278$	−0.267100	−	9.99155i	−0.0160196	−	0.599254i
$279$	−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	$0.574602\pi$
$282$	−0.181858	−	6.80286i	−0.0108295	−	0.405104i
$283$	−3.97529	−	6.88540i	−0.236306	−	0.409294i	0.723345	−	0.690487i	$-0.242604\pi$
$283$	−3.97529	−	6.88540i	−0.236306	−	0.409294i	−0.959651	+	0.281192i	$0.909270\pi$
$284$	1.64650	+	30.7738i	0.0977019	+	1.82609i
$285$		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
$292$	−2.37849	+	1.54830i	−0.139190	+	0.0906077i
$293$			2.11501i			0.123560i	0.998090	+	0.0617801i	$0.0196777\pi$
$293$			2.11501i			0.123560i	−0.998090	+	0.0617801i	$0.980322\pi$
$294$	3.56141	−	6.32116i	0.207706	−	0.368657i
$295$		0			0
$296$	11.4454	+	5.43617i	0.665251	+	0.315971i
$297$	9.32902	−	5.38611i	0.541325	−	0.312534i
$298$	10.9225	+	5.92271i	0.632723	+	0.343093i
$299$	−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
$304$	5.22162	−	11.7972i	0.299480	−	0.676618i
$305$		0			0
$306$	4.94067	−	0.132077i	0.282439	−	0.00755032i
$307$	−18.6560			−1.06475			−0.532376	−	0.846508i	$-0.678701\pi$
$307$	−18.6560			−1.06475			−0.532376	+	0.846508i	$0.678701\pi$
$308$	10.5131	+	9.60034i	0.599037	+	0.547030i
$309$	−9.82137			−0.558718
$310$		0			0
$311$	4.09153	+	7.08673i	0.232009	+	0.401852i	0.958399	−	0.285431i	$-0.0921367\pi$
$311$	4.09153	+	7.08673i	0.232009	+	0.401852i	−0.726390	+	0.687283i	$0.758803\pi$
$312$	4.65030	+	6.74253i	0.263271	+	0.381721i
$313$	20.2427	+	11.6871i	1.14419	+	0.660597i	0.947464	−	0.319863i	$-0.103637\pi$
$313$	20.2427	+	11.6871i	1.14419	+	0.660597i	0.196723	+	0.980459i	$0.436970\pi$
$314$	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	0.218300	+	0.975882i	$0.429949\pi$
$317$	−13.1039	+	22.6966i	−0.735988	+	1.27477i	−0.954288	+	0.298887i	$0.903385\pi$
$318$	−1.47234	−	0.798373i	−0.0825646	−	0.0447705i
$319$	12.0680	−	6.96749i	0.675680	−	0.390104i
$320$		0			0
$321$		−	3.97890i		−	0.222081i
$322$	17.8397	+	4.42580i	0.994167	+	0.246640i
$323$		−	4.57675i		−	0.254657i
$324$	4.86000	+	7.46587i	0.270000	+	0.414771i
$325$		0			0
$326$	7.22606	−	13.3261i	0.400214	−	0.738064i
$327$	−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	$-0.153081\pi$
$331$	16.9060	+	9.76067i	0.929237	+	0.536495i	0.0426665	+	0.999089i	$0.486415\pi$
$332$	−10.5084	+	0.562234i	−0.576724	+	0.0308566i
$333$	5.51654	+	9.55493i	0.302305	+	0.523607i
$334$	−0.499824	−	18.6972i	−0.0273491	−	1.02307i
$335$		0			0
$336$	4.91682	−	5.99881i	0.268234	−	0.327262i
$337$	31.7520			1.72964			0.864820	−	0.502082i	$-0.167433\pi$
$337$	31.7520			1.72964			0.864820	+	0.502082i	$0.167433\pi$
$338$	−0.0987052	−	3.69233i	−0.00536886	−	0.200836i
$339$	−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
$346$	7.58666	−	13.9911i	0.407861	−	0.752167i
$347$	15.9212	−	9.19210i	0.854694	−	0.493458i	−0.00753782	−	0.999972i	$-0.502399\pi$
$347$	15.9212	−	9.19210i	0.854694	−	0.493458i	0.862232	+	0.506514i	$0.169066\pi$
$348$	−4.14175	−	6.36251i	−0.222021	−	0.341066i
$349$			2.37390i			0.127072i	0.997980	+	0.0635360i	$0.0202378\pi$
$349$			2.37390i			0.127072i	−0.997980	+	0.0635360i	$0.979762\pi$
$350$		0			0
$351$			15.8195i			0.844384i
$352$	9.29826	+	12.0494i	0.495599	+	0.642238i
$353$	1.86560	−	1.07710i	0.0992958	−	0.0573284i	−0.449530	−	0.893265i	$-0.648408\pi$
$353$	1.86560	−	1.07710i	0.0992958	−	0.0573284i	0.548826	+	0.835937i	$0.315075\pi$
$354$	6.95654	+	3.77217i	0.369736	+	0.200489i
$355$		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	$-0.376140\pi$
$359$	−4.40004	−	2.54037i	−0.232225	−	0.134075i	−0.611598	+	0.791168i	$0.709473\pi$
$360$		0			0
$361$	4.29874	+	7.44564i	0.226250	+	0.391876i
$362$	0.0943096	−	0.00252113i	0.00495680	−	0.000132508i
$363$	−2.75648			−0.144678
$364$	−19.9292	+	6.32124i	−1.04457	+	0.331323i
$365$		0			0
$366$	−14.8165	+	0.396082i	−0.774471	+	0.0207036i
$367$	6.77267	+	11.7306i	0.353530	+	0.612333i	0.986865	−	0.161545i	$-0.0516478\pi$
$367$	6.77267	+	11.7306i	0.353530	+	0.612333i	−0.633335	+	0.773878i	$0.718314\pi$
$368$	17.9682	+	7.95296i	0.936657	+	0.414577i
$369$	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	$-0.892462\pi$
$373$	−3.56700	+	6.17822i	−0.184692	+	0.319896i	0.758781	+	0.651346i	$0.225795\pi$
$374$	4.74644	+	2.57375i	0.245433	+	0.133086i
$375$		0			0
$376$	16.7747	+	7.96743i	0.865091	+	0.410889i
$377$			20.4642i			1.05396i
$378$	14.3955	−	4.14605i	0.740425	−	0.213250i
$379$			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
$382$	−11.7704	+	21.7066i	−0.602224	+	1.11061i
$383$	−4.94358	+	8.56254i	−0.252605	+	0.437525i	−0.964242	−	0.265022i	$-0.914621\pi$
$383$	−4.94358	+	8.56254i	−0.252605	+	0.437525i	0.711637	+	0.702547i	$0.247954\pi$
$384$	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
$388$	−0.892372	−	16.6788i	−0.0453033	−	0.846739i
$389$	−15.9811	−	27.6802i	−0.810276	−	1.40344i	−0.912671	−	0.408696i	$-0.865984\pi$
$389$	−15.9811	−	27.6802i	−0.810276	−	1.40344i	0.102395	−	0.994744i	$-0.467350\pi$
$390$		0			0
$391$	6.97078			0.352527
$392$	10.9753	+	16.4785i	0.554339	+	0.832291i
$393$	−10.3658			−0.522886
$394$	−0.451208	−	16.8786i	−0.0227315	−	0.850331i
$395$		0			0
$396$	0.708053	+	13.2338i	0.0355810	+	0.665025i
$397$	15.1344	+	8.73784i	0.759573	+	0.438539i	0.829142	−	0.559038i	$-0.188829\pi$
$397$	15.1344	+	8.73784i	0.759573	+	0.438539i	−0.0695697	+	0.997577i	$0.522163\pi$
$398$	−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	−0.563744	−	0.825950i	$-0.690639\pi$
$401$	8.67926	−	15.0329i	0.433422	−	0.750708i	0.997165	+	0.0752415i	$0.0239728\pi$
$402$	−1.49534	+	2.75767i	−0.0745809	+	0.137540i
$403$	26.1252	−	15.0834i	1.30139	−	0.751358i
$404$	0.468239	−	0.304805i	0.0232957	−	0.0151646i
$405$		0			0
$406$	18.6221	−	5.36334i	0.924197	−	0.266178i
$407$			12.0531i			0.597448i
$408$	1.26203	−	2.65710i	0.0624798	−	0.131546i
$409$	−6.32187	+	3.64993i	−0.312596	+	0.180478i	−0.648088	−	0.761566i	$-0.724431\pi$
$409$	−6.32187	+	3.64993i	−0.312596	+	0.180478i	0.335491	+	0.942043i	$0.391098\pi$
$410$		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
$416$	−22.1520	+	2.97793i	−1.08609	+	0.146005i
$417$	−2.58995	−	4.48592i	−0.126830	−	0.219677i
$418$	12.2678	−	0.327950i	0.600038	−	0.0160405i
$419$	17.9278			0.875831			0.437915	−	0.899016i	$-0.355717\pi$
$419$	17.9278			0.875831			0.437915	+	0.899016i	$0.355717\pi$
$420$		0			0
$421$	12.6334			0.615716			0.307858	−	0.951432i	$-0.400388\pi$
$421$	12.6334			0.615716			0.307858	+	0.951432i	$0.400388\pi$
$422$	−20.0232	+	0.535271i	−0.974715	+	0.0260566i
$423$	8.08522	+	14.0040i	0.393117	+	0.680898i
$424$	3.76241	−	2.59492i	0.182719	−	0.126020i
$425$		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	$-0.954991\pi$
$431$	−28.2962	+	16.3368i	−1.36298	+	0.786918i	−0.372962	+	0.927847i	$0.621658\pi$
$432$	15.9236	−	1.70882i	0.766124	−	0.0822156i
$433$			23.5884i			1.13359i	0.823860	+	0.566794i	$0.191816\pi$
$433$			23.5884i			1.13359i	−0.823860	+	0.566794i	$0.808184\pi$
$434$	−20.5727	−	19.8204i	−0.987520	−	0.951409i
$435$		0			0
$436$	−9.72946	−	14.9463i	−0.465957	−	0.715797i
$437$	13.7212	−	7.92195i	0.656375	−	0.378958i
$438$	−0.701095	+	1.29294i	−0.0334996	+	0.0617790i
$439$	−9.19501	+	15.9262i	−0.438854	+	0.760117i	−0.997601	−	0.0692207i	$-0.977949\pi$
$439$	−9.19501	+	15.9262i	−0.438854	+	0.760117i	0.558748	+	0.829338i	$0.311282\pi$
$440$		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	0.568008	−	0.823023i	$-0.307714\pi$
$443$	2.93092	+	1.69217i	0.139252	+	0.0803973i	−0.428755	+	0.903421i	$0.641048\pi$
$444$	6.55717	−	0.350830i	0.311189	−	0.0166497i
$445$		0			0
$446$	0.114677	+	4.28980i	0.00543013	+	0.203128i
$447$	6.43914			0.304561
$448$	8.51556	+	19.3774i	0.402322	+	0.915498i
$449$	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
$452$	2.10021	−	0.112368i	0.0987855	−	0.00528535i
$453$	−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	$-0.669301\pi$
$457$	10.5352	−	18.2475i	0.492816	−	0.853582i	0.999966	+	0.00827601i	$0.00263437\pi$
$458$	−4.33524	+	7.99492i	−0.202572	+	0.373578i
$459$	4.92023	−	2.84070i	0.229657	−	0.132592i
$460$		0			0
$461$			29.6708i			1.38191i	0.722899	+	0.690954i	$0.242809\pi$
$461$			29.6708i			1.38191i	−0.722899	+	0.690954i	$0.757191\pi$
$462$	7.16111	+	1.77658i	0.333165	+	0.0826540i
$463$			15.0481i			0.699342i	0.936873	+	0.349671i	$0.113707\pi$
$463$			15.0481i			0.699342i	−0.936873	+	0.349671i	$0.886293\pi$
$464$	20.5988	−	2.21053i	0.956274	−	0.102621i
$465$		0			0
$466$	−21.7196	−	11.7774i	−1.00614	−	0.545578i
$467$	−2.57299	+	4.45656i	−0.119064	+	0.206225i	−0.919397	−	0.393331i	$-0.871323\pi$
$467$	−2.57299	+	4.45656i	−0.119064	+	0.206225i	0.800333	+	0.599556i	$0.204656\pi$
$468$	−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
$472$	−17.7767	+	12.2605i	−0.818240	+	0.564337i
$473$	−12.4863	−	21.6269i	−0.574120	−	0.994405i
$474$	−12.6538	+	0.338268i	−0.581208	+	0.0155372i
$475$		0			0
$476$	5.54471	+	5.06333i	0.254142	+	0.232077i
$477$	3.97974			0.182220
$478$	4.55907	−	0.121875i	0.208527	−	0.00557445i
$479$	−19.9783	−	34.6035i	−0.912834	−	1.58107i	−0.810042	−	0.586372i	$-0.800556\pi$
$479$	−19.9783	−	34.6035i	−0.912834	−	1.58107i	−0.102792	−	0.994703i	$-0.532778\pi$
$480$		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
$486$	18.9909	+	10.2978i	0.861443	+	0.467116i
$487$	−10.5871	+	6.11246i	−0.479747	+	0.276982i	−0.720311	−	0.693651i	$-0.756001\pi$
$487$	−10.5871	+	6.11246i	−0.479747	+	0.276982i	0.240564	+	0.970633i	$0.422668\pi$
$488$	17.3529	−	36.5351i	0.785529	−	1.65386i
$489$		−	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	$-0.173284\pi$
$492$	0.399874	−	0.260303i	0.0180277	−	0.0117354i
$493$	6.36483	−	3.67473i	0.286657	−	0.165502i
$494$	−8.59085	+	15.8430i	−0.386521	+	0.712811i
$495$		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	$-0.303312\pi$
$499$	3.64376	+	2.10372i	0.163117	+	0.0941756i	−0.416219	+	0.909264i	$0.636645\pi$
$500$		0			0
$501$	−4.84657	−	8.39451i	−0.216529	−	0.375039i
$502$	−0.573105	−	21.4385i	−0.0255789	−	0.956847i
$503$	−43.1904			−1.92576			−0.962882	−	0.269924i	$-0.913001\pi$
$503$	−43.1904			−1.92576			−0.962882	+	0.269924i	$0.913001\pi$
$504$	−3.47575	+	18.0996i	−0.154822	+	0.806219i
$505$		0			0
$506$	0.499495	+	18.6849i	0.0222053	+	0.830646i
$507$	−0.957101	−	1.65775i	−0.0425064	−	0.0736232i
$508$	0.183546	+	3.43056i	0.00814355	+	0.152206i
$509$	32.3532	+	18.6791i	1.43403	+	0.827937i	0.997425	−	0.0717169i	$-0.0228478\pi$
$509$	32.3532	+	18.6791i	1.43403	+	0.827937i	0.436604	+	0.899654i	$0.356181\pi$
$510$		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
$514$	3.18966	−	5.88227i	0.140690	−	0.259456i
$515$		0			0
$516$	−11.4021	+	7.42235i	−0.501951	+	0.326751i
$517$			17.6653i			0.776921i
$518$	−4.03606	+	16.2687i	−0.177334	+	0.714807i
$519$		−	8.24817i		−	0.362055i
$520$		0			0
$521$	13.9610	−	8.06040i	0.611643	−	0.353132i	−0.161965	−	0.986796i	$-0.551783\pi$
$521$	13.9610	−	8.06040i	0.611643	−	0.353132i	0.773608	+	0.633664i	$0.218450\pi$
$522$	15.8580	+	8.59897i	0.694085	+	0.376367i
$523$	7.98356	−	13.8279i	0.349097	−	0.604653i	−0.636993	−	0.770870i	$-0.719822\pi$
$523$	7.98356	−	13.8279i	0.349097	−	0.604653i	0.986089	+	0.166217i	$0.0531552\pi$
$524$	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
$528$	7.21269	+	3.19243i	0.313892	+	0.138933i
$529$	0.565805	+	0.980002i	0.0246002	+	0.0426088i
$530$		0			0
$531$	−18.8036			−0.816007
$532$	16.6684	+	3.66532i	0.722667	+	0.158912i
$533$	−1.28614			−0.0557090
$534$	4.91637	−	0.131427i	0.212752	−	0.00568740i
$535$		0			0
$536$	−4.86025	−	7.04694i	−0.209931	−	0.304382i
$537$	−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	−0.664771	−	0.747047i	$-0.731471\pi$
$541$	7.31686	−	12.6732i	0.314576	−	0.544862i	0.979347	+	0.202185i	$0.0648042\pi$
$542$	−32.8099	−	17.7911i	−1.40931	−	0.764194i
$543$	0.0423423	−	0.0244463i	0.00181708	−	0.00104909i
$544$	4.90401	+	6.35502i	0.210258	+	0.272469i
$545$		0			0
$546$	−7.51768	+	7.80301i	−0.321727	+	0.333938i
$547$			16.5936i			0.709493i	0.934963	+	0.354747i	$0.115433\pi$
$547$			16.5936i			0.709493i	−0.934963	+	0.354747i	$0.884567\pi$
$548$	16.2259	+	24.9261i	0.693137	+	1.06479i
$549$	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
$556$	14.1151	−	0.755202i	0.598611	−	0.0320277i
$557$	−12.3878	−	21.4562i	−0.524886	−	0.909129i	−0.999580	−	0.0289782i	$-0.990775\pi$
$557$	−12.3878	−	21.4562i	−0.524886	−	0.909129i	0.474694	−	0.880151i	$-0.342559\pi$
$558$	−0.710626	−	26.5828i	−0.0300832	−	1.12534i
$559$	36.6734			1.55112
$560$		0			0
$561$	2.79817			0.118139
$562$	−0.294240	−	11.0068i	−0.0124118	−	0.464294i
$563$	−11.9762	−	20.7434i	−0.504737	−	0.874230i	−0.999985	−	0.00547814i	$-0.998256\pi$
$563$	−11.9762	−	20.7434i	−0.504737	−	0.874230i	0.495248	−	0.868751i	$-0.335077\pi$
$564$	9.61039	−	0.514188i	0.404670	−	0.0216512i
$565$		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	−0.753889	−	0.657002i	$-0.771824\pi$
$569$	4.58078	−	7.93415i	0.192036	−	0.332617i	0.945925	+	0.324385i	$0.105157\pi$
$570$		0			0
$571$	21.4132	−	12.3629i	0.896114	−	0.517372i	0.0201768	−	0.999796i	$-0.493577\pi$
$571$	21.4132	−	12.3629i	0.896114	−	0.517372i	0.875938	+	0.482425i	$0.160244\pi$
$572$	−11.5993	−	17.8188i	−0.484993	−	0.745040i
$573$			12.7967i			0.534589i
$574$	0.337078	+	1.17037i	0.0140694	+	0.0488502i
$575$		0			0
$576$	−7.00053	+	18.4172i	−0.291689	+	0.767383i
$577$	8.23042	−	4.75184i	0.342637	−	0.197822i	−0.318801	−	0.947822i	$-0.603280\pi$
$577$	8.23042	−	4.75184i	0.342637	−	0.197822i	0.661438	+	0.750000i	$0.269947\pi$
$578$	−18.6311	−	10.1027i	−0.774953	−	0.420217i
$579$	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
$584$	−2.27874	−	3.30397i	−0.0942949	−	0.136719i
$585$		0			0
$586$	−2.99001	+	0.0799304i	−0.123516	+	0.00330190i
$587$	14.2100			0.586508			0.293254	−	0.956035i	$-0.405262\pi$
$587$	14.2100			0.586508			0.293254	+	0.956035i	$0.405262\pi$
$588$	9.07087	+	4.79591i	0.374076	+	0.197780i
$589$	−24.6248			−1.01465
$590$		0			0
$591$	−4.37516	−	7.57801i	−0.179970	−	0.311717i
$592$	−7.25262	+	16.3859i	−0.298081	+	0.673457i
$593$	15.3781	+	8.87854i	0.631502	+	0.364598i	0.781334	−	0.624114i	$-0.214540\pi$
$593$	15.3781	+	8.87854i	0.631502	+	0.364598i	−0.149831	+	0.988712i	$0.547873\pi$
$594$	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
$598$	−24.1303	−	13.0846i	−0.986759	−	0.535069i
$599$	−18.1537	+	10.4811i	−0.741741	+	0.428244i	−0.822702	−	0.568473i	$-0.807534\pi$
$599$	−18.1537	+	10.4811i	−0.741741	+	0.428244i	0.0809612	+	0.996717i	$0.474201\pi$
$600$		0			0
$601$		−	20.7196i		−	0.845169i	−0.906324	−	0.422585i	$-0.861123\pi$
$601$		−	20.7196i		−	0.845169i	0.906324	−	0.422585i	$-0.138877\pi$
$602$	−9.61154	−	33.3722i	−0.391737	−	1.36015i
$603$		−	7.45401i		−	0.303551i
$604$	0.503402	−	0.327696i	0.0204831	−	0.0133337i
$605$		0			0
$606$	0.138020	−	0.254533i	0.00560669	−	0.0103397i
$607$	−1.60263	+	2.77584i	−0.0650487	+	0.112668i	−0.896716	−	0.442607i	$-0.854054\pi$
$607$	−1.60263	+	2.77584i	−0.0650487	+	0.112668i	0.831667	+	0.555275i	$0.187387\pi$
$608$	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
$612$	0.373436	+	6.97968i	0.0150952	+	0.282137i
$613$	−2.39778	−	4.15308i	−0.0968454	−	0.167741i	0.813532	−	0.581520i	$-0.197542\pi$
$613$	−2.39778	−	4.15308i	−0.0968454	−	0.167741i	−0.910377	+	0.413779i	$0.864209\pi$
$614$	−0.705046	−	26.3741i	−0.0284534	−	1.06437i
$615$		0			0
$616$	−13.1748	+	15.2252i	−0.530827	+	0.613442i
$617$	−8.95961			−0.360700			−0.180350	−	0.983602i	$-0.557723\pi$
$617$	−8.95961			−0.360700			−0.180350	+	0.983602i	$0.557723\pi$
$618$	−0.371169	−	13.8846i	−0.0149306	−	0.558519i
$619$	12.8347	+	22.2303i	0.515868	+	0.893510i	0.999830	+	0.0184212i	$0.00586397\pi$
$619$	12.8347	+	22.2303i	0.515868	+	0.893510i	−0.483962	+	0.875089i	$0.660803\pi$
$620$		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
$626$	−15.7572	+	29.0590i	−0.629785	+	1.16143i
$627$	5.50790	−	3.17999i	0.219964	−	0.126996i
$628$	−32.2405	+	20.9873i	−1.28653	+	0.837485i
$629$			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	$0.988904\pi$
$632$	14.8200	−	31.2022i	0.589507	−	1.24116i
$633$	−8.98985	+	5.19029i	−0.357314	+	0.206296i
$634$	−32.5816	−	17.6673i	−1.29398	−	0.701660i
$635$		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	0.916084	+	0.400986i	$0.131332\pi$
$641$	20.3887	+	35.3143i	0.805306	+	1.39483i	−0.110778	+	0.993845i	$0.535334\pi$
$642$	5.62501	−	0.150371i	0.222001	−	0.00593466i
$643$	−35.0077			−1.38057			−0.690285	−	0.723538i	$-0.742515\pi$
$643$	−35.0077			−1.38057			−0.690285	+	0.723538i	$0.742515\pi$
$644$	−5.58260	+	25.3874i	−0.219985	+	1.00040i
$645$		0			0
$646$	6.47019	−	0.172965i	0.254566	−	0.00680520i
$647$	12.1215	+	20.9951i	0.476547	+	0.825404i	0.999639	−	0.0268724i	$-0.00855480\pi$
$647$	12.1215	+	20.9951i	0.476547	+	0.825404i	−0.523092	+	0.852276i	$0.675221\pi$
$648$	−10.3709	+	7.15277i	−0.407407	+	0.280987i
$649$	−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	−0.0404346	−	0.999182i	$-0.512874\pi$
$653$	21.5956	−	37.4046i	0.845100	−	1.46376i	0.885534	−	0.464574i	$-0.153792\pi$
$654$	−8.12475	−	4.40564i	−0.317703	−	0.172274i
$655$		0			0
$656$	0.138929	+	1.29460i	0.00542425	+	0.0505457i
$657$		−	3.49483i		−	0.136346i
$658$	−5.91538	+	23.8439i	−0.230606	+	0.929534i
$659$		−	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	−0.183702	−	0.982982i	$-0.558808\pi$
$661$	14.8021	−	8.54599i	0.575735	−	0.332400i	0.759436	+	0.650582i	$0.225475\pi$
$662$	−13.1598	+	24.2690i	−0.511471	+	0.943241i
$663$	−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
$668$	26.4135	−	1.41321i	1.02197	−	0.0546787i
$669$	1.11198	+	1.92600i	0.0429915	+	0.0744634i
$670$		0			0
$671$	38.4748			1.48530
$672$	8.66638	+	6.72424i	0.334313	+	0.259393i
$673$	−3.77972			−0.145697			−0.0728487	−	0.997343i	$-0.523209\pi$
$673$	−3.77972			−0.145697			−0.0728487	+	0.997343i	$0.523209\pi$
$674$	1.19997	+	44.8880i	0.0462211	+	1.72902i
$675$		0			0
$676$	5.21614	−	0.279081i	0.200621	−	0.0107339i
$677$	24.0534	+	13.8872i	0.924446	+	0.533729i	0.885051	−	0.465494i	$-0.154123\pi$
$677$	24.0534	+	13.8872i	0.924446	+	0.533729i	0.0393956	+	0.999224i	$0.487457\pi$
$678$	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
$682$	13.8478	−	25.5378i	0.530261	−	0.977893i
$683$	9.67614	−	5.58652i	0.370247	−	0.213762i	−0.303319	−	0.952889i	$-0.598095\pi$
$683$	9.67614	−	5.58652i	0.370247	−	0.213762i	0.673567	+	0.739127i	$0.264761\pi$
$684$	8.66713	+	13.3144i	0.331396	+	0.509087i
$685$		0			0
$686$	−18.4755	+	18.5649i	−0.705399	+	0.708811i
$687$			4.71324i			0.179821i
$688$	−3.96145	−	36.9146i	−0.151029	−	1.40736i
$689$	−5.52935	+	3.19237i	−0.210652	+	0.121620i
$690$		0			0
$691$	17.7057	−	30.6672i	0.673556	−	1.16663i	−0.303332	−	0.952885i	$-0.598099\pi$
$691$	17.7057	−	30.6672i	0.673556	−	1.16663i	0.976889	−	0.213749i	$-0.0685675\pi$
$692$	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
$696$	8.83821	−	6.09568i	0.335012	−	0.231056i
$697$	0.230952	+	0.400020i	0.00874791	+	0.0151518i
$698$	−3.35600	+	0.0897145i	−0.127027	+	0.00339574i
$699$	−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	$0.486473\pi$
$702$	−22.3642	+	0.597852i	−0.844083	+	0.0225645i
$703$	7.22434	+	12.5129i	0.272471	+	0.471934i
$704$	−16.6830	+	13.6004i	−0.628764	+	0.512584i
$705$		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	−0.975774	−	0.218780i	$-0.929792\pi$
$709$	−7.94601	+	13.7629i	−0.298418	+	0.516876i	0.677356	+	0.735656i	$0.263126\pi$
$710$		0			0
$711$	26.0485	−	15.0391i	0.976893	−	0.564010i
$712$	−5.75799	+	12.1230i	−0.215790	+	0.454327i
$713$		−	37.5056i		−	1.40460i
$714$	3.77685	+	0.936989i	0.141345	+	0.0350660i
$715$		0			0
$716$	1.35093	−	0.879403i	0.0504866	−	0.0328648i
$717$	2.04689	−	1.18177i	0.0764425	−	0.0441341i
$718$	3.42505	−	6.31638i	0.127822	−	0.235725i
$719$	18.0142	−	31.2015i	0.671817	−	1.16362i	−0.305572	−	0.952169i	$-0.598848\pi$
$719$	18.0142	−	31.2015i	0.671817	−	1.16362i	0.977388	−	0.211452i	$-0.0678191\pi$
$720$		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
$724$	0.00712830	+	0.133231i	0.000264921	+	0.00495149i
$725$		0			0
$726$	−0.104173	−	3.89686i	−0.00386622	−	0.144626i
$727$	−51.4779			−1.90921			−0.954604	−	0.297878i	$-0.903721\pi$
$727$	−51.4779			−1.90921			−0.954604	+	0.297878i	$0.903721\pi$
$728$	−9.68955	−	27.9352i	−0.359119	−	1.03535i
$729$	−2.16686			−0.0802541
$730$		0			0
$731$	−6.58541	−	11.4063i	−0.243570	−	0.421876i
$732$	−1.11989	−	20.9312i	−0.0413923	−	0.773641i
$733$	−31.1280	−	17.9717i	−1.14974	−	0.663801i	−0.200914	−	0.979609i	$-0.564391\pi$
$733$	−31.1280	−	17.9717i	−1.14974	−	0.663801i	−0.948823	+	0.315807i	$0.897725\pi$
$734$	−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
$738$	−0.540432	+	0.996651i	−0.0198936	+	0.0366872i
$739$	−15.7903	+	9.11653i	−0.580855	+	0.335357i	−0.761473	−	0.648196i	$-0.775524\pi$
$739$	−15.7903	+	9.11653i	−0.580855	+	0.335357i	0.180618	+	0.983553i	$0.442190\pi$
$740$		0			0
$741$			9.33993i			0.343111i
$742$	4.35416	+	4.19495i	0.159846	+	0.154001i
$743$			29.1171i			1.06820i	0.845420	+	0.534102i	$0.179350\pi$
$743$			29.1171i			1.06820i	−0.845420	+	0.534102i	$0.820650\pi$
$744$	−14.2963	−	6.79024i	−0.524127	−	0.248942i
$745$		0			0
$746$	−8.86901	−	4.80921i	−0.324717	−	0.176078i
$747$	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	$-0.620775\pi$
$751$	−37.2703	−	21.5180i	−1.36001	−	0.785203i	−0.989625	+	0.143675i	$0.954108\pi$
$752$	−10.6297	+	24.0157i	−0.387624	+	0.875762i
$753$	−5.55715	−	9.62527i	−0.202514	−	0.350764i
$754$	−28.9304	+	0.773382i	−1.05358	+	0.0281649i
$755$		0			0
$756$	6.40535	+	20.1944i	0.232960	+	0.734462i
$757$	−10.6531			−0.387193			−0.193597	−	0.981081i	$-0.562015\pi$
$757$	−10.6531			−0.387193			−0.193597	+	0.981081i	$0.562015\pi$
$758$	−22.9637	+	0.613879i	−0.834081	+	0.0222971i
$759$	4.84339	+	8.38899i	0.175804	+	0.304501i
$760$		0			0
$761$	12.3298	+	7.11864i	0.446956	+	0.258050i	0.706544	−	0.707669i	$-0.250253\pi$
$761$	12.3298	+	7.11864i	0.446956	+	0.258050i	−0.259588	+	0.965720i	$0.583587\pi$
$762$	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
$766$	−12.2918	−	6.66519i	−0.444119	−	0.240823i
$767$	26.1252	−	15.0834i	0.943327	−	0.544630i
$768$	7.88456	+	8.68011i	0.284509	+	0.313216i
$769$			35.5770i			1.28294i	0.767149	+	0.641469i	$0.221675\pi$
$769$			35.5770i			1.28294i	−0.767149	+	0.641469i	$0.778325\pi$
$770$		0			0
$771$		−	3.46777i		−	0.124889i
$772$	18.7635	+	28.8242i	0.675313	+	1.03741i
$773$	10.2930	−	5.94268i	0.370214	−	0.213743i	−0.303338	−	0.952883i	$-0.598101\pi$
$773$	10.2930	−	5.94268i	0.370214	−	0.213743i	0.673552	+	0.739140i	$0.264768\pi$
$774$	15.4100	−	28.4188i	0.553902	−	1.02149i
$775$		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
$782$	0.263440	+	9.85465i	0.00942058	+	0.352401i
$783$	20.7365			0.741061
$784$	−22.8810	+	16.1387i	−0.817180	+	0.576382i
$785$		0			0
$786$	−0.391745	−	14.6542i	−0.0139731	−	0.522700i
$787$	−23.1890	−	40.1645i	−0.826597	−	1.43171i	−0.900692	−	0.434457i	$-0.856940\pi$
$787$	−23.1890	−	40.1645i	−0.826597	−	1.43171i	0.0740951	−	0.997251i	$-0.476393\pi$
$788$	23.8444	−	1.27575i	0.849420	−	0.0454468i
$789$	−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
$794$	−11.7808	+	21.7258i	−0.418085	+	0.771020i
$795$		0			0
$796$	−16.9344	−	26.0144i	−0.600223	−	0.922056i
$797$		−	9.09251i		−	0.322073i	−0.986948	−	0.161037i	$-0.948516\pi$
$797$		−	9.09251i		−	0.322073i	0.986948	−	0.161037i	$-0.0514837\pi$
$798$	8.49918	−	2.44785i	0.300868	−	0.0866530i
$799$			9.31691i			0.329609i
$800$		0			0
$801$	−10.1206	+	5.84312i	−0.357593	+	0.206457i
$802$	21.5802	+	11.7018i	0.762023	+	0.413206i
$803$	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
$808$	0.448602	+	0.650434i	0.0157818	+	0.0228822i
$809$	8.66128	+	15.0018i	0.304515	+	0.527435i	0.977153	−	0.212536i	$-0.0681724\pi$
$809$	8.66128	+	15.0018i	0.304515	+	0.527435i	−0.672639	+	0.739971i	$0.734839\pi$
$810$		0			0
$811$	16.4459			0.577493			0.288746	−	0.957406i	$-0.406762\pi$
$811$	16.4459			0.577493			0.288746	+	0.957406i	$0.406762\pi$
$812$	8.28597	+	26.1235i	0.290781	+	0.916754i
$813$	−19.3424			−0.678368
$814$	−17.0395	+	0.455509i	−0.597235	+	0.0159656i
$815$		0			0
$816$	3.80406	+	1.68373i	0.133169	+	0.0589422i
$817$	−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	0.146226	+	0.989251i	$0.453287\pi$
$821$	−22.4527	+	38.8892i	−0.783603	+	1.35724i	−0.929830	+	0.367990i	$0.880046\pi$
$822$	13.5497	+	7.34733i	0.472601	+	0.256267i
$823$	−20.5328	+	11.8546i	−0.715729	+	0.413226i	−0.813179	−	0.582014i	$-0.802265\pi$
$823$	−20.5328	+	11.8546i	−0.715729	+	0.413226i	0.0974497	+	0.995240i	$0.468931\pi$
$824$	34.2371	+	16.2614i	1.19270	+	0.566493i
$825$		0			0
$826$	−20.5727	−	19.8204i	−0.715815	−	0.689640i
$827$		−	8.20536i		−	0.285328i	−0.989771	−	0.142664i	$-0.954433\pi$
$827$		−	8.20536i		−	0.285328i	0.989771	−	0.142664i	$-0.0455669\pi$
$828$	−20.2789	+	13.2008i	−0.704740	+	0.458759i
$829$	19.1548	−	11.0590i	0.665272	−	0.384095i	−0.129011	−	0.991643i	$-0.541180\pi$
$829$	19.1548	−	11.0590i	0.665272	−	0.384095i	0.794283	+	0.607548i	$0.207847\pi$
$830$		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
$836$	0.927251	+	17.3307i	0.0320696	+	0.599395i
$837$	−15.2841	−	26.4729i	−0.528296	−	0.915036i
$838$	0.677528	+	25.3447i	0.0234048	+	0.875518i
$839$	3.64977			0.126004			0.0630020	−	0.998013i	$-0.479933\pi$
$839$	3.64977			0.126004			0.0630020	+	0.998013i	$0.479933\pi$
$840$		0			0
$841$	−2.17525			−0.0750086
$842$	0.477443	+	17.8600i	0.0164538	+	0.615496i
$843$	−2.85312	−	4.94174i	−0.0982665	−	0.170203i
$844$	−1.51343	−	28.2868i	−0.0520946	−	0.973670i
$845$		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
$852$	−18.9292	+	12.3222i	−0.648505	+	0.422152i
$853$		−	1.03474i		−	0.0354290i	−0.999843	−	0.0177145i	$-0.994361\pi$
$853$		−	1.03474i		−	0.0354290i	0.999843	−	0.0177145i	$-0.00563899\pi$
$854$	51.9317	+	12.8836i	1.77706	+	0.440867i
$855$		0			0
$856$	−6.58794	+	13.8703i	−0.225171	+	0.474079i
$857$	42.0132	−	24.2563i	1.43514	−	0.828581i	0.437637	−	0.899152i	$-0.355815\pi$
$857$	42.0132	−	24.2563i	1.43514	−	0.828581i	0.997507	+	0.0705709i	$0.0224821\pi$
$858$	−9.68623	−	5.25235i	−0.330682	−	0.179312i
$859$	12.4674	−	21.5941i	0.425382	−	0.736783i	−0.571074	−	0.820898i	$-0.693473\pi$
$859$	12.4674	−	21.5941i	0.425382	−	0.736783i	0.996456	+	0.0841157i	$0.0268065\pi$
$860$		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	0.585369	−	0.810767i	$-0.300950\pi$
$863$	5.16765	+	2.98354i	0.175909	+	0.101561i	−0.409460	+	0.912328i	$0.634283\pi$
$864$	3.01756	+	22.4467i	0.102659	+	0.763653i
$865$		0			0
$866$	−33.3472	+	0.891454i	−1.13318	+	0.0302928i
$867$	−10.9836			−0.373023
$868$	27.2428	−	29.8328i	0.924680	−	1.01259i
$869$	32.8588			1.11466
$870$		0			0
$871$	5.97927	+	10.3564i	0.202600	+	0.350913i
$872$	20.7620	−	14.3195i	0.703090	−	0.484918i
$873$	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	0.425270	+	0.905066i	$0.360179\pi$
$877$	−16.9149	+	29.2974i	−0.571175	+	0.989304i	−0.996446	+	0.0842381i	$0.973154\pi$
$878$	−22.8625	−	12.3972i	−0.771573	−	0.418384i
$879$	−1.34243	+	0.775051i	−0.0452789	+	0.0261418i
$880$		0			0
$881$		−	20.9239i		−	0.704944i	−0.935822	−	0.352472i	$-0.885341\pi$
$881$		−	20.9239i		−	0.704944i	0.935822	−	0.352472i	$-0.114659\pi$
$882$	−24.3796	+	0.256417i	−0.820905	+	0.00863401i
$883$			14.7876i			0.497642i	0.968549	+	0.248821i	$0.0800432\pi$
$883$			14.7876i			0.497642i	−0.968549	+	0.248821i	$0.919957\pi$
$884$	−6.11763	−	9.39783i	−0.205758	−	0.316083i
$885$		0			0
$886$	−2.28147	+	4.20742i	−0.0766473	+	0.141351i
$887$	3.69958	−	6.40786i	0.124220	−	0.215155i	−0.797208	−	0.603705i	$-0.793691\pi$
$887$	3.69958	−	6.40786i	0.124220	−	0.215155i	0.921428	+	0.388550i	$0.127024\pi$
$888$	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
$892$	−6.06020	+	0.324241i	−0.202910	+	0.0108564i
$893$	10.5882	+	18.3393i	0.354321	+	0.613702i
$894$	0.243348	+	9.10306i	0.00813877	+	0.304452i
$895$		0			0
$896$	−27.0722	+	12.7708i	−0.904420	+	0.426643i
$897$	−14.2255			−0.474976
$898$	0.449775	+	16.8250i	0.0150092	+	0.561457i
$899$	−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
$906$	0.148385	−	0.273648i	0.00492977	−	0.00909135i
$907$	16.0320	−	9.25608i	0.532334	−	0.307343i	−0.209632	−	0.977780i	$-0.567227\pi$
$907$	16.0320	−	9.25608i	0.532334	−	0.307343i	0.741966	+	0.670437i	$0.233893\pi$
$908$	−16.1231	−	24.7681i	−0.535063	−	0.821958i
$909$			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	$-0.0574912\pi$
$912$	9.40136	−	1.00890i	0.311310	−	0.0334079i
$913$	12.2602	−	7.07841i	0.405752	−	0.234261i
$914$	26.1948	+	14.2041i	0.866446	+	0.469829i
$915$		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	$-0.247703\pi$
$919$	13.9555	+	8.05723i	0.460351	+	0.265784i	−0.251841	+	0.967769i	$0.581036\pi$
$920$		0			0
$921$	−6.83653	−	11.8412i	−0.225271	−	0.390181i
$922$	−41.9459	+	1.12132i	−1.38141	+	0.0369287i
$923$	60.8834			2.00400
$924$	−2.24093	+	10.1909i	−0.0737213	+	0.335255i
$925$		0			0
$926$	−21.2736	+	0.568696i	−0.699093	+	0.0186885i
$927$	16.5018	+	28.5820i	0.541991	+	0.938757i
$928$	3.90352	+	29.0371i	0.128139	+	0.953190i
$929$	−42.7419	−	24.6770i	−1.40232	−	0.809627i	−0.407686	−	0.913122i	$-0.633664\pi$
$929$	−42.7419	−	24.6770i	−1.40232	−	0.809627i	−0.994630	+	0.103495i	$0.966998\pi$
$930$		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
$934$	−6.39751	−	3.46904i	−0.209333	−	0.113511i
$935$		0			0
$936$	11.8086	−	24.8620i	0.385976	−	0.812641i
$937$			31.3085i			1.02280i	0.859342	+	0.511402i	$0.170874\pi$
$937$			31.3085i			1.02280i	−0.859342	+	0.511402i	$0.829126\pi$
$938$	7.85708	−	8.15529i	0.256543	−	0.266280i
$939$			17.1311i			0.559054i
$940$		0			0
$941$	37.9492	−	21.9100i	1.23711	−	0.714245i	0.268606	−	0.963250i	$-0.413437\pi$
$941$	37.9492	−	21.9100i	1.23711	−	0.714245i	0.968502	+	0.249005i	$0.0801035\pi$
$942$	−9.50335	+	17.5258i	−0.309636	+	0.571022i
$943$	−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	0.279736	−	0.960077i	$-0.409753\pi$
$947$	−12.6739	−	7.31729i	−0.411847	−	0.237780i	−0.691583	+	0.722297i	$0.743086\pi$
$948$	−0.956425	−	17.8760i	−0.0310633	−	0.580586i
$949$	2.80340	+	4.85563i	0.0910021	+	0.157620i
$950$		0			0
$951$	−19.2078			−0.622857
$952$	−6.94853	+	8.02996i	−0.225203	+	0.260253i
$953$	28.2044			0.913630			0.456815	−	0.889562i	$-0.348990\pi$
$953$	28.2044			0.913630			0.456815	+	0.889562i	$0.348990\pi$
$954$	0.150403	+	5.62620i	0.00486946	+	0.182155i
$955$		0			0
$956$	0.344593	+	6.44059i	0.0111449	+	0.208303i
$957$	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
$962$	11.9324	−	22.0053i	0.384715	−	0.709480i
$963$	−11.5793	+	6.68534i	−0.373139	+	0.215432i
$964$	34.3396	−	22.3538i	1.10600	−	0.719966i
$965$		0			0
$966$	3.72828	+	12.9450i	0.119956	+	0.416497i
$967$		−	8.88824i		−	0.285827i	−0.989735	−	0.142913i	$-0.954353\pi$
$967$		−	8.88824i		−	0.285827i	0.989735	−	0.142913i	$-0.0456470\pi$
$968$	9.60903	+	4.56396i	0.308846	+	0.146691i
$969$	2.90493	−	1.67716i	0.0933198	−	0.0538782i
$970$		0			0
$971$	−4.37105	+	7.57089i	−0.140274	+	0.242961i	−0.927600	−	0.373576i	$-0.878132\pi$
$971$	−4.37105	+	7.57089i	−0.140274	+	0.242961i	0.787326	+	0.616537i	$0.211465\pi$
$972$	−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
$976$	52.3057	+	23.1512i	1.67427	+	0.741052i
$977$	20.9907	+	36.3569i	0.671551	+	1.16316i	0.977464	+	0.211100i	$0.0677047\pi$
$977$	20.9907	+	36.3569i	0.671551	+	1.16316i	−0.305914	+	0.952059i	$0.598962\pi$
$978$	11.1063	−	0.296899i	0.355139	−	0.00949378i
$979$	−12.7666			−0.408022
$980$		0			0
$981$	21.9613			0.701170
$982$	32.4468	−	0.867385i	1.03542	−	0.0276794i
$983$	5.50236	+	9.53036i	0.175498	+	0.303971i	0.940333	−	0.340254i	$-0.110513\pi$
$983$	5.50236	+	9.53036i	0.175498	+	0.303971i	−0.764836	+	0.644226i	$0.777180\pi$
$984$	0.383105	+	0.555468i	0.0122129	+	0.0177077i
$985$		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	$-0.469323\pi$
$991$	31.6799	−	18.2904i	1.00634	−	0.581013i	0.910119	+	0.414346i	$0.135990\pi$
$992$	34.1926	−	26.3856i	1.08562	−	0.837743i
$993$			14.3073i			0.454028i
$994$	−15.9566	−	55.4028i	−0.506112	−	1.75727i
$995$		0			0
$996$	−4.20769	−	6.46381i	−0.133326	−	0.204814i
$997$	−12.5263	+	7.23204i	−0.396711	+	0.229041i	−0.685064	−	0.728483i	$-0.740226\pi$
$997$	−12.5263	+	7.23204i	−0.396711	+	0.229041i	0.288353	+	0.957524i	$0.406892\pi$
$998$	−2.83635	+	5.23071i	−0.0897830	+	0.165575i
$999$	−8.96801	+	15.5331i	−0.283735	+	0.491444i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.1	✓	32	5.2	odd	4
140.2.s.b.19.6	yes	32	20.7	even	4
140.2.s.b.19.11	yes	32	20.3	even	4
140.2.s.b.19.16	yes	32	5.3	odd	4
140.2.s.b.59.1	yes	32	140.3	odd	12
140.2.s.b.59.6	yes	32	35.3	even	12
140.2.s.b.59.11	yes	32	35.17	even	12
140.2.s.b.59.16	yes	32	140.87	odd	12
700.2.p.e.451.3		32	7.3	odd	6	inner
700.2.p.e.451.8		32	140.59	even	6	inner
700.2.p.e.451.9		32	28.3	even	6	inner
700.2.p.e.451.14		32	35.24	odd	6	inner
700.2.p.e.551.3		32	4.3	odd	2	inner
700.2.p.e.551.8		32	5.4	even	2	inner
700.2.p.e.551.9		32	1.1	even	1	trivial
700.2.p.e.551.14		32	20.19	odd	2	inner
980.2.c.d.979.9		32	35.23	odd	12
980.2.c.d.979.10		32	35.33	even	12
980.2.c.d.979.11		32	140.107	even	12
980.2.c.d.979.12		32	140.47	odd	12
980.2.c.d.979.21		32	140.103	odd	12
980.2.c.d.979.22		32	140.23	even	12
980.2.c.d.979.23		32	35.12	even	12
980.2.c.d.979.24		32	35.2	odd	12
980.2.s.e.19.1		32	35.27	even	4
980.2.s.e.19.6		32	140.27	odd	4
980.2.s.e.19.11		32	140.83	odd	4
980.2.s.e.19.16		32	35.13	even	4
980.2.s.e.619.1		32	140.123	even	12
980.2.s.e.619.6		32	35.18	odd	12
980.2.s.e.619.11		32	35.32	odd	12
980.2.s.e.619.16		32	140.67	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	700.2.p.e.551.9

Level	$700$
Weight	$2$
Character	700.551
Analytic conductor	$5.590$
Analytic rank	$0$
Dimension	$32$
Inner twists	$8$