LMFDB - Embedded newform 125.2.d.b.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [125,2,Mod(26,125)] 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("125.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(125, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$125 = 5^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	125.d (of order $5$ , degree $4$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625$ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$5^{2}$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.1
Root			$0.644389 + 0.983224i$ of defining polynomial
Character	$\chi$	$=$	125.101
Dual form			125.2.d.b.26.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.644389 + 1.98322i) q^{2} +(1.77862 + 1.29224i) q^{3} +(-1.89991 - 1.38036i) q^{4} +(-3.70892 + 2.69469i) q^{6} +0.992398 q^{7} +(0.587785 - 0.427051i) q^{8} +(0.566541 + 1.74363i) q^{9} +(0.618034 - 1.90211i) q^{11} +(-1.59545 - 4.91027i) q^{12} +(-1.04264 - 3.20892i) q^{13} +(-0.639490 + 1.96815i) q^{14} +(-0.983224 - 3.02605i) q^{16} +(-2.34171 + 1.70135i) q^{17} -3.82309 q^{18} +(2.09089 - 1.51912i) q^{19} +(1.76510 + 1.28242i) q^{21} +(3.37406 + 2.45140i) q^{22} +(-1.40591 + 4.32696i) q^{23} +1.59730 q^{24} +7.03588 q^{26} +(0.792578 - 2.43930i) q^{27} +(-1.88546 - 1.36987i) q^{28} +(4.35599 + 3.16481i) q^{29} +(-0.110461 + 0.0802548i) q^{31} +8.08800 q^{32} +(3.55723 - 2.58448i) q^{33} +(-1.86519 - 5.74046i) q^{34} +(1.33047 - 4.09478i) q^{36} +(-0.664110 - 2.04392i) q^{37} +(1.66541 + 5.12561i) q^{38} +(2.29224 - 7.05479i) q^{39} +(2.66780 + 8.21064i) q^{41} +(-3.68073 + 2.67421i) q^{42} +4.64398 q^{43} +(-3.79981 + 2.76073i) q^{44} +(-7.67537 - 5.57648i) q^{46} +(-8.03054 - 5.83453i) q^{47} +(2.16161 - 6.65275i) q^{48} -6.01515 q^{49} -6.36356 q^{51} +(-2.44856 + 7.53588i) q^{52} +(-6.12038 - 4.44672i) q^{53} +(4.32696 + 3.14372i) q^{54} +(0.583317 - 0.423805i) q^{56} +5.68196 q^{57} +(-9.08347 + 6.59953i) q^{58} +(1.51967 + 4.67706i) q^{59} +(-0.855890 + 2.63416i) q^{61} +(-0.0879833 - 0.270785i) q^{62} +(0.562235 + 1.73038i) q^{63} +(-3.24537 + 9.98822i) q^{64} +(2.83337 + 8.72020i) q^{66} +(-1.76833 + 1.28477i) q^{67} +6.79751 q^{68} +(-8.09205 + 5.87922i) q^{69} +(-7.80098 - 5.66774i) q^{71} +(1.07763 + 0.782941i) q^{72} +(0.239775 - 0.737953i) q^{73} +4.48150 q^{74} -6.06943 q^{76} +(0.613336 - 1.88765i) q^{77} +(12.5141 + 9.09205i) q^{78} +(-12.8236 - 9.31689i) q^{79} +(9.01153 - 6.54726i) q^{81} -18.0026 q^{82} +(1.43285 - 1.04103i) q^{83} +(-1.58332 - 4.87295i) q^{84} +(-2.99252 + 9.21004i) q^{86} +(3.65794 + 11.2580i) q^{87} +(-0.449028 - 1.38197i) q^{88} +(4.48322 - 13.7979i) q^{89} +(-1.03472 - 3.18453i) q^{91} +(8.64388 - 6.28015i) q^{92} -0.300177 q^{93} +(16.7460 - 12.1667i) q^{94} +(14.3855 + 10.4516i) q^{96} +(13.7768 + 10.0095i) q^{97} +(3.87609 - 11.9294i) q^{98} +3.66673 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 2 q^{4} - 18 q^{6} - 2 q^{9} - 8 q^{11} - 26 q^{14} + 6 q^{16} + 10 q^{19} - 8 q^{21} + 40 q^{24} + 12 q^{26} + 10 q^{29} - 18 q^{31} - 26 q^{34} + 46 q^{36} + 6 q^{39} - 8 q^{41} + 4 q^{44} - 38 q^{46}+ \cdots + 16 q^{99}+O(q^{100})$ 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9 - 8 * q^11 - 26 * q^14 + 6 * q^16 + 10 * q^19 - 8 * q^21 + 40 * q^24 + 12 * q^26 + 10 * q^29 - 18 * q^31 - 26 * q^34 + 46 * q^36 + 6 * q^39 - 8 * q^41 + 4 * q^44 - 38 * q^46 - 28 * q^49 - 8 * q^51 + 10 * q^54 + 20 * q^56 - 18 * q^61 - 8 * q^64 + 24 * q^66 - 34 * q^69 + 12 * q^71 + 24 * q^74 - 40 * q^76 - 30 * q^79 + 56 * q^81 - 36 * q^84 - 18 * q^86 + 50 * q^89 + 12 * q^91 + 54 * q^94 + 32 * q^96 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.644389	+	1.98322i	−0.455652	+	1.40235i	0.414717	+	0.909950i	$0.363881\pi$
$2$	−0.644389	+	1.98322i	−0.455652	+	1.40235i	−0.870369	+	0.492401i	$0.836119\pi$
$3$	1.77862	+	1.29224i	1.02689	+	0.746076i	0.967683	−	0.252170i	$-0.0811443\pi$
$3$	1.77862	+	1.29224i	1.02689	+	0.746076i	0.0592022	+	0.998246i	$0.481144\pi$
$4$	−1.89991	−	1.38036i	−0.949953	−	0.690182i
$5$		0			0
$5$		0			0
$6$	−3.70892	+	2.69469i	−1.51416	+	1.10010i
$7$	0.992398			0.375091			0.187546	−	0.982256i	$-0.439947\pi$
$7$	0.992398			0.375091			0.187546	+	0.982256i	$0.439947\pi$
$8$	0.587785	−	0.427051i	0.207813	−	0.150985i
$9$	0.566541	+	1.74363i	0.188847	+	0.581211i
$10$		0			0
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	−0.813625	−	0.581390i	$-0.802509\pi$
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	0.999969	+	0.00788181i	$0.00250889\pi$
$12$	−1.59545	−	4.91027i	−0.460565	−	1.41747i
$13$	−1.04264	−	3.20892i	−0.289177	−	0.889995i	−0.985115	−	0.171894i	$-0.945011\pi$
$13$	−1.04264	−	3.20892i	−0.289177	−	0.889995i	0.695938	−	0.718101i	$-0.254989\pi$
$14$	−0.639490	+	1.96815i	−0.170911	+	0.526010i
$15$		0			0
$16$	−0.983224	−	3.02605i	−0.245806	−	0.756513i
$17$	−2.34171	+	1.70135i	−0.567948	+	0.412638i	−0.834359	−	0.551221i	$-0.814162\pi$
$17$	−2.34171	+	1.70135i	−0.567948	+	0.412638i	0.266411	+	0.963859i	$0.414162\pi$
$18$	−3.82309			−0.901111
$19$	2.09089	−	1.51912i	0.479683	−	0.348510i	−0.321520	−	0.946903i	$-0.604194\pi$
$19$	2.09089	−	1.51912i	0.479683	−	0.348510i	0.801203	+	0.598393i	$0.204194\pi$
$20$		0			0
$21$	1.76510	+	1.28242i	0.385176	+	0.279847i
$22$	3.37406	+	2.45140i	0.719352	+	0.522640i
$23$	−1.40591	+	4.32696i	−0.293153	+	0.902233i	0.690682	+	0.723158i	$0.257310\pi$
$23$	−1.40591	+	4.32696i	−0.293153	+	0.902233i	−0.983835	+	0.179075i	$0.942690\pi$
$24$	1.59730			0.326047
$25$		0			0
$26$	7.03588			1.37985
$27$	0.792578	−	2.43930i	0.152532	−	0.469444i
$28$	−1.88546	−	1.36987i	−0.356319	−	0.258881i
$29$	4.35599	+	3.16481i	0.808886	+	0.587690i	0.913508	−	0.406822i	$-0.133363\pi$
$29$	4.35599	+	3.16481i	0.808886	+	0.587690i	−0.104621	+	0.994512i	$0.533363\pi$
$30$		0			0
$31$	−0.110461	+	0.0802548i	−0.0198394	+	0.0144142i	−0.597661	−	0.801749i	$-0.703903\pi$
$31$	−0.110461	+	0.0802548i	−0.0198394	+	0.0144142i	0.577821	+	0.816163i	$0.303903\pi$
$32$	8.08800			1.42977
$33$	3.55723	−	2.58448i	0.619235	−	0.449901i
$34$	−1.86519	−	5.74046i	−0.319877	−	0.984482i
$35$		0			0
$36$	1.33047	−	4.09478i	0.221746	−	0.682463i
$37$	−0.664110	−	2.04392i	−0.109179	−	0.336018i	0.881510	−	0.472166i	$-0.156528\pi$
$37$	−0.664110	−	2.04392i	−0.109179	−	0.336018i	−0.990689	+	0.136148i	$0.956528\pi$
$38$	1.66541	+	5.12561i	0.270165	+	0.831483i
$39$	2.29224	−	7.05479i	0.367052	−	1.12967i
$40$		0			0
$41$	2.66780	+	8.21064i	0.416640	+	1.28229i	0.910776	+	0.412902i	$0.135485\pi$
$41$	2.66780	+	8.21064i	0.416640	+	1.28229i	−0.494135	+	0.869385i	$0.664515\pi$
$42$	−3.68073	+	2.67421i	−0.567949	+	0.412639i
$43$	4.64398			0.708200			0.354100	−	0.935208i	$-0.384787\pi$
$43$	4.64398			0.708200			0.354100	+	0.935208i	$0.384787\pi$
$44$	−3.79981	+	2.76073i	−0.572843	+	0.416195i
$45$		0			0
$46$	−7.67537	−	5.57648i	−1.13167	−	0.822208i
$47$	−8.03054	−	5.83453i	−1.17137	−	0.851054i	−0.180202	−	0.983630i	$-0.557675\pi$
$47$	−8.03054	−	5.83453i	−1.17137	−	0.851054i	−0.991173	+	0.132576i	$0.957675\pi$
$48$	2.16161	−	6.65275i	0.312001	−	0.960242i
$49$	−6.01515			−0.859306
$50$		0			0
$51$	−6.36356			−0.891077
$52$	−2.44856	+	7.53588i	−0.339554	+	1.04504i
$53$	−6.12038	−	4.44672i	−0.840699	−	0.610804i	0.0818665	−	0.996643i	$-0.473912\pi$
$53$	−6.12038	−	4.44672i	−0.840699	−	0.610804i	−0.922566	+	0.385839i	$0.873912\pi$
$54$	4.32696	+	3.14372i	0.588824	+	0.427806i
$55$		0			0
$56$	0.583317	−	0.423805i	0.0779490	−	0.0566333i
$57$	5.68196			0.752594
$58$	−9.08347	+	6.59953i	−1.19272	+	0.866561i
$59$	1.51967	+	4.67706i	0.197844	+	0.608901i	0.999932	+	0.0116948i	$0.00372266\pi$
$59$	1.51967	+	4.67706i	0.197844	+	0.608901i	−0.802088	+	0.597206i	$0.796277\pi$
$60$		0			0
$61$	−0.855890	+	2.63416i	−0.109585	+	0.337269i	−0.990779	−	0.135486i	$-0.956740\pi$
$61$	−0.855890	+	2.63416i	−0.109585	+	0.337269i	0.881194	+	0.472755i	$0.156740\pi$
$62$	−0.0879833	−	0.270785i	−0.0111739	−	0.0343897i
$63$	0.562235	+	1.73038i	0.0708349	+	0.218007i
$64$	−3.24537	+	9.98822i	−0.405671	+	1.24853i
$65$		0			0
$66$	2.83337	+	8.72020i	0.348763	+	1.07338i
$67$	−1.76833	+	1.28477i	−0.216036	+	0.156959i	−0.690540	−	0.723294i	$-0.742627\pi$
$67$	−1.76833	+	1.28477i	−0.216036	+	0.156959i	0.474505	+	0.880253i	$0.342627\pi$
$68$	6.79751			0.824319
$69$	−8.09205	+	5.87922i	−0.974169	+	0.707775i
$70$		0			0
$71$	−7.80098	−	5.66774i	−0.925806	−	0.672637i	0.0191565	−	0.999816i	$-0.493902\pi$
$71$	−7.80098	−	5.66774i	−0.925806	−	0.672637i	−0.944962	+	0.327179i	$0.893902\pi$
$72$	1.07763	+	0.782941i	0.126999	+	0.0922704i
$73$	0.239775	−	0.737953i	0.0280636	−	0.0863708i	−0.936044	−	0.351884i	$-0.885541\pi$
$73$	0.239775	−	0.737953i	0.0280636	−	0.0863708i	0.964107	+	0.265513i	$0.0855413\pi$
$74$	4.48150			0.520963
$75$		0			0
$76$	−6.06943			−0.696212
$77$	0.613336	−	1.88765i	0.0698961	−	0.215118i
$78$	12.5141	+	9.09205i	1.41695	+	1.02947i
$79$	−12.8236	−	9.31689i	−1.44277	−	1.04823i	−0.987455	−	0.157900i	$-0.949527\pi$
$79$	−12.8236	−	9.31689i	−1.44277	−	1.04823i	−0.455313	−	0.890332i	$-0.650473\pi$
$80$		0			0
$81$	9.01153	−	6.54726i	1.00128	−	0.727474i
$82$	−18.0026			−1.98806
$83$	1.43285	−	1.04103i	0.157276	−	0.114268i	−0.506364	−	0.862320i	$-0.669011\pi$
$83$	1.43285	−	1.04103i	0.157276	−	0.114268i	0.663640	+	0.748052i	$0.269011\pi$
$84$	−1.58332	−	4.87295i	−0.172754	−	0.531682i
$85$		0			0
$86$	−2.99252	+	9.21004i	−0.322692	+	0.993144i
$87$	3.65794	+	11.2580i	0.392172	+	1.20698i
$88$	−0.449028	−	1.38197i	−0.0478665	−	0.147318i
$89$	4.48322	−	13.7979i	0.475221	−	1.46258i	−0.370439	−	0.928857i	$-0.620793\pi$
$89$	4.48322	−	13.7979i	0.475221	−	1.46258i	0.845660	−	0.533722i	$-0.179207\pi$
$90$		0			0
$91$	−1.03472	−	3.18453i	−0.108468	−	0.333830i
$92$	8.64388	−	6.28015i	0.901187	−	0.654750i
$93$	−0.300177			−0.0311269
$94$	16.7460	−	12.1667i	1.72721	−	1.25490i
$95$		0			0
$96$	14.3855	+	10.4516i	1.46821	+	1.06672i
$97$	13.7768	+	10.0095i	1.39883	+	1.01631i	0.994831	+	0.101545i	$0.0323786\pi$
$97$	13.7768	+	10.0095i	1.39883	+	1.01631i	0.403995	+	0.914761i	$0.367621\pi$
$98$	3.87609	−	11.9294i	0.391544	−	1.20505i
$99$	3.66673			0.368520
$100$		0			0
$101$	−2.54716			−0.253452			−0.126726	−	0.991938i	$-0.540447\pi$
$101$	−2.54716			−0.253452			−0.126726	+	0.991938i	$0.540447\pi$
$102$	4.10060	−	12.6204i	0.406020	−	1.24960i
$103$	−8.22400	−	5.97509i	−0.810335	−	0.588743i	0.103593	−	0.994620i	$-0.466966\pi$
$103$	−8.22400	−	5.97509i	−0.810335	−	0.588743i	−0.913928	+	0.405877i	$0.866966\pi$
$104$	−1.98322	−	1.44090i	−0.194471	−	0.141292i
$105$		0			0
$106$	12.7627	−	9.27268i	1.23963	−	0.900642i
$107$	−4.81720			−0.465697			−0.232848	−	0.972513i	$-0.574805\pi$
$107$	−4.81720			−0.465697			−0.232848	+	0.972513i	$0.574805\pi$
$108$	−4.87295	+	3.54040i	−0.468900	+	0.340676i
$109$	5.02903	+	15.4778i	0.481694	+	1.48250i	0.836713	+	0.547642i	$0.184474\pi$
$109$	5.02903	+	15.4778i	0.481694	+	1.48250i	−0.355019	+	0.934859i	$0.615526\pi$
$110$		0			0
$111$	1.46004	−	4.49354i	0.138581	−	0.426508i
$112$	−0.975750	−	3.00305i	−0.0921997	−	0.283762i
$113$	2.08804	+	6.42633i	0.196426	+	0.604538i	0.999957	+	0.00927487i	$0.00295233\pi$
$113$	2.08804	+	6.42633i	0.196426	+	0.604538i	−0.803531	+	0.595264i	$0.797048\pi$
$114$	−3.66139	+	11.2686i	−0.342921	+	1.05540i
$115$		0			0
$116$	−3.90738	−	12.0257i	−0.362791	−	1.11656i
$117$	5.00449	−	3.63597i	0.462665	−	0.336146i
$118$	−10.2549			−0.944041
$119$	−2.32391	+	1.68842i	−0.213032	+	0.154777i
$120$		0			0
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$	−4.67260	−	3.39484i	−0.423037	−	0.307355i
$123$	−5.86513	+	18.0510i	−0.528841	+	1.62761i
$124$	0.320647			0.0287950
$125$		0			0
$126$	−3.79403			−0.337999
$127$	−0.460687	+	1.41785i	−0.0408793	+	0.125814i	−0.969413	−	0.245433i	$-0.921070\pi$
$127$	−0.460687	+	1.41785i	−0.0408793	+	0.125814i	0.928534	+	0.371247i	$0.121070\pi$
$128$	−4.63093	−	3.36457i	−0.409320	−	0.297389i
$129$	8.25985	+	6.00114i	0.727240	+	0.528370i
$130$		0			0
$131$	−11.4190	+	8.29640i	−0.997684	+	0.724860i	−0.961590	−	0.274489i	$-0.911491\pi$
$131$	−11.4190	+	8.29640i	−0.997684	+	0.724860i	−0.0360934	+	0.999348i	$0.511491\pi$
$132$	−10.3259			−0.898757
$133$	2.07500	−	1.50757i	0.179925	−	0.130723i
$134$	−1.40849	−	4.33488i	−0.121675	−	0.374476i
$135$		0			0
$136$	−0.649858	+	2.00006i	−0.0557249	+	0.171504i
$137$	−0.213051	−	0.655703i	−0.0182022	−	0.0560205i	0.941543	−	0.336893i	$-0.109376\pi$
$137$	−0.213051	−	0.655703i	−0.0182022	−	0.0560205i	−0.959745	+	0.280873i	$0.909376\pi$
$138$	−6.44539	−	19.8369i	−0.548668	−	1.68863i
$139$	−5.12099	+	15.7608i	−0.434356	+	1.33681i	0.459388	+	0.888236i	$0.348069\pi$
$139$	−5.12099	+	15.7608i	−0.434356	+	1.33681i	−0.893745	+	0.448576i	$0.851931\pi$
$140$		0			0
$141$	−6.74364	−	20.7548i	−0.567917	−	1.74787i
$142$	16.2673	−	11.8189i	1.36512	−	0.991817i
$143$	−6.74812			−0.564307
$144$	4.71929	−	3.42877i	0.393274	−	0.285731i
$145$		0			0
$146$	1.30902	+	0.951057i	0.108335	+	0.0787100i
$147$	−10.6986	−	7.77302i	−0.882409	−	0.641108i
$148$	−1.55961	+	4.79997i	−0.128199	+	0.394555i
$149$	3.21156			0.263101			0.131551	−	0.991309i	$-0.458004\pi$
$149$	3.21156			0.263101			0.131551	+	0.991309i	$0.458004\pi$
$150$		0			0
$151$	17.6863			1.43929			0.719647	−	0.694340i	$-0.244304\pi$
$151$	17.6863			1.43929			0.719647	+	0.694340i	$0.244304\pi$
$152$	0.580252	−	1.78583i	0.0470647	−	0.144850i
$153$	−4.29321	−	3.11920i	−0.347085	−	0.252172i
$154$	3.34841	+	2.43277i	0.269823	+	0.196038i
$155$		0			0
$156$	−14.0932	+	10.2393i	−1.12836	+	0.819802i
$157$	1.65512			0.132093			0.0660465	−	0.997817i	$-0.478961\pi$
$157$	1.65512			0.132093			0.0660465	+	0.997817i	$0.478961\pi$
$158$	26.7409	−	19.4284i	2.12739	−	1.54564i
$159$	−5.13959	−	15.8180i	−0.407596	−	1.25445i
$160$		0			0
$161$	−1.39523	+	4.29407i	−0.109959	+	0.338420i
$162$	7.17776	+	22.0909i	0.563938	+	1.73562i
$163$	0.275932	+	0.849231i	0.0216127	+	0.0665169i	0.961281	−	0.275570i	$-0.0888664\pi$
$163$	0.275932	+	0.849231i	0.0216127	+	0.0665169i	−0.939668	+	0.342086i	$0.888866\pi$
$164$	6.26510	−	19.2820i	0.489222	−	1.50567i
$165$		0			0
$166$	1.14128	+	3.51249i	0.0885803	+	0.272622i
$167$	−4.20331	+	3.05388i	−0.325262	+	0.236317i	−0.738417	−	0.674344i	$-0.764427\pi$
$167$	−4.20331	+	3.05388i	−0.325262	+	0.236317i	0.413156	+	0.910660i	$0.364427\pi$
$168$	1.58516			0.122297
$169$	1.30713	−	0.949687i	0.100549	−	0.0730529i
$170$		0			0
$171$	3.83337	+	2.78510i	0.293145	+	0.212982i
$172$	−8.82312	−	6.41037i	−0.672757	−	0.488786i
$173$	−1.78137	+	5.48250i	−0.135435	+	0.416827i	−0.995657	−	0.0930924i	$-0.970325\pi$
$173$	−1.78137	+	5.48250i	−0.135435	+	0.416827i	0.860222	+	0.509919i	$0.170325\pi$
$174$	−24.6842			−1.87130
$175$		0			0
$176$	−6.36356			−0.479671
$177$	−3.34098	+	10.2825i	−0.251123	+	0.772878i
$178$	24.4755	+	17.7825i	1.83451	+	1.33285i
$179$	−7.01326	−	5.09543i	−0.524196	−	0.380850i	0.293986	−	0.955810i	$-0.405018\pi$
$179$	−7.01326	−	5.09543i	−0.524196	−	0.380850i	−0.818182	+	0.574959i	$0.805018\pi$
$180$		0			0
$181$	−11.5616	+	8.39996i	−0.859363	+	0.624364i	−0.927712	−	0.373297i	$-0.878227\pi$
$181$	−11.5616	+	8.39996i	−0.859363	+	0.624364i	0.0683483	+	0.997662i	$0.478227\pi$
$182$	6.98240			0.517570
$183$	−4.92627	+	3.57914i	−0.364160	+	0.264578i
$184$	1.02146	+	3.14372i	0.0753027	+	0.231758i
$185$		0			0
$186$	0.193431	−	0.595318i	0.0141830	−	0.0436508i
$187$	1.78891	+	5.50569i	0.130818	+	0.402616i
$188$	7.20351	+	22.1701i	0.525370	+	1.61692i
$189$	0.786553	−	2.42076i	0.0572133	−	0.176084i
$190$		0			0
$191$	−0.391326	−	1.20438i	−0.0283154	−	0.0871458i	0.935900	−	0.352265i	$-0.114589\pi$
$191$	−0.391326	−	1.20438i	−0.0283154	−	0.0871458i	−0.964216	+	0.265120i	$0.914589\pi$
$192$	−18.6795	+	13.5714i	−1.34807	+	0.979433i
$193$	21.1730			1.52406			0.762031	−	0.647540i	$-0.224202\pi$
$193$	21.1730			1.52406			0.762031	+	0.647540i	$0.224202\pi$
$194$	−28.7286	+	20.8726i	−2.06260	+	1.49856i
$195$		0			0
$196$	11.4282	+	8.30308i	0.816301	+	0.593077i
$197$	9.87108	+	7.17176i	0.703285	+	0.510967i	0.881001	−	0.473115i	$-0.156871\pi$
$197$	9.87108	+	7.17176i	0.703285	+	0.510967i	−0.177715	+	0.984082i	$0.556871\pi$
$198$	−2.36280	+	7.27195i	−0.167917	+	0.516795i
$199$	10.4065			0.737695			0.368848	−	0.929490i	$-0.379752\pi$
$199$	10.4065			0.737695			0.368848	+	0.929490i	$0.379752\pi$
$200$		0			0
$201$	−4.80540			−0.338947
$202$	1.64136	−	5.05159i	0.115486	−	0.355429i
$203$	4.32287	+	3.14075i	0.303406	+	0.220438i
$204$	12.0902	+	8.78402i	0.846481	+	0.615005i
$205$		0			0
$206$	17.1494	−	12.4598i	1.19485	−	0.868113i
$207$	−8.34114			−0.579749
$208$	−8.68522	+	6.31018i	−0.602212	+	0.437532i
$209$	−1.59730	−	4.91598i	−0.110487	−	0.340045i
$210$		0			0
$211$	−2.67537	+	8.23395i	−0.184180	+	0.566848i	−0.999933	−	0.0115520i	$-0.996323\pi$
$211$	−2.67537	+	8.23395i	−0.184180	+	0.566848i	0.815753	+	0.578400i	$0.196323\pi$
$212$	5.49007	+	16.8967i	0.377060	+	1.16047i
$213$	−6.55086	−	20.1615i	−0.448858	−	1.38144i
$214$	3.10415	−	9.55359i	0.212195	−	0.653070i
$215$		0			0
$216$	−0.575842	−	1.77226i	−0.0391811	−	0.120587i
$217$	−0.109622	+	0.0796448i	−0.00744160	+	0.00540664i
$218$	−33.9365			−2.29847
$219$	1.38008	−	1.00269i	0.0932573	−	0.0677554i
$220$		0			0
$221$	7.90107	+	5.74046i	0.531484	+	0.386145i
$222$	7.97087	+	5.79117i	0.534970	+	0.388678i
$223$	8.75859	−	26.9562i	0.586518	−	1.80512i	−0.00656747	−	0.999978i	$-0.502091\pi$
$223$	8.75859	−	26.9562i	0.586518	−	1.80512i	0.593086	−	0.805139i	$-0.297909\pi$
$224$	8.02652			0.536295
$225$		0			0
$226$	−14.0904			−0.937277
$227$	6.87299	−	21.1529i	0.456176	−	1.40397i	−0.413572	−	0.910471i	$-0.635719\pi$
$227$	6.87299	−	21.1529i	0.456176	−	1.40397i	0.869749	−	0.493495i	$-0.164281\pi$
$228$	−10.7952	−	7.84317i	−0.714929	−	0.519427i
$229$	−2.00280	−	1.45512i	−0.132348	−	0.0961568i	0.519641	−	0.854384i	$-0.326066\pi$
$229$	−2.00280	−	1.45512i	−0.132348	−	0.0961568i	−0.651990	+	0.758228i	$0.726066\pi$
$230$		0			0
$231$	3.53019	−	2.56484i	0.232270	−	0.168754i
$232$	3.91192			0.256830
$233$	−4.81854	+	3.50088i	−0.315673	+	0.229350i	−0.734327	−	0.678796i	$-0.762502\pi$
$233$	−4.81854	+	3.50088i	−0.315673	+	0.229350i	0.418654	+	0.908146i	$0.362502\pi$
$234$	3.98612	+	12.2680i	0.260581	+	0.801985i
$235$		0			0
$236$	3.56881	−	10.9837i	0.232310	−	0.714976i
$237$	−10.7686	−	33.1424i	−0.699496	−	2.15283i
$238$	−1.85101	−	5.69683i	−0.119983	−	0.369271i
$239$	−2.17314	+	6.68823i	−0.140569	+	0.432626i	−0.996415	−	0.0846050i	$-0.973037\pi$
$239$	−2.17314	+	6.68823i	−0.140569	+	0.432626i	0.855846	+	0.517231i	$0.173037\pi$
$240$		0			0
$241$	0.364567	+	1.12202i	0.0234838	+	0.0722758i	0.962112	−	0.272656i	$-0.0879021\pi$
$241$	0.364567	+	1.12202i	0.0234838	+	0.0722758i	−0.938628	+	0.344932i	$0.887902\pi$
$242$	−11.8092	+	8.57990i	−0.759125	+	0.551537i
$243$	16.7942			1.07735
$244$	5.26220	−	3.82322i	0.336878	−	0.244756i
$245$		0			0
$246$	−32.0198	−	23.2637i	−2.04151	−	1.48324i
$247$	−7.05479	−	5.12561i	−0.448886	−	0.326135i
$248$	−0.0306546	+	0.0943452i	−0.00194657	+	0.00599093i
$249$	3.89375			0.246757
$250$		0			0
$251$	4.60867			0.290897			0.145448	−	0.989366i	$-0.453538\pi$
$251$	4.60867			0.290897			0.145448	+	0.989366i	$0.453538\pi$
$252$	1.32036	−	4.06365i	0.0831748	−	0.255986i
$253$	7.36146	+	5.34841i	0.462811	+	0.336252i
$254$	−2.51505	−	1.82729i	−0.157808	−	0.114654i
$255$		0			0
$256$	−7.33616	+	5.33003i	−0.458510	+	0.333127i
$257$	−9.75542			−0.608526			−0.304263	−	0.952588i	$-0.598410\pi$
$257$	−9.75542			−0.608526			−0.304263	+	0.952588i	$0.598410\pi$
$258$	−17.2242	+	12.5141i	−1.07233	+	0.779092i
$259$	−0.659062	−	2.02838i	−0.0409521	−	0.126038i
$260$		0			0
$261$	−3.05043	+	9.38824i	−0.188817	+	0.581118i
$262$	−9.09534	−	27.9926i	−0.561912	−	1.72939i
$263$	0.307728	+	0.947088i	0.0189753	+	0.0584000i	0.960096	−	0.279671i	$-0.0902255\pi$
$263$	0.307728	+	0.947088i	0.0189753	+	0.0584000i	−0.941121	+	0.338071i	$0.890225\pi$
$264$	0.987184	−	3.03824i	0.0607570	−	0.186991i
$265$		0			0
$266$	1.65275	+	5.08664i	0.101337	+	0.311882i
$267$	25.8042	−	18.7479i	1.57919	−	1.14735i
$268$	5.13310			0.313554
$269$	2.66048	−	1.93295i	0.162212	−	0.117854i	−0.503718	−	0.863868i	$-0.668035\pi$
$269$	2.66048	−	1.93295i	0.162212	−	0.117854i	0.665930	+	0.746014i	$0.268035\pi$
$270$		0			0
$271$	−9.82960	−	7.14162i	−0.597105	−	0.433823i	0.247745	−	0.968825i	$-0.420311\pi$
$271$	−9.82960	−	7.14162i	−0.597105	−	0.433823i	−0.844850	+	0.535003i	$0.820311\pi$
$272$	7.45080	+	5.41332i	0.451771	+	0.328231i
$273$	2.27482	−	7.00116i	0.137678	−	0.423730i
$274$	1.43769			0.0868543
$275$		0			0
$276$	23.4896			1.41391
$277$	−3.66697	+	11.2858i	−0.220327	+	0.678096i	0.778406	+	0.627762i	$0.216029\pi$
$277$	−3.66697	+	11.2858i	−0.220327	+	0.678096i	−0.998732	+	0.0503346i	$0.983971\pi$
$278$	−27.9572	−	20.3121i	−1.67676	−	1.21824i
$279$	−0.202516	−	0.147136i	−0.0121243	−	0.00880883i
$280$		0			0
$281$	19.9355	−	14.4840i	1.18925	−	0.864041i	0.196066	−	0.980591i	$-0.437183\pi$
$281$	19.9355	−	14.4840i	1.18925	−	0.864041i	0.993185	+	0.116549i	$0.0371833\pi$
$282$	45.5069			2.70990
$283$	2.72107	−	1.97697i	0.161751	−	0.117519i	−0.503965	−	0.863724i	$-0.668126\pi$
$283$	2.72107	−	1.97697i	0.161751	−	0.117519i	0.665716	+	0.746205i	$0.268126\pi$
$284$	6.99759	+	21.5364i	0.415231	+	1.27795i
$285$		0			0
$286$	4.34841	−	13.3830i	0.257127	−	0.791356i
$287$	2.64752	+	8.14823i	0.156278	+	0.480975i
$288$	4.58219	+	14.1025i	0.270008	+	0.830999i
$289$	−2.66428	+	8.19982i	−0.156723	+	0.482342i
$290$		0			0
$291$	11.5691	+	35.6060i	0.678192	+	2.08726i
$292$	−1.47419	+	1.07106i	−0.0862707	+	0.0626793i
$293$	−8.96340			−0.523647			−0.261824	−	0.965116i	$-0.584324\pi$
$293$	−8.96340			−0.523647			−0.261824	+	0.965116i	$0.584324\pi$
$294$	22.3097	−	16.2090i	1.30113	−	0.945326i
$295$		0			0
$296$	−1.26321	−	0.917777i	−0.0734227	−	0.0533447i
$297$	−4.14999	−	3.01515i	−0.240807	−	0.174956i
$298$	−2.06949	+	6.36925i	−0.119883	+	0.368961i
$299$	15.3507			0.887756
$300$		0			0
$301$	4.60867			0.265640
$302$	−11.3969	+	35.0760i	−0.655817	+	2.01840i
$303$	−4.53042	−	3.29155i	−0.260266	−	0.189094i
$304$	−6.65275	−	4.83351i	−0.381561	−	0.277221i
$305$		0			0
$306$	8.95256	−	6.50442i	0.511784	−	0.371833i
$307$	9.48133			0.541128			0.270564	−	0.962702i	$-0.412790\pi$
$307$	9.48133			0.541128			0.270564	+	0.962702i	$0.412790\pi$
$308$	−3.77093	+	2.73974i	−0.214869	+	0.156111i
$309$	−6.90610	−	21.2548i	−0.392874	−	1.20914i
$310$		0			0
$311$	9.06409	−	27.8964i	0.513978	−	1.58186i	−0.271157	−	0.962535i	$-0.587406\pi$
$311$	9.06409	−	27.8964i	0.513978	−	1.58186i	0.785135	−	0.619325i	$-0.212594\pi$
$312$	−1.66541	−	5.12561i	−0.0942853	−	0.290180i
$313$	5.83735	+	17.9655i	0.329947	+	1.01547i	0.969158	+	0.246440i	$0.0792608\pi$
$313$	5.83735	+	17.9655i	0.329947	+	1.01547i	−0.639212	+	0.769031i	$0.720739\pi$
$314$	−1.06654	+	3.28248i	−0.0601884	+	0.185241i
$315$		0			0
$316$	11.5030	+	35.4024i	0.647092	+	1.99154i
$317$	−18.4369	+	13.3952i	−1.03552	+	0.752351i	−0.969406	−	0.245461i	$-0.921061\pi$
$317$	−18.4369	+	13.3952i	−1.03552	+	0.752351i	−0.0661157	+	0.997812i	$0.521061\pi$
$318$	34.6826			1.94490
$319$	8.71197	−	6.32962i	0.487777	−	0.354391i
$320$		0			0
$321$	−8.56796	−	6.22499i	−0.478217	−	0.347445i
$322$	−7.61703	−	5.53409i	−0.424480	−	0.308403i
$323$	−2.31170	+	7.11468i	−0.128626	+	0.395871i
$324$	−26.1587			−1.45326
$325$		0			0
$326$	−1.86202			−0.103128
$327$	−11.0563	+	34.0277i	−0.611414	+	1.88174i
$328$	5.07446	+	3.68681i	0.280190	+	0.203570i
$329$	−7.96950	−	5.79018i	−0.439373	−	0.319223i
$330$		0			0
$331$	−2.39711	+	1.74160i	−0.131757	+	0.0957272i	−0.651712	−	0.758467i	$-0.725949\pi$
$331$	−2.39711	+	1.74160i	−0.131757	+	0.0957272i	0.519955	+	0.854194i	$0.325949\pi$
$332$	−4.15928			−0.228270
$333$	3.18760	−	2.31593i	0.174680	−	0.126912i
$334$	−3.34797	−	10.3040i	−0.183193	−	0.563809i
$335$		0			0
$336$	2.14518	−	6.60218i	0.117029	−	0.360178i
$337$	−5.81332	−	17.8916i	−0.316672	−	0.974615i	−0.975061	−	0.221937i	$-0.928762\pi$
$337$	−5.81332	−	17.8916i	−0.316672	−	0.974615i	0.658389	−	0.752678i	$-0.271238\pi$
$338$	1.04114	+	3.20430i	0.0566306	+	0.174291i
$339$	−4.59054	+	14.1282i	−0.249324	+	0.767340i
$340$		0			0
$341$	0.0843849	+	0.259710i	0.00456970	+	0.0140641i
$342$	−7.99366	+	5.80773i	−0.432248	+	0.314046i
$343$	−12.9162			−0.697410
$344$	2.72966	−	1.98321i	0.147173	−	0.106928i
$345$		0			0
$346$	−9.72514	−	7.06573i	−0.522827	−	0.379856i
$347$	18.3956	+	13.3652i	0.987526	+	0.717480i	0.959378	−	0.282124i	$-0.0910389\pi$
$347$	18.3956	+	13.3652i	0.987526	+	0.717480i	0.0281483	+	0.999604i	$0.491039\pi$
$348$	8.59035	−	26.4384i	0.460491	−	1.41725i
$349$	1.93849			0.103765			0.0518824	−	0.998653i	$-0.483478\pi$
$349$	1.93849			0.103765			0.0518824	+	0.998653i	$0.483478\pi$
$350$		0			0
$351$	−8.65392			−0.461912
$352$	4.99866	−	15.3843i	0.266430	−	0.819986i
$353$	−4.24689	−	3.08555i	−0.226039	−	0.164227i	0.469002	−	0.883197i	$-0.344614\pi$
$353$	−4.24689	−	3.08555i	−0.226039	−	0.164227i	−0.695041	+	0.718970i	$0.744614\pi$
$354$	−18.2396	−	13.2518i	−0.969422	−	0.704326i
$355$		0			0
$356$	−27.5639	+	20.0263i	−1.46088	+	1.06139i
$357$	−6.31519			−0.334235
$358$	14.6246	−	10.6254i	0.772937	−	0.561571i
$359$	6.98184	+	21.4879i	0.368488	+	1.13409i	0.947768	+	0.318960i	$0.103334\pi$
$359$	6.98184	+	21.4879i	0.368488	+	1.13409i	−0.579281	+	0.815128i	$0.696666\pi$
$360$		0			0
$361$	−3.80723	+	11.7174i	−0.200380	+	0.616708i
$362$	−9.20887	−	28.3420i	−0.484007	−	1.48962i
$363$	4.75560	+	14.6362i	0.249604	+	0.768203i
$364$	−2.42994	+	7.47860i	−0.127364	+	0.391985i
$365$		0			0
$366$	−3.92381	−	12.0762i	−0.205101	−	0.631236i
$367$	5.90479	−	4.29008i	0.308228	−	0.223940i	−0.422908	−	0.906173i	$-0.638991\pi$
$367$	5.90479	−	4.29008i	0.308228	−	0.223940i	0.731136	+	0.682232i	$0.238991\pi$
$368$	14.4759			0.754610
$369$	−12.8049	+	9.30333i	−0.666598	+	0.484312i
$370$		0			0
$371$	−6.07386	−	4.41292i	−0.315339	−	0.229107i
$372$	0.570308	+	0.414353i	0.0295691	+	0.0214832i
$373$	−6.89335	+	21.2156i	−0.356924	+	1.09850i	0.597961	+	0.801525i	$0.295978\pi$
$373$	−6.89335	+	21.2156i	−0.356924	+	1.09850i	−0.954885	+	0.296975i	$0.904022\pi$
$374$	−12.0718			−0.624216
$375$		0			0
$376$	−7.21188			−0.371924
$377$	5.61390	−	17.2778i	0.289130	−	0.889852i
$378$	4.29407	+	3.11982i	0.220863	+	0.160466i
$379$	26.6544	+	19.3655i	1.36914	+	0.994740i	0.997804	+	0.0662429i	$0.0211012\pi$
$379$	26.6544	+	19.3655i	1.36914	+	0.994740i	0.371339	+	0.928497i	$0.378899\pi$
$380$		0			0
$381$	−2.65159	+	1.92649i	−0.135845	+	0.0986971i
$382$	2.64072			0.135111
$383$	16.7468	−	12.1673i	0.855722	−	0.621719i	−0.0709955	−	0.997477i	$-0.522618\pi$
$383$	16.7468	−	12.1673i	0.855722	−	0.621719i	0.926718	+	0.375758i	$0.122618\pi$
$384$	−3.88882	−	11.9686i	−0.198450	−	0.610768i
$385$		0			0
$386$	−13.6436	+	41.9907i	−0.694441	+	2.13727i
$387$	2.63100	+	8.09739i	0.133741	+	0.411614i
$388$	−12.3580	−	38.0341i	−0.627383	−	1.93089i
$389$	−0.353657	+	1.08844i	−0.0179311	+	0.0551863i	−0.959622	−	0.281294i	$-0.909236\pi$
$389$	−0.353657	+	1.08844i	−0.0179311	+	0.0551863i	0.941691	+	0.336480i	$0.109236\pi$
$390$		0			0
$391$	−4.06943	−	12.5244i	−0.205800	−	0.633388i
$392$	−3.53561	+	2.56877i	−0.178575	+	0.129743i
$393$	−31.0310			−1.56531
$394$	−20.5840	+	14.9552i	−1.03701	+	0.753430i
$395$		0			0
$396$	−6.96645	−	5.06142i	−0.350077	−	0.254346i
$397$	3.79035	+	2.75385i	0.190232	+	0.138212i	0.678825	−	0.734300i	$-0.262490\pi$
$397$	3.79035	+	2.75385i	0.190232	+	0.138212i	−0.488593	+	0.872512i	$0.662490\pi$
$398$	−6.70581	+	20.6384i	−0.336132	+	1.03451i
$399$	5.63877			0.282292
$400$		0			0
$401$	−24.0851			−1.20275			−0.601376	−	0.798966i	$-0.705381\pi$
$401$	−24.0851			−1.20275			−0.601376	+	0.798966i	$0.705381\pi$
$402$	3.09655	−	9.53019i	0.154442	−	0.475323i
$403$	0.372703	+	0.270785i	0.0185657	+	0.0134888i
$404$	4.83937	+	3.51601i	0.240768	+	0.174928i
$405$		0			0
$406$	−9.01443	+	6.54936i	−0.447378	+	0.325039i
$407$	−4.29821			−0.213054
$408$	−3.74041	+	2.71756i	−0.185178	+	0.134539i
$409$	−0.586930	−	1.80638i	−0.0290218	−	0.0893199i	0.935496	−	0.353336i	$-0.114953\pi$
$409$	−0.586930	−	1.80638i	−0.0290218	−	0.0893199i	−0.964518	+	0.264016i	$0.914953\pi$
$410$		0			0
$411$	0.468391	−	1.44156i	0.0231040	−	0.0711068i
$412$	7.37705	+	22.7042i	0.363441	+	1.11856i
$413$	1.50812	+	4.64151i	0.0742096	+	0.228394i
$414$	5.37494	−	16.5423i	0.264164	−	0.813012i
$415$		0			0
$416$	−8.43290	−	25.9538i	−0.413457	−	1.27249i
$417$	−29.4750	+	21.4148i	−1.44340	+	1.04869i
$418$	10.7788			0.527207
$419$	1.88344	−	1.36840i	0.0920120	−	0.0668507i	−0.540828	−	0.841133i	$-0.681889\pi$
$419$	1.88344	−	1.36840i	0.0920120	−	0.0668507i	0.632840	+	0.774283i	$0.281889\pi$
$420$		0			0
$421$	19.3760	+	14.0775i	0.944329	+	0.686095i	0.949459	−	0.313892i	$-0.101633\pi$
$421$	19.3760	+	14.0775i	0.944329	+	0.686095i	−0.00513010	+	0.999987i	$0.501633\pi$
$422$	−14.6058	−	10.6117i	−0.710998	−	0.516571i
$423$	5.62366	−	17.3078i	0.273431	−	0.841536i
$424$	−5.49645			−0.266931
$425$		0			0
$426$	44.2060			2.14179
$427$	−0.849384	+	2.61413i	−0.0411045	+	0.126507i
$428$	9.15224	+	6.64949i	0.442390	+	0.321415i
$429$	−12.0023	−	8.72020i	−0.579478	−	0.421015i
$430$		0			0
$431$	−0.964563	+	0.700796i	−0.0464614	+	0.0337562i	−0.610774	−	0.791805i	$-0.709141\pi$
$431$	−0.964563	+	0.700796i	−0.0464614	+	0.0337562i	0.564312	+	0.825561i	$0.309141\pi$
$432$	−8.16074			−0.392634
$433$	−20.7220	+	15.0554i	−0.995837	+	0.723518i	−0.961192	−	0.275882i	$-0.911030\pi$
$433$	−20.7220	+	15.0554i	−0.995837	+	0.723518i	−0.0346454	+	0.999400i	$0.511030\pi$
$434$	−0.0873145	−	0.268726i	−0.00419123	−	0.0128993i
$435$		0			0
$436$	11.8102	−	36.3482i	0.565608	−	1.74076i
$437$	3.63356	+	11.1829i	0.173817	+	0.534953i
$438$	1.09925	+	3.38313i	0.0525240	+	0.161652i
$439$	5.98693	−	18.4259i	0.285741	−	0.879420i	−0.700435	−	0.713716i	$-0.747011\pi$
$439$	5.98693	−	18.4259i	0.285741	−	0.879420i	0.986176	−	0.165703i	$-0.0529894\pi$
$440$		0			0
$441$	−3.40783	−	10.4882i	−0.162277	−	0.499439i
$442$	−16.4760	+	11.9705i	−0.783683	+	0.569379i
$443$	−2.46263			−0.117003			−0.0585016	−	0.998287i	$-0.518632\pi$
$443$	−2.46263			−0.117003			−0.0585016	+	0.998287i	$0.518632\pi$
$444$	−8.97666	+	6.52192i	−0.426013	+	0.309517i
$445$		0			0
$446$	47.8162	+	34.7405i	2.26416	+	1.64501i
$447$	5.71214	+	4.15011i	0.270175	+	0.196294i
$448$	−3.22070	+	9.91229i	−0.152164	+	0.468312i
$449$	−14.3585			−0.677618			−0.338809	−	0.940855i	$-0.610024\pi$
$449$	−14.3585			−0.677618			−0.338809	+	0.940855i	$0.610024\pi$
$450$		0			0
$451$	17.2664			0.813041
$452$	4.90359	−	15.0917i	0.230645	−	0.709853i
$453$	31.4572	+	22.8550i	1.47799	+	1.07382i
$454$	37.5220	+	27.2614i	1.76100	+	1.27944i
$455$		0			0
$456$	3.33977	−	2.42649i	0.156399	−	0.113631i
$457$	25.1964			1.17864			0.589319	−	0.807901i	$-0.299396\pi$
$457$	25.1964			1.17864			0.589319	+	0.807901i	$0.299396\pi$
$458$	4.17640	−	3.03433i	0.195150	−	0.141785i
$459$	2.29413	+	7.06059i	0.107081	+	0.329560i
$460$		0			0
$461$	8.90758	−	27.4147i	0.414867	−	1.27683i	−0.497502	−	0.867463i	$-0.665749\pi$
$461$	8.90758	−	27.4147i	0.414867	−	1.27683i	0.912370	−	0.409367i	$-0.134251\pi$
$462$	2.81183	+	8.65392i	0.130818	+	0.402617i
$463$	−9.85134	−	30.3193i	−0.457831	−	1.40906i	−0.867780	−	0.496949i	$-0.834453\pi$
$463$	−9.85134	−	30.3193i	−0.457831	−	1.40906i	0.409949	−	0.912108i	$-0.365547\pi$
$464$	5.29397	−	16.2932i	0.245766	−	0.756391i
$465$		0			0
$466$	−3.83801	−	11.8122i	−0.177792	−	0.547189i
$467$	34.8683	−	25.3333i	1.61351	−	1.17229i	0.762847	−	0.646580i	$-0.223801\pi$
$467$	34.8683	−	25.3333i	1.61351	−	1.17229i	0.850666	−	0.525706i	$-0.176199\pi$
$468$	−14.5270			−0.671512
$469$	−1.75489	+	1.27500i	−0.0810331	+	0.0588740i
$470$		0			0
$471$	2.94383	+	2.13882i	0.135644	+	0.0985514i
$472$	2.89058	+	2.10013i	0.133050	+	0.0966663i
$473$	2.87013	−	8.83337i	0.131969	−	0.406159i
$474$	72.6679			3.33775
$475$		0			0
$476$	6.74584			0.309195
$477$	4.28600	−	13.1910i	0.196243	−	0.603973i
$478$	−11.8639	−	8.61964i	−0.542643	−	0.394253i
$479$	−17.0107	−	12.3590i	−0.777237	−	0.564696i	0.126912	−	0.991914i	$-0.459494\pi$
$479$	−17.0107	−	12.3590i	−0.777237	−	0.564696i	−0.904148	+	0.427218i	$0.859494\pi$
$480$		0			0
$481$	−5.86635	+	4.26216i	−0.267483	+	0.194338i
$482$	−2.46014			−0.112057
$483$	−8.03054	+	5.83453i	−0.365402	+	0.265480i
$484$	−5.07990	−	15.6343i	−0.230904	−	0.710651i
$485$		0			0
$486$	−10.8220	+	33.3067i	−0.490895	+	1.51082i
$487$	8.62744	+	26.5525i	0.390947	+	1.20321i	0.932073	+	0.362269i	$0.117998\pi$
$487$	8.62744	+	26.5525i	0.390947	+	1.20321i	−0.541127	+	0.840941i	$0.682002\pi$
$488$	0.621840	+	1.91383i	0.0281494	+	0.0866349i
$489$	−0.606634	+	1.86703i	−0.0274329	+	0.0844299i
$490$		0			0
$491$	4.62322	+	14.2288i	0.208643	+	0.642137i	0.999544	+	0.0301930i	$0.00961220\pi$
$491$	4.62322	+	14.2288i	0.208643	+	0.642137i	−0.790901	+	0.611944i	$0.790388\pi$
$492$	36.0602	−	26.1993i	1.62572	−	1.18115i
$493$	−15.5849			−0.701909
$494$	14.7113	−	10.6884i	0.661891	−	0.480892i
$495$		0			0
$496$	0.351464	+	0.255353i	0.0157812	+	0.0114657i
$497$	−7.74168	−	5.62466i	−0.347262	−	0.252300i
$498$	−2.50909	+	7.72218i	−0.112435	+	0.346039i
$499$	−44.3253			−1.98427			−0.992137	−	0.125160i	$-0.960056\pi$
$499$	−44.3253			−1.98427			−0.992137	+	0.125160i	$0.960056\pi$
$500$		0			0
$501$	−11.4224			−0.510316
$502$	−2.96978	+	9.14003i	−0.132548	+	0.407940i
$503$	19.1100	+	13.8842i	0.852071	+	0.619066i	0.925716	−	0.378219i	$-0.123463\pi$
$503$	19.1100	+	13.8842i	0.852071	+	0.619066i	−0.0736453	+	0.997284i	$0.523463\pi$
$504$	1.06943	+	0.776989i	0.0476364	+	0.0346098i
$505$		0			0
$506$	−15.3507	+	11.1530i	−0.682424	+	0.495810i
$507$	3.55211			0.157755
$508$	2.83241	−	2.05786i	0.125668	−	0.0913029i
$509$	−8.25552	−	25.4079i	−0.365920	−	1.12618i	−0.949403	−	0.314060i	$-0.898311\pi$
$509$	−8.25552	−	25.4079i	−0.365920	−	1.12618i	0.583484	−	0.812125i	$-0.301689\pi$
$510$		0			0
$511$	0.237953	−	0.732343i	0.0105264	−	0.0323970i
$512$	−9.38103	−	28.8718i	−0.414587	−	1.27597i
$513$	−2.04840	−	6.30434i	−0.0904392	−	0.278343i
$514$	6.28628	−	19.3472i	0.277276	−	0.853367i
$515$		0			0
$516$	−7.40921	−	22.8032i	−0.326172	−	1.00385i
$517$	−16.0611	+	11.6691i	−0.706366	+	0.513205i
$518$	4.44743			0.195409
$519$	−10.2531	+	7.44931i	−0.450061	+	0.326988i
$520$		0			0
$521$	−26.4607	−	19.2249i	−1.15927	−	0.842256i	−0.169581	−	0.985516i	$-0.554241\pi$
$521$	−26.4607	−	19.2249i	−1.15927	−	0.842256i	−0.989685	+	0.143260i	$0.954241\pi$
$522$	−16.6533	−	12.0994i	−0.728896	−	0.529574i
$523$	0.0729175	−	0.224417i	0.00318846	−	0.00981307i	−0.949450	−	0.313919i	$-0.898358\pi$
$523$	0.0729175	−	0.224417i	0.00318846	−	0.00981307i	0.952638	+	0.304106i	$0.0983578\pi$
$524$	33.1471			1.44804
$525$		0			0
$526$	−2.07658			−0.0905434
$527$	0.122127	−	0.375867i	0.00531992	−	0.0163730i
$528$	−11.3183	−	8.22325i	−0.492567	−	0.357871i
$529$	1.86142	+	1.35240i	0.0809313	+	0.0588001i
$530$		0			0
$531$	−7.29413	+	5.29949i	−0.316538	+	0.229978i
$532$	−6.02330			−0.261143
$533$	23.5658	−	17.1215i	1.02075	−	0.741616i
$534$	20.5533	+	63.2564i	0.889427	+	2.73737i
$535$		0			0
$536$	−0.490737	+	1.51033i	−0.0211966	+	0.0652364i
$537$	−5.88938	−	18.1256i	−0.254145	−	0.782179i
$538$	2.11909	+	6.52190i	0.0913606	+	0.281179i
$539$	−3.71756	+	11.4415i	−0.160127	+	0.492820i
$540$		0			0
$541$	−10.3698	−	31.9148i	−0.445830	−	1.37213i	−0.881570	−	0.472053i	$-0.843513\pi$
$541$	−10.3698	−	31.9148i	−0.445830	−	1.37213i	0.435740	−	0.900073i	$-0.356487\pi$
$542$	20.4975	−	14.8923i	0.880443	−	0.639680i
$543$	−31.4183			−1.34829
$544$	−18.9397	+	13.7605i	−0.812035	+	0.589978i
$545$		0			0
$546$	12.4190	+	9.02294i	0.531485	+	0.386146i
$547$	−31.1573	−	22.6371i	−1.33219	−	0.967892i	−0.999693	−	0.0247869i	$-0.992109\pi$
$547$	−31.1573	−	22.6371i	−1.33219	−	0.967892i	−0.332496	−	0.943105i	$-0.607891\pi$
$548$	−0.500332	+	1.53986i	−0.0213731	+	0.0657797i
$549$	−5.07790			−0.216720
$550$		0			0
$551$	13.9156			0.592825
$552$	−2.24566	+	6.91144i	−0.0955818	+	0.294170i
$553$	−12.7261	−	9.24607i	−0.541170	−	0.393183i
$554$	−20.0193	−	14.5448i	−0.850537	−	0.617951i
$555$		0			0
$556$	31.4850	−	22.8752i	1.33526	−	0.970124i
$557$	4.33445			0.183657			0.0918283	−	0.995775i	$-0.470729\pi$
$557$	4.33445			0.183657			0.0918283	+	0.995775i	$0.470729\pi$
$558$	0.422304	−	0.306821i	0.0178775	−	0.0129888i
$559$	−4.84201	−	14.9022i	−0.204795	−	0.630294i
$560$		0			0
$561$	−3.93290	+	12.1042i	−0.166047	+	0.511040i
$562$	15.8788	+	48.8698i	0.669805	+	2.06145i
$563$	−10.7853	−	33.1936i	−0.454544	−	1.39894i	−0.871669	−	0.490094i	$-0.836962\pi$
$563$	−10.7853	−	33.1936i	−0.454544	−	1.39894i	0.417125	−	0.908849i	$-0.363038\pi$
$564$	−15.8369	+	48.7408i	−0.666852	+	2.05236i
$565$		0			0
$566$	2.16735	+	6.67043i	0.0911007	+	0.280379i
$567$	8.94303	−	6.49749i	0.375572	−	0.272869i
$568$	−7.00572			−0.293953
$569$	33.9501	−	24.6662i	1.42326	−	1.03406i	0.432038	−	0.901855i	$-0.357795\pi$
$569$	33.9501	−	24.6662i	1.42326	−	1.03406i	0.991223	−	0.132204i	$-0.0422054\pi$
$570$		0			0
$571$	11.1913	+	8.13093i	0.468340	+	0.340269i	0.796794	−	0.604251i	$-0.206528\pi$
$571$	11.1913	+	8.13093i	0.468340	+	0.340269i	−0.328454	+	0.944520i	$0.606528\pi$
$572$	12.8208	+	9.31486i	0.536065	+	0.389474i
$573$	0.860328	−	2.64782i	0.0359407	−	0.110614i
$574$	−17.8658			−0.745704
$575$		0			0
$576$	−19.2544			−0.802268
$577$	3.94902	−	12.1538i	0.164400	−	0.505970i	−0.834592	−	0.550869i	$-0.814296\pi$
$577$	3.94902	−	12.1538i	0.164400	−	0.505970i	0.998992	+	0.0448986i	$0.0142965\pi$
$578$	−14.5453	−	10.5677i	−0.605003	−	0.439560i
$579$	37.6586	+	27.3606i	1.56504	+	1.13707i
$580$		0			0
$581$	1.42196	−	1.03311i	0.0589928	−	0.0428608i
$582$	−78.0696			−3.23609
$583$	−12.2408	+	8.89344i	−0.506961	+	0.368329i
$584$	−0.174207	−	0.536154i	−0.00720874	−	0.0221862i
$585$		0			0
$586$	5.77591	−	17.7764i	0.238601	−	0.734337i
$587$	3.76597	+	11.5905i	0.155438	+	0.478390i	0.998205	−	0.0598889i	$-0.0190746\pi$
$587$	3.76597	+	11.5905i	0.155438	+	0.478390i	−0.842767	+	0.538279i	$0.819075\pi$
$588$	9.59683	+	29.5360i	0.395767	+	1.21804i
$589$	−0.109046	+	0.335608i	−0.00449315	+	0.0138285i
$590$		0			0
$591$	8.28923	+	25.5116i	0.340973	+	1.04941i
$592$	−5.53204	+	4.01926i	−0.227365	+	0.165191i
$593$	31.2580			1.28361			0.641807	−	0.766866i	$-0.278185\pi$
$593$	31.2580			1.28361			0.641807	+	0.766866i	$0.278185\pi$
$594$	8.65392	−	6.28744i	0.355074	−	0.257977i
$595$		0			0
$596$	−6.10167	−	4.43312i	−0.249934	−	0.181588i
$597$	18.5091	+	13.4477i	0.757528	+	0.550376i
$598$	−9.89184	+	30.4440i	−0.404508	+	1.24495i
$599$	−33.3707			−1.36349			−0.681746	−	0.731589i	$-0.738779\pi$
$599$	−33.3707			−1.36349			−0.681746	+	0.731589i	$0.738779\pi$
$600$		0			0
$601$	−46.8052			−1.90922			−0.954611	−	0.297854i	$-0.903729\pi$
$601$	−46.8052			−1.90922			−0.954611	+	0.297854i	$0.903729\pi$
$602$	−2.96978	+	9.14003i	−0.121039	+	0.372520i
$603$	−3.24199	−	2.35544i	−0.132024	−	0.0959211i
$604$	−33.6024	−	24.4136i	−1.36726	−	0.993374i
$605$		0			0
$606$	9.44722	−	6.86381i	0.383767	−	0.278823i
$607$	−30.7401			−1.24770			−0.623851	−	0.781543i	$-0.714433\pi$
$607$	−30.7401			−1.24770			−0.623851	+	0.781543i	$0.714433\pi$
$608$	16.9111	−	12.2867i	0.685837	−	0.498289i
$609$	3.63013	+	11.1724i	0.147100	+	0.452728i
$610$		0			0
$611$	−10.3496	+	31.8527i	−0.418699	+	1.28862i
$612$	3.85107	+	11.8524i	0.155670	+	0.479104i
$613$	11.8321	+	36.4154i	0.477894	+	1.47081i	0.842015	+	0.539454i	$0.181369\pi$
$613$	11.8321	+	36.4154i	0.477894	+	1.47081i	−0.364121	+	0.931352i	$0.618631\pi$
$614$	−6.10966	+	18.8036i	−0.246566	+	0.758852i
$615$		0			0
$616$	−0.445615	−	1.37146i	−0.0179543	−	0.0552577i
$617$	0.344080	−	0.249989i	0.0138521	−	0.0100642i	−0.580838	−	0.814019i	$-0.697275\pi$
$617$	0.344080	−	0.249989i	0.0138521	−	0.0100642i	0.594690	+	0.803955i	$0.297275\pi$
$618$	46.6032			1.87466
$619$	−6.07691	+	4.41513i	−0.244252	+	0.177459i	−0.703175	−	0.711016i	$-0.748235\pi$
$619$	−6.07691	+	4.41513i	−0.244252	+	0.177459i	0.458924	+	0.888476i	$0.348235\pi$
$620$		0			0
$621$	9.44047	+	6.85890i	0.378833	+	0.275238i
$622$	49.4840	+	35.9523i	1.98413	+	1.44155i
$623$	4.44914	−	13.6931i	0.178251	−	0.548601i
$624$	−23.6020			−0.944834
$625$		0			0
$626$	−39.3912			−1.57439
$627$	3.51165	−	10.8077i	0.140242	−	0.431619i
$628$	−3.14458	−	2.28467i	−0.125482	−	0.0911682i
$629$	5.03258	+	3.65638i	0.200662	+	0.145789i
$630$		0			0
$631$	9.11889	−	6.62526i	0.363017	−	0.263747i	−0.391292	−	0.920266i	$-0.627972\pi$
$631$	9.11889	−	6.62526i	0.363017	−	0.263747i	0.754309	+	0.656519i	$0.227972\pi$
$632$	−11.5163			−0.458094
$633$	−15.3987	+	11.1878i	−0.612044	+	0.444676i
$634$	−14.6852	−	45.1963i	−0.583223	−	1.79498i
$635$		0			0
$636$	−12.0699	+	37.1473i	−0.478602	+	1.47298i
$637$	6.27165	+	19.3021i	0.248492	+	0.764779i
$638$	6.93916	+	21.3565i	0.274724	+	0.845513i
$639$	5.46290	−	16.8131i	0.216109	−	0.665115i
$640$		0			0
$641$	8.05994	+	24.8060i	0.318349	+	0.979776i	0.974354	+	0.225020i	$0.0722448\pi$
$641$	8.05994	+	24.8060i	0.318349	+	0.979776i	−0.656006	+	0.754756i	$0.727755\pi$
$642$	17.8666	−	12.9809i	0.705140	−	0.512314i
$643$	31.9492			1.25995			0.629977	−	0.776614i	$-0.283064\pi$
$643$	31.9492			1.25995			0.629977	+	0.776614i	$0.283064\pi$
$644$	8.57817	−	6.23241i	0.338027	−	0.245591i
$645$		0			0
$646$	−12.6204	−	9.16923i	−0.496542	−	0.360759i
$647$	−5.98214	−	4.34628i	−0.235182	−	0.170870i	0.463952	−	0.885860i	$-0.346431\pi$
$647$	−5.98214	−	4.34628i	−0.235182	−	0.170870i	−0.699134	+	0.714990i	$0.746431\pi$
$648$	2.50083	−	7.69677i	0.0982419	−	0.302358i
$649$	9.83550			0.386077
$650$		0			0
$651$	−0.297895			−0.0116754
$652$	0.648002	−	1.99435i	0.0253777	−	0.0781046i
$653$	15.1167	+	10.9829i	0.591563	+	0.429796i	0.842874	−	0.538111i	$-0.180862\pi$
$653$	15.1167	+	10.9829i	0.591563	+	0.429796i	−0.251311	+	0.967906i	$0.580862\pi$
$654$	−60.3601	−	43.8542i	−2.36027	−	1.71483i
$655$		0			0
$656$	22.2228	−	16.1458i	0.867654	−	0.630388i
$657$	1.42256			0.0554994
$658$	16.6187	−	12.0742i	0.647863	−	0.470700i
$659$	3.02885	+	9.32184i	0.117987	+	0.363128i	0.992558	−	0.121770i	$-0.0388570\pi$
$659$	3.02885	+	9.32184i	0.117987	+	0.363128i	−0.874571	+	0.484897i	$0.838857\pi$
$660$		0			0
$661$	−8.70145	+	26.7803i	−0.338447	+	1.04163i	0.626552	+	0.779380i	$0.284466\pi$
$661$	−8.70145	+	26.7803i	−0.338447	+	1.04163i	−0.964999	+	0.262253i	$0.915534\pi$
$662$	−1.90932	−	5.87628i	−0.0742078	−	0.228388i
$663$	6.63492	+	20.4202i	0.257679	+	0.793054i
$664$	0.397637	−	1.22380i	0.0154313	−	0.0474927i
$665$		0			0
$666$	2.53895	+	7.81409i	0.0983824	+	0.302790i
$667$	−19.8181	+	14.3987i	−0.767361	+	0.557521i
$668$	12.2014			0.472085
$669$	50.4120	−	36.6265i	1.94904	−	1.41606i
$670$		0			0
$671$	4.48150	+	3.25600i	0.173006	+	0.125696i
$672$	14.2761	+	10.3722i	0.550713	+	0.400116i
$673$	12.0595	−	37.1153i	0.464859	−	1.43069i	−0.394301	−	0.918981i	$-0.629013\pi$
$673$	12.0595	−	37.1153i	0.464859	−	1.43069i	0.859160	−	0.511707i	$-0.170987\pi$
$674$	39.2290			1.51104
$675$		0			0
$676$	−3.79434			−0.145936
$677$	−1.55600	+	4.78888i	−0.0598020	+	0.184052i	−0.976495	−	0.215541i	$-0.930848\pi$
$677$	−1.55600	+	4.78888i	−0.0598020	+	0.184052i	0.916693	+	0.399593i	$0.130848\pi$
$678$	−25.0614	−	18.2081i	−0.962476	−	0.699280i
$679$	13.6721	+	9.93337i	0.524687	+	0.381208i
$680$		0			0
$681$	39.5590	−	28.7413i	1.51591	−	1.10137i
$682$	−0.569440			−0.0218050
$683$	−24.5384	+	17.8282i	−0.938937	+	0.682178i	−0.948165	−	0.317780i	$-0.897063\pi$
$683$	−24.5384	+	17.8282i	−0.938937	+	0.682178i	0.00922734	+	0.999957i	$0.497063\pi$
$684$	−3.43858	−	10.5829i	−0.131478	−	0.404646i
$685$		0			0
$686$	8.32306	−	25.6157i	0.317776	−	0.978013i
$687$	−1.68185	−	5.17619i	−0.0641664	−	0.197484i
$688$	−4.56607	−	14.0529i	−0.174080	−	0.535762i
$689$	−7.88781	+	24.2762i	−0.300502	+	0.924849i
$690$		0			0
$691$	−6.56134	−	20.1937i	−0.249605	−	0.768205i	−0.994845	−	0.101409i	$-0.967665\pi$
$691$	−6.56134	−	20.1937i	−0.249605	−	0.768205i	0.745240	−	0.666796i	$-0.232335\pi$
$692$	10.9523	−	7.95730i	0.416344	−	0.302491i
$693$	3.63886			0.138229
$694$	−38.3600	+	27.8702i	−1.45613	+	1.05794i
$695$		0			0
$696$	6.95781	+	5.05514i	0.263735	+	0.191615i
$697$	−20.2164	−	14.6881i	−0.765751	−	0.556350i
$698$	−1.24914	+	3.84445i	−0.0472806	+	0.145515i
$699$	−13.0943			−0.495273
$700$		0			0
$701$	32.7698			1.23770			0.618849	−	0.785510i	$-0.287599\pi$
$701$	32.7698			1.23770			0.618849	+	0.785510i	$0.287599\pi$
$702$	5.57648	−	17.1627i	0.210471	−	0.647763i
$703$	−4.49354	−	3.26475i	−0.169477	−	0.123132i
$704$	16.9930	+	12.3461i	0.640447	+	0.465312i
$705$		0			0
$706$	8.85599	−	6.43425i	0.333299	−	0.242156i
$707$	−2.52780			−0.0950676
$708$	20.5411	−	14.9240i	0.771982	−	0.560878i
$709$	6.13273	+	18.8746i	0.230320	+	0.708851i	0.997708	+	0.0676683i	$0.0215560\pi$
$709$	6.13273	+	18.8746i	0.230320	+	0.708851i	−0.767388	+	0.641183i	$0.778444\pi$
$710$		0			0
$711$	8.98015	−	27.6381i	0.336782	−	1.03651i
$712$	−3.25725	−	10.0248i	−0.122071	−	0.375695i
$713$	−0.191960	−	0.590793i	−0.00718897	−	0.0221254i
$714$	4.06943	−	12.5244i	0.152295	−	0.468715i
$715$		0			0
$716$	6.29100	+	19.3617i	0.235106	+	0.723580i
$717$	−12.5080	+	9.08759i	−0.467120	+	0.339382i
$718$	−47.1144			−1.75829
$719$	−19.5945	+	14.2362i	−0.730751	+	0.530922i	−0.889801	−	0.456349i	$-0.849157\pi$
$719$	−19.5945	+	14.2362i	−0.730751	+	0.530922i	0.159050	+	0.987271i	$0.449157\pi$
$720$		0			0
$721$	−8.16149	−	5.92967i	−0.303950	−	0.220832i
$722$	−20.7850	−	15.1012i	−0.773537	−	0.562008i
$723$	−0.801498	+	2.46676i	−0.0298080	+	0.0917397i
$724$	33.5609			1.24728
$725$		0			0
$726$	−32.0914			−1.19102
$727$	1.81242	−	5.57804i	0.0672188	−	0.206878i	−0.911805	−	0.410623i	$-0.865311\pi$
$727$	1.81242	−	5.57804i	0.0672188	−	0.206878i	0.979024	+	0.203745i	$0.0653113\pi$
$728$	−1.96815	−	1.42994i	−0.0729444	−	0.0529972i
$729$	2.83585	+	2.06037i	0.105032	+	0.0763099i
$730$		0			0
$731$	−10.8748	+	7.90103i	−0.402220	+	0.292230i
$732$	14.3000			0.528542
$733$	−27.9123	+	20.2795i	−1.03096	+	0.749039i	−0.968501	−	0.249008i	$-0.919895\pi$
$733$	−27.9123	+	20.2795i	−1.03096	+	0.749039i	−0.0624625	+	0.998047i	$0.519895\pi$
$734$	4.70321	+	14.4750i	0.173599	+	0.534282i
$735$		0			0
$736$	−11.3710	+	34.9964i	−0.419142	+	1.28999i
$737$	1.35088	+	4.15759i	0.0497604	+	0.153147i
$738$	−10.1992	−	31.3900i	−0.375439	−	1.15548i
$739$	12.2282	−	37.6345i	0.449821	−	1.38441i	−0.427288	−	0.904116i	$-0.640531\pi$
$739$	12.2282	−	37.6345i	0.449821	−	1.38441i	0.877109	−	0.480291i	$-0.159469\pi$
$740$		0			0
$741$	−5.92426	−	18.2330i	−0.217633	−	0.669805i
$742$	12.6657	−	9.20219i	0.464974	−	0.337823i
$743$	−29.7058			−1.08980			−0.544900	−	0.838501i	$-0.683433\pi$
$743$	−29.7058			−1.08980			−0.544900	+	0.838501i	$0.683433\pi$
$744$	−0.176440	+	0.128191i	−0.00646859	+	0.00469971i
$745$		0			0
$746$	−37.6332	−	27.3421i	−1.37785	−	1.00107i
$747$	2.62694	+	1.90858i	0.0961147	+	0.0698314i
$748$	4.20109	−	12.9296i	0.153607	−	0.472754i
$749$	−4.78058			−0.174679
$750$		0			0
$751$	26.8870			0.981122			0.490561	−	0.871407i	$-0.336792\pi$
$751$	26.8870			0.981122			0.490561	+	0.871407i	$0.336792\pi$
$752$	−9.75977	+	30.0375i	−0.355902	+	1.09535i
$753$	8.19707	+	5.95552i	0.298718	+	0.217031i
$754$	30.6482	+	22.2672i	1.11614	+	0.810925i
$755$		0			0
$756$	−4.83591	+	3.51349i	−0.175880	+	0.127784i
$757$	44.6792			1.62389			0.811947	−	0.583731i	$-0.198408\pi$
$757$	44.6792			1.62389			0.811947	+	0.583731i	$0.198408\pi$
$758$	−55.5819	+	40.3826i	−2.01883	+	1.46676i
$759$	6.18178	+	19.0256i	0.224384	+	0.690584i
$760$		0			0
$761$	6.27550	−	19.3140i	0.227487	−	0.700132i	−0.770543	−	0.637388i	$-0.780015\pi$
$761$	6.27550	−	19.3140i	0.227487	−	0.700132i	0.998030	−	0.0627441i	$-0.0199852\pi$
$762$	−2.11201	−	6.50010i	−0.0765100	−	0.235474i
$763$	4.99080	+	15.3601i	0.180679	+	0.556073i
$764$	−0.918996	+	2.82838i	−0.0332481	+	0.102327i
$765$		0			0
$766$	13.3390	+	41.0531i	0.481957	+	1.48331i
$767$	13.4239	−	9.75300i	0.484707	−	0.352160i
$768$	−19.9359			−0.719375
$769$	−21.0811	+	15.3163i	−0.760205	+	0.552321i	−0.898973	−	0.438004i	$-0.855686\pi$
$769$	−21.0811	+	15.3163i	−0.760205	+	0.552321i	0.138768	+	0.990325i	$0.455686\pi$
$770$		0			0
$771$	−17.3511	−	12.6063i	−0.624886	−	0.454007i
$772$	−40.2266	−	29.2264i	−1.44779	−	1.05188i
$773$	4.24295	−	13.0585i	0.152608	−	0.469680i	−0.845302	−	0.534288i	$-0.820580\pi$
$773$	4.24295	−	13.0585i	0.152608	−	0.469680i	0.997911	+	0.0646079i	$0.0205797\pi$
$774$	−17.7543			−0.638166
$775$		0			0
$776$	12.3724			0.444142
$777$	1.44894	−	4.45938i	0.0519805	−	0.159979i
$778$	−1.93074	−	1.40276i	−0.0692203	−	0.0502915i
$779$	18.0510	+	13.1148i	0.646745	+	0.469888i
$780$		0			0
$781$	−15.6020	+	11.3355i	−0.558282	+	0.405616i
$782$	27.4610			0.982005
$783$	11.1724	−	8.11722i	0.399269	−	0.290086i
$784$	5.91424	+	18.2021i	0.211223	+	0.650077i
$785$		0			0
$786$	19.9960	−	61.5414i	0.713234	−	2.19511i
$787$	−6.07714	−	18.7035i	−0.216627	−	0.666708i	−0.999034	−	0.0439412i	$-0.986009\pi$
$787$	−6.07714	−	18.7035i	−0.216627	−	0.666708i	0.782408	−	0.622767i	$-0.213991\pi$
$788$	−8.85450	−	27.2513i	−0.315429	−	0.970789i
$789$	−0.676537	+	2.08217i	−0.0240853	+	0.0741271i
$790$		0			0
$791$	2.07217	+	6.37748i	0.0736779	+	0.226757i
$792$	2.15525	−	1.56588i	0.0765835	−	0.0556412i
$793$	9.34520			0.331858
$794$	−7.90396	+	5.74257i	−0.280501	+	0.203796i
$795$		0			0
$796$	−19.7713	−	14.3647i	−0.700776	−	0.509144i
$797$	−8.85396	−	6.43278i	−0.313623	−	0.227861i	0.419826	−	0.907604i	$-0.362091\pi$
$797$	−8.85396	−	6.43278i	−0.313623	−	0.227861i	−0.733450	+	0.679744i	$0.762091\pi$
$798$	−3.63356	+	11.1829i	−0.128627	+	0.395872i
$799$	28.7318			1.01646
$800$		0			0
$801$	26.5985			0.939812
$802$	15.5202	−	47.7661i	0.548036	−	1.68668i
$803$	−1.25548	−	0.912160i	−0.0443049	−	0.0321894i
$804$	9.12982	+	6.63320i	0.321984	+	0.233935i
$805$		0			0
$806$	−0.777193	+	0.564664i	−0.0273754	+	0.0198894i
$807$	7.22982			0.254502
$808$	−1.49718	+	1.08777i	−0.0526707	+	0.0382675i
$809$	5.08109	+	15.6380i	0.178641	+	0.549802i	0.999781	−	0.0209255i	$-0.00666128\pi$
$809$	5.08109	+	15.6380i	0.178641	+	0.549802i	−0.821140	+	0.570727i	$0.806661\pi$
$810$		0			0
$811$	6.99839	−	21.5388i	0.245747	−	0.756331i	−0.749766	−	0.661703i	$-0.769834\pi$
$811$	6.99839	−	21.5388i	0.245747	−	0.756331i	0.995513	−	0.0946276i	$-0.0301660\pi$
$812$	−3.87768	−	11.9343i	−0.136080	−	0.418811i
$813$	−8.25439	−	25.4044i	−0.289494	−	0.890972i
$814$	2.76972	−	8.52431i	0.0970785	−	0.298777i
$815$		0			0
$816$	6.25680	+	19.2565i	0.219032	+	0.674111i
$817$	9.71004	−	7.05476i	0.339711	−	0.246815i
$818$	3.96067			0.138482
$819$	4.96645	−	3.60834i	0.173542	−	0.126085i
$820$		0			0
$821$	32.1820	+	23.3816i	1.12316	+	0.816024i	0.984685	−	0.174342i	$-0.0557800\pi$
$821$	32.1820	+	23.3816i	1.12316	+	0.816024i	0.138475	+	0.990366i	$0.455780\pi$
$822$	2.55711	+	1.85785i	0.0891894	+	0.0647999i
$823$	5.11738	−	15.7497i	0.178381	−	0.548999i	−0.821391	−	0.570365i	$-0.806802\pi$
$823$	5.11738	−	15.7497i	0.178381	−	0.548999i	0.999772	+	0.0213662i	$0.00680160\pi$
$824$	−7.38562			−0.257290
$825$		0			0
$826$	−10.1770			−0.354102
$827$	−8.04561	+	24.7618i	−0.279773	+	0.861053i	0.708144	+	0.706068i	$0.249533\pi$
$827$	−8.04561	+	24.7618i	−0.279773	+	0.861053i	−0.987917	+	0.154985i	$0.950467\pi$
$828$	15.8474	+	11.5138i	0.550735	+	0.400132i
$829$	−4.16123	−	3.02331i	−0.144526	−	0.105004i	0.513173	−	0.858285i	$-0.328470\pi$
$829$	−4.16123	−	3.02331i	−0.144526	−	0.105004i	−0.657699	+	0.753281i	$0.728470\pi$
$830$		0			0
$831$	−21.1061	+	15.3345i	−0.732162	+	0.531947i
$832$	35.4352			1.22849
$833$	14.0857	−	10.2339i	0.488041	−	0.354583i
$834$	−23.4771	−	72.2550i	−0.812944	−	2.50199i
$835$		0			0
$836$	−3.75112	+	11.5447i	−0.129735	+	0.399283i
$837$	0.108217	+	0.333057i	0.00374052	+	0.0115121i
$838$	1.50017	+	4.61706i	0.0518227	+	0.159494i
$839$	11.9177	−	36.6788i	0.411444	−	1.26629i	−0.503950	−	0.863733i	$-0.668120\pi$
$839$	11.9177	−	36.6788i	0.411444	−	1.26629i	0.915393	−	0.402560i	$-0.131880\pi$
$840$		0			0
$841$	−0.00289251	−	0.00890222i	−9.97416e−5	−	0.000306973i
$842$	−40.4045	+	29.3556i	−1.39243	+	1.01166i
$843$	54.1744			1.86586
$844$	16.4488	−	11.9507i	0.566191	−	0.411362i
$845$		0			0
$846$	30.7015	+	22.3059i	1.05554	+	0.766894i
$847$	5.62007	+	4.08322i	0.193108	+	0.140301i
$848$	−7.43830	+	22.8927i	−0.255432	+	0.786139i
$849$	7.39447			0.253777
$850$		0			0
$851$	9.77764			0.335173
$852$	−15.3841	+	47.3475i	−0.527052	+	1.62210i
$853$	−7.40059	−	5.37684i	−0.253391	−	0.184100i	0.453837	−	0.891085i	$-0.350055\pi$
$853$	−7.40059	−	5.37684i	−0.253391	−	0.184100i	−0.707228	+	0.706985i	$0.750055\pi$
$854$	−4.63708	−	3.36904i	−0.158678	−	0.115286i
$855$		0			0
$856$	−2.83148	+	2.05719i	−0.0967780	+	0.0703134i
$857$	−13.6712			−0.466998			−0.233499	−	0.972357i	$-0.575018\pi$
$857$	−13.6712			−0.466998			−0.233499	+	0.972357i	$0.575018\pi$
$858$	25.0283	−	18.1841i	0.854451	−	0.620795i
$859$	−11.0182	−	33.9105i	−0.375936	−	1.15701i	−0.942845	−	0.333232i	$-0.891861\pi$
$859$	−11.0182	−	33.9105i	−0.375936	−	1.15701i	0.566909	−	0.823780i	$-0.308139\pi$
$860$		0			0
$861$	−5.82055	+	17.9138i	−0.198364	+	0.610501i
$862$	−0.768282	−	2.36453i	−0.0261678	−	0.0805362i
$863$	10.4860	+	32.2725i	0.356947	+	1.09857i	0.954872	+	0.297017i	$0.0959918\pi$
$863$	10.4860	+	32.2725i	0.356947	+	1.09857i	−0.597926	+	0.801552i	$0.704008\pi$
$864$	6.41037	−	19.7291i	0.218085	−	0.671197i
$865$		0			0
$866$	−16.5053	−	50.7980i	−0.560872	−	1.72619i
$867$	−15.3349	+	11.1414i	−0.520800	+	0.378383i
$868$	0.318210			0.0108007
$869$	−25.6472	+	18.6338i	−0.870022	+	0.632108i
$870$		0			0
$871$	5.96645	+	4.33488i	0.202165	+	0.146882i
$872$	9.56578	+	6.94995i	0.323938	+	0.235355i
$873$	−9.64769	+	29.6925i	−0.326525	+	1.00494i
$874$	−24.5197			−0.829391
$875$		0			0
$876$	−4.00610			−0.135354
$877$	8.86851	−	27.2945i	0.299468	−	0.921668i	−0.682216	−	0.731151i	$-0.738983\pi$
$877$	8.86851	−	27.2945i	0.299468	−	0.921668i	0.981684	−	0.190517i	$-0.0610165\pi$
$878$	32.6847	+	23.7469i	1.10306	+	0.801418i
$879$	−15.9425	−	11.5829i	−0.537726	−	0.390680i
$880$		0			0
$881$	−6.73943	+	4.89648i	−0.227057	+	0.164967i	−0.695498	−	0.718528i	$-0.744816\pi$
$881$	−6.73943	+	4.89648i	−0.227057	+	0.164967i	0.468441	+	0.883495i	$0.344816\pi$
$882$	22.9964			0.774331
$883$	40.7069	−	29.5753i	1.36990	−	0.995289i	0.372152	−	0.928172i	$-0.378620\pi$
$883$	40.7069	−	29.5753i	1.36990	−	0.995289i	0.997745	−	0.0671169i	$-0.0213800\pi$
$884$	−7.08737	−	21.8127i	−0.238374	−	0.733640i
$885$		0			0
$886$	1.58689	−	4.88395i	0.0533127	−	0.164080i
$887$	3.74486	+	11.5255i	0.125740	+	0.386988i	0.994035	−	0.109060i	$-0.0347840\pi$
$887$	3.74486	+	11.5255i	0.125740	+	0.386988i	−0.868295	+	0.496048i	$0.834784\pi$
$888$	−1.06078	−	3.26475i	−0.0355975	−	0.109558i
$889$	−0.457185	+	1.40707i	−0.0153335	+	0.0471916i
$890$		0			0
$891$	−6.88420	−	21.1874i	−0.230629	−	0.709804i
$892$	−53.8498	+	39.1242i	−1.80302	+	1.30997i
$893$	−25.6543			−0.858490
$894$	−11.9114	+	8.65417i	−0.398378	+	0.289439i
$895$		0			0
$896$	−4.59573	−	3.33899i	−0.153532	−	0.111548i
$897$	27.3031	+	19.8369i	0.911624	+	0.662333i
$898$	9.25243	−	28.4761i	0.308758	−	0.950259i
$899$	−0.735159			−0.0245189
$900$		0			0
$901$	21.8976			0.729514
$902$	−11.1262	+	34.2431i	−0.370463	+	1.14017i
$903$	8.19707	+	5.95552i	0.272781	+	0.198187i
$904$	3.97169	+	2.88560i	0.132096	+	0.0959737i
$905$		0			0
$906$	−65.5973	+	47.6592i	−2.17932	+	1.58337i
$907$	−31.9105			−1.05957			−0.529786	−	0.848132i	$-0.677728\pi$
$907$	−31.9105			−1.05957			−0.529786	+	0.848132i	$0.677728\pi$
$908$	−42.2567	+	30.7013i	−1.40234	+	1.01886i
$909$	−1.44307	−	4.44132i	−0.0478637	−	0.147309i
$910$		0			0
$911$	−7.62900	+	23.4797i	−0.252760	+	0.777916i	0.741503	+	0.670950i	$0.234114\pi$
$911$	−7.62900	+	23.4797i	−0.252760	+	0.777916i	−0.994263	+	0.106966i	$0.965886\pi$
$912$	−5.58664	−	17.1939i	−0.184992	−	0.569347i
$913$	−1.09460	−	3.36884i	−0.0362260	−	0.111492i
$914$	−16.2363	+	49.9701i	−0.537048	+	1.65286i
$915$		0			0
$916$	1.79654	+	5.52917i	0.0593592	+	0.182689i
$917$	−11.3322	+	8.23333i	−0.374223	+	0.271889i
$918$	−15.4810			−0.510951
$919$	15.7637	−	11.4530i	0.519997	−	0.377800i	−0.296606	−	0.955000i	$-0.595855\pi$
$919$	15.7637	−	11.4530i	0.519997	−	0.377800i	0.816603	+	0.577200i	$0.195855\pi$
$920$		0			0
$921$	16.8637	+	12.2522i	0.555676	+	0.403723i
$922$	48.6296	+	35.3314i	1.60153	+	1.16358i
$923$	−10.0537	+	30.9422i	−0.330922	+	1.01847i
$924$	−10.2474			−0.337116
$925$		0			0
$926$	66.4781			2.18461
$927$	5.75913	−	17.7248i	0.189155	−	0.582158i
$928$	35.2312	+	25.5970i	1.15652	+	0.840262i
$929$	−9.51748	−	6.91485i	−0.312258	−	0.226869i	0.420607	−	0.907243i	$-0.361817\pi$
$929$	−9.51748	−	6.91485i	−0.312258	−	0.226869i	−0.732865	+	0.680374i	$0.761817\pi$
$930$		0			0
$931$	−12.5770	+	9.13773i	−0.412195	+	0.299477i
$932$	13.9873			0.458168
$933$	52.1704	−	37.9040i	1.70798	−	1.24092i
$934$	27.7729	+	85.4762i	0.908757	+	2.79687i
$935$		0			0
$936$	1.38882	−	4.27434i	0.0453950	−	0.139711i
$937$	−6.51046	−	20.0371i	−0.212688	−	0.654585i	−0.999310	−	0.0371502i	$-0.988172\pi$
$937$	−6.51046	−	20.0371i	−0.212688	−	0.654585i	0.786622	−	0.617435i	$-0.211828\pi$
$938$	−1.39778	−	4.30193i	−0.0456392	−	0.140463i
$939$	−12.8334	+	39.4970i	−0.418801	+	1.28894i
$940$		0			0
$941$	−0.694380	−	2.13708i	−0.0226362	−	0.0696669i	0.939100	−	0.343643i	$-0.111661\pi$
$941$	−0.694380	−	2.13708i	−0.0226362	−	0.0696669i	−0.961736	+	0.273976i	$0.911661\pi$
$942$	−6.13872	+	4.46004i	−0.200010	+	0.145316i
$943$	−39.2778			−1.27906
$944$	12.6588	−	9.19719i	0.412010	−	0.299343i
$945$		0			0
$946$	15.6691	+	11.3842i	0.509445	+	0.370134i
$947$	5.46592	+	3.97122i	0.177619	+	0.129047i	0.673042	−	0.739604i	$-0.264987\pi$
$947$	5.46592	+	3.97122i	0.177619	+	0.129047i	−0.495424	+	0.868651i	$0.664987\pi$
$948$	−25.2891	+	77.8320i	−0.821353	+	2.52787i
$949$	−2.61803			−0.0849850
$950$		0			0
$951$	−50.1021			−1.62467
$952$	−0.644918	+	1.98485i	−0.0209019	+	0.0643295i
$953$	−48.5033	−	35.2397i	−1.57118	−	1.14153i	−0.926020	−	0.377475i	$-0.876793\pi$
$953$	−48.5033	−	35.2397i	−1.57118	−	1.14153i	−0.645156	−	0.764051i	$-0.723207\pi$
$954$	23.3988	+	17.0002i	0.757564	+	0.550402i
$955$		0			0
$956$	13.3610	−	9.70730i	0.432124	−	0.313957i
$957$	23.6747			0.765293
$958$	35.4721	−	25.7720i	1.14605	−	0.832654i
$959$	−0.211431	−	0.650719i	−0.00682748	−	0.0210128i
$960$		0			0
$961$	−9.57377	+	29.4650i	−0.308831	+	0.950485i
$962$	−4.67260	−	14.3808i	−0.150651	−	0.463655i
$963$	−2.72914	−	8.39944i	−0.0879454	−	0.270668i
$964$	0.856155	−	2.63497i	0.0275749	−	0.0848668i
$965$		0			0
$966$	−6.39639	−	19.6861i	−0.205801	−	0.633389i
$967$	7.32645	−	5.32298i	0.235603	−	0.171175i	−0.463719	−	0.885982i	$-0.653485\pi$
$967$	7.32645	−	5.32298i	0.235603	−	0.171175i	0.699322	+	0.714807i	$0.253485\pi$
$968$	5.08580			0.163464
$969$	−13.3055	+	9.66701i	−0.427434	+	0.310549i
$970$		0			0
$971$	−38.3076	−	27.8321i	−1.22935	−	0.893175i	−0.232509	−	0.972594i	$-0.574693\pi$
$971$	−38.3076	−	27.8321i	−1.22935	−	0.893175i	−0.996841	+	0.0794192i	$0.974693\pi$
$972$	−31.9074	−	23.1821i	−1.02343	−	0.743566i
$973$	−5.08206	+	15.6410i	−0.162923	+	0.501426i
$974$	−58.2191			−1.86546
$975$		0			0
$976$	8.81263			0.282085
$977$	−1.46618	+	4.51245i	−0.0469074	+	0.144366i	−0.971767	−	0.235943i	$-0.924182\pi$
$977$	−1.46618	+	4.51245i	−0.0469074	+	0.144366i	0.924860	+	0.380309i	$0.124182\pi$
$978$	−3.31183	−	2.40618i	−0.105900	−	0.0769412i
$979$	−23.4745	−	17.0552i	−0.750247	−	0.545086i
$980$		0			0
$981$	−24.1384	+	17.5376i	−0.770680	+	0.559932i
$982$	−31.1981			−0.995570
$983$	−15.0199	+	10.9126i	−0.479059	+	0.348057i	−0.800961	−	0.598716i	$-0.795678\pi$
$983$	−15.0199	+	10.9126i	−0.479059	+	0.348057i	0.321902	+	0.946773i	$0.395678\pi$
$984$	4.26127	+	13.1148i	0.135844	+	0.418086i
$985$		0			0
$986$	10.0427	−	30.9084i	0.319826	−	0.984323i
$987$	−6.69238	−	20.5970i	−0.213021	−	0.655610i
$988$	6.32825	+	19.4764i	0.201328	+	0.619625i
$989$	−6.52903	+	20.0943i	−0.207611	+	0.638961i
$990$		0			0
$991$	−12.2741	−	37.7758i	−0.389900	−	1.19999i	−0.932863	−	0.360232i	$-0.882698\pi$
$991$	−12.2741	−	37.7758i	−0.389900	−	1.19999i	0.542963	−	0.839757i	$-0.317302\pi$
$992$	−0.893411	+	0.649101i	−0.0283658	+	0.0206090i
$993$	−6.51411			−0.206719
$994$	16.1436	−	11.7290i	0.512044	−	0.372022i
$995$		0			0
$996$	−7.39777	−	5.37479i	−0.234407	−	0.170307i
$997$	−24.5063	−	17.8048i	−0.776121	−	0.563885i	0.127691	−	0.991814i	$-0.459243\pi$
$997$	−24.5063	−	17.8048i	−0.776121	−	0.563885i	−0.903812	+	0.427929i	$0.859243\pi$
$998$	28.5627	−	87.9070i	0.904137	−	2.78265i
$999$	−5.51210			−0.174395

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	125.2.d.b.101.1		16
5.2	odd	4		25.2.e.a.4.1	✓	8
5.3	odd	4		125.2.e.b.24.2		8
5.4	even	2	inner	125.2.d.b.101.4		16
15.2	even	4		225.2.m.a.154.2		8
20.7	even	4		400.2.y.c.129.1		8
25.2	odd	20		625.2.e.a.249.1		8
25.3	odd	20		625.2.e.a.374.1		8
25.4	even	10		625.2.d.o.251.1		16
25.6	even	5	inner	125.2.d.b.26.1		16
25.8	odd	20		25.2.e.a.19.1	yes	8
25.9	even	10		625.2.a.f.1.7		8
25.11	even	5		625.2.d.o.376.4		16
25.12	odd	20		625.2.b.c.624.2		8
25.13	odd	20		625.2.b.c.624.7		8
25.14	even	10		625.2.d.o.376.1		16
25.16	even	5		625.2.a.f.1.2		8
25.17	odd	20		125.2.e.b.99.2		8
25.19	even	10	inner	125.2.d.b.26.4		16
25.21	even	5		625.2.d.o.251.4		16
25.22	odd	20		625.2.e.i.374.2		8
25.23	odd	20		625.2.e.i.249.2		8
75.8	even	20		225.2.m.a.19.2		8
75.41	odd	10		5625.2.a.x.1.7		8
75.59	odd	10		5625.2.a.x.1.2		8
100.59	odd	10		10000.2.a.bj.1.2		8
100.83	even	20		400.2.y.c.369.1		8
100.91	odd	10		10000.2.a.bj.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.1	✓	8	5.2	odd	4
25.2.e.a.19.1	yes	8	25.8	odd	20
125.2.d.b.26.1		16	25.6	even	5	inner
125.2.d.b.26.4		16	25.19	even	10	inner
125.2.d.b.101.1		16	1.1	even	1	trivial
125.2.d.b.101.4		16	5.4	even	2	inner
125.2.e.b.24.2		8	5.3	odd	4
125.2.e.b.99.2		8	25.17	odd	20
225.2.m.a.19.2		8	75.8	even	20
225.2.m.a.154.2		8	15.2	even	4
400.2.y.c.129.1		8	20.7	even	4
400.2.y.c.369.1		8	100.83	even	20
625.2.a.f.1.2		8	25.16	even	5
625.2.a.f.1.7		8	25.9	even	10
625.2.b.c.624.2		8	25.12	odd	20
625.2.b.c.624.7		8	25.13	odd	20
625.2.d.o.251.1		16	25.4	even	10
625.2.d.o.251.4		16	25.21	even	5
625.2.d.o.376.1		16	25.14	even	10
625.2.d.o.376.4		16	25.11	even	5
625.2.e.a.249.1		8	25.2	odd	20
625.2.e.a.374.1		8	25.3	odd	20
625.2.e.i.249.2		8	25.23	odd	20
625.2.e.i.374.2		8	25.22	odd	20
5625.2.a.x.1.2		8	75.59	odd	10
5625.2.a.x.1.7		8	75.41	odd	10
10000.2.a.bj.1.2		8	100.59	odd	10
10000.2.a.bj.1.7		8	100.91	odd	10

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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

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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	125.2.d.b.101.1

Level	$125$
Weight	$2$
Character	125.101
Analytic conductor	$0.998$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$