LMFDB - Embedded newform 125.2.d.b.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(26,125)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			101.4
Root			$-0.644389 - 0.983224i$ of defining polynomial
Character	$\chi$	$=$	125.101
Dual form			125.2.d.b.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.644389 - 1.98322i) q^{2} +(-1.77862 - 1.29224i) q^{3} +(-1.89991 - 1.38036i) q^{4} +(-3.70892 + 2.69469i) q^{6} -0.992398 q^{7} +(-0.587785 + 0.427051i) q^{8} +(0.566541 + 1.74363i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.636119\pi$
$2$	0.644389	−	1.98322i	0.455652	−	1.40235i	0.870369	−	0.492401i	$-0.163881\pi$
$3$	−1.77862	−	1.29224i	−1.02689	−	0.746076i	−0.0592022	−	0.998246i	$-0.518856\pi$
$3$	−1.77862	−	1.29224i	−1.02689	−	0.746076i	−0.967683	+	0.252170i	$0.918856\pi$
$4$	−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	$-0.560053\pi$
$7$	−0.992398			−0.375091			−0.187546	+	0.982256i	$0.560053\pi$
$8$	−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	$0.0549886\pi$
$13$	1.04264	+	3.20892i	0.289177	+	0.889995i	−0.695938	+	0.718101i	$0.745011\pi$
$14$	−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	−0.266411	−	0.963859i	$-0.585838\pi$
$17$	2.34171	−	1.70135i	0.567948	−	0.412638i	0.834359	+	0.551221i	$0.185838\pi$
$18$	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	$-0.742690\pi$
$23$	1.40591	−	4.32696i	0.293153	−	0.902233i	0.983835	−	0.179075i	$-0.0573104\pi$
$24$	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	0.990689	−	0.136148i	$-0.0434722\pi$
$37$	0.664110	+	2.04392i	0.109179	+	0.336018i	−0.881510	+	0.472166i	$0.843472\pi$
$38$	−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	$-0.615213\pi$
$43$	−4.64398			−0.708200			−0.354100	+	0.935208i	$0.615213\pi$
$44$	−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	0.991173	−	0.132576i	$-0.0423248\pi$
$47$	8.03054	+	5.83453i	1.17137	+	0.851054i	0.180202	+	0.983630i	$0.442325\pi$
$48$	−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	0.922566	−	0.385839i	$-0.126088\pi$
$53$	6.12038	+	4.44672i	0.840699	+	0.610804i	−0.0818665	+	0.996643i	$0.526088\pi$
$54$	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	−0.474505	−	0.880253i	$-0.657373\pi$
$67$	1.76833	−	1.28477i	0.216036	−	0.156959i	0.690540	+	0.723294i	$0.257373\pi$
$68$	−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	−0.964107	−	0.265513i	$-0.914459\pi$
$73$	−0.239775	+	0.737953i	−0.0280636	+	0.0863708i	0.936044	+	0.351884i	$0.114459\pi$
$74$	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	−0.663640	−	0.748052i	$-0.730989\pi$
$83$	−1.43285	+	1.04103i	−0.157276	+	0.114268i	0.506364	+	0.862320i	$0.330989\pi$
$84$	−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	$-0.967621\pi$
$97$	−13.7768	−	10.0095i	−1.39883	−	1.01631i	−0.403995	−	0.914761i	$-0.632379\pi$
$98$	−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	0.913928	−	0.405877i	$-0.133034\pi$
$103$	8.22400	+	5.97509i	0.810335	+	0.588743i	−0.103593	+	0.994620i	$0.533034\pi$
$104$	−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	$-0.425195\pi$
$107$	4.81720			0.465697			0.232848	+	0.972513i	$0.425195\pi$
$108$	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	$-0.997048\pi$
$113$	−2.08804	−	6.42633i	−0.196426	−	0.604538i	0.803531	−	0.595264i	$-0.202952\pi$
$114$	−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	−0.928534	−	0.371247i	$-0.878930\pi$
$127$	0.460687	−	1.41785i	0.0408793	−	0.125814i	0.969413	+	0.245433i	$0.0789303\pi$
$128$	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	0.959745	−	0.280873i	$-0.0906239\pi$
$137$	0.213051	+	0.655703i	0.0182022	+	0.0560205i	−0.941543	+	0.336893i	$0.890624\pi$
$138$	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	$-0.521039\pi$
$157$	−1.65512			−0.132093			−0.0660465	+	0.997817i	$0.521039\pi$
$158$	−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	0.939668	−	0.342086i	$-0.111134\pi$
$163$	−0.275932	−	0.849231i	−0.0216127	−	0.0665169i	−0.961281	+	0.275570i	$0.911134\pi$
$164$	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	−0.413156	−	0.910660i	$-0.635573\pi$
$167$	4.20331	−	3.05388i	0.325262	−	0.236317i	0.738417	+	0.674344i	$0.235573\pi$
$168$	−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	−0.860222	−	0.509919i	$-0.829675\pi$
$173$	1.78137	−	5.48250i	0.135435	−	0.416827i	0.995657	+	0.0930924i	$0.0296752\pi$
$174$	−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	$-0.775798\pi$
$193$	−21.1730			−1.52406			−0.762031	+	0.647540i	$0.775798\pi$
$194$	−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	0.177715	−	0.984082i	$-0.443129\pi$
$197$	−9.87108	−	7.17176i	−0.703285	−	0.510967i	−0.881001	+	0.473115i	$0.843129\pi$
$198$	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	$0.497909\pi$
$223$	−8.75859	+	26.9562i	−0.586518	+	1.80512i	−0.593086	+	0.805139i	$0.702091\pi$
$224$	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	$0.364281\pi$
$227$	−6.87299	+	21.1529i	−0.456176	+	1.40397i	−0.869749	+	0.493495i	$0.835719\pi$
$228$	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	−0.418654	−	0.908146i	$-0.637498\pi$
$233$	4.81854	−	3.50088i	0.315673	−	0.229350i	0.734327	+	0.678796i	$0.237498\pi$
$234$	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	$-0.401590\pi$
$257$	9.75542			0.608526			0.304263	+	0.952588i	$0.401590\pi$
$258$	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	0.941121	−	0.338071i	$-0.109775\pi$
$263$	−0.307728	−	0.947088i	−0.0189753	−	0.0584000i	−0.960096	+	0.279671i	$0.909775\pi$
$264$	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	$-0.783971\pi$
$277$	3.66697	−	11.2858i	0.220327	−	0.678096i	0.998732	−	0.0503346i	$-0.0160288\pi$
$278$	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	−0.665716	−	0.746205i	$-0.731874\pi$
$283$	−2.72107	+	1.97697i	−0.161751	+	0.117519i	0.503965	+	0.863724i	$0.331874\pi$
$284$	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	$-0.415676\pi$
$293$	8.96340			0.523647			0.261824	+	0.965116i	$0.415676\pi$
$294$	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	$-0.587210\pi$
$307$	−9.48133			−0.541128			−0.270564	+	0.962702i	$0.587210\pi$
$308$	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	$-0.920739\pi$
$313$	−5.83735	−	17.9655i	−0.329947	−	1.01547i	0.639212	−	0.769031i	$-0.279261\pi$
$314$	−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	0.0661157	−	0.997812i	$-0.478939\pi$
$317$	18.4369	−	13.3952i	1.03552	−	0.752351i	0.969406	+	0.245461i	$0.0789394\pi$
$318$	−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	$0.0712381\pi$
$337$	5.81332	+	17.8916i	0.316672	+	0.974615i	−0.658389	+	0.752678i	$0.728762\pi$
$338$	−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	−0.0281483	−	0.999604i	$-0.508961\pi$
$347$	−18.3956	−	13.3652i	−0.987526	−	0.717480i	−0.959378	+	0.282124i	$0.908961\pi$
$348$	−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	0.695041	−	0.718970i	$-0.255386\pi$
$353$	4.24689	+	3.08555i	0.226039	+	0.164227i	−0.469002	+	0.883197i	$0.655386\pi$
$354$	−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	−0.731136	−	0.682232i	$-0.761009\pi$
$367$	−5.90479	+	4.29008i	−0.308228	+	0.223940i	0.422908	+	0.906173i	$0.361009\pi$
$368$	−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	$-0.704022\pi$
$373$	6.89335	−	21.2156i	0.356924	−	1.09850i	0.954885	−	0.296975i	$-0.0959778\pi$
$374$	−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	−0.926718	−	0.375758i	$-0.877382\pi$
$383$	−16.7468	+	12.1673i	−0.855722	+	0.621719i	0.0709955	+	0.997477i	$0.477382\pi$
$384$	−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	0.488593	−	0.872512i	$-0.337510\pi$
$397$	−3.79035	−	2.75385i	−0.190232	−	0.138212i	−0.678825	+	0.734300i	$0.737510\pi$
$398$	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	0.0346454	−	0.999400i	$-0.488970\pi$
$433$	20.7220	−	15.0554i	0.995837	−	0.723518i	0.961192	+	0.275882i	$0.0889698\pi$
$434$	−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	$-0.481368\pi$
$443$	2.46263			0.117003			0.0585016	+	0.998287i	$0.481368\pi$
$444$	−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	$-0.700604\pi$
$457$	−25.1964			−1.17864			−0.589319	+	0.807901i	$0.700604\pi$
$458$	−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	$0.165547\pi$
$463$	9.85134	+	30.3193i	0.457831	+	1.40906i	−0.409949	+	0.912108i	$0.634453\pi$
$464$	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	$0.776199\pi$
$467$	−34.8683	+	25.3333i	−1.61351	+	1.17229i	−0.850666	+	0.525706i	$0.823801\pi$
$468$	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	$-0.882002\pi$
$487$	−8.62744	−	26.5525i	−0.390947	−	1.20321i	0.541127	−	0.840941i	$-0.317998\pi$
$488$	−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	0.0736453	−	0.997284i	$-0.476537\pi$
$503$	−19.1100	−	13.8842i	−0.852071	−	0.619066i	−0.925716	+	0.378219i	$0.876537\pi$
$504$	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	−0.952638	−	0.304106i	$-0.901642\pi$
$523$	−0.0729175	+	0.224417i	−0.00318846	+	0.00981307i	0.949450	+	0.313919i	$0.101642\pi$
$524$	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	$0.00789072\pi$
$547$	31.1573	+	22.6371i	1.33219	+	0.967892i	0.332496	+	0.943105i	$0.392109\pi$
$548$	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	$-0.529271\pi$
$557$	−4.33445			−0.183657			−0.0918283	+	0.995775i	$0.529271\pi$
$558$	−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	$0.163038\pi$
$563$	10.7853	+	33.1936i	0.454544	+	1.39894i	−0.417125	+	0.908849i	$0.636962\pi$
$564$	−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	−0.998992	−	0.0448986i	$-0.985704\pi$
$577$	−3.94902	+	12.1538i	−0.164400	+	0.505970i	0.834592	+	0.550869i	$0.185704\pi$
$578$	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	0.842767	−	0.538279i	$-0.180925\pi$
$587$	−3.76597	−	11.5905i	−0.155438	−	0.478390i	−0.998205	+	0.0598889i	$0.980925\pi$
$588$	−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	$-0.721815\pi$
$593$	−31.2580			−1.28361			−0.641807	+	0.766866i	$0.721815\pi$
$594$	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	$-0.285567\pi$
$607$	30.7401			1.24770			0.623851	+	0.781543i	$0.285567\pi$
$608$	−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	$-0.818631\pi$
$613$	−11.8321	−	36.4154i	−0.477894	−	1.47081i	0.364121	−	0.931352i	$-0.381369\pi$
$614$	−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	−0.594690	−	0.803955i	$-0.702725\pi$
$617$	−0.344080	+	0.249989i	−0.0138521	+	0.0100642i	0.580838	+	0.814019i	$0.302725\pi$
$618$	−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	$-0.716936\pi$
$643$	−31.9492			−1.25995			−0.629977	+	0.776614i	$0.716936\pi$
$644$	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	0.699134	−	0.714990i	$-0.253569\pi$
$647$	5.98214	+	4.34628i	0.235182	+	0.170870i	−0.463952	+	0.885860i	$0.653569\pi$
$648$	−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	0.251311	−	0.967906i	$-0.419138\pi$
$653$	−15.1167	−	10.9829i	−0.591563	−	0.429796i	−0.842874	+	0.538111i	$0.819138\pi$
$654$	−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	$0.370987\pi$
$673$	−12.0595	+	37.1153i	−0.464859	+	1.43069i	−0.859160	+	0.511707i	$0.829013\pi$
$674$	39.2290			1.51104
$675$		0			0
$676$	−3.79434			−0.145936
$677$	1.55600	−	4.78888i	0.0598020	−	0.184052i	−0.916693	−	0.399593i	$-0.869152\pi$
$677$	1.55600	−	4.78888i	0.0598020	−	0.184052i	0.976495	+	0.215541i	$0.0691515\pi$
$678$	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	−0.00922734	−	0.999957i	$-0.502937\pi$
$683$	24.5384	−	17.8282i	0.938937	−	0.682178i	0.948165	+	0.317780i	$0.102937\pi$
$684$	−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	−0.979024	−	0.203745i	$-0.934689\pi$
$727$	−1.81242	+	5.57804i	−0.0672188	+	0.206878i	0.911805	+	0.410623i	$0.134689\pi$
$728$	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	0.0624625	−	0.998047i	$-0.480105\pi$
$733$	27.9123	−	20.2795i	1.03096	−	0.749039i	0.968501	+	0.249008i	$0.0801046\pi$
$734$	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	$-0.316567\pi$
$743$	29.7058			1.08980			0.544900	+	0.838501i	$0.316567\pi$
$744$	−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	$-0.801592\pi$
$757$	−44.6792			−1.62389			−0.811947	+	0.583731i	$0.801592\pi$
$758$	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	−0.997911	−	0.0646079i	$-0.979420\pi$
$773$	−4.24295	+	13.0585i	−0.152608	+	0.469680i	0.845302	+	0.534288i	$0.179420\pi$
$774$	−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	$0.0139914\pi$
$787$	6.07714	+	18.7035i	0.216627	+	0.666708i	−0.782408	+	0.622767i	$0.786009\pi$
$788$	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	0.733450	−	0.679744i	$-0.237909\pi$
$797$	8.85396	+	6.43278i	0.313623	+	0.227861i	−0.419826	+	0.907604i	$0.637909\pi$
$798$	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	−0.999772	−	0.0213662i	$-0.993198\pi$
$823$	−5.11738	+	15.7497i	−0.178381	+	0.548999i	0.821391	+	0.570365i	$0.193198\pi$
$824$	−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	$-0.750467\pi$
$827$	8.04561	−	24.7618i	0.279773	−	0.861053i	0.987917	−	0.154985i	$-0.0495329\pi$
$828$	−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	0.707228	−	0.706985i	$-0.249945\pi$
$853$	7.40059	+	5.37684i	0.253391	+	0.184100i	−0.453837	+	0.891085i	$0.649945\pi$
$854$	−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	$-0.424982\pi$
$857$	13.6712			0.466998			0.233499	+	0.972357i	$0.424982\pi$
$858$	−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	$-0.904008\pi$
$863$	−10.4860	−	32.2725i	−0.356947	−	1.09857i	0.597926	−	0.801552i	$-0.295992\pi$
$864$	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	$0.261017\pi$
$877$	−8.86851	+	27.2945i	−0.299468	+	0.921668i	−0.981684	+	0.190517i	$0.938983\pi$
$878$	−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	$0.621380\pi$
$883$	−40.7069	+	29.5753i	−1.36990	+	0.995289i	−0.997745	+	0.0671169i	$0.978620\pi$
$884$	−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	0.868295	−	0.496048i	$-0.165216\pi$
$887$	−3.74486	−	11.5255i	−0.125740	−	0.386988i	−0.994035	+	0.109060i	$0.965216\pi$
$888$	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	$-0.322272\pi$
$907$	31.9105			1.05957			0.529786	+	0.848132i	$0.322272\pi$
$908$	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	$0.0118280\pi$
$937$	6.51046	+	20.0371i	0.212688	+	0.654585i	−0.786622	+	0.617435i	$0.788172\pi$
$938$	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	0.495424	−	0.868651i	$-0.335013\pi$
$947$	−5.46592	−	3.97122i	−0.177619	−	0.129047i	−0.673042	+	0.739604i	$0.735013\pi$
$948$	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	$0.123207\pi$
$953$	48.5033	+	35.2397i	1.57118	+	1.14153i	0.645156	+	0.764051i	$0.276793\pi$
$954$	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	−0.699322	−	0.714807i	$-0.746515\pi$
$967$	−7.32645	+	5.32298i	−0.235603	+	0.171175i	0.463719	+	0.885982i	$0.346515\pi$
$968$	−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	−0.924860	−	0.380309i	$-0.875818\pi$
$977$	1.46618	−	4.51245i	0.0469074	−	0.144366i	0.971767	+	0.235943i	$0.0758178\pi$
$978$	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	−0.321902	−	0.946773i	$-0.604322\pi$
$983$	15.0199	−	10.9126i	0.479059	−	0.348057i	0.800961	+	0.598716i	$0.204322\pi$
$984$	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	0.903812	−	0.427929i	$-0.140757\pi$
$997$	24.5063	+	17.8048i	0.776121	+	0.563885i	−0.127691	+	0.991814i	$0.540757\pi$
$998$	−28.5627	+	87.9070i	−0.904137	+	2.78265i
$999$	−5.51210			−0.174395

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.1	✓	8	5.3	odd	4
25.2.e.a.19.1	yes	8	25.17	odd	20
125.2.d.b.26.1		16	25.19	even	10	inner
125.2.d.b.26.4		16	25.6	even	5	inner
125.2.d.b.101.1		16	5.4	even	2	inner
125.2.d.b.101.4		16	1.1	even	1	trivial
125.2.e.b.24.2		8	5.2	odd	4
125.2.e.b.99.2		8	25.8	odd	20
225.2.m.a.19.2		8	75.17	even	20
225.2.m.a.154.2		8	15.8	even	4
400.2.y.c.129.1		8	20.3	even	4
400.2.y.c.369.1		8	100.67	even	20
625.2.a.f.1.2		8	25.9	even	10
625.2.a.f.1.7		8	25.16	even	5
625.2.b.c.624.2		8	25.13	odd	20
625.2.b.c.624.7		8	25.12	odd	20
625.2.d.o.251.1		16	25.21	even	5
625.2.d.o.251.4		16	25.4	even	10
625.2.d.o.376.1		16	25.11	even	5
625.2.d.o.376.4		16	25.14	even	10
625.2.e.a.249.1		8	25.23	odd	20
625.2.e.a.374.1		8	25.22	odd	20
625.2.e.i.249.2		8	25.2	odd	20
625.2.e.i.374.2		8	25.3	odd	20
5625.2.a.x.1.2		8	75.41	odd	10
5625.2.a.x.1.7		8	75.59	odd	10
10000.2.a.bj.1.2		8	100.91	odd	10
10000.2.a.bj.1.7		8	100.59	odd	10

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.644389 - 1.98322i) q^{2} +(-1.77862 - 1.29224i) q^{3} +(-1.89991 - 1.38036i) q^{4} +(-3.70892 + 2.69469i) q^{6} -0.992398 q^{7} +(-0.587785 + 0.427051i) q^{8} +(0.566541 + 1.74363i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9	\( 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9} - 8 q^{11} - 26 q^{14} + 6 q^{16} + 10 q^{19} - 8 q^{21} + 40 q^{24} + 12 q^{26} + 10 q^{29} - 18 q^{31} - 26 q^{34} + 46 q^{36} + 6 q^{39} - 8 q^{41} + 4 q^{44} - 38 q^{46} - 28 q^{49} - 8 q^{51} + 10 q^{54} + 20 q^{56} - 18 q^{61} - 8 q^{64} + 24 q^{66} - 34 q^{69} + 12 q^{71} + 24 q^{74} - 40 q^{76} - 30 q^{79} + 56 q^{81} - 36 q^{84} - 18 q^{86} + 50 q^{89} + 12 q^{91} + 54 q^{94} + 32 q^{96} + 16 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

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