LMFDB - Embedded newform 125.2.e.a.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(24,125)]

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([1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("125.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.e (of order $10$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			74.1
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	125.74
Dual form			125.2.e.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.363271 - 0.500000i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.500000 - 1.53884i) q^{4} +(0.190983 + 0.587785i) q^{6} -1.61803i q^{7} +(-2.12663 + 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +(0.618034 - 0.449028i) q^{11} +(-0.951057 + 1.30902i) q^{12} +(2.85317 - 3.92705i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-1.50000 - 1.08981i) q^{16} +(0.726543 - 0.236068i) q^{17} +1.23607i q^{18} +(1.80902 + 5.56758i) q^{19} +(-0.500000 + 1.53884i) q^{21} +(-0.449028 - 0.145898i) q^{22} +(4.84104 + 6.66312i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(2.93893 + 4.04508i) q^{27} +(-2.48990 - 0.809017i) q^{28} +(0.427051 - 1.31433i) q^{29} +(-0.927051 - 2.85317i) q^{31} +5.61803i q^{32} +(-0.726543 + 0.236068i) q^{33} +(-0.381966 - 0.277515i) q^{34} +(-2.61803 + 1.90211i) q^{36} +(2.48990 - 3.42705i) q^{37} +(2.12663 - 2.92705i) q^{38} +(-3.92705 + 2.85317i) q^{39} +(4.23607 + 3.07768i) q^{41} +(0.951057 - 0.309017i) q^{42} -1.85410i q^{43} +(-0.381966 - 1.17557i) q^{44} +(1.57295 - 4.84104i) q^{46} +(-1.53884 - 0.500000i) q^{47} +(1.08981 + 1.50000i) q^{48} +4.38197 q^{49} -0.763932 q^{51} +(-4.61653 - 6.35410i) q^{52} +(-5.20431 - 1.69098i) q^{53} +(0.954915 - 2.93893i) q^{54} +(1.11803 + 3.44095i) q^{56} -5.85410i q^{57} +(-0.812299 + 0.263932i) q^{58} +(-3.35410 - 2.43690i) q^{59} +(3.80902 - 2.76741i) q^{61} +(-1.08981 + 1.50000i) q^{62} +(-1.90211 + 2.61803i) q^{63} +(-0.190983 + 0.138757i) q^{64} +(0.381966 + 0.277515i) q^{66} +(-8.78402 + 2.85410i) q^{67} -1.23607i q^{68} +(-2.54508 - 7.83297i) q^{69} +(-1.35410 + 4.16750i) q^{71} +(4.25325 + 1.38197i) q^{72} +(-5.29007 - 7.28115i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(-0.726543 - 1.00000i) q^{77} +(2.85317 + 0.927051i) q^{78} +(-0.954915 + 2.93893i) q^{79} +(0.309017 + 0.951057i) q^{81} -3.23607i q^{82} +(-1.67760 + 0.545085i) q^{83} +(2.11803 + 1.53884i) q^{84} +(-0.927051 + 0.673542i) q^{86} +(-0.812299 + 1.11803i) q^{87} +(-1.00406 + 1.38197i) q^{88} +(7.23607 - 5.25731i) q^{89} +(-6.35410 - 4.61653i) q^{91} +(12.6740 - 4.11803i) q^{92} +3.00000i q^{93} +(0.309017 + 0.951057i) q^{94} +(1.73607 - 5.34307i) q^{96} +(2.71441 + 0.881966i) q^{97} +(-1.59184 - 2.19098i) q^{98} -1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} - 2 q^{14} - 12 q^{16} + 10 q^{19} - 4 q^{21} - 24 q^{26} - 10 q^{29} + 6 q^{31} - 12 q^{34} - 12 q^{36} - 18 q^{39} + 16 q^{41} - 12 q^{44} + 26 q^{46} + 44 q^{49}+ \cdots - 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 - 2 * q^14 - 12 * q^16 + 10 * q^19 - 4 * q^21 - 24 * q^26 - 10 * q^29 + 6 * q^31 - 12 * q^34 - 12 * q^36 - 18 * q^39 + 16 * q^41 - 12 * q^44 + 26 * q^46 + 44 * q^49 - 24 * q^51 + 30 * q^54 + 26 * q^61 - 6 * q^64 + 12 * q^66 + 2 * q^69 + 16 * q^71 - 12 * q^74 + 40 * q^76 - 30 * q^79 - 2 * q^81 + 8 * q^84 + 6 * q^86 + 40 * q^89 - 24 * q^91 - 2 * q^94 - 4 * q^96 - 48 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.363271	−	0.500000i	−0.256872	−	0.353553i	0.661031	−	0.750358i	$-0.270119\pi$
$2$	−0.363271	−	0.500000i	−0.256872	−	0.353553i	−0.917903	+	0.396805i	$0.870119\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i	0.0213149	−	0.999773i	$-0.493215\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i	−0.570408	+	0.821362i	$0.693215\pi$
$4$	0.500000	−	1.53884i	0.250000	−	0.769421i
$5$		0			0
$5$		0			0
$6$	0.190983	+	0.587785i	0.0779685	+	0.239962i
$7$		−	1.61803i		−	0.611559i	−0.952102	−	0.305780i	$-0.901083\pi$
$7$		−	1.61803i		−	0.611559i	0.952102	−	0.305780i	$-0.0989171\pi$
$8$	−2.12663	+	0.690983i	−0.751876	+	0.244299i
$9$	−1.61803	−	1.17557i	−0.539345	−	0.391857i
$10$		0			0
$11$	0.618034	−	0.449028i	0.186344	−	0.135387i	−0.490702	−	0.871327i	$-0.663260\pi$
$11$	0.618034	−	0.449028i	0.186344	−	0.135387i	0.677046	+	0.735940i	$0.263260\pi$
$12$	−0.951057	+	1.30902i	−0.274546	+	0.377881i
$13$	2.85317	−	3.92705i	0.791327	−	1.08917i	−0.202615	−	0.979259i	$-0.564944\pi$
$13$	2.85317	−	3.92705i	0.791327	−	1.08917i	0.993942	−	0.109909i	$-0.0350561\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$		0			0
$16$	−1.50000	−	1.08981i	−0.375000	−	0.272453i
$17$	0.726543	−	0.236068i	0.176212	−	0.0572549i	−0.219582	−	0.975594i	$-0.570469\pi$
$17$	0.726543	−	0.236068i	0.176212	−	0.0572549i	0.395794	+	0.918339i	$0.370469\pi$
$18$			1.23607i			0.291344i
$19$	1.80902	+	5.56758i	0.415017	+	1.27729i	0.912236	+	0.409666i	$0.134355\pi$
$19$	1.80902	+	5.56758i	0.415017	+	1.27729i	−0.497219	+	0.867625i	$0.665645\pi$
$20$		0			0
$21$	−0.500000	+	1.53884i	−0.109109	+	0.335803i
$22$	−0.449028	−	0.145898i	−0.0957331	−	0.0311056i
$23$	4.84104	+	6.66312i	1.00943	+	1.38936i	0.919359	+	0.393421i	$0.128708\pi$
$23$	4.84104	+	6.66312i	1.00943	+	1.38936i	0.0900679	+	0.995936i	$0.471292\pi$
$24$	2.23607			0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	2.93893	+	4.04508i	0.565597	+	0.778477i
$28$	−2.48990	−	0.809017i	−0.470547	−	0.152890i
$29$	0.427051	−	1.31433i	0.0793014	−	0.244065i	−0.903544	−	0.428495i	$-0.859044\pi$
$29$	0.427051	−	1.31433i	0.0793014	−	0.244065i	0.982846	+	0.184430i	$0.0590440\pi$
$30$		0			0
$31$	−0.927051	−	2.85317i	−0.166503	−	0.512444i	0.832641	−	0.553814i	$-0.186828\pi$
$31$	−0.927051	−	2.85317i	−0.166503	−	0.512444i	−0.999144	+	0.0413693i	$0.986828\pi$
$32$			5.61803i			0.993137i
$33$	−0.726543	+	0.236068i	−0.126475	+	0.0410942i
$34$	−0.381966	−	0.277515i	−0.0655066	−	0.0475934i
$35$		0			0
$36$	−2.61803	+	1.90211i	−0.436339	+	0.317019i
$37$	2.48990	−	3.42705i	0.409337	−	0.563404i	−0.553720	−	0.832703i	$-0.686792\pi$
$37$	2.48990	−	3.42705i	0.409337	−	0.563404i	0.963057	+	0.269299i	$0.0867921\pi$
$38$	2.12663	−	2.92705i	0.344984	−	0.474830i
$39$	−3.92705	+	2.85317i	−0.628831	+	0.456873i
$40$		0			0
$41$	4.23607	+	3.07768i	0.661563	+	0.480653i	0.867190	−	0.497977i	$-0.165924\pi$
$41$	4.23607	+	3.07768i	0.661563	+	0.480653i	−0.205628	+	0.978630i	$0.565924\pi$
$42$	0.951057	−	0.309017i	0.146751	−	0.0476824i
$43$		−	1.85410i		−	0.282748i	−0.989956	−	0.141374i	$-0.954848\pi$
$43$		−	1.85410i		−	0.282748i	0.989956	−	0.141374i	$-0.0451520\pi$
$44$	−0.381966	−	1.17557i	−0.0575835	−	0.177224i
$45$		0			0
$46$	1.57295	−	4.84104i	0.231919	−	0.713772i
$47$	−1.53884	−	0.500000i	−0.224463	−	0.0729325i	0.194626	−	0.980877i	$-0.437651\pi$
$47$	−1.53884	−	0.500000i	−0.224463	−	0.0729325i	−0.419089	+	0.907945i	$0.637651\pi$
$48$	1.08981	+	1.50000i	0.157301	+	0.216506i
$49$	4.38197			0.625995
$50$		0			0
$51$	−0.763932			−0.106972
$52$	−4.61653	−	6.35410i	−0.640197	−	0.881155i
$53$	−5.20431	−	1.69098i	−0.714867	−	0.232274i	−0.0710707	−	0.997471i	$-0.522642\pi$
$53$	−5.20431	−	1.69098i	−0.714867	−	0.232274i	−0.643796	+	0.765197i	$0.722642\pi$
$54$	0.954915	−	2.93893i	0.129947	−	0.399937i
$55$		0			0
$56$	1.11803	+	3.44095i	0.149404	+	0.459817i
$57$		−	5.85410i		−	0.775395i
$58$	−0.812299	+	0.263932i	−0.106660	+	0.0346560i
$59$	−3.35410	−	2.43690i	−0.436667	−	0.317257i	0.347642	−	0.937627i	$-0.386982\pi$
$59$	−3.35410	−	2.43690i	−0.436667	−	0.317257i	−0.784309	+	0.620370i	$0.786982\pi$
$60$		0			0
$61$	3.80902	−	2.76741i	0.487695	−	0.354331i	−0.316602	−	0.948558i	$-0.602542\pi$
$61$	3.80902	−	2.76741i	0.487695	−	0.354331i	0.804297	+	0.594227i	$0.202542\pi$
$62$	−1.08981	+	1.50000i	−0.138406	+	0.190500i
$63$	−1.90211	+	2.61803i	−0.239644	+	0.329841i
$64$	−0.190983	+	0.138757i	−0.0238729	+	0.0173447i
$65$		0			0
$66$	0.381966	+	0.277515i	0.0470168	+	0.0341597i
$67$	−8.78402	+	2.85410i	−1.07314	+	0.348684i	−0.791709	−	0.610898i	$-0.790809\pi$
$67$	−8.78402	+	2.85410i	−1.07314	+	0.348684i	−0.281430	+	0.959582i	$0.590809\pi$
$68$		−	1.23607i		−	0.149895i
$69$	−2.54508	−	7.83297i	−0.306392	−	0.942978i
$70$		0			0
$71$	−1.35410	+	4.16750i	−0.160702	+	0.494591i	−0.998694	−	0.0510922i	$-0.983730\pi$
$71$	−1.35410	+	4.16750i	−0.160702	+	0.494591i	0.837992	+	0.545683i	$0.183730\pi$
$72$	4.25325	+	1.38197i	0.501251	+	0.162866i
$73$	−5.29007	−	7.28115i	−0.619156	−	0.852194i	0.378136	−	0.925750i	$-0.376565\pi$
$73$	−5.29007	−	7.28115i	−0.619156	−	0.852194i	−0.997291	+	0.0735557i	$0.976565\pi$
$74$	−2.61803			−0.304340
$75$		0			0
$76$	9.47214			1.08653
$77$	−0.726543	−	1.00000i	−0.0827972	−	0.113961i
$78$	2.85317	+	0.927051i	0.323058	+	0.104968i
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	−0.990295	−	0.138985i	$-0.955616\pi$
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	0.882858	+	0.469640i	$0.155616\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	3.23607i		−	0.357364i
$83$	−1.67760	+	0.545085i	−0.184140	+	0.0598308i	−0.399636	−	0.916674i	$-0.630863\pi$
$83$	−1.67760	+	0.545085i	−0.184140	+	0.0598308i	0.215495	+	0.976505i	$0.430863\pi$
$84$	2.11803	+	1.53884i	0.231096	+	0.167901i
$85$		0			0
$86$	−0.927051	+	0.673542i	−0.0999665	+	0.0726299i
$87$	−0.812299	+	1.11803i	−0.0870876	+	0.119866i
$88$	−1.00406	+	1.38197i	−0.107033	+	0.147318i
$89$	7.23607	−	5.25731i	0.767022	−	0.557274i	−0.134034	−	0.990977i	$-0.542793\pi$
$89$	7.23607	−	5.25731i	0.767022	−	0.557274i	0.901056	+	0.433703i	$0.142793\pi$
$90$		0			0
$91$	−6.35410	−	4.61653i	−0.666091	−	0.483943i
$92$	12.6740	−	4.11803i	1.32136	−	0.429335i
$93$			3.00000i			0.311086i
$94$	0.309017	+	0.951057i	0.0318727	+	0.0980940i
$95$		0			0
$96$	1.73607	−	5.34307i	0.177187	−	0.545325i
$97$	2.71441	+	0.881966i	0.275607	+	0.0895501i	0.443559	−	0.896245i	$-0.353716\pi$
$97$	2.71441	+	0.881966i	0.275607	+	0.0895501i	−0.167953	+	0.985795i	$0.553716\pi$
$98$	−1.59184	−	2.19098i	−0.160800	−	0.221323i
$99$	−1.52786			−0.153556
$100$		0			0
$101$	−7.47214			−0.743505			−0.371753	−	0.928332i	$-0.621243\pi$
$101$	−7.47214			−0.743505			−0.371753	+	0.928332i	$0.621243\pi$
$102$	0.277515	+	0.381966i	0.0274780	+	0.0378203i
$103$	10.9964	+	3.57295i	1.08351	+	0.352053i	0.795735	−	0.605645i	$-0.207085\pi$
$103$	10.9964	+	3.57295i	1.08351	+	0.352053i	0.287773	+	0.957699i	$0.407085\pi$
$104$	−3.35410	+	10.3229i	−0.328897	+	1.01224i
$105$		0			0
$106$	1.04508	+	3.21644i	0.101508	+	0.312408i
$107$			10.4164i			1.00699i	0.863998	+	0.503496i	$0.167953\pi$
$107$			10.4164i			1.00699i	−0.863998	+	0.503496i	$0.832047\pi$
$108$	7.69421	−	2.50000i	0.740376	−	0.240563i
$109$	8.09017	+	5.87785i	0.774898	+	0.562996i	0.903443	−	0.428707i	$-0.141031\pi$
$109$	8.09017	+	5.87785i	0.774898	+	0.562996i	−0.128546	+	0.991704i	$0.541031\pi$
$110$		0			0
$111$	−3.42705	+	2.48990i	−0.325281	+	0.236331i
$112$	−1.76336	+	2.42705i	−0.166621	+	0.229335i
$113$	−5.96361	+	8.20820i	−0.561009	+	0.772163i	−0.991454	−	0.130454i	$-0.958357\pi$
$113$	−5.96361	+	8.20820i	−0.561009	+	0.772163i	0.430445	+	0.902617i	$0.358357\pi$
$114$	−2.92705	+	2.12663i	−0.274143	+	0.199177i
$115$		0			0
$116$	−1.80902	−	1.31433i	−0.167963	−	0.122032i
$117$	−9.23305	+	3.00000i	−0.853596	+	0.277350i
$118$			2.56231i			0.235879i
$119$	−0.381966	−	1.17557i	−0.0350148	−	0.107764i
$120$		0			0
$121$	−3.21885	+	9.90659i	−0.292622	+	0.900599i
$122$	−2.76741	−	0.899187i	−0.250550	−	0.0814086i
$123$	−3.07768	−	4.23607i	−0.277505	−	0.381953i
$124$	−4.85410			−0.435911
$125$		0			0
$126$	2.00000			0.178174
$127$	9.33905	+	12.8541i	0.828707	+	1.14062i	0.988162	+	0.153412i	$0.0490262\pi$
$127$	9.33905	+	12.8541i	0.828707	+	1.14062i	−0.159455	+	0.987205i	$0.550974\pi$
$128$	10.8249	+	3.51722i	0.956794	+	0.310881i
$129$	−0.572949	+	1.76336i	−0.0504453	+	0.155255i
$130$		0			0
$131$	−5.50000	−	16.9273i	−0.480537	−	1.47894i	−0.838342	−	0.545145i	$-0.816475\pi$
$131$	−5.50000	−	16.9273i	−0.480537	−	1.47894i	0.357805	−	0.933797i	$-0.383525\pi$
$132$			1.23607i			0.107586i
$133$	9.00854	−	2.92705i	0.781139	−	0.253808i
$134$	4.61803	+	3.35520i	0.398937	+	0.289845i
$135$		0			0
$136$	−1.38197	+	1.00406i	−0.118503	+	0.0860972i
$137$	3.49396	−	4.80902i	0.298509	−	0.410862i	−0.633246	−	0.773951i	$-0.718278\pi$
$137$	3.49396	−	4.80902i	0.298509	−	0.410862i	0.931755	+	0.363089i	$0.118278\pi$
$138$	−2.99193	+	4.11803i	−0.254690	+	0.350550i
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	−0.402869	−	0.915258i	$-0.631987\pi$
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	0.745968	+	0.665981i	$0.231987\pi$
$140$		0			0
$141$	1.30902	+	0.951057i	0.110239	+	0.0800934i
$142$	2.57565	−	0.836881i	0.216144	−	0.0702295i
$143$		−	3.70820i		−	0.310096i
$144$	1.14590	+	3.52671i	0.0954915	+	0.293893i
$145$		0			0
$146$	−1.71885	+	5.29007i	−0.142253	+	0.437809i
$147$	−4.16750	−	1.35410i	−0.343729	−	0.111684i
$148$	−4.02874	−	5.54508i	−0.331160	−	0.455803i
$149$	−13.9443			−1.14236			−0.571180	−	0.820825i	$-0.693514\pi$
$149$	−13.9443			−1.14236			−0.571180	+	0.820825i	$0.693514\pi$
$150$		0			0
$151$	−5.56231			−0.452654			−0.226327	−	0.974051i	$-0.572672\pi$
$151$	−5.56231			−0.452654			−0.226327	+	0.974051i	$0.572672\pi$
$152$	−7.69421	−	10.5902i	−0.624083	−	0.858976i
$153$	−1.45309	−	0.472136i	−0.117475	−	0.0381699i
$154$	−0.236068	+	0.726543i	−0.0190229	+	0.0585465i
$155$		0			0
$156$	2.42705	+	7.46969i	0.194320	+	0.598054i
$157$		−	9.18034i		−	0.732671i	−0.930483	−	0.366335i	$-0.880612\pi$
$157$		−	9.18034i		−	0.732671i	0.930483	−	0.366335i	$-0.119388\pi$
$158$	1.81636	−	0.590170i	0.144502	−	0.0469514i
$159$	4.42705	+	3.21644i	0.351088	+	0.255080i
$160$		0			0
$161$	10.7812	−	7.83297i	0.849674	−	0.617324i
$162$	0.363271	−	0.500000i	0.0285413	−	0.0392837i
$163$	−6.46564	+	8.89919i	−0.506428	+	0.697038i	−0.983312	−	0.181928i	$-0.941766\pi$
$163$	−6.46564	+	8.89919i	−0.506428	+	0.697038i	0.476884	+	0.878966i	$0.341766\pi$
$164$	6.85410	−	4.97980i	0.535215	−	0.388857i
$165$		0			0
$166$	0.881966	+	0.640786i	0.0684538	+	0.0497346i
$167$	5.29007	−	1.71885i	0.409358	−	0.133008i	−0.0970971	−	0.995275i	$-0.530956\pi$
$167$	5.29007	−	1.71885i	0.409358	−	0.133008i	0.506455	+	0.862267i	$0.330956\pi$
$168$		−	3.61803i		−	0.279137i
$169$	−3.26393	−	10.0453i	−0.251072	−	0.772719i
$170$		0			0
$171$	3.61803	−	11.1352i	0.276678	−	0.851527i
$172$	−2.85317	−	0.927051i	−0.217552	−	0.0706870i
$173$	−9.92684	−	13.6631i	−0.754723	−	1.03879i	−0.997635	−	0.0687392i	$-0.978102\pi$
$173$	−9.92684	−	13.6631i	−0.754723	−	1.03879i	0.242911	−	0.970049i	$-0.421898\pi$
$174$	0.854102			0.0647493
$175$		0			0
$176$	−1.41641			−0.106766
$177$	2.43690	+	3.35410i	0.183168	+	0.252110i
$178$	−5.25731	−	1.70820i	−0.394052	−	0.128035i
$179$	2.92705	−	9.00854i	0.218778	−	0.673330i	−0.780086	−	0.625673i	$-0.784825\pi$
$179$	2.92705	−	9.00854i	0.218778	−	0.673330i	0.998864	−	0.0476570i	$-0.0151754\pi$
$180$		0			0
$181$	4.23607	+	13.0373i	0.314864	+	0.969053i	0.975810	+	0.218619i	$0.0701553\pi$
$181$	4.23607	+	13.0373i	0.314864	+	0.969053i	−0.660946	+	0.750434i	$0.729845\pi$
$182$			4.85410i			0.359810i
$183$	−4.47777	+	1.45492i	−0.331006	+	0.107550i
$184$	−14.8992	−	10.8249i	−1.09838	−	0.798022i
$185$		0			0
$186$	1.50000	−	1.08981i	0.109985	−	0.0799090i
$187$	0.343027	−	0.472136i	0.0250846	−	0.0345260i
$188$	−1.53884	+	2.11803i	−0.112232	+	0.154474i
$189$	6.54508	−	4.75528i	0.476085	−	0.345896i
$190$		0			0
$191$	19.5623	+	14.2128i	1.41548	+	1.02841i	0.992497	+	0.122267i	$0.0390165\pi$
$191$	19.5623	+	14.2128i	1.41548	+	1.02841i	0.422982	+	0.906138i	$0.360984\pi$
$192$	0.224514	−	0.0729490i	0.0162029	−	0.00526464i
$193$			5.70820i			0.410886i	0.978669	+	0.205443i	$0.0658634\pi$
$193$			5.70820i			0.410886i	−0.978669	+	0.205443i	$0.934137\pi$
$194$	−0.545085	−	1.67760i	−0.0391348	−	0.120445i
$195$		0			0
$196$	2.19098	−	6.74315i	0.156499	−	0.481654i
$197$	−9.23305	−	3.00000i	−0.657828	−	0.213741i	−0.0389652	−	0.999241i	$-0.512406\pi$
$197$	−9.23305	−	3.00000i	−0.657828	−	0.213741i	−0.618862	+	0.785499i	$0.712406\pi$
$198$	0.555029	+	0.763932i	0.0394442	+	0.0542903i
$199$	−2.56231			−0.181637			−0.0908185	−	0.995867i	$-0.528948\pi$
$199$	−2.56231			−0.181637			−0.0908185	+	0.995867i	$0.528948\pi$
$200$		0			0
$201$	9.23607			0.651462
$202$	2.71441	+	3.73607i	0.190985	+	0.262869i
$203$	−2.12663	−	0.690983i	−0.149260	−	0.0484975i
$204$	−0.381966	+	1.17557i	−0.0267430	+	0.0823064i
$205$		0			0
$206$	−2.20820	−	6.79615i	−0.153853	−	0.473510i
$207$		−	16.4721i		−	1.14489i
$208$	−8.55951	+	2.78115i	−0.593495	+	0.192838i
$209$	3.61803	+	2.62866i	0.250265	+	0.181828i
$210$		0			0
$211$	−10.6631	+	7.74721i	−0.734079	+	0.533340i	−0.890851	−	0.454295i	$-0.849891\pi$
$211$	−10.6631	+	7.74721i	−0.734079	+	0.533340i	0.156772	+	0.987635i	$0.449891\pi$
$212$	−5.20431	+	7.16312i	−0.357434	+	0.491965i
$213$	2.57565	−	3.54508i	0.176481	−	0.242905i
$214$	5.20820	−	3.78398i	0.356025	−	0.258668i
$215$		0			0
$216$	−9.04508	−	6.57164i	−0.615440	−	0.447143i
$217$	−4.61653	+	1.50000i	−0.313390	+	0.101827i
$218$		−	6.18034i		−	0.418585i
$219$	2.78115	+	8.55951i	0.187933	+	0.578398i
$220$		0			0
$221$	1.14590	−	3.52671i	0.0770814	−	0.237232i
$222$	2.48990	+	0.809017i	0.167111	+	0.0542977i
$223$	13.0373	+	17.9443i	0.873041	+	1.20164i	0.978300	+	0.207193i	$0.0664327\pi$
$223$	13.0373	+	17.9443i	0.873041	+	1.20164i	−0.105260	+	0.994445i	$0.533567\pi$
$224$	9.09017			0.607363
$225$		0			0
$226$	6.27051			0.417108
$227$	−11.3067	−	15.5623i	−0.750451	−	1.03291i	−0.997949	−	0.0640182i	$-0.979608\pi$
$227$	−11.3067	−	15.5623i	−0.750451	−	1.03291i	0.247498	−	0.968888i	$-0.420392\pi$
$228$	−9.00854	−	2.92705i	−0.596605	−	0.193849i
$229$	−2.56231	+	7.88597i	−0.169322	+	0.521119i	−0.999329	−	0.0366339i	$-0.988336\pi$
$229$	−2.56231	+	7.88597i	−0.169322	+	0.521119i	0.830007	+	0.557753i	$0.188336\pi$
$230$		0			0
$231$	0.381966	+	1.17557i	0.0251315	+	0.0773469i
$232$			3.09017i			0.202880i
$233$	14.2128	−	4.61803i	0.931115	−	0.302537i	0.196096	−	0.980585i	$-0.437174\pi$
$233$	14.2128	−	4.61803i	0.931115	−	0.302537i	0.735018	+	0.678047i	$0.237174\pi$
$234$	4.85410	+	3.52671i	0.317323	+	0.230548i
$235$		0			0
$236$	−5.42705	+	3.94298i	−0.353271	+	0.256666i
$237$	1.81636	−	2.50000i	0.117985	−	0.162392i
$238$	−0.449028	+	0.618034i	−0.0291062	+	0.0400612i
$239$	−23.8435	+	17.3233i	−1.54231	+	1.12055i	−0.593436	+	0.804881i	$0.702229\pi$
$239$	−23.8435	+	17.3233i	−1.54231	+	1.12055i	−0.948869	+	0.315669i	$0.897771\pi$
$240$		0			0
$241$	−9.28115	−	6.74315i	−0.597852	−	0.434365i	0.247264	−	0.968948i	$-0.420468\pi$
$241$	−9.28115	−	6.74315i	−0.597852	−	0.434365i	−0.845116	+	0.534584i	$0.820468\pi$
$242$	6.12261	−	1.98936i	0.393576	−	0.127881i
$243$		−	16.0000i		−	1.02640i
$244$	−2.35410	−	7.24518i	−0.150706	−	0.463825i
$245$		0			0
$246$	−1.00000	+	3.07768i	−0.0637577	+	0.196226i
$247$	27.0256	+	8.78115i	1.71960	+	0.558731i
$248$	3.94298	+	5.42705i	0.250380	+	0.344618i
$249$	1.76393			0.111785
$250$		0			0
$251$	−6.81966			−0.430453			−0.215227	−	0.976564i	$-0.569049\pi$
$251$	−6.81966			−0.430453			−0.215227	+	0.976564i	$0.569049\pi$
$252$	3.07768	+	4.23607i	0.193876	+	0.266847i
$253$	5.98385	+	1.94427i	0.376202	+	0.122235i
$254$	3.03444	−	9.33905i	0.190398	−	0.585984i
$255$		0			0
$256$	−2.02786	−	6.24112i	−0.126742	−	0.390070i
$257$			16.1459i			1.00715i	0.863951	+	0.503577i	$0.167983\pi$
$257$			16.1459i			1.00715i	−0.863951	+	0.503577i	$0.832017\pi$
$258$	1.08981	−	0.354102i	0.0678488	−	0.0220454i
$259$	−5.54508	−	4.02874i	−0.344555	−	0.250334i
$260$		0			0
$261$	−2.23607	+	1.62460i	−0.138409	+	0.100560i
$262$	−6.46564	+	8.89919i	−0.399448	+	0.549794i
$263$	12.9843	−	17.8713i	0.800645	−	1.10199i	−0.192055	−	0.981384i	$-0.561515\pi$
$263$	12.9843	−	17.8713i	0.800645	−	1.10199i	0.992700	−	0.120609i	$-0.0384847\pi$
$264$	1.38197	−	1.00406i	0.0850541	−	0.0617954i
$265$		0			0
$266$	−4.73607	−	3.44095i	−0.290387	−	0.210978i
$267$	−8.50651	+	2.76393i	−0.520590	+	0.169150i
$268$			14.9443i			0.912867i
$269$	5.32624	+	16.3925i	0.324746	+	0.999467i	0.971555	+	0.236814i	$0.0761033\pi$
$269$	5.32624	+	16.3925i	0.324746	+	0.999467i	−0.646808	+	0.762652i	$0.723897\pi$
$270$		0			0
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	−0.997640	−	0.0686657i	$-0.978126\pi$
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	0.847468	+	0.530846i	$0.178126\pi$
$272$	−1.34708	−	0.437694i	−0.0816790	−	0.0265391i
$273$	4.61653	+	6.35410i	0.279405	+	0.384568i
$274$	−3.67376			−0.221940
$275$		0			0
$276$	−13.3262			−0.802145
$277$	6.63715	+	9.13525i	0.398788	+	0.548884i	0.960439	−	0.278490i	$-0.0898338\pi$
$277$	6.63715	+	9.13525i	0.398788	+	0.548884i	−0.561651	+	0.827374i	$0.689834\pi$
$278$	−2.93893	−	0.954915i	−0.176265	−	0.0572720i
$279$	−1.85410	+	5.70634i	−0.111002	+	0.341630i
$280$		0			0
$281$	−0.336881	−	1.03681i	−0.0200966	−	0.0618511i	0.940505	−	0.339779i	$-0.110352\pi$
$281$	−0.336881	−	1.03681i	−0.0200966	−	0.0618511i	−0.960602	+	0.277928i	$0.910352\pi$
$282$		−	1.00000i		−	0.0595491i
$283$	−22.0131	+	7.15248i	−1.30854	+	0.425171i	−0.878545	−	0.477660i	$-0.841485\pi$
$283$	−22.0131	+	7.15248i	−1.30854	+	0.425171i	−0.429996	+	0.902831i	$0.641485\pi$
$284$	5.73607	+	4.16750i	0.340373	+	0.247295i
$285$		0			0
$286$	−1.85410	+	1.34708i	−0.109635	+	0.0796547i
$287$	4.97980	−	6.85410i	0.293948	−	0.404585i
$288$	6.60440	−	9.09017i	0.389168	−	0.535643i
$289$	−13.2812	+	9.64932i	−0.781244	+	0.567607i
$290$		0			0
$291$	−2.30902	−	1.67760i	−0.135357	−	0.0983426i
$292$	−13.8496	+	4.50000i	−0.810485	+	0.263343i
$293$			28.4721i			1.66336i	0.555255	+	0.831680i	$0.312621\pi$
$293$			28.4721i			1.66336i	−0.555255	+	0.831680i	$0.687379\pi$
$294$	0.836881	+	2.57565i	0.0488079	+	0.150215i
$295$		0			0
$296$	−2.92705	+	9.00854i	−0.170131	+	0.523611i
$297$	3.63271	+	1.18034i	0.210791	+	0.0684903i
$298$	5.06555	+	6.97214i	0.293440	+	0.403885i
$299$	39.9787			2.31203
$300$		0			0
$301$	−3.00000			−0.172917
$302$	2.02063	+	2.78115i	0.116274	+	0.160037i
$303$	7.10642	+	2.30902i	0.408253	+	0.132650i
$304$	3.35410	−	10.3229i	0.192371	−	0.592057i
$305$		0			0
$306$	0.291796	+	0.898056i	0.0166809	+	0.0513384i
$307$			4.76393i			0.271892i	0.990716	+	0.135946i	$0.0434074\pi$
$307$			4.76393i			0.271892i	−0.990716	+	0.135946i	$0.956593\pi$
$308$	−1.90211	+	0.618034i	−0.108383	+	0.0352158i
$309$	−9.35410	−	6.79615i	−0.532136	−	0.386620i
$310$		0			0
$311$	23.8713	−	17.3435i	1.35362	−	0.983461i	0.354796	−	0.934944i	$-0.384550\pi$
$311$	23.8713	−	17.3435i	1.35362	−	0.983461i	0.998822	−	0.0485178i	$-0.0154498\pi$
$312$	6.37988	−	8.78115i	0.361190	−	0.497135i
$313$	12.4822	−	17.1803i	0.705538	−	0.971090i	−0.294343	−	0.955700i	$-0.595101\pi$
$313$	12.4822	−	17.1803i	0.705538	−	0.971090i	0.999882	−	0.0153904i	$-0.00489912\pi$
$314$	−4.59017	+	3.33495i	−0.259038	+	0.188202i
$315$		0			0
$316$	4.04508	+	2.93893i	0.227554	+	0.165328i
$317$	22.4948	−	7.30902i	1.26344	−	0.410515i	0.400719	−	0.916201i	$-0.368761\pi$
$317$	22.4948	−	7.30902i	1.26344	−	0.410515i	0.862718	+	0.505686i	$0.168761\pi$
$318$		−	3.38197i		−	0.189651i
$319$	−0.326238	−	1.00406i	−0.0182658	−	0.0562164i
$320$		0			0
$321$	3.21885	−	9.90659i	0.179659	−	0.552932i
$322$	−7.83297	−	2.54508i	−0.436514	−	0.141832i
$323$	2.62866	+	3.61803i	0.146262	+	0.201313i
$324$	1.61803			0.0898908
$325$		0			0
$326$	6.79837			0.376527
$327$	−5.87785	−	8.09017i	−0.325046	−	0.447387i
$328$	−11.1352	−	3.61803i	−0.614837	−	0.199773i
$329$	−0.809017	+	2.48990i	−0.0446026	+	0.137273i
$330$		0			0
$331$	5.29180	+	16.2865i	0.290863	+	0.895186i	0.984580	+	0.174937i	$0.0559722\pi$
$331$	5.29180	+	16.2865i	0.290863	+	0.895186i	−0.693716	+	0.720248i	$0.744028\pi$
$332$			2.85410i			0.156639i
$333$	−8.05748	+	2.61803i	−0.441547	+	0.143467i
$334$	−2.78115	−	2.02063i	−0.152178	−	0.110564i
$335$		0			0
$336$	2.42705	−	1.76336i	0.132406	−	0.0961989i
$337$	0.673542	−	0.927051i	0.0366902	−	0.0504997i	−0.790278	−	0.612749i	$-0.790064\pi$
$337$	0.673542	−	0.927051i	0.0366902	−	0.0504997i	0.826968	+	0.562249i	$0.190064\pi$
$338$	−3.83698	+	5.28115i	−0.208704	+	0.287257i
$339$	8.20820	−	5.96361i	0.445808	−	0.323899i
$340$		0			0
$341$	−1.85410	−	1.34708i	−0.100405	−	0.0729487i
$342$	−6.88191	+	2.23607i	−0.372131	+	0.120913i
$343$		−	18.4164i		−	0.994393i
$344$	1.28115	+	3.94298i	0.0690751	+	0.212591i
$345$		0			0
$346$	−3.22542	+	9.92684i	−0.173400	+	0.533670i
$347$	−29.5685	−	9.60739i	−1.58732	−	0.515752i	−0.623391	−	0.781910i	$-0.714246\pi$
$347$	−29.5685	−	9.60739i	−1.58732	−	0.515752i	−0.963929	+	0.266158i	$0.914246\pi$
$348$	1.31433	+	1.80902i	0.0704554	+	0.0969735i
$349$	−8.29180			−0.443850			−0.221925	−	0.975064i	$-0.571234\pi$
$349$	−8.29180			−0.443850			−0.221925	+	0.975064i	$0.571234\pi$
$350$		0			0
$351$	24.2705			1.29546
$352$	2.52265	+	3.47214i	0.134458	+	0.185065i
$353$	−22.9111	−	7.44427i	−1.21944	−	0.396219i	−0.372559	−	0.928008i	$-0.621520\pi$
$353$	−22.9111	−	7.44427i	−1.21944	−	0.396219i	−0.846876	+	0.531790i	$0.821520\pi$
$354$	0.791796	−	2.43690i	0.0420835	−	0.129520i
$355$		0			0
$356$	−4.47214	−	13.7638i	−0.237023	−	0.729481i
$357$			1.23607i			0.0654197i
$358$	−5.56758	+	1.80902i	−0.294256	+	0.0956095i
$359$	−23.2533	−	16.8945i	−1.22726	−	0.891658i	−0.230580	−	0.973053i	$-0.574062\pi$
$359$	−23.2533	−	16.8945i	−1.22726	−	0.891658i	−0.996682	+	0.0813956i	$0.974062\pi$
$360$		0			0
$361$	−12.3541	+	8.97578i	−0.650216	+	0.472409i
$362$	4.97980	−	6.85410i	0.261732	−	0.360244i
$363$	6.12261	−	8.42705i	0.321354	−	0.442305i
$364$	−10.2812	+	7.46969i	−0.538879	+	0.391518i
$365$		0			0
$366$	2.35410	+	1.71036i	0.123051	+	0.0894017i
$367$	5.17155	−	1.68034i	0.269953	−	0.0877130i	−0.170913	−	0.985286i	$-0.554672\pi$
$367$	5.17155	−	1.68034i	0.269953	−	0.0877130i	0.440866	+	0.897573i	$0.354672\pi$
$368$		−	15.2705i		−	0.796030i
$369$	−3.23607	−	9.95959i	−0.168463	−	0.518476i
$370$		0			0
$371$	−2.73607	+	8.42075i	−0.142050	+	0.437184i
$372$	4.61653	+	1.50000i	0.239356	+	0.0777714i
$373$	3.09793	+	4.26393i	0.160405	+	0.220778i	0.881653	−	0.471899i	$-0.156431\pi$
$373$	3.09793	+	4.26393i	0.160405	+	0.220778i	−0.721248	+	0.692677i	$0.756431\pi$
$374$	−0.360680			−0.0186503
$375$		0			0
$376$	3.61803			0.186586
$377$	−3.94298	−	5.42705i	−0.203074	−	0.279507i
$378$	−4.75528	−	1.54508i	−0.244585	−	0.0794706i
$379$	10.6910	−	32.9035i	0.549159	−	1.69014i	−0.161732	−	0.986835i	$-0.551708\pi$
$379$	10.6910	−	32.9035i	0.549159	−	1.69014i	0.710891	−	0.703303i	$-0.248292\pi$
$380$		0			0
$381$	−4.90983	−	15.1109i	−0.251538	−	0.774155i
$382$		−	14.9443i		−	0.764615i
$383$	−10.8046	+	3.51064i	−0.552092	+	0.179385i	−0.571760	−	0.820421i	$-0.693739\pi$
$383$	−10.8046	+	3.51064i	−0.552092	+	0.179385i	0.0196680	+	0.999807i	$0.493739\pi$
$384$	−9.20820	−	6.69015i	−0.469904	−	0.341405i
$385$		0			0
$386$	2.85410	−	2.07363i	0.145270	−	0.105545i
$387$	−2.17963	+	3.00000i	−0.110797	+	0.152499i
$388$	2.71441	−	3.73607i	0.137803	−	0.189670i
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	−0.235988	−	0.971756i	$-0.575833\pi$
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	0.851270	+	0.524727i	$0.175833\pi$
$390$		0			0
$391$	5.09017	+	3.69822i	0.257421	+	0.187027i
$392$	−9.31881	+	3.02786i	−0.470671	+	0.152930i
$393$			17.7984i			0.897809i
$394$	1.85410	+	5.70634i	0.0934083	+	0.287481i
$395$		0			0
$396$	−0.763932	+	2.35114i	−0.0383890	+	0.118149i
$397$	−0.0327561	−	0.0106431i	−0.00164398	−	0.000534163i	0.308195	−	0.951323i	$-0.400275\pi$
$397$	−0.0327561	−	0.0106431i	−0.00164398	−	0.000534163i	−0.309839	+	0.950789i	$0.600275\pi$
$398$	0.930812	+	1.28115i	0.0466574	+	0.0642184i
$399$	−9.47214			−0.474200
$400$		0			0
$401$	−22.5967			−1.12843			−0.564214	−	0.825629i	$-0.690821\pi$
$401$	−22.5967			−1.12843			−0.564214	+	0.825629i	$0.690821\pi$
$402$	−3.35520	−	4.61803i	−0.167342	−	0.230327i
$403$	−13.8496	−	4.50000i	−0.689897	−	0.224161i
$404$	−3.73607	+	11.4984i	−0.185876	+	0.572069i
$405$		0			0
$406$	0.427051	+	1.31433i	0.0211942	+	0.0652290i
$407$		−	3.23607i		−	0.160406i
$408$	1.62460	−	0.527864i	0.0804296	−	0.0261332i
$409$	22.9894	+	16.7027i	1.13675	+	0.825898i	0.986663	−	0.162775i	$-0.0520445\pi$
$409$	22.9894	+	16.7027i	1.13675	+	0.825898i	0.150087	+	0.988673i	$0.452045\pi$
$410$		0			0
$411$	−4.80902	+	3.49396i	−0.237211	+	0.172344i
$412$	10.9964	−	15.1353i	0.541754	−	0.745660i
$413$	−3.94298	+	5.42705i	−0.194022	+	0.267048i
$414$	−8.23607	+	5.98385i	−0.404781	+	0.294090i
$415$		0			0
$416$	22.0623	+	16.0292i	1.08169	+	0.785896i
$417$	−4.75528	+	1.54508i	−0.232867	+	0.0756631i
$418$		−	2.76393i		−	0.135188i
$419$	0.163119	+	0.502029i	0.00796888	+	0.0245257i	0.954962	−	0.296728i	$-0.0958956\pi$
$419$	0.163119	+	0.502029i	0.00796888	+	0.0245257i	−0.946993	+	0.321254i	$0.895896\pi$
$420$		0			0
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	−0.354429	−	0.935083i	$-0.615325\pi$
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	0.836367	−	0.548170i	$-0.184675\pi$
$422$	7.74721	+	2.51722i	0.377128	+	0.122536i
$423$	1.90211	+	2.61803i	0.0924839	+	0.127293i
$424$	12.2361			0.594236
$425$		0			0
$426$	−2.70820			−0.131213
$427$	−4.47777	−	6.16312i	−0.216694	−	0.298254i
$428$	16.0292	+	5.20820i	0.774801	+	0.251748i
$429$	−1.14590	+	3.52671i	−0.0553245	+	0.170271i
$430$		0			0
$431$	7.36475	+	22.6664i	0.354747	+	1.09180i	0.956156	+	0.292858i	$0.0946064\pi$
$431$	7.36475	+	22.6664i	0.354747	+	1.09180i	−0.601409	+	0.798942i	$0.705394\pi$
$432$		−	9.27051i		−	0.446028i
$433$	19.1599	−	6.22542i	0.920765	−	0.299175i	0.189985	−	0.981787i	$-0.439156\pi$
$433$	19.1599	−	6.22542i	0.920765	−	0.299175i	0.730781	+	0.682612i	$0.239156\pi$
$434$	2.42705	+	1.76336i	0.116502	+	0.0846438i
$435$		0			0
$436$	13.0902	−	9.51057i	0.626905	−	0.455473i
$437$	−28.3399	+	39.0066i	−1.35568	+	1.86594i
$438$	3.26944	−	4.50000i	0.156220	−	0.215018i
$439$	4.83688	−	3.51420i	0.230852	−	0.167724i	−0.466346	−	0.884602i	$-0.654430\pi$
$439$	4.83688	−	3.51420i	0.230852	−	0.167724i	0.697198	+	0.716879i	$0.254430\pi$
$440$		0			0
$441$	−7.09017	−	5.15131i	−0.337627	−	0.245300i
$442$	−2.17963	+	0.708204i	−0.103674	+	0.0336858i
$443$		−	12.0557i		−	0.572785i	−0.958112	−	0.286392i	$-0.907544\pi$
$443$		−	12.0557i		−	0.572785i	0.958112	−	0.286392i	$-0.0924561\pi$
$444$	2.11803	+	6.51864i	0.100517	+	0.309361i
$445$		0			0
$446$	4.23607	−	13.0373i	0.200584	−	0.617333i
$447$	13.2618	+	4.30902i	0.627261	+	0.203810i
$448$	0.224514	+	0.309017i	0.0106073	+	0.0145997i
$449$	−20.3262			−0.959254			−0.479627	−	0.877472i	$-0.659228\pi$
$449$	−20.3262			−0.959254			−0.479627	+	0.877472i	$0.659228\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	9.64932	+	13.2812i	0.453866	+	0.624693i
$453$	5.29007	+	1.71885i	0.248549	+	0.0807585i
$454$	−3.67376	+	11.3067i	−0.172418	+	0.530649i
$455$		0			0
$456$	4.04508	+	12.4495i	0.189428	+	0.583001i
$457$			5.41641i			0.253369i	0.991943	+	0.126684i	$0.0404336\pi$
$457$			5.41641i			0.253369i	−0.991943	+	0.126684i	$0.959566\pi$
$458$	4.87380	−	1.58359i	0.227738	−	0.0739964i
$459$	3.09017	+	2.24514i	0.144237	+	0.104794i
$460$		0			0
$461$	−18.7533	+	13.6251i	−0.873428	+	0.634582i	−0.931505	−	0.363730i	$-0.881503\pi$
$461$	−18.7533	+	13.6251i	−0.873428	+	0.634582i	0.0580768	+	0.998312i	$0.481503\pi$
$462$	0.449028	−	0.618034i	0.0208907	−	0.0287535i
$463$	−9.47781	+	13.0451i	−0.440471	+	0.606257i	−0.970317	−	0.241838i	$-0.922250\pi$
$463$	−9.47781	+	13.0451i	−0.440471	+	0.606257i	0.529846	+	0.848094i	$0.322250\pi$
$464$	−2.07295	+	1.50609i	−0.0962342	+	0.0699183i
$465$		0			0
$466$	−7.47214	−	5.42882i	−0.346140	−	0.251485i
$467$	27.0584	−	8.79180i	1.25211	−	0.406836i	0.393435	−	0.919353i	$-0.371287\pi$
$467$	27.0584	−	8.79180i	1.25211	−	0.406836i	0.858677	+	0.512517i	$0.171287\pi$
$468$			15.7082i			0.726112i
$469$	4.61803	+	14.2128i	0.213241	+	0.656288i
$470$		0			0
$471$	−2.83688	+	8.73102i	−0.130717	+	0.402304i
$472$	8.81678	+	2.86475i	0.405825	+	0.131861i
$473$	−0.832544	−	1.14590i	−0.0382804	−	0.0526884i
$474$	−1.90983			−0.0877214
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	6.43288	+	8.85410i	0.294541	+	0.405401i
$478$	17.3233	+	5.62868i	0.792349	+	0.257450i
$479$	1.28115	−	3.94298i	0.0585374	−	0.180160i	−0.917512	−	0.397708i	$-0.869806\pi$
$479$	1.28115	−	3.94298i	0.0585374	−	0.180160i	0.976050	+	0.217548i	$0.0698059\pi$
$480$		0			0
$481$	−6.35410	−	19.5559i	−0.289722	−	0.891673i
$482$			7.09017i			0.322948i
$483$	−12.6740	+	4.11803i	−0.576687	+	0.187377i
$484$	13.6353	+	9.90659i	0.619784	+	0.450300i
$485$		0			0
$486$	−8.00000	+	5.81234i	−0.362887	+	0.263653i
$487$	−5.63309	+	7.75329i	−0.255260	+	0.351335i	−0.917345	−	0.398094i	$-0.869672\pi$
$487$	−5.63309	+	7.75329i	−0.255260	+	0.351335i	0.662085	+	0.749429i	$0.269672\pi$
$488$	−6.18812	+	8.51722i	−0.280123	+	0.385556i
$489$	8.89919	−	6.46564i	0.402435	−	0.292386i
$490$		0			0
$491$	−30.1353	−	21.8945i	−1.35999	−	0.988087i	−0.998446	−	0.0557300i	$-0.982251\pi$
$491$	−30.1353	−	21.8945i	−1.35999	−	0.988087i	−0.361539	−	0.932357i	$-0.617749\pi$
$492$	−8.05748	+	2.61803i	−0.363259	+	0.118030i
$493$		−	1.05573i		−	0.0475476i
$494$	−5.42705	−	16.7027i	−0.244175	−	0.751492i
$495$		0			0
$496$	−1.71885	+	5.29007i	−0.0771785	+	0.237531i
$497$	6.74315	+	2.19098i	0.302472	+	0.0982790i
$498$	−0.640786	−	0.881966i	−0.0287143	−	0.0395218i
$499$	12.5623			0.562366			0.281183	−	0.959654i	$-0.409273\pi$
$499$	12.5623			0.562366			0.281183	+	0.959654i	$0.409273\pi$
$500$		0			0
$501$	−5.56231			−0.248506
$502$	2.47739	+	3.40983i	0.110571	+	0.152188i
$503$	10.0656	+	3.27051i	0.448803	+	0.145825i	0.524693	−	0.851291i	$-0.324180\pi$
$503$	10.0656	+	3.27051i	0.448803	+	0.145825i	−0.0758907	+	0.997116i	$0.524180\pi$
$504$	2.23607	−	6.88191i	0.0996024	−	0.306545i
$505$		0			0
$506$	−1.20163	−	3.69822i	−0.0534188	−	0.164406i
$507$			10.5623i			0.469088i
$508$	24.4500	−	7.94427i	1.08479	−	0.352470i
$509$	−3.78115	−	2.74717i	−0.167597	−	0.121766i	0.500825	−	0.865548i	$-0.333030\pi$
$509$	−3.78115	−	2.74717i	−0.167597	−	0.121766i	−0.668422	+	0.743782i	$0.733030\pi$
$510$		0			0
$511$	−11.7812	+	8.55951i	−0.521168	+	0.378650i
$512$	10.9964	−	15.1353i	0.485977	−	0.668890i
$513$	−17.2048	+	23.6803i	−0.759609	+	1.04551i
$514$	8.07295	−	5.86534i	0.356083	−	0.258709i
$515$		0			0
$516$	2.42705	+	1.76336i	0.106845	+	0.0776274i
$517$	−1.17557	+	0.381966i	−0.0517015	+	0.0167988i
$518$			4.23607i			0.186122i
$519$	5.21885	+	16.0620i	0.229082	+	0.705042i
$520$		0			0
$521$	−4.74671	+	14.6089i	−0.207957	+	0.640026i	0.791622	+	0.611011i	$0.209237\pi$
$521$	−4.74671	+	14.6089i	−0.207957	+	0.640026i	−0.999579	+	0.0290150i	$0.990763\pi$
$522$	1.62460	+	0.527864i	0.0711067	+	0.0231040i
$523$	−11.6699	−	16.0623i	−0.510291	−	0.702356i	0.473677	−	0.880699i	$-0.342926\pi$
$523$	−11.6699	−	16.0623i	−0.510291	−	0.702356i	−0.983968	+	0.178343i	$0.942926\pi$
$524$	−28.7984			−1.25806
$525$		0			0
$526$	−13.6525			−0.595276
$527$	−1.34708	−	1.85410i	−0.0586799	−	0.0807660i
$528$	1.34708	+	0.437694i	0.0586243	+	0.0190482i
$529$	−13.8541	+	42.6385i	−0.602352	+	1.85385i
$530$		0			0
$531$	2.56231	+	7.88597i	0.111195	+	0.342222i
$532$		−	15.3262i		−	0.664477i
$533$	24.1724	−	7.85410i	1.04702	−	0.340199i
$534$	4.47214	+	3.24920i	0.193528	+	0.140607i
$535$		0			0
$536$	16.7082	−	12.1392i	0.721684	−	0.524334i
$537$	−5.56758	+	7.66312i	−0.240259	+	0.330688i
$538$	6.26137	−	8.61803i	0.269947	−	0.371550i
$539$	2.70820	−	1.96763i	0.116651	−	0.0847516i
$540$		0			0
$541$	10.6180	+	7.71445i	0.456505	+	0.331670i	0.792159	−	0.610315i	$-0.208957\pi$
$541$	10.6180	+	7.71445i	0.456505	+	0.331670i	−0.335654	+	0.941985i	$0.608957\pi$
$542$	4.70228	−	1.52786i	0.201980	−	0.0656274i
$543$		−	13.7082i		−	0.588275i
$544$	1.32624	+	4.08174i	0.0568620	+	0.175003i
$545$		0			0
$546$	1.50000	−	4.61653i	0.0641941	−	0.197569i
$547$	−33.0095	−	10.7254i	−1.41138	−	0.458586i	−0.498529	−	0.866873i	$-0.666126\pi$
$547$	−33.0095	−	10.7254i	−1.41138	−	0.458586i	−0.912854	+	0.408287i	$0.866126\pi$
$548$	−5.65334	−	7.78115i	−0.241499	−	0.332394i
$549$	−9.41641			−0.401882
$550$		0			0
$551$	8.09017			0.344653
$552$	10.8249	+	14.8992i	0.460738	+	0.634152i
$553$	4.75528	+	1.54508i	0.202215	+	0.0657037i
$554$	2.15654	−	6.63715i	0.0916227	−	0.281986i
$555$		0			0
$556$	−2.50000	−	7.69421i	−0.106024	−	0.326307i
$557$			9.23607i			0.391345i	0.980669	+	0.195672i	$0.0626889\pi$
$557$			9.23607i			0.391345i	−0.980669	+	0.195672i	$0.937311\pi$
$558$	3.52671	−	1.14590i	0.149298	−	0.0485097i
$559$	−7.28115	−	5.29007i	−0.307960	−	0.223746i
$560$		0			0
$561$	−0.472136	+	0.343027i	−0.0199336	+	0.0144826i
$562$	−0.396027	+	0.545085i	−0.0167054	+	0.0229930i
$563$	−5.65334	+	7.78115i	−0.238260	+	0.327936i	−0.911356	−	0.411618i	$-0.864964\pi$
$563$	−5.65334	+	7.78115i	−0.238260	+	0.327936i	0.673097	+	0.739555i	$0.264964\pi$
$564$	2.11803	−	1.53884i	0.0891853	−	0.0647969i
$565$		0			0
$566$	11.5729	+	8.40824i	0.486447	+	0.353425i
$567$	1.53884	−	0.500000i	0.0646253	−	0.0209980i
$568$		−	9.79837i		−	0.411131i
$569$	−9.10739	−	28.0297i	−0.381802	−	1.17506i	−0.938774	−	0.344534i	$-0.888037\pi$
$569$	−9.10739	−	28.0297i	−0.381802	−	1.17506i	0.556972	−	0.830531i	$-0.311963\pi$
$570$		0			0
$571$	9.92705	−	30.5523i	0.415434	−	1.27857i	−0.496428	−	0.868078i	$-0.665355\pi$
$571$	9.92705	−	30.5523i	0.415434	−	1.27857i	0.911862	−	0.410497i	$-0.134645\pi$
$572$	−5.70634	−	1.85410i	−0.238594	−	0.0775239i
$573$	−14.2128	−	19.5623i	−0.593750	−	0.817227i
$574$	−5.23607			−0.218549
$575$		0			0
$576$	0.472136			0.0196723
$577$	−22.2048	−	30.5623i	−0.924399	−	1.27233i	−0.962005	−	0.273033i	$-0.911973\pi$
$577$	−22.2048	−	30.5623i	−0.924399	−	1.27233i	0.0376062	−	0.999293i	$-0.488027\pi$
$578$	9.64932	+	3.13525i	0.401359	+	0.130409i
$579$	1.76393	−	5.42882i	0.0733065	−	0.225614i
$580$		0			0
$581$	0.881966	+	2.71441i	0.0365901	+	0.112613i
$582$			1.76393i			0.0731173i
$583$	−3.97574	+	1.29180i	−0.164658	+	0.0535007i
$584$	16.2812	+	11.8290i	0.673719	+	0.489485i
$585$		0			0
$586$	14.2361	−	10.3431i	0.588087	−	0.427270i
$587$	10.9964	−	15.1353i	0.453870	−	0.624699i	−0.519353	−	0.854560i	$-0.673827\pi$
$587$	10.9964	−	15.1353i	0.453870	−	0.624699i	0.973224	+	0.229861i	$0.0738271\pi$
$588$	−4.16750	+	5.73607i	−0.171865	+	0.236551i
$589$	14.2082	−	10.3229i	0.585439	−	0.425346i
$590$		0			0
$591$	7.85410	+	5.70634i	0.323075	+	0.234727i
$592$	−7.46969	+	2.42705i	−0.307003	+	0.0997512i
$593$			22.0902i			0.907135i	0.891222	+	0.453567i	$0.149849\pi$
$593$			22.0902i			0.907135i	−0.891222	+	0.453567i	$0.850151\pi$
$594$	−0.729490	−	2.24514i	−0.0299313	−	0.0921192i
$595$		0			0
$596$	−6.97214	+	21.4580i	−0.285590	+	0.878955i
$597$	2.43690	+	0.791796i	0.0997356	+	0.0324061i
$598$	−14.5231	−	19.9894i	−0.593894	−	0.817426i
$599$	0.527864			0.0215679			0.0107840	−	0.999942i	$-0.496567\pi$
$599$	0.527864			0.0215679			0.0107840	+	0.999942i	$0.496567\pi$
$600$		0			0
$601$	36.2705			1.47950			0.739752	−	0.672879i	$-0.234943\pi$
$601$	36.2705			1.47950			0.739752	+	0.672879i	$0.234943\pi$
$602$	1.08981	+	1.50000i	0.0444175	+	0.0611354i
$603$	17.5680	+	5.70820i	0.715426	+	0.232456i
$604$	−2.78115	+	8.55951i	−0.113164	+	0.348281i
$605$		0			0
$606$	−1.42705	−	4.39201i	−0.0579700	−	0.178413i
$607$		−	15.4377i		−	0.626597i	−0.949655	−	0.313298i	$-0.898566\pi$
$607$		−	15.4377i		−	0.626597i	0.949655	−	0.313298i	$-0.101434\pi$
$608$	−31.2789	+	10.1631i	−1.26853	+	0.412169i
$609$	1.80902	+	1.31433i	0.0733051	+	0.0532592i
$610$		0			0
$611$	−6.35410	+	4.61653i	−0.257059	+	0.186765i
$612$	−1.45309	+	2.00000i	−0.0587375	+	0.0808452i
$613$	−18.7966	+	25.8713i	−0.759188	+	1.04493i	0.238093	+	0.971242i	$0.423478\pi$
$613$	−18.7966	+	25.8713i	−0.759188	+	1.04493i	−0.997281	+	0.0736905i	$0.976522\pi$
$614$	2.38197	−	1.73060i	0.0961283	−	0.0698413i
$615$		0			0
$616$	2.23607	+	1.62460i	0.0900937	+	0.0654569i
$617$	−9.28605	+	3.01722i	−0.373842	+	0.121469i	−0.489911	−	0.871772i	$-0.662971\pi$
$617$	−9.28605	+	3.01722i	−0.373842	+	0.121469i	0.116069	+	0.993241i	$0.462971\pi$
$618$			7.14590i			0.287450i
$619$	−12.1976	−	37.5402i	−0.490261	−	1.50887i	−0.824213	−	0.566279i	$-0.808382\pi$
$619$	−12.1976	−	37.5402i	−0.490261	−	1.50887i	0.333952	−	0.942590i	$-0.391618\pi$
$620$		0			0
$621$	−12.7254	+	39.1648i	−0.510654	+	1.57163i
$622$	−17.3435	−	5.63525i	−0.695412	−	0.225953i
$623$	−8.50651	−	11.7082i	−0.340806	−	0.469079i
$624$	9.00000			0.360288
$625$		0			0
$626$	−13.1246			−0.524565
$627$	−2.62866	−	3.61803i	−0.104978	−	0.144490i
$628$	−14.1271	−	4.59017i	−0.563732	−	0.183168i
$629$	1.00000	−	3.07768i	0.0398726	−	0.122715i
$630$		0			0
$631$	−1.78115	−	5.48183i	−0.0709066	−	0.218228i	0.909323	−	0.416090i	$-0.136600\pi$
$631$	−1.78115	−	5.48183i	−0.0709066	−	0.218228i	−0.980230	+	0.197862i	$0.936600\pi$
$632$		−	6.90983i		−	0.274858i
$633$	12.5352	−	4.07295i	0.498231	−	0.161885i
$634$	−11.8262	−	8.59226i	−0.469680	−	0.341242i
$635$		0			0
$636$	7.16312	−	5.20431i	0.284036	−	0.206364i
$637$	12.5025	−	17.2082i	0.495367	−	0.681814i
$638$	−0.383516	+	0.527864i	−0.0151835	+	0.0208983i
$639$	7.09017	−	5.15131i	0.280483	−	0.203783i
$640$		0			0
$641$	−8.16312	−	5.93085i	−0.322424	−	0.234255i	0.414785	−	0.909919i	$-0.363857\pi$
$641$	−8.16312	−	5.93085i	−0.322424	−	0.234255i	−0.737209	+	0.675665i	$0.763857\pi$
$642$	−6.12261	+	1.98936i	−0.241640	+	0.0785137i
$643$		−	22.8328i		−	0.900438i	−0.892918	−	0.450219i	$-0.851346\pi$
$643$		−	22.8328i		−	0.900438i	0.892918	−	0.450219i	$-0.148654\pi$
$644$	−6.66312	−	20.5070i	−0.262564	−	0.808088i
$645$		0			0
$646$	0.854102	−	2.62866i	0.0336042	−	0.103423i
$647$	29.0462	+	9.43769i	1.14193	+	0.371034i	0.818096	−	0.575082i	$-0.195030\pi$
$647$	29.0462	+	9.43769i	1.14193	+	0.371034i	0.323829	+	0.946116i	$0.395030\pi$
$648$	−1.31433	−	1.80902i	−0.0516317	−	0.0710649i
$649$	−3.16718			−0.124323
$650$		0			0
$651$	4.85410			0.190247
$652$	10.4616	+	14.3992i	0.409709	+	0.563916i
$653$	−7.52270	−	2.44427i	−0.294386	−	0.0956518i	0.158101	−	0.987423i	$-0.449463\pi$
$653$	−7.52270	−	2.44427i	−0.294386	−	0.0956518i	−0.452487	+	0.891771i	$0.649463\pi$
$654$	−1.90983	+	5.87785i	−0.0746803	+	0.229842i
$655$		0			0
$656$	−3.00000	−	9.23305i	−0.117130	−	0.360490i
$657$			18.0000i			0.702247i
$658$	1.53884	−	0.500000i	0.0599903	−	0.0194920i
$659$	19.7984	+	14.3844i	0.771235	+	0.560335i	0.902336	−	0.431034i	$-0.141851\pi$
$659$	19.7984	+	14.3844i	0.771235	+	0.560335i	−0.131101	+	0.991369i	$0.541851\pi$
$660$		0			0
$661$	32.9164	−	23.9152i	1.28030	−	0.930192i	0.280738	−	0.959784i	$-0.409421\pi$
$661$	32.9164	−	23.9152i	1.28030	−	0.930192i	0.999562	+	0.0295922i	$0.00942086\pi$
$662$	6.22088	−	8.56231i	0.241781	−	0.332783i
$663$	−2.17963	+	3.00000i	−0.0846497	+	0.116510i
$664$	3.19098	−	2.31838i	0.123834	−	0.0899708i
$665$		0			0
$666$	4.23607	+	3.07768i	0.164144	+	0.119258i
$667$	10.8249	−	3.51722i	0.419142	−	0.136187i
$668$		−	9.00000i		−	0.348220i
$669$	−6.85410	−	21.0948i	−0.264995	−	0.815570i
$670$		0			0
$671$	1.11146	−	3.42071i	0.0429073	−	0.132055i
$672$	−8.64527	−	2.80902i	−0.333498	−	0.108360i
$673$	−5.98385	−	8.23607i	−0.230661	−	0.317477i	0.677961	−	0.735098i	$-0.262864\pi$
$673$	−5.98385	−	8.23607i	−0.230661	−	0.317477i	−0.908621	+	0.417621i	$0.862864\pi$
$674$	−0.708204			−0.0272790
$675$		0			0
$676$	−17.0902			−0.657314
$677$	−4.92680	−	6.78115i	−0.189352	−	0.260621i	0.703777	−	0.710421i	$-0.251495\pi$
$677$	−4.92680	−	6.78115i	−0.189352	−	0.260621i	−0.893129	+	0.449800i	$0.851495\pi$
$678$	−5.96361	−	1.93769i	−0.229031	−	0.0744167i
$679$	1.42705	−	4.39201i	0.0547652	−	0.168550i
$680$		0			0
$681$	5.94427	+	18.2946i	0.227785	+	0.701050i
$682$			1.41641i			0.0542371i
$683$	−4.30625	+	1.39919i	−0.164774	+	0.0535384i	−0.390242	−	0.920712i	$-0.627609\pi$
$683$	−4.30625	+	1.39919i	−0.164774	+	0.0535384i	0.225468	+	0.974251i	$0.427609\pi$
$684$	−15.3262	−	11.1352i	−0.586013	−	0.425764i
$685$		0			0
$686$	−9.20820	+	6.69015i	−0.351571	+	0.255431i
$687$	4.87380	−	6.70820i	0.185947	−	0.255934i
$688$	−2.02063	+	2.78115i	−0.0770356	+	0.106030i
$689$	−21.4894	+	15.6129i	−0.818679	+	0.594805i
$690$		0			0
$691$	−2.20820	−	1.60435i	−0.0840040	−	0.0610325i	0.544991	−	0.838442i	$-0.316533\pi$
$691$	−2.20820	−	1.60435i	−0.0840040	−	0.0610325i	−0.628995	+	0.777410i	$0.716533\pi$
$692$	−25.9888	+	8.44427i	−0.987946	+	0.321003i
$693$			2.47214i			0.0939087i
$694$	5.93769	+	18.2743i	0.225392	+	0.693685i
$695$		0			0
$696$	0.954915	−	2.93893i	0.0361960	−	0.111400i
$697$	3.80423	+	1.23607i	0.144095	+	0.0468194i
$698$	3.01217	+	4.14590i	0.114012	+	0.156925i
$699$	−14.9443			−0.565244
$700$		0			0
$701$	35.0132			1.32243			0.661214	−	0.750197i	$-0.270041\pi$
$701$	35.0132			1.32243			0.661214	+	0.750197i	$0.270041\pi$
$702$	−8.81678	−	12.1353i	−0.332768	−	0.458016i
$703$	23.5847	+	7.66312i	0.889512	+	0.289020i
$704$	−0.0557281	+	0.171513i	−0.00210033	+	0.00646416i
$705$		0			0
$706$	4.60081	+	14.1598i	0.173154	+	0.532913i
$707$			12.0902i			0.454698i
$708$	6.37988	−	2.07295i	0.239771	−	0.0779062i
$709$	27.1353	+	19.7149i	1.01909	+	0.740409i	0.966095	−	0.258186i	$-0.0831247\pi$
$709$	27.1353	+	19.7149i	1.01909	+	0.740409i	0.0529906	+	0.998595i	$0.483125\pi$
$710$		0			0
$711$	5.00000	−	3.63271i	0.187515	−	0.136237i
$712$	−11.7557	+	16.1803i	−0.440564	+	0.606384i
$713$	14.5231	−	19.9894i	0.543895	−	0.748607i
$714$	0.618034	−	0.449028i	0.0231293	−	0.0168044i
$715$		0			0
$716$	−12.3992	−	9.00854i	−0.463379	−	0.336665i
$717$	28.0297	−	9.10739i	1.04679	−	0.340122i
$718$			17.7639i			0.662944i
$719$	11.3435	+	34.9116i	0.423040	+	1.30198i	0.904859	+	0.425712i	$0.139976\pi$
$719$	11.3435	+	34.9116i	0.423040	+	1.30198i	−0.481819	+	0.876271i	$0.660024\pi$
$720$		0			0
$721$	5.78115	−	17.7926i	0.215301	−	0.662630i
$722$	8.97578	+	2.91641i	0.334044	+	0.108537i
$723$	6.74315	+	9.28115i	0.250781	+	0.345170i
$724$	22.1803			0.824326
$725$		0			0
$726$	−6.43769			−0.238925
$727$	−2.60841	−	3.59017i	−0.0967406	−	0.133152i	0.757903	−	0.652368i	$-0.226224\pi$
$727$	−2.60841	−	3.59017i	−0.0967406	−	0.133152i	−0.854643	+	0.519216i	$0.826224\pi$
$728$	16.7027	+	5.42705i	0.619045	+	0.201140i
$729$	−4.01722	+	12.3637i	−0.148786	+	0.457916i
$730$		0			0
$731$	−0.437694	−	1.34708i	−0.0161887	−	0.0498237i
$732$			7.61803i			0.281571i
$733$	25.6583	−	8.33688i	0.947710	−	0.307930i	0.205925	−	0.978568i	$-0.433980\pi$
$733$	25.6583	−	8.33688i	0.947710	−	0.307930i	0.741785	+	0.670638i	$0.233980\pi$
$734$	−2.71885	−	1.97536i	−0.100354	−	0.0729118i
$735$		0			0
$736$	−37.4336	+	27.1971i	−1.37982	+	1.00250i
$737$	−4.14725	+	5.70820i	−0.152766	+	0.210264i
$738$	−3.80423	+	5.23607i	−0.140035	+	0.192742i
$739$	−25.0623	+	18.2088i	−0.921932	+	0.669823i	−0.944004	−	0.329934i	$-0.892974\pi$
$739$	−25.0623	+	18.2088i	−0.921932	+	0.669823i	0.0220723	+	0.999756i	$0.492974\pi$
$740$		0			0
$741$	−22.9894	−	16.7027i	−0.844535	−	0.613591i
$742$	5.20431	−	1.69098i	0.191056	−	0.0620779i
$743$			16.3607i			0.600215i	0.953905	+	0.300108i	$0.0970226\pi$
$743$			16.3607i			0.600215i	−0.953905	+	0.300108i	$0.902977\pi$
$744$	−2.07295	−	6.37988i	−0.0759980	−	0.233898i
$745$		0			0
$746$	1.00658	−	3.09793i	0.0368534	−	0.113423i
$747$	3.35520	+	1.09017i	0.122760	+	0.0398872i
$748$	−0.555029	−	0.763932i	−0.0202939	−	0.0279321i
$749$	16.8541			0.615835
$750$		0			0
$751$	−40.8885			−1.49204			−0.746022	−	0.665921i	$-0.768039\pi$
$751$	−40.8885			−1.49204			−0.746022	+	0.665921i	$0.768039\pi$
$752$	1.76336	+	2.42705i	0.0643030	+	0.0885054i
$753$	6.48588	+	2.10739i	0.236359	+	0.0767976i
$754$	−1.28115	+	3.94298i	−0.0466568	+	0.143595i
$755$		0			0
$756$	−4.04508	−	12.4495i	−0.147118	−	0.452784i
$757$			3.58359i			0.130248i	0.997877	+	0.0651239i	$0.0207443\pi$
$757$			3.58359i			0.130248i	−0.997877	+	0.0651239i	$0.979256\pi$
$758$	−20.3355	+	6.60739i	−0.738617	+	0.239991i
$759$	−5.09017	−	3.69822i	−0.184761	−	0.134237i
$760$		0			0
$761$	−30.2984	+	22.0131i	−1.09832	+	0.797973i	−0.980784	−	0.195096i	$-0.937498\pi$
$761$	−30.2984	+	22.0131i	−1.09832	+	0.797973i	−0.117531	+	0.993069i	$0.537498\pi$
$762$	−5.77185	+	7.94427i	−0.209092	+	0.287791i
$763$	9.51057	−	13.0902i	0.344306	−	0.473896i
$764$	31.6525	−	22.9969i	1.14515	−	0.831998i
$765$		0			0
$766$	5.68034	+	4.12701i	0.205239	+	0.149115i
$767$	−19.1396	+	6.21885i	−0.691092	+	0.224550i
$768$			6.56231i			0.236797i
$769$	4.14590	+	12.7598i	0.149505	+	0.460129i	0.997563	−	0.0697749i	$-0.0222281\pi$
$769$	4.14590	+	12.7598i	0.149505	+	0.460129i	−0.848058	+	0.529904i	$0.822228\pi$
$770$		0			0
$771$	4.98936	−	15.3557i	0.179687	−	0.553021i
$772$	8.78402	+	2.85410i	0.316144	+	0.102721i
$773$	19.4904	+	26.8262i	0.701021	+	0.964873i	0.999944	+	0.0105954i	$0.00337269\pi$
$773$	19.4904	+	26.8262i	0.701021	+	0.964873i	−0.298923	+	0.954277i	$0.596627\pi$
$774$	2.29180			0.0823769
$775$		0			0
$776$	−6.38197			−0.229099
$777$	4.02874	+	5.54508i	0.144530	+	0.198929i
$778$	−8.81678	−	2.86475i	−0.316097	−	0.102706i
$779$	−9.47214	+	29.1522i	−0.339374	+	1.04449i
$780$		0			0
$781$	1.03444	+	3.18368i	0.0370152	+	0.113921i
$782$		−	3.88854i		−	0.139054i
$783$	6.57164	−	2.13525i	0.234851	−	0.0763078i
$784$	−6.57295	−	4.77553i	−0.234748	−	0.170555i
$785$		0			0
$786$	8.89919	−	6.46564i	0.317423	−	0.230622i
$787$	−20.0907	+	27.6525i	−0.716156	+	0.985704i	0.283487	+	0.958976i	$0.408509\pi$
$787$	−20.0907	+	27.6525i	−0.716156	+	0.985704i	−0.999643	+	0.0267281i	$0.991491\pi$
$788$	−9.23305	+	12.7082i	−0.328914	+	0.452711i
$789$	−17.8713	+	12.9843i	−0.636236	+	0.462252i
$790$		0			0
$791$	13.2812	+	9.64932i	0.472223	+	0.343090i
$792$	3.24920	−	1.05573i	0.115455	−	0.0375137i
$793$		−	22.8541i		−	0.811573i
$794$	0.00657781	+	0.0202444i	0.000233438	+	0.000718447i
$795$		0			0
$796$	−1.28115	+	3.94298i	−0.0454093	+	0.139755i
$797$	13.5393	+	4.39919i	0.479587	+	0.155827i	0.538827	−	0.842417i	$-0.318868\pi$
$797$	13.5393	+	4.39919i	0.479587	+	0.155827i	−0.0592400	+	0.998244i	$0.518868\pi$
$798$	3.44095	+	4.73607i	0.121808	+	0.167655i
$799$	−1.23607			−0.0437289
$800$		0			0
$801$	−17.8885			−0.632061
$802$	8.20875	+	11.2984i	0.289861	+	0.398959i
$803$	−6.53888	−	2.12461i	−0.230752	−	0.0749759i
$804$	4.61803	−	14.2128i	0.162866	−	0.501248i
$805$		0			0
$806$	2.78115	+	8.55951i	0.0979619	+	0.301496i
$807$		−	17.2361i		−	0.606738i
$808$	15.8904	−	5.16312i	0.559024	−	0.181638i
$809$	−12.9271	−	9.39205i	−0.454491	−	0.330207i	0.336875	−	0.941549i	$-0.390630\pi$
$809$	−12.9271	−	9.39205i	−0.454491	−	0.330207i	−0.791366	+	0.611342i	$0.790630\pi$
$810$		0			0
$811$	1.04508	−	0.759299i	0.0366979	−	0.0266626i	−0.569285	−	0.822140i	$-0.692780\pi$
$811$	1.04508	−	0.759299i	0.0366979	−	0.0266626i	0.605983	+	0.795478i	$0.292780\pi$
$812$	−2.12663	+	2.92705i	−0.0746300	+	0.102719i
$813$	4.70228	−	6.47214i	0.164916	−	0.226988i
$814$	−1.61803	+	1.17557i	−0.0567121	+	0.0412037i
$815$		0			0
$816$	1.14590	+	0.832544i	0.0401145	+	0.0291449i
$817$	10.3229	−	3.35410i	0.361151	−	0.117345i
$818$		−	17.5623i		−	0.614052i
$819$	4.85410	+	14.9394i	0.169616	+	0.522025i
$820$		0			0
$821$	6.08359	−	18.7234i	0.212319	−	0.653450i	−0.787014	−	0.616935i	$-0.788374\pi$
$821$	6.08359	−	18.7234i	0.212319	−	0.653450i	0.999333	−	0.0365154i	$-0.0116258\pi$
$822$	3.49396	+	1.13525i	0.121866	+	0.0395966i
$823$	20.1562	+	27.7426i	0.702601	+	0.967048i	0.999925	+	0.0122710i	$0.00390607\pi$
$823$	20.1562	+	27.7426i	0.702601	+	0.967048i	−0.297323	+	0.954777i	$0.596094\pi$
$824$	−25.8541			−0.900670
$825$		0			0
$826$	4.14590			0.144254
$827$	17.6538	+	24.2984i	0.613883	+	0.844937i	0.996890	−	0.0788082i	$-0.0251115\pi$
$827$	17.6538	+	24.2984i	0.613883	+	0.844937i	−0.383007	+	0.923745i	$0.625111\pi$
$828$	−25.3480	−	8.23607i	−0.880904	−	0.286223i
$829$	9.00658	−	27.7194i	0.312811	−	0.962734i	−0.663835	−	0.747879i	$-0.731072\pi$
$829$	9.00658	−	27.7194i	0.312811	−	0.962734i	0.976646	−	0.214855i	$-0.0689279\pi$
$830$		0			0
$831$	−3.48936	−	10.7391i	−0.121044	−	0.372537i
$832$			1.14590i			0.0397269i
$833$	3.18368	−	1.03444i	0.110308	−	0.0358413i
$834$	2.50000	+	1.81636i	0.0865679	+	0.0628953i
$835$		0			0
$836$	5.85410	−	4.25325i	0.202468	−	0.147102i
$837$	8.81678	−	12.1353i	0.304752	−	0.419456i
$838$	0.191758	−	0.263932i	0.00662416	−	0.00911738i
$839$	3.35410	−	2.43690i	0.115796	−	0.0841311i	−0.528380	−	0.849008i	$-0.677200\pi$
$839$	3.35410	−	2.43690i	0.115796	−	0.0841311i	0.644176	+	0.764877i	$0.277200\pi$
$840$		0			0
$841$	21.9164	+	15.9232i	0.755738	+	0.549076i
$842$	−18.8091	+	6.11146i	−0.648205	+	0.210615i
$843$			1.09017i			0.0375474i
$844$	6.59017	+	20.2825i	0.226843	+	0.698151i
$845$		0			0
$846$	0.618034	−	1.90211i	0.0212484	−	0.0653960i
$847$	16.0292	+	5.20820i	0.550770	+	0.178956i
$848$	5.96361	+	8.20820i	0.204791	+	0.281871i
$849$	23.1459			0.794365
$850$		0			0
$851$	34.8885			1.19596
$852$	−4.16750	−	5.73607i	−0.142776	−	0.196514i
$853$	−44.9897	−	14.6180i	−1.54042	−	0.500512i	−0.588926	−	0.808187i	$-0.700449\pi$
$853$	−44.9897	−	14.6180i	−1.54042	−	0.500512i	−0.951491	+	0.307675i	$0.900449\pi$
$854$	−1.45492	+	4.47777i	−0.0497862	+	0.153226i
$855$		0			0
$856$	−7.19756	−	22.1518i	−0.246008	−	0.757133i
$857$		−	40.6869i		−	1.38984i	−0.719088	−	0.694919i	$-0.755440\pi$
$857$		−	40.6869i		−	1.38984i	0.719088	−	0.694919i	$-0.244560\pi$
$858$	2.17963	−	0.708204i	0.0744113	−	0.0241777i
$859$	−22.9894	−	16.7027i	−0.784387	−	0.569890i	0.121906	−	0.992542i	$-0.461099\pi$
$859$	−22.9894	−	16.7027i	−0.784387	−	0.569890i	−0.906292	+	0.422651i	$0.861099\pi$
$860$		0			0
$861$	−6.85410	+	4.97980i	−0.233587	+	0.169711i
$862$	8.65778	−	11.9164i	0.294885	−	0.405874i
$863$	24.4297	−	33.6246i	0.831597	−	1.14460i	−0.156027	−	0.987753i	$-0.549869\pi$
$863$	24.4297	−	33.6246i	0.831597	−	1.14460i	0.987624	−	0.156842i	$-0.0501314\pi$
$864$	−22.7254	+	16.5110i	−0.773135	+	0.561715i
$865$		0			0
$866$	−10.0729	−	7.31843i	−0.342293	−	0.248690i
$867$	15.6129	−	5.07295i	0.530243	−	0.172286i
$868$			7.85410i			0.266586i
$869$	0.729490	+	2.24514i	0.0247463	+	0.0761612i
$870$		0			0
$871$	−13.8541	+	42.6385i	−0.469428	+	1.44475i
$872$	−21.2663	−	6.90983i	−0.720167	−	0.233996i
$873$	−3.35520	−	4.61803i	−0.113556	−	0.156297i
$874$	29.7984			1.00795
$875$		0			0
$876$	14.5623			0.492015
$877$	−17.9516	−	24.7082i	−0.606181	−	0.834337i	0.390075	−	0.920783i	$-0.372449\pi$
$877$	−17.9516	−	24.7082i	−0.606181	−	0.834337i	−0.996257	+	0.0864462i	$0.972449\pi$
$878$	−3.51420	−	1.14183i	−0.118598	−	0.0385350i
$879$	8.79837	−	27.0786i	0.296762	−	0.913339i
$880$		0			0
$881$	1.34752	+	4.14725i	0.0453992	+	0.139725i	0.971187	−	0.238320i	$-0.0765967\pi$
$881$	1.34752	+	4.14725i	0.0453992	+	0.139725i	−0.925787	+	0.378044i	$0.876597\pi$
$882$			5.41641i			0.182380i
$883$	−45.0957	+	14.6525i	−1.51759	+	0.493095i	−0.945090	−	0.326809i	$-0.894026\pi$
$883$	−45.0957	+	14.6525i	−1.51759	+	0.493095i	−0.572500	+	0.819904i	$0.694026\pi$
$884$	−4.85410	−	3.52671i	−0.163261	−	0.118616i
$885$		0			0
$886$	−6.02786	+	4.37950i	−0.202510	+	0.147132i
$887$	−3.46120	+	4.76393i	−0.116216	+	0.159957i	−0.863162	−	0.504927i	$-0.831519\pi$
$887$	−3.46120	+	4.76393i	−0.116216	+	0.159957i	0.746946	+	0.664885i	$0.231519\pi$
$888$	5.56758	−	7.66312i	0.186836	−	0.257157i
$889$	20.7984	−	15.1109i	0.697555	−	0.506803i
$890$		0			0
$891$	0.618034	+	0.449028i	0.0207049	+	0.0150430i
$892$	34.1320	−	11.0902i	1.14283	−	0.371326i
$893$		−	9.47214i		−	0.316973i
$894$	−2.66312	−	8.19624i	−0.0890680	−	0.274123i
$895$		0			0
$896$	5.69098	−	17.5150i	0.190122	−	0.585137i
$897$	−38.0220	−	12.3541i	−1.26952	−	0.412491i
$898$	7.38394	+	10.1631i	0.246405	+	0.339148i
$899$	−4.14590			−0.138273
$900$		0			0
$901$	−4.18034			−0.139267
$902$	−1.45309	−	2.00000i	−0.0483824	−	0.0665927i
$903$	2.85317	+	0.927051i	0.0949475	+	0.0308503i
$904$	7.01064	−	21.5765i	0.233171	−	0.717625i
$905$		0			0
$906$	−1.06231	−	3.26944i	−0.0352927	−	0.108620i
$907$			47.2492i			1.56888i	0.620202	+	0.784442i	$0.287051\pi$
$907$			47.2492i			1.56888i	−0.620202	+	0.784442i	$0.712949\pi$
$908$	−29.6013	+	9.61803i	−0.982352	+	0.319186i
$909$	12.0902	+	8.78402i	0.401006	+	0.291348i
$910$		0			0
$911$	28.9336	−	21.0215i	0.958614	−	0.696474i	0.00578548	−	0.999983i	$-0.498158\pi$
$911$	28.9336	−	21.0215i	0.958614	−	0.696474i	0.952828	+	0.303510i	$0.0981584\pi$
$912$	−6.37988	+	8.78115i	−0.211259	+	0.290773i
$913$	−0.792055	+	1.09017i	−0.0262132	+	0.0360794i
$914$	2.70820	−	1.96763i	0.0895794	−	0.0650833i
$915$		0			0
$916$	10.8541	+	7.88597i	0.358630	+	0.260560i
$917$	−27.3889	+	8.89919i	−0.904461	+	0.293877i
$918$		−	2.36068i		−	0.0779140i
$919$	0.551663	+	1.69784i	0.0181977	+	0.0560067i	0.959743	−	0.280880i	$-0.0906262\pi$
$919$	0.551663	+	1.69784i	0.0181977	+	0.0560067i	−0.941545	+	0.336886i	$0.890626\pi$
$920$		0			0
$921$	1.47214	−	4.53077i	0.0485085	−	0.149294i
$922$	13.6251	+	4.42705i	0.448718	+	0.145797i
$923$	12.5025	+	17.2082i	0.411525	+	0.566415i
$924$	2.00000			0.0657952
$925$		0			0
$926$	9.96556			0.327489
$927$	−13.5923	−	18.7082i	−0.446430	−	0.614458i
$928$	7.38394	+	2.39919i	0.242390	+	0.0787572i
$929$	11.3197	−	34.8383i	0.371386	−	1.14301i	−0.574499	−	0.818506i	$-0.694803\pi$
$929$	11.3197	−	34.8383i	0.371386	−	1.14301i	0.945885	−	0.324503i	$-0.105197\pi$
$930$		0			0
$931$	7.92705	+	24.3970i	0.259799	+	0.799578i
$932$		−	24.1803i		−	0.792053i
$933$	−28.0624	+	9.11803i	−0.918722	+	0.298511i
$934$	−14.2254	−	10.3354i	−0.465470	−	0.338184i
$935$		0			0
$936$	17.5623	−	12.7598i	0.574042	−	0.417066i
$937$	30.1360	−	41.4787i	0.984502	−	1.35505i	0.0501333	−	0.998743i	$-0.484035\pi$
$937$	30.1360	−	41.4787i	0.984502	−	1.35505i	0.934369	−	0.356308i	$-0.115965\pi$
$938$	5.42882	−	7.47214i	0.177257	−	0.243974i
$939$	−17.1803	+	12.4822i	−0.560659	+	0.407343i
$940$		0			0
$941$	15.8435	+	11.5109i	0.516482	+	0.375246i	0.815277	−	0.579071i	$-0.196585\pi$
$941$	15.8435	+	11.5109i	0.516482	+	0.375246i	−0.298795	+	0.954317i	$0.596585\pi$
$942$	5.39607	−	1.75329i	0.175813	−	0.0571252i
$943$			43.1246i			1.40433i
$944$	2.37539	+	7.31069i	0.0773123	+	0.237943i
$945$		0			0
$946$	−0.270510	+	0.832544i	−0.00879503	+	0.0270683i
$947$	−27.2501	−	8.85410i	−0.885510	−	0.287720i	−0.169267	−	0.985570i	$-0.554140\pi$
$947$	−27.2501	−	8.85410i	−0.885510	−	0.287720i	−0.716243	+	0.697851i	$0.754140\pi$
$948$	−2.93893	−	4.04508i	−0.0954519	−	0.131378i
$949$	−43.6869			−1.41814
$950$		0			0
$951$	−23.6525			−0.766984
$952$	1.62460	+	2.23607i	0.0526535	+	0.0724714i
$953$	−33.0422	−	10.7361i	−1.07034	−	0.347775i	−0.279721	−	0.960081i	$-0.590242\pi$
$953$	−33.0422	−	10.7361i	−1.07034	−	0.347775i	−0.790621	+	0.612306i	$0.790242\pi$
$954$	2.09017	−	6.43288i	0.0676718	−	0.208272i
$955$		0			0
$956$	14.7361	+	45.3530i	0.476598	+	1.46682i
$957$			1.05573i			0.0341268i
$958$	−2.43690	+	0.791796i	−0.0787326	+	0.0255818i
$959$	−7.78115	−	5.65334i	−0.251267	−	0.182556i
$960$		0			0
$961$	17.7984	−	12.9313i	0.574141	−	0.417138i
$962$	−7.46969	+	10.2812i	−0.240833	+	0.331478i
$963$	12.2452	−	16.8541i	0.394597	−	0.543116i
$964$	−15.0172	+	10.9106i	−0.483672	+	0.351408i
$965$		0			0
$966$	6.66312	+	4.84104i	0.214382	+	0.155758i
$967$	−37.9363	+	12.3262i	−1.21995	+	0.396385i	−0.847063	−	0.531493i	$-0.821631\pi$
$967$	−37.9363	+	12.3262i	−1.21995	+	0.396385i	−0.372885	+	0.927878i	$0.621631\pi$
$968$		−	23.2918i		−	0.748627i
$969$	−1.38197	−	4.25325i	−0.0443951	−	0.136634i
$970$		0			0
$971$	1.04508	−	3.21644i	0.0335384	−	0.103220i	−0.932886	−	0.360172i	$-0.882718\pi$
$971$	1.04508	−	3.21644i	0.0335384	−	0.103220i	0.966424	+	0.256951i	$0.0827180\pi$
$972$	−24.6215	−	8.00000i	−0.789734	−	0.256600i
$973$	−4.75528	−	6.54508i	−0.152447	−	0.209826i
$974$	5.92299			0.189785
$975$		0			0
$976$	−8.72949			−0.279424
$977$	19.7804	+	27.2254i	0.632832	+	0.871019i	0.998208	−	0.0598416i	$-0.0190595\pi$
$977$	19.7804	+	27.2254i	0.632832	+	0.871019i	−0.365376	+	0.930860i	$0.619060\pi$
$978$	−6.46564	−	2.10081i	−0.206748	−	0.0671766i
$979$	2.11146	−	6.49839i	0.0674824	−	0.207690i
$980$		0			0
$981$	−6.18034	−	19.0211i	−0.197323	−	0.607298i
$982$			23.0213i			0.734639i
$983$	7.02067	−	2.28115i	0.223924	−	0.0727575i	−0.194906	−	0.980822i	$-0.562440\pi$
$983$	7.02067	−	2.28115i	0.223924	−	0.0727575i	0.418830	+	0.908064i	$0.362440\pi$
$984$	9.47214	+	6.88191i	0.301961	+	0.219387i
$985$		0			0
$986$	−0.527864	+	0.383516i	−0.0168106	+	0.0122136i
$987$	1.53884	−	2.11803i	0.0489819	−	0.0674178i
$988$	27.0256	−	37.1976i	0.859799	−	1.18341i
$989$	12.3541	−	8.97578i	0.392838	−	0.285413i
$990$		0			0
$991$	−23.7533	−	17.2578i	−0.754548	−	0.548211i	0.142685	−	0.989768i	$-0.454426\pi$
$991$	−23.7533	−	17.2578i	−0.754548	−	0.548211i	−0.897233	+	0.441557i	$0.854426\pi$
$992$	16.0292	−	5.20820i	0.508928	−	0.165361i
$993$		−	17.1246i		−	0.543433i
$994$	−1.35410	−	4.16750i	−0.0429495	−	0.132185i
$995$		0			0
$996$	0.881966	−	2.71441i	0.0279462	−	0.0860094i
$997$	−10.3556	−	3.36475i	−0.327966	−	0.106563i	0.140406	−	0.990094i	$-0.455159\pi$
$997$	−10.3556	−	3.36475i	−0.327966	−	0.106563i	−0.468372	+	0.883531i	$0.655159\pi$
$998$	−4.56352	−	6.28115i	−0.144456	−	0.198826i
$999$	21.1803			0.670116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.e.a.74.1		8
5.2	odd	4		125.2.d.a.51.1		4
5.3	odd	4		25.2.d.a.11.1	✓	4
5.4	even	2	inner	125.2.e.a.74.2		8
15.8	even	4		225.2.h.b.136.1		4
20.3	even	4		400.2.u.b.161.1		4
25.2	odd	20		625.2.d.b.126.1		4
25.3	odd	20		625.2.a.b.1.2		2
25.4	even	10		625.2.b.a.624.2		4
25.6	even	5		625.2.e.c.124.2		8
25.8	odd	20		625.2.d.h.501.1		4
25.9	even	10	inner	125.2.e.a.49.1		8
25.11	even	5		625.2.e.c.499.1		8
25.12	odd	20		125.2.d.a.76.1		4
25.13	odd	20		25.2.d.a.16.1	yes	4
25.14	even	10		625.2.e.c.499.2		8
25.16	even	5	inner	125.2.e.a.49.2		8
25.17	odd	20		625.2.d.b.501.1		4
25.19	even	10		625.2.e.c.124.1		8
25.21	even	5		625.2.b.a.624.3		4
25.22	odd	20		625.2.a.c.1.1		2
25.23	odd	20		625.2.d.h.126.1		4
75.38	even	20		225.2.h.b.91.1		4
75.47	even	20		5625.2.a.d.1.2		2
75.53	even	20		5625.2.a.f.1.1		2
100.3	even	20		10000.2.a.c.1.2		2
100.47	even	20		10000.2.a.l.1.1		2
100.63	even	20		400.2.u.b.241.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	5.3	odd	4
25.2.d.a.16.1	yes	4	25.13	odd	20
125.2.d.a.51.1		4	5.2	odd	4
125.2.d.a.76.1		4	25.12	odd	20
125.2.e.a.49.1		8	25.9	even	10	inner
125.2.e.a.49.2		8	25.16	even	5	inner
125.2.e.a.74.1		8	1.1	even	1	trivial
125.2.e.a.74.2		8	5.4	even	2	inner
225.2.h.b.91.1		4	75.38	even	20
225.2.h.b.136.1		4	15.8	even	4
400.2.u.b.161.1		4	20.3	even	4
400.2.u.b.241.1		4	100.63	even	20
625.2.a.b.1.2		2	25.3	odd	20
625.2.a.c.1.1		2	25.22	odd	20
625.2.b.a.624.2		4	25.4	even	10
625.2.b.a.624.3		4	25.21	even	5
625.2.d.b.126.1		4	25.2	odd	20
625.2.d.b.501.1		4	25.17	odd	20
625.2.d.h.126.1		4	25.23	odd	20
625.2.d.h.501.1		4	25.8	odd	20
625.2.e.c.124.1		8	25.19	even	10
625.2.e.c.124.2		8	25.6	even	5
625.2.e.c.499.1		8	25.11	even	5
625.2.e.c.499.2		8	25.14	even	10
5625.2.a.d.1.2		2	75.47	even	20
5625.2.a.f.1.1		2	75.53	even	20
10000.2.a.c.1.2		2	100.3	even	20
10000.2.a.l.1.1		2	100.47	even	20

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.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.363271 - 0.500000i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.500000 - 1.53884i) q^{4} +(0.190983 + 0.587785i) q^{6} -1.61803i q^{7} +(-2.12663 + 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +(0.618034 - 0.449028i) q^{11} +(-0.951057 + 1.30902i) q^{12} +(2.85317 - 3.92705i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-1.50000 - 1.08981i) q^{16} +(0.726543 - 0.236068i) q^{17} +1.23607i q^{18} +(1.80902 + 5.56758i) q^{19} +(-0.500000 + 1.53884i) q^{21} +(-0.449028 - 0.145898i) q^{22} +(4.84104 + 6.66312i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(2.93893 + 4.04508i) q^{27} +(-2.48990 - 0.809017i) q^{28} +(0.427051 - 1.31433i) q^{29} +(-0.927051 - 2.85317i) q^{31} +5.61803i q^{32} +(-0.726543 + 0.236068i) q^{33} +(-0.381966 - 0.277515i) q^{34} +(-2.61803 + 1.90211i) q^{36} +(2.48990 - 3.42705i) q^{37} +(2.12663 - 2.92705i) q^{38} +(-3.92705 + 2.85317i) q^{39} +(4.23607 + 3.07768i) q^{41} +(0.951057 - 0.309017i) q^{42} -1.85410i q^{43} +(-0.381966 - 1.17557i) q^{44} +(1.57295 - 4.84104i) q^{46} +(-1.53884 - 0.500000i) q^{47} +(1.08981 + 1.50000i) q^{48} +4.38197 q^{49} -0.763932 q^{51} +(-4.61653 - 6.35410i) q^{52} +(-5.20431 - 1.69098i) q^{53} +(0.954915 - 2.93893i) q^{54} +(1.11803 + 3.44095i) q^{56} -5.85410i q^{57} +(-0.812299 + 0.263932i) q^{58} +(-3.35410 - 2.43690i) q^{59} +(3.80902 - 2.76741i) q^{61} +(-1.08981 + 1.50000i) q^{62} +(-1.90211 + 2.61803i) q^{63} +(-0.190983 + 0.138757i) q^{64} +(0.381966 + 0.277515i) q^{66} +(-8.78402 + 2.85410i) q^{67} -1.23607i q^{68} +(-2.54508 - 7.83297i) q^{69} +(-1.35410 + 4.16750i) q^{71} +(4.25325 + 1.38197i) q^{72} +(-5.29007 - 7.28115i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(-0.726543 - 1.00000i) q^{77} +(2.85317 + 0.927051i) q^{78} +(-0.954915 + 2.93893i) q^{79} +(0.309017 + 0.951057i) q^{81} -3.23607i q^{82} +(-1.67760 + 0.545085i) q^{83} +(2.11803 + 1.53884i) q^{84} +(-0.927051 + 0.673542i) q^{86} +(-0.812299 + 1.11803i) q^{87} +(-1.00406 + 1.38197i) q^{88} +(7.23607 - 5.25731i) q^{89} +(-6.35410 - 4.61653i) q^{91} +(12.6740 - 4.11803i) q^{92} +3.00000i q^{93} +(0.309017 + 0.951057i) q^{94} +(1.73607 - 5.34307i) q^{96} +(2.71441 + 0.881966i) q^{97} +(-1.59184 - 2.19098i) q^{98} -1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} - 2 q^{14} - 12 q^{16} + 10 q^{19} - 4 q^{21} - 24 q^{26} - 10 q^{29} + 6 q^{31} - 12 q^{34} - 12 q^{36} - 18 q^{39} + 16 q^{41} - 12 q^{44} + 26 q^{46} + 44 q^{49}+ \cdots - 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 - 2 * q^14 - 12 * q^16 + 10 * q^19 - 4 * q^21 - 24 * q^26 - 10 * q^29 + 6 * q^31 - 12 * q^34 - 12 * q^36 - 18 * q^39 + 16 * q^41 - 12 * q^44 + 26 * q^46 + 44 * q^49 - 24 * q^51 + 30 * q^54 + 26 * q^61 - 6 * q^64 + 12 * q^66 + 2 * q^69 + 16 * q^71 - 12 * q^74 + 40 * q^76 - 30 * q^79 - 2 * q^81 + 8 * q^84 + 6 * q^86 + 40 * q^89 - 24 * q^91 - 2 * q^94 - 4 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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