LMFDB - Embedded newform 125.2.d.a.76.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			76.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	125.76
Dual form			125.2.d.a.51.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.190983 - 0.587785i) q^{6} +1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +(1.61803 - 1.17557i) q^{9} +(0.618034 + 0.449028i) q^{11} +(-1.30902 + 0.951057i) q^{12} +(-3.92705 + 2.85317i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(0.236068 - 0.726543i) q^{17} +1.23607 q^{18} +(-1.80902 + 5.56758i) q^{19} +(-0.500000 - 1.53884i) q^{21} +(0.145898 + 0.449028i) q^{22} +(6.66312 + 4.84104i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-4.04508 - 2.93893i) q^{27} +(-0.809017 - 2.48990i) q^{28} +(-0.427051 - 1.31433i) q^{29} +(-0.927051 + 2.85317i) q^{31} -5.61803 q^{32} +(0.236068 - 0.726543i) q^{33} +(0.381966 - 0.277515i) q^{34} +(-2.61803 - 1.90211i) q^{36} +(3.42705 - 2.48990i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(3.92705 + 2.85317i) q^{39} +(4.23607 - 3.07768i) q^{41} +(0.309017 - 0.951057i) q^{42} -1.85410 q^{43} +(0.381966 - 1.17557i) q^{44} +(1.57295 + 4.84104i) q^{46} +(0.500000 + 1.53884i) q^{47} +(1.50000 + 1.08981i) q^{48} -4.38197 q^{49} -0.763932 q^{51} +(6.35410 + 4.61653i) q^{52} +(-1.69098 - 5.20431i) q^{53} +(-0.954915 - 2.93893i) q^{54} +(1.11803 - 3.44095i) q^{56} +5.85410 q^{57} +(0.263932 - 0.812299i) q^{58} +(3.35410 - 2.43690i) q^{59} +(3.80902 + 2.76741i) q^{61} +(-1.50000 + 1.08981i) q^{62} +(2.61803 - 1.90211i) q^{63} +(0.190983 + 0.138757i) q^{64} +(0.381966 - 0.277515i) q^{66} +(-2.85410 + 8.78402i) q^{67} -1.23607 q^{68} +(2.54508 - 7.83297i) q^{69} +(-1.35410 - 4.16750i) q^{71} +(-1.38197 - 4.25325i) q^{72} +(-7.28115 - 5.29007i) q^{73} +2.61803 q^{74} +9.47214 q^{76} +(1.00000 + 0.726543i) q^{77} +(0.927051 + 2.85317i) q^{78} +(0.954915 + 2.93893i) q^{79} +(0.309017 - 0.951057i) q^{81} +3.23607 q^{82} +(0.545085 - 1.67760i) q^{83} +(-2.11803 + 1.53884i) q^{84} +(-0.927051 - 0.673542i) q^{86} +(-1.11803 + 0.812299i) q^{87} +(1.38197 - 1.00406i) q^{88} +(-7.23607 - 5.25731i) q^{89} +(-6.35410 + 4.61653i) q^{91} +(4.11803 - 12.6740i) q^{92} +3.00000 q^{93} +(-0.309017 + 0.951057i) q^{94} +(1.73607 + 5.34307i) q^{96} +(-0.881966 - 2.71441i) q^{97} +(-2.19098 - 1.59184i) q^{98} +1.52786 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{7} + 5 q^{8} + 2 q^{9} - 2 q^{11} - 3 q^{12} - 9 q^{13} + q^{14} - 6 q^{16} - 8 q^{17} - 4 q^{18} - 5 q^{19} - 2 q^{21} + 14 q^{22} + 11 q^{23} - 12 q^{26}+ \cdots + 24 q^{99}+O(q^{100})$ 4 * q + 2 * q^2 + q^3 - 2 * q^4 + 3 * q^6 + 2 * q^7 + 5 * q^8 + 2 * q^9 - 2 * q^11 - 3 * q^12 - 9 * q^13 + q^14 - 6 * q^16 - 8 * q^17 - 4 * q^18 - 5 * q^19 - 2 * q^21 + 14 * q^22 + 11 * q^23 - 12 * q^26 - 5 * q^27 - q^28 + 5 * q^29 + 3 * q^31 - 18 * q^32 - 8 * q^33 + 6 * q^34 - 6 * q^36 + 7 * q^37 - 5 * q^38 + 9 * q^39 + 8 * q^41 - q^42 + 6 * q^43 + 6 * q^44 + 13 * q^46 + 2 * q^47 + 6 * q^48 - 22 * q^49 - 12 * q^51 + 12 * q^52 - 9 * q^53 - 15 * q^54 + 10 * q^57 + 10 * q^58 + 13 * q^61 - 6 * q^62 + 6 * q^63 + 3 * q^64 + 6 * q^66 + 2 * q^67 + 4 * q^68 - q^69 + 8 * q^71 - 10 * q^72 - 9 * q^73 + 6 * q^74 + 20 * q^76 + 4 * q^77 - 3 * q^78 + 15 * q^79 - q^81 + 4 * q^82 - 9 * q^83 - 4 * q^84 + 3 * q^86 + 10 * q^88 - 20 * q^89 - 12 * q^91 + 12 * q^92 + 12 * q^93 + q^94 - 2 * q^96 - 8 * q^97 - 11 * q^98 + 24 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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

)

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

$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	0.750358	−	0.661031i	$-0.229881\pi$
$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	−0.396805	+	0.917903i	$0.629881\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i	0.821362	−	0.570408i	$-0.193215\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i	−0.999773	+	0.0213149i	$0.993215\pi$
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$		0			0
$5$		0			0
$6$	0.190983	−	0.587785i	0.0779685	−	0.239962i
$7$	1.61803			0.611559			0.305780	−	0.952102i	$-0.401083\pi$
$7$	1.61803			0.611559			0.305780	+	0.952102i	$0.401083\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	1.61803	−	1.17557i	0.539345	−	0.391857i
$10$		0			0
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	0.677046	−	0.735940i	$-0.263260\pi$
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	−0.490702	+	0.871327i	$0.663260\pi$
$12$	−1.30902	+	0.951057i	−0.377881	+	0.274546i
$13$	−3.92705	+	2.85317i	−1.08917	+	0.791327i	−0.979259	−	0.202615i	$-0.935056\pi$
$13$	−3.92705	+	2.85317i	−1.08917	+	0.791327i	−0.109909	+	0.993942i	$0.535056\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$		0			0
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	0.236068	−	0.726543i	0.0572549	−	0.176212i	−0.918339	−	0.395794i	$-0.870469\pi$
$17$	0.236068	−	0.726543i	0.0572549	−	0.176212i	0.975594	+	0.219582i	$0.0704693\pi$
$18$	1.23607			0.291344
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	0.497219	+	0.867625i	$0.334355\pi$
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	−0.912236	+	0.409666i	$0.865645\pi$
$20$		0			0
$21$	−0.500000	−	1.53884i	−0.109109	−	0.335803i
$22$	0.145898	+	0.449028i	0.0311056	+	0.0957331i
$23$	6.66312	+	4.84104i	1.38936	+	1.00943i	0.995936	+	0.0900679i	$0.0287084\pi$
$23$	6.66312	+	4.84104i	1.38936	+	1.00943i	0.393421	+	0.919359i	$0.371292\pi$
$24$	−2.23607			−0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	−4.04508	−	2.93893i	−0.778477	−	0.565597i
$28$	−0.809017	−	2.48990i	−0.152890	−	0.470547i
$29$	−0.427051	−	1.31433i	−0.0793014	−	0.244065i	0.903544	−	0.428495i	$-0.140956\pi$
$29$	−0.427051	−	1.31433i	−0.0793014	−	0.244065i	−0.982846	+	0.184430i	$0.940956\pi$
$30$		0			0
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	−0.999144	−	0.0413693i	$-0.986828\pi$
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	0.832641	+	0.553814i	$0.186828\pi$
$32$	−5.61803			−0.993137
$33$	0.236068	−	0.726543i	0.0410942	−	0.126475i
$34$	0.381966	−	0.277515i	0.0655066	−	0.0475934i
$35$		0			0
$36$	−2.61803	−	1.90211i	−0.436339	−	0.317019i
$37$	3.42705	−	2.48990i	0.563404	−	0.409337i	−0.269299	−	0.963057i	$-0.586792\pi$
$37$	3.42705	−	2.48990i	0.563404	−	0.409337i	0.832703	+	0.553720i	$0.186792\pi$
$38$	−2.92705	+	2.12663i	−0.474830	+	0.344984i
$39$	3.92705	+	2.85317i	0.628831	+	0.456873i
$40$		0			0
$41$	4.23607	−	3.07768i	0.661563	−	0.480653i	−0.205628	−	0.978630i	$-0.565924\pi$
$41$	4.23607	−	3.07768i	0.661563	−	0.480653i	0.867190	+	0.497977i	$0.165924\pi$
$42$	0.309017	−	0.951057i	0.0476824	−	0.146751i
$43$	−1.85410			−0.282748			−0.141374	−	0.989956i	$-0.545152\pi$
$43$	−1.85410			−0.282748			−0.141374	+	0.989956i	$0.545152\pi$
$44$	0.381966	−	1.17557i	0.0575835	−	0.177224i
$45$		0			0
$46$	1.57295	+	4.84104i	0.231919	+	0.713772i
$47$	0.500000	+	1.53884i	0.0729325	+	0.224463i	0.980877	−	0.194626i	$-0.0623494\pi$
$47$	0.500000	+	1.53884i	0.0729325	+	0.224463i	−0.907945	+	0.419089i	$0.862349\pi$
$48$	1.50000	+	1.08981i	0.216506	+	0.157301i
$49$	−4.38197			−0.625995
$50$		0			0
$51$	−0.763932			−0.106972
$52$	6.35410	+	4.61653i	0.881155	+	0.640197i
$53$	−1.69098	−	5.20431i	−0.232274	−	0.714867i	−0.997471	−	0.0710707i	$-0.977358\pi$
$53$	−1.69098	−	5.20431i	−0.232274	−	0.714867i	0.765197	−	0.643796i	$-0.222642\pi$
$54$	−0.954915	−	2.93893i	−0.129947	−	0.399937i
$55$		0			0
$56$	1.11803	−	3.44095i	0.149404	−	0.459817i
$57$	5.85410			0.775395
$58$	0.263932	−	0.812299i	0.0346560	−	0.106660i
$59$	3.35410	−	2.43690i	0.436667	−	0.317257i	−0.347642	−	0.937627i	$-0.613018\pi$
$59$	3.35410	−	2.43690i	0.436667	−	0.317257i	0.784309	+	0.620370i	$0.213018\pi$
$60$		0			0
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	0.804297	−	0.594227i	$-0.202542\pi$
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	−0.316602	+	0.948558i	$0.602542\pi$
$62$	−1.50000	+	1.08981i	−0.190500	+	0.138406i
$63$	2.61803	−	1.90211i	0.329841	−	0.239644i
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$		0			0
$66$	0.381966	−	0.277515i	0.0470168	−	0.0341597i
$67$	−2.85410	+	8.78402i	−0.348684	+	1.07314i	0.610898	+	0.791709i	$0.290809\pi$
$67$	−2.85410	+	8.78402i	−0.348684	+	1.07314i	−0.959582	+	0.281430i	$0.909191\pi$
$68$	−1.23607			−0.149895
$69$	2.54508	−	7.83297i	0.306392	−	0.942978i
$70$		0			0
$71$	−1.35410	−	4.16750i	−0.160702	−	0.494591i	0.837992	−	0.545683i	$-0.183730\pi$
$71$	−1.35410	−	4.16750i	−0.160702	−	0.494591i	−0.998694	+	0.0510922i	$0.983730\pi$
$72$	−1.38197	−	4.25325i	−0.162866	−	0.501251i
$73$	−7.28115	−	5.29007i	−0.852194	−	0.619156i	0.0735557	−	0.997291i	$-0.476565\pi$
$73$	−7.28115	−	5.29007i	−0.852194	−	0.619156i	−0.925750	+	0.378136i	$0.876565\pi$
$74$	2.61803			0.304340
$75$		0			0
$76$	9.47214			1.08653
$77$	1.00000	+	0.726543i	0.113961	+	0.0827972i
$78$	0.927051	+	2.85317i	0.104968	+	0.323058i
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	0.990295	−	0.138985i	$-0.0443839\pi$
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	−0.882858	+	0.469640i	$0.844384\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.23607			0.357364
$83$	0.545085	−	1.67760i	0.0598308	−	0.184140i	−0.916674	−	0.399636i	$-0.869137\pi$
$83$	0.545085	−	1.67760i	0.0598308	−	0.184140i	0.976505	+	0.215495i	$0.0691366\pi$
$84$	−2.11803	+	1.53884i	−0.231096	+	0.167901i
$85$		0			0
$86$	−0.927051	−	0.673542i	−0.0999665	−	0.0726299i
$87$	−1.11803	+	0.812299i	−0.119866	+	0.0870876i
$88$	1.38197	−	1.00406i	0.147318	−	0.107033i
$89$	−7.23607	−	5.25731i	−0.767022	−	0.557274i	0.134034	−	0.990977i	$-0.457207\pi$
$89$	−7.23607	−	5.25731i	−0.767022	−	0.557274i	−0.901056	+	0.433703i	$0.857207\pi$
$90$		0			0
$91$	−6.35410	+	4.61653i	−0.666091	+	0.483943i
$92$	4.11803	−	12.6740i	0.429335	−	1.32136i
$93$	3.00000			0.311086
$94$	−0.309017	+	0.951057i	−0.0318727	+	0.0980940i
$95$		0			0
$96$	1.73607	+	5.34307i	0.177187	+	0.545325i
$97$	−0.881966	−	2.71441i	−0.0895501	−	0.275607i	0.896245	−	0.443559i	$-0.146284\pi$
$97$	−0.881966	−	2.71441i	−0.0895501	−	0.275607i	−0.985795	+	0.167953i	$0.946284\pi$
$98$	−2.19098	−	1.59184i	−0.221323	−	0.160800i
$99$	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	$0.621243\pi$
$102$	−0.381966	−	0.277515i	−0.0378203	−	0.0274780i
$103$	3.57295	+	10.9964i	0.352053	+	1.08351i	0.957699	+	0.287773i	$0.0929150\pi$
$103$	3.57295	+	10.9964i	0.352053	+	1.08351i	−0.605645	+	0.795735i	$0.707085\pi$
$104$	3.35410	+	10.3229i	0.328897	+	1.01224i
$105$		0			0
$106$	1.04508	−	3.21644i	0.101508	−	0.312408i
$107$	−10.4164			−1.00699			−0.503496	−	0.863998i	$-0.667953\pi$
$107$	−10.4164			−1.00699			−0.503496	+	0.863998i	$0.667953\pi$
$108$	−2.50000	+	7.69421i	−0.240563	+	0.740376i
$109$	−8.09017	+	5.87785i	−0.774898	+	0.562996i	−0.903443	−	0.428707i	$-0.858969\pi$
$109$	−8.09017	+	5.87785i	−0.774898	+	0.562996i	0.128546	+	0.991704i	$0.458969\pi$
$110$		0			0
$111$	−3.42705	−	2.48990i	−0.325281	−	0.236331i
$112$	−2.42705	+	1.76336i	−0.229335	+	0.166621i
$113$	8.20820	−	5.96361i	0.772163	−	0.561009i	−0.130454	−	0.991454i	$-0.541643\pi$
$113$	8.20820	−	5.96361i	0.772163	−	0.561009i	0.902617	+	0.430445i	$0.141643\pi$
$114$	2.92705	+	2.12663i	0.274143	+	0.199177i
$115$		0			0
$116$	−1.80902	+	1.31433i	−0.167963	+	0.122032i
$117$	−3.00000	+	9.23305i	−0.277350	+	0.853596i
$118$	2.56231			0.235879
$119$	0.381966	−	1.17557i	0.0350148	−	0.107764i
$120$		0			0
$121$	−3.21885	−	9.90659i	−0.292622	−	0.900599i
$122$	0.899187	+	2.76741i	0.0814086	+	0.250550i
$123$	−4.23607	−	3.07768i	−0.381953	−	0.277505i
$124$	4.85410			0.435911
$125$		0			0
$126$	2.00000			0.178174
$127$	−12.8541	−	9.33905i	−1.14062	−	0.828707i	−0.153412	−	0.988162i	$-0.549026\pi$
$127$	−12.8541	−	9.33905i	−1.14062	−	0.828707i	−0.987205	+	0.159455i	$0.949026\pi$
$128$	3.51722	+	10.8249i	0.310881	+	0.956794i
$129$	0.572949	+	1.76336i	0.0504453	+	0.155255i
$130$		0			0
$131$	−5.50000	+	16.9273i	−0.480537	+	1.47894i	0.357805	+	0.933797i	$0.383525\pi$
$131$	−5.50000	+	16.9273i	−0.480537	+	1.47894i	−0.838342	+	0.545145i	$0.816475\pi$
$132$	−1.23607			−0.107586
$133$	−2.92705	+	9.00854i	−0.253808	+	0.781139i
$134$	−4.61803	+	3.35520i	−0.398937	+	0.289845i
$135$		0			0
$136$	−1.38197	−	1.00406i	−0.118503	−	0.0860972i
$137$	4.80902	−	3.49396i	0.410862	−	0.298509i	−0.363089	−	0.931755i	$-0.618278\pi$
$137$	4.80902	−	3.49396i	0.410862	−	0.298509i	0.773951	+	0.633246i	$0.218278\pi$
$138$	4.11803	−	2.99193i	0.350550	−	0.254690i
$139$	−4.04508	−	2.93893i	−0.343100	−	0.249276i	0.402869	−	0.915258i	$-0.368013\pi$
$139$	−4.04508	−	2.93893i	−0.343100	−	0.249276i	−0.745968	+	0.665981i	$0.768013\pi$
$140$		0			0
$141$	1.30902	−	0.951057i	0.110239	−	0.0800934i
$142$	0.836881	−	2.57565i	0.0702295	−	0.216144i
$143$	−3.70820			−0.310096
$144$	−1.14590	+	3.52671i	−0.0954915	+	0.293893i
$145$		0			0
$146$	−1.71885	−	5.29007i	−0.142253	−	0.437809i
$147$	1.35410	+	4.16750i	0.111684	+	0.343729i
$148$	−5.54508	−	4.02874i	−0.455803	−	0.331160i
$149$	13.9443			1.14236			0.571180	−	0.820825i	$-0.306486\pi$
$149$	13.9443			1.14236			0.571180	+	0.820825i	$0.306486\pi$
$150$		0			0
$151$	−5.56231			−0.452654			−0.226327	−	0.974051i	$-0.572672\pi$
$151$	−5.56231			−0.452654			−0.226327	+	0.974051i	$0.572672\pi$
$152$	10.5902	+	7.69421i	0.858976	+	0.624083i
$153$	−0.472136	−	1.45309i	−0.0381699	−	0.117475i
$154$	0.236068	+	0.726543i	0.0190229	+	0.0585465i
$155$		0			0
$156$	2.42705	−	7.46969i	0.194320	−	0.598054i
$157$	9.18034			0.732671			0.366335	−	0.930483i	$-0.380612\pi$
$157$	9.18034			0.732671			0.366335	+	0.930483i	$0.380612\pi$
$158$	−0.590170	+	1.81636i	−0.0469514	+	0.144502i
$159$	−4.42705	+	3.21644i	−0.351088	+	0.255080i
$160$		0			0
$161$	10.7812	+	7.83297i	0.849674	+	0.617324i
$162$	0.500000	−	0.363271i	0.0392837	−	0.0285413i
$163$	8.89919	−	6.46564i	0.697038	−	0.506428i	−0.181928	−	0.983312i	$-0.558234\pi$
$163$	8.89919	−	6.46564i	0.697038	−	0.506428i	0.878966	+	0.476884i	$0.158234\pi$
$164$	−6.85410	−	4.97980i	−0.535215	−	0.388857i
$165$		0			0
$166$	0.881966	−	0.640786i	0.0684538	−	0.0497346i
$167$	1.71885	−	5.29007i	0.133008	−	0.409358i	−0.862267	−	0.506455i	$-0.830956\pi$
$167$	1.71885	−	5.29007i	0.133008	−	0.409358i	0.995275	+	0.0970971i	$0.0309557\pi$
$168$	−3.61803			−0.279137
$169$	3.26393	−	10.0453i	0.251072	−	0.772719i
$170$		0			0
$171$	3.61803	+	11.1352i	0.276678	+	0.851527i
$172$	0.927051	+	2.85317i	0.0706870	+	0.217552i
$173$	−13.6631	−	9.92684i	−1.03879	−	0.754723i	−0.0687392	−	0.997635i	$-0.521898\pi$
$173$	−13.6631	−	9.92684i	−1.03879	−	0.754723i	−0.970049	+	0.242911i	$0.921898\pi$
$174$	−0.854102			−0.0647493
$175$		0			0
$176$	−1.41641			−0.106766
$177$	−3.35410	−	2.43690i	−0.252110	−	0.183168i
$178$	−1.70820	−	5.25731i	−0.128035	−	0.394052i
$179$	−2.92705	−	9.00854i	−0.218778	−	0.673330i	−0.998864	−	0.0476570i	$-0.984825\pi$
$179$	−2.92705	−	9.00854i	−0.218778	−	0.673330i	0.780086	−	0.625673i	$-0.215175\pi$
$180$		0			0
$181$	4.23607	−	13.0373i	0.314864	−	0.969053i	−0.660946	−	0.750434i	$-0.729845\pi$
$181$	4.23607	−	13.0373i	0.314864	−	0.969053i	0.975810	−	0.218619i	$-0.0701553\pi$
$182$	−4.85410			−0.359810
$183$	1.45492	−	4.47777i	0.107550	−	0.331006i
$184$	14.8992	−	10.8249i	1.09838	−	0.798022i
$185$		0			0
$186$	1.50000	+	1.08981i	0.109985	+	0.0799090i
$187$	0.472136	−	0.343027i	0.0345260	−	0.0250846i
$188$	2.11803	−	1.53884i	0.154474	−	0.112232i
$189$	−6.54508	−	4.75528i	−0.476085	−	0.345896i
$190$		0			0
$191$	19.5623	−	14.2128i	1.41548	−	1.02841i	0.422982	−	0.906138i	$-0.360984\pi$
$191$	19.5623	−	14.2128i	1.41548	−	1.02841i	0.992497	−	0.122267i	$-0.0390165\pi$
$192$	0.0729490	−	0.224514i	0.00526464	−	0.0162029i
$193$	5.70820			0.410886			0.205443	−	0.978669i	$-0.434137\pi$
$193$	5.70820			0.410886			0.205443	+	0.978669i	$0.434137\pi$
$194$	0.545085	−	1.67760i	0.0391348	−	0.120445i
$195$		0			0
$196$	2.19098	+	6.74315i	0.156499	+	0.481654i
$197$	3.00000	+	9.23305i	0.213741	+	0.657828i	0.999241	+	0.0389652i	$0.0124062\pi$
$197$	3.00000	+	9.23305i	0.213741	+	0.657828i	−0.785499	+	0.618862i	$0.787594\pi$
$198$	0.763932	+	0.555029i	0.0542903	+	0.0394442i
$199$	2.56231			0.181637			0.0908185	−	0.995867i	$-0.471052\pi$
$199$	2.56231			0.181637			0.0908185	+	0.995867i	$0.471052\pi$
$200$		0			0
$201$	9.23607			0.651462
$202$	−3.73607	−	2.71441i	−0.262869	−	0.190985i
$203$	−0.690983	−	2.12663i	−0.0484975	−	0.149260i
$204$	0.381966	+	1.17557i	0.0267430	+	0.0823064i
$205$		0			0
$206$	−2.20820	+	6.79615i	−0.153853	+	0.473510i
$207$	16.4721			1.14489
$208$	2.78115	−	8.55951i	0.192838	−	0.593495i
$209$	−3.61803	+	2.62866i	−0.250265	+	0.181828i
$210$		0			0
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	0.156772	−	0.987635i	$-0.449891\pi$
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	−0.890851	+	0.454295i	$0.849891\pi$
$212$	−7.16312	+	5.20431i	−0.491965	+	0.357434i
$213$	−3.54508	+	2.57565i	−0.242905	+	0.176481i
$214$	−5.20820	−	3.78398i	−0.356025	−	0.258668i
$215$		0			0
$216$	−9.04508	+	6.57164i	−0.615440	+	0.447143i
$217$	−1.50000	+	4.61653i	−0.101827	+	0.313390i
$218$	−6.18034			−0.418585
$219$	−2.78115	+	8.55951i	−0.187933	+	0.578398i
$220$		0			0
$221$	1.14590	+	3.52671i	0.0770814	+	0.237232i
$222$	−0.809017	−	2.48990i	−0.0542977	−	0.167111i
$223$	17.9443	+	13.0373i	1.20164	+	0.873041i	0.994445	−	0.105260i	$-0.0335673\pi$
$223$	17.9443	+	13.0373i	1.20164	+	0.873041i	0.207193	+	0.978300i	$0.433567\pi$
$224$	−9.09017			−0.607363
$225$		0			0
$226$	6.27051			0.417108
$227$	15.5623	+	11.3067i	1.03291	+	0.750451i	0.968888	−	0.247498i	$-0.0796084\pi$
$227$	15.5623	+	11.3067i	1.03291	+	0.750451i	0.0640182	+	0.997949i	$0.479608\pi$
$228$	−2.92705	−	9.00854i	−0.193849	−	0.596605i
$229$	2.56231	+	7.88597i	0.169322	+	0.521119i	0.999329	−	0.0366339i	$-0.0116635\pi$
$229$	2.56231	+	7.88597i	0.169322	+	0.521119i	−0.830007	+	0.557753i	$0.811664\pi$
$230$		0			0
$231$	0.381966	−	1.17557i	0.0251315	−	0.0773469i
$232$	−3.09017			−0.202880
$233$	−4.61803	+	14.2128i	−0.302537	+	0.931115i	0.678047	+	0.735018i	$0.262826\pi$
$233$	−4.61803	+	14.2128i	−0.302537	+	0.931115i	−0.980585	+	0.196096i	$0.937174\pi$
$234$	−4.85410	+	3.52671i	−0.317323	+	0.230548i
$235$		0			0
$236$	−5.42705	−	3.94298i	−0.353271	−	0.256666i
$237$	2.50000	−	1.81636i	0.162392	−	0.117985i
$238$	0.618034	−	0.449028i	0.0400612	−	0.0291062i
$239$	23.8435	+	17.3233i	1.54231	+	1.12055i	0.948869	+	0.315669i	$0.102229\pi$
$239$	23.8435	+	17.3233i	1.54231	+	1.12055i	0.593436	+	0.804881i	$0.297771\pi$
$240$		0			0
$241$	−9.28115	+	6.74315i	−0.597852	+	0.434365i	−0.845116	−	0.534584i	$-0.820468\pi$
$241$	−9.28115	+	6.74315i	−0.597852	+	0.434365i	0.247264	+	0.968948i	$0.420468\pi$
$242$	1.98936	−	6.12261i	0.127881	−	0.393576i
$243$	−16.0000			−1.02640
$244$	2.35410	−	7.24518i	0.150706	−	0.463825i
$245$		0			0
$246$	−1.00000	−	3.07768i	−0.0637577	−	0.196226i
$247$	−8.78115	−	27.0256i	−0.558731	−	1.71960i
$248$	5.42705	+	3.94298i	0.344618	+	0.250380i
$249$	−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	$0.569049\pi$
$252$	−4.23607	−	3.07768i	−0.266847	−	0.193876i
$253$	1.94427	+	5.98385i	0.122235	+	0.376202i
$254$	−3.03444	−	9.33905i	−0.190398	−	0.585984i
$255$		0			0
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	−16.1459			−1.00715			−0.503577	−	0.863951i	$-0.667983\pi$
$257$	−16.1459			−1.00715			−0.503577	+	0.863951i	$0.667983\pi$
$258$	−0.354102	+	1.08981i	−0.0220454	+	0.0678488i
$259$	5.54508	−	4.02874i	0.344555	−	0.250334i
$260$		0			0
$261$	−2.23607	−	1.62460i	−0.138409	−	0.100560i
$262$	−8.89919	+	6.46564i	−0.549794	+	0.399448i
$263$	−17.8713	+	12.9843i	−1.10199	+	0.800645i	−0.981384	−	0.192055i	$-0.938485\pi$
$263$	−17.8713	+	12.9843i	−1.10199	+	0.800645i	−0.120609	+	0.992700i	$0.538485\pi$
$264$	−1.38197	−	1.00406i	−0.0850541	−	0.0617954i
$265$		0			0
$266$	−4.73607	+	3.44095i	−0.290387	+	0.210978i
$267$	−2.76393	+	8.50651i	−0.169150	+	0.520590i
$268$	14.9443			0.912867
$269$	−5.32624	+	16.3925i	−0.324746	+	0.999467i	0.646808	+	0.762652i	$0.276103\pi$
$269$	−5.32624	+	16.3925i	−0.324746	+	0.999467i	−0.971555	+	0.236814i	$0.923897\pi$
$270$		0			0
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	0.847468	−	0.530846i	$-0.178126\pi$
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	−0.997640	+	0.0686657i	$0.978126\pi$
$272$	0.437694	+	1.34708i	0.0265391	+	0.0816790i
$273$	6.35410	+	4.61653i	0.384568	+	0.279405i
$274$	3.67376			0.221940
$275$		0			0
$276$	−13.3262			−0.802145
$277$	−9.13525	−	6.63715i	−0.548884	−	0.398788i	0.278490	−	0.960439i	$-0.410166\pi$
$277$	−9.13525	−	6.63715i	−0.548884	−	0.398788i	−0.827374	+	0.561651i	$0.810166\pi$
$278$	−0.954915	−	2.93893i	−0.0572720	−	0.176265i
$279$	1.85410	+	5.70634i	0.111002	+	0.341630i
$280$		0			0
$281$	−0.336881	+	1.03681i	−0.0200966	+	0.0618511i	−0.960602	−	0.277928i	$-0.910352\pi$
$281$	−0.336881	+	1.03681i	−0.0200966	+	0.0618511i	0.940505	+	0.339779i	$0.110352\pi$
$282$	1.00000			0.0595491
$283$	7.15248	−	22.0131i	0.425171	−	1.30854i	−0.477660	−	0.878545i	$-0.658515\pi$
$283$	7.15248	−	22.0131i	0.425171	−	1.30854i	0.902831	−	0.429996i	$-0.141485\pi$
$284$	−5.73607	+	4.16750i	−0.340373	+	0.247295i
$285$		0			0
$286$	−1.85410	−	1.34708i	−0.109635	−	0.0796547i
$287$	6.85410	−	4.97980i	0.404585	−	0.293948i
$288$	−9.09017	+	6.60440i	−0.535643	+	0.389168i
$289$	13.2812	+	9.64932i	0.781244	+	0.567607i
$290$		0			0
$291$	−2.30902	+	1.67760i	−0.135357	+	0.0983426i
$292$	−4.50000	+	13.8496i	−0.263343	+	0.810485i
$293$	28.4721			1.66336			0.831680	−	0.555255i	$-0.187379\pi$
$293$	28.4721			1.66336			0.831680	+	0.555255i	$0.187379\pi$
$294$	−0.836881	+	2.57565i	−0.0488079	+	0.150215i
$295$		0			0
$296$	−2.92705	−	9.00854i	−0.170131	−	0.523611i
$297$	−1.18034	−	3.63271i	−0.0684903	−	0.210791i
$298$	6.97214	+	5.06555i	0.403885	+	0.293440i
$299$	−39.9787			−2.31203
$300$		0			0
$301$	−3.00000			−0.172917
$302$	−2.78115	−	2.02063i	−0.160037	−	0.116274i
$303$	2.30902	+	7.10642i	0.132650	+	0.408253i
$304$	−3.35410	−	10.3229i	−0.192371	−	0.592057i
$305$		0			0
$306$	0.291796	−	0.898056i	0.0166809	−	0.0513384i
$307$	−4.76393			−0.271892			−0.135946	−	0.990716i	$-0.543407\pi$
$307$	−4.76393			−0.271892			−0.135946	+	0.990716i	$0.543407\pi$
$308$	0.618034	−	1.90211i	0.0352158	−	0.108383i
$309$	9.35410	−	6.79615i	0.532136	−	0.386620i
$310$		0			0
$311$	23.8713	+	17.3435i	1.35362	+	0.983461i	0.998822	+	0.0485178i	$0.0154498\pi$
$311$	23.8713	+	17.3435i	1.35362	+	0.983461i	0.354796	+	0.934944i	$0.384550\pi$
$312$	8.78115	−	6.37988i	0.497135	−	0.361190i
$313$	−17.1803	+	12.4822i	−0.971090	+	0.705538i	−0.955700	−	0.294343i	$-0.904899\pi$
$313$	−17.1803	+	12.4822i	−0.971090	+	0.705538i	−0.0153904	+	0.999882i	$0.504899\pi$
$314$	4.59017	+	3.33495i	0.259038	+	0.188202i
$315$		0			0
$316$	4.04508	−	2.93893i	0.227554	−	0.165328i
$317$	7.30902	−	22.4948i	0.410515	−	1.26344i	−0.505686	−	0.862718i	$-0.668761\pi$
$317$	7.30902	−	22.4948i	0.410515	−	1.26344i	0.916201	−	0.400719i	$-0.131239\pi$
$318$	−3.38197			−0.189651
$319$	0.326238	−	1.00406i	0.0182658	−	0.0562164i
$320$		0			0
$321$	3.21885	+	9.90659i	0.179659	+	0.552932i
$322$	2.54508	+	7.83297i	0.141832	+	0.436514i
$323$	3.61803	+	2.62866i	0.201313	+	0.146262i
$324$	−1.61803			−0.0898908
$325$		0			0
$326$	6.79837			0.376527
$327$	8.09017	+	5.87785i	0.447387	+	0.325046i
$328$	−3.61803	−	11.1352i	−0.199773	−	0.614837i
$329$	0.809017	+	2.48990i	0.0446026	+	0.137273i
$330$		0			0
$331$	5.29180	−	16.2865i	0.290863	−	0.895186i	−0.693716	−	0.720248i	$-0.744028\pi$
$331$	5.29180	−	16.2865i	0.290863	−	0.895186i	0.984580	−	0.174937i	$-0.0559722\pi$
$332$	−2.85410			−0.156639
$333$	2.61803	−	8.05748i	0.143467	−	0.441547i
$334$	2.78115	−	2.02063i	0.152178	−	0.110564i
$335$		0			0
$336$	2.42705	+	1.76336i	0.132406	+	0.0961989i
$337$	0.927051	−	0.673542i	0.0504997	−	0.0366902i	−0.562249	−	0.826968i	$-0.690064\pi$
$337$	0.927051	−	0.673542i	0.0504997	−	0.0366902i	0.612749	+	0.790278i	$0.290064\pi$
$338$	5.28115	−	3.83698i	0.287257	−	0.208704i
$339$	−8.20820	−	5.96361i	−0.445808	−	0.323899i
$340$		0			0
$341$	−1.85410	+	1.34708i	−0.100405	+	0.0729487i
$342$	−2.23607	+	6.88191i	−0.120913	+	0.372131i
$343$	−18.4164			−0.994393
$344$	−1.28115	+	3.94298i	−0.0690751	+	0.212591i
$345$		0			0
$346$	−3.22542	−	9.92684i	−0.173400	−	0.533670i
$347$	9.60739	+	29.5685i	0.515752	+	1.58732i	0.781910	+	0.623391i	$0.214246\pi$
$347$	9.60739	+	29.5685i	0.515752	+	1.58732i	−0.266158	+	0.963929i	$0.585754\pi$
$348$	1.80902	+	1.31433i	0.0969735	+	0.0704554i
$349$	8.29180			0.443850			0.221925	−	0.975064i	$-0.428766\pi$
$349$	8.29180			0.443850			0.221925	+	0.975064i	$0.428766\pi$
$350$		0			0
$351$	24.2705			1.29546
$352$	−3.47214	−	2.52265i	−0.185065	−	0.134458i
$353$	−7.44427	−	22.9111i	−0.396219	−	1.21944i	−0.928008	−	0.372559i	$-0.878480\pi$
$353$	−7.44427	−	22.9111i	−0.396219	−	1.21944i	0.531790	−	0.846876i	$-0.321520\pi$
$354$	−0.791796	−	2.43690i	−0.0420835	−	0.129520i
$355$		0			0
$356$	−4.47214	+	13.7638i	−0.237023	+	0.729481i
$357$	−1.23607			−0.0654197
$358$	1.80902	−	5.56758i	0.0956095	−	0.294256i
$359$	23.2533	−	16.8945i	1.22726	−	0.891658i	0.230580	−	0.973053i	$-0.425938\pi$
$359$	23.2533	−	16.8945i	1.22726	−	0.891658i	0.996682	+	0.0813956i	$0.0259377\pi$
$360$		0			0
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$	6.85410	−	4.97980i	0.360244	−	0.261732i
$363$	−8.42705	+	6.12261i	−0.442305	+	0.321354i
$364$	10.2812	+	7.46969i	0.538879	+	0.391518i
$365$		0			0
$366$	2.35410	−	1.71036i	0.123051	−	0.0894017i
$367$	1.68034	−	5.17155i	0.0877130	−	0.269953i	−0.897573	−	0.440866i	$-0.854672\pi$
$367$	1.68034	−	5.17155i	0.0877130	−	0.269953i	0.985286	+	0.170913i	$0.0546716\pi$
$368$	−15.2705			−0.796030
$369$	3.23607	−	9.95959i	0.168463	−	0.518476i
$370$		0			0
$371$	−2.73607	−	8.42075i	−0.142050	−	0.437184i
$372$	−1.50000	−	4.61653i	−0.0777714	−	0.239356i
$373$	4.26393	+	3.09793i	0.220778	+	0.160405i	0.692677	−	0.721248i	$-0.256431\pi$
$373$	4.26393	+	3.09793i	0.220778	+	0.160405i	−0.471899	+	0.881653i	$0.656431\pi$
$374$	0.360680			0.0186503
$375$		0			0
$376$	3.61803			0.186586
$377$	5.42705	+	3.94298i	0.279507	+	0.203074i
$378$	−1.54508	−	4.75528i	−0.0794706	−	0.244585i
$379$	−10.6910	−	32.9035i	−0.549159	−	1.69014i	−0.710891	−	0.703303i	$-0.751708\pi$
$379$	−10.6910	−	32.9035i	−0.549159	−	1.69014i	0.161732	−	0.986835i	$-0.448292\pi$
$380$		0			0
$381$	−4.90983	+	15.1109i	−0.251538	+	0.774155i
$382$	14.9443			0.764615
$383$	3.51064	−	10.8046i	0.179385	−	0.552092i	−0.820421	−	0.571760i	$-0.806261\pi$
$383$	3.51064	−	10.8046i	0.179385	−	0.552092i	0.999807	+	0.0196680i	$0.00626093\pi$
$384$	9.20820	−	6.69015i	0.469904	−	0.341405i
$385$		0			0
$386$	2.85410	+	2.07363i	0.145270	+	0.105545i
$387$	−3.00000	+	2.17963i	−0.152499	+	0.110797i
$388$	−3.73607	+	2.71441i	−0.189670	+	0.137803i
$389$	−12.1353	−	8.81678i	−0.615282	−	0.447028i	0.235988	−	0.971756i	$-0.424167\pi$
$389$	−12.1353	−	8.81678i	−0.615282	−	0.447028i	−0.851270	+	0.524727i	$0.824167\pi$
$390$		0			0
$391$	5.09017	−	3.69822i	0.257421	−	0.187027i
$392$	−3.02786	+	9.31881i	−0.152930	+	0.470671i
$393$	17.7984			0.897809
$394$	−1.85410	+	5.70634i	−0.0934083	+	0.287481i
$395$		0			0
$396$	−0.763932	−	2.35114i	−0.0383890	−	0.118149i
$397$	0.0106431	+	0.0327561i	0.000534163	+	0.00164398i	0.951323	−	0.308195i	$-0.0997249\pi$
$397$	0.0106431	+	0.0327561i	0.000534163	+	0.00164398i	−0.950789	+	0.309839i	$0.899725\pi$
$398$	1.28115	+	0.930812i	0.0642184	+	0.0466574i
$399$	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	$0.690821\pi$
$402$	4.61803	+	3.35520i	0.230327	+	0.167342i
$403$	−4.50000	−	13.8496i	−0.224161	−	0.689897i
$404$	3.73607	+	11.4984i	0.185876	+	0.572069i
$405$		0			0
$406$	0.427051	−	1.31433i	0.0211942	−	0.0652290i
$407$	3.23607			0.160406
$408$	−0.527864	+	1.62460i	−0.0261332	+	0.0804296i
$409$	−22.9894	+	16.7027i	−1.13675	+	0.825898i	−0.986663	−	0.162775i	$-0.947955\pi$
$409$	−22.9894	+	16.7027i	−1.13675	+	0.825898i	−0.150087	+	0.988673i	$0.547955\pi$
$410$		0			0
$411$	−4.80902	−	3.49396i	−0.237211	−	0.172344i
$412$	15.1353	−	10.9964i	0.745660	−	0.541754i
$413$	5.42705	−	3.94298i	0.267048	−	0.194022i
$414$	8.23607	+	5.98385i	0.404781	+	0.294090i
$415$		0			0
$416$	22.0623	−	16.0292i	1.08169	−	0.785896i
$417$	−1.54508	+	4.75528i	−0.0756631	+	0.232867i
$418$	−2.76393			−0.135188
$419$	−0.163119	+	0.502029i	−0.00796888	+	0.0245257i	−0.954962	−	0.296728i	$-0.904104\pi$
$419$	−0.163119	+	0.502029i	−0.00796888	+	0.0245257i	0.946993	+	0.321254i	$0.104104\pi$
$420$		0			0
$421$	9.88854	+	30.4338i	0.481938	+	1.48325i	0.836367	+	0.548170i	$0.184675\pi$
$421$	9.88854	+	30.4338i	0.481938	+	1.48325i	−0.354429	+	0.935083i	$0.615325\pi$
$422$	−2.51722	−	7.74721i	−0.122536	−	0.377128i
$423$	2.61803	+	1.90211i	0.127293	+	0.0924839i
$424$	−12.2361			−0.594236
$425$		0			0
$426$	−2.70820			−0.131213
$427$	6.16312	+	4.47777i	0.298254	+	0.216694i
$428$	5.20820	+	16.0292i	0.251748	+	0.774801i
$429$	1.14590	+	3.52671i	0.0553245	+	0.170271i
$430$		0			0
$431$	7.36475	−	22.6664i	0.354747	−	1.09180i	−0.601409	−	0.798942i	$-0.705394\pi$
$431$	7.36475	−	22.6664i	0.354747	−	1.09180i	0.956156	−	0.292858i	$-0.0946064\pi$
$432$	9.27051			0.446028
$433$	−6.22542	+	19.1599i	−0.299175	+	0.920765i	0.682612	+	0.730781i	$0.260844\pi$
$433$	−6.22542	+	19.1599i	−0.299175	+	0.920765i	−0.981787	+	0.189985i	$0.939156\pi$
$434$	−2.42705	+	1.76336i	−0.116502	+	0.0846438i
$435$		0			0
$436$	13.0902	+	9.51057i	0.626905	+	0.455473i
$437$	−39.0066	+	28.3399i	−1.86594	+	1.35568i
$438$	−4.50000	+	3.26944i	−0.215018	+	0.156220i
$439$	−4.83688	−	3.51420i	−0.230852	−	0.167724i	0.466346	−	0.884602i	$-0.345570\pi$
$439$	−4.83688	−	3.51420i	−0.230852	−	0.167724i	−0.697198	+	0.716879i	$0.745570\pi$
$440$		0			0
$441$	−7.09017	+	5.15131i	−0.337627	+	0.245300i
$442$	−0.708204	+	2.17963i	−0.0336858	+	0.103674i
$443$	−12.0557			−0.572785			−0.286392	−	0.958112i	$-0.592456\pi$
$443$	−12.0557			−0.572785			−0.286392	+	0.958112i	$0.592456\pi$
$444$	−2.11803	+	6.51864i	−0.100517	+	0.309361i
$445$		0			0
$446$	4.23607	+	13.0373i	0.200584	+	0.617333i
$447$	−4.30902	−	13.2618i	−0.203810	−	0.627261i
$448$	0.309017	+	0.224514i	0.0145997	+	0.0106073i
$449$	20.3262			0.959254			0.479627	−	0.877472i	$-0.340772\pi$
$449$	20.3262			0.959254			0.479627	+	0.877472i	$0.340772\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−13.2812	−	9.64932i	−0.624693	−	0.453866i
$453$	1.71885	+	5.29007i	0.0807585	+	0.248549i
$454$	3.67376	+	11.3067i	0.172418	+	0.530649i
$455$		0			0
$456$	4.04508	−	12.4495i	0.189428	−	0.583001i
$457$	−5.41641			−0.253369			−0.126684	−	0.991943i	$-0.540434\pi$
$457$	−5.41641			−0.253369			−0.126684	+	0.991943i	$0.540434\pi$
$458$	−1.58359	+	4.87380i	−0.0739964	+	0.227738i
$459$	−3.09017	+	2.24514i	−0.144237	+	0.104794i
$460$		0			0
$461$	−18.7533	−	13.6251i	−0.873428	−	0.634582i	0.0580768	−	0.998312i	$-0.481503\pi$
$461$	−18.7533	−	13.6251i	−0.873428	−	0.634582i	−0.931505	+	0.363730i	$0.881503\pi$
$462$	0.618034	−	0.449028i	0.0287535	−	0.0208907i
$463$	13.0451	−	9.47781i	0.606257	−	0.440471i	−0.241838	−	0.970317i	$-0.577750\pi$
$463$	13.0451	−	9.47781i	0.606257	−	0.440471i	0.848094	+	0.529846i	$0.177750\pi$
$464$	2.07295	+	1.50609i	0.0962342	+	0.0699183i
$465$		0			0
$466$	−7.47214	+	5.42882i	−0.346140	+	0.251485i
$467$	8.79180	−	27.0584i	0.406836	−	1.25211i	−0.512517	−	0.858677i	$-0.671287\pi$
$467$	8.79180	−	27.0584i	0.406836	−	1.25211i	0.919353	−	0.393435i	$-0.128713\pi$
$468$	15.7082			0.726112
$469$	−4.61803	+	14.2128i	−0.213241	+	0.656288i
$470$		0			0
$471$	−2.83688	−	8.73102i	−0.130717	−	0.402304i
$472$	−2.86475	−	8.81678i	−0.131861	−	0.405825i
$473$	−1.14590	−	0.832544i	−0.0526884	−	0.0382804i
$474$	1.90983			0.0877214
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	−8.85410	−	6.43288i	−0.405401	−	0.294541i
$478$	5.62868	+	17.3233i	0.257450	+	0.792349i
$479$	−1.28115	−	3.94298i	−0.0585374	−	0.180160i	0.917512	−	0.397708i	$-0.130194\pi$
$479$	−1.28115	−	3.94298i	−0.0585374	−	0.180160i	−0.976050	+	0.217548i	$0.930194\pi$
$480$		0			0
$481$	−6.35410	+	19.5559i	−0.289722	+	0.891673i
$482$	−7.09017			−0.322948
$483$	4.11803	−	12.6740i	0.187377	−	0.576687i
$484$	−13.6353	+	9.90659i	−0.619784	+	0.450300i
$485$		0			0
$486$	−8.00000	−	5.81234i	−0.362887	−	0.263653i
$487$	−7.75329	+	5.63309i	−0.351335	+	0.255260i	−0.749429	−	0.662085i	$-0.769672\pi$
$487$	−7.75329	+	5.63309i	−0.351335	+	0.255260i	0.398094	+	0.917345i	$0.369672\pi$
$488$	8.51722	−	6.18812i	0.385556	−	0.280123i
$489$	−8.89919	−	6.46564i	−0.402435	−	0.292386i
$490$		0			0
$491$	−30.1353	+	21.8945i	−1.35999	+	0.988087i	−0.361539	+	0.932357i	$0.617749\pi$
$491$	−30.1353	+	21.8945i	−1.35999	+	0.988087i	−0.998446	+	0.0557300i	$0.982251\pi$
$492$	−2.61803	+	8.05748i	−0.118030	+	0.363259i
$493$	−1.05573			−0.0475476
$494$	5.42705	−	16.7027i	0.244175	−	0.751492i
$495$		0			0
$496$	−1.71885	−	5.29007i	−0.0771785	−	0.237531i
$497$	−2.19098	−	6.74315i	−0.0982790	−	0.302472i
$498$	−0.881966	−	0.640786i	−0.0395218	−	0.0287143i
$499$	−12.5623			−0.562366			−0.281183	−	0.959654i	$-0.590727\pi$
$499$	−12.5623			−0.562366			−0.281183	+	0.959654i	$0.590727\pi$
$500$		0			0
$501$	−5.56231			−0.248506
$502$	−3.40983	−	2.47739i	−0.152188	−	0.110571i
$503$	3.27051	+	10.0656i	0.145825	+	0.448803i	0.997116	−	0.0758907i	$-0.0241800\pi$
$503$	3.27051	+	10.0656i	0.145825	+	0.448803i	−0.851291	+	0.524693i	$0.824180\pi$
$504$	−2.23607	−	6.88191i	−0.0996024	−	0.306545i
$505$		0			0
$506$	−1.20163	+	3.69822i	−0.0534188	+	0.164406i
$507$	−10.5623			−0.469088
$508$	−7.94427	+	24.4500i	−0.352470	+	1.08479i
$509$	3.78115	−	2.74717i	0.167597	−	0.121766i	−0.500825	−	0.865548i	$-0.666970\pi$
$509$	3.78115	−	2.74717i	0.167597	−	0.121766i	0.668422	+	0.743782i	$0.266970\pi$
$510$		0			0
$511$	−11.7812	−	8.55951i	−0.521168	−	0.378650i
$512$	15.1353	−	10.9964i	0.668890	−	0.485977i
$513$	23.6803	−	17.2048i	1.04551	−	0.759609i
$514$	−8.07295	−	5.86534i	−0.356083	−	0.258709i
$515$		0			0
$516$	2.42705	−	1.76336i	0.106845	−	0.0776274i
$517$	−0.381966	+	1.17557i	−0.0167988	+	0.0517015i
$518$	4.23607			0.186122
$519$	−5.21885	+	16.0620i	−0.229082	+	0.705042i
$520$		0			0
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	−0.999579	−	0.0290150i	$-0.990763\pi$
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	0.791622	−	0.611011i	$-0.209237\pi$
$522$	−0.527864	−	1.62460i	−0.0231040	−	0.0711067i
$523$	−16.0623	−	11.6699i	−0.702356	−	0.510291i	0.178343	−	0.983968i	$-0.442926\pi$
$523$	−16.0623	−	11.6699i	−0.702356	−	0.510291i	−0.880699	+	0.473677i	$0.842926\pi$
$524$	28.7984			1.25806
$525$		0			0
$526$	−13.6525			−0.595276
$527$	1.85410	+	1.34708i	0.0807660	+	0.0586799i
$528$	0.437694	+	1.34708i	0.0190482	+	0.0586243i
$529$	13.8541	+	42.6385i	0.602352	+	1.85385i
$530$		0			0
$531$	2.56231	−	7.88597i	0.111195	−	0.342222i
$532$	15.3262			0.664477
$533$	−7.85410	+	24.1724i	−0.340199	+	1.04702i
$534$	−4.47214	+	3.24920i	−0.193528	+	0.140607i
$535$		0			0
$536$	16.7082	+	12.1392i	0.721684	+	0.524334i
$537$	−7.66312	+	5.56758i	−0.330688	+	0.240259i
$538$	−8.61803	+	6.26137i	−0.371550	+	0.269947i
$539$	−2.70820	−	1.96763i	−0.116651	−	0.0847516i
$540$		0			0
$541$	10.6180	−	7.71445i	0.456505	−	0.331670i	−0.335654	−	0.941985i	$-0.608957\pi$
$541$	10.6180	−	7.71445i	0.456505	−	0.331670i	0.792159	+	0.610315i	$0.208957\pi$
$542$	1.52786	−	4.70228i	0.0656274	−	0.201980i
$543$	−13.7082			−0.588275
$544$	−1.32624	+	4.08174i	−0.0568620	+	0.175003i
$545$		0			0
$546$	1.50000	+	4.61653i	0.0641941	+	0.197569i
$547$	10.7254	+	33.0095i	0.458586	+	1.41138i	0.866873	+	0.498529i	$0.166126\pi$
$547$	10.7254	+	33.0095i	0.458586	+	1.41138i	−0.408287	+	0.912854i	$0.633874\pi$
$548$	−7.78115	−	5.65334i	−0.332394	−	0.241499i
$549$	9.41641			0.401882
$550$		0			0
$551$	8.09017			0.344653
$552$	−14.8992	−	10.8249i	−0.634152	−	0.460738i
$553$	1.54508	+	4.75528i	0.0657037	+	0.202215i
$554$	−2.15654	−	6.63715i	−0.0916227	−	0.281986i
$555$		0			0
$556$	−2.50000	+	7.69421i	−0.106024	+	0.326307i
$557$	−9.23607			−0.391345			−0.195672	−	0.980669i	$-0.562689\pi$
$557$	−9.23607			−0.391345			−0.195672	+	0.980669i	$0.562689\pi$
$558$	−1.14590	+	3.52671i	−0.0485097	+	0.149298i
$559$	7.28115	−	5.29007i	0.307960	−	0.223746i
$560$		0			0
$561$	−0.472136	−	0.343027i	−0.0199336	−	0.0144826i
$562$	−0.545085	+	0.396027i	−0.0229930	+	0.0167054i
$563$	7.78115	−	5.65334i	0.327936	−	0.238260i	−0.411618	−	0.911356i	$-0.635036\pi$
$563$	7.78115	−	5.65334i	0.327936	−	0.238260i	0.739555	+	0.673097i	$0.235036\pi$
$564$	−2.11803	−	1.53884i	−0.0891853	−	0.0647969i
$565$		0			0
$566$	11.5729	−	8.40824i	0.486447	−	0.353425i
$567$	0.500000	−	1.53884i	0.0209980	−	0.0646253i
$568$	−9.79837			−0.411131
$569$	9.10739	−	28.0297i	0.381802	−	1.17506i	−0.556972	−	0.830531i	$-0.688037\pi$
$569$	9.10739	−	28.0297i	0.381802	−	1.17506i	0.938774	−	0.344534i	$-0.111963\pi$
$570$		0			0
$571$	9.92705	+	30.5523i	0.415434	+	1.27857i	0.911862	+	0.410497i	$0.134645\pi$
$571$	9.92705	+	30.5523i	0.415434	+	1.27857i	−0.496428	+	0.868078i	$0.665355\pi$
$572$	1.85410	+	5.70634i	0.0775239	+	0.238594i
$573$	−19.5623	−	14.2128i	−0.817227	−	0.593750i
$574$	5.23607			0.218549
$575$		0			0
$576$	0.472136			0.0196723
$577$	30.5623	+	22.2048i	1.27233	+	0.924399i	0.999293	−	0.0376062i	$-0.0119732\pi$
$577$	30.5623	+	22.2048i	1.27233	+	0.924399i	0.273033	+	0.962005i	$0.411973\pi$
$578$	3.13525	+	9.64932i	0.130409	+	0.401359i
$579$	−1.76393	−	5.42882i	−0.0733065	−	0.225614i
$580$		0			0
$581$	0.881966	−	2.71441i	0.0365901	−	0.112613i
$582$	−1.76393			−0.0731173
$583$	1.29180	−	3.97574i	0.0535007	−	0.164658i
$584$	−16.2812	+	11.8290i	−0.673719	+	0.489485i
$585$		0			0
$586$	14.2361	+	10.3431i	0.588087	+	0.427270i
$587$	15.1353	−	10.9964i	0.624699	−	0.453870i	−0.229861	−	0.973224i	$-0.573827\pi$
$587$	15.1353	−	10.9964i	0.624699	−	0.453870i	0.854560	+	0.519353i	$0.173827\pi$
$588$	5.73607	−	4.16750i	0.236551	−	0.171865i
$589$	−14.2082	−	10.3229i	−0.585439	−	0.425346i
$590$		0			0
$591$	7.85410	−	5.70634i	0.323075	−	0.234727i
$592$	−2.42705	+	7.46969i	−0.0997512	+	0.307003i
$593$	22.0902			0.907135			0.453567	−	0.891222i	$-0.350151\pi$
$593$	22.0902			0.907135			0.453567	+	0.891222i	$0.350151\pi$
$594$	0.729490	−	2.24514i	0.0299313	−	0.0921192i
$595$		0			0
$596$	−6.97214	−	21.4580i	−0.285590	−	0.878955i
$597$	−0.791796	−	2.43690i	−0.0324061	−	0.0997356i
$598$	−19.9894	−	14.5231i	−0.817426	−	0.593894i
$599$	−0.527864			−0.0215679			−0.0107840	−	0.999942i	$-0.503433\pi$
$599$	−0.527864			−0.0215679			−0.0107840	+	0.999942i	$0.503433\pi$
$600$		0			0
$601$	36.2705			1.47950			0.739752	−	0.672879i	$-0.234943\pi$
$601$	36.2705			1.47950			0.739752	+	0.672879i	$0.234943\pi$
$602$	−1.50000	−	1.08981i	−0.0611354	−	0.0444175i
$603$	5.70820	+	17.5680i	0.232456	+	0.715426i
$604$	2.78115	+	8.55951i	0.113164	+	0.348281i
$605$		0			0
$606$	−1.42705	+	4.39201i	−0.0579700	+	0.178413i
$607$	15.4377			0.626597			0.313298	−	0.949655i	$-0.398566\pi$
$607$	15.4377			0.626597			0.313298	+	0.949655i	$0.398566\pi$
$608$	10.1631	−	31.2789i	0.412169	−	1.26853i
$609$	−1.80902	+	1.31433i	−0.0733051	+	0.0532592i
$610$		0			0
$611$	−6.35410	−	4.61653i	−0.257059	−	0.186765i
$612$	−2.00000	+	1.45309i	−0.0808452	+	0.0587375i
$613$	25.8713	−	18.7966i	1.04493	−	0.759188i	0.0736905	−	0.997281i	$-0.476522\pi$
$613$	25.8713	−	18.7966i	1.04493	−	0.759188i	0.971242	+	0.238093i	$0.0765223\pi$
$614$	−2.38197	−	1.73060i	−0.0961283	−	0.0698413i
$615$		0			0
$616$	2.23607	−	1.62460i	0.0900937	−	0.0654569i
$617$	−3.01722	+	9.28605i	−0.121469	+	0.373842i	−0.993241	−	0.116069i	$-0.962971\pi$
$617$	−3.01722	+	9.28605i	−0.121469	+	0.373842i	0.871772	+	0.489911i	$0.162971\pi$
$618$	7.14590			0.287450
$619$	12.1976	−	37.5402i	0.490261	−	1.50887i	−0.333952	−	0.942590i	$-0.608382\pi$
$619$	12.1976	−	37.5402i	0.490261	−	1.50887i	0.824213	−	0.566279i	$-0.191618\pi$
$620$		0			0
$621$	−12.7254	−	39.1648i	−0.510654	−	1.57163i
$622$	5.63525	+	17.3435i	0.225953	+	0.695412i
$623$	−11.7082	−	8.50651i	−0.469079	−	0.340806i
$624$	−9.00000			−0.360288
$625$		0			0
$626$	−13.1246			−0.524565
$627$	3.61803	+	2.62866i	0.144490	+	0.104978i
$628$	−4.59017	−	14.1271i	−0.183168	−	0.563732i
$629$	−1.00000	−	3.07768i	−0.0398726	−	0.122715i
$630$		0			0
$631$	−1.78115	+	5.48183i	−0.0709066	+	0.218228i	−0.980230	−	0.197862i	$-0.936600\pi$
$631$	−1.78115	+	5.48183i	−0.0709066	+	0.218228i	0.909323	+	0.416090i	$0.136600\pi$
$632$	6.90983			0.274858
$633$	−4.07295	+	12.5352i	−0.161885	+	0.498231i
$634$	11.8262	−	8.59226i	0.469680	−	0.341242i
$635$		0			0
$636$	7.16312	+	5.20431i	0.284036	+	0.206364i
$637$	17.2082	−	12.5025i	0.681814	−	0.495367i
$638$	0.527864	−	0.383516i	0.0208983	−	0.0151835i
$639$	−7.09017	−	5.15131i	−0.280483	−	0.203783i
$640$		0			0
$641$	−8.16312	+	5.93085i	−0.322424	+	0.234255i	−0.737209	−	0.675665i	$-0.763857\pi$
$641$	−8.16312	+	5.93085i	−0.322424	+	0.234255i	0.414785	+	0.909919i	$0.363857\pi$
$642$	−1.98936	+	6.12261i	−0.0785137	+	0.241640i
$643$	−22.8328			−0.900438			−0.450219	−	0.892918i	$-0.648654\pi$
$643$	−22.8328			−0.900438			−0.450219	+	0.892918i	$0.648654\pi$
$644$	6.66312	−	20.5070i	0.262564	−	0.808088i
$645$		0			0
$646$	0.854102	+	2.62866i	0.0336042	+	0.103423i
$647$	−9.43769	−	29.0462i	−0.371034	−	1.14193i	−0.946116	−	0.323829i	$-0.895030\pi$
$647$	−9.43769	−	29.0462i	−0.371034	−	1.14193i	0.575082	−	0.818096i	$-0.304970\pi$
$648$	−1.80902	−	1.31433i	−0.0710649	−	0.0516317i
$649$	3.16718			0.124323
$650$		0			0
$651$	4.85410			0.190247
$652$	−14.3992	−	10.4616i	−0.563916	−	0.409709i
$653$	−2.44427	−	7.52270i	−0.0956518	−	0.294386i	0.891771	−	0.452487i	$-0.149463\pi$
$653$	−2.44427	−	7.52270i	−0.0956518	−	0.294386i	−0.987423	+	0.158101i	$0.949463\pi$
$654$	1.90983	+	5.87785i	0.0746803	+	0.229842i
$655$		0			0
$656$	−3.00000	+	9.23305i	−0.117130	+	0.360490i
$657$	−18.0000			−0.702247
$658$	−0.500000	+	1.53884i	−0.0194920	+	0.0599903i
$659$	−19.7984	+	14.3844i	−0.771235	+	0.560335i	−0.902336	−	0.431034i	$-0.858149\pi$
$659$	−19.7984	+	14.3844i	−0.771235	+	0.560335i	0.131101	+	0.991369i	$0.458149\pi$
$660$		0			0
$661$	32.9164	+	23.9152i	1.28030	+	0.930192i	0.999562	−	0.0295922i	$-0.00942086\pi$
$661$	32.9164	+	23.9152i	1.28030	+	0.930192i	0.280738	+	0.959784i	$0.409421\pi$
$662$	8.56231	−	6.22088i	0.332783	−	0.241781i
$663$	3.00000	−	2.17963i	0.116510	−	0.0846497i
$664$	−3.19098	−	2.31838i	−0.123834	−	0.0899708i
$665$		0			0
$666$	4.23607	−	3.07768i	0.164144	−	0.119258i
$667$	3.51722	−	10.8249i	0.136187	−	0.419142i
$668$	−9.00000			−0.348220
$669$	6.85410	−	21.0948i	0.264995	−	0.815570i
$670$		0			0
$671$	1.11146	+	3.42071i	0.0429073	+	0.132055i
$672$	2.80902	+	8.64527i	0.108360	+	0.333498i
$673$	−8.23607	−	5.98385i	−0.317477	−	0.230661i	0.417621	−	0.908621i	$-0.362864\pi$
$673$	−8.23607	−	5.98385i	−0.317477	−	0.230661i	−0.735098	+	0.677961i	$0.762864\pi$
$674$	0.708204			0.0272790
$675$		0			0
$676$	−17.0902			−0.657314
$677$	6.78115	+	4.92680i	0.260621	+	0.189352i	0.710421	−	0.703777i	$-0.248505\pi$
$677$	6.78115	+	4.92680i	0.260621	+	0.189352i	−0.449800	+	0.893129i	$0.648505\pi$
$678$	−1.93769	−	5.96361i	−0.0744167	−	0.229031i
$679$	−1.42705	−	4.39201i	−0.0547652	−	0.168550i
$680$		0			0
$681$	5.94427	−	18.2946i	0.227785	−	0.701050i
$682$	−1.41641			−0.0542371
$683$	1.39919	−	4.30625i	0.0535384	−	0.164774i	−0.920712	−	0.390242i	$-0.872391\pi$
$683$	1.39919	−	4.30625i	0.0535384	−	0.164774i	0.974251	+	0.225468i	$0.0723912\pi$
$684$	15.3262	−	11.1352i	0.586013	−	0.425764i
$685$		0			0
$686$	−9.20820	−	6.69015i	−0.351571	−	0.255431i
$687$	6.70820	−	4.87380i	0.255934	−	0.185947i
$688$	2.78115	−	2.02063i	0.106030	−	0.0770356i
$689$	21.4894	+	15.6129i	0.818679	+	0.594805i
$690$		0			0
$691$	−2.20820	+	1.60435i	−0.0840040	+	0.0610325i	−0.628995	−	0.777410i	$-0.716533\pi$
$691$	−2.20820	+	1.60435i	−0.0840040	+	0.0610325i	0.544991	+	0.838442i	$0.316533\pi$
$692$	−8.44427	+	25.9888i	−0.321003	+	0.987946i
$693$	2.47214			0.0939087
$694$	−5.93769	+	18.2743i	−0.225392	+	0.693685i
$695$		0			0
$696$	0.954915	+	2.93893i	0.0361960	+	0.111400i
$697$	−1.23607	−	3.80423i	−0.0468194	−	0.144095i
$698$	4.14590	+	3.01217i	0.156925	+	0.114012i
$699$	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	$0.270041\pi$
$702$	12.1353	+	8.81678i	0.458016	+	0.332768i
$703$	7.66312	+	23.5847i	0.289020	+	0.889512i
$704$	0.0557281	+	0.171513i	0.00210033	+	0.00646416i
$705$		0			0
$706$	4.60081	−	14.1598i	0.173154	−	0.532913i
$707$	−12.0902			−0.454698
$708$	−2.07295	+	6.37988i	−0.0779062	+	0.239771i
$709$	−27.1353	+	19.7149i	−1.01909	+	0.740409i	−0.966095	−	0.258186i	$-0.916875\pi$
$709$	−27.1353	+	19.7149i	−1.01909	+	0.740409i	−0.0529906	+	0.998595i	$0.516875\pi$
$710$		0			0
$711$	5.00000	+	3.63271i	0.187515	+	0.136237i
$712$	−16.1803	+	11.7557i	−0.606384	+	0.440564i
$713$	−19.9894	+	14.5231i	−0.748607	+	0.543895i
$714$	−0.618034	−	0.449028i	−0.0231293	−	0.0168044i
$715$		0			0
$716$	−12.3992	+	9.00854i	−0.463379	+	0.336665i
$717$	9.10739	−	28.0297i	0.340122	−	1.04679i
$718$	17.7639			0.662944
$719$	−11.3435	+	34.9116i	−0.423040	+	1.30198i	0.481819	+	0.876271i	$0.339976\pi$
$719$	−11.3435	+	34.9116i	−0.423040	+	1.30198i	−0.904859	+	0.425712i	$0.860024\pi$
$720$		0			0
$721$	5.78115	+	17.7926i	0.215301	+	0.662630i
$722$	−2.91641	−	8.97578i	−0.108537	−	0.334044i
$723$	9.28115	+	6.74315i	0.345170	+	0.250781i
$724$	−22.1803			−0.824326
$725$		0			0
$726$	−6.43769			−0.238925
$727$	3.59017	+	2.60841i	0.133152	+	0.0967406i	0.652368	−	0.757903i	$-0.273776\pi$
$727$	3.59017	+	2.60841i	0.133152	+	0.0967406i	−0.519216	+	0.854643i	$0.673776\pi$
$728$	5.42705	+	16.7027i	0.201140	+	0.619045i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$		0			0
$731$	−0.437694	+	1.34708i	−0.0161887	+	0.0498237i
$732$	−7.61803			−0.281571
$733$	−8.33688	+	25.6583i	−0.307930	+	0.947710i	0.670638	+	0.741785i	$0.266020\pi$
$733$	−8.33688	+	25.6583i	−0.307930	+	0.947710i	−0.978568	+	0.205925i	$0.933980\pi$
$734$	2.71885	−	1.97536i	0.100354	−	0.0729118i
$735$		0			0
$736$	−37.4336	−	27.1971i	−1.37982	−	1.00250i
$737$	−5.70820	+	4.14725i	−0.210264	+	0.152766i
$738$	5.23607	−	3.80423i	0.192742	−	0.140035i
$739$	25.0623	+	18.2088i	0.921932	+	0.669823i	0.944004	−	0.329934i	$-0.107026\pi$
$739$	25.0623	+	18.2088i	0.921932	+	0.669823i	−0.0220723	+	0.999756i	$0.507026\pi$
$740$		0			0
$741$	−22.9894	+	16.7027i	−0.844535	+	0.613591i
$742$	1.69098	−	5.20431i	0.0620779	−	0.191056i
$743$	16.3607			0.600215			0.300108	−	0.953905i	$-0.402977\pi$
$743$	16.3607			0.600215			0.300108	+	0.953905i	$0.402977\pi$
$744$	2.07295	−	6.37988i	0.0759980	−	0.233898i
$745$		0			0
$746$	1.00658	+	3.09793i	0.0368534	+	0.113423i
$747$	−1.09017	−	3.35520i	−0.0398872	−	0.122760i
$748$	−0.763932	−	0.555029i	−0.0279321	−	0.0202939i
$749$	−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	$0.768039\pi$
$752$	−2.42705	−	1.76336i	−0.0885054	−	0.0643030i
$753$	2.10739	+	6.48588i	0.0767976	+	0.236359i
$754$	1.28115	+	3.94298i	0.0466568	+	0.143595i
$755$		0			0
$756$	−4.04508	+	12.4495i	−0.147118	+	0.452784i
$757$	−3.58359			−0.130248			−0.0651239	−	0.997877i	$-0.520744\pi$
$757$	−3.58359			−0.130248			−0.0651239	+	0.997877i	$0.520744\pi$
$758$	6.60739	−	20.3355i	0.239991	−	0.738617i
$759$	5.09017	−	3.69822i	0.184761	−	0.134237i
$760$		0			0
$761$	−30.2984	−	22.0131i	−1.09832	−	0.797973i	−0.117531	−	0.993069i	$-0.537498\pi$
$761$	−30.2984	−	22.0131i	−1.09832	−	0.797973i	−0.980784	+	0.195096i	$0.937498\pi$
$762$	−7.94427	+	5.77185i	−0.287791	+	0.209092i
$763$	−13.0902	+	9.51057i	−0.473896	+	0.344306i
$764$	−31.6525	−	22.9969i	−1.14515	−	0.831998i
$765$		0			0
$766$	5.68034	−	4.12701i	0.205239	−	0.149115i
$767$	−6.21885	+	19.1396i	−0.224550	+	0.691092i
$768$	6.56231			0.236797
$769$	−4.14590	+	12.7598i	−0.149505	+	0.460129i	−0.997563	−	0.0697749i	$-0.977772\pi$
$769$	−4.14590	+	12.7598i	−0.149505	+	0.460129i	0.848058	+	0.529904i	$0.177772\pi$
$770$		0			0
$771$	4.98936	+	15.3557i	0.179687	+	0.553021i
$772$	−2.85410	−	8.78402i	−0.102721	−	0.316144i
$773$	26.8262	+	19.4904i	0.964873	+	0.701021i	0.954277	−	0.298923i	$-0.0966273\pi$
$773$	26.8262	+	19.4904i	0.964873	+	0.701021i	0.0105954	+	0.999944i	$0.496627\pi$
$774$	−2.29180			−0.0823769
$775$		0			0
$776$	−6.38197			−0.229099
$777$	−5.54508	−	4.02874i	−0.198929	−	0.144530i
$778$	−2.86475	−	8.81678i	−0.102706	−	0.316097i
$779$	9.47214	+	29.1522i	0.339374	+	1.04449i
$780$		0			0
$781$	1.03444	−	3.18368i	0.0370152	−	0.113921i
$782$	3.88854			0.139054
$783$	−2.13525	+	6.57164i	−0.0763078	+	0.234851i
$784$	6.57295	−	4.77553i	0.234748	−	0.170555i
$785$		0			0
$786$	8.89919	+	6.46564i	0.317423	+	0.230622i
$787$	−27.6525	+	20.0907i	−0.985704	+	0.716156i	−0.958976	−	0.283487i	$-0.908509\pi$
$787$	−27.6525	+	20.0907i	−0.985704	+	0.716156i	−0.0267281	+	0.999643i	$0.508509\pi$
$788$	12.7082	−	9.23305i	0.452711	−	0.328914i
$789$	17.8713	+	12.9843i	0.636236	+	0.462252i
$790$		0			0
$791$	13.2812	−	9.64932i	0.472223	−	0.343090i
$792$	1.05573	−	3.24920i	0.0375137	−	0.115455i
$793$	−22.8541			−0.811573
$794$	−0.00657781	+	0.0202444i	−0.000233438	+	0.000718447i
$795$		0			0
$796$	−1.28115	−	3.94298i	−0.0454093	−	0.139755i
$797$	−4.39919	−	13.5393i	−0.155827	−	0.479587i	0.842417	−	0.538827i	$-0.181132\pi$
$797$	−4.39919	−	13.5393i	−0.155827	−	0.479587i	−0.998244	+	0.0592400i	$0.981132\pi$
$798$	4.73607	+	3.44095i	0.167655	+	0.121808i
$799$	1.23607			0.0437289
$800$		0			0
$801$	−17.8885			−0.632061
$802$	−11.2984	−	8.20875i	−0.398959	−	0.289861i
$803$	−2.12461	−	6.53888i	−0.0749759	−	0.230752i
$804$	−4.61803	−	14.2128i	−0.162866	−	0.501248i
$805$		0			0
$806$	2.78115	−	8.55951i	0.0979619	−	0.301496i
$807$	17.2361			0.606738
$808$	−5.16312	+	15.8904i	−0.181638	+	0.559024i
$809$	12.9271	−	9.39205i	0.454491	−	0.330207i	−0.336875	−	0.941549i	$-0.609370\pi$
$809$	12.9271	−	9.39205i	0.454491	−	0.330207i	0.791366	+	0.611342i	$0.209370\pi$
$810$		0			0
$811$	1.04508	+	0.759299i	0.0366979	+	0.0266626i	0.605983	−	0.795478i	$-0.292780\pi$
$811$	1.04508	+	0.759299i	0.0366979	+	0.0266626i	−0.569285	+	0.822140i	$0.692780\pi$
$812$	−2.92705	+	2.12663i	−0.102719	+	0.0746300i
$813$	−6.47214	+	4.70228i	−0.226988	+	0.164916i
$814$	1.61803	+	1.17557i	0.0567121	+	0.0412037i
$815$		0			0
$816$	1.14590	−	0.832544i	0.0401145	−	0.0291449i
$817$	3.35410	−	10.3229i	0.117345	−	0.361151i
$818$	−17.5623			−0.614052
$819$	−4.85410	+	14.9394i	−0.169616	+	0.522025i
$820$		0			0
$821$	6.08359	+	18.7234i	0.212319	+	0.653450i	0.999333	+	0.0365154i	$0.0116258\pi$
$821$	6.08359	+	18.7234i	0.212319	+	0.653450i	−0.787014	+	0.616935i	$0.788374\pi$
$822$	−1.13525	−	3.49396i	−0.0395966	−	0.121866i
$823$	27.7426	+	20.1562i	0.967048	+	0.702601i	0.954777	−	0.297323i	$-0.0960939\pi$
$823$	27.7426	+	20.1562i	0.967048	+	0.702601i	0.0122710	+	0.999925i	$0.496094\pi$
$824$	25.8541			0.900670
$825$		0			0
$826$	4.14590			0.144254
$827$	−24.2984	−	17.6538i	−0.844937	−	0.613883i	0.0788082	−	0.996890i	$-0.474889\pi$
$827$	−24.2984	−	17.6538i	−0.844937	−	0.613883i	−0.923745	+	0.383007i	$0.874889\pi$
$828$	−8.23607	−	25.3480i	−0.286223	−	0.880904i
$829$	−9.00658	−	27.7194i	−0.312811	−	0.962734i	−0.976646	−	0.214855i	$-0.931072\pi$
$829$	−9.00658	−	27.7194i	−0.312811	−	0.962734i	0.663835	−	0.747879i	$-0.268928\pi$
$830$		0			0
$831$	−3.48936	+	10.7391i	−0.121044	+	0.372537i
$832$	−1.14590			−0.0397269
$833$	−1.03444	+	3.18368i	−0.0358413	+	0.110308i
$834$	−2.50000	+	1.81636i	−0.0865679	+	0.0628953i
$835$		0			0
$836$	5.85410	+	4.25325i	0.202468	+	0.147102i
$837$	12.1353	−	8.81678i	0.419456	−	0.304752i
$838$	−0.263932	+	0.191758i	−0.00911738	+	0.00662416i
$839$	−3.35410	−	2.43690i	−0.115796	−	0.0841311i	0.528380	−	0.849008i	$-0.322800\pi$
$839$	−3.35410	−	2.43690i	−0.115796	−	0.0841311i	−0.644176	+	0.764877i	$0.722800\pi$
$840$		0			0
$841$	21.9164	−	15.9232i	0.755738	−	0.549076i
$842$	−6.11146	+	18.8091i	−0.210615	+	0.648205i
$843$	1.09017			0.0375474
$844$	−6.59017	+	20.2825i	−0.226843	+	0.698151i
$845$		0			0
$846$	0.618034	+	1.90211i	0.0212484	+	0.0653960i
$847$	−5.20820	−	16.0292i	−0.178956	−	0.550770i
$848$	8.20820	+	5.96361i	0.281871	+	0.204791i
$849$	−23.1459			−0.794365
$850$		0			0
$851$	34.8885			1.19596
$852$	5.73607	+	4.16750i	0.196514	+	0.142776i
$853$	−14.6180	−	44.9897i	−0.500512	−	1.54042i	−0.808187	−	0.588926i	$-0.799551\pi$
$853$	−14.6180	−	44.9897i	−0.500512	−	1.54042i	0.307675	−	0.951491i	$-0.400449\pi$
$854$	1.45492	+	4.47777i	0.0497862	+	0.153226i
$855$		0			0
$856$	−7.19756	+	22.1518i	−0.246008	+	0.757133i
$857$	40.6869			1.38984			0.694919	−	0.719088i	$-0.255440\pi$
$857$	40.6869			1.38984			0.694919	+	0.719088i	$0.255440\pi$
$858$	−0.708204	+	2.17963i	−0.0241777	+	0.0744113i
$859$	22.9894	−	16.7027i	0.784387	−	0.569890i	−0.121906	−	0.992542i	$-0.538901\pi$
$859$	22.9894	−	16.7027i	0.784387	−	0.569890i	0.906292	+	0.422651i	$0.138901\pi$
$860$		0			0
$861$	−6.85410	−	4.97980i	−0.233587	−	0.169711i
$862$	11.9164	−	8.65778i	0.405874	−	0.294885i
$863$	−33.6246	+	24.4297i	−1.14460	+	0.831597i	−0.987753	−	0.156027i	$-0.950131\pi$
$863$	−33.6246	+	24.4297i	−1.14460	+	0.831597i	−0.156842	+	0.987624i	$0.550131\pi$
$864$	22.7254	+	16.5110i	0.773135	+	0.561715i
$865$		0			0
$866$	−10.0729	+	7.31843i	−0.342293	+	0.248690i
$867$	5.07295	−	15.6129i	0.172286	−	0.530243i
$868$	7.85410			0.266586
$869$	−0.729490	+	2.24514i	−0.0247463	+	0.0761612i
$870$		0			0
$871$	−13.8541	−	42.6385i	−0.469428	−	1.44475i
$872$	6.90983	+	21.2663i	0.233996	+	0.720167i
$873$	−4.61803	−	3.35520i	−0.156297	−	0.113556i
$874$	−29.7984			−1.00795
$875$		0			0
$876$	14.5623			0.492015
$877$	24.7082	+	17.9516i	0.834337	+	0.606181i	0.920783	−	0.390075i	$-0.127551\pi$
$877$	24.7082	+	17.9516i	0.834337	+	0.606181i	−0.0864462	+	0.996257i	$0.527551\pi$
$878$	−1.14183	−	3.51420i	−0.0385350	−	0.118598i
$879$	−8.79837	−	27.0786i	−0.296762	−	0.913339i
$880$		0			0
$881$	1.34752	−	4.14725i	0.0453992	−	0.139725i	−0.925787	−	0.378044i	$-0.876597\pi$
$881$	1.34752	−	4.14725i	0.0453992	−	0.139725i	0.971187	+	0.238320i	$0.0765967\pi$
$882$	−5.41641			−0.182380
$883$	14.6525	−	45.0957i	0.493095	−	1.51759i	−0.326809	−	0.945090i	$-0.605974\pi$
$883$	14.6525	−	45.0957i	0.493095	−	1.51759i	0.819904	−	0.572500i	$-0.194026\pi$
$884$	4.85410	−	3.52671i	0.163261	−	0.118616i
$885$		0			0
$886$	−6.02786	−	4.37950i	−0.202510	−	0.147132i
$887$	−4.76393	+	3.46120i	−0.159957	+	0.116216i	−0.664885	−	0.746946i	$-0.731519\pi$
$887$	−4.76393	+	3.46120i	−0.159957	+	0.116216i	0.504927	+	0.863162i	$0.331519\pi$
$888$	−7.66312	+	5.56758i	−0.257157	+	0.186836i
$889$	−20.7984	−	15.1109i	−0.697555	−	0.506803i
$890$		0			0
$891$	0.618034	−	0.449028i	0.0207049	−	0.0150430i
$892$	11.0902	−	34.1320i	0.371326	−	1.14283i
$893$	−9.47214			−0.316973
$894$	2.66312	−	8.19624i	0.0890680	−	0.274123i
$895$		0			0
$896$	5.69098	+	17.5150i	0.190122	+	0.585137i
$897$	12.3541	+	38.0220i	0.412491	+	1.26952i
$898$	10.1631	+	7.38394i	0.339148	+	0.246405i
$899$	4.14590			0.138273
$900$		0			0
$901$	−4.18034			−0.139267
$902$	2.00000	+	1.45309i	0.0665927	+	0.0483824i
$903$	0.927051	+	2.85317i	0.0308503	+	0.0949475i
$904$	−7.01064	−	21.5765i	−0.233171	−	0.717625i
$905$		0			0
$906$	−1.06231	+	3.26944i	−0.0352927	+	0.108620i
$907$	−47.2492			−1.56888			−0.784442	−	0.620202i	$-0.787051\pi$
$907$	−47.2492			−1.56888			−0.784442	+	0.620202i	$0.787051\pi$
$908$	9.61803	−	29.6013i	0.319186	−	0.982352i
$909$	−12.0902	+	8.78402i	−0.401006	+	0.291348i
$910$		0			0
$911$	28.9336	+	21.0215i	0.958614	+	0.696474i	0.952828	−	0.303510i	$-0.0981584\pi$
$911$	28.9336	+	21.0215i	0.958614	+	0.696474i	0.00578548	+	0.999983i	$0.498158\pi$
$912$	−8.78115	+	6.37988i	−0.290773	+	0.211259i
$913$	1.09017	−	0.792055i	0.0360794	−	0.0262132i
$914$	−2.70820	−	1.96763i	−0.0895794	−	0.0650833i
$915$		0			0
$916$	10.8541	−	7.88597i	0.358630	−	0.260560i
$917$	−8.89919	+	27.3889i	−0.293877	+	0.904461i
$918$	−2.36068			−0.0779140
$919$	−0.551663	+	1.69784i	−0.0181977	+	0.0560067i	−0.959743	−	0.280880i	$-0.909374\pi$
$919$	−0.551663	+	1.69784i	−0.0181977	+	0.0560067i	0.941545	+	0.336886i	$0.109374\pi$
$920$		0			0
$921$	1.47214	+	4.53077i	0.0485085	+	0.149294i
$922$	−4.42705	−	13.6251i	−0.145797	−	0.448718i
$923$	17.2082	+	12.5025i	0.566415	+	0.411525i
$924$	−2.00000			−0.0657952
$925$		0			0
$926$	9.96556			0.327489
$927$	18.7082	+	13.5923i	0.614458	+	0.446430i
$928$	2.39919	+	7.38394i	0.0787572	+	0.242390i
$929$	−11.3197	−	34.8383i	−0.371386	−	1.14301i	−0.945885	−	0.324503i	$-0.894803\pi$
$929$	−11.3197	−	34.8383i	−0.371386	−	1.14301i	0.574499	−	0.818506i	$-0.305197\pi$
$930$		0			0
$931$	7.92705	−	24.3970i	0.259799	−	0.799578i
$932$	24.1803			0.792053
$933$	9.11803	−	28.0624i	0.298511	−	0.918722i
$934$	14.2254	−	10.3354i	0.465470	−	0.338184i
$935$		0			0
$936$	17.5623	+	12.7598i	0.574042	+	0.417066i
$937$	41.4787	−	30.1360i	1.35505	−	0.984502i	0.356308	−	0.934369i	$-0.384035\pi$
$937$	41.4787	−	30.1360i	1.35505	−	0.984502i	0.998743	−	0.0501333i	$-0.0159646\pi$
$938$	−7.47214	+	5.42882i	−0.243974	+	0.177257i
$939$	17.1803	+	12.4822i	0.560659	+	0.407343i
$940$		0			0
$941$	15.8435	−	11.5109i	0.516482	−	0.375246i	−0.298795	−	0.954317i	$-0.596585\pi$
$941$	15.8435	−	11.5109i	0.516482	−	0.375246i	0.815277	+	0.579071i	$0.196585\pi$
$942$	1.75329	−	5.39607i	0.0571252	−	0.175813i
$943$	43.1246			1.40433
$944$	−2.37539	+	7.31069i	−0.0773123	+	0.237943i
$945$		0			0
$946$	−0.270510	−	0.832544i	−0.00879503	−	0.0270683i
$947$	8.85410	+	27.2501i	0.287720	+	0.885510i	0.985570	+	0.169267i	$0.0541399\pi$
$947$	8.85410	+	27.2501i	0.287720	+	0.885510i	−0.697851	+	0.716243i	$0.745860\pi$
$948$	−4.04508	−	2.93893i	−0.131378	−	0.0954519i
$949$	43.6869			1.41814
$950$		0			0
$951$	−23.6525			−0.766984
$952$	−2.23607	−	1.62460i	−0.0724714	−	0.0526535i
$953$	−10.7361	−	33.0422i	−0.347775	−	1.07034i	−0.960081	−	0.279721i	$-0.909758\pi$
$953$	−10.7361	−	33.0422i	−0.347775	−	1.07034i	0.612306	−	0.790621i	$-0.290242\pi$
$954$	−2.09017	−	6.43288i	−0.0676718	−	0.208272i
$955$		0			0
$956$	14.7361	−	45.3530i	0.476598	−	1.46682i
$957$	−1.05573			−0.0341268
$958$	0.791796	−	2.43690i	0.0255818	−	0.0787326i
$959$	7.78115	−	5.65334i	0.251267	−	0.182556i
$960$		0			0
$961$	17.7984	+	12.9313i	0.574141	+	0.417138i
$962$	−10.2812	+	7.46969i	−0.331478	+	0.240833i
$963$	−16.8541	+	12.2452i	−0.543116	+	0.394597i
$964$	15.0172	+	10.9106i	0.483672	+	0.351408i
$965$		0			0
$966$	6.66312	−	4.84104i	0.214382	−	0.155758i
$967$	−12.3262	+	37.9363i	−0.396385	+	1.21995i	0.531493	+	0.847063i	$0.321631\pi$
$967$	−12.3262	+	37.9363i	−0.396385	+	1.21995i	−0.927878	+	0.372885i	$0.878369\pi$
$968$	−23.2918			−0.748627
$969$	1.38197	−	4.25325i	0.0443951	−	0.136634i
$970$		0			0
$971$	1.04508	+	3.21644i	0.0335384	+	0.103220i	0.966424	−	0.256951i	$-0.0827180\pi$
$971$	1.04508	+	3.21644i	0.0335384	+	0.103220i	−0.932886	+	0.360172i	$0.882718\pi$
$972$	8.00000	+	24.6215i	0.256600	+	0.789734i
$973$	−6.54508	−	4.75528i	−0.209826	−	0.152447i
$974$	−5.92299			−0.189785
$975$		0			0
$976$	−8.72949			−0.279424
$977$	−27.2254	−	19.7804i	−0.871019	−	0.632832i	0.0598416	−	0.998208i	$-0.480940\pi$
$977$	−27.2254	−	19.7804i	−0.871019	−	0.632832i	−0.930860	+	0.365376i	$0.880940\pi$
$978$	−2.10081	−	6.46564i	−0.0671766	−	0.206748i
$979$	−2.11146	−	6.49839i	−0.0674824	−	0.207690i
$980$		0			0
$981$	−6.18034	+	19.0211i	−0.197323	+	0.607298i
$982$	−23.0213			−0.734639
$983$	−2.28115	+	7.02067i	−0.0727575	+	0.223924i	−0.980822	−	0.194906i	$-0.937560\pi$
$983$	−2.28115	+	7.02067i	−0.0727575	+	0.223924i	0.908064	+	0.418830i	$0.137560\pi$
$984$	−9.47214	+	6.88191i	−0.301961	+	0.219387i
$985$		0			0
$986$	−0.527864	−	0.383516i	−0.0168106	−	0.0122136i
$987$	2.11803	−	1.53884i	0.0674178	−	0.0489819i
$988$	−37.1976	+	27.0256i	−1.18341	+	0.859799i
$989$	−12.3541	−	8.97578i	−0.392838	−	0.285413i
$990$		0			0
$991$	−23.7533	+	17.2578i	−0.754548	+	0.548211i	−0.897233	−	0.441557i	$-0.854426\pi$
$991$	−23.7533	+	17.2578i	−0.754548	+	0.548211i	0.142685	+	0.989768i	$0.454426\pi$
$992$	5.20820	−	16.0292i	0.165361	−	0.508928i
$993$	−17.1246			−0.543433
$994$	1.35410	−	4.16750i	0.0429495	−	0.132185i
$995$		0			0
$996$	0.881966	+	2.71441i	0.0279462	+	0.0860094i
$997$	3.36475	+	10.3556i	0.106563	+	0.327966i	0.990094	−	0.140406i	$-0.0448408\pi$
$997$	3.36475	+	10.3556i	0.106563	+	0.327966i	−0.883531	+	0.468372i	$0.844841\pi$
$998$	−6.28115	−	4.56352i	−0.198826	−	0.144456i
$999$	−21.1803			−0.670116

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	25.14	even	10
25.2.d.a.16.1	yes	4	5.4	even	2
125.2.d.a.51.1		4	25.11	even	5	inner
125.2.d.a.76.1		4	1.1	even	1	trivial
125.2.e.a.49.1		8	5.2	odd	4
125.2.e.a.49.2		8	5.3	odd	4
125.2.e.a.74.1		8	25.23	odd	20
125.2.e.a.74.2		8	25.2	odd	20
225.2.h.b.91.1		4	15.14	odd	2
225.2.h.b.136.1		4	75.14	odd	10
400.2.u.b.161.1		4	100.39	odd	10
400.2.u.b.241.1		4	20.19	odd	2
625.2.a.b.1.2		2	25.19	even	10
625.2.a.c.1.1		2	25.6	even	5
625.2.b.a.624.2		4	25.17	odd	20
625.2.b.a.624.3		4	25.8	odd	20
625.2.d.b.126.1		4	25.21	even	5
625.2.d.b.501.1		4	25.16	even	5
625.2.d.h.126.1		4	25.4	even	10
625.2.d.h.501.1		4	25.9	even	10
625.2.e.c.124.1		8	25.12	odd	20
625.2.e.c.124.2		8	25.13	odd	20
625.2.e.c.499.1		8	25.3	odd	20
625.2.e.c.499.2		8	25.22	odd	20
5625.2.a.d.1.2		2	75.56	odd	10
5625.2.a.f.1.1		2	75.44	odd	10
10000.2.a.c.1.2		2	100.19	odd	10
10000.2.a.l.1.1		2	100.31	odd	10

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	125.2.d.a.76.1

Level	$125$
Weight	$2$
Character	125.76
Analytic conductor	$0.998$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$