LMFDB - Embedded newform 325.2.m.b.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(49,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("325.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.m (of order $6$, degree $2$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$0.665665 + 1.24775i$ of defining polynomial
Character	$\chi$	$=$	325.199
Dual form			325.2.m.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.747754 - 1.29515i) q^{2} +(-0.0820885 - 0.0473938i) q^{3} +(-0.118272 - 0.204852i) q^{4} +(-0.122764 + 0.0708778i) q^{6} +(2.41342 + 4.18016i) q^{7} +2.63726 q^{8} +(-1.49551 - 2.59030i) q^{9} +O(q^{10})$	\(q+(0.747754 - 1.29515i) q^{2} +(-0.0820885 - 0.0473938i) q^{3} +(-0.118272 - 0.204852i) q^{4} +(-0.122764 + 0.0708778i) q^{6} +(2.41342 + 4.18016i) q^{7} +2.63726 q^{8} +(-1.49551 - 2.59030i) q^{9} +(-0.926118 - 0.534695i) q^{11} +0.0224214i q^{12} +(3.59030 + 0.331331i) q^{13} +7.21857 q^{14} +(2.20857 - 3.82535i) q^{16} +(3.08209 - 1.77944i) q^{17} -4.47309 q^{18} +(-4.96410 + 2.86603i) q^{19} -0.457524i q^{21} +(-1.38502 + 0.799640i) q^{22} +(-6.13649 - 3.54290i) q^{23} +(-0.216489 - 0.124990i) q^{24} +(3.11378 - 4.40221i) q^{26} +0.567874i q^{27} +(0.570878 - 0.988789i) q^{28} +(0.736543 - 1.27573i) q^{29} -1.46410i q^{31} +(-0.665665 - 1.15297i) q^{32} +(0.0506824 + 0.0877845i) q^{33} -5.32235i q^{34} +(-0.353752 + 0.612717i) q^{36} +(-0.0126991 + 0.0219955i) q^{37} +8.57233i q^{38} +(-0.279019 - 0.197356i) q^{39} +(-0.232051 - 0.133975i) q^{41} +(-0.592562 - 0.342116i) q^{42} +(-3.08209 + 1.77944i) q^{43} +0.252957i q^{44} +(-9.17716 + 5.29844i) q^{46} -6.51793 q^{47} +(-0.362596 + 0.209345i) q^{48} +(-8.14918 + 14.1148i) q^{49} -0.337339 q^{51} +(-0.356756 - 0.774668i) q^{52} +0.991015i q^{53} +(0.735481 + 0.424630i) q^{54} +(6.36482 + 11.0242i) q^{56} +0.543327 q^{57} +(-1.10151 - 1.90786i) q^{58} +(7.55440 - 4.36153i) q^{59} +(-3.16867 - 5.48830i) q^{61} +(-1.89623 - 1.09479i) q^{62} +(7.21857 - 12.5029i) q^{63} +6.84325 q^{64} +0.151592 q^{66} +(-2.58658 + 4.48009i) q^{67} +(-0.729047 - 0.420915i) q^{68} +(0.335823 + 0.581663i) q^{69} +(-6.72458 + 3.88244i) q^{71} +(-3.94405 - 6.83129i) q^{72} +10.1088 q^{73} +(0.0189916 + 0.0328945i) q^{74} +(1.17422 + 0.677939i) q^{76} -5.16177i q^{77} +(-0.464243 + 0.213797i) q^{78} -8.78347 q^{79} +(-4.45961 + 7.72427i) q^{81} +(-0.347034 + 0.200360i) q^{82} +0.725474 q^{83} +(-0.0937250 + 0.0541121i) q^{84} +5.32235i q^{86} +(-0.120923 + 0.0698151i) q^{87} +(-2.44242 - 1.41013i) q^{88} +(-11.6970 - 6.75327i) q^{89} +(7.27987 + 15.8077i) q^{91} +1.67610i q^{92} +(-0.0693893 + 0.120186i) q^{93} +(-4.87381 + 8.44168i) q^{94} +0.126194i q^{96} +(1.71935 + 2.97800i) q^{97} +(12.1872 + 21.1088i) q^{98} +3.19856i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9	$ 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9} + 8 q^{13} - 4 q^{14} - 2 q^{16} + 18 q^{17} - 40 q^{18} - 12 q^{19} + 6 q^{22} + 6 q^{23} + 12 q^{24} + 10 q^{26} + 8 q^{28} + 8 q^{29} - 4 q^{32} - 18 q^{33} + 20 q^{36} - 2 q^{37} + 12 q^{41} - 42 q^{42} - 18 q^{43} - 42 q^{46} - 16 q^{47} - 6 q^{48} - 12 q^{49} - 8 q^{51} + 16 q^{52} - 18 q^{54} + 12 q^{56} - 28 q^{57} + 22 q^{58} + 12 q^{59} - 28 q^{61} + 12 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} + 12 q^{68} + 16 q^{69} + 12 q^{72} - 16 q^{73} - 10 q^{74} + 54 q^{76} + 18 q^{78} + 16 q^{79} + 8 q^{81} - 6 q^{82} + 24 q^{83} + 30 q^{84} + 54 q^{87} + 42 q^{88} - 24 q^{89} + 28 q^{91} + 8 q^{93} - 32 q^{94} - 2 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9 + 8 * q^13 - 4 * q^14 - 2 * q^16 + 18 * q^17 - 40 * q^18 - 12 * q^19 + 6 * q^22 + 6 * q^23 + 12 * q^24 + 10 * q^26 + 8 * q^28 + 8 * q^29 - 4 * q^32 - 18 * q^33 + 20 * q^36 - 2 * q^37 + 12 * q^41 - 42 * q^42 - 18 * q^43 - 42 * q^46 - 16 * q^47 - 6 * q^48 - 12 * q^49 - 8 * q^51 + 16 * q^52 - 18 * q^54 + 12 * q^56 - 28 * q^57 + 22 * q^58 + 12 * q^59 - 28 * q^61 + 12 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 + 12 * q^68 + 16 * q^69 + 12 * q^72 - 16 * q^73 - 10 * q^74 + 54 * q^76 + 18 * q^78 + 16 * q^79 + 8 * q^81 - 6 * q^82 + 24 * q^83 + 30 * q^84 + 54 * q^87 + 42 * q^88 - 24 * q^89 + 28 * q^91 + 8 * q^93 - 32 * q^94 - 2 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.747754	−	1.29515i	0.528742	−	0.915808i	−0.470696	−	0.882295i	$-0.655997\pi$
$2$	0.747754	−	1.29515i	0.528742	−	0.915808i	0.999438	−	0.0335125i	$-0.0106693\pi$
$3$	−0.0820885	−	0.0473938i	−0.0473938	−	0.0273628i	0.476116	−	0.879383i	$-0.342044\pi$
$3$	−0.0820885	−	0.0473938i	−0.0473938	−	0.0273628i	−0.523510	+	0.852020i	$0.675378\pi$
$4$	−0.118272	−	0.204852i	−0.0591358	−	0.102426i
$5$		0			0
$5$		0			0
$6$	−0.122764	+	0.0708778i	−0.0501182	+	0.0289357i
$7$	2.41342	+	4.18016i	0.912187	+	1.57995i	0.810969	+	0.585089i	$0.198941\pi$
$7$	2.41342	+	4.18016i	0.912187	+	1.57995i	0.101218	+	0.994864i	$0.467726\pi$
$8$	2.63726			0.932413
$9$	−1.49551	−	2.59030i	−0.498503	−	0.863432i
$10$		0			0
$11$	−0.926118	−	0.534695i	−0.279235	−	0.161217i	0.353842	−	0.935305i	$-0.384875\pi$
$11$	−0.926118	−	0.534695i	−0.279235	−	0.161217i	−0.633077	+	0.774089i	$0.718208\pi$
$12$			0.0224214i			0.00647249i
$13$	3.59030	+	0.331331i	0.995769	+	0.0918946i
$13$	3.59030	+	0.331331i	0.995769	+	0.0918946i
$14$	7.21857			1.92924
$15$		0			0
$16$	2.20857	−	3.82535i	0.552142	−	0.956337i
$17$	3.08209	−	1.77944i	0.747516	−	0.431579i	−0.0772795	−	0.997009i	$-0.524623\pi$
$17$	3.08209	−	1.77944i	0.747516	−	0.431579i	0.824796	+	0.565431i	$0.191290\pi$
$18$	−4.47309			−1.05432
$19$	−4.96410	+	2.86603i	−1.13884	+	0.657511i	−0.946144	−	0.323747i	$-0.895057\pi$
$19$	−4.96410	+	2.86603i	−1.13884	+	0.657511i	−0.192699	+	0.981258i	$0.561724\pi$
$20$		0			0
$21$		−	0.457524i		−	0.0998400i
$22$	−1.38502	+	0.799640i	−0.295287	+	0.170484i
$23$	−6.13649	−	3.54290i	−1.27955	−	0.738746i	−0.302781	−	0.953060i	$-0.597915\pi$
$23$	−6.13649	−	3.54290i	−1.27955	−	0.738746i	−0.976765	+	0.214314i	$0.931248\pi$
$24$	−0.216489	−	0.124990i	−0.0441906	−	0.0255135i
$25$		0			0
$26$	3.11378	−	4.40221i	0.610662	−	0.863344i
$27$			0.567874i			0.109287i
$28$	0.570878	−	0.988789i	0.107886	−	0.186864i
$29$	0.736543	−	1.27573i	0.136773	−	0.236897i	−0.789501	−	0.613750i	$-0.789660\pi$
$29$	0.736543	−	1.27573i	0.136773	−	0.236897i	0.926273	+	0.376853i	$0.122994\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	−0.665665	−	1.15297i	−0.117674	−	0.203818i
$33$	0.0506824	+	0.0877845i	0.00882268	+	0.0152813i
$34$		−	5.32235i		−	0.912775i
$35$		0			0
$36$	−0.353752	+	0.612717i	−0.0589587	+	0.102119i
$37$	−0.0126991	+	0.0219955i	−0.00208772	+	0.00361604i	−0.867067	−	0.498191i	$-0.833998\pi$
$37$	−0.0126991	+	0.0219955i	−0.00208772	+	0.00361604i	0.864980	+	0.501807i	$0.167331\pi$
$38$			8.57233i			1.39061i
$39$	−0.279019	−	0.197356i	−0.0446788	−	0.0316023i
$40$		0			0
$41$	−0.232051	−	0.133975i	−0.0362402	−	0.0209233i	0.481770	−	0.876297i	$-0.339994\pi$
$41$	−0.232051	−	0.133975i	−0.0362402	−	0.0209233i	−0.518011	+	0.855374i	$0.673327\pi$
$42$	−0.592562	−	0.342116i	−0.0914342	−	0.0527896i
$43$	−3.08209	+	1.77944i	−0.470014	+	0.271363i	−0.716246	−	0.697848i	$-0.754141\pi$
$43$	−3.08209	+	1.77944i	−0.470014	+	0.271363i	0.246232	+	0.969211i	$0.420808\pi$
$44$			0.252957i			0.0381347i
$45$		0			0
$46$	−9.17716	+	5.29844i	−1.35310	+	0.781212i
$47$	−6.51793			−0.950738			−0.475369	−	0.879787i	$-0.657685\pi$
$47$	−6.51793			−0.950738			−0.475369	+	0.879787i	$0.657685\pi$
$48$	−0.362596	+	0.209345i	−0.0523362	+	0.0302163i
$49$	−8.14918	+	14.1148i	−1.16417	+	2.01640i
$50$		0			0
$51$	−0.337339			−0.0472368
$52$	−0.356756	−	0.774668i	−0.0494732	−	0.107427i
$53$			0.991015i			0.136126i	0.997681	+	0.0680632i	$0.0216820\pi$
$53$			0.991015i			0.136126i	−0.997681	+	0.0680632i	$0.978318\pi$
$54$	0.735481	+	0.424630i	0.100086	+	0.0577848i
$55$		0			0
$56$	6.36482	+	11.0242i	0.850535	+	1.47317i
$57$	0.543327			0.0719655
$58$	−1.10151	−	1.90786i	−0.144635	−	0.250515i
$59$	7.55440	−	4.36153i	0.983499	−	0.567823i	0.0801741	−	0.996781i	$-0.474452\pi$
$59$	7.55440	−	4.36153i	0.983499	−	0.567823i	0.903325	+	0.428958i	$0.141119\pi$
$60$		0			0
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	0.588697	−	0.808354i	$-0.299641\pi$
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	−0.994403	+	0.105650i	$0.966308\pi$
$62$	−1.89623	−	1.09479i	−0.240821	−	0.139038i
$63$	7.21857	−	12.5029i	0.909455	−	1.57522i
$64$	6.84325			0.855406
$65$		0			0
$66$	0.151592			0.0186597
$67$	−2.58658	+	4.48009i	−0.316001	+	0.547330i	−0.979650	−	0.200714i	$-0.935674\pi$
$67$	−2.58658	+	4.48009i	−0.316001	+	0.547330i	0.663649	+	0.748044i	$0.269007\pi$
$68$	−0.729047	−	0.420915i	−0.0884099	−	0.0510435i
$69$	0.335823	+	0.581663i	0.0404283	+	0.0700240i
$70$		0			0
$71$	−6.72458	+	3.88244i	−0.798061	+	0.460761i	−0.842793	−	0.538238i	$-0.819090\pi$
$71$	−6.72458	+	3.88244i	−0.798061	+	0.460761i	0.0447317	+	0.998999i	$0.485757\pi$
$72$	−3.94405	−	6.83129i	−0.464810	−	0.805075i
$73$	10.1088			1.18314			0.591572	−	0.806252i	$-0.298507\pi$
$73$	10.1088			1.18314			0.591572	+	0.806252i	$0.298507\pi$
$74$	0.0189916	+	0.0328945i	0.00220773	+	0.00382391i
$75$		0			0
$76$	1.17422	+	0.677939i	0.134693	+	0.0777649i
$77$		−	5.16177i		−	0.588238i
$78$	−0.464243	+	0.213797i	−0.0525651	+	0.0242077i
$79$	−8.78347			−0.988218			−0.494109	−	0.869400i	$-0.664506\pi$
$79$	−8.78347			−0.988218			−0.494109	+	0.869400i	$0.664506\pi$
$80$		0			0
$81$	−4.45961	+	7.72427i	−0.495512	+	0.858252i
$82$	−0.347034	+	0.200360i	−0.0383235	+	0.0221261i
$83$	0.725474			0.0796311			0.0398155	−	0.999207i	$-0.487323\pi$
$83$	0.725474			0.0796311			0.0398155	+	0.999207i	$0.487323\pi$
$84$	−0.0937250	+	0.0541121i	−0.0102262	+	0.00590412i
$85$		0			0
$86$			5.32235i			0.573923i
$87$	−0.120923	+	0.0698151i	−0.0129643	+	0.00748497i
$88$	−2.44242	−	1.41013i	−0.260363	−	0.150320i
$89$	−11.6970	−	6.75327i	−1.23988	−	0.715845i	−0.270810	−	0.962633i	$-0.587292\pi$
$89$	−11.6970	−	6.75327i	−1.23988	−	0.715845i	−0.969070	+	0.246788i	$0.920625\pi$
$90$		0			0
$91$	7.27987	+	15.8077i	0.763138	+	1.65709i
$92$			1.67610i			0.174745i
$93$	−0.0693893	+	0.120186i	−0.00719534	+	0.0124627i
$94$	−4.87381	+	8.44168i	−0.502695	+	0.870693i
$95$		0			0
$96$			0.126194i			0.0128796i
$97$	1.71935	+	2.97800i	0.174574	+	0.302371i	0.940014	−	0.341137i	$-0.110812\pi$
$97$	1.71935	+	2.97800i	0.174574	+	0.302371i	−0.765440	+	0.643507i	$0.777479\pi$
$98$	12.1872	+	21.1088i	1.23109	+	2.13231i
$99$			3.19856i			0.321467i
$100$		0			0
$101$	1.42763	−	2.47273i	0.142055	−	0.246046i	−0.786215	−	0.617953i	$-0.787962\pi$
$101$	1.42763	−	2.47273i	0.142055	−	0.246046i	0.928270	+	0.371906i	$0.121296\pi$
$102$	−0.252246	+	0.436903i	−0.0249761	+	0.0432599i
$103$			5.54488i			0.546354i	0.961964	+	0.273177i	$0.0880744\pi$
$103$			5.54488i			0.546354i	−0.961964	+	0.273177i	$0.911926\pi$
$104$	9.46855	+	0.873806i	0.928468	+	0.0856838i
$105$		0			0
$106$	1.28351	+	0.741035i	0.124666	+	0.0719757i
$107$	−3.84611	−	2.22056i	−0.371818	−	0.214669i	0.302434	−	0.953170i	$-0.402201\pi$
$107$	−3.84611	−	2.22056i	−0.371818	−	0.214669i	−0.674252	+	0.738501i	$0.735534\pi$
$108$	0.116330	−	0.0671633i	0.0111939	−	0.00646280i
$109$		−	13.7804i		−	1.31993i	−0.751298	−	0.659963i	$-0.770572\pi$
$109$		−	13.7804i		−	1.31993i	0.751298	−	0.659963i	$-0.229428\pi$
$110$		0			0
$111$	0.00208490	−	0.00120372i	0.000197890	−	0.000114252i
$112$	21.3208			2.01463
$113$	−6.96630	+	4.02200i	−0.655334	+	0.378358i	−0.790497	−	0.612466i	$-0.790178\pi$
$113$	−6.96630	+	4.02200i	−0.655334	+	0.378358i	0.135163	+	0.990823i	$0.456844\pi$
$114$	0.406275	−	0.703689i	0.0380511	−	0.0659065i
$115$		0			0
$116$	−0.348448			−0.0323526
$117$	−4.51107	−	9.79543i	−0.417049	−	0.905588i
$118$		−	13.0454i		−	1.20093i
$119$	14.8767	+	8.58909i	1.36375	+	0.787361i
$120$		0			0
$121$	−4.92820	−	8.53590i	−0.448018	−	0.775991i
$122$	−9.47754			−0.858056
$123$	0.0126991	+	0.0219955i	0.00114504	+	0.00198327i
$124$	−0.299925	+	0.173162i	−0.0269340	+	0.0155504i
$125$		0			0
$126$	−10.7954	−	18.6982i	−0.961734	−	1.66577i
$127$	−0.611979	−	0.353326i	−0.0543044	−	0.0313526i	0.472602	−	0.881276i	$-0.343315\pi$
$127$	−0.611979	−	0.353326i	−0.0543044	−	0.0313526i	−0.526906	+	0.849923i	$0.676648\pi$
$128$	6.44840	−	11.1690i	0.569963	−	0.987205i
$129$	0.337339			0.0297010
$130$		0			0
$131$	6.26554			0.547423			0.273711	−	0.961812i	$-0.411749\pi$
$131$	6.26554			0.547423			0.273711	+	0.961812i	$0.411749\pi$
$132$	0.0119886	−	0.0207648i	0.00104347	−	0.00180735i
$133$	−23.9609	−	13.8338i	−2.07767	−	1.19955i
$134$	3.86825	+	6.70001i	0.334166	+	0.578793i
$135$		0			0
$136$	8.12828	−	4.69286i	0.696994	−	0.402410i
$137$	8.15290	+	14.1212i	0.696549	+	1.20646i	0.969656	+	0.244475i	$0.0786155\pi$
$137$	8.15290	+	14.1212i	0.696549	+	1.20646i	−0.273107	+	0.961984i	$0.588051\pi$
$138$	1.00445			0.0855046
$139$	−3.41264	−	5.91087i	−0.289456	−	0.501353i	0.684224	−	0.729272i	$-0.260141\pi$
$139$	−3.41264	−	5.91087i	−0.289456	−	0.501353i	−0.973680	+	0.227919i	$0.926808\pi$
$140$		0			0
$141$	0.535047	+	0.308909i	0.0450591	+	0.0260149i
$142$			11.6124i			0.974494i
$143$	−3.14788	−	2.22656i	−0.263239	−	0.186195i
$144$	−13.2117			−1.10098
$145$		0			0
$146$	7.55889	−	13.0924i	0.625578	−	1.08353i
$147$	1.33791	−	0.772442i	0.110349	−	0.0637099i
$148$	0.00600778			0.000493837
$149$	7.30887	−	4.21978i	0.598766	−	0.345698i	−0.169790	−	0.985480i	$-0.554309\pi$
$149$	7.30887	−	4.21978i	0.598766	−	0.345698i	0.768556	+	0.639783i	$0.220976\pi$
$150$		0			0
$151$			1.37017i			0.111503i	0.998445	+	0.0557513i	$0.0177554\pi$
$151$			1.37017i			0.111503i	−0.998445	+	0.0557513i	$0.982245\pi$
$152$	−13.0916	+	7.55846i	−1.06187	+	0.613072i
$153$	−9.21857	−	5.32235i	−0.745278	−	0.430286i
$154$	−6.68525	−	3.85973i	−0.538713	−	0.311026i
$155$		0			0
$156$	−0.00742888	+	0.0804993i	−0.000594787	+	0.00644510i
$157$		−	11.9700i		−	0.955311i	−0.878547	−	0.477656i	$-0.841487\pi$
$157$		−	11.9700i		−	0.955311i	0.878547	−	0.477656i	$-0.158513\pi$
$158$	−6.56787	+	11.3759i	−0.522512	+	0.905017i
$159$	0.0469680	−	0.0813509i	0.00372480	−	0.00645155i
$160$		0			0
$161$		−	34.2020i		−	2.69550i
$162$	6.66938	+	11.5517i	0.523996	+	0.907588i
$163$	11.2857	+	19.5474i	0.883962	+	1.53107i	0.846899	+	0.531754i	$0.178467\pi$
$163$	11.2857	+	19.5474i	0.883962	+	1.53107i	0.0370630	+	0.999313i	$0.488200\pi$
$164$			0.0633815i			0.00494927i
$165$		0			0
$166$	0.542476	−	0.939595i	0.0421043	−	0.0729267i
$167$	4.09850	−	7.09881i	0.317152	−	0.549323i	−0.662741	−	0.748849i	$-0.730607\pi$
$167$	4.09850	−	7.09881i	0.317152	−	0.549323i	0.979893	+	0.199526i	$0.0639403\pi$
$168$		−	1.20661i		−	0.0930922i
$169$	12.7804	+	2.37915i	0.983111	+	0.183012i
$170$		0			0
$171$	14.8477	+	8.57233i	1.13543	+	0.655542i
$172$	0.729047	+	0.420915i	0.0555893	+	0.0320945i
$173$	7.93948	−	4.58386i	0.603628	−	0.348505i	−0.166840	−	0.985984i	$-0.553356\pi$
$173$	7.93948	−	4.58386i	0.603628	−	0.348505i	0.770467	+	0.637479i	$0.220023\pi$
$174$			0.208818i			0.0158305i
$175$		0			0
$176$	−4.09079	+	2.36182i	−0.308355	+	0.178029i
$177$	−0.826838			−0.0621490
$178$	−17.4930	+	10.0996i	−1.31115	+	0.756994i
$179$	5.01850	−	8.69229i	0.375100	−	0.649693i	−0.615242	−	0.788338i	$-0.710942\pi$
$179$	5.01850	−	8.69229i	0.375100	−	0.649693i	0.990342	+	0.138646i	$0.0442750\pi$
$180$		0			0
$181$	−17.0238			−1.26537			−0.632686	−	0.774408i	$-0.718048\pi$
$181$	−17.0238			−1.26537			−0.632686	+	0.774408i	$0.718048\pi$
$182$	25.9168	+	2.39174i	1.92108	+	0.177287i
$183$			0.600701i			0.0444051i
$184$	−16.1835	−	9.34356i	−1.19307	−	0.688817i
$185$		0			0
$186$	0.103772	+	0.179739i	0.00760895	+	0.0131791i
$187$	−3.80584			−0.278310
$188$	0.770886	+	1.33521i	0.0562226	+	0.0973804i
$189$	−2.37381	+	1.37052i	−0.172669	+	0.0996905i
$190$		0			0
$191$	1.93870	+	3.35793i	0.140280	+	0.242971i	0.927602	−	0.373570i	$-0.121867\pi$
$191$	1.93870	+	3.35793i	0.140280	+	0.242971i	−0.787322	+	0.616542i	$0.788533\pi$
$192$	−0.561752	−	0.324328i	−0.0405410	−	0.0234063i
$193$	−0.626972	+	1.08595i	−0.0451304	+	0.0781681i	−0.887708	−	0.460406i	$-0.847704\pi$
$193$	−0.626972	+	1.08595i	−0.0451304	+	0.0781681i	0.842578	+	0.538575i	$0.181037\pi$
$194$	5.14261			0.369218
$195$		0			0
$196$	3.85527			0.275376
$197$	7.64098	−	13.2346i	0.544397	−	0.942923i	−0.454247	−	0.890876i	$-0.650092\pi$
$197$	7.64098	−	13.2346i	0.544397	−	0.942923i	0.998645	−	0.0520479i	$-0.0165749\pi$
$198$	4.14261	+	2.39174i	0.294402	+	0.169973i
$199$	6.61480	+	11.4572i	0.468911	+	0.812177i	0.999368	−	0.0355340i	$-0.0113132\pi$
$199$	6.61480	+	11.4572i	0.468911	+	0.812177i	−0.530458	+	0.847711i	$0.677980\pi$
$200$		0			0
$201$	0.424657	−	0.245176i	0.0299530	−	0.0172934i
$202$	−2.13504	−	3.69799i	−0.150221	−	0.260190i
$203$	7.11035			0.499049
$204$	0.0398976	+	0.0691046i	0.00279339	+	0.00483829i
$205$		0			0
$206$	7.18144	+	4.14621i	0.500355	+	0.288880i
$207$			21.1937i			1.47307i
$208$	9.19686	−	13.0024i	0.637688	−	0.901552i
$209$	6.12979			0.424007
$210$		0			0
$211$	2.40521	−	4.16595i	0.165582	−	0.286796i	−0.771280	−	0.636496i	$-0.780383\pi$
$211$	2.40521	−	4.16595i	0.165582	−	0.286796i	0.936862	+	0.349700i	$0.113717\pi$
$212$	0.203012	−	0.117209i	0.0139429	−	0.00804994i
$213$	0.736014			0.0504309
$214$	−5.75189	+	3.32086i	−0.393191	+	0.227009i
$215$		0			0
$216$			1.49763i			0.101901i
$217$	6.12019	−	3.53349i	0.415465	−	0.239869i
$218$	−17.8477	−	10.3044i	−1.20880	−	0.697900i
$219$	−0.829815	−	0.479094i	−0.0560737	−	0.0323742i
$220$		0			0
$221$	11.6552	−	5.36754i	0.784013	−	0.361060i
$222$		−	0.00360034i		−	0.000241639i
$223$	7.35661	−	12.7420i	0.492635	−	0.853269i	−0.507329	−	0.861753i	$-0.669367\pi$
$223$	7.35661	−	12.7420i	0.492635	−	0.853269i	0.999964	+	0.00848317i	$0.00270031\pi$
$224$	3.21306	−	5.56518i	0.214682	−	0.371839i
$225$		0			0
$226$			12.0299i			0.800214i
$227$	−7.45140	−	12.9062i	−0.494567	−	0.856615i	0.505413	−	0.862877i	$-0.331340\pi$
$227$	−7.45140	−	12.9062i	−0.494567	−	0.856615i	−0.999980	+	0.00626222i	$0.998007\pi$
$228$	−0.0642602	−	0.111302i	−0.00425573	−	0.00737115i
$229$		−	19.3074i		−	1.27587i	−0.770092	−	0.637933i	$-0.779790\pi$
$229$		−	19.3074i		−	1.27587i	0.770092	−	0.637933i	$-0.220210\pi$
$230$		0			0
$231$	−0.244636	+	0.423722i	−0.0160959	+	0.0278788i
$232$	1.94246	−	3.36444i	0.127529	−	0.220886i
$233$			21.1937i			1.38845i	0.719759	+	0.694224i	$0.244252\pi$
$233$			21.1937i			1.38845i	−0.719759	+	0.694224i	$0.755748\pi$
$234$	−16.0597	−	1.48207i	−1.04986	−	0.0968860i
$235$		0			0
$236$	−1.78694	−	1.03169i	−0.116320	−	0.0671573i
$237$	0.721022	+	0.416282i	0.0468354	+	0.0270404i
$238$	22.2483	−	12.8451i	1.44214	−	0.832621i
$239$			14.8971i			0.963612i	0.876278	+	0.481806i	$0.160019\pi$
$239$			14.8971i			0.963612i	−0.876278	+	0.481806i	$0.839981\pi$
$240$		0			0
$241$	−8.13343	+	4.69584i	−0.523921	+	0.302486i	−0.738537	−	0.674213i	$-0.764483\pi$
$241$	−8.13343	+	4.69584i	−0.523921	+	0.302486i	0.214617	+	0.976698i	$0.431150\pi$
$242$	−14.7403			−0.947544
$243$	2.20754	−	1.27453i	0.141614	−	0.0817609i
$244$	−0.749527	+	1.29822i	−0.0479835	+	0.0831099i
$245$		0			0
$246$	0.0379833			0.00242173
$247$	−18.7722	+	8.64512i	−1.19445	+	0.550076i
$248$		−	3.86122i		−	0.245188i
$249$	−0.0595530	−	0.0343829i	−0.00377402	−	0.00217893i
$250$		0			0
$251$	5.65817	+	9.80024i	0.357140	+	0.618585i	0.987482	−	0.157733i	$-0.0504184\pi$
$251$	5.65817	+	9.80024i	0.357140	+	0.618585i	−0.630341	+	0.776318i	$0.717085\pi$
$252$	−3.41501			−0.215125
$253$	3.78874	+	6.56229i	0.238196	+	0.412568i
$254$	−0.915219	+	0.528402i	−0.0574260	+	0.0331549i
$255$		0			0
$256$	−2.80038	−	4.85040i	−0.175024	−	0.303150i
$257$	22.9773	+	13.2660i	1.43329	+	0.827508i	0.997370	−	0.0724788i	$-0.0230910\pi$
$257$	22.9773	+	13.2660i	1.43329	+	0.827508i	0.435917	+	0.899987i	$0.356424\pi$
$258$	0.252246	−	0.436903i	0.0157042	−	0.0272004i
$259$	−0.122593			−0.00761758
$260$		0			0
$261$	−4.40602			−0.272726
$262$	4.68508	−	8.11480i	0.289445	−	0.501334i
$263$	12.2463	+	7.07038i	0.755137	+	0.435979i	0.827547	−	0.561396i	$-0.189736\pi$
$263$	12.2463	+	7.07038i	0.755137	+	0.435979i	−0.0724100	+	0.997375i	$0.523069\pi$
$264$	0.133663	+	0.231511i	0.00822638	+	0.0142485i
$265$		0			0
$266$	−35.8337	+	20.6886i	−2.19711	+	1.26850i
$267$	0.640126	+	1.10873i	0.0391751	+	0.0678532i
$268$	1.22368			0.0747479
$269$	12.3872	+	21.4553i	0.755264	+	1.30815i	0.945243	+	0.326367i	$0.105824\pi$
$269$	12.3872	+	21.4553i	0.755264	+	1.30815i	−0.189980	+	0.981788i	$0.560842\pi$
$270$		0			0
$271$	16.2095	+	9.35856i	0.984657	+	0.568492i	0.903673	−	0.428224i	$-0.140860\pi$
$271$	16.2095	+	9.35856i	0.984657	+	0.568492i	0.0809839	+	0.996715i	$0.474194\pi$
$272$		−	15.7201i		−	0.953170i
$273$	0.151592	−	1.64265i	0.00917476	−	0.0994176i
$274$	24.3854			1.47318
$275$		0			0
$276$	0.0794367	−	0.137588i	0.00478152	−	0.00828184i
$277$	−19.6282	+	11.3323i	−1.17934	+	0.680893i	−0.955862	−	0.293815i	$-0.905075\pi$
$277$	−19.6282	+	11.3323i	−1.17934	+	0.680893i	−0.223480	+	0.974709i	$0.571742\pi$
$278$	−10.2073			−0.612191
$279$	−3.79246	+	2.18958i	−0.227048	+	0.131086i
$280$		0			0
$281$			27.8384i			1.66070i	0.557241	+	0.830351i	$0.311860\pi$
$281$			27.8384i			1.66070i	−0.557241	+	0.830351i	$0.688140\pi$
$282$	0.800167	−	0.461976i	0.0476492	−	0.0275103i
$283$	6.85898	+	3.96004i	0.407724	+	0.235400i	0.689811	−	0.723989i	$-0.257693\pi$
$283$	6.85898	+	3.96004i	0.407724	+	0.235400i	−0.282087	+	0.959389i	$0.591027\pi$
$284$	1.59065	+	0.918364i	0.0943879	+	0.0544949i
$285$		0			0
$286$	−5.23757	+	2.41204i	−0.309704	+	0.142627i
$287$		−	1.29335i		−	0.0763439i
$288$	−1.99102	+	3.44854i	−0.117322	+	0.203207i
$289$	−2.16715	+	3.75362i	−0.127480	+	0.220801i
$290$		0			0
$291$		−	0.325946i		−	0.0191073i
$292$	−1.19558	−	2.07081i	−0.0699662	−	0.121185i
$293$	0.136485	+	0.236400i	0.00797356	+	0.0138106i	0.869985	−	0.493079i	$-0.164129\pi$
$293$	0.136485	+	0.236400i	0.00797356	+	0.0138106i	−0.862011	+	0.506889i	$0.830795\pi$
$294$		−	2.31038i		−	0.134744i
$295$		0			0
$296$	−0.0334909	+	0.0580080i	−0.00194662	+	0.00337165i
$297$	0.303639	−	0.525918i	0.0176189	−	0.0305169i
$298$		−	12.6214i		−	0.731139i
$299$	−20.8579	−	14.7533i	−1.20624	−	0.853204i
$300$		0			0
$301$	−14.8767	−	8.58909i	−0.857481	−	0.495067i
$302$	1.77457	+	1.02455i	0.102115	+	0.0589560i
$303$	−0.234385	+	0.135322i	−0.0134650	+	0.00777404i
$304$			25.3192i			1.45216i
$305$		0			0
$306$	−13.7864	+	7.95961i	−0.788119	+	0.455021i
$307$	−6.85224			−0.391078			−0.195539	−	0.980696i	$-0.562646\pi$
$307$	−6.85224			−0.391078			−0.195539	+	0.980696i	$0.562646\pi$
$308$	−1.05740	+	0.610491i	−0.0602510	+	0.0347859i
$309$	0.262793	−	0.455171i	0.0149498	−	0.0258938i
$310$		0			0
$311$	−10.6447			−0.603605			−0.301803	−	0.953370i	$-0.597588\pi$
$311$	−10.6447			−0.603605			−0.301803	+	0.953370i	$0.597588\pi$
$312$	−0.735846	−	0.520480i	−0.0416591	−	0.0294664i
$313$			17.8236i			1.00745i	0.863865	+	0.503724i	$0.168037\pi$
$313$			17.8236i			1.00745i	−0.863865	+	0.503724i	$0.831963\pi$
$314$	−15.5029	−	8.95062i	−0.874881	−	0.505113i
$315$		0			0
$316$	1.03883	+	1.79931i	0.0584390	+	0.101219i
$317$	8.17161			0.458963			0.229482	−	0.973313i	$-0.426297\pi$
$317$	8.17161			0.458963			0.229482	+	0.973313i	$0.426297\pi$
$318$	−0.0702410	−	0.121661i	−0.00393892	−	0.00682241i
$319$	−1.36425	+	0.787651i	−0.0763835	+	0.0441000i
$320$		0			0
$321$	0.210481	+	0.364564i	0.0117479	+	0.0203480i
$322$	−44.2967	−	25.5747i	−2.46856	−	1.42522i
$323$	−10.1999	+	17.6667i	−0.567536	+	0.983001i
$324$	2.10978			0.117210
$325$		0			0
$326$	33.7556			1.86955
$327$	−0.653107	+	1.13122i	−0.0361169	+	0.0625563i
$328$	−0.611979	−	0.353326i	−0.0337909	−	0.0195092i
$329$	−15.7305	−	27.2460i	−0.867250	−	1.50212i
$330$		0			0
$331$	21.5983	−	12.4698i	1.18715	−	0.685400i	0.229490	−	0.973311i	$-0.426294\pi$
$331$	21.5983	−	12.4698i	1.18715	−	0.685400i	0.957657	+	0.287911i	$0.0929608\pi$
$332$	−0.0858029	−	0.148615i	−0.00470905	−	0.00815631i
$333$	0.0759666			0.00416294
$334$	−6.12934	−	10.6163i	−0.335383	−	0.580900i
$335$		0			0
$336$	−1.75019	−	1.01047i	−0.0954807	−	0.0551258i
$337$		−	19.6057i		−	1.06799i	−0.845487	−	0.533996i	$-0.820690\pi$
$337$		−	19.6057i		−	1.06799i	0.845487	−	0.533996i	$-0.179310\pi$
$338$	12.6380	−	14.7735i	0.687415	−	0.803575i
$339$	0.762471			0.0414117
$340$		0			0
$341$	−0.782847	+	1.35593i	−0.0423936	+	0.0734278i
$342$	22.2049	−	12.8200i	1.20070	−	0.693225i
$343$	−44.8817			−2.42339
$344$	−8.12828	+	4.69286i	−0.438247	+	0.253022i
$345$		0			0
$346$		−	13.7104i		−	0.737076i
$347$	−14.7926	+	8.54049i	−0.794107	+	0.458478i	−0.841406	−	0.540403i	$-0.818272\pi$
$347$	−14.7926	+	8.54049i	−0.794107	+	0.458478i	0.0472996	+	0.998881i	$0.484938\pi$
$348$	0.0286036	+	0.0165143i	0.00153331	+	0.000885259i
$349$	24.5708	+	14.1860i	1.31525	+	0.759357i	0.982960	−	0.183822i	$-0.0588469\pi$
$349$	24.5708	+	14.1860i	1.31525	+	0.759357i	0.332286	+	0.943179i	$0.392180\pi$
$350$		0			0
$351$	−0.188154	+	2.03883i	−0.0100429	+	0.108825i
$352$			1.42371i			0.0758840i
$353$	10.6260	−	18.4047i	0.565564	−	0.979586i	−0.431433	−	0.902145i	$-0.641992\pi$
$353$	10.6260	−	18.4047i	0.565564	−	0.979586i	0.996997	−	0.0774407i	$-0.0246749\pi$
$354$	−0.618272	+	1.07088i	−0.0328608	+	0.0569165i
$355$		0			0
$356$			3.19488i			0.169328i
$357$	−0.814139	−	1.41013i	−0.0430888	−	0.0746320i
$358$	−7.50520	−	12.9994i	−0.396662	−	0.687039i
$359$			32.6519i			1.72330i	0.507502	+	0.861650i	$0.330569\pi$
$359$			32.6519i			1.72330i	−0.507502	+	0.861650i	$0.669431\pi$
$360$		0			0
$361$	6.92820	−	12.0000i	0.364642	−	0.631579i
$362$	−12.7296	+	22.0484i	−0.669055	+	1.15884i
$363$			0.934265i			0.0490362i
$364$	2.37724	−	3.36090i	0.124601	−	0.176159i
$365$		0			0
$366$	0.777997	+	0.449176i	0.0406665	+	0.0234788i
$367$	−5.12546	−	2.95918i	−0.267547	−	0.154468i	0.360226	−	0.932865i	$-0.382700\pi$
$367$	−5.12546	−	2.95918i	−0.267547	−	0.154468i	−0.627772	+	0.778397i	$0.716033\pi$
$368$	−27.1057	+	15.6495i	−1.41298	+	0.815785i
$369$			0.801440i			0.0417213i
$370$		0			0
$371$	−4.14261	+	2.39174i	−0.215073	+	0.124173i
$372$	0.0328271			0.00170201
$373$	−11.5342	+	6.65926i	−0.597217	+	0.344803i	−0.767946	−	0.640515i	$-0.778721\pi$
$373$	−11.5342	+	6.65926i	−0.597217	+	0.344803i	0.170729	+	0.985318i	$0.445388\pi$
$374$	−2.84583	+	4.92912i	−0.147154	+	0.254879i
$375$		0			0
$376$	−17.1895			−0.886480
$377$	3.06710	−	4.33621i	0.157963	−	0.223326i
$378$			4.09924i			0.210842i
$379$	22.0131	+	12.7093i	1.13074	+	0.652832i	0.944120	−	0.329601i	$-0.106914\pi$
$379$	22.0131	+	12.7093i	1.13074	+	0.652832i	0.186617	+	0.982433i	$0.440248\pi$
$380$		0			0
$381$	0.0334909	+	0.0580080i	0.00171579	+	0.00297184i
$382$	5.79869			0.296687
$383$	−5.41342	−	9.37632i	−0.276613	−	0.479107i	0.693928	−	0.720044i	$-0.255879\pi$
$383$	−5.41342	−	9.37632i	−0.276613	−	0.479107i	−0.970541	+	0.240937i	$0.922545\pi$
$384$	−1.05868	+	0.611228i	−0.0540254	+	0.0311916i
$385$		0			0
$386$	0.937641	+	1.62404i	0.0477247	+	0.0826615i
$387$	9.21857	+	5.32235i	0.468606	+	0.270550i
$388$	0.406701	−	0.704427i	0.0206471	−	0.0357618i
$389$	−23.0370			−1.16802			−0.584011	−	0.811746i	$-0.698518\pi$
$389$	−23.0370			−1.16802			−0.584011	+	0.811746i	$0.698518\pi$
$390$		0			0
$391$	−25.2176			−1.27531
$392$	−21.4915	+	37.2244i	−1.08549	+	1.88012i
$393$	−0.514329	−	0.296948i	−0.0259444	−	0.0149790i
$394$	−11.4271	−	19.7924i	−0.575691	−	0.997126i
$395$		0			0
$396$	0.655233	−	0.378299i	0.0329267	−	0.0190102i
$397$	10.5432	+	18.2614i	0.529149	+	0.916512i	0.999422	+	0.0339917i	$0.0108220\pi$
$397$	10.5432	+	18.2614i	0.529149	+	0.916512i	−0.470273	+	0.882521i	$0.655845\pi$
$398$	19.7850			0.991731
$399$	1.31128	+	2.27120i	0.0656459	+	0.113702i
$400$		0			0
$401$	−17.1273	−	9.88845i	−0.855296	−	0.493805i	0.00713812	−	0.999975i	$-0.497728\pi$
$401$	−17.1273	−	9.88845i	−0.855296	−	0.493805i	−0.862434	+	0.506169i	$0.831061\pi$
$402$		−	0.733324i		−	0.0365749i
$403$	0.485102	−	5.25656i	0.0241646	−	0.261848i
$404$	−0.675394			−0.0336021
$405$		0			0
$406$	5.31679	−	9.20895i	0.263868	−	0.457033i
$407$	0.0235218	−	0.0135803i	0.00116593	−	0.000673151i
$408$	−0.889650			−0.0440443
$409$	27.6096	−	15.9404i	1.36521	−	0.788204i	0.374897	−	0.927066i	$-0.377678\pi$
$409$	27.6096	−	15.9404i	1.36521	−	0.788204i	0.990312	+	0.138862i	$0.0443446\pi$
$410$		0			0
$411$		−	1.54559i		−	0.0762382i
$412$	1.13588	−	0.655802i	0.0559609	−	0.0323090i
$413$	36.4639	+	21.0524i	1.79427	+	1.03592i
$414$	27.4490	+	15.8477i	1.34905	+	0.778872i
$415$		0			0
$416$	−2.00792	−	4.36004i	−0.0984465	−	0.213769i
$417$			0.646952i			0.0316814i
$418$	4.58358	−	7.93899i	0.224190	−	0.388309i
$419$	15.3648	−	26.6127i	0.750621	−	1.30011i	−0.196902	−	0.980423i	$-0.563088\pi$
$419$	15.3648	−	26.6127i	0.750621	−	1.30011i	0.947522	−	0.319690i	$-0.103579\pi$
$420$		0			0
$421$			17.9820i			0.876391i	0.898880	+	0.438195i	$0.144382\pi$
$421$			17.9820i			0.876391i	−0.898880	+	0.438195i	$0.855618\pi$
$422$	−3.59701	−	6.23021i	−0.175100	−	0.303282i
$423$	9.74761	+	16.8834i	0.473945	+	0.820897i
$424$			2.61357i			0.126926i
$425$		0			0
$426$	0.550357	−	0.953247i	0.0266649	−	0.0461850i
$427$	15.2947	−	26.4911i	0.740160	−	1.28200i
$428$			1.05051i			0.0507785i
$429$	0.152879	+	0.331965i	0.00738107	+	0.0160274i
$430$		0			0
$431$	−4.24308	−	2.44974i	−0.204382	−	0.118000i	0.394316	−	0.918975i	$-0.370982\pi$
$431$	−4.24308	−	2.44974i	−0.204382	−	0.118000i	−0.598698	+	0.800975i	$0.704315\pi$
$432$	2.17232	+	1.25419i	0.104516	+	0.0603421i
$433$	16.6618	−	9.61972i	0.800717	−	0.462294i	−0.0430048	−	0.999075i	$-0.513693\pi$
$433$	16.6618	−	9.61972i	0.800717	−	0.462294i	0.843722	+	0.536781i	$0.180360\pi$
$434$		−	10.5687i		−	0.507315i
$435$		0			0
$436$	−2.82296	+	1.62983i	−0.135195	+	0.0780549i
$437$	40.6162			1.94294
$438$	−1.24100	+	0.716489i	−0.0592970	+	0.0342352i
$439$	4.27987	−	7.41295i	0.204267	−	0.353801i	−0.745632	−	0.666358i	$-0.767852\pi$
$439$	4.27987	−	7.41295i	0.204267	−	0.353801i	0.949899	+	0.312557i	$0.101186\pi$
$440$		0			0
$441$	48.7487			2.32137
$442$	1.76346	−	19.1088i	0.0838791	−	0.908913i
$443$		−	37.9652i		−	1.80378i	−0.431965	−	0.901891i	$-0.642179\pi$
$443$		−	37.9652i		−	1.80378i	0.431965	−	0.901891i	$-0.357821\pi$
$444$	−0.000493170	0	0.000284732i	−2.34048e−5	0	1.35128e-5i
$445$		0			0
$446$	−11.0019	−	19.0558i	−0.520954	−	0.902318i
$447$	−0.799965			−0.0378370
$448$	16.5156	+	28.6059i	0.780290	+	1.35150i
$449$	−23.1283	+	13.3531i	−1.09149	+	0.630173i	−0.933973	−	0.357344i	$-0.883683\pi$
$449$	−23.1283	+	13.3531i	−1.09149	+	0.630173i	−0.157518	+	0.987516i	$0.550349\pi$
$450$		0			0
$451$	0.143271	+	0.248153i	0.00674637	+	0.0116851i
$452$	1.64783	+	0.951375i	0.0775074	+	0.0447489i
$453$	0.0649373	−	0.112475i	0.00305102	−	0.00528453i
$454$	−22.2873			−1.04599
$455$		0			0
$456$	1.43290			0.0671016
$457$	2.13563	−	3.69903i	0.0999007	−	0.173033i	−0.811743	−	0.584015i	$-0.801481\pi$
$457$	2.13563	−	3.69903i	0.0999007	−	0.173033i	0.911643	+	0.410982i	$0.134814\pi$
$458$	−25.0059	−	14.4371i	−1.16845	−	0.674604i
$459$	1.01050	+	1.75024i	0.0471661	+	0.0816941i
$460$		0			0
$461$	17.8767	−	10.3211i	0.832603	−	0.480704i	−0.0221401	−	0.999755i	$-0.507048\pi$
$461$	17.8767	−	10.3211i	0.832603	−	0.480704i	0.854743	+	0.519051i	$0.173715\pi$
$462$	0.365855	+	0.633679i	0.0170211	+	0.0294814i
$463$	−32.1040			−1.49200			−0.745999	−	0.665947i	$-0.768028\pi$
$463$	−32.1040			−1.49200			−0.745999	+	0.665947i	$0.768028\pi$
$464$	−3.25341	−	5.63507i	−0.151036	−	0.261602i
$465$		0			0
$466$	27.4490	+	15.8477i	1.27155	+	0.734131i
$467$			23.3774i			1.08178i	0.841095	+	0.540888i	$0.181912\pi$
$467$			23.3774i			1.08178i	−0.841095	+	0.540888i	$0.818088\pi$
$468$	−1.47309	+	2.08262i	−0.0680934	+	0.0962694i
$469$	−24.9700			−1.15301
$470$		0			0
$471$	−0.567304	+	0.982600i	−0.0261400	+	0.0452758i
$472$	19.9229	−	11.5025i	0.917027	−	0.529446i
$473$	3.80584			0.174993
$474$	1.07829	−	0.622553i	0.0495277	−	0.0285948i
$475$		0			0
$476$		−	4.06338i		−	0.186245i
$477$	2.56702	−	1.48207i	0.117536	−	0.0678594i
$478$	19.2939	+	11.1393i	0.882483	+	0.509502i
$479$	4.48198	+	2.58767i	0.204787	+	0.118234i	0.598886	−	0.800834i	$-0.295610\pi$
$479$	4.48198	+	2.58767i	0.204787	+	0.118234i	−0.394100	+	0.919068i	$0.628943\pi$
$480$		0			0
$481$	−0.0528814	+	0.0747629i	−0.00241119	+	0.00340889i
$482$			14.0453i			0.639747i
$483$	−1.62096	+	2.80759i	−0.0737564	+	0.127750i
$484$	−1.16573	+	2.01911i	−0.0529879	+	0.0917777i
$485$		0			0
$486$		−	3.81213i		−	0.172922i
$487$	15.3865	+	26.6501i	0.697227	+	1.20763i	0.969424	+	0.245391i	$0.0789165\pi$
$487$	15.3865	+	26.6501i	0.697227	+	1.20763i	−0.272197	+	0.962242i	$0.587750\pi$
$488$	−8.35661	−	14.4741i	−0.378286	−	0.655211i
$489$		−	2.13948i		−	0.0967508i
$490$		0			0
$491$	17.8992	−	31.0023i	0.807778	−	1.39911i	−0.106622	−	0.994300i	$-0.534003\pi$
$491$	17.8992	−	31.0023i	0.807778	−	1.39911i	0.914400	−	0.404813i	$-0.132663\pi$
$492$	0.00300389	−	0.00520289i	0.000135426	−	0.000234565i
$493$		−	5.24255i		−	0.236113i
$494$	−2.84028	+	30.7772i	−0.127790	+	1.38473i
$495$		0			0
$496$	−5.60070	−	3.23357i	−0.251479	−	0.145191i
$497$	−32.4585	−	18.7399i	−1.45596	−	0.840600i
$498$	−0.0890620	+	0.0514200i	−0.00399096	+	0.00230418i
$499$		−	28.8971i		−	1.29361i	−0.762655	−	0.646805i	$-0.776105\pi$
$499$		−	28.8971i		−	1.29361i	0.762655	−	0.646805i	$-0.223895\pi$
$500$		0			0
$501$	−0.672879	+	0.388487i	−0.0300620	+	0.0173563i
$502$	16.9237			0.755340
$503$	−6.80974	+	3.93161i	−0.303631	+	0.175302i	−0.644073	−	0.764964i	$-0.722757\pi$
$503$	−6.80974	+	3.93161i	−0.303631	+	0.175302i	0.340442	+	0.940266i	$0.389423\pi$
$504$	19.0373	−	32.9735i	0.847988	−	1.46876i
$505$		0			0
$506$	11.3322			0.503777
$507$	−0.936370	−	0.801014i	−0.0415856	−	0.0355743i
$508$			0.167154i			0.00741625i
$509$	−24.2585	−	14.0057i	−1.07524	−	0.620790i	−0.145631	−	0.989339i	$-0.546521\pi$
$509$	−24.2585	−	14.0057i	−1.07524	−	0.620790i	−0.929608	+	0.368549i	$0.879855\pi$
$510$		0			0
$511$	24.3968	+	42.2564i	1.07925	+	1.86931i
$512$	17.4176			0.769757
$513$	−1.62754	−	2.81898i	−0.0718577	−	0.124461i
$514$	34.3628	−	19.8394i	1.51568	−	0.875076i
$515$		0			0
$516$	−0.0398976	−	0.0691046i	−0.00175639	−	0.00304216i
$517$	6.03637	+	3.48510i	0.265479	+	0.153275i
$518$	−0.0916696	+	0.158776i	−0.00402773	+	0.00697623i
$519$	−0.868986			−0.0381443
$520$		0			0
$521$	−37.5609			−1.64557			−0.822786	−	0.568351i	$-0.807581\pi$
$521$	−37.5609			−1.64557			−0.822786	+	0.568351i	$0.807581\pi$
$522$	−3.29462	+	5.70645i	−0.144202	+	0.249765i
$523$	39.2401	+	22.6553i	1.71585	+	0.990647i	0.926151	+	0.377154i	$0.123097\pi$
$523$	39.2401	+	22.6553i	1.71585	+	0.990647i	0.789700	+	0.613493i	$0.210236\pi$
$524$	−0.741035	−	1.28351i	−0.0323723	−	0.0560704i
$525$		0			0
$526$	18.3144	−	10.5738i	0.798545	−	0.461040i
$527$	−2.60529	−	4.51249i	−0.113488	−	0.196567i
$528$	0.447742			0.0194855
$529$	13.6043	+	23.5633i	0.591491	+	1.02449i
$530$		0			0
$531$	−22.5953	−	13.0454i	−0.980553	−	0.566123i
$532$			6.54460i			0.283744i
$533$	−0.788741	−	0.557894i	−0.0341642	−	0.0241651i
$534$	1.91463			0.0828540
$535$		0			0
$536$	−6.82149	+	11.8152i	−0.294644	+	0.510338i
$537$	−0.823922	+	0.475691i	−0.0355548	+	0.0205276i
$538$	37.0504			1.59736
$539$	15.0942	−	8.71465i	0.650154	−	0.375367i
$540$		0			0
$541$		−	19.7445i		−	0.848882i	−0.905456	−	0.424441i	$-0.860471\pi$
$541$		−	19.7445i		−	0.848882i	0.905456	−	0.424441i	$-0.139529\pi$
$542$	24.2414	−	13.9958i	1.04126	−	0.601171i
$543$	1.39746	+	0.806824i	0.0599708	+	0.0346242i
$544$	−4.10328	−	2.36903i	−0.175927	−	0.101571i
$545$		0			0
$546$	−2.01412	−	1.42463i	−0.0861963	−	0.0609685i
$547$			11.8312i			0.505867i	0.967484	+	0.252934i	$0.0813954\pi$
$547$			11.8312i			0.505867i	−0.967484	+	0.252934i	$0.918605\pi$
$548$	1.92851	−	3.34028i	0.0823820	−	0.142690i
$549$	−9.47754	+	16.4156i	−0.404491	+	0.700600i
$550$		0			0
$551$			8.44381i			0.359718i
$552$	0.885654	+	1.53400i	0.0376959	+	0.0652913i
$553$	−21.1982	−	36.7164i	−0.901439	−	1.56134i
$554$			33.8952i			1.44007i
$555$		0			0
$556$	−0.807237	+	1.39818i	−0.0342345	+	0.0592958i
$557$	−2.02310	+	3.50412i	−0.0857217	+	0.148474i	−0.905699	−	0.423922i	$-0.860653\pi$
$557$	−2.02310	+	3.50412i	−0.0857217	+	0.148474i	0.819977	+	0.572397i	$0.193986\pi$
$558$			6.54905i			0.277244i
$559$	−11.6552	+	5.36754i	−0.492962	+	0.227023i
$560$		0			0
$561$	0.312415	+	0.180373i	0.0131902	+	0.00761536i
$562$	36.0549	+	20.8163i	1.52088	+	0.878083i
$563$	−3.37686	+	1.94963i	−0.142318	+	0.0821671i	−0.569468	−	0.822013i	$-0.692851\pi$
$563$	−3.37686	+	1.94963i	−0.142318	+	0.0821671i	0.427151	+	0.904181i	$0.359517\pi$
$564$		−	0.146141i		−	0.00615364i
$565$		0			0
$566$	10.2577	−	5.92226i	0.431162	−	0.248931i
$567$	−43.0516			−1.80800
$568$	−17.7345	+	10.2390i	−0.744123	+	0.429619i
$569$	8.66778	−	15.0130i	0.363372	−	0.629379i	−0.625141	−	0.780512i	$-0.714959\pi$
$569$	8.66778	−	15.0130i	0.363372	−	0.629379i	0.988514	+	0.151133i	$0.0482920\pi$
$570$		0			0
$571$	−29.5118			−1.23503			−0.617515	−	0.786559i	$-0.711860\pi$
$571$	−29.5118			−1.23503			−0.617515	+	0.786559i	$0.711860\pi$
$572$	−0.0838123	+	0.908189i	−0.00350437	+	0.0379733i
$573$		−	0.367530i		−	0.0153538i
$574$	−1.67508	−	0.967106i	−0.0699163	−	0.0403662i
$575$		0			0
$576$	−10.2341	−	17.7260i	−0.426422	−	0.738585i
$577$	−28.3684			−1.18099			−0.590496	−	0.807041i	$-0.701068\pi$
$577$	−28.3684			−1.18099			−0.590496	+	0.807041i	$0.701068\pi$
$578$	3.24100	+	5.61357i	0.134808	+	0.233494i
$579$	0.102934	−	0.0594291i	0.00427780	−	0.00246979i
$580$		0			0
$581$	1.75087	+	3.03260i	0.0726384	+	0.125813i
$582$	−0.422149	−	0.243728i	−0.0174986	−	0.0101028i
$583$	0.529891	−	0.917797i	0.0219458	−	0.0380113i
$584$	26.6595			1.10318
$585$		0			0
$586$	0.408230			0.0168638
$587$	17.1939	−	29.7806i	0.709667	−	1.22918i	−0.255314	−	0.966858i	$-0.582179\pi$
$587$	17.1939	−	29.7806i	0.709667	−	1.22918i	0.964981	−	0.262320i	$-0.0844877\pi$
$588$	−0.316473	−	0.182716i	−0.0130511	−	0.00753507i
$589$	4.19615	+	7.26795i	0.172899	+	0.299471i
$590$		0			0
$591$	−1.25447	+	0.724270i	−0.0516021	+	0.0297925i
$592$	0.0560937	+	0.0971572i	0.00230544	+	0.00399314i
$593$	−5.47612			−0.224877			−0.112439	−	0.993659i	$-0.535866\pi$
$593$	−5.47612			−0.224877			−0.112439	+	0.993659i	$0.535866\pi$
$594$	−0.454095	−	0.786515i	−0.0186317	−	0.0322711i
$595$		0			0
$596$	−1.72886	−	0.998159i	−0.0708170	−	0.0408862i
$597$		−	1.25400i		−	0.0513229i
$598$	−34.7043	+	15.9823i	−1.41916	+	0.653564i
$599$	−38.6039			−1.57731			−0.788657	−	0.614833i	$-0.789223\pi$
$599$	−38.6039			−1.57731			−0.788657	+	0.614833i	$0.789223\pi$
$600$		0			0
$601$	−3.28948	+	5.69754i	−0.134181	+	0.232408i	−0.925284	−	0.379275i	$-0.876174\pi$
$601$	−3.28948	+	5.69754i	−0.134181	+	0.232408i	0.791104	+	0.611682i	$0.209507\pi$
$602$	−22.2483	+	12.8451i	−0.906772	+	0.523525i
$603$	15.4730			0.630109
$604$	0.280682	−	0.162052i	0.0114208	−	0.00659379i
$605$		0			0
$606$			0.404750i			0.0164418i
$607$	14.5201	−	8.38318i	0.589352	−	0.340263i	−0.175489	−	0.984481i	$-0.556151\pi$
$607$	14.5201	−	8.38318i	0.589352	−	0.340263i	0.764841	+	0.644219i	$0.222817\pi$
$608$	6.60886	+	3.81563i	0.268025	+	0.154744i
$609$	−0.583678	−	0.336986i	−0.0236518	−	0.0136554i
$610$		0			0
$611$	−23.4013	−	2.15959i	−0.946715	−	0.0873677i
$612$			2.51793i			0.101781i
$613$	−14.3894	+	24.9232i	−0.581184	+	1.00664i	0.414155	+	0.910206i	$0.364077\pi$
$613$	−14.3894	+	24.9232i	−0.581184	+	1.00664i	−0.995339	+	0.0964341i	$0.969256\pi$
$614$	−5.12379	+	8.87466i	−0.206779	+	0.358152i
$615$		0			0
$616$		−	13.6129i		−	0.548481i
$617$	−18.6645	−	32.3279i	−0.751406	−	1.30147i	−0.947141	−	0.320817i	$-0.896043\pi$
$617$	−18.6645	−	32.3279i	−0.751406	−	1.30147i	0.195735	−	0.980657i	$-0.437291\pi$
$618$	−0.393009	−	0.680712i	−0.0158091	−	0.0273822i
$619$		−	12.7535i		−	0.512606i	−0.966597	−	0.256303i	$-0.917496\pi$
$619$		−	12.7535i		−	0.512606i	0.966597	−	0.256303i	$-0.0825045\pi$
$620$		0			0
$621$	2.01192	−	3.48475i	0.0807356	−	0.139838i
$622$	−7.95961	+	13.7864i	−0.319151	+	0.552786i
$623$		−	65.1939i		−	2.61194i
$624$	−1.37119	+	0.631470i	−0.0548914	+	0.0252790i
$625$		0			0
$626$	23.0842	+	13.3276i	0.922629	+	0.532680i
$627$	−0.503185	−	0.290514i	−0.0200953	−	0.0116020i
$628$	−2.45209	+	1.41571i	−0.0978489	+	0.0564931i
$629$			0.0903896i			0.00360407i
$630$		0			0
$631$	24.8759	−	14.3621i	0.990294	−	0.571746i	0.0849315	−	0.996387i	$-0.472933\pi$
$631$	24.8759	−	14.3621i	0.990294	−	0.571746i	0.905362	+	0.424641i	$0.139600\pi$
$632$	−23.1643			−0.921427
$633$	−0.394880	+	0.227984i	−0.0156951	+	0.00906156i
$634$	6.11035	−	10.5834i	0.242673	−	0.420322i
$635$		0			0
$636$	−0.0222199			−0.000881077
$637$	−33.9346	+	47.9762i	−1.34454	+	1.90089i
$638$			2.35588i			0.0932701i
$639$	20.1133	+	11.6124i	0.795671	+	0.459381i
$640$		0			0
$641$	−11.1985	−	19.3964i	−0.442315	−	0.766112i	0.555546	−	0.831486i	$-0.312509\pi$
$641$	−11.1985	−	19.3964i	−0.442315	−	0.766112i	−0.997861	+	0.0653739i	$0.979176\pi$
$642$	0.629552			0.0248464
$643$	7.08209	+	12.2665i	0.279290	+	0.483745i	0.971209	−	0.238231i	$-0.0765675\pi$
$643$	7.08209	+	12.2665i	0.279290	+	0.483745i	−0.691918	+	0.721976i	$0.743234\pi$
$644$	−7.00637	+	4.04513i	−0.276090	+	0.159400i
$645$		0			0
$646$	15.2540	+	26.4207i	0.600160	+	1.03951i
$647$	20.4466	+	11.8048i	0.803838	+	0.464096i	0.844812	−	0.535064i	$-0.179713\pi$
$647$	20.4466	+	11.8048i	0.803838	+	0.464096i	−0.0409732	+	0.999160i	$0.513046\pi$
$648$	−11.7612	+	20.3709i	−0.462022	+	0.800246i
$649$	−9.32835			−0.366170
$650$		0			0
$651$	−0.669862			−0.0262540
$652$	2.66955	−	4.62379i	0.104548	−	0.181082i
$653$	−28.8183	−	16.6383i	−1.12775	−	0.651105i	−0.184380	−	0.982855i	$-0.559028\pi$
$653$	−28.8183	−	16.6383i	−1.12775	−	0.651105i	−0.943367	+	0.331750i	$0.892361\pi$
$654$	0.976727	+	1.69174i	0.0381930	+	0.0661523i
$655$		0			0
$656$	−1.02500	+	0.591784i	−0.0400195	+	0.0231053i
$657$	−15.1178	−	26.1848i	−0.589801	−	1.02156i
$658$	−47.0502			−1.83421
$659$	11.5454	+	19.9972i	0.449745	+	0.778982i	0.998369	−	0.0570875i	$-0.0181814\pi$
$659$	11.5454	+	19.9972i	0.449745	+	0.778982i	−0.548624	+	0.836069i	$0.684848\pi$
$660$		0			0
$661$	11.6364	+	6.71826i	0.452602	+	0.261310i	0.708929	−	0.705280i	$-0.249179\pi$
$661$	11.6364	+	6.71826i	0.452602	+	0.261310i	−0.256326	+	0.966590i	$0.582512\pi$
$662$		−	37.2972i		−	1.44960i
$663$	−1.21114	−	0.111771i	−0.0470370	−	0.00434081i
$664$	1.91326			0.0742491
$665$		0			0
$666$	0.0568043	−	0.0983879i	0.00220112	−	0.00381245i
$667$	−9.03957	+	5.21900i	−0.350014	+	0.202080i
$668$	−1.93895			−0.0750200
$669$	−1.20779	+	0.697316i	−0.0466957	+	0.0269598i
$670$		0			0
$671$			6.77708i			0.261626i
$672$	−0.527510	+	0.304558i	−0.0203491	+	0.0117486i
$673$	−1.68463	−	0.972620i	−0.0649376	−	0.0374918i	0.467180	−	0.884162i	$-0.345270\pi$
$673$	−1.68463	−	0.972620i	−0.0649376	−	0.0374918i	−0.532117	+	0.846671i	$0.678603\pi$
$674$	−25.3923	−	14.6603i	−0.978075	−	0.564692i
$675$		0			0
$676$	−1.02419	−	2.89949i	−0.0393919	−	0.111519i
$677$		−	24.8683i		−	0.955768i	−0.878423	−	0.477884i	$-0.841404\pi$
$677$		−	24.8683i		−	0.955768i	0.878423	−	0.477884i	$-0.158596\pi$
$678$	0.570140	−	0.987512i	0.0218961	−	0.0379252i
$679$	−8.29903	+	14.3743i	−0.318488	+	0.551637i
$680$		0			0
$681$			1.41260i			0.0541310i
$682$	1.17075	+	2.02781i	0.0448305	+	0.0776487i
$683$	−7.31107	−	12.6631i	−0.279750	−	0.484542i	0.691572	−	0.722307i	$-0.256918\pi$
$683$	−7.31107	−	12.6631i	−0.279750	−	0.484542i	−0.971323	+	0.237766i	$0.923585\pi$
$684$		−	4.05545i		−	0.155064i
$685$		0			0
$686$	−33.5605	+	58.1285i	−1.28135	+	2.21935i
$687$	−0.915049	+	1.58491i	−0.0349113	+	0.0604681i
$688$			15.7201i			0.599323i
$689$	−0.328354	+	3.55804i	−0.0125093	+	0.135550i
$690$		0			0
$691$	−3.05231	−	1.76225i	−0.116115	−	0.0670393i	0.440817	−	0.897597i	$-0.354689\pi$
$691$	−3.05231	−	1.76225i	−0.116115	−	0.0670393i	−0.556933	+	0.830558i	$0.688022\pi$
$692$	−1.87803	−	1.08428i	−0.0713920	−	0.0412182i
$693$	−13.3705	+	7.71947i	−0.507904	+	0.293238i
$694$			25.5447i			0.969665i
$695$		0			0
$696$	−0.318907	+	0.184121i	−0.0120881	+	0.00697909i
$697$	−0.953601			−0.0361202
$698$	36.7458	−	21.2152i	1.39085	−	0.803008i
$699$	1.00445	−	1.73976i	0.0379919	−	0.0658038i
$700$		0			0
$701$	1.53457			0.0579599			0.0289800	−	0.999580i	$-0.490774\pi$
$701$	1.53457			0.0579599			0.0289800	+	0.999580i	$0.490774\pi$
$702$	2.49990	+	1.76823i	0.0943526	+	0.0667377i
$703$		−	0.145584i		−	0.00549081i
$704$	−6.33766	−	3.65905i	−0.238860	−	0.137906i
$705$		0			0
$706$	−15.8912	−	27.5244i	−0.598075	−	1.03590i
$707$	13.7819			0.518322
$708$	0.0977915	+	0.169380i	0.00367523	+	0.00636568i
$709$	−12.1289	+	7.00262i	−0.455510	+	0.262989i	−0.710155	−	0.704046i	$-0.751375\pi$
$709$	−12.1289	+	7.00262i	−0.455510	+	0.262989i	0.254644	+	0.967035i	$0.418042\pi$
$710$		0			0
$711$	13.1357	+	22.7518i	0.492629	+	0.853259i
$712$	−30.8481	−	17.8101i	−1.15608	−	0.667463i
$713$	−5.18717	+	8.98444i	−0.194261	+	0.336470i
$714$	−2.43510			−0.0911314
$715$		0			0
$716$	−2.37418			−0.0887274
$717$	0.706029	−	1.22288i	0.0263671	−	0.0456692i
$718$	42.2890	+	24.4156i	1.57821	+	0.911181i
$719$	−11.2381	−	19.4649i	−0.419109	−	0.725918i	0.576741	−	0.816927i	$-0.304324\pi$
$719$	−11.2381	−	19.4649i	−0.419109	−	0.725918i	−0.995850	+	0.0910091i	$0.970991\pi$
$720$		0			0
$721$	−23.1785	+	13.3821i	−0.863213	+	0.498376i
$722$	−10.3612	−	17.9461i	−0.385603	−	0.667884i
$723$	0.890215			0.0331074
$724$	2.01344	+	3.48737i	0.0748288	+	0.129607i
$725$		0			0
$726$	1.21001	+	0.698600i	0.0449077	+	0.0259275i
$727$		−	10.3421i		−	0.383566i	−0.981437	−	0.191783i	$-0.938573\pi$
$727$		−	10.3421i		−	0.383566i	0.981437	−	0.191783i	$-0.0614270\pi$
$728$	19.1989	+	41.6890i	0.711560	+	1.54510i
$729$	26.5160			0.982075
$730$		0			0
$731$	−6.33285	+	10.9688i	−0.234229	+	0.405696i
$732$	0.123055	−	0.0710459i	0.00454824	−	0.00262593i
$733$	27.3533			1.01032			0.505159	−	0.863026i	$-0.331434\pi$
$733$	27.3533			1.01032			0.505159	+	0.863026i	$0.331434\pi$
$734$	−7.66516	+	4.42548i	−0.282926	+	0.163348i
$735$		0			0
$736$			9.43355i			0.347725i
$737$	4.79096	−	2.76606i	0.176477	−	0.101889i
$738$	1.03798	+	0.599280i	0.0382087	+	0.0220598i
$739$	−11.6495	−	6.72583i	−0.428533	−	0.247413i	0.270189	−	0.962807i	$-0.412914\pi$
$739$	−11.6495	−	6.72583i	−0.428533	−	0.247413i	−0.698721	+	0.715394i	$0.746247\pi$
$740$		0			0
$741$	1.95071	+	0.180021i	0.0716610	+	0.00661324i
$742$			7.15372i			0.262621i
$743$	−8.19632	+	14.1964i	−0.300694	+	0.520817i	−0.976293	−	0.216452i	$-0.930552\pi$
$743$	−8.19632	+	14.1964i	−0.300694	+	0.520817i	0.675599	+	0.737269i	$0.263885\pi$
$744$	−0.182998	+	0.316962i	−0.00670903	+	0.0116204i
$745$		0			0
$746$			19.9179i			0.729248i
$747$	−1.08495	−	1.87919i	−0.0396963	−	0.0687560i
$748$	0.450122	+	0.779635i	0.0164581	+	0.0285063i
$749$		−	21.4365i		−	0.783274i
$750$		0			0
$751$	−13.8328	+	23.9590i	−0.504764	+	0.874277i	0.495221	+	0.868767i	$0.335087\pi$
$751$	−13.8328	+	23.9590i	−0.504764	+	0.874277i	−0.999985	+	0.00551009i	$0.998246\pi$
$752$	−14.3953	+	24.9334i	−0.524942	+	0.909226i
$753$		−	1.07265i		−	0.0390895i
$754$	−3.32260	−	7.21476i	−0.121002	−	0.262746i
$755$		0			0
$756$	0.561508	+	0.324187i	0.0204218	+	0.0117906i
$757$	19.9167	+	11.4989i	0.723885	+	0.417935i	0.816181	−	0.577797i	$-0.196087\pi$
$757$	19.9167	+	11.4989i	0.723885	+	0.417935i	−0.0922961	+	0.995732i	$0.529421\pi$
$758$	32.9208	−	19.0068i	1.19574	−	0.690359i
$759$		−	0.718251i		−	0.0260709i
$760$		0			0
$761$	6.63759	−	3.83221i	0.240612	−	0.138918i	−0.374846	−	0.927087i	$-0.622304\pi$
$761$	6.63759	−	3.83221i	0.240612	−	0.138918i	0.615458	+	0.788170i	$0.288971\pi$
$762$	0.100172			0.00362885
$763$	57.6045	−	33.2580i	2.08542	−	1.20402i
$764$	0.458587	−	0.794296i	0.0165911	−	0.0287366i
$765$		0			0
$766$	−16.1916			−0.585027
$767$	28.5676	−	13.1562i	1.03152	−	0.475042i
$768$			0.530882i			0.0191566i
$769$	−6.26219	−	3.61548i	−0.225820	−	0.130377i	0.382822	−	0.923822i	$-0.374952\pi$
$769$	−6.26219	−	3.61548i	−0.225820	−	0.130377i	−0.608642	+	0.793445i	$0.708286\pi$
$770$		0			0
$771$	−1.25745	−	2.17797i	−0.0452859	−	0.0784375i
$772$	0.296612			0.0106753
$773$	−16.7998	−	29.0981i	−0.604246	−	1.04658i	−0.992170	−	0.124893i	$-0.960141\pi$
$773$	−16.7998	−	29.0981i	−0.604246	−	1.04658i	0.387924	−	0.921691i	$-0.373192\pi$
$774$	13.7864	−	7.95961i	0.495544	−	0.286102i
$775$		0			0
$776$	4.53438	+	7.85378i	0.162775	+	0.281934i
$777$	0.0100635	+	0.00581016i	0.000361026	+	0.000208438i
$778$	−17.2260	+	29.8363i	−0.617582	+	1.06968i
$779$	1.53590			0.0550293
$780$		0			0
$781$	8.30368			0.297129
$782$	−18.8565	+	32.6605i	−0.674309	+	1.16794i
$783$	0.724454	+	0.418264i	0.0258899	+	0.0149475i
$784$	35.9960	+	62.3470i	1.28557	+	2.22668i
$785$		0			0
$786$	−0.769182	+	0.444088i	−0.0274358	+	0.0158401i
$787$	−1.48584	−	2.57355i	−0.0529645	−	0.0917371i	0.838328	−	0.545167i	$-0.183534\pi$
$787$	−1.48584	−	2.57355i	−0.0529645	−	0.0917371i	−0.891292	+	0.453430i	$0.850200\pi$
$788$	−3.61484			−0.128773
$789$	−0.670185	−	1.16079i	−0.0238592	−	0.0413254i
$790$		0			0
$791$	−33.6252	−	19.4135i	−1.19557	−	0.690265i
$792$			8.43544i			0.299740i
$793$	−9.55802	−	20.7545i	−0.339415	−	0.737013i
$794$	31.5349			1.11913
$795$		0			0
$796$	1.56469	−	2.71012i	0.0554588	−	0.0960575i
$797$	−19.5506	+	11.2875i	−0.692517	+	0.399825i	−0.804554	−	0.593879i	$-0.797596\pi$
$797$	−19.5506	+	11.2875i	−0.692517	+	0.399825i	0.112037	+	0.993704i	$0.464262\pi$
$798$	3.92205			0.138839
$799$	−20.0888	+	11.5983i	−0.710692	+	0.410318i
$800$		0			0
$801$			40.3983i			1.42740i
$802$	−25.6140	+	14.7882i	−0.904462	+	0.522191i
$803$	−9.36194	−	5.40512i	−0.330376	−	0.190742i
$804$	−0.100450	−	0.0579946i	−0.00354259	−	0.00204531i
$805$		0			0
$806$	−6.44528	−	4.55889i	−0.227025	−	0.160580i
$807$		−	2.34831i		−	0.0826646i
$808$	3.76505	−	6.52125i	0.132454	−	0.229417i
$809$	6.82921	−	11.8285i	0.240102	−	0.415869i	−0.720641	−	0.693308i	$-0.756152\pi$
$809$	6.82921	−	11.8285i	0.240102	−	0.415869i	0.960743	+	0.277439i	$0.0894857\pi$
$810$		0			0
$811$			14.1147i			0.495636i	0.968807	+	0.247818i	$0.0797135\pi$
$811$			14.1147i			0.495636i	−0.968807	+	0.247818i	$0.920287\pi$
$812$	−0.840952	−	1.45657i	−0.0295116	−	0.0511157i
$813$	−0.887075	−	1.53646i	−0.0311111	−	0.0538860i
$814$		−	0.0406189i		−	0.00142369i
$815$		0			0
$816$	−0.745035	+	1.29044i	−0.0260814	+	0.0451744i
$817$	10.1999	−	17.6667i	0.356848	−	0.618079i
$818$		−	47.6781i		−	1.66703i
$819$	30.0594	−	42.4975i	1.05036	−	1.48498i
$820$		0			0
$821$	−1.37318	−	0.792808i	−0.0479244	−	0.0276692i	0.475846	−	0.879528i	$-0.342142\pi$
$821$	−1.37318	−	0.792808i	−0.0479244	−	0.0276692i	−0.523771	+	0.851859i	$0.675475\pi$
$822$	−2.00176	−	1.15572i	−0.0698195	−	0.0403103i
$823$	−16.0776	+	9.28238i	−0.560428	+	0.323563i	−0.753317	−	0.657657i	$-0.771548\pi$
$823$	−16.0776	+	9.28238i	−0.560428	+	0.323563i	0.192889	+	0.981221i	$0.438214\pi$
$824$			14.6233i			0.509427i
$825$		0			0
$826$	54.5320	−	31.4840i	1.89741	−	1.09547i
$827$	−9.01023			−0.313316			−0.156658	−	0.987653i	$-0.550072\pi$
$827$	−9.01023			−0.313316			−0.156658	+	0.987653i	$0.550072\pi$
$828$	4.34159	−	2.50662i	0.150881	−	0.0871110i
$829$	−23.5588	+	40.8051i	−0.818233	+	1.41722i	0.0887506	+	0.996054i	$0.471713\pi$
$829$	−23.5588	+	40.8051i	−0.818233	+	1.41722i	−0.906983	+	0.421167i	$0.861621\pi$
$830$		0			0
$831$	2.14833			0.0745247
$832$	24.5693	+	2.26738i	0.851787	+	0.0786072i
$833$			58.0041i			2.00972i
$834$	0.837898	+	0.483761i	0.0290141	+	0.0167513i
$835$		0			0
$836$	−0.724980	−	1.25570i	−0.0250740	−	0.0434294i
$837$	0.831425			0.0287383
$838$	−22.9782	−	39.7994i	−0.793769	−	1.37485i
$839$	−46.3121	+	26.7383i	−1.59887	+	0.923108i	−0.607164	+	0.794576i	$0.707693\pi$
$839$	−46.3121	+	26.7383i	−1.59887	+	0.923108i	−0.991705	+	0.128531i	$0.958974\pi$
$840$		0			0
$841$	13.4150	+	23.2355i	0.462586	+	0.801223i
$842$	23.2894	+	13.4461i	0.802605	+	0.463384i
$843$	1.31937	−	2.28521i	0.0454415	−	0.0787070i
$844$	−1.13787			−0.0391672
$845$		0			0
$846$	29.1553			1.00238
$847$	23.7876	−	41.2014i	0.817353	−	1.41570i
$848$	3.79098	+	2.18872i	0.130183	+	0.0751611i
$849$	−0.375362	−	0.650146i	−0.0128824	−	0.0223130i
$850$		0			0
$851$	0.155856	−	0.0899835i	0.00534268	−	0.00308460i
$852$	−0.0870495	−	0.150774i	−0.00298227	−	0.00516544i
$853$	27.7756			0.951019			0.475510	−	0.879711i	$-0.342264\pi$
$853$	27.7756			0.951019			0.475510	+	0.879711i	$0.342264\pi$
$854$	−22.8733	−	39.6177i	−0.782707	−	1.35569i
$855$		0			0
$856$	−10.1432	−	5.85619i	−0.346688	−	0.200160i
$857$			53.6917i			1.83407i	0.398801	+	0.917037i	$0.369426\pi$
$857$			53.6917i			1.83407i	−0.398801	+	0.917037i	$0.630574\pi$
$858$	0.544260	+	0.0502271i	0.0185807	+	0.00171472i
$859$	−2.08958			−0.0712955			−0.0356477	−	0.999364i	$-0.511349\pi$
$859$	−2.08958			−0.0712955			−0.0356477	+	0.999364i	$0.511349\pi$
$860$		0			0
$861$	−0.0612966	+	0.106169i	−0.00208898	+	0.00361823i
$862$	−6.34556	+	3.66361i	−0.216131	+	0.124783i
$863$	−1.75413			−0.0597113			−0.0298557	−	0.999554i	$-0.509505\pi$
$863$	−1.75413			−0.0597113			−0.0298557	+	0.999554i	$0.509505\pi$
$864$	0.654739	−	0.378014i	0.0222747	−	0.0128603i
$865$		0			0
$866$		−	28.7727i		−	0.977737i
$867$	0.355797	−	0.205419i	0.0120835	−	0.00697640i
$868$	−1.44769	−	0.835823i	−0.0491377	−	0.0283697i
$869$	8.13453	+	4.69647i	0.275945	+	0.159317i
$870$		0			0
$871$	−10.7710	+	15.2278i	−0.364961	+	0.515975i
$872$		−	36.3426i		−	1.23072i
$873$	5.14261	−	8.90726i	0.174051	−	0.301465i
$874$	30.3709	−	52.6040i	1.02731	−	1.77936i
$875$		0			0
$876$			0.226653i			0.00765789i
$877$	10.7836	+	18.6777i	0.364136	+	0.630702i	0.988637	−	0.150322i	$-0.0480311\pi$
$877$	10.7836	+	18.6777i	0.364136	+	0.630702i	−0.624501	+	0.781024i	$0.714698\pi$
$878$	−6.40058	−	11.0861i	−0.216009	−	0.374139i
$879$		−	0.0258742i		−	0.000872716i
$880$		0			0
$881$	12.5132	−	21.6734i	0.421579	−	0.730196i	−0.574515	−	0.818494i	$-0.694809\pi$
$881$	12.5132	−	21.6734i	0.421579	−	0.730196i	0.996094	+	0.0882978i	$0.0281427\pi$
$882$	36.4520	−	63.1367i	1.22740	−	2.12592i
$883$			48.7832i			1.64169i	0.571154	+	0.820843i	$0.306496\pi$
$883$			48.7832i			1.64169i	−0.571154	+	0.820843i	$0.693504\pi$
$884$	−2.47803	−	1.75277i	−0.0833452	−	0.0589519i
$885$		0			0
$886$	−49.1705	−	28.3886i	−1.65192	−	0.953734i
$887$	−29.2659	−	16.8967i	−0.982651	−	0.567334i	−0.0795819	−	0.996828i	$-0.525359\pi$
$887$	−29.2659	−	16.8967i	−0.982651	−	0.567334i	−0.903070	+	0.429494i	$0.858692\pi$
$888$	0.00549844	−	0.00317453i	0.000184516	−	0.000106530i
$889$		−	3.41090i		−	0.114398i
$890$		0			0
$891$	8.26025	−	4.76906i	0.276729	−	0.159769i
$892$	−3.48031			−0.116530
$893$	32.3557	−	18.6806i	1.08274	−	0.625121i
$894$	−0.598177	+	1.03607i	−0.0200060	+	0.0346515i
$895$		0			0
$896$	62.2508			2.07965
$897$	1.01298	+	2.19961i	0.0338225	+	0.0734428i
$898$			39.9394i			1.33279i
$899$	−1.86780	−	1.07837i	−0.0622946	−	0.0359658i
$900$		0			0
$901$	1.76346	+	3.05440i	0.0587493	+	0.101757i
$902$	0.428526			0.0142683
$903$	0.814139	+	1.41013i	0.0270929	+	0.0469262i
$904$	−18.3720	+	10.6071i	−0.611043	+	0.352786i
$905$		0			0
$906$	−0.0971143	−	0.168207i	−0.00322641	−	0.00558830i
$907$	29.9879	+	17.3135i	0.995731	+	0.574885i	0.906982	−	0.421169i	$-0.138380\pi$
$907$	29.9879	+	17.3135i	0.995731	+	0.574885i	0.0887485	+	0.996054i	$0.471713\pi$
$908$	−1.76258	+	3.05288i	−0.0584932	+	0.101313i
$909$	−8.54015			−0.283259
$910$		0			0
$911$	31.1865			1.03326			0.516628	−	0.856210i	$-0.327187\pi$
$911$	31.1865			1.03326			0.516628	+	0.856210i	$0.327187\pi$
$912$	1.19997	−	2.07842i	0.0397351	−	0.0688233i
$913$	−0.671874	−	0.387907i	−0.0222358	−	0.0128378i
$914$	−3.19386	−	5.53192i	−0.105643	−	0.182980i
$915$		0			0
$916$	−3.95516	+	2.28351i	−0.130682	+	0.0754493i
$917$	15.1214	+	26.1910i	0.499352	+	0.864903i
$918$	3.02242			0.0997548
$919$	−25.9610	−	44.9658i	−0.856374	−	1.48328i	−0.875364	−	0.483464i	$-0.839379\pi$
$919$	−25.9610	−	44.9658i	−0.856374	−	1.48328i	0.0189904	−	0.999820i	$-0.493955\pi$
$920$		0			0
$921$	0.562490	+	0.324753i	0.0185347	+	0.0107010i
$922$		−	30.8707i		−	1.01667i
$923$	−25.4296	+	11.7110i	−0.837026	+	0.385474i
$924$	0.115734			0.00380736
$925$		0			0
$926$	−24.0059	+	41.5794i	−0.788882	+	1.36638i
$927$	14.3629	−	8.29242i	0.471739	−	0.272359i
$928$	−1.96117			−0.0643784
$929$	17.7462	−	10.2457i	0.582232	−	0.336152i	−0.179788	−	0.983705i	$-0.557541\pi$
$929$	17.7462	−	10.2457i	0.582232	−	0.336152i	0.762020	+	0.647553i	$0.224208\pi$
$930$		0			0
$931$		−	93.4231i		−	3.06182i
$932$	4.34159	−	2.50662i	0.142213	−	0.0821070i
$933$	0.873806	+	0.504492i	0.0286071	+	0.0165163i
$934$	30.2771	+	17.4805i	0.990698	+	0.571980i
$935$		0			0
$936$	−11.8969	−	25.8331i	−0.388862	−	0.844382i
$937$			39.6806i			1.29631i	0.761510	+	0.648154i	$0.224459\pi$
$937$			39.6806i			1.29631i	−0.761510	+	0.648154i	$0.775541\pi$
$938$	−18.6714	+	32.3399i	−0.609644	+	1.05593i
$939$	0.844727	−	1.46311i	0.0275666	−	0.0477468i
$940$		0			0
$941$			19.6189i			0.639557i	0.947492	+	0.319779i	$0.103609\pi$
$941$			19.6189i			0.639557i	−0.947492	+	0.319779i	$0.896391\pi$
$942$	0.848408	+	1.46949i	0.0276426	+	0.0478784i
$943$	0.949318	+	1.64427i	0.0309140	+	0.0535447i
$944$		−	38.5309i		−	1.25408i
$945$		0			0
$946$	2.84583	−	4.92912i	0.0925259	−	0.160260i
$947$	−28.6062	+	49.5474i	−0.929576	+	1.61007i	−0.145544	+	0.989352i	$0.546493\pi$
$947$	−28.6062	+	49.5474i	−0.929576	+	1.61007i	−0.784032	+	0.620721i	$0.786840\pi$
$948$		−	0.196937i		−	0.00639623i
$949$	36.2936	+	3.34935i	1.17814	+	0.108725i
$950$		0			0
$951$	−0.670795	−	0.387283i	−0.0217520	−	0.0125585i
$952$	39.2339	+	22.6517i	1.27158	+	0.734146i
$953$	−23.7958	+	13.7385i	−0.770820	+	0.445033i	−0.833167	−	0.553021i	$-0.813475\pi$
$953$	−23.7958	+	13.7385i	−0.770820	+	0.445033i	0.0623470	+	0.998055i	$0.480141\pi$
$954$		−	4.43290i		−	0.143520i
$955$		0			0
$956$	3.05170	−	1.76190i	0.0986991	−	0.0569840i
$957$	0.149319			0.00482680
$958$	6.70283	−	3.86988i	0.216559	−	0.125030i
$959$	−39.3527	+	68.1609i	−1.27077	+	2.20103i
$960$		0			0
$961$	28.8564			0.930852
$962$	0.0572867	+	0.124393i	0.00184700	+	0.00401061i
$963$			13.2834i			0.428053i
$964$	1.92391	+	1.11077i	0.0619649	+	0.0357755i
$965$		0			0
$966$	2.42416	+	4.19877i	0.0779962	+	0.135093i
$967$	10.3643			0.333293			0.166647	−	0.986017i	$-0.446706\pi$
$967$	10.3643			0.333293			0.166647	+	0.986017i	$0.446706\pi$
$968$	−12.9970	−	22.5114i	−0.417738	−	0.723544i
$969$	1.67458	−	0.966821i	0.0537953	−	0.0310588i
$970$		0			0
$971$	−20.8758	−	36.1579i	−0.669935	−	1.16036i	−0.977922	−	0.208971i	$-0.932989\pi$
$971$	−20.8758	−	36.1579i	−0.669935	−	1.16036i	0.307987	−	0.951391i	$-0.400345\pi$
$972$	−0.522180	−	0.301481i	−0.0167489	−	0.00966999i
$973$	16.4723	−	28.5308i	0.528077	−	0.914656i
$974$	46.0212			1.47461
$975$		0			0
$976$	−27.9929			−0.896030
$977$	−6.89691	+	11.9458i	−0.220652	+	0.382180i	−0.955006	−	0.296586i	$-0.904152\pi$
$977$	−6.89691	+	11.9458i	−0.220652	+	0.382180i	0.734354	+	0.678766i	$0.237485\pi$
$978$	−2.77095	−	1.59981i	−0.0886051	−	0.0511562i
$979$	7.22187	+	12.5087i	0.230812	+	0.399778i
$980$		0			0
$981$	−35.6954	+	20.6088i	−1.13967	+	0.657987i
$982$	−26.7683	−	46.3641i	−0.854212	−	1.47954i
$983$	−37.9997			−1.21200			−0.606002	−	0.795463i	$-0.707227\pi$
$983$	−37.9997			−1.21200			−0.606002	+	0.795463i	$0.707227\pi$
$984$	0.0334909	+	0.0580080i	0.00106765	+	0.00184923i
$985$		0			0
$986$	−6.78988	−	3.92014i	−0.216234	−	0.124843i
$987$			2.98211i			0.0949217i
$988$	3.99119	+	2.82306i	0.126977	+	0.0898134i
$989$	25.2176			0.801873
$990$		0			0
$991$	26.2765	−	45.5122i	0.834700	−	1.44574i	−0.0595748	−	0.998224i	$-0.518974\pi$
$991$	26.2765	−	45.5122i	0.834700	−	1.44574i	0.894275	−	0.447519i	$-0.147692\pi$
$992$	−1.68806	+	0.974602i	−0.0535960	+	0.0309436i
$993$	−2.36396			−0.0750179
$994$	−48.5419	+	28.0257i	−1.53966	+	0.888920i
$995$		0			0
$996$			0.0162661i			0.000515411i
$997$	−16.0994	+	9.29497i	−0.509872	+	0.294375i	−0.732781	−	0.680465i	$-0.761778\pi$
$997$	−16.0994	+	9.29497i	−0.509872	+	0.294375i	0.222909	+	0.974839i	$0.428445\pi$
$998$	−37.4260	−	21.6079i	−1.18470	−	0.683986i
$999$	−0.0124907	−	0.00721150i	−0.000395188	−	0.000228162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.m.b.199.4		8
5.2	odd	4		65.2.m.a.56.4	yes	8
5.3	odd	4		325.2.n.d.251.1		8
5.4	even	2		325.2.m.c.199.1		8
13.10	even	6		325.2.m.c.49.1		8
15.2	even	4		585.2.bu.c.316.1		8
20.7	even	4		1040.2.da.b.641.3		8
65.2	even	12		845.2.e.m.146.4		8
65.7	even	12		845.2.a.l.1.4		4
65.12	odd	4		845.2.m.g.316.1		8
65.17	odd	12		845.2.c.g.506.7		8
65.22	odd	12		845.2.c.g.506.2		8
65.23	odd	12		325.2.n.d.101.1		8
65.32	even	12		845.2.a.m.1.1		4
65.33	even	12		4225.2.a.bl.1.1		4
65.37	even	12		845.2.e.n.146.1		8
65.42	odd	12		845.2.m.g.361.1		8
65.47	even	4		845.2.e.n.191.1		8
65.49	even	6	inner	325.2.m.b.49.4		8
65.57	even	4		845.2.e.m.191.4		8
65.58	even	12		4225.2.a.bi.1.4		4
65.62	odd	12		65.2.m.a.36.4	✓	8
195.32	odd	12		7605.2.a.cf.1.4		4
195.62	even	12		585.2.bu.c.361.1		8
195.137	odd	12		7605.2.a.cj.1.1		4
260.127	even	12		1040.2.da.b.881.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	65.62	odd	12
65.2.m.a.56.4	yes	8	5.2	odd	4
325.2.m.b.49.4		8	65.49	even	6	inner
325.2.m.b.199.4		8	1.1	even	1	trivial
325.2.m.c.49.1		8	13.10	even	6
325.2.m.c.199.1		8	5.4	even	2
325.2.n.d.101.1		8	65.23	odd	12
325.2.n.d.251.1		8	5.3	odd	4
585.2.bu.c.316.1		8	15.2	even	4
585.2.bu.c.361.1		8	195.62	even	12
845.2.a.l.1.4		4	65.7	even	12
845.2.a.m.1.1		4	65.32	even	12
845.2.c.g.506.2		8	65.22	odd	12
845.2.c.g.506.7		8	65.17	odd	12
845.2.e.m.146.4		8	65.2	even	12
845.2.e.m.191.4		8	65.57	even	4
845.2.e.n.146.1		8	65.37	even	12
845.2.e.n.191.1		8	65.47	even	4
845.2.m.g.316.1		8	65.12	odd	4
845.2.m.g.361.1		8	65.42	odd	12
1040.2.da.b.641.3		8	20.7	even	4
1040.2.da.b.881.3		8	260.127	even	12
4225.2.a.bi.1.4		4	65.58	even	12
4225.2.a.bl.1.1		4	65.33	even	12
7605.2.a.cf.1.4		4	195.32	odd	12
7605.2.a.cj.1.1		4	195.137	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.747754 - 1.29515i) q^{2} +(-0.0820885 - 0.0473938i) q^{3} +(-0.118272 - 0.204852i) q^{4} +(-0.122764 + 0.0708778i) q^{6} +(2.41342 + 4.18016i) q^{7} +2.63726 q^{8} +(-1.49551 - 2.59030i) q^{9} +O(q^{10})\)	\(q+(0.747754 - 1.29515i) q^{2} +(-0.0820885 - 0.0473938i) q^{3} +(-0.118272 - 0.204852i) q^{4} +(-0.122764 + 0.0708778i) q^{6} +(2.41342 + 4.18016i) q^{7} +2.63726 q^{8} +(-1.49551 - 2.59030i) q^{9} +(-0.926118 - 0.534695i) q^{11} +0.0224214i q^{12} +(3.59030 + 0.331331i) q^{13} +7.21857 q^{14} +(2.20857 - 3.82535i) q^{16} +(3.08209 - 1.77944i) q^{17} -4.47309 q^{18} +(-4.96410 + 2.86603i) q^{19} -0.457524i q^{21} +(-1.38502 + 0.799640i) q^{22} +(-6.13649 - 3.54290i) q^{23} +(-0.216489 - 0.124990i) q^{24} +(3.11378 - 4.40221i) q^{26} +0.567874i q^{27} +(0.570878 - 0.988789i) q^{28} +(0.736543 - 1.27573i) q^{29} -1.46410i q^{31} +(-0.665665 - 1.15297i) q^{32} +(0.0506824 + 0.0877845i) q^{33} -5.32235i q^{34} +(-0.353752 + 0.612717i) q^{36} +(-0.0126991 + 0.0219955i) q^{37} +8.57233i q^{38} +(-0.279019 - 0.197356i) q^{39} +(-0.232051 - 0.133975i) q^{41} +(-0.592562 - 0.342116i) q^{42} +(-3.08209 + 1.77944i) q^{43} +0.252957i q^{44} +(-9.17716 + 5.29844i) q^{46} -6.51793 q^{47} +(-0.362596 + 0.209345i) q^{48} +(-8.14918 + 14.1148i) q^{49} -0.337339 q^{51} +(-0.356756 - 0.774668i) q^{52} +0.991015i q^{53} +(0.735481 + 0.424630i) q^{54} +(6.36482 + 11.0242i) q^{56} +0.543327 q^{57} +(-1.10151 - 1.90786i) q^{58} +(7.55440 - 4.36153i) q^{59} +(-3.16867 - 5.48830i) q^{61} +(-1.89623 - 1.09479i) q^{62} +(7.21857 - 12.5029i) q^{63} +6.84325 q^{64} +0.151592 q^{66} +(-2.58658 + 4.48009i) q^{67} +(-0.729047 - 0.420915i) q^{68} +(0.335823 + 0.581663i) q^{69} +(-6.72458 + 3.88244i) q^{71} +(-3.94405 - 6.83129i) q^{72} +10.1088 q^{73} +(0.0189916 + 0.0328945i) q^{74} +(1.17422 + 0.677939i) q^{76} -5.16177i q^{77} +(-0.464243 + 0.213797i) q^{78} -8.78347 q^{79} +(-4.45961 + 7.72427i) q^{81} +(-0.347034 + 0.200360i) q^{82} +0.725474 q^{83} +(-0.0937250 + 0.0541121i) q^{84} +5.32235i q^{86} +(-0.120923 + 0.0698151i) q^{87} +(-2.44242 - 1.41013i) q^{88} +(-11.6970 - 6.75327i) q^{89} +(7.27987 + 15.8077i) q^{91} +1.67610i q^{92} +(-0.0693893 + 0.120186i) q^{93} +(-4.87381 + 8.44168i) q^{94} +0.126194i q^{96} +(1.71935 + 2.97800i) q^{97} +(12.1872 + 21.1088i) q^{98} +3.19856i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9	\( 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9} + 8 q^{13} - 4 q^{14} - 2 q^{16} + 18 q^{17} - 40 q^{18} - 12 q^{19} + 6 q^{22} + 6 q^{23} + 12 q^{24} + 10 q^{26} + 8 q^{28} + 8 q^{29} - 4 q^{32} - 18 q^{33} + 20 q^{36} - 2 q^{37} + 12 q^{41} - 42 q^{42} - 18 q^{43} - 42 q^{46} - 16 q^{47} - 6 q^{48} - 12 q^{49} - 8 q^{51} + 16 q^{52} - 18 q^{54} + 12 q^{56} - 28 q^{57} + 22 q^{58} + 12 q^{59} - 28 q^{61} + 12 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} + 12 q^{68} + 16 q^{69} + 12 q^{72} - 16 q^{73} - 10 q^{74} + 54 q^{76} + 18 q^{78} + 16 q^{79} + 8 q^{81} - 6 q^{82} + 24 q^{83} + 30 q^{84} + 54 q^{87} + 42 q^{88} - 24 q^{89} + 28 q^{91} + 8 q^{93} - 32 q^{94} - 2 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9 + 8 * q^13 - 4 * q^14 - 2 * q^16 + 18 * q^17 - 40 * q^18 - 12 * q^19 + 6 * q^22 + 6 * q^23 + 12 * q^24 + 10 * q^26 + 8 * q^28 + 8 * q^29 - 4 * q^32 - 18 * q^33 + 20 * q^36 - 2 * q^37 + 12 * q^41 - 42 * q^42 - 18 * q^43 - 42 * q^46 - 16 * q^47 - 6 * q^48 - 12 * q^49 - 8 * q^51 + 16 * q^52 - 18 * q^54 + 12 * q^56 - 28 * q^57 + 22 * q^58 + 12 * q^59 - 28 * q^61 + 12 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 + 12 * q^68 + 16 * q^69 + 12 * q^72 - 16 * q^73 - 10 * q^74 + 54 * q^76 + 18 * q^78 + 16 * q^79 + 8 * q^81 - 6 * q^82 + 24 * q^83 + 30 * q^84 + 54 * q^87 + 42 * q^88 - 24 * q^89 + 28 * q^91 + 8 * q^93 - 32 * q^94 - 2 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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