LMFDB - Embedded newform 325.2.n.d.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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([0, 5]))

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

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

chi := DirichletCharacter("325.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, degree $2$, 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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	325.101
Dual form			325.2.n.d.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05628 + 0.609843i) q^{2} +(1.16612 + 2.01978i) q^{3} +(-0.256182 + 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-3.11786 - 1.80010i) q^{7} -3.06430i q^{8} +(-1.21969 + 2.11256i) q^{9} +O(q^{10})$	\(q+(-1.05628 + 0.609843i) q^{2} +(1.16612 + 2.01978i) q^{3} +(-0.256182 + 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-3.11786 - 1.80010i) q^{7} -3.06430i q^{8} +(-1.21969 + 2.11256i) q^{9} +(-4.65213 + 2.68591i) q^{11} -1.19496 q^{12} +(-1.81988 + 3.11256i) q^{13} +4.39111 q^{14} +(1.35638 + 2.34932i) q^{16} +(0.565928 - 0.980215i) q^{17} -2.97527i q^{18} +(-1.96410 - 1.13397i) q^{19} -8.39654i q^{21} +(3.27597 - 5.67414i) q^{22} +(1.94644 + 3.37133i) q^{23} +(6.18922 - 3.57335i) q^{24} +(0.0241312 - 4.39758i) q^{26} +1.30752 q^{27} +(1.59748 - 0.922305i) q^{28} +(0.0123639 + 0.0214150i) q^{29} +5.46410i q^{31} +(2.44209 + 1.40994i) q^{32} +(-10.8499 - 6.26420i) q^{33} +1.38051i q^{34} +(-0.624924 - 1.08240i) q^{36} +(-7.53794 + 4.35203i) q^{37} +2.76619 q^{38} +(-8.40891 - 0.0461428i) q^{39} +(3.23205 - 1.86603i) q^{41} +(5.12058 + 8.86910i) q^{42} +(0.565928 - 0.980215i) q^{43} -2.75232i q^{44} +(-4.11196 - 2.37404i) q^{46} +2.58535i q^{47} +(-3.16341 + 5.47918i) q^{48} +(2.98070 + 5.16273i) q^{49} +2.63977 q^{51} +(-0.914884 - 1.60490i) q^{52} +4.43937 q^{53} +(-1.38111 + 0.797382i) q^{54} +(-5.51603 + 9.55405i) q^{56} -5.28942i q^{57} +(-0.0261196 - 0.0150801i) q^{58} +(-0.148458 - 0.0857123i) q^{59} +(-1.68012 + 2.91005i) q^{61} +(-3.33225 - 5.77162i) q^{62} +(7.60563 - 4.39111i) q^{63} -8.86488 q^{64} +15.2807 q^{66} +(-5.54239 + 3.19990i) q^{67} +(0.289961 + 0.502227i) q^{68} +(-4.53957 + 7.86276i) q^{69} +(9.35076 + 5.39866i) q^{71} +(6.47351 + 3.73748i) q^{72} -4.70308i q^{73} +(5.30812 - 9.19393i) q^{74} +(1.00633 - 0.581008i) q^{76} +19.3396 q^{77} +(8.91030 - 5.07938i) q^{78} -11.9826 q^{79} +(5.18379 + 8.97859i) q^{81} +(-2.27597 + 3.94209i) q^{82} +12.1286i q^{83} +(3.72572 + 2.15104i) q^{84} +1.38051i q^{86} +(-0.0288357 + 0.0499450i) q^{87} +(8.23042 + 14.2555i) q^{88} +(13.9898 - 8.07702i) q^{89} +(11.2771 - 6.42856i) q^{91} -1.99457 q^{92} +(-11.0363 + 6.37182i) q^{93} +(-1.57666 - 2.73086i) q^{94} +6.57666i q^{96} +(10.5379 + 6.08408i) q^{97} +(-6.29692 - 3.63553i) q^{98} -13.1039i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 2 q^{4} - 18 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 2 * q^4 - 18 * q^6 + 6 * q^7 - 4 * q^9	$ 8 q - 2 q^{3} + 2 q^{4} - 18 q^{6} + 6 q^{7} - 4 q^{9} - 20 q^{12} + 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} + 12 q^{22} + 10 q^{23} - 12 q^{24} + 10 q^{26} + 4 q^{27} + 18 q^{28} - 8 q^{29} - 6 q^{32} - 42 q^{33} + 20 q^{36} - 6 q^{37} + 16 q^{38} + 12 q^{41} - 4 q^{42} + 2 q^{43} - 42 q^{46} - 28 q^{48} + 12 q^{49} - 8 q^{51} + 6 q^{52} + 24 q^{53} + 18 q^{54} + 12 q^{56} - 36 q^{58} - 12 q^{59} - 28 q^{61} - 4 q^{62} + 24 q^{63} - 8 q^{64} + 12 q^{66} - 6 q^{67} + 14 q^{68} - 16 q^{69} + 48 q^{72} + 10 q^{74} + 54 q^{76} + 36 q^{77} + 56 q^{78} - 16 q^{79} + 8 q^{81} - 4 q^{82} - 30 q^{84} - 22 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 30 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^4 - 18 * q^6 + 6 * q^7 - 4 * q^9 - 20 * q^12 + 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 + 12 * q^22 + 10 * q^23 - 12 * q^24 + 10 * q^26 + 4 * q^27 + 18 * q^28 - 8 * q^29 - 6 * q^32 - 42 * q^33 + 20 * q^36 - 6 * q^37 + 16 * q^38 + 12 * q^41 - 4 * q^42 + 2 * q^43 - 42 * q^46 - 28 * q^48 + 12 * q^49 - 8 * q^51 + 6 * q^52 + 24 * q^53 + 18 * q^54 + 12 * q^56 - 36 * q^58 - 12 * q^59 - 28 * q^61 - 4 * q^62 + 24 * q^63 - 8 * q^64 + 12 * q^66 - 6 * q^67 + 14 * q^68 - 16 * q^69 + 48 * q^72 + 10 * q^74 + 54 * q^76 + 36 * q^77 + 56 * q^78 - 16 * q^79 + 8 * q^81 - 4 * q^82 - 30 * q^84 - 22 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.05628	+	0.609843i	−0.746903	+	0.431224i	−0.824574	−	0.565755i	$-0.808585\pi$
$2$	−1.05628	+	0.609843i	−0.746903	+	0.431224i	0.0776710	+	0.996979i	$0.475252\pi$
$3$	1.16612	+	2.01978i	0.673262	+	1.16612i	0.976974	+	0.213359i	$0.0684405\pi$
$3$	1.16612	+	2.01978i	0.673262	+	1.16612i	−0.303712	+	0.952764i	$0.598226\pi$
$4$	−0.256182	+	0.443720i	−0.128091	+	0.221860i
$5$		0			0
$5$		0			0
$6$	−2.46350	−	1.42231i	−1.00572	−	0.580654i
$7$	−3.11786	−	1.80010i	−1.17844	−	0.680373i	−0.222787	−	0.974867i	$-0.571516\pi$
$7$	−3.11786	−	1.80010i	−1.17844	−	0.680373i	−0.955653	+	0.294494i	$0.904849\pi$
$8$		−	3.06430i		−	1.08339i
$9$	−1.21969	+	2.11256i	−0.406562	+	0.704187i
$10$		0			0
$11$	−4.65213	+	2.68591i	−1.40267	+	0.809832i	−0.994666	−	0.103149i	$-0.967108\pi$
$11$	−4.65213	+	2.68591i	−1.40267	+	0.809832i	−0.408004	+	0.912980i	$0.633775\pi$
$12$	−1.19496			−0.344955
$13$	−1.81988	+	3.11256i	−0.504745	+	0.863269i
$13$	−1.81988	+	3.11256i	−0.504745	+	0.863269i
$14$	4.39111			1.17357
$15$		0			0
$16$	1.35638	+	2.34932i	0.339094	+	0.587329i
$17$	0.565928	−	0.980215i	0.137258	−	0.237737i	−0.789200	−	0.614136i	$-0.789505\pi$
$17$	0.565928	−	0.980215i	0.137258	−	0.237737i	0.926458	+	0.376399i	$0.122838\pi$
$18$		−	2.97527i		−	0.701278i
$19$	−1.96410	−	1.13397i	−0.450596	−	0.260152i	0.257486	−	0.966282i	$-0.417106\pi$
$19$	−1.96410	−	1.13397i	−0.450596	−	0.260152i	−0.708082	+	0.706130i	$0.750439\pi$
$20$		0			0
$21$		−	8.39654i		−	1.83228i
$22$	3.27597	−	5.67414i	0.698438	−	1.20973i
$23$	1.94644	+	3.37133i	0.405860	+	0.702970i	0.994421	−	0.105483i	$-0.0336387\pi$
$23$	1.94644	+	3.37133i	0.405860	+	0.702970i	−0.588561	+	0.808453i	$0.700305\pi$
$24$	6.18922	−	3.57335i	1.26337	−	0.729407i
$25$		0			0
$26$	0.0241312	−	4.39758i	0.00473251	−	0.862436i
$27$	1.30752			0.251632
$28$	1.59748	−	0.922305i	0.301895	−	0.174299i
$29$	0.0123639	+	0.0214150i	0.00229593	+	0.00397666i	0.867171	−	0.498010i	$-0.165936\pi$
$29$	0.0123639	+	0.0214150i	0.00229593	+	0.00397666i	−0.864875	+	0.501987i	$0.832603\pi$
$30$		0			0
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	2.44209	+	1.40994i	0.431705	+	0.249245i
$33$	−10.8499	−	6.26420i	−1.88873	−	1.09046i
$34$			1.38051i			0.236755i
$35$		0			0
$36$	−0.624924	−	1.08240i	−0.104154	−	0.180400i
$37$	−7.53794	+	4.35203i	−1.23923	+	0.715470i	−0.968937	−	0.247309i	$-0.920454\pi$
$37$	−7.53794	+	4.35203i	−1.23923	+	0.715470i	−0.270293	+	0.962778i	$0.587121\pi$
$38$	2.76619			0.448735
$39$	−8.40891	−	0.0461428i	−1.34650	−	0.00738877i
$40$		0			0
$41$	3.23205	−	1.86603i	0.504762	−	0.291424i	−0.225916	−	0.974147i	$-0.572538\pi$
$41$	3.23205	−	1.86603i	0.504762	−	0.291424i	0.730678	+	0.682723i	$0.239204\pi$
$42$	5.12058	+	8.86910i	0.790122	+	1.36853i
$43$	0.565928	−	0.980215i	0.0863031	−	0.149481i	−0.819643	−	0.572875i	$-0.805828\pi$
$43$	0.565928	−	0.980215i	0.0863031	−	0.149481i	0.905946	+	0.423394i	$0.139161\pi$
$44$		−	2.75232i		−	0.414929i
$45$		0			0
$46$	−4.11196	−	2.37404i	−0.606276	−	0.350034i
$47$			2.58535i			0.377113i	0.982062	+	0.188556i	$0.0603808\pi$
$47$			2.58535i			0.377113i	−0.982062	+	0.188556i	$0.939619\pi$
$48$	−3.16341	+	5.47918i	−0.456598	+	0.790852i
$49$	2.98070	+	5.16273i	0.425815	+	0.737533i
$50$		0			0
$51$	2.63977			0.369641
$52$	−0.914884	−	1.60490i	−0.126872	−	0.222560i
$53$	4.43937			0.609795			0.304897	−	0.952385i	$-0.401378\pi$
$53$	4.43937			0.609795			0.304897	+	0.952385i	$0.401378\pi$
$54$	−1.38111	+	0.797382i	−0.187945	+	0.108510i
$55$		0			0
$56$	−5.51603	+	9.55405i	−0.737111	+	1.27671i
$57$		−	5.28942i		−	0.700600i
$58$	−0.0261196	−	0.0150801i	−0.00342967	−	0.00198012i
$59$	−0.148458	−	0.0857123i	−0.0193276	−	0.0111588i	0.490305	−	0.871551i	$-0.336885\pi$
$59$	−0.148458	−	0.0857123i	−0.0193276	−	0.0111588i	−0.509633	+	0.860392i	$0.670219\pi$
$60$		0			0
$61$	−1.68012	+	2.91005i	−0.215117	+	0.372594i	−0.953309	−	0.301997i	$-0.902347\pi$
$61$	−1.68012	+	2.91005i	−0.215117	+	0.372594i	0.738192	+	0.674591i	$0.235680\pi$
$62$	−3.33225	−	5.77162i	−0.423196	−	0.732997i
$63$	7.60563	−	4.39111i	0.958219	−	0.553228i
$64$	−8.86488			−1.10811
$65$		0			0
$66$	15.2807			1.88093
$67$	−5.54239	+	3.19990i	−0.677111	+	0.390930i	−0.798766	−	0.601642i	$-0.794513\pi$
$67$	−5.54239	+	3.19990i	−0.677111	+	0.390930i	0.121655	+	0.992572i	$0.461180\pi$
$68$	0.289961	+	0.502227i	0.0351629	+	0.0609040i
$69$	−4.53957	+	7.86276i	−0.546500	+	0.946566i
$70$		0			0
$71$	9.35076	+	5.39866i	1.10973	+	0.640703i	0.938760	−	0.344573i	$-0.111976\pi$
$71$	9.35076	+	5.39866i	1.10973	+	0.640703i	0.170971	+	0.985276i	$0.445309\pi$
$72$	6.47351	+	3.73748i	0.762911	+	0.440467i
$73$		−	4.70308i		−	0.550454i	−0.961379	−	0.275227i	$-0.911247\pi$
$73$		−	4.70308i		−	0.550454i	0.961379	−	0.275227i	$-0.0887531\pi$
$74$	5.30812	−	9.19393i	0.617056	−	1.06877i
$75$		0			0
$76$	1.00633	−	0.581008i	0.115435	−	0.0666462i
$77$	19.3396			2.20395
$78$	8.91030	−	5.07938i	1.00889	−	0.575126i
$79$	−11.9826			−1.34815			−0.674075	−	0.738663i	$-0.735457\pi$
$79$	−11.9826			−1.34815			−0.674075	+	0.738663i	$0.735457\pi$
$80$		0			0
$81$	5.18379	+	8.97859i	0.575976	+	0.997621i
$82$	−2.27597	+	3.94209i	−0.251338	+	0.435331i
$83$			12.1286i			1.33129i	0.746270	+	0.665643i	$0.231843\pi$
$83$			12.1286i			1.33129i	−0.746270	+	0.665643i	$0.768157\pi$
$84$	3.72572	+	2.15104i	0.406509	+	0.234698i
$85$		0			0
$86$			1.38051i			0.148864i
$87$	−0.0288357	+	0.0499450i	−0.00309152	+	0.00535466i
$88$	8.23042	+	14.2555i	0.877366	+	1.51964i
$89$	13.9898	−	8.07702i	1.48292	−	0.856162i	0.483105	−	0.875562i	$-0.339509\pi$
$89$	13.9898	−	8.07702i	1.48292	−	0.856162i	0.999812	+	0.0194001i	$0.00617565\pi$
$90$		0			0
$91$	11.2771	−	6.42856i	1.18216	−	0.673896i
$92$	−1.99457			−0.207948
$93$	−11.0363	+	6.37182i	−1.14441	+	0.660727i
$94$	−1.57666	−	2.73086i	−0.162620	−	0.281666i
$95$		0			0
$96$			6.57666i			0.671228i
$97$	10.5379	+	6.08408i	1.06997	+	0.617745i	0.928172	−	0.372151i	$-0.121380\pi$
$97$	10.5379	+	6.08408i	1.06997	+	0.617745i	0.141794	+	0.989896i	$0.454713\pi$
$98$	−6.29692	−	3.63553i	−0.636085	−	0.367244i
$99$		−	13.1039i		−	1.31699i
$100$		0			0
$101$	−2.02721	−	3.51122i	−0.201714	−	0.349380i	0.747366	−	0.664412i	$-0.231318\pi$
$101$	−2.02721	−	3.51122i	−0.201714	−	0.349380i	−0.949081	+	0.315032i	$0.897985\pi$
$102$	−2.78833	+	1.60984i	−0.276086	+	0.159398i
$103$	−17.9035			−1.76408			−0.882041	−	0.471173i	$-0.843831\pi$
$103$	−17.9035			−1.76408			−0.882041	+	0.471173i	$0.843831\pi$
$104$	9.53781	+	5.57666i	0.935259	+	0.546837i
$105$		0			0
$106$	−4.68922	+	2.70732i	−0.455457	+	0.262958i
$107$	−4.56593	−	7.90842i	−0.441405	−	0.764536i	0.556389	−	0.830922i	$-0.312186\pi$
$107$	−4.56593	−	7.90842i	−0.441405	−	0.764536i	−0.997794	+	0.0663862i	$0.978853\pi$
$108$	−0.334963	+	0.580172i	−0.0322318	+	0.0558271i
$109$			7.37605i			0.706498i	0.935529	+	0.353249i	$0.114923\pi$
$109$			7.37605i			0.706498i	−0.935529	+	0.353249i	$0.885077\pi$
$110$		0			0
$111$	−17.5803	−	10.1500i	−1.66865	−	0.963396i
$112$		−	9.76645i		−	0.922843i
$113$	3.53794	−	6.12789i	0.332821	−	0.576463i	−0.650243	−	0.759727i	$-0.725333\pi$
$113$	3.53794	−	6.12789i	0.332821	−	0.576463i	0.983064	+	0.183263i	$0.0586661\pi$
$114$	3.22572	+	5.58710i	0.302116	+	0.523280i
$115$		0			0
$116$	−0.0126697			−0.00117635
$117$	−4.35578	−	7.64096i	−0.402692	−	0.706407i
$118$	0.209084			0.0192478
$119$	−3.52897	+	2.03745i	−0.323500	+	0.186773i
$120$		0			0
$121$	8.92820	−	15.4641i	0.811655	−	1.40583i
$122$		−	4.09843i		−	0.371055i
$123$	7.53794	+	4.35203i	0.679673	+	0.392409i
$124$	−2.42453	−	1.39980i	−0.217729	−	0.125706i
$125$		0			0
$126$	−5.35578	+	9.27648i	−0.477131	+	0.826415i
$127$	5.71806	+	9.90396i	0.507395	+	0.878835i	0.999963	+	0.00856072i	$0.00272499\pi$
$127$	5.71806	+	9.90396i	0.507395	+	0.878835i	−0.492568	+	0.870274i	$0.663942\pi$
$128$	4.47962	−	2.58631i	0.395946	−	0.228600i
$129$	2.63977			0.232418
$130$		0			0
$131$	−10.5680			−0.923328			−0.461664	−	0.887055i	$-0.652747\pi$
$131$	−10.5680			−0.923328			−0.461664	+	0.887055i	$0.652747\pi$
$132$	5.55910	−	3.20955i	0.483858	−	0.279355i
$133$	4.08253	+	7.07115i	0.354000	+	0.613146i
$134$	3.90288	−	6.75998i	0.337157	−	0.583974i
$135$		0			0
$136$	−3.00367	−	1.73417i	−0.257563	−	0.148704i
$137$	−3.27940	−	1.89336i	−0.280178	−	0.161761i	0.353326	−	0.935500i	$-0.385051\pi$
$137$	−3.27940	−	1.89336i	−0.280178	−	0.161761i	−0.633504	+	0.773739i	$0.718384\pi$
$138$		−	11.0737i		−	0.942656i
$139$	−1.00693	+	1.74406i	−0.0854068	+	0.147929i	−0.905564	−	0.424209i	$-0.860552\pi$
$139$	−1.00693	+	1.74406i	−0.0854068	+	0.147929i	0.820158	+	0.572138i	$0.193886\pi$
$140$		0			0
$141$	−5.22186	+	3.01484i	−0.439760	+	0.253895i
$142$	−13.1694			−1.10515
$143$	0.106280	−	19.3681i	0.00888757	−	1.61964i
$144$	−6.61742			−0.551452
$145$		0			0
$146$	2.86814	+	4.96777i	0.237369	+	0.411136i
$147$	−6.95174	+	12.0408i	−0.573370	+	0.993105i
$148$		−	4.45965i		−	0.366581i
$149$	4.77855	+	2.75890i	0.391474	+	0.226018i	0.682799	−	0.730607i	$-0.260763\pi$
$149$	4.77855	+	2.75890i	0.391474	+	0.226018i	−0.291324	+	0.956624i	$0.594096\pi$
$150$		0			0
$151$			4.88961i			0.397911i	0.980009	+	0.198956i	$0.0637549\pi$
$151$			4.88961i			0.397911i	−0.980009	+	0.198956i	$0.936245\pi$
$152$	−3.47484	+	6.01859i	−0.281846	+	0.488172i
$153$	1.38051	+	2.39111i	0.111608	+	0.193310i
$154$	−20.4280	+	11.7941i	−1.64614	+	0.950397i
$155$		0			0
$156$	2.17469	−	3.71938i	0.174114	−	0.297789i
$157$	−10.0405			−0.801323			−0.400661	−	0.916226i	$-0.631220\pi$
$157$	−10.0405			−0.801323			−0.400661	+	0.916226i	$0.631220\pi$
$158$	12.6570	−	7.30752i	1.00694	−	0.581355i
$159$	5.17686	+	8.96658i	0.410551	+	0.711096i
$160$		0			0
$161$		−	14.0151i		−	1.10454i
$162$	−10.9511	−	6.32260i	−0.860397	−	0.496750i
$163$	−5.87273	−	3.39062i	−0.459988	−	0.265574i	0.252051	−	0.967714i	$-0.418895\pi$
$163$	−5.87273	−	3.39062i	−0.459988	−	0.265574i	−0.712039	+	0.702140i	$0.752228\pi$
$164$			1.91217i			0.149315i
$165$		0			0
$166$	−7.39654	−	12.8112i	−0.574083	−	0.994341i
$167$	9.08444	−	5.24490i	0.702975	−	0.405863i	−0.105479	−	0.994421i	$-0.533638\pi$
$167$	9.08444	−	5.24490i	0.702975	−	0.405863i	0.808455	+	0.588559i	$0.200304\pi$
$168$	−25.7295			−1.98507
$169$	−6.37605	−	11.3290i	−0.490466	−	0.871460i
$170$		0			0
$171$	4.79118	−	2.76619i	0.366391	−	0.211536i
$172$	0.289961	+	0.502227i	0.0221093	+	0.0382944i
$173$	2.22923	−	3.86113i	0.169485	−	0.293557i	−0.768754	−	0.639545i	$-0.779123\pi$
$173$	2.22923	−	3.86113i	0.169485	−	0.293557i	0.938239	+	0.345988i	$0.112456\pi$
$174$		−	0.0703412i		−	0.00533255i
$175$		0			0
$176$	−12.6201	−	7.28621i	−0.951275	−	0.549219i
$177$		−	0.399804i		−	0.0300511i
$178$	−9.85143	+	17.0632i	−0.738396	+	1.27894i
$179$	9.31564	+	16.1352i	0.696284	+	1.20600i	0.969746	+	0.244116i	$0.0784979\pi$
$179$	9.31564	+	16.1352i	0.696284	+	1.20600i	−0.273462	+	0.961883i	$0.588169\pi$
$180$		0			0
$181$	−18.0900			−1.34462			−0.672310	−	0.740270i	$-0.734698\pi$
$181$	−18.0900			−1.34462			−0.672310	+	0.740270i	$0.734698\pi$
$182$	−7.99131	+	13.6676i	−0.592355	+	1.01311i
$183$	−7.83690			−0.579320
$184$	10.3307	−	5.96446i	0.761593	−	0.439706i
$185$		0			0
$186$	7.77162	−	13.4608i	0.569843	−	0.986997i
$187$			6.08012i			0.444622i
$188$	−1.14717	−	0.662321i	−0.0836662	−	0.0483047i
$189$	−4.07666	−	2.35366i	−0.296533	−	0.171204i
$190$		0			0
$191$	−13.6682	+	23.6740i	−0.988994	+	1.71299i	−0.366361	+	0.930473i	$0.619397\pi$
$191$	−13.6682	+	23.6740i	−0.988994	+	1.71299i	−0.622632	+	0.782515i	$0.713937\pi$
$192$	−10.3375	−	17.9052i	−0.746048	−	1.29219i
$193$	18.8511	−	10.8837i	1.35693	−	0.783425i	0.367723	−	0.929935i	$-0.380137\pi$
$193$	18.8511	−	10.8837i	1.35693	−	0.783425i	0.989209	+	0.146510i	$0.0468041\pi$
$194$	−14.8413			−1.06555
$195$		0			0
$196$	−3.05441			−0.218172
$197$	1.46940	−	0.848360i	0.104691	−	0.0604432i	−0.446741	−	0.894664i	$-0.647415\pi$
$197$	1.46940	−	0.848360i	0.104691	−	0.0604432i	0.551431	+	0.834220i	$0.314082\pi$
$198$	7.99131	+	13.8413i	0.567917	+	0.983662i
$199$	12.6627	−	21.9325i	0.897637	−	1.55475i	0.0671309	−	0.997744i	$-0.478615\pi$
$199$	12.6627	−	21.9325i	0.897637	−	1.55475i	0.830506	−	0.557009i	$-0.188051\pi$
$200$		0			0
$201$	−12.9262	−	7.46296i	−0.911746	−	0.526397i
$202$	4.28259	+	2.47256i	0.301322	+	0.173968i
$203$		−	0.0890252i		−	0.00624834i
$204$	−0.676260	+	1.17132i	−0.0473477	+	0.0820086i
$205$		0			0
$206$	18.9111	−	10.9183i	1.31760	−	0.760715i
$207$	−9.49617			−0.660030
$208$	−9.78083	−	0.0536711i	−0.678179	−	0.00372142i
$209$	12.1830			0.842716
$210$		0			0
$211$	0.167753	+	0.290558i	0.0115486	+	0.0200028i	0.871742	−	0.489965i	$-0.162991\pi$
$211$	0.167753	+	0.290558i	0.0115486	+	0.0200028i	−0.860193	+	0.509968i	$0.829657\pi$
$212$	−1.13729	+	1.96984i	−0.0781092	+	0.135289i
$213$			25.1820i			1.72544i
$214$	9.64579	+	5.56900i	0.659373	+	0.380689i
$215$		0			0
$216$		−	4.00663i		−	0.272616i
$217$	9.83592	−	17.0363i	0.667706	−	1.15650i
$218$	−4.49824	−	7.79118i	−0.304659	−	0.527685i
$219$	9.49922	−	5.48438i	0.641898	−	0.370600i
$220$		0			0
$221$	2.02106	+	3.54536i	0.135951	+	0.238487i
$222$	24.7597			1.66176
$223$	10.6493	−	6.14838i	0.713130	−	0.411726i	−0.0990887	−	0.995079i	$-0.531593\pi$
$223$	10.6493	−	6.14838i	0.713130	−	0.411726i	0.812219	+	0.583353i	$0.198259\pi$
$224$	−5.07606	−	8.79200i	−0.339159	−	0.587440i
$225$		0			0
$226$			8.63036i			0.574083i
$227$	−6.60974	−	3.81613i	−0.438704	−	0.253286i	0.264344	−	0.964428i	$-0.414845\pi$
$227$	−6.60974	−	3.81613i	−0.438704	−	0.253286i	−0.703048	+	0.711143i	$0.748178\pi$
$228$	2.34702	+	1.35505i	0.155435	+	0.0897406i
$229$			14.4008i			0.951631i	0.879545	+	0.475815i	$0.157847\pi$
$229$			14.4008i			0.951631i	−0.879545	+	0.475815i	$0.842153\pi$
$230$		0			0
$231$	22.5523	+	39.0618i	1.48384	+	2.57008i
$232$	0.0656218	−	0.0378868i	0.00430828	−	0.00248739i
$233$	9.49617			0.622115			0.311057	−	0.950391i	$-0.399317\pi$
$233$	9.49617			0.622115			0.311057	+	0.950391i	$0.399317\pi$
$234$	9.26071	+	5.41465i	0.605392	+	0.353966i
$235$		0			0
$236$	0.0760645	−	0.0439159i	0.00495138	−	0.00285868i
$237$	−13.9732	−	24.2023i	−0.907657	−	1.57211i
$238$	2.48505	−	4.30423i	0.161082	−	0.279002i
$239$		−	19.9143i		−	1.28815i	−0.764962	−	0.644076i	$-0.777242\pi$
$239$		−	19.9143i		−	1.28815i	0.764962	−	0.644076i	$-0.222758\pi$
$240$		0			0
$241$	20.1493	+	11.6332i	1.29793	+	0.749360i	0.980046	−	0.198770i	$-0.0636947\pi$
$241$	20.1493	+	11.6332i	1.29793	+	0.749360i	0.317883	+	0.948130i	$0.397028\pi$
$242$			21.7792i			1.40002i
$243$	−10.1286	+	17.5432i	−0.649750	+	1.12540i
$244$	−0.860832	−	1.49100i	−0.0551091	−	0.0954518i
$245$		0			0
$246$	−10.6162			−0.676866
$247$	7.10400	−	4.04968i	0.452017	−	0.257675i
$248$	16.7436			1.06322
$249$	−24.4972	+	14.1434i	−1.55244	+	0.896304i
$250$		0			0
$251$	5.92008	−	10.2539i	0.373672	−	0.647219i	−0.616455	−	0.787390i	$-0.711432\pi$
$251$	5.92008	−	10.2539i	0.373672	−	0.647219i	0.990127	+	0.140171i	$0.0447652\pi$
$252$			4.49969i			0.283454i
$253$	−18.1101	−	10.4559i	−1.13858	−	0.657357i
$254$	−12.0797	−	6.97424i	−0.757950	−	0.437603i
$255$		0			0
$256$	5.71040	−	9.89070i	0.356900	−	0.618169i
$257$	2.77501	+	4.80646i	0.173100	+	0.299819i	0.939502	−	0.342543i	$-0.111288\pi$
$257$	2.77501	+	4.80646i	0.173100	+	0.299819i	−0.766402	+	0.642361i	$0.777955\pi$
$258$	−2.78833	+	1.60984i	−0.173594	+	0.100224i
$259$	31.3363			1.94714
$260$		0			0
$261$	−0.0603205			−0.00373375
$262$	11.1627	−	6.44481i	0.689636	−	0.398161i
$263$	3.42983	+	5.94065i	0.211493	+	0.366316i	0.952182	−	0.305532i	$-0.0988342\pi$
$263$	3.42983	+	5.94065i	0.211493	+	0.366316i	−0.740689	+	0.671848i	$0.765501\pi$
$264$	−19.1954	+	33.2474i	−1.18139	+	2.04623i
$265$		0			0
$266$	−8.62459	−	4.97941i	−0.528807	−	0.305307i
$267$	32.6277	+	18.8376i	1.99678	+	1.15284i
$268$		−	3.27903i		−	0.200299i
$269$	0.710994	−	1.23148i	0.0433501	−	0.0750845i	−0.843536	−	0.537072i	$-0.819530\pi$
$269$	0.710994	−	1.23148i	0.0433501	−	0.0750845i	0.886886	+	0.461988i	$0.152864\pi$
$270$		0			0
$271$	8.63381	−	4.98473i	0.524467	−	0.302801i	−0.214294	−	0.976769i	$-0.568745\pi$
$271$	8.63381	−	4.98473i	0.524467	−	0.302801i	0.738760	+	0.673968i	$0.235412\pi$
$272$	3.07045			0.186173
$273$	26.1347	+	15.2807i	1.58175	+	0.924831i
$274$	4.61862			0.279021
$275$		0			0
$276$	−2.32591	−	4.02860i	−0.140003	−	0.242493i
$277$	8.76187	−	15.1760i	0.526449	−	0.911837i	−0.473076	−	0.881022i	$-0.656856\pi$
$277$	8.76187	−	15.1760i	0.526449	−	0.911837i	0.999525	−	0.0308154i	$-0.00981039\pi$
$278$		−	2.45628i		−	0.147318i
$279$	−11.5432	−	6.66449i	−0.691076	−	0.398993i
$280$		0			0
$281$		−	10.7352i		−	0.640406i	−0.947349	−	0.320203i	$-0.896249\pi$
$281$		−	10.7352i		−	0.640406i	0.947349	−	0.320203i	$-0.103751\pi$
$282$	3.67716	−	6.36903i	0.218972	−	0.379270i
$283$	−0.659192	−	1.14175i	−0.0391849	−	0.0678702i	0.845768	−	0.533551i	$-0.179143\pi$
$283$	−0.659192	−	1.14175i	−0.0391849	−	0.0678702i	−0.884953	+	0.465681i	$0.845809\pi$
$284$	−4.79099	+	2.76608i	−0.284293	+	0.164137i
$285$		0			0
$286$	11.6992	+	20.5229i	0.691790	+	1.21355i
$287$	−13.4361			−0.793109
$288$	−5.95717	+	3.43937i	−0.351030	+	0.202667i
$289$	7.85945	+	13.6130i	0.462321	+	0.800763i
$290$		0			0
$291$			28.3792i			1.66362i
$292$	2.08685	+	1.20485i	0.122124	+	0.0705082i
$293$	−16.2316	−	9.37133i	−0.948261	−	0.547479i	−0.0557207	−	0.998446i	$-0.517746\pi$
$293$	−16.2316	−	9.37133i	−0.948261	−	0.547479i	−0.892540	+	0.450968i	$0.851079\pi$
$294$		−	16.9579i		−	0.989004i
$295$		0			0
$296$	13.3359	+	23.0985i	0.775134	+	1.34257i
$297$	−6.08275	+	3.51187i	−0.352957	+	0.203780i
$298$	−6.72998			−0.389857
$299$	−14.0357	−	0.0770194i	−0.811708	−	0.00445415i
$300$		0			0
$301$	−3.52897	+	2.03745i	−0.203406	+	0.117437i
$302$	−2.98190	−	5.16480i	−0.171589	−	0.297201i
$303$	4.72794	−	8.18904i	0.271613	−	0.470448i
$304$		−	6.15239i		−	0.352864i
$305$		0			0
$306$	−2.91641	−	1.68379i	−0.166720	−	0.0962558i
$307$			14.3043i			0.816387i	0.912895	+	0.408194i	$0.133841\pi$
$307$			14.3043i			0.816387i	−0.912895	+	0.408194i	$0.866159\pi$
$308$	−4.95445	+	8.58137i	−0.282306	+	0.488969i
$309$	−20.8777	−	36.1612i	−1.18769	−	2.05714i
$310$		0			0
$311$	−2.76102			−0.156563			−0.0782815	−	0.996931i	$-0.524943\pi$
$311$	−2.76102			−0.156563			−0.0782815	+	0.996931i	$0.524943\pi$
$312$	−0.141395	+	25.7674i	−0.00800494	+	1.45879i
$313$	16.3858			0.926179			0.463090	−	0.886311i	$-0.346741\pi$
$313$	16.3858			0.926179			0.463090	+	0.886311i	$0.346741\pi$
$314$	10.6056	−	6.12316i	0.598510	−	0.345550i
$315$		0			0
$316$	3.06973	−	5.31693i	0.172686	−	0.299101i
$317$		−	1.78575i		−	0.100297i	−0.998742	−	0.0501487i	$-0.984030\pi$
$317$		−	1.78575i		−	0.100297i	0.998742	−	0.0501487i	$-0.0159695\pi$
$318$	−10.9364	−	6.31414i	−0.613284	−	0.354080i
$319$	−0.115037	−	0.0664168i	−0.00644085	−	0.00371863i
$320$		0			0
$321$	10.6489	−	18.4444i	0.594362	−	1.02946i
$322$	8.54702	+	14.8039i	0.476307	+	0.824987i
$323$	−2.22308	+	1.28349i	−0.123695	+	0.0714156i
$324$	−5.31197			−0.295110
$325$		0			0
$326$	8.27099			0.458088
$327$	−14.8980	+	8.60139i	−0.823864	+	0.475658i
$328$	−5.71806	−	9.90396i	−0.315727	−	0.546855i
$329$	4.65389	−	8.06077i	0.256577	−	0.444405i
$330$		0			0
$331$	−6.25652	−	3.61220i	−0.343889	−	0.198545i	0.318101	−	0.948057i	$-0.396955\pi$
$331$	−6.25652	−	3.61220i	−0.343889	−	0.198545i	−0.661991	+	0.749512i	$0.730288\pi$
$332$	−5.38170	−	3.10713i	−0.295359	−	0.170526i
$333$		−	21.2325i		−	1.16353i
$334$	−6.39714	+	11.0802i	−0.350036	+	0.606280i
$335$		0			0
$336$	19.7261	−	11.3889i	1.07615	−	0.621315i
$337$	−4.36219			−0.237624			−0.118812	−	0.992917i	$-0.537909\pi$
$337$	−4.36219			−0.237624			−0.118812	+	0.992917i	$0.537909\pi$
$338$	13.6438	+	8.07818i	0.742125	+	0.439395i
$339$	16.5027			0.896303
$340$		0			0
$341$	−14.6761	−	25.4197i	−0.794754	−	1.37655i
$342$	−3.37388	+	5.84374i	−0.182439	+	0.315993i
$343$			3.73913i			0.201894i
$344$	−3.00367	−	1.73417i	−0.161947	−	0.0935002i
$345$		0			0
$346$			5.43792i			0.292344i
$347$	−13.3536	+	23.1291i	−0.716858	+	1.24163i	0.245381	+	0.969427i	$0.421087\pi$
$347$	−13.3536	+	23.1291i	−0.716858	+	1.24163i	−0.962239	+	0.272207i	$0.912246\pi$
$348$	−0.0147744	−	0.0255900i	−0.000791991	−	0.00137177i
$349$	−20.4131	+	11.7855i	−1.09269	+	0.630865i	−0.934292	−	0.356510i	$-0.883967\pi$
$349$	−20.4131	+	11.7855i	−1.09269	+	0.630865i	−0.158399	+	0.987375i	$0.550633\pi$
$350$		0			0
$351$	−2.37953	+	4.06973i	−0.127010	+	0.217226i
$352$	−15.1479			−0.807385
$353$	−4.96862	+	2.86863i	−0.264453	+	0.152682i	−0.626364	−	0.779531i	$-0.715458\pi$
$353$	−4.96862	+	2.86863i	−0.264453	+	0.152682i	0.361911	+	0.932213i	$0.382124\pi$
$354$	0.243818	+	0.422305i	0.0129588	+	0.0224453i
$355$		0			0
$356$			8.27675i			0.438667i
$357$	−8.23042	−	4.75184i	−0.435600	−	0.251494i
$358$	−19.6799	−	11.3622i	−1.04011	−	0.600509i
$359$			24.7583i			1.30669i	0.757059	+	0.653347i	$0.226636\pi$
$359$			24.7583i			1.30669i	−0.757059	+	0.653347i	$0.773364\pi$
$360$		0			0
$361$	−6.92820	−	12.0000i	−0.364642	−	0.631579i
$362$	19.1081	−	11.0321i	1.00430	−	0.579833i
$363$	41.6455			2.18582
$364$	−0.0364951	+	6.65074i	−0.00191286	+	0.348593i
$365$		0			0
$366$	8.27796	−	4.77928i	0.432696	−	0.249817i
$367$	13.0268	+	22.5630i	0.679992	+	1.17778i	0.974983	+	0.222280i	$0.0713500\pi$
$367$	13.0268	+	22.5630i	0.679992	+	1.17778i	−0.294991	+	0.955500i	$0.595317\pi$
$368$	−5.28021	+	9.14558i	−0.275250	+	0.476747i
$369$			9.10387i			0.473928i
$370$		0			0
$371$	−13.8413	−	7.99131i	−0.718607	−	0.414888i
$372$		−	6.52938i		−	0.338532i
$373$	6.60224	−	11.4354i	0.341851	−	0.592103i	−0.642926	−	0.765929i	$-0.722280\pi$
$373$	6.60224	−	11.4354i	0.341851	−	0.592103i	0.984776	+	0.173826i	$0.0556129\pi$
$374$	−3.70792	−	6.42231i	−0.191732	−	0.332089i
$375$		0			0
$376$	7.92229			0.408561
$377$	−0.0891563		0.000489234i	−0.00459178		2.51968e-5i
$378$	5.74146			0.295309
$379$	22.5147	−	12.9989i	1.15650	−	0.667707i	0.206039	−	0.978544i	$-0.433943\pi$
$379$	22.5147	−	12.9989i	1.15650	−	0.667707i	0.950463	+	0.310837i	$0.100609\pi$
$380$		0			0
$381$	−13.3359	+	23.0985i	−0.683220	+	1.18337i
$382$		−	33.3418i		−	1.70591i
$383$	−8.31401	−	4.80010i	−0.424826	−	0.245274i	0.272314	−	0.962208i	$-0.412211\pi$
$383$	−8.31401	−	4.80010i	−0.424826	−	0.245274i	−0.697140	+	0.716935i	$0.745544\pi$
$384$	10.4476	+	6.03191i	0.533151	+	0.307815i
$385$		0			0
$386$	−13.2747	+	22.9924i	−0.675664	+	1.17028i
$387$	1.38051	+	2.39111i	0.0701752	+	0.121547i
$388$	−5.39926	+	3.11726i	−0.274106	+	0.158255i
$389$	−5.63129			−0.285518			−0.142759	−	0.989758i	$-0.545597\pi$
$389$	−5.63129			−0.285518			−0.142759	+	0.989758i	$0.545597\pi$
$390$		0			0
$391$	4.40617			0.222829
$392$	15.8201	−	9.13376i	0.799038	−	0.461325i
$393$	−12.3236	−	21.3450i	−0.621641	−	1.07671i
$394$	−1.03473	+	1.79221i	−0.0521291	+	0.0902903i
$395$		0			0
$396$	5.81445	+	3.35697i	0.292187	+	0.168694i
$397$	14.5196	+	8.38291i	0.728719	+	0.420726i	0.817953	−	0.575285i	$-0.195109\pi$
$397$	14.5196	+	8.38291i	0.728719	+	0.420726i	−0.0892344	+	0.996011i	$0.528442\pi$
$398$			30.8891i			1.54833i
$399$	−9.52147	+	16.4917i	−0.476670	+	0.825616i
$400$		0			0
$401$	12.0187	−	6.93902i	0.600187	−	0.346518i	−0.168928	−	0.985628i	$-0.554031\pi$
$401$	12.0187	−	6.93902i	0.600187	−	0.346518i	0.769115	+	0.639110i	$0.220697\pi$
$402$	18.2050			0.907980
$403$	−17.0073	−	9.94402i	−0.847196	−	0.495347i
$404$	2.07733			0.103351
$405$		0			0
$406$	0.0542914	+	0.0940355i	0.00269444	+	0.00466690i
$407$	23.3783	−	40.4924i	1.15882	−	2.00713i
$408$		−	8.08903i		−	0.400466i
$409$	−25.4829	−	14.7125i	−1.26005	−	0.727489i	−0.286964	−	0.957941i	$-0.592646\pi$
$409$	−25.4829	−	14.7125i	−1.26005	−	0.727489i	−0.973083	+	0.230453i	$0.925979\pi$
$410$		0			0
$411$		−	8.83157i		−	0.435629i
$412$	4.58655	−	7.94413i	0.225963	−	0.391379i
$413$	0.308581	+	0.534478i	0.0151843	+	0.0262999i
$414$	10.0306	−	5.79118i	0.492978	−	0.284621i
$415$		0			0
$416$	−8.83284	+	5.03522i	−0.433066	+	0.246872i
$417$	−4.69683			−0.230005
$418$	−12.8687	+	7.42973i	−0.629427	+	0.363400i
$419$	−3.48397	−	6.03440i	−0.170203	−	0.294800i	0.768288	−	0.640104i	$-0.221109\pi$
$419$	−3.48397	−	6.03440i	−0.170203	−	0.294800i	−0.938491	+	0.345305i	$0.887776\pi$
$420$		0			0
$421$			7.12125i			0.347069i	0.984828	+	0.173534i	$0.0555188\pi$
$421$			7.12125i			0.347069i	−0.984828	+	0.173534i	$0.944481\pi$
$422$	−0.354389	−	0.204607i	−0.0172514	−	0.00996010i
$423$	−5.46171	−	3.15332i	−0.265558	−	0.153320i
$424$		−	13.6036i		−	0.660647i
$425$		0			0
$426$	−15.3571	−	26.5993i	−0.744054	−	1.28874i
$427$	10.4767	−	6.04875i	0.507005	−	0.292720i
$428$	4.67883			0.226160
$429$	39.2433	−	22.3709i	1.89468	−	1.08008i
$430$		0			0
$431$	26.1664	−	15.1072i	1.26039	−	0.727687i	0.287241	−	0.957858i	$-0.407262\pi$
$431$	26.1664	−	15.1072i	1.26039	−	0.727687i	0.973150	+	0.230171i	$0.0739286\pi$
$432$	1.77349	+	3.07177i	0.0853270	+	0.147791i
$433$	−0.600065	+	1.03934i	−0.0288373	+	0.0499476i	−0.880084	−	0.474818i	$-0.842514\pi$
$433$	−0.600065	+	1.03934i	−0.0288373	+	0.0499476i	0.851247	+	0.524766i	$0.175847\pi$
$434$			23.9935i			1.15172i
$435$		0			0
$436$	−3.27290	−	1.88961i	−0.156744	−	0.0904960i
$437$		−	8.82884i		−	0.422341i
$438$	−6.68922	+	11.5861i	−0.319623	+	0.553604i
$439$	−8.27705	−	14.3363i	−0.395042	−	0.684233i	0.598064	−	0.801448i	$-0.295937\pi$
$439$	−8.27705	−	14.3363i	−0.395042	−	0.684233i	−0.993107	+	0.117215i	$0.962603\pi$
$440$		0			0
$441$	−14.5421			−0.692481
$442$	−4.29692	−	2.51236i	−0.204383	−	0.119501i
$443$	−4.55949			−0.216628			−0.108314	−	0.994117i	$-0.534545\pi$
$443$	−4.55949			−0.216628			−0.108314	+	0.994117i	$0.534545\pi$
$444$	9.00753	−	5.20050i	0.427478	−	0.246805i
$445$		0			0
$446$	−7.49910	+	12.9888i	−0.355093	+	0.615038i
$447$			12.8689i			0.608676i
$448$	27.6395	+	15.9577i	1.30584	+	0.753929i
$449$	11.9963	+	6.92608i	0.566142	+	0.326862i	0.755607	−	0.655025i	$-0.227342\pi$
$449$	11.9963	+	6.92608i	0.566142	+	0.326862i	−0.189465	+	0.981887i	$0.560675\pi$
$450$		0			0
$451$	−10.0239	+	17.3620i	−0.472009	+	0.817544i
$452$	1.81271	+	3.13971i	0.0852628	+	0.147680i
$453$	−9.87596	+	5.70189i	−0.464013	+	0.267898i
$454$	9.30897			0.436892
$455$		0			0
$456$	−16.2083			−0.759025
$457$	−34.7402	+	20.0573i	−1.62508	+	0.938240i	−0.639548	+	0.768751i	$0.720878\pi$
$457$	−34.7402	+	20.0573i	−1.62508	+	0.938240i	−0.985532	+	0.169489i	$0.945788\pi$
$458$	−8.78222	−	15.2113i	−0.410366	−	0.710775i
$459$	0.739961	−	1.28165i	0.0345384	−	0.0598223i
$460$		0			0
$461$	6.52897	+	3.76950i	0.304084	+	0.175563i	0.644276	−	0.764793i	$-0.277159\pi$
$461$	6.52897	+	3.76950i	0.304084	+	0.175563i	−0.340192	+	0.940356i	$0.610492\pi$
$462$	−47.6432	−	27.5068i	−2.21656	−	1.27973i
$463$			23.3031i			1.08299i	0.840705	+	0.541494i	$0.182141\pi$
$463$			23.3031i			1.08299i	−0.840705	+	0.541494i	$0.817859\pi$
$464$	−0.0335403	+	0.0580936i	−0.00155707	+	0.00269693i
$465$		0			0
$466$	−10.0306	+	5.79118i	−0.464659	+	0.268271i
$467$	−22.6297			−1.04718			−0.523589	−	0.851971i	$-0.675407\pi$
$467$	−22.6297			−1.04718			−0.523589	+	0.851971i	$0.675407\pi$
$468$	4.50632	+	0.0247279i	0.208305	+	0.00114305i
$469$	23.0405			1.06391
$470$		0			0
$471$	−11.7085	−	20.2797i	−0.539500	−	0.934441i
$472$	−0.262648	+	0.454919i	−0.0120893	+	0.0209394i
$473$			6.08012i			0.279564i
$474$	29.5192	+	17.0429i	1.35586	+	0.782808i
$475$		0			0
$476$		−	2.08783i		−	0.0956956i
$477$	−5.41465	+	9.37844i	−0.247920	+	0.429409i
$478$	12.1446	+	21.0351i	0.555482	+	0.962124i
$479$	−17.8789	+	10.3224i	−0.816910	+	0.471643i	−0.849350	−	0.527831i	$-0.823006\pi$
$479$	−17.8789	+	10.3224i	−0.816910	+	0.471643i	0.0324399	+	0.999474i	$0.489672\pi$
$480$		0			0
$481$	0.172207	−	31.3825i	0.00785198	−	1.43092i
$482$	−28.3777			−1.29257
$483$	28.3075	−	16.3433i	1.28804	−	0.743648i
$484$	4.57449	+	7.92325i	0.207931	+	0.360148i
$485$		0			0
$486$		−	24.7074i		−	1.12075i
$487$	2.62929	+	1.51802i	0.119145	+	0.0687882i	0.558388	−	0.829580i	$-0.311420\pi$
$487$	2.62929	+	1.51802i	0.119145	+	0.0687882i	−0.439243	+	0.898368i	$0.644753\pi$
$488$	8.91725	+	5.14838i	0.403665	+	0.233056i
$489$		−	15.8155i		−	0.715203i
$490$		0			0
$491$	5.33401	+	9.23877i	0.240720	+	0.416940i	0.960920	−	0.276827i	$-0.0892830\pi$
$491$	5.33401	+	9.23877i	0.240720	+	0.416940i	−0.720199	+	0.693767i	$0.755950\pi$
$492$	−3.86217	+	2.22982i	−0.174120	+	0.100528i
$493$	0.0279884			0.00126053
$494$	−5.03414	+	8.60992i	−0.226497	+	0.387379i
$495$		0			0
$496$	−12.8369	+	7.41139i	−0.576394	+	0.332781i
$497$	−19.4362	−	33.6646i	−0.871835	−	1.51006i
$498$	17.2506	−	29.8789i	0.773016	−	1.33890i
$499$			33.9143i			1.51821i	0.650966	+	0.759107i	$0.274364\pi$
$499$			33.9143i			1.51821i	−0.650966	+	0.759107i	$0.725636\pi$
$500$		0			0
$501$	21.1872	+	12.2324i	0.946572	+	0.546504i
$502$			14.4413i			0.644546i
$503$	−6.31380	+	10.9358i	−0.281518	+	0.487604i	−0.971759	−	0.235976i	$-0.924171\pi$
$503$	−6.31380	+	10.9358i	−0.281518	+	0.487604i	0.690241	+	0.723580i	$0.257505\pi$
$504$	−13.4557	−	23.3059i	−0.599363	−	1.03813i
$505$		0			0
$506$	25.5058			1.13387
$507$	15.4468	−	26.0893i	0.686019	−	1.15866i
$508$	−5.85945			−0.259971
$509$	−20.9168	+	12.0763i	−0.927120	+	0.535273i	−0.885899	−	0.463877i	$-0.846458\pi$
$509$	−20.9168	+	12.0763i	−0.927120	+	0.535273i	−0.0412201	+	0.999150i	$0.513124\pi$
$510$		0			0
$511$	−8.46601	+	14.6636i	−0.374514	+	0.648678i
$512$			24.2750i			1.07281i
$513$	−2.56810	−	1.48269i	−0.113384	−	0.0654625i
$514$	−5.86238	−	3.38465i	−0.258578	−	0.149290i
$515$		0			0
$516$	−0.676260	+	1.17132i	−0.0297707	+	0.0515644i
$517$	−6.94402	−	12.0274i	−0.305398	−	0.528964i
$518$	−33.0999	+	19.1103i	−1.45433	+	0.839656i
$519$	10.3982			0.456431
$520$		0			0
$521$	−24.7521			−1.08441			−0.542205	−	0.840246i	$-0.682410\pi$
$521$	−24.7521			−1.08441			−0.542205	+	0.840246i	$0.682410\pi$
$522$	0.0637154	−	0.0367861i	0.00278875	−	0.00161008i
$523$	18.5163	+	32.0712i	0.809662	+	1.40238i	0.913098	+	0.407739i	$0.133683\pi$
$523$	18.5163	+	32.0712i	0.809662	+	1.40238i	−0.103436	+	0.994636i	$0.532984\pi$
$524$	2.70732	−	4.68922i	0.118270	−	0.204850i
$525$		0			0
$526$	−7.24573	−	4.18332i	−0.315929	−	0.182402i
$527$	5.35600	+	3.09229i	0.233311	+	0.134702i
$528$		−	33.9865i		−	1.47907i
$529$	3.92277	−	6.79444i	0.170555	−	0.295410i
$530$		0			0
$531$	0.362145	−	0.209084i	0.0157157	−	0.00907348i
$532$	−4.18348			−0.181377
$533$	−0.0738376	+	13.4559i	−0.00319826	+	0.582840i
$534$	−45.9519			−1.98854
$535$		0			0
$536$	9.80545	+	16.9835i	0.423531	+	0.733577i
$537$	−21.7264	+	37.6312i	−0.937562	+	1.62391i
$538$			1.73438i			0.0747744i
$539$	−27.7332	−	16.0118i	−1.19456	−	0.689677i
$540$		0			0
$541$			8.38144i			0.360346i	0.983635	+	0.180173i	$0.0576658\pi$
$541$			8.38144i			0.360346i	−0.983635	+	0.180173i	$0.942334\pi$
$542$	−6.07981	+	10.5305i	−0.261150	+	0.452326i
$543$	−21.0952	−	36.5379i	−0.905281	−	1.56799i
$544$	2.76409	−	1.59585i	0.118509	−	0.0684215i
$545$		0			0
$546$	−36.9245	−	0.202618i	−1.58022	−	0.00867126i
$547$	22.7842			0.974181			0.487091	−	0.873351i	$-0.338058\pi$
$547$	22.7842			0.974181			0.487091	+	0.873351i	$0.338058\pi$
$548$	1.68025	−	0.970090i	0.0717765	−	0.0414402i
$549$	−4.09843	−	7.09870i	−0.174917	−	0.302965i
$550$		0			0
$551$		−	0.0560816i		−	0.00238915i
$552$	24.0938	+	13.9106i	1.02550	+	0.592074i
$553$	37.3601	+	21.5699i	1.58871	+	0.917245i
$554$			21.3735i			0.908071i
$555$		0			0
$556$	−0.515915	−	0.893592i	−0.0218797	−	0.0378967i
$557$	−24.3810	+	14.0764i	−1.03306	+	0.596435i	−0.917858	−	0.396908i	$-0.870083\pi$
$557$	−24.3810	+	14.0764i	−1.03306	+	0.596435i	−0.115197	+	0.993343i	$0.536750\pi$
$558$	16.2572			0.688222
$559$	2.02106	+	3.54536i	0.0854816	+	0.149953i
$560$		0			0
$561$	−12.2805	+	7.09017i	−0.518484	+	0.299347i
$562$	6.54676	+	11.3393i	0.276159	+	0.478321i
$563$	9.06514	−	15.7013i	0.382050	−	0.661731i	−0.609305	−	0.792936i	$-0.708551\pi$
$563$	9.06514	−	15.7013i	0.382050	−	0.661731i	0.991355	+	0.131206i	$0.0418848\pi$
$564$		−	3.08939i		−	0.130087i
$565$		0			0
$566$	1.39258	+	0.804007i	0.0585346	+	0.0337950i
$567$		−	37.3253i		−	1.56752i
$568$	16.5431	−	28.6535i	0.694133	−	1.20227i
$569$	20.2992	+	35.1593i	0.850988	+	1.47395i	0.880317	+	0.474385i	$0.157330\pi$
$569$	20.2992	+	35.1593i	0.850988	+	1.47395i	−0.0293292	+	0.999570i	$0.509337\pi$
$570$		0			0
$571$	−24.7159			−1.03433			−0.517164	−	0.855886i	$-0.673012\pi$
$571$	−24.7159			−1.03433			−0.517164	+	0.855886i	$0.673012\pi$
$572$	8.56677	+	5.00891i	0.358195	+	0.209433i
$573$	−63.7551			−2.66341
$574$	14.1923	−	8.19393i	0.592375	−	0.342008i
$575$		0			0
$576$	10.8124	−	18.7276i	0.450516	−	0.780317i
$577$		−	23.0691i		−	0.960379i	−0.877165	−	0.480189i	$-0.840568\pi$
$577$		−	23.0691i		−	0.960379i	0.877165	−	0.480189i	$-0.159432\pi$
$578$	−16.6036	−	9.58607i	−0.690617	−	0.398728i
$579$	43.9654	+	25.3834i	1.82714	+	1.05490i
$580$		0			0
$581$	21.8327	−	37.8153i	0.905771	−	1.56884i
$582$	−17.3068	−	29.9763i	−0.717392	−	1.24256i
$583$	−20.6525	+	11.9237i	−0.855341	+	0.493831i
$584$	−14.4116			−0.596358
$585$		0			0
$586$	22.8602			0.944345
$587$	17.6256	−	10.1762i	0.727487	−	0.420015i	−0.0900152	−	0.995940i	$-0.528692\pi$
$587$	17.6256	−	10.1762i	0.727487	−	0.420015i	0.817502	+	0.575926i	$0.195358\pi$
$588$	−3.56182	−	6.16925i	−0.146887	−	0.254416i
$589$	6.19615	−	10.7321i	0.255308	−	0.442206i
$590$		0			0
$591$	3.42701	+	1.97859i	0.140968	+	0.0813881i
$592$	−20.4486	−	11.8060i	−0.840432	−	0.485223i
$593$			10.3834i			0.426395i	0.977009	+	0.213198i	$0.0683878\pi$
$593$			10.3834i			0.426395i	−0.977009	+	0.213198i	$0.931612\pi$
$594$	4.28339	−	7.41904i	0.175750	−	0.304407i
$595$		0			0
$596$	−2.44836	+	1.41356i	−0.100289	+	0.0579017i
$597$	59.0652			2.41738
$598$	14.8726	−	8.47825i	0.608187	−	0.346701i
$599$	−31.5965			−1.29100			−0.645499	−	0.763761i	$-0.723351\pi$
$599$	−31.5965			−1.29100			−0.645499	+	0.763761i	$0.723351\pi$
$600$		0			0
$601$	21.9423	+	38.0051i	0.895044	+	1.55026i	0.833751	+	0.552141i	$0.186189\pi$
$601$	21.9423	+	38.0051i	0.895044	+	1.55026i	0.0612928	+	0.998120i	$0.480478\pi$
$602$	2.48505	−	4.30423i	0.101283	−	0.175428i
$603$		−	15.6115i		−	0.635750i
$604$	−2.16962	−	1.25263i	−0.0882806	−	0.0509688i
$605$		0			0
$606$			11.5332i			0.468505i
$607$	1.08770	−	1.88395i	0.0441484	−	0.0764673i	−0.843107	−	0.537746i	$-0.819276\pi$
$607$	1.08770	−	1.88395i	0.0441484	−	0.0764673i	0.887255	+	0.461279i	$0.152609\pi$
$608$	−3.19768	−	5.53854i	−0.129683	−	0.224617i
$609$	0.179812	−	0.103814i	0.00728634	−	0.00420677i
$610$		0			0
$611$	−8.04707	−	4.70504i	−0.325550	−	0.190346i
$612$	−1.41465			−0.0571837
$613$	12.7843	−	7.38100i	0.516352	−	0.298116i	−0.219089	−	0.975705i	$-0.570309\pi$
$613$	12.7843	−	7.38100i	0.516352	−	0.298116i	0.735441	+	0.677589i	$0.236975\pi$
$614$	−8.72336	−	15.1093i	−0.352046	−	0.609762i
$615$		0			0
$616$		−	59.2622i		−	2.38774i
$617$	−17.5779	−	10.1486i	−0.707659	−	0.408567i	0.102535	−	0.994729i	$-0.467305\pi$
$617$	−17.5779	−	10.1486i	−0.707659	−	0.408567i	−0.810194	+	0.586162i	$0.800638\pi$
$618$	44.1053	+	25.4642i	1.77418	+	1.02432i
$619$		−	9.94207i		−	0.399605i	−0.979836	−	0.199803i	$-0.935970\pi$
$619$		−	9.94207i		−	0.399605i	0.979836	−	0.199803i	$-0.0640301\pi$
$620$		0			0
$621$	2.54500	+	4.40807i	0.102127	+	0.176890i
$622$	2.91641	−	1.68379i	0.116937	−	0.0675138i
$623$	−58.1577			−2.33004
$624$	−11.2973	−	19.8178i	−0.452252	−	0.793345i
$625$		0			0
$626$	−17.3080	+	9.99276i	−0.691766	+	0.399391i
$627$	14.2069	+	24.6070i	0.567368	+	0.982711i
$628$	2.57221	−	4.45519i	0.102642	−	0.177782i
$629$			9.85174i			0.392815i
$630$		0			0
$631$	0.843006	+	0.486710i	0.0335596	+	0.0193756i	0.516686	−	0.856175i	$-0.327165\pi$
$631$	0.843006	+	0.486710i	0.0335596	+	0.0193756i	−0.483126	+	0.875551i	$0.660499\pi$
$632$			36.7183i			1.46058i
$633$	−0.391243	+	0.677652i	−0.0155505	+	0.0269342i
$634$	1.08903	+	1.88625i	0.0432507	+	0.0749124i
$635$		0			0
$636$	−5.30487			−0.210352
$637$	−21.4938	−	0.117945i	−0.851617	−	0.00467314i
$638$	0.162015			0.00641425
$639$	−22.8100	+	13.1694i	−0.902350	+	0.520972i
$640$		0			0
$641$	−6.31047	+	10.9301i	−0.249249	+	0.431711i	−0.963318	−	0.268364i	$-0.913517\pi$
$641$	−6.31047	+	10.9301i	−0.249249	+	0.431711i	0.714069	+	0.700075i	$0.246850\pi$
$642$			25.9766i			1.02521i
$643$	8.62599	+	4.98022i	0.340176	+	0.196401i	0.660350	−	0.750958i	$-0.270408\pi$
$643$	8.62599	+	4.98022i	0.340176	+	0.196401i	−0.320174	+	0.947359i	$0.603741\pi$
$644$	6.21878	+	3.59042i	0.245054	+	0.141482i
$645$		0			0
$646$	1.56546	−	2.71146i	0.0615923	−	0.106681i
$647$	18.1381	+	31.4162i	0.713084	+	1.23510i	0.963694	+	0.267009i	$0.0860354\pi$
$647$	18.1381	+	31.4162i	0.713084	+	1.23510i	−0.250610	+	0.968088i	$0.580631\pi$
$648$	27.5131	−	15.8847i	1.08081	−	0.624009i
$649$	0.920861			0.0361470
$650$		0			0
$651$	45.8796			1.79816
$652$	3.00898	−	1.73723i	0.117841	−	0.0680353i
$653$	6.87769	+	11.9125i	0.269145	+	0.466172i	0.968641	−	0.248464i	$-0.0799257\pi$
$653$	6.87769	+	11.9125i	0.269145	+	0.466172i	−0.699497	+	0.714636i	$0.746592\pi$
$654$	10.4910	−	18.1709i	0.410231	−	0.710540i
$655$		0			0
$656$	8.76776	+	5.06207i	0.342324	+	0.197641i
$657$	9.93555	+	5.73629i	0.387623	+	0.223794i
$658$			11.3526i			0.442570i
$659$	1.29092	−	2.23593i	0.0502869	−	0.0870995i	−0.839786	−	0.542917i	$-0.817320\pi$
$659$	1.29092	−	2.23593i	0.0502869	−	0.0870995i	0.890073	+	0.455818i	$0.150653\pi$
$660$		0			0
$661$	−21.5437	+	12.4382i	−0.837951	+	0.483791i	−0.856567	−	0.516036i	$-0.827407\pi$
$661$	−21.5437	+	12.4382i	−0.837951	+	0.483791i	0.0186163	+	0.999827i	$0.494074\pi$
$662$	8.81151			0.342469
$663$	−4.80406	+	8.21643i	−0.186574	+	0.319100i
$664$	37.1656			1.44231
$665$		0			0
$666$	12.9485	+	22.4274i	0.501743	+	0.869045i
$667$	−0.0481312	+	0.0833657i	−0.00186365	+	0.00322793i
$668$			5.37460i			0.207949i
$669$	24.8368	+	14.3395i	0.960246	+	0.554398i
$670$		0			0
$671$		−	18.0506i		−	0.696834i
$672$	11.8386	−	20.5051i	0.456685	−	0.791002i
$673$	−21.6611	−	37.5181i	−0.834974	−	1.44622i	−0.894052	−	0.447964i	$-0.852149\pi$
$673$	−21.6611	−	37.5181i	−0.834974	−	1.44622i	0.0590774	−	0.998253i	$-0.481184\pi$
$674$	4.60770	−	2.66025i	0.177482	−	0.102469i
$675$		0			0
$676$	6.66033	+	0.0730977i	0.256167	+	0.00281145i
$677$	41.3625			1.58969			0.794845	−	0.606813i	$-0.207552\pi$
$677$	41.3625			1.58969			0.794845	+	0.606813i	$0.207552\pi$
$678$	−17.4315	+	10.0641i	−0.669451	+	0.386508i
$679$	−21.9039	−	37.9386i	−0.840594	−	1.45595i
$680$		0			0
$681$		−	17.8003i		−	0.682110i
$682$	31.0041	+	17.9002i	1.18721	+	0.685435i
$683$	−2.27495	−	1.31344i	−0.0870484	−	0.0502574i	0.455844	−	0.890060i	$-0.349338\pi$
$683$	−2.27495	−	1.31344i	−0.0870484	−	0.0502574i	−0.542892	+	0.839802i	$0.682671\pi$
$684$			2.83459i			0.108383i
$685$		0			0
$686$	−2.28028	−	3.94957i	−0.0870617	−	0.150795i
$687$	−29.0865	+	16.7931i	−1.10972	+	0.640696i
$688$	3.07045			0.117060
$689$	−8.07914	+	13.8178i	−0.307791	+	0.526417i
$690$		0			0
$691$	−13.2288	+	7.63765i	−0.503247	+	0.290550i	−0.730053	−	0.683390i	$-0.760505\pi$
$691$	−13.2288	+	7.63765i	−0.503247	+	0.290550i	0.226806	+	0.973940i	$0.427172\pi$
$692$	1.14218	+	1.97831i	0.0434190	+	0.0752039i
$693$	−23.5882	+	40.8560i	−0.896043	+	1.55199i
$694$		−	32.5744i		−	1.23651i
$695$		0			0
$696$	0.153046	+	0.0883613i	0.00580120	+	0.00334933i
$697$		−	4.22414i		−	0.160001i
$698$	14.3747	−	24.8976i	0.544089	−	0.942390i
$699$	11.0737	+	19.1802i	0.418846	+	0.725463i
$700$		0			0
$701$	48.1947			1.82029			0.910144	−	0.414292i	$-0.135971\pi$
$701$	48.1947			1.82029			0.910144	+	0.414292i	$0.135971\pi$
$702$	0.0315519	−	5.74991i	0.00119085	−	0.217017i
$703$	19.7404			0.744522
$704$	41.2406	−	23.8103i	1.55431	−	0.897383i
$705$		0			0
$706$	3.49884	−	6.06016i	0.131680	−	0.228077i
$707$			14.5967i			0.548964i
$708$	0.177401	+	0.102423i	0.00666715	+	0.00384928i
$709$	−33.6624	−	19.4350i	−1.26422	−	0.729896i	−0.290329	−	0.956927i	$-0.593765\pi$
$709$	−33.6624	−	19.4350i	−1.26422	−	0.729896i	−0.973887	+	0.227031i	$0.927098\pi$
$710$		0			0
$711$	14.6150	−	25.3140i	0.548107	−	0.949349i
$712$	−24.7504	−	42.8689i	−0.927560	−	1.60658i
$713$	−18.4213	+	10.6355i	−0.689882	+	0.398304i
$714$	11.5915			0.433801
$715$		0			0
$716$	−9.54600			−0.356751
$717$	40.2227	−	23.2226i	1.50214	−	0.867263i
$718$	−15.0987	−	26.1517i	−0.563478	−	0.975973i
$719$	3.30830	−	5.73015i	0.123379	−	0.213698i	−0.797719	−	0.603029i	$-0.793960\pi$
$719$	3.30830	−	5.73015i	0.123379	−	0.213698i	0.921098	+	0.389331i	$0.127294\pi$
$720$		0			0
$721$	55.8205	+	32.2280i	2.07887	+	1.20023i
$722$	14.6362	+	8.45024i	0.544705	+	0.314485i
$723$			54.2629i			2.01806i
$724$	4.63433	−	8.02690i	0.172234	−	0.298317i
$725$		0			0
$726$	−43.9893	+	25.3973i	−1.63260	+	0.942581i
$727$	−18.3735			−0.681435			−0.340717	−	0.940166i	$-0.610670\pi$
$727$	−18.3735			−0.681435			−0.340717	+	0.940166i	$0.610670\pi$
$728$	−19.6990	−	34.5562i	−0.730094	−	1.28074i
$729$	−16.1420			−0.597853
$730$		0			0
$731$	−0.640548	−	1.10946i	−0.0236915	−	0.0410349i
$732$	2.00767	−	3.47739i	0.0742057	−	0.128528i
$733$		−	0.791131i		−	0.0292211i	−0.999893	−	0.0146105i	$-0.995349\pi$
$733$		−	0.791131i		−	0.0292211i	0.999893	−	0.0146105i	$-0.00465084\pi$
$734$	−27.5198	−	15.8886i	−1.01578	−	0.586458i
$735$		0			0
$736$			10.9774i			0.404634i
$737$	17.1893	−	29.7727i	0.633175	−	1.09669i
$738$	−5.55193	−	9.61623i	−0.204369	−	0.353978i
$739$	−27.0073	+	15.5926i	−0.993478	+	0.573585i	−0.906312	−	0.422609i	$-0.861114\pi$
$739$	−27.0073	+	15.5926i	−0.993478	+	0.573585i	−0.0871658	+	0.996194i	$0.527781\pi$
$740$		0			0
$741$	16.4636	+	9.62612i	0.604806	+	0.353624i
$742$	19.4938			0.715639
$743$	−4.81773	+	2.78152i	−0.176745	+	0.102044i	−0.585763	−	0.810483i	$-0.699205\pi$
$743$	−4.81773	+	2.78152i	−0.176745	+	0.102044i	0.409017	+	0.912527i	$0.365872\pi$
$744$	19.5251	+	33.8185i	0.715826	+	1.23985i
$745$		0			0
$746$			16.1053i			0.589658i
$747$	−25.6224	−	14.7931i	−0.937474	−	0.541251i
$748$	−2.69787	−	1.55762i	−0.0986439	−	0.0569521i
$749$			32.8765i			1.20128i
$750$		0			0
$751$	−17.6048	−	30.4925i	−0.642410	−	1.11269i	−0.984893	−	0.173163i	$-0.944601\pi$
$751$	−17.6048	−	30.4925i	−0.642410	−	1.11269i	0.342483	−	0.939524i	$-0.388732\pi$
$752$	−6.07381	+	3.50672i	−0.221489	+	0.127877i
$753$	27.6142			1.00632
$754$	0.0944723	−	0.0538546i	0.00344048	−	0.00196127i
$755$		0			0
$756$	2.08873	−	1.20593i	0.0759665	−	0.0438593i
$757$	25.0223	+	43.3399i	0.909451	+	1.57522i	0.814828	+	0.579703i	$0.196831\pi$
$757$	25.0223	+	43.3399i	0.909451	+	1.57522i	0.0946237	+	0.995513i	$0.469835\pi$
$758$	−15.8545	+	27.4609i	−0.575863	+	0.997424i
$759$		−	48.7715i		−	1.77029i
$760$		0			0
$761$	38.8161	+	22.4105i	1.40708	+	0.812379i	0.995106	−	0.0988165i	$-0.0315057\pi$
$761$	38.8161	+	22.4105i	1.40708	+	0.812379i	0.411975	+	0.911195i	$0.364839\pi$
$762$		−	32.5313i		−	1.17848i
$763$	13.2776	−	22.9975i	0.480682	−	0.832566i
$764$	−7.00307	−	12.1297i	−0.253362	−	0.438836i
$765$		0			0
$766$	11.7092			0.423072
$767$	0.536961	−	0.306098i	0.0193885	−	0.0110526i
$768$	26.6361			0.961148
$769$	−34.0897	+	19.6817i	−1.22930	+	0.709739i	−0.966884	−	0.255215i	$-0.917854\pi$
$769$	−34.0897	+	19.6817i	−1.22930	+	0.709739i	−0.262420	+	0.964954i	$0.584521\pi$
$770$		0			0
$771$	−6.47201	+	11.2099i	−0.233084	+	0.403713i
$772$			11.1528i			0.401399i
$773$	42.2452	+	24.3902i	1.51945	+	0.877256i	0.999737	+	0.0229167i	$0.00729525\pi$
$773$	42.2452	+	24.3902i	1.51945	+	0.877256i	0.519715	+	0.854340i	$0.326038\pi$
$774$	−2.91641	−	1.68379i	−0.104828	−	0.0605225i
$775$		0			0
$776$	18.6434	−	32.2914i	0.669260	−	1.15919i
$777$	36.5420	+	63.2926i	1.31094	+	2.27061i
$778$	5.94822	−	3.43420i	0.213254	−	0.123122i
$779$	−8.46410			−0.303258
$780$		0			0
$781$	−58.0013			−2.07545
$782$	−4.65415	+	2.68707i	−0.166432	+	0.0960895i
$783$	0.0161661	+	0.0280005i	0.000577728	+	0.00100066i
$784$	−8.08592	+	14.0052i	−0.288783	+	0.500187i
$785$		0			0
$786$	26.0342	+	15.0309i	0.928611	+	0.536134i
$787$	−34.5204	−	19.9304i	−1.23052	−	0.710442i	−0.263382	−	0.964692i	$-0.584838\pi$
$787$	−34.5204	−	19.9304i	−1.23052	−	0.710442i	−0.967139	+	0.254250i	$0.918171\pi$
$788$			0.869338i			0.0309689i
$789$	−7.99922	+	13.8551i	−0.284780	+	0.493253i
$790$		0			0
$791$	−22.0616	+	12.7373i	−0.784420	+	0.452885i
$792$	−40.1541			−1.42682
$793$	−6.00008	−	10.5254i	−0.213069	−	0.373768i
$794$	−20.4490			−0.725709
$795$		0			0
$796$	6.48793	+	11.2374i	0.229958	+	0.398300i
$797$	−13.1059	+	22.7001i	−0.464235	+	0.804079i	−0.999167	−	0.0408167i	$-0.987004\pi$
$797$	−13.1059	+	22.7001i	−0.464235	+	0.804079i	0.534932	+	0.844895i	$0.320337\pi$
$798$		−	23.2264i		−	0.822206i
$799$	2.53420	+	1.46312i	0.0896537	+	0.0517616i
$800$		0			0
$801$			39.4057i			1.39233i
$802$	−8.46343	+	14.6591i	−0.298854	+	0.517630i
$803$	12.6321	+	21.8794i	0.445775	+	0.772106i
$804$	6.62293	−	3.82375i	0.233573	−	0.134853i
$805$		0			0
$806$	24.0288	+	0.131855i	0.846379	+	0.00464440i
$807$	3.31643			0.116744
$808$	−10.7594	+	6.21196i	−0.378515	+	0.218536i
$809$	−11.1068	−	19.2376i	−0.390495	−	0.676357i	0.602020	−	0.798481i	$-0.294363\pi$
$809$	−11.1068	−	19.2376i	−0.390495	−	0.676357i	−0.992515	+	0.122124i	$0.961029\pi$
$810$		0			0
$811$			19.0950i			0.670515i	0.942127	+	0.335257i	$0.108823\pi$
$811$			19.0950i			0.670515i	−0.942127	+	0.335257i	$0.891177\pi$
$812$	0.0395023	+	0.0228066i	0.00138626	+	0.000800356i
$813$	20.1362	+	11.6256i	0.706207	+	0.407729i
$814$			57.0284i			1.99885i
$815$		0			0
$816$	3.58052	+	6.20164i	0.125343	+	0.217101i
$817$	−2.22308	+	1.28349i	−0.0777757	+	0.0449038i
$818$	35.8894			1.25484
$819$	−0.173754	+	31.6643i	−0.00607145	+	1.10644i
$820$		0			0
$821$	−29.5820	+	17.0792i	−1.03242	+	0.596068i	−0.917677	−	0.397327i	$-0.869938\pi$
$821$	−29.5820	+	17.0792i	−1.03242	+	0.596068i	−0.114743	+	0.993395i	$0.536604\pi$
$822$	5.38588	+	9.32861i	0.187854	+	0.325373i
$823$	−2.03970	+	3.53286i	−0.0710995	+	0.123148i	−0.899383	−	0.437161i	$-0.855984\pi$
$823$	−2.03970	+	3.53286i	−0.0710995	+	0.123148i	0.828284	+	0.560309i	$0.189317\pi$
$824$			54.8616i			1.91119i
$825$		0			0
$826$	−0.651896	−	0.376372i	−0.0226824	−	0.0130957i
$827$		−	54.8780i		−	1.90830i	−0.299337	−	0.954148i	$-0.596765\pi$
$827$		−	54.8780i		−	1.90830i	0.299337	−	0.954148i	$-0.403235\pi$
$828$	2.43275	−	4.21364i	0.0845438	−	0.146434i
$829$	4.07475	+	7.05768i	0.141522	+	0.245123i	0.928070	−	0.372406i	$-0.121467\pi$
$829$	4.07475	+	7.05768i	0.141522	+	0.245123i	−0.786548	+	0.617529i	$0.788134\pi$
$830$		0			0
$831$	40.8697			1.41775
$832$	16.1330	−	27.5925i	0.559313	−	0.956597i
$833$	6.74745			0.233785
$834$	4.96116	−	2.86433i	0.171791	−	0.0991836i
$835$		0			0
$836$	−3.12107	+	5.40585i	−0.107944	+	0.186965i
$837$			7.14441i			0.246947i
$838$	7.36008	+	4.24935i	0.254250	+	0.146791i
$839$	−18.9543	−	10.9433i	−0.654374	−	0.377803i	0.135756	−	0.990742i	$-0.456654\pi$
$839$	−18.9543	−	10.9433i	−0.654374	−	0.377803i	−0.790130	+	0.612939i	$0.789987\pi$
$840$		0			0
$841$	14.4997	−	25.1142i	0.499989	−	0.866007i
$842$	−4.34285	−	7.52204i	−0.149664	−	0.259226i
$843$	21.6827	−	12.5185i	0.746792	−	0.431160i
$844$	−0.171902			−0.00591710
$845$		0			0
$846$	7.69213			0.264461
$847$	−55.6738	+	32.1433i	−1.91297	+	1.10446i
$848$	6.02147	+	10.4295i	0.206778	+	0.358150i
$849$	1.53740	−	2.66285i	0.0527633	−	0.0913888i
$850$		0			0
$851$	−29.3442	−	16.9419i	−1.00591	−	0.580761i
$852$	−11.1738	−	6.45118i	−0.382807	−	0.221014i
$853$		−	19.2240i		−	0.658217i	−0.944292	−	0.329108i	$-0.893252\pi$
$853$		−	19.2240i		−	0.658217i	0.944292	−	0.329108i	$-0.106748\pi$
$854$	−7.37758	+	12.7783i	−0.252456	+	0.437266i
$855$		0			0
$856$	−24.2337	+	13.9914i	−0.828292	+	0.478215i
$857$	−27.8197			−0.950302			−0.475151	−	0.879904i	$-0.657607\pi$
$857$	−27.8197			−0.950302			−0.475151	+	0.879904i	$0.657607\pi$
$858$	−27.8091	+	47.5622i	−0.949388	+	1.62375i
$859$	45.7355			1.56048			0.780238	−	0.625482i	$-0.215098\pi$
$859$	45.7355			1.56048			0.780238	+	0.625482i	$0.215098\pi$
$860$		0			0
$861$	−15.6682	−	27.1381i	−0.533970	−	0.924862i
$862$	−18.4260	+	31.9148i	−0.627593	+	1.08702i
$863$		−	54.8186i		−	1.86605i	−0.359814	−	0.933024i	$-0.617160\pi$
$863$		−	54.8186i		−	1.86605i	0.359814	−	0.933024i	$-0.382840\pi$
$864$	3.19308	+	1.84352i	0.108631	+	0.0627180i
$865$		0			0
$866$		−	1.46378i		−	0.0497413i
$867$	−18.3302	+	31.7488i	−0.622526	+	1.07825i
$868$	5.03957	+	8.72879i	0.171054	+	0.296274i
$869$	55.7447	−	32.1842i	1.89101	−	1.09177i
$870$		0			0
$871$	0.126618	−	23.0745i	0.00429030	−	0.781849i
$872$	22.6024			0.765415
$873$	−25.7060	+	14.8413i	−0.870015	+	0.502304i
$874$	5.38421	+	9.32572i	0.182124	+	0.315447i
$875$		0			0
$876$			5.61999i			0.189882i
$877$	−23.7113	−	13.6897i	−0.800673	−	0.462269i	0.0430336	−	0.999074i	$-0.486298\pi$
$877$	−23.7113	−	13.6897i	−0.800673	−	0.462269i	−0.843706	+	0.536805i	$0.819631\pi$
$878$	17.4858	+	10.0954i	0.590116	+	0.340704i
$879$		−	43.7125i		−	1.47439i
$880$		0			0
$881$	−17.2213	−	29.8282i	−0.580200	−	1.00494i	−0.995455	−	0.0952310i	$-0.969641\pi$
$881$	−17.2213	−	29.8282i	−0.580200	−	1.00494i	0.415255	−	0.909705i	$-0.363692\pi$
$882$	15.3605	−	8.86841i	0.517216	−	0.298615i
$883$	−17.3592			−0.584183			−0.292092	−	0.956390i	$-0.594351\pi$
$883$	−17.3592			−0.584183			−0.292092	+	0.956390i	$0.594351\pi$
$884$	−2.09091	−	0.0114736i	−0.0703248	−	0.000385899i
$885$		0			0
$886$	4.81610	−	2.78058i	0.161800	−	0.0934153i
$887$	−15.5714	−	26.9704i	−0.522835	−	0.905577i	−0.999647	−	0.0265716i	$-0.991541\pi$
$887$	−15.5714	−	26.9704i	−0.522835	−	0.905577i	0.476812	−	0.879005i	$-0.341792\pi$
$888$	−31.1026	+	53.8714i	−1.04374	+	1.80780i
$889$		−	41.1722i		−	1.38087i
$890$		0			0
$891$	−48.2313	−	27.8464i	−1.61581	−	0.932888i
$892$			6.30042i			0.210954i
$893$	2.93173	−	5.07790i	0.0981065	−	0.169925i
$894$	−7.84799	−	13.5931i	−0.262476	−	0.454622i
$895$		0			0
$896$	−18.6224			−0.622132
$897$	−16.2118	−	28.4390i	−0.541298	−	0.949550i
$898$	−16.8953			−0.563804
$899$	−0.117014	+	0.0675578i	−0.00390262	+	0.00225318i
$900$		0			0
$901$	2.51236	−	4.35154i	0.0836990	−	0.144971i
$902$		−	24.4521i		−	0.814167i
$903$	−8.23042	−	4.75184i	−0.273891	−	0.158131i
$904$	−18.7777	−	10.8413i	−0.624536	−	0.360576i
$905$		0			0
$906$	6.95452	−	12.0456i	0.231048	−	0.400188i
$907$	−8.80284	−	15.2470i	−0.292294	−	0.506267i	0.682058	−	0.731298i	$-0.261085\pi$
$907$	−8.80284	−	15.2470i	−0.292294	−	0.506267i	−0.974352	+	0.225031i	$0.927752\pi$
$908$	3.38659	−	1.95525i	0.112388	−	0.0648872i
$909$	9.89022			0.328038
$910$		0			0
$911$	50.0232			1.65734			0.828671	−	0.559737i	$-0.189098\pi$
$911$	50.0232			1.65734			0.828671	+	0.559737i	$0.189098\pi$
$912$	12.4265	−	7.17445i	0.411483	−	0.237570i
$913$	−32.5763	−	56.4238i	−1.07812	−	1.86735i
$914$	24.4636	−	42.3722i	0.809184	−	1.40155i
$915$		0			0
$916$	−6.38992	−	3.68922i	−0.211129	−	0.121895i
$917$	32.9495	+	19.0234i	1.08809	+	0.628207i
$918$			1.80504i			0.0595752i
$919$	3.80778	−	6.59527i	0.125607	−	0.217558i	−0.796363	−	0.604819i	$-0.793245\pi$
$919$	3.80778	−	6.59527i	0.125607	−	0.217558i	0.921970	+	0.387261i	$0.126579\pi$
$920$		0			0
$921$	−28.8915	+	16.6805i	−0.952008	+	0.549642i
$922$	−9.19522			−0.302828
$923$	−33.8209	+	19.2799i	−1.11323	+	0.634604i
$924$	−23.1100			−0.760264
$925$		0			0
$926$	−14.2113	−	24.6146i	−0.467011	−	0.808887i
$927$	21.8366	−	37.8222i	0.717209	−	1.24224i
$928$			0.0697297i			0.00228899i
$929$	12.2317	+	7.06196i	0.401308	+	0.231695i	0.687048	−	0.726612i	$-0.258906\pi$
$929$	12.2317	+	7.06196i	0.401308	+	0.231695i	−0.285740	+	0.958307i	$0.592239\pi$
$930$		0			0
$931$		−	13.5202i		−	0.443106i
$932$	−2.43275	+	4.21364i	−0.0796873	+	0.138022i
$933$	−3.21969	−	5.57666i	−0.105408	−	0.182572i
$934$	23.9033	−	13.8006i	0.782140	−	0.451569i
$935$		0			0
$936$	−23.4142	+	13.3474i	−0.765316	+	0.436274i
$937$	23.9317			0.781815			0.390908	−	0.920430i	$-0.372161\pi$
$937$	23.9317			0.781815			0.390908	+	0.920430i	$0.372161\pi$
$938$	−24.3373	+	14.0511i	−0.794640	+	0.458786i
$939$	19.1078	+	33.0958i	0.623561	+	1.08004i
$940$		0			0
$941$		−	25.3591i		−	0.826683i	−0.910576	−	0.413342i	$-0.864362\pi$
$941$		−	25.3591i		−	0.826683i	0.910576	−	0.413342i	$-0.135638\pi$
$942$	24.7349	+	14.2807i	0.805908	+	0.465291i
$943$	12.5820	+	7.26420i	0.409725	+	0.236555i
$944$		−	0.465033i		−	0.0151355i
$945$		0			0
$946$	−3.70792	−	6.42231i	−0.120555	−	0.208807i
$947$	35.8727	−	20.7111i	1.16571	−	0.673021i	0.213042	−	0.977043i	$-0.431663\pi$
$947$	35.8727	−	20.7111i	1.16571	−	0.673021i	0.952665	+	0.304022i	$0.0983296\pi$
$948$	14.3187			0.465051
$949$	14.6386	+	8.55906i	0.475190	+	0.277839i
$950$		0			0
$951$	3.60682	−	2.08240i	0.116959	−	0.0675264i
$952$	6.24335	+	10.8138i	0.202348	+	0.350477i
$953$	−12.1513	+	21.0466i	−0.393619	+	0.681767i	−0.992924	−	0.118753i	$-0.962110\pi$
$953$	−12.1513	+	21.0466i	−0.393619	+	0.681767i	0.599305	+	0.800521i	$0.295444\pi$
$954$		−	13.2083i		−	0.427636i
$955$		0			0
$956$	8.83639	+	5.10169i	0.285789	+	0.165001i
$957$		−	0.309801i		−	0.0100144i
$958$	12.5901	−	21.8067i	0.406768	−	0.704543i
$959$	6.81647	+	11.8065i	0.220115	+	0.381251i
$960$		0			0
$961$	1.14359			0.0368901
$962$	18.9565	+	33.2537i	0.611182	+	1.07214i
$963$	22.2760			0.717834
$964$	−10.3238	+	5.96043i	−0.332506	+	0.191972i
$965$		0			0
$966$	−19.9338	+	34.5263i	−0.641358	+	1.11086i
$967$		−	23.6784i		−	0.761445i	−0.924689	−	0.380722i	$-0.875675\pi$
$967$		−	23.6784i		−	0.761445i	0.924689	−	0.380722i	$-0.124325\pi$
$968$	−47.3866	−	27.3587i	−1.52306	−	0.879341i
$969$	−5.18477	−	2.99343i	−0.166559	−	0.0961627i
$970$		0			0
$971$	8.48609	−	14.6983i	0.272332	−	0.471692i	−0.697127	−	0.716948i	$-0.745539\pi$
$971$	8.48609	−	14.6983i	0.272332	−	0.471692i	0.969458	+	0.245256i	$0.0788719\pi$
$972$	−5.18953	−	8.98852i	−0.166454	−	0.288307i
$973$	6.27895	−	3.62515i	0.201294	−	0.116217i
$974$	−3.70303			−0.118653
$975$		0			0
$976$	−9.11550			−0.291780
$977$	−21.6501	+	12.4997i	−0.692649	+	0.399901i	−0.804604	−	0.593812i	$-0.797622\pi$
$977$	−21.6501	+	12.4997i	−0.692649	+	0.399901i	0.111955	+	0.993713i	$0.464289\pi$
$978$	9.64500	+	16.7056i	0.308413	+	0.534187i
$979$	−43.3883	+	75.1507i	−1.38669	+	2.40183i
$980$		0			0
$981$	−15.5824	−	8.99648i	−0.497506	−	0.287235i
$982$	−11.2684	−	6.50582i	−0.359589	−	0.207609i
$983$		−	27.3418i		−	0.872068i	−0.899930	−	0.436034i	$-0.856383\pi$
$983$		−	27.3418i		−	0.872068i	0.899930	−	0.436034i	$-0.143617\pi$
$984$	13.3359	−	23.0985i	0.425134	−	0.736353i
$985$		0			0
$986$	−0.0295635	+	0.0170685i	−0.000941495	+	0.000543573i
$987$	21.7080			0.690975
$988$	−0.0229901	+	4.18964i	−0.000731414	+	0.133290i
$989$	4.40617			0.140108
$990$		0			0
$991$	−8.03802	−	13.9223i	−0.255336	−	0.442255i	0.709651	−	0.704554i	$-0.248853\pi$
$991$	−8.03802	−	13.9223i	−0.255336	−	0.442255i	−0.964987	+	0.262299i	$0.915519\pi$
$992$	−7.70406	+	13.3438i	−0.244604	+	0.423667i
$993$		−	16.8491i		−	0.534690i
$994$	41.0602	+	23.7061i	1.30235	+	0.751913i
$995$		0			0
$996$		−	14.4932i		−	0.459234i
$997$	−17.2806	+	29.9309i	−0.547282	+	0.947920i	0.451178	+	0.892434i	$0.351004\pi$
$997$	−17.2806	+	29.9309i	−0.547282	+	0.947920i	−0.998459	+	0.0554858i	$0.982329\pi$
$998$	−20.6824	−	35.8230i	−0.654691	−	1.13396i
$999$	−9.85600	+	5.69036i	−0.311830	+	0.180035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.d.101.2		8
5.2	odd	4		325.2.m.b.49.2		8
5.3	odd	4		325.2.m.c.49.3		8
5.4	even	2		65.2.m.a.36.3	✓	8
13.2	odd	12		4225.2.a.bi.1.2		4
13.4	even	6	inner	325.2.n.d.251.2		8
13.11	odd	12		4225.2.a.bl.1.3		4
15.14	odd	2		585.2.bu.c.361.2		8
20.19	odd	2		1040.2.da.b.881.4		8
65.4	even	6		65.2.m.a.56.3	yes	8
65.9	even	6		845.2.m.g.316.2		8
65.17	odd	12		325.2.m.c.199.3		8
65.19	odd	12		845.2.e.m.191.2		8
65.24	odd	12		845.2.a.l.1.2		4
65.29	even	6		845.2.c.g.506.6		8
65.34	odd	4		845.2.e.n.146.3		8
65.43	odd	12		325.2.m.b.199.2		8
65.44	odd	4		845.2.e.m.146.2		8
65.49	even	6		845.2.c.g.506.3		8
65.54	odd	12		845.2.a.m.1.3		4
65.59	odd	12		845.2.e.n.191.3		8
65.64	even	2		845.2.m.g.361.2		8
195.89	even	12		7605.2.a.cj.1.3		4
195.119	even	12		7605.2.a.cf.1.2		4
195.134	odd	6		585.2.bu.c.316.2		8
260.199	odd	6		1040.2.da.b.641.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	5.4	even	2
65.2.m.a.56.3	yes	8	65.4	even	6
325.2.m.b.49.2		8	5.2	odd	4
325.2.m.b.199.2		8	65.43	odd	12
325.2.m.c.49.3		8	5.3	odd	4
325.2.m.c.199.3		8	65.17	odd	12
325.2.n.d.101.2		8	1.1	even	1	trivial
325.2.n.d.251.2		8	13.4	even	6	inner
585.2.bu.c.316.2		8	195.134	odd	6
585.2.bu.c.361.2		8	15.14	odd	2
845.2.a.l.1.2		4	65.24	odd	12
845.2.a.m.1.3		4	65.54	odd	12
845.2.c.g.506.3		8	65.49	even	6
845.2.c.g.506.6		8	65.29	even	6
845.2.e.m.146.2		8	65.44	odd	4
845.2.e.m.191.2		8	65.19	odd	12
845.2.e.n.146.3		8	65.34	odd	4
845.2.e.n.191.3		8	65.59	odd	12
845.2.m.g.316.2		8	65.9	even	6
845.2.m.g.361.2		8	65.64	even	2
1040.2.da.b.641.4		8	260.199	odd	6
1040.2.da.b.881.4		8	20.19	odd	2
4225.2.a.bi.1.2		4	13.2	odd	12
4225.2.a.bl.1.3		4	13.11	odd	12
7605.2.a.cf.1.2		4	195.119	even	12
7605.2.a.cj.1.3		4	195.89	even	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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05628 + 0.609843i) q^{2} +(1.16612 + 2.01978i) q^{3} +(-0.256182 + 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-3.11786 - 1.80010i) q^{7} -3.06430i q^{8} +(-1.21969 + 2.11256i) q^{9} +O(q^{10})\)	\(q+(-1.05628 + 0.609843i) q^{2} +(1.16612 + 2.01978i) q^{3} +(-0.256182 + 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-3.11786 - 1.80010i) q^{7} -3.06430i q^{8} +(-1.21969 + 2.11256i) q^{9} +(-4.65213 + 2.68591i) q^{11} -1.19496 q^{12} +(-1.81988 + 3.11256i) q^{13} +4.39111 q^{14} +(1.35638 + 2.34932i) q^{16} +(0.565928 - 0.980215i) q^{17} -2.97527i q^{18} +(-1.96410 - 1.13397i) q^{19} -8.39654i q^{21} +(3.27597 - 5.67414i) q^{22} +(1.94644 + 3.37133i) q^{23} +(6.18922 - 3.57335i) q^{24} +(0.0241312 - 4.39758i) q^{26} +1.30752 q^{27} +(1.59748 - 0.922305i) q^{28} +(0.0123639 + 0.0214150i) q^{29} +5.46410i q^{31} +(2.44209 + 1.40994i) q^{32} +(-10.8499 - 6.26420i) q^{33} +1.38051i q^{34} +(-0.624924 - 1.08240i) q^{36} +(-7.53794 + 4.35203i) q^{37} +2.76619 q^{38} +(-8.40891 - 0.0461428i) q^{39} +(3.23205 - 1.86603i) q^{41} +(5.12058 + 8.86910i) q^{42} +(0.565928 - 0.980215i) q^{43} -2.75232i q^{44} +(-4.11196 - 2.37404i) q^{46} +2.58535i q^{47} +(-3.16341 + 5.47918i) q^{48} +(2.98070 + 5.16273i) q^{49} +2.63977 q^{51} +(-0.914884 - 1.60490i) q^{52} +4.43937 q^{53} +(-1.38111 + 0.797382i) q^{54} +(-5.51603 + 9.55405i) q^{56} -5.28942i q^{57} +(-0.0261196 - 0.0150801i) q^{58} +(-0.148458 - 0.0857123i) q^{59} +(-1.68012 + 2.91005i) q^{61} +(-3.33225 - 5.77162i) q^{62} +(7.60563 - 4.39111i) q^{63} -8.86488 q^{64} +15.2807 q^{66} +(-5.54239 + 3.19990i) q^{67} +(0.289961 + 0.502227i) q^{68} +(-4.53957 + 7.86276i) q^{69} +(9.35076 + 5.39866i) q^{71} +(6.47351 + 3.73748i) q^{72} -4.70308i q^{73} +(5.30812 - 9.19393i) q^{74} +(1.00633 - 0.581008i) q^{76} +19.3396 q^{77} +(8.91030 - 5.07938i) q^{78} -11.9826 q^{79} +(5.18379 + 8.97859i) q^{81} +(-2.27597 + 3.94209i) q^{82} +12.1286i q^{83} +(3.72572 + 2.15104i) q^{84} +1.38051i q^{86} +(-0.0288357 + 0.0499450i) q^{87} +(8.23042 + 14.2555i) q^{88} +(13.9898 - 8.07702i) q^{89} +(11.2771 - 6.42856i) q^{91} -1.99457 q^{92} +(-11.0363 + 6.37182i) q^{93} +(-1.57666 - 2.73086i) q^{94} +6.57666i q^{96} +(10.5379 + 6.08408i) q^{97} +(-6.29692 - 3.63553i) q^{98} -13.1039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{4} - 18 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 2 * q^4 - 18 * q^6 + 6 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 2 q^{4} - 18 q^{6} + 6 q^{7} - 4 q^{9} - 20 q^{12} + 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} + 12 q^{22} + 10 q^{23} - 12 q^{24} + 10 q^{26} + 4 q^{27} + 18 q^{28} - 8 q^{29} - 6 q^{32} - 42 q^{33} + 20 q^{36} - 6 q^{37} + 16 q^{38} + 12 q^{41} - 4 q^{42} + 2 q^{43} - 42 q^{46} - 28 q^{48} + 12 q^{49} - 8 q^{51} + 6 q^{52} + 24 q^{53} + 18 q^{54} + 12 q^{56} - 36 q^{58} - 12 q^{59} - 28 q^{61} - 4 q^{62} + 24 q^{63} - 8 q^{64} + 12 q^{66} - 6 q^{67} + 14 q^{68} - 16 q^{69} + 48 q^{72} + 10 q^{74} + 54 q^{76} + 36 q^{77} + 56 q^{78} - 16 q^{79} + 8 q^{81} - 4 q^{82} - 30 q^{84} - 22 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 30 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^4 - 18 * q^6 + 6 * q^7 - 4 * q^9 - 20 * q^12 + 4 * q^14 - 2 * q^16 + 2 * q^17 + 12 * q^19 + 12 * q^22 + 10 * q^23 - 12 * q^24 + 10 * q^26 + 4 * q^27 + 18 * q^28 - 8 * q^29 - 6 * q^32 - 42 * q^33 + 20 * q^36 - 6 * q^37 + 16 * q^38 + 12 * q^41 - 4 * q^42 + 2 * q^43 - 42 * q^46 - 28 * q^48 + 12 * q^49 - 8 * q^51 + 6 * q^52 + 24 * q^53 + 18 * q^54 + 12 * q^56 - 36 * q^58 - 12 * q^59 - 28 * q^61 - 4 * q^62 + 24 * q^63 - 8 * q^64 + 12 * q^66 - 6 * q^67 + 14 * q^68 - 16 * q^69 + 48 * q^72 + 10 * q^74 + 54 * q^76 + 36 * q^77 + 56 * q^78 - 16 * q^79 + 8 * q^81 - 4 * q^82 - 30 * q^84 - 22 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^91 - 44 * q^92 + 32 * q^94 + 30 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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