LMFDB - Embedded newform 325.2.n.d.251.2

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			251.2
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	325.251
Dual form			325.2.n.d.101.2

$q$-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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.05628	−	0.609843i	−0.746903	−	0.431224i	0.0776710	−	0.996979i	$-0.475252\pi$
$2$	−1.05628	−	0.609843i	−0.746903	−	0.431224i	−0.824574	+	0.565755i	$0.808585\pi$
$3$	1.16612	−	2.01978i	0.673262	−	1.16612i	−0.303712	−	0.952764i	$-0.598226\pi$
$3$	1.16612	−	2.01978i	0.673262	−	1.16612i	0.976974	−	0.213359i	$-0.0684405\pi$
$4$	−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	−0.955653	−	0.294494i	$-0.904849\pi$
$7$	−3.11786	+	1.80010i	−1.17844	+	0.680373i	−0.222787	+	0.974867i	$0.571516\pi$
$8$			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	−0.408004	−	0.912980i	$-0.633775\pi$
$11$	−4.65213	−	2.68591i	−1.40267	−	0.809832i	−0.994666	+	0.103149i	$0.967108\pi$
$12$	−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	0.926458	−	0.376399i	$-0.122838\pi$
$17$	0.565928	+	0.980215i	0.137258	+	0.237737i	−0.789200	+	0.614136i	$0.789505\pi$
$18$			2.97527i			0.701278i
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	−0.708082	−	0.706130i	$-0.750439\pi$
$19$	−1.96410	+	1.13397i	−0.450596	+	0.260152i	0.257486	+	0.966282i	$0.417106\pi$
$20$		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	−0.588561	−	0.808453i	$-0.700305\pi$
$23$	1.94644	−	3.37133i	0.405860	−	0.702970i	0.994421	+	0.105483i	$0.0336387\pi$
$24$	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	−0.864875	−	0.501987i	$-0.832603\pi$
$29$	0.0123639	−	0.0214150i	0.00229593	−	0.00397666i	0.867171	+	0.498010i	$0.165936\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	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	−0.270293	−	0.962778i	$-0.587121\pi$
$37$	−7.53794	−	4.35203i	−1.23923	−	0.715470i	−0.968937	+	0.247309i	$0.920454\pi$
$38$	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	0.730678	−	0.682723i	$-0.239204\pi$
$41$	3.23205	+	1.86603i	0.504762	+	0.291424i	−0.225916	+	0.974147i	$0.572538\pi$
$42$	5.12058	−	8.86910i	0.790122	−	1.36853i
$43$	0.565928	+	0.980215i	0.0863031	+	0.149481i	0.905946	−	0.423394i	$-0.139161\pi$
$43$	0.565928	+	0.980215i	0.0863031	+	0.149481i	−0.819643	+	0.572875i	$0.805828\pi$
$44$			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	$-0.939619\pi$
$47$		−	2.58535i		−	0.377113i	0.982062	−	0.188556i	$-0.0603808\pi$
$48$	−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	−0.509633	−	0.860392i	$-0.670219\pi$
$59$	−0.148458	+	0.0857123i	−0.0193276	+	0.0111588i	0.490305	+	0.871551i	$0.336885\pi$
$60$		0			0
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	0.738192	−	0.674591i	$-0.235680\pi$
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	−0.953309	+	0.301997i	$0.902347\pi$
$62$	−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	0.121655	−	0.992572i	$-0.461180\pi$
$67$	−5.54239	−	3.19990i	−0.677111	−	0.390930i	−0.798766	+	0.601642i	$0.794513\pi$
$68$	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	0.170971	−	0.985276i	$-0.445309\pi$
$71$	9.35076	−	5.39866i	1.10973	−	0.640703i	0.938760	+	0.344573i	$0.111976\pi$
$72$	6.47351	−	3.73748i	0.762911	−	0.440467i
$73$			4.70308i			0.550454i	0.961379	+	0.275227i	$0.0887531\pi$
$73$			4.70308i			0.550454i	−0.961379	+	0.275227i	$0.911247\pi$
$74$	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	$-0.768157\pi$
$83$		−	12.1286i		−	1.33129i	0.746270	−	0.665643i	$-0.231843\pi$
$84$	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	0.999812	−	0.0194001i	$-0.00617565\pi$
$89$	13.9898	+	8.07702i	1.48292	+	0.856162i	0.483105	+	0.875562i	$0.339509\pi$
$90$		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	0.141794	−	0.989896i	$-0.454713\pi$
$97$	10.5379	−	6.08408i	1.06997	−	0.617745i	0.928172	+	0.372151i	$0.121380\pi$
$98$	−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	−0.949081	−	0.315032i	$-0.897985\pi$
$101$	−2.02721	+	3.51122i	−0.201714	+	0.349380i	0.747366	+	0.664412i	$0.231318\pi$
$102$	−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	−0.997794	−	0.0663862i	$-0.978853\pi$
$107$	−4.56593	+	7.90842i	−0.441405	+	0.764536i	0.556389	+	0.830922i	$0.312186\pi$
$108$	−0.334963	−	0.580172i	−0.0322318	−	0.0558271i
$109$		−	7.37605i		−	0.706498i	−0.935529	−	0.353249i	$-0.885077\pi$
$109$		−	7.37605i		−	0.706498i	0.935529	−	0.353249i	$-0.114923\pi$
$110$		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	0.983064	−	0.183263i	$-0.0586661\pi$
$113$	3.53794	+	6.12789i	0.332821	+	0.576463i	−0.650243	+	0.759727i	$0.725333\pi$
$114$	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	−0.492568	−	0.870274i	$-0.663942\pi$
$127$	5.71806	−	9.90396i	0.507395	−	0.878835i	0.999963	−	0.00856072i	$-0.00272499\pi$
$128$	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	−0.633504	−	0.773739i	$-0.718384\pi$
$137$	−3.27940	+	1.89336i	−0.280178	+	0.161761i	0.353326	+	0.935500i	$0.385051\pi$
$138$			11.0737i			0.942656i
$139$	−1.00693	−	1.74406i	−0.0854068	−	0.147929i	0.820158	−	0.572138i	$-0.193886\pi$
$139$	−1.00693	−	1.74406i	−0.0854068	−	0.147929i	−0.905564	+	0.424209i	$0.860552\pi$
$140$		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	−0.291324	−	0.956624i	$-0.594096\pi$
$149$	4.77855	−	2.75890i	0.391474	−	0.226018i	0.682799	+	0.730607i	$0.260763\pi$
$150$		0			0
$151$		−	4.88961i		−	0.397911i	−0.980009	−	0.198956i	$-0.936245\pi$
$151$		−	4.88961i		−	0.397911i	0.980009	−	0.198956i	$-0.0637549\pi$
$152$	−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	−0.712039	−	0.702140i	$-0.752228\pi$
$163$	−5.87273	+	3.39062i	−0.459988	+	0.265574i	0.252051	+	0.967714i	$0.418895\pi$
$164$		−	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	0.808455	−	0.588559i	$-0.200304\pi$
$167$	9.08444	+	5.24490i	0.702975	+	0.405863i	−0.105479	+	0.994421i	$0.533638\pi$
$168$	−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	0.938239	−	0.345988i	$-0.112456\pi$
$173$	2.22923	+	3.86113i	0.169485	+	0.293557i	−0.768754	+	0.639545i	$0.779123\pi$
$174$			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	−0.273462	−	0.961883i	$-0.588169\pi$
$179$	9.31564	−	16.1352i	0.696284	−	1.20600i	0.969746	−	0.244116i	$-0.0784979\pi$
$180$		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	−0.622632	−	0.782515i	$-0.713937\pi$
$191$	−13.6682	−	23.6740i	−0.988994	−	1.71299i	−0.366361	−	0.930473i	$-0.619397\pi$
$192$	−10.3375	+	17.9052i	−0.746048	+	1.29219i
$193$	18.8511	+	10.8837i	1.35693	+	0.783425i	0.989209	−	0.146510i	$-0.0468041\pi$
$193$	18.8511	+	10.8837i	1.35693	+	0.783425i	0.367723	+	0.929935i	$0.380137\pi$
$194$	−14.8413			−1.06555
$195$		0			0
$196$	−3.05441			−0.218172
$197$	1.46940	+	0.848360i	0.104691	+	0.0604432i	0.551431	−	0.834220i	$-0.314082\pi$
$197$	1.46940	+	0.848360i	0.104691	+	0.0604432i	−0.446741	+	0.894664i	$0.647415\pi$
$198$	7.99131	−	13.8413i	0.567917	−	0.983662i
$199$	12.6627	+	21.9325i	0.897637	+	1.55475i	0.830506	+	0.557009i	$0.188051\pi$
$199$	12.6627	+	21.9325i	0.897637	+	1.55475i	0.0671309	+	0.997744i	$0.478615\pi$
$200$		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	−0.860193	−	0.509968i	$-0.829657\pi$
$211$	0.167753	−	0.290558i	0.0115486	−	0.0200028i	0.871742	+	0.489965i	$0.162991\pi$
$212$	−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	0.812219	−	0.583353i	$-0.198259\pi$
$223$	10.6493	+	6.14838i	0.713130	+	0.411726i	−0.0990887	+	0.995079i	$0.531593\pi$
$224$	−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	−0.703048	−	0.711143i	$-0.748178\pi$
$227$	−6.60974	+	3.81613i	−0.438704	+	0.253286i	0.264344	+	0.964428i	$0.414845\pi$
$228$	2.34702	−	1.35505i	0.155435	−	0.0897406i
$229$		−	14.4008i		−	0.951631i	−0.879545	−	0.475815i	$-0.842153\pi$
$229$		−	14.4008i		−	0.951631i	0.879545	−	0.475815i	$-0.157847\pi$
$230$		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	$0.222758\pi$
$239$			19.9143i			1.28815i	−0.764962	+	0.644076i	$0.777242\pi$
$240$		0			0
$241$	20.1493	−	11.6332i	1.29793	−	0.749360i	0.317883	−	0.948130i	$-0.397028\pi$
$241$	20.1493	−	11.6332i	1.29793	−	0.749360i	0.980046	+	0.198770i	$0.0636947\pi$
$242$		−	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	0.990127	−	0.140171i	$-0.0447652\pi$
$251$	5.92008	+	10.2539i	0.373672	+	0.647219i	−0.616455	+	0.787390i	$0.711432\pi$
$252$		−	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	−0.766402	−	0.642361i	$-0.777955\pi$
$257$	2.77501	−	4.80646i	0.173100	−	0.299819i	0.939502	+	0.342543i	$0.111288\pi$
$258$	−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	−0.740689	−	0.671848i	$-0.765501\pi$
$263$	3.42983	−	5.94065i	0.211493	−	0.366316i	0.952182	+	0.305532i	$0.0988342\pi$
$264$	−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	0.886886	−	0.461988i	$-0.152864\pi$
$269$	0.710994	+	1.23148i	0.0433501	+	0.0750845i	−0.843536	+	0.537072i	$0.819530\pi$
$270$		0			0
$271$	8.63381	+	4.98473i	0.524467	+	0.302801i	0.738760	−	0.673968i	$-0.235412\pi$
$271$	8.63381	+	4.98473i	0.524467	+	0.302801i	−0.214294	+	0.976769i	$0.568745\pi$
$272$	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	0.999525	+	0.0308154i	$0.00981039\pi$
$277$	8.76187	+	15.1760i	0.526449	+	0.911837i	−0.473076	+	0.881022i	$0.656856\pi$
$278$			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	$0.103751\pi$
$281$			10.7352i			0.640406i	−0.947349	+	0.320203i	$0.896249\pi$
$282$	3.67716	+	6.36903i	0.218972	+	0.379270i
$283$	−0.659192	+	1.14175i	−0.0391849	+	0.0678702i	−0.884953	−	0.465681i	$-0.845809\pi$
$283$	−0.659192	+	1.14175i	−0.0391849	+	0.0678702i	0.845768	+	0.533551i	$0.179143\pi$
$284$	−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	−0.892540	−	0.450968i	$-0.851079\pi$
$293$	−16.2316	+	9.37133i	−0.948261	+	0.547479i	−0.0557207	+	0.998446i	$0.517746\pi$
$294$			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	$-0.866159\pi$
$307$		−	14.3043i		−	0.816387i	0.912895	−	0.408194i	$-0.133841\pi$
$308$	−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	$0.0159695\pi$
$317$			1.78575i			0.100297i	−0.998742	+	0.0501487i	$0.984030\pi$
$318$	−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	−0.661991	−	0.749512i	$-0.730288\pi$
$331$	−6.25652	+	3.61220i	−0.343889	+	0.198545i	0.318101	+	0.948057i	$0.396955\pi$
$332$	−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	−0.962239	−	0.272207i	$-0.912246\pi$
$347$	−13.3536	−	23.1291i	−0.716858	−	1.24163i	0.245381	−	0.969427i	$-0.421087\pi$
$348$	−0.0147744	+	0.0255900i	−0.000791991	+	0.00137177i
$349$	−20.4131	−	11.7855i	−1.09269	−	0.630865i	−0.158399	−	0.987375i	$-0.550633\pi$
$349$	−20.4131	−	11.7855i	−1.09269	−	0.630865i	−0.934292	+	0.356510i	$0.883967\pi$
$350$		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	0.361911	−	0.932213i	$-0.382124\pi$
$353$	−4.96862	−	2.86863i	−0.264453	−	0.152682i	−0.626364	+	0.779531i	$0.715458\pi$
$354$	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	$-0.773364\pi$
$359$		−	24.7583i		−	1.30669i	0.757059	−	0.653347i	$-0.226636\pi$
$360$		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	−0.294991	−	0.955500i	$-0.595317\pi$
$367$	13.0268	−	22.5630i	0.679992	−	1.17778i	0.974983	−	0.222280i	$-0.0713500\pi$
$368$	−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	0.984776	−	0.173826i	$-0.0556129\pi$
$373$	6.60224	+	11.4354i	0.341851	+	0.592103i	−0.642926	+	0.765929i	$0.722280\pi$
$374$	−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	0.950463	−	0.310837i	$-0.100609\pi$
$379$	22.5147	+	12.9989i	1.15650	+	0.667707i	0.206039	+	0.978544i	$0.433943\pi$
$380$		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	−0.697140	−	0.716935i	$-0.745544\pi$
$383$	−8.31401	+	4.80010i	−0.424826	+	0.245274i	0.272314	+	0.962208i	$0.412211\pi$
$384$	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	−0.0892344	−	0.996011i	$-0.528442\pi$
$397$	14.5196	−	8.38291i	0.728719	−	0.420726i	0.817953	+	0.575285i	$0.195109\pi$
$398$		−	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	0.769115	−	0.639110i	$-0.220697\pi$
$401$	12.0187	+	6.93902i	0.600187	+	0.346518i	−0.168928	+	0.985628i	$0.554031\pi$
$402$	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	−0.973083	−	0.230453i	$-0.925979\pi$
$409$	−25.4829	+	14.7125i	−1.26005	+	0.727489i	−0.286964	+	0.957941i	$0.592646\pi$
$410$		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	−0.938491	−	0.345305i	$-0.887776\pi$
$419$	−3.48397	+	6.03440i	−0.170203	+	0.294800i	0.768288	+	0.640104i	$0.221109\pi$
$420$		0			0
$421$		−	7.12125i		−	0.347069i	−0.984828	−	0.173534i	$-0.944481\pi$
$421$		−	7.12125i		−	0.347069i	0.984828	−	0.173534i	$-0.0555188\pi$
$422$	−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	0.973150	−	0.230171i	$-0.0739286\pi$
$431$	26.1664	+	15.1072i	1.26039	+	0.727687i	0.287241	+	0.957858i	$0.407262\pi$
$432$	1.77349	−	3.07177i	0.0853270	−	0.147791i
$433$	−0.600065	−	1.03934i	−0.0288373	−	0.0499476i	0.851247	−	0.524766i	$-0.175847\pi$
$433$	−0.600065	−	1.03934i	−0.0288373	−	0.0499476i	−0.880084	+	0.474818i	$0.842514\pi$
$434$		−	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	−0.993107	−	0.117215i	$-0.962603\pi$
$439$	−8.27705	+	14.3363i	−0.395042	+	0.684233i	0.598064	+	0.801448i	$0.295937\pi$
$440$		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	−0.189465	−	0.981887i	$-0.560675\pi$
$449$	11.9963	−	6.92608i	0.566142	−	0.326862i	0.755607	+	0.655025i	$0.227342\pi$
$450$		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	−0.985532	−	0.169489i	$-0.945788\pi$
$457$	−34.7402	−	20.0573i	−1.62508	−	0.938240i	−0.639548	−	0.768751i	$-0.720878\pi$
$458$	−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	−0.340192	−	0.940356i	$-0.610492\pi$
$461$	6.52897	−	3.76950i	0.304084	−	0.175563i	0.644276	+	0.764793i	$0.277159\pi$
$462$	−47.6432	+	27.5068i	−2.21656	+	1.27973i
$463$		−	23.3031i		−	1.08299i	−0.840705	−	0.541494i	$-0.817859\pi$
$463$		−	23.3031i		−	1.08299i	0.840705	−	0.541494i	$-0.182141\pi$
$464$	−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	0.0324399	−	0.999474i	$-0.489672\pi$
$479$	−17.8789	−	10.3224i	−0.816910	−	0.471643i	−0.849350	+	0.527831i	$0.823006\pi$
$480$		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	−0.439243	−	0.898368i	$-0.644753\pi$
$487$	2.62929	−	1.51802i	0.119145	−	0.0687882i	0.558388	+	0.829580i	$0.311420\pi$
$488$	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	−0.720199	−	0.693767i	$-0.755950\pi$
$491$	5.33401	−	9.23877i	0.240720	−	0.416940i	0.960920	+	0.276827i	$0.0892830\pi$
$492$	−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	$-0.725636\pi$
$499$		−	33.9143i		−	1.51821i	0.650966	−	0.759107i	$-0.274364\pi$
$500$		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	0.690241	−	0.723580i	$-0.257505\pi$
$503$	−6.31380	−	10.9358i	−0.281518	−	0.487604i	−0.971759	+	0.235976i	$0.924171\pi$
$504$	−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	−0.0412201	−	0.999150i	$-0.513124\pi$
$509$	−20.9168	−	12.0763i	−0.927120	−	0.535273i	−0.885899	+	0.463877i	$0.846458\pi$
$510$		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	−0.103436	−	0.994636i	$-0.532984\pi$
$523$	18.5163	−	32.0712i	0.809662	−	1.40238i	0.913098	−	0.407739i	$-0.133683\pi$
$524$	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	$-0.942334\pi$
$541$		−	8.38144i		−	0.360346i	0.983635	−	0.180173i	$-0.0576658\pi$
$542$	−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	−0.115197	−	0.993343i	$-0.536750\pi$
$557$	−24.3810	−	14.0764i	−1.03306	−	0.596435i	−0.917858	+	0.396908i	$0.870083\pi$
$558$	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	0.991355	−	0.131206i	$-0.0418848\pi$
$563$	9.06514	+	15.7013i	0.382050	+	0.661731i	−0.609305	+	0.792936i	$0.708551\pi$
$564$			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	−0.0293292	−	0.999570i	$-0.509337\pi$
$569$	20.2992	−	35.1593i	0.850988	−	1.47395i	0.880317	−	0.474385i	$-0.157330\pi$
$570$		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	$0.159432\pi$
$577$			23.0691i			0.960379i	−0.877165	+	0.480189i	$0.840568\pi$
$578$	−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	0.817502	−	0.575926i	$-0.195358\pi$
$587$	17.6256	+	10.1762i	0.727487	+	0.420015i	−0.0900152	+	0.995940i	$0.528692\pi$
$588$	−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	$-0.931612\pi$
$593$		−	10.3834i		−	0.426395i	0.977009	−	0.213198i	$-0.0683878\pi$
$594$	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	0.0612928	−	0.998120i	$-0.480478\pi$
$601$	21.9423	−	38.0051i	0.895044	−	1.55026i	0.833751	−	0.552141i	$-0.186189\pi$
$602$	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	0.887255	−	0.461279i	$-0.152609\pi$
$607$	1.08770	+	1.88395i	0.0441484	+	0.0764673i	−0.843107	+	0.537746i	$0.819276\pi$
$608$	−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	0.735441	−	0.677589i	$-0.236975\pi$
$613$	12.7843	+	7.38100i	0.516352	+	0.298116i	−0.219089	+	0.975705i	$0.570309\pi$
$614$	−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	−0.810194	−	0.586162i	$-0.800638\pi$
$617$	−17.5779	+	10.1486i	−0.707659	+	0.408567i	0.102535	+	0.994729i	$0.467305\pi$
$618$	44.1053	−	25.4642i	1.77418	−	1.02432i
$619$			9.94207i			0.399605i	0.979836	+	0.199803i	$0.0640301\pi$
$619$			9.94207i			0.399605i	−0.979836	+	0.199803i	$0.935970\pi$
$620$		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	−0.483126	−	0.875551i	$-0.660499\pi$
$631$	0.843006	−	0.486710i	0.0335596	−	0.0193756i	0.516686	+	0.856175i	$0.327165\pi$
$632$		−	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	0.714069	−	0.700075i	$-0.246850\pi$
$641$	−6.31047	−	10.9301i	−0.249249	−	0.431711i	−0.963318	+	0.268364i	$0.913517\pi$
$642$		−	25.9766i		−	1.02521i
$643$	8.62599	−	4.98022i	0.340176	−	0.196401i	−0.320174	−	0.947359i	$-0.603741\pi$
$643$	8.62599	−	4.98022i	0.340176	−	0.196401i	0.660350	+	0.750958i	$0.270408\pi$
$644$	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	−0.250610	−	0.968088i	$-0.580631\pi$
$647$	18.1381	−	31.4162i	0.713084	−	1.23510i	0.963694	−	0.267009i	$-0.0860354\pi$
$648$	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	−0.699497	−	0.714636i	$-0.746592\pi$
$653$	6.87769	−	11.9125i	0.269145	−	0.466172i	0.968641	+	0.248464i	$0.0799257\pi$
$654$	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	0.890073	−	0.455818i	$-0.150653\pi$
$659$	1.29092	+	2.23593i	0.0502869	+	0.0870995i	−0.839786	+	0.542917i	$0.817320\pi$
$660$		0			0
$661$	−21.5437	−	12.4382i	−0.837951	−	0.483791i	0.0186163	−	0.999827i	$-0.494074\pi$
$661$	−21.5437	−	12.4382i	−0.837951	−	0.483791i	−0.856567	+	0.516036i	$0.827407\pi$
$662$	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	0.0590774	+	0.998253i	$0.481184\pi$
$673$	−21.6611	+	37.5181i	−0.834974	+	1.44622i	−0.894052	+	0.447964i	$0.852149\pi$
$674$	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	−0.542892	−	0.839802i	$-0.682671\pi$
$683$	−2.27495	+	1.31344i	−0.0870484	+	0.0502574i	0.455844	+	0.890060i	$0.349338\pi$
$684$		−	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	0.226806	−	0.973940i	$-0.427172\pi$
$691$	−13.2288	−	7.63765i	−0.503247	−	0.290550i	−0.730053	+	0.683390i	$0.760505\pi$
$692$	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	−0.973887	−	0.227031i	$-0.927098\pi$
$709$	−33.6624	+	19.4350i	−1.26422	+	0.729896i	−0.290329	+	0.956927i	$0.593765\pi$
$710$		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	0.921098	−	0.389331i	$-0.127294\pi$
$719$	3.30830	+	5.73015i	0.123379	+	0.213698i	−0.797719	+	0.603029i	$0.793960\pi$
$720$		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	$0.00465084\pi$
$733$			0.791131i			0.0292211i	−0.999893	+	0.0146105i	$0.995349\pi$
$734$	−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	−0.0871658	−	0.996194i	$-0.527781\pi$
$739$	−27.0073	−	15.5926i	−0.993478	−	0.573585i	−0.906312	+	0.422609i	$0.861114\pi$
$740$		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	0.409017	−	0.912527i	$-0.365872\pi$
$743$	−4.81773	−	2.78152i	−0.176745	−	0.102044i	−0.585763	+	0.810483i	$0.699205\pi$
$744$	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	0.342483	+	0.939524i	$0.388732\pi$
$751$	−17.6048	+	30.4925i	−0.642410	+	1.11269i	−0.984893	+	0.173163i	$0.944601\pi$
$752$	−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	0.0946237	−	0.995513i	$-0.469835\pi$
$757$	25.0223	−	43.3399i	0.909451	−	1.57522i	0.814828	−	0.579703i	$-0.196831\pi$
$758$	−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	0.411975	−	0.911195i	$-0.364839\pi$
$761$	38.8161	−	22.4105i	1.40708	−	0.812379i	0.995106	+	0.0988165i	$0.0315057\pi$
$762$			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	−0.262420	−	0.964954i	$-0.584521\pi$
$769$	−34.0897	−	19.6817i	−1.22930	−	0.709739i	−0.966884	+	0.255215i	$0.917854\pi$
$770$		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	0.519715	−	0.854340i	$-0.326038\pi$
$773$	42.2452	−	24.3902i	1.51945	−	0.877256i	0.999737	−	0.0229167i	$-0.00729525\pi$
$774$	−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	−0.967139	−	0.254250i	$-0.918171\pi$
$787$	−34.5204	+	19.9304i	−1.23052	+	0.710442i	−0.263382	+	0.964692i	$0.584838\pi$
$788$		−	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	0.534932	−	0.844895i	$-0.320337\pi$
$797$	−13.1059	−	22.7001i	−0.464235	−	0.804079i	−0.999167	+	0.0408167i	$0.987004\pi$
$798$			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	−0.992515	−	0.122124i	$-0.961029\pi$
$809$	−11.1068	+	19.2376i	−0.390495	+	0.676357i	0.602020	+	0.798481i	$0.294363\pi$
$810$		0			0
$811$		−	19.0950i		−	0.670515i	−0.942127	−	0.335257i	$-0.891177\pi$
$811$		−	19.0950i		−	0.670515i	0.942127	−	0.335257i	$-0.108823\pi$
$812$	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	−0.114743	−	0.993395i	$-0.536604\pi$
$821$	−29.5820	−	17.0792i	−1.03242	−	0.596068i	−0.917677	+	0.397327i	$0.869938\pi$
$822$	5.38588	−	9.32861i	0.187854	−	0.325373i
$823$	−2.03970	−	3.53286i	−0.0710995	−	0.123148i	0.828284	−	0.560309i	$-0.189317\pi$
$823$	−2.03970	−	3.53286i	−0.0710995	−	0.123148i	−0.899383	+	0.437161i	$0.855984\pi$
$824$		−	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	$0.403235\pi$
$827$			54.8780i			1.90830i	−0.299337	+	0.954148i	$0.596765\pi$
$828$	2.43275	+	4.21364i	0.0845438	+	0.146434i
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	−0.786548	−	0.617529i	$-0.788134\pi$
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	0.928070	+	0.372406i	$0.121467\pi$
$830$		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	−0.790130	−	0.612939i	$-0.789987\pi$
$839$	−18.9543	+	10.9433i	−0.654374	+	0.377803i	0.135756	+	0.990742i	$0.456654\pi$
$840$		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	$0.106748\pi$
$853$			19.2240i			0.658217i	−0.944292	+	0.329108i	$0.893252\pi$
$854$	−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	$0.382840\pi$
$863$			54.8186i			1.86605i	−0.359814	+	0.933024i	$0.617160\pi$
$864$	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	−0.843706	−	0.536805i	$-0.819631\pi$
$877$	−23.7113	+	13.6897i	−0.800673	+	0.462269i	0.0430336	+	0.999074i	$0.486298\pi$
$878$	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	0.415255	+	0.909705i	$0.363692\pi$
$881$	−17.2213	+	29.8282i	−0.580200	+	1.00494i	−0.995455	+	0.0952310i	$0.969641\pi$
$882$	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	0.476812	+	0.879005i	$0.341792\pi$
$887$	−15.5714	+	26.9704i	−0.522835	+	0.905577i	−0.999647	+	0.0265716i	$0.991541\pi$
$888$	−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	−0.974352	−	0.225031i	$-0.927752\pi$
$907$	−8.80284	+	15.2470i	−0.292294	+	0.506267i	0.682058	+	0.731298i	$0.261085\pi$
$908$	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	0.921970	−	0.387261i	$-0.126579\pi$
$919$	3.80778	+	6.59527i	0.125607	+	0.217558i	−0.796363	+	0.604819i	$0.793245\pi$
$920$		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	−0.285740	−	0.958307i	$-0.592239\pi$
$929$	12.2317	−	7.06196i	0.401308	−	0.231695i	0.687048	+	0.726612i	$0.258906\pi$
$930$		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	$0.135638\pi$
$941$			25.3591i			0.826683i	−0.910576	+	0.413342i	$0.864362\pi$
$942$	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	0.952665	−	0.304022i	$-0.0983296\pi$
$947$	35.8727	+	20.7111i	1.16571	+	0.673021i	0.213042	+	0.977043i	$0.431663\pi$
$948$	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	0.599305	−	0.800521i	$-0.295444\pi$
$953$	−12.1513	−	21.0466i	−0.393619	−	0.681767i	−0.992924	+	0.118753i	$0.962110\pi$
$954$			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	$0.124325\pi$
$967$			23.6784i			0.761445i	−0.924689	+	0.380722i	$0.875675\pi$
$968$	−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	0.969458	−	0.245256i	$-0.0788719\pi$
$971$	8.48609	+	14.6983i	0.272332	+	0.471692i	−0.697127	+	0.716948i	$0.745539\pi$
$972$	−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	0.111955	−	0.993713i	$-0.464289\pi$
$977$	−21.6501	−	12.4997i	−0.692649	−	0.399901i	−0.804604	+	0.593812i	$0.797622\pi$
$978$	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	$0.143617\pi$
$983$			27.3418i			0.872068i	−0.899930	+	0.436034i	$0.856383\pi$
$984$	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	−0.964987	−	0.262299i	$-0.915519\pi$
$991$	−8.03802	+	13.9223i	−0.255336	+	0.442255i	0.709651	+	0.704554i	$0.248853\pi$
$992$	−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	−0.998459	−	0.0554858i	$-0.982329\pi$
$997$	−17.2806	−	29.9309i	−0.547282	−	0.947920i	0.451178	−	0.892434i	$-0.351004\pi$
$998$	−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.251.2		8
5.2	odd	4		325.2.m.c.199.3		8
5.3	odd	4		325.2.m.b.199.2		8
5.4	even	2		65.2.m.a.56.3	yes	8
13.6	odd	12		4225.2.a.bl.1.3		4
13.7	odd	12		4225.2.a.bi.1.2		4
13.10	even	6	inner	325.2.n.d.101.2		8
15.14	odd	2		585.2.bu.c.316.2		8
20.19	odd	2		1040.2.da.b.641.4		8
65.4	even	6		845.2.c.g.506.6		8
65.9	even	6		845.2.c.g.506.3		8
65.19	odd	12		845.2.a.l.1.2		4
65.23	odd	12		325.2.m.c.49.3		8
65.24	odd	12		845.2.e.m.146.2		8
65.29	even	6		845.2.m.g.361.2		8
65.34	odd	4		845.2.e.m.191.2		8
65.44	odd	4		845.2.e.n.191.3		8
65.49	even	6		65.2.m.a.36.3	✓	8
65.54	odd	12		845.2.e.n.146.3		8
65.59	odd	12		845.2.a.m.1.3		4
65.62	odd	12		325.2.m.b.49.2		8
65.64	even	2		845.2.m.g.316.2		8
195.59	even	12		7605.2.a.cf.1.2		4
195.149	even	12		7605.2.a.cj.1.3		4
195.179	odd	6		585.2.bu.c.361.2		8
260.179	odd	6		1040.2.da.b.881.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	65.49	even	6
65.2.m.a.56.3	yes	8	5.4	even	2
325.2.m.b.49.2		8	65.62	odd	12
325.2.m.b.199.2		8	5.3	odd	4
325.2.m.c.49.3		8	65.23	odd	12
325.2.m.c.199.3		8	5.2	odd	4
325.2.n.d.101.2		8	13.10	even	6	inner
325.2.n.d.251.2		8	1.1	even	1	trivial
585.2.bu.c.316.2		8	15.14	odd	2
585.2.bu.c.361.2		8	195.179	odd	6
845.2.a.l.1.2		4	65.19	odd	12
845.2.a.m.1.3		4	65.59	odd	12
845.2.c.g.506.3		8	65.9	even	6
845.2.c.g.506.6		8	65.4	even	6
845.2.e.m.146.2		8	65.24	odd	12
845.2.e.m.191.2		8	65.34	odd	4
845.2.e.n.146.3		8	65.54	odd	12
845.2.e.n.191.3		8	65.44	odd	4
845.2.m.g.316.2		8	65.64	even	2
845.2.m.g.361.2		8	65.29	even	6
1040.2.da.b.641.4		8	20.19	odd	2
1040.2.da.b.881.4		8	260.179	odd	6
4225.2.a.bi.1.2		4	13.7	odd	12
4225.2.a.bl.1.3		4	13.6	odd	12
7605.2.a.cf.1.2		4	195.59	even	12
7605.2.a.cj.1.3		4	195.149	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

Groups

Database

Properties

Related objects

Downloads

Learn more