LMFDB - Embedded newform 325.2.m.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("325.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			49.3
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	325.49
Dual form			325.2.m.c.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.609843 + 1.05628i) q^{2} +(-2.01978 + 1.16612i) q^{3} +(0.256182 - 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-1.80010 + 3.11786i) q^{7} +3.06430 q^{8} +(1.21969 - 2.11256i) q^{9} +O(q^{10})$	\(q+(0.609843 + 1.05628i) q^{2} +(-2.01978 + 1.16612i) q^{3} +(0.256182 - 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-1.80010 + 3.11786i) q^{7} +3.06430 q^{8} +(1.21969 - 2.11256i) q^{9} +(-4.65213 + 2.68591i) q^{11} +1.19496i q^{12} +(-3.11256 - 1.81988i) q^{13} -4.39111 q^{14} +(1.35638 + 2.34932i) q^{16} +(-0.980215 - 0.565928i) q^{17} +2.97527 q^{18} +(1.96410 + 1.13397i) q^{19} -8.39654i q^{21} +(-5.67414 - 3.27597i) q^{22} +(-3.37133 + 1.94644i) q^{23} +(-6.18922 + 3.57335i) q^{24} +(0.0241312 - 4.39758i) q^{26} -1.30752i q^{27} +(0.922305 + 1.59748i) q^{28} +(-0.0123639 - 0.0214150i) q^{29} +5.46410i q^{31} +(1.40994 - 2.44209i) q^{32} +(6.26420 - 10.8499i) q^{33} -1.38051i q^{34} +(-0.624924 - 1.08240i) q^{36} +(4.35203 + 7.53794i) q^{37} +2.76619i q^{38} +(8.40891 + 0.0461428i) q^{39} +(3.23205 - 1.86603i) q^{41} +(8.86910 - 5.12058i) q^{42} +(0.980215 + 0.565928i) q^{43} +2.75232i q^{44} +(-4.11196 - 2.37404i) q^{46} +2.58535 q^{47} +(-5.47918 - 3.16341i) q^{48} +(-2.98070 - 5.16273i) q^{49} +2.63977 q^{51} +(-1.60490 + 0.914884i) q^{52} +4.43937i q^{53} +(1.38111 - 0.797382i) q^{54} +(-5.51603 + 9.55405i) q^{56} -5.28942 q^{57} +(0.0150801 - 0.0261196i) q^{58} +(0.148458 + 0.0857123i) q^{59} +(-1.68012 + 2.91005i) q^{61} +(-5.77162 + 3.33225i) q^{62} +(4.39111 + 7.60563i) q^{63} +8.86488 q^{64} +15.2807 q^{66} +(3.19990 + 5.54239i) q^{67} +(-0.502227 + 0.289961i) q^{68} +(4.53957 - 7.86276i) q^{69} +(9.35076 + 5.39866i) q^{71} +(3.73748 - 6.47351i) q^{72} +4.70308 q^{73} +(-5.30812 + 9.19393i) q^{74} +(1.00633 - 0.581008i) q^{76} -19.3396i q^{77} +(5.07938 + 8.91030i) q^{78} +11.9826 q^{79} +(5.18379 + 8.97859i) q^{81} +(3.94209 + 2.27597i) q^{82} -12.1286 q^{83} +(-3.72572 - 2.15104i) q^{84} +1.38051i q^{86} +(0.0499450 + 0.0288357i) q^{87} +(-14.2555 + 8.23042i) q^{88} +(-13.9898 + 8.07702i) q^{89} +(11.2771 - 6.42856i) q^{91} +1.99457i q^{92} +(-6.37182 - 11.0363i) q^{93} +(1.57666 + 2.73086i) q^{94} +6.57666i q^{96} +(6.08408 - 10.5379i) q^{97} +(3.63553 - 6.29692i) q^{98} +13.1039i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9	$ 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9} - 8 q^{13} - 4 q^{14} - 2 q^{16} - 18 q^{17} + 40 q^{18} - 12 q^{19} - 6 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{26} - 8 q^{28} + 8 q^{29} + 4 q^{32} + 18 q^{33} + 20 q^{36} + 2 q^{37} + 12 q^{41} + 42 q^{42} + 18 q^{43} - 42 q^{46} + 16 q^{47} + 6 q^{48} - 12 q^{49} - 8 q^{51} - 16 q^{52} - 18 q^{54} + 12 q^{56} + 28 q^{57} - 22 q^{58} + 12 q^{59} - 28 q^{61} - 12 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 12 q^{68} + 16 q^{69} - 12 q^{72} + 16 q^{73} - 10 q^{74} + 54 q^{76} - 18 q^{78} + 16 q^{79} + 8 q^{81} + 6 q^{82} - 24 q^{83} + 30 q^{84} - 54 q^{87} - 42 q^{88} - 24 q^{89} + 28 q^{91} - 8 q^{93} - 32 q^{94} + 2 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9 - 8 * q^13 - 4 * q^14 - 2 * q^16 - 18 * q^17 + 40 * q^18 - 12 * q^19 - 6 * q^22 - 6 * q^23 + 12 * q^24 + 10 * q^26 - 8 * q^28 + 8 * q^29 + 4 * q^32 + 18 * q^33 + 20 * q^36 + 2 * q^37 + 12 * q^41 + 42 * q^42 + 18 * q^43 - 42 * q^46 + 16 * q^47 + 6 * q^48 - 12 * q^49 - 8 * q^51 - 16 * q^52 - 18 * q^54 + 12 * q^56 + 28 * q^57 - 22 * q^58 + 12 * q^59 - 28 * q^61 - 12 * q^62 + 4 * q^63 + 8 * q^64 + 12 * q^66 + 30 * q^67 - 12 * q^68 + 16 * q^69 - 12 * q^72 + 16 * q^73 - 10 * q^74 + 54 * q^76 - 18 * q^78 + 16 * q^79 + 8 * q^81 + 6 * q^82 - 24 * q^83 + 30 * q^84 - 54 * q^87 - 42 * q^88 - 24 * q^89 + 28 * q^91 - 8 * q^93 - 32 * q^94 + 2 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.609843	+	1.05628i	0.431224	+	0.746903i	0.996979	−	0.0776710i	$-0.0247484\pi$
$2$	0.609843	+	1.05628i	0.431224	+	0.746903i	−0.565755	+	0.824574i	$0.691415\pi$
$3$	−2.01978	+	1.16612i	−1.16612	+	0.673262i	−0.952764	−	0.303712i	$-0.901774\pi$
$3$	−2.01978	+	1.16612i	−1.16612	+	0.673262i	−0.213359	+	0.976974i	$0.568441\pi$
$4$	0.256182	−	0.443720i	0.128091	−	0.221860i
$5$		0			0
$5$		0			0
$6$	−2.46350	−	1.42231i	−1.00572	−	0.580654i
$7$	−1.80010	+	3.11786i	−0.680373	+	1.17844i	0.294494	+	0.955653i	$0.404849\pi$
$7$	−1.80010	+	3.11786i	−0.680373	+	1.17844i	−0.974867	+	0.222787i	$0.928484\pi$
$8$	3.06430			1.08339
$9$	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	$0.633775\pi$
$12$			1.19496i			0.344955i
$13$	−3.11256	−	1.81988i	−0.863269	−	0.504745i
$13$	−3.11256	−	1.81988i	−0.863269	−	0.504745i
$14$	−4.39111			−1.17357
$15$		0			0
$16$	1.35638	+	2.34932i	0.339094	+	0.587329i
$17$	−0.980215	−	0.565928i	−0.237737	−	0.137258i	0.376399	−	0.926458i	$-0.377162\pi$
$17$	−0.980215	−	0.565928i	−0.237737	−	0.137258i	−0.614136	+	0.789200i	$0.710495\pi$
$18$	2.97527			0.701278
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	0.708082	−	0.706130i	$-0.249561\pi$
$19$	1.96410	+	1.13397i	0.450596	+	0.260152i	−0.257486	+	0.966282i	$0.582894\pi$
$20$		0			0
$21$		−	8.39654i		−	1.83228i
$22$	−5.67414	−	3.27597i	−1.20973	−	0.698438i
$23$	−3.37133	+	1.94644i	−0.702970	+	0.405860i	−0.808453	−	0.588561i	$-0.799695\pi$
$23$	−3.37133	+	1.94644i	−0.702970	+	0.405860i	0.105483	+	0.994421i	$0.466361\pi$
$24$	−6.18922	+	3.57335i	−1.26337	+	0.729407i
$25$		0			0
$26$	0.0241312	−	4.39758i	0.00473251	−	0.862436i
$27$		−	1.30752i		−	0.251632i
$28$	0.922305	+	1.59748i	0.174299	+	0.301895i
$29$	−0.0123639	−	0.0214150i	−0.00229593	−	0.00397666i	0.864875	−	0.501987i	$-0.167397\pi$
$29$	−0.0123639	−	0.0214150i	−0.00229593	−	0.00397666i	−0.867171	+	0.498010i	$0.834064\pi$
$30$		0			0
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	1.40994	−	2.44209i	0.249245	−	0.431705i
$33$	6.26420	−	10.8499i	1.09046	−	1.88873i
$34$		−	1.38051i		−	0.236755i
$35$		0			0
$36$	−0.624924	−	1.08240i	−0.104154	−	0.180400i
$37$	4.35203	+	7.53794i	0.715470	+	1.23923i	0.962778	+	0.270293i	$0.0871205\pi$
$37$	4.35203	+	7.53794i	0.715470	+	1.23923i	−0.247309	+	0.968937i	$0.579546\pi$
$38$			2.76619i			0.448735i
$39$	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	$0.239204\pi$
$42$	8.86910	−	5.12058i	1.36853	−	0.790122i
$43$	0.980215	+	0.565928i	0.149481	+	0.0863031i	0.572875	−	0.819643i	$-0.305828\pi$
$43$	0.980215	+	0.565928i	0.149481	+	0.0863031i	−0.423394	+	0.905946i	$0.639161\pi$
$44$			2.75232i			0.414929i
$45$		0			0
$46$	−4.11196	−	2.37404i	−0.606276	−	0.350034i
$47$	2.58535			0.377113			0.188556	−	0.982062i	$-0.439619\pi$
$47$	2.58535			0.377113			0.188556	+	0.982062i	$0.439619\pi$
$48$	−5.47918	−	3.16341i	−0.790852	−	0.456598i
$49$	−2.98070	−	5.16273i	−0.425815	−	0.737533i
$50$		0			0
$51$	2.63977			0.369641
$52$	−1.60490	+	0.914884i	−0.222560	+	0.126872i
$53$			4.43937i			0.609795i	0.952385	+	0.304897i	$0.0986222\pi$
$53$			4.43937i			0.609795i	−0.952385	+	0.304897i	$0.901378\pi$
$54$	1.38111	−	0.797382i	0.187945	−	0.108510i
$55$		0			0
$56$	−5.51603	+	9.55405i	−0.737111	+	1.27671i
$57$	−5.28942			−0.700600
$58$	0.0150801	−	0.0261196i	0.00198012	−	0.00342967i
$59$	0.148458	+	0.0857123i	0.0193276	+	0.0111588i	0.509633	−	0.860392i	$-0.329781\pi$
$59$	0.148458	+	0.0857123i	0.0193276	+	0.0111588i	−0.490305	+	0.871551i	$0.663115\pi$
$60$		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	$0.235680\pi$
$62$	−5.77162	+	3.33225i	−0.732997	+	0.423196i
$63$	4.39111	+	7.60563i	0.553228	+	0.958219i
$64$	8.86488			1.10811
$65$		0			0
$66$	15.2807			1.88093
$67$	3.19990	+	5.54239i	0.390930	+	0.677111i	0.992572	−	0.121655i	$-0.0388200\pi$
$67$	3.19990	+	5.54239i	0.390930	+	0.677111i	−0.601642	+	0.798766i	$0.705487\pi$
$68$	−0.502227	+	0.289961i	−0.0609040	+	0.0351629i
$69$	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	$0.445309\pi$
$72$	3.73748	−	6.47351i	0.440467	−	0.762911i
$73$	4.70308			0.550454			0.275227	−	0.961379i	$-0.411247\pi$
$73$	4.70308			0.550454			0.275227	+	0.961379i	$0.411247\pi$
$74$	−5.30812	+	9.19393i	−0.617056	+	1.06877i
$75$		0			0
$76$	1.00633	−	0.581008i	0.115435	−	0.0666462i
$77$		−	19.3396i		−	2.20395i
$78$	5.07938	+	8.91030i	0.575126	+	1.00889i
$79$	11.9826			1.34815			0.674075	−	0.738663i	$-0.264543\pi$
$79$	11.9826			1.34815			0.674075	+	0.738663i	$0.264543\pi$
$80$		0			0
$81$	5.18379	+	8.97859i	0.575976	+	0.997621i
$82$	3.94209	+	2.27597i	0.435331	+	0.251338i
$83$	−12.1286			−1.33129			−0.665643	−	0.746270i	$-0.731843\pi$
$83$	−12.1286			−1.33129			−0.665643	+	0.746270i	$0.731843\pi$
$84$	−3.72572	−	2.15104i	−0.406509	−	0.234698i
$85$		0			0
$86$			1.38051i			0.148864i
$87$	0.0499450	+	0.0288357i	0.00535466	+	0.00309152i
$88$	−14.2555	+	8.23042i	−1.51964	+	0.877366i
$89$	−13.9898	+	8.07702i	−1.48292	+	0.856162i	−0.999812	−	0.0194001i	$-0.993824\pi$
$89$	−13.9898	+	8.07702i	−1.48292	+	0.856162i	−0.483105	+	0.875562i	$0.660491\pi$
$90$		0			0
$91$	11.2771	−	6.42856i	1.18216	−	0.673896i
$92$			1.99457i			0.207948i
$93$	−6.37182	−	11.0363i	−0.660727	−	1.14441i
$94$	1.57666	+	2.73086i	0.162620	+	0.281666i
$95$		0			0
$96$			6.57666i			0.671228i
$97$	6.08408	−	10.5379i	0.617745	−	1.06997i	−0.372151	−	0.928172i	$-0.621380\pi$
$97$	6.08408	−	10.5379i	0.617745	−	1.06997i	0.989896	−	0.141794i	$-0.0452869\pi$
$98$	3.63553	−	6.29692i	0.367244	−	0.636085i
$99$			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	$0.897985\pi$
$102$	1.60984	+	2.78833i	0.159398	+	0.276086i
$103$		−	17.9035i		−	1.76408i	−0.471173	−	0.882041i	$-0.656169\pi$
$103$		−	17.9035i		−	1.76408i	0.471173	−	0.882041i	$-0.343831\pi$
$104$	−9.53781	−	5.57666i	−0.935259	−	0.546837i
$105$		0			0
$106$	−4.68922	+	2.70732i	−0.455457	+	0.262958i
$107$	−7.90842	+	4.56593i	−0.764536	+	0.441405i	−0.830922	−	0.556389i	$-0.812186\pi$
$107$	−7.90842	+	4.56593i	−0.764536	+	0.441405i	0.0663862	+	0.997794i	$0.478853\pi$
$108$	−0.580172	−	0.334963i	−0.0558271	−	0.0322318i
$109$		−	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
$112$	−9.76645			−0.922843
$113$	6.12789	+	3.53794i	0.576463	+	0.332821i	0.759727	−	0.650243i	$-0.225333\pi$
$113$	6.12789	+	3.53794i	0.576463	+	0.332821i	−0.183263	+	0.983064i	$0.558666\pi$
$114$	−3.22572	−	5.58710i	−0.302116	−	0.523280i
$115$		0			0
$116$	−0.0126697			−0.00117635
$117$	−7.64096	+	4.35578i	−0.706407	+	0.402692i
$118$			0.209084i			0.0192478i
$119$	3.52897	−	2.03745i	0.323500	−	0.186773i
$120$		0			0
$121$	8.92820	−	15.4641i	0.811655	−	1.40583i
$122$	−4.09843			−0.371055
$123$	−4.35203	+	7.53794i	−0.392409	+	0.679673i
$124$	2.42453	+	1.39980i	0.217729	+	0.125706i
$125$		0			0
$126$	−5.35578	+	9.27648i	−0.477131	+	0.826415i
$127$	9.90396	−	5.71806i	0.878835	−	0.507395i	0.00856072	−	0.999963i	$-0.497275\pi$
$127$	9.90396	−	5.71806i	0.878835	−	0.507395i	0.870274	+	0.492568i	$0.163942\pi$
$128$	2.58631	+	4.47962i	0.228600	+	0.395946i
$129$	−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	$0.652747\pi$
$132$	−3.20955	−	5.55910i	−0.279355	−	0.483858i
$133$	−7.07115	+	4.08253i	−0.613146	+	0.354000i
$134$	−3.90288	+	6.75998i	−0.337157	+	0.583974i
$135$		0			0
$136$	−3.00367	−	1.73417i	−0.257563	−	0.148704i
$137$	−1.89336	+	3.27940i	−0.161761	+	0.280178i	−0.935500	−	0.353326i	$-0.885051\pi$
$137$	−1.89336	+	3.27940i	−0.161761	+	0.280178i	0.773739	+	0.633504i	$0.218384\pi$
$138$	11.0737			0.942656
$139$	1.00693	−	1.74406i	0.0854068	−	0.147929i	−0.820158	−	0.572138i	$-0.806114\pi$
$139$	1.00693	−	1.74406i	0.0854068	−	0.147929i	0.905564	+	0.424209i	$0.139448\pi$
$140$		0			0
$141$	−5.22186	+	3.01484i	−0.439760	+	0.253895i
$142$			13.1694i			1.10515i
$143$	19.3681	+	0.106280i	1.61964	+	0.00888757i
$144$	6.61742			0.551452
$145$		0			0
$146$	2.86814	+	4.96777i	0.237369	+	0.411136i
$147$	12.0408	+	6.95174i	0.993105	+	0.573370i
$148$	4.45965			0.366581
$149$	−4.77855	−	2.75890i	−0.391474	−	0.226018i	0.291324	−	0.956624i	$-0.405904\pi$
$149$	−4.77855	−	2.75890i	−0.391474	−	0.226018i	−0.682799	+	0.730607i	$0.739237\pi$
$150$		0			0
$151$			4.88961i			0.397911i	0.980009	+	0.198956i	$0.0637549\pi$
$151$			4.88961i			0.397911i	−0.980009	+	0.198956i	$0.936245\pi$
$152$	6.01859	+	3.47484i	0.488172	+	0.281846i
$153$	−2.39111	+	1.38051i	−0.193310	+	0.111608i
$154$	20.4280	−	11.7941i	1.64614	−	0.950397i
$155$		0			0
$156$	2.17469	−	3.71938i	0.174114	−	0.297789i
$157$			10.0405i			0.801323i	0.916226	+	0.400661i	$0.131220\pi$
$157$			10.0405i			0.801323i	−0.916226	+	0.400661i	$0.868780\pi$
$158$	7.30752	+	12.6570i	0.581355	+	1.00694i
$159$	−5.17686	−	8.96658i	−0.410551	−	0.711096i
$160$		0			0
$161$		−	14.0151i		−	1.10454i
$162$	−6.32260	+	10.9511i	−0.496750	+	0.860397i
$163$	3.39062	−	5.87273i	0.265574	−	0.459988i	−0.702140	−	0.712039i	$-0.747772\pi$
$163$	3.39062	−	5.87273i	0.265574	−	0.459988i	0.967714	+	0.252051i	$0.0811052\pi$
$164$		−	1.91217i		−	0.149315i
$165$		0			0
$166$	−7.39654	−	12.8112i	−0.574083	−	0.994341i
$167$	−5.24490	−	9.08444i	−0.405863	−	0.702975i	0.588559	−	0.808455i	$-0.299696\pi$
$167$	−5.24490	−	9.08444i	−0.405863	−	0.702975i	−0.994421	+	0.105479i	$0.966362\pi$
$168$		−	25.7295i		−	1.98507i
$169$	6.37605	+	11.3290i	0.490466	+	0.871460i
$170$		0			0
$171$	4.79118	−	2.76619i	0.366391	−	0.211536i
$172$	0.502227	−	0.289961i	0.0382944	−	0.0221093i
$173$	3.86113	+	2.22923i	0.293557	+	0.169485i	0.639545	−	0.768754i	$-0.279123\pi$
$173$	3.86113	+	2.22923i	0.293557	+	0.169485i	−0.345988	+	0.938239i	$0.612456\pi$
$174$			0.0703412i			0.00533255i
$175$		0			0
$176$	−12.6201	−	7.28621i	−0.951275	−	0.549219i
$177$	−0.399804			−0.0300511
$178$	−17.0632	−	9.85143i	−1.27894	−	0.738396i
$179$	−9.31564	−	16.1352i	−0.696284	−	1.20600i	−0.969746	−	0.244116i	$-0.921502\pi$
$179$	−9.31564	−	16.1352i	−0.696284	−	1.20600i	0.273462	−	0.961883i	$-0.411831\pi$
$180$		0			0
$181$	−18.0900			−1.34462			−0.672310	−	0.740270i	$-0.734698\pi$
$181$	−18.0900			−1.34462			−0.672310	+	0.740270i	$0.734698\pi$
$182$	13.6676	+	7.99131i	1.01311	+	0.592355i
$183$		−	7.83690i		−	0.579320i
$184$	−10.3307	+	5.96446i	−0.761593	+	0.439706i
$185$		0			0
$186$	7.77162	−	13.4608i	0.569843	−	0.986997i
$187$	6.08012			0.444622
$188$	0.662321	−	1.14717i	0.0483047	−	0.0836662i
$189$	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	$0.713937\pi$
$192$	−17.9052	+	10.3375i	−1.29219	+	0.746048i
$193$	10.8837	+	18.8511i	0.783425	+	1.35693i	0.929935	+	0.367723i	$0.119863\pi$
$193$	10.8837	+	18.8511i	0.783425	+	1.35693i	−0.146510	+	0.989209i	$0.546804\pi$
$194$	14.8413			1.06555
$195$		0			0
$196$	−3.05441			−0.218172
$197$	−0.848360	−	1.46940i	−0.0604432	−	0.104691i	0.834220	−	0.551431i	$-0.185918\pi$
$197$	−0.848360	−	1.46940i	−0.0604432	−	0.104691i	−0.894664	+	0.446741i	$0.852585\pi$
$198$	−13.8413	+	7.99131i	−0.983662	+	0.567917i
$199$	−12.6627	+	21.9325i	−0.897637	+	1.55475i	−0.0671309	+	0.997744i	$0.521385\pi$
$199$	−12.6627	+	21.9325i	−0.897637	+	1.55475i	−0.830506	+	0.557009i	$0.811949\pi$
$200$		0			0
$201$	−12.9262	−	7.46296i	−0.911746	−	0.526397i
$202$	2.47256	−	4.28259i	0.173968	−	0.301322i
$203$	0.0890252			0.00624834
$204$	0.676260	−	1.17132i	0.0473477	−	0.0820086i
$205$		0			0
$206$	18.9111	−	10.9183i	1.31760	−	0.760715i
$207$			9.49617i			0.660030i
$208$	0.0536711	−	9.78083i	0.00372142	−	0.678179i
$209$	−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	$0.829657\pi$
$212$	1.96984	+	1.13729i	0.135289	+	0.0781092i
$213$	−25.1820			−1.72544
$214$	−9.64579	−	5.56900i	−0.659373	−	0.380689i
$215$		0			0
$216$		−	4.00663i		−	0.272616i
$217$	−17.0363	−	9.83592i	−1.15650	−	0.667706i
$218$	7.79118	−	4.49824i	0.527685	−	0.304659i
$219$	−9.49922	+	5.48438i	−0.641898	+	0.370600i
$220$		0			0
$221$	2.02106	+	3.54536i	0.135951	+	0.238487i
$222$		−	24.7597i		−	1.66176i
$223$	6.14838	+	10.6493i	0.411726	+	0.713130i	0.995079	−	0.0990887i	$-0.0315928\pi$
$223$	6.14838	+	10.6493i	0.411726	+	0.713130i	−0.583353	+	0.812219i	$0.698259\pi$
$224$	5.07606	+	8.79200i	0.339159	+	0.587440i
$225$		0			0
$226$			8.63036i			0.574083i
$227$	−3.81613	+	6.60974i	−0.253286	+	0.438704i	−0.964428	−	0.264344i	$-0.914845\pi$
$227$	−3.81613	+	6.60974i	−0.253286	+	0.438704i	0.711143	+	0.703048i	$0.248178\pi$
$228$	−1.35505	+	2.34702i	−0.0897406	+	0.155435i
$229$		−	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
$232$	−0.0378868	−	0.0656218i	−0.00248739	−	0.00430828i
$233$			9.49617i			0.622115i	0.950391	+	0.311057i	$0.100683\pi$
$233$			9.49617i			0.622115i	−0.950391	+	0.311057i	$0.899317\pi$
$234$	−9.26071	−	5.41465i	−0.605392	−	0.353966i
$235$		0			0
$236$	0.0760645	−	0.0439159i	0.00495138	−	0.00285868i
$237$	−24.2023	+	13.9732i	−1.57211	+	0.907657i
$238$	4.30423	+	2.48505i	0.279002	+	0.161082i
$239$			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	0.980046	−	0.198770i	$-0.0636947\pi$
$241$	20.1493	+	11.6332i	1.29793	+	0.749360i	0.317883	+	0.948130i	$0.397028\pi$
$242$	21.7792			1.40002
$243$	−17.5432	−	10.1286i	−1.12540	−	0.649750i
$244$	0.860832	+	1.49100i	0.0551091	+	0.0954518i
$245$		0			0
$246$	−10.6162			−0.676866
$247$	−4.04968	−	7.10400i	−0.257675	−	0.452017i
$248$			16.7436i			1.06322i
$249$	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	$0.0447652\pi$
$252$	4.49969			0.283454
$253$	10.4559	−	18.1101i	0.657357	−	1.13858i
$254$	12.0797	+	6.97424i	0.757950	+	0.437603i
$255$		0			0
$256$	5.71040	−	9.89070i	0.356900	−	0.618169i
$257$	4.80646	−	2.77501i	0.299819	−	0.173100i	−0.342543	−	0.939502i	$-0.611288\pi$
$257$	4.80646	−	2.77501i	0.299819	−	0.173100i	0.642361	+	0.766402i	$0.277955\pi$
$258$	−1.60984	−	2.78833i	−0.100224	−	0.173594i
$259$	−31.3363			−1.94714
$260$		0			0
$261$	−0.0603205			−0.00373375
$262$	−6.44481	−	11.1627i	−0.398161	−	0.689636i
$263$	−5.94065	+	3.42983i	−0.366316	+	0.211493i	−0.671848	−	0.740689i	$-0.734499\pi$
$263$	−5.94065	+	3.42983i	−0.366316	+	0.211493i	0.305532	+	0.952182i	$0.401166\pi$
$264$	19.1954	−	33.2474i	1.18139	−	2.04623i
$265$		0			0
$266$	−8.62459	−	4.97941i	−0.528807	−	0.305307i
$267$	18.8376	−	32.6277i	1.15284	−	1.99678i
$268$	3.27903			0.200299
$269$	−0.710994	+	1.23148i	−0.0433501	+	0.0750845i	−0.886886	−	0.461988i	$-0.847136\pi$
$269$	−0.710994	+	1.23148i	−0.0433501	+	0.0750845i	0.843536	+	0.537072i	$0.180470\pi$
$270$		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	$0.235412\pi$
$272$		−	3.07045i		−	0.186173i
$273$	−15.2807	+	26.1347i	−0.924831	+	1.58175i
$274$	−4.61862			−0.279021
$275$		0			0
$276$	−2.32591	−	4.02860i	−0.140003	−	0.242493i
$277$	−15.1760	−	8.76187i	−0.911837	−	0.526449i	−0.0308154	−	0.999525i	$-0.509810\pi$
$277$	−15.1760	−	8.76187i	−0.911837	−	0.526449i	−0.881022	+	0.473076i	$0.843144\pi$
$278$	2.45628			0.147318
$279$	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	$-0.103751\pi$
$282$	−6.36903	−	3.67716i	−0.379270	−	0.218972i
$283$	1.14175	−	0.659192i	0.0678702	−	0.0391849i	−0.465681	−	0.884953i	$-0.654191\pi$
$283$	1.14175	−	0.659192i	0.0678702	−	0.0391849i	0.533551	+	0.845768i	$0.320857\pi$
$284$	4.79099	−	2.76608i	0.284293	−	0.164137i
$285$		0			0
$286$	11.6992	+	20.5229i	0.691790	+	1.21355i
$287$			13.4361i			0.793109i
$288$	−3.43937	−	5.95717i	−0.202667	−	0.351030i
$289$	−7.85945	−	13.6130i	−0.462321	−	0.800763i
$290$		0			0
$291$			28.3792i			1.66362i
$292$	1.20485	−	2.08685i	0.0705082	−	0.122124i
$293$	9.37133	−	16.2316i	0.547479	−	0.948261i	−0.450968	−	0.892540i	$-0.648921\pi$
$293$	9.37133	−	16.2316i	0.547479	−	0.948261i	0.998446	−	0.0557207i	$-0.0177456\pi$
$294$			16.9579i			0.989004i
$295$		0			0
$296$	13.3359	+	23.0985i	0.775134	+	1.34257i
$297$	3.51187	+	6.08275i	0.203780	+	0.352957i
$298$		−	6.72998i		−	0.389857i
$299$	14.0357	+	0.0770194i	0.811708	+	0.00445415i
$300$		0			0
$301$	−3.52897	+	2.03745i	−0.203406	+	0.117437i
$302$	−5.16480	+	2.98190i	−0.297201	+	0.171589i
$303$	8.18904	+	4.72794i	0.470448	+	0.271613i
$304$			6.15239i			0.352864i
$305$		0			0
$306$	−2.91641	−	1.68379i	−0.166720	−	0.0962558i
$307$	14.3043			0.816387			0.408194	−	0.912895i	$-0.366159\pi$
$307$	14.3043			0.816387			0.408194	+	0.912895i	$0.366159\pi$
$308$	−8.58137	−	4.95445i	−0.488969	−	0.282306i
$309$	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	$0.524943\pi$
$312$	25.7674	+	0.141395i	1.45879	+	0.00800494i
$313$			16.3858i			0.926179i	0.886311	+	0.463090i	$0.153259\pi$
$313$			16.3858i			0.926179i	−0.886311	+	0.463090i	$0.846741\pi$
$314$	−10.6056	+	6.12316i	−0.598510	+	0.345550i
$315$		0			0
$316$	3.06973	−	5.31693i	0.172686	−	0.299101i
$317$	−1.78575			−0.100297			−0.0501487	−	0.998742i	$-0.515970\pi$
$317$	−1.78575			−0.100297			−0.0501487	+	0.998742i	$0.515970\pi$
$318$	6.31414	−	10.9364i	0.354080	−	0.613284i
$319$	0.115037	+	0.0664168i	0.00644085	+	0.00371863i
$320$		0			0
$321$	10.6489	−	18.4444i	0.594362	−	1.02946i
$322$	14.8039	−	8.54702i	0.824987	−	0.476307i
$323$	−1.28349	−	2.22308i	−0.0714156	−	0.123695i
$324$	5.31197			0.295110
$325$		0			0
$326$	8.27099			0.458088
$327$	8.60139	+	14.8980i	0.475658	+	0.823864i
$328$	9.90396	−	5.71806i	0.546855	−	0.315727i
$329$	−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	$0.730288\pi$
$332$	−3.10713	+	5.38170i	−0.170526	+	0.295359i
$333$	21.2325			1.16353
$334$	6.39714	−	11.0802i	0.350036	−	0.606280i
$335$		0			0
$336$	19.7261	−	11.3889i	1.07615	−	0.621315i
$337$			4.36219i			0.237624i	0.992917	+	0.118812i	$0.0379085\pi$
$337$			4.36219i			0.237624i	−0.992917	+	0.118812i	$0.962091\pi$
$338$	−8.07818	+	13.6438i	−0.439395	+	0.742125i
$339$	−16.5027			−0.896303
$340$		0			0
$341$	−14.6761	−	25.4197i	−0.794754	−	1.37655i
$342$	5.84374	+	3.37388i	0.315993	+	0.182439i
$343$	−3.73913			−0.201894
$344$	3.00367	+	1.73417i	0.161947	+	0.0935002i
$345$		0			0
$346$			5.43792i			0.292344i
$347$	23.1291	+	13.3536i	1.24163	+	0.716858i	0.969427	−	0.245381i	$-0.0789130\pi$
$347$	23.1291	+	13.3536i	1.24163	+	0.716858i	0.272207	+	0.962239i	$0.412246\pi$
$348$	0.0255900	−	0.0147744i	0.00137177	−	0.000791991i
$349$	20.4131	−	11.7855i	1.09269	−	0.630865i	0.158399	−	0.987375i	$-0.449367\pi$
$349$	20.4131	−	11.7855i	1.09269	−	0.630865i	0.934292	+	0.356510i	$0.116033\pi$
$350$		0			0
$351$	−2.37953	+	4.06973i	−0.127010	+	0.217226i
$352$			15.1479i			0.807385i
$353$	−2.86863	−	4.96862i	−0.152682	−	0.264453i	0.779531	−	0.626364i	$-0.215458\pi$
$353$	−2.86863	−	4.96862i	−0.152682	−	0.264453i	−0.932213	+	0.361911i	$0.882124\pi$
$354$	−0.243818	−	0.422305i	−0.0129588	−	0.0224453i
$355$		0			0
$356$			8.27675i			0.438667i
$357$	−4.75184	+	8.23042i	−0.251494	+	0.435600i
$358$	11.3622	−	19.6799i	0.600509	−	1.04011i
$359$		−	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
$362$	−11.0321	−	19.1081i	−0.579833	−	1.00430i
$363$			41.6455i			2.18582i
$364$	0.0364951	−	6.65074i	0.00191286	−	0.348593i
$365$		0			0
$366$	8.27796	−	4.77928i	0.432696	−	0.249817i
$367$	22.5630	−	13.0268i	1.17778	−	0.679992i	0.222280	−	0.974983i	$-0.428650\pi$
$367$	22.5630	−	13.0268i	1.17778	−	0.679992i	0.955500	+	0.294991i	$0.0953167\pi$
$368$	−9.14558	−	5.28021i	−0.476747	−	0.275250i
$369$		−	9.10387i		−	0.473928i
$370$		0			0
$371$	−13.8413	−	7.99131i	−0.718607	−	0.414888i
$372$	−6.52938			−0.338532
$373$	11.4354	+	6.60224i	0.592103	+	0.341851i	0.765929	−	0.642926i	$-0.222280\pi$
$373$	11.4354	+	6.60224i	0.592103	+	0.341851i	−0.173826	+	0.984776i	$0.555613\pi$
$374$	3.70792	+	6.42231i	0.191732	+	0.332089i
$375$		0			0
$376$	7.92229			0.408561
$377$	−0.000489234		0.0891563i	−2.51968e−5		0.00459178i
$378$			5.74146i			0.295309i
$379$	−22.5147	+	12.9989i	−1.15650	+	0.667707i	−0.950463	−	0.310837i	$-0.899391\pi$
$379$	−22.5147	+	12.9989i	−1.15650	+	0.667707i	−0.206039	+	0.978544i	$0.566057\pi$
$380$		0			0
$381$	−13.3359	+	23.0985i	−0.683220	+	1.18337i
$382$	−33.3418			−1.70591
$383$	4.80010	−	8.31401i	0.245274	−	0.424826i	−0.716935	−	0.697140i	$-0.754456\pi$
$383$	4.80010	−	8.31401i	0.245274	−	0.424826i	0.962208	+	0.272314i	$0.0877889\pi$
$384$	−10.4476	−	6.03191i	−0.533151	−	0.307815i
$385$		0			0
$386$	−13.2747	+	22.9924i	−0.675664	+	1.17028i
$387$	2.39111	−	1.38051i	0.121547	−	0.0701752i
$388$	−3.11726	−	5.39926i	−0.158255	−	0.274106i
$389$	5.63129			0.285518			0.142759	−	0.989758i	$-0.454403\pi$
$389$	5.63129			0.285518			0.142759	+	0.989758i	$0.454403\pi$
$390$		0			0
$391$	4.40617			0.222829
$392$	−9.13376	−	15.8201i	−0.461325	−	0.799038i
$393$	21.3450	−	12.3236i	1.07671	−	0.621641i
$394$	1.03473	−	1.79221i	0.0521291	−	0.0902903i
$395$		0			0
$396$	5.81445	+	3.35697i	0.292187	+	0.168694i
$397$	8.38291	−	14.5196i	0.420726	−	0.728719i	−0.575285	−	0.817953i	$-0.695109\pi$
$397$	8.38291	−	14.5196i	0.420726	−	0.728719i	0.996011	+	0.0892344i	$0.0284420\pi$
$398$	−30.8891			−1.54833
$399$	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	$0.220697\pi$
$402$		−	18.2050i		−	0.907980i
$403$	9.94402	−	17.0073i	0.495347	−	0.847196i
$404$	−2.07733			−0.103351
$405$		0			0
$406$	0.0542914	+	0.0940355i	0.00269444	+	0.00466690i
$407$	−40.4924	−	23.3783i	−2.00713	−	1.15882i
$408$	8.08903			0.400466
$409$	25.4829	+	14.7125i	1.26005	+	0.727489i	0.973083	−	0.230453i	$-0.0740208\pi$
$409$	25.4829	+	14.7125i	1.26005	+	0.727489i	0.286964	+	0.957941i	$0.407354\pi$
$410$		0			0
$411$		−	8.83157i		−	0.435629i
$412$	−7.94413	−	4.58655i	−0.391379	−	0.225963i
$413$	−0.534478	+	0.308581i	−0.0262999	+	0.0151843i
$414$	−10.0306	+	5.79118i	−0.492978	+	0.284621i
$415$		0			0
$416$	−8.83284	+	5.03522i	−0.433066	+	0.246872i
$417$			4.69683i			0.230005i
$418$	−7.42973	−	12.8687i	−0.363400	−	0.629427i
$419$	3.48397	+	6.03440i	0.170203	+	0.294800i	0.938491	−	0.345305i	$-0.112224\pi$
$419$	3.48397	+	6.03440i	0.170203	+	0.294800i	−0.768288	+	0.640104i	$0.778891\pi$
$420$		0			0
$421$			7.12125i			0.347069i	0.984828	+	0.173534i	$0.0555188\pi$
$421$			7.12125i			0.347069i	−0.984828	+	0.173534i	$0.944481\pi$
$422$	−0.204607	+	0.354389i	−0.00996010	+	0.0172514i
$423$	3.15332	−	5.46171i	0.153320	−	0.265558i
$424$			13.6036i			0.660647i
$425$		0			0
$426$	−15.3571	−	26.5993i	−0.744054	−	1.28874i
$427$	−6.04875	−	10.4767i	−0.292720	−	0.507005i
$428$			4.67883i			0.226160i
$429$	−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	$0.0739286\pi$
$432$	3.07177	−	1.77349i	0.147791	−	0.0853270i
$433$	−1.03934	−	0.600065i	−0.0499476	−	0.0288373i	0.474818	−	0.880084i	$-0.342514\pi$
$433$	−1.03934	−	0.600065i	−0.0499476	−	0.0288373i	−0.524766	+	0.851247i	$0.675847\pi$
$434$		−	23.9935i		−	1.15172i
$435$		0			0
$436$	−3.27290	−	1.88961i	−0.156744	−	0.0904960i
$437$	−8.82884			−0.422341
$438$	−11.5861	−	6.68922i	−0.553604	−	0.319623i
$439$	8.27705	+	14.3363i	0.395042	+	0.684233i	0.993107	−	0.117215i	$-0.0373966\pi$
$439$	8.27705	+	14.3363i	0.395042	+	0.684233i	−0.598064	+	0.801448i	$0.704063\pi$
$440$		0			0
$441$	−14.5421			−0.692481
$442$	−2.51236	+	4.29692i	−0.119501	+	0.204383i
$443$		−	4.55949i		−	0.216628i	−0.994117	−	0.108314i	$-0.965455\pi$
$443$		−	4.55949i		−	0.216628i	0.994117	−	0.108314i	$-0.0345452\pi$
$444$	−9.00753	+	5.20050i	−0.427478	+	0.246805i
$445$		0			0
$446$	−7.49910	+	12.9888i	−0.355093	+	0.615038i
$447$	12.8689			0.608676
$448$	−15.9577	+	27.6395i	−0.753929	+	1.30584i
$449$	−11.9963	−	6.92608i	−0.566142	−	0.326862i	0.189465	−	0.981887i	$-0.439325\pi$
$449$	−11.9963	−	6.92608i	−0.566142	−	0.326862i	−0.755607	+	0.655025i	$0.772658\pi$
$450$		0			0
$451$	−10.0239	+	17.3620i	−0.472009	+	0.817544i
$452$	3.13971	−	1.81271i	0.147680	−	0.0852628i
$453$	−5.70189	−	9.87596i	−0.267898	−	0.464013i
$454$	−9.30897			−0.436892
$455$		0			0
$456$	−16.2083			−0.759025
$457$	20.0573	+	34.7402i	0.938240	+	1.62508i	0.768751	+	0.639548i	$0.220878\pi$
$457$	20.0573	+	34.7402i	0.938240	+	1.62508i	0.169489	+	0.985532i	$0.445788\pi$
$458$	15.2113	−	8.78222i	0.710775	−	0.410366i
$459$	−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	$0.610492\pi$
$462$	−27.5068	+	47.6432i	−1.27973	+	2.21656i
$463$	−23.3031			−1.08299			−0.541494	−	0.840705i	$-0.682141\pi$
$463$	−23.3031			−1.08299			−0.541494	+	0.840705i	$0.682141\pi$
$464$	0.0335403	−	0.0580936i	0.00155707	−	0.00269693i
$465$		0			0
$466$	−10.0306	+	5.79118i	−0.464659	+	0.268271i
$467$			22.6297i			1.04718i	0.851971	+	0.523589i	$0.175407\pi$
$467$			22.6297i			1.04718i	−0.851971	+	0.523589i	$0.824593\pi$
$468$	−0.0247279	+	4.50632i	−0.00114305	+	0.208305i
$469$	−23.0405			−1.06391
$470$		0			0
$471$	−11.7085	−	20.2797i	−0.539500	−	0.934441i
$472$	0.454919	+	0.262648i	0.0209394	+	0.0120893i
$473$	−6.08012			−0.279564
$474$	−29.5192	−	17.0429i	−1.35586	−	0.782808i
$475$		0			0
$476$		−	2.08783i		−	0.0956956i
$477$	9.37844	+	5.41465i	0.429409	+	0.247920i
$478$	−21.0351	+	12.1446i	−0.962124	+	0.555482i
$479$	17.8789	−	10.3224i	0.816910	−	0.471643i	−0.0324399	−	0.999474i	$-0.510328\pi$
$479$	17.8789	−	10.3224i	0.816910	−	0.471643i	0.849350	+	0.527831i	$0.176994\pi$
$480$		0			0
$481$	0.172207	−	31.3825i	0.00785198	−	1.43092i
$482$			28.3777i			1.29257i
$483$	16.3433	+	28.3075i	0.743648	+	1.28804i
$484$	−4.57449	−	7.92325i	−0.207931	−	0.360148i
$485$		0			0
$486$		−	24.7074i		−	1.12075i
$487$	1.51802	−	2.62929i	0.0687882	−	0.119145i	−0.829580	−	0.558388i	$-0.811420\pi$
$487$	1.51802	−	2.62929i	0.0687882	−	0.119145i	0.898368	+	0.439243i	$0.144753\pi$
$488$	−5.14838	+	8.91725i	−0.233056	+	0.403665i
$489$			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	$0.755950\pi$
$492$	2.22982	+	3.86217i	0.100528	+	0.174120i
$493$			0.0279884i			0.00126053i
$494$	5.03414	−	8.60992i	0.226497	−	0.387379i
$495$		0			0
$496$	−12.8369	+	7.41139i	−0.576394	+	0.332781i
$497$	−33.6646	+	19.4362i	−1.51006	+	0.871835i
$498$	29.8789	+	17.2506i	1.33890	+	0.773016i
$499$		−	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
$502$	14.4413			0.644546
$503$	−10.9358	−	6.31380i	−0.487604	−	0.281518i	0.235976	−	0.971759i	$-0.424171\pi$
$503$	−10.9358	−	6.31380i	−0.487604	−	0.281518i	−0.723580	+	0.690241i	$0.757505\pi$
$504$	13.4557	+	23.3059i	0.599363	+	1.03813i
$505$		0			0
$506$	25.5058			1.13387
$507$	−26.0893	−	15.4468i	−1.15866	−	0.686019i
$508$		−	5.85945i		−	0.259971i
$509$	20.9168	−	12.0763i	0.927120	−	0.535273i	0.0412201	−	0.999150i	$-0.486876\pi$
$509$	20.9168	−	12.0763i	0.927120	−	0.535273i	0.885899	+	0.463877i	$0.153542\pi$
$510$		0			0
$511$	−8.46601	+	14.6636i	−0.374514	+	0.648678i
$512$	24.2750			1.07281
$513$	1.48269	−	2.56810i	0.0654625	−	0.113384i
$514$	5.86238	+	3.38465i	0.258578	+	0.149290i
$515$		0			0
$516$	−0.676260	+	1.17132i	−0.0297707	+	0.0515644i
$517$	−12.0274	+	6.94402i	−0.528964	+	0.305398i
$518$	−19.1103	−	33.0999i	−0.839656	−	1.45433i
$519$	−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	$0.682410\pi$
$522$	−0.0367861	−	0.0637154i	−0.00161008	−	0.00278875i
$523$	−32.0712	+	18.5163i	−1.40238	+	0.809662i	−0.994636	−	0.103436i	$-0.967016\pi$
$523$	−32.0712	+	18.5163i	−1.40238	+	0.809662i	−0.407739	+	0.913098i	$0.633683\pi$
$524$	−2.70732	+	4.68922i	−0.118270	+	0.204850i
$525$		0			0
$526$	−7.24573	−	4.18332i	−0.315929	−	0.182402i
$527$	3.09229	−	5.35600i	0.134702	−	0.233311i
$528$	33.9865			1.47907
$529$	−3.92277	+	6.79444i	−0.170555	+	0.295410i
$530$		0			0
$531$	0.362145	−	0.209084i	0.0157157	−	0.00907348i
$532$			4.18348i			0.181377i
$533$	−13.4559	−	0.0738376i	−0.582840	−	0.00319826i
$534$	45.9519			1.98854
$535$		0			0
$536$	9.80545	+	16.9835i	0.423531	+	0.733577i
$537$	37.6312	+	21.7264i	1.62391	+	0.937562i
$538$	−1.73438			−0.0747744
$539$	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	$0.942334\pi$
$542$	10.5305	+	6.07981i	0.452326	+	0.261150i
$543$	36.5379	−	21.0952i	1.56799	−	0.905281i
$544$	−2.76409	+	1.59585i	−0.118509	+	0.0684215i
$545$		0			0
$546$	−36.9245	−	0.202618i	−1.58022	−	0.00867126i
$547$		−	22.7842i		−	0.974181i	−0.873351	−	0.487091i	$-0.838058\pi$
$547$		−	22.7842i		−	0.974181i	0.873351	−	0.487091i	$-0.161942\pi$
$548$	0.970090	+	1.68025i	0.0414402	+	0.0717765i
$549$	4.09843	+	7.09870i	0.174917	+	0.302965i
$550$		0			0
$551$		−	0.0560816i		−	0.00238915i
$552$	13.9106	−	24.0938i	0.592074	−	1.02550i
$553$	−21.5699	+	37.3601i	−0.917245	+	1.58871i
$554$		−	21.3735i		−	0.908071i
$555$		0			0
$556$	−0.515915	−	0.893592i	−0.0218797	−	0.0378967i
$557$	14.0764	+	24.3810i	0.596435	+	1.03306i	0.993343	+	0.115197i	$0.0367499\pi$
$557$	14.0764	+	24.3810i	0.596435	+	1.03306i	−0.396908	+	0.917858i	$0.629917\pi$
$558$			16.2572i			0.688222i
$559$	−2.02106	−	3.54536i	−0.0854816	−	0.149953i
$560$		0			0
$561$	−12.2805	+	7.09017i	−0.518484	+	0.299347i
$562$	11.3393	−	6.54676i	0.478321	−	0.276159i
$563$	15.7013	+	9.06514i	0.661731	+	0.382050i	0.792936	−	0.609305i	$-0.208551\pi$
$563$	15.7013	+	9.06514i	0.661731	+	0.382050i	−0.131206	+	0.991355i	$0.541885\pi$
$564$			3.08939i			0.130087i
$565$		0			0
$566$	1.39258	+	0.804007i	0.0585346	+	0.0337950i
$567$	−37.3253			−1.56752
$568$	28.6535	+	16.5431i	1.20227	+	0.694133i
$569$	−20.2992	−	35.1593i	−0.850988	−	1.47395i	−0.880317	−	0.474385i	$-0.842670\pi$
$569$	−20.2992	−	35.1593i	−0.850988	−	1.47395i	0.0293292	−	0.999570i	$-0.490663\pi$
$570$		0			0
$571$	−24.7159			−1.03433			−0.517164	−	0.855886i	$-0.673012\pi$
$571$	−24.7159			−1.03433			−0.517164	+	0.855886i	$0.673012\pi$
$572$	5.00891	−	8.56677i	0.209433	−	0.358195i
$573$		−	63.7551i		−	2.66341i
$574$	−14.1923	+	8.19393i	−0.592375	+	0.342008i
$575$		0			0
$576$	10.8124	−	18.7276i	0.450516	−	0.780317i
$577$	−23.0691			−0.960379			−0.480189	−	0.877165i	$-0.659432\pi$
$577$	−23.0691			−0.960379			−0.480189	+	0.877165i	$0.659432\pi$
$578$	9.58607	−	16.6036i	0.398728	−	0.690617i
$579$	−43.9654	−	25.3834i	−1.82714	−	1.05490i
$580$		0			0
$581$	21.8327	−	37.8153i	0.905771	−	1.56884i
$582$	−29.9763	+	17.3068i	−1.24256	+	0.717392i
$583$	−11.9237	−	20.6525i	−0.493831	−	0.855341i
$584$	14.4116			0.596358
$585$		0			0
$586$	22.8602			0.944345
$587$	−10.1762	−	17.6256i	−0.420015	−	0.727487i	0.575926	−	0.817502i	$-0.304642\pi$
$587$	−10.1762	−	17.6256i	−0.420015	−	0.727487i	−0.995940	+	0.0900152i	$0.971308\pi$
$588$	6.16925	−	3.56182i	0.254416	−	0.146887i
$589$	−6.19615	+	10.7321i	−0.255308	+	0.442206i
$590$		0			0
$591$	3.42701	+	1.97859i	0.140968	+	0.0813881i
$592$	−11.8060	+	20.4486i	−0.485223	+	0.840432i
$593$	−10.3834			−0.426395			−0.213198	−	0.977009i	$-0.568388\pi$
$593$	−10.3834			−0.426395			−0.213198	+	0.977009i	$0.568388\pi$
$594$	−4.28339	+	7.41904i	−0.175750	+	0.304407i
$595$		0			0
$596$	−2.44836	+	1.41356i	−0.100289	+	0.0579017i
$597$		−	59.0652i		−	2.41738i
$598$	8.47825	+	14.8726i	0.346701	+	0.608187i
$599$	31.5965			1.29100			0.645499	−	0.763761i	$-0.276649\pi$
$599$	31.5965			1.29100			0.645499	+	0.763761i	$0.276649\pi$
$600$		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	$0.480478\pi$
$602$	−4.30423	−	2.48505i	−0.175428	−	0.101283i
$603$	15.6115			0.635750
$604$	2.16962	+	1.25263i	0.0882806	+	0.0509688i
$605$		0			0
$606$			11.5332i			0.468505i
$607$	−1.88395	−	1.08770i	−0.0764673	−	0.0441484i	0.461279	−	0.887255i	$-0.347391\pi$
$607$	−1.88395	−	1.08770i	−0.0764673	−	0.0441484i	−0.537746	+	0.843107i	$0.680724\pi$
$608$	5.53854	−	3.19768i	0.224617	−	0.129683i
$609$	−0.179812	+	0.103814i	−0.00728634	+	0.00420677i
$610$		0			0
$611$	−8.04707	−	4.70504i	−0.325550	−	0.190346i
$612$			1.41465i			0.0571837i
$613$	7.38100	+	12.7843i	0.298116	+	0.516352i	0.975705	−	0.219089i	$-0.0703085\pi$
$613$	7.38100	+	12.7843i	0.298116	+	0.516352i	−0.677589	+	0.735441i	$0.736975\pi$
$614$	8.72336	+	15.1093i	0.352046	+	0.609762i
$615$		0			0
$616$		−	59.2622i		−	2.38774i
$617$	−10.1486	+	17.5779i	−0.408567	+	0.707659i	−0.994729	−	0.102535i	$-0.967305\pi$
$617$	−10.1486	+	17.5779i	−0.408567	+	0.707659i	0.586162	+	0.810194i	$0.300638\pi$
$618$	−25.4642	+	44.1053i	−1.02432	+	1.77418i
$619$			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
$622$	−1.68379	−	2.91641i	−0.0675138	−	0.116937i
$623$		−	58.1577i		−	2.33004i
$624$	11.2973	+	19.8178i	0.452252	+	0.793345i
$625$		0			0
$626$	−17.3080	+	9.99276i	−0.691766	+	0.399391i
$627$	24.6070	−	14.2069i	0.982711	−	0.567368i
$628$	4.45519	+	2.57221i	0.177782	+	0.102642i
$629$		−	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	$0.660499\pi$
$632$	36.7183			1.46058
$633$	−0.677652	−	0.391243i	−0.0269342	−	0.0155505i
$634$	−1.08903	−	1.88625i	−0.0432507	−	0.0749124i
$635$		0			0
$636$	−5.30487			−0.210352
$637$	−0.117945	+	21.4938i	−0.00467314	+	0.851617i
$638$			0.162015i			0.00641425i
$639$	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	$0.246850\pi$
$642$	25.9766			1.02521
$643$	−4.98022	+	8.62599i	−0.196401	+	0.340176i	−0.947359	−	0.320174i	$-0.896259\pi$
$643$	−4.98022	+	8.62599i	−0.196401	+	0.340176i	0.750958	+	0.660350i	$0.229592\pi$
$644$	−6.21878	−	3.59042i	−0.245054	−	0.141482i
$645$		0			0
$646$	1.56546	−	2.71146i	0.0615923	−	0.106681i
$647$	31.4162	−	18.1381i	1.23510	−	0.713084i	0.267009	−	0.963694i	$-0.413965\pi$
$647$	31.4162	−	18.1381i	1.23510	−	0.713084i	0.968088	+	0.250610i	$0.0806313\pi$
$648$	15.8847	+	27.5131i	0.624009	+	1.08081i
$649$	−0.920861			−0.0361470
$650$		0			0
$651$	45.8796			1.79816
$652$	−1.73723	−	3.00898i	−0.0680353	−	0.117841i
$653$	−11.9125	+	6.87769i	−0.466172	+	0.269145i	−0.714636	−	0.699497i	$-0.753408\pi$
$653$	−11.9125	+	6.87769i	−0.466172	+	0.269145i	0.248464	+	0.968641i	$0.420074\pi$
$654$	−10.4910	+	18.1709i	−0.410231	+	0.710540i
$655$		0			0
$656$	8.76776	+	5.06207i	0.342324	+	0.197641i
$657$	5.73629	−	9.93555i	0.223794	−	0.387623i
$658$	−11.3526			−0.442570
$659$	−1.29092	+	2.23593i	−0.0502869	+	0.0870995i	−0.890073	−	0.455818i	$-0.849347\pi$
$659$	−1.29092	+	2.23593i	−0.0502869	+	0.0870995i	0.839786	+	0.542917i	$0.182680\pi$
$660$		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	$0.494074\pi$
$662$		−	8.81151i		−	0.342469i
$663$	−8.21643	−	4.80406i	−0.319100	−	0.186574i
$664$	−37.1656			−1.44231
$665$		0			0
$666$	12.9485	+	22.4274i	0.501743	+	0.869045i
$667$	0.0833657	+	0.0481312i	0.00322793	+	0.00186365i
$668$	−5.37460			−0.207949
$669$	−24.8368	−	14.3395i	−0.960246	−	0.554398i
$670$		0			0
$671$		−	18.0506i		−	0.696834i
$672$	−20.5051	−	11.8386i	−0.791002	−	0.456685i
$673$	37.5181	−	21.6611i	1.44622	−	0.834974i	0.447964	−	0.894052i	$-0.352149\pi$
$673$	37.5181	−	21.6611i	1.44622	−	0.834974i	0.998253	+	0.0590774i	$0.0188159\pi$
$674$	−4.60770	+	2.66025i	−0.177482	+	0.102469i
$675$		0			0
$676$	6.66033	+	0.0730977i	0.256167	+	0.00281145i
$677$		−	41.3625i		−	1.58969i	−0.606813	−	0.794845i	$-0.707552\pi$
$677$		−	41.3625i		−	1.58969i	0.606813	−	0.794845i	$-0.292448\pi$
$678$	−10.0641	−	17.4315i	−0.386508	−	0.669451i
$679$	21.9039	+	37.9386i	0.840594	+	1.45595i
$680$		0			0
$681$		−	17.8003i		−	0.682110i
$682$	17.9002	−	31.0041i	0.685435	−	1.18721i
$683$	1.31344	−	2.27495i	0.0502574	−	0.0870484i	−0.839802	−	0.542892i	$-0.817329\pi$
$683$	1.31344	−	2.27495i	0.0502574	−	0.0870484i	0.890060	+	0.455844i	$0.150662\pi$
$684$		−	2.83459i		−	0.108383i
$685$		0			0
$686$	−2.28028	−	3.94957i	−0.0870617	−	0.150795i
$687$	16.7931	+	29.0865i	0.640696	+	1.10972i
$688$			3.07045i			0.117060i
$689$	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	$0.427172\pi$
$692$	1.97831	−	1.14218i	0.0752039	−	0.0434190i
$693$	−40.8560	−	23.5882i	−1.55199	−	0.896043i
$694$			32.5744i			1.23651i
$695$		0			0
$696$	0.153046	+	0.0883613i	0.00580120	+	0.00334933i
$697$	−4.22414			−0.160001
$698$	24.8976	+	14.3747i	0.942390	+	0.544089i
$699$	−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	$0.135971\pi$
$702$	−5.74991	−	0.0315519i	−0.217017	−	0.00119085i
$703$			19.7404i			0.744522i
$704$	−41.2406	+	23.8103i	−1.55431	+	0.897383i
$705$		0			0
$706$	3.49884	−	6.06016i	0.131680	−	0.228077i
$707$	14.5967			0.548964
$708$	−0.102423	+	0.177401i	−0.00384928	+	0.00666715i
$709$	33.6624	+	19.4350i	1.26422	+	0.729896i	0.973887	−	0.227031i	$-0.0729019\pi$
$709$	33.6624	+	19.4350i	1.26422	+	0.729896i	0.290329	+	0.956927i	$0.406235\pi$
$710$		0			0
$711$	14.6150	−	25.3140i	0.548107	−	0.949349i
$712$	−42.8689	+	24.7504i	−1.60658	+	0.927560i
$713$	−10.6355	−	18.4213i	−0.398304	−	0.689882i
$714$	−11.5915			−0.433801
$715$		0			0
$716$	−9.54600			−0.356751
$717$	−23.2226	−	40.2227i	−0.867263	−	1.50214i
$718$	26.1517	−	15.0987i	0.975973	−	0.563478i
$719$	−3.30830	+	5.73015i	−0.123379	+	0.213698i	−0.921098	−	0.389331i	$-0.872706\pi$
$719$	−3.30830	+	5.73015i	−0.123379	+	0.213698i	0.797719	+	0.603029i	$0.206040\pi$
$720$		0			0
$721$	55.8205	+	32.2280i	2.07887	+	1.20023i
$722$	8.45024	−	14.6362i	0.314485	−	0.544705i
$723$	−54.2629			−2.01806
$724$	−4.63433	+	8.02690i	−0.172234	+	0.298317i
$725$		0			0
$726$	−43.9893	+	25.3973i	−1.63260	+	0.942581i
$727$			18.3735i			0.681435i	0.940166	+	0.340717i	$0.110670\pi$
$727$			18.3735i			0.681435i	−0.940166	+	0.340717i	$0.889330\pi$
$728$	34.5562	−	19.6990i	1.28074	−	0.730094i
$729$	16.1420			0.597853
$730$		0			0
$731$	−0.640548	−	1.10946i	−0.0236915	−	0.0410349i
$732$	−3.47739	−	2.00767i	−0.128528	−	0.0742057i
$733$	0.791131			0.0292211			0.0146105	−	0.999893i	$-0.495349\pi$
$733$	0.791131			0.0292211			0.0146105	+	0.999893i	$0.495349\pi$
$734$	27.5198	+	15.8886i	1.01578	+	0.586458i
$735$		0			0
$736$			10.9774i			0.404634i
$737$	−29.7727	−	17.1893i	−1.09669	−	0.633175i
$738$	9.61623	−	5.55193i	0.353978	−	0.204369i
$739$	27.0073	−	15.5926i	0.993478	−	0.573585i	0.0871658	−	0.996194i	$-0.472219\pi$
$739$	27.0073	−	15.5926i	0.993478	−	0.573585i	0.906312	+	0.422609i	$0.138886\pi$
$740$		0			0
$741$	16.4636	+	9.62612i	0.604806	+	0.353624i
$742$		−	19.4938i		−	0.715639i
$743$	−2.78152	−	4.81773i	−0.102044	−	0.176745i	0.810483	−	0.585763i	$-0.199205\pi$
$743$	−2.78152	−	4.81773i	−0.102044	−	0.176745i	−0.912527	+	0.409017i	$0.865872\pi$
$744$	−19.5251	−	33.8185i	−0.715826	−	1.23985i
$745$		0			0
$746$			16.1053i			0.589658i
$747$	−14.7931	+	25.6224i	−0.541251	+	0.937474i
$748$	1.55762	−	2.69787i	0.0569521	−	0.0986439i
$749$		−	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	$-0.388732\pi$
$752$	3.50672	+	6.07381i	0.127877	+	0.221489i
$753$			27.6142i			1.00632i
$754$	−0.0944723	+	0.0538546i	−0.00344048	+	0.00196127i
$755$		0			0
$756$	2.08873	−	1.20593i	0.0759665	−	0.0438593i
$757$	43.3399	−	25.0223i	1.57522	−	0.909451i	0.579703	−	0.814828i	$-0.303169\pi$
$757$	43.3399	−	25.0223i	1.57522	−	0.909451i	0.995513	−	0.0946237i	$-0.0301648\pi$
$758$	−27.4609	−	15.8545i	−0.997424	−	0.575863i
$759$			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	$0.364839\pi$
$762$	−32.5313			−1.17848
$763$	22.9975	+	13.2776i	0.832566	+	0.480682i
$764$	7.00307	+	12.1297i	0.253362	+	0.438836i
$765$		0			0
$766$	11.7092			0.423072
$767$	−0.306098	−	0.536961i	−0.0110526	−	0.0193885i
$768$			26.6361i			0.961148i
$769$	34.0897	−	19.6817i	1.22930	−	0.709739i	0.262420	−	0.964954i	$-0.415479\pi$
$769$	34.0897	−	19.6817i	1.22930	−	0.709739i	0.966884	+	0.255215i	$0.0821461\pi$
$770$		0			0
$771$	−6.47201	+	11.2099i	−0.233084	+	0.403713i
$772$	11.1528			0.401399
$773$	−24.3902	+	42.2452i	−0.877256	+	1.51945i	−0.0229167	+	0.999737i	$0.507295\pi$
$773$	−24.3902	+	42.2452i	−0.877256	+	1.51945i	−0.854340	+	0.519715i	$0.826038\pi$
$774$	2.91641	+	1.68379i	0.104828	+	0.0605225i
$775$		0			0
$776$	18.6434	−	32.2914i	0.669260	−	1.15919i
$777$	63.2926	−	36.5420i	2.27061	−	1.31094i
$778$	3.43420	+	5.94822i	0.123122	+	0.213254i
$779$	8.46410			0.303258
$780$		0			0
$781$	−58.0013			−2.07545
$782$	2.68707	+	4.65415i	0.0960895	+	0.166432i
$783$	−0.0280005	+	0.0161661i	−0.00100066	+	0.000577728i
$784$	8.08592	−	14.0052i	0.288783	−	0.500187i
$785$		0			0
$786$	26.0342	+	15.0309i	0.928611	+	0.536134i
$787$	−19.9304	+	34.5204i	−0.710442	+	1.23052i	0.254250	+	0.967139i	$0.418171\pi$
$787$	−19.9304	+	34.5204i	−0.710442	+	1.23052i	−0.964692	+	0.263382i	$0.915162\pi$
$788$	−0.869338			−0.0309689
$789$	7.99922	−	13.8551i	0.284780	−	0.493253i
$790$		0			0
$791$	−22.0616	+	12.7373i	−0.784420	+	0.452885i
$792$			40.1541i			1.42682i
$793$	10.5254	−	6.00008i	0.373768	−	0.213069i
$794$	20.4490			0.725709
$795$		0			0
$796$	6.48793	+	11.2374i	0.229958	+	0.398300i
$797$	22.7001	+	13.1059i	0.804079	+	0.464235i	0.844895	−	0.534932i	$-0.179663\pi$
$797$	22.7001	+	13.1059i	0.804079	+	0.464235i	−0.0408167	+	0.999167i	$0.512996\pi$
$798$	23.2264			0.822206
$799$	−2.53420	−	1.46312i	−0.0896537	−	0.0517616i
$800$		0			0
$801$			39.4057i			1.39233i
$802$	14.6591	+	8.46343i	0.517630	+	0.298854i
$803$	−21.8794	+	12.6321i	−0.772106	+	0.445775i
$804$	−6.62293	+	3.82375i	−0.233573	+	0.134853i
$805$		0			0
$806$	24.0288	+	0.131855i	0.846379	+	0.00464440i
$807$		−	3.31643i		−	0.116744i
$808$	−6.21196	−	10.7594i	−0.218536	−	0.378515i
$809$	11.1068	+	19.2376i	0.390495	+	0.676357i	0.992515	−	0.122124i	$-0.0389705\pi$
$809$	11.1068	+	19.2376i	0.390495	+	0.676357i	−0.602020	+	0.798481i	$0.705637\pi$
$810$		0			0
$811$			19.0950i			0.670515i	0.942127	+	0.335257i	$0.108823\pi$
$811$			19.0950i			0.670515i	−0.942127	+	0.335257i	$0.891177\pi$
$812$	0.0228066	−	0.0395023i	0.000800356	−	0.00138626i
$813$	−11.6256	+	20.1362i	−0.407729	+	0.706207i
$814$		−	57.0284i		−	1.99885i
$815$		0			0
$816$	3.58052	+	6.20164i	0.125343	+	0.217101i
$817$	1.28349	+	2.22308i	0.0449038	+	0.0777757i
$818$			35.8894i			1.25484i
$819$	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	$0.536604\pi$
$822$	9.32861	−	5.38588i	0.325373	−	0.187854i
$823$	−3.53286	−	2.03970i	−0.123148	−	0.0710995i	0.437161	−	0.899383i	$-0.355984\pi$
$823$	−3.53286	−	2.03970i	−0.123148	−	0.0710995i	−0.560309	+	0.828284i	$0.689317\pi$
$824$		−	54.8616i		−	1.91119i
$825$		0			0
$826$	−0.651896	−	0.376372i	−0.0226824	−	0.0130957i
$827$	−54.8780			−1.90830			−0.954148	−	0.299337i	$-0.903235\pi$
$827$	−54.8780			−1.90830			−0.954148	+	0.299337i	$0.903235\pi$
$828$	4.21364	+	2.43275i	0.146434	+	0.0845438i
$829$	−4.07475	−	7.05768i	−0.141522	−	0.245123i	0.786548	−	0.617529i	$-0.211866\pi$
$829$	−4.07475	−	7.05768i	−0.141522	−	0.245123i	−0.928070	+	0.372406i	$0.878533\pi$
$830$		0			0
$831$	40.8697			1.41775
$832$	−27.5925	−	16.1330i	−0.956597	−	0.559313i
$833$			6.74745i			0.233785i
$834$	−4.96116	+	2.86433i	−0.171791	+	0.0991836i
$835$		0			0
$836$	−3.12107	+	5.40585i	−0.107944	+	0.186965i
$837$	7.14441			0.246947
$838$	−4.24935	+	7.36008i	−0.146791	+	0.254250i
$839$	18.9543	+	10.9433i	0.654374	+	0.377803i	0.790130	−	0.612939i	$-0.210013\pi$
$839$	18.9543	+	10.9433i	0.654374	+	0.377803i	−0.135756	+	0.990742i	$0.543346\pi$
$840$		0			0
$841$	14.4997	−	25.1142i	0.499989	−	0.866007i
$842$	−7.52204	+	4.34285i	−0.259226	+	0.149664i
$843$	12.5185	+	21.6827i	0.431160	+	0.746792i
$844$	0.171902			0.00591710
$845$		0			0
$846$	7.69213			0.264461
$847$	32.1433	+	55.6738i	1.10446	+	1.91297i
$848$	−10.4295	+	6.02147i	−0.358150	+	0.206778i
$849$	−1.53740	+	2.66285i	−0.0527633	+	0.0913888i
$850$		0			0
$851$	−29.3442	−	16.9419i	−1.00591	−	0.580761i
$852$	−6.45118	+	11.1738i	−0.221014	+	0.382807i
$853$	19.2240			0.658217			0.329108	−	0.944292i	$-0.393252\pi$
$853$	19.2240			0.658217			0.329108	+	0.944292i	$0.393252\pi$
$854$	7.37758	−	12.7783i	0.252456	−	0.437266i
$855$		0			0
$856$	−24.2337	+	13.9914i	−0.828292	+	0.478215i
$857$			27.8197i			0.950302i	0.879904	+	0.475151i	$0.157607\pi$
$857$			27.8197i			0.950302i	−0.879904	+	0.475151i	$0.842393\pi$
$858$	−47.5622	−	27.8091i	−1.62375	−	0.949388i
$859$	−45.7355			−1.56048			−0.780238	−	0.625482i	$-0.784902\pi$
$859$	−45.7355			−1.56048			−0.780238	+	0.625482i	$0.784902\pi$
$860$		0			0
$861$	−15.6682	−	27.1381i	−0.533970	−	0.924862i
$862$	31.9148	+	18.4260i	1.08702	+	0.627593i
$863$	54.8186			1.86605			0.933024	−	0.359814i	$-0.117160\pi$
$863$	54.8186			1.86605			0.933024	+	0.359814i	$0.117160\pi$
$864$	−3.19308	−	1.84352i	−0.108631	−	0.0627180i
$865$		0			0
$866$		−	1.46378i		−	0.0497413i
$867$	31.7488	+	18.3302i	1.07825	+	0.622526i
$868$	−8.72879	+	5.03957i	−0.296274	+	0.171054i
$869$	−55.7447	+	32.1842i	−1.89101	+	1.09177i
$870$		0			0
$871$	0.126618	−	23.0745i	0.00429030	−	0.781849i
$872$		−	22.6024i		−	0.765415i
$873$	−14.8413	−	25.7060i	−0.502304	−	0.870015i
$874$	−5.38421	−	9.32572i	−0.182124	−	0.315447i
$875$		0			0
$876$			5.61999i			0.189882i
$877$	−13.6897	+	23.7113i	−0.462269	+	0.800673i	−0.999074	−	0.0430336i	$-0.986298\pi$
$877$	−13.6897	+	23.7113i	−0.462269	+	0.800673i	0.536805	+	0.843706i	$0.319631\pi$
$878$	−10.0954	+	17.4858i	−0.340704	+	0.590116i
$879$			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	$-0.363692\pi$
$882$	−8.86841	−	15.3605i	−0.298615	−	0.517216i
$883$		−	17.3592i		−	0.584183i	−0.956390	−	0.292092i	$-0.905649\pi$
$883$		−	17.3592i		−	0.584183i	0.956390	−	0.292092i	$-0.0943512\pi$
$884$	2.09091	+	0.0114736i	0.0703248	+	0.000385899i
$885$		0			0
$886$	4.81610	−	2.78058i	0.161800	−	0.0934153i
$887$	−26.9704	+	15.5714i	−0.905577	+	0.522835i	−0.879005	−	0.476812i	$-0.841792\pi$
$887$	−26.9704	+	15.5714i	−0.905577	+	0.522835i	−0.0265716	+	0.999647i	$0.508459\pi$
$888$	−53.8714	−	31.1026i	−1.80780	−	1.04374i
$889$			41.1722i			1.38087i
$890$		0			0
$891$	−48.2313	−	27.8464i	−1.61581	−	0.932888i
$892$	6.30042			0.210954
$893$	5.07790	+	2.93173i	0.169925	+	0.0981065i
$894$	7.84799	+	13.5931i	0.262476	+	0.454622i
$895$		0			0
$896$	−18.6224			−0.622132
$897$	−28.4390	+	16.2118i	−0.949550	+	0.541298i
$898$		−	16.8953i		−	0.563804i
$899$	0.117014	−	0.0675578i	0.00390262	−	0.00225318i
$900$		0			0
$901$	2.51236	−	4.35154i	0.0836990	−	0.144971i
$902$	−24.4521			−0.814167
$903$	4.75184	−	8.23042i	0.158131	−	0.273891i
$904$	18.7777	+	10.8413i	0.624536	+	0.360576i
$905$		0			0
$906$	6.95452	−	12.0456i	0.231048	−	0.400188i
$907$	−15.2470	+	8.80284i	−0.506267	+	0.292294i	−0.731298	−	0.682058i	$-0.761085\pi$
$907$	−15.2470	+	8.80284i	−0.506267	+	0.292294i	0.225031	+	0.974352i	$0.427752\pi$
$908$	1.95525	+	3.38659i	0.0648872	+	0.112388i
$909$	−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	$0.189098\pi$
$912$	−7.17445	−	12.4265i	−0.237570	−	0.411483i
$913$	56.4238	−	32.5763i	1.86735	−	1.07812i
$914$	−24.4636	+	42.3722i	−0.809184	+	1.40155i
$915$		0			0
$916$	−6.38992	−	3.68922i	−0.211129	−	0.121895i
$917$	19.0234	−	32.9495i	0.628207	−	1.08809i
$918$	−1.80504			−0.0595752
$919$	−3.80778	+	6.59527i	−0.125607	+	0.217558i	−0.921970	−	0.387261i	$-0.873421\pi$
$919$	−3.80778	+	6.59527i	−0.125607	+	0.217558i	0.796363	+	0.604819i	$0.206755\pi$
$920$		0			0
$921$	−28.8915	+	16.6805i	−0.952008	+	0.549642i
$922$			9.19522i			0.302828i
$923$	−19.2799	−	33.8209i	−0.634604	−	1.11323i
$924$	23.1100			0.760264
$925$		0			0
$926$	−14.2113	−	24.6146i	−0.467011	−	0.808887i
$927$	−37.8222	−	21.8366i	−1.24224	−	0.717209i
$928$	−0.0697297			−0.00228899
$929$	−12.2317	−	7.06196i	−0.401308	−	0.231695i	0.285740	−	0.958307i	$-0.407761\pi$
$929$	−12.2317	−	7.06196i	−0.401308	−	0.231695i	−0.687048	+	0.726612i	$0.741094\pi$
$930$		0			0
$931$		−	13.5202i		−	0.443106i
$932$	4.21364	+	2.43275i	0.138022	+	0.0796873i
$933$	5.57666	−	3.21969i	0.182572	−	0.105408i
$934$	−23.9033	+	13.8006i	−0.782140	+	0.451569i
$935$		0			0
$936$	−23.4142	+	13.3474i	−0.765316	+	0.436274i
$937$		−	23.9317i		−	0.781815i	−0.920430	−	0.390908i	$-0.872161\pi$
$937$		−	23.9317i		−	0.781815i	0.920430	−	0.390908i	$-0.127839\pi$
$938$	−14.0511	−	24.3373i	−0.458786	−	0.794640i
$939$	−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	$-0.135638\pi$
$942$	14.2807	−	24.7349i	0.465291	−	0.805908i
$943$	−7.26420	+	12.5820i	−0.236555	+	0.409725i
$944$			0.465033i			0.0151355i
$945$		0			0
$946$	−3.70792	−	6.42231i	−0.120555	−	0.208807i
$947$	−20.7111	−	35.8727i	−0.673021	−	1.16571i	−0.977043	−	0.213042i	$-0.931663\pi$
$947$	−20.7111	−	35.8727i	−0.673021	−	1.16571i	0.304022	−	0.952665i	$-0.401670\pi$
$948$			14.3187i			0.465051i
$949$	−14.6386	−	8.55906i	−0.475190	−	0.277839i
$950$		0			0
$951$	3.60682	−	2.08240i	0.116959	−	0.0675264i
$952$	10.8138	−	6.24335i	0.350477	−	0.202348i
$953$	−21.0466	−	12.1513i	−0.681767	−	0.393619i	0.118753	−	0.992924i	$-0.462110\pi$
$953$	−21.0466	−	12.1513i	−0.681767	−	0.393619i	−0.800521	+	0.599305i	$0.795444\pi$
$954$			13.2083i			0.427636i
$955$		0			0
$956$	8.83639	+	5.10169i	0.285789	+	0.165001i
$957$	−0.309801			−0.0100144
$958$	21.8067	+	12.5901i	0.704543	+	0.406768i
$959$	−6.81647	−	11.8065i	−0.220115	−	0.381251i
$960$		0			0
$961$	1.14359			0.0368901
$962$	33.2537	−	18.9565i	1.07214	−	0.611182i
$963$			22.2760i			0.717834i
$964$	10.3238	−	5.96043i	0.332506	−	0.191972i
$965$		0			0
$966$	−19.9338	+	34.5263i	−0.641358	+	1.11086i
$967$	−23.6784			−0.761445			−0.380722	−	0.924689i	$-0.624325\pi$
$967$	−23.6784			−0.761445			−0.380722	+	0.924689i	$0.624325\pi$
$968$	27.3587	−	47.3866i	0.879341	−	1.52306i
$969$	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	$0.0788719\pi$
$972$	−8.98852	+	5.18953i	−0.288307	+	0.166454i
$973$	3.62515	+	6.27895i	0.116217	+	0.201294i
$974$	3.70303			0.118653
$975$		0			0
$976$	−9.11550			−0.291780
$977$	12.4997	+	21.6501i	0.399901	+	0.692649i	0.993713	−	0.111955i	$-0.0357112\pi$
$977$	12.4997	+	21.6501i	0.399901	+	0.692649i	−0.593812	+	0.804604i	$0.702378\pi$
$978$	−16.7056	+	9.64500i	−0.534187	+	0.308413i
$979$	43.3883	−	75.1507i	1.38669	−	2.40183i
$980$		0			0
$981$	−15.5824	−	8.99648i	−0.497506	−	0.287235i
$982$	−6.50582	+	11.2684i	−0.207609	+	0.359589i
$983$	27.3418			0.872068			0.436034	−	0.899930i	$-0.356383\pi$
$983$	27.3418			0.872068			0.436034	+	0.899930i	$0.356383\pi$
$984$	−13.3359	+	23.0985i	−0.425134	+	0.736353i
$985$		0			0
$986$	−0.0295635	+	0.0170685i	−0.000941495	+	0.000543573i
$987$		−	21.7080i		−	0.690975i
$988$	−4.18964	−	0.0229901i	−0.133290	−	0.000731414i
$989$	−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	$0.915519\pi$
$992$	13.3438	+	7.70406i	0.423667	+	0.244604i
$993$	16.8491			0.534690
$994$	−41.0602	−	23.7061i	−1.30235	−	0.751913i
$995$		0			0
$996$		−	14.4932i		−	0.459234i
$997$	29.9309	+	17.2806i	0.947920	+	0.547282i	0.892434	−	0.451178i	$-0.148996\pi$
$997$	29.9309	+	17.2806i	0.947920	+	0.547282i	0.0554858	+	0.998459i	$0.482329\pi$
$998$	35.8230	−	20.6824i	1.13396	−	0.654691i
$999$	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.m.c.49.3		8
5.2	odd	4		325.2.n.d.101.2		8
5.3	odd	4		65.2.m.a.36.3	✓	8
5.4	even	2		325.2.m.b.49.2		8
13.4	even	6		325.2.m.b.199.2		8
15.8	even	4		585.2.bu.c.361.2		8
20.3	even	4		1040.2.da.b.881.4		8
65.2	even	12		4225.2.a.bi.1.2		4
65.3	odd	12		845.2.c.g.506.6		8
65.4	even	6	inner	325.2.m.c.199.3		8
65.8	even	4		845.2.e.n.146.3		8
65.17	odd	12		325.2.n.d.251.2		8
65.18	even	4		845.2.e.m.146.2		8
65.23	odd	12		845.2.c.g.506.3		8
65.28	even	12		845.2.a.m.1.3		4
65.33	even	12		845.2.e.n.191.3		8
65.37	even	12		4225.2.a.bl.1.3		4
65.38	odd	4		845.2.m.g.361.2		8
65.43	odd	12		65.2.m.a.56.3	yes	8
65.48	odd	12		845.2.m.g.316.2		8
65.58	even	12		845.2.e.m.191.2		8
65.63	even	12		845.2.a.l.1.2		4
195.128	odd	12		7605.2.a.cj.1.3		4
195.158	odd	12		7605.2.a.cf.1.2		4
195.173	even	12		585.2.bu.c.316.2		8
260.43	even	12		1040.2.da.b.641.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	5.3	odd	4
65.2.m.a.56.3	yes	8	65.43	odd	12
325.2.m.b.49.2		8	5.4	even	2
325.2.m.b.199.2		8	13.4	even	6
325.2.m.c.49.3		8	1.1	even	1	trivial
325.2.m.c.199.3		8	65.4	even	6	inner
325.2.n.d.101.2		8	5.2	odd	4
325.2.n.d.251.2		8	65.17	odd	12
585.2.bu.c.316.2		8	195.173	even	12
585.2.bu.c.361.2		8	15.8	even	4
845.2.a.l.1.2		4	65.63	even	12
845.2.a.m.1.3		4	65.28	even	12
845.2.c.g.506.3		8	65.23	odd	12
845.2.c.g.506.6		8	65.3	odd	12
845.2.e.m.146.2		8	65.18	even	4
845.2.e.m.191.2		8	65.58	even	12
845.2.e.n.146.3		8	65.8	even	4
845.2.e.n.191.3		8	65.33	even	12
845.2.m.g.316.2		8	65.48	odd	12
845.2.m.g.361.2		8	65.38	odd	4
1040.2.da.b.641.4		8	260.43	even	12
1040.2.da.b.881.4		8	20.3	even	4
4225.2.a.bi.1.2		4	65.2	even	12
4225.2.a.bl.1.3		4	65.37	even	12
7605.2.a.cf.1.2		4	195.158	odd	12
7605.2.a.cj.1.3		4	195.128	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.609843 + 1.05628i) q^{2} +(-2.01978 + 1.16612i) q^{3} +(0.256182 - 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-1.80010 + 3.11786i) q^{7} +3.06430 q^{8} +(1.21969 - 2.11256i) q^{9} +O(q^{10})\)	\(q+(0.609843 + 1.05628i) q^{2} +(-2.01978 + 1.16612i) q^{3} +(0.256182 - 0.443720i) q^{4} +(-2.46350 - 1.42231i) q^{6} +(-1.80010 + 3.11786i) q^{7} +3.06430 q^{8} +(1.21969 - 2.11256i) q^{9} +(-4.65213 + 2.68591i) q^{11} +1.19496i q^{12} +(-3.11256 - 1.81988i) q^{13} -4.39111 q^{14} +(1.35638 + 2.34932i) q^{16} +(-0.980215 - 0.565928i) q^{17} +2.97527 q^{18} +(1.96410 + 1.13397i) q^{19} -8.39654i q^{21} +(-5.67414 - 3.27597i) q^{22} +(-3.37133 + 1.94644i) q^{23} +(-6.18922 + 3.57335i) q^{24} +(0.0241312 - 4.39758i) q^{26} -1.30752i q^{27} +(0.922305 + 1.59748i) q^{28} +(-0.0123639 - 0.0214150i) q^{29} +5.46410i q^{31} +(1.40994 - 2.44209i) q^{32} +(6.26420 - 10.8499i) q^{33} -1.38051i q^{34} +(-0.624924 - 1.08240i) q^{36} +(4.35203 + 7.53794i) q^{37} +2.76619i q^{38} +(8.40891 + 0.0461428i) q^{39} +(3.23205 - 1.86603i) q^{41} +(8.86910 - 5.12058i) q^{42} +(0.980215 + 0.565928i) q^{43} +2.75232i q^{44} +(-4.11196 - 2.37404i) q^{46} +2.58535 q^{47} +(-5.47918 - 3.16341i) q^{48} +(-2.98070 - 5.16273i) q^{49} +2.63977 q^{51} +(-1.60490 + 0.914884i) q^{52} +4.43937i q^{53} +(1.38111 - 0.797382i) q^{54} +(-5.51603 + 9.55405i) q^{56} -5.28942 q^{57} +(0.0150801 - 0.0261196i) q^{58} +(0.148458 + 0.0857123i) q^{59} +(-1.68012 + 2.91005i) q^{61} +(-5.77162 + 3.33225i) q^{62} +(4.39111 + 7.60563i) q^{63} +8.86488 q^{64} +15.2807 q^{66} +(3.19990 + 5.54239i) q^{67} +(-0.502227 + 0.289961i) q^{68} +(4.53957 - 7.86276i) q^{69} +(9.35076 + 5.39866i) q^{71} +(3.73748 - 6.47351i) q^{72} +4.70308 q^{73} +(-5.30812 + 9.19393i) q^{74} +(1.00633 - 0.581008i) q^{76} -19.3396i q^{77} +(5.07938 + 8.91030i) q^{78} +11.9826 q^{79} +(5.18379 + 8.97859i) q^{81} +(3.94209 + 2.27597i) q^{82} -12.1286 q^{83} +(-3.72572 - 2.15104i) q^{84} +1.38051i q^{86} +(0.0499450 + 0.0288357i) q^{87} +(-14.2555 + 8.23042i) q^{88} +(-13.9898 + 8.07702i) q^{89} +(11.2771 - 6.42856i) q^{91} +1.99457i q^{92} +(-6.37182 - 11.0363i) q^{93} +(1.57666 + 2.73086i) q^{94} +6.57666i q^{96} +(6.08408 - 10.5379i) q^{97} +(3.63553 - 6.29692i) q^{98} +13.1039i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9	\( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9} - 8 q^{13} - 4 q^{14} - 2 q^{16} - 18 q^{17} + 40 q^{18} - 12 q^{19} - 6 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{26} - 8 q^{28} + 8 q^{29} + 4 q^{32} + 18 q^{33} + 20 q^{36} + 2 q^{37} + 12 q^{41} + 42 q^{42} + 18 q^{43} - 42 q^{46} + 16 q^{47} + 6 q^{48} - 12 q^{49} - 8 q^{51} - 16 q^{52} - 18 q^{54} + 12 q^{56} + 28 q^{57} - 22 q^{58} + 12 q^{59} - 28 q^{61} - 12 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 12 q^{68} + 16 q^{69} - 12 q^{72} + 16 q^{73} - 10 q^{74} + 54 q^{76} - 18 q^{78} + 16 q^{79} + 8 q^{81} + 6 q^{82} - 24 q^{83} + 30 q^{84} - 54 q^{87} - 42 q^{88} - 24 q^{89} + 28 q^{91} - 8 q^{93} - 32 q^{94} + 2 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 6 * q^3 - 2 * q^4 - 18 * q^6 - 10 * q^7 - 12 * q^8 + 4 * q^9 - 8 * q^13 - 4 * q^14 - 2 * q^16 - 18 * q^17 + 40 * q^18 - 12 * q^19 - 6 * q^22 - 6 * q^23 + 12 * q^24 + 10 * q^26 - 8 * q^28 + 8 * q^29 + 4 * q^32 + 18 * q^33 + 20 * q^36 + 2 * q^37 + 12 * q^41 + 42 * q^42 + 18 * q^43 - 42 * q^46 + 16 * q^47 + 6 * q^48 - 12 * q^49 - 8 * q^51 - 16 * q^52 - 18 * q^54 + 12 * q^56 + 28 * q^57 - 22 * q^58 + 12 * q^59 - 28 * q^61 - 12 * q^62 + 4 * q^63 + 8 * q^64 + 12 * q^66 + 30 * q^67 - 12 * q^68 + 16 * q^69 - 12 * q^72 + 16 * q^73 - 10 * q^74 + 54 * q^76 - 18 * q^78 + 16 * q^79 + 8 * q^81 + 6 * q^82 - 24 * q^83 + 30 * q^84 - 54 * q^87 - 42 * q^88 - 24 * q^89 + 28 * q^91 - 8 * q^93 - 32 * q^94 + 2 * q^97 - 24 * q^98

Introduction

L-functions

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