LMFDB - Embedded newform 845.2.e.m.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
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:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.2
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.m.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})$	\(q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +(0.609843 - 1.05628i) q^{10} +(-2.68591 + 4.65213i) q^{11} -1.19496 q^{12} +4.39111 q^{14} +(1.16612 - 2.01978i) q^{15} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +2.97527 q^{18} +(-1.13397 - 1.96410i) q^{19} +(-0.256182 - 0.443720i) q^{20} +8.39654 q^{21} +(-3.27597 - 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} +(3.57335 - 6.18922i) q^{24} +1.00000 q^{25} -1.30752 q^{27} +(0.922305 - 1.59748i) q^{28} +(0.0123639 - 0.0214150i) q^{29} +(1.42231 + 2.46350i) q^{30} +5.46410 q^{31} +(-1.40994 - 2.44209i) q^{32} +(-6.26420 - 10.8499i) q^{33} -1.38051 q^{34} +(1.80010 + 3.11786i) q^{35} +(0.624924 - 1.08240i) q^{36} +(4.35203 - 7.53794i) q^{37} +2.76619 q^{38} +3.06430 q^{40} +(-1.86603 + 3.23205i) q^{41} +(-5.12058 + 8.86910i) q^{42} +(0.565928 + 0.980215i) q^{43} -2.75232 q^{44} +(1.21969 + 2.11256i) q^{45} +(2.37404 + 4.11196i) q^{46} +2.58535 q^{47} +(3.16341 + 5.47918i) q^{48} +(-2.98070 + 5.16273i) q^{49} +(-0.609843 + 1.05628i) q^{50} -2.63977 q^{51} -4.43937 q^{53} +(0.797382 - 1.38111i) q^{54} +(2.68591 - 4.65213i) q^{55} +(5.51603 + 9.55405i) q^{56} +5.28942 q^{57} +(0.0150801 + 0.0261196i) q^{58} +(0.0857123 + 0.148458i) q^{59} +1.19496 q^{60} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} +(-4.39111 + 7.60563i) q^{63} +8.86488 q^{64} +15.2807 q^{66} +(-3.19990 + 5.54239i) q^{67} +(-0.289961 + 0.502227i) q^{68} +(4.53957 + 7.86276i) q^{69} -4.39111 q^{70} +(5.39866 + 9.35076i) q^{71} +(3.73748 + 6.47351i) q^{72} -4.70308 q^{73} +(5.30812 + 9.19393i) q^{74} +(-1.16612 + 2.01978i) q^{75} +(0.581008 - 1.00633i) q^{76} +19.3396 q^{77} -11.9826 q^{79} +(-1.35638 + 2.34932i) q^{80} +(5.18379 - 8.97859i) q^{81} +(-2.27597 - 3.94209i) q^{82} -12.1286 q^{83} +(2.15104 + 3.72572i) q^{84} +(-0.565928 - 0.980215i) q^{85} -1.38051 q^{86} +(0.0288357 + 0.0499450i) q^{87} +(8.23042 - 14.2555i) q^{88} +(8.07702 - 13.9898i) q^{89} -2.97527 q^{90} +1.99457 q^{92} +(-6.37182 + 11.0363i) q^{93} +(-1.57666 + 2.73086i) q^{94} +(1.13397 + 1.96410i) q^{95} +6.57666 q^{96} +(-6.08408 - 10.5379i) q^{97} +(-3.63553 - 6.29692i) q^{98} +13.1039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 40 q^{18} - 16 q^{19} + 2 q^{20} + 8 q^{21} - 12 q^{22} + 10 q^{23} + 24 q^{24} + 8 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} - 4 q^{30} + 16 q^{31} - 4 q^{32} - 18 q^{33} - 8 q^{34} + 10 q^{35} - 20 q^{36} + 2 q^{37} + 16 q^{38} - 12 q^{40} - 8 q^{41} + 4 q^{42} + 2 q^{43} + 24 q^{44} + 4 q^{45} - 16 q^{46} + 16 q^{47} + 28 q^{48} - 12 q^{49} - 2 q^{50} + 8 q^{51} - 24 q^{53} + 16 q^{54} - 12 q^{56} - 28 q^{57} - 22 q^{58} - 12 q^{59} + 20 q^{60} - 28 q^{61} - 4 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} - 14 q^{68} + 16 q^{69} - 4 q^{70} - 4 q^{71} - 12 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 20 q^{76} + 36 q^{77} - 16 q^{79} + 2 q^{80} + 8 q^{81} - 4 q^{82} - 24 q^{83} + 28 q^{84} - 2 q^{85} - 8 q^{86} + 22 q^{87} + 18 q^{88} + 12 q^{89} - 40 q^{90} + 44 q^{92} - 8 q^{93} + 32 q^{94} + 16 q^{95} + 8 q^{96} - 2 q^{97} + 24 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9 + 2 * q^10 - 20 * q^12 + 4 * q^14 - 2 * q^15 - 2 * q^16 + 2 * q^17 + 40 * q^18 - 16 * q^19 + 2 * q^20 + 8 * q^21 - 12 * q^22 + 10 * q^23 + 24 * q^24 + 8 * q^25 - 4 * q^27 - 8 * q^28 - 8 * q^29 - 4 * q^30 + 16 * q^31 - 4 * q^32 - 18 * q^33 - 8 * q^34 + 10 * q^35 - 20 * q^36 + 2 * q^37 + 16 * q^38 - 12 * q^40 - 8 * q^41 + 4 * q^42 + 2 * q^43 + 24 * q^44 + 4 * q^45 - 16 * q^46 + 16 * q^47 + 28 * q^48 - 12 * q^49 - 2 * q^50 + 8 * q^51 - 24 * q^53 + 16 * q^54 - 12 * q^56 - 28 * q^57 - 22 * q^58 - 12 * q^59 + 20 * q^60 - 28 * q^61 - 4 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 - 14 * q^68 + 16 * q^69 - 4 * q^70 - 4 * q^71 - 12 * q^72 - 16 * q^73 + 10 * q^74 + 2 * q^75 - 20 * q^76 + 36 * q^77 - 16 * q^79 + 2 * q^80 + 8 * q^81 - 4 * q^82 - 24 * q^83 + 28 * q^84 - 2 * q^85 - 8 * q^86 + 22 * q^87 + 18 * q^88 + 12 * q^89 - 40 * q^90 + 44 * q^92 - 8 * q^93 + 32 * q^94 + 16 * q^95 + 8 * q^96 - 2 * q^97 + 24 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.975252\pi$
$2$	−0.609843	+	1.05628i	−0.431224	+	0.746903i	0.565755	+	0.824574i	$0.308585\pi$
$3$	−1.16612	+	2.01978i	−0.673262	+	1.16612i	0.303712	+	0.952764i	$0.401774\pi$
$3$	−1.16612	+	2.01978i	−0.673262	+	1.16612i	−0.976974	+	0.213359i	$0.931559\pi$
$4$	0.256182	+	0.443720i	0.128091	+	0.221860i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.42231	−	2.46350i	−0.580654	−	1.00572i
$7$	−1.80010	−	3.11786i	−0.680373	−	1.17844i	−0.974867	−	0.222787i	$-0.928484\pi$
$7$	−1.80010	−	3.11786i	−0.680373	−	1.17844i	0.294494	−	0.955653i	$-0.404849\pi$
$8$	−3.06430			−1.08339
$9$	−1.21969	−	2.11256i	−0.406562	−	0.704187i
$10$	0.609843	−	1.05628i	0.192849	−	0.334025i
$11$	−2.68591	+	4.65213i	−0.809832	+	1.40267i	0.103149	+	0.994666i	$0.467108\pi$
$11$	−2.68591	+	4.65213i	−0.809832	+	1.40267i	−0.912980	+	0.408004i	$0.866225\pi$
$12$	−1.19496			−0.344955
$13$		0			0
$13$		0			0
$14$	4.39111			1.17357
$15$	1.16612	−	2.01978i	0.301092	−	0.521506i
$16$	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	$0.789505\pi$
$18$	2.97527			0.701278
$19$	−1.13397	−	1.96410i	−0.260152	−	0.450596i	0.706130	−	0.708082i	$-0.250439\pi$
$19$	−1.13397	−	1.96410i	−0.260152	−	0.450596i	−0.966282	+	0.257486i	$0.917106\pi$
$20$	−0.256182	−	0.443720i	−0.0572840	−	0.0992188i
$21$	8.39654			1.83228
$22$	−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	$0.0336387\pi$
$24$	3.57335	−	6.18922i	0.729407	−	1.26337i
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.30752			−0.251632
$28$	0.922305	−	1.59748i	0.174299	−	0.301895i
$29$	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	$0.165936\pi$
$30$	1.42231	+	2.46350i	0.259676	+	0.449772i
$31$	5.46410			0.981382			0.490691	−	0.871334i	$-0.336744\pi$
$31$	5.46410			0.981382			0.490691	+	0.871334i	$0.336744\pi$
$32$	−1.40994	−	2.44209i	−0.249245	−	0.431705i
$33$	−6.26420	−	10.8499i	−1.09046	−	1.88873i
$34$	−1.38051			−0.236755
$35$	1.80010	+	3.11786i	0.304272	+	0.527015i
$36$	0.624924	−	1.08240i	0.104154	−	0.180400i
$37$	4.35203	−	7.53794i	0.715470	−	1.23923i	−0.247309	−	0.968937i	$-0.579546\pi$
$37$	4.35203	−	7.53794i	0.715470	−	1.23923i	0.962778	−	0.270293i	$-0.0871205\pi$
$38$	2.76619			0.448735
$39$		0			0
$40$	3.06430			0.484508
$41$	−1.86603	+	3.23205i	−0.291424	+	0.504762i	−0.974147	−	0.225916i	$-0.927462\pi$
$41$	−1.86603	+	3.23205i	−0.291424	+	0.504762i	0.682723	+	0.730678i	$0.260796\pi$
$42$	−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	$0.805828\pi$
$44$	−2.75232			−0.414929
$45$	1.21969	+	2.11256i	0.181820	+	0.314922i
$46$	2.37404	+	4.11196i	0.350034	+	0.606276i
$47$	2.58535			0.377113			0.188556	−	0.982062i	$-0.439619\pi$
$47$	2.58535			0.377113			0.188556	+	0.982062i	$0.439619\pi$
$48$	3.16341	+	5.47918i	0.456598	+	0.790852i
$49$	−2.98070	+	5.16273i	−0.425815	+	0.737533i
$50$	−0.609843	+	1.05628i	−0.0862449	+	0.149381i
$51$	−2.63977			−0.369641
$52$		0			0
$53$	−4.43937			−0.609795			−0.304897	−	0.952385i	$-0.598622\pi$
$53$	−4.43937			−0.609795			−0.304897	+	0.952385i	$0.598622\pi$
$54$	0.797382	−	1.38111i	0.108510	−	0.187945i
$55$	2.68591	−	4.65213i	0.362168	−	0.627293i
$56$	5.51603	+	9.55405i	0.737111	+	1.27671i
$57$	5.28942			0.700600
$58$	0.0150801	+	0.0261196i	0.00198012	+	0.00342967i
$59$	0.0857123	+	0.148458i	0.0111588	+	0.0193276i	0.871551	−	0.490305i	$-0.163115\pi$
$59$	0.0857123	+	0.148458i	0.0111588	+	0.0193276i	−0.860392	+	0.509633i	$0.829781\pi$
$60$	1.19496			0.154269
$61$	−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
$63$	−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	$-0.961180\pi$
$67$	−3.19990	+	5.54239i	−0.390930	+	0.677111i	0.601642	+	0.798766i	$0.294513\pi$
$68$	−0.289961	+	0.502227i	−0.0351629	+	0.0609040i
$69$	4.53957	+	7.86276i	0.546500	+	0.946566i
$70$	−4.39111			−0.524838
$71$	5.39866	+	9.35076i	0.640703	+	1.10973i	0.985276	+	0.170971i	$0.0546905\pi$
$71$	5.39866	+	9.35076i	0.640703	+	1.10973i	−0.344573	+	0.938760i	$0.611976\pi$
$72$	3.73748	+	6.47351i	0.440467	+	0.762911i
$73$	−4.70308			−0.550454			−0.275227	−	0.961379i	$-0.588753\pi$
$73$	−4.70308			−0.550454			−0.275227	+	0.961379i	$0.588753\pi$
$74$	5.30812	+	9.19393i	0.617056	+	1.06877i
$75$	−1.16612	+	2.01978i	−0.134652	+	0.233225i
$76$	0.581008	−	1.00633i	0.0666462	−	0.115435i
$77$	19.3396			2.20395
$78$		0			0
$79$	−11.9826			−1.34815			−0.674075	−	0.738663i	$-0.735457\pi$
$79$	−11.9826			−1.34815			−0.674075	+	0.738663i	$0.735457\pi$
$80$	−1.35638	+	2.34932i	−0.151648	+	0.262661i
$81$	5.18379	−	8.97859i	0.575976	−	0.997621i
$82$	−2.27597	−	3.94209i	−0.251338	−	0.435331i
$83$	−12.1286			−1.33129			−0.665643	−	0.746270i	$-0.731843\pi$
$83$	−12.1286			−1.33129			−0.665643	+	0.746270i	$0.731843\pi$
$84$	2.15104	+	3.72572i	0.234698	+	0.406509i
$85$	−0.565928	−	0.980215i	−0.0613835	−	0.106319i
$86$	−1.38051			−0.148864
$87$	0.0288357	+	0.0499450i	0.00309152	+	0.00535466i
$88$	8.23042	−	14.2555i	0.877366	−	1.51964i
$89$	8.07702	−	13.9898i	0.856162	−	1.48292i	−0.0194001	−	0.999812i	$-0.506176\pi$
$89$	8.07702	−	13.9898i	0.856162	−	1.48292i	0.875562	−	0.483105i	$-0.160491\pi$
$90$	−2.97527			−0.313621
$91$		0			0
$92$	1.99457			0.207948
$93$	−6.37182	+	11.0363i	−0.660727	+	1.14441i
$94$	−1.57666	+	2.73086i	−0.162620	+	0.281666i
$95$	1.13397	+	1.96410i	0.116343	+	0.201513i
$96$	6.57666			0.671228
$97$	−6.08408	−	10.5379i	−0.617745	−	1.06997i	−0.989896	−	0.141794i	$-0.954713\pi$
$97$	−6.08408	−	10.5379i	−0.617745	−	1.06997i	0.372151	−	0.928172i	$-0.378620\pi$
$98$	−3.63553	−	6.29692i	−0.367244	−	0.636085i
$99$	13.1039			1.31699
$100$	0.256182	+	0.443720i	0.0256182	+	0.0443720i
$101$	2.02721	−	3.51122i	0.201714	−	0.349380i	−0.747366	−	0.664412i	$-0.768682\pi$
$101$	2.02721	−	3.51122i	0.201714	−	0.349380i	0.949081	+	0.315032i	$0.102015\pi$
$102$	1.60984	−	2.78833i	0.159398	−	0.276086i
$103$	−17.9035			−1.76408			−0.882041	−	0.471173i	$-0.843831\pi$
$103$	−17.9035			−1.76408			−0.882041	+	0.471173i	$0.843831\pi$
$104$		0			0
$105$	−8.39654			−0.819419
$106$	2.70732	−	4.68922i	0.262958	−	0.455457i
$107$	4.56593	−	7.90842i	0.441405	−	0.764536i	−0.556389	−	0.830922i	$-0.687814\pi$
$107$	4.56593	−	7.90842i	0.441405	−	0.764536i	0.997794	+	0.0663862i	$0.0211469\pi$
$108$	−0.334963	−	0.580172i	−0.0322318	−	0.0558271i
$109$	7.37605			0.706498			0.353249	−	0.935529i	$-0.385077\pi$
$109$	7.37605			0.706498			0.353249	+	0.935529i	$0.385077\pi$
$110$	3.27597	+	5.67414i	0.312351	+	0.541008i
$111$	10.1500	+	17.5803i	0.963396	+	1.66865i
$112$	−9.76645			−0.922843
$113$	−3.53794	−	6.12789i	−0.332821	−	0.576463i	0.650243	−	0.759727i	$-0.274667\pi$
$113$	−3.53794	−	6.12789i	−0.332821	−	0.576463i	−0.983064	+	0.183263i	$0.941334\pi$
$114$	−3.22572	+	5.58710i	−0.302116	+	0.523280i
$115$	−1.94644	+	3.37133i	−0.181506	+	0.314378i
$116$	0.0126697			0.00117635
$117$		0			0
$118$	−0.209084			−0.0192478
$119$	2.03745	−	3.52897i	0.186773	−	0.323500i
$120$	−3.57335	+	6.18922i	−0.326201	+	0.564996i
$121$	−8.92820	−	15.4641i	−0.811655	−	1.40583i
$122$	4.09843			0.371055
$123$	−4.35203	−	7.53794i	−0.392409	−	0.679673i
$124$	1.39980	+	2.42453i	0.125706	+	0.217729i
$125$	−1.00000			−0.0894427
$126$	−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	$-0.00272499\pi$
$128$	−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
$133$	−4.08253	+	7.07115i	−0.354000	+	0.613146i
$134$	−3.90288	−	6.75998i	−0.337157	−	0.583974i
$135$	1.30752			0.112533
$136$	−1.73417	−	3.00367i	−0.148704	−	0.257563i
$137$	−1.89336	−	3.27940i	−0.161761	−	0.280178i	0.773739	−	0.633504i	$-0.218384\pi$
$137$	−1.89336	−	3.27940i	−0.161761	−	0.280178i	−0.935500	+	0.353326i	$0.885051\pi$
$138$	−11.0737			−0.942656
$139$	−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	$0.860552\pi$
$140$	−0.922305	+	1.59748i	−0.0779490	+	0.135012i
$141$	−3.01484	+	5.22186i	−0.253895	+	0.439760i
$142$	−13.1694			−1.10515
$143$		0			0
$144$	−6.61742			−0.551452
$145$	−0.0123639	+	0.0214150i	−0.00102677	+	0.00177842i
$146$	2.86814	−	4.96777i	0.237369	−	0.411136i
$147$	−6.95174	−	12.0408i	−0.573370	−	0.993105i
$148$	4.45965			0.366581
$149$	2.75890	+	4.77855i	0.226018	+	0.391474i	0.956624	−	0.291324i	$-0.0940959\pi$
$149$	2.75890	+	4.77855i	0.226018	+	0.391474i	−0.730607	+	0.682799i	$0.760763\pi$
$150$	−1.42231	−	2.46350i	−0.116131	−	0.201144i
$151$	−4.88961			−0.397911			−0.198956	−	0.980009i	$-0.563755\pi$
$151$	−4.88961			−0.397911			−0.198956	+	0.980009i	$0.563755\pi$
$152$	3.47484	+	6.01859i	0.281846	+	0.488172i
$153$	1.38051	−	2.39111i	0.111608	−	0.193310i
$154$	−11.7941	+	20.4280i	−0.950397	+	1.64614i
$155$	−5.46410			−0.438887
$156$		0			0
$157$	10.0405			0.801323			0.400661	−	0.916226i	$-0.368780\pi$
$157$	10.0405			0.801323			0.400661	+	0.916226i	$0.368780\pi$
$158$	7.30752	−	12.6570i	0.581355	−	1.00694i
$159$	5.17686	−	8.96658i	0.410551	−	0.711096i
$160$	1.40994	+	2.44209i	0.111466	+	0.193064i
$161$	−14.0151			−1.10454
$162$	6.32260	+	10.9511i	0.496750	+	0.860397i
$163$	−3.39062	−	5.87273i	−0.265574	−	0.459988i	0.702140	−	0.712039i	$-0.252228\pi$
$163$	−3.39062	−	5.87273i	−0.265574	−	0.459988i	−0.967714	+	0.252051i	$0.918895\pi$
$164$	−1.91217			−0.149315
$165$	6.26420	+	10.8499i	0.487667	+	0.844664i
$166$	7.39654	−	12.8112i	0.574083	−	0.994341i
$167$	−5.24490	+	9.08444i	−0.405863	+	0.702975i	−0.994421	−	0.105479i	$-0.966362\pi$
$167$	−5.24490	+	9.08444i	−0.405863	+	0.702975i	0.588559	+	0.808455i	$0.299696\pi$
$168$	−25.7295			−1.98507
$169$		0			0
$170$	1.38051			0.105880
$171$	−2.76619	+	4.79118i	−0.211536	+	0.366391i
$172$	−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	$0.779123\pi$
$174$	−0.0703412			−0.00533255
$175$	−1.80010	−	3.11786i	−0.136075	−	0.235688i
$176$	7.28621	+	12.6201i	0.549219	+	0.951275i
$177$	−0.399804			−0.0300511
$178$	9.85143	+	17.0632i	0.738396	+	1.27894i
$179$	−9.31564	+	16.1352i	−0.696284	+	1.20600i	0.273462	+	0.961883i	$0.411831\pi$
$179$	−9.31564	+	16.1352i	−0.696284	+	1.20600i	−0.969746	+	0.244116i	$0.921502\pi$
$180$	−0.624924	+	1.08240i	−0.0465791	+	0.0806773i
$181$	18.0900			1.34462			0.672310	−	0.740270i	$-0.265302\pi$
$181$	18.0900			1.34462			0.672310	+	0.740270i	$0.265302\pi$
$182$		0			0
$183$	7.83690			0.579320
$184$	−5.96446	+	10.3307i	−0.439706	+	0.761593i
$185$	−4.35203	+	7.53794i	−0.319968	+	0.554200i
$186$	−7.77162	−	13.4608i	−0.569843	−	0.986997i
$187$	−6.08012			−0.444622
$188$	0.662321	+	1.14717i	0.0483047	+	0.0836662i
$189$	2.35366	+	4.07666i	0.171204	+	0.296533i
$190$	−2.76619			−0.200680
$191$	−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
$193$	−10.8837	+	18.8511i	−0.783425	+	1.35693i	0.146510	+	0.989209i	$0.453196\pi$
$193$	−10.8837	+	18.8511i	−0.783425	+	1.35693i	−0.929935	+	0.367723i	$0.880137\pi$
$194$	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	$-0.814082\pi$
$197$	0.848360	−	1.46940i	0.0604432	−	0.104691i	0.894664	+	0.446741i	$0.147415\pi$
$198$	−7.99131	+	13.8413i	−0.567917	+	0.983662i
$199$	−12.6627	−	21.9325i	−0.897637	−	1.55475i	−0.830506	−	0.557009i	$-0.811949\pi$
$199$	−12.6627	−	21.9325i	−0.897637	−	1.55475i	−0.0671309	−	0.997744i	$-0.521385\pi$
$200$	−3.06430			−0.216679
$201$	−7.46296	−	12.9262i	−0.526397	−	0.911746i
$202$	2.47256	+	4.28259i	0.173968	+	0.301322i
$203$	−0.0890252			−0.00624834
$204$	−0.676260	−	1.17132i	−0.0473477	−	0.0820086i
$205$	1.86603	−	3.23205i	0.130329	−	0.225736i
$206$	10.9183	−	18.9111i	0.760715	−	1.31760i
$207$	−9.49617			−0.660030
$208$		0			0
$209$	12.1830			0.842716
$210$	5.12058	−	8.86910i	0.353353	−	0.612026i
$211$	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
$213$	−25.1820			−1.72544
$214$	5.56900	+	9.64579i	0.380689	+	0.659373i
$215$	−0.565928	−	0.980215i	−0.0385959	−	0.0668501i
$216$	4.00663			0.272616
$217$	−9.83592	−	17.0363i	−0.667706	−	1.15650i
$218$	−4.49824	+	7.79118i	−0.304659	+	0.527685i
$219$	5.48438	−	9.49922i	0.370600	−	0.641898i
$220$	2.75232			0.185562
$221$		0			0
$222$	−24.7597			−1.66176
$223$	6.14838	−	10.6493i	0.411726	−	0.713130i	−0.583353	−	0.812219i	$-0.698259\pi$
$223$	6.14838	−	10.6493i	0.411726	−	0.713130i	0.995079	+	0.0990887i	$0.0315928\pi$
$224$	−5.07606	+	8.79200i	−0.339159	+	0.587440i
$225$	−1.21969	−	2.11256i	−0.0813125	−	0.140837i
$226$	8.63036			0.574083
$227$	3.81613	+	6.60974i	0.253286	+	0.438704i	0.964428	−	0.264344i	$-0.0851554\pi$
$227$	3.81613	+	6.60974i	0.253286	+	0.438704i	−0.711143	+	0.703048i	$0.751822\pi$
$228$	1.35505	+	2.34702i	0.0897406	+	0.155435i
$229$	−14.4008			−0.951631			−0.475815	−	0.879545i	$-0.657847\pi$
$229$	−14.4008			−0.951631			−0.475815	+	0.879545i	$0.657847\pi$
$230$	−2.37404	−	4.11196i	−0.156540	−	0.271135i
$231$	−22.5523	+	39.0618i	−1.48384	+	2.57008i
$232$	−0.0378868	+	0.0656218i	−0.00248739	+	0.00430828i
$233$	9.49617			0.622115			0.311057	−	0.950391i	$-0.399317\pi$
$233$	9.49617			0.622115			0.311057	+	0.950391i	$0.399317\pi$
$234$		0			0
$235$	−2.58535			−0.168650
$236$	−0.0439159	+	0.0760645i	−0.00285868	+	0.00495138i
$237$	13.9732	−	24.2023i	0.907657	−	1.57211i
$238$	2.48505	+	4.30423i	0.161082	+	0.279002i
$239$	−19.9143			−1.28815			−0.644076	−	0.764962i	$-0.722758\pi$
$239$	−19.9143			−1.28815			−0.644076	+	0.764962i	$0.722758\pi$
$240$	−3.16341	−	5.47918i	−0.204197	−	0.353680i
$241$	−11.6332	−	20.1493i	−0.749360	−	1.29793i	−0.948130	−	0.317883i	$-0.897028\pi$
$241$	−11.6332	−	20.1493i	−0.749360	−	1.29793i	0.198770	−	0.980046i	$-0.436305\pi$
$242$	21.7792			1.40002
$243$	10.1286	+	17.5432i	0.649750	+	1.12540i
$244$	0.860832	−	1.49100i	0.0551091	−	0.0954518i
$245$	2.98070	−	5.16273i	0.190430	−	0.329835i
$246$	10.6162			0.676866
$247$		0			0
$248$	−16.7436			−1.06322
$249$	14.1434	−	24.4972i	0.896304	−	1.55244i
$250$	0.609843	−	1.05628i	0.0385699	−	0.0668050i
$251$	−5.92008	−	10.2539i	−0.373672	−	0.647219i	0.616455	−	0.787390i	$-0.288568\pi$
$251$	−5.92008	−	10.2539i	−0.373672	−	0.647219i	−0.990127	+	0.140171i	$0.955235\pi$
$252$	−4.49969			−0.283454
$253$	10.4559	+	18.1101i	0.657357	+	1.13858i
$254$	6.97424	+	12.0797i	0.437603	+	0.757950i
$255$	2.63977			0.165309
$256$	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	$0.111288\pi$
$258$	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
$263$	−3.42983	+	5.94065i	−0.211493	+	0.366316i	−0.952182	−	0.305532i	$-0.901166\pi$
$263$	−3.42983	+	5.94065i	−0.211493	+	0.366316i	0.740689	+	0.671848i	$0.234499\pi$
$264$	19.1954	+	33.2474i	1.18139	+	2.04623i
$265$	4.43937			0.272709
$266$	−4.97941	−	8.62459i	−0.305307	−	0.528807i
$267$	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	$-0.152864\pi$
$269$	0.710994	+	1.23148i	0.0433501	+	0.0750845i	−0.843536	+	0.537072i	$0.819530\pi$
$270$	−0.797382	+	1.38111i	−0.0485271	+	0.0840514i
$271$	4.98473	−	8.63381i	0.302801	−	0.524467i	−0.673968	−	0.738760i	$-0.735412\pi$
$271$	4.98473	−	8.63381i	0.302801	−	0.524467i	0.976769	+	0.214294i	$0.0687449\pi$
$272$	3.07045			0.186173
$273$		0			0
$274$	4.61862			0.279021
$275$	−2.68591	+	4.65213i	−0.161966	+	0.280534i
$276$	−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	$0.656856\pi$
$278$	2.45628			0.147318
$279$	−6.66449	−	11.5432i	−0.398993	−	0.691076i
$280$	−5.51603	−	9.55405i	−0.329646	−	0.570964i
$281$	10.7352			0.640406			0.320203	−	0.947349i	$-0.396249\pi$
$281$	10.7352			0.640406			0.320203	+	0.947349i	$0.396249\pi$
$282$	−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	$0.179143\pi$
$284$	−2.76608	+	4.79099i	−0.164137	+	0.284293i
$285$	−5.28942			−0.313318
$286$		0			0
$287$	13.4361			0.793109
$288$	−3.43937	+	5.95717i	−0.202667	+	0.351030i
$289$	7.85945	−	13.6130i	0.462321	−	0.800763i
$290$	−0.0150801	−	0.0261196i	−0.000885536	−	0.00153379i
$291$	28.3792			1.66362
$292$	−1.20485	−	2.08685i	−0.0705082	−	0.122124i
$293$	−9.37133	−	16.2316i	−0.547479	−	0.948261i	−0.998446	−	0.0557207i	$-0.982254\pi$
$293$	−9.37133	−	16.2316i	−0.547479	−	0.948261i	0.450968	−	0.892540i	$-0.351079\pi$
$294$	16.9579			0.989004
$295$	−0.0857123	−	0.148458i	−0.00499036	−	0.00864356i
$296$	−13.3359	+	23.0985i	−0.775134	+	1.34257i
$297$	3.51187	−	6.08275i	0.203780	−	0.352957i
$298$	−6.72998			−0.389857
$299$		0			0
$300$	−1.19496			−0.0689910
$301$	2.03745	−	3.52897i	0.117437	−	0.203406i
$302$	2.98190	−	5.16480i	0.171589	−	0.297201i
$303$	4.72794	+	8.18904i	0.271613	+	0.470448i
$304$	−6.15239			−0.352864
$305$	1.68012	+	2.91005i	0.0962032	+	0.166629i
$306$	1.68379	+	2.91641i	0.0962558	+	0.166720i
$307$	14.3043			0.816387			0.408194	−	0.912895i	$-0.366159\pi$
$307$	14.3043			0.816387			0.408194	+	0.912895i	$0.366159\pi$
$308$	4.95445	+	8.58137i	0.282306	+	0.488969i
$309$	20.8777	−	36.1612i	1.18769	−	2.05714i
$310$	3.33225	−	5.77162i	0.189259	−	0.327806i
$311$	2.76102			0.156563			0.0782815	−	0.996931i	$-0.475057\pi$
$311$	2.76102			0.156563			0.0782815	+	0.996931i	$0.475057\pi$
$312$		0			0
$313$	−16.3858			−0.926179			−0.463090	−	0.886311i	$-0.653259\pi$
$313$	−16.3858			−0.926179			−0.463090	+	0.886311i	$0.653259\pi$
$314$	−6.12316	+	10.6056i	−0.345550	+	0.598510i
$315$	4.39111	−	7.60563i	0.247411	−	0.428529i
$316$	−3.06973	−	5.31693i	−0.172686	−	0.299101i
$317$	1.78575			0.100297			0.0501487	−	0.998742i	$-0.484030\pi$
$317$	1.78575			0.100297			0.0501487	+	0.998742i	$0.484030\pi$
$318$	6.31414	+	10.9364i	0.354080	+	0.613284i
$319$	0.0664168	+	0.115037i	0.00371863	+	0.00644085i
$320$	−8.86488			−0.495562
$321$	10.6489	+	18.4444i	0.594362	+	1.02946i
$322$	8.54702	−	14.8039i	0.476307	−	0.824987i
$323$	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
$328$	5.71806	−	9.90396i	0.315727	−	0.546855i
$329$	−4.65389	−	8.06077i	−0.256577	−	0.444405i
$330$	−15.2807			−0.841176
$331$	−3.61220	−	6.25652i	−0.198545	−	0.343889i	0.749512	−	0.661991i	$-0.230288\pi$
$331$	−3.61220	−	6.25652i	−0.198545	−	0.343889i	−0.948057	+	0.318101i	$0.896955\pi$
$332$	−3.10713	−	5.38170i	−0.170526	−	0.295359i
$333$	−21.2325			−1.16353
$334$	−6.39714	−	11.0802i	−0.350036	−	0.606280i
$335$	3.19990	−	5.54239i	0.174829	−	0.302813i
$336$	11.3889	−	19.7261i	0.621315	−	1.07615i
$337$	−4.36219			−0.237624			−0.118812	−	0.992917i	$-0.537909\pi$
$337$	−4.36219			−0.237624			−0.118812	+	0.992917i	$0.537909\pi$
$338$		0			0
$339$	16.5027			0.896303
$340$	0.289961	−	0.502227i	0.0157253	−	0.0272371i
$341$	−14.6761	+	25.4197i	−0.794754	+	1.37655i
$342$	−3.37388	−	5.84374i	−0.182439	−	0.315993i
$343$	−3.73913			−0.201894
$344$	−1.73417	−	3.00367i	−0.0935002	−	0.161947i
$345$	−4.53957	−	7.86276i	−0.244402	−	0.423317i
$346$	−5.43792			−0.292344
$347$	13.3536	+	23.1291i	0.716858	+	1.24163i	0.962239	+	0.272207i	$0.0877537\pi$
$347$	13.3536	+	23.1291i	0.716858	+	1.24163i	−0.245381	+	0.969427i	$0.578913\pi$
$348$	−0.0147744	+	0.0255900i	−0.000791991	+	0.00137177i
$349$	−11.7855	+	20.4131i	−0.630865	+	1.09269i	0.356510	+	0.934292i	$0.383967\pi$
$349$	−11.7855	+	20.4131i	−0.630865	+	1.09269i	−0.987375	+	0.158399i	$0.949367\pi$
$350$	4.39111			0.234715
$351$		0			0
$352$	15.1479			0.807385
$353$	−2.86863	+	4.96862i	−0.152682	+	0.264453i	−0.932213	−	0.361911i	$-0.882124\pi$
$353$	−2.86863	+	4.96862i	−0.152682	+	0.264453i	0.779531	+	0.626364i	$0.215458\pi$
$354$	0.243818	−	0.422305i	0.0129588	−	0.0224453i
$355$	−5.39866	−	9.35076i	−0.286531	−	0.496287i
$356$	8.27675			0.438667
$357$	4.75184	+	8.23042i	0.251494	+	0.435600i
$358$	−11.3622	−	19.6799i	−0.600509	−	1.04011i
$359$	−24.7583			−1.30669			−0.653347	−	0.757059i	$-0.726636\pi$
$359$	−24.7583			−1.30669			−0.653347	+	0.757059i	$0.726636\pi$
$360$	−3.73748	−	6.47351i	−0.196983	−	0.341184i
$361$	6.92820	−	12.0000i	0.364642	−	0.631579i
$362$	−11.0321	+	19.1081i	−0.579833	+	1.00430i
$363$	41.6455			2.18582
$364$		0			0
$365$	4.70308			0.246171
$366$	−4.77928	+	8.27796i	−0.249817	+	0.432696i
$367$	−13.0268	+	22.5630i	−0.679992	+	1.17778i	0.294991	+	0.955500i	$0.404683\pi$
$367$	−13.0268	+	22.5630i	−0.679992	+	1.17778i	−0.974983	+	0.222280i	$0.928650\pi$
$368$	−5.28021	−	9.14558i	−0.275250	−	0.476747i
$369$	9.10387			0.473928
$370$	−5.30812	−	9.19393i	−0.275956	−	0.477969i
$371$	7.99131	+	13.8413i	0.414888	+	0.718607i
$372$	−6.52938			−0.338532
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	0.642926	−	0.765929i	$-0.277720\pi$
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	−0.984776	+	0.173826i	$0.944387\pi$
$374$	3.70792	−	6.42231i	0.191732	−	0.332089i
$375$	1.16612	−	2.01978i	0.0602183	−	0.104301i
$376$	−7.92229			−0.408561
$377$		0			0
$378$	−5.74146			−0.295309
$379$	−12.9989	+	22.5147i	−0.667707	+	1.15650i	0.310837	+	0.950463i	$0.399391\pi$
$379$	−12.9989	+	22.5147i	−0.667707	+	1.15650i	−0.978544	+	0.206039i	$0.933943\pi$
$380$	−0.581008	+	1.00633i	−0.0298051	+	0.0516239i
$381$	13.3359	+	23.0985i	0.683220	+	1.18337i
$382$	33.3418			1.70591
$383$	4.80010	+	8.31401i	0.245274	+	0.424826i	0.962208	−	0.272314i	$-0.0877889\pi$
$383$	4.80010	+	8.31401i	0.245274	+	0.424826i	−0.716935	+	0.697140i	$0.754456\pi$
$384$	−6.03191	−	10.4476i	−0.307815	−	0.533151i
$385$	−19.3396			−0.985637
$386$	−13.2747	−	22.9924i	−0.675664	−	1.17028i
$387$	1.38051	−	2.39111i	0.0701752	−	0.121547i
$388$	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
$393$	12.3236	−	21.3450i	0.621641	−	1.07671i
$394$	1.03473	+	1.79221i	0.0521291	+	0.0902903i
$395$	11.9826			0.602911
$396$	3.35697	+	5.81445i	0.168694	+	0.292187i
$397$	8.38291	+	14.5196i	0.420726	+	0.728719i	0.996011	−	0.0892344i	$-0.0284420\pi$
$397$	8.38291	+	14.5196i	0.420726	+	0.728719i	−0.575285	+	0.817953i	$0.695109\pi$
$398$	30.8891			1.54833
$399$	−9.52147	−	16.4917i	−0.476670	−	0.825616i
$400$	1.35638	−	2.34932i	0.0678189	−	0.117466i
$401$	6.93902	−	12.0187i	0.346518	−	0.600187i	−0.639110	−	0.769115i	$-0.720697\pi$
$401$	6.93902	−	12.0187i	0.346518	−	0.600187i	0.985628	+	0.168928i	$0.0540307\pi$
$402$	18.2050			0.907980
$403$		0			0
$404$	2.07733			0.103351
$405$	−5.18379	+	8.97859i	−0.257585	+	0.446149i
$406$	0.0542914	−	0.0940355i	0.00269444	−	0.00466690i
$407$	23.3783	+	40.4924i	1.15882	+	2.00713i
$408$	8.08903			0.400466
$409$	−14.7125	−	25.4829i	−0.727489	−	1.26005i	−0.957941	−	0.286964i	$-0.907354\pi$
$409$	−14.7125	−	25.4829i	−0.727489	−	1.26005i	0.230453	−	0.973083i	$-0.425979\pi$
$410$	2.27597	+	3.94209i	0.112402	+	0.194686i
$411$	8.83157			0.435629
$412$	−4.58655	−	7.94413i	−0.225963	−	0.391379i
$413$	0.308581	−	0.534478i	0.0151843	−	0.0262999i
$414$	5.79118	−	10.0306i	0.284621	−	0.492978i
$415$	12.1286			0.595369
$416$		0			0
$417$	4.69683			0.230005
$418$	−7.42973	+	12.8687i	−0.363400	+	0.629427i
$419$	−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	$0.221109\pi$
$420$	−2.15104	−	3.72572i	−0.104960	−	0.181796i
$421$	7.12125			0.347069			0.173534	−	0.984828i	$-0.444481\pi$
$421$	7.12125			0.347069			0.173534	+	0.984828i	$0.444481\pi$
$422$	0.204607	+	0.354389i	0.00996010	+	0.0172514i
$423$	−3.15332	−	5.46171i	−0.153320	−	0.265558i
$424$	13.6036			0.660647
$425$	0.565928	+	0.980215i	0.0274515	+	0.0475474i
$426$	15.3571	−	26.5993i	0.744054	−	1.28874i
$427$	−6.04875	+	10.4767i	−0.292720	+	0.507005i
$428$	4.67883			0.226160
$429$		0			0
$430$	1.38051			0.0665740
$431$	−15.1072	+	26.1664i	−0.727687	+	1.26039i	0.230171	+	0.973150i	$0.426071\pi$
$431$	−15.1072	+	26.1664i	−0.727687	+	1.26039i	−0.957858	+	0.287241i	$0.907262\pi$
$432$	−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	$0.842514\pi$
$434$	23.9935			1.15172
$435$	−0.0288357	−	0.0499450i	−0.00138257	−	0.00239468i
$436$	1.88961	+	3.27290i	0.0904960	+	0.156744i
$437$	−8.82884			−0.422341
$438$	6.68922	+	11.5861i	0.319623	+	0.553604i
$439$	8.27705	−	14.3363i	0.395042	−	0.684233i	−0.598064	−	0.801448i	$-0.704063\pi$
$439$	8.27705	−	14.3363i	0.395042	−	0.684233i	0.993107	+	0.117215i	$0.0373966\pi$
$440$	−8.23042	+	14.2555i	−0.392370	+	0.679605i
$441$	14.5421			0.692481
$442$		0			0
$443$	4.55949			0.216628			0.108314	−	0.994117i	$-0.465455\pi$
$443$	4.55949			0.216628			0.108314	+	0.994117i	$0.465455\pi$
$444$	−5.20050	+	9.00753i	−0.246805	+	0.427478i
$445$	−8.07702	+	13.9898i	−0.382887	+	0.663180i
$446$	7.49910	+	12.9888i	0.355093	+	0.615038i
$447$	−12.8689			−0.608676
$448$	−15.9577	−	27.6395i	−0.753929	−	1.30584i
$449$	−6.92608	−	11.9963i	−0.326862	−	0.566142i	0.655025	−	0.755607i	$-0.272658\pi$
$449$	−6.92608	−	11.9963i	−0.326862	−	0.566142i	−0.981887	+	0.189465i	$0.939325\pi$
$450$	2.97527			0.140256
$451$	−10.0239	−	17.3620i	−0.472009	−	0.817544i
$452$	1.81271	−	3.13971i	0.0852628	−	0.147680i
$453$	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	−0.169489	+	0.985532i	$0.554212\pi$
$457$	−20.0573	+	34.7402i	−0.938240	+	1.62508i	−0.768751	+	0.639548i	$0.779122\pi$
$458$	8.78222	−	15.2113i	0.410366	−	0.710775i
$459$	−0.739961	−	1.28165i	−0.0345384	−	0.0598223i
$460$	−1.99457			−0.0929972
$461$	3.76950	+	6.52897i	0.175563	+	0.304084i	0.940356	−	0.340192i	$-0.110492\pi$
$461$	3.76950	+	6.52897i	0.175563	+	0.304084i	−0.764793	+	0.644276i	$0.777159\pi$
$462$	−27.5068	−	47.6432i	−1.27973	−	2.21656i
$463$	23.3031			1.08299			0.541494	−	0.840705i	$-0.317859\pi$
$463$	23.3031			1.08299			0.541494	+	0.840705i	$0.317859\pi$
$464$	−0.0335403	−	0.0580936i	−0.00155707	−	0.00269693i
$465$	6.37182	−	11.0363i	0.295486	−	0.511797i
$466$	−5.79118	+	10.0306i	−0.268271	+	0.464659i
$467$	−22.6297			−1.04718			−0.523589	−	0.851971i	$-0.675407\pi$
$467$	−22.6297			−1.04718			−0.523589	+	0.851971i	$0.675407\pi$
$468$		0			0
$469$	23.0405			1.06391
$470$	1.57666	−	2.73086i	0.0727260	−	0.125965i
$471$	−11.7085	+	20.2797i	−0.539500	+	0.934441i
$472$	−0.262648	−	0.454919i	−0.0120893	−	0.0209394i
$473$	−6.08012			−0.279564
$474$	17.0429	+	29.5192i	0.782808	+	1.35586i
$475$	−1.13397	−	1.96410i	−0.0520303	−	0.0901192i
$476$	2.08783			0.0956956
$477$	5.41465	+	9.37844i	0.247920	+	0.429409i
$478$	12.1446	−	21.0351i	0.555482	−	0.962124i
$479$	−10.3224	+	17.8789i	−0.471643	+	0.816910i	−0.999474	−	0.0324399i	$-0.989672\pi$
$479$	−10.3224	+	17.8789i	−0.471643	+	0.816910i	0.527831	+	0.849350i	$0.323006\pi$
$480$	−6.57666			−0.300182
$481$		0			0
$482$	28.3777			1.29257
$483$	16.3433	−	28.3075i	0.743648	−	1.28804i
$484$	4.57449	−	7.92325i	0.207931	−	0.360148i
$485$	6.08408	+	10.5379i	0.276264	+	0.478503i
$486$	−24.7074			−1.12075
$487$	−1.51802	−	2.62929i	−0.0687882	−	0.119145i	0.829580	−	0.558388i	$-0.188580\pi$
$487$	−1.51802	−	2.62929i	−0.0687882	−	0.119145i	−0.898368	+	0.439243i	$0.855247\pi$
$488$	5.14838	+	8.91725i	0.233056	+	0.403665i
$489$	15.8155			0.715203
$490$	3.63553	+	6.29692i	0.164236	+	0.284466i
$491$	−5.33401	+	9.23877i	−0.240720	+	0.416940i	−0.960920	−	0.276827i	$-0.910717\pi$
$491$	−5.33401	+	9.23877i	−0.240720	+	0.416940i	0.720199	+	0.693767i	$0.244050\pi$
$492$	2.22982	−	3.86217i	0.100528	−	0.174120i
$493$	0.0279884			0.00126053
$494$		0			0
$495$	−13.1039			−0.588975
$496$	7.41139	−	12.8369i	0.332781	−	0.576394i
$497$	19.4362	−	33.6646i	0.871835	−	1.51006i
$498$	17.2506	+	29.8789i	0.773016	+	1.33890i
$499$	33.9143			1.51821			0.759107	−	0.650966i	$-0.225636\pi$
$499$	33.9143			1.51821			0.759107	+	0.650966i	$0.225636\pi$
$500$	−0.256182	−	0.443720i	−0.0114568	−	0.0198438i
$501$	−12.2324	−	21.1872i	−0.546504	−	0.946572i
$502$	14.4413			0.644546
$503$	6.31380	+	10.9358i	0.281518	+	0.487604i	0.971759	−	0.235976i	$-0.0758286\pi$
$503$	6.31380	+	10.9358i	0.281518	+	0.487604i	−0.690241	+	0.723580i	$0.742495\pi$
$504$	13.4557	−	23.3059i	0.599363	−	1.03813i
$505$	−2.02721	+	3.51122i	−0.0902095	+	0.156247i
$506$	−25.5058			−1.13387
$507$		0			0
$508$	5.85945			0.259971
$509$	12.0763	−	20.9168i	0.535273	−	0.927120i	−0.463877	−	0.885899i	$-0.653542\pi$
$509$	12.0763	−	20.9168i	0.535273	−	0.927120i	0.999150	−	0.0412201i	$-0.0131245\pi$
$510$	−1.60984	+	2.78833i	−0.0712851	+	0.123469i
$511$	8.46601	+	14.6636i	0.374514	+	0.648678i
$512$	−24.2750			−1.07281
$513$	1.48269	+	2.56810i	0.0654625	+	0.113384i
$514$	3.38465	+	5.86238i	0.149290	+	0.258578i
$515$	17.9035			0.788921
$516$	−0.676260	−	1.17132i	−0.0297707	−	0.0515644i
$517$	−6.94402	+	12.0274i	−0.305398	+	0.528964i
$518$	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
$523$	−18.5163	+	32.0712i	−0.809662	+	1.40238i	0.103436	+	0.994636i	$0.467016\pi$
$523$	−18.5163	+	32.0712i	−0.809662	+	1.40238i	−0.913098	+	0.407739i	$0.866317\pi$
$524$	−2.70732	−	4.68922i	−0.118270	−	0.204850i
$525$	8.39654			0.366455
$526$	−4.18332	−	7.24573i	−0.182402	−	0.315929i
$527$	3.09229	+	5.35600i	0.134702	+	0.233311i
$528$	−33.9865			−1.47907
$529$	3.92277	+	6.79444i	0.170555	+	0.295410i
$530$	−2.70732	+	4.68922i	−0.117599	+	0.203687i
$531$	0.209084	−	0.362145i	0.00907348	−	0.0157157i
$532$	−4.18348			−0.181377
$533$		0			0
$534$	−45.9519			−1.98854
$535$	−4.56593	+	7.90842i	−0.197402	+	0.341911i
$536$	9.80545	−	16.9835i	0.423531	−	0.733577i
$537$	−21.7264	−	37.6312i	−0.937562	−	1.62391i
$538$	−1.73438			−0.0747744
$539$	−16.0118	−	27.7332i	−0.689677	−	1.19456i
$540$	0.334963	+	0.580172i	0.0144145	+	0.0249666i
$541$	−8.38144			−0.360346			−0.180173	−	0.983635i	$-0.557666\pi$
$541$	−8.38144			−0.360346			−0.180173	+	0.983635i	$0.557666\pi$
$542$	6.07981	+	10.5305i	0.261150	+	0.452326i
$543$	−21.0952	+	36.5379i	−0.905281	+	1.56799i
$544$	1.59585	−	2.76409i	0.0684215	−	0.118509i
$545$	−7.37605			−0.315955
$546$		0			0
$547$	−22.7842			−0.974181			−0.487091	−	0.873351i	$-0.661942\pi$
$547$	−22.7842			−0.974181			−0.487091	+	0.873351i	$0.661942\pi$
$548$	0.970090	−	1.68025i	0.0414402	−	0.0717765i
$549$	−4.09843	+	7.09870i	−0.174917	+	0.302965i
$550$	−3.27597	−	5.67414i	−0.139688	−	0.241946i
$551$	−0.0560816			−0.00238915
$552$	−13.9106	−	24.0938i	−0.592074	−	1.02550i
$553$	21.5699	+	37.3601i	0.917245	+	1.58871i
$554$	−21.3735			−0.908071
$555$	−10.1500	−	17.5803i	−0.430844	−	0.746244i
$556$	0.515915	−	0.893592i	0.0218797	−	0.0378967i
$557$	14.0764	−	24.3810i	0.596435	−	1.03306i	−0.396908	−	0.917858i	$-0.629917\pi$
$557$	14.0764	−	24.3810i	0.596435	−	1.03306i	0.993343	−	0.115197i	$-0.0367499\pi$
$558$	16.2572			0.688222
$559$		0			0
$560$	9.76645			0.412708
$561$	7.09017	−	12.2805i	0.299347	−	0.518484i
$562$	−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	$0.708551\pi$
$564$	−3.08939			−0.130087
$565$	3.53794	+	6.12789i	0.148842	+	0.257802i
$566$	−0.804007	−	1.39258i	−0.0337950	−	0.0585346i
$567$	−37.3253			−1.56752
$568$	−16.5431	−	28.6535i	−0.694133	−	1.20227i
$569$	−20.2992	+	35.1593i	−0.850988	+	1.47395i	0.0293292	+	0.999570i	$0.490663\pi$
$569$	−20.2992	+	35.1593i	−0.850988	+	1.47395i	−0.880317	+	0.474385i	$0.842670\pi$
$570$	3.22572	−	5.58710i	0.135110	−	0.234018i
$571$	24.7159			1.03433			0.517164	−	0.855886i	$-0.326988\pi$
$571$	24.7159			1.03433			0.517164	+	0.855886i	$0.326988\pi$
$572$		0			0
$573$	63.7551			2.66341
$574$	−8.19393	+	14.1923i	−0.342008	+	0.592375i
$575$	1.94644	−	3.37133i	0.0811720	−	0.140594i
$576$	−10.8124	−	18.7276i	−0.450516	−	0.780317i
$577$	23.0691			0.960379			0.480189	−	0.877165i	$-0.340568\pi$
$577$	23.0691			0.960379			0.480189	+	0.877165i	$0.340568\pi$
$578$	9.58607	+	16.6036i	0.398728	+	0.690617i
$579$	−25.3834	−	43.9654i	−1.05490	−	1.82714i
$580$	−0.0126697			−0.000526079
$581$	21.8327	+	37.8153i	0.905771	+	1.56884i
$582$	−17.3068	+	29.9763i	−0.717392	+	1.24256i
$583$	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	$-0.695358\pi$
$587$	10.1762	−	17.6256i	0.420015	−	0.727487i	0.995940	+	0.0900152i	$0.0286916\pi$
$588$	3.56182	−	6.16925i	0.146887	−	0.254416i
$589$	−6.19615	−	10.7321i	−0.255308	−	0.442206i
$590$	0.209084			0.00860786
$591$	1.97859	+	3.42701i	0.0813881	+	0.140968i
$592$	−11.8060	−	20.4486i	−0.485223	−	0.840432i
$593$	10.3834			0.426395			0.213198	−	0.977009i	$-0.431612\pi$
$593$	10.3834			0.426395			0.213198	+	0.977009i	$0.431612\pi$
$594$	4.28339	+	7.41904i	0.175750	+	0.304407i
$595$	−2.03745	+	3.52897i	−0.0835273	+	0.144674i
$596$	−1.41356	+	2.44836i	−0.0579017	+	0.100289i
$597$	59.0652			2.41738
$598$		0			0
$599$	−31.5965			−1.29100			−0.645499	−	0.763761i	$-0.723351\pi$
$599$	−31.5965			−1.29100			−0.645499	+	0.763761i	$0.723351\pi$
$600$	3.57335	−	6.18922i	0.145881	−	0.252674i
$601$	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
$603$	15.6115			0.635750
$604$	−1.25263	−	2.16962i	−0.0509688	−	0.0882806i
$605$	8.92820	+	15.4641i	0.362983	+	0.628705i
$606$	−11.5332			−0.468505
$607$	−1.08770	−	1.88395i	−0.0441484	−	0.0764673i	0.843107	−	0.537746i	$-0.180724\pi$
$607$	−1.08770	−	1.88395i	−0.0441484	−	0.0764673i	−0.887255	+	0.461279i	$0.847391\pi$
$608$	−3.19768	+	5.53854i	−0.129683	+	0.224617i
$609$	0.103814	−	0.179812i	0.00420677	−	0.00728634i
$610$	−4.09843			−0.165941
$611$		0			0
$612$	1.41465			0.0571837
$613$	7.38100	−	12.7843i	0.298116	−	0.516352i	−0.677589	−	0.735441i	$-0.736975\pi$
$613$	7.38100	−	12.7843i	0.298116	−	0.516352i	0.975705	+	0.219089i	$0.0703085\pi$
$614$	−8.72336	+	15.1093i	−0.352046	+	0.609762i
$615$	4.35203	+	7.53794i	0.175491	+	0.303959i
$616$	−59.2622			−2.38774
$617$	10.1486	+	17.5779i	0.408567	+	0.707659i	0.994729	−	0.102535i	$-0.0326953\pi$
$617$	10.1486	+	17.5779i	0.408567	+	0.707659i	−0.586162	+	0.810194i	$0.699362\pi$
$618$	25.4642	+	44.1053i	1.02432	+	1.77418i
$619$	9.94207			0.399605			0.199803	−	0.979836i	$-0.435970\pi$
$619$	9.94207			0.399605			0.199803	+	0.979836i	$0.435970\pi$
$620$	−1.39980	−	2.42453i	−0.0562175	−	0.0973716i
$621$	−2.54500	+	4.40807i	−0.102127	+	0.176890i
$622$	−1.68379	+	2.91641i	−0.0675138	+	0.116937i
$623$	−58.1577			−2.33004
$624$		0			0
$625$	1.00000			0.0400000
$626$	9.99276	−	17.3080i	0.399391	−	0.691766i
$627$	−14.2069	+	24.6070i	−0.567368	+	0.982711i
$628$	2.57221	+	4.45519i	0.102642	+	0.177782i
$629$	9.85174			0.392815
$630$	5.35578	+	9.27648i	0.213379	+	0.369584i
$631$	−0.486710	−	0.843006i	−0.0193756	−	0.0335596i	0.856175	−	0.516686i	$-0.172835\pi$
$631$	−0.486710	−	0.843006i	−0.0193756	−	0.0335596i	−0.875551	+	0.483126i	$0.839501\pi$
$632$	36.7183			1.46058
$633$	0.391243	+	0.677652i	0.0155505	+	0.0269342i
$634$	−1.08903	+	1.88625i	−0.0432507	+	0.0749124i
$635$	−5.71806	+	9.90396i	−0.226914	+	0.393027i
$636$	5.30487			0.210352
$637$		0			0
$638$	−0.162015			−0.00641425
$639$	13.1694	−	22.8100i	0.520972	−	0.902350i
$640$	2.58631	−	4.47962i	0.102233	−	0.177072i
$641$	6.31047	+	10.9301i	0.249249	+	0.431711i	0.963318	−	0.268364i	$-0.0864830\pi$
$641$	6.31047	+	10.9301i	0.249249	+	0.431711i	−0.714069	+	0.700075i	$0.753150\pi$
$642$	−25.9766			−1.02521
$643$	−4.98022	−	8.62599i	−0.196401	−	0.340176i	0.750958	−	0.660350i	$-0.229592\pi$
$643$	−4.98022	−	8.62599i	−0.196401	−	0.340176i	−0.947359	+	0.320174i	$0.896259\pi$
$644$	−3.59042	−	6.21878i	−0.141482	−	0.245054i
$645$	2.63977			0.103941
$646$	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	$-0.0860354\pi$
$648$	−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
$653$	−6.87769	+	11.9125i	−0.269145	+	0.466172i	−0.968641	−	0.248464i	$-0.920074\pi$
$653$	−6.87769	+	11.9125i	−0.269145	+	0.466172i	0.699497	+	0.714636i	$0.253408\pi$
$654$	−10.4910	−	18.1709i	−0.410231	−	0.710540i
$655$	10.5680			0.412925
$656$	5.06207	+	8.76776i	0.197641	+	0.342324i
$657$	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	$-0.150653\pi$
$659$	1.29092	+	2.23593i	0.0502869	+	0.0870995i	−0.839786	+	0.542917i	$0.817320\pi$
$660$	−3.20955	+	5.55910i	−0.124932	+	0.216388i
$661$	−12.4382	+	21.5437i	−0.483791	+	0.837951i	−0.999827	−	0.0186163i	$-0.994074\pi$
$661$	−12.4382	+	21.5437i	−0.483791	+	0.837951i	0.516036	+	0.856567i	$0.327407\pi$
$662$	8.81151			0.342469
$663$		0			0
$664$	37.1656			1.44231
$665$	4.08253	−	7.07115i	0.158314	−	0.274207i
$666$	12.9485	−	22.4274i	0.501743	−	0.869045i
$667$	−0.0481312	−	0.0833657i	−0.00186365	−	0.00322793i
$668$	−5.37460			−0.207949
$669$	14.3395	+	24.8368i	0.554398	+	0.960246i
$670$	3.90288	+	6.75998i	0.150781	+	0.261161i
$671$	18.0506			0.696834
$672$	−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	$0.852149\pi$
$674$	2.66025	−	4.60770i	0.102469	−	0.177482i
$675$	−1.30752			−0.0503264
$676$		0			0
$677$	−41.3625			−1.58969			−0.794845	−	0.606813i	$-0.792448\pi$
$677$	−41.3625			−1.58969			−0.794845	+	0.606813i	$0.792448\pi$
$678$	−10.0641	+	17.4315i	−0.386508	+	0.669451i
$679$	−21.9039	+	37.9386i	−0.840594	+	1.45595i
$680$	1.73417	+	3.00367i	0.0665024	+	0.115186i
$681$	−17.8003			−0.682110
$682$	−17.9002	−	31.0041i	−0.685435	−	1.18721i
$683$	−1.31344	−	2.27495i	−0.0502574	−	0.0870484i	0.839802	−	0.542892i	$-0.182671\pi$
$683$	−1.31344	−	2.27495i	−0.0502574	−	0.0870484i	−0.890060	+	0.455844i	$0.849338\pi$
$684$	−2.83459			−0.108383
$685$	1.89336	+	3.27940i	0.0723416	+	0.125299i
$686$	2.28028	−	3.94957i	0.0870617	−	0.150795i
$687$	16.7931	−	29.0865i	0.640696	−	1.10972i
$688$	3.07045			0.117060
$689$		0			0
$690$	11.0737			0.421569
$691$	7.63765	−	13.2288i	0.290550	−	0.503247i	−0.683390	−	0.730053i	$-0.739495\pi$
$691$	7.63765	−	13.2288i	0.290550	−	0.503247i	0.973940	+	0.226806i	$0.0728285\pi$
$692$	−1.14218	+	1.97831i	−0.0434190	+	0.0752039i
$693$	−23.5882	−	40.8560i	−0.896043	−	1.55199i
$694$	−32.5744			−1.23651
$695$	1.00693	+	1.74406i	0.0381951	+	0.0661558i
$696$	−0.0883613	−	0.153046i	−0.00334933	−	0.00580120i
$697$	−4.22414			−0.160001
$698$	−14.3747	−	24.8976i	−0.544089	−	0.942390i
$699$	−11.0737	+	19.1802i	−0.418846	+	0.725463i
$700$	0.922305	−	1.59748i	0.0348599	−	0.0603790i
$701$	−48.1947			−1.82029			−0.910144	−	0.414292i	$-0.864029\pi$
$701$	−48.1947			−1.82029			−0.910144	+	0.414292i	$0.864029\pi$
$702$		0			0
$703$	−19.7404			−0.744522
$704$	−23.8103	+	41.2406i	−0.897383	+	1.55431i
$705$	3.01484	−	5.22186i	0.113546	−	0.196667i
$706$	−3.49884	−	6.06016i	−0.131680	−	0.228077i
$707$	−14.5967			−0.548964
$708$	−0.102423	−	0.177401i	−0.00384928	−	0.00666715i
$709$	19.4350	+	33.6624i	0.729896	+	1.26422i	0.956927	+	0.290329i	$0.0937647\pi$
$709$	19.4350	+	33.6624i	0.729896	+	1.26422i	−0.227031	+	0.973887i	$0.572902\pi$
$710$	13.1694			0.494237
$711$	14.6150	+	25.3140i	0.548107	+	0.949349i
$712$	−24.7504	+	42.8689i	−0.927560	+	1.60658i
$713$	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
$718$	15.0987	−	26.1517i	0.563478	−	0.975973i
$719$	−3.30830	−	5.73015i	−0.123379	−	0.213698i	0.797719	−	0.603029i	$-0.206040\pi$
$719$	−3.30830	−	5.73015i	−0.123379	−	0.213698i	−0.921098	+	0.389331i	$0.872706\pi$
$720$	6.61742			0.246617
$721$	32.2280	+	55.8205i	1.20023	+	2.07887i
$722$	8.45024	+	14.6362i	0.314485	+	0.544705i
$723$	54.2629			2.01806
$724$	4.63433	+	8.02690i	0.172234	+	0.298317i
$725$	0.0123639	−	0.0214150i	0.000459185	−	0.000795332i
$726$	−25.3973	+	43.9893i	−0.942581	+	1.63260i
$727$	−18.3735			−0.681435			−0.340717	−	0.940166i	$-0.610670\pi$
$727$	−18.3735			−0.681435			−0.340717	+	0.940166i	$0.610670\pi$
$728$		0			0
$729$	−16.1420			−0.597853
$730$	−2.86814	+	4.96777i	−0.106155	+	0.183866i
$731$	−0.640548	+	1.10946i	−0.0236915	+	0.0410349i
$732$	2.00767	+	3.47739i	0.0742057	+	0.128528i
$733$	0.791131			0.0292211			0.0146105	−	0.999893i	$-0.495349\pi$
$733$	0.791131			0.0292211			0.0146105	+	0.999893i	$0.495349\pi$
$734$	−15.8886	−	27.5198i	−0.586458	−	1.01578i
$735$	6.95174	+	12.0408i	0.256419	+	0.444130i
$736$	−10.9774			−0.404634
$737$	−17.1893	−	29.7727i	−0.633175	−	1.09669i
$738$	−5.55193	+	9.61623i	−0.204369	+	0.353978i
$739$	−15.5926	+	27.0073i	−0.573585	+	0.993478i	0.422609	+	0.906312i	$0.361114\pi$
$739$	−15.5926	+	27.0073i	−0.573585	+	0.993478i	−0.996194	+	0.0871658i	$0.972219\pi$
$740$	−4.45965			−0.163940
$741$		0			0
$742$	−19.4938			−0.715639
$743$	−2.78152	+	4.81773i	−0.102044	+	0.176745i	−0.912527	−	0.409017i	$-0.865872\pi$
$743$	−2.78152	+	4.81773i	−0.102044	+	0.176745i	0.810483	+	0.585763i	$0.199205\pi$
$744$	19.5251	−	33.8185i	0.715826	−	1.23985i
$745$	−2.75890	−	4.77855i	−0.101078	−	0.175073i
$746$	16.1053			0.589658
$747$	14.7931	+	25.6224i	0.541251	+	0.937474i
$748$	−1.55762	−	2.69787i	−0.0569521	−	0.0986439i
$749$	−32.8765			−1.20128
$750$	1.42231	+	2.46350i	0.0519352	+	0.0899545i
$751$	17.6048	−	30.4925i	0.642410	−	1.11269i	−0.342483	−	0.939524i	$-0.611268\pi$
$751$	17.6048	−	30.4925i	0.642410	−	1.11269i	0.984893	−	0.173163i	$-0.0553987\pi$
$752$	3.50672	−	6.07381i	0.127877	−	0.221489i
$753$	27.6142			1.00632
$754$		0			0
$755$	4.88961			0.177951
$756$	−1.20593	+	2.08873i	−0.0438593	+	0.0759665i
$757$	−25.0223	+	43.3399i	−0.909451	+	1.57522i	−0.0946237	+	0.995513i	$0.530165\pi$
$757$	−25.0223	+	43.3399i	−0.909451	+	1.57522i	−0.814828	+	0.579703i	$0.803169\pi$
$758$	−15.8545	−	27.4609i	−0.575863	−	0.997424i
$759$	−48.7715			−1.77029
$760$	−3.47484	−	6.01859i	−0.126046	−	0.218317i
$761$	−22.4105	−	38.8161i	−0.812379	−	1.40708i	−0.911195	−	0.411975i	$-0.864839\pi$
$761$	−22.4105	−	38.8161i	−0.812379	−	1.40708i	0.0988165	−	0.995106i	$-0.468494\pi$
$762$	−32.5313			−1.17848
$763$	−13.2776	−	22.9975i	−0.480682	−	0.832566i
$764$	7.00307	−	12.1297i	0.253362	−	0.438836i
$765$	−1.38051	+	2.39111i	−0.0499124	+	0.0864508i
$766$	−11.7092			−0.423072
$767$		0			0
$768$	−26.6361			−0.961148
$769$	19.6817	−	34.0897i	0.709739	−	1.22930i	−0.255215	−	0.966884i	$-0.582146\pi$
$769$	19.6817	−	34.0897i	0.709739	−	1.22930i	0.964954	−	0.262420i	$-0.0845205\pi$
$770$	11.7941	−	20.4280i	0.425031	−	0.736175i
$771$	6.47201	+	11.2099i	0.233084	+	0.403713i
$772$	−11.1528			−0.401399
$773$	−24.3902	−	42.2452i	−0.877256	−	1.51945i	−0.854340	−	0.519715i	$-0.826038\pi$
$773$	−24.3902	−	42.2452i	−0.877256	−	1.51945i	−0.0229167	−	0.999737i	$-0.507295\pi$
$774$	1.68379	+	2.91641i	0.0605225	+	0.104828i
$775$	5.46410			0.196276
$776$	18.6434	+	32.2914i	0.669260	+	1.15919i
$777$	36.5420	−	63.2926i	1.31094	−	2.27061i
$778$	−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
$783$	−0.0161661	+	0.0280005i	−0.000577728	+	0.00100066i
$784$	8.08592	+	14.0052i	0.288783	+	0.500187i
$785$	−10.0405			−0.358363
$786$	15.0309	+	26.0342i	0.536134	+	0.928611i
$787$	−19.9304	−	34.5204i	−0.710442	−	1.23052i	−0.964692	−	0.263382i	$-0.915162\pi$
$787$	−19.9304	−	34.5204i	−0.710442	−	1.23052i	0.254250	−	0.967139i	$-0.418171\pi$
$788$	0.869338			0.0309689
$789$	−7.99922	−	13.8551i	−0.284780	−	0.493253i
$790$	−7.30752	+	12.6570i	−0.259990	+	0.450316i
$791$	−12.7373	+	22.0616i	−0.452885	+	0.784420i
$792$	−40.1541			−1.42682
$793$		0			0
$794$	−20.4490			−0.725709
$795$	−5.17686	+	8.96658i	−0.183604	+	0.318012i
$796$	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	$0.987004\pi$
$798$	23.2264			0.822206
$799$	1.46312	+	2.53420i	0.0517616	+	0.0896537i
$800$	−1.40994	−	2.44209i	−0.0498490	−	0.0863409i
$801$	−39.4057			−1.39233
$802$	8.46343	+	14.6591i	0.298854	+	0.517630i
$803$	12.6321	−	21.8794i	0.445775	−	0.772106i
$804$	3.82375	−	6.62293i	0.134853	−	0.233573i
$805$	14.0151			0.493968
$806$		0			0
$807$	−3.31643			−0.116744
$808$	−6.21196	+	10.7594i	−0.218536	+	0.378515i
$809$	−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	$0.294363\pi$
$810$	−6.32260	−	10.9511i	−0.222153	−	0.384781i
$811$	19.0950			0.670515			0.335257	−	0.942127i	$-0.391177\pi$
$811$	19.0950			0.670515			0.335257	+	0.942127i	$0.391177\pi$
$812$	−0.0228066	−	0.0395023i	−0.000800356	−	0.00138626i
$813$	11.6256	+	20.1362i	0.407729	+	0.706207i
$814$	−57.0284			−1.99885
$815$	3.39062	+	5.87273i	0.118768	+	0.205713i
$816$	−3.58052	+	6.20164i	−0.125343	+	0.217101i
$817$	1.28349	−	2.22308i	0.0449038	−	0.0777757i
$818$	35.8894			1.25484
$819$		0			0
$820$	1.91217			0.0667758
$821$	17.0792	−	29.5820i	0.596068	−	1.03242i	−0.397327	−	0.917677i	$-0.630062\pi$
$821$	17.0792	−	29.5820i	0.596068	−	1.03242i	0.993395	−	0.114743i	$-0.0366044\pi$
$822$	−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	$0.855984\pi$
$824$	54.8616			1.91119
$825$	−6.26420	−	10.8499i	−0.218091	−	0.377745i
$826$	0.376372	+	0.651896i	0.0130957	+	0.0226824i
$827$	−54.8780			−1.90830			−0.954148	−	0.299337i	$-0.903235\pi$
$827$	−54.8780			−1.90830			−0.954148	+	0.299337i	$0.903235\pi$
$828$	−2.43275	−	4.21364i	−0.0845438	−	0.146434i
$829$	−4.07475	+	7.05768i	−0.141522	+	0.245123i	−0.928070	−	0.372406i	$-0.878533\pi$
$829$	−4.07475	+	7.05768i	−0.141522	+	0.245123i	0.786548	+	0.617529i	$0.211866\pi$
$830$	−7.39654	+	12.8112i	−0.256738	+	0.444683i
$831$	−40.8697			−1.41775
$832$		0			0
$833$	−6.74745			−0.233785
$834$	−2.86433	+	4.96116i	−0.0991836	+	0.171791i
$835$	5.24490	−	9.08444i	0.181507	−	0.314380i
$836$	3.12107	+	5.40585i	0.107944	+	0.186965i
$837$	−7.14441			−0.246947
$838$	−4.24935	−	7.36008i	−0.146791	−	0.254250i
$839$	10.9433	+	18.9543i	0.377803	+	0.654374i	0.990742	−	0.135756i	$-0.0433463\pi$
$839$	10.9433	+	18.9543i	0.377803	+	0.654374i	−0.612939	+	0.790130i	$0.710013\pi$
$840$	25.7295			0.887752
$841$	14.4997	+	25.1142i	0.499989	+	0.866007i
$842$	−4.34285	+	7.52204i	−0.149664	+	0.259226i
$843$	−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
$848$	−6.02147	+	10.4295i	−0.206778	+	0.358150i
$849$	−1.53740	−	2.66285i	−0.0527633	−	0.0913888i
$850$	−1.38051			−0.0473511
$851$	−16.9419	−	29.3442i	−0.580761	−	1.00591i
$852$	−6.45118	−	11.1738i	−0.221014	−	0.382807i
$853$	−19.2240			−0.658217			−0.329108	−	0.944292i	$-0.606748\pi$
$853$	−19.2240			−0.658217			−0.329108	+	0.944292i	$0.606748\pi$
$854$	−7.37758	−	12.7783i	−0.252456	−	0.437266i
$855$	2.76619	−	4.79118i	0.0946016	−	0.163855i
$856$	−13.9914	+	24.2337i	−0.478215	+	0.828292i
$857$	−27.8197			−0.950302			−0.475151	−	0.879904i	$-0.657607\pi$
$857$	−27.8197			−0.950302			−0.475151	+	0.879904i	$0.657607\pi$
$858$		0			0
$859$	45.7355			1.56048			0.780238	−	0.625482i	$-0.215098\pi$
$859$	45.7355			1.56048			0.780238	+	0.625482i	$0.215098\pi$
$860$	0.289961	−	0.502227i	0.00988758	−	0.0171258i
$861$	−15.6682	+	27.1381i	−0.533970	+	0.924862i
$862$	−18.4260	−	31.9148i	−0.627593	−	1.08702i
$863$	54.8186			1.86605			0.933024	−	0.359814i	$-0.117160\pi$
$863$	54.8186			1.86605			0.933024	+	0.359814i	$0.117160\pi$
$864$	1.84352	+	3.19308i	0.0627180	+	0.108631i
$865$	−2.22923	−	3.86113i	−0.0757960	−	0.131283i
$866$	1.46378			0.0497413
$867$	18.3302	+	31.7488i	0.622526	+	1.07825i
$868$	5.03957	−	8.72879i	0.171054	−	0.296274i
$869$	32.1842	−	55.7447i	1.09177	−	1.89101i
$870$	0.0703412			0.00238479
$871$		0			0
$872$	−22.6024			−0.765415
$873$	−14.8413	+	25.7060i	−0.502304	+	0.870015i
$874$	5.38421	−	9.32572i	0.182124	−	0.315447i
$875$	1.80010	+	3.11786i	0.0608544	+	0.105403i
$876$	5.61999			0.189882
$877$	13.6897	+	23.7113i	0.462269	+	0.800673i	0.999074	−	0.0430336i	$-0.0137022\pi$
$877$	13.6897	+	23.7113i	0.462269	+	0.800673i	−0.536805	+	0.843706i	$0.680369\pi$
$878$	10.0954	+	17.4858i	0.340704	+	0.590116i
$879$	43.7125			1.47439
$880$	−7.28621	−	12.6201i	−0.245618	−	0.425423i
$881$	17.2213	−	29.8282i	0.580200	−	1.00494i	−0.415255	−	0.909705i	$-0.636308\pi$
$881$	17.2213	−	29.8282i	0.580200	−	1.00494i	0.995455	−	0.0952310i	$-0.0303590\pi$
$882$	−8.86841	+	15.3605i	−0.298615	+	0.517216i
$883$	−17.3592			−0.584183			−0.292092	−	0.956390i	$-0.594351\pi$
$883$	−17.3592			−0.584183			−0.292092	+	0.956390i	$0.594351\pi$
$884$		0			0
$885$	0.399804			0.0134393
$886$	−2.78058	+	4.81610i	−0.0934153	+	0.161800i
$887$	15.5714	−	26.9704i	0.522835	−	0.905577i	−0.476812	−	0.879005i	$-0.658208\pi$
$887$	15.5714	−	26.9704i	0.522835	−	0.905577i	0.999647	−	0.0265716i	$-0.00845898\pi$
$888$	−31.1026	−	53.8714i	−1.04374	−	1.80780i
$889$	−41.1722			−1.38087
$890$	−9.85143	−	17.0632i	−0.330221	−	0.571959i
$891$	27.8464	+	48.2313i	0.932888	+	1.61581i
$892$	6.30042			0.210954
$893$	−2.93173	−	5.07790i	−0.0981065	−	0.169925i
$894$	7.84799	−	13.5931i	0.262476	−	0.454622i
$895$	9.31564	−	16.1352i	0.311388	−	0.539339i
$896$	18.6224			0.622132
$897$		0			0
$898$	16.8953			0.563804
$899$	0.0675578	−	0.117014i	0.00225318	−	0.00390262i
$900$	0.624924	−	1.08240i	0.0208308	−	0.0360800i
$901$	−2.51236	−	4.35154i	−0.0836990	−	0.144971i
$902$	24.4521			0.814167
$903$	4.75184	+	8.23042i	0.158131	+	0.273891i
$904$	10.8413	+	18.7777i	0.360576	+	0.624536i
$905$	−18.0900			−0.601332
$906$	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	$0.261085\pi$
$908$	−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
$913$	32.5763	−	56.4238i	1.07812	−	1.86735i
$914$	−24.4636	−	42.3722i	−0.809184	−	1.40155i
$915$	−7.83690			−0.259080
$916$	−3.68922	−	6.38992i	−0.121895	−	0.211129i
$917$	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	$-0.126579\pi$
$919$	3.80778	+	6.59527i	0.125607	+	0.217558i	−0.796363	+	0.604819i	$0.793245\pi$
$920$	5.96446	−	10.3307i	0.196642	−	0.340595i
$921$	−16.6805	+	28.8915i	−0.549642	+	0.952008i
$922$	−9.19522			−0.302828
$923$		0			0
$924$	−23.1100			−0.760264
$925$	4.35203	−	7.53794i	0.143094	−	0.247846i
$926$	−14.2113	+	24.6146i	−0.467011	+	0.808887i
$927$	21.8366	+	37.8222i	0.717209	+	1.24224i
$928$	−0.0697297			−0.00228899
$929$	7.06196	+	12.2317i	0.231695	+	0.401308i	0.958307	−	0.285740i	$-0.0922394\pi$
$929$	7.06196	+	12.2317i	0.231695	+	0.401308i	−0.726612	+	0.687048i	$0.758906\pi$
$930$	7.77162	+	13.4608i	0.254841	+	0.441398i
$931$	13.5202			0.443106
$932$	2.43275	+	4.21364i	0.0796873	+	0.138022i
$933$	−3.21969	+	5.57666i	−0.105408	+	0.182572i
$934$	13.8006	−	23.9033i	0.451569	−	0.782140i
$935$	6.08012			0.198841
$936$		0			0
$937$	−23.9317			−0.781815			−0.390908	−	0.920430i	$-0.627839\pi$
$937$	−23.9317			−0.781815			−0.390908	+	0.920430i	$0.627839\pi$
$938$	−14.0511	+	24.3373i	−0.458786	+	0.794640i
$939$	19.1078	−	33.0958i	0.623561	−	1.08004i
$940$	−0.662321	−	1.14717i	−0.0216025	−	0.0374167i
$941$	−25.3591			−0.826683			−0.413342	−	0.910576i	$-0.635638\pi$
$941$	−25.3591			−0.826683			−0.413342	+	0.910576i	$0.635638\pi$
$942$	−14.2807	−	24.7349i	−0.465291	−	0.805908i
$943$	7.26420	+	12.5820i	0.236555	+	0.409725i
$944$	0.465033			0.0151355
$945$	−2.35366	−	4.07666i	−0.0765646	−	0.132614i
$946$	3.70792	−	6.42231i	0.120555	−	0.208807i
$947$	−20.7111	+	35.8727i	−0.673021	+	1.16571i	0.304022	+	0.952665i	$0.401670\pi$
$947$	−20.7111	+	35.8727i	−0.673021	+	1.16571i	−0.977043	+	0.213042i	$0.931663\pi$
$948$	14.3187			0.465051
$949$		0			0
$950$	2.76619			0.0897470
$951$	−2.08240	+	3.60682i	−0.0675264	+	0.116959i
$952$	−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	$0.962110\pi$
$954$	−13.2083			−0.427636
$955$	13.6682	+	23.6740i	0.442291	+	0.766071i
$956$	−5.10169	−	8.83639i	−0.165001	−	0.285789i
$957$	−0.309801			−0.0100144
$958$	−12.5901	−	21.8067i	−0.406768	−	0.704543i
$959$	−6.81647	+	11.8065i	−0.220115	+	0.381251i
$960$	10.3375	−	17.9052i	0.333643	−	0.577886i
$961$	−1.14359			−0.0368901
$962$		0			0
$963$	−22.2760			−0.717834
$964$	5.96043	−	10.3238i	0.191972	−	0.332506i
$965$	10.8837	−	18.8511i	0.350358	−	0.606839i
$966$	19.9338	+	34.5263i	0.641358	+	1.11086i
$967$	23.6784			0.761445			0.380722	−	0.924689i	$-0.375675\pi$
$967$	23.6784			0.761445			0.380722	+	0.924689i	$0.375675\pi$
$968$	27.3587	+	47.3866i	0.879341	+	1.52306i
$969$	2.99343	+	5.18477i	0.0961627	+	0.166559i
$970$	−14.8413			−0.476527
$971$	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
$973$	−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	$-0.964289\pi$
$977$	−12.4997	+	21.6501i	−0.399901	+	0.692649i	0.593812	+	0.804604i	$0.297622\pi$
$978$	−9.64500	+	16.7056i	−0.308413	+	0.534187i
$979$	43.3883	+	75.1507i	1.38669	+	2.40183i
$980$	3.05441			0.0975696
$981$	−8.99648	−	15.5824i	−0.287235	−	0.497506i
$982$	−6.50582	−	11.2684i	−0.207609	−	0.359589i
$983$	−27.3418			−0.872068			−0.436034	−	0.899930i	$-0.643617\pi$
$983$	−27.3418			−0.872068			−0.436034	+	0.899930i	$0.643617\pi$
$984$	13.3359	+	23.0985i	0.425134	+	0.736353i
$985$	−0.848360	+	1.46940i	−0.0270310	+	0.0468191i
$986$	−0.0170685	+	0.0295635i	−0.000543573	+	0.000941495i
$987$	21.7080			0.690975
$988$		0			0
$989$	4.40617			0.140108
$990$	7.99131	−	13.8413i	0.253980	−	0.439907i
$991$	−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
$993$	16.8491			0.534690
$994$	23.7061	+	41.0602i	0.751913	+	1.30235i
$995$	12.6627	+	21.9325i	0.401436	+	0.695307i
$996$	14.4932			0.459234
$997$	17.2806	+	29.9309i	0.547282	+	0.947920i	0.998459	+	0.0554858i	$0.0176708\pi$
$997$	17.2806	+	29.9309i	0.547282	+	0.947920i	−0.451178	+	0.892434i	$0.648996\pi$
$998$	−20.6824	+	35.8230i	−0.654691	+	1.13396i
$999$	−5.69036	+	9.85600i	−0.180035	+	0.311830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.m.191.2		8
13.2	odd	12		845.2.m.g.361.2		8
13.3	even	3	inner	845.2.e.m.146.2		8
13.4	even	6		845.2.a.l.1.2		4
13.5	odd	4		65.2.m.a.56.3	yes	8
13.6	odd	12		845.2.c.g.506.3		8
13.7	odd	12		845.2.c.g.506.6		8
13.8	odd	4		845.2.m.g.316.2		8
13.9	even	3		845.2.a.m.1.3		4
13.10	even	6		845.2.e.n.146.3		8
13.11	odd	12		65.2.m.a.36.3	✓	8
13.12	even	2		845.2.e.n.191.3		8
39.5	even	4		585.2.bu.c.316.2		8
39.11	even	12		585.2.bu.c.361.2		8
39.17	odd	6		7605.2.a.cj.1.3		4
39.35	odd	6		7605.2.a.cf.1.2		4
52.11	even	12		1040.2.da.b.881.4		8
52.31	even	4		1040.2.da.b.641.4		8
65.4	even	6		4225.2.a.bl.1.3		4
65.9	even	6		4225.2.a.bi.1.2		4
65.18	even	4		325.2.m.c.199.3		8
65.24	odd	12		325.2.n.d.101.2		8
65.37	even	12		325.2.m.c.49.3		8
65.44	odd	4		325.2.n.d.251.2		8
65.57	even	4		325.2.m.b.199.2		8
65.63	even	12		325.2.m.b.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	13.11	odd	12
65.2.m.a.56.3	yes	8	13.5	odd	4
325.2.m.b.49.2		8	65.63	even	12
325.2.m.b.199.2		8	65.57	even	4
325.2.m.c.49.3		8	65.37	even	12
325.2.m.c.199.3		8	65.18	even	4
325.2.n.d.101.2		8	65.24	odd	12
325.2.n.d.251.2		8	65.44	odd	4
585.2.bu.c.316.2		8	39.5	even	4
585.2.bu.c.361.2		8	39.11	even	12
845.2.a.l.1.2		4	13.4	even	6
845.2.a.m.1.3		4	13.9	even	3
845.2.c.g.506.3		8	13.6	odd	12
845.2.c.g.506.6		8	13.7	odd	12
845.2.e.m.146.2		8	13.3	even	3	inner
845.2.e.m.191.2		8	1.1	even	1	trivial
845.2.e.n.146.3		8	13.10	even	6
845.2.e.n.191.3		8	13.12	even	2
845.2.m.g.316.2		8	13.8	odd	4
845.2.m.g.361.2		8	13.2	odd	12
1040.2.da.b.641.4		8	52.31	even	4
1040.2.da.b.881.4		8	52.11	even	12
4225.2.a.bi.1.2		4	65.9	even	6
4225.2.a.bl.1.3		4	65.4	even	6
7605.2.a.cf.1.2		4	39.35	odd	6
7605.2.a.cj.1.3		4	39.17	odd	6

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})\)	\(q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +(0.609843 - 1.05628i) q^{10} +(-2.68591 + 4.65213i) q^{11} -1.19496 q^{12} +4.39111 q^{14} +(1.16612 - 2.01978i) q^{15} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +2.97527 q^{18} +(-1.13397 - 1.96410i) q^{19} +(-0.256182 - 0.443720i) q^{20} +8.39654 q^{21} +(-3.27597 - 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} +(3.57335 - 6.18922i) q^{24} +1.00000 q^{25} -1.30752 q^{27} +(0.922305 - 1.59748i) q^{28} +(0.0123639 - 0.0214150i) q^{29} +(1.42231 + 2.46350i) q^{30} +5.46410 q^{31} +(-1.40994 - 2.44209i) q^{32} +(-6.26420 - 10.8499i) q^{33} -1.38051 q^{34} +(1.80010 + 3.11786i) q^{35} +(0.624924 - 1.08240i) q^{36} +(4.35203 - 7.53794i) q^{37} +2.76619 q^{38} +3.06430 q^{40} +(-1.86603 + 3.23205i) q^{41} +(-5.12058 + 8.86910i) q^{42} +(0.565928 + 0.980215i) q^{43} -2.75232 q^{44} +(1.21969 + 2.11256i) q^{45} +(2.37404 + 4.11196i) q^{46} +2.58535 q^{47} +(3.16341 + 5.47918i) q^{48} +(-2.98070 + 5.16273i) q^{49} +(-0.609843 + 1.05628i) q^{50} -2.63977 q^{51} -4.43937 q^{53} +(0.797382 - 1.38111i) q^{54} +(2.68591 - 4.65213i) q^{55} +(5.51603 + 9.55405i) q^{56} +5.28942 q^{57} +(0.0150801 + 0.0261196i) q^{58} +(0.0857123 + 0.148458i) q^{59} +1.19496 q^{60} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} +(-4.39111 + 7.60563i) q^{63} +8.86488 q^{64} +15.2807 q^{66} +(-3.19990 + 5.54239i) q^{67} +(-0.289961 + 0.502227i) q^{68} +(4.53957 + 7.86276i) q^{69} -4.39111 q^{70} +(5.39866 + 9.35076i) q^{71} +(3.73748 + 6.47351i) q^{72} -4.70308 q^{73} +(5.30812 + 9.19393i) q^{74} +(-1.16612 + 2.01978i) q^{75} +(0.581008 - 1.00633i) q^{76} +19.3396 q^{77} -11.9826 q^{79} +(-1.35638 + 2.34932i) q^{80} +(5.18379 - 8.97859i) q^{81} +(-2.27597 - 3.94209i) q^{82} -12.1286 q^{83} +(2.15104 + 3.72572i) q^{84} +(-0.565928 - 0.980215i) q^{85} -1.38051 q^{86} +(0.0288357 + 0.0499450i) q^{87} +(8.23042 - 14.2555i) q^{88} +(8.07702 - 13.9898i) q^{89} -2.97527 q^{90} +1.99457 q^{92} +(-6.37182 + 11.0363i) q^{93} +(-1.57666 + 2.73086i) q^{94} +(1.13397 + 1.96410i) q^{95} +6.57666 q^{96} +(-6.08408 - 10.5379i) q^{97} +(-3.63553 - 6.29692i) q^{98} +13.1039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 40 q^{18} - 16 q^{19} + 2 q^{20} + 8 q^{21} - 12 q^{22} + 10 q^{23} + 24 q^{24} + 8 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} - 4 q^{30} + 16 q^{31} - 4 q^{32} - 18 q^{33} - 8 q^{34} + 10 q^{35} - 20 q^{36} + 2 q^{37} + 16 q^{38} - 12 q^{40} - 8 q^{41} + 4 q^{42} + 2 q^{43} + 24 q^{44} + 4 q^{45} - 16 q^{46} + 16 q^{47} + 28 q^{48} - 12 q^{49} - 2 q^{50} + 8 q^{51} - 24 q^{53} + 16 q^{54} - 12 q^{56} - 28 q^{57} - 22 q^{58} - 12 q^{59} + 20 q^{60} - 28 q^{61} - 4 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} - 14 q^{68} + 16 q^{69} - 4 q^{70} - 4 q^{71} - 12 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 20 q^{76} + 36 q^{77} - 16 q^{79} + 2 q^{80} + 8 q^{81} - 4 q^{82} - 24 q^{83} + 28 q^{84} - 2 q^{85} - 8 q^{86} + 22 q^{87} + 18 q^{88} + 12 q^{89} - 40 q^{90} + 44 q^{92} - 8 q^{93} + 32 q^{94} + 16 q^{95} + 8 q^{96} - 2 q^{97} + 24 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9 + 2 * q^10 - 20 * q^12 + 4 * q^14 - 2 * q^15 - 2 * q^16 + 2 * q^17 + 40 * q^18 - 16 * q^19 + 2 * q^20 + 8 * q^21 - 12 * q^22 + 10 * q^23 + 24 * q^24 + 8 * q^25 - 4 * q^27 - 8 * q^28 - 8 * q^29 - 4 * q^30 + 16 * q^31 - 4 * q^32 - 18 * q^33 - 8 * q^34 + 10 * q^35 - 20 * q^36 + 2 * q^37 + 16 * q^38 - 12 * q^40 - 8 * q^41 + 4 * q^42 + 2 * q^43 + 24 * q^44 + 4 * q^45 - 16 * q^46 + 16 * q^47 + 28 * q^48 - 12 * q^49 - 2 * q^50 + 8 * q^51 - 24 * q^53 + 16 * q^54 - 12 * q^56 - 28 * q^57 - 22 * q^58 - 12 * q^59 + 20 * q^60 - 28 * q^61 - 4 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 - 14 * q^68 + 16 * q^69 - 4 * q^70 - 4 * q^71 - 12 * q^72 - 16 * q^73 + 10 * q^74 + 2 * q^75 - 20 * q^76 + 36 * q^77 - 16 * q^79 + 2 * q^80 + 8 * q^81 - 4 * q^82 - 24 * q^83 + 28 * q^84 - 2 * q^85 - 8 * q^86 + 22 * q^87 + 18 * q^88 + 12 * q^89 - 40 * q^90 + 44 * q^92 - 8 * q^93 + 32 * q^94 + 16 * q^95 + 8 * q^96 - 2 * q^97 + 24 * q^98 + 48 * q^99

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