LMFDB - Embedded newform 845.2.m.g.316.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.2
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	845.316
Dual form			845.2.m.g.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.05628	−	0.609843i	−0.746903	−	0.431224i	0.0776710	−	0.996979i	$-0.475252\pi$
$2$	−1.05628	−	0.609843i	−0.746903	−	0.431224i	−0.824574	+	0.565755i	$0.808585\pi$
$3$	−1.16612	+	2.01978i	−0.673262	+	1.16612i	0.303712	+	0.952764i	$0.401774\pi$
$3$	−1.16612	+	2.01978i	−0.673262	+	1.16612i	−0.976974	+	0.213359i	$0.931559\pi$
$4$	−0.256182	−	0.443720i	−0.128091	−	0.221860i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.46350	−	1.42231i	1.00572	−	0.580654i
$7$	−3.11786	+	1.80010i	−1.17844	+	0.680373i	−0.955653	−	0.294494i	$-0.904849\pi$
$7$	−3.11786	+	1.80010i	−1.17844	+	0.680373i	−0.222787	+	0.974867i	$0.571516\pi$
$8$			3.06430i			1.08339i
$9$	−1.21969	−	2.11256i	−0.406562	−	0.704187i
$10$	−0.609843	+	1.05628i	−0.192849	+	0.334025i
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.994666	−	0.103149i	$-0.0328917\pi$
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.408004	+	0.912980i	$0.366225\pi$
$12$	1.19496			0.344955
$13$		0			0
$13$		0			0
$14$	4.39111			1.17357
$15$	2.01978	+	1.16612i	0.521506	+	0.301092i
$16$	1.35638	−	2.34932i	0.339094	−	0.587329i
$17$	−0.565928	−	0.980215i	−0.137258	−	0.237737i	0.789200	−	0.614136i	$-0.210495\pi$
$17$	−0.565928	−	0.980215i	−0.137258	−	0.237737i	−0.926458	+	0.376399i	$0.877162\pi$
$18$			2.97527i			0.701278i
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	−0.257486	−	0.966282i	$-0.582894\pi$
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	0.708082	+	0.706130i	$0.249561\pi$
$20$	−0.443720	+	0.256182i	−0.0992188	+	0.0572840i
$21$		−	8.39654i		−	1.83228i
$22$	−3.27597	−	5.67414i	−0.698438	−	1.20973i
$23$	−1.94644	+	3.37133i	−0.405860	+	0.702970i	−0.994421	−	0.105483i	$-0.966361\pi$
$23$	−1.94644	+	3.37133i	−0.405860	+	0.702970i	0.588561	+	0.808453i	$0.299695\pi$
$24$	−6.18922	−	3.57335i	−1.26337	−	0.729407i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−1.30752			−0.251632
$28$	1.59748	+	0.922305i	0.301895	+	0.174299i
$29$	0.0123639	−	0.0214150i	0.00229593	−	0.00397666i	−0.864875	−	0.501987i	$-0.832603\pi$
$29$	0.0123639	−	0.0214150i	0.00229593	−	0.00397666i	0.867171	+	0.498010i	$0.165936\pi$
$30$	−1.42231	−	2.46350i	−0.259676	−	0.449772i
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	2.44209	−	1.40994i	0.431705	−	0.249245i
$33$	−10.8499	+	6.26420i	−1.88873	+	1.09046i
$34$			1.38051i			0.236755i
$35$	1.80010	+	3.11786i	0.304272	+	0.527015i
$36$	−0.624924	+	1.08240i	−0.104154	+	0.180400i
$37$	−7.53794	−	4.35203i	−1.23923	−	0.715470i	−0.270293	−	0.962778i	$-0.587121\pi$
$37$	−7.53794	−	4.35203i	−1.23923	−	0.715470i	−0.968937	+	0.247309i	$0.920454\pi$
$38$	−2.76619			−0.448735
$39$		0			0
$40$	3.06430			0.484508
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	0.225916	−	0.974147i	$-0.427462\pi$
$41$	−3.23205	−	1.86603i	−0.504762	−	0.291424i	−0.730678	+	0.682723i	$0.760796\pi$
$42$	−5.12058	+	8.86910i	−0.790122	+	1.36853i
$43$	−0.565928	−	0.980215i	−0.0863031	−	0.149481i	0.819643	−	0.572875i	$-0.194172\pi$
$43$	−0.565928	−	0.980215i	−0.0863031	−	0.149481i	−0.905946	+	0.423394i	$0.860839\pi$
$44$		−	2.75232i		−	0.414929i
$45$	−2.11256	+	1.21969i	−0.314922	+	0.181820i
$46$	4.11196	−	2.37404i	0.606276	−	0.350034i
$47$		−	2.58535i		−	0.377113i	−0.982062	−	0.188556i	$-0.939619\pi$
$47$		−	2.58535i		−	0.377113i	0.982062	−	0.188556i	$-0.0603808\pi$
$48$	3.16341	+	5.47918i	0.456598	+	0.790852i
$49$	2.98070	−	5.16273i	0.425815	−	0.737533i
$50$	1.05628	+	0.609843i	0.149381	+	0.0862449i
$51$	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	$0.598622\pi$
$54$	1.38111	+	0.797382i	0.187945	+	0.108510i
$55$	2.68591	−	4.65213i	0.362168	−	0.627293i
$56$	−5.51603	−	9.55405i	−0.737111	−	1.27671i
$57$			5.28942i			0.700600i
$58$	−0.0261196	+	0.0150801i	−0.00342967	+	0.00198012i
$59$	0.148458	−	0.0857123i	0.0193276	−	0.0111588i	−0.490305	−	0.871551i	$-0.663115\pi$
$59$	0.148458	−	0.0857123i	0.0193276	−	0.0111588i	0.509633	+	0.860392i	$0.329781\pi$
$60$		−	1.19496i		−	0.154269i
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	0.738192	−	0.674591i	$-0.235680\pi$
$61$	−1.68012	−	2.91005i	−0.215117	−	0.372594i	−0.953309	+	0.301997i	$0.902347\pi$
$62$	3.33225	−	5.77162i	0.423196	−	0.732997i
$63$	7.60563	+	4.39111i	0.958219	+	0.553228i
$64$	−8.86488			−1.10811
$65$		0			0
$66$	15.2807			1.88093
$67$	−5.54239	−	3.19990i	−0.677111	−	0.390930i	0.121655	−	0.992572i	$-0.461180\pi$
$67$	−5.54239	−	3.19990i	−0.677111	−	0.390930i	−0.798766	+	0.601642i	$0.794513\pi$
$68$	−0.289961	+	0.502227i	−0.0351629	+	0.0609040i
$69$	−4.53957	−	7.86276i	−0.546500	−	0.946566i
$70$		−	4.39111i		−	0.524838i
$71$	−9.35076	+	5.39866i	−1.10973	+	0.640703i	−0.938760	−	0.344573i	$-0.888024\pi$
$71$	−9.35076	+	5.39866i	−1.10973	+	0.640703i	−0.170971	+	0.985276i	$0.554691\pi$
$72$	6.47351	−	3.73748i	0.762911	−	0.440467i
$73$			4.70308i			0.550454i	0.961379	+	0.275227i	$0.0887531\pi$
$73$			4.70308i			0.550454i	−0.961379	+	0.275227i	$0.911247\pi$
$74$	5.30812	+	9.19393i	0.617056	+	1.06877i
$75$	1.16612	−	2.01978i	0.134652	−	0.233225i
$76$	−1.00633	−	0.581008i	−0.115435	−	0.0666462i
$77$	−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	$0.735457\pi$
$80$	−2.34932	−	1.35638i	−0.262661	−	0.151648i
$81$	5.18379	−	8.97859i	0.575976	−	0.997621i
$82$	2.27597	+	3.94209i	0.251338	+	0.435331i
$83$		−	12.1286i		−	1.33129i	−0.746270	−	0.665643i	$-0.768157\pi$
$83$		−	12.1286i		−	1.33129i	0.746270	−	0.665643i	$-0.231843\pi$
$84$	−3.72572	+	2.15104i	−0.406509	+	0.234698i
$85$	−0.980215	+	0.565928i	−0.106319	+	0.0613835i
$86$			1.38051i			0.148864i
$87$	0.0288357	+	0.0499450i	0.00309152	+	0.00535466i
$88$	−8.23042	+	14.2555i	−0.877366	+	1.51964i
$89$	−13.9898	−	8.07702i	−1.48292	−	0.856162i	−0.483105	−	0.875562i	$-0.660491\pi$
$89$	−13.9898	−	8.07702i	−1.48292	−	0.856162i	−0.999812	+	0.0194001i	$0.993824\pi$
$90$	2.97527			0.313621
$91$		0			0
$92$	1.99457			0.207948
$93$	−11.0363	−	6.37182i	−1.14441	−	0.660727i
$94$	−1.57666	+	2.73086i	−0.162620	+	0.281666i
$95$	−1.13397	−	1.96410i	−0.116343	−	0.201513i
$96$			6.57666i			0.671228i
$97$	10.5379	−	6.08408i	1.06997	−	0.617745i	0.141794	−	0.989896i	$-0.454713\pi$
$97$	10.5379	−	6.08408i	1.06997	−	0.617745i	0.928172	+	0.372151i	$0.121380\pi$
$98$	−6.29692	+	3.63553i	−0.636085	+	0.367244i
$99$		−	13.1039i		−	1.31699i
$100$	0.256182	+	0.443720i	0.0256182	+	0.0443720i
$101$	−2.02721	+	3.51122i	−0.201714	+	0.349380i	−0.949081	−	0.315032i	$-0.897985\pi$
$101$	−2.02721	+	3.51122i	−0.201714	+	0.349380i	0.747366	+	0.664412i	$0.231318\pi$
$102$	−2.78833	−	1.60984i	−0.276086	−	0.159398i
$103$	17.9035			1.76408			0.882041	−	0.471173i	$-0.156169\pi$
$103$	17.9035			1.76408			0.882041	+	0.471173i	$0.156169\pi$
$104$		0			0
$105$	−8.39654			−0.819419
$106$	4.68922	+	2.70732i	0.455457	+	0.262958i
$107$	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
$109$			7.37605i			0.706498i	0.935529	+	0.353249i	$0.114923\pi$
$109$			7.37605i			0.706498i	−0.935529	+	0.353249i	$0.885077\pi$
$110$	−5.67414	+	3.27597i	−0.541008	+	0.312351i
$111$	17.5803	−	10.1500i	1.66865	−	0.963396i
$112$			9.76645i			0.922843i
$113$	−3.53794	−	6.12789i	−0.332821	−	0.576463i	0.650243	−	0.759727i	$-0.274667\pi$
$113$	−3.53794	−	6.12789i	−0.332821	−	0.576463i	−0.983064	+	0.183263i	$0.941334\pi$
$114$	3.22572	−	5.58710i	0.302116	−	0.523280i
$115$	3.37133	+	1.94644i	0.314378	+	0.181506i
$116$	−0.0126697			−0.00117635
$117$		0			0
$118$	−0.209084			−0.0192478
$119$	3.52897	+	2.03745i	0.323500	+	0.186773i
$120$	−3.57335	+	6.18922i	−0.326201	+	0.564996i
$121$	8.92820	+	15.4641i	0.811655	+	1.40583i
$122$			4.09843i			0.371055i
$123$	7.53794	−	4.35203i	0.679673	−	0.392409i
$124$	2.42453	−	1.39980i	0.217729	−	0.125706i
$125$			1.00000i			0.0894427i
$126$	−5.35578	−	9.27648i	−0.477131	−	0.826415i
$127$	−5.71806	+	9.90396i	−0.507395	+	0.878835i	0.492568	+	0.870274i	$0.336058\pi$
$127$	−5.71806	+	9.90396i	−0.507395	+	0.878835i	−0.999963	+	0.00856072i	$0.997275\pi$
$128$	4.47962	+	2.58631i	0.395946	+	0.228600i
$129$	2.63977			0.232418
$130$		0			0
$131$	−10.5680			−0.923328			−0.461664	−	0.887055i	$-0.652747\pi$
$131$	−10.5680			−0.923328			−0.461664	+	0.887055i	$0.652747\pi$
$132$	5.55910	+	3.20955i	0.483858	+	0.279355i
$133$	−4.08253	+	7.07115i	−0.354000	+	0.613146i
$134$	3.90288	+	6.75998i	0.337157	+	0.583974i
$135$			1.30752i			0.112533i
$136$	3.00367	−	1.73417i	0.257563	−	0.148704i
$137$	−3.27940	+	1.89336i	−0.280178	+	0.161761i	−0.633504	−	0.773739i	$-0.718384\pi$
$137$	−3.27940	+	1.89336i	−0.280178	+	0.161761i	0.353326	+	0.935500i	$0.385051\pi$
$138$			11.0737i			0.942656i
$139$	−1.00693	−	1.74406i	−0.0854068	−	0.147929i	0.820158	−	0.572138i	$-0.193886\pi$
$139$	−1.00693	−	1.74406i	−0.0854068	−	0.147929i	−0.905564	+	0.424209i	$0.860552\pi$
$140$	0.922305	−	1.59748i	0.0779490	−	0.135012i
$141$	5.22186	+	3.01484i	0.439760	+	0.253895i
$142$	13.1694			1.10515
$143$		0			0
$144$	−6.61742			−0.551452
$145$	−0.0214150	−	0.0123639i	−0.00177842	−	0.00102677i
$146$	2.86814	−	4.96777i	0.237369	−	0.411136i
$147$	6.95174	+	12.0408i	0.573370	+	0.993105i
$148$			4.45965i			0.366581i
$149$	−4.77855	+	2.75890i	−0.391474	+	0.226018i	−0.682799	−	0.730607i	$-0.739237\pi$
$149$	−4.77855	+	2.75890i	−0.391474	+	0.226018i	0.291324	+	0.956624i	$0.405904\pi$
$150$	−2.46350	+	1.42231i	−0.201144	+	0.116131i
$151$			4.88961i			0.397911i	0.980009	+	0.198956i	$0.0637549\pi$
$151$			4.88961i			0.397911i	−0.980009	+	0.198956i	$0.936245\pi$
$152$	3.47484	+	6.01859i	0.281846	+	0.488172i
$153$	−1.38051	+	2.39111i	−0.111608	+	0.193310i
$154$	20.4280	+	11.7941i	1.64614	+	0.950397i
$155$	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	$0.368780\pi$
$158$	12.6570	+	7.30752i	1.00694	+	0.581355i
$159$	5.17686	−	8.96658i	0.410551	−	0.711096i
$160$	−1.40994	−	2.44209i	−0.111466	−	0.193064i
$161$		−	14.0151i		−	1.10454i
$162$	−10.9511	+	6.32260i	−0.860397	+	0.496750i
$163$	−5.87273	+	3.39062i	−0.459988	+	0.265574i	−0.712039	−	0.702140i	$-0.752228\pi$
$163$	−5.87273	+	3.39062i	−0.459988	+	0.265574i	0.252051	+	0.967714i	$0.418895\pi$
$164$			1.91217i			0.149315i
$165$	6.26420	+	10.8499i	0.487667	+	0.844664i
$166$	−7.39654	+	12.8112i	−0.574083	+	0.994341i
$167$	9.08444	+	5.24490i	0.702975	+	0.405863i	0.808455	−	0.588559i	$-0.200304\pi$
$167$	9.08444	+	5.24490i	0.702975	+	0.405863i	−0.105479	+	0.994421i	$0.533638\pi$
$168$	25.7295			1.98507
$169$		0			0
$170$	1.38051			0.105880
$171$	−4.79118	−	2.76619i	−0.366391	−	0.211536i
$172$	−0.289961	+	0.502227i	−0.0221093	+	0.0382944i
$173$	−2.22923	−	3.86113i	−0.169485	−	0.293557i	0.768754	−	0.639545i	$-0.220877\pi$
$173$	−2.22923	−	3.86113i	−0.169485	−	0.293557i	−0.938239	+	0.345988i	$0.887544\pi$
$174$		−	0.0703412i		−	0.00533255i
$175$	3.11786	−	1.80010i	0.235688	−	0.136075i
$176$	12.6201	−	7.28621i	0.951275	−	0.549219i
$177$			0.399804i			0.0300511i
$178$	9.85143	+	17.0632i	0.738396	+	1.27894i
$179$	9.31564	−	16.1352i	0.696284	−	1.20600i	−0.273462	−	0.961883i	$-0.588169\pi$
$179$	9.31564	−	16.1352i	0.696284	−	1.20600i	0.969746	−	0.244116i	$-0.0784979\pi$
$180$	1.08240	+	0.624924i	0.0806773	+	0.0465791i
$181$	−18.0900			−1.34462			−0.672310	−	0.740270i	$-0.734698\pi$
$181$	−18.0900			−1.34462			−0.672310	+	0.740270i	$0.734698\pi$
$182$		0			0
$183$	7.83690			0.579320
$184$	−10.3307	−	5.96446i	−0.761593	−	0.439706i
$185$	−4.35203	+	7.53794i	−0.319968	+	0.554200i
$186$	7.77162	+	13.4608i	0.569843	+	0.986997i
$187$		−	6.08012i		−	0.444622i
$188$	−1.14717	+	0.662321i	−0.0836662	+	0.0483047i
$189$	4.07666	−	2.35366i	0.296533	−	0.171204i
$190$			2.76619i			0.200680i
$191$	−13.6682	−	23.6740i	−0.988994	−	1.71299i	−0.622632	−	0.782515i	$-0.713937\pi$
$191$	−13.6682	−	23.6740i	−0.988994	−	1.71299i	−0.366361	−	0.930473i	$-0.619397\pi$
$192$	10.3375	−	17.9052i	0.746048	−	1.29219i
$193$	18.8511	+	10.8837i	1.35693	+	0.783425i	0.989209	−	0.146510i	$-0.0468041\pi$
$193$	18.8511	+	10.8837i	1.35693	+	0.783425i	0.367723	+	0.929935i	$0.380137\pi$
$194$	−14.8413			−1.06555
$195$		0			0
$196$	−3.05441			−0.218172
$197$	1.46940	+	0.848360i	0.104691	+	0.0604432i	0.551431	−	0.834220i	$-0.314082\pi$
$197$	1.46940	+	0.848360i	0.104691	+	0.0604432i	−0.446741	+	0.894664i	$0.647415\pi$
$198$	−7.99131	+	13.8413i	−0.567917	+	0.983662i
$199$	12.6627	+	21.9325i	0.897637	+	1.55475i	0.830506	+	0.557009i	$0.188051\pi$
$199$	12.6627	+	21.9325i	0.897637	+	1.55475i	0.0671309	+	0.997744i	$0.478615\pi$
$200$		−	3.06430i		−	0.216679i
$201$	12.9262	−	7.46296i	0.911746	−	0.526397i
$202$	4.28259	−	2.47256i	0.301322	−	0.173968i
$203$			0.0890252i			0.00624834i
$204$	−0.676260	−	1.17132i	−0.0473477	−	0.0820086i
$205$	−1.86603	+	3.23205i	−0.130329	+	0.225736i
$206$	−18.9111	−	10.9183i	−1.31760	−	0.760715i
$207$	9.49617			0.660030
$208$		0			0
$209$	12.1830			0.842716
$210$	8.86910	+	5.12058i	0.612026	+	0.353353i
$211$	0.167753	−	0.290558i	0.0115486	−	0.0200028i	−0.860193	−	0.509968i	$-0.829657\pi$
$211$	0.167753	−	0.290558i	0.0115486	−	0.0200028i	0.871742	+	0.489965i	$0.162991\pi$
$212$	1.13729	+	1.96984i	0.0781092	+	0.135289i
$213$		−	25.1820i		−	1.72544i
$214$	−9.64579	+	5.56900i	−0.659373	+	0.380689i
$215$	−0.980215	+	0.565928i	−0.0668501	+	0.0385959i
$216$		−	4.00663i		−	0.272616i
$217$	−9.83592	−	17.0363i	−0.667706	−	1.15650i
$218$	4.49824	−	7.79118i	0.304659	−	0.527685i
$219$	−9.49922	−	5.48438i	−0.641898	−	0.370600i
$220$	−2.75232			−0.185562
$221$		0			0
$222$	−24.7597			−1.66176
$223$	10.6493	+	6.14838i	0.713130	+	0.411726i	0.812219	−	0.583353i	$-0.198259\pi$
$223$	10.6493	+	6.14838i	0.713130	+	0.411726i	−0.0990887	+	0.995079i	$0.531593\pi$
$224$	−5.07606	+	8.79200i	−0.339159	+	0.587440i
$225$	1.21969	+	2.11256i	0.0813125	+	0.140837i
$226$			8.63036i			0.574083i
$227$	−6.60974	+	3.81613i	−0.438704	+	0.253286i	−0.703048	−	0.711143i	$-0.748178\pi$
$227$	−6.60974	+	3.81613i	−0.438704	+	0.253286i	0.264344	+	0.964428i	$0.414845\pi$
$228$	2.34702	−	1.35505i	0.155435	−	0.0897406i
$229$			14.4008i			0.951631i	0.879545	+	0.475815i	$0.157847\pi$
$229$			14.4008i			0.951631i	−0.879545	+	0.475815i	$0.842153\pi$
$230$	−2.37404	−	4.11196i	−0.156540	−	0.271135i
$231$	22.5523	−	39.0618i	1.48384	−	2.57008i
$232$	0.0656218	+	0.0378868i	0.00430828	+	0.00248739i
$233$	−9.49617			−0.622115			−0.311057	−	0.950391i	$-0.600683\pi$
$233$	−9.49617			−0.622115			−0.311057	+	0.950391i	$0.600683\pi$
$234$		0			0
$235$	−2.58535			−0.168650
$236$	−0.0760645	−	0.0439159i	−0.00495138	−	0.00285868i
$237$	13.9732	−	24.2023i	0.907657	−	1.57211i
$238$	−2.48505	−	4.30423i	−0.161082	−	0.279002i
$239$		−	19.9143i		−	1.28815i	−0.764962	−	0.644076i	$-0.777242\pi$
$239$		−	19.9143i		−	1.28815i	0.764962	−	0.644076i	$-0.222758\pi$
$240$	5.47918	−	3.16341i	0.353680	−	0.204197i
$241$	−20.1493	+	11.6332i	−1.29793	+	0.749360i	−0.980046	−	0.198770i	$-0.936305\pi$
$241$	−20.1493	+	11.6332i	−1.29793	+	0.749360i	−0.317883	+	0.948130i	$0.602972\pi$
$242$		−	21.7792i		−	1.40002i
$243$	10.1286	+	17.5432i	0.649750	+	1.12540i
$244$	−0.860832	+	1.49100i	−0.0551091	+	0.0954518i
$245$	−5.16273	−	2.98070i	−0.329835	−	0.190430i
$246$	−10.6162			−0.676866
$247$		0			0
$248$	−16.7436			−1.06322
$249$	24.4972	+	14.1434i	1.55244	+	0.896304i
$250$	0.609843	−	1.05628i	0.0385699	−	0.0668050i
$251$	5.92008	+	10.2539i	0.373672	+	0.647219i	0.990127	−	0.140171i	$-0.0447652\pi$
$251$	5.92008	+	10.2539i	0.373672	+	0.647219i	−0.616455	+	0.787390i	$0.711432\pi$
$252$		−	4.49969i		−	0.283454i
$253$	−18.1101	+	10.4559i	−1.13858	+	0.657357i
$254$	12.0797	−	6.97424i	0.757950	−	0.437603i
$255$		−	2.63977i		−	0.165309i
$256$	5.71040	+	9.89070i	0.356900	+	0.618169i
$257$	−2.77501	+	4.80646i	−0.173100	+	0.299819i	−0.939502	−	0.342543i	$-0.888712\pi$
$257$	−2.77501	+	4.80646i	−0.173100	+	0.299819i	0.766402	+	0.642361i	$0.222045\pi$
$258$	−2.78833	−	1.60984i	−0.173594	−	0.100224i
$259$	31.3363			1.94714
$260$		0			0
$261$	−0.0603205			−0.00373375
$262$	11.1627	+	6.44481i	0.689636	+	0.398161i
$263$	−3.42983	+	5.94065i	−0.211493	+	0.366316i	−0.952182	−	0.305532i	$-0.901166\pi$
$263$	−3.42983	+	5.94065i	−0.211493	+	0.366316i	0.740689	+	0.671848i	$0.234499\pi$
$264$	−19.1954	−	33.2474i	−1.18139	−	2.04623i
$265$			4.43937i			0.272709i
$266$	8.62459	−	4.97941i	0.528807	−	0.305307i
$267$	32.6277	−	18.8376i	1.99678	−	1.15284i
$268$			3.27903i			0.200299i
$269$	0.710994	+	1.23148i	0.0433501	+	0.0750845i	0.886886	−	0.461988i	$-0.152864\pi$
$269$	0.710994	+	1.23148i	0.0433501	+	0.0750845i	−0.843536	+	0.537072i	$0.819530\pi$
$270$	0.797382	−	1.38111i	0.0485271	−	0.0840514i
$271$	−8.63381	−	4.98473i	−0.524467	−	0.302801i	0.214294	−	0.976769i	$-0.431255\pi$
$271$	−8.63381	−	4.98473i	−0.524467	−	0.302801i	−0.738760	+	0.673968i	$0.764588\pi$
$272$	−3.07045			−0.186173
$273$		0			0
$274$	4.61862			0.279021
$275$	−4.65213	−	2.68591i	−0.280534	−	0.161966i
$276$	−2.32591	+	4.02860i	−0.140003	+	0.242493i
$277$	−8.76187	−	15.1760i	−0.526449	−	0.911837i	−0.999525	−	0.0308154i	$-0.990190\pi$
$277$	−8.76187	−	15.1760i	−0.526449	−	0.911837i	0.473076	−	0.881022i	$-0.343144\pi$
$278$			2.45628i			0.147318i
$279$	11.5432	−	6.66449i	0.691076	−	0.398993i
$280$	−9.55405	+	5.51603i	−0.570964	+	0.329646i
$281$		−	10.7352i		−	0.640406i	−0.947349	−	0.320203i	$-0.896249\pi$
$281$		−	10.7352i		−	0.640406i	0.947349	−	0.320203i	$-0.103751\pi$
$282$	−3.67716	−	6.36903i	−0.218972	−	0.379270i
$283$	0.659192	−	1.14175i	0.0391849	−	0.0678702i	−0.845768	−	0.533551i	$-0.820857\pi$
$283$	0.659192	−	1.14175i	0.0391849	−	0.0678702i	0.884953	+	0.465681i	$0.154191\pi$
$284$	4.79099	+	2.76608i	0.284293	+	0.164137i
$285$	5.28942			0.313318
$286$		0			0
$287$	13.4361			0.793109
$288$	−5.95717	−	3.43937i	−0.351030	−	0.202667i
$289$	7.85945	−	13.6130i	0.462321	−	0.800763i
$290$	0.0150801	+	0.0261196i	0.000885536	+	0.00153379i
$291$			28.3792i			1.66362i
$292$	2.08685	−	1.20485i	0.122124	−	0.0705082i
$293$	−16.2316	+	9.37133i	−0.948261	+	0.547479i	−0.892540	−	0.450968i	$-0.851079\pi$
$293$	−16.2316	+	9.37133i	−0.948261	+	0.547479i	−0.0557207	+	0.998446i	$0.517746\pi$
$294$		−	16.9579i		−	0.989004i
$295$	−0.0857123	−	0.148458i	−0.00499036	−	0.00864356i
$296$	13.3359	−	23.0985i	0.775134	−	1.34257i
$297$	−6.08275	−	3.51187i	−0.352957	−	0.203780i
$298$	6.72998			0.389857
$299$		0			0
$300$	−1.19496			−0.0689910
$301$	3.52897	+	2.03745i	0.203406	+	0.117437i
$302$	2.98190	−	5.16480i	0.171589	−	0.297201i
$303$	−4.72794	−	8.18904i	−0.271613	−	0.470448i
$304$		−	6.15239i		−	0.352864i
$305$	−2.91005	+	1.68012i	−0.166629	+	0.0962032i
$306$	2.91641	−	1.68379i	0.166720	−	0.0962558i
$307$		−	14.3043i		−	0.816387i	−0.912895	−	0.408194i	$-0.866159\pi$
$307$		−	14.3043i		−	0.816387i	0.912895	−	0.408194i	$-0.133841\pi$
$308$	4.95445	+	8.58137i	0.282306	+	0.488969i
$309$	−20.8777	+	36.1612i	−1.18769	+	2.05714i
$310$	−5.77162	−	3.33225i	−0.327806	−	0.189259i
$311$	−2.76102			−0.156563			−0.0782815	−	0.996931i	$-0.524943\pi$
$311$	−2.76102			−0.156563			−0.0782815	+	0.996931i	$0.524943\pi$
$312$		0			0
$313$	−16.3858			−0.926179			−0.463090	−	0.886311i	$-0.653259\pi$
$313$	−16.3858			−0.926179			−0.463090	+	0.886311i	$0.653259\pi$
$314$	−10.6056	−	6.12316i	−0.598510	−	0.345550i
$315$	4.39111	−	7.60563i	0.247411	−	0.428529i
$316$	3.06973	+	5.31693i	0.172686	+	0.299101i
$317$			1.78575i			0.100297i	0.998742	+	0.0501487i	$0.0159695\pi$
$317$			1.78575i			0.100297i	−0.998742	+	0.0501487i	$0.984030\pi$
$318$	−10.9364	+	6.31414i	−0.613284	+	0.354080i
$319$	0.115037	−	0.0664168i	0.00644085	−	0.00371863i
$320$			8.86488i			0.495562i
$321$	10.6489	+	18.4444i	0.594362	+	1.02946i
$322$	−8.54702	+	14.8039i	−0.476307	+	0.824987i
$323$	−2.22308	−	1.28349i	−0.123695	−	0.0714156i
$324$	−5.31197			−0.295110
$325$		0			0
$326$	8.27099			0.458088
$327$	−14.8980	−	8.60139i	−0.823864	−	0.475658i
$328$	5.71806	−	9.90396i	0.315727	−	0.546855i
$329$	4.65389	+	8.06077i	0.256577	+	0.444405i
$330$		−	15.2807i		−	0.841176i
$331$	6.25652	−	3.61220i	0.343889	−	0.198545i	−0.318101	−	0.948057i	$-0.603045\pi$
$331$	6.25652	−	3.61220i	0.343889	−	0.198545i	0.661991	+	0.749512i	$0.269712\pi$
$332$	−5.38170	+	3.10713i	−0.295359	+	0.170526i
$333$			21.2325i			1.16353i
$334$	−6.39714	−	11.0802i	−0.350036	−	0.606280i
$335$	−3.19990	+	5.54239i	−0.174829	+	0.302813i
$336$	−19.7261	−	11.3889i	−1.07615	−	0.621315i
$337$	4.36219			0.237624			0.118812	−	0.992917i	$-0.462091\pi$
$337$	4.36219			0.237624			0.118812	+	0.992917i	$0.462091\pi$
$338$		0			0
$339$	16.5027			0.896303
$340$	0.502227	+	0.289961i	0.0272371	+	0.0157253i
$341$	−14.6761	+	25.4197i	−0.794754	+	1.37655i
$342$	3.37388	+	5.84374i	0.182439	+	0.315993i
$343$		−	3.73913i		−	0.201894i
$344$	3.00367	−	1.73417i	0.161947	−	0.0935002i
$345$	−7.86276	+	4.53957i	−0.423317	+	0.244402i
$346$			5.43792i			0.292344i
$347$	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
$349$	20.4131	+	11.7855i	1.09269	+	0.630865i	0.934292	−	0.356510i	$-0.116033\pi$
$349$	20.4131	+	11.7855i	1.09269	+	0.630865i	0.158399	+	0.987375i	$0.449367\pi$
$350$	−4.39111			−0.234715
$351$		0			0
$352$	15.1479			0.807385
$353$	−4.96862	−	2.86863i	−0.264453	−	0.152682i	0.361911	−	0.932213i	$-0.382124\pi$
$353$	−4.96862	−	2.86863i	−0.264453	−	0.152682i	−0.626364	+	0.779531i	$0.715458\pi$
$354$	0.243818	−	0.422305i	0.0129588	−	0.0224453i
$355$	5.39866	+	9.35076i	0.286531	+	0.496287i
$356$			8.27675i			0.438667i
$357$	−8.23042	+	4.75184i	−0.435600	+	0.251494i
$358$	−19.6799	+	11.3622i	−1.04011	+	0.600509i
$359$			24.7583i			1.30669i	0.757059	+	0.653347i	$0.226636\pi$
$359$			24.7583i			1.30669i	−0.757059	+	0.653347i	$0.773364\pi$
$360$	−3.73748	−	6.47351i	−0.196983	−	0.341184i
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	19.1081	+	11.0321i	1.00430	+	0.579833i
$363$	−41.6455			−2.18582
$364$		0			0
$365$	4.70308			0.246171
$366$	−8.27796	−	4.77928i	−0.432696	−	0.249817i
$367$	−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
$369$			9.10387i			0.473928i
$370$	9.19393	−	5.30812i	0.477969	−	0.275956i
$371$	13.8413	−	7.99131i	0.718607	−	0.414888i
$372$			6.52938i			0.338532i
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	0.642926	−	0.765929i	$-0.277720\pi$
$373$	−6.60224	−	11.4354i	−0.341851	−	0.592103i	−0.984776	+	0.173826i	$0.944387\pi$
$374$	−3.70792	+	6.42231i	−0.191732	+	0.332089i
$375$	−2.01978	−	1.16612i	−0.104301	−	0.0602183i
$376$	7.92229			0.408561
$377$		0			0
$378$	−5.74146			−0.295309
$379$	−22.5147	−	12.9989i	−1.15650	−	0.667707i	−0.206039	−	0.978544i	$-0.566057\pi$
$379$	−22.5147	−	12.9989i	−1.15650	−	0.667707i	−0.950463	+	0.310837i	$0.899391\pi$
$380$	−0.581008	+	1.00633i	−0.0298051	+	0.0516239i
$381$	−13.3359	−	23.0985i	−0.683220	−	1.18337i
$382$			33.3418i			1.70591i
$383$	−8.31401	+	4.80010i	−0.424826	+	0.245274i	−0.697140	−	0.716935i	$-0.745544\pi$
$383$	−8.31401	+	4.80010i	−0.424826	+	0.245274i	0.272314	+	0.962208i	$0.412211\pi$
$384$	−10.4476	+	6.03191i	−0.533151	+	0.307815i
$385$			19.3396i			0.985637i
$386$	−13.2747	−	22.9924i	−0.675664	−	1.17028i
$387$	−1.38051	+	2.39111i	−0.0701752	+	0.121547i
$388$	−5.39926	−	3.11726i	−0.274106	−	0.158255i
$389$	−5.63129			−0.285518			−0.142759	−	0.989758i	$-0.545597\pi$
$389$	−5.63129			−0.285518			−0.142759	+	0.989758i	$0.545597\pi$
$390$		0			0
$391$	4.40617			0.222829
$392$	15.8201	+	9.13376i	0.799038	+	0.461325i
$393$	12.3236	−	21.3450i	0.621641	−	1.07671i
$394$	−1.03473	−	1.79221i	−0.0521291	−	0.0902903i
$395$			11.9826i			0.602911i
$396$	−5.81445	+	3.35697i	−0.292187	+	0.168694i
$397$	14.5196	−	8.38291i	0.728719	−	0.420726i	−0.0892344	−	0.996011i	$-0.528442\pi$
$397$	14.5196	−	8.38291i	0.728719	−	0.420726i	0.817953	+	0.575285i	$0.195109\pi$
$398$		−	30.8891i		−	1.54833i
$399$	−9.52147	−	16.4917i	−0.476670	−	0.825616i
$400$	−1.35638	+	2.34932i	−0.0678189	+	0.117466i
$401$	−12.0187	−	6.93902i	−0.600187	−	0.346518i	0.168928	−	0.985628i	$-0.445969\pi$
$401$	−12.0187	−	6.93902i	−0.600187	−	0.346518i	−0.769115	+	0.639110i	$0.779303\pi$
$402$	−18.2050			−0.907980
$403$		0			0
$404$	2.07733			0.103351
$405$	−8.97859	−	5.18379i	−0.446149	−	0.257585i
$406$	0.0542914	−	0.0940355i	0.00269444	−	0.00466690i
$407$	−23.3783	−	40.4924i	−1.15882	−	2.00713i
$408$			8.08903i			0.400466i
$409$	25.4829	−	14.7125i	1.26005	−	0.727489i	0.286964	−	0.957941i	$-0.407354\pi$
$409$	25.4829	−	14.7125i	1.26005	−	0.727489i	0.973083	+	0.230453i	$0.0740208\pi$
$410$	3.94209	−	2.27597i	0.194686	−	0.112402i
$411$		−	8.83157i		−	0.435629i
$412$	−4.58655	−	7.94413i	−0.225963	−	0.391379i
$413$	−0.308581	+	0.534478i	−0.0151843	+	0.0262999i
$414$	−10.0306	−	5.79118i	−0.492978	−	0.284621i
$415$	−12.1286			−0.595369
$416$		0			0
$417$	4.69683			0.230005
$418$	−12.8687	−	7.42973i	−0.629427	−	0.363400i
$419$	−3.48397	+	6.03440i	−0.170203	+	0.294800i	−0.938491	−	0.345305i	$-0.887776\pi$
$419$	−3.48397	+	6.03440i	−0.170203	+	0.294800i	0.768288	+	0.640104i	$0.221109\pi$
$420$	2.15104	+	3.72572i	0.104960	+	0.181796i
$421$			7.12125i			0.347069i	0.984828	+	0.173534i	$0.0555188\pi$
$421$			7.12125i			0.347069i	−0.984828	+	0.173534i	$0.944481\pi$
$422$	−0.354389	+	0.204607i	−0.0172514	+	0.00996010i
$423$	−5.46171	+	3.15332i	−0.265558	+	0.153320i
$424$		−	13.6036i		−	0.660647i
$425$	0.565928	+	0.980215i	0.0274515	+	0.0475474i
$426$	−15.3571	+	26.5993i	−0.744054	+	1.28874i
$427$	10.4767	+	6.04875i	0.507005	+	0.292720i
$428$	−4.67883			−0.226160
$429$		0			0
$430$	1.38051			0.0665740
$431$	−26.1664	−	15.1072i	−1.26039	−	0.727687i	−0.287241	−	0.957858i	$-0.592738\pi$
$431$	−26.1664	−	15.1072i	−1.26039	−	0.727687i	−0.973150	+	0.230171i	$0.926071\pi$
$432$	−1.77349	+	3.07177i	−0.0853270	+	0.147791i
$433$	0.600065	+	1.03934i	0.0288373	+	0.0499476i	0.880084	−	0.474818i	$-0.157486\pi$
$433$	0.600065	+	1.03934i	0.0288373	+	0.0499476i	−0.851247	+	0.524766i	$0.824153\pi$
$434$			23.9935i			1.15172i
$435$	0.0499450	−	0.0288357i	0.00239468	−	0.00138257i
$436$	3.27290	−	1.88961i	0.156744	−	0.0904960i
$437$			8.82884i			0.422341i
$438$	6.68922	+	11.5861i	0.319623	+	0.553604i
$439$	−8.27705	+	14.3363i	−0.395042	+	0.684233i	−0.993107	−	0.117215i	$-0.962603\pi$
$439$	−8.27705	+	14.3363i	−0.395042	+	0.684233i	0.598064	+	0.801448i	$0.295937\pi$
$440$	14.2555	+	8.23042i	0.679605	+	0.392370i
$441$	−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	$0.465455\pi$
$444$	−9.00753	−	5.20050i	−0.427478	−	0.246805i
$445$	−8.07702	+	13.9898i	−0.382887	+	0.663180i
$446$	−7.49910	−	12.9888i	−0.355093	−	0.615038i
$447$		−	12.8689i		−	0.608676i
$448$	27.6395	−	15.9577i	1.30584	−	0.753929i
$449$	−11.9963	+	6.92608i	−0.566142	+	0.326862i	−0.755607	−	0.655025i	$-0.772658\pi$
$449$	−11.9963	+	6.92608i	−0.566142	+	0.326862i	0.189465	+	0.981887i	$0.439325\pi$
$450$		−	2.97527i		−	0.140256i
$451$	−10.0239	−	17.3620i	−0.472009	−	0.817544i
$452$	−1.81271	+	3.13971i	−0.0852628	+	0.147680i
$453$	−9.87596	−	5.70189i	−0.464013	−	0.267898i
$454$	9.30897			0.436892
$455$		0			0
$456$	−16.2083			−0.759025
$457$	−34.7402	−	20.0573i	−1.62508	−	0.938240i	−0.985532	−	0.169489i	$-0.945788\pi$
$457$	−34.7402	−	20.0573i	−1.62508	−	0.938240i	−0.639548	−	0.768751i	$-0.720878\pi$
$458$	8.78222	−	15.2113i	0.410366	−	0.710775i
$459$	0.739961	+	1.28165i	0.0345384	+	0.0598223i
$460$		−	1.99457i		−	0.0929972i
$461$	−6.52897	+	3.76950i	−0.304084	+	0.175563i	−0.644276	−	0.764793i	$-0.722841\pi$
$461$	−6.52897	+	3.76950i	−0.304084	+	0.175563i	0.340192	+	0.940356i	$0.389508\pi$
$462$	−47.6432	+	27.5068i	−2.21656	+	1.27973i
$463$		−	23.3031i		−	1.08299i	−0.840705	−	0.541494i	$-0.817859\pi$
$463$		−	23.3031i		−	1.08299i	0.840705	−	0.541494i	$-0.182141\pi$
$464$	−0.0335403	−	0.0580936i	−0.00155707	−	0.00269693i
$465$	−6.37182	+	11.0363i	−0.295486	+	0.511797i
$466$	10.0306	+	5.79118i	0.464659	+	0.268271i
$467$	22.6297			1.04718			0.523589	−	0.851971i	$-0.324593\pi$
$467$	22.6297			1.04718			0.523589	+	0.851971i	$0.324593\pi$
$468$		0			0
$469$	23.0405			1.06391
$470$	2.73086	+	1.57666i	0.125965	+	0.0727260i
$471$	−11.7085	+	20.2797i	−0.539500	+	0.934441i
$472$	0.262648	+	0.454919i	0.0120893	+	0.0209394i
$473$		−	6.08012i		−	0.279564i
$474$	−29.5192	+	17.0429i	−1.35586	+	0.782808i
$475$	−1.96410	+	1.13397i	−0.0901192	+	0.0520303i
$476$		−	2.08783i		−	0.0956956i
$477$	5.41465	+	9.37844i	0.247920	+	0.429409i
$478$	−12.1446	+	21.0351i	−0.555482	+	0.962124i
$479$	17.8789	+	10.3224i	0.816910	+	0.471643i	0.849350	−	0.527831i	$-0.176994\pi$
$479$	17.8789	+	10.3224i	0.816910	+	0.471643i	−0.0324399	+	0.999474i	$0.510328\pi$
$480$	6.57666			0.300182
$481$		0			0
$482$	28.3777			1.29257
$483$	28.3075	+	16.3433i	1.28804	+	0.743648i
$484$	4.57449	−	7.92325i	0.207931	−	0.360148i
$485$	−6.08408	−	10.5379i	−0.276264	−	0.478503i
$486$		−	24.7074i		−	1.12075i
$487$	2.62929	−	1.51802i	0.119145	−	0.0687882i	−0.439243	−	0.898368i	$-0.644753\pi$
$487$	2.62929	−	1.51802i	0.119145	−	0.0687882i	0.558388	+	0.829580i	$0.311420\pi$
$488$	8.91725	−	5.14838i	0.403665	−	0.233056i
$489$		−	15.8155i		−	0.715203i
$490$	3.63553	+	6.29692i	0.164236	+	0.284466i
$491$	5.33401	−	9.23877i	0.240720	−	0.416940i	−0.720199	−	0.693767i	$-0.755950\pi$
$491$	5.33401	−	9.23877i	0.240720	−	0.416940i	0.960920	+	0.276827i	$0.0892830\pi$
$492$	−3.86217	−	2.22982i	−0.174120	−	0.100528i
$493$	−0.0279884			−0.00126053
$494$		0			0
$495$	−13.1039			−0.588975
$496$	12.8369	+	7.41139i	0.576394	+	0.332781i
$497$	19.4362	−	33.6646i	0.871835	−	1.51006i
$498$	−17.2506	−	29.8789i	−0.773016	−	1.33890i
$499$			33.9143i			1.51821i	0.650966	+	0.759107i	$0.274364\pi$
$499$			33.9143i			1.51821i	−0.650966	+	0.759107i	$0.725636\pi$
$500$	0.443720	−	0.256182i	0.0198438	−	0.0114568i
$501$	−21.1872	+	12.2324i	−0.946572	+	0.546504i
$502$		−	14.4413i		−	0.644546i
$503$	6.31380	+	10.9358i	0.281518	+	0.487604i	0.971759	−	0.235976i	$-0.0758286\pi$
$503$	6.31380	+	10.9358i	0.281518	+	0.487604i	−0.690241	+	0.723580i	$0.742495\pi$
$504$	−13.4557	+	23.3059i	−0.599363	+	1.03813i
$505$	3.51122	+	2.02721i	0.156247	+	0.0902095i
$506$	25.5058			1.13387
$507$		0			0
$508$	5.85945			0.259971
$509$	20.9168	+	12.0763i	0.927120	+	0.535273i	0.885899	−	0.463877i	$-0.153542\pi$
$509$	20.9168	+	12.0763i	0.927120	+	0.535273i	0.0412201	+	0.999150i	$0.486876\pi$
$510$	−1.60984	+	2.78833i	−0.0712851	+	0.123469i
$511$	−8.46601	−	14.6636i	−0.374514	−	0.648678i
$512$		−	24.2750i		−	1.07281i
$513$	−2.56810	+	1.48269i	−0.113384	+	0.0654625i
$514$	5.86238	−	3.38465i	0.258578	−	0.149290i
$515$		−	17.9035i		−	0.788921i
$516$	−0.676260	−	1.17132i	−0.0297707	−	0.0515644i
$517$	6.94402	−	12.0274i	0.305398	−	0.528964i
$518$	−33.0999	−	19.1103i	−1.45433	−	0.839656i
$519$	10.3982			0.456431
$520$		0			0
$521$	−24.7521			−1.08441			−0.542205	−	0.840246i	$-0.682410\pi$
$521$	−24.7521			−1.08441			−0.542205	+	0.840246i	$0.682410\pi$
$522$	0.0637154	+	0.0367861i	0.00278875	+	0.00161008i
$523$	−18.5163	+	32.0712i	−0.809662	+	1.40238i	0.103436	+	0.994636i	$0.467016\pi$
$523$	−18.5163	+	32.0712i	−0.809662	+	1.40238i	−0.913098	+	0.407739i	$0.866317\pi$
$524$	2.70732	+	4.68922i	0.118270	+	0.204850i
$525$			8.39654i			0.366455i
$526$	7.24573	−	4.18332i	0.315929	−	0.182402i
$527$	5.35600	−	3.09229i	0.233311	−	0.134702i
$528$			33.9865i			1.47907i
$529$	3.92277	+	6.79444i	0.170555	+	0.295410i
$530$	2.70732	−	4.68922i	0.117599	−	0.203687i
$531$	−0.362145	−	0.209084i	−0.0157157	−	0.00907348i
$532$	4.18348			0.181377
$533$		0			0
$534$	−45.9519			−1.98854
$535$	−7.90842	−	4.56593i	−0.341911	−	0.197402i
$536$	9.80545	−	16.9835i	0.423531	−	0.733577i
$537$	21.7264	+	37.6312i	0.937562	+	1.62391i
$538$		−	1.73438i		−	0.0747744i
$539$	27.7332	−	16.0118i	1.19456	−	0.689677i
$540$	0.580172	−	0.334963i	0.0249666	−	0.0144145i
$541$			8.38144i			0.360346i	0.983635	+	0.180173i	$0.0576658\pi$
$541$			8.38144i			0.360346i	−0.983635	+	0.180173i	$0.942334\pi$
$542$	6.07981	+	10.5305i	0.261150	+	0.452326i
$543$	21.0952	−	36.5379i	0.905281	−	1.56799i
$544$	−2.76409	−	1.59585i	−0.118509	−	0.0684215i
$545$	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	$0.661942\pi$
$548$	1.68025	+	0.970090i	0.0717765	+	0.0414402i
$549$	−4.09843	+	7.09870i	−0.174917	+	0.302965i
$550$	3.27597	+	5.67414i	0.139688	+	0.241946i
$551$		−	0.0560816i		−	0.00238915i
$552$	24.0938	−	13.9106i	1.02550	−	0.592074i
$553$	37.3601	−	21.5699i	1.58871	−	0.917245i
$554$			21.3735i			0.908071i
$555$	−10.1500	−	17.5803i	−0.430844	−	0.746244i
$556$	−0.515915	+	0.893592i	−0.0218797	+	0.0378967i
$557$	−24.3810	−	14.0764i	−1.03306	−	0.596435i	−0.115197	−	0.993343i	$-0.536750\pi$
$557$	−24.3810	−	14.0764i	−1.03306	−	0.596435i	−0.917858	+	0.396908i	$0.870083\pi$
$558$	−16.2572			−0.688222
$559$		0			0
$560$	9.76645			0.412708
$561$	12.2805	+	7.09017i	0.518484	+	0.299347i
$562$	−6.54676	+	11.3393i	−0.276159	+	0.478321i
$563$	−9.06514	−	15.7013i	−0.382050	−	0.661731i	0.609305	−	0.792936i	$-0.291449\pi$
$563$	−9.06514	−	15.7013i	−0.382050	−	0.661731i	−0.991355	+	0.131206i	$0.958115\pi$
$564$		−	3.08939i		−	0.130087i
$565$	−6.12789	+	3.53794i	−0.257802	+	0.148842i
$566$	−1.39258	+	0.804007i	−0.0585346	+	0.0337950i
$567$			37.3253i			1.56752i
$568$	−16.5431	−	28.6535i	−0.694133	−	1.20227i
$569$	20.2992	−	35.1593i	0.850988	−	1.47395i	−0.0293292	−	0.999570i	$-0.509337\pi$
$569$	20.2992	−	35.1593i	0.850988	−	1.47395i	0.880317	−	0.474385i	$-0.157330\pi$
$570$	−5.58710	−	3.22572i	−0.234018	−	0.135110i
$571$	−24.7159			−1.03433			−0.517164	−	0.855886i	$-0.673012\pi$
$571$	−24.7159			−1.03433			−0.517164	+	0.855886i	$0.673012\pi$
$572$		0			0
$573$	63.7551			2.66341
$574$	−14.1923	−	8.19393i	−0.592375	−	0.342008i
$575$	1.94644	−	3.37133i	0.0811720	−	0.140594i
$576$	10.8124	+	18.7276i	0.450516	+	0.780317i
$577$			23.0691i			0.960379i	0.877165	+	0.480189i	$0.159432\pi$
$577$			23.0691i			0.960379i	−0.877165	+	0.480189i	$0.840568\pi$
$578$	−16.6036	+	9.58607i	−0.690617	+	0.398728i
$579$	−43.9654	+	25.3834i	−1.82714	+	1.05490i
$580$			0.0126697i			0.000526079i
$581$	21.8327	+	37.8153i	0.905771	+	1.56884i
$582$	17.3068	−	29.9763i	0.717392	−	1.24256i
$583$	−20.6525	−	11.9237i	−0.855341	−	0.493831i
$584$	−14.4116			−0.596358
$585$		0			0
$586$	22.8602			0.944345
$587$	17.6256	+	10.1762i	0.727487	+	0.420015i	0.817502	−	0.575926i	$-0.195358\pi$
$587$	17.6256	+	10.1762i	0.727487	+	0.420015i	−0.0900152	+	0.995940i	$0.528692\pi$
$588$	3.56182	−	6.16925i	0.146887	−	0.254416i
$589$	6.19615	+	10.7321i	0.255308	+	0.442206i
$590$			0.209084i			0.00860786i
$591$	−3.42701	+	1.97859i	−0.140968	+	0.0813881i
$592$	−20.4486	+	11.8060i	−0.840432	+	0.485223i
$593$		−	10.3834i		−	0.426395i	−0.977009	−	0.213198i	$-0.931612\pi$
$593$		−	10.3834i		−	0.426395i	0.977009	−	0.213198i	$-0.0683878\pi$
$594$	4.28339	+	7.41904i	0.175750	+	0.304407i
$595$	2.03745	−	3.52897i	0.0835273	−	0.144674i
$596$	2.44836	+	1.41356i	0.100289	+	0.0579017i
$597$	−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	$0.723351\pi$
$600$	6.18922	+	3.57335i	0.252674	+	0.145881i
$601$	21.9423	−	38.0051i	0.895044	−	1.55026i	0.0612928	−	0.998120i	$-0.480478\pi$
$601$	21.9423	−	38.0051i	0.895044	−	1.55026i	0.833751	−	0.552141i	$-0.186189\pi$
$602$	−2.48505	−	4.30423i	−0.101283	−	0.175428i
$603$			15.6115i			0.635750i
$604$	2.16962	−	1.25263i	0.0882806	−	0.0509688i
$605$	15.4641	−	8.92820i	0.628705	−	0.362983i
$606$			11.5332i			0.468505i
$607$	−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
$609$	−0.179812	−	0.103814i	−0.00728634	−	0.00420677i
$610$	4.09843			0.165941
$611$		0			0
$612$	1.41465			0.0571837
$613$	12.7843	+	7.38100i	0.516352	+	0.298116i	0.735441	−	0.677589i	$-0.236975\pi$
$613$	12.7843	+	7.38100i	0.516352	+	0.298116i	−0.219089	+	0.975705i	$0.570309\pi$
$614$	−8.72336	+	15.1093i	−0.352046	+	0.609762i
$615$	−4.35203	−	7.53794i	−0.175491	−	0.303959i
$616$		−	59.2622i		−	2.38774i
$617$	−17.5779	+	10.1486i	−0.707659	+	0.408567i	−0.810194	−	0.586162i	$-0.800638\pi$
$617$	−17.5779	+	10.1486i	−0.707659	+	0.408567i	0.102535	+	0.994729i	$0.467305\pi$
$618$	44.1053	−	25.4642i	1.77418	−	1.02432i
$619$		−	9.94207i		−	0.399605i	−0.979836	−	0.199803i	$-0.935970\pi$
$619$		−	9.94207i		−	0.399605i	0.979836	−	0.199803i	$-0.0640301\pi$
$620$	−1.39980	−	2.42453i	−0.0562175	−	0.0973716i
$621$	2.54500	−	4.40807i	0.102127	−	0.176890i
$622$	2.91641	+	1.68379i	0.116937	+	0.0675138i
$623$	58.1577			2.33004
$624$		0			0
$625$	1.00000			0.0400000
$626$	17.3080	+	9.99276i	0.691766	+	0.399391i
$627$	−14.2069	+	24.6070i	−0.567368	+	0.982711i
$628$	−2.57221	−	4.45519i	−0.102642	−	0.177782i
$629$			9.85174i			0.392815i
$630$	−9.27648	+	5.35578i	−0.369584	+	0.213379i
$631$	−0.843006	+	0.486710i	−0.0335596	+	0.0193756i	−0.516686	−	0.856175i	$-0.672835\pi$
$631$	−0.843006	+	0.486710i	−0.0335596	+	0.0193756i	0.483126	+	0.875551i	$0.339501\pi$
$632$		−	36.7183i		−	1.46058i
$633$	0.391243	+	0.677652i	0.0155505	+	0.0269342i
$634$	1.08903	−	1.88625i	0.0432507	−	0.0749124i
$635$	9.90396	+	5.71806i	0.393027	+	0.226914i
$636$	−5.30487			−0.210352
$637$		0			0
$638$	−0.162015			−0.00641425
$639$	22.8100	+	13.1694i	0.902350	+	0.520972i
$640$	2.58631	−	4.47962i	0.102233	−	0.177072i
$641$	−6.31047	−	10.9301i	−0.249249	−	0.431711i	0.714069	−	0.700075i	$-0.246850\pi$
$641$	−6.31047	−	10.9301i	−0.249249	−	0.431711i	−0.963318	+	0.268364i	$0.913517\pi$
$642$		−	25.9766i		−	1.02521i
$643$	8.62599	−	4.98022i	0.340176	−	0.196401i	−0.320174	−	0.947359i	$-0.603741\pi$
$643$	8.62599	−	4.98022i	0.340176	−	0.196401i	0.660350	+	0.750958i	$0.270408\pi$
$644$	−6.21878	+	3.59042i	−0.245054	+	0.141482i
$645$		−	2.63977i		−	0.103941i
$646$	1.56546	+	2.71146i	0.0615923	+	0.106681i
$647$	−18.1381	+	31.4162i	−0.713084	+	1.23510i	0.250610	+	0.968088i	$0.419369\pi$
$647$	−18.1381	+	31.4162i	−0.713084	+	1.23510i	−0.963694	+	0.267009i	$0.913965\pi$
$648$	27.5131	+	15.8847i	1.08081	+	0.624009i
$649$	0.920861			0.0361470
$650$		0			0
$651$	45.8796			1.79816
$652$	3.00898	+	1.73723i	0.117841	+	0.0680353i
$653$	−6.87769	+	11.9125i	−0.269145	+	0.466172i	−0.968641	−	0.248464i	$-0.920074\pi$
$653$	−6.87769	+	11.9125i	−0.269145	+	0.466172i	0.699497	+	0.714636i	$0.253408\pi$
$654$	10.4910	+	18.1709i	0.410231	+	0.710540i
$655$			10.5680i			0.412925i
$656$	−8.76776	+	5.06207i	−0.342324	+	0.197641i
$657$	9.93555	−	5.73629i	0.387623	−	0.223794i
$658$		−	11.3526i		−	0.442570i
$659$	1.29092	+	2.23593i	0.0502869	+	0.0870995i	0.890073	−	0.455818i	$-0.150653\pi$
$659$	1.29092	+	2.23593i	0.0502869	+	0.0870995i	−0.839786	+	0.542917i	$0.817320\pi$
$660$	3.20955	−	5.55910i	0.124932	−	0.216388i
$661$	21.5437	+	12.4382i	0.837951	+	0.483791i	0.856567	−	0.516036i	$-0.172593\pi$
$661$	21.5437	+	12.4382i	0.837951	+	0.483791i	−0.0186163	+	0.999827i	$0.505926\pi$
$662$	−8.81151			−0.342469
$663$		0			0
$664$	37.1656			1.44231
$665$	7.07115	+	4.08253i	0.274207	+	0.158314i
$666$	12.9485	−	22.4274i	0.501743	−	0.869045i
$667$	0.0481312	+	0.0833657i	0.00186365	+	0.00322793i
$668$		−	5.37460i		−	0.207949i
$669$	−24.8368	+	14.3395i	−0.960246	+	0.554398i
$670$	6.75998	−	3.90288i	0.261161	−	0.150781i
$671$		−	18.0506i		−	0.696834i
$672$	−11.8386	−	20.5051i	−0.456685	−	0.791002i
$673$	21.6611	−	37.5181i	0.834974	−	1.44622i	−0.0590774	−	0.998253i	$-0.518816\pi$
$673$	21.6611	−	37.5181i	0.834974	−	1.44622i	0.894052	−	0.447964i	$-0.147851\pi$
$674$	−4.60770	−	2.66025i	−0.177482	−	0.102469i
$675$	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	$0.792448\pi$
$678$	−17.4315	−	10.0641i	−0.669451	−	0.386508i
$679$	−21.9039	+	37.9386i	−0.840594	+	1.45595i
$680$	−1.73417	−	3.00367i	−0.0665024	−	0.115186i
$681$		−	17.8003i		−	0.682110i
$682$	31.0041	−	17.9002i	1.18721	−	0.685435i
$683$	−2.27495	+	1.31344i	−0.0870484	+	0.0502574i	−0.542892	−	0.839802i	$-0.682671\pi$
$683$	−2.27495	+	1.31344i	−0.0870484	+	0.0502574i	0.455844	+	0.890060i	$0.349338\pi$
$684$			2.83459i			0.108383i
$685$	1.89336	+	3.27940i	0.0723416	+	0.125299i
$686$	−2.28028	+	3.94957i	−0.0870617	+	0.150795i
$687$	−29.0865	−	16.7931i	−1.10972	−	0.640696i
$688$	−3.07045			−0.117060
$689$		0			0
$690$	11.0737			0.421569
$691$	13.2288	+	7.63765i	0.503247	+	0.290550i	0.730053	−	0.683390i	$-0.239495\pi$
$691$	13.2288	+	7.63765i	0.503247	+	0.290550i	−0.226806	+	0.973940i	$0.572828\pi$
$692$	−1.14218	+	1.97831i	−0.0434190	+	0.0752039i
$693$	23.5882	+	40.8560i	0.896043	+	1.55199i
$694$		−	32.5744i		−	1.23651i
$695$	−1.74406	+	1.00693i	−0.0661558	+	0.0381951i
$696$	−0.153046	+	0.0883613i	−0.00580120	+	0.00334933i
$697$			4.22414i			0.160001i
$698$	−14.3747	−	24.8976i	−0.544089	−	0.942390i
$699$	11.0737	−	19.1802i	0.418846	−	0.725463i
$700$	−1.59748	−	0.922305i	−0.0603790	−	0.0348599i
$701$	48.1947			1.82029			0.910144	−	0.414292i	$-0.135971\pi$
$701$	48.1947			1.82029			0.910144	+	0.414292i	$0.135971\pi$
$702$		0			0
$703$	−19.7404			−0.744522
$704$	−41.2406	−	23.8103i	−1.55431	−	0.897383i
$705$	3.01484	−	5.22186i	0.113546	−	0.196667i
$706$	3.49884	+	6.06016i	0.131680	+	0.228077i
$707$		−	14.5967i		−	0.548964i
$708$	0.177401	−	0.102423i	0.00666715	−	0.00384928i
$709$	33.6624	−	19.4350i	1.26422	−	0.729896i	0.290329	−	0.956927i	$-0.406235\pi$
$709$	33.6624	−	19.4350i	1.26422	−	0.729896i	0.973887	+	0.227031i	$0.0729019\pi$
$710$		−	13.1694i		−	0.494237i
$711$	14.6150	+	25.3140i	0.548107	+	0.949349i
$712$	24.7504	−	42.8689i	0.927560	−	1.60658i
$713$	−18.4213	−	10.6355i	−0.689882	−	0.398304i
$714$	11.5915			0.433801
$715$		0			0
$716$	−9.54600			−0.356751
$717$	40.2227	+	23.2226i	1.50214	+	0.867263i
$718$	15.0987	−	26.1517i	0.563478	−	0.975973i
$719$	3.30830	+	5.73015i	0.123379	+	0.213698i	0.921098	−	0.389331i	$-0.127294\pi$
$719$	3.30830	+	5.73015i	0.123379	+	0.213698i	−0.797719	+	0.603029i	$0.793960\pi$
$720$			6.61742i			0.246617i
$721$	−55.8205	+	32.2280i	−2.07887	+	1.20023i
$722$	14.6362	−	8.45024i	0.544705	−	0.314485i
$723$		−	54.2629i		−	2.01806i
$724$	4.63433	+	8.02690i	0.172234	+	0.298317i
$725$	−0.0123639	+	0.0214150i	−0.000459185	+	0.000795332i
$726$	43.9893	+	25.3973i	1.63260	+	0.942581i
$727$	18.3735			0.681435			0.340717	−	0.940166i	$-0.389330\pi$
$727$	18.3735			0.681435			0.340717	+	0.940166i	$0.389330\pi$
$728$		0			0
$729$	−16.1420			−0.597853
$730$	−4.96777	−	2.86814i	−0.183866	−	0.106155i
$731$	−0.640548	+	1.10946i	−0.0236915	+	0.0410349i
$732$	−2.00767	−	3.47739i	−0.0742057	−	0.128528i
$733$			0.791131i			0.0292211i	0.999893	+	0.0146105i	$0.00465084\pi$
$733$			0.791131i			0.0292211i	−0.999893	+	0.0146105i	$0.995349\pi$
$734$	27.5198	−	15.8886i	1.01578	−	0.586458i
$735$	12.0408	−	6.95174i	0.444130	−	0.256419i
$736$			10.9774i			0.404634i
$737$	−17.1893	−	29.7727i	−0.633175	−	1.09669i
$738$	5.55193	−	9.61623i	0.204369	−	0.353978i
$739$	27.0073	+	15.5926i	0.993478	+	0.573585i	0.906312	−	0.422609i	$-0.138886\pi$
$739$	27.0073	+	15.5926i	0.993478	+	0.573585i	0.0871658	+	0.996194i	$0.472219\pi$
$740$	4.45965			0.163940
$741$		0			0
$742$	−19.4938			−0.715639
$743$	−4.81773	−	2.78152i	−0.176745	−	0.102044i	0.409017	−	0.912527i	$-0.365872\pi$
$743$	−4.81773	−	2.78152i	−0.176745	−	0.102044i	−0.585763	+	0.810483i	$0.699205\pi$
$744$	19.5251	−	33.8185i	0.715826	−	1.23985i
$745$	2.75890	+	4.77855i	0.101078	+	0.175073i
$746$			16.1053i			0.589658i
$747$	−25.6224	+	14.7931i	−0.937474	+	0.541251i
$748$	−2.69787	+	1.55762i	−0.0986439	+	0.0569521i
$749$			32.8765i			1.20128i
$750$	1.42231	+	2.46350i	0.0519352	+	0.0899545i
$751$	−17.6048	+	30.4925i	−0.642410	+	1.11269i	0.342483	+	0.939524i	$0.388732\pi$
$751$	−17.6048	+	30.4925i	−0.642410	+	1.11269i	−0.984893	+	0.173163i	$0.944601\pi$
$752$	−6.07381	−	3.50672i	−0.221489	−	0.127877i
$753$	−27.6142			−1.00632
$754$		0			0
$755$	4.88961			0.177951
$756$	−2.08873	−	1.20593i	−0.0759665	−	0.0438593i
$757$	−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
$759$		−	48.7715i		−	1.77029i
$760$	6.01859	−	3.47484i	0.218317	−	0.126046i
$761$	−38.8161	+	22.4105i	−1.40708	+	0.812379i	−0.995106	−	0.0988165i	$-0.968494\pi$
$761$	−38.8161	+	22.4105i	−1.40708	+	0.812379i	−0.411975	+	0.911195i	$0.635161\pi$
$762$			32.5313i			1.17848i
$763$	−13.2776	−	22.9975i	−0.480682	−	0.832566i
$764$	−7.00307	+	12.1297i	−0.253362	+	0.438836i
$765$	2.39111	+	1.38051i	0.0864508	+	0.0499124i
$766$	11.7092			0.423072
$767$		0			0
$768$	−26.6361			−0.961148
$769$	34.0897	+	19.6817i	1.22930	+	0.709739i	0.966884	−	0.255215i	$-0.0821461\pi$
$769$	34.0897	+	19.6817i	1.22930	+	0.709739i	0.262420	+	0.964954i	$0.415479\pi$
$770$	11.7941	−	20.4280i	0.425031	−	0.736175i
$771$	−6.47201	−	11.2099i	−0.233084	−	0.403713i
$772$		−	11.1528i		−	0.401399i
$773$	42.2452	−	24.3902i	1.51945	−	0.877256i	0.519715	−	0.854340i	$-0.326038\pi$
$773$	42.2452	−	24.3902i	1.51945	−	0.877256i	0.999737	−	0.0229167i	$-0.00729525\pi$
$774$	2.91641	−	1.68379i	0.104828	−	0.0605225i
$775$		−	5.46410i		−	0.196276i
$776$	18.6434	+	32.2914i	0.669260	+	1.15919i
$777$	−36.5420	+	63.2926i	−1.31094	+	2.27061i
$778$	5.94822	+	3.43420i	0.213254	+	0.123122i
$779$	−8.46410			−0.303258
$780$		0			0
$781$	−58.0013			−2.07545
$782$	−4.65415	−	2.68707i	−0.166432	−	0.0960895i
$783$	−0.0161661	+	0.0280005i	−0.000577728	+	0.00100066i
$784$	−8.08592	−	14.0052i	−0.288783	−	0.500187i
$785$		−	10.0405i		−	0.358363i
$786$	−26.0342	+	15.0309i	−0.928611	+	0.536134i
$787$	−34.5204	+	19.9304i	−1.23052	+	0.710442i	−0.967139	−	0.254250i	$-0.918171\pi$
$787$	−34.5204	+	19.9304i	−1.23052	+	0.710442i	−0.263382	+	0.964692i	$0.584838\pi$
$788$		−	0.869338i		−	0.0309689i
$789$	−7.99922	−	13.8551i	−0.284780	−	0.493253i
$790$	7.30752	−	12.6570i	0.259990	−	0.450316i
$791$	22.0616	+	12.7373i	0.784420	+	0.452885i
$792$	40.1541			1.42682
$793$		0			0
$794$	−20.4490			−0.725709
$795$	−8.96658	−	5.17686i	−0.318012	−	0.183604i
$796$	6.48793	−	11.2374i	0.229958	−	0.398300i
$797$	13.1059	+	22.7001i	0.464235	+	0.804079i	0.999167	−	0.0408167i	$-0.0129960\pi$
$797$	13.1059	+	22.7001i	0.464235	+	0.804079i	−0.534932	+	0.844895i	$0.679663\pi$
$798$			23.2264i			0.822206i
$799$	−2.53420	+	1.46312i	−0.0896537	+	0.0517616i
$800$	−2.44209	+	1.40994i	−0.0863409	+	0.0498490i
$801$			39.4057i			1.39233i
$802$	8.46343	+	14.6591i	0.298854	+	0.517630i
$803$	−12.6321	+	21.8794i	−0.445775	+	0.772106i
$804$	−6.62293	−	3.82375i	−0.233573	−	0.134853i
$805$	−14.0151			−0.493968
$806$		0			0
$807$	−3.31643			−0.116744
$808$	−10.7594	−	6.21196i	−0.378515	−	0.218536i
$809$	−11.1068	+	19.2376i	−0.390495	+	0.676357i	−0.992515	−	0.122124i	$-0.961029\pi$
$809$	−11.1068	+	19.2376i	−0.390495	+	0.676357i	0.602020	+	0.798481i	$0.294363\pi$
$810$	6.32260	+	10.9511i	0.222153	+	0.384781i
$811$			19.0950i			0.670515i	0.942127	+	0.335257i	$0.108823\pi$
$811$			19.0950i			0.670515i	−0.942127	+	0.335257i	$0.891177\pi$
$812$	0.0395023	−	0.0228066i	0.00138626	−	0.000800356i
$813$	20.1362	−	11.6256i	0.706207	−	0.407729i
$814$			57.0284i			1.99885i
$815$	3.39062	+	5.87273i	0.118768	+	0.205713i
$816$	3.58052	−	6.20164i	0.125343	−	0.217101i
$817$	−2.22308	−	1.28349i	−0.0777757	−	0.0449038i
$818$	−35.8894			−1.25484
$819$		0			0
$820$	1.91217			0.0667758
$821$	29.5820	+	17.0792i	1.03242	+	0.596068i	0.917677	−	0.397327i	$-0.130062\pi$
$821$	29.5820	+	17.0792i	1.03242	+	0.596068i	0.114743	+	0.993395i	$0.463396\pi$
$822$	−5.38588	+	9.32861i	−0.187854	+	0.325373i
$823$	2.03970	+	3.53286i	0.0710995	+	0.123148i	0.899383	−	0.437161i	$-0.144016\pi$
$823$	2.03970	+	3.53286i	0.0710995	+	0.123148i	−0.828284	+	0.560309i	$0.810683\pi$
$824$			54.8616i			1.91119i
$825$	10.8499	−	6.26420i	0.377745	−	0.218091i
$826$	0.651896	−	0.376372i	0.0226824	−	0.0130957i
$827$			54.8780i			1.90830i	0.299337	+	0.954148i	$0.403235\pi$
$827$			54.8780i			1.90830i	−0.299337	+	0.954148i	$0.596765\pi$
$828$	−2.43275	−	4.21364i	−0.0845438	−	0.146434i
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	−0.786548	−	0.617529i	$-0.788134\pi$
$829$	4.07475	−	7.05768i	0.141522	−	0.245123i	0.928070	+	0.372406i	$0.121467\pi$
$830$	12.8112	+	7.39654i	0.444683	+	0.256738i
$831$	40.8697			1.41775
$832$		0			0
$833$	−6.74745			−0.233785
$834$	−4.96116	−	2.86433i	−0.171791	−	0.0991836i
$835$	5.24490	−	9.08444i	0.181507	−	0.314380i
$836$	−3.12107	−	5.40585i	−0.107944	−	0.186965i
$837$		−	7.14441i		−	0.246947i
$838$	7.36008	−	4.24935i	0.254250	−	0.146791i
$839$	18.9543	−	10.9433i	0.654374	−	0.377803i	−0.135756	−	0.990742i	$-0.543346\pi$
$839$	18.9543	−	10.9433i	0.654374	−	0.377803i	0.790130	+	0.612939i	$0.210013\pi$
$840$		−	25.7295i		−	0.887752i
$841$	14.4997	+	25.1142i	0.499989	+	0.866007i
$842$	4.34285	−	7.52204i	0.149664	−	0.259226i
$843$	21.6827	+	12.5185i	0.746792	+	0.431160i
$844$	−0.171902			−0.00591710
$845$		0			0
$846$	7.69213			0.264461
$847$	−55.6738	−	32.1433i	−1.91297	−	1.10446i
$848$	−6.02147	+	10.4295i	−0.206778	+	0.358150i
$849$	1.53740	+	2.66285i	0.0527633	+	0.0913888i
$850$		−	1.38051i		−	0.0473511i
$851$	29.3442	−	16.9419i	1.00591	−	0.580761i
$852$	−11.1738	+	6.45118i	−0.382807	+	0.221014i
$853$			19.2240i			0.658217i	0.944292	+	0.329108i	$0.106748\pi$
$853$			19.2240i			0.658217i	−0.944292	+	0.329108i	$0.893252\pi$
$854$	−7.37758	−	12.7783i	−0.252456	−	0.437266i
$855$	−2.76619	+	4.79118i	−0.0946016	+	0.163855i
$856$	24.2337	+	13.9914i	0.828292	+	0.478215i
$857$	27.8197			0.950302			0.475151	−	0.879904i	$-0.342393\pi$
$857$	27.8197			0.950302			0.475151	+	0.879904i	$0.342393\pi$
$858$		0			0
$859$	45.7355			1.56048			0.780238	−	0.625482i	$-0.215098\pi$
$859$	45.7355			1.56048			0.780238	+	0.625482i	$0.215098\pi$
$860$	0.502227	+	0.289961i	0.0171258	+	0.00988758i
$861$	−15.6682	+	27.1381i	−0.533970	+	0.924862i
$862$	18.4260	+	31.9148i	0.627593	+	1.08702i
$863$			54.8186i			1.86605i	0.359814	+	0.933024i	$0.382840\pi$
$863$			54.8186i			1.86605i	−0.359814	+	0.933024i	$0.617160\pi$
$864$	−3.19308	+	1.84352i	−0.108631	+	0.0627180i
$865$	−3.86113	+	2.22923i	−0.131283	+	0.0757960i
$866$		−	1.46378i		−	0.0497413i
$867$	18.3302	+	31.7488i	0.622526	+	1.07825i
$868$	−5.03957	+	8.72879i	−0.171054	+	0.296274i
$869$	−55.7447	−	32.1842i	−1.89101	−	1.09177i
$870$	−0.0703412			−0.00238479
$871$		0			0
$872$	−22.6024			−0.765415
$873$	−25.7060	−	14.8413i	−0.870015	−	0.502304i
$874$	5.38421	−	9.32572i	0.182124	−	0.315447i
$875$	−1.80010	−	3.11786i	−0.0608544	−	0.105403i
$876$			5.61999i			0.189882i
$877$	−23.7113	+	13.6897i	−0.800673	+	0.462269i	−0.843706	−	0.536805i	$-0.819631\pi$
$877$	−23.7113	+	13.6897i	−0.800673	+	0.462269i	0.0430336	+	0.999074i	$0.486298\pi$
$878$	17.4858	−	10.0954i	0.590116	−	0.340704i
$879$		−	43.7125i		−	1.47439i
$880$	−7.28621	−	12.6201i	−0.245618	−	0.425423i
$881$	−17.2213	+	29.8282i	−0.580200	+	1.00494i	0.415255	+	0.909705i	$0.363692\pi$
$881$	−17.2213	+	29.8282i	−0.580200	+	1.00494i	−0.995455	+	0.0952310i	$0.969641\pi$
$882$	15.3605	+	8.86841i	0.517216	+	0.298615i
$883$	17.3592			0.584183			0.292092	−	0.956390i	$-0.405649\pi$
$883$	17.3592			0.584183			0.292092	+	0.956390i	$0.405649\pi$
$884$		0			0
$885$	0.399804			0.0134393
$886$	−4.81610	−	2.78058i	−0.161800	−	0.0934153i
$887$	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
$889$		−	41.1722i		−	1.38087i
$890$	17.0632	−	9.85143i	0.571959	−	0.330221i
$891$	48.2313	−	27.8464i	1.61581	−	0.932888i
$892$		−	6.30042i		−	0.210954i
$893$	−2.93173	−	5.07790i	−0.0981065	−	0.169925i
$894$	−7.84799	+	13.5931i	−0.262476	+	0.454622i
$895$	−16.1352	−	9.31564i	−0.539339	−	0.311388i
$896$	−18.6224			−0.622132
$897$		0			0
$898$	16.8953			0.563804
$899$	0.117014	+	0.0675578i	0.00390262	+	0.00225318i
$900$	0.624924	−	1.08240i	0.0208308	−	0.0360800i
$901$	2.51236	+	4.35154i	0.0836990	+	0.144971i
$902$			24.4521i			0.814167i
$903$	−8.23042	+	4.75184i	−0.273891	+	0.158131i
$904$	18.7777	−	10.8413i	0.624536	−	0.360576i
$905$			18.0900i			0.601332i
$906$	6.95452	+	12.0456i	0.231048	+	0.400188i
$907$	8.80284	−	15.2470i	0.292294	−	0.506267i	−0.682058	−	0.731298i	$-0.738915\pi$
$907$	8.80284	−	15.2470i	0.292294	−	0.506267i	0.974352	+	0.225031i	$0.0722482\pi$
$908$	3.38659	+	1.95525i	0.112388	+	0.0648872i
$909$	9.89022			0.328038
$910$		0			0
$911$	50.0232			1.65734			0.828671	−	0.559737i	$-0.189098\pi$
$911$	50.0232			1.65734			0.828671	+	0.559737i	$0.189098\pi$
$912$	12.4265	+	7.17445i	0.411483	+	0.237570i
$913$	32.5763	−	56.4238i	1.07812	−	1.86735i
$914$	24.4636	+	42.3722i	0.809184	+	1.40155i
$915$		−	7.83690i		−	0.259080i
$916$	6.38992	−	3.68922i	0.211129	−	0.121895i
$917$	32.9495	−	19.0234i	1.08809	−	0.628207i
$918$		−	1.80504i		−	0.0595752i
$919$	3.80778	+	6.59527i	0.125607	+	0.217558i	0.921970	−	0.387261i	$-0.126579\pi$
$919$	3.80778	+	6.59527i	0.125607	+	0.217558i	−0.796363	+	0.604819i	$0.793245\pi$
$920$	−5.96446	+	10.3307i	−0.196642	+	0.340595i
$921$	28.8915	+	16.6805i	0.952008	+	0.549642i
$922$	9.19522			0.302828
$923$		0			0
$924$	−23.1100			−0.760264
$925$	7.53794	+	4.35203i	0.247846	+	0.143094i
$926$	−14.2113	+	24.6146i	−0.467011	+	0.808887i
$927$	−21.8366	−	37.8222i	−0.717209	−	1.24224i
$928$		−	0.0697297i		−	0.00228899i
$929$	−12.2317	+	7.06196i	−0.401308	+	0.231695i	−0.687048	−	0.726612i	$-0.741094\pi$
$929$	−12.2317	+	7.06196i	−0.401308	+	0.231695i	0.285740	+	0.958307i	$0.407761\pi$
$930$	13.4608	−	7.77162i	0.441398	−	0.254841i
$931$		−	13.5202i		−	0.443106i
$932$	2.43275	+	4.21364i	0.0796873	+	0.138022i
$933$	3.21969	−	5.57666i	0.105408	−	0.182572i
$934$	−23.9033	−	13.8006i	−0.782140	−	0.451569i
$935$	−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	$0.627839\pi$
$938$	−24.3373	−	14.0511i	−0.794640	−	0.458786i
$939$	19.1078	−	33.0958i	0.623561	−	1.08004i
$940$	0.662321	+	1.14717i	0.0216025	+	0.0374167i
$941$		−	25.3591i		−	0.826683i	−0.910576	−	0.413342i	$-0.864362\pi$
$941$		−	25.3591i		−	0.826683i	0.910576	−	0.413342i	$-0.135638\pi$
$942$	24.7349	−	14.2807i	0.805908	−	0.465291i
$943$	12.5820	−	7.26420i	0.409725	−	0.236555i
$944$		−	0.465033i		−	0.0151355i
$945$	−2.35366	−	4.07666i	−0.0765646	−	0.132614i
$946$	−3.70792	+	6.42231i	−0.120555	+	0.208807i
$947$	35.8727	+	20.7111i	1.16571	+	0.673021i	0.952665	−	0.304022i	$-0.0983296\pi$
$947$	35.8727	+	20.7111i	1.16571	+	0.673021i	0.213042	+	0.977043i	$0.431663\pi$
$948$	−14.3187			−0.465051
$949$		0			0
$950$	2.76619			0.0897470
$951$	−3.60682	−	2.08240i	−0.116959	−	0.0675264i
$952$	−6.24335	+	10.8138i	−0.202348	+	0.350477i
$953$	12.1513	+	21.0466i	0.393619	+	0.681767i	0.992924	−	0.118753i	$-0.0378897\pi$
$953$	12.1513	+	21.0466i	0.393619	+	0.681767i	−0.599305	+	0.800521i	$0.704556\pi$
$954$		−	13.2083i		−	0.427636i
$955$	−23.6740	+	13.6682i	−0.766071	+	0.442291i
$956$	−8.83639	+	5.10169i	−0.285789	+	0.165001i
$957$			0.309801i			0.0100144i
$958$	−12.5901	−	21.8067i	−0.406768	−	0.704543i
$959$	6.81647	−	11.8065i	0.220115	−	0.381251i
$960$	−17.9052	−	10.3375i	−0.577886	−	0.333643i
$961$	1.14359			0.0368901
$962$		0			0
$963$	−22.2760			−0.717834
$964$	10.3238	+	5.96043i	0.332506	+	0.191972i
$965$	10.8837	−	18.8511i	0.350358	−	0.606839i
$966$	−19.9338	−	34.5263i	−0.641358	−	1.11086i
$967$			23.6784i			0.761445i	0.924689	+	0.380722i	$0.124325\pi$
$967$			23.6784i			0.761445i	−0.924689	+	0.380722i	$0.875675\pi$
$968$	−47.3866	+	27.3587i	−1.52306	+	0.879341i
$969$	5.18477	−	2.99343i	0.166559	−	0.0961627i
$970$			14.8413i			0.476527i
$971$	8.48609	+	14.6983i	0.272332	+	0.471692i	0.969458	−	0.245256i	$-0.0788719\pi$
$971$	8.48609	+	14.6983i	0.272332	+	0.471692i	−0.697127	+	0.716948i	$0.745539\pi$
$972$	5.18953	−	8.98852i	0.166454	−	0.288307i
$973$	6.27895	+	3.62515i	0.201294	+	0.116217i
$974$	−3.70303			−0.118653
$975$		0			0
$976$	−9.11550			−0.291780
$977$	−21.6501	−	12.4997i	−0.692649	−	0.399901i	0.111955	−	0.993713i	$-0.464289\pi$
$977$	−21.6501	−	12.4997i	−0.692649	−	0.399901i	−0.804604	+	0.593812i	$0.797622\pi$
$978$	−9.64500	+	16.7056i	−0.308413	+	0.534187i
$979$	−43.3883	−	75.1507i	−1.38669	−	2.40183i
$980$			3.05441i			0.0975696i
$981$	15.5824	−	8.99648i	0.497506	−	0.287235i
$982$	−11.2684	+	6.50582i	−0.359589	+	0.207609i
$983$			27.3418i			0.872068i	0.899930	+	0.436034i	$0.143617\pi$
$983$			27.3418i			0.872068i	−0.899930	+	0.436034i	$0.856383\pi$
$984$	13.3359	+	23.0985i	0.425134	+	0.736353i
$985$	0.848360	−	1.46940i	0.0270310	−	0.0468191i
$986$	0.0295635	+	0.0170685i	0.000941495	+	0.000543573i
$987$	−21.7080			−0.690975
$988$		0			0
$989$	4.40617			0.140108
$990$	13.8413	+	7.99131i	0.439907	+	0.253980i
$991$	−8.03802	+	13.9223i	−0.255336	+	0.442255i	−0.964987	−	0.262299i	$-0.915519\pi$
$991$	−8.03802	+	13.9223i	−0.255336	+	0.442255i	0.709651	+	0.704554i	$0.248853\pi$
$992$	7.70406	+	13.3438i	0.244604	+	0.423667i
$993$			16.8491i			0.534690i
$994$	−41.0602	+	23.7061i	−1.30235	+	0.751913i
$995$	21.9325	−	12.6627i	0.695307	−	0.401436i
$996$		−	14.4932i		−	0.459234i
$997$	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
$999$	9.85600	+	5.69036i	0.311830	+	0.180035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.g.316.2		8
13.2	odd	12		845.2.e.m.146.2		8
13.3	even	3		65.2.m.a.36.3	✓	8
13.4	even	6		845.2.c.g.506.3		8
13.5	odd	4		845.2.e.m.191.2		8
13.6	odd	12		845.2.a.m.1.3		4
13.7	odd	12		845.2.a.l.1.2		4
13.8	odd	4		845.2.e.n.191.3		8
13.9	even	3		845.2.c.g.506.6		8
13.10	even	6	inner	845.2.m.g.361.2		8
13.11	odd	12		845.2.e.n.146.3		8
13.12	even	2		65.2.m.a.56.3	yes	8
39.20	even	12		7605.2.a.cj.1.3		4
39.29	odd	6		585.2.bu.c.361.2		8
39.32	even	12		7605.2.a.cf.1.2		4
39.38	odd	2		585.2.bu.c.316.2		8
52.3	odd	6		1040.2.da.b.881.4		8
52.51	odd	2		1040.2.da.b.641.4		8
65.3	odd	12		325.2.m.b.49.2		8
65.12	odd	4		325.2.m.b.199.2		8
65.19	odd	12		4225.2.a.bi.1.2		4
65.29	even	6		325.2.n.d.101.2		8
65.38	odd	4		325.2.m.c.199.3		8
65.42	odd	12		325.2.m.c.49.3		8
65.59	odd	12		4225.2.a.bl.1.3		4
65.64	even	2		325.2.n.d.251.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	13.3	even	3
65.2.m.a.56.3	yes	8	13.12	even	2
325.2.m.b.49.2		8	65.3	odd	12
325.2.m.b.199.2		8	65.12	odd	4
325.2.m.c.49.3		8	65.42	odd	12
325.2.m.c.199.3		8	65.38	odd	4
325.2.n.d.101.2		8	65.29	even	6
325.2.n.d.251.2		8	65.64	even	2
585.2.bu.c.316.2		8	39.38	odd	2
585.2.bu.c.361.2		8	39.29	odd	6
845.2.a.l.1.2		4	13.7	odd	12
845.2.a.m.1.3		4	13.6	odd	12
845.2.c.g.506.3		8	13.4	even	6
845.2.c.g.506.6		8	13.9	even	3
845.2.e.m.146.2		8	13.2	odd	12
845.2.e.m.191.2		8	13.5	odd	4
845.2.e.n.146.3		8	13.11	odd	12
845.2.e.n.191.3		8	13.8	odd	4
845.2.m.g.316.2		8	1.1	even	1	trivial
845.2.m.g.361.2		8	13.10	even	6	inner
1040.2.da.b.641.4		8	52.51	odd	2
1040.2.da.b.881.4		8	52.3	odd	6
4225.2.a.bi.1.2		4	65.19	odd	12
4225.2.a.bl.1.3		4	65.59	odd	12
7605.2.a.cf.1.2		4	39.32	even	12
7605.2.a.cj.1.3		4	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

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

Introduction

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