LMFDB - Embedded newform 845.2.e.n.191.3

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			191.3
Root			$1.40994 + 0.109843i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.n.146.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.609843 - 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} +1.00000 q^{5} +(1.42231 + 2.46350i) q^{6} +(1.80010 + 3.11786i) q^{7} +3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})$	\(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	−0.565755	−	0.824574i	$-0.691415\pi$
$2$	0.609843	−	1.05628i	0.431224	−	0.746903i	0.996979	+	0.0776710i	$0.0247484\pi$
$3$	−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	$0.0715156\pi$
$7$	1.80010	+	3.11786i	0.680373	+	1.17844i	−0.294494	+	0.955653i	$0.595151\pi$
$8$	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	$-0.532892\pi$
$11$	2.68591	−	4.65213i	0.809832	−	1.40267i	0.912980	−	0.408004i	$-0.133775\pi$
$12$	−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	0.966282	−	0.257486i	$-0.0828941\pi$
$19$	1.13397	+	1.96410i	0.260152	+	0.450596i	−0.706130	+	0.708082i	$0.749561\pi$
$20$	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	$-0.663256\pi$
$31$	−5.46410			−0.981382			−0.490691	+	0.871334i	$0.663256\pi$
$32$	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	$0.420454\pi$
$37$	−4.35203	+	7.53794i	−0.715470	+	1.23923i	−0.962778	+	0.270293i	$0.912879\pi$
$38$	2.76619			0.448735
$39$		0			0
$40$	3.06430			0.484508
$41$	1.86603	−	3.23205i	0.291424	−	0.504762i	−0.682723	−	0.730678i	$-0.739204\pi$
$41$	1.86603	−	3.23205i	0.291424	−	0.504762i	0.974147	+	0.225916i	$0.0725376\pi$
$42$	−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	$-0.560381\pi$
$47$	−2.58535			−0.377113			−0.188556	+	0.982062i	$0.560381\pi$
$48$	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	0.860392	−	0.509633i	$-0.170219\pi$
$59$	−0.0857123	−	0.148458i	−0.0111588	−	0.0193276i	−0.871551	+	0.490305i	$0.836885\pi$
$60$	−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	−0.601642	−	0.798766i	$-0.705487\pi$
$67$	3.19990	−	5.54239i	0.390930	−	0.677111i	0.992572	+	0.121655i	$0.0388200\pi$
$68$	−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	$-0.945309\pi$
$71$	−5.39866	−	9.35076i	−0.640703	−	1.10973i	0.344573	−	0.938760i	$-0.388024\pi$
$72$	−3.73748	−	6.47351i	−0.440467	−	0.762911i
$73$	4.70308			0.550454			0.275227	−	0.961379i	$-0.411247\pi$
$73$	4.70308			0.550454			0.275227	+	0.961379i	$0.411247\pi$
$74$	5.30812	+	9.19393i	0.617056	+	1.06877i
$75$	−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	$-0.268157\pi$
$83$	12.1286			1.33129			0.665643	+	0.746270i	$0.268157\pi$
$84$	−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	$0.493824\pi$
$89$	−8.07702	+	13.9898i	−0.856162	+	1.48292i	−0.875562	+	0.483105i	$0.839509\pi$
$90$	−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	$0.0452869\pi$
$97$	6.08408	+	10.5379i	0.617745	+	1.06997i	−0.372151	+	0.928172i	$0.621380\pi$
$98$	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	$-0.614923\pi$
$109$	−7.37605			−0.706498			−0.353249	+	0.935529i	$0.614923\pi$
$110$	−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	0.935500	−	0.353326i	$-0.114949\pi$
$137$	1.89336	+	3.27940i	0.161761	+	0.280178i	−0.773739	+	0.633504i	$0.781616\pi$
$138$	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	0.730607	−	0.682799i	$-0.239237\pi$
$149$	−2.75890	−	4.77855i	−0.226018	−	0.391474i	−0.956624	+	0.291324i	$0.905904\pi$
$150$	1.42231	+	2.46350i	0.116131	+	0.201144i
$151$	4.88961			0.397911			0.198956	−	0.980009i	$-0.436245\pi$
$151$	4.88961			0.397911			0.198956	+	0.980009i	$0.436245\pi$
$152$	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	0.967714	−	0.252051i	$-0.0811052\pi$
$163$	3.39062	+	5.87273i	0.265574	+	0.459988i	−0.702140	+	0.712039i	$0.747772\pi$
$164$	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	−0.588559	−	0.808455i	$-0.700304\pi$
$167$	5.24490	−	9.08444i	0.405863	−	0.702975i	0.994421	+	0.105479i	$0.0336377\pi$
$168$	−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	$-0.546804\pi$
$193$	10.8837	−	18.8511i	0.783425	−	1.35693i	0.929935	−	0.367723i	$-0.119863\pi$
$194$	14.8413			1.06555
$195$		0			0
$196$	−3.05441			−0.218172
$197$	−0.848360	+	1.46940i	−0.0604432	+	0.104691i	−0.894664	−	0.446741i	$-0.852585\pi$
$197$	−0.848360	+	1.46940i	−0.0604432	+	0.104691i	0.834220	+	0.551431i	$0.185918\pi$
$198$	−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	−0.995079	−	0.0990887i	$-0.968407\pi$
$223$	−6.14838	+	10.6493i	−0.411726	+	0.713130i	0.583353	+	0.812219i	$0.301741\pi$
$224$	−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	0.711143	−	0.703048i	$-0.248178\pi$
$227$	−3.81613	−	6.60974i	−0.253286	−	0.438704i	−0.964428	+	0.264344i	$0.914845\pi$
$228$	−1.35505	−	2.34702i	−0.0897406	−	0.155435i
$229$	14.4008			0.951631			0.475815	−	0.879545i	$-0.342153\pi$
$229$	14.4008			0.951631			0.475815	+	0.879545i	$0.342153\pi$
$230$	−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	$-0.277242\pi$
$239$	19.9143			1.28815			0.644076	+	0.764962i	$0.277242\pi$
$240$	3.16341	+	5.47918i	0.204197	+	0.353680i
$241$	11.6332	+	20.1493i	0.749360	+	1.29793i	0.948130	+	0.317883i	$0.102972\pi$
$241$	11.6332	+	20.1493i	0.749360	+	1.29793i	−0.198770	+	0.980046i	$0.563695\pi$
$242$	−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	−0.976769	−	0.214294i	$-0.931255\pi$
$271$	−4.98473	+	8.63381i	−0.302801	+	0.524467i	0.673968	+	0.738760i	$0.264588\pi$
$272$	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	$-0.603751\pi$
$281$	−10.7352			−0.640406			−0.320203	+	0.947349i	$0.603751\pi$
$282$	−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	$0.0177456\pi$
$293$	9.37133	+	16.2316i	0.547479	+	0.948261i	−0.450968	+	0.892540i	$0.648921\pi$
$294$	−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	$-0.633841\pi$
$307$	−14.3043			−0.816387			−0.408194	+	0.912895i	$0.633841\pi$
$308$	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	$-0.515970\pi$
$317$	−1.78575			−0.100297			−0.0501487	+	0.998742i	$0.515970\pi$
$318$	−6.31414	−	10.9364i	−0.354080	−	0.613284i
$319$	−0.0664168	−	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	0.948057	−	0.318101i	$-0.103045\pi$
$331$	3.61220	+	6.25652i	0.198545	+	0.343889i	−0.749512	+	0.661991i	$0.769712\pi$
$332$	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	$-0.616033\pi$
$349$	11.7855	−	20.4131i	0.630865	−	1.09269i	0.987375	−	0.158399i	$-0.0506333\pi$
$350$	4.39111			0.234715
$351$		0			0
$352$	15.1479			0.807385
$353$	2.86863	−	4.96862i	0.152682	−	0.264453i	−0.779531	−	0.626364i	$-0.784542\pi$
$353$	2.86863	−	4.96862i	0.152682	−	0.264453i	0.932213	+	0.361911i	$0.117876\pi$
$354$	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	$-0.273364\pi$
$359$	24.7583			1.30669			0.653347	+	0.757059i	$0.273364\pi$
$360$	−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	$-0.600609\pi$
$379$	12.9989	−	22.5147i	0.667707	−	1.15650i	0.978544	−	0.206039i	$-0.0660572\pi$
$380$	−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	0.716935	−	0.697140i	$-0.245544\pi$
$383$	−4.80010	−	8.31401i	−0.245274	−	0.424826i	−0.962208	+	0.272314i	$0.912211\pi$
$384$	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	0.575285	−	0.817953i	$-0.304891\pi$
$397$	−8.38291	−	14.5196i	−0.420726	−	0.728719i	−0.996011	+	0.0892344i	$0.971558\pi$
$398$	−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	−0.985628	−	0.168928i	$-0.945969\pi$
$401$	−6.93902	+	12.0187i	−0.346518	+	0.600187i	0.639110	+	0.769115i	$0.279303\pi$
$402$	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	$0.0926459\pi$
$409$	14.7125	+	25.4829i	0.727489	+	1.26005i	−0.230453	+	0.973083i	$0.574021\pi$
$410$	−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	$-0.555519\pi$
$421$	−7.12125			−0.347069			−0.173534	+	0.984828i	$0.555519\pi$
$422$	−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	$-0.573929\pi$
$431$	15.1072	−	26.1664i	0.727687	−	1.26039i	0.957858	−	0.287241i	$-0.0927381\pi$
$432$	−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	0.981887	−	0.189465i	$-0.0606754\pi$
$449$	6.92608	+	11.9963i	0.326862	+	0.566142i	−0.655025	+	0.755607i	$0.727342\pi$
$450$	−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	$-0.445788\pi$
$457$	20.0573	−	34.7402i	0.938240	−	1.62508i	0.768751	−	0.639548i	$-0.220878\pi$
$458$	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	0.764793	−	0.644276i	$-0.222841\pi$
$461$	−3.76950	−	6.52897i	−0.175563	−	0.304084i	−0.940356	+	0.340192i	$0.889508\pi$
$462$	27.5068	+	47.6432i	1.27973	+	2.21656i
$463$	−23.3031			−1.08299			−0.541494	−	0.840705i	$-0.682141\pi$
$463$	−23.3031			−1.08299			−0.541494	+	0.840705i	$0.682141\pi$
$464$	−0.0335403	−	0.0580936i	−0.00155707	−	0.00269693i
$465$	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	−0.527831	−	0.849350i	$-0.676994\pi$
$479$	10.3224	−	17.8789i	0.471643	−	0.816910i	0.999474	+	0.0324399i	$0.0103278\pi$
$480$	−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	0.898368	−	0.439243i	$-0.144753\pi$
$487$	1.51802	+	2.62929i	0.0687882	+	0.119145i	−0.829580	+	0.558388i	$0.811420\pi$
$488$	−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	$-0.774364\pi$
$499$	−33.9143			−1.51821			−0.759107	+	0.650966i	$0.774364\pi$
$500$	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	$0.346458\pi$
$509$	−12.0763	+	20.9168i	−0.535273	+	0.927120i	−0.999150	+	0.0412201i	$0.986876\pi$
$510$	−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	$-0.442334\pi$
$541$	8.38144			0.360346			0.180173	+	0.983635i	$0.442334\pi$
$542$	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	$0.370083\pi$
$557$	−14.0764	+	24.3810i	−0.596435	+	1.03306i	−0.993343	+	0.115197i	$0.963250\pi$
$558$	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	$-0.659432\pi$
$577$	−23.0691			−0.960379			−0.480189	+	0.877165i	$0.659432\pi$
$578$	−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	−0.995940	−	0.0900152i	$-0.971308\pi$
$587$	−10.1762	+	17.6256i	−0.420015	+	0.727487i	0.575926	+	0.817502i	$0.304642\pi$
$588$	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	$-0.568388\pi$
$593$	−10.3834			−0.426395			−0.213198	+	0.977009i	$0.568388\pi$
$594$	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	−0.975705	−	0.219089i	$-0.929691\pi$
$613$	−7.38100	+	12.7843i	−0.298116	+	0.516352i	0.677589	+	0.735441i	$0.263025\pi$
$614$	−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	0.586162	−	0.810194i	$-0.300638\pi$
$617$	−10.1486	−	17.5779i	−0.408567	−	0.707659i	−0.994729	+	0.102535i	$0.967305\pi$
$618$	−25.4642	−	44.1053i	−1.02432	−	1.77418i
$619$	−9.94207			−0.399605			−0.199803	−	0.979836i	$-0.564030\pi$
$619$	−9.94207			−0.399605			−0.199803	+	0.979836i	$0.564030\pi$
$620$	−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	0.875551	−	0.483126i	$-0.160499\pi$
$631$	0.486710	+	0.843006i	0.0193756	+	0.0335596i	−0.856175	+	0.516686i	$0.827165\pi$
$632$	−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	0.947359	−	0.320174i	$-0.103741\pi$
$643$	4.98022	+	8.62599i	0.196401	+	0.340176i	−0.750958	+	0.660350i	$0.770408\pi$
$644$	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	−0.516036	−	0.856567i	$-0.672593\pi$
$661$	12.4382	−	21.5437i	0.483791	−	0.837951i	0.999827	+	0.0186163i	$0.00592609\pi$
$662$	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	0.890060	−	0.455844i	$-0.150662\pi$
$683$	1.31344	+	2.27495i	0.0502574	+	0.0870484i	−0.839802	+	0.542892i	$0.817329\pi$
$684$	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	−0.973940	−	0.226806i	$-0.927172\pi$
$691$	−7.63765	+	13.2288i	−0.290550	+	0.503247i	0.683390	+	0.730053i	$0.260505\pi$
$692$	−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	$-0.906235\pi$
$709$	−19.4350	−	33.6624i	−0.729896	−	1.26422i	0.227031	−	0.973887i	$-0.427098\pi$
$710$	−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	$-0.504651\pi$
$733$	−0.791131			−0.0292211			−0.0146105	+	0.999893i	$0.504651\pi$
$734$	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	$-0.638886\pi$
$739$	15.5926	−	27.0073i	0.573585	−	0.993478i	0.996194	−	0.0871658i	$-0.0277810\pi$
$740$	−4.45965			−0.163940
$741$		0			0
$742$	−19.4938			−0.715639
$743$	2.78152	−	4.81773i	0.102044	−	0.176745i	−0.810483	−	0.585763i	$-0.800795\pi$
$743$	2.78152	−	4.81773i	0.102044	−	0.176745i	0.912527	+	0.409017i	$0.134128\pi$
$744$	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	$0.135161\pi$
$761$	22.4105	+	38.8161i	0.812379	+	1.40708i	−0.0988165	+	0.995106i	$0.531506\pi$
$762$	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	$0.417854\pi$
$769$	−19.6817	+	34.0897i	−0.709739	+	1.22930i	−0.964954	+	0.262420i	$0.915479\pi$
$770$	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	$0.173962\pi$
$773$	24.3902	+	42.2452i	0.877256	+	1.51945i	0.0229167	+	0.999737i	$0.492705\pi$
$774$	−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	$0.0848381\pi$
$787$	19.9304	+	34.5204i	0.710442	+	1.23052i	−0.254250	+	0.967139i	$0.581829\pi$
$788$	−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	$-0.608823\pi$
$811$	−19.0950			−0.670515			−0.335257	+	0.942127i	$0.608823\pi$
$812$	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	$0.369938\pi$
$821$	−17.0792	+	29.5820i	−0.596068	+	1.03242i	−0.993395	+	0.114743i	$0.963396\pi$
$822$	−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	$-0.0967654\pi$
$827$	54.8780			1.90830			0.954148	+	0.299337i	$0.0967654\pi$
$828$	−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	0.612939	−	0.790130i	$-0.289987\pi$
$839$	−10.9433	−	18.9543i	−0.377803	−	0.654374i	−0.990742	+	0.135756i	$0.956654\pi$
$840$	−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	$-0.393252\pi$
$853$	19.2240			0.658217			0.329108	+	0.944292i	$0.393252\pi$
$854$	−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	$-0.882840\pi$
$863$	−54.8186			−1.86605			−0.933024	+	0.359814i	$0.882840\pi$
$864$	−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	0.536805	−	0.843706i	$-0.319631\pi$
$877$	−13.6897	−	23.7113i	−0.462269	−	0.800673i	−0.999074	+	0.0430336i	$0.986298\pi$
$878$	−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	0.726612	−	0.687048i	$-0.241094\pi$
$929$	−7.06196	−	12.2317i	−0.231695	−	0.401308i	−0.958307	+	0.285740i	$0.907761\pi$
$930$	−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	$-0.364362\pi$
$941$	25.3591			0.826683			0.413342	+	0.910576i	$0.364362\pi$
$942$	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	$-0.598330\pi$
$947$	20.7111	−	35.8727i	0.673021	−	1.16571i	0.977043	−	0.213042i	$-0.0683371\pi$
$948$	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	$-0.624325\pi$
$967$	−23.6784			−0.761445			−0.380722	+	0.924689i	$0.624325\pi$
$968$	−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	−0.593812	−	0.804604i	$-0.702378\pi$
$977$	12.4997	−	21.6501i	0.399901	−	0.692649i	0.993713	+	0.111955i	$0.0357112\pi$
$978$	−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	$-0.356383\pi$
$983$	27.3418			0.872068			0.436034	+	0.899930i	$0.356383\pi$
$984$	13.3359	+	23.0985i	0.425134	+	0.736353i
$985$	−0.848360	+	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.n.191.3		8
13.2	odd	12		65.2.m.a.36.3	✓	8
13.3	even	3	inner	845.2.e.n.146.3		8
13.4	even	6		845.2.a.m.1.3		4
13.5	odd	4		845.2.m.g.316.2		8
13.6	odd	12		845.2.c.g.506.6		8
13.7	odd	12		845.2.c.g.506.3		8
13.8	odd	4		65.2.m.a.56.3	yes	8
13.9	even	3		845.2.a.l.1.2		4
13.10	even	6		845.2.e.m.146.2		8
13.11	odd	12		845.2.m.g.361.2		8
13.12	even	2		845.2.e.m.191.2		8
39.2	even	12		585.2.bu.c.361.2		8
39.8	even	4		585.2.bu.c.316.2		8
39.17	odd	6		7605.2.a.cf.1.2		4
39.35	odd	6		7605.2.a.cj.1.3		4
52.15	even	12		1040.2.da.b.881.4		8
52.47	even	4		1040.2.da.b.641.4		8
65.2	even	12		325.2.m.c.49.3		8
65.4	even	6		4225.2.a.bi.1.2		4
65.8	even	4		325.2.m.c.199.3		8
65.9	even	6		4225.2.a.bl.1.3		4
65.28	even	12		325.2.m.b.49.2		8
65.34	odd	4		325.2.n.d.251.2		8
65.47	even	4		325.2.m.b.199.2		8
65.54	odd	12		325.2.n.d.101.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	13.2	odd	12
65.2.m.a.56.3	yes	8	13.8	odd	4
325.2.m.b.49.2		8	65.28	even	12
325.2.m.b.199.2		8	65.47	even	4
325.2.m.c.49.3		8	65.2	even	12
325.2.m.c.199.3		8	65.8	even	4
325.2.n.d.101.2		8	65.54	odd	12
325.2.n.d.251.2		8	65.34	odd	4
585.2.bu.c.316.2		8	39.8	even	4
585.2.bu.c.361.2		8	39.2	even	12
845.2.a.l.1.2		4	13.9	even	3
845.2.a.m.1.3		4	13.4	even	6
845.2.c.g.506.3		8	13.7	odd	12
845.2.c.g.506.6		8	13.6	odd	12
845.2.e.m.146.2		8	13.10	even	6
845.2.e.m.191.2		8	13.12	even	2
845.2.e.n.146.3		8	13.3	even	3	inner
845.2.e.n.191.3		8	1.1	even	1	trivial
845.2.m.g.316.2		8	13.5	odd	4
845.2.m.g.361.2		8	13.11	odd	12
1040.2.da.b.641.4		8	52.47	even	4
1040.2.da.b.881.4		8	52.15	even	12
4225.2.a.bi.1.2		4	65.4	even	6
4225.2.a.bl.1.3		4	65.9	even	6
7605.2.a.cf.1.2		4	39.17	odd	6
7605.2.a.cj.1.3		4	39.35	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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