LMFDB - Embedded newform 961.2.c.c.521.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(439,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("961.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.c.439.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.618034 q^{2} +(0.618034 + 1.07047i) q^{3} -1.61803 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.381966 - 0.661585i) q^{6} +(2.11803 + 3.66854i) q^{7} +2.23607 q^{8} +(0.736068 - 1.27491i) q^{9} +(0.309017 - 0.535233i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.00000 - 1.73205i) q^{12} +(0.618034 - 1.07047i) q^{13} +(-1.30902 - 2.26728i) q^{14} -1.23607 q^{15} +1.85410 q^{16} +(2.61803 + 4.53457i) q^{17} +(-0.454915 + 0.787936i) q^{18} +(-1.11803 - 1.93649i) q^{19} +(0.809017 - 1.40126i) q^{20} +(-2.61803 + 4.53457i) q^{21} +(-0.618034 + 1.07047i) q^{22} +7.70820 q^{23} +(1.38197 + 2.39364i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.381966 + 0.661585i) q^{26} +5.52786 q^{27} +(-3.42705 - 5.93583i) q^{28} -7.23607 q^{29} +0.763932 q^{30} -5.61803 q^{32} +2.47214 q^{33} +(-1.61803 - 2.80252i) q^{34} -4.23607 q^{35} +(-1.19098 + 2.06284i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.690983 + 1.19682i) q^{38} +1.52786 q^{39} +(-1.11803 + 1.93649i) q^{40} +(-3.50000 + 6.06218i) q^{41} +(1.61803 - 2.80252i) q^{42} +(-1.61803 - 2.80252i) q^{43} +(-1.61803 + 2.80252i) q^{44} +(0.736068 + 1.27491i) q^{45} -4.76393 q^{46} -6.47214 q^{47} +(1.14590 + 1.98475i) q^{48} +(-5.47214 + 9.47802i) q^{49} +(-1.23607 - 2.14093i) q^{50} +(-3.23607 + 5.60503i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-0.763932 + 1.32317i) q^{53} -3.41641 q^{54} +(1.00000 + 1.73205i) q^{55} +(4.73607 + 8.20311i) q^{56} +(1.38197 - 2.39364i) q^{57} +4.47214 q^{58} +(1.11803 + 1.93649i) q^{59} +2.00000 q^{60} +14.1803 q^{61} +6.23607 q^{63} -0.236068 q^{64} +(0.618034 + 1.07047i) q^{65} -1.52786 q^{66} +(-4.00000 + 6.92820i) q^{67} +(-4.23607 - 7.33708i) q^{68} +(4.76393 + 8.25137i) q^{69} +2.61803 q^{70} +(-6.59017 + 11.4145i) q^{71} +(1.64590 - 2.85078i) q^{72} +(-0.236068 + 0.408882i) q^{73} +(0.618034 + 1.07047i) q^{74} +(-2.47214 + 4.28187i) q^{75} +(1.80902 + 3.13331i) q^{76} +8.47214 q^{77} -0.944272 q^{78} +(0.854102 + 1.47935i) q^{79} +(-0.927051 + 1.60570i) q^{80} +(1.20820 + 2.09267i) q^{81} +(2.16312 - 3.74663i) q^{82} +(1.47214 - 2.54981i) q^{83} +(4.23607 - 7.33708i) q^{84} -5.23607 q^{85} +(1.00000 + 1.73205i) q^{86} +(-4.47214 - 7.74597i) q^{87} +(2.23607 - 3.87298i) q^{88} +1.70820 q^{89} +(-0.454915 - 0.787936i) q^{90} +5.23607 q^{91} -12.4721 q^{92} +4.00000 q^{94} +2.23607 q^{95} +(-3.47214 - 6.01392i) q^{96} +1.94427 q^{97} +(3.38197 - 5.85774i) q^{98} +(-1.47214 - 2.54981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 6 q^{6} + 4 q^{7} - 6 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 2 q^{13} - 3 q^{14} + 4 q^{15} - 6 q^{16} + 6 q^{17} - 13 q^{18} + q^{20} - 6 q^{21} + 2 q^{22}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 6 * q^6 + 4 * q^7 - 6 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 2 * q^13 - 3 * q^14 + 4 * q^15 - 6 * q^16 + 6 * q^17 - 13 * q^18 + q^20 - 6 * q^21 + 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 6 * q^26 + 40 * q^27 - 7 * q^28 - 20 * q^29 + 12 * q^30 - 18 * q^32 - 8 * q^33 - 2 * q^34 - 8 * q^35 - 7 * q^36 - 4 * q^37 + 5 * q^38 + 24 * q^39 - 14 * q^41 + 2 * q^42 - 2 * q^43 - 2 * q^44 - 6 * q^45 - 28 * q^46 - 8 * q^47 + 18 * q^48 - 4 * q^49 + 4 * q^50 - 4 * q^51 - 4 * q^52 - 12 * q^53 + 40 * q^54 + 4 * q^55 + 10 * q^56 + 10 * q^57 + 8 * q^60 + 12 * q^61 + 16 * q^63 + 8 * q^64 - 2 * q^65 - 24 * q^66 - 16 * q^67 - 8 * q^68 + 28 * q^69 + 6 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 2 * q^74 + 8 * q^75 + 5 * q^76 + 16 * q^77 + 32 * q^78 - 10 * q^79 + 3 * q^80 - 22 * q^81 - 7 * q^82 - 12 * q^83 + 8 * q^84 - 12 * q^85 + 4 * q^86 - 20 * q^89 - 13 * q^90 + 12 * q^91 - 32 * q^92 + 16 * q^94 + 4 * q^96 - 28 * q^97 + 18 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.618034			−0.437016			−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034			−0.437016			−0.218508	+	0.975835i	$0.570119\pi$
$3$	0.618034	+	1.07047i	0.356822	+	0.618034i	0.987428	−	0.158069i	$-0.0505269\pi$
$3$	0.618034	+	1.07047i	0.356822	+	0.618034i	−0.630606	+	0.776103i	$0.717194\pi$
$4$	−1.61803			−0.809017
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−0.381966	−	0.661585i	−0.155937	−	0.270091i
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	0.919260	+	0.393651i	$0.128788\pi$
$7$	2.11803	+	3.66854i	0.800542	+	1.38658i	−0.118718	+	0.992928i	$0.537879\pi$
$8$	2.23607			0.790569
$9$	0.736068	−	1.27491i	0.245356	−	0.424969i
$10$	0.309017	−	0.535233i	0.0977198	−	0.169256i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	0.618034	−	1.07047i	0.171412	−	0.296894i	−0.767502	−	0.641047i	$-0.778500\pi$
$13$	0.618034	−	1.07047i	0.171412	−	0.296894i	0.938914	+	0.344153i	$0.111834\pi$
$14$	−1.30902	−	2.26728i	−0.349850	−	0.605957i
$15$	−1.23607			−0.319151
$16$	1.85410			0.463525
$17$	2.61803	+	4.53457i	0.634967	+	1.09979i	0.986522	+	0.163627i	$0.0523194\pi$
$17$	2.61803	+	4.53457i	0.634967	+	1.09979i	−0.351556	+	0.936167i	$0.614347\pi$
$18$	−0.454915	+	0.787936i	−0.107225	+	0.185718i
$19$	−1.11803	−	1.93649i	−0.256495	−	0.444262i	0.708806	−	0.705404i	$-0.249234\pi$
$19$	−1.11803	−	1.93649i	−0.256495	−	0.444262i	−0.965300	+	0.261142i	$0.915901\pi$
$20$	0.809017	−	1.40126i	0.180902	−	0.313331i
$21$	−2.61803	+	4.53457i	−0.571302	+	0.989524i
$22$	−0.618034	+	1.07047i	−0.131765	+	0.228224i
$23$	7.70820			1.60727			0.803636	−	0.595121i	$-0.202896\pi$
$23$	7.70820			1.60727			0.803636	+	0.595121i	$0.202896\pi$
$24$	1.38197	+	2.39364i	0.282093	+	0.488599i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−0.381966	+	0.661585i	−0.0749097	+	0.129747i
$27$	5.52786			1.06384
$28$	−3.42705	−	5.93583i	−0.647652	−	1.12177i
$29$	−7.23607			−1.34370			−0.671852	−	0.740685i	$-0.734501\pi$
$29$	−7.23607			−1.34370			−0.671852	+	0.740685i	$0.734501\pi$
$30$	0.763932			0.139474
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	2.47214			0.430344
$34$	−1.61803	−	2.80252i	−0.277491	−	0.480628i
$35$	−4.23607			−0.716026
$36$	−1.19098	+	2.06284i	−0.198497	+	0.343807i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	0.690983	+	1.19682i	0.112092	+	0.194149i
$39$	1.52786			0.244654
$40$	−1.11803	+	1.93649i	−0.176777	+	0.306186i
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	0.451896	+	0.892071i	$0.350748\pi$
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	−0.998504	+	0.0546823i	$0.982585\pi$
$42$	1.61803	−	2.80252i	0.249668	−	0.432438i
$43$	−1.61803	−	2.80252i	−0.246748	−	0.427380i	0.715874	−	0.698230i	$-0.246029\pi$
$43$	−1.61803	−	2.80252i	−0.246748	−	0.427380i	−0.962622	+	0.270850i	$0.912695\pi$
$44$	−1.61803	+	2.80252i	−0.243928	+	0.422495i
$45$	0.736068	+	1.27491i	0.109727	+	0.190052i
$46$	−4.76393			−0.702403
$47$	−6.47214			−0.944058			−0.472029	−	0.881583i	$-0.656478\pi$
$47$	−6.47214			−0.944058			−0.472029	+	0.881583i	$0.656478\pi$
$48$	1.14590	+	1.98475i	0.165396	+	0.286475i
$49$	−5.47214	+	9.47802i	−0.781734	+	1.35400i
$50$	−1.23607	−	2.14093i	−0.174806	−	0.302774i
$51$	−3.23607	+	5.60503i	−0.453140	+	0.784862i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−0.763932	+	1.32317i	−0.104934	+	0.181751i	−0.913711	−	0.406364i	$-0.866797\pi$
$53$	−0.763932	+	1.32317i	−0.104934	+	0.181751i	0.808777	+	0.588115i	$0.200130\pi$
$54$	−3.41641			−0.464914
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	4.73607	+	8.20311i	0.632884	+	1.09619i
$57$	1.38197	−	2.39364i	0.183046	−	0.317045i
$58$	4.47214			0.587220
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	0.929580	−	0.368620i	$-0.120170\pi$
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	−0.784024	+	0.620730i	$0.786836\pi$
$60$	2.00000			0.258199
$61$	14.1803			1.81561			0.907803	−	0.419396i	$-0.137758\pi$
$61$	14.1803			1.81561			0.907803	+	0.419396i	$0.137758\pi$
$62$		0			0
$63$	6.23607			0.785671
$64$	−0.236068			−0.0295085
$65$	0.618034	+	1.07047i	0.0766577	+	0.132775i
$66$	−1.52786			−0.188067
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	−4.23607	−	7.33708i	−0.513699	−	0.889752i
$69$	4.76393	+	8.25137i	0.573510	+	0.993348i
$70$	2.61803			0.312915
$71$	−6.59017	+	11.4145i	−0.782109	+	1.35465i	0.148602	+	0.988897i	$0.452523\pi$
$71$	−6.59017	+	11.4145i	−0.782109	+	1.35465i	−0.930711	+	0.365756i	$0.880811\pi$
$72$	1.64590	−	2.85078i	0.193971	−	0.335968i
$73$	−0.236068	+	0.408882i	−0.0276297	+	0.0478560i	−0.879510	−	0.475881i	$-0.842129\pi$
$73$	−0.236068	+	0.408882i	−0.0276297	+	0.0478560i	0.851880	+	0.523737i	$0.175463\pi$
$74$	0.618034	+	1.07047i	0.0718450	+	0.124439i
$75$	−2.47214	+	4.28187i	−0.285458	+	0.494427i
$76$	1.80902	+	3.13331i	0.207508	+	0.359415i
$77$	8.47214			0.965489
$78$	−0.944272			−0.106918
$79$	0.854102	+	1.47935i	0.0960940	+	0.166440i	0.910065	−	0.414466i	$-0.136032\pi$
$79$	0.854102	+	1.47935i	0.0960940	+	0.166440i	−0.813971	+	0.580906i	$0.802698\pi$
$80$	−0.927051	+	1.60570i	−0.103647	+	0.179523i
$81$	1.20820	+	2.09267i	0.134245	+	0.232519i
$82$	2.16312	−	3.74663i	0.238877	−	0.413746i
$83$	1.47214	−	2.54981i	0.161588	−	0.279878i	−0.773850	−	0.633368i	$-0.781672\pi$
$83$	1.47214	−	2.54981i	0.161588	−	0.279878i	0.935438	+	0.353490i	$0.115005\pi$
$84$	4.23607	−	7.33708i	0.462193	−	0.800542i
$85$	−5.23607			−0.567931
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	−4.47214	−	7.74597i	−0.479463	−	0.830455i
$88$	2.23607	−	3.87298i	0.238366	−	0.412861i
$89$	1.70820			0.181069			0.0905346	−	0.995893i	$-0.471142\pi$
$89$	1.70820			0.181069			0.0905346	+	0.995893i	$0.471142\pi$
$90$	−0.454915	−	0.787936i	−0.0479523	−	0.0830557i
$91$	5.23607			0.548889
$92$	−12.4721			−1.30031
$93$		0			0
$94$	4.00000			0.412568
$95$	2.23607			0.229416
$96$	−3.47214	−	6.01392i	−0.354373	−	0.613793i
$97$	1.94427			0.197411			0.0987055	−	0.995117i	$-0.468530\pi$
$97$	1.94427			0.197411			0.0987055	+	0.995117i	$0.468530\pi$
$98$	3.38197	−	5.85774i	0.341630	−	0.591721i
$99$	−1.47214	−	2.54981i	−0.147955	−	0.256266i
$100$	−3.23607	−	5.60503i	−0.323607	−	0.560503i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	2.00000	−	3.46410i	0.198030	−	0.342997i
$103$	−0.881966	+	1.52761i	−0.0869027	+	0.150520i	−0.906200	−	0.422848i	$-0.861030\pi$
$103$	−0.881966	+	1.52761i	−0.0869027	+	0.150520i	0.819298	+	0.573368i	$0.194364\pi$
$104$	1.38197	−	2.39364i	0.135513	−	0.234715i
$105$	−2.61803	−	4.53457i	−0.255494	−	0.442529i
$106$	0.472136	−	0.817763i	0.0458579	−	0.0794282i
$107$	−5.11803	−	8.86469i	−0.494779	−	0.856982i	0.505203	−	0.863001i	$-0.331418\pi$
$107$	−5.11803	−	8.86469i	−0.494779	−	0.856982i	−0.999982	+	0.00601821i	$0.998084\pi$
$108$	−8.94427			−0.860663
$109$	3.94427			0.377793			0.188896	−	0.981997i	$-0.439509\pi$
$109$	3.94427			0.377793			0.188896	+	0.981997i	$0.439509\pi$
$110$	−0.618034	−	1.07047i	−0.0589272	−	0.102065i
$111$	1.23607	−	2.14093i	0.117322	−	0.203208i
$112$	3.92705	+	6.80185i	0.371071	+	0.642715i
$113$	2.73607	−	4.73901i	0.257388	−	0.445808i	−0.708154	−	0.706058i	$-0.750472\pi$
$113$	2.73607	−	4.73901i	0.257388	−	0.445808i	0.965541	+	0.260250i	$0.0838049\pi$
$114$	−0.854102	+	1.47935i	−0.0799940	+	0.138554i
$115$	−3.85410	+	6.67550i	−0.359397	+	0.622494i
$116$	11.7082			1.08708
$117$	−0.909830	−	1.57587i	−0.0841138	−	0.145689i
$118$	−0.690983	−	1.19682i	−0.0636101	−	0.110176i
$119$	−11.0902	+	19.2087i	−1.01663	+	1.76086i
$120$	−2.76393			−0.252311
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−8.76393			−0.793449
$123$	−8.65248			−0.780167
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−3.85410			−0.343351
$127$	1.76393	+	3.05522i	0.156524	+	0.271107i	0.933613	−	0.358284i	$-0.116638\pi$
$127$	1.76393	+	3.05522i	0.156524	+	0.271107i	−0.777089	+	0.629391i	$0.783305\pi$
$128$	11.3820			1.00603
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	−0.381966	−	0.661585i	−0.0335006	−	0.0580248i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	−4.00000			−0.348155
$133$	4.73607	−	8.20311i	0.410669	−	0.711300i
$134$	2.47214	−	4.28187i	0.213560	−	0.369897i
$135$	−2.76393	+	4.78727i	−0.237881	+	0.412023i
$136$	5.85410	+	10.1396i	0.501985	+	0.869464i
$137$	9.85410	−	17.0678i	0.841893	−	1.45820i	−0.0463998	−	0.998923i	$-0.514775\pi$
$137$	9.85410	−	17.0678i	0.841893	−	1.45820i	0.888293	−	0.459278i	$-0.151892\pi$
$138$	−2.94427	−	5.09963i	−0.250633	−	0.434109i
$139$	13.4164			1.13796			0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164			1.13796			0.568982	+	0.822350i	$0.307337\pi$
$140$	6.85410			0.579277
$141$	−4.00000	−	6.92820i	−0.336861	−	0.583460i
$142$	4.07295	−	7.05455i	0.341794	−	0.592005i
$143$	−1.23607	−	2.14093i	−0.103365	−	0.179034i
$144$	1.36475	−	2.36381i	0.113729	−	0.196984i
$145$	3.61803	−	6.26662i	0.300461	−	0.520414i
$146$	0.145898	−	0.252703i	0.0120746	−	0.0209138i
$147$	−13.5279			−1.11576
$148$	1.61803	+	2.80252i	0.133002	+	0.230365i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$	1.52786	−	2.64634i	0.124750	−	0.216073i
$151$	−8.18034			−0.665707			−0.332853	−	0.942979i	$-0.608011\pi$
$151$	−8.18034			−0.665707			−0.332853	+	0.942979i	$0.608011\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	7.70820			0.623171
$154$	−5.23607			−0.421934
$155$		0			0
$156$	−2.47214			−0.197929
$157$	−14.8885			−1.18824			−0.594118	−	0.804378i	$-0.702499\pi$
$157$	−14.8885			−1.18824			−0.594118	+	0.804378i	$0.702499\pi$
$158$	−0.527864	−	0.914287i	−0.0419946	−	0.0727368i
$159$	−1.88854			−0.149771
$160$	2.80902	−	4.86536i	0.222072	−	0.384640i
$161$	16.3262	+	28.2779i	1.28669	+	2.22861i
$162$	−0.746711	−	1.29334i	−0.0586672	−	0.101615i
$163$	−2.70820			−0.212123			−0.106061	−	0.994360i	$-0.533824\pi$
$163$	−2.70820			−0.212123			−0.106061	+	0.994360i	$0.533824\pi$
$164$	5.66312	−	9.80881i	0.442215	−	0.765939i
$165$	−1.23607	+	2.14093i	−0.0962278	+	0.166671i
$166$	−0.909830	+	1.57587i	−0.0706165	+	0.122311i
$167$	1.23607	+	2.14093i	0.0956498	+	0.165670i	0.909880	−	0.414872i	$-0.136174\pi$
$167$	1.23607	+	2.14093i	0.0956498	+	0.165670i	−0.814230	+	0.580543i	$0.802840\pi$
$168$	−5.85410	+	10.1396i	−0.451654	+	0.782287i
$169$	5.73607	+	9.93516i	0.441236	+	0.764243i
$170$	3.23607			0.248195
$171$	−3.29180			−0.251730
$172$	2.61803	+	4.53457i	0.199623	+	0.345758i
$173$	7.47214	−	12.9421i	0.568096	−	0.983971i	−0.428658	−	0.903467i	$-0.641014\pi$
$173$	7.47214	−	12.9421i	0.568096	−	0.983971i	0.996754	−	0.0805044i	$-0.0256531\pi$
$174$	2.76393	+	4.78727i	0.209533	+	0.362922i
$175$	−8.47214	+	14.6742i	−0.640433	+	1.10926i
$176$	1.85410	−	3.21140i	0.139758	−	0.242068i
$177$	−1.38197	+	2.39364i	−0.103875	+	0.179917i
$178$	−1.05573			−0.0791302
$179$	−5.85410	−	10.1396i	−0.437556	−	0.757869i	0.559944	−	0.828530i	$-0.310823\pi$
$179$	−5.85410	−	10.1396i	−0.437556	−	0.757869i	−0.997500	+	0.0706608i	$0.977489\pi$
$180$	−1.19098	−	2.06284i	−0.0887706	−	0.153755i
$181$	9.09017	−	15.7446i	0.675667	−	1.17029i	−0.300606	−	0.953748i	$-0.597189\pi$
$181$	9.09017	−	15.7446i	0.675667	−	1.17029i	0.976273	−	0.216541i	$-0.0694776\pi$
$182$	−3.23607			−0.239873
$183$	8.76393	+	15.1796i	0.647848	+	1.12211i
$184$	17.2361			1.27066
$185$	2.00000			0.147043
$186$		0			0
$187$	10.4721			0.765798
$188$	10.4721			0.763759
$189$	11.7082	+	20.2792i	0.851647	+	1.47510i
$190$	−1.38197			−0.100258
$191$	−1.59017	+	2.75426i	−0.115061	+	0.199291i	−0.917804	−	0.397034i	$-0.870040\pi$
$191$	−1.59017	+	2.75426i	−0.115061	+	0.199291i	0.802743	+	0.596325i	$0.203373\pi$
$192$	−0.145898	−	0.252703i	−0.0105293	−	0.0182373i
$193$	2.73607	+	4.73901i	0.196946	+	0.341121i	0.947537	−	0.319646i	$-0.103564\pi$
$193$	2.73607	+	4.73901i	0.196946	+	0.341121i	−0.750590	+	0.660768i	$0.770231\pi$
$194$	−1.20163			−0.0862717
$195$	−0.763932	+	1.32317i	−0.0547063	+	0.0947541i
$196$	8.85410	−	15.3358i	0.632436	−	1.09541i
$197$	−7.70820	+	13.3510i	−0.549187	+	0.951219i	0.449144	+	0.893460i	$0.351729\pi$
$197$	−7.70820	+	13.3510i	−0.549187	+	0.951219i	−0.998331	+	0.0577599i	$0.981604\pi$
$198$	0.909830	+	1.57587i	0.0646588	+	0.111992i
$199$	−0.527864	+	0.914287i	−0.0374193	+	0.0648121i	−0.884129	−	0.467244i	$-0.845247\pi$
$199$	−0.527864	+	0.914287i	−0.0374193	+	0.0648121i	0.846709	+	0.532056i	$0.178580\pi$
$200$	4.47214	+	7.74597i	0.316228	+	0.547723i
$201$	−9.88854			−0.697484
$202$	1.85410			0.130454
$203$	−15.3262	−	26.5458i	−1.07569	−	1.86315i
$204$	5.23607	−	9.06914i	0.366598	−	0.634967i
$205$	−3.50000	−	6.06218i	−0.244451	−	0.423401i
$206$	0.545085	−	0.944115i	0.0379779	−	0.0657796i
$207$	5.67376	−	9.82724i	0.394354	−	0.683041i
$208$	1.14590	−	1.98475i	0.0794537	−	0.137618i
$209$	−4.47214			−0.309344
$210$	1.61803	+	2.80252i	0.111655	+	0.193392i
$211$	−0.409830	−	0.709846i	−0.0282139	−	0.0488678i	0.851574	−	0.524235i	$-0.175649\pi$
$211$	−0.409830	−	0.709846i	−0.0282139	−	0.0488678i	−0.879788	+	0.475367i	$0.842315\pi$
$212$	1.23607	−	2.14093i	0.0848935	−	0.147040i
$213$	−16.2918			−1.11630
$214$	3.16312	+	5.47868i	0.216226	+	0.374515i
$215$	3.23607			0.220698
$216$	12.3607			0.841038
$217$		0			0
$218$	−2.43769			−0.165101
$219$	−0.583592			−0.0394355
$220$	−1.61803	−	2.80252i	−0.109088	−	0.188946i
$221$	6.47214			0.435363
$222$	−0.763932	+	1.32317i	−0.0512718	+	0.0888053i
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	0.925188	−	0.379509i	$-0.123907\pi$
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	−0.791258	+	0.611482i	$0.790574\pi$
$224$	−11.8992	−	20.6100i	−0.795048	−	1.37706i
$225$	5.88854			0.392570
$226$	−1.69098	+	2.92887i	−0.112483	+	0.194825i
$227$	−1.23607	+	2.14093i	−0.0820407	+	0.142099i	−0.904126	−	0.427265i	$-0.859477\pi$
$227$	−1.23607	+	2.14093i	−0.0820407	+	0.142099i	0.822086	+	0.569364i	$0.192810\pi$
$228$	−2.23607	+	3.87298i	−0.148087	+	0.256495i
$229$	6.70820	+	11.6190i	0.443291	+	0.767802i	0.997931	−	0.0642881i	$-0.0204776\pi$
$229$	6.70820	+	11.6190i	0.443291	+	0.767802i	−0.554641	+	0.832090i	$0.687144\pi$
$230$	2.38197	−	4.12569i	0.157062	−	0.272040i
$231$	5.23607	+	9.06914i	0.344508	+	0.596705i
$232$	−16.1803			−1.06229
$233$	0.0557281			0.00365087			0.00182543	−	0.999998i	$-0.499419\pi$
$233$	0.0557281			0.00365087			0.00182543	+	0.999998i	$0.499419\pi$
$234$	0.562306	+	0.973942i	0.0367591	+	0.0636686i
$235$	3.23607	−	5.60503i	0.211098	−	0.365632i
$236$	−1.80902	−	3.13331i	−0.117757	−	0.203961i
$237$	−1.05573	+	1.82857i	−0.0685769	+	0.118779i
$238$	6.85410	−	11.8717i	0.444285	−	0.769525i
$239$	0.854102	−	1.47935i	0.0552473	−	0.0956911i	−0.837079	−	0.547082i	$-0.815739\pi$
$239$	0.854102	−	1.47935i	0.0552473	−	0.0956911i	0.892326	+	0.451391i	$0.149072\pi$
$240$	−2.29180			−0.147935
$241$	−15.1803	−	26.2931i	−0.977852	−	1.69369i	−0.670184	−	0.742195i	$-0.733785\pi$
$241$	−15.1803	−	26.2931i	−0.977852	−	1.69369i	−0.307667	−	0.951494i	$-0.599548\pi$
$242$	−2.16312	−	3.74663i	−0.139051	−	0.240843i
$243$	6.79837	−	11.7751i	0.436116	−	0.755375i
$244$	−22.9443			−1.46886
$245$	−5.47214	−	9.47802i	−0.349602	−	0.605528i
$246$	5.34752			0.340946
$247$	−2.76393			−0.175865
$248$		0			0
$249$	3.63932			0.230633
$250$	5.56231			0.351791
$251$	−12.0902	−	20.9408i	−0.763125	−	1.32177i	−0.941232	−	0.337760i	$-0.890331\pi$
$251$	−12.0902	−	20.9408i	−0.763125	−	1.32177i	0.178108	−	0.984011i	$-0.443002\pi$
$252$	−10.0902			−0.635621
$253$	7.70820	−	13.3510i	0.484611	−	0.839370i
$254$	−1.09017	−	1.88823i	−0.0684033	−	0.118478i
$255$	−3.23607	−	5.60503i	−0.202650	−	0.351001i
$256$	−6.56231			−0.410144
$257$	7.97214	−	13.8081i	0.497288	−	0.861328i	−0.502707	−	0.864457i	$-0.667663\pi$
$257$	7.97214	−	13.8081i	0.497288	−	0.861328i	0.999995	+	0.00312852i	$0.000995840\pi$
$258$	−1.23607	+	2.14093i	−0.0769542	+	0.133289i
$259$	4.23607	−	7.33708i	0.263216	−	0.455904i
$260$	−1.00000	−	1.73205i	−0.0620174	−	0.107417i
$261$	−5.32624	+	9.22531i	−0.329686	+	0.571033i
$262$	3.70820	+	6.42280i	0.229094	+	0.396802i
$263$	18.7639			1.15703			0.578517	−	0.815670i	$-0.303632\pi$
$263$	18.7639			1.15703			0.578517	+	0.815670i	$0.303632\pi$
$264$	5.52786			0.340217
$265$	−0.763932	−	1.32317i	−0.0469280	−	0.0812816i
$266$	−2.92705	+	5.06980i	−0.179469	+	0.310849i
$267$	1.05573	+	1.82857i	0.0646095	+	0.111907i
$268$	6.47214	−	11.2101i	0.395349	−	0.684764i
$269$	−14.4721	+	25.0665i	−0.882382	+	1.52833i	−0.0336962	+	0.999432i	$0.510728\pi$
$269$	−14.4721	+	25.0665i	−0.882382	+	1.52833i	−0.848686	+	0.528898i	$0.822605\pi$
$270$	1.70820	−	2.95870i	0.103958	−	0.180061i
$271$	−8.18034			−0.496920			−0.248460	−	0.968642i	$-0.579924\pi$
$271$	−8.18034			−0.496920			−0.248460	+	0.968642i	$0.579924\pi$
$272$	4.85410	+	8.40755i	0.294323	+	0.509783i
$273$	3.23607	+	5.60503i	0.195856	+	0.339232i
$274$	−6.09017	+	10.5485i	−0.367921	+	0.637257i
$275$	8.00000			0.482418
$276$	−7.70820	−	13.3510i	−0.463979	−	0.803636i
$277$	−18.6525			−1.12072			−0.560359	−	0.828250i	$-0.689337\pi$
$277$	−18.6525			−1.12072			−0.560359	+	0.828250i	$0.689337\pi$
$278$	−8.29180			−0.497309
$279$		0			0
$280$	−9.47214			−0.566068
$281$	17.0000			1.01413			0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000			1.01413			0.507067	+	0.861906i	$0.330729\pi$
$282$	2.47214	+	4.28187i	0.147214	+	0.254981i
$283$	21.8885			1.30114			0.650569	−	0.759447i	$-0.274530\pi$
$283$	21.8885			1.30114			0.650569	+	0.759447i	$0.274530\pi$
$284$	10.6631	−	18.4691i	0.632740	−	1.09594i
$285$	1.38197	+	2.39364i	0.0818606	+	0.141787i
$286$	0.763932	+	1.32317i	0.0451722	+	0.0782406i
$287$	−29.6525			−1.75033
$288$	−4.13525	+	7.16247i	−0.243672	+	0.422053i
$289$	−5.20820	+	9.02087i	−0.306365	+	0.530640i
$290$	−2.23607	+	3.87298i	−0.131306	+	0.227429i
$291$	1.20163	+	2.08128i	0.0704406	+	0.122007i
$292$	0.381966	−	0.661585i	0.0223529	−	0.0387163i
$293$	−4.23607	−	7.33708i	−0.247474	−	0.428637i	0.715350	−	0.698766i	$-0.246267\pi$
$293$	−4.23607	−	7.33708i	−0.247474	−	0.428637i	−0.962824	+	0.270129i	$0.912934\pi$
$294$	8.36068			0.487605
$295$	−2.23607			−0.130189
$296$	−2.23607	−	3.87298i	−0.129969	−	0.225113i
$297$	5.52786	−	9.57454i	0.320759	−	0.555571i
$298$	3.09017	+	5.35233i	0.179009	+	0.310052i
$299$	4.76393	−	8.25137i	0.275505	−	0.477189i
$300$	4.00000	−	6.92820i	0.230940	−	0.400000i
$301$	6.85410	−	11.8717i	0.395064	−	0.684271i
$302$	5.05573			0.290924
$303$	−1.85410	−	3.21140i	−0.106515	−	0.184490i
$304$	−2.07295	−	3.59045i	−0.118892	−	0.205927i
$305$	−7.09017	+	12.2805i	−0.405982	+	0.703181i
$306$	−4.76393			−0.272336
$307$	7.64590	+	13.2431i	0.436374	+	0.755823i	0.997407	−	0.0719712i	$-0.0229290\pi$
$307$	7.64590	+	13.2431i	0.436374	+	0.755823i	−0.561032	+	0.827794i	$0.689596\pi$
$308$	−13.7082			−0.781097
$309$	−2.18034			−0.124035
$310$		0			0
$311$	−6.81966			−0.386707			−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966			−0.386707			−0.193354	+	0.981129i	$0.561936\pi$
$312$	3.41641			0.193416
$313$	10.6180	+	18.3910i	0.600167	+	1.03952i	0.992795	+	0.119822i	$0.0382325\pi$
$313$	10.6180	+	18.3910i	0.600167	+	1.03952i	−0.392629	+	0.919697i	$0.628434\pi$
$314$	9.20163			0.519278
$315$	−3.11803	+	5.40059i	−0.175681	+	0.304289i
$316$	−1.38197	−	2.39364i	−0.0777417	−	0.134653i
$317$	−10.9721	−	19.0043i	−0.616257	−	1.06739i	−0.990163	−	0.139921i	$-0.955315\pi$
$317$	−10.9721	−	19.0043i	−0.616257	−	1.06739i	0.373906	−	0.927467i	$-0.378018\pi$
$318$	1.16718			0.0654524
$319$	−7.23607	+	12.5332i	−0.405142	+	0.701727i
$320$	0.118034	−	0.204441i	0.00659830	−	0.0114286i
$321$	6.32624	−	10.9574i	0.353096	−	0.611581i
$322$	−10.0902	−	17.4767i	−0.562303	−	0.973938i
$323$	5.85410	−	10.1396i	0.325731	−	0.564183i
$324$	−1.95492	−	3.38601i	−0.108606	−	0.188112i
$325$	4.94427			0.274259
$326$	1.67376			0.0927011
$327$	2.43769	+	4.22221i	0.134805	+	0.233489i
$328$	−7.82624	+	13.5554i	−0.432132	+	0.748474i
$329$	−13.7082	−	23.7433i	−0.755758	−	1.30901i
$330$	0.763932	−	1.32317i	0.0420531	−	0.0728381i
$331$	1.00000	−	1.73205i	0.0549650	−	0.0952021i	−0.837234	−	0.546845i	$-0.815829\pi$
$331$	1.00000	−	1.73205i	0.0549650	−	0.0952021i	0.892199	+	0.451643i	$0.149162\pi$
$332$	−2.38197	+	4.12569i	−0.130727	+	0.226426i
$333$	−2.94427			−0.161345
$334$	−0.763932	−	1.32317i	−0.0418005	−	0.0724006i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$	−4.85410	+	8.40755i	−0.264813	+	0.458670i
$337$	19.2361			1.04786			0.523928	−	0.851763i	$-0.324466\pi$
$337$	19.2361			1.04786			0.523928	+	0.851763i	$0.324466\pi$
$338$	−3.54508	−	6.14027i	−0.192827	−	0.333987i
$339$	6.76393			0.367366
$340$	8.47214			0.459466
$341$		0			0
$342$	2.03444			0.110010
$343$	−16.7082			−0.902158
$344$	−3.61803	−	6.26662i	−0.195071	−	0.337873i
$345$	−9.52786			−0.512963
$346$	−4.61803	+	7.99867i	−0.248267	+	0.430011i
$347$	0.909830	+	1.57587i	0.0488422	+	0.0845972i	0.889413	−	0.457105i	$-0.151114\pi$
$347$	0.909830	+	1.57587i	0.0488422	+	0.0845972i	−0.840571	+	0.541702i	$0.817780\pi$
$348$	7.23607	+	12.5332i	0.387894	+	0.671852i
$349$	27.8885			1.49284			0.746420	−	0.665475i	$-0.231771\pi$
$349$	27.8885			1.49284			0.746420	+	0.665475i	$0.231771\pi$
$350$	5.23607	−	9.06914i	0.279880	−	0.484766i
$351$	3.41641	−	5.91739i	0.182354	−	0.315847i
$352$	−5.61803	+	9.73072i	−0.299442	+	0.518649i
$353$	−9.70820	−	16.8151i	−0.516716	−	0.894978i	−0.999812	−	0.0194102i	$-0.993821\pi$
$353$	−9.70820	−	16.8151i	−0.516716	−	0.894978i	0.483096	−	0.875567i	$-0.339512\pi$
$354$	0.854102	−	1.47935i	0.0453950	−	0.0786265i
$355$	−6.59017	−	11.4145i	−0.349770	−	0.605819i
$356$	−2.76393			−0.146488
$357$	−27.4164			−1.45103
$358$	3.61803	+	6.26662i	0.191219	+	0.331201i
$359$	−8.88197	+	15.3840i	−0.468772	+	0.811937i	−0.999363	−	0.0356909i	$-0.988637\pi$
$359$	−8.88197	+	15.3840i	−0.468772	+	0.811937i	0.530591	+	0.847628i	$0.321970\pi$
$360$	1.64590	+	2.85078i	0.0867464	+	0.150249i
$361$	7.00000	−	12.1244i	0.368421	−	0.638124i
$362$	−5.61803	+	9.73072i	−0.295277	+	0.511435i
$363$	−4.32624	+	7.49326i	−0.227069	+	0.393294i
$364$	−8.47214			−0.444061
$365$	−0.236068	−	0.408882i	−0.0123564	−	0.0214018i
$366$	−5.41641	−	9.38149i	−0.283120	−	0.490379i
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	−0.529607	−	0.848243i	$-0.677661\pi$
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	0.999404	+	0.0345320i	$0.0109941\pi$
$368$	14.2918			0.745011
$369$	5.15248	+	8.92435i	0.268227	+	0.464583i
$370$	−1.23607			−0.0642601
$371$	−6.47214			−0.336017
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	−6.47214			−0.334666
$375$	−5.56231	−	9.63420i	−0.287236	−	0.497508i
$376$	−14.4721			−0.746343
$377$	−4.47214	+	7.74597i	−0.230327	+	0.398938i
$378$	−7.23607	−	12.5332i	−0.372183	−	0.644640i
$379$	18.9443	+	32.8124i	0.973102	+	1.68546i	0.686062	+	0.727543i	$0.259338\pi$
$379$	18.9443	+	32.8124i	0.973102	+	1.68546i	0.287040	+	0.957919i	$0.407329\pi$
$380$	−3.61803			−0.185601
$381$	−2.18034	+	3.77646i	−0.111702	+	0.193474i
$382$	0.982779	−	1.70222i	0.0502834	−	0.0870933i
$383$	5.94427	−	10.2958i	0.303738	−	0.526090i	−0.673241	−	0.739423i	$-0.735099\pi$
$383$	5.94427	−	10.2958i	0.303738	−	0.526090i	0.976980	+	0.213333i	$0.0684319\pi$
$384$	7.03444	+	12.1840i	0.358975	+	0.621763i
$385$	−4.23607	+	7.33708i	−0.215890	+	0.373932i
$386$	−1.69098	−	2.92887i	−0.0860688	−	0.149075i
$387$	−4.76393			−0.242164
$388$	−3.14590			−0.159709
$389$	8.94427	+	15.4919i	0.453493	+	0.785472i	0.998600	−	0.0528939i	$-0.0168445\pi$
$389$	8.94427	+	15.4919i	0.453493	+	0.785472i	−0.545108	+	0.838366i	$0.683511\pi$
$390$	0.472136	−	0.817763i	0.0239075	−	0.0414091i
$391$	20.1803	+	34.9534i	1.02056	+	1.76767i
$392$	−12.2361	+	21.1935i	−0.618015	+	1.07043i
$393$	7.41641	−	12.8456i	0.374108	−	0.647975i
$394$	4.76393	−	8.25137i	0.240003	−	0.415698i
$395$	−1.70820			−0.0859491
$396$	2.38197	+	4.12569i	0.119698	+	0.207324i
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	0.940389	−	0.340099i	$-0.110461\pi$
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	−0.764730	+	0.644351i	$0.777127\pi$
$398$	0.326238	−	0.565061i	0.0163528	−	0.0283239i
$399$	11.7082			0.586143
$400$	3.70820	+	6.42280i	0.185410	+	0.321140i
$401$	−15.8197			−0.789996			−0.394998	−	0.918682i	$-0.629255\pi$
$401$	−15.8197			−0.789996			−0.394998	+	0.918682i	$0.629255\pi$
$402$	6.11146			0.304812
$403$		0			0
$404$	4.85410			0.241501
$405$	−2.41641			−0.120072
$406$	9.47214	+	16.4062i	0.470094	+	0.814227i
$407$	−4.00000			−0.198273
$408$	−7.23607	+	12.5332i	−0.358239	+	0.620488i
$409$	−13.0902	−	22.6728i	−0.647267	−	1.12110i	−0.983773	−	0.179418i	$-0.942578\pi$
$409$	−13.0902	−	22.6728i	−0.647267	−	1.12110i	0.336506	−	0.941681i	$-0.390755\pi$
$410$	2.16312	+	3.74663i	0.106829	+	0.185033i
$411$	24.3607			1.20162
$412$	1.42705	−	2.47172i	0.0703058	−	0.121773i
$413$	−4.73607	+	8.20311i	−0.233047	+	0.403649i
$414$	−3.50658	+	6.07357i	−0.172339	+	0.298500i
$415$	1.47214	+	2.54981i	0.0722643	+	0.125165i
$416$	−3.47214	+	6.01392i	−0.170235	+	0.294856i
$417$	8.29180	+	14.3618i	0.406051	+	0.703301i
$418$	2.76393			0.135188
$419$	30.1246			1.47168			0.735842	−	0.677153i	$-0.236787\pi$
$419$	30.1246			1.47168			0.735842	+	0.677153i	$0.236787\pi$
$420$	4.23607	+	7.33708i	0.206699	+	0.358013i
$421$	7.68034	−	13.3027i	0.374317	−	0.648336i	−0.615908	−	0.787818i	$-0.711211\pi$
$421$	7.68034	−	13.3027i	0.374317	−	0.648336i	0.990225	+	0.139483i	$0.0445439\pi$
$422$	0.253289	+	0.438709i	0.0123299	+	0.0213560i
$423$	−4.76393	+	8.25137i	−0.231630	+	0.401195i
$424$	−1.70820	+	2.95870i	−0.0829577	+	0.143687i
$425$	−10.4721	+	18.1383i	−0.507973	+	0.879835i
$426$	10.0689			0.487839
$427$	30.0344	+	52.0212i	1.45347	+	2.51748i
$428$	8.28115	+	14.3434i	0.400285	+	0.693313i
$429$	1.52786	−	2.64634i	0.0737660	−	0.127766i
$430$	−2.00000			−0.0964486
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	10.2492			0.493116
$433$	12.1803			0.585350			0.292675	−	0.956212i	$-0.405455\pi$
$433$	12.1803			0.585350			0.292675	+	0.956212i	$0.405455\pi$
$434$		0			0
$435$	8.94427			0.428845
$436$	−6.38197			−0.305641
$437$	−8.61803	−	14.9269i	−0.412256	−	0.714049i
$438$	0.360680			0.0172339
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	0.494539	+	0.869155i	$0.335337\pi$
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	−0.999980	+	0.00629443i	$0.997996\pi$
$440$	2.23607	+	3.87298i	0.106600	+	0.184637i
$441$	8.05573	+	13.9529i	0.383606	+	0.664425i
$442$	−4.00000			−0.190261
$443$	−8.64590	+	14.9751i	−0.410779	+	0.711490i	−0.994975	−	0.100122i	$-0.968077\pi$
$443$	−8.64590	+	14.9751i	−0.410779	+	0.711490i	0.584196	+	0.811613i	$0.301410\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$	−0.854102	+	1.47935i	−0.0404883	+	0.0701278i
$446$	−1.23607	−	2.14093i	−0.0585295	−	0.101376i
$447$	6.18034	−	10.7047i	0.292320	−	0.506313i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−31.3050			−1.47737			−0.738686	−	0.674050i	$-0.764553\pi$
$449$	−31.3050			−1.47737			−0.738686	+	0.674050i	$0.764553\pi$
$450$	−3.63932			−0.171559
$451$	7.00000	+	12.1244i	0.329617	+	0.570914i
$452$	−4.42705	+	7.66788i	−0.208231	+	0.360667i
$453$	−5.05573	−	8.75678i	−0.237539	−	0.411429i
$454$	0.763932	−	1.32317i	0.0358531	−	0.0620994i
$455$	−2.61803	+	4.53457i	−0.122735	+	0.212584i
$456$	3.09017	−	5.35233i	0.144710	−	0.250646i
$457$	20.9443			0.979732			0.489866	−	0.871798i	$-0.337046\pi$
$457$	20.9443			0.979732			0.489866	+	0.871798i	$0.337046\pi$
$458$	−4.14590	−	7.18091i	−0.193725	−	0.335542i
$459$	14.4721	+	25.0665i	0.675501	+	1.17000i
$460$	6.23607	−	10.8012i	0.290758	−	0.503608i
$461$	10.3607			0.482545			0.241272	−	0.970457i	$-0.422435\pi$
$461$	10.3607			0.482545			0.241272	+	0.970457i	$0.422435\pi$
$462$	−3.23607	−	5.60503i	−0.150556	−	0.260770i
$463$	29.4164			1.36710			0.683548	−	0.729905i	$-0.260436\pi$
$463$	29.4164			1.36710			0.683548	+	0.729905i	$0.260436\pi$
$464$	−13.4164			−0.622841
$465$		0			0
$466$	−0.0344419			−0.00159549
$467$	−8.70820			−0.402968			−0.201484	−	0.979492i	$-0.564576\pi$
$467$	−8.70820			−0.402968			−0.201484	+	0.979492i	$0.564576\pi$
$468$	1.47214	+	2.54981i	0.0680495	+	0.117865i
$469$	−33.8885			−1.56483
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	−9.20163	−	15.9377i	−0.423989	−	0.734370i
$472$	2.50000	+	4.33013i	0.115072	+	0.199310i
$473$	−6.47214			−0.297589
$474$	0.652476	−	1.13012i	0.0299692	−	0.0519082i
$475$	4.47214	−	7.74597i	0.205196	−	0.355409i
$476$	17.9443	−	31.0804i	0.822474	−	1.42457i
$477$	1.12461	+	1.94788i	0.0514924	+	0.0891875i
$478$	−0.527864	+	0.914287i	−0.0241439	+	0.0418185i
$479$	−18.3541	−	31.7902i	−0.838620	−	1.45253i	−0.891048	−	0.453908i	$-0.850029\pi$
$479$	−18.3541	−	31.7902i	−0.838620	−	1.45253i	0.0524281	−	0.998625i	$-0.483304\pi$
$480$	6.94427			0.316961
$481$	−2.47214			−0.112720
$482$	9.38197	+	16.2500i	0.427337	+	0.740169i
$483$	−20.1803	+	34.9534i	−0.918237	+	1.59043i
$484$	−5.66312	−	9.80881i	−0.257414	−	0.445855i
$485$	−0.972136	+	1.68379i	−0.0441424	+	0.0764569i
$486$	−4.20163	+	7.27743i	−0.190590	+	0.330111i
$487$	−7.38197	+	12.7859i	−0.334509	+	0.579386i	−0.983390	−	0.181503i	$-0.941904\pi$
$487$	−7.38197	+	12.7859i	−0.334509	+	0.579386i	0.648882	+	0.760889i	$0.275237\pi$
$488$	31.7082			1.43536
$489$	−1.67376	−	2.89904i	−0.0756901	−	0.131099i
$490$	3.38197	+	5.85774i	0.152782	+	0.264626i
$491$	−20.1803	+	34.9534i	−0.910726	+	1.57742i	−0.0976849	+	0.995217i	$0.531144\pi$
$491$	−20.1803	+	34.9534i	−0.910726	+	1.57742i	−0.813041	+	0.582206i	$0.802190\pi$
$492$	14.0000			0.631169
$493$	−18.9443	−	32.8124i	−0.853207	−	1.47780i
$494$	1.70820			0.0768557
$495$	2.94427			0.132335
$496$		0			0
$497$	−55.8328			−2.50444
$498$	−2.24922			−0.100790
$499$	−16.7082	−	28.9395i	−0.747962	−	1.29551i	−0.948798	−	0.315883i	$-0.897699\pi$
$499$	−16.7082	−	28.9395i	−0.747962	−	1.29551i	0.200836	−	0.979625i	$-0.435634\pi$
$500$	14.5623			0.651246
$501$	−1.52786	+	2.64634i	−0.0682599	+	0.118230i
$502$	7.47214	+	12.9421i	0.333498	+	0.577635i
$503$	0.826238	+	1.43109i	0.0368401	+	0.0638090i	0.883858	−	0.467756i	$-0.154937\pi$
$503$	0.826238	+	1.43109i	0.0368401	+	0.0638090i	−0.847017	+	0.531565i	$0.821604\pi$
$504$	13.9443			0.621127
$505$	1.50000	−	2.59808i	0.0667491	−	0.115613i
$506$	−4.76393	+	8.25137i	−0.211783	+	0.366818i
$507$	−7.09017	+	12.2805i	−0.314886	+	0.545398i
$508$	−2.85410	−	4.94345i	−0.126630	−	0.219330i
$509$	−9.79837	+	16.9713i	−0.434305	+	0.752239i	−0.997239	−	0.0742635i	$-0.976339\pi$
$509$	−9.79837	+	16.9713i	−0.434305	+	0.752239i	0.562933	+	0.826502i	$0.309673\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	−2.00000			−0.0884748
$512$	−18.7082			−0.826794
$513$	−6.18034	−	10.7047i	−0.272869	−	0.472622i
$514$	−4.92705	+	8.53390i	−0.217323	+	0.376414i
$515$	−0.881966	−	1.52761i	−0.0388641	−	0.0673145i
$516$	−3.23607	+	5.60503i	−0.142460	+	0.246748i
$517$	−6.47214	+	11.2101i	−0.284644	+	0.493018i
$518$	−2.61803	+	4.53457i	−0.115030	+	0.199237i
$519$	18.4721			0.810837
$520$	1.38197	+	2.39364i	0.0606032	+	0.104968i
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	0.843288	−	0.537461i	$-0.180617\pi$
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	−0.887099	+	0.461579i	$0.847283\pi$
$522$	3.29180	−	5.70156i	0.144078	−	0.249550i
$523$	4.29180			0.187667			0.0938336	−	0.995588i	$-0.470088\pi$
$523$	4.29180			0.187667			0.0938336	+	0.995588i	$0.470088\pi$
$524$	9.70820	+	16.8151i	0.424105	+	0.734571i
$525$	−20.9443			−0.914083
$526$	−11.5967			−0.505642
$527$		0			0
$528$	4.58359			0.199475
$529$	36.4164			1.58332
$530$	0.472136	+	0.817763i	0.0205083	+	0.0355214i
$531$	3.29180			0.142852
$532$	−7.66312	+	13.2729i	−0.332238	+	0.575454i
$533$	4.32624	+	7.49326i	0.187390	+	0.324569i
$534$	−0.652476	−	1.13012i	−0.0282354	−	0.0489051i
$535$	10.2361			0.442544
$536$	−8.94427	+	15.4919i	−0.386334	+	0.669150i
$537$	7.23607	−	12.5332i	0.312259	−	0.540849i
$538$	8.94427	−	15.4919i	0.385615	−	0.667905i
$539$	10.9443	+	18.9560i	0.471403	+	0.816494i
$540$	4.47214	−	7.74597i	0.192450	−	0.333333i
$541$	−9.68034	−	16.7668i	−0.416190	−	0.720863i	0.579362	−	0.815070i	$-0.303302\pi$
$541$	−9.68034	−	16.7668i	−0.416190	−	0.720863i	−0.995553	+	0.0942074i	$0.969968\pi$
$542$	5.05573			0.217162
$543$	22.4721			0.964372
$544$	−14.7082	−	25.4754i	−0.630609	−	1.09225i
$545$	−1.97214	+	3.41584i	−0.0844770	+	0.146318i
$546$	−2.00000	−	3.46410i	−0.0855921	−	0.148250i
$547$	−14.0623	+	24.3566i	−0.601261	+	1.04141i	0.391370	+	0.920234i	$0.372001\pi$
$547$	−14.0623	+	24.3566i	−0.601261	+	1.04141i	−0.992630	+	0.121181i	$0.961332\pi$
$548$	−15.9443	+	27.6163i	−0.681106	+	1.17971i
$549$	10.4377	−	18.0786i	0.445470	−	0.771577i
$550$	−4.94427			−0.210824
$551$	8.09017	+	14.0126i	0.344653	+	0.596956i
$552$	10.6525	+	18.4506i	0.453399	+	0.785311i
$553$	−3.61803	+	6.26662i	−0.153854	+	0.266484i
$554$	11.5279			0.489772
$555$	1.23607	+	2.14093i	0.0524682	+	0.0908775i
$556$	−21.7082			−0.920633
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	−7.85410			−0.331896
$561$	6.47214	+	11.2101i	0.273254	+	0.473289i
$562$	−10.5066			−0.443193
$563$	19.7705	−	34.2435i	0.833228	−	1.44319i	−0.0622377	−	0.998061i	$-0.519824\pi$
$563$	19.7705	−	34.2435i	0.833228	−	1.44319i	0.895465	−	0.445131i	$-0.146843\pi$
$564$	6.47214	+	11.2101i	0.272526	+	0.472029i
$565$	2.73607	+	4.73901i	0.115107	+	0.199372i
$566$	−13.5279			−0.568619
$567$	−5.11803	+	8.86469i	−0.214937	+	0.372282i
$568$	−14.7361	+	25.5236i	−0.618312	+	1.07095i
$569$	7.23607	−	12.5332i	0.303352	−	0.525421i	−0.673541	−	0.739150i	$-0.735228\pi$
$569$	7.23607	−	12.5332i	0.303352	−	0.525421i	0.976893	+	0.213729i	$0.0685610\pi$
$570$	−0.854102	−	1.47935i	−0.0357744	−	0.0619631i
$571$	2.90983	−	5.03997i	0.121773	−	0.210916i	−0.798694	−	0.601737i	$-0.794475\pi$
$571$	2.90983	−	5.03997i	0.121773	−	0.210916i	0.920467	+	0.390821i	$0.127809\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$	−3.93112			−0.164225
$574$	18.3262			0.764922
$575$	15.4164	+	26.7020i	0.642909	+	1.11355i
$576$	−0.173762	+	0.300965i	−0.00724009	+	0.0125402i
$577$	−12.4164	−	21.5058i	−0.516902	−	0.895300i	−0.999807	−	0.0196278i	$-0.993752\pi$
$577$	−12.4164	−	21.5058i	−0.516902	−	0.895300i	0.482906	−	0.875672i	$-0.339581\pi$
$578$	3.21885	−	5.57521i	0.133886	−	0.231898i
$579$	−3.38197	+	5.85774i	−0.140550	+	0.243439i
$580$	−5.85410	+	10.1396i	−0.243078	+	0.421024i
$581$	12.4721			0.517431
$582$	−0.742646	−	1.28630i	−0.0307837	−	0.0533189i
$583$	1.52786	+	2.64634i	0.0632777	+	0.109600i
$584$	−0.527864	+	0.914287i	−0.0218432	+	0.0378335i
$585$	1.81966			0.0752337
$586$	2.61803	+	4.53457i	0.108150	+	0.187321i
$587$	−2.47214			−0.102036			−0.0510180	−	0.998698i	$-0.516247\pi$
$587$	−2.47214			−0.102036			−0.0510180	+	0.998698i	$0.516247\pi$
$588$	21.8885			0.902668
$589$		0			0
$590$	1.38197			0.0568946
$591$	−19.0557			−0.783848
$592$	−1.85410	−	3.21140i	−0.0762031	−	0.131988i
$593$	−15.4721			−0.635364			−0.317682	−	0.948197i	$-0.602905\pi$
$593$	−15.4721			−0.635364			−0.317682	+	0.948197i	$0.602905\pi$
$594$	−3.41641	+	5.91739i	−0.140177	+	0.242794i
$595$	−11.0902	−	19.2087i	−0.454653	−	0.787481i
$596$	8.09017	+	14.0126i	0.331386	+	0.573978i
$597$	−1.30495			−0.0534081
$598$	−2.94427	+	5.09963i	−0.120400	+	0.208539i
$599$	−17.2984	+	29.9617i	−0.706792	+	1.22420i	0.259248	+	0.965811i	$0.416525\pi$
$599$	−17.2984	+	29.9617i	−0.706792	+	1.22420i	−0.966041	+	0.258390i	$0.916808\pi$
$600$	−5.52786	+	9.57454i	−0.225674	+	0.390879i
$601$	−18.2705	−	31.6455i	−0.745270	−	1.29084i	−0.950069	−	0.312041i	$-0.898987\pi$
$601$	−18.2705	−	31.6455i	−0.745270	−	1.29084i	0.204799	−	0.978804i	$-0.434346\pi$
$602$	−4.23607	+	7.33708i	−0.172649	+	0.299037i
$603$	5.88854	+	10.1993i	0.239800	+	0.415346i
$604$	13.2361			0.538568
$605$	−7.00000			−0.284590
$606$	1.14590	+	1.98475i	0.0465489	+	0.0806251i
$607$	−6.76393	+	11.7155i	−0.274540	+	0.475516i	−0.970019	−	0.243030i	$-0.921859\pi$
$607$	−6.76393	+	11.7155i	−0.274540	+	0.475516i	0.695479	+	0.718546i	$0.255192\pi$
$608$	6.28115	+	10.8793i	0.254734	+	0.441213i
$609$	18.9443	−	32.8124i	0.767661	−	1.32963i
$610$	4.38197	−	7.58979i	0.177421	−	0.307302i
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$	−12.4721			−0.504156
$613$	−4.05573	−	7.02473i	−0.163809	−	0.283726i	0.772422	−	0.635109i	$-0.219045\pi$
$613$	−4.05573	−	7.02473i	−0.163809	−	0.283726i	−0.936232	+	0.351383i	$0.885712\pi$
$614$	−4.72542	−	8.18468i	−0.190703	−	0.330307i
$615$	4.32624	−	7.49326i	0.174451	−	0.302158i
$616$	18.9443			0.763286
$617$	−11.7639	−	20.3757i	−0.473598	−	0.820296i	0.525945	−	0.850519i	$-0.323712\pi$
$617$	−11.7639	−	20.3757i	−0.473598	−	0.820296i	−0.999543	+	0.0302226i	$0.990378\pi$
$618$	1.34752			0.0542054
$619$	16.1803			0.650343			0.325171	−	0.945655i	$-0.394578\pi$
$619$	16.1803			0.650343			0.325171	+	0.945655i	$0.394578\pi$
$620$		0			0
$621$	42.6099			1.70988
$622$	4.21478			0.168997
$623$	3.61803	+	6.26662i	0.144953	+	0.251067i
$624$	2.83282			0.113403
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−6.56231	−	11.3662i	−0.262282	−	0.454287i
$627$	−2.76393	−	4.78727i	−0.110381	−	0.191185i
$628$	24.0902			0.961302
$629$	5.23607	−	9.06914i	0.208776	−	0.361610i
$630$	1.92705	−	3.33775i	0.0767755	−	0.132979i
$631$	−5.18034	+	8.97261i	−0.206226	+	0.357194i	−0.950523	−	0.310655i	$-0.899452\pi$
$631$	−5.18034	+	8.97261i	−0.206226	+	0.357194i	0.744297	+	0.667849i	$0.232785\pi$
$632$	1.90983	+	3.30792i	0.0759690	+	0.131582i
$633$	0.506578	−	0.877419i	0.0201347	−	0.0348743i
$634$	6.78115	+	11.7453i	0.269314	+	0.466466i
$635$	−3.52786			−0.139999
$636$	3.05573			0.121168
$637$	6.76393	+	11.7155i	0.267997	+	0.464184i
$638$	4.47214	−	7.74597i	0.177054	−	0.306666i
$639$	9.70163	+	16.8037i	0.383790	+	0.664744i
$640$	−5.69098	+	9.85707i	−0.224956	+	0.389635i
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$	−3.90983	+	6.77202i	−0.154309	+	0.267270i
$643$	−28.4721			−1.12283			−0.561416	−	0.827534i	$-0.689743\pi$
$643$	−28.4721			−1.12283			−0.561416	+	0.827534i	$0.689743\pi$
$644$	−26.4164	−	45.7546i	−1.04095	−	1.80298i
$645$	2.00000	+	3.46410i	0.0787499	+	0.136399i
$646$	−3.61803	+	6.26662i	−0.142350	+	0.246557i
$647$	−16.9443			−0.666148			−0.333074	−	0.942901i	$-0.608086\pi$
$647$	−16.9443			−0.666148			−0.333074	+	0.942901i	$0.608086\pi$
$648$	2.70163	+	4.67935i	0.106130	+	0.183822i
$649$	4.47214			0.175547
$650$	−3.05573			−0.119856
$651$		0			0
$652$	4.38197			0.171611
$653$	15.3050			0.598929			0.299465	−	0.954107i	$-0.403192\pi$
$653$	15.3050			0.598929			0.299465	+	0.954107i	$0.403192\pi$
$654$	−1.50658	−	2.60947i	−0.0589119	−	0.102038i
$655$	12.0000			0.468879
$656$	−6.48936	+	11.2399i	−0.253367	+	0.438844i
$657$	0.347524	+	0.601929i	0.0135582	+	0.0234835i
$658$	8.47214	+	14.6742i	0.330278	+	0.572059i
$659$	−5.65248			−0.220189			−0.110095	−	0.993921i	$-0.535115\pi$
$659$	−5.65248			−0.220189			−0.110095	+	0.993921i	$0.535115\pi$
$660$	2.00000	−	3.46410i	0.0778499	−	0.134840i
$661$	22.6803	−	39.2835i	0.882163	−	1.52795i	0.0332318	−	0.999448i	$-0.489420\pi$
$661$	22.6803	−	39.2835i	0.882163	−	1.52795i	0.848931	−	0.528503i	$-0.177247\pi$
$662$	−0.618034	+	1.07047i	−0.0240206	+	0.0416049i
$663$	4.00000	+	6.92820i	0.155347	+	0.269069i
$664$	3.29180	−	5.70156i	0.127746	−	0.221263i
$665$	4.73607	+	8.20311i	0.183657	+	0.318103i
$666$	1.81966			0.0705104
$667$	−55.7771			−2.15970
$668$	−2.00000	−	3.46410i	−0.0773823	−	0.134030i
$669$	−2.47214	+	4.28187i	−0.0955783	+	0.165546i
$670$	2.47214	+	4.28187i	0.0955069	+	0.165423i
$671$	14.1803	−	24.5611i	0.547426	−	0.948170i
$672$	14.7082	−	25.4754i	0.567381	−	0.982733i
$673$	23.5066	−	40.7146i	0.906112	−	1.56943i	0.0866944	−	0.996235i	$-0.472370\pi$
$673$	23.5066	−	40.7146i	0.906112	−	1.56943i	0.819418	−	0.573197i	$-0.194297\pi$
$674$	−11.8885			−0.457930
$675$	11.0557	+	19.1491i	0.425535	+	0.737049i
$676$	−9.28115	−	16.0754i	−0.356967	−	0.618286i
$677$	21.3607	−	36.9978i	0.820958	−	1.42194i	−0.0840123	−	0.996465i	$-0.526774\pi$
$677$	21.3607	−	36.9978i	0.820958	−	1.42194i	0.904970	−	0.425476i	$-0.139893\pi$
$678$	−4.18034			−0.160545
$679$	4.11803	+	7.13264i	0.158036	+	0.273726i
$680$	−11.7082			−0.448989
$681$	−3.05573			−0.117096
$682$		0			0
$683$	−17.1803			−0.657387			−0.328694	−	0.944437i	$-0.606608\pi$
$683$	−17.1803			−0.657387			−0.328694	+	0.944437i	$0.606608\pi$
$684$	5.32624			0.203654
$685$	9.85410	+	17.0678i	0.376506	+	0.652127i
$686$	10.3262			0.394258
$687$	−8.29180	+	14.3618i	−0.316352	+	0.547937i
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$	0.944272	+	1.63553i	0.0359739	+	0.0623086i
$690$	5.88854			0.224173
$691$	9.59017	−	16.6107i	0.364827	−	0.631899i	−0.623921	−	0.781487i	$-0.714461\pi$
$691$	9.59017	−	16.6107i	0.364827	−	0.631899i	0.988748	+	0.149588i	$0.0477947\pi$
$692$	−12.0902	+	20.9408i	−0.459599	+	0.796049i
$693$	6.23607	−	10.8012i	0.236889	−	0.410303i
$694$	−0.562306	−	0.973942i	−0.0213448	−	0.0369703i
$695$	−6.70820	+	11.6190i	−0.254457	+	0.440732i
$696$	−10.0000	−	17.3205i	−0.379049	−	0.656532i
$697$	−36.6525			−1.38831
$698$	−17.2361			−0.652395
$699$	0.0344419	+	0.0596550i	0.00130271	+	0.00225636i
$700$	13.7082	−	23.7433i	0.518121	−	0.897413i
$701$	−3.50000	−	6.06218i	−0.132193	−	0.228965i	0.792329	−	0.610095i	$-0.208869\pi$
$701$	−3.50000	−	6.06218i	−0.132193	−	0.228965i	−0.924522	+	0.381129i	$0.875535\pi$
$702$	−2.11146	+	3.65715i	−0.0796918	+	0.138030i
$703$	−2.23607	+	3.87298i	−0.0843349	+	0.146072i
$704$	−0.236068	+	0.408882i	−0.00889715	+	0.0154103i
$705$	8.00000			0.301297
$706$	6.00000	+	10.3923i	0.225813	+	0.391120i
$707$	−6.35410	−	11.0056i	−0.238971	−	0.413909i
$708$	2.23607	−	3.87298i	0.0840366	−	0.145556i
$709$	−34.4721			−1.29463			−0.647314	−	0.762223i	$-0.724108\pi$
$709$	−34.4721			−1.29463			−0.647314	+	0.762223i	$0.724108\pi$
$710$	4.07295	+	7.05455i	0.152855	+	0.264753i
$711$	2.51471			0.0943089
$712$	3.81966			0.143148
$713$		0			0
$714$	16.9443			0.634123
$715$	2.47214			0.0924526
$716$	9.47214	+	16.4062i	0.353990	+	0.613129i
$717$	2.11146			0.0788538
$718$	5.48936	−	9.50785i	0.204861	−	0.354830i
$719$	−18.0902	−	31.3331i	−0.674649	−	1.16853i	−0.976571	−	0.215194i	$-0.930961\pi$
$719$	−18.0902	−	31.3331i	−0.674649	−	1.16853i	0.301922	−	0.953333i	$-0.402372\pi$
$720$	1.36475	+	2.36381i	0.0508610	+	0.0880939i
$721$	−7.47214			−0.278277
$722$	−4.32624	+	7.49326i	−0.161006	+	0.278870i
$723$	18.7639	−	32.5001i	0.697838	−	1.20869i
$724$	−14.7082	+	25.4754i	−0.546626	+	0.946784i
$725$	−14.4721	−	25.0665i	−0.537482	−	0.930946i
$726$	2.67376	−	4.63109i	0.0992326	−	0.171876i
$727$	19.8820	+	34.4366i	0.737381	+	1.27718i	0.953671	+	0.300853i	$0.0972712\pi$
$727$	19.8820	+	34.4366i	0.737381	+	1.27718i	−0.216289	+	0.976329i	$0.569395\pi$
$728$	11.7082			0.433935
$729$	24.0557			0.890953
$730$	0.145898	+	0.252703i	0.00539993	+	0.00935295i
$731$	8.47214	−	14.6742i	0.313353	−	0.542744i
$732$	−14.1803	−	24.5611i	−0.524120	−	0.907803i
$733$	2.73607	−	4.73901i	0.101059	−	0.175039i	−0.811062	−	0.584960i	$-0.801110\pi$
$733$	2.73607	−	4.73901i	0.101059	−	0.175039i	0.912121	+	0.409921i	$0.134444\pi$
$734$	−5.56231	+	9.63420i	−0.205308	+	0.355605i
$735$	6.76393	−	11.7155i	0.249491	−	0.432132i
$736$	−43.3050			−1.59624
$737$	8.00000	+	13.8564i	0.294684	+	0.510407i
$738$	−3.18441	−	5.51555i	−0.117220	−	0.203030i
$739$	−8.09017	+	14.0126i	−0.297602	+	0.515461i	−0.975587	−	0.219614i	$-0.929520\pi$
$739$	−8.09017	+	14.0126i	−0.297602	+	0.515461i	0.677985	+	0.735076i	$0.262853\pi$
$740$	−3.23607			−0.118960
$741$	−1.70820	−	2.95870i	−0.0627524	−	0.108690i
$742$	4.00000			0.146845
$743$	−27.8197			−1.02060			−0.510302	−	0.859995i	$-0.670466\pi$
$743$	−27.8197			−1.02060			−0.510302	+	0.859995i	$0.670466\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	−11.7426			−0.429929
$747$	−2.16718	−	3.75367i	−0.0792931	−	0.137340i
$748$	−16.9443			−0.619544
$749$	21.6803	−	37.5515i	0.792182	−	1.37210i
$750$	3.43769	+	5.95426i	0.125527	+	0.217419i
$751$	−22.7705	−	39.4397i	−0.830908	−	1.43917i	−0.897319	−	0.441382i	$-0.854488\pi$
$751$	−22.7705	−	39.4397i	−0.830908	−	1.43917i	0.0664116	−	0.997792i	$-0.478845\pi$
$752$	−12.0000			−0.437595
$753$	14.9443	−	25.8842i	0.544600	−	0.943274i
$754$	2.76393	−	4.78727i	0.100656	−	0.174342i
$755$	4.09017	−	7.08438i	0.148857	−	0.257827i
$756$	−18.9443	−	32.8124i	−0.688997	−	1.19338i
$757$	−11.3262	+	19.6176i	−0.411659	+	0.713015i	−0.995071	−	0.0991617i	$-0.968384\pi$
$757$	−11.3262	+	19.6176i	−0.411659	+	0.713015i	0.583412	+	0.812176i	$0.301717\pi$
$758$	−11.7082	−	20.2792i	−0.425261	−	0.736574i
$759$	19.0557			0.691679
$760$	5.00000			0.181369
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	0.883581	−	0.468278i	$-0.155125\pi$
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	−0.847331	+	0.531065i	$0.821792\pi$
$762$	1.34752	−	2.33398i	0.0488156	−	0.0845512i
$763$	8.35410	+	14.4697i	0.302439	+	0.523839i
$764$	2.57295	−	4.45648i	0.0930860	−	0.161230i
$765$	−3.85410	+	6.67550i	−0.139345	+	0.241353i
$766$	−3.67376	+	6.36314i	−0.132738	+	0.229910i
$767$	2.76393			0.0997998
$768$	−4.05573	−	7.02473i	−0.146348	−	0.253483i
$769$	1.31966	+	2.28572i	0.0475882	+	0.0824251i	0.888838	−	0.458221i	$-0.151513\pi$
$769$	1.31966	+	2.28572i	0.0475882	+	0.0824251i	−0.841250	+	0.540646i	$0.818180\pi$
$770$	2.61803	−	4.53457i	0.0943474	−	0.163414i
$771$	19.7082			0.709774
$772$	−4.42705	−	7.66788i	−0.159333	−	0.275973i
$773$	−29.1246			−1.04754			−0.523770	−	0.851860i	$-0.675475\pi$
$773$	−29.1246			−1.04754			−0.523770	+	0.851860i	$0.675475\pi$
$774$	2.94427			0.105830
$775$		0			0
$776$	4.34752			0.156067
$777$	10.4721			0.375686
$778$	−5.52786	−	9.57454i	−0.198184	−	0.343264i
$779$	15.6525			0.560808
$780$	1.23607	−	2.14093i	0.0442583	−	0.0766577i
$781$	13.1803	+	22.8290i	0.471630	+	0.816887i
$782$	−12.4721	−	21.6024i	−0.446003	−	0.772499i
$783$	−40.0000			−1.42948
$784$	−10.1459	+	17.5732i	−0.362354	+	0.627615i
$785$	7.44427	−	12.8939i	0.265697	−	0.460201i
$786$	−4.58359	+	7.93901i	−0.163491	+	0.283175i
$787$	19.3262	+	33.4740i	0.688906	+	1.19322i	0.972192	+	0.234185i	$0.0752421\pi$
$787$	19.3262	+	33.4740i	0.688906	+	1.19322i	−0.283286	+	0.959035i	$0.591425\pi$
$788$	12.4721	−	21.6024i	0.444301	−	0.769553i
$789$	11.5967	+	20.0862i	0.412855	+	0.715086i
$790$	1.05573			0.0375611
$791$	23.1803			0.824198
$792$	−3.29180	−	5.70156i	−0.116969	−	0.202596i
$793$	8.76393	−	15.1796i	0.311216	−	0.539043i
$794$	−2.16312	−	3.74663i	−0.0767662	−	0.132963i
$795$	0.944272	−	1.63553i	0.0334899	−	0.0580062i
$796$	0.854102	−	1.47935i	0.0302728	−	0.0524341i
$797$	−14.2918	+	24.7541i	−0.506241	+	0.876836i	0.493733	+	0.869614i	$0.335632\pi$
$797$	−14.2918	+	24.7541i	−0.506241	+	0.876836i	−0.999974	+	0.00722199i	$0.997701\pi$
$798$	−7.23607			−0.256154
$799$	−16.9443	−	29.3483i	−0.599445	−	1.03827i
$800$	−11.2361	−	19.4614i	−0.397255	−	0.688066i
$801$	1.25735	−	2.17780i	0.0444264	−	0.0769488i
$802$	9.77709			0.345241
$803$	0.472136	+	0.817763i	0.0166613	+	0.0288582i
$804$	16.0000			0.564276
$805$	−32.6525			−1.15085
$806$		0			0
$807$	−35.7771			−1.25941
$808$	−6.70820			−0.235994
$809$	−1.70820	−	2.95870i	−0.0600573	−	0.104022i	0.834434	−	0.551109i	$-0.185795\pi$
$809$	−1.70820	−	2.95870i	−0.0600573	−	0.104022i	−0.894491	+	0.447086i	$0.852462\pi$
$810$	1.49342			0.0524735
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	−0.508347	−	0.861152i	$-0.669743\pi$
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	0.999953	+	0.00966502i	$0.00307652\pi$
$812$	24.7984	+	42.9520i	0.870252	+	1.50732i
$813$	−5.05573	−	8.75678i	−0.177312	−	0.307114i
$814$	2.47214			0.0866483
$815$	1.35410	−	2.34537i	0.0474321	−	0.0821548i
$816$	−6.00000	+	10.3923i	−0.210042	+	0.363803i
$817$	−3.61803	+	6.26662i	−0.126579	+	0.219241i
$818$	8.09017	+	14.0126i	0.282866	+	0.489939i
$819$	3.85410	−	6.67550i	0.134673	−	0.233261i
$820$	5.66312	+	9.80881i	0.197765	+	0.342538i
$821$	36.5410			1.27529			0.637645	−	0.770330i	$-0.279909\pi$
$821$	36.5410			1.27529			0.637645	+	0.770330i	$0.279909\pi$
$822$	−15.0557			−0.525129
$823$	−13.8541	−	23.9960i	−0.482924	−	0.836448i	0.516884	−	0.856055i	$-0.327092\pi$
$823$	−13.8541	−	23.9960i	−0.482924	−	0.836448i	−0.999808	+	0.0196071i	$0.993758\pi$
$824$	−1.97214	+	3.41584i	−0.0687026	+	0.118996i
$825$	4.94427	+	8.56373i	0.172137	+	0.298151i
$826$	2.92705	−	5.06980i	0.101845	−	0.176401i
$827$	24.3262	−	42.1343i	0.845906	−	1.46515i	−0.0389257	−	0.999242i	$-0.512394\pi$
$827$	24.3262	−	42.1343i	0.845906	−	1.46515i	0.884832	−	0.465910i	$-0.154273\pi$
$828$	−9.18034	+	15.9008i	−0.319039	+	0.552592i
$829$	36.8328			1.27926			0.639628	−	0.768684i	$-0.279088\pi$
$829$	36.8328			1.27926			0.639628	+	0.768684i	$0.279088\pi$
$830$	−0.909830	−	1.57587i	−0.0315807	−	0.0546993i
$831$	−11.5279	−	19.9668i	−0.399897	−	0.692642i
$832$	−0.145898	+	0.252703i	−0.00505810	+	0.00876089i
$833$	−57.3050			−1.98550
$834$	−5.12461	−	8.87609i	−0.177451	−	0.307354i
$835$	−2.47214			−0.0855518
$836$	7.23607			0.250265
$837$		0			0
$838$	−18.6180			−0.643149
$839$	11.0557			0.381686			0.190843	−	0.981621i	$-0.438878\pi$
$839$	11.0557			0.381686			0.190843	+	0.981621i	$0.438878\pi$
$840$	−5.85410	−	10.1396i	−0.201986	−	0.349850i
$841$	23.3607			0.805541
$842$	−4.74671	+	8.22154i	−0.163582	+	0.283333i
$843$	10.5066	+	18.1979i	0.361866	+	0.626770i
$844$	0.663119	+	1.14856i	0.0228255	+	0.0395349i
$845$	−11.4721			−0.394653
$846$	2.94427	−	5.09963i	0.101226	−	0.175329i
$847$	−14.8262	+	25.6798i	−0.509436	+	0.882368i
$848$	−1.41641	+	2.45329i	−0.0486396	+	0.0842463i
$849$	13.5279	+	23.4309i	0.464275	+	0.804148i
$850$	6.47214	−	11.2101i	0.221992	−	0.384502i
$851$	−7.70820	−	13.3510i	−0.264234	−	0.457666i
$852$	26.3607			0.903102
$853$	37.4164			1.28111			0.640557	−	0.767911i	$-0.278704\pi$
$853$	37.4164			1.28111			0.640557	+	0.767911i	$0.278704\pi$
$854$	−18.5623	−	32.1509i	−0.635189	−	1.10018i
$855$	1.64590	−	2.85078i	0.0562885	−	0.0974946i
$856$	−11.4443	−	19.8221i	−0.391157	−	0.677504i
$857$	−25.8328	+	44.7437i	−0.882432	+	1.52842i	−0.0338034	+	0.999429i	$0.510762\pi$
$857$	−25.8328	+	44.7437i	−0.882432	+	1.52842i	−0.848629	+	0.528989i	$0.822571\pi$
$858$	−0.944272	+	1.63553i	−0.0322369	+	0.0558360i
$859$	18.9443	−	32.8124i	0.646370	−	1.11955i	−0.337613	−	0.941285i	$-0.609620\pi$
$859$	18.9443	−	32.8124i	0.646370	−	1.11955i	0.983983	−	0.178261i	$-0.0570472\pi$
$860$	−5.23607			−0.178548
$861$	−18.3262	−	31.7420i	−0.624557	−	1.08176i
$862$	3.70820	+	6.42280i	0.126302	+	0.218761i
$863$	−16.0902	+	27.8690i	−0.547716	+	0.948672i	0.450715	+	0.892668i	$0.351169\pi$
$863$	−16.0902	+	27.8690i	−0.547716	+	0.948672i	−0.998431	+	0.0560035i	$0.982164\pi$
$864$	−31.0557			−1.05654
$865$	7.47214	+	12.9421i	0.254060	+	0.440045i
$866$	−7.52786			−0.255807
$867$	−12.8754			−0.437271
$868$		0			0
$869$	3.41641			0.115894
$870$	−5.52786			−0.187412
$871$	4.94427	+	8.56373i	0.167530	+	0.290171i
$872$	8.81966			0.298671
$873$	1.43112	−	2.47877i	0.0484359	−	0.0838935i
$874$	5.32624	+	9.22531i	0.180163	+	0.312051i
$875$	−19.0623	−	33.0169i	−0.644424	−	1.11617i
$876$	0.944272			0.0319040
$877$	17.9721	−	31.1287i	0.606876	−	1.05114i	−0.384876	−	0.922968i	$-0.625756\pi$
$877$	17.9721	−	31.1287i	0.606876	−	1.05114i	0.991752	−	0.128172i	$-0.0409108\pi$
$878$	6.54508	−	11.3364i	0.220886	−	0.382586i
$879$	5.23607	−	9.06914i	0.176608	−	0.305894i
$880$	1.85410	+	3.21140i	0.0625018	+	0.108256i
$881$	12.1803	−	21.0970i	0.410366	−	0.710775i	−0.584564	−	0.811348i	$-0.698734\pi$
$881$	12.1803	−	21.0970i	0.410366	−	0.710775i	0.994930	+	0.100573i	$0.0320676\pi$
$882$	−4.97871	−	8.62339i	−0.167642	−	0.290364i
$883$	−39.7771			−1.33861			−0.669303	−	0.742990i	$-0.733407\pi$
$883$	−39.7771			−1.33861			−0.669303	+	0.742990i	$0.733407\pi$
$884$	−10.4721			−0.352216
$885$	−1.38197	−	2.39364i	−0.0464543	−	0.0804612i
$886$	5.34346	−	9.25514i	0.179517	−	0.310933i
$887$	15.5344	+	26.9064i	0.521596	+	0.903430i	0.999684	+	0.0251185i	$0.00799631\pi$
$887$	15.5344	+	26.9064i	0.521596	+	0.903430i	−0.478089	+	0.878311i	$0.658670\pi$
$888$	2.76393	−	4.78727i	0.0927515	−	0.160650i
$889$	−7.47214	+	12.9421i	−0.250607	+	0.434065i
$890$	0.527864	−	0.914287i	0.0176940	−	0.0306470i
$891$	4.83282			0.161905
$892$	−3.23607	−	5.60503i	−0.108352	−	0.187670i
$893$	7.23607	+	12.5332i	0.242146	+	0.419409i
$894$	−3.81966	+	6.61585i	−0.127749	+	0.221267i
$895$	11.7082			0.391362
$896$	24.1074	+	41.7552i	0.805371	+	1.39494i
$897$	11.7771			0.393226
$898$	19.3475			0.645635
$899$		0			0
$900$	−9.52786			−0.317595
$901$	−8.00000			−0.266519
$902$	−4.32624	−	7.49326i	−0.144048	−	0.249498i
$903$	16.9443			0.563870
$904$	6.11803	−	10.5967i	0.203483	−	0.352443i
$905$	9.09017	+	15.7446i	0.302167	+	0.523369i
$906$	3.12461	+	5.41199i	0.103808	+	0.179801i
$907$	−19.7639			−0.656251			−0.328125	−	0.944634i	$-0.606417\pi$
$907$	−19.7639			−0.656251			−0.328125	+	0.944634i	$0.606417\pi$
$908$	2.00000	−	3.46410i	0.0663723	−	0.114960i
$909$	−2.20820	+	3.82472i	−0.0732415	+	0.126858i
$910$	1.61803	−	2.80252i	0.0536373	−	0.0929025i
$911$	−2.09017	−	3.62028i	−0.0692504	−	0.119945i	0.829321	−	0.558772i	$-0.188727\pi$
$911$	−2.09017	−	3.62028i	−0.0692504	−	0.119945i	−0.898572	+	0.438827i	$0.855394\pi$
$912$	2.56231	−	4.43804i	0.0848464	−	0.146958i
$913$	−2.94427	−	5.09963i	−0.0974412	−	0.168773i
$914$	−12.9443			−0.428158
$915$	−17.5279			−0.579453
$916$	−10.8541	−	18.7999i	−0.358630	−	0.621165i
$917$	25.4164	−	44.0225i	0.839324	−	1.45375i
$918$	−8.94427	−	15.4919i	−0.295205	−	0.511310i
$919$	2.76393	−	4.78727i	0.0911737	−	0.157917i	−0.816832	−	0.576876i	$-0.804271\pi$
$919$	2.76393	−	4.78727i	0.0911737	−	0.157917i	0.908005	+	0.418959i	$0.137605\pi$
$920$	−8.61803	+	14.9269i	−0.284128	+	0.492124i
$921$	−9.45085	+	16.3694i	−0.311416	+	0.539388i
$922$	−6.40325			−0.210880
$923$	8.14590	+	14.1091i	0.268125	+	0.464407i
$924$	−8.47214	−	14.6742i	−0.278713	−	0.482745i
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$	−18.1803			−0.597443
$927$	1.29837	+	2.24885i	0.0426442	+	0.0738619i
$928$	40.6525			1.33448
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		0			0
$931$	24.4721			0.802042
$932$	−0.0901699			−0.00295361
$933$	−4.21478	−	7.30022i	−0.137986	−	0.238998i
$934$	5.38197			0.176103
$935$	−5.23607	+	9.06914i	−0.171238	+	0.296592i
$936$	−2.03444	−	3.52376i	−0.0664978	−	0.115178i
$937$	−13.4721	−	23.3344i	−0.440115	−	0.762302i	0.557582	−	0.830122i	$-0.311729\pi$
$937$	−13.4721	−	23.3344i	−0.440115	−	0.762302i	−0.997698	+	0.0678194i	$0.978396\pi$
$938$	20.9443			0.683855
$939$	−13.1246	+	22.7325i	−0.428306	+	0.741847i
$940$	−5.23607	+	9.06914i	−0.170782	+	0.295803i
$941$	−19.0000	+	32.9090i	−0.619382	+	1.07280i	0.370216	+	0.928946i	$0.379284\pi$
$941$	−19.0000	+	32.9090i	−0.619382	+	1.07280i	−0.989599	+	0.143856i	$0.954050\pi$
$942$	5.68692	+	9.85003i	0.185290	+	0.320931i
$943$	−26.9787	+	46.7285i	−0.878548	+	1.52169i
$944$	2.07295	+	3.59045i	0.0674687	+	0.116859i
$945$	−23.4164			−0.761736
$946$	4.00000			0.130051
$947$	−15.4721	−	26.7985i	−0.502777	−	0.870835i	−0.999995	−	0.00320942i	$-0.998978\pi$
$947$	−15.4721	−	26.7985i	−0.502777	−	0.870835i	0.497218	−	0.867626i	$-0.334355\pi$
$948$	1.70820	−	2.95870i	0.0554799	−	0.0960940i
$949$	0.291796	+	0.505406i	0.00947210	+	0.0164062i
$950$	−2.76393	+	4.78727i	−0.0896738	+	0.155320i
$951$	13.5623	−	23.4906i	0.439788	−	0.761735i
$952$	−24.7984	+	42.9520i	−0.803720	+	1.39208i
$953$	−32.2918			−1.04603			−0.523017	−	0.852322i	$-0.675194\pi$
$953$	−32.2918			−1.04603			−0.523017	+	0.852322i	$0.675194\pi$
$954$	−0.695048	−	1.20386i	−0.0225030	−	0.0389764i
$955$	−1.59017	−	2.75426i	−0.0514567	−	0.0891256i
$956$	−1.38197	+	2.39364i	−0.0446960	+	0.0774157i
$957$	−17.8885			−0.578254
$958$	11.3435	+	19.6474i	0.366491	+	0.634780i
$959$	83.4853			2.69588
$960$	0.291796			0.00941768
$961$		0			0
$962$	1.52786			0.0492603
$963$	−15.0689			−0.485588
$964$	24.5623	+	42.5432i	0.791099	+	1.37022i
$965$	−5.47214			−0.176154
$966$	12.4721	−	21.6024i	0.401284	−	0.695045i
$967$	7.81966	+	13.5440i	0.251463	+	0.435547i	0.963929	−	0.266160i	$-0.0857549\pi$
$967$	7.81966	+	13.5440i	0.251463	+	0.435547i	−0.712466	+	0.701707i	$0.752422\pi$
$968$	7.82624	+	13.5554i	0.251545	+	0.435688i
$969$	14.4721			0.464912
$970$	0.600813	−	1.04064i	0.0192909	−	0.0334129i
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	−0.549058	−	0.835784i	$-0.685013\pi$
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	0.998339	+	0.0576061i	$0.0183467\pi$
$972$	−11.0000	+	19.0526i	−0.352825	+	0.611111i
$973$	28.4164	+	49.2187i	0.910988	+	1.57788i
$974$	4.56231	−	7.90215i	0.146186	−	0.253201i
$975$	3.05573	+	5.29268i	0.0978616	+	0.169501i
$976$	26.2918			0.841580
$977$	33.2492			1.06374			0.531868	−	0.846827i	$-0.321490\pi$
$977$	33.2492			1.06374			0.531868	+	0.846827i	$0.321490\pi$
$978$	1.03444	+	1.79171i	0.0330778	+	0.0572924i
$979$	1.70820	−	2.95870i	0.0545944	−	0.0945603i
$980$	8.85410	+	15.3358i	0.282834	+	0.489883i
$981$	2.90325	−	5.02858i	0.0926937	−	0.160550i
$982$	12.4721	−	21.6024i	0.398002	−	0.689359i
$983$	24.2361	−	41.9781i	0.773011	−	1.33889i	−0.162895	−	0.986643i	$-0.552083\pi$
$983$	24.2361	−	41.9781i	0.773011	−	1.33889i	0.935906	−	0.352250i	$-0.114583\pi$
$984$	−19.3475			−0.616777
$985$	−7.70820	−	13.3510i	−0.245604	−	0.425398i
$986$	11.7082	+	20.2792i	0.372865	+	0.645821i
$987$	16.9443	−	29.3483i	0.539342	−	0.934168i
$988$	4.47214			0.142278
$989$	−12.4721	−	21.6024i	−0.396591	−	0.686916i
$990$	−1.81966			−0.0578326
$991$	−50.5410			−1.60549			−0.802744	−	0.596324i	$-0.796628\pi$
$991$	−50.5410			−1.60549			−0.802744	+	0.596324i	$0.796628\pi$
$992$		0			0
$993$	2.47214			0.0784509
$994$	34.5066			1.09448
$995$	−0.527864	−	0.914287i	−0.0167344	−	0.0289849i
$996$	−5.88854			−0.186586
$997$	−7.68034	+	13.3027i	−0.243239	+	0.421302i	−0.961635	−	0.274332i	$-0.911543\pi$
$997$	−7.68034	+	13.3027i	−0.243239	+	0.421302i	0.718396	+	0.695634i	$0.244877\pi$
$998$	10.3262	+	17.8856i	0.326871	+	0.566158i
$999$	−5.52786	−	9.57454i	−0.174894	−	0.302925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.c.521.1		4
31.2	even	5		961.2.g.d.844.1		8
31.3	odd	30		961.2.d.c.628.1		4
31.4	even	5		961.2.g.e.338.1		8
31.5	even	3	inner	961.2.c.c.439.1		4
31.6	odd	6		31.2.a.a.1.1	✓	2
31.7	even	15		961.2.d.g.388.1		4
31.8	even	5		961.2.g.e.732.1		8
31.9	even	15		961.2.g.e.816.1		8
31.10	even	15		961.2.g.d.547.1		8
31.11	odd	30		961.2.g.h.235.1		8
31.12	odd	30		961.2.d.c.531.1		4
31.13	odd	30		961.2.g.a.846.1		8
31.14	even	15		961.2.d.g.374.1		4
31.15	odd	10		961.2.g.a.448.1		8
31.16	even	5		961.2.g.d.448.1		8
31.17	odd	30		961.2.d.d.374.1		4
31.18	even	15		961.2.g.d.846.1		8
31.19	even	15		961.2.d.a.531.1		4
31.20	even	15		961.2.g.e.235.1		8
31.21	odd	30		961.2.g.a.547.1		8
31.22	odd	30		961.2.g.h.816.1		8
31.23	odd	10		961.2.g.h.732.1		8
31.24	odd	30		961.2.d.d.388.1		4
31.25	even	3		961.2.a.f.1.1		2
31.26	odd	6		961.2.c.e.439.1		4
31.27	odd	10		961.2.g.h.338.1		8
31.28	even	15		961.2.d.a.628.1		4
31.29	odd	10		961.2.g.a.844.1		8
31.30	odd	2		961.2.c.e.521.1		4
93.56	odd	6		8649.2.a.c.1.2		2
93.68	even	6		279.2.a.a.1.2		2
124.99	even	6		496.2.a.i.1.1		2
155.37	even	12		775.2.b.d.249.2		4
155.68	even	12		775.2.b.d.249.3		4
155.99	odd	6		775.2.a.d.1.2		2
217.6	even	6		1519.2.a.a.1.1		2
248.37	odd	6		1984.2.a.r.1.1		2
248.99	even	6		1984.2.a.n.1.2		2
341.285	even	6		3751.2.a.b.1.2		2
372.347	odd	6		4464.2.a.bf.1.2		2
403.285	odd	6		5239.2.a.f.1.2		2
465.254	even	6		6975.2.a.y.1.1		2
527.254	odd	6		8959.2.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.1	✓	2	31.6	odd	6
279.2.a.a.1.2		2	93.68	even	6
496.2.a.i.1.1		2	124.99	even	6
775.2.a.d.1.2		2	155.99	odd	6
775.2.b.d.249.2		4	155.37	even	12
775.2.b.d.249.3		4	155.68	even	12
961.2.a.f.1.1		2	31.25	even	3
961.2.c.c.439.1		4	31.5	even	3	inner
961.2.c.c.521.1		4	1.1	even	1	trivial
961.2.c.e.439.1		4	31.26	odd	6
961.2.c.e.521.1		4	31.30	odd	2
961.2.d.a.531.1		4	31.19	even	15
961.2.d.a.628.1		4	31.28	even	15
961.2.d.c.531.1		4	31.12	odd	30
961.2.d.c.628.1		4	31.3	odd	30
961.2.d.d.374.1		4	31.17	odd	30
961.2.d.d.388.1		4	31.24	odd	30
961.2.d.g.374.1		4	31.14	even	15
961.2.d.g.388.1		4	31.7	even	15
961.2.g.a.448.1		8	31.15	odd	10
961.2.g.a.547.1		8	31.21	odd	30
961.2.g.a.844.1		8	31.29	odd	10
961.2.g.a.846.1		8	31.13	odd	30
961.2.g.d.448.1		8	31.16	even	5
961.2.g.d.547.1		8	31.10	even	15
961.2.g.d.844.1		8	31.2	even	5
961.2.g.d.846.1		8	31.18	even	15
961.2.g.e.235.1		8	31.20	even	15
961.2.g.e.338.1		8	31.4	even	5
961.2.g.e.732.1		8	31.8	even	5
961.2.g.e.816.1		8	31.9	even	15
961.2.g.h.235.1		8	31.11	odd	30
961.2.g.h.338.1		8	31.27	odd	10
961.2.g.h.732.1		8	31.23	odd	10
961.2.g.h.816.1		8	31.22	odd	30
1519.2.a.a.1.1		2	217.6	even	6
1984.2.a.n.1.2		2	248.99	even	6
1984.2.a.r.1.1		2	248.37	odd	6
3751.2.a.b.1.2		2	341.285	even	6
4464.2.a.bf.1.2		2	372.347	odd	6
5239.2.a.f.1.2		2	403.285	odd	6
6975.2.a.y.1.1		2	465.254	even	6
8649.2.a.c.1.2		2	93.56	odd	6
8959.2.a.b.1.1		2	527.254	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +(0.618034 + 1.07047i) q^{3} -1.61803 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.381966 - 0.661585i) q^{6} +(2.11803 + 3.66854i) q^{7} +2.23607 q^{8} +(0.736068 - 1.27491i) q^{9} +(0.309017 - 0.535233i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.00000 - 1.73205i) q^{12} +(0.618034 - 1.07047i) q^{13} +(-1.30902 - 2.26728i) q^{14} -1.23607 q^{15} +1.85410 q^{16} +(2.61803 + 4.53457i) q^{17} +(-0.454915 + 0.787936i) q^{18} +(-1.11803 - 1.93649i) q^{19} +(0.809017 - 1.40126i) q^{20} +(-2.61803 + 4.53457i) q^{21} +(-0.618034 + 1.07047i) q^{22} +7.70820 q^{23} +(1.38197 + 2.39364i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.381966 + 0.661585i) q^{26} +5.52786 q^{27} +(-3.42705 - 5.93583i) q^{28} -7.23607 q^{29} +0.763932 q^{30} -5.61803 q^{32} +2.47214 q^{33} +(-1.61803 - 2.80252i) q^{34} -4.23607 q^{35} +(-1.19098 + 2.06284i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(0.690983 + 1.19682i) q^{38} +1.52786 q^{39} +(-1.11803 + 1.93649i) q^{40} +(-3.50000 + 6.06218i) q^{41} +(1.61803 - 2.80252i) q^{42} +(-1.61803 - 2.80252i) q^{43} +(-1.61803 + 2.80252i) q^{44} +(0.736068 + 1.27491i) q^{45} -4.76393 q^{46} -6.47214 q^{47} +(1.14590 + 1.98475i) q^{48} +(-5.47214 + 9.47802i) q^{49} +(-1.23607 - 2.14093i) q^{50} +(-3.23607 + 5.60503i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-0.763932 + 1.32317i) q^{53} -3.41641 q^{54} +(1.00000 + 1.73205i) q^{55} +(4.73607 + 8.20311i) q^{56} +(1.38197 - 2.39364i) q^{57} +4.47214 q^{58} +(1.11803 + 1.93649i) q^{59} +2.00000 q^{60} +14.1803 q^{61} +6.23607 q^{63} -0.236068 q^{64} +(0.618034 + 1.07047i) q^{65} -1.52786 q^{66} +(-4.00000 + 6.92820i) q^{67} +(-4.23607 - 7.33708i) q^{68} +(4.76393 + 8.25137i) q^{69} +2.61803 q^{70} +(-6.59017 + 11.4145i) q^{71} +(1.64590 - 2.85078i) q^{72} +(-0.236068 + 0.408882i) q^{73} +(0.618034 + 1.07047i) q^{74} +(-2.47214 + 4.28187i) q^{75} +(1.80902 + 3.13331i) q^{76} +8.47214 q^{77} -0.944272 q^{78} +(0.854102 + 1.47935i) q^{79} +(-0.927051 + 1.60570i) q^{80} +(1.20820 + 2.09267i) q^{81} +(2.16312 - 3.74663i) q^{82} +(1.47214 - 2.54981i) q^{83} +(4.23607 - 7.33708i) q^{84} -5.23607 q^{85} +(1.00000 + 1.73205i) q^{86} +(-4.47214 - 7.74597i) q^{87} +(2.23607 - 3.87298i) q^{88} +1.70820 q^{89} +(-0.454915 - 0.787936i) q^{90} +5.23607 q^{91} -12.4721 q^{92} +4.00000 q^{94} +2.23607 q^{95} +(-3.47214 - 6.01392i) q^{96} +1.94427 q^{97} +(3.38197 - 5.85774i) q^{98} +(-1.47214 - 2.54981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 6 q^{6} + 4 q^{7} - 6 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 2 q^{13} - 3 q^{14} + 4 q^{15} - 6 q^{16} + 6 q^{17} - 13 q^{18} + q^{20} - 6 q^{21} + 2 q^{22}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 6 * q^6 + 4 * q^7 - 6 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 2 * q^13 - 3 * q^14 + 4 * q^15 - 6 * q^16 + 6 * q^17 - 13 * q^18 + q^20 - 6 * q^21 + 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 6 * q^26 + 40 * q^27 - 7 * q^28 - 20 * q^29 + 12 * q^30 - 18 * q^32 - 8 * q^33 - 2 * q^34 - 8 * q^35 - 7 * q^36 - 4 * q^37 + 5 * q^38 + 24 * q^39 - 14 * q^41 + 2 * q^42 - 2 * q^43 - 2 * q^44 - 6 * q^45 - 28 * q^46 - 8 * q^47 + 18 * q^48 - 4 * q^49 + 4 * q^50 - 4 * q^51 - 4 * q^52 - 12 * q^53 + 40 * q^54 + 4 * q^55 + 10 * q^56 + 10 * q^57 + 8 * q^60 + 12 * q^61 + 16 * q^63 + 8 * q^64 - 2 * q^65 - 24 * q^66 - 16 * q^67 - 8 * q^68 + 28 * q^69 + 6 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 2 * q^74 + 8 * q^75 + 5 * q^76 + 16 * q^77 + 32 * q^78 - 10 * q^79 + 3 * q^80 - 22 * q^81 - 7 * q^82 - 12 * q^83 + 8 * q^84 - 12 * q^85 + 4 * q^86 - 20 * q^89 - 13 * q^90 + 12 * q^91 - 32 * q^92 + 16 * q^94 + 4 * q^96 - 28 * q^97 + 18 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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