LMFDB - Embedded newform 961.2.c.i.439.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [16,4,-3,16,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			439.7
Root			$1.14660i$ of defining polynomial
Character	$\chi$	$=$	961.439
Dual form			961.2.c.i.521.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.07212 q^{2} +(-1.06970 + 1.85277i) q^{3} +2.29369 q^{4} +(-1.17396 - 2.03335i) q^{5} +(-2.21654 + 3.83916i) q^{6} +(1.83727 - 3.18225i) q^{7} +0.608557 q^{8} +(-0.788498 - 1.36572i) q^{9} +(-2.43258 - 4.21335i) q^{10} +(-2.14032 - 3.70714i) q^{11} +(-2.45355 + 4.24967i) q^{12} +(-1.04360 - 1.80757i) q^{13} +(3.80705 - 6.59400i) q^{14} +5.02310 q^{15} -3.32637 q^{16} +(1.06405 - 1.84298i) q^{17} +(-1.63386 - 2.82993i) q^{18} +(0.310008 - 0.536949i) q^{19} +(-2.69269 - 4.66387i) q^{20} +(3.93064 + 6.80807i) q^{21} +(-4.43500 - 7.68165i) q^{22} +3.35388 q^{23} +(-0.650970 + 1.12751i) q^{24} +(-0.256344 + 0.444001i) q^{25} +(-2.16247 - 3.74550i) q^{26} -3.04436 q^{27} +(4.21412 - 7.29908i) q^{28} +1.37742 q^{29} +10.4085 q^{30} -8.10976 q^{32} +9.15797 q^{33} +(2.20483 - 3.81888i) q^{34} -8.62750 q^{35} +(-1.80857 - 3.13253i) q^{36} +(0.137239 - 0.237704i) q^{37} +(0.642374 - 1.11262i) q^{38} +4.46534 q^{39} +(-0.714418 - 1.23741i) q^{40} +(2.13896 + 3.70478i) q^{41} +(8.14477 + 14.1071i) q^{42} +(0.134846 - 0.233560i) q^{43} +(-4.90923 - 8.50303i) q^{44} +(-1.85132 + 3.20659i) q^{45} +6.94964 q^{46} +5.37916 q^{47} +(3.55821 - 6.16299i) q^{48} +(-3.25113 - 5.63112i) q^{49} +(-0.531176 + 0.920024i) q^{50} +(2.27641 + 3.94286i) q^{51} +(-2.39369 - 4.14600i) q^{52} +(4.75434 + 8.23476i) q^{53} -6.30829 q^{54} +(-5.02528 + 8.70405i) q^{55} +(1.11808 - 1.93658i) q^{56} +(0.663228 + 1.14874i) q^{57} +2.85417 q^{58} +(2.91372 - 5.04671i) q^{59} +11.5214 q^{60} -2.22719 q^{61} -5.79474 q^{63} -10.1517 q^{64} +(-2.45028 + 4.24401i) q^{65} +18.9764 q^{66} +(6.80719 + 11.7904i) q^{67} +(2.44059 - 4.22722i) q^{68} +(-3.58763 + 6.21395i) q^{69} -17.8772 q^{70} +(0.667962 + 1.15694i) q^{71} +(-0.479846 - 0.831117i) q^{72} +(-7.08301 - 12.2681i) q^{73} +(0.284375 - 0.492552i) q^{74} +(-0.548420 - 0.949892i) q^{75} +(0.711061 - 1.23159i) q^{76} -15.7294 q^{77} +9.25272 q^{78} +(4.33831 - 7.51417i) q^{79} +(3.90501 + 6.76368i) q^{80} +(5.62204 - 9.73765i) q^{81} +(4.43218 + 7.67676i) q^{82} +(-2.59274 - 4.49076i) q^{83} +(9.01566 + 15.6156i) q^{84} -4.99657 q^{85} +(0.279418 - 0.483966i) q^{86} +(-1.47342 + 2.55203i) q^{87} +(-1.30251 - 2.25601i) q^{88} -5.01258 q^{89} +(-3.83617 + 6.64444i) q^{90} -7.66950 q^{91} +7.69274 q^{92} +11.1463 q^{94} -1.45574 q^{95} +(8.67498 - 15.0255i) q^{96} +6.71398 q^{97} +(-6.73673 - 11.6684i) q^{98} +(-3.37528 + 5.84615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * q^99

Character values

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

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

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 $

$2$	2.07212			1.46521			0.732606	−	0.680653i	$-0.238304\pi$
$2$	2.07212			1.46521			0.732606	+	0.680653i	$0.238304\pi$
$3$	−1.06970	+	1.85277i	−0.617589	+	1.06970i	0.372335	+	0.928098i	$0.378557\pi$
$3$	−1.06970	+	1.85277i	−0.617589	+	1.06970i	−0.989924	+	0.141597i	$0.954776\pi$
$4$	2.29369			1.14684
$5$	−1.17396	−	2.03335i	−0.525009	−	0.909342i	−0.999576	−	0.0291228i	$-0.990729\pi$
$5$	−1.17396	−	2.03335i	−0.525009	−	0.909342i	0.474567	−	0.880219i	$-0.342605\pi$
$6$	−2.21654	+	3.83916i	−0.904898	+	1.56733i
$7$	1.83727	−	3.18225i	0.694423	−	1.20278i	−0.275952	−	0.961171i	$-0.588993\pi$
$7$	1.83727	−	3.18225i	0.694423	−	1.20278i	0.970375	−	0.241604i	$-0.0776736\pi$
$8$	0.608557			0.215157
$9$	−0.788498	−	1.36572i	−0.262833	−	0.455239i
$10$	−2.43258	−	4.21335i	−0.769249	−	1.33238i
$11$	−2.14032	−	3.70714i	−0.645331	−	1.11775i	−0.984225	−	0.176921i	$-0.943386\pi$
$11$	−2.14032	−	3.70714i	−0.645331	−	1.11775i	0.338894	−	0.940825i	$-0.389947\pi$
$12$	−2.45355	+	4.24967i	−0.708278	+	1.22677i
$13$	−1.04360	−	1.80757i	−0.289442	−	0.501329i	0.684234	−	0.729262i	$-0.260137\pi$
$13$	−1.04360	−	1.80757i	−0.289442	−	0.501329i	−0.973677	+	0.227933i	$0.926803\pi$
$14$	3.80705	−	6.59400i	1.01748	−	1.76232i
$15$	5.02310			1.29696
$16$	−3.32637			−0.831593
$17$	1.06405	−	1.84298i	0.258069	−	0.446989i	−0.707656	−	0.706558i	$-0.750247\pi$
$17$	1.06405	−	1.84298i	0.258069	−	0.446989i	0.965725	+	0.259569i	$0.0835805\pi$
$18$	−1.63386	−	2.82993i	−0.385105	−	0.667022i
$19$	0.310008	−	0.536949i	0.0711206	−	0.123185i	−0.828272	−	0.560326i	$-0.810676\pi$
$19$	0.310008	−	0.536949i	0.0711206	−	0.123185i	0.899393	+	0.437142i	$0.144009\pi$
$20$	−2.69269	−	4.66387i	−0.602103	−	1.04287i
$21$	3.93064	+	6.80807i	0.857736	+	1.48564i
$22$	−4.43500	−	7.68165i	−0.945546	−	1.63773i
$23$	3.35388			0.699331			0.349666	−	0.936875i	$-0.386295\pi$
$23$	3.35388			0.699331			0.349666	+	0.936875i	$0.386295\pi$
$24$	−0.650970	+	1.12751i	−0.132879	+	0.230153i
$25$	−0.256344	+	0.444001i	−0.0512688	+	0.0888002i
$26$	−2.16247	−	3.74550i	−0.424094	−	0.734553i
$27$	−3.04436			−0.585888
$28$	4.21412	−	7.29908i	0.796395	−	1.37940i
$29$	1.37742			0.255780			0.127890	−	0.991788i	$-0.459180\pi$
$29$	1.37742			0.255780			0.127890	+	0.991788i	$0.459180\pi$
$30$	10.4085			1.90032
$31$		0			0
$31$		0			0
$32$	−8.10976			−1.43362
$33$	9.15797			1.59420
$34$	2.20483	−	3.81888i	0.378126	−	0.654933i
$35$	−8.62750			−1.45831
$36$	−1.80857	−	3.13253i	−0.301428	−	0.522089i
$37$	0.137239	−	0.237704i	0.0225619	−	0.0390783i	−0.854524	−	0.519412i	$-0.826151\pi$
$37$	0.137239	−	0.237704i	0.0225619	−	0.0390783i	0.877086	+	0.480334i	$0.159484\pi$
$38$	0.642374	−	1.11262i	0.104207	−	0.180491i
$39$	4.46534			0.715026
$40$	−0.714418	−	1.23741i	−0.112959	−	0.195652i
$41$	2.13896	+	3.70478i	0.334049	+	0.578590i	0.983302	−	0.181983i	$-0.0582516\pi$
$41$	2.13896	+	3.70478i	0.334049	+	0.578590i	−0.649253	+	0.760573i	$0.724918\pi$
$42$	8.14477	+	14.1071i	1.25676	+	2.17678i
$43$	0.134846	−	0.233560i	0.0205639	−	0.0356176i	−0.855560	−	0.517703i	$-0.826787\pi$
$43$	0.134846	−	0.233560i	0.0205639	−	0.0356176i	0.876124	+	0.482085i	$0.160121\pi$
$44$	−4.90923	−	8.50303i	−0.740094	−	1.28188i
$45$	−1.85132	+	3.20659i	−0.275979	+	0.478010i
$46$	6.94964			1.02467
$47$	5.37916			0.784631			0.392316	−	0.919831i	$-0.371674\pi$
$47$	5.37916			0.784631			0.392316	+	0.919831i	$0.371674\pi$
$48$	3.55821	−	6.16299i	0.513583	−	0.889552i
$49$	−3.25113	−	5.63112i	−0.464447	−	0.804445i
$50$	−0.531176	+	0.920024i	−0.0751197	+	0.130111i
$51$	2.27641	+	3.94286i	0.318761	+	0.552111i
$52$	−2.39369	−	4.14600i	−0.331945	−	0.574946i
$53$	4.75434	+	8.23476i	0.653059	+	1.13113i	0.982377	+	0.186912i	$0.0598480\pi$
$53$	4.75434	+	8.23476i	0.653059	+	1.13113i	−0.329317	+	0.944219i	$0.606819\pi$
$54$	−6.30829			−0.858450
$55$	−5.02528	+	8.70405i	−0.677609	+	1.17365i
$56$	1.11808	−	1.93658i	0.149410	−	0.258786i
$57$	0.663228	+	1.14874i	0.0878467	+	0.152155i
$58$	2.85417			0.374771
$59$	2.91372	−	5.04671i	0.379334	−	0.657026i	−0.611632	−	0.791143i	$-0.709487\pi$
$59$	2.91372	−	5.04671i	0.379334	−	0.657026i	0.990965	+	0.134117i	$0.0428198\pi$
$60$	11.5214			1.48741
$61$	−2.22719			−0.285162			−0.142581	−	0.989783i	$-0.545540\pi$
$61$	−2.22719			−0.285162			−0.142581	+	0.989783i	$0.545540\pi$
$62$		0			0
$63$	−5.79474			−0.730068
$64$	−10.1517			−1.26896
$65$	−2.45028	+	4.24401i	−0.303920	+	0.526404i
$66$	18.9764			2.33584
$67$	6.80719	+	11.7904i	0.831631	+	1.44043i	0.896744	+	0.442550i	$0.145926\pi$
$67$	6.80719	+	11.7904i	0.831631	+	1.44043i	−0.0651129	+	0.997878i	$0.520741\pi$
$68$	2.44059	−	4.22722i	0.295965	−	0.512626i
$69$	−3.58763	+	6.21395i	−0.431899	+	0.748072i
$70$	−17.8772			−2.13674
$71$	0.667962	+	1.15694i	0.0792725	+	0.137304i	0.902936	−	0.429774i	$-0.141407\pi$
$71$	0.667962	+	1.15694i	0.0792725	+	0.137304i	−0.823664	+	0.567079i	$0.808074\pi$
$72$	−0.479846	−	0.831117i	−0.0565503	−	0.0979481i
$73$	−7.08301	−	12.2681i	−0.829004	−	1.43588i	−0.898821	−	0.438316i	$-0.855575\pi$
$73$	−7.08301	−	12.2681i	−0.829004	−	1.43588i	0.0698172	−	0.997560i	$-0.477758\pi$
$74$	0.284375	−	0.492552i	0.0330579	−	0.0572580i
$75$	−0.548420	−	0.949892i	−0.0633261	−	0.109684i
$76$	0.711061	−	1.23159i	0.0815643	−	0.141273i
$77$	−15.7294			−1.79253
$78$	9.25272			1.04766
$79$	4.33831	−	7.51417i	0.488098	−	0.845410i	−0.511809	−	0.859100i	$-0.671024\pi$
$79$	4.33831	−	7.51417i	0.488098	−	0.845410i	0.999906	+	0.0136894i	$0.00435762\pi$
$80$	3.90501	+	6.76368i	0.436594	+	0.756203i
$81$	5.62204	−	9.73765i	0.624671	−	1.08196i
$82$	4.43218	+	7.67676i	0.489452	+	0.847756i
$83$	−2.59274	−	4.49076i	−0.284590	−	0.492925i	0.687920	−	0.725787i	$-0.258524\pi$
$83$	−2.59274	−	4.49076i	−0.284590	−	0.492925i	−0.972510	+	0.232862i	$0.925191\pi$
$84$	9.01566	+	15.6156i	0.983689	+	1.70380i
$85$	−4.99657			−0.541954
$86$	0.279418	−	0.483966i	0.0301304	−	0.0521874i
$87$	−1.47342	+	2.55203i	−0.157967	+	0.273607i
$88$	−1.30251	−	2.25601i	−0.138848	−	0.240491i
$89$	−5.01258			−0.531333			−0.265666	−	0.964065i	$-0.585592\pi$
$89$	−5.01258			−0.531333			−0.265666	+	0.964065i	$0.585592\pi$
$90$	−3.83617	+	6.64444i	−0.404367	+	0.700385i
$91$	−7.66950			−0.803982
$92$	7.69274			0.802024
$93$		0			0
$94$	11.1463			1.14965
$95$	−1.45574			−0.149356
$96$	8.67498	−	15.0255i	0.885386	−	1.53353i
$97$	6.71398			0.681702			0.340851	−	0.940117i	$-0.389285\pi$
$97$	6.71398			0.681702			0.340851	+	0.940117i	$0.389285\pi$
$98$	−6.73673	−	11.6684i	−0.680512	−	1.17868i
$99$	−3.37528	+	5.84615i	−0.339228	+	0.587560i
$100$	−0.587973	+	1.01840i	−0.0587973	+	0.101840i
$101$	−18.0626			−1.79730			−0.898648	−	0.438671i	$-0.855450\pi$
$101$	−18.0626			−1.79730			−0.898648	+	0.438671i	$0.855450\pi$
$102$	4.71700	+	8.17008i	0.467053	+	0.808959i
$103$	−1.95766	−	3.39077i	−0.192894	−	0.334102i	0.753314	−	0.657661i	$-0.228454\pi$
$103$	−1.95766	−	3.39077i	−0.192894	−	0.334102i	−0.946208	+	0.323559i	$0.895121\pi$
$104$	−0.635089	−	1.10001i	−0.0622756	−	0.107865i
$105$	9.22880	−	15.9847i	0.900638	−	1.55995i
$106$	9.85157	+	17.0634i	0.956870	+	1.65735i
$107$	−5.55781	+	9.62641i	−0.537294	+	0.930620i	0.461755	+	0.887008i	$0.347220\pi$
$107$	−5.55781	+	9.62641i	−0.537294	+	0.930620i	−0.999049	+	0.0436127i	$0.986113\pi$
$108$	−6.98282			−0.671922
$109$	18.0934			1.73303			0.866516	−	0.499150i	$-0.166354\pi$
$109$	18.0934			1.73303			0.866516	+	0.499150i	$0.166354\pi$
$110$	−10.4130	+	18.0358i	−0.992840	+	1.71965i
$111$	0.293607	+	0.508542i	0.0278679	+	0.0482687i
$112$	−6.11145	+	10.5853i	−0.577477	+	1.00022i
$113$	−8.76938	−	15.1890i	−0.824954	−	1.42886i	−0.901955	−	0.431830i	$-0.857868\pi$
$113$	−8.76938	−	15.1890i	−0.824954	−	1.42886i	0.0770012	−	0.997031i	$-0.475465\pi$
$114$	1.37429	+	2.38034i	0.128714	+	0.222939i
$115$	−3.93730	−	6.81961i	−0.367155	−	0.635932i
$116$	3.15936			0.293339
$117$	−1.64575	+	2.85053i	−0.152150	+	0.263531i
$118$	6.03758	−	10.4574i	0.555804	−	0.962681i
$119$	−3.90988	−	6.77211i	−0.358418	−	0.620798i
$120$	3.05684			0.279050
$121$	−3.66195	+	6.34268i	−0.332904	+	0.576607i
$122$	−4.61500			−0.417823
$123$	−9.15213			−0.825220
$124$		0			0
$125$	−10.5358			−0.942352
$126$	−12.0074			−1.06970
$127$	−7.09914	+	12.2961i	−0.629947	+	1.09110i	0.357615	+	0.933869i	$0.383590\pi$
$127$	−7.09914	+	12.2961i	−0.629947	+	1.09110i	−0.987562	+	0.157231i	$0.949743\pi$
$128$	−4.81596			−0.425675
$129$	0.288489	+	0.499677i	0.0254000	+	0.0439941i
$130$	−5.07728	+	8.79410i	−0.445307	+	0.771294i
$131$	−3.59426	+	6.22543i	−0.314032	+	0.543919i	−0.979231	−	0.202747i	$-0.935013\pi$
$131$	−3.59426	+	6.22543i	−0.314032	+	0.543919i	0.665200	+	0.746666i	$0.268346\pi$
$132$	21.0055			1.82830
$133$	−1.13914	−	1.97304i	−0.0987756	−	0.171084i
$134$	14.1053	+	24.4312i	1.21852	+	2.11053i
$135$	3.57395	+	6.19026i	0.307596	+	0.532773i
$136$	0.647532	−	1.12156i	0.0555254	−	0.0961728i
$137$	3.78883	+	6.56244i	0.323701	+	0.560667i	0.981249	−	0.192746i	$-0.0617394\pi$
$137$	3.78883	+	6.56244i	0.323701	+	0.560667i	−0.657547	+	0.753413i	$0.728406\pi$
$138$	−7.43400	+	12.8761i	−0.632824	+	1.09608i
$139$	20.0982			1.70471			0.852354	−	0.522965i	$-0.175174\pi$
$139$	20.0982			1.70471			0.852354	+	0.522965i	$0.175174\pi$
$140$	−19.7888			−1.67246
$141$	−5.75407	+	9.96634i	−0.484580	+	0.839317i
$142$	1.38410	+	2.39733i	0.116151	+	0.201179i
$143$	−4.46728	+	7.73755i	−0.373572	+	0.647046i
$144$	2.62284	+	4.54289i	0.218570	+	0.378574i
$145$	−1.61703	−	2.80077i	−0.134287	−	0.232591i
$146$	−14.6769	−	25.4211i	−1.21467	−	2.10386i
$147$	13.9109			1.14735
$148$	0.314782	−	0.545219i	0.0258749	−	0.0448167i
$149$	−6.15749	+	10.6651i	−0.504441	+	0.873717i	0.495546	+	0.868582i	$0.334968\pi$
$149$	−6.15749	+	10.6651i	−0.504441	+	0.873717i	−0.999987	+	0.00513554i	$0.998365\pi$
$150$	−1.13639	−	1.96829i	−0.0927862	−	0.160710i
$151$	19.8770			1.61756			0.808782	−	0.588108i	$-0.200127\pi$
$151$	19.8770			1.61756			0.808782	+	0.588108i	$0.200127\pi$
$152$	0.188657	−	0.326764i	0.0153021	−	0.0265040i
$153$	−3.35599			−0.271316
$154$	−32.5932			−2.62644
$155$		0			0
$156$	10.2421			0.820023
$157$	−5.80462			−0.463259			−0.231629	−	0.972804i	$-0.574406\pi$
$157$	−5.80462			−0.463259			−0.231629	+	0.972804i	$0.574406\pi$
$158$	8.98950	−	15.5703i	0.715166	−	1.23870i
$159$	−20.3428			−1.61329
$160$	9.52050	+	16.4900i	0.752662	+	1.30365i
$161$	6.16198	−	10.6729i	0.485632	−	0.841139i
$162$	11.6495	−	20.1776i	0.915274	−	1.58530i
$163$	17.7833			1.39290			0.696449	−	0.717607i	$-0.254762\pi$
$163$	17.7833			1.39290			0.696449	+	0.717607i	$0.254762\pi$
$164$	4.90610	+	8.49761i	0.383102	+	0.663552i
$165$	−10.7510	−	18.6214i	−0.836968	−	1.44967i
$166$	−5.37247	−	9.30539i	−0.416985	−	0.722239i
$167$	1.09102	−	1.88969i	0.0844253	−	0.146229i	−0.820721	−	0.571329i	$-0.806428\pi$
$167$	1.09102	−	1.88969i	0.0844253	−	0.146229i	0.905146	+	0.425100i	$0.139761\pi$
$168$	2.39202	+	4.14310i	0.184548	+	0.319647i
$169$	4.32180	−	7.48558i	0.332446	−	0.575814i
$170$	−10.3535			−0.794077
$171$	−0.977762			−0.0747713
$172$	0.309295	−	0.535715i	0.0235835	−	0.0408479i
$173$	2.75396	+	4.77000i	0.209380	+	0.362657i	0.951519	−	0.307589i	$-0.0995221\pi$
$173$	2.75396	+	4.77000i	0.209380	+	0.362657i	−0.742139	+	0.670246i	$0.766189\pi$
$174$	−3.05310	+	5.28812i	−0.231455	+	0.400891i
$175$	0.941947	+	1.63150i	0.0712045	+	0.123330i
$176$	7.11950	+	12.3313i	0.536653	+	0.929510i
$177$	6.23359	+	10.7969i	0.468545	+	0.811544i
$178$	−10.3867			−0.778514
$179$	6.06695	−	10.5083i	0.453465	−	0.785424i	−0.545134	−	0.838349i	$-0.683521\pi$
$179$	6.06695	−	10.5083i	0.453465	−	0.785424i	0.998598	+	0.0529251i	$0.0168545\pi$
$180$	−4.24636	+	7.35491i	−0.316505	+	0.548202i
$181$	4.82344	+	8.35444i	0.358523	+	0.620980i	0.987714	−	0.156270i	$-0.0499471\pi$
$181$	4.82344	+	8.35444i	0.358523	+	0.620980i	−0.629191	+	0.777251i	$0.716614\pi$
$182$	−15.8921			−1.17800
$183$	2.38241	−	4.12646i	0.176113	−	0.305037i
$184$	2.04102			0.150466
$185$	−0.644448			−0.0473808
$186$		0			0
$187$	−9.10960			−0.666160
$188$	12.3381			0.899850
$189$	−5.59332	+	9.68791i	−0.406854	+	0.704692i
$190$	−3.01647			−0.218838
$191$	−5.23270	−	9.06331i	−0.378625	−	0.655798i	0.612237	−	0.790674i	$-0.290270\pi$
$191$	−5.23270	−	9.06331i	−0.378625	−	0.655798i	−0.990862	+	0.134876i	$0.956936\pi$
$192$	10.8592	−	18.8087i	0.783695	−	1.35740i
$193$	0.895325	−	1.55075i	0.0644469	−	0.111625i	−0.832002	−	0.554773i	$-0.812805\pi$
$193$	0.895325	−	1.55075i	0.0644469	−	0.111625i	0.896449	+	0.443148i	$0.146138\pi$
$194$	13.9122			0.998837
$195$	−5.24211	−	9.07959i	−0.375395	−	0.650203i
$196$	−7.45707	−	12.9160i	−0.532648	−	0.922573i
$197$	3.19848	+	5.53993i	0.227882	+	0.394704i	0.957180	−	0.289493i	$-0.0934866\pi$
$197$	3.19848	+	5.53993i	0.227882	+	0.394704i	−0.729298	+	0.684196i	$0.760153\pi$
$198$	−6.99398	+	12.1139i	−0.497041	+	0.860900i
$199$	0.463578	+	0.802941i	0.0328622	+	0.0569190i	0.881989	−	0.471270i	$-0.156204\pi$
$199$	0.463578	+	0.802941i	0.0328622	+	0.0569190i	−0.849127	+	0.528189i	$0.822871\pi$
$200$	−0.156000	+	0.270200i	−0.0110309	+	0.0191060i
$201$	−29.1265			−2.05443
$202$	−37.4279			−2.63342
$203$	2.53069	−	4.38328i	0.177619	−	0.307646i
$204$	5.22137	+	9.04369i	0.365569	+	0.633185i
$205$	5.02208	−	8.69850i	0.350757	−	0.607530i
$206$	−4.05651	−	7.02608i	−0.282630	−	0.489530i
$207$	−2.64452	−	4.58045i	−0.183807	−	0.318363i
$208$	3.47140	+	6.01264i	0.240698	+	0.416902i
$209$	−2.65406			−0.183585
$210$	19.1232	−	33.1223i	1.31963	−	2.28566i
$211$	3.09072	−	5.35328i	0.212774	−	0.368535i	−0.739808	−	0.672818i	$-0.765084\pi$
$211$	3.09072	−	5.35328i	0.212774	−	0.368535i	0.952582	+	0.304283i	$0.0984169\pi$
$212$	10.9050	+	18.8880i	0.748957	+	1.29723i
$213$	−2.85806			−0.195831
$214$	−11.5165	+	19.9471i	−0.787249	+	1.36356i
$215$	−0.633214			−0.0431848
$216$	−1.85267			−0.126058
$217$		0			0
$218$	37.4917			2.53926
$219$	30.3067			2.04793
$220$	−11.5264	+	19.9644i	−0.777112	+	1.34600i
$221$	−4.44175			−0.298785
$222$	0.608389	+	1.05376i	0.0408324	+	0.0707238i
$223$	7.94891	−	13.7679i	0.532298	−	0.921968i	−0.466991	−	0.884262i	$-0.654662\pi$
$223$	7.94891	−	13.7679i	0.532298	−	0.921968i	0.999289	−	0.0377054i	$-0.0120048\pi$
$224$	−14.8998	+	25.8073i	−0.995536	+	1.72432i
$225$	0.808507			0.0539005
$226$	−18.1712	−	31.4735i	−1.20873	−	2.09358i
$227$	2.32248	+	4.02265i	0.154148	+	0.266993i	0.932749	−	0.360527i	$-0.117403\pi$
$227$	2.32248	+	4.02265i	0.154148	+	0.266993i	−0.778600	+	0.627520i	$0.784070\pi$
$228$	1.52124	+	2.63486i	0.100746	+	0.174498i
$229$	−9.70918	+	16.8168i	−0.641601	+	1.11129i	0.343474	+	0.939162i	$0.388396\pi$
$229$	−9.70918	+	16.8168i	−0.641601	+	1.11129i	−0.985075	+	0.172123i	$0.944937\pi$
$230$	−8.15857	−	14.1311i	−0.537960	−	0.931774i
$231$	16.8257	−	29.1429i	1.10705	−	1.91746i
$232$	0.838236			0.0550329
$233$	−14.2485			−0.933449			−0.466724	−	0.884403i	$-0.654566\pi$
$233$	−14.2485			−0.933449			−0.466724	+	0.884403i	$0.654566\pi$
$234$	−3.41020	+	5.90664i	−0.222932	+	0.386129i
$235$	−6.31490	−	10.9377i	−0.411939	−	0.713499i
$236$	6.68316	−	11.5756i	0.435037	−	0.753506i
$237$	9.28134	+	16.0757i	0.602888	+	1.04423i
$238$	−8.10175	−	14.0326i	−0.525158	−	0.909601i
$239$	−3.40076	−	5.89029i	−0.219977	−	0.381011i	0.734824	−	0.678258i	$-0.237265\pi$
$239$	−3.40076	−	5.89029i	−0.219977	−	0.381011i	−0.954801	+	0.297247i	$0.903932\pi$
$240$	−16.7087			−1.07854
$241$	−5.75256	+	9.96373i	−0.370555	+	0.641820i	−0.989651	−	0.143495i	$-0.954166\pi$
$241$	−5.75256	+	9.96373i	−0.370555	+	0.641820i	0.619096	+	0.785315i	$0.287499\pi$
$242$	−7.58800	+	13.1428i	−0.487775	+	0.844851i
$243$	7.46119	+	12.9232i	0.478636	+	0.829021i
$244$	−5.10847			−0.327037
$245$	−7.63336	+	13.2214i	−0.487677	+	0.844682i
$246$	−18.9643			−1.20912
$247$	−1.29410			−0.0823413
$248$		0			0
$249$	11.0938			0.703039
$250$	−21.8315			−1.38074
$251$	−3.64720	+	6.31714i	−0.230209	+	0.398734i	−0.957870	−	0.287203i	$-0.907274\pi$
$251$	−3.64720	+	6.31714i	−0.230209	+	0.398734i	0.727660	+	0.685938i	$0.240608\pi$
$252$	−13.2913			−0.837274
$253$	−7.17837	−	12.4333i	−0.451300	−	0.781675i
$254$	−14.7103	+	25.4790i	−0.923005	+	1.59869i
$255$	5.34481	−	9.25748i	0.334705	−	0.579726i
$256$	10.3241			0.645254
$257$	12.3278	+	21.3525i	0.768990	+	1.33193i	0.938111	+	0.346334i	$0.112574\pi$
$257$	12.3278	+	21.3525i	0.768990	+	1.33193i	−0.169121	+	0.985595i	$0.554093\pi$
$258$	0.597784	+	1.03539i	0.0372164	+	0.0644607i
$259$	−0.504289	−	0.873454i	−0.0313350	−	0.0542738i
$260$	−5.62018	+	9.73443i	−0.348548	+	0.603704i
$261$	−1.08609	−	1.88116i	−0.0672273	−	0.116441i
$262$	−7.44774	+	12.8999i	−0.460123	+	0.796956i
$263$	26.2870			1.62093			0.810463	−	0.585790i	$-0.199215\pi$
$263$	26.2870			1.62093			0.810463	+	0.585790i	$0.199215\pi$
$264$	5.57314			0.343003
$265$	11.1628	−	19.3345i	0.685724	−	1.18771i
$266$	−2.36043	−	4.08838i	−0.144727	−	0.250675i
$267$	5.36194	−	9.28715i	0.328145	−	0.568364i
$268$	15.6136	+	27.0435i	0.953751	+	1.65195i
$269$	−10.4399	−	18.0824i	−0.636532	−	1.10251i	−0.986188	−	0.165627i	$-0.947035\pi$
$269$	−10.4399	−	18.0824i	−0.636532	−	1.10251i	0.349657	−	0.936878i	$-0.386298\pi$
$270$	7.40565	+	12.8270i	0.450694	+	0.780624i
$271$	21.0108			1.27632			0.638159	−	0.769905i	$-0.279696\pi$
$271$	21.0108			1.27632			0.638159	+	0.769905i	$0.279696\pi$
$272$	−3.53941	+	6.13044i	−0.214608	+	0.371713i
$273$	8.20403	−	14.2098i	0.496530	−	0.860016i
$274$	7.85091	+	13.5982i	0.474291	+	0.821496i
$275$	2.19463			0.132341
$276$	−8.22889	+	14.2529i	−0.495321	+	0.857922i
$277$	4.75928			0.285958			0.142979	−	0.989726i	$-0.454332\pi$
$277$	4.75928			0.285958			0.142979	+	0.989726i	$0.454332\pi$
$278$	41.6459			2.49776
$279$		0			0
$280$	−5.25032			−0.313767
$281$	−6.65481			−0.396993			−0.198496	−	0.980102i	$-0.563606\pi$
$281$	−6.65481			−0.396993			−0.198496	+	0.980102i	$0.563606\pi$
$282$	−11.9231	+	20.6515i	−0.710012	+	1.22978i
$283$	−7.24625			−0.430745			−0.215372	−	0.976532i	$-0.569096\pi$
$283$	−7.24625			−0.430745			−0.215372	+	0.976532i	$0.569096\pi$
$284$	1.53210	+	2.65367i	0.0909132	+	0.157466i
$285$	1.55720	−	2.69715i	0.0922406	−	0.159765i
$286$	−9.25674	+	16.0331i	−0.547362	+	0.948059i
$287$	15.7194			0.927885
$288$	6.39453	+	11.0756i	0.376801	+	0.652639i
$289$	6.23561	+	10.8004i	0.366801	+	0.635318i
$290$	−3.35067	−	5.80354i	−0.196758	−	0.340795i
$291$	−7.18192	+	12.4395i	−0.421012	+	0.729214i
$292$	−16.2462	−	28.1393i	−0.950738	−	1.64673i
$293$	−6.75576	+	11.7013i	−0.394676	+	0.683598i	−0.993060	−	0.117611i	$-0.962476\pi$
$293$	−6.75576	+	11.7013i	−0.394676	+	0.683598i	0.598384	+	0.801209i	$0.295810\pi$
$294$	28.8250			1.68111
$295$	−13.6823			−0.796615
$296$	0.0835174	−	0.144656i	0.00485435	−	0.00840798i
$297$	6.51591	+	11.2859i	0.378092	+	0.654874i
$298$	−12.7591	+	22.0993i	−0.739112	+	1.28018i
$299$	−3.50010	−	6.06236i	−0.202416	−	0.350595i
$300$	−1.25791	−	2.17876i	−0.0726252	−	0.125791i
$301$	−0.495498	−	0.858227i	−0.0285600	−	0.0494674i
$302$	41.1875			2.37007
$303$	19.3215	−	33.4658i	1.10999	−	1.92256i
$304$	−1.03120	+	1.78609i	−0.0591434	+	0.102439i
$305$	2.61462	+	4.52866i	0.149713	+	0.259310i
$306$	−6.95402			−0.397535
$307$	11.3629	−	19.6811i	0.648516	−	1.12326i	−0.334962	−	0.942232i	$-0.608723\pi$
$307$	11.3629	−	19.6811i	0.648516	−	1.12326i	0.983477	−	0.181030i	$-0.0579433\pi$
$308$	−36.0783			−2.05575
$309$	8.37640			0.476517
$310$		0			0
$311$	9.49330			0.538315			0.269158	−	0.963096i	$-0.413255\pi$
$311$	9.49330			0.538315			0.269158	+	0.963096i	$0.413255\pi$
$312$	2.71741			0.153843
$313$	14.0485	−	24.3328i	0.794070	−	1.37537i	−0.129359	−	0.991598i	$-0.541292\pi$
$313$	14.0485	−	24.3328i	0.794070	−	1.37537i	0.923428	−	0.383771i	$-0.125375\pi$
$314$	−12.0279			−0.678772
$315$	6.80276	+	11.7827i	0.383292	+	0.663882i
$316$	9.95072	−	17.2352i	0.559772	−	0.969553i
$317$	7.90841	−	13.6978i	0.444181	−	0.769344i	−0.553814	−	0.832640i	$-0.686828\pi$
$317$	7.90841	−	13.6978i	0.444181	−	0.769344i	0.997995	+	0.0632968i	$0.0201615\pi$
$318$	−42.1528			−2.36381
$319$	−2.94811	−	5.10628i	−0.165063	−	0.285897i
$320$	11.9176	+	20.6419i	0.666214	+	1.15392i
$321$	−11.8903	−	20.5947i	−0.663654	−	1.14948i
$322$	12.7684	−	22.1155i	0.711553	−	1.23245i
$323$	−0.659725	−	1.14268i	−0.0367081	−	0.0635802i
$324$	12.8952	−	22.3351i	0.716400	−	1.24084i
$325$	1.07008			0.0593575
$326$	36.8492			2.04089
$327$	−19.3544	+	33.5228i	−1.07030	+	1.85382i
$328$	1.30168	+	2.25457i	0.0718730	+	0.124488i
$329$	9.88298	−	17.1178i	0.544866	−	0.943736i
$330$	−22.2775	−	38.5857i	−1.22633	−	2.12407i
$331$	6.47206	+	11.2099i	0.355737	+	0.616154i	0.987244	−	0.159216i	$-0.0508967\pi$
$331$	6.47206	+	11.2099i	0.355737	+	0.616154i	−0.631507	+	0.775370i	$0.717563\pi$
$332$	−5.94693	−	10.3004i	−0.326380	−	0.565308i
$333$	−0.432849			−0.0237200
$334$	2.26072	−	3.91568i	0.123701	−	0.214256i
$335$	15.9827	−	27.6828i	0.873228	−	1.51247i
$336$	−13.0748	−	22.6462i	−0.713287	−	1.23545i
$337$	27.8663			1.51797			0.758987	−	0.651105i	$-0.225694\pi$
$337$	27.8663			1.51797			0.758987	+	0.651105i	$0.225694\pi$
$338$	8.95530	−	15.5110i	0.487104	−	0.843689i
$339$	37.5223			2.03793
$340$	−11.4606			−0.621537
$341$		0			0
$342$	−2.02604			−0.109556
$343$	1.82899			0.0987564
$344$	0.0820615	−	0.142135i	0.00442446	−	0.00766339i
$345$	16.8469			0.907004
$346$	5.70655	+	9.88403i	0.306786	+	0.531369i
$347$	2.66175	−	4.61029i	0.142890	−	0.247493i	−0.785693	−	0.618616i	$-0.787694\pi$
$347$	2.66175	−	4.61029i	0.142890	−	0.247493i	0.928584	+	0.371123i	$0.121027\pi$
$348$	−3.37956	+	5.85356i	−0.181163	+	0.313784i
$349$	−4.09791			−0.219356			−0.109678	−	0.993967i	$-0.534982\pi$
$349$	−4.09791			−0.219356			−0.109678	+	0.993967i	$0.534982\pi$
$350$	1.95183	+	3.38067i	0.104330	+	0.180704i
$351$	3.17710	+	5.50289i	0.169581	+	0.293723i
$352$	17.3575	+	30.0641i	0.925157	+	1.60242i
$353$	10.8947	−	18.8701i	0.579865	−	1.00436i	−0.415629	−	0.909534i	$-0.636438\pi$
$353$	10.8947	−	18.8701i	0.579865	−	1.00436i	0.995494	−	0.0948220i	$-0.0302282\pi$
$354$	12.9167	+	22.3725i	0.686517	+	1.18908i
$355$	1.56832	−	2.71640i	0.0832376	−	0.144172i
$356$	−11.4973			−0.609355
$357$	16.7295			0.885421
$358$	12.5714	−	21.7744i	0.664422	−	1.15081i
$359$	3.54072	+	6.13270i	0.186872	+	0.323671i	0.944206	−	0.329356i	$-0.106832\pi$
$359$	3.54072	+	6.13270i	0.186872	+	0.323671i	−0.757334	+	0.653028i	$0.773498\pi$
$360$	−1.12663	+	1.95139i	−0.0593789	+	0.102847i
$361$	9.30779	+	16.1216i	0.489884	+	0.848503i
$362$	9.99475	+	17.3114i	0.525312	+	0.909867i
$363$	−7.83434	−	13.5695i	−0.411196	−	0.712212i
$364$	−17.5914			−0.922042
$365$	−16.6303	+	28.8045i	−0.870469	+	1.50770i
$366$	4.93665	−	8.55053i	0.258043	−	0.446943i
$367$	−8.05884	−	13.9583i	−0.420668	−	0.728619i	0.575337	−	0.817917i	$-0.304871\pi$
$367$	−8.05884	−	13.9583i	−0.420668	−	0.728619i	−0.996005	+	0.0892980i	$0.971538\pi$
$368$	−11.1562			−0.581559
$369$	3.37313	−	5.84243i	0.175598	−	0.304145i
$370$	−1.33537			−0.0694228
$371$	34.9401			1.81400
$372$		0			0
$373$	−9.81895			−0.508406			−0.254203	−	0.967151i	$-0.581813\pi$
$373$	−9.81895			−0.508406			−0.254203	+	0.967151i	$0.581813\pi$
$374$	−18.8762			−0.976065
$375$	11.2701	−	19.5204i	0.581986	−	1.00803i
$376$	3.27352			0.168819
$377$	−1.43747	−	2.48977i	−0.0740335	−	0.128230i
$378$	−11.5900	+	20.0745i	−0.596127	+	1.03252i
$379$	6.90781	−	11.9647i	0.354830	−	0.614584i	−0.632258	−	0.774758i	$-0.717872\pi$
$379$	6.90781	−	11.9647i	0.354830	−	0.614584i	0.987089	+	0.160173i	$0.0512053\pi$
$380$	−3.33902			−0.171288
$381$	−15.1878	−	26.3061i	−0.778097	−	1.34770i
$382$	−10.8428	−	18.7803i	−0.554766	−	0.960882i
$383$	5.15301	+	8.92528i	0.263307	+	0.456060i	0.967119	−	0.254326i	$-0.0818536\pi$
$383$	5.15301	+	8.92528i	0.263307	+	0.456060i	−0.703812	+	0.710386i	$0.748520\pi$
$384$	5.15161	−	8.92286i	0.262892	−	0.455343i
$385$	18.4656	+	31.9834i	0.941095	+	1.63002i
$386$	1.85522	−	3.21334i	0.0944283	−	0.163555i
$387$	−0.425304			−0.0216194
$388$	15.3998			0.781806
$389$	−12.6827	+	21.9671i	−0.643039	+	1.11378i	0.341712	+	0.939805i	$0.388993\pi$
$389$	−12.6827	+	21.9671i	−0.643039	+	1.11378i	−0.984751	+	0.173971i	$0.944340\pi$
$390$	−10.8623	−	18.8140i	−0.550033	−	0.952685i
$391$	3.56868	−	6.18113i	0.180476	−	0.312593i
$392$	−1.97849	−	3.42685i	−0.0999290	−	0.173082i
$393$	−7.68952	−	13.3186i	−0.387885	−	0.671837i
$394$	6.62764	+	11.4794i	0.333896	+	0.578324i
$395$	−20.3719			−1.02502
$396$	−7.74183	+	13.4092i	−0.389042	+	0.673840i
$397$	−8.37941	+	14.5136i	−0.420550	+	0.728415i	−0.995993	−	0.0894272i	$-0.971496\pi$
$397$	−8.37941	+	14.5136i	−0.420550	+	0.728415i	0.575443	+	0.817842i	$0.304830\pi$
$398$	0.960590	+	1.66379i	0.0481500	+	0.0833983i
$399$	4.87412			0.244011
$400$	0.852696	−	1.47691i	0.0426348	−	0.0738456i
$401$	27.6236			1.37946			0.689728	−	0.724069i	$-0.257730\pi$
$401$	27.6236			1.37946			0.689728	+	0.724069i	$0.257730\pi$
$402$	−60.3537			−3.01017
$403$		0			0
$404$	−41.4300			−2.06122
$405$	−26.4001			−1.31183
$406$	5.24389	−	9.08268i	0.260250	−	0.450766i
$407$	−1.17494			−0.0582395
$408$	1.38532	+	2.39945i	0.0685838	+	0.118791i
$409$	−11.3053	+	19.5814i	−0.559013	+	0.968239i	0.438566	+	0.898699i	$0.355486\pi$
$409$	−11.3053	+	19.5814i	−0.559013	+	0.968239i	−0.997579	+	0.0695399i	$0.977847\pi$
$410$	10.4064	−	18.0244i	0.513934	−	0.890159i
$411$	−16.2116			−0.799657
$412$	−4.49026	−	7.77736i	−0.221219	−	0.383163i
$413$	−10.7066	−	18.5443i	−0.526836	−	0.912507i
$414$	−5.47977	−	9.49125i	−0.269316	−	0.466469i
$415$	−6.08752	+	10.5439i	−0.298825	+	0.517580i
$416$	8.46334	+	14.6589i	0.414949	+	0.718714i
$417$	−21.4990	+	37.2373i	−1.05281	+	1.82352i
$418$	−5.49954			−0.268991
$419$	−6.19097			−0.302449			−0.151224	−	0.988499i	$-0.548322\pi$
$419$	−6.19097			−0.302449			−0.151224	+	0.988499i	$0.548322\pi$
$420$	21.1680	−	36.6640i	1.03289	−	1.78902i
$421$	−3.27967	−	5.68055i	−0.159841	−	0.276853i	0.774970	−	0.631998i	$-0.217765\pi$
$421$	−3.27967	−	5.68055i	−0.159841	−	0.276853i	−0.934811	+	0.355145i	$0.884432\pi$
$422$	6.40434	−	11.0926i	0.311759	−	0.539982i
$423$	−4.24146	−	7.34642i	−0.206227	−	0.357195i
$424$	2.89329	+	5.01132i	0.140510	+	0.243371i
$425$	0.545524	+	0.944875i	0.0264618	+	0.0458332i
$426$	−5.92226			−0.286934
$427$	−4.09195	+	7.08746i	−0.198023	+	0.342986i
$428$	−12.7479	+	22.0800i	−0.616192	+	1.06728i
$429$	−9.55725	−	16.5536i	−0.461428	−	0.799217i
$430$	−1.31210			−0.0632749
$431$	−11.7339	+	20.3236i	−0.565200	+	0.978955i	0.431831	+	0.901954i	$0.357868\pi$
$431$	−11.7339	+	20.3236i	−0.565200	+	0.978955i	−0.997031	+	0.0770004i	$0.975466\pi$
$432$	10.1267			0.487220
$433$	−24.3130			−1.16841			−0.584203	−	0.811607i	$-0.698593\pi$
$433$	−24.3130			−1.16841			−0.584203	+	0.811607i	$0.698593\pi$
$434$		0			0
$435$	6.91890			0.331736
$436$	41.5006			1.98752
$437$	1.03973	−	1.80086i	0.0497369	−	0.0861468i
$438$	62.7991			3.00066
$439$	−7.25318	−	12.5629i	−0.346175	−	0.599593i	0.639391	−	0.768881i	$-0.279186\pi$
$439$	−7.25318	−	12.5629i	−0.346175	−	0.599593i	−0.985567	+	0.169288i	$0.945853\pi$
$440$	−3.05817	+	5.29690i	−0.145792	+	0.252520i
$441$	−5.12701	+	8.88025i	−0.244143	+	0.422869i
$442$	−9.20385			−0.437782
$443$	8.28299	+	14.3466i	0.393537	+	0.681626i	0.992913	−	0.118841i	$-0.0379180\pi$
$443$	8.28299	+	14.3466i	0.393537	+	0.681626i	−0.599376	+	0.800467i	$0.704585\pi$
$444$	0.673443	+	1.16644i	0.0319602	+	0.0553566i
$445$	5.88455	+	10.1923i	0.278954	+	0.483163i
$446$	16.4711	−	28.5288i	0.779929	−	1.35088i
$447$	−13.1733	−	22.8168i	−0.623074	−	1.07920i
$448$	−18.6514	+	32.3051i	−0.881194	+	1.52627i
$449$	−6.81731			−0.321729			−0.160864	−	0.986977i	$-0.551428\pi$
$449$	−6.81731			−0.321729			−0.160864	+	0.986977i	$0.551428\pi$
$450$	1.67533			0.0789756
$451$	9.15611	−	15.8588i	0.431144	−	0.746764i
$452$	−20.1142	−	34.8388i	−0.946093	−	1.63868i
$453$	−21.2623	+	36.8274i	−0.998990	+	1.73030i
$454$	4.81246	+	8.33542i	0.225860	+	0.391201i
$455$	9.00365	+	15.5948i	0.422098	+	0.731095i
$456$	0.403612	+	0.699076i	0.0189008	+	0.0327372i
$457$	−21.4277			−1.00235			−0.501174	−	0.865347i	$-0.667098\pi$
$457$	−21.4277			−1.00235			−0.501174	+	0.865347i	$0.667098\pi$
$458$	−20.1186	+	34.8465i	−0.940081	+	1.62827i
$459$	−3.23934	+	5.61070i	−0.151200	+	0.261885i
$460$	−9.03094	−	15.6420i	−0.421070	−	0.729314i
$461$	8.67451			0.404012			0.202006	−	0.979384i	$-0.435254\pi$
$461$	8.67451			0.404012			0.202006	+	0.979384i	$0.435254\pi$
$462$	34.8648	−	60.3876i	1.62206	−	2.80949i
$463$	−3.64987			−0.169624			−0.0848120	−	0.996397i	$-0.527029\pi$
$463$	−3.64987			−0.169624			−0.0848120	+	0.996397i	$0.527029\pi$
$464$	−4.58180			−0.212705
$465$		0			0
$466$	−29.5246			−1.36770
$467$	−3.08111			−0.142577			−0.0712884	−	0.997456i	$-0.522711\pi$
$467$	−3.08111			−0.142577			−0.0712884	+	0.997456i	$0.522711\pi$
$468$	−3.77484	+	6.53822i	−0.174492	+	0.302229i
$469$	50.0266			2.31002
$470$	−13.0852	−	22.6643i	−0.603577	−	1.04543i
$471$	6.20917	−	10.7546i	0.286104	−	0.495546i
$472$	1.77316	−	3.07121i	0.0816164	−	0.141364i
$473$	−1.15446			−0.0530820
$474$	19.2321	+	33.3109i	0.883358	+	1.53002i
$475$	0.158937	+	0.275287i	0.00729254	+	0.0126311i
$476$	−8.96804	−	15.5331i	−0.411050	−	0.711959i
$477$	7.49758	−	12.9862i	0.343291	−	0.594597i
$478$	−7.04679	−	12.2054i	−0.322313	−	0.558262i
$479$	8.70511	−	15.0777i	0.397747	−	0.688918i	−0.595701	−	0.803206i	$-0.703126\pi$
$479$	8.70511	−	15.0777i	0.397747	−	0.688918i	0.993448	+	0.114289i	$0.0364589\pi$
$480$	−40.7362			−1.85934
$481$	−0.572888			−0.0261215
$482$	−11.9200	+	20.6461i	−0.542941	+	0.940402i
$483$	13.1829	+	22.8334i	0.599842	+	1.03896i
$484$	−8.39936	+	14.5481i	−0.381789	+	0.661278i
$485$	−7.88192	−	13.6519i	−0.357900	−	0.619900i
$486$	15.4605	+	26.7784i	0.701302	+	1.21469i
$487$	14.3868	+	24.9187i	0.651929	+	1.12917i	0.982654	+	0.185447i	$0.0593732\pi$
$487$	14.3868	+	24.9187i	0.651929	+	1.12917i	−0.330726	+	0.943727i	$0.607294\pi$
$488$	−1.35537			−0.0613547
$489$	−19.0227	+	32.9484i	−0.860238	+	1.48998i
$490$	−15.8172	+	27.3963i	−0.714550	+	1.23764i
$491$	−4.91284	−	8.50929i	−0.221713	−	0.384019i	0.733615	−	0.679565i	$-0.237832\pi$
$491$	−4.91284	−	8.50929i	−0.221713	−	0.384019i	−0.955328	+	0.295546i	$0.904498\pi$
$492$	−20.9921			−0.946399
$493$	1.46563	−	2.53855i	0.0660088	−	0.114331i
$494$	−2.68152			−0.120647
$495$	15.8497			0.712391
$496$		0			0
$497$	4.90891			0.220195
$498$	22.9876			1.03010
$499$	−5.42400	+	9.39465i	−0.242812	+	0.420562i	−0.961514	−	0.274756i	$-0.911403\pi$
$499$	−5.42400	+	9.39465i	−0.242812	+	0.420562i	0.718702	+	0.695318i	$0.244736\pi$
$500$	−24.1659			−1.08073
$501$	2.33411	+	4.04280i	0.104280	+	0.180619i
$502$	−7.55745	+	13.0899i	−0.337305	+	0.584230i
$503$	−4.28047	+	7.41400i	−0.190857	+	0.330574i	−0.945534	−	0.325522i	$-0.894460\pi$
$503$	−4.28047	+	7.41400i	−0.190857	+	0.330574i	0.754678	+	0.656096i	$0.227793\pi$
$504$	−3.52642			−0.157079
$505$	21.2047	+	36.7276i	0.943596	+	1.63436i
$506$	−14.8745	−	25.7633i	−0.661250	−	1.14532i
$507$	9.24602	+	16.0146i	0.410630	+	0.711232i
$508$	−16.2832	+	28.2033i	−0.722451	+	1.25132i
$509$	−19.7912	−	34.2793i	−0.877228	−	1.51940i	−0.854370	−	0.519665i	$-0.826057\pi$
$509$	−19.7912	−	34.2793i	−0.877228	−	1.51940i	−0.0228575	−	0.999739i	$-0.507276\pi$
$510$	11.0751	−	19.1826i	0.490414	−	0.849421i
$511$	−52.0536			−2.30272
$512$	31.0247			1.37111
$513$	−0.943776	+	1.63467i	−0.0416687	+	0.0721723i
$514$	25.5448	+	44.2449i	1.12673	+	1.95156i
$515$	−4.59641	+	7.96122i	−0.202542	+	0.350813i
$516$	0.661703	+	1.14610i	0.0291299	+	0.0504544i
$517$	−11.5131	−	19.9413i	−0.506347	−	0.877019i
$518$	−1.04495	−	1.80990i	−0.0459124	−	0.0795225i
$519$	−11.7836			−0.517243
$520$	−1.49113	+	2.58272i	−0.0653905	+	0.113260i
$521$	0.674660	−	1.16855i	0.0295574	−	0.0511949i	−0.850868	−	0.525379i	$-0.823924\pi$
$521$	0.674660	−	1.16855i	0.0295574	−	0.0511949i	0.880426	+	0.474184i	$0.157257\pi$
$522$	−2.25051	−	3.89800i	−0.0985022	−	0.170611i
$523$	−28.4729			−1.24503			−0.622517	−	0.782607i	$-0.713890\pi$
$523$	−28.4729			−1.24503			−0.622517	+	0.782607i	$0.713890\pi$
$524$	−8.24410	+	14.2792i	−0.360145	+	0.623790i
$525$	−4.03039			−0.175900
$526$	54.4699			2.37500
$527$		0			0
$528$	−30.4628			−1.32572
$529$	−11.7515			−0.510936
$530$	23.1306	−	40.0634i	1.00473	−	1.74024i
$531$	−9.18985			−0.398805
$532$	−2.61282	−	4.52554i	−0.113280	−	0.196207i
$533$	4.46443	−	7.73262i	0.193376	−	0.334937i
$534$	11.1106	−	19.2441i	0.480802	−	0.832773i
$535$	26.0985			1.12834
$536$	4.14256	+	7.17513i	0.178931	+	0.309918i
$537$	12.9796	+	22.4813i	0.560110	+	0.970139i
$538$	−21.6327	−	37.4690i	−0.932653	−	1.61540i
$539$	−13.9169	+	24.1048i	−0.599444	+	1.03827i
$540$	8.19752	+	14.1985i	0.352765	+	0.611007i
$541$	7.15480	−	12.3925i	0.307609	−	0.532794i	−0.670230	−	0.742154i	$-0.733804\pi$
$541$	7.15480	−	12.3925i	0.307609	−	0.532794i	0.977839	+	0.209359i	$0.0671378\pi$
$542$	43.5370			1.87008
$543$	−20.6384			−0.885680
$544$	−8.62916	+	14.9461i	−0.369972	+	0.640810i
$545$	−21.2408	−	36.7902i	−0.909857	−	1.57592i
$546$	16.9997	−	29.4444i	0.727522	−	1.26011i
$547$	−21.1835	−	36.6908i	−0.905739	−	1.56879i	−0.819922	−	0.572475i	$-0.805983\pi$
$547$	−21.1835	−	36.6908i	−0.905739	−	1.56879i	−0.0858173	−	0.996311i	$-0.527350\pi$
$548$	8.69038	+	15.0522i	0.371235	+	0.642998i
$549$	1.75613	+	3.04171i	0.0749499	+	0.129817i
$550$	4.54755			0.193908
$551$	0.427010	−	0.739602i	0.0181912	−	0.0315081i
$552$	−2.18327	+	3.78154i	−0.0929263	+	0.160953i
$553$	−15.9413	−	27.6111i	−0.677893	−	1.17414i
$554$	9.86181			0.418988
$555$	0.689363	−	1.19401i	0.0292618	−	0.0506830i
$556$	46.0990			1.95503
$557$	−27.3019			−1.15682			−0.578409	−	0.815747i	$-0.696326\pi$
$557$	−27.3019			−1.15682			−0.578409	+	0.815747i	$0.696326\pi$
$558$		0			0
$559$	−0.562902			−0.0238082
$560$	28.6983			1.21272
$561$	9.74450	−	16.8780i	0.411413	−	0.712588i
$562$	−13.7896			−0.581678
$563$	−2.59399	−	4.49293i	−0.109324	−	0.189354i	0.806173	−	0.591680i	$-0.201535\pi$
$563$	−2.59399	−	4.49293i	−0.109324	−	0.189354i	−0.915497	+	0.402326i	$0.868202\pi$
$564$	−13.1980	+	22.8597i	−0.555737	+	0.962565i
$565$	−20.5897	+	35.6624i	−0.866216	+	1.50033i
$566$	−15.0151			−0.631132
$567$	−20.6584	−	35.7814i	−0.867571	−	1.50268i
$568$	0.406493	+	0.704066i	0.0170561	+	0.0295420i
$569$	1.18392	+	2.05060i	0.0496323	+	0.0859657i	0.889774	−	0.456401i	$-0.150862\pi$
$569$	1.18392	+	2.05060i	0.0496323	+	0.0859657i	−0.840142	+	0.542367i	$0.817528\pi$
$570$	3.22671	−	5.58882i	0.135152	−	0.234090i
$571$	10.1810	+	17.6340i	0.426060	+	0.737958i	0.996519	−	0.0833685i	$-0.0265678\pi$
$571$	10.1810	+	17.6340i	0.426060	+	0.737958i	−0.570459	+	0.821326i	$0.693235\pi$
$572$	−10.2465	+	17.7475i	−0.428429	+	0.742061i
$573$	22.3896			0.935339
$574$	32.5724			1.35955
$575$	−0.859746	+	1.48912i	−0.0358539	+	0.0621008i
$576$	8.00457	+	13.8643i	0.333524	+	0.577680i
$577$	−12.7909	+	22.1544i	−0.532491	+	0.922302i	0.466789	+	0.884369i	$0.345411\pi$
$577$	−12.7909	+	22.1544i	−0.532491	+	0.922302i	−0.999280	+	0.0379330i	$0.987923\pi$
$578$	12.9209	+	22.3797i	0.537441	+	0.930874i
$579$	1.91545	+	3.31766i	0.0796034	+	0.137877i
$580$	−3.70895	−	6.42409i	−0.154006	−	0.266746i
$581$	−19.0543			−0.790504
$582$	−14.8818	+	25.7761i	−0.616871	+	1.06845i
$583$	20.3516	−	35.2501i	0.842879	−	1.45991i
$584$	−4.31041	−	7.46585i	−0.178366	−	0.308939i
$585$	7.72816			0.319520
$586$	−13.9988	+	24.2466i	−0.578283	+	1.00162i
$587$	−39.9619			−1.64940			−0.824702	−	0.565567i	$-0.808657\pi$
$587$	−39.9619			−1.64940			−0.824702	+	0.565567i	$0.808657\pi$
$588$	31.9072			1.31583
$589$		0			0
$590$	−28.3514			−1.16721
$591$	−13.6856			−0.562950
$592$	−0.456506	+	0.790692i	−0.0187623	+	0.0324973i
$593$	−20.9772			−0.861429			−0.430715	−	0.902488i	$-0.641738\pi$
$593$	−20.9772			−0.861429			−0.430715	+	0.902488i	$0.641738\pi$
$594$	13.5018	+	23.3857i	0.553984	+	0.959529i
$595$	−9.18005	+	15.9003i	−0.376345	+	0.651849i
$596$	−14.1233	+	24.4624i	−0.578515	+	1.00202i
$597$	−1.98355			−0.0811813
$598$	−7.25264	−	12.5619i	−0.296582	−	0.513696i
$599$	−10.4707	−	18.1358i	−0.427820	−	0.741007i	0.568859	−	0.822435i	$-0.307385\pi$
$599$	−10.4707	−	18.1358i	−0.427820	−	0.741007i	−0.996679	+	0.0814285i	$0.974052\pi$
$600$	−0.333745	−	0.578063i	−0.0136251	−	0.0235993i
$601$	−8.30933	+	14.3922i	−0.338945	+	0.587070i	−0.984235	−	0.176868i	$-0.943403\pi$
$601$	−8.30933	+	14.3922i	−0.338945	+	0.587070i	0.645290	+	0.763938i	$0.276737\pi$
$602$	−1.02673	−	1.77835i	−0.0418465	−	0.0724802i
$603$	10.7349	−	18.5934i	0.437160	−	0.757183i
$604$	45.5915			1.85509
$605$	17.1958			0.699111
$606$	40.0365	−	69.3452i	1.62637	−	2.81696i
$607$	−14.7757	−	25.5922i	−0.599726	−	1.03876i	−0.992861	−	0.119275i	$-0.961943\pi$
$607$	−14.7757	−	25.5922i	−0.599726	−	1.03876i	0.393135	−	0.919481i	$-0.371390\pi$
$608$	−2.51409	+	4.35453i	−0.101960	+	0.176599i
$609$	5.41413	+	9.37755i	0.219392	+	0.379997i
$610$	5.41781	+	9.38392i	0.219361	+	0.379944i
$611$	−5.61369	−	9.72320i	−0.227106	−	0.393359i
$612$	−7.69760			−0.311157
$613$	18.5499	−	32.1294i	0.749224	−	1.29769i	−0.198971	−	0.980005i	$-0.563760\pi$
$613$	18.5499	−	32.1294i	0.749224	−	1.29769i	0.948195	−	0.317689i	$-0.102907\pi$
$614$	23.5453	−	40.7817i	0.950212	−	1.64582i
$615$	10.7442	+	18.6095i	0.433248	+	0.750407i
$616$	−9.57222			−0.385676
$617$	13.1716	−	22.8138i	0.530267	−	0.918450i	−0.469109	−	0.883140i	$-0.655425\pi$
$617$	13.1716	−	22.8138i	0.530267	−	0.918450i	0.999376	−	0.0353098i	$-0.0112418\pi$
$618$	17.3569			0.698198
$619$	26.3796			1.06029			0.530144	−	0.847908i	$-0.322138\pi$
$619$	26.3796			1.06029			0.530144	+	0.847908i	$0.322138\pi$
$620$		0			0
$621$	−10.2104			−0.409730
$622$	19.6713			0.788746
$623$	−9.20947	+	15.9513i	−0.368970	+	0.639074i
$624$	−14.8534			−0.594611
$625$	13.6503	+	23.6430i	0.546012	+	0.945720i
$626$	29.1103	−	50.4204i	1.16348	−	2.01521i
$627$	2.83904	−	4.91736i	0.113380	−	0.196381i
$628$	−13.3140			−0.531286
$629$	−0.292056	−	0.505856i	−0.0116450	−	0.0201698i
$630$	14.0962	+	24.4153i	0.561604	+	0.972727i
$631$	9.98562	+	17.2956i	0.397521	+	0.688527i	0.993419	−	0.114533i	$-0.0365371\pi$
$631$	9.98562	+	17.2956i	0.397521	+	0.688527i	−0.595898	+	0.803060i	$0.703204\pi$
$632$	2.64011	−	4.57280i	0.105018	−	0.181896i
$633$	6.61226	+	11.4528i	0.262814	+	0.455207i
$634$	16.3872	−	28.3834i	0.650819	−	1.12725i
$635$	33.3363			1.32291
$636$	−46.6600			−1.85019
$637$	−6.78575	+	11.7533i	−0.268861	+	0.465681i
$638$	−6.10885	−	10.5808i	−0.241852	−	0.418899i
$639$	1.05337	−	1.82450i	0.0416708	−	0.0721760i
$640$	5.65373	+	9.79254i	0.223483	+	0.387084i
$641$	11.6475	+	20.1740i	0.460048	+	0.796826i	0.998963	−	0.0455342i	$-0.0144990\pi$
$641$	11.6475	+	20.1740i	0.460048	+	0.796826i	−0.538915	+	0.842360i	$0.681166\pi$
$642$	−24.6382	−	42.6747i	−0.972393	−	1.68423i
$643$	38.8939			1.53382			0.766912	−	0.641752i	$-0.221792\pi$
$643$	38.8939			1.53382			0.766912	+	0.641752i	$0.221792\pi$
$644$	14.1337	−	24.4802i	0.556944	−	0.964655i
$645$	0.677346	−	1.17320i	0.0266705	−	0.0461946i
$646$	−1.36703	−	2.36777i	−0.0537851	−	0.0931585i
$647$	2.23041			0.0876865			0.0438432	−	0.999038i	$-0.486040\pi$
$647$	2.23041			0.0876865			0.0438432	+	0.999038i	$0.486040\pi$
$648$	3.42133	−	5.92591i	0.134402	−	0.232792i
$649$	−24.9452			−0.979184
$650$	2.21734			0.0869713
$651$		0			0
$652$	40.7894			1.59744
$653$	−28.5732			−1.11816			−0.559078	−	0.829115i	$-0.688845\pi$
$653$	−28.5732			−1.11816			−0.559078	+	0.829115i	$0.688845\pi$
$654$	−40.1047	+	69.4634i	−1.56822	+	2.71623i
$655$	16.8780			0.659478
$656$	−7.11497	−	12.3235i	−0.277793	−	0.481151i
$657$	−11.1699	+	19.3468i	−0.435778	+	0.754790i
$658$	20.4787	−	35.4702i	0.798344	−	1.38277i
$659$	5.13778			0.200140			0.100070	−	0.994980i	$-0.468093\pi$
$659$	5.13778			0.200140			0.100070	+	0.994980i	$0.468093\pi$
$660$	−24.6595	−	42.7116i	−0.959872	−	1.66255i
$661$	2.94772	+	5.10561i	0.114653	+	0.198585i	0.917641	−	0.397410i	$-0.130091\pi$
$661$	2.94772	+	5.10561i	0.114653	+	0.198585i	−0.802988	+	0.595995i	$0.796758\pi$
$662$	13.4109	+	23.2284i	0.521229	+	0.902796i
$663$	4.75132	−	8.22953i	0.184526	−	0.319609i
$664$	−1.57783	−	2.73288i	−0.0612316	−	0.106056i
$665$	−2.67459	+	4.63253i	−0.103716	+	0.179642i
$666$	−0.896916			−0.0347548
$667$	4.61968			0.178875
$668$	2.50245	−	4.33437i	0.0968226	−	0.167702i
$669$	17.0058	+	29.4550i	0.657483	+	1.13879i
$670$	33.1181	−	57.3622i	1.27946	−	2.21609i
$671$	4.76690	+	8.25651i	0.184024	+	0.318739i
$672$	−31.8766	−	55.2118i	−1.22966	−	2.12984i
$673$	13.6317	+	23.6107i	0.525462	+	0.910127i	0.999560	+	0.0296547i	$0.00944077\pi$
$673$	13.6317	+	23.6107i	0.525462	+	0.910127i	−0.474098	+	0.880472i	$0.657226\pi$
$674$	57.7424			2.22415
$675$	0.780405	−	1.35170i	0.0300378	−	0.0520270i
$676$	9.91286	−	17.1696i	0.381264	−	0.660368i
$677$	−1.31511	−	2.27784i	−0.0505438	−	0.0875444i	0.839647	−	0.543133i	$-0.182762\pi$
$677$	−1.31511	−	2.27784i	−0.0505438	−	0.0875444i	−0.890190	+	0.455589i	$0.849429\pi$
$678$	77.7507			2.98600
$679$	12.3354	−	21.3655i	0.473389	−	0.819935i
$680$	−3.04070			−0.116605
$681$	−9.93738			−0.380801
$682$		0			0
$683$	29.5859			1.13207			0.566037	−	0.824380i	$-0.308476\pi$
$683$	29.5859			1.13207			0.566037	+	0.824380i	$0.308476\pi$
$684$	−2.24268			−0.0857510
$685$	8.89583	−	15.4080i	0.339892	−	0.588710i
$686$	3.78990			0.144699
$687$	−20.7717	−	35.9777i	−0.792492	−	1.37264i
$688$	−0.448549	+	0.776909i	−0.0171008	+	0.0296194i
$689$	9.92326	−	17.1876i	0.378046	−	0.654795i
$690$	34.9087			1.32895
$691$	−8.42291	−	14.5889i	−0.320423	−	0.554988i	0.660153	−	0.751131i	$-0.270492\pi$
$691$	−8.42291	−	14.5889i	−0.320423	−	0.554988i	−0.980575	+	0.196143i	$0.937158\pi$
$692$	6.31673	+	10.9409i	0.240126	+	0.415911i
$693$	12.4026	+	21.4819i	0.471136	+	0.816031i
$694$	5.51548	−	9.55309i	0.209365	−	0.362630i
$695$	−23.5944	−	40.8667i	−0.894987	−	1.55016i
$696$	−0.896657	+	1.55306i	−0.0339877	+	0.0588684i
$697$	9.10379			0.344831
$698$	−8.49136			−0.321403
$699$	15.2415	−	26.3991i	0.576488	−	0.998506i
$700$	2.16053	+	3.74215i	0.0816604	+	0.141440i
$701$	−10.6122	+	18.3808i	−0.400816	+	0.694233i	−0.993825	−	0.110963i	$-0.964607\pi$
$701$	−10.6122	+	18.3808i	−0.400816	+	0.694233i	0.593009	+	0.805196i	$0.297940\pi$
$702$	6.58333	+	11.4027i	0.248472	+	0.430366i
$703$	−0.0850900	−	0.147380i	−0.00320923	−	0.00555855i
$704$	21.7278	+	37.6337i	0.818898	+	1.41837i
$705$	27.0201			1.01764
$706$	22.5751	−	39.1012i	0.849625	−	1.47159i
$707$	−33.1859	+	57.4796i	−1.24808	+	2.16174i
$708$	14.2979	+	24.7647i	0.537348	+	0.930714i
$709$	−51.3442			−1.92827			−0.964136	−	0.265407i	$-0.914494\pi$
$709$	−51.3442			−1.92827			−0.964136	+	0.265407i	$0.914494\pi$
$710$	3.24974	−	5.62872i	0.121961	−	0.211242i
$711$	−13.6830			−0.513152
$712$	−3.05044			−0.114320
$713$		0			0
$714$	34.6656			1.29733
$715$	20.9775			0.784515
$716$	13.9157	−	24.1027i	0.520053	−	0.900759i
$717$	14.5511			0.543421
$718$	7.33679	+	12.7077i	0.273807	+	0.474247i
$719$	−20.0999	+	34.8141i	−0.749601	+	1.29835i	0.198413	+	0.980119i	$0.436421\pi$
$719$	−20.0999	+	34.8141i	−0.749601	+	1.29835i	−0.948014	+	0.318229i	$0.896912\pi$
$720$	6.15819	−	10.6663i	0.229502	−	0.397509i
$721$	−14.3870			−0.535800
$722$	19.2869	+	33.4058i	0.717783	+	1.24324i
$723$	−12.3070	−	21.3163i	−0.457701	−	0.792762i
$724$	11.0635	+	19.1625i	0.411170	+	0.712167i
$725$	−0.353093	+	0.611574i	−0.0131135	+	0.0227133i
$726$	−16.2337	−	28.1176i	−0.602489	−	1.04354i
$727$	10.7419	−	18.6056i	0.398396	−	0.690042i	−0.595132	−	0.803628i	$-0.702900\pi$
$727$	10.7419	−	18.6056i	0.398396	−	0.690042i	0.993528	+	0.113586i	$0.0362337\pi$
$728$	−4.66732			−0.172983
$729$	1.80740			0.0669407
$730$	−34.4600	+	59.6864i	−1.27542	+	2.20909i
$731$	−0.286965	−	0.497038i	−0.0106138	−	0.0183836i
$732$	5.46451	−	9.46481i	0.201974	−	0.349830i
$733$	−11.2357	−	19.4607i	−0.414999	−	0.718799i	0.580430	−	0.814310i	$-0.302885\pi$
$733$	−11.2357	−	19.4607i	−0.414999	−	0.718799i	−0.995428	+	0.0955115i	$0.969551\pi$
$734$	−16.6989	−	28.9233i	−0.616368	−	1.06758i
$735$	−16.3307	−	28.2857i	−0.602368	−	1.04333i
$736$	−27.1991			−1.00257
$737$	29.1392	−	50.4705i	1.07335	−	1.85910i
$738$	6.98953	−	12.1062i	0.257288	−	0.445636i
$739$	26.2750	+	45.5097i	0.966542	+	1.67410i	0.705413	+	0.708797i	$0.250762\pi$
$739$	26.2750	+	45.5097i	0.966542	+	1.67410i	0.261129	+	0.965304i	$0.415905\pi$
$740$	−1.47816			−0.0543383
$741$	1.38429	−	2.39766i	0.0508531	−	0.0880802i
$742$	72.4000			2.65789
$743$	17.4032			0.638460			0.319230	−	0.947677i	$-0.396576\pi$
$743$	17.4032			0.638460			0.319230	+	0.947677i	$0.396576\pi$
$744$		0			0
$745$	28.9145			1.05934
$746$	−20.3461			−0.744922
$747$	−4.08874	+	7.08190i	−0.149599	+	0.259113i
$748$	−20.8946			−0.763981
$749$	20.4224	+	35.3727i	0.746219	+	1.29249i
$750$	23.3530	−	40.4487i	0.852732	−	1.47698i
$751$	11.2220	−	19.4370i	0.409496	−	0.709268i	−0.585337	−	0.810790i	$-0.699038\pi$
$751$	11.2220	−	19.4370i	0.409496	−	0.709268i	0.994833	+	0.101522i	$0.0323712\pi$
$752$	−17.8931			−0.652494
$753$	−7.80280	−	13.5148i	−0.284350	−	0.492508i
$754$	−2.97861	−	5.15911i	−0.108475	−	0.187884i
$755$	−23.3347	−	40.4168i	−0.849236	−	1.47092i
$756$	−12.8293	+	22.2210i	−0.466598	+	0.808172i
$757$	−7.39642	−	12.8110i	−0.268827	−	0.465623i	0.699732	−	0.714405i	$-0.253303\pi$
$757$	−7.39642	−	12.8110i	−0.268827	−	0.465623i	−0.968559	+	0.248783i	$0.919969\pi$
$758$	14.3138	−	24.7923i	0.519902	−	0.900496i
$759$	30.7147			1.11487
$760$	−0.885901			−0.0321350
$761$	−9.95063	+	17.2350i	−0.360710	+	0.624768i	−0.988078	−	0.153955i	$-0.950799\pi$
$761$	−9.95063	+	17.2350i	−0.360710	+	0.624768i	0.627368	+	0.778723i	$0.284132\pi$
$762$	−31.4710	−	54.5095i	−1.14008	−	1.97467i
$763$	33.2424	−	57.5776i	1.20346	−	2.08445i
$764$	−12.0022	−	20.7884i	−0.434224	−	0.752098i
$765$	3.93979	+	6.82391i	0.142443	+	0.246719i
$766$	10.6777	+	18.4943i	0.385800	+	0.668225i
$767$	−12.1630			−0.439181
$768$	−11.0436	+	19.1281i	−0.398502	+	0.690226i
$769$	−2.09853	+	3.63477i	−0.0756751	+	0.131073i	−0.901380	−	0.433030i	$-0.857445\pi$
$769$	−2.09853	+	3.63477i	−0.0756751	+	0.131073i	0.825705	+	0.564103i	$0.190778\pi$
$770$	38.2630	+	66.2734i	1.37890	+	2.38833i
$771$	−52.7482			−1.89968
$772$	2.05360	−	3.55693i	0.0739105	−	0.128017i
$773$	−11.8786			−0.427245			−0.213622	−	0.976916i	$-0.568526\pi$
$773$	−11.8786			−0.427245			−0.213622	+	0.976916i	$0.568526\pi$
$774$	−0.881281			−0.0316770
$775$		0			0
$776$	4.08584			0.146673
$777$	2.15774			0.0774086
$778$	−26.2801	+	45.5185i	−0.942187	+	1.63192i
$779$	2.65237			0.0950311
$780$	−12.0238	−	20.8258i	−0.430519	−	0.745682i
$781$	2.85931	−	4.95246i	0.102314	−	0.177213i
$782$	7.39473	−	12.8081i	0.264435	−	0.458015i
$783$	−4.19336			−0.149858
$784$	10.8145	+	18.7312i	0.386231	+	0.668971i
$785$	6.81436	+	11.8028i	0.243215	+	0.421261i
$786$	−15.9336	−	27.5978i	−0.568333	−	0.984382i
$787$	0.992015	−	1.71822i	0.0353615	−	0.0612480i	−0.847803	−	0.530311i	$-0.822075\pi$
$787$	0.992015	−	1.71822i	0.0353615	−	0.0612480i	0.883165	+	0.469063i	$0.155408\pi$
$788$	7.33631	+	12.7069i	0.261345	+	0.452663i
$789$	−28.1191	+	48.7037i	−1.00107	+	1.73390i
$790$	−42.2131			−1.50187
$791$	−64.4469			−2.29147
$792$	−2.05405	+	3.55771i	−0.0729874	+	0.126418i
$793$	2.32429	+	4.02579i	0.0825380	+	0.142960i
$794$	−17.3632	+	30.0739i	−0.616195	+	1.06728i
$795$	23.8815	+	41.3640i	0.846991	+	1.46703i
$796$	1.06330	+	1.84170i	0.0376878	+	0.0652772i
$797$	−25.1932	−	43.6358i	−0.892388	−	1.54566i	−0.837005	−	0.547196i	$-0.815695\pi$
$797$	−25.1932	−	43.6358i	−0.892388	−	1.54566i	−0.0553833	−	0.998465i	$-0.517638\pi$
$798$	10.0998			0.357528
$799$	5.72368	−	9.91370i	0.202489	−	0.350721i
$800$	2.07889	−	3.60074i	0.0734998	−	0.127305i
$801$	3.95241	+	6.84577i	0.139652	+	0.241884i
$802$	57.2394			2.02119
$803$	−30.3198	+	52.5155i	−1.06996	+	1.85323i
$804$	−66.8071			−2.35611
$805$	−28.9356			−1.01984
$806$		0			0
$807$	44.6701			1.57246
$808$	−10.9921			−0.386701
$809$	−7.78621	+	13.4861i	−0.273748	+	0.474146i	−0.969819	−	0.243828i	$-0.921597\pi$
$809$	−7.78621	+	13.4861i	−0.273748	+	0.474146i	0.696070	+	0.717974i	$0.254930\pi$
$810$	−54.7042			−1.92211
$811$	−10.3694	−	17.9604i	−0.364119	−	0.630673i	0.624515	−	0.781013i	$-0.285297\pi$
$811$	−10.3694	−	17.9604i	−0.364119	−	0.630673i	−0.988634	+	0.150340i	$0.951963\pi$
$812$	5.80460	−	10.0539i	0.203702	−	0.352822i
$813$	−22.4752	+	38.9282i	−0.788240	+	1.36527i
$814$	−2.43461			−0.0853332
$815$	−20.8768	−	36.1597i	−0.731284	−	1.26662i
$816$	−7.57219	−	13.1154i	−0.265080	−	0.459131i
$817$	−0.0836067	−	0.144811i	−0.00292503	−	0.00506630i
$818$	−23.4260	+	40.5751i	−0.819072	+	1.41867i
$819$	6.04738	+	10.4744i	0.211313	+	0.366004i
$820$	11.5191	−	19.9516i	0.402264	−	0.696742i
$821$	−19.5948			−0.683861			−0.341931	−	0.939725i	$-0.611081\pi$
$821$	−19.5948			−0.683861			−0.341931	+	0.939725i	$0.611081\pi$
$822$	−33.5923			−1.17167
$823$	1.05031	−	1.81919i	0.0366115	−	0.0634130i	−0.847139	−	0.531371i	$-0.821677\pi$
$823$	1.05031	−	1.81919i	0.0366115	−	0.0634130i	0.883751	+	0.467958i	$0.155010\pi$
$824$	−1.19135	−	2.06347i	−0.0415025	−	0.0718845i
$825$	−2.34759	+	4.06615i	−0.0817326	+	0.141565i
$826$	−22.1853	−	38.4261i	−0.771927	−	1.33702i
$827$	−1.75257	−	3.03554i	−0.0609429	−	0.105556i	0.833944	−	0.551849i	$-0.186077\pi$
$827$	−1.75257	−	3.03554i	−0.0609429	−	0.105556i	−0.894887	+	0.446293i	$0.852744\pi$
$828$	−6.06571	−	10.5061i	−0.210798	−	0.365113i
$829$	2.08859			0.0725399			0.0362699	−	0.999342i	$-0.488452\pi$
$829$	2.08859			0.0725399			0.0362699	+	0.999342i	$0.488452\pi$
$830$	−12.6141	+	21.8482i	−0.437841	+	0.758363i
$831$	−5.09098	+	8.81784i	−0.176604	+	0.305888i
$832$	10.5943	+	18.3498i	0.367290	+	0.636166i
$833$	−13.8374			−0.479437
$834$	−44.5485	+	77.1603i	−1.54259	+	2.67184i
$835$	−5.12321			−0.177296
$836$	−6.08759			−0.210544
$837$		0			0
$838$	−12.8284			−0.443151
$839$	−10.7734			−0.371938			−0.185969	−	0.982556i	$-0.559542\pi$
$839$	−10.7734			−0.371938			−0.185969	+	0.982556i	$0.559542\pi$
$840$	5.61624	−	9.72762i	0.193779	−	0.335635i
$841$	−27.1027			−0.934577
$842$	−6.79587	−	11.7708i	−0.234201	−	0.405648i
$843$	7.11863	−	12.3298i	0.245178	−	0.424662i
$844$	7.08914	−	12.2788i	0.244018	−	0.422652i
$845$	−20.2944			−0.698149
$846$	−8.78882	−	15.2227i	−0.302166	−	0.523366i
$847$	13.4560	+	23.3064i	0.462353	+	0.800818i
$848$	−15.8147	−	27.3919i	−0.543079	−	0.940641i
$849$	7.75128	−	13.4256i	0.266023	−	0.460766i
$850$	1.13039	+	1.95790i	0.0387721	+	0.0671553i
$851$	0.460281	−	0.797230i	0.0157782	−	0.0273287i
$852$	−6.55551			−0.224588
$853$	32.6504			1.11793			0.558964	−	0.829192i	$-0.311199\pi$
$853$	32.6504			1.11793			0.558964	+	0.829192i	$0.311199\pi$
$854$	−8.47901	+	14.6861i	−0.290146	+	0.502547i
$855$	1.14785	+	1.98813i	0.0392556	+	0.0679927i
$856$	−3.38224	+	5.85822i	−0.115603	+	0.200230i
$857$	21.8669	+	37.8746i	0.746959	+	1.29377i	0.949274	+	0.314450i	$0.101820\pi$
$857$	21.8669	+	37.8746i	0.746959	+	1.29377i	−0.202315	+	0.979321i	$0.564846\pi$
$858$	−19.8038	−	34.3012i	−0.676090	−	1.17102i
$859$	−12.1832	−	21.1018i	−0.415684	−	0.719985i	0.579816	−	0.814747i	$-0.303124\pi$
$859$	−12.1832	−	21.1018i	−0.415684	−	0.719985i	−0.995500	+	0.0947619i	$0.969791\pi$
$860$	−1.45239			−0.0495262
$861$	−16.8149	+	29.1243i	−0.573052	+	0.992555i
$862$	−24.3140	+	42.1130i	−0.828137	+	1.43438i
$863$	−21.7570	−	37.6842i	−0.740616	−	1.28279i	−0.952215	−	0.305429i	$-0.901200\pi$
$863$	−21.7570	−	37.6842i	−0.740616	−	1.28279i	0.211599	−	0.977357i	$-0.432133\pi$
$864$	24.6891			0.839939
$865$	6.46606	−	11.1995i	0.219853	−	0.380796i
$866$	−50.3794			−1.71196
$867$	−26.6808			−0.906129
$868$		0			0
$869$	−37.1415			−1.25994
$870$	14.3368			0.486063
$871$	14.2080	−	24.6089i	0.481419	−	0.833842i
$872$	11.0108			0.372874
$873$	−5.29396	−	9.16941i	−0.179173	−	0.310338i
$874$	2.15444	−	3.73160i	0.0728751	−	0.126223i
$875$	−19.3571	+	33.5275i	−0.654391	+	1.13344i
$876$	69.5140			2.34866
$877$	19.1219	+	33.1201i	0.645701	+	1.11839i	0.984139	+	0.177398i	$0.0567681\pi$
$877$	19.1219	+	33.1201i	0.645701	+	1.11839i	−0.338438	+	0.940989i	$0.609899\pi$
$878$	−15.0295	−	26.0318i	−0.507220	−	0.878530i
$879$	−14.4532	−	25.0337i	−0.487495	−	0.844366i
$880$	16.7160	−	28.9529i	0.563495	−	0.976002i
$881$	20.3707	+	35.2831i	0.686307	+	1.18872i	0.973024	+	0.230703i	$0.0741025\pi$
$881$	20.3707	+	35.2831i	0.686307	+	1.18872i	−0.286718	+	0.958015i	$0.592564\pi$
$882$	−10.6238	+	18.4009i	−0.357722	+	0.619592i
$883$	−33.1160			−1.11444			−0.557222	−	0.830364i	$-0.688133\pi$
$883$	−33.1160			−1.11444			−0.557222	+	0.830364i	$0.688133\pi$
$884$	−10.1880			−0.342659
$885$	14.6359	−	25.3501i	0.491981	−	0.852135i
$886$	17.1634	+	29.7278i	0.576615	+	0.998726i
$887$	−6.23376	+	10.7972i	−0.209309	+	0.362534i	−0.951497	−	0.307658i	$-0.900455\pi$
$887$	−6.23376	+	10.7972i	−0.209309	+	0.362534i	0.742188	+	0.670192i	$0.233788\pi$
$888$	0.178676	+	0.309477i	0.00599599	+	0.0103854i
$889$	26.0861	+	45.1824i	0.874899	+	1.51537i
$890$	12.1935	+	21.1198i	0.408727	+	0.707936i
$891$	−48.1318			−1.61248
$892$	18.2323	−	31.5793i	0.610463	−	1.05735i
$893$	1.66758	−	2.88834i	0.0558035	−	0.0966545i
$894$	−27.2966	−	47.2791i	−0.912936	−	1.58125i
$895$	−28.4893			−0.952292
$896$	−8.84823	+	15.3256i	−0.295598	+	0.511992i
$897$	14.9762			0.500040
$898$	−14.1263			−0.471401
$899$		0			0
$900$	1.85446			0.0618154
$901$	20.2354			0.674137
$902$	18.9726	−	32.8615i	0.631717	−	1.09417i
$903$	2.12013			0.0705534
$904$	−5.33666	−	9.24337i	−0.177495	−	0.307430i
$905$	11.3250	−	19.6155i	0.376456	−	0.652041i
$906$	−44.0581	+	76.3108i	−1.46373	+	2.53526i
$907$	16.9013			0.561197			0.280599	−	0.959825i	$-0.409467\pi$
$907$	16.9013			0.561197			0.280599	+	0.959825i	$0.409467\pi$
$908$	5.32704	+	9.22671i	0.176784	+	0.306199i
$909$	14.2423	+	24.6684i	0.472388	+	0.818200i
$910$	18.6567	+	32.3143i	0.618462	+	1.07121i
$911$	−27.2348	+	47.1721i	−0.902330	+	1.56288i	−0.0778682	+	0.996964i	$0.524811\pi$
$911$	−27.2348	+	47.1721i	−0.902330	+	1.56288i	−0.824462	+	0.565918i	$0.808522\pi$
$912$	−2.20614	−	3.82115i	−0.0730527	−	0.126531i
$913$	−11.0986	+	19.2233i	−0.367310	+	0.636199i
$914$	−44.4009			−1.46865
$915$	−11.1874			−0.369844
$916$	−22.2698	+	38.5725i	−0.735816	+	1.27447i
$917$	13.2072	+	22.8756i	0.436142	+	0.755419i
$918$	−6.71231	+	11.6261i	−0.221539	+	0.383717i
$919$	4.38366	+	7.59272i	0.144604	+	0.250461i	0.929225	−	0.369514i	$-0.120476\pi$
$919$	4.38366	+	7.59272i	0.144604	+	0.250461i	−0.784621	+	0.619975i	$0.787143\pi$
$920$	−2.39607	−	4.15012i	−0.0789961	−	0.136825i
$921$	24.3097	+	42.1057i	0.801032	+	1.38743i
$922$	17.9746			0.591963
$923$	1.39417	−	2.41477i	0.0458897	−	0.0794832i
$924$	38.5928	−	66.8447i	1.26961	−	2.19903i
$925$	0.0703606	+	0.121868i	0.00231344	+	0.00400700i
$926$	−7.56298			−0.248535
$927$	−3.08722	+	5.34722i	−0.101398	+	0.175626i
$928$	−11.1705			−0.366690
$929$	44.2868			1.45300			0.726501	−	0.687165i	$-0.241145\pi$
$929$	44.2868			1.45300			0.726501	+	0.687165i	$0.241145\pi$
$930$		0			0
$931$	−4.03150			−0.132127
$932$	−32.6816			−1.07052
$933$	−10.1549	+	17.5889i	−0.332458	+	0.575834i
$934$	−6.38443			−0.208905
$935$	10.6943	+	18.5230i	0.349740	+	0.605767i
$936$	−1.00153	+	1.73471i	−0.0327361	+	0.0567006i
$937$	25.7583	−	44.6147i	0.841486	−	1.45750i	−0.0471516	−	0.998888i	$-0.515014\pi$
$937$	25.7583	−	44.6147i	0.841486	−	1.45750i	0.888638	−	0.458609i	$-0.151652\pi$
$938$	103.661			3.38466
$939$	30.0553	+	52.0573i	0.980818	+	1.69883i
$940$	−14.4844	−	25.0877i	−0.472429	−	0.818271i
$941$	19.5985	+	33.9456i	0.638893	+	1.10660i	0.985676	+	0.168650i	$0.0539407\pi$
$941$	19.5985	+	33.9456i	0.638893	+	1.10660i	−0.346783	+	0.937945i	$0.612726\pi$
$942$	12.8662	−	22.2848i	0.419202	−	0.726080i
$943$	7.17380	+	12.4254i	0.233611	+	0.404626i
$944$	−9.69211	+	16.7872i	−0.315451	+	0.546378i
$945$	26.2652			0.854408
$946$	−2.39217			−0.0777763
$947$	28.4582	−	49.2910i	0.924766	−	1.60174i	0.132829	−	0.991139i	$-0.457594\pi$
$947$	28.4582	−	49.2910i	0.924766	−	1.60174i	0.791937	−	0.610603i	$-0.209073\pi$
$948$	21.2885	+	36.8727i	0.691418	+	1.19757i
$949$	−14.7837	+	25.6060i	−0.479898	+	0.831207i
$950$	0.329337	+	0.570429i	0.0106851	+	0.0185072i
$951$	16.9192	+	29.3049i	0.548642	+	0.950276i
$952$	−2.37938	−	4.12121i	−0.0771162	−	0.133569i
$953$	15.2738			0.494768			0.247384	−	0.968918i	$-0.420429\pi$
$953$	15.2738			0.494768			0.247384	+	0.968918i	$0.420429\pi$
$954$	15.5359	−	26.9090i	0.502993	−	0.871210i
$955$	−12.2859	+	21.2798i	−0.397563	+	0.688599i
$956$	−7.80028	−	13.5105i	−0.252279	−	0.436960i
$957$	12.6143			0.407764
$958$	18.0381	−	31.2428i	0.582783	−	1.00941i
$959$	27.8444			0.899142
$960$	−50.9928			−1.64579
$961$		0			0
$962$	−1.18709			−0.0382735
$963$	17.5293			0.564874
$964$	−13.1946	+	22.8537i	−0.424969	+	0.736067i
$965$	−4.20429			−0.135341
$966$	27.3165	+	47.3136i	0.878895	+	1.52229i
$967$	5.64979	−	9.78573i	0.181685	−	0.314688i	−0.760769	−	0.649022i	$-0.775178\pi$
$967$	5.64979	−	9.78573i	0.181685	−	0.314688i	0.942455	+	0.334334i	$0.108511\pi$
$968$	−2.22850	+	3.85988i	−0.0716267	+	0.124061i
$969$	2.82282			0.0906820
$970$	−16.3323	−	28.2884i	−0.524398	−	0.908285i
$971$	7.93411	+	13.7423i	0.254618	+	0.441011i	0.964792	−	0.263016i	$-0.0847171\pi$
$971$	7.93411	+	13.7423i	0.254618	+	0.441011i	−0.710174	+	0.704026i	$0.751384\pi$
$972$	17.1136	+	29.6417i	0.548920	+	0.950758i
$973$	36.9259	−	63.9575i	1.18379	−	2.05038i
$974$	29.8112	+	51.6345i	0.955213	+	1.65448i
$975$	−1.14466	+	1.98261i	−0.0366585	+	0.0634945i
$976$	7.40846			0.237139
$977$	−16.5600			−0.529800			−0.264900	−	0.964276i	$-0.585339\pi$
$977$	−16.5600			−0.529800			−0.264900	+	0.964276i	$0.585339\pi$
$978$	−39.4174	+	68.2730i	−1.26043	+	2.18313i
$979$	10.7285	+	18.5824i	0.342885	+	0.593895i
$980$	−17.5085	+	30.3257i	−0.559290	+	0.968718i
$981$	−14.2666	−	24.7105i	−0.455497	−	0.788944i
$982$	−10.1800	−	17.6323i	−0.324857	−	0.562669i
$983$	10.8249	+	18.7493i	0.345261	+	0.598010i	0.985401	−	0.170249i	$-0.0544571\pi$
$983$	10.8249	+	18.7493i	0.345261	+	0.598010i	−0.640140	+	0.768258i	$0.721124\pi$
$984$	−5.56959			−0.177552
$985$	7.50975	−	13.0073i	0.239280	−	0.414446i
$986$	3.03697	−	5.26019i	0.0967169	−	0.167519i
$987$	21.1436	+	36.6217i	0.673007	+	1.16568i
$988$	−2.96825			−0.0944326
$989$	0.452257	−	0.783333i	0.0143809	−	0.0249085i
$990$	32.8425			1.04380
$991$	−32.3028			−1.02613			−0.513066	−	0.858349i	$-0.671490\pi$
$991$	−32.3028			−1.02613			−0.513066	+	0.858349i	$0.671490\pi$
$992$		0			0
$993$	−27.6925			−0.878796
$994$	10.1719			0.322632
$995$	1.08844	−	1.88523i	0.0345059	−	0.0597659i
$996$	25.4456			0.806276
$997$	5.74360	+	9.94821i	0.181902	+	0.315063i	0.942528	−	0.334127i	$-0.108441\pi$
$997$	5.74360	+	9.94821i	0.181902	+	0.315063i	−0.760626	+	0.649190i	$0.775108\pi$
$998$	−11.2392	+	19.4669i	−0.355771	+	0.616213i
$999$	−0.417804	+	0.723658i	−0.0132187	+	0.0228955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.i.439.7		16
31.2	even	5		961.2.g.l.547.2		16
31.3	odd	30		31.2.g.a.14.2	✓	16
31.4	even	5		961.2.g.m.235.1		16
31.5	even	3		961.2.a.j.1.7		8
31.6	odd	6		961.2.c.j.521.7		16
31.7	even	15		961.2.g.n.338.1		16
31.8	even	5		961.2.g.n.816.1		16
31.9	even	15		961.2.d.q.374.1		16
31.10	even	15		961.2.d.n.531.4		16
31.11	odd	30		961.2.d.p.388.1		16
31.12	odd	30		961.2.g.k.844.2		16
31.13	odd	30		961.2.d.o.628.4		16
31.14	even	15		961.2.g.m.732.1		16
31.15	odd	10		961.2.g.k.846.2		16
31.16	even	5		961.2.g.j.846.2		16
31.17	odd	30		961.2.g.s.732.1		16
31.18	even	15		961.2.d.n.628.4		16
31.19	even	15		961.2.g.j.844.2		16
31.20	even	15		961.2.d.q.388.1		16
31.21	odd	30		961.2.d.o.531.4		16
31.22	odd	30		961.2.d.p.374.1		16
31.23	odd	10		961.2.g.t.816.1		16
31.24	odd	30		961.2.g.t.338.1		16
31.25	even	3	inner	961.2.c.i.521.7		16
31.26	odd	6		961.2.a.i.1.7		8
31.27	odd	10		961.2.g.s.235.1		16
31.28	even	15		961.2.g.l.448.2		16
31.29	odd	10		31.2.g.a.20.2	yes	16
31.30	odd	2		961.2.c.j.439.7		16
93.5	odd	6		8649.2.a.be.1.2		8
93.26	even	6		8649.2.a.bf.1.2		8
93.29	even	10		279.2.y.c.82.1		16
93.65	even	30		279.2.y.c.262.1		16
124.3	even	30		496.2.bg.c.417.2		16
124.91	even	10		496.2.bg.c.113.2		16
155.3	even	60		775.2.ck.a.324.2		32
155.29	odd	10		775.2.bl.a.51.1		16
155.34	odd	30		775.2.bl.a.76.1		16
155.122	even	20		775.2.ck.a.299.2		32
155.127	even	60		775.2.ck.a.324.3		32
155.153	even	20		775.2.ck.a.299.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.2	✓	16	31.3	odd	30
31.2.g.a.20.2	yes	16	31.29	odd	10
279.2.y.c.82.1		16	93.29	even	10
279.2.y.c.262.1		16	93.65	even	30
496.2.bg.c.113.2		16	124.91	even	10
496.2.bg.c.417.2		16	124.3	even	30
775.2.bl.a.51.1		16	155.29	odd	10
775.2.bl.a.76.1		16	155.34	odd	30
775.2.ck.a.299.2		32	155.122	even	20
775.2.ck.a.299.3		32	155.153	even	20
775.2.ck.a.324.2		32	155.3	even	60
775.2.ck.a.324.3		32	155.127	even	60
961.2.a.i.1.7		8	31.26	odd	6
961.2.a.j.1.7		8	31.5	even	3
961.2.c.i.439.7		16	1.1	even	1	trivial
961.2.c.i.521.7		16	31.25	even	3	inner
961.2.c.j.439.7		16	31.30	odd	2
961.2.c.j.521.7		16	31.6	odd	6
961.2.d.n.531.4		16	31.10	even	15
961.2.d.n.628.4		16	31.18	even	15
961.2.d.o.531.4		16	31.21	odd	30
961.2.d.o.628.4		16	31.13	odd	30
961.2.d.p.374.1		16	31.22	odd	30
961.2.d.p.388.1		16	31.11	odd	30
961.2.d.q.374.1		16	31.9	even	15
961.2.d.q.388.1		16	31.20	even	15
961.2.g.j.844.2		16	31.19	even	15
961.2.g.j.846.2		16	31.16	even	5
961.2.g.k.844.2		16	31.12	odd	30
961.2.g.k.846.2		16	31.15	odd	10
961.2.g.l.448.2		16	31.28	even	15
961.2.g.l.547.2		16	31.2	even	5
961.2.g.m.235.1		16	31.4	even	5
961.2.g.m.732.1		16	31.14	even	15
961.2.g.n.338.1		16	31.7	even	15
961.2.g.n.816.1		16	31.8	even	5
961.2.g.s.235.1		16	31.27	odd	10
961.2.g.s.732.1		16	31.17	odd	30
961.2.g.t.338.1		16	31.24	odd	30
961.2.g.t.816.1		16	31.23	odd	10
8649.2.a.be.1.2		8	93.5	odd	6
8649.2.a.bf.1.2		8	93.26	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.07212 q^{2} +(-1.06970 + 1.85277i) q^{3} +2.29369 q^{4} +(-1.17396 - 2.03335i) q^{5} +(-2.21654 + 3.83916i) q^{6} +(1.83727 - 3.18225i) q^{7} +0.608557 q^{8} +(-0.788498 - 1.36572i) q^{9} +(-2.43258 - 4.21335i) q^{10} +(-2.14032 - 3.70714i) q^{11} +(-2.45355 + 4.24967i) q^{12} +(-1.04360 - 1.80757i) q^{13} +(3.80705 - 6.59400i) q^{14} +5.02310 q^{15} -3.32637 q^{16} +(1.06405 - 1.84298i) q^{17} +(-1.63386 - 2.82993i) q^{18} +(0.310008 - 0.536949i) q^{19} +(-2.69269 - 4.66387i) q^{20} +(3.93064 + 6.80807i) q^{21} +(-4.43500 - 7.68165i) q^{22} +3.35388 q^{23} +(-0.650970 + 1.12751i) q^{24} +(-0.256344 + 0.444001i) q^{25} +(-2.16247 - 3.74550i) q^{26} -3.04436 q^{27} +(4.21412 - 7.29908i) q^{28} +1.37742 q^{29} +10.4085 q^{30} -8.10976 q^{32} +9.15797 q^{33} +(2.20483 - 3.81888i) q^{34} -8.62750 q^{35} +(-1.80857 - 3.13253i) q^{36} +(0.137239 - 0.237704i) q^{37} +(0.642374 - 1.11262i) q^{38} +4.46534 q^{39} +(-0.714418 - 1.23741i) q^{40} +(2.13896 + 3.70478i) q^{41} +(8.14477 + 14.1071i) q^{42} +(0.134846 - 0.233560i) q^{43} +(-4.90923 - 8.50303i) q^{44} +(-1.85132 + 3.20659i) q^{45} +6.94964 q^{46} +5.37916 q^{47} +(3.55821 - 6.16299i) q^{48} +(-3.25113 - 5.63112i) q^{49} +(-0.531176 + 0.920024i) q^{50} +(2.27641 + 3.94286i) q^{51} +(-2.39369 - 4.14600i) q^{52} +(4.75434 + 8.23476i) q^{53} -6.30829 q^{54} +(-5.02528 + 8.70405i) q^{55} +(1.11808 - 1.93658i) q^{56} +(0.663228 + 1.14874i) q^{57} +2.85417 q^{58} +(2.91372 - 5.04671i) q^{59} +11.5214 q^{60} -2.22719 q^{61} -5.79474 q^{63} -10.1517 q^{64} +(-2.45028 + 4.24401i) q^{65} +18.9764 q^{66} +(6.80719 + 11.7904i) q^{67} +(2.44059 - 4.22722i) q^{68} +(-3.58763 + 6.21395i) q^{69} -17.8772 q^{70} +(0.667962 + 1.15694i) q^{71} +(-0.479846 - 0.831117i) q^{72} +(-7.08301 - 12.2681i) q^{73} +(0.284375 - 0.492552i) q^{74} +(-0.548420 - 0.949892i) q^{75} +(0.711061 - 1.23159i) q^{76} -15.7294 q^{77} +9.25272 q^{78} +(4.33831 - 7.51417i) q^{79} +(3.90501 + 6.76368i) q^{80} +(5.62204 - 9.73765i) q^{81} +(4.43218 + 7.67676i) q^{82} +(-2.59274 - 4.49076i) q^{83} +(9.01566 + 15.6156i) q^{84} -4.99657 q^{85} +(0.279418 - 0.483966i) q^{86} +(-1.47342 + 2.55203i) q^{87} +(-1.30251 - 2.25601i) q^{88} -5.01258 q^{89} +(-3.83617 + 6.64444i) q^{90} -7.66950 q^{91} +7.69274 q^{92} +11.1463 q^{94} -1.45574 q^{95} +(8.67498 - 15.0255i) q^{96} +6.71398 q^{97} +(-6.73673 - 11.6684i) q^{98} +(-3.37528 + 5.84615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 16 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} - 18 q^{11} - 8 q^{13} + 9 q^{14} + 36 q^{15} + 8 q^{16} - 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 16 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 - 18 * q^11 - 8 * q^13 + 9 * q^14 + 36 * q^15 + 8 * q^16 - 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 + q^21 - 4 * q^22 + 44 * q^23 - 30 * q^24 - 13 * q^25 - 9 * q^26 + 36 * q^27 + 5 * q^28 + 24 * q^29 + 22 * q^30 - 42 * q^32 + 12 * q^33 + 7 * q^34 - 24 * q^35 + q^36 + 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 + 6 * q^42 + 2 * q^43 - 4 * q^44 + 36 * q^46 - 36 * q^47 + q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 + q^52 - 6 * q^53 - 14 * q^54 - 28 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 4 * q^59 - 80 * q^60 + 60 * q^61 - 46 * q^63 + 18 * q^64 - 3 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 23 * q^75 + 33 * q^76 - 48 * q^77 - 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 - 39 * q^83 - 8 * q^84 - 52 * q^85 + 16 * q^86 + 15 * q^87 + 17 * q^88 + 54 * q^89 - 8 * q^90 + 32 * q^91 + 64 * q^92 + 44 * q^94 - 12 * q^95 + 12 * q^96 + 68 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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