LMFDB - Embedded newform 961.2.d.p.531.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == 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:	$4$ over $\Q(\zeta_{5})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.3
Root			$1.03739i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.p.628.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.391401 + 1.20461i) q^{2} +(0.458679 - 1.41167i) q^{3} +(0.320145 - 0.232599i) q^{4} -3.80032 q^{5} +1.88004 q^{6} +(-1.77093 + 1.28666i) q^{7} +(2.45490 + 1.78359i) q^{8} +(0.644632 + 0.468353i) q^{9} +(-1.48745 - 4.57790i) q^{10} +(0.769048 - 0.558746i) q^{11} +(-0.181509 - 0.558626i) q^{12} +(0.0519589 - 0.159913i) q^{13} +(-2.24306 - 1.62968i) q^{14} +(-1.74313 + 5.36479i) q^{15} +(-0.943109 + 2.90259i) q^{16} +(5.32063 + 3.86566i) q^{17} +(-0.311872 + 0.959844i) q^{18} +(-0.356248 - 1.09642i) q^{19} +(-1.21665 + 0.883950i) q^{20} +(1.00404 + 3.09013i) q^{21} +(0.974077 + 0.707709i) q^{22} +(3.74454 + 2.72056i) q^{23} +(3.64384 - 2.64741i) q^{24} +9.44244 q^{25} +0.212969 q^{26} +(4.55935 - 3.31256i) q^{27} +(-0.267679 + 0.823832i) q^{28} +(0.413068 + 1.27129i) q^{29} -7.14474 q^{30} +2.20322 q^{32} +(-0.436018 - 1.34192i) q^{33} +(-2.57411 + 7.92230i) q^{34} +(6.73010 - 4.88970i) q^{35} +0.315314 q^{36} -3.87165 q^{37} +(1.18132 - 0.858279i) q^{38} +(-0.201911 - 0.146697i) q^{39} +(-9.32941 - 6.77821i) q^{40} +(0.101420 + 0.312139i) q^{41} +(-3.32941 + 2.41896i) q^{42} +(2.97601 + 9.15922i) q^{43} +(0.116243 - 0.357759i) q^{44} +(-2.44981 - 1.77989i) q^{45} +(-1.81160 + 5.57554i) q^{46} +(1.74242 - 5.36260i) q^{47} +(3.66491 + 2.66271i) q^{48} +(-0.682410 + 2.10024i) q^{49} +(3.69578 + 11.3745i) q^{50} +(7.89748 - 5.73786i) q^{51} +(-0.0205612 - 0.0632808i) q^{52} +(5.93248 + 4.31020i) q^{53} +(5.77487 + 4.19569i) q^{54} +(-2.92263 + 2.12341i) q^{55} -6.64232 q^{56} -1.71118 q^{57} +(-1.36973 + 0.995171i) q^{58} +(-0.819859 + 2.52327i) q^{59} +(0.689791 + 2.12296i) q^{60} -1.74967 q^{61} -1.74421 q^{63} +(2.74856 + 8.45921i) q^{64} +(-0.197460 + 0.607720i) q^{65} +(1.44584 - 1.05046i) q^{66} +0.552007 q^{67} +2.60252 q^{68} +(5.55807 - 4.03817i) q^{69} +(8.52436 + 6.19331i) q^{70} +(-0.919843 - 0.668305i) q^{71} +(0.747159 + 2.29952i) q^{72} +(6.40952 - 4.65679i) q^{73} +(-1.51537 - 4.66383i) q^{74} +(4.33104 - 13.3296i) q^{75} +(-0.369076 - 0.268150i) q^{76} +(-0.643016 + 1.97900i) q^{77} +(0.0976845 - 0.300642i) q^{78} +(-3.67478 - 2.66989i) q^{79} +(3.58412 - 11.0308i) q^{80} +(-1.84627 - 5.68225i) q^{81} +(-0.336310 + 0.244343i) q^{82} +(0.100862 + 0.310421i) q^{83} +(1.04020 + 0.755748i) q^{84} +(-20.2201 - 14.6908i) q^{85} +(-9.86847 + 7.16986i) q^{86} +1.98411 q^{87} +2.88451 q^{88} +(11.9008 - 8.64641i) q^{89} +(1.18521 - 3.64772i) q^{90} +(0.113737 + 0.350048i) q^{91} +1.83159 q^{92} +7.14183 q^{94} +(1.35386 + 4.16674i) q^{95} +(1.01057 - 3.11022i) q^{96} +(-12.5553 + 9.12195i) q^{97} -2.79707 q^{98} +0.757443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} - 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} + 4 q^{11} - 5 q^{12} + 9 q^{13} - 18 q^{14} + 4 q^{15} - 2 q^{16} + 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 - 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 + 4 * q^11 - 5 * q^12 + 9 * q^13 - 18 * q^14 + 4 * q^15 - 2 * q^16 + 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 + 2 * q^21 - 8 * q^22 + 21 * q^23 + 5 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 - 56 * q^34 + 21 * q^35 - 2 * q^36 + 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 + 12 * q^42 - 16 * q^43 + 37 * q^44 - 5 * q^45 - 16 * q^46 + 4 * q^47 + 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 - 18 * q^52 + 3 * q^53 + 39 * q^54 + 29 * q^55 + 60 * q^56 + 34 * q^57 + 10 * q^58 - 3 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 9 * q^65 + 20 * q^66 - 26 * q^67 - 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 - 9 * q^73 + 64 * q^74 + 19 * q^75 + 9 * q^76 - 42 * q^77 + 15 * q^78 + 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 + 67 * q^83 + 39 * q^84 - 63 * q^85 - 23 * q^86 - 30 * q^87 + 34 * q^88 + 26 * q^89 - 24 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 4 * q^96 - 37 * q^97 + 20 * q^98 - 12 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.391401	+	1.20461i	0.276763	+	0.851788i	0.988748	+	0.149593i	$0.0477964\pi$
$2$	0.391401	+	1.20461i	0.276763	+	0.851788i	−0.711985	+	0.702195i	$0.752204\pi$
$3$	0.458679	−	1.41167i	0.264818	−	0.815027i	−0.726917	−	0.686725i	$-0.759048\pi$
$3$	0.458679	−	1.41167i	0.264818	−	0.815027i	0.991735	−	0.128301i	$-0.0409524\pi$
$4$	0.320145	−	0.232599i	0.160072	−	0.116299i
$5$	−3.80032			−1.69956			−0.849778	−	0.527141i	$-0.823264\pi$
$5$	−3.80032			−1.69956			−0.849778	+	0.527141i	$0.823264\pi$
$6$	1.88004			0.767521
$7$	−1.77093	+	1.28666i	−0.669349	+	0.486310i	−0.869807	−	0.493392i	$-0.835757\pi$
$7$	−1.77093	+	1.28666i	−0.669349	+	0.486310i	0.200459	+	0.979702i	$0.435757\pi$
$8$	2.45490	+	1.78359i	0.867938	+	0.630594i
$9$	0.644632	+	0.468353i	0.214877	+	0.156118i
$10$	−1.48745	−	4.57790i	−0.470373	−	1.44766i
$11$	0.769048	−	0.558746i	0.231877	−	0.168468i	−0.465780	−	0.884901i	$-0.654226\pi$
$11$	0.769048	−	0.558746i	0.231877	−	0.168468i	0.697657	+	0.716432i	$0.254226\pi$
$12$	−0.181509	−	0.558626i	−0.0523970	−	0.161261i
$13$	0.0519589	−	0.159913i	0.0144108	−	0.0443519i	−0.943593	−	0.331109i	$-0.892577\pi$
$13$	0.0519589	−	0.159913i	0.0144108	−	0.0443519i	0.958003	+	0.286757i	$0.0925772\pi$
$14$	−2.24306	−	1.62968i	−0.599484	−	0.435550i
$15$	−1.74313	+	5.36479i	−0.450073	+	1.38518i
$16$	−0.943109	+	2.90259i	−0.235777	+	0.725648i
$17$	5.32063	+	3.86566i	1.29044	+	0.937560i	0.999814	−	0.0192759i	$-0.00613610\pi$
$17$	5.32063	+	3.86566i	1.29044	+	0.937560i	0.290627	+	0.956836i	$0.406136\pi$
$18$	−0.311872	+	0.959844i	−0.0735090	+	0.226237i
$19$	−0.356248	−	1.09642i	−0.0817288	−	0.251535i	0.901840	−	0.432071i	$-0.142217\pi$
$19$	−0.356248	−	1.09642i	−0.0817288	−	0.251535i	−0.983568	+	0.180535i	$0.942217\pi$
$20$	−1.21665	+	0.883950i	−0.272052	+	0.197657i
$21$	1.00404	+	3.09013i	0.219100	+	0.674321i
$22$	0.974077	+	0.707709i	0.207674	+	0.150884i
$23$	3.74454	+	2.72056i	0.780790	+	0.567277i	0.905216	−	0.424952i	$-0.139709\pi$
$23$	3.74454	+	2.72056i	0.780790	+	0.567277i	−0.124426	+	0.992229i	$0.539709\pi$
$24$	3.64384	−	2.64741i	0.743797	−	0.540400i
$25$	9.44244			1.88849
$26$	0.212969			0.0417667
$27$	4.55935	−	3.31256i	0.877446	−	0.637502i
$28$	−0.267679	+	0.823832i	−0.0505866	+	0.155690i
$29$	0.413068	+	1.27129i	0.0767047	+	0.236073i	0.982056	−	0.188591i	$-0.0603921\pi$
$29$	0.413068	+	1.27129i	0.0767047	+	0.236073i	−0.905351	+	0.424664i	$0.860392\pi$
$30$	−7.14474			−1.30444
$31$		0			0
$31$		0			0
$32$	2.20322			0.389479
$33$	−0.436018	−	1.34192i	−0.0759010	−	0.233599i
$34$	−2.57411	+	7.92230i	−0.441457	+	1.35866i
$35$	6.73010	−	4.88970i	1.13759	−	0.826511i
$36$	0.315314			0.0525523
$37$	−3.87165			−0.636495			−0.318248	−	0.948008i	$-0.603094\pi$
$37$	−3.87165			−0.636495			−0.318248	+	0.948008i	$0.603094\pi$
$38$	1.18132	−	0.858279i	0.191635	−	0.139231i
$39$	−0.201911	−	0.146697i	−0.0323317	−	0.0234904i
$40$	−9.32941	−	6.77821i	−1.47511	−	1.07173i
$41$	0.101420	+	0.312139i	0.0158392	+	0.0487480i	0.958664	−	0.284542i	$-0.0918414\pi$
$41$	0.101420	+	0.312139i	0.0158392	+	0.0487480i	−0.942825	+	0.333289i	$0.891841\pi$
$42$	−3.32941	+	2.41896i	−0.513739	+	0.373253i
$43$	2.97601	+	9.15922i	0.453837	+	1.39677i	0.872495	+	0.488624i	$0.162501\pi$
$43$	2.97601	+	9.15922i	0.453837	+	1.39677i	−0.418657	+	0.908144i	$0.637499\pi$
$44$	0.116243	−	0.357759i	0.0175243	−	0.0539342i
$45$	−2.44981	−	1.77989i	−0.365196	−	0.265330i
$46$	−1.81160	+	5.57554i	−0.267106	+	0.822068i
$47$	1.74242	−	5.36260i	0.254157	−	0.782216i	−0.739837	−	0.672786i	$-0.765097\pi$
$47$	1.74242	−	5.36260i	0.254157	−	0.782216i	0.993994	−	0.109430i	$-0.0349026\pi$
$48$	3.66491	+	2.66271i	0.528984	+	0.384329i
$49$	−0.682410	+	2.10024i	−0.0974871	+	0.300035i
$50$	3.69578	+	11.3745i	0.522663	+	1.60859i
$51$	7.89748	−	5.73786i	1.10587	−	0.803461i
$52$	−0.0205612	−	0.0632808i	−0.00285132	−	0.00877547i
$53$	5.93248	+	4.31020i	0.814888	+	0.592051i	0.915244	−	0.402901i	$-0.131998\pi$
$53$	5.93248	+	4.31020i	0.814888	+	0.592051i	−0.100355	+	0.994952i	$0.531998\pi$
$54$	5.77487	+	4.19569i	0.785861	+	0.570961i
$55$	−2.92263	+	2.12341i	−0.394087	+	0.286321i
$56$	−6.64232			−0.887617
$57$	−1.71118			−0.226651
$58$	−1.36973	+	0.995171i	−0.179855	+	0.130672i
$59$	−0.819859	+	2.52327i	−0.106737	+	0.328501i	−0.990134	−	0.140123i	$-0.955250\pi$
$59$	−0.819859	+	2.52327i	−0.106737	+	0.328501i	0.883398	+	0.468624i	$0.155250\pi$
$60$	0.689791	+	2.12296i	0.0890516	+	0.274073i
$61$	−1.74967			−0.224023			−0.112011	−	0.993707i	$-0.535729\pi$
$61$	−1.74967			−0.224023			−0.112011	+	0.993707i	$0.535729\pi$
$62$		0			0
$63$	−1.74421			−0.219749
$64$	2.74856	+	8.45921i	0.343570	+	1.05740i
$65$	−0.197460	+	0.607720i	−0.0244919	+	0.0753784i
$66$	1.44584	−	1.05046i	0.177970	−	0.129303i
$67$	0.552007			0.0674383			0.0337192	−	0.999431i	$-0.489265\pi$
$67$	0.552007			0.0674383			0.0337192	+	0.999431i	$0.489265\pi$
$68$	2.60252			0.315602
$69$	5.55807	−	4.03817i	0.669113	−	0.486139i
$70$	8.52436	+	6.19331i	1.01886	+	0.740242i
$71$	−0.919843	−	0.668305i	−0.109165	−	0.0793132i	0.531863	−	0.846830i	$-0.321492\pi$
$71$	−0.919843	−	0.668305i	−0.109165	−	0.0793132i	−0.641029	+	0.767517i	$0.721492\pi$
$72$	0.747159	+	2.29952i	0.0880535	+	0.271001i
$73$	6.40952	−	4.65679i	0.750177	−	0.545036i	−0.145705	−	0.989328i	$-0.546545\pi$
$73$	6.40952	−	4.65679i	0.750177	−	0.545036i	0.895882	+	0.444293i	$0.146545\pi$
$74$	−1.51537	−	4.66383i	−0.176158	−	0.542159i
$75$	4.33104	−	13.3296i	0.500106	−	1.53917i
$76$	−0.369076	−	0.268150i	−0.0423359	−	0.0307589i
$77$	−0.643016	+	1.97900i	−0.0732785	+	0.225528i
$78$	0.0976845	−	0.300642i	0.0110606	−	0.0340410i
$79$	−3.67478	−	2.66989i	−0.413445	−	0.300386i	0.361550	−	0.932353i	$-0.382248\pi$
$79$	−3.67478	−	2.66989i	−0.413445	−	0.300386i	−0.774995	+	0.631967i	$0.782248\pi$
$80$	3.58412	−	11.0308i	0.400716	−	1.23328i
$81$	−1.84627	−	5.68225i	−0.205142	−	0.631361i
$82$	−0.336310	+	0.244343i	−0.0371392	+	0.0269832i
$83$	0.100862	+	0.310421i	0.0110710	+	0.0340731i	0.956439	−	0.291931i	$-0.0942977\pi$
$83$	0.100862	+	0.310421i	0.0110710	+	0.0340731i	−0.945368	+	0.326004i	$0.894298\pi$
$84$	1.04020	+	0.755748i	0.113495	+	0.0824589i
$85$	−20.2201	−	14.6908i	−2.19318	−	1.59344i
$86$	−9.86847	+	7.16986i	−1.06414	+	0.773146i
$87$	1.98411			0.212719
$88$	2.88451			0.307490
$89$	11.9008	−	8.64641i	1.26148	−	0.916518i	0.262649	−	0.964891i	$-0.415404\pi$
$89$	11.9008	−	8.64641i	1.26148	−	0.916518i	0.998829	+	0.0483734i	$0.0154037\pi$
$90$	1.18521	−	3.64772i	0.124933	−	0.384503i
$91$	0.113737	+	0.350048i	0.0119229	+	0.0366950i
$92$	1.83159			0.190957
$93$		0			0
$94$	7.14183			0.736623
$95$	1.35386	+	4.16674i	0.138903	+	0.427498i
$96$	1.01057	−	3.11022i	0.103141	−	0.317436i
$97$	−12.5553	+	9.12195i	−1.27480	+	0.926193i	−0.999383	−	0.0351325i	$-0.988815\pi$
$97$	−12.5553	+	9.12195i	−1.27480	+	0.926193i	−0.275413	+	0.961326i	$0.588815\pi$
$98$	−2.79707			−0.282546
$99$	0.757443			0.0761259
$100$	3.02295	−	2.19630i	0.302295	−	0.219630i
$101$	−3.94282	−	2.86463i	−0.392326	−	0.285041i	0.374082	−	0.927396i	$-0.377958\pi$
$101$	−3.94282	−	2.86463i	−0.392326	−	0.285041i	−0.766408	+	0.642354i	$0.777958\pi$
$102$	10.0030	+	7.26758i	0.990441	+	0.719598i
$103$	0.596594	+	1.83613i	0.0587842	+	0.180919i	0.976137	−	0.217156i	$-0.0696782\pi$
$103$	0.596594	+	1.83613i	0.0587842	+	0.180919i	−0.917353	+	0.398076i	$0.869678\pi$
$104$	0.412773	−	0.299897i	0.0404757	−	0.0294073i
$105$	−3.81568	−	11.7435i	−0.372373	−	1.14604i
$106$	−2.87012	+	8.83334i	−0.278771	+	0.857969i
$107$	−10.1350	−	7.36349i	−0.979785	−	0.711855i	−0.0221241	−	0.999755i	$-0.507043\pi$
$107$	−10.1350	−	7.36349i	−0.979785	−	0.711855i	−0.957660	+	0.287900i	$0.907043\pi$
$108$	0.689153	−	2.12100i	0.0663138	−	0.204093i
$109$	−3.17128	+	9.76021i	−0.303754	+	0.934858i	0.676385	+	0.736548i	$0.263545\pi$
$109$	−3.17128	+	9.76021i	−0.303754	+	0.934858i	−0.980139	+	0.198310i	$0.936455\pi$
$110$	−3.70181	−	2.68952i	−0.352953	−	0.256436i
$111$	−1.77584	+	5.46548i	−0.168555	+	0.518760i
$112$	−2.06446	−	6.35374i	−0.195073	−	0.600372i
$113$	3.10901	−	2.25882i	0.292471	−	0.212492i	−0.431868	−	0.901937i	$-0.642145\pi$
$113$	3.10901	−	2.25882i	0.292471	−	0.212492i	0.724338	+	0.689445i	$0.242145\pi$
$114$	−0.669758	−	2.06130i	−0.0627286	−	0.193059i
$115$	−14.2304	−	10.3390i	−1.32699	−	0.964118i
$116$	0.427942	+	0.310918i	0.0397334	+	0.0288680i
$117$	0.108390	−	0.0787500i	0.0100207	−	0.00728044i
$118$	−3.36045			−0.309354
$119$	−14.3962			−1.31970
$120$	−13.8478	+	10.0610i	−1.26412	+	0.918439i
$121$	−3.11995	+	9.60222i	−0.283632	+	0.872929i
$122$	−0.684825	−	2.10767i	−0.0620011	−	0.190820i
$123$	0.487156			0.0439254
$124$		0			0
$125$	−16.8827			−1.51003
$126$	−0.682685	−	2.10109i	−0.0608184	−	0.187180i
$127$	2.26939	−	6.98445i	0.201375	−	0.619770i	−0.798467	−	0.602038i	$-0.794356\pi$
$127$	2.26939	−	6.98445i	0.201375	−	0.619770i	0.999843	−	0.0177317i	$-0.00564447\pi$
$128$	−5.54936	+	4.03184i	−0.490499	+	0.356368i
$129$	14.2948			1.25859
$130$	−0.809352			−0.0709849
$131$	−10.5445	+	7.66100i	−0.921274	+	0.669345i	−0.943841	−	0.330401i	$-0.892816\pi$
$131$	−10.5445	+	7.66100i	−0.921274	+	0.669345i	0.0225669	+	0.999745i	$0.492816\pi$
$132$	−0.451719	−	0.328193i	−0.0393171	−	0.0285655i
$133$	2.04160	+	1.48331i	0.177029	+	0.128619i
$134$	0.216056	+	0.664953i	0.0186644	+	0.0574431i
$135$	−17.3270	+	12.5888i	−1.49127	+	1.08347i
$136$	6.16685	+	18.9796i	0.528803	+	1.62749i
$137$	−0.0415008	+	0.127726i	−0.00354565	+	0.0109124i	−0.952814	−	0.303556i	$-0.901826\pi$
$137$	−0.0415008	+	0.127726i	−0.00354565	+	0.0109124i	0.949268	+	0.314468i	$0.101826\pi$
$138$	7.03986	+	5.11476i	0.599273	+	0.435397i
$139$	3.56219	−	10.9633i	0.302141	−	0.929894i	−0.678588	−	0.734519i	$-0.737408\pi$
$139$	3.56219	−	10.9633i	0.302141	−	0.929894i	0.980729	−	0.195375i	$-0.0625924\pi$
$140$	1.01727	−	3.13083i	0.0859748	−	0.264603i
$141$	−6.77100	−	4.91942i	−0.570221	−	0.414290i
$142$	0.445019	−	1.36963i	0.0373452	−	0.114937i
$143$	−0.0493919	−	0.152013i	−0.00413036	−	0.0127119i
$144$	−1.96739	+	1.42940i	−0.163950	+	0.119116i
$145$	−1.56979	−	4.83132i	−0.130364	−	0.401219i
$146$	8.11830	+	5.89829i	0.671876	+	0.488146i
$147$	2.65184	+	1.92667i	0.218720	+	0.158909i
$148$	−1.23949	+	0.900541i	−0.101885	+	0.0740240i
$149$	−5.44108			−0.445751			−0.222875	−	0.974847i	$-0.571544\pi$
$149$	−5.44108			−0.445751			−0.222875	+	0.974847i	$0.571544\pi$
$150$	17.7521			1.44945
$151$	−11.0748	+	8.04630i	−0.901253	+	0.654799i	−0.938788	−	0.344497i	$-0.888050\pi$
$151$	−11.0748	+	8.04630i	−0.901253	+	0.654799i	0.0375344	+	0.999295i	$0.488050\pi$
$152$	1.08101	−	3.32700i	0.0876812	−	0.269855i
$153$	1.61935	+	4.98386i	0.130917	+	0.402921i
$154$	−2.63560			−0.212383
$155$		0			0
$156$	−0.0987625			−0.00790733
$157$	−4.65236	−	14.3185i	−0.371299	−	1.14274i	−0.945942	−	0.324336i	$-0.894859\pi$
$157$	−4.65236	−	14.3185i	−0.371299	−	1.14274i	0.574644	−	0.818404i	$-0.305141\pi$
$158$	1.77785	−	5.47167i	0.141439	−	0.435303i
$159$	8.80566	−	6.39769i	0.698335	−	0.507370i
$160$	−8.37296			−0.661941
$161$	−10.1317			−0.798493
$162$	6.12225	−	4.44808i	0.481010	−	0.349474i
$163$	−13.7841	−	10.0147i	−1.07965	−	0.784415i	−0.102032	−	0.994781i	$-0.532534\pi$
$163$	−13.7841	−	10.0147i	−1.07965	−	0.784415i	−0.977623	+	0.210366i	$0.932534\pi$
$164$	0.105072	+	0.0763395i	0.00820477	+	0.00596111i
$165$	1.65701	+	5.09975i	0.128998	+	0.397015i
$166$	−0.334459	+	0.242998i	−0.0259590	+	0.0188603i
$167$	−5.00553	−	15.4054i	−0.387340	−	1.19211i	−0.934769	−	0.355257i	$-0.884393\pi$
$167$	−5.00553	−	15.4054i	−0.387340	−	1.19211i	0.547429	−	0.836852i	$-0.315607\pi$
$168$	−3.04669	+	9.37675i	−0.235057	+	0.723432i
$169$	10.4943	+	7.62459i	0.807258	+	0.586507i
$170$	9.78245	−	30.1073i	0.750280	−	2.30912i
$171$	0.283861	−	0.873636i	0.0217074	−	0.0668086i
$172$	3.08318	+	2.24006i	0.235090	+	0.170803i
$173$	−0.720386	+	2.21712i	−0.0547699	+	0.168564i	−0.974700	−	0.223519i	$-0.928246\pi$
$173$	−0.720386	+	2.21712i	−0.0547699	+	0.168564i	0.919930	+	0.392083i	$0.128246\pi$
$174$	0.776582	+	2.39007i	0.0588725	+	0.181191i
$175$	−16.7219	+	12.1492i	−1.26406	+	0.918391i
$176$	0.896515	+	2.75919i	0.0675774	+	0.207982i
$177$	3.18596	+	2.31474i	0.239472	+	0.173986i
$178$	15.0735	+	10.9516i	1.12981	+	0.820854i
$179$	13.7295	−	9.97508i	1.02619	−	0.745573i	0.0586497	−	0.998279i	$-0.481321\pi$
$179$	13.7295	−	9.97508i	1.02619	−	0.745573i	0.967543	+	0.252706i	$0.0813205\pi$
$180$	−1.19829			−0.0893155
$181$	−7.33576			−0.545263			−0.272631	−	0.962119i	$-0.587894\pi$
$181$	−7.33576			−0.545263			−0.272631	+	0.962119i	$0.587894\pi$
$182$	−0.377154	+	0.274018i	−0.0279565	+	0.0203116i
$183$	−0.802538	+	2.46996i	−0.0593253	+	0.182584i
$184$	4.34009	+	13.3574i	0.319956	+	0.984723i
$185$	14.7135			1.08176
$186$		0			0
$187$	6.25174			0.457173
$188$	−0.689510	−	2.12209i	−0.0502877	−	0.154770i
$189$	−3.81216	+	11.7326i	−0.277294	+	0.853422i
$190$	−4.48939	+	3.26173i	−0.325695	+	0.236631i
$191$	7.82276			0.566035			0.283018	−	0.959115i	$-0.408665\pi$
$191$	7.82276			0.566035			0.283018	+	0.959115i	$0.408665\pi$
$192$	13.2023			0.952793
$193$	3.74697	−	2.72233i	0.269713	−	0.195958i	−0.444705	−	0.895677i	$-0.646692\pi$
$193$	3.74697	−	2.72233i	0.269713	−	0.195958i	0.714418	+	0.699719i	$0.246692\pi$
$194$	−15.9025	−	11.5539i	−1.14174	−	0.829520i
$195$	0.767328	+	0.557497i	0.0549495	+	0.0399232i
$196$	0.270044	+	0.831109i	0.0192888	+	0.0593649i
$197$	18.1093	−	13.1572i	1.29024	−	0.937412i	0.290427	−	0.956897i	$-0.406203\pi$
$197$	18.1093	−	13.1572i	1.29024	−	0.937412i	0.999810	+	0.0194848i	$0.00620261\pi$
$198$	0.296464	+	0.912424i	0.0210688	+	0.0648431i
$199$	−8.22101	+	25.3017i	−0.582772	+	1.79359i	0.0252665	+	0.999681i	$0.491957\pi$
$199$	−8.22101	+	25.3017i	−0.582772	+	1.79359i	−0.608039	+	0.793907i	$0.708043\pi$
$200$	23.1802	+	16.8414i	1.63909	+	1.19087i
$201$	0.253194	−	0.779250i	0.0178589	−	0.0549640i
$202$	1.90753	−	5.87078i	0.134214	−	0.413067i
$203$	−2.36723	−	1.71989i	−0.166147	−	0.120713i
$204$	1.19372	−	3.67389i	0.0835771	−	0.257224i
$205$	−0.385429	−	1.18623i	−0.0269195	−	0.0828498i
$206$	−1.97831	+	1.43733i	−0.137835	+	0.100143i
$207$	1.13966	+	3.50753i	0.0792122	+	0.243790i
$208$	0.415159	+	0.301631i	0.0287861	+	0.0209143i
$209$	−0.886591	−	0.644146i	−0.0613268	−	0.0445565i
$210$	12.6528	−	9.19282i	0.873128	−	0.634365i
$211$	1.32614			0.0912951			0.0456476	−	0.998958i	$-0.485465\pi$
$211$	1.32614			0.0912951			0.0456476	+	0.998958i	$0.485465\pi$
$212$	2.90180			0.199296
$213$	−1.36534	+	0.991975i	−0.0935514	+	0.0679690i
$214$	4.90329	−	15.0908i	0.335182	−	1.03158i
$215$	−11.3098	−	34.8080i	−0.771322	−	2.37388i
$216$	17.1010			1.16357
$217$		0			0
$218$	−12.9985			−0.880368
$219$	−3.63393	−	11.1841i	−0.245558	−	0.755750i
$220$	−0.441761	+	1.35960i	−0.0297835	+	0.0916642i
$221$	0.894623	−	0.649982i	0.0601788	−	0.0437225i
$222$	−7.27884			−0.488524
$223$	−12.1199			−0.811612			−0.405806	−	0.913959i	$-0.633009\pi$
$223$	−12.1199			−0.811612			−0.405806	+	0.913959i	$0.633009\pi$
$224$	−3.90176	+	2.83479i	−0.260697	+	0.189407i
$225$	6.08690	+	4.42239i	0.405793	+	0.294826i
$226$	3.93787	+	2.86103i	0.261943	+	0.190313i
$227$	−4.91404	−	15.1238i	−0.326156	−	1.00381i	−0.970916	−	0.239420i	$-0.923043\pi$
$227$	−4.91404	−	15.1238i	−0.326156	−	1.00381i	0.644760	−	0.764385i	$-0.276957\pi$
$228$	−0.547825	+	0.398018i	−0.0362806	+	0.0263594i
$229$	−5.03655	−	15.5009i	−0.332824	−	1.02433i	−0.967784	−	0.251783i	$-0.918983\pi$
$229$	−5.03655	−	15.5009i	−0.332824	−	1.02433i	0.634959	−	0.772545i	$-0.281017\pi$
$230$	6.88467	−	21.1888i	0.453961	−	1.39715i
$231$	2.49875	+	1.81545i	0.164406	+	0.119448i
$232$	−1.25342	+	3.85764i	−0.0822912	+	0.253266i
$233$	−1.58308	+	4.87223i	−0.103711	+	0.319190i	−0.989426	−	0.145040i	$-0.953669\pi$
$233$	−1.58308	+	4.87223i	−0.103711	+	0.319190i	0.885715	+	0.464230i	$0.153669\pi$
$234$	0.137287	+	0.0997448i	0.00897473	+	0.00652052i
$235$	−6.62174	+	20.3796i	−0.431955	+	1.32942i
$236$	0.324435	+	0.998509i	0.0211189	+	0.0649974i
$237$	−5.45453	+	3.96295i	−0.354310	+	0.257421i
$238$	−5.63470	−	17.3418i	−0.365244	−	1.12410i
$239$	−6.93166	−	5.03614i	−0.448372	−	0.325761i	0.340581	−	0.940215i	$-0.389376\pi$
$239$	−6.93166	−	5.03614i	−0.448372	−	0.325761i	−0.788952	+	0.614454i	$0.789376\pi$
$240$	−13.9278	−	10.1192i	−0.899037	−	0.653189i
$241$	5.53915	−	4.02443i	0.356808	−	0.259236i	−0.394912	−	0.918719i	$-0.629225\pi$
$241$	5.53915	−	4.02443i	0.356808	−	0.259236i	0.751719	+	0.659483i	$0.229225\pi$
$242$	−12.7881			−0.822049
$243$	8.03869			0.515682
$244$	−0.560149	+	0.406972i	−0.0358598	+	0.0260537i
$245$	2.59338	−	7.98159i	0.165685	−	0.509925i
$246$	0.190674	+	0.586833i	0.0121569	+	0.0374151i
$247$	−0.193842			−0.0123338
$248$		0			0
$249$	0.484474			0.0307023
$250$	−6.60791	−	20.3370i	−0.417921	−	1.28623i
$251$	7.00421	−	21.5567i	0.442102	−	1.36065i	−0.443529	−	0.896260i	$-0.646274\pi$
$251$	7.00421	−	21.5567i	0.442102	−	1.36065i	0.885631	−	0.464389i	$-0.153726\pi$
$252$	−0.558399	+	0.405700i	−0.0351758	+	0.0255567i
$253$	4.39983			0.276615
$254$	9.30178			0.583645
$255$	−30.0130	+	21.8057i	−1.87949	+	1.36553i
$256$	7.36284	+	5.34941i	0.460177	+	0.334338i
$257$	13.4769	+	9.79154i	0.840666	+	0.610779i	0.922557	−	0.385862i	$-0.126096\pi$
$257$	13.4769	+	9.79154i	0.840666	+	0.610779i	−0.0818908	+	0.996641i	$0.526096\pi$
$258$	5.59501	+	17.2197i	0.348330	+	1.07205i
$259$	6.85642	−	4.98148i	0.426037	−	0.309534i
$260$	0.0781391	+	0.240488i	0.00484598	+	0.0149144i
$261$	−0.329136	+	1.01298i	−0.0203730	+	0.0627017i
$262$	−13.3556	−	9.70343i	−0.825114	−	0.599480i
$263$	−7.59760	+	23.3830i	−0.468488	+	1.44186i	0.386054	+	0.922476i	$0.373838\pi$
$263$	−7.59760	+	23.3830i	−0.468488	+	1.44186i	−0.854542	+	0.519382i	$0.826162\pi$
$264$	1.32306	−	4.07197i	0.0814289	−	0.250612i
$265$	−22.5453	−	16.3801i	−1.38495	−	1.00622i
$266$	−0.987724	+	3.03990i	−0.0605613	+	0.186388i
$267$	−6.74723	−	20.7658i	−0.412924	−	1.27085i
$268$	0.176722	−	0.128396i	0.0107950	−	0.00784304i
$269$	3.86708	+	11.9017i	0.235780	+	0.725657i	0.997017	+	0.0771830i	$0.0245926\pi$
$269$	3.86708	+	11.9017i	0.235780	+	0.725657i	−0.761237	+	0.648474i	$0.775407\pi$
$270$	−21.9464	−	15.9450i	−1.33561	−	0.970380i
$271$	21.9788	+	15.9685i	1.33512	+	0.970020i	0.999608	+	0.0279826i	$0.00890831\pi$
$271$	21.9788	+	15.9685i	1.33512	+	0.970020i	0.335509	+	0.942037i	$0.391092\pi$
$272$	−16.2384	+	11.7979i	−0.984595	+	0.715350i
$273$	0.546320			0.0330648
$274$	−0.170104			−0.0102763
$275$	7.26169	−	5.27593i	0.437896	−	0.318150i
$276$	0.840112	−	2.58560i	0.0505688	−	0.155635i
$277$	−4.68387	−	14.4155i	−0.281427	−	0.866142i	−0.987447	−	0.157951i	$-0.949511\pi$
$277$	−4.68387	−	14.4155i	−0.281427	−	0.866142i	0.706020	−	0.708192i	$-0.250489\pi$
$278$	14.6007			0.875694
$279$		0			0
$280$	25.2430			1.50855
$281$	9.34706	+	28.7673i	0.557599	+	1.71611i	0.688980	+	0.724780i	$0.258059\pi$
$281$	9.34706	+	28.7673i	0.557599	+	1.71611i	−0.131381	+	0.991332i	$0.541941\pi$
$282$	3.27580	−	10.0819i	0.195071	−	0.600368i
$283$	−2.54462	+	1.84877i	−0.151262	+	0.109898i	−0.660842	−	0.750525i	$-0.729801\pi$
$283$	−2.54462	+	1.84877i	−0.151262	+	0.109898i	0.509580	+	0.860423i	$0.329801\pi$
$284$	−0.449930			−0.0266984
$285$	6.50303			0.385206
$286$	0.163784	−	0.118996i	0.00968474	−	0.00703637i
$287$	−0.581224	−	0.422284i	−0.0343086	−	0.0249266i
$288$	1.42027	+	1.03189i	0.0836902	+	0.0608045i
$289$	8.11244	+	24.9675i	0.477202	+	1.46868i
$290$	5.20543	−	3.78197i	0.305673	−	0.222085i
$291$	7.11832	+	21.9079i	0.417283	+	1.28427i
$292$	0.968810	−	2.98169i	0.0566953	−	0.174490i
$293$	−1.53720	−	1.11684i	−0.0898041	−	0.0652465i	0.541977	−	0.840393i	$-0.317676\pi$
$293$	−1.53720	−	1.11684i	−0.0898041	−	0.0652465i	−0.631781	+	0.775147i	$0.717676\pi$
$294$	−1.28295	+	3.94853i	−0.0748234	+	0.230283i
$295$	3.11573	−	9.58922i	0.181405	−	0.558306i
$296$	−9.50451	−	6.90543i	−0.552438	−	0.401370i
$297$	1.65548	−	5.09503i	0.0960605	−	0.295644i
$298$	−2.12965	−	6.55438i	−0.123367	−	0.379685i
$299$	0.629615	−	0.457442i	0.0364116	−	0.0264546i
$300$	−1.71388	−	5.27479i	−0.0989511	−	0.304540i
$301$	−17.0551	−	12.3912i	−0.983038	−	0.714219i
$302$	−14.0273	−	10.1915i	−0.807183	−	0.586453i
$303$	−5.85239	+	4.25201i	−0.336211	+	0.244272i
$304$	3.51843			0.201796
$305$	6.64932			0.380739
$306$	−5.36979	+	3.90138i	−0.306970	+	0.223027i
$307$	7.02337	−	21.6157i	0.400845	−	1.23367i	−0.523471	−	0.852044i	$-0.675363\pi$
$307$	7.02337	−	21.6157i	0.400845	−	1.23367i	0.924315	−	0.381629i	$-0.124637\pi$
$308$	0.254455	+	0.783131i	0.0144989	+	0.0446230i
$309$	2.86565			0.163021
$310$		0			0
$311$	15.8754			0.900213			0.450106	−	0.892975i	$-0.351386\pi$
$311$	15.8754			0.900213			0.450106	+	0.892975i	$0.351386\pi$
$312$	−0.234025	−	0.720254i	−0.0132490	−	0.0407764i
$313$	1.96206	−	6.03859i	0.110902	−	0.341321i	−0.880168	−	0.474662i	$-0.842570\pi$
$313$	1.96206	−	6.03859i	0.110902	−	0.341321i	0.991070	+	0.133341i	$0.0425704\pi$
$314$	15.4272	−	11.2085i	0.870610	−	0.632535i
$315$	6.62855			0.373476
$316$	−1.79747			−0.101116
$317$	12.3788	−	8.99370i	0.695261	−	0.505137i	−0.183124	−	0.983090i	$-0.558621\pi$
$317$	12.3788	−	8.99370i	0.695261	−	0.505137i	0.878385	+	0.477953i	$0.158621\pi$
$318$	11.1533	+	8.10332i	0.625444	+	0.454412i
$319$	1.02800	+	0.746884i	0.0575568	+	0.0418175i
$320$	−10.4454	−	32.1477i	−0.583917	−	1.79711i
$321$	−15.0435	+	10.9297i	−0.839646	+	0.610038i
$322$	−3.96558	−	12.2048i	−0.220993	−	0.680146i
$323$	2.34292	−	7.21076i	0.130363	−	0.401217i
$324$	−1.91276	−	1.38970i	−0.106264	−	0.0772056i
$325$	0.490618	−	1.50997i	0.0272146	−	0.0837580i
$326$	6.66873	−	20.5243i	0.369347	−	1.13673i
$327$	12.3236	+	8.95359i	0.681495	+	0.495135i
$328$	−0.307752	+	0.947162i	−0.0169927	+	0.0522983i
$329$	3.81413	+	11.7387i	0.210280	+	0.647175i
$330$	−5.49465	+	3.99209i	−0.302470	+	0.219758i
$331$	−2.77125	−	8.52903i	−0.152322	−	0.468798i	0.845558	−	0.533884i	$-0.179268\pi$
$331$	−2.77125	−	8.52903i	−0.152322	−	0.468798i	−0.997880	+	0.0650856i	$0.979268\pi$
$332$	0.104494	+	0.0759193i	0.00573485	+	0.00416661i
$333$	−2.49579	−	1.81330i	−0.136768	−	0.0993681i
$334$	16.5984	−	12.0594i	0.908222	−	0.659862i
$335$	−2.09780			−0.114615
$336$	−9.91629			−0.540978
$337$	3.53441	−	2.56790i	0.192532	−	0.139882i	−0.487343	−	0.873210i	$-0.662034\pi$
$337$	3.53441	−	2.56790i	0.192532	−	0.139882i	0.679875	+	0.733328i	$0.262034\pi$
$338$	−5.07715	+	15.6259i	−0.276161	+	0.849935i
$339$	−1.76268	−	5.42496i	−0.0957354	−	0.294643i
$340$	−9.89040			−0.536382
$341$		0			0
$342$	1.16349			0.0629145
$343$	−6.22883	−	19.1704i	−0.336325	−	1.03510i
$344$	−9.03048	+	27.7929i	−0.486891	+	1.49850i
$345$	−21.1224	+	15.3464i	−1.13719	+	0.826220i
$346$	−2.95272			−0.158739
$347$	24.4053			1.31015			0.655073	−	0.755566i	$-0.272638\pi$
$347$	24.4053			1.31015			0.655073	+	0.755566i	$0.272638\pi$
$348$	0.635201	−	0.461501i	0.0340504	−	0.0247390i
$349$	−10.5527	−	7.66702i	−0.564875	−	0.410406i	0.268365	−	0.963317i	$-0.413517\pi$
$349$	−10.5527	−	7.66702i	−0.564875	−	0.410406i	−0.833240	+	0.552911i	$0.813517\pi$
$350$	−21.1800	−	15.3882i	−1.13212	−	0.822531i
$351$	−0.292823	−	0.901215i	−0.0156297	−	0.0481033i
$352$	1.69439	−	1.23104i	0.0903111	−	0.0656148i
$353$	3.34505	+	10.2950i	0.178039	+	0.547948i	0.999759	−	0.0219433i	$-0.00698534\pi$
$353$	3.34505	+	10.2950i	0.178039	+	0.547948i	−0.821720	+	0.569891i	$0.806985\pi$
$354$	−1.54136	+	4.74383i	−0.0819226	+	0.252132i
$355$	3.49570	+	2.53977i	0.185532	+	0.134797i
$356$	1.79882	−	5.53621i	0.0953374	−	0.293418i
$357$	−6.60324	+	20.3227i	−0.349481	+	1.07559i
$358$	17.3898	+	12.6345i	0.919081	+	0.667752i
$359$	10.4396	−	32.1299i	0.550983	−	1.69575i	−0.155338	−	0.987861i	$-0.549647\pi$
$359$	10.4396	−	32.1299i	0.550983	−	1.69575i	0.706321	−	0.707891i	$-0.250353\pi$
$360$	−2.83944	−	8.73891i	−0.149652	−	0.460581i
$361$	14.2961	−	10.3867i	0.752427	−	0.546670i
$362$	−2.87123	−	8.83673i	−0.150908	−	0.464448i
$363$	12.1241	+	8.80866i	0.636349	+	0.462335i
$364$	0.117833	+	0.0856108i	0.00617613	+	0.00448722i
$365$	−24.3582	+	17.6973i	−1.27497	+	0.926318i
$366$	−3.28945			−0.171942
$367$	22.6313			1.18135			0.590673	−	0.806911i	$-0.298862\pi$
$367$	22.6313			1.18135			0.590673	+	0.806911i	$0.298862\pi$
$368$	−11.4282	+	8.30306i	−0.595735	+	0.432827i
$369$	−0.0808125	+	0.248715i	−0.00420693	+	0.0129476i
$370$	5.75889	+	17.7240i	0.299390	+	0.921429i
$371$	−16.0517			−0.833365
$372$		0			0
$373$	−32.9720			−1.70723			−0.853613	−	0.520908i	$-0.825593\pi$
$373$	−32.9720			−1.70723			−0.853613	+	0.520908i	$0.825593\pi$
$374$	2.44694	+	7.53091i	0.126528	+	0.389414i
$375$	−7.74373	+	23.8327i	−0.399884	+	1.23072i
$376$	13.8421	−	10.0569i	0.713854	−	0.518645i
$377$	0.224759			0.0115757
$378$	−15.6253			−0.803679
$379$	26.2865	−	19.0982i	1.35025	−	0.981011i	0.351246	−	0.936283i	$-0.385758\pi$
$379$	26.2865	−	19.0982i	1.35025	−	0.981011i	0.998999	−	0.0447276i	$-0.0142420\pi$
$380$	1.40261	+	1.01905i	0.0719523	+	0.0522764i
$381$	−8.81880	−	6.40724i	−0.451801	−	0.328253i
$382$	3.06184	+	9.42337i	0.156657	+	0.482142i
$383$	21.6658	−	15.7411i	1.10707	−	0.804335i	0.124872	−	0.992173i	$-0.460148\pi$
$383$	21.6658	−	15.7411i	1.10707	−	0.804335i	0.982200	+	0.187838i	$0.0601481\pi$
$384$	3.14625	+	9.68317i	0.160556	+	0.494142i
$385$	2.44367	−	7.52084i	0.124541	−	0.383297i
$386$	4.74591	+	3.44811i	0.241561	+	0.175504i
$387$	−2.37131	+	7.29815i	−0.120541	+	0.370986i
$388$	−1.89775	+	5.84069i	−0.0963439	+	0.296516i
$389$	14.3499	+	10.4258i	0.727571	+	0.528611i	0.888794	−	0.458307i	$-0.151544\pi$
$389$	14.3499	+	10.4258i	0.727571	+	0.528611i	−0.161223	+	0.986918i	$0.551544\pi$
$390$	−0.371232	+	1.14254i	−0.0187981	+	0.0578546i
$391$	9.40649	+	28.9502i	0.475707	+	1.46407i
$392$	−5.42122	+	3.93874i	−0.273813	+	0.198937i
$393$	5.97827	+	18.3992i	0.301564	+	0.928117i
$394$	22.9373	+	16.6649i	1.15557	+	0.839568i
$395$	13.9653	+	10.1464i	0.702673	+	0.510522i
$396$	0.242491	−	0.176180i	0.0121857	−	0.00885340i
$397$	9.94953			0.499352			0.249676	−	0.968329i	$-0.419676\pi$
$397$	9.94953			0.499352			0.249676	+	0.968329i	$0.419676\pi$
$398$	−33.6964			−1.68905
$399$	3.03038	−	2.20170i	0.151709	−	0.110223i
$400$	−8.90525	+	27.4075i	−0.445262	+	1.37038i
$401$	6.14807	+	18.9218i	0.307020	+	0.944911i	0.978916	+	0.204265i	$0.0654804\pi$
$401$	6.14807	+	18.9218i	0.307020	+	0.944911i	−0.671896	+	0.740646i	$0.734520\pi$
$402$	1.03779			0.0517604
$403$		0			0
$404$	−1.92858			−0.0959506
$405$	7.01643	+	21.5944i	0.348649	+	1.07303i
$406$	1.14526	−	3.52475i	0.0568384	−	0.174931i
$407$	−2.97748	+	2.16327i	−0.147588	+	0.107229i
$408$	29.6215			1.46648
$409$	−24.3255			−1.20282			−0.601410	−	0.798941i	$-0.705394\pi$
$409$	−24.3255			−1.20282			−0.601410	+	0.798941i	$0.705394\pi$
$410$	1.27809	−	0.928583i	0.0631201	−	0.0458595i
$411$	0.161271	+	0.117171i	0.00795493	+	0.00577960i
$412$	0.618077	+	0.449060i	0.0304505	+	0.0221236i
$413$	−1.79466	−	5.52340i	−0.0883096	−	0.271789i
$414$	−3.77913	+	2.74570i	−0.185734	+	0.134944i
$415$	−0.383308	−	1.17970i	−0.0188158	−	0.0579092i
$416$	0.114477	−	0.352324i	0.00561270	−	0.0172741i
$417$	−13.8426	−	10.0573i	−0.677876	−	0.492506i
$418$	0.428931	−	1.32012i	0.0209797	−	0.0645689i
$419$	−1.36176	+	4.19106i	−0.0665263	+	0.204747i	−0.978794	−	0.204848i	$-0.934330\pi$
$419$	−1.36176	+	4.19106i	−0.0665263	+	0.204747i	0.912267	+	0.409595i	$0.134330\pi$
$420$	−3.95309	−	2.87209i	−0.192891	−	0.140143i
$421$	−3.83913	+	11.8156i	−0.187108	+	0.575858i	−0.999978	−	0.00658617i	$-0.997904\pi$
$421$	−3.83913	+	11.8156i	−0.187108	+	0.575858i	0.812871	+	0.582444i	$0.197904\pi$
$422$	0.519052	+	1.59748i	0.0252671	+	0.0777641i
$423$	3.63481	−	2.64084i	0.176730	−	0.128402i
$424$	6.87602	+	21.1622i	0.333929	+	1.02773i
$425$	50.2397	+	36.5013i	2.43698	+	1.77057i
$426$	−1.72934	−	1.25644i	−0.0837867	−	0.0608746i
$427$	3.09855	−	2.25123i	0.149949	−	0.108945i
$428$	−4.95739			−0.239625
$429$	−0.237246			−0.0114544
$430$	37.5033	−	27.2478i	1.80857	−	1.31400i
$431$	−5.73699	+	17.6566i	−0.276341	+	0.850491i	0.712520	+	0.701652i	$0.247554\pi$
$431$	−5.73699	+	17.6566i	−0.276341	+	0.850491i	−0.988861	+	0.148839i	$0.952446\pi$
$432$	5.31504	+	16.3580i	0.255720	+	0.787025i
$433$	−36.1204			−1.73584			−0.867918	−	0.496708i	$-0.834542\pi$
$433$	−36.1204			−1.73584			−0.867918	+	0.496708i	$0.834542\pi$
$434$		0			0
$435$	−7.54024			−0.361527
$436$	1.25494	+	3.86231i	0.0601008	+	0.184971i
$437$	1.64889	−	5.07477i	0.0788772	−	0.242759i
$438$	12.0501	−	8.75492i	0.575777	−	0.418326i
$439$	−19.0094			−0.907268			−0.453634	−	0.891188i	$-0.649873\pi$
$439$	−19.0094			−0.907268			−0.453634	+	0.891188i	$0.649873\pi$
$440$	−10.9621			−0.522596
$441$	−1.42356	+	1.03427i	−0.0677884	+	0.0492512i
$442$	1.13313	+	0.823268i	0.0538975	+	0.0391588i
$443$	−10.0755	−	7.32030i	−0.478703	−	0.347798i	0.322121	−	0.946699i	$-0.395604\pi$
$443$	−10.0755	−	7.32030i	−0.478703	−	0.347798i	−0.800823	+	0.598901i	$0.795604\pi$
$444$	0.702737	+	2.16280i	0.0333504	+	0.102642i
$445$	−45.2267	+	32.8591i	−2.14395	+	1.55767i
$446$	−4.74376	−	14.5998i	−0.224624	−	0.691321i
$447$	−2.49571	+	7.68099i	−0.118043	+	0.363299i
$448$	−15.7516	−	11.4442i	−0.744193	−	0.540688i
$449$	7.86034	−	24.1916i	0.370952	−	1.14167i	−0.575217	−	0.818001i	$-0.695082\pi$
$449$	7.86034	−	24.1916i	0.370952	−	1.14167i	0.946169	−	0.323673i	$-0.104918\pi$
$450$	−2.94483	+	9.06327i	−0.138821	+	0.427247i
$451$	0.252404	+	0.183382i	0.0118852	+	0.00863512i
$452$	0.469932	−	1.44630i	0.0221037	−	0.0680283i
$453$	6.27894	+	19.3246i	0.295010	+	0.907948i
$454$	16.2950	−	11.8390i	0.764761	−	0.555631i
$455$	−0.432239	−	1.33029i	−0.0202637	−	0.0623651i
$456$	−4.20078	−	3.05204i	−0.196719	−	0.142925i
$457$	−25.8675	−	18.7938i	−1.21003	−	0.879138i	−0.214796	−	0.976659i	$-0.568909\pi$
$457$	−25.8675	−	18.7938i	−1.21003	−	0.879138i	−0.995233	+	0.0975213i	$0.968909\pi$
$458$	16.7012	−	12.1341i	0.780397	−	0.566991i
$459$	37.0638			1.72999
$460$	−6.96064			−0.324542
$461$	−15.6545	+	11.3737i	−0.729105	+	0.529726i	−0.889280	−	0.457363i	$-0.848794\pi$
$461$	−15.6545	+	11.3737i	−0.729105	+	0.529726i	0.160175	+	0.987089i	$0.448794\pi$
$462$	−1.20889	+	3.72059i	−0.0562428	+	0.173098i
$463$	0.0128126	+	0.0394332i	0.000595453	+	0.00183262i	0.951354	−	0.308101i	$-0.0996933\pi$
$463$	0.0128126	+	0.0394332i	0.000595453	+	0.00183262i	−0.950758	+	0.309933i	$0.899693\pi$
$464$	−4.07961			−0.189391
$465$		0			0
$466$	−6.48875			−0.300586
$467$	7.82069	+	24.0696i	0.361898	+	1.11381i	0.951901	+	0.306407i	$0.0991269\pi$
$467$	7.82069	+	24.0696i	0.361898	+	1.11381i	−0.590002	+	0.807402i	$0.700873\pi$
$468$	0.0163833	−	0.0504228i	0.000757321	−	0.00233079i
$469$	−0.977565	+	0.710243i	−0.0451398	+	0.0327960i
$470$	−27.1412			−1.25193
$471$	−22.3469			−1.02969
$472$	−6.51314	+	4.73208i	−0.299792	+	0.217811i
$473$	7.40637	+	5.38105i	0.340545	+	0.247421i
$474$	−6.90872	−	5.01948i	−0.317328	−	0.230552i
$475$	−3.36385	−	10.3529i	−0.154344	−	0.475022i
$476$	−4.60888	+	3.34854i	−0.211248	+	0.153480i
$477$	1.80557	+	5.55698i	0.0826715	+	0.254437i
$478$	3.35353	−	10.3211i	0.153387	−	0.472076i
$479$	17.1845	+	12.4852i	0.785178	+	0.570465i	0.906528	−	0.422145i	$-0.138723\pi$
$479$	17.1845	+	12.4852i	0.785178	+	0.570465i	−0.121351	+	0.992610i	$0.538723\pi$
$480$	−3.84050	+	11.8198i	−0.175294	+	0.539499i
$481$	−0.201166	+	0.619127i	−0.00917240	+	0.0282298i
$482$	7.01589	+	5.09734i	0.319565	+	0.232178i
$483$	−4.64721	+	14.3026i	−0.211455	+	0.650793i
$484$	1.23463	+	3.79979i	0.0561195	+	0.172718i
$485$	47.7141	−	34.6663i	2.16659	−	1.57412i
$486$	3.14636	+	9.68349i	0.142722	+	0.439252i
$487$	−21.6509	−	15.7303i	−0.981095	−	0.712807i	−0.0231422	−	0.999732i	$-0.507367\pi$
$487$	−21.6509	−	15.7303i	−0.981095	−	0.712807i	−0.957953	+	0.286925i	$0.907367\pi$
$488$	−4.29527	−	3.12070i	−0.194438	−	0.141267i
$489$	−20.4600	+	14.8650i	−0.925231	+	0.672220i
$490$	10.6298			0.480203
$491$	−12.5664			−0.567113			−0.283557	−	0.958955i	$-0.591514\pi$
$491$	−12.5664			−0.567113			−0.283557	+	0.958955i	$0.591514\pi$
$492$	0.155960	−	0.113312i	0.00703124	−	0.00510849i
$493$	−2.71660	+	8.36085i	−0.122350	+	0.376554i
$494$	−0.0758699	−	0.233503i	−0.00341355	−	0.0105058i
$495$	−2.87853			−0.129380
$496$		0			0
$497$	2.48886			0.111640
$498$	0.189624	+	0.583602i	0.00849725	+	0.0261518i
$499$	−7.11678	+	21.9032i	−0.318591	+	0.980521i	0.655661	+	0.755056i	$0.272390\pi$
$499$	−7.11678	+	21.9032i	−0.318591	+	0.980521i	−0.974251	+	0.225465i	$0.927610\pi$
$500$	−5.40490	+	3.92689i	−0.241715	+	0.175616i
$501$	−24.0433			−1.07417
$502$	28.7089			1.28134
$503$	−0.535228	+	0.388866i	−0.0238646	+	0.0173387i	−0.599654	−	0.800260i	$-0.704695\pi$
$503$	−0.535228	+	0.388866i	−0.0238646	+	0.0173387i	0.575789	+	0.817598i	$0.304695\pi$
$504$	−4.28185	−	3.11095i	−0.190729	−	0.138573i
$505$	14.9840	+	10.8865i	0.666779	+	0.484443i
$506$	1.72210	+	5.30008i	0.0765567	+	0.235617i
$507$	15.5769	−	11.3173i	0.691795	−	0.502619i
$508$	−0.898043	−	2.76389i	−0.0398442	−	0.122628i
$509$	−3.60543	+	11.0964i	−0.159808	+	0.491838i	−0.998616	−	0.0525889i	$-0.983253\pi$
$509$	−3.60543	+	11.0964i	−0.159808	+	0.491838i	0.838808	+	0.544427i	$0.183253\pi$
$510$	−38.0145	−	27.6191i	−1.68331	−	1.22300i
$511$	−5.35912	+	16.4937i	−0.237074	+	0.729638i
$512$	−7.80146	+	24.0104i	−0.344779	+	1.06112i
$513$	−5.25620	−	3.81886i	−0.232067	−	0.168607i
$514$	−6.52011	+	20.0668i	−0.287590	+	0.885110i
$515$	−2.26725	−	6.97788i	−0.0999069	−	0.307482i
$516$	4.57641	−	3.32495i	0.201465	−	0.146373i
$517$	−1.65633	−	5.09767i	−0.0728454	−	0.224195i
$518$	8.68435	+	6.30955i	0.381568	+	0.277226i
$519$	2.79941	+	2.03389i	0.122880	+	0.0892779i
$520$	−1.56867	+	1.13970i	−0.0687907	+	0.0499794i
$521$	−31.9184			−1.39837			−0.699186	−	0.714940i	$-0.746454\pi$
$521$	−31.9184			−1.39837			−0.699186	+	0.714940i	$0.746454\pi$
$522$	−1.34907			−0.0590470
$523$	0.00335774	−	0.00243954i	0.000146824	−	0.000106674i	−0.587712	−	0.809070i	$-0.699971\pi$
$523$	0.00335774	−	0.00243954i	0.000146824	−	0.000106674i	0.587859	+	0.808964i	$0.299971\pi$
$524$	−1.59381	+	4.90526i	−0.0696261	+	0.214287i
$525$	9.48061	+	29.1783i	0.413768	+	1.27345i
$526$	−31.1411			−1.35782
$527$		0			0
$528$	4.30627			0.187406
$529$	−0.487316	−	1.49980i	−0.0211876	−	0.0652088i
$530$	10.9074	−	33.5695i	0.473787	−	1.45817i
$531$	−1.71029	+	1.24260i	−0.0742201	+	0.0539241i
$532$	0.998624			0.0432958
$533$	0.0551848			0.00239032
$534$	22.3739	−	16.2556i	0.968212	−	0.703447i
$535$	38.5161	+	27.9836i	1.66520	+	1.20984i
$536$	1.35512	+	0.984553i	0.0585323	+	0.0425262i
$537$	−7.78406	−	23.9569i	−0.335907	−	1.03382i
$538$	−12.8233	+	9.31665i	−0.552851	+	0.401669i
$539$	0.648696	+	1.99648i	0.0279413	+	0.0859945i
$540$	−2.61900	+	8.06046i	−0.112704	+	0.346867i
$541$	−23.6840	−	17.2074i	−1.01825	−	0.739805i	−0.0523303	−	0.998630i	$-0.516665\pi$
$541$	−23.6840	−	17.2074i	−1.01825	−	0.739805i	−0.965924	+	0.258825i	$0.916665\pi$
$542$	−10.6333	+	32.7260i	−0.456740	+	1.40570i
$543$	−3.36476	+	10.3557i	−0.144395	+	0.444404i
$544$	11.7225	+	8.51692i	0.502599	+	0.365160i
$545$	12.0519	−	37.0919i	0.516246	−	1.58884i
$546$	0.213830	+	0.658102i	0.00915110	+	0.0281642i
$547$	−33.3034	+	24.1964i	−1.42395	+	1.03456i	−0.432848	+	0.901467i	$0.642491\pi$
$547$	−33.3034	+	24.1964i	−1.42395	+	1.03456i	−0.991103	+	0.133094i	$0.957509\pi$
$548$	0.0164227	+	0.0505439i	0.000701543	+	0.00215913i
$549$	−1.12790	−	0.819464i	−0.0481374	−	0.0349739i
$550$	9.19767	+	6.68250i	0.392190	+	0.284943i
$551$	1.24671	−	0.905789i	0.0531117	−	0.0385879i
$552$	20.8469			0.887305
$553$	9.94300			0.422820
$554$	15.5318	−	11.2845i	0.659881	−	0.479432i
$555$	6.74877	−	20.7706i	0.286469	−	0.881662i
$556$	−1.40963	−	4.33840i	−0.0597817	−	0.183989i
$557$	−5.73810			−0.243131			−0.121566	−	0.992583i	$-0.538791\pi$
$557$	−5.73810			−0.243131			−0.121566	+	0.992583i	$0.538791\pi$
$558$		0			0
$559$	1.61931			0.0684894
$560$	7.84559	+	24.1462i	0.331537	+	1.02037i
$561$	2.86754	−	8.82538i	0.121068	−	0.372608i
$562$	−30.9949	+	22.5191i	−1.30744	+	0.949911i
$563$	−14.2942			−0.602428			−0.301214	−	0.953557i	$-0.597392\pi$
$563$	−14.2942			−0.602428			−0.301214	+	0.953557i	$0.597392\pi$
$564$	−3.31195			−0.139458
$565$	−11.8152	+	8.58426i	−0.497070	+	0.361142i
$566$	−3.22302	−	2.34166i	−0.135474	−	0.0984273i
$567$	10.5807	+	7.68734i	0.444348	+	0.322838i
$568$	−1.06614	−	3.28125i	−0.0447343	−	0.137678i
$569$	−11.6189	+	8.44165i	−0.487091	+	0.353892i	−0.804065	−	0.594542i	$-0.797333\pi$
$569$	−11.6189	+	8.44165i	−0.487091	+	0.353892i	0.316974	+	0.948434i	$0.397333\pi$
$570$	2.54530	+	7.83362i	0.106611	+	0.328114i
$571$	10.3147	−	31.7453i	0.431656	−	1.32850i	−0.464819	−	0.885406i	$-0.653881\pi$
$571$	10.3147	−	31.7453i	0.431656	−	1.32850i	0.896475	−	0.443095i	$-0.146119\pi$
$572$	−0.0511705	−	0.0371775i	−0.00213955	−	0.00155447i
$573$	3.58813	−	11.0431i	0.149896	−	0.461334i
$574$	0.281195	−	0.865430i	0.0117369	−	0.0361224i
$575$	35.3575	+	25.6888i	1.47451	+	1.07130i
$576$	−2.19008	+	6.74037i	−0.0912533	+	0.280849i
$577$	−6.94658	−	21.3794i	−0.289190	−	0.890035i	−0.985111	−	0.171917i	$-0.945004\pi$
$577$	−6.94658	−	21.3794i	−0.289190	−	0.890035i	0.695921	−	0.718118i	$-0.254996\pi$
$578$	−26.9009	+	19.5446i	−1.11893	+	0.812950i
$579$	−2.12437	−	6.53815i	−0.0882859	−	0.271716i
$580$	−1.62632	−	1.18159i	−0.0675292	−	0.0490628i
$581$	−0.578024	−	0.419959i	−0.0239805	−	0.0174228i
$582$	−23.6044	+	17.1496i	−0.978433	+	0.710873i
$583$	6.97067			0.288695
$584$	24.0405			0.994804
$585$	−0.411917	+	0.299275i	−0.0170307	+	0.0123735i
$586$	0.743695	−	2.28886i	0.0307217	−	0.0945518i
$587$	−1.98271	−	6.10214i	−0.0818350	−	0.251862i	0.901765	−	0.432227i	$-0.142272\pi$
$587$	−1.98271	−	6.10214i	−0.0818350	−	0.251862i	−0.983600	+	0.180365i	$0.942272\pi$
$588$	1.29711			0.0534920
$589$		0			0
$590$	12.7708			0.525764
$591$	−10.2672	−	31.5993i	−0.422338	−	1.29982i
$592$	3.65139	−	11.2378i	0.150071	−	0.461871i
$593$	16.8762	−	12.2613i	0.693023	−	0.503510i	−0.184630	−	0.982808i	$-0.559109\pi$
$593$	16.8762	−	12.2613i	0.693023	−	0.503510i	0.877652	+	0.479298i	$0.159109\pi$
$594$	6.78548			0.278412
$595$	54.7103			2.24290
$596$	−1.74193	+	1.26559i	−0.0713523	+	0.0518405i
$597$	31.9467	+	23.2107i	1.30749	+	0.949950i
$598$	0.797472	+	0.579397i	0.0326110	+	0.0236933i
$599$	−3.57174	−	10.9927i	−0.145937	−	0.449149i	0.851193	−	0.524853i	$-0.175880\pi$
$599$	−3.57174	−	10.9927i	−0.145937	−	0.449149i	−0.997130	+	0.0757040i	$0.975880\pi$
$600$	34.4068	−	24.9980i	1.40465	−	1.02054i
$601$	1.33416	+	4.10611i	0.0544213	+	0.167492i	0.974573	−	0.224071i	$-0.0719347\pi$
$601$	1.33416	+	4.10611i	0.0544213	+	0.167492i	−0.920152	+	0.391562i	$0.871935\pi$
$602$	8.25122	−	25.3946i	0.336295	−	1.03501i
$603$	0.355841	+	0.258534i	0.0144910	+	0.0105283i
$604$	−1.67397	+	5.15196i	−0.0681130	+	0.209630i
$605$	11.8568	−	36.4915i	0.482048	−	1.48359i
$606$	−7.41265	−	5.38560i	−0.301118	−	0.218775i
$607$	13.8777	−	42.7112i	0.563279	−	1.73360i	−0.109730	−	0.993961i	$-0.534999\pi$
$607$	13.8777	−	42.7112i	0.563279	−	1.73360i	0.673009	−	0.739634i	$-0.265001\pi$
$608$	−0.784894	−	2.41565i	−0.0318316	−	0.0979677i
$609$	−3.51371	+	2.55286i	−0.142383	+	0.103447i
$610$	2.60255	+	8.00984i	0.105374	+	0.324309i
$611$	−0.767016	−	0.557270i	−0.0310301	−	0.0225447i
$612$	1.67767	+	1.21890i	0.0678157	+	0.0492710i
$613$	2.10762	−	1.53128i	0.0851260	−	0.0618477i	−0.544408	−	0.838820i	$-0.683246\pi$
$613$	2.10762	−	1.53128i	0.0851260	−	0.0618477i	0.629534	+	0.776973i	$0.283246\pi$
$614$	28.7874			1.16177
$615$	−1.85135			−0.0746536
$616$	−5.10826	+	3.71137i	−0.205818	+	0.149535i
$617$	−7.72134	+	23.7639i	−0.310850	+	0.956697i	0.666580	+	0.745434i	$0.267758\pi$
$617$	−7.72134	+	23.7639i	−0.310850	+	0.956697i	−0.977429	+	0.211263i	$0.932242\pi$
$618$	1.12162	+	3.45199i	0.0451181	+	0.138859i
$619$	31.9083			1.28250			0.641252	−	0.767330i	$-0.278415\pi$
$619$	31.9083			1.28250			0.641252	+	0.767330i	$0.278415\pi$
$620$		0			0
$621$	26.0847			1.04674
$622$	6.21366	+	19.1237i	0.249145	+	0.766790i
$623$	−9.95046	+	30.6244i	−0.398657	+	1.22694i
$624$	0.616227	−	0.447715i	0.0246688	−	0.0179229i
$625$	16.9474			0.677898
$626$	8.04209			0.321427
$627$	−1.31598	+	0.956115i	−0.0525552	+	0.0381836i
$628$	−4.81989	−	3.50185i	−0.192335	−	0.139739i
$629$	−20.5996	−	14.9665i	−0.821360	−	0.596753i
$630$	2.59442	+	7.98481i	0.103364	+	0.318122i
$631$	0.291045	−	0.211456i	0.0115863	−	0.00841795i	−0.581977	−	0.813205i	$-0.697721\pi$
$631$	0.291045	−	0.211456i	0.0115863	−	0.00841795i	0.593563	+	0.804787i	$0.297721\pi$
$632$	−4.25924	−	13.1086i	−0.169424	−	0.521432i
$633$	0.608271	−	1.87207i	0.0241766	−	0.0744080i
$634$	15.6790	+	11.3914i	0.622691	+	0.452412i
$635$	−8.62439	+	26.5432i	−0.342249	+	1.05333i
$636$	1.33099	−	4.09637i	0.0527773	−	0.162432i
$637$	0.300399	+	0.218252i	0.0119022	+	0.00864747i
$638$	−0.497344	+	1.53067i	−0.0196900	+	0.0605997i
$639$	−0.279958	−	0.861622i	−0.0110750	−	0.0340852i
$640$	21.0893	−	15.3223i	0.833629	−	0.605667i
$641$	−9.51986	−	29.2991i	−0.376012	−	1.15725i	−0.942793	−	0.333378i	$-0.891812\pi$
$641$	−9.51986	−	29.2991i	−0.376012	−	1.15725i	0.566781	−	0.823868i	$-0.308188\pi$
$642$	−19.0541	−	13.8436i	−0.752006	−	0.546364i
$643$	1.41726	+	1.02970i	0.0558915	+	0.0406075i	0.615380	−	0.788230i	$-0.289002\pi$
$643$	1.41726	+	1.02970i	0.0558915	+	0.0406075i	−0.559489	+	0.828838i	$0.689002\pi$
$644$	−3.24362	+	2.35663i	−0.127817	+	0.0928642i
$645$	−54.3248			−2.13904
$646$	9.60317			0.377832
$647$	19.9426	−	14.4891i	0.784024	−	0.569626i	−0.122160	−	0.992510i	$-0.538982\pi$
$647$	19.9426	−	14.4891i	0.784024	−	0.569626i	0.906184	+	0.422884i	$0.138982\pi$
$648$	5.60238	−	17.2423i	0.220082	−	0.677343i
$649$	0.779354	+	2.39861i	0.0305923	+	0.0941535i
$650$	2.01095			0.0788760
$651$		0			0
$652$	−6.74233			−0.264050
$653$	−0.0882751	−	0.271683i	−0.00345447	−	0.0106318i	0.949314	−	0.314328i	$-0.101779\pi$
$653$	−0.0882751	−	0.271683i	−0.00345447	−	0.0106318i	−0.952769	+	0.303696i	$0.901779\pi$
$654$	−5.96212	+	18.3495i	−0.233138	+	0.717524i
$655$	40.0723	−	29.1143i	1.56576	−	1.13759i
$656$	−1.00166			−0.0391083
$657$	6.31280			0.246286
$658$	−12.6477	+	9.18907i	−0.493058	+	0.358227i
$659$	−30.2772	−	21.9977i	−1.17943	−	0.856908i	−0.187325	−	0.982298i	$-0.559982\pi$
$659$	−30.2772	−	21.9977i	−1.17943	−	0.856908i	−0.992107	+	0.125391i	$0.959982\pi$
$660$	1.71668	+	1.24724i	0.0668215	+	0.0485487i
$661$	1.29527	+	3.98642i	0.0503801	+	0.155054i	0.973081	−	0.230462i	$-0.0740236\pi$
$661$	1.29527	+	3.98642i	0.0503801	+	0.155054i	−0.922701	+	0.385516i	$0.874024\pi$
$662$	9.18948	−	6.67655i	0.357159	−	0.259491i
$663$	−0.507213	−	1.56104i	−0.0196985	−	0.0606259i
$664$	−0.306058	+	0.941949i	−0.0118773	+	0.0365547i
$665$	−7.75874	−	5.63706i	−0.300871	−	0.218596i
$666$	1.20746	−	3.71618i	0.0467881	−	0.143999i
$667$	−1.91188	+	5.88417i	−0.0740284	+	0.227836i
$668$	−5.18578	−	3.76769i	−0.200644	−	0.145776i
$669$	−5.55916	+	17.1093i	−0.214929	+	0.661485i
$670$	−0.821083	−	2.52703i	−0.0317212	−	0.0976278i
$671$	−1.34558	+	0.977623i	−0.0519457	+	0.0377407i
$672$	2.21213	+	6.80824i	0.0853348	+	0.262634i
$673$	−8.06806	−	5.86179i	−0.311001	−	0.225955i	0.421325	−	0.906910i	$-0.361565\pi$
$673$	−8.06806	−	5.86179i	−0.311001	−	0.225955i	−0.732326	+	0.680954i	$0.761565\pi$
$674$	4.47669	+	3.25250i	0.172436	+	0.125282i
$675$	43.0513	−	31.2786i	1.65705	−	1.20391i
$676$	5.13318			0.197430
$677$	−47.7577			−1.83548			−0.917738	−	0.397186i	$-0.869987\pi$
$677$	−47.7577			−1.83548			−0.917738	+	0.397186i	$0.869987\pi$
$678$	5.84504	−	4.24667i	0.224477	−	0.163092i
$679$	10.4977	−	32.3087i	0.402865	−	1.23989i
$680$	−23.4360	−	72.1287i	−0.898730	−	2.76601i
$681$	−23.6038			−0.904500
$682$		0			0
$683$	27.7600			1.06221			0.531104	−	0.847307i	$-0.321777\pi$
$683$	27.7600			1.06221			0.531104	+	0.847307i	$0.321777\pi$
$684$	−0.112330	−	0.345716i	−0.00429504	−	0.0132188i
$685$	0.157716	−	0.485401i	0.00602603	−	0.0185462i
$686$	20.6548	−	15.0066i	0.788606	−	0.572956i
$687$	−24.1923			−0.922993
$688$	−29.3922			−1.12057
$689$	0.997501	−	0.724727i	0.0380018	−	0.0276099i
$690$	−26.7537	−	19.4377i	−1.01850	−	0.739981i
$691$	−30.7677	−	22.3540i	−1.17046	−	0.850388i	−0.179394	−	0.983777i	$-0.557414\pi$
$691$	−30.7677	−	22.3540i	−1.17046	−	0.850388i	−0.991064	+	0.133390i	$0.957414\pi$
$692$	0.285072	+	0.877360i	0.0108368	+	0.0333522i
$693$	−1.34138	+	0.974569i	−0.0509548	+	0.0370208i
$694$	9.55227	+	29.3989i	0.362599	+	1.11597i
$695$	−13.5375	+	41.6640i	−0.513505	+	1.58041i
$696$	4.87078	+	3.53883i	0.184627	+	0.134139i
$697$	−0.667006	+	2.05283i	−0.0252646	+	0.0777566i
$698$	5.10540	−	15.7128i	0.193242	−	0.594739i
$699$	6.15184	+	4.46957i	0.232684	+	0.169055i
$700$	−2.52754	+	7.77898i	−0.0955322	+	0.294018i
$701$	12.6871	+	39.0468i	0.479184	+	1.47478i	0.840230	+	0.542230i	$0.182420\pi$
$701$	12.6871	+	39.0468i	0.479184	+	1.47478i	−0.361046	+	0.932548i	$0.617580\pi$
$702$	0.971001	−	0.705474i	0.0366481	−	0.0266264i
$703$	1.37927	+	4.24494i	0.0520200	+	0.160101i
$704$	6.84033	+	4.96979i	0.257804	+	0.187306i
$705$	25.7320	+	18.6954i	0.969123	+	0.704109i
$706$	−11.0922	+	8.05896i	−0.417461	+	0.303303i
$707$	10.6683			0.401221
$708$	1.55837			0.0585673
$709$	−34.0319	+	24.7256i	−1.27809	+	0.928590i	−0.999494	−	0.0318175i	$-0.989870\pi$
$709$	−34.0319	+	24.7256i	−1.27809	+	0.928590i	−0.278600	+	0.960407i	$0.589870\pi$
$710$	−1.69121	+	5.20502i	−0.0634702	+	0.195341i
$711$	−1.11843	−	3.44219i	−0.0419446	−	0.129092i
$712$	44.6368			1.67284
$713$		0			0
$714$	−27.0654			−1.01290
$715$	0.187705	+	0.577696i	0.00701977	+	0.0216046i
$716$	2.07524	−	6.38694i	0.0775555	−	0.238691i
$717$	−10.2888	+	7.47522i	−0.384241	+	0.279167i
$718$	42.7901			1.59691
$719$	−33.2690			−1.24072			−0.620362	−	0.784316i	$-0.713014\pi$
$719$	−33.2690			−1.24072			−0.620362	+	0.784316i	$0.713014\pi$
$720$	7.47673	−	5.43216i	0.278641	−	0.202445i
$721$	−3.41899	−	2.48404i	−0.127330	−	0.0925106i
$722$	18.1075	+	13.1558i	0.673890	+	0.489610i
$723$	−3.14046	−	9.66535i	−0.116795	−	0.359458i
$724$	−2.34850	+	1.70629i	−0.0872815	+	0.0634137i
$725$	3.90037	+	12.0041i	0.144856	+	0.445821i
$726$	−5.86562	+	18.0525i	−0.217693	+	0.669991i
$727$	26.4734	+	19.2340i	0.981843	+	0.713351i	0.958120	−	0.286368i	$-0.0924479\pi$
$727$	26.4734	+	19.2340i	0.981843	+	0.713351i	0.0237235	+	0.999719i	$0.492448\pi$
$728$	−0.345127	+	1.06219i	−0.0127913	+	0.0393675i
$729$	9.22600	−	28.3947i	0.341704	−	1.05166i
$730$	−30.8522	−	22.4154i	−1.14189	−	0.829631i
$731$	−19.5722	+	60.2370i	−0.723904	+	2.22795i
$732$	0.317581	+	0.977413i	0.0117381	+	0.0361262i
$733$	8.06097	−	5.85664i	0.297739	−	0.216320i	−0.428879	−	0.903362i	$-0.641091\pi$
$733$	8.06097	−	5.85664i	0.297739	−	0.216320i	0.726618	+	0.687042i	$0.241091\pi$
$734$	8.85793	+	27.2619i	0.326952	+	1.00626i
$735$	−10.0778	−	7.32197i	−0.371726	−	0.270075i
$736$	8.25005	+	5.99401i	0.304101	+	0.220942i
$737$	0.424520	−	0.308432i	0.0156374	−	0.0113612i
$738$	−0.331235			−0.0121929
$739$	30.9584			1.13882			0.569412	−	0.822052i	$-0.307171\pi$
$739$	30.9584			1.13882			0.569412	+	0.822052i	$0.307171\pi$
$740$	4.71045	−	3.42234i	0.173160	−	0.125808i
$741$	−0.0889110	+	0.273640i	−0.00326623	+	0.0100524i
$742$	−6.28267	−	19.3361i	−0.230644	−	0.709850i
$743$	1.11003			0.0407231			0.0203615	−	0.999793i	$-0.493518\pi$
$743$	1.11003			0.0407231			0.0203615	+	0.999793i	$0.493518\pi$
$744$		0			0
$745$	20.6778			0.757578
$746$	−12.9053	−	39.7184i	−0.472496	−	1.45419i
$747$	−0.0803677	+	0.247346i	−0.00294050	+	0.00904993i
$748$	2.00146	−	1.45415i	0.0731807	−	0.0531689i
$749$	27.4226			1.00200
$750$	−31.7401			−1.15898
$751$	−22.7781	+	16.5493i	−0.831185	+	0.603892i	−0.919894	−	0.392166i	$-0.871726\pi$
$751$	−22.7781	+	16.5493i	−0.831185	+	0.603892i	0.0887090	+	0.996058i	$0.471726\pi$
$752$	13.9222	+	10.1150i	0.507689	+	0.368857i
$753$	−27.2183	−	19.7752i	−0.991889	−	0.720649i
$754$	0.0879708	+	0.270746i	0.00320371	+	0.00986000i
$755$	42.0877	−	30.5785i	1.53173	−	1.11287i
$756$	1.50855	+	4.64284i	0.0548654	+	0.168858i
$757$	11.9659	−	36.8271i	0.434906	−	1.33850i	−0.458276	−	0.888810i	$-0.651533\pi$
$757$	11.9659	−	36.8271i	0.434906	−	1.33850i	0.893183	−	0.449694i	$-0.148467\pi$
$758$	33.2945	+	24.1899i	1.20931	+	0.878615i
$759$	2.01811	−	6.21110i	0.0732527	−	0.225449i
$760$	−4.10817	+	12.6436i	−0.149019	+	0.458633i
$761$	−35.1412	−	25.5315i	−1.27387	−	0.925518i	−0.274517	−	0.961582i	$-0.588518\pi$
$761$	−35.1412	−	25.5315i	−1.27387	−	0.925518i	−0.999349	+	0.0360644i	$0.988518\pi$
$762$	4.26653	−	13.1310i	0.154560	−	0.475687i
$763$	−6.94191	−	21.3650i	−0.251314	−	0.773465i
$764$	2.50442	−	1.81956i	0.0906066	−	0.0658295i
$765$	−6.15406	−	18.9403i	−0.222501	−	0.684787i
$766$	27.4420	+	19.9378i	0.991518	+	0.720380i
$767$	0.360904	+	0.262212i	0.0130315	+	0.00946793i
$768$	10.9288	−	7.94021i	0.394358	−	0.286518i
$769$	−3.11019			−0.112156			−0.0560781	−	0.998426i	$-0.517860\pi$
$769$	−3.11019			−0.112156			−0.0560781	+	0.998426i	$0.517860\pi$
$770$	10.0161			0.360956
$771$	20.0040	−	14.5337i	0.720425	−	0.523419i
$772$	0.566361	−	1.74308i	0.0203838	−	0.0627348i
$773$	6.68718	+	20.5810i	0.240521	+	0.740248i	0.996341	+	0.0854684i	$0.0272387\pi$
$773$	6.68718	+	20.5810i	0.240521	+	0.740248i	−0.755820	+	0.654780i	$0.772761\pi$
$774$	−9.71956			−0.349362
$775$		0			0
$776$	−47.0918			−1.69050
$777$	−3.88730	−	11.9639i	−0.139456	−	0.429202i
$778$	−6.94248	+	21.3668i	−0.248900	+	0.766036i
$779$	0.306104	−	0.222398i	0.0109673	−	0.00796823i
$780$	0.375329			0.0134389
$781$	−1.08082			−0.0386747
$782$	−31.1920	+	22.6623i	−1.11542	+	0.810402i
$783$	6.09455	+	4.42795i	0.217801	+	0.158242i
$784$	−5.45255	−	3.96151i	−0.194734	−	0.141483i
$785$	17.6805	+	54.4148i	0.631042	+	1.94215i
$786$	−19.8240	+	14.4030i	−0.707097	+	0.513736i
$787$	−2.43398	−	7.49103i	−0.0867621	−	0.267026i	0.898257	−	0.439470i	$-0.144834\pi$
$787$	−2.43398	−	7.49103i	−0.0867621	−	0.267026i	−0.985019	+	0.172444i	$0.944834\pi$
$788$	2.73726	−	8.42442i	0.0975109	−	0.300108i
$789$	29.5242	+	21.4506i	1.05109	+	0.763661i
$790$	−6.75642	+	20.7941i	−0.240383	+	0.739822i
$791$	−2.59950	+	8.00044i	−0.0924276	+	0.284463i
$792$	1.85945	+	1.35097i	0.0660726	+	0.0480046i
$793$	−0.0909111	+	0.279795i	−0.00322835	+	0.00993583i
$794$	3.89426	+	11.9853i	0.138202	+	0.425342i
$795$	−33.4643	+	24.3133i	−1.18686	+	0.862303i
$796$	3.25322	+	10.0124i	0.115307	+	0.354880i
$797$	−23.8807	−	17.3503i	−0.845897	−	0.614580i	0.0781144	−	0.996944i	$-0.475110\pi$
$797$	−23.8807	−	17.3503i	−0.845897	−	0.614580i	−0.924012	+	0.382364i	$0.875110\pi$
$798$	3.83828	+	2.78868i	0.135874	+	0.0987181i
$799$	30.0007	−	21.7968i	1.06135	−	0.771116i
$800$	20.8038			0.735526
$801$	11.7212			0.414148
$802$	−20.3870	+	14.8121i	−0.719892	+	0.523032i
$803$	2.32726	−	7.16258i	0.0821274	−	0.252762i
$804$	−0.100194	−	0.308365i	−0.00353357	−	0.0108752i
$805$	38.5039			1.35708
$806$		0			0
$807$	18.5749			0.653869
$808$	−4.56992	−	14.0648i	−0.160769	−	0.494796i
$809$	−0.657442	+	2.02340i	−0.0231144	+	0.0711389i	−0.961948	−	0.273231i	$-0.911908\pi$
$809$	−0.657442	+	2.02340i	−0.0231144	+	0.0711389i	0.938834	+	0.344370i	$0.111908\pi$
$810$	−23.2665	+	16.9041i	−0.817503	+	0.593950i
$811$	7.20504			0.253003			0.126502	−	0.991966i	$-0.459625\pi$
$811$	7.20504			0.253003			0.126502	+	0.991966i	$0.459625\pi$
$812$	−1.15790			−0.0406343
$813$	32.6235	−	23.7023i	1.14416	−	0.831277i
$814$	−3.77129	−	2.74000i	−0.132183	−	0.0960369i
$815$	52.3840	+	38.0592i	1.83493	+	1.33316i
$816$	9.20646	+	28.3346i	0.322291	+	0.991909i
$817$	8.98213	−	6.52590i	0.314245	−	0.228312i
$818$	−9.52104	−	29.3027i	−0.332895	−	1.02455i
$819$	−0.0906270	+	0.278921i	−0.00316676	+	0.00974630i
$820$	−0.399308	−	0.290115i	−0.0139445	−	0.0101312i
$821$	12.9972	−	40.0012i	0.453604	−	1.39605i	−0.419161	−	0.907912i	$-0.637676\pi$
$821$	12.9972	−	40.0012i	0.453604	−	1.39605i	0.872766	−	0.488139i	$-0.162324\pi$
$822$	−0.0780229	+	0.240130i	−0.00272136	+	0.00837549i
$823$	24.4104	+	17.7352i	0.850895	+	0.618211i	0.925393	−	0.379010i	$-0.123735\pi$
$823$	24.4104	+	17.7352i	0.850895	+	0.618211i	−0.0744980	+	0.997221i	$0.523735\pi$
$824$	−1.81032	+	5.57159i	−0.0630655	+	0.194096i
$825$	−4.11707	−	12.6710i	−0.143338	−	0.441149i
$826$	5.95111	−	4.32374i	0.207066	−	0.150442i
$827$	−1.19604	−	3.68102i	−0.0415903	−	0.128002i	0.928105	−	0.372317i	$-0.121437\pi$
$827$	−1.19604	−	3.68102i	−0.0415903	−	0.128002i	−0.969696	+	0.244316i	$0.921437\pi$
$828$	1.18070	+	0.857832i	0.0410323	+	0.0298117i
$829$	−10.6561	−	7.74208i	−0.370100	−	0.268894i	0.387152	−	0.922016i	$-0.373459\pi$
$829$	−10.6561	−	7.74208i	−0.370100	−	0.268894i	−0.757253	+	0.653122i	$0.773459\pi$
$830$	1.27105	−	0.923472i	0.0441188	−	0.0320542i
$831$	−22.4983			−0.780456
$832$	1.49555			0.0518488
$833$	−11.7497	+	8.53663i	−0.407102	+	0.295777i
$834$	6.69704	−	20.6114i	0.231900	−	0.713714i
$835$	19.0226	+	58.5456i	0.658305	+	2.02605i
$836$	−0.433665			−0.0149986
$837$		0			0
$838$	−5.58159			−0.192813
$839$	−10.5835	−	32.5727i	−0.365384	−	1.12454i	−0.949740	−	0.313039i	$-0.898653\pi$
$839$	−10.5835	−	32.5727i	−0.365384	−	1.12454i	0.584356	−	0.811497i	$-0.301347\pi$
$840$	11.5784	−	35.6346i	0.399493	−	1.22951i
$841$	22.0159	−	15.9955i	0.759170	−	0.551569i
$842$	−15.7358			−0.542293
$843$	44.8971			1.54634
$844$	0.424556	−	0.308458i	0.0146138	−	0.0106176i
$845$	−39.8819	−	28.9759i	−1.37198	−	0.996801i
$846$	4.60385	+	3.34489i	0.158284	+	0.115000i
$847$	−6.82954	−	21.0192i	−0.234666	−	0.722227i
$848$	−18.1057	+	13.1546i	−0.621753	+	0.451730i
$849$	1.44269	+	4.44015i	0.0495131	+	0.152386i
$850$	−24.3059	+	74.8058i	−0.833685	+	2.56582i
$851$	−14.4975	−	10.5331i	−0.496969	−	0.361069i
$852$	−0.206373	+	0.635151i	−0.00707023	+	0.0217599i
$853$	−4.46464	+	13.7407i	−0.152866	+	0.470474i	−0.997938	−	0.0641782i	$-0.979557\pi$
$853$	−4.46464	+	13.7407i	−0.152866	+	0.470474i	0.845072	+	0.534652i	$0.179557\pi$
$854$	3.92463	+	2.85141i	0.134298	+	0.0975732i
$855$	−1.07876	+	3.32010i	−0.0368930	+	0.113545i
$856$	−11.7469	−	36.1533i	−0.401501	−	1.23569i
$857$	−22.5174	+	16.3599i	−0.769180	+	0.558842i	−0.901712	−	0.432337i	$-0.857689\pi$
$857$	−22.5174	+	16.3599i	−0.769180	+	0.558842i	0.132532	+	0.991179i	$0.457689\pi$
$858$	−0.0928585	−	0.285789i	−0.00317014	−	0.00975668i
$859$	38.2828	+	27.8141i	1.30619	+	0.949005i	0.999996	−	0.00296341i	$-0.000943285\pi$
$859$	38.2828	+	27.8141i	1.30619	+	0.949005i	0.306197	+	0.951968i	$0.400943\pi$
$860$	−11.7171	−	8.51294i	−0.399548	−	0.290289i
$861$	−0.862719	+	0.626802i	−0.0294014	+	0.0213614i
$862$	−23.5148			−0.800919
$863$	26.0534			0.886867			0.443434	−	0.896307i	$-0.353760\pi$
$863$	26.0534			0.886867			0.443434	+	0.896307i	$0.353760\pi$
$864$	10.0453	−	7.29831i	0.341747	−	0.248294i
$865$	2.73770	−	8.42577i	0.0930845	−	0.286485i
$866$	−14.1376	−	43.5110i	−0.480414	−	1.47856i
$867$	38.9668			1.32338
$868$		0			0
$869$	−4.31787			−0.146474
$870$	−2.95126	−	9.08305i	−0.100057	−	0.307944i
$871$	0.0286816	−	0.0882730i	0.000971840	−	0.00299102i
$872$	−25.1934	+	18.3041i	−0.853156	+	0.619854i
$873$	−12.3658			−0.418520
$874$	6.75849			0.228609
$875$	29.8981	−	21.7222i	1.01074	−	0.734345i
$876$	−3.76478	−	2.73527i	−0.127200	−	0.0924164i
$877$	27.7667	+	20.1737i	0.937613	+	0.681216i	0.947845	−	0.318732i	$-0.103257\pi$
$877$	27.7667	+	20.1737i	0.937613	+	0.681216i	−0.0102317	+	0.999948i	$0.503257\pi$
$878$	−7.44030	−	22.8989i	−0.251098	−	0.772800i
$879$	−2.28169	+	1.65774i	−0.0769594	+	0.0559143i
$880$	−3.40704	−	10.4858i	−0.114851	−	0.353476i
$881$	−1.12318	+	3.45678i	−0.0378408	+	0.116462i	−0.968193	−	0.250206i	$-0.919502\pi$
$881$	−1.12318	+	3.45678i	−0.0378408	+	0.116462i	0.930352	+	0.366668i	$0.119502\pi$
$882$	−1.80308	−	1.31001i	−0.0607129	−	0.0441105i
$883$	12.1930	−	37.5262i	0.410327	−	1.26286i	−0.506037	−	0.862512i	$-0.668890\pi$
$883$	12.1930	−	37.5262i	0.410327	−	1.26286i	0.916364	−	0.400345i	$-0.131110\pi$
$884$	0.135224	−	0.416176i	0.00454807	−	0.0139975i
$885$	−12.1077	−	8.79674i	−0.406995	−	0.295699i
$886$	4.87453	−	15.0022i	0.163763	−	0.504010i
$887$	−13.0723	−	40.2323i	−0.438924	−	1.35087i	−0.889012	−	0.457884i	$-0.848607\pi$
$887$	−13.0723	−	40.2323i	−0.438924	−	1.35087i	0.450088	−	0.892984i	$-0.351393\pi$
$888$	−14.1077	+	10.2498i	−0.473423	+	0.343962i
$889$	4.96766	+	15.2889i	0.166610	+	0.512773i
$890$	−57.2842	−	41.6194i	−1.92017	−	1.39509i
$891$	−4.59481	−	3.33832i	−0.153932	−	0.111838i
$892$	−3.88014	+	2.81908i	−0.129917	+	0.0943899i
$893$	−6.50038			−0.217527
$894$	−10.2294			−0.342123
$895$	−52.1766	+	37.9085i	−1.74407	+	1.26714i
$896$	4.63993	−	14.2802i	0.155009	−	0.477069i
$897$	−0.356965	−	1.09863i	−0.0119187	−	0.0366821i
$898$	32.2180			1.07513
$899$		0			0
$900$	2.97733			0.0992444
$901$	14.9027	+	45.8659i	0.496482	+	1.52801i
$902$	−0.122113	+	0.375824i	−0.00406590	+	0.0125136i
$903$	−25.3151	+	18.3925i	−0.842433	+	0.612064i
$904$	11.6611			0.387843
$905$	27.8782			0.926704
$906$	−20.8210	+	15.1273i	−0.691731	+	0.502572i
$907$	26.1863	+	19.0254i	0.869501	+	0.631730i	0.930453	−	0.366411i	$-0.119414\pi$
$907$	26.1863	+	19.0254i	0.869501	+	0.631730i	−0.0609518	+	0.998141i	$0.519414\pi$
$908$	−5.09099	−	3.69882i	−0.168950	−	0.122750i
$909$	−1.20001	−	3.69326i	−0.0398020	−	0.122498i
$910$	1.43331	−	1.04136i	0.0475136	−	0.0345207i
$911$	−8.36223	−	25.7363i	−0.277053	−	0.852682i	−0.988669	−	0.150113i	$-0.952036\pi$
$911$	−8.36223	−	25.7363i	−0.277053	−	0.852682i	0.711616	−	0.702569i	$-0.247964\pi$
$912$	1.61383	−	4.96685i	0.0534392	−	0.164469i
$913$	0.251014	+	0.182372i	0.00830736	+	0.00603565i
$914$	12.5146	−	38.5161i	0.413948	−	1.27400i
$915$	3.04990	−	9.38663i	0.100827	−	0.310312i
$916$	−5.21791	−	3.79104i	−0.172405	−	0.125259i
$917$	8.81643	−	27.1342i	0.291144	−	0.896050i
$918$	14.5068	+	44.6474i	0.478796	+	1.47358i
$919$	−16.7992	+	12.2053i	−0.554154	+	0.402617i	−0.829315	−	0.558782i	$-0.811269\pi$
$919$	−16.7992	+	12.2053i	−0.554154	+	0.402617i	0.275161	+	0.961398i	$0.411269\pi$
$920$	−16.4937	−	50.7625i	−0.543782	−	1.67359i
$921$	−27.2927	−	19.8293i	−0.899325	−	0.653398i
$922$	−19.8281	−	14.4059i	−0.653003	−	0.474434i
$923$	−0.154665	+	0.112370i	−0.00509085	+	0.00369872i
$924$	1.22223			0.0402085
$925$	−36.5578			−1.20201
$926$	−0.0424867	+	0.0308684i	−0.00139620	+	0.00101440i
$927$	−0.475372	+	1.46304i	−0.0156133	+	0.0480527i
$928$	0.910081	+	2.80094i	0.0298749	+	0.0919454i
$929$	−20.6589			−0.677798			−0.338899	−	0.940823i	$-0.610055\pi$
$929$	−20.6589			−0.677798			−0.338899	+	0.940823i	$0.610055\pi$
$930$		0			0
$931$	2.54585			0.0834368
$932$	0.626458	+	1.92804i	0.0205203	+	0.0631551i
$933$	7.28172	−	22.4108i	0.238393	−	0.733697i
$934$	−25.9335	+	18.8418i	−0.848569	+	0.616521i
$935$	−23.7586			−0.776990
$936$	0.406544			0.0132883
$937$	−2.36282	+	1.71669i	−0.0771898	+	0.0560817i	−0.625711	−	0.780055i	$-0.715191\pi$
$937$	−2.36282	+	1.71669i	−0.0771898	+	0.0560817i	0.548521	+	0.836137i	$0.315191\pi$
$938$	−1.23819	−	0.899594i	−0.0404282	−	0.0293728i
$939$	−7.62453	−	5.53954i	−0.248817	−	0.180776i
$940$	2.62036	+	8.06463i	0.0854667	+	0.263039i
$941$	−26.5763	+	19.3088i	−0.866362	+	0.629449i	−0.929608	−	0.368549i	$-0.879855\pi$
$941$	−26.5763	+	19.3088i	−0.866362	+	0.629449i	0.0632463	+	0.997998i	$0.479855\pi$
$942$	−8.74660	−	26.9193i	−0.284980	−	0.877077i
$943$	−0.469423	+	1.44474i	−0.0152865	+	0.0470471i
$944$	−6.55079	−	4.75943i	−0.213210	−	0.154906i
$945$	14.4874	−	44.5877i	0.471276	−	1.45044i
$946$	−3.58319	+	11.0279i	−0.116500	+	0.358549i
$947$	−31.6526	−	22.9969i	−1.02857	−	0.747300i	−0.0605485	−	0.998165i	$-0.519285\pi$
$947$	−31.6526	−	22.9969i	−1.02857	−	0.747300i	−0.968022	+	0.250865i	$0.919285\pi$
$948$	−0.824463	+	2.53744i	−0.0267773	+	0.0824121i
$949$	−0.411649	−	1.26693i	−0.0133627	−	0.0411262i
$950$	11.1545	−	8.10424i	0.361901	−	0.262936i
$951$	−7.01824	−	21.5999i	−0.227582	−	0.700426i
$952$	−35.3413	−	25.6770i	−1.14542	−	0.832195i
$953$	−4.87008	−	3.53832i	−0.157757	−	0.114617i	0.506106	−	0.862471i	$-0.331084\pi$
$953$	−4.87008	−	3.53832i	−0.157757	−	0.114617i	−0.663863	+	0.747854i	$0.731084\pi$
$954$	−5.98729	+	4.35002i	−0.193846	+	0.140837i
$955$	−29.7290			−0.962008
$956$	−3.39053			−0.109658
$957$	1.52587	−	1.10861i	0.0493245	−	0.0358363i
$958$	−8.31382	+	25.5873i	−0.268607	+	0.826688i
$959$	−0.0908447	−	0.279591i	−0.00293353	−	0.00902848i
$960$	−50.1729			−1.61932
$961$		0			0
$962$	−0.824543			−0.0265843
$963$	−3.08462	−	9.49348i	−0.0994005	−	0.305923i
$964$	0.837252	−	2.57680i	0.0269661	−	0.0829931i
$965$	−14.2397	+	10.3457i	−0.458391	+	0.333041i
$966$	−19.0480			−0.612860
$967$	26.3103			0.846083			0.423042	−	0.906110i	$-0.360962\pi$
$967$	26.3103			0.846083			0.423042	+	0.906110i	$0.360962\pi$
$968$	−24.7856	+	18.0078i	−0.796639	+	0.578792i
$969$	−9.10455	−	6.61484i	−0.292480	−	0.212499i
$970$	60.4348	+	43.9084i	1.94044	+	1.40981i
$971$	−1.46346	−	4.50408i	−0.0469648	−	0.144543i	0.924824	−	0.380395i	$-0.124212\pi$
$971$	−1.46346	−	4.50408i	−0.0469648	−	0.144543i	−0.971789	+	0.235852i	$0.924212\pi$
$972$	2.57355	−	1.86979i	0.0825465	−	0.0599735i
$973$	7.79760	+	23.9985i	0.249979	+	0.769358i
$974$	10.4747	−	32.2377i	0.335630	−	1.03296i
$975$	−1.90654	−	1.38518i	−0.0610580	−	0.0443613i
$976$	1.65013	−	5.07859i	0.0528195	−	0.162562i
$977$	−5.33982	+	16.4343i	−0.170836	+	0.525780i	−0.999419	−	0.0340871i	$-0.989148\pi$
$977$	−5.33982	+	16.4343i	−0.170836	+	0.525780i	0.828583	+	0.559867i	$0.189148\pi$
$978$	−25.9146	−	18.8281i	−0.828658	−	0.602055i
$979$	4.32111	−	13.2990i	0.138103	−	0.425038i
$980$	−1.02625	−	3.15848i	−0.0327824	−	0.100894i
$981$	−6.61553	+	4.80646i	−0.211218	+	0.153459i
$982$	−4.91850	−	15.1376i	−0.156956	−	0.483060i
$983$	33.1426	+	24.0795i	1.05709	+	0.768017i	0.973547	−	0.228487i	$-0.0733779\pi$
$983$	33.1426	+	24.0795i	1.05709	+	0.768017i	0.0835383	+	0.996505i	$0.473378\pi$
$984$	1.19592	+	0.868886i	0.0381245	+	0.0276991i
$985$	−68.8213	+	50.0016i	−2.19283	+	1.59318i
$986$	−11.1348			−0.354605
$987$	18.3206			0.583150
$988$	−0.0620574	+	0.0450873i	−0.00197431	+	0.00143442i
$989$	−13.7745	+	42.3934i	−0.438003	+	1.34803i
$990$	−1.12666	−	3.46750i	−0.0358076	−	0.110204i
$991$	14.1338			0.448975			0.224487	−	0.974477i	$-0.427929\pi$
$991$	14.1338			0.448975			0.224487	+	0.974477i	$0.427929\pi$
$992$		0			0
$993$	−13.3113			−0.422420
$994$	0.974142	+	2.99810i	0.0308979	+	0.0950940i
$995$	31.2425	−	96.1545i	0.990453	−	3.04830i
$996$	0.155102	−	0.112688i	0.00491459	−	0.00357066i
$997$	15.4538			0.489428			0.244714	−	0.969595i	$-0.421306\pi$
$997$	15.4538			0.489428			0.244714	+	0.969595i	$0.421306\pi$
$998$	−29.1703			−0.923370
$999$	−17.6522	+	12.8251i	−0.558490	+	0.405767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.p.531.3		16
31.2	even	5		961.2.d.o.388.2		16
31.3	odd	30		961.2.c.i.439.6		16
31.4	even	5		961.2.d.o.374.2		16
31.5	even	3		961.2.g.t.844.2		16
31.6	odd	6		961.2.g.m.547.2		16
31.7	even	15		31.2.g.a.10.1	✓	16
31.8	even	5	inner	961.2.d.p.628.3		16
31.9	even	15		961.2.g.s.448.2		16
31.10	even	15		31.2.g.a.28.1	yes	16
31.11	odd	30		961.2.g.j.732.1		16
31.12	odd	30		961.2.g.j.235.1		16
31.13	odd	30		961.2.c.i.521.6		16
31.14	even	15		961.2.g.t.846.2		16
31.15	odd	10		961.2.a.j.1.6		8
31.16	even	5		961.2.a.i.1.6		8
31.17	odd	30		961.2.g.n.846.2		16
31.18	even	15		961.2.c.j.521.6		16
31.19	even	15		961.2.g.k.235.1		16
31.20	even	15		961.2.g.k.732.1		16
31.21	odd	30		961.2.g.l.338.1		16
31.22	odd	30		961.2.g.m.448.2		16
31.23	odd	10		961.2.d.q.628.3		16
31.24	odd	30		961.2.g.l.816.1		16
31.25	even	3		961.2.g.s.547.2		16
31.26	odd	6		961.2.g.n.844.2		16
31.27	odd	10		961.2.d.n.374.2		16
31.28	even	15		961.2.c.j.439.6		16
31.29	odd	10		961.2.d.n.388.2		16
31.30	odd	2		961.2.d.q.531.3		16
93.38	odd	30		279.2.y.c.10.2		16
93.41	odd	30		279.2.y.c.28.2		16
93.47	odd	10		8649.2.a.bf.1.3		8
93.77	even	10		8649.2.a.be.1.3		8
124.7	odd	30		496.2.bg.c.289.2		16
124.103	odd	30		496.2.bg.c.369.2		16
155.7	odd	60		775.2.ck.a.599.4		32
155.38	odd	60		775.2.ck.a.599.1		32
155.69	even	30		775.2.bl.a.351.2		16
155.72	odd	60		775.2.ck.a.524.1		32
155.103	odd	60		775.2.ck.a.524.4		32
155.134	even	30		775.2.bl.a.276.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.1	✓	16	31.7	even	15
31.2.g.a.28.1	yes	16	31.10	even	15
279.2.y.c.10.2		16	93.38	odd	30
279.2.y.c.28.2		16	93.41	odd	30
496.2.bg.c.289.2		16	124.7	odd	30
496.2.bg.c.369.2		16	124.103	odd	30
775.2.bl.a.276.2		16	155.134	even	30
775.2.bl.a.351.2		16	155.69	even	30
775.2.ck.a.524.1		32	155.72	odd	60
775.2.ck.a.524.4		32	155.103	odd	60
775.2.ck.a.599.1		32	155.38	odd	60
775.2.ck.a.599.4		32	155.7	odd	60
961.2.a.i.1.6		8	31.16	even	5
961.2.a.j.1.6		8	31.15	odd	10
961.2.c.i.439.6		16	31.3	odd	30
961.2.c.i.521.6		16	31.13	odd	30
961.2.c.j.439.6		16	31.28	even	15
961.2.c.j.521.6		16	31.18	even	15
961.2.d.n.374.2		16	31.27	odd	10
961.2.d.n.388.2		16	31.29	odd	10
961.2.d.o.374.2		16	31.4	even	5
961.2.d.o.388.2		16	31.2	even	5
961.2.d.p.531.3		16	1.1	even	1	trivial
961.2.d.p.628.3		16	31.8	even	5	inner
961.2.d.q.531.3		16	31.30	odd	2
961.2.d.q.628.3		16	31.23	odd	10
961.2.g.j.235.1		16	31.12	odd	30
961.2.g.j.732.1		16	31.11	odd	30
961.2.g.k.235.1		16	31.19	even	15
961.2.g.k.732.1		16	31.20	even	15
961.2.g.l.338.1		16	31.21	odd	30
961.2.g.l.816.1		16	31.24	odd	30
961.2.g.m.448.2		16	31.22	odd	30
961.2.g.m.547.2		16	31.6	odd	6
961.2.g.n.844.2		16	31.26	odd	6
961.2.g.n.846.2		16	31.17	odd	30
961.2.g.s.448.2		16	31.9	even	15
961.2.g.s.547.2		16	31.25	even	3
961.2.g.t.844.2		16	31.5	even	3
961.2.g.t.846.2		16	31.14	even	15
8649.2.a.be.1.3		8	93.77	even	10
8649.2.a.bf.1.3		8	93.47	odd	10

Overview	Random
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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.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.391401 + 1.20461i) q^{2} +(0.458679 - 1.41167i) q^{3} +(0.320145 - 0.232599i) q^{4} -3.80032 q^{5} +1.88004 q^{6} +(-1.77093 + 1.28666i) q^{7} +(2.45490 + 1.78359i) q^{8} +(0.644632 + 0.468353i) q^{9} +(-1.48745 - 4.57790i) q^{10} +(0.769048 - 0.558746i) q^{11} +(-0.181509 - 0.558626i) q^{12} +(0.0519589 - 0.159913i) q^{13} +(-2.24306 - 1.62968i) q^{14} +(-1.74313 + 5.36479i) q^{15} +(-0.943109 + 2.90259i) q^{16} +(5.32063 + 3.86566i) q^{17} +(-0.311872 + 0.959844i) q^{18} +(-0.356248 - 1.09642i) q^{19} +(-1.21665 + 0.883950i) q^{20} +(1.00404 + 3.09013i) q^{21} +(0.974077 + 0.707709i) q^{22} +(3.74454 + 2.72056i) q^{23} +(3.64384 - 2.64741i) q^{24} +9.44244 q^{25} +0.212969 q^{26} +(4.55935 - 3.31256i) q^{27} +(-0.267679 + 0.823832i) q^{28} +(0.413068 + 1.27129i) q^{29} -7.14474 q^{30} +2.20322 q^{32} +(-0.436018 - 1.34192i) q^{33} +(-2.57411 + 7.92230i) q^{34} +(6.73010 - 4.88970i) q^{35} +0.315314 q^{36} -3.87165 q^{37} +(1.18132 - 0.858279i) q^{38} +(-0.201911 - 0.146697i) q^{39} +(-9.32941 - 6.77821i) q^{40} +(0.101420 + 0.312139i) q^{41} +(-3.32941 + 2.41896i) q^{42} +(2.97601 + 9.15922i) q^{43} +(0.116243 - 0.357759i) q^{44} +(-2.44981 - 1.77989i) q^{45} +(-1.81160 + 5.57554i) q^{46} +(1.74242 - 5.36260i) q^{47} +(3.66491 + 2.66271i) q^{48} +(-0.682410 + 2.10024i) q^{49} +(3.69578 + 11.3745i) q^{50} +(7.89748 - 5.73786i) q^{51} +(-0.0205612 - 0.0632808i) q^{52} +(5.93248 + 4.31020i) q^{53} +(5.77487 + 4.19569i) q^{54} +(-2.92263 + 2.12341i) q^{55} -6.64232 q^{56} -1.71118 q^{57} +(-1.36973 + 0.995171i) q^{58} +(-0.819859 + 2.52327i) q^{59} +(0.689791 + 2.12296i) q^{60} -1.74967 q^{61} -1.74421 q^{63} +(2.74856 + 8.45921i) q^{64} +(-0.197460 + 0.607720i) q^{65} +(1.44584 - 1.05046i) q^{66} +0.552007 q^{67} +2.60252 q^{68} +(5.55807 - 4.03817i) q^{69} +(8.52436 + 6.19331i) q^{70} +(-0.919843 - 0.668305i) q^{71} +(0.747159 + 2.29952i) q^{72} +(6.40952 - 4.65679i) q^{73} +(-1.51537 - 4.66383i) q^{74} +(4.33104 - 13.3296i) q^{75} +(-0.369076 - 0.268150i) q^{76} +(-0.643016 + 1.97900i) q^{77} +(0.0976845 - 0.300642i) q^{78} +(-3.67478 - 2.66989i) q^{79} +(3.58412 - 11.0308i) q^{80} +(-1.84627 - 5.68225i) q^{81} +(-0.336310 + 0.244343i) q^{82} +(0.100862 + 0.310421i) q^{83} +(1.04020 + 0.755748i) q^{84} +(-20.2201 - 14.6908i) q^{85} +(-9.86847 + 7.16986i) q^{86} +1.98411 q^{87} +2.88451 q^{88} +(11.9008 - 8.64641i) q^{89} +(1.18521 - 3.64772i) q^{90} +(0.113737 + 0.350048i) q^{91} +1.83159 q^{92} +7.14183 q^{94} +(1.35386 + 4.16674i) q^{95} +(1.01057 - 3.11022i) q^{96} +(-12.5553 + 9.12195i) q^{97} -2.79707 q^{98} +0.757443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} - 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} + 4 q^{11} - 5 q^{12} + 9 q^{13} - 18 q^{14} + 4 q^{15} - 2 q^{16} + 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 - 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 + 4 * q^11 - 5 * q^12 + 9 * q^13 - 18 * q^14 + 4 * q^15 - 2 * q^16 + 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 + 2 * q^21 - 8 * q^22 + 21 * q^23 + 5 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 - 56 * q^34 + 21 * q^35 - 2 * q^36 + 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 + 12 * q^42 - 16 * q^43 + 37 * q^44 - 5 * q^45 - 16 * q^46 + 4 * q^47 + 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 - 18 * q^52 + 3 * q^53 + 39 * q^54 + 29 * q^55 + 60 * q^56 + 34 * q^57 + 10 * q^58 - 3 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 9 * q^65 + 20 * q^66 - 26 * q^67 - 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 - 9 * q^73 + 64 * q^74 + 19 * q^75 + 9 * q^76 - 42 * q^77 + 15 * q^78 + 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 + 67 * q^83 + 39 * q^84 - 63 * q^85 - 23 * q^86 - 30 * q^87 + 34 * q^88 + 26 * q^89 - 24 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 4 * q^96 - 37 * q^97 + 20 * q^98 - 12 * q^99

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