LMFDB - Embedded newform 968.2.o.h.269.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(245,968)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("968.245"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.10
Character	$\chi$	$=$	968.269
Dual form			968.2.o.h.493.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41418 - 0.00927596i) q^{2} +(0.784953 - 1.08039i) q^{3} +(1.99983 - 0.0262358i) q^{4} +(1.83667 + 0.596771i) q^{5} +(1.10004 - 1.53516i) q^{6} +(-1.48802 + 1.08111i) q^{7} +(2.82788 - 0.0556526i) q^{8} +(0.375949 + 1.15705i) q^{9} +(2.60293 + 0.826906i) q^{10} +(1.54142 - 2.18120i) q^{12} +(-0.152835 + 0.0496591i) q^{13} +(-2.09431 + 1.54270i) q^{14} +(2.08645 - 1.51589i) q^{15} +(3.99862 - 0.104934i) q^{16} +(-1.67315 + 5.14942i) q^{17} +(0.542394 + 1.63280i) q^{18} +(1.64430 - 2.26318i) q^{19} +(3.68868 + 1.14525i) q^{20} +2.45628i q^{21} +4.44137 q^{23} +(2.15962 - 3.09891i) q^{24} +(-1.02786 - 0.746783i) q^{25} +(-0.215676 + 0.0716448i) q^{26} +(5.35542 + 1.74008i) q^{27} +(-2.94743 + 2.20108i) q^{28} +(-4.90770 - 6.75487i) q^{29} +(2.93656 - 2.16310i) q^{30} +(-2.79918 - 8.61500i) q^{31} +(5.65381 - 0.185487i) q^{32} +(-2.31837 + 7.29774i) q^{34} +(-3.37819 + 1.09764i) q^{35} +(0.782190 + 2.30404i) q^{36} +(0.353889 + 0.487087i) q^{37} +(2.30434 - 3.21580i) q^{38} +(-0.0663168 + 0.204102i) q^{39} +(5.22710 + 1.58538i) q^{40} +(-9.51720 - 6.91465i) q^{41} +(0.0227843 + 3.47362i) q^{42} +4.47936i q^{43} +2.34948i q^{45} +(6.28091 - 0.0411980i) q^{46} +(-5.09323 - 3.70045i) q^{47} +(3.02536 - 4.40246i) q^{48} +(-1.11771 + 3.43995i) q^{49} +(-1.46051 - 1.04655i) q^{50} +(4.25006 + 5.84971i) q^{51} +(-0.304341 + 0.103319i) q^{52} +(-11.1474 + 3.62200i) q^{53} +(7.58968 + 2.41112i) q^{54} +(-4.14779 + 3.14007i) q^{56} +(-1.15443 - 3.55298i) q^{57} +(-7.00305 - 9.50710i) q^{58} +(5.66097 + 7.79166i) q^{59} +(4.13277 - 3.08626i) q^{60} +(3.16618 + 1.02875i) q^{61} +(-4.03847 - 12.1572i) q^{62} +(-1.81033 - 1.31528i) q^{63} +(7.99381 - 0.314758i) q^{64} -0.310343 q^{65} -5.76864i q^{67} +(-3.21091 + 10.3418i) q^{68} +(3.48627 - 4.79843i) q^{69} +(-4.76720 + 1.58360i) q^{70} +(2.97557 - 9.15788i) q^{71} +(1.12753 + 3.25108i) q^{72} +(-0.551701 + 0.400834i) q^{73} +(0.504983 + 0.685547i) q^{74} +(-1.61364 + 0.524303i) q^{75} +(3.22893 - 4.56911i) q^{76} +(-0.0918909 + 0.289253i) q^{78} +(-1.78571 - 5.49584i) q^{79} +(7.40678 + 2.19353i) q^{80} +(3.13098 - 2.27479i) q^{81} +(-13.5232 - 9.69030i) q^{82} +(-2.78089 - 0.903567i) q^{83} +(0.0644424 + 4.91213i) q^{84} +(-6.14604 + 8.45931i) q^{85} +(0.0415504 + 6.33463i) q^{86} -11.1502 q^{87} +5.74214 q^{89} +(0.0217937 + 3.32260i) q^{90} +(0.173735 - 0.239126i) q^{91} +(8.88198 - 0.116523i) q^{92} +(-11.5048 - 3.73814i) q^{93} +(-7.23708 - 5.18586i) q^{94} +(4.37063 - 3.17545i) q^{95} +(4.23757 - 6.25395i) q^{96} +(-1.66198 - 5.11506i) q^{97} +(-1.54873 + 4.87509i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100}) $ 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.41418	−	0.00927596i	0.999978	−	0.00655910i
$2$	1.41418	−	0.00927596i	0.999978	−	0.00655910i
$3$	0.784953	−	1.08039i	0.453193	−	0.623766i	−0.519887	−	0.854235i	$-0.674026\pi$
$3$	0.784953	−	1.08039i	0.453193	−	0.623766i	0.973080	+	0.230469i	$0.0740260\pi$
$4$	1.99983	−	0.0262358i	0.999914	−	0.0131179i
$5$	1.83667	+	0.596771i	0.821384	+	0.266884i	0.689412	−	0.724369i	$-0.257869\pi$
$5$	1.83667	+	0.596771i	0.821384	+	0.266884i	0.131972	+	0.991253i	$0.457869\pi$
$6$	1.10004	−	1.53516i	0.449091	−	0.626725i
$7$	−1.48802	+	1.08111i	−0.562420	+	0.408622i	−0.832344	−	0.554259i	$-0.813002\pi$
$7$	−1.48802	+	1.08111i	−0.562420	+	0.408622i	0.269924	+	0.962882i	$0.413002\pi$
$8$	2.82788	−	0.0556526i	0.999806	−	0.0196762i
$9$	0.375949	+	1.15705i	0.125316	+	0.385684i
$10$	2.60293	+	0.826906i	0.823117	+	0.261491i
$11$		0			0
$11$		0			0
$12$	1.54142	−	2.18120i	0.444971	−	0.629657i
$13$	−0.152835	+	0.0496591i	−0.0423888	+	0.0137730i	−0.330135	−	0.943934i	$-0.607094\pi$
$13$	−0.152835	+	0.0496591i	−0.0423888	+	0.0137730i	0.287746	+	0.957707i	$0.407094\pi$
$14$	−2.09431	+	1.54270i	−0.559728	+	0.412303i
$15$	2.08645	−	1.51589i	0.538718	−	0.391402i
$16$	3.99862	−	0.104934i	0.999656	−	0.0262336i
$17$	−1.67315	+	5.14942i	−0.405798	+	1.24892i	0.514429	+	0.857533i	$0.328004\pi$
$17$	−1.67315	+	5.14942i	−0.405798	+	1.24892i	−0.920227	+	0.391385i	$0.871996\pi$
$18$	0.542394	+	1.63280i	0.127843	+	0.384854i
$19$	1.64430	−	2.26318i	0.377227	−	0.519209i	−0.577620	−	0.816306i	$-0.696018\pi$
$19$	1.64430	−	2.26318i	0.377227	−	0.519209i	0.954847	+	0.297097i	$0.0960184\pi$
$20$	3.68868	+	1.14525i	0.824815	+	0.256086i
$21$			2.45628i			0.536003i
$22$		0			0
$23$	4.44137			0.926090			0.463045	−	0.886335i	$-0.346757\pi$
$23$	4.44137			0.926090			0.463045	+	0.886335i	$0.346757\pi$
$24$	2.15962	−	3.09891i	0.440831	−	0.632562i
$25$	−1.02786	−	0.746783i	−0.205572	−	0.149357i
$26$	−0.215676	+	0.0716448i	−0.0422976	+	0.0140507i
$27$	5.35542	+	1.74008i	1.03065	+	0.334879i
$28$	−2.94743	+	2.20108i	−0.557012	+	0.415965i
$29$	−4.90770	−	6.75487i	−0.911337	−	1.25435i	−0.966708	−	0.255882i	$-0.917634\pi$
$29$	−4.90770	−	6.75487i	−0.911337	−	1.25435i	0.0553705	−	0.998466i	$-0.482366\pi$
$30$	2.93656	−	2.16310i	0.536140	−	0.394927i
$31$	−2.79918	−	8.61500i	−0.502748	−	1.54730i	−0.804523	−	0.593921i	$-0.797579\pi$
$31$	−2.79918	−	8.61500i	−0.502748	−	1.54730i	0.301775	−	0.953379i	$-0.402421\pi$
$32$	5.65381	−	0.185487i	0.999462	−	0.0327898i
$33$		0			0
$34$	−2.31837	+	7.29774i	−0.397597	+	1.25155i
$35$	−3.37819	+	1.09764i	−0.571018	+	0.185535i
$36$	0.782190	+	2.30404i	0.130365	+	0.384007i
$37$	0.353889	+	0.487087i	0.0581791	+	0.0800766i	0.837115	−	0.547027i	$-0.184240\pi$
$37$	0.353889	+	0.487087i	0.0581791	+	0.0800766i	−0.778936	+	0.627103i	$0.784240\pi$
$38$	2.30434	−	3.21580i	0.373814	−	0.521672i
$39$	−0.0663168	+	0.204102i	−0.0106192	+	0.0326825i
$40$	5.22710	+	1.58538i	0.826477	+	0.250671i
$41$	−9.51720	−	6.91465i	−1.48634	−	1.07989i	−0.975446	−	0.220241i	$-0.929316\pi$
$41$	−9.51720	−	6.91465i	−1.48634	−	1.07989i	−0.510891	−	0.859646i	$-0.670684\pi$
$42$	0.0227843	+	3.47362i	0.00351570	+	0.535992i
$43$			4.47936i			0.683096i	0.939864	+	0.341548i	$0.110951\pi$
$43$			4.47936i			0.683096i	−0.939864	+	0.341548i	$0.889049\pi$
$44$		0			0
$45$			2.34948i			0.350240i
$46$	6.28091	−	0.0411980i	0.926070	−	0.00607431i
$47$	−5.09323	−	3.70045i	−0.742924	−	0.539766i	0.150702	−	0.988579i	$-0.451847\pi$
$47$	−5.09323	−	3.70045i	−0.742924	−	0.539766i	−0.893625	+	0.448814i	$0.851847\pi$
$48$	3.02536	−	4.40246i	0.436673	−	0.635440i
$49$	−1.11771	+	3.43995i	−0.159672	+	0.491421i
$50$	−1.46051	−	1.04655i	−0.206547	−	0.148005i
$51$	4.25006	+	5.84971i	0.595128	+	0.819123i
$52$	−0.304341	+	0.103319i	−0.0422045	+	0.0143278i
$53$	−11.1474	+	3.62200i	−1.53121	+	0.497521i	−0.948935	−	0.315471i	$-0.897838\pi$
$53$	−11.1474	+	3.62200i	−1.53121	+	0.497521i	−0.582276	+	0.812991i	$0.697838\pi$
$54$	7.58968	+	2.41112i	1.03282	+	0.328111i
$55$		0			0
$56$	−4.14779	+	3.14007i	−0.554271	+	0.419610i
$57$	−1.15443	−	3.55298i	−0.152908	−	0.470603i
$58$	−7.00305	−	9.50710i	−0.919545	−	1.24834i
$59$	5.66097	+	7.79166i	0.736995	+	1.01439i	0.998786	+	0.0492625i	$0.0156871\pi$
$59$	5.66097	+	7.79166i	0.736995	+	1.01439i	−0.261790	+	0.965125i	$0.584313\pi$
$60$	4.13277	−	3.08626i	0.533538	−	0.398435i
$61$	3.16618	+	1.02875i	0.405388	+	0.131718i	0.504611	−	0.863347i	$-0.331636\pi$
$61$	3.16618	+	1.02875i	0.405388	+	0.131718i	−0.0992234	+	0.995065i	$0.531636\pi$
$62$	−4.03847	−	12.1572i	−0.512886	−	1.54397i
$63$	−1.81033	−	1.31528i	−0.228080	−	0.165710i
$64$	7.99381	−	0.314758i	0.999226	−	0.0393447i
$65$	−0.310343			−0.0384933
$66$		0			0
$67$		−	5.76864i		−	0.704751i	−0.935859	−	0.352376i	$-0.885374\pi$
$67$		−	5.76864i		−	0.704751i	0.935859	−	0.352376i	$-0.114626\pi$
$68$	−3.21091	+	10.3418i	−0.389380	+	1.25413i
$69$	3.48627	−	4.79843i	0.419697	−	0.577664i
$70$	−4.76720	+	1.58360i	−0.569789	+	0.189276i
$71$	2.97557	−	9.15788i	0.353136	−	1.08684i	−0.603947	−	0.797025i	$-0.706406\pi$
$71$	2.97557	−	9.15788i	0.353136	−	1.08684i	0.957083	−	0.289815i	$-0.0935939\pi$
$72$	1.12753	+	3.25108i	0.132881	+	0.383144i
$73$	−0.551701	+	0.400834i	−0.0645717	+	0.0469141i	−0.619603	−	0.784915i	$-0.712706\pi$
$73$	−0.551701	+	0.400834i	−0.0645717	+	0.0469141i	0.555031	+	0.831830i	$0.312706\pi$
$74$	0.504983	+	0.685547i	0.0587030	+	0.0796933i
$75$	−1.61364	+	0.524303i	−0.186327	+	0.0605413i
$76$	3.22893	−	4.56911i	0.370384	−	0.524113i
$77$		0			0
$78$	−0.0918909	+	0.289253i	−0.0104046	+	0.0327515i
$79$	−1.78571	−	5.49584i	−0.200908	−	0.618330i	−0.999857	−	0.0169315i	$-0.994610\pi$
$79$	−1.78571	−	5.49584i	−0.200908	−	0.618330i	0.798949	−	0.601399i	$-0.205390\pi$
$80$	7.40678	+	2.19353i	0.828103	+	0.245244i
$81$	3.13098	−	2.27479i	0.347886	−	0.252754i
$82$	−13.5232	−	9.69030i	−1.49339	−	1.07011i
$83$	−2.78089	−	0.903567i	−0.305243	−	0.0991794i	0.152391	−	0.988320i	$-0.451303\pi$
$83$	−2.78089	−	0.903567i	−0.305243	−	0.0991794i	−0.457633	+	0.889141i	$0.651303\pi$
$84$	0.0644424	+	4.91213i	0.00703125	+	0.535957i
$85$	−6.14604	+	8.45931i	−0.666632	+	0.917540i
$86$	0.0415504	+	6.33463i	0.00448049	+	0.683081i
$87$	−11.1502			−1.19543
$88$		0			0
$89$	5.74214			0.608666			0.304333	−	0.952566i	$-0.401566\pi$
$89$	5.74214			0.608666			0.304333	+	0.952566i	$0.401566\pi$
$90$	0.0217937	+	3.32260i	0.00229726	+	0.350232i
$91$	0.173735	−	0.239126i	0.0182124	−	0.0250672i
$92$	8.88198	−	0.116523i	0.926010	−	0.0121484i
$93$	−11.5048	−	3.73814i	−1.19299	−	0.387628i
$94$	−7.23708	−	5.18586i	−0.746448	−	0.534881i
$95$	4.37063	−	3.17545i	0.448417	−	0.325794i
$96$	4.23757	−	6.25395i	0.432496	−	0.638291i
$97$	−1.66198	−	5.11506i	−0.168749	−	0.519355i	0.830544	−	0.556953i	$-0.188030\pi$
$97$	−1.66198	−	5.11506i	−0.168749	−	0.519355i	−0.999293	+	0.0375974i	$0.988030\pi$
$98$	−1.54873	+	4.87509i	−0.156446	+	0.492458i
$99$		0			0
$100$	−2.07513	−	1.46647i	−0.207513	−	0.146647i
$101$	8.86259	−	2.87963i	0.881861	−	0.286534i	0.167131	−	0.985935i	$-0.446550\pi$
$101$	8.86259	−	2.87963i	0.881861	−	0.286534i	0.714730	+	0.699401i	$0.246550\pi$
$102$	6.06463	+	8.23314i	0.600488	+	0.815202i
$103$	−1.35802	+	0.986656i	−0.133809	+	0.0972181i	−0.652676	−	0.757637i	$-0.726354\pi$
$103$	−1.35802	+	0.986656i	−0.133809	+	0.0972181i	0.518867	+	0.854855i	$0.326354\pi$
$104$	−0.429435	+	0.148936i	−0.0421096	+	0.0146043i
$105$	−1.46583	+	4.51137i	−0.143051	+	0.440265i
$106$	−15.7308	+	5.22558i	−1.52791	+	0.507553i
$107$	−6.62834	+	9.12312i	−0.640786	+	0.881966i	−0.998657	−	0.0518051i	$-0.983503\pi$
$107$	−6.62834	+	9.12312i	−0.640786	+	0.881966i	0.357872	+	0.933771i	$0.383503\pi$
$108$	10.7556	+	3.33936i	1.03495	+	0.321330i
$109$			19.6373i			1.88092i	0.339910	+	0.940458i	$0.389603\pi$
$109$			19.6373i			1.88092i	−0.339910	+	0.940458i	$0.610397\pi$
$110$		0			0
$111$	0.804032			0.0763154
$112$	−5.83660	+	4.47911i	−0.551507	+	0.423236i
$113$	10.4489	+	7.59158i	0.982951	+	0.714155i	0.958366	−	0.285542i	$-0.0921737\pi$
$113$	10.4489	+	7.59158i	0.982951	+	0.714155i	0.0245845	+	0.999698i	$0.492174\pi$
$114$	−1.66554	−	5.01385i	−0.155992	−	0.469590i
$115$	8.15734	+	2.65048i	0.760676	+	0.247159i
$116$	−9.99178	−	13.3798i	−0.927713	−	1.24229i
$117$	−0.114916	−	0.158169i	−0.0106240	−	0.0146227i
$118$	8.07792	+	10.9663i	0.743633	+	1.00953i
$119$	−3.07742	−	9.47133i	−0.282107	−	0.868235i
$120$	5.81586	−	4.40288i	0.530913	−	0.401926i
$121$		0			0
$122$	4.48710	+	1.42548i	0.406243	+	0.129057i
$123$	−14.9411	+	4.85466i	−1.34719	+	0.437730i
$124$	−5.82391	−	17.1551i	−0.523002	−	1.54057i
$125$	−7.11781	−	9.79682i	−0.636636	−	0.876254i
$126$	−2.57233	−	1.84325i	−0.229162	−	0.164210i
$127$	−0.348311	+	1.07199i	−0.0309076	+	0.0951238i	−0.965320	−	0.261068i	$-0.915925\pi$
$127$	−0.348311	+	1.07199i	−0.0309076	+	0.0951238i	0.934413	+	0.356192i	$0.115925\pi$
$128$	11.3018	−	0.519275i	0.998946	−	0.0458979i
$129$	4.83947	+	3.51608i	0.426092	+	0.309574i
$130$	−0.438882	+	0.00287873i	−0.0384925	+	0.000252481i
$131$		−	10.9554i		−	0.957178i	−0.878039	−	0.478589i	$-0.841148\pi$
$131$		−	10.9554i		−	0.957178i	0.878039	−	0.478589i	$-0.158852\pi$
$132$		0			0
$133$			5.14534i			0.446157i
$134$	−0.0535097	−	8.15791i	−0.00462253	−	0.704736i
$135$	8.79771	+	6.39191i	0.757186	+	0.550128i
$136$	−4.44488	+	14.6551i	−0.381145	+	1.25666i
$137$	−3.14435	+	9.67732i	−0.268640	+	0.826789i	0.722192	+	0.691692i	$0.243135\pi$
$137$	−3.14435	+	9.67732i	−0.268640	+	0.826789i	−0.990832	+	0.135097i	$0.956865\pi$
$138$	4.88571	−	6.81820i	0.415899	−	0.580404i
$139$	10.7769	+	14.8331i	0.914083	+	1.25813i	0.965753	+	0.259463i	$0.0835454\pi$
$139$	10.7769	+	14.8331i	0.914083	+	1.25813i	−0.0516706	+	0.998664i	$0.516455\pi$
$140$	−6.72700	+	2.28372i	−0.568535	+	0.193010i
$141$	−7.99588	+	2.59802i	−0.673375	+	0.218793i
$142$	4.12306	−	12.9785i	0.345999	−	1.08913i
$143$		0			0
$144$	1.62469	+	4.58717i	0.135391	+	0.382264i
$145$	−4.98273	−	15.3353i	−0.413793	−	1.27352i
$146$	−0.776488	+	0.571970i	−0.0642626	+	0.0473366i
$147$	2.83915	+	3.90776i	0.234170	+	0.322307i
$148$	0.720497	+	0.964805i	0.0592245	+	0.0793065i
$149$	8.05442	+	2.61704i	0.659844	+	0.214396i	0.619750	−	0.784800i	$-0.287234\pi$
$149$	8.05442	+	2.61704i	0.659844	+	0.214396i	0.0400944	+	0.999196i	$0.487234\pi$
$150$	−2.27712	+	0.756429i	−0.185926	+	0.0617622i
$151$	−8.14723	−	5.91931i	−0.663012	−	0.481707i	0.204666	−	0.978832i	$-0.434389\pi$
$151$	−8.14723	−	5.91931i	−0.663012	−	0.481707i	−0.867679	+	0.497125i	$0.834389\pi$
$152$	4.52392	−	6.49151i	0.366938	−	0.526531i
$153$	−6.58717			−0.532541
$154$		0			0
$155$		−	17.4934i		−	1.40510i
$156$	−0.127267	+	0.409909i	−0.0101895	+	0.0328190i
$157$	−5.13706	+	7.07056i	−0.409982	+	0.564292i	−0.963214	−	0.268735i	$-0.913394\pi$
$157$	−5.13706	+	7.07056i	−0.409982	+	0.564292i	0.553232	+	0.833027i	$0.313394\pi$
$158$	−2.57630	−	7.75556i	−0.204959	−	0.616999i
$159$	−4.83697	+	14.8867i	−0.383597	+	1.18059i
$160$	10.4949	+	3.03335i	0.829694	+	0.239807i
$161$	−6.60887	+	4.80163i	−0.520852	+	0.378421i
$162$	4.40667	−	3.24601i	0.346221	−	0.255030i
$163$	23.2283	−	7.54735i	1.81938	−	0.591154i	0.819549	−	0.573009i	$-0.194224\pi$
$163$	23.2283	−	7.54735i	1.81938	−	0.591154i	0.999835	−	0.0181445i	$-0.00577589\pi$
$164$	−19.2142	−	13.5784i	−1.50037	−	1.06030i
$165$		0			0
$166$	−3.94107	−	1.25201i	−0.305887	−	0.0971751i
$167$	2.27586	+	7.00438i	0.176112	+	0.542016i	0.999682	−	0.0251977i	$-0.00802153\pi$
$167$	2.27586	+	7.00438i	0.176112	+	0.542016i	−0.823571	+	0.567213i	$0.808022\pi$
$168$	0.136698	+	6.94605i	0.0105465	+	0.535900i
$169$	−10.4963	+	7.62603i	−0.807410	+	0.586618i
$170$	−8.61316	+	12.0200i	−0.660600	+	0.921893i
$171$	3.23679	+	1.05170i	0.247523	+	0.0804253i
$172$	0.117520	+	8.95794i	0.00896079	+	0.683037i
$173$	0.812921	−	1.11889i	0.0618052	−	0.0850676i	−0.776996	−	0.629506i	$-0.783257\pi$
$173$	0.812921	−	1.11889i	0.0618052	−	0.0850676i	0.838801	+	0.544439i	$0.183257\pi$
$174$	−15.7685	+	0.103429i	−1.19541	+	0.00784095i
$175$	2.33684			0.176648
$176$		0			0
$177$	12.8617			0.966741
$178$	8.12044	−	0.0532639i	0.608653	−	0.00399230i
$179$	−5.81718	+	8.00667i	−0.434797	+	0.598446i	−0.969046	−	0.246881i	$-0.920594\pi$
$179$	−5.81718	+	8.00667i	−0.434797	+	0.598446i	0.534249	+	0.845327i	$0.320594\pi$
$180$	0.0616406	+	4.69856i	0.00459442	+	0.350210i
$181$	−11.1086	−	3.60942i	−0.825699	−	0.268286i	−0.134467	−	0.990918i	$-0.542932\pi$
$181$	−11.1086	−	3.60942i	−0.825699	−	0.268286i	−0.691233	+	0.722632i	$0.742932\pi$
$182$	0.243475	−	0.339779i	0.0180476	−	0.0251861i
$183$	3.59676	−	2.61320i	0.265880	−	0.193173i
$184$	12.5597	−	0.247174i	0.925911	−	0.0182219i
$185$	0.359299	+	1.10581i	0.0264162	+	0.0813007i
$186$	−16.3046	−	5.17970i	−1.19551	−	0.379794i
$187$		0			0
$188$	−10.2827	−	7.26663i	−0.749940	−	0.529974i
$189$	−9.85021	+	3.20053i	−0.716498	+	0.232804i
$190$	6.15142	−	4.53121i	0.446271	−	0.328728i
$191$	−9.78115	+	7.10642i	−0.707739	+	0.514203i	−0.882443	−	0.470418i	$-0.844103\pi$
$191$	−9.78115	+	7.10642i	−0.707739	+	0.514203i	0.174704	+	0.984621i	$0.444103\pi$
$192$	5.93470	−	8.88353i	0.428300	−	0.641114i
$193$	4.09819	−	12.6129i	0.294994	−	0.907900i	−0.688229	−	0.725494i	$-0.741612\pi$
$193$	4.09819	−	12.6129i	0.294994	−	0.907900i	0.983223	−	0.182406i	$-0.0583885\pi$
$194$	−2.39779	−	7.21821i	−0.172152	−	0.518237i
$195$	−0.243604	+	0.335293i	−0.0174449	+	0.0240108i
$196$	−2.14497	+	6.90863i	−0.153212	+	0.493474i
$197$		−	11.6835i		−	0.832415i	−0.909270	−	0.416208i	$-0.863359\pi$
$197$		−	11.6835i		−	0.832415i	0.909270	−	0.416208i	$-0.136641\pi$
$198$		0			0
$199$	−24.9329			−1.76745			−0.883725	−	0.468007i	$-0.844972\pi$
$199$	−24.9329			−1.76745			−0.883725	+	0.468007i	$0.844972\pi$
$200$	−2.94822	−	2.05461i	−0.208471	−	0.145283i
$201$	−6.23240	−	4.52811i	−0.439600	−	0.319388i
$202$	12.5066	−	4.15454i	0.879963	−	0.292312i
$203$	14.6056	+	4.74564i	1.02511	+	0.333078i
$204$	8.65287	+	11.5869i	0.605822	+	0.811246i
$205$	−13.3535	−	18.3795i	−0.932649	−	1.28368i
$206$	−1.91133	+	1.40791i	−0.133169	+	0.0980937i
$207$	1.66973	+	5.13890i	0.116054	+	0.357178i
$208$	−0.605919	+	0.214606i	−0.0420129	+	0.0148802i
$209$		0			0
$210$	−2.03111	+	6.39350i	−0.140160	+	0.441194i
$211$	5.67063	−	1.84250i	0.390382	−	0.126843i	−0.107248	−	0.994232i	$-0.534204\pi$
$211$	5.67063	−	1.84250i	0.390382	−	0.126843i	0.497630	+	0.867390i	$0.334204\pi$
$212$	−22.1978	+	7.53585i	−1.52455	+	0.517564i
$213$	−7.55844	−	10.4033i	−0.517895	−	0.712822i
$214$	−9.28906	+	12.9633i	−0.634987	+	0.886150i
$215$	−2.67315	+	8.22711i	−0.182307	+	0.561084i
$216$	15.2413	+	4.62269i	1.03704	+	0.314534i
$217$	13.4790	+	9.79310i	0.915017	+	0.664799i
$218$	0.182155	+	27.7708i	0.0123371	+	1.88088i
$219$			0.910690i			0.0615387i
$220$		0			0
$221$		−	0.870099i		−	0.0585292i
$222$	1.13705	−	0.00745818i	0.0763137	−	0.000500560i
$223$	−0.839768	−	0.610127i	−0.0562350	−	0.0408571i	0.559313	−	0.828957i	$-0.311065\pi$
$223$	−0.839768	−	0.610127i	−0.0562350	−	0.0408571i	−0.615548	+	0.788100i	$0.711065\pi$
$224$	−8.21248	+	6.38842i	−0.548719	+	0.426844i
$225$	0.477645	−	1.47004i	0.0318430	−	0.0980026i
$226$	14.8471	+	10.6390i	0.987614	+	0.707693i
$227$	3.91237	+	5.38491i	0.259673	+	0.357409i	0.918870	−	0.394562i	$-0.129104\pi$
$227$	3.91237	+	5.38491i	0.259673	+	0.357409i	−0.659197	+	0.751971i	$0.729104\pi$
$228$	−2.40188	−	7.07505i	−0.159068	−	0.468557i
$229$	−15.5864	+	5.06432i	−1.02998	+	0.334660i	−0.774781	−	0.632230i	$-0.782140\pi$
$229$	−15.5864	+	5.06432i	−1.02998	+	0.334660i	−0.255196	+	0.966889i	$0.582140\pi$
$230$	11.5606	+	3.67260i	0.762281	+	0.242164i
$231$		0			0
$232$	−14.2543	−	18.8288i	−0.935842	−	1.23617i
$233$	4.96721	+	15.2875i	0.325413	+	1.00152i	0.971254	+	0.238046i	$0.0765070\pi$
$233$	4.96721	+	15.2875i	0.325413	+	1.00152i	−0.645841	+	0.763472i	$0.723493\pi$
$234$	−0.163980	−	0.222614i	−0.0107197	−	0.0145527i
$235$	−7.14627	−	9.83599i	−0.466171	−	0.641629i
$236$	11.5254	+	15.4335i	0.750239	+	1.00463i
$237$	−7.33937	−	2.38471i	−0.476743	−	0.154903i
$238$	−4.43989	−	13.3656i	−0.287795	−	0.866366i
$239$	−2.03922	−	1.48158i	−0.131906	−	0.0958356i	0.519876	−	0.854242i	$-0.325978\pi$
$239$	−2.03922	−	1.48158i	−0.131906	−	0.0958356i	−0.651782	+	0.758406i	$0.725978\pi$
$240$	8.18385	−	6.28042i	0.528265	−	0.405400i
$241$	−6.11179			−0.393695			−0.196848	−	0.980434i	$-0.563070\pi$
$241$	−6.11179			−0.393695			−0.196848	+	0.980434i	$0.563070\pi$
$242$		0			0
$243$			11.7248i			0.752144i
$244$	6.35880	+	1.97426i	0.407081	+	0.126389i
$245$	−4.10572	+	5.65104i	−0.262305	+	0.361032i
$246$	−21.0844	+	7.00397i	−1.34429	+	0.446557i
$247$	−0.138919	+	0.427547i	−0.00883918	+	0.0272042i
$248$	−8.39520	−	24.2064i	−0.533096	−	1.53711i
$249$	−3.15908	+	2.29520i	−0.200198	+	0.145453i
$250$	−10.1568	−	13.7885i	−0.642370	−	0.872060i
$251$	−0.465437	+	0.151230i	−0.0293782	+	0.00954554i	−0.323669	−	0.946170i	$-0.604916\pi$
$251$	−0.465437	+	0.151230i	−0.0293782	+	0.00954554i	0.294291	+	0.955716i	$0.404916\pi$
$252$	−3.65485	−	2.58284i	−0.230234	−	0.162703i
$253$		0			0
$254$	−0.482632	+	1.51922i	−0.0302830	+	0.0953245i
$255$	4.31503	+	13.2803i	0.270218	+	0.831645i
$256$	15.9780	−	0.839185i	0.998624	−	0.0524491i
$257$	−8.16186	+	5.92994i	−0.509123	+	0.369900i	−0.812491	−	0.582974i	$-0.801889\pi$
$257$	−8.16186	+	5.92994i	−0.509123	+	0.369900i	0.303368	+	0.952874i	$0.401889\pi$
$258$	6.87652	+	4.92749i	0.428113	+	0.306772i
$259$	−1.05319	−	0.342203i	−0.0654422	−	0.0212635i
$260$	−0.620632	+	0.00814210i	−0.0384900	+	0.000504952i
$261$	5.97070	−	8.21796i	0.369577	−	0.508679i
$262$	−0.101622	−	15.4929i	−0.00627822	−	0.957157i
$263$	−3.98466			−0.245705			−0.122852	−	0.992425i	$-0.539204\pi$
$263$	−3.98466			−0.245705			−0.122852	+	0.992425i	$0.539204\pi$
$264$		0			0
$265$	−22.6356			−1.39049
$266$	0.0477280	+	7.27645i	0.00292639	+	0.446148i
$267$	4.50731	−	6.20378i	0.275843	−	0.379665i
$268$	−0.151345	−	11.5363i	−0.00924486	−	0.704690i
$269$	−2.56851	−	0.834559i	−0.156605	−	0.0508840i	0.229666	−	0.973270i	$-0.426237\pi$
$269$	−2.56851	−	0.834559i	−0.156605	−	0.0508840i	−0.386270	+	0.922386i	$0.626237\pi$
$270$	12.5009	+	8.95772i	0.760778	+	0.545150i
$271$	18.0905	−	13.1435i	1.09892	−	0.798413i	0.118037	−	0.993009i	$-0.462340\pi$
$271$	18.0905	−	13.1435i	1.09892	−	0.798413i	0.980883	+	0.194596i	$0.0623397\pi$
$272$	−6.14994	+	20.7662i	−0.372895	+	1.25913i
$273$	−0.121977	−	0.375405i	−0.00738235	−	0.0227205i
$274$	−4.35692	+	13.7147i	−0.263211	+	0.828534i
$275$		0			0
$276$	6.84604	−	9.68751i	0.412083	−	0.583119i
$277$	29.9455	−	9.72988i	1.79925	−	0.584612i	0.799381	−	0.600824i	$-0.205161\pi$
$277$	29.9455	−	9.72988i	1.79925	−	0.584612i	0.999869	+	0.0162128i	$0.00516091\pi$
$278$	15.3781	+	20.8767i	0.922315	+	1.25210i
$279$	8.91566	−	6.47761i	0.533767	−	0.387804i
$280$	−9.49203	+	3.29200i	−0.567257	+	0.196735i
$281$	2.95754	−	9.10236i	0.176432	−	0.543001i	−0.823264	−	0.567658i	$-0.807849\pi$
$281$	2.95754	−	9.10236i	0.176432	−	0.543001i	0.999696	+	0.0246572i	$0.00784941\pi$
$282$	−11.2835	+	3.74825i	−0.671925	+	0.223205i
$283$	9.63949	−	13.2676i	0.573008	−	0.788678i	−0.419899	−	0.907571i	$-0.637934\pi$
$283$	9.63949	−	13.2676i	0.573008	−	0.788678i	0.992907	+	0.118893i	$0.0379345\pi$
$284$	5.71037	−	18.3922i	0.338848	−	1.09138i
$285$		−	7.21458i		−	0.427355i
$286$		0			0
$287$	21.6373			1.27721
$288$	2.34017	+	6.47203i	0.137896	+	0.381368i
$289$	−9.96380	−	7.23913i	−0.586106	−	0.425831i
$290$	−7.18874	−	21.6406i	−0.422137	−	1.27078i
$291$	−6.83086	−	2.21948i	−0.400432	−	0.130108i
$292$	−1.09279	+	0.816073i	−0.0639507	+	0.0477571i
$293$	−5.88297	−	8.09722i	−0.343687	−	0.473044i	0.601827	−	0.798627i	$-0.294440\pi$
$293$	−5.88297	−	8.09722i	−0.343687	−	0.473044i	−0.945514	+	0.325582i	$0.894440\pi$
$294$	4.05133	+	5.49995i	0.236279	+	0.320764i
$295$	5.74751	+	17.6890i	0.334633	+	1.02989i
$296$	1.02786	+	1.35773i	0.0597434	+	0.0789164i
$297$		0			0
$298$	11.4147	+	3.62626i	0.661236	+	0.210064i
$299$	−0.678797	+	0.220555i	−0.0392559	+	0.0127550i
$300$	−3.21325	+	1.09085i	−0.185517	+	0.0629804i
$301$	−4.84269	−	6.66540i	−0.279128	−	0.384187i
$302$	−11.5766	−	8.29542i	−0.666158	−	0.477348i
$303$	3.84558	−	11.8355i	0.220923	−	0.679930i
$304$	6.33743	−	9.22214i	0.363477	−	0.528926i
$305$	5.20130	+	3.77897i	0.297826	+	0.216383i
$306$	−9.31546	+	0.0611023i	−0.532530	+	0.00349299i
$307$		−	18.8436i		−	1.07546i	−0.843117	−	0.537731i	$-0.819282\pi$
$307$		−	18.8436i		−	1.07546i	0.843117	−	0.537731i	$-0.180718\pi$
$308$		0			0
$309$			2.24167i			0.127524i
$310$	−0.162268	−	24.7389i	−0.00921621	−	1.40507i
$311$	1.29169	+	0.938466i	0.0732449	+	0.0532155i	0.623805	−	0.781580i	$-0.285586\pi$
$311$	1.29169	+	0.938466i	0.0732449	+	0.0532155i	−0.550560	+	0.834795i	$0.685586\pi$
$312$	−0.176177	+	0.580867i	−0.00997407	+	0.0328851i
$313$	1.21795	−	3.74846i	0.0688424	−	0.211875i	−0.910717	−	0.413032i	$-0.864470\pi$
$313$	1.21795	−	3.74846i	0.0688424	−	0.211875i	0.979559	+	0.201156i	$0.0644699\pi$
$314$	−7.19916	+	10.0467i	−0.406272	+	0.566969i
$315$	−2.54006	−	3.49609i	−0.143116	−	0.196982i
$316$	−3.71529	−	10.9439i	−0.209002	−	0.615642i
$317$	1.84870	−	0.600679i	0.103833	−	0.0337375i	−0.256640	−	0.966507i	$-0.582615\pi$
$317$	1.84870	−	0.600679i	0.103833	−	0.0337375i	0.360473	+	0.932770i	$0.382615\pi$
$318$	−6.70228	+	21.0974i	−0.375845	+	1.18308i
$319$		0			0
$320$	14.8698	+	4.19236i	0.831249	+	0.234360i
$321$	4.65364	+	14.3224i	0.259741	+	0.799401i
$322$	−9.30162	+	6.85168i	−0.518359	+	0.381829i
$323$	8.90291	+	12.2538i	0.495371	+	0.681820i
$324$	6.20173	−	4.63133i	0.344541	−	0.257296i
$325$	0.194177	+	0.0630920i	0.0107710	+	0.00349972i
$326$	32.7791	−	10.8888i	1.81547	−	0.603075i
$327$	21.2161	+	15.4144i	1.17325	+	0.852417i
$328$	−27.2983	−	19.0241i	−1.50730	−	1.05043i
$329$	11.5795			0.638396
$330$		0			0
$331$		−	7.52148i		−	0.413418i	−0.978402	−	0.206709i	$-0.933725\pi$
$331$		−	7.52148i		−	0.413418i	0.978402	−	0.206709i	$-0.0662753\pi$
$332$	−5.58501	−	1.73402i	−0.306517	−	0.0951667i
$333$	−0.430541	+	0.592589i	−0.0235935	+	0.0324737i
$334$	3.28346	+	9.88437i	0.179663	+	0.540849i
$335$	3.44255	−	10.5951i	0.188087	−	0.578872i
$336$	0.257748	+	9.82172i	0.0140613	+	0.535819i
$337$	−6.85426	+	4.97991i	−0.373375	+	0.271273i	−0.758609	−	0.651546i	$-0.774121\pi$
$337$	−6.85426	+	4.97991i	−0.373375	+	0.271273i	0.385234	+	0.922819i	$0.374121\pi$
$338$	−14.7730	+	10.8820i	−0.803545	+	0.591901i
$339$	16.4038	−	5.32992i	0.890932	−	0.289481i
$340$	−12.0691	+	17.0784i	−0.654539	+	0.926206i
$341$		0			0
$342$	4.58717	+	1.45727i	0.248046	+	0.0788000i
$343$	−6.03442	−	18.5720i	−0.325828	−	1.00280i
$344$	0.249288	+	12.6671i	0.0134407	+	0.682963i
$345$	9.26669	−	6.73264i	0.498902	−	0.362473i
$346$	1.13924	−	1.58986i	0.0612459	−	0.0854712i
$347$	16.4045	+	5.33015i	0.880640	+	0.286137i	0.714223	−	0.699918i	$-0.246780\pi$
$347$	16.4045	+	5.33015i	0.880640	+	0.286137i	0.166417	+	0.986055i	$0.446780\pi$
$348$	−22.2986	+	0.292536i	−1.19533	+	0.0156816i
$349$	−2.74841	+	3.78287i	−0.147119	+	0.202492i	−0.876216	−	0.481918i	$-0.839940\pi$
$349$	−2.74841	+	3.78287i	−0.147119	+	0.202492i	0.729097	+	0.684410i	$0.239940\pi$
$350$	3.30471	−	0.0216764i	0.176644	−	0.00115865i
$351$	−0.904906			−0.0483003
$352$		0			0
$353$	−5.45055			−0.290104			−0.145052	−	0.989424i	$-0.546335\pi$
$353$	−5.45055			−0.290104			−0.145052	+	0.989424i	$0.546335\pi$
$354$	18.1887	−	0.119304i	0.966720	−	0.00634095i
$355$	10.9303	−	15.0443i	0.580120	−	0.798467i
$356$	11.4833	−	0.150650i	0.608614	−	0.00798443i
$357$	−12.6484	−	4.10971i	−0.669424	−	0.217509i
$358$	−8.15229	+	11.3769i	−0.430862	+	0.601285i
$359$	−22.6668	+	16.4684i	−1.19631	+	0.869167i	−0.993916	−	0.110138i	$-0.964871\pi$
$359$	−22.6668	+	16.4684i	−1.19631	+	0.869167i	−0.202389	+	0.979305i	$0.564871\pi$
$360$	0.130755	+	6.64405i	0.00689138	+	0.350172i
$361$	3.45305	+	10.6274i	0.181740	+	0.559337i
$362$	−15.7431	−	5.00134i	−0.827441	−	0.262864i
$363$		0			0
$364$	0.341167	−	0.482769i	0.0178820	−	0.0253040i
$365$	−1.25250	+	0.406962i	−0.0655588	+	0.0213013i
$366$	5.06224	−	3.72891i	0.264607	−	0.194913i
$367$	23.3315	−	16.9513i	1.21789	−	0.884851i	0.221969	−	0.975054i	$-0.428752\pi$
$367$	23.3315	−	16.9513i	1.21789	−	0.884851i	0.995923	+	0.0902031i	$0.0287516\pi$
$368$	17.7594	−	0.466052i	0.925771	−	0.0242946i
$369$	4.42263	−	13.6115i	0.230233	−	0.708584i
$370$	0.518372	+	1.56048i	0.0269489	+	0.0811257i
$371$	12.6718	−	17.4412i	0.657886	−	0.905503i
$372$	−23.1057	−	7.17381i	−1.19798	−	0.371945i
$373$		−	1.34080i		−	0.0694239i	−0.999397	−	0.0347119i	$-0.988949\pi$
$373$		−	1.34080i		−	0.0694239i	0.999397	−	0.0347119i	$-0.0110514\pi$
$374$		0			0
$375$	−16.1716			−0.835096
$376$	−14.6090	−	10.1810i	−0.753400	−	0.525043i
$377$	1.08551	+	0.788669i	0.0559066	+	0.0406185i
$378$	−13.9003	+	4.61750i	−0.714955	+	0.237499i
$379$	−8.29554	−	2.69538i	−0.426113	−	0.138453i	0.0881065	−	0.996111i	$-0.471918\pi$
$379$	−8.29554	−	2.69538i	−0.426113	−	0.138453i	−0.514220	+	0.857658i	$0.671918\pi$
$380$	8.65720	−	6.46502i	0.444105	−	0.331648i
$381$	0.884766	+	1.21778i	0.0453279	+	0.0623885i
$382$	−13.7664	+	10.1405i	−0.704351	+	0.518834i
$383$	2.39882	+	7.38281i	0.122574	+	0.377244i	0.993451	−	0.114256i	$-0.0364486\pi$
$383$	2.39882	+	7.38281i	0.122574	+	0.377244i	−0.870877	+	0.491501i	$0.836449\pi$
$384$	8.31034	−	12.6180i	0.424085	−	0.643909i
$385$		0			0
$386$	5.67860	−	17.8750i	0.289033	−	0.909815i
$387$	−5.18285	+	1.68401i	−0.263459	+	0.0856031i
$388$	−3.45788	−	10.1856i	−0.175547	−	0.517097i
$389$	22.6849	+	31.2230i	1.15017	+	1.58307i	0.742357	+	0.670005i	$0.233708\pi$
$389$	22.6849	+	31.2230i	1.15017	+	1.58307i	0.407811	+	0.913066i	$0.366292\pi$
$390$	−0.341391	+	0.476425i	−0.0172870	+	0.0241247i
$391$	−7.43107	+	22.8705i	−0.375805	+	1.15661i
$392$	−2.96930	+	9.78996i	−0.149972	+	0.494468i
$393$	−11.8362	−	8.59947i	−0.597055	−	0.433786i
$394$	−0.108376	−	16.5226i	−0.00545989	−	0.832397i
$395$		−	11.1597i		−	0.561506i
$396$		0			0
$397$			20.4200i			1.02485i	0.858732	+	0.512426i	$0.171253\pi$
$397$			20.4200i			1.02485i	−0.858732	+	0.512426i	$0.828747\pi$
$398$	−35.2597	+	0.231277i	−1.76741	+	0.0115929i
$399$	5.55899	+	4.03884i	0.278298	+	0.202195i
$400$	−4.18838	−	2.87825i	−0.209419	−	0.143912i
$401$	1.53349	−	4.71959i	0.0765788	−	0.235685i	−0.905438	−	0.424478i	$-0.860458\pi$
$401$	1.53349	−	4.71959i	0.0765788	−	0.235685i	0.982017	+	0.188793i	$0.0604575\pi$
$402$	−8.85576	−	6.34576i	−0.441685	−	0.316498i
$403$	0.855627	+	1.17767i	0.0426218	+	0.0586639i
$404$	17.6481	−	5.99128i	0.878026	−	0.298078i
$405$	7.10810	−	2.30956i	0.353204	−	0.114763i
$406$	20.6990	+	6.57572i	1.02727	+	0.326347i
$407$		0			0
$408$	12.3442	+	16.3057i	0.611130	+	0.807255i
$409$	−4.74087	−	14.5909i	−0.234421	−	0.721473i	−0.997198	−	0.0748112i	$-0.976165\pi$
$409$	−4.74087	−	14.5909i	−0.234421	−	0.721473i	0.762777	−	0.646662i	$-0.223835\pi$
$410$	−19.0548	−	25.8681i	−0.941049	−	1.27754i
$411$	7.98716	+	10.9934i	0.393977	+	0.542263i
$412$	−2.68991	+	2.00877i	−0.132522	+	0.0989650i
$413$	−16.8473	−	5.47403i	−0.829003	−	0.269359i
$414$	2.40897	+	7.25186i	0.118395	+	0.356410i
$415$	−4.56836	−	3.31911i	−0.224252	−	0.162929i
$416$	−0.854890	+	0.309112i	−0.0419144	+	0.0151555i
$417$	24.4849			1.19903
$418$		0			0
$419$			12.0628i			0.589306i	0.955604	+	0.294653i	$0.0952041\pi$
$419$			12.0628i			0.589306i	−0.955604	+	0.294653i	$0.904796\pi$
$420$	−2.81306	+	9.06043i	−0.137263	+	0.442104i
$421$	8.40779	−	11.5723i	0.409771	−	0.564001i	−0.553392	−	0.832921i	$-0.686667\pi$
$421$	8.40779	−	11.5723i	0.409771	−	0.564001i	0.963162	+	0.268920i	$0.0866668\pi$
$422$	8.00221	−	2.65823i	0.389542	−	0.129401i
$423$	2.36682	−	7.28431i	0.115079	−	0.354175i
$424$	−31.3219	+	10.8630i	−1.52113	+	0.527553i
$425$	5.56526	−	4.04340i	0.269955	−	0.196133i
$426$	−10.7855	−	14.6421i	−0.522560	−	0.709410i
$427$	−5.82355	+	1.89219i	−0.281821	+	0.0915693i
$428$	−13.0162	+	18.4186i	−0.629161	+	0.890296i
$429$		0			0
$430$	−3.70401	+	11.6594i	−0.178623	+	0.562268i
$431$	5.85649	+	18.0244i	0.282097	+	0.868205i	0.987254	+	0.159154i	$0.0508766\pi$
$431$	5.85649	+	18.0244i	0.282097	+	0.868205i	−0.705157	+	0.709051i	$0.749123\pi$
$432$	21.5969	+	6.39596i	1.03908	+	0.307726i
$433$	13.2784	−	9.64733i	0.638120	−	0.463621i	−0.221084	−	0.975255i	$-0.570959\pi$
$433$	13.2784	−	9.64733i	0.638120	−	0.463621i	0.859204	+	0.511634i	$0.170959\pi$
$434$	19.1527	+	13.7242i	0.919358	+	0.658783i
$435$	−20.4793	−	6.65414i	−0.981909	−	0.319041i
$436$	0.515202	+	39.2713i	0.0246737	+	1.88075i
$437$	7.30293	−	10.0516i	0.349347	−	0.480834i
$438$	0.00844753	+	1.28788i	0.000403639	+	0.0615374i
$439$	24.5482			1.17162			0.585810	−	0.810448i	$-0.300776\pi$
$439$	24.5482			1.17162			0.585810	+	0.810448i	$0.300776\pi$
$440$		0			0
$441$	−4.40040			−0.209543
$442$	−0.00807100	−	1.23048i	−0.000383899	−	0.0585279i
$443$	−6.50558	+	8.95416i	−0.309089	+	0.425425i	−0.935097	−	0.354392i	$-0.884688\pi$
$443$	−6.50558	+	8.95416i	−0.309089	+	0.425425i	0.626008	+	0.779817i	$0.284688\pi$
$444$	1.60793	−	0.0210945i	0.0763088	−	0.00100110i
$445$	10.5464	+	3.42674i	0.499949	+	0.162443i
$446$	−1.19325	−	0.855042i	−0.0565018	−	0.0404874i
$447$	9.14978	−	6.64770i	0.432770	−	0.314426i
$448$	−11.5547	+	9.11058i	−0.545908	+	0.430434i
$449$	8.23984	+	25.3596i	0.388862	+	1.19679i	0.933639	+	0.358214i	$0.116614\pi$
$449$	8.23984	+	25.3596i	0.388862	+	1.19679i	−0.544777	+	0.838581i	$0.683386\pi$
$450$	0.661841	−	2.08333i	0.0311995	−	0.0982093i
$451$		0			0
$452$	21.0952	+	14.9077i	0.992234	+	0.701200i
$453$	−12.7904	+	4.15585i	−0.600945	+	0.195259i
$454$	5.58275	+	7.57896i	0.262012	+	0.355698i
$455$	0.461798	−	0.335516i	0.0216494	−	0.0157292i
$456$	−3.46233	−	9.98314i	−0.162138	−	0.467503i
$457$	−1.01449	+	3.12228i	−0.0474558	+	0.146054i	−0.971977	−	0.235078i	$-0.924466\pi$
$457$	−1.01449	+	3.12228i	−0.0474558	+	0.146054i	0.924521	+	0.381132i	$0.124466\pi$
$458$	−21.9950	+	7.30645i	−1.02776	+	0.341408i
$459$	−17.9208	+	24.6659i	−0.836471	+	1.15130i
$460$	16.3828	+	5.08649i	0.763853	+	0.237159i
$461$		−	3.17514i		−	0.147881i	−0.997263	−	0.0739406i	$-0.976442\pi$
$461$		−	3.17514i		−	0.147881i	0.997263	−	0.0739406i	$-0.0235575\pi$
$462$		0			0
$463$	21.8696			1.01637			0.508184	−	0.861248i	$-0.330317\pi$
$463$	21.8696			1.01637			0.508184	+	0.861248i	$0.330317\pi$
$464$	−20.3329	−	26.4952i	−0.943930	−	1.23001i
$465$	−18.8998	−	13.7315i	−0.876456	−	0.636782i
$466$	7.16636	+	21.5733i	0.331975	+	0.999362i
$467$	4.71472	+	1.53190i	0.218171	+	0.0708881i	0.416063	−	0.909336i	$-0.363410\pi$
$467$	4.71472	+	1.53190i	0.218171	+	0.0708881i	−0.197892	+	0.980224i	$0.563410\pi$
$468$	−0.233963	−	0.313296i	−0.0108149	−	0.0144821i
$469$	6.23655	+	8.58387i	0.287977	+	0.396366i
$470$	−10.1974	−	13.8436i	−0.470370	−	0.638558i
$471$	3.60664	+	11.1001i	0.166185	+	0.511466i
$472$	16.4422	+	21.7188i	0.756812	+	0.999690i
$473$		0			0
$474$	−10.4013	−	3.30433i	−0.477749	−	0.151773i
$475$	−3.38021	+	1.09830i	−0.155095	+	0.0503933i
$476$	−6.40280	−	18.8603i	−0.293472	−	0.864460i
$477$	−8.38170	−	11.5364i	−0.383772	−	0.528217i
$478$	−2.89758	−	2.07631i	−0.132532	−	0.0949683i
$479$	10.9832	−	33.8027i	0.501834	−	1.54449i	−0.304196	−	0.952610i	$-0.598388\pi$
$479$	10.9832	−	33.8027i	0.501834	−	1.54449i	0.806029	−	0.591876i	$-0.201612\pi$
$480$	11.5152	−	8.95758i	0.525595	−	0.408856i
$481$	−0.0782750	−	0.0568701i	−0.00356903	−	0.00259305i
$482$	−8.64320	+	0.0566928i	−0.393687	+	0.00258229i
$483$			10.9092i			0.496387i
$484$		0			0
$485$		−	10.3865i		−	0.471627i
$486$	0.108758	+	16.5810i	0.00493338	+	0.752128i
$487$	−8.21531	−	5.96877i	−0.372271	−	0.270471i	0.385881	−	0.922549i	$-0.373898\pi$
$487$	−8.21531	−	5.96877i	−0.372271	−	0.270471i	−0.758152	+	0.652078i	$0.773898\pi$
$488$	9.01083	+	2.73299i	0.407901	+	0.123716i
$489$	10.0790	−	31.0201i	0.455790	−	1.40278i
$490$	−5.75382	+	8.02969i	−0.259931	+	0.362744i
$491$	0.216048	+	0.297365i	0.00975013	+	0.0134199i	0.813864	−	0.581055i	$-0.197360\pi$
$491$	0.216048	+	0.297365i	0.00975013	+	0.0134199i	−0.804114	+	0.594475i	$0.797360\pi$
$492$	−29.7523	+	10.1005i	−1.34134	+	0.455364i
$493$	42.9950	−	13.9699i	1.93640	−	0.629173i
$494$	−0.192490	+	0.605919i	−0.00866055	+	0.0272616i
$495$		0			0
$496$	−12.0969	−	34.1544i	−0.543166	−	1.53358i
$497$	5.47297	+	16.8441i	0.245496	+	0.755560i
$498$	−4.44622	+	3.27514i	−0.199240	+	0.146763i
$499$	−18.3285	−	25.2271i	−0.820498	−	1.12932i	−0.989618	−	0.143723i	$-0.954093\pi$
$499$	−18.3285	−	25.2271i	−0.820498	−	1.12932i	0.169120	−	0.985595i	$-0.445907\pi$
$500$	−14.4914	−	19.4052i	−0.648076	−	0.867828i
$501$	9.35394	+	3.03928i	0.417903	+	0.135785i
$502$	−0.656811	+	0.218184i	−0.0293149	+	0.00973803i
$503$	16.3425	+	11.8735i	0.728675	+	0.529413i	0.889144	−	0.457628i	$-0.151301\pi$
$503$	16.3425	+	11.8735i	0.728675	+	0.529413i	−0.160469	+	0.987041i	$0.551301\pi$
$504$	−5.19259	−	3.61870i	−0.231296	−	0.161190i
$505$	17.9962			0.800818
$506$		0			0
$507$			17.3262i			0.769486i
$508$	−0.668438	+	2.15294i	−0.0296571	+	0.0955211i
$509$	12.9435	−	17.8153i	0.573712	−	0.789647i	−0.419276	−	0.907859i	$-0.637716\pi$
$509$	12.9435	−	17.8153i	0.573712	−	0.789647i	0.992988	+	0.118211i	$0.0377160\pi$
$510$	6.22543	+	18.7408i	0.275667	+	0.829855i
$511$	0.387597	−	1.19290i	0.0171463	−	0.0527709i
$512$	22.5880	−	1.33497i	0.998258	−	0.0589980i
$513$	12.7440	−	9.25906i	0.562661	−	0.408797i
$514$	−11.4874	+	8.46173i	−0.506686	+	0.373231i
$515$	−3.08304	+	1.00174i	−0.135855	+	0.0441419i
$516$	9.77036	+	6.90459i	0.430116	+	0.303958i
$517$		0			0
$518$	−1.49258	−	0.474168i	−0.0655802	−	0.0208338i
$519$	−0.570738	−	1.75655i	−0.0250526	−	0.0771040i
$520$	−0.877612	+	0.0172714i	−0.0384858	+	0.000757400i
$521$	−29.2152	+	21.2261i	−1.27994	+	0.929931i	−0.999551	−	0.0299549i	$-0.990464\pi$
$521$	−29.2152	+	21.2261i	−1.27994	+	0.929931i	−0.280390	+	0.959886i	$0.590464\pi$
$522$	8.36743	−	11.6771i	0.366232	−	0.511092i
$523$	−32.8484	−	10.6731i	−1.43636	−	0.466702i	−0.515599	−	0.856830i	$-0.672431\pi$
$523$	−32.8484	−	10.6731i	−1.43636	−	0.466702i	−0.920760	+	0.390128i	$0.872431\pi$
$524$	−0.287424	−	21.9089i	−0.0125562	−	0.957095i
$525$	1.83430	−	2.52470i	0.0800556	−	0.110187i
$526$	−5.63504	+	0.0369616i	−0.245699	+	0.00161160i
$527$	49.0457			2.13646
$528$		0			0
$529$	−3.27421			−0.142357
$530$	−32.0109	+	0.209967i	−1.39046	+	0.00912038i
$531$	−6.88712	+	9.47931i	−0.298876	+	0.411367i
$532$	0.134992	+	10.2898i	0.00585265	+	0.446119i
$533$	1.79794	+	0.584185i	0.0778773	+	0.0253039i
$534$	6.31662	−	8.81509i	0.273347	−	0.381466i
$535$	−17.6185	+	12.8006i	−0.761714	+	0.553417i
$536$	−0.321040	−	16.3130i	−0.0138668	−	0.704615i
$537$	4.08415	+	12.5697i	0.176244	+	0.542423i
$538$	−3.64008	−	1.15639i	−0.156935	−	0.0498557i
$539$		0			0
$540$	17.7616	+	12.5519i	0.764338	+	0.540148i
$541$	−5.84449	+	1.89899i	−0.251274	+	0.0816440i	−0.431946	−	0.901899i	$-0.642173\pi$
$541$	−5.84449	+	1.89899i	−0.251274	+	0.0816440i	0.180672	+	0.983543i	$0.442173\pi$
$542$	25.4614	−	18.7552i	1.09366	−	0.805603i
$543$	−12.6194	+	9.16850i	−0.541548	+	0.393458i
$544$	−8.50451	+	29.4242i	−0.364628	+	1.26155i
$545$	−11.7190	+	36.0673i	−0.501986	+	1.54496i
$546$	−0.175979	−	0.529760i	−0.00753122	−	0.0226716i
$547$	10.1881	−	14.0228i	0.435613	−	0.599571i	−0.533617	−	0.845726i	$-0.679168\pi$
$547$	10.1881	−	14.0228i	0.435613	−	0.599571i	0.969230	+	0.246156i	$0.0791675\pi$
$548$	−6.03427	+	19.4355i	−0.257771	+	0.830242i
$549$			4.05020i			0.172858i
$550$		0			0
$551$	−23.3572			−0.995050
$552$	9.59170	−	13.7634i	0.408250	−	0.585810i
$553$	8.59880	+	6.24739i	0.365658	+	0.265666i
$554$	42.2581	−	14.0376i	1.79538	−	0.596401i
$555$	1.47674	+	0.479823i	0.0626843	+	0.0203674i
$556$	21.9411	+	29.3809i	0.930508	+	1.24603i
$557$	22.4316	+	30.8745i	0.950458	+	1.30819i	0.951323	+	0.308194i	$0.0997246\pi$
$557$	22.4316	+	30.8745i	0.950458	+	1.30819i	−0.000865126		1.00000i	$0.500275\pi$
$558$	12.5483	−	9.24322i	0.531212	−	0.391297i
$559$	−0.222441	−	0.684603i	−0.00940825	−	0.0289556i
$560$	−13.3929	+	4.74354i	−0.565954	+	0.200451i
$561$		0			0
$562$	4.09806	−	12.8998i	0.172866	−	0.544147i
$563$	31.5875	−	10.2634i	1.33126	−	0.432551i	0.444910	−	0.895575i	$-0.353236\pi$
$563$	31.5875	−	10.2634i	1.33126	−	0.432551i	0.886346	+	0.463024i	$0.153236\pi$
$564$	−15.9222	+	5.40537i	−0.670447	+	0.227607i
$565$	14.6608	+	20.1788i	0.616784	+	0.848930i
$566$	13.5089	−	18.8523i	0.567823	−	0.792419i
$567$	−2.19967	+	6.76988i	−0.0923773	+	0.284308i
$568$	7.90491	−	26.0630i	0.331683	−	1.09358i
$569$	6.66229	+	4.84044i	0.279298	+	0.202922i	0.718611	−	0.695412i	$-0.244778\pi$
$569$	6.66229	+	4.84044i	0.279298	+	0.202922i	−0.439313	+	0.898334i	$0.644778\pi$
$570$	−0.0669222	−	10.2027i	−0.00280306	−	0.427346i
$571$			32.7618i			1.37104i	0.728055	+	0.685518i	$0.240424\pi$
$571$			32.7618i			1.37104i	−0.728055	+	0.685518i	$0.759576\pi$
$572$		0			0
$573$			16.1457i			0.674496i
$574$	30.5992	−	0.200707i	1.27718	−	0.00837736i
$575$	−4.56510	−	3.31674i	−0.190378	−	0.138318i
$576$	3.36946	+	9.13092i	0.140394	+	0.380455i
$577$	−2.01113	+	6.18961i	−0.0837243	+	0.257677i	−0.984151	−	0.177330i	$-0.943254\pi$
$577$	−2.01113	+	6.18961i	−0.0837243	+	0.257677i	0.900427	+	0.435007i	$0.143254\pi$
$578$	−14.1578	−	10.1450i	−0.588887	−	0.421978i
$579$	−10.4101	−	14.3282i	−0.432628	−	0.595461i
$580$	−10.3669	−	30.5371i	−0.430463	−	1.26799i
$581$	5.11490	−	1.66193i	0.212202	−	0.0689485i
$582$	−9.68067	−	3.07539i	−0.401277	−	0.127479i
$583$		0			0
$584$	−1.53784	+	1.16421i	−0.0636361	+	0.0481755i
$585$	−0.116673	−	0.359083i	−0.00482384	−	0.0148463i
$586$	−8.39471	−	11.3964i	−0.346782	−	0.470780i
$587$	5.85038	+	8.05235i	0.241471	+	0.332356i	0.912501	−	0.409074i	$-0.134148\pi$
$587$	5.85038	+	8.05235i	0.241471	+	0.332356i	−0.671031	+	0.741430i	$0.734148\pi$
$588$	5.78034	+	7.74036i	0.238377	+	0.319207i
$589$	−24.1000	−	7.83056i	−0.993022	−	0.322652i
$590$	8.29211	+	24.9622i	0.341381	+	1.02768i
$591$	−12.6228	−	9.17099i	−0.519232	−	0.377244i
$592$	1.46618	+	1.91054i	0.0602597	+	0.0785228i
$593$	−8.80877			−0.361733			−0.180867	−	0.983508i	$-0.557890\pi$
$593$	−8.80877			−0.361733			−0.180867	+	0.983508i	$0.557890\pi$
$594$		0			0
$595$		−	19.2322i		−	0.788444i
$596$	16.1761	+	5.02232i	0.662600	+	0.205722i
$597$	−19.5712	+	26.9374i	−0.800995	+	1.10247i
$598$	−0.957898	+	0.318201i	−0.0391714	+	0.0130122i
$599$	9.86213	−	30.3525i	0.402956	−	1.24017i	−0.519635	−	0.854388i	$-0.673932\pi$
$599$	9.86213	−	30.3525i	0.402956	−	1.24017i	0.922590	−	0.385781i	$-0.126068\pi$
$600$	−4.53400	+	1.57247i	−0.185100	+	0.0641958i
$601$	8.92461	−	6.48411i	0.364042	−	0.264492i	−0.390694	−	0.920521i	$-0.627765\pi$
$601$	8.92461	−	6.48411i	0.364042	−	0.264492i	0.754736	+	0.656028i	$0.227765\pi$
$602$	−6.91028	−	9.38117i	−0.281642	−	0.382348i
$603$	6.67462	−	2.16871i	0.271811	−	0.0883169i
$604$	−16.4484	−	11.6239i	−0.669274	−	0.472968i
$605$		0			0
$606$	5.32857	−	16.7732i	0.216458	−	0.681364i
$607$	−3.77492	−	11.6180i	−0.153219	−	0.471560i	0.844757	−	0.535150i	$-0.179745\pi$
$607$	−3.77492	−	11.6180i	−0.153219	−	0.471560i	−0.997976	+	0.0635899i	$0.979745\pi$
$608$	8.87675	−	13.1006i	0.360000	−	0.531299i
$609$	16.5918	−	12.0547i	0.672335	−	0.488480i
$610$	7.39065	+	5.29590i	0.299238	+	0.214425i
$611$	0.962185	+	0.312633i	0.0389258	+	0.0126478i
$612$	−13.1732	+	0.172820i	−0.532495	+	0.00698583i
$613$	−2.10123	+	2.89209i	−0.0848678	+	0.116810i	−0.849340	−	0.527846i	$-0.823000\pi$
$613$	−2.10123	+	2.89209i	−0.0848678	+	0.116810i	0.764472	+	0.644657i	$0.223000\pi$
$614$	−0.174793	−	26.6483i	−0.00705406	−	1.07544i
$615$	−30.3390			−1.22339
$616$		0			0
$617$	30.5057			1.22811			0.614057	−	0.789262i	$-0.289537\pi$
$617$	30.5057			1.22811			0.614057	+	0.789262i	$0.289537\pi$
$618$	0.0207937	+	3.17013i	0.000836443	+	0.127521i
$619$	6.23749	−	8.58517i	0.250706	−	0.345067i	−0.665053	−	0.746797i	$-0.731591\pi$
$619$	6.23749	−	8.58517i	0.250706	−	0.345067i	0.915758	+	0.401730i	$0.131591\pi$
$620$	−0.458954	−	34.9838i	−0.0184320	−	1.40498i
$621$	23.7854	+	7.72834i	0.954475	+	0.310128i
$622$	1.83539	+	1.31518i	0.0735923	+	0.0527339i
$623$	−8.54445	+	6.20791i	−0.342326	+	0.248715i
$624$	−0.243759	+	0.823087i	−0.00975816	+	0.0329498i
$625$	−5.26358	−	16.1996i	−0.210543	−	0.647986i
$626$	1.68763	−	5.31230i	0.0674513	−	0.212322i
$627$		0			0
$628$	−10.0877	+	14.2747i	−0.402545	+	0.569622i
$629$	−3.10032	+	1.00736i	−0.123618	+	0.0401659i
$630$	−3.62453	−	4.92055i	−0.144405	−	0.196039i
$631$	−3.47259	+	2.52298i	−0.138241	+	0.100438i	−0.654757	−	0.755840i	$-0.727229\pi$
$631$	−3.47259	+	2.52298i	−0.138241	+	0.100438i	0.516515	+	0.856278i	$0.327229\pi$
$632$	−5.35562	−	15.4422i	−0.213035	−	0.614257i
$633$	2.46055	−	7.57279i	0.0977980	−	0.300991i
$634$	2.60883	−	0.866618i	0.103610	−	0.0344178i
$635$	−1.27947	+	1.76103i	−0.0507741	+	0.0698845i
$636$	−9.28255	+	29.8977i	−0.368077	+	1.18552i
$637$		−	0.581249i		−	0.0230299i
$638$		0			0
$639$	11.7148			0.463431
$640$	21.0676	+	5.79084i	0.832768	+	0.228903i
$641$	21.4880	+	15.6119i	0.848724	+	0.616634i	0.924794	−	0.380469i	$-0.124237\pi$
$641$	21.4880	+	15.6119i	0.848724	+	0.616634i	−0.0760700	+	0.997102i	$0.524237\pi$
$642$	6.71396	+	20.2114i	0.264979	+	0.797680i
$643$	−26.6880	−	8.67146i	−1.05247	−	0.341969i	−0.268834	−	0.963187i	$-0.586638\pi$
$643$	−26.6880	−	8.67146i	−1.05247	−	0.341969i	−0.783638	+	0.621218i	$0.786638\pi$
$644$	−13.0906	+	9.77582i	−0.515843	+	0.385221i
$645$	6.79023	+	9.34595i	0.267365	+	0.367996i
$646$	12.7040	+	17.2465i	0.499832	+	0.678556i
$647$	−9.98071	−	30.7175i	−0.392382	−	1.20763i	−0.930981	−	0.365066i	$-0.881046\pi$
$647$	−9.98071	−	30.7175i	−0.392382	−	1.20763i	0.538599	−	0.842562i	$-0.318954\pi$
$648$	8.72742	−	6.60707i	0.342846	−	0.259550i
$649$		0			0
$650$	0.275188	+	0.0874225i	0.0107937	+	0.00342899i
$651$	21.1608	−	6.87557i	0.829358	−	0.269475i
$652$	46.2547	−	15.7028i	1.81147	−	0.614969i
$653$	−19.3499	−	26.6329i	−0.757220	−	1.04222i	−0.997440	−	0.0715057i	$-0.977220\pi$
$653$	−19.3499	−	26.6329i	−0.757220	−	1.04222i	0.240220	−	0.970718i	$-0.422780\pi$
$654$	30.1464	+	21.6020i	1.17882	+	0.844703i
$655$	6.53786	−	20.1215i	0.255455	−	0.786211i
$656$	−38.7813	−	26.6504i	−1.51415	−	1.04052i
$657$	−0.671198	−	0.487654i	−0.0261859	−	0.0190252i
$658$	16.3755	−	0.107411i	0.638382	−	0.00418730i
$659$			3.99602i			0.155663i	0.996967	+	0.0778314i	$0.0247996\pi$
$659$			3.99602i			0.155663i	−0.996967	+	0.0778314i	$0.975200\pi$
$660$		0			0
$661$		−	19.2377i		−	0.748258i	−0.927377	−	0.374129i	$-0.877942\pi$
$661$		−	19.2377i		−	0.748258i	0.927377	−	0.374129i	$-0.122058\pi$
$662$	−0.0697690	−	10.6367i	−0.00271165	−	0.413409i
$663$	−0.940050	−	0.682986i	−0.0365085	−	0.0265250i
$664$	−7.91432	−	2.40041i	−0.307135	−	0.0931542i
$665$	−3.07059	+	9.45029i	−0.119072	+	0.366467i
$666$	−0.603367	+	0.842023i	−0.0233800	+	0.0326277i
$667$	−21.7969	−	30.0009i	−0.843981	−	1.16164i
$668$	4.73510	+	13.9479i	0.183206	+	0.539659i
$669$	−1.31836	+	0.428360i	−0.0509706	+	0.0165613i
$670$	4.77012	−	15.0153i	0.184286	−	0.580093i
$671$		0			0
$672$	0.455608	+	13.8873i	0.0175755	+	0.535715i
$673$	−1.67241	−	5.14714i	−0.0644666	−	0.198408i	0.913635	−	0.406535i	$-0.133263\pi$
$673$	−1.67241	−	5.14714i	−0.0644666	−	0.198408i	−0.978102	+	0.208127i	$0.933263\pi$
$674$	−9.64699	+	7.10609i	−0.371588	+	0.273716i
$675$	−4.20515	−	5.78789i	−0.161856	−	0.222776i
$676$	−20.7908	+	15.5261i	−0.799645	+	0.597159i
$677$	39.0944	+	12.7025i	1.50252	+	0.488198i	0.940751	−	0.339098i	$-0.110122\pi$
$677$	39.0944	+	12.7025i	1.50252	+	0.488198i	0.561767	+	0.827296i	$0.310122\pi$
$678$	23.1485	−	7.68964i	0.889014	−	0.295319i
$679$	8.00303	+	5.81454i	0.307128	+	0.223142i
$680$	−16.9095	+	24.2639i	−0.648449	+	0.930480i
$681$	8.88885			0.340621
$682$		0			0
$683$			35.8592i			1.37211i	0.727548	+	0.686057i	$0.240660\pi$
$683$			35.8592i			1.37211i	−0.727548	+	0.686057i	$0.759340\pi$
$684$	6.50061	+	2.01829i	0.248557	+	0.0771713i
$685$	−11.5503	+	15.8976i	−0.441314	+	0.607416i
$686$	−8.70605	−	26.2083i	−0.332399	−	1.00064i
$687$	−6.76310	+	20.8147i	−0.258028	+	0.794130i
$688$	0.470038	+	17.9113i	0.0179200	+	0.682861i
$689$	1.52385	−	1.10714i	0.0580539	−	0.0421786i
$690$	13.0423	−	9.60715i	0.496514	−	0.365738i
$691$	−42.9366	+	13.9509i	−1.63338	+	0.530719i	−0.975046	−	0.222004i	$-0.928740\pi$
$691$	−42.9366	+	13.9509i	−1.63338	+	0.530719i	−0.658338	+	0.752722i	$0.728740\pi$
$692$	1.59635	−	2.25891i	0.0606840	−	0.0858710i
$693$		0			0
$694$	23.2484	+	7.38564i	0.882498	+	0.280355i
$695$	10.9416	+	33.6748i	0.415039	+	1.27736i
$696$	−31.5315	+	0.620540i	−1.19520	+	0.0235215i
$697$	51.5301	−	37.4388i	1.95184	−	1.41810i
$698$	−3.85167	+	5.37516i	−0.145788	+	0.203453i
$699$	20.4156	+	6.63342i	0.772188	+	0.250899i
$700$	4.67327	−	0.0613088i	0.176633	−	0.00231725i
$701$	10.9250	−	15.0369i	0.412631	−	0.567937i	−0.551227	−	0.834355i	$-0.685840\pi$
$701$	10.9250	−	15.0369i	0.412631	−	0.567937i	0.963858	+	0.266418i	$0.0858401\pi$
$702$	−1.27970	+	0.00839387i	−0.0482993	+	0.000316806i
$703$	1.68426			0.0635232
$704$		0			0
$705$	−16.2362			−0.611492
$706$	−7.70808	+	0.0505591i	−0.290097	+	0.00190282i
$707$	−10.0746	+	13.8664i	−0.378892	+	0.521501i
$708$	25.7211	−	0.337436i	0.966658	−	0.0126816i
$709$	25.9356	+	8.42699i	0.974032	+	0.316482i	0.752443	−	0.658658i	$-0.228876\pi$
$709$	25.9356	+	8.42699i	0.974032	+	0.316482i	0.221589	+	0.975140i	$0.428876\pi$
$710$	15.3179	−	21.3768i	0.574871	−	0.802255i
$711$	5.68764	−	4.13231i	0.213303	−	0.154974i
$712$	16.2381	−	0.319565i	0.608548	−	0.0119762i
$713$	−12.4322	−	38.2624i	−0.465590	−	1.43294i
$714$	−17.9253	−	5.69456i	−0.670836	−	0.213114i
$715$		0			0
$716$	−11.4233	+	16.1646i	−0.426909	+	0.604099i
$717$	−3.20139	+	1.04019i	−0.119558	+	0.0388467i
$718$	−31.9022	+	23.4995i	−1.19058	+	0.876995i
$719$	−27.6522	+	20.0905i	−1.03125	+	0.749249i	−0.968559	−	0.248784i	$-0.919969\pi$
$719$	−27.6522	+	20.0905i	−1.03125	+	0.749249i	−0.0626934	+	0.998033i	$0.519969\pi$
$720$	0.246541	+	9.39469i	0.00918804	+	0.350119i
$721$	0.954074	−	2.93634i	0.0355316	−	0.109355i
$722$	4.98183	+	14.9971i	0.185404	+	0.558133i
$723$	−4.79747	+	6.60315i	−0.178420	+	0.245574i
$724$	−22.3101	−	6.92677i	−0.829148	−	0.257431i
$725$			10.6080i			0.393973i
$726$		0			0
$727$	−25.0380			−0.928608			−0.464304	−	0.885676i	$-0.653696\pi$
$727$	−25.0380			−0.928608			−0.464304	+	0.885676i	$0.653696\pi$
$728$	0.477994	−	0.685888i	0.0177156	−	0.0254207i
$729$	22.0603	+	16.0277i	0.817048	+	0.593620i
$730$	−1.76749	+	0.587136i	−0.0654177	+	0.0217309i
$731$	−23.0661	−	7.49463i	−0.853130	−	0.277199i
$732$	7.12434	−	5.32031i	0.263323	−	0.196644i
$733$	−10.1507	−	13.9713i	−0.374926	−	0.516041i	0.579306	−	0.815110i	$-0.303324\pi$
$733$	−10.1507	−	13.9713i	−0.374926	−	0.516041i	−0.954231	+	0.299069i	$0.903324\pi$
$734$	32.8377	−	24.1887i	1.21206	−	0.892820i
$735$	2.88256	+	8.87160i	0.106325	+	0.327234i
$736$	25.1107	−	0.823818i	0.925592	−	0.0303663i
$737$		0			0
$738$	6.12815	−	19.2901i	0.225580	−	0.710079i
$739$	−16.4235	+	5.33633i	−0.604149	+	0.196300i	−0.595090	−	0.803659i	$-0.702884\pi$
$739$	−16.4235	+	5.33633i	−0.604149	+	0.196300i	−0.00905903	+	0.999959i	$0.502884\pi$
$740$	0.747549	+	2.20200i	0.0274804	+	0.0809472i
$741$	0.352875	+	0.485691i	0.0129632	+	0.0178423i
$742$	17.7584	−	24.7826i	0.651933	−	0.909799i
$743$	−10.7035	+	32.9421i	−0.392675	+	1.20853i	0.538083	+	0.842892i	$0.319149\pi$
$743$	−10.7035	+	32.9421i	−0.392675	+	1.20853i	−0.930758	+	0.365636i	$0.880851\pi$
$744$	−32.7423	−	9.93075i	−1.20039	−	0.364079i
$745$	13.2316	+	9.61329i	0.484767	+	0.352204i
$746$	−0.0124372	−	1.89613i	−0.000455358	−	0.0694224i
$747$		−	3.55734i		−	0.130156i
$748$		0			0
$749$		−	20.7414i		−	0.757875i
$750$	−22.8696	+	0.150007i	−0.835078	+	0.00547748i
$751$	−41.7069	−	30.3019i	−1.52191	−	1.10573i	−0.960532	−	0.278170i	$-0.910272\pi$
$751$	−41.7069	−	30.3019i	−1.52191	−	1.10573i	−0.561376	−	0.827561i	$-0.689728\pi$
$752$	−20.7542	−	14.2622i	−0.756828	−	0.520090i
$753$	−0.201958	+	0.621564i	−0.00735978	+	0.0226511i
$754$	1.54243	+	1.10525i	0.0561718	+	0.0402510i
$755$	−11.4313	−	15.7339i	−0.416028	−	0.572614i
$756$	−19.6148	+	6.65893i	−0.713382	+	0.242183i
$757$	31.0091	−	10.0755i	1.12704	−	0.366199i	0.314592	−	0.949227i	$-0.398132\pi$
$757$	31.0091	−	10.0755i	1.12704	−	0.366199i	0.812452	+	0.583028i	$0.198132\pi$
$758$	−11.7564	−	3.73482i	−0.427012	−	0.135655i
$759$		0			0
$760$	12.1829	−	9.22302i	0.441920	−	0.334554i
$761$	0.862449	+	2.65435i	0.0312638	+	0.0962200i	0.965471	−	0.260511i	$-0.0838912\pi$
$761$	0.862449	+	2.65435i	0.0312638	+	0.0962200i	−0.934207	+	0.356731i	$0.883891\pi$
$762$	1.26252	+	1.71395i	0.0457362	+	0.0620899i
$763$	−21.2302	−	29.2208i	−0.768584	−	1.05787i
$764$	−19.3742	+	14.4682i	−0.700933	+	0.523442i
$765$	−12.0985	−	3.93103i	−0.437421	−	0.142127i
$766$	3.46085	+	10.4184i	0.125046	+	0.376432i
$767$	−1.25212	−	0.909719i	−0.0452115	−	0.0328481i
$768$	11.6353	−	17.9212i	0.419853	−	0.646677i
$769$	−23.1604			−0.835187			−0.417593	−	0.908634i	$-0.637126\pi$
$769$	−23.1604			−0.835187			−0.417593	+	0.908634i	$0.637126\pi$
$770$		0			0
$771$			13.4728i			0.485209i
$772$	7.86477	−	25.3312i	0.283059	−	0.911691i
$773$	12.2208	−	16.8205i	0.439552	−	0.604992i	−0.530560	−	0.847647i	$-0.678018\pi$
$773$	12.2208	−	16.8205i	0.439552	−	0.604992i	0.970113	+	0.242656i	$0.0780185\pi$
$774$	−7.31388	+	2.42958i	−0.262892	+	0.0873293i
$775$	−3.55637	+	10.9454i	−0.127749	+	0.393170i
$776$	−4.98455	−	14.3723i	−0.178935	−	0.515934i
$777$	−1.19642	+	0.869250i	−0.0429213	+	0.0311842i
$778$	32.3702	+	43.9447i	1.16053	+	1.57549i
$779$	−31.2982	+	10.1694i	−1.12137	+	0.364356i
$780$	−0.478370	+	0.676919i	−0.0171284	+	0.0242376i
$781$		0			0
$782$	−10.2968	+	32.4120i	−0.368211	+	1.15905i
$783$	−14.5288	−	44.7149i	−0.519216	−	1.59798i
$784$	−4.10832	+	13.8723i	−0.146726	+	0.495441i
$785$	−13.6546	+	9.92065i	−0.487353	+	0.354083i
$786$	−16.8183	−	12.0514i	−0.599887	−	0.429860i
$787$	38.4107	+	12.4804i	1.36919	+	0.444878i	0.899101	−	0.437740i	$-0.144221\pi$
$787$	38.4107	+	12.4804i	1.36919	+	0.444878i	0.470091	+	0.882618i	$0.344221\pi$
$788$	−0.306526	−	23.3650i	−0.0109195	−	0.832343i
$789$	−3.12777	+	4.30501i	−0.111352	+	0.153262i
$790$	−0.103517	−	15.7819i	−0.00368297	−	0.561494i
$791$	−23.7556			−0.844651
$792$		0			0
$793$	−0.534990			−0.0189981
$794$	0.189415	+	28.8776i	0.00672210	+	1.02483i
$795$	−17.7679	+	24.4554i	−0.630161	+	0.867342i
$796$	−49.8616	+	0.654136i	−1.76730	+	0.0231852i
$797$	29.5959	+	9.61629i	1.04834	+	0.340627i	0.782017	−	0.623257i	$-0.214191\pi$
$797$	29.5959	+	9.61629i	1.04834	+	0.340627i	0.266324	+	0.963884i	$0.414191\pi$
$798$	7.89890	+	5.66010i	0.279618	+	0.200365i
$799$	27.5769	−	20.0358i	0.975600	−	0.708815i
$800$	−5.94984	−	4.03152i	−0.210359	−	0.142536i
$801$	2.15875	+	6.64396i	0.0762758	+	0.234753i
$802$	2.12486	−	6.68859i	0.0750313	−	0.236182i
$803$		0			0
$804$	−12.5825	−	8.89192i	−0.443752	−	0.313594i
$805$	−15.0038	+	4.87503i	−0.528814	+	0.171822i
$806$	1.22094	+	1.65750i	0.0430057	+	0.0583831i
$807$	−2.91781	+	2.11991i	−0.102712	+	0.0746245i
$808$	24.9021	−	8.63648i	0.876052	−	0.303830i
$809$	−7.30059	+	22.4689i	−0.256675	+	0.789965i	0.736820	+	0.676089i	$0.236327\pi$
$809$	−7.30059	+	22.4689i	−0.256675	+	0.789965i	−0.993495	+	0.113876i	$0.963673\pi$
$810$	10.0307	−	3.33208i	0.352444	−	0.117077i
$811$	15.4575	−	21.2754i	0.542785	−	0.747080i	−0.446226	−	0.894920i	$-0.647232\pi$
$811$	15.4575	−	21.2754i	0.542785	−	0.747080i	0.989011	+	0.147840i	$0.0472322\pi$
$812$	29.3331	+	9.10727i	1.02939	+	0.319602i
$813$		−	29.8619i		−	1.04730i
$814$		0			0
$815$	47.1669			1.65218
$816$	17.6082	+	22.9448i	0.616411	+	0.803229i
$817$	10.1376	+	7.36539i	0.354669	+	0.257682i
$818$	−6.83980	−	20.5902i	−0.239148	−	0.719920i
$819$	0.341997	+	0.111122i	0.0119503	+	0.00388290i
$820$	−27.1869	−	36.4055i	−0.949408	−	1.27134i
$821$	32.6964	+	45.0027i	1.14111	+	1.57060i	0.765001	+	0.644029i	$0.222738\pi$
$821$	32.6964	+	45.0027i	1.14111	+	1.57060i	0.376110	+	0.926575i	$0.377262\pi$
$822$	11.3973	+	15.4726i	0.397526	+	0.539668i
$823$	8.68247	+	26.7219i	0.302652	+	0.931467i	0.980543	+	0.196304i	$0.0628941\pi$
$823$	8.68247	+	26.7219i	0.302652	+	0.931467i	−0.677891	+	0.735162i	$0.737106\pi$
$824$	−3.78539	+	2.86572i	−0.131870	+	0.0998321i
$825$		0			0
$826$	−23.8760	−	7.58500i	−0.830752	−	0.263916i
$827$	36.6684	−	11.9143i	1.27509	−	0.414301i	0.408239	−	0.912875i	$-0.366143\pi$
$827$	36.6684	−	11.9143i	1.27509	−	0.414301i	0.866847	+	0.498574i	$0.166143\pi$
$828$	3.47400	+	10.2331i	0.120730	+	0.355625i
$829$	26.1318	+	35.9674i	0.907595	+	1.24920i	0.967981	+	0.251023i	$0.0807669\pi$
$829$	26.1318	+	35.9674i	0.907595	+	1.24920i	−0.0603858	+	0.998175i	$0.519233\pi$
$830$	−6.49129	−	4.65146i	−0.225316	−	0.161454i
$831$	12.9937	−	39.9904i	0.450746	−	1.38725i
$832$	−1.20610	+	0.445071i	−0.0418141	+	0.0154301i
$833$	−15.8437	−	11.5111i	−0.548950	−	0.398835i
$834$	34.6262	−	0.227121i	1.19901	−	0.00786457i
$835$			14.2229i			0.492204i
$836$		0			0
$837$		−	51.0077i		−	1.76308i
$838$	0.111894	+	17.0590i	0.00386531	+	0.589293i
$839$	32.1892	+	23.3868i	1.11129	+	0.807403i	0.982867	−	0.184316i	$-0.0590070\pi$
$839$	32.1892	+	23.3868i	1.11129	+	0.807403i	0.128428	+	0.991719i	$0.459007\pi$
$840$	−3.89413	+	12.8392i	−0.134360	+	0.442994i
$841$	−12.5813	+	38.7212i	−0.433837	+	1.33521i
$842$	11.7828	−	16.4434i	0.406063	−	0.566677i
$843$	−7.51261	−	10.3402i	−0.258748	−	0.356136i
$844$	11.2919	−	3.83345i	0.388685	−	0.131953i
$845$	−23.8293	+	7.74261i	−0.819753	+	0.266354i
$846$	3.27954	−	10.3233i	0.112753	−	0.354923i
$847$		0			0
$848$	−44.1941	+	15.6528i	−1.51763	+	0.537518i
$849$	−6.76772	−	20.8289i	−0.232268	−	0.714846i
$850$	7.83279	−	5.76972i	0.268662	−	0.197900i
$851$	1.57175	+	2.16333i	0.0538791	+	0.0741582i
$852$	−15.3885	−	20.6065i	−0.527202	−	0.705967i
$853$	−3.98990	−	1.29640i	−0.136612	−	0.0443878i	0.239913	−	0.970794i	$-0.422881\pi$
$853$	−3.98990	−	1.29640i	−0.136612	−	0.0443878i	−0.376525	+	0.926407i	$0.622881\pi$
$854$	−8.21802	+	2.72992i	−0.281215	+	0.0934159i
$855$	5.31730	+	3.86324i	0.181848	+	0.132120i
$856$	−18.2364	+	26.1680i	−0.623308	+	0.894403i
$857$	−43.4106			−1.48288			−0.741438	−	0.671021i	$-0.765856\pi$
$857$	−43.4106			−1.48288			−0.741438	+	0.671021i	$0.765856\pi$
$858$		0			0
$859$		−	31.7672i		−	1.08388i	−0.840416	−	0.541941i	$-0.817690\pi$
$859$		−	31.7672i		−	1.08388i	0.840416	−	0.541941i	$-0.182310\pi$
$860$	−5.12999	+	16.5229i	−0.174931	+	0.563427i
$861$	16.9843	−	23.3769i	0.578823	−	0.796681i
$862$	8.44934	+	25.4355i	0.287786	+	0.866336i
$863$	−15.7898	+	48.5960i	−0.537491	+	1.65423i	0.200713	+	0.979650i	$0.435674\pi$
$863$	−15.7898	+	48.5960i	−0.537491	+	1.65423i	−0.738204	+	0.674577i	$0.764326\pi$
$864$	30.6013	+	8.84472i	1.04108	+	0.300904i
$865$	2.16079	−	1.56991i	0.0734690	−	0.0533784i
$866$	18.6886	−	13.7663i	0.635065	−	0.467797i
$867$	−15.6422	+	5.08247i	−0.531238	+	0.172610i
$868$	27.2127	+	19.2309i	0.923659	+	0.652739i
$869$		0			0
$870$	−29.0232	−	9.22020i	−0.983980	−	0.312594i
$871$	0.286465	+	0.881650i	0.00970651	+	0.0298736i
$872$	1.09287	+	55.5320i	0.0370092	+	1.88055i
$873$	5.29357	−	3.84600i	0.179160	−	0.130167i
$874$	10.2344	−	14.2826i	0.346185	−	0.483115i
$875$	21.1829	+	6.88276i	0.716114	+	0.232680i
$876$	0.0238927	+	1.82122i	0.000807260	+	0.0615334i
$877$	−26.9742	+	37.1267i	−0.910852	+	1.25368i	0.0560223	+	0.998430i	$0.482158\pi$
$877$	−26.9742	+	37.1267i	−0.910852	+	1.25368i	−0.966875	+	0.255251i	$0.917842\pi$
$878$	34.7156	−	0.227708i	1.17159	−	0.00768477i
$879$	−13.3660			−0.450825
$880$		0			0
$881$	−19.3333			−0.651356			−0.325678	−	0.945481i	$-0.605593\pi$
$881$	−19.3333			−0.651356			−0.325678	+	0.945481i	$0.605593\pi$
$882$	−6.22298	+	0.0408180i	−0.209539	+	0.00137441i
$883$	13.2759	−	18.2727i	0.446768	−	0.614924i	−0.524931	−	0.851145i	$-0.675909\pi$
$883$	13.2759	−	18.2727i	0.446768	−	0.614924i	0.971699	+	0.236221i	$0.0759089\pi$
$884$	−0.0228278	−	1.74005i	−0.000767780	−	0.0585241i
$885$	23.6226	+	7.67546i	0.794066	+	0.258008i
$886$	−9.11702	+	12.7232i	−0.306292	+	0.427443i
$887$	−27.6688	+	20.1025i	−0.929026	+	0.674977i	−0.945754	−	0.324883i	$-0.894675\pi$
$887$	−27.6688	+	20.1025i	−0.929026	+	0.674977i	0.0167283	+	0.999860i	$0.494675\pi$
$888$	2.27371	−	0.0447465i	0.0763006	−	0.00150159i
$889$	−0.640648	−	1.97171i	−0.0214867	−	0.0661291i
$890$	14.9464	+	4.74821i	0.501003	+	0.159160i
$891$		0			0
$892$	−1.69540	−	1.19812i	−0.0567662	−	0.0401159i
$893$	−16.7495	+	5.44226i	−0.560502	+	0.182118i
$894$	12.8778	−	9.48594i	0.430698	−	0.317257i
$895$	−15.4624	+	11.2341i	−0.516851	+	0.375514i
$896$	−16.2559	+	12.9912i	−0.543073	+	0.434006i
$897$	−0.294538	+	0.906494i	−0.00983433	+	0.0302669i
$898$	11.8879	+	35.7867i	0.396704	+	1.19422i
$899$	−44.4557	+	61.1880i	−1.48268	+	2.04073i
$900$	0.916639	−	2.95236i	0.0305546	−	0.0984119i
$901$		−	63.4627i		−	2.11425i
$902$		0			0
$903$	−11.0025			−0.366142
$904$	29.9707	+	20.8866i	0.996812	+	0.694676i
$905$	−18.2489	−	13.2586i	−0.606615	−	0.440732i
$906$	−18.0494	+	5.99577i	−0.599651	+	0.199196i
$907$	−16.3872	−	5.32452i	−0.544127	−	0.176798i	0.0240396	−	0.999711i	$-0.492347\pi$
$907$	−16.3872	−	5.32452i	−0.544127	−	0.176798i	−0.568167	+	0.822913i	$0.692347\pi$
$908$	7.96534	+	10.6662i	0.264339	+	0.353972i
$909$	6.66377	+	9.17189i	0.221023	+	0.304213i
$910$	0.649954	−	0.478764i	0.0215458	−	0.0158709i
$911$	−8.69988	−	26.7755i	−0.288240	−	0.887111i	−0.985409	−	0.170204i	$-0.945557\pi$
$911$	−8.69988	−	26.7755i	−0.288240	−	0.887111i	0.697169	−	0.716907i	$-0.254443\pi$
$912$	−4.98897	−	14.0859i	−0.165201	−	0.466430i
$913$		0			0
$914$	−1.40571	+	4.42488i	−0.0464968	+	0.146362i
$915$	8.16555	−	2.65315i	0.269945	−	0.0877104i
$916$	−31.0372	+	10.5367i	−1.02550	+	0.348142i
$917$	11.8440	+	16.3019i	0.391124	+	0.538336i
$918$	−25.1145	+	35.0483i	−0.828902	+	1.15677i
$919$	−0.579296	+	1.78289i	−0.0191092	+	0.0588121i	−0.960156	−	0.279463i	$-0.909843\pi$
$919$	−0.579296	+	1.78289i	−0.0191092	+	0.0588121i	0.941047	+	0.338275i	$0.109843\pi$
$920$	23.2155	+	7.04126i	0.765392	+	0.232144i
$921$	−20.3585	−	14.7913i	−0.670836	−	0.487391i
$922$	−0.0294525	−	4.49024i	−0.000969967	−	0.147878i
$923$			1.54741i			0.0509336i
$924$		0			0
$925$		−	0.764935i		−	0.0251509i
$926$	30.9277	−	0.202862i	1.01635	−	0.00666646i
$927$	−1.65216	−	1.20036i	−0.0542640	−	0.0394251i
$928$	−29.0002	−	37.2805i	−0.951977	−	1.22379i
$929$	7.18636	−	22.1173i	0.235777	−	0.725646i	−0.761241	−	0.648469i	$-0.775409\pi$
$929$	7.18636	−	22.1173i	0.235777	−	0.725646i	0.997017	−	0.0771767i	$-0.0245905\pi$
$930$	−26.8551	−	19.2435i	−0.880614	−	0.631020i
$931$	5.94738	+	8.18587i	0.194917	+	0.268281i
$932$	10.3347	+	30.4421i	0.338523	+	0.997163i
$933$	2.02783	−	0.658881i	0.0663880	−	0.0215708i
$934$	6.68168	+	2.12266i	0.218631	+	0.0694555i
$935$		0			0
$936$	−0.333772	−	0.440887i	−0.0109097	−	0.0144109i
$937$	3.43830	+	10.5820i	0.112325	+	0.345699i	0.991380	−	0.131021i	$-0.0418255\pi$
$937$	3.43830	+	10.5820i	0.112325	+	0.345699i	−0.879055	+	0.476720i	$0.841826\pi$
$938$	8.89925	+	12.0813i	0.290571	+	0.394469i
$939$	−3.09378	−	4.25822i	−0.100962	−	0.138962i
$940$	−14.5494	−	19.4828i	−0.474548	−	0.635459i
$941$	22.4376	+	7.29043i	0.731446	+	0.237661i	0.650979	−	0.759096i	$-0.274359\pi$
$941$	22.4376	+	7.29043i	0.731446	+	0.237661i	0.0804673	+	0.996757i	$0.474359\pi$
$942$	5.20342	+	15.6641i	0.169537	+	0.510365i
$943$	−42.2694	−	30.7105i	−1.37648	−	1.00007i
$944$	23.4537	+	30.5619i	0.763353	+	0.994704i
$945$	−20.0016			−0.650652
$946$		0			0
$947$			23.1038i			0.750772i	0.926869	+	0.375386i	$0.122490\pi$
$947$			23.1038i			0.750772i	−0.926869	+	0.375386i	$0.877510\pi$
$948$	−14.7400	−	4.57645i	−0.478734	−	0.148636i
$949$	0.0644141	−	0.0886585i	0.00209097	−	0.00287798i
$950$	−4.77004	+	1.58455i	−0.154761	+	0.0514095i
$951$	0.802171	−	2.46883i	0.0260122	−	0.0800572i
$952$	−9.22968	−	26.6125i	−0.299136	−	0.862516i
$953$	2.23259	−	1.62207i	0.0723208	−	0.0525441i	−0.551037	−	0.834481i	$-0.685768\pi$
$953$	2.23259	−	1.62207i	0.0723208	−	0.0525441i	0.623358	+	0.781936i	$0.285768\pi$
$954$	−11.9603	−	16.2369i	−0.387228	−	0.525688i
$955$	−22.2057	+	7.21506i	−0.718558	+	0.233474i
$956$	−4.11696	−	2.90941i	−0.133152	−	0.0940970i
$957$		0			0
$958$	15.2187	−	47.9051i	0.491692	−	1.54774i
$959$	−5.78341	−	17.7995i	−0.186756	−	0.574776i
$960$	16.2015	−	12.7745i	0.522902	−	0.412295i
$961$	−41.3033	+	30.0086i	−1.33236	+	0.968019i
$962$	−0.111223	−	0.0796987i	−0.00358596	−	0.00256959i
$963$	−13.0479	−	4.23950i	−0.420461	−	0.136616i
$964$	−12.2225	+	0.160348i	−0.393661	+	0.00516446i
$965$	15.0541	−	20.7202i	0.484608	−	0.667005i
$966$	0.101194	+	15.4277i	0.00325585	+	0.496377i
$967$	−50.7176			−1.63097			−0.815484	−	0.578780i	$-0.803529\pi$
$967$	−50.7176			−1.63097			−0.815484	+	0.578780i	$0.803529\pi$
$968$		0			0
$969$	20.2273			0.649794
$970$	−0.0963448	−	14.6884i	−0.00309345	−	0.471617i
$971$	22.8597	−	31.4637i	0.733604	−	1.00972i	−0.265357	−	0.964150i	$-0.585490\pi$
$971$	22.8597	−	31.4637i	0.733604	−	1.00972i	0.998961	−	0.0455693i	$-0.0145102\pi$
$972$	0.307609	+	23.4475i	0.00986656	+	0.752079i
$973$	−32.0725	−	10.4210i	−1.02820	−	0.334082i
$974$	−11.6733	−	8.36473i	−0.374037	−	0.268023i
$975$	0.220584	−	0.160264i	0.00706435	−	0.00513255i
$976$	12.7683	+	3.78136i	0.408704	+	0.121038i
$977$	−5.28994	−	16.2808i	−0.169240	−	0.520868i	0.830083	−	0.557639i	$-0.188293\pi$
$977$	−5.28994	−	16.2808i	−0.169240	−	0.520868i	−0.999324	+	0.0367712i	$0.988293\pi$
$978$	13.9659	−	43.9616i	0.446579	−	1.40574i
$979$		0			0
$980$	−8.06248	+	11.4088i	−0.257546	+	0.364442i
$981$	−22.7214	+	7.38264i	−0.725440	+	0.235710i
$982$	0.308290	+	0.418525i	0.00983794	+	0.0133557i
$983$	4.68117	−	3.40107i	0.149306	−	0.108477i	−0.510624	−	0.859804i	$-0.670586\pi$
$983$	4.68117	−	3.40107i	0.149306	−	0.108477i	0.659931	+	0.751327i	$0.270586\pi$
$984$	−41.9814	+	14.5599i	−1.33832	+	0.464152i
$985$	6.97237	−	21.4588i	0.222158	−	0.683733i
$986$	60.6732	−	20.1548i	1.93223	−	0.641861i
$987$	9.08932	−	12.5104i	0.289316	−	0.398210i
$988$	−0.266596	+	0.858666i	−0.00848155	+	0.0273178i
$989$			19.8945i			0.632608i
$990$		0			0
$991$	−4.97362			−0.157992			−0.0789961	−	0.996875i	$-0.525171\pi$
$991$	−4.97362			−0.157992			−0.0789961	+	0.996875i	$0.525171\pi$
$992$	−17.4240	−	48.1884i	−0.553214	−	1.52998i
$993$	−8.12616	−	5.90400i	−0.257876	−	0.187358i
$994$	7.89603	+	23.7698i	0.250447	+	0.753934i
$995$	−45.7936	−	14.8792i	−1.45176	−	0.471704i
$996$	−6.25740	+	4.67289i	−0.198273	+	0.148066i
$997$	−13.1312	−	18.0736i	−0.415870	−	0.572396i	0.548768	−	0.835975i	$-0.315097\pi$
$997$	−13.1312	−	18.0736i	−0.415870	−	0.572396i	−0.964638	+	0.263579i	$0.915097\pi$
$998$	−26.1539	−	35.5057i	−0.827887	−	1.12391i
$999$	1.04765	+	3.22435i	0.0331463	+	0.102014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.h.269.10		40
8.5	even	2	inner	968.2.o.h.269.3		40
11.2	odd	10		968.2.o.g.493.8		40
11.3	even	5		968.2.c.d.485.7		10
11.4	even	5	inner	968.2.o.h.245.6		40
11.5	even	5	inner	968.2.o.h.565.2		40
11.6	odd	10		968.2.o.g.565.9		40
11.7	odd	10		968.2.o.g.245.5		40
11.8	odd	10		88.2.c.a.45.4	yes	10
11.9	even	5	inner	968.2.o.h.493.3		40
11.10	odd	2		968.2.o.g.269.1		40
33.8	even	10		792.2.f.g.397.7		10
44.3	odd	10		3872.2.c.f.1937.4		10
44.19	even	10		352.2.c.a.177.4		10
88.3	odd	10		3872.2.c.f.1937.7		10
88.5	even	10	inner	968.2.o.h.565.6		40
88.13	odd	10		968.2.o.g.493.1		40
88.19	even	10		352.2.c.a.177.7		10
88.21	odd	2		968.2.o.g.269.8		40
88.29	odd	10		968.2.o.g.245.9		40
88.37	even	10	inner	968.2.o.h.245.2		40
88.53	even	10	inner	968.2.o.h.493.10		40
88.61	odd	10		968.2.o.g.565.5		40
88.69	even	10		968.2.c.d.485.8		10
88.85	odd	10		88.2.c.a.45.3	✓	10
132.107	odd	10		3168.2.f.g.1585.3		10
176.19	even	20		2816.2.a.q.1.4		5
176.85	odd	20		2816.2.a.o.1.4		5
176.107	even	20		2816.2.a.p.1.2		5
176.173	odd	20		2816.2.a.r.1.2		5
264.107	odd	10		3168.2.f.g.1585.8		10
264.173	even	10		792.2.f.g.397.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.3	✓	10	88.85	odd	10
88.2.c.a.45.4	yes	10	11.8	odd	10
352.2.c.a.177.4		10	44.19	even	10
352.2.c.a.177.7		10	88.19	even	10
792.2.f.g.397.7		10	33.8	even	10
792.2.f.g.397.8		10	264.173	even	10
968.2.c.d.485.7		10	11.3	even	5
968.2.c.d.485.8		10	88.69	even	10
968.2.o.g.245.5		40	11.7	odd	10
968.2.o.g.245.9		40	88.29	odd	10
968.2.o.g.269.1		40	11.10	odd	2
968.2.o.g.269.8		40	88.21	odd	2
968.2.o.g.493.1		40	88.13	odd	10
968.2.o.g.493.8		40	11.2	odd	10
968.2.o.g.565.5		40	88.61	odd	10
968.2.o.g.565.9		40	11.6	odd	10
968.2.o.h.245.2		40	88.37	even	10	inner
968.2.o.h.245.6		40	11.4	even	5	inner
968.2.o.h.269.3		40	8.5	even	2	inner
968.2.o.h.269.10		40	1.1	even	1	trivial
968.2.o.h.493.3		40	11.9	even	5	inner
968.2.o.h.493.10		40	88.53	even	10	inner
968.2.o.h.565.2		40	11.5	even	5	inner
968.2.o.h.565.6		40	88.5	even	10	inner
2816.2.a.o.1.4		5	176.85	odd	20
2816.2.a.p.1.2		5	176.107	even	20
2816.2.a.q.1.4		5	176.19	even	20
2816.2.a.r.1.2		5	176.173	odd	20
3168.2.f.g.1585.3		10	132.107	odd	10
3168.2.f.g.1585.8		10	264.107	odd	10
3872.2.c.f.1937.4		10	44.3	odd	10
3872.2.c.f.1937.7		10	88.3	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41418 - 0.00927596i) q^{2} +(0.784953 - 1.08039i) q^{3} +(1.99983 - 0.0262358i) q^{4} +(1.83667 + 0.596771i) q^{5} +(1.10004 - 1.53516i) q^{6} +(-1.48802 + 1.08111i) q^{7} +(2.82788 - 0.0556526i) q^{8} +(0.375949 + 1.15705i) q^{9} +(2.60293 + 0.826906i) q^{10} +(1.54142 - 2.18120i) q^{12} +(-0.152835 + 0.0496591i) q^{13} +(-2.09431 + 1.54270i) q^{14} +(2.08645 - 1.51589i) q^{15} +(3.99862 - 0.104934i) q^{16} +(-1.67315 + 5.14942i) q^{17} +(0.542394 + 1.63280i) q^{18} +(1.64430 - 2.26318i) q^{19} +(3.68868 + 1.14525i) q^{20} +2.45628i q^{21} +4.44137 q^{23} +(2.15962 - 3.09891i) q^{24} +(-1.02786 - 0.746783i) q^{25} +(-0.215676 + 0.0716448i) q^{26} +(5.35542 + 1.74008i) q^{27} +(-2.94743 + 2.20108i) q^{28} +(-4.90770 - 6.75487i) q^{29} +(2.93656 - 2.16310i) q^{30} +(-2.79918 - 8.61500i) q^{31} +(5.65381 - 0.185487i) q^{32} +(-2.31837 + 7.29774i) q^{34} +(-3.37819 + 1.09764i) q^{35} +(0.782190 + 2.30404i) q^{36} +(0.353889 + 0.487087i) q^{37} +(2.30434 - 3.21580i) q^{38} +(-0.0663168 + 0.204102i) q^{39} +(5.22710 + 1.58538i) q^{40} +(-9.51720 - 6.91465i) q^{41} +(0.0227843 + 3.47362i) q^{42} +4.47936i q^{43} +2.34948i q^{45} +(6.28091 - 0.0411980i) q^{46} +(-5.09323 - 3.70045i) q^{47} +(3.02536 - 4.40246i) q^{48} +(-1.11771 + 3.43995i) q^{49} +(-1.46051 - 1.04655i) q^{50} +(4.25006 + 5.84971i) q^{51} +(-0.304341 + 0.103319i) q^{52} +(-11.1474 + 3.62200i) q^{53} +(7.58968 + 2.41112i) q^{54} +(-4.14779 + 3.14007i) q^{56} +(-1.15443 - 3.55298i) q^{57} +(-7.00305 - 9.50710i) q^{58} +(5.66097 + 7.79166i) q^{59} +(4.13277 - 3.08626i) q^{60} +(3.16618 + 1.02875i) q^{61} +(-4.03847 - 12.1572i) q^{62} +(-1.81033 - 1.31528i) q^{63} +(7.99381 - 0.314758i) q^{64} -0.310343 q^{65} -5.76864i q^{67} +(-3.21091 + 10.3418i) q^{68} +(3.48627 - 4.79843i) q^{69} +(-4.76720 + 1.58360i) q^{70} +(2.97557 - 9.15788i) q^{71} +(1.12753 + 3.25108i) q^{72} +(-0.551701 + 0.400834i) q^{73} +(0.504983 + 0.685547i) q^{74} +(-1.61364 + 0.524303i) q^{75} +(3.22893 - 4.56911i) q^{76} +(-0.0918909 + 0.289253i) q^{78} +(-1.78571 - 5.49584i) q^{79} +(7.40678 + 2.19353i) q^{80} +(3.13098 - 2.27479i) q^{81} +(-13.5232 - 9.69030i) q^{82} +(-2.78089 - 0.903567i) q^{83} +(0.0644424 + 4.91213i) q^{84} +(-6.14604 + 8.45931i) q^{85} +(0.0415504 + 6.33463i) q^{86} -11.1502 q^{87} +5.74214 q^{89} +(0.0217937 + 3.32260i) q^{90} +(0.173735 - 0.239126i) q^{91} +(8.88198 - 0.116523i) q^{92} +(-11.5048 - 3.73814i) q^{93} +(-7.23708 - 5.18586i) q^{94} +(4.37063 - 3.17545i) q^{95} +(4.23757 - 6.25395i) q^{96} +(-1.66198 - 5.11506i) q^{97} +(-1.54873 + 4.87509i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100}) \) 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

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