LMFDB - Embedded newform 968.2.o.h.269.3

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			269.3
Character	$\chi$	$=$	968.269
Dual form			968.2.o.h.493.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14955 + 0.823732i) q^{2} +(-0.784953 + 1.08039i) q^{3} +(0.642933 - 1.89384i) q^{4} +(-1.83667 - 0.596771i) q^{5} +(0.0123875 - 1.88856i) q^{6} +(-1.48802 + 1.08111i) q^{7} +(0.820934 + 2.70667i) 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} +(0.820012 - 2.46853i) q^{14} +(2.08645 - 1.51589i) q^{15} +(-3.17328 - 2.43523i) q^{16} +(-1.67315 + 5.14942i) q^{17} +(-1.38527 - 1.02041i) q^{18} +(-1.64430 + 2.26318i) q^{19} +(-2.31105 + 3.09468i) q^{20} -2.45628i q^{21} +4.44137 q^{23} +(-3.56867 - 1.23768i) q^{24} +(-1.02786 - 0.746783i) q^{25} +(-0.134786 + 0.182981i) q^{26} +(-5.35542 - 1.74008i) q^{27} +(1.09076 + 3.51317i) q^{28} +(4.90770 + 6.75487i) q^{29} +(-1.14979 + 3.46127i) 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} +(2.43299 + 0.0319184i) q^{36} +(-0.353889 - 0.487087i) q^{37} +(0.0259490 - 3.95610i) q^{38} +(-0.0663168 + 0.204102i) q^{39} +(0.107476 - 5.46117i) q^{40} +(-9.51720 - 6.91465i) q^{41} +(2.02331 + 2.82361i) q^{42} -4.47936i q^{43} -2.34948i q^{45} +(-5.10558 + 3.65850i) q^{46} +(-5.09323 - 3.70045i) q^{47} +(5.12187 - 1.51685i) q^{48} +(-1.11771 + 3.43995i) q^{49} +(1.79672 + 0.0117851i) q^{50} +(-4.25006 - 5.84971i) q^{51} +(0.00421610 - 0.321373i) 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} +(-11.2059 - 3.72244i) q^{58} +(-5.66097 - 7.79166i) q^{59} +(-1.52942 - 4.92602i) q^{60} +(-3.16618 - 1.02875i) q^{61} +(10.3143 + 7.59760i) q^{62} +(-1.81033 - 1.31528i) q^{63} +(-6.65213 + 4.44400i) q^{64} -0.310343 q^{65} +5.76864i q^{67} +(8.67647 + 6.47941i) q^{68} +(-3.48627 + 4.79843i) q^{69} +(-2.97924 + 4.04451i) q^{70} +(2.97557 - 9.15788i) q^{71} +(-2.82313 + 1.96744i) q^{72} +(-0.551701 + 0.400834i) q^{73} +(0.808043 + 0.268421i) 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} +(4.37499 + 6.36643i) q^{80} +(3.13098 - 2.27479i) q^{81} +(16.6363 + 0.109122i) q^{82} +(2.78089 + 0.903567i) q^{83} +(-4.65180 - 1.57922i) q^{84} +(6.14604 - 8.45931i) q^{85} +(3.68979 + 5.14925i) q^{86} -11.1502 q^{87} +5.74214 q^{89} +(1.93534 + 2.70085i) q^{90} +(-0.173735 + 0.239126i) q^{91} +(2.85550 - 8.41126i) q^{92} +(11.5048 + 3.73814i) q^{93} +(8.90310 + 0.0583975i) q^{94} +(4.37063 - 3.17545i) q^{95} +(-4.63837 + 5.96275i) 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 $

$2$	−1.14955	+	0.823732i	−0.812855	+	0.582466i
$2$	−1.14955	+	0.823732i	−0.812855	+	0.582466i
$3$	−0.784953	+	1.08039i	−0.453193	+	0.623766i	−0.973080	−	0.230469i	$-0.925974\pi$
$3$	−0.784953	+	1.08039i	−0.453193	+	0.623766i	0.519887	+	0.854235i	$0.325974\pi$
$4$	0.642933	−	1.89384i	0.321466	−	0.946921i
$5$	−1.83667	−	0.596771i	−0.821384	−	0.266884i	−0.131972	−	0.991253i	$-0.542131\pi$
$5$	−1.83667	−	0.596771i	−0.821384	−	0.266884i	−0.689412	+	0.724369i	$0.742131\pi$
$6$	0.0123875	−	1.88856i	0.00505718	−	0.771001i
$7$	−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	$0.413002\pi$
$8$	0.820934	+	2.70667i	0.290244	+	0.956953i
$9$	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	−0.287746	−	0.957707i	$-0.592906\pi$
$13$	0.152835	−	0.0496591i	0.0423888	−	0.0137730i	0.330135	+	0.943934i	$0.392906\pi$
$14$	0.820012	−	2.46853i	0.219158	−	0.659742i
$15$	2.08645	−	1.51589i	0.538718	−	0.391402i
$16$	−3.17328	−	2.43523i	−0.793319	−	0.608806i
$17$	−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	$0.871996\pi$
$18$	−1.38527	−	1.02041i	−0.326512	−	0.240513i
$19$	−1.64430	+	2.26318i	−0.377227	+	0.519209i	−0.954847	−	0.297097i	$-0.903982\pi$
$19$	−1.64430	+	2.26318i	−0.377227	+	0.519209i	0.577620	+	0.816306i	$0.303982\pi$
$20$	−2.31105	+	3.09468i	−0.516765	+	0.691992i
$21$		−	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	$0.346757\pi$
$24$	−3.56867	−	1.23768i	−0.728451	−	0.252639i
$25$	−1.02786	−	0.746783i	−0.205572	−	0.149357i
$26$	−0.134786	+	0.182981i	−0.0264337	+	0.0358855i
$27$	−5.35542	−	1.74008i	−1.03065	−	0.334879i
$28$	1.09076	+	3.51317i	0.206134	+	0.663926i
$29$	4.90770	+	6.75487i	0.911337	+	1.25435i	0.966708	+	0.255882i	$0.0823660\pi$
$29$	4.90770	+	6.75487i	0.911337	+	1.25435i	−0.0553705	+	0.998466i	$0.517634\pi$
$30$	−1.14979	+	3.46127i	−0.209922	+	0.631938i
$31$	−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
$36$	2.43299	+	0.0319184i	0.405498	+	0.00531974i
$37$	−0.353889	−	0.487087i	−0.0581791	−	0.0800766i	0.778936	−	0.627103i	$-0.215760\pi$
$37$	−0.353889	−	0.487087i	−0.0581791	−	0.0800766i	−0.837115	+	0.547027i	$0.815760\pi$
$38$	0.0259490	−	3.95610i	0.00420948	−	0.641764i
$39$	−0.0663168	+	0.204102i	−0.0106192	+	0.0326825i
$40$	0.107476	−	5.46117i	0.0169934	−	0.863487i
$41$	−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	$-0.670684\pi$
$42$	2.02331	+	2.82361i	0.312204	+	0.435693i
$43$		−	4.47936i		−	0.683096i	−0.939864	−	0.341548i	$-0.889049\pi$
$43$		−	4.47936i		−	0.683096i	0.939864	−	0.341548i	$-0.110951\pi$
$44$		0			0
$45$		−	2.34948i		−	0.350240i
$46$	−5.10558	+	3.65850i	−0.752777	+	0.539416i
$47$	−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	$0.851847\pi$
$48$	5.12187	−	1.51685i	0.739279	−	0.218939i
$49$	−1.11771	+	3.43995i	−0.159672	+	0.491421i
$50$	1.79672	+	0.0117851i	0.254095	+	0.00166667i
$51$	−4.25006	−	5.84971i	−0.595128	−	0.819123i
$52$	0.00421610	−	0.321373i	0.000584668	−	0.0445664i
$53$	11.1474	−	3.62200i	1.53121	−	0.497521i	0.582276	−	0.812991i	$-0.302162\pi$
$53$	11.1474	−	3.62200i	1.53121	−	0.497521i	0.948935	+	0.315471i	$0.102162\pi$
$54$	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
$58$	−11.2059	−	3.72244i	−1.47140	−	0.488780i
$59$	−5.66097	−	7.79166i	−0.736995	−	1.01439i	−0.998786	−	0.0492625i	$-0.984313\pi$
$59$	−5.66097	−	7.79166i	−0.736995	−	1.01439i	0.261790	−	0.965125i	$-0.415687\pi$
$60$	−1.52942	−	4.92602i	−0.197447	−	0.635946i
$61$	−3.16618	−	1.02875i	−0.405388	−	0.131718i	0.0992234	−	0.995065i	$-0.468364\pi$
$61$	−3.16618	−	1.02875i	−0.405388	−	0.131718i	−0.504611	+	0.863347i	$0.668364\pi$
$62$	10.3143	+	7.59760i	1.30991	+	0.964897i
$63$	−1.81033	−	1.31528i	−0.228080	−	0.165710i
$64$	−6.65213	+	4.44400i	−0.831517	+	0.555500i
$65$	−0.310343			−0.0384933
$66$		0			0
$67$			5.76864i			0.704751i	0.935859	+	0.352376i	$0.114626\pi$
$67$			5.76864i			0.704751i	−0.935859	+	0.352376i	$0.885374\pi$
$68$	8.67647	+	6.47941i	1.05218	+	0.785743i
$69$	−3.48627	+	4.79843i	−0.419697	+	0.577664i
$70$	−2.97924	+	4.04451i	−0.356087	+	0.483412i
$71$	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	$-0.0935939\pi$
$72$	−2.82313	+	1.96744i	−0.332709	+	0.231864i
$73$	−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	$0.312706\pi$
$74$	0.808043	+	0.268421i	0.0939330	+	0.0312033i
$75$	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	$-0.205390\pi$
$80$	4.37499	+	6.36643i	0.489139	+	0.711788i
$81$	3.13098	−	2.27479i	0.347886	−	0.252754i
$82$	16.6363	+	0.109122i	1.83717	+	0.0120505i
$83$	2.78089	+	0.903567i	0.305243	+	0.0991794i	0.457633	−	0.889141i	$-0.348697\pi$
$83$	2.78089	+	0.903567i	0.305243	+	0.0991794i	−0.152391	+	0.988320i	$0.548697\pi$
$84$	−4.65180	−	1.57922i	−0.507553	−	0.172307i
$85$	6.14604	−	8.45931i	0.666632	−	0.917540i
$86$	3.68979	+	5.14925i	0.397880	+	0.555258i
$87$	−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	$0.401566\pi$
$90$	1.93534	+	2.70085i	0.204003	+	0.284694i
$91$	−0.173735	+	0.239126i	−0.0182124	+	0.0250672i
$92$	2.85550	−	8.41126i	0.297707	−	0.876934i
$93$	11.5048	+	3.73814i	1.19299	+	0.387628i
$94$	8.90310	+	0.0583975i	0.918284	+	0.00602325i
$95$	4.37063	−	3.17545i	0.448417	−	0.325794i
$96$	−4.63837	+	5.96275i	−0.473402	+	0.608570i
$97$	−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	−0.714730	−	0.699401i	$-0.753450\pi$
$101$	−8.86259	+	2.87963i	−0.881861	+	0.286534i	−0.167131	+	0.985935i	$0.553450\pi$
$102$	9.70425	+	3.22363i	0.960864	+	0.319186i
$103$	−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	$0.326354\pi$
$104$	0.259878	+	0.372907i	0.0254832	+	0.0365666i
$105$	−1.46583	+	4.51137i	−0.143051	+	0.440265i
$106$	−9.83092	+	13.3461i	−0.954863	+	1.29629i
$107$	6.62834	−	9.12312i	0.640786	−	0.881966i	−0.357872	−	0.933771i	$-0.616497\pi$
$107$	6.62834	−	9.12312i	0.640786	−	0.881966i	0.998657	+	0.0518051i	$0.0164975\pi$
$108$	−6.73861	+	9.02356i	−0.648423	+	0.868292i
$109$		−	19.6373i		−	1.88092i	−0.339910	−	0.940458i	$-0.610397\pi$
$109$		−	19.6373i		−	1.88092i	0.339910	−	0.940458i	$-0.389603\pi$
$110$		0			0
$111$	0.804032			0.0763154
$112$	7.35467	+	0.193006i	0.694951	+	0.0182373i
$113$	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	$0.492174\pi$
$114$	4.25378	+	3.13338i	0.398403	+	0.293468i
$115$	−8.15734	−	2.65048i	−0.760676	−	0.247159i
$116$	15.9480	−	4.95149i	1.48073	−	0.459734i
$117$	0.114916	+	0.158169i	0.0106240	+	0.0146227i
$118$	12.9258	+	4.29378i	1.18992	+	0.395275i
$119$	−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
$124$	−18.1151	−	0.237653i	−1.62679	−	0.0213419i
$125$	7.11781	+	9.79682i	0.636636	+	0.876254i
$126$	3.16450	+	0.0207567i	0.281916	+	0.00184915i
$127$	−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	$0.115925\pi$
$128$	3.98630	−	10.5882i	0.352343	−	0.935871i
$129$	4.83947	+	3.51608i	0.426092	+	0.309574i
$130$	0.356755	−	0.255639i	0.0312895	−	0.0224210i
$131$			10.9554i			0.957178i	0.878039	+	0.478589i	$0.158852\pi$
$131$			10.9554i			0.957178i	−0.878039	+	0.478589i	$0.841148\pi$
$132$		0			0
$133$		−	5.14534i		−	0.446157i
$134$	−4.75181	−	6.63134i	−0.410494	−	0.572860i
$135$	8.79771	+	6.39191i	0.757186	+	0.550128i
$136$	−15.3113	−	0.301326i	−1.31294	−	0.0258385i
$137$	−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	$0.956865\pi$
$138$	0.0550175	−	8.38779i	0.00468340	−	0.714016i
$139$	−10.7769	−	14.8331i	−0.914083	−	1.25813i	−0.965753	−	0.259463i	$-0.916455\pi$
$139$	−10.7769	−	14.8331i	−0.914083	−	1.25813i	0.0516706	−	0.998664i	$-0.483545\pi$
$140$	0.0931906	−	7.10347i	0.00787605	−	0.600352i
$141$	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
$146$	0.304028	−	0.915232i	0.0251616	−	0.0757452i
$147$	−2.83915	−	3.90776i	−0.234170	−	0.322307i
$148$	−1.14999	+	0.357047i	−0.0945288	+	0.0293490i
$149$	−8.05442	−	2.61704i	−0.659844	−	0.214396i	−0.0400944	−	0.999196i	$-0.512766\pi$
$149$	−8.05442	−	2.61704i	−0.659844	−	0.214396i	−0.619750	+	0.784800i	$0.712766\pi$
$150$	−1.42308	+	1.93192i	−0.116194	+	0.157741i
$151$	−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	$0.834389\pi$
$152$	−7.47554	−	2.59265i	−0.606346	−	0.210291i
$153$	−6.58717			−0.532541
$154$		0			0
$155$			17.4934i			1.40510i
$156$	0.343900	+	0.256818i	0.0275340	+	0.0205619i
$157$	5.13706	−	7.07056i	0.409982	−	0.564292i	−0.553232	−	0.833027i	$-0.686606\pi$
$157$	5.13706	−	7.07056i	0.409982	−	0.564292i	0.963214	+	0.268735i	$0.0866057\pi$
$158$	6.57986	+	4.84680i	0.523465	+	0.385591i
$159$	−4.83697	+	14.8867i	−0.383597	+	1.18059i
$160$	−10.2735	−	3.71471i	−0.812192	−	0.293674i
$161$	−6.60887	+	4.80163i	−0.520852	+	0.378421i
$162$	−1.72540	+	5.19407i	−0.135560	+	0.408084i
$163$	−23.2283	+	7.54735i	−1.81938	+	0.591154i	−0.819549	+	0.573009i	$0.805776\pi$
$163$	−23.2283	+	7.54735i	−1.81938	+	0.591154i	−0.999835	+	0.0181445i	$0.994224\pi$
$164$	−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	$0.808022\pi$
$168$	6.64833	−	2.01644i	0.512930	−	0.155572i
$169$	−10.4963	+	7.62603i	−0.807410	+	0.586618i
$170$	−0.0969920	+	14.7871i	−0.00743895	+	1.13412i
$171$	−3.23679	−	1.05170i	−0.247523	−	0.0804253i
$172$	−8.48320	−	2.87992i	−0.646838	−	0.219592i
$173$	−0.812921	+	1.11889i	−0.0618052	+	0.0850676i	−0.838801	−	0.544439i	$-0.816743\pi$
$173$	−0.812921	+	1.11889i	−0.0618052	+	0.0850676i	0.776996	+	0.629506i	$0.216743\pi$
$174$	12.8178	−	9.18480i	0.971712	−	0.696298i
$175$	2.33684			0.176648
$176$		0			0
$177$	12.8617			0.966741
$178$	−6.60088	+	4.72998i	−0.494757	+	0.354527i
$179$	5.81718	−	8.00667i	0.434797	−	0.598446i	−0.534249	−	0.845327i	$-0.679406\pi$
$179$	5.81718	−	8.00667i	0.434797	−	0.598446i	0.969046	+	0.246881i	$0.0794056\pi$
$180$	−4.44955	−	1.51056i	−0.331650	−	0.112590i
$181$	11.1086	+	3.60942i	0.825699	+	0.268286i	0.691233	−	0.722632i	$-0.257068\pi$
$181$	11.1086	+	3.60942i	0.825699	+	0.268286i	0.134467	+	0.990918i	$0.457068\pi$
$182$	0.00274175	−	0.417999i	0.000203232	−	0.0309841i
$183$	3.59676	−	2.61320i	0.265880	−	0.193173i
$184$	3.64607	+	12.0213i	0.268792	+	0.886224i
$185$	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
$190$	−2.40854	+	7.25056i	−0.174734	+	0.526011i
$191$	−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	$0.444103\pi$
$192$	0.420340	−	10.6753i	0.0303354	−	0.770420i
$193$	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	$-0.0583885\pi$
$194$	6.12397	+	4.51099i	0.439675	+	0.323870i
$195$	0.243604	−	0.335293i	0.0174449	−	0.0240108i
$196$	5.79611	+	4.32842i	0.414008	+	0.309173i
$197$			11.6835i			0.832415i	0.909270	+	0.416208i	$0.136641\pi$
$197$			11.6835i			0.832415i	−0.909270	+	0.416208i	$0.863359\pi$
$198$		0			0
$199$	−24.9329			−1.76745			−0.883725	−	0.468007i	$-0.844972\pi$
$199$	−24.9329			−1.76745			−0.883725	+	0.468007i	$0.844972\pi$
$200$	1.17749	−	3.39513i	0.0832612	−	0.240072i
$201$	−6.23240	−	4.52811i	−0.439600	−	0.319388i
$202$	7.81596	−	10.6107i	0.549929	−	0.746565i
$203$	−14.6056	−	4.74564i	−1.02511	−	0.333078i
$204$	−13.8109	+	4.28798i	−0.966958	+	0.300219i
$205$	13.3535	+	18.3795i	0.932649	+	1.28368i
$206$	0.748368	−	2.25285i	0.0521412	−	0.156964i
$207$	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	−0.497630	−	0.867390i	$-0.665796\pi$
$211$	−5.67063	+	1.84250i	−0.390382	+	0.126843i	0.107248	+	0.994232i	$0.465796\pi$
$212$	0.307511	−	23.4401i	0.0211200	−	1.60987i
$213$	7.55844	+	10.4033i	0.517895	+	0.712822i
$214$	−0.104603	+	15.9475i	−0.00715053	+	1.09015i
$215$	−2.67315	+	8.22711i	−0.182307	+	0.561084i
$216$	0.313381	−	15.9238i	0.0213229	−	1.08348i
$217$	13.4790	+	9.79310i	0.915017	+	0.664799i
$218$	16.1759	+	22.5741i	1.09557	+	1.52891i
$219$		−	0.910690i		−	0.0615387i
$220$		0			0
$221$			0.870099i			0.0585292i
$222$	−0.924276	+	0.662307i	−0.0620333	+	0.0444511i
$223$	−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	$0.711065\pi$
$224$	−8.61355	+	5.83640i	−0.575517	+	0.389961i
$225$	0.477645	−	1.47004i	0.0318430	−	0.0980026i
$226$	−18.2650	−	0.119804i	−1.21497	−	0.00796926i
$227$	−3.91237	−	5.38491i	−0.259673	−	0.357409i	0.659197	−	0.751971i	$-0.270896\pi$
$227$	−3.91237	−	5.38491i	−0.259673	−	0.357409i	−0.918870	+	0.394562i	$0.870896\pi$
$228$	−7.47100	−	0.0980123i	−0.494779	−	0.00649102i
$229$	15.5864	−	5.06432i	1.02998	−	0.334660i	0.255196	−	0.966889i	$-0.417860\pi$
$229$	15.5864	−	5.06432i	1.02998	−	0.334660i	0.774781	+	0.632230i	$0.217860\pi$
$230$	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	$0.723493\pi$
$234$	−0.262391	−	0.0871628i	−0.0171530	−	0.00569801i
$235$	7.14627	+	9.83599i	0.466171	+	0.641629i
$236$	−18.3958	+	5.71147i	−1.19746	+	0.371785i
$237$	7.33937	+	2.38471i	0.476743	+	0.154903i
$238$	11.3395	+	8.35280i	0.735029	+	0.541431i
$239$	−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	$0.725978\pi$
$240$	−10.3124	−	0.270625i	−0.665663	−	0.0174687i
$241$	−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
$244$	−3.98394	+	5.33482i	−0.255045	+	0.341527i
$245$	4.10572	−	5.65104i	0.262305	−	0.361032i
$246$	−13.1766	+	17.8881i	−0.840110	+	1.14051i
$247$	−0.138919	+	0.427547i	−0.00883918	+	0.0272042i
$248$	21.0200	−	14.6488i	1.33477	−	0.930201i
$249$	−3.15908	+	2.29520i	−0.200198	+	0.145453i
$250$	−16.2522	−	5.39878i	−1.02788	−	0.341449i
$251$	0.465437	−	0.151230i	0.0293782	−	0.00954554i	−0.294291	−	0.955716i	$-0.595084\pi$
$251$	0.465437	−	0.151230i	0.0293782	−	0.00954554i	0.323669	+	0.946170i	$0.395084\pi$
$252$	−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
$256$	4.13935	+	15.4553i	0.258710	+	0.965955i
$257$	−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	$0.401889\pi$
$258$	−8.45953	−	0.0554881i	−0.526667	−	0.00345454i
$259$	1.05319	+	0.342203i	0.0654422	+	0.0212635i
$260$	−0.199530	+	0.587740i	−0.0123743	+	0.0364501i
$261$	−5.97070	+	8.21796i	−0.369577	+	0.508679i
$262$	−9.02431	−	12.5938i	−0.557524	−	0.778047i
$263$	−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
$266$	4.23838	+	5.91482i	0.259872	+	0.362661i
$267$	−4.50731	+	6.20378i	−0.275843	+	0.379665i
$268$	10.9249	+	3.70884i	0.667344	+	0.226554i
$269$	2.56851	+	0.834559i	0.156605	+	0.0508840i	0.386270	−	0.922386i	$-0.373763\pi$
$269$	2.56851	+	0.834559i	0.156605	+	0.0508840i	−0.229666	+	0.973270i	$0.573763\pi$
$270$	−15.3786	−	0.100872i	−0.935914	−	0.00613888i
$271$	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	$0.0623397\pi$
$272$	17.8494	−	12.2660i	1.08228	−	0.743738i
$273$	−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	−0.999869	−	0.0162128i	$-0.994839\pi$
$277$	−29.9455	+	9.72988i	−1.79925	+	0.584612i	−0.799381	+	0.600824i	$0.794839\pi$
$278$	24.6071	+	8.17414i	1.47583	+	0.490252i
$279$	8.91566	−	6.47761i	0.533767	−	0.387804i
$280$	5.74422	+	8.24256i	0.343283	+	0.492587i
$281$	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	$0.00784941\pi$
$282$	−7.05160	+	9.57302i	−0.419917	+	0.570065i
$283$	−9.63949	+	13.2676i	−0.573008	+	0.788678i	−0.992907	−	0.118893i	$-0.962066\pi$
$283$	−9.63949	+	13.2676i	−0.573008	+	0.788678i	0.419899	+	0.907571i	$0.362066\pi$
$284$	−15.4305	−	11.5232i	−0.915631	−	0.683774i
$285$			7.21458i			0.427355i
$286$		0			0
$287$	21.6373			1.27721
$288$	1.91093	+	6.61149i	0.112603	+	0.389586i
$289$	−9.96380	−	7.23913i	−0.586106	−	0.425831i
$290$	18.3600	+	13.5242i	1.07814	+	0.794170i
$291$	6.83086	+	2.21948i	0.400432	+	0.130108i
$292$	0.404410	+	1.30254i	0.0236663	+	0.0762256i
$293$	5.88297	+	8.09722i	0.343687	+	0.473044i	0.945514	−	0.325582i	$-0.105560\pi$
$293$	5.88297	+	8.09722i	0.343687	+	0.473044i	−0.601827	+	0.798627i	$0.705560\pi$
$294$	6.48270	+	2.15347i	0.378079	+	0.125593i
$295$	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
$300$	0.0445138	−	3.39307i	0.00257001	−	0.195899i
$301$	4.84269	+	6.66540i	0.279128	+	0.384187i
$302$	14.2416	+	0.0934139i	0.819511	+	0.00537537i
$303$	3.84558	−	11.8355i	0.220923	−	0.679930i
$304$	10.7292	−	3.17746i	0.615359	−	0.182240i
$305$	5.20130	+	3.77897i	0.297826	+	0.216383i
$306$	7.57228	−	5.42606i	0.432879	−	0.310187i
$307$			18.8436i			1.07546i	0.843117	+	0.537731i	$0.180718\pi$
$307$			18.8436i			1.07546i	−0.843117	+	0.537731i	$0.819282\pi$
$308$		0			0
$309$		−	2.24167i		−	0.127524i
$310$	−14.4099	−	20.1095i	−0.818425	−	1.14215i
$311$	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	$0.685586\pi$
$312$	−0.606879	−	0.0119434i	−0.0343578	−	0.000676160i
$313$	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	$0.0644699\pi$
$314$	−0.0810691	+	12.3595i	−0.00457499	+	0.697488i
$315$	2.54006	+	3.49609i	0.143116	+	0.196982i
$316$	−11.5563	−	0.151608i	−0.650095	−	0.00852862i
$317$	−1.84870	+	0.600679i	−0.103833	+	0.0337375i	−0.360473	−	0.932770i	$-0.617385\pi$
$317$	−1.84870	+	0.600679i	−0.103833	+	0.0337375i	0.256640	+	0.966507i	$0.417385\pi$
$318$	−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
$322$	3.64198	−	10.9636i	0.202960	−	0.610980i
$323$	−8.90291	−	12.2538i	−0.495371	−	0.681820i
$324$	−2.29508	−	7.39211i	−0.127504	−	0.410673i
$325$	−0.194177	−	0.0630920i	−0.0107710	−	0.00349972i
$326$	20.4852	−	27.8100i	1.13457	−	1.54025i
$327$	21.2161	+	15.4144i	1.17325	+	0.852417i
$328$	10.9027	−	31.4364i	0.602000	−	1.73578i
$329$	11.5795			0.638396
$330$		0			0
$331$			7.52148i			0.413418i	0.978402	+	0.206709i	$0.0662753\pi$
$331$			7.52148i			0.413418i	−0.978402	+	0.206709i	$0.933725\pi$
$332$	3.49914	−	4.68564i	0.192040	−	0.257158i
$333$	0.430541	−	0.592589i	0.0235935	−	0.0324737i
$334$	−8.38595	−	6.17719i	−0.458859	−	0.338001i
$335$	3.44255	−	10.5951i	0.188087	−	0.578872i
$336$	−5.98159	+	7.79444i	−0.326322	+	0.425222i
$337$	−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	$0.374121\pi$
$338$	5.78426	−	17.4127i	0.314622	−	0.947124i
$339$	−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
$344$	12.1241	−	3.67726i	0.653690	−	0.198264i
$345$	9.26669	−	6.73264i	0.498902	−	0.362473i
$346$	0.0128289	−	1.95585i	0.000689685	−	0.105147i
$347$	−16.4045	−	5.33015i	−0.880640	−	0.286137i	−0.166417	−	0.986055i	$-0.553220\pi$
$347$	−16.4045	−	5.33015i	−0.880640	−	0.286137i	−0.714223	+	0.699918i	$0.753220\pi$
$348$	−7.16885	+	21.1168i	−0.384291	+	1.13198i
$349$	2.74841	−	3.78287i	0.147119	−	0.202492i	−0.729097	−	0.684410i	$-0.760060\pi$
$349$	2.74841	−	3.78287i	0.147119	−	0.202492i	0.876216	+	0.481918i	$0.160060\pi$
$350$	−2.68631	+	1.92493i	−0.143589	+	0.102892i
$351$	−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	$0.546335\pi$
$354$	−14.7851	+	10.5946i	−0.785820	+	0.563094i
$355$	−10.9303	+	15.0443i	−0.580120	+	0.798467i
$356$	3.69181	−	10.8747i	0.195666	−	0.576359i
$357$	12.6484	+	4.10971i	0.669424	+	0.217509i
$358$	−0.0918022	+	13.9959i	−0.00485190	+	0.739705i
$359$	−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	$0.564871\pi$
$360$	6.35927	−	1.92877i	0.335163	−	0.101655i
$361$	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
$366$	−1.98208	+	5.96677i	−0.103605	+	0.311888i
$367$	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	$0.0287516\pi$
$368$	−14.0937	−	10.8157i	−0.734685	−	0.563810i
$369$	4.42263	−	13.6115i	0.230233	−	0.708584i
$370$	−1.32392	−	0.975218i	−0.0688275	−	0.0506992i
$371$	−12.6718	+	17.4412i	−0.657886	+	0.905503i
$372$	14.4763	−	19.3849i	0.750560	−	1.00506i
$373$			1.34080i			0.0694239i	0.999397	+	0.0347119i	$0.0110514\pi$
$373$			1.34080i			0.0694239i	−0.999397	+	0.0347119i	$0.988949\pi$
$374$		0			0
$375$	−16.1716			−0.835096
$376$	5.83469	−	16.8235i	0.300901	−	0.867607i
$377$	1.08551	+	0.788669i	0.0559066	+	0.0406185i
$378$	−8.68694	+	11.7931i	−0.446808	+	0.606572i
$379$	8.29554	+	2.69538i	0.426113	+	0.138453i	0.514220	−	0.857658i	$-0.328082\pi$
$379$	8.29554	+	2.69538i	0.426113	+	0.138453i	−0.0881065	+	0.996111i	$0.528082\pi$
$380$	−3.20378	−	10.3189i	−0.164350	−	0.529347i
$381$	−0.884766	−	1.21778i	−0.0453279	−	0.0623885i
$382$	5.39014	−	16.2262i	0.275784	−	0.830206i
$383$	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
$388$	−10.7557	−	0.141104i	−0.546035	−	0.00716346i
$389$	−22.6849	−	31.2230i	−1.15017	−	1.58307i	−0.742357	−	0.670005i	$-0.766292\pi$
$389$	−22.6849	−	31.2230i	−1.15017	−	1.58307i	−0.407811	−	0.913066i	$-0.633708\pi$
$390$	−0.00384437	+	0.586101i	−0.000194667	+	0.0296784i
$391$	−7.43107	+	22.8705i	−0.375805	+	1.15661i
$392$	−10.2284	−	0.201294i	−0.516611	−	0.0101669i
$393$	−11.8362	−	8.59947i	−0.597055	−	0.433786i
$394$	−9.62407	−	13.4308i	−0.484854	−	0.676633i
$395$			11.1597i			0.561506i
$396$		0			0
$397$		−	20.4200i		−	1.02485i	−0.858732	−	0.512426i	$-0.828747\pi$
$397$		−	20.4200i		−	1.02485i	0.858732	−	0.512426i	$-0.171253\pi$
$398$	28.6617	−	20.5381i	1.43668	−	1.02948i
$399$	5.55899	+	4.03884i	0.278298	+	0.202195i
$400$	1.44309	+	4.87281i	0.0721547	+	0.243641i
$401$	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	$0.0604575\pi$
$402$	10.8944	+	0.0714590i	0.543363	+	0.00356405i
$403$	−0.855627	−	1.17767i	−0.0426218	−	0.0586639i
$404$	−0.244483	+	18.6358i	−0.0121635	+	0.927164i
$405$	−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	$-0.223835\pi$
$410$	−30.4903	−	10.1285i	−1.50581	−	0.500210i
$411$	−7.98716	−	10.9934i	−0.393977	−	0.542263i
$412$	0.995458	+	3.20622i	0.0490427	+	0.157959i
$413$	16.8473	+	5.47403i	0.829003	+	0.269359i
$414$	−6.15252	−	4.53202i	−0.302380	−	0.222737i
$415$	−4.56836	−	3.31911i	−0.224252	−	0.162929i
$416$	0.873312	−	0.252414i	0.0428176	−	0.0123756i
$417$	24.4849			1.19903
$418$		0			0
$419$		−	12.0628i		−	0.589306i	−0.955604	−	0.294653i	$-0.904796\pi$
$419$		−	12.0628i		−	0.589306i	0.955604	−	0.294653i	$-0.0952041\pi$
$420$	7.60139	+	5.67657i	0.370910	+	0.276988i
$421$	−8.40779	+	11.5723i	−0.409771	+	0.564001i	−0.963162	−	0.268920i	$-0.913333\pi$
$421$	−8.40779	+	11.5723i	−0.409771	+	0.564001i	0.553392	+	0.832921i	$0.313333\pi$
$422$	5.00095	−	6.78912i	0.243442	−	0.330489i
$423$	2.36682	−	7.28431i	0.115079	−	0.354175i
$424$	18.9548	+	27.1989i	0.920529	+	1.32089i
$425$	5.56526	−	4.04340i	0.269955	−	0.196133i
$426$	−17.2583	−	5.73299i	−0.836169	−	0.277764i
$427$	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	$0.749123\pi$
$432$	12.7567	+	18.5634i	0.613758	+	0.893132i
$433$	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	$0.170959\pi$
$434$	−23.5617	−	0.154547i	−1.13100	−	0.00741849i
$435$	20.4793	+	6.65414i	0.981909	+	0.319041i
$436$	−37.1900	−	12.6255i	−1.78108	−	0.604651i
$437$	−7.30293	+	10.0516i	−0.349347	+	0.480834i
$438$	0.750164	+	1.04688i	0.0358442	+	0.0500221i
$439$	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
$442$	−0.716728	−	1.00022i	−0.0340913	−	0.0475757i
$443$	6.50558	−	8.95416i	0.309089	−	0.425425i	−0.626008	−	0.779817i	$-0.715312\pi$
$443$	6.50558	−	8.95416i	0.309089	−	0.425425i	0.935097	+	0.354392i	$0.115312\pi$
$444$	0.516939	−	1.52271i	0.0245328	−	0.0722646i
$445$	−10.5464	−	3.42674i	−0.499949	−	0.162443i
$446$	1.46794	+	0.00962855i	0.0695088	+	0.000455925i
$447$	9.14978	−	6.64770i	0.432770	−	0.314426i
$448$	5.09408	−	13.8045i	0.240673	−	0.652201i
$449$	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
$454$	8.93318	+	2.96749i	0.419255	+	0.139271i
$455$	0.461798	−	0.335516i	0.0216494	−	0.0157292i
$456$	8.66902	−	6.04143i	0.405964	−	0.282916i
$457$	−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	$0.124466\pi$
$458$	−13.7457	+	18.6607i	−0.642294	+	0.871956i
$459$	17.9208	−	24.6659i	0.836471	−	1.15130i
$460$	−10.2642	+	13.7446i	−0.478571	+	0.640847i
$461$			3.17514i			0.147881i	0.997263	+	0.0739406i	$0.0235575\pi$
$461$			3.17514i			0.147881i	−0.997263	+	0.0739406i	$0.976442\pi$
$462$		0			0
$463$	21.8696			1.01637			0.508184	−	0.861248i	$-0.330317\pi$
$463$	21.8696			1.01637			0.508184	+	0.861248i	$0.330317\pi$
$464$	0.876147	−	33.3864i	0.0406741	−	1.54993i
$465$	−18.8998	−	13.7315i	−0.876456	−	0.636782i
$466$	−18.3029	−	13.4821i	−0.847864	−	0.624547i
$467$	−4.71472	−	1.53190i	−0.218171	−	0.0708881i	0.197892	−	0.980224i	$-0.436590\pi$
$467$	−4.71472	−	1.53190i	−0.218171	−	0.0708881i	−0.416063	+	0.909336i	$0.636590\pi$
$468$	0.373430	−	0.115942i	0.0172618	−	0.00535940i
$469$	−6.23655	−	8.58387i	−0.287977	−	0.396366i
$470$	−16.3172	−	5.42036i	−0.752657	−	0.250023i
$471$	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
$476$	−19.9158	−	0.261276i	−0.912838	−	0.0119756i
$477$	8.38170	+	11.5364i	0.383772	+	0.528217i
$478$	3.56461	+	0.0233812i	0.163042	+	0.00106943i
$479$	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	$-0.201612\pi$
$480$	12.0776	−	8.18356i	0.551263	−	0.373527i
$481$	−0.0782750	−	0.0568701i	−0.00356903	−	0.00259305i
$482$	7.02582	−	5.03448i	0.320017	−	0.229314i
$483$		−	10.9092i		−	0.496387i
$484$		0			0
$485$			10.3865i			0.471627i
$486$	9.65806	+	13.4782i	0.438098	+	0.611384i
$487$	−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	$0.773898\pi$
$488$	0.185274	−	9.41434i	0.00838696	−	0.426167i
$489$	10.0790	−	31.0201i	0.455790	−	1.40278i
$490$	−0.0647933	+	9.87817i	−0.00292706	+	0.446250i
$491$	−0.216048	−	0.297365i	−0.00975013	−	0.0134199i	0.804114	−	0.594475i	$-0.202640\pi$
$491$	−0.216048	−	0.297365i	−0.00975013	−	0.0134199i	−0.813864	+	0.581055i	$0.802640\pi$
$492$	0.412165	−	31.4173i	0.0185818	−	1.41640i
$493$	−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
$498$	1.74089	−	5.24069i	0.0780110	−	0.234841i
$499$	18.3285	+	25.2271i	0.820498	+	1.12932i	0.989618	+	0.143723i	$0.0459073\pi$
$499$	18.3285	+	25.2271i	0.820498	+	1.12932i	−0.169120	+	0.985595i	$0.554093\pi$
$500$	23.1299	−	7.18131i	1.03440	−	0.321158i
$501$	−9.35394	−	3.03928i	−0.417903	−	0.135785i
$502$	−0.410471	+	0.557242i	−0.0183202	+	0.0248709i
$503$	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	$0.551301\pi$
$504$	2.07387	−	5.97972i	0.0923775	−	0.266358i
$505$	17.9962			0.800818
$506$		0			0
$507$		−	17.3262i		−	0.769486i
$508$	1.80624	+	1.34886i	0.0801390	+	0.0598462i
$509$	−12.9435	+	17.8153i	−0.573712	+	0.789647i	−0.992988	−	0.118211i	$-0.962284\pi$
$509$	−12.9435	+	17.8153i	−0.573712	+	0.789647i	0.419276	+	0.907859i	$0.362284\pi$
$510$	−15.8998	−	11.7120i	−0.704053	−	0.518614i
$511$	0.387597	−	1.19290i	0.0171463	−	0.0527709i
$512$	−17.4894	−	14.3569i	−0.772930	−	0.634492i
$513$	12.7440	−	9.25906i	0.562661	−	0.408797i
$514$	4.49779	−	13.5399i	0.198389	−	0.597222i
$515$	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
$520$	−0.254771	−	0.839996i	−0.0111724	−	0.0368363i
$521$	−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	$0.590464\pi$
$522$	0.0942248	−	14.3652i	0.00412411	−	0.628748i
$523$	32.8484	+	10.6731i	1.43636	+	0.466702i	0.920760	−	0.390128i	$-0.127569\pi$
$523$	32.8484	+	10.6731i	1.43636	+	0.466702i	0.515599	+	0.856830i	$0.327569\pi$
$524$	20.7478	+	7.04358i	0.906372	+	0.307700i
$525$	−1.83430	+	2.52470i	−0.0800556	+	0.110187i
$526$	4.58057	−	3.28229i	0.199722	−	0.143115i
$527$	49.0457			2.13646
$528$		0			0
$529$	−3.27421			−0.142357
$530$	26.0208	−	18.6456i	1.13027	−	0.809915i
$531$	6.88712	−	9.47931i	0.298876	−	0.411367i
$532$	−9.74445	−	3.30810i	−0.422476	−	0.143425i
$533$	−1.79794	−	0.584185i	−0.0778773	−	0.0253039i
$534$	0.0711308	−	10.8444i	0.00307813	−	0.469282i
$535$	−17.6185	+	12.8006i	−0.761714	+	0.553417i
$536$	−15.6138	+	4.73567i	−0.674413	+	0.204550i
$537$	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	−0.180672	−	0.983543i	$-0.557827\pi$
$541$	5.84449	−	1.89899i	0.251274	−	0.0816440i	0.431946	+	0.901899i	$0.357827\pi$
$542$	−9.96922	+	30.0109i	−0.428215	+	1.28908i
$543$	−12.6194	+	9.16850i	−0.541548	+	0.393458i
$544$	−10.4148	+	28.8035i	−0.446532	+	1.23494i
$545$	−11.7190	+	36.0673i	−0.501986	+	1.54496i
$546$	0.449451	+	0.331071i	0.0192347	+	0.0141685i
$547$	−10.1881	+	14.0228i	−0.435613	+	0.599571i	−0.969230	−	0.246156i	$-0.920832\pi$
$547$	−10.1881	+	14.0228i	−0.435613	+	0.599571i	0.533617	+	0.845726i	$0.320832\pi$
$548$	16.3057	+	12.1768i	0.696545	+	0.520166i
$549$		−	4.05020i		−	0.172858i
$550$		0			0
$551$	−23.3572			−0.995050
$552$	−15.8498	−	5.49698i	−0.674611	−	0.233967i
$553$	8.59880	+	6.24739i	0.365658	+	0.265666i
$554$	26.4090	−	35.8520i	1.12201	−	1.52321i
$555$	−1.47674	−	0.479823i	−0.0626843	−	0.0203674i
$556$	−35.0203	+	10.8730i	−1.48519	+	0.461119i
$557$	−22.4316	−	30.8745i	−0.950458	−	1.30819i	−0.951323	−	0.308194i	$-0.900275\pi$
$557$	−22.4316	−	30.8745i	−0.950458	−	1.30819i	0.000865126	−	1.00000i	$-0.499725\pi$
$558$	−4.91319	+	14.7904i	−0.207992	+	0.626130i
$559$	−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	−0.886346	−	0.463024i	$-0.846764\pi$
$563$	−31.5875	+	10.2634i	−1.33126	+	0.432551i	−0.444910	+	0.895575i	$0.646764\pi$
$564$	0.220574	−	16.8133i	0.00928785	−	0.707967i
$565$	−14.6608	−	20.1788i	−0.616784	−	0.848930i
$566$	0.152123	−	23.1921i	0.00639420	−	0.974839i
$567$	−2.19967	+	6.76988i	−0.0923773	+	0.284308i
$568$	27.2301	+	0.535888i	1.14255	+	0.0224854i
$569$	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	$0.644778\pi$
$570$	−5.94288	−	8.29352i	−0.248920	−	0.347378i
$571$		−	32.7618i		−	1.37104i	−0.728055	−	0.685518i	$-0.759576\pi$
$571$		−	32.7618i		−	1.37104i	0.728055	−	0.685518i	$-0.240424\pi$
$572$		0			0
$573$		−	16.1457i		−	0.674496i
$574$	−24.8732	+	17.8234i	−1.03819	+	0.743933i
$575$	−4.56510	−	3.31674i	−0.190378	−	0.138318i
$576$	−7.64280	−	6.02615i	−0.318450	−	0.251090i
$577$	−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	$0.143254\pi$
$578$	17.4170	+	0.114242i	0.724451	+	0.00475185i
$579$	10.4101	+	14.3282i	0.432628	+	0.595461i
$580$	−32.2461	−	0.423038i	−1.33895	−	0.0175657i
$581$	−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
$586$	−13.4327	−	4.46217i	−0.554900	−	0.184330i
$587$	−5.85038	−	8.05235i	−0.241471	−	0.332356i	0.671031	−	0.741430i	$-0.265852\pi$
$587$	−5.85038	−	8.05235i	−0.241471	−	0.332356i	−0.912501	+	0.409074i	$0.865852\pi$
$588$	−9.22607	+	2.86448i	−0.380477	+	0.118129i
$589$	24.1000	+	7.83056i	0.993022	+	0.322652i
$590$	−21.1781	−	15.6000i	−0.871887	−	0.642242i
$591$	−12.6228	−	9.17099i	−0.519232	−	0.377244i
$592$	−0.0631780	+	2.40746i	−0.00259660	+	0.0989461i
$593$	−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
$596$	−10.1347	+	13.5712i	−0.415134	+	0.555899i
$597$	19.5712	−	26.9374i	0.800995	−	1.10247i
$598$	−0.598634	+	0.812685i	−0.0244800	+	0.0332332i
$599$	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	$-0.126068\pi$
$600$	2.74381	+	3.93717i	0.112016	+	0.160734i
$601$	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	$0.227765\pi$
$602$	−11.0574	−	3.67313i	−0.450667	−	0.149706i
$603$	−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	$0.979745\pi$
$608$	−9.71633	+	12.4906i	−0.394049	+	0.506560i
$609$	16.5918	−	12.0547i	0.672335	−	0.488480i
$610$	−9.09201	−	0.0596367i	−0.368125	−	0.00241462i
$611$	−0.962185	−	0.312633i	−0.0389258	−	0.0126478i
$612$	−4.23511	+	12.4751i	−0.171194	+	0.504274i
$613$	2.10123	−	2.89209i	0.0848678	−	0.116810i	−0.764472	−	0.644657i	$-0.777000\pi$
$613$	2.10123	−	2.89209i	0.0848678	−	0.116810i	0.849340	+	0.527846i	$0.177000\pi$
$614$	−15.5221	−	21.6617i	−0.626420	−	0.874194i
$615$	−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	$0.289537\pi$
$618$	1.84653	+	2.57691i	0.0742785	+	0.103659i
$619$	−6.23749	+	8.58517i	−0.250706	+	0.345067i	−0.915758	−	0.401730i	$-0.868409\pi$
$619$	−6.23749	+	8.58517i	−0.250706	+	0.345067i	0.665053	+	0.746797i	$0.268409\pi$
$620$	33.1297	+	11.2471i	1.33052	+	0.451693i
$621$	−23.7854	−	7.72834i	−0.954475	−	0.310128i
$622$	−2.25790	−	0.0148101i	−0.0905337	−	0.000593832i
$623$	−8.54445	+	6.20791i	−0.342326	+	0.248715i
$624$	0.707476	−	0.486176i	0.0283217	−	0.0194626i
$625$	−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
$630$	−5.79976	−	1.92660i	−0.231068	−	0.0767577i
$631$	−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	$0.327229\pi$
$632$	13.4095	−	9.34504i	0.533401	−	0.371726i
$633$	2.46055	−	7.57279i	0.0977980	−	0.300991i
$634$	1.63037	−	2.21334i	0.0647504	−	0.0879030i
$635$	1.27947	−	1.76103i	0.0507741	−	0.0698845i
$636$	25.0832	+	18.7316i	0.994612	+	0.742756i
$637$			0.581249i			0.0230299i
$638$		0			0
$639$	11.7148			0.463431
$640$	−13.6402	+	17.0681i	−0.539178	+	0.674675i
$641$	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	$0.524237\pi$
$642$	−17.1474	−	12.6310i	−0.676755	−	0.498506i
$643$	26.6880	+	8.67146i	1.05247	+	0.341969i	0.783638	−	0.621218i	$-0.213362\pi$
$643$	26.6880	+	8.67146i	1.05247	+	0.341969i	0.268834	+	0.963187i	$0.413362\pi$
$644$	4.84446	+	15.6033i	0.190899	+	0.614855i
$645$	−6.79023	−	9.34595i	−0.267365	−	0.367996i
$646$	20.3282	+	6.75276i	0.799802	+	0.265684i
$647$	−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
$652$	−0.640777	+	48.8432i	−0.0250947	+	1.91285i
$653$	19.3499	+	26.6329i	0.757220	+	1.04222i	0.997440	+	0.0715057i	$0.0227804\pi$
$653$	19.3499	+	26.6329i	0.757220	+	1.04222i	−0.240220	+	0.970718i	$0.577220\pi$
$654$	−37.0863	−	0.243258i	−1.45019	−	0.00951212i
$655$	6.53786	−	20.1215i	0.255455	−	0.786211i
$656$	13.3620	+	45.1186i	0.521697	+	1.76159i
$657$	−0.671198	−	0.487654i	−0.0261859	−	0.0190252i
$658$	−13.3112	+	9.53836i	−0.518923	+	0.371844i
$659$		−	3.99602i		−	0.155663i	−0.996967	−	0.0778314i	$-0.975200\pi$
$659$		−	3.99602i		−	0.155663i	0.996967	−	0.0778314i	$-0.0247996\pi$
$660$		0			0
$661$			19.2377i			0.748258i	0.927377	+	0.374129i	$0.122058\pi$
$661$			19.2377i			0.748258i	−0.927377	+	0.374129i	$0.877942\pi$
$662$	−6.19568	−	8.64632i	−0.240802	−	0.336049i
$663$	−0.940050	−	0.682986i	−0.0365085	−	0.0265250i
$664$	−0.162728	+	8.26873i	−0.00631509	+	0.320889i
$665$	−3.07059	+	9.45029i	−0.119072	+	0.366467i
$666$	−0.00679446	+	1.03586i	−0.000263280	+	0.0401388i
$667$	21.7969	+	30.0009i	0.843981	+	1.16164i
$668$	14.7284	+	0.193223i	0.569860	+	0.00747601i
$669$	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	$0.933263\pi$
$674$	3.77721	−	11.3707i	0.145493	−	0.437984i
$675$	4.20515	+	5.78789i	0.161856	+	0.222776i
$676$	7.69406	+	24.7814i	0.295926	+	0.953131i
$677$	−39.0944	−	12.7025i	−1.50252	−	0.488198i	−0.561767	−	0.827296i	$-0.689878\pi$
$677$	−39.0944	−	12.7025i	−1.50252	−	0.488198i	−0.940751	+	0.339098i	$0.889878\pi$
$678$	14.4666	−	19.6393i	0.555585	−	0.754244i
$679$	8.00303	+	5.81454i	0.307128	+	0.223142i
$680$	27.9421	+	9.69079i	1.07153	+	0.371625i
$681$	8.88885			0.340621
$682$		0			0
$683$		−	35.8592i		−	1.37211i	−0.727548	−	0.686057i	$-0.759340\pi$
$683$		−	35.8592i		−	1.37211i	0.727548	−	0.686057i	$-0.240660\pi$
$684$	−4.07278	+	5.45380i	−0.155727	+	0.208531i
$685$	11.5503	−	15.8976i	0.441314	−	0.607416i
$686$	22.2353	+	16.3788i	0.848946	+	0.625344i
$687$	−6.76310	+	20.8147i	−0.258028	+	0.794130i
$688$	−10.9082	+	14.2142i	−0.415873	+	0.541913i
$689$	1.52385	−	1.10714i	0.0580539	−	0.0421786i
$690$	−5.10664	+	15.3728i	−0.194406	+	0.585232i
$691$	42.9366	−	13.9509i	1.63338	−	0.530719i	0.658338	−	0.752722i	$-0.271260\pi$
$691$	42.9366	−	13.9509i	1.63338	−	0.530719i	0.975046	+	0.222004i	$0.0712598\pi$
$692$	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
$696$	−9.15361	−	30.1800i	−0.346967	−	1.14397i
$697$	51.5301	−	37.4388i	1.95184	−	1.41810i
$698$	−0.0433733	+	6.61255i	−0.00164170	+	0.250289i
$699$	−20.4156	−	6.63342i	−0.772188	−	0.250899i
$700$	1.50243	−	4.42560i	0.0567864	−	0.167272i
$701$	−10.9250	+	15.0369i	−0.412631	+	0.567937i	−0.963858	−	0.266418i	$-0.914160\pi$
$701$	−10.9250	+	15.0369i	−0.412631	+	0.567937i	0.551227	+	0.834355i	$0.314160\pi$
$702$	1.04024	−	0.745400i	0.0392611	−	0.0281333i
$703$	1.68426			0.0635232
$704$		0			0
$705$	−16.2362			−0.611492
$706$	6.26568	−	4.48979i	0.235812	−	0.168975i
$707$	10.0746	−	13.8664i	0.378892	−	0.521501i
$708$	8.26918	−	24.3579i	0.310775	−	0.915428i
$709$	−25.9356	−	8.42699i	−0.974032	−	0.316482i	−0.221589	−	0.975140i	$-0.571124\pi$
$709$	−25.9356	−	8.42699i	−0.974032	−	0.316482i	−0.752443	+	0.658658i	$0.771124\pi$
$710$	0.172493	−	26.2978i	0.00647356	−	0.986939i
$711$	5.68764	−	4.13231i	0.213303	−	0.154974i
$712$	4.71392	+	15.5421i	0.176662	+	0.582465i
$713$	−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
$718$	12.4911	−	37.6025i	0.466162	−	1.40331i
$719$	−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	$0.519969\pi$
$720$	−5.72152	+	7.45555i	−0.213228	+	0.277852i
$721$	0.954074	−	2.93634i	0.0355316	−	0.109355i
$722$	−12.7236	−	9.37235i	−0.473523	−	0.348803i
$723$	4.79747	−	6.60315i	0.178420	−	0.245574i
$724$	13.9778	−	18.7174i	0.519480	−	0.695627i
$725$		−	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	$0.653696\pi$
$728$	−0.789860	−	0.273937i	−0.0292742	−	0.0101528i
$729$	22.0603	+	16.0277i	0.817048	+	0.593620i
$730$	−1.10458	+	1.49955i	−0.0408825	+	0.0555007i
$731$	23.0661	+	7.49463i	0.853130	+	0.277199i
$732$	−2.63651	−	8.49181i	−0.0974483	−	0.313866i
$733$	10.1507	+	13.9713i	0.374926	+	0.516041i	0.954231	−	0.299069i	$-0.0966762\pi$
$733$	10.1507	+	13.9713i	0.374926	+	0.516041i	−0.579306	+	0.815110i	$0.696676\pi$
$734$	−12.8574	+	38.7052i	−0.474574	+	1.42864i
$735$	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	0.00905903	−	0.999959i	$-0.497116\pi$
$739$	16.4235	−	5.33633i	0.604149	−	0.196300i	0.595090	+	0.803659i	$0.297116\pi$
$740$	2.32523	+	0.0305048i	0.0854773	+	0.00112138i
$741$	−0.352875	−	0.485691i	−0.0129632	−	0.0178423i
$742$	0.199976	−	30.4877i	0.00734135	−	1.11924i
$743$	−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	$0.880851\pi$
$744$	−0.673223	+	34.2085i	−0.0246816	+	1.25415i
$745$	13.2316	+	9.61329i	0.484767	+	0.352204i
$746$	−1.10446	−	1.54131i	−0.0404371	−	0.0564315i
$747$			3.55734i			0.130156i
$748$		0			0
$749$			20.7414i			0.757875i
$750$	18.5900	−	13.3210i	0.678812	−	0.486415i
$751$	−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	$-0.689728\pi$
$752$	7.15079	+	24.1457i	0.260763	+	0.880503i
$753$	−0.201958	+	0.621564i	−0.00735978	+	0.0226511i
$754$	−1.89750	−	0.0124462i	−0.0691029	−	0.000453262i
$755$	11.4313	+	15.7339i	0.416028	+	0.572614i
$756$	0.271728	−	20.7125i	0.00988264	−	0.753305i
$757$	−31.0091	+	10.0755i	−1.12704	+	0.366199i	−0.812452	−	0.583028i	$-0.801868\pi$
$757$	−31.0091	+	10.0755i	−1.12704	+	0.366199i	−0.314592	+	0.949227i	$0.601868\pi$
$758$	−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	$0.883891\pi$
$762$	2.02020	+	0.671085i	0.0731842	+	0.0243108i
$763$	21.2302	+	29.2208i	0.768584	+	1.05787i
$764$	7.16982	+	23.0929i	0.259395	+	0.835472i
$765$	12.0985	+	3.93103i	0.437421	+	0.142127i
$766$	−8.83902	−	6.51093i	−0.319367	−	0.235249i
$767$	−1.25212	−	0.909719i	−0.0452115	−	0.0328481i
$768$	−19.9470	−	7.65953i	−0.719775	−	0.276389i
$769$	−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
$772$	−21.2521	−	15.8706i	−0.764878	−	0.571196i
$773$	−12.2208	+	16.8205i	−0.439552	+	0.604992i	−0.970113	−	0.242656i	$-0.921982\pi$
$773$	−12.2208	+	16.8205i	−0.439552	+	0.604992i	0.530560	+	0.847647i	$0.321982\pi$
$774$	−4.57078	+	6.20514i	−0.164293	+	0.223039i
$775$	−3.55637	+	10.9454i	−0.127749	+	0.393170i
$776$	12.4804	−	8.69756i	0.448020	−	0.312224i
$777$	−1.19642	+	0.869250i	−0.0429213	+	0.0311842i
$778$	51.7968	+	17.2062i	1.85701	+	0.616873i
$779$	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
$784$	11.9238	−	8.19404i	0.425852	−	0.292644i
$785$	−13.6546	+	9.92065i	−0.487353	+	0.354083i
$786$	20.6899	+	0.135710i	0.737985	+	0.00484062i
$787$	−38.4107	−	12.4804i	−1.36919	−	0.444878i	−0.470091	−	0.882618i	$-0.655779\pi$
$787$	−38.4107	−	12.4804i	−1.36919	−	0.444878i	−0.899101	+	0.437740i	$0.855779\pi$
$788$	22.1267	+	7.51170i	0.788231	+	0.267593i
$789$	3.12777	−	4.30501i	0.111352	−	0.153262i
$790$	−9.19260	−	12.8286i	−0.327058	−	0.456423i
$791$	−23.7556			−0.844651
$792$		0			0
$793$	−0.534990			−0.0189981
$794$	16.8206	+	23.4738i	0.596941	+	0.833055i
$795$	17.7679	−	24.4554i	0.630161	−	0.867342i
$796$	−16.0302	+	47.2191i	−0.568175	+	1.67363i
$797$	−29.5959	−	9.61629i	−1.04834	−	0.340627i	−0.266324	−	0.963884i	$-0.585809\pi$
$797$	−29.5959	−	9.61629i	−1.04834	−	0.340627i	−0.782017	+	0.623257i	$0.785809\pi$
$798$	−9.71727	−	0.0637379i	−0.343988	−	0.00225630i
$799$	27.5769	−	20.0358i	0.975600	−	0.708815i
$800$	−5.67280	−	4.41282i	−0.200564	−	0.156017i
$801$	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
$806$	1.95367	+	0.648983i	0.0688151	+	0.0228595i
$807$	−2.91781	+	2.11991i	−0.102712	+	0.0746245i
$808$	−15.0698	−	21.6241i	−0.530154	−	0.760734i
$809$	−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	$0.963673\pi$
$810$	6.26866	−	8.51012i	0.220258	−	0.299015i
$811$	−15.4575	+	21.2754i	−0.542785	+	0.747080i	−0.989011	−	0.147840i	$-0.952768\pi$
$811$	−15.4575	+	21.2754i	−0.542785	+	0.747080i	0.446226	+	0.894920i	$0.352768\pi$
$812$	−18.3779	+	24.6095i	−0.644937	+	0.863624i
$813$			29.8619i			1.04730i
$814$		0			0
$815$	47.1669			1.65218
$816$	−0.758742	+	28.9126i	−0.0265613	+	1.01214i
$817$	10.1376	+	7.36539i	0.354669	+	0.257682i
$818$	17.4688	+	12.8678i	0.610784	+	0.449911i
$819$	−0.341997	−	0.111122i	−0.0119503	−	0.00388290i
$820$	43.3933	−	13.4726i	1.51536	−	0.470485i
$821$	−32.6964	−	45.0027i	−1.14111	−	1.57060i	−0.765001	−	0.644029i	$-0.777262\pi$
$821$	−32.6964	−	45.0027i	−1.14111	−	1.57060i	−0.376110	−	0.926575i	$-0.622738\pi$
$822$	18.2372	+	6.05817i	0.636097	+	0.211303i
$823$	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	−0.866847	−	0.498574i	$-0.833857\pi$
$827$	−36.6684	+	11.9143i	−1.27509	+	0.414301i	−0.408239	+	0.912875i	$0.633857\pi$
$828$	10.8058	+	0.141762i	0.375527	+	0.00492656i
$829$	−26.1318	−	35.9674i	−0.907595	−	1.24920i	−0.967981	−	0.251023i	$-0.919233\pi$
$829$	−26.1318	−	35.9674i	−0.907595	−	1.24920i	0.0603858	−	0.998175i	$-0.480767\pi$
$830$	7.98562	+	0.0523796i	0.277185	+	0.00181812i
$831$	12.9937	−	39.9904i	0.450746	−	1.38725i
$832$	−0.795994	+	1.00954i	−0.0275961	+	0.0349994i
$833$	−15.8437	−	11.5111i	−0.548950	−	0.398835i
$834$	−28.1467	+	20.1690i	−0.974639	+	0.698396i
$835$		−	14.2229i		−	0.492204i
$836$		0			0
$837$			51.0077i			1.76308i
$838$	9.93650	+	13.8668i	0.343251	+	0.479020i
$839$	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	$0.459007\pi$
$840$	−13.4142	−	0.263990i	−0.462832	−	0.00910853i
$841$	−12.5813	+	38.7212i	−0.433837	+	1.33521i
$842$	0.132685	−	20.2287i	0.00457263	−	0.697128i
$843$	7.51261	+	10.3402i	0.258748	+	0.356136i
$844$	−0.156430	+	11.9239i	−0.00538453	+	0.410437i
$845$	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
$850$	−3.06687	+	9.23236i	−0.105193	+	0.316668i
$851$	−1.57175	−	2.16333i	−0.0538791	−	0.0741582i
$852$	24.5618	−	7.62587i	0.841472	−	0.261258i
$853$	3.98990	+	1.29640i	0.136612	+	0.0443878i	0.376525	−	0.926407i	$-0.377119\pi$
$853$	3.98990	+	1.29640i	0.136612	+	0.0443878i	−0.239913	+	0.970794i	$0.577119\pi$
$854$	−5.13581	+	6.97221i	−0.175744	+	0.238584i
$855$	5.31730	+	3.86324i	0.181848	+	0.132120i
$856$	30.1347	+	10.4512i	1.02998	+	0.357216i
$857$	−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	$0.182310\pi$
$859$			31.7672i			1.08388i	−0.840416	+	0.541941i	$0.817690\pi$
$860$	13.8622	+	10.3520i	0.472697	+	0.353000i
$861$	−16.9843	+	23.3769i	−0.578823	+	0.796681i
$862$	−21.5796	−	15.8958i	−0.735004	−	0.541413i
$863$	−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	$0.764326\pi$
$864$	−29.9558	−	10.8314i	−1.01912	−	0.368493i
$865$	2.16079	−	1.56991i	0.0734690	−	0.0533784i
$866$	−7.31740	+	22.0279i	−0.248655	+	0.748540i
$867$	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
$872$	53.1518	−	16.1210i	1.79995	−	0.545925i
$873$	5.29357	−	3.84600i	0.179160	−	0.130167i
$874$	0.115249	−	17.5705i	0.00389836	−	0.594331i
$875$	−21.1829	−	6.88276i	−0.716114	−	0.232680i
$876$	−1.72470	−	0.585512i	−0.0582723	−	0.0197826i
$877$	26.9742	−	37.1267i	0.910852	−	1.25368i	−0.0560223	−	0.998430i	$-0.517842\pi$
$877$	26.9742	−	37.1267i	0.910852	−	1.25368i	0.966875	−	0.255251i	$-0.0821582\pi$
$878$	−28.2194	+	20.2211i	−0.952357	+	0.682429i
$879$	−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	$0.605593\pi$
$882$	5.05849	−	3.62475i	0.170328	−	0.122052i
$883$	−13.2759	+	18.2727i	−0.446768	+	0.614924i	−0.971699	−	0.236221i	$-0.924091\pi$
$883$	−13.2759	+	18.2727i	−0.446768	+	0.614924i	0.524931	+	0.851145i	$0.324091\pi$
$884$	1.64783	+	0.559415i	0.0554225	+	0.0188152i
$885$	−23.6226	−	7.67546i	−0.794066	−	0.258008i
$886$	−0.102666	+	15.6521i	−0.00344913	+	0.525843i
$887$	−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	$0.494675\pi$
$888$	0.660058	+	2.17625i	0.0221501	+	0.0730302i
$889$	−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
$894$	−5.04221	+	15.1788i	−0.168637	+	0.507656i
$895$	−15.4624	+	11.2341i	−0.516851	+	0.375514i
$896$	5.51529	+	20.0651i	0.184253	+	0.670328i
$897$	−0.294538	+	0.906494i	−0.00983433	+	0.0302669i
$898$	−30.3616	−	22.3648i	−1.01318	−	0.746322i
$899$	44.4557	−	61.1880i	1.48268	−	2.04073i
$900$	−2.47693	−	1.84972i	−0.0825643	−	0.0616573i
$901$			63.4627i			2.11425i
$902$		0			0
$903$	−11.0025			−0.366142
$904$	−11.9700	+	34.5139i	−0.398117	+	1.14792i
$905$	−18.2489	−	13.2586i	−0.606615	−	0.440732i
$906$	−11.2799	+	15.3132i	−0.374749	+	0.508747i
$907$	16.3872	+	5.32452i	0.544127	+	0.176798i	0.568167	−	0.822913i	$-0.307653\pi$
$907$	16.3872	+	5.32452i	0.544127	+	0.176798i	−0.0240396	+	0.999711i	$0.507653\pi$
$908$	−12.7136	+	3.94727i	−0.421914	+	0.130995i
$909$	−6.66377	−	9.17189i	−0.221023	−	0.304213i
$910$	−0.254485	+	0.766090i	−0.00843610	+	0.0253956i
$911$	−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
$916$	0.429965	−	32.7741i	0.0142065	−	1.08289i
$917$	−11.8440	−	16.3019i	−0.391124	−	0.538336i
$918$	−0.282812	+	43.1166i	−0.00933419	+	1.42306i
$919$	−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	$0.109843\pi$
$920$	0.477340	−	24.2551i	0.0157374	−	0.799667i
$921$	−20.3585	−	14.7913i	−0.670836	−	0.487391i
$922$	−2.61547	−	3.64999i	−0.0861358	−	0.120206i
$923$		−	1.54741i		−	0.0509336i
$924$		0			0
$925$			0.764935i			0.0251509i
$926$	−25.1403	+	18.0147i	−0.826160	+	0.592000i
$927$	−1.65216	−	1.20036i	−0.0542640	−	0.0394251i
$928$	26.4943	+	39.1011i	0.869717	+	1.28356i
$929$	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	$-0.0245905\pi$
$930$	33.0373	+	0.216700i	1.08334	+	0.00710586i
$931$	−5.94738	−	8.18587i	−0.194917	−	0.268281i
$932$	32.1457	+	0.421721i	1.05297	+	0.0138139i
$933$	−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	$0.841826\pi$
$938$	14.2400	+	4.73035i	0.464954	+	0.154451i
$939$	3.09378	+	4.25822i	0.100962	+	0.138962i
$940$	23.2224	−	7.21002i	0.757431	−	0.235165i
$941$	−22.4376	−	7.29043i	−0.731446	−	0.237661i	−0.0804673	−	0.996757i	$-0.525641\pi$
$941$	−22.4376	−	7.29043i	−0.731446	−	0.237661i	−0.650979	+	0.759096i	$0.725641\pi$
$942$	−13.2895	−	9.78923i	−0.432996	−	0.318950i
$943$	−42.2694	−	30.7105i	−1.37648	−	1.00007i
$944$	−1.01062	+	38.5108i	−0.0328930	+	1.25342i
$945$	−20.0016			−0.650652
$946$		0			0
$947$		−	23.1038i		−	0.750772i	−0.926869	−	0.375386i	$-0.877510\pi$
$947$		−	23.1038i		−	0.750772i	0.926869	−	0.375386i	$-0.122490\pi$
$948$	9.23498	−	12.3664i	0.299938	−	0.401642i
$949$	−0.0644141	+	0.0886585i	−0.00209097	+	0.00287798i
$950$	−2.98102	+	4.04693i	−0.0967170	+	0.131300i
$951$	0.802171	−	2.46883i	0.0260122	−	0.0800572i
$952$	23.1094	−	16.1049i	0.748980	−	0.521963i
$953$	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	$0.285768\pi$
$954$	−19.1381	−	6.35743i	−0.619619	−	0.205829i
$955$	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
$960$	−7.14271	+	19.3561i	−0.230530	+	0.624715i
$961$	−41.3033	+	30.0086i	−1.33236	+	0.968019i
$962$	0.136827		0.000897479i	0.00441147		2.89359e-5i
$963$	13.0479	+	4.23950i	0.420461	+	0.136616i
$964$	−3.92947	+	11.5748i	−0.126560	+	0.372798i
$965$	−15.0541	+	20.7202i	−0.484608	+	0.667005i
$966$	8.98628	+	12.5407i	0.289129	+	0.403491i
$967$	−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
$970$	−8.55569	−	11.9398i	−0.274707	−	0.383364i
$971$	−22.8597	+	31.4637i	−0.733604	+	1.00972i	0.265357	+	0.964150i	$0.414510\pi$
$971$	−22.8597	+	31.4637i	−0.733604	+	1.00972i	−0.998961	+	0.0455693i	$0.985490\pi$
$972$	−22.2048	−	7.53823i	−0.712221	−	0.241789i
$973$	32.0725	+	10.4210i	1.02820	+	0.334082i
$974$	14.3606	+	0.0941945i	0.460143	+	0.00301819i
$975$	0.220584	−	0.160264i	0.00706435	−	0.00513255i
$976$	7.54191	+	10.9749i	0.241411	+	0.351297i
$977$	−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
$982$	0.493308	+	0.163870i	0.0157421	+	0.00522931i
$983$	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	$0.270586\pi$
$984$	25.4056	+	36.4553i	0.809901	+	1.16215i
$985$	6.97237	−	21.4588i	0.222158	−	0.683733i
$986$	37.9174	−	51.4754i	1.20754	−	1.63931i
$987$	−9.08932	+	12.5104i	−0.289316	+	0.398210i
$988$	0.720392	+	0.537974i	0.0229187	+	0.0171152i
$989$		−	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	$0.525171\pi$
$992$	−14.2281	−	49.2268i	−0.451742	−	1.56295i
$993$	−8.12616	−	5.90400i	−0.257876	−	0.187358i
$994$	−20.1665	−	14.8549i	−0.639641	−	0.471168i
$995$	45.7936	+	14.8792i	1.45176	+	0.471704i
$996$	2.31568	+	7.45846i	0.0733751	+	0.236330i
$997$	13.1312	+	18.0736i	0.415870	+	0.572396i	0.964638	−	0.263579i	$-0.0849028\pi$
$997$	13.1312	+	18.0736i	0.415870	+	0.572396i	−0.548768	+	0.835975i	$0.684903\pi$
$998$	−41.8499	−	13.9020i	−1.32474	−	0.440060i
$999$	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.269.3		40
8.5	even	2	inner	968.2.o.h.269.10		40
11.2	odd	10		968.2.o.g.493.1		40
11.3	even	5		968.2.c.d.485.8		10
11.4	even	5	inner	968.2.o.h.245.2		40
11.5	even	5	inner	968.2.o.h.565.6		40
11.6	odd	10		968.2.o.g.565.5		40
11.7	odd	10		968.2.o.g.245.9		40
11.8	odd	10		88.2.c.a.45.3	✓	10
11.9	even	5	inner	968.2.o.h.493.10		40
11.10	odd	2		968.2.o.g.269.8		40
33.8	even	10		792.2.f.g.397.8		10
44.3	odd	10		3872.2.c.f.1937.7		10
44.19	even	10		352.2.c.a.177.7		10
88.3	odd	10		3872.2.c.f.1937.4		10
88.5	even	10	inner	968.2.o.h.565.2		40
88.13	odd	10		968.2.o.g.493.8		40
88.19	even	10		352.2.c.a.177.4		10
88.21	odd	2		968.2.o.g.269.1		40
88.29	odd	10		968.2.o.g.245.5		40
88.37	even	10	inner	968.2.o.h.245.6		40
88.53	even	10	inner	968.2.o.h.493.3		40
88.61	odd	10		968.2.o.g.565.9		40
88.69	even	10		968.2.c.d.485.7		10
88.85	odd	10		88.2.c.a.45.4	yes	10
132.107	odd	10		3168.2.f.g.1585.8		10
176.19	even	20		2816.2.a.p.1.2		5
176.85	odd	20		2816.2.a.r.1.2		5
176.107	even	20		2816.2.a.q.1.4		5
176.173	odd	20		2816.2.a.o.1.4		5
264.107	odd	10		3168.2.f.g.1585.3		10
264.173	even	10		792.2.f.g.397.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.3	✓	10	11.8	odd	10
88.2.c.a.45.4	yes	10	88.85	odd	10
352.2.c.a.177.4		10	88.19	even	10
352.2.c.a.177.7		10	44.19	even	10
792.2.f.g.397.7		10	264.173	even	10
792.2.f.g.397.8		10	33.8	even	10
968.2.c.d.485.7		10	88.69	even	10
968.2.c.d.485.8		10	11.3	even	5
968.2.o.g.245.5		40	88.29	odd	10
968.2.o.g.245.9		40	11.7	odd	10
968.2.o.g.269.1		40	88.21	odd	2
968.2.o.g.269.8		40	11.10	odd	2
968.2.o.g.493.1		40	11.2	odd	10
968.2.o.g.493.8		40	88.13	odd	10
968.2.o.g.565.5		40	11.6	odd	10
968.2.o.g.565.9		40	88.61	odd	10
968.2.o.h.245.2		40	11.4	even	5	inner
968.2.o.h.245.6		40	88.37	even	10	inner
968.2.o.h.269.3		40	1.1	even	1	trivial
968.2.o.h.269.10		40	8.5	even	2	inner
968.2.o.h.493.3		40	88.53	even	10	inner
968.2.o.h.493.10		40	11.9	even	5	inner
968.2.o.h.565.2		40	88.5	even	10	inner
968.2.o.h.565.6		40	11.5	even	5	inner
2816.2.a.o.1.4		5	176.173	odd	20
2816.2.a.p.1.2		5	176.19	even	20
2816.2.a.q.1.4		5	176.107	even	20
2816.2.a.r.1.2		5	176.85	odd	20
3168.2.f.g.1585.3		10	264.107	odd	10
3168.2.f.g.1585.8		10	132.107	odd	10
3872.2.c.f.1937.4		10	88.3	odd	10
3872.2.c.f.1937.7		10	44.3	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+(-1.14955 + 0.823732i) q^{2} +(-0.784953 + 1.08039i) q^{3} +(0.642933 - 1.89384i) q^{4} +(-1.83667 - 0.596771i) q^{5} +(0.0123875 - 1.88856i) q^{6} +(-1.48802 + 1.08111i) q^{7} +(0.820934 + 2.70667i) 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} +(0.820012 - 2.46853i) q^{14} +(2.08645 - 1.51589i) q^{15} +(-3.17328 - 2.43523i) q^{16} +(-1.67315 + 5.14942i) q^{17} +(-1.38527 - 1.02041i) q^{18} +(-1.64430 + 2.26318i) q^{19} +(-2.31105 + 3.09468i) q^{20} -2.45628i q^{21} +4.44137 q^{23} +(-3.56867 - 1.23768i) q^{24} +(-1.02786 - 0.746783i) q^{25} +(-0.134786 + 0.182981i) q^{26} +(-5.35542 - 1.74008i) q^{27} +(1.09076 + 3.51317i) q^{28} +(4.90770 + 6.75487i) q^{29} +(-1.14979 + 3.46127i) 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} +(2.43299 + 0.0319184i) q^{36} +(-0.353889 - 0.487087i) q^{37} +(0.0259490 - 3.95610i) q^{38} +(-0.0663168 + 0.204102i) q^{39} +(0.107476 - 5.46117i) q^{40} +(-9.51720 - 6.91465i) q^{41} +(2.02331 + 2.82361i) q^{42} -4.47936i q^{43} -2.34948i q^{45} +(-5.10558 + 3.65850i) q^{46} +(-5.09323 - 3.70045i) q^{47} +(5.12187 - 1.51685i) q^{48} +(-1.11771 + 3.43995i) q^{49} +(1.79672 + 0.0117851i) q^{50} +(-4.25006 - 5.84971i) q^{51} +(0.00421610 - 0.321373i) 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} +(-11.2059 - 3.72244i) q^{58} +(-5.66097 - 7.79166i) q^{59} +(-1.52942 - 4.92602i) q^{60} +(-3.16618 - 1.02875i) q^{61} +(10.3143 + 7.59760i) q^{62} +(-1.81033 - 1.31528i) q^{63} +(-6.65213 + 4.44400i) q^{64} -0.310343 q^{65} +5.76864i q^{67} +(8.67647 + 6.47941i) q^{68} +(-3.48627 + 4.79843i) q^{69} +(-2.97924 + 4.04451i) q^{70} +(2.97557 - 9.15788i) q^{71} +(-2.82313 + 1.96744i) q^{72} +(-0.551701 + 0.400834i) q^{73} +(0.808043 + 0.268421i) 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} +(4.37499 + 6.36643i) q^{80} +(3.13098 - 2.27479i) q^{81} +(16.6363 + 0.109122i) q^{82} +(2.78089 + 0.903567i) q^{83} +(-4.65180 - 1.57922i) q^{84} +(6.14604 - 8.45931i) q^{85} +(3.68979 + 5.14925i) q^{86} -11.1502 q^{87} +5.74214 q^{89} +(1.93534 + 2.70085i) q^{90} +(-0.173735 + 0.239126i) q^{91} +(2.85550 - 8.41126i) q^{92} +(11.5048 + 3.73814i) q^{93} +(8.90310 + 0.0583975i) q^{94} +(4.37063 - 3.17545i) q^{95} +(-4.63837 + 5.96275i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more