LMFDB - Embedded newform 950.2.bb.c.243.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			243.3
Character	$\chi$	$=$	950.243
Dual form			950.2.bb.c.907.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 - 0.906308i) q^{2} +(1.84087 + 1.28899i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.390238 - 2.21315i) q^{6} +(-0.947246 - 3.53517i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.701247 + 1.92666i) q^{9} +O(q^{10})$	\(q+(-0.422618 - 0.906308i) q^{2} +(1.84087 + 1.28899i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.390238 - 2.21315i) q^{6} +(-0.947246 - 3.53517i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.701247 + 1.92666i) q^{9} +(-1.01780 - 1.76288i) q^{11} +(-2.17071 + 0.581641i) q^{12} +(0.228201 + 0.325905i) q^{13} +(-2.80363 + 2.35253i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(3.29740 - 1.53760i) q^{17} +(1.44979 - 1.44979i) q^{18} +(2.20191 - 3.76186i) q^{19} +(2.81305 - 7.72879i) q^{21} +(-1.16757 + 1.66746i) q^{22} +(-0.331390 - 3.78781i) q^{23} +(1.44453 + 1.72152i) q^{24} +(0.198929 - 0.344554i) q^{26} +(0.552380 - 2.06151i) q^{27} +(3.31698 + 1.54673i) q^{28} +(-4.56508 + 1.66155i) q^{29} +(-3.28120 - 1.89440i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(0.398700 - 4.55716i) q^{33} +(-2.78709 - 2.33864i) q^{34} +(-1.92666 - 0.701247i) q^{36} +(7.90769 + 7.90769i) q^{37} +(-4.33997 - 0.405773i) q^{38} +0.894100i q^{39} +(-1.75160 + 0.308853i) q^{41} +(-8.19351 + 0.716839i) q^{42} +(-0.840994 - 0.0735774i) q^{43} +(2.00467 + 0.353477i) q^{44} +(-3.29287 + 1.90114i) q^{46} +(1.80812 - 3.87752i) q^{47} +(0.949745 - 2.03674i) q^{48} +(-5.53799 + 3.19736i) q^{49} +(8.05206 + 1.41979i) q^{51} +(-0.396343 - 0.0346755i) q^{52} +(11.2417 - 0.983524i) q^{53} +(-2.10181 + 0.370605i) q^{54} -3.65988i q^{56} +(8.90244 - 4.08686i) q^{57} +(3.43516 + 3.43516i) q^{58} +(-5.19883 - 1.89222i) q^{59} +(-7.06628 - 5.92932i) q^{61} +(-0.330216 + 3.77439i) q^{62} +(6.14682 - 4.30405i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-4.29869 + 1.56459i) q^{66} +(13.1012 + 6.10920i) q^{67} +(-0.941657 + 3.51431i) q^{68} +(4.27241 - 7.40003i) q^{69} +(5.65737 + 6.74219i) q^{71} +(0.178696 + 2.04251i) q^{72} +(6.07023 - 8.66918i) q^{73} +(3.82487 - 10.5087i) q^{74} +(1.46640 + 4.10484i) q^{76} +(-5.26797 + 5.26797i) q^{77} +(0.810330 - 0.377863i) q^{78} +(-0.813612 - 4.61423i) q^{79} +(8.38601 - 7.03670i) q^{81} +(1.02017 + 1.45696i) q^{82} +(1.85941 - 0.498229i) q^{83} +(4.11240 + 7.12289i) q^{84} +(0.288736 + 0.793294i) q^{86} +(-10.5454 - 2.82564i) q^{87} +(-0.526850 - 1.96623i) q^{88} +(-1.99769 + 11.3295i) q^{89} +(0.935969 - 1.11544i) q^{91} +(3.11464 + 2.18090i) q^{92} +(-3.59840 - 7.71679i) q^{93} -4.27837 q^{94} -2.24729 q^{96} +(3.74799 + 8.03759i) q^{97} +(5.23825 + 3.66786i) q^{98} +(2.68274 - 3.19716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{6}+O(q^{10}) $ 72 * q + 24 * q^6	$ 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) $ 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$3$	1.84087	+	1.28899i	1.06283	+	0.744200i	0.967913	−	0.251285i	$-0.0808533\pi$
$3$	1.84087	+	1.28899i	1.06283	+	0.744200i	0.0949146	+	0.995485i	$0.469742\pi$
$4$	−0.642788	+	0.766044i	−0.321394	+	0.383022i
$5$		0			0
$5$		0			0
$6$	0.390238	−	2.21315i	0.159314	−	0.903514i
$7$	−0.947246	−	3.53517i	−0.358026	−	1.33617i	−0.876634	−	0.481158i	$-0.840216\pi$
$7$	−0.947246	−	3.53517i	−0.358026	−	1.33617i	0.518609	−	0.855012i	$-0.326450\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.701247	+	1.92666i	0.233749	+	0.642220i
$10$		0			0
$11$	−1.01780	−	1.76288i	−0.306877	−	0.531527i	0.670800	−	0.741638i	$-0.265951\pi$
$11$	−1.01780	−	1.76288i	−0.306877	−	0.531527i	−0.977678	+	0.210111i	$0.932617\pi$
$12$	−2.17071	+	0.581641i	−0.626631	+	0.167905i
$13$	0.228201	+	0.325905i	0.0632917	+	0.0903899i	0.849550	−	0.527508i	$-0.176873\pi$
$13$	0.228201	+	0.325905i	0.0632917	+	0.0903899i	−0.786258	+	0.617898i	$0.787985\pi$
$14$	−2.80363	+	2.35253i	−0.749302	+	0.628739i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	3.29740	−	1.53760i	0.799738	−	0.372924i	0.0206090	−	0.999788i	$-0.493440\pi$
$17$	3.29740	−	1.53760i	0.799738	−	0.372924i	0.779129	+	0.626864i	$0.215662\pi$
$18$	1.44979	−	1.44979i	0.341718	−	0.341718i
$19$	2.20191	−	3.76186i	0.505152	−	0.863030i
$19$	2.20191	−	3.76186i	0.505152	−	0.863030i
$20$		0			0
$21$	2.81305	−	7.72879i	0.613858	−	1.68656i
$22$	−1.16757	+	1.66746i	−0.248926	+	0.355504i
$23$	−0.331390	−	3.78781i	−0.0690997	−	0.789813i	−0.949128	−	0.314891i	$-0.898032\pi$
$23$	−0.331390	−	3.78781i	−0.0690997	−	0.789813i	0.880028	−	0.474922i	$-0.157524\pi$
$24$	1.44453	+	1.72152i	0.294863	+	0.351404i
$25$		0			0
$26$	0.198929	−	0.344554i	0.0390131	−	0.0675727i
$27$	0.552380	−	2.06151i	0.106306	−	0.396738i
$28$	3.31698	+	1.54673i	0.626850	+	0.292305i
$29$	−4.56508	+	1.66155i	−0.847714	+	0.308542i	−0.729108	−	0.684399i	$-0.760065\pi$
$29$	−4.56508	+	1.66155i	−0.847714	+	0.308542i	−0.118606	+	0.992941i	$0.537842\pi$
$30$		0			0
$31$	−3.28120	−	1.89440i	−0.589321	−	0.340245i	0.175508	−	0.984478i	$-0.443843\pi$
$31$	−3.28120	−	1.89440i	−0.589321	−	0.340245i	−0.764829	+	0.644233i	$0.777177\pi$
$32$	−0.819152	+	0.573576i	−0.144807	+	0.101395i
$33$	0.398700	−	4.55716i	0.0694047	−	0.793300i
$34$	−2.78709	−	2.33864i	−0.477981	−	0.401074i
$35$		0			0
$36$	−1.92666	−	0.701247i	−0.321110	−	0.116874i
$37$	7.90769	+	7.90769i	1.30002	+	1.30002i	0.928378	+	0.371638i	$0.121204\pi$
$37$	7.90769	+	7.90769i	1.30002	+	1.30002i	0.371638	+	0.928378i	$0.378796\pi$
$38$	−4.33997	−	0.405773i	−0.704036	−	0.0658251i
$39$			0.894100i			0.143171i
$40$		0			0
$41$	−1.75160	+	0.308853i	−0.273553	+	0.0482348i	−0.308742	−	0.951146i	$-0.599908\pi$
$41$	−1.75160	+	0.308853i	−0.273553	+	0.0482348i	0.0351886	+	0.999381i	$0.488797\pi$
$42$	−8.19351	+	0.716839i	−1.26429	+	0.110611i
$43$	−0.840994	−	0.0735774i	−0.128250	−	0.0112205i	0.0228498	−	0.999739i	$-0.492726\pi$
$43$	−0.840994	−	0.0735774i	−0.128250	−	0.0112205i	−0.151100	+	0.988518i	$0.548282\pi$
$44$	2.00467	+	0.353477i	0.302215	+	0.0532887i
$45$		0			0
$46$	−3.29287	+	1.90114i	−0.485507	+	0.280308i
$47$	1.80812	−	3.87752i	0.263741	−	0.565595i	−0.729186	−	0.684315i	$-0.760101\pi$
$47$	1.80812	−	3.87752i	0.263741	−	0.565595i	0.992928	+	0.118720i	$0.0378791\pi$
$48$	0.949745	−	2.03674i	0.137084	−	0.293977i
$49$	−5.53799	+	3.19736i	−0.791141	+	0.456765i
$50$		0			0
$51$	8.05206	+	1.41979i	1.12751	+	0.198811i
$52$	−0.396343	−	0.0346755i	−0.0549629	−	0.00480863i
$53$	11.2417	−	0.983524i	1.54417	−	0.135097i	0.717010	−	0.697063i	$-0.245510\pi$
$53$	11.2417	−	0.983524i	1.54417	−	0.135097i	0.827160	+	0.561966i	$0.189955\pi$
$54$	−2.10181	+	0.370605i	−0.286020	+	0.0504330i
$55$		0			0
$56$		−	3.65988i		−	0.489072i
$57$	8.90244	−	4.08686i	1.17916	−	0.541318i
$58$	3.43516	+	3.43516i	0.451059	+	0.451059i
$59$	−5.19883	−	1.89222i	−0.676830	−	0.246346i	−0.0193440	−	0.999813i	$-0.506158\pi$
$59$	−5.19883	−	1.89222i	−0.676830	−	0.246346i	−0.657486	+	0.753467i	$0.728380\pi$
$60$		0			0
$61$	−7.06628	−	5.92932i	−0.904745	−	0.759171i	0.0663671	−	0.997795i	$-0.478859\pi$
$61$	−7.06628	−	5.92932i	−0.904745	−	0.759171i	−0.971112	+	0.238624i	$0.923304\pi$
$62$	−0.330216	+	3.77439i	−0.0419375	+	0.479347i
$63$	6.14682	−	4.30405i	0.774426	−	0.542259i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−4.29869	+	1.56459i	−0.529132	+	0.192588i
$67$	13.1012	+	6.10920i	1.60057	+	0.746358i	0.998637	−	0.0521887i	$-0.0166197\pi$
$67$	13.1012	+	6.10920i	1.60057	+	0.746358i	0.601933	+	0.798547i	$0.294397\pi$
$68$	−0.941657	+	3.51431i	−0.114193	+	0.426173i
$69$	4.27241	−	7.40003i	0.514338	−	0.890859i
$70$		0			0
$71$	5.65737	+	6.74219i	0.671406	+	0.800150i	0.988975	−	0.148085i	$-0.0473109\pi$
$71$	5.65737	+	6.74219i	0.671406	+	0.800150i	−0.317569	+	0.948235i	$0.602866\pi$
$72$	0.178696	+	2.04251i	0.0210595	+	0.240712i
$73$	6.07023	−	8.66918i	0.710466	−	1.01465i	−0.287908	−	0.957658i	$-0.592960\pi$
$73$	6.07023	−	8.66918i	0.710466	−	1.01465i	0.998375	−	0.0569931i	$-0.0181513\pi$
$74$	3.82487	−	10.5087i	0.444632	−	1.22162i
$75$		0			0
$76$	1.46640	+	4.10484i	0.168207	+	0.470857i
$77$	−5.26797	+	5.26797i	−0.600340	+	0.600340i
$78$	0.810330	−	0.377863i	0.0917518	−	0.0427845i
$79$	−0.813612	−	4.61423i	−0.0915386	−	0.519141i	−0.995753	−	0.0920627i	$-0.970654\pi$
$79$	−0.813612	−	4.61423i	−0.0915386	−	0.519141i	0.904215	−	0.427078i	$-0.140457\pi$
$80$		0			0
$81$	8.38601	−	7.03670i	0.931779	−	0.781855i
$82$	1.02017	+	1.45696i	0.112659	+	0.160894i
$83$	1.85941	−	0.498229i	0.204097	−	0.0546877i	−0.155322	−	0.987864i	$-0.549641\pi$
$83$	1.85941	−	0.498229i	0.204097	−	0.0546877i	0.359419	+	0.933176i	$0.382975\pi$
$84$	4.11240	+	7.12289i	0.448700	+	0.777171i
$85$		0			0
$86$	0.288736	+	0.793294i	0.0311352	+	0.0855431i
$87$	−10.5454	−	2.82564i	−1.13059	−	0.302941i
$88$	−0.526850	−	1.96623i	−0.0561624	−	0.209601i
$89$	−1.99769	+	11.3295i	−0.211755	+	1.20092i	0.674694	+	0.738097i	$0.264275\pi$
$89$	−1.99769	+	11.3295i	−0.211755	+	1.20092i	−0.886450	+	0.462825i	$0.846836\pi$
$90$		0			0
$91$	0.935969	−	1.11544i	0.0981162	−	0.116930i
$92$	3.11464	+	2.18090i	0.324724	+	0.227374i
$93$	−3.59840	−	7.71679i	−0.373136	−	0.800194i
$94$	−4.27837			−0.441281
$95$		0			0
$96$	−2.24729			−0.229363
$97$	3.74799	+	8.03759i	0.380551	+	0.816094i	0.999529	+	0.0306856i	$0.00976907\pi$
$97$	3.74799	+	8.03759i	0.380551	+	0.816094i	−0.618978	+	0.785408i	$0.712453\pi$
$98$	5.23825	+	3.66786i	0.529143	+	0.370510i
$99$	2.68274	−	3.19716i	0.269625	−	0.321327i
$100$		0			0
$101$	−1.12745	+	6.39408i	−0.112185	+	0.636235i	0.875920	+	0.482456i	$0.160255\pi$
$101$	−1.12745	+	6.39408i	−0.112185	+	0.636235i	−0.988105	+	0.153778i	$0.950856\pi$
$102$	−2.11618	−	7.89767i	−0.209533	−	0.781986i
$103$	−15.6168	−	4.18451i	−1.53877	−	0.412312i	−0.612902	−	0.790159i	$-0.709998\pi$
$103$	−15.6168	−	4.18451i	−1.53877	−	0.412312i	−0.925868	+	0.377847i	$0.876665\pi$
$104$	0.136075	+	0.373863i	0.0133433	+	0.0366603i
$105$		0			0
$106$	−5.64233	−	9.77281i	−0.548032	−	0.949219i
$107$	−12.3055	+	3.29724i	−1.18961	+	0.318756i	−0.798733	−	0.601685i	$-0.794496\pi$
$107$	−12.3055	+	3.29724i	−1.18961	+	0.318756i	−0.390881	+	0.920441i	$0.627830\pi$
$108$	1.22415	+	1.74826i	0.117793	+	0.168226i
$109$	−7.69581	+	6.45755i	−0.737124	+	0.618521i	−0.932064	−	0.362294i	$-0.881993\pi$
$109$	−7.69581	+	6.45755i	−0.737124	+	0.618521i	0.194939	+	0.980815i	$0.437549\pi$
$110$		0			0
$111$	4.36409	+	24.7500i	0.414221	+	2.34916i
$112$	−3.31698	+	1.54673i	−0.313425	+	0.146152i
$113$	−11.5628	+	11.5628i	−1.08774	+	1.08774i	−0.0919767	+	0.995761i	$0.529319\pi$
$113$	−11.5628	+	11.5628i	−1.08774	+	1.08774i	−0.995761	+	0.0919767i	$0.970681\pi$
$114$	−7.46629	−	6.34116i	−0.699282	−	0.593904i
$115$		0			0
$116$	1.66155	−	4.56508i	0.154271	−	0.423857i
$117$	−0.467883	+	0.668206i	−0.0432558	+	0.0617757i
$118$	0.482187	+	5.51142i	0.0443889	+	0.507368i
$119$	−8.55915	−	10.2004i	−0.784616	−	0.935069i
$120$		0			0
$121$	3.42818	−	5.93778i	0.311653	−	0.539798i
$122$	−2.38744	+	8.91006i	−0.216149	+	0.806679i
$123$	−3.62257	−	1.68923i	−0.326636	−	0.152313i
$124$	3.56031	−	1.29585i	0.319725	−	0.116370i
$125$		0			0
$126$	−6.49855	−	3.75194i	−0.578937	−	0.334249i
$127$	4.21307	−	2.95002i	0.373849	−	0.261772i	−0.371518	−	0.928426i	$-0.621163\pi$
$127$	4.21307	−	2.95002i	0.373849	−	0.261772i	0.745368	+	0.666653i	$0.232274\pi$
$128$	0.0871557	−	0.996195i	0.00770355	−	0.0880520i
$129$	−1.45332	−	1.21948i	−0.127958	−	0.107369i
$130$		0			0
$131$	7.43460	+	2.70597i	0.649564	+	0.236422i	0.645724	−	0.763571i	$-0.276556\pi$
$131$	7.43460	+	2.70597i	0.649564	+	0.236422i	0.00383987	+	0.999993i	$0.498778\pi$
$132$	3.23471	+	3.23471i	0.281545	+	0.281545i
$133$	−15.3846	−	4.22071i	−1.33401	−	0.365982i
$134$		−	14.4556i		−	1.24877i
$135$		0			0
$136$	3.58301	−	0.631781i	0.307240	−	0.0541748i
$137$	−0.0646282	+	0.00565423i	−0.00552156	+	0.000483074i	−0.0899162	−	0.995949i	$-0.528660\pi$
$137$	−0.0646282	+	0.00565423i	−0.00552156	+	0.000483074i	0.0843946	+	0.996432i	$0.473104\pi$
$138$	−8.51230	−	0.744730i	−0.724615	−	0.0633956i
$139$	17.1262	+	3.01982i	1.45263	+	0.256137i	0.843583	−	0.536998i	$-0.180442\pi$
$139$	17.1262	+	3.01982i	1.45263	+	0.256137i	0.609045	+	0.793136i	$0.291553\pi$
$140$		0			0
$141$	8.32661	−	4.80737i	0.701227	−	0.404854i
$142$	3.71959	−	7.97669i	0.312141	−	0.669389i
$143$	0.342268	−	0.733996i	0.0286219	−	0.0613798i
$144$	1.77562	−	1.02515i	0.147968	−	0.0854295i
$145$		0			0
$146$	−10.4223	−	1.83774i	−0.862559	−	0.152092i
$147$	−14.3161	−	1.25250i	−1.18077	−	0.103304i
$148$	−11.1406	+	0.974677i	−0.915752	+	0.0801179i
$149$	−15.4981	+	2.73273i	−1.26965	+	0.223874i	−0.767582	−	0.640951i	$-0.778540\pi$
$149$	−15.4981	+	2.73273i	−1.26965	+	0.223874i	−0.502073	+	0.864825i	$0.667429\pi$
$150$		0			0
$151$			9.12444i			0.742536i	0.928526	+	0.371268i	$0.121077\pi$
$151$			9.12444i			0.742536i	−0.928526	+	0.371268i	$0.878923\pi$
$152$	3.10052	−	3.06378i	0.251485	−	0.248506i
$153$	5.27473	+	5.27473i	0.426437	+	0.426437i
$154$	7.00074	+	2.54806i	0.564135	+	0.205328i
$155$		0			0
$156$	−0.684920	−	0.574716i	−0.0548375	−	0.0460141i
$157$	1.49617	−	17.1013i	0.119407	−	1.36483i	−0.666045	−	0.745911i	$-0.732014\pi$
$157$	1.49617	−	17.1013i	0.119407	−	1.36483i	0.785453	−	0.618922i	$-0.212430\pi$
$158$	−3.83806	+	2.68744i	−0.305340	+	0.213801i
$159$	21.9623	+	12.6800i	1.74173	+	1.00559i
$160$		0			0
$161$	−13.0766	+	4.75951i	−1.03058	+	0.375102i
$162$	−9.92150	−	4.62647i	−0.779506	−	0.363490i
$163$	−4.17250	+	15.5720i	−0.326816	+	1.21969i	0.585659	+	0.810558i	$0.300836\pi$
$163$	−4.17250	+	15.5720i	−0.326816	+	1.21969i	−0.912474	+	0.409134i	$0.865831\pi$
$164$	0.889308	−	1.54033i	0.0694433	−	0.120279i
$165$		0			0
$166$	−1.23737	−	1.47464i	−0.0960386	−	0.114454i
$167$	−0.984333	−	11.2510i	−0.0761700	−	0.870627i	−0.934135	−	0.356919i	$-0.883827\pi$
$167$	−0.984333	−	11.2510i	−0.0761700	−	0.870627i	0.857965	−	0.513708i	$-0.171728\pi$
$168$	4.71756	−	6.73737i	0.363967	−	0.519799i
$169$	4.39212	−	12.0673i	0.337856	−	0.928251i
$170$		0			0
$171$	8.79191	+	1.60433i	0.672334	+	0.122686i
$172$	0.596944	−	0.596944i	0.0455165	−	0.0455165i
$173$	−19.6625	+	9.16877i	−1.49491	+	0.697088i	−0.986460	−	0.164003i	$-0.947559\pi$
$173$	−19.6625	+	9.16877i	−1.49491	+	0.697088i	−0.508451	+	0.861091i	$0.669782\pi$
$174$	1.89580	+	10.7516i	0.143720	+	0.815076i
$175$		0			0
$176$	−1.55936	+	1.30845i	−0.117541	+	0.0986285i
$177$	−7.13132	−	10.1846i	−0.536023	−	0.765520i
$178$	11.1123	−	2.97752i	0.832899	−	0.223175i
$179$	11.0624	+	19.1607i	0.826843	+	1.43213i	0.900503	+	0.434851i	$0.143199\pi$
$179$	11.0624	+	19.1607i	0.826843	+	1.43213i	−0.0736594	+	0.997283i	$0.523468\pi$
$180$		0			0
$181$	−4.62297	−	12.7015i	−0.343623	−	0.944096i	−0.984334	−	0.176314i	$-0.943583\pi$
$181$	−4.62297	−	12.7015i	−0.343623	−	0.944096i	0.640711	−	0.767782i	$-0.278640\pi$
$182$	−1.40649	−	0.376869i	−0.104256	−	0.0279354i
$183$	−5.36528	−	20.0235i	−0.396613	−	1.48018i
$184$	0.660259	−	3.74451i	0.0486749	−	0.276049i
$185$		0			0
$186$	−5.47304	+	6.52251i	−0.401303	+	0.478254i
$187$	−6.06669	−	4.24794i	−0.443641	−	0.310640i
$188$	1.80812	+	3.87752i	0.131871	+	0.282798i
$189$	−7.81103			−0.568169
$190$		0			0
$191$	−14.2634			−1.03207			−0.516033	−	0.856569i	$-0.672592\pi$
$191$	−14.2634			−1.03207			−0.516033	+	0.856569i	$0.672592\pi$
$192$	0.949745	+	2.03674i	0.0685420	+	0.146989i
$193$	4.09257	+	2.86565i	0.294590	+	0.206274i	0.711522	−	0.702664i	$-0.248006\pi$
$193$	4.09257	+	2.86565i	0.294590	+	0.206274i	−0.416933	+	0.908937i	$0.636895\pi$
$194$	5.70056	−	6.79366i	0.409276	−	0.487757i
$195$		0			0
$196$	1.11043	−	6.29757i	0.0793165	−	0.449826i
$197$	−2.56441	−	9.57051i	−0.182707	−	0.681870i	−0.995110	−	0.0987743i	$-0.968508\pi$
$197$	−2.56441	−	9.57051i	−0.182707	−	0.681870i	0.812403	−	0.583096i	$-0.198159\pi$
$198$	−4.03138	−	1.08021i	−0.286498	−	0.0767669i
$199$	3.43559	+	9.43920i	0.243542	+	0.669127i	0.999888	+	0.0149552i	$0.00476057\pi$
$199$	3.43559	+	9.43920i	0.243542	+	0.669127i	−0.756346	+	0.654172i	$0.773017\pi$
$200$		0			0
$201$	16.2430	+	28.1336i	1.14569	+	1.98439i
$202$	6.27148	−	1.68044i	0.441260	−	0.118235i
$203$	10.1981	+	14.5644i	0.715768	+	1.02222i
$204$	−6.26339	+	5.25561i	−0.438525	+	0.367966i
$205$		0			0
$206$	2.80749	+	15.9221i	0.195607	+	1.10934i
$207$	7.06543	−	3.29467i	0.491082	−	0.228995i
$208$	0.281327	−	0.281327i	0.0195065	−	0.0195065i
$209$	−8.87279	−	0.0528762i	−0.613744	−	0.00365753i
$210$		0			0
$211$	5.63145	−	15.4723i	0.387685	−	1.06516i	−0.580356	−	0.814363i	$-0.697086\pi$
$211$	5.63145	−	15.4723i	0.387685	−	1.06516i	0.968041	−	0.250793i	$-0.0806913\pi$
$212$	−6.47262	+	9.24386i	−0.444541	+	0.634871i
$213$	1.72386	+	19.7038i	0.118117	+	1.35008i
$214$	8.18883	+	9.75907i	0.559777	+	0.667116i
$215$		0			0
$216$	1.06712	−	1.84830i	0.0726080	−	0.125761i
$217$	−3.58893	+	13.3941i	−0.243632	+	0.909249i
$218$	9.10491	+	4.24569i	0.616663	+	0.287554i
$219$	22.3490	−	8.13438i	1.51021	−	0.549670i
$220$		0			0
$221$	1.25359	+	0.723758i	0.0843253	+	0.0486852i
$222$	20.5868	−	14.4150i	1.38169	−	0.967472i
$223$	−1.76268	+	20.1475i	−0.118038	+	1.34918i	0.674011	+	0.738721i	$0.264570\pi$
$223$	−1.76268	+	20.1475i	−0.118038	+	1.34918i	−0.792049	+	0.610457i	$0.790986\pi$
$224$	2.80363	+	2.35253i	0.187325	+	0.157185i
$225$		0			0
$226$	15.3661	+	5.59281i	1.02214	+	0.372028i
$227$	16.9824	+	16.9824i	1.12716	+	1.12716i	0.990637	+	0.136525i	$0.0435932\pi$
$227$	16.9824	+	16.9824i	1.12716	+	1.12716i	0.136525	+	0.990637i	$0.456407\pi$
$228$	−2.59166	+	9.44665i	−0.171637	+	0.625620i
$229$			8.20517i			0.542213i	0.962549	+	0.271107i	$0.0873896\pi$
$229$			8.20517i			0.542213i	−0.962549	+	0.271107i	$0.912610\pi$
$230$		0			0
$231$	−16.4880	+	2.90728i	−1.08483	+	0.191285i
$232$	−4.83957	+	0.423407i	−0.317733	+	0.0277980i
$233$	9.93045	+	0.868802i	0.650566	+	0.0569171i	0.407661	−	0.913133i	$-0.366344\pi$
$233$	9.93045	+	0.868802i	0.650566	+	0.0569171i	0.242904	+	0.970050i	$0.421900\pi$
$234$	0.803337	+	0.141650i	0.0525158	+	0.00925995i
$235$		0			0
$236$	4.79127	−	2.76624i	0.311885	−	0.180067i
$237$	4.44994	−	9.54294i	0.289055	−	0.619880i
$238$	−5.62745	+	12.0681i	−0.364773	+	0.782259i
$239$	−9.17350	+	5.29632i	−0.593384	+	0.342591i	−0.766435	−	0.642322i	$-0.777971\pi$
$239$	−9.17350	+	5.29632i	−0.593384	+	0.342591i	0.173050	+	0.984913i	$0.444638\pi$
$240$		0			0
$241$	−5.98759	−	1.05577i	−0.385695	−	0.0680084i	−0.0225612	−	0.999745i	$-0.507182\pi$
$241$	−5.98759	−	1.05577i	−0.385695	−	0.0680084i	−0.363134	+	0.931737i	$0.618293\pi$
$242$	−6.83027	−	0.597571i	−0.439066	−	0.0384133i
$243$	18.1295	−	1.58612i	1.16301	−	0.101750i
$244$	9.08424	−	1.60180i	0.581559	−	0.102545i
$245$		0			0
$246$			3.99707i			0.254844i
$247$	1.72849	−	0.140849i	0.109981	−	0.00896201i
$248$	−2.67909	−	2.67909i	−0.170122	−	0.170122i
$249$	4.06516	+	1.47960i	0.257619	+	0.0937656i
$250$		0			0
$251$	4.99608	+	4.19221i	0.315350	+	0.264610i	0.786699	−	0.617337i	$-0.211788\pi$
$251$	4.99608	+	4.19221i	0.315350	+	0.264610i	−0.471349	+	0.881947i	$0.656233\pi$
$252$	−0.654006	+	7.47533i	−0.0411985	+	0.470901i
$253$	−6.34015	+	4.43942i	−0.398602	+	0.279104i
$254$	−4.45415	−	2.57160i	−0.279478	−	0.161357i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	14.0201	+	6.53770i	0.874553	+	0.407811i	0.807450	−	0.589936i	$-0.200847\pi$
$257$	14.0201	+	6.53770i	0.874553	+	0.407811i	0.0671022	+	0.997746i	$0.478625\pi$
$258$	−0.491025	+	1.83253i	−0.0305699	+	0.114088i
$259$	20.4645	−	35.4456i	1.27160	−	2.20248i
$260$		0			0
$261$	−6.40249	−	7.63019i	−0.396304	−	0.472297i
$262$	−0.689553	−	7.88163i	−0.0426008	−	0.486929i
$263$	11.4410	−	16.3395i	0.705484	−	1.00754i	−0.293190	−	0.956054i	$-0.594717\pi$
$263$	11.4410	−	16.3395i	0.705484	−	1.00754i	0.998674	−	0.0514815i	$-0.0163943\pi$
$264$	1.56459	−	4.29869i	0.0962941	−	0.264566i
$265$		0			0
$266$	2.67654	+	15.7269i	0.164109	+	0.964279i
$267$	−18.2811	+	18.2811i	−1.11879	+	1.11879i
$268$	−13.1012	+	6.10920i	−0.800285	+	0.373179i
$269$	2.78396	+	15.7886i	0.169741	+	0.962651i	0.944040	+	0.329831i	$0.106992\pi$
$269$	2.78396	+	15.7886i	0.169741	+	0.962651i	−0.774299	+	0.632820i	$0.781897\pi$
$270$		0			0
$271$	−0.427071	+	0.358355i	−0.0259427	+	0.0217685i	−0.655667	−	0.755050i	$-0.727612\pi$
$271$	−0.427071	+	0.358355i	−0.0259427	+	0.0217685i	0.629724	+	0.776819i	$0.283168\pi$
$272$	−2.08683	−	2.98031i	−0.126533	−	0.180708i
$273$	3.16080	−	0.846933i	0.191300	−	0.0512587i
$274$	0.0324375	+	0.0561834i	0.00195962	+	0.00339416i
$275$		0			0
$276$	2.92250	+	8.02950i	0.175914	+	0.483319i
$277$	23.4935	+	6.29506i	1.41159	+	0.378233i	0.882491	−	0.470330i	$-0.155865\pi$
$277$	23.4935	+	6.29506i	1.41159	+	0.378233i	0.529095	+	0.848563i	$0.322532\pi$
$278$	−4.50097	−	16.7979i	−0.269950	−	1.00747i
$279$	1.34894	−	7.65020i	0.0807587	−	0.458005i
$280$		0			0
$281$	−16.7044	+	19.9075i	−0.996502	+	1.18758i	−0.0142727	+	0.999898i	$0.504543\pi$
$281$	−16.7044	+	19.9075i	−0.996502	+	1.18758i	−0.982229	+	0.187686i	$0.939901\pi$
$282$	−7.87594	−	5.51479i	−0.469005	−	0.328401i
$283$	−10.6442	−	22.8265i	−0.632730	−	1.35689i	−0.917284	−	0.398233i	$-0.869623\pi$
$283$	−10.6442	−	22.8265i	−0.632730	−	1.35689i	0.284554	−	0.958660i	$-0.408154\pi$
$284$	−8.80130			−0.522261
$285$		0			0
$286$	−0.809875			−0.0478889
$287$	2.75104	+	5.89963i	0.162389	+	0.348244i
$288$	−1.67951	−	1.17601i	−0.0989663	−	0.0692970i
$289$	−2.41875	+	2.88255i	−0.142279	+	0.169562i
$290$		0			0
$291$	−3.46082	+	19.6273i	−0.202877	+	1.15057i
$292$	2.73911	+	10.2225i	0.160294	+	0.598227i
$293$	15.6986	+	4.20642i	0.917121	+	0.245742i	0.686354	−	0.727267i	$-0.259210\pi$
$293$	15.6986	+	4.20642i	0.917121	+	0.245742i	0.230767	+	0.973009i	$0.425877\pi$
$294$	4.91510	+	13.5041i	0.286654	+	0.787576i
$295$		0			0
$296$	5.59158	+	9.68490i	0.325004	+	0.562923i
$297$	−4.19640	+	1.12442i	−0.243500	+	0.0652455i
$298$	9.02648	+	12.8912i	0.522890	+	0.746764i
$299$	1.15884	−	0.972385i	0.0670177	−	0.0562345i
$300$		0			0
$301$	0.536520	+	3.04275i	0.0309245	+	0.175381i
$302$	8.26955	−	3.85615i	0.475859	−	0.221897i
$303$	−10.3174	+	10.3174i	−0.592719	+	0.592719i
$304$	−4.08707	−	1.51521i	−0.234409	−	0.0869035i
$305$		0			0
$306$	2.55133	−	7.00973i	0.145850	−	0.400720i
$307$	13.4826	−	19.2552i	0.769494	−	1.09895i	−0.222778	−	0.974869i	$-0.571512\pi$
$307$	13.4826	−	19.2552i	0.769494	−	1.09895i	0.992272	−	0.124082i	$-0.0395987\pi$
$308$	−0.649313	−	7.42168i	−0.0369980	−	0.422889i
$309$	−23.3547	−	27.8331i	−1.32860	−	1.58337i
$310$		0			0
$311$	−5.83904	+	10.1135i	−0.331102	+	0.573485i	−0.982728	−	0.185055i	$-0.940754\pi$
$311$	−5.83904	+	10.1135i	−0.331102	+	0.573485i	0.651626	+	0.758540i	$0.274087\pi$
$312$	−0.231410	+	0.863634i	−0.0131010	+	0.0488936i
$313$	4.39298	+	2.04848i	0.248306	+	0.115787i	0.542787	−	0.839870i	$-0.317369\pi$
$313$	4.39298	+	2.04848i	0.248306	+	0.115787i	−0.294481	+	0.955657i	$0.595147\pi$
$314$	−16.1314	+	5.87133i	−0.910345	+	0.331338i
$315$		0			0
$316$	4.05768	+	2.34270i	0.228262	+	0.131787i
$317$	−23.5662	+	16.5012i	−1.32361	+	0.926802i	−0.999813	−	0.0193247i	$-0.993848\pi$
$317$	−23.5662	+	16.5012i	−1.32361	+	0.926802i	−0.323797	+	0.946127i	$0.604959\pi$
$318$	2.21026	−	25.2634i	0.123945	−	1.41670i
$319$	7.57543	+	6.35654i	0.424143	+	0.355898i
$320$		0			0
$321$	−26.9029	−	9.79185i	−1.50157	−	0.546528i
$322$	9.84001	+	9.84001i	0.548362	+	0.548362i
$323$	1.47632	−	15.7900i	0.0821445	−	0.878581i
$324$			10.9472i			0.608176i
$325$		0			0
$326$	15.8764	−	2.79944i	0.879312	−	0.155046i
$327$	−22.4907	+	1.96768i	−1.24374	+	0.108813i
$328$	−1.77185	−	0.155017i	−0.0978339	−	0.00855936i
$329$	−15.4204	−	2.71904i	−0.850157	−	0.149906i
$330$		0			0
$331$	16.3599	−	9.44539i	0.899221	−	0.519166i	0.0222740	−	0.999752i	$-0.492909\pi$
$331$	16.3599	−	9.44539i	0.899221	−	0.519166i	0.876948	+	0.480586i	$0.159576\pi$
$332$	−0.813543	+	1.74465i	−0.0446490	+	0.0957501i
$333$	−9.69018	+	20.7807i	−0.531019	+	1.13877i
$334$	−9.78085	+	5.64698i	−0.535184	+	0.308989i
$335$		0			0
$336$	−8.09985	−	1.42822i	−0.441883	−	0.0779159i
$337$	4.83922	+	0.423377i	0.263609	+	0.0230628i	0.218194	−	0.975905i	$-0.429983\pi$
$337$	4.83922	+	0.423377i	0.263609	+	0.0230628i	0.0454151	+	0.998968i	$0.485539\pi$
$338$	−12.7928	+	1.11923i	−0.695839	+	0.0608780i
$339$	−36.1900	+	6.38128i	−1.96557	+	0.346583i
$340$		0			0
$341$			7.71246i			0.417653i
$342$	−2.26160	−	8.64619i	−0.122294	−	0.467533i
$343$	−1.56643	−	1.56643i	−0.0845791	−	0.0845791i
$344$	−0.793294	−	0.288736i	−0.0427716	−	0.0155676i
$345$		0			0
$346$	16.6194	+	13.9454i	0.893467	+	0.749708i
$347$	−2.05622	+	23.5028i	−0.110384	+	1.26169i	0.715805	+	0.698300i	$0.246060\pi$
$347$	−2.05622	+	23.5028i	−0.110384	+	1.26169i	−0.826189	+	0.563394i	$0.809496\pi$
$348$	8.94305	−	6.26199i	0.479398	−	0.335678i
$349$	27.7330	+	16.0117i	1.48451	+	0.857085i	0.999845	−	0.0176130i	$-0.00560669\pi$
$349$	27.7330	+	16.0117i	1.48451	+	0.857085i	0.484669	+	0.874698i	$0.338940\pi$
$350$		0			0
$351$	0.797911	−	0.290416i	0.0425893	−	0.0155013i
$352$	1.84487	+	0.860279i	0.0983321	+	0.0458530i
$353$	−1.43103	+	5.34067i	−0.0761660	+	0.284255i	−0.993495	−	0.113874i	$-0.963674\pi$
$353$	−1.43103	+	5.34067i	−0.0761660	+	0.284255i	0.917329	+	0.398130i	$0.130341\pi$
$354$	−6.21654	+	10.7674i	−0.330405	+	0.572279i
$355$		0			0
$356$	−7.39479	−	8.81277i	−0.391923	−	0.467076i
$357$	−2.60806	−	29.8103i	−0.138033	−	1.57773i
$358$	12.6903	−	18.1236i	0.670702	−	0.957861i
$359$	9.48616	−	26.0630i	0.500660	−	1.37555i	−0.389971	−	0.920827i	$-0.627515\pi$
$359$	9.48616	−	26.0630i	0.500660	−	1.37555i	0.890631	−	0.454726i	$-0.150263\pi$
$360$		0			0
$361$	−9.30322	−	16.5665i	−0.489643	−	0.871923i
$362$	−9.55773	+	9.55773i	−0.502343	+	0.502343i
$363$	13.9646	−	6.51179i	0.732951	−	0.341781i
$364$	0.252851	+	1.43399i	0.0132530	+	0.0751613i
$365$		0			0
$366$	−15.8800	+	13.3249i	−0.830060	+	0.696503i
$367$	−5.06478	−	7.23325i	−0.264379	−	0.377573i	0.664911	−	0.746922i	$-0.268469\pi$
$367$	−5.06478	−	7.23325i	−0.264379	−	0.377573i	−0.929291	+	0.369350i	$0.879580\pi$
$368$	−3.67272	+	0.984102i	−0.191454	+	0.0512999i
$369$	−1.82336	−	3.15815i	−0.0949201	−	0.164406i
$370$		0			0
$371$	−14.1256	−	38.8098i	−0.733365	−	2.01490i
$372$	8.22441	+	2.20372i	0.426416	+	0.114258i
$373$	−2.17694	−	8.12447i	−0.112718	−	0.420669i	0.886388	−	0.462943i	$-0.153206\pi$
$373$	−2.17694	−	8.12447i	−0.112718	−	0.420669i	−0.999106	+	0.0422739i	$0.986540\pi$
$374$	−1.28605	+	7.29355i	−0.0665000	+	0.377141i
$375$		0			0
$376$	2.75009	−	3.27742i	0.141825	−	0.169020i
$377$	−1.58327	−	1.10861i	−0.0815423	−	0.0570966i
$378$	3.30108	+	7.07920i	0.169789	+	0.364115i
$379$	37.0435			1.90280			0.951399	−	0.307962i	$-0.0996471\pi$
$379$	37.0435			1.90280			0.951399	+	0.307962i	$0.0996471\pi$
$380$		0			0
$381$	11.5583			0.592148
$382$	6.02799	+	12.9271i	0.308419	+	0.661406i
$383$	−21.8129	−	15.2735i	−1.11459	−	0.780442i	−0.136915	−	0.990583i	$-0.543719\pi$
$383$	−21.8129	−	15.2735i	−1.11459	−	0.780442i	−0.977671	+	0.210141i	$0.932608\pi$
$384$	1.44453	−	1.72152i	0.0737158	−	0.0878511i
$385$		0			0
$386$	0.867564	−	4.92020i	0.0441579	−	0.250432i
$387$	−0.447985	−	1.67190i	−0.0227724	−	0.0849877i
$388$	−8.56631	−	2.29534i	−0.434889	−	0.116528i
$389$	10.3560	+	28.4529i	0.525071	+	1.44262i	0.864810	+	0.502100i	$0.167439\pi$
$389$	10.3560	+	28.4529i	0.525071	+	1.44262i	−0.339739	+	0.940520i	$0.610339\pi$
$390$		0			0
$391$	−6.91688	−	11.9804i	−0.349802	−	0.605874i
$392$	−6.17682	+	1.65507i	−0.311977	+	0.0835939i
$393$	10.1982	+	14.5645i	0.514430	+	0.734682i
$394$	−7.59006	+	6.36881i	−0.382382	+	0.320856i
$395$		0			0
$396$	0.724737	+	4.11019i	0.0364194	+	0.206545i
$397$	12.9106	−	6.02029i	0.647962	−	0.302150i	−0.0707119	−	0.997497i	$-0.522527\pi$
$397$	12.9106	−	6.02029i	0.647962	−	0.302150i	0.718674	+	0.695347i	$0.244749\pi$
$398$	7.10288	−	7.10288i	0.356035	−	0.356035i
$399$	−22.8806	−	27.6004i	−1.14546	−	1.38175i
$400$		0			0
$401$	−2.57197	+	7.06642i	−0.128438	+	0.352880i	−0.987198	−	0.159497i	$-0.949013\pi$
$401$	−2.57197	+	7.06642i	−0.128438	+	0.352880i	0.858761	+	0.512377i	$0.171235\pi$
$402$	18.6332	−	26.6109i	0.929338	−	1.32723i
$403$	−0.131379	−	1.50167i	−0.00654444	−	0.0748033i
$404$	−4.17344	−	4.97371i	−0.207636	−	0.247451i
$405$		0			0
$406$	8.88995	−	15.3978i	0.441201	−	0.764182i
$407$	5.89185	−	21.9887i	0.292048	−	1.08994i
$408$	7.41022	+	3.45544i	0.366861	+	0.171070i
$409$	−9.23982	+	3.36302i	−0.456880	+	0.166291i	−0.560200	−	0.828358i	$-0.689276\pi$
$409$	−9.23982	+	3.36302i	−0.456880	+	0.166291i	0.103320	+	0.994648i	$0.467053\pi$
$410$		0			0
$411$	−0.126260	−	0.0728965i	−0.00622797	−	0.00359572i
$412$	13.2438	−	9.27342i	0.652476	−	0.456868i
$413$	−1.76475	+	20.1711i	−0.0868375	+	0.992557i
$414$	−5.97196	−	5.01107i	−0.293506	−	0.246281i
$415$		0			0
$416$	−0.373863	−	0.136075i	−0.0183302	−	0.00667163i
$417$	27.6347	+	27.6347i	1.35328	+	1.35328i
$418$	3.70188	+	8.06383i	0.181065	+	0.394415i
$419$			22.6846i			1.10821i	0.832446	+	0.554107i	$0.186940\pi$
$419$			22.6846i			1.10821i	−0.832446	+	0.554107i	$0.813060\pi$
$420$		0			0
$421$	15.7480	−	2.77679i	0.767510	−	0.135333i	0.223833	−	0.974627i	$-0.428143\pi$
$421$	15.7480	−	2.77679i	0.767510	−	0.135333i	0.543677	+	0.839295i	$0.317032\pi$
$422$	−16.4026	+	1.43504i	−0.798466	+	0.0698568i
$423$	8.73861	+	0.764529i	0.424886	+	0.0371727i
$424$	11.1132	+	1.95956i	0.539706	+	0.0951648i
$425$		0			0
$426$	17.1292	−	9.88953i	0.829911	−	0.479149i
$427$	−14.2676	+	30.5971i	−0.690459	+	1.48070i
$428$	5.38397	−	11.5460i	0.260244	−	0.558095i
$429$	1.57619	−	0.910012i	0.0760990	−	0.0439358i
$430$		0			0
$431$	−11.1562	−	1.96715i	−0.537377	−	0.0947541i	−0.101628	−	0.994822i	$-0.532405\pi$
$431$	−11.1562	−	1.96715i	−0.537377	−	0.0947541i	−0.435749	+	0.900068i	$0.643516\pi$
$432$	−2.12611	−	0.186011i	−0.102293	−	0.00894944i
$433$	0.262954	−	0.0230055i	0.0126367	−	0.00110557i	−0.0808356	−	0.996727i	$-0.525759\pi$
$433$	0.262954	−	0.0230055i	0.0126367	−	0.00110557i	0.0934724	+	0.995622i	$0.470203\pi$
$434$	13.6559	−	2.40790i	0.655504	−	0.115583i
$435$		0			0
$436$		−	10.0462i		−	0.481124i
$437$	−14.9789	−	7.09376i	−0.716538	−	0.339340i
$438$	−16.8174	−	16.8174i	−0.803564	−	0.803564i
$439$	−13.1779	−	4.79637i	−0.628948	−	0.228918i	0.00782562	−	0.999969i	$-0.497509\pi$
$439$	−13.1779	−	4.79637i	−0.628948	−	0.228918i	−0.636773	+	0.771051i	$0.719731\pi$
$440$		0			0
$441$	−10.0437	−	8.42768i	−0.478272	−	0.401318i
$442$	0.126159	−	1.44201i	0.00600079	−	0.0685893i
$443$	20.6262	−	14.4427i	0.979983	−	0.686191i	0.0303444	−	0.999540i	$-0.490340\pi$
$443$	20.6262	−	14.4427i	0.979983	−	0.686191i	0.949638	+	0.313348i	$0.101451\pi$
$444$	−21.7648	−	12.5659i	−1.03291	−	0.596351i
$445$		0			0
$446$	19.0048	−	6.91718i	0.899904	−	0.327538i
$447$	−32.0525	−	14.9463i	−1.51603	−	0.706937i
$448$	0.947246	−	3.53517i	0.0447532	−	0.167021i
$449$	8.85846	−	15.3433i	0.418057	−	0.724095i	−0.577687	−	0.816258i	$-0.696045\pi$
$449$	8.85846	−	15.3433i	0.418057	−	0.724095i	0.995744	+	0.0921629i	$0.0293780\pi$
$450$		0			0
$451$	2.32724	+	2.77349i	0.109585	+	0.130599i
$452$	−1.42520	−	16.2901i	−0.0670356	−	0.766220i
$453$	−11.7613	+	16.7969i	−0.552595	+	0.789188i
$454$	8.21421	−	22.5683i	0.385512	−	1.05919i
$455$		0			0
$456$	9.65685	−	1.64349i	0.452224	−	0.0769634i
$457$	−22.0911	+	22.0911i	−1.03338	+	1.03338i	−0.0339529	+	0.999423i	$0.510810\pi$
$457$	−22.0911	+	22.0911i	−1.03338	+	1.03338i	−0.999423	+	0.0339529i	$0.989190\pi$
$458$	7.43641	−	3.46766i	0.347481	−	0.162033i
$459$	−1.34837	−	7.64697i	−0.0629364	−	0.356930i
$460$		0			0
$461$	8.00960	−	6.72085i	0.373044	−	0.313021i	−0.436920	−	0.899500i	$-0.643931\pi$
$461$	8.00960	−	6.72085i	0.373044	−	0.313021i	0.809964	+	0.586479i	$0.199486\pi$
$462$	9.60303	+	13.7145i	0.446773	+	0.638058i
$463$	22.5965	−	6.05471i	1.05015	−	0.281386i	0.307835	−	0.951440i	$-0.400396\pi$
$463$	22.5965	−	6.05471i	1.05015	−	0.281386i	0.742312	+	0.670054i	$0.233729\pi$
$464$	2.42903	+	4.20720i	0.112765	+	0.195314i
$465$		0			0
$466$	−3.40939	−	9.36722i	−0.157937	−	0.433928i
$467$	−25.3644	−	6.79636i	−1.17372	−	0.314498i	−0.381289	−	0.924456i	$-0.624520\pi$
$467$	−25.3644	−	6.79636i	−1.17372	−	0.314498i	−0.792434	+	0.609958i	$0.791186\pi$
$468$	−0.211126	−	0.787934i	−0.00975932	−	0.0364223i
$469$	9.18699	−	52.1020i	0.424216	−	2.40585i
$470$		0			0
$471$	24.7977	−	29.5528i	1.14262	−	1.36172i
$472$	−4.53194	−	3.17330i	−0.208599	−	0.146063i
$473$	0.726253	+	1.55745i	0.0333931	+	0.0716118i
$474$	−10.5295			−0.483634
$475$		0			0
$476$	13.3157			0.610323
$477$	9.77814	+	20.9693i	0.447710	+	0.960118i
$478$	8.67698	+	6.07569i	0.396876	+	0.277896i
$479$	−10.6969	+	12.7481i	−0.488755	+	0.582475i	−0.952900	−	0.303284i	$-0.901917\pi$
$479$	−10.6969	+	12.7481i	−0.488755	+	0.582475i	0.464146	+	0.885759i	$0.346361\pi$
$480$		0			0
$481$	−0.772613	+	4.38170i	−0.0352281	+	0.199788i
$482$	1.57361	+	5.87279i	0.0716760	+	0.267498i
$483$	−30.2074	−	8.09405i	−1.37448	−	0.368292i
$484$	2.34501	+	6.44287i	0.106591	+	0.292858i
$485$		0			0
$486$	−9.09937	−	15.7606i	−0.412756	−	0.714914i
$487$	−3.93208	+	1.05360i	−0.178180	+	0.0477431i	−0.346806	−	0.937937i	$-0.612734\pi$
$487$	−3.93208	+	1.05360i	−0.178180	+	0.0477431i	0.168626	+	0.985680i	$0.446067\pi$
$488$	−5.29089	−	7.55617i	−0.239507	−	0.342052i
$489$	−27.7532	+	23.2877i	−1.25504	+	1.05311i
$490$		0			0
$491$	−5.77015	−	32.7241i	−0.260403	−	1.47682i	−0.781813	−	0.623513i	$-0.785705\pi$
$491$	−5.77015	−	32.7241i	−0.260403	−	1.47682i	0.521409	−	0.853307i	$-0.325406\pi$
$492$	3.62257	−	1.68923i	0.163318	−	0.0761565i
$493$	−12.4981	+	12.4981i	−0.562886	+	0.562886i
$494$	−0.858144	−	1.50702i	−0.0386097	−	0.0678039i
$495$		0			0
$496$	−1.29585	+	3.56031i	−0.0581852	+	0.159863i
$497$	18.4759	−	26.3863i	0.828756	−	1.18359i
$498$	−0.377040	−	4.30959i	−0.0168956	−	0.193117i
$499$	0.189710	+	0.226087i	0.00849258	+	0.0101211i	0.770274	−	0.637713i	$-0.220119\pi$
$499$	0.189710	+	0.226087i	0.00849258	+	0.0101211i	−0.761781	+	0.647834i	$0.775675\pi$
$500$		0			0
$501$	12.6904	−	21.9804i	0.566965	−	0.982012i
$502$	1.68800	−	6.29969i	0.0753390	−	0.281169i
$503$	31.4925	+	14.6852i	1.40418	+	0.654781i	0.969340	−	0.245725i	$-0.0790260\pi$
$503$	31.4925	+	14.6852i	1.40418	+	0.654781i	0.434843	+	0.900506i	$0.356804\pi$
$504$	7.05134	−	2.56648i	0.314092	−	0.114320i
$505$		0			0
$506$	6.70294	+	3.86995i	0.297982	+	0.172040i
$507$	23.6399	−	16.5529i	1.04989	−	0.735138i
$508$	−0.448260	+	5.12364i	−0.0198883	+	0.227325i
$509$	−7.54692	−	6.33262i	−0.334512	−	0.280689i	0.460024	−	0.887907i	$-0.347841\pi$
$509$	−7.54692	−	6.33262i	−0.334512	−	0.280689i	−0.794535	+	0.607218i	$0.792285\pi$
$510$		0			0
$511$	−36.3971	−	13.2474i	−1.61011	−	0.586032i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−6.53883	−	6.61723i	−0.288696	−	0.292158i
$514$		−	15.4695i		−	0.682331i
$515$		0			0
$516$	1.86835	−	0.329441i	0.0822497	−	0.0145028i
$517$	−8.67589	+	0.759042i	−0.381565	+	0.0333826i
$518$	−40.7733	−	3.56720i	−1.79147	−	0.156734i
$519$	−48.0146	−	8.46626i	−2.10761	−	0.371628i
$520$		0			0
$521$	22.9420	−	13.2456i	1.00511	−	0.580300i	0.0953526	−	0.995444i	$-0.469602\pi$
$521$	22.9420	−	13.2456i	1.00511	−	0.580300i	0.909756	+	0.415144i	$0.136269\pi$
$522$	−4.20949	+	9.02729i	−0.184244	+	0.395114i
$523$	13.7727	−	29.5357i	0.602239	−	1.29151i	−0.334803	−	0.942288i	$-0.608670\pi$
$523$	13.7727	−	29.5357i	0.602239	−	1.29151i	0.937042	−	0.349218i	$-0.113553\pi$
$524$	−6.85177	+	3.95587i	−0.299321	+	0.172813i
$525$		0			0
$526$	−19.6438	−	3.46373i	−0.856510	−	0.151026i
$527$	−13.7323	−	1.20142i	−0.598187	−	0.0523346i
$528$	−4.55716	+	0.398700i	−0.198325	+	0.0173512i
$529$	8.41290	−	1.48342i	0.365778	−	0.0644966i
$530$		0			0
$531$		−	11.3433i		−	0.492257i
$532$	13.1223	−	9.07225i	0.568922	−	0.393332i
$533$	−0.500373	−	0.500373i	−0.0216736	−	0.0216736i
$534$	24.2942	+	8.84238i	1.05131	+	0.382647i
$535$		0			0
$536$	11.0736	+	9.29189i	0.478308	+	0.401348i
$537$	−4.33346	+	49.5316i	−0.187003	+	2.13745i
$538$	13.1328	−	9.19570i	0.566196	−	0.396455i
$539$	11.2731	+	6.50852i	0.485566	+	0.280342i
$540$		0			0
$541$	−13.6337	+	4.96227i	−0.586160	+	0.213345i	−0.618039	−	0.786147i	$-0.712073\pi$
$541$	−13.6337	+	4.96227i	−0.586160	+	0.213345i	0.0318799	+	0.999492i	$0.489851\pi$
$542$	0.505268	+	0.235610i	0.0217031	+	0.0101203i
$543$	7.86185	−	29.3408i	0.337384	−	1.25914i
$544$	−1.81914	+	3.15085i	−0.0779950	+	0.135091i
$545$		0			0
$546$	−2.10339	−	2.50672i	−0.0900169	−	0.107278i
$547$	0.899184	+	10.2777i	0.0384463	+	0.439444i	0.990885	+	0.134712i	$0.0430111\pi$
$547$	0.899184	+	10.2777i	0.0384463	+	0.439444i	−0.952438	+	0.304731i	$0.901433\pi$
$548$	0.0372108	−	0.0531425i	0.00158957	−	0.00227014i
$549$	6.46856	−	17.7722i	0.276072	−	0.758501i
$550$		0			0
$551$	−3.80134	+	20.8318i	−0.161943	+	0.887463i
$552$	6.04210	−	6.04210i	0.257169	−	0.257169i
$553$	−15.5414	+	7.24707i	−0.660887	+	0.308177i
$554$	−4.22351	−	23.9527i	−0.179440	−	1.01765i
$555$		0			0
$556$	−13.3218	+	11.1784i	−0.564972	+	0.474068i
$557$	−21.4053	−	30.5699i	−0.906970	−	1.29529i	−0.955050	−	0.296444i	$-0.904199\pi$
$557$	−21.4053	−	30.5699i	−0.906970	−	1.29529i	0.0480799	−	0.998843i	$-0.484690\pi$
$558$	−7.50352	+	2.01056i	−0.317649	+	0.0851139i
$559$	−0.167937	−	0.290875i	−0.00710296	−	0.0123027i
$560$		0			0
$561$	−5.69244	−	15.6398i	−0.240335	−	0.660315i
$562$	25.1020	+	6.72605i	1.05886	+	0.283721i
$563$	−2.49018	−	9.29350i	−0.104949	−	0.391674i	0.893391	−	0.449281i	$-0.148320\pi$
$563$	−2.49018	−	9.29350i	−0.104949	−	0.391674i	−0.998339	+	0.0576067i	$0.981653\pi$
$564$	−1.66958	+	9.46867i	−0.0703021	+	0.398703i
$565$		0			0
$566$	−16.1894	+	19.2938i	−0.680491	+	0.810978i
$567$	−32.8196	−	22.9805i	−1.37829	−	0.965090i
$568$	3.71959	+	7.97669i	0.156071	+	0.334694i
$569$	−19.0127			−0.797055			−0.398527	−	0.917156i	$-0.630479\pi$
$569$	−19.0127			−0.797055			−0.398527	+	0.917156i	$0.630479\pi$
$570$		0			0
$571$	0.873418			0.0365514			0.0182757	−	0.999833i	$-0.494182\pi$
$571$	0.873418			0.0365514			0.0182757	+	0.999833i	$0.494182\pi$
$572$	0.342268	+	0.733996i	0.0143109	+	0.0306899i
$573$	−26.2571	−	18.3854i	−1.09691	−	0.768063i
$574$	4.18424	−	4.98658i	0.174647	−	0.208136i
$575$		0			0
$576$	−0.356032	+	2.01916i	−0.0148347	+	0.0841316i
$577$	2.00055	+	7.46617i	0.0832841	+	0.310821i	0.994984	−	0.100037i	$-0.0318961\pi$
$577$	2.00055	+	7.46617i	0.0832841	+	0.310821i	−0.911700	+	0.410857i	$0.865229\pi$
$578$	3.63468	+	0.973910i	0.151183	+	0.0405093i
$579$	3.84010	+	10.5506i	0.159589	+	0.438467i
$580$		0			0
$581$	−3.52265	−	6.10141i	−0.146144	−	0.253129i
$582$	19.2510	−	5.15828i	0.797979	−	0.213818i
$583$	−13.1756	−	18.8167i	−0.545679	−	0.779310i
$584$	8.10714	−	6.80270i	0.335476	−	0.281498i
$585$		0			0
$586$	−2.82219	−	16.0055i	−0.116584	−	0.661179i
$587$	31.1379	−	14.5198i	1.28520	−	0.599297i	0.344577	−	0.938758i	$-0.388022\pi$
$587$	31.1379	−	14.5198i	1.28520	−	0.599297i	0.940620	+	0.339461i	$0.110245\pi$
$588$	10.1617	−	10.1617i	0.419060	−	0.419060i
$589$	−14.3514	+	8.17213i	−0.591338	+	0.336727i
$590$		0			0
$591$	7.61556	−	20.9236i	0.313262	−	0.860681i
$592$	6.41440	−	9.16071i	0.263630	−	0.376503i
$593$	0.638147	+	7.29405i	0.0262055	+	0.299531i	0.997975	+	0.0636002i	$0.0202582\pi$
$593$	0.638147	+	7.29405i	0.0262055	+	0.299531i	−0.971770	+	0.235931i	$0.924186\pi$
$594$	2.79255	+	3.32803i	0.114580	+	0.136551i
$595$		0			0
$596$	7.86860	−	13.6288i	0.322310	−	0.558258i
$597$	−5.84258	+	21.8048i	−0.239121	+	0.892411i
$598$	−1.37103	−	0.639321i	−0.0560655	−	0.0261438i
$599$	0.0335506	−	0.0122114i	0.00137084	−	0.000498945i	−0.341335	−	0.939942i	$-0.610879\pi$
$599$	0.0335506	−	0.0122114i	0.00137084	−	0.000498945i	0.342705	+	0.939443i	$0.388657\pi$
$600$		0			0
$601$	27.8767	+	16.0946i	1.13711	+	0.656512i	0.945714	−	0.325000i	$-0.105364\pi$
$601$	27.8767	+	16.0946i	1.13711	+	0.656512i	0.191399	+	0.981512i	$0.438698\pi$
$602$	2.53093	−	1.77218i	0.103153	−	0.0722285i
$603$	−2.58316	+	29.5257i	−0.105194	+	1.20238i
$604$	−6.98972	−	5.86508i	−0.284408	−	0.238647i
$605$		0			0
$606$	13.7111	+	4.99042i	0.556974	+	0.202722i
$607$	18.1942	+	18.1942i	0.738478	+	0.738478i	0.972283	−	0.233806i	$-0.0751179\pi$
$607$	18.1942	+	18.1942i	0.738478	+	0.738478i	−0.233806	+	0.972283i	$0.575118\pi$
$608$	0.354019	+	4.34450i	0.0143574	+	0.176193i
$609$			39.9566i			1.61912i
$610$		0			0
$611$	1.67632	−	0.295581i	0.0678167	−	0.0119579i
$612$	−7.43121	+	0.650147i	−0.300389	+	0.0262806i
$613$	47.8974	+	4.19048i	1.93456	+	0.169252i	0.988126	−	0.153647i	$-0.0491020\pi$
$613$	47.8974	+	4.19048i	1.93456	+	0.169252i	0.946433	+	0.322899i	$0.104658\pi$
$614$	−23.1491	−	4.08182i	−0.934223	−	0.164729i
$615$		0			0
$616$	−6.45191	+	3.72501i	−0.259955	+	0.150085i
$617$	−13.5042	+	28.9599i	−0.543659	+	1.16588i	0.422126	+	0.906537i	$0.361284\pi$
$617$	−13.5042	+	28.9599i	−0.543659	+	1.16588i	−0.965785	+	0.259343i	$0.916494\pi$
$618$	−15.3552	+	32.9294i	−0.617677	+	1.32461i
$619$	−6.33757	+	3.65900i	−0.254728	+	0.147067i	−0.621927	−	0.783075i	$-0.713650\pi$
$619$	−6.33757	+	3.65900i	−0.254728	+	0.147067i	0.367199	+	0.930142i	$0.380317\pi$
$620$		0			0
$621$	−7.99166	−	1.40915i	−0.320694	−	0.0565470i
$622$	11.6337	+	1.01781i	0.466467	+	0.0408106i
$623$	41.9440	−	3.66962i	1.68045	−	0.147020i
$624$	0.880516	−	0.155259i	0.0352489	−	0.00621533i
$625$		0			0
$626$		−	4.84712i		−	0.193730i
$627$	−16.2655	−	11.5343i	−0.649582	−	0.460635i
$628$	12.1386	+	12.1386i	0.484384	+	0.484384i
$629$	38.2337	+	13.9159i	1.52448	+	0.554865i
$630$		0			0
$631$	−3.97788	−	3.33784i	−0.158357	−	0.132877i	0.560166	−	0.828380i	$-0.310737\pi$
$631$	−3.97788	−	3.33784i	−0.158357	−	0.132877i	−0.718523	+	0.695503i	$0.755182\pi$
$632$	0.408360	−	4.66758i	0.0162437	−	0.185666i
$633$	30.3104	−	21.2236i	1.20473	−	0.843562i
$634$	24.9147	+	14.3845i	0.989490	+	0.571282i
$635$		0			0
$636$	−23.8305	+	8.67360i	−0.944942	+	0.343931i
$637$	−2.30581	−	1.07522i	−0.0913596	−	0.0426017i
$638$	2.55947	−	9.55206i	0.101330	−	0.378170i
$639$	−9.02269	+	15.6278i	−0.356932	+	0.618224i
$640$		0			0
$641$	7.52712	+	8.97047i	0.297303	+	0.354312i	0.893930	−	0.448207i	$-0.147937\pi$
$641$	7.52712	+	8.97047i	0.297303	+	0.354312i	−0.596627	+	0.802519i	$0.703493\pi$
$642$	2.49522	+	28.5205i	0.0984786	+	1.12562i
$643$	−1.15385	+	1.64787i	−0.0455035	+	0.0649858i	−0.841259	−	0.540632i	$-0.818185\pi$
$643$	−1.15385	+	1.64787i	−0.0455035	+	0.0649858i	0.795756	+	0.605618i	$0.207074\pi$
$644$	4.75951	−	13.0766i	0.187551	−	0.515292i
$645$		0			0
$646$	−14.9346	+	5.33516i	−0.587592	+	0.209909i
$647$	19.1316	−	19.1316i	0.752140	−	0.752140i	−0.222739	−	0.974878i	$-0.571500\pi$
$647$	19.1316	−	19.1316i	0.752140	−	0.752140i	0.974878	+	0.222739i	$0.0714996\pi$
$648$	9.92150	−	4.62647i	0.389753	−	0.181745i
$649$	1.95560	+	11.0908i	0.0767642	+	0.435351i
$650$		0			0
$651$	−23.8716	+	20.0307i	−0.935602	+	0.785063i
$652$	−9.24680	−	13.2058i	−0.362133	−	0.517179i
$653$	−5.77046	+	1.54619i	−0.225816	+	0.0605071i	−0.369953	−	0.929051i	$-0.620626\pi$
$653$	−5.77046	+	1.54619i	−0.225816	+	0.0605071i	0.144137	+	0.989558i	$0.453959\pi$
$654$	11.2883	+	19.5519i	0.441408	+	0.764541i
$655$		0			0
$656$	0.608323	+	1.67135i	0.0237510	+	0.0652554i
$657$	20.9593	+	5.61602i	0.817700	+	0.219102i
$658$	4.05268	+	15.1248i	0.157990	+	0.589626i
$659$	2.71452	−	15.3948i	0.105743	−	0.599697i	−0.885178	−	0.465252i	$-0.845964\pi$
$659$	2.71452	−	15.3948i	0.105743	−	0.599697i	0.990921	−	0.134445i	$-0.0429252\pi$
$660$		0			0
$661$	−0.941384	+	1.12190i	−0.0366156	+	0.0436368i	−0.784041	−	0.620708i	$-0.786845\pi$
$661$	−0.941384	+	1.12190i	−0.0366156	+	0.0436368i	0.747426	+	0.664345i	$0.231290\pi$
$662$	−15.4744	−	10.8353i	−0.601431	−	0.421126i
$663$	1.37477	+	2.94821i	0.0533917	+	0.114499i
$664$	1.92501			0.0747048
$665$		0			0
$666$	22.9289			0.888478
$667$	7.80647	+	16.7410i	0.302268	+	0.648215i
$668$	9.25147	+	6.47795i	0.357950	+	0.250639i
$669$	−29.2149	+	34.8169i	−1.12951	+	1.34610i
$670$		0			0
$671$	−3.26061	+	18.4918i	−0.125874	+	0.713869i
$672$	2.12874	+	7.94455i	0.0821178	+	0.306468i
$673$	−22.5231	−	6.03504i	−0.868201	−	0.232634i	−0.202891	−	0.979201i	$-0.565034\pi$
$673$	−22.5231	−	6.03504i	−0.868201	−	0.232634i	−0.665310	+	0.746567i	$0.731700\pi$
$674$	−1.66143	−	4.56475i	−0.0639961	−	0.175828i
$675$		0			0
$676$	6.42085	+	11.1212i	0.246956	+	0.427740i
$677$	19.4948	−	5.22361i	0.749245	−	0.200760i	0.136062	−	0.990700i	$-0.456555\pi$
$677$	19.4948	−	5.22361i	0.749245	−	0.200760i	0.613183	+	0.789941i	$0.289889\pi$
$678$	21.0780	+	30.1025i	0.809494	+	1.15608i
$679$	24.8640	−	20.8634i	0.954192	−	0.800663i
$680$		0			0
$681$	9.37223	+	53.1526i	0.359145	+	2.03681i
$682$	6.98987	−	3.25943i	0.267656	−	0.124810i
$683$	8.02116	−	8.02116i	0.306921	−	0.306921i	−0.536793	−	0.843714i	$-0.680364\pi$
$683$	8.02116	−	8.02116i	0.306921	−	0.306921i	0.843714	+	0.536793i	$0.180364\pi$
$684$	−6.88032	+	5.70375i	−0.263076	+	0.218088i
$685$		0			0
$686$	−0.757665	+	2.08167i	−0.0289278	+	0.0794784i
$687$	−10.5764	+	15.1047i	−0.403515	+	0.576279i
$688$	0.0735774	+	0.840994i	0.00280511	+	0.0320626i
$689$	2.88591	+	3.43930i	0.109945	+	0.131027i
$690$		0			0
$691$	−6.21068	+	10.7572i	−0.236265	+	0.409223i	−0.959640	−	0.281233i	$-0.909257\pi$
$691$	−6.21068	+	10.7572i	−0.236265	+	0.409223i	0.723374	+	0.690456i	$0.242590\pi$
$692$	5.61512	−	20.9559i	0.213455	−	0.796624i
$693$	−13.8437	−	6.45543i	−0.525879	−	0.245222i
$694$	22.1697	−	8.06912i	0.841551	−	0.306300i
$695$		0			0
$696$	−9.45479	−	5.45873i	−0.358383	−	0.206912i
$697$	−5.30082	+	3.71168i	−0.200783	+	0.140590i
$698$	2.79102	−	31.9015i	0.105642	−	1.20749i
$699$	17.1608	+	14.3996i	0.649081	+	0.544644i
$700$		0			0
$701$	−19.8105	−	7.21044i	−0.748233	−	0.272334i	−0.0603709	−	0.998176i	$-0.519228\pi$
$701$	−19.8105	−	7.21044i	−0.748233	−	0.272334i	−0.687862	+	0.725842i	$0.741451\pi$
$702$	−0.600418	−	0.600418i	−0.0226613	−	0.0226613i
$703$	47.1596	−	12.3356i	1.77866	−	0.465248i
$704$		−	2.03559i		−	0.0767193i
$705$		0			0
$706$	5.44507	−	0.960113i	0.204928	−	0.0361343i
$707$	23.6721	−	2.07104i	0.890282	−	0.0778896i
$708$	12.3858	+	1.08361i	0.465486	+	0.0407247i
$709$	−11.4026	−	2.01058i	−0.428232	−	0.0755088i	−0.0446217	−	0.999004i	$-0.514208\pi$
$709$	−11.4026	−	2.01058i	−0.428232	−	0.0755088i	−0.383610	+	0.923495i	$0.625319\pi$
$710$		0			0
$711$	8.31950	−	4.80326i	0.312006	−	0.180137i
$712$	−4.86191	+	10.4264i	−0.182208	+	0.390746i
$713$	−6.08827	+	13.0563i	−0.228008	+	0.488964i
$714$	−25.9151	+	14.9621i	−0.969848	+	0.559942i
$715$		0			0
$716$	−21.7887	−	3.84193i	−0.814281	−	0.143580i
$717$	−23.7141	−	2.07472i	−0.885621	−	0.0774818i
$718$	−27.6301	+	2.41732i	−1.03115	+	0.0902137i
$719$	−27.0863	+	4.77604i	−1.01015	+	0.178116i	−0.654145	−	0.756369i	$-0.726972\pi$
$719$	−27.0863	+	4.77604i	−1.01015	+	0.178116i	−0.356002	+	0.934485i	$0.615860\pi$
$720$		0			0
$721$			59.1719i			2.20368i
$722$	−11.0827	+	15.4329i	−0.412454	+	0.574353i
$723$	−9.66151	−	9.66151i	−0.359315	−	0.359315i
$724$	12.7015	+	4.62297i	0.472048	+	0.171811i
$725$		0			0
$726$	−11.8034	−	9.90421i	−0.438065	−	0.367580i
$727$	0.752266	−	8.59844i	0.0279000	−	0.318899i	−0.969401	−	0.245481i	$-0.921054\pi$
$727$	0.752266	−	8.59844i	0.0279000	−	0.318899i	0.997301	−	0.0734172i	$-0.0233905\pi$
$728$	1.19277	−	0.835190i	0.0442072	−	0.0309542i
$729$	6.97700	+	4.02817i	0.258407	+	0.149192i
$730$		0			0
$731$	−2.88623	+	1.05050i	−0.106751	+	0.0388542i
$732$	18.7876	+	8.76081i	0.694410	+	0.323809i
$733$	−2.61866	+	9.77299i	−0.0967226	+	0.360974i	−0.997275	−	0.0737739i	$-0.976496\pi$
$733$	−2.61866	+	9.77299i	−0.0967226	+	0.360974i	0.900552	+	0.434747i	$0.143162\pi$
$734$	−4.41509	+	7.64715i	−0.162964	+	0.282262i
$735$		0			0
$736$	2.44406	+	2.91271i	0.0900891	+	0.107364i
$737$	−2.56462	−	29.3138i	−0.0944691	−	1.07979i
$738$	−2.09167	+	2.98721i	−0.0769954	+	0.109961i
$739$	−5.21626	+	14.3316i	−0.191883	+	0.527195i	−0.997905	−	0.0646905i	$-0.979394\pi$
$739$	−5.21626	+	14.3316i	−0.191883	+	0.527195i	0.806022	+	0.591885i	$0.201616\pi$
$740$		0			0
$741$	3.36348	+	1.96872i	0.123561	+	0.0723229i
$742$	−29.2039	+	29.2039i	−1.07211	+	1.07211i
$743$	−12.9587	+	6.04272i	−0.475407	+	0.221686i	−0.645527	−	0.763737i	$-0.723362\pi$
$743$	−12.9587	+	6.04272i	−0.475407	+	0.221686i	0.170120	+	0.985423i	$0.445584\pi$
$744$	−1.47853	−	8.38518i	−0.0542057	−	0.307416i
$745$		0			0
$746$	−6.44325	+	5.40653i	−0.235904	+	0.197947i
$747$	2.26383	+	3.23308i	0.0828290	+	0.118292i
$748$	7.15371	−	1.91683i	0.261566	−	0.0700863i
$749$	23.3126	+	40.3786i	0.851824	+	1.47540i
$750$		0			0
$751$	−0.373454	−	1.02606i	−0.0136275	−	0.0374414i	0.932692	−	0.360673i	$-0.117453\pi$
$751$	−0.373454	−	1.02606i	−0.0136275	−	0.0374414i	−0.946320	+	0.323232i	$0.895231\pi$
$752$	−4.13259	−	1.10732i	−0.150700	−	0.0403800i
$753$	3.79342	+	14.1572i	0.138240	+	0.515918i
$754$	−0.335629	+	1.90345i	−0.0122229	+	0.0693194i
$755$		0			0
$756$	5.02083	−	5.98360i	0.182606	−	0.217621i
$757$	−15.3020	−	10.7146i	−0.556160	−	0.389428i	0.261435	−	0.965221i	$-0.415804\pi$
$757$	−15.3020	−	10.7146i	−0.556160	−	0.389428i	−0.817595	+	0.575793i	$0.804693\pi$
$758$	−15.6553	−	33.5728i	−0.568625	−	1.21942i
$759$	−17.3938			−0.631354
$760$		0			0
$761$	33.7464			1.22330			0.611652	−	0.791127i	$-0.290505\pi$
$761$	33.7464			1.22330			0.611652	+	0.791127i	$0.290505\pi$
$762$	−4.88474	−	10.4754i	−0.176955	−	0.379482i
$763$	30.1184	+	21.0891i	1.09036	+	0.763477i
$764$	9.16835	−	10.9264i	0.331699	−	0.395304i
$765$		0			0
$766$	−4.62401	+	26.2241i	−0.167072	+	0.947514i
$767$	−0.569696	−	2.12613i	−0.0205705	−	0.0767702i
$768$	−2.17071	−	0.581641i	−0.0783289	−	0.0209882i
$769$	−10.2512	−	28.1649i	−0.369667	−	1.01565i	−0.975488	−	0.220051i	$-0.929377\pi$
$769$	−10.2512	−	28.1649i	−0.369667	−	1.01565i	0.605821	−	0.795601i	$-0.292845\pi$
$770$		0			0
$771$	17.3822	+	30.1069i	0.626006	+	1.08427i
$772$	−4.82587	+	1.29309i	−0.173687	+	0.0465392i
$773$	8.28226	+	11.8283i	0.297892	+	0.425434i	0.939997	−	0.341183i	$-0.110828\pi$
$773$	8.28226	+	11.8283i	0.297892	+	0.425434i	−0.642105	+	0.766617i	$0.721939\pi$
$774$	−1.32593	+	1.11259i	−0.0476597	+	0.0399912i
$775$		0			0
$776$	1.54000	+	8.73377i	0.0552827	+	0.313524i
$777$	83.3616	−	38.8721i	2.99058	−	1.39453i
$778$	21.4104	−	21.4104i	0.767602	−	0.767602i
$779$	−2.69498	+	7.26933i	−0.0965578	+	0.260451i
$780$		0			0
$781$	6.12759	−	16.8354i	0.219262	−	0.602418i
$782$	−7.93472	+	11.3320i	−0.283745	+	0.405230i
$783$	0.903649	+	10.3288i	0.0322938	+	0.369120i
$784$	4.11044	+	4.89864i	0.146802	+	0.174951i
$785$		0			0
$786$	8.88998	−	15.3979i	0.317095	−	0.549225i
$787$	−5.87046	+	21.9089i	−0.209259	+	0.780967i	0.778849	+	0.627211i	$0.215804\pi$
$787$	−5.87046	+	21.9089i	−0.209259	+	0.780967i	−0.988109	+	0.153756i	$0.950863\pi$
$788$	8.97980	+	4.18735i	0.319892	+	0.149168i
$789$	42.1229	−	15.3315i	1.49962	−	0.545816i
$790$		0			0
$791$	51.8294	+	29.9237i	1.84284	+	1.06396i
$792$	3.41881	−	2.39388i	0.121482	−	0.0850627i
$793$	0.319860	−	3.65602i	0.0113586	−	0.129829i
$794$	−10.9125	−	9.15665i	−0.387269	−	0.324957i
$795$		0			0
$796$	−9.43920	−	3.43559i	−0.334564	−	0.121771i
$797$	−37.2856	−	37.2856i	−1.32072	−	1.32072i	−0.913190	−	0.407534i	$-0.866389\pi$
$797$	−37.2856	−	37.2856i	−1.32072	−	1.32072i	−0.407534	−	0.913190i	$-0.633611\pi$
$798$	−15.3447	+	32.4013i	−0.543196	+	1.14699i
$799$		−	15.5659i		−	0.550683i
$800$		0			0
$801$	−23.2289	+	4.09589i	−0.820754	+	0.144721i
$802$	7.49131	−	0.655405i	0.264527	−	0.0231431i
$803$	−21.4610	−	1.87759i	−0.757341	−	0.0662587i
$804$	−31.9924	−	5.64112i	−1.12828	−	0.198947i
$805$		0			0
$806$	−1.30545	+	0.753701i	−0.0459825	+	0.0265480i
$807$	−15.2265	+	32.6534i	−0.535999	+	1.14945i
$808$	−2.74394	+	5.88440i	−0.0965315	+	0.207012i
$809$	32.1500	−	18.5618i	1.13033	−	0.652598i	0.186314	−	0.982490i	$-0.440346\pi$
$809$	32.1500	−	18.5618i	1.13033	−	0.652598i	0.944019	+	0.329892i	$0.107012\pi$
$810$		0			0
$811$	−33.1066	−	5.83759i	−1.16253	−	0.204985i	−0.441090	−	0.897463i	$-0.645408\pi$
$811$	−33.1066	−	5.83759i	−1.16253	−	0.204985i	−0.721440	+	0.692477i	$0.756519\pi$
$812$	−17.7122	−	1.54962i	−0.621577	−	0.0543810i
$813$	−1.24810	+	0.109195i	−0.0437728	+	0.00382962i
$814$	−22.4185	+	3.95299i	−0.785769	+	0.138552i
$815$		0			0
$816$		−	8.17627i		−	0.286227i
$817$	−2.12858	+	3.00169i	−0.0744695	+	0.105016i
$818$	6.95285	+	6.95285i	0.243101	+	0.243101i
$819$	2.80543	+	1.02109i	0.0980295	+	0.0356798i
$820$		0			0
$821$	−36.4020	−	30.5449i	−1.27044	−	1.06602i	−0.994488	−	0.104852i	$-0.966563\pi$
$821$	−36.4020	−	30.5449i	−1.27044	−	1.06602i	−0.275950	−	0.961172i	$-0.588992\pi$
$822$	−0.0127067	+	0.145238i	−0.000443197	+	0.00506576i
$823$	−44.5572	+	31.1993i	−1.55317	+	1.08754i	−0.594086	+	0.804402i	$0.702486\pi$
$823$	−44.5572	+	31.1993i	−1.55317	+	1.08754i	−0.959080	+	0.283137i	$0.908625\pi$
$824$	−14.0016	−	8.08385i	−0.487771	−	0.281614i
$825$		0			0
$826$	19.0271	−	6.92529i	0.662037	−	0.240962i
$827$	36.4111	+	16.9788i	1.26614	+	0.590410i	0.935493	−	0.353345i	$-0.114956\pi$
$827$	36.4111	+	16.9788i	1.26614	+	0.590410i	0.330646	+	0.943755i	$0.392733\pi$
$828$	−2.01771	+	7.53021i	−0.0701204	+	0.261693i
$829$	1.42975	−	2.47640i	0.0496573	−	0.0860089i	−0.840128	−	0.542388i	$-0.817520\pi$
$829$	1.42975	−	2.47640i	0.0496573	−	0.0860089i	0.889786	+	0.456379i	$0.150854\pi$
$830$		0			0
$831$	35.1342	+	41.8713i	1.21879	+	1.45250i
$832$	0.0346755	+	0.396343i	0.00120216	+	0.0137407i
$833$	−13.3447	+	19.0582i	−0.462367	+	0.660328i
$834$	13.3666	−	36.7244i	0.462847	−	1.27166i
$835$		0			0
$836$	5.74383	−	6.76296i	0.198654	−	0.233902i
$837$	−5.71780	+	5.71780i	−0.197636	+	0.197636i
$838$	20.5592	−	9.58691i	0.710206	−	0.331174i
$839$	−5.21072	−	29.5514i	−0.179894	−	1.02023i	−0.932342	−	0.361578i	$-0.882238\pi$
$839$	−5.21072	−	29.5514i	−0.179894	−	1.02023i	0.752448	−	0.658652i	$-0.228873\pi$
$840$		0			0
$841$	−4.13612	+	3.47061i	−0.142625	+	0.119676i
$842$	−9.17202	−	13.0990i	−0.316089	−	0.451421i
$843$	−56.4113	+	15.1154i	−1.94291	+	0.520601i
$844$	8.23263	+	14.2593i	0.283379	+	0.490827i
$845$		0			0
$846$	−3.00020	−	8.24297i	−0.103149	−	0.283399i
$847$	−24.2384	−	6.49466i	−0.832841	−	0.223159i
$848$	−2.92069	−	10.9002i	−0.100297	−	0.374313i
$849$	9.82862	−	55.7408i	0.337317	−	1.91302i
$850$		0			0
$851$	27.3323	−	32.5733i	0.936939	−	1.11660i
$852$	−16.2021	−	11.3448i	−0.555073	−	0.388667i
$853$	15.0441	+	32.2621i	0.515100	+	1.10463i	0.976117	+	0.217244i	$0.0697067\pi$
$853$	15.0441	+	32.2621i	0.515100	+	1.10463i	−0.461018	+	0.887391i	$0.652516\pi$
$854$	33.7601			1.15525
$855$		0			0
$856$	−12.7396			−0.435429
$857$	3.36904	+	7.22494i	0.115084	+	0.246799i	0.955410	−	0.295283i	$-0.0954139\pi$
$857$	3.36904	+	7.22494i	0.115084	+	0.246799i	−0.840325	+	0.542082i	$0.817636\pi$
$858$	−1.49088	−	1.04392i	−0.0508977	−	0.0356389i
$859$	3.63063	−	4.32681i	0.123875	−	0.147629i	−0.700542	−	0.713611i	$-0.747058\pi$
$859$	3.63063	−	4.32681i	0.123875	−	0.147629i	0.824418	+	0.565982i	$0.191503\pi$
$860$		0			0
$861$	−2.54026	+	14.4065i	−0.0865718	+	0.490973i
$862$	2.93199	+	10.9423i	0.0998640	+	0.372698i
$863$	−3.20720	−	0.859366i	−0.109174	−	0.0292532i	0.203818	−	0.979009i	$-0.434665\pi$
$863$	−3.20720	−	0.859366i	−0.109174	−	0.0292532i	−0.312993	+	0.949756i	$0.601331\pi$
$864$	0.729950	+	2.00552i	0.0248334	+	0.0682292i
$865$		0			0
$866$	−0.131979	−	0.228594i	−0.00448483	−	0.00776795i
$867$	−8.16818	+	2.18866i	−0.277406	+	0.0743307i
$868$	−7.95353	−	11.3588i	−0.269960	−	0.385544i
$869$	−7.30621	+	6.13064i	−0.247846	+	0.207968i
$870$		0			0
$871$	0.998697	+	5.66389i	0.0338395	+	0.191914i
$872$	−9.10491	+	4.24569i	−0.308331	+	0.143777i
$873$	−12.8574	+	12.8574i	−0.435158	+	0.435158i
$874$	−0.0987673	+	16.5735i	−0.00334085	+	0.560605i
$875$		0			0
$876$	−8.13438	+	22.3490i	−0.274835	+	0.755103i
$877$	3.89826	−	5.56729i	0.131635	−	0.187994i	−0.747924	−	0.663785i	$-0.768949\pi$
$877$	3.89826	−	5.56729i	0.131635	−	0.187994i	0.879559	+	0.475791i	$0.157838\pi$
$878$	1.22224	+	13.9703i	0.0412486	+	0.471474i
$879$	23.4770	+	27.9788i	0.791860	+	0.943702i
$880$		0			0
$881$	−17.0976	+	29.6140i	−0.576034	+	0.997720i	0.419895	+	0.907573i	$0.362067\pi$
$881$	−17.0976	+	29.6140i	−0.576034	+	0.997720i	−0.995928	+	0.0901468i	$0.971266\pi$
$882$	−3.39341	+	12.6644i	−0.114262	+	0.426432i
$883$	−49.4000	−	23.0356i	−1.66244	−	0.775210i	−0.999651	−	0.0264069i	$-0.991593\pi$
$883$	−49.4000	−	23.0356i	−1.66244	−	0.775210i	−0.662792	−	0.748803i	$-0.730629\pi$
$884$	−1.36022	+	0.495080i	−0.0457492	+	0.0166513i
$885$		0			0
$886$	−21.8065	−	12.5900i	−0.732604	−	0.422969i
$887$	33.3094	−	23.3235i	1.11842	−	0.783127i	0.140083	−	0.990140i	$-0.455263\pi$
$887$	33.3094	−	23.3235i	1.11842	−	0.783127i	0.978338	+	0.207013i	$0.0663742\pi$
$888$	−2.19038	+	25.0362i	−0.0735043	+	0.840159i
$889$	−14.4197	−	12.0995i	−0.483620	−	0.405805i
$890$		0			0
$891$	−20.9401	−	7.62157i	−0.701519	−	0.255332i
$892$	−14.3009	−	14.3009i	−0.478829	−	0.478829i
$893$	−10.6054	−	15.3398i	−0.354896	−	0.513328i
$894$			35.3660i			1.18282i
$895$		0			0
$896$	−3.60428	+	0.635531i	−0.120410	+	0.0212316i
$897$	3.38668	−	0.296296i	0.113078	−	0.00989304i
$898$	−17.6495	−	1.54413i	−0.588972	−	0.0515283i
$899$	18.1266	+	3.19620i	0.604555	+	0.106599i
$900$		0			0
$901$	35.5562	−	20.5284i	1.18455	−	0.683900i
$902$	1.53011	−	3.28132i	0.0509470	−	0.109256i
$903$	−2.93442	+	6.29289i	−0.0976514	+	0.209414i
$904$	−14.1615	+	8.17614i	−0.471004	+	0.271934i
$905$		0			0
$906$	20.1937	+	3.56070i	0.670892	+	0.118296i
$907$	38.0915	+	3.33257i	1.26481	+	0.110656i	0.699746	−	0.714392i	$-0.253297\pi$
$907$	38.0915	+	3.33257i	1.26481	+	0.110656i	0.565062	+	0.825048i	$0.308852\pi$
$908$	−23.9253	+	2.09320i	−0.793990	+	0.0694652i
$909$	−13.1098	+	2.31162i	−0.434826	+	0.0766715i
$910$		0			0
$911$		−	10.9349i		−	0.362288i	−0.983457	−	0.181144i	$-0.942020\pi$
$911$		−	10.9349i		−	0.362288i	0.983457	−	0.181144i	$-0.0579801\pi$
$912$	−5.57067	−	8.05751i	−0.184463	−	0.266811i
$913$	−2.77082	−	2.77082i	−0.0917008	−	0.0917008i
$914$	29.3574	+	10.6852i	0.971056	+	0.353436i
$915$		0			0
$916$	−6.28553	−	5.27418i	−0.207680	−	0.174264i
$917$	2.52368	−	28.8458i	0.0833393	−	0.952573i
$918$	−6.36067	+	4.45379i	−0.209933	+	0.146997i
$919$	41.8138	+	24.1412i	1.37931	+	0.796345i	0.992076	−	0.125636i	$-0.0400972\pi$
$919$	41.8138	+	24.1412i	1.37931	+	0.796345i	0.387234	+	0.921981i	$0.373431\pi$
$920$		0			0
$921$	49.6396	−	18.0673i	1.63568	−	0.595339i
$922$	−9.47616	−	4.41881i	−0.312081	−	0.145526i
$923$	−0.906296	+	3.38234i	−0.0298311	+	0.111331i
$924$	8.37118	−	14.4993i	0.275392	−	0.476992i
$925$		0			0
$926$	−15.0371	−	17.9205i	−0.494150	−	0.588905i
$927$	−2.88911	−	33.0226i	−0.0948907	−	1.08461i
$928$	2.78647	−	3.97948i	0.0914702	−	0.130633i
$929$	2.79049	−	7.66681i	0.0915530	−	0.251540i	−0.885461	−	0.464713i	$-0.846158\pi$
$929$	2.79049	−	7.66681i	0.0915530	−	0.251540i	0.977014	+	0.213173i	$0.0683798\pi$
$930$		0			0
$931$	−0.166108	+	27.8734i	−0.00544397	+	0.913515i
$932$	−7.04871	+	7.04871i	−0.230888	+	0.230888i
$933$	−23.7852	+	11.0912i	−0.778692	+	0.363110i
$934$	4.55985	+	25.8602i	0.149203	+	0.846171i
$935$		0			0
$936$	−0.624885	+	0.524341i	−0.0204250	+	0.0171386i
$937$	−4.79704	−	6.85088i	−0.156712	−	0.223809i	0.733116	−	0.680103i	$-0.238065\pi$
$937$	−4.79704	−	6.85088i	−0.156712	−	0.223809i	−0.889829	+	0.456295i	$0.849176\pi$
$938$	−51.1031	+	13.6930i	−1.66857	+	0.447093i
$939$	5.44644	+	9.43350i	0.177738	+	0.307851i
$940$		0			0
$941$	9.65059	+	26.5148i	0.314600	+	0.864357i	0.991712	+	0.128477i	$0.0410089\pi$
$941$	9.65059	+	26.5148i	0.314600	+	0.864357i	−0.677112	+	0.735880i	$0.736769\pi$
$942$	−37.2639	−	9.98482i	−1.21412	−	0.325323i
$943$	1.75034	+	6.53236i	0.0569989	+	0.212723i
$944$	−0.960705	+	5.44843i	−0.0312683	+	0.177331i
$945$		0			0
$946$	1.10461	−	1.31642i	0.0359138	−	0.0428004i
$947$	11.1199	+	7.78627i	0.361350	+	0.253020i	0.740126	−	0.672469i	$-0.234766\pi$
$947$	11.1199	+	7.78627i	0.361350	+	0.253020i	−0.378776	+	0.925488i	$0.623655\pi$
$948$	4.44994	+	9.54294i	0.144527	+	0.309940i
$949$	4.21057			0.136681
$950$		0			0
$951$	−64.6523			−2.09650
$952$	−5.62745	−	12.0681i	−0.182387	−	0.391129i
$953$	−14.4384	−	10.1098i	−0.467704	−	0.327490i	0.315855	−	0.948808i	$-0.397709\pi$
$953$	−14.4384	−	10.1098i	−0.467704	−	0.327490i	−0.783559	+	0.621318i	$0.786598\pi$
$954$	14.8722	−	17.7240i	0.481506	−	0.573836i
$955$		0			0
$956$	1.83939	−	10.4317i	0.0594902	−	0.337386i
$957$	5.75186	+	21.4662i	0.185931	+	0.693905i
$958$	16.0744	+	4.30712i	0.519341	+	0.139157i
$959$	0.0812075	+	0.223116i	0.00262233	+	0.00720478i
$960$		0			0
$961$	−8.32249	−	14.4150i	−0.268467	−	0.464999i
$962$	4.29769	−	1.15156i	0.138563	−	0.0371279i
$963$	−14.9818	−	21.3963i	−0.482783	−	0.689485i
$964$	4.65752	−	3.90812i	0.150009	−	0.125872i
$965$		0			0
$966$	5.43050	+	30.7979i	0.174723	+	0.990906i
$967$	21.6762	−	10.1078i	0.697059	−	0.325044i	−0.0415896	−	0.999135i	$-0.513242\pi$
$967$	21.6762	−	10.1078i	0.697059	−	0.325044i	0.738648	+	0.674091i	$0.235464\pi$
$968$	4.84818	−	4.84818i	0.155826	−	0.155826i
$969$	23.0709	−	27.1645i	0.741146	−	0.872649i
$970$		0			0
$971$	1.15941	−	3.18546i	0.0372073	−	0.102226i	−0.919698	−	0.392627i	$-0.871566\pi$
$971$	1.15941	−	3.18546i	0.0372073	−	0.102226i	0.956905	+	0.290401i	$0.0937886\pi$
$972$	−10.4384	+	14.9075i	−0.334811	+	0.478159i
$973$	−5.54719	−	63.4047i	−0.177835	−	2.03266i
$974$	2.61666	+	3.11841i	0.0838431	+	0.0999203i
$975$		0			0
$976$	−4.61219	+	7.98855i	−0.147633	+	0.255707i
$977$	−7.39660	+	27.6045i	−0.236638	+	0.883146i	0.740765	+	0.671764i	$0.234463\pi$
$977$	−7.39660	+	27.6045i	−0.236638	+	0.883146i	−0.977404	+	0.211382i	$0.932204\pi$
$978$	32.8348	+	15.3111i	1.04994	+	0.489596i
$979$	22.0057	−	8.00942i	0.703306	−	0.255982i
$980$		0			0
$981$	−17.8382	−	10.2989i	−0.569528	−	0.328817i
$982$	−27.2196	+	19.0594i	−0.868612	+	0.608208i
$983$	2.03577	−	23.2689i	0.0649309	−	0.742164i	−0.892036	−	0.451965i	$-0.850723\pi$
$983$	2.03577	−	23.2689i	0.0649309	−	0.742164i	0.956966	−	0.290198i	$-0.0937213\pi$
$984$	−3.06193	−	2.56926i	−0.0976107	−	0.0819051i
$985$		0			0
$986$	16.6090	+	6.04520i	0.528940	+	0.192518i
$987$	−24.8822	−	24.8822i	−0.792010	−	0.792010i
$988$	−1.00315	+	1.41464i	−0.0319146	+	0.0450056i
$989$			3.20991i			0.102069i
$990$		0			0
$991$	27.9141	−	4.92201i	0.886721	−	0.156353i	0.288305	−	0.957539i	$-0.406908\pi$
$991$	27.9141	−	4.92201i	0.886721	−	0.156353i	0.598416	+	0.801186i	$0.295797\pi$
$992$	3.77439	−	0.330216i	0.119837	−	0.0104844i
$993$	42.2915	+	3.70003i	1.34208	+	0.117417i
$994$	−31.7223	−	5.59350i	−1.00617	−	0.177415i
$995$		0			0
$996$	−3.74647	+	2.16302i	−0.118711	+	0.0685381i
$997$	11.7072	−	25.1061i	0.370770	−	0.795119i	−0.629072	−	0.777347i	$-0.716565\pi$
$997$	11.7072	−	25.1061i	0.370770	−	0.795119i	0.999842	−	0.0177719i	$-0.00565726\pi$
$998$	0.124730	−	0.267484i	0.00394826	−	0.00846706i
$999$	20.6698	−	11.9337i	0.653964	−	0.377566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.c.243.3	✓	72
5.2	odd	4	inner	950.2.bb.c.357.6	yes	72
5.3	odd	4	inner	950.2.bb.c.357.1	yes	72
5.4	even	2	inner	950.2.bb.c.243.4	yes	72
19.14	odd	18	inner	950.2.bb.c.793.6	yes	72
95.14	odd	18	inner	950.2.bb.c.793.1	yes	72
95.33	even	36	inner	950.2.bb.c.907.4	yes	72
95.52	even	36	inner	950.2.bb.c.907.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.c.243.3	✓	72	1.1	even	1	trivial
950.2.bb.c.243.4	yes	72	5.4	even	2	inner
950.2.bb.c.357.1	yes	72	5.3	odd	4	inner
950.2.bb.c.357.6	yes	72	5.2	odd	4	inner
950.2.bb.c.793.1	yes	72	95.14	odd	18	inner
950.2.bb.c.793.6	yes	72	19.14	odd	18	inner
950.2.bb.c.907.3	yes	72	95.52	even	36	inner
950.2.bb.c.907.4	yes	72	95.33	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.422618 - 0.906308i) q^{2} +(1.84087 + 1.28899i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.390238 - 2.21315i) q^{6} +(-0.947246 - 3.53517i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.701247 + 1.92666i) q^{9} +O(q^{10})\)	\(q+(-0.422618 - 0.906308i) q^{2} +(1.84087 + 1.28899i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.390238 - 2.21315i) q^{6} +(-0.947246 - 3.53517i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.701247 + 1.92666i) q^{9} +(-1.01780 - 1.76288i) q^{11} +(-2.17071 + 0.581641i) q^{12} +(0.228201 + 0.325905i) q^{13} +(-2.80363 + 2.35253i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(3.29740 - 1.53760i) q^{17} +(1.44979 - 1.44979i) q^{18} +(2.20191 - 3.76186i) q^{19} +(2.81305 - 7.72879i) q^{21} +(-1.16757 + 1.66746i) q^{22} +(-0.331390 - 3.78781i) q^{23} +(1.44453 + 1.72152i) q^{24} +(0.198929 - 0.344554i) q^{26} +(0.552380 - 2.06151i) q^{27} +(3.31698 + 1.54673i) q^{28} +(-4.56508 + 1.66155i) q^{29} +(-3.28120 - 1.89440i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(0.398700 - 4.55716i) q^{33} +(-2.78709 - 2.33864i) q^{34} +(-1.92666 - 0.701247i) q^{36} +(7.90769 + 7.90769i) q^{37} +(-4.33997 - 0.405773i) q^{38} +0.894100i q^{39} +(-1.75160 + 0.308853i) q^{41} +(-8.19351 + 0.716839i) q^{42} +(-0.840994 - 0.0735774i) q^{43} +(2.00467 + 0.353477i) q^{44} +(-3.29287 + 1.90114i) q^{46} +(1.80812 - 3.87752i) q^{47} +(0.949745 - 2.03674i) q^{48} +(-5.53799 + 3.19736i) q^{49} +(8.05206 + 1.41979i) q^{51} +(-0.396343 - 0.0346755i) q^{52} +(11.2417 - 0.983524i) q^{53} +(-2.10181 + 0.370605i) q^{54} -3.65988i q^{56} +(8.90244 - 4.08686i) q^{57} +(3.43516 + 3.43516i) q^{58} +(-5.19883 - 1.89222i) q^{59} +(-7.06628 - 5.92932i) q^{61} +(-0.330216 + 3.77439i) q^{62} +(6.14682 - 4.30405i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-4.29869 + 1.56459i) q^{66} +(13.1012 + 6.10920i) q^{67} +(-0.941657 + 3.51431i) q^{68} +(4.27241 - 7.40003i) q^{69} +(5.65737 + 6.74219i) q^{71} +(0.178696 + 2.04251i) q^{72} +(6.07023 - 8.66918i) q^{73} +(3.82487 - 10.5087i) q^{74} +(1.46640 + 4.10484i) q^{76} +(-5.26797 + 5.26797i) q^{77} +(0.810330 - 0.377863i) q^{78} +(-0.813612 - 4.61423i) q^{79} +(8.38601 - 7.03670i) q^{81} +(1.02017 + 1.45696i) q^{82} +(1.85941 - 0.498229i) q^{83} +(4.11240 + 7.12289i) q^{84} +(0.288736 + 0.793294i) q^{86} +(-10.5454 - 2.82564i) q^{87} +(-0.526850 - 1.96623i) q^{88} +(-1.99769 + 11.3295i) q^{89} +(0.935969 - 1.11544i) q^{91} +(3.11464 + 2.18090i) q^{92} +(-3.59840 - 7.71679i) q^{93} -4.27837 q^{94} -2.24729 q^{96} +(3.74799 + 8.03759i) q^{97} +(5.23825 + 3.66786i) q^{98} +(2.68274 - 3.19716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{6}+O(q^{10}) \) 72 * q + 24 * q^6	\( 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) \) 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Introduction

L-functions

Modular forms

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Database

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