LMFDB - Embedded newform 930.2.j.g.497.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.18
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.37273 - 1.05623i) q^{3} -1.00000i q^{4} +(0.0887404 - 2.23431i) q^{5} +(0.223801 - 1.71753i) q^{6} +(-1.91575 - 1.91575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.768771 - 2.89983i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.37273 - 1.05623i) q^{3} -1.00000i q^{4} +(0.0887404 - 2.23431i) q^{5} +(0.223801 - 1.71753i) q^{6} +(-1.91575 - 1.91575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.768771 - 2.89983i) q^{9} +(-1.51714 - 1.64264i) q^{10} +2.90133i q^{11} +(-1.05623 - 1.37273i) q^{12} +(-3.30346 + 3.30346i) q^{13} -2.70928 q^{14} +(-2.23812 - 3.16083i) q^{15} -1.00000 q^{16} +(1.96263 - 1.96263i) q^{17} +(-1.50688 - 2.59409i) q^{18} -4.24049i q^{19} +(-2.23431 - 0.0887404i) q^{20} +(-4.65327 - 0.606339i) q^{21} +(2.05155 + 2.05155i) q^{22} +(1.11948 + 1.11948i) q^{23} +(-1.71753 - 0.223801i) q^{24} +(-4.98425 - 0.396546i) q^{25} +4.67179i q^{26} +(-2.00756 - 4.79267i) q^{27} +(-1.91575 + 1.91575i) q^{28} +8.88469 q^{29} +(-3.81763 - 0.652455i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.06446 + 3.98274i) q^{33} -2.77557i q^{34} +(-4.45037 + 4.11036i) q^{35} +(-2.89983 - 0.768771i) q^{36} +(2.16001 + 2.16001i) q^{37} +(-2.99848 - 2.99848i) q^{38} +(-1.04555 + 8.02395i) q^{39} +(-1.64264 + 1.51714i) q^{40} +3.64400i q^{41} +(-3.71910 + 2.86161i) q^{42} +(1.90276 - 1.90276i) q^{43} +2.90133 q^{44} +(-6.41088 - 1.97500i) q^{45} +1.58318 q^{46} +(-2.85601 + 2.85601i) q^{47} +(-1.37273 + 1.05623i) q^{48} +0.340178i q^{49} +(-3.80480 + 3.24400i) q^{50} +(0.621177 - 4.76714i) q^{51} +(3.30346 + 3.30346i) q^{52} +(-2.41379 - 2.41379i) q^{53} +(-4.80849 - 1.96937i) q^{54} +(6.48246 + 0.257465i) q^{55} +2.70928i q^{56} +(-4.47891 - 5.82104i) q^{57} +(6.28243 - 6.28243i) q^{58} +14.8240 q^{59} +(-3.16083 + 2.23812i) q^{60} -6.35938 q^{61} +(0.707107 - 0.707107i) q^{62} +(-7.02811 + 4.08256i) q^{63} +1.00000i q^{64} +(7.08779 + 7.67409i) q^{65} +(4.98313 + 0.649321i) q^{66} +(-0.273727 - 0.273727i) q^{67} +(-1.96263 - 1.96263i) q^{68} +(2.71916 + 0.354318i) q^{69} +(-0.240422 + 6.05335i) q^{70} -12.0879i q^{71} +(-2.59409 + 1.50688i) q^{72} +(4.09656 - 4.09656i) q^{73} +3.05472 q^{74} +(-7.26087 + 4.72015i) q^{75} -4.24049 q^{76} +(5.55822 - 5.55822i) q^{77} +(4.93447 + 6.41311i) q^{78} -17.5965i q^{79} +(-0.0887404 + 2.23431i) q^{80} +(-7.81798 - 4.45860i) q^{81} +(2.57670 + 2.57670i) q^{82} +(0.573218 + 0.573218i) q^{83} +(-0.606339 + 4.65327i) q^{84} +(-4.21095 - 4.55928i) q^{85} -2.69091i q^{86} +(12.1963 - 9.38425i) q^{87} +(2.05155 - 2.05155i) q^{88} +1.57133 q^{89} +(-5.92971 + 3.13664i) q^{90} +12.6572 q^{91} +(1.11948 - 1.11948i) q^{92} +(1.37273 - 1.05623i) q^{93} +4.03900i q^{94} +(-9.47455 - 0.376302i) q^{95} +(-0.223801 + 1.71753i) q^{96} +(5.85296 + 5.85296i) q^{97} +(0.240542 + 0.240542i) q^{98} +(8.41336 + 2.23046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 - 8 * q^7	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.37273	−	1.05623i	0.792546	−	0.609813i
$3$	1.37273	−	1.05623i	0.792546	−	0.609813i
$4$		−	1.00000i		−	0.500000i
$5$	0.0887404	−	2.23431i	0.0396859	−	0.999212i
$5$	0.0887404	−	2.23431i	0.0396859	−	0.999212i
$6$	0.223801	−	1.71753i	0.0913665	−	0.701179i
$7$	−1.91575	−	1.91575i	−0.724085	−	0.724085i	0.245350	−	0.969435i	$-0.421097\pi$
$7$	−1.91575	−	1.91575i	−0.724085	−	0.724085i	−0.969435	+	0.245350i	$0.921097\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.768771	−	2.89983i	0.256257	−	0.966609i
$10$	−1.51714	−	1.64264i	−0.479763	−	0.519449i
$11$			2.90133i			0.874784i	0.899271	+	0.437392i	$0.144098\pi$
$11$			2.90133i			0.874784i	−0.899271	+	0.437392i	$0.855902\pi$
$12$	−1.05623	−	1.37273i	−0.304906	−	0.396273i
$13$	−3.30346	+	3.30346i	−0.916214	+	0.916214i	−0.996752	−	0.0805372i	$-0.974336\pi$
$13$	−3.30346	+	3.30346i	−0.916214	+	0.916214i	0.0805372	+	0.996752i	$0.474336\pi$
$14$	−2.70928			−0.724085
$15$	−2.23812	−	3.16083i	−0.577879	−	0.816122i
$16$	−1.00000			−0.250000
$17$	1.96263	−	1.96263i	0.476007	−	0.476007i	−0.427845	−	0.903852i	$-0.640727\pi$
$17$	1.96263	−	1.96263i	0.476007	−	0.476007i	0.903852	+	0.427845i	$0.140727\pi$
$18$	−1.50688	−	2.59409i	−0.355176	−	0.611433i
$19$		−	4.24049i		−	0.972834i	−0.873727	−	0.486417i	$-0.838304\pi$
$19$		−	4.24049i		−	0.972834i	0.873727	−	0.486417i	$-0.161696\pi$
$20$	−2.23431	−	0.0887404i	−0.499606	−	0.0198430i
$21$	−4.65327	−	0.606339i	−1.01543	−	0.132314i
$22$	2.05155	+	2.05155i	0.437392	+	0.437392i
$23$	1.11948	+	1.11948i	0.233427	+	0.233427i	0.814122	−	0.580694i	$-0.197219\pi$
$23$	1.11948	+	1.11948i	0.233427	+	0.233427i	−0.580694	+	0.814122i	$0.697219\pi$
$24$	−1.71753	−	0.223801i	−0.350590	−	0.0456832i
$25$	−4.98425	−	0.396546i	−0.996850	−	0.0793093i
$26$			4.67179i			0.916214i
$27$	−2.00756	−	4.79267i	−0.386355	−	0.922350i
$28$	−1.91575	+	1.91575i	−0.362042	+	0.362042i
$29$	8.88469			1.64985			0.824923	−	0.565245i	$-0.191219\pi$
$29$	8.88469			1.64985			0.824923	+	0.565245i	$0.191219\pi$
$30$	−3.81763	−	0.652455i	−0.697001	−	0.119121i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.06446	+	3.98274i	0.533455	+	0.693306i
$34$		−	2.77557i		−	0.476007i
$35$	−4.45037	+	4.11036i	−0.752250	+	0.694778i
$36$	−2.89983	−	0.768771i	−0.483304	−	0.128129i
$37$	2.16001	+	2.16001i	0.355104	+	0.355104i	0.862004	−	0.506901i	$-0.169209\pi$
$37$	2.16001	+	2.16001i	0.355104	+	0.355104i	−0.506901	+	0.862004i	$0.669209\pi$
$38$	−2.99848	−	2.99848i	−0.486417	−	0.486417i
$39$	−1.04555	+	8.02395i	−0.167423	+	1.28486i
$40$	−1.64264	+	1.51714i	−0.259725	+	0.239882i
$41$			3.64400i			0.569098i	0.958662	+	0.284549i	$0.0918438\pi$
$41$			3.64400i			0.569098i	−0.958662	+	0.284549i	$0.908156\pi$
$42$	−3.71910	+	2.86161i	−0.573870	+	0.441556i
$43$	1.90276	−	1.90276i	0.290168	−	0.290168i	−0.546979	−	0.837147i	$-0.684222\pi$
$43$	1.90276	−	1.90276i	0.290168	−	0.290168i	0.837147	+	0.546979i	$0.184222\pi$
$44$	2.90133			0.437392
$45$	−6.41088	−	1.97500i	−0.955677	−	0.294416i
$46$	1.58318			0.233427
$47$	−2.85601	+	2.85601i	−0.416591	+	0.416591i	−0.884027	−	0.467436i	$-0.845178\pi$
$47$	−2.85601	+	2.85601i	−0.416591	+	0.416591i	0.467436	+	0.884027i	$0.345178\pi$
$48$	−1.37273	+	1.05623i	−0.198136	+	0.152453i
$49$			0.340178i			0.0485969i
$50$	−3.80480	+	3.24400i	−0.538080	+	0.458770i
$51$	0.621177	−	4.76714i	0.0869822	−	0.667532i
$52$	3.30346	+	3.30346i	0.458107	+	0.458107i
$53$	−2.41379	−	2.41379i	−0.331560	−	0.331560i	0.521619	−	0.853179i	$-0.325328\pi$
$53$	−2.41379	−	2.41379i	−0.331560	−	0.331560i	−0.853179	+	0.521619i	$0.825328\pi$
$54$	−4.80849	−	1.96937i	−0.654353	−	0.267998i
$55$	6.48246	+	0.257465i	0.874095	+	0.0347166i
$56$			2.70928i			0.362042i
$57$	−4.47891	−	5.82104i	−0.593247	−	0.771016i
$58$	6.28243	−	6.28243i	0.824923	−	0.824923i
$59$	14.8240			1.92992			0.964959	−	0.262401i	$-0.0845143\pi$
$59$	14.8240			1.92992			0.964959	+	0.262401i	$0.0845143\pi$
$60$	−3.16083	+	2.23812i	−0.408061	+	0.288940i
$61$	−6.35938			−0.814235			−0.407117	−	0.913376i	$-0.633466\pi$
$61$	−6.35938			−0.814235			−0.407117	+	0.913376i	$0.633466\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	−7.02811	+	4.08256i	−0.885458	+	0.514355i
$64$			1.00000i			0.125000i
$65$	7.08779	+	7.67409i	0.879132	+	0.951853i
$66$	4.98313	+	0.649321i	0.613380	+	0.0799259i
$67$	−0.273727	−	0.273727i	−0.0334411	−	0.0334411i	0.690189	−	0.723630i	$-0.257528\pi$
$67$	−0.273727	−	0.273727i	−0.0334411	−	0.0334411i	−0.723630	+	0.690189i	$0.757528\pi$
$68$	−1.96263	−	1.96263i	−0.238004	−	0.238004i
$69$	2.71916	+	0.354318i	0.327349	+	0.0426549i
$70$	−0.240422	+	6.05335i	−0.0287360	+	0.723514i
$71$		−	12.0879i		−	1.43457i	−0.696780	−	0.717285i	$-0.745385\pi$
$71$		−	12.0879i		−	1.43457i	0.696780	−	0.717285i	$-0.254615\pi$
$72$	−2.59409	+	1.50688i	−0.305716	+	0.177588i
$73$	4.09656	−	4.09656i	0.479466	−	0.479466i	−0.425495	−	0.904961i	$-0.639900\pi$
$73$	4.09656	−	4.09656i	0.479466	−	0.479466i	0.904961	+	0.425495i	$0.139900\pi$
$74$	3.05472			0.355104
$75$	−7.26087	+	4.72015i	−0.838413	+	0.545036i
$76$	−4.24049			−0.486417
$77$	5.55822	−	5.55822i	0.633418	−	0.633418i
$78$	4.93447	+	6.41311i	0.558719	+	0.726142i
$79$		−	17.5965i		−	1.97976i	−0.141917	−	0.989879i	$-0.545327\pi$
$79$		−	17.5965i		−	1.97976i	0.141917	−	0.989879i	$-0.454673\pi$
$80$	−0.0887404	+	2.23431i	−0.00992148	+	0.249803i
$81$	−7.81798	−	4.45860i	−0.868665	−	0.495401i
$82$	2.57670	+	2.57670i	0.284549	+	0.284549i
$83$	0.573218	+	0.573218i	0.0629188	+	0.0629188i	0.737866	−	0.674947i	$-0.235834\pi$
$83$	0.573218	+	0.573218i	0.0629188	+	0.0629188i	−0.674947	+	0.737866i	$0.735834\pi$
$84$	−0.606339	+	4.65327i	−0.0661570	+	0.507713i
$85$	−4.21095	−	4.55928i	−0.456741	−	0.494523i
$86$		−	2.69091i		−	0.290168i
$87$	12.1963	−	9.38425i	1.30758	−	1.00610i
$88$	2.05155	−	2.05155i	0.218696	−	0.218696i
$89$	1.57133			0.166560			0.0832801	−	0.996526i	$-0.473460\pi$
$89$	1.57133			0.166560			0.0832801	+	0.996526i	$0.473460\pi$
$90$	−5.92971	+	3.13664i	−0.625047	+	0.330631i
$91$	12.6572			1.32683
$92$	1.11948	−	1.11948i	0.116714	−	0.116714i
$93$	1.37273	−	1.05623i	0.142345	−	0.109526i
$94$			4.03900i			0.416591i
$95$	−9.47455	−	0.376302i	−0.972068	−	0.0386078i
$96$	−0.223801	+	1.71753i	−0.0228416	+	0.175295i
$97$	5.85296	+	5.85296i	0.594278	+	0.594278i	0.938784	−	0.344506i	$-0.111954\pi$
$97$	5.85296	+	5.85296i	0.594278	+	0.594278i	−0.344506	+	0.938784i	$0.611954\pi$
$98$	0.240542	+	0.240542i	0.0242984	+	0.0242984i
$99$	8.41336	+	2.23046i	0.845574	+	0.224170i
$100$	−0.396546	+	4.98425i	−0.0396546	+	0.498425i
$101$			4.48698i			0.446472i	0.974764	+	0.223236i	$0.0716620\pi$
$101$			4.48698i			0.446472i	−0.974764	+	0.223236i	$0.928338\pi$
$102$	−2.93164	−	3.81011i	−0.290275	−	0.377257i
$103$	−10.0236	+	10.0236i	−0.987656	+	0.987656i	−0.999925	−	0.0122685i	$-0.996095\pi$
$103$	−10.0236	+	10.0236i	−0.987656	+	0.987656i	0.0122685	+	0.999925i	$0.496095\pi$
$104$	4.67179			0.458107
$105$	−1.76768	+	10.3430i	−0.172508	+	1.00938i
$106$	−3.41362			−0.331560
$107$	−6.69006	+	6.69006i	−0.646753	+	0.646753i	−0.952207	−	0.305454i	$-0.901192\pi$
$107$	−6.69006	+	6.69006i	−0.646753	+	0.646753i	0.305454	+	0.952207i	$0.401192\pi$
$108$	−4.79267	+	2.00756i	−0.461175	+	0.193177i
$109$		−	2.59911i		−	0.248950i	−0.992223	−	0.124475i	$-0.960275\pi$
$109$		−	2.59911i		−	0.248950i	0.992223	−	0.124475i	$-0.0397246\pi$
$110$	4.76585	−	4.40174i	0.454406	−	0.419689i
$111$	5.24657	+	0.683649i	0.497983	+	0.0648891i
$112$	1.91575	+	1.91575i	0.181021	+	0.181021i
$113$	4.81572	+	4.81572i	0.453025	+	0.453025i	0.896357	−	0.443332i	$-0.146204\pi$
$113$	4.81572	+	4.81572i	0.453025	+	0.453025i	−0.443332	+	0.896357i	$0.646204\pi$
$114$	−7.28317	−	0.949026i	−0.682131	−	0.0888844i
$115$	2.60060	−	2.40191i	0.242507	−	0.223980i
$116$		−	8.88469i		−	0.824923i
$117$	7.03985	+	12.1191i	0.650834	+	1.12041i
$118$	10.4821	−	10.4821i	0.964959	−	0.964959i
$119$	−7.51980			−0.689339
$120$	−0.652455	+	3.81763i	−0.0595607	+	0.348500i
$121$	2.58228			0.234753
$122$	−4.49676	+	4.49676i	−0.407117	+	0.407117i
$123$	3.84889	+	5.00223i	0.347043	+	0.451036i
$124$		−	1.00000i		−	0.0898027i
$125$	−1.32831	+	11.1012i	−0.118808	+	0.992917i
$126$	−2.08281	+	7.85643i	−0.185552	+	0.699906i
$127$	−4.59947	−	4.59947i	−0.408137	−	0.408137i	0.472952	−	0.881088i	$-0.343189\pi$
$127$	−4.59947	−	4.59947i	−0.408137	−	0.408137i	−0.881088	+	0.472952i	$0.843189\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.602228	−	4.62171i	0.0530232	−	0.406919i
$130$	10.4382	+	0.414577i	0.915493	+	0.0363608i
$131$			3.27542i			0.286175i	0.989710	+	0.143088i	$0.0457030\pi$
$131$			3.27542i			0.286175i	−0.989710	+	0.143088i	$0.954297\pi$
$132$	3.98274	−	3.06446i	0.346653	−	0.266727i
$133$	−8.12370	+	8.12370i	−0.704414	+	0.704414i
$134$	−0.387109			−0.0334411
$135$	−10.8865	+	4.06020i	−0.936956	+	0.349446i
$136$	−2.77557			−0.238004
$137$	7.69947	−	7.69947i	0.657810	−	0.657810i	−0.297052	−	0.954861i	$-0.596003\pi$
$137$	7.69947	−	7.69947i	0.657810	−	0.657810i	0.954861	+	0.297052i	$0.0960033\pi$
$138$	2.17328	−	1.67220i	0.185002	−	0.142347i
$139$		−	13.2282i		−	1.12200i	−0.827816	−	0.560999i	$-0.810417\pi$
$139$		−	13.2282i		−	1.12200i	0.827816	−	0.560999i	$-0.189583\pi$
$140$	4.11036	+	4.45037i	0.347389	+	0.376125i
$141$	−0.903934	+	6.93711i	−0.0761249	+	0.584210i
$142$	−8.54744	−	8.54744i	−0.717285	−	0.717285i
$143$	−9.58443	−	9.58443i	−0.801490	−	0.801490i
$144$	−0.768771	+	2.89983i	−0.0640643	+	0.241652i
$145$	0.788431	−	19.8511i	0.0654756	−	1.64855i
$146$		−	5.79341i		−	0.479466i
$147$	0.359305	+	0.466973i	0.0296350	+	0.0385152i
$148$	2.16001	−	2.16001i	0.177552	−	0.177552i
$149$	−7.97282			−0.653159			−0.326580	−	0.945170i	$-0.605896\pi$
$149$	−7.97282			−0.653159			−0.326580	+	0.945170i	$0.605896\pi$
$150$	−1.79656	+	8.47186i	−0.146689	+	0.691724i
$151$	21.7180			1.76739			0.883693	−	0.468067i	$-0.155049\pi$
$151$	21.7180			1.76739			0.883693	+	0.468067i	$0.155049\pi$
$152$	−2.99848	+	2.99848i	−0.243209	+	0.243209i
$153$	−4.18247	−	7.20009i	−0.338132	−	0.582093i
$154$		−	7.86051i		−	0.633418i
$155$	0.0887404	−	2.23431i	0.00712780	−	0.179464i
$156$	8.02395	+	1.04555i	0.642430	+	0.0837113i
$157$	17.3950	+	17.3950i	1.38827	+	1.38827i	0.828957	+	0.559313i	$0.188935\pi$
$157$	17.3950	+	17.3950i	1.38827	+	1.38827i	0.559313	+	0.828957i	$0.311065\pi$
$158$	−12.4426	−	12.4426i	−0.989879	−	0.989879i
$159$	−5.86299	−	0.763972i	−0.464966	−	0.0605869i
$160$	1.51714	+	1.64264i	0.119941	+	0.129862i
$161$		−	4.28927i		−	0.338042i
$162$	−8.68086	+	2.37544i	−0.682033	+	0.186632i
$163$	−3.25399	+	3.25399i	−0.254872	+	0.254872i	−0.822965	−	0.568093i	$-0.807682\pi$
$163$	−3.25399	+	3.25399i	−0.254872	+	0.254872i	0.568093	+	0.822965i	$0.307682\pi$
$164$	3.64400			0.284549
$165$	9.17061	−	6.49352i	0.713931	−	0.505520i
$166$	0.810652			0.0629188
$167$	−5.50723	+	5.50723i	−0.426162	+	0.426162i	−0.887319	−	0.461157i	$-0.847435\pi$
$167$	−5.50723	+	5.50723i	−0.426162	+	0.426162i	0.461157	+	0.887319i	$0.347435\pi$
$168$	2.86161	+	3.71910i	0.220778	+	0.286935i
$169$		−	8.82567i		−	0.678898i
$170$	−6.20148	−	0.246306i	−0.475632	−	0.0188908i
$171$	−12.2967	−	3.25996i	−0.940350	−	0.249296i
$172$	−1.90276	−	1.90276i	−0.145084	−	0.145084i
$173$	4.80907	+	4.80907i	0.365627	+	0.365627i	0.865879	−	0.500253i	$-0.166760\pi$
$173$	4.80907	+	4.80907i	0.365627	+	0.365627i	−0.500253	+	0.865879i	$0.666760\pi$
$174$	1.98840	−	15.2597i	0.150741	−	1.15684i
$175$	8.78888	+	10.3082i	0.664377	+	0.779230i
$176$		−	2.90133i		−	0.218696i
$177$	20.3493	−	15.6575i	1.52955	−	1.17689i
$178$	1.11109	−	1.11109i	0.0832801	−	0.0832801i
$179$	4.62728			0.345859			0.172929	−	0.984934i	$-0.444677\pi$
$179$	4.62728			0.345859			0.172929	+	0.984934i	$0.444677\pi$
$180$	−1.97500	+	6.41088i	−0.147208	+	0.477839i
$181$	1.05315			0.0782799			0.0391400	−	0.999234i	$-0.487538\pi$
$181$	1.05315			0.0782799			0.0391400	+	0.999234i	$0.487538\pi$
$182$	8.94998	−	8.94998i	0.663417	−	0.663417i
$183$	−8.72970	+	6.71694i	−0.645318	+	0.496531i
$184$		−	1.58318i		−	0.116714i
$185$	5.01781	−	4.63445i	0.368916	−	0.340731i
$186$	0.223801	−	1.71753i	0.0164099	−	0.125935i
$187$	5.69423	+	5.69423i	0.416403	+	0.416403i
$188$	2.85601	+	2.85601i	0.208296	+	0.208296i
$189$	−5.33557	+	13.0275i	−0.388106	+	0.947613i
$190$	−6.96560	+	6.43343i	−0.505338	+	0.466730i
$191$			15.2760i			1.10533i	0.833403	+	0.552665i	$0.186389\pi$
$191$			15.2760i			1.10533i	−0.833403	+	0.552665i	$0.813611\pi$
$192$	1.05623	+	1.37273i	0.0762266	+	0.0990682i
$193$	−3.97848	+	3.97848i	−0.286377	+	0.286377i	−0.835646	−	0.549269i	$-0.814906\pi$
$193$	−3.97848	+	3.97848i	−0.286377	+	0.286377i	0.549269	+	0.835646i	$0.314906\pi$
$194$	8.27734			0.594278
$195$	17.8352	+	3.04814i	1.27720	+	0.218281i
$196$	0.340178			0.0242984
$197$	−6.44042	+	6.44042i	−0.458861	+	0.458861i	−0.898282	−	0.439420i	$-0.855184\pi$
$197$	−6.44042	+	6.44042i	−0.458861	+	0.458861i	0.439420	+	0.898282i	$0.355184\pi$
$198$	7.52631	−	4.37197i	0.534872	−	0.310702i
$199$			21.9690i			1.55734i	0.627433	+	0.778671i	$0.284106\pi$
$199$			21.9690i			1.55734i	−0.627433	+	0.778671i	$0.715894\pi$
$200$	3.24400	+	3.80480i	0.229385	+	0.269040i
$201$	−0.664872	−	0.0866354i	−0.0468964	−	0.00611079i
$202$	3.17278	+	3.17278i	0.223236	+	0.223236i
$203$	−17.0208	−	17.0208i	−1.19463	−	1.19463i
$204$	−4.76714	−	0.621177i	−0.333766	−	0.0434911i
$205$	8.14182	+	0.323370i	0.568649	+	0.0225852i
$206$			14.1755i			0.987656i
$207$	4.10691	−	2.38567i	0.285450	−	0.165815i
$208$	3.30346	−	3.30346i	0.229054	−	0.229054i
$209$	12.3031			0.851020
$210$	6.06368	+	8.56356i	0.418434	+	0.590941i
$211$	18.0161			1.24028			0.620140	−	0.784491i	$-0.287076\pi$
$211$	18.0161			1.24028			0.620140	+	0.784491i	$0.287076\pi$
$212$	−2.41379	+	2.41379i	−0.165780	+	0.165780i
$213$	−12.7676	−	16.5934i	−0.874819	−	1.13696i
$214$			9.46118i			0.646753i
$215$	−4.08249	−	4.42020i	−0.278424	−	0.301455i
$216$	−1.96937	+	4.80849i	−0.133999	+	0.327176i
$217$	−1.91575	−	1.91575i	−0.130049	−	0.130049i
$218$	−1.83785	−	1.83785i	−0.124475	−	0.124475i
$219$	1.29657	−	9.95037i	0.0876143	−	0.672384i
$220$	0.257465	−	6.48246i	0.0173583	−	0.437048i
$221$			12.9669i			0.872249i
$222$	4.19330	−	3.22647i	0.281436	−	0.216547i
$223$	−8.01367	+	8.01367i	−0.536635	+	0.536635i	−0.922539	−	0.385904i	$-0.873890\pi$
$223$	−8.01367	+	8.01367i	−0.536635	+	0.536635i	0.385904	+	0.922539i	$0.373890\pi$
$224$	2.70928			0.181021
$225$	−4.98166	+	14.1486i	−0.332111	+	0.943240i
$226$	6.81046			0.453025
$227$	5.35234	−	5.35234i	0.355248	−	0.355248i	−0.506810	−	0.862058i	$-0.669175\pi$
$227$	5.35234	−	5.35234i	0.355248	−	0.355248i	0.862058	+	0.506810i	$0.169175\pi$
$228$	−5.82104	+	4.47891i	−0.385508	+	0.296623i
$229$			7.11285i			0.470030i	0.971992	+	0.235015i	$0.0755140\pi$
$229$			7.11285i			0.470030i	−0.971992	+	0.235015i	$0.924486\pi$
$230$	0.140492	−	3.53731i	0.00926378	−	0.233243i
$231$	1.75919	−	13.5007i	0.115746	−	0.888279i
$232$	−6.28243	−	6.28243i	−0.412461	−	0.412461i
$233$	−18.5150	−	18.5150i	−1.21296	−	1.21296i	−0.970049	−	0.242910i	$-0.921898\pi$
$233$	−18.5150	−	18.5150i	−1.21296	−	1.21296i	−0.242910	−	0.970049i	$-0.578102\pi$
$234$	13.5474	+	3.59154i	0.885621	+	0.234786i
$235$	6.12775	+	6.63464i	0.399730	+	0.432796i
$236$		−	14.8240i		−	0.964959i
$237$	−18.5859	−	24.1552i	−1.20728	−	1.56905i
$238$	−5.31730	+	5.31730i	−0.344669	+	0.344669i
$239$	−3.09406			−0.200138			−0.100069	−	0.994981i	$-0.531906\pi$
$239$	−3.09406			−0.200138			−0.100069	+	0.994981i	$0.531906\pi$
$240$	2.23812	+	3.16083i	0.144470	+	0.204031i
$241$	25.4115			1.63690			0.818448	−	0.574580i	$-0.194835\pi$
$241$	25.4115			1.63690			0.818448	+	0.574580i	$0.194835\pi$
$242$	1.82595	−	1.82595i	0.117376	−	0.117376i
$243$	−15.4413	+	2.13710i	−0.990558	+	0.137095i
$244$			6.35938i			0.407117i
$245$	0.760062	+	0.0301875i	0.0485586	+	0.00192861i
$246$	6.25869	+	0.815532i	0.399039	+	0.0519964i
$247$	14.0083	+	14.0083i	0.891325	+	0.891325i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	1.39232	+	0.181425i	0.0882347	+	0.0114973i
$250$	6.91044	+	8.78896i	0.437055	+	0.555863i
$251$			27.5814i			1.74092i	0.492240	+	0.870460i	$0.336178\pi$
$251$			27.5814i			1.74092i	−0.492240	+	0.870460i	$0.663822\pi$
$252$	4.08256	+	7.02811i	0.257177	+	0.442729i
$253$	−3.24798	+	3.24798i	−0.204199	+	0.204199i
$254$	−6.50463			−0.408137
$255$	−10.5961	−	1.81094i	−0.663555	−	0.113405i
$256$	1.00000			0.0625000
$257$	5.60832	−	5.60832i	0.349837	−	0.349837i	−0.510212	−	0.860049i	$-0.670433\pi$
$257$	5.60832	−	5.60832i	0.349837	−	0.349837i	0.860049	+	0.510212i	$0.170433\pi$
$258$	−2.84221	−	3.69389i	−0.176948	−	0.229971i
$259$		−	8.27607i		−	0.514250i
$260$	7.67409	−	7.08779i	0.475927	−	0.439566i
$261$	6.83029	−	25.7641i	0.422785	−	1.59476i
$262$	2.31607	+	2.31607i	0.143088	+	0.143088i
$263$	−8.31992	−	8.31992i	−0.513028	−	0.513028i	0.402425	−	0.915453i	$-0.368167\pi$
$263$	−8.31992	−	8.31992i	−0.513028	−	0.513028i	−0.915453	+	0.402425i	$0.868167\pi$
$264$	0.649321	−	4.98313i	0.0399630	−	0.306690i
$265$	−5.60735	+	5.17895i	−0.344457	+	0.318140i
$266$			11.4887i			0.704414i
$267$	2.15700	−	1.65968i	0.132007	−	0.101570i
$268$	−0.273727	+	0.273727i	−0.0167206	+	0.0167206i
$269$	20.0647			1.22337			0.611685	−	0.791102i	$-0.290492\pi$
$269$	20.0647			1.22337			0.611685	+	0.791102i	$0.290492\pi$
$270$	−4.82689	+	10.5689i	−0.293755	+	0.643201i
$271$	−22.2178			−1.34963			−0.674817	−	0.737985i	$-0.735777\pi$
$271$	−22.2178			−1.34963			−0.674817	+	0.737985i	$0.735777\pi$
$272$	−1.96263	+	1.96263i	−0.119002	+	0.119002i
$273$	17.3749	−	13.3689i	1.05158	−	0.809120i
$274$		−	10.8887i		−	0.657810i
$275$	1.15051	−	14.4610i	0.0693785	−	0.872029i
$276$	0.354318	−	2.71916i	0.0213274	−	0.163674i
$277$	3.09681	+	3.09681i	0.186069	+	0.186069i	0.793994	−	0.607925i	$-0.207998\pi$
$277$	3.09681	+	3.09681i	0.186069	+	0.186069i	−0.607925	+	0.793994i	$0.707998\pi$
$278$	−9.35372	−	9.35372i	−0.560999	−	0.560999i
$279$	0.768771	−	2.89983i	0.0460251	−	0.173608i
$280$	6.05335	+	0.240422i	0.361757	+	0.0143680i
$281$			19.9689i			1.19125i	0.803264	+	0.595623i	$0.203095\pi$
$281$			19.9689i			1.19125i	−0.803264	+	0.595623i	$0.796905\pi$
$282$	4.26610	+	5.54446i	0.254043	+	0.330168i
$283$	8.77383	−	8.77383i	0.521550	−	0.521550i	−0.396489	−	0.918039i	$-0.629772\pi$
$283$	8.77383	−	8.77383i	0.521550	−	0.521550i	0.918039	+	0.396489i	$0.129772\pi$
$284$	−12.0879			−0.717285
$285$	−13.4034	+	9.49071i	−0.793952	+	0.562181i
$286$	−13.5544			−0.801490
$287$	6.98099	−	6.98099i	0.412075	−	0.412075i
$288$	1.50688	+	2.59409i	0.0887940	+	0.152858i
$289$			9.29619i			0.546835i
$290$	−13.4794	−	14.5944i	−0.791535	−	0.857011i
$291$	14.2166	+	1.85248i	0.833391	+	0.108594i
$292$	−4.09656	−	4.09656i	−0.239733	−	0.239733i
$293$	17.6917	+	17.6917i	1.03356	+	1.03356i	0.999417	+	0.0341415i	$0.0108697\pi$
$293$	17.6917	+	17.6917i	1.03356	+	1.03356i	0.0341415	+	0.999417i	$0.489130\pi$
$294$	0.584267	+	0.0761323i	0.0340751	+	0.00444013i
$295$	1.31549	−	33.1213i	0.0765906	−	1.92840i
$296$		−	3.05472i		−	0.177552i
$297$	13.9051	−	5.82459i	0.806857	−	0.337977i
$298$	−5.63764	+	5.63764i	−0.326580	+	0.326580i
$299$	−7.39630			−0.427739
$300$	4.72015	+	7.26087i	0.272518	+	0.419206i
$301$	−7.29041			−0.420212
$302$	15.3570	−	15.3570i	0.883693	−	0.883693i
$303$	4.73927	+	6.15941i	0.272264	+	0.353849i
$304$			4.24049i			0.243209i
$305$	−0.564334	+	14.2088i	−0.0323137	+	0.813593i
$306$	−8.04868	−	2.13378i	−0.460113	−	0.121980i
$307$	−23.4513	−	23.4513i	−1.33843	−	1.33843i	−0.897577	−	0.440858i	$-0.854674\pi$
$307$	−23.4513	−	23.4513i	−1.33843	−	1.33843i	−0.440858	−	0.897577i	$-0.645326\pi$
$308$	−5.55822	−	5.55822i	−0.316709	−	0.316709i
$309$	−3.17250	+	24.3469i	−0.180477	+	1.38505i
$310$	−1.51714	−	1.64264i	−0.0861680	−	0.0932958i
$311$		−	30.2426i		−	1.71490i	−0.514569	−	0.857449i	$-0.672048\pi$
$311$		−	30.2426i		−	1.71490i	0.514569	−	0.857449i	$-0.327952\pi$
$312$	6.41311	−	4.93447i	0.363071	−	0.279360i
$313$	−0.474602	+	0.474602i	−0.0268261	+	0.0268261i	−0.720393	−	0.693567i	$-0.756038\pi$
$313$	−0.474602	+	0.474602i	−0.0268261	+	0.0268261i	0.693567	+	0.720393i	$0.256038\pi$
$314$	24.6002			1.38827
$315$	8.49802	+	16.0652i	0.478809	+	0.905173i
$316$	−17.5965			−0.989879
$317$	−24.1351	+	24.1351i	−1.35556	+	1.35556i	−0.476250	+	0.879310i	$0.658004\pi$
$317$	−24.1351	+	24.1351i	−1.35556	+	1.35556i	−0.879310	+	0.476250i	$0.841996\pi$
$318$	−4.68597	+	3.60555i	−0.262776	+	0.202189i
$319$			25.7774i			1.44326i
$320$	2.23431	+	0.0887404i	0.124902	+	0.00496074i
$321$	−2.11742	+	16.2499i	−0.118183	+	0.906979i
$322$	−3.03298	−	3.03298i	−0.169021	−	0.169021i
$323$	−8.32250	−	8.32250i	−0.463076	−	0.463076i
$324$	−4.45860	+	7.81798i	−0.247700	+	0.434332i
$325$	17.7752	−	15.1553i	0.985993	−	0.840664i
$326$			4.60184i			0.254872i
$327$	−2.74525	−	3.56788i	−0.151813	−	0.197304i
$328$	2.57670	−	2.57670i	0.142274	−	0.142274i
$329$	10.9428			0.603295
$330$	1.89299	−	11.0762i	0.104206	−	0.609725i
$331$	5.54933			0.305019			0.152509	−	0.988302i	$-0.451265\pi$
$331$	5.54933			0.305019			0.152509	+	0.988302i	$0.451265\pi$
$332$	0.573218	−	0.573218i	0.0314594	−	0.0314594i
$333$	7.92421	−	4.60310i	0.434244	−	0.252248i
$334$			7.78839i			0.426162i
$335$	−0.635881	+	0.587300i	−0.0347419	+	0.0320876i
$336$	4.65327	+	0.606339i	0.253856	+	0.0330785i
$337$	23.5853	+	23.5853i	1.28477	+	1.28477i	0.937921	+	0.346850i	$0.112749\pi$
$337$	23.5853	+	23.5853i	1.28477	+	1.28477i	0.346850	+	0.937921i	$0.387251\pi$
$338$	−6.24069	−	6.24069i	−0.339449	−	0.339449i
$339$	11.6972	+	1.52419i	0.635304	+	0.0827826i
$340$	−4.55928	+	4.21095i	−0.247261	+	0.228371i
$341$			2.90133i			0.157116i
$342$	−11.0002	+	6.38992i	−0.594823	+	0.345527i
$343$	−12.7585	+	12.7585i	−0.688896	+	0.688896i
$344$	−2.69091			−0.145084
$345$	1.03295	−	6.04400i	0.0556124	−	0.325398i
$346$	6.80105			0.365627
$347$	16.6402	−	16.6402i	0.893292	−	0.893292i	−0.101540	−	0.994831i	$-0.532377\pi$
$347$	16.6402	−	16.6402i	0.893292	−	0.893292i	0.994831	+	0.101540i	$0.0323769\pi$
$348$	−9.38425	−	12.1963i	−0.503048	−	0.653789i
$349$			16.8810i			0.903618i	0.892115	+	0.451809i	$0.149221\pi$
$349$			16.8810i			0.903618i	−0.892115	+	0.451809i	$0.850779\pi$
$350$	13.5037	+	1.07435i	0.721804	+	0.0574266i
$351$	22.4643	+	9.20051i	1.19905	+	0.491087i
$352$	−2.05155	−	2.05155i	−0.109348	−	0.109348i
$353$	9.96055	+	9.96055i	0.530146	+	0.530146i	0.920616	−	0.390469i	$-0.127687\pi$
$353$	9.96055	+	9.96055i	0.530146	+	0.530146i	−0.390469	+	0.920616i	$0.627687\pi$
$354$	3.31762	−	25.4606i	0.176330	−	1.35322i
$355$	−27.0081	−	1.07269i	−1.43344	−	0.0569322i
$356$		−	1.57133i		−	0.0832801i
$357$	−10.3226	+	7.94261i	−0.546332	+	0.420368i
$358$	3.27198	−	3.27198i	0.172929	−	0.172929i
$359$	−22.7592			−1.20118			−0.600592	−	0.799555i	$-0.705069\pi$
$359$	−22.7592			−1.20118			−0.600592	+	0.799555i	$0.705069\pi$
$360$	3.13664	+	5.92971i	0.165315	+	0.312523i
$361$	1.01827			0.0535933
$362$	0.744689	−	0.744689i	0.0391400	−	0.0391400i
$363$	3.54477	−	2.72747i	0.186052	−	0.143155i
$364$		−	12.6572i		−	0.663417i
$365$	−8.78944	−	9.51650i	−0.460061	−	0.498117i
$366$	−1.42324	+	10.9224i	−0.0743938	+	0.570924i
$367$	−9.10560	−	9.10560i	−0.475308	−	0.475308i	0.428319	−	0.903627i	$-0.359106\pi$
$367$	−9.10560	−	9.10560i	−0.475308	−	0.475308i	−0.903627	+	0.428319i	$0.859106\pi$
$368$	−1.11948	−	1.11948i	−0.0583568	−	0.0583568i
$369$	10.5670	+	2.80140i	0.550095	+	0.145835i
$370$	0.271077	−	6.82517i	0.0140926	−	0.354824i
$371$			9.24843i			0.480155i
$372$	−1.05623	−	1.37273i	−0.0547628	−	0.0711727i
$373$	24.2260	−	24.2260i	1.25437	−	1.25437i	0.300632	−	0.953740i	$-0.402802\pi$
$373$	24.2260	−	24.2260i	1.25437	−	1.25437i	0.953740	−	0.300632i	$-0.0971977\pi$
$374$	8.05286			0.416403
$375$	9.90192	+	16.6419i	0.511333	+	0.859383i
$376$	4.03900			0.208296
$377$	−29.3502	+	29.3502i	−1.51161	+	1.51161i
$378$	5.43903	+	12.9847i	0.279754	+	0.667860i
$379$		−	22.6743i		−	1.16470i	−0.812938	−	0.582350i	$-0.802133\pi$
$379$		−	22.6743i		−	1.16470i	0.812938	−	0.582350i	$-0.197867\pi$
$380$	−0.376302	+	9.47455i	−0.0193039	+	0.486034i
$381$	−11.1719	−	1.45574i	−0.572354	−	0.0745800i
$382$	10.8017	+	10.8017i	0.552665	+	0.552665i
$383$	7.99408	+	7.99408i	0.408478	+	0.408478i	0.881208	−	0.472729i	$-0.156731\pi$
$383$	7.99408	+	7.99408i	0.408478	+	0.408478i	−0.472729	+	0.881208i	$0.656731\pi$
$384$	1.71753	+	0.223801i	0.0876474	+	0.0114208i
$385$	−11.9255	−	12.9120i	−0.607781	−	0.658057i
$386$			5.62642i			0.286377i
$387$	−4.05488	−	6.98045i	−0.206121	−	0.354836i
$388$	5.85296	−	5.85296i	0.297139	−	0.297139i
$389$	−26.6848			−1.35297			−0.676486	−	0.736456i	$-0.736498\pi$
$389$	−26.6848			−1.35297			−0.676486	+	0.736456i	$0.736498\pi$
$390$	14.7667	−	10.4560i	0.747743	−	0.529461i
$391$	4.39424			0.222226
$392$	0.240542	−	0.240542i	0.0121492	−	0.0121492i
$393$	3.45959	+	4.49627i	0.174513	+	0.226807i
$394$			9.10813i			0.458861i
$395$	−39.3159	−	1.56152i	−1.97820	−	0.0785685i
$396$	2.23046	−	8.41336i	0.112085	−	0.422787i
$397$	−11.8906	−	11.8906i	−0.596775	−	0.596775i	0.342678	−	0.939453i	$-0.388666\pi$
$397$	−11.8906	−	11.8906i	−0.596775	−	0.596775i	−0.939453	+	0.342678i	$0.888666\pi$
$398$	15.5344	+	15.5344i	0.778671	+	0.778671i
$399$	−2.57117	+	19.7321i	−0.128720	+	0.987841i
$400$	4.98425	+	0.396546i	0.249213	+	0.0198273i
$401$			26.4186i			1.31928i	0.751581	+	0.659640i	$0.229291\pi$
$401$			26.4186i			1.31928i	−0.751581	+	0.659640i	$0.770709\pi$
$402$	−0.531396	+	0.408875i	−0.0265036	+	0.0203928i
$403$	−3.30346	+	3.30346i	−0.164557	+	0.164557i
$404$	4.48698			0.223236
$405$	−10.6557	+	17.0721i	−0.529484	+	0.848320i
$406$	−24.0711			−1.19463
$407$	−6.26691	+	6.26691i	−0.310639	+	0.310639i
$408$	−3.81011	+	2.93164i	−0.188629	+	0.145138i
$409$			12.8238i			0.634097i	0.948409	+	0.317049i	$0.102692\pi$
$409$			12.8238i			0.634097i	−0.948409	+	0.317049i	$0.897308\pi$
$410$	5.98579	−	5.52848i	0.295617	−	0.273032i
$411$	2.43690	−	18.7017i	0.120204	−	0.922485i
$412$	10.0236	+	10.0236i	0.493828	+	0.493828i
$413$	−28.3990	−	28.3990i	−1.39742	−	1.39742i
$414$	1.21710	−	4.59095i	0.0598174	−	0.225633i
$415$	1.33161	−	1.22988i	0.0653662	−	0.0603723i
$416$		−	4.67179i		−	0.229054i
$417$	−13.9719	−	18.1587i	−0.684209	−	0.889235i
$418$	8.69957	−	8.69957i	0.425510	−	0.425510i
$419$	4.99777			0.244157			0.122079	−	0.992520i	$-0.461044\pi$
$419$	4.99777			0.244157			0.122079	+	0.992520i	$0.461044\pi$
$420$	10.3430	+	1.76768i	0.504688	+	0.0862540i
$421$	−28.0690			−1.36800			−0.683999	−	0.729483i	$-0.739761\pi$
$421$	−28.0690			−1.36800			−0.683999	+	0.729483i	$0.739761\pi$
$422$	12.7393	−	12.7393i	0.620140	−	0.620140i
$423$	6.08631	+	10.4775i	0.295926	+	0.509435i
$424$			3.41362i			0.165780i
$425$	−10.5605	+	9.00395i	−0.512259	+	0.436756i
$426$	−20.7613	−	2.70529i	−1.00589	−	0.131072i
$427$	12.1830	+	12.1830i	0.589575	+	0.589575i
$428$	6.69006	+	6.69006i	0.323376	+	0.323376i
$429$	−23.2801	−	3.03350i	−1.12398	−	0.146459i
$430$	−6.01231	−	0.238792i	−0.289939	−	0.0115156i
$431$			23.1372i			1.11448i	0.830351	+	0.557240i	$0.188140\pi$
$431$			23.1372i			1.11448i	−0.830351	+	0.557240i	$0.811860\pi$
$432$	2.00756	+	4.79267i	0.0965887	+	0.230588i
$433$	−6.74329	+	6.74329i	−0.324062	+	0.324062i	−0.850323	−	0.526261i	$-0.823593\pi$
$433$	−6.74329	+	6.74329i	−0.324062	+	0.324062i	0.526261	+	0.850323i	$0.323593\pi$
$434$	−2.70928			−0.130049
$435$	−19.8850	−	28.0830i	−0.953412	−	1.34648i
$436$	−2.59911			−0.124475
$437$	4.74713	−	4.74713i	0.227086	−	0.227086i
$438$	−6.11916	−	7.95279i	−0.292385	−	0.379999i
$439$		−	13.4623i		−	0.642519i	−0.946991	−	0.321260i	$-0.895894\pi$
$439$		−	13.4623i		−	0.642519i	0.946991	−	0.321260i	$-0.104106\pi$
$440$	−4.40174	−	4.76585i	−0.209845	−	0.227203i
$441$	0.986458	+	0.261519i	0.0469742	+	0.0124533i
$442$	9.16899	+	9.16899i	0.436125	+	0.436125i
$443$	−22.6140	−	22.6140i	−1.07442	−	1.07442i	−0.996998	−	0.0774260i	$-0.975330\pi$
$443$	−22.6140	−	22.6140i	−1.07442	−	1.07442i	−0.0774260	−	0.996998i	$-0.524670\pi$
$444$	0.683649	−	5.24657i	0.0324446	−	0.248991i
$445$	0.139440	−	3.51082i	0.00661009	−	0.166429i
$446$			11.3330i			0.536635i
$447$	−10.9445	+	8.42111i	−0.517658	+	0.398305i
$448$	1.91575	−	1.91575i	0.0905106	−	0.0905106i
$449$	38.6253			1.82284			0.911420	−	0.411477i	$-0.134987\pi$
$449$	38.6253			1.82284			0.911420	+	0.411477i	$0.134987\pi$
$450$	6.48201	+	13.5271i	0.305565	+	0.637676i
$451$	−10.5725			−0.497838
$452$	4.81572	−	4.81572i	0.226513	−	0.226513i
$453$	29.8129	−	22.9391i	1.40073	−	1.07777i
$454$		−	7.56936i		−	0.355248i
$455$	1.12320	−	28.2800i	0.0526566	−	1.32579i
$456$	−0.949026	+	7.28317i	−0.0444422	+	0.341066i
$457$	−23.8871	−	23.8871i	−1.11739	−	1.11739i	−0.992123	−	0.125267i	$-0.960021\pi$
$457$	−23.8871	−	23.8871i	−1.11739	−	1.11739i	−0.125267	−	0.992123i	$-0.539979\pi$
$458$	5.02954	+	5.02954i	0.235015	+	0.235015i
$459$	−13.3463	−	5.46614i	−0.622953	−	0.255138i
$460$	−2.40191	−	2.60060i	−0.111990	−	0.121254i
$461$			38.8078i			1.80746i	0.428103	+	0.903730i	$0.359182\pi$
$461$			38.8078i			1.80746i	−0.428103	+	0.903730i	$0.640818\pi$
$462$	−8.30248	−	10.7903i	−0.386266	−	0.502012i
$463$	−13.0546	+	13.0546i	−0.606697	+	0.606697i	−0.942081	−	0.335384i	$-0.891134\pi$
$463$	−13.0546	+	13.0546i	−0.606697	+	0.606697i	0.335384	+	0.942081i	$0.391134\pi$
$464$	−8.88469			−0.412461
$465$	−2.23812	−	3.16083i	−0.103790	−	0.146580i
$466$	−26.1842			−1.21296
$467$	−0.563836	+	0.563836i	−0.0260912	+	0.0260912i	−0.720032	−	0.693941i	$-0.755873\pi$
$467$	−0.563836	+	0.563836i	−0.0260912	+	0.0260912i	0.693941	+	0.720032i	$0.255873\pi$
$468$	12.1191	−	7.03985i	0.560204	−	0.325417i
$469$			1.04878i			0.0484284i
$470$	9.02437	+	0.358423i	0.416263	+	0.0165328i
$471$	42.2516	+	5.50555i	1.94685	+	0.253683i
$472$	−10.4821	−	10.4821i	−0.482479	−	0.482479i
$473$	5.52053	+	5.52053i	0.253834	+	0.253834i
$474$	−30.2225	−	3.93811i	−1.38816	−	0.180883i
$475$	−1.68155	+	21.1356i	−0.0771548	+	0.969770i
$476$			7.51980i			0.344669i
$477$	−8.85523	+	5.14392i	−0.405453	+	0.235524i
$478$	−2.18783	+	2.18783i	−0.100069	+	0.100069i
$479$	25.6542			1.17217			0.586085	−	0.810250i	$-0.300669\pi$
$479$	25.6542			1.17217			0.586085	+	0.810250i	$0.300669\pi$
$480$	3.81763	+	0.652455i	0.174250	+	0.0297804i
$481$	−14.2710			−0.650702
$482$	17.9686	−	17.9686i	0.818448	−	0.818448i
$483$	−4.53045	−	5.88801i	−0.206142	−	0.267914i
$484$		−	2.58228i		−	0.117376i
$485$	13.5967	−	12.5579i	0.617394	−	0.570225i
$486$	−9.40747	+	12.4298i	−0.426731	+	0.563827i
$487$	−21.6393	−	21.6393i	−0.980569	−	0.980569i	0.0192455	−	0.999815i	$-0.493874\pi$
$487$	−21.6393	−	21.6393i	−0.980569	−	0.980569i	−0.999815	+	0.0192455i	$0.993874\pi$
$488$	4.49676	+	4.49676i	0.203559	+	0.203559i
$489$	−1.02990	+	7.90380i	−0.0465735	+	0.357422i
$490$	0.558791	−	0.516099i	0.0252436	−	0.0233150i
$491$		−	31.0783i		−	1.40254i	−0.712894	−	0.701272i	$-0.752616\pi$
$491$		−	31.0783i		−	1.40254i	0.712894	−	0.701272i	$-0.247384\pi$
$492$	5.00223	−	3.84889i	0.225518	−	0.173521i
$493$	17.4373	−	17.4373i	0.785338	−	0.785338i
$494$	19.8107			0.891325
$495$	5.73013	−	18.6001i	0.257550	−	0.836012i
$496$	−1.00000			−0.0449013
$497$	−23.1574	+	23.1574i	−1.03875	+	1.03875i
$498$	1.11281	−	0.856232i	0.0498660	−	0.0383687i
$499$			1.44024i			0.0644741i	0.999480	+	0.0322371i	$0.0102632\pi$
$499$			1.44024i			0.0644741i	−0.999480	+	0.0322371i	$0.989737\pi$
$500$	11.1012	+	1.32831i	0.496459	+	0.0594039i
$501$	−1.74305	+	13.3768i	−0.0778738	+	0.597632i
$502$	19.5030	+	19.5030i	0.870460	+	0.870460i
$503$	−23.2644	−	23.2644i	−1.03731	−	1.03731i	−0.999277	−	0.0380312i	$-0.987891\pi$
$503$	−23.2644	−	23.2644i	−1.03731	−	1.03731i	−0.0380312	−	0.999277i	$-0.512109\pi$
$504$	7.85643	+	2.08281i	0.349953	+	0.0927759i
$505$	10.0253	+	0.398177i	0.446120	+	0.0177186i
$506$			4.59333i			0.204199i
$507$	−9.32190	−	12.1153i	−0.414000	−	0.538057i
$508$	−4.59947	+	4.59947i	−0.204068	+	0.204068i
$509$	6.33245			0.280681			0.140340	−	0.990103i	$-0.455180\pi$
$509$	6.33245			0.280681			0.140340	+	0.990103i	$0.455180\pi$
$510$	−8.77311	+	6.21206i	−0.388480	+	0.275075i
$511$	−15.6960			−0.694348
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−20.3233	+	8.51303i	−0.897294	+	0.375859i
$514$		−	7.93136i		−	0.349837i
$515$	21.5063	+	23.2853i	0.947682	+	1.02607i
$516$	−4.62171	−	0.602228i	−0.203460	−	0.0265116i
$517$	−8.28622	−	8.28622i	−0.364428	−	0.364428i
$518$	−5.85207	−	5.85207i	−0.257125	−	0.257125i
$519$	11.6810	+	1.52208i	0.512740	+	0.0668120i
$520$	0.414577	−	10.4382i	0.0181804	−	0.457746i
$521$			31.9649i			1.40041i	0.713942	+	0.700204i	$0.246908\pi$
$521$			31.9649i			1.40041i	−0.713942	+	0.700204i	$0.753092\pi$
$522$	−13.3882	−	23.0477i	−0.585985	−	1.00877i
$523$	−27.4388	+	27.4388i	−1.19981	+	1.19981i	−0.225592	+	0.974222i	$0.572431\pi$
$523$	−27.4388	+	27.4388i	−1.19981	+	1.19981i	−0.974222	+	0.225592i	$0.927569\pi$
$524$	3.27542			0.143088
$525$	22.9526	+	4.86738i	1.00173	+	0.212430i
$526$	−11.7661			−0.513028
$527$	1.96263	−	1.96263i	0.0854934	−	0.0854934i
$528$	−3.06446	−	3.98274i	−0.133364	−	0.173327i
$529$		−	20.4935i		−	0.891023i
$530$	−0.302926	+	7.62707i	−0.0131583	+	0.331299i
$531$	11.3962	−	42.9870i	0.494555	−	1.86548i
$532$	8.12370	+	8.12370i	0.352207	+	0.352207i
$533$	−12.0378	−	12.0378i	−0.521415	−	0.521415i
$534$	0.351664	−	2.69880i	0.0152180	−	0.116788i
$535$	14.3540	+	15.5413i	0.620576	+	0.671910i
$536$			0.387109i			0.0167206i
$537$	6.35200	−	4.88745i	0.274109	−	0.210909i
$538$	14.1879	−	14.1879i	0.611685	−	0.611685i
$539$	−0.986970			−0.0425118
$540$	4.06020	+	10.8865i	0.174723	+	0.468478i
$541$	−40.6794			−1.74894			−0.874471	−	0.485077i	$-0.838791\pi$
$541$	−40.6794			−1.74894			−0.874471	+	0.485077i	$0.838791\pi$
$542$	−15.7103	+	15.7103i	−0.674817	+	0.674817i
$543$	1.44569	−	1.11236i	0.0620404	−	0.0477361i
$544$			2.77557i			0.119002i
$545$	−5.80722	−	0.230646i	−0.248754	−	0.00987980i
$546$	2.83269	−	21.7391i	0.121228	−	0.930348i
$547$	−31.1133	−	31.1133i	−1.33031	−	1.33031i	−0.905090	−	0.425221i	$-0.860197\pi$
$547$	−31.1133	−	31.1133i	−1.33031	−	1.33031i	−0.425221	−	0.905090i	$-0.639803\pi$
$548$	−7.69947	−	7.69947i	−0.328905	−	0.328905i
$549$	−4.88891	+	18.4411i	−0.208653	+	0.787046i
$550$	−9.41191	−	11.0390i	−0.401325	−	0.470704i
$551$		−	37.6754i		−	1.60503i
$552$	−1.67220	−	2.17328i	−0.0711735	−	0.0925009i
$553$	−33.7104	+	33.7104i	−1.43351	+	1.43351i
$554$	4.37955			0.186069
$555$	1.99306	−	11.6618i	0.0846009	−	0.495015i
$556$	−13.2282			−0.560999
$557$	8.03267	−	8.03267i	0.340355	−	0.340355i	−0.516146	−	0.856501i	$-0.672634\pi$
$557$	8.03267	−	8.03267i	0.340355	−	0.340355i	0.856501	+	0.516146i	$0.172634\pi$
$558$	−1.50688	−	2.59409i	−0.0637915	−	0.109817i
$559$			12.5714i			0.531712i
$560$	4.45037	−	4.11036i	0.188063	−	0.173695i
$561$	13.8310	+	1.80224i	0.583947	+	0.0760906i
$562$	14.1202	+	14.1202i	0.595623	+	0.595623i
$563$	6.17647	+	6.17647i	0.260307	+	0.260307i	0.825179	−	0.564872i	$-0.191074\pi$
$563$	6.17647	+	6.17647i	0.260307	+	0.260307i	−0.564872	+	0.825179i	$0.691074\pi$
$564$	6.93711	+	0.903934i	0.292105	+	0.0380625i
$565$	11.1872	−	10.3325i	0.470647	−	0.434690i
$566$		−	12.4081i		−	0.521550i
$567$	6.43572	+	23.5188i	0.270275	+	0.987699i
$568$	−8.54744	+	8.54744i	−0.358643	+	0.358643i
$569$	−27.6543			−1.15933			−0.579663	−	0.814856i	$-0.696816\pi$
$569$	−27.6543			−1.15933			−0.579663	+	0.814856i	$0.696816\pi$
$570$	−2.76673	+	16.1886i	−0.115885	+	0.678066i
$571$	−36.6788			−1.53496			−0.767480	−	0.641073i	$-0.778490\pi$
$571$	−36.6788			−1.53496			−0.767480	+	0.641073i	$0.778490\pi$
$572$	−9.58443	+	9.58443i	−0.400745	+	0.400745i
$573$	16.1349	+	20.9698i	0.674045	+	0.876025i
$574$		−	9.87261i		−	0.412075i
$575$	−5.13583	−	6.02368i	−0.214179	−	0.251205i
$576$	2.89983	+	0.768771i	0.120826	+	0.0320321i
$577$	−9.40792	−	9.40792i	−0.391657	−	0.391657i	0.483621	−	0.875278i	$-0.339321\pi$
$577$	−9.40792	−	9.40792i	−0.391657	−	0.391657i	−0.875278	+	0.483621i	$0.839321\pi$
$578$	6.57340	+	6.57340i	0.273417	+	0.273417i
$579$	−1.25920	+	9.66356i	−0.0523306	+	0.401604i
$580$	−19.8511	−	0.788431i	−0.824273	−	0.0327378i
$581$		−	2.19628i		−	0.0911171i
$582$	11.3625	−	8.74274i	0.470993	−	0.362398i
$583$	7.00321	−	7.00321i	0.290043	−	0.290043i
$584$	−5.79341			−0.239733
$585$	27.7024	−	14.6537i	1.14535	−	0.605857i
$586$	25.0198			1.03356
$587$	12.7521	−	12.7521i	0.526336	−	0.526336i	−0.393142	−	0.919478i	$-0.628612\pi$
$587$	12.7521	−	12.7521i	0.526336	−	0.526336i	0.919478	+	0.393142i	$0.128612\pi$
$588$	0.466973	−	0.359305i	0.0192576	−	0.0148175i
$589$		−	4.24049i		−	0.174726i
$590$	−22.4901	−	24.3505i	−0.925903	−	1.00249i
$591$	−2.03841	+	15.6435i	−0.0838490	+	0.643488i
$592$	−2.16001	−	2.16001i	−0.0887759	−	0.0887759i
$593$	14.7098	+	14.7098i	0.604060	+	0.604060i	0.941387	−	0.337327i	$-0.109523\pi$
$593$	14.7098	+	14.7098i	0.604060	+	0.604060i	−0.337327	+	0.941387i	$0.609523\pi$
$594$	5.71380	−	13.9510i	0.234440	−	0.572417i
$595$	−0.667310	+	16.8015i	−0.0273570	+	0.688796i
$596$			7.97282i			0.326580i
$597$	23.2042	+	30.1575i	0.949687	+	1.23426i
$598$	−5.22997	+	5.22997i	−0.213869	+	0.213869i
$599$	−12.3761			−0.505672			−0.252836	−	0.967509i	$-0.581363\pi$
$599$	−12.3761			−0.505672			−0.252836	+	0.967509i	$0.581363\pi$
$600$	8.47186	+	1.79656i	0.345862	+	0.0733443i
$601$	−3.08324			−0.125768			−0.0628840	−	0.998021i	$-0.520030\pi$
$601$	−3.08324			−0.125768			−0.0628840	+	0.998021i	$0.520030\pi$
$602$	−5.15510	+	5.15510i	−0.210106	+	0.210106i
$603$	−1.00420	+	0.583328i	−0.0408940	+	0.0237550i
$604$		−	21.7180i		−	0.883693i
$605$	0.229152	−	5.76960i	0.00931637	−	0.234568i
$606$	7.70653	+	1.00419i	0.313057	+	0.0407925i
$607$	2.34458	+	2.34458i	0.0951637	+	0.0951637i	0.753086	−	0.657922i	$-0.228564\pi$
$607$	2.34458	+	2.34458i	0.0951637	+	0.0951637i	−0.657922	+	0.753086i	$0.728564\pi$
$608$	2.99848	+	2.99848i	0.121604	+	0.121604i
$609$	−41.3428	−	5.38714i	−1.67530	−	0.218298i
$610$	9.64809	+	10.4462i	0.390640	+	0.422954i
$611$		−	18.8694i		−	0.763374i
$612$	−7.20009	+	4.18247i	−0.291046	+	0.169066i
$613$	−16.9016	+	16.9016i	−0.682651	+	0.682651i	−0.960597	−	0.277946i	$-0.910346\pi$
$613$	−16.9016	+	16.9016i	−0.682651	+	0.682651i	0.277946	+	0.960597i	$0.410346\pi$
$614$	−33.1651			−1.33843
$615$	11.5181	−	8.15570i	0.464453	−	0.328870i
$616$	−7.86051			−0.316709
$617$	−8.24437	+	8.24437i	−0.331906	+	0.331906i	−0.853310	−	0.521404i	$-0.825408\pi$
$617$	−8.24437	+	8.24437i	−0.331906	+	0.331906i	0.521404	+	0.853310i	$0.325408\pi$
$618$	14.9726	+	19.4592i	0.602285	+	0.782763i
$619$			6.74980i			0.271297i	0.990757	+	0.135649i	$0.0433118\pi$
$619$			6.74980i			0.271297i	−0.990757	+	0.135649i	$0.956688\pi$
$620$	−2.23431	−	0.0887404i	−0.0897319	−	0.00356390i
$621$	3.11787	−	7.61271i	0.125116	−	0.305487i
$622$	−21.3847	−	21.3847i	−0.857449	−	0.857449i
$623$	−3.01026	−	3.01026i	−0.120604	−	0.120604i
$624$	1.04555	−	8.02395i	0.0418556	−	0.321215i
$625$	24.6855	+	3.95297i	0.987420	+	0.158119i
$626$			0.671189i			0.0268261i
$627$	16.8888	−	12.9948i	0.674472	−	0.518963i
$628$	17.3950	−	17.3950i	0.694135	−	0.694135i
$629$	8.47859			0.338064
$630$	17.3688	+	5.35083i	0.691991	+	0.213182i
$631$	23.0189			0.916370			0.458185	−	0.888857i	$-0.348500\pi$
$631$	23.0189			0.916370			0.458185	+	0.888857i	$0.348500\pi$
$632$	−12.4426	+	12.4426i	−0.494939	+	0.494939i
$633$	24.7312	−	19.0291i	0.982978	−	0.756338i
$634$			34.1321i			1.35556i
$635$	−10.6848	+	9.86846i	−0.424013	+	0.391618i
$636$	−0.763972	+	5.86299i	−0.0302935	+	0.232483i
$637$	−1.12376	−	1.12376i	−0.0445252	−	0.0445252i
$638$	18.2274	+	18.2274i	0.721629	+	0.721629i
$639$	−35.0528	−	9.29283i	−1.38667	−	0.367619i
$640$	1.64264	−	1.51714i	0.0649311	−	0.0599704i
$641$		−	3.39221i		−	0.133984i	−0.997754	−	0.0669922i	$-0.978660\pi$
$641$		−	3.39221i		−	0.133984i	0.997754	−	0.0669922i	$-0.0213403\pi$
$642$	9.99315	+	12.9876i	0.394398	+	0.512581i
$643$	2.30668	−	2.30668i	0.0909665	−	0.0909665i	−0.660159	−	0.751126i	$-0.729511\pi$
$643$	2.30668	−	2.30668i	0.0909665	−	0.0909665i	0.751126	+	0.660159i	$0.229511\pi$
$644$	−4.28927			−0.169021
$645$	−10.2729	−	1.75569i	−0.404494	−	0.0691304i
$646$	−11.7698			−0.463076
$647$	−6.67626	+	6.67626i	−0.262471	+	0.262471i	−0.826057	−	0.563586i	$-0.809421\pi$
$647$	−6.67626	+	6.67626i	−0.262471	+	0.262471i	0.563586	+	0.826057i	$0.309421\pi$
$648$	2.37544	+	8.68086i	0.0933160	+	0.341016i
$649$			43.0093i			1.68826i
$650$	1.85258	−	23.2854i	0.0726643	−	0.913328i
$651$	−4.65327	−	0.606339i	−0.182376	−	0.0237643i
$652$	3.25399	+	3.25399i	0.127436	+	0.127436i
$653$	31.9988	+	31.9988i	1.25221	+	1.25221i	0.954727	+	0.297482i	$0.0961469\pi$
$653$	31.9988	+	31.9988i	1.25221	+	1.25221i	0.297482	+	0.954727i	$0.403853\pi$
$654$	−4.46406	−	0.581685i	−0.174558	−	0.0227457i
$655$	7.31830	+	0.290662i	0.285950	+	0.0113571i
$656$		−	3.64400i		−	0.142274i
$657$	−8.73000	−	15.0286i	−0.340590	−	0.586323i
$658$	7.73771	−	7.73771i	0.301647	−	0.301647i
$659$	29.7863			1.16031			0.580154	−	0.814507i	$-0.302992\pi$
$659$	29.7863			1.16031			0.580154	+	0.814507i	$0.302992\pi$
$660$	−6.49352	−	9.17061i	−0.252760	−	0.356965i
$661$	−4.65941			−0.181230			−0.0906149	−	0.995886i	$-0.528883\pi$
$661$	−4.65941			−0.181230			−0.0906149	+	0.995886i	$0.528883\pi$
$662$	3.92397	−	3.92397i	0.152509	−	0.152509i
$663$	13.6960	+	17.8001i	0.531909	+	0.691297i
$664$		−	0.810652i		−	0.0314594i
$665$	17.4299	+	18.8717i	0.675904	+	0.731815i
$666$	2.34838	−	8.85815i	0.0909978	−	0.343246i
$667$	9.94622	+	9.94622i	0.385119	+	0.385119i
$668$	5.50723	+	5.50723i	0.213081	+	0.213081i
$669$	−2.53635	+	19.4649i	−0.0980609	+	0.752555i
$670$	−0.0343522	+	0.864920i	−0.00132714	+	0.0334148i
$671$		−	18.4507i		−	0.712280i
$672$	3.71910	−	2.86161i	0.143468	−	0.110389i
$673$	3.34653	−	3.34653i	0.128999	−	0.128999i	−0.639659	−	0.768658i	$-0.720925\pi$
$673$	3.34653	−	3.34653i	0.128999	−	0.128999i	0.768658	+	0.639659i	$0.220925\pi$
$674$	33.3546			1.28477
$675$	8.10566	+	24.6840i	0.311987	+	0.950086i
$676$	−8.82567			−0.339449
$677$	27.0736	−	27.0736i	1.04052	−	1.04052i	0.0413797	−	0.999143i	$-0.486825\pi$
$677$	27.0736	−	27.0736i	1.04052	−	1.04052i	0.999143	−	0.0413797i	$-0.0131753\pi$
$678$	9.34892	−	7.19339i	0.359043	−	0.276261i
$679$		−	22.4256i		−	0.860615i
$680$	−0.246306	+	6.20148i	−0.00944539	+	0.237816i
$681$	1.69403	−	13.0006i	0.0649154	−	0.498184i
$682$	2.05155	+	2.05155i	0.0785579	+	0.0785579i
$683$	13.1461	+	13.1461i	0.503023	+	0.503023i	0.912376	−	0.409353i	$-0.134246\pi$
$683$	13.1461	+	13.1461i	0.503023	+	0.503023i	−0.409353	+	0.912376i	$0.634246\pi$
$684$	−3.25996	+	12.2967i	−0.124648	+	0.470175i
$685$	−16.5197	−	17.8862i	−0.631186	−	0.683397i
$686$			18.0433i			0.688896i
$687$	7.51278	+	9.76402i	0.286630	+	0.372520i
$688$	−1.90276	+	1.90276i	−0.0725420	+	0.0725420i
$689$	15.9477			0.607560
$690$	−3.54334	−	5.00416i	−0.134893	−	0.190505i
$691$	48.1196			1.83055			0.915277	−	0.402825i	$-0.131972\pi$
$691$	48.1196			1.83055			0.915277	+	0.402825i	$0.131972\pi$
$692$	4.80907	−	4.80907i	0.182813	−	0.182813i
$693$	−11.8449	−	20.3909i	−0.449949	−	0.774585i
$694$		−	23.5328i		−	0.893292i
$695$	−29.5558	−	1.17387i	−1.12111	−	0.0445275i
$696$	−15.2597	−	1.98840i	−0.578419	−	0.0753703i
$697$	7.15182	+	7.15182i	0.270894	+	0.270894i
$698$	11.9367	+	11.9367i	0.451809	+	0.451809i
$699$	−44.9721	−	5.86005i	−1.70100	−	0.221647i
$700$	10.3082	−	8.78888i	0.389615	−	0.332189i
$701$		−	37.7930i		−	1.42742i	−0.700441	−	0.713710i	$-0.747013\pi$
$701$		−	37.7930i		−	1.42742i	0.700441	−	0.713710i	$-0.252987\pi$
$702$	22.3904	−	9.37890i	0.845071	−	0.353984i
$703$	9.15950	−	9.15950i	0.345457	−	0.345457i
$704$	−2.90133			−0.109348
$705$	15.4194	+	2.63527i	0.580729	+	0.0992499i
$706$	14.0863			0.530146
$707$	8.59593	−	8.59593i	0.323283	−	0.323283i
$708$	−15.6575	−	20.3493i	−0.588444	−	0.764774i
$709$			0.477518i			0.0179336i	0.999960	+	0.00896678i	$0.00285425\pi$
$709$			0.477518i			0.0179336i	−0.999960	+	0.00896678i	$0.997146\pi$
$710$	−19.8561	+	18.3391i	−0.745186	+	0.688254i
$711$	−51.0267	−	13.5277i	−1.91365	−	0.507327i
$712$	−1.11109	−	1.11109i	−0.0416400	−	0.0416400i
$713$	1.11948	+	1.11948i	0.0419248	+	0.0419248i
$714$	−1.68294	+	12.9155i	−0.0629824	+	0.483350i
$715$	−22.2651	+	20.5640i	−0.832666	+	0.769051i
$716$		−	4.62728i		−	0.172929i
$717$	−4.24730	+	3.26802i	−0.158618	+	0.122047i
$718$	−16.0932	+	16.0932i	−0.600592	+	0.600592i
$719$	−21.9720			−0.819419			−0.409709	−	0.912216i	$-0.634370\pi$
$719$	−21.9720			−0.819419			−0.409709	+	0.912216i	$0.634370\pi$
$720$	6.41088	+	1.97500i	0.238919	+	0.0736040i
$721$	38.4054			1.43029
$722$	0.720027	−	0.720027i	0.0267966	−	0.0267966i
$723$	34.8831	−	26.8403i	1.29732	−	0.998201i
$724$		−	1.05315i		−	0.0391400i
$725$	−44.2835	−	3.52319i	−1.64465	−	0.130848i
$726$	0.577917	−	4.43514i	0.0214485	−	0.164604i
$727$	−1.73275	−	1.73275i	−0.0642643	−	0.0642643i	0.674244	−	0.738508i	$-0.264470\pi$
$727$	−1.73275	−	1.73275i	−0.0642643	−	0.0642643i	−0.738508	+	0.674244i	$0.764470\pi$
$728$	−8.94998	−	8.94998i	−0.331708	−	0.331708i
$729$	−18.9394	+	19.2431i	−0.701460	+	0.712709i
$730$	−12.9443	−	0.514110i	−0.479089	−	0.0190281i
$731$		−	7.46881i		−	0.276244i
$732$	6.71694	+	8.72970i	0.248265	+	0.322659i
$733$	−19.5415	+	19.5415i	−0.721781	+	0.721781i	−0.968968	−	0.247187i	$-0.920494\pi$
$733$	−19.5415	+	19.5415i	−0.721781	+	0.721781i	0.247187	+	0.968968i	$0.420494\pi$
$734$	−12.8773			−0.475308
$735$	1.07524	−	0.761359i	0.0396610	−	0.0280831i
$736$	−1.58318			−0.0583568
$737$	0.794174	−	0.794174i	0.0292538	−	0.0292538i
$738$	9.45287	−	5.49109i	0.347965	−	0.202130i
$739$		−	30.5281i		−	1.12299i	−0.827479	−	0.561496i	$-0.810226\pi$
$739$		−	30.5281i		−	1.12299i	0.827479	−	0.561496i	$-0.189774\pi$
$740$	−4.63445	−	5.01781i	−0.170366	−	0.184458i
$741$	34.0255	+	4.43365i	1.24996	+	0.162874i
$742$	6.53963	+	6.53963i	0.240077	+	0.240077i
$743$	19.1485	+	19.1485i	0.702491	+	0.702491i	0.964945	−	0.262453i	$-0.0845316\pi$
$743$	19.1485	+	19.1485i	0.702491	+	0.702491i	−0.262453	+	0.964945i	$0.584532\pi$
$744$	−1.71753	−	0.223801i	−0.0629677	−	0.00820495i
$745$	−0.707511	+	17.8137i	−0.0259212	+	0.652644i
$746$		−	34.2607i		−	1.25437i
$747$	2.10290	−	1.22156i	0.0769413	−	0.0446945i
$748$	5.69423	−	5.69423i	0.208202	−	0.208202i
$749$	25.6330			0.936608
$750$	18.7693	+	4.76587i	0.685358	+	0.174025i
$751$	−14.2636			−0.520488			−0.260244	−	0.965543i	$-0.583803\pi$
$751$	−14.2636			−0.520488			−0.260244	+	0.965543i	$0.583803\pi$
$752$	2.85601	−	2.85601i	0.104148	−	0.104148i
$753$	29.1322	+	37.8617i	1.06163	+	1.37976i
$754$			41.5075i			1.51161i
$755$	1.92726	−	48.5247i	0.0701403	−	1.76599i
$756$	13.0275	+	5.33557i	0.473807	+	0.194053i
$757$	−24.6042	−	24.6042i	−0.894256	−	0.894256i	0.100665	−	0.994920i	$-0.467903\pi$
$757$	−24.6042	−	24.6042i	−0.894256	−	0.894256i	−0.994920	+	0.100665i	$0.967903\pi$
$758$	−16.0331	−	16.0331i	−0.582350	−	0.582350i
$759$	−1.02799	+	7.88919i	−0.0373138	+	0.286359i
$760$	6.43343	+	6.96560i	0.233365	+	0.252669i
$761$			45.8447i			1.66187i	0.556372	+	0.830934i	$0.312193\pi$
$761$			45.8447i			1.66187i	−0.556372	+	0.830934i	$0.687807\pi$
$762$	−8.92910	+	6.87036i	−0.323467	+	0.248887i
$763$	−4.97925	+	4.97925i	−0.180261	+	0.180261i
$764$	15.2760			0.552665
$765$	−16.4584	+	8.70597i	−0.595053	+	0.314765i
$766$	11.3053			0.408478
$767$	−48.9704	+	48.9704i	−1.76822	+	1.76822i
$768$	1.37273	−	1.05623i	0.0495341	−	0.0381133i
$769$			41.2994i			1.48929i	0.667459	+	0.744646i	$0.267382\pi$
$769$			41.2994i			1.48929i	−0.667459	+	0.744646i	$0.732618\pi$
$770$	−17.5628	−	0.697545i	−0.632919	−	0.0251378i
$771$	1.77505	−	13.6224i	0.0639268	−	0.490597i
$772$	3.97848	+	3.97848i	0.143189	+	0.143189i
$773$	11.0109	+	11.0109i	0.396035	+	0.396035i	0.876832	−	0.480797i	$-0.159653\pi$
$773$	11.0109	+	11.0109i	0.396035	+	0.396035i	−0.480797	+	0.876832i	$0.659653\pi$
$774$	−7.80316	−	2.06869i	−0.280479	−	0.0743575i
$775$	−4.98425	−	0.396546i	−0.179040	−	0.0142444i
$776$		−	8.27734i		−	0.297139i
$777$	−8.74141	−	11.3608i	−0.313596	−	0.407567i
$778$	−18.8690	+	18.8690i	−0.676486	+	0.676486i
$779$	15.4523			0.553638
$780$	3.04814	−	17.8352i	0.109141	−	0.638602i
$781$	35.0710			1.25494
$782$	3.10719	−	3.10719i	0.111113	−	0.111113i
$783$	−17.8365	−	42.5814i	−0.637426	−	1.52174i
$784$		−	0.340178i		−	0.0121492i
$785$	40.4093	−	37.3220i	1.44227	−	1.33208i
$786$	5.62564	+	0.733044i	0.200660	+	0.0261468i
$787$	−15.1463	−	15.1463i	−0.539907	−	0.539907i	0.383595	−	0.923502i	$-0.374686\pi$
$787$	−15.1463	−	15.1463i	−0.539907	−	0.539907i	−0.923502	+	0.383595i	$0.874686\pi$
$788$	6.44042	+	6.44042i	0.229431	+	0.229431i
$789$	−20.2087	−	2.63328i	−0.719449	−	0.0937471i
$790$	−28.9047	+	26.6964i	−1.02838	+	0.949814i
$791$		−	18.4514i		−	0.656057i
$792$	−4.37197	−	7.52631i	−0.155351	−	0.267436i
$793$	21.0079	−	21.0079i	0.746014	−	0.746014i
$794$	−16.8159			−0.596775
$795$	−2.22723	+	13.0319i	−0.0789918	+	0.462195i
$796$	21.9690			0.778671
$797$	12.7552	−	12.7552i	0.451812	−	0.451812i	−0.444143	−	0.895956i	$-0.646492\pi$
$797$	12.7552	−	12.7552i	0.451812	−	0.451812i	0.895956	+	0.444143i	$0.146492\pi$
$798$	12.1346	+	15.7708i	0.429561	+	0.558280i
$799$			11.2106i			0.396601i
$800$	3.80480	−	3.24400i	0.134520	−	0.114693i
$801$	1.20799	−	4.55657i	0.0426822	−	0.160998i
$802$	18.6808	+	18.6808i	0.659640	+	0.659640i
$803$	11.8855	+	11.8855i	0.419430	+	0.419430i
$804$	−0.0866354	+	0.664872i	−0.00305540	+	0.0234482i
$805$	−9.58355	−	0.380632i	−0.337776	−	0.0134155i
$806$			4.67179i			0.164557i
$807$	27.5435	−	21.1929i	0.969576	−	0.746026i
$808$	3.17278	−	3.17278i	0.111618	−	0.111618i
$809$	28.8348			1.01378			0.506889	−	0.862012i	$-0.330796\pi$
$809$	28.8348			1.01378			0.506889	+	0.862012i	$0.330796\pi$
$810$	4.53712	+	19.6065i	0.159418	+	0.688902i
$811$	11.5785			0.406577			0.203288	−	0.979119i	$-0.434837\pi$
$811$	11.5785			0.406577			0.203288	+	0.979119i	$0.434837\pi$
$812$	−17.0208	+	17.0208i	−0.597314	+	0.597314i
$813$	−30.4990	+	23.4670i	−1.06965	+	0.823024i
$814$			8.86275i			0.310639i
$815$	6.98165	+	7.55917i	0.244557	+	0.264786i
$816$	−0.621177	+	4.76714i	−0.0217455	+	0.166883i
$817$	−8.06862	−	8.06862i	−0.282285	−	0.282285i
$818$	9.06782	+	9.06782i	0.317049	+	0.317049i
$819$	9.73048	−	36.7036i	0.340010	−	1.28253i
$820$	0.323370	−	8.14182i	0.0112926	−	0.284325i
$821$		−	34.8823i		−	1.21740i	−0.793401	−	0.608700i	$-0.791691\pi$
$821$		−	34.8823i		−	1.21740i	0.793401	−	0.608700i	$-0.208309\pi$
$822$	−11.5009	−	14.9472i	−0.401141	−	0.521344i
$823$	0.867175	−	0.867175i	0.0302278	−	0.0302278i	−0.691831	−	0.722059i	$-0.743196\pi$
$823$	0.867175	−	0.867175i	0.0302278	−	0.0302278i	0.722059	+	0.691831i	$0.243196\pi$
$824$	14.1755			0.493828
$825$	−13.6947	−	21.0662i	−0.476789	−	0.733430i
$826$	−40.1623			−1.39742
$827$	4.78759	−	4.78759i	0.166481	−	0.166481i	−0.618950	−	0.785431i	$-0.712442\pi$
$827$	4.78759	−	4.78759i	0.166481	−	0.166481i	0.785431	+	0.618950i	$0.212442\pi$
$828$	−2.38567	−	4.10691i	−0.0829077	−	0.142725i
$829$		−	32.9815i		−	1.14549i	−0.819732	−	0.572747i	$-0.805878\pi$
$829$		−	32.9815i		−	1.14549i	0.819732	−	0.572747i	$-0.194122\pi$
$830$	0.0719376	−	1.81125i	0.00249699	−	0.0628693i
$831$	7.52200	+	0.980147i	0.260935	+	0.0340009i
$832$	−3.30346	−	3.30346i	−0.114527	−	0.114527i
$833$	0.667643	+	0.667643i	0.0231325	+	0.0231325i
$834$	−22.7198	−	2.96048i	−0.786722	−	0.102513i
$835$	11.8161	+	12.7935i	0.408914	+	0.442739i
$836$		−	12.3031i		−	0.425510i
$837$	−2.00756	−	4.79267i	−0.0693914	−	0.165659i
$838$	3.53396	−	3.53396i	0.122079	−	0.122079i
$839$	−20.5395			−0.709103			−0.354552	−	0.935036i	$-0.615366\pi$
$839$	−20.5395			−0.709103			−0.354552	+	0.935036i	$0.615366\pi$
$840$	8.56356	−	6.06368i	0.295471	−	0.209217i
$841$	49.9377			1.72199
$842$	−19.8478	+	19.8478i	−0.683999	+	0.683999i
$843$	21.0917	+	27.4119i	0.726437	+	0.944117i
$844$		−	18.0161i		−	0.620140i
$845$	−19.7192	−	0.783193i	−0.678363	−	0.0269427i
$846$	11.7124	+	3.10507i	0.402681	+	0.106754i
$847$	−4.94699	−	4.94699i	−0.169981	−	0.169981i
$848$	2.41379	+	2.41379i	0.0828900	+	0.0828900i
$849$	2.77694	−	21.3112i	0.0953044	−	0.731400i
$850$	−1.10064	+	13.8342i	−0.0377518	+	0.474508i
$851$			4.83617i			0.165782i
$852$	−16.5934	+	12.7676i	−0.568481	+	0.437410i
$853$	1.03640	−	1.03640i	0.0354856	−	0.0354856i	−0.689141	−	0.724627i	$-0.742012\pi$
$853$	1.03640	−	1.03640i	0.0354856	−	0.0354856i	0.724627	+	0.689141i	$0.242012\pi$
$854$	17.2293			0.589575
$855$	−8.37497	+	27.1852i	−0.286418	+	0.929716i
$856$	9.46118			0.323376
$857$	−31.2113	+	31.2113i	−1.06616	+	1.06616i	−0.0685081	+	0.997651i	$0.521824\pi$
$857$	−31.2113	+	31.2113i	−1.06616	+	1.06616i	−0.997651	+	0.0685081i	$0.978176\pi$
$858$	−18.6066	+	14.3165i	−0.635217	+	0.488759i
$859$			16.6854i			0.569297i	0.958632	+	0.284649i	$0.0918770\pi$
$859$			16.6854i			0.569297i	−0.958632	+	0.284649i	$0.908123\pi$
$860$	−4.42020	+	4.08249i	−0.150727	+	0.139212i
$861$	2.20950	−	16.9565i	0.0752996	−	0.577876i
$862$	16.3605	+	16.3605i	0.557240	+	0.557240i
$863$	35.1418	+	35.1418i	1.19624	+	1.19624i	0.975283	+	0.220958i	$0.0709185\pi$
$863$	35.1418	+	35.1418i	1.19624	+	1.19624i	0.220958	+	0.975283i	$0.429082\pi$
$864$	4.80849	+	1.96937i	0.163588	+	0.0669994i
$865$	11.1717	−	10.3182i	0.379849	−	0.350828i
$866$			9.53645i			0.324062i
$867$	9.81888	+	12.7611i	0.333467	+	0.433391i
$868$	−1.91575	+	1.91575i	−0.0650247	+	0.0650247i
$869$	51.0532			1.73186
$870$	−33.9185	−	5.79686i	−1.14994	−	0.196532i
$871$	1.80849			0.0612785
$872$	−1.83785	+	1.83785i	−0.0622375	+	0.0622375i
$873$	21.4722	−	12.4730i	0.726722	−	0.422146i
$874$		−	6.71346i		−	0.227086i
$875$	23.8117	−	18.7223i	0.804983	−	0.632929i
$876$	−9.95037	−	1.29657i	−0.336192	−	0.0438071i
$877$	−15.4995	−	15.4995i	−0.523382	−	0.523382i	0.395209	−	0.918591i	$-0.370672\pi$
$877$	−15.4995	−	15.4995i	−0.523382	−	0.523382i	−0.918591	+	0.395209i	$0.870672\pi$
$878$	−9.51926	−	9.51926i	−0.321260	−	0.321260i
$879$	42.9723	+	5.59946i	1.44942	+	0.188865i
$880$	−6.48246	−	0.257465i	−0.218524	−	0.00867915i
$881$		−	26.0266i		−	0.876860i	−0.898765	−	0.438430i	$-0.855535\pi$
$881$		−	26.0266i		−	0.876860i	0.898765	−	0.438430i	$-0.144465\pi$
$882$	0.882453	−	0.512609i	0.0297137	−	0.0172604i
$883$	−11.4063	+	11.4063i	−0.383853	+	0.383853i	−0.872488	−	0.488635i	$-0.837495\pi$
$883$	−11.4063	+	11.4063i	−0.383853	+	0.383853i	0.488635	+	0.872488i	$0.337495\pi$
$884$	12.9669			0.436125
$885$	−33.1778	−	46.8560i	−1.11526	−	1.57505i
$886$	−31.9810			−1.07442
$887$	−22.9825	+	22.9825i	−0.771677	+	0.771677i	−0.978400	−	0.206722i	$-0.933720\pi$
$887$	−22.9825	+	22.9825i	−0.771677	+	0.771677i	0.206722	+	0.978400i	$0.433720\pi$
$888$	−3.22647	−	4.19330i	−0.108273	−	0.140718i
$889$			17.6228i			0.591051i
$890$	−2.38393	−	2.58113i	−0.0799094	−	0.0865195i
$891$	12.9359	−	22.6826i	0.433369	−	0.759894i
$892$	8.01367	+	8.01367i	0.268318	+	0.268318i
$893$	12.1109	+	12.1109i	0.405274	+	0.405274i
$894$	−1.78433	+	13.6936i	−0.0596768	+	0.457981i
$895$	0.410626	−	10.3388i	0.0137257	−	0.345586i
$896$		−	2.70928i		−	0.0905106i
$897$	−10.1531	+	7.81217i	−0.339003	+	0.260841i
$898$	27.3122	−	27.3122i	0.911420	−	0.911420i
$899$	8.88469			0.296321
$900$	14.1486	+	4.98166i	0.471620	+	0.166055i
$901$	−9.47475			−0.315650
$902$	−7.47586	+	7.47586i	−0.248919	+	0.248919i
$903$	−10.0078	+	7.70032i	−0.333037	+	0.256251i
$904$		−	6.81046i		−	0.226513i
$905$	0.0934569	−	2.35306i	0.00310661	−	0.0782183i
$906$	4.86052	−	37.3014i	0.161480	−	1.23925i
$907$	37.4360	+	37.4360i	1.24304	+	1.24304i	0.958733	+	0.284309i	$0.0917642\pi$
$907$	37.4360	+	37.4360i	1.24304	+	1.24304i	0.284309	+	0.958733i	$0.408236\pi$
$908$	−5.35234	−	5.35234i	−0.177624	−	0.177624i
$909$	13.0115	+	3.44946i	0.431563	+	0.114411i
$910$	−19.2028	−	20.7912i	−0.636566	−	0.689222i
$911$			47.6038i			1.57718i	0.614917	+	0.788592i	$0.289189\pi$
$911$			47.6038i			1.57718i	−0.614917	+	0.788592i	$0.710811\pi$
$912$	4.47891	+	5.82104i	0.148312	+	0.192754i
$913$	−1.66309	+	1.66309i	−0.0550404	+	0.0550404i
$914$	−33.7814			−1.11739
$915$	14.2330	+	20.1009i	0.470530	+	0.664515i
$916$	7.11285			0.235015
$917$	6.27488	−	6.27488i	0.207215	−	0.207215i
$918$	−13.3024	+	5.57213i	−0.439045	+	0.183908i
$919$		−	45.0152i		−	1.48491i	−0.669894	−	0.742457i	$-0.733660\pi$
$919$		−	45.0152i		−	1.48491i	0.669894	−	0.742457i	$-0.266340\pi$
$920$	−3.53731	−	0.140492i	−0.116622	−	0.00463189i
$921$	−56.9621	−	7.42239i	−1.87697	−	0.244576i
$922$	27.4413	+	27.4413i	0.903730	+	0.903730i
$923$	39.9319	+	39.9319i	1.31437	+	1.31437i
$924$	−13.5007	−	1.75919i	−0.444139	−	0.0578731i
$925$	−9.90949	−	11.6226i	−0.325822	−	0.382148i
$926$			18.4619i			0.606697i
$927$	21.3609	+	36.7726i	0.701583	+	1.20777i
$928$	−6.28243	+	6.28243i	−0.206231	+	0.206231i
$929$	20.3848			0.668805			0.334402	−	0.942430i	$-0.391466\pi$
$929$	20.3848			0.668805			0.334402	+	0.942430i	$0.391466\pi$
$930$	−3.81763	−	0.652455i	−0.125185	−	0.0213948i
$931$	1.44252			0.0472767
$932$	−18.5150	+	18.5150i	−0.606479	+	0.606479i
$933$	−31.9430	−	41.5148i	−1.04577	−	1.35913i
$934$			0.797384i			0.0260912i
$935$	13.2280	−	12.2174i	0.432601	−	0.399550i
$936$	3.59154	−	13.5474i	0.117393	−	0.442810i
$937$	−22.8348	−	22.8348i	−0.745980	−	0.745980i	0.227742	−	0.973722i	$-0.426866\pi$
$937$	−22.8348	−	22.8348i	−0.745980	−	0.745980i	−0.973722	+	0.227742i	$0.926866\pi$
$938$	0.741603	+	0.741603i	0.0242142	+	0.0242142i
$939$	−0.150213	+	1.15279i	−0.00490201	+	0.0376198i
$940$	6.63464	−	6.12775i	0.216398	−	0.199865i
$941$		−	41.6503i		−	1.35776i	−0.734249	−	0.678880i	$-0.762465\pi$
$941$		−	41.6503i		−	1.35776i	0.734249	−	0.678880i	$-0.237535\pi$
$942$	33.7694	−	25.9834i	1.10027	−	0.846584i
$943$	−4.07938	+	4.07938i	−0.132843	+	0.132843i
$944$	−14.8240			−0.482479
$945$	28.6340	+	13.0774i	0.931464	+	0.425407i
$946$	7.80721			0.253834
$947$	18.0697	−	18.0697i	0.587188	−	0.587188i	−0.349681	−	0.936869i	$-0.613710\pi$
$947$	18.0697	−	18.0697i	0.587188	−	0.587188i	0.936869	+	0.349681i	$0.113710\pi$
$948$	−24.1552	+	18.5859i	−0.784524	+	0.603640i
$949$			27.0656i			0.878588i
$950$	13.7561	+	16.1342i	0.446308	+	0.523462i
$951$	−7.63881	+	58.6230i	−0.247705	+	1.90098i
$952$	5.31730	+	5.31730i	0.172335	+	0.172335i
$953$	−15.7901	−	15.7901i	−0.511491	−	0.511491i	0.403492	−	0.914983i	$-0.367796\pi$
$953$	−15.7901	−	15.7901i	−0.511491	−	0.511491i	−0.914983	+	0.403492i	$0.867796\pi$
$954$	−2.62429	+	9.89890i	−0.0849645	+	0.320489i
$955$	34.1312	+	1.35560i	1.10446	+	0.0438661i
$956$			3.09406i			0.100069i
$957$	27.2268	+	35.3854i	0.880118	+	1.14385i
$958$	18.1402	−	18.1402i	0.586085	−	0.586085i
$959$	−29.5005			−0.952620
$960$	3.16083	−	2.23812i	0.102015	−	0.0722349i
$961$	1.00000			0.0322581
$962$	−10.0911	+	10.0911i	−0.325351	+	0.325351i
$963$	14.2569	+	24.5432i	0.459422	+	0.790892i
$964$		−	25.4115i		−	0.818448i
$965$	8.53610	+	9.24220i	0.274787	+	0.297517i
$966$	−7.36696	−	0.959945i	−0.237028	−	0.0308857i
$967$	18.4888	+	18.4888i	0.594560	+	0.594560i	0.938860	−	0.344300i	$-0.111884\pi$
$967$	18.4888	+	18.4888i	0.594560	+	0.594560i	−0.344300	+	0.938860i	$0.611884\pi$
$968$	−1.82595	−	1.82595i	−0.0586881	−	0.0586881i
$969$	−20.2150	−	2.63409i	−0.649399	−	0.0846192i
$970$	0.734534	−	18.4941i	0.0235845	−	0.593810i
$971$			3.15628i			0.101290i	0.998717	+	0.0506449i	$0.0161277\pi$
$971$			3.15628i			0.101290i	−0.998717	+	0.0506449i	$0.983872\pi$
$972$	2.13710	+	15.4413i	0.0685476	+	0.495279i
$973$	−25.3418	+	25.3418i	−0.812421	+	0.812421i
$974$	−30.6026			−0.980569
$975$	8.39317	−	39.5788i	0.268797	−	1.26754i
$976$	6.35938			0.203559
$977$	−18.0776	+	18.0776i	−0.578353	+	0.578353i	−0.934449	−	0.356096i	$-0.884108\pi$
$977$	−18.0776	+	18.0776i	−0.578353	+	0.578353i	0.356096	+	0.934449i	$0.384108\pi$
$978$	4.86058	+	6.31708i	0.155424	+	0.201998i
$979$			4.55893i			0.145704i
$980$	0.0301875	−	0.760062i	0.000964306	−	0.0242793i
$981$	−7.53698	−	1.99812i	−0.240637	−	0.0637952i
$982$	−21.9757	−	21.9757i	−0.701272	−	0.701272i
$983$	−23.0754	−	23.0754i	−0.735990	−	0.735990i	0.235810	−	0.971799i	$-0.424226\pi$
$983$	−23.0754	−	23.0754i	−0.735990	−	0.735990i	−0.971799	+	0.235810i	$0.924226\pi$
$984$	0.815532	−	6.25869i	0.0259982	−	0.199520i
$985$	13.8184	+	14.9614i	0.440289	+	0.476710i
$986$		−	24.6601i		−	0.785338i
$987$	15.0215	−	11.5580i	0.478139	−	0.367897i
$988$	14.0083	−	14.0083i	0.445662	−	0.445662i
$989$	4.26019			0.135466
$990$	−9.10043	−	17.2041i	−0.289231	−	0.546781i
$991$	37.5448			1.19265			0.596324	−	0.802744i	$-0.296627\pi$
$991$	37.5448			1.19265			0.596324	+	0.802744i	$0.296627\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	7.61773	−	5.86135i	0.241741	−	0.186004i
$994$			32.7495i			1.03875i
$995$	49.0855	+	1.94954i	1.55611	+	0.0618045i
$996$	0.181425	−	1.39232i	0.00574867	−	0.0441174i
$997$	22.8215	+	22.8215i	0.722763	+	0.722763i	0.969167	−	0.246404i	$-0.0792491\pi$
$997$	22.8215	+	22.8215i	0.722763	+	0.722763i	−0.246404	+	0.969167i	$0.579249\pi$
$998$	1.01841	+	1.01841i	0.0322371	+	0.0322371i
$999$	6.01588	−	14.6886i	0.190334	−	0.464726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.18	yes	40
3.2	odd	2	inner	930.2.j.g.497.9	✓	40
5.3	odd	4	inner	930.2.j.g.683.9	yes	40
15.8	even	4	inner	930.2.j.g.683.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.9	✓	40	3.2	odd	2	inner
930.2.j.g.497.18	yes	40	1.1	even	1	trivial
930.2.j.g.683.9	yes	40	5.3	odd	4	inner
930.2.j.g.683.18	yes	40	15.8	even	4	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.37273 - 1.05623i) q^{3} -1.00000i q^{4} +(0.0887404 - 2.23431i) q^{5} +(0.223801 - 1.71753i) q^{6} +(-1.91575 - 1.91575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.768771 - 2.89983i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.37273 - 1.05623i) q^{3} -1.00000i q^{4} +(0.0887404 - 2.23431i) q^{5} +(0.223801 - 1.71753i) q^{6} +(-1.91575 - 1.91575i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.768771 - 2.89983i) q^{9} +(-1.51714 - 1.64264i) q^{10} +2.90133i q^{11} +(-1.05623 - 1.37273i) q^{12} +(-3.30346 + 3.30346i) q^{13} -2.70928 q^{14} +(-2.23812 - 3.16083i) q^{15} -1.00000 q^{16} +(1.96263 - 1.96263i) q^{17} +(-1.50688 - 2.59409i) q^{18} -4.24049i q^{19} +(-2.23431 - 0.0887404i) q^{20} +(-4.65327 - 0.606339i) q^{21} +(2.05155 + 2.05155i) q^{22} +(1.11948 + 1.11948i) q^{23} +(-1.71753 - 0.223801i) q^{24} +(-4.98425 - 0.396546i) q^{25} +4.67179i q^{26} +(-2.00756 - 4.79267i) q^{27} +(-1.91575 + 1.91575i) q^{28} +8.88469 q^{29} +(-3.81763 - 0.652455i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.06446 + 3.98274i) q^{33} -2.77557i q^{34} +(-4.45037 + 4.11036i) q^{35} +(-2.89983 - 0.768771i) q^{36} +(2.16001 + 2.16001i) q^{37} +(-2.99848 - 2.99848i) q^{38} +(-1.04555 + 8.02395i) q^{39} +(-1.64264 + 1.51714i) q^{40} +3.64400i q^{41} +(-3.71910 + 2.86161i) q^{42} +(1.90276 - 1.90276i) q^{43} +2.90133 q^{44} +(-6.41088 - 1.97500i) q^{45} +1.58318 q^{46} +(-2.85601 + 2.85601i) q^{47} +(-1.37273 + 1.05623i) q^{48} +0.340178i q^{49} +(-3.80480 + 3.24400i) q^{50} +(0.621177 - 4.76714i) q^{51} +(3.30346 + 3.30346i) q^{52} +(-2.41379 - 2.41379i) q^{53} +(-4.80849 - 1.96937i) q^{54} +(6.48246 + 0.257465i) q^{55} +2.70928i q^{56} +(-4.47891 - 5.82104i) q^{57} +(6.28243 - 6.28243i) q^{58} +14.8240 q^{59} +(-3.16083 + 2.23812i) q^{60} -6.35938 q^{61} +(0.707107 - 0.707107i) q^{62} +(-7.02811 + 4.08256i) q^{63} +1.00000i q^{64} +(7.08779 + 7.67409i) q^{65} +(4.98313 + 0.649321i) q^{66} +(-0.273727 - 0.273727i) q^{67} +(-1.96263 - 1.96263i) q^{68} +(2.71916 + 0.354318i) q^{69} +(-0.240422 + 6.05335i) q^{70} -12.0879i q^{71} +(-2.59409 + 1.50688i) q^{72} +(4.09656 - 4.09656i) q^{73} +3.05472 q^{74} +(-7.26087 + 4.72015i) q^{75} -4.24049 q^{76} +(5.55822 - 5.55822i) q^{77} +(4.93447 + 6.41311i) q^{78} -17.5965i q^{79} +(-0.0887404 + 2.23431i) q^{80} +(-7.81798 - 4.45860i) q^{81} +(2.57670 + 2.57670i) q^{82} +(0.573218 + 0.573218i) q^{83} +(-0.606339 + 4.65327i) q^{84} +(-4.21095 - 4.55928i) q^{85} -2.69091i q^{86} +(12.1963 - 9.38425i) q^{87} +(2.05155 - 2.05155i) q^{88} +1.57133 q^{89} +(-5.92971 + 3.13664i) q^{90} +12.6572 q^{91} +(1.11948 - 1.11948i) q^{92} +(1.37273 - 1.05623i) q^{93} +4.03900i q^{94} +(-9.47455 - 0.376302i) q^{95} +(-0.223801 + 1.71753i) q^{96} +(5.85296 + 5.85296i) q^{97} +(0.240542 + 0.240542i) q^{98} +(8.41336 + 2.23046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 - 8 * q^7	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more