LMFDB - Embedded newform 930.2.be.b.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, 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:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.76107 + 1.37790i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.28122 - 4.78156i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.76107 + 1.37790i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.28122 - 4.78156i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.270942 - 2.21959i) q^{10} +(3.29801 + 1.90410i) q^{11} +(0.965926 + 0.258819i) q^{12} +(3.08420 - 0.826410i) q^{13} +(-4.28703 + 2.47512i) q^{14} +(1.78675 - 1.34444i) q^{15} -1.00000 q^{16} +(2.72631 + 0.730514i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.78421 + 1.60747i) q^{19} +(-1.37790 + 1.76107i) q^{20} +(-4.28703 - 2.47512i) q^{21} +(-0.985637 - 3.67845i) q^{22} +(-0.0663633 - 0.0663633i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.20276 + 4.85318i) q^{25} +(-2.76522 - 1.59650i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.78156 + 1.28122i) q^{28} -4.25970 q^{29} +(-2.21409 - 0.312763i) q^{30} +(3.04284 + 4.66274i) q^{31} +(0.707107 + 0.707107i) q^{32} +(2.69281 - 2.69281i) q^{33} +(-1.41124 - 2.44435i) q^{34} +(8.84485 - 6.65529i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.83984 - 2.10068i) q^{37} +(3.10539 + 0.832086i) q^{38} -3.19300i q^{39} +(2.21959 - 0.270942i) q^{40} +(2.84370 - 4.92543i) q^{41} +(1.28122 + 4.78156i) q^{42} +(1.79574 - 6.70179i) q^{43} +(-1.90410 + 3.29801i) q^{44} +(-0.836183 - 2.07384i) q^{45} +0.0938519i q^{46} +(4.45449 + 4.45449i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-15.1596 - 8.75242i) q^{49} +(2.58124 - 4.28220i) q^{50} +(1.41124 - 2.44435i) q^{51} +(0.826410 + 3.08420i) q^{52} +(4.79801 - 1.28562i) q^{53} +1.00000 q^{54} +(3.18436 + 7.89760i) q^{55} +(-2.47512 - 4.28703i) q^{56} +(0.832086 + 3.10539i) q^{57} +(3.01207 + 3.01207i) q^{58} +(8.46975 - 4.89001i) q^{59} +(1.34444 + 1.78675i) q^{60} +10.8712i q^{61} +(1.14544 - 5.44867i) q^{62} +(-3.50035 + 3.50035i) q^{63} -1.00000i q^{64} +(6.57023 + 2.79437i) q^{65} -3.80821 q^{66} +(3.91121 - 1.04801i) q^{67} +(-0.730514 + 2.72631i) q^{68} +(-0.0812782 + 0.0469260i) q^{69} +(-10.9603 - 1.54825i) q^{70} +(6.02746 - 10.4399i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-7.48712 + 2.00617i) q^{73} +(4.05820 + 7.02901i) q^{74} +(4.99911 + 0.0943161i) q^{75} +(-1.60747 - 2.78421i) q^{76} +(13.3301 - 13.3301i) q^{77} +(-2.25779 + 2.25779i) q^{78} +(-5.93732 - 10.2837i) q^{79} +(-1.76107 - 1.37790i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.49360 + 1.47201i) q^{82} +(-6.49523 + 1.74039i) q^{83} +(2.47512 - 4.28703i) q^{84} +(3.79466 + 5.04309i) q^{85} +(-6.00866 + 3.46910i) q^{86} +(-1.10249 + 4.11456i) q^{87} +(3.67845 - 0.985637i) q^{88} -12.2236 q^{89} +(-0.875153 + 2.05769i) q^{90} -15.8061i q^{91} +(0.0663633 - 0.0663633i) q^{92} +(5.29140 - 1.73235i) q^{93} -6.29959i q^{94} +(-7.11814 - 1.00551i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-9.58031 - 9.58031i) q^{97} +(4.53059 + 16.9084i) q^{98} +(-1.90410 - 3.29801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	1.76107	+	1.37790i	0.787576	+	0.616217i
$5$	1.76107	+	1.37790i	0.787576	+	0.616217i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	1.28122	−	4.78156i	0.484254	−	1.80726i	−0.0991429	−	0.995073i	$-0.531610\pi$
$7$	1.28122	−	4.78156i	0.484254	−	1.80726i	0.583397	−	0.812187i	$-0.301723\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.270942	−	2.21959i	−0.0856795	−	0.701897i
$11$	3.29801	+	1.90410i	0.994386	+	0.574109i	0.906583	−	0.422029i	$-0.138682\pi$
$11$	3.29801	+	1.90410i	0.994386	+	0.574109i	0.0878038	+	0.996138i	$0.472015\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	3.08420	−	0.826410i	0.855405	−	0.229205i	0.195639	−	0.980676i	$-0.437322\pi$
$13$	3.08420	−	0.826410i	0.855405	−	0.229205i	0.659766	+	0.751471i	$0.270655\pi$
$14$	−4.28703	+	2.47512i	−1.14576	+	0.661503i
$15$	1.78675	−	1.34444i	0.461337	−	0.347133i
$16$	−1.00000			−0.250000
$17$	2.72631	+	0.730514i	0.661228	+	0.177176i	0.573800	−	0.818995i	$-0.305469\pi$
$17$	2.72631	+	0.730514i	0.661228	+	0.177176i	0.0874279	+	0.996171i	$0.472135\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−2.78421	+	1.60747i	−0.638742	+	0.368778i	−0.784130	−	0.620597i	$-0.786890\pi$
$19$	−2.78421	+	1.60747i	−0.638742	+	0.368778i	0.145388	+	0.989375i	$0.453557\pi$
$20$	−1.37790	+	1.76107i	−0.308109	+	0.393788i
$21$	−4.28703	−	2.47512i	−0.935507	−	0.540115i
$22$	−0.985637	−	3.67845i	−0.210139	−	0.784248i
$23$	−0.0663633	−	0.0663633i	−0.0138377	−	0.0138377i	0.700154	−	0.713992i	$-0.253115\pi$
$23$	−0.0663633	−	0.0663633i	−0.0138377	−	0.0138377i	−0.713992	+	0.700154i	$0.753115\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	1.20276	+	4.85318i	0.240553	+	0.970636i
$26$	−2.76522	−	1.59650i	−0.542305	−	0.313100i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.78156	+	1.28122i	0.903630	+	0.242127i
$29$	−4.25970			−0.791007			−0.395504	−	0.918464i	$-0.629430\pi$
$29$	−4.25970			−0.791007			−0.395504	+	0.918464i	$0.629430\pi$
$30$	−2.21409	−	0.312763i	−0.404235	−	0.0571024i
$31$	3.04284	+	4.66274i	0.546510	+	0.837452i
$31$	3.04284	+	4.66274i	0.546510	+	0.837452i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	2.69281	−	2.69281i	0.468758	−	0.468758i
$34$	−1.41124	−	2.44435i	−0.242026	−	0.419202i
$35$	8.84485	−	6.65529i	1.49505	−	1.12495i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−7.83984	−	2.10068i	−1.28886	−	0.345349i	−0.451634	−	0.892204i	$-0.649159\pi$
$37$	−7.83984	−	2.10068i	−1.28886	−	0.345349i	−0.837228	+	0.546854i	$0.815825\pi$
$38$	3.10539	+	0.832086i	0.503760	+	0.134982i
$39$		−	3.19300i		−	0.511290i
$40$	2.21959	−	0.270942i	0.350948	−	0.0428397i
$41$	2.84370	−	4.92543i	0.444111	−	0.769223i	−0.553879	−	0.832597i	$-0.686853\pi$
$41$	2.84370	−	4.92543i	0.444111	−	0.769223i	0.997990	+	0.0633745i	$0.0201863\pi$
$42$	1.28122	+	4.78156i	0.197696	+	0.737811i
$43$	1.79574	−	6.70179i	0.273848	−	1.02201i	−0.682762	−	0.730641i	$-0.739221\pi$
$43$	1.79574	−	6.70179i	0.273848	−	1.02201i	0.956610	−	0.291373i	$-0.0941120\pi$
$44$	−1.90410	+	3.29801i	−0.287055	+	0.497193i
$45$	−0.836183	−	2.07384i	−0.124651	−	0.309149i
$46$			0.0938519i			0.0138377i
$47$	4.45449	+	4.45449i	0.649754	+	0.649754i	0.952933	−	0.303180i	$-0.0980483\pi$
$47$	4.45449	+	4.45449i	0.649754	+	0.649754i	−0.303180	+	0.952933i	$0.598048\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	−15.1596	−	8.75242i	−2.16566	−	1.25035i
$50$	2.58124	−	4.28220i	0.365042	−	0.605594i
$51$	1.41124	−	2.44435i	0.197614	−	0.342277i
$52$	0.826410	+	3.08420i	0.114602	+	0.427702i
$53$	4.79801	−	1.28562i	0.659057	−	0.176594i	0.0862368	−	0.996275i	$-0.472516\pi$
$53$	4.79801	−	1.28562i	0.659057	−	0.176594i	0.572821	+	0.819681i	$0.305849\pi$
$54$	1.00000			0.136083
$55$	3.18436	+	7.89760i	0.429379	+	1.06491i
$56$	−2.47512	−	4.28703i	−0.330752	−	0.572879i
$57$	0.832086	+	3.10539i	0.110212	+	0.411318i
$58$	3.01207	+	3.01207i	0.395504	+	0.395504i
$59$	8.46975	−	4.89001i	1.10267	−	0.636625i	0.165747	−	0.986168i	$-0.446997\pi$
$59$	8.46975	−	4.89001i	1.10267	−	0.636625i	0.936920	+	0.349543i	$0.113663\pi$
$60$	1.34444	+	1.78675i	0.173566	+	0.230669i
$61$			10.8712i			1.39191i	0.718085	+	0.695956i	$0.245019\pi$
$61$			10.8712i			1.39191i	−0.718085	+	0.695956i	$0.754981\pi$
$62$	1.14544	−	5.44867i	0.145471	−	0.691981i
$63$	−3.50035	+	3.50035i	−0.441002	+	0.441002i
$64$		−	1.00000i		−	0.125000i
$65$	6.57023	+	2.79437i	0.814936	+	0.346599i
$66$	−3.80821			−0.468758
$67$	3.91121	−	1.04801i	0.477831	−	0.128034i	−0.0118617	−	0.999930i	$-0.503776\pi$
$67$	3.91121	−	1.04801i	0.477831	−	0.128034i	0.489692	+	0.871895i	$0.337109\pi$
$68$	−0.730514	+	2.72631i	−0.0885878	+	0.330614i
$69$	−0.0812782	+	0.0469260i	−0.00978474	+	0.00564922i
$70$	−10.9603	−	1.54825i	−1.31000	−	0.185051i
$71$	6.02746	−	10.4399i	0.715327	−	1.23898i	−0.247506	−	0.968886i	$-0.579611\pi$
$71$	6.02746	−	10.4399i	0.715327	−	1.23898i	0.962833	−	0.270097i	$-0.0870558\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−7.48712	+	2.00617i	−0.876301	+	0.234804i	−0.668810	−	0.743433i	$-0.733196\pi$
$73$	−7.48712	+	2.00617i	−0.876301	+	0.234804i	−0.207490	+	0.978237i	$0.566530\pi$
$74$	4.05820	+	7.02901i	0.471756	+	0.817105i
$75$	4.99911	+	0.0943161i	0.577248	+	0.0108907i
$76$	−1.60747	−	2.78421i	−0.184389	−	0.319371i
$77$	13.3301	−	13.3301i	1.51910	−	1.51910i
$78$	−2.25779	+	2.25779i	−0.255645	+	0.255645i
$79$	−5.93732	−	10.2837i	−0.668001	−	1.15701i	−0.978462	−	0.206426i	$-0.933817\pi$
$79$	−5.93732	−	10.2837i	−0.668001	−	1.15701i	0.310461	−	0.950586i	$-0.399516\pi$
$80$	−1.76107	−	1.37790i	−0.196894	−	0.154054i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−5.49360	+	1.47201i	−0.606667	+	0.162556i
$83$	−6.49523	+	1.74039i	−0.712945	+	0.191033i	−0.597021	−	0.802225i	$-0.703649\pi$
$83$	−6.49523	+	1.74039i	−0.712945	+	0.191033i	−0.115923	+	0.993258i	$0.536983\pi$
$84$	2.47512	−	4.28703i	0.270058	−	0.467753i
$85$	3.79466	+	5.04309i	0.411589	+	0.546999i
$86$	−6.00866	+	3.46910i	−0.647931	+	0.374083i
$87$	−1.10249	+	4.11456i	−0.118200	+	0.441127i
$88$	3.67845	−	0.985637i	0.392124	−	0.105069i
$89$	−12.2236			−1.29570			−0.647849	−	0.761768i	$-0.724331\pi$
$89$	−12.2236			−1.29570			−0.647849	+	0.761768i	$0.724331\pi$
$90$	−0.875153	+	2.05769i	−0.0922493	+	0.216900i
$91$		−	15.8061i		−	1.65693i
$92$	0.0663633	−	0.0663633i	0.00691886	−	0.00691886i
$93$	5.29140	−	1.73235i	0.548693	−	0.179637i
$94$		−	6.29959i		−	0.649754i
$95$	−7.11814	−	1.00551i	−0.730306	−	0.103163i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−9.58031	−	9.58031i	−0.972733	−	0.972733i	0.0269052	−	0.999638i	$-0.491435\pi$
$97$	−9.58031	−	9.58031i	−0.972733	−	0.972733i	−0.999638	+	0.0269052i	$0.991435\pi$
$98$	4.53059	+	16.9084i	0.457658	+	1.70800i
$99$	−1.90410	−	3.29801i	−0.191370	−	0.331462i
$100$	−4.85318	+	1.20276i	−0.485318	+	0.120276i
$101$	−10.4110			−1.03593			−0.517965	−	0.855402i	$-0.673310\pi$
$101$	−10.4110			−1.03593			−0.517965	+	0.855402i	$0.673310\pi$
$102$	−2.72631	+	0.730514i	−0.269945	+	0.0723316i
$103$	−0.169917	−	0.634139i	−0.0167424	−	0.0624836i	0.957049	−	0.289925i	$-0.0936305\pi$
$103$	−0.169917	−	0.634139i	−0.0167424	−	0.0624836i	−0.973792	+	0.227442i	$0.926964\pi$
$104$	1.59650	−	2.76522i	0.156550	−	0.271152i
$105$	−4.13930	−	10.2660i	−0.403955	−	1.00186i
$106$	−4.30178	−	2.48363i	−0.417826	−	0.241232i
$107$	−2.41983	+	9.03094i	−0.233934	+	0.873054i	0.744692	+	0.667408i	$0.232596\pi$
$107$	−2.41983	+	9.03094i	−0.233934	+	0.873054i	−0.978626	+	0.205646i	$0.934070\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			10.8715i			1.04130i	0.853769	+	0.520652i	$0.174311\pi$
$109$			10.8715i			1.04130i	−0.853769	+	0.520652i	$0.825689\pi$
$110$	3.33277	−	7.83613i	0.317767	−	0.747146i
$111$	−4.05820	+	7.02901i	−0.385187	+	0.667164i
$112$	−1.28122	+	4.78156i	−0.121063	+	0.451815i
$113$	−2.55659	−	9.54132i	−0.240504	−	0.897572i	−0.975590	−	0.219599i	$-0.929525\pi$
$113$	−2.55659	−	9.54132i	−0.240504	−	0.897572i	0.735087	−	0.677973i	$-0.237141\pi$
$114$	1.60747	−	2.78421i	0.150553	−	0.260765i
$115$	−0.0254284	−	0.208313i	−0.00237122	−	0.0194253i
$116$		−	4.25970i		−	0.395504i
$117$	−3.08420	−	0.826410i	−0.285135	−	0.0764017i
$118$	−9.44677	−	2.53126i	−0.869646	−	0.233021i
$119$	6.98599	−	12.1001i	0.640405	−	1.10921i
$120$	0.312763	−	2.21409i	0.0285512	−	0.202118i
$121$	1.75123	+	3.03322i	0.159203	+	0.275747i
$122$	7.68708	−	7.68708i	0.695956	−	0.695956i
$123$	−4.02160	−	4.02160i	−0.362615	−	0.362615i
$124$	−4.66274	+	3.04284i	−0.418726	+	0.273255i
$125$	−4.56906	+	10.2041i	−0.408669	+	0.912683i
$126$	4.95024			0.441002
$127$	0.547093	+	0.146593i	0.0485466	+	0.0130080i	0.283011	−	0.959117i	$-0.408667\pi$
$127$	0.547093	+	0.146593i	0.0485466	+	0.0130080i	−0.234464	+	0.972125i	$0.575333\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−6.00866	−	3.46910i	−0.529033	−	0.305438i
$130$	−2.66994	−	6.62177i	−0.234169	−	0.580767i
$131$	10.8884	+	18.8593i	0.951325	+	1.64774i	0.742562	+	0.669777i	$0.233610\pi$
$131$	10.8884	+	18.8593i	0.951325	+	1.64774i	0.208763	+	0.977966i	$0.433056\pi$
$132$	2.69281	+	2.69281i	0.234379	+	0.234379i
$133$	4.11902	+	15.3724i	0.357164	+	1.33296i
$134$	−3.50670	−	2.02459i	−0.302932	−	0.174898i
$135$	−2.21959	+	0.270942i	−0.191032	+	0.0233190i
$136$	2.44435	−	1.41124i	0.209601	−	0.121013i
$137$	0.224469	+	0.837732i	0.0191777	+	0.0715722i	0.974852	−	0.222855i	$-0.0715377\pi$
$137$	0.224469	+	0.837732i	0.0191777	+	0.0715722i	−0.955674	+	0.294427i	$0.904871\pi$
$138$	0.0906540	+	0.0242907i	0.00771698	+	0.00206776i
$139$	10.1621			0.861934			0.430967	−	0.902368i	$-0.358172\pi$
$139$	10.1621			0.861934			0.430967	+	0.902368i	$0.358172\pi$
$140$	6.65529	+	8.84485i	0.562475	+	0.747526i
$141$	5.45561	−	3.14980i	0.459445	−	0.265261i
$142$	−11.6442	+	3.12004i	−0.977155	+	0.261828i
$143$	11.7453	+	3.14714i	0.982191	+	0.263177i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−7.50165	−	5.86946i	−0.622978	−	0.487432i
$146$	6.71277	+	3.87562i	0.555552	+	0.320748i
$147$	−12.3778	+	12.3778i	−1.02090	+	1.02090i
$148$	2.10068	−	7.83984i	0.172675	−	0.644431i
$149$	5.57254	−	3.21731i	0.456521	−	0.263572i	−0.254060	−	0.967189i	$-0.581766\pi$
$149$	5.57254	−	3.21731i	0.456521	−	0.263572i	0.710580	+	0.703616i	$0.248433\pi$
$150$	−3.46821	−	3.60160i	−0.283178	−	0.294069i
$151$			5.07526i			0.413018i	0.978445	+	0.206509i	$0.0662103\pi$
$151$			5.07526i			0.413018i	−0.978445	+	0.206509i	$0.933790\pi$
$152$	−0.832086	+	3.10539i	−0.0674911	+	0.251880i
$153$	−1.99580	−	1.99580i	−0.161351	−	0.161351i
$154$	−18.8515			−1.51910
$155$	−1.06614	+	12.4042i	−0.0856341	+	0.996327i
$156$	3.19300			0.255645
$157$	−11.3713	−	11.3713i	−0.907532	−	0.907532i	0.0885405	−	0.996073i	$-0.471780\pi$
$157$	−11.3713	−	11.3713i	−0.907532	−	0.907532i	−0.996073	+	0.0885405i	$0.971780\pi$
$158$	−3.07338	+	11.4700i	−0.244505	+	0.912506i
$159$		−	4.96727i		−	0.393930i
$160$	0.270942	+	2.21959i	0.0214199	+	0.175474i
$161$	−0.402346	+	0.232295i	−0.0317093	+	0.0183074i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−4.22636	+	4.22636i	−0.331034	+	0.331034i	−0.852979	−	0.521945i	$-0.825207\pi$
$163$	−4.22636	+	4.22636i	−0.331034	+	0.331034i	0.521945	+	0.852979i	$0.325207\pi$
$164$	4.92543	+	2.84370i	0.384611	+	0.222055i
$165$	8.45267	−	1.03180i	0.658040	−	0.0803259i
$166$	5.82347	+	3.36218i	0.451989	+	0.260956i
$167$	14.2540	+	3.81935i	1.10301	+	0.295550i	0.763989	−	0.645229i	$-0.223238\pi$
$167$	14.2540	+	3.81935i	1.10301	+	0.295550i	0.339020	+	0.940779i	$0.389905\pi$
$168$	−4.78156	+	1.28122i	−0.368905	+	0.0988479i
$169$	−2.42896	+	1.40236i	−0.186843	+	0.107874i
$170$	0.882769	−	6.24923i	0.0677053	−	0.479294i
$171$	3.21493			0.245852
$172$	6.70179	+	1.79574i	0.511007	+	0.136924i
$173$	4.12075	+	15.3789i	0.313295	+	1.16923i	0.925566	+	0.378586i	$0.123589\pi$
$173$	4.12075	+	15.3789i	0.313295	+	1.16923i	−0.612271	+	0.790648i	$0.709744\pi$
$174$	3.68901	−	2.12985i	0.279663	−	0.161464i
$175$	24.7468	+	0.466887i	1.87068	+	0.0352934i
$176$	−3.29801	−	1.90410i	−0.248597	−	0.143527i
$177$	−2.53126	−	9.44677i	−0.190261	−	0.710063i
$178$	8.64339	+	8.64339i	0.647849	+	0.647849i
$179$	2.03246	+	3.52033i	0.151913	+	0.263122i	0.931931	−	0.362636i	$-0.118123\pi$
$179$	2.03246	+	3.52033i	0.151913	+	0.263122i	−0.780017	+	0.625758i	$0.784790\pi$
$180$	2.07384	−	0.836183i	0.154575	−	0.0623254i
$181$	2.17797	+	1.25745i	0.161887	+	0.0934654i	0.578755	−	0.815502i	$-0.303539\pi$
$181$	2.17797	+	1.25745i	0.161887	+	0.0934654i	−0.416868	+	0.908967i	$0.636872\pi$
$182$	−11.1766	+	11.1766i	−0.828466	+	0.828466i
$183$	10.5008	+	2.81367i	0.776238	+	0.207992i
$184$	−0.0938519			−0.00691886
$185$	−10.9120	−	14.5020i	−0.802266	−	1.06621i
$186$	−4.96655	−	2.51663i	−0.364165	−	0.184528i
$187$	7.60042	+	7.60042i	0.555798	+	0.555798i
$188$	−4.45449	+	4.45449i	−0.324877	+	0.324877i
$189$	2.47512	+	4.28703i	0.180038	+	0.311836i
$190$	4.32228	+	5.74429i	0.313571	+	0.416734i
$191$	−0.688757	+	1.19296i	−0.0498367	+	0.0863197i	−0.889868	−	0.456219i	$-0.849203\pi$
$191$	−0.688757	+	1.19296i	−0.0498367	+	0.0863197i	0.840031	+	0.542539i	$0.182537\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	25.5979	+	6.85892i	1.84257	+	0.493716i	0.999058	−	0.0433886i	$-0.0138154\pi$
$193$	25.5979	+	6.85892i	1.84257	+	0.493716i	0.843516	+	0.537105i	$0.180482\pi$
$194$			13.5486i			0.972733i
$195$	4.39965	−	5.62312i	0.315066	−	0.402680i
$196$	8.75242	−	15.1596i	0.625173	−	1.08283i
$197$	6.00179	+	22.3990i	0.427610	+	1.59586i	0.758156	+	0.652073i	$0.226100\pi$
$197$	6.00179	+	22.3990i	0.427610	+	1.59586i	−0.330546	+	0.943790i	$0.607233\pi$
$198$	−0.985637	+	3.67845i	−0.0700462	+	0.261416i
$199$	−11.6482	+	20.1753i	−0.825720	+	1.43019i	0.0756473	+	0.997135i	$0.475898\pi$
$199$	−11.6482	+	20.1753i	−0.825720	+	1.43019i	−0.901368	+	0.433055i	$0.857436\pi$
$200$	4.28220	+	2.58124i	0.302797	+	0.182521i
$201$		−	4.04918i		−	0.285607i
$202$	7.36167	+	7.36167i	0.517965	+	0.517965i
$203$	−5.45760	+	20.3680i	−0.383048	+	1.42956i
$204$	2.44435	+	1.41124i	0.171138	+	0.0988068i
$205$	11.7947	−	4.75570i	0.823780	−	0.332153i
$206$	−0.328255	+	0.568554i	−0.0228706	+	0.0396130i
$207$	0.0242907	+	0.0906540i	0.00168832	+	0.00630089i
$208$	−3.08420	+	0.826410i	−0.213851	+	0.0573012i
$209$	−12.2431			−0.846875
$210$	−4.33222	+	10.1861i	−0.298951	+	0.702906i
$211$	−9.49428	−	16.4446i	−0.653613	−	1.13209i	−0.982240	−	0.187631i	$-0.939919\pi$
$211$	−9.49428	−	16.4446i	−0.653613	−	1.13209i	0.328627	−	0.944460i	$-0.393414\pi$
$212$	1.28562	+	4.79801i	0.0882969	+	0.329529i
$213$	−8.52411	−	8.52411i	−0.584062	−	0.584062i
$214$	8.09692	−	4.67476i	0.553494	−	0.319560i
$215$	12.3969	−	9.32800i	0.845459	−	0.636164i
$216$			1.00000i			0.0680414i
$217$	26.1937	−	8.57556i	1.77814	−	0.582147i
$218$	7.68734	−	7.68734i	0.520652	−	0.520652i
$219$			7.75123i			0.523780i
$220$	−7.89760	+	3.18436i	−0.532456	+	0.214689i
$221$	9.01221			0.606227
$222$	7.83984	−	2.10068i	0.526175	−	0.140988i
$223$	−3.41922	+	12.7607i	−0.228968	+	0.854519i	0.751808	+	0.659382i	$0.229182\pi$
$223$	−3.41922	+	12.7607i	−0.228968	+	0.854519i	−0.980776	+	0.195137i	$0.937485\pi$
$224$	4.28703	−	2.47512i	0.286439	−	0.165376i
$225$	1.38497	−	4.80436i	0.0923312	−	0.320291i
$226$	−4.93895	+	8.55451i	−0.328534	+	0.569038i
$227$	−22.1264	+	5.92875i	−1.46858	+	0.393505i	−0.902444	−	0.430807i	$-0.858229\pi$
$227$	−22.1264	+	5.92875i	−1.46858	+	0.393505i	−0.566136	+	0.824312i	$0.691562\pi$
$228$	−3.10539	+	0.832086i	−0.205659	+	0.0551062i
$229$	−5.91839	−	10.2510i	−0.391098	−	0.677402i	0.601496	−	0.798875i	$-0.294571\pi$
$229$	−5.91839	−	10.2510i	−0.391098	−	0.677402i	−0.992595	+	0.121474i	$0.961238\pi$
$230$	−0.129319	+	0.165280i	−0.00852704	+	0.0108983i
$231$	−9.42577	−	16.3259i	−0.620170	−	1.07417i
$232$	−3.01207	+	3.01207i	−0.197752	+	0.197752i
$233$	−8.90502	+	8.90502i	−0.583387	+	0.583387i	−0.935832	−	0.352445i	$-0.885350\pi$
$233$	−8.90502	+	8.90502i	−0.583387	+	0.583387i	0.352445	+	0.935832i	$0.385350\pi$
$234$	1.59650	+	2.76522i	0.104367	+	0.180768i
$235$	1.70683	+	13.9825i	0.111341	+	0.912120i
$236$	4.89001	+	8.46975i	0.318313	+	0.551333i
$237$	−11.4700	+	3.07338i	−0.745058	+	0.199638i
$238$	−13.4959	+	3.61621i	−0.874809	+	0.234404i
$239$	−6.25027	+	10.8258i	−0.404296	+	0.700261i	−0.994239	−	0.107183i	$-0.965817\pi$
$239$	−6.25027	+	10.8258i	−0.404296	+	0.700261i	0.589943	+	0.807445i	$0.299150\pi$
$240$	−1.78675	+	1.34444i	−0.115334	+	0.0867832i
$241$	10.7344	−	6.19749i	0.691461	−	0.399215i	−0.112698	−	0.993629i	$-0.535949\pi$
$241$	10.7344	−	6.19749i	0.691461	−	0.399215i	0.804159	+	0.594414i	$0.202616\pi$
$242$	0.906504	−	3.38312i	0.0582723	−	0.217475i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−10.8712			−0.695956
$245$	−14.6373	−	36.3022i	−0.935140	−	2.31926i
$246$			5.68740i			0.362615i
$247$	−7.25866	+	7.25866i	−0.461857	+	0.461857i
$248$	5.44867	+	1.14544i	0.345991	+	0.0727355i
$249$			6.72436i			0.426139i
$250$	10.4462	−	3.98457i	0.660676	−	0.252007i
$251$	2.50839	−	1.44822i	0.158328	−	0.0914108i	−0.418743	−	0.908105i	$-0.637529\pi$
$251$	2.50839	−	1.44822i	0.158328	−	0.0914108i	0.577071	+	0.816694i	$0.304196\pi$
$252$	−3.50035	−	3.50035i	−0.220501	−	0.220501i
$253$	−0.0925039	−	0.345229i	−0.00581567	−	0.0217044i
$254$	−0.283196	−	0.490510i	−0.0177693	−	0.0307773i
$255$	5.85338	−	2.36012i	0.366553	−	0.147796i
$256$	1.00000			0.0625000
$257$	−1.99224	+	0.533820i	−0.124273	+	0.0332988i	−0.320419	−	0.947276i	$-0.603824\pi$
$257$	−1.99224	+	0.533820i	−0.124273	+	0.0332988i	0.196147	+	0.980575i	$0.437157\pi$
$258$	1.79574	+	6.70179i	0.111798	+	0.417235i
$259$	−20.0890	+	34.7952i	−1.24827	+	2.16207i
$260$	−2.79437	+	6.57023i	−0.173299	+	0.407468i
$261$	3.68901	+	2.12985i	0.228344	+	0.131835i
$262$	5.63626	−	21.0348i	0.348209	−	1.29953i
$263$	−3.77451	−	3.77451i	−0.232746	−	0.232746i	0.581092	−	0.813838i	$-0.302626\pi$
$263$	−3.77451	−	3.77451i	−0.232746	−	0.232746i	−0.813838	+	0.581092i	$0.802626\pi$
$264$		−	3.80821i		−	0.234379i
$265$	10.2211	+	4.34712i	0.627878	+	0.267041i
$266$	7.95734	−	13.7825i	0.487896	−	0.845060i
$267$	−3.16370	+	11.8071i	−0.193615	+	0.722582i
$268$	1.04801	+	3.91121i	0.0640172	+	0.238915i
$269$	4.13528	−	7.16252i	0.252133	−	0.436707i	−0.711980	−	0.702200i	$-0.752201\pi$
$269$	4.13528	−	7.16252i	0.252133	−	0.436707i	0.964113	+	0.265493i	$0.0855347\pi$
$270$	1.76107	+	1.37790i	0.107176	+	0.0838566i
$271$		−	15.3433i		−	0.932040i	−0.884774	−	0.466020i	$-0.845688\pi$
$271$		−	15.3433i		−	0.932040i	0.884774	−	0.466020i	$-0.154312\pi$
$272$	−2.72631	−	0.730514i	−0.165307	−	0.0442939i
$273$	−15.2675	−	4.09093i	−0.924034	−	0.247594i
$274$	0.433642	−	0.751090i	0.0261973	−	0.0453750i
$275$	−5.27425	+	18.2960i	−0.318049	+	1.10329i
$276$	−0.0469260	−	0.0812782i	−0.00282461	−	0.00489237i
$277$	−15.8017	+	15.8017i	−0.949429	+	0.949429i	−0.998781	−	0.0493520i	$-0.984284\pi$
$277$	−15.8017	+	15.8017i	−0.949429	+	0.949429i	0.0493520	+	0.998781i	$0.484284\pi$
$278$	−7.18566	−	7.18566i	−0.430967	−	0.430967i
$279$	−0.303809	−	5.55947i	−0.0181886	−	0.332837i
$280$	1.54825	−	10.9603i	0.0925256	−	0.655000i
$281$	−7.22510			−0.431014			−0.215507	−	0.976502i	$-0.569140\pi$
$281$	−7.22510			−0.431014			−0.215507	+	0.976502i	$0.569140\pi$
$282$	−6.08494	−	1.63045i	−0.362353	−	0.0970922i
$283$	18.2073	−	18.2073i	1.08231	−	1.08231i	0.0860181	−	0.996294i	$-0.472586\pi$
$283$	18.2073	−	18.2073i	1.08231	−	1.08231i	0.996294	−	0.0860181i	$-0.0274143\pi$
$284$	10.4399	+	6.02746i	0.619492	+	0.357664i
$285$	−2.81356	+	6.61535i	−0.166661	+	0.391859i
$286$	−6.07981	−	10.5305i	−0.359507	−	0.622684i
$287$	−19.9079	−	19.9079i	−1.17512	−	1.17512i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−7.82330	−	4.51678i	−0.460194	−	0.265693i
$290$	1.15413	+	9.45481i	0.0677731	+	0.555205i
$291$	−11.7334	+	6.77430i	−0.687826	+	0.397117i
$292$	−2.00617	−	7.48712i	−0.117402	−	0.438150i
$293$	21.1681	+	5.67196i	1.23665	+	0.331360i	0.817166	−	0.576402i	$-0.195544\pi$
$293$	21.1681	+	5.67196i	1.23665	+	0.331360i	0.419485	+	0.907762i	$0.362211\pi$
$294$	17.5048			1.02090
$295$	21.6538	+	3.05883i	1.26073	+	0.178092i
$296$	−7.02901	+	4.05820i	−0.408553	+	0.235878i
$297$	−3.67845	+	0.985637i	−0.213445	+	0.0571925i
$298$	−6.21536	−	1.66540i	−0.360046	−	0.0964741i
$299$	−0.259521	−	0.149835i	−0.0150085	−	0.00866517i
$300$	−0.0943161	+	4.99911i	−0.00544534	+	0.288624i
$301$	−29.7443	−	17.1729i	−1.71443	−	0.989829i
$302$	3.58875	−	3.58875i	0.206509	−	0.206509i
$303$	−2.69456	+	10.0562i	−0.154798	+	0.577715i
$304$	2.78421	−	1.60747i	0.159686	−	0.0921945i
$305$	−14.9794	+	19.1449i	−0.857720	+	1.09624i
$306$			2.82249i			0.161351i
$307$	−2.62614	+	9.80090i	−0.149882	+	0.559367i	0.849608	+	0.527415i	$0.176839\pi$
$307$	−2.62614	+	9.80090i	−0.149882	+	0.559367i	−0.999489	+	0.0319513i	$0.989828\pi$
$308$	13.3301	+	13.3301i	0.759550	+	0.759550i
$309$	−0.656509			−0.0373475
$310$	9.52494	−	8.01720i	0.540980	−	0.455346i
$311$	−15.4120			−0.873937			−0.436969	−	0.899477i	$-0.643948\pi$
$311$	−15.4120			−0.873937			−0.436969	+	0.899477i	$0.643948\pi$
$312$	−2.25779	−	2.25779i	−0.127822	−	0.127822i
$313$	−0.247940	+	0.925323i	−0.0140144	+	0.0523024i	−0.972579	−	0.232573i	$-0.925286\pi$
$313$	−0.247940	+	0.925323i	−0.0140144	+	0.0523024i	0.958565	+	0.284875i	$0.0919522\pi$
$314$			16.0815i			0.907532i
$315$	−10.9875	+	1.34123i	−0.619076	+	0.0755696i
$316$	10.2837	−	5.93732i	0.578506	−	0.334000i
$317$	2.85826	−	10.6672i	0.160536	−	0.599128i	−0.838032	−	0.545621i	$-0.816294\pi$
$317$	2.85826	−	10.6672i	0.160536	−	0.599128i	0.998568	−	0.0535061i	$-0.0170397\pi$
$318$	−3.51239	+	3.51239i	−0.196965	+	0.196965i
$319$	−14.0485	−	8.11092i	−0.786567	−	0.454125i
$320$	1.37790	−	1.76107i	0.0770272	−	0.0984470i
$321$	8.09692	+	4.67476i	0.451926	+	0.260920i
$322$	0.448759	+	0.120245i	0.0250083	+	0.00670097i
$323$	−8.76491	+	2.34855i	−0.487693	+	0.130677i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	7.72028	+	13.9742i	0.428244	+	0.775151i
$326$	5.97698			0.331034
$327$	10.5011	+	2.81376i	0.580712	+	0.155601i
$328$	−1.47201	−	5.49360i	−0.0812779	−	0.303333i
$329$	27.0066	−	15.5922i	1.48892	−	0.859628i
$330$	−6.70654	−	5.24735i	−0.369183	−	0.288857i
$331$	3.31055	+	1.91135i	0.181964	+	0.105057i	0.588215	−	0.808704i	$-0.299831\pi$
$331$	3.31055	+	1.91135i	0.181964	+	0.105057i	−0.406251	+	0.913762i	$0.633164\pi$
$332$	−1.74039	−	6.49523i	−0.0955165	−	0.356472i
$333$	5.73916	+	5.73916i	0.314504	+	0.314504i
$334$	−7.37842	−	12.7798i	−0.403729	−	0.699280i
$335$	8.33198	+	3.54366i	0.455225	+	0.193611i
$336$	4.28703	+	2.47512i	0.233877	+	0.135029i
$337$	−5.75111	+	5.75111i	−0.313283	+	0.313283i	−0.846180	−	0.532897i	$-0.821103\pi$
$337$	−5.75111	+	5.75111i	−0.313283	+	0.313283i	0.532897	+	0.846180i	$0.321103\pi$
$338$	2.70916	+	0.725917i	0.147359	+	0.0394847i
$339$	−9.87790			−0.536494
$340$	−5.04309	+	3.79466i	−0.273500	+	0.205794i
$341$	1.15697	+	21.1716i	0.0626533	+	1.14651i
$342$	−2.27330	−	2.27330i	−0.122926	−	0.122926i
$343$	−36.7706	+	36.7706i	−1.98543	+	1.98543i
$344$	−3.46910	−	6.00866i	−0.187042	−	0.323965i
$345$	−0.207796	−	0.0293534i	−0.0111874	−	0.00158033i
$346$	7.96069	−	13.7883i	0.427969	−	0.741264i
$347$	33.5255	+	8.98312i	1.79974	+	0.482239i	0.993938	−	0.109943i	$-0.0350668\pi$
$347$	33.5255	+	8.98312i	1.79974	+	0.482239i	0.805804	+	0.592182i	$0.201734\pi$
$348$	−4.11456	−	1.10249i	−0.220563	−	0.0590998i
$349$			29.3837i			1.57288i	0.617669	+	0.786438i	$0.288077\pi$
$349$			29.3837i			1.57288i	−0.617669	+	0.786438i	$0.711923\pi$
$350$	−17.1685	−	17.8288i	−0.917694	−	0.952987i
$351$	−1.59650	+	2.76522i	−0.0852150	+	0.147597i
$352$	0.985637	+	3.67845i	0.0525346	+	0.196062i
$353$	5.38379	−	20.0926i	0.286550	−	1.06942i	−0.661149	−	0.750255i	$-0.729931\pi$
$353$	5.38379	−	20.0926i	0.286550	−	1.06942i	0.947699	−	0.319165i	$-0.103403\pi$
$354$	−4.89001	+	8.46975i	−0.259901	+	0.450162i
$355$	24.9999	−	10.0801i	1.32686	−	0.534997i
$356$		−	12.2236i		−	0.647849i
$357$	−9.87968	−	9.87968i	−0.522888	−	0.522888i
$358$	1.05208	−	3.92641i	0.0556041	−	0.207517i
$359$	−11.9758	−	6.91422i	−0.632058	−	0.364919i	0.149491	−	0.988763i	$-0.452237\pi$
$359$	−11.9758	−	6.91422i	−0.632058	−	0.364919i	−0.781549	+	0.623844i	$0.785570\pi$
$360$	−2.05769	−	0.875153i	−0.108450	−	0.0461246i
$361$	−4.33211	+	7.50343i	−0.228006	+	0.394917i
$362$	−0.650903	−	2.42920i	−0.0342107	−	0.127676i
$363$	3.38312	−	0.906504i	0.177568	−	0.0475791i
$364$	15.8061			0.828466
$365$	−15.9497	−	6.78352i	−0.834844	−	0.355066i
$366$	−5.43559	−	9.41472i	−0.284123	−	0.492115i
$367$	−2.49148	−	9.29833i	−0.130054	−	0.485369i	0.869915	−	0.493201i	$-0.164173\pi$
$367$	−2.49148	−	9.29833i	−0.130054	−	0.485369i	−0.999969	+	0.00783271i	$0.997507\pi$
$368$	0.0663633	+	0.0663633i	0.00345943	+	0.00345943i
$369$	−4.92543	+	2.84370i	−0.256408	+	0.148037i
$370$	−2.53851	+	17.9704i	−0.131971	+	0.934237i
$371$		−	24.5891i		−	1.27660i
$372$	1.73235	+	5.29140i	0.0898183	+	0.274346i
$373$	19.2112	−	19.2112i	0.994716	−	0.994716i	−0.00526988	−	0.999986i	$-0.501677\pi$
$373$	19.2112	−	19.2112i	0.994716	−	0.994716i	0.999986	+	0.00526988i	$0.00167746\pi$
$374$		−	10.7486i		−	0.555798i
$375$	8.67384	+	7.05439i	0.447915	+	0.364287i
$376$	6.29959			0.324877
$377$	−13.1378	+	3.52026i	−0.676631	+	0.181303i
$378$	1.28122	−	4.78156i	0.0658986	−	0.245937i
$379$	−3.20135	+	1.84830i	−0.164442	+	0.0949407i	−0.579963	−	0.814643i	$-0.696933\pi$
$379$	−3.20135	+	1.84830i	−0.164442	+	0.0949407i	0.415520	+	0.909584i	$0.363599\pi$
$380$	1.00551	−	7.11814i	0.0515816	−	0.365153i
$381$	0.283196	−	0.490510i	0.0145086	−	0.0251296i
$382$	1.33058	−	0.356527i	0.0680782	−	0.0182415i
$383$	−17.1367	+	4.59178i	−0.875647	+	0.234629i	−0.668528	−	0.743687i	$-0.733075\pi$
$383$	−17.1367	+	4.59178i	−0.875647	+	0.234629i	−0.207119	+	0.978316i	$0.566409\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	41.8427	−	5.10768i	2.13250	−	0.260311i
$386$	−13.2504	−	22.9504i	−0.674429	−	1.16814i
$387$	−4.90605	+	4.90605i	−0.249389	+	0.249389i
$388$	9.58031	−	9.58031i	0.486366	−	0.486366i
$389$	−7.08645	−	12.2741i	−0.359297	−	0.622321i	0.628546	−	0.777772i	$-0.283650\pi$
$389$	−7.08645	−	12.2741i	−0.359297	−	0.622321i	−0.987844	+	0.155451i	$0.950317\pi$
$390$	−7.08717	+	0.865120i	−0.358873	+	0.0438070i
$391$	−0.132448	−	0.229407i	−0.00669818	−	0.0116016i
$392$	−16.9084	+	4.53059i	−0.854002	+	0.228829i
$393$	21.0348	−	5.63626i	1.06107	−	0.284312i
$394$	11.5946	−	20.0824i	0.584126	−	1.01174i
$395$	3.71395	−	26.2915i	0.186869	−	1.32287i
$396$	3.29801	−	1.90410i	0.165731	−	0.0956849i
$397$	7.76562	−	28.9817i	0.389745	−	1.45455i	−0.440803	−	0.897604i	$-0.645306\pi$
$397$	7.76562	−	28.9817i	0.389745	−	1.45455i	0.830549	−	0.556946i	$-0.188027\pi$
$398$	22.5026	−	6.02956i	1.12795	−	0.302235i
$399$	15.9147			0.796730
$400$	−1.20276	−	4.85318i	−0.0601381	−	0.242659i
$401$			22.1175i			1.10450i	0.833680	+	0.552248i	$0.186230\pi$
$401$			22.1175i			1.10450i	−0.833680	+	0.552248i	$0.813770\pi$
$402$	−2.86321	+	2.86321i	−0.142804	+	0.142804i
$403$	13.2381	+	11.8662i	0.659436	+	0.591098i
$404$		−	10.4110i		−	0.517965i
$405$	−0.312763	+	2.21409i	−0.0155413	+	0.110019i
$406$	18.2615	−	10.5433i	0.906302	−	0.523254i
$407$	−21.8559	−	21.8559i	−1.08336	−	1.08336i
$408$	−0.730514	−	2.72631i	−0.0361658	−	0.134973i
$409$	10.2929	+	17.8278i	0.508950	+	0.881528i	0.999946	+	0.0103660i	$0.00329966\pi$
$409$	10.2929	+	17.8278i	0.508950	+	0.881528i	−0.490996	+	0.871162i	$0.663367\pi$
$410$	−11.7029	−	4.97734i	−0.577966	−	0.245813i
$411$	0.867284			0.0427799
$412$	0.634139	−	0.169917i	0.0312418	−	0.00837121i
$413$	−12.5303	−	46.7638i	−0.616576	−	2.30109i
$414$	0.0469260	−	0.0812782i	0.00230629	−	0.00399460i
$415$	−13.8367	−	5.88485i	−0.679216	−	0.288876i
$416$	2.76522	+	1.59650i	0.135576	+	0.0782749i
$417$	2.63013	−	9.81579i	0.128798	−	0.480681i
$418$	8.65720	+	8.65720i	0.423438	+	0.423438i
$419$			24.5442i			1.19906i	0.800351	+	0.599532i	$0.204646\pi$
$419$			24.5442i			1.19906i	−0.800351	+	0.599532i	$0.795354\pi$
$420$	10.2660	−	4.13930i	0.500929	−	0.201977i
$421$	−11.5957	+	20.0844i	−0.565142	+	0.978855i	0.431894	+	0.901924i	$0.357845\pi$
$421$	−11.5957	+	20.0844i	−0.565142	+	0.978855i	−0.997036	+	0.0769308i	$0.975488\pi$
$422$	−4.91460	+	18.3415i	−0.239239	+	0.892852i
$423$	−1.63045	−	6.08494i	−0.0792754	−	0.295860i
$424$	2.48363	−	4.30178i	0.120616	−	0.208913i
$425$	−0.266206	+	14.1099i	−0.0129129	+	0.684432i
$426$			12.0549i			0.584062i
$427$	51.9812	+	13.9283i	2.51555	+	0.674039i
$428$	−9.03094	−	2.41983i	−0.436527	−	0.116967i
$429$	6.07981	−	10.5305i	0.293536	−	0.508420i
$430$	−15.3618	−	2.17001i	−0.740811	−	0.104647i
$431$	0.408836	+	0.708125i	0.0196930	+	0.0341092i	0.875704	−	0.482848i	$-0.160398\pi$
$431$	0.408836	+	0.708125i	0.0196930	+	0.0341092i	−0.856011	+	0.516958i	$0.827064\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	3.93211	+	3.93211i	0.188965	+	0.188965i	0.795249	−	0.606283i	$-0.207340\pi$
$433$	3.93211	+	3.93211i	0.188965	+	0.188965i	−0.606283	+	0.795249i	$0.707340\pi$
$434$	−24.5856	−	12.4579i	−1.18015	−	0.597999i
$435$	−7.61104	+	5.72691i	−0.364921	+	0.274584i
$436$	−10.8715			−0.520652
$437$	0.291446	+	0.0780928i	0.0139418	+	0.00373569i
$438$	5.48095	−	5.48095i	0.261890	−	0.261890i
$439$	−2.52783	−	1.45945i	−0.120647	−	0.0696555i	0.438462	−	0.898750i	$-0.355523\pi$
$439$	−2.52783	−	1.45945i	−0.120647	−	0.0696555i	−0.559109	+	0.829094i	$0.688857\pi$
$440$	7.83613	+	3.33277i	0.373573	+	0.158883i
$441$	8.75242	+	15.1596i	0.416782	+	0.721888i
$442$	−6.37260	−	6.37260i	−0.303114	−	0.303114i
$443$	1.65965	+	6.19391i	0.0788525	+	0.294281i	0.994079	−	0.108658i	$-0.0346553\pi$
$443$	1.65965	+	6.19391i	0.0788525	+	0.294281i	−0.915227	+	0.402939i	$0.867989\pi$
$444$	−7.02901	−	4.05820i	−0.333582	−	0.192594i
$445$	−21.5267	−	16.8429i	−1.02046	−	0.798432i
$446$	11.4409	−	6.60542i	0.541743	−	0.312776i
$447$	−1.66540	−	6.21536i	−0.0787708	−	0.293977i
$448$	−4.78156	−	1.28122i	−0.225908	−	0.0605317i
$449$	34.5634			1.63115			0.815574	−	0.578652i	$-0.196421\pi$
$449$	34.5634			1.63115			0.815574	+	0.578652i	$0.196421\pi$
$450$	−4.37651	+	2.41788i	−0.206311	+	0.113980i
$451$	18.7571	−	10.8294i	0.883236	−	0.509936i
$452$	9.54132	−	2.55659i	0.448786	−	0.120252i
$453$	4.90232	+	1.31357i	0.230331	+	0.0617170i
$454$	19.8380	+	11.4535i	0.931043	+	0.537538i
$455$	21.7793	−	27.8358i	1.02103	−	1.30496i
$456$	2.78421	+	1.60747i	0.130383	+	0.0752765i
$457$	−25.1795	+	25.1795i	−1.17785	+	1.17785i	−0.197555	+	0.980292i	$0.563300\pi$
$457$	−25.1795	+	25.1795i	−1.17785	+	1.17785i	−0.980292	+	0.197555i	$0.936700\pi$
$458$	−3.06358	+	11.4335i	−0.143152	+	0.534250i
$459$	−2.44435	+	1.41124i	−0.114092	+	0.0658712i
$460$	0.208313	−	0.0254284i	0.00971264	−	0.00118561i
$461$			39.0187i			1.81728i	0.417580	+	0.908640i	$0.362878\pi$
$461$			39.0187i			1.81728i	−0.417580	+	0.908640i	$0.637122\pi$
$462$	−4.87914	+	18.2092i	−0.226998	+	0.847168i
$463$	−2.10310	−	2.10310i	−0.0977391	−	0.0977391i	0.656546	−	0.754286i	$-0.272017\pi$
$463$	−2.10310	−	2.10310i	−0.0977391	−	0.0977391i	−0.754286	+	0.656546i	$0.772017\pi$
$464$	4.25970			0.197752
$465$	11.7056	+	4.24024i	0.542833	+	0.196637i
$466$	12.5936			0.583387
$467$	−18.9416	−	18.9416i	−0.876515	−	0.876515i	0.116657	−	0.993172i	$-0.462782\pi$
$467$	−18.9416	−	18.9416i	−0.876515	−	0.876515i	−0.993172	+	0.116657i	$0.962782\pi$
$468$	0.826410	−	3.08420i	0.0382008	−	0.142567i
$469$		−	20.0444i		−	0.925565i
$470$	8.68023	−	11.0941i	0.400389	−	0.511730i
$471$	−13.9270	+	8.04075i	−0.641722	+	0.370498i
$472$	2.53126	−	9.44677i	0.116510	−	0.434823i
$473$	18.6833	−	18.6833i	0.859058	−	0.859058i
$474$	10.2837	+	5.93732i	0.472348	+	0.272710i
$475$	−11.1501	−	11.5789i	−0.511600	−	0.531276i
$476$	12.1001	+	6.98599i	0.554607	+	0.320202i
$477$	−4.79801	−	1.28562i	−0.219686	−	0.0588646i
$478$	12.0746	−	3.23538i	0.552279	−	0.147983i
$479$	−33.2255	+	19.1828i	−1.51811	+	0.876483i	−0.518340	+	0.855175i	$0.673450\pi$
$479$	−33.2255	+	19.1828i	−1.51811	+	0.876483i	−0.999773	+	0.0213081i	$0.993217\pi$
$480$	2.21409	+	0.312763i	0.101059	+	0.0142756i
$481$	−25.9157			−1.18165
$482$	−11.9726	−	3.20806i	−0.545338	−	0.146123i
$483$	0.120245	+	0.448759i	0.00547132	+	0.0204192i
$484$	−3.03322	+	1.75123i	−0.137874	+	0.0796014i
$485$	−3.67089	−	30.0724i	−0.166686	−	1.36552i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	2.45375	+	9.15751i	0.111190	+	0.414966i	0.998974	−	0.0452944i	$-0.0144226\pi$
$487$	2.45375	+	9.15751i	0.111190	+	0.414966i	−0.887784	+	0.460261i	$0.847756\pi$
$488$	7.68708	+	7.68708i	0.347978	+	0.347978i
$489$	2.98849	+	5.17622i	0.135144	+	0.234077i
$490$	−15.3194	+	36.0196i	−0.692061	+	1.62720i
$491$	37.0216	+	21.3744i	1.67076	+	0.964614i	0.967213	+	0.253966i	$0.0817353\pi$
$491$	37.0216	+	21.3744i	1.67076	+	0.964614i	0.703548	+	0.710648i	$0.251598\pi$
$492$	4.02160	−	4.02160i	0.181308	−	0.181308i
$493$	−11.6133	−	3.11177i	−0.523036	−	0.140147i
$494$	10.2653			0.461857
$495$	1.19107	−	8.43171i	0.0535344	−	0.378977i
$496$	−3.04284	−	4.66274i	−0.136628	−	0.209363i
$497$	−42.1964	−	42.1964i	−1.89277	−	1.89277i
$498$	4.75484	−	4.75484i	0.213070	−	0.213070i
$499$	−13.4860	−	23.3584i	−0.603716	−	1.04567i	−0.992253	−	0.124234i	$-0.960353\pi$
$499$	−13.4860	−	23.3584i	−0.603716	−	1.04567i	0.388537	−	0.921433i	$-0.372981\pi$
$500$	−10.2041	−	4.56906i	−0.456341	−	0.204335i
$501$	7.37842	−	12.7798i	0.329644	−	0.570959i
$502$	−2.79774	−	0.749653i	−0.124869	−	0.0334587i
$503$	−17.3425	−	4.64691i	−0.773264	−	0.207196i	−0.149451	−	0.988769i	$-0.547751\pi$
$503$	−17.3425	−	4.64691i	−0.773264	−	0.207196i	−0.623813	+	0.781574i	$0.714417\pi$
$504$			4.95024i			0.220501i
$505$	−18.3345	−	14.3453i	−0.815874	−	0.638358i
$506$	−0.178704	+	0.309524i	−0.00794436	+	0.0137600i
$507$	0.725917	+	2.70916i	0.0322391	+	0.120318i
$508$	−0.146593	+	0.547093i	−0.00650402	+	0.0242733i
$509$	−13.8668	+	24.0180i	−0.614634	+	1.06458i	0.375814	+	0.926695i	$0.377363\pi$
$509$	−13.8668	+	24.0180i	−0.614634	+	1.06458i	−0.990449	+	0.137883i	$0.955970\pi$
$510$	−5.80782	−	2.47011i	−0.257174	−	0.109378i
$511$			38.3704i			1.69741i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.832086	−	3.10539i	0.0367375	−	0.137106i
$514$	1.78620	+	1.03126i	0.0787858	+	0.0454870i
$515$	0.574546	−	1.35090i	0.0253175	−	0.0595276i
$516$	3.46910	−	6.00866i	0.152719	−	0.264517i
$517$	6.20911	+	23.1727i	0.273077	+	1.01914i
$518$	38.8091	−	10.3989i	1.70517	−	0.456899i
$519$	15.9214			0.698871
$520$	6.62177	−	2.66994i	0.290384	−	0.117084i
$521$	7.83899	+	13.5775i	0.343433	+	0.594843i	0.985068	−	0.172167i	$-0.0550770\pi$
$521$	7.83899	+	13.5775i	0.343433	+	0.594843i	−0.641635	+	0.767010i	$0.721744\pi$
$522$	−1.10249	−	4.11456i	−0.0482548	−	0.180089i
$523$	−5.29009	−	5.29009i	−0.231320	−	0.231320i	0.581924	−	0.813243i	$-0.302300\pi$
$523$	−5.29009	−	5.29009i	−0.231320	−	0.231320i	−0.813243	+	0.581924i	$0.802300\pi$
$524$	−18.8593	+	10.8884i	−0.823872	+	0.475663i
$525$	6.85592	−	23.7827i	0.299217	−	1.03796i
$526$			5.33796i			0.232746i
$527$	4.88955	+	14.9349i	0.212992	+	0.650575i
$528$	−2.69281	+	2.69281i	−0.117190	+	0.117190i
$529$		−	22.9912i		−	0.999617i
$530$	−4.15354	−	10.3013i	−0.180418	−	0.447460i
$531$	−9.78002			−0.424417
$532$	−15.3724	+	4.11902i	−0.666478	+	0.178582i
$533$	4.70012	−	17.5411i	0.203585	−	0.759789i
$534$	10.5859	−	6.11180i	0.458099	−	0.264483i
$535$	−16.7053	+	12.5699i	−0.722232	+	0.543442i
$536$	2.02459	−	3.50670i	0.0874491	−	0.151466i
$537$	3.92641	−	1.05208i	0.169437	−	0.0454006i
$538$	−7.98876	+	2.14058i	−0.344420	+	0.0922870i
$539$	−33.3311	−	57.7311i	−1.43567	−	2.48665i
$540$	−0.270942	−	2.21959i	−0.0116595	−	0.0955160i
$541$	−15.3333	−	26.5580i	−0.659229	−	1.14182i	−0.980816	−	0.194937i	$-0.937550\pi$
$541$	−15.3333	−	26.5580i	−0.659229	−	1.14182i	0.321587	−	0.946880i	$-0.395784\pi$
$542$	−10.8494	+	10.8494i	−0.466020	+	0.466020i
$543$	1.77830	−	1.77830i	0.0763142	−	0.0763142i
$544$	1.41124	+	2.44435i	0.0605066	+	0.104800i
$545$	−14.9799	+	19.1456i	−0.641670	+	0.820106i
$546$	7.90306	+	13.6885i	0.338220	+	0.585814i
$547$	41.2312	−	11.0479i	1.76292	−	0.472373i	0.775614	−	0.631207i	$-0.217440\pi$
$547$	41.2312	−	11.0479i	1.76292	−	0.472373i	0.987305	+	0.158834i	$0.0507735\pi$
$548$	−0.837732	+	0.224469i	−0.0357861	+	0.00958886i
$549$	5.43559	−	9.41472i	0.231985	−	0.401810i
$550$	16.6667	−	9.20777i	0.710670	−	0.392621i
$551$	11.8599	−	6.84733i	0.505250	−	0.291706i
$552$	−0.0242907	+	0.0906540i	−0.00103388	+	0.00385849i
$553$	−56.7793	+	15.2140i	−2.41450	+	0.646964i
$554$	22.3469			0.949429
$555$	−16.8321	+	6.78679i	−0.714482	+	0.288083i
$556$			10.1621i			0.430967i
$557$	−9.27769	+	9.27769i	−0.393108	+	0.393108i	−0.875794	−	0.482685i	$-0.839661\pi$
$557$	−9.27769	+	9.27769i	−0.393108	+	0.393108i	0.482685	+	0.875794i	$0.339661\pi$
$558$	−3.71631	+	4.14596i	−0.157324	+	0.175513i
$559$		−	22.1537i		−	0.937003i
$560$	−8.84485	+	6.65529i	−0.373763	+	0.281237i
$561$	9.30858	−	5.37431i	0.393009	−	0.226904i
$562$	5.10892	+	5.10892i	0.215507	+	0.215507i
$563$	−10.3901	−	38.7762i	−0.437889	−	1.63422i	−0.734057	−	0.679088i	$-0.762376\pi$
$563$	−10.3901	−	38.7762i	−0.437889	−	1.63422i	0.296168	−	0.955136i	$-0.404291\pi$
$564$	3.14980	+	5.45561i	0.132630	+	0.229723i
$565$	8.64468	−	20.3257i	0.363684	−	0.855109i
$566$	−25.7490			−1.08231
$567$	4.78156	−	1.28122i	0.200807	−	0.0538060i
$568$	−3.12004	−	11.6442i	−0.130914	−	0.488578i
$569$	15.9628	−	27.6484i	0.669195	−	1.15908i	−0.308935	−	0.951083i	$-0.599973\pi$
$569$	15.9628	−	27.6484i	0.669195	−	1.15908i	0.978130	−	0.207996i	$-0.0666941\pi$
$570$	6.66724	−	2.68827i	0.279260	−	0.112599i
$571$	−39.9030	−	23.0380i	−1.66989	−	0.964111i	−0.967694	−	0.252126i	$-0.918870\pi$
$571$	−39.9030	−	23.0380i	−1.66989	−	0.964111i	−0.702195	−	0.711985i	$-0.747796\pi$
$572$	−3.14714	+	11.7453i	−0.131589	+	0.491096i
$573$	0.974049	+	0.974049i	0.0406915	+	0.0406915i
$574$			28.1540i			1.17512i
$575$	0.242254	−	0.401893i	0.0101027	−	0.0167601i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−0.885291	+	3.30395i	−0.0368551	+	0.137545i	−0.981902	−	0.189390i	$-0.939349\pi$
$577$	−0.885291	+	3.30395i	−0.0368551	+	0.137545i	0.945047	+	0.326935i	$0.106016\pi$
$578$	2.33806	+	8.72575i	0.0972504	+	0.362943i
$579$	13.2504	−	22.9504i	0.550669	−	0.953786i
$580$	5.86946	−	7.50165i	0.243716	−	0.311489i
$581$			33.2872i			1.38099i
$582$	13.0869	+	3.50664i	0.542471	+	0.145355i
$583$	18.2718	+	4.89592i	0.756742	+	0.202768i
$584$	−3.87562	+	6.71277i	−0.160374	+	0.277776i
$585$	−4.29280	−	5.70511i	−0.177485	−	0.235877i
$586$	−10.9574	−	18.9788i	−0.452646	−	0.784006i
$587$	28.4945	−	28.4945i	1.17609	−	1.17609i	0.195363	−	0.980731i	$-0.437411\pi$
$587$	28.4945	−	28.4945i	1.17609	−	1.17609i	0.980731	−	0.195363i	$-0.0625885\pi$
$588$	−12.3778	−	12.3778i	−0.510452	−	0.510452i
$589$	−15.9671	−	8.09079i	−0.657913	−	0.333375i
$590$	−13.1486	−	17.4745i	−0.541321	−	0.719413i
$591$	23.1892			0.953874
$592$	7.83984	+	2.10068i	0.322215	+	0.0863373i
$593$	−0.813967	+	0.813967i	−0.0334256	+	0.0334256i	−0.723622	−	0.690196i	$-0.757524\pi$
$593$	−0.813967	+	0.813967i	−0.0334256	+	0.0334256i	0.690196	+	0.723622i	$0.257524\pi$
$594$	3.29801	+	1.90410i	0.135319	+	0.0781264i
$595$	28.9756	−	11.6831i	1.18788	−	0.478962i
$596$	3.21731	+	5.57254i	0.131786	+	0.228260i
$597$	16.4731	+	16.4731i	0.674198	+	0.674198i
$598$	0.0775602	+	0.289459i	0.00317167	+	0.0118368i
$599$	12.6450	+	7.30059i	0.516660	+	0.298294i	0.735567	−	0.677452i	$-0.236916\pi$
$599$	12.6450	+	7.30059i	0.516660	+	0.298294i	−0.218907	+	0.975746i	$0.570249\pi$
$600$	3.60160	−	3.46821i	0.147035	−	0.141589i
$601$	1.72837	−	0.997873i	0.0705016	−	0.0407041i	−0.464335	−	0.885660i	$-0.653707\pi$
$601$	1.72837	−	0.997873i	0.0705016	−	0.0407041i	0.534836	+	0.844956i	$0.320373\pi$
$602$	8.88934	+	33.1755i	0.362302	+	1.35213i
$603$	−3.91121	−	1.04801i	−0.159277	−	0.0426781i
$604$	−5.07526			−0.206509
$605$	−1.09544	+	7.75475i	−0.0445359	+	0.315275i
$606$	9.01616	−	5.20548i	0.366257	−	0.211458i
$607$	29.8737	−	8.00465i	1.21254	−	0.324899i	0.404781	−	0.914414i	$-0.367348\pi$
$607$	29.8737	−	8.00465i	1.21254	−	0.324899i	0.807757	+	0.589515i	$0.200681\pi$
$608$	−3.10539	−	0.832086i	−0.125940	−	0.0337455i
$609$	18.2615	+	10.5433i	0.739993	+	0.427235i
$610$	24.1296	−	2.94546i	0.976978	−	0.119258i
$611$	17.4198	+	10.0573i	0.704729	+	0.406875i
$612$	1.99580	−	1.99580i	0.0806754	−	0.0806754i
$613$	3.33571	−	12.4490i	0.134728	−	0.502812i	−0.865271	−	0.501305i	$-0.832854\pi$
$613$	3.33571	−	12.4490i	0.134728	−	0.502812i	0.999999	−	0.00150709i	$-0.000479722\pi$
$614$	8.78724	−	5.07332i	0.354624	−	0.204742i
$615$	−1.54096	−	12.6237i	−0.0621373	−	0.509037i
$616$		−	18.8515i		−	0.759550i
$617$	5.70705	−	21.2990i	0.229757	−	0.857465i	−0.750686	−	0.660660i	$-0.770277\pi$
$617$	5.70705	−	21.2990i	0.229757	−	0.857465i	0.980443	−	0.196805i	$-0.0630567\pi$
$618$	0.464222	+	0.464222i	0.0186737	+	0.0186737i
$619$	49.3272			1.98263			0.991314	−	0.131519i	$-0.0419856\pi$
$619$	49.3272			1.98263			0.991314	+	0.131519i	$0.0419856\pi$
$620$	−12.4042	−	1.06614i	−0.498163	−	0.0428170i
$621$	0.0938519			0.00376615
$622$	10.8980	+	10.8980i	0.436969	+	0.436969i
$623$	−15.6611	+	58.4479i	−0.627447	+	2.34167i
$624$			3.19300i			0.127822i
$625$	−22.1067	+	11.6744i	−0.884269	+	0.466978i
$626$	0.829622	−	0.478983i	0.0331584	−	0.0191440i
$627$	−3.16876	+	11.8260i	−0.126548	+	0.472283i
$628$	11.3713	−	11.3713i	0.453766	−	0.453766i
$629$	−19.8393	−	11.4542i	−0.791044	−	0.456709i
$630$	8.71773	+	6.82095i	0.347323	+	0.271753i
$631$	−11.9938	−	6.92461i	−0.477465	−	0.275665i	0.241894	−	0.970303i	$-0.422231\pi$
$631$	−11.9938	−	6.92461i	−0.477465	−	0.275665i	−0.719359	+	0.694638i	$0.755565\pi$
$632$	−11.4700	−	3.07338i	−0.456253	−	0.122253i
$633$	−18.3415	+	4.91460i	−0.729010	+	0.195338i
$634$	−9.56392	+	5.52173i	−0.379832	+	0.219296i
$635$	0.761480	+	1.01200i	0.0302184	+	0.0401601i
$636$	4.96727			0.196965
$637$	−53.9885	−	14.4662i	−2.13910	−	0.573171i
$638$	4.19852	+	15.6691i	0.166221	+	0.620346i
$639$	−10.4399	+	6.02746i	−0.412994	+	0.238442i
$640$	−2.21959	+	0.270942i	−0.0877371	+	0.0107099i
$641$	−23.8999	−	13.7986i	−0.943989	−	0.545012i	−0.0527805	−	0.998606i	$-0.516808\pi$
$641$	−23.8999	−	13.7986i	−0.943989	−	0.545012i	−0.891209	+	0.453594i	$0.850142\pi$
$642$	−2.41983	−	9.03094i	−0.0955032	−	0.356423i
$643$	17.7038	+	17.7038i	0.698171	+	0.698171i	0.964016	−	0.265845i	$-0.0856508\pi$
$643$	17.7038	+	17.7038i	0.698171	+	0.698171i	−0.265845	+	0.964016i	$0.585651\pi$
$644$	−0.232295	−	0.402346i	−0.00915369	−	0.0158547i
$645$	−5.80161	−	14.3887i	−0.228438	−	0.566555i
$646$	7.85841	+	4.53705i	0.309185	+	0.178508i
$647$	2.98146	−	2.98146i	0.117213	−	0.117213i	−0.646067	−	0.763280i	$-0.723587\pi$
$647$	2.98146	−	2.98146i	0.117213	−	0.117213i	0.763280	+	0.646067i	$0.223587\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	37.2444			1.46197
$650$	4.42221	−	15.3403i	0.173453	−	0.601698i
$651$	−1.50393	−	27.5207i	−0.0589435	−	1.07862i
$652$	−4.22636	−	4.22636i	−0.165517	−	0.165517i
$653$	1.83390	−	1.83390i	0.0717661	−	0.0717661i	−0.670313	−	0.742079i	$-0.733840\pi$
$653$	1.83390	−	1.83390i	0.0717661	−	0.0717661i	0.742079	+	0.670313i	$0.233840\pi$
$654$	−5.43577	−	9.41502i	−0.212555	−	0.368157i
$655$	−6.81098	+	48.2158i	−0.266127	+	1.88395i
$656$	−2.84370	+	4.92543i	−0.111028	+	0.192306i
$657$	7.48712	+	2.00617i	0.292100	+	0.0782680i
$658$	−30.1219	−	8.07114i	−1.17427	−	0.314646i
$659$		−	3.51707i		−	0.137006i	−0.997651	−	0.0685029i	$-0.978178\pi$
$659$		−	3.51707i		−	0.137006i	0.997651	−	0.0685029i	$-0.0218222\pi$
$660$	1.03180	+	8.45267i	0.0401629	+	0.329020i
$661$	−4.10725	+	7.11397i	−0.159754	+	0.276701i	−0.934780	−	0.355228i	$-0.884403\pi$
$661$	−4.10725	+	7.11397i	−0.159754	+	0.276701i	0.775026	+	0.631929i	$0.217737\pi$
$662$	−0.989386	−	3.69244i	−0.0384536	−	0.143511i
$663$	2.33253	−	8.70513i	0.0905881	−	0.338079i
$664$	−3.36218	+	5.82347i	−0.130478	+	0.225994i
$665$	−13.9278	+	32.7475i	−0.540096	+	1.26990i
$666$		−	8.11640i		−	0.314504i
$667$	0.282688	+	0.282688i	0.0109457	+	0.0109457i
$668$	−3.81935	+	14.2540i	−0.147775	+	0.551504i
$669$	11.4409	+	6.60542i	0.442332	+	0.255380i
$670$	−3.38586	−	8.39735i	−0.130807	−	0.324418i
$671$	−20.6999	+	35.8532i	−0.799109	+	1.38410i
$672$	−1.28122	−	4.78156i	−0.0494240	−	0.184453i
$673$	−19.5310	+	5.23332i	−0.752866	+	0.201730i	−0.614789	−	0.788692i	$-0.710759\pi$
$673$	−19.5310	+	5.23332i	−0.752866	+	0.201730i	−0.138077	+	0.990422i	$0.544092\pi$
$674$	8.13330			0.313283
$675$	−4.28220	−	2.58124i	−0.164822	−	0.0993518i
$676$	−1.40236	−	2.42896i	−0.0539370	−	0.0934217i
$677$	8.20423	+	30.6186i	0.315314	+	1.17677i	0.923697	+	0.383125i	$0.125152\pi$
$677$	8.20423	+	30.6186i	0.315314	+	1.17677i	−0.608382	+	0.793644i	$0.708181\pi$
$678$	6.98473	+	6.98473i	0.268247	+	0.268247i
$679$	−58.0833	+	33.5344i	−2.22903	+	1.28693i
$680$	6.24923	+	0.882769i	0.239647	+	0.0338526i
$681$			22.9069i			0.877796i
$682$	14.1525	−	15.7887i	0.541927	−	0.604581i
$683$	−4.85715	+	4.85715i	−0.185854	+	0.185854i	−0.793901	−	0.608047i	$-0.791953\pi$
$683$	−4.85715	+	4.85715i	−0.185854	+	0.185854i	0.608047	+	0.793901i	$0.291953\pi$
$684$			3.21493i			0.122926i
$685$	−0.759006	+	1.78460i	−0.0290001	+	0.0681862i
$686$	52.0015			1.98543
$687$	−11.4335	+	3.06358i	−0.436213	+	0.116883i
$688$	−1.79574	+	6.70179i	−0.0684620	+	0.255504i
$689$	13.7356	−	7.93025i	0.523284	−	0.302118i
$690$	0.126178	+	0.167690i	0.00480352	+	0.00638385i
$691$	−4.31689	+	7.47707i	−0.164222	+	0.284441i	−0.936379	−	0.350991i	$-0.885845\pi$
$691$	−4.31689	+	7.47707i	−0.164222	+	0.284441i	0.772157	+	0.635432i	$0.219178\pi$
$692$	−15.3789	+	4.12075i	−0.584617	+	0.156648i
$693$	−18.2092	+	4.87914i	−0.691710	+	0.185343i
$694$	−17.3541	−	30.0581i	−0.658751	−	1.14099i
$695$	17.8961	+	14.0023i	0.678839	+	0.531139i
$696$	2.12985	+	3.68901i	0.0807318	+	0.139832i
$697$	11.3509	−	11.3509i	0.429946	−	0.429946i
$698$	20.7774	−	20.7774i	0.786438	−	0.786438i
$699$	6.29680	+	10.9064i	0.238167	+	0.412517i
$700$	−0.466887	+	24.7468i	−0.0176467	+	0.935340i
$701$	3.55477	+	6.15704i	0.134262	+	0.232548i	0.925315	−	0.379199i	$-0.123800\pi$
$701$	3.55477	+	6.15704i	0.134262	+	0.232548i	−0.791053	+	0.611747i	$0.790467\pi$
$702$	3.08420	−	0.826410i	0.116406	−	0.0311908i
$703$	25.2045	−	6.75354i	0.950607	−	0.254715i
$704$	1.90410	−	3.29801i	0.0717637	−	0.124298i
$705$	13.9478	+	1.97028i	0.525306	+	0.0742050i
$706$	−18.0145	+	10.4007i	−0.677985	+	0.391435i
$707$	−13.3387	+	49.7807i	−0.501653	+	1.87220i
$708$	9.44677	−	2.53126i	0.355031	−	0.0951304i
$709$	25.2446			0.948082			0.474041	−	0.880503i	$-0.342795\pi$
$709$	25.2446			0.948082			0.474041	+	0.880503i	$0.342795\pi$
$710$	−24.8053	−	10.5499i	−0.930927	−	0.395931i
$711$			11.8746i			0.445334i
$712$	−8.64339	+	8.64339i	−0.323925	+	0.323925i
$713$	0.107502	−	0.511368i	0.00402597	−	0.0191509i
$714$			13.9720i			0.522888i
$715$	16.3479	+	21.7262i	0.611376	+	0.812515i
$716$	−3.52033	+	2.03246i	−0.131561	+	0.0759567i
$717$	8.83921	+	8.83921i	0.330106	+	0.330106i
$718$	3.57907	+	13.3573i	0.133570	+	0.498488i
$719$	13.6631	+	23.6652i	0.509549	+	0.882565i	0.999939	+	0.0110615i	$0.00352104\pi$
$719$	13.6631	+	23.6652i	0.509549	+	0.882565i	−0.490390	+	0.871503i	$0.663146\pi$
$720$	0.836183	+	2.07384i	0.0311627	+	0.0772873i
$721$	−3.24988			−0.121032
$722$	8.36899	−	2.24246i	0.311461	−	0.0834558i
$723$	−3.20806	−	11.9726i	−0.119309	−	0.445267i
$724$	−1.25745	+	2.17797i	−0.0467327	+	0.0809434i
$725$	−5.12341	−	20.6731i	−0.190279	−	0.767780i
$726$	−3.03322	−	1.75123i	−0.112573	−	0.0649943i
$727$	8.58131	−	32.0259i	0.318263	−	1.18777i	−0.602650	−	0.798006i	$-0.705888\pi$
$727$	8.58131	−	32.0259i	0.318263	−	1.18777i	0.920913	−	0.389768i	$-0.127445\pi$
$728$	−11.1766	−	11.1766i	−0.414233	−	0.414233i
$729$		−	1.00000i		−	0.0370370i
$730$	6.48145	+	16.0748i	0.239889	+	0.594955i
$731$	9.79150	−	16.9594i	0.362152	−	0.627265i
$732$	−2.81367	+	10.5008i	−0.103996	+	0.388119i
$733$	−6.32211	−	23.5945i	−0.233513	−	0.871481i	−0.978814	−	0.204753i	$-0.934361\pi$
$733$	−6.32211	−	23.5945i	−0.233513	−	0.871481i	0.745301	−	0.666728i	$-0.232306\pi$
$734$	−4.81317	+	8.33665i	−0.177657	+	0.307711i
$735$	−38.8536	+	4.74280i	−1.43314	+	0.174941i
$736$		−	0.0938519i		−	0.00345943i
$737$	14.8947	+	3.99103i	0.548654	+	0.147011i
$738$	5.49360	+	1.47201i	0.202222	+	0.0541853i
$739$	12.6173	−	21.8538i	0.464135	−	0.803905i	−0.535027	−	0.844835i	$-0.679699\pi$
$739$	12.6173	−	21.8538i	0.464135	−	0.803905i	0.999162	+	0.0409300i	$0.0130321\pi$
$740$	14.5020	−	10.9120i	0.533104	−	0.401133i
$741$	5.13265	+	8.89000i	0.188552	+	0.326582i
$742$	−17.3871	+	17.3871i	−0.638302	+	0.638302i
$743$	−9.23630	−	9.23630i	−0.338847	−	0.338847i	0.517086	−	0.855933i	$-0.327017\pi$
$743$	−9.23630	−	9.23630i	−0.338847	−	0.338847i	−0.855933	+	0.517086i	$0.827017\pi$
$744$	2.51663	−	4.96655i	0.0922641	−	0.182082i
$745$	14.2468	+	2.01251i	0.521963	+	0.0737326i
$746$	−27.1687			−0.994716
$747$	6.49523	+	1.74039i	0.237648	+	0.0636776i
$748$	−7.60042	+	7.60042i	−0.277899	+	0.277899i
$749$	40.0817	+	23.1412i	1.46455	+	0.845559i
$750$	−1.14513	−	11.1215i	−0.0418141	−	0.406101i
$751$	19.9768	+	34.6008i	0.728964	+	1.26260i	0.957321	+	0.289025i	$0.0933312\pi$
$751$	19.9768	+	34.6008i	0.728964	+	1.26260i	−0.228357	+	0.973577i	$0.573335\pi$
$752$	−4.45449	−	4.45449i	−0.162438	−	0.162438i
$753$	−0.749653	−	2.79774i	−0.0273189	−	0.101955i
$754$	11.7790	+	6.80063i	0.428967	+	0.247664i
$755$	−6.99321	+	8.93790i	−0.254509	+	0.325284i
$756$	−4.28703	+	2.47512i	−0.155918	+	0.0900192i
$757$	2.64418	+	9.86820i	0.0961042	+	0.358666i	0.997185	−	0.0749863i	$-0.0238913\pi$
$757$	2.64418	+	9.86820i	0.0961042	+	0.358666i	−0.901080	+	0.433652i	$0.857225\pi$
$758$	3.57064	+	0.956749i	0.129691	+	0.0347507i
$759$	−0.357408			−0.0129731
$760$	−5.74429	+	4.32228i	−0.208367	+	0.156786i
$761$	−44.3011	+	25.5773i	−1.60591	+	0.927175i	−0.615643	+	0.788026i	$0.711103\pi$
$761$	−44.3011	+	25.5773i	−1.60591	+	0.927175i	−0.990271	+	0.139149i	$0.955563\pi$
$762$	−0.547093	+	0.146593i	−0.0198191	+	0.00531051i
$763$	51.9829	+	13.9288i	1.88191	+	0.504256i
$764$	−1.19296	−	0.688757i	−0.0431598	−	0.0249183i
$765$	−0.764731	−	6.26477i	−0.0276489	−	0.226503i
$766$	15.3644	+	8.87063i	0.555138	+	0.320509i
$767$	22.0813	−	22.0813i	0.797309	−	0.797309i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−9.02002	+	5.20771i	−0.325270	+	0.187795i	−0.653739	−	0.756720i	$-0.726801\pi$
$769$	−9.02002	+	5.20771i	−0.325270	+	0.187795i	0.328469	+	0.944515i	$0.393467\pi$
$770$	−33.1990	−	25.9756i	−1.19641	−	0.936096i
$771$			2.06252i			0.0742799i
$772$	−6.85892	+	25.5979i	−0.246858	+	0.921287i
$773$	−14.5357	−	14.5357i	−0.522812	−	0.522812i	0.395607	−	0.918420i	$-0.370534\pi$
$773$	−14.5357	−	14.5357i	−0.522812	−	0.522812i	−0.918420	+	0.395607i	$0.870534\pi$
$774$	6.93821			0.249389
$775$	−18.9693	+	20.3756i	−0.681397	+	0.731914i
$776$	−13.5486			−0.486366
$777$	28.4102	+	28.4102i	1.01921	+	1.01921i
$778$	−3.66821	+	13.6900i	−0.131512	+	0.490809i
$779$			18.2846i			0.655113i
$780$	5.62312	+	4.39965i	0.201340	+	0.157533i
$781$	39.7572	−	22.9538i	1.42262	−	0.821352i
$782$	−0.0685601	+	0.255870i	−0.00245170	+	0.00914988i
$783$	3.01207	−	3.01207i	0.107642	−	0.107642i
$784$	15.1596	+	8.75242i	0.541416	+	0.312587i
$785$	−4.35716	−	35.6944i	−0.155514	−	1.27399i
$786$	−18.8593	−	10.8884i	−0.672688	−	0.388377i
$787$	−0.621799	−	0.166611i	−0.0221648	−	0.00593903i	0.247720	−	0.968832i	$-0.420319\pi$
$787$	−0.621799	−	0.166611i	−0.0221648	−	0.00593903i	−0.269884	+	0.962893i	$0.586985\pi$
$788$	−22.3990	+	6.00179i	−0.797931	+	0.213805i
$789$	−4.62281	+	2.66898i	−0.164576	+	0.0950183i
$790$	−21.2170	+	15.9647i	−0.754869	+	0.568000i
$791$	−48.8979			−1.73861
$792$	−3.67845	−	0.985637i	−0.130708	−	0.0350231i
$793$	8.98405	+	33.5289i	0.319033	+	1.19065i
$794$	−25.9843	+	15.0020i	−0.922148	+	0.532402i
$795$	6.84441	−	8.74772i	0.242746	−	0.310250i
$796$	−20.1753	−	11.6482i	−0.715095	−	0.412860i
$797$	−5.38599	−	20.1008i	−0.190781	−	0.712006i	−0.993319	−	0.115404i	$-0.963184\pi$
$797$	−5.38599	−	20.1008i	−0.190781	−	0.712006i	0.802537	−	0.596602i	$-0.203483\pi$
$798$	−11.2534	−	11.2534i	−0.398365	−	0.398365i
$799$	8.89026	+	15.3984i	0.314515	+	0.544756i
$800$	−2.58124	+	4.28220i	−0.0912605	+	0.151399i
$801$	10.5859	+	6.11180i	0.374036	+	0.215950i
$802$	15.6395	−	15.6395i	0.552248	−	0.552248i
$803$	−28.5125	−	7.63991i	−1.00618	−	0.269606i
$804$	4.04918			0.142804
$805$	−1.02864	−	0.145306i	−0.0362548	−	0.00512137i
$806$	−0.970063	−	17.7514i	−0.0341690	−	0.625267i
$807$	−5.84818	−	5.84818i	−0.205866	−	0.205866i
$808$	−7.36167	+	7.36167i	−0.258983	+	0.258983i
$809$	22.7704	+	39.4396i	0.800566	+	1.38662i	0.919244	+	0.393688i	$0.128801\pi$
$809$	22.7704	+	39.4396i	0.800566	+	1.38662i	−0.118678	+	0.992933i	$0.537866\pi$
$810$	1.78675	−	1.34444i	0.0627801	−	0.0472388i
$811$	23.1236	−	40.0513i	0.811980	−	1.40639i	−0.0994966	−	0.995038i	$-0.531723\pi$
$811$	23.1236	−	40.0513i	0.811980	−	1.40639i	0.911476	−	0.411352i	$-0.134943\pi$
$812$	−20.3680	−	5.45760i	−0.714778	−	0.191524i
$813$	−14.8205	−	3.97114i	−0.519778	−	0.139274i
$814$			30.9089i			1.08336i
$815$	−13.2665	+	1.61942i	−0.464704	+	0.0567257i
$816$	−1.41124	+	2.44435i	−0.0494034	+	0.0855692i
$817$	5.77318	+	21.5458i	0.201978	+	0.753793i
$818$	5.32799	−	19.8843i	0.186289	−	0.695239i
$819$	−7.90306	+	13.6885i	−0.276155	+	0.478315i
$820$	4.75570	+	11.7947i	0.166076	+	0.411890i
$821$			6.79565i			0.237170i	0.992944	+	0.118585i	$0.0378358\pi$
$821$			6.79565i			0.237170i	−0.992944	+	0.118585i	$0.962164\pi$
$822$	−0.613262	−	0.613262i	−0.0213900	−	0.0213900i
$823$	11.1991	−	41.7956i	0.390376	−	1.45690i	−0.439139	−	0.898419i	$-0.644717\pi$
$823$	11.1991	−	41.7956i	0.390376	−	1.45690i	0.829515	−	0.558484i	$-0.188617\pi$
$824$	−0.568554	−	0.328255i	−0.0198065	−	0.0114353i
$825$	16.3075	+	9.82989i	0.567755	+	0.342233i
$826$	−24.2067	+	41.9272i	−0.842259	+	1.45884i
$827$	2.76327	+	10.3127i	0.0960882	+	0.358606i	0.997182	−	0.0750177i	$-0.0239013\pi$
$827$	2.76327	+	10.3127i	0.0960882	+	0.358606i	−0.901094	+	0.433624i	$0.857235\pi$
$828$	−0.0906540	+	0.0242907i	−0.00315044	+	0.000844159i
$829$	−49.6771			−1.72536			−0.862679	−	0.505752i	$-0.831215\pi$
$829$	−49.6771			−1.72536			−0.862679	+	0.505752i	$0.831215\pi$
$830$	5.62280	+	13.9452i	0.195170	+	0.484046i
$831$	11.1735	+	19.3530i	0.387603	+	0.671348i
$832$	−0.826410	−	3.08420i	−0.0286506	−	0.106926i
$833$	−34.9362	−	34.9362i	−1.21047	−	1.21047i
$834$	−8.80060	+	5.08103i	−0.304740	+	0.175942i
$835$	19.8397	+	26.3668i	0.686580	+	0.912461i
$836$		−	12.2431i		−	0.423438i
$837$	−5.44867	−	1.14544i	−0.188333	−	0.0395922i
$838$	17.3554	−	17.3554i	0.599532	−	0.599532i
$839$			5.23222i			0.180636i	0.995913	+	0.0903182i	$0.0287884\pi$
$839$			5.23222i			0.180636i	−0.995913	+	0.0903182i	$0.971212\pi$
$840$	−10.1861	−	4.33222i	−0.351453	−	0.149476i
$841$	−10.8549			−0.374307
$842$	22.4013	−	6.00240i	0.771999	−	0.206856i
$843$	−1.86999	+	6.97892i	−0.0644060	+	0.240367i
$844$	16.4446	−	9.49428i	0.566045	−	0.326806i
$845$	−6.20991	−	0.877214i	−0.213627	−	0.0301771i
$846$	−3.14980	+	5.45561i	−0.108292	+	0.187568i
$847$	16.7472	−	4.48741i	0.575442	−	0.154189i
$848$	−4.79801	+	1.28562i	−0.164764	+	0.0441485i
$849$	−12.8745	−	22.2993i	−0.441852	−	0.765310i
$850$	10.1655	−	9.78899i	0.348672	−	0.335760i
$851$	0.380870	+	0.659686i	0.0130560	+	0.0226137i
$852$	8.52411	−	8.52411i	0.292031	−	0.292031i
$853$	−9.74809	+	9.74809i	−0.333768	+	0.333768i	−0.854016	−	0.520247i	$-0.825840\pi$
$853$	−9.74809	+	9.74809i	−0.333768	+	0.333768i	0.520247	+	0.854016i	$0.325840\pi$
$854$	−26.9075	−	46.6051i	−0.920754	−	1.59479i
$855$	5.66173	+	4.42987i	0.193627	+	0.151498i
$856$	4.67476	+	8.09692i	0.159780	+	0.276747i
$857$	−0.795132	+	0.213055i	−0.0271612	+	0.00727782i	−0.272374	−	0.962191i	$-0.587809\pi$
$857$	−0.795132	+	0.213055i	−0.0271612	+	0.00727782i	0.245213	+	0.969469i	$0.421142\pi$
$858$	−11.7453	+	3.14714i	−0.400978	+	0.107442i
$859$	−3.07000	+	5.31740i	−0.104747	+	0.181427i	−0.913635	−	0.406536i	$-0.866737\pi$
$859$	−3.07000	+	5.31740i	−0.104747	+	0.181427i	0.808888	+	0.587963i	$0.200070\pi$
$860$	9.32800	+	12.3969i	0.318082	+	0.422729i
$861$	−24.3820	+	14.0770i	−0.830938	+	0.479742i
$862$	0.211629	−	0.789811i	0.00720812	−	0.0269011i
$863$	−8.55057	+	2.29112i	−0.291065	+	0.0779906i	−0.401397	−	0.915904i	$-0.631475\pi$
$863$	−8.55057	+	2.29112i	−0.291065	+	0.0779906i	0.110332	+	0.993895i	$0.464809\pi$
$864$	−1.00000			−0.0340207
$865$	−13.9336	+	32.7613i	−0.473758	+	1.11392i
$866$		−	5.56085i		−	0.188965i
$867$	−6.38769	+	6.38769i	−0.216937	+	0.216937i
$868$	8.57556	+	26.1937i	0.291073	+	0.889072i
$869$		−	45.2211i		−	1.53402i
$870$	9.43135	+	1.33228i	0.319753	+	0.0451684i
$871$	11.1969	−	6.46453i	0.379392	−	0.219042i
$872$	7.68734	+	7.68734i	0.260326	+	0.260326i
$873$	3.50664	+	13.0869i	0.118682	+	0.442926i
$874$	−0.150864	−	0.261304i	−0.00510304	−	0.00883873i
$875$	42.9376	+	34.9209i	1.45156	+	1.18054i
$876$	−7.75123			−0.261890
$877$	−23.2137	+	6.22009i	−0.783871	+	0.210038i	−0.628491	−	0.777817i	$-0.716327\pi$
$877$	−23.2137	+	6.22009i	−0.783871	+	0.210038i	−0.155380	+	0.987855i	$0.549660\pi$
$878$	0.755464	+	2.81943i	0.0254957	+	0.0951512i
$879$	10.9574	−	18.9788i	0.369584	−	0.640138i
$880$	−3.18436	−	7.89760i	−0.107345	−	0.266228i
$881$	12.8076	+	7.39450i	0.431501	+	0.249127i	0.699986	−	0.714157i	$-0.253190\pi$
$881$	12.8076	+	7.39450i	0.431501	+	0.249127i	−0.268485	+	0.963284i	$0.586523\pi$
$882$	4.53059	−	16.9084i	0.152553	−	0.569335i
$883$	8.51290	+	8.51290i	0.286482	+	0.286482i	0.835687	−	0.549205i	$-0.185070\pi$
$883$	8.51290	+	8.51290i	0.286482	+	0.286482i	−0.549205	+	0.835687i	$0.685070\pi$
$884$			9.01221i			0.303114i
$885$	8.55902	−	20.1243i	0.287708	−	0.676471i
$886$	3.20620	−	5.55331i	0.107714	−	0.186567i
$887$	1.68486	−	6.28800i	0.0565722	−	0.211130i	−0.931854	−	0.362834i	$-0.881809\pi$
$887$	1.68486	−	6.28800i	0.0565722	−	0.211130i	0.988426	+	0.151704i	$0.0484759\pi$
$888$	2.10068	+	7.83984i	0.0704941	+	0.263088i
$889$	1.40189	−	2.42814i	0.0470178	−	0.0814372i
$890$	3.31189	+	27.1314i	0.111015	+	0.909447i
$891$			3.80821i			0.127580i
$892$	−12.7607	−	3.41922i	−0.427260	−	0.114484i
$893$	−19.5627	−	5.24180i	−0.654640	−	0.175410i
$894$	−3.21731	+	5.57254i	−0.107603	+	0.186374i
$895$	−1.27136	+	9.00009i	−0.0424968	+	0.300840i
$896$	2.47512	+	4.28703i	0.0826879	+	0.143220i
$897$	−0.211898	+	0.211898i	−0.00707508	+	0.00707508i
$898$	−24.4400	−	24.4400i	−0.815574	−	0.815574i
$899$	−12.9616	−	19.8619i	−0.432294	−	0.662431i
$900$	4.80436	+	1.38497i	0.160145	+	0.0461656i
$901$	14.0200			0.467075
$902$	−20.9208	−	5.60571i	−0.696586	−	0.186650i
$903$	−24.2861	+	24.2861i	−0.808192	+	0.808192i
$904$	−8.55451	−	4.93895i	−0.284519	−	0.164267i
$905$	2.10291	+	5.21549i	0.0699032	+	0.173369i
$906$	−2.53763	−	4.39530i	−0.0843070	−	0.146024i
$907$	−32.4883	−	32.4883i	−1.07876	−	1.07876i	−0.996621	−	0.0821345i	$-0.973826\pi$
$907$	−32.4883	−	32.4883i	−1.07876	−	1.07876i	−0.0821345	−	0.996621i	$-0.526174\pi$
$908$	−5.92875	−	22.1264i	−0.196753	−	0.734290i
$909$	9.01616	+	5.20548i	0.299047	+	0.172655i
$910$	−35.0832	+	4.28255i	−1.16300	+	0.141965i
$911$	4.58548	−	2.64743i	0.151924	−	0.0877132i	−0.422111	−	0.906544i	$-0.638711\pi$
$911$	4.58548	−	2.64743i	0.151924	−	0.0877132i	0.574035	+	0.818831i	$0.305377\pi$
$912$	−0.832086	−	3.10539i	−0.0275531	−	0.102830i
$913$	−24.7352	−	6.62778i	−0.818616	−	0.219348i
$914$	35.6092			1.17785
$915$	14.6156	+	19.4241i	0.483178	+	0.642141i
$916$	10.2510	−	5.91839i	0.338701	−	0.195549i
$917$	104.127	−	27.9008i	3.43858	−	0.921366i
$918$	2.72631	+	0.730514i	0.0899818	+	0.0241105i
$919$	−1.21572	−	0.701896i	−0.0401029	−	0.0231534i	0.479815	−	0.877370i	$-0.340704\pi$
$919$	−1.21572	−	0.701896i	−0.0401029	−	0.0231534i	−0.519917	+	0.854217i	$0.674037\pi$
$920$	−0.165280	−	0.129319i	−0.00544913	−	0.00426352i
$921$	8.78724	+	5.07332i	0.289549	+	0.167171i
$922$	27.5904	−	27.5904i	0.908640	−	0.908640i
$923$	9.96230	−	37.1798i	0.327913	−	1.22379i
$924$	16.3259	−	9.42577i	0.537083	−	0.310085i
$925$	0.765507	−	40.5748i	0.0251697	−	1.33409i
$926$			2.97423i			0.0977391i
$927$	−0.169917	+	0.634139i	−0.00558081	+	0.0208279i
$928$	−3.01207	−	3.01207i	−0.0988759	−	0.0988759i
$929$	43.5414			1.42855			0.714274	−	0.699866i	$-0.246757\pi$
$929$	43.5414			1.42855			0.714274	+	0.699866i	$0.246757\pi$
$930$	−5.27878	−	11.2754i	−0.173098	−	0.369735i
$931$	56.2769			1.84440
$932$	−8.90502	−	8.90502i	−0.291694	−	0.291694i
$933$	−3.98893	+	14.8869i	−0.130592	+	0.487375i
$934$			26.7875i			0.876515i
$935$	2.91226	+	23.8576i	0.0952410	+	0.780226i
$936$	−2.76522	+	1.59650i	−0.0903841	+	0.0521833i
$937$	13.3344	−	49.7645i	0.435614	−	1.62574i	−0.303977	−	0.952679i	$-0.598315\pi$
$937$	13.3344	−	49.7645i	0.435614	−	1.62574i	0.739591	−	0.673056i	$-0.235019\pi$
$938$	−14.1735	+	14.1735i	−0.462783	+	0.462783i
$939$	0.829622	+	0.478983i	0.0270737	+	0.0156310i
$940$	−13.9825	+	1.70683i	−0.456060	+	0.0556705i
$941$	−32.8415	−	18.9611i	−1.07060	−	0.618113i	−0.142257	−	0.989830i	$-0.545436\pi$
$941$	−32.8415	−	18.9611i	−1.07060	−	0.618113i	−0.928346	+	0.371717i	$0.878769\pi$
$942$	15.5335	+	4.16220i	0.506110	+	0.135612i
$943$	−0.515585	+	0.138151i	−0.0167898	+	0.00449880i
$944$	−8.46975	+	4.89001i	−0.275667	+	0.159156i
$945$	−1.54825	+	10.9603i	−0.0503646	+	0.356537i
$946$	−26.4221			−0.859058
$947$	−6.95895	−	1.86465i	−0.226136	−	0.0605929i	0.143972	−	0.989582i	$-0.454012\pi$
$947$	−6.95895	−	1.86465i	−0.226136	−	0.0605929i	−0.370108	+	0.928989i	$0.620679\pi$
$948$	−3.07338	−	11.4700i	−0.0998189	−	0.372529i
$949$	−21.4339	+	12.3749i	−0.695773	+	0.401705i
$950$	−0.303220	+	16.0718i	−0.00983775	+	0.521438i
$951$	−9.56392	−	5.52173i	−0.310131	−	0.179054i
$952$	−3.61621	−	13.4959i	−0.117202	−	0.437405i
$953$	9.89637	+	9.89637i	0.320575	+	0.320575i	0.848988	−	0.528413i	$-0.177213\pi$
$953$	9.89637	+	9.89637i	0.320575	+	0.320575i	−0.528413	+	0.848988i	$0.677213\pi$
$954$	2.48363	+	4.30178i	0.0804106	+	0.139275i
$955$	−2.85674	+	1.15185i	−0.0924419	+	0.0372731i
$956$	−10.8258	−	6.25027i	−0.350131	−	0.202148i
$957$	−11.4706	+	11.4706i	−0.370791	+	0.370791i
$958$	37.0583	+	9.92973i	1.19730	+	0.320815i
$959$	4.29326			0.138637
$960$	−1.34444	−	1.78675i	−0.0433916	−	0.0576672i
$961$	−12.4822	+	28.3759i	−0.402653	+	0.915353i
$962$	18.3252	+	18.3252i	0.590827	+	0.590827i
$963$	6.61111	−	6.61111i	0.213040	−	0.213040i
$964$	6.19749	+	10.7344i	0.199608	+	0.345731i
$965$	35.6288	+	47.3505i	1.14693	+	1.52426i
$966$	0.232295	−	0.402346i	0.00747396	−	0.0129453i
$967$	34.1653	+	9.15457i	1.09868	+	0.294391i	0.762228	−	0.647308i	$-0.224105\pi$
$967$	34.1653	+	9.15457i	1.09868	+	0.294391i	0.336455	+	0.941700i	$0.390772\pi$
$968$	3.38312	+	0.906504i	0.108738	+	0.0291361i
$969$			9.07411i			0.291502i
$970$	−18.6687	+	23.8601i	−0.599415	+	0.766101i
$971$	−9.01049	+	15.6066i	−0.289160	+	0.500840i	−0.973610	−	0.228220i	$-0.926709\pi$
$971$	−9.01049	+	15.6066i	−0.289160	+	0.500840i	0.684449	+	0.729061i	$0.260043\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	13.0198	−	48.5905i	0.417395	−	1.55774i
$974$	4.74028	−	8.21040i	0.151888	−	0.263078i
$975$	15.4962	−	3.84043i	0.496276	−	0.122992i
$976$		−	10.8712i		−	0.347978i
$977$	7.03507	+	7.03507i	0.225072	+	0.225072i	0.810630	−	0.585558i	$-0.199125\pi$
$977$	7.03507	+	7.03507i	0.225072	+	0.225072i	−0.585558	+	0.810630i	$0.699125\pi$
$978$	1.54696	−	5.77332i	0.0494662	−	0.184610i
$979$	−40.3135	−	23.2750i	−1.28843	−	0.743873i
$980$	36.3022	−	14.6373i	1.15963	−	0.467570i
$981$	5.43577	−	9.41502i	0.173551	−	0.300599i
$982$	−11.0642	−	41.2922i	−0.353073	−	1.31769i
$983$	10.9529	−	2.93483i	0.349344	−	0.0936064i	−0.0798802	−	0.996804i	$-0.525454\pi$
$983$	10.9529	−	2.93483i	0.349344	−	0.0936064i	0.429224	+	0.903198i	$0.358787\pi$
$984$	−5.68740			−0.181308
$985$	−20.2941	+	47.7162i	−0.646623	+	1.52036i
$986$	6.01148	+	10.4122i	0.191445	+	0.331592i
$987$	−8.07114	−	30.1219i	−0.256907	−	0.958791i
$988$	−7.25866	−	7.25866i	−0.230929	−	0.230929i
$989$	−0.563925	+	0.325582i	−0.0179318	+	0.0103529i
$990$	−6.80433	+	5.11991i	−0.216256	+	0.162721i
$991$			14.0657i			0.446811i	0.974726	+	0.223405i	$0.0717174\pi$
$991$			14.0657i			0.446811i	−0.974726	+	0.223405i	$0.928283\pi$
$992$	−1.14544	+	5.44867i	−0.0363677	+	0.172995i
$993$	2.70305	−	2.70305i	0.0857788	−	0.0857788i
$994$			59.6747i			1.89277i
$995$	−48.3130	+	19.4801i	−1.53163	+	0.617560i
$996$	−6.72436			−0.213070
$997$	40.3029	−	10.7991i	1.27640	−	0.342012i	0.443924	−	0.896065i	$-0.353586\pi$
$997$	40.3029	−	10.7991i	1.27640	−	0.342012i	0.832481	+	0.554053i	$0.186920\pi$
$998$	−6.98086	+	26.0529i	−0.220975	+	0.824691i
$999$	7.02901	−	4.05820i	0.222388	−	0.128396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.6	yes	64
5.3	odd	4		930.2.be.a.223.1	✓	64
31.26	odd	6		930.2.be.a.367.1	yes	64
155.88	even	12	inner	930.2.be.b.553.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.1	✓	64	5.3	odd	4
930.2.be.a.367.1	yes	64	31.26	odd	6
930.2.be.b.37.6	yes	64	1.1	even	1	trivial
930.2.be.b.553.6	yes	64	155.88	even	12	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.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.76107 + 1.37790i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.28122 - 4.78156i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.76107 + 1.37790i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.28122 - 4.78156i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.270942 - 2.21959i) q^{10} +(3.29801 + 1.90410i) q^{11} +(0.965926 + 0.258819i) q^{12} +(3.08420 - 0.826410i) q^{13} +(-4.28703 + 2.47512i) q^{14} +(1.78675 - 1.34444i) q^{15} -1.00000 q^{16} +(2.72631 + 0.730514i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.78421 + 1.60747i) q^{19} +(-1.37790 + 1.76107i) q^{20} +(-4.28703 - 2.47512i) q^{21} +(-0.985637 - 3.67845i) q^{22} +(-0.0663633 - 0.0663633i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.20276 + 4.85318i) q^{25} +(-2.76522 - 1.59650i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.78156 + 1.28122i) q^{28} -4.25970 q^{29} +(-2.21409 - 0.312763i) q^{30} +(3.04284 + 4.66274i) q^{31} +(0.707107 + 0.707107i) q^{32} +(2.69281 - 2.69281i) q^{33} +(-1.41124 - 2.44435i) q^{34} +(8.84485 - 6.65529i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.83984 - 2.10068i) q^{37} +(3.10539 + 0.832086i) q^{38} -3.19300i q^{39} +(2.21959 - 0.270942i) q^{40} +(2.84370 - 4.92543i) q^{41} +(1.28122 + 4.78156i) q^{42} +(1.79574 - 6.70179i) q^{43} +(-1.90410 + 3.29801i) q^{44} +(-0.836183 - 2.07384i) q^{45} +0.0938519i q^{46} +(4.45449 + 4.45449i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-15.1596 - 8.75242i) q^{49} +(2.58124 - 4.28220i) q^{50} +(1.41124 - 2.44435i) q^{51} +(0.826410 + 3.08420i) q^{52} +(4.79801 - 1.28562i) q^{53} +1.00000 q^{54} +(3.18436 + 7.89760i) q^{55} +(-2.47512 - 4.28703i) q^{56} +(0.832086 + 3.10539i) q^{57} +(3.01207 + 3.01207i) q^{58} +(8.46975 - 4.89001i) q^{59} +(1.34444 + 1.78675i) q^{60} +10.8712i q^{61} +(1.14544 - 5.44867i) q^{62} +(-3.50035 + 3.50035i) q^{63} -1.00000i q^{64} +(6.57023 + 2.79437i) q^{65} -3.80821 q^{66} +(3.91121 - 1.04801i) q^{67} +(-0.730514 + 2.72631i) q^{68} +(-0.0812782 + 0.0469260i) q^{69} +(-10.9603 - 1.54825i) q^{70} +(6.02746 - 10.4399i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-7.48712 + 2.00617i) q^{73} +(4.05820 + 7.02901i) q^{74} +(4.99911 + 0.0943161i) q^{75} +(-1.60747 - 2.78421i) q^{76} +(13.3301 - 13.3301i) q^{77} +(-2.25779 + 2.25779i) q^{78} +(-5.93732 - 10.2837i) q^{79} +(-1.76107 - 1.37790i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.49360 + 1.47201i) q^{82} +(-6.49523 + 1.74039i) q^{83} +(2.47512 - 4.28703i) q^{84} +(3.79466 + 5.04309i) q^{85} +(-6.00866 + 3.46910i) q^{86} +(-1.10249 + 4.11456i) q^{87} +(3.67845 - 0.985637i) q^{88} -12.2236 q^{89} +(-0.875153 + 2.05769i) q^{90} -15.8061i q^{91} +(0.0663633 - 0.0663633i) q^{92} +(5.29140 - 1.73235i) q^{93} -6.29959i q^{94} +(-7.11814 - 1.00551i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-9.58031 - 9.58031i) q^{97} +(4.53059 + 16.9084i) q^{98} +(-1.90410 - 3.29801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more