LMFDB - Embedded newform 483.2.bb.a.26.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(26,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 55, 48]))

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

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

chi := DirichletCharacter("483.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bb (of order $66$, degree $20$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			26.14
Character	$\chi$	$=$	483.26
Dual form			483.2.bb.a.353.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.660745 + 1.65046i) q^{2} +(0.966959 + 1.43701i) q^{3} +(-0.839971 - 0.800910i) q^{4} +(0.513695 + 1.48422i) q^{5} +(-3.01064 + 0.646433i) q^{6} +(2.47761 + 0.928150i) q^{7} +(-1.35743 + 0.619916i) q^{8} +(-1.12998 + 2.77905i) q^{9} +(-2.78908 - 0.132860i) q^{10} +(-0.721058 - 1.80111i) q^{11} +(0.338697 - 1.98149i) q^{12} +(-0.133458 + 0.207665i) q^{13} +(-3.16894 + 3.47592i) q^{14} +(-1.63612 + 2.17337i) q^{15} +(-0.236682 - 4.96857i) q^{16} +(-0.335175 - 1.38161i) q^{17} +(-3.84009 - 3.70123i) q^{18} +(6.45388 + 1.56570i) q^{19} +(0.757242 - 1.65813i) q^{20} +(1.06199 + 4.45782i) q^{21} +3.44911 q^{22} +(-3.05688 + 3.69533i) q^{23} +(-2.20340 - 1.35120i) q^{24} +(1.99123 - 1.56592i) q^{25} +(-0.254561 - 0.357481i) q^{26} +(-5.08617 + 1.06344i) q^{27} +(-1.33775 - 2.76396i) q^{28} +(-0.330102 + 1.12423i) q^{29} +(-2.50600 - 4.13639i) q^{30} +(-3.70658 - 2.63945i) q^{31} +(5.53641 + 1.91617i) q^{32} +(1.89098 - 2.77777i) q^{33} +(2.50176 + 0.359699i) q^{34} +(-0.104848 + 4.15411i) q^{35} +(3.17492 - 1.42931i) q^{36} +(-4.60809 + 0.888136i) q^{37} +(-6.84849 + 9.61736i) q^{38} +(-0.427464 + 0.00902317i) q^{39} +(-1.61740 - 1.69628i) q^{40} +(3.52132 - 4.06383i) q^{41} +(-8.05917 - 1.19272i) q^{42} +(3.26330 - 7.14562i) q^{43} +(-0.836864 + 2.09039i) q^{44} +(-4.70521 - 0.249557i) q^{45} +(-4.07918 - 7.48694i) q^{46} +(3.99663 - 6.92236i) q^{47} +(6.91101 - 5.14452i) q^{48} +(5.27708 + 4.59918i) q^{49} +(1.26879 + 4.32111i) q^{50} +(1.66128 - 1.81761i) q^{51} +(0.278422 - 0.0675443i) q^{52} +(0.244094 - 0.473475i) q^{53} +(1.60549 - 9.09719i) q^{54} +(2.30285 - 1.99543i) q^{55} +(-3.93855 + 0.276013i) q^{56} +(3.99073 + 10.7882i) q^{57} +(-1.63738 - 1.28765i) q^{58} +(0.328910 - 6.90467i) q^{59} +(3.11497 - 0.515181i) q^{60} +(-0.163471 + 1.71195i) q^{61} +(6.80541 - 4.37357i) q^{62} +(-5.37903 + 5.83662i) q^{63} +(-0.305895 + 0.353021i) q^{64} +(-0.376778 - 0.0914053i) q^{65} +(3.33514 + 4.95639i) q^{66} +(-6.00365 + 4.72132i) q^{67} +(-0.825009 + 1.42896i) q^{68} +(-8.26610 - 0.819531i) q^{69} +(-6.78692 - 2.91786i) q^{70} +(9.45929 - 1.36004i) q^{71} +(-0.188916 - 4.47286i) q^{72} +(-9.18005 + 9.62776i) q^{73} +(1.57894 - 8.19230i) q^{74} +(4.17567 + 1.34723i) q^{75} +(-4.16709 - 6.48412i) q^{76} +(-0.114793 - 5.13170i) q^{77} +(0.267552 - 0.711475i) q^{78} +(1.61002 - 0.830025i) q^{79} +(7.25289 - 2.90362i) q^{80} +(-6.44629 - 6.28055i) q^{81} +(4.38049 + 8.49696i) q^{82} +(2.79068 + 3.22061i) q^{83} +(2.67828 - 4.59500i) q^{84} +(1.87844 - 1.20720i) q^{85} +(9.63737 + 10.1074i) q^{86} +(-1.93472 + 0.612720i) q^{87} +(2.09532 + 1.99789i) q^{88} +(1.49651 + 2.10156i) q^{89} +(3.52083 - 7.60087i) q^{90} +(-0.523400 + 0.390642i) q^{91} +(5.52732 - 0.655678i) q^{92} +(0.208788 - 7.87862i) q^{93} +(8.78434 + 11.1702i) q^{94} +(0.991485 + 10.3833i) q^{95} +(2.59993 + 9.80872i) q^{96} +(1.67674 + 1.45290i) q^{97} +(-11.0776 + 5.67072i) q^{98} +(5.82018 + 0.0313649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 27 q^{3} - 74 q^{4} - 36 q^{7} - 13 q^{9} - 54 q^{10} - 15 q^{12} - 64 q^{15} + 38 q^{16} + 43 q^{18} - 54 q^{19} - 70 q^{21} - 160 q^{22} - 66 q^{24} + 34 q^{25} - 76 q^{28} - 23 q^{30} - 54 q^{31}+ \cdots + 196 q^{99}+O(q^{100}) $ 1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9 - 54 * q^10 - 15 * q^12 - 64 * q^15 + 38 * q^16 + 43 * q^18 - 54 * q^19 - 70 * q^21 - 160 * q^22 - 66 * q^24 + 34 * q^25 - 76 * q^28 - 23 * q^30 - 54 * q^31 - 3 * q^33 - 28 * q^36 + 26 * q^37 + 5 * q^39 - 30 * q^40 - 68 * q^42 - 176 * q^43 - 96 * q^45 - 22 * q^46 - 128 * q^49 - 23 * q^51 - 102 * q^52 + 21 * q^54 - 36 * q^57 + 58 * q^58 - 43 * q^60 - 126 * q^61 + 41 * q^63 + 40 * q^64 - 132 * q^66 - 10 * q^67 + 20 * q^70 + 59 * q^72 - 30 * q^73 - 81 * q^75 + 164 * q^78 - 14 * q^79 - 97 * q^81 - 66 * q^82 + 24 * q^84 - 56 * q^85 - 399 * q^87 - 74 * q^88 - 156 * q^91 + 8 * q^93 - 126 * q^94 - 117 * q^96 + 196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.660745	+	1.65046i	−0.467217	+	1.16705i	0.488447	+	0.872594i	$0.337564\pi$
$2$	−0.660745	+	1.65046i	−0.467217	+	1.16705i	−0.955664	+	0.294459i	$0.904861\pi$
$3$	0.966959	+	1.43701i	0.558274	+	0.829657i
$3$	0.966959	+	1.43701i	0.558274	+	0.829657i
$4$	−0.839971	−	0.800910i	−0.419985	−	0.400455i
$5$	0.513695	+	1.48422i	0.229731	+	0.663765i	0.999671	+	0.0256486i	$0.00816510\pi$
$5$	0.513695	+	1.48422i	0.229731	+	0.663765i	−0.769940	+	0.638117i	$0.779714\pi$
$6$	−3.01064	+	0.646433i	−1.22909	+	0.263905i
$7$	2.47761	+	0.928150i	0.936448	+	0.350808i
$7$	2.47761	+	0.928150i	0.936448	+	0.350808i
$8$	−1.35743	+	0.619916i	−0.479923	+	0.219173i
$9$	−1.12998	+	2.77905i	−0.376660	+	0.926352i
$10$	−2.78908	−	0.132860i	−0.881984	−	0.0420141i
$11$	−0.721058	−	1.80111i	−0.217407	−	0.543056i	0.779069	−	0.626939i	$-0.215692\pi$
$11$	−0.721058	−	1.80111i	−0.217407	−	0.543056i	−0.996476	+	0.0838821i	$0.973268\pi$
$12$	0.338697	−	1.98149i	0.0977733	−	0.572007i
$13$	−0.133458	+	0.207665i	−0.0370146	+	0.0575958i	−0.859268	−	0.511526i	$-0.829080\pi$
$13$	−0.133458	+	0.207665i	−0.0370146	+	0.0575958i	0.822253	+	0.569122i	$0.192717\pi$
$14$	−3.16894	+	3.47592i	−0.846935	+	0.928980i
$15$	−1.63612	+	2.17337i	−0.422444	+	0.561161i
$16$	−0.236682	−	4.96857i	−0.0591706	−	1.24214i
$17$	−0.335175	−	1.38161i	−0.0812919	−	0.335090i	0.916614	−	0.399774i	$-0.130911\pi$
$17$	−0.335175	−	1.38161i	−0.0812919	−	0.335090i	−0.997906	+	0.0646839i	$0.979396\pi$
$18$	−3.84009	−	3.70123i	−0.905119	−	0.872389i
$19$	6.45388	+	1.56570i	1.48062	+	0.359195i	0.893043	−	0.449971i	$-0.148566\pi$
$19$	6.45388	+	1.56570i	1.48062	+	0.359195i	0.587580	+	0.809166i	$0.300081\pi$
$20$	0.757242	−	1.65813i	0.169324	−	0.370769i
$21$	1.06199	+	4.45782i	0.231745	+	0.972777i
$22$	3.44911			0.735352
$23$	−3.05688	+	3.69533i	−0.637404	+	0.770529i
$23$	−3.05688	+	3.69533i	−0.637404	+	0.770529i
$24$	−2.20340	−	1.35120i	−0.449767	−	0.275812i
$25$	1.99123	−	1.56592i	0.398245	−	0.313183i
$26$	−0.254561	−	0.357481i	−0.0499235	−	0.0701077i
$27$	−5.08617	+	1.06344i	−0.978833	+	0.204660i
$28$	−1.33775	−	2.76396i	−0.252811	−	0.522339i
$29$	−0.330102	+	1.12423i	−0.0612985	+	0.208763i	−0.984448	−	0.175679i	$-0.943788\pi$
$29$	−0.330102	+	1.12423i	−0.0612985	+	0.208763i	0.923149	+	0.384442i	$0.125606\pi$
$30$	−2.50600	−	4.13639i	−0.457531	−	0.755199i
$31$	−3.70658	−	2.63945i	−0.665722	−	0.474058i	0.196557	−	0.980492i	$-0.437024\pi$
$31$	−3.70658	−	2.63945i	−0.665722	−	0.474058i	−0.862279	+	0.506434i	$0.830963\pi$
$32$	5.53641	+	1.91617i	0.978708	+	0.338734i
$33$	1.89098	−	2.77777i	0.329178	−	0.483548i
$34$	2.50176	+	0.359699i	0.429048	+	0.0616878i
$35$	−0.104848	+	4.15411i	−0.0177226	+	0.702173i
$36$	3.17492	−	1.42931i	0.529154	−	0.238219i
$37$	−4.60809	+	0.888136i	−0.757565	+	0.146009i	−0.553386	−	0.832925i	$-0.686664\pi$
$37$	−4.60809	+	0.888136i	−0.757565	+	0.146009i	−0.204179	+	0.978934i	$0.565452\pi$
$38$	−6.84849	+	9.61736i	−1.11097	+	1.56014i
$39$	−0.427464	+	0.00902317i	−0.0684490	+	0.00144486i
$40$	−1.61740	−	1.69628i	−0.255733	−	0.268205i
$41$	3.52132	−	4.06383i	0.549938	−	0.634663i	−0.410930	−	0.911667i	$-0.634796\pi$
$41$	3.52132	−	4.06383i	0.549938	−	0.634663i	0.960869	+	0.277004i	$0.0893415\pi$
$42$	−8.05917	−	1.19272i	−1.24356	−	0.184040i
$43$	3.26330	−	7.14562i	0.497648	−	1.08970i	−0.479578	−	0.877499i	$-0.659210\pi$
$43$	3.26330	−	7.14562i	0.497648	−	1.08970i	0.977227	−	0.212198i	$-0.0680623\pi$
$44$	−0.836864	+	2.09039i	−0.126162	+	0.315138i
$45$	−4.70521	−	0.249557i	−0.701411	−	0.0372018i
$46$	−4.07918	−	7.48694i	−0.601442	−	1.10389i
$47$	3.99663	−	6.92236i	0.582968	−	1.00973i	−0.412157	−	0.911113i	$-0.635225\pi$
$47$	3.99663	−	6.92236i	0.582968	−	1.00973i	0.995125	−	0.0986176i	$-0.0314421\pi$
$48$	6.91101	−	5.14452i	0.997519	−	0.742547i
$49$	5.27708	+	4.59918i	0.753868	+	0.657026i
$50$	1.26879	+	4.32111i	0.179434	+	0.611098i
$51$	1.66128	−	1.81761i	0.232626	−	0.254516i
$52$	0.278422	−	0.0675443i	0.0386101	−	0.00936671i
$53$	0.244094	−	0.473475i	0.0335288	−	0.0650368i	−0.871476	−	0.490438i	$-0.836837\pi$
$53$	0.244094	−	0.473475i	0.0335288	−	0.0650368i	0.905005	+	0.425401i	$0.139867\pi$
$54$	1.60549	−	9.09719i	0.218479	−	1.23797i
$55$	2.30285	−	1.99543i	0.310517	−	0.269064i
$56$	−3.93855	+	0.276013i	−0.526310	+	0.0368838i
$57$	3.99073	+	10.7882i	0.528585	+	1.42894i
$58$	−1.63738	−	1.28765i	−0.214998	−	0.169076i
$59$	0.328910	−	6.90467i	0.0428204	−	0.898911i	−0.870624	−	0.491948i	$-0.836285\pi$
$59$	0.328910	−	6.90467i	0.0428204	−	0.898911i	0.913445	−	0.406963i	$-0.133412\pi$
$60$	3.11497	−	0.515181i	0.402140	−	0.0665095i
$61$	−0.163471	+	1.71195i	−0.0209303	+	0.219193i	0.978955	+	0.204074i	$0.0654185\pi$
$61$	−0.163471	+	1.71195i	−0.0209303	+	0.219193i	−0.999886	+	0.0151181i	$0.995188\pi$
$62$	6.80541	−	4.37357i	0.864288	−	0.555444i
$63$	−5.37903	+	5.83662i	−0.677694	+	0.735344i
$64$	−0.305895	+	0.353021i	−0.0382368	+	0.0441276i
$65$	−0.376778	−	0.0914053i	−0.0467335	−	0.0113374i
$66$	3.33514	+	4.95639i	0.410528	+	0.610089i
$67$	−6.00365	+	4.72132i	−0.733463	+	0.576801i	−0.913490	−	0.406860i	$-0.866624\pi$
$67$	−6.00365	+	4.72132i	−0.733463	+	0.576801i	0.180028	+	0.983662i	$0.442381\pi$
$68$	−0.825009	+	1.42896i	−0.100047	+	0.173286i
$69$	−8.26610	−	0.819531i	−0.995121	−	0.0986600i
$70$	−6.78692	−	2.91786i	−0.811192	−	0.348751i
$71$	9.45929	−	1.36004i	1.12261	−	0.161407i	0.444086	−	0.895984i	$-0.353528\pi$
$71$	9.45929	−	1.36004i	1.12261	−	0.161407i	0.678525	+	0.734577i	$0.262619\pi$
$72$	−0.188916	−	4.47286i	−0.0222639	−	0.527131i
$73$	−9.18005	+	9.62776i	−1.07444	+	1.12684i	−0.0829675	+	0.996552i	$0.526440\pi$
$73$	−9.18005	+	9.62776i	−1.07444	+	1.12684i	−0.991476	+	0.130291i	$0.958409\pi$
$74$	1.57894	−	8.19230i	0.183548	−	0.952335i
$75$	4.17567	+	1.34723i	0.482165	+	0.155564i
$76$	−4.16709	−	6.48412i	−0.477998	−	0.743780i
$77$	−0.114793	−	5.13170i	−0.0130819	−	0.584812i
$78$	0.267552	−	0.711475i	0.0302943	−	0.0805587i
$79$	1.61002	−	0.830025i	0.181142	−	0.0933851i	−0.365270	−	0.930901i	$-0.619023\pi$
$79$	1.61002	−	0.830025i	0.181142	−	0.0933851i	0.546412	+	0.837516i	$0.315993\pi$
$80$	7.25289	−	2.90362i	0.810898	−	0.324635i
$81$	−6.44629	−	6.28055i	−0.716255	−	0.697839i
$82$	4.38049	+	8.49696i	0.483744	+	0.938333i
$83$	2.79068	+	3.22061i	0.306317	+	0.353508i	0.887948	−	0.459944i	$-0.152131\pi$
$83$	2.79068	+	3.22061i	0.306317	+	0.353508i	−0.581631	+	0.813453i	$0.697585\pi$
$84$	2.67828	−	4.59500i	0.292224	−	0.501355i
$85$	1.87844	−	1.20720i	0.203746	−	0.130939i
$86$	9.63737	+	10.1074i	1.03922	+	1.08991i
$87$	−1.93472	+	0.612720i	−0.207423	+	0.0656905i
$88$	2.09532	+	1.99789i	0.223362	+	0.212975i
$89$	1.49651	+	2.10156i	0.158630	+	0.222765i	0.886240	−	0.463226i	$-0.153308\pi$
$89$	1.49651	+	2.10156i	0.158630	+	0.222765i	−0.727610	+	0.685991i	$0.759369\pi$
$90$	3.52083	−	7.60087i	0.371128	−	0.801202i
$91$	−0.523400	+	0.390642i	−0.0548673	+	0.0409504i
$92$	5.52732	−	0.655678i	0.576263	−	0.0683592i
$93$	0.208788	−	7.87862i	0.0216503	−	0.816975i
$94$	8.78434	+	11.1702i	0.906035	+	1.15212i
$95$	0.991485	+	10.3833i	0.101724	+	1.06530i
$96$	2.59993	+	9.80872i	0.265354	+	1.00110i
$97$	1.67674	+	1.45290i	0.170247	+	0.147520i	0.735817	−	0.677180i	$-0.236798\pi$
$97$	1.67674	+	1.45290i	0.170247	+	0.147520i	−0.565570	+	0.824700i	$0.691344\pi$
$98$	−11.0776	+	5.67072i	−1.11900	+	0.572830i
$99$	5.82018	+	0.0313649i	0.584950	+	0.00315229i
$100$	−2.92673	−	0.279469i	−0.292673	−	0.0279469i
$101$	−2.29146	+	6.62072i	−0.228008	+	0.658787i	0.771731	+	0.635949i	$0.219391\pi$
$101$	−2.29146	+	6.62072i	−0.228008	+	0.658787i	−0.999739	+	0.0228375i	$0.992730\pi$
$102$	1.90221	+	3.94286i	0.188347	+	0.390401i
$103$	−8.33820	+	10.6029i	−0.821587	+	1.04473i	0.176584	+	0.984286i	$0.443495\pi$
$103$	−8.33820	+	10.6029i	−0.821587	+	1.04473i	−0.998171	+	0.0604479i	$0.980747\pi$
$104$	0.0524248	−	0.364622i	0.00514067	−	0.0357541i
$105$	−6.07087	+	3.86619i	−0.592456	+	0.377301i
$106$	0.620169	+	0.715713i	0.0602362	+	0.0695162i
$107$	−1.20372	+	12.6059i	−0.116368	+	1.21866i	0.729014	+	0.684499i	$0.239979\pi$
$107$	−1.20372	+	12.6059i	−0.116368	+	1.21866i	−0.845382	+	0.534163i	$0.820627\pi$
$108$	5.12395	+	3.18030i	0.493053	+	0.306025i
$109$	−1.16396	−	4.79789i	−0.111487	−	0.459555i	−1.00000		0.000703207i	$-0.999776\pi$
$109$	−1.16396	−	4.79789i	−0.111487	−	0.459555i	0.888513	−	0.458851i	$-0.151739\pi$
$110$	1.77179	+	5.11925i	0.168933	+	0.488101i
$111$	−5.73209	−	5.76306i	−0.544066	−	0.547006i
$112$	4.02517	−	12.5298i	0.380343	−	1.18396i
$113$	18.0719	−	2.59834i	1.70006	−	0.244431i	0.777112	−	0.629362i	$-0.216684\pi$
$113$	18.0719	−	2.59834i	1.70006	−	0.244431i	0.922945	+	0.384931i	$0.125775\pi$
$114$	−20.4424	−	0.541737i	−1.91461	−	0.0507383i
$115$	−7.05500	−	2.63883i	−0.657883	−	0.246072i
$116$	1.17768	−	0.679934i	0.109345	−	0.0631303i
$117$	−0.426307	−	0.605544i	−0.0394121	−	0.0559825i
$118$	11.1786	+	5.10508i	1.02907	+	0.469961i
$119$	0.451909	−	3.73418i	0.0414264	−	0.342312i
$120$	0.873606	−	3.96444i	0.0797490	−	0.361903i
$121$	5.23698	−	4.99345i	0.476089	−	0.453950i
$122$	−2.71749	−	1.40096i	−0.246030	−	0.126837i
$123$	9.24472	+	1.13062i	0.833569	+	0.101944i
$124$	0.999461	+	5.18570i	0.0897543	+	0.465689i
$125$	9.95345	+	6.39669i	0.890263	+	0.572138i
$126$	−6.07894	−	12.7344i	−0.541555	−	1.13447i
$127$	−1.86736	+	12.9878i	−0.165702	+	1.15248i	0.721943	+	0.691952i	$0.243249\pi$
$127$	−1.86736	+	12.9878i	−0.165702	+	1.15248i	−0.887645	+	0.460528i	$0.847660\pi$
$128$	4.98863	+	9.67659i	0.440937	+	0.855298i
$129$	13.4238	−	2.22014i	1.18190	−	0.195473i
$130$	0.399815	−	0.561461i	0.0350661	−	0.0492434i
$131$	0.181784	+	3.81612i	0.0158826	+	0.333416i	0.992799	+	0.119793i	$0.0382232\pi$
$131$	0.181784	+	3.81612i	0.0158826	+	0.333416i	−0.976916	+	0.213623i	$0.931474\pi$
$132$	−3.81311	+	0.818738i	−0.331889	+	0.0712620i
$133$	14.5370	+	9.86935i	1.26052	+	0.855781i
$134$	−3.82548	−	13.0284i	−0.330471	−	1.12548i
$135$	−4.19113	−	7.00273i	−0.360715	−	0.602699i
$136$	1.31146	+	1.66765i	0.112457	+	0.143000i
$137$	−11.5627	+	6.67573i	−0.987869	+	0.570346i	−0.904637	−	0.426184i	$-0.859858\pi$
$137$	−11.5627	+	6.67573i	−0.987869	+	0.570346i	−0.0832323	+	0.996530i	$0.526524\pi$
$138$	6.81439	−	13.1014i	0.580079	−	1.11526i
$139$		−	16.8016i		−	1.42509i	−0.701627	−	0.712545i	$-0.747543\pi$
$139$		−	16.8016i		−	1.42509i	0.701627	−	0.712545i	$-0.252457\pi$
$140$	3.41514	−	3.40536i	0.288632	−	0.287805i
$141$	13.8121	−	0.950459i	1.16319	−	0.0800431i
$142$	−4.00548	+	16.5108i	−0.336133	+	1.38556i
$143$	0.470259	+	0.0906349i	0.0393250	+	0.00757927i
$144$	14.0754	+	4.95663i	1.17295	+	0.413053i
$145$	−1.83817	+	0.0875630i	−0.152652	+	0.00727171i
$146$	−9.82457	−	21.5128i	−0.813087	−	1.78041i
$147$	−1.50634	+	12.0304i	−0.124241	+	0.992252i
$148$	4.58197	+	2.94466i	0.376636	+	0.242049i
$149$	13.3138	−	16.9298i	1.09071	−	1.38695i	0.175254	−	0.984523i	$-0.443925\pi$
$149$	13.3138	−	16.9298i	1.09071	−	1.38695i	0.915454	−	0.402424i	$-0.131832\pi$
$150$	−4.98260	+	6.00161i	−0.406828	+	0.490029i
$151$	−0.672176	+	14.1107i	−0.0547009	+	1.14831i	0.790011	+	0.613093i	$0.210075\pi$
$151$	−0.672176	+	14.1107i	−0.0547009	+	1.14831i	−0.844712	+	0.535221i	$0.820228\pi$
$152$	−9.73127	+	1.87555i	−0.789311	+	0.152127i
$153$	4.21831	+	0.629722i	0.341030	+	0.0509100i
$154$	8.54553	+	3.20129i	0.688618	+	0.257967i
$155$	2.01348	−	6.85727i	0.161726	−	0.550789i
$156$	0.366284	+	0.334781i	0.0293262	+	0.0268039i
$157$	7.52395	−	7.89089i	0.600476	−	0.629761i	−0.351407	−	0.936223i	$-0.614297\pi$
$157$	7.52395	−	7.89089i	0.600476	−	0.629761i	0.951883	+	0.306462i	$0.0991451\pi$
$158$	0.306109	+	3.20572i	0.0243527	+	0.255033i
$159$	0.916416	−	0.107067i	0.0726765	−	0.00849098i
$160$			9.20160i			0.727450i
$161$	−11.0036	+	6.31833i	−0.867203	+	0.497954i
$162$	14.6252	−	6.48951i	1.14906	−	0.509864i
$163$	12.3504	+	4.94437i	0.967361	+	0.387273i	0.800915	−	0.598778i	$-0.204347\pi$
$163$	12.3504	+	4.94437i	0.967361	+	0.387273i	0.166445	+	0.986051i	$0.446771\pi$
$164$	−6.21257	+	0.593228i	−0.485120	+	0.0463234i
$165$	5.09422	+	1.37971i	0.396585	+	0.107411i
$166$	−7.15943	+	2.47790i	−0.555679	+	0.192322i
$167$	−2.87103	−	0.843012i	−0.222167	−	0.0652342i	0.168754	−	0.985658i	$-0.446026\pi$
$167$	−2.87103	−	0.843012i	−0.222167	−	0.0652342i	−0.390922	+	0.920424i	$0.627844\pi$
$168$	−4.20504	−	5.39282i	−0.324426	−	0.416065i
$169$	5.37508	+	11.7698i	0.413468	+	0.905368i
$170$	0.751268	+	3.89795i	0.0576196	+	0.298959i
$171$	−11.6439	+	16.1665i	−0.890432	+	1.23628i
$172$	−8.46408	+	3.38851i	−0.645380	+	0.258371i
$173$	−12.9554	−	10.1882i	−0.984979	−	0.774596i	−0.0107005	−	0.999943i	$-0.503406\pi$
$173$	−12.9554	−	10.1882i	−0.984979	−	0.774596i	−0.974279	+	0.225347i	$0.927649\pi$
$174$	0.267082	−	3.59802i	0.0202474	−	0.272766i
$175$	6.38688	−	2.03157i	0.482803	−	0.153572i
$176$	−8.77831	+	4.00892i	−0.661690	+	0.302184i
$177$	10.2401	−	6.20389i	0.769693	−	0.466313i
$178$	−4.45735	+	1.08134i	−0.334093	+	0.0810501i
$179$	−0.518737	+	2.69146i	−0.0387722	+	0.201170i	−0.996149	−	0.0876709i	$-0.972058\pi$
$179$	−0.518737	+	2.69146i	−0.0387722	+	0.201170i	0.957377	+	0.288840i	$0.0932697\pi$
$180$	3.75236	+	3.97807i	0.279685	+	0.296508i
$181$	−14.6341	−	6.68316i	−1.08774	−	0.496755i	−0.210887	−	0.977510i	$-0.567635\pi$
$181$	−14.6341	−	6.68316i	−1.08774	−	0.496755i	−0.876855	+	0.480755i	$0.840363\pi$
$182$	−0.298906	−	1.12197i	−0.0221564	−	0.0831657i
$183$	−2.61815	+	1.42047i	−0.193539	+	0.105005i
$184$	1.85870	−	6.91115i	0.137025	−	0.509497i
$185$	−3.68534	−	6.38320i	−0.270952	−	0.469302i
$186$	12.8654	+	5.55036i	0.943337	+	0.406972i
$187$	−2.24676	+	1.59991i	−0.164299	+	0.116997i
$188$	−8.90124	+	2.61364i	−0.649190	+	0.190619i
$189$	−13.5886	−	2.08593i	−0.988422	−	0.151729i
$190$	−17.7924	−	5.22431i	−1.29079	−	0.379011i
$191$	12.4553	−	0.593317i	0.901231	−	0.0429309i	0.408150	−	0.912915i	$-0.366174\pi$
$191$	12.4553	−	0.593317i	0.901231	−	0.0429309i	0.493080	+	0.869984i	$0.335871\pi$
$192$	−0.803081	−	0.0982157i	−0.0579574	−	0.00708810i
$193$	7.74509	−	22.3780i	0.557504	−	1.61080i	−0.215573	−	0.976488i	$-0.569162\pi$
$193$	7.74509	−	22.3780i	0.557504	−	1.61080i	0.773076	−	0.634313i	$-0.218717\pi$
$194$	−3.50586	+	1.80739i	−0.251706	+	0.129763i
$195$	−0.232979	−	0.629817i	−0.0166839	−	0.0451022i
$196$	−0.749056	−	8.08964i	−0.0535040	−	0.577832i
$197$	8.70289	−	13.5420i	0.620055	−	0.964825i	−0.379165	−	0.925329i	$-0.623789\pi$
$197$	8.70289	−	13.5420i	0.620055	−	0.964825i	0.999220	−	0.0394955i	$-0.0125751\pi$
$198$	−3.89742	+	9.58525i	−0.276978	+	0.681194i
$199$	−17.7597	−	12.6466i	−1.25895	−	0.896497i	−0.261320	−	0.965252i	$-0.584158\pi$
$199$	−17.7597	−	12.6466i	−1.25895	−	0.896497i	−0.997634	+	0.0687551i	$0.978097\pi$
$200$	−1.73221	+	3.36001i	−0.122485	+	0.237589i
$201$	−12.5899	−	4.06196i	−0.888020	−	0.286509i
$202$	−9.41318	−	8.15657i	−0.662309	−	0.573894i
$203$	−1.86131	+	2.47900i	−0.130639	+	0.173992i
$204$	−2.85117	+	0.196200i	−0.199622	+	0.0137367i
$205$	7.84052	+	3.13887i	0.547605	+	0.219228i
$206$	−11.9902	−	20.7677i	−0.835399	−	1.44695i
$207$	−6.81531	−	12.6709i	−0.473697	−	0.880688i
$208$	1.06338	+	0.613945i	0.0737324	+	0.0425694i
$209$	−1.83363	−	12.7531i	−0.126834	−	0.882153i
$210$	−2.36970	−	12.5743i	−0.163525	−	0.867710i
$211$	0.478008	−	0.140356i	0.0329074	−	0.00966249i	−0.265237	−	0.964183i	$-0.585450\pi$
$211$	0.478008	−	0.140356i	0.0329074	−	0.00966249i	0.298145	+	0.954521i	$0.403632\pi$
$212$	−0.584243	+	0.202208i	−0.0401260	+	0.0138877i
$213$	11.1011	+	12.2780i	0.760637	+	0.841272i
$214$	−20.0103	−	10.3160i	−1.36787	−	0.705187i
$215$	12.2820	+	1.17279i	0.837629	+	0.0799839i
$216$	6.24485	−	4.59654i	0.424908	−	0.312755i
$217$	−6.73366	−	9.97977i	−0.457110	−	0.677471i
$218$	8.68781	+	1.24912i	0.588413	+	0.0846010i
$219$	−22.7119	−	3.88215i	−1.53473	−	0.262331i
$220$	−3.53250	−	0.168273i	−0.238161	−	0.0113450i
$221$	0.331643	+	0.114783i	0.0223087	+	0.00772113i
$222$	13.2992	−	5.65268i	0.892581	−	0.379383i
$223$	4.32843	+	6.73517i	0.289853	+	0.451020i	0.955391	−	0.295344i	$-0.0954342\pi$
$223$	4.32843	+	6.73517i	0.289853	+	0.451020i	−0.665538	+	0.746364i	$0.731798\pi$
$224$	11.9386	+	9.88613i	0.797678	+	0.660545i
$225$	2.10172	+	7.30318i	0.140115	+	0.486879i
$226$	−7.65243	+	31.5437i	−0.509032	+	2.09826i
$227$	−26.4154	+	2.52236i	−1.75325	+	0.167415i	−0.921666	−	0.387983i	$-0.873172\pi$
$227$	−26.4154	+	2.52236i	−1.75325	+	0.167415i	−0.831584	+	0.555398i	$0.812566\pi$
$228$	5.28832	−	12.2580i	0.350228	−	0.811807i
$229$	−10.2656	−	5.92686i	−0.678371	−	0.391658i	0.120870	−	0.992668i	$-0.461432\pi$
$229$	−10.2656	−	5.92686i	−0.678371	−	0.391658i	−0.799241	+	0.601010i	$0.794765\pi$
$230$	9.01685	−	9.90042i	0.594553	−	0.652814i
$231$	7.26330	−	5.12711i	0.477890	−	0.337339i
$232$	−0.248835	−	1.73069i	−0.0163368	−	0.113625i
$233$	−14.7897	+	10.5317i	−0.968904	+	0.689953i	−0.950775	−	0.309882i	$-0.899710\pi$
$233$	−14.7897	+	10.5317i	−0.968904	+	0.689953i	−0.0181290	+	0.999836i	$0.505771\pi$
$234$	1.28111	−	0.303492i	0.0837486	−	0.0198399i
$235$	12.3274	+	2.37591i	0.804150	+	0.154987i
$236$	−5.80630	+	5.53629i	−0.377958	+	0.360382i
$237$	2.74958	+	1.51102i	0.178604	+	0.0981510i
$238$	5.86452	+	3.21320i	0.380140	+	0.208281i
$239$	−0.249259	+	0.215984i	−0.0161232	+	0.0139708i	−0.662885	−	0.748721i	$-0.730668\pi$
$239$	−0.249259	+	0.215984i	−0.0161232	+	0.0139708i	0.646762	+	0.762692i	$0.276123\pi$
$240$	11.1858	+	7.61478i	0.722039	+	0.491532i
$241$	−6.30340	−	15.7451i	−0.406038	−	1.01423i	−0.980643	−	0.195803i	$-0.937269\pi$
$241$	−6.30340	−	15.7451i	−0.406038	−	1.01423i	0.574606	−	0.818430i	$-0.305155\pi$
$242$	4.78119	+	11.9428i	0.307347	+	0.767715i
$243$	2.79190	−	15.3364i	0.179100	−	0.983831i
$244$	1.50843	−	1.30706i	0.0965672	−	0.0836760i
$245$	−4.11541	+	10.1949i	−0.262924	+	0.651331i
$246$	−7.97444	+	14.5110i	−0.508432	+	0.925188i
$247$	−1.18646	+	1.13129i	−0.0754928	+	0.0719822i
$248$	6.66765	+	1.28508i	0.423396	+	0.0816029i
$249$	−1.92957	+	7.12443i	−0.122282	+	0.451492i
$250$	−17.1342	+	12.2012i	−1.08366	+	0.771671i
$251$	2.49230	+	17.3343i	0.157312	+	1.09413i	0.903559	+	0.428463i	$0.140945\pi$
$251$	2.49230	+	17.3343i	0.157312	+	1.09413i	−0.746247	+	0.665669i	$0.768146\pi$
$252$	9.19283	−	0.594468i	0.579094	−	0.0374480i
$253$	8.85990	+	2.84125i	0.557017	+	0.178628i
$254$	−20.2020	−	11.6636i	−1.26759	−	0.731842i
$255$	3.55113	+	1.53202i	0.222381	+	0.0959388i
$256$	−20.1970	+	1.92858i	−1.26232	+	0.120536i
$257$	6.10171	−	25.1516i	0.380614	−	1.56891i	−0.383317	−	0.923617i	$-0.625218\pi$
$257$	6.10171	−	25.1516i	0.380614	−	1.56891i	0.763932	−	0.645297i	$-0.223266\pi$
$258$	−5.20544	+	23.6224i	−0.324076	+	1.47067i
$259$	−12.2413	−	2.07654i	−0.760640	−	0.129030i
$260$	0.243275	+	0.378543i	0.0150873	+	0.0234762i
$261$	−2.75127	−	2.18772i	−0.170300	−	0.135417i
$262$	−6.41847	−	2.22146i	−0.396535	−	0.137242i
$263$	−6.70146	−	0.319230i	−0.413230	−	0.0196846i	−0.160062	−	0.987107i	$-0.551169\pi$
$263$	−6.70146	−	0.319230i	−0.413230	−	0.0196846i	−0.253168	+	0.967422i	$0.581472\pi$
$264$	−0.844885	+	4.94287i	−0.0519991	+	0.304212i
$265$	0.828133	+	0.119068i	0.0508718	+	0.00731426i
$266$	−25.8942	+	17.4716i	−1.58768	+	1.07125i
$267$	−1.57289	+	4.18262i	−0.0962592	+	0.255972i
$268$	8.82425	+	0.842613i	0.539027	+	0.0514708i
$269$	13.5927	+	7.00754i	0.828764	+	0.427257i	0.819764	−	0.572702i	$-0.194105\pi$
$269$	13.5927	+	7.00754i	0.828764	+	0.427257i	0.00900005	+	0.999959i	$0.497135\pi$
$270$	14.3270	−	2.29028i	0.871913	−	0.139382i
$271$	−19.1250	+	6.61924i	−1.16176	+	0.402090i	−0.838863	−	0.544343i	$-0.816779\pi$
$271$	−19.1250	+	6.61924i	−1.16176	+	0.402090i	−0.322900	+	0.946433i	$0.604658\pi$
$272$	−6.78530	+	1.99234i	−0.411419	+	0.120804i
$273$	−1.06746	−	0.374395i	−0.0646058	−	0.0226594i
$274$	−3.37804	−	23.4948i	−0.204075	−	1.41937i
$275$	−4.25618	−	2.45731i	−0.256658	−	0.148181i
$276$	6.28691	+	7.30879i	0.378427	+	0.439937i
$277$	6.53799	+	11.3241i	0.392830	+	0.680401i	0.992822	−	0.119605i	$-0.0381628\pi$
$277$	6.53799	+	11.3241i	0.392830	+	0.680401i	−0.599992	+	0.800006i	$0.704829\pi$
$278$	27.7303	+	11.1015i	1.66315	+	0.665827i
$279$	11.5235	−	7.31828i	0.689896	−	0.438134i
$280$	−2.43288	−	5.70390i	−0.145392	−	0.340873i
$281$	−20.8671	−	18.0814i	−1.24483	−	1.07865i	−0.993859	−	0.110651i	$-0.964706\pi$
$281$	−20.8671	−	18.0814i	−1.24483	−	1.07865i	−0.250966	−	0.967996i	$-0.580748\pi$
$282$	−7.55756	+	23.4243i	−0.450046	+	1.39490i
$283$	12.0928	−	23.4568i	0.718843	−	1.39436i	−0.191911	−	0.981412i	$-0.561468\pi$
$283$	12.0928	−	23.4568i	0.718843	−	1.39436i	0.910754	−	0.412949i	$-0.135501\pi$
$284$	−9.03480	−	6.43365i	−0.536117	−	0.381767i
$285$	−13.9622	+	11.4650i	−0.827047	+	0.679128i
$286$	−0.460311	+	0.716257i	−0.0272187	+	0.0423532i
$287$	12.4963	−	6.80025i	0.737633	−	0.401406i
$288$	−11.5812	+	13.2207i	−0.682427	+	0.779040i
$289$	13.3137	−	6.86369i	0.783159	−	0.403746i
$290$	1.07005	−	3.09169i	0.0628352	−	0.181550i
$291$	−0.466494	+	3.81438i	−0.0273463	+	0.223603i
$292$	15.4219	−	0.734638i	0.902501	−	0.0429914i
$293$	−11.9928	−	3.52140i	−0.700627	−	0.205723i	−0.0880296	−	0.996118i	$-0.528057\pi$
$293$	−11.9928	−	3.52140i	−0.700627	−	0.205723i	−0.612597	+	0.790395i	$0.709875\pi$
$294$	−18.8604	−	10.4352i	−1.09996	−	0.608593i
$295$	10.4170	−	3.05872i	0.606503	−	0.178085i
$296$	5.70457	−	4.06220i	0.331571	−	0.236111i
$297$	5.58280	+	8.39397i	0.323947	+	0.487067i
$298$	19.1450	+	33.1602i	1.10904	+	1.92092i
$299$	−0.359424	−	1.12798i	−0.0207860	−	0.0652326i
$300$	−2.42843	−	4.47597i	−0.140205	−	0.258420i
$301$	14.7174	−	14.6752i	0.848296	−	0.845866i
$302$	−22.8451	−	10.4330i	−1.31459	−	0.600351i
$303$	−11.7298	+	3.10913i	−0.673858	+	0.178615i
$304$	6.25175	−	32.4372i	0.358562	−	1.86040i
$305$	−2.62489	+	0.636791i	−0.150301	+	0.0364626i
$306$	−3.82656	+	6.54607i	−0.218750	+	0.374214i
$307$	−22.3129	+	10.1899i	−1.27346	+	0.581571i	−0.933402	−	0.358832i	$-0.883175\pi$
$307$	−22.3129	+	10.1899i	−1.27346	+	0.581571i	−0.340061	+	0.940403i	$0.610448\pi$
$308$	−4.01361	+	4.40242i	−0.228697	+	0.250851i
$309$	−23.2991	−	1.72950i	−1.32544	−	0.0983877i
$310$	9.98727	+	7.85407i	0.567239	+	0.446081i
$311$	−0.696789	+	0.278952i	−0.0395113	+	0.0158179i	−0.391334	−	0.920249i	$-0.627986\pi$
$311$	−0.696789	+	0.278952i	−0.0395113	+	0.0158179i	0.351823	+	0.936067i	$0.385562\pi$
$312$	0.574657	−	0.277240i	0.0325336	−	0.0156956i
$313$	−4.23836	−	21.9907i	−0.239566	−	1.24299i	−0.880000	−	0.474974i	$-0.842457\pi$
$313$	−4.23836	−	21.9907i	−0.239566	−	1.24299i	0.640434	−	0.768013i	$-0.278755\pi$
$314$	8.05219	+	17.6318i	0.454412	+	0.995023i
$315$	−11.4260	−	4.98544i	−0.643784	−	0.280898i
$316$	−2.01715	−	0.592288i	−0.113473	−	0.0333188i
$317$	22.6146	−	7.82699i	1.27016	−	0.439607i	0.392883	−	0.919588i	$-0.371478\pi$
$317$	22.6146	−	7.82699i	1.27016	−	0.439607i	0.877279	+	0.479981i	$0.159356\pi$
$318$	−0.428807	+	1.58325i	−0.0240463	+	0.0887844i
$319$	2.26288	−	0.216079i	0.126697	−	0.0120981i
$320$	−0.681099	−	0.272671i	−0.0380746	−	0.0152428i
$321$	−19.2788	+	10.4597i	−1.07604	+	0.583802i
$322$	−3.15760	−	22.3358i	−0.175966	−	1.24472i
$323$		−	9.44153i		−	0.525341i
$324$	0.384536	+	10.4384i	0.0213631	+	0.579910i
$325$	0.0594407	+	0.622491i	0.00329718	+	0.0345296i
$326$	−16.3210	+	17.1169i	−0.903935	+	0.948020i
$327$	5.76911	−	6.31198i	0.319032	−	0.349053i
$328$	−2.26071	+	7.69927i	−0.124827	+	0.425121i
$329$	16.3271	−	13.4414i	0.900140	−	0.741050i
$330$	−5.64315	+	7.49618i	−0.310645	+	0.412651i
$331$	−15.2225	+	2.93389i	−0.836702	+	0.161261i	−0.589567	−	0.807720i	$-0.700701\pi$
$331$	−15.2225	+	2.93389i	−0.836702	+	0.161261i	−0.247136	+	0.968981i	$0.579489\pi$
$332$	0.235336	−	4.94031i	0.0129157	−	0.271134i
$333$	2.73887	−	13.8097i	0.150089	−	0.756767i
$334$	3.28838	−	4.18152i	0.179932	−	0.228802i
$335$	−10.0915	−	6.48544i	−0.551360	−	0.354338i
$336$	21.8977	−	6.33165i	1.19462	−	0.345420i
$337$	9.05466	+	19.8269i	0.493239	+	1.08004i	0.978608	+	0.205733i	$0.0659578\pi$
$337$	9.05466	+	19.8269i	0.493239	+	1.08004i	−0.485369	+	0.874309i	$0.661315\pi$
$338$	−22.9771	+	1.09454i	−1.24979	+	0.0595349i
$339$	21.2086	+	23.4569i	1.15189	+	1.27400i
$340$	−2.54470	−	0.490450i	−0.138005	−	0.0265984i
$341$	−2.08128	+	8.57917i	−0.112708	+	0.464588i
$342$	−18.9885	−	29.8998i	−1.02678	−	1.61679i
$343$	8.80579	+	16.2929i	0.475468	+	0.879733i
$344$			11.7226i			0.632042i
$345$	−3.02989	−	12.6897i	−0.163124	−	0.683192i
$346$	25.3755	−	14.6505i	1.36419	−	0.787618i
$347$	3.25136	+	4.13444i	0.174542	+	0.221948i	0.865451	−	0.500993i	$-0.167032\pi$
$347$	3.25136	+	4.13444i	0.174542	+	0.221948i	−0.690909	+	0.722942i	$0.742789\pi$
$348$	2.11584	+	1.03487i	0.113421	+	0.0554747i
$349$	5.38492	+	18.3394i	0.288248	+	0.981684i	0.968564	+	0.248764i	$0.0800245\pi$
$349$	5.38492	+	18.3394i	0.288248	+	0.981684i	−0.680316	+	0.732919i	$0.738157\pi$
$350$	−0.867069	+	11.8837i	−0.0463468	+	0.635208i
$351$	0.457950	−	1.19814i	0.0244436	−	0.0639521i
$352$	−0.540828	−	11.3534i	−0.0288262	−	0.605137i
$353$	17.6565	−	24.7951i	0.939760	−	1.31971i	−0.00774647	−	0.999970i	$-0.502466\pi$
$353$	17.6565	−	24.7951i	0.939760	−	1.31971i	0.947506	−	0.319738i	$-0.103595\pi$
$354$	3.47318	+	21.0001i	0.184597	+	1.11614i
$355$	6.87780	+	13.3411i	0.365036	+	0.708070i
$356$	0.426133	−	2.96382i	0.0225850	−	0.157082i
$357$	5.80302	−	2.96140i	0.307128	−	0.156734i
$358$	−4.09941	−	2.63453i	−0.216660	−	0.139239i
$359$	1.87832	+	9.74563i	0.0991338	+	0.514355i	0.997219	+	0.0745326i	$0.0237465\pi$
$359$	1.87832	+	9.74563i	0.0991338	+	0.514355i	−0.898085	+	0.439822i	$0.855041\pi$
$360$	6.54168	−	2.57808i	0.344777	−	0.135877i
$361$	22.3133	+	11.5033i	1.17439	+	0.605438i
$362$	20.6997	−	19.7371i	1.08795	−	1.03736i
$363$	12.2396	+	2.69712i	0.642411	+	0.141562i
$364$	0.752510	+	0.0910686i	0.0394423	+	0.00477329i
$365$	−19.0055	−	8.67952i	−0.994793	−	0.454307i
$366$	−0.614508	−	5.25973i	−0.0321208	−	0.274931i
$367$	15.7911	−	9.11701i	0.824290	−	0.475904i	−0.0276036	−	0.999619i	$-0.508788\pi$
$367$	15.7911	−	9.11701i	0.824290	−	0.475904i	0.851894	+	0.523715i	$0.175454\pi$
$368$	19.0840	+	14.3137i	0.994823	+	0.746155i
$369$	7.31457	+	14.3780i	0.380781	+	0.748488i
$370$	12.9703	−	1.86485i	0.674294	−	0.0969488i
$371$	1.04422	−	0.946531i	0.0542134	−	0.0491414i
$372$	−6.48545	+	6.45059i	−0.336255	+	0.334448i
$373$	−3.72055	−	10.7498i	−0.192643	−	0.556605i	0.806770	−	0.590865i	$-0.201214\pi$
$373$	−3.72055	−	10.7498i	−0.192643	−	0.556605i	−0.999413	+	0.0342607i	$0.989092\pi$
$374$	−1.15605	−	4.76532i	−0.0597781	−	0.246409i
$375$	0.432484	+	20.4885i	0.0223334	+	1.05802i
$376$	−1.13385	+	11.8742i	−0.0584736	+	0.612364i
$377$	−0.189407	−	0.218587i	−0.00975496	−	0.0112578i
$378$	12.4213	−	21.0491i	0.638884	−	1.08265i
$379$	1.72436	−	11.9932i	0.0885743	−	0.616048i	−0.896387	−	0.443272i	$-0.853817\pi$
$379$	1.72436	−	11.9932i	0.0885743	−	0.616048i	0.984961	−	0.172775i	$-0.0552735\pi$
$380$	7.48328	−	9.51576i	0.383884	−	0.488148i
$381$	−20.4692	+	9.87526i	−1.04867	+	0.505925i
$382$	−7.25050	+	20.9489i	−0.370968	+	1.07184i
$383$	−1.75624	−	0.167701i	−0.0897398	−	0.00856911i	0.0500895	−	0.998745i	$-0.484049\pi$
$383$	−1.75624	−	0.167701i	−0.0897398	−	0.00856911i	−0.139829	+	0.990176i	$0.544655\pi$
$384$	−9.08153	+	16.5256i	−0.463440	+	0.843316i
$385$	7.55763	−	2.80651i	0.385173	−	0.143033i
$386$	31.8164	+	27.5691i	1.61941	+	1.40323i
$387$	16.1706	+	17.1433i	0.821999	+	0.871443i
$388$	−0.244767	−	2.56331i	−0.0124262	−	0.130133i
$389$	−13.7309	−	17.4602i	−0.696184	−	0.885270i	0.301488	−	0.953470i	$-0.402517\pi$
$389$	−13.7309	−	17.4602i	−0.696184	−	0.885270i	−0.997672	+	0.0682004i	$0.978274\pi$
$390$	1.19343	+	0.0316266i	0.0604316	+	0.00160147i
$391$	6.13009	+	2.98484i	0.310012	+	0.150950i
$392$	−10.0143	−	2.97171i	−0.505801	−	0.150094i
$393$	−5.30802	+	3.95126i	−0.267754	+	0.199315i
$394$	16.6001	+	23.3116i	0.836301	+	1.17442i
$395$	2.05900	+	1.96326i	0.103600	+	0.0987822i
$396$	−4.86366	−	4.68779i	−0.244408	−	0.235570i
$397$	−7.13461	−	7.48257i	−0.358076	−	0.375539i	0.519914	−	0.854219i	$-0.325964\pi$
$397$	−7.13461	−	7.48257i	−0.358076	−	0.375539i	−0.877990	+	0.478679i	$0.841116\pi$
$398$	32.6075	−	20.9555i	1.63446	−	1.05041i
$399$	−0.125651	+	30.4330i	−0.00629044	+	1.52356i
$400$	−8.25166	−	9.52292i	−0.412583	−	0.476146i
$401$	−16.3453	−	31.7054i	−0.816244	−	1.58329i	−0.812257	−	0.583300i	$-0.801761\pi$
$401$	−16.3453	−	31.7054i	−0.816244	−	1.58329i	−0.00398679	−	0.999992i	$-0.501269\pi$
$402$	15.0228	−	18.0952i	0.749269	−	0.902504i
$403$	1.04279	−	0.417471i	0.0519452	−	0.0207957i
$404$	7.22736	−	3.72596i	0.359575	−	0.185374i
$405$	6.01032	−	12.7940i	0.298655	−	0.635741i
$406$	−2.86165	−	4.71002i	−0.142021	−	0.233754i
$407$	4.92233	+	7.65929i	0.243991	+	0.379657i
$408$	−1.12830	+	3.49713i	−0.0558594	+	0.173134i
$409$	1.33065	−	6.90405i	0.0657962	−	0.341383i	−0.934081	−	0.357062i	$-0.883779\pi$
$409$	1.33065	−	6.90405i	0.0657962	−	0.341383i	0.999877	+	0.0156783i	$0.00499076\pi$
$410$	−10.3612	+	10.8665i	−0.511701	+	0.536657i
$411$	−20.7737	−	10.1605i	−1.02469	−	0.501182i
$412$	15.4958	−	2.22796i	0.763424	−	0.109764i
$413$	7.22348	−	16.8018i	0.355444	−	0.826761i
$414$	25.4160	−	2.87617i	1.24913	−	0.141356i
$415$	−3.34656	+	5.79641i	−0.164276	+	0.284534i
$416$	−1.13680	+	0.893988i	−0.0557361	+	0.0438314i
$417$	24.1440	−	16.2464i	1.18233	−	0.795591i
$418$	22.2601	+	5.40025i	1.08878	+	0.264135i
$419$	−4.41138	+	5.09101i	−0.215510	+	0.248712i	−0.853203	−	0.521579i	$-0.825343\pi$
$419$	−4.41138	+	5.09101i	−0.215510	+	0.248712i	0.637693	+	0.770291i	$0.279889\pi$
$420$	8.19583	+	1.61474i	0.399915	+	0.0787912i
$421$	−15.4065	+	9.90113i	−0.750865	+	0.482551i	−0.859249	−	0.511558i	$-0.829069\pi$
$421$	−15.4065	+	9.90113i	−0.750865	+	0.482551i	0.108384	+	0.994109i	$0.465432\pi$
$422$	−0.0841896	+	0.881673i	−0.00409829	+	0.0429192i
$423$	14.7215	+	18.9290i	0.715785	+	0.920358i
$424$	−0.0378241	+	0.794026i	−0.00183690	+	0.0385613i
$425$	−2.83090	−	2.22624i	−0.137319	−	0.107989i
$426$	−27.5993	+	10.2094i	−1.33719	+	0.494647i
$427$	−1.99396	+	4.08981i	−0.0964946	+	0.197920i
$428$	11.1073	−	9.62454i	0.536892	−	0.465220i
$429$	0.324478	+	0.763405i	0.0156659	+	0.0368576i
$430$	−10.0510	+	19.4961i	−0.484700	+	0.940187i
$431$	−22.9713	+	5.57278i	−1.10649	+	0.268431i	−0.747070	−	0.664745i	$-0.768540\pi$
$431$	−22.9713	+	5.57278i	−1.10649	+	0.268431i	−0.359419	+	0.933176i	$0.617025\pi$
$432$	6.48760	+	25.0193i	0.312135	+	1.20374i
$433$	0.285889	+	0.973649i	0.0137390	+	0.0467906i	0.966077	−	0.258254i	$-0.0831470\pi$
$433$	0.285889	+	0.973649i	0.0137390	+	0.0467906i	−0.952338	+	0.305044i	$0.901329\pi$
$434$	20.9205	−	4.51955i	1.00421	−	0.216945i
$435$	−1.90327	−	2.55680i	−0.0912547	−	0.122589i
$436$	−2.86499	+	4.96231i	−0.137208	+	0.237652i
$437$	−25.5145	+	19.0631i	−1.22053	+	0.911911i
$438$	21.4141	−	34.9200i	1.02321	−	1.66854i
$439$	7.16489	−	17.8970i	0.341962	−	0.854179i	−0.653314	−	0.757087i	$-0.726622\pi$
$439$	7.16489	−	17.8970i	0.341962	−	0.854179i	0.995275	−	0.0970916i	$-0.0309540\pi$
$440$	−1.88895	+	4.13623i	−0.0900524	+	0.197187i
$441$	−18.7444	+	9.46830i	−0.892589	+	0.450871i
$442$	−0.408576	+	0.471522i	−0.0194340	+	0.0224280i
$443$	1.93635	+	2.03078i	0.0919985	+	0.0964853i	0.768124	−	0.640302i	$-0.221191\pi$
$443$	1.93635	+	2.03078i	0.0919985	+	0.0964853i	−0.676125	+	0.736787i	$0.736342\pi$
$444$	0.199090	+	9.43169i	0.00944839	+	0.447608i
$445$	−2.35043	+	3.30072i	−0.111421	+	0.156469i
$446$	−13.9761	+	2.69368i	−0.661789	+	0.127549i
$447$	37.2022	+	2.76153i	1.75960	+	0.130616i
$448$	−1.08554	+	0.590732i	−0.0512871	+	0.0279094i
$449$	22.8270	+	3.28203i	1.07727	+	0.154889i	0.658035	−	0.752987i	$-0.271388\pi$
$449$	22.8270	+	3.28203i	1.07727	+	0.154889i	0.419239	+	0.907876i	$0.362297\pi$
$450$	−13.4423	−	1.35672i	−0.633677	−	0.0639566i
$451$	−9.85849	−	3.41206i	−0.464218	−	0.160668i
$452$	−17.2609	−	12.2914i	−0.811883	−	0.578139i
$453$	−20.9272	+	12.6786i	−0.983244	+	0.595691i
$454$	13.2908	−	45.2642i	0.623767	−	2.12436i
$455$	−0.848669	−	0.576172i	−0.0397862	−	0.0270114i
$456$	−12.1049	−	12.1703i	−0.566865	−	0.569928i
$457$	4.31902	+	6.06522i	0.202035	+	0.283719i	0.903146	−	0.429334i	$-0.141252\pi$
$457$	4.31902	+	6.06522i	0.202035	+	0.283719i	−0.701111	+	0.713052i	$0.747312\pi$
$458$	16.5650	−	13.0269i	0.774032	−	0.608706i
$459$	3.17402	+	6.67066i	0.148151	+	0.311360i
$460$	3.81253	+	7.86697i	0.177760	+	0.366799i
$461$	−33.2899			−1.55046			−0.775232	−	0.631677i	$-0.782367\pi$
$461$	−33.2899			−1.55046			−0.775232	+	0.631677i	$0.782367\pi$
$462$	3.66291	+	15.3755i	0.170414	+	0.715333i
$463$	−7.90404	+	17.3074i	−0.367332	+	0.804345i	0.632231	+	0.774780i	$0.282139\pi$
$463$	−7.90404	+	17.3074i	−0.367332	+	0.804345i	−0.999563	+	0.0295648i	$0.990588\pi$
$464$	5.66392	+	1.37405i	0.262941	+	0.0637888i
$465$	11.8009	−	3.73732i	0.547254	−	0.173314i
$466$	−7.60993	−	31.3685i	−0.352523	−	1.45312i
$467$	−0.809332	−	16.9900i	−0.0374514	−	0.786202i	−0.936989	−	0.349359i	$-0.886399\pi$
$467$	−0.809332	−	16.9900i	−0.0374514	−	0.786202i	0.899538	−	0.436843i	$-0.143904\pi$
$468$	−0.126901	+	0.850072i	−0.00586602	+	0.0392946i
$469$	−19.2568	+	6.12530i	−0.889196	+	0.282840i
$470$	−12.0666	+	18.7760i	−0.556591	+	0.866073i
$471$	18.6146	+	3.18180i	0.857716	+	0.146610i
$472$	3.83384	+	9.57648i	0.176467	+	0.440793i
$473$	−15.2231	−	0.725166i	−0.699959	−	0.0333432i
$474$	−4.31064	+	3.53968i	−0.197994	+	0.162583i
$475$	15.3029	−	6.98860i	0.702145	−	0.320659i
$476$	−3.37033	+	2.77466i	−0.154479	+	0.127176i
$477$	1.03999	+	1.21337i	0.0476180	+	0.0555563i
$478$	−0.191777	−	0.554102i	−0.00877166	−	0.0253440i
$479$	11.4399	+	10.9080i	0.522704	+	0.498398i	0.904865	−	0.425698i	$-0.139972\pi$
$479$	11.4399	+	10.9080i	0.522704	+	0.498398i	−0.382161	+	0.924096i	$0.624820\pi$
$480$	−13.2228	+	8.89757i	−0.603534	+	0.406117i
$481$	0.430551	−	1.07546i	0.0196314	−	0.0490370i
$482$	30.1517			1.37337
$483$	−19.7195	−	9.70265i	−0.897268	−	0.441486i
$484$	−8.39822			−0.381737
$485$	−1.29510	+	3.23501i	−0.0588075	+	0.146894i
$486$	23.4674	+	14.7414i	1.06450	+	0.668682i
$487$	24.8654	+	23.7091i	1.12676	+	1.07436i	0.996560	+	0.0828722i	$0.0264093\pi$
$487$	24.8654	+	23.7091i	1.12676	+	1.07436i	0.130197	+	0.991488i	$0.458439\pi$
$488$	−0.839364	−	2.42518i	−0.0379962	−	0.109783i
$489$	4.83727	+	22.5287i	0.218749	+	1.01878i
$490$	−14.1071	−	13.5286i	−0.637295	−	0.611159i
$491$	4.92902	−	2.25101i	0.222444	−	0.101587i	−0.301076	−	0.953600i	$-0.597346\pi$
$491$	4.92902	−	2.25101i	0.222444	−	0.101587i	0.523520	+	0.852013i	$0.324619\pi$
$492$	−6.85977	−	8.35388i	−0.309263	−	0.376622i
$493$	1.66388	+	0.0792605i	0.0749375	+	0.00356971i
$494$	−1.08320	−	2.70570i	−0.0487355	−	0.121735i
$495$	2.94324	+	8.65456i	0.132289	+	0.388994i
$496$	−12.2370	+	19.0411i	−0.549457	+	0.854972i
$497$	24.6987	+	5.40999i	1.10789	+	0.242671i
$498$	−10.4836	−	7.89212i	−0.469783	−	0.353654i
$499$	−0.166242	−	3.48985i	−0.00744203	−	0.156227i	−0.999529	−	0.0306775i	$-0.990234\pi$
$499$	−0.166242	−	3.48985i	−0.00744203	−	0.156227i	0.992087	−	0.125550i	$-0.0400695\pi$
$500$	−3.23743	−	13.3449i	−0.144782	−	0.596800i
$501$	−1.56476	−	4.94086i	−0.0699083	−	0.220741i
$502$	−30.2564	−	7.34012i	−1.35041	−	0.327606i
$503$	2.79573	−	6.12180i	0.124656	−	0.272957i	−0.837008	−	0.547191i	$-0.815697\pi$
$503$	2.79573	−	6.12180i	0.124656	−	0.272957i	0.961663	+	0.274234i	$0.0884243\pi$
$504$	3.68342	−	11.2573i	0.164073	−	0.501441i
$505$	−11.0038			−0.489661
$506$	−10.5435	+	12.7456i	−0.468716	+	0.566610i
$507$	−11.7158	+	19.1049i	−0.520316	+	0.848480i
$508$	11.9706	−	9.41378i	0.531109	−	0.417669i
$509$	14.0855	+	19.7803i	0.624329	+	0.876747i	0.998723	−	0.0505227i	$-0.0160887\pi$
$509$	14.0855	+	19.7803i	0.624329	+	0.876747i	−0.374394	+	0.927270i	$0.622149\pi$
$510$	−4.87493	+	4.84873i	−0.215866	+	0.214705i
$511$	−31.6806	+	15.3333i	−1.40147	+	0.678307i
$512$	4.02770	−	13.7171i	0.178001	−	0.606216i
$513$	−34.4906	−	1.10005i	−1.52280	−	0.0485683i
$514$	37.4801	+	26.6894i	1.65318	+	1.17722i
$515$	−20.0204	−	6.92911i	−0.882202	−	0.305333i
$516$	−13.0537	−	8.88640i	−0.574658	−	0.391202i
$517$	−15.3498	−	2.20696i	−0.675082	−	0.0970621i
$518$	11.5157	−	18.8318i	0.505969	−	0.827422i
$519$	2.11323	−	28.4686i	0.0927604	−	1.24963i
$520$	0.568112	−	0.109495i	0.0249133	−	0.00480165i
$521$	6.99857	−	9.82812i	0.306613	−	0.430578i	−0.632305	−	0.774720i	$-0.717891\pi$
$521$	6.99857	−	9.82812i	0.306613	−	0.430578i	0.938918	+	0.344142i	$0.111830\pi$
$522$	5.42864	−	3.09534i	0.237605	−	0.135480i
$523$	−8.20983	−	8.61022i	−0.358991	−	0.376499i	0.519327	−	0.854575i	$-0.326183\pi$
$523$	−8.20983	−	8.61022i	−0.358991	−	0.376499i	−0.878318	+	0.478077i	$0.841334\pi$
$524$	2.90368	−	3.35102i	0.126848	−	0.146390i
$525$	9.09524	+	7.21355i	0.396949	+	0.314825i
$526$	4.95483	−	10.8496i	0.216041	−	0.473064i
$527$	−2.40433	+	6.00573i	−0.104734	+	0.261614i
$528$	−14.2491	−	8.73803i	−0.620113	−	0.380274i
$529$	−4.31092	−	22.5924i	−0.187431	−	0.982278i
$530$	−0.743702	+	1.28813i	−0.0323043	+	0.0559527i
$531$	18.8168	+	8.71619i	0.816579	+	0.378251i
$532$	−4.30618	−	19.9328i	−0.186697	−	0.864196i
$533$	0.373964	+	1.27360i	0.0161982	+	0.0551659i
$534$	−5.86398	−	5.35964i	−0.253759	−	0.231934i
$535$	−19.3284	+	4.68901i	−0.835639	+	0.202724i
$536$	5.22269	−	10.1306i	0.225586	−	0.437576i
$537$	−4.36925	+	1.85711i	−0.188547	+	0.0801401i
$538$	−20.5470	+	17.8041i	−0.885844	+	0.767589i
$539$	4.47858	−	12.8209i	0.192906	−	0.552235i
$540$	−2.08813	+	9.23880i	−0.0898589	+	0.397575i
$541$	−30.9974	−	24.3766i	−1.33268	−	1.04803i	−0.994255	−	0.107040i	$-0.965863\pi$
$541$	−30.9974	−	24.3766i	−1.33268	−	1.04803i	−0.338428	−	0.940992i	$-0.609895\pi$
$542$	1.71197	−	35.9388i	0.0735356	−	1.54370i
$543$	−4.54681	−	27.4916i	−0.195122	−	1.17978i
$544$	0.791733	−	8.29141i	0.0339453	−	0.355491i
$545$	6.52323	−	4.19223i	0.279424	−	0.179575i
$546$	1.32324	−	1.51443i	0.0566296	−	0.0648115i
$547$	9.09574	−	10.4970i	0.388906	−	0.448821i	−0.527210	−	0.849735i	$-0.676762\pi$
$547$	9.09574	−	10.4970i	0.388906	−	0.448821i	0.916116	+	0.400914i	$0.131307\pi$
$548$	15.0590	+	3.65327i	0.643289	+	0.156060i
$549$	−4.57288	−	2.38876i	−0.195166	−	0.101950i
$550$	6.86795	−	5.40101i	0.292850	−	0.230300i
$551$	−3.89064	+	6.73878i	−0.165747	+	0.287082i
$552$	11.7287	−	4.01183i	0.499205	−	0.170755i
$553$	4.75939	−	0.562132i	0.202390	−	0.0239043i
$554$	−23.0100	+	3.30834i	−0.977601	+	0.140558i
$555$	5.60913	−	11.4682i	0.238094	−	0.486796i
$556$	−13.4565	+	14.1128i	−0.570685	+	0.598517i
$557$	−0.753341	+	3.90871i	−0.0319201	+	0.165617i	−0.994391	−	0.105768i	$-0.966270\pi$
$557$	−0.753341	+	3.90871i	−0.0319201	+	0.165617i	0.962471	+	0.271386i	$0.0874819\pi$
$558$	4.46442	+	23.8547i	0.188994	+	1.00985i
$559$	1.04838	+	1.63131i	0.0443418	+	0.0689971i
$560$	20.6648	−	0.462259i	0.873248	−	0.0195340i
$561$	−4.47160	−	1.68156i	−0.188791	−	0.0709955i
$562$	43.6305	−	22.4931i	1.84044	−	0.948814i
$563$	−28.7924	+	11.5267i	−1.21345	+	0.485794i	−0.888035	−	0.459776i	$-0.847930\pi$
$563$	−28.7924	+	11.5267i	−1.21345	+	0.485794i	−0.325419	+	0.945570i	$0.605505\pi$
$564$	−12.3630	−	10.2639i	−0.520574	−	0.432187i
$565$	13.1399	+	25.4879i	0.552802	+	1.07229i
$566$	30.7243	+	35.4577i	1.29144	+	1.49040i
$567$	−10.1421	−	21.5439i	−0.425927	−	0.904757i
$568$	−11.9972	+	7.71012i	−0.503391	+	0.323509i
$569$	13.4763	+	14.1335i	0.564955	+	0.592508i	0.942799	−	0.333361i	$-0.108183\pi$
$569$	13.4763	+	14.1335i	0.564955	+	0.592508i	−0.377844	+	0.925869i	$0.623334\pi$
$570$	−9.69712	−	30.6194i	−0.406168	−	1.28251i
$571$	−22.5526	−	21.5039i	−0.943797	−	0.899908i	0.0513133	−	0.998683i	$-0.483659\pi$
$571$	−22.5526	−	21.5039i	−0.943797	−	0.899908i	−0.995110	+	0.0987744i	$0.968508\pi$
$572$	−0.322413	−	0.452766i	−0.0134808	−	0.0189311i
$573$	12.8963	+	17.3246i	0.538752	+	0.723745i
$574$	2.96668	+	25.1179i	0.123827	+	1.04840i
$575$	−0.300365	+	12.1451i	−0.0125261	+	0.506484i
$576$	−0.635410	−	1.24900i	−0.0264754	−	0.0520418i
$577$	23.0660	+	29.3309i	0.960252	+	1.22106i	0.975235	+	0.221172i	$0.0709881\pi$
$577$	23.0660	+	29.3309i	0.960252	+	1.22106i	−0.0149831	+	0.999888i	$0.504769\pi$
$578$	2.53129	+	26.5089i	0.105288	+	1.10262i
$579$	39.6465	−	10.5088i	1.64765	−	0.436732i
$580$	1.61414	+	1.39866i	0.0670236	+	0.0580763i
$581$	3.92499	+	10.5696i	0.162836	+	0.438500i
$582$	−5.98726	−	3.29027i	−0.248180	−	0.136386i
$583$	−1.02879	−	0.0982374i	−0.0426081	−	0.00406858i
$584$	6.49284	−	18.7598i	0.268676	−	0.776287i
$585$	0.679771	−	0.943799i	0.0281051	−	0.0390213i
$586$	13.7361	−	17.4669i	0.567434	−	0.721551i
$587$	2.85749	−	19.8742i	0.117941	−	0.820298i	−0.841876	−	0.539671i	$-0.818549\pi$
$587$	2.85749	−	19.8742i	0.117941	−	0.820298i	0.959817	−	0.280627i	$-0.0905423\pi$
$588$	10.9006	−	8.89875i	0.449532	−	0.366978i
$589$	−19.7893	−	22.8381i	−0.815403	−	0.941026i
$590$	−1.83471	+	19.2140i	−0.0755338	+	0.791026i
$591$	27.8752	−	0.588407i	1.14663	−	0.0242038i
$592$	5.50342	+	22.6854i	0.226189	+	0.932364i
$593$	−1.14186	−	3.29919i	−0.0468905	−	0.135481i	0.919124	−	0.393967i	$-0.128898\pi$
$593$	−1.14186	−	3.29919i	−0.0468905	−	0.135481i	−0.966015	+	0.258486i	$0.916776\pi$
$594$	−17.5427	+	3.66793i	−0.719787	+	0.150497i
$595$	5.77450	−	1.24749i	0.236732	−	0.0511423i
$596$	−24.7425	+	3.55743i	−1.01349	+	0.145718i
$597$	1.00039	−	37.7497i	0.0409432	−	1.54499i
$598$	2.09917	+	0.152091i	0.0858415	+	0.00621945i
$599$	11.5710	−	6.68055i	0.472780	−	0.272960i	−0.244623	−	0.969618i	$-0.578664\pi$
$599$	11.5710	−	6.68055i	0.472780	−	0.272960i	0.717403	+	0.696659i	$0.245331\pi$
$600$	−6.50333	+	0.759801i	−0.265497	+	0.0310187i
$601$	−22.8087	−	10.4164i	−0.930386	−	0.424893i	−0.108211	−	0.994128i	$-0.534512\pi$
$601$	−22.8087	−	10.4164i	−0.930386	−	0.424893i	−0.822175	+	0.569235i	$0.807239\pi$
$602$	14.4965	+	33.9870i	0.590831	+	1.38521i
$603$	−6.33681	−	22.0195i	−0.258055	−	0.896702i
$604$	11.8660	−	11.3142i	0.482822	−	0.460370i
$605$	10.1016	+	5.20775i	0.410689	+	0.211725i
$606$	2.61889	−	21.4139i	0.106385	−	0.869880i
$607$	−0.0247571	−	0.128452i	−0.00100486	−	0.00521371i	0.981423	−	0.191857i	$-0.0614511\pi$
$607$	−0.0247571	−	0.128452i	−0.00100486	−	0.00521371i	−0.982428	+	0.186644i	$0.940239\pi$
$608$	32.7312	+	21.0351i	1.32743	+	0.853085i
$609$	−5.36216	−	0.277625i	−0.217286	−	0.0112499i
$610$	0.683383	−	4.75304i	0.0276694	−	0.192445i
$611$	0.904148	+	1.75380i	0.0365779	+	0.0709513i
$612$	−3.03891	−	3.90744i	−0.122841	−	0.157949i
$613$	12.6778	−	17.8035i	0.512052	−	0.719076i	−0.474909	−	0.880035i	$-0.657519\pi$
$613$	12.6778	−	17.8035i	0.512052	−	0.719076i	0.986961	+	0.160959i	$0.0514586\pi$
$614$	−2.07499	−	43.5595i	−0.0837400	−	1.75792i
$615$	3.07088	+	14.3020i	0.123830	+	0.576714i
$616$	3.33705	+	6.89475i	0.134454	+	0.277797i
$617$	−2.60088	−	8.85779i	−0.104708	−	0.356601i	0.890427	−	0.455126i	$-0.150406\pi$
$617$	−2.60088	−	8.85779i	−0.104708	−	0.356601i	−0.995135	+	0.0985248i	$0.968588\pi$
$618$	18.2493	−	37.3116i	0.734093	−	1.50089i
$619$	1.37296	+	1.74586i	0.0551840	+	0.0701721i	0.812862	−	0.582457i	$-0.197908\pi$
$619$	1.37296	+	1.74586i	0.0551840	+	0.0701721i	−0.757678	+	0.652629i	$0.773666\pi$
$620$	−7.18332	+	4.14729i	−0.288489	+	0.166559i
$621$	11.6180	−	22.0459i	0.466216	−	0.884671i
$622$		−	1.33434i		−	0.0535021i
$623$	1.75721	+	6.59582i	0.0704011	+	0.264256i
$624$	0.146005	+	2.12175i	0.00584489	+	0.0849380i
$625$	−1.39497	+	5.75016i	−0.0557989	+	0.230006i
$626$	39.0953	+	7.53499i	1.56256	+	0.301159i
$627$	16.5533	−	14.9667i	0.661076	−	0.597712i
$628$	−12.6398	+	0.602107i	−0.504382	+	0.0240267i
$629$	2.77157	+	6.06889i	0.110510	+	0.241983i
$630$	15.7780	−	15.5641i	0.628609	−	0.620089i
$631$	−2.34423	−	1.50654i	−0.0933222	−	0.0599746i	0.493147	−	0.869946i	$-0.335846\pi$
$631$	−2.34423	−	1.50654i	−0.0933222	−	0.0599746i	−0.586470	+	0.809971i	$0.699483\pi$
$632$	−1.67094	+	2.12478i	−0.0664666	+	0.0845191i
$633$	0.663907	+	0.551183i	0.0263879	+	0.0219075i
$634$	−2.02434	+	42.4962i	−0.0803969	+	1.68774i
$635$	−20.2361	+	3.90018i	−0.803044	+	0.154774i
$636$	−0.855514	−	0.644034i	−0.0339233	−	0.0255376i
$637$	−1.65935	+	0.482065i	−0.0657460	+	0.0191001i
$638$	−1.13856	+	3.87757i	−0.0450759	+	0.153515i
$639$	−6.90918	+	27.8247i	−0.273323	+	1.10073i
$640$	−11.7996	+	12.3751i	−0.466420	+	0.489167i
$641$	2.08923	+	21.8794i	0.0825195	+	0.864183i	0.938066	+	0.346457i	$0.112615\pi$
$641$	2.08923	+	21.8794i	0.0825195	+	0.864183i	−0.855546	+	0.517726i	$0.826779\pi$
$642$	−4.52493	−	38.7300i	−0.178585	−	1.52855i
$643$			17.2151i			0.678898i	0.940624	+	0.339449i	$0.110241\pi$
$643$			17.2151i			0.678898i	−0.940624	+	0.339449i	$0.889759\pi$
$644$	14.3031	+	3.50567i	0.563621	+	0.138143i
$645$	10.1909	+	18.7834i	0.401267	+	0.739597i
$646$	15.5829	+	6.23845i	0.613100	+	0.245448i
$647$	−40.7505	+	3.89120i	−1.60207	+	0.152979i	−0.857470	−	0.514534i	$-0.827965\pi$
$647$	−40.7505	+	3.89120i	−1.60207	+	0.152979i	−0.744598	+	0.667513i	$0.767359\pi$
$648$	12.6438	+	4.52923i	0.496695	+	0.177925i
$649$	−12.6733	+	4.38626i	−0.497469	+	0.172176i
$650$	−1.06667	−	0.313203i	−0.0418384	−	0.0122848i
$651$	7.82984	−	19.3263i	0.306876	−	0.757459i
$652$	−6.41401	−	14.0447i	−0.251192	−	0.550034i
$653$	−6.03356	−	31.3051i	−0.236111	−	1.22506i	−0.885512	−	0.464616i	$-0.846192\pi$
$653$	−6.03356	−	31.3051i	−0.236111	−	1.22506i	0.649401	−	0.760446i	$-0.275020\pi$
$654$	6.60577	+	13.6923i	0.258306	+	0.535411i
$655$	−5.57060	+	2.23013i	−0.217661	+	0.0871384i
$656$	−21.0248	−	16.5341i	−0.820882	−	0.645549i
$657$	−16.3828	−	36.3910i	−0.639154	−	1.41975i
$658$	11.3965	+	35.8285i	0.444283	+	1.39674i
$659$	−4.76260	+	2.17501i	−0.185525	+	0.0847262i	−0.506012	−	0.862527i	$-0.668881\pi$
$659$	−4.76260	+	2.17501i	−0.185525	+	0.0847262i	0.320487	+	0.947253i	$0.396153\pi$
$660$	−3.17397	−	5.23894i	−0.123547	−	0.203925i
$661$	−10.2406	+	2.48433i	−0.398312	+	0.0966293i	−0.429911	−	0.902871i	$-0.641455\pi$
$661$	−10.2406	+	2.48433i	−0.398312	+	0.0966293i	0.0315995	+	0.999501i	$0.489940\pi$
$662$	5.21590	−	27.0626i	0.202722	−	1.05182i
$663$	0.155742	+	0.587564i	0.00604851	+	0.0228191i
$664$	−5.78465	−	2.64176i	−0.224488	−	0.102520i
$665$	−7.18075	+	26.6460i	−0.278458	+	1.03329i
$666$	20.9827	+	13.6451i	0.813062	+	0.528736i
$667$	−3.14530	−	4.65646i	−0.121786	−	0.180299i
$668$	1.73641	+	3.00755i	0.0671836	+	0.116365i
$669$	−5.49307	+	12.7326i	−0.212374	+	0.492272i
$670$	17.3719	−	12.3705i	0.671136	−	0.477914i
$671$	3.20129	−	0.939983i	0.123584	−	0.0362876i
$672$	−2.66235	+	26.7153i	−0.102702	+	1.03056i
$673$	42.9095	+	12.5994i	1.65404	+	0.485669i	0.969864	−	0.243649i	$-0.0783444\pi$
$673$	42.9095	+	12.5994i	1.65404	+	0.485669i	0.684175	+	0.729318i	$0.260163\pi$
$674$	−38.7064	+	1.84381i	−1.49092	+	0.0710211i
$675$	−8.46244	+	10.0821i	−0.325720	+	0.388059i
$676$	4.91163	−	14.1912i	0.188909	−	0.545817i
$677$	14.1040	−	7.27111i	0.542061	−	0.279452i	−0.165374	−	0.986231i	$-0.552883\pi$
$677$	14.1040	−	7.27111i	0.542061	−	0.279452i	0.707434	+	0.706779i	$0.249853\pi$
$678$	−52.7282	+	19.5049i	−2.02501	+	0.749082i
$679$	2.80579	+	5.15599i	0.107676	+	0.197869i
$680$	−1.80148	+	2.80316i	−0.0690837	+	0.107496i
$681$	−29.1673	−	35.5201i	−1.11769	−	1.36113i
$682$	−12.7844	−	9.10373i	−0.489540	−	0.348600i
$683$	−15.5119	+	30.0888i	−0.593545	+	1.15132i	0.380461	+	0.924797i	$0.375765\pi$
$683$	−15.5119	+	30.0888i	−0.593545	+	1.15132i	−0.974006	+	0.226521i	$0.927265\pi$
$684$	22.7285	−	4.25365i	0.869044	−	0.162642i
$685$	−15.8480	−	13.7324i	−0.605521	−	0.524687i
$686$	−32.7092	+	3.76818i	−1.24884	+	0.143870i
$687$	−1.40950	−	20.4828i	−0.0537757	−	0.781468i
$688$	−36.2759	−	14.5227i	−1.38301	−	0.553672i
$689$	0.0657479	+	0.113879i	0.00250479	+	0.00433843i
$690$	22.9459	+	3.38397i	0.873535	+	0.128826i
$691$	32.3472	+	18.6757i	1.23055	+	0.710456i	0.967144	−	0.254230i	$-0.0818220\pi$
$691$	32.3472	+	18.6757i	1.23055	+	0.710456i	0.263402	+	0.964686i	$0.415155\pi$
$692$	2.72228	+	18.9339i	0.103486	+	0.719759i
$693$	14.3910	+	5.47971i	0.546669	+	0.208157i
$694$	−8.97206	+	2.63443i	−0.340575	+	0.100002i
$695$	24.9373	−	8.63088i	0.945925	−	0.327388i
$696$	2.24640	−	2.03108i	0.0851495	−	0.0769880i
$697$	−6.79488	−	3.50300i	−0.257374	−	0.132686i
$698$	−33.8265	−	3.23004i	−1.28035	−	0.122259i
$699$	−29.4351	−	11.0692i	−1.11334	−	0.418674i
$700$	−6.99190	−	3.40886i	−0.264269	−	0.128843i
$701$	−46.6130	−	6.70194i	−1.76055	−	0.253129i	−0.815199	−	0.579181i	$-0.803372\pi$
$701$	−46.6130	−	6.70194i	−1.76055	−	0.253129i	−0.945352	+	0.326052i	$0.894281\pi$
$702$	1.67490	+	1.54749i	0.0632150	+	0.0584064i
$703$	−31.1306	−	1.48293i	−1.17411	−	0.0559299i
$704$	0.856399	+	0.296403i	0.0322768	+	0.0111711i
$705$	8.50588	+	20.0120i	0.320350	+	0.753694i
$706$	29.2569	+	45.5246i	1.10110	+	1.71334i
$707$	−11.8224	+	14.2767i	−0.444625	+	0.536932i
$708$	−13.5701	−	2.99032i	−0.509997	−	0.112383i
$709$	4.37765	−	18.0449i	0.164406	−	0.677692i	−0.828621	−	0.559809i	$-0.810874\pi$
$709$	4.37765	−	18.0449i	0.164406	−	0.677692i	0.993028	−	0.117882i	$-0.0376105\pi$
$710$	−26.5634	+	2.53650i	−0.996906	+	0.0951930i
$711$	0.487390	+	5.41226i	0.0182786	+	0.202975i
$712$	−3.33420	−	1.92500i	−0.124954	−	0.0721424i
$713$	21.0842	−	5.62857i	0.789610	−	0.210791i
$714$	1.05336	+	11.5344i	0.0394211	+	0.431664i
$715$	0.107047	+	0.744528i	0.00400333	+	0.0278438i
$716$	2.59135	−	1.84529i	0.0968432	−	0.0689617i
$717$	−0.551393	−	0.149339i	−0.0205922	−	0.00557717i
$718$	−17.3259	−	3.33929i	−0.646596	−	0.124621i
$719$	2.51721	−	2.40016i	0.0938762	−	0.0895108i	−0.641688	−	0.766966i	$-0.721766\pi$
$719$	2.51721	−	2.40016i	0.0938762	−	0.0895108i	0.735564	+	0.677455i	$0.236917\pi$
$720$	−0.126303	+	23.4372i	−0.00470704	+	0.873454i
$721$	−30.4999	+	18.5307i	−1.13587	+	0.690119i
$722$	−33.7292	+	29.2266i	−1.25527	+	1.08770i
$723$	16.5307	−	24.2829i	0.614785	−	0.903092i
$724$	6.93958	+	17.3342i	0.257908	+	0.644222i
$725$	1.10314	+	2.75550i	0.0409694	+	0.102337i
$726$	−12.5387	+	18.4188i	−0.465356	+	0.683588i
$727$	−12.1224	+	10.5041i	−0.449595	+	0.389576i	−0.850018	−	0.526754i	$-0.823409\pi$
$727$	−12.1224	+	10.5041i	−0.449595	+	0.389576i	0.400423	+	0.916331i	$0.368863\pi$
$728$	0.468312	−	0.854733i	0.0173568	−	0.0316785i
$729$	24.7382	−	10.8177i	0.916229	−	0.400655i
$730$	26.8830	−	25.6329i	0.994984	−	0.948716i
$731$	−10.9662	−	2.11357i	−0.405601	−	0.0781732i
$732$	3.33684	+	0.903748i	0.123333	+	0.0334035i
$733$	−15.2823	+	10.8825i	−0.564463	+	0.401952i	−0.826359	−	0.563144i	$-0.809592\pi$
$733$	−15.2823	+	10.8825i	−0.564463	+	0.401952i	0.261896	+	0.965096i	$0.415652\pi$
$734$	4.61337	+	32.0867i	0.170282	+	1.18434i
$735$	−18.6296	+	3.94422i	−0.687165	+	0.145485i
$736$	−24.0050	+	14.6013i	−0.884837	+	0.538213i
$737$	12.8326	+	7.40892i	0.472696	+	0.272911i
$738$	−28.5634	+	2.57222i	−1.05143	+	0.0946848i
$739$	−7.90177	+	0.754527i	−0.290671	+	0.0277557i	−0.239373	−	0.970928i	$-0.576942\pi$
$739$	−7.90177	+	0.754527i	−0.290671	+	0.0277557i	−0.0512981	+	0.998683i	$0.516336\pi$
$740$	−2.01679	+	8.31333i	−0.0741388	+	0.305604i
$741$	−2.77293	−	0.611044i	−0.101866	−	0.0224473i
$742$	0.872246	+	2.34887i	0.0320212	+	0.0862296i
$743$	19.7635	+	30.7526i	0.725051	+	1.12820i	0.986623	+	0.163018i	$0.0521228\pi$
$743$	19.7635	+	30.7526i	0.725051	+	1.12820i	−0.261572	+	0.965184i	$0.584241\pi$
$744$	4.60067	+	10.8241i	0.168669	+	0.396830i
$745$	31.9669	+	11.0639i	1.17118	+	0.405348i
$746$	20.2005	+	0.962269i	0.739593	+	0.0352312i
$747$	−12.1037	+	4.11622i	−0.442850	+	0.150605i
$748$	3.16859	+	0.455575i	0.115855	+	0.0166575i
$749$	−14.6825	+	30.1153i	−0.536488	+	1.10039i
$750$	−34.1013	−	12.8239i	−1.24520	−	0.468262i
$751$	2.36240	+	0.225582i	0.0862052	+	0.00823160i	0.138069	−	0.990423i	$-0.455910\pi$
$751$	2.36240	+	0.225582i	0.0862052	+	0.00823160i	−0.0518643	+	0.998654i	$0.516516\pi$
$752$	−35.3402	−	18.2191i	−1.28872	−	0.664383i
$753$	−22.4996	+	20.3430i	−0.819930	+	0.741341i
$754$	0.485920	−	0.168178i	0.0176962	−	0.00612470i
$755$	−21.2888	+	6.25095i	−0.774778	+	0.227495i
$756$	9.74335	+	12.6353i	0.354362	+	0.459543i
$757$	5.42865	+	37.7571i	0.197308	+	1.37230i	0.812055	+	0.583581i	$0.198349\pi$
$757$	5.42865	+	37.7571i	0.197308	+	1.37230i	−0.614748	+	0.788724i	$0.710742\pi$
$758$	18.6549	+	10.7704i	0.677577	+	0.391199i
$759$	4.48426	+	15.4791i	0.162768	+	0.561856i
$760$	−7.78264	−	13.4799i	−0.282306	−	0.488969i
$761$	8.74845	+	3.50235i	0.317131	+	0.126960i	0.524767	−	0.851246i	$-0.324153\pi$
$761$	8.74845	+	3.50235i	0.317131	+	0.126960i	−0.207636	+	0.978206i	$0.566577\pi$
$762$	−2.77379	−	40.3087i	−0.100484	−	1.46023i
$763$	1.56934	−	12.9676i	0.0568138	−	0.469459i
$764$	−10.9372	−	9.47717i	−0.395696	−	0.342872i
$765$	1.23228	+	6.58440i	0.0445531	+	0.238060i
$766$	1.43721	−	2.78780i	0.0519286	−	0.100727i
$767$	1.38996	+	0.989786i	0.0501885	+	0.0357391i
$768$	−22.3011	−	27.1584i	−0.804722	−	0.979996i
$769$	−15.0558	+	23.4274i	−0.542928	+	0.844812i	−0.998981	−	0.0451407i	$-0.985626\pi$
$769$	−15.0558	+	23.4274i	−0.542928	+	0.844812i	0.456053	+	0.889953i	$0.349263\pi$
$770$	−0.361632	+	14.3280i	−0.0130323	+	0.516344i
$771$	42.0431	−	15.5524i	1.51415	−	0.560105i
$772$	−24.4284	+	12.5937i	−0.879197	+	0.453258i
$773$	−0.558782	+	1.61450i	−0.0200980	+	0.0580694i	−0.954604	−	0.297879i	$-0.903721\pi$
$773$	−0.558782	+	1.61450i	−0.0200980	+	0.0580694i	0.934506	+	0.355948i	$0.115842\pi$
$774$	−38.9790	+	15.3616i	−1.40107	+	0.552163i
$775$	−11.5138	+	0.548470i	−0.413588	+	0.0197016i
$776$	−3.17673	−	0.932772i	−0.114038	−	0.0334845i
$777$	−8.85288	−	19.5988i	−0.317595	−	0.703104i
$778$	37.8901	−	11.1255i	1.35843	−	0.398870i
$779$	29.0889	−	20.7141i	1.04222	−	0.742161i
$780$	−0.308732	+	0.715623i	−0.0110544	+	0.0256234i
$781$	−9.27028	−	16.0566i	−0.331717	−	0.574550i
$782$	−8.97679	+	8.14527i	−0.321009	+	0.291274i
$783$	0.483406	−	6.06904i	0.0172755	−	0.216890i
$784$	21.6024	−	27.3081i	0.771513	−	0.975288i
$785$	15.5769	+	7.11371i	0.555962	+	0.253899i
$786$	−3.01415	−	11.3715i	−0.107511	−	0.405606i
$787$	−9.71824	+	50.4230i	−0.346418	+	1.79739i	0.222435	+	0.974947i	$0.428599\pi$
$787$	−9.71824	+	50.4230i	−0.346418	+	1.79739i	−0.568853	+	0.822439i	$0.692613\pi$
$788$	−18.1561	+	4.40462i	−0.646783	+	0.156908i
$789$	−6.02130	−	9.93873i	−0.214364	−	0.353828i
$790$	−4.60076	+	2.10110i	−0.163688	+	0.0747536i
$791$	47.1866	+	10.3357i	1.67776	+	0.367496i
$792$	−7.91991	+	3.56544i	−0.281422	+	0.126693i
$793$	−0.333695	−	0.262420i	−0.0118498	−	0.00931882i
$794$	17.0638	−	6.83133i	0.605573	−	0.242435i
$795$	0.629670	+	1.30517i	0.0223321	+	0.0462895i
$796$	4.78882	+	24.8468i	0.169735	+	0.880670i
$797$	9.01600	+	19.7423i	0.319363	+	0.699308i	0.999427	−	0.0338452i	$-0.0107753\pi$
$797$	9.01600	+	19.7423i	0.319363	+	0.699308i	−0.680064	+	0.733153i	$0.738048\pi$
$798$	−50.1455	−	20.3159i	−1.77513	−	0.719173i
$799$	−10.9036	−	3.20158i	−0.385741	−	0.113264i
$800$	14.0248	−	4.85403i	0.495852	−	0.171616i
$801$	−7.53138	+	1.78417i	−0.266108	+	0.0630406i
$802$	63.1286	−	6.02805i	2.22915	−	0.212858i
$803$	23.9600	+	9.59215i	0.845531	+	0.338500i
$804$	7.32185	+	13.4953i	0.258222	+	0.475942i
$805$	−15.0303	−	13.0861i	−0.529749	−	0.461224i
$806$			1.99693i			0.0703389i
$807$	3.07373	+	26.3089i	0.108200	+	0.926116i
$808$	−0.993811	−	10.4077i	−0.0349621	−	0.366140i
$809$	32.3464	−	33.9239i	1.13724	−	1.19270i	0.158550	−	0.987351i	$-0.449318\pi$
$809$	32.3464	−	33.9239i	1.13724	−	1.19270i	0.978688	−	0.205351i	$-0.0658335\pi$
$810$	17.1448	+	18.3734i	0.602406	+	0.645575i
$811$	8.65769	−	29.4854i	0.304013	−	1.03537i	−0.655847	−	0.754893i	$-0.727689\pi$
$811$	8.65769	−	29.4854i	0.304013	−	1.03537i	0.959860	−	0.280479i	$-0.0904933\pi$
$812$	3.54891	−	0.591545i	0.124542	−	0.0207592i
$813$	−28.0050	−	21.0823i	−0.982179	−	0.739388i
$814$	−15.8938	+	3.06327i	−0.557076	+	0.107368i
$815$	−0.994195	+	20.8707i	−0.0348251	+	0.731069i
$816$	−9.42412	−	7.82401i	−0.329910	−	0.273895i
$817$	32.2488	−	41.0077i	1.12824	−	1.43468i
$818$	10.5156	+	6.75800i	0.367671	+	0.236288i
$819$	−0.494185	−	1.89598i	−0.0172682	−	0.0662508i
$820$	−4.07185	−	8.91611i	−0.142195	−	0.311364i
$821$	−23.0137	+	1.09628i	−0.803185	+	0.0382604i	−0.445159	−	0.895451i	$-0.646853\pi$
$821$	−23.0137	+	1.09628i	−0.803185	+	0.0382604i	−0.358025	+	0.933712i	$0.616550\pi$
$822$	30.4957	−	27.5727i	1.06366	−	0.961710i
$823$	−39.2244	−	7.55988i	−1.36728	−	0.263521i	−0.547788	−	0.836617i	$-0.684530\pi$
$823$	−39.2244	−	7.55988i	−1.36728	−	0.263521i	−0.819488	+	0.573096i	$0.805742\pi$
$824$	4.74560	−	19.5616i	0.165321	−	0.681462i
$825$	−0.584385	−	8.49229i	−0.0203457	−	0.295663i
$826$	22.9578	+	23.0238i	0.798804	+	0.801099i
$827$			40.3559i			1.40331i	0.712516	+	0.701656i	$0.247556\pi$
$827$			40.3559i			1.40331i	−0.712516	+	0.701656i	$0.752444\pi$
$828$	−4.42360	+	16.1016i	−0.153731	+	0.559570i
$829$	−35.0405	+	20.2306i	−1.21701	+	0.702639i	−0.964276	−	0.264898i	$-0.914662\pi$
$829$	−35.0405	+	20.2306i	−1.21701	+	0.702639i	−0.252730	+	0.967537i	$0.581328\pi$
$830$	−7.35552	−	9.35331i	−0.255314	−	0.324658i
$831$	−9.95089	+	20.3451i	−0.345193	+	0.705764i
$832$	−0.0324859	−	0.110637i	−0.00112625	−	0.00383565i
$833$	4.58553	−	8.83239i	0.158879	−	0.306024i
$834$	10.8611	+	50.5834i	0.376089	+	1.75156i
$835$	−0.223618	−	4.69431i	−0.00773860	−	0.162453i
$836$	−8.67393	+	12.1808i	−0.299994	+	0.421283i
$837$	21.6592	+	9.48292i	0.748651	+	0.327778i
$838$	−5.48771	−	10.6447i	−0.189570	−	0.367714i
$839$	−6.40818	+	44.5699i	−0.221235	+	1.53872i	0.512142	+	0.858901i	$0.328852\pi$
$839$	−6.40818	+	44.5699i	−0.221235	+	1.53872i	−0.733377	+	0.679822i	$0.762057\pi$
$840$	5.84405	−	9.01150i	0.201639	−	0.310926i
$841$	23.2414	+	14.9364i	0.801429	+	0.515047i
$842$	−6.16169	−	31.9699i	−0.212346	−	1.10175i
$843$	5.80553	−	47.4701i	0.199953	−	1.63496i
$844$	−0.513925	−	0.264947i	−0.0176900	−	0.00911985i
$845$	−14.7079	+	14.0239i	−0.505966	+	0.482437i
$846$	−40.9687	+	11.7901i	−1.40853	+	0.405351i
$847$	17.6099	−	7.51111i	0.605082	−	0.258085i
$848$	−2.41027	−	1.10073i	−0.0827690	−	0.0377993i
$849$	45.4008	−	5.30430i	1.55815	−	0.182043i
$850$	5.54482	−	3.20131i	0.190186	−	0.109804i
$851$	10.8044	−	19.7433i	0.370371	−	0.676792i
$852$	0.508922	−	19.2041i	0.0174354	−	0.657923i
$853$	−2.10640	+	0.302854i	−0.0721217	+	0.0103695i	−0.178281	−	0.983980i	$-0.557054\pi$
$853$	−2.10640	+	0.302854i	−0.0721217	+	0.0103695i	0.106160	+	0.994349i	$0.466145\pi$
$854$	−5.43257	−	5.99328i	−0.185899	−	0.205086i
$855$	−29.9761	−	8.97753i	−1.02516	−	0.307025i
$856$	−6.18066	−	17.8578i	−0.211251	−	0.610368i
$857$	−11.2382	−	46.3245i	−0.383890	−	1.58242i	−0.756222	−	0.654316i	$-0.772957\pi$
$857$	−11.2382	−	46.3245i	−0.383890	−	1.58242i	0.372332	−	0.928100i	$-0.378558\pi$
$858$	−1.47437	+	0.0311219i	−0.0503341	+	0.00106248i
$859$	5.07810	−	53.1803i	0.173263	−	1.81449i	−0.323092	−	0.946368i	$-0.604722\pi$
$859$	5.07810	−	53.1803i	0.173263	−	1.81449i	0.496355	−	0.868120i	$-0.334672\pi$
$860$	−9.37726	−	10.8219i	−0.319762	−	0.369025i
$861$	21.8554	+	11.3817i	0.744830	+	0.387888i
$862$	5.98052	−	41.5954i	0.203697	−	1.41675i
$863$	4.32282	−	5.49692i	0.147151	−	0.187117i	−0.706890	−	0.707323i	$-0.749902\pi$
$863$	4.32282	−	5.49692i	0.147151	−	0.187117i	0.854041	+	0.520206i	$0.174145\pi$
$864$	−30.1968	−	3.85830i	−1.02732	−	0.131262i
$865$	8.46649	−	24.4623i	0.287869	−	0.831744i
$866$	−1.79587	−	0.171485i	−0.0610261	−	0.00582729i
$867$	22.7370	+	12.4950i	0.772188	+	0.424352i
$868$	−2.33683	+	13.7758i	−0.0793172	+	0.467580i
$869$	−2.65589	−	2.30134i	−0.0900949	−	0.0780677i
$870$	5.47747	−	1.45188i	0.185704	−	0.0492233i
$871$	−0.179217	−	1.87684i	−0.00607253	−	0.0635944i
$872$	4.55427	+	5.79123i	0.154227	+	0.196116i
$873$	−5.93238	+	3.01800i	−0.200781	+	0.102144i
$874$	−14.6043	−	54.7066i	−0.493997	−	1.85048i
$875$	18.7236	+	25.0868i	0.632975	+	0.848088i
$876$	15.9681	+	21.4511i	0.539511	+	0.724765i
$877$	15.7765	+	22.1550i	0.532735	+	0.748121i	0.989978	−	0.141220i	$-0.0451026\pi$
$877$	15.7765	+	22.1550i	0.532735	+	0.748121i	−0.457243	+	0.889342i	$0.651163\pi$
$878$	24.8042	+	23.6508i	0.837101	+	0.798174i
$879$	−6.53626	−	20.6388i	−0.220463	−	0.696129i
$880$	−10.4595	−	10.9696i	−0.352590	−	0.369786i
$881$	32.4236	−	20.8374i	1.09238	−	0.702029i	0.134994	−	0.990846i	$-0.456898\pi$
$881$	32.4236	−	20.8374i	1.09238	−	0.702029i	0.957384	+	0.288817i	$0.0932620\pi$
$882$	−3.24181	−	37.1930i	−0.109158	−	1.25235i
$883$	12.5915	+	14.5314i	0.423737	+	0.489019i	0.926972	−	0.375131i	$-0.122402\pi$
$883$	12.5915	+	14.5314i	0.423737	+	0.489019i	−0.503234	+	0.864150i	$0.667857\pi$
$884$	−0.186640	−	0.362031i	−0.00627738	−	0.0121764i
$885$	14.4682	+	12.0117i	0.486345	+	0.403769i
$886$	−4.63116	+	1.85403i	−0.155587	+	0.0622875i
$887$	13.3874	−	6.90170i	0.449506	−	0.231736i	−0.218582	−	0.975819i	$-0.570143\pi$
$887$	13.3874	−	6.90170i	0.449506	−	0.231736i	0.668088	+	0.744082i	$0.267113\pi$
$888$	11.3535	+	4.26952i	0.380999	+	0.143276i
$889$	−16.6812	+	30.4455i	−0.559470	+	1.02111i
$890$	−3.89468	−	6.06023i	−0.130550	−	0.203140i
$891$	−6.66385	+	16.1391i	−0.223247	+	0.540682i
$892$	1.75851	−	9.12403i	0.0588794	−	0.305495i
$893$	36.6321	−	38.4186i	1.22585	−	1.28563i
$894$	−29.1390	+	59.5761i	−0.974552	+	1.99252i
$895$	−4.26121	+	0.612670i	−0.142437	+	0.0204793i
$896$	3.37854	+	28.6050i	0.112869	+	0.955625i
$897$	1.27336	−	1.60720i	0.0425164	−	0.0536629i
$898$	−20.4997	+	35.5065i	−0.684084	+	1.18487i
$899$	4.19088	−	3.29575i	0.139774	−	0.109919i
$900$	4.08381	−	7.81775i	0.136127	−	0.260592i
$901$	−0.735972	−	0.178545i	−0.0245188	−	0.00594819i
$902$	12.1454	−	14.0166i	0.404398	−	0.466700i
$903$	35.3195	+	6.95864i	1.17536	+	0.231569i
$904$	−22.9205	+	14.7301i	−0.762323	+	0.489915i
$905$	2.40185	−	25.1534i	0.0798404	−	0.836126i
$906$	−7.09796	−	42.9168i	−0.235814	−	1.42582i
$907$	1.43441	−	30.1119i	0.0476287	−	0.999850i	−0.840946	−	0.541118i	$-0.818001\pi$
$907$	1.43441	−	30.1119i	0.0476287	−	0.999850i	0.888575	−	0.458731i	$-0.151696\pi$
$908$	24.2083	+	19.0376i	0.803382	+	0.631787i
$909$	−15.8101	−	13.8494i	−0.524387	−	0.459354i
$910$	1.51170	−	1.01999i	0.0501125	−	0.0338124i
$911$	−20.1002	+	17.4169i	−0.665948	+	0.577048i	−0.920849	−	0.389920i	$-0.872503\pi$
$911$	−20.1002	+	17.4169i	−0.665948	+	0.577048i	0.254900	+	0.966967i	$0.417957\pi$
$912$	52.6576	−	22.3816i	1.74367	−	0.741129i
$913$	3.78846	−	7.34858i	0.125380	−	0.243202i
$914$	−12.8642	+	3.12082i	−0.425509	+	0.103227i
$915$	−3.45324	−	3.15623i	−0.114160	−	0.104342i
$916$	3.87594	+	13.2002i	0.128065	+	0.436148i
$917$	−3.09154	+	9.62357i	−0.102092	+	0.317798i
$918$	−13.1069	+	0.830991i	−0.432592	+	0.0274268i
$919$	−12.2711	+	21.2542i	−0.404786	+	0.701110i	−0.994297	−	0.106650i	$-0.965987\pi$
$919$	−12.2711	+	21.2542i	−0.404786	+	0.701110i	0.589510	+	0.807761i	$0.299321\pi$
$920$	11.2125	−	0.791493i	0.369665	−	0.0260948i
$921$	−36.2187	−	22.2105i	−1.19345	−	0.731861i
$922$	21.9961	−	54.9436i	0.724403	−	1.80947i
$923$	−0.979985	+	2.14587i	−0.0322566	+	0.0706321i
$924$	−10.2073	−	1.51063i	−0.335796	−	0.0496961i
$925$	−7.78499	+	8.98436i	−0.255969	+	0.295404i
$926$	−23.3427	−	24.4811i	−0.767089	−	0.804500i
$927$	−20.0440	−	35.1534i	−0.658331	−	1.15459i
$928$	−3.98179	+	5.59164i	−0.130709	+	0.183554i
$929$	23.1895	−	4.46942i	0.760824	−	0.146637i	0.205940	−	0.978565i	$-0.433975\pi$
$929$	23.1895	−	4.46942i	0.760824	−	0.146637i	0.554884	+	0.831928i	$0.312763\pi$
$930$	−1.62908	+	21.9463i	−0.0534197	+	0.719649i
$931$	26.8567	+	37.9449i	0.880193	+	1.24359i
$932$	20.8578	+	2.99890i	0.683221	+	0.0982323i
$933$	−1.07462	−	0.731555i	−0.0351816	−	0.0239500i
$934$	28.5761	+	9.89027i	0.935037	+	0.323620i
$935$	−3.52877	−	2.51283i	−0.115403	−	0.0821782i
$936$	0.954066	+	0.557707i	0.0311846	+	0.0182292i
$937$	6.80900	−	23.1893i	0.222440	−	0.757563i	−0.770342	−	0.637631i	$-0.779914\pi$
$937$	6.80900	−	23.1893i	0.222440	−	0.757563i	0.992782	−	0.119931i	$-0.0382675\pi$
$938$	2.61426	−	35.8298i	0.0853586	−	1.16989i
$939$	27.5025	−	27.3547i	0.897509	−	0.892685i
$940$	−8.45175	−	11.8688i	−0.275666	−	0.387118i
$941$	−18.7710	+	14.7617i	−0.611917	+	0.481217i	−0.875369	−	0.483456i	$-0.839381\pi$
$941$	−18.7710	+	14.7617i	−0.611917	+	0.481217i	0.263452	+	0.964673i	$0.415139\pi$
$942$	−17.5509	+	28.6203i	−0.571841	+	0.932501i
$943$	4.25289	+	25.4351i	0.138493	+	0.828281i
$944$	−34.3842			−1.11911
$945$	−3.88439	−	21.2400i	−0.126359	−	0.690937i
$946$	11.2555	−	24.6460i	0.365946	−	0.801311i
$947$	−16.5225	−	4.00832i	−0.536910	−	0.130253i	−0.0418699	−	0.999123i	$-0.513332\pi$
$947$	−16.5225	−	4.00832i	−0.536910	−	0.130253i	−0.495040	+	0.868870i	$0.664847\pi$
$948$	−1.09938	−	3.47138i	−0.0357061	−	0.112745i
$949$	−0.774194	−	3.19127i	−0.0251314	−	0.103593i
$950$	1.42310	+	29.8745i	0.0461714	+	0.969257i
$951$	33.1148	+	24.9290i	1.07382	+	0.808377i
$952$	1.70144	+	5.34902i	0.0551441	+	0.173363i
$953$	9.22806	−	14.3591i	0.298926	−	0.465138i	−0.659004	−	0.752139i	$-0.729022\pi$
$953$	9.22806	−	14.3591i	0.298926	−	0.465138i	0.957930	+	0.287001i	$0.0926583\pi$
$954$	−2.68979	+	0.914742i	−0.0870850	+	0.0296159i
$955$	7.27882	+	18.1816i	0.235537	+	0.588343i
$956$	0.382354	+	0.0182138i	0.0123662	+	0.000589075i
$957$	2.49862	+	3.04284i	0.0807689	+	0.0983610i
$958$	−25.5621	+	11.6738i	−0.825873	+	0.377163i
$959$	−34.8439	+	5.80792i	−1.12517	+	0.187547i
$960$	−0.266765	−	1.24241i	−0.00860980	−	0.0400985i
$961$	−3.36702	−	9.72838i	−0.108614	−	0.313819i
$962$	1.49053	+	1.42122i	0.0480566	+	0.0458219i
$963$	−33.6724	−	17.5897i	−1.08508	−	0.566819i
$964$	−7.31577	+	18.2739i	−0.235625	+	0.588563i
$965$	37.1925			1.19727
$966$	29.0434	−	26.1353i	0.934457	−	0.840889i
$967$	−10.0731			−0.323928			−0.161964	−	0.986797i	$-0.551783\pi$
$967$	−10.0731			−0.323928			−0.161964	+	0.986797i	$0.551783\pi$
$968$	−4.01330	+	10.0247i	−0.128992	+	0.322207i
$969$	13.5675	−	9.12958i	0.435852	−	0.293284i
$970$	−4.48352	−	4.27503i	−0.143957	−	0.137263i
$971$	1.59493	+	4.60826i	0.0511838	+	0.147886i	0.967695	−	0.252122i	$-0.0811285\pi$
$971$	1.59493	+	4.60826i	0.0511838	+	0.147886i	−0.916512	+	0.400008i	$0.869007\pi$
$972$	−14.6282	+	10.6461i	−0.469200	+	0.341473i
$973$	15.5944	−	41.6277i	0.499932	−	1.33452i
$974$	−55.5606	+	25.3737i	−1.78028	+	0.813024i
$975$	−0.837048	+	0.687340i	−0.0268070	+	0.0220125i
$976$	8.54463	+	0.407031i	0.273507	+	0.0130287i
$977$	−14.1319	−	35.2997i	−0.452119	−	1.12934i	−0.962955	−	0.269661i	$-0.913088\pi$
$977$	−14.1319	−	35.2997i	−0.452119	−	1.12934i	0.510836	−	0.859678i	$-0.329336\pi$
$978$	−40.3789	−	6.90197i	−1.29117	−	0.220701i
$979$	2.70608	−	4.21074i	0.0864866	−	0.134576i
$980$	11.6221	−	5.26738i	0.371253	−	0.168260i
$981$	14.6488	+	2.18682i	0.467702	+	0.0698199i
$982$	0.458376	+	9.62250i	0.0146274	+	0.307066i
$983$	−8.41248	−	34.6767i	−0.268316	−	1.10602i	−0.933283	−	0.359142i	$-0.883069\pi$
$983$	−8.41248	−	34.6767i	−0.268316	−	1.10602i	0.664966	−	0.746873i	$-0.268446\pi$
$984$	−13.2499	+	4.19622i	−0.422392	+	0.133771i
$985$	24.5699	+	5.96060i	0.782863	+	0.189921i
$986$	−1.23022	+	2.69380i	−0.0391781	+	0.0857882i
$987$	35.1030	+	10.4648i	1.11734	+	0.333098i
$988$	1.90265			0.0605315
$989$	16.4299	+	33.9023i	0.522441	+	1.07803i
$990$	−16.2288	−	0.860748i	−0.515784	−	0.0273564i
$991$	−1.94725	+	1.53134i	−0.0618565	+	0.0486445i	−0.648609	−	0.761122i	$-0.724649\pi$
$991$	−1.94725	+	1.53134i	−0.0618565	+	0.0486445i	0.586752	+	0.809767i	$0.300406\pi$
$992$	−15.4635	−	21.7155i	−0.490968	−	0.689467i
$993$	−18.9355	−	19.0378i	−0.600901	−	0.604148i
$994$	−25.2485	+	37.1897i	−0.800835	+	1.17958i
$995$	9.64738	−	32.8559i	0.305842	−	1.04160i
$996$	7.32681	−	4.43889i	0.232159	−	0.140652i
$997$	−22.5930	−	16.0884i	−0.715527	−	0.509524i	0.163353	−	0.986568i	$-0.447769\pi$
$997$	−22.5930	−	16.0884i	−0.715527	−	0.509524i	−0.878880	+	0.477043i	$0.841708\pi$
$998$	5.86971	+	2.03153i	0.185803	+	0.0643069i
$999$	22.4930	−	9.41764i	0.711647	−	0.297961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bb.a.26.14	✓	1200
3.2	odd	2	inner	483.2.bb.a.26.47	yes	1200
7.3	odd	6	inner	483.2.bb.a.164.14	yes	1200
21.17	even	6	inner	483.2.bb.a.164.47	yes	1200
23.8	even	11	inner	483.2.bb.a.215.47	yes	1200
69.8	odd	22	inner	483.2.bb.a.215.14	yes	1200
161.31	odd	66	inner	483.2.bb.a.353.47	yes	1200
483.353	even	66	inner	483.2.bb.a.353.14	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bb.a.26.14	✓	1200	1.1	even	1	trivial
483.2.bb.a.26.47	yes	1200	3.2	odd	2	inner
483.2.bb.a.164.14	yes	1200	7.3	odd	6	inner
483.2.bb.a.164.47	yes	1200	21.17	even	6	inner
483.2.bb.a.215.14	yes	1200	69.8	odd	22	inner
483.2.bb.a.215.47	yes	1200	23.8	even	11	inner
483.2.bb.a.353.14	yes	1200	483.353	even	66	inner
483.2.bb.a.353.47	yes	1200	161.31	odd	66	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bb (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.660745 + 1.65046i) q^{2} +(0.966959 + 1.43701i) q^{3} +(-0.839971 - 0.800910i) q^{4} +(0.513695 + 1.48422i) q^{5} +(-3.01064 + 0.646433i) q^{6} +(2.47761 + 0.928150i) q^{7} +(-1.35743 + 0.619916i) q^{8} +(-1.12998 + 2.77905i) q^{9} +(-2.78908 - 0.132860i) q^{10} +(-0.721058 - 1.80111i) q^{11} +(0.338697 - 1.98149i) q^{12} +(-0.133458 + 0.207665i) q^{13} +(-3.16894 + 3.47592i) q^{14} +(-1.63612 + 2.17337i) q^{15} +(-0.236682 - 4.96857i) q^{16} +(-0.335175 - 1.38161i) q^{17} +(-3.84009 - 3.70123i) q^{18} +(6.45388 + 1.56570i) q^{19} +(0.757242 - 1.65813i) q^{20} +(1.06199 + 4.45782i) q^{21} +3.44911 q^{22} +(-3.05688 + 3.69533i) q^{23} +(-2.20340 - 1.35120i) q^{24} +(1.99123 - 1.56592i) q^{25} +(-0.254561 - 0.357481i) q^{26} +(-5.08617 + 1.06344i) q^{27} +(-1.33775 - 2.76396i) q^{28} +(-0.330102 + 1.12423i) q^{29} +(-2.50600 - 4.13639i) q^{30} +(-3.70658 - 2.63945i) q^{31} +(5.53641 + 1.91617i) q^{32} +(1.89098 - 2.77777i) q^{33} +(2.50176 + 0.359699i) q^{34} +(-0.104848 + 4.15411i) q^{35} +(3.17492 - 1.42931i) q^{36} +(-4.60809 + 0.888136i) q^{37} +(-6.84849 + 9.61736i) q^{38} +(-0.427464 + 0.00902317i) q^{39} +(-1.61740 - 1.69628i) q^{40} +(3.52132 - 4.06383i) q^{41} +(-8.05917 - 1.19272i) q^{42} +(3.26330 - 7.14562i) q^{43} +(-0.836864 + 2.09039i) q^{44} +(-4.70521 - 0.249557i) q^{45} +(-4.07918 - 7.48694i) q^{46} +(3.99663 - 6.92236i) q^{47} +(6.91101 - 5.14452i) q^{48} +(5.27708 + 4.59918i) q^{49} +(1.26879 + 4.32111i) q^{50} +(1.66128 - 1.81761i) q^{51} +(0.278422 - 0.0675443i) q^{52} +(0.244094 - 0.473475i) q^{53} +(1.60549 - 9.09719i) q^{54} +(2.30285 - 1.99543i) q^{55} +(-3.93855 + 0.276013i) q^{56} +(3.99073 + 10.7882i) q^{57} +(-1.63738 - 1.28765i) q^{58} +(0.328910 - 6.90467i) q^{59} +(3.11497 - 0.515181i) q^{60} +(-0.163471 + 1.71195i) q^{61} +(6.80541 - 4.37357i) q^{62} +(-5.37903 + 5.83662i) q^{63} +(-0.305895 + 0.353021i) q^{64} +(-0.376778 - 0.0914053i) q^{65} +(3.33514 + 4.95639i) q^{66} +(-6.00365 + 4.72132i) q^{67} +(-0.825009 + 1.42896i) q^{68} +(-8.26610 - 0.819531i) q^{69} +(-6.78692 - 2.91786i) q^{70} +(9.45929 - 1.36004i) q^{71} +(-0.188916 - 4.47286i) q^{72} +(-9.18005 + 9.62776i) q^{73} +(1.57894 - 8.19230i) q^{74} +(4.17567 + 1.34723i) q^{75} +(-4.16709 - 6.48412i) q^{76} +(-0.114793 - 5.13170i) q^{77} +(0.267552 - 0.711475i) q^{78} +(1.61002 - 0.830025i) q^{79} +(7.25289 - 2.90362i) q^{80} +(-6.44629 - 6.28055i) q^{81} +(4.38049 + 8.49696i) q^{82} +(2.79068 + 3.22061i) q^{83} +(2.67828 - 4.59500i) q^{84} +(1.87844 - 1.20720i) q^{85} +(9.63737 + 10.1074i) q^{86} +(-1.93472 + 0.612720i) q^{87} +(2.09532 + 1.99789i) q^{88} +(1.49651 + 2.10156i) q^{89} +(3.52083 - 7.60087i) q^{90} +(-0.523400 + 0.390642i) q^{91} +(5.52732 - 0.655678i) q^{92} +(0.208788 - 7.87862i) q^{93} +(8.78434 + 11.1702i) q^{94} +(0.991485 + 10.3833i) q^{95} +(2.59993 + 9.80872i) q^{96} +(1.67674 + 1.45290i) q^{97} +(-11.0776 + 5.67072i) q^{98} +(5.82018 + 0.0313649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 27 q^{3} - 74 q^{4} - 36 q^{7} - 13 q^{9} - 54 q^{10} - 15 q^{12} - 64 q^{15} + 38 q^{16} + 43 q^{18} - 54 q^{19} - 70 q^{21} - 160 q^{22} - 66 q^{24} + 34 q^{25} - 76 q^{28} - 23 q^{30} - 54 q^{31}+ \cdots + 196 q^{99}+O(q^{100}) \) 1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9 - 54 * q^10 - 15 * q^12 - 64 * q^15 + 38 * q^16 + 43 * q^18 - 54 * q^19 - 70 * q^21 - 160 * q^22 - 66 * q^24 + 34 * q^25 - 76 * q^28 - 23 * q^30 - 54 * q^31 - 3 * q^33 - 28 * q^36 + 26 * q^37 + 5 * q^39 - 30 * q^40 - 68 * q^42 - 176 * q^43 - 96 * q^45 - 22 * q^46 - 128 * q^49 - 23 * q^51 - 102 * q^52 + 21 * q^54 - 36 * q^57 + 58 * q^58 - 43 * q^60 - 126 * q^61 + 41 * q^63 + 40 * q^64 - 132 * q^66 - 10 * q^67 + 20 * q^70 + 59 * q^72 - 30 * q^73 - 81 * q^75 + 164 * q^78 - 14 * q^79 - 97 * q^81 - 66 * q^82 + 24 * q^84 - 56 * q^85 - 399 * q^87 - 74 * q^88 - 156 * q^91 + 8 * q^93 - 126 * q^94 - 117 * q^96 + 196 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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