LMFDB - Embedded newform 135.2.q.a.113.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.8
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.576956 - 0.0504771i) q^{2} +(-1.73138 - 0.0483220i) q^{3} +(-1.63929 - 0.289050i) q^{4} +(2.18512 + 0.474625i) q^{5} +(0.996489 + 0.115275i) q^{6} +(2.78018 + 1.94671i) q^{7} +(2.05006 + 0.549311i) q^{8} +(2.99533 + 0.167327i) q^{9} +O(q^{10})$	\(q+(-0.576956 - 0.0504771i) q^{2} +(-1.73138 - 0.0483220i) q^{3} +(-1.63929 - 0.289050i) q^{4} +(2.18512 + 0.474625i) q^{5} +(0.996489 + 0.115275i) q^{6} +(2.78018 + 1.94671i) q^{7} +(2.05006 + 0.549311i) q^{8} +(2.99533 + 0.167327i) q^{9} +(-1.23676 - 0.384136i) q^{10} +(1.55726 - 4.27854i) q^{11} +(2.82425 + 0.579668i) q^{12} +(0.357151 + 4.08225i) q^{13} +(-1.50578 - 1.26350i) q^{14} +(-3.76032 - 0.927343i) q^{15} +(1.97331 + 0.718227i) q^{16} +(0.284890 - 0.0763360i) q^{17} +(-1.71973 - 0.247736i) q^{18} +(-4.26213 + 2.46074i) q^{19} +(-3.44484 - 1.40965i) q^{20} +(-4.71948 - 3.50482i) q^{21} +(-1.11444 + 2.38992i) q^{22} +(0.869642 + 1.24198i) q^{23} +(-3.52287 - 1.05013i) q^{24} +(4.54946 + 2.07422i) q^{25} -2.37331i q^{26} +(-5.17796 - 0.434446i) q^{27} +(-3.99482 - 3.99482i) q^{28} +(5.57542 - 4.67834i) q^{29} +(2.12273 + 0.724846i) q^{30} +(0.591015 - 3.35181i) q^{31} +(-4.94931 - 2.30790i) q^{32} +(-2.90295 + 7.33251i) q^{33} +(-0.168222 + 0.0296621i) q^{34} +(5.15107 + 5.57332i) q^{35} +(-4.86183 - 1.14010i) q^{36} +(1.28961 + 4.81289i) q^{37} +(2.58327 - 1.20460i) q^{38} +(-0.421100 - 7.08518i) q^{39} +(4.21889 + 2.17331i) q^{40} +(-2.42980 + 2.89573i) q^{41} +(2.54602 + 2.26035i) q^{42} +(-4.02865 - 8.63947i) q^{43} +(-3.78950 + 6.56361i) q^{44} +(6.46573 + 1.78729i) q^{45} +(-0.439054 - 0.760463i) q^{46} +(1.09911 - 1.56969i) q^{47} +(-3.38184 - 1.33888i) q^{48} +(1.54562 + 4.24655i) q^{49} +(-2.52014 - 1.42638i) q^{50} +(-0.496940 + 0.118400i) q^{51} +(0.594504 - 6.79521i) q^{52} +(-1.39575 + 1.39575i) q^{53} +(2.96552 + 0.512025i) q^{54} +(5.43349 - 8.60998i) q^{55} +(4.63018 + 5.51804i) q^{56} +(7.49825 - 4.05451i) q^{57} +(-3.45292 + 2.41776i) q^{58} +(-9.34637 + 3.40180i) q^{59} +(5.89619 + 2.60710i) q^{60} +(-0.249603 - 1.41557i) q^{61} +(-0.510179 + 1.90402i) q^{62} +(8.00183 + 6.29622i) q^{63} +(-0.898191 - 0.518571i) q^{64} +(-1.15712 + 9.08971i) q^{65} +(2.04500 - 4.08400i) q^{66} +(-9.46116 + 0.827744i) q^{67} +(-0.489081 + 0.0427890i) q^{68} +(-1.44566 - 2.19235i) q^{69} +(-2.69061 - 3.47557i) q^{70} +(0.728237 + 0.420448i) q^{71} +(6.04868 + 1.98840i) q^{72} +(0.166069 - 0.619776i) q^{73} +(-0.501107 - 2.84192i) q^{74} +(-7.77660 - 3.81109i) q^{75} +(7.69812 - 2.80189i) q^{76} +(12.6585 - 8.86359i) q^{77} +(-0.114683 + 4.10909i) q^{78} +(9.56341 + 11.3972i) q^{79} +(3.97103 + 2.50599i) q^{80} +(8.94400 + 1.00240i) q^{81} +(1.54806 - 1.54806i) q^{82} +(0.830405 - 9.49158i) q^{83} +(6.72350 + 7.10957i) q^{84} +(0.658748 - 0.0315873i) q^{85} +(1.88826 + 5.18795i) q^{86} +(-9.87923 + 7.83055i) q^{87} +(5.54271 - 7.91582i) q^{88} +(-6.19767 - 10.7347i) q^{89} +(-3.64022 - 1.35756i) q^{90} +(-6.95400 + 12.0447i) q^{91} +(-1.06660 - 2.28733i) q^{92} +(-1.18524 + 5.77469i) q^{93} +(-0.713371 + 0.850162i) q^{94} +(-10.4812 + 3.35409i) q^{95} +(8.45759 + 4.23500i) q^{96} +(-4.11255 + 1.91772i) q^{97} +(-0.677399 - 2.52809i) q^{98} +(5.38042 - 12.5551i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.576956	−	0.0504771i	−0.407969	−	0.0356927i	−0.118676	−	0.992933i	$-0.537865\pi$
$2$	−0.576956	−	0.0504771i	−0.407969	−	0.0356927i	−0.289294	+	0.957240i	$0.593420\pi$
$3$	−1.73138	−	0.0483220i	−0.999611	−	0.0278987i
$3$	−1.73138	−	0.0483220i	−0.999611	−	0.0278987i
$4$	−1.63929	−	0.289050i	−0.819643	−	0.144525i
$5$	2.18512	+	0.474625i	0.977214	+	0.212259i
$5$	2.18512	+	0.474625i	0.977214	+	0.212259i
$6$	0.996489	+	0.115275i	0.406815	+	0.0470606i
$7$	2.78018	+	1.94671i	1.05081	+	0.735785i	0.965456	−	0.260565i	$-0.0839089\pi$
$7$	2.78018	+	1.94671i	1.05081	+	0.735785i	0.0853543	+	0.996351i	$0.472798\pi$
$8$	2.05006	+	0.549311i	0.724804	+	0.194211i
$9$	2.99533	+	0.167327i	0.998443	+	0.0557757i
$10$	−1.23676	−	0.384136i	−0.391097	−	0.121474i
$11$	1.55726	−	4.27854i	0.469531	−	1.29003i	−0.448594	−	0.893736i	$-0.648075\pi$
$11$	1.55726	−	4.27854i	0.469531	−	1.29003i	0.918125	−	0.396291i	$-0.129703\pi$
$12$	2.82425	+	0.579668i	0.815292	+	0.167336i
$13$	0.357151	+	4.08225i	0.0990558	+	1.13221i	0.869239	+	0.494391i	$0.164609\pi$
$13$	0.357151	+	4.08225i	0.0990558	+	1.13221i	−0.770184	+	0.637822i	$0.779835\pi$
$14$	−1.50578	−	1.26350i	−0.402436	−	0.337684i
$15$	−3.76032	−	0.927343i	−0.970911	−	0.239439i
$16$	1.97331	+	0.718227i	0.493328	+	0.179557i
$17$	0.284890	−	0.0763360i	0.0690959	−	0.0185142i	−0.224105	−	0.974565i	$-0.571946\pi$
$17$	0.284890	−	0.0763360i	0.0690959	−	0.0185142i	0.293201	+	0.956051i	$0.405279\pi$
$18$	−1.71973	−	0.247736i	−0.405344	−	0.0583919i
$19$	−4.26213	+	2.46074i	−0.977799	+	0.564532i	−0.901605	−	0.432561i	$-0.857610\pi$
$19$	−4.26213	+	2.46074i	−0.977799	+	0.564532i	−0.0761939	+	0.997093i	$0.524277\pi$
$20$	−3.44484	−	1.40965i	−0.770289	−	0.315208i
$21$	−4.71948	−	3.50482i	−1.02987	−	0.764815i
$22$	−1.11444	+	2.38992i	−0.237599	+	0.509533i
$23$	0.869642	+	1.24198i	0.181333	+	0.258970i	0.899520	−	0.436880i	$-0.143917\pi$
$23$	0.869642	+	1.24198i	0.181333	+	0.258970i	−0.718187	+	0.695850i	$0.755028\pi$
$24$	−3.52287	−	1.05013i	−0.719104	−	0.214356i
$25$	4.54946	+	2.07422i	0.909893	+	0.414844i
$26$		−	2.37331i		−	0.465444i
$27$	−5.17796	−	0.434446i	−0.996499	−	0.0836092i
$28$	−3.99482	−	3.99482i	−0.754950	−	0.754950i
$29$	5.57542	−	4.67834i	1.03533	−	0.868745i	0.0438548	−	0.999038i	$-0.486036\pi$
$29$	5.57542	−	4.67834i	1.03533	−	0.868745i	0.991476	+	0.130293i	$0.0415917\pi$
$30$	2.12273	+	0.724846i	0.387556	+	0.132338i
$31$	0.591015	−	3.35181i	0.106149	−	0.602003i	−0.884606	−	0.466340i	$-0.845572\pi$
$31$	0.591015	−	3.35181i	0.106149	−	0.602003i	0.990755	−	0.135663i	$-0.0433165\pi$
$32$	−4.94931	−	2.30790i	−0.874922	−	0.407983i
$33$	−2.90295	+	7.33251i	−0.505339	+	1.27643i
$34$	−0.168222	+	0.0296621i	−0.0288498	+	0.00508701i
$35$	5.15107	+	5.57332i	0.870690	+	0.942063i
$36$	−4.86183	−	1.14010i	−0.810306	−	0.190016i
$37$	1.28961	+	4.81289i	0.212011	+	0.791234i	0.987198	+	0.159502i	$0.0509890\pi$
$37$	1.28961	+	4.81289i	0.212011	+	0.791234i	−0.775187	+	0.631732i	$0.782344\pi$
$38$	2.58327	−	1.20460i	0.419062	−	0.195412i
$39$	−0.421100	−	7.08518i	−0.0674300	−	1.13454i
$40$	4.21889	+	2.17331i	0.667066	+	0.343631i
$41$	−2.42980	+	2.89573i	−0.379472	+	0.452237i	−0.921647	−	0.388028i	$-0.873156\pi$
$41$	−2.42980	+	2.89573i	−0.379472	+	0.452237i	0.542176	+	0.840265i	$0.317601\pi$
$42$	2.54602	+	2.26035i	0.392859	+	0.348780i
$43$	−4.02865	−	8.63947i	−0.614364	−	1.31751i	−0.929627	−	0.368503i	$-0.879871\pi$
$43$	−4.02865	−	8.63947i	−0.614364	−	1.31751i	0.315263	−	0.949004i	$-0.397907\pi$
$44$	−3.78950	+	6.56361i	−0.571289	+	0.989502i
$45$	6.46573	+	1.78729i	0.963853	+	0.266433i
$46$	−0.439054	−	0.760463i	−0.0647349	−	0.112124i
$47$	1.09911	−	1.56969i	0.160322	−	0.228963i	−0.730952	−	0.682429i	$-0.760924\pi$
$47$	1.09911	−	1.56969i	0.160322	−	0.228963i	0.891274	+	0.453466i	$0.149813\pi$
$48$	−3.38184	−	1.33888i	−0.488126	−	0.193250i
$49$	1.54562	+	4.24655i	0.220802	+	0.606650i
$50$	−2.52014	−	1.42638i	−0.356401	−	0.201720i
$51$	−0.496940	+	0.118400i	−0.0695855	+	0.0165793i
$52$	0.594504	−	6.79521i	0.0824429	−	0.942327i
$53$	−1.39575	+	1.39575i	−0.191721	+	0.191721i	−0.796439	−	0.604719i	$-0.793286\pi$
$53$	−1.39575	+	1.39575i	−0.191721	+	0.191721i	0.604719	+	0.796439i	$0.293286\pi$
$54$	2.96552	+	0.512025i	0.403557	+	0.0696777i
$55$	5.43349	−	8.60998i	0.732652	−	1.16097i
$56$	4.63018	+	5.51804i	0.618734	+	0.737379i
$57$	7.49825	−	4.05451i	0.993168	−	0.537033i
$58$	−3.45292	+	2.41776i	−0.453391	+	0.317468i
$59$	−9.34637	+	3.40180i	−1.21679	+	0.442877i	−0.869055	−	0.494715i	$-0.835272\pi$
$59$	−9.34637	+	3.40180i	−1.21679	+	0.442877i	−0.347738	+	0.937592i	$0.613050\pi$
$60$	5.89619	+	2.60710i	0.761195	+	0.336575i
$61$	−0.249603	−	1.41557i	−0.0319584	−	0.181245i	0.964650	−	0.263534i	$-0.0848881\pi$
$61$	−0.249603	−	1.41557i	−0.0319584	−	0.181245i	−0.996609	+	0.0822889i	$0.973777\pi$
$62$	−0.510179	+	1.90402i	−0.0647928	+	0.241810i
$63$	8.00183	+	6.29622i	1.00814	+	0.793250i
$64$	−0.898191	−	0.518571i	−0.112274	−	0.0648214i
$65$	−1.15712	+	9.08971i	−0.143523	+	1.12744i
$66$	2.04500	−	4.08400i	0.251722	−	0.502706i
$67$	−9.46116	+	0.827744i	−1.15586	+	0.101125i	−0.648922	−	0.760855i	$-0.724780\pi$
$67$	−9.46116	+	0.827744i	−1.15586	+	0.101125i	−0.506943	+	0.861980i	$0.669224\pi$
$68$	−0.489081	+	0.0427890i	−0.0593097	+	0.00518893i
$69$	−1.44566	−	2.19235i	−0.174037	−	0.263928i
$70$	−2.69061	−	3.47557i	−0.321590	−	0.415410i
$71$	0.728237	+	0.420448i	0.0864258	+	0.0498980i	0.542590	−	0.839998i	$-0.317444\pi$
$71$	0.728237	+	0.420448i	0.0864258	+	0.0498980i	−0.456164	+	0.889896i	$0.650777\pi$
$72$	6.04868	+	1.98840i	0.712844	+	0.234335i
$73$	0.166069	−	0.619776i	0.0194369	−	0.0725393i	−0.955526	−	0.294906i	$-0.904712\pi$
$73$	0.166069	−	0.619776i	0.0194369	−	0.0725393i	0.974963	+	0.222367i	$0.0713783\pi$
$74$	−0.501107	−	2.84192i	−0.0582526	−	0.330367i
$75$	−7.77660	−	3.81109i	−0.897965	−	0.440067i
$76$	7.69812	−	2.80189i	0.883035	−	0.321398i
$77$	12.6585	−	8.86359i	1.44257	−	1.01010i
$78$	−0.114683	+	4.10909i	−0.0129853	+	0.465263i
$79$	9.56341	+	11.3972i	1.07597	+	1.28229i	0.957219	+	0.289364i	$0.0934436\pi$
$79$	9.56341	+	11.3972i	1.07597	+	1.28229i	0.118748	+	0.992924i	$0.462112\pi$
$80$	3.97103	+	2.50599i	0.443974	+	0.280178i
$81$	8.94400	+	1.00240i	0.993778	+	0.111378i
$82$	1.54806	−	1.54806i	0.170954	−	0.170954i
$83$	0.830405	−	9.49158i	0.0911488	−	1.04184i	−0.803571	−	0.595209i	$-0.797069\pi$
$83$	0.830405	−	9.49158i	0.0911488	−	1.04184i	0.894720	−	0.446627i	$-0.147375\pi$
$84$	6.72350	+	7.10957i	0.733594	+	0.775718i
$85$	0.658748	−	0.0315873i	0.0714513	−	0.00342612i
$86$	1.88826	+	5.18795i	0.203616	+	0.559431i
$87$	−9.87923	+	7.83055i	−1.05916	+	0.839523i
$88$	5.54271	−	7.91582i	0.590855	−	0.843829i
$89$	−6.19767	−	10.7347i	−0.656952	−	1.13787i	−0.981401	−	0.191971i	$-0.938512\pi$
$89$	−6.19767	−	10.7347i	−0.656952	−	1.13787i	0.324448	−	0.945903i	$-0.394821\pi$
$90$	−3.64022	−	1.35756i	−0.383713	−	0.143099i
$91$	−6.95400	+	12.0447i	−0.728977	+	1.26263i
$92$	−1.06660	−	2.28733i	−0.111200	−	0.238470i
$93$	−1.18524	+	5.77469i	−0.122903	+	0.598807i
$94$	−0.713371	+	0.850162i	−0.0735786	+	0.0876876i
$95$	−10.4812	+	3.35409i	−1.07534	+	0.344123i
$96$	8.45759	+	4.23500i	0.863200	+	0.432233i
$97$	−4.11255	+	1.91772i	−0.417567	+	0.194715i	−0.620035	−	0.784574i	$-0.712882\pi$
$97$	−4.11255	+	1.91772i	−0.417567	+	0.194715i	0.202468	+	0.979289i	$0.435104\pi$
$98$	−0.677399	−	2.52809i	−0.0684277	−	0.255376i
$99$	5.38042	−	12.5551i	0.540753	−	1.26183i
$100$	−6.85831	−	4.71526i	−0.685831	−	0.471526i
$101$	−8.64670	+	1.52465i	−0.860378	+	0.151708i	−0.586394	−	0.810026i	$-0.699453\pi$
$101$	−8.64670	+	1.52465i	−0.860378	+	0.151708i	−0.273985	+	0.961734i	$0.588342\pi$
$102$	0.292689	−	0.0432274i	0.0289805	−	0.00428015i
$103$	−2.78831	−	1.30021i	−0.274741	−	0.128114i	0.280365	−	0.959893i	$-0.409544\pi$
$103$	−2.78831	−	1.30021i	−0.274741	−	0.128114i	−0.555106	+	0.831780i	$0.687322\pi$
$104$	−1.51025	+	8.56503i	−0.148092	+	0.839871i
$105$	−8.64913	−	9.89843i	−0.844068	−	0.965987i
$106$	0.875738	−	0.734831i	0.0850592	−	0.0713731i
$107$	−0.840083	−	0.840083i	−0.0812138	−	0.0812138i	0.665333	−	0.746547i	$-0.268290\pi$
$107$	−0.840083	−	0.840083i	−0.0812138	−	0.0812138i	−0.746547	+	0.665333i	$0.768290\pi$
$108$	8.36257	+	2.20887i	0.804689	+	0.212549i
$109$		−	15.3404i		−	1.46935i	−0.678422	−	0.734673i	$-0.737336\pi$
$109$		−	15.3404i		−	1.46935i	0.678422	−	0.734673i	$-0.262664\pi$
$110$	−3.56949	+	4.69331i	−0.340338	+	0.447490i
$111$	−2.00023	−	8.39524i	−0.189854	−	0.796841i
$112$	4.08799	+	5.83826i	0.386279	+	0.551664i
$113$	1.57466	−	3.37688i	0.148132	−	0.317670i	−0.818215	−	0.574912i	$-0.805036\pi$
$113$	1.57466	−	3.37688i	0.148132	−	0.317670i	0.966347	+	0.257242i	$0.0828139\pi$
$114$	−4.53082	+	1.96078i	−0.424350	+	0.183644i
$115$	1.31080	+	3.12662i	0.122232	+	0.291559i
$116$	−10.4920	+	6.05755i	−0.974156	+	0.562429i
$117$	0.386714	+	12.2875i	0.0357517	+	1.13598i
$118$	5.56415	−	1.49091i	0.512222	−	0.137249i
$119$	0.940649	+	0.342368i	0.0862292	+	0.0313849i
$120$	−7.19947	−	3.96669i	−0.657219	−	0.362108i
$121$	−7.45432	−	6.25492i	−0.677665	−	0.568629i
$122$	0.0725561	+	0.829320i	0.00656892	+	0.0750831i
$123$	4.34683	−	4.89618i	0.391941	−	0.441474i
$124$	−1.93768	+	5.32374i	−0.174009	+	0.478086i
$125$	8.95663	+	6.69170i	0.801105	+	0.598523i
$126$	−4.29889	−	4.03655i	−0.382975	−	0.359605i
$127$	−17.0553	−	4.56996i	−1.51342	−	0.405518i	−0.595847	−	0.803098i	$-0.703184\pi$
$127$	−17.0553	−	4.56996i	−1.51342	−	0.405518i	−0.917568	+	0.397579i	$0.869850\pi$
$128$	9.43875	+	6.60908i	0.834275	+	0.584166i
$129$	6.55764	+	15.1529i	0.577368	+	1.33413i
$130$	1.12643	−	5.18595i	0.0987945	−	0.454838i
$131$	−4.36693	−	0.770008i	−0.381540	−	0.0672759i	−0.0204113	−	0.999792i	$-0.506498\pi$
$131$	−4.36693	−	0.770008i	−0.381540	−	0.0672759i	−0.361129	+	0.932516i	$0.617609\pi$
$132$	6.87823	−	11.1810i	0.598673	−	0.973179i
$133$	−16.6398	−	1.45580i	−1.44286	−	0.126234i
$134$	5.50045			0.475167
$135$	−11.1082	−	3.40690i	−0.956045	−	0.293219i
$136$	0.625972			0.0536767
$137$	−17.1191	−	1.49772i	−1.46258	−	0.127959i	−0.672107	−	0.740454i	$-0.734610\pi$
$137$	−17.1191	−	1.49772i	−1.46258	−	0.127959i	−0.790474	+	0.612495i	$0.790166\pi$
$138$	0.723420	+	1.33786i	0.0615816	+	0.113887i
$139$	3.49278	+	0.615871i	0.296254	+	0.0522375i	0.319799	−	0.947485i	$-0.396384\pi$
$139$	3.49278	+	0.615871i	0.296254	+	0.0522375i	−0.0235459	+	0.999723i	$0.507496\pi$
$140$	−6.83310	−	10.6252i	−0.577503	−	0.897992i
$141$	−1.97882	+	2.66461i	−0.166647	+	0.224401i
$142$	−0.398938	−	0.279339i	−0.0334781	−	0.0234416i
$143$	18.0222	+	4.82905i	1.50710	+	0.403825i
$144$	5.79054	+	2.48151i	0.482545	+	0.206793i
$145$	14.4034	−	7.57647i	1.19614	−	0.629192i
$146$	−0.127099	+	0.349201i	−0.0105188	+	0.0289001i
$147$	−2.47084	−	7.42706i	−0.203792	−	0.612574i
$148$	−0.722872	−	8.26246i	−0.0594197	−	0.679170i
$149$	−2.74544	−	2.30369i	−0.224915	−	0.188726i	0.523366	−	0.852108i	$-0.324676\pi$
$149$	−2.74544	−	2.30369i	−0.224915	−	0.188726i	−0.748281	+	0.663382i	$0.769120\pi$
$150$	4.29438	+	2.59137i	0.350635	+	0.211585i
$151$	18.4206	+	6.70454i	1.49904	+	0.545607i	0.955813	−	0.293976i	$-0.0949785\pi$
$151$	18.4206	+	6.70454i	1.49904	+	0.545607i	0.543231	+	0.839583i	$0.317201\pi$
$152$	−10.0893	+	2.70342i	−0.818351	+	0.219276i
$153$	0.866112	−	0.180982i	0.0700210	−	0.0146315i
$154$	−7.75081	+	4.47493i	−0.624578	+	0.360600i
$155$	2.88229	−	7.04359i	0.231511	−	0.565755i
$156$	−1.35767	+	11.7363i	−0.108700	+	0.939660i
$157$	0.239187	−	0.512939i	0.0190892	−	0.0409370i	−0.896532	−	0.442979i	$-0.853922\pi$
$157$	0.239187	−	0.512939i	0.0190892	−	0.0409370i	0.915621	+	0.402042i	$0.131699\pi$
$158$	−4.94237	−	7.05843i	−0.393193	−	0.561538i
$159$	2.48401	−	2.34912i	0.196995	−	0.186297i
$160$	−9.71943	−	7.39209i	−0.768388	−	0.584396i
$161$			5.14586i			0.405551i
$162$	−5.10970	−	1.02981i	−0.401456	−	0.0809093i
$163$	3.48997	+	3.48997i	0.273355	+	0.273355i	0.830449	−	0.557094i	$-0.188084\pi$
$163$	3.48997	+	3.48997i	0.273355	+	0.273355i	−0.557094	+	0.830449i	$0.688084\pi$
$164$	4.82015	−	4.04459i	0.376391	−	0.315829i
$165$	−9.82347	+	14.6446i	−0.764756	+	1.14008i
$166$	−0.958215	+	5.43431i	−0.0743719	+	0.421784i
$167$	13.2832	+	6.19404i	1.02788	+	0.479309i	0.862039	−	0.506843i	$-0.169188\pi$
$167$	13.2832	+	6.19404i	1.02788	+	0.479309i	0.165844	+	0.986152i	$0.446965\pi$
$168$	−7.74995	−	9.77754i	−0.597922	−	0.754354i
$169$	−3.73474	+	0.658535i	−0.287288	+	0.0506566i
$170$	−0.381663	−	0.0150272i	−0.0292722	−	0.00115253i
$171$	−13.1782	+	6.65756i	−1.00776	+	0.509116i
$172$	4.10687	+	15.3270i	0.313146	+	1.16868i
$173$	−8.49331	+	3.96050i	−0.645735	+	0.301111i	−0.717759	−	0.696292i	$-0.754832\pi$
$173$	−8.49331	+	3.96050i	−0.645735	+	0.301111i	0.0720241	+	0.997403i	$0.477054\pi$
$174$	6.09514	−	4.01921i	0.462071	−	0.304695i
$175$	8.61045	+	14.6232i	0.650889	+	1.10541i
$176$	6.14592	−	7.32442i	0.463266	−	0.552099i
$177$	16.3465	−	5.43816i	1.22868	−	0.408757i
$178$	3.03393	+	6.50628i	0.227403	+	0.487666i
$179$	10.1322	−	17.5496i	0.757320	−	1.31172i	−0.186893	−	0.982380i	$-0.559842\pi$
$179$	10.1322	−	17.5496i	0.757320	−	1.31172i	0.944213	−	0.329336i	$-0.106825\pi$
$180$	−10.0826	−	4.79879i	−0.751509	−	0.357681i
$181$	5.71685	+	9.90188i	0.424930	+	0.736001i	0.996414	−	0.0846126i	$-0.0269653\pi$
$181$	5.71685	+	9.90188i	0.424930	+	0.736001i	−0.571484	+	0.820613i	$0.693632\pi$
$182$	4.62013	−	6.59823i	0.342467	−	0.489094i
$183$	0.363754	+	2.46294i	0.0268894	+	0.182066i
$184$	1.10058	+	3.02383i	0.0811361	+	0.222920i
$185$	0.533632	+	11.1288i	0.0392334	+	0.818206i
$186$	0.975318	−	3.27191i	0.0715138	−	0.239908i
$187$	0.117041	−	1.33779i	0.00855889	−	0.0978286i
$188$	−2.25547	+	2.25547i	−0.164497	+	0.164497i
$189$	−13.5499	−	11.2878i	−0.985613	−	0.821067i
$190$	6.21648	−	1.40610i	0.450991	−	0.102010i
$191$	−3.38340	−	4.03218i	−0.244814	−	0.291758i	0.629619	−	0.776904i	$-0.283211\pi$
$191$	−3.38340	−	4.03218i	−0.244814	−	0.291758i	−0.874433	+	0.485146i	$0.838767\pi$
$192$	1.53005	+	0.941244i	0.110422	+	0.0679284i
$193$	8.91213	−	6.24034i	0.641509	−	0.449189i	−0.207021	−	0.978336i	$-0.566377\pi$
$193$	8.91213	−	6.24034i	0.641509	−	0.449189i	0.848530	+	0.529147i	$0.177488\pi$
$194$	2.46956	−	0.898848i	0.177304	−	0.0645335i
$195$	2.44265	−	15.6818i	0.174921	−	1.12300i
$196$	−1.30624	−	7.40806i	−0.0933030	−	0.529147i
$197$	2.41739	−	9.02182i	0.172232	−	0.642778i	−0.824775	−	0.565461i	$-0.808698\pi$
$197$	2.41739	−	9.02182i	0.172232	−	0.642778i	0.997007	−	0.0773166i	$-0.0246352\pi$
$198$	−3.73801	+	6.97212i	−0.265649	+	0.495487i
$199$	10.1326	+	5.85008i	0.718284	+	0.414701i	0.814121	−	0.580696i	$-0.197219\pi$
$199$	10.1326	+	5.85008i	0.718284	+	0.414701i	−0.0958368	+	0.995397i	$0.530553\pi$
$200$	8.18726	+	6.75133i	0.578927	+	0.477391i
$201$	16.4208	−	0.975955i	1.15824	−	0.0688386i
$202$	5.06572	−	0.443193i	0.356423	−	0.0311830i
$203$	24.6080	−	2.15293i	1.72715	−	0.151106i
$204$	0.848850	−	0.0504506i	0.0594314	−	0.00353225i
$205$	−6.68379	+	5.17426i	−0.466816	+	0.361386i
$206$	1.54310	+	0.890911i	0.107513	+	0.0620727i
$207$	2.39705	+	3.86565i	0.166606	+	0.268681i
$208$	−2.22721	+	8.31207i	−0.154429	+	0.576339i
$209$	3.89112	+	22.0677i	0.269155	+	1.52645i
$210$	4.49052	+	6.14754i	0.309875	+	0.424220i
$211$	−13.7093	+	4.98977i	−0.943786	+	0.343510i	−0.767660	−	0.640858i	$-0.778579\pi$
$211$	−13.7093	+	4.98977i	−0.943786	+	0.343510i	−0.176126	+	0.984368i	$0.556357\pi$
$212$	2.69147	−	1.88459i	0.184851	−	0.129434i
$213$	−1.24054	−	0.763143i	−0.0850001	−	0.0522897i
$214$	0.442286	+	0.527096i	0.0302340	+	0.0360315i
$215$	−4.70257	−	20.7903i	−0.320712	−	1.41789i
$216$	−10.3765	−	3.73495i	−0.706029	−	0.254131i
$217$	8.16812	−	8.16812i	0.554488	−	0.554488i
$218$	−0.774340	+	8.85074i	−0.0524449	+	0.599448i
$219$	−0.317476	+	1.06504i	−0.0214530	+	0.0719688i
$220$	−11.3958	+	12.5437i	−0.768302	+	0.845694i
$221$	0.413372	+	1.13573i	0.0278064	+	0.0763974i
$222$	0.730279	+	4.94465i	0.0490131	+	0.331863i
$223$	−11.8646	+	16.9444i	−0.794514	+	1.13468i	0.193618	+	0.981077i	$0.437978\pi$
$223$	−11.8646	+	16.9444i	−0.794514	+	1.13468i	−0.988132	+	0.153607i	$0.950911\pi$
$224$	−9.26718	−	16.0512i	−0.619190	−	1.07247i
$225$	13.2801	+	6.97422i	0.885338	+	0.464948i
$226$	−1.07897	+	1.86883i	−0.0717718	+	0.124312i
$227$	−4.17394	−	8.95104i	−0.277034	−	0.594101i	0.717728	−	0.696324i	$-0.245182\pi$
$227$	−4.17394	−	8.95104i	−0.277034	−	0.594101i	−0.994762	+	0.102223i	$0.967405\pi$
$228$	−13.4637	+	4.47913i	−0.891658	+	0.296638i
$229$	17.3346	−	20.6585i	1.14550	−	1.36515i	0.225024	−	0.974353i	$-0.427754\pi$
$229$	17.3346	−	20.6585i	1.14550	−	1.36515i	0.920475	−	0.390800i	$-0.127802\pi$
$230$	−0.598449	−	1.87009i	−0.0394605	−	0.123310i
$231$	−22.3450	+	14.7345i	−1.47019	+	0.969460i
$232$	13.9998	−	6.52821i	0.919131	−	0.428598i
$233$	−1.67108	−	6.23657i	−0.109476	−	0.408571i	0.889338	−	0.457250i	$-0.151166\pi$
$233$	−1.67108	−	6.23657i	−0.109476	−	0.408571i	−0.998814	+	0.0486789i	$0.984499\pi$
$234$	0.397119	−	7.10884i	0.0259605	−	0.464720i
$235$	3.14669	−	2.90829i	0.205268	−	0.189716i
$236$	16.3047	−	2.87495i	1.06134	−	0.187143i
$237$	−16.0071	−	20.1950i	−1.03977	−	1.31181i
$238$	−0.525432	−	0.245013i	−0.0340587	−	0.0158818i
$239$	−2.94647	+	16.7103i	−0.190591	+	1.08090i	0.727967	+	0.685612i	$0.240465\pi$
$239$	−2.94647	+	16.7103i	−0.190591	+	1.08090i	−0.918558	+	0.395286i	$0.870646\pi$
$240$	−6.75425	−	4.53070i	−0.435985	−	0.292455i
$241$	−3.88280	+	3.25805i	−0.250113	+	0.209870i	−0.759221	−	0.650833i	$-0.774420\pi$
$241$	−3.88280	+	3.25805i	−0.250113	+	0.209870i	0.509108	+	0.860703i	$0.329975\pi$
$242$	3.98508	+	3.98508i	0.256171	+	0.256171i
$243$	−15.4370	−	2.16772i	−0.990284	−	0.139059i
$244$			2.39267i			0.153175i
$245$	1.36184	+	10.0128i	0.0870045	+	0.639693i
$246$	−2.75508	+	2.60547i	−0.175657	+	0.166118i
$247$	−11.5676	−	16.5202i	−0.736028	−	1.05116i
$248$	3.05280	−	6.54675i	0.193853	−	0.415719i
$249$	−1.89640	+	16.3934i	−0.120179	+	1.03889i
$250$	−4.82980	−	4.31292i	−0.305464	−	0.272773i
$251$	−7.62764	+	4.40382i	−0.481452	+	0.277967i	−0.721022	−	0.692913i	$-0.756327\pi$
$251$	−7.62764	+	4.40382i	−0.481452	+	0.277967i	0.239569	+	0.970879i	$0.422994\pi$
$252$	−11.2974	−	12.6342i	−0.711667	−	0.795882i
$253$	6.66810	−	1.78671i	0.419220	−	0.112330i
$254$	9.60949	+	3.49757i	0.602953	+	0.219457i
$255$	−1.14207	+	0.0228575i	−0.0715190	+	0.00143139i
$256$	−3.52314	−	2.95627i	−0.220196	−	0.184767i
$257$	2.26790	+	25.9222i	0.141468	+	1.61698i	0.652753	+	0.757571i	$0.273614\pi$
$257$	2.26790	+	25.9222i	0.141468	+	1.61698i	−0.511286	+	0.859411i	$0.670831\pi$
$258$	−3.01860	−	9.07354i	−0.187930	−	0.564894i
$259$	−5.78393	+	15.8912i	−0.359396	+	0.987432i
$260$	4.52424	−	14.5662i	0.280581	−	0.903355i
$261$	17.4830	−	13.0802i	1.08217	−	0.809647i
$262$	2.48066	+	0.664690i	0.153256	+	0.0410647i
$263$	−4.72837	−	3.31084i	−0.291564	−	0.204155i	0.418638	−	0.908153i	$-0.362507\pi$
$263$	−4.72837	−	3.31084i	−0.291564	−	0.204155i	−0.710202	+	0.703998i	$0.751396\pi$
$264$	−9.97903	+	13.4374i	−0.614167	+	0.827016i
$265$	−3.71232	+	2.38741i	−0.228046	+	0.146658i
$266$	9.52696	+	1.67986i	0.584136	+	0.102999i
$267$	10.2118	+	18.8853i	0.624951	+	1.15576i
$268$	15.7488	+	1.37784i	0.962011	+	0.0841651i
$269$	−21.3254			−1.30023			−0.650116	−	0.759835i	$-0.725280\pi$
$269$	−21.3254			−1.30023			−0.650116	+	0.759835i	$0.725280\pi$
$270$	6.23699	+	2.52634i	0.379571	+	0.153748i
$271$	13.8664			0.842325			0.421162	−	0.906985i	$-0.361622\pi$
$271$	13.8664			0.842325			0.421162	+	0.906985i	$0.361622\pi$
$272$	0.617003	+	0.0539808i	0.0374113	+	0.00327306i
$273$	12.6220	−	20.5178i	0.763919	−	1.24180i
$274$	9.80135	+	1.72824i	0.592121	+	0.104407i
$275$	15.9593	−	16.2349i	0.962383	−	0.979004i
$276$	1.73615	+	4.01176i	0.104504	+	0.241480i
$277$	−3.39790	−	2.37923i	−0.204160	−	0.142954i	0.467025	−	0.884244i	$-0.345326\pi$
$277$	−3.39790	−	2.37923i	−0.204160	−	0.142954i	−0.671185	+	0.741290i	$0.734215\pi$
$278$	−1.98409	−	0.531636i	−0.118998	−	0.0318854i
$279$	2.33113	−	9.94089i	0.139561	−	0.595146i
$280$	7.49849	+	14.2552i	0.448121	+	0.851908i
$281$	4.59659	−	12.6290i	0.274210	−	0.753385i	−0.723781	−	0.690029i	$-0.757598\pi$
$281$	4.59659	−	12.6290i	0.274210	−	0.753385i	0.997991	−	0.0633553i	$-0.0201801\pi$
$282$	1.27620	−	1.43748i	0.0759963	−	0.0856007i
$283$	1.01502	+	11.6017i	0.0603367	+	0.689651i	0.964780	+	0.263058i	$0.0847310\pi$
$283$	1.01502	+	11.6017i	0.0603367	+	0.689651i	−0.904443	+	0.426594i	$0.859713\pi$
$284$	−1.07226	−	0.899731i	−0.0636268	−	0.0533892i
$285$	18.3089	−	5.30073i	1.08453	−	0.313988i
$286$	−10.1543	−	3.69586i	−0.600435	−	0.218541i
$287$	−12.3924	+	3.32054i	−0.731502	+	0.196005i
$288$	−14.4386	−	7.74108i	−0.850805	−	0.456147i
$289$	−14.6471	+	8.45651i	−0.861594	+	0.497441i
$290$	−8.69257	+	3.64425i	−0.510445	+	0.213998i
$291$	7.21305	−	3.12156i	0.422836	−	0.182989i
$292$	−0.451380	+	0.967988i	−0.0264150	+	0.0566472i
$293$	−15.1248	−	21.6004i	−0.883598	−	1.26191i	−0.964204	−	0.265162i	$-0.914574\pi$
$293$	−15.1248	−	21.6004i	−0.883598	−	1.26191i	0.0806060	−	0.996746i	$-0.474314\pi$
$294$	1.05067	+	4.40981i	0.0612764	+	0.257185i
$295$	−22.0375	+	2.99731i	−1.28307	+	0.174510i
$296$			10.5751i			0.614665i
$297$	−9.92222	+	21.4775i	−0.575746	+	1.24625i
$298$	1.46771	+	1.46771i	0.0850222	+	0.0850222i
$299$	−4.75947	+	3.99367i	−0.275248	+	0.230960i
$300$	11.6465	+	8.49530i	0.672410	+	0.490476i
$301$	5.61812	−	31.8619i	0.323823	−	1.83649i
$302$	−10.2894	−	4.79804i	−0.592090	−	0.276096i
$303$	15.0444	−	2.22191i	0.864276	−	0.127645i
$304$	−10.1779	+	1.79463i	−0.583741	+	0.102929i
$305$	0.126452	−	3.21165i	0.00724063	−	0.183899i
$306$	−0.508844	+	0.0606996i	−0.0290887	+	0.00346997i
$307$	4.69578	+	17.5249i	0.268003	+	1.00020i	0.960387	+	0.278670i	$0.0898936\pi$
$307$	4.69578	+	17.5249i	0.268003	+	1.00020i	−0.692384	+	0.721529i	$0.743440\pi$
$308$	−23.3129	+	10.8710i	−1.32838	+	0.619433i
$309$	4.76479	+	2.38589i	0.271059	+	0.135729i
$310$	−2.01849	+	3.91835i	−0.114643	+	0.222547i
$311$	11.0997	−	13.2281i	0.629405	−	0.750095i	−0.353252	−	0.935528i	$-0.614924\pi$
$311$	11.0997	−	13.2281i	0.629405	−	0.750095i	0.982657	+	0.185433i	$0.0593687\pi$
$312$	3.02869	−	14.7563i	0.171466	−	0.835412i
$313$	−6.31743	−	13.5478i	−0.357082	−	0.765766i	0.642918	−	0.765935i	$-0.277724\pi$
$313$	−6.31743	−	13.5478i	−0.357082	−	0.765766i	−1.00000		0.000169586i	$0.999946\pi$
$314$	−0.163892	+	0.283870i	−0.00924897	+	0.0160197i
$315$	14.4966	+	17.5558i	0.816790	+	0.989160i
$316$	−12.3828	−	21.4476i	−0.696586	−	1.20652i
$317$	−8.90361	+	12.7157i	−0.500077	+	0.714183i	−0.987260	−	0.159116i	$-0.949135\pi$
$317$	−8.90361	+	12.7157i	−0.500077	+	0.714183i	0.487183	+	0.873300i	$0.338024\pi$
$318$	−1.55174	+	1.22995i	−0.0870173	+	0.0689723i
$319$	−11.3340	−	31.1400i	−0.634585	−	1.74351i
$320$	−1.71653	−	1.55944i	−0.0959567	−	0.0871754i
$321$	1.41390	+	1.49509i	0.0789165	+	0.0834480i
$322$	0.259748	−	2.96894i	0.0144752	−	0.165452i
$323$	−1.02639	+	1.02639i	−0.0571100	+	0.0571100i
$324$	−14.3720	−	4.22848i	−0.798446	−	0.234916i
$325$	−6.84264	+	19.3129i	−0.379562	+	1.07129i
$326$	−1.83739	−	2.18972i	−0.101764	−	0.121277i
$327$	−0.741279	+	26.5600i	−0.0409928	+	1.46877i
$328$	−6.57189	+	4.60169i	−0.362872	+	0.254086i
$329$	6.11145	−	2.22439i	0.336935	−	0.122634i
$330$	6.40692	−	7.95341i	0.352690	−	0.437821i
$331$	0.733175	+	4.15804i	0.0402990	+	0.228547i	0.998305	−	0.0582018i	$-0.0185367\pi$
$331$	0.733175	+	4.15804i	0.0402990	+	0.228547i	−0.958006	+	0.286749i	$0.907426\pi$
$332$	−4.10481	+	15.3194i	−0.225281	+	0.840760i
$333$	3.05748	+	14.6320i	0.167549	+	0.801828i
$334$	−7.35114	−	4.24418i	−0.402237	−	0.232231i
$335$	−21.0666	−	2.68178i	−1.15099	−	0.146521i
$336$	−6.79574	−	10.3058i	−0.370738	−	0.562225i
$337$	−4.83165	+	0.422715i	−0.263197	+	0.0230267i	−0.217990	−	0.975951i	$-0.569950\pi$
$337$	−4.83165	+	0.422715i	−0.263197	+	0.0230267i	−0.0452064	+	0.998978i	$0.514395\pi$
$338$	2.18802	−	0.191427i	0.119013	−	0.0104123i
$339$	−2.88951	+	5.77056i	−0.156937	+	0.313414i
$340$	−1.08901	−	0.138631i	−0.0590597	−	0.00751830i
$341$	−13.4205	−	7.74832i	−0.726760	−	0.419595i
$342$	7.93931	−	3.17592i	0.429309	−	0.171734i
$343$	2.17930	−	8.13327i	0.117671	−	0.439155i
$344$	−3.51321	−	19.9244i	−0.189419	−	1.07425i
$345$	−2.11840	−	5.47669i	−0.114051	−	0.294855i
$346$	5.10018	−	1.85631i	0.274187	−	0.0997961i
$347$	15.3139	−	10.7229i	0.822092	−	0.575635i	−0.0850901	−	0.996373i	$-0.527118\pi$
$347$	15.3139	−	10.7229i	0.822092	−	0.575635i	0.907182	+	0.420738i	$0.138229\pi$
$348$	18.4583	−	9.98091i	0.989468	−	0.535033i
$349$	−5.80311	−	6.91588i	−0.310634	−	0.370199i	0.588029	−	0.808840i	$-0.299904\pi$
$349$	−5.80311	−	6.91588i	−0.310634	−	0.370199i	−0.898662	+	0.438641i	$0.855460\pi$
$350$	−4.22971	−	8.87156i	−0.226088	−	0.474205i
$351$	−0.0757929	−	21.2929i	−0.00404552	−	1.13653i
$352$	−17.5818	+	17.5818i	−0.937112	+	0.937112i
$353$	−3.00095	+	34.3010i	−0.159724	+	1.82566i	0.319069	+	0.947731i	$0.396630\pi$
$353$	−3.00095	+	34.3010i	−0.159724	+	1.82566i	−0.478794	+	0.877927i	$0.658926\pi$
$354$	−9.70569	+	2.31246i	−0.515852	+	0.122906i
$355$	1.39173	+	1.26437i	0.0738652	+	0.0671056i
$356$	7.05689	+	19.3887i	0.374015	+	1.02760i
$357$	−1.61207	−	0.638223i	−0.0853200	−	0.0337783i
$358$	−6.73171	+	9.61388i	−0.355782	+	0.508109i
$359$	2.43212	+	4.21256i	0.128363	+	0.222330i	0.923042	−	0.384698i	$-0.125695\pi$
$359$	2.43212	+	4.21256i	0.128363	+	0.222330i	−0.794680	+	0.607029i	$0.792361\pi$
$360$	12.2733	+	7.21573i	0.646861	+	0.380302i
$361$	2.61048	−	4.52148i	0.137394	−	0.237973i
$362$	−2.79855	−	6.00152i	−0.147089	−	0.315433i
$363$	12.6040	+	11.1898i	0.661537	+	0.587313i
$364$	14.8811	−	17.7346i	0.779982	−	0.929546i
$365$	0.657040	−	1.27546i	0.0343910	−	0.0667608i
$366$	−0.0855476	−	1.43937i	−0.00447164	−	0.0752371i
$367$	16.1484	−	7.53013i	0.842941	−	0.393070i	0.0473310	−	0.998879i	$-0.484928\pi$
$367$	16.1484	−	7.53013i	0.842941	−	0.393070i	0.795610	+	0.605810i	$0.207151\pi$
$368$	0.824053	+	3.07541i	0.0429568	+	0.160317i
$369$	−7.76260	+	8.26709i	−0.404105	+	0.430368i
$370$	0.253868	−	6.44777i	0.0131980	−	0.335203i
$371$	−6.59754	+	1.16332i	−0.342527	+	0.0603968i
$372$	3.61211	−	9.12377i	0.187279	−	0.473046i
$373$	1.45346	+	0.677762i	0.0752575	+	0.0350932i	0.459883	−	0.887980i	$-0.347891\pi$
$373$	1.45346	+	0.677762i	0.0752575	+	0.0350932i	−0.384625	+	0.923073i	$0.625669\pi$
$374$	−0.135055	+	0.765936i	−0.00698353	+	0.0396056i
$375$	−15.1839	−	12.0186i	−0.784095	−	0.620640i
$376$	3.11548	−	2.61420i	0.160669	−	0.134817i
$377$	21.0894	+	21.0894i	1.08616	+	1.08616i
$378$	7.24794	+	7.19652i	0.372794	+	0.370149i
$379$		−	16.2538i		−	0.834901i	−0.908700	−	0.417451i	$-0.862924\pi$
$379$		−	16.2538i		−	0.834901i	0.908700	−	0.417451i	$-0.137076\pi$
$380$	18.1511	−	2.46873i	0.931133	−	0.126643i
$381$	29.3084	+	8.73647i	1.50151	+	0.447583i
$382$	1.74854	+	2.49717i	0.0894631	+	0.127767i
$383$	−14.0616	+	30.1551i	−0.718512	+	1.54085i	0.118066	+	0.993006i	$0.462331\pi$
$383$	−14.0616	+	30.1551i	−0.718512	+	1.54085i	−0.836578	+	0.547848i	$0.815447\pi$
$384$	−16.0227	−	11.8989i	−0.817653	−	0.607214i
$385$	31.8672	−	13.3599i	1.62410	−	0.680885i
$386$	−5.45690	+	3.15054i	−0.277749	+	0.160358i
$387$	−10.6215	−	26.5522i	−0.539922	−	1.34972i
$388$	7.29597	−	1.95495i	0.370397	−	0.0992475i
$389$	11.1086	+	4.04319i	0.563227	+	0.204998i	0.607914	−	0.794003i	$-0.292007\pi$
$389$	11.1086	+	4.04319i	0.563227	+	0.204998i	−0.0446865	+	0.999001i	$0.514229\pi$
$390$	−2.20087	+	8.92441i	−0.111445	+	0.451905i
$391$	0.342560	+	0.287442i	0.0173240	+	0.0145366i
$392$	0.835926	+	9.55468i	0.0422207	+	0.482584i
$393$	7.52359	+	1.54419i	0.379515	+	0.0778942i
$394$	−1.85012	+	5.08317i	−0.0932078	+	0.256086i
$395$	15.4878	+	29.4433i	0.779273	+	1.48145i
$396$	−12.4491	+	19.0261i	−0.625590	+	0.956098i
$397$	12.4793	+	3.34381i	0.626317	+	0.167821i	0.557998	−	0.829842i	$-0.311570\pi$
$397$	12.4793	+	3.34381i	0.626317	+	0.167821i	0.0683192	+	0.997664i	$0.478236\pi$
$398$	−5.55079	−	3.88671i	−0.278236	−	0.194823i
$399$	28.7395	+	3.32460i	1.43877	+	0.166438i
$400$	7.48775	+	7.36063i	0.374387	+	0.368031i
$401$	−7.99873	−	1.41039i	−0.399437	−	0.0704316i	−0.0296788	−	0.999559i	$-0.509448\pi$
$401$	−7.99873	−	1.41039i	−0.399437	−	0.0704316i	−0.369758	+	0.929128i	$0.620560\pi$
$402$	−9.52336	−	0.265793i	−0.474982	−	0.0132565i
$403$	13.8940	+	1.21557i	0.692111	+	0.0605519i
$404$	14.6151			0.727129
$405$	19.0679	+	6.43540i	0.947493	+	0.319778i
$406$	−14.3064			−0.710016
$407$	22.6004	+	1.97728i	1.12026	+	0.0980100i
$408$	−1.08379	−	0.0302482i	−0.0536558	−	0.00149751i
$409$	21.0475	+	3.71124i	1.04073	+	0.183509i	0.667793	−	0.744347i	$-0.267239\pi$
$409$	21.0475	+	3.71124i	1.04073	+	0.183509i	0.372938	+	0.927856i	$0.378350\pi$
$410$	4.11743	−	2.64794i	0.203346	−	0.130772i
$411$	29.5672	+	3.42035i	1.45844	+	0.168714i
$412$	4.19501	+	2.93738i	0.206673	+	0.144714i
$413$	−32.6069	−	8.73700i	−1.60448	−	0.429919i
$414$	−1.18786	−	2.35130i	−0.0583804	−	0.115560i
$415$	6.31947	−	20.3461i	0.310210	−	0.998749i
$416$	7.65378	−	21.0286i	0.375258	−	1.03101i
$417$	−6.01755	−	1.23508i	−0.294681	−	0.0604822i
$418$	−1.13110	−	12.9285i	−0.0553237	−	0.632353i
$419$	−2.15215	−	1.80587i	−0.105139	−	0.0882223i	0.588703	−	0.808350i	$-0.299639\pi$
$419$	−2.15215	−	1.80587i	−0.105139	−	0.0882223i	−0.693842	+	0.720127i	$0.744083\pi$
$420$	11.3172	+	18.7264i	0.552225	+	0.913754i
$421$	−4.87917	−	1.77587i	−0.237796	−	0.0865507i	0.220373	−	0.975416i	$-0.429272\pi$
$421$	−4.87917	−	1.77587i	−0.237796	−	0.0865507i	−0.458169	+	0.888865i	$0.651495\pi$
$422$	8.16152	−	2.18687i	0.397297	−	0.106455i
$423$	3.55485	−	4.51783i	0.172843	−	0.219664i
$424$	−3.62806	+	2.09466i	−0.176194	+	0.101726i
$425$	1.45443	+	0.243636i	0.0705504	+	0.0118181i
$426$	0.677213	+	0.502919i	0.0328111	+	0.0243665i
$427$	2.06175	−	4.42144i	0.0997752	−	0.213969i
$428$	1.13431	+	1.61996i	0.0548289	+	0.0783038i
$429$	−30.9699	−	9.23177i	−1.49524	−	0.445714i
$430$	1.66374	+	12.2325i	0.0802325	+	0.589903i
$431$		−	12.2810i		−	0.591553i	−0.955257	−	0.295776i	$-0.904422\pi$
$431$		−	12.2810i		−	0.591553i	0.955257	−	0.295776i	$-0.0955783\pi$
$432$	−9.90569	−	4.57625i	−0.476588	−	0.220175i
$433$	10.5318	+	10.5318i	0.506127	+	0.506127i	0.913335	−	0.407209i	$-0.133498\pi$
$433$	10.5318	+	10.5318i	0.506127	+	0.506127i	−0.407209	+	0.913335i	$0.633498\pi$
$434$	−5.12495	+	4.30034i	−0.246005	+	0.206423i
$435$	−25.3038	+	12.4217i	−1.21323	+	0.595576i
$436$	−4.43415	+	25.1473i	−0.212357	+	1.20434i
$437$	−6.76271	−	3.15350i	−0.323504	−	0.150852i
$438$	0.236930	−	0.598457i	0.0113209	−	0.0285954i
$439$	−0.587913	+	0.103665i	−0.0280596	+	0.00494766i	−0.187660	−	0.982234i	$-0.560090\pi$
$439$	−0.587913	+	0.103665i	−0.0280596	+	0.00494766i	0.159601	+	0.987182i	$0.448979\pi$
$440$	15.8685	−	14.6663i	0.756502	−	0.699187i
$441$	3.91907	+	12.9784i	0.186622	+	0.618021i
$442$	−0.181169	−	0.676131i	−0.00861732	−	0.0321603i
$443$	20.1220	−	9.38303i	0.956024	−	0.445801i	0.118956	−	0.992900i	$-0.462045\pi$
$443$	20.1220	−	9.38303i	0.956024	−	0.445801i	0.837068	+	0.547098i	$0.184268\pi$
$444$	0.852305	+	14.3404i	0.0404486	+	0.680564i
$445$	−8.44769	−	26.3981i	−0.400459	−	1.25139i
$446$	7.70067	−	9.17730i	0.364637	−	0.434558i
$447$	4.64206	+	4.12123i	0.219562	+	0.194927i
$448$	−1.48763	−	3.19024i	−0.0702840	−	0.150724i
$449$	−2.87636	+	4.98200i	−0.135744	+	0.235115i	−0.925881	−	0.377814i	$-0.876676\pi$
$449$	−2.87636	+	4.98200i	−0.135744	+	0.235115i	0.790137	+	0.612930i	$0.210009\pi$
$450$	−7.30998	−	4.69416i	−0.344596	−	0.221285i
$451$	8.60564	+	14.9054i	0.405224	+	0.701868i
$452$	−3.55741	+	5.08051i	−0.167327	+	0.238967i
$453$	−31.5690	−	12.4982i	−1.48324	−	0.587216i
$454$	1.95636	+	5.37504i	0.0918163	+	0.252263i
$455$	−20.9120	+	23.0185i	−0.980370	+	1.07912i
$456$	17.5990	−	4.19311i	0.824150	−	0.196360i
$457$	2.29810	−	26.2674i	0.107501	−	1.22874i	−0.730440	−	0.682977i	$-0.760685\pi$
$457$	2.29810	−	26.2674i	0.107501	−	1.22874i	0.837941	−	0.545761i	$-0.183759\pi$
$458$	−11.0441	+	11.0441i	−0.516055	+	0.516055i
$459$	−1.50831	+	0.271495i	−0.0704019	+	0.0126723i
$460$	−1.24502	−	5.50431i	−0.0580493	−	0.256640i
$461$	−21.8021	−	25.9827i	−1.01542	−	1.21013i	−0.977518	−	0.210853i	$-0.932376\pi$
$461$	−21.8021	−	25.9827i	−1.01542	−	1.21013i	−0.0379057	−	0.999281i	$-0.512069\pi$
$462$	13.6358	−	7.37326i	0.634395	−	0.343035i
$463$	−14.3797	+	10.0688i	−0.668283	+	0.467937i	−0.857829	−	0.513935i	$-0.828187\pi$
$463$	−14.3797	+	10.0688i	−0.668283	+	0.467937i	0.189546	+	0.981872i	$0.439298\pi$
$464$	14.3622	−	5.22740i	0.666746	−	0.242676i
$465$	−5.33069	+	12.0558i	−0.247205	+	0.559075i
$466$	0.649338	+	3.68258i	0.0300800	+	0.170592i
$467$	1.95125	−	7.28218i	0.0902933	−	0.336979i	−0.905971	−	0.423341i	$-0.860857\pi$
$467$	1.95125	−	7.28218i	0.0902933	−	0.336979i	0.996264	+	0.0863616i	$0.0275240\pi$
$468$	2.91776	−	20.2544i	0.134873	−	0.936261i
$469$	−27.9151	−	16.1168i	−1.28900	−	0.744205i
$470$	−1.96231	+	1.51912i	−0.0905144	+	0.0700718i
$471$	−0.438910	+	0.876532i	−0.0202239	+	0.0403885i
$472$	−21.0292	+	1.83982i	−0.967948	+	0.0846845i
$473$	−43.2379	+	3.78283i	−1.98808	+	0.173935i
$474$	8.21602	+	12.4596i	0.377374	+	0.572289i
$475$	−24.4945	+	2.35446i	−1.12388	+	0.108030i
$476$	−1.44303	−	0.833134i	−0.0661412	−	0.0381867i
$477$	−4.41427	+	3.94718i	−0.202115	+	0.180729i
$478$	2.54347	−	9.49236i	0.116336	−	0.434171i
$479$	2.36842	+	13.4320i	0.108216	+	0.613722i	0.989887	+	0.141858i	$0.0453076\pi$
$479$	2.36842	+	13.4320i	0.108216	+	0.613722i	−0.881671	+	0.471864i	$0.843581\pi$
$480$	16.4708	+	13.2682i	0.751785	+	0.605606i
$481$	−19.1869	+	6.98344i	−0.874845	+	0.318418i
$482$	2.40466	−	1.68376i	0.109529	−	0.0766932i
$483$	0.248658	−	8.90943i	0.0113143	−	0.405393i
$484$	10.4118	+	12.4083i	0.473262	+	0.564012i
$485$	−9.89660	+	2.23851i	−0.449382	+	0.101646i
$486$	8.79705	+	2.02990i	0.399042	+	0.0920779i
$487$	17.1622	−	17.1622i	0.777696	−	0.777696i	−0.201743	−	0.979439i	$-0.564661\pi$
$487$	17.1622	−	17.1622i	0.777696	−	0.777696i	0.979439	+	0.201743i	$0.0646605\pi$
$488$	0.265887	−	3.03910i	0.0120361	−	0.137574i
$489$	−5.87381	−	6.21109i	−0.265623	−	0.280875i
$490$	−0.280303	−	5.84568i	−0.0126628	−	0.264081i
$491$	12.1283	+	33.3223i	0.547344	+	1.50382i	0.837282	+	0.546771i	$0.184143\pi$
$491$	12.1283	+	33.3223i	0.547344	+	1.50382i	−0.289938	+	0.957046i	$0.593635\pi$
$492$	−8.54094	+	6.76979i	−0.385056	+	0.305206i
$493$	1.23126	−	1.75842i	0.0554530	−	0.0791951i
$494$	5.84009	+	10.1153i	0.262758	+	0.455111i
$495$	17.7158	−	24.8806i	0.796265	−	1.11830i
$496$	3.57362	−	6.18969i	0.160460	−	0.277925i
$497$	1.20614	+	2.58658i	0.0541030	+	0.116024i
$498$	1.92163	−	9.36253i	0.0861101	−	0.419545i
$499$	−25.8228	+	30.7744i	−1.15599	+	1.37765i	−0.242815	+	0.970073i	$0.578071\pi$
$499$	−25.8228	+	30.7744i	−1.15599	+	1.37765i	−0.913171	+	0.407578i	$0.866374\pi$
$500$	−12.7482	−	13.5585i	−0.570118	−	0.606355i
$501$	−22.6989	−	11.3661i	−1.01411	−	0.507799i
$502$	4.62310	−	2.15579i	0.206339	−	0.0962176i
$503$	−1.01183	−	3.77620i	−0.0451153	−	0.168372i	0.939693	−	0.342020i	$-0.111111\pi$
$503$	−1.01183	−	3.77620i	−0.0451153	−	0.168372i	−0.984808	+	0.173648i	$0.944445\pi$
$504$	12.9456	+	17.3031i	0.576643	+	0.770741i
$505$	−19.6177	−	0.772406i	−0.872975	−	0.0343716i
$506$	−3.93739	+	0.694268i	−0.175038	+	0.0308640i
$507$	6.49806	−	0.959703i	0.288589	−	0.0426219i
$508$	26.6376	+	12.4213i	1.18185	+	0.551107i
$509$	−4.88932	+	27.7287i	−0.216715	+	1.22905i	0.661190	+	0.750219i	$0.270052\pi$
$509$	−4.88932	+	27.7287i	−0.216715	+	1.22905i	−0.877905	+	0.478835i	$0.841059\pi$
$510$	0.660076	+	0.0444605i	0.0292287	+	0.00196874i
$511$	1.66822	−	1.39980i	0.0737978	−	0.0619237i
$512$	−14.4119	−	14.4119i	−0.636923	−	0.636923i
$513$	23.1382	−	10.8899i	1.02158	−	0.480803i
$514$		−	15.0704i		−	0.664728i
$515$	−5.47567	−	4.16451i	−0.241287	−	0.183510i
$516$	−6.36990	−	26.7353i	−0.280419	−	1.17696i
$517$	−5.00438	−	7.14699i	−0.220092	−	0.314324i
$518$	4.13921	−	8.87657i	0.181867	−	0.390014i
$519$	14.8965	−	6.44670i	0.653884	−	0.282979i
$520$	−7.36524	+	17.9988i	−0.322987	+	0.789299i
$521$	20.7682	−	11.9905i	0.909872	−	0.525315i	0.0294818	−	0.999565i	$-0.490614\pi$
$521$	20.7682	−	11.9905i	0.909872	−	0.525315i	0.880390	+	0.474251i	$0.157281\pi$
$522$	−10.7472	+	6.66423i	−0.470392	+	0.291685i
$523$	−8.27760	+	2.21798i	−0.361954	+	0.0969853i	−0.435213	−	0.900328i	$-0.643327\pi$
$523$	−8.27760	+	2.21798i	−0.361954	+	0.0969853i	0.0732586	+	0.997313i	$0.476660\pi$
$524$	6.93607	+	2.52452i	0.303004	+	0.110284i
$525$	−14.2013	−	25.7343i	−0.619796	−	1.12314i
$526$	2.56094	+	2.14888i	0.111662	+	0.0936957i
$527$	−0.0874898	−	1.00001i	−0.00381111	−	0.0435612i
$528$	−10.9948	+	12.3843i	−0.478488	+	0.538959i
$529$	7.08023	−	19.4528i	0.307836	−	0.845773i
$530$	2.26236	−	1.19004i	0.0982705	−	0.0516922i
$531$	−28.5647	+	8.62561i	−1.23960	+	0.374320i
$532$	26.8566	+	7.19621i	1.16438	+	0.311995i
$533$	−12.6889	−	8.88487i	−0.549618	−	0.384846i
$534$	−4.93848	−	11.4114i	−0.213709	−	0.493821i
$535$	−1.43695	−	2.23440i	−0.0621249	−	0.0966016i
$536$	−19.8506	−	3.50020i	−0.857415	−	0.151185i
$537$	−18.3908	+	29.8953i	−0.793620	+	1.29008i
$538$	12.3038	+	1.07644i	0.530455	+	0.0464088i
$539$	20.5759			0.886268
$540$	17.2248	+	8.79572i	0.741238	+	0.378508i
$541$	−24.1490			−1.03825			−0.519123	−	0.854700i	$-0.673741\pi$
$541$	−24.1490			−1.03825			−0.519123	+	0.854700i	$0.673741\pi$
$542$	−8.00031	−	0.699936i	−0.343643	−	0.0300648i
$543$	−9.41955	−	17.4201i	−0.404231	−	0.747569i
$544$	−1.58618	−	0.279687i	−0.0680070	−	0.0119915i
$545$	7.28094	−	33.5206i	0.311881	−	1.43586i
$546$	−8.31803	+	11.2008i	−0.355979	+	0.479349i
$547$	−8.43453	−	5.90592i	−0.360634	−	0.252519i	0.379190	−	0.925319i	$-0.376203\pi$
$547$	−8.43453	−	5.90592i	−0.360634	−	0.252519i	−0.739825	+	0.672800i	$0.765092\pi$
$548$	27.6301	+	7.40347i	1.18030	+	0.316261i
$549$	−0.510780	−	4.28186i	−0.0217996	−	0.182745i
$550$	−10.0273	+	8.56127i	−0.427566	+	0.365054i
$551$	−12.2510	+	33.6593i	−0.521910	+	1.43394i
$552$	−1.75941	−	5.28857i	−0.0748853	−	0.225096i
$553$	4.40099	+	50.3035i	0.187149	+	2.13912i
$554$	1.84034	+	1.54423i	0.0781886	+	0.0656080i
$555$	−0.386152	−	19.2939i	−0.0163912	−	0.818982i
$556$	−5.54764	−	2.01918i	−0.235272	−	0.0856322i
$557$	0.0136213	−	0.00364981i	0.000577152	−	0.000154647i	−0.258530	−	0.966003i	$-0.583238\pi$
$557$	0.0136213	−	0.00364981i	0.000577152	−	0.000154647i	0.259108	+	0.965848i	$0.416572\pi$
$558$	−1.84675	+	5.61779i	−0.0781791	+	0.237820i
$559$	33.8297	−	19.5316i	1.43084	−	0.826098i
$560$	6.16176	+	14.6975i	0.260382	+	0.621084i
$561$	−0.267287	+	2.31056i	−0.0112849	+	0.0975517i
$562$	−3.28951	+	7.05437i	−0.138759	+	0.297571i
$563$	−8.54312	−	12.2008i	−0.360050	−	0.514204i	0.597734	−	0.801695i	$-0.296068\pi$
$563$	−8.54312	−	12.2008i	−0.360050	−	0.514204i	−0.957783	+	0.287490i	$0.907179\pi$
$564$	4.01406	−	3.79608i	0.169022	−	0.159844i
$565$	5.04357	−	6.63150i	0.212185	−	0.278989i
$566$		−	6.74492i		−	0.283510i
$567$	22.9146	+	20.1982i	0.962322	+	0.848244i
$568$	1.26197	+	1.26197i	0.0529511	+	0.0529511i
$569$	21.1007	−	17.7056i	0.884589	−	0.742258i	−0.0825286	−	0.996589i	$-0.526300\pi$
$569$	21.1007	−	17.7056i	0.884589	−	0.742258i	0.967117	+	0.254331i	$0.0818551\pi$
$570$	−10.8310	+	2.13410i	−0.453661	+	0.0893878i
$571$	−3.36410	+	19.0788i	−0.140783	+	0.798421i	0.829873	+	0.557952i	$0.188413\pi$
$571$	−3.36410	+	19.0788i	−0.140783	+	0.798421i	−0.970657	+	0.240470i	$0.922699\pi$
$572$	−28.1478	−	13.1255i	−1.17692	−	0.548805i
$573$	5.66310	+	7.14471i	0.236579	+	0.298475i
$574$	7.31750	−	1.29027i	0.305426	−	0.0538549i
$575$	1.38027	+	7.45416i	0.0575613	+	0.310860i
$576$	−2.60361	−	1.70358i	−0.108484	−	0.0709826i
$577$	−6.81468	−	25.4327i	−0.283699	−	1.05878i	−0.949785	−	0.312904i	$-0.898698\pi$
$577$	−6.81468	−	25.4327i	−0.283699	−	1.05878i	0.666086	−	0.745875i	$-0.267968\pi$
$578$	8.87759	−	4.13969i	0.369259	−	0.172188i
$579$	−15.7318	+	10.3737i	−0.653791	+	0.431117i
$580$	−25.8013	+	8.25670i	−1.07134	+	0.342841i
$581$	20.7860	−	24.7718i	0.862348	−	1.02771i
$582$	−4.31918	+	1.43691i	−0.179036	+	0.0595618i
$583$	3.79821	+	8.14529i	0.157306	+	0.337344i
$584$	0.680899	−	1.17935i	0.0281758	−	0.0488020i
$585$	−4.98691	+	27.0331i	−0.206184	+	1.11768i
$586$	7.63599	+	13.2259i	0.315440	+	0.546358i
$587$	11.8655	−	16.9456i	0.489740	−	0.699421i	−0.495882	−	0.868390i	$-0.665155\pi$
$587$	11.8655	−	16.9456i	0.489740	−	0.699421i	0.985621	+	0.168969i	$0.0540439\pi$
$588$	1.90362	+	12.8893i	0.0785041	+	0.531544i
$589$	5.72896	+	15.7402i	0.236058	+	0.648563i
$590$	12.8659	−	0.616929i	0.529683	−	0.0253985i
$591$	−4.62136	+	15.5034i	−0.190097	+	0.637723i
$592$	−0.911944	+	10.4236i	−0.0374807	+	0.428406i
$593$	25.1558	−	25.1558i	1.03302	−	1.03302i	0.0335886	−	0.999436i	$-0.489306\pi$
$593$	25.1558	−	25.1558i	1.03302	−	1.03302i	0.999436	−	0.0335886i	$-0.0106936\pi$
$594$	6.80881	−	11.8907i	0.279369	−	0.487883i
$595$	1.89293	+	1.19457i	0.0776026	+	0.0489726i
$596$	3.83467	+	4.56998i	0.157074	+	0.187194i
$597$	−17.2607	−	10.6183i	−0.706435	−	0.434579i
$598$	2.94760	−	2.06393i	0.120536	−	0.0844003i
$599$	−22.0669	+	8.03169i	−0.901629	+	0.328166i	−0.750905	−	0.660410i	$-0.770383\pi$
$599$	−22.0669	+	8.03169i	−0.901629	+	0.328166i	−0.150723	+	0.988576i	$0.548160\pi$
$600$	−13.8490	−	12.0847i	−0.565383	−	0.493357i
$601$	−0.359287	−	2.03762i	−0.0146556	−	0.0831161i	0.976603	−	0.215052i	$-0.0689920\pi$
$601$	−0.359287	−	2.03762i	−0.0146556	−	0.0831161i	−0.991258	+	0.131935i	$0.957881\pi$
$602$	−4.84970	+	18.0993i	−0.197659	+	0.737674i
$603$	−28.4778	+	0.896260i	−1.15971	+	0.0364985i
$604$	−28.2586	−	16.3151i	−1.14983	−	0.663853i
$605$	−13.3198	−	17.2057i	−0.541527	−	0.699512i
$606$	−8.79209	+	0.522549i	−0.357154	+	0.0212271i
$607$	27.2557	−	2.38456i	1.10627	−	0.0967864i	0.480651	−	0.876912i	$-0.340401\pi$
$607$	27.2557	−	2.38456i	1.10627	−	0.0967864i	0.625623	+	0.780126i	$0.284845\pi$
$608$	26.7737	−	2.34240i	1.08582	−	0.0949967i
$609$	−42.7098	+	2.53842i	−1.73069	+	0.102862i
$610$	−0.235072	+	1.84660i	−0.00951779	+	0.0747665i
$611$	6.80042	+	3.92623i	0.275116	+	0.158838i
$612$	−1.47212	+	0.0463308i	−0.0595068	+	0.00187281i
$613$	−2.44513	+	9.12534i	−0.0987578	+	0.368569i	−0.997562	−	0.0697805i	$-0.977770\pi$
$613$	−2.44513	+	9.12534i	−0.0987578	+	0.368569i	0.898805	+	0.438350i	$0.144437\pi$
$614$	−1.82465	−	10.3481i	−0.0736370	−	0.417616i
$615$	11.8222	−	8.63561i	0.476717	−	0.348222i
$616$	30.8195	−	11.2174i	1.24175	−	0.451962i
$617$	26.3513	−	18.4514i	1.06086	−	0.742826i	0.0933483	−	0.995634i	$-0.470243\pi$
$617$	26.3513	−	18.4514i	1.06086	−	0.742826i	0.967516	+	0.252808i	$0.0813541\pi$
$618$	−2.62864	−	1.61707i	−0.105739	−	0.0650480i
$619$	19.6122	+	23.3729i	0.788279	+	0.939435i	0.999276	−	0.0380520i	$-0.0121153\pi$
$619$	19.6122	+	23.3729i	0.788279	+	0.939435i	−0.210996	+	0.977487i	$0.567671\pi$
$620$	−6.76084	+	10.7133i	−0.271522	+	0.430257i
$621$	−3.96340	−	6.80872i	−0.159046	−	0.273225i
$622$	−7.07174	+	7.07174i	−0.283551	+	0.283551i
$623$	3.66660	−	41.9094i	0.146899	−	1.67907i
$624$	4.25780	−	14.2837i	0.170448	−	0.571806i
$625$	16.3952	+	18.8732i	0.655809	+	0.754927i
$626$	2.96103	+	8.13536i	0.118346	+	0.325154i
$627$	−5.67065	−	38.3955i	−0.226464	−	1.53337i
$628$	−0.540361	+	0.771716i	−0.0215628	+	0.0307948i
$629$	0.734793	+	1.27270i	0.0292981	+	0.0507459i
$630$	−7.47772	−	10.8607i	−0.297920	−	0.432700i
$631$	−13.5982	+	23.5528i	−0.541338	+	0.937624i	0.457490	+	0.889215i	$0.348749\pi$
$631$	−13.5982	+	23.5528i	−0.541338	+	0.937624i	−0.998828	+	0.0484094i	$0.984585\pi$
$632$	13.3449	+	28.6182i	0.530832	+	1.13837i
$633$	23.9770	−	7.97671i	0.953002	−	0.317046i
$634$	5.77884	−	6.88695i	0.229507	−	0.273516i
$635$	−35.0988	−	18.0808i	−1.39286	−	0.717513i
$636$	−4.75101	+	3.13287i	−0.188390	+	0.124226i
$637$	−16.7835	+	7.82626i	−0.664985	+	0.310088i
$638$	4.96739	+	18.5385i	0.196661	+	0.733948i
$639$	2.11096	+	1.38123i	0.0835082	+	0.0546408i
$640$	17.4879	+	18.9215i	0.691271	+	0.747937i
$641$	47.3771	−	8.35386i	1.87128	−	0.329957i	0.881459	−	0.472261i	$-0.156562\pi$
$641$	47.3771	−	8.35386i	1.87128	−	0.329957i	0.989823	+	0.142304i	$0.0454509\pi$
$642$	−0.740293	−	0.933973i	−0.0292170	−	0.0368610i
$643$	1.29754	+	0.605053i	0.0511700	+	0.0238610i	0.448035	−	0.894016i	$-0.352124\pi$
$643$	1.29754	+	0.605053i	0.0511700	+	0.0238610i	−0.396865	+	0.917877i	$0.629902\pi$
$644$	1.48741	−	8.43554i	0.0586123	−	0.332407i
$645$	7.13728	+	36.2232i	0.281030	+	1.42629i
$646$	0.643993	−	0.540374i	0.0253376	−	0.0212607i
$647$	−3.76082	−	3.76082i	−0.147853	−	0.147853i	0.629305	−	0.777158i	$-0.283340\pi$
$647$	−3.76082	−	3.76082i	−0.147853	−	0.147853i	−0.777158	+	0.629305i	$0.783340\pi$
$648$	17.7851	+	6.96801i	0.698664	+	0.273729i
$649$			45.2862i			1.77764i
$650$	4.92276	−	10.7973i	0.193087	−	0.423504i
$651$	−14.5368	+	13.7474i	−0.569742	+	0.538803i
$652$	−4.71228	−	6.72983i	−0.184547	−	0.263561i
$653$	−14.6726	+	31.4655i	−0.574184	+	1.23134i	0.377997	+	0.925807i	$0.376613\pi$
$653$	−14.6726	+	31.4655i	−0.574184	+	1.23134i	−0.952181	+	0.305535i	$0.901165\pi$
$654$	1.76836	−	15.2866i	0.0691483	−	0.597751i
$655$	−9.17678	−	3.75521i	−0.358567	−	0.146728i
$656$	−6.87455	+	3.96902i	−0.268406	+	0.154964i
$657$	0.601135	−	1.82865i	0.0234525	−	0.0713423i
$658$	−3.63832	+	0.974884i	−0.141836	+	0.0380049i
$659$	29.5525	+	10.7562i	1.15120	+	0.419003i	0.845946	−	0.533268i	$-0.179036\pi$
$659$	29.5525	+	10.7562i	1.15120	+	0.419003i	0.305254	+	0.952271i	$0.401258\pi$
$660$	20.3365	−	21.1671i	0.791597	−	0.823930i
$661$	18.2275	+	15.2947i	0.708967	+	0.594894i	0.924309	−	0.381645i	$-0.124642\pi$
$661$	18.2275	+	15.2947i	0.708967	+	0.594894i	−0.215342	+	0.976539i	$0.569087\pi$
$662$	−0.213124	−	2.43602i	−0.00828329	−	0.0946785i
$663$	−0.660821	−	1.98635i	−0.0256642	−	0.0771434i
$664$	6.91620	−	19.0021i	0.268401	−	0.737425i
$665$	−35.6690	−	11.0788i	−1.38318	−	0.429616i
$666$	−1.02545	−	8.59634i	−0.0397355	−	0.333101i
$667$	10.6590	+	2.85607i	0.412719	+	0.110588i
$668$	−19.9845	−	13.9933i	−0.773224	−	0.541417i
$669$	21.3609	−	28.7639i	0.825861	−	1.11208i
$670$	12.0191	+	2.61065i	0.464340	+	0.100858i
$671$	−6.44526	−	1.13647i	−0.248816	−	0.0438730i
$672$	15.2694	+	28.2385i	0.589028	+	1.08933i
$673$	−1.83430	−	0.160481i	−0.0707073	−	0.00618608i	0.0517472	−	0.998660i	$-0.483521\pi$
$673$	−1.83430	−	0.160481i	−0.0707073	−	0.00618608i	−0.122454	+	0.992474i	$0.539077\pi$
$674$	2.80899			0.108198
$675$	−22.6558	−	12.7167i	−0.872022	−	0.489467i
$676$	6.31265			0.242794
$677$	11.1662	+	0.976915i	0.429151	+	0.0375459i	0.299686	−	0.954038i	$-0.403118\pi$
$677$	11.1662	+	0.976915i	0.429151	+	0.0375459i	0.129466	+	0.991584i	$0.458674\pi$
$678$	1.95840	−	3.18350i	0.0752120	−	0.122262i
$679$	−15.1669	−	2.67433i	−0.582052	−	0.102631i
$680$	1.36782	+	0.297102i	0.0524536	+	0.0113933i
$681$	6.79413	+	15.6993i	0.260352	+	0.601599i
$682$	7.35191	+	5.14787i	0.281519	+	0.197122i
$683$	31.7505	+	8.50752i	1.21490	+	0.325531i	0.808682	−	0.588246i	$-0.200181\pi$
$683$	31.7505	+	8.50752i	1.21490	+	0.325531i	0.406216	+	0.913777i	$0.366848\pi$
$684$	23.5272	−	7.10447i	0.899586	−	0.271646i
$685$	−36.6963	−	11.3978i	−1.40209	−	0.435489i
$686$	−1.66791	+	4.58253i	−0.0636809	+	0.174962i
$687$	−31.0109	+	34.9300i	−1.18314	+	1.33266i
$688$	−1.74469	−	19.9419i	−0.0665155	−	0.760276i
$689$	−6.19628	−	5.19930i	−0.236060	−	0.198078i
$690$	0.945774	+	3.26674i	0.0360050	+	0.124363i
$691$	35.2185	+	12.8185i	1.33977	+	0.487638i	0.909742	−	0.415175i	$-0.136280\pi$
$691$	35.2185	+	12.8185i	1.33977	+	0.487638i	0.430033	+	0.902813i	$0.358502\pi$
$692$	15.0677	−	4.03739i	0.572790	−	0.153479i
$693$	39.3995	−	24.4313i	1.49666	−	0.928067i
$694$	−9.37669	+	5.41364i	−0.355934	+	0.205499i
$695$	7.33982	+	3.00351i	0.278415	+	0.113930i
$696$	−24.5544	+	10.6263i	−0.930731	+	0.402789i
$697$	−0.471178	+	1.01044i	−0.0178471	+	0.0382733i
$698$	2.99905	+	4.28308i	0.113516	+	0.162117i
$699$	2.59191	+	10.8786i	0.0980351	+	0.411466i
$700$	−9.88815	−	26.4604i	−0.373737	−	1.00011i
$701$			8.75525i			0.330681i	0.986237	+	0.165341i	$0.0528724\pi$
$701$			8.75525i			0.330681i	−0.986237	+	0.165341i	$0.947128\pi$
$702$	−1.03108	+	12.2889i	−0.0389154	+	0.463814i
$703$	−17.3398	−	17.3398i	−0.653981	−	0.653981i
$704$	−3.61744	+	3.03539i	−0.136337	+	0.114401i
$705$	−5.58865	+	4.88329i	−0.210481	+	0.183915i
$706$	3.46283	−	19.6387i	0.130325	−	0.739112i
$707$	−27.0074	−	12.5938i	−1.01572	−	0.473638i
$708$	−28.3684	+	4.18975i	−1.06615	+	0.157460i
$709$	7.84342	−	1.38301i	0.294566	−	0.0519399i	−0.0244124	−	0.999702i	$-0.507771\pi$
$709$	7.84342	−	1.38301i	0.294566	−	0.0519399i	0.318978	+	0.947762i	$0.396660\pi$
$710$	−0.739144	−	0.799734i	−0.0277396	−	0.0300135i
$711$	26.7385	+	35.7387i	1.00277	+	1.34030i
$712$	−6.80890	−	25.4112i	−0.255174	−	0.952323i
$713$	4.67685	−	2.18085i	0.175149	−	0.0816735i
$714$	0.897880	+	0.449599i	0.0336023	+	0.0168258i
$715$	37.0887	+	19.1058i	1.38704	+	0.714517i
$716$	−21.6823	+	25.8400i	−0.810307	+	0.965687i
$717$	5.90893	−	28.7894i	0.220673	−	1.07516i
$718$	−1.19059	−	2.55323i	−0.0444324	−	0.0952856i
$719$	−4.35425	+	7.54179i	−0.162386	+	0.281261i	−0.935724	−	0.352733i	$-0.885252\pi$
$719$	−4.35425	+	7.54179i	−0.162386	+	0.281261i	0.773338	+	0.633994i	$0.218586\pi$
$720$	11.4752	+	8.17073i	0.427656	+	0.304505i
$721$	−5.22089	−	9.04285i	−0.194436	−	0.336773i
$722$	−1.73436	+	2.47693i	−0.0645463	+	0.0921816i
$723$	6.88002	−	5.45329i	0.255871	−	0.202810i
$724$	−6.50941	−	17.8845i	−0.241920	−	0.664671i
$725$	35.0691	−	9.71927i	1.30243	−	0.360965i
$726$	−6.70711	−	7.09225i	−0.248924	−	0.263218i
$727$	−3.05305	+	34.8965i	−0.113231	+	1.29424i	0.700774	+	0.713383i	$0.252838\pi$
$727$	−3.05305	+	34.8965i	−0.113231	+	1.29424i	−0.814005	+	0.580857i	$0.802717\pi$
$728$	−20.8724	+	20.8724i	−0.773581	+	0.773581i
$729$	26.6225	+	4.49909i	0.986019	+	0.166633i
$730$	−0.443465	+	0.702720i	−0.0164134	+	0.0260088i
$731$	−1.80722	−	2.15377i	−0.0668426	−	0.0796599i
$732$	0.115618	−	4.14261i	0.00427338	−	0.153115i
$733$	15.4172	−	10.7952i	0.569447	−	0.398731i	−0.253090	−	0.967443i	$-0.581447\pi$
$733$	15.4172	−	10.7952i	0.569447	−	0.398731i	0.822537	+	0.568711i	$0.192558\pi$
$734$	−9.69703	+	3.52943i	−0.357924	+	0.130274i
$735$	−1.87401	−	17.4017i	−0.0691241	−	0.641872i
$736$	−1.43777	−	8.15398i	−0.0529968	−	0.300560i
$737$	−11.1919	+	41.7689i	−0.412261	+	1.53858i
$738$	4.89598	−	4.37791i	0.180223	−	0.161153i
$739$	9.05915	+	5.23030i	0.333246	+	0.192400i	0.657281	−	0.753645i	$-0.271706\pi$
$739$	9.05915	+	5.23030i	0.333246	+	0.192400i	−0.324035	+	0.946045i	$0.605040\pi$
$740$	2.34201	−	18.3975i	0.0860940	−	0.676307i
$741$	19.2296	+	29.1617i	0.706415	+	1.07128i
$742$	3.86521	−	0.338162i	0.141896	−	0.0124143i
$743$	26.5503	−	2.32285i	0.974035	−	0.0852170i	0.410987	−	0.911641i	$-0.365184\pi$
$743$	26.5503	−	2.32285i	0.974035	−	0.0852170i	0.563048	+	0.826424i	$0.309629\pi$
$744$	−5.60190	+	11.1874i	−0.205376	+	0.410149i
$745$	−4.90570	−	6.33689i	−0.179731	−	0.232166i
$746$	−0.804373	−	0.464405i	−0.0294502	−	0.0170031i
$747$	4.07554	−	28.2915i	0.149116	−	1.03513i
$748$	−0.578551	+	2.15918i	−0.0211539	+	0.0789475i
$749$	−0.700190	−	3.97098i	−0.0255844	−	0.145096i
$750$	8.15380	+	7.70067i	0.297735	+	0.281189i
$751$	−33.4699	+	12.1820i	−1.22133	+	0.444529i	−0.870621	−	0.491954i	$-0.836283\pi$
$751$	−33.4699	+	12.1820i	−1.22133	+	0.444529i	−0.350712	+	0.936483i	$0.614061\pi$
$752$	3.29628	−	2.30808i	0.120203	−	0.0841670i
$753$	13.4191	−	7.25609i	0.489020	−	0.264427i
$754$	−11.1031	−	13.2322i	−0.404352	−	0.481888i
$755$	37.0689	+	23.3930i	1.34908	+	0.851360i
$756$	18.9495	+	22.4205i	0.689186	+	0.815427i
$757$	−23.2266	+	23.2266i	−0.844185	+	0.844185i	−0.989400	−	0.145215i	$-0.953613\pi$
$757$	−23.2266	+	23.2266i	−0.844185	+	0.844185i	0.145215	+	0.989400i	$0.453613\pi$
$758$	−0.820445	+	9.37772i	−0.0297999	+	0.340614i
$759$	−11.6313	+	2.77126i	−0.422191	+	0.100590i
$760$	−23.3294	+	1.11866i	−0.846247	+	0.0405780i
$761$	−11.0481	−	30.3545i	−0.400494	−	1.10035i	−0.962041	−	0.272904i	$-0.912016\pi$
$761$	−11.0481	−	30.3545i	−0.400494	−	1.10035i	0.561547	−	0.827445i	$-0.310206\pi$
$762$	−16.4686	−	6.51996i	−0.596596	−	0.236193i
$763$	29.8633	−	42.6492i	1.08112	−	1.54400i
$764$	4.38086	+	7.58787i	0.158494	+	0.274519i
$765$	1.97845	+	0.0156119i	0.0715311	+	0.000564451i
$766$	9.63504	−	16.6884i	0.348128	−	0.602976i
$767$	−17.2251	−	36.9393i	−0.621961	−	1.33380i
$768$	5.95703	+	5.28866i	0.214956	+	0.190838i
$769$	−24.2180	+	28.8618i	−0.873322	+	1.04078i	0.125492	+	0.992095i	$0.459949\pi$
$769$	−24.2180	+	28.8618i	−0.873322	+	1.04078i	−0.998814	+	0.0486900i	$0.984495\pi$
$770$	−19.0603	+	6.09952i	−0.686887	+	0.219812i
$771$	−2.67397	−	44.9906i	−0.0963008	−	1.62030i
$772$	−16.4133	+	7.65364i	−0.590727	+	0.275461i
$773$	1.80797	+	6.74744i	0.0650282	+	0.242689i	0.990788	−	0.135424i	$-0.0432398\pi$
$773$	1.80797	+	6.74744i	0.0650282	+	0.242689i	−0.925759	+	0.378113i	$0.876573\pi$
$774$	4.78787	+	15.8556i	0.172097	+	0.569917i
$775$	9.64119	−	14.0231i	0.346322	−	0.503723i
$776$	−9.48439	+	1.67235i	−0.340470	+	0.0600340i
$777$	10.7821	−	27.2342i	0.386804	−	0.977021i
$778$	−6.20507	−	2.89347i	−0.222463	−	0.103736i
$779$	3.23050	−	18.3211i	0.115745	−	0.656421i
$780$	−8.53702	+	25.0009i	−0.305674	+	0.895176i
$781$	2.93295	−	2.46104i	0.104949	−	0.0880630i
$782$	−0.183133	−	0.183133i	−0.00654881	−	0.00654881i
$783$	−30.9018	+	21.8020i	−1.10434	+	0.779140i
$784$			9.48986i			0.338924i
$785$	0.766105	−	1.00731i	0.0273435	−	0.0359523i
$786$	−4.26283	−	1.27070i	−0.152050	−	0.0453244i
$787$	−8.41019	−	12.0110i	−0.299791	−	0.428146i	0.640790	−	0.767717i	$-0.278607\pi$
$787$	−8.41019	−	12.0110i	−0.299791	−	0.428146i	−0.940581	+	0.339571i	$0.889718\pi$
$788$	−6.57055	+	14.0906i	−0.234066	+	0.501956i
$789$	8.02660	+	5.96079i	0.285754	+	0.212210i
$790$	−7.44954	−	17.7693i	−0.265043	−	0.632202i
$791$	10.9516	−	6.32294i	0.389396	−	0.224818i
$792$	17.9268	−	22.7830i	0.637001	−	0.809560i
$793$	5.68957	−	1.52451i	0.202042	−	0.0541371i
$794$	−7.03121	−	2.55915i	−0.249528	−	0.0908209i
$795$	6.54280	−	3.95412i	0.232049	−	0.140238i
$796$	−14.9193	−	12.5188i	−0.528801	−	0.443717i
$797$	4.08425	+	46.6832i	0.144672	+	1.65360i	0.628035	+	0.778185i	$0.283859\pi$
$797$	4.08425	+	46.6832i	0.144672	+	1.65360i	−0.483364	+	0.875420i	$0.660585\pi$
$798$	−16.4136	−	3.36883i	−0.581035	−	0.119255i
$799$	0.193301	−	0.531090i	0.00683850	−	0.0187886i
$800$	−17.7296	−	20.7657i	−0.626836	−	0.734177i
$801$	−16.7679	−	33.1910i	−0.592464	−	1.17275i
$802$	4.54372	+	1.21749i	0.160444	+	0.0429909i
$803$	−2.39312	−	1.67568i	−0.0844515	−	0.0591335i
$804$	−27.2005	−	3.14658i	−0.959289	−	0.110971i
$805$	−2.44235	+	11.2443i	−0.0860816	+	0.396310i
$806$	−7.95488	−	1.40266i	−0.280199	−	0.0494066i
$807$	36.9223	+	1.03048i	1.29973	+	0.0362748i
$808$	−18.5637	−	1.62411i	−0.653069	−	0.0571362i
$809$	−48.2320			−1.69575			−0.847874	−	0.530198i	$-0.822118\pi$
$809$	−48.2320			−1.69575			−0.847874	+	0.530198i	$0.822118\pi$
$810$	−10.6765	−	4.67544i	−0.375134	−	0.164278i
$811$	−25.8197			−0.906653			−0.453326	−	0.891345i	$-0.649763\pi$
$811$	−25.8197			−0.906653			−0.453326	+	0.891345i	$0.649763\pi$
$812$	−40.9619	−	3.58370i	−1.43748	−	0.125763i
$813$	−24.0080	−	0.670052i	−0.841997	−	0.0234998i
$814$	−12.9396	−	2.28160i	−0.453533	−	0.0799702i
$815$	5.96956	+	9.28241i	0.209105	+	0.325149i
$816$	−1.06566	−	0.123276i	−0.0373054	−	0.00431552i
$817$	38.4301	+	26.9091i	1.34450	+	0.941429i
$818$	−11.9561	−	3.20364i	−0.418036	−	0.112013i
$819$	−22.8449	+	34.9142i	−0.798266	+	1.22000i
$820$	12.4523	−	6.55013i	0.434852	−	0.228741i
$821$	−16.5087	+	45.3573i	−0.576158	+	1.58298i	0.218443	+	0.975850i	$0.429902\pi$
$821$	−16.5087	+	45.3573i	−0.576158	+	1.58298i	−0.794601	+	0.607132i	$0.792320\pi$
$822$	−16.8863	−	3.46586i	−0.588978	−	0.120886i
$823$	−1.90579	−	21.7833i	−0.0664316	−	0.759316i	−0.954228	−	0.299080i	$-0.903320\pi$
$823$	−1.90579	−	21.7833i	−0.0664316	−	0.759316i	0.887796	−	0.460236i	$-0.152235\pi$
$824$	−5.00198	−	4.19716i	−0.174252	−	0.146215i
$825$	−28.4161	+	27.3376i	−0.989321	+	0.951773i
$826$	18.3717	+	6.68676i	0.639234	+	0.232662i
$827$	−11.9876	+	3.21205i	−0.416848	+	0.111694i	−0.461146	−	0.887324i	$-0.652562\pi$
$827$	−11.9876	+	3.21205i	−0.416848	+	0.111694i	0.0442980	+	0.999018i	$0.485895\pi$
$828$	−2.81208	−	7.02977i	−0.0977266	−	0.244301i
$829$	36.4705	−	21.0563i	1.26667	−	0.731314i	0.292316	−	0.956322i	$-0.405574\pi$
$829$	36.4705	−	21.0563i	1.26667	−	0.731314i	0.974357	+	0.225008i	$0.0722408\pi$
$830$	−4.67306	+	11.4198i	−0.162204	+	0.396387i
$831$	5.76807	+	4.28354i	0.200092	+	0.148594i
$832$	1.79615	−	3.85185i	0.0622702	−	0.133539i
$833$	0.764495	+	1.09181i	0.0264882	+	0.0378290i
$834$	3.40952	+	1.01634i	0.118062	+	0.0351929i
$835$	26.0854	+	19.8392i	0.902723	+	0.686564i
$836$		−	37.2999i		−	1.29005i
$837$	−4.51643	+	17.0988i	−0.156111	+	0.591020i
$838$	1.15054	+	1.15054i	0.0397447	+	0.0397447i
$839$	−12.1068	+	10.1589i	−0.417975	+	0.350723i	−0.827392	−	0.561625i	$-0.810176\pi$
$839$	−12.1068	+	10.1589i	−0.417975	+	0.350723i	0.409417	+	0.912347i	$0.365732\pi$
$840$	−12.2939	−	25.0434i	−0.424179	−	0.864079i
$841$	4.16273	−	23.6080i	0.143542	−	0.814069i
$842$	2.72543	+	1.27089i	0.0939244	+	0.0437976i
$843$	−8.56869	+	21.6435i	−0.295121	+	0.745441i
$844$	23.9157	−	4.21699i	0.823213	−	0.145155i
$845$	−8.47339	−	0.333623i	−0.291494	−	0.0114770i
$846$	−2.27904	+	2.42715i	−0.0783549	+	0.0834472i
$847$	−8.54789	−	31.9012i	−0.293709	−	1.09614i
$848$	−3.75671	+	1.75178i	−0.129006	+	0.0601564i
$849$	−1.19676	−	20.1360i	−0.0410728	−	0.691066i
$850$	−0.826846	−	0.213983i	−0.0283606	−	0.00733955i
$851$	−4.85600	+	5.78716i	−0.166462	+	0.198381i
$852$	1.81301	+	1.60959i	0.0621125	+	0.0551435i
$853$	−1.32236	−	2.83580i	−0.0452766	−	0.0970960i	0.882368	−	0.470560i	$-0.155948\pi$
$853$	−1.32236	−	2.83580i	−0.0452766	−	0.0970960i	−0.927645	+	0.373463i	$0.878170\pi$
$854$	−1.41272	+	2.44691i	−0.0483424	+	0.0837314i
$855$	−31.9558	+	8.29283i	−1.09286	+	0.283609i
$856$	−1.26075	−	2.18368i	−0.0430915	−	0.0746367i
$857$	9.61006	−	13.7246i	0.328273	−	0.468823i	−0.620759	−	0.784001i	$-0.713175\pi$
$857$	9.61006	−	13.7246i	0.328273	−	0.468823i	0.949032	+	0.315178i	$0.102064\pi$
$858$	17.4023	+	6.88960i	0.594105	+	0.235207i
$859$	12.0888	+	33.2138i	0.412465	+	1.13324i	0.955875	+	0.293772i	$0.0949107\pi$
$859$	12.0888	+	33.2138i	0.412465	+	1.13324i	−0.543410	+	0.839467i	$0.682867\pi$
$860$	1.69939	+	35.4406i	0.0579489	+	1.20851i
$861$	21.6164	−	5.15028i	0.736686	−	0.175521i
$862$	−0.619907	+	7.08557i	−0.0211141	+	0.241336i
$863$	18.3310	−	18.3310i	0.623993	−	0.623993i	−0.322557	−	0.946550i	$-0.604542\pi$
$863$	18.3310	−	18.3310i	0.623993	−	0.623993i	0.946550	+	0.322557i	$0.104542\pi$
$864$	24.6247	+	14.1004i	0.837748	+	0.479706i
$865$	−20.4386	+	4.62301i	−0.694934	+	0.157187i
$866$	−5.54478	−	6.60801i	−0.188419	−	0.224549i
$867$	25.7683	−	13.9336i	0.875137	−	0.473211i
$868$	−15.7509	+	11.0289i	−0.534620	+	0.374345i
$869$	63.6561	−	23.1689i	2.15939	−	0.785952i
$870$	15.2262	−	5.88953i	0.516217	−	0.199674i
$871$	−6.75812	−	38.3272i	−0.228990	−	1.29867i
$872$	8.42666	−	31.4487i	0.285363	−	1.06499i
$873$	−12.6393	+	5.05605i	−0.427777	+	0.171121i
$874$	3.74260	+	2.16079i	0.126595	+	0.0730899i
$875$	11.8743	+	36.0401i	0.401425	+	1.21838i
$876$	0.828284	−	1.65414i	0.0279851	−	0.0558882i
$877$	0.651619	−	0.0570093i	0.0220036	−	0.00192507i	−0.0761486	−	0.997096i	$-0.524262\pi$
$877$	0.651619	−	0.0570093i	0.0220036	−	0.00192507i	0.0981522	+	0.995171i	$0.468707\pi$
$878$	0.344433	−	0.0301339i	0.0116240	−	0.00101697i
$879$	25.1429	+	38.1293i	0.848048	+	1.28607i
$880$	16.9059	−	13.0877i	0.569897	−	0.441186i
$881$	47.1502	+	27.2222i	1.58853	+	0.917139i	0.993550	+	0.113399i	$0.0361738\pi$
$881$	47.1502	+	27.2222i	1.58853	+	0.917139i	0.594981	+	0.803740i	$0.297160\pi$
$882$	−1.60602	−	7.68581i	−0.0540774	−	0.258795i
$883$	6.18571	−	23.0854i	0.208166	−	0.776885i	−0.780296	−	0.625411i	$-0.784931\pi$
$883$	6.18571	−	23.0854i	0.208166	−	0.776885i	0.988461	−	0.151474i	$-0.0484020\pi$
$884$	−0.349351	−	1.98127i	−0.0117500	−	0.0666373i
$885$	38.3000	−	4.12458i	1.28744	−	0.138646i
$886$	−12.0831	+	4.39790i	−0.405940	+	0.147750i
$887$	3.61660	−	2.53237i	0.121433	−	0.0850286i	−0.511282	−	0.859413i	$-0.670829\pi$
$887$	3.61660	−	2.53237i	0.121433	−	0.0850286i	0.632715	+	0.774384i	$0.281940\pi$
$888$	0.511009	−	18.3095i	0.0171483	−	0.614425i
$889$	−38.5206	−	45.9070i	−1.29194	−	1.53967i
$890$	3.54145	+	15.6570i	0.118710	+	0.524822i
$891$	18.2169	−	36.7062i	0.610290	−	1.22971i
$892$	24.3473	−	24.3473i	0.815208	−	0.815208i
$893$	−0.821942	+	9.39484i	−0.0275052	+	0.314386i
$894$	−2.47024	−	2.61208i	−0.0826171	−	0.0873612i
$895$	30.4696	−	33.5388i	1.01849	−	1.12108i
$896$	13.3755	+	36.7489i	0.446845	+	1.22770i
$897$	8.43343	−	6.68457i	0.281584	−	0.223191i
$898$	1.91101	−	2.72921i	0.0637713	−	0.0910748i
$899$	−12.3857	−	21.4527i	−0.413088	−	0.715489i
$900$	−19.7539	−	15.2713i	−0.658464	−	0.509045i
$901$	−0.291088	+	0.504180i	−0.00969756	+	0.0167967i
$902$	−4.21269	−	9.03415i	−0.140267	−	0.300804i
$903$	−11.2667	+	54.8935i	−0.374932	+	1.82674i
$904$	5.08311	−	6.05781i	0.169062	−	0.201480i
$905$	7.79231	+	24.3501i	0.259025	+	0.809425i
$906$	17.5830	+	8.80442i	0.584157	+	0.292507i
$907$	−41.6059	+	19.4012i	−1.38150	+	0.644205i	−0.964350	−	0.264632i	$-0.914750\pi$
$907$	−41.6059	+	19.4012i	−1.38150	+	0.644205i	−0.417152	+	0.908837i	$0.636972\pi$
$908$	4.25498	+	15.8798i	0.141206	+	0.526989i
$909$	−26.1548	+	3.11999i	−0.867501	+	0.103484i
$910$	13.2272	−	12.2251i	0.438478	−	0.405257i
$911$	−48.2873	+	8.51435i	−1.59983	+	0.282093i	−0.901204	−	0.433395i	$-0.857315\pi$
$911$	−48.2873	+	8.51435i	−1.59983	+	0.282093i	−0.698625	+	0.715488i	$0.746204\pi$
$912$	17.7084	−	2.61537i	0.586385	−	0.0866036i
$913$	−39.3169	−	18.3338i	−1.30120	−	0.606759i
$914$	−2.65181	+	15.0391i	−0.0877139	+	0.497451i
$915$	−0.374130	+	5.55446i	−0.0123683	+	0.183625i
$916$	−34.3876	+	28.8547i	−1.13620	+	0.953385i
$917$	−10.6419	−	10.6419i	−0.351426	−	0.351426i
$918$	0.883933	−	0.0805056i	0.0291742	−	0.00265708i
$919$			45.6321i			1.50526i	0.658442	+	0.752632i	$0.271216\pi$
$919$			45.6321i			1.50526i	−0.658442	+	0.752632i	$0.728784\pi$
$920$	0.969719	+	7.12978i	0.0319707	+	0.235062i
$921$	−7.28333	−	30.5691i	−0.239994	−	1.00729i
$922$	11.2673	+	16.0914i	0.371069	+	0.529941i
$923$	−1.45628	+	3.12301i	−0.0479342	+	0.102795i
$924$	40.8888	−	17.6953i	1.34514	−	0.582132i
$925$	−4.11596	+	24.5710i	−0.135332	+	0.807890i
$926$	8.80472	−	5.08341i	0.289341	−	0.167051i
$927$	−8.13436	−	4.36112i	−0.267167	−	0.143238i
$928$	−38.3916	+	10.2870i	−1.26027	+	0.337687i
$929$	−37.4112	−	13.6166i	−1.22742	−	0.446745i	−0.354707	−	0.934977i	$-0.615419\pi$
$929$	−37.4112	−	13.6166i	−1.22742	−	0.446745i	−0.872713	+	0.488233i	$0.837642\pi$
$930$	3.68411	−	6.68660i	0.120807	−	0.219262i
$931$	−17.0373	−	14.2960i	−0.558374	−	0.468531i
$932$	0.936701	+	10.7065i	0.0306827	+	0.350704i
$933$	−19.8569	+	22.3664i	−0.650086	+	0.732244i
$934$	−1.49337	+	4.10300i	−0.0488646	+	0.134254i
$935$	0.890694	−	2.86767i	0.0291288	−	0.0937827i
$936$	−5.95685	+	25.4024i	−0.194706	+	0.830303i
$937$	1.08557	+	0.290876i	0.0354639	+	0.00950252i	0.276507	−	0.961012i	$-0.410823\pi$
$937$	1.08557	+	0.290876i	0.0354639	+	0.00950252i	−0.241043	+	0.970514i	$0.577490\pi$
$938$	15.2923	+	10.7078i	0.499310	+	0.349621i
$939$	10.2832	+	23.7616i	0.335580	+	0.775430i
$940$	−5.99897	+	3.85797i	−0.195665	+	0.125833i
$941$	−52.2436	−	9.21195i	−1.70309	−	0.300301i	−0.764319	−	0.644839i	$-0.776925\pi$
$941$	−52.2436	−	9.21195i	−1.70309	−	0.300301i	−0.938773	+	0.344538i	$0.888036\pi$
$942$	0.297476	−	0.483566i	0.00969230	−	0.0157554i
$943$	−5.70949	−	0.499516i	−0.185927	−	0.0162665i
$944$	−20.8866			−0.679799
$945$	−24.2507	−	31.0963i	−0.788876	−	1.01156i
$946$	25.1373			0.817285
$947$	55.3718	+	4.84441i	1.79934	+	0.157422i	0.937097	−	0.349068i	$-0.113502\pi$
$947$	55.3718	+	4.84441i	1.79934	+	0.157422i	0.862246	+	0.506490i	$0.169057\pi$
$948$	20.4029	+	37.7322i	0.662654	+	1.22549i
$949$	2.58940	+	0.456580i	0.0840553	+	0.0148212i
$950$	14.2511	−	0.122009i	0.462366	−	0.00395849i
$951$	16.0299	−	21.5854i	0.519807	−	0.699954i
$952$	1.74032	+	1.21858i	0.0564040	+	0.0394945i
$953$	−59.1867	−	15.8590i	−1.91725	−	0.513724i	−0.990389	−	0.138307i	$-0.955834\pi$
$953$	−59.1867	−	15.8590i	−1.91725	−	0.513724i	−0.926856	−	0.375417i	$-0.877499\pi$
$954$	2.74608	−	2.05453i	0.0889076	−	0.0665178i
$955$	−5.47935	−	10.4166i	−0.177308	−	0.337074i
$956$	9.66022	−	26.5412i	0.312434	−	0.858405i
$957$	18.1188	+	54.4628i	0.585696	+	1.76053i
$958$	−0.688466	−	7.86920i	−0.0222433	−	0.254242i
$959$	−44.6785	−	37.4897i	−1.44274	−	1.21061i
$960$	2.89660	+	2.78293i	0.0934873	+	0.0898185i
$961$	18.2451	+	6.64068i	0.588552	+	0.214216i
$962$	11.4225	−	3.06064i	0.368275	−	0.0986791i
$963$	−2.37576	−	2.65689i	−0.0765577	−	0.0856172i
$964$	7.30675	−	4.21855i	0.235335	−	0.135870i
$965$	22.4359	−	9.40595i	0.722236	−	0.302788i
$966$	−0.593187	+	5.12779i	−0.0190855	+	0.164984i
$967$	−2.27975	+	4.88895i	−0.0733120	+	0.157218i	−0.939548	−	0.342417i	$-0.888755\pi$
$967$	−2.27975	+	4.88895i	−0.0733120	+	0.157218i	0.866236	+	0.499635i	$0.166532\pi$
$968$	−11.8459	−	16.9177i	−0.380741	−	0.543754i
$969$	1.82667	−	1.72748i	0.0586811	−	0.0554945i
$970$	5.82290	−	0.791971i	0.186962	−	0.0254287i
$971$			49.9614i			1.60334i	0.597769	+	0.801668i	$0.296054\pi$
$971$			49.9614i			1.60334i	−0.597769	+	0.801668i	$0.703946\pi$
$972$	24.6791	+	8.01558i	0.791581	+	0.257100i
$973$	8.51164	+	8.51164i	0.272871	+	0.272871i
$974$	−10.7682	+	9.03556i	−0.345034	+	0.289518i
$975$	12.7804	−	33.1072i	0.409301	−	1.06028i
$976$	0.524155	−	2.97263i	0.0167778	−	0.0951516i
$977$	−30.2308	−	14.0969i	−0.967169	−	0.450998i	−0.126155	−	0.992011i	$-0.540264\pi$
$977$	−30.2308	−	14.0969i	−0.967169	−	0.450998i	−0.841015	+	0.541012i	$0.818041\pi$
$978$	3.07541	+	3.88002i	0.0983408	+	0.124069i
$979$	−55.5801	+	9.80028i	−1.77635	+	0.313218i
$980$	0.661759	−	16.8075i	0.0211391	−	0.536894i
$981$	2.56687	−	45.9496i	0.0819537	−	1.46706i
$982$	−5.31550	−	19.8377i	−0.169625	−	0.633047i
$983$	16.4610	−	7.67588i	0.525024	−	0.244823i	−0.141990	−	0.989868i	$-0.545350\pi$
$983$	16.4610	−	7.67588i	0.525024	−	0.244823i	0.667014	+	0.745045i	$0.267572\pi$
$984$	11.6008	−	7.64969i	0.369819	−	0.243863i
$985$	9.56425	−	18.5664i	0.304742	−	0.591574i
$986$	−0.799140	+	0.952378i	−0.0254498	+	0.0303299i
$987$	−10.6887	+	3.55593i	−0.340225	+	0.113187i
$988$	14.1874	+	30.4250i	0.451361	+	0.967947i
$989$	7.22655	−	12.5167i	0.229791	−	0.398009i
$990$	−11.4771	+	13.4607i	−0.364767	+	0.427811i
$991$	3.17299	+	5.49579i	0.100793	+	0.174579i	0.912012	−	0.410164i	$-0.134529\pi$
$991$	3.17299	+	5.49579i	0.100793	+	0.174579i	−0.811218	+	0.584743i	$0.801195\pi$
$992$	−10.6608	+	15.2251i	−0.338480	+	0.483399i
$993$	−1.06848	−	7.23457i	−0.0339071	−	0.229582i
$994$	−0.565329	−	1.55323i	−0.0179311	−	0.0492654i
$995$	19.3644	+	17.5923i	0.613893	+	0.557714i
$996$	7.84724	−	26.3253i	0.248649	−	0.834148i
$997$	1.87448	−	21.4254i	0.0593654	−	0.678549i	−0.906958	−	0.421220i	$-0.861602\pi$
$997$	1.87448	−	21.4254i	0.0593654	−	0.678549i	0.966324	−	0.257329i	$-0.0828425\pi$
$998$	16.4520	−	16.4520i	0.520779	−	0.520779i
$999$	−4.58661	−	25.4812i	−0.145114	−	0.806190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.113.8	yes	192
3.2	odd	2		405.2.r.a.368.9		192
5.2	odd	4	inner	135.2.q.a.32.9	✓	192
5.3	odd	4		675.2.ba.b.32.8		192
5.4	even	2		675.2.ba.b.518.9		192
15.2	even	4		405.2.r.a.287.8		192
27.11	odd	18	inner	135.2.q.a.38.9	yes	192
27.16	even	9		405.2.r.a.278.8		192
135.38	even	36		675.2.ba.b.632.9		192
135.92	even	36	inner	135.2.q.a.92.8	yes	192
135.97	odd	36		405.2.r.a.197.9		192
135.119	odd	18		675.2.ba.b.443.8		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.9	✓	192	5.2	odd	4	inner
135.2.q.a.38.9	yes	192	27.11	odd	18	inner
135.2.q.a.92.8	yes	192	135.92	even	36	inner
135.2.q.a.113.8	yes	192	1.1	even	1	trivial
405.2.r.a.197.9		192	135.97	odd	36
405.2.r.a.278.8		192	27.16	even	9
405.2.r.a.287.8		192	15.2	even	4
405.2.r.a.368.9		192	3.2	odd	2
675.2.ba.b.32.8		192	5.3	odd	4
675.2.ba.b.443.8		192	135.119	odd	18
675.2.ba.b.518.9		192	5.4	even	2
675.2.ba.b.632.9		192	135.38	even	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576956 - 0.0504771i) q^{2} +(-1.73138 - 0.0483220i) q^{3} +(-1.63929 - 0.289050i) q^{4} +(2.18512 + 0.474625i) q^{5} +(0.996489 + 0.115275i) q^{6} +(2.78018 + 1.94671i) q^{7} +(2.05006 + 0.549311i) q^{8} +(2.99533 + 0.167327i) q^{9} +O(q^{10})\)	\(q+(-0.576956 - 0.0504771i) q^{2} +(-1.73138 - 0.0483220i) q^{3} +(-1.63929 - 0.289050i) q^{4} +(2.18512 + 0.474625i) q^{5} +(0.996489 + 0.115275i) q^{6} +(2.78018 + 1.94671i) q^{7} +(2.05006 + 0.549311i) q^{8} +(2.99533 + 0.167327i) q^{9} +(-1.23676 - 0.384136i) q^{10} +(1.55726 - 4.27854i) q^{11} +(2.82425 + 0.579668i) q^{12} +(0.357151 + 4.08225i) q^{13} +(-1.50578 - 1.26350i) q^{14} +(-3.76032 - 0.927343i) q^{15} +(1.97331 + 0.718227i) q^{16} +(0.284890 - 0.0763360i) q^{17} +(-1.71973 - 0.247736i) q^{18} +(-4.26213 + 2.46074i) q^{19} +(-3.44484 - 1.40965i) q^{20} +(-4.71948 - 3.50482i) q^{21} +(-1.11444 + 2.38992i) q^{22} +(0.869642 + 1.24198i) q^{23} +(-3.52287 - 1.05013i) q^{24} +(4.54946 + 2.07422i) q^{25} -2.37331i q^{26} +(-5.17796 - 0.434446i) q^{27} +(-3.99482 - 3.99482i) q^{28} +(5.57542 - 4.67834i) q^{29} +(2.12273 + 0.724846i) q^{30} +(0.591015 - 3.35181i) q^{31} +(-4.94931 - 2.30790i) q^{32} +(-2.90295 + 7.33251i) q^{33} +(-0.168222 + 0.0296621i) q^{34} +(5.15107 + 5.57332i) q^{35} +(-4.86183 - 1.14010i) q^{36} +(1.28961 + 4.81289i) q^{37} +(2.58327 - 1.20460i) q^{38} +(-0.421100 - 7.08518i) q^{39} +(4.21889 + 2.17331i) q^{40} +(-2.42980 + 2.89573i) q^{41} +(2.54602 + 2.26035i) q^{42} +(-4.02865 - 8.63947i) q^{43} +(-3.78950 + 6.56361i) q^{44} +(6.46573 + 1.78729i) q^{45} +(-0.439054 - 0.760463i) q^{46} +(1.09911 - 1.56969i) q^{47} +(-3.38184 - 1.33888i) q^{48} +(1.54562 + 4.24655i) q^{49} +(-2.52014 - 1.42638i) q^{50} +(-0.496940 + 0.118400i) q^{51} +(0.594504 - 6.79521i) q^{52} +(-1.39575 + 1.39575i) q^{53} +(2.96552 + 0.512025i) q^{54} +(5.43349 - 8.60998i) q^{55} +(4.63018 + 5.51804i) q^{56} +(7.49825 - 4.05451i) q^{57} +(-3.45292 + 2.41776i) q^{58} +(-9.34637 + 3.40180i) q^{59} +(5.89619 + 2.60710i) q^{60} +(-0.249603 - 1.41557i) q^{61} +(-0.510179 + 1.90402i) q^{62} +(8.00183 + 6.29622i) q^{63} +(-0.898191 - 0.518571i) q^{64} +(-1.15712 + 9.08971i) q^{65} +(2.04500 - 4.08400i) q^{66} +(-9.46116 + 0.827744i) q^{67} +(-0.489081 + 0.0427890i) q^{68} +(-1.44566 - 2.19235i) q^{69} +(-2.69061 - 3.47557i) q^{70} +(0.728237 + 0.420448i) q^{71} +(6.04868 + 1.98840i) q^{72} +(0.166069 - 0.619776i) q^{73} +(-0.501107 - 2.84192i) q^{74} +(-7.77660 - 3.81109i) q^{75} +(7.69812 - 2.80189i) q^{76} +(12.6585 - 8.86359i) q^{77} +(-0.114683 + 4.10909i) q^{78} +(9.56341 + 11.3972i) q^{79} +(3.97103 + 2.50599i) q^{80} +(8.94400 + 1.00240i) q^{81} +(1.54806 - 1.54806i) q^{82} +(0.830405 - 9.49158i) q^{83} +(6.72350 + 7.10957i) q^{84} +(0.658748 - 0.0315873i) q^{85} +(1.88826 + 5.18795i) q^{86} +(-9.87923 + 7.83055i) q^{87} +(5.54271 - 7.91582i) q^{88} +(-6.19767 - 10.7347i) q^{89} +(-3.64022 - 1.35756i) q^{90} +(-6.95400 + 12.0447i) q^{91} +(-1.06660 - 2.28733i) q^{92} +(-1.18524 + 5.77469i) q^{93} +(-0.713371 + 0.850162i) q^{94} +(-10.4812 + 3.35409i) q^{95} +(8.45759 + 4.23500i) q^{96} +(-4.11255 + 1.91772i) q^{97} +(-0.677399 - 2.52809i) q^{98} +(5.38042 - 12.5551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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