LMFDB - Embedded newform 91.2.ba.a.59.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(45,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("91.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.ba (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.5
Character	$\chi$	$=$	91.59
Dual form			91.2.ba.a.54.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.203761 + 0.203761i) q^{2} +(0.923129 - 0.532969i) q^{3} -1.91696i q^{4} +(0.499383 + 0.133809i) q^{5} +(0.296695 + 0.0794993i) q^{6} +(-2.60732 + 0.449339i) q^{7} +(0.798123 - 0.798123i) q^{8} +(-0.931889 + 1.61408i) q^{9} +O(q^{10})$	\(q+(0.203761 + 0.203761i) q^{2} +(0.923129 - 0.532969i) q^{3} -1.91696i q^{4} +(0.499383 + 0.133809i) q^{5} +(0.296695 + 0.0794993i) q^{6} +(-2.60732 + 0.449339i) q^{7} +(0.798123 - 0.798123i) q^{8} +(-0.931889 + 1.61408i) q^{9} +(0.0744896 + 0.129020i) q^{10} +(3.69793 + 0.990856i) q^{11} +(-1.02168 - 1.76960i) q^{12} +(1.12494 + 3.42557i) q^{13} +(-0.622826 - 0.439711i) q^{14} +(0.532311 - 0.142632i) q^{15} -3.50867 q^{16} -4.52032 q^{17} +(-0.518768 + 0.139003i) q^{18} +(0.797839 + 2.97757i) q^{19} +(0.256508 - 0.957300i) q^{20} +(-2.16740 + 1.80442i) q^{21} +(0.551594 + 0.955389i) q^{22} -8.67873i q^{23} +(0.311396 - 1.16214i) q^{24} +(-4.09865 - 2.36636i) q^{25} +(-0.468776 + 0.927215i) q^{26} +5.18448i q^{27} +(0.861367 + 4.99813i) q^{28} +(1.26720 - 2.19486i) q^{29} +(0.137527 + 0.0794012i) q^{30} +(0.270595 + 1.00987i) q^{31} +(-2.31118 - 2.31118i) q^{32} +(3.94176 - 1.05619i) q^{33} +(-0.921063 - 0.921063i) q^{34} +(-1.36218 - 0.124491i) q^{35} +(3.09413 + 1.78640i) q^{36} +(-0.129500 + 0.129500i) q^{37} +(-0.444144 + 0.769281i) q^{38} +(2.86419 + 2.56268i) q^{39} +(0.505366 - 0.291773i) q^{40} +(1.79081 + 6.68338i) q^{41} +(-0.809301 - 0.0739629i) q^{42} +(4.59244 - 2.65145i) q^{43} +(1.89943 - 7.08879i) q^{44} +(-0.681349 + 0.681349i) q^{45} +(1.76838 - 1.76838i) q^{46} +(2.42047 - 9.03333i) q^{47} +(-3.23896 + 1.87001i) q^{48} +(6.59619 - 2.34314i) q^{49} +(-0.352973 - 1.31731i) q^{50} +(-4.17284 + 2.40919i) q^{51} +(6.56668 - 2.15648i) q^{52} +(0.512534 - 0.887735i) q^{53} +(-1.05639 + 1.05639i) q^{54} +(1.71410 + 0.989634i) q^{55} +(-1.72233 + 2.43959i) q^{56} +(2.32346 + 2.32346i) q^{57} +(0.705432 - 0.189020i) q^{58} +(0.368467 + 0.368467i) q^{59} +(-0.273421 - 1.02042i) q^{60} +(-7.39280 - 4.26823i) q^{61} +(-0.150636 + 0.260909i) q^{62} +(1.70446 - 4.62715i) q^{63} +6.07549i q^{64} +(0.103406 + 1.86120i) q^{65} +(1.01838 + 0.587965i) q^{66} +(-1.83243 + 6.83871i) q^{67} +8.66528i q^{68} +(-4.62549 - 8.01158i) q^{69} +(-0.252192 - 0.302924i) q^{70} +(1.96522 - 7.33429i) q^{71} +(0.544472 + 2.03200i) q^{72} +(-11.9468 + 3.20113i) q^{73} -0.0527740 q^{74} -5.04477 q^{75} +(5.70790 - 1.52943i) q^{76} +(-10.0869 - 0.921852i) q^{77} +(0.0614358 + 1.10578i) q^{78} +(3.77800 + 6.54369i) q^{79} +(-1.75217 - 0.469493i) q^{80} +(-0.0325003 - 0.0562921i) q^{81} +(-0.996914 + 1.72671i) q^{82} +(6.42827 - 6.42827i) q^{83} +(3.45900 + 4.15483i) q^{84} +(-2.25737 - 0.604861i) q^{85} +(1.47602 + 0.395498i) q^{86} -2.70152i q^{87} +(3.74222 - 2.16057i) q^{88} +(8.56976 + 8.56976i) q^{89} -0.277664 q^{90} +(-4.47233 - 8.42605i) q^{91} -16.6368 q^{92} +(0.788024 + 0.788024i) q^{93} +(2.33384 - 1.34744i) q^{94} +1.59371i q^{95} +(-3.36530 - 0.901729i) q^{96} +(-13.1956 - 3.53575i) q^{97} +(1.82148 + 0.866604i) q^{98} +(-5.04538 + 5.04538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 12 q^{6} - 6 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 6 * q^3 - 6 * q^5 - 12 * q^6 - 6 * q^7 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 12 q^{6} - 6 q^{7} - 4 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{11} - 8 q^{12} - 20 q^{14} + 10 q^{15} + 4 q^{16} - 12 q^{17} + 2 q^{18} + 14 q^{19} + 36 q^{20} - 6 q^{21} - 8 q^{22} - 18 q^{24} + 24 q^{26} + 2 q^{28} - 8 q^{29} - 30 q^{30} - 4 q^{31} + 10 q^{32} - 12 q^{33} - 12 q^{34} - 20 q^{35} + 54 q^{36} - 10 q^{37} - 20 q^{39} + 48 q^{40} - 18 q^{41} - 10 q^{42} + 48 q^{43} - 6 q^{44} - 6 q^{45} + 24 q^{46} - 6 q^{47} - 12 q^{48} - 50 q^{49} + 10 q^{50} - 12 q^{51} - 26 q^{52} + 12 q^{53} - 30 q^{54} + 6 q^{55} + 54 q^{56} + 12 q^{57} - 46 q^{58} + 42 q^{59} + 10 q^{60} + 30 q^{61} + 36 q^{62} + 54 q^{63} + 28 q^{65} + 66 q^{66} - 10 q^{67} - 42 q^{69} - 88 q^{70} - 42 q^{71} + 46 q^{72} + 40 q^{73} + 12 q^{74} - 40 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} + 30 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} + 104 q^{84} - 54 q^{85} - 18 q^{86} - 6 q^{88} + 72 q^{90} + 26 q^{91} - 156 q^{92} + 20 q^{93} - 18 q^{94} - 66 q^{96} - 62 q^{97} - 56 q^{98} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 6 * q^3 - 6 * q^5 - 12 * q^6 - 6 * q^7 - 4 * q^8 + 6 * q^9 - 6 * q^10 + 2 * q^11 - 8 * q^12 - 20 * q^14 + 10 * q^15 + 4 * q^16 - 12 * q^17 + 2 * q^18 + 14 * q^19 + 36 * q^20 - 6 * q^21 - 8 * q^22 - 18 * q^24 + 24 * q^26 + 2 * q^28 - 8 * q^29 - 30 * q^30 - 4 * q^31 + 10 * q^32 - 12 * q^33 - 12 * q^34 - 20 * q^35 + 54 * q^36 - 10 * q^37 - 20 * q^39 + 48 * q^40 - 18 * q^41 - 10 * q^42 + 48 * q^43 - 6 * q^44 - 6 * q^45 + 24 * q^46 - 6 * q^47 - 12 * q^48 - 50 * q^49 + 10 * q^50 - 12 * q^51 - 26 * q^52 + 12 * q^53 - 30 * q^54 + 6 * q^55 + 54 * q^56 + 12 * q^57 - 46 * q^58 + 42 * q^59 + 10 * q^60 + 30 * q^61 + 36 * q^62 + 54 * q^63 + 28 * q^65 + 66 * q^66 - 10 * q^67 - 42 * q^69 - 88 * q^70 - 42 * q^71 + 46 * q^72 + 40 * q^73 + 12 * q^74 - 40 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 + 30 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 + 104 * q^84 - 54 * q^85 - 18 * q^86 - 6 * q^88 + 72 * q^90 + 26 * q^91 - 156 * q^92 + 20 * q^93 - 18 * q^94 - 66 * q^96 - 62 * q^97 - 56 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.203761	+	0.203761i	0.144081	+	0.144081i	0.775468	−	0.631387i	$-0.217514\pi$
$2$	0.203761	+	0.203761i	0.144081	+	0.144081i	−0.631387	+	0.775468i	$0.717514\pi$
$3$	0.923129	−	0.532969i	0.532969	−	0.307710i	−0.209256	−	0.977861i	$-0.567104\pi$
$3$	0.923129	−	0.532969i	0.532969	−	0.307710i	0.742224	+	0.670151i	$0.233771\pi$
$4$		−	1.91696i		−	0.958482i
$5$	0.499383	+	0.133809i	0.223331	+	0.0598414i	0.368749	−	0.929529i	$-0.379786\pi$
$5$	0.499383	+	0.133809i	0.223331	+	0.0598414i	−0.145418	+	0.989370i	$0.546453\pi$
$6$	0.296695	+	0.0794993i	0.121125	+	0.0324554i
$7$	−2.60732	+	0.449339i	−0.985473	+	0.169834i
$7$	−2.60732	+	0.449339i	−0.985473	+	0.169834i
$8$	0.798123	−	0.798123i	0.282179	−	0.282179i
$9$	−0.931889	+	1.61408i	−0.310630	+	0.538026i
$10$	0.0744896	+	0.129020i	0.0235557	+	0.0407996i
$11$	3.69793	+	0.990856i	1.11497	+	0.298754i	0.768845	−	0.639435i	$-0.220832\pi$
$11$	3.69793	+	0.990856i	1.11497	+	0.298754i	0.346122	+	0.938190i	$0.387498\pi$
$12$	−1.02168	−	1.76960i	−0.294934	−	0.510841i
$13$	1.12494	+	3.42557i	0.312003	+	0.950081i
$13$	1.12494	+	3.42557i	0.312003	+	0.950081i
$14$	−0.622826	−	0.439711i	−0.166457	−	0.117518i
$15$	0.532311	−	0.142632i	0.137442	−	0.0368275i
$16$	−3.50867			−0.877169
$17$	−4.52032			−1.09634			−0.548169	−	0.836368i	$-0.684675\pi$
$17$	−4.52032			−1.09634			−0.548169	+	0.836368i	$0.684675\pi$
$18$	−0.518768	+	0.139003i	−0.122275	+	0.0327634i
$19$	0.797839	+	2.97757i	0.183037	+	0.683103i	0.995042	+	0.0994528i	$0.0317092\pi$
$19$	0.797839	+	2.97757i	0.183037	+	0.683103i	−0.812006	+	0.583650i	$0.801624\pi$
$20$	0.256508	−	0.957300i	0.0573569	−	0.214059i
$21$	−2.16740	+	1.80442i	−0.472966	+	0.393756i
$22$	0.551594	+	0.955389i	0.117600	+	0.203690i
$23$		−	8.67873i		−	1.80964i	−0.425795	−	0.904820i	$-0.640006\pi$
$23$		−	8.67873i		−	1.80964i	0.425795	−	0.904820i	$-0.359994\pi$
$24$	0.311396	−	1.16214i	0.0635634	−	0.237222i
$25$	−4.09865	−	2.36636i	−0.819730	−	0.473271i
$26$	−0.468776	+	0.927215i	−0.0919346	+	0.181842i
$27$			5.18448i			0.997754i
$28$	0.861367	+	4.99813i	0.162783	+	0.944557i
$29$	1.26720	−	2.19486i	0.235314	−	0.407575i	−0.724050	−	0.689747i	$-0.757722\pi$
$29$	1.26720	−	2.19486i	0.235314	−	0.407575i	0.959364	+	0.282172i	$0.0910549\pi$
$30$	0.137527	+	0.0794012i	0.0251089	+	0.0144966i
$31$	0.270595	+	1.00987i	0.0486002	+	0.181378i	0.985959	−	0.166987i	$-0.0534036\pi$
$31$	0.270595	+	1.00987i	0.0486002	+	0.181378i	−0.937359	+	0.348365i	$0.886737\pi$
$32$	−2.31118	−	2.31118i	−0.408562	−	0.408562i
$33$	3.94176	−	1.05619i	0.686172	−	0.183859i
$34$	−0.921063	−	0.921063i	−0.157961	−	0.157961i
$35$	−1.36218	−	0.124491i	−0.230250	−	0.0210428i
$36$	3.09413	+	1.78640i	0.515688	+	0.297733i
$37$	−0.129500	+	0.129500i	−0.0212897	+	0.0212897i	−0.717671	−	0.696382i	$-0.754792\pi$
$37$	−0.129500	+	0.129500i	−0.0212897	+	0.0212897i	0.696382	+	0.717671i	$0.254792\pi$
$38$	−0.444144	+	0.769281i	−0.0720497	+	0.124794i
$39$	2.86419	+	2.56268i	0.458637	+	0.410357i
$40$	0.505366	−	0.291773i	0.0799053	−	0.0461334i
$41$	1.79081	+	6.68338i	0.279677	+	1.04377i	0.952642	+	0.304094i	$0.0983538\pi$
$41$	1.79081	+	6.68338i	0.279677	+	1.04377i	−0.672965	+	0.739674i	$0.734980\pi$
$42$	−0.809301	−	0.0739629i	−0.124878	−	0.0114127i
$43$	4.59244	−	2.65145i	0.700341	−	0.404342i	−0.107134	−	0.994245i	$-0.534167\pi$
$43$	4.59244	−	2.65145i	0.700341	−	0.404342i	0.807474	+	0.589903i	$0.200834\pi$
$44$	1.89943	−	7.08879i	0.286351	−	1.06867i
$45$	−0.681349	+	0.681349i	−0.101569	+	0.101569i
$46$	1.76838	−	1.76838i	0.260734	−	0.260734i
$47$	2.42047	−	9.03333i	0.353063	−	1.31765i	−0.529843	−	0.848096i	$-0.677749\pi$
$47$	2.42047	−	9.03333i	0.353063	−	1.31765i	0.882905	−	0.469551i	$-0.155584\pi$
$48$	−3.23896	+	1.87001i	−0.467503	+	0.269913i
$49$	6.59619	−	2.34314i	0.942313	−	0.334734i
$50$	−0.352973	−	1.31731i	−0.0499179	−	0.186296i
$51$	−4.17284	+	2.40919i	−0.584314	+	0.337354i
$52$	6.56668	−	2.15648i	0.910635	−	0.299050i
$53$	0.512534	−	0.887735i	0.0704019	−	0.121940i	−0.828676	−	0.559729i	$-0.810905\pi$
$53$	0.512534	−	0.887735i	0.0704019	−	0.121940i	0.899078	+	0.437789i	$0.144238\pi$
$54$	−1.05639	+	1.05639i	−0.143757	+	0.143757i
$55$	1.71410	+	0.989634i	0.231129	+	0.133442i
$56$	−1.72233	+	2.43959i	−0.230156	+	0.326003i
$57$	2.32346	+	2.32346i	0.307750	+	0.307750i
$58$	0.705432	−	0.189020i	0.0926278	−	0.0248195i
$59$	0.368467	+	0.368467i	0.0479703	+	0.0479703i	0.730685	−	0.682715i	$-0.239201\pi$
$59$	0.368467	+	0.368467i	0.0479703	+	0.0479703i	−0.682715	+	0.730685i	$0.739201\pi$
$60$	−0.273421	−	1.02042i	−0.0352985	−	0.131736i
$61$	−7.39280	−	4.26823i	−0.946551	−	0.546491i	−0.0545432	−	0.998511i	$-0.517370\pi$
$61$	−7.39280	−	4.26823i	−0.946551	−	0.546491i	−0.892008	+	0.452020i	$0.850704\pi$
$62$	−0.150636	+	0.260909i	−0.0191308	+	0.0331355i
$63$	1.70446	−	4.62715i	0.214742	−	0.582966i
$64$			6.07549i			0.759437i
$65$	0.103406	+	1.86120i	0.0128259	+	0.230853i
$66$	1.01838	+	0.587965i	0.125355	+	0.0723735i
$67$	−1.83243	+	6.83871i	−0.223867	+	0.835482i	0.758989	+	0.651104i	$0.225694\pi$
$67$	−1.83243	+	6.83871i	−0.223867	+	0.835482i	−0.982855	+	0.184378i	$0.940973\pi$
$68$			8.66528i			1.05082i
$69$	−4.62549	−	8.01158i	−0.556843	−	0.964481i
$70$	−0.252192	−	0.302924i	−0.0301427	−	0.0362064i
$71$	1.96522	−	7.33429i	0.233228	−	0.870420i	−0.745711	−	0.666269i	$-0.767890\pi$
$71$	1.96522	−	7.33429i	0.233228	−	0.870420i	0.978940	−	0.204150i	$-0.0654432\pi$
$72$	0.544472	+	2.03200i	0.0641666	+	0.239473i
$73$	−11.9468	+	3.20113i	−1.39826	+	0.374664i	−0.877721	−	0.479171i	$-0.840937\pi$
$73$	−11.9468	+	3.20113i	−1.39826	+	0.374664i	−0.520543	+	0.853835i	$0.674271\pi$
$74$	−0.0527740			−0.00613485
$75$	−5.04477			−0.582520
$76$	5.70790	−	1.52943i	0.654741	−	0.175437i
$77$	−10.0869	−	0.921852i	−1.14951	−	0.105055i
$78$	0.0614358	+	1.10578i	0.00695623	+	0.125205i
$79$	3.77800	+	6.54369i	0.425058	+	0.736222i	0.996426	−	0.0844720i	$-0.0269204\pi$
$79$	3.77800	+	6.54369i	0.425058	+	0.736222i	−0.571368	+	0.820694i	$0.693587\pi$
$80$	−1.75217	−	0.469493i	−0.195899	−	0.0524910i
$81$	−0.0325003	−	0.0562921i	−0.00361114	−	0.00625468i
$82$	−0.996914	+	1.72671i	−0.110091	+	0.190683i
$83$	6.42827	−	6.42827i	0.705594	−	0.705594i	−0.260011	−	0.965606i	$-0.583726\pi$
$83$	6.42827	−	6.42827i	0.705594	−	0.705594i	0.965606	+	0.260011i	$0.0837262\pi$
$84$	3.45900	+	4.15483i	0.377408	+	0.453330i
$85$	−2.25737	−	0.604861i	−0.244846	−	0.0656064i
$86$	1.47602	+	0.395498i	0.159163	+	0.0426477i
$87$		−	2.70152i		−	0.289633i
$88$	3.74222	−	2.16057i	0.398922	−	0.230318i
$89$	8.56976	+	8.56976i	0.908393	+	0.908393i	0.996143	−	0.0877495i	$-0.0279675\pi$
$89$	8.56976	+	8.56976i	0.908393	+	0.908393i	−0.0877495	+	0.996143i	$0.527967\pi$
$90$	−0.277664			−0.0292684
$91$	−4.47233	−	8.42605i	−0.468827	−	0.883290i
$92$	−16.6368			−1.73451
$93$	0.788024	+	0.788024i	0.0817143	+	0.0817143i
$94$	2.33384	−	1.34744i	0.240717	−	0.138978i
$95$			1.59371i			0.163511i
$96$	−3.36530	−	0.901729i	−0.343469	−	0.0920323i
$97$	−13.1956	−	3.53575i	−1.33981	−	0.359001i	−0.483446	−	0.875374i	$-0.660615\pi$
$97$	−13.1956	−	3.53575i	−1.33981	−	0.359001i	−0.856364	+	0.516373i	$0.827282\pi$
$98$	1.82148	+	0.866604i	0.183998	+	0.0875403i
$99$	−5.04538	+	5.04538i	−0.507079	+	0.507079i
$100$	−4.53622	+	7.85696i	−0.453622	+	0.785696i
$101$	0.555807	+	0.962686i	0.0553049	+	0.0957909i	0.892352	−	0.451339i	$-0.149054\pi$
$101$	0.555807	+	0.962686i	0.0553049	+	0.0957909i	−0.837048	+	0.547130i	$0.815720\pi$
$102$	−1.34116	−	0.359362i	−0.132794	−	0.0355821i
$103$	0.214188	+	0.370984i	0.0211046	+	0.0365542i	0.876385	−	0.481612i	$-0.159948\pi$
$103$	0.214188	+	0.370984i	0.0211046	+	0.0365542i	−0.855280	+	0.518166i	$0.826615\pi$
$104$	3.63187	+	1.83618i	0.356134	+	0.180052i
$105$	−1.32381	+	0.611076i	−0.129191	+	0.0596349i
$106$	0.285320	−	0.0764512i	0.0277127	−	0.00742559i
$107$	5.01634			0.484948			0.242474	−	0.970158i	$-0.422041\pi$
$107$	5.01634			0.484948			0.242474	+	0.970158i	$0.422041\pi$
$108$	9.93846			0.956329
$109$	−0.820253	+	0.219786i	−0.0785660	+	0.0210517i	−0.297888	−	0.954601i	$-0.596282\pi$
$109$	−0.820253	+	0.219786i	−0.0785660	+	0.0210517i	0.219322	+	0.975653i	$0.429616\pi$
$110$	0.147617	+	0.550914i	0.0140747	+	0.0525276i
$111$	−0.0505257	+	0.188564i	−0.00479569	+	0.0178977i
$112$	9.14822	−	1.57658i	0.864426	−	0.148973i
$113$	2.44889	+	4.24160i	0.230372	+	0.399016i	0.957918	−	0.287043i	$-0.0926724\pi$
$113$	2.44889	+	4.24160i	0.230372	+	0.399016i	−0.727546	+	0.686059i	$0.759339\pi$
$114$			0.946860i			0.0886816i
$115$	1.16129	−	4.33401i	0.108291	−	0.404149i
$116$	−4.20747	−	2.42918i	−0.390653	−	0.225544i
$117$	−6.57746	−	1.37650i	−0.608086	−	0.127257i
$118$			0.150158i			0.0138232i
$119$	11.7859	−	2.03116i	1.08041	−	0.186196i
$120$	0.311012	−	0.538688i	0.0283914	−	0.0491753i
$121$	3.16658	+	1.82822i	0.287871	+	0.166202i
$122$	−0.636663	−	2.37606i	−0.0576408	−	0.215118i
$123$	5.21518	+	5.21518i	0.470237	+	0.470237i
$124$	1.93589	−	0.518720i	0.173848	−	0.0465824i
$125$	−3.55803	−	3.55803i	−0.318240	−	0.318240i
$126$	1.29013	−	0.595529i	0.114934	−	0.0530539i
$127$	−3.00665	−	1.73589i	−0.266797	−	0.154035i	0.360634	−	0.932707i	$-0.382560\pi$
$127$	−3.00665	−	1.73589i	−0.266797	−	0.154035i	−0.627431	+	0.778672i	$0.715894\pi$
$128$	−5.86030	+	5.86030i	−0.517982	+	0.517982i
$129$	2.82628	−	4.89525i	0.248840	−	0.431003i
$130$	−0.358169	+	0.400309i	−0.0314135	+	0.0351094i
$131$	15.0157	−	8.66932i	1.31193	−	0.757442i	0.329512	−	0.944151i	$-0.393116\pi$
$131$	15.0157	−	8.66932i	1.31193	−	0.757442i	0.982415	+	0.186710i	$0.0597823\pi$
$132$	−2.02468	−	7.55620i	−0.176226	−	0.657683i
$133$	−3.41816	−	7.40498i	−0.296392	−	0.642093i
$134$	−1.76684	+	1.02008i	−0.152631	+	0.0881218i
$135$	−0.693732	+	2.58904i	−0.0597070	+	0.222829i
$136$	−3.60777	+	3.60777i	−0.309364	+	0.309364i
$137$	−6.67957	+	6.67957i	−0.570674	+	0.570674i	−0.932317	−	0.361643i	$-0.882216\pi$
$137$	−6.67957	+	6.67957i	−0.570674	+	0.570674i	0.361643	+	0.932317i	$0.382216\pi$
$138$	0.689952	−	2.57494i	0.0587327	−	0.219193i
$139$	13.1525	−	7.59358i	1.11558	−	0.644079i	0.175310	−	0.984513i	$-0.443907\pi$
$139$	13.1525	−	7.59358i	1.11558	−	0.644079i	0.940268	+	0.340434i	$0.110574\pi$
$140$	−0.238644	+	2.61124i	−0.0201691	+	0.220690i
$141$	−2.58007	−	9.62897i	−0.217281	−	0.810905i
$142$	1.89487	−	1.09401i	0.159014	−	0.0918069i
$143$	0.765718	+	13.7821i	0.0640325	+	1.15252i
$144$	3.26969	−	5.66328i	0.272475	−	0.471940i
$145$	0.926513	−	0.926513i	0.0769427	−	0.0769427i
$146$	−3.08655	−	1.78202i	−0.255444	−	0.147481i
$147$	4.84031	−	5.67858i	0.399222	−	0.468361i
$148$	0.248247	+	0.248247i	0.0204057	+	0.0204057i
$149$	13.8760	−	3.71806i	1.13677	−	0.304595i	0.359116	−	0.933293i	$-0.383078\pi$
$149$	13.8760	−	3.71806i	1.13677	−	0.304595i	0.777650	+	0.628698i	$0.216412\pi$
$150$	−1.02793	−	1.02793i	−0.0839298	−	0.0839298i
$151$	1.28473	+	4.79468i	0.104550	+	0.390185i	0.998294	−	0.0583923i	$-0.0185974\pi$
$151$	1.28473	+	4.79468i	0.104550	+	0.390185i	−0.893744	+	0.448578i	$0.851931\pi$
$152$	3.01324	+	1.73970i	0.244406	+	0.141108i
$153$	4.21243	−	7.29615i	0.340555	−	0.589859i
$154$	−1.86747	−	2.24315i	−0.150485	−	0.180758i
$155$			0.540522i			0.0434157i
$156$	4.91256	−	5.49054i	0.393320	−	0.439595i
$157$	3.02404	+	1.74593i	0.241345	+	0.139340i	0.615795	−	0.787907i	$-0.288835\pi$
$157$	3.02404	+	1.74593i	0.241345	+	0.139340i	−0.374450	+	0.927247i	$0.622168\pi$
$158$	−0.563538	+	2.10315i	−0.0448327	+	0.167318i
$159$		−	1.09266i		−	0.0866534i
$160$	−0.844906	−	1.46342i	−0.0667957	−	0.115693i
$161$	3.89969	+	22.6282i	0.307339	+	1.78335i
$162$	0.00484784	−	0.0180924i	0.000380882	−	0.00142147i
$163$	0.594214	+	2.21764i	0.0465424	+	0.173699i	0.985285	−	0.170921i	$-0.0546744\pi$
$163$	0.594214	+	2.21764i	0.0465424	+	0.173699i	−0.938742	+	0.344620i	$0.888008\pi$
$164$	12.8118	−	3.43291i	1.00043	−	0.268065i
$165$	2.10978			0.164246
$166$	2.61966			0.203325
$167$	−20.2547	+	5.42723i	−1.56736	+	0.419972i	−0.934983	−	0.354693i	$-0.884585\pi$
$167$	−20.2547	+	5.42723i	−1.56736	+	0.419972i	−0.632372	+	0.774665i	$0.717919\pi$
$168$	−0.289710	+	3.17000i	−0.0223516	+	0.244571i
$169$	−10.4690	+	7.70714i	−0.805308	+	0.592857i
$170$	−0.336717	−	0.583210i	−0.0258250	−	0.0447302i
$171$	−5.54954	−	1.48699i	−0.424384	−	0.113713i
$172$	−5.08273	−	8.80354i	−0.387554	−	0.671263i
$173$	−10.0438	+	17.3963i	−0.763613	+	1.32262i	0.177363	+	0.984145i	$0.443243\pi$
$173$	−10.0438	+	17.3963i	−0.763613	+	1.32262i	−0.940977	+	0.338472i	$0.890090\pi$
$174$	0.550463	−	0.550463i	0.0417305	−	0.0417305i
$175$	11.7498	+	4.32815i	0.888199	+	0.327178i
$176$	−12.9748	−	3.47659i	−0.978013	−	0.262058i
$177$	0.536524	+	0.143761i	0.0403276	+	0.0108058i
$178$			3.49236i			0.261764i
$179$	−18.5574	+	10.7141i	−1.38704	+	0.800810i	−0.992981	−	0.118274i	$-0.962264\pi$
$179$	−18.5574	+	10.7141i	−1.38704	+	0.800810i	−0.394062	+	0.919084i	$0.628931\pi$
$180$	1.30612	+	1.30612i	0.0973525	+	0.0973525i
$181$	19.7532			1.46824			0.734121	−	0.679019i	$-0.237595\pi$
$181$	19.7532			1.46824			0.734121	+	0.679019i	$0.237595\pi$
$182$	0.805613	−	2.62818i	0.0597160	−	0.194814i
$183$	−9.09934			−0.672643
$184$	−6.92669	−	6.92669i	−0.510642	−	0.510642i
$185$	−0.0819984	+	0.0473418i	−0.00602864	+	0.00348064i
$186$			0.321137i			0.0235469i
$187$	−16.7158	−	4.47898i	−1.22238	−	0.327536i
$188$	−17.3166	−	4.63996i	−1.26294	−	0.338404i
$189$	−2.32959	−	13.5176i	−0.169453	−	0.983259i
$190$	−0.324735	+	0.324735i	−0.0235588	+	0.0235588i
$191$	2.14939	−	3.72284i	0.155524	−	0.269376i	−0.777726	−	0.628604i	$-0.783627\pi$
$191$	2.14939	−	3.72284i	0.155524	−	0.269376i	0.933250	+	0.359228i	$0.116960\pi$
$192$	3.23805	+	5.60846i	0.233686	+	0.404756i
$193$	13.0919	+	3.50795i	0.942372	+	0.252508i	0.697123	−	0.716952i	$-0.254463\pi$
$193$	13.0919	+	3.50795i	0.942372	+	0.252508i	0.245250	+	0.969460i	$0.421130\pi$
$194$	−1.96830	−	3.40919i	−0.141315	−	0.244766i
$195$	1.08742	+	1.66301i	0.0778716	+	0.119091i
$196$	−4.49171	−	12.6447i	−0.320836	−	0.903189i
$197$	3.69905	−	0.991158i	0.263546	−	0.0706171i	−0.124626	−	0.992204i	$-0.539773\pi$
$197$	3.69905	−	0.991158i	0.263546	−	0.0706171i	0.388173	+	0.921587i	$0.373106\pi$
$198$	−2.05610			−0.146121
$199$	−10.5082			−0.744906			−0.372453	−	0.928051i	$-0.621483\pi$
$199$	−10.5082			−0.744906			−0.372453	+	0.928051i	$0.621483\pi$
$200$	−5.15987	+	1.38258i	−0.364858	+	0.0977634i
$201$	1.95325	+	7.28964i	0.137772	+	0.514171i
$202$	−0.0829059	+	0.309409i	−0.00583324	+	0.0217700i
$203$	−2.31776	+	6.29210i	−0.162675	+	0.441619i
$204$	4.61832	+	7.99917i	0.323347	+	0.560054i
$205$			3.57720i			0.249842i
$206$	−0.0319489	+	0.119235i	−0.00222599	+	0.00830750i
$207$	14.0081	+	8.08761i	0.973633	+	0.562128i
$208$	−3.94706	−	12.0192i	−0.273680	−	0.833381i
$209$			11.8014i			0.816319i
$210$	−0.394254	−	0.145228i	−0.0272061	−	0.0100217i
$211$	−3.87722	+	6.71554i	−0.266919	+	0.462317i	−0.968065	−	0.250701i	$-0.919339\pi$
$211$	−3.87722	+	6.71554i	−0.266919	+	0.462317i	0.701146	+	0.713018i	$0.252672\pi$
$212$	−1.70175	−	0.982508i	−0.116877	−	0.0674790i
$213$	−2.09480	−	7.81789i	−0.143533	−	0.535673i
$214$	1.02213	+	1.02213i	0.0698715	+	0.0698715i
$215$	2.64818	−	0.709577i	0.180604	−	0.0483927i
$216$	4.13785	+	4.13785i	0.281545	+	0.281545i
$217$	−1.15930	−	2.51147i	−0.0786984	−	0.170490i
$218$	−0.211919	−	0.122352i	−0.0143530	−	0.00828669i
$219$	−9.32231	+	9.32231i	−0.629943	+	0.629943i
$220$	1.89709	−	3.28586i	0.127902	−	0.221533i
$221$	−5.08511	−	15.4846i	−0.342061	−	1.04161i
$222$	−0.0487172	+	0.0281269i	−0.00326968	+	0.00188775i
$223$	−6.07469	−	22.6710i	−0.406791	−	1.51817i	−0.800728	−	0.599028i	$-0.795554\pi$
$223$	−6.07469	−	22.6710i	−0.406791	−	1.51817i	0.393937	−	0.919138i	$-0.371113\pi$
$224$	7.06447	+	4.98746i	0.472015	+	0.333239i
$225$	7.63897	−	4.41036i	0.509265	−	0.294024i
$226$	−0.365284	+	1.36326i	−0.0242983	+	0.0906825i
$227$	−4.35743	+	4.35743i	−0.289213	+	0.289213i	−0.836769	−	0.547556i	$-0.815558\pi$
$227$	−4.35743	+	4.35743i	−0.289213	+	0.289213i	0.547556	+	0.836769i	$0.315558\pi$
$228$	4.45399	−	4.45399i	0.294973	−	0.294973i
$229$	−2.94756	+	11.0005i	−0.194780	+	0.726931i	0.797543	+	0.603262i	$0.206133\pi$
$229$	−2.94756	+	11.0005i	−0.194780	+	0.726931i	−0.992324	+	0.123669i	$0.960534\pi$
$230$	1.11973	−	0.646475i	0.0738326	−	0.0426273i
$231$	−9.80281	+	4.52501i	−0.644978	+	0.297724i
$232$	−0.740385	−	2.76315i	−0.0486086	−	0.181410i
$233$	12.9075	−	7.45218i	0.845602	−	0.488208i	−0.0135628	−	0.999908i	$-0.504317\pi$
$233$	12.9075	−	7.45218i	0.845602	−	0.488208i	0.859164	+	0.511700i	$0.170984\pi$
$234$	−1.05975	−	1.62070i	−0.0692781	−	0.105949i
$235$	2.41749	−	4.18721i	0.157700	−	0.273144i
$236$	0.706338	−	0.706338i	0.0459787	−	0.0459787i
$237$	6.97516	+	4.02711i	0.453085	+	0.261589i
$238$	2.81537	+	1.98763i	0.182493	+	0.128839i
$239$	20.4619	+	20.4619i	1.32357	+	1.32357i	0.910864	+	0.412706i	$0.135416\pi$
$239$	20.4619	+	20.4619i	1.32357	+	1.32357i	0.412706	+	0.910864i	$0.364584\pi$
$240$	−1.86771	+	0.500451i	−0.120560	+	0.0323039i
$241$	13.0056	+	13.0056i	0.837762	+	0.837762i	0.988564	−	0.150802i	$-0.0481855\pi$
$241$	13.0056	+	13.0056i	0.837762	+	0.837762i	−0.150802	+	0.988564i	$0.548185\pi$
$242$	0.272704	+	1.01774i	0.0175301	+	0.0654230i
$243$	−13.5297	−	7.81137i	−0.867930	−	0.501099i
$244$	−8.18205	+	14.1717i	−0.523802	+	0.907252i
$245$	3.60756	−	0.287492i	0.230479	−	0.0183672i
$246$			2.12530i			0.135504i
$247$	−9.30235	+	6.08266i	−0.591895	+	0.387030i
$248$	1.02197	+	0.590035i	0.0648952	+	0.0374672i
$249$	2.50806	−	9.36019i	0.158942	−	0.593178i
$250$		−	1.44997i		−	0.0917043i
$251$	3.43367	+	5.94730i	0.216731	+	0.375390i	0.953807	−	0.300421i	$-0.0971271\pi$
$251$	3.43367	+	5.94730i	0.216731	+	0.375390i	−0.737075	+	0.675811i	$0.763794\pi$
$252$	−8.87007	−	3.26739i	−0.558762	−	0.205826i
$253$	8.59937	−	32.0933i	0.540638	−	2.01769i
$254$	−0.258931	−	0.966343i	−0.0162468	−	0.0606338i
$255$	−2.40622	+	0.644744i	−0.150683	+	0.0403754i
$256$	9.76279			0.610175
$257$	8.32966			0.519590			0.259795	−	0.965664i	$-0.416345\pi$
$257$	8.32966			0.519590			0.259795	+	0.965664i	$0.416345\pi$
$258$	1.57334	−	0.421576i	0.0979521	−	0.0262462i
$259$	0.279458	−	0.395836i	0.0173647	−	0.0245961i
$260$	3.56785	−	0.198225i	0.221269	−	0.0122934i
$261$	2.36179	+	4.09073i	0.146191	+	0.253210i
$262$	4.82607	+	1.29314i	0.298156	+	0.0798906i
$263$	1.35186	+	2.34149i	0.0833593	+	0.144383i	0.904691	−	0.426069i	$-0.140102\pi$
$263$	1.35186	+	2.34149i	0.0833593	+	0.144383i	−0.821332	+	0.570451i	$0.806768\pi$
$264$	2.30304	−	3.98898i	0.141742	−	0.245505i
$265$	0.374738	−	0.374738i	0.0230200	−	0.0230200i
$266$	0.812357	−	2.20533i	0.0498088	−	0.135217i
$267$	12.4784	+	3.34358i	0.763666	+	0.204624i
$268$	13.1096	+	3.51270i	0.800794	+	0.214572i
$269$		−	23.3633i		−	1.42448i	−0.701934	−	0.712242i	$-0.747680\pi$
$269$		−	23.3633i		−	1.42448i	0.701934	−	0.712242i	$-0.252320\pi$
$270$	−0.668901	+	0.386190i	−0.0407080	+	0.0235028i
$271$	−9.39907	−	9.39907i	−0.570953	−	0.570953i	0.361442	−	0.932395i	$-0.382285\pi$
$271$	−9.39907	−	9.39907i	−0.570953	−	0.570953i	−0.932395	+	0.361442i	$0.882285\pi$
$272$	15.8603			0.961673
$273$	−8.61935	−	5.39472i	−0.521667	−	0.326503i
$274$	−2.72207			−0.164446
$275$	−12.8118	−	12.8118i	−0.772579	−	0.772579i
$276$	−15.3579	+	8.86689i	−0.924437	+	0.533724i
$277$		−	4.84110i		−	0.290873i	−0.989368	−	0.145437i	$-0.953541\pi$
$277$		−	4.84110i		−	0.290873i	0.989368	−	0.145437i	$-0.0464587\pi$
$278$	4.22723	+	1.13268i	0.253532	+	0.0679338i
$279$	−1.88218	−	0.504328i	−0.112683	−	0.0301933i
$280$	−1.18654	+	0.987825i	−0.0709095	+	0.0590338i
$281$	8.60836	−	8.60836i	0.513532	−	0.513532i	−0.402075	−	0.915607i	$-0.631711\pi$
$281$	8.60836	−	8.60836i	0.513532	−	0.513532i	0.915607	+	0.402075i	$0.131711\pi$
$282$	1.43629	−	2.48772i	0.0855297	−	0.148142i
$283$	−0.527867	−	0.914293i	−0.0313784	−	0.0543491i	0.849910	−	0.526928i	$-0.176656\pi$
$283$	−0.527867	−	0.914293i	−0.0313784	−	0.0543491i	−0.881288	+	0.472579i	$0.843323\pi$
$284$	−14.0596	−	3.76725i	−0.834281	−	0.223545i
$285$	0.849397	+	1.47120i	0.0503140	+	0.0871463i
$286$	−2.65224	+	2.96428i	−0.156830	+	0.175282i
$287$	−7.67230	−	16.6210i	−0.452882	−	0.981107i
$288$	5.88418	−	1.57666i	0.346729	−	0.0929056i
$289$	3.43328			0.201958
$290$	0.377574			0.0221719
$291$	−14.0657	+	3.76889i	−0.824544	+	0.220936i
$292$	6.13645	+	22.9015i	0.359108	+	1.34021i
$293$	−5.31237	+	19.8260i	−0.310352	+	1.15825i	0.617888	+	0.786266i	$0.287989\pi$
$293$	−5.31237	+	19.8260i	−0.310352	+	1.15825i	−0.928240	+	0.371983i	$0.878678\pi$
$294$	2.14334	−	0.170806i	0.125002	−	0.00996160i
$295$	0.134702	+	0.233311i	0.00784266	+	0.0135839i
$296$			0.206714i			0.0120150i
$297$	−5.13708	+	19.1718i	−0.298083	+	1.11246i
$298$	3.58498	+	2.06979i	0.207672	+	0.119900i
$299$	29.7295	−	9.76308i	1.71930	−	0.564614i
$300$			9.67064i			0.558335i
$301$	−10.7825	+	8.97672i	−0.621495	+	0.517410i
$302$	−0.715189	+	1.23874i	−0.0411545	+	0.0712817i
$303$	1.02616	+	0.592456i	0.0589515	+	0.0340357i
$304$	−2.79936	−	10.4473i	−0.160554	−	0.599196i
$305$	−3.12071	−	3.12071i	−0.178691	−	0.178691i
$306$	2.34500	−	0.628340i	0.134055	−	0.0359198i
$307$	7.23927	+	7.23927i	0.413167	+	0.413167i	0.882840	−	0.469673i	$-0.155628\pi$
$307$	7.23927	+	7.23927i	0.413167	+	0.413167i	−0.469673	+	0.882840i	$0.655628\pi$
$308$	−1.76716	+	19.3362i	−0.100693	+	1.10178i
$309$	0.395446	+	0.228311i	0.0224961	+	0.0129881i
$310$	−0.110137	+	0.110137i	−0.00625536	+	0.00625536i
$311$	4.86207	−	8.42134i	0.275702	−	0.477531i	−0.694610	−	0.719387i	$-0.744423\pi$
$311$	4.86207	−	8.42134i	0.275702	−	0.477531i	0.970312	+	0.241856i	$0.0777562\pi$
$312$	4.33131	−	0.240642i	0.245212	−	0.0136236i
$313$	14.4470	−	8.34100i	0.816595	−	0.471461i	−0.0326459	−	0.999467i	$-0.510393\pi$
$313$	14.4470	−	8.34100i	0.816595	−	0.471461i	0.849241	+	0.528006i	$0.177060\pi$
$314$	0.260429	+	0.971933i	0.0146968	+	0.0548494i
$315$	1.47033	−	2.08265i	0.0828440	−	0.117344i
$316$	12.5440	−	7.24228i	0.705655	−	0.407410i
$317$	2.75827	−	10.2940i	0.154920	−	0.578170i	−0.844192	−	0.536041i	$-0.819919\pi$
$317$	2.75827	−	10.2940i	0.154920	−	0.578170i	0.999112	−	0.0421288i	$-0.0134140\pi$
$318$	0.222641	−	0.222641i	0.0124851	−	0.0124851i
$319$	6.86081	−	6.86081i	0.384132	−	0.384132i
$320$	−0.812958	+	3.03400i	−0.0454457	+	0.169606i
$321$	4.63073	−	2.67355i	0.258462	−	0.149223i
$322$	−3.81613	+	5.40534i	−0.212665	+	0.301228i
$323$	−3.60649	−	13.4596i	−0.200670	−	0.748911i
$324$	−0.107910	+	0.0623018i	−0.00599499	+	0.00346121i
$325$	3.49536	−	16.7022i	0.193887	−	0.926472i
$326$	−0.330790	+	0.572944i	−0.0183207	+	0.0317325i
$327$	−0.640060	+	0.640060i	−0.0353954	+	0.0353954i
$328$	6.76344	+	3.90488i	0.373449	+	0.215611i
$329$	−2.25191	+	24.6404i	−0.124152	+	1.35847i
$330$	0.429889	+	0.429889i	0.0236646	+	0.0236646i
$331$	−33.1191	+	8.87424i	−1.82039	+	0.487772i	−0.996838	−	0.0794669i	$-0.974678\pi$
$331$	−33.1191	+	8.87424i	−1.82039	+	0.487772i	−0.823553	+	0.567239i	$0.808012\pi$
$332$	−12.3228	−	12.3228i	−0.676299	−	0.676299i
$333$	−0.0883435	−	0.329703i	−0.00484120	−	0.0180676i
$334$	−5.23296	−	3.02125i	−0.286335	−	0.165316i
$335$	−1.83017	+	3.16994i	−0.0999927	+	0.173192i
$336$	7.60472	−	6.33111i	0.414871	−	0.345390i
$337$			32.8040i			1.78695i	0.449117	+	0.893473i	$0.351739\pi$
$337$			32.8040i			1.78695i	−0.449117	+	0.893473i	$0.648261\pi$
$338$	−3.70358	−	0.562758i	−0.201448	−	0.0306100i
$339$	4.52128	+	2.61036i	0.245562	+	0.141775i
$340$	−1.15950	+	4.32730i	−0.0628825	+	0.234681i
$341$			4.00255i			0.216750i
$342$	−0.827787	−	1.43377i	−0.0447616	−	0.0775293i
$343$	−16.1455	+	9.07323i	−0.871774	+	0.489908i
$344$	1.54915	−	5.78151i	0.0835247	−	0.311718i
$345$	−1.23787	−	4.61978i	−0.0666445	−	0.248721i
$346$	−5.59121	+	1.49816i	−0.300585	+	0.0805416i
$347$	9.06551			0.486662			0.243331	−	0.969943i	$-0.421760\pi$
$347$	9.06551			0.486662			0.243331	+	0.969943i	$0.421760\pi$
$348$	−5.17871			−0.277608
$349$	−27.6016	+	7.39582i	−1.47748	+	0.395889i	−0.905488	−	0.424372i	$-0.860495\pi$
$349$	−27.6016	+	7.39582i	−1.47748	+	0.395889i	−0.571990	+	0.820261i	$0.693828\pi$
$350$	1.51223	+	3.27605i	0.0808322	+	0.175112i
$351$	−17.7598	+	5.83225i	−0.947947	+	0.311303i
$352$	−6.25651	−	10.8366i	−0.333473	−	0.577593i
$353$	−19.4183	−	5.20313i	−1.03353	−	0.276935i	−0.298103	−	0.954534i	$-0.596354\pi$
$353$	−19.4183	−	5.20313i	−1.03353	−	0.276935i	−0.735431	+	0.677599i	$0.763020\pi$
$354$	0.0800296	+	0.138615i	0.00425353	+	0.00736733i
$355$	1.96279	−	3.39966i	0.104174	−	0.180435i
$356$	16.4279	−	16.4279i	0.870678	−	0.870678i
$357$	9.79736	−	8.15653i	0.518531	−	0.431689i
$358$	−5.96438	−	1.59815i	−0.315227	−	0.0844649i
$359$	−29.7920	−	7.98274i	−1.57236	−	0.421313i	−0.635811	−	0.771845i	$-0.719334\pi$
$359$	−29.7920	−	7.98274i	−1.57236	−	0.421313i	−0.936551	+	0.350532i	$0.886001\pi$
$360$			1.08760i			0.0573216i
$361$	8.22508	−	4.74875i	0.432899	−	0.249934i
$362$	4.02492	+	4.02492i	0.211545	+	0.211545i
$363$	3.89754			0.204568
$364$	−16.1524	+	8.57328i	−0.846617	+	0.449362i
$365$	−6.39436			−0.334696
$366$	−1.85409	−	1.85409i	−0.0969147	−	0.0969147i
$367$	4.59522	−	2.65305i	0.239869	−	0.138488i	−0.375248	−	0.926925i	$-0.622442\pi$
$367$	4.59522	−	2.65305i	0.239869	−	0.138488i	0.615116	+	0.788436i	$0.289109\pi$
$368$			30.4508i			1.58736i
$369$	−12.4563	−	3.33766i	−0.648451	−	0.173752i
$370$	−0.0263544	−	0.00706165i	−0.00137010	−	0.000367118i
$371$	−0.937444	+	2.54491i	−0.0486696	+	0.132125i
$372$	1.51061	−	1.51061i	0.0783216	−	0.0783216i
$373$	12.2831	−	21.2749i	0.635993	−	1.10157i	−0.350311	−	0.936633i	$-0.613924\pi$
$373$	12.2831	−	21.2749i	0.635993	−	1.10157i	0.986304	−	0.164938i	$-0.0527425\pi$
$374$	−2.49338	−	4.31866i	−0.128930	−	0.223313i
$375$	−5.18083	−	1.38820i	−0.267537	−	0.0716863i
$376$	−5.27788	−	9.14155i	−0.272186	−	0.471439i
$377$	8.94417	+	1.87179i	0.460648	+	0.0964022i
$378$	2.27967	−	3.22903i	0.117254	−	0.166083i
$379$	21.0045	−	5.62815i	1.07893	−	0.289099i	0.324773	−	0.945792i	$-0.394712\pi$
$379$	21.0045	−	5.62815i	1.07893	−	0.289099i	0.754158	+	0.656693i	$0.228045\pi$
$380$	3.05508			0.156722
$381$	−3.70070			−0.189593
$382$	1.19653	−	0.320609i	0.0612198	−	0.0164038i
$383$	3.03913	+	11.3422i	0.155292	+	0.579558i	0.999080	+	0.0428816i	$0.0136538\pi$
$383$	3.03913	+	11.3422i	0.155292	+	0.579558i	−0.843788	+	0.536677i	$0.819679\pi$
$384$	−2.28645	+	8.53317i	−0.116680	+	0.435456i
$385$	−4.91387	−	1.81008i	−0.250434	−	0.0922501i
$386$	1.95282	+	3.38239i	0.0993961	+	0.172159i
$387$			9.88341i			0.502402i
$388$	−6.77790	+	25.2955i	−0.344096	+	1.28418i
$389$	−30.3210	−	17.5058i	−1.53733	−	0.887580i	−0.998994	−	0.0448528i	$-0.985718\pi$
$389$	−30.3210	−	17.5058i	−1.53733	−	0.887580i	−0.538341	−	0.842727i	$-0.680949\pi$
$390$	−0.117284	+	0.560430i	−0.00593890	+	0.0283785i
$391$			39.2306i			1.98398i
$392$	3.39446	−	7.13468i	0.171446	−	0.360356i
$393$	9.24095	−	16.0058i	0.466144	−	0.807385i
$394$	0.955680	+	0.551762i	0.0481465	+	0.0277974i
$395$	1.01106	+	3.77334i	0.0508721	+	0.189857i
$396$	9.67180	+	9.67180i	0.486026	+	0.486026i
$397$	7.73441	−	2.07243i	0.388179	−	0.104012i	−0.0594508	−	0.998231i	$-0.518935\pi$
$397$	7.73441	−	2.07243i	0.388179	−	0.104012i	0.447630	+	0.894219i	$0.352268\pi$
$398$	−2.14116	−	2.14116i	−0.107326	−	0.107326i
$399$	−7.10202	−	5.01398i	−0.355546	−	0.251013i
$400$	14.3808	+	8.30277i	0.719041	+	0.415139i
$401$	19.3159	−	19.3159i	0.964591	−	0.964591i	−0.0348028	−	0.999394i	$-0.511080\pi$
$401$	19.3159	−	19.3159i	0.964591	−	0.964591i	0.999394	+	0.0348028i	$0.0110803\pi$
$402$	−1.08735	+	1.88334i	−0.0542319	+	0.0939323i
$403$	−3.15498	+	2.06299i	−0.157161	+	0.102765i
$404$	1.84543	−	1.06546i	0.0918138	−	0.0530087i
$405$	−0.00869768	−	0.0324602i	−0.000432191	−	0.00161296i
$406$	−1.75435	+	0.809813i	−0.0870670	+	0.0401904i
$407$	−0.607197	+	0.350565i	−0.0300976	+	0.0173769i
$408$	−1.40761	+	5.25326i	−0.0696870	+	0.260075i
$409$	4.04580	−	4.04580i	0.200052	−	0.200052i	−0.599970	−	0.800022i	$-0.704821\pi$
$409$	4.04580	−	4.04580i	0.200052	−	0.200052i	0.800022	+	0.599970i	$0.204821\pi$
$410$	−0.728892	+	0.728892i	−0.0359974	+	0.0359974i
$411$	−2.60610	+	9.72610i	−0.128549	+	0.479753i
$412$	0.711163	−	0.410590i	0.0350365	−	0.0202283i
$413$	−1.12628	−	0.795144i	−0.0554205	−	0.0391265i
$414$	1.20637	+	4.50225i	0.0592900	+	0.221273i
$415$	4.07033	−	2.35001i	0.199805	−	0.115357i
$416$	5.31714	−	10.5170i	0.260694	−	0.515640i
$417$	8.09428	−	14.0197i	0.396379	−	0.686548i
$418$	−2.40466	+	2.40466i	−0.117616	+	0.117616i
$419$	−13.3221	−	7.69152i	−0.650828	−	0.375755i	0.137946	−	0.990440i	$-0.455950\pi$
$419$	−13.3221	−	7.69152i	−0.650828	−	0.375755i	−0.788773	+	0.614684i	$0.789283\pi$
$420$	1.17141	+	2.53770i	0.0571590	+	0.123827i
$421$	4.76255	+	4.76255i	0.232112	+	0.232112i	0.813574	−	0.581462i	$-0.197519\pi$
$421$	4.76255	+	4.76255i	0.232112	+	0.232112i	−0.581462	+	0.813574i	$0.697519\pi$
$422$	−2.15839	+	0.578338i	−0.105069	+	0.0281531i
$423$	12.3249	+	12.3249i	0.599257	+	0.599257i
$424$	−0.299456	−	1.11759i	−0.0145429	−	0.0542748i
$425$	18.5272	+	10.6967i	0.898701	+	0.518865i
$426$	1.16614	−	2.01982i	0.0564997	−	0.0978604i
$427$	21.1932	+	7.80676i	1.02561	+	0.377796i
$428$		−	9.61614i		−	0.464814i
$429$	8.05231	+	12.3146i	0.388769	+	0.594554i
$430$	0.684178	+	0.395010i	0.0329940	+	0.0190491i
$431$	4.36813	−	16.3021i	0.210406	−	0.785244i	−0.777328	−	0.629095i	$-0.783425\pi$
$431$	4.36813	−	16.3021i	0.210406	−	0.785244i	0.987734	−	0.156149i	$-0.0499079\pi$
$432$		−	18.1907i		−	0.875198i
$433$	−4.63490	−	8.02787i	−0.222739	−	0.385795i	0.732900	−	0.680337i	$-0.238166\pi$
$433$	−4.63490	−	8.02787i	−0.222739	−	0.385795i	−0.955639	+	0.294542i	$0.904833\pi$
$434$	0.275518	−	0.747958i	0.0132253	−	0.0359031i
$435$	0.361488	−	1.34909i	0.0173320	−	0.0646841i
$436$	0.421322	+	1.57240i	0.0201777	+	0.0753041i
$437$	25.8416	−	6.92422i	1.23617	−	0.331231i
$438$	−3.79904			−0.181525
$439$	−17.4133			−0.831090			−0.415545	−	0.909573i	$-0.636409\pi$
$439$	−17.4133			−0.831090			−0.415545	+	0.909573i	$0.636409\pi$
$440$	2.15791	−	0.578210i	0.102874	−	0.0275651i
$441$	−2.36491	+	12.8303i	−0.112615	+	0.610967i
$442$	2.11902	−	4.19131i	0.100791	−	0.199360i
$443$	−5.09769	−	8.82945i	−0.242198	−	0.419500i	0.719142	−	0.694863i	$-0.244535\pi$
$443$	−5.09769	−	8.82945i	−0.242198	−	0.419500i	−0.961340	+	0.275363i	$0.911202\pi$
$444$	0.361471	+	0.0968559i	0.0171547	+	0.00459658i
$445$	3.13288	+	5.42631i	0.148513	+	0.257232i
$446$	3.38168	−	5.85725i	0.160127	−	0.277349i
$447$	10.8277	−	10.8277i	0.512133	−	0.512133i
$448$	−2.72996	−	15.8407i	−0.128978	−	0.748404i
$449$	−17.5974	−	4.71520i	−0.830471	−	0.222524i	−0.181552	−	0.983381i	$-0.558112\pi$
$449$	−17.5974	−	4.71520i	−0.830471	−	0.222524i	−0.648919	+	0.760857i	$0.724779\pi$
$450$	2.45518	+	0.657863i	0.115738	+	0.0310120i
$451$			26.4891i			1.24732i
$452$	8.13099	−	4.69443i	0.382449	−	0.220807i
$453$	3.74139	+	3.74139i	0.175786	+	0.175786i
$454$	−1.77575			−0.0833399
$455$	−1.10592	−	4.80627i	−0.0518464	−	0.225321i
$456$	3.70882			0.173681
$457$	23.8543	+	23.8543i	1.11586	+	1.11586i	0.992343	+	0.123515i	$0.0394167\pi$
$457$	23.8543	+	23.8543i	1.11586	+	1.11586i	0.123515	+	0.992343i	$0.460583\pi$
$458$	−2.84206	+	1.64086i	−0.132801	+	0.0766725i
$459$		−	23.4355i		−	1.09388i
$460$	−8.30814	−	2.22616i	−0.387369	−	0.103795i
$461$	−10.9633	−	2.93760i	−0.510611	−	0.136818i	−0.00569051	−	0.999984i	$-0.501811\pi$
$461$	−10.9633	−	2.93760i	−0.510611	−	0.136818i	−0.504920	+	0.863166i	$0.668478\pi$
$462$	−2.91945	−	1.07541i	−0.135825	−	0.0500326i
$463$	−4.05208	+	4.05208i	−0.188316	+	0.188316i	−0.794968	−	0.606652i	$-0.792512\pi$
$463$	−4.05208	+	4.05208i	−0.188316	+	0.188316i	0.606652	+	0.794968i	$0.292512\pi$
$464$	−4.44620	+	7.70105i	−0.206410	+	0.357512i
$465$	0.288081	+	0.498971i	0.0133594	+	0.0231392i
$466$	4.14851	+	1.11159i	0.192176	+	0.0514934i
$467$	−18.1856	−	31.4984i	−0.841529	−	1.45757i	−0.888602	−	0.458680i	$-0.848322\pi$
$467$	−18.1856	−	31.4984i	−0.841529	−	1.45757i	0.0470722	−	0.998891i	$-0.485011\pi$
$468$	−2.63870	+	12.6087i	−0.121974	+	0.582839i
$469$	1.70482	−	18.6541i	0.0787211	−	0.861364i
$470$	1.34578	−	0.360600i	0.0620762	−	0.0166333i
$471$	3.72211			0.171506
$472$	0.588164			0.0270725
$473$	19.6097	−	5.25440i	0.901655	−	0.241598i
$474$	0.600696	+	2.24183i	0.0275909	+	0.102971i
$475$	3.77594	−	14.0920i	0.173252	−	0.646585i
$476$	−3.89365	−	22.5931i	−0.178465	−	1.03555i
$477$	0.955249	+	1.65454i	0.0437379	+	0.0757562i
$478$			8.33866i			0.381401i
$479$	6.29114	−	23.4789i	0.287449	−	1.07278i	−0.659581	−	0.751633i	$-0.729266\pi$
$479$	6.29114	−	23.4789i	0.287449	−	1.07278i	0.947031	−	0.321143i	$-0.104067\pi$
$480$	−1.55991	−	0.900617i	−0.0712000	−	0.0411073i
$481$	−0.589291	−	0.297930i	−0.0268693	−	0.0135844i
$482$			5.30005i			0.241411i
$483$	15.6600	+	18.8103i	0.712556	+	0.855899i
$484$	3.50464	−	6.07021i	0.159302	−	0.275919i
$485$	−6.11654	−	3.53139i	−0.277738	−	0.160352i
$486$	−1.16517	−	4.34847i	−0.0528531	−	0.197250i
$487$	18.8377	+	18.8377i	0.853616	+	0.853616i	0.990577	−	0.136960i	$-0.0437333\pi$
$487$	18.8377	+	18.8377i	0.853616	+	0.853616i	−0.136960	+	0.990577i	$0.543733\pi$
$488$	−9.30694	+	2.49379i	−0.421305	+	0.112888i
$489$	1.73047	+	1.73047i	0.0782544	+	0.0782544i
$490$	0.793659	+	0.676499i	0.0358538	+	0.0305611i
$491$	−15.2520	−	8.80574i	−0.688313	−	0.397398i	0.114667	−	0.993404i	$-0.463420\pi$
$491$	−15.2520	−	8.80574i	−0.688313	−	0.397398i	−0.802980	+	0.596006i	$0.796753\pi$
$492$	9.99730	−	9.99730i	0.450713	−	0.450713i
$493$	−5.72816	+	9.92147i	−0.257983	+	0.446840i
$494$	−3.13486	−	0.656048i	−0.141044	−	0.0295170i
$495$	−3.19469	+	1.84446i	−0.143591	+	0.0829022i
$496$	−0.949428	−	3.54331i	−0.0426306	−	0.159099i
$497$	−1.82836	+	20.0058i	−0.0820130	+	0.897385i
$498$	2.41828	−	1.39620i	0.108366	−	0.0625650i
$499$	−3.93339	+	14.6796i	−0.176083	+	0.657149i	0.820282	+	0.571959i	$0.193816\pi$
$499$	−3.93339	+	14.6796i	−0.176083	+	0.657149i	−0.996365	+	0.0851901i	$0.972850\pi$
$500$	−6.82061	+	6.82061i	−0.305027	+	0.305027i
$501$	−15.8051	+	15.8051i	−0.706122	+	0.706122i
$502$	−0.512177	+	1.91147i	−0.0228596	+	0.0853132i
$503$	3.91743	−	2.26173i	0.174669	−	0.100845i	−0.410116	−	0.912033i	$-0.634512\pi$
$503$	3.91743	−	2.26173i	0.174669	−	0.100845i	0.584786	+	0.811188i	$0.301179\pi$
$504$	−2.33266	−	5.05340i	−0.103905	−	0.225096i
$505$	0.148744	+	0.555122i	0.00661904	+	0.0247026i
$506$	8.29156	−	4.78713i	0.368605	−	0.212814i
$507$	−5.55657	+	12.6943i	−0.246776	+	0.563775i
$508$	−3.32764	+	5.76364i	−0.147640	+	0.255720i
$509$	−27.1759	+	27.1759i	−1.20455	+	1.20455i	−0.231785	+	0.972767i	$0.574457\pi$
$509$	−27.1759	+	27.1759i	−1.20455	+	1.20455i	−0.972767	+	0.231785i	$0.925543\pi$
$510$	−0.621666	−	0.358919i	−0.0275278	−	0.0158932i
$511$	29.7106	−	13.7145i	1.31432	−	0.606694i
$512$	13.7099	+	13.7099i	0.605896	+	0.605896i
$513$	−15.4372	+	4.13638i	−0.681568	+	0.182626i
$514$	1.69726	+	1.69726i	0.0748628	+	0.0748628i
$515$	0.0573207	+	0.213924i	0.00252585	+	0.00942660i
$516$	−9.38402	−	5.41787i	−0.413108	−	0.238508i
$517$	17.9015	−	31.0063i	0.787306	−	1.36365i
$518$	0.137598	−	0.0237134i	0.00604573	−	0.00104191i
$519$			21.4121i			0.939885i
$520$	1.56800	+	1.40294i	0.0687612	+	0.0615228i
$521$	31.7542	+	18.3333i	1.39117	+	0.803195i	0.993445	−	0.114308i	$-0.0364649\pi$
$521$	31.7542	+	18.3333i	1.39117	+	0.803195i	0.397729	+	0.917503i	$0.369798\pi$
$522$	−0.352291	+	1.31477i	−0.0154194	+	0.0575459i
$523$		−	10.5291i		−	0.460407i	−0.973143	−	0.230203i	$-0.926061\pi$
$523$		−	10.5291i		−	0.460407i	0.973143	−	0.230203i	$-0.0739391\pi$
$524$	−16.6188	−	28.7845i	−0.725994	−	1.25746i
$525$	13.1533	−	2.26681i	0.574058	−	0.0989319i
$526$	−0.201648	+	0.752560i	−0.00879226	+	0.0328132i
$527$	−1.22317	−	4.56495i	−0.0532823	−	0.198852i
$528$	−13.8303	+	3.70583i	−0.601888	+	0.161275i
$529$	−52.3203			−2.27479
$530$	0.152714			0.00663346
$531$	−0.938106	+	0.251365i	−0.0407103	+	0.0109083i
$532$	−14.1951	+	6.55248i	−0.615434	+	0.284086i
$533$	−20.8798	+	13.6530i	−0.904404	+	0.591375i
$534$	1.86132	+	3.22390i	0.0805472	+	0.139512i
$535$	2.50508	+	0.671233i	0.108304	+	0.0290199i
$536$	3.99563	+	6.92064i	0.172585	+	0.298926i
$537$	−11.4206	+	19.7810i	−0.492834	+	0.853613i
$538$	4.76052	−	4.76052i	0.205241	−	0.205241i
$539$	26.7139	−	2.12887i	1.15065	−	0.0916971i
$540$	4.96310	+	1.32986i	0.213578	+	0.0572280i
$541$	−11.8482	−	3.17473i	−0.509396	−	0.136492i	−0.00503858	−	0.999987i	$-0.501604\pi$
$541$	−11.8482	−	3.17473i	−0.509396	−	0.136492i	−0.504357	+	0.863495i	$0.668271\pi$
$542$		−	3.83032i		−	0.164526i
$543$	18.2347	−	10.5278i	0.782527	−	0.451792i
$544$	10.4473	+	10.4473i	0.447922	+	0.447922i
$545$	−0.439030			−0.0188060
$546$	−0.657053	−	2.85552i	−0.0281193	−	0.122205i
$547$	−46.5673			−1.99108			−0.995538	−	0.0943609i	$-0.969919\pi$
$547$	−46.5673			−1.99108			−0.995538	+	0.0943609i	$0.969919\pi$
$548$	12.8045	+	12.8045i	0.546980	+	0.546980i
$549$	13.7785	−	7.95504i	0.588054	−	0.339513i
$550$		−	5.22107i		−	0.222627i
$551$	7.54639	+	2.02205i	0.321487	+	0.0861421i
$552$	−10.0859	−	2.70252i	−0.429286	−	0.115027i
$553$	−12.7908	−	15.3638i	−0.543919	−	0.653337i
$554$	0.986426	−	0.986426i	0.0419092	−	0.0419092i
$555$	−0.0504634	+	0.0874051i	−0.00214205	+	0.00371014i
$556$	−14.5566	−	25.2128i	−0.617338	−	1.06926i
$557$	18.1529	+	4.86405i	0.769163	+	0.206097i	0.622002	−	0.783016i	$-0.286320\pi$
$557$	18.1529	+	4.86405i	0.769163	+	0.206097i	0.147161	+	0.989113i	$0.452986\pi$
$558$	−0.280752	−	0.486276i	−0.0118852	−	0.0205857i
$559$	14.2489	+	12.7490i	0.602666	+	0.539224i
$560$	4.77943	+	0.436798i	0.201968	+	0.0184581i
$561$	−17.8180	+	4.77432i	−0.752276	+	0.201572i
$562$	3.50809			0.147980
$563$	−18.7069			−0.788402			−0.394201	−	0.919024i	$-0.628979\pi$
$563$	−18.7069			−0.788402			−0.394201	+	0.919024i	$0.628979\pi$
$564$	−18.4584	+	4.94591i	−0.777238	+	0.208260i
$565$	0.655368	+	2.44587i	0.0275715	+	0.102898i
$566$	0.0787383	−	0.293855i	0.00330962	−	0.0123517i
$567$	0.110033	+	0.132168i	0.00462094	+	0.00555052i
$568$	−4.28518	−	7.42215i	−0.179802	−	0.311426i
$569$			6.74956i			0.282956i	0.989941	+	0.141478i	$0.0451855\pi$
$569$			6.74956i			0.282956i	−0.989941	+	0.141478i	$0.954815\pi$
$570$	−0.126699	+	0.472846i	−0.00530683	+	0.0198054i
$571$	5.33385	+	3.07950i	0.223215	+	0.128873i	0.607438	−	0.794367i	$-0.292197\pi$
$571$	5.33385	+	3.07950i	0.223215	+	0.128873i	−0.384223	+	0.923240i	$0.625531\pi$
$572$	26.4199	−	1.46785i	1.10467	−	0.0613740i
$573$		−	4.58222i		−	0.191425i
$574$	1.82339	−	4.95002i	0.0761070	−	0.206610i
$575$	−20.5369	+	35.5710i	−0.856450	+	1.48341i
$576$	−9.80633	−	5.66169i	−0.408597	−	0.235904i
$577$	−5.24075	−	19.5588i	−0.218175	−	0.814242i	−0.985025	−	0.172414i	$-0.944843\pi$
$577$	−5.24075	−	19.5588i	−0.218175	−	0.814242i	0.766849	−	0.641827i	$-0.221823\pi$
$578$	0.699567	+	0.699567i	0.0290982	+	0.0290982i
$579$	13.9551	−	3.73926i	0.579954	−	0.155398i
$580$	−1.77609	−	1.77609i	−0.0737482	−	0.0737482i
$581$	−13.8721	+	19.6490i	−0.575510	+	0.815178i
$582$	−3.63398	−	2.09808i	−0.150633	−	0.0869682i
$583$	2.77493	−	2.77493i	0.114926	−	0.114926i
$584$	−6.98010	+	12.0899i	−0.288839	+	0.500283i
$585$	−3.10048	−	1.56753i	−0.128189	−	0.0648092i
$586$	−5.12222	+	2.95731i	−0.211597	+	0.122165i
$587$	3.35452	+	12.5192i	0.138456	+	0.516725i	0.999960	+	0.00897355i	$0.00285641\pi$
$587$	3.35452	+	12.5192i	0.138456	+	0.516725i	−0.861504	+	0.507751i	$0.830477\pi$
$588$	−10.8856	−	9.27870i	−0.448916	−	0.382647i
$589$	−2.79108	+	1.61143i	−0.115004	+	0.0663979i
$590$	−0.0200926	+	0.0749865i	−0.000827199	+	0.00308715i
$591$	2.88644	−	2.88644i	0.118732	−	0.118732i
$592$	0.454373	−	0.454373i	0.0186746	−	0.0186746i
$593$	−0.677366	+	2.52797i	−0.0278161	+	0.103811i	−0.978438	−	0.206540i	$-0.933780\pi$
$593$	−0.677366	+	2.52797i	−0.0278161	+	0.103811i	0.950622	+	0.310351i	$0.100446\pi$
$594$	−4.95320	+	2.85973i	−0.203232	+	0.117336i
$595$	6.15747	+	0.562738i	0.252432	+	0.0230700i
$596$	−7.12739	−	26.5998i	−0.291949	−	1.08957i
$597$	−9.70041	+	5.60053i	−0.397011	+	0.229215i
$598$	8.04704	+	4.06838i	0.329068	+	0.166368i
$599$	−11.8359	+	20.5003i	−0.483600	+	0.837620i	−0.999823	−	0.0188345i	$-0.994004\pi$
$599$	−11.8359	+	20.5003i	−0.483600	+	0.837620i	0.516222	+	0.856455i	$0.327338\pi$
$600$	−4.02635	+	4.02635i	−0.164375	+	0.164375i
$601$	−39.8779	−	23.0235i	−1.62665	−	0.939149i	−0.985082	−	0.172087i	$-0.944949\pi$
$601$	−39.8779	−	23.0235i	−1.62665	−	0.939149i	−0.641573	−	0.767062i	$-0.721718\pi$
$602$	−4.02616	−	0.367955i	−0.164094	−	0.0149967i
$603$	−9.33060	−	9.33060i	−0.379971	−	0.379971i
$604$	9.19122	−	2.46278i	0.373986	−	0.100209i
$605$	1.33670	+	1.33670i	0.0543447	+	0.0543447i
$606$	0.0883725	+	0.329811i	0.00358989	+	0.0133976i
$607$	7.28556	+	4.20632i	0.295712	+	0.170729i	0.640515	−	0.767946i	$-0.278721\pi$
$607$	7.28556	+	4.20632i	0.295712	+	0.170729i	−0.344803	+	0.938675i	$0.612054\pi$
$608$	5.03775	−	8.72564i	0.204308	−	0.353872i
$609$	1.21390	+	7.04371i	0.0491896	+	0.285426i
$610$		−	1.27176i		−	0.0514919i
$611$	33.6672	−	1.87050i	1.36203	−	0.0756725i
$612$	−13.9865	−	8.07508i	−0.565369	−	0.326416i
$613$	−5.48728	+	20.4788i	−0.221629	+	0.827131i	0.762098	+	0.647462i	$0.224169\pi$
$613$	−5.48728	+	20.4788i	−0.221629	+	0.827131i	−0.983727	+	0.179669i	$0.942497\pi$
$614$			2.95016i			0.119059i
$615$	1.90653	+	3.30221i	0.0768788	+	0.133158i
$616$	−8.78633	+	7.31483i	−0.354011	+	0.294723i
$617$	7.51730	−	28.0549i	0.302635	−	1.12945i	−0.632327	−	0.774702i	$-0.717900\pi$
$617$	7.51730	−	28.0549i	0.302635	−	1.12945i	0.934962	−	0.354748i	$-0.115433\pi$
$618$	0.0340556	+	0.127097i	0.00136992	+	0.00511259i
$619$	24.8662	−	6.66289i	0.999458	−	0.267804i	0.278240	−	0.960512i	$-0.410249\pi$
$619$	24.8662	−	6.66289i	0.999458	−	0.267804i	0.721218	+	0.692708i	$0.243582\pi$
$620$	1.03616			0.0416132
$621$	44.9947			1.80557
$622$	2.70664	−	0.725241i	0.108526	−	0.0290795i
$623$	−26.1948	−	18.4933i	−1.04947	−	0.740920i
$624$	−10.0495	−	8.99160i	−0.402302	−	0.359952i
$625$	10.5311	+	18.2403i	0.421242	+	0.729613i
$626$	4.64331	+	1.24417i	0.185584	+	0.0497270i
$627$	6.28977	+	10.8942i	0.251189	+	0.435073i
$628$	3.34689	−	5.79698i	0.133555	−	0.231325i
$629$	0.585381	−	0.585381i	0.0233407	−	0.0233407i
$630$	0.723958	−	0.124765i	0.0288432	−	0.00497077i
$631$	4.24248	+	1.13677i	0.168891	+	0.0452541i	0.342273	−	0.939600i	$-0.388803\pi$
$631$	4.24248	+	1.13677i	0.168891	+	0.0452541i	−0.173383	+	0.984855i	$0.555470\pi$
$632$	8.23797	+	2.20736i	0.327689	+	0.0878040i
$633$			8.26574i			0.328534i
$634$	2.65954	−	1.53549i	0.105624	−	0.0609820i
$635$	−1.26919	−	1.26919i	−0.0503664	−	0.0503664i
$636$	−2.09458			−0.0830557
$637$	15.4469	+	19.9598i	0.612029	+	0.790835i
$638$	2.79593			0.110692
$639$	10.0068	+	10.0068i	0.395861	+	0.395861i
$640$	−3.71070	+	2.14237i	−0.146678	+	0.0846847i
$641$			20.1136i			0.794439i	0.917724	+	0.397220i	$0.130025\pi$
$641$			20.1136i			0.794439i	−0.917724	+	0.397220i	$0.869975\pi$
$642$	1.48832	+	0.398795i	0.0587395	+	0.0157392i
$643$	3.80955	+	1.02077i	0.150234	+	0.0402551i	0.333152	−	0.942873i	$-0.391888\pi$
$643$	3.80955	+	1.02077i	0.150234	+	0.0402551i	−0.182918	+	0.983128i	$0.558554\pi$
$644$	43.3774	−	7.47556i	1.70931	−	0.294578i
$645$	2.06643	−	2.06643i	0.0813654	−	0.0813654i
$646$	2.00767	−	3.47739i	0.0789909	−	0.136816i
$647$	−3.76152	−	6.51515i	−0.147881	−	0.256137i	0.782563	−	0.622571i	$-0.213912\pi$
$647$	−3.76152	−	6.51515i	−0.147881	−	0.256137i	−0.930444	+	0.366434i	$0.880579\pi$
$648$	−0.0708672	−	0.0189888i	−0.00278393	−	0.000745951i
$649$	0.997466	+	1.72766i	0.0391540	+	0.0678167i
$650$	4.11547	−	2.69104i	0.161422	−	0.105551i
$651$	−2.40872	−	1.70054i	−0.0944051	−	0.0666493i
$652$	4.25113	−	1.13909i	0.166487	−	0.0446100i
$653$	−10.5828			−0.414136			−0.207068	−	0.978327i	$-0.566392\pi$
$653$	−10.5828			−0.414136			−0.207068	+	0.978327i	$0.566392\pi$
$654$	−0.260838			−0.0101996
$655$	8.65863	−	2.32007i	0.338320	−	0.0906527i
$656$	−6.28336	−	23.4498i	−0.245324	−	0.915561i
$657$	5.96619	−	22.2661i	0.232763	−	0.868685i
$658$	−5.47959	+	4.56189i	−0.213617	+	0.177841i
$659$	2.76883	+	4.79576i	0.107858	+	0.186816i	0.914902	−	0.403675i	$-0.132267\pi$
$659$	2.76883	+	4.79576i	0.107858	+	0.186816i	−0.807044	+	0.590491i	$0.798934\pi$
$660$		−	4.04436i		−	0.157427i
$661$	3.44429	−	12.8542i	0.133967	−	0.499972i	−0.866033	−	0.499987i	$-0.833338\pi$
$661$	3.44429	−	12.8542i	0.133967	−	0.499972i	1.00000		1.48350e-5i	$4.72214e-6\pi$
$662$	−8.55659	−	4.94015i	−0.332561	−	0.192004i
$663$	−12.9470	−	11.5841i	−0.502821	−	0.449890i
$664$		−	10.2611i		−	0.398208i
$665$	−0.716116	−	4.15530i	−0.0277698	−	0.161136i
$666$	0.0491795	−	0.0851813i	0.00190567	−	0.00330071i
$667$	−19.0486	−	10.9977i	−0.737564	−	0.425833i
$668$	10.4038	+	38.8275i	0.402535	+	1.50228i
$669$	−17.6907	−	17.6907i	−0.683961	−	0.683961i
$670$	−1.01883	+	0.272994i	−0.0393607	+	0.0105467i
$671$	−23.1088	−	23.1088i	−0.892106	−	0.892106i
$672$	9.17957	+	0.838931i	0.354110	+	0.0323625i
$673$	12.8942	+	7.44448i	0.497035	+	0.286963i	0.727488	−	0.686120i	$-0.240687\pi$
$673$	12.8942	+	7.44448i	0.497035	+	0.286963i	−0.230453	+	0.973083i	$0.574021\pi$
$674$	−6.68416	+	6.68416i	−0.257464	+	0.257464i
$675$	12.2683	−	21.2494i	0.472208	−	0.817889i
$676$	14.7743	+	20.0687i	0.568243	+	0.771873i
$677$	10.7184	−	6.18827i	0.411942	−	0.237835i	−0.279682	−	0.960093i	$-0.590229\pi$
$677$	10.7184	−	6.18827i	0.411942	−	0.237835i	0.691624	+	0.722258i	$0.256896\pi$
$678$	0.389370	+	1.45315i	0.0149536	+	0.0558078i
$679$	35.9938	+	3.28952i	1.38132	+	0.126240i
$680$	−2.28441	+	1.31891i	−0.0876033	+	0.0505778i
$681$	−1.70010	+	6.34484i	−0.0651478	+	0.243135i
$682$	−0.815563	+	0.815563i	−0.0312295	+	0.0312295i
$683$	20.0999	−	20.0999i	0.769102	−	0.769102i	−0.208847	−	0.977948i	$-0.566971\pi$
$683$	20.0999	−	20.0999i	0.769102	−	0.769102i	0.977948	+	0.208847i	$0.0669709\pi$
$684$	−2.85051	+	10.6383i	−0.108992	+	0.406764i
$685$	−4.22945	+	2.44188i	−0.161599	+	0.0932993i
$686$	−5.13858	−	1.44105i	−0.196192	−	0.0550195i
$687$	3.14192	+	11.7258i	0.119872	+	0.447367i
$688$	−16.1134	+	9.30306i	−0.614317	+	0.354676i
$689$	3.61757	+	0.757066i	0.137818	+	0.0288419i
$690$	0.689102	−	1.19356i	0.0262336	−	0.0454380i
$691$	−8.27743	+	8.27743i	−0.314888	+	0.314888i	−0.846800	−	0.531912i	$-0.821474\pi$
$691$	−8.27743	+	8.27743i	−0.314888	+	0.314888i	0.531912	+	0.846800i	$0.321474\pi$
$692$	33.3481	+	19.2535i	1.26770	+	0.731909i
$693$	10.8878	−	15.4220i	0.413593	−	0.585832i
$694$	1.84719	+	1.84719i	0.0701186	+	0.0701186i
$695$	7.58422	−	2.03219i	0.287686	−	0.0770852i
$696$	−2.15614	−	2.15614i	−0.0817284	−	0.0817284i
$697$	−8.09501	−	30.2110i	−0.306621	−	1.14432i
$698$	−7.13109	−	4.11714i	−0.269916	−	0.155836i
$699$	7.94355	−	13.7586i	0.300453	−	0.520399i
$700$	8.29691	−	22.5239i	0.313594	−	0.851322i
$701$			0.431477i			0.0162966i	0.999967	+	0.00814832i	$0.00259372\pi$
$701$			0.431477i			0.0162966i	−0.999967	+	0.00814832i	$0.997406\pi$
$702$	−4.80713	−	2.43036i	−0.181433	−	0.0917281i
$703$	−0.488916	−	0.282276i	−0.0184398	−	0.0106462i
$704$	−6.01994	+	22.4667i	−0.226885	+	0.846747i
$705$		−	5.15378i		−	0.194103i
$706$	−2.89650	−	5.01689i	−0.109011	−	0.188813i
$707$	−1.88174	−	2.26028i	−0.0707700	−	0.0850066i
$708$	0.275585	−	1.02850i	0.0103571	−	0.0386533i
$709$	−1.09881	−	4.10081i	−0.0412666	−	0.154009i	0.942218	−	0.335000i	$-0.108736\pi$
$709$	−1.09881	−	4.10081i	−0.0412666	−	0.154009i	−0.983485	+	0.180991i	$0.942070\pi$
$710$	1.09266	−	0.292776i	0.0410067	−	0.0109877i
$711$	−14.0827			−0.528142
$712$	13.6795			0.512659
$713$	8.76441	−	2.34842i	0.328230	−	0.0879488i
$714$	3.65830	+	0.334336i	0.136908	+	0.0125122i
$715$	−1.46179	+	6.98503i	−0.0546680	+	0.261225i
$716$	20.5385	+	35.5738i	0.767562	+	1.32946i
$717$	29.7945	+	7.98342i	1.11270	+	0.298146i
$718$	−4.44387	−	7.69701i	−0.165844	−	0.287250i
$719$	5.89574	−	10.2117i	0.219874	−	0.380833i	−0.734895	−	0.678180i	$-0.762769\pi$
$719$	5.89574	−	10.2117i	0.219874	−	0.380833i	0.954769	+	0.297348i	$0.0961021\pi$
$720$	2.39063	−	2.39063i	0.0890935	−	0.0890935i
$721$	−0.725153	−	0.871030i	−0.0270061	−	0.0324388i
$722$	2.64356	+	0.708339i	0.0983830	+	0.0263616i
$723$	18.9374	+	5.07425i	0.704289	+	0.188714i
$724$		−	37.8661i		−	1.40728i
$725$	−10.3876	+	5.99731i	−0.385787	+	0.222734i
$726$	0.794166	+	0.794166i	0.0294743	+	0.0294743i
$727$	−9.73102			−0.360904			−0.180452	−	0.983584i	$-0.557756\pi$
$727$	−9.73102			−0.360904			−0.180452	+	0.983584i	$0.557756\pi$
$728$	−10.2945	−	3.15556i	−0.381539	−	0.116953i
$729$	−16.4579			−0.609550
$730$	−1.30292	−	1.30292i	−0.0482232	−	0.0482232i
$731$	−20.7593	+	11.9854i	−0.767810	+	0.443295i
$732$			17.4431i			0.644716i
$733$	−14.6487	−	3.92510i	−0.541061	−	0.144977i	−0.0220699	−	0.999756i	$-0.507026\pi$
$733$	−14.6487	−	3.92510i	−0.541061	−	0.144977i	−0.518991	+	0.854779i	$0.673692\pi$
$734$	1.47691	+	0.395738i	0.0545139	+	0.0146069i
$735$	3.17702	−	2.18811i	0.117186	−	0.0807096i
$736$	−20.0581	+	20.0581i	−0.739350	+	0.739350i
$737$	−13.5524	+	23.4734i	−0.499207	+	0.864653i
$738$	−1.85803	−	3.21820i	−0.0683949	−	0.118463i
$739$	−2.26822	−	0.607767i	−0.0834378	−	0.0223571i	0.216859	−	0.976203i	$-0.430419\pi$
$739$	−2.26822	−	0.607767i	−0.0834378	−	0.0223571i	−0.300296	+	0.953846i	$0.597086\pi$
$740$	0.0907525	+	0.157188i	0.00333613	+	0.00577834i
$741$	−5.34541	+	10.5729i	−0.196368	+	0.388407i
$742$	−0.709566	+	0.327538i	−0.0260490	+	0.0120243i
$743$	27.0211	−	7.24029i	0.991309	−	0.265620i	0.273509	−	0.961870i	$-0.411816\pi$
$743$	27.0211	−	7.24029i	0.991309	−	0.265620i	0.717800	+	0.696249i	$0.245149\pi$
$744$	1.25788			0.0461161
$745$	7.42695			0.272102
$746$	6.83779	−	1.83218i	0.250349	−	0.0670809i
$747$	4.38530	+	16.3662i	0.160450	+	0.598807i
$748$	−8.58605	+	32.0436i	−0.313937	+	1.17163i
$749$	−13.0792	+	2.25404i	−0.477903	+	0.0823607i
$750$	−0.772789	−	1.33851i	−0.0282183	−	0.0488755i
$751$		−	5.21551i		−	0.190317i	−0.995462	−	0.0951584i	$-0.969664\pi$
$751$		−	5.21551i		−	0.190317i	0.995462	−	0.0951584i	$-0.0303358\pi$
$752$	−8.49266	+	31.6950i	−0.309695	+	1.15580i
$753$	6.33944	+	3.66008i	0.231022	+	0.133381i
$754$	1.44107	+	2.20387i	0.0524808	+	0.0802601i
$755$			2.56629i			0.0933969i
$756$	−25.9127	+	4.46574i	−0.942436	+	0.162417i
$757$	10.3674	−	17.9569i	0.376811	−	0.652656i	−0.613785	−	0.789473i	$-0.710354\pi$
$757$	10.3674	−	17.9569i	0.376811	−	0.652656i	0.990596	+	0.136817i	$0.0436872\pi$
$758$	5.42669	+	3.13310i	0.197106	+	0.113799i
$759$	−9.16639	−	34.2094i	−0.332719	−	1.24172i
$760$	1.27198	+	1.27198i	0.0461394	+	0.0461394i
$761$	−37.9896	+	10.1793i	−1.37712	+	0.368999i	−0.870075	−	0.492919i	$-0.835930\pi$
$761$	−37.9896	+	10.1793i	−1.37712	+	0.368999i	−0.507048	+	0.861918i	$0.669263\pi$
$762$	−0.754057	−	0.754057i	−0.0273166	−	0.0273166i
$763$	2.03990	−	0.941624i	0.0738494	−	0.0340891i
$764$	−7.13656	−	4.12029i	−0.258192	−	0.149067i
$765$	3.07991	−	3.07991i	0.111354	−	0.111354i
$766$	−1.69184	+	2.93034i	−0.0611285	+	0.105878i
$767$	−0.847704	+	1.67671i	−0.0306088	+	0.0605426i
$768$	9.01232	−	5.20326i	0.325204	−	0.187757i
$769$	−2.96518	−	11.0662i	−0.106927	−	0.399057i	0.891630	−	0.452765i	$-0.149563\pi$
$769$	−2.96518	−	11.0662i	−0.106927	−	0.399057i	−0.998557	+	0.0537084i	$0.982896\pi$
$770$	−0.632431	−	1.37008i	−0.0227912	−	0.0493741i
$771$	7.68935	−	4.43945i	0.276925	−	0.159883i
$772$	6.72462	−	25.0966i	0.242024	−	0.903247i
$773$	−33.1308	+	33.1308i	−1.19163	+	1.19163i	−0.215021	+	0.976609i	$0.568982\pi$
$773$	−33.1308	+	33.1308i	−1.19163	+	1.19163i	−0.976609	+	0.215021i	$0.931018\pi$
$774$	−2.01385	+	2.01385i	−0.0723864	+	0.0723864i
$775$	1.28065	−	4.77944i	0.0460022	−	0.171682i
$776$	−13.3537	+	7.70974i	−0.479369	+	0.276764i
$777$	0.0470070	−	0.514350i	0.00168637	−	0.0184522i
$778$	−2.61122	−	9.74522i	−0.0936169	−	0.349383i
$779$	−18.4715	+	10.6645i	−0.661810	+	0.382096i
$780$	3.18794	−	2.08454i	0.114146	−	0.0746385i
$781$	14.5344	−	25.1744i	0.520083	−	0.900811i
$782$	−7.99365	+	7.99365i	−0.285852	+	0.285852i
$783$	11.3792	+	6.56979i	0.406660	+	0.234785i
$784$	−23.1439	+	8.22131i	−0.826567	+	0.293618i
$785$	1.27653	+	1.27653i	0.0455615	+	0.0455615i
$786$	5.14429	−	1.37841i	0.183491	−	0.0491662i
$787$	−5.73431	−	5.73431i	−0.204406	−	0.204406i	0.597479	−	0.801885i	$-0.296169\pi$
$787$	−5.73431	−	5.73431i	−0.204406	−	0.204406i	−0.801885	+	0.597479i	$0.796169\pi$
$788$	−1.90001	−	7.09094i	−0.0676852	−	0.252604i
$789$	2.49588	+	1.44100i	0.0888558	+	0.0513009i
$790$	−0.562843	+	0.974873i	−0.0200251	+	0.0346844i
$791$	−8.29094	−	9.95880i	−0.294792	−	0.354094i
$792$			8.05366i			0.286174i
$793$	6.30463	−	30.1260i	0.223884	−	1.06981i
$794$	1.99825	+	1.15369i	0.0709152	+	0.0409429i
$795$	0.146208	−	0.545655i	0.00518546	−	0.0193524i
$796$			20.1438i			0.713978i
$797$	5.11594	+	8.86106i	0.181216	+	0.313875i	0.942295	−	0.334784i	$-0.108663\pi$
$797$	5.11594	+	8.86106i	0.181216	+	0.313875i	−0.761079	+	0.648659i	$0.775330\pi$
$798$	−0.425461	−	2.46876i	−0.0150612	−	0.0873933i
$799$	−10.9413	+	40.8335i	−0.387076	+	1.44459i
$800$	4.00363	+	14.9418i	0.141550	+	0.528271i
$801$	−21.8183	+	5.84621i	−0.770913	+	0.206566i
$802$	7.87165			0.277958
$803$	−47.3501			−1.67095
$804$	13.9740	−	3.74431i	0.492824	−	0.132052i
$805$	−1.08042	+	11.8219i	−0.0380798	+	0.416669i
$806$	−1.06322	−	0.222505i	−0.0374502	−	0.00783740i
$807$	−12.4519	−	21.5673i	−0.438328	−	0.759206i
$808$	1.21194	+	0.324740i	0.0426361	+	0.0114243i
$809$	−5.83752	−	10.1109i	−0.205236	−	0.355480i	0.744972	−	0.667096i	$-0.232463\pi$
$809$	−5.83752	−	10.1109i	−0.205236	−	0.355480i	−0.950208	+	0.311616i	$0.899130\pi$
$810$	0.00484186	−	0.00838635i	0.000170126	−	0.000294666i
$811$	19.1328	−	19.1328i	0.671843	−	0.671843i	−0.286298	−	0.958141i	$-0.592425\pi$
$811$	19.1328	−	19.1328i	0.671843	−	0.671843i	0.958141	+	0.286298i	$0.0924246\pi$
$812$	12.0617	+	4.44306i	0.423283	+	0.155921i
$813$	−13.6860	−	3.66714i	−0.479988	−	0.128612i
$814$	−0.195154	−	0.0522914i	−0.00684015	−	0.00183281i
$815$			1.18696i			0.0415775i
$816$	14.6411	−	8.45306i	0.512542	−	0.295916i
$817$	11.5589	+	11.5589i	0.404395	+	0.404395i
$818$	1.64875			0.0576472
$819$	17.7680	+	0.633455i	0.620865	+	0.0221347i
$820$	6.85735			0.239469
$821$	−19.1916	−	19.1916i	−0.669791	−	0.669791i	0.287876	−	0.957668i	$-0.407051\pi$
$821$	−19.1916	−	19.1916i	−0.669791	−	0.669791i	−0.957668	+	0.287876i	$0.907051\pi$
$822$	−2.51282	+	1.45078i	−0.0876446	+	0.0506016i
$823$		−	27.7780i		−	0.968282i	−0.874990	−	0.484141i	$-0.839132\pi$
$823$		−	27.7780i		−	0.968282i	0.874990	−	0.484141i	$-0.160868\pi$
$824$	0.467039	+	0.125143i	0.0162701	+	0.00435956i
$825$	−18.6552	−	4.99864i	−0.649491	−	0.174030i
$826$	−0.0674720	−	0.391510i	−0.00234765	−	0.0136224i
$827$	30.1851	−	30.1851i	1.04964	−	1.04964i	0.0509356	−	0.998702i	$-0.483780\pi$
$827$	30.1851	−	30.1851i	1.04964	−	1.04964i	0.998702	−	0.0509356i	$-0.0162203\pi$
$828$	15.5036	−	26.8531i	0.538789	−	0.933210i
$829$	13.9806	+	24.2150i	0.485565	+	0.841023i	0.999862	−	0.0165887i	$-0.00528058\pi$
$829$	13.9806	+	24.2150i	0.485565	+	0.841023i	−0.514297	+	0.857612i	$0.671947\pi$
$830$	1.30821	+	0.350535i	0.0454088	+	0.0121672i
$831$	−2.58015	−	4.46896i	−0.0895046	−	0.155026i
$832$	−20.8120	+	6.83459i	−0.721527	+	0.236947i
$833$	−29.8169	+	10.5917i	−1.03309	+	0.366982i
$834$	4.50596	−	1.20737i	0.156029	−	0.0418078i
$835$	−10.8411			−0.375171
$836$	22.6228			0.782427
$837$	−5.23567	+	1.40289i	−0.180971	+	0.0484911i
$838$	−1.14729	−	4.28175i	−0.0396325	−	0.147911i
$839$	−8.74827	+	32.6490i	−0.302024	+	1.12717i	0.633453	+	0.773781i	$0.281637\pi$
$839$	−8.74827	+	32.6490i	−0.302024	+	1.12717i	−0.935477	+	0.353387i	$0.885030\pi$
$840$	−0.568852	+	1.54428i	−0.0196273	+	0.0532827i
$841$	11.2884	+	19.5521i	0.389255	+	0.674209i
$842$			1.94084i			0.0668857i
$843$	3.35864	−	12.5346i	0.115678	−	0.431715i
$844$	12.8734	+	7.43249i	0.443122	+	0.255837i
$845$	−6.25933	+	2.44797i	−0.215328	+	0.0842127i
$846$			5.02266i			0.172683i
$847$	−9.07775	−	3.34389i	−0.311915	−	0.114897i
$848$	−1.79831	+	3.11477i	−0.0617544	+	0.106962i
$849$	−0.974579	−	0.562673i	−0.0334475	−	0.0193109i
$850$	1.59555	+	5.95468i	0.0547269	+	0.204244i
$851$	1.12389	+	1.12389i	0.0385266	+	0.0385266i
$852$	−14.9866	+	4.01565i	−0.513433	+	0.137574i
$853$	18.1560	+	18.1560i	0.621649	+	0.621649i	0.945953	−	0.324304i	$-0.105130\pi$
$853$	18.1560	+	18.1560i	0.621649	+	0.621649i	−0.324304	+	0.945953i	$0.605130\pi$
$854$	2.72764	+	5.90906i	0.0933379	+	0.202204i
$855$	−2.57237	−	1.48516i	−0.0879733	−	0.0507914i
$856$	4.00366	−	4.00366i	0.136842	−	0.136842i
$857$	−0.942085	+	1.63174i	−0.0321810	+	0.0557392i	−0.881667	−	0.471871i	$-0.843579\pi$
$857$	−0.942085	+	1.63174i	−0.0321810	+	0.0557392i	0.849486	+	0.527611i	$0.176912\pi$
$858$	−0.868486	+	4.14997i	−0.0296496	+	0.141678i
$859$	−1.31631	+	0.759972i	−0.0449119	+	0.0259299i	−0.522288	−	0.852769i	$-0.674921\pi$
$859$	−1.31631	+	0.759972i	−0.0449119	+	0.0259299i	0.477376	+	0.878699i	$0.341588\pi$
$860$	−1.36023	−	5.07646i	−0.0463835	−	0.173106i
$861$	−15.9410	−	11.2542i	−0.543268	−	0.383543i
$862$	4.21178	−	2.43167i	0.143454	−	0.0828231i
$863$	2.37770	−	8.87371i	0.0809380	−	0.302065i	−0.913576	−	0.406668i	$-0.866691\pi$
$863$	2.37770	−	8.87371i	0.0809380	−	0.302065i	0.994514	+	0.104603i	$0.0333573\pi$
$864$	11.9822	−	11.9822i	0.407644	−	0.407644i
$865$	−7.34348	+	7.34348i	−0.249686	+	0.249686i
$866$	0.691356	−	2.58017i	0.0234932	−	0.0876779i
$867$	3.16936	−	1.82983i	0.107637	−	0.0621443i
$868$	−4.81439	+	2.22234i	−0.163411	+	0.0754310i
$869$	7.48691	+	27.9415i	0.253976	+	0.947851i
$870$	0.348549	−	0.201235i	0.0118169	−	0.00682251i
$871$	−25.4878	+	1.41607i	−0.863622	+	0.0479817i
$872$	−0.479247	+	0.830080i	−0.0162293	+	0.0281100i
$873$	18.0038	−	18.0038i	0.609336	−	0.609336i
$874$	6.67638	+	3.85461i	0.225832	+	0.130384i
$875$	10.8757	+	7.67814i	0.367664	+	0.259568i
$876$	17.8705	+	17.8705i	0.603789	+	0.603789i
$877$	2.74004	−	0.734191i	0.0925245	−	0.0247919i	−0.212260	−	0.977213i	$-0.568082\pi$
$877$	2.74004	−	0.734191i	0.0925245	−	0.0247919i	0.304784	+	0.952421i	$0.401416\pi$
$878$	−3.54814	−	3.54814i	−0.119744	−	0.119744i
$879$	5.66265	+	21.1333i	0.190997	+	0.712809i
$880$	−6.01421	−	3.47230i	−0.202739	−	0.117051i
$881$	−16.7491	+	29.0103i	−0.564292	+	0.977383i	0.432823	+	0.901479i	$0.357517\pi$
$881$	−16.7491	+	29.0103i	−0.564292	+	0.977383i	−0.997115	+	0.0759037i	$0.975816\pi$
$882$	−3.09619	+	2.13244i	−0.104254	+	0.0718029i
$883$		−	36.3459i		−	1.22314i	−0.791192	−	0.611568i	$-0.790539\pi$
$883$		−	36.3459i		−	1.22314i	0.791192	−	0.611568i	$-0.209461\pi$
$884$	−29.6835	+	9.74796i	−0.998364	+	0.327859i
$885$	0.248695	+	0.143584i	0.00835978	+	0.00482652i
$886$	0.760387	−	2.83780i	0.0255457	−	0.0953378i
$887$		−	24.5633i		−	0.824754i	−0.911013	−	0.412377i	$-0.864699\pi$
$887$		−	24.5633i		−	0.824754i	0.911013	−	0.412377i	$-0.135301\pi$
$888$	0.110172	+	0.190823i	0.00369713	+	0.00640361i
$889$	8.61929	+	3.17501i	0.289082	+	0.106486i
$890$	−0.467311	+	1.74403i	−0.0156643	+	0.0584599i
$891$	−0.0644062	−	0.240367i	−0.00215769	−	0.00805260i
$892$	−43.4596	+	11.6450i	−1.45513	+	0.389902i
$893$	28.8286			0.964712
$894$	4.41253			0.147577
$895$	−10.7009	+	2.86730i	−0.357691	+	0.0958431i
$896$	12.6464	−	17.9129i	0.422486	−	0.598428i
$897$	22.2408	−	24.8575i	0.742598	−	0.829968i
$898$	−2.62488	−	4.54642i	−0.0875934	−	0.151716i
$899$	2.55943	+	0.685797i	0.0853617	+	0.0228726i
$900$	−8.45450	−	14.6436i	−0.281817	−	0.488121i
$901$	−2.31682	+	4.01284i	−0.0771843	+	0.133687i
$902$	−5.39743	+	5.39743i	−0.179715	+	0.179715i
$903$	−5.16936	+	14.0334i	−0.172026	+	0.467003i
$904$	5.33983	+	1.43080i	0.177600	+	0.0475878i
$905$	9.86440	+	2.64316i	0.327904	+	0.0878616i
$906$			1.52469i			0.0506546i
$907$	−29.6238	+	17.1033i	−0.983641	+	0.567905i	−0.903367	−	0.428868i	$-0.858913\pi$
$907$	−29.6238	+	17.1033i	−0.983641	+	0.567905i	−0.0802733	+	0.996773i	$0.525579\pi$
$908$	8.35303	+	8.35303i	0.277205	+	0.277205i
$909$	−2.07180			−0.0687173
$910$	0.753985	−	1.20467i	0.0249944	−	0.0399345i
$911$	49.8898			1.65292			0.826462	−	0.562993i	$-0.190350\pi$
$911$	49.8898			1.65292			0.826462	+	0.562993i	$0.190350\pi$
$912$	−8.15227	−	8.15227i	−0.269949	−	0.269949i
$913$	30.1408	−	17.4018i	0.997514	−	0.575915i
$914$			9.72114i			0.321547i
$915$	−4.54406	−	1.21758i	−0.150222	−	0.0402519i
$916$	21.0875	+	5.65037i	0.696750	+	0.186694i
$917$	−35.2552	+	29.3508i	−1.16423	+	0.969248i
$918$	4.77523	−	4.77523i	0.157606	−	0.157606i
$919$	1.35826	−	2.35258i	0.0448049	−	0.0776044i	−0.842753	−	0.538300i	$-0.819067\pi$
$919$	1.35826	−	2.35258i	0.0448049	−	0.0776044i	0.887558	+	0.460696i	$0.152400\pi$
$920$	−2.53222	−	4.38593i	−0.0834848	−	0.144600i
$921$	10.5411	+	2.82448i	0.347341	+	0.0930696i
$922$	−1.63532	−	2.83245i	−0.0538563	−	0.0932818i
$923$	27.3348	−	1.51869i	0.899737	−	0.0499882i
$924$	8.67427	+	18.7916i	0.285363	+	0.618199i
$925$	0.837217	−	0.224332i	0.0275275	−	0.00737598i
$926$	−1.65131			−0.0542654
$927$	−0.798397			−0.0262228
$928$	−8.00144	+	2.14398i	−0.262660	+	0.0703796i
$929$	−6.50346	−	24.2713i	−0.213372	−	0.796314i	−0.986733	−	0.162349i	$-0.948093\pi$
$929$	−6.50346	−	24.2713i	−0.213372	−	0.796314i	0.773362	−	0.633965i	$-0.218574\pi$
$930$	−0.0429711	+	0.160370i	−0.00140908	+	0.00525875i
$931$	12.2396	+	17.7712i	0.401135	+	0.582428i
$932$	−14.2855	−	24.7433i	−0.467939	−	0.810494i
$933$		−	10.3653i		−	0.339345i
$934$	2.71262	−	10.1236i	0.0887597	−	0.331256i
$935$	−7.74826	−	4.47346i	−0.253395	−	0.146298i
$936$	−6.34823	+	4.15100i	−0.207499	+	0.135680i
$937$			3.14878i			0.102866i	0.998676	+	0.0514330i	$0.0163789\pi$
$937$			3.14878i			0.102866i	−0.998676	+	0.0514330i	$0.983621\pi$
$938$	4.14834	−	3.45359i	0.135448	−	0.112764i
$939$	8.89099	−	15.3996i	0.290146	−	0.502548i
$940$	−8.02674	−	4.63424i	−0.261803	−	0.151152i
$941$	2.50587	+	9.35203i	0.0816890	+	0.304867i	0.994667	−	0.103142i	$-0.0328897\pi$
$941$	2.50587	+	9.35203i	0.0816890	+	0.304867i	−0.912978	+	0.408010i	$0.866223\pi$
$942$	0.758419	+	0.758419i	0.0247106	+	0.0247106i
$943$	58.0032	−	15.5419i	1.88884	−	0.506114i
$944$	−1.29283	−	1.29283i	−0.0420781	−	0.0420781i
$945$	0.645420	−	7.06218i	0.0209955	−	0.229733i
$946$	5.06633	+	2.92504i	0.164720	+	0.0951014i
$947$	−31.0712	+	31.0712i	−1.00968	+	1.00968i	−0.00972566	+	0.999953i	$0.503096\pi$
$947$	−31.0712	+	31.0712i	−1.00968	+	1.00968i	−0.999953	+	0.00972566i	$0.996904\pi$
$948$	7.71982	−	13.3711i	0.250728	−	0.434274i
$949$	−24.4051	−	37.3234i	−0.792224	−	1.21157i
$950$	3.64078	−	2.10201i	0.118123	−	0.0681981i
$951$	−2.94015	−	10.9728i	−0.0953408	−	0.355817i
$952$	7.78548	−	11.0277i	0.252329	−	0.357410i
$953$	−17.0074	+	9.81922i	−0.550923	+	0.318076i	−0.749494	−	0.662011i	$-0.769703\pi$
$953$	−17.0074	+	9.81922i	−0.550923	+	0.318076i	0.198571	+	0.980086i	$0.436370\pi$
$954$	−0.142488	+	0.531772i	−0.00461322	+	0.0172168i
$955$	1.57152	−	1.57152i	0.0508532	−	0.0508532i
$956$	39.2247	−	39.2247i	1.26862	−	1.26862i
$957$	2.67682	−	9.99001i	0.0865292	−	0.322931i
$958$	6.06595	−	3.50218i	0.195982	−	0.113150i
$959$	14.4143	−	20.4171i	0.465464	−	0.659303i
$960$	0.866562	+	3.23405i	0.0279682	+	0.104379i
$961$	25.9002	−	14.9535i	0.835489	−	0.482370i
$962$	−0.0593678	−	0.180781i	−0.00191409	−	0.00582860i
$963$	−4.67467	+	8.09677i	−0.150639	+	0.260915i
$964$	24.9312	−	24.9312i	0.802980	−	0.802980i
$965$	6.06846	+	3.50363i	0.195351	+	0.112786i
$966$	−0.641904	+	7.02370i	−0.0206529	+	0.225984i
$967$	−22.4539	−	22.4539i	−0.722068	−	0.722068i	0.246958	−	0.969026i	$-0.420569\pi$
$967$	−22.4539	−	22.4539i	−0.722068	−	0.722068i	−0.969026	+	0.246958i	$0.920569\pi$
$968$	3.98646	−	1.06817i	0.128130	−	0.0343323i
$969$	−10.5028	−	10.5028i	−0.337398	−	0.337398i
$970$	−0.526753	−	1.96587i	−0.0169130	−	0.0631202i
$971$	33.8453	+	19.5406i	1.08615	+	0.627087i	0.932548	−	0.361046i	$-0.117580\pi$
$971$	33.8453	+	19.5406i	1.08615	+	0.627087i	0.153599	+	0.988133i	$0.450914\pi$
$972$	−14.9741	+	25.9359i	−0.480295	+	0.831895i
$973$	−30.8805	+	25.7088i	−0.989985	+	0.824186i
$974$			7.67675i			0.245979i
$975$	−5.67509	−	17.2812i	−0.181748	−	0.553441i
$976$	25.9389	+	14.9758i	0.830285	+	0.479365i
$977$	6.98547	−	26.0701i	0.223485	−	0.834057i	−0.759521	−	0.650483i	$-0.774567\pi$
$977$	6.98547	−	26.0701i	0.223485	−	0.834057i	0.983006	−	0.183574i	$-0.0587668\pi$
$978$			0.705202i			0.0225499i
$979$	23.1989	+	40.1817i	0.741441	+	1.28421i
$980$	−0.551112	−	6.91556i	−0.0176046	−	0.220909i
$981$	0.409633	−	1.52877i	0.0130786	−	0.0488099i
$982$	−1.31349	−	4.90202i	−0.0419152	−	0.156430i
$983$	12.0465	−	3.22784i	0.384223	−	0.102952i	−0.0615370	−	0.998105i	$-0.519600\pi$
$983$	12.0465	−	3.22784i	0.384223	−	0.102952i	0.445760	+	0.895153i	$0.352934\pi$
$984$	8.32470			0.265382
$985$	1.97987			0.0630839
$986$	−3.18878	+	0.854431i	−0.101551	+	0.0272106i
$987$	11.0537	+	23.9464i	0.351844	+	0.762223i
$988$	11.6602	+	17.8323i	0.370961	+	0.567320i
$989$	−23.0112	−	39.8565i	−0.731713	−	1.26736i
$990$	−1.02678	−	0.275125i	−0.0326332	−	0.00874405i
$991$	11.0564	+	19.1502i	0.351218	+	0.608327i	0.986463	−	0.163983i	$-0.0524343\pi$
$991$	11.0564	+	19.1502i	0.351218	+	0.608327i	−0.635245	+	0.772311i	$0.719101\pi$
$992$	1.70860	−	2.95938i	0.0542481	−	0.0939606i
$993$	−25.8435	+	25.8435i	−0.820119	+	0.820119i
$994$	−4.44895	+	3.70386i	−0.141112	+	0.117479i
$995$	−5.24761	−	1.40609i	−0.166361	−	0.0445762i
$996$	−17.9431	−	4.80785i	−0.568550	−	0.152343i
$997$			34.5702i			1.09485i	0.836855	+	0.547424i	$0.184392\pi$
$997$			34.5702i			1.09485i	−0.836855	+	0.547424i	$0.815608\pi$
$998$	−3.79260	+	2.18966i	−0.120053	+	0.0693123i
$999$	−0.671390	−	0.671390i	−0.0212418	−	0.0212418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.ba.a.59.5	yes	28
3.2	odd	2		819.2.et.b.514.3		28
7.2	even	3		637.2.x.a.215.5		28
7.3	odd	6		637.2.bd.a.293.3		28
7.4	even	3		637.2.bd.b.293.3		28
7.5	odd	6		91.2.w.a.33.5	✓	28
7.6	odd	2		637.2.bb.a.423.5		28
13.2	odd	12		91.2.w.a.80.5	yes	28
21.5	even	6		819.2.gh.b.397.3		28
39.2	even	12		819.2.gh.b.262.3		28
91.2	odd	12		637.2.bb.a.509.5		28
91.41	even	12		637.2.x.a.80.5		28
91.54	even	12	inner	91.2.ba.a.54.5	yes	28
91.67	odd	12		637.2.bd.a.587.3		28
91.80	even	12		637.2.bd.b.587.3		28
273.236	odd	12		819.2.et.b.145.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.5	✓	28	7.5	odd	6
91.2.w.a.80.5	yes	28	13.2	odd	12
91.2.ba.a.54.5	yes	28	91.54	even	12	inner
91.2.ba.a.59.5	yes	28	1.1	even	1	trivial
637.2.x.a.80.5		28	91.41	even	12
637.2.x.a.215.5		28	7.2	even	3
637.2.bb.a.423.5		28	7.6	odd	2
637.2.bb.a.509.5		28	91.2	odd	12
637.2.bd.a.293.3		28	7.3	odd	6
637.2.bd.a.587.3		28	91.67	odd	12
637.2.bd.b.293.3		28	7.4	even	3
637.2.bd.b.587.3		28	91.80	even	12
819.2.et.b.145.3		28	273.236	odd	12
819.2.et.b.514.3		28	3.2	odd	2
819.2.gh.b.262.3		28	39.2	even	12
819.2.gh.b.397.3		28	21.5	even	6

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.ba (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203761 + 0.203761i) q^{2} +(0.923129 - 0.532969i) q^{3} -1.91696i q^{4} +(0.499383 + 0.133809i) q^{5} +(0.296695 + 0.0794993i) q^{6} +(-2.60732 + 0.449339i) q^{7} +(0.798123 - 0.798123i) q^{8} +(-0.931889 + 1.61408i) q^{9} +O(q^{10})\)	\(q+(0.203761 + 0.203761i) q^{2} +(0.923129 - 0.532969i) q^{3} -1.91696i q^{4} +(0.499383 + 0.133809i) q^{5} +(0.296695 + 0.0794993i) q^{6} +(-2.60732 + 0.449339i) q^{7} +(0.798123 - 0.798123i) q^{8} +(-0.931889 + 1.61408i) q^{9} +(0.0744896 + 0.129020i) q^{10} +(3.69793 + 0.990856i) q^{11} +(-1.02168 - 1.76960i) q^{12} +(1.12494 + 3.42557i) q^{13} +(-0.622826 - 0.439711i) q^{14} +(0.532311 - 0.142632i) q^{15} -3.50867 q^{16} -4.52032 q^{17} +(-0.518768 + 0.139003i) q^{18} +(0.797839 + 2.97757i) q^{19} +(0.256508 - 0.957300i) q^{20} +(-2.16740 + 1.80442i) q^{21} +(0.551594 + 0.955389i) q^{22} -8.67873i q^{23} +(0.311396 - 1.16214i) q^{24} +(-4.09865 - 2.36636i) q^{25} +(-0.468776 + 0.927215i) q^{26} +5.18448i q^{27} +(0.861367 + 4.99813i) q^{28} +(1.26720 - 2.19486i) q^{29} +(0.137527 + 0.0794012i) q^{30} +(0.270595 + 1.00987i) q^{31} +(-2.31118 - 2.31118i) q^{32} +(3.94176 - 1.05619i) q^{33} +(-0.921063 - 0.921063i) q^{34} +(-1.36218 - 0.124491i) q^{35} +(3.09413 + 1.78640i) q^{36} +(-0.129500 + 0.129500i) q^{37} +(-0.444144 + 0.769281i) q^{38} +(2.86419 + 2.56268i) q^{39} +(0.505366 - 0.291773i) q^{40} +(1.79081 + 6.68338i) q^{41} +(-0.809301 - 0.0739629i) q^{42} +(4.59244 - 2.65145i) q^{43} +(1.89943 - 7.08879i) q^{44} +(-0.681349 + 0.681349i) q^{45} +(1.76838 - 1.76838i) q^{46} +(2.42047 - 9.03333i) q^{47} +(-3.23896 + 1.87001i) q^{48} +(6.59619 - 2.34314i) q^{49} +(-0.352973 - 1.31731i) q^{50} +(-4.17284 + 2.40919i) q^{51} +(6.56668 - 2.15648i) q^{52} +(0.512534 - 0.887735i) q^{53} +(-1.05639 + 1.05639i) q^{54} +(1.71410 + 0.989634i) q^{55} +(-1.72233 + 2.43959i) q^{56} +(2.32346 + 2.32346i) q^{57} +(0.705432 - 0.189020i) q^{58} +(0.368467 + 0.368467i) q^{59} +(-0.273421 - 1.02042i) q^{60} +(-7.39280 - 4.26823i) q^{61} +(-0.150636 + 0.260909i) q^{62} +(1.70446 - 4.62715i) q^{63} +6.07549i q^{64} +(0.103406 + 1.86120i) q^{65} +(1.01838 + 0.587965i) q^{66} +(-1.83243 + 6.83871i) q^{67} +8.66528i q^{68} +(-4.62549 - 8.01158i) q^{69} +(-0.252192 - 0.302924i) q^{70} +(1.96522 - 7.33429i) q^{71} +(0.544472 + 2.03200i) q^{72} +(-11.9468 + 3.20113i) q^{73} -0.0527740 q^{74} -5.04477 q^{75} +(5.70790 - 1.52943i) q^{76} +(-10.0869 - 0.921852i) q^{77} +(0.0614358 + 1.10578i) q^{78} +(3.77800 + 6.54369i) q^{79} +(-1.75217 - 0.469493i) q^{80} +(-0.0325003 - 0.0562921i) q^{81} +(-0.996914 + 1.72671i) q^{82} +(6.42827 - 6.42827i) q^{83} +(3.45900 + 4.15483i) q^{84} +(-2.25737 - 0.604861i) q^{85} +(1.47602 + 0.395498i) q^{86} -2.70152i q^{87} +(3.74222 - 2.16057i) q^{88} +(8.56976 + 8.56976i) q^{89} -0.277664 q^{90} +(-4.47233 - 8.42605i) q^{91} -16.6368 q^{92} +(0.788024 + 0.788024i) q^{93} +(2.33384 - 1.34744i) q^{94} +1.59371i q^{95} +(-3.36530 - 0.901729i) q^{96} +(-13.1956 - 3.53575i) q^{97} +(1.82148 + 0.866604i) q^{98} +(-5.04538 + 5.04538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 12 q^{6} - 6 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 6 * q^3 - 6 * q^5 - 12 * q^6 - 6 * q^7 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} - 6 q^{3} - 6 q^{5} - 12 q^{6} - 6 q^{7} - 4 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{11} - 8 q^{12} - 20 q^{14} + 10 q^{15} + 4 q^{16} - 12 q^{17} + 2 q^{18} + 14 q^{19} + 36 q^{20} - 6 q^{21} - 8 q^{22} - 18 q^{24} + 24 q^{26} + 2 q^{28} - 8 q^{29} - 30 q^{30} - 4 q^{31} + 10 q^{32} - 12 q^{33} - 12 q^{34} - 20 q^{35} + 54 q^{36} - 10 q^{37} - 20 q^{39} + 48 q^{40} - 18 q^{41} - 10 q^{42} + 48 q^{43} - 6 q^{44} - 6 q^{45} + 24 q^{46} - 6 q^{47} - 12 q^{48} - 50 q^{49} + 10 q^{50} - 12 q^{51} - 26 q^{52} + 12 q^{53} - 30 q^{54} + 6 q^{55} + 54 q^{56} + 12 q^{57} - 46 q^{58} + 42 q^{59} + 10 q^{60} + 30 q^{61} + 36 q^{62} + 54 q^{63} + 28 q^{65} + 66 q^{66} - 10 q^{67} - 42 q^{69} - 88 q^{70} - 42 q^{71} + 46 q^{72} + 40 q^{73} + 12 q^{74} - 40 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} + 30 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} + 104 q^{84} - 54 q^{85} - 18 q^{86} - 6 q^{88} + 72 q^{90} + 26 q^{91} - 156 q^{92} + 20 q^{93} - 18 q^{94} - 66 q^{96} - 62 q^{97} - 56 q^{98} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^3 - 6 * q^5 - 12 * q^6 - 6 * q^7 - 4 * q^8 + 6 * q^9 - 6 * q^10 + 2 * q^11 - 8 * q^12 - 20 * q^14 + 10 * q^15 + 4 * q^16 - 12 * q^17 + 2 * q^18 + 14 * q^19 + 36 * q^20 - 6 * q^21 - 8 * q^22 - 18 * q^24 + 24 * q^26 + 2 * q^28 - 8 * q^29 - 30 * q^30 - 4 * q^31 + 10 * q^32 - 12 * q^33 - 12 * q^34 - 20 * q^35 + 54 * q^36 - 10 * q^37 - 20 * q^39 + 48 * q^40 - 18 * q^41 - 10 * q^42 + 48 * q^43 - 6 * q^44 - 6 * q^45 + 24 * q^46 - 6 * q^47 - 12 * q^48 - 50 * q^49 + 10 * q^50 - 12 * q^51 - 26 * q^52 + 12 * q^53 - 30 * q^54 + 6 * q^55 + 54 * q^56 + 12 * q^57 - 46 * q^58 + 42 * q^59 + 10 * q^60 + 30 * q^61 + 36 * q^62 + 54 * q^63 + 28 * q^65 + 66 * q^66 - 10 * q^67 - 42 * q^69 - 88 * q^70 - 42 * q^71 + 46 * q^72 + 40 * q^73 + 12 * q^74 - 40 * q^75 - 52 * q^76 - 62 * q^78 + 4 * q^79 + 30 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 + 104 * q^84 - 54 * q^85 - 18 * q^86 - 6 * q^88 + 72 * q^90 + 26 * q^91 - 156 * q^92 + 20 * q^93 - 18 * q^94 - 66 * q^96 - 62 * q^97 - 56 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more