LMFDB - Embedded newform 370.2.o.c.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			181.1
Character	$\chi$	$=$	370.181
Dual form			370.2.o.c.231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.420953 - 2.38734i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.766044 - 0.642788i) q^{5} +2.42417 q^{6} +(0.480222 - 0.402954i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.70313 + 0.983860i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.420953 - 2.38734i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.766044 - 0.642788i) q^{5} +2.42417 q^{6} +(0.480222 - 0.402954i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.70313 + 0.983860i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.10221 - 1.90908i) q^{11} +(-0.420953 + 2.38734i) q^{12} +(-2.96072 - 1.07761i) q^{13} +(0.313443 + 0.542899i) q^{14} +(-1.85702 - 1.55823i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.15412 + 0.784035i) q^{17} +(-0.499519 - 2.83291i) q^{18} +(-0.443644 - 2.51603i) q^{19} +(-0.939693 + 0.342020i) q^{20} +(-1.16414 - 0.976831i) q^{21} +(1.68868 + 1.41697i) q^{22} +(-2.44767 - 4.23950i) q^{23} +(-2.27798 - 0.829116i) q^{24} +(0.173648 - 0.984808i) q^{25} +(1.57536 - 2.72861i) q^{26} +(-0.149555 - 0.259037i) q^{27} +(-0.589080 + 0.214408i) q^{28} +(-0.0272111 + 0.0471310i) q^{29} +(1.85702 - 1.55823i) q^{30} +5.29459 q^{31} +(-0.766044 + 0.642788i) q^{32} +(-5.02160 - 1.82771i) q^{33} +(-0.398065 - 2.25754i) q^{34} +(0.108858 - 0.617362i) q^{35} +2.87661 q^{36} +(-1.02258 - 5.99619i) q^{37} +2.55484 q^{38} +(-1.32631 + 7.52187i) q^{39} +(-0.173648 - 0.984808i) q^{40} +(-0.166409 - 0.0605677i) q^{41} +(1.16414 - 0.976831i) q^{42} +2.99960 q^{43} +(-1.68868 + 1.41697i) q^{44} +(-1.43831 + 2.49122i) q^{45} +(4.60012 - 1.67431i) q^{46} +(1.99372 + 3.45323i) q^{47} +(1.21209 - 2.09940i) q^{48} +(-1.14730 + 6.50664i) q^{49} +(0.939693 + 0.342020i) q^{50} +(2.77854 + 4.81258i) q^{51} +(2.41360 + 2.02525i) q^{52} +(2.52707 + 2.12046i) q^{53} +(0.281071 - 0.102302i) q^{54} +(-0.382792 - 2.17092i) q^{55} +(-0.108858 - 0.617362i) q^{56} +(-5.81987 + 2.11826i) q^{57} +(-0.0416898 - 0.0349819i) q^{58} +(8.62512 + 7.23734i) q^{59} +(1.21209 + 2.09940i) q^{60} +(2.66384 + 0.969558i) q^{61} +(-0.919396 + 5.21415i) q^{62} +(-0.901654 + 1.56171i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.96072 + 1.07761i) q^{65} +(2.67194 - 4.62794i) q^{66} +(5.80763 - 4.87318i) q^{67} +2.29236 q^{68} +(-9.09078 + 7.62807i) q^{69} +(0.589080 + 0.214408i) q^{70} +(2.24551 + 12.7349i) q^{71} +(-0.499519 + 2.83291i) q^{72} +0.767684 q^{73} +(6.08267 + 0.0341800i) q^{74} -2.42417 q^{75} +(-0.443644 + 2.51603i) q^{76} +(-0.239967 - 1.36092i) q^{77} +(-7.17729 - 2.61232i) q^{78} +(9.07425 - 7.61420i) q^{79} +1.00000 q^{80} +(-7.16630 + 6.01324i) q^{81} +(0.0885441 - 0.153363i) q^{82} +(0.541536 - 0.197103i) q^{83} +(0.759840 + 1.31608i) q^{84} +(-1.14618 + 1.98525i) q^{85} +(-0.520875 + 2.95403i) q^{86} +(0.123972 + 0.0451223i) q^{87} +(-1.10221 - 1.90908i) q^{88} +(-4.52050 - 3.79315i) q^{89} +(-2.20361 - 1.84905i) q^{90} +(-1.85603 + 0.675540i) q^{91} +(0.850068 + 4.82098i) q^{92} +(-2.22877 - 12.6400i) q^{93} +(-3.74697 + 1.36379i) q^{94} +(-1.95712 - 1.64222i) q^{95} +(1.85702 + 1.55823i) q^{96} +(-3.01586 - 5.22363i) q^{97} +(-6.20856 - 2.25973i) q^{98} +(-1.10115 + 6.24491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9	$ 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31} - 39 q^{33} - 21 q^{34} + 6 q^{35} + 54 q^{36} - 12 q^{37} - 36 q^{38} - 18 q^{39} + 27 q^{41} - 36 q^{42} - 24 q^{43} - 9 q^{44} - 27 q^{45} + 3 q^{46} - 6 q^{47} - 3 q^{48} - 27 q^{49} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 9 q^{54} + 9 q^{55} - 6 q^{56} - 27 q^{57} + 27 q^{58} + 51 q^{59} - 3 q^{60} - 3 q^{62} - 27 q^{63} - 12 q^{64} + 15 q^{66} - 18 q^{69} + 3 q^{70} - 66 q^{71} + 6 q^{72} + 42 q^{73} - 42 q^{74} + 6 q^{75} - 6 q^{76} + 69 q^{77} + 36 q^{78} - 30 q^{79} + 24 q^{80} - 90 q^{81} + 24 q^{82} + 57 q^{83} + 6 q^{84} - 6 q^{86} + 6 q^{87} + 15 q^{88} - 57 q^{89} + 6 q^{90} + 3 q^{91} + 15 q^{92} - 72 q^{93} + 3 q^{94} - 15 q^{95} - 3 q^{97} - 72 q^{98} + 63 q^{99}+O(q^{100}) $ 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−0.420953	−	2.38734i	−0.243037	−	1.37833i	−0.825007	−	0.565123i	$-0.808829\pi$
$3$	−0.420953	−	2.38734i	−0.243037	−	1.37833i	0.581969	−	0.813211i	$-0.302282\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$	2.42417			0.989664
$7$	0.480222	−	0.402954i	0.181507	−	0.152302i	−0.547507	−	0.836801i	$-0.684423\pi$
$7$	0.480222	−	0.402954i	0.181507	−	0.152302i	0.729014	+	0.684498i	$0.239979\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.70313	+	0.983860i	−0.901044	+	0.327953i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.10221	−	1.90908i	0.332328	−	0.575609i	−0.650640	−	0.759386i	$-0.725499\pi$
$11$	1.10221	−	1.90908i	0.332328	−	0.575609i	0.982968	+	0.183778i	$0.0588326\pi$
$12$	−0.420953	+	2.38734i	−0.121519	+	0.689167i
$13$	−2.96072	−	1.07761i	−0.821155	−	0.298876i	−0.102931	−	0.994688i	$-0.532822\pi$
$13$	−2.96072	−	1.07761i	−0.821155	−	0.298876i	−0.718223	+	0.695813i	$0.755044\pi$
$14$	0.313443	+	0.542899i	0.0837711	+	0.145096i
$15$	−1.85702	−	1.55823i	−0.479482	−	0.402333i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.15412	+	0.784035i	−0.522450	+	0.190156i	−0.589764	−	0.807576i	$-0.700779\pi$
$17$	−2.15412	+	0.784035i	−0.522450	+	0.190156i	0.0673140	+	0.997732i	$0.478557\pi$
$18$	−0.499519	−	2.83291i	−0.117738	−	0.667724i
$19$	−0.443644	−	2.51603i	−0.101779	−	0.577216i	−0.992458	−	0.122584i	$-0.960882\pi$
$19$	−0.443644	−	2.51603i	−0.101779	−	0.577216i	0.890679	−	0.454632i	$-0.150229\pi$
$20$	−0.939693	+	0.342020i	−0.210122	+	0.0764780i
$21$	−1.16414	−	0.976831i	−0.254037	−	0.213162i
$22$	1.68868	+	1.41697i	0.360028	+	0.302099i
$23$	−2.44767	−	4.23950i	−0.510375	−	0.883996i	−0.999928	−	0.0120221i	$-0.996173\pi$
$23$	−2.44767	−	4.23950i	−0.510375	−	0.883996i	0.489552	−	0.871974i	$-0.337160\pi$
$24$	−2.27798	−	0.829116i	−0.464990	−	0.169243i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	1.57536	−	2.72861i	0.308954	−	0.535125i
$27$	−0.149555	−	0.259037i	−0.0287819	−	0.0498517i
$28$	−0.589080	+	0.214408i	−0.111326	+	0.0405192i
$29$	−0.0272111	+	0.0471310i	−0.00505297	+	0.00875201i	−0.868541	−	0.495618i	$-0.834942\pi$
$29$	−0.0272111	+	0.0471310i	−0.00505297	+	0.00875201i	0.863488	+	0.504370i	$0.168275\pi$
$30$	1.85702	−	1.55823i	0.339045	−	0.284492i
$31$	5.29459			0.950937			0.475468	−	0.879733i	$-0.342279\pi$
$31$	5.29459			0.950937			0.475468	+	0.879733i	$0.342279\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−5.02160	−	1.82771i	−0.874149	−	0.318164i
$34$	−0.398065	−	2.25754i	−0.0682675	−	0.387164i
$35$	0.108858	−	0.617362i	0.0184003	−	0.104353i
$36$	2.87661			0.479436
$37$	−1.02258	−	5.99619i	−0.168112	−	0.985768i
$37$	−1.02258	−	5.99619i	−0.168112	−	0.985768i
$38$	2.55484			0.414450
$39$	−1.32631	+	7.52187i	−0.212379	+	1.20446i
$40$	−0.173648	−	0.984808i	−0.0274562	−	0.155712i
$41$	−0.166409	−	0.0605677i	−0.0259886	−	0.00945909i	0.328993	−	0.944332i	$-0.393291\pi$
$41$	−0.166409	−	0.0605677i	−0.0259886	−	0.00945909i	−0.354982	+	0.934873i	$0.615513\pi$
$42$	1.16414	−	0.976831i	0.179631	−	0.150728i
$43$	2.99960			0.457435			0.228717	−	0.973493i	$-0.426547\pi$
$43$	2.99960			0.457435			0.228717	+	0.973493i	$0.426547\pi$
$44$	−1.68868	+	1.41697i	−0.254578	+	0.213616i
$45$	−1.43831	+	2.49122i	−0.214410	+	0.371369i
$46$	4.60012	−	1.67431i	0.678251	−	0.246863i
$47$	1.99372	+	3.45323i	0.290814	+	0.503705i	0.974002	−	0.226537i	$-0.0727405\pi$
$47$	1.99372	+	3.45323i	0.290814	+	0.503705i	−0.683188	+	0.730242i	$0.739407\pi$
$48$	1.21209	−	2.09940i	0.174950	−	0.303022i
$49$	−1.14730	+	6.50664i	−0.163899	+	0.929520i
$50$	0.939693	+	0.342020i	0.132893	+	0.0483690i
$51$	2.77854	+	4.81258i	0.389074	+	0.673896i
$52$	2.41360	+	2.02525i	0.334706	+	0.280851i
$53$	2.52707	+	2.12046i	0.347119	+	0.291268i	0.799632	−	0.600490i	$-0.205028\pi$
$53$	2.52707	+	2.12046i	0.347119	+	0.291268i	−0.452513	+	0.891758i	$0.649472\pi$
$54$	0.281071	−	0.102302i	0.0382490	−	0.0139215i
$55$	−0.382792	−	2.17092i	−0.0516157	−	0.292727i
$56$	−0.108858	−	0.617362i	−0.0145467	−	0.0824985i
$57$	−5.81987	+	2.11826i	−0.770861	+	0.280570i
$58$	−0.0416898	−	0.0349819i	−0.00547414	−	0.00459335i
$59$	8.62512	+	7.23734i	1.12290	+	0.942221i	0.998747	−	0.0500424i	$-0.0159356\pi$
$59$	8.62512	+	7.23734i	1.12290	+	0.942221i	0.124149	+	0.992264i	$0.460380\pi$
$60$	1.21209	+	2.09940i	0.156480	+	0.271031i
$61$	2.66384	+	0.969558i	0.341070	+	0.124139i	0.506876	−	0.862019i	$-0.330800\pi$
$61$	2.66384	+	0.969558i	0.341070	+	0.124139i	−0.165806	+	0.986158i	$0.553023\pi$
$62$	−0.919396	+	5.21415i	−0.116763	+	0.662198i
$63$	−0.901654	+	1.56171i	−0.113598	+	0.196757i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.96072	+	1.07761i	−0.367232	+	0.133661i
$66$	2.67194	−	4.62794i	0.328893	−	0.569659i
$67$	5.80763	−	4.87318i	0.709515	−	0.595354i	−0.214948	−	0.976626i	$-0.568958\pi$
$67$	5.80763	−	4.87318i	0.709515	−	0.595354i	0.924463	+	0.381271i	$0.124514\pi$
$68$	2.29236			0.277990
$69$	−9.09078	+	7.62807i	−1.09440	+	0.918312i
$70$	0.589080	+	0.214408i	0.0704085	+	0.0256266i
$71$	2.24551	+	12.7349i	0.266493	+	1.51136i	0.764749	+	0.644328i	$0.222863\pi$
$71$	2.24551	+	12.7349i	0.266493	+	1.51136i	−0.498256	+	0.867030i	$0.666026\pi$
$72$	−0.499519	+	2.83291i	−0.0588688	+	0.333862i
$73$	0.767684			0.0898506			0.0449253	−	0.998990i	$-0.485695\pi$
$73$	0.767684			0.0898506			0.0449253	+	0.998990i	$0.485695\pi$
$74$	6.08267	+	0.0341800i	0.707096	+	0.00397334i
$75$	−2.42417			−0.279919
$76$	−0.443644	+	2.51603i	−0.0508894	+	0.288608i
$77$	−0.239967	−	1.36092i	−0.0273468	−	0.155091i
$78$	−7.17729	−	2.61232i	−0.812668	−	0.295787i
$79$	9.07425	−	7.61420i	1.02093	−	0.856664i	0.0311880	−	0.999514i	$-0.490071\pi$
$79$	9.07425	−	7.61420i	1.02093	−	0.856664i	0.989744	+	0.142850i	$0.0456265\pi$
$80$	1.00000			0.111803
$81$	−7.16630	+	6.01324i	−0.796255	+	0.668137i
$82$	0.0885441	−	0.153363i	0.00977806	−	0.0169361i
$83$	0.541536	−	0.197103i	0.0594413	−	0.0216349i	−0.312128	−	0.950040i	$-0.601042\pi$
$83$	0.541536	−	0.197103i	0.0594413	−	0.0216349i	0.371570	+	0.928405i	$0.378820\pi$
$84$	0.759840	+	1.31608i	0.0829053	+	0.143596i
$85$	−1.14618	+	1.98525i	−0.124321	+	0.215330i
$86$	−0.520875	+	2.95403i	−0.0561674	+	0.318541i
$87$	0.123972	+	0.0451223i	0.0132912	+	0.00483762i
$88$	−1.10221	−	1.90908i	−0.117496	−	0.203508i
$89$	−4.52050	−	3.79315i	−0.479172	−	0.402073i	0.370955	−	0.928651i	$-0.379030\pi$
$89$	−4.52050	−	3.79315i	−0.479172	−	0.402073i	−0.850127	+	0.526578i	$0.823475\pi$
$90$	−2.20361	−	1.84905i	−0.232281	−	0.194907i
$91$	−1.85603	+	0.675540i	−0.194565	+	0.0708158i
$92$	0.850068	+	4.82098i	0.0886257	+	0.502622i
$93$	−2.22877	−	12.6400i	−0.231113	−	1.31071i
$94$	−3.74697	+	1.36379i	−0.386470	+	0.140664i
$95$	−1.95712	−	1.64222i	−0.200797	−	0.168488i
$96$	1.85702	+	1.55823i	0.189532	+	0.159036i
$97$	−3.01586	−	5.22363i	−0.306214	−	0.530379i	0.671317	−	0.741171i	$-0.265729\pi$
$97$	−3.01586	−	5.22363i	−0.306214	−	0.530379i	−0.977531	+	0.210792i	$0.932396\pi$
$98$	−6.20856	−	2.25973i	−0.627160	−	0.228267i
$99$	−1.10115	+	6.24491i	−0.110669	+	0.627637i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.723264	+	1.25273i	0.0719675	+	0.124651i	0.899764	−	0.436378i	$-0.143739\pi$
$101$	0.723264	+	1.25273i	0.0719675	+	0.124651i	−0.827796	+	0.561029i	$0.810406\pi$
$102$	−5.22195	+	1.90064i	−0.517050	+	0.188191i
$103$	5.61541	−	9.72618i	0.553303	−	0.958349i	−0.444730	−	0.895665i	$-0.646700\pi$
$103$	5.61541	−	9.72618i	0.553303	−	0.958349i	0.998033	−	0.0626847i	$-0.0199662\pi$
$104$	−2.41360	+	2.02525i	−0.236673	+	0.198592i
$105$	−1.51968			−0.148306
$106$	−2.52707	+	2.12046i	−0.245450	+	0.205957i
$107$	4.73736	+	1.72426i	0.457978	+	0.166690i	0.560699	−	0.828020i	$-0.310533\pi$
$107$	4.73736	+	1.72426i	0.457978	+	0.166690i	−0.102721	+	0.994710i	$0.532755\pi$
$108$	0.0519399	+	0.294566i	0.00499792	+	0.0283446i
$109$	1.37042	−	7.77206i	0.131263	−	0.744428i	−0.846127	−	0.532982i	$-0.821071\pi$
$109$	1.37042	−	7.77206i	0.131263	−	0.744428i	0.977390	−	0.211447i	$-0.0678175\pi$
$110$	2.20441			0.210183
$111$	−13.8845	+	4.96537i	−1.31786	+	0.471292i
$112$	0.626886			0.0592351
$113$	−2.38245	+	13.5116i	−0.224122	+	1.27106i	0.640234	+	0.768180i	$0.278837\pi$
$113$	−2.38245	+	13.5116i	−0.224122	+	1.27106i	−0.864356	+	0.502880i	$0.832274\pi$
$114$	−1.07547	−	6.09929i	−0.100727	−	0.571250i
$115$	−4.60012	−	1.67431i	−0.428964	−	0.156130i
$116$	0.0416898	−	0.0349819i	0.00387080	−	0.00324799i
$117$	9.06343			0.837914
$118$	−8.62512	+	7.23734i	−0.794007	+	0.666251i
$119$	−0.718525	+	1.24452i	−0.0658671	+	0.114085i
$120$	−2.27798	+	0.829116i	−0.207950	+	0.0756876i
$121$	3.07028	+	5.31788i	0.279116	+	0.483444i
$122$	−1.41740	+	2.45501i	−0.128325	+	0.222266i
$123$	−0.0745459	+	0.422771i	−0.00672157	+	0.0381199i
$124$	−4.97529	−	1.81086i	−0.446794	−	0.162620i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−1.38141	−	1.15914i	−0.123066	−	0.103265i
$127$	7.19836	+	6.04014i	0.638751	+	0.535976i	0.903635	−	0.428304i	$-0.140889\pi$
$127$	7.19836	+	6.04014i	0.638751	+	0.535976i	−0.264883	+	0.964281i	$0.585333\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−1.26269	−	7.16108i	−0.111174	−	0.630498i
$130$	−0.547118	−	3.10286i	−0.0479854	−	0.272139i
$131$	−13.8768	+	5.05076i	−1.21243	+	0.441287i	−0.867544	−	0.497360i	$-0.834303\pi$
$131$	−13.8768	+	5.05076i	−1.21243	+	0.441287i	−0.344881	+	0.938646i	$0.612081\pi$
$132$	4.09365	+	3.43498i	0.356306	+	0.298977i
$133$	−1.22689	−	1.02948i	−0.106385	−	0.0892677i
$134$	3.79066	+	6.56562i	0.327463	+	0.567183i
$135$	−0.281071	−	0.102302i	−0.0241908	−	0.00880472i
$136$	−0.398065	+	2.25754i	−0.0341338	+	0.193582i
$137$	−3.69639	+	6.40234i	−0.315804	+	0.546989i	−0.979608	−	0.200918i	$-0.935608\pi$
$137$	−3.69639	+	6.40234i	−0.315804	+	0.546989i	0.663804	+	0.747907i	$0.268941\pi$
$138$	−5.93358	−	10.2773i	−0.505100	−	0.874859i
$139$	16.5294	−	6.01622i	1.40201	−	0.510289i	0.473234	−	0.880937i	$-0.343087\pi$
$139$	16.5294	−	6.01622i	1.40201	−	0.510289i	0.928773	+	0.370648i	$0.120864\pi$
$140$	−0.313443	+	0.542899i	−0.0264908	+	0.0458833i
$141$	7.40478	−	6.21335i	0.623595	−	0.523258i
$142$	−12.9314			−1.08518
$143$	−5.32057	+	4.46449i	−0.444928	+	0.373339i
$144$	−2.70313	−	0.983860i	−0.225261	−	0.0819883i
$145$	0.00945031	+	0.0535954i	0.000784806	+	0.00445085i
$146$	−0.133307	+	0.756021i	−0.0110326	+	0.0625688i
$147$	16.0165			1.32102
$148$	−1.08990	+	5.98432i	−0.0895896	+	0.491908i
$149$	13.5027			1.10618			0.553091	−	0.833121i	$-0.313448\pi$
$149$	13.5027			1.10618			0.553091	+	0.833121i	$0.313448\pi$
$150$	0.420953	−	2.38734i	0.0343707	−	0.194926i
$151$	2.02519	+	11.4854i	0.164807	+	0.934669i	0.949263	+	0.314484i	$0.101831\pi$
$151$	2.02519	+	11.4854i	0.164807	+	0.934669i	−0.784455	+	0.620185i	$0.787057\pi$
$152$	−2.40077	−	0.873807i	−0.194728	−	0.0708751i
$153$	5.05148	−	4.23870i	0.408388	−	0.342678i
$154$	1.38192			0.111358
$155$	4.05589	−	3.40330i	0.325777	−	0.273359i
$156$	3.81895	−	6.61462i	0.305761	−	0.529594i
$157$	23.2622	−	8.46673i	1.85652	−	0.675719i	0.875074	−	0.483989i	$-0.160813\pi$
$157$	23.2622	−	8.46673i	1.85652	−	0.675719i	0.981448	−	0.191729i	$-0.0614095\pi$
$158$	5.92279	+	10.2586i	0.471192	+	0.816129i
$159$	3.99849	−	6.92559i	0.317101	−	0.549235i
$160$	−0.173648	+	0.984808i	−0.0137281	+	0.0778559i
$161$	−2.88375	−	1.04960i	−0.227271	−	0.0827200i
$162$	−4.67747	−	8.10161i	−0.367497	−	0.636523i
$163$	−18.1577	−	15.2362i	−1.42222	−	1.19339i	−0.950136	−	0.311836i	$-0.899056\pi$
$163$	−18.1577	−	15.2362i	−1.42222	−	1.19339i	−0.472088	−	0.881551i	$-0.656500\pi$
$164$	0.135657	+	0.113830i	0.0105931	+	0.00888864i
$165$	−5.02160	+	1.82771i	−0.390931	+	0.142287i
$166$	0.100072	+	0.567535i	0.00776708	+	0.0440493i
$167$	−2.92570	−	16.5925i	−0.226398	−	1.28397i	−0.859995	−	0.510302i	$-0.829533\pi$
$167$	−2.92570	−	16.5925i	−0.226398	−	1.28397i	0.633597	−	0.773663i	$-0.281578\pi$
$168$	−1.42803	+	0.519761i	−0.110175	+	0.0401004i
$169$	−2.35399	−	1.97523i	−0.181076	−	0.151941i
$170$	−1.75605	−	1.47350i	−0.134683	−	0.113013i
$171$	3.67465	+	6.36467i	0.281007	+	0.486719i
$172$	−2.81870	−	1.02592i	−0.214924	−	0.0782259i
$173$	−0.366739	+	2.07988i	−0.0278826	+	0.158130i	−0.995570	−	0.0940225i	$-0.970027\pi$
$173$	−0.366739	+	2.07988i	−0.0278826	+	0.158130i	0.967687	+	0.252153i	$0.0811386\pi$
$174$	−0.0659644	+	0.114254i	−0.00500075	+	0.00866155i
$175$	−0.313443	−	0.542899i	−0.0236941	−	0.0410393i
$176$	2.07147	−	0.753954i	0.156143	−	0.0568314i
$177$	13.6472	−	23.6377i	1.02579	−	1.77672i
$178$	4.52050	−	3.79315i	0.338825	−	0.284308i
$179$	25.9954			1.94299			0.971495	−	0.237059i	$-0.0761834\pi$
$179$	25.9954			1.94299			0.971495	+	0.237059i	$0.0761834\pi$
$180$	2.20361	−	1.84905i	0.164248	−	0.137820i
$181$	−10.4268	−	3.79503i	−0.775015	−	0.282083i	−0.0759228	−	0.997114i	$-0.524190\pi$
$181$	−10.4268	−	3.79503i	−0.775015	−	0.282083i	−0.699093	+	0.715031i	$0.746412\pi$
$182$	−0.342981	−	1.94514i	−0.0254234	−	0.144183i
$183$	1.19332	−	6.76764i	0.0882125	−	0.500278i
$184$	−4.89535			−0.360890
$185$	−4.63762	−	3.93605i	−0.340965	−	0.289384i
$186$	12.8350			0.941108
$187$	−0.877499	+	4.97655i	−0.0641691	+	0.363921i
$188$	−0.692412	−	3.92686i	−0.0504993	−	0.286396i
$189$	−0.176200	−	0.0641314i	−0.0128166	−	0.00466488i
$190$	1.95712	−	1.64222i	0.141985	−	0.119139i
$191$	17.6972			1.28053			0.640263	−	0.768156i	$-0.278826\pi$
$191$	17.6972			1.28053			0.640263	+	0.768156i	$0.278826\pi$
$192$	−1.85702	+	1.55823i	−0.134019	+	0.112455i
$193$	−3.27226	+	5.66773i	−0.235543	+	0.407972i	−0.959430	−	0.281946i	$-0.909020\pi$
$193$	−3.27226	+	5.66773i	−0.235543	+	0.407972i	0.723888	+	0.689918i	$0.242353\pi$
$194$	5.66797	−	2.06297i	0.406936	−	0.148113i
$195$	3.81895	+	6.61462i	0.273481	+	0.473683i
$196$	3.30351	−	5.72184i	0.235965	−	0.408703i
$197$	−2.43142	+	13.7892i	−0.173231	+	0.982443i	0.766935	+	0.641725i	$0.221781\pi$
$197$	−2.43142	+	13.7892i	−0.173231	+	0.982443i	−0.940166	+	0.340718i	$0.889330\pi$
$198$	−5.95882	−	2.16883i	−0.423475	−	0.154132i
$199$	−9.68678	−	16.7780i	−0.686677	−	1.18936i	−0.972906	−	0.231199i	$-0.925735\pi$
$199$	−9.68678	−	16.7780i	−0.686677	−	1.18936i	0.286229	−	0.958161i	$-0.407598\pi$
$200$	−0.766044	−	0.642788i	−0.0541675	−	0.0454519i
$201$	−14.0787	−	11.8134i	−0.993035	−	0.833256i
$202$	−1.35929	+	0.494742i	−0.0956395	+	0.0348099i
$203$	0.00592427	+	0.0335982i	0.000415802	+	0.00235813i
$204$	−0.964978	−	5.47266i	−0.0675620	−	0.383163i
$205$	−0.166409	+	0.0605677i	−0.0116225	+	0.00423023i
$206$	8.60331	+	7.21904i	0.599421	+	0.502974i
$207$	10.7875	+	9.05175i	0.749780	+	0.629140i
$208$	−1.57536	−	2.72861i	−0.109232	−	0.189195i
$209$	−5.29228	−	1.92623i	−0.366075	−	0.133240i
$210$	0.263890	−	1.49659i	0.0182101	−	0.103275i
$211$	−13.0135	+	22.5401i	−0.895887	+	1.55172i	−0.0631845	+	0.998002i	$0.520126\pi$
$211$	−13.0135	+	22.5401i	−0.895887	+	1.55172i	−0.832703	+	0.553720i	$0.813208\pi$
$212$	−1.64943	−	2.85689i	−0.113283	−	0.196212i
$213$	29.4574	−	10.7216i	2.01839	−	0.734633i
$214$	−2.52070	+	4.36598i	−0.172311	+	0.298452i
$215$	2.29783	−	1.92811i	0.156710	−	0.131496i
$216$	−0.299110			−0.0203519
$217$	2.54258	−	2.13348i	0.172602	−	0.144830i
$218$	7.41601	+	2.69921i	0.502276	+	0.182813i
$219$	−0.323159	−	1.83273i	−0.0218371	−	0.123844i
$220$	−0.382792	+	2.17092i	−0.0258079	+	0.146364i
$221$	7.22261			0.485846
$222$	−2.47892	−	14.5358i	−0.166374	−	0.975579i
$223$	−13.3172			−0.891784			−0.445892	−	0.895087i	$-0.647113\pi$
$223$	−13.3172			−0.891784			−0.445892	+	0.895087i	$0.647113\pi$
$224$	−0.108858	+	0.617362i	−0.00727335	+	0.0412492i
$225$	0.499519	+	2.83291i	0.0333012	+	0.188861i
$226$	−12.8926	−	4.69251i	−0.857601	−	0.312141i
$227$	−9.49454	+	7.96686i	−0.630175	+	0.528779i	−0.900983	−	0.433854i	$-0.857153\pi$
$227$	−9.49454	+	7.96686i	−0.630175	+	0.528779i	0.270809	+	0.962633i	$0.412709\pi$
$228$	6.19338			0.410166
$229$	13.2586	−	11.1253i	0.876150	−	0.735177i	−0.0892336	−	0.996011i	$-0.528442\pi$
$229$	13.2586	−	11.1253i	0.876150	−	0.735177i	0.965384	+	0.260833i	$0.0839973\pi$
$230$	2.44767	−	4.23950i	0.161395	−	0.279544i
$231$	−3.14797	+	1.14577i	−0.207121	+	0.0753860i
$232$	0.0272111	+	0.0471310i	0.00178650	+	0.00309430i
$233$	−11.1390	+	19.2933i	−0.729738	+	1.26394i	0.227255	+	0.973835i	$0.427025\pi$
$233$	−11.1390	+	19.2933i	−0.729738	+	1.26394i	−0.956994	+	0.290109i	$0.906309\pi$
$234$	−1.57385	+	8.92573i	−0.102886	+	0.583493i
$235$	3.74697	+	1.36379i	0.244425	+	0.0889636i
$236$	−5.62965	−	9.75084i	−0.366459	−	0.634726i
$237$	−21.9975	−	18.4581i	−1.42889	−	1.19898i
$238$	−1.10084	−	0.923718i	−0.0713571	−	0.0598758i
$239$	−12.9990	+	4.73124i	−0.840834	+	0.306038i	−0.726297	−	0.687381i	$-0.758760\pi$
$239$	−12.9990	+	4.73124i	−0.840834	+	0.306038i	−0.114536	+	0.993419i	$0.536538\pi$
$240$	−0.420953	−	2.38734i	−0.0271724	−	0.154102i
$241$	−3.40828	−	19.3293i	−0.219547	−	1.24511i	−0.872840	−	0.488007i	$-0.837724\pi$
$241$	−3.40828	−	19.3293i	−0.219547	−	1.24511i	0.653293	−	0.757105i	$-0.273387\pi$
$242$	−5.77024	+	2.10020i	−0.370925	+	0.135006i
$243$	16.6849	+	14.0003i	1.07034	+	0.898122i
$244$	−2.17158	−	1.82217i	−0.139021	−	0.116653i
$245$	3.30351	+	5.72184i	0.211053	+	0.365555i
$246$	−0.403403	−	0.146827i	−0.0257200	−	0.00936133i
$247$	−1.39780	+	7.92732i	−0.0889399	+	0.504403i
$248$	2.64730	−	4.58525i	0.168103	−	0.291164i
$249$	−0.698514	−	1.20986i	−0.0442665	−	0.0766718i
$250$	0.939693	−	0.342020i	0.0594314	−	0.0216313i
$251$	1.17718	−	2.03893i	0.0743029	−	0.128696i	−0.826480	−	0.562966i	$-0.809660\pi$
$251$	1.17718	−	2.03893i	0.0743029	−	0.128696i	0.900783	+	0.434270i	$0.142994\pi$
$252$	1.38141	−	1.15914i	0.0870209	−	0.0730192i
$253$	−10.7914			−0.678448
$254$	−7.19836	+	6.04014i	−0.451665	+	0.378992i
$255$	5.22195	+	1.90064i	0.327011	+	0.119022i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−1.85898	+	10.5428i	−0.115960	+	0.657641i	0.870311	+	0.492503i	$0.163918\pi$
$257$	−1.85898	+	10.5428i	−0.115960	+	0.657641i	−0.986270	+	0.165138i	$0.947193\pi$
$258$	7.27155			0.452707
$259$	−2.90726	−	2.46745i	−0.180648	−	0.153320i
$260$	3.15073			0.195400
$261$	0.0271849	−	0.154173i	0.00168270	−	0.00954308i
$262$	−2.56434	−	14.5431i	−0.158425	−	0.898474i
$263$	−11.3864	−	4.14432i	−0.702117	−	0.255550i	−0.0338026	−	0.999429i	$-0.510762\pi$
$263$	−11.3864	−	4.14432i	−0.702117	−	0.255550i	−0.668315	+	0.743879i	$0.732984\pi$
$264$	−4.09365	+	3.43498i	−0.251947	+	0.211408i
$265$	3.29885			0.202647
$266$	1.22689	−	1.02948i	0.0752256	−	0.0631218i
$267$	−7.15263	+	12.3887i	−0.437734	+	0.758177i
$268$	−7.12412	+	2.59297i	−0.435175	+	0.158391i
$269$	−8.59822	−	14.8926i	−0.524243	−	0.908015i	−0.999602	−	0.0282234i	$-0.991015\pi$
$269$	−8.59822	−	14.8926i	−0.524243	−	0.908015i	0.475359	−	0.879792i	$-0.342318\pi$
$270$	0.149555	−	0.259037i	0.00910163	−	0.0157645i
$271$	1.10934	−	6.29135i	0.0673873	−	0.382173i	−0.932398	−	0.361434i	$-0.882287\pi$
$271$	1.10934	−	6.29135i	0.0673873	−	0.382173i	0.999785	−	0.0207383i	$-0.00660169\pi$
$272$	−2.15412	−	0.784035i	−0.130613	−	0.0475391i
$273$	2.39405	+	4.14661i	0.144894	+	0.250964i
$274$	−5.66320	−	4.75199i	−0.342127	−	0.287078i
$275$	−1.68868	−	1.41697i	−0.101831	−	0.0854465i
$276$	11.1515	−	4.05881i	0.671241	−	0.244312i
$277$	3.52797	+	20.0081i	0.211975	+	1.20217i	0.886079	+	0.463534i	$0.153419\pi$
$277$	3.52797	+	20.0081i	0.211975	+	1.20217i	−0.674104	+	0.738636i	$0.735470\pi$
$278$	3.05451	+	17.3230i	0.183198	+	1.03896i
$279$	−14.3120	+	5.20914i	−0.856836	+	0.311863i
$280$	−0.480222	−	0.402954i	−0.0286988	−	0.0240811i
$281$	−4.62472	−	3.88060i	−0.275888	−	0.231497i	0.494336	−	0.869271i	$-0.335411\pi$
$281$	−4.62472	−	3.88060i	−0.275888	−	0.231497i	−0.770224	+	0.637774i	$0.779856\pi$
$282$	4.83312	+	8.37122i	0.287808	+	0.498499i
$283$	−3.19924	−	1.16443i	−0.190175	−	0.0692181i	0.245177	−	0.969478i	$-0.421154\pi$
$283$	−3.19924	−	1.16443i	−0.190175	−	0.0692181i	−0.435352	+	0.900260i	$0.643376\pi$
$284$	2.24551	−	12.7349i	0.133247	−	0.755679i
$285$	−3.09669	+	5.36362i	−0.183432	+	0.317714i
$286$	−3.47275	−	6.01499i	−0.205348	−	0.355674i
$287$	−0.104319	+	0.0379691i	−0.00615776	+	0.00224124i
$288$	1.43831	−	2.49122i	0.0847530	−	0.146797i
$289$	−8.99725	+	7.54959i	−0.529250	+	0.444093i
$290$	−0.0544222			−0.00319578
$291$	−11.2011	+	9.39881i	−0.656618	+	0.550968i
$292$	−0.721387	−	0.262563i	−0.0422160	−	0.0153654i
$293$	2.19179	+	12.4302i	0.128046	+	0.726183i	0.979452	+	0.201676i	$0.0646389\pi$
$293$	2.19179	+	12.4302i	0.128046	+	0.726183i	−0.851407	+	0.524506i	$0.824250\pi$
$294$	−2.78124	+	15.7732i	−0.162205	+	0.919913i
$295$	11.2593			0.655542
$296$	−5.70415	−	2.11251i	−0.331547	−	0.122787i
$297$	−0.659362			−0.0382601
$298$	−2.34471	+	13.2975i	−0.135826	+	0.770306i
$299$	2.67833	+	15.1896i	0.154892	+	0.878436i
$300$	2.27798	+	0.829116i	0.131519	+	0.0478690i
$301$	1.44047	−	1.20870i	0.0830276	−	0.0696684i
$302$	−11.6626			−0.671106
$303$	2.68624	−	2.25402i	0.154320	−	0.129490i
$304$	1.27742	−	2.21256i	0.0732651	−	0.126899i
$305$	2.66384	−	0.969558i	0.152531	−	0.0555167i
$306$	3.29712	+	5.71078i	0.188484	+	0.326464i
$307$	−9.06649	+	15.7036i	−0.517452	+	0.896253i	0.482343	+	0.875983i	$0.339786\pi$
$307$	−9.06649	+	15.7036i	−0.517452	+	0.896253i	−0.999795	+	0.0202701i	$0.993547\pi$
$308$	−0.239967	+	1.36092i	−0.0136734	+	0.0775457i
$309$	−25.5836	−	9.31166i	−1.45540	−	0.529722i
$310$	2.64730	+	4.58525i	0.150356	+	0.260425i
$311$	−18.6662	−	15.6628i	−1.05846	−	0.888155i	−0.0645040	−	0.997917i	$-0.520547\pi$
$311$	−18.6662	−	15.6628i	−1.05846	−	0.888155i	−0.993958	+	0.109763i	$0.964991\pi$
$312$	5.85098	+	4.90955i	0.331246	+	0.277949i
$313$	0.729697	−	0.265588i	0.0412449	−	0.0150119i	−0.321315	−	0.946972i	$-0.604125\pi$
$313$	0.729697	−	0.265588i	0.0412449	−	0.0150119i	0.362560	+	0.931960i	$0.381903\pi$
$314$	4.29867	+	24.3790i	0.242588	+	1.37579i
$315$	0.313141	+	1.77591i	0.0176435	+	0.100061i
$316$	−11.1312	+	4.05143i	−0.626180	+	0.227911i
$317$	−11.0117	−	9.23989i	−0.618477	−	0.518964i	0.278847	−	0.960335i	$-0.410048\pi$
$317$	−11.0117	−	9.23989i	−0.618477	−	0.518964i	−0.897324	+	0.441372i	$0.854492\pi$
$318$	6.12604	+	5.14036i	0.343532	+	0.288257i
$319$	0.0599845	+	0.103896i	0.00335849	+	0.00581707i
$320$	−0.939693	−	0.342020i	−0.0525304	−	0.0191195i
$321$	2.12219	−	12.0355i	0.118449	−	0.671759i
$322$	1.53441	−	2.65768i	0.0855094	−	0.148107i
$323$	2.92831	+	5.07199i	0.162936	+	0.282213i
$324$	8.79076	−	3.19958i	0.488376	−	0.177754i
$325$	−1.57536	+	2.72861i	−0.0873855	+	0.151356i
$326$	18.1577	−	15.2362i	1.00566	−	0.843852i
$327$	−19.1315			−1.05797
$328$	−0.135657	+	0.113830i	−0.00749043	+	0.00628522i
$329$	2.34892	+	0.854938i	0.129500	+	0.0471343i
$330$	−0.927955	−	5.26269i	−0.0510822	−	0.289702i
$331$	1.89796	−	10.7639i	0.104321	−	0.591635i	−0.887168	−	0.461446i	$-0.847331\pi$
$331$	1.89796	−	10.7639i	0.104321	−	0.591635i	0.991489	−	0.130189i	$-0.0415583\pi$
$332$	−0.576290			−0.0316280
$333$	8.66359	+	15.2024i	0.474762	+	0.833088i
$334$	16.8485			0.921907
$335$	1.31648	−	7.46615i	0.0719272	−	0.407919i
$336$	−0.263890	−	1.49659i	−0.0143964	−	0.0816458i
$337$	16.5983	+	6.04130i	0.904169	+	0.329091i	0.751922	−	0.659252i	$-0.229127\pi$
$337$	16.5983	+	6.04130i	0.904169	+	0.329091i	0.152247	+	0.988343i	$0.451349\pi$
$338$	2.35399	−	1.97523i	0.128040	−	0.107438i
$339$	33.2596			1.80642
$340$	1.75605	−	1.47350i	0.0952353	−	0.0799119i
$341$	5.83573	−	10.1078i	0.316023	−	0.547367i
$342$	−6.90608	+	2.51361i	−0.373438	+	0.135920i
$343$	4.26502	+	7.38724i	0.230290	+	0.398873i
$344$	1.49980	−	2.59773i	0.0808638	−	0.140060i
$345$	−2.06071	+	11.6869i	−0.110945	+	0.629200i
$346$	−1.98460	−	0.722335i	−0.106693	−	0.0388329i
$347$	9.18087	+	15.9017i	0.492855	+	0.853650i	0.999966	−	0.00823078i	$-0.00261997\pi$
$347$	9.18087	+	15.9017i	0.492855	+	0.853650i	−0.507111	+	0.861881i	$0.669287\pi$
$348$	−0.101063	−	0.0848022i	−0.00541756	−	0.00454587i
$349$	−22.1878	−	18.6178i	−1.18769	−	0.996588i	−0.999897	−	0.0143792i	$-0.995423\pi$
$349$	−22.1878	−	18.6178i	−1.18769	−	0.996588i	−0.187791	−	0.982209i	$-0.560133\pi$
$350$	0.589080	−	0.214408i	0.0314877	−	0.0114606i
$351$	0.163648	+	0.928097i	0.00873491	+	0.0495381i
$352$	0.382792	+	2.17092i	0.0204029	+	0.115711i
$353$	13.9117	−	5.06346i	0.740447	−	0.269501i	0.0558667	−	0.998438i	$-0.482208\pi$
$353$	13.9117	−	5.06346i	0.740447	−	0.269501i	0.684580	+	0.728938i	$0.259986\pi$
$354$	20.9088	+	17.5446i	1.11129	+	0.932483i
$355$	9.90602	+	8.31214i	0.525757	+	0.441162i
$356$	2.95054	+	5.11049i	0.156379	+	0.270856i
$357$	3.27357	+	1.19148i	0.173256	+	0.0630599i
$358$	−4.51406	+	25.6005i	−0.238576	+	1.35303i
$359$	1.51687	−	2.62729i	0.0800571	−	0.138663i	−0.823217	−	0.567727i	$-0.807823\pi$
$359$	1.51687	−	2.62729i	0.0800571	−	0.138663i	0.903274	+	0.429064i	$0.141156\pi$
$360$	1.43831	+	2.49122i	0.0758054	+	0.131299i
$361$	11.7206	−	4.26594i	0.616873	−	0.224523i
$362$	5.54797	−	9.60936i	0.291595	−	0.505057i
$363$	11.4032	−	9.56840i	0.598511	−	0.502211i
$364$	1.97515			0.103526
$365$	0.588080	−	0.493458i	0.0307815	−	0.0258288i
$366$	6.45760	+	2.35038i	0.337544	+	0.122856i
$367$	−3.49170	−	19.8024i	−0.182265	−	1.03368i	−0.929419	−	0.369027i	$-0.879691\pi$
$367$	−3.49170	−	19.8024i	−0.182265	−	1.03368i	0.747153	−	0.664652i	$-0.231420\pi$
$368$	0.850068	−	4.82098i	0.0443129	−	0.251311i
$369$	0.509414			0.0265191
$370$	4.68156	−	3.88368i	0.243383	−	0.201903i
$371$	2.06800			0.107365
$372$	−2.22877	+	12.6400i	−0.115557	+	0.655354i
$373$	2.24457	+	12.7296i	0.116219	+	0.659113i	0.986139	+	0.165920i	$0.0530593\pi$
$373$	2.24457	+	12.7296i	0.116219	+	0.659113i	−0.869920	+	0.493193i	$0.835830\pi$
$374$	−4.74856	−	1.72834i	−0.245542	−	0.0893701i
$375$	−1.85702	+	1.55823i	−0.0958963	+	0.0804666i
$376$	3.98744			0.205637
$377$	0.131353	−	0.110218i	0.00676504	−	0.00567654i
$378$	0.0937539	−	0.162387i	0.00482218	−	0.00835226i
$379$	1.62637	−	0.591949i	0.0835409	−	0.0304064i	−0.299912	−	0.953967i	$-0.596957\pi$
$379$	1.62637	−	0.591949i	0.0835409	−	0.0304064i	0.383453	+	0.923561i	$0.374735\pi$
$380$	1.27742	+	2.21256i	0.0655303	+	0.113502i
$381$	11.3897	−	19.7276i	0.583513	−	1.01067i
$382$	−3.07309	+	17.4283i	−0.157233	+	0.891712i
$383$	7.15686	+	2.60488i	0.365698	+	0.133103i	0.518332	−	0.855180i	$-0.326553\pi$
$383$	7.15686	+	2.60488i	0.365698	+	0.133103i	−0.152633	+	0.988283i	$0.548775\pi$
$384$	−1.21209	−	2.09940i	−0.0618540	−	0.107134i
$385$	−1.05861	−	0.888278i	−0.0539517	−	0.0452709i
$386$	−5.01340	−	4.20674i	−0.255175	−	0.214118i
$387$	−8.10831	+	2.95119i	−0.412169	+	0.150017i
$388$	1.04740	+	5.94009i	0.0531736	+	0.301562i
$389$	−1.59955	−	9.07151i	−0.0811005	−	0.459944i	−0.998130	−	0.0611247i	$-0.980531\pi$
$389$	−1.59955	−	9.07151i	−0.0811005	−	0.459944i	0.917030	−	0.398819i	$-0.130580\pi$
$390$	−7.17729	+	2.61232i	−0.363436	+	0.132280i
$391$	8.59649	+	7.21331i	0.434743	+	0.364793i
$392$	5.06127	+	4.24691i	0.255633	+	0.214501i
$393$	17.8994	+	31.0027i	0.902905	+	1.56388i
$394$	−13.1575	−	4.78895i	−0.662867	−	0.241264i
$395$	2.05696	−	11.6656i	0.103497	−	0.586961i
$396$	3.17062	−	5.49168i	0.159330	−	0.275967i
$397$	3.80784	+	6.59538i	0.191110	+	0.331013i	0.945618	−	0.325278i	$-0.105458\pi$
$397$	3.80784	+	6.59538i	0.191110	+	0.331013i	−0.754508	+	0.656291i	$0.772125\pi$
$398$	18.2052	−	6.62615i	0.912544	−	0.332139i
$399$	−1.94127	+	3.36238i	−0.0971851	+	0.168329i
$400$	0.766044	−	0.642788i	0.0383022	−	0.0321394i
$401$	−15.7686			−0.787447			−0.393724	−	0.919229i	$-0.628813\pi$
$401$	−15.7686			−0.787447			−0.393724	+	0.919229i	$0.628813\pi$
$402$	14.0787	−	11.8134i	0.702182	−	0.589201i
$403$	−15.6758	−	5.70552i	−0.780866	−	0.284212i
$404$	−0.251187	−	1.42455i	−0.0124970	−	0.0708741i
$405$	−1.62447	+	9.21281i	−0.0807204	+	0.457788i
$406$	−0.0341165			−0.00169317
$407$	−12.5743	−	4.65685i	−0.623285	−	0.230832i
$408$	5.55709			0.275117
$409$	−6.30594	+	35.7628i	−0.311809	+	1.76836i	0.277773	+	0.960647i	$0.410404\pi$
$409$	−6.30594	+	35.7628i	−0.311809	+	1.76836i	−0.589582	+	0.807709i	$0.700707\pi$
$410$	−0.0307510	−	0.174398i	−0.00151869	−	0.00861290i
$411$	16.8406	+	6.12948i	0.830686	+	0.302345i
$412$	−8.60331	+	7.21904i	−0.423855	+	0.355656i
$413$	7.05830			0.347316
$414$	−10.7875	+	9.05175i	−0.530175	+	0.444869i
$415$	0.288145	−	0.499082i	0.0141445	−	0.0244990i
$416$	2.96072	−	1.07761i	0.145161	−	0.0528343i
$417$	−21.3209	−	36.9289i	−1.04409	−	1.80841i
$418$	2.81596	−	4.87739i	0.137733	−	0.238561i
$419$	−0.826127	+	4.68520i	−0.0403589	+	0.228887i	−0.998315	−	0.0580282i	$-0.981519\pi$
$419$	−0.826127	+	4.68520i	−0.0403589	+	0.228887i	0.957956	+	0.286915i	$0.0926298\pi$
$420$	1.42803	+	0.519761i	0.0696808	+	0.0253617i
$421$	13.4192	+	23.2428i	0.654014	+	1.13278i	0.982140	+	0.188151i	$0.0602494\pi$
$421$	13.4192	+	23.2428i	0.654014	+	1.13278i	−0.328126	+	0.944634i	$0.606417\pi$
$422$	−19.9379	−	16.7299i	−0.970560	−	0.814396i
$423$	−8.78678	−	7.37299i	−0.427228	−	0.358487i
$424$	3.09991	−	1.12827i	0.150545	−	0.0547938i
$425$	0.398065	+	2.25754i	0.0193090	+	0.109507i
$426$	5.44351	+	30.8717i	0.263739	+	1.49574i
$427$	1.66992	−	0.607802i	0.0808132	−	0.0294136i
$428$	−3.86193	−	3.24055i	−0.186674	−	0.156638i
$429$	12.8980	+	10.8227i	0.622720	+	0.522524i
$430$	1.49980	+	2.59773i	0.0723268	+	0.125274i
$431$	−2.26314	−	0.823717i	−0.109012	−	0.0396770i	0.286938	−	0.957949i	$-0.407362\pi$
$431$	−2.26314	−	0.823717i	−0.109012	−	0.0396770i	−0.395950	+	0.918272i	$0.629585\pi$
$432$	0.0519399	−	0.294566i	0.00249896	−	0.0141723i
$433$	0.592988	−	1.02708i	0.0284972	−	0.0493586i	−0.851425	−	0.524476i	$-0.824261\pi$
$433$	0.592988	−	1.02708i	0.0284972	−	0.0493586i	0.879922	+	0.475118i	$0.157595\pi$
$434$	1.65955	+	2.87443i	0.0796611	+	0.137977i
$435$	0.123972	−	0.0451223i	0.00594403	−	0.00216345i
$436$	−3.94598	+	6.83464i	−0.188978	+	0.327320i
$437$	−9.58079	+	8.03924i	−0.458312	+	0.384569i
$438$	1.86100			0.0889220
$439$	−17.8668	+	14.9920i	−0.852737	+	0.715531i	−0.960391	−	0.278657i	$-0.910111\pi$
$439$	−17.8668	+	14.9920i	−0.852737	+	0.715531i	0.107654	+	0.994188i	$0.465666\pi$
$440$	−2.07147	−	0.753954i	−0.0987535	−	0.0359433i
$441$	−3.30033	−	18.7171i	−0.157158	−	0.891290i
$442$	−1.25419	+	7.11289i	−0.0596559	+	0.338326i
$443$	7.00455			0.332796			0.166398	−	0.986059i	$-0.446786\pi$
$443$	7.00455			0.332796			0.166398	+	0.986059i	$0.446786\pi$
$444$	14.7454	+	0.0828581i	0.699787	+	0.00393227i
$445$	−5.90109			−0.279738
$446$	2.31250	−	13.1149i	0.109500	−	0.621006i
$447$	−5.68399	−	32.2355i	−0.268844	−	1.52469i
$448$	−0.589080	−	0.214408i	−0.0278314	−	0.0101298i
$449$	−24.9588	+	20.9429i	−1.17788	+	0.988356i	−0.177886	+	0.984051i	$0.556926\pi$
$449$	−24.9588	+	20.9429i	−1.17788	+	0.988356i	−0.999991	+	0.00430495i	$0.998630\pi$
$450$	−2.87661			−0.135605
$451$	−0.299045	+	0.250929i	−0.0140815	+	0.0118158i
$452$	6.86000	−	11.8819i	0.322667	−	0.558876i
$453$	26.5671	−	9.66963i	1.24823	−	0.454319i
$454$	−6.19712	−	10.7337i	−0.290845	−	0.503759i
$455$	−0.987573	+	1.71053i	−0.0462982	+	0.0801908i
$456$	−1.07547	+	6.09929i	−0.0503634	+	0.285625i
$457$	26.3312	+	9.58376i	1.23172	+	0.448309i	0.874186	−	0.485591i	$-0.161396\pi$
$457$	26.3312	+	9.58376i	1.23172	+	0.448309i	0.357533	+	0.933900i	$0.383618\pi$
$458$	8.65391	+	14.9890i	0.404371	+	0.700391i
$459$	0.525253	+	0.440739i	0.0245167	+	0.0205720i
$460$	3.75005	+	3.14667i	0.174847	+	0.146714i
$461$	−1.44118	+	0.524546i	−0.0671224	+	0.0244306i	−0.375363	−	0.926878i	$-0.622482\pi$
$461$	−1.44118	+	0.524546i	−0.0671224	+	0.0244306i	0.308241	+	0.951308i	$0.400260\pi$
$462$	−0.581722	−	3.29911i	−0.0270641	−	0.153488i
$463$	−1.62797	−	9.23269i	−0.0756583	−	0.429080i	−0.998984	−	0.0450623i	$-0.985651\pi$
$463$	−1.62797	−	9.23269i	−0.0756583	−	0.429080i	0.923326	−	0.384017i	$-0.125460\pi$
$464$	−0.0511401	+	0.0186135i	−0.00237412	+	0.000864109i
$465$	−9.83218	−	8.25018i	−0.455957	−	0.382593i
$466$	−17.0659	−	14.3200i	−0.790562	−	0.663361i
$467$	−8.40673	−	14.5609i	−0.389017	−	0.673797i	0.603301	−	0.797514i	$-0.293852\pi$
$467$	−8.40673	−	14.5609i	−0.389017	−	0.673797i	−0.992318	+	0.123717i	$0.960519\pi$
$468$	−8.51684	−	3.09987i	−0.393691	−	0.143292i
$469$	0.825285	−	4.68042i	0.0381081	−	0.216122i
$470$	−1.99372	+	3.45323i	−0.0919635	+	0.159285i
$471$	−30.0053	−	51.9707i	−1.38257	−	2.39468i
$472$	10.5803	−	3.85091i	0.486997	−	0.177252i
$473$	3.30618	−	5.72647i	0.152018	−	0.263303i
$474$	21.9975	−	18.4581i	1.01038	−	0.847810i
$475$	−2.55484			−0.117224
$476$	1.10084	−	0.923718i	0.0504571	−	0.0423386i
$477$	−8.91723	−	3.24561i	−0.408292	−	0.148606i
$478$	−2.40211	−	13.6231i	−0.109870	−	0.623104i
$479$	7.42962	−	42.1355i	0.339468	−	1.92522i	−0.0381831	−	0.999271i	$-0.512157\pi$
$479$	7.42962	−	42.1355i	0.339468	−	1.92522i	0.377651	−	0.925948i	$-0.376732\pi$
$480$	2.42417			0.110648
$481$	−3.43399	+	18.8550i	−0.156577	+	0.859713i
$482$	19.6275			0.894009
$483$	−1.29183	+	7.32634i	−0.0587804	+	0.333360i
$484$	−1.06630	−	6.04727i	−0.0484681	−	0.274876i
$485$	−5.66797	−	2.06297i	−0.257369	−	0.0936747i
$486$	−16.6849	+	14.0003i	−0.756844	+	0.635068i
$487$	−13.5262			−0.612929			−0.306465	−	0.951882i	$-0.599146\pi$
$487$	−13.5262			−0.612929			−0.306465	+	0.951882i	$0.599146\pi$
$488$	2.17158	−	1.82217i	0.0983028	−	0.0824859i
$489$	−28.7304	+	49.7625i	−1.29923	+	2.25034i
$490$	−6.20856	+	2.25973i	−0.280474	+	0.102084i
$491$	2.34854	+	4.06779i	0.105988	+	0.183577i	0.914141	−	0.405395i	$-0.132866\pi$
$491$	2.34854	+	4.06779i	0.105988	+	0.183577i	−0.808153	+	0.588972i	$0.799533\pi$
$492$	0.214646	−	0.371778i	0.00967700	−	0.0167611i
$493$	0.0216636	−	0.122860i	0.000975677	−	0.00553334i
$494$	−7.56416	−	2.75313i	−0.340328	−	0.123869i
$495$	3.17062	+	5.49168i	0.142509	+	0.246833i
$496$	4.05589	+	3.40330i	0.182115	+	0.152813i
$497$	6.20994	+	5.21076i	0.278554	+	0.233735i
$498$	1.31278	−	0.477811i	0.0588269	−	0.0214112i
$499$	0.987365	+	5.59963i	0.0442005	+	0.250674i	0.998900	−	0.0468992i	$-0.0149340\pi$
$499$	0.987365	+	5.59963i	0.0442005	+	0.250674i	−0.954699	+	0.297573i	$0.903823\pi$
$500$	0.173648	+	0.984808i	0.00776578	+	0.0440419i
$501$	−38.3804	+	13.9693i	−1.71471	+	0.624103i
$502$	1.80354	+	1.51335i	0.0804960	+	0.0675442i
$503$	−29.0803	−	24.4013i	−1.29663	−	1.08800i	−0.990717	−	0.135940i	$-0.956595\pi$
$503$	−29.0803	−	24.4013i	−1.29663	−	1.08800i	−0.305911	−	0.952060i	$-0.598961\pi$
$504$	0.901654	+	1.56171i	0.0401629	+	0.0695641i
$505$	1.35929	+	0.494742i	0.0604877	+	0.0220157i
$506$	1.87390	−	10.6274i	0.0833051	−	0.472447i
$507$	−3.72464	+	6.45126i	−0.165417	+	0.286510i
$508$	−4.69840	−	8.13786i	−0.208458	−	0.361059i
$509$	25.5019	−	9.28194i	1.13035	−	0.411415i	0.291933	−	0.956439i	$-0.405702\pi$
$509$	25.5019	−	9.28194i	1.13035	−	0.411415i	0.838420	+	0.545024i	$0.183480\pi$
$510$	−2.77854	+	4.81258i	−0.123036	+	0.213104i
$511$	0.368659	−	0.309342i	0.0163085	−	0.0136845i
$512$	−1.00000			−0.0441942
$513$	−0.585395	+	0.491204i	−0.0258458	+	0.0216872i
$514$	−10.0598	−	3.66147i	−0.443719	−	0.161501i
$515$	−1.95021	−	11.0602i	−0.0859367	−	0.487371i
$516$	−1.26269	+	7.16108i	−0.0555869	+	0.315249i
$517$	8.78997			0.386583
$518$	2.93481	−	2.43462i	0.128948	−	0.106971i
$519$	5.11977			0.224733
$520$	−0.547118	+	3.10286i	−0.0239927	+	0.136069i
$521$	3.70813	+	21.0298i	0.162456	+	0.921334i	0.951649	+	0.307188i	$0.0993881\pi$
$521$	3.70813	+	21.0298i	0.162456	+	0.921334i	−0.789193	+	0.614146i	$0.789501\pi$
$522$	0.147110	+	0.0535438i	0.00643885	+	0.00234355i
$523$	11.9038	−	9.98849i	0.520518	−	0.436766i	−0.344294	−	0.938862i	$-0.611882\pi$
$523$	11.9038	−	9.98849i	0.520518	−	0.436766i	0.864812	+	0.502095i	$0.167437\pi$
$524$	14.7674			0.645118
$525$	−1.16414	+	0.976831i	−0.0508073	+	0.0426324i
$526$	6.05859	−	10.4938i	0.264167	−	0.457551i
$527$	−11.4052	+	4.15114i	−0.496817	+	0.180827i
$528$	−2.67194	−	4.62794i	−0.116281	−	0.201405i
$529$	−0.482215	+	0.835222i	−0.0209659	+	0.0363140i
$530$	−0.572839	+	3.24873i	−0.0248826	+	0.141116i
$531$	−30.4354	−	11.0776i	−1.32078	−	0.480726i
$532$	0.800797	+	1.38702i	0.0347190	+	0.0601350i
$533$	0.427420	+	0.358648i	0.0185136	+	0.0155348i
$534$	−10.9585	−	9.19524i	−0.474219	−	0.397917i
$535$	4.73736	−	1.72426i	0.204814	−	0.0745462i
$536$	−1.31648	−	7.46615i	−0.0568634	−	0.322489i
$537$	−10.9429	−	62.0601i	−0.472219	−	2.67809i
$538$	16.1594	−	5.88153i	0.696680	−	0.253571i
$539$	11.1571	+	9.36194i	0.480571	+	0.403247i
$540$	0.229132	+	0.192264i	0.00986025	+	0.00827373i
$541$	−1.78616	−	3.09371i	−0.0767928	−	0.133009i	0.825072	−	0.565028i	$-0.191135\pi$
$541$	−1.78616	−	3.09371i	−0.0767928	−	0.133009i	−0.901865	+	0.432019i	$0.857801\pi$
$542$	6.00314	+	2.18496i	0.257857	+	0.0938523i
$543$	−4.67087	+	26.4898i	−0.200446	+	1.13679i
$544$	1.14618	−	1.98525i	0.0491421	−	0.0851167i
$545$	−3.94598	−	6.83464i	−0.169027	−	0.292764i
$546$	−4.49934	+	1.63763i	−0.192554	+	0.0700839i
$547$	19.7577	−	34.2213i	0.844777	−	1.46320i	−0.0410371	−	0.999158i	$-0.513066\pi$
$547$	19.7577	−	34.2213i	0.844777	−	1.46320i	0.885814	−	0.464040i	$-0.153600\pi$
$548$	5.66320	−	4.75199i	0.241920	−	0.202995i
$549$	−8.15462			−0.348031
$550$	1.68868	−	1.41697i	0.0720055	−	0.0604198i
$551$	0.130655	+	0.0475545i	0.00556609	+	0.00202589i
$552$	2.06071	+	11.6869i	0.0877097	+	0.497427i
$553$	1.28948	−	7.31302i	0.0548344	−	0.310981i
$554$	−20.3168			−0.863176
$555$	−7.44447	+	12.7285i	−0.316000	+	0.540294i
$556$	−17.5902			−0.745992
$557$	−5.94633	+	33.7233i	−0.251954	+	1.42890i	0.551817	+	0.833965i	$0.313935\pi$
$557$	−5.94633	+	33.7233i	−0.251954	+	1.42890i	−0.803771	+	0.594938i	$0.797176\pi$
$558$	−2.64475	−	14.9991i	−0.111961	−	0.634963i
$559$	−8.88096	−	3.23241i	−0.375625	−	0.136716i
$560$	0.480222	−	0.402954i	0.0202931	−	0.0170279i
$561$	12.2501			0.517200
$562$	4.62472	−	3.88060i	0.195082	−	0.163693i
$563$	−14.6705	+	25.4100i	−0.618288	+	1.07091i	0.371510	+	0.928429i	$0.378840\pi$
$563$	−14.6705	+	25.4100i	−0.618288	+	1.07091i	−0.989798	+	0.142477i	$0.954493\pi$
$564$	−9.08330	+	3.30605i	−0.382476	+	0.139210i
$565$	6.86000	+	11.8819i	0.288602	+	0.499874i
$566$	1.70228	−	2.94844i	0.0715522	−	0.123932i
$567$	−1.01836	+	5.77538i	−0.0427669	+	0.242543i
$568$	12.1515	+	4.42280i	0.509867	+	0.185576i
$569$	5.39668	+	9.34733i	0.226241	+	0.391861i	0.956691	−	0.291105i	$-0.0940230\pi$
$569$	5.39668	+	9.34733i	0.226241	+	0.391861i	−0.730450	+	0.682966i	$0.760690\pi$
$570$	−4.74440	−	3.98103i	−0.198721	−	0.166747i
$571$	−9.88397	−	8.29363i	−0.413631	−	0.347078i	0.412103	−	0.911137i	$-0.364794\pi$
$571$	−9.88397	−	8.29363i	−0.413631	−	0.347078i	−0.825734	+	0.564060i	$0.809239\pi$
$572$	6.52664	−	2.37550i	0.272893	−	0.0993248i
$573$	−7.44970	−	42.2493i	−0.311216	−	1.76499i
$574$	−0.0192774	−	0.109328i	−0.000804623	−	0.00456324i
$575$	−4.60012	+	1.67431i	−0.191838	+	0.0698235i
$576$	2.20361	+	1.84905i	0.0918172	+	0.0770438i
$577$	35.9633	+	30.1768i	1.49717	+	1.25628i	0.885034	+	0.465525i	$0.154135\pi$
$577$	35.9633	+	30.1768i	1.49717	+	1.25628i	0.612138	+	0.790751i	$0.290310\pi$
$578$	−5.87253	−	10.1715i	−0.244265	−	0.423080i
$579$	14.9083	+	5.42617i	0.619567	+	0.225504i
$580$	0.00945031	−	0.0535954i	0.000392403	−	0.00222543i
$581$	0.180634	−	0.312868i	0.00749397	−	0.0129799i
$582$	−7.31097	−	12.6630i	−0.303050	−	0.524897i
$583$	6.83347	−	2.48718i	0.283014	−	0.103009i
$584$	0.383842	−	0.664834i	0.0158835	−	0.0275110i
$585$	6.94299	−	5.82586i	0.287057	−	0.240870i
$586$	−12.6220			−0.521410
$587$	27.6369	−	23.1901i	1.14070	−	0.957158i	0.141235	−	0.989976i	$-0.454893\pi$
$587$	27.6369	−	23.1901i	1.14070	−	0.957158i	0.999461	+	0.0328177i	$0.0104481\pi$
$588$	−15.0506	−	5.47798i	−0.620677	−	0.225908i
$589$	−2.34891	−	13.3213i	−0.0967852	−	0.548896i
$590$	−1.95516	+	11.0882i	−0.0804925	+	0.456496i
$591$	33.9432			1.39624
$592$	3.07093	−	5.25065i	0.126215	−	0.215801i
$593$	13.4004			0.550288			0.275144	−	0.961403i	$-0.411274\pi$
$593$	13.4004			0.550288			0.275144	+	0.961403i	$0.411274\pi$
$594$	0.114497	−	0.649345i	0.00469787	−	0.0266429i
$595$	0.249541	+	1.41522i	0.0102302	+	0.0580183i
$596$	−12.6884	−	4.61819i	−0.519736	−	0.189168i
$597$	−35.9772	+	30.1884i	−1.47245	+	1.23553i
$598$	−15.4239			−0.630731
$599$	32.8297	−	27.5474i	1.34139	−	1.12556i	0.360119	−	0.932907i	$-0.382736\pi$
$599$	32.8297	−	27.5474i	1.34139	−	1.12556i	0.981268	−	0.192650i	$-0.0617082\pi$
$600$	−1.21209	+	2.09940i	−0.0494832	+	0.0857075i
$601$	−10.9451	+	3.98368i	−0.446459	+	0.162498i	−0.555459	−	0.831544i	$-0.687457\pi$
$601$	−10.9451	+	3.98368i	−0.446459	+	0.162498i	0.109000	+	0.994042i	$0.465235\pi$
$602$	0.940203	+	1.62848i	0.0383198	+	0.0663719i
$603$	−10.9043	+	18.8868i	−0.444056	+	0.769128i
$604$	2.02519	−	11.4854i	0.0824037	−	0.467334i
$605$	5.77024	+	2.10020i	0.234594	+	0.0853851i
$606$	1.75332	+	3.03684i	0.0712237	+	0.123363i
$607$	25.3313	+	21.2554i	1.02816	+	0.862732i	0.990631	−	0.136563i	$-0.0436058\pi$
$607$	25.3313	+	21.2554i	1.02816	+	0.862732i	0.0375326	+	0.999295i	$0.488050\pi$
$608$	1.95712	+	1.64222i	0.0793718	+	0.0666008i
$609$	0.0777166	−	0.0282865i	0.00314924	−	0.00114623i
$610$	0.492257	+	2.79173i	0.0199309	+	0.113034i
$611$	−2.18160	−	12.3725i	−0.0882582	−	0.500537i
$612$	−6.19656	+	2.25536i	−0.250481	+	0.0911677i
$613$	36.9533	+	31.0075i	1.49253	+	1.25238i	0.891389	+	0.453238i	$0.149731\pi$
$613$	36.9533	+	31.0075i	1.49253	+	1.25238i	0.601141	+	0.799143i	$0.294713\pi$
$614$	−13.8907	−	11.6556i	−0.560581	−	0.470384i
$615$	0.214646	+	0.371778i	0.00865537	+	0.0149915i
$616$	−1.29858	−	0.472643i	−0.0523211	−	0.0190433i
$617$	6.46089	−	36.6415i	0.260106	−	1.47513i	−0.522514	−	0.852631i	$-0.675006\pi$
$617$	6.46089	−	36.6415i	0.260106	−	1.47513i	0.782619	−	0.622501i	$-0.213883\pi$
$618$	13.6127	−	23.5779i	0.547584	−	0.948444i
$619$	−10.4957	−	18.1790i	−0.421856	−	0.730676i	0.574265	−	0.818670i	$-0.305288\pi$
$619$	−10.4957	−	18.1790i	−0.421856	−	0.730676i	−0.996121	+	0.0879932i	$0.971955\pi$
$620$	−4.97529	+	1.81086i	−0.199812	+	0.0727258i
$621$	−0.732124	+	1.26808i	−0.0293791	+	0.0508861i
$622$	18.6662	−	15.6628i	0.748446	−	0.628020i
$623$	−3.69931			−0.148210
$624$	−5.85098	+	4.90955i	−0.234227	+	0.196539i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	0.134843	+	0.764730i	0.00538939	+	0.0305648i
$627$	−2.37078	+	13.4453i	−0.0946797	+	0.536955i
$628$	−24.7551			−0.987835
$629$	6.90399	+	12.1148i	0.275280	+	0.483047i
$630$	−1.80331			−0.0718455
$631$	−1.69153	+	9.59315i	−0.0673388	+	0.381897i	0.932449	+	0.361301i	$0.117667\pi$
$631$	−1.69153	+	9.59315i	−0.0673388	+	0.381897i	−0.999788	+	0.0205959i	$0.993444\pi$
$632$	−2.05696	−	11.6656i	−0.0818217	−	0.464034i
$633$	59.2890	+	21.5794i	2.35653	+	0.857705i
$634$	11.0117	−	9.23989i	0.437329	−	0.366963i
$635$	9.39680			0.372900
$636$	−6.12604	+	5.14036i	−0.242913	+	0.203829i
$637$	10.4085	−	18.0280i	0.412398	−	0.714294i
$638$	−0.112734	+	0.0410318i	−0.00446318	+	0.00162446i
$639$	−18.5993	−	32.2149i	−0.735777	−	1.27440i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	3.30527	−	18.7451i	0.130550	−	0.740387i	−0.847305	−	0.531106i	$-0.821776\pi$
$641$	3.30527	−	18.7451i	0.130550	−	0.740387i	0.977856	−	0.209281i	$-0.0671124\pi$
$642$	11.4842	+	4.17990i	0.453245	+	0.164968i
$643$	4.91017	+	8.50466i	0.193638	+	0.335391i	0.946453	−	0.322841i	$-0.104638\pi$
$643$	4.91017	+	8.50466i	0.193638	+	0.335391i	−0.752815	+	0.658232i	$0.771305\pi$
$644$	2.35086	+	1.97260i	0.0926367	+	0.0777314i
$645$	−5.57033	−	4.67406i	−0.219331	−	0.184041i
$646$	−5.50343	+	2.00308i	−0.216529	+	0.0788103i
$647$	−2.55913	−	14.5136i	−0.100610	−	0.570587i	−0.992883	−	0.119091i	$-0.962002\pi$
$647$	−2.55913	−	14.5136i	−0.100610	−	0.570587i	0.892273	−	0.451495i	$-0.149109\pi$
$648$	1.62447	+	9.21281i	0.0638151	+	0.361913i
$649$	23.3233	−	8.48899i	0.915520	−	0.333222i
$650$	−2.41360	−	2.02525i	−0.0946691	−	0.0794368i
$651$	−6.16366	−	5.17192i	−0.241573	−	0.202704i
$652$	11.8516	+	20.5276i	0.464145	+	0.803923i
$653$	−30.8993	−	11.2464i	−1.20918	−	0.440107i	−0.342763	−	0.939422i	$-0.611363\pi$
$653$	−30.8993	−	11.2464i	−1.20918	−	0.440107i	−0.866421	+	0.499315i	$0.833585\pi$
$654$	3.32214	−	18.8408i	0.129906	−	0.736734i
$655$	−7.38371	+	12.7890i	−0.288506	+	0.499706i
$656$	−0.0885441	−	0.153363i	−0.00345707	−	0.00598782i
$657$	−2.07515	+	0.755294i	−0.0809594	+	0.0294668i
$658$	−1.24984	+	2.16478i	−0.0487237	+	0.0843919i
$659$	2.41783	−	2.02880i	0.0941851	−	0.0790307i	−0.594479	−	0.804111i	$-0.702642\pi$
$659$	2.41783	−	2.02880i	0.0941851	−	0.0790307i	0.688664	+	0.725080i	$0.258197\pi$
$660$	5.34388			0.208010
$661$	14.8860	−	12.4908i	0.578997	−	0.485837i	−0.305620	−	0.952153i	$-0.598864\pi$
$661$	14.8860	−	12.4908i	0.578997	−	0.485837i	0.884618	+	0.466317i	$0.154419\pi$
$662$	10.2708	+	3.73825i	0.399184	+	0.145291i
$663$	−3.04038	−	17.2429i	−0.118079	−	0.669657i
$664$	0.100072	−	0.567535i	0.00388354	−	0.0220246i
$665$	−1.60159			−0.0621072
$666$	−16.4759	+	5.89210i	−0.638427	+	0.228314i
$667$	0.266416			0.0103156
$668$	−2.92570	+	16.5925i	−0.113199	+	0.641983i
$669$	5.60591	+	31.7927i	0.216737	+	1.22918i
$670$	7.12412	+	2.59297i	0.275229	+	0.100175i
$671$	4.78706	−	4.01682i	0.184802	−	0.155068i
$672$	1.51968			0.0586229
$673$	13.0373	−	10.9396i	0.502551	−	0.421691i	−0.355948	−	0.934506i	$-0.615842\pi$
$673$	13.0373	−	10.9396i	0.502551	−	0.421691i	0.858499	+	0.512815i	$0.171397\pi$
$674$	−8.83179	+	15.2971i	−0.340188	+	0.589223i
$675$	−0.281071	+	0.102302i	−0.0108184	+	0.00393759i
$676$	1.53646	+	2.66122i	0.0590945	+	0.102355i
$677$	−22.0633	+	38.2147i	−0.847960	+	1.46871i	0.0350652	+	0.999385i	$0.488836\pi$
$677$	−22.0633	+	38.2147i	−0.847960	+	1.46871i	−0.883025	+	0.469325i	$0.844497\pi$
$678$	−5.77547	+	32.7543i	−0.221806	+	1.25792i
$679$	−3.55317	−	1.29325i	−0.136358	−	0.0496303i
$680$	1.14618	+	1.98525i	0.0439541	+	0.0761307i
$681$	23.0164	+	19.3131i	0.881990	+	0.740078i
$682$	8.94086	+	7.50227i	0.342363	+	0.287277i
$683$	6.65458	−	2.42207i	0.254630	−	0.0926779i	−0.211551	−	0.977367i	$-0.567852\pi$
$683$	6.65458	−	2.42207i	0.254630	−	0.0926779i	0.466182	+	0.884689i	$0.345629\pi$
$684$	−1.27619	−	7.23764i	−0.0487964	−	0.276738i
$685$	1.28374	+	7.28048i	0.0490493	+	0.278173i
$686$	−8.01562	+	2.91745i	−0.306038	+	0.111389i
$687$	−32.1410	−	26.9695i	−1.22626	−	1.02895i
$688$	2.29783	+	1.92811i	0.0876038	+	0.0735083i
$689$	−5.19689	−	9.00128i	−0.197986	−	0.342921i
$690$	−11.1515	−	4.05881i	−0.424530	−	0.154516i
$691$	2.35585	−	13.3607i	0.0896209	−	0.508266i	−0.906643	−	0.421900i	$-0.861363\pi$
$691$	2.35585	−	13.3607i	0.0896209	−	0.508266i	0.996263	−	0.0863660i	$-0.0275254\pi$
$692$	1.05598	−	1.82902i	0.0401424	−	0.0695287i
$693$	1.98762	+	3.44266i	0.0755034	+	0.130776i
$694$	−17.2544	+	6.28009i	−0.654968	+	0.238389i
$695$	8.79512	−	15.2336i	0.333618	−	0.577843i
$696$	0.101063	−	0.0848022i	0.00383079	−	0.00321442i
$697$	0.405951			0.0153765
$698$	22.1878	−	18.6178i	0.839822	−	0.704694i
$699$	50.7486	+	18.4710i	1.91949	+	0.698637i
$700$	0.108858	+	0.617362i	0.00411443	+	0.0233341i
$701$	−0.587511	+	3.33194i	−0.0221900	+	0.125846i	−0.993891	−	0.110371i	$-0.964796\pi$
$701$	−0.587511	+	3.33194i	−0.0221900	+	0.125846i	0.971701	+	0.236216i	$0.0759073\pi$
$702$	−0.942414			−0.0355691
$703$	−14.6329	+	5.23302i	−0.551891	+	0.197367i
$704$	−2.20441			−0.0830820
$705$	1.67853	−	9.51940i	0.0632170	−	0.358521i
$706$	2.57078	+	14.5796i	0.0967528	+	0.548712i
$707$	0.852121	+	0.310147i	0.0320473	+	0.0116643i
$708$	−20.9088	+	17.5446i	−0.785801	+	0.659365i
$709$	−26.4033			−0.991597			−0.495798	−	0.868438i	$-0.665124\pi$
$709$	−26.4033			−0.991597			−0.495798	+	0.868438i	$0.665124\pi$
$710$	−9.90602	+	8.31214i	−0.371766	+	0.311949i
$711$	−17.0376	+	29.5100i	−0.638959	+	1.10671i
$712$	−5.54521	+	2.01829i	−0.207815	+	0.0756386i
$713$	−12.9594	−	22.4464i	−0.485335	−	0.840624i
$714$	−1.74183	+	3.01694i	−0.0651863	+	0.112906i
$715$	−1.20607	+	6.83999i	−0.0451046	+	0.255801i
$716$	−24.4277	−	8.89097i	−0.912907	−	0.332271i
$717$	16.7671	+	29.0414i	0.626177	+	1.08457i
$718$	2.32397	+	1.95004i	0.0867299	+	0.0727750i
$719$	11.1383	+	9.34616i	0.415389	+	0.348553i	0.826406	−	0.563075i	$-0.190382\pi$
$719$	11.1383	+	9.34616i	0.415389	+	0.348553i	−0.411017	+	0.911628i	$0.634826\pi$
$720$	−2.70313	+	0.983860i	−0.100740	+	0.0366663i
$721$	−1.22256	−	6.93349i	−0.0455305	−	0.258217i
$722$	2.16588	+	12.2833i	0.0806056	+	0.457137i
$723$	−44.7110	+	16.2735i	−1.66282	+	0.605218i
$724$	8.49998	+	7.13233i	0.315899	+	0.265071i
$725$	0.0416898	+	0.0349819i	0.00154832	+	0.00129920i
$726$	7.44289	+	12.8915i	0.276232	+	0.478447i
$727$	−6.61159	−	2.40642i	−0.245210	−	0.0892492i	0.216491	−	0.976285i	$-0.430539\pi$
$727$	−6.61159	−	2.40642i	−0.245210	−	0.0892492i	−0.461702	+	0.887035i	$0.652761\pi$
$728$	−0.342981	+	1.94514i	−0.0127117	+	0.0720917i
$729$	12.3676	−	21.4214i	0.458060	−	0.793384i
$730$	0.383842	+	0.664834i	0.0142066	+	0.0246066i
$731$	−6.46149	+	2.35179i	−0.238987	+	0.0869841i
$732$	−3.43602	+	5.95136i	−0.126999	+	0.219969i
$733$	18.9531	−	15.9036i	0.700049	−	0.587411i	−0.221738	−	0.975106i	$-0.571173\pi$
$733$	18.9531	−	15.9036i	0.700049	−	0.587411i	0.921788	+	0.387695i	$0.126729\pi$
$734$	20.1079			0.742197
$735$	12.2694	−	10.2952i	0.452563	−	0.379745i
$736$	4.60012	+	1.67431i	0.169563	+	0.0617158i
$737$	−2.90207	−	16.4585i	−0.106899	−	0.606256i
$738$	−0.0884589	+	0.501675i	−0.00325622	+	0.0184669i
$739$	−40.4501			−1.48798			−0.743991	−	0.668190i	$-0.767069\pi$
$739$	−40.4501			−1.48798			−0.743991	+	0.668190i	$0.767069\pi$
$740$	3.01173	+	5.28483i	0.110713	+	0.194274i
$741$	19.5136			0.716852
$742$	−0.359105	+	2.03658i	−0.0131832	+	0.0747654i
$743$	7.72748	+	43.8247i	0.283494	+	1.60777i	0.710617	+	0.703579i	$0.248416\pi$
$743$	7.72748	+	43.8247i	0.283494	+	1.60777i	−0.427124	+	0.904193i	$0.640473\pi$
$744$	−12.0610	−	4.38983i	−0.442176	−	0.160939i
$745$	10.3436	−	8.67935i	0.378962	−	0.317987i
$746$	−12.9260			−0.473253
$747$	−1.26992	+	1.06559i	−0.0464640	+	0.0389879i
$748$	2.52666	−	4.37630i	0.0923838	−	0.160013i
$749$	2.96979	−	1.08091i	0.108514	−	0.0394957i
$750$	−1.21209	−	2.09940i	−0.0442591	−	0.0766591i
$751$	6.01741	−	10.4225i	0.219578	−	0.380321i	−0.735101	−	0.677958i	$-0.762865\pi$
$751$	6.01741	−	10.4225i	0.219578	−	0.380321i	0.954679	+	0.297637i	$0.0961985\pi$
$752$	−0.692412	+	3.92686i	−0.0252497	+	0.143198i
$753$	−5.36317	−	1.95204i	−0.195445	−	0.0711361i
$754$	0.0857347	+	0.148497i	0.00312228	+	0.00540794i
$755$	8.93406	+	7.49657i	0.325144	+	0.272828i
$756$	0.143639	+	0.120528i	0.00522411	+	0.00438355i
$757$	36.2464	−	13.1926i	1.31740	−	0.479494i	0.414775	−	0.909924i	$-0.363860\pi$
$757$	36.2464	−	13.1926i	1.31740	−	0.479494i	0.902624	+	0.430430i	$0.141638\pi$
$758$	0.300541	+	1.70445i	0.0109161	+	0.0619084i
$759$	4.54266	+	25.7627i	0.164888	+	0.935127i
$760$	−2.40077	+	0.873807i	−0.0870849	+	0.0316963i
$761$	32.6847	+	27.4257i	1.18482	+	0.994182i	0.999935	+	0.0114218i	$0.00363576\pi$
$761$	32.6847	+	27.4257i	1.18482	+	0.994182i	0.184885	+	0.982760i	$0.440809\pi$
$762$	17.4501	+	14.6424i	0.632150	+	0.530436i
$763$	−2.47368	−	4.28454i	−0.0895532	−	0.155111i
$764$	−16.6299	−	6.05280i	−0.601650	−	0.218983i
$765$	1.14508	−	6.49406i	0.0414004	−	0.234793i
$766$	−3.80809	+	6.59580i	−0.137592	+	0.238316i
$767$	−17.7375	−	30.7222i	−0.640464	−	1.10932i
$768$	2.27798	−	0.829116i	0.0821994	−	0.0299181i
$769$	−19.4966	+	33.7692i	−0.703067	+	1.21775i	0.264318	+	0.964436i	$0.414853\pi$
$769$	−19.4966	+	33.7692i	−0.703067	+	1.21775i	−0.967385	+	0.253312i	$0.918480\pi$
$770$	1.05861	−	0.888278i	0.0381496	−	0.0320113i
$771$	25.9518			0.934632
$772$	5.01340	−	4.20674i	0.180436	−	0.151404i
$773$	−35.1045	−	12.7770i	−1.26262	−	0.459556i	−0.377972	−	0.925817i	$-0.623379\pi$
$773$	−35.1045	−	12.7770i	−1.26262	−	0.459556i	−0.884647	+	0.466261i	$0.845601\pi$
$774$	−1.49836	−	8.49760i	−0.0538573	−	0.305440i
$775$	0.919396	−	5.21415i	0.0330257	−	0.187298i
$776$	−6.03173			−0.216526
$777$	−4.66684	+	7.97931i	−0.167422	+	0.286256i
$778$	9.21145			0.330247
$779$	−0.0785641	+	0.445559i	−0.00281485	+	0.0159638i
$780$	−1.32631	−	7.52187i	−0.0474895	−	0.269326i
$781$	26.7870	+	9.74967i	0.958514	+	0.348871i
$782$	−8.59649	+	7.21331i	−0.307410	+	0.257947i
$783$	0.0162782			0.000581736
$784$	−5.06127	+	4.24691i	−0.180760	+	0.151675i
$785$	12.3775	−	21.4385i	0.441773	−	0.765173i
$786$	−33.6399	+	12.2439i	−1.19989	+	0.436726i
$787$	3.41283	+	5.91120i	0.121654	+	0.210711i	0.920420	−	0.390931i	$-0.127847\pi$
$787$	3.41283	+	5.91120i	0.121654	+	0.210711i	−0.798766	+	0.601642i	$0.794513\pi$
$788$	7.00098	−	12.1261i	0.249400	−	0.431973i
$789$	−5.10077	+	28.9279i	−0.181592	+	1.02986i
$790$	11.1312	+	4.05143i	0.396031	+	0.144143i
$791$	4.30043	+	7.44857i	0.152906	+	0.264841i
$792$	4.85768	+	4.07607i	0.172610	+	0.144837i
$793$	−6.84206	−	5.74117i	−0.242969	−	0.203875i
$794$	−7.15641	+	2.60472i	−0.253971	+	0.0924380i
$795$	−1.38866	−	7.87549i	−0.0492507	−	0.279315i
$796$	3.36418	+	19.0792i	0.119240	+	0.676245i
$797$	−33.3580	+	12.1413i	−1.18160	+	0.430068i	−0.856767	−	0.515703i	$-0.827531\pi$
$797$	−33.3580	+	12.1413i	−1.18160	+	0.430068i	−0.324835	+	0.945771i	$0.605309\pi$
$798$	−2.97420	−	2.49565i	−0.105285	−	0.0883450i
$799$	−7.00216	−	5.87551i	−0.247719	−	0.207861i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	15.9514	+	5.80584i	0.563616	+	0.205139i
$802$	2.73819	−	15.5291i	0.0966889	−	0.548350i
$803$	0.846147	−	1.46557i	0.0298599	−	0.0517188i
$804$	9.18922	+	15.9162i	0.324079	+	0.561321i
$805$	−2.88375	+	1.04960i	−0.101639	+	0.0369935i
$806$	8.34091	−	14.4469i	0.293796	−	0.508870i
$807$	−31.9342	+	26.7960i	−1.12414	+	0.943264i
$808$	1.44653			0.0508887
$809$	−0.976340	+	0.819247i	−0.0343263	+	0.0288032i	−0.659789	−	0.751451i	$-0.729355\pi$
$809$	−0.976340	+	0.819247i	−0.0343263	+	0.0288032i	0.625463	+	0.780254i	$0.284910\pi$
$810$	−8.79076	−	3.19958i	−0.308876	−	0.112422i
$811$	−2.22559	−	12.6220i	−0.0781511	−	0.443217i	−0.998625	−	0.0524139i	$-0.983309\pi$
$811$	−2.22559	−	12.6220i	−0.0781511	−	0.443217i	0.920474	−	0.390803i	$-0.127803\pi$
$812$	0.00592427	−	0.0335982i	0.000207901	−	0.00117907i
$813$	−15.4866			−0.543139
$814$	6.76961	−	11.5746i	0.237275	−	0.405690i
$815$	−23.7032			−0.830288
$816$	−0.964978	+	5.47266i	−0.0337810	+	0.191581i
$817$	−1.33075	−	7.54708i	−0.0465572	−	0.264039i
$818$	−34.1244	−	12.4203i	−1.19313	−	0.434265i
$819$	4.35246	−	3.65215i	0.152087	−	0.127616i
$820$	0.177088			0.00618419
$821$	24.6092	−	20.6496i	0.858867	−	0.720675i	−0.102857	−	0.994696i	$-0.532798\pi$
$821$	24.6092	−	20.6496i	0.858867	−	0.720675i	0.961724	+	0.274021i	$0.0883539\pi$
$822$	−8.96070	+	15.5204i	−0.312540	+	0.541336i
$823$	−11.6585	+	4.24335i	−0.406390	+	0.147914i	−0.537123	−	0.843504i	$-0.680489\pi$
$823$	−11.6585	+	4.24335i	−0.406390	+	0.147914i	0.130733	+	0.991418i	$0.458267\pi$
$824$	−5.61541	−	9.72618i	−0.195622	−	0.338828i
$825$	−2.67194	+	4.62794i	−0.0930250	+	0.161124i
$826$	−1.22566	+	6.95107i	−0.0426462	+	0.241858i
$827$	47.2617	+	17.2019i	1.64345	+	0.598167i	0.987637	−	0.156756i	$-0.0501036\pi$
$827$	47.2617	+	17.2019i	1.64345	+	0.598167i	0.655813	+	0.754923i	$0.272326\pi$
$828$	−7.04101	−	12.1954i	−0.244692	−	0.423819i
$829$	3.37343	+	2.83064i	0.117164	+	0.0983123i	0.699487	−	0.714645i	$-0.253412\pi$
$829$	3.37343	+	2.83064i	0.117164	+	0.0983123i	−0.582323	+	0.812957i	$0.697856\pi$
$830$	0.441464	+	0.370432i	0.0153234	+	0.0128579i
$831$	46.2811	−	16.8449i	1.60547	−	0.584345i
$832$	0.547118	+	3.10286i	0.0189679	+	0.107572i
$833$	−2.63002	−	14.9156i	−0.0911248	−	0.516794i
$834$	40.0702	−	14.5843i	1.38752	−	0.505015i
$835$	−12.9067	−	10.8300i	−0.446654	−	0.374787i
$836$	4.31431	+	3.62013i	0.149213	+	0.125205i
$837$	−0.791832	−	1.37149i	−0.0273697	−	0.0474058i
$838$	−4.47056	−	1.62715i	−0.154433	−	0.0562090i
$839$	−1.92636	+	10.9250i	−0.0665055	+	0.377171i	0.933330	+	0.359020i	$0.116889\pi$
$839$	−1.92636	+	10.9250i	−0.0665055	+	0.377171i	−0.999835	+	0.0181511i	$0.994222\pi$
$840$	−0.759840	+	1.31608i	−0.0262170	+	0.0454091i
$841$	14.4985	+	25.1122i	0.499949	+	0.865937i
$842$	−25.2199	+	9.17930i	−0.869136	+	0.316340i
$843$	−7.31754	+	12.6743i	−0.252029	+	0.436528i
$844$	19.9379	−	16.7299i	0.686289	−	0.575865i
$845$	−3.07291			−0.105711
$846$	8.78678	−	7.37299i	0.302096	−	0.253488i
$847$	3.61728	+	1.31658i	0.124291	+	0.0452383i
$848$	0.572839	+	3.24873i	0.0196714	+	0.111562i
$849$	−1.43316	+	8.12786i	−0.0491860	+	0.278948i
$850$	−2.29236			−0.0786274
$851$	−22.9179	+	19.0120i	−0.785615	+	0.651722i
$852$	−31.3479			−1.07396
$853$	7.64178	−	43.3387i	0.261649	−	1.48389i	−0.516760	−	0.856131i	$-0.672862\pi$
$853$	7.64178	−	43.3387i	0.261649	−	1.48389i	0.778409	−	0.627757i	$-0.216027\pi$
$854$	0.308589	+	1.75010i	0.0105597	+	0.0598871i
$855$	6.90608	+	2.51361i	0.236183	+	0.0859635i
$856$	3.86193	−	3.24055i	0.131998	−	0.110760i
$857$	−26.9038			−0.919015			−0.459508	−	0.888174i	$-0.651974\pi$
$857$	−26.9038			−0.919015			−0.459508	+	0.888174i	$0.651974\pi$
$858$	−12.8980	+	10.8227i	−0.440330	+	0.369480i
$859$	−11.5471	+	20.0001i	−0.393981	+	0.682396i	−0.992971	−	0.118361i	$-0.962236\pi$
$859$	−11.5471	+	20.0001i	−0.393981	+	0.682396i	0.598989	+	0.800757i	$0.295569\pi$
$860$	−2.81870	+	1.02592i	−0.0961169	+	0.0349837i
$861$	0.134559	+	0.233062i	0.00458575	+	0.00794275i
$862$	1.20419	−	2.08572i	0.0410150	−	0.0710400i
$863$	−1.51899	+	8.61460i	−0.0517069	+	0.293244i	−0.999685	−	0.0250906i	$-0.992013\pi$
$863$	−1.51899	+	8.61460i	−0.0517069	+	0.293244i	0.947978	+	0.318335i	$0.103124\pi$
$864$	0.281071	+	0.102302i	0.00956224	+	0.00348037i
$865$	1.05598	+	1.82902i	0.0359045	+	0.0621884i
$866$	0.908510	+	0.762330i	0.0308724	+	0.0259050i
$867$	21.8109	+	18.3015i	0.740736	+	0.621551i
$868$	−3.11894	+	1.13520i	−0.105864	+	0.0385312i
$869$	−4.53440	−	25.7159i	−0.153819	−	0.872351i
$870$	0.0229092	+	0.129924i	0.000776694	+	0.00440485i
$871$	−22.4462	+	8.16973i	−0.760559	+	0.276821i
$872$	−6.04559	−	5.07285i	−0.204730	−	0.171788i
$873$	13.2916	+	11.1530i	0.449852	+	0.377471i
$874$	−6.25342	−	10.8312i	−0.211525	−	0.366372i
$875$	−0.589080	−	0.214408i	−0.0199145	−	0.00724830i
$876$	−0.323159	+	1.83273i	−0.0109185	+	0.0619221i
$877$	−20.8920	+	36.1860i	−0.705473	+	1.22192i	0.261047	+	0.965326i	$0.415932\pi$
$877$	−20.8920	+	36.1860i	−0.705473	+	1.22192i	−0.966521	+	0.256589i	$0.917401\pi$
$878$	−11.6617	−	20.1987i	−0.393565	−	0.681674i
$879$	28.7526	−	10.4651i	0.969802	−	0.352979i
$880$	1.10221	−	1.90908i	0.0371554	−	0.0643550i
$881$	16.1265	−	13.5317i	0.543315	−	0.455895i	−0.329355	−	0.944206i	$-0.606831\pi$
$881$	16.1265	−	13.5317i	0.543315	−	0.455895i	0.872670	+	0.488311i	$0.162387\pi$
$882$	19.0058			0.639959
$883$	−34.3680	+	28.8381i	−1.15657	+	0.970481i	−0.999853	−	0.0171618i	$-0.994537\pi$
$883$	−34.3680	+	28.8381i	−1.15657	+	0.970481i	−0.156722	+	0.987643i	$0.550093\pi$
$884$	−6.78704	−	2.47028i	−0.228273	−	0.0830845i
$885$	−4.73964	−	26.8798i	−0.159321	−	0.903555i
$886$	−1.21633	+	6.89814i	−0.0408633	+	0.231747i
$887$	−41.2400			−1.38470			−0.692352	−	0.721560i	$-0.743425\pi$
$887$	−41.2400			−1.38470			−0.692352	+	0.721560i	$0.743425\pi$
$888$	−2.64212	+	14.5070i	−0.0886636	+	0.486824i
$889$	5.89072			0.197568
$890$	1.02471	−	5.81144i	0.0343485	−	0.194800i
$891$	3.58100	+	20.3088i	0.119968	+	0.680372i
$892$	12.5140	+	4.55474i	0.419001	+	0.152504i
$893$	7.80391	−	6.54826i	0.261148	−	0.219129i
$894$	32.7328			1.09475
$895$	19.9137	−	16.7095i	0.665640	−	0.558539i
$896$	0.313443	−	0.542899i	0.0104714	−	0.0181370i
$897$	35.1353	−	12.7882i	1.17313	−	0.426986i
$898$	−16.2907	−	28.2163i	−0.543627	−	0.941589i
$899$	−0.144072	+	0.249539i	−0.00480506	+	0.00832260i
$900$	0.499519	−	2.83291i	0.0166506	−	0.0944304i
$901$	−7.10611	−	2.58641i	−0.236739	−	0.0861659i
$902$	−0.195188	−	0.338075i	−0.00649904	−	0.0112567i
$903$	−3.49196	−	2.93010i	−0.116205	−	0.0975077i
$904$	10.5101	+	8.81904i	0.349561	+	0.293317i
$905$	−10.4268	+	3.79503i	−0.346597	+	0.126151i
$906$	4.90940	+	27.8426i	0.163104	+	0.925009i
$907$	5.18492	+	29.4052i	0.172163	+	0.976383i	0.941368	+	0.337381i	$0.109541\pi$
$907$	5.18492	+	29.4052i	0.172163	+	0.976383i	−0.769206	+	0.639001i	$0.779348\pi$
$908$	11.6468	−	4.23908i	0.386512	−	0.140679i
$909$	−3.18759	−	2.67471i	−0.105726	−	0.0887144i
$910$	−1.51305	−	1.26960i	−0.0501571	−	0.0420868i
$911$	−2.99046	−	5.17964i	−0.0990785	−	0.171609i	0.812225	−	0.583344i	$-0.198256\pi$
$911$	−2.99046	−	5.17964i	−0.0990785	−	0.171609i	−0.911303	+	0.411735i	$0.864923\pi$
$912$	−5.81987	−	2.11826i	−0.192715	−	0.0701426i
$913$	0.220600	−	1.25108i	0.00730078	−	0.0414048i
$914$	−14.0105	+	24.2669i	−0.463427	+	0.802678i
$915$	−3.43602	−	5.95136i	−0.113591	−	0.196746i
$916$	−16.2640	+	5.91962i	−0.537379	+	0.195590i
$917$	−4.62875	+	8.01722i	−0.152855	+	0.264752i
$918$	−0.525253	+	0.440739i	−0.0173359	+	0.0145466i
$919$	−11.3787			−0.375350			−0.187675	−	0.982231i	$-0.560095\pi$
$919$	−11.3787			−0.375350			−0.187675	+	0.982231i	$0.560095\pi$
$920$	−3.75005	+	3.14667i	−0.123636	+	0.103743i
$921$	41.3065	+	15.0343i	1.36110	+	0.495398i
$922$	−0.266319	−	1.51037i	−0.00877075	−	0.0497414i
$923$	7.07500	−	40.1243i	0.232876	−	1.32071i
$924$	3.35000			0.110207
$925$	−6.08267	−	0.0341800i	−0.199997	−	0.00112383i
$926$	9.37512			0.308086
$927$	−5.61001	+	31.8159i	−0.184257	+	1.04497i
$928$	−0.00945031	−	0.0535954i	−0.000310222	−	0.00175935i
$929$	9.66551	+	3.51796i	0.317115	+	0.115420i	0.495674	−	0.868509i	$-0.334921\pi$
$929$	9.66551	+	3.51796i	0.317115	+	0.115420i	−0.178559	+	0.983929i	$0.557143\pi$
$930$	9.83218	−	8.25018i	0.322410	−	0.270534i
$931$	16.8799			0.553216
$932$	17.0659	−	14.3200i	0.559012	−	0.469067i
$933$	−29.5349	+	51.1559i	−0.966928	+	1.67477i
$934$	15.7995	−	5.75054i	0.516975	−	0.188163i
$935$	2.52666	+	4.37630i	0.0826306	+	0.143120i
$936$	4.53171	−	7.84916i	0.148124	−	0.256558i
$937$	−2.38594	+	13.5313i	−0.0779451	+	0.442049i	0.920712	+	0.390243i	$0.127609\pi$
$937$	−2.38594	+	13.5313i	−0.0779451	+	0.442049i	−0.998657	+	0.0518061i	$0.983502\pi$
$938$	4.46601	+	1.62549i	0.145820	+	0.0530743i
$939$	−0.941218	−	1.63024i	−0.0307155	−	0.0532008i
$940$	−3.05456	−	2.56308i	−0.0996287	−	0.0835984i
$941$	39.1966	+	32.8899i	1.27777	+	1.07218i	0.993547	+	0.113422i	$0.0361813\pi$
$941$	39.1966	+	32.8899i	1.27777	+	1.07218i	0.284227	+	0.958757i	$0.408263\pi$
$942$	56.3915	−	20.5248i	1.83733	−	0.668735i
$943$	0.150537	+	0.853738i	0.00490216	+	0.0278015i
$944$	1.95516	+	11.0882i	0.0636349	+	0.360892i
$945$	−0.176200	+	0.0641314i	−0.00573178	+	0.00208620i
$946$	5.06536	+	4.25034i	0.164689	+	0.138191i
$947$	13.0490	+	10.9494i	0.424035	+	0.355807i	0.829695	−	0.558216i	$-0.188514\pi$
$947$	13.0490	+	10.9494i	0.424035	+	0.355807i	−0.405661	+	0.914024i	$0.632959\pi$
$948$	14.3579	+	24.8686i	0.466322	+	0.807694i
$949$	−2.27289	−	0.827266i	−0.0737813	−	0.0268542i
$950$	0.443644	−	2.51603i	0.0143937	−	0.0816307i
$951$	−17.4234	+	30.1782i	−0.564992	+	0.978595i
$952$	0.718525	+	1.24452i	0.0232875	+	0.0403352i
$953$	−22.5863	+	8.22073i	−0.731641	+	0.266296i	−0.680859	−	0.732414i	$-0.738394\pi$
$953$	−22.5863	+	8.22073i	−0.731641	+	0.266296i	−0.0507818	+	0.998710i	$0.516171\pi$
$954$	4.74476	−	8.21816i	0.153617	−	0.266073i
$955$	13.5568	−	11.3755i	0.438689	−	0.368104i
$956$	13.8332			0.447398
$957$	0.222785	−	0.186939i	0.00720163	−	0.00604288i
$958$	40.2052	+	14.6335i	1.29897	+	0.472787i
$959$	0.804761	+	4.56403i	0.0259871	+	0.147380i
$960$	−0.420953	+	2.38734i	−0.0135862	+	0.0770512i
$961$	−2.96731			−0.0957196
$962$	−17.9722	−	6.65595i	−0.579447	−	0.214597i
$963$	−14.5021			−0.467325
$964$	−3.40828	+	19.3293i	−0.109773	+	0.622556i
$965$	1.13645	+	6.44510i	0.0365835	+	0.207475i
$966$	−6.99071	−	2.54441i	−0.224922	−	0.0818651i
$967$	−8.37954	+	7.03127i	−0.269468	+	0.226110i	−0.767501	−	0.641047i	$-0.778500\pi$
$967$	−8.37954	+	7.03127i	−0.269468	+	0.226110i	0.498033	+	0.867158i	$0.334056\pi$
$968$	6.14056			0.197365
$969$	10.8759	−	9.12596i	0.349384	−	0.293168i
$970$	3.01586	−	5.22363i	0.0968335	−	0.167721i
$971$	−38.0922	+	13.8644i	−1.22244	+	0.444931i	−0.871001	−	0.491281i	$-0.836529\pi$
$971$	−38.0922	+	13.8644i	−1.22244	+	0.444931i	−0.351436	+	0.936212i	$0.614307\pi$
$972$	−10.8903	−	18.8626i	−0.349307	−	0.605018i
$973$	5.51354	−	9.54972i	0.176756	−	0.306150i
$974$	2.34879	−	13.3207i	0.0752602	−	0.426822i
$975$	7.17729	+	2.61232i	0.229857	+	0.0836612i
$976$	1.41740	+	2.45501i	0.0453698	+	0.0785828i
$977$	−0.950469	−	0.797538i	−0.0304082	−	0.0255155i	0.627457	−	0.778651i	$-0.284096\pi$
$977$	−0.950469	−	0.797538i	−0.0304082	−	0.0255155i	−0.657865	+	0.753136i	$0.728540\pi$
$978$	−44.0175	−	36.9351i	−1.40752	−	1.18105i
$979$	−12.2239	+	4.44915i	−0.390679	+	0.142195i
$980$	−1.14730	−	6.50664i	−0.0366490	−	0.207847i
$981$	3.94218	+	22.3572i	0.125864	+	0.713811i
$982$	−4.41381	+	1.60650i	−0.140850	+	0.0512653i
$983$	9.38233	+	7.87271i	0.299250	+	0.251100i	0.780032	−	0.625740i	$-0.215203\pi$
$983$	9.38233	+	7.87271i	0.299250	+	0.251100i	−0.480782	+	0.876840i	$0.659647\pi$
$984$	0.328857	+	0.275944i	0.0104836	+	0.00879677i
$985$	7.00098	+	12.1261i	0.223070	+	0.386368i
$986$	0.117232	+	0.0426689i	0.00373342	+	0.00135885i
$987$	1.05224	−	5.96758i	0.0334933	−	0.189950i
$988$	4.02481	−	6.97117i	0.128046	−	0.221782i
$989$	−7.34204	−	12.7168i	−0.233463	−	0.404370i
$990$	−5.95882	+	2.16883i	−0.189384	+	0.0689301i
$991$	13.7506	−	23.8168i	0.436803	−	0.756564i	−0.560638	−	0.828061i	$-0.689444\pi$
$991$	13.7506	−	23.8168i	0.436803	−	0.756564i	0.997441	+	0.0714965i	$0.0227775\pi$
$992$	−4.05589	+	3.40330i	−0.128775	+	0.108055i
$993$	−26.4960			−0.840824
$994$	−6.20994	+	5.21076i	−0.196967	+	0.165275i
$995$	−18.2052	−	6.62615i	−0.577143	−	0.210063i
$996$	0.242591	+	1.37580i	0.00768680	+	0.0435940i
$997$	−8.60142	+	48.7811i	−0.272410	+	1.54491i	0.474662	+	0.880168i	$0.342570\pi$
$997$	−8.60142	+	48.7811i	−0.272410	+	1.54491i	−0.747072	+	0.664743i	$0.768541\pi$
$998$	−5.68601			−0.179988
$999$	−1.40030	+	1.16165i	−0.0443036	+	0.0367529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.c.181.1	✓	24
37.9	even	9	inner	370.2.o.c.231.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.c.181.1	✓	24	1.1	even	1	trivial
370.2.o.c.231.1	yes	24	37.9	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.420953 - 2.38734i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.766044 - 0.642788i) q^{5} +2.42417 q^{6} +(0.480222 - 0.402954i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.70313 + 0.983860i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.420953 - 2.38734i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.766044 - 0.642788i) q^{5} +2.42417 q^{6} +(0.480222 - 0.402954i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.70313 + 0.983860i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.10221 - 1.90908i) q^{11} +(-0.420953 + 2.38734i) q^{12} +(-2.96072 - 1.07761i) q^{13} +(0.313443 + 0.542899i) q^{14} +(-1.85702 - 1.55823i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.15412 + 0.784035i) q^{17} +(-0.499519 - 2.83291i) q^{18} +(-0.443644 - 2.51603i) q^{19} +(-0.939693 + 0.342020i) q^{20} +(-1.16414 - 0.976831i) q^{21} +(1.68868 + 1.41697i) q^{22} +(-2.44767 - 4.23950i) q^{23} +(-2.27798 - 0.829116i) q^{24} +(0.173648 - 0.984808i) q^{25} +(1.57536 - 2.72861i) q^{26} +(-0.149555 - 0.259037i) q^{27} +(-0.589080 + 0.214408i) q^{28} +(-0.0272111 + 0.0471310i) q^{29} +(1.85702 - 1.55823i) q^{30} +5.29459 q^{31} +(-0.766044 + 0.642788i) q^{32} +(-5.02160 - 1.82771i) q^{33} +(-0.398065 - 2.25754i) q^{34} +(0.108858 - 0.617362i) q^{35} +2.87661 q^{36} +(-1.02258 - 5.99619i) q^{37} +2.55484 q^{38} +(-1.32631 + 7.52187i) q^{39} +(-0.173648 - 0.984808i) q^{40} +(-0.166409 - 0.0605677i) q^{41} +(1.16414 - 0.976831i) q^{42} +2.99960 q^{43} +(-1.68868 + 1.41697i) q^{44} +(-1.43831 + 2.49122i) q^{45} +(4.60012 - 1.67431i) q^{46} +(1.99372 + 3.45323i) q^{47} +(1.21209 - 2.09940i) q^{48} +(-1.14730 + 6.50664i) q^{49} +(0.939693 + 0.342020i) q^{50} +(2.77854 + 4.81258i) q^{51} +(2.41360 + 2.02525i) q^{52} +(2.52707 + 2.12046i) q^{53} +(0.281071 - 0.102302i) q^{54} +(-0.382792 - 2.17092i) q^{55} +(-0.108858 - 0.617362i) q^{56} +(-5.81987 + 2.11826i) q^{57} +(-0.0416898 - 0.0349819i) q^{58} +(8.62512 + 7.23734i) q^{59} +(1.21209 + 2.09940i) q^{60} +(2.66384 + 0.969558i) q^{61} +(-0.919396 + 5.21415i) q^{62} +(-0.901654 + 1.56171i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.96072 + 1.07761i) q^{65} +(2.67194 - 4.62794i) q^{66} +(5.80763 - 4.87318i) q^{67} +2.29236 q^{68} +(-9.09078 + 7.62807i) q^{69} +(0.589080 + 0.214408i) q^{70} +(2.24551 + 12.7349i) q^{71} +(-0.499519 + 2.83291i) q^{72} +0.767684 q^{73} +(6.08267 + 0.0341800i) q^{74} -2.42417 q^{75} +(-0.443644 + 2.51603i) q^{76} +(-0.239967 - 1.36092i) q^{77} +(-7.17729 - 2.61232i) q^{78} +(9.07425 - 7.61420i) q^{79} +1.00000 q^{80} +(-7.16630 + 6.01324i) q^{81} +(0.0885441 - 0.153363i) q^{82} +(0.541536 - 0.197103i) q^{83} +(0.759840 + 1.31608i) q^{84} +(-1.14618 + 1.98525i) q^{85} +(-0.520875 + 2.95403i) q^{86} +(0.123972 + 0.0451223i) q^{87} +(-1.10221 - 1.90908i) q^{88} +(-4.52050 - 3.79315i) q^{89} +(-2.20361 - 1.84905i) q^{90} +(-1.85603 + 0.675540i) q^{91} +(0.850068 + 4.82098i) q^{92} +(-2.22877 - 12.6400i) q^{93} +(-3.74697 + 1.36379i) q^{94} +(-1.95712 - 1.64222i) q^{95} +(1.85702 + 1.55823i) q^{96} +(-3.01586 - 5.22363i) q^{97} +(-6.20856 - 2.25973i) q^{98} +(-1.10115 + 6.24491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9	\( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31} - 39 q^{33} - 21 q^{34} + 6 q^{35} + 54 q^{36} - 12 q^{37} - 36 q^{38} - 18 q^{39} + 27 q^{41} - 36 q^{42} - 24 q^{43} - 9 q^{44} - 27 q^{45} + 3 q^{46} - 6 q^{47} - 3 q^{48} - 27 q^{49} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 9 q^{54} + 9 q^{55} - 6 q^{56} - 27 q^{57} + 27 q^{58} + 51 q^{59} - 3 q^{60} - 3 q^{62} - 27 q^{63} - 12 q^{64} + 15 q^{66} - 18 q^{69} + 3 q^{70} - 66 q^{71} + 6 q^{72} + 42 q^{73} - 42 q^{74} + 6 q^{75} - 6 q^{76} + 69 q^{77} + 36 q^{78} - 30 q^{79} + 24 q^{80} - 90 q^{81} + 24 q^{82} + 57 q^{83} + 6 q^{84} - 6 q^{86} + 6 q^{87} + 15 q^{88} - 57 q^{89} + 6 q^{90} + 3 q^{91} + 15 q^{92} - 72 q^{93} + 3 q^{94} - 15 q^{95} - 3 q^{97} - 72 q^{98} + 63 q^{99}+O(q^{100}) \) 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more