LMFDB - Embedded newform 190.2.k.d.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(61,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("190.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.k (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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} + \cdots + 64 $ x^18 + 24x^16 - 12x^15 + 393x^14 - 222x^13 + 3518x^12 - 2478x^11 + 22809x^10 - 12862x^9 + 77397x^8 - 24822x^7 + 178501x^6 - 39408x^5 + 132588x^4 + 45584x^3 + 50640x^2 + 1824x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.1
Root			$1.15990 + 2.00901i$ of defining polynomial
Character	$\chi$	$=$	190.161
Dual form			190.2.k.d.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-1.77707 + 1.49114i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(1.77707 + 1.49114i) q^{6} +(2.45837 - 4.25802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.413538 - 2.34529i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.77707 + 1.49114i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(1.77707 + 1.49114i) q^{6} +(2.45837 - 4.25802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.413538 - 2.34529i) q^{9} +(-0.173648 + 0.984808i) q^{10} +(-1.42329 - 2.46520i) q^{11} +(1.15990 - 2.00901i) q^{12} +(-5.02662 - 4.21784i) q^{13} +(-4.62023 - 1.68163i) q^{14} +(2.17990 - 0.793418i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.380503 - 2.15794i) q^{17} -2.38147 q^{18} +(4.17271 + 1.26036i) q^{19} +1.00000 q^{20} +(1.98061 + 11.2326i) q^{21} +(-2.18060 + 1.82974i) q^{22} +(2.49728 - 0.908934i) q^{23} +(-2.17990 - 0.793418i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-3.28089 + 5.68268i) q^{26} +(-0.717435 - 1.24263i) q^{27} +(-0.853783 + 4.84205i) q^{28} +(-1.32004 + 7.48630i) q^{29} +(-1.15990 - 2.00901i) q^{30} +(2.70769 - 4.68986i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(6.20524 + 2.25852i) q^{33} +(-2.05908 + 0.749444i) q^{34} +(-3.76644 + 3.16042i) q^{35} +(0.413538 + 2.34529i) q^{36} -2.06252 q^{37} +(0.516628 - 4.32817i) q^{38} +15.2220 q^{39} +(-0.173648 - 0.984808i) q^{40} +(-7.16810 + 6.01475i) q^{41} +(10.7180 - 3.90103i) q^{42} +(-1.62951 - 0.593093i) q^{43} +(2.18060 + 1.82974i) q^{44} +(-1.19073 + 2.06241i) q^{45} +(-1.32877 - 2.30150i) q^{46} +(-0.521812 + 2.95934i) q^{47} +(-0.402829 + 2.28456i) q^{48} +(-8.58718 - 14.8734i) q^{49} +(0.500000 - 0.866025i) q^{50} +(3.89396 + 3.26742i) q^{51} +(6.16606 + 2.24426i) q^{52} +(3.96752 - 1.44406i) q^{53} +(-1.09917 + 0.922316i) q^{54} +(0.494302 + 2.80333i) q^{55} +4.91674 q^{56} +(-9.29456 + 3.98234i) q^{57} +7.60179 q^{58} +(-0.167500 - 0.949937i) q^{59} +(-1.77707 + 1.49114i) q^{60} +(7.04727 - 2.56500i) q^{61} +(-5.08880 - 1.85217i) q^{62} +(-8.96967 - 7.52644i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.28089 + 5.68268i) q^{65} +(1.14668 - 6.50315i) q^{66} +(0.333326 - 1.89039i) q^{67} +(1.09561 + 1.89766i) q^{68} +(-3.08249 + 5.33902i) q^{69} +(3.76644 + 3.16042i) q^{70} +(5.79354 + 2.10868i) q^{71} +(2.23785 - 0.814510i) q^{72} +(-3.04659 + 2.55639i) q^{73} +(0.358153 + 2.03119i) q^{74} -2.31980 q^{75} +(-4.35213 + 0.242800i) q^{76} -13.9959 q^{77} +(-2.64328 - 14.9908i) q^{78} +(11.7380 - 9.84938i) q^{79} +(-0.939693 + 0.342020i) q^{80} +(9.84141 + 3.58198i) q^{81} +(7.16810 + 6.01475i) q^{82} +(0.656032 - 1.13628i) q^{83} +(-5.70293 - 9.87776i) q^{84} +(-0.380503 + 2.15794i) q^{85} +(-0.301121 + 1.70774i) q^{86} +(-8.81731 - 15.2720i) q^{87} +(1.42329 - 2.46520i) q^{88} +(-8.25512 - 6.92687i) q^{89} +(2.23785 + 0.814510i) q^{90} +(-30.3170 + 11.0345i) q^{91} +(-2.03580 + 1.70824i) q^{92} +(2.18147 + 12.3718i) q^{93} +3.00499 q^{94} +(-3.49000 - 2.61150i) q^{95} +2.31980 q^{96} +(0.356724 + 2.02308i) q^{97} +(-13.1563 + 11.0395i) q^{98} +(-6.37020 + 2.31856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q + 9 * q^8 - 18 * q^9	$ 18 q + 9 q^{8} - 18 q^{9} - 12 q^{11} - 6 q^{13} + 6 q^{14} - 42 q^{18} + 18 q^{20} + 12 q^{21} - 3 q^{22} + 9 q^{23} - 9 q^{26} - 18 q^{27} + 3 q^{28} - 6 q^{29} - 6 q^{31} + 66 q^{33} + 18 q^{34} + 3 q^{35} - 18 q^{36} - 12 q^{37} - 6 q^{38} + 48 q^{39} - 21 q^{41} + 42 q^{42} + 18 q^{43} + 3 q^{44} - 21 q^{45} + 18 q^{46} - 54 q^{47} - 39 q^{49} + 9 q^{50} + 42 q^{51} + 12 q^{52} - 24 q^{53} - 54 q^{54} - 6 q^{55} - 18 q^{57} - 30 q^{59} + 48 q^{61} - 30 q^{62} - 57 q^{63} - 9 q^{64} + 9 q^{65} + 24 q^{66} - 6 q^{67} - 6 q^{68} - 30 q^{69} - 3 q^{70} + 30 q^{71} + 6 q^{73} - 3 q^{74} - 21 q^{76} + 30 q^{77} - 24 q^{78} + 30 q^{79} + 18 q^{81} + 21 q^{82} + 6 q^{83} + 6 q^{84} + 36 q^{86} + 24 q^{87} + 12 q^{88} + 30 q^{89} - 60 q^{91} - 18 q^{92} - 12 q^{93} + 6 q^{94} - 12 q^{95} - 12 q^{97} - 18 q^{98} + 171 q^{99}+O(q^{100}) $ 18 * q + 9 * q^8 - 18 * q^9 - 12 * q^11 - 6 * q^13 + 6 * q^14 - 42 * q^18 + 18 * q^20 + 12 * q^21 - 3 * q^22 + 9 * q^23 - 9 * q^26 - 18 * q^27 + 3 * q^28 - 6 * q^29 - 6 * q^31 + 66 * q^33 + 18 * q^34 + 3 * q^35 - 18 * q^36 - 12 * q^37 - 6 * q^38 + 48 * q^39 - 21 * q^41 + 42 * q^42 + 18 * q^43 + 3 * q^44 - 21 * q^45 + 18 * q^46 - 54 * q^47 - 39 * q^49 + 9 * q^50 + 42 * q^51 + 12 * q^52 - 24 * q^53 - 54 * q^54 - 6 * q^55 - 18 * q^57 - 30 * q^59 + 48 * q^61 - 30 * q^62 - 57 * q^63 - 9 * q^64 + 9 * q^65 + 24 * q^66 - 6 * q^67 - 6 * q^68 - 30 * q^69 - 3 * q^70 + 30 * q^71 + 6 * q^73 - 3 * q^74 - 21 * q^76 + 30 * q^77 - 24 * q^78 + 30 * q^79 + 18 * q^81 + 21 * q^82 + 6 * q^83 + 6 * q^84 + 36 * q^86 + 24 * q^87 + 12 * q^88 + 30 * q^89 - 60 * q^91 - 18 * q^92 - 12 * q^93 + 6 * q^94 - 12 * q^95 - 12 * q^97 - 18 * q^98 + 171 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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
$3$	−1.77707	+	1.49114i	−1.02599	+	0.860909i	−0.990369	−	0.138456i	$-0.955786\pi$
$3$	−1.77707	+	1.49114i	−1.02599	+	0.860909i	−0.0356229	+	0.999365i	$0.511342\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$	1.77707	+	1.49114i	0.725486	+	0.608755i
$7$	2.45837	−	4.25802i	0.929177	−	1.60938i	0.144475	−	0.989508i	$-0.453851\pi$
$7$	2.45837	−	4.25802i	0.929177	−	1.60938i	0.784702	−	0.619873i	$-0.212816\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.413538	−	2.34529i	0.137846	−	0.781763i
$10$	−0.173648	+	0.984808i	−0.0549124	+	0.311424i
$11$	−1.42329	−	2.46520i	−0.429137	−	0.743287i	0.567660	−	0.823263i	$-0.307849\pi$
$11$	−1.42329	−	2.46520i	−0.429137	−	0.743287i	−0.996797	+	0.0799763i	$0.974516\pi$
$12$	1.15990	−	2.00901i	0.334834	−	0.579950i
$13$	−5.02662	−	4.21784i	−1.39413	−	1.16982i	−0.963634	−	0.267227i	$-0.913893\pi$
$13$	−5.02662	−	4.21784i	−1.39413	−	1.16982i	−0.430500	−	0.902590i	$-0.641663\pi$
$14$	−4.62023	−	1.68163i	−1.23481	−	0.449433i
$15$	2.17990	−	0.793418i	0.562847	−	0.204860i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.380503	−	2.15794i	−0.0922855	−	0.523377i	−0.995545	−	0.0942832i	$-0.969944\pi$
$17$	−0.380503	−	2.15794i	−0.0922855	−	0.523377i	0.903260	−	0.429094i	$-0.141167\pi$
$18$	−2.38147			−0.561317
$19$	4.17271	+	1.26036i	0.957285	+	0.289146i
$19$	4.17271	+	1.26036i	0.957285	+	0.289146i
$20$	1.00000			0.223607
$21$	1.98061	+	11.2326i	0.432204	+	2.45115i
$22$	−2.18060	+	1.82974i	−0.464906	+	0.390102i
$23$	2.49728	−	0.908934i	0.520718	−	0.189526i	−0.0682711	−	0.997667i	$-0.521748\pi$
$23$	2.49728	−	0.908934i	0.520718	−	0.189526i	0.588989	+	0.808141i	$0.299526\pi$
$24$	−2.17990	−	0.793418i	−0.444970	−	0.161956i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	−3.28089	+	5.68268i	−0.643436	+	1.11446i
$27$	−0.717435	−	1.24263i	−0.138070	−	0.239145i
$28$	−0.853783	+	4.84205i	−0.161350	+	0.915061i
$29$	−1.32004	+	7.48630i	−0.245125	+	1.39017i	0.575079	+	0.818098i	$0.304971\pi$
$29$	−1.32004	+	7.48630i	−0.245125	+	1.39017i	−0.820203	+	0.572072i	$0.806140\pi$
$30$	−1.15990	−	2.00901i	−0.211768	−	0.366792i
$31$	2.70769	−	4.68986i	0.486316	−	0.842324i	−0.513560	−	0.858054i	$-0.671674\pi$
$31$	2.70769	−	4.68986i	0.486316	−	0.842324i	0.999876	+	0.0157295i	$0.00500705\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	6.20524	+	2.25852i	1.08019	+	0.393158i
$34$	−2.05908	+	0.749444i	−0.353130	+	0.128529i
$35$	−3.76644	+	3.16042i	−0.636645	+	0.534209i
$36$	0.413538	+	2.34529i	0.0689229	+	0.390881i
$37$	−2.06252			−0.339076			−0.169538	−	0.985524i	$-0.554228\pi$
$37$	−2.06252			−0.339076			−0.169538	+	0.985524i	$0.554228\pi$
$38$	0.516628	−	4.32817i	0.0838081	−	0.702123i
$39$	15.2220			2.43748
$40$	−0.173648	−	0.984808i	−0.0274562	−	0.155712i
$41$	−7.16810	+	6.01475i	−1.11947	+	0.939346i	−0.998578	−	0.0533193i	$-0.983020\pi$
$41$	−7.16810	+	6.01475i	−1.11947	+	0.939346i	−0.120892	+	0.992666i	$0.538575\pi$
$42$	10.7180	−	3.90103i	1.65382	−	0.601942i
$43$	−1.62951	−	0.593093i	−0.248498	−	0.0904459i	0.214768	−	0.976665i	$-0.431100\pi$
$43$	−1.62951	−	0.593093i	−0.248498	−	0.0904459i	−0.463266	+	0.886219i	$0.653323\pi$
$44$	2.18060	+	1.82974i	0.328738	+	0.275844i
$45$	−1.19073	+	2.06241i	−0.177504	+	0.307446i
$46$	−1.32877	−	2.30150i	−0.195917	−	0.339338i
$47$	−0.521812	+	2.95934i	−0.0761140	+	0.431664i	0.922809	+	0.385259i	$0.125888\pi$
$47$	−0.521812	+	2.95934i	−0.0761140	+	0.431664i	−0.998923	+	0.0464056i	$0.985223\pi$
$48$	−0.402829	+	2.28456i	−0.0581433	+	0.329747i
$49$	−8.58718	−	14.8734i	−1.22674	−	2.12478i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	3.89396	+	3.26742i	0.545264	+	0.457531i
$52$	6.16606	+	2.24426i	0.855079	+	0.311223i
$53$	3.96752	−	1.44406i	0.544981	−	0.198357i	−0.0548340	−	0.998495i	$-0.517463\pi$
$53$	3.96752	−	1.44406i	0.544981	−	0.198357i	0.599815	+	0.800139i	$0.295241\pi$
$54$	−1.09917	+	0.922316i	−0.149579	+	0.125511i
$55$	0.494302	+	2.80333i	0.0666517	+	0.378000i
$56$	4.91674			0.657027
$57$	−9.29456	+	3.98234i	−1.23109	+	0.527474i
$58$	7.60179			0.998163
$59$	−0.167500	−	0.949937i	−0.0218066	−	0.123671i	0.971961	−	0.235141i	$-0.0755553\pi$
$59$	−0.167500	−	0.949937i	−0.0218066	−	0.123671i	−0.993768	+	0.111470i	$0.964444\pi$
$60$	−1.77707	+	1.49114i	−0.229419	+	0.192505i
$61$	7.04727	−	2.56500i	0.902311	−	0.328414i	0.151132	−	0.988514i	$-0.451708\pi$
$61$	7.04727	−	2.56500i	0.902311	−	0.328414i	0.751178	+	0.660099i	$0.229486\pi$
$62$	−5.08880	−	1.85217i	−0.646278	−	0.235226i
$63$	−8.96967	−	7.52644i	−1.13007	−	0.948243i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	3.28089	+	5.68268i	0.406945	+	0.704849i
$66$	1.14668	−	6.50315i	0.141147	−	0.800483i
$67$	0.333326	−	1.89039i	0.0407223	−	0.230948i	−0.957653	−	0.287924i	$-0.907035\pi$
$67$	0.333326	−	1.89039i	0.0407223	−	0.230948i	0.998376	+	0.0569765i	$0.0181460\pi$
$68$	1.09561	+	1.89766i	0.132863	+	0.230125i
$69$	−3.08249	+	5.33902i	−0.371088	+	0.642743i
$70$	3.76644	+	3.16042i	0.450176	+	0.377743i
$71$	5.79354	+	2.10868i	0.687567	+	0.250254i	0.662093	−	0.749422i	$-0.269668\pi$
$71$	5.79354	+	2.10868i	0.687567	+	0.250254i	0.0254738	+	0.999675i	$0.491891\pi$
$72$	2.23785	−	0.814510i	0.263733	−	0.0959909i
$73$	−3.04659	+	2.55639i	−0.356576	+	0.299203i	−0.803424	−	0.595407i	$-0.796991\pi$
$73$	−3.04659	+	2.55639i	−0.356576	+	0.299203i	0.446848	+	0.894610i	$0.352546\pi$
$74$	0.358153	+	2.03119i	0.0416344	+	0.236121i
$75$	−2.31980			−0.267867
$76$	−4.35213	+	0.242800i	−0.499224	+	0.0278511i
$77$	−13.9959			−1.59498
$78$	−2.64328	−	14.9908i	−0.299292	−	1.69737i
$79$	11.7380	−	9.84938i	1.32063	−	1.10814i	0.334461	−	0.942409i	$-0.391446\pi$
$79$	11.7380	−	9.84938i	1.32063	−	1.10814i	0.986171	−	0.165732i	$-0.0529988\pi$
$80$	−0.939693	+	0.342020i	−0.105061	+	0.0382390i
$81$	9.84141	+	3.58198i	1.09349	+	0.397998i
$82$	7.16810	+	6.01475i	0.791584	+	0.664218i
$83$	0.656032	−	1.13628i	0.0720089	−	0.124723i	−0.827773	−	0.561064i	$-0.810392\pi$
$83$	0.656032	−	1.13628i	0.0720089	−	0.124723i	0.899782	+	0.436340i	$0.143726\pi$
$84$	−5.70293	−	9.87776i	−0.622240	−	1.07775i
$85$	−0.380503	+	2.15794i	−0.0412713	+	0.234061i
$86$	−0.301121	+	1.70774i	−0.0324708	+	0.184151i
$87$	−8.81731	−	15.2720i	−0.945315	−	1.63733i
$88$	1.42329	−	2.46520i	0.151723	−	0.262792i
$89$	−8.25512	−	6.92687i	−0.875041	−	0.734247i	0.0901123	−	0.995932i	$-0.471277\pi$
$89$	−8.25512	−	6.92687i	−0.875041	−	0.734247i	−0.965153	+	0.261685i	$0.915722\pi$
$90$	2.23785	+	0.814510i	0.235890	+	0.0858569i
$91$	−30.3170	+	11.0345i	−3.17808	+	1.15673i
$92$	−2.03580	+	1.70824i	−0.212247	+	0.178096i
$93$	2.18147	+	12.3718i	0.226208	+	1.28289i
$94$	3.00499			0.309941
$95$	−3.49000	−	2.61150i	−0.358066	−	0.267934i
$96$	2.31980			0.236764
$97$	0.356724	+	2.02308i	0.0362198	+	0.205413i	0.997547	−	0.0699948i	$-0.0222983\pi$
$97$	0.356724	+	2.02308i	0.0362198	+	0.205413i	−0.961328	+	0.275408i	$0.911187\pi$
$98$	−13.1563	+	11.0395i	−1.32899	+	1.11515i
$99$	−6.37020	+	2.31856i	−0.640229	+	0.233024i
$100$	−0.939693	−	0.342020i	−0.0939693	−	0.0342020i
$101$	−3.83762	−	3.22015i	−0.381857	−	0.320416i	0.431574	−	0.902078i	$-0.357959\pi$
$101$	−3.83762	−	3.22015i	−0.381857	−	0.320416i	−0.813431	+	0.581661i	$0.802403\pi$
$102$	2.54161	−	4.40219i	0.251656	−	0.435882i
$103$	4.51744	+	7.82444i	0.445117	+	0.770965i	0.998060	−	0.0622537i	$-0.0198288\pi$
$103$	4.51744	+	7.82444i	0.445117	+	0.770965i	−0.552943	+	0.833219i	$0.686495\pi$
$104$	1.13944	−	6.46210i	0.111732	−	0.633661i
$105$	1.98061	−	11.2326i	0.193287	−	1.09619i
$106$	−2.11108	−	3.65649i	−0.205046	−	0.355150i
$107$	−2.98391	+	5.16829i	−0.288466	+	0.499637i	−0.973444	−	0.228926i	$-0.926478\pi$
$107$	−2.98391	+	5.16829i	−0.288466	+	0.499637i	0.684978	+	0.728564i	$0.259812\pi$
$108$	1.09917	+	0.922316i	0.105768	+	0.0887499i
$109$	14.8753	+	5.41417i	1.42480	+	0.518583i	0.935435	−	0.353499i	$-0.115008\pi$
$109$	14.8753	+	5.41417i	1.42480	+	0.518583i	0.489360	+	0.872082i	$0.337230\pi$
$110$	2.67490	−	0.973585i	0.255042	−	0.0928277i
$111$	3.66524	−	3.07550i	0.347889	−	0.291914i
$112$	−0.853783	−	4.84205i	−0.0806750	−	0.457530i
$113$	18.2051			1.71259			0.856296	−	0.516485i	$-0.172760\pi$
$113$	18.2051			1.71259			0.856296	+	0.516485i	$0.172760\pi$
$114$	5.53582	+	8.46183i	0.518477	+	0.792523i
$115$	−2.65755			−0.247817
$116$	−1.32004	−	7.48630i	−0.122562	−	0.695085i
$117$	−11.9707	+	10.0446i	−1.10670	+	0.928628i
$118$	−0.906420	+	0.329910i	−0.0834427	+	0.0303707i
$119$	−10.1240	−	3.68482i	−0.928063	−	0.337787i
$120$	1.77707	+	1.49114i	0.162223	+	0.136122i
$121$	1.44851	−	2.50890i	0.131683	−	0.228082i
$122$	−3.74977	−	6.49480i	−0.339489	−	0.588012i
$123$	3.76939	−	21.3773i	0.339874	−	1.92752i
$124$	−0.940372	+	5.33311i	−0.0844479	+	0.478928i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−5.85453	+	10.1404i	−0.521563	+	0.903374i
$127$	5.85989	+	4.91703i	0.519981	+	0.436316i	0.864625	−	0.502418i	$-0.167556\pi$
$127$	5.85989	+	4.91703i	0.519981	+	0.436316i	−0.344644	+	0.938733i	$0.612000\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	3.78014	−	1.37586i	0.332823	−	0.121137i
$130$	5.02662	−	4.21784i	0.440864	−	0.369929i
$131$	−2.31209	−	13.1125i	−0.202008	−	1.14564i	−0.902079	−	0.431571i	$-0.857960\pi$
$131$	−2.31209	−	13.1125i	−0.202008	−	1.14564i	0.700071	−	0.714073i	$-0.253152\pi$
$132$	−6.60347			−0.574759
$133$	15.6247	−	14.6691i	1.35483	−	1.27197i
$134$	−1.91955			−0.165824
$135$	0.249162	+	1.41307i	0.0214445	+	0.121618i
$136$	1.67858	−	1.40849i	0.143937	−	0.120777i
$137$	6.79047	−	2.47153i	0.580149	−	0.211157i	−0.0352423	−	0.999379i	$-0.511220\pi$
$137$	6.79047	−	2.47153i	0.580149	−	0.211157i	0.615391	+	0.788222i	$0.288998\pi$
$138$	5.79318	+	2.10854i	0.493148	+	0.179491i
$139$	−1.84752	−	1.55026i	−0.156705	−	0.131491i	0.561064	−	0.827772i	$-0.310392\pi$
$139$	−1.84752	−	1.55026i	−0.156705	−	0.131491i	−0.717769	+	0.696281i	$0.754837\pi$
$140$	2.45837	−	4.25802i	0.207770	−	0.359869i
$141$	−3.48549	−	6.03705i	−0.293531	−	0.508411i
$142$	1.07060	−	6.07169i	0.0898430	−	0.509525i
$143$	−3.24351	+	18.3948i	−0.271236	+	1.53825i
$144$	−1.19073	−	2.06241i	−0.0992279	−	0.171868i
$145$	3.80089	−	6.58334i	0.315647	−	0.546717i
$146$	3.04659	+	2.55639i	0.252137	+	0.211568i
$147$	37.4384	+	13.6264i	3.08786	+	1.12389i
$148$	1.93814	−	0.705424i	0.159314	−	0.0579855i
$149$	−5.34602	+	4.48584i	−0.437963	+	0.367495i	−0.834946	−	0.550331i	$-0.814501\pi$
$149$	−5.34602	+	4.48584i	−0.437963	+	0.367495i	0.396983	+	0.917826i	$0.370057\pi$
$150$	0.402829	+	2.28456i	0.0328908	+	0.186533i
$151$	−5.69362			−0.463340			−0.231670	−	0.972794i	$-0.574419\pi$
$151$	−5.69362			−0.463340			−0.231670	+	0.972794i	$0.574419\pi$
$152$	0.994851	+	4.24385i	0.0806931	+	0.344222i
$153$	−5.21834			−0.421878
$154$	2.43036	+	13.7832i	0.195844	+	1.11068i
$155$	−4.14843	+	3.48094i	−0.333210	+	0.279596i
$156$	−14.3040	+	5.20624i	−1.14524	+	0.416833i
$157$	4.99337	+	1.81744i	0.398514	+	0.145047i	0.533500	−	0.845800i	$-0.320877\pi$
$157$	4.99337	+	1.81744i	0.398514	+	0.145047i	−0.134985	+	0.990848i	$0.543099\pi$
$158$	−11.7380	−	9.84938i	−0.933828	−	0.783575i
$159$	−4.89727	+	8.48232i	−0.388379	+	0.672692i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	2.26897	−	12.8680i	0.178820	−	1.01414i
$162$	1.81862	−	10.3139i	0.142884	−	0.810337i
$163$	2.23679	+	3.87424i	0.175199	+	0.303454i	0.940230	−	0.340540i	$-0.110610\pi$
$163$	2.23679	+	3.87424i	0.175199	+	0.303454i	−0.765031	+	0.643993i	$0.777276\pi$
$164$	4.67865	−	8.10365i	0.365341	−	0.632789i
$165$	−5.05856	−	4.24463i	−0.393808	−	0.330444i
$166$	−1.23294	−	0.448753i	−0.0956945	−	0.0348300i
$167$	−3.42872	+	1.24795i	−0.265322	+	0.0965694i	−0.471256	−	0.881997i	$-0.656199\pi$
$167$	−3.42872	+	1.24795i	−0.265322	+	0.0965694i	0.205934	+	0.978566i	$0.433977\pi$
$168$	−8.73739	+	7.33154i	−0.674104	+	0.565641i
$169$	5.21936	+	29.6004i	0.401489	+	2.27696i
$170$	2.19123			0.168060
$171$	4.68148	−	9.26500i	0.358002	−	0.708512i
$172$	1.73409			0.132223
$173$	−0.204264	−	1.15844i	−0.0155299	−	0.0880746i	0.976058	−	0.217512i	$-0.0697941\pi$
$173$	−0.204264	−	1.15844i	−0.0155299	−	0.0880746i	−0.991588	+	0.129437i	$0.958683\pi$
$174$	−13.5089	+	11.3353i	−1.02411	+	0.859328i
$175$	4.62023	−	1.68163i	0.349256	−	0.127119i
$176$	−2.67490	−	0.973585i	−0.201628	−	0.0733867i
$177$	1.71415	+	1.43834i	0.128843	+	0.108112i
$178$	−5.38815	+	9.33254i	−0.403859	+	0.699504i
$179$	−2.16529	−	3.75038i	−0.161841	−	0.280317i	0.773688	−	0.633567i	$-0.218410\pi$
$179$	−2.16529	−	3.75038i	−0.161841	−	0.280317i	−0.935529	+	0.353250i	$0.885077\pi$
$180$	0.413538	−	2.34529i	0.0308233	−	0.174807i
$181$	0.237758	−	1.34839i	0.0176724	−	0.100225i	−0.974696	−	0.223536i	$-0.928240\pi$
$181$	0.237758	−	1.34839i	0.0176724	−	0.100225i	0.992368	+	0.123311i	$0.0393511\pi$
$182$	16.1313	+	27.9403i	1.19573	+	2.07107i
$183$	−8.69872	+	15.0666i	−0.643028	+	1.11376i
$184$	2.03580	+	1.70824i	0.150081	+	0.125933i
$185$	1.93814	+	0.705424i	0.142495	+	0.0518638i
$186$	11.8050	−	4.29667i	0.865584	−	0.315047i
$187$	−4.77819	+	4.00938i	−0.349416	+	0.293195i
$188$	−0.521812	−	2.95934i	−0.0380570	−	0.215832i
$189$	−7.05488			−0.513167
$190$	−1.96579	+	3.89046i	−0.142614	+	0.282243i
$191$	13.6338			0.986505			0.493252	−	0.869886i	$-0.335808\pi$
$191$	13.6338			0.986505			0.493252	+	0.869886i	$0.335808\pi$
$192$	−0.402829	−	2.28456i	−0.0290717	−	0.164874i
$193$	−3.99835	+	3.35501i	−0.287807	+	0.241499i	−0.775248	−	0.631657i	$-0.782375\pi$
$193$	−3.99835	+	3.35501i	−0.287807	+	0.241499i	0.487441	+	0.873156i	$0.337931\pi$
$194$	1.93040	−	0.702609i	0.138595	−	0.0504444i
$195$	−14.3040	−	5.20624i	−1.02433	−	0.372827i
$196$	13.1563	+	11.0395i	0.939737	+	0.788533i
$197$	−1.42771	+	2.47286i	−0.101720	+	0.176184i	−0.912393	−	0.409315i	$-0.865768\pi$
$197$	−1.42771	+	2.47286i	−0.101720	+	0.176184i	0.810674	+	0.585498i	$0.199101\pi$
$198$	3.38951	+	5.87080i	0.240882	+	0.417220i
$199$	−0.254330	+	1.44238i	−0.0180290	+	0.102247i	−0.992494	−	0.122290i	$-0.960976\pi$
$199$	−0.254330	+	1.44238i	−0.0180290	+	0.102247i	0.974465	+	0.224538i	$0.0720872\pi$
$200$	−0.173648	+	0.984808i	−0.0122788	+	0.0696364i
$201$	2.22649	+	3.85639i	0.157044	+	0.272009i
$202$	−2.50483	+	4.33849i	−0.176239	+	0.305255i
$203$	28.6317	+	24.0248i	2.00955	+	1.68621i
$204$	−4.77666	−	1.73856i	−0.334433	−	0.121724i
$205$	8.79298	−	3.20038i	0.614128	−	0.223524i
$206$	6.92112	−	5.80751i	0.482218	−	0.404629i
$207$	−1.09900	−	6.23271i	−0.0763855	−	0.433203i
$208$	−6.56179			−0.454978
$209$	−2.83192	−	12.0804i	−0.195888	−	0.835621i
$210$	−11.4059			−0.787079
$211$	0.227567	+	1.29059i	0.0156663	+	0.0888482i	0.991638	−	0.129047i	$-0.0411919\pi$
$211$	0.227567	+	1.29059i	0.0156663	+	0.0888482i	−0.975972	+	0.217896i	$0.930081\pi$
$212$	−3.23435	+	2.71395i	−0.222136	+	0.186395i
$213$	−13.4399	+	4.89171i	−0.920883	+	0.335174i
$214$	5.60792	+	2.04112i	0.383350	+	0.139528i
$215$	1.32839	+	1.11465i	0.0905954	+	0.0760186i
$216$	0.717435	−	1.24263i	0.0488152	−	0.0845505i
$217$	−13.3130	−	23.0588i	−0.903747	−	1.56534i
$218$	2.74884	−	15.5895i	0.186175	−	1.05585i
$219$	1.60206	−	9.08576i	0.108257	−	0.613959i
$220$	−1.42329	−	2.46520i	−0.0959579	−	0.166204i
$221$	−7.18919	+	12.4520i	−0.483597	+	0.837615i
$222$	−3.66524	−	3.07550i	−0.245995	−	0.206414i
$223$	−26.4339	−	9.62115i	−1.77014	−	0.644280i	−0.999979	−	0.00643379i	$-0.997952\pi$
$223$	−26.4339	−	9.62115i	−1.77014	−	0.644280i	−0.770164	−	0.637846i	$-0.779826\pi$
$224$	−4.62023	+	1.68163i	−0.308702	+	0.112358i
$225$	1.82431	−	1.53078i	0.121621	−	0.102052i
$226$	−3.16128	−	17.9285i	−0.210285	−	1.19259i
$227$	12.6466			0.839382			0.419691	−	0.907667i	$-0.362138\pi$
$227$	12.6466			0.839382			0.419691	+	0.907667i	$0.362138\pi$
$228$	7.37199	−	6.92110i	0.488222	−	0.458361i
$229$	13.7440			0.908227			0.454113	−	0.890944i	$-0.349956\pi$
$229$	13.7440			0.908227			0.454113	+	0.890944i	$0.349956\pi$
$230$	0.461478	+	2.61717i	0.0304290	+	0.172571i
$231$	24.8716	−	20.8698i	1.63643	−	1.37313i
$232$	−7.14334	+	2.59996i	−0.468983	+	0.170696i
$233$	−23.1335	−	8.41990i	−1.51552	−	0.551606i	−0.555499	−	0.831517i	$-0.687473\pi$
$233$	−23.1335	−	8.41990i	−1.51552	−	0.551606i	−0.960026	+	0.279911i	$0.909695\pi$
$234$	11.9707	+	10.0446i	0.782552	+	0.656639i
$235$	1.50250	−	2.60240i	0.0980121	−	0.169762i
$236$	0.482296	+	0.835361i	0.0313948	+	0.0543774i
$237$	−6.17251	+	35.0061i	−0.400948	+	2.27389i
$238$	−1.87083	+	10.6100i	−0.121268	+	0.687746i
$239$	8.14698	+	14.1110i	0.526984	+	0.912763i	0.999506	+	0.0314439i	$0.0100106\pi$
$239$	8.14698	+	14.1110i	0.526984	+	0.912763i	−0.472522	+	0.881319i	$0.656656\pi$
$240$	1.15990	−	2.00901i	0.0748712	−	0.129681i
$241$	−14.7500	−	12.3767i	−0.950133	−	0.797256i	0.0291873	−	0.999574i	$-0.490708\pi$
$241$	−14.7500	−	12.3767i	−0.950133	−	0.797256i	−0.979320	+	0.202318i	$0.935153\pi$
$242$	−2.72232	−	0.990842i	−0.174997	−	0.0636938i
$243$	−18.7851	+	6.83722i	−1.20506	+	0.438608i
$244$	−5.74499	+	4.82062i	−0.367785	+	0.308608i
$245$	2.98230	+	16.9134i	0.190532	+	1.08056i
$246$	−21.7070			−1.38399
$247$	−15.6586	−	23.9351i	−0.996335	−	1.52296i
$248$	5.41539			0.343877
$249$	0.528538	+	2.99749i	0.0334947	+	0.189958i
$250$	−0.766044	+	0.642788i	−0.0484489	+	0.0406535i
$251$	26.0953	−	9.49792i	1.64712	−	0.599504i	0.658860	−	0.752266i	$-0.271039\pi$
$251$	26.0953	−	9.49792i	1.64712	−	0.599504i	0.988263	+	0.152762i	$0.0488169\pi$
$252$	11.0029	+	4.00474i	0.693119	+	0.252275i
$253$	−5.79505	−	4.86262i	−0.364331	−	0.305710i
$254$	3.82477	−	6.62470i	0.239987	−	0.415671i
$255$	−2.54161	−	4.40219i	−0.159161	−	0.275676i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.26963	−	12.8717i	0.141576	−	0.802915i	−0.828478	−	0.560022i	$-0.810793\pi$
$257$	2.26963	−	12.8717i	0.141576	−	0.802915i	0.970053	−	0.242893i	$-0.0780962\pi$
$258$	−2.01137	−	3.48379i	−0.125222	−	0.216891i
$259$	−5.07044	+	8.78226i	−0.315062	+	0.545703i
$260$	−5.02662	−	4.21784i	−0.311738	−	0.261579i
$261$	17.0116	+	6.19173i	1.05299	+	0.383259i
$262$	−12.5118	+	4.55392i	−0.772981	+	0.281342i
$263$	11.5336	−	9.67780i	0.711190	−	0.596759i	−0.213743	−	0.976890i	$-0.568566\pi$
$263$	11.5336	−	9.67780i	0.711190	−	0.596759i	0.924933	+	0.380131i	$0.124121\pi$
$264$	1.14668	+	6.50315i	0.0705734	+	0.400241i
$265$	−4.22215			−0.259365
$266$	−17.1594	−	12.8401i	−1.05211	−	0.787276i
$267$	24.9988			1.52990
$268$	0.333326	+	1.89039i	0.0203612	+	0.115474i
$269$	18.7339	−	15.7196i	1.14222	−	0.958439i	0.142714	−	0.989764i	$-0.454417\pi$
$269$	18.7339	−	15.7196i	1.14222	−	0.958439i	0.999509	+	0.0313248i	$0.00997262\pi$
$270$	1.34834	−	0.490754i	0.0820571	−	0.0298663i
$271$	−8.41094	−	3.06133i	−0.510928	−	0.185963i	0.0736745	−	0.997282i	$-0.476527\pi$
$271$	−8.41094	−	3.06133i	−0.510928	−	0.185963i	−0.584603	+	0.811320i	$0.698750\pi$
$272$	−1.67858	−	1.40849i	−0.101779	−	0.0854025i
$273$	37.4214	−	64.8158i	2.26485	−	3.92283i
$274$	−3.61313	−	6.25813i	−0.218277	−	0.378067i
$275$	0.494302	−	2.80333i	0.0298075	−	0.169047i
$276$	1.07054	−	6.07131i	0.0644387	−	0.365450i
$277$	3.90071	+	6.75622i	0.234371	+	0.405942i	0.959090	−	0.283103i	$-0.0913637\pi$
$277$	3.90071	+	6.75622i	0.234371	+	0.405942i	−0.724719	+	0.689045i	$0.758030\pi$
$278$	−1.20589	+	2.08866i	−0.0723242	+	0.125269i
$279$	−9.87935	−	8.28976i	−0.591461	−	0.496295i
$280$	−4.62023	−	1.68163i	−0.276111	−	0.100496i
$281$	−17.1947	+	6.25837i	−1.02575	+	0.373343i	−0.799462	−	0.600717i	$-0.794882\pi$
$281$	−17.1947	+	6.25837i	−1.02575	+	0.373343i	−0.226290	+	0.974060i	$0.572660\pi$
$282$	−5.34008	+	4.48086i	−0.317997	+	0.266831i
$283$	1.25513	+	7.11822i	0.0746100	+	0.423134i	0.999119	+	0.0419735i	$0.0133645\pi$
$283$	1.25513	+	7.11822i	0.0746100	+	0.423134i	−0.924509	+	0.381161i	$0.875524\pi$
$284$	−6.16536			−0.365847
$285$	10.0961	−	0.563248i	0.598040	−	0.0333639i
$286$	18.6786			1.10449
$287$	7.98910	+	45.3084i	0.471582	+	2.67447i
$288$	−1.82431	+	1.53078i	−0.107499	+	0.0902020i
$289$	11.4629	−	4.17214i	0.674286	−	0.245420i
$290$	−7.14334	−	2.59996i	−0.419471	−	0.152675i
$291$	−3.65062	−	3.06323i	−0.214003	−	0.179570i
$292$	1.98852	−	3.44421i	0.116369	−	0.201557i
$293$	−5.69330	−	9.86109i	−0.332606	−	0.576091i	0.650416	−	0.759578i	$-0.274595\pi$
$293$	−5.69330	−	9.86109i	−0.332606	−	0.576091i	−0.983022	+	0.183488i	$0.941261\pi$
$294$	6.91833	−	39.2358i	0.403485	−	2.28828i
$295$	−0.167500	+	0.949937i	−0.00975220	+	0.0553075i
$296$	−1.03126	−	1.78620i	−0.0599408	−	0.103821i
$297$	−2.04223	+	3.53724i	−0.118502	+	0.205252i
$298$	5.34602	+	4.48584i	0.309687	+	0.259858i
$299$	−16.3866	−	5.96423i	−0.947662	−	0.344921i
$300$	2.17990	−	0.793418i	0.125856	−	0.0458080i
$301$	−6.53135	+	5.48045i	−0.376461	+	0.315888i
$302$	0.988686	+	5.60712i	0.0568925	+	0.322653i
$303$	11.6214			0.667632
$304$	4.00662	−	1.71667i	0.229796	−	0.0984580i
$305$	−7.49955			−0.429423
$306$	0.906156	+	5.13906i	0.0518015	+	0.293781i
$307$	3.78649	−	3.17725i	0.216107	−	0.181335i	−0.528308	−	0.849053i	$-0.677173\pi$
$307$	3.78649	−	3.17725i	0.216107	−	0.181335i	0.744414	+	0.667718i	$0.232729\pi$
$308$	13.1518	−	4.78687i	0.749394	−	0.272757i
$309$	−19.6951	−	7.16844i	−1.12042	−	0.407798i
$310$	4.14843	+	3.48094i	0.235615	+	0.197704i
$311$	−12.0586	+	20.8861i	−0.683782	+	1.18434i	0.290036	+	0.957016i	$0.406333\pi$
$311$	−12.0586	+	20.8861i	−0.683782	+	1.18434i	−0.973818	+	0.227329i	$0.927001\pi$
$312$	7.61102	+	13.1827i	0.430889	+	0.746322i
$313$	−5.37886	+	30.5050i	−0.304031	+	1.72424i	0.324001	+	0.946057i	$0.394972\pi$
$313$	−5.37886	+	30.5050i	−0.304031	+	1.72424i	−0.628031	+	0.778188i	$0.716139\pi$
$314$	0.922737	−	5.23310i	0.0520731	−	0.295321i
$315$	5.85453	+	10.1404i	0.329866	+	0.571344i
$316$	−7.66146	+	13.2700i	−0.430991	+	0.746498i
$317$	−5.29378	−	4.44201i	−0.297328	−	0.249488i	0.481903	−	0.876225i	$-0.339946\pi$
$317$	−5.29378	−	4.44201i	−0.297328	−	0.249488i	−0.779231	+	0.626737i	$0.784390\pi$
$318$	9.20386	+	3.34993i	0.516127	+	0.187855i
$319$	20.3340	−	7.40098i	1.13849	−	0.414376i
$320$	0.766044	−	0.642788i	0.0428232	−	0.0359329i
$321$	−2.40401	−	13.6338i	−0.134179	−	0.760966i
$322$	−13.0665			−0.728166
$323$	1.13205	−	9.48402i	0.0629890	−	0.527705i
$324$	−10.4730			−0.581834
$325$	−1.13944	−	6.46210i	−0.0632049	−	0.358453i
$326$	3.42697	−	2.87557i	0.189802	−	0.159263i
$327$	−34.5077	+	12.5598i	−1.90828	+	0.694557i
$328$	−8.79298	−	3.20038i	−0.485511	−	0.176712i
$329$	11.3181	+	9.49705i	0.623989	+	0.523589i
$330$	−3.30174	+	5.71878i	−0.181755	+	0.314808i
$331$	−2.08943	−	3.61900i	−0.114845	−	0.198918i	0.802873	−	0.596151i	$-0.203304\pi$
$331$	−2.08943	−	3.61900i	−0.114845	−	0.198918i	−0.917718	+	0.397233i	$0.869971\pi$
$332$	−0.227838	+	1.29213i	−0.0125042	+	0.0709149i
$333$	−0.852930	+	4.83721i	−0.0467403	+	0.265077i
$334$	1.82438	+	3.15992i	0.0998258	+	0.172903i
$335$	−0.959775	+	1.66238i	−0.0524381	+	0.0908255i
$336$	8.73739	+	7.33154i	0.476664	+	0.399968i
$337$	−16.1638	−	5.88315i	−0.880500	−	0.320476i	−0.138088	−	0.990420i	$-0.544096\pi$
$337$	−16.1638	−	5.88315i	−0.880500	−	0.320476i	−0.742411	+	0.669944i	$0.766318\pi$
$338$	28.2444	−	10.2801i	1.53629	−	0.559165i
$339$	−32.3517	+	27.1463i	−1.75710	+	1.47439i
$340$	−0.380503	−	2.15794i	−0.0206357	−	0.117031i
$341$	−15.4153			−0.834784
$342$	−9.93717	−	3.00151i	−0.537341	−	0.162303i
$343$	−50.0247			−2.70108
$344$	−0.301121	−	1.70774i	−0.0162354	−	0.0920754i
$345$	4.72264	−	3.96277i	0.254259	−	0.213348i
$346$	−1.10537	+	0.402322i	−0.0594251	+	0.0216290i
$347$	−17.3494	−	6.31466i	−0.931364	−	0.338989i	−0.168614	−	0.985682i	$-0.553929\pi$
$347$	−17.3494	−	6.31466i	−0.931364	−	0.338989i	−0.762750	+	0.646693i	$0.776151\pi$
$348$	13.5089	+	11.3353i	0.724153	+	0.607637i
$349$	−12.3704	+	21.4262i	−0.662174	+	1.14692i	0.317870	+	0.948134i	$0.397033\pi$
$349$	−12.3704	+	21.4262i	−0.662174	+	1.14692i	−0.980043	+	0.198784i	$0.936301\pi$
$350$	−2.45837	−	4.25802i	−0.131405	−	0.227601i
$351$	−1.63495	+	9.27227i	−0.0872672	+	0.494917i
$352$	−0.494302	+	2.80333i	−0.0263464	+	0.149418i
$353$	3.20496	+	5.55115i	0.170583	+	0.295458i	0.938624	−	0.344943i	$-0.112102\pi$
$353$	3.20496	+	5.55115i	0.170583	+	0.295458i	−0.768041	+	0.640401i	$0.778768\pi$
$354$	1.11883	−	1.93787i	0.0594651	−	0.102997i
$355$	−4.72294	−	3.96302i	−0.250668	−	0.210335i
$356$	10.1264	+	3.68571i	0.536698	+	0.195342i
$357$	23.4856	−	8.54805i	1.24299	−	0.452411i
$358$	−3.31741	+	2.78364i	−0.175331	+	0.147120i
$359$	−6.39293	−	36.2561i	−0.337406	−	1.91353i	−0.402051	−	0.915617i	$-0.631703\pi$
$359$	−6.39293	−	36.2561i	−0.337406	−	1.91353i	0.0646449	−	0.997908i	$-0.479409\pi$
$360$	−2.38147			−0.125514
$361$	15.8230	+	10.5182i	0.832789	+	0.553591i
$362$	−1.36920			−0.0719633
$363$	1.16701	+	6.61843i	0.0612520	+	0.347377i
$364$	24.7146	−	20.7380i	1.29540	−	1.08697i
$365$	3.73719	−	1.36023i	0.195613	−	0.0711975i
$366$	16.3483	+	5.95028i	0.854537	+	0.311026i
$367$	11.2025	+	9.39999i	0.584764	+	0.490676i	0.886508	−	0.462714i	$-0.153124\pi$
$367$	11.2025	+	9.39999i	0.584764	+	0.490676i	−0.301743	+	0.953389i	$0.597569\pi$
$368$	1.32877	−	2.30150i	0.0692671	−	0.119974i
$369$	11.1420	+	19.2986i	0.580032	+	1.00464i
$370$	0.358153	−	2.03119i	0.0186195	−	0.105596i
$371$	3.60480	−	20.4438i	0.187152	−	1.06139i
$372$	−6.28130	−	10.8795i	−0.325670	−	0.564078i
$373$	6.77871	−	11.7411i	0.350989	−	0.607930i	−0.635434	−	0.772155i	$-0.719179\pi$
$373$	6.77871	−	11.7411i	0.350989	−	0.607930i	0.986423	+	0.164225i	$0.0525123\pi$
$374$	4.77819	+	4.00938i	0.247075	+	0.207320i
$375$	2.17990	+	0.793418i	0.112569	+	0.0409719i
$376$	−2.82377	+	1.02777i	−0.145625	+	0.0530031i
$377$	38.2113	−	32.0631i	1.96798	−	1.65133i
$378$	1.22507	+	6.94770i	0.0630107	+	0.357351i
$379$	30.2899			1.55589			0.777944	−	0.628333i	$-0.216262\pi$
$379$	30.2899			1.55589			0.777944	+	0.628333i	$0.216262\pi$
$380$	4.17271	+	1.26036i	0.214055	+	0.0646551i
$381$	−17.7454			−0.909124
$382$	−2.36748	−	13.4266i	−0.121131	−	0.686967i
$383$	−21.9571	+	18.4242i	−1.12196	+	0.941433i	−0.998702	−	0.0509425i	$-0.983777\pi$
$383$	−21.9571	+	18.4242i	−1.12196	+	0.941433i	−0.123254	+	0.992375i	$0.539333\pi$
$384$	−2.17990	+	0.793418i	−0.111242	+	0.0404889i
$385$	13.1518	+	4.78687i	0.670278	+	0.243961i
$386$	3.99835	+	3.35501i	0.203511	+	0.170766i
$387$	−2.06484	+	3.57641i	−0.104962	+	0.181799i
$388$	−1.02715	−	1.77907i	−0.0521454	−	0.0903186i
$389$	2.97395	−	16.8661i	0.150785	−	0.855145i	−0.811754	−	0.584000i	$-0.801487\pi$
$389$	2.97395	−	16.8661i	0.150785	−	0.855145i	0.962539	−	0.271145i	$-0.0874021\pi$
$390$	−2.64328	+	14.9908i	−0.133848	+	0.759087i
$391$	−2.91165	−	5.04312i	−0.147248	−	0.255041i
$392$	8.58718	−	14.8734i	0.433718	−	0.751222i
$393$	23.6613	+	19.8542i	1.19355	+	1.00151i
$394$	2.68321	+	0.976608i	0.135178	+	0.0492008i
$395$	−14.3988	+	5.24075i	−0.724484	+	0.263691i
$396$	5.19303	−	4.35747i	0.260960	−	0.218971i
$397$	4.53308	+	25.7084i	0.227509	+	1.29027i	0.857831	+	0.513932i	$0.171812\pi$
$397$	4.53308	+	25.7084i	0.227509	+	1.29027i	−0.630322	+	0.776334i	$0.717077\pi$
$398$	1.46463			0.0734151
$399$	−5.89259	+	49.3665i	−0.294998	+	2.47142i
$400$	1.00000			0.0500000
$401$	−1.61683	−	9.16948i	−0.0807405	−	0.457902i	−0.998195	−	0.0600607i	$-0.980871\pi$
$401$	−1.61683	−	9.16948i	−0.0807405	−	0.457902i	0.917454	−	0.397841i	$-0.130241\pi$
$402$	3.41117	−	2.86232i	0.170134	−	0.142759i
$403$	−33.3916	+	12.1536i	−1.66336	+	0.605412i
$404$	4.70754	+	1.71340i	0.234209	+	0.0852450i
$405$	−8.02279	−	6.73192i	−0.398656	−	0.334512i
$406$	18.6880	−	32.3686i	0.927471	−	1.60643i
$407$	2.93556	+	5.08453i	0.145510	+	0.252031i
$408$	−0.882690	+	5.00598i	−0.0436997	+	0.247833i
$409$	2.53175	−	14.3583i	0.125187	−	0.709972i	−0.856009	−	0.516960i	$-0.827063\pi$
$409$	2.53175	−	14.3583i	0.125187	−	0.709972i	0.981196	−	0.193012i	$-0.0618255\pi$
$410$	−4.67865	−	8.10365i	−0.231062	−	0.400211i
$411$	−8.38174	+	14.5176i	−0.413441	+	0.716101i
$412$	−6.92112	−	5.80751i	−0.340979	−	0.286116i
$413$	−4.45663	−	1.62208i	−0.219297	−	0.0798174i
$414$	−5.94718	+	2.16460i	−0.292288	+	0.106384i
$415$	−1.00510	+	0.843379i	−0.0493384	+	0.0413999i
$416$	1.13944	+	6.46210i	0.0558658	+	0.316831i
$417$	5.59483			0.273980
$418$	−11.4051	+	4.88664i	−0.557844	+	0.239013i
$419$	14.5969			0.713103			0.356552	−	0.934276i	$-0.383952\pi$
$419$	14.5969			0.713103			0.356552	+	0.934276i	$0.383952\pi$
$420$	1.98061	+	11.2326i	0.0966437	+	0.548094i
$421$	−30.0605	+	25.2237i	−1.46506	+	1.22933i	−0.544478	+	0.838775i	$0.683272\pi$
$421$	−30.0605	+	25.2237i	−1.46506	+	1.22933i	−0.920580	+	0.390554i	$0.872283\pi$
$422$	1.23147	−	0.448219i	0.0599471	−	0.0218190i
$423$	6.72472	+	2.44760i	0.326967	+	0.119006i
$424$	3.23435	+	2.71395i	0.157074	+	0.131801i
$425$	1.09561	−	1.89766i	0.0531451	−	0.0920500i
$426$	7.15120	+	12.3862i	0.346477	+	0.600115i
$427$	6.40299	−	36.3132i	0.309862	−	1.75732i
$428$	1.03630	−	5.87716i	0.0500916	−	0.284083i
$429$	−21.6653	−	37.5254i	−1.04601	−	1.81174i
$430$	0.867044	−	1.50177i	0.0418126	−	0.0724215i
$431$	16.7585	+	14.0620i	0.807228	+	0.677345i	0.949944	−	0.312419i	$-0.101139\pi$
$431$	16.7585	+	14.0620i	0.807228	+	0.677345i	−0.142716	+	0.989764i	$0.545584\pi$
$432$	−1.34834	−	0.490754i	−0.0648718	−	0.0236114i
$433$	1.03524	−	0.376798i	0.0497507	−	0.0181078i	−0.317025	−	0.948417i	$-0.602684\pi$
$433$	1.03524	−	0.376798i	0.0497507	−	0.0181078i	0.366776	+	0.930309i	$0.380462\pi$
$434$	−20.3967	+	17.1149i	−0.979075	+	0.821542i
$435$	3.06222	+	17.3667i	0.146822	+	0.832670i
$436$	−15.8300			−0.758118
$437$	11.5660	−	0.645253i	0.553276	−	0.0308666i
$438$	−9.22592			−0.440832
$439$	−0.732304	−	4.15310i	−0.0349510	−	0.198217i	0.962333	−	0.271875i	$-0.0876437\pi$
$439$	−0.732304	−	4.15310i	−0.0349510	−	0.198217i	−0.997284	+	0.0736582i	$0.976533\pi$
$440$	−2.18060	+	1.82974i	−0.103956	+	0.0872295i
$441$	−38.4336	+	13.9887i	−1.83017	+	0.666128i
$442$	13.5113	+	4.91770i	0.642665	+	0.233911i
$443$	5.80899	+	4.87432i	0.275993	+	0.231586i	0.770269	−	0.637719i	$-0.220122\pi$
$443$	5.80899	+	4.87432i	0.275993	+	0.231586i	−0.494275	+	0.869305i	$0.664567\pi$
$444$	−2.39232	+	4.14362i	−0.113534	+	0.196647i
$445$	5.38815	+	9.33254i	0.255423	+	0.442405i
$446$	−4.88478	+	27.7030i	−0.231301	+	1.31177i
$447$	2.81124	−	15.9433i	0.132967	−	0.754093i
$448$	2.45837	+	4.25802i	0.116147	+	0.201173i
$449$	−14.8487	+	25.7188i	−0.700756	+	1.21374i	0.267446	+	0.963573i	$0.413820\pi$
$449$	−14.8487	+	25.7188i	−0.700756	+	1.21374i	−0.968202	+	0.250171i	$0.919513\pi$
$450$	−1.82431	−	1.53078i	−0.0859988	−	0.0721616i
$451$	25.0298	+	9.11012i	1.17861	+	0.428979i
$452$	−17.1072	+	6.22651i	−0.804655	+	0.292871i
$453$	10.1180	−	8.48997i	0.475383	−	0.398894i
$454$	−2.19605	−	12.4544i	−0.103066	−	0.584515i
$455$	32.2626			1.51250
$456$	−8.09609	−	6.05816i	−0.379134	−	0.283699i
$457$	9.12576			0.426885			0.213442	−	0.976956i	$-0.431532\pi$
$457$	9.12576			0.426885			0.213442	+	0.976956i	$0.431532\pi$
$458$	−2.38661	−	13.5352i	−0.111519	−	0.632456i
$459$	−2.40854	+	2.02101i	−0.112421	+	0.0943324i
$460$	2.49728	−	0.908934i	0.116436	−	0.0423793i
$461$	24.7943	+	9.02439i	1.15479	+	0.420308i	0.847232	−	0.531223i	$-0.178267\pi$
$461$	24.7943	+	9.02439i	1.15479	+	0.420308i	0.307554	+	0.951531i	$0.400490\pi$
$462$	−24.8716	−	20.8698i	−1.15713	−	0.970949i
$463$	7.86094	−	13.6156i	0.365329	−	0.632768i	−0.623500	−	0.781823i	$-0.714290\pi$
$463$	7.86094	−	13.6156i	0.365329	−	0.632768i	0.988829	+	0.149055i	$0.0476232\pi$
$464$	3.80089	+	6.58334i	0.176452	+	0.305624i
$465$	2.18147	−	12.3718i	0.101163	−	0.573726i
$466$	−4.27489	+	24.2441i	−0.198031	+	1.12309i
$467$	3.44966	+	5.97499i	0.159631	+	0.276490i	0.934736	−	0.355344i	$-0.115636\pi$
$467$	3.44966	+	5.97499i	0.159631	+	0.276490i	−0.775104	+	0.631833i	$0.782303\pi$
$468$	7.81335	−	13.5331i	0.361172	−	0.625568i
$469$	−7.22988	−	6.06659i	−0.333845	−	0.280129i
$470$	−2.82377	−	1.02777i	−0.130251	−	0.0474074i
$471$	−11.5836	+	4.21609i	−0.533745	+	0.194267i
$472$	0.738920	−	0.620028i	0.0340116	−	0.0285391i
$473$	0.857164	+	4.86122i	0.0394124	+	0.223519i
$474$	35.5461			1.63269
$475$	2.38634	+	3.64766i	0.109493	+	0.167366i
$476$	10.7737			0.493812
$477$	−1.74602	−	9.90216i	−0.0799447	−	0.453389i
$478$	12.4819	−	10.4735i	0.570908	−	0.479049i
$479$	3.42858	−	1.24790i	0.156656	−	0.0570180i	−0.262502	−	0.964931i	$-0.584548\pi$
$479$	3.42858	−	1.24790i	0.156656	−	0.0570180i	0.419158	+	0.907913i	$0.362325\pi$
$480$	−2.17990	−	0.793418i	−0.0994983	−	0.0362144i
$481$	10.3675	+	8.69938i	0.472718	+	0.396657i
$482$	−9.62739	+	16.6751i	−0.438516	+	0.759532i
$483$	15.1558	+	26.2506i	0.689612	+	1.19444i
$484$	−0.503064	+	2.85302i	−0.0228665	+	0.129683i
$485$	0.356724	−	2.02308i	0.0161980	−	0.0918635i
$486$	9.99534	+	17.3124i	0.453398	+	0.785308i
$487$	11.2575	−	19.4986i	0.510128	−	0.883568i	−0.489803	−	0.871833i	$-0.662931\pi$
$487$	11.2575	−	19.4986i	0.510128	−	0.883568i	0.999931	−	0.0117346i	$-0.00373533\pi$
$488$	5.74499	+	4.82062i	0.260063	+	0.218219i
$489$	−9.75196	−	3.54942i	−0.440999	−	0.160510i
$490$	16.1386	−	5.87398i	0.729069	−	0.265359i
$491$	19.2746	−	16.1733i	0.869849	−	0.729890i	−0.0942175	−	0.995552i	$-0.530035\pi$
$491$	19.2746	−	16.1733i	0.869849	−	0.729890i	0.964066	+	0.265662i	$0.0855905\pi$
$492$	3.76939	+	21.3773i	0.169937	+	0.963761i
$493$	16.6573			0.750205
$494$	−20.8524	+	19.5770i	−0.938195	+	0.880813i
$495$	6.77902			0.304694
$496$	−0.940372	−	5.33311i	−0.0422239	−	0.239464i
$497$	23.2215	−	19.4851i	1.04163	−	0.874027i
$498$	2.86017	−	1.04102i	0.128167	−	0.0466490i
$499$	−29.8561	−	10.8667i	−1.33654	−	0.486461i	−0.427819	−	0.903864i	$-0.640718\pi$
$499$	−29.8561	−	10.8667i	−1.33654	−	0.486461i	−0.908721	+	0.417403i	$0.862940\pi$
$500$	0.766044	+	0.642788i	0.0342585	+	0.0287463i
$501$	4.23220	−	7.33039i	0.189081	−	0.327498i
$502$	−13.8850	−	24.0496i	−0.619719	−	1.07339i
$503$	−4.43880	+	25.1737i	−0.197917	+	1.12244i	0.710287	+	0.703912i	$0.248565\pi$
$503$	−4.43880	+	25.1737i	−0.197917	+	1.12244i	−0.908204	+	0.418528i	$0.862546\pi$
$504$	2.03326	−	11.5312i	0.0905685	−	0.513640i
$505$	2.50483	+	4.33849i	0.111463	+	0.193060i
$506$	−3.78245	+	6.55139i	−0.168150	+	0.291245i
$507$	−53.4135	−	44.8192i	−2.37218	−	1.99049i
$508$	−7.18822	−	2.61630i	−0.318926	−	0.116079i
$509$	−9.28595	+	3.37981i	−0.411592	+	0.149807i	−0.539513	−	0.841977i	$-0.681392\pi$
$509$	−9.28595	+	3.37981i	−0.411592	+	0.149807i	0.127921	+	0.991784i	$0.459170\pi$
$510$	−3.89396	+	3.26742i	−0.172428	+	0.144684i
$511$	3.39553	+	19.2570i	0.150209	+	0.851879i
$512$	−1.00000			−0.0441942
$513$	−1.42748	−	6.08937i	−0.0630248	−	0.268852i
$514$	−13.0703			−0.576505
$515$	−1.56889	−	8.89763i	−0.0691336	−	0.392076i
$516$	−3.08160	+	2.58577i	−0.135660	+	0.113832i
$517$	8.03806	−	2.92562i	0.353514	−	0.128668i
$518$	9.52932	+	3.46839i	0.418694	+	0.152392i
$519$	2.09039	+	1.75404i	0.0917578	+	0.0769940i
$520$	−3.28089	+	5.68268i	−0.143877	+	0.249202i
$521$	2.14888	+	3.72196i	0.0941440	+	0.163062i	0.909251	−	0.416248i	$-0.136655\pi$
$521$	2.14888	+	3.72196i	0.0941440	+	0.163062i	−0.815107	+	0.579310i	$0.803322\pi$
$522$	3.14362	−	17.8284i	0.137593	−	0.780327i
$523$	4.32437	−	24.5247i	0.189092	−	1.07239i	−0.731493	−	0.681849i	$-0.761176\pi$
$523$	4.32437	−	24.5247i	0.189092	−	1.07239i	0.920585	−	0.390543i	$-0.127713\pi$
$524$	6.65739	+	11.5309i	0.290829	+	0.503731i
$525$	−5.70293	+	9.87776i	−0.248896	+	0.431101i
$526$	−11.5336	−	9.67780i	−0.502887	−	0.421972i
$527$	−11.1507	−	4.05853i	−0.485733	−	0.176792i
$528$	6.20524	−	2.25852i	0.270048	−	0.0982895i
$529$	−12.2088	+	10.2444i	−0.530817	+	0.445408i
$530$	0.733169	+	4.15801i	0.0318468	+	0.180612i
$531$	−2.29714			−0.0996876
$532$	−9.66531	+	19.1284i	−0.419044	+	0.829320i
$533$	61.4006			2.65955
$534$	−4.34100	−	24.6191i	−0.187854	−	1.06537i
$535$	4.57162	−	3.83604i	0.197648	−	0.165847i
$536$	1.80379	−	0.656525i	0.0779118	−	0.0283576i
$537$	9.44020	+	3.43595i	0.407375	+	0.148272i
$538$	−18.7339	−	15.7196i	−0.807674	−	0.677719i
$539$	−24.4440	+	42.3383i	−1.05288	+	1.82364i
$540$	−0.717435	−	1.24263i	−0.0308735	−	0.0534744i
$541$	−3.80139	+	21.5587i	−0.163434	+	0.926882i	0.787230	+	0.616660i	$0.211515\pi$
$541$	−3.80139	+	21.5587i	−0.163434	+	0.926882i	−0.950664	+	0.310222i	$0.899596\pi$
$542$	−1.55428	+	8.81475i	−0.0667620	+	0.378626i
$543$	1.58813	+	2.75072i	0.0681531	+	0.118045i
$544$	−1.09561	+	1.89766i	−0.0469741	+	0.0813615i
$545$	−12.1265	−	10.1753i	−0.519440	−	0.435862i
$546$	−70.3292	−	25.5978i	−3.00981	−	1.09548i
$547$	−2.78367	+	1.01317i	−0.119021	+	0.0433202i	−0.400844	−	0.916146i	$-0.631283\pi$
$547$	−2.78367	+	1.01317i	−0.119021	+	0.0433202i	0.281823	+	0.959466i	$0.409061\pi$
$548$	−5.53564	+	4.64495i	−0.236471	+	0.198423i
$549$	−3.10135	−	17.5886i	−0.132362	−	0.750663i
$550$	−2.84657			−0.121378
$551$	−14.9435	+	29.5744i	−0.636617	+	1.25991i
$552$	−6.16497			−0.262399
$553$	−13.0825	−	74.1943i	−0.556322	−	3.15506i
$554$	5.97623	−	5.01465i	0.253906	−	0.213052i
$555$	−4.49609	+	1.63644i	−0.190848	+	0.0694631i
$556$	2.26632	+	0.824874i	0.0961135	+	0.0349825i
$557$	−23.5710	−	19.7784i	−0.998734	−	0.838038i	−0.0119259	−	0.999929i	$-0.503796\pi$
$557$	−23.5710	−	19.7784i	−0.998734	−	0.838038i	−0.986809	+	0.161891i	$0.948241\pi$
$558$	−6.44829	+	11.1688i	−0.272978	+	0.472811i
$559$	5.68936	+	9.85426i	0.240634	+	0.416791i
$560$	−0.853783	+	4.84205i	−0.0360789	+	0.204614i
$561$	2.51264	−	14.2499i	0.106084	−	0.601631i
$562$	9.14912	+	15.8467i	0.385933	+	0.668455i
$563$	17.7546	−	30.7518i	0.748266	−	1.29603i	−0.200387	−	0.979717i	$-0.564220\pi$
$563$	17.7546	−	30.7518i	0.748266	−	1.29603i	0.948653	−	0.316318i	$-0.102447\pi$
$564$	5.34008	+	4.48086i	0.224858	+	0.188678i
$565$	−17.1072	−	6.22651i	−0.719705	−	0.261951i
$566$	6.79213	−	2.47213i	0.285494	−	0.103911i
$567$	39.4460	−	33.0991i	1.65658	−	1.39003i
$568$	1.07060	+	6.07169i	0.0449215	+	0.254763i
$569$	33.0813			1.38684			0.693421	−	0.720533i	$-0.256103\pi$
$569$	33.0813			1.38684			0.693421	+	0.720533i	$0.256103\pi$
$570$	−2.30786	−	9.84488i	−0.0966654	−	0.412357i
$571$	2.29342			0.0959766			0.0479883	−	0.998848i	$-0.484719\pi$
$571$	2.29342			0.0959766			0.0479883	+	0.998848i	$0.484719\pi$
$572$	−3.24351	−	18.3948i	−0.135618	−	0.769127i
$573$	−24.2282	+	20.3298i	−1.01215	+	0.849291i
$574$	43.2328	−	15.7355i	1.80450	−	0.656785i
$575$	2.49728	+	0.908934i	0.104144	+	0.0379052i
$576$	1.82431	+	1.53078i	0.0760129	+	0.0637824i
$577$	7.85178	−	13.5997i	0.326874	−	0.566162i	−0.655016	−	0.755615i	$-0.727338\pi$
$577$	7.85178	−	13.5997i	0.326874	−	0.566162i	0.981890	+	0.189453i	$0.0606715\pi$
$578$	−6.09926	−	10.5642i	−0.253696	−	0.439414i
$579$	2.10255	−	11.9242i	0.0873792	−	0.495552i
$580$	−1.32004	+	7.48630i	−0.0548115	+	0.310852i
$581$	−3.22554	−	5.58680i	−0.133818	−	0.231780i
$582$	−2.38277	+	4.12708i	−0.0987691	+	0.171073i
$583$	−9.20682	−	7.72544i	−0.381308	−	0.319955i
$584$	−3.73719	−	1.36023i	−0.154646	−	0.0562865i
$585$	14.6843	−	5.34464i	0.607121	−	0.220974i
$586$	−8.72264	+	7.31917i	−0.360329	+	0.302352i
$587$	−4.60359	−	26.1082i	−0.190010	−	1.07760i	−0.919347	−	0.393448i	$-0.871282\pi$
$587$	−4.60359	−	26.1082i	−0.190010	−	1.07760i	0.729337	−	0.684155i	$-0.239829\pi$
$588$	−39.8411			−1.64302
$589$	17.2093	−	16.1568i	0.709098	−	0.665728i
$590$	0.964592			0.0397116
$591$	−1.15024	−	6.52335i	−0.0473146	−	0.268335i
$592$	−1.57998	+	1.32576i	−0.0649369	+	0.0544885i
$593$	2.75254	−	1.00184i	0.113033	−	0.0411408i	−0.284884	−	0.958562i	$-0.591955\pi$
$593$	2.75254	−	1.00184i	0.113033	−	0.0411408i	0.397918	+	0.917421i	$0.369733\pi$
$594$	3.83813	+	1.39697i	0.157481	+	0.0573182i
$595$	8.25314	+	6.92521i	0.338346	+	0.283906i
$596$	3.48937	−	6.04376i	0.142930	−	0.247562i
$597$	−1.69882	−	2.94244i	−0.0695281	−	0.120426i
$598$	−3.02812	+	17.1733i	−0.123829	+	0.702270i
$599$	6.43428	−	36.4906i	0.262897	−	1.49097i	−0.512059	−	0.858950i	$-0.671117\pi$
$599$	6.43428	−	36.4906i	0.262897	−	1.49097i	0.774956	−	0.632015i	$-0.217772\pi$
$600$	−1.15990	−	2.00901i	−0.0473527	−	0.0820173i
$601$	4.84799	−	8.39697i	0.197754	−	0.342520i	−0.750046	−	0.661386i	$-0.769969\pi$
$601$	4.84799	−	8.39697i	0.197754	−	0.342520i	0.947800	+	0.318866i	$0.103302\pi$
$602$	6.53135	+	5.48045i	0.266198	+	0.223367i
$603$	−4.29566	−	1.56349i	−0.174933	−	0.0636704i
$604$	5.35025	−	1.94733i	0.217699	−	0.0792358i
$605$	−2.21925	+	1.86217i	−0.0902255	+	0.0757082i
$606$	−2.01803	−	11.4448i	−0.0819771	−	0.464915i
$607$	−38.0294			−1.54357			−0.771783	−	0.635886i	$-0.780635\pi$
$607$	−38.0294			−1.54357			−0.771783	+	0.635886i	$0.780635\pi$
$608$	−2.38634	−	3.64766i	−0.0967787	−	0.147932i
$609$	−86.7049			−3.51346
$610$	1.30228	+	7.38561i	0.0527279	+	0.299035i
$611$	15.1050	−	12.6746i	0.611081	−	0.512758i
$612$	4.90364	−	1.78478i	0.198218	−	0.0721454i
$613$	21.4696	+	7.81429i	0.867149	+	0.315616i	0.737012	−	0.675880i	$-0.236236\pi$
$613$	21.4696	+	7.81429i	0.867149	+	0.315616i	0.130137	+	0.991496i	$0.458458\pi$
$614$	−3.78649	−	3.17725i	−0.152810	−	0.128223i
$615$	−10.8535	+	18.7988i	−0.437656	+	0.758043i
$616$	−6.99793	−	12.1208i	−0.281955	−	0.488360i
$617$	−4.41886	+	25.0606i	−0.177896	+	1.00890i	0.756851	+	0.653588i	$0.226737\pi$
$617$	−4.41886	+	25.0606i	−0.177896	+	1.00890i	−0.934747	+	0.355313i	$0.884374\pi$
$618$	−3.63951	+	20.6407i	−0.146403	+	0.830291i
$619$	−7.95778	−	13.7833i	−0.319850	−	0.553997i	0.660606	−	0.750733i	$-0.270299\pi$
$619$	−7.95778	−	13.7833i	−0.319850	−	0.553997i	−0.980457	+	0.196736i	$0.936966\pi$
$620$	2.70769	−	4.68986i	0.108744	−	0.188349i
$621$	−2.92110	−	2.45110i	−0.117220	−	0.0983591i
$622$	22.6628	+	8.24858i	0.908695	+	0.330738i
$623$	−49.7889	+	18.1217i	−1.99475	+	0.726030i
$624$	11.6608	−	9.78453i	0.466804	−	0.391695i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	30.9756			1.23803
$627$	23.0461	+	17.2450i	0.920372	+	0.688698i
$628$	−5.31383			−0.212045
$629$	0.784795	+	4.45079i	0.0312918	+	0.177465i
$630$	8.96967	−	7.52644i	0.357360	−	0.299861i
$631$	18.7345	−	6.81880i	0.745808	−	0.271452i	0.0589675	−	0.998260i	$-0.481219\pi$
$631$	18.7345	−	6.81880i	0.745808	−	0.271452i	0.686841	+	0.726808i	$0.258997\pi$
$632$	14.3988	+	5.24075i	0.572755	+	0.208466i
$633$	−2.32886	−	1.95414i	−0.0925637	−	0.0776702i
$634$	−3.45527	+	5.98470i	−0.137226	+	0.237683i
$635$	−3.82477	−	6.62470i	−0.151781	−	0.262893i
$636$	1.70080	−	9.64574i	0.0674413	−	0.382478i
$637$	−19.5692	+	110.982i	−0.775360	+	4.39728i
$638$	−10.8195	−	18.7399i	−0.428349	−	0.741922i
$639$	7.34130	−	12.7155i	0.290417	−	0.503018i
$640$	−0.766044	−	0.642788i	−0.0302806	−	0.0254084i
$641$	−2.28156	−	0.830421i	−0.0901163	−	0.0327996i	0.296569	−	0.955012i	$-0.404158\pi$
$641$	−2.28156	−	0.830421i	−0.0901163	−	0.0327996i	−0.386685	+	0.922212i	$0.626380\pi$
$642$	−13.0093	+	4.73498i	−0.513434	+	0.186875i
$643$	−5.12827	+	4.30313i	−0.202239	+	0.169699i	−0.738282	−	0.674492i	$-0.764363\pi$
$643$	−5.12827	+	4.30313i	−0.202239	+	0.169699i	0.536043	+	0.844191i	$0.319918\pi$
$644$	2.26897	+	12.8680i	0.0894099	+	0.507069i
$645$	−4.02274			−0.158395
$646$	−9.53651	+	0.532031i	−0.375209	+	0.0209325i
$647$	28.2280			1.10976			0.554878	−	0.831932i	$-0.312765\pi$
$647$	28.2280			1.10976			0.554878	+	0.831932i	$0.312765\pi$
$648$	1.81862	+	10.3139i	0.0714421	+	0.405168i
$649$	−2.10339	+	1.76495i	−0.0825652	+	0.0692805i
$650$	−6.16606	+	2.24426i	−0.241853	+	0.0880273i
$651$	58.0421	+	21.1256i	2.27485	+	0.827977i
$652$	−3.42697	−	2.87557i	−0.134210	−	0.112616i
$653$	−8.49136	+	14.7075i	−0.332293	+	0.575548i	−0.982961	−	0.183814i	$-0.941156\pi$
$653$	−8.49136	+	14.7075i	−0.332293	+	0.575548i	0.650668	+	0.759362i	$0.274489\pi$
$654$	18.3612	+	31.8025i	0.717978	+	1.24358i
$655$	−2.31209	+	13.1125i	−0.0903407	+	0.512347i
$656$	−1.62488	+	9.21513i	−0.0634408	+	0.359791i
$657$	4.73559	+	8.20228i	0.184753	+	0.320002i
$658$	7.38739	−	12.7953i	0.287990	−	0.498814i
$659$	−14.0188	−	11.7632i	−0.546095	−	0.458228i	0.327521	−	0.944844i	$-0.393787\pi$
$659$	−14.0188	−	11.7632i	−0.546095	−	0.458228i	−0.873616	+	0.486616i	$0.838231\pi$
$660$	6.20524	+	2.25852i	0.241539	+	0.0879128i
$661$	−5.11150	+	1.86043i	−0.198814	+	0.0723625i	−0.439508	−	0.898239i	$-0.644847\pi$
$661$	−5.11150	+	1.86043i	−0.198814	+	0.0723625i	0.240694	+	0.970601i	$0.422625\pi$
$662$	−3.20119	+	2.68612i	−0.124418	+	0.104399i
$663$	−5.79203	−	32.8482i	−0.224944	−	1.27572i
$664$	1.31206			0.0509180
$665$	−19.6995	+	8.44045i	−0.763915	+	0.327306i
$666$	4.91183			0.190329
$667$	3.50806	+	19.8952i	0.135833	+	0.770344i
$668$	2.79512	−	2.34538i	0.108146	−	0.0907456i
$669$	61.3213	−	22.3191i	2.37082	−	0.862907i
$670$	1.80379	+	0.656525i	0.0696864	+	0.0253638i
$671$	−16.3535	−	13.7222i	−0.631321	−	0.529741i
$672$	5.70293	−	9.87776i	0.219995	−	0.381043i
$673$	14.9572	+	25.9066i	0.576557	+	0.998626i	0.995871	+	0.0907847i	$0.0289375\pi$
$673$	14.9572	+	25.9066i	0.576557	+	0.998626i	−0.419313	+	0.907842i	$0.637729\pi$
$674$	−2.98695	+	16.9399i	−0.115053	+	0.652499i
$675$	0.249162	−	1.41307i	0.00959026	−	0.0543891i
$676$	−15.0285	−	26.0302i	−0.578021	−	1.00116i
$677$	15.7282	−	27.2420i	0.604483	−	1.04700i	−0.387650	−	0.921807i	$-0.626713\pi$
$677$	15.7282	−	27.2420i	0.604483	−	1.04700i	0.992133	−	0.125189i	$-0.0399537\pi$
$678$	32.3517	+	27.1463i	1.24246	+	1.04255i
$679$	9.49130	+	3.45455i	0.364243	+	0.132573i
$680$	−2.05908	+	0.749444i	−0.0789622	+	0.0287399i
$681$	−22.4738	+	18.8578i	−0.861199	+	0.722631i
$682$	2.67684	+	15.1811i	0.102501	+	0.581314i
$683$	−49.8920			−1.90906			−0.954532	−	0.298109i	$-0.903644\pi$
$683$	−49.8920			−1.90906			−0.954532	+	0.298109i	$0.903644\pi$
$684$	−1.23033	+	10.3074i	−0.0470430	+	0.394114i
$685$	−7.22627			−0.276101
$686$	8.68670	+	49.2647i	0.331660	+	1.88094i
$687$	−24.4240	+	20.4941i	−0.931833	+	0.781900i
$688$	−1.62951	+	0.593093i	−0.0621245	+	0.0226115i
$689$	−26.0341	−	9.47562i	−0.991818	−	0.360992i
$690$	−4.72264	−	3.96277i	−0.179788	−	0.150860i
$691$	−9.36370	+	16.2184i	−0.356212	+	0.616977i	−0.987325	−	0.158714i	$-0.949265\pi$
$691$	−9.36370	+	16.2184i	−0.356212	+	0.616977i	0.631113	+	0.775691i	$0.282599\pi$
$692$	0.588156	+	1.01872i	0.0223583	+	0.0387258i
$693$	−5.78782	+	32.8243i	−0.219861	+	1.24689i
$694$	−3.20604	+	18.1823i	−0.121699	+	0.690192i
$695$	1.20589	+	2.08866i	0.0457419	+	0.0792272i
$696$	8.81731	−	15.2720i	0.334219	−	0.578885i
$697$	15.7069	+	13.1797i	0.594943	+	0.499217i
$698$	23.2488	+	8.46187i	0.879980	+	0.320286i
$699$	53.6650	−	19.5325i	2.02980	−	0.738786i
$700$	−3.76644	+	3.16042i	−0.142358	+	0.119453i
$701$	−3.10915	−	17.6329i	−0.117431	−	0.665984i	−0.985518	−	0.169572i	$-0.945761\pi$
$701$	−3.10915	−	17.6329i	−0.117431	−	0.665984i	0.868087	−	0.496412i	$-0.165350\pi$
$702$	9.41531			0.355358
$703$	−8.60630	−	2.59952i	−0.324593	−	0.0980426i
$704$	2.84657			0.107284
$705$	1.21050	+	6.86508i	0.0455900	+	0.258554i
$706$	4.91028	−	4.12021i	0.184801	−	0.155066i
$707$	−23.1458	+	8.42437i	−0.870486	+	0.316831i
$708$	−2.10271	−	0.765324i	−0.0790247	−	0.0287627i
$709$	20.6673	+	17.3419i	0.776177	+	0.651290i	0.942283	−	0.334818i	$-0.108675\pi$
$709$	20.6673	+	17.3419i	0.776177	+	0.651290i	−0.166106	+	0.986108i	$0.553119\pi$
$710$	−3.08268	+	5.33936i	−0.115691	+	0.200382i
$711$	−18.2455	−	31.6022i	−0.684260	−	1.18517i
$712$	1.87128	−	10.6126i	0.0701293	−	0.397723i
$713$	2.49908	−	14.1730i	0.0935913	−	0.530783i
$714$	−12.4964	−	21.6444i	−0.467667	−	0.810023i
$715$	9.33930	−	16.1761i	0.349270	−	0.604953i
$716$	3.31741	+	2.78364i	0.123977	+	0.104029i
$717$	−35.5192	−	12.9279i	−1.32649	−	0.482802i
$718$	−34.5952	+	12.5916i	−1.29108	+	0.469915i
$719$	32.4936	−	27.2653i	1.21180	−	1.01683i	0.212593	−	0.977141i	$-0.431809\pi$
$719$	32.4936	−	27.2653i	1.21180	−	1.01683i	0.999212	−	0.0396842i	$-0.0126352\pi$
$720$	0.413538	+	2.34529i	0.0154116	+	0.0874037i
$721$	44.4222			1.65437
$722$	7.61079	−	17.4091i	0.283244	−	0.647899i
$723$	44.6672			1.66119
$724$	0.237758	+	1.34839i	0.00883622	+	0.0501127i
$725$	−5.82331	+	4.88633i	−0.216272	+	0.181474i
$726$	6.31523	−	2.29856i	0.234380	−	0.0853074i
$727$	40.4476	+	14.7217i	1.50012	+	0.545999i	0.956092	−	0.293068i	$-0.0946761\pi$
$727$	40.4476	+	14.7217i	1.50012	+	0.545999i	0.544028	+	0.839067i	$0.316898\pi$
$728$	−24.7146	−	20.7380i	−0.915984	−	0.768602i
$729$	7.47766	−	12.9517i	0.276950	−	0.479692i
$730$	−1.98852	−	3.44421i	−0.0735983	−	0.127476i
$731$	−0.659826	+	3.74206i	−0.0244045	+	0.138405i
$732$	3.02104	−	17.1331i	0.111661	−	0.633259i
$733$	15.1979	+	26.3235i	0.561347	+	0.972282i	0.997379	+	0.0723507i	$0.0230501\pi$
$733$	15.1979	+	26.3235i	0.561347	+	0.972282i	−0.436032	+	0.899931i	$0.643617\pi$
$734$	7.31190	−	12.6646i	0.269887	−	0.467458i
$735$	−30.5200	−	25.6093i	−1.12575	−	0.944615i
$736$	−2.49728	−	0.908934i	−0.0920508	−	0.0335038i
$737$	−5.13461	+	1.86885i	−0.189136	+	0.0688398i
$738$	17.0706	−	14.3239i	0.628378	−	0.527272i
$739$	−6.40630	−	36.3319i	−0.235659	−	1.33649i	−0.841221	−	0.540692i	$-0.818162\pi$
$739$	−6.40630	−	36.3319i	−0.235659	−	1.33649i	0.605561	−	0.795799i	$-0.292949\pi$
$740$	−2.06252			−0.0758198
$741$	63.5171	+	19.1852i	2.33336	+	0.704787i
$742$	−20.7592			−0.762095
$743$	4.26670	+	24.1976i	0.156530	+	0.887725i	0.957374	+	0.288852i	$0.0932736\pi$
$743$	4.26670	+	24.1976i	0.156530	+	0.887725i	−0.800844	+	0.598873i	$0.795615\pi$
$744$	−9.62352	+	8.07509i	−0.352815	+	0.296047i
$745$	6.55786	−	2.38687i	0.240262	−	0.0874480i
$746$	−12.7398	−	4.63691i	−0.466438	−	0.169769i
$747$	−2.39361	−	2.00848i	−0.0875778	−	0.0734865i
$748$	3.11874	−	5.40182i	0.114033	−	0.197510i
$749$	14.6711	+	25.4112i	0.536072	+	0.928503i
$750$	0.402829	−	2.28456i	0.0147092	−	0.0834202i
$751$	1.64514	−	9.33008i	0.0600322	−	0.340459i	−0.939967	−	0.341264i	$-0.889145\pi$
$751$	1.64514	−	9.33008i	0.0600322	−	0.340459i	1.00000		0.000804564i	$0.000256101\pi$
$752$	1.50250	+	2.60240i	0.0547904	+	0.0948998i
$753$	−32.2105	+	55.7902i	−1.17382	+	2.03311i
$754$	−38.2113	−	32.0631i	−1.39157	−	1.16767i
$755$	5.35025	+	1.94733i	0.194716	+	0.0708707i
$756$	6.62942	−	2.41291i	0.241110	−	0.0877568i
$757$	−5.41985	+	4.54780i	−0.196988	+	0.165292i	−0.735946	−	0.677040i	$-0.763262\pi$
$757$	−5.41985	+	4.54780i	−0.196988	+	0.165292i	0.538958	+	0.842332i	$0.318818\pi$
$758$	−5.25979	−	29.8298i	−0.191044	−	1.08347i
$759$	17.5490			0.636990
$760$	0.516628	−	4.32817i	0.0187401	−	0.156999i
$761$	−45.9880			−1.66706			−0.833531	−	0.552472i	$-0.813684\pi$
$761$	−45.9880			−1.66706			−0.833531	+	0.552472i	$0.813684\pi$
$762$	3.08146	+	17.4758i	0.111629	+	0.633082i
$763$	59.6227	−	50.0293i	2.15849	−	1.81118i
$764$	−12.8116	+	4.66302i	−0.463506	+	0.168702i
$765$	4.90364	+	1.78478i	0.177291	+	0.0645288i
$766$	21.9571	+	18.4242i	0.793342	+	0.665693i
$767$	−3.16472	+	5.48146i	−0.114272	+	0.197924i
$768$	1.15990	+	2.00901i	0.0418543	+	0.0724937i
$769$	−7.83899	+	44.4571i	−0.282681	+	1.60317i	0.430771	+	0.902461i	$0.358242\pi$
$769$	−7.83899	+	44.4571i	−0.282681	+	1.60317i	−0.713452	+	0.700704i	$0.752869\pi$
$770$	2.43036	−	13.7832i	0.0875839	−	0.496713i
$771$	15.1602	+	26.2582i	0.545981	+	0.945667i
$772$	2.60974	−	4.52019i	0.0939264	−	0.162685i
$773$	−0.590996	−	0.495905i	−0.0212567	−	0.0178364i	0.632097	−	0.774889i	$-0.282194\pi$
$773$	−0.590996	−	0.495905i	−0.0212567	−	0.0178364i	−0.653354	+	0.757052i	$0.726639\pi$
$774$	3.88063	+	1.41243i	0.139486	+	0.0507689i
$775$	5.08880	−	1.85217i	0.182795	−	0.0665320i
$776$	−1.57368	+	1.32047i	−0.0564918	+	0.0474022i
$777$	−4.08504	−	23.1674i	−0.146550	−	0.831127i
$778$	−17.1263			−0.614007
$779$	−37.4911	+	16.0634i	−1.34326	+	0.575532i
$780$	15.2220			0.545036
$781$	−3.04755	−	17.2835i	−0.109050	−	0.618452i
$782$	−4.46090	+	3.74314i	−0.159521	+	0.133854i
$783$	10.2498	−	3.73061i	0.366297	−	0.133321i
$784$	−16.1386	−	5.87398i	−0.576379	−	0.209785i
$785$	−4.07063	−	3.41567i	−0.145287	−	0.121910i
$786$	15.4438	−	26.7494i	0.550862	−	0.954121i
$787$	6.76358	+	11.7149i	0.241095	+	0.417590i	0.961027	−	0.276456i	$-0.0891600\pi$
$787$	6.76358	+	11.7149i	0.241095	+	0.417590i	−0.719931	+	0.694045i	$0.755827\pi$
$788$	0.495837	−	2.81203i	0.0176635	−	0.100174i
$789$	−6.06499	+	34.3963i	−0.215919	+	1.22454i
$790$	7.66146	+	13.2700i	0.272582	+	0.472127i
$791$	44.7549	−	77.5178i	1.59130	−	2.75621i
$792$	−5.19303	−	4.35747i	−0.184526	−	0.154836i
$793$	−46.2427	−	16.8310i	−1.64213	−	0.597685i
$794$	24.5306	−	8.92842i	0.870560	−	0.316858i
$795$	7.50305	−	6.29581i	0.266106	−	0.223289i
$796$	−0.254330	−	1.44238i	−0.00901448	−	0.0511237i
$797$	−33.8026			−1.19735			−0.598674	−	0.800992i	$-0.704306\pi$
$797$	−33.8026			−1.19735			−0.598674	+	0.800992i	$0.704306\pi$
$798$	49.6398	−	2.76935i	1.75723	−	0.0980338i
$799$	6.58463			0.232947
$800$	−0.173648	−	0.984808i	−0.00613939	−	0.0348182i
$801$	−19.6593	+	16.4961i	−0.694628	+	0.582862i
$802$	−8.74942	+	3.18453i	−0.308953	+	0.112450i
$803$	10.6382	+	3.87198i	0.375413	+	0.136639i
$804$	−3.41117	−	2.86232i	−0.120303	−	0.100946i
$805$	−6.53324	+	11.3159i	−0.230266	+	0.398833i
$806$	17.7673	+	30.7739i	0.625827	+	1.08396i
$807$	−9.85131	+	55.8695i	−0.346782	+	1.96670i
$808$	0.869918	−	4.93355i	0.0306036	−	0.173562i
$809$	6.45477	+	11.1800i	0.226938	+	0.393068i	0.956899	−	0.290421i	$-0.0937953\pi$
$809$	6.45477	+	11.1800i	0.226938	+	0.393068i	−0.729961	+	0.683488i	$0.760462\pi$
$810$	−5.23651	+	9.06990i	−0.183992	+	0.318684i
$811$	42.3134	+	35.5052i	1.48582	+	1.24675i	0.899681	+	0.436547i	$0.143799\pi$
$811$	42.3134	+	35.5052i	1.48582	+	1.24675i	0.586143	+	0.810208i	$0.300646\pi$
$812$	−35.1220	−	12.7834i	−1.23254	−	0.448608i
$813$	19.5117	−	7.10168i	0.684305	−	0.249067i
$814$	4.49753	−	3.77388i	0.157638	−	0.132274i
$815$	−0.776830	−	4.40562i	−0.0272112	−	0.154322i
$816$	5.08321			0.177948
$817$	−6.05196	−	4.52857i	−0.211731	−	0.158435i
$818$	−14.5798			−0.509771
$819$	13.3418	+	75.6652i	0.466201	+	2.64396i
$820$	−7.16810	+	6.01475i	−0.250321	+	0.210044i
$821$	−48.4375	+	17.6298i	−1.69048	+	0.615285i	−0.994686	−	0.102955i	$-0.967170\pi$
$821$	−48.4375	+	17.6298i	−1.69048	+	0.615285i	−0.695796	+	0.718240i	$0.744948\pi$
$822$	15.7525	+	5.73345i	0.549432	+	0.199977i
$823$	−20.5172	−	17.2160i	−0.715186	−	0.600112i	0.210863	−	0.977516i	$-0.432373\pi$
$823$	−20.5172	−	17.2160i	−0.715186	−	0.600112i	−0.926049	+	0.377403i	$0.876817\pi$
$824$	−4.51744	+	7.82444i	−0.157373	+	0.272577i
$825$	3.30174	+	5.71878i	0.114952	+	0.199102i
$826$	−0.823552	+	4.67060i	−0.0286551	+	0.162511i
$827$	−0.785414	+	4.45430i	−0.0273115	+	0.154891i	−0.995414	−	0.0956647i	$-0.969502\pi$
$827$	−0.785414	+	4.45430i	−0.0273115	+	0.154891i	0.968102	+	0.250556i	$0.0806134\pi$
$828$	3.16443	+	5.48096i	0.109972	+	0.190476i
$829$	6.55868	−	11.3600i	0.227792	−	0.394548i	−0.729361	−	0.684129i	$-0.760183\pi$
$829$	6.55868	−	11.3600i	0.227792	−	0.394548i	0.957154	+	0.289581i	$0.0935160\pi$
$830$	1.00510	+	0.843379i	0.0348875	+	0.0292741i
$831$	−17.0063	−	6.18978i	−0.589941	−	0.214721i
$832$	6.16606	−	2.24426i	0.213770	−	0.0778059i
$833$	−28.8285	+	24.1900i	−0.998849	+	0.838134i
$834$	−0.971531	−	5.50983i	−0.0336414	−	0.190790i
$835$	3.64877			0.126271
$836$	6.79288	+	10.3833i	0.234937	+	0.359114i
$837$	−7.77037			−0.268583
$838$	−2.53472	−	14.3751i	−0.0875604	−	0.496580i
$839$	−19.2974	+	16.1924i	−0.666220	+	0.559025i	−0.911944	−	0.410315i	$-0.865419\pi$
$839$	−19.2974	+	16.1924i	−0.666220	+	0.559025i	0.245724	+	0.969340i	$0.420974\pi$
$840$	10.7180	−	3.90103i	0.369806	−	0.134598i
$841$	−27.0511	−	9.84578i	−0.932796	−	0.339510i
$842$	30.0605	+	25.2237i	1.03595	+	0.869267i
$843$	21.2241	−	36.7613i	0.730998	−	1.26613i
$844$	−0.655252	−	1.13493i	−0.0225547	−	0.0390659i
$845$	5.21936	−	29.6004i	0.179551	−	1.01829i
$846$	1.24268	−	7.04758i	0.0427241	−	0.242301i
$847$	−7.12197	−	12.3356i	−0.244714	−	0.423857i
$848$	2.11108	−	3.65649i	0.0724946	−	0.125564i
$849$	−12.8447	−	10.7780i	−0.440829	−	0.369900i
$850$	−2.05908	−	0.749444i	−0.0706259	−	0.0257057i
$851$	−5.15068	+	1.87470i	−0.176563	+	0.0642638i
$852$	10.9563	−	9.19340i	0.375356	−	0.314961i
$853$	−5.90914	−	33.5124i	−0.202325	−	1.14744i	−0.901594	−	0.432583i	$-0.857602\pi$
$853$	−5.90914	−	33.5124i	−0.202325	−	1.14744i	0.699269	−	0.714859i	$-0.253509\pi$
$854$	−36.8734			−1.26178
$855$	−7.56797	+	7.10509i	−0.258819	+	0.242989i
$856$	−5.96783			−0.203976
$857$	−0.187890	−	1.06558i	−0.00641819	−	0.0363994i	0.981430	−	0.191818i	$-0.0614384\pi$
$857$	−0.187890	−	1.06558i	−0.00641819	−	0.0363994i	−0.987849	+	0.155419i	$0.950327\pi$
$858$	−33.1932	+	27.8524i	−1.13320	+	0.950864i
$859$	−32.0734	+	11.6737i	−1.09433	+	0.398303i	−0.825223	−	0.564807i	$-0.808950\pi$
$859$	−32.0734	+	11.6737i	−1.09433	+	0.398303i	−0.269106	+	0.963111i	$0.586728\pi$
$860$	−1.62951	−	0.593093i	−0.0555658	−	0.0202243i
$861$	−81.7583	−	68.6034i	−2.78632	−	2.33800i
$862$	10.9383	−	18.9457i	0.372561	−	0.645294i
$863$	17.1608	+	29.7233i	0.584160	+	1.01179i	0.994980	+	0.100078i	$0.0319091\pi$
$863$	17.1608	+	29.7233i	0.584160	+	1.01179i	−0.410820	+	0.911716i	$0.634758\pi$
$864$	−0.249162	+	1.41307i	−0.00847668	+	0.0480736i
$865$	−0.204264	+	1.15844i	−0.00694520	+	0.0393882i
$866$	−0.550842	−	0.954087i	−0.0187184	−	0.0324212i
$867$	−14.1491	+	24.5069i	−0.480527	+	0.832297i
$868$	20.3967	+	17.1149i	0.692311	+	0.580918i
$869$	−40.9873	−	14.9182i	−1.39040	−	0.506064i
$870$	16.5711	−	6.03139i	0.561814	−	0.204483i
$871$	−9.64886	+	8.09635i	−0.326939	+	0.274334i
$872$	2.74884	+	15.5895i	0.0930876	+	0.527926i
$873$	4.89223			0.165577
$874$	−2.64386	−	11.2782i	−0.0894300	−	0.381492i
$875$	−4.91674			−0.166216
$876$	1.60206	+	9.08576i	0.0541287	+	0.306979i
$877$	1.21443	−	1.01903i	0.0410084	−	0.0344102i	−0.622053	−	0.782975i	$-0.713701\pi$
$877$	1.21443	−	1.01903i	0.0410084	−	0.0344102i	0.663062	+	0.748565i	$0.269257\pi$
$878$	−3.96284	+	1.44236i	−0.133740	+	0.0486772i
$879$	24.8216	+	9.03434i	0.837213	+	0.304721i
$880$	2.18060	+	1.82974i	0.0735080	+	0.0616806i
$881$	8.41502	−	14.5752i	0.283509	−	0.491052i	−0.688737	−	0.725011i	$-0.741835\pi$
$881$	8.41502	−	14.5752i	0.283509	−	0.491052i	0.972247	+	0.233959i	$0.0751680\pi$
$882$	20.4501	+	35.4206i	0.688591	+	1.19267i
$883$	−8.30743	+	47.1138i	−0.279567	+	1.58550i	0.444503	+	0.895778i	$0.353380\pi$
$883$	−8.30743	+	47.1138i	−0.279567	+	1.58550i	−0.724070	+	0.689727i	$0.757731\pi$
$884$	2.49678	−	14.1599i	0.0839758	−	0.476250i
$885$	−1.11883	−	1.93787i	−0.0376090	−	0.0651408i
$886$	3.79155	−	6.56715i	0.127380	−	0.220628i
$887$	23.6487	+	19.8436i	0.794045	+	0.666283i	0.946743	−	0.321990i	$-0.104352\pi$
$887$	23.6487	+	19.8436i	0.794045	+	0.666283i	−0.152698	+	0.988273i	$0.548796\pi$
$888$	4.49609	+	1.63644i	0.150879	+	0.0549154i
$889$	35.3426	−	12.8637i	1.18535	−	0.431433i
$890$	8.25512	−	6.92687i	0.276712	−	0.232189i
$891$	−5.17683	−	29.3593i	−0.173430	−	0.983573i
$892$	28.1303			0.941874
$893$	−5.90720	+	11.6908i	−0.197677	+	0.391218i
$894$	−16.1893			−0.541450
$895$	0.751996	+	4.26478i	0.0251364	+	0.142556i
$896$	3.76644	−	3.16042i	0.125828	−	0.105582i
$897$	38.0136	−	13.8358i	1.26924	−	0.461965i
$898$	27.9065	+	10.1571i	0.931252	+	0.338948i
$899$	31.5354	+	26.4614i	1.05177	+	0.882537i
$900$	−1.19073	+	2.06241i	−0.0396911	+	0.0687471i
$901$	−4.62585	−	8.01220i	−0.154109	−	0.266925i
$902$	4.62533	−	26.2315i	0.154007	−	0.873415i
$903$	3.43455	−	19.4783i	0.114295	−	0.648197i
$904$	9.10255	+	15.7661i	0.302746	+	0.524372i
$905$	−0.684598	+	1.18576i	−0.0227568	+	0.0394159i
$906$	−10.1180	−	8.48997i	−0.336146	−	0.282060i
$907$	21.3569	+	7.77328i	0.709145	+	0.258108i	0.671310	−	0.741176i	$-0.265732\pi$
$907$	21.3569	+	7.77328i	0.709145	+	0.258108i	0.0378346	+	0.999284i	$0.487954\pi$
$908$	−11.8839	+	4.32538i	−0.394380	+	0.143543i
$909$	−9.13917	+	7.66868i	−0.303127	+	0.254354i
$910$	−5.60235	−	31.7725i	−0.185716	−	1.05325i
$911$	−58.5516			−1.93990			−0.969950	−	0.243305i	$-0.921768\pi$
$911$	−58.5516			−1.93990			−0.969950	+	0.243305i	$0.921768\pi$
$912$	−4.56025	+	9.02508i	−0.151005	+	0.298850i
$913$	−3.73489			−0.123607
$914$	−1.58467	−	8.98712i	−0.0524163	−	0.297267i
$915$	13.3272	−	11.1829i	0.440584	−	0.369694i
$916$	−12.9151	+	4.70071i	−0.426727	+	0.155316i
$917$	−61.5173	−	22.3905i	−2.03148	−	0.739398i
$918$	2.40854	+	2.02101i	0.0794937	+	0.0667031i
$919$	−4.56100	+	7.89988i	−0.150454	+	0.260593i	−0.931394	−	0.364012i	$-0.881407\pi$
$919$	−4.56100	+	7.89988i	−0.150454	+	0.260593i	0.780941	+	0.624605i	$0.214740\pi$
$920$	−1.32877	−	2.30150i	−0.0438083	−	0.0758783i
$921$	−1.99115	+	11.2924i	−0.0656106	+	0.372096i
$922$	4.58180	−	25.9847i	0.150894	−	0.855760i
$923$	−20.2279	−	35.0357i	−0.665809	−	1.15322i
$924$	−16.2338	+	28.1178i	−0.534053	+	0.925006i
$925$	−1.57998	−	1.32576i	−0.0519495	−	0.0435908i
$926$	−14.7737	−	5.37720i	−0.485495	−	0.176706i
$927$	20.2187	−	7.35901i	0.664069	−	0.241701i
$928$	5.82331	−	4.88633i	0.191159	−	0.160402i
$929$	9.58024	+	54.3323i	0.314318	+	1.78258i	0.576021	+	0.817435i	$0.304605\pi$
$929$	9.58024	+	54.3323i	0.314318	+	1.78258i	−0.261703	+	0.965148i	$0.584284\pi$
$930$	−12.5626			−0.411944
$931$	−17.0859	−	72.8854i	−0.559969	−	2.38872i
$932$	24.6181			0.806394
$933$	−9.71512	−	55.0972i	−0.318059	−	1.80380i
$934$	5.28519	−	4.43480i	0.172937	−	0.145111i
$935$	5.86132	−	2.13335i	0.191686	−	0.0697679i
$936$	−14.6843	−	5.34464i	−0.479971	−	0.174695i
$937$	35.4722	+	29.7647i	1.15883	+	0.972370i	0.999889	−	0.0149184i	$-0.00474886\pi$
$937$	35.4722	+	29.7647i	1.15883	+	0.972370i	0.158937	+	0.987289i	$0.449193\pi$
$938$	−4.71897	+	8.17349i	−0.154080	+	0.266874i
$939$	−35.9286	−	62.2301i	−1.17248	−	2.03080i
$940$	−0.521812	+	2.95934i	−0.0170196	+	0.0965230i
$941$	−3.80849	+	21.5990i	−0.124153	+	0.704107i	0.857654	+	0.514227i	$0.171921\pi$
$941$	−3.80849	+	21.5990i	−0.124153	+	0.704107i	−0.981807	+	0.189880i	$0.939190\pi$
$942$	6.16351	+	10.6755i	0.200818	+	0.347827i
$943$	−12.4337	+	21.5358i	−0.404898	+	0.701303i
$944$	−0.738920	−	0.620028i	−0.0240498	−	0.0201802i
$945$	6.62942	+	2.41291i	0.215655	+	0.0784920i
$946$	4.63852	−	1.68828i	0.150811	−	0.0548908i
$947$	11.2050	−	9.40207i	0.364112	−	0.305526i	−0.442315	−	0.896860i	$-0.645843\pi$
$947$	11.2050	−	9.40207i	0.364112	−	0.305526i	0.806427	+	0.591333i	$0.201398\pi$
$948$	−6.17251	−	35.0061i	−0.200474	−	1.13694i
$949$	26.0965			0.847127
$950$	3.17786	−	2.98349i	0.103103	−	0.0967973i
$951$	16.0310			0.519842
$952$	−1.87083	−	10.6100i	−0.0606341	−	0.343873i
$953$	5.48071	−	4.59886i	0.177538	−	0.148972i	−0.549688	−	0.835370i	$-0.685254\pi$
$953$	5.48071	−	4.59886i	0.177538	−	0.148972i	0.727226	+	0.686398i	$0.240809\pi$
$954$	−9.44853	+	3.43898i	−0.305908	+	0.111341i
$955$	−12.8116	−	4.66302i	−0.414572	−	0.150892i
$956$	−12.4819	−	10.4735i	−0.403693	−	0.338739i
$957$	−25.0991	+	43.4729i	−0.811339	+	1.40528i
$958$	−1.82431	−	3.15979i	−0.0589407	−	0.102088i
$959$	6.16967	−	34.9899i	0.199229	−	1.12988i
$960$	−0.402829	+	2.28456i	−0.0130012	+	0.0737337i
$961$	0.836797	+	1.44938i	0.0269935	+	0.0467540i
$962$	6.76691	−	11.7206i	0.218174	−	0.377889i
$963$	10.8872	+	9.13542i	0.350834	+	0.294385i
$964$	18.0936	+	6.58553i	0.582755	+	0.212105i
$965$	4.90470	−	1.78516i	0.157888	−	0.0574665i
$966$	23.2200	−	19.4839i	0.747092	−	0.626885i
$967$	−1.87290	−	10.6217i	−0.0602283	−	0.341572i	0.939772	−	0.341803i	$-0.111037\pi$
$967$	−1.87290	−	10.6217i	−0.0602283	−	0.341572i	−1.00000		0.000231267i	$0.999926\pi$
$968$	2.89703			0.0931141
$969$	12.1303	+	18.5418i	0.389680	+	0.595649i
$970$	−2.05429			−0.0659594
$971$	−9.79260	−	55.5366i	−0.314260	−	1.78225i	−0.576341	−	0.817209i	$-0.695520\pi$
$971$	−9.79260	−	55.5366i	−0.314260	−	1.78225i	0.262082	−	0.965046i	$-0.415591\pi$
$972$	15.3138	−	12.8498i	0.491189	−	0.412156i
$973$	−11.1429	+	4.05570i	−0.357226	+	0.130020i
$974$	−21.1573	−	7.70061i	−0.677922	−	0.246744i
$975$	11.6608	+	9.78453i	0.373443	+	0.313356i
$976$	3.74977	−	6.49480i	0.120027	−	0.207893i
$977$	−8.86235	−	15.3500i	−0.283532	−	0.491091i	0.688720	−	0.725027i	$-0.258173\pi$
$977$	−8.86235	−	15.3500i	−0.283532	−	0.491091i	−0.972252	+	0.233936i	$0.924839\pi$
$978$	−1.80209	+	10.2202i	−0.0576245	+	0.326805i
$979$	−5.32674	+	30.2095i	−0.170243	+	0.965499i
$980$	−8.58718	−	14.8734i	−0.274307	−	0.475114i
$981$	18.8493	−	32.6479i	0.601811	−	1.04237i
$982$	−19.2746	−	16.1733i	−0.615076	−	0.516110i
$983$	26.6978	+	9.71721i	0.851528	+	0.309931i	0.730663	−	0.682738i	$-0.239211\pi$
$983$	26.6978	+	9.71721i	0.851528	+	0.309931i	0.120865	+	0.992669i	$0.461433\pi$
$984$	20.3979	−	7.42424i	0.650263	−	0.236676i
$985$	2.18737	−	1.83542i	0.0696955	−	0.0584814i
$986$	−2.89250	−	16.4042i	−0.0921160	−	0.522416i
$987$	−34.2745			−1.09097
$988$	22.9006	+	17.1361i	0.728565	+	0.545172i
$989$	−4.60842			−0.146539
$990$	−1.17716	−	6.67603i	−0.0374127	−	0.212178i
$991$	−17.7636	+	14.9054i	−0.564279	+	0.473487i	−0.879742	−	0.475451i	$-0.842285\pi$
$991$	−17.7636	+	14.9054i	−0.564279	+	0.473487i	0.315463	+	0.948938i	$0.397840\pi$
$992$	−5.08880	+	1.85217i	−0.161570	+	0.0588065i
$993$	9.10948	+	3.31558i	0.289081	+	0.105217i
$994$	−23.2215	−	19.4851i	−0.736540	−	0.618031i
$995$	0.732314	−	1.26840i	0.0232159	−	0.0402111i
$996$	−1.52186	−	2.63595i	−0.0482221	−	0.0835231i
$997$	5.29489	−	30.0288i	0.167691	−	0.951022i	−0.778555	−	0.627576i	$-0.784047\pi$
$997$	5.29489	−	30.0288i	0.167691	−	0.951022i	0.946246	−	0.323447i	$-0.104842\pi$
$998$	−5.51718	+	31.2895i	−0.174643	+	0.990451i
$999$	1.47972	+	2.56296i	0.0468164	+	0.0810884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.k.d.161.1	yes	18
5.2	odd	4		950.2.u.g.199.6		36
5.3	odd	4		950.2.u.g.199.1		36
5.4	even	2		950.2.l.i.351.3		18
19.6	even	9		3610.2.a.bi.1.3		9
19.13	odd	18		3610.2.a.bj.1.7		9
19.17	even	9	inner	190.2.k.d.131.1	✓	18
95.17	odd	36		950.2.u.g.549.1		36
95.74	even	18		950.2.l.i.701.3		18
95.93	odd	36		950.2.u.g.549.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.1	✓	18	19.17	even	9	inner
190.2.k.d.161.1	yes	18	1.1	even	1	trivial
950.2.l.i.351.3		18	5.4	even	2
950.2.l.i.701.3		18	95.74	even	18
950.2.u.g.199.1		36	5.3	odd	4
950.2.u.g.199.6		36	5.2	odd	4
950.2.u.g.549.1		36	95.17	odd	36
950.2.u.g.549.6		36	95.93	odd	36
3610.2.a.bi.1.3		9	19.6	even	9
3610.2.a.bj.1.7		9	19.13	odd	18

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.77707 + 1.49114i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(1.77707 + 1.49114i) q^{6} +(2.45837 - 4.25802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.413538 - 2.34529i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.77707 + 1.49114i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.939693 - 0.342020i) q^{5} +(1.77707 + 1.49114i) q^{6} +(2.45837 - 4.25802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.413538 - 2.34529i) q^{9} +(-0.173648 + 0.984808i) q^{10} +(-1.42329 - 2.46520i) q^{11} +(1.15990 - 2.00901i) q^{12} +(-5.02662 - 4.21784i) q^{13} +(-4.62023 - 1.68163i) q^{14} +(2.17990 - 0.793418i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.380503 - 2.15794i) q^{17} -2.38147 q^{18} +(4.17271 + 1.26036i) q^{19} +1.00000 q^{20} +(1.98061 + 11.2326i) q^{21} +(-2.18060 + 1.82974i) q^{22} +(2.49728 - 0.908934i) q^{23} +(-2.17990 - 0.793418i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-3.28089 + 5.68268i) q^{26} +(-0.717435 - 1.24263i) q^{27} +(-0.853783 + 4.84205i) q^{28} +(-1.32004 + 7.48630i) q^{29} +(-1.15990 - 2.00901i) q^{30} +(2.70769 - 4.68986i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(6.20524 + 2.25852i) q^{33} +(-2.05908 + 0.749444i) q^{34} +(-3.76644 + 3.16042i) q^{35} +(0.413538 + 2.34529i) q^{36} -2.06252 q^{37} +(0.516628 - 4.32817i) q^{38} +15.2220 q^{39} +(-0.173648 - 0.984808i) q^{40} +(-7.16810 + 6.01475i) q^{41} +(10.7180 - 3.90103i) q^{42} +(-1.62951 - 0.593093i) q^{43} +(2.18060 + 1.82974i) q^{44} +(-1.19073 + 2.06241i) q^{45} +(-1.32877 - 2.30150i) q^{46} +(-0.521812 + 2.95934i) q^{47} +(-0.402829 + 2.28456i) q^{48} +(-8.58718 - 14.8734i) q^{49} +(0.500000 - 0.866025i) q^{50} +(3.89396 + 3.26742i) q^{51} +(6.16606 + 2.24426i) q^{52} +(3.96752 - 1.44406i) q^{53} +(-1.09917 + 0.922316i) q^{54} +(0.494302 + 2.80333i) q^{55} +4.91674 q^{56} +(-9.29456 + 3.98234i) q^{57} +7.60179 q^{58} +(-0.167500 - 0.949937i) q^{59} +(-1.77707 + 1.49114i) q^{60} +(7.04727 - 2.56500i) q^{61} +(-5.08880 - 1.85217i) q^{62} +(-8.96967 - 7.52644i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.28089 + 5.68268i) q^{65} +(1.14668 - 6.50315i) q^{66} +(0.333326 - 1.89039i) q^{67} +(1.09561 + 1.89766i) q^{68} +(-3.08249 + 5.33902i) q^{69} +(3.76644 + 3.16042i) q^{70} +(5.79354 + 2.10868i) q^{71} +(2.23785 - 0.814510i) q^{72} +(-3.04659 + 2.55639i) q^{73} +(0.358153 + 2.03119i) q^{74} -2.31980 q^{75} +(-4.35213 + 0.242800i) q^{76} -13.9959 q^{77} +(-2.64328 - 14.9908i) q^{78} +(11.7380 - 9.84938i) q^{79} +(-0.939693 + 0.342020i) q^{80} +(9.84141 + 3.58198i) q^{81} +(7.16810 + 6.01475i) q^{82} +(0.656032 - 1.13628i) q^{83} +(-5.70293 - 9.87776i) q^{84} +(-0.380503 + 2.15794i) q^{85} +(-0.301121 + 1.70774i) q^{86} +(-8.81731 - 15.2720i) q^{87} +(1.42329 - 2.46520i) q^{88} +(-8.25512 - 6.92687i) q^{89} +(2.23785 + 0.814510i) q^{90} +(-30.3170 + 11.0345i) q^{91} +(-2.03580 + 1.70824i) q^{92} +(2.18147 + 12.3718i) q^{93} +3.00499 q^{94} +(-3.49000 - 2.61150i) q^{95} +2.31980 q^{96} +(0.356724 + 2.02308i) q^{97} +(-13.1563 + 11.0395i) q^{98} +(-6.37020 + 2.31856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q + 9 * q^8 - 18 * q^9	\( 18 q + 9 q^{8} - 18 q^{9} - 12 q^{11} - 6 q^{13} + 6 q^{14} - 42 q^{18} + 18 q^{20} + 12 q^{21} - 3 q^{22} + 9 q^{23} - 9 q^{26} - 18 q^{27} + 3 q^{28} - 6 q^{29} - 6 q^{31} + 66 q^{33} + 18 q^{34} + 3 q^{35} - 18 q^{36} - 12 q^{37} - 6 q^{38} + 48 q^{39} - 21 q^{41} + 42 q^{42} + 18 q^{43} + 3 q^{44} - 21 q^{45} + 18 q^{46} - 54 q^{47} - 39 q^{49} + 9 q^{50} + 42 q^{51} + 12 q^{52} - 24 q^{53} - 54 q^{54} - 6 q^{55} - 18 q^{57} - 30 q^{59} + 48 q^{61} - 30 q^{62} - 57 q^{63} - 9 q^{64} + 9 q^{65} + 24 q^{66} - 6 q^{67} - 6 q^{68} - 30 q^{69} - 3 q^{70} + 30 q^{71} + 6 q^{73} - 3 q^{74} - 21 q^{76} + 30 q^{77} - 24 q^{78} + 30 q^{79} + 18 q^{81} + 21 q^{82} + 6 q^{83} + 6 q^{84} + 36 q^{86} + 24 q^{87} + 12 q^{88} + 30 q^{89} - 60 q^{91} - 18 q^{92} - 12 q^{93} + 6 q^{94} - 12 q^{95} - 12 q^{97} - 18 q^{98} + 171 q^{99}+O(q^{100}) \) 18 * q + 9 * q^8 - 18 * q^9 - 12 * q^11 - 6 * q^13 + 6 * q^14 - 42 * q^18 + 18 * q^20 + 12 * q^21 - 3 * q^22 + 9 * q^23 - 9 * q^26 - 18 * q^27 + 3 * q^28 - 6 * q^29 - 6 * q^31 + 66 * q^33 + 18 * q^34 + 3 * q^35 - 18 * q^36 - 12 * q^37 - 6 * q^38 + 48 * q^39 - 21 * q^41 + 42 * q^42 + 18 * q^43 + 3 * q^44 - 21 * q^45 + 18 * q^46 - 54 * q^47 - 39 * q^49 + 9 * q^50 + 42 * q^51 + 12 * q^52 - 24 * q^53 - 54 * q^54 - 6 * q^55 - 18 * q^57 - 30 * q^59 + 48 * q^61 - 30 * q^62 - 57 * q^63 - 9 * q^64 + 9 * q^65 + 24 * q^66 - 6 * q^67 - 6 * q^68 - 30 * q^69 - 3 * q^70 + 30 * q^71 + 6 * q^73 - 3 * q^74 - 21 * q^76 + 30 * q^77 - 24 * q^78 + 30 * q^79 + 18 * q^81 + 21 * q^82 + 6 * q^83 + 6 * q^84 + 36 * q^86 + 24 * q^87 + 12 * q^88 + 30 * q^89 - 60 * q^91 - 18 * q^92 - 12 * q^93 + 6 * q^94 - 12 * q^95 - 12 * q^97 - 18 * q^98 + 171 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more