LMFDB - Embedded newform 37.2.h.a.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(3,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("37.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.h (of order $18$, 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:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
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} + 30x^{16} + 333x^{14} + 1826x^{12} + 5490x^{10} + 9432x^{8} + 9385x^{6} + 5316x^{4} + 1584x^{2} + 192 $ x^18 + 30x^16 + 333x^14 + 1826x^12 + 5490x^10 + 9432x^8 + 9385x^6 + 5316x^4 + 1584x^2 + 192
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			30.1
Root			$-1.77531i$ of defining polynomial
Character	$\chi$	$=$	37.30
Dual form			37.2.h.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841146 - 2.31103i) q^{2} +(2.14040 + 0.779043i) q^{3} +(-3.10124 + 2.60225i) q^{4} +(-2.84116 + 0.500973i) q^{5} -5.60182i q^{6} +(0.251492 + 1.42628i) q^{7} +(4.36277 + 2.51884i) q^{8} +(1.67628 + 1.40657i) q^{9} +O(q^{10})$	\(q+(-0.841146 - 2.31103i) q^{2} +(2.14040 + 0.779043i) q^{3} +(-3.10124 + 2.60225i) q^{4} +(-2.84116 + 0.500973i) q^{5} -5.60182i q^{6} +(0.251492 + 1.42628i) q^{7} +(4.36277 + 2.51884i) q^{8} +(1.67628 + 1.40657i) q^{9} +(3.54759 + 6.14461i) q^{10} +(1.43354 - 2.48297i) q^{11} +(-8.66517 + 3.15386i) q^{12} +(-0.863812 - 1.02945i) q^{13} +(3.08464 - 1.78092i) q^{14} +(-6.47150 - 1.14110i) q^{15} +(0.745411 - 4.22743i) q^{16} +(0.409304 - 0.487789i) q^{17} +(1.84062 - 5.05706i) q^{18} +(0.636155 - 1.74782i) q^{19} +(7.50746 - 8.94704i) q^{20} +(-0.572841 + 3.24874i) q^{21} +(-6.94403 - 1.22442i) q^{22} +(-6.38349 + 3.68551i) q^{23} +(7.37579 + 8.79012i) q^{24} +(3.12274 - 1.13658i) q^{25} +(-1.65250 + 2.86221i) q^{26} +(-0.924515 - 1.60131i) q^{27} +(-4.49149 - 3.76880i) q^{28} +(8.44060 + 4.87318i) q^{29} +(2.80636 + 15.9157i) q^{30} -2.28766i q^{31} +(-0.474419 + 0.0836529i) q^{32} +(5.00269 - 4.19776i) q^{33} +(-1.47158 - 0.535611i) q^{34} +(-1.42906 - 3.92630i) q^{35} -8.85879 q^{36} +(4.38799 - 4.21255i) q^{37} -4.57436 q^{38} +(-1.04692 - 2.87639i) q^{39} +(-13.6572 - 4.97081i) q^{40} +(-4.07527 + 3.41956i) q^{41} +(7.98978 - 1.40881i) q^{42} +5.16051i q^{43} +(2.01555 + 11.4307i) q^{44} +(-5.46723 - 3.15650i) q^{45} +(13.8868 + 11.6524i) q^{46} +(-5.53593 - 9.58852i) q^{47} +(4.88883 - 8.46770i) q^{48} +(4.60681 - 1.67674i) q^{49} +(-5.25336 - 6.26071i) q^{50} +(1.25608 - 0.725200i) q^{51} +(5.35778 + 0.944721i) q^{52} +(-1.46342 + 8.29949i) q^{53} +(-2.92301 + 3.48351i) q^{54} +(-2.82902 + 7.77267i) q^{55} +(-2.49538 + 6.85601i) q^{56} +(2.72325 - 3.24545i) q^{57} +(4.16229 - 23.6055i) q^{58} +(5.35027 + 0.943396i) q^{59} +(23.0391 - 13.3016i) q^{60} +(0.559486 + 0.666770i) q^{61} +(-5.28685 + 1.92425i) q^{62} +(-1.58459 + 2.74459i) q^{63} +(-3.70027 - 6.40906i) q^{64} +(2.96995 + 2.49209i) q^{65} +(-13.9091 - 8.03045i) q^{66} +(0.975073 + 5.52991i) q^{67} +2.57786i q^{68} +(-16.5344 + 2.91546i) q^{69} +(-7.87176 + 6.60519i) q^{70} +(0.480027 + 0.174716i) q^{71} +(3.77030 + 10.3588i) q^{72} -3.16083 q^{73} +(-13.4263 - 6.59740i) q^{74} +7.56936 q^{75} +(2.57540 + 7.07585i) q^{76} +(3.90194 + 1.42019i) q^{77} +(-5.76680 + 4.83892i) q^{78} +(3.22119 - 0.567982i) q^{79} +12.3842i q^{80} +(-1.87129 - 10.6126i) q^{81} +(11.3306 + 6.54173i) q^{82} +(-3.83406 - 3.21716i) q^{83} +(-6.67753 - 11.5658i) q^{84} +(-0.918527 + 1.59094i) q^{85} +(11.9261 - 4.34074i) q^{86} +(14.2699 + 17.0062i) q^{87} +(12.5084 - 7.22174i) q^{88} +(-0.860158 - 0.151669i) q^{89} +(-2.69604 + 15.2900i) q^{90} +(1.25105 - 1.49094i) q^{91} +(10.2061 - 28.0411i) q^{92} +(1.78218 - 4.89651i) q^{93} +(-17.5028 + 20.8590i) q^{94} +(-0.931805 + 5.28453i) q^{95} +(-1.08062 - 0.190542i) q^{96} +(-11.4492 + 6.61021i) q^{97} +(-7.75001 - 9.23610i) q^{98} +(5.89547 - 2.14578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−0.841146	−	2.31103i	−0.594780	−	1.63414i	−0.761518	−	0.648144i	$-0.775546\pi$
$2$	−0.841146	−	2.31103i	−0.594780	−	1.63414i	0.166738	−	0.986001i	$-0.446677\pi$
$3$	2.14040	+	0.779043i	1.23576	+	0.449780i	0.875567	−	0.483097i	$-0.160488\pi$
$3$	2.14040	+	0.779043i	1.23576	+	0.449780i	0.360195	+	0.932877i	$0.382710\pi$
$4$	−3.10124	+	2.60225i	−1.55062	+	1.30113i
$5$	−2.84116	+	0.500973i	−1.27060	+	0.224042i	−0.767986	−	0.640467i	$-0.778741\pi$
$5$	−2.84116	+	0.500973i	−1.27060	+	0.224042i	−0.502618	+	0.864508i	$0.667630\pi$
$6$		−	5.60182i		−	2.28693i
$7$	0.251492	+	1.42628i	0.0950551	+	0.539084i	0.994730	+	0.102525i	$0.0326921\pi$
$7$	0.251492	+	1.42628i	0.0950551	+	0.539084i	−0.899675	+	0.436560i	$0.856197\pi$
$8$	4.36277	+	2.51884i	1.54247	+	0.890546i
$9$	1.67628	+	1.40657i	0.558760	+	0.468855i
$10$	3.54759	+	6.14461i	1.12185	+	1.94310i
$11$	1.43354	−	2.48297i	0.432229	−	0.748643i	−0.564836	−	0.825203i	$-0.691060\pi$
$11$	1.43354	−	2.48297i	0.432229	−	0.748643i	0.997065	+	0.0765604i	$0.0243938\pi$
$12$	−8.66517	+	3.15386i	−2.50142	+	0.910442i
$13$	−0.863812	−	1.02945i	−0.239578	−	0.285518i	0.632836	−	0.774286i	$-0.281891\pi$
$13$	−0.863812	−	1.02945i	−0.239578	−	0.285518i	−0.872414	+	0.488768i	$0.837446\pi$
$14$	3.08464	−	1.78092i	0.824405	−	0.475970i
$15$	−6.47150	−	1.14110i	−1.67093	−	0.294631i
$16$	0.745411	−	4.22743i	0.186353	−	1.05686i
$17$	0.409304	−	0.487789i	0.0992707	−	0.118306i	−0.714122	−	0.700021i	$-0.753174\pi$
$17$	0.409304	−	0.487789i	0.0992707	−	0.118306i	0.813393	+	0.581715i	$0.197618\pi$
$18$	1.84062	−	5.05706i	0.433838	−	1.19196i
$19$	0.636155	−	1.74782i	0.145944	−	0.400978i	−0.845084	−	0.534634i	$-0.820450\pi$
$19$	0.636155	−	1.74782i	0.145944	−	0.400978i	0.991028	+	0.133656i	$0.0426718\pi$
$20$	7.50746	−	8.94704i	1.67872	−	2.00062i
$21$	−0.572841	+	3.24874i	−0.125004	+	0.708934i
$22$	−6.94403	−	1.22442i	−1.48047	−	0.261047i
$23$	−6.38349	+	3.68551i	−1.33105	+	0.768481i	−0.985460	−	0.169905i	$-0.945654\pi$
$23$	−6.38349	+	3.68551i	−1.33105	+	0.768481i	−0.345588	+	0.938386i	$0.612321\pi$
$24$	7.37579	+	8.79012i	1.50558	+	1.79428i
$25$	3.12274	−	1.13658i	0.624548	−	0.227317i
$26$	−1.65250	+	2.86221i	−0.324082	+	0.561326i
$27$	−0.924515	−	1.60131i	−0.177923	−	0.308172i
$28$	−4.49149	−	3.76880i	−0.848811	−	0.712237i
$29$	8.44060	+	4.87318i	1.56738	+	0.904927i	0.996473	+	0.0839118i	$0.0267414\pi$
$29$	8.44060	+	4.87318i	1.56738	+	0.904927i	0.570906	+	0.821015i	$0.306592\pi$
$30$	2.80636	+	15.9157i	0.512369	+	2.90579i
$31$		−	2.28766i		−	0.410876i	−0.978670	−	0.205438i	$-0.934138\pi$
$31$		−	2.28766i		−	0.410876i	0.978670	−	0.205438i	$-0.0658618\pi$
$32$	−0.474419	+	0.0836529i	−0.0838662	+	0.0147879i
$33$	5.00269	−	4.19776i	0.870857	−	0.730736i
$34$	−1.47158	−	0.535611i	−0.252374	−	0.0918565i
$35$	−1.42906	−	3.92630i	−0.241555	−	0.663666i
$36$	−8.85879			−1.47646
$37$	4.38799	−	4.21255i	0.721381	−	0.692539i
$37$	4.38799	−	4.21255i	0.721381	−	0.692539i
$38$	−4.57436			−0.742060
$39$	−1.04692	−	2.87639i	−0.167641	−	0.460590i
$40$	−13.6572	−	4.97081i	−2.15939	−	0.785953i
$41$	−4.07527	+	3.41956i	−0.636451	+	0.534046i	−0.902926	−	0.429796i	$-0.858585\pi$
$41$	−4.07527	+	3.41956i	−0.636451	+	0.534046i	0.266475	+	0.963842i	$0.414141\pi$
$42$	7.98978	−	1.40881i	1.23285	−	0.217385i
$43$			5.16051i			0.786970i	0.919331	+	0.393485i	$0.128731\pi$
$43$			5.16051i			0.786970i	−0.919331	+	0.393485i	$0.871269\pi$
$44$	2.01555	+	11.4307i	0.303855	+	1.72325i
$45$	−5.46723	−	3.15650i	−0.815006	−	0.470544i
$46$	13.8868	+	11.6524i	2.04749	+	1.71805i
$47$	−5.53593	−	9.58852i	−0.807499	−	1.39863i	−0.914591	−	0.404380i	$-0.867487\pi$
$47$	−5.53593	−	9.58852i	−0.807499	−	1.39863i	0.107092	−	0.994249i	$-0.465846\pi$
$48$	4.88883	−	8.46770i	0.705642	−	1.22221i
$49$	4.60681	−	1.67674i	0.658116	−	0.239535i
$50$	−5.25336	−	6.26071i	−0.742937	−	0.885398i
$51$	1.25608	−	0.725200i	0.175887	−	0.101548i
$52$	5.35778	+	0.944721i	0.742991	+	0.131009i
$53$	−1.46342	+	8.29949i	−0.201017	+	1.14002i	0.702569	+	0.711616i	$0.252036\pi$
$53$	−1.46342	+	8.29949i	−0.201017	+	1.14002i	−0.903586	+	0.428407i	$0.859075\pi$
$54$	−2.92301	+	3.48351i	−0.397772	+	0.474046i
$55$	−2.82902	+	7.77267i	−0.381465	+	1.04807i
$56$	−2.49538	+	6.85601i	−0.333460	+	0.916173i
$57$	2.72325	−	3.24545i	0.360704	−	0.429870i
$58$	4.16229	−	23.6055i	0.546536	−	3.09956i
$59$	5.35027	+	0.943396i	0.696545	+	0.122820i	0.510700	−	0.859759i	$-0.329386\pi$
$59$	5.35027	+	0.943396i	0.696545	+	0.122820i	0.185846	+	0.982579i	$0.440498\pi$
$60$	23.0391	−	13.3016i	2.97434	−	1.71723i
$61$	0.559486	+	0.666770i	0.0716348	+	0.0853711i	0.800672	−	0.599103i	$-0.204476\pi$
$61$	0.559486	+	0.666770i	0.0716348	+	0.0853711i	−0.729037	+	0.684474i	$0.760032\pi$
$62$	−5.28685	+	1.92425i	−0.671430	+	0.244381i
$63$	−1.58459	+	2.74459i	−0.199639	+	0.345786i
$64$	−3.70027	−	6.40906i	−0.462534	−	0.801132i
$65$	2.96995	+	2.49209i	0.368377	+	0.309105i
$66$	−13.9091	−	8.03045i	−1.71210	−	0.988480i
$67$	0.975073	+	5.52991i	0.119124	+	0.675586i	0.984625	+	0.174679i	$0.0558889\pi$
$67$	0.975073	+	5.52991i	0.119124	+	0.675586i	−0.865501	+	0.500907i	$0.833000\pi$
$68$			2.57786i			0.312612i
$69$	−16.5344	+	2.91546i	−1.99051	+	0.350980i
$70$	−7.87176	+	6.60519i	−0.940855	+	0.789471i
$71$	0.480027	+	0.174716i	0.0569687	+	0.0207349i	0.370347	−	0.928893i	$-0.379239\pi$
$71$	0.480027	+	0.174716i	0.0569687	+	0.0207349i	−0.313379	+	0.949628i	$0.601461\pi$
$72$	3.77030	+	10.3588i	0.444334	+	1.22080i
$73$	−3.16083			−0.369947			−0.184973	−	0.982744i	$-0.559220\pi$
$73$	−3.16083			−0.369947			−0.184973	+	0.982744i	$0.559220\pi$
$74$	−13.4263	−	6.59740i	−1.56077	−	0.766932i
$75$	7.56936			0.874035
$76$	2.57540	+	7.07585i	0.295419	+	0.811656i
$77$	3.90194	+	1.42019i	0.444667	+	0.161846i
$78$	−5.76680	+	4.83892i	−0.652962	+	0.547900i
$79$	3.22119	−	0.567982i	0.362412	−	0.0639030i	0.0105225	−	0.999945i	$-0.496651\pi$
$79$	3.22119	−	0.567982i	0.362412	−	0.0639030i	0.351889	+	0.936042i	$0.385539\pi$
$80$			12.3842i			1.38460i
$81$	−1.87129	−	10.6126i	−0.207921	−	1.17918i
$82$	11.3306	+	6.54173i	1.25126	+	0.722413i
$83$	−3.83406	−	3.21716i	−0.420843	−	0.353129i	0.407641	−	0.913142i	$-0.366352\pi$
$83$	−3.83406	−	3.21716i	−0.420843	−	0.353129i	−0.828484	+	0.560013i	$0.810796\pi$
$84$	−6.67753	−	11.5658i	−0.728578	−	1.26193i
$85$	−0.918527	+	1.59094i	−0.0996282	+	0.172561i
$86$	11.9261	−	4.34074i	1.28602	−	0.468074i
$87$	14.2699	+	17.0062i	1.52989	+	1.82325i
$88$	12.5084	−	7.22174i	1.33340	−	0.769840i
$89$	−0.860158	−	0.151669i	−0.0911766	−	0.0160769i	0.127874	−	0.991790i	$-0.459185\pi$
$89$	−0.860158	−	0.151669i	−0.0911766	−	0.0160769i	−0.219050	+	0.975714i	$0.570296\pi$
$90$	−2.69604	+	15.2900i	−0.284188	+	1.61171i
$91$	1.25105	−	1.49094i	0.131145	−	0.156293i
$92$	10.2061	−	28.0411i	1.06406	−	2.92349i
$93$	1.78218	−	4.89651i	0.184804	−	0.507744i
$94$	−17.5028	+	20.8590i	−1.80528	+	2.15145i
$95$	−0.931805	+	5.28453i	−0.0956012	+	0.542181i
$96$	−1.08062	−	0.190542i	−0.110290	−	0.0194471i
$97$	−11.4492	+	6.61021i	−1.16249	+	0.671165i	−0.951900	−	0.306409i	$-0.900872\pi$
$97$	−11.4492	+	6.61021i	−1.16249	+	0.671165i	−0.210592	+	0.977574i	$0.567539\pi$
$98$	−7.75001	−	9.23610i	−0.782869	−	0.932987i
$99$	5.89547	−	2.14578i	0.592518	−	0.215659i
$100$	−6.72669	+	11.6510i	−0.672669	+	1.16510i
$101$	0.897121	+	1.55386i	0.0892669	+	0.154615i	0.907201	−	0.420696i	$-0.138214\pi$
$101$	0.897121	+	1.55386i	0.0892669	+	0.154615i	−0.817935	+	0.575311i	$0.804881\pi$
$102$	−2.73251	−	2.29285i	−0.270558	−	0.227025i
$103$	−14.4610	−	8.34904i	−1.42488	−	0.822655i	−0.428170	−	0.903698i	$-0.640842\pi$
$103$	−14.4610	−	8.34904i	−1.42488	−	0.822655i	−0.996711	+	0.0810425i	$0.974175\pi$
$104$	−1.17558	−	6.66706i	−0.115275	−	0.653759i
$105$		−	9.51716i		−	0.928780i
$106$	20.4113	−	3.59907i	1.98252	−	0.349572i
$107$	−4.15304	+	3.48482i	−0.401490	+	0.336890i	−0.821069	−	0.570829i	$-0.806622\pi$
$107$	−4.15304	+	3.48482i	−0.401490	+	0.336890i	0.419579	+	0.907719i	$0.362178\pi$
$108$	7.03415	+	2.56022i	0.676861	+	0.246357i
$109$	−1.39101	−	3.82177i	−0.133235	−	0.366060i	0.855078	−	0.518499i	$-0.173509\pi$
$109$	−1.39101	−	3.82177i	−0.133235	−	0.366060i	−0.988313	+	0.152440i	$0.951287\pi$
$110$	20.3425			1.93958
$111$	12.6738	−	5.59812i	1.20294	−	0.531350i
$112$	6.21698			0.587450
$113$	3.65921	+	10.0536i	0.344229	+	0.945762i	0.984153	+	0.177323i	$0.0567438\pi$
$113$	3.65921	+	10.0536i	0.344229	+	0.945762i	−0.639924	+	0.768439i	$0.721034\pi$
$114$	−9.79098	−	3.56362i	−0.917009	−	0.333764i
$115$	16.2902	−	13.6691i	1.51906	−	1.27465i
$116$	−38.8576	+	6.85164i	−3.60784	+	0.636159i
$117$		−	2.94066i		−	0.271864i
$118$	−2.32014	−	13.1582i	−0.213586	−	1.21131i
$119$	0.798662	+	0.461108i	0.0732132	+	0.0422697i
$120$	−25.3594	−	21.2790i	−2.31498	−	1.94250i
$121$	1.38991	+	2.40740i	0.126356	+	0.218855i
$122$	1.07031	−	1.85384i	0.0969017	−	0.167839i
$123$	−11.3867	+	4.14442i	−1.02670	+	0.373690i
$124$	5.95306	+	7.09458i	0.534601	+	0.637112i
$125$	4.18956	−	2.41885i	0.374726	−	0.216348i
$126$	7.67570	+	1.35343i	0.683806	+	0.120573i
$127$	1.32583	−	7.51915i	0.117648	−	0.667216i	−0.867757	−	0.496989i	$-0.834439\pi$
$127$	1.32583	−	7.51915i	0.117648	−	0.667216i	0.985405	−	0.170227i	$-0.0544501\pi$
$128$	−12.3184	+	14.6805i	−1.08880	+	1.29758i
$129$	−4.02026	+	11.0456i	−0.353964	+	0.972508i
$130$	3.26112	−	8.95986i	0.286019	−	0.785832i
$131$	4.79709	−	5.71695i	0.419123	−	0.499492i	−0.514628	−	0.857413i	$-0.672070\pi$
$131$	4.79709	−	5.71695i	0.419123	−	0.499492i	0.933752	+	0.357922i	$0.116514\pi$
$132$	−4.59094	+	26.0365i	−0.399590	+	2.26619i
$133$	2.65287	+	0.467773i	0.230033	+	0.0405611i
$134$	11.9596	−	6.90488i	1.03315	−	0.596491i
$135$	3.42890	+	4.08641i	0.295113	+	0.351702i
$136$	3.01436	−	1.09714i	0.258479	−	0.0940787i
$137$	−5.81227	+	10.0671i	−0.496576	+	0.860095i	−0.999992	−	0.00394934i	$-0.998743\pi$
$137$	−5.81227	+	10.0671i	−0.496576	+	0.860095i	0.503416	+	0.864044i	$0.332076\pi$
$138$	20.6456	+	35.7591i	1.75747	+	3.04402i
$139$	9.84996	+	8.26509i	0.835462	+	0.701036i	0.956538	−	0.291607i	$-0.0941900\pi$
$139$	9.84996	+	8.26509i	0.835462	+	0.701036i	−0.121076	+	0.992643i	$0.538634\pi$
$140$	14.6491	+	8.45765i	1.23807	+	0.714802i
$141$	−4.37926	−	24.8360i	−0.368800	−	2.09157i
$142$		−	1.25632i		−	0.105428i
$143$	−3.79441	+	0.669056i	−0.317304	+	0.0559493i
$144$	7.19568	−	6.03789i	0.599640	−	0.503158i
$145$	−26.4224	−	9.61697i	−2.19426	−	0.798646i
$146$	2.65872	+	7.30477i	0.220037	+	0.604547i
$147$	11.1667			0.921013
$148$	−2.64610	+	24.4828i	−0.217508	+	2.01247i
$149$	−0.277891			−0.0227657			−0.0113829	−	0.999935i	$-0.503623\pi$
$149$	−0.277891			−0.0227657			−0.0113829	+	0.999935i	$0.503623\pi$
$150$	−6.36694	−	17.4930i	−0.519858	−	1.42830i
$151$	−9.04205	−	3.29104i	−0.735832	−	0.267821i	−0.0532005	−	0.998584i	$-0.516942\pi$
$151$	−9.04205	−	3.29104i	−0.735832	−	0.267821i	−0.682631	+	0.730763i	$0.739164\pi$
$152$	7.17788	−	6.02296i	0.582203	−	0.488526i
$153$	1.37221	−	0.241958i	0.110937	−	0.0195612i
$154$		−	10.2121i		−	0.822913i
$155$	1.14605	+	6.49960i	0.0920533	+	0.522060i
$156$	10.7318	+	6.19602i	0.859234	+	0.496079i
$157$	−4.99851	−	4.19425i	−0.398924	−	0.334737i	0.421153	−	0.906989i	$-0.361625\pi$
$157$	−4.99851	−	4.19425i	−0.398924	−	0.334737i	−0.820078	+	0.572252i	$0.806070\pi$
$158$	−4.02211	−	6.96650i	−0.319982	−	0.554225i
$159$	−9.59797	+	16.6242i	−0.761169	+	1.31838i
$160$	1.30599	−	0.475342i	0.103248	−	0.0375791i
$161$	−6.86197	−	8.17778i	−0.540799	−	0.644499i
$162$	−22.9521	+	13.2514i	−1.80328	+	1.04113i
$163$	−9.22022	−	1.62577i	−0.722183	−	0.127340i	−0.199537	−	0.979890i	$-0.563944\pi$
$163$	−9.22022	−	1.62577i	−0.722183	−	0.127340i	−0.522646	+	0.852550i	$0.675055\pi$
$164$	3.73986	−	21.2098i	0.292034	−	1.65621i
$165$	−12.1105	+	14.4327i	−0.942800	+	1.12358i
$166$	−4.20994	+	11.5667i	−0.326755	+	0.897752i
$167$	−2.13679	+	5.87080i	−0.165350	+	0.454296i	−0.994501	−	0.104730i	$-0.966602\pi$
$167$	−2.13679	+	5.87080i	−0.165350	+	0.454296i	0.829151	+	0.559025i	$0.188825\pi$
$168$	−10.6822	+	12.7306i	−0.824153	+	0.982187i
$169$	1.94383	−	11.0240i	0.149525	−	0.848000i
$170$	4.44931	+	0.784534i	0.341247	+	0.0601710i
$171$	3.52480	−	2.03504i	0.269548	−	0.155624i
$172$	−13.4289	−	16.0040i	−1.02395	−	1.22029i
$173$	22.8408	−	8.31338i	1.73655	−	0.632054i	0.737493	−	0.675355i	$-0.236010\pi$
$173$	22.8408	−	8.31338i	1.73655	−	0.632054i	0.999062	+	0.0433007i	$0.0137874\pi$
$174$	27.2987	−	47.2827i	2.06951	−	3.58449i
$175$	2.40643	+	4.16807i	0.181909	+	0.315076i
$176$	−9.42801	−	7.91104i	−0.710663	−	0.596317i
$177$	10.7168	+	6.18733i	0.805522	+	0.465068i
$178$	0.373007	+	2.11543i	0.0279580	+	0.158558i
$179$		−	16.5110i		−	1.23409i	−0.786927	−	0.617045i	$-0.788329\pi$
$179$		−	16.5110i		−	1.23409i	0.786927	−	0.617045i	$-0.211671\pi$
$180$	25.1692	−	4.43801i	1.87600	−	0.330790i
$181$	2.79042	−	2.34144i	0.207410	−	0.174038i	−0.533165	−	0.846011i	$-0.678998\pi$
$181$	2.79042	−	2.34144i	0.207410	−	0.174038i	0.740575	+	0.671973i	$0.234553\pi$
$182$	−4.49792	−	1.63711i	−0.333408	−	0.121351i
$183$	0.678083	+	1.86302i	0.0501254	+	0.137718i
$184$	−37.1329			−2.73747
$185$	−10.3566	+	14.1668i	−0.761432	+	1.04156i
$186$	−12.8151			−0.939645
$187$	−0.624410	−	1.71555i	−0.0456614	−	0.125454i
$188$	42.1200	+	15.3304i	3.07192	+	1.11809i
$189$	2.05141	−	1.72134i	0.149218	−	0.125209i
$190$	12.9965	−	2.29163i	0.942865	−	0.166252i
$191$		−	8.78784i		−	0.635866i	−0.948113	−	0.317933i	$-0.897011\pi$
$191$		−	8.78784i		−	0.635866i	0.948113	−	0.317933i	$-0.102989\pi$
$192$	−2.92714	−	16.6006i	−0.211248	−	1.19805i
$193$	9.10990	+	5.25960i	0.655745	+	0.378594i	0.790654	−	0.612264i	$-0.209741\pi$
$193$	9.10990	+	5.25960i	0.655745	+	0.378594i	−0.134909	+	0.990858i	$0.543074\pi$
$194$	24.9068	+	20.8993i	1.78821	+	1.50048i
$195$	4.41545	+	7.64779i	0.316197	+	0.547669i
$196$	−9.92354	+	17.1881i	−0.708824	+	1.22772i
$197$	14.0980	−	5.13126i	1.00444	−	0.365587i	0.213147	−	0.977020i	$-0.431629\pi$
$197$	14.0980	−	5.13126i	1.00444	−	0.365587i	0.791296	+	0.611433i	$0.209407\pi$
$198$	−9.91791	−	11.8197i	−0.704835	−	0.839990i
$199$	−9.44027	+	5.45034i	−0.669203	+	0.386364i	−0.795774	−	0.605593i	$-0.792936\pi$
$199$	−9.44027	+	5.45034i	−0.669203	+	0.386364i	0.126572	+	0.991957i	$0.459603\pi$
$200$	16.4867	+	2.90704i	1.16578	+	0.205559i
$201$	−2.22099	+	12.5959i	−0.156656	+	0.888443i
$202$	2.83641	−	3.38030i	0.199569	−	0.237837i
$203$	−4.82779	+	13.2642i	−0.338844	+	0.930968i
$204$	−2.00826	+	5.51766i	−0.140607	+	0.386314i
$205$	9.86539	−	11.7571i	0.689029	−	0.821152i
$206$	−7.13110	+	40.4425i	−0.496847	+	2.81776i
$207$	−15.8844	−	2.80085i	−1.10404	−	0.194673i
$208$	−4.99583	+	2.88435i	−0.346399	+	0.199993i
$209$	−3.42783	−	4.08513i	−0.237108	−	0.282574i
$210$	−21.9945	+	8.00533i	−1.51776	+	0.552420i
$211$	−2.27056	+	3.93273i	−0.156312	+	0.270740i	−0.933536	−	0.358484i	$-0.883294\pi$
$211$	−2.27056	+	3.93273i	−0.156312	+	0.270740i	0.777224	+	0.629224i	$0.216627\pi$
$212$	−17.0589	−	29.5469i	−1.17161	−	2.02929i
$213$	0.891340	+	0.747923i	0.0610736	+	0.0512468i
$214$	11.5468	+	6.66656i	0.789325	+	0.455717i
$215$	−2.58527	−	14.6618i	−0.176314	−	0.999928i
$216$		−	9.31483i		−	0.633794i
$217$	3.26285	−	0.575328i	0.221497	−	0.0390558i
$218$	−7.66219	+	6.42934i	−0.518949	+	0.435450i
$219$	−6.76544	−	2.46242i	−0.457166	−	0.166395i
$220$	−11.4530	−	31.4668i	−0.772159	−	2.12149i
$221$	−0.855716			−0.0575617
$222$	−23.5979	−	24.5807i	−1.58379	−	1.64975i
$223$	1.64789			0.110351			0.0551756	−	0.998477i	$-0.482428\pi$
$223$	1.64789			0.110351			0.0551756	+	0.998477i	$0.482428\pi$
$224$	−0.238625	−	0.655618i	−0.0159438	−	0.0438053i
$225$	6.83326	+	2.48710i	0.455551	+	0.165807i
$226$	20.1562	−	16.9131i	1.34077	−	1.12504i
$227$	15.8787	−	2.79985i	1.05391	−	0.185833i	0.380256	−	0.924881i	$-0.375836\pi$
$227$	15.8787	−	2.79985i	1.05391	−	0.185833i	0.673652	+	0.739049i	$0.264725\pi$
$228$			17.1515i			1.13589i
$229$	4.10288	+	23.2686i	0.271126	+	1.53763i	0.751005	+	0.660297i	$0.229570\pi$
$229$	4.10288	+	23.2686i	0.271126	+	1.53763i	−0.479879	+	0.877335i	$0.659319\pi$
$230$	−45.2920	−	26.1493i	−2.98647	−	1.72424i
$231$	7.24533	+	6.07955i	0.476708	+	0.400005i
$232$	24.5496	+	42.5211i	1.61176	+	2.79165i
$233$	11.7613	−	20.3712i	0.770510	−	1.33456i	−0.166773	−	0.985995i	$-0.553335\pi$
$233$	11.7613	−	20.3712i	0.770510	−	1.33456i	0.937283	−	0.348568i	$-0.113332\pi$
$234$	−6.79594	+	2.47352i	−0.444265	+	0.161699i
$235$	20.5320	+	24.4691i	1.33936	+	1.59619i
$236$	−19.0474	+	10.9970i	−1.23988	+	0.715846i
$237$	7.33711	+	1.29373i	0.476597	+	0.0840369i
$238$	0.393842	−	2.23359i	0.0255290	−	0.144782i
$239$	11.1037	−	13.2329i	0.718239	−	0.855964i	−0.276219	−	0.961095i	$-0.589082\pi$
$239$	11.1037	−	13.2329i	0.718239	−	0.855964i	0.994458	+	0.105131i	$0.0335261\pi$
$240$	−9.64785	+	26.5072i	−0.622766	+	1.71104i
$241$	−5.67360	+	15.5881i	−0.365468	+	1.00412i	0.611596	+	0.791170i	$0.290528\pi$
$241$	−5.67360	+	15.5881i	−0.365468	+	1.00412i	−0.977064	+	0.212946i	$0.931694\pi$
$242$	4.39445	−	5.23711i	0.282486	−	0.336654i
$243$	3.29913	−	18.7103i	0.211639	−	1.20027i
$244$	−3.47020	−	0.611891i	−0.222157	−	0.0391723i
$245$	−12.2487	+	7.07178i	−0.782539	+	0.451799i
$246$	19.1558	+	22.8290i	1.22133	+	1.45552i
$247$	−2.34881	+	0.854898i	−0.149451	+	0.0543959i
$248$	5.76225	−	9.98052i	0.365904	−	0.633764i
$249$	−5.70013	−	9.87291i	−0.361231	−	0.625670i
$250$	−9.11406	−	7.64760i	−0.576424	−	0.483677i
$251$	−14.5088	−	8.37666i	−0.915788	−	0.528730i	−0.0334990	−	0.999439i	$-0.510665\pi$
$251$	−14.5088	−	8.37666i	−0.915788	−	0.528730i	−0.882289	+	0.470708i	$0.843998\pi$
$252$	−2.22792	−	12.6351i	−0.140345	−	0.795939i
$253$			21.1333i			1.32864i
$254$	−18.4922	+	3.26067i	−1.16030	+	0.204593i
$255$	−3.20542	+	2.68967i	−0.200731	+	0.168434i
$256$	30.3800	+	11.0574i	1.89875	+	0.691089i
$257$	8.38370	+	23.0340i	0.522961	+	1.43682i	0.867209	+	0.497944i	$0.165912\pi$
$257$	8.38370	+	23.0340i	0.522961	+	1.43682i	−0.344248	+	0.938879i	$0.611866\pi$
$258$	28.9082			1.79975
$259$	7.11183	+	5.19909i	0.441908	+	0.323056i
$260$	−15.6956			−0.973399
$261$	7.29435	+	20.0411i	0.451509	+	1.24051i
$262$	−17.2471	−	6.27743i	−1.06553	−	0.387821i
$263$	−12.5527	+	10.5329i	−0.774031	+	0.649489i	−0.941738	−	0.336348i	$-0.890808\pi$
$263$	−12.5527	+	10.5329i	−0.774031	+	0.649489i	0.167707	+	0.985837i	$0.446364\pi$
$264$	32.3991	−	5.71283i	1.99403	−	0.351601i
$265$		−	24.3133i		−	1.49355i
$266$	−1.15042	−	6.52434i	−0.0705366	−	0.400033i
$267$	−1.72293	−	0.994733i	−0.105441	−	0.0608766i
$268$	−17.4142	−	14.6122i	−1.06374	−	0.892583i
$269$	−8.69998	−	15.0688i	−0.530447	−	0.918761i	−0.999369	−	0.0355214i	$-0.988691\pi$
$269$	−8.69998	−	15.0688i	−0.530447	−	0.918761i	0.468922	−	0.883240i	$-0.344643\pi$
$270$	6.55960	−	11.3616i	0.399205	−	0.691443i
$271$	−2.64225	+	0.961701i	−0.160505	+	0.0584192i	−0.421023	−	0.907050i	$-0.638329\pi$
$271$	−2.64225	+	0.961701i	−0.160505	+	0.0584192i	0.260518	+	0.965469i	$0.416107\pi$
$272$	−1.75700	−	2.09391i	−0.106534	−	0.126962i
$273$	3.83925	−	2.21659i	0.232362	−	0.134154i
$274$	28.1545	+	4.96439i	1.70087	+	0.299910i
$275$	1.65448	−	9.38300i	0.0997687	−	0.565816i
$276$	43.6904	−	52.0682i	2.62985	−	3.13414i
$277$	7.59101	−	20.8561i	0.456100	−	1.25312i	−0.472266	−	0.881456i	$-0.656564\pi$
$277$	7.59101	−	20.8561i	0.456100	−	1.25312i	0.928366	−	0.371667i	$-0.121214\pi$
$278$	10.8156	−	29.7157i	0.648678	−	1.78223i
$279$	3.21774	−	3.83476i	0.192641	−	0.229581i
$280$	3.65510	−	20.7291i	0.218434	−	1.23880i
$281$	−0.813808	−	0.143496i	−0.0485477	−	0.00856027i	0.149322	−	0.988789i	$-0.452291\pi$
$281$	−0.813808	−	0.143496i	−0.0485477	−	0.00856027i	−0.197869	+	0.980228i	$0.563402\pi$
$282$	−53.7131	+	31.0113i	−3.19857	+	1.84670i
$283$	−18.5213	−	22.0728i	−1.10098	−	1.31209i	−0.945997	−	0.324176i	$-0.894913\pi$
$283$	−18.5213	−	22.0728i	−1.10098	−	1.31209i	−0.154980	−	0.987918i	$-0.549531\pi$
$284$	−1.94333	+	0.707316i	−0.115316	+	0.0419715i
$285$	−6.11131	+	10.5851i	−0.362003	+	0.627007i
$286$	4.73786	+	8.20621i	0.280155	+	0.485243i
$287$	−5.90216	−	4.95250i	−0.348394	−	0.292337i
$288$	−0.912922	−	0.527076i	−0.0537944	−	0.0310582i
$289$	2.88161	+	16.3424i	0.169506	+	0.961319i
$290$			69.1522i			4.06076i
$291$	−29.6556	+	5.22907i	−1.73844	+	0.306534i
$292$	9.80249	−	8.22527i	0.573648	−	0.481347i
$293$	−2.54298	−	0.925570i	−0.148563	−	0.0540723i	0.266669	−	0.963788i	$-0.414077\pi$
$293$	−2.54298	−	0.925570i	−0.148563	−	0.0540723i	−0.415231	+	0.909716i	$0.636299\pi$
$294$	−9.39281	−	25.8065i	−0.547800	−	1.50507i
$295$	−15.6736			−0.912550
$296$	29.7545	−	7.32571i	1.72945	−	0.425798i
$297$	−5.30132			−0.307614
$298$	0.233747	+	0.642215i	0.0135406	+	0.0372025i
$299$	9.30818	+	3.38790i	0.538306	+	0.195927i
$300$	−23.4744	+	19.6974i	−1.35530	+	1.13723i
$301$	−7.36035	+	1.29783i	−0.424243	+	0.0748055i
$302$			23.6647i			1.36175i
$303$	0.709677	+	4.02478i	0.0407699	+	0.231218i
$304$	−6.91460	−	3.99215i	−0.396580	−	0.228965i
$305$	−1.92362	−	1.61411i	−0.110146	−	0.0924237i
$306$	−1.71341	−	2.96771i	−0.0979489	−	0.169652i
$307$	−8.78442	+	15.2151i	−0.501353	+	0.868369i	0.498646	+	0.866806i	$0.333831\pi$
$307$	−8.78442	+	15.2151i	−0.501353	+	0.868369i	−0.999999	+	0.00156318i	$0.999502\pi$
$308$	−15.7966	+	5.74948i	−0.900092	+	0.327607i
$309$	−24.4480	−	29.1360i	−1.39080	−	1.65749i
$310$	14.0568	−	8.11568i	0.798371	−	0.460939i
$311$	−4.39059	−	0.774179i	−0.248967	−	0.0438997i	0.0477716	−	0.998858i	$-0.484788\pi$
$311$	−4.39059	−	0.774179i	−0.248967	−	0.0438997i	−0.296739	+	0.954959i	$0.595899\pi$
$312$	2.67771	−	15.1860i	0.151595	−	0.859739i
$313$	12.9678	−	15.4545i	0.732985	−	0.873537i	−0.262838	−	0.964840i	$-0.584659\pi$
$313$	12.9678	−	15.4545i	0.732985	−	0.873537i	0.995823	+	0.0913024i	$0.0291030\pi$
$314$	−5.48855	+	15.0797i	−0.309737	+	0.850995i
$315$	3.12710	−	8.59165i	0.176192	−	0.484084i
$316$	−8.51165	+	10.1438i	−0.478818	+	0.570633i
$317$	−1.48509	+	8.42239i	−0.0834112	+	0.473049i	0.914277	+	0.405090i	$0.132760\pi$
$317$	−1.48509	+	8.42239i	−0.0834112	+	0.473049i	−0.997688	+	0.0679587i	$0.978351\pi$
$318$	46.4923	+	8.19784i	2.60716	+	0.459712i
$319$	24.1999	−	13.9718i	1.35493	−	0.782272i
$320$	13.7238	+	16.3554i	0.767184	+	0.914295i
$321$	−11.6040	+	4.22351i	−0.647672	+	0.235733i
$322$	−13.1272	+	22.7369i	−0.731549	+	1.26708i
$323$	−0.592187	−	1.02570i	−0.0329502	−	0.0570714i
$324$	33.4201	+	28.0428i	1.85667	+	1.55793i
$325$	−3.86752	−	2.23291i	−0.214531	−	0.123860i
$326$	3.99834	+	22.6757i	0.221447	+	1.25589i
$327$		−	9.26379i		−	0.512289i
$328$	−26.3928	+	4.65376i	−1.45730	+	0.256961i
$329$	12.2837	−	10.3072i	0.677222	−	0.568257i
$330$	43.5411	+	15.8477i	2.39686	+	0.872385i
$331$	−3.54657	−	9.74413i	−0.194937	−	0.535586i	0.803258	−	0.595631i	$-0.203098\pi$
$331$	−3.54657	−	9.74413i	−0.194937	−	0.535586i	−0.998196	+	0.0600450i	$0.980876\pi$
$332$	20.2622			1.11203
$333$	13.2807	−	0.889416i	0.727779	−	0.0487397i
$334$	15.3649			0.840732
$335$	−5.54067	−	15.2229i	−0.302719	−	0.831714i
$336$	13.3068	+	4.84329i	0.725948	+	0.264223i
$337$	−18.3101	+	15.3640i	−0.997415	+	0.836930i	−0.986624	−	0.163011i	$-0.947879\pi$
$337$	−18.3101	+	15.3640i	−0.997415	+	0.836930i	−0.0107907	+	0.999942i	$0.503435\pi$
$338$	−27.1118	+	4.78055i	−1.47469	+	0.260027i
$339$			24.3694i			1.32356i
$340$	−1.29144	−	7.32411i	−0.0700381	−	0.397206i
$341$	−5.68018	−	3.27946i	−0.307599	−	0.177592i
$342$	−7.66791	−	6.43414i	−0.414633	−	0.347919i
$343$	8.61909	+	14.9287i	0.465387	+	0.806074i
$344$	−12.9985	+	22.5141i	−0.700833	+	1.21388i
$345$	45.5162	−	16.5666i	2.45051	−	0.891914i
$346$	−38.4249	−	45.7930i	−2.06574	−	2.46185i
$347$	26.6673	−	15.3964i	1.43158	−	0.826521i	0.434335	−	0.900751i	$-0.356983\pi$
$347$	26.6673	−	15.3964i	1.43158	−	0.826521i	0.997241	+	0.0742306i	$0.0236501\pi$
$348$	−88.5086	−	15.6064i	−4.74456	−	0.836593i
$349$	−2.68233	+	15.2123i	−0.143582	+	0.814294i	0.824913	+	0.565260i	$0.191224\pi$
$349$	−2.68233	+	15.2123i	−0.143582	+	0.814294i	−0.968495	+	0.249034i	$0.919887\pi$
$350$	7.60836	−	9.06730i	0.406684	−	0.484667i
$351$	−0.849860	+	2.33497i	−0.0453622	+	0.124632i
$352$	−0.472392	+	1.29789i	−0.0251786	+	0.0691776i
$353$	−8.03901	+	9.58052i	−0.427873	+	0.509919i	−0.936307	−	0.351181i	$-0.885780\pi$
$353$	−8.03901	+	9.58052i	−0.427873	+	0.509919i	0.508434	+	0.861101i	$0.330225\pi$
$354$	5.28474	−	29.9712i	0.280881	−	1.59295i
$355$	−1.45136	−	0.255914i	−0.0770302	−	0.0135825i
$356$	3.06224	−	1.76799i	0.162298	−	0.0937030i
$357$	1.35023	+	1.60915i	0.0714620	+	0.0851651i
$358$	−38.1574	+	13.8882i	−2.01668	+	0.734013i
$359$	−2.15674	+	3.73559i	−0.113829	+	0.197157i	−0.917311	−	0.398172i	$-0.869645\pi$
$359$	−2.15674	+	3.73559i	−0.113829	+	0.197157i	0.803482	+	0.595329i	$0.202978\pi$
$360$	−15.9015	−	27.5422i	−0.838082	−	1.45160i
$361$	11.9047	+	9.98920i	0.626561	+	0.525747i
$362$	−7.75828	−	4.47925i	−0.407766	−	0.235424i
$363$	1.09951	+	6.23561i	0.0577091	+	0.327284i
$364$			7.87930i			0.412988i
$365$	8.98041	−	1.58349i	0.470056	−	0.0828836i
$366$	3.73512	−	3.13414i	0.195238	−	0.163824i
$367$	21.4032	+	7.79014i	1.11724	+	0.406642i	0.833644	−	0.552302i	$-0.186251\pi$
$367$	21.4032	+	7.79014i	1.11724	+	0.406642i	0.283595	+	0.958944i	$0.408473\pi$
$368$	10.8219	+	29.7330i	0.564132	+	1.54994i
$369$	−11.6411			−0.606013
$370$	41.4512	+	12.0181i	2.15495	+	0.624789i
$371$	−12.2055			−0.633676
$372$	7.21496	+	19.8230i	0.374078	+	1.02777i
$373$	20.8605	+	7.59260i	1.08012	+	0.393130i	0.819950	−	0.572435i	$-0.194001\pi$
$373$	20.8605	+	7.59260i	1.08012	+	0.393130i	0.260165	+	0.965564i	$0.416223\pi$
$374$	−3.43948	+	2.88606i	−0.177851	+	0.149235i
$375$	10.8517	−	1.91345i	0.560381	−	0.0988103i
$376$		−	55.7766i		−	2.87646i
$377$	−2.27439	−	12.8987i	−0.117137	−	0.664317i
$378$	−5.70359	−	3.29297i	−0.293361	−	0.169372i
$379$	−5.05313	−	4.24008i	−0.259562	−	0.217798i	0.503715	−	0.863870i	$-0.331966\pi$
$379$	−5.05313	−	4.24008i	−0.259562	−	0.217798i	−0.763277	+	0.646072i	$0.776411\pi$
$380$	−10.8619	−	18.8134i	−0.557205	−	0.965107i
$381$	8.69554	−	15.0611i	0.445486	−	0.771605i
$382$	−20.3090	+	7.39186i	−1.03910	+	0.378200i
$383$	−3.03672	−	3.61902i	−0.155169	−	0.184923i	0.682859	−	0.730550i	$-0.260736\pi$
$383$	−3.03672	−	3.61902i	−0.155169	−	0.184923i	−0.838028	+	0.545627i	$0.816292\pi$
$384$	−37.8029	+	21.8255i	−1.92912	+	1.11378i
$385$	−11.7975	−	2.08022i	−0.601256	−	0.106018i
$386$	4.49234	−	25.4773i	0.228654	−	1.29676i
$387$	−7.25859	+	8.65046i	−0.368975	+	0.439727i
$388$	18.3054	−	50.2936i	0.929314	−	2.55327i
$389$	−11.0492	+	30.3573i	−0.560215	+	1.53918i	0.259110	+	0.965848i	$0.416571\pi$
$389$	−11.0492	+	30.3573i	−0.560215	+	1.53918i	−0.819325	+	0.573329i	$0.805652\pi$
$390$	13.9602	−	16.6371i	0.706903	−	0.842455i
$391$	−0.815034	+	4.62229i	−0.0412180	+	0.233759i
$392$	24.3219	+	4.28861i	1.22844	+	0.216607i
$393$	14.7214	−	8.49943i	0.742598	−	0.428739i
$394$	−23.7170	−	28.2648i	−1.19485	−	1.42396i
$395$	−8.86735	+	3.22745i	−0.446165	+	0.162391i
$396$	−12.6994	+	21.9961i	−0.638171	+	1.10534i
$397$	−11.7914	−	20.4233i	−0.591794	−	1.02502i	−0.993991	−	0.109465i	$-0.965086\pi$
$397$	−11.7914	−	20.4233i	−0.591794	−	1.02502i	0.402196	−	0.915553i	$-0.368247\pi$
$398$	20.5365	+	17.2322i	1.02940	+	0.863772i
$399$	5.31380	+	3.06793i	0.266023	+	0.153588i
$400$	−2.47711	−	14.0484i	−0.123856	−	0.702420i
$401$		−	19.5173i		−	0.974645i	−0.873222	−	0.487323i	$-0.837974\pi$
$401$		−	19.5173i		−	0.974645i	0.873222	−	0.487323i	$-0.162026\pi$
$402$	30.9776	−	5.46218i	1.54502	−	0.272429i
$403$	−2.35503	+	1.97611i	−0.117313	+	0.0984369i
$404$	−6.82573	−	2.48436i	−0.339593	−	0.123602i
$405$	10.6333	+	29.2147i	0.528372	+	1.45169i
$406$	34.7149			1.72287
$407$	−4.16926	−	16.9341i	−0.206662	−	0.839392i
$408$	7.30666			0.361733
$409$	−4.11939	−	11.3179i	−0.203691	−	0.559635i	0.795219	−	0.606322i	$-0.207356\pi$
$409$	−4.11939	−	11.3179i	−0.203691	−	0.559635i	−0.998910	+	0.0466872i	$0.985134\pi$
$410$	−35.4693	−	12.9098i	−1.75170	−	0.637567i
$411$	−20.2833	+	17.0197i	−1.00050	+	0.839522i
$412$	66.5733	−	11.7387i	3.27983	−	0.578322i
$413$			7.86825i			0.387171i
$414$	6.88826	+	39.0653i	0.338540	+	1.91995i
$415$	12.5049	+	7.21969i	0.613840	+	0.354401i
$416$	0.495925	+	0.416131i	0.0243147	+	0.0204025i
$417$	14.6440	+	25.3642i	0.717120	+	1.24209i
$418$	−6.55755	+	11.3580i	−0.320740	+	0.555538i
$419$	−30.9985	+	11.2825i	−1.51438	+	0.551188i	−0.959737	−	0.280901i	$-0.909367\pi$
$419$	−30.9985	+	11.2825i	−1.51438	+	0.551188i	−0.554641	+	0.832090i	$0.687144\pi$
$420$	24.7661	+	29.5150i	1.20846	+	1.44019i
$421$	−1.57499	+	0.909320i	−0.0767602	+	0.0443175i	−0.537889	−	0.843016i	$-0.680778\pi$
$421$	−1.57499	+	0.909320i	−0.0767602	+	0.0443175i	0.461129	+	0.887333i	$0.347445\pi$
$422$	10.9985	+	1.93934i	0.535400	+	0.0944054i
$423$	4.20711	−	23.8597i	0.204556	−	1.16010i
$424$	−27.2897	+	32.5226i	−1.32531	+	1.57944i
$425$	0.723735	−	1.98845i	0.0351063	−	0.0964538i
$426$	0.978725	−	2.68902i	0.0474194	−	0.130284i
$427$	−0.810296	+	0.965673i	−0.0392130	+	0.0467322i
$428$	3.81122	−	21.6145i	0.184222	−	1.04478i
$429$	−8.64278	−	1.52395i	−0.417277	−	0.0735772i
$430$	−31.7093	+	18.3074i	−1.52916	+	0.882860i
$431$	13.1774	+	15.7042i	0.634732	+	0.756444i	0.983528	−	0.180754i	$-0.0578539\pi$
$431$	13.1774	+	15.7042i	0.634732	+	0.756444i	−0.348796	+	0.937199i	$0.613409\pi$
$432$	−7.45856	+	2.71469i	−0.358850	+	0.130611i
$433$	12.4606	−	21.5824i	0.598820	−	1.03719i	−0.394176	−	0.919035i	$-0.628970\pi$
$433$	12.4606	−	21.5824i	0.598820	−	1.03719i	0.992996	−	0.118151i	$-0.0376967\pi$
$434$	−4.07413	−	7.05660i	−0.195565	−	0.338728i
$435$	−49.0625	−	41.1683i	−2.35237	−	1.97387i
$436$	14.2591	+	8.23249i	0.682886	+	0.394265i
$437$	2.38072	+	13.5017i	0.113885	+	0.645876i
$438$			17.7064i			0.846044i
$439$	38.4292	−	6.77611i	1.83413	−	0.323406i	0.853771	−	0.520648i	$-0.174310\pi$
$439$	38.4292	−	6.77611i	1.83413	−	0.323406i	0.980355	+	0.197243i	$0.0631986\pi$
$440$	−31.9205	+	26.7845i	−1.52175	+	1.27690i
$441$	10.0808	+	3.66910i	0.480036	+	0.174719i
$442$	0.719782	+	1.97759i	0.0342366	+	0.0940642i
$443$	−3.65524			−0.173666			−0.0868329	−	0.996223i	$-0.527675\pi$
$443$	−3.65524			−0.173666			−0.0868329	+	0.996223i	$0.527675\pi$
$444$	−24.7369	+	50.3416i	−1.17396	+	2.38911i
$445$	2.51983			0.119451
$446$	−1.38612	−	3.80833i	−0.0656347	−	0.180330i
$447$	−0.594799	−	0.216489i	−0.0281330	−	0.0102396i
$448$	8.21054	−	6.88946i	0.387911	−	0.325496i
$449$	0.769825	−	0.135741i	0.0363303	−	0.00640601i	−0.155453	−	0.987843i	$-0.549684\pi$
$449$	0.769825	−	0.135741i	0.0363303	−	0.00640601i	0.191784	+	0.981437i	$0.438573\pi$
$450$		−	17.8839i		−	0.843055i
$451$	2.64858	+	15.0209i	0.124717	+	0.707305i
$452$	−37.5100	−	21.6564i	−1.76432	−	1.01863i
$453$	−16.7898	−	14.0883i	−0.788852	−	0.661926i
$454$	−19.8269	−	34.3411i	−0.930521	−	1.61171i
$455$	−2.80750	+	4.86273i	−0.131618	+	0.227968i
$456$	20.0557	−	7.29968i	0.939194	−	0.341839i
$457$	14.3796	+	17.1370i	0.672651	+	0.801634i	0.989142	−	0.146961i	$-0.0469493\pi$
$457$	14.3796	+	17.1370i	0.672651	+	0.801634i	−0.316492	+	0.948595i	$0.602505\pi$
$458$	50.3233	−	29.0542i	2.35145	−	1.35761i
$459$	−1.15951	−	0.204452i	−0.0541211	−	0.00954302i
$460$	−14.9494	+	84.7821i	−0.697018	+	3.95299i
$461$	−14.0359	+	16.7274i	−0.653719	+	0.779072i	−0.986470	−	0.163943i	$-0.947579\pi$
$461$	−14.0359	+	16.7274i	−0.653719	+	0.779072i	0.332751	+	0.943015i	$0.392023\pi$
$462$	7.95565	−	21.8580i	0.370130	−	1.01692i
$463$	−5.30211	+	14.5674i	−0.246410	+	0.677006i	0.753401	+	0.657562i	$0.228412\pi$
$463$	−5.30211	+	14.5674i	−0.246410	+	0.677006i	−0.999811	+	0.0194446i	$0.993810\pi$
$464$	26.8928	−	32.0496i	1.24847	−	1.48786i
$465$	−2.61045	+	14.8046i	−0.121057	+	0.686546i
$466$	−56.9715	−	10.0456i	−2.63915	−	0.465354i
$467$	−5.88301	+	3.39656i	−0.272233	+	0.157174i	−0.629902	−	0.776674i	$-0.716905\pi$
$467$	−5.88301	+	3.39656i	−0.272233	+	0.157174i	0.357669	+	0.933849i	$0.383572\pi$
$468$	7.65233	+	9.11969i	0.353729	+	0.421558i
$469$	−7.64199	+	2.78146i	−0.352875	+	0.128436i
$470$	39.2784	−	68.0323i	1.81178	−	3.13809i
$471$	−7.43132	−	12.8714i	−0.342417	−	0.593084i
$472$	20.9657	+	17.5923i	0.965024	+	0.809751i
$473$	12.8134	+	7.39781i	0.589160	+	0.340152i
$474$	−3.18173	−	18.0445i	−0.146142	−	0.828812i
$475$		−	6.18103i		−	0.283605i
$476$	−3.67676	+	0.648312i	−0.168524	+	0.0297153i
$477$	−14.1269	+	11.8539i	−0.646826	+	0.542751i
$478$	−39.9214	−	14.5302i	−1.82596	−	0.664596i
$479$	−4.28164	−	11.7637i	−0.195633	−	0.537497i	0.802626	−	0.596483i	$-0.203436\pi$
$479$	−4.28164	−	11.7637i	−0.195633	−	0.537497i	−0.998259	+	0.0589857i	$0.981213\pi$
$480$	3.16566			0.144492
$481$	−8.12701	−	0.878369i	−0.370560	−	0.0400502i
$482$	40.7968			1.85824
$483$	−8.31654	−	22.8495i	−0.378416	−	1.03969i
$484$	−10.5751	−	3.84903i	−0.480687	−	0.174956i
$485$	29.2175	−	24.5164i	1.32670	−	1.11323i
$486$	−46.0151	+	8.11370i	−2.08729	+	0.368045i
$487$			21.6934i			0.983023i	0.870871	+	0.491511i	$0.163555\pi$
$487$			21.6934i			0.983023i	−0.870871	+	0.491511i	$0.836445\pi$
$488$	0.761418	+	4.31822i	0.0344678	+	0.195477i
$489$	−18.4684	−	10.6627i	−0.835171	−	0.482186i
$490$	26.6460	+	22.3587i	1.20374	+	1.01006i
$491$	13.6363	+	23.6187i	0.615396	+	1.06590i	0.990315	+	0.138840i	$0.0443373\pi$
$491$	13.6363	+	23.6187i	0.615396	+	1.06590i	−0.374919	+	0.927058i	$0.622329\pi$
$492$	24.5281	−	42.4839i	1.10581	−	1.91532i
$493$	5.83185	−	2.12262i	0.262653	−	0.0955980i
$494$	3.95139	+	4.70908i	0.177782	+	0.211872i
$495$	−15.6750	+	9.04996i	−0.704539	+	0.406766i
$496$	−9.67093	−	1.70525i	−0.434237	−	0.0765678i
$497$	−0.128471	+	0.728594i	−0.00576270	+	0.0326819i
$498$	−18.0219	+	21.4777i	−0.807583	+	0.962440i
$499$	−11.8679	+	32.6067i	−0.531279	+	1.45968i	0.326271	+	0.945276i	$0.394208\pi$
$499$	−11.8679	+	32.6067i	−0.531279	+	1.45968i	−0.857550	+	0.514401i	$0.828014\pi$
$500$	−6.69841	+	18.4037i	−0.299562	+	0.823040i
$501$	−9.14720	+	10.9012i	−0.408667	+	0.487030i
$502$	−7.15469	+	40.5763i	−0.319330	+	1.81101i
$503$	14.5930	+	2.57314i	0.650669	+	0.114731i	0.489234	−	0.872153i	$-0.337277\pi$
$503$	14.5930	+	2.57314i	0.650669	+	0.114731i	0.161435	+	0.986883i	$0.448388\pi$
$504$	−13.8264	+	7.98267i	−0.615876	+	0.355576i
$505$	−3.32730	−	3.96533i	−0.148063	−	0.176455i
$506$	48.8397	−	17.7762i	2.17119	−	0.790249i
$507$	12.7487	−	22.0815i	0.566191	−	0.980672i
$508$	15.4550	+	26.7688i	0.685705	+	1.18768i
$509$	−11.5452	−	9.68756i	−0.511731	−	0.429393i	0.350007	−	0.936747i	$-0.386179\pi$
$509$	−11.5452	−	9.68756i	−0.511731	−	0.429393i	−0.861738	+	0.507354i	$0.830624\pi$
$510$	8.91213	+	5.14542i	0.394636	+	0.227843i
$511$	−0.794923	−	4.50823i	−0.0351653	−	0.199433i
$512$		−	41.1821i		−	1.82001i
$513$	−3.38693	+	0.597207i	−0.149537	+	0.0263673i
$514$	46.1804	−	38.7499i	2.03693	−	1.70919i
$515$	45.2685	+	16.4764i	1.99477	+	0.726037i
$516$	−16.2755	−	44.7167i	−0.716491	−	1.96854i
$517$	−31.7440			−1.39610
$518$	6.03316	−	20.8088i	0.265082	−	0.914288i
$519$	55.3650			2.43025
$520$	6.68003	+	18.3532i	0.292939	+	0.804843i
$521$	−0.101246	−	0.0368504i	−0.00443566	−	0.00161445i	0.339801	−	0.940497i	$-0.389640\pi$
$521$	−0.101246	−	0.0368504i	−0.00443566	−	0.00161445i	−0.344237	+	0.938883i	$0.611862\pi$
$522$	40.1799	−	33.7149i	1.75863	−	1.47566i
$523$	−22.2611	+	3.92523i	−0.973409	+	0.171638i	−0.637664	−	0.770315i	$-0.720099\pi$
$523$	−22.2611	+	3.92523i	−0.973409	+	0.171638i	−0.335745	+	0.941953i	$0.608988\pi$
$524$			30.2129i			1.31986i
$525$	1.90364	+	10.7961i	0.0830815	+	0.471178i
$526$	34.9006	+	20.1499i	1.52174	+	0.878576i
$527$	−1.11589	−	0.936347i	−0.0486091	−	0.0407879i
$528$	−14.0167	−	24.2776i	−0.609998	−	1.05655i
$529$	15.6659	−	27.1342i	0.681127	−	1.17975i
$530$	−56.1888	+	20.4510i	−2.44068	+	0.888336i
$531$	7.64159	+	9.10690i	0.331617	+	0.395206i
$532$	−9.44447	+	5.45277i	−0.409470	+	0.236408i
$533$	7.04054	+	1.24144i	0.304960	+	0.0537726i
$534$	−0.849623	+	4.81845i	−0.0367668	+	0.208515i
$535$	10.0536	−	11.9815i	0.434657	−	0.518004i
$536$	−9.67497	+	26.5818i	−0.417895	+	1.14816i
$537$	12.8628	−	35.3402i	0.555070	−	1.52504i
$538$	−27.5065	+	32.7810i	−1.18589	+	1.41329i
$539$	2.44076	−	13.8423i	0.105131	−	0.596228i
$540$	−21.2677	−	3.75007i	−0.915217	−	0.161377i
$541$	8.14169	−	4.70061i	0.350039	−	0.202095i	−0.314664	−	0.949203i	$-0.601892\pi$
$541$	8.14169	−	4.70061i	0.350039	−	0.202095i	0.664702	+	0.747108i	$0.268558\pi$
$542$	4.44504	+	5.29739i	0.190931	+	0.227542i
$543$	7.79670	−	2.83777i	0.334588	−	0.121780i
$544$	−0.153376	+	0.265656i	−0.00657596	+	0.0113899i
$545$	5.86669	+	10.1614i	0.251301	+	0.435267i
$546$	−8.35197	−	7.00814i	−0.357432	−	0.299921i
$547$	−9.86753	−	5.69702i	−0.421905	−	0.243587i	0.273987	−	0.961733i	$-0.411657\pi$
$547$	−9.86753	−	5.69702i	−0.421905	−	0.243587i	−0.695892	+	0.718146i	$0.744991\pi$
$548$	−8.17199	−	46.3457i	−0.349090	−	1.97979i
$549$			1.90465i			0.0812883i
$550$	−23.0761	+	4.06893i	−0.983966	+	0.173500i
$551$	13.8870	−	11.6526i	0.591605	−	0.496415i
$552$	−79.4793	−	28.9281i	−3.38286	−	1.23126i
$553$	1.62021	+	4.45148i	0.0688982	+	0.189296i
$554$	−54.5843			−2.31906
$555$	−33.2038	+	22.2544i	−1.40942	+	0.944645i
$556$	−52.0550			−2.20762
$557$	−8.03908	−	22.0872i	−0.340627	−	0.935864i	−0.985213	−	0.171333i	$-0.945193\pi$
$557$	−8.03908	−	22.0872i	−0.340627	−	0.935864i	0.644587	−	0.764531i	$-0.277029\pi$
$558$	−11.5688	−	4.21071i	−0.489747	−	0.178253i
$559$	5.31249	−	4.45771i	0.224694	−	0.188541i
$560$	−17.6634	+	3.11454i	−0.746416	+	0.131613i
$561$		−	4.15842i		−	0.175568i
$562$	0.352907	+	2.00144i	0.0148865	+	0.0844255i
$563$	23.5707	+	13.6085i	0.993385	+	0.573531i	0.906285	−	0.422668i	$-0.138906\pi$
$563$	23.5707	+	13.6085i	0.993385	+	0.573531i	0.0871009	+	0.996199i	$0.472240\pi$
$564$	78.2107	+	65.6265i	3.29326	+	2.76338i
$565$	−15.4330	−	26.7307i	−0.649269	−	1.12457i
$566$	−35.4318	+	61.3698i	−1.48931	+	2.57956i
$567$	14.6660	−	5.33798i	0.615914	−	0.224174i
$568$	1.65416	+	1.97136i	0.0694072	+	0.0827163i
$569$	−29.1899	+	16.8528i	−1.22371	+	0.706507i	−0.965706	−	0.259638i	$-0.916397\pi$
$569$	−29.1899	+	16.8528i	−1.22371	+	0.706507i	−0.258000	+	0.966145i	$0.583063\pi$
$570$	29.6030	+	5.21981i	1.23993	+	0.218634i
$571$	6.55743	−	37.1890i	0.274420	−	1.55631i	−0.466379	−	0.884585i	$-0.654442\pi$
$571$	6.55743	−	37.1890i	0.274420	−	1.55631i	0.740799	−	0.671727i	$-0.234447\pi$
$572$	10.0263	−	11.9489i	0.419221	−	0.499609i
$573$	6.84610	−	18.8095i	0.286000	−	0.785778i
$574$	−6.48080	+	17.8058i	−0.270503	+	0.743202i
$575$	−15.7451	+	18.7642i	−0.656615	+	0.782523i
$576$	2.81207	−	15.9480i	0.117170	−	0.664502i
$577$	−45.0407	−	7.94189i	−1.87507	−	0.330625i	−0.884380	−	0.466767i	$-0.845419\pi$
$577$	−45.0407	−	7.94189i	−1.87507	−	0.330625i	−0.990689	+	0.136142i	$0.956530\pi$
$578$	35.3440	−	20.4059i	1.47012	−	0.848772i
$579$	15.4014	+	18.3547i	0.640060	+	0.762794i
$580$	106.968	−	38.9332i	4.44161	−	1.61661i
$581$	3.62434	−	6.27754i	0.150363	−	0.260436i
$582$	37.0292	+	64.1365i	1.53491	+	2.65854i
$583$	18.5095	+	15.5313i	0.766585	+	0.643241i
$584$	−13.7900	−	7.96163i	−0.570632	−	0.329455i
$585$	1.47319	+	8.35487i	0.0609088	+	0.345431i
$586$			6.65544i			0.274934i
$587$	8.88682	−	1.56699i	0.366798	−	0.0646764i	0.0127887	−	0.999918i	$-0.495929\pi$
$587$	8.88682	−	1.56699i	0.366798	−	0.0646764i	0.354010	+	0.935242i	$0.384818\pi$
$588$	−34.6306	+	29.0585i	−1.42814	+	1.19835i
$589$	−3.99842	−	1.45530i	−0.164752	−	0.0599648i
$590$	13.1838	+	36.2221i	0.542767	+	1.49124i
$591$	34.1729			1.40569
$592$	−14.5374	−	21.6900i	−0.597484	−	0.891454i
$593$	−7.32788			−0.300920			−0.150460	−	0.988616i	$-0.548075\pi$
$593$	−7.32788			−0.300920			−0.150460	+	0.988616i	$0.548075\pi$
$594$	4.45919	+	12.2515i	0.182963	+	0.502686i
$595$	−2.50013	−	0.909971i	−0.102495	−	0.0373052i
$596$	0.861808	−	0.723143i	0.0353010	−	0.0296211i
$597$	−24.4520	+	4.31155i	−1.00075	+	0.176460i
$598$		−	24.3612i		−	0.996204i
$599$	−5.37230	−	30.4678i	−0.219506	−	1.24488i	−0.872914	−	0.487875i	$-0.837772\pi$
$599$	−5.37230	−	30.4678i	−0.219506	−	1.24488i	0.653408	−	0.757006i	$-0.273339\pi$
$600$	33.0234	+	19.0660i	1.34817	+	0.778368i
$601$	−23.6298	−	19.8278i	−0.963880	−	0.808791i	0.0176998	−	0.999843i	$-0.494366\pi$
$601$	−23.6298	−	19.8278i	−0.963880	−	0.808791i	−0.981580	+	0.191052i	$0.938810\pi$
$602$	9.19044	+	15.9183i	0.374575	+	0.648782i
$603$	−6.14369	+	10.6412i	−0.250190	+	0.433342i
$604$	36.6057	−	13.3234i	1.48947	−	0.542121i
$605$	−5.15500	−	6.14349i	−0.209581	−	0.249769i
$606$	8.70444	−	5.02551i	0.353594	−	0.204148i
$607$	1.62505	+	0.286539i	0.0659586	+	0.0116303i	0.206530	−	0.978440i	$-0.433783\pi$
$607$	1.62505	+	0.286539i	0.0659586	+	0.0116303i	−0.140572	+	0.990071i	$0.544894\pi$
$608$	−0.155594	+	0.882416i	−0.00631016	+	0.0357867i
$609$	−20.6668	+	24.6298i	−0.837462	+	0.998048i
$610$	−2.11221	+	5.80325i	−0.0855209	+	0.234967i
$611$	−5.08890	+	13.9816i	−0.205875	+	0.565637i
$612$	−3.62593	+	4.32122i	−0.146570	+	0.174675i
$613$	−0.618131	+	3.50560i	−0.0249661	+	0.141590i	−0.994743	−	0.102404i	$-0.967347\pi$
$613$	−0.618131	+	3.50560i	−0.0249661	+	0.141590i	0.969777	+	0.243994i	$0.0784577\pi$
$614$	42.5514	+	7.50296i	1.71724	+	0.302795i
$615$	30.2752	−	17.4794i	1.22081	−	0.704837i
$616$	13.4460	+	16.0243i	0.541755	+	0.645639i
$617$	−40.0535	+	14.5783i	−1.61249	+	0.586900i	−0.981931	−	0.189239i	$-0.939398\pi$
$617$	−40.0535	+	14.5783i	−1.61249	+	0.586900i	−0.630562	+	0.776139i	$0.717176\pi$
$618$	−46.7698	+	81.0077i	−1.88136	+	3.25861i
$619$	11.0480	+	19.1357i	0.444058	+	0.769130i	0.997986	−	0.0634340i	$-0.0202052\pi$
$619$	11.0480	+	19.1357i	0.444058	+	0.769130i	−0.553928	+	0.832564i	$0.686872\pi$
$620$	−20.4678	−	17.1745i	−0.822006	−	0.689745i
$621$	11.8033	+	6.81461i	0.473648	+	0.273461i
$622$	1.90397	+	10.7980i	0.0763424	+	0.432959i
$623$		−	1.26497i		−	0.0506800i
$624$	−12.9401	+	2.28169i	−0.518019	+	0.0913408i
$625$	−23.4198	+	19.6516i	−0.936793	+	0.786063i
$626$	−46.6235	−	16.9696i	−1.86345	−	0.678241i
$627$	−4.15444	−	11.4142i	−0.165912	−	0.455841i
$628$	26.4161			1.05412
$629$	−0.258816	−	3.86462i	−0.0103197	−	0.154093i
$630$	−22.4859			−0.895860
$631$	−6.66923	−	18.3236i	−0.265498	−	0.729449i	−0.998773	−	0.0495176i	$-0.984232\pi$
$631$	−6.66923	−	18.3236i	−0.265498	−	0.729449i	0.733275	−	0.679932i	$-0.237991\pi$
$632$	15.4839	+	5.63569i	0.615918	+	0.224176i
$633$	−7.92368	+	6.64875i	−0.314938	+	0.264264i
$634$	20.7136	−	3.65236i	0.822641	−	0.145054i
$635$			22.0273i			0.874126i
$636$	−13.4946	−	76.5320i	−0.535098	−	3.03469i
$637$	−5.70555	−	3.29410i	−0.226062	−	0.130517i
$638$	−52.6449	−	44.1744i	−2.08423	−	1.74888i
$639$	0.558911	+	0.968061i	0.0221102	+	0.0382959i
$640$	27.6439	−	47.8806i	1.09272	−	1.89265i
$641$	3.63893	−	1.32446i	0.143729	−	0.0523131i	−0.269154	−	0.963097i	$-0.586744\pi$
$641$	3.63893	−	1.32446i	0.143729	−	0.0523131i	0.412883	+	0.910784i	$0.364522\pi$
$642$	19.5213	+	23.2646i	0.770445	+	0.918180i
$643$	23.9860	−	13.8483i	0.945916	−	0.546125i	0.0541060	−	0.998535i	$-0.482769\pi$
$643$	23.9860	−	13.8483i	0.945916	−	0.546125i	0.891810	+	0.452410i	$0.149436\pi$
$644$	42.5613	+	7.50470i	1.67715	+	0.295727i
$645$	5.88866	−	33.3962i	0.231866	−	1.31498i
$646$	−1.87230	+	2.23132i	−0.0736648	+	0.0877903i
$647$	−4.10055	+	11.2662i	−0.161209	+	0.442919i	−0.993829	−	0.110927i	$-0.964618\pi$
$647$	−4.10055	+	11.2662i	−0.161209	+	0.442919i	0.832619	+	0.553846i	$0.186840\pi$
$648$	18.5675	−	51.0139i	0.729402	−	2.00402i
$649$	10.0123	−	11.9321i	0.393015	−	0.468378i
$650$	−1.90718	+	10.8162i	−0.0748057	+	0.424244i
$651$	7.43201	+	1.31046i	0.291284	+	0.0513611i
$652$	32.8248	−	18.9514i	1.28552	−	0.742194i
$653$	3.19325	+	3.80556i	0.124961	+	0.148923i	0.824898	−	0.565282i	$-0.191233\pi$
$653$	3.19325	+	3.80556i	0.124961	+	0.148923i	−0.699936	+	0.714205i	$0.746788\pi$
$654$	−21.4089	+	7.79220i	−0.837154	+	0.304699i
$655$	−10.7652	+	18.6460i	−0.420633	+	0.728558i
$656$	11.4182	+	19.7769i	0.445806	+	0.772159i
$657$	−5.29843	−	4.44591i	−0.206711	−	0.173452i
$658$	−34.1527	−	19.7181i	−1.33141	−	0.768691i
$659$	−3.28827	−	18.6487i	−0.128093	−	0.726451i	−0.979423	−	0.201820i	$-0.935314\pi$
$659$	−3.28827	−	18.6487i	−0.128093	−	0.726451i	0.851330	−	0.524631i	$-0.175797\pi$
$660$		−	76.2738i		−	2.96896i
$661$	15.6808	−	2.76495i	0.609912	−	0.107544i	0.139843	−	0.990174i	$-0.455340\pi$
$661$	15.6808	−	2.76495i	0.609912	−	0.107544i	0.470069	+	0.882630i	$0.344229\pi$
$662$	−19.5358	+	16.3925i	−0.759280	+	0.637111i
$663$	−1.83158	−	0.666639i	−0.0711325	−	0.0258901i
$664$	−8.62359	−	23.6931i	−0.334660	−	0.919471i
$665$	−7.77158			−0.301369
$666$	−13.2265	−	29.9440i	−0.512516	−	1.16031i
$667$	−71.8406			−2.78168
$668$	−8.65057	−	23.7672i	−0.334700	−	0.919582i
$669$	3.52716	+	1.28378i	0.136368	+	0.0496338i
$670$	−30.5200	+	25.6093i	−1.17909	+	0.989374i
$671$	2.45761	−	0.433344i	0.0948752	−	0.0167290i
$672$		−	1.58918i		−	0.0613041i
$673$	0.349701	+	1.98325i	0.0134800	+	0.0764488i	0.990806	−	0.135293i	$-0.0431975\pi$
$673$	0.349701	+	1.98325i	0.0134800	+	0.0764488i	−0.977326	+	0.211742i	$0.932086\pi$
$674$	50.9081	+	29.3918i	1.96091	+	1.13213i
$675$	−4.70704	−	3.94967i	−0.181174	−	0.152023i
$676$	22.6589	+	39.2464i	0.871497	+	1.50948i
$677$	−3.35870	+	5.81744i	−0.129085	+	0.223583i	−0.923323	−	0.384025i	$-0.874537\pi$
$677$	−3.35870	+	5.81744i	−0.129085	+	0.223583i	0.794237	+	0.607608i	$0.207871\pi$
$678$	56.3184	−	20.4982i	2.16289	−	0.787229i
$679$	−12.3074	−	14.6674i	−0.472315	−	0.562883i
$680$	−8.01463	+	4.62725i	−0.307347	+	0.177447i
$681$	36.1681	+	6.37741i	1.38596	+	0.244383i
$682$	−2.80105	+	15.8856i	−0.107258	+	0.608290i
$683$	3.27490	−	3.90287i	0.125311	−	0.149339i	−0.699741	−	0.714396i	$-0.746701\pi$
$683$	3.27490	−	3.90287i	0.125311	−	0.149339i	0.825052	+	0.565057i	$0.191146\pi$
$684$	−5.63556	+	15.4836i	−0.215481	+	0.592029i
$685$	11.4702	−	31.5141i	0.438254	−	1.20409i
$686$	27.2508	−	32.4762i	1.04044	−	1.23995i
$687$	−9.34541	+	53.0005i	−0.356550	+	2.02209i
$688$	21.8157	+	3.84670i	0.831716	+	0.146654i
$689$	9.80805	−	5.66268i	0.373657	−	0.215731i
$690$	−76.5716	−	91.2545i	−2.91503	−	3.47400i
$691$	4.84765	−	1.76440i	0.184413	−	0.0671209i	−0.248163	−	0.968718i	$-0.579827\pi$
$691$	4.84765	−	1.76440i	0.184413	−	0.0671209i	0.432576	+	0.901597i	$0.357605\pi$
$692$	−49.2014	+	85.2193i	−1.87036	+	3.23955i
$693$	4.54315	+	7.86897i	0.172580	+	0.298917i
$694$	−58.0126	−	48.6783i	−2.20213	−	1.84780i
$695$	−32.1259	−	18.5479i	−1.21860	−	0.703561i
$696$	19.4202	+	110.137i	0.736120	+	4.17475i
$697$			3.38751i			0.128311i
$698$	37.4122	−	6.59678i	1.41607	−	0.249692i
$699$	41.0440	−	34.4400i	1.55243	−	1.30264i
$700$	−18.3093	−	6.66404i	−0.692026	−	0.251877i
$701$	16.4100	+	45.0861i	0.619797	+	1.70288i	0.707484	+	0.706730i	$0.249830\pi$
$701$	16.4100	+	45.0861i	0.619797	+	1.70288i	−0.0876869	+	0.996148i	$0.527947\pi$
$702$	6.11104			0.230646
$703$	−4.57134	−	10.3492i	−0.172411	−	0.390329i
$704$	−21.2180			−0.799683
$705$	24.8843	+	68.3691i	0.937198	+	2.57493i
$706$	28.9028	+	10.5198i	1.08777	+	0.395917i
$707$	−1.99062	+	1.67033i	−0.0748651	+	0.0628193i
$708$	−49.3363	+	8.69932i	−1.85417	+	0.326941i
$709$			39.6235i			1.48809i	0.668129	+	0.744046i	$0.267095\pi$
$709$			39.6235i			1.48809i	−0.668129	+	0.744046i	$0.732905\pi$
$710$	0.629381	+	3.56940i	0.0236202	+	0.133957i
$711$	6.19851	+	3.57871i	0.232462	+	0.134212i
$712$	−3.37064	−	2.82830i	−0.126320	−	0.105995i
$713$	8.43118	+	14.6032i	0.315750	+	0.546895i
$714$	2.58304	−	4.47396i	0.0966679	−	0.167434i
$715$	10.4453	−	3.80179i	0.390633	−	0.142179i
$716$	42.9658	+	51.2047i	1.60571	+	1.91361i
$717$	34.0754	−	19.6734i	1.27257	−	0.734717i
$718$	10.4472	+	1.84212i	0.389886	+	0.0687474i
$719$	−6.07958	+	34.4790i	−0.226730	+	1.28585i	0.632620	+	0.774463i	$0.281980\pi$
$719$	−6.07958	+	34.4790i	−0.226730	+	1.28585i	−0.859350	+	0.511388i	$0.829131\pi$
$720$	−17.4192	+	20.7594i	−0.649177	+	0.773659i
$721$	8.27128	−	22.7251i	0.308038	−	0.846329i
$722$	13.0718	−	35.9144i	0.486481	−	1.33660i
$723$	−24.2875	+	28.9448i	−0.903264	+	1.07647i
$724$	−2.56075	+	14.5227i	−0.0951695	+	0.539733i
$725$	31.8966	+	5.62422i	1.18461	+	0.208878i
$726$	13.4858	−	7.78604i	0.500506	−	0.288967i
$727$	−3.91285	−	4.66316i	−0.145120	−	0.172947i	0.688588	−	0.725153i	$-0.258231\pi$
$727$	−3.91285	−	4.66316i	−0.145120	−	0.172947i	−0.833708	+	0.552206i	$0.813786\pi$
$728$	9.21347	−	3.35343i	0.341474	−	0.124286i
$729$	5.47305	−	9.47961i	0.202706	−	0.351097i
$730$	−11.2133	−	19.4220i	−0.415024	−	0.718842i
$731$	2.51724	+	2.11221i	0.0931035	+	0.0781231i
$732$	−6.95094	−	4.01313i	−0.256914	−	0.148330i
$733$	0.767589	+	4.35322i	0.0283516	+	0.160790i	0.995697	−	0.0926737i	$-0.0295414\pi$
$733$	0.767589	+	4.35322i	0.0283516	+	0.160790i	−0.967345	+	0.253463i	$0.918430\pi$
$734$		−	56.0161i		−	2.06759i
$735$	−31.7263	+	5.59421i	−1.17024	+	0.206345i
$736$	2.72014	−	2.28247i	0.100266	−	0.0841330i
$737$	15.1284	+	5.50629i	0.557262	+	0.202827i
$738$	9.79189	+	26.9030i	0.360445	+	0.990313i
$739$	19.8773			0.731198			0.365599	−	0.930773i	$-0.380864\pi$
$739$	19.8773			0.731198			0.365599	+	0.930773i	$0.380864\pi$
$740$	−4.74721	−	70.8851i	−0.174511	−	2.60579i
$741$	−5.69341			−0.209153
$742$	10.2666	+	28.2072i	0.376898	+	1.03552i
$743$	−46.9483	−	17.0878i	−1.72237	−	0.626890i	−0.724325	−	0.689459i	$-0.757848\pi$
$743$	−46.9483	−	17.0878i	−1.72237	−	0.626890i	−0.998041	+	0.0625694i	$0.980071\pi$
$744$	20.1088	−	16.8733i	0.737224	−	0.618604i
$745$	0.789533	−	0.139216i	0.0289262	−	0.00510048i
$746$		−	54.5957i		−	1.99889i
$747$	−1.90181	−	10.7857i	−0.0695837	−	0.394629i
$748$	6.40075	+	3.69548i	0.234035	+	0.135120i
$749$	−6.01479	−	5.04701i	−0.219776	−	0.184414i
$750$	−13.5499	−	23.4692i	−0.494774	−	0.856974i
$751$	4.66637	−	8.08239i	0.170278	−	0.294930i	−0.768239	−	0.640163i	$-0.778867\pi$
$751$	4.66637	−	8.08239i	0.170278	−	0.294930i	0.938517	+	0.345233i	$0.112200\pi$
$752$	−44.6614	+	16.2554i	−1.62863	+	0.592774i
$753$	−24.5289	−	29.2324i	−0.893883	−	1.06529i
$754$	−27.8962	+	16.1059i	−1.01592	+	0.586541i
$755$	27.3386	+	4.82054i	0.994954	+	0.175437i
$756$	−1.88257	+	10.6766i	−0.0684682	+	0.388303i
$757$	19.5011	−	23.2405i	0.708779	−	0.844690i	−0.284710	−	0.958614i	$-0.591897\pi$
$757$	19.5011	−	23.2405i	0.708779	−	0.844690i	0.993490	+	0.113923i	$0.0363418\pi$
$758$	−5.54853	+	15.2445i	−0.201532	+	0.553704i
$759$	−16.4638	+	45.2338i	−0.597597	+	1.64188i
$760$	−17.3762	+	20.7081i	−0.630299	+	0.751162i
$761$	5.95667	−	33.7819i	0.215929	−	1.22459i	−0.663358	−	0.748302i	$-0.730869\pi$
$761$	5.95667	−	33.7819i	0.215929	−	1.22459i	0.879287	−	0.476292i	$-0.158020\pi$
$762$	−42.1209	−	7.42705i	−1.52588	−	0.269054i
$763$	5.10110	−	2.94512i	0.184672	−	0.106621i
$764$	22.8682	+	27.2532i	0.827341	+	0.985987i
$765$	−3.77746	+	1.37488i	−0.136574	+	0.0497090i
$766$	−5.80934	+	10.0621i	−0.209900	+	0.363558i
$767$	−3.65044	−	6.32275i	−0.131810	−	0.228301i
$768$	56.4113	+	47.3347i	2.03557	+	1.70804i
$769$	15.2691	+	8.81563i	0.550618	+	0.317900i	0.749371	−	0.662150i	$-0.230356\pi$
$769$	15.2691	+	8.81563i	0.550618	+	0.317900i	−0.198753	+	0.980050i	$0.563689\pi$
$770$	5.11598	+	29.0141i	0.184367	+	1.04560i
$771$			55.8333i			2.01079i
$772$	−41.9388	+	7.39494i	−1.50941	+	0.266150i
$773$	−6.77749	+	5.68699i	−0.243769	+	0.204547i	−0.756484	−	0.654012i	$-0.773084\pi$
$773$	−6.77749	+	5.68699i	−0.243769	+	0.204547i	0.512714	+	0.858559i	$0.328640\pi$
$774$	26.0970	+	9.49853i	0.938037	+	0.341418i
$775$	−2.60012	−	7.14376i	−0.0933989	−	0.256611i
$776$	−66.6003			−2.39081
$777$	11.1719	+	16.6686i	0.400788	+	0.597981i
$778$	79.4506			2.84844
$779$	3.38427	+	9.29822i	0.121254	+	0.333143i
$780$	−33.5949	−	12.2275i	−1.20289	−	0.437816i
$781$	1.12195	−	0.941429i	0.0401466	−	0.0336870i
$782$	11.3678	−	2.00445i	0.406512	−	0.0716790i
$783$		−	18.0213i		−	0.644029i
$784$	−3.65435	−	20.7249i	−0.130513	−	0.740174i
$785$	16.3028	+	9.41240i	0.581870	+	0.335943i
$786$	−32.0253	−	26.8724i	−1.14230	−	0.958508i
$787$	−23.0575	−	39.9368i	−0.821911	−	1.42359i	−0.904257	−	0.426988i	$-0.859575\pi$
$787$	−23.0575	−	39.9368i	−0.821911	−	1.42359i	0.0823459	−	0.996604i	$-0.473759\pi$
$788$	−30.3686	+	52.5999i	−1.08184	+	1.87379i
$789$	−35.0734	+	12.7657i	−1.24865	+	0.454470i
$790$	14.9175	+	17.7780i	0.530740	+	0.632511i
$791$	−13.4190	+	7.74746i	−0.477125	+	0.275468i
$792$	31.1255	+	5.48826i	1.10599	+	0.195017i
$793$	0.203116	−	1.15193i	0.00721285	−	0.0409061i
$794$	−37.2806	+	44.4293i	−1.32304	+	1.57674i
$795$	18.9411	−	52.0402i	0.671771	−	1.84568i
$796$	15.0934	−	41.4688i	0.534971	−	1.46982i
$797$	25.5181	−	30.4113i	0.903898	−	1.07722i	−0.0927727	−	0.995687i	$-0.529573\pi$
$797$	25.5181	−	30.4113i	0.903898	−	1.07722i	0.996670	−	0.0815360i	$-0.0259826\pi$
$798$	2.62038	−	14.8609i	0.0927606	−	0.526071i
$799$	−6.94305	−	1.22425i	−0.245627	−	0.0433107i
$800$	−1.38641	+	0.800443i	−0.0490169	+	0.0282999i
$801$	−1.22853	−	1.46411i	−0.0434081	−	0.0517317i
$802$	−45.1050	+	16.4169i	−1.59271	+	0.579700i
$803$	−4.53118	+	7.84823i	−0.159902	+	0.276958i
$804$	−25.8898	−	44.8424i	−0.913061	−	1.58147i
$805$	23.5928	+	19.7967i	0.831537	+	0.697742i
$806$	6.54777	+	3.78036i	0.230635	+	0.133157i
$807$	−6.88221	−	39.0309i	−0.242265	−	1.37395i
$808$			9.03883i			0.317985i
$809$	−24.1279	+	4.25440i	−0.848292	+	0.149577i	−0.580864	−	0.814001i	$-0.697285\pi$
$809$	−24.1279	+	4.25440i	−0.848292	+	0.149577i	−0.267429	+	0.963578i	$0.586174\pi$
$810$	58.5718	−	49.1476i	2.05800	−	1.72687i
$811$	−23.5403	−	8.56798i	−0.826613	−	0.300862i	−0.106145	−	0.994351i	$-0.533851\pi$
$811$	−23.5403	−	8.56798i	−0.826613	−	0.300862i	−0.720468	+	0.693488i	$0.756073\pi$
$812$	−19.5448	−	53.6988i	−0.685886	−	1.88446i
$813$	−6.40469			−0.224622
$814$	−35.6283	+	23.8793i	−1.24877	+	0.836970i
$815$	27.0106			0.946138
$816$	−2.12944	−	5.85058i	−0.0745452	−	0.204811i
$817$	9.01965	+	3.28288i	0.315557	+	0.114854i
$818$	−22.6910	+	19.0400i	−0.793374	+	0.665720i
$819$	4.19421	−	0.739552i	0.146557	−	0.0258420i
$820$			62.1339i			2.16981i
$821$	0.657092	+	3.72655i	0.0229327	+	0.130058i	0.994125	−	0.108240i	$-0.0345216\pi$
$821$	0.657092	+	3.72655i	0.0229327	+	0.130058i	−0.971192	+	0.238298i	$0.923411\pi$
$822$	56.3944	+	32.5593i	1.96698	+	1.13564i
$823$	22.4077	+	18.8023i	0.781082	+	0.655406i	0.943521	−	0.331313i	$-0.107491\pi$
$823$	22.4077	+	18.8023i	0.781082	+	0.655406i	−0.162439	+	0.986719i	$0.551936\pi$
$824$	−42.0599	−	72.8498i	−1.46522	−	2.53784i
$825$	10.8510	−	18.7945i	0.377783	−	0.654340i
$826$	18.1838	−	6.61835i	0.632694	−	0.230282i
$827$	−0.869232	−	1.03591i	−0.0302262	−	0.0360222i	0.750720	−	0.660621i	$-0.229707\pi$
$827$	−0.869232	−	1.03591i	−0.0302262	−	0.0360222i	−0.780946	+	0.624599i	$0.785263\pi$
$828$	56.5499	−	32.6491i	1.96525	−	1.13464i
$829$	37.5106	+	6.61414i	1.30280	+	0.229719i	0.781634	−	0.623737i	$-0.214387\pi$
$829$	37.5106	+	6.61414i	1.30280	+	0.229719i	0.521165	+	0.853456i	$0.325498\pi$
$830$	6.16650	−	34.9720i	0.214042	−	1.21389i
$831$	32.4956	−	38.7268i	1.12726	−	1.34342i
$832$	−3.40147	+	9.34547i	−0.117925	+	0.323996i
$833$	1.06769	−	2.93345i	0.0369932	−	0.101638i
$834$	46.2996	−	55.1777i	1.60322	−	1.91065i
$835$	3.12986	−	17.7503i	0.108313	−	0.614275i
$836$	21.2611	+	3.74890i	0.735329	+	0.129658i
$837$	−3.66324	+	2.11497i	−0.126620	+	0.0731042i
$838$	52.1486	+	62.1483i	1.80144	+	2.14688i
$839$	10.1555	−	3.69628i	0.350605	−	0.127610i	−0.160713	−	0.987001i	$-0.551379\pi$
$839$	10.1555	−	3.69628i	0.350605	−	0.127610i	0.511319	+	0.859391i	$0.329157\pi$
$840$	23.9723	−	41.5212i	0.827121	−	1.43262i
$841$	32.9958	+	57.1504i	1.13779	+	1.97070i
$842$	3.42626	+	2.87497i	0.118077	+	0.0990781i
$843$	−1.63009	−	0.941131i	−0.0561432	−	0.0324143i
$844$	−3.19238	−	18.1049i	−0.109886	−	0.623197i
$845$			32.2947i			1.11097i
$846$	−58.6792	+	10.3467i	−2.01743	+	0.355728i
$847$	−3.08408	+	2.58785i	−0.105970	+	0.0889196i
$848$	33.9947	+	12.3731i	1.16738	+	0.424893i
$849$	−22.4474	−	61.6736i	−0.770391	−	2.11663i
$850$	−5.20412			−0.178500
$851$	−12.4853	+	43.0627i	−0.427990	+	1.47617i
$852$	−4.71054			−0.161381
$853$	14.6360	+	40.2121i	0.501127	+	1.37683i	0.890176	+	0.455618i	$0.150582\pi$
$853$	14.6360	+	40.2121i	0.501127	+	1.37683i	−0.389049	+	0.921217i	$0.627196\pi$
$854$	2.91328	+	1.06035i	0.0996902	+	0.0362843i
$855$	−8.99500	+	7.54770i	−0.307623	+	0.258126i
$856$	−26.8965	+	4.74257i	−0.919302	+	0.162098i
$857$		−	26.7181i		−	0.912672i	−0.889808	−	0.456336i	$-0.849162\pi$
$857$		−	26.7181i		−	0.912672i	0.889808	−	0.456336i	$-0.150838\pi$
$858$	3.74793	+	21.2556i	0.127952	+	0.725653i
$859$	−44.2982	−	25.5756i	−1.51143	−	0.872627i	−0.999911	−	0.0133579i	$-0.995748\pi$
$859$	−44.2982	−	25.5756i	−1.51143	−	0.872627i	−0.511524	−	0.859269i	$-0.670919\pi$
$860$	46.1713	+	38.7423i	1.57443	+	1.32110i
$861$	−8.77479	−	15.1984i	−0.299044	−	0.517959i
$862$	25.2088	−	43.6628i	0.858614	−	1.48716i
$863$	−27.0688	+	9.85225i	−0.921434	+	0.335375i	−0.758809	−	0.651313i	$-0.774218\pi$
$863$	−27.0688	+	9.85225i	−0.921434	+	0.335375i	−0.162625	+	0.986688i	$0.551996\pi$
$864$	0.572561	+	0.682352i	0.0194789	+	0.0232141i
$865$	−60.7296	+	35.0622i	−2.06487	+	1.19215i
$866$	−60.3589	−	10.6429i	−2.05108	−	0.361660i
$867$	−6.56364	+	37.2243i	−0.222913	+	1.26420i
$868$	−8.62174	+	10.2750i	−0.292641	+	0.348756i
$869$	3.20742	−	8.81233i	0.108804	−	0.298938i
$870$	−53.8725	+	148.014i	−1.82645	+	5.01813i
$871$	4.85049	−	5.78059i	0.164353	−	0.195868i
$872$	3.55779	−	20.1772i	0.120482	−	0.683288i
$873$	−28.4898	−	5.02352i	−0.964233	−	0.170020i
$874$	29.2004	−	16.8589i	0.987718	−	0.570259i
$875$	4.50360	+	5.36718i	0.152250	+	0.181444i
$876$	27.3891	−	9.96882i	0.925392	−	0.336815i
$877$	21.4317	−	37.1209i	0.723699	−	1.25348i	−0.235809	−	0.971799i	$-0.575774\pi$
$877$	21.4317	−	37.1209i	0.723699	−	1.25348i	0.959507	−	0.281683i	$-0.0908928\pi$
$878$	−47.9844	−	83.1113i	−1.61939	−	2.80487i
$879$	−4.72194	−	3.96218i	−0.159267	−	0.133641i
$880$	30.7497	+	17.7533i	1.03657	+	0.598465i
$881$	1.95748	+	11.1014i	0.0659492	+	0.374016i	0.999864	+	0.0165195i	$0.00525857\pi$
$881$	1.95748	+	11.1014i	0.0659492	+	0.374016i	−0.933914	+	0.357497i	$0.883630\pi$
$882$		−	26.3832i		−	0.888368i
$883$	−11.4118	+	2.01222i	−0.384039	+	0.0677165i	−0.362335	−	0.932048i	$-0.618020\pi$
$883$	−11.4118	+	2.01222i	−0.384039	+	0.0677165i	−0.0217043	+	0.999764i	$0.506909\pi$
$884$	2.65378	−	2.22679i	0.0892564	−	0.0748950i
$885$	−33.5477	−	12.2104i	−1.12769	−	0.410447i
$886$	3.07459	+	8.44737i	0.103293	+	0.283795i
$887$	−19.0553			−0.639815			−0.319907	−	0.947449i	$-0.603652\pi$
$887$	−19.0553			−0.639815			−0.319907	+	0.947449i	$0.603652\pi$
$888$	69.3937	+	7.50008i	2.32870	+	0.251686i
$889$	11.0579			0.370869
$890$	−2.11954	−	5.82339i	−0.0710472	−	0.195201i
$891$	−29.0334	−	10.5673i	−0.972655	−	0.354018i
$892$	−5.11052	+	4.28823i	−0.171113	+	0.143581i
$893$	−20.2807	+	3.57604i	−0.678668	+	0.119668i
$894$			1.55670i			0.0520637i
$895$	8.27157	+	46.9104i	0.276488	+	1.56804i
$896$	−24.0364	−	13.8774i	−0.803001	−	0.463613i
$897$	17.2839	+	14.5029i	0.577094	+	0.484239i
$898$	−0.961237	−	1.66491i	−0.0320769	−	0.0555588i
$899$	11.1482	−	19.3092i	0.371812	−	0.643998i
$900$	−27.6637	+	10.0688i	−0.922123	+	0.335625i
$901$	3.44942	+	4.11085i	0.114917	+	0.136952i
$902$	32.4858	−	18.7557i	1.08166	−	0.624496i
$903$	−16.7652	−	2.95615i	−0.557910	−	0.0983745i
$904$	−9.35916	+	53.0784i	−0.311281	+	1.76536i
$905$	−6.75502	+	8.05032i	−0.224544	+	0.267602i
$906$	−18.4358	+	50.6520i	−0.612489	+	1.68280i
$907$	7.26152	−	19.9509i	0.241115	−	0.662457i	−0.758823	−	0.651297i	$-0.774225\pi$
$907$	7.26152	−	19.9509i	0.241115	−	0.662457i	0.999938	−	0.0111605i	$-0.00355257\pi$
$908$	−41.9579	+	50.0035i	−1.39242	+	1.65942i
$909$	−0.681779	+	3.86656i	−0.0226132	+	0.128246i
$910$	13.5994	+	2.39795i	0.450817	+	0.0794912i
$911$	−12.3199	+	7.11292i	−0.408178	+	0.235662i	−0.690007	−	0.723803i	$-0.742392\pi$
$911$	−12.3199	+	7.11292i	−0.408178	+	0.235662i	0.281829	+	0.959465i	$0.409059\pi$
$912$	−11.6900	−	13.9316i	−0.387094	−	0.461320i
$913$	−13.4844	+	4.90792i	−0.446268	+	0.162428i
$914$	27.5087	−	47.6464i	0.909907	−	1.57600i
$915$	−2.85986	−	4.95343i	−0.0945441	−	0.163755i
$916$	−73.2748	−	61.4848i	−2.42107	−	2.03152i
$917$	9.36041	+	5.40424i	0.309108	+	0.178464i
$918$	0.502819	+	2.85163i	0.0165955	+	0.0941178i
$919$			14.4599i			0.476988i	0.971144	+	0.238494i	$0.0766537\pi$
$919$			14.4599i			0.476988i	−0.971144	+	0.238494i	$0.923346\pi$
$920$	105.500	−	18.6026i	3.47824	−	0.613308i
$921$	−30.6554	+	25.7229i	−1.01013	+	0.847598i
$922$	50.4637	+	18.3673i	1.66193	+	0.604895i
$923$	−0.234792	−	0.645086i	−0.00772827	−	0.0212333i
$924$	−38.2901			−1.25965
$925$	8.91463	−	18.1420i	0.293111	−	0.596505i
$926$	38.1256			1.25289
$927$	−12.4971	−	34.3356i	−0.410460	−	1.12773i
$928$	−4.41203	−	1.60585i	−0.144832	−	0.0527146i
$929$	35.7520	−	29.9995i	1.17299	−	0.984252i	0.172987	−	0.984924i	$-0.444658\pi$
$929$	35.7520	−	29.9995i	1.17299	−	0.984252i	1.00000		0.000671835i	$0.000213852\pi$
$930$	36.4096	−	6.41999i	1.19392	−	0.210520i
$931$		−	9.11855i		−	0.298848i
$932$	16.5363	+	93.7821i	0.541665	+	3.07193i
$933$	−8.79450	−	5.07751i	−0.287919	−	0.166230i
$934$	12.7980	+	10.7388i	0.418764	+	0.351385i
$935$	2.63349	+	4.56135i	0.0861245	+	0.149172i
$936$	7.40705	−	12.8294i	0.242107	−	0.419342i
$937$	−3.55157	+	1.29267i	−0.116025	+	0.0422296i	−0.399380	−	0.916785i	$-0.630775\pi$
$937$	−3.55157	+	1.29267i	−0.116025	+	0.0422296i	0.283355	+	0.959015i	$0.408552\pi$
$938$	12.8561	+	15.3213i	0.419765	+	0.500257i
$939$	39.7960	−	22.9763i	1.29869	−	0.749802i
$940$	−127.350	−	22.4552i	−4.15369	−	0.732407i
$941$	6.00827	−	34.0746i	0.195864	−	1.11080i	−0.715319	−	0.698798i	$-0.753719\pi$
$941$	6.00827	−	34.0746i	0.195864	−	1.11080i	0.911183	−	0.412002i	$-0.135170\pi$
$942$	−23.4954	+	28.0007i	−0.765522	+	0.912314i
$943$	13.4116	−	36.8482i	0.436743	−	1.19994i
$944$	7.97629	−	21.9147i	0.259606	−	0.713262i
$945$	−4.96603	+	5.91828i	−0.161545	+	0.192522i
$946$	6.31863	−	35.8347i	0.205436	−	1.16509i
$947$	23.8688	+	4.20871i	0.775632	+	0.136765i	0.547433	−	0.836850i	$-0.315605\pi$
$947$	23.8688	+	4.20871i	0.775632	+	0.136765i	0.228199	+	0.973615i	$0.426716\pi$
$948$	−26.1208	+	15.0808i	−0.848364	+	0.489803i
$949$	2.73036	+	3.25392i	0.0886313	+	0.105627i
$950$	−14.2845	+	5.19915i	−0.463452	+	0.168683i
$951$	−9.74010	+	16.8703i	−0.315844	+	0.547058i
$952$	2.32292	+	4.02341i	0.0752861	+	0.130399i
$953$	−12.3734	−	10.3826i	−0.400815	−	0.336324i	0.419993	−	0.907527i	$-0.362032\pi$
$953$	−12.3734	−	10.3826i	−0.400815	−	0.336324i	−0.820809	+	0.571203i	$0.806477\pi$
$954$	39.2774	+	22.6768i	1.27165	+	0.734189i
$955$	4.40247	+	24.9676i	0.142460	+	0.807934i
$956$			69.9330i			2.26180i
$957$	62.6822	−	11.0526i	2.02623	−	0.357278i
$958$	−23.5848	+	19.7900i	−0.761989	+	0.639385i
$959$	−15.8203	−	5.75813i	−0.510866	−	0.185940i
$960$	16.6329	+	45.6986i	0.536825	+	1.47491i
$961$	25.7666			0.831181
$962$	4.80607	+	19.5206i	0.154954	+	0.629369i
$963$	−11.8633			−0.382289
$964$	−22.9689	−	63.1065i	−0.739778	−	2.03252i
$965$	−28.5176	−	10.3795i	−0.918013	−	0.334129i
$966$	−45.8105	+	38.4395i	−1.47393	+	1.23677i
$967$	15.3906	−	2.71378i	0.494928	−	0.0872692i	0.0793875	−	0.996844i	$-0.474704\pi$
$967$	15.3906	−	2.71378i	0.494928	−	0.0872692i	0.415541	+	0.909575i	$0.363592\pi$
$968$			14.0039i			0.450102i
$969$	−0.468456	−	2.65675i	−0.0150490	−	0.0853470i
$970$	−81.2343	−	46.9006i	−2.60828	−	1.50589i
$971$	6.02864	+	5.05863i	0.193468	+	0.162339i	0.734376	−	0.678743i	$-0.237475\pi$
$971$	6.02864	+	5.05863i	0.193468	+	0.162339i	−0.540908	+	0.841082i	$0.681919\pi$
$972$	38.4575	+	66.6103i	1.23352	+	2.13653i
$973$	−9.31118	+	16.1274i	−0.298503	+	0.517022i
$974$	50.1341	−	18.2473i	1.60640	−	0.584682i
$975$	−6.53851	−	7.79229i	−0.209400	−	0.249553i
$976$	3.23577	−	1.86817i	0.103575	−	0.0597988i
$977$	−17.0021	−	2.99793i	−0.543945	−	0.0959123i	−0.105078	−	0.994464i	$-0.533509\pi$
$977$	−17.0021	−	2.99793i	−0.543945	−	0.0959123i	−0.438868	+	0.898552i	$0.644620\pi$
$978$	−9.10729	+	51.6500i	−0.291219	+	1.65158i
$979$	−1.60966	+	1.91832i	−0.0514450	+	0.0613098i
$980$	19.5836	−	53.8055i	0.625575	−	1.71875i
$981$	3.04385	−	8.36291i	0.0971827	−	0.267007i
$982$	43.1134	−	51.3806i	1.37581	−	1.63962i
$983$	−4.26382	+	24.1813i	−0.135995	+	0.771264i	0.838167	+	0.545413i	$0.183627\pi$
$983$	−4.26382	+	24.1813i	−0.135995	+	0.771264i	−0.974162	+	0.225851i	$0.927484\pi$
$984$	−60.1167	−	10.6002i	−1.91645	−	0.337922i
$985$	−37.4841	+	21.6415i	−1.19434	+	0.689554i
$986$	−9.81088	−	11.6921i	−0.312442	−	0.372354i
$987$	34.3218	−	12.4921i	1.09248	−	0.397629i
$988$	5.05958	−	8.76345i	0.160967	−	0.278803i
$989$	−19.0191	−	32.9420i	−0.604772	−	1.04750i
$990$	34.0997	+	28.6130i	1.08376	+	0.909382i
$991$	37.7019	+	21.7672i	1.19764	+	0.691458i	0.960029	−	0.279902i	$-0.0903018\pi$
$991$	37.7019	+	21.7672i	1.19764	+	0.691458i	0.237612	+	0.971360i	$0.423635\pi$
$992$	0.191369	+	1.08531i	0.00607598	+	0.0344586i
$993$		−	23.6193i		−	0.749535i
$994$	1.79186	−	0.315954i	0.0568345	−	0.0100215i
$995$	24.0908	−	20.2146i	0.763730	−	0.640846i
$996$	43.3693	+	15.7851i	1.37421	+	0.500171i
$997$	7.79472	+	21.4158i	0.246861	+	0.678246i	0.999797	+	0.0201517i	$0.00641491\pi$
$997$	7.79472	+	21.4158i	0.246861	+	0.678246i	−0.752936	+	0.658094i	$0.771363\pi$
$998$	85.3377			2.70132
$999$	−10.8023	−	3.13195i	−0.341771	−	0.0990905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.h.a.30.1	yes	18
3.2	odd	2		333.2.bl.d.289.3		18
4.3	odd	2		592.2.bq.d.289.1		18
5.2	odd	4		925.2.ba.a.474.6		36
5.3	odd	4		925.2.ba.a.474.1		36
5.4	even	2		925.2.bb.a.326.3		18
37.4	even	18		1369.2.b.g.1368.3		18
37.13	odd	36		1369.2.a.m.1.16		18
37.21	even	18	inner	37.2.h.a.21.1	✓	18
37.24	odd	36		1369.2.a.m.1.3		18
37.33	even	9		1369.2.b.g.1368.16		18
111.95	odd	18		333.2.bl.d.280.3		18
148.95	odd	18		592.2.bq.d.465.1		18
185.58	odd	36		925.2.ba.a.724.6		36
185.132	odd	36		925.2.ba.a.724.1		36
185.169	even	18		925.2.bb.a.576.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.21.1	✓	18	37.21	even	18	inner
37.2.h.a.30.1	yes	18	1.1	even	1	trivial
333.2.bl.d.280.3		18	111.95	odd	18
333.2.bl.d.289.3		18	3.2	odd	2
592.2.bq.d.289.1		18	4.3	odd	2
592.2.bq.d.465.1		18	148.95	odd	18
925.2.ba.a.474.1		36	5.3	odd	4
925.2.ba.a.474.6		36	5.2	odd	4
925.2.ba.a.724.1		36	185.132	odd	36
925.2.ba.a.724.6		36	185.58	odd	36
925.2.bb.a.326.3		18	5.4	even	2
925.2.bb.a.576.3		18	185.169	even	18
1369.2.a.m.1.3		18	37.24	odd	36
1369.2.a.m.1.16		18	37.13	odd	36
1369.2.b.g.1368.3		18	37.4	even	18
1369.2.b.g.1368.16		18	37.33	even	9

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841146 - 2.31103i) q^{2} +(2.14040 + 0.779043i) q^{3} +(-3.10124 + 2.60225i) q^{4} +(-2.84116 + 0.500973i) q^{5} -5.60182i q^{6} +(0.251492 + 1.42628i) q^{7} +(4.36277 + 2.51884i) q^{8} +(1.67628 + 1.40657i) q^{9} +O(q^{10})\)	\(q+(-0.841146 - 2.31103i) q^{2} +(2.14040 + 0.779043i) q^{3} +(-3.10124 + 2.60225i) q^{4} +(-2.84116 + 0.500973i) q^{5} -5.60182i q^{6} +(0.251492 + 1.42628i) q^{7} +(4.36277 + 2.51884i) q^{8} +(1.67628 + 1.40657i) q^{9} +(3.54759 + 6.14461i) q^{10} +(1.43354 - 2.48297i) q^{11} +(-8.66517 + 3.15386i) q^{12} +(-0.863812 - 1.02945i) q^{13} +(3.08464 - 1.78092i) q^{14} +(-6.47150 - 1.14110i) q^{15} +(0.745411 - 4.22743i) q^{16} +(0.409304 - 0.487789i) q^{17} +(1.84062 - 5.05706i) q^{18} +(0.636155 - 1.74782i) q^{19} +(7.50746 - 8.94704i) q^{20} +(-0.572841 + 3.24874i) q^{21} +(-6.94403 - 1.22442i) q^{22} +(-6.38349 + 3.68551i) q^{23} +(7.37579 + 8.79012i) q^{24} +(3.12274 - 1.13658i) q^{25} +(-1.65250 + 2.86221i) q^{26} +(-0.924515 - 1.60131i) q^{27} +(-4.49149 - 3.76880i) q^{28} +(8.44060 + 4.87318i) q^{29} +(2.80636 + 15.9157i) q^{30} -2.28766i q^{31} +(-0.474419 + 0.0836529i) q^{32} +(5.00269 - 4.19776i) q^{33} +(-1.47158 - 0.535611i) q^{34} +(-1.42906 - 3.92630i) q^{35} -8.85879 q^{36} +(4.38799 - 4.21255i) q^{37} -4.57436 q^{38} +(-1.04692 - 2.87639i) q^{39} +(-13.6572 - 4.97081i) q^{40} +(-4.07527 + 3.41956i) q^{41} +(7.98978 - 1.40881i) q^{42} +5.16051i q^{43} +(2.01555 + 11.4307i) q^{44} +(-5.46723 - 3.15650i) q^{45} +(13.8868 + 11.6524i) q^{46} +(-5.53593 - 9.58852i) q^{47} +(4.88883 - 8.46770i) q^{48} +(4.60681 - 1.67674i) q^{49} +(-5.25336 - 6.26071i) q^{50} +(1.25608 - 0.725200i) q^{51} +(5.35778 + 0.944721i) q^{52} +(-1.46342 + 8.29949i) q^{53} +(-2.92301 + 3.48351i) q^{54} +(-2.82902 + 7.77267i) q^{55} +(-2.49538 + 6.85601i) q^{56} +(2.72325 - 3.24545i) q^{57} +(4.16229 - 23.6055i) q^{58} +(5.35027 + 0.943396i) q^{59} +(23.0391 - 13.3016i) q^{60} +(0.559486 + 0.666770i) q^{61} +(-5.28685 + 1.92425i) q^{62} +(-1.58459 + 2.74459i) q^{63} +(-3.70027 - 6.40906i) q^{64} +(2.96995 + 2.49209i) q^{65} +(-13.9091 - 8.03045i) q^{66} +(0.975073 + 5.52991i) q^{67} +2.57786i q^{68} +(-16.5344 + 2.91546i) q^{69} +(-7.87176 + 6.60519i) q^{70} +(0.480027 + 0.174716i) q^{71} +(3.77030 + 10.3588i) q^{72} -3.16083 q^{73} +(-13.4263 - 6.59740i) q^{74} +7.56936 q^{75} +(2.57540 + 7.07585i) q^{76} +(3.90194 + 1.42019i) q^{77} +(-5.76680 + 4.83892i) q^{78} +(3.22119 - 0.567982i) q^{79} +12.3842i q^{80} +(-1.87129 - 10.6126i) q^{81} +(11.3306 + 6.54173i) q^{82} +(-3.83406 - 3.21716i) q^{83} +(-6.67753 - 11.5658i) q^{84} +(-0.918527 + 1.59094i) q^{85} +(11.9261 - 4.34074i) q^{86} +(14.2699 + 17.0062i) q^{87} +(12.5084 - 7.22174i) q^{88} +(-0.860158 - 0.151669i) q^{89} +(-2.69604 + 15.2900i) q^{90} +(1.25105 - 1.49094i) q^{91} +(10.2061 - 28.0411i) q^{92} +(1.78218 - 4.89651i) q^{93} +(-17.5028 + 20.8590i) q^{94} +(-0.931805 + 5.28453i) q^{95} +(-1.08062 - 0.190542i) q^{96} +(-11.4492 + 6.61021i) q^{97} +(-7.75001 - 9.23610i) q^{98} +(5.89547 - 2.14578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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