LMFDB - Embedded newform 418.2.v.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	418.13
Dual form			418.2.v.a.193.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.374607 + 0.927184i) q^{2} +(0.885806 + 3.08917i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(3.09438 - 1.64531i) q^{5} +(-2.53240 + 1.97853i) q^{6} +(-0.131685 - 0.295769i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-6.21419 + 3.88306i) q^{9} +O(q^{10})$	\(q+(0.374607 + 0.927184i) q^{2} +(0.885806 + 3.08917i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(3.09438 - 1.64531i) q^{5} +(-2.53240 + 1.97853i) q^{6} +(-0.131685 - 0.295769i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-6.21419 + 3.88306i) q^{9} +(2.68468 + 2.25272i) q^{10} +(-2.29389 - 2.39543i) q^{11} +(-2.78312 - 1.60683i) q^{12} +(0.200703 + 5.74739i) q^{13} +(0.224902 - 0.232893i) q^{14} +(7.82368 + 8.10166i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-1.50229 + 2.40417i) q^{17} +(-5.92819 - 4.30708i) q^{18} +(4.30368 - 0.691628i) q^{19} +(-1.08298 + 3.33308i) q^{20} +(0.797034 - 0.668791i) q^{21} +(1.36170 - 3.02420i) q^{22} +(1.47805 - 8.38244i) q^{23} +(0.447256 - 3.18239i) q^{24} +(4.07219 - 6.03726i) q^{25} +(-5.25370 + 2.33910i) q^{26} +(-10.3354 - 9.30600i) q^{27} +(0.300185 + 0.121282i) q^{28} +(1.00192 + 4.01848i) q^{29} +(-4.58092 + 10.2889i) q^{30} +(-1.56465 + 1.40882i) q^{31} +(0.939693 - 0.342020i) q^{32} +(5.36796 - 9.20810i) q^{33} +(-2.79187 - 0.492282i) q^{34} +(-0.894116 - 0.698560i) q^{35} +(1.77272 - 7.10998i) q^{36} +(1.81791 - 2.50214i) q^{37} +(2.25345 + 3.73121i) q^{38} +(-17.5769 + 5.71108i) q^{39} +(-3.49607 + 0.244469i) q^{40} +(3.30445 - 0.947537i) q^{41} +(0.918667 + 0.488464i) q^{42} +(7.48959 - 1.32062i) q^{43} +(3.31409 + 0.129662i) q^{44} +(-12.8402 + 22.2400i) q^{45} +(8.32575 - 1.76969i) q^{46} +(-8.02055 - 0.560852i) q^{47} +(3.11821 - 0.777456i) q^{48} +(4.61378 - 5.12412i) q^{49} +(7.12312 + 1.51407i) q^{50} +(-8.75762 - 2.51121i) q^{51} +(-4.13685 - 3.99491i) q^{52} +(3.78327 - 7.11530i) q^{53} +(4.75668 - 13.0689i) q^{54} +(-11.0394 - 3.63822i) q^{55} +0.323759i q^{56} +(5.94878 + 12.6822i) q^{57} +(-3.35055 + 2.43431i) q^{58} +(-0.551718 - 7.88994i) q^{59} +(-11.2558 - 0.393060i) q^{60} +(-0.420135 - 2.98941i) q^{61} +(-1.89237 - 0.922968i) q^{62} +(1.96680 + 1.32663i) q^{63} +(0.669131 + 0.743145i) q^{64} +(10.0773 + 17.4544i) q^{65} +(10.5485 + 1.52768i) q^{66} +(1.69360 - 2.01835i) q^{67} +(-0.589417 - 2.77299i) q^{68} +(27.2041 - 2.85926i) q^{69} +(0.312752 - 1.09069i) q^{70} +(3.15696 + 5.93738i) q^{71} +(7.25633 - 1.01981i) q^{72} +(-2.13158 + 1.43777i) q^{73} +(3.00095 + 0.748221i) q^{74} +(22.2573 + 7.23184i) q^{75} +(-2.61536 + 3.48710i) q^{76} +(-0.406424 + 0.993902i) q^{77} +(-11.8796 - 14.1576i) q^{78} +(-5.05391 + 6.46871i) q^{79} +(-1.53632 - 3.14992i) q^{80} +(9.95603 - 20.4129i) q^{81} +(2.11641 + 2.70888i) q^{82} +(1.08446 - 5.10196i) q^{83} +(-0.108757 + 1.03475i) q^{84} +(-0.693055 + 9.91114i) q^{85} +(4.03010 + 6.44951i) q^{86} +(-11.5263 + 6.65470i) q^{87} +(1.12126 + 3.12134i) q^{88} +(3.40719 + 9.36118i) q^{89} +(-25.4306 - 3.57403i) q^{90} +(1.67347 - 0.816206i) q^{91} +(4.75971 + 7.05656i) q^{92} +(-5.73807 - 3.58554i) q^{93} +(-2.48454 - 7.64662i) q^{94} +(12.1793 - 9.22106i) q^{95} +(1.88894 + 2.59991i) q^{96} +(-5.09720 + 2.05940i) q^{97} +(6.47935 + 2.35829i) q^{98} +(23.5562 + 5.97838i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$3$	0.885806	+	3.08917i	0.511420	+	1.78353i	0.614562	+	0.788868i	$0.289333\pi$
$3$	0.885806	+	3.08917i	0.511420	+	1.78353i	−0.103142	+	0.994667i	$0.532890\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	3.09438	−	1.64531i	1.38385	−	0.735806i	0.400290	−	0.916388i	$-0.368909\pi$
$5$	3.09438	−	1.64531i	1.38385	−	0.735806i	0.983560	+	0.180582i	$0.0577982\pi$
$6$	−2.53240	+	1.97853i	−1.03385	+	0.807731i
$7$	−0.131685	−	0.295769i	−0.0497722	−	0.111790i	0.886948	−	0.461870i	$-0.152821\pi$
$7$	−0.131685	−	0.295769i	−0.0497722	−	0.111790i	−0.936720	+	0.350080i	$0.886155\pi$
$8$	−0.913545	−	0.406737i	−0.322987	−	0.143803i
$9$	−6.21419	+	3.88306i	−2.07140	+	1.29435i
$10$	2.68468	+	2.25272i	0.848971	+	0.712372i
$11$	−2.29389	−	2.39543i	−0.691632	−	0.722250i
$11$	−2.29389	−	2.39543i	−0.691632	−	0.722250i
$12$	−2.78312	−	1.60683i	−0.803416	−	0.463853i
$13$	0.200703	+	5.74739i	0.0556651	+	1.59404i	0.630777	+	0.775964i	$0.282736\pi$
$13$	0.200703	+	5.74739i	0.0556651	+	1.59404i	−0.575112	+	0.818075i	$0.695042\pi$
$14$	0.224902	−	0.232893i	0.0601076	−	0.0622433i
$15$	7.82368	+	8.10166i	2.02007	+	2.09184i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	−1.50229	+	2.40417i	−0.364359	+	0.583096i	−0.978537	−	0.206072i	$-0.933932\pi$
$17$	−1.50229	+	2.40417i	−0.364359	+	0.583096i	0.614178	+	0.789167i	$0.289488\pi$
$18$	−5.92819	−	4.30708i	−1.39729	−	1.01519i
$19$	4.30368	−	0.691628i	0.987332	−	0.158670i
$19$	4.30368	−	0.691628i	0.987332	−	0.158670i
$20$	−1.08298	+	3.33308i	−0.242162	+	0.745299i
$21$	0.797034	−	0.668791i	0.173927	−	0.145942i
$22$	1.36170	−	3.02420i	0.290316	−	0.644761i
$23$	1.47805	−	8.38244i	0.308195	−	1.74786i	−0.299877	−	0.953978i	$-0.596946\pi$
$23$	1.47805	−	8.38244i	0.308195	−	1.74786i	0.608072	−	0.793882i	$-0.291943\pi$
$24$	0.447256	−	3.18239i	0.0912957	−	0.649603i
$25$	4.07219	−	6.03726i	0.814437	−	1.20745i
$26$	−5.25370	+	2.33910i	−1.03034	+	0.458735i
$27$	−10.3354	−	9.30600i	−1.98904	−	1.79094i
$28$	0.300185	+	0.121282i	0.0567295	+	0.0229202i
$29$	1.00192	+	4.01848i	0.186052	+	0.746214i	0.988719	+	0.149786i	$0.0478583\pi$
$29$	1.00192	+	4.01848i	0.186052	+	0.746214i	−0.802667	+	0.596428i	$0.796586\pi$
$30$	−4.58092	+	10.2889i	−0.836358	+	1.87849i
$31$	−1.56465	+	1.40882i	−0.281020	+	0.253032i	−0.797571	−	0.603225i	$-0.793882\pi$
$31$	−1.56465	+	1.40882i	−0.281020	+	0.253032i	0.516551	+	0.856256i	$0.327216\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	5.36796	−	9.20810i	0.934443	−	1.60292i
$34$	−2.79187	−	0.492282i	−0.478802	−	0.0844257i
$35$	−0.894116	−	0.698560i	−0.151133	−	0.118078i
$36$	1.77272	−	7.10998i	0.295453	−	1.18500i
$37$	1.81791	−	2.50214i	0.298863	−	0.411350i	−0.633005	−	0.774148i	$-0.718179\pi$
$37$	1.81791	−	2.50214i	0.298863	−	0.411350i	0.931868	+	0.362798i	$0.118179\pi$
$38$	2.25345	+	3.73121i	0.365558	+	0.605283i
$39$	−17.5769	+	5.71108i	−2.81456	+	0.914505i
$40$	−3.49607	+	0.244469i	−0.552777	+	0.0386539i
$41$	3.30445	−	0.947537i	0.516069	−	0.147980i	−0.00748652	−	0.999972i	$-0.502383\pi$
$41$	3.30445	−	0.947537i	0.516069	−	0.147980i	0.523555	+	0.851992i	$0.324605\pi$
$42$	0.918667	+	0.488464i	0.141753	+	0.0753716i
$43$	7.48959	−	1.32062i	1.14215	−	0.201392i	0.429605	−	0.903017i	$-0.358653\pi$
$43$	7.48959	−	1.32062i	1.14215	−	0.201392i	0.712547	+	0.701625i	$0.247542\pi$
$44$	3.31409	+	0.129662i	0.499618	+	0.0195473i
$45$	−12.8402	+	22.2400i	−1.91411	+	3.31534i
$46$	8.32575	−	1.76969i	1.22756	−	0.260927i
$47$	−8.02055	−	0.560852i	−1.16992	−	0.0818086i	−0.528454	−	0.848962i	$-0.677228\pi$
$47$	−8.02055	−	0.560852i	−1.16992	−	0.0818086i	−0.641464	+	0.767153i	$0.721672\pi$
$48$	3.11821	−	0.777456i	0.450074	−	0.112216i
$49$	4.61378	−	5.12412i	0.659111	−	0.732017i
$50$	7.12312	+	1.51407i	1.00736	+	0.214121i
$51$	−8.75762	−	2.51121i	−1.22631	−	0.351639i
$52$	−4.13685	−	3.99491i	−0.573677	−	0.553994i
$53$	3.78327	−	7.11530i	0.519673	−	0.977362i	−0.475546	−	0.879691i	$-0.657750\pi$
$53$	3.78327	−	7.11530i	0.519673	−	0.977362i	0.995219	−	0.0976712i	$-0.0311393\pi$
$54$	4.75668	−	13.0689i	0.647302	−	1.77845i
$55$	−11.0394	−	3.63822i	−1.48855	−	0.490578i
$56$			0.323759i			0.0432642i
$57$	5.94878	+	12.6822i	0.787936	+	1.67979i
$58$	−3.35055	+	2.43431i	−0.439948	+	0.319641i
$59$	−0.551718	−	7.88994i	−0.0718276	−	1.02718i	−0.891109	−	0.453790i	$-0.850072\pi$
$59$	−0.551718	−	7.88994i	−0.0718276	−	1.02718i	0.819281	−	0.573392i	$-0.194373\pi$
$60$	−11.2558	−	0.393060i	−1.45311	−	0.0507438i
$61$	−0.420135	−	2.98941i	−0.0537927	−	0.382755i	−0.998496	−	0.0548282i	$-0.982539\pi$
$61$	−0.420135	−	2.98941i	−0.0537927	−	0.382755i	0.944703	−	0.327927i	$-0.106350\pi$
$62$	−1.89237	−	0.922968i	−0.240331	−	0.117217i
$63$	1.96680	+	1.32663i	0.247794	+	0.167139i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	10.0773	+	17.4544i	1.24994	+	2.16495i
$66$	10.5485	+	1.52768i	1.29843	+	0.188044i
$67$	1.69360	−	2.01835i	0.206906	−	0.246581i	−0.652605	−	0.757698i	$-0.726324\pi$
$67$	1.69360	−	2.01835i	0.206906	−	0.246581i	0.859511	+	0.511118i	$0.170768\pi$
$68$	−0.589417	−	2.77299i	−0.0714773	−	0.336274i
$69$	27.2041	−	2.85926i	3.27499	−	0.344215i
$70$	0.312752	−	1.09069i	0.0373810	−	0.130363i
$71$	3.15696	+	5.93738i	0.374662	+	0.704637i	0.996941	−	0.0781587i	$-0.0249041\pi$
$71$	3.15696	+	5.93738i	0.374662	+	0.704637i	−0.622279	+	0.782796i	$0.713793\pi$
$72$	7.25633	−	1.01981i	0.855167	−	0.120186i
$73$	−2.13158	+	1.43777i	−0.249483	+	0.168278i	−0.677568	−	0.735460i	$-0.736966\pi$
$73$	−2.13158	+	1.43777i	−0.249483	+	0.168278i	0.428085	+	0.903738i	$0.359188\pi$
$74$	3.00095	+	0.748221i	0.348853	+	0.0869789i
$75$	22.2573	+	7.23184i	2.57005	+	0.835061i
$76$	−2.61536	+	3.48710i	−0.300003	+	0.399998i
$77$	−0.406424	+	0.993902i	−0.0463163	+	0.113266i
$78$	−11.8796	−	14.1576i	−1.34510	−	1.60303i
$79$	−5.05391	+	6.46871i	−0.568610	+	0.727787i	−0.983263	−	0.182192i	$-0.941681\pi$
$79$	−5.05391	+	6.46871i	−0.568610	+	0.727787i	0.414653	+	0.909980i	$0.363903\pi$
$80$	−1.53632	−	3.14992i	−0.171766	−	0.352172i
$81$	9.95603	−	20.4129i	1.10623	−	2.26810i
$82$	2.11641	+	2.70888i	0.233718	+	0.299146i
$83$	1.08446	−	5.10196i	0.119034	−	0.560013i	−0.877696	−	0.479217i	$-0.840921\pi$
$83$	1.08446	−	5.10196i	0.119034	−	0.560013i	0.996731	−	0.0807956i	$-0.0257461\pi$
$84$	−0.108757	+	1.03475i	−0.0118664	+	0.112901i
$85$	−0.693055	+	9.91114i	−0.0751723	+	1.07501i
$86$	4.03010	+	6.44951i	0.434577	+	0.695469i
$87$	−11.5263	+	6.65470i	−1.23575	+	0.713459i
$88$	1.12126	+	3.12134i	0.119527	+	0.332736i
$89$	3.40719	+	9.36118i	0.361161	+	0.992283i	0.978619	+	0.205679i	$0.0659403\pi$
$89$	3.40719	+	9.36118i	0.361161	+	0.992283i	−0.617458	+	0.786604i	$0.711837\pi$
$90$	−25.4306	−	3.57403i	−2.68062	−	0.376736i
$91$	1.67347	−	0.816206i	0.175427	−	0.0855616i
$92$	4.75971	+	7.05656i	0.496234	+	0.735697i
$93$	−5.73807	−	3.58554i	−0.595010	−	0.371804i
$94$	−2.48454	−	7.64662i	−0.256261	−	0.788689i
$95$	12.1793	−	9.22106i	1.24957	−	0.946061i
$96$	1.88894	+	2.59991i	0.192790	+	0.265352i
$97$	−5.09720	+	2.05940i	−0.517543	+	0.209101i	−0.618492	−	0.785791i	$-0.712256\pi$
$97$	−5.09720	+	2.05940i	−0.517543	+	0.209101i	0.100950	+	0.994892i	$0.467812\pi$
$98$	6.47935	+	2.35829i	0.654513	+	0.238223i
$99$	23.5562	+	5.97838i	2.36749	+	0.600850i
$100$	1.26455	+	7.17162i	0.126455	+	0.717162i
$101$	−7.96667	+	0.278202i	−0.792713	+	0.0276821i	−0.428394	−	0.903592i	$-0.640920\pi$
$101$	−7.96667	+	0.278202i	−0.792713	+	0.0276821i	−0.364319	+	0.931274i	$0.618698\pi$
$102$	−0.952312	−	9.06064i	−0.0942929	−	0.897137i
$103$	−14.4903	−	1.52299i	−1.42777	−	0.150064i	−0.641107	−	0.767451i	$-0.721525\pi$
$103$	−14.4903	−	1.52299i	−1.42777	−	0.150064i	−0.786660	+	0.617387i	$0.788191\pi$
$104$	2.15432	−	5.33213i	0.211249	−	0.522859i
$105$	1.36596	−	3.38087i	0.133304	−	0.329939i
$106$	8.01443	+	0.842351i	0.778431	+	0.0818163i
$107$	−0.310913	−	2.95814i	−0.0300571	−	0.285975i	−0.999218	−	0.0395448i	$-0.987409\pi$
$107$	−0.310913	−	2.95814i	−0.0300571	−	0.285975i	0.969161	−	0.246430i	$-0.0792575\pi$
$108$	13.8991	−	0.485368i	1.33744	−	0.0467046i
$109$	2.88044	+	16.3358i	0.275896	+	1.56469i	0.736100	+	0.676873i	$0.236665\pi$
$109$	2.88044	+	16.3358i	0.275896	+	1.56469i	−0.460203	+	0.887814i	$0.652224\pi$
$110$	−0.762128	−	11.5984i	−0.0726661	−	1.10587i
$111$	9.33988	+	3.39944i	0.886502	+	0.322660i
$112$	−0.300185	+	0.121282i	−0.0283648	+	0.0114601i
$113$	−3.88509	−	5.34737i	−0.365479	−	0.503039i	0.586186	−	0.810176i	$-0.300629\pi$
$113$	−3.88509	−	5.34737i	−0.365479	−	0.503039i	−0.951665	+	0.307138i	$0.900629\pi$
$114$	−9.53024	+	10.2664i	−0.892589	+	0.961540i
$115$	−9.21808	−	28.3703i	−0.859590	−	2.64555i
$116$	−3.51219	−	2.19466i	−0.326099	−	0.203769i
$117$	−23.5647	−	34.9360i	−2.17855	−	3.22984i
$118$	7.10874	−	3.46717i	0.654413	−	0.319178i
$119$	0.908906	+	0.127738i	0.0833193	+	0.0117098i
$120$	−3.85205	−	10.5834i	−0.351642	−	0.966129i
$121$	−0.476180	+	10.9897i	−0.0432891	+	0.999063i
$122$	2.61435	−	1.50940i	0.236692	−	0.136654i
$123$	5.85421	+	9.36870i	0.527856	+	0.844747i
$124$	0.146869	−	2.10032i	0.0131892	−	0.188614i
$125$	0.836061	−	7.95459i	0.0747796	−	0.711480i
$126$	−0.493248	+	2.32055i	−0.0439421	+	0.206731i
$127$	−1.55197	−	1.98643i	−0.137715	−	0.176267i	0.714209	−	0.699932i	$-0.246787\pi$
$127$	−1.55197	−	1.98643i	−0.137715	−	0.176267i	−0.851924	+	0.523665i	$0.824564\pi$
$128$	−0.438371	+	0.898794i	−0.0387469	+	0.0794429i
$129$	10.7139	+	21.9668i	0.943309	+	1.93407i
$130$	−12.4084	+	15.8820i	−1.08829	+	1.39295i
$131$	−5.15159	−	6.13943i	−0.450097	−	0.536404i	0.492511	−	0.870306i	$-0.336079\pi$
$131$	−5.15159	−	6.13943i	−0.450097	−	0.536404i	−0.942608	+	0.333902i	$0.891635\pi$
$132$	2.53509	+	10.3527i	0.220651	+	0.901083i
$133$	−0.771291	−	1.18182i	−0.0668794	−	0.102477i
$134$	2.50581	+	0.814189i	0.216469	+	0.0703352i
$135$	−47.2928	−	11.7914i	−4.07032	−	1.01484i
$136$	2.35027	−	1.58528i	0.201534	−	0.135937i
$137$	−9.88961	+	1.38989i	−0.844927	+	0.118747i	−0.548336	−	0.836258i	$-0.684739\pi$
$137$	−9.88961	+	1.38989i	−0.844927	+	0.118747i	−0.296591	+	0.955005i	$0.595850\pi$
$138$	12.8419	+	24.1521i	1.09317	+	2.05596i
$139$	−2.23046	+	7.77855i	−0.189185	+	0.659768i	0.808292	+	0.588782i	$0.200392\pi$
$139$	−2.23046	+	7.77855i	−0.189185	+	0.659768i	−0.997477	+	0.0709861i	$0.977385\pi$
$140$	1.12843	−	0.118603i	0.0953700	−	0.0100238i
$141$	−5.37209	−	25.2737i	−0.452411	−	2.12843i
$142$	−4.32242	+	5.15126i	−0.362730	+	0.432284i
$143$	13.3071	−	13.6646i	1.11279	−	1.14269i
$144$	3.66382	+	6.34593i	0.305318	+	0.528827i
$145$	9.71199	+	10.7863i	0.806537	+	0.895750i
$146$	−2.13158	−	1.43777i	−0.176411	−	0.118991i
$147$	19.9162	+	9.71378i	1.64266	+	0.801179i
$148$	0.430437	+	3.06272i	0.0353817	+	0.251754i
$149$	2.81358	+	0.0982525i	0.230498	+	0.00804916i	0.149916	−	0.988699i	$-0.452100\pi$
$149$	2.81358	+	0.0982525i	0.230498	+	0.00804916i	0.0805822	+	0.996748i	$0.474322\pi$
$150$	1.63249	+	23.3457i	0.133292	+	1.90617i
$151$	1.49654	−	1.08730i	0.121787	−	0.0884834i	−0.525224	−	0.850964i	$-0.676019\pi$
$151$	1.49654	−	1.08730i	0.121787	−	0.0884834i	0.647011	+	0.762480i	$0.276019\pi$
$152$	−4.21292	−	1.11863i	−0.341713	−	0.0907329i
$153$		−	20.7734i		−	1.67943i
$154$	−1.07378	−	0.00450777i	−0.0865276	−	0.000363246i
$155$	−2.52369	+	6.93377i	−0.202707	+	0.556934i
$156$	8.67651	−	16.3181i	0.694677	−	1.30650i
$157$	−4.22032	−	4.07552i	−0.336818	−	0.325262i	0.506944	−	0.861979i	$-0.330775\pi$
$157$	−4.22032	−	4.07552i	−0.336818	−	0.325262i	−0.843762	+	0.536718i	$0.819664\pi$
$158$	−7.89092	−	2.26268i	−0.627768	−	0.180009i
$159$	25.3316	+	5.38441i	2.00893	+	0.427011i
$160$	2.34504	−	2.60443i	0.185392	−	0.205898i
$161$	−2.67390	+	0.666679i	−0.210733	+	0.0525416i
$162$	22.6561	+	1.58427i	1.78003	+	0.124472i
$163$	−4.29963	+	0.913914i	−0.336773	+	0.0715833i	−0.373194	−	0.927753i	$-0.621737\pi$
$163$	−4.29963	+	0.913914i	−0.336773	+	0.0715833i	0.0364214	+	0.999337i	$0.488404\pi$
$164$	−1.71881	+	2.97707i	−0.134217	+	0.232470i
$165$	1.46034	−	37.3254i	0.113687	−	2.90577i
$166$	5.13670	−	0.905739i	0.398685	−	0.0702990i
$167$	−18.2855	−	9.72255i	−1.41497	−	0.752353i	−0.426603	−	0.904439i	$-0.640290\pi$
$167$	−18.2855	−	9.72255i	−1.41497	−	0.752353i	−0.988367	+	0.152086i	$0.951401\pi$
$168$	−1.00015	+	0.286788i	−0.0771632	+	0.0221262i
$169$	−20.0239	+	1.40020i	−1.54030	+	0.107708i
$170$	−9.44908	+	3.07019i	−0.724711	+	0.235473i
$171$	−24.0583	+	21.0093i	−1.83978	+	1.60663i
$172$	−4.47018	+	6.15268i	−0.340848	+	0.469137i
$173$	3.88286	−	15.5733i	0.295208	−	1.18402i	−0.621162	−	0.783682i	$-0.713339\pi$
$173$	3.88286	−	15.5733i	0.295208	−	1.18402i	0.916370	−	0.400333i	$-0.131105\pi$
$174$	−10.4880	−	8.19409i	−0.795090	−	0.621192i
$175$	−2.32188	−	0.409410i	−0.175518	−	0.0309485i
$176$	−2.47403	+	2.20889i	−0.186487	+	0.166501i
$177$	23.8847	−	8.69331i	1.79528	−	0.653429i
$178$	−7.40318	+	6.66585i	−0.554892	+	0.499627i
$179$	−0.959000	+	2.15395i	−0.0716790	+	0.160994i	−0.945832	−	0.324658i	$-0.894751\pi$
$179$	−0.959000	+	2.15395i	−0.0716790	+	0.160994i	0.874153	+	0.485651i	$0.161418\pi$
$180$	−6.21267	−	24.9177i	−0.463065	−	1.85725i
$181$	−2.78943	−	1.12700i	−0.207337	−	0.0837694i	0.268589	−	0.963255i	$-0.413443\pi$
$181$	−2.78943	−	1.12700i	−0.207337	−	0.0837694i	−0.475926	+	0.879485i	$0.657887\pi$
$182$	1.38367	+	1.24586i	0.102564	+	0.0923491i
$183$	8.86266	−	3.94591i	0.655147	−	0.291690i
$184$	−4.75971	+	7.05656i	−0.350891	+	0.520217i
$185$	1.50851	−	10.7336i	0.110908	−	0.789152i
$186$	1.17494	−	6.66341i	0.0861508	−	0.488585i
$187$	9.20509	−	1.91625i	0.673143	−	0.140130i
$188$	6.15910	−	5.16810i	0.449199	−	0.376922i
$189$	−1.39142	+	4.28234i	−0.101211	+	0.311494i
$190$	13.1121	+	7.83817i	0.951249	+	0.568640i
$191$	21.2039	+	15.4055i	1.53426	+	1.11471i	0.953810	+	0.300411i	$0.0971239\pi$
$191$	21.2039	+	15.4055i	1.53426	+	1.11471i	0.580451	+	0.814295i	$0.302876\pi$
$192$	−1.70298	+	2.72534i	−0.122902	+	0.196685i
$193$	−0.145366	+	4.16275i	−0.0104637	+	0.299641i	0.982865	+	0.184326i	$0.0590102\pi$
$193$	−0.145366	+	4.16275i	−0.0104637	+	0.299641i	−0.993329	+	0.115316i	$0.963212\pi$
$194$	−3.81889	−	3.95458i	−0.274180	−	0.283922i
$195$	−44.9931	+	46.5917i	−3.22202	+	3.33650i
$196$	0.240638	+	6.89098i	0.0171885	+	0.492213i
$197$	0.938704	+	0.541961i	0.0668799	+	0.0386131i	0.533067	−	0.846073i	$-0.321039\pi$
$197$	0.938704	+	0.541961i	0.0668799	+	0.0386131i	−0.466187	+	0.884686i	$0.654373\pi$
$198$	3.28127	+	24.0805i	0.233190	+	1.71133i
$199$	0.643824	+	0.540232i	0.0456395	+	0.0382961i	0.665322	−	0.746556i	$-0.268294\pi$
$199$	0.643824	+	0.540232i	0.0456395	+	0.0382961i	−0.619683	+	0.784853i	$0.712739\pi$
$200$	−6.17570	+	3.85901i	−0.436688	+	0.272873i
$201$	7.73523	+	3.44395i	0.545601	+	0.242917i
$202$	−3.24231	−	7.28235i	−0.228128	−	0.512384i
$203$	1.05661	−	0.825510i	0.0741591	−	0.0579395i
$204$	8.04414	−	4.27714i	0.563202	−	0.299460i
$205$	8.66625	−	8.36890i	0.605277	−	0.584509i
$206$	−4.01606	−	14.0056i	−0.279812	−	0.975820i
$207$	23.3646	+	57.8295i	1.62395	+	4.01943i
$208$	5.75089			0.398753
$209$	−11.5289	−	8.72265i	−0.797470	−	0.603358i
$210$	3.64638			0.251624
$211$	−0.185170	−	0.458312i	−0.0127476	−	0.0315515i	0.920676	−	0.390328i	$-0.127638\pi$
$211$	−0.185170	−	0.458312i	−0.0127476	−	0.0315515i	−0.933423	+	0.358777i	$0.883194\pi$
$212$	2.22125	+	7.74640i	0.152556	+	0.532025i
$213$	−15.5451	+	15.0118i	−1.06513	+	1.02859i
$214$	2.62627	−	1.39641i	0.179528	−	0.0954569i
$215$	21.0028	−	16.4092i	1.43238	−	1.11910i
$216$	5.65673	+	12.7052i	0.384892	+	0.864481i
$217$	0.622727	+	0.277256i	0.0422734	+	0.0188213i
$218$	−14.0673	+	8.79020i	−0.952755	+	0.595348i
$219$	−6.32969	−	5.31124i	−0.427721	−	0.358900i
$220$	10.4684	−	5.05149i	0.705779	−	0.340571i
$221$	−14.1192	−	8.15172i	−0.949759	−	0.548344i
$222$	0.346876	+	9.93323i	0.0232808	+	0.666675i
$223$	−15.6493	+	16.2054i	−1.04796	+	1.08519i	−0.0517086	+	0.998662i	$0.516467\pi$
$223$	−15.6493	+	16.2054i	−1.04796	+	1.08519i	−0.996249	+	0.0865299i	$0.972422\pi$
$224$	−0.224902	−	0.232893i	−0.0150269	−	0.0155608i
$225$	−1.86230	+	53.3293i	−0.124153	+	3.55528i
$226$	3.50262	−	5.60536i	0.232991	−	0.372863i
$227$	−11.0499	−	8.02820i	−0.733406	−	0.532850i	0.157233	−	0.987561i	$-0.449743\pi$
$227$	−11.0499	−	8.02820i	−0.733406	−	0.532850i	−0.890639	+	0.454711i	$0.849743\pi$
$228$	−13.0890	−	4.99041i	−0.866838	−	0.330498i
$229$	−1.77088	+	5.45020i	−0.117023	+	0.360160i	−0.992364	−	0.123347i	$-0.960637\pi$
$229$	−1.77088	+	5.45020i	−0.117023	+	0.360160i	0.875341	+	0.483507i	$0.160637\pi$
$230$	22.8514	−	19.1746i	1.50677	−	1.26433i
$231$	−3.43035	−	0.375110i	−0.225700	−	0.0246805i
$232$	0.719165	−	4.07859i	0.0472155	−	0.267772i
$233$	−1.02486	+	7.29229i	−0.0671411	+	0.477734i	0.927457	+	0.373931i	$0.121990\pi$
$233$	−1.02486	+	7.29229i	−0.0671411	+	0.477734i	−0.994598	+	0.103803i	$0.966899\pi$
$234$	23.5647	−	34.9360i	1.54047	−	2.28384i
$235$	−25.7414	+	11.4608i	−1.67919	+	0.747622i
$236$	5.87768	+	5.29229i	0.382605	+	0.344499i
$237$	−24.4598	−	9.88239i	−1.58883	−	0.641930i
$238$	0.222045	+	0.890575i	0.0143931	+	0.0577274i
$239$	9.53556	−	21.4172i	0.616804	−	1.38536i	−0.287212	−	0.957867i	$-0.592728\pi$
$239$	9.53556	−	21.4172i	0.616804	−	1.38536i	0.904016	−	0.427498i	$-0.140605\pi$
$240$	8.36976	−	7.53617i	0.540266	−	0.486458i
$241$	−6.82930	+	2.48566i	−0.439914	+	0.160116i	−0.552475	−	0.833529i	$-0.686317\pi$
$241$	−6.82930	+	2.48566i	−0.439914	+	0.160116i	0.112561	+	0.993645i	$0.464094\pi$
$242$	−10.3678	+	3.67530i	−0.666470	+	0.236257i
$243$	30.7892	+	5.42896i	1.97513	+	0.348268i
$244$	2.37884	+	1.85855i	0.152290	+	0.118982i
$245$	5.84601	−	23.4471i	0.373488	−	1.49798i
$246$	−6.49348	+	8.93750i	−0.414009	+	0.569835i
$247$	4.83882	+	24.5961i	0.307886	+	1.56501i
$248$	2.00240	−	0.650620i	0.127153	−	0.0413144i
$249$	16.7215	−	1.16928i	1.05968	−	0.0741000i
$250$	7.68856	−	2.20466i	0.486267	−	0.139435i
$251$	11.9420	+	6.34966i	0.753770	+	0.400787i	0.801439	−	0.598076i	$-0.204068\pi$
$251$	11.9420	+	6.34966i	0.753770	+	0.400787i	−0.0476688	+	0.998863i	$0.515179\pi$
$252$	−2.33635	+	0.411962i	−0.147176	+	0.0259512i
$253$	−23.4700	+	15.6878i	−1.47555	+	0.986283i
$254$	1.26041	−	2.18309i	0.0790852	−	0.136980i
$255$	−31.2312	+	6.63839i	−1.95577	+	0.415712i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	19.7106	−	4.91440i	1.22951	−	0.306552i	0.427585	−	0.903975i	$-0.359364\pi$
$257$	19.7106	−	4.91440i	1.22951	−	0.306552i	0.801926	+	0.597423i	$0.203809\pi$
$258$	−16.3538	+	18.1627i	−1.01814	+	1.13076i
$259$	−0.979448	−	0.208188i	−0.0608600	−	0.0129362i
$260$	−19.3739	−	5.55536i	−1.20152	−	0.344529i
$261$	−21.8301	−	21.0811i	−1.35125	−	1.30489i
$262$	3.76256	−	7.07634i	0.232452	−	0.437178i
$263$	7.81371	−	21.4680i	0.481814	−	1.32377i	−0.426123	−	0.904665i	$-0.640121\pi$
$263$	7.81371	−	21.4680i	0.481814	−	1.32377i	0.907937	−	0.419107i	$-0.137657\pi$
$264$	−8.64915	+	6.22867i	−0.532318	+	0.383348i
$265$		−	28.2421i		−	1.73490i
$266$	0.806832	−	1.15785i	0.0494700	−	0.0709921i
$267$	−25.9002	+	18.8176i	−1.58507	+	1.15162i
$268$	0.183792	+	2.62835i	0.0112269	+	0.160552i
$269$	−6.69826	−	0.233908i	−0.408400	−	0.0142616i	−0.170037	−	0.985438i	$-0.554389\pi$
$269$	−6.69826	−	0.233908i	−0.408400	−	0.0142616i	−0.238363	+	0.971176i	$0.576611\pi$
$270$	−6.78338	−	48.2663i	−0.412824	−	2.93739i
$271$	−18.7624	−	9.15101i	−1.13973	−	0.555885i	−0.230872	−	0.972984i	$-0.574158\pi$
$271$	−18.7624	−	9.15101i	−1.13973	−	0.555885i	−0.908861	+	0.417100i	$0.863047\pi$
$272$	2.35027	+	1.58528i	0.142506	+	0.0961216i
$273$	4.00377	+	4.44664i	0.242319	+	0.269123i
$274$	−4.99340	−	8.64883i	−0.301662	−	0.522495i
$275$	−23.8030	+	4.09415i	−1.43537	+	0.246887i
$276$	−17.5828	+	20.9543i	−1.05836	+	1.26130i
$277$	−0.786360	−	3.69953i	−0.0472478	−	0.222283i	0.948189	−	0.317707i	$-0.102913\pi$
$277$	−0.786360	−	3.69953i	−0.0472478	−	0.222283i	−0.995437	+	0.0954235i	$0.969579\pi$
$278$	−8.04769	+	0.845847i	−0.482669	+	0.0507305i
$279$	4.25253	−	14.8303i	0.254592	−	0.887868i
$280$	0.532685	+	1.00184i	0.0318340	+	0.0598711i
$281$	−4.83884	+	0.680055i	−0.288661	+	0.0405687i	−0.282017	−	0.959409i	$-0.591004\pi$
$281$	−4.83884	+	0.680055i	−0.288661	+	0.0405687i	−0.00664353	+	0.999978i	$0.502115\pi$
$282$	21.4209	−	14.4486i	1.27560	−	0.860401i
$283$	−11.9480	−	2.97896i	−0.710233	−	0.177081i	−0.129979	−	0.991517i	$-0.541491\pi$
$283$	−11.9480	−	2.97896i	−0.710233	−	0.177081i	−0.580254	+	0.814436i	$0.697047\pi$
$284$	−6.39537	−	2.07798i	−0.379496	−	0.123306i
$285$	39.2739	+	29.4559i	2.32639	+	1.74481i
$286$	17.6545	+	7.21926i	1.04393	+	0.426884i
$287$	−0.715398	−	0.852579i	−0.0422286	−	0.0503261i
$288$	−4.51135	+	5.77426i	−0.265834	+	0.340252i
$289$	3.92917	+	8.05599i	0.231128	+	0.473882i
$290$	−6.36267	+	13.0454i	−0.373629	+	0.766052i
$291$	−10.8770	−	13.9219i	−0.637620	−	0.816117i
$292$	0.534572	−	2.51497i	0.0312835	−	0.147177i
$293$	−2.97592	+	28.3140i	−0.173855	+	1.65412i	0.465382	+	0.885110i	$0.345917\pi$
$293$	−2.97592	+	28.3140i	−0.173855	+	1.65412i	−0.639237	+	0.769010i	$0.720750\pi$
$294$	−1.54572	+	22.1048i	−0.0901482	+	1.28918i
$295$	−14.6886	−	23.5067i	−0.855205	−	1.36861i
$296$	−2.67846	+	1.54641i	−0.155682	+	0.0898833i
$297$	1.41625	+	46.1045i	0.0821791	+	2.67526i
$298$	0.962889	+	2.64552i	0.0557787	+	0.153251i
$299$	48.4738	+	6.81255i	2.80331	+	0.393980i
$300$	−21.0342	+	10.2591i	−1.21441	+	0.592308i
$301$	−1.37686	−	2.04128i	−0.0793610	−	0.117658i
$302$	1.56874	+	0.980260i	0.0902711	+	0.0564076i
$303$	−7.91634	−	24.3640i	−0.454782	−	1.39967i
$304$	−0.541010	−	4.32519i	−0.0310291	−	0.248067i
$305$	−6.21858	−	8.55914i	−0.356075	−	0.490095i
$306$	19.2608	−	7.78186i	1.10107	−	0.444860i
$307$	−7.18600	−	2.61549i	−0.410127	−	0.149274i	0.128714	−	0.991682i	$-0.458915\pi$
$307$	−7.18600	−	2.61549i	−0.410127	−	0.149274i	−0.538840	+	0.842408i	$0.681137\pi$
$308$	−0.398065	−	0.997279i	−0.0226819	−	0.0568253i
$309$	−8.13078	−	46.1120i	−0.462544	−	2.62322i
$310$	−7.37427	+	0.257515i	−0.418831	+	0.0146259i
$311$	−0.236773	−	2.25274i	−0.0134262	−	0.127741i	0.985756	−	0.168183i	$-0.0537901\pi$
$311$	−0.236773	−	2.25274i	−0.0134262	−	0.127741i	−0.999182	+	0.0404420i	$0.987123\pi$
$312$	18.3802	+	1.93184i	1.04057	+	0.109369i
$313$	1.90245	−	4.70872i	0.107533	−	0.266153i	−0.863818	−	0.503804i	$-0.831933\pi$
$313$	1.90245	−	4.70872i	0.107533	−	0.266153i	0.971350	+	0.237652i	$0.0763777\pi$
$314$	2.19779	−	5.43973i	0.124029	−	0.306982i
$315$	8.26876	+	0.869081i	0.465892	+	0.0489672i
$316$	−0.858065	−	8.16395i	−0.0482699	−	0.459258i
$317$	11.0157	−	0.384677i	0.618703	−	0.0216056i	0.276166	−	0.961110i	$-0.410936\pi$
$317$	11.0157	−	0.384677i	0.618703	−	0.0216056i	0.342537	+	0.939504i	$0.388714\pi$
$318$	4.49707	+	25.5041i	0.252183	+	1.43020i
$319$	7.32771	−	11.6180i	0.410273	−	0.650482i
$320$	3.29325	+	1.19865i	0.184098	+	0.0670063i
$321$	8.86281	−	3.58081i	0.494674	−	0.199861i
$322$	−1.61980	−	2.22946i	−0.0902677	−	0.124243i
$323$	−4.80258	+	11.3858i	−0.267223	+	0.633522i
$324$	7.01822	+	21.5998i	0.389901	+	1.19999i
$325$	35.5158	+	22.1927i	1.97006	+	1.23103i
$326$	−2.45804	−	3.64419i	−0.136138	−	0.201833i
$327$	−47.9126	+	23.3685i	−2.64957	+	1.29228i
$328$	−3.40417	−	0.478424i	−0.187964	−	0.0264166i
$329$	0.890302	+	2.44609i	0.0490840	+	0.134857i
$330$	35.1545	−	12.6283i	1.93519	−	0.695166i
$331$	21.1289	−	12.1988i	1.16135	−	0.670506i	0.209723	−	0.977761i	$-0.432744\pi$
$331$	21.1289	−	12.1988i	1.16135	−	0.670506i	0.951627	+	0.307255i	$0.0994104\pi$
$332$	2.76403	+	4.42337i	0.151696	+	0.242764i
$333$	−1.58090	+	22.6079i	−0.0866326	+	1.23890i
$334$	2.16474	−	20.5961i	0.118449	−	1.12697i
$335$	1.91982	−	9.03204i	0.104891	−	0.493473i
$336$	−0.640568	−	0.819889i	−0.0349458	−	0.0447286i
$337$	10.8518	−	22.2495i	0.591136	−	1.21201i	−0.368201	−	0.929746i	$-0.620026\pi$
$337$	10.8518	−	22.2495i	0.591136	−	1.21201i	0.959337	−	0.282262i	$-0.0910849\pi$
$338$	−8.79932	−	18.0413i	−0.478620	−	0.981316i
$339$	13.0775	−	16.7385i	0.710274	−	0.909109i
$340$	−6.38632	−	7.61092i	−0.346347	−	0.412760i
$341$	6.96387	+	0.516347i	0.377115	+	0.0279618i
$342$	−28.4919	−	14.4362i	−1.54067	−	0.780620i
$343$	−4.27851	−	1.39017i	−0.231018	−	0.0750623i
$344$	−7.37922	−	1.83985i	−0.397861	−	0.0991979i
$345$	79.4754	−	53.6069i	4.27881	−	2.88610i
$346$	15.8938	−	2.23373i	0.854458	−	0.120086i
$347$	15.1810	+	28.5514i	0.814960	+	1.53272i	0.845990	+	0.533199i	$0.179010\pi$
$347$	15.1810	+	28.5514i	0.814960	+	1.53272i	−0.0310294	+	0.999518i	$0.509879\pi$
$348$	3.66857	−	12.7938i	0.196656	−	0.685821i
$349$	−15.2954	+	1.60761i	−0.818742	+	0.0860533i	−0.504634	−	0.863334i	$-0.668372\pi$
$349$	−15.2954	+	1.60761i	−0.818742	+	0.0860533i	−0.314109	+	0.949387i	$0.601706\pi$
$350$	−0.490193	−	2.30618i	−0.0262019	−	0.123270i
$351$	51.4109	−	61.2691i	2.74411	−	3.27030i
$352$	−2.97483	−	1.46641i	−0.158559	−	0.0781601i
$353$	0.771094	+	1.33557i	0.0410412	+	0.0710855i	0.885816	−	0.464036i	$-0.153599\pi$
$353$	0.771094	+	1.33557i	0.0410412	+	0.0710855i	−0.844775	+	0.535121i	$0.820266\pi$
$354$	17.0076	+	18.8889i	0.903946	+	1.00393i
$355$	19.5377	+	13.1783i	1.03695	+	0.699433i
$356$	−8.95375	−	4.36704i	−0.474548	−	0.231452i
$357$	0.410509	+	2.92092i	0.0217264	+	0.154592i
$358$	−2.35635	−	0.0822857i	−0.124537	−	0.00434894i
$359$	1.81311	+	25.9287i	0.0956923	+	1.36846i	0.773767	+	0.633470i	$0.218370\pi$
$359$	1.81311	+	25.9287i	0.0956923	+	1.36846i	−0.678075	+	0.734993i	$0.737185\pi$
$360$	20.7760	−	15.0946i	1.09499	−	0.795556i
$361$	18.0433	−	5.95309i	0.949647	−	0.313320i
$362$		−	3.00850i		−	0.158123i
$363$	−34.3709	+	8.26373i	−1.80400	+	0.433733i
$364$	−0.636809	+	1.74962i	−0.0333779	+	0.0917050i
$365$	−4.23035	+	7.95613i	−0.221427	+	0.416443i
$366$	6.97859	+	6.73915i	0.364777	+	0.352261i
$367$	21.0855	+	6.04616i	1.10065	+	0.315607i	0.776322	−	0.630337i	$-0.217083\pi$
$367$	21.0855	+	6.04616i	1.10065	+	0.315607i	0.324331	+	0.945944i	$0.394861\pi$
$368$	−8.32575	−	1.76969i	−0.434010	−	0.0922516i
$369$	−16.8552	+	18.7196i	−0.877445	+	0.974502i
$370$	10.5171	−	2.62222i	0.546760	−	0.136323i
$371$	−2.60269	−	0.181997i	−0.135125	−	0.00944884i
$372$	6.61835	−	1.40677i	0.343146	−	0.0729378i
$373$	−4.42226	+	7.65958i	−0.228976	+	0.396598i	−0.957505	−	0.288417i	$-0.906871\pi$
$373$	−4.42226	+	7.65958i	−0.228976	+	0.396598i	0.728529	+	0.685015i	$0.240204\pi$
$374$	5.22500	+	7.81697i	0.270179	+	0.404206i
$375$	25.3137	−	4.46349i	1.30719	−	0.230494i
$376$	7.09902	+	3.77462i	0.366104	+	0.194661i
$377$	−22.8947	+	6.56495i	−1.17914	+	0.338112i
$378$	−4.49175	+	0.314094i	−0.231031	+	0.0161552i
$379$	−16.0439	+	5.21297i	−0.824118	+	0.267772i	−0.690566	−	0.723270i	$-0.742638\pi$
$379$	−16.0439	+	5.21297i	−0.824118	+	0.267772i	−0.133552	+	0.991042i	$0.542638\pi$
$380$	−2.35556	+	15.0935i	−0.120838	+	0.774281i
$381$	4.76169	−	6.55391i	0.243949	−	0.335767i
$382$	−6.34065	+	25.4309i	−0.324416	+	1.30116i
$383$	−14.7997	−	11.5628i	−0.756231	−	0.590832i	0.162040	−	0.986784i	$-0.448193\pi$
$383$	−14.7997	−	11.5628i	−0.756231	−	0.590832i	−0.918271	+	0.395952i	$0.870415\pi$
$384$	−3.16484	−	0.558047i	−0.161505	−	0.0284777i
$385$	0.377647	+	3.74421i	0.0192467	+	0.190823i
$386$	−3.91409	+	1.42461i	−0.199222	+	0.0725109i
$387$	−41.4137	+	37.2891i	−2.10518	+	1.89551i
$388$	2.23604	−	5.02223i	0.113518	−	0.254965i
$389$	3.37134	+	13.5217i	0.170934	+	0.685578i	0.993195	+	0.116467i	$0.0371569\pi$
$389$	3.37134	+	13.5217i	0.170934	+	0.685578i	−0.822261	+	0.569111i	$0.807288\pi$
$390$	−60.0538	−	24.2633i	−3.04094	−	1.22862i
$391$	17.9323	+	16.1463i	0.906876	+	0.816555i
$392$	−6.29906	+	2.80452i	−0.318151	+	0.141650i
$393$	14.4024	−	21.3525i	0.726507	−	1.07709i
$394$	−0.150853	+	1.07337i	−0.00759986	+	0.0540758i
$395$	−4.99569	+	28.3319i	−0.251360	+	1.42553i
$396$	−21.0979	+	12.0631i	−1.06021	+	0.606192i
$397$	−4.12030	+	3.45734i	−0.206792	+	0.173519i	−0.740302	−	0.672275i	$-0.765317\pi$
$397$	−4.12030	+	3.45734i	−0.206792	+	0.173519i	0.533510	+	0.845794i	$0.320873\pi$
$398$	−0.259714	+	0.799318i	−0.0130183	+	0.0400662i
$399$	2.96763	−	3.42951i	0.148567	−	0.171690i
$400$	−5.89147	−	4.28040i	−0.294573	−	0.214020i
$401$	17.7820	−	28.4572i	0.887993	−	1.42109i	−0.0189453	−	0.999821i	$-0.506031\pi$
$401$	17.7820	−	28.4572i	0.887993	−	1.42109i	0.906938	−	0.421265i	$-0.138414\pi$
$402$	−0.295503	+	8.46211i	−0.0147384	+	0.422052i
$403$	−8.41107	−	8.70992i	−0.418985	−	0.433872i
$404$	5.53748	−	5.73423i	0.275500	−	0.285289i
$405$	−2.77781	−	79.5461i	−0.138031	−	3.95268i
$406$	1.16121	+	0.670426i	0.0576299	+	0.0332727i
$407$	−10.1638	+	1.38494i	−0.503801	+	0.0686491i
$408$	6.97909	+	5.85615i	0.345516	+	0.289923i
$409$	−25.7334	+	16.0800i	−1.27243	+	0.795105i	−0.986598	−	0.163173i	$-0.947827\pi$
$409$	−25.7334	+	16.0800i	−1.27243	+	0.795105i	−0.285837	+	0.958278i	$0.592272\pi$
$410$	11.0059	+	4.90016i	0.543545	+	0.242002i
$411$	−13.0539	−	29.3195i	−0.643902	−	1.44623i
$412$	11.4814	−	8.97023i	0.565647	−	0.441931i
$413$	−2.26095	+	1.20217i	−0.111254	+	0.0591547i
$414$	−44.8660	+	43.3266i	−2.20504	+	2.12939i
$415$	−5.03860	−	17.5717i	−0.247335	−	0.862560i
$416$	2.15432	+	5.33213i	0.105624	+	0.261429i
$417$	−26.0051			−1.27347
$418$	3.76870	−	13.9570i	0.184333	−	0.682657i
$419$	−15.8722			−0.775408			−0.387704	−	0.921784i	$-0.626732\pi$
$419$	−15.8722			−0.775408			−0.387704	+	0.921784i	$0.626732\pi$
$420$	1.36596	+	3.38087i	0.0666520	+	0.164969i
$421$	−7.86865	−	27.4412i	−0.383494	−	1.33740i	−0.882299	−	0.470689i	$-0.844005\pi$
$421$	−7.86865	−	27.4412i	−0.383494	−	1.33740i	0.498805	−	0.866714i	$-0.333772\pi$
$422$	0.355574	−	0.343373i	0.0173091	−	0.0167152i
$423$	52.0191	−	27.6590i	2.52925	−	1.34483i
$424$	−6.35025	+	4.96136i	−0.308395	+	0.240945i
$425$	8.39698	+	18.8599i	0.407313	+	0.914841i
$426$	−19.7420	−	8.78969i	−0.956501	−	0.425862i
$427$	−0.828850	+	0.517923i	−0.0401109	+	0.0250641i
$428$	2.27855	+	1.91193i	0.110138	+	0.0924167i
$429$	53.9999	+	29.0037i	2.60714	+	1.40031i
$430$	23.0821	+	13.3265i	1.11312	+	0.642660i
$431$	−0.405729	−	11.6185i	−0.0195433	−	0.559646i	−0.969189	−	0.246319i	$-0.920779\pi$
$431$	−0.405729	−	11.6185i	−0.0195433	−	0.559646i	0.949645	−	0.313326i	$-0.101443\pi$
$432$	−9.66103	+	10.0043i	−0.464816	+	0.481331i
$433$	18.6585	+	19.3215i	0.896672	+	0.928531i	0.997797	−	0.0663426i	$-0.0211330\pi$
$433$	18.6585	+	19.3215i	0.896672	+	0.928531i	−0.101125	+	0.994874i	$0.532244\pi$
$434$	−0.0237896	+	0.681244i	−0.00114194	+	0.0327008i
$435$	−24.7177	+	39.5565i	−1.18512	+	1.89659i
$436$	−13.4198	−	9.75007i	−0.642693	−	0.466944i
$437$	0.563525	−	37.0976i	0.0269571	−	1.77462i
$438$	2.55335	−	7.85841i	0.122004	−	0.375489i
$439$	−17.7442	+	14.8891i	−0.846884	+	0.710620i	−0.959101	−	0.283064i	$-0.908649\pi$
$439$	−17.7442	+	14.8891i	−0.846884	+	0.710620i	0.112217	+	0.993684i	$0.464205\pi$
$440$	8.60519	+	7.81381i	0.410236	+	0.372509i
$441$	−8.77365	+	49.7578i	−0.417793	+	2.36942i
$442$	2.26900	−	16.1448i	0.107925	−	0.767928i
$443$	2.23793	−	3.31786i	0.106327	−	0.157636i	−0.772119	−	0.635478i	$-0.780803\pi$
$443$	2.23793	−	3.31786i	0.106327	−	0.157636i	0.878446	+	0.477842i	$0.158581\pi$
$444$	−9.07999	+	4.04267i	−0.430917	+	0.191857i
$445$	25.9452	+	23.3612i	1.22992	+	1.10743i
$446$	−20.8877	−	8.43918i	−0.989062	−	0.399607i
$447$	2.18877	+	8.77868i	0.103525	+	0.415217i
$448$	0.131685	−	0.295769i	0.00622152	−	0.0139738i
$449$	0.990012	−	0.891411i	0.0467216	−	0.0420683i	−0.645439	−	0.763812i	$-0.723326\pi$
$449$	0.990012	−	0.891411i	0.0467216	−	0.0420683i	0.692161	+	0.721743i	$0.256659\pi$
$450$	−50.1437	+	18.2508i	−2.36380	+	0.860351i
$451$	−9.84980	−	5.74205i	−0.463809	−	0.270383i
$452$	6.50930	+	1.14777i	0.306172	+	0.0539863i
$453$	4.68451	+	3.65994i	0.220098	+	0.171959i
$454$	3.30426	−	13.2527i	0.155077	−	0.621979i
$455$	3.83544	−	5.27903i	0.179808	−	0.247485i
$456$	−0.276184	−	14.0053i	−0.0129335	−	0.655859i
$457$	39.3318	−	12.7797i	1.83986	−	0.597808i	0.841524	−	0.540219i	$-0.181659\pi$
$457$	39.3318	−	12.7797i	1.83986	−	0.597808i	0.998340	−	0.0575890i	$-0.0183413\pi$
$458$	−5.71672	+	0.399752i	−0.267125	+	0.0186792i
$459$	37.8999	−	10.8676i	1.76901	−	0.507257i
$460$	26.3386	+	14.0045i	1.22804	+	0.652963i
$461$	19.6413	−	3.46330i	0.914788	−	0.161302i	0.303611	−	0.952796i	$-0.401808\pi$
$461$	19.6413	−	3.46330i	0.914788	−	0.161302i	0.611177	+	0.791494i	$0.290696\pi$
$462$	−0.937235	−	3.32108i	−0.0436041	−	0.154511i
$463$	2.16038	−	3.74188i	0.100401	−	0.173900i	−0.811449	−	0.584424i	$-0.801321\pi$
$463$	2.16038	−	3.74188i	0.100401	−	0.173900i	0.911850	+	0.410523i	$0.134654\pi$
$464$	4.05100	−	0.861067i	0.188063	−	0.0399740i
$465$	−23.6551	−	1.65413i	−1.09698	−	0.0767083i
$466$	−7.14522	+	1.78150i	−0.330996	+	0.0825265i
$467$	−12.7968	+	14.2123i	−0.592167	+	0.657668i	−0.962516	−	0.271224i	$-0.912571\pi$
$467$	−12.7968	+	14.2123i	−0.592167	+	0.657668i	0.370349	+	0.928893i	$0.379238\pi$
$468$	41.2196	+	8.76150i	1.90538	+	0.405000i
$469$	−0.819987	−	0.235127i	−0.0378635	−	0.0108572i
$470$	−20.2692	−	19.5737i	−0.934948	−	0.902869i
$471$	8.85159	−	16.6474i	0.407860	−	0.767073i
$472$	−2.70511	+	7.43222i	−0.124513	+	0.342096i
$473$	−20.3437	−	14.9114i	−0.935404	−	0.685629i
$474$		−	26.3807i		−	1.21171i
$475$	13.3498	−	28.7989i	0.612533	−	1.32138i
$476$	−0.742547	+	0.539492i	−0.0340346	+	0.0247276i
$477$	4.11915	+	58.9065i	0.188603	+	2.69715i
$478$	23.4298	+	0.818186i	1.07165	+	0.0374230i
$479$	0.836803	+	5.95416i	0.0382345	+	0.272053i	0.999998	−	0.00182754i	$-0.000581724\pi$
$479$	0.836803	+	5.95416i	0.0382345	+	0.272053i	−0.961764	+	0.273880i	$0.911693\pi$
$480$	10.1228	+	4.93721i	0.462040	+	0.225352i
$481$	14.7457	+	9.94607i	0.672344	+	0.453502i
$482$	−4.86297	−	5.40087i	−0.221502	−	0.246003i
$483$	−4.42805	−	7.66960i	−0.201483	−	0.348979i
$484$	−7.29154	−	8.23610i	−0.331434	−	0.374368i
$485$	−12.3843	+	14.7591i	−0.562344	+	0.670175i
$486$	6.50018	+	30.5809i	0.294854	+	1.38718i
$487$	29.0599	−	3.05432i	1.31683	−	0.138405i	0.580075	−	0.814563i	$-0.303023\pi$
$487$	29.0599	−	3.05432i	1.31683	−	0.138405i	0.736756	+	0.676159i	$0.236357\pi$
$488$	−0.832092	+	2.90185i	−0.0376670	+	0.131361i
$489$	−6.63188	−	12.4727i	−0.299904	−	0.564037i
$490$	23.9297	−	3.36310i	1.08103	−	0.151929i
$491$	−0.523083	+	0.352824i	−0.0236064	+	0.0159227i	−0.570939	−	0.820992i	$-0.693421\pi$
$491$	−0.523083	+	0.352824i	−0.0236064	+	0.0159227i	0.547333	+	0.836915i	$0.315643\pi$
$492$	−10.7192	−	2.67260i	−0.483259	−	0.120490i
$493$	−11.1663	−	3.62814i	−0.502904	−	0.163403i
$494$	−20.9925	+	13.7003i	−0.944495	+	0.616407i
$495$	82.7284	−	20.2580i	3.71836	−	0.910529i
$496$	1.35336	+	1.61287i	0.0607675	+	0.0724199i
$497$	1.34037	−	1.71559i	0.0601237	−	0.0769549i
$498$	7.34810	+	15.0658i	0.329276	+	0.675117i
$499$	13.7390	−	28.1691i	0.615042	−	1.26102i	−0.333015	−	0.942921i	$-0.608066\pi$
$499$	13.7390	−	28.1691i	0.615042	−	1.26102i	0.948057	−	0.318101i	$-0.103045\pi$
$500$	4.92431	+	6.30283i	0.220222	+	0.281871i
$501$	13.8373	−	65.0992i	0.618203	−	2.90842i
$502$	−1.41376	+	13.4510i	−0.0630992	+	0.600348i
$503$	1.37188	−	19.6187i	0.0611689	−	0.874757i	−0.865984	−	0.500072i	$-0.833307\pi$
$503$	1.37188	−	19.6187i	0.0611689	−	0.874757i	0.927153	−	0.374684i	$-0.122249\pi$
$504$	−1.25718	−	2.01190i	−0.0559991	−	0.0896173i
$505$	−24.1942	+	13.9685i	−1.07663	+	0.621591i
$506$	−23.3375	−	15.8843i	−1.03748	−	0.706143i
$507$	−22.0627	−	60.6169i	−0.979841	−	2.69209i
$508$	2.49629	+	0.350830i	0.110755	+	0.0155656i
$509$	−12.2207	+	5.96042i	−0.541672	+	0.264191i	−0.688831	−	0.724922i	$-0.741876\pi$
$509$	−12.2207	+	5.96042i	−0.541672	+	0.264191i	0.147159	+	0.989113i	$0.452987\pi$
$510$	−17.8544	−	26.4702i	−0.790606	−	1.17212i
$511$	0.705945	+	0.441123i	0.0312292	+	0.0195141i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−50.9163	−	32.9018i	−2.24801	−	1.45265i
$514$	11.9403	+	16.4344i	0.526662	+	0.724888i
$515$	−47.3442	+	19.1283i	−2.08623	+	0.842893i
$516$	−22.9664	−	8.35909i	−1.01104	−	0.367988i
$517$	17.0547	+	20.4992i	0.750067	+	0.901554i
$518$	−0.173879	−	0.986117i	−0.00763981	−	0.0433275i
$519$	51.5480	−	1.80010i	2.26271	−	0.0790155i
$520$	−2.10673	−	20.0442i	−0.0923862	−	0.878996i
$521$	1.69691	+	0.178353i	0.0743431	+	0.00781377i	0.141627	−	0.989920i	$-0.454767\pi$
$521$	1.69691	+	0.178353i	0.0743431	+	0.00781377i	−0.0672839	+	0.997734i	$0.521433\pi$
$522$	11.3684	−	28.1377i	0.497580	−	1.23155i
$523$	−2.61605	+	6.47495i	−0.114392	+	0.283130i	−0.973509	−	0.228650i	$-0.926569\pi$
$523$	−2.61605	+	6.47495i	−0.114392	+	0.283130i	0.859117	+	0.511779i	$0.171013\pi$
$524$	7.97055	+	0.837738i	0.348195	+	0.0365968i
$525$	−0.791997	−	7.53535i	−0.0345656	−	0.328870i
$526$	22.8318	−	0.797305i	0.995515	−	0.0347642i
$527$	−1.03648	−	5.87814i	−0.0451496	−	0.256056i
$528$	−9.01515	−	5.68605i	−0.392334	−	0.247454i
$529$	−46.4677	−	16.9129i	−2.02034	−	0.735342i
$530$	26.1857	−	10.5797i	1.13743	−	0.459552i
$531$	34.0656	+	46.8872i	1.47832	+	2.03473i
$532$	1.37578	+	0.314345i	0.0596476	+	0.0136286i
$533$	6.10908	+	18.8018i	0.264614	+	0.814397i
$534$	−27.1498	−	16.9650i	−1.17488	−	0.734149i
$535$	−5.82916	−	8.64208i	−0.252016	−	0.373630i
$536$	−2.36812	+	1.15501i	−0.102287	+	0.0498887i
$537$	−7.50341	−	1.05454i	−0.323796	−	0.0455066i
$538$	−2.29233	−	6.29814i	−0.0988296	−	0.271532i
$539$	−22.8579	+	0.702155i	−0.984561	+	0.0302440i
$540$	42.2106	−	24.3703i	1.81646	−	1.04873i
$541$	−14.6323	−	23.4166i	−0.629094	−	1.00676i	−0.997038	−	0.0769124i	$-0.975494\pi$
$541$	−14.6323	−	23.4166i	−0.629094	−	1.00676i	0.367944	−	0.929848i	$-0.380062\pi$
$542$	1.45617	−	20.8242i	0.0625478	−	0.894475i
$543$	1.01061	−	9.61533i	0.0433695	−	0.412633i
$544$	−0.589417	+	2.77299i	−0.0252711	+	0.118891i
$545$	35.7907	+	45.8100i	1.53311	+	1.96229i
$546$	−2.62301	+	5.37797i	−0.112255	+	0.230156i
$547$	12.0363	+	24.6781i	0.514635	+	1.05516i	0.984979	+	0.172675i	$0.0552411\pi$
$547$	12.0363	+	24.6781i	0.514635	+	1.05516i	−0.470344	+	0.882483i	$0.655870\pi$
$548$	6.14849	−	7.86971i	0.262650	−	0.336177i
$549$	14.2189	+	16.9454i	0.606847	+	0.723212i
$550$	−12.7128	−	20.5360i	−0.542075	−	0.875660i
$551$	7.09124	+	16.6013i	0.302097	+	0.707239i
$552$	−26.0151	−	8.45283i	−1.10728	−	0.359776i
$553$	2.57877	+	0.642959i	0.109660	+	0.0273414i
$554$	3.13557	−	2.11497i	0.133218	−	0.0898564i
$555$	34.4943	−	4.84786i	1.46420	−	0.205780i
$556$	−3.79897	−	7.14483i	−0.161112	−	0.303008i
$557$	−3.18248	+	11.0986i	−0.134846	+	0.470265i	−0.999484	−	0.0321318i	$-0.989770\pi$
$557$	−3.18248	+	11.0986i	−0.134846	+	0.470265i	0.864637	+	0.502396i	$0.167548\pi$
$558$	15.3435	−	1.61266i	0.649541	−	0.0682695i
$559$	9.09328	+	42.7805i	0.384605	+	1.80942i
$560$	−0.729338	+	0.869192i	−0.0308202	+	0.0367300i
$561$	14.0736	+	26.7387i	0.594186	+	1.12891i
$562$	−2.44320	−	4.23174i	−0.103060	−	0.178505i
$563$	16.8520	+	18.7160i	0.710226	+	0.788786i	0.984969	−	0.172732i	$-0.0552594\pi$
$563$	16.8520	+	18.7160i	0.710226	+	0.788786i	−0.274743	+	0.961518i	$0.588593\pi$
$564$	21.4209	+	14.4486i	0.901984	+	0.608396i
$565$	−20.8201	−	10.1546i	−0.875907	−	0.427208i
$566$	−1.71374	−	12.1939i	−0.0720339	−	0.512548i
$567$	−7.34856	−	0.256617i	−0.308610	−	0.0107769i
$568$	−0.469077	−	6.70811i	−0.0196820	−	0.281466i
$569$	−21.5668	+	15.6692i	−0.904126	+	0.656886i	−0.939522	−	0.342487i	$-0.888731\pi$
$569$	−21.5668	+	15.6692i	−0.904126	+	0.656886i	0.0353963	+	0.999373i	$0.488731\pi$
$570$	−12.5987	+	47.4485i	−0.527702	+	1.98740i
$571$			12.0765i			0.505388i	0.967546	+	0.252694i	$0.0813166\pi$
$571$			12.0765i			0.505388i	−0.967546	+	0.252694i	$0.918683\pi$
$572$	−0.0800708	+	19.0734i	−0.00334793	+	0.797498i
$573$	−28.8078	+	79.1489i	−1.20346	+	3.30649i
$574$	0.522504	−	0.982687i	0.0218089	−	0.0410166i
$575$	−44.5881	−	43.0582i	−1.85945	−	1.79565i
$576$	−7.04378	−	2.01977i	−0.293491	−	0.0841572i
$577$	−25.6406	−	5.45008i	−1.06743	−	0.226890i	−0.359482	−	0.933152i	$-0.617046\pi$
$577$	−25.6406	−	5.45008i	−1.06743	−	0.226890i	−0.707950	+	0.706263i	$0.750380\pi$
$578$	−5.99749	+	6.66089i	−0.249463	+	0.277057i
$579$	−12.9882	+	3.23833i	−0.539772	+	0.134580i
$580$	−14.4790	−	1.01247i	−0.601207	−	0.0420405i
$581$	−1.65181	+	0.351103i	−0.0685286	+	0.0145662i
$582$	8.83358	−	15.3002i	0.366164	−	0.634214i
$583$	−25.7226	+	7.25912i	−1.06532	+	0.300642i
$584$	2.53209	−	0.446476i	0.104779	−	0.0184753i
$585$	−130.399	−	69.3343i	−5.39133	−	2.86662i
$586$	−27.3671	+	7.84738i	−1.13052	+	0.324172i
$587$	33.6881	−	2.35570i	1.39046	−	0.0972302i	0.645203	−	0.764011i	$-0.276773\pi$
$587$	33.6881	−	2.35570i	1.39046	−	0.0972302i	0.745254	+	0.666781i	$0.232328\pi$
$588$	−21.0743	+	6.84745i	−0.869088	+	0.282384i
$589$	−5.75939	+	7.14527i	−0.237311	+	0.294416i
$590$	16.2926	−	22.4248i	0.670756	−	0.923216i
$591$	−0.842702	+	3.37989i	−0.0346641	+	0.139030i
$592$	−2.43718	−	1.90413i	−0.100167	−	0.0782593i
$593$	−27.9571	−	4.92959i	−1.14806	−	0.202434i	−0.432931	−	0.901427i	$-0.642521\pi$
$593$	−27.9571	−	4.92959i	−1.14806	−	0.202434i	−0.715128	+	0.698993i	$0.753632\pi$
$594$	−42.2168	+	18.5842i	−1.73218	+	0.762518i
$595$	3.02267	−	1.10016i	0.123918	−	0.0451023i
$596$	−2.09217	+	1.88380i	−0.0856988	+	0.0771636i
$597$	−1.09857	+	2.46742i	−0.0449614	+	0.100985i
$598$	11.8421	+	47.4961i	0.484260	+	1.94226i
$599$	6.30829	+	2.54872i	0.257750	+	0.104138i	0.499845	−	0.866115i	$-0.333390\pi$
$599$	6.30829	+	2.54872i	0.257750	+	0.104138i	−0.242095	+	0.970252i	$0.577835\pi$
$600$	−17.3916	−	15.6595i	−0.710010	−	0.639296i
$601$	−27.4269	+	12.2112i	−1.11877	+	0.498107i	−0.880953	−	0.473204i	$-0.843097\pi$
$601$	−27.4269	+	12.2112i	−1.11877	+	0.498107i	−0.237814	+	0.971311i	$0.576431\pi$
$602$	1.37686	−	2.04128i	0.0561167	−	0.0831965i
$603$	−2.68697	+	19.1188i	−0.109422	+	0.778576i
$604$	−0.321219	+	1.82173i	−0.0130702	+	0.0741250i
$605$	16.6080	+	34.7898i	0.675211	+	1.41441i
$606$	19.6244	−	16.4668i	0.797186	−	0.668918i
$607$	0.440126	−	1.35457i	0.0178642	−	0.0549803i	−0.941727	−	0.336378i	$-0.890798\pi$
$607$	0.440126	−	1.35457i	0.0178642	−	0.0549803i	0.959591	+	0.281398i	$0.0907980\pi$
$608$	3.80758	−	2.12186i	0.154418	−	0.0860529i
$609$	3.48609	+	2.53279i	0.141264	+	0.102634i
$610$	5.60637	−	8.97207i	0.226995	−	0.363269i
$611$	1.61368	−	46.2098i	0.0652826	−	1.86945i
$612$	14.4304	+	14.9432i	0.583316	+	0.604041i
$613$	−17.4482	+	18.0681i	−0.704726	+	0.729766i	−0.972291	−	0.233774i	$-0.924892\pi$
$613$	−17.4482	+	18.0681i	−0.704726	+	0.729766i	0.267564	+	0.963540i	$0.413781\pi$
$614$	−0.266883	−	7.64253i	−0.0107705	−	0.308427i
$615$	33.5296	+	19.3583i	1.35204	+	0.780603i
$616$	0.775543	−	0.742667i	0.0312475	−	0.0299229i
$617$	25.7780	+	21.6303i	1.03778	+	0.870803i	0.991756	−	0.128138i	$-0.0408999\pi$
$617$	25.7780	+	21.6303i	1.03778	+	0.870803i	0.0460257	+	0.998940i	$0.485344\pi$
$618$	39.7084	−	24.8126i	1.59731	−	0.998108i
$619$	34.0823	+	15.1744i	1.36989	+	0.609912i	0.954083	−	0.299543i	$-0.0968342\pi$
$619$	34.0823	+	15.1744i	1.36989	+	0.609912i	0.415802	+	0.909455i	$0.363501\pi$
$620$	−3.00122	−	6.74084i	−0.120532	−	0.270719i
$621$	−93.2831	+	72.8808i	−3.74332	+	2.92460i
$622$	2.00001	−	1.06342i	0.0801931	−	0.0426394i
$623$	2.32007	−	2.24047i	0.0929517	−	0.0897624i
$624$	5.09418	+	17.7655i	0.203930	+	0.711189i
$625$	3.13921	+	7.76982i	0.125568	+	0.310793i
$626$	5.07852			0.202978
$627$	16.7334	−	43.3413i	0.668268	−	1.73089i
$628$	5.86694			0.234116
$629$	3.28454	+	8.12951i	0.130963	+	0.324145i
$630$	2.29173	+	7.99222i	0.0913048	+	0.318418i
$631$	3.67851	−	3.55229i	0.146439	−	0.141414i	−0.617831	−	0.786311i	$-0.711988\pi$
$631$	3.67851	−	3.55229i	0.146439	−	0.141414i	0.764270	+	0.644896i	$0.223100\pi$
$632$	7.24804	−	3.85385i	0.288312	−	0.153298i
$633$	1.25178	−	0.977998i	0.0497538	−	0.0388719i
$634$	4.48322	+	10.0695i	0.178051	+	0.399910i
$635$	−8.07070	−	3.59331i	−0.320276	−	0.142596i
$636$	−21.9624	+	13.7236i	−0.870865	+	0.544177i
$637$	30.3763	+	25.4887i	1.20355	+	1.00990i
$638$	13.5170	+	2.44197i	0.535143	+	0.0966783i
$639$	−42.6731	−	24.6373i	−1.68812	−	0.974638i
$640$	0.122309	+	3.50247i	0.00483469	+	0.138447i
$641$	16.7649	−	17.3606i	0.662174	−	0.685701i	−0.301292	−	0.953532i	$-0.597418\pi$
$641$	16.7649	−	17.3606i	0.662174	−	0.685701i	0.963466	+	0.267831i	$0.0863068\pi$
$642$	6.64013	+	6.87606i	0.262065	+	0.271376i
$643$	0.963369	−	27.5873i	0.0379916	−	1.08794i	−0.819384	−	0.573245i	$-0.805684\pi$
$643$	0.963369	−	27.5873i	0.0379916	−	1.08794i	0.857376	−	0.514691i	$-0.172093\pi$
$644$	1.46033	−	2.33702i	0.0575451	−	0.0920914i
$645$	69.2953	+	50.3460i	2.72850	+	1.98237i
$646$	−12.3558	−	0.187689i	−0.486132	−	0.00738452i
$647$	−7.96392	+	24.5104i	−0.313094	+	0.963604i	0.663438	+	0.748231i	$0.269097\pi$
$647$	−7.96392	+	24.5104i	−0.313094	+	0.963604i	−0.976532	+	0.215373i	$0.930903\pi$
$648$	−17.3980	+	14.5986i	−0.683456	+	0.573488i
$649$	−17.6342	+	19.4202i	−0.692204	+	0.762310i
$650$	−7.27229	+	41.2432i	−0.285243	+	1.61769i
$651$	−0.304876	+	2.16931i	−0.0119490	+	0.0850218i
$652$	2.45804	−	3.64419i	0.0962641	−	0.142717i
$653$	28.8270	−	12.8346i	1.12809	−	0.502257i	0.244092	−	0.969752i	$-0.421510\pi$
$653$	28.8270	−	12.8346i	1.12809	−	0.502257i	0.883995	+	0.467496i	$0.154844\pi$
$654$	−39.6153	−	35.6698i	−1.54908	−	1.39480i
$655$	−26.0423	−	10.5218i	−1.01756	−	0.411119i
$656$	−0.831636	−	3.33551i	−0.0324699	−	0.130230i
$657$	7.66311	−	17.2116i	0.298967	−	0.671490i
$658$	−1.93446	+	1.74179i	−0.0754130	+	0.0679022i
$659$	−38.4420	+	13.9918i	−1.49749	+	0.545042i	−0.955409	−	0.295285i	$-0.904585\pi$
$659$	−38.4420	+	13.9918i	−1.49749	+	0.545042i	−0.542080	+	0.840327i	$0.682363\pi$
$660$	24.8779	+	27.8640i	0.968371	+	1.08461i
$661$	−25.9325	−	4.57259i	−1.00866	−	0.177853i	−0.355178	−	0.934799i	$-0.615580\pi$
$661$	−25.9325	−	4.57259i	−1.00866	−	0.177853i	−0.653478	+	0.756945i	$0.726691\pi$
$662$	19.2256	+	15.0206i	0.747222	+	0.583794i
$663$	12.6752	−	50.8375i	0.492264	−	1.97436i
$664$	−3.06585	+	4.21979i	−0.118978	+	0.163759i
$665$	−4.33113	−	2.38798i	−0.167954	−	0.0926019i
$666$	−21.5539	+	7.00328i	−0.835196	+	0.271372i
$667$	35.1656	−	2.45902i	1.36162	−	0.0952135i
$668$	19.9073	−	5.70833i	0.770237	−	0.220862i
$669$	−63.9235	−	33.9887i	−2.47143	−	1.31408i
$670$	9.09354	−	1.60344i	0.351314	−	0.0619462i
$671$	−6.19719	+	7.86378i	−0.239240	+	0.303578i
$672$	0.520227	−	0.901060i	0.0200682	−	0.0347591i
$673$	29.2639	−	6.22024i	1.12804	−	0.239773i	0.394155	−	0.919044i	$-0.371037\pi$
$673$	29.2639	−	6.22024i	1.12804	−	0.239773i	0.733887	+	0.679271i	$0.237704\pi$
$674$	24.6946	+	1.72681i	0.951199	+	0.0665143i
$675$	−98.2703	+	24.5015i	−3.78242	+	0.943064i
$676$	13.4313	−	14.9170i	0.516588	−	0.573730i
$677$	−28.9371	−	6.15077i	−1.11214	−	0.236393i	−0.385025	−	0.922906i	$-0.625807\pi$
$677$	−28.9371	−	6.15077i	−1.11214	−	0.236393i	−0.727118	+	0.686513i	$0.759141\pi$
$678$	20.4186	+	5.85493i	0.784170	+	0.224857i
$679$	1.28033	+	1.23640i	0.0491346	+	0.0474488i
$680$	4.66436	−	8.77239i	0.178870	−	0.336406i
$681$	15.0125	−	41.2464i	0.575279	−	1.58057i
$682$	2.12996	+	6.65021i	0.0815605	+	0.254650i
$683$			19.2497i			0.736571i	0.929713	+	0.368285i	$0.120055\pi$
$683$			19.2497i			0.736571i	−0.929713	+	0.368285i	$0.879945\pi$
$684$	2.71175	−	31.8251i	0.103686	−	1.21686i
$685$	−28.3154	+	20.5724i	−1.08188	+	0.786030i
$686$	−0.313813	−	4.48774i	−0.0119814	−	0.171343i
$687$	−18.4053	−	0.642726i	−0.702205	−	0.0245215i
$688$	−1.05843	−	7.53111i	−0.0403522	−	0.287121i
$689$	41.6537	+	20.3159i	1.58688	+	0.773973i
$690$	79.4754	+	53.6069i	3.02558	+	2.04078i
$691$	22.7485	+	25.2648i	0.865393	+	0.961117i	0.999555	−	0.0298428i	$-0.00950067\pi$
$691$	22.7485	+	25.2648i	0.865393	+	0.961117i	−0.134161	+	0.990960i	$0.542834\pi$
$692$	8.02502	+	13.8997i	0.305066	+	0.528389i
$693$	−1.33378	−	7.75447i	−0.0506662	−	0.294568i
$694$	−20.7855	+	24.7711i	−0.789005	+	0.940299i
$695$	5.89624	+	27.7396i	0.223657	+	1.05222i
$696$	13.2365	−	1.39121i	0.501728	−	0.0527337i
$697$	−2.68621	+	9.36793i	−0.101747	+	0.354836i
$698$	−7.22030	−	13.5794i	−0.273292	−	0.513988i
$699$	−23.4350	+	3.29357i	−0.886393	+	0.124574i
$700$	1.95462	−	1.31841i	0.0738777	−	0.0498312i
$701$	18.2423	+	4.54831i	0.689002	+	0.171787i	0.570661	−	0.821186i	$-0.306687\pi$
$701$	18.2423	+	4.54831i	0.689002	+	0.171787i	0.118341	+	0.992973i	$0.462243\pi$
$702$	76.0665	+	24.7155i	2.87095	+	0.932827i
$703$	6.09317	−	12.0257i	0.229808	−	0.453560i
$704$	0.245243	−	3.30755i	0.00924295	−	0.124658i
$705$	−58.2064	−	69.3677i	−2.19218	−	2.61254i
$706$	−0.949466	+	1.21526i	−0.0357336	+	0.0457370i
$707$	1.13137	+	2.31966i	0.0425496	+	0.0872397i
$708$	−11.1423	+	22.8451i	−0.418754	+	0.858572i
$709$	15.4848	+	19.8197i	0.581545	+	0.744344i	0.985358	−	0.170498i	$-0.0545375\pi$
$709$	15.4848	+	19.8197i	0.581545	+	0.744344i	−0.403813	+	0.914842i	$0.632315\pi$
$710$	−4.89979	+	23.0517i	−0.183886	+	0.865115i
$711$	6.28760	−	59.8225i	0.235803	−	2.24352i
$712$	0.694911	−	9.93769i	0.0260429	−	0.372431i
$713$	9.49672	+	15.1979i	0.355655	+	0.569167i
$714$	−2.55445	+	1.47481i	−0.0955979	+	0.0551935i
$715$	18.6946	−	64.1779i	0.699140	−	2.40012i
$716$	−0.806412	−	2.21560i	−0.0301370	−	0.0828008i
$717$	74.6082	+	10.4855i	2.78629	+	0.391588i
$718$	−23.3615	+	11.3941i	−0.871842	+	0.425226i
$719$	10.1045	+	14.9805i	0.376833	+	0.558678i	0.968976	−	0.247155i	$-0.0794958\pi$
$719$	10.1045	+	14.9805i	0.376833	+	0.558678i	−0.592143	+	0.805833i	$0.701718\pi$
$720$	21.7783	+	13.6086i	0.811629	+	0.507162i
$721$	1.45769	+	4.48632i	0.0542874	+	0.167079i
$722$	12.2787	+	14.4994i	0.456968	+	0.539612i
$723$	−13.7281	−	18.8951i	−0.510553	−	0.702716i
$724$	2.78943	−	1.12700i	0.103668	−	0.0418847i
$725$	28.3407	+	10.3152i	1.05255	+	0.383095i
$726$	−20.5375	−	28.7725i	−0.762220	−	1.06785i
$727$	−4.89886	−	27.7828i	−0.181689	−	1.03041i	−0.930136	−	0.367214i	$-0.880312\pi$
$727$	−4.89886	−	27.7828i	−0.181689	−	1.03041i	0.748448	−	0.663194i	$-0.230799\pi$
$728$	−1.86077	+	0.0649796i	−0.0689648	+	0.00240830i
$729$	3.38026	+	32.1610i	0.125195	+	1.19115i
$730$	−8.96151	−	0.941892i	−0.331680	−	0.0348610i
$731$	−8.07655	+	19.9902i	−0.298722	+	0.739363i
$732$	−3.63420	+	8.99497i	−0.134324	+	0.332464i
$733$	−21.4030	−	2.24954i	−0.790537	−	0.0830888i	−0.299350	−	0.954143i	$-0.596770\pi$
$733$	−21.4030	−	2.24954i	−0.790537	−	0.0830888i	−0.491186	+	0.871054i	$0.663437\pi$
$734$	2.29285	+	21.8150i	0.0846307	+	0.805208i
$735$	77.6105	−	2.71022i	2.86271	−	0.0999680i
$736$	−1.47805	−	8.38244i	−0.0544817	−	0.308981i
$737$	−8.71974	+	0.572969i	−0.321196	+	0.0211056i
$738$	−23.6705	−	8.61537i	−0.871325	−	0.317136i
$739$	20.6759	−	8.35362i	0.760576	−	0.307293i	0.0386408	−	0.999253i	$-0.487697\pi$
$739$	20.6759	−	8.35362i	0.760576	−	0.307293i	0.721935	+	0.691960i	$0.243253\pi$
$740$	6.37107	+	8.76903i	0.234205	+	0.322356i
$741$	−71.6954	+	36.7353i	−2.63380	+	1.34951i
$742$	−0.806238	−	2.48135i	−0.0295979	−	0.0910931i
$743$	35.7355	+	22.3300i	1.31101	+	0.819210i	0.991716	−	0.128446i	$-0.0409990\pi$
$743$	35.7355	+	22.3300i	1.31101	+	0.819210i	0.319293	+	0.947656i	$0.396555\pi$
$744$	3.78362	+	5.60944i	0.138714	+	0.205652i
$745$	8.86796	−	4.32519i	0.324897	−	0.158463i
$746$	−8.75845	−	1.23092i	−0.320670	−	0.0450672i
$747$	13.0722	+	35.9156i	0.478287	+	1.31408i
$748$	−5.29045	+	7.77283i	−0.193438	+	0.284203i
$749$	−0.833985	+	0.481501i	−0.0304731	+	0.0175937i
$750$	13.6212	+	21.7984i	0.497374	+	0.795965i
$751$	−3.23968	+	46.3296i	−0.118218	+	1.69059i	0.470618	+	0.882337i	$0.344031\pi$
$751$	−3.23968	+	46.3296i	−0.118218	+	1.69059i	−0.588835	+	0.808253i	$0.700413\pi$
$752$	−0.840423	+	7.99609i	−0.0306471	+	0.291587i
$753$	−9.03692	+	42.5154i	−0.329324	+	1.54935i
$754$	−14.6634	−	18.7683i	−0.534010	−	0.683502i
$755$	2.84192	−	5.82681i	0.103428	−	0.212059i
$756$	−1.97386	−	4.04701i	−0.0717886	−	0.147188i
$757$	−15.3097	+	19.5955i	−0.556440	+	0.712210i	−0.981178	−	0.193106i	$-0.938144\pi$
$757$	−15.3097	+	19.5955i	−0.556440	+	0.712210i	0.424738	+	0.905316i	$0.360366\pi$
$758$	−10.8435	−	12.9228i	−0.393854	−	0.469377i
$759$	−69.2522	−	58.6067i	−2.51370	−	2.12729i
$760$	−14.8769	+	3.47009i	−0.539641	+	0.125874i
$761$	32.7941	+	10.6554i	1.18879	+	0.386260i	0.835624	−	0.549303i	$-0.185107\pi$
$761$	32.7941	+	10.6554i	1.18879	+	0.386260i	0.353162	+	0.935562i	$0.385107\pi$
$762$	7.86044	+	1.95983i	0.284754	+	0.0709970i
$763$	4.45231	−	3.00312i	0.161185	−	0.108720i
$764$	−25.9544	+	3.64765i	−0.938998	+	0.131967i
$765$	−34.1788	−	64.2809i	−1.23574	−	2.32408i
$766$	5.17678	−	18.0536i	0.187045	−	0.652302i
$767$	45.2358	−	4.75447i	1.63337	−	0.171674i
$768$	−0.668159	−	3.14344i	−0.0241101	−	0.113429i
$769$	−10.9838	+	13.0900i	−0.396086	+	0.472037i	−0.926822	−	0.375500i	$-0.877471\pi$
$769$	−10.9838	+	13.0900i	−0.396086	+	0.472037i	0.530736	+	0.847537i	$0.321916\pi$
$770$	−3.33010	+	1.75275i	−0.120008	+	0.0631649i
$771$	32.6412	+	56.5362i	1.17554	+	2.03610i
$772$	−2.78712	−	3.09541i	−0.100311	−	0.111406i
$773$	−20.0530	−	13.5259i	−0.721258	−	0.486495i	0.142886	−	0.989739i	$-0.454362\pi$
$773$	−20.0530	−	13.5259i	−0.721258	−	0.486495i	−0.864144	+	0.503245i	$0.832139\pi$
$774$	−50.0877	−	24.4294i	−1.80036	−	0.878097i
$775$	2.13386	+	15.1832i	0.0766505	+	0.545397i
$776$	5.49416	+	0.191860i	0.197229	+	0.00688739i
$777$	−0.224472	−	3.21010i	−0.00805289	−	0.115162i
$778$	−11.2742	+	8.19117i	−0.404199	+	0.293668i
$779$	13.5660	−	6.36335i	0.486051	−	0.227991i
$780$		−	64.7702i		−	2.31914i
$781$	6.98087	−	21.1819i	0.249795	−	0.757949i
$782$	−8.25305	+	22.6751i	−0.295129	+	0.810859i
$783$	27.0408	−	50.8563i	0.966359	−	1.81746i
$784$	−4.95998	−	4.78979i	−0.177142	−	0.171064i
$785$	−19.7648	−	5.66746i	−0.705436	−	0.202280i
$786$	25.1929	+	5.35492i	0.898602	+	0.191004i
$787$	−10.4415	+	11.5965i	−0.372200	+	0.413370i	−0.899925	−	0.436045i	$-0.856379\pi$
$787$	−10.4415	+	11.5965i	−0.372200	+	0.413370i	0.527724	+	0.849416i	$0.323045\pi$
$788$	−1.05173	+	0.262225i	−0.0374662	+	0.00934136i
$789$	73.2397	+	5.12142i	2.60740	+	0.182327i
$790$	−28.1403	+	5.98141i	−1.00119	+	0.212809i
$791$	−1.06998	+	1.85326i	−0.0380441	+	0.0658943i
$792$	−19.0881	−	15.0427i	−0.678265	−	0.534519i
$793$	17.0970	−	3.01466i	0.607132	−	0.107054i
$794$	−4.74908	−	2.52513i	−0.168539	−	0.0896136i
$795$	87.2448	−	25.0171i	3.09426	−	0.887264i
$796$	−0.838405	+	0.0586270i	−0.0297165	+	0.00207798i
$797$	0.292688	−	0.0951000i	0.0103675	−	0.00336861i	−0.303829	−	0.952727i	$-0.598265\pi$
$797$	0.292688	−	0.0951000i	0.0103675	−	0.00336861i	0.314196	+	0.949358i	$0.398265\pi$
$798$	4.29148	+	1.46682i	0.151917	+	0.0519247i
$799$	13.3976	−	18.4402i	0.473972	−	0.652366i
$800$	1.76174	−	7.06594i	0.0622868	−	0.249819i
$801$	−57.5230	−	44.9419i	−2.03247	−	1.58794i
$802$	33.0463	+	5.82696i	1.16691	+	0.205757i
$803$	8.33368	+	1.80798i	0.294089	+	0.0638021i
$804$	−7.95663	+	2.89598i	−0.280609	+	0.102133i
$805$	−7.17718	+	6.46236i	−0.252962	+	0.227768i
$806$	4.92485	−	11.0614i	0.173471	−	0.389621i
$807$	−5.21077	−	20.8993i	−0.183428	−	0.735689i
$808$	7.39107	+	2.98618i	0.260017	+	0.105054i
$809$	1.20309	+	1.08327i	0.0422984	+	0.0380857i	0.690009	−	0.723801i	$-0.257607\pi$
$809$	1.20309	+	1.08327i	0.0422984	+	0.0380857i	−0.647710	+	0.761887i	$0.724273\pi$
$810$	72.7133	−	32.3740i	2.55488	−	1.13751i
$811$	14.6241	−	21.6811i	0.513522	−	0.761327i	−0.479716	−	0.877424i	$-0.659260\pi$
$811$	14.6241	−	21.6811i	0.513522	−	0.761327i	0.993238	+	0.116097i	$0.0370382\pi$
$812$	−0.186610	+	1.32780i	−0.00654874	+	0.0465967i
$813$	11.6493	−	66.0662i	0.408557	−	2.31704i
$814$	−5.09152	−	8.90490i	−0.178458	−	0.312117i
$815$	−11.8010	+	9.90223i	−0.413372	+	0.346860i
$816$	−2.81531	+	8.66465i	−0.0985557	+	0.303323i
$817$	31.3194	−	10.8635i	1.09573	−	0.380066i
$818$	−24.5490	−	17.8359i	−0.858337	−	0.623618i
$819$	−7.22989	+	11.5702i	−0.252633	+	0.404297i
$820$	−0.420452	+	12.0402i	−0.0146828	+	0.420461i
$821$	−37.7141	−	39.0541i	−1.31623	−	1.36300i	−0.888354	−	0.459159i	$-0.848151\pi$
$821$	−37.7141	−	39.0541i	−1.31623	−	1.36300i	−0.427876	−	0.903837i	$-0.640738\pi$
$822$	22.2945	−	23.0867i	0.777611	−	0.805240i
$823$	−0.389944	−	11.1665i	−0.0135926	−	0.389241i	−0.987054	−	0.160389i	$-0.948725\pi$
$823$	−0.389944	−	11.1665i	−0.0135926	−	0.389241i	0.973461	−	0.228852i	$-0.0734972\pi$
$824$	12.6180	+	7.28503i	0.439571	+	0.253786i
$825$	−33.7324	−	69.9049i	−1.17441	−	2.43378i
$826$	−1.96159	−	1.64597i	−0.0682526	−	0.0572707i
$827$	−42.9137	+	26.8155i	−1.49226	+	0.932465i	−0.494252	+	0.869319i	$0.664558\pi$
$827$	−42.9137	+	26.8155i	−1.49226	+	0.932465i	−0.998004	+	0.0631463i	$0.979887\pi$
$828$	−56.9788	−	25.3686i	−1.98015	−	0.881620i
$829$	13.3146	+	29.9051i	0.462435	+	1.03865i	0.982795	+	0.184699i	$0.0591310\pi$
$829$	13.3146	+	29.9051i	0.462435	+	1.03865i	−0.520360	+	0.853947i	$0.674202\pi$
$830$	14.4047	−	11.2542i	0.499994	−	0.390638i
$831$	10.7319	−	5.70627i	0.372287	−	0.197948i
$832$	−4.13685	+	3.99491i	−0.143419	+	0.138498i
$833$	5.38800	+	18.7902i	0.186683	+	0.651041i
$834$	−9.74166	−	24.1115i	−0.337326	−	0.834912i
$835$	−72.5788			−2.51169
$836$	14.3525	−	1.73409i	0.496390	−	0.0599748i
$837$	29.2817			1.01212
$838$	−5.94583	−	14.7164i	−0.205395	−	0.508371i
$839$	5.03514	+	17.5596i	0.173832	+	0.606226i	0.999137	+	0.0415377i	$0.0132257\pi$
$839$	5.03514	+	17.5596i	0.173832	+	0.606226i	−0.825305	+	0.564688i	$0.808997\pi$
$840$	−2.62299	+	2.53299i	−0.0905017	+	0.0873965i
$841$	10.4611	−	5.56227i	0.360728	−	0.191803i
$842$	22.4954	−	17.5753i	0.775243	−	0.605686i
$843$	−6.38708	−	14.3456i	−0.219983	−	0.494089i
$844$	0.451571	+	0.201052i	0.0155437	+	0.00692050i
$845$	−59.6577	+	37.2783i	−2.05229	+	1.28241i
$846$	45.1317	+	37.8700i	1.55166	+	1.30200i
$847$	3.31311	−	1.30634i	0.113840	−	0.0448862i
$848$	−6.97893	−	4.02929i	−0.239658	−	0.138366i
$849$	−1.38105	−	39.5481i	−0.0473975	−	1.35729i
$850$	−14.3411	+	14.8506i	−0.491894	+	0.509371i
$851$	−18.2871	−	18.9369i	−0.626874	−	0.649147i
$852$	0.754188	−	21.5971i	0.0258380	−	0.739905i
$853$	13.9102	−	22.2610i	0.476277	−	0.762202i	−0.519455	−	0.854498i	$-0.673865\pi$
$853$	13.9102	−	22.2610i	0.476277	−	0.762202i	0.995732	+	0.0922960i	$0.0294206\pi$
$854$	−0.790703	−	0.574479i	−0.0270573	−	0.0196583i
$855$	−39.8785	+	104.594i	−1.36382	+	3.57705i
$856$	−0.919152	+	2.82886i	−0.0314160	+	0.0966884i
$857$	40.5809	−	34.0514i	1.38622	−	1.16317i	0.419371	−	0.907815i	$-0.362251\pi$
$857$	40.5809	−	34.0514i	1.38622	−	1.16317i	0.966846	−	0.255360i	$-0.0821939\pi$
$858$	−6.66303	+	60.9328i	−0.227472	+	2.08021i
$859$	5.58024	−	31.6471i	0.190395	−	1.07979i	−0.728430	−	0.685120i	$-0.759750\pi$
$859$	5.58024	−	31.6471i	0.190395	−	1.07979i	0.918825	−	0.394665i	$-0.129139\pi$
$860$	−3.70938	+	26.3936i	−0.126489	+	0.900014i
$861$	2.00006	−	2.96521i	0.0681618	−	0.101054i
$862$	10.6205	−	4.72857i	0.361737	−	0.161056i
$863$	−33.0276	−	29.7382i	−1.12427	−	1.01230i	−0.999798	−	0.0200781i	$-0.993609\pi$
$863$	−33.0276	−	29.7382i	−1.12427	−	1.01230i	−0.124476	−	0.992223i	$-0.539725\pi$
$864$	−12.8949	−	5.20988i	−0.438693	−	0.177244i
$865$	−13.6079	−	54.5782i	−0.462682	−	1.85572i
$866$	−10.9250	+	24.5378i	−0.371245	+	0.833830i
$867$	−21.4059	+	19.2739i	−0.726982	+	0.654577i
$868$	−0.640550	+	0.233141i	−0.0217417	+	0.00791333i
$869$	27.0885	−	2.73219i	0.918913	−	0.0926831i
$870$	−45.9356	−	8.09968i	−1.55736	−	0.274605i
$871$	11.9402	+	9.32867i	0.404577	+	0.316090i
$872$	4.01296	−	16.0951i	0.135896	−	0.545048i
$873$	23.6782	−	32.5903i	0.801386	−	1.10301i
$874$	34.6074	−	13.3745i	1.17061	−	0.452400i
$875$	−2.46282	+	0.800218i	−0.0832585	+	0.0270523i
$876$	8.24269	−	0.576385i	0.278495	−	0.0194743i
$877$	33.5395	−	9.61730i	1.13255	−	0.324753i	0.343542	−	0.939137i	$-0.388373\pi$
$877$	33.5395	−	9.61730i	1.13255	−	0.324753i	0.789007	+	0.614384i	$0.210596\pi$
$878$	−20.4521	−	10.8746i	−0.690224	−	0.366999i
$879$	−90.1029	+	15.8876i	−3.03909	+	0.535874i
$880$	−4.02128	+	10.9057i	−0.135557	+	0.367631i
$881$	24.2068	−	41.9273i	0.815547	−	1.41257i	−0.0933883	−	0.995630i	$-0.529770\pi$
$881$	24.2068	−	41.9273i	0.815547	−	1.41257i	0.908935	−	0.416938i	$-0.136897\pi$
$882$	−49.4213	+	10.5048i	−1.66410	+	0.353716i
$883$	−49.6408	−	3.47122i	−1.67055	−	0.116816i	−0.797135	−	0.603801i	$-0.793652\pi$
$883$	−49.6408	−	3.47122i	−1.67055	−	0.116816i	−0.873411	+	0.486985i	$0.838097\pi$
$884$	15.8192	−	3.94416i	0.532056	−	0.132656i
$885$	59.6051	−	66.1981i	2.00360	−	2.22523i
$886$	3.91461	+	0.832077i	0.131514	+	0.0279542i
$887$	4.81557	+	1.38084i	0.161691	+	0.0463641i	0.355506	−	0.934674i	$-0.384308\pi$
$887$	4.81557	+	1.38084i	0.161691	+	0.0463641i	−0.193815	+	0.981038i	$0.562086\pi$
$888$	−7.14973	−	6.90441i	−0.239929	−	0.231697i
$889$	−0.383154	+	0.720608i	−0.0128506	+	0.0241684i
$890$	−11.9409	+	32.8072i	−0.400258	+	1.09970i
$891$	−71.7357	+	22.9758i	−2.40324	+	0.769720i
$892$		−	22.5281i		−	0.754297i
$893$	−34.9058	+	3.13351i	−1.16808	+	0.104859i
$894$	−7.31952	+	5.31794i	−0.244801	+	0.177859i
$895$	0.576407	+	8.24300i	0.0192671	+	0.275533i
$896$	0.323562	+	0.0112990i	0.0108095	+	0.000377475i
$897$	21.8932	+	155.779i	0.730994	+	5.20129i
$898$	1.19737	+	0.583995i	0.0399567	+	0.0194882i
$899$	−7.22898	−	4.87601i	−0.241100	−	0.162624i
$900$	−35.7060	−	39.6555i	−1.19020	−	1.32185i
$901$	11.4228	+	19.7849i	0.380548	+	0.659129i
$902$	1.63414	−	11.2836i	0.0544108	−	0.375702i
$903$	5.08624	−	6.06155i	0.169260	−	0.201716i
$904$	1.37424	+	6.46528i	0.0457065	+	0.215032i
$905$	−10.4858	+	1.10211i	−0.348561	+	0.0366352i
$906$	−1.63859	+	5.71444i	−0.0544385	+	0.189850i
$907$	−5.42833	−	10.2092i	−0.180245	−	0.338991i	0.776404	−	0.630236i	$-0.217042\pi$
$907$	−5.42833	−	10.2092i	−0.180245	−	0.338991i	−0.956649	+	0.291245i	$0.905931\pi$
$908$	13.5255	−	1.90088i	0.448858	−	0.0630829i
$909$	48.4261	−	32.6638i	1.60619	−	1.08339i
$910$	6.33142	+	1.57860i	0.209884	+	0.0523301i
$911$	−8.37874	−	2.72242i	−0.277600	−	0.0901977i	0.166908	−	0.985972i	$-0.446622\pi$
$911$	−8.37874	−	2.72242i	−0.277600	−	0.0901977i	−0.444508	+	0.895775i	$0.646622\pi$
$912$	12.8820	−	5.50256i	0.426567	−	0.182208i
$913$	−14.7090	+	9.10558i	−0.486797	+	0.301351i
$914$	26.5831	+	31.6805i	0.879290	+	1.04790i
$915$	20.9322	−	26.7920i	0.691997	−	0.885716i
$916$	−2.51217	−	5.15070i	−0.0830043	−	0.170184i
$917$	−1.13747	+	2.33215i	−0.0375624	+	0.0770144i
$918$	24.2738	+	31.0691i	0.801155	+	1.02543i
$919$	−2.56746	+	12.0790i	−0.0846927	+	0.398448i	−0.999991	−	0.00432962i	$-0.998622\pi$
$919$	−2.56746	+	12.0790i	−0.0846927	+	0.398448i	0.915298	+	0.402778i	$0.131955\pi$
$920$	−3.11812	+	29.6669i	−0.102801	+	0.978089i
$921$	1.71430	−	24.5156i	0.0564881	−	0.807817i
$922$	10.5689	+	16.9138i	0.348068	+	0.557025i
$923$	−33.4908	+	19.3359i	−1.10236	+	0.636450i
$924$	2.72816	−	2.11309i	0.0897499	−	0.0695155i
$925$	−7.70322	−	21.1644i	−0.253280	−	0.695882i
$926$	4.27871	+	0.601333i	0.140607	+	0.0197610i
$927$	95.9591	−	46.8024i	3.15171	−	1.53719i
$928$	2.31590	+	3.43346i	0.0760231	+	0.112709i
$929$	−12.4249	−	7.76395i	−0.407648	−	0.254727i	0.310562	−	0.950553i	$-0.399483\pi$
$929$	−12.4249	−	7.76395i	−0.407648	−	0.254727i	−0.718210	+	0.695826i	$0.755038\pi$
$930$	−7.32769	−	22.5523i	−0.240284	−	0.739519i
$931$	16.3122	−	25.2436i	0.534612	−	0.827325i
$932$	−4.32843	−	5.95757i	−0.141782	−	0.195147i
$933$	6.74938	−	2.72693i	0.220965	−	0.0892756i
$934$	−17.9712	−	6.54099i	−0.588037	−	0.214028i
$935$	25.3313	−	21.0749i	0.828420	−	0.689222i
$936$	7.31762	+	41.5003i	0.239184	+	1.35648i
$937$	−36.0102	+	1.25750i	−1.17640	+	0.0410809i	−0.616416	−	0.787421i	$-0.711416\pi$
$937$	−36.0102	+	1.25750i	−1.17640	+	0.0410809i	−0.559986	+	0.828502i	$0.689194\pi$
$938$	−0.0891661	−	0.848359i	−0.00291138	−	0.0276999i
$939$	16.2313	+	1.70597i	0.529687	+	0.0556723i
$940$	10.5555	−	26.1257i	0.344282	−	0.852127i
$941$	3.49842	−	8.65888i	0.114045	−	0.282272i	−0.859357	−	0.511377i	$-0.829136\pi$
$941$	3.49842	−	8.65888i	0.114045	−	0.282272i	0.973402	+	0.229105i	$0.0735800\pi$
$942$	18.7511	+	1.97082i	0.610943	+	0.0642127i
$943$	−3.05852	−	29.0999i	−0.0995992	−	0.947623i
$944$	−7.90438	+	0.276027i	−0.257266	+	0.00898392i
$945$	2.74021	+	15.5405i	0.0891390	+	0.505533i
$946$	6.20477	−	24.4483i	0.201734	−	0.794882i
$947$	−32.4701	−	11.8181i	−1.05514	−	0.384038i	−0.244537	−	0.969640i	$-0.578636\pi$
$947$	−32.4701	−	11.8181i	−1.05514	−	0.384038i	−0.810599	+	0.585602i	$0.800858\pi$
$948$	24.4598	−	9.88239i	0.794416	−	0.320965i
$949$	−8.69124	−	11.9625i	−0.282129	−	0.388318i
$950$	31.7028	+	1.58951i	1.02857	+	0.0515704i
$951$	10.9461	+	33.6887i	0.354952	+	1.09243i
$952$	−0.778371	−	0.486380i	−0.0252272	−	0.0157637i
$953$	31.4600	+	46.6414i	1.01909	+	1.51086i	0.851051	+	0.525082i	$0.175965\pi$
$953$	31.4600	+	46.6414i	1.01909	+	1.51086i	0.168038	+	0.985780i	$0.446257\pi$
$954$	−53.0741	+	25.8860i	−1.71834	+	0.838090i
$955$	90.9600	+	12.7836i	2.94339	+	0.413667i
$956$	8.01834	+	22.0302i	0.259332	+	0.712508i
$957$	42.3809	+	12.3453i	1.36998	+	0.399067i
$958$	−5.20713	+	3.00634i	−0.168235	+	0.0971304i
$959$	1.71340	+	2.74201i	0.0553286	+	0.0885442i
$960$	−0.785641	+	11.2352i	−0.0253565	+	0.362614i
$961$	−2.77702	+	26.4215i	−0.0895812	+	0.852308i
$962$	−3.69802	+	17.3978i	−0.119229	+	0.560928i
$963$	13.4187	+	17.1752i	0.432412	+	0.553463i
$964$	3.18590	−	6.53207i	0.102611	−	0.210384i
$965$	6.39921	+	13.1203i	0.205998	+	0.422358i
$966$	5.45235	−	6.97869i	0.175427	−	0.224536i
$967$	−29.8995	−	35.6328i	−0.961503	−	1.14588i	−0.989246	−	0.146260i	$-0.953276\pi$
$967$	−29.8995	−	35.6328i	−0.961503	−	1.14588i	0.0277429	−	0.999615i	$-0.491168\pi$
$968$	4.90492	−	9.84590i	0.157650	−	0.316459i
$969$	−39.4268	−	4.75042i	−1.26657	−	0.152605i
$970$	−18.3236	−	5.95371i	−0.588336	−	0.191162i
$971$	15.9734	+	3.98262i	0.512611	+	0.127808i	0.489635	−	0.871928i	$-0.337130\pi$
$971$	15.9734	+	3.98262i	0.512611	+	0.127808i	0.0229764	+	0.999736i	$0.492686\pi$
$972$	−25.9191	+	17.4827i	−0.831357	+	0.560757i
$973$	2.59437	−	0.364615i	0.0831718	−	0.0116890i
$974$	13.7180	+	25.7997i	0.439552	+	0.826677i
$975$	−37.0971	+	129.373i	−1.18806	+	4.14325i
$976$	−3.00225	+	0.315550i	−0.0960998	+	0.0101005i
$977$	−4.90760	−	23.0885i	−0.157008	−	0.738665i	−0.984245	−	0.176811i	$-0.943422\pi$
$977$	−4.90760	−	23.0885i	−0.157008	−	0.738665i	0.827237	−	0.561854i	$-0.189912\pi$
$978$	9.08018	−	10.8213i	0.290352	−	0.346028i
$979$	14.6084	−	29.6352i	0.466885	−	0.947144i
$980$	12.0824	+	20.9274i	0.385959	+	0.668501i
$981$	−81.3325	−	90.3289i	−2.59675	−	2.88398i
$982$	−0.523083	−	0.352824i	−0.0166923	−	0.0112591i
$983$	−46.2533	−	22.5592i	−1.47525	−	0.719528i	−0.487148	−	0.873319i	$-0.661963\pi$
$983$	−46.2533	−	22.5592i	−1.47525	−	0.719528i	−0.988103	+	0.153791i	$0.950852\pi$
$984$	−1.53750	−	10.9399i	−0.0490136	−	0.348750i
$985$	3.79641	+	0.132573i	0.120964	+	0.00422414i
$986$	−0.819005	−	11.7123i	−0.0260824	−	0.372996i
$987$	−6.76775	+	4.91706i	−0.215420	+	0.156512i
$988$	−20.5666	−	14.3316i	−0.654312	−	0.455950i
$989$		−	64.7330i		−	2.05839i
$990$	49.7735	+	69.1156i	1.58190	+	2.19664i
$991$	−0.705768	+	1.93908i	−0.0224195	+	0.0615970i	−0.950398	−	0.311038i	$-0.899323\pi$
$991$	−0.705768	+	1.93908i	−0.0224195	+	0.0615970i	0.927978	+	0.372635i	$0.121546\pi$
$992$	−0.988449	+	1.85900i	−0.0313833	+	0.0590234i
$993$	56.4003	+	54.4651i	1.78981	+	1.72840i
$994$	2.09278	+	0.600095i	0.0663790	+	0.0190339i
$995$	2.88109	+	0.612394i	0.0913366	+	0.0194142i
$996$	−11.2162	+	12.4568i	−0.355398	+	0.394709i
$997$	13.4091	−	3.34326i	0.424669	−	0.105882i	−0.0237234	−	0.999719i	$-0.507552\pi$
$997$	13.4091	−	3.34326i	0.424669	−	0.105882i	0.448393	+	0.893837i	$0.351997\pi$
$998$	31.2646	+	2.18624i	0.989665	+	0.0692041i
$999$	−42.0737	+	8.94305i	−1.33115	+	0.282946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.13.10	✓	240
11.6	odd	10		418.2.v.b.127.1	yes	240
19.3	odd	18		418.2.v.b.79.1	yes	240
209.193	even	90	inner	418.2.v.a.193.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.13.10	✓	240	1.1	even	1	trivial
418.2.v.a.193.10	yes	240	209.193	even	90	inner
418.2.v.b.79.1	yes	240	19.3	odd	18
418.2.v.b.127.1	yes	240	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.374607 + 0.927184i) q^{2} +(0.885806 + 3.08917i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(3.09438 - 1.64531i) q^{5} +(-2.53240 + 1.97853i) q^{6} +(-0.131685 - 0.295769i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-6.21419 + 3.88306i) q^{9} +O(q^{10})\)	\(q+(0.374607 + 0.927184i) q^{2} +(0.885806 + 3.08917i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(3.09438 - 1.64531i) q^{5} +(-2.53240 + 1.97853i) q^{6} +(-0.131685 - 0.295769i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-6.21419 + 3.88306i) q^{9} +(2.68468 + 2.25272i) q^{10} +(-2.29389 - 2.39543i) q^{11} +(-2.78312 - 1.60683i) q^{12} +(0.200703 + 5.74739i) q^{13} +(0.224902 - 0.232893i) q^{14} +(7.82368 + 8.10166i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-1.50229 + 2.40417i) q^{17} +(-5.92819 - 4.30708i) q^{18} +(4.30368 - 0.691628i) q^{19} +(-1.08298 + 3.33308i) q^{20} +(0.797034 - 0.668791i) q^{21} +(1.36170 - 3.02420i) q^{22} +(1.47805 - 8.38244i) q^{23} +(0.447256 - 3.18239i) q^{24} +(4.07219 - 6.03726i) q^{25} +(-5.25370 + 2.33910i) q^{26} +(-10.3354 - 9.30600i) q^{27} +(0.300185 + 0.121282i) q^{28} +(1.00192 + 4.01848i) q^{29} +(-4.58092 + 10.2889i) q^{30} +(-1.56465 + 1.40882i) q^{31} +(0.939693 - 0.342020i) q^{32} +(5.36796 - 9.20810i) q^{33} +(-2.79187 - 0.492282i) q^{34} +(-0.894116 - 0.698560i) q^{35} +(1.77272 - 7.10998i) q^{36} +(1.81791 - 2.50214i) q^{37} +(2.25345 + 3.73121i) q^{38} +(-17.5769 + 5.71108i) q^{39} +(-3.49607 + 0.244469i) q^{40} +(3.30445 - 0.947537i) q^{41} +(0.918667 + 0.488464i) q^{42} +(7.48959 - 1.32062i) q^{43} +(3.31409 + 0.129662i) q^{44} +(-12.8402 + 22.2400i) q^{45} +(8.32575 - 1.76969i) q^{46} +(-8.02055 - 0.560852i) q^{47} +(3.11821 - 0.777456i) q^{48} +(4.61378 - 5.12412i) q^{49} +(7.12312 + 1.51407i) q^{50} +(-8.75762 - 2.51121i) q^{51} +(-4.13685 - 3.99491i) q^{52} +(3.78327 - 7.11530i) q^{53} +(4.75668 - 13.0689i) q^{54} +(-11.0394 - 3.63822i) q^{55} +0.323759i q^{56} +(5.94878 + 12.6822i) q^{57} +(-3.35055 + 2.43431i) q^{58} +(-0.551718 - 7.88994i) q^{59} +(-11.2558 - 0.393060i) q^{60} +(-0.420135 - 2.98941i) q^{61} +(-1.89237 - 0.922968i) q^{62} +(1.96680 + 1.32663i) q^{63} +(0.669131 + 0.743145i) q^{64} +(10.0773 + 17.4544i) q^{65} +(10.5485 + 1.52768i) q^{66} +(1.69360 - 2.01835i) q^{67} +(-0.589417 - 2.77299i) q^{68} +(27.2041 - 2.85926i) q^{69} +(0.312752 - 1.09069i) q^{70} +(3.15696 + 5.93738i) q^{71} +(7.25633 - 1.01981i) q^{72} +(-2.13158 + 1.43777i) q^{73} +(3.00095 + 0.748221i) q^{74} +(22.2573 + 7.23184i) q^{75} +(-2.61536 + 3.48710i) q^{76} +(-0.406424 + 0.993902i) q^{77} +(-11.8796 - 14.1576i) q^{78} +(-5.05391 + 6.46871i) q^{79} +(-1.53632 - 3.14992i) q^{80} +(9.95603 - 20.4129i) q^{81} +(2.11641 + 2.70888i) q^{82} +(1.08446 - 5.10196i) q^{83} +(-0.108757 + 1.03475i) q^{84} +(-0.693055 + 9.91114i) q^{85} +(4.03010 + 6.44951i) q^{86} +(-11.5263 + 6.65470i) q^{87} +(1.12126 + 3.12134i) q^{88} +(3.40719 + 9.36118i) q^{89} +(-25.4306 - 3.57403i) q^{90} +(1.67347 - 0.816206i) q^{91} +(4.75971 + 7.05656i) q^{92} +(-5.73807 - 3.58554i) q^{93} +(-2.48454 - 7.64662i) q^{94} +(12.1793 - 9.22106i) q^{95} +(1.88894 + 2.59991i) q^{96} +(-5.09720 + 2.05940i) q^{97} +(6.47935 + 2.35829i) q^{98} +(23.5562 + 5.97838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

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