LMFDB - Embedded newform 414.2.m.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	414.13
Dual form			414.2.m.a.223.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(-0.431117 - 1.67754i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(2.15343 + 3.02407i) q^{5} +(-1.72628 - 0.141264i) q^{6} +(-1.21686 - 5.01596i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.62828 + 1.44643i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(-0.431117 - 1.67754i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(2.15343 + 3.02407i) q^{5} +(-1.72628 - 0.141264i) q^{6} +(-1.21686 - 5.01596i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.62828 + 1.44643i) q^{9} +(3.56206 - 1.04592i) q^{10} +(-1.22830 - 0.236735i) q^{11} +(-0.698106 + 1.58513i) q^{12} +(0.668652 - 2.75622i) q^{13} +(-5.13808 - 0.490627i) q^{14} +(4.14461 - 4.91619i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.942149 - 6.55279i) q^{17} +(0.507252 + 2.95680i) q^{18} +(0.510319 - 3.54935i) q^{19} +(0.176645 - 3.70824i) q^{20} +(-7.88986 + 4.20379i) q^{21} +(-0.625453 + 1.08332i) q^{22} +(2.00181 + 4.35807i) q^{23} +(1.26962 + 1.17816i) q^{24} +(-2.87239 + 8.29923i) q^{25} +(-2.38594 - 1.53335i) q^{26} +(3.55954 + 3.78546i) q^{27} +(-2.14415 + 4.69502i) q^{28} +(-0.959618 + 0.754652i) q^{29} +(-3.29023 - 5.52459i) q^{30} +(-0.144500 - 3.03342i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.132407 + 2.16258i) q^{33} +(-6.50054 - 1.25288i) q^{34} +(12.5482 - 14.4814i) q^{35} +(2.96009 + 0.487722i) q^{36} +(1.13582 + 2.48711i) q^{37} +(-3.18723 - 1.64313i) q^{38} +(-4.91194 + 0.0665624i) q^{39} +(-3.44651 - 1.37978i) q^{40} +(3.27499 + 4.59908i) q^{41} +(1.39207 + 8.83085i) q^{42} +(-0.0514617 + 1.08031i) q^{43} +(0.819169 + 0.945371i) q^{44} +(-10.0339 - 4.83330i) q^{45} +(4.77311 - 0.466330i) q^{46} +(2.78533 + 4.82433i) q^{47} +(1.52861 - 0.814459i) q^{48} +(-17.4573 + 8.99984i) q^{49} +(6.90331 + 5.42882i) q^{50} +(-10.5864 + 4.40551i) q^{51} +(-2.22938 + 1.75320i) q^{52} +(7.49162 + 2.19974i) q^{53} +(4.74147 - 2.12566i) q^{54} +(-1.92915 - 4.22426i) q^{55} +(3.73552 + 3.56181i) q^{56} +(-6.17418 + 0.674102i) q^{57} +(0.399286 + 1.15366i) q^{58} +(3.36911 - 13.8877i) q^{59} +(-6.29687 + 1.30235i) q^{60} +(4.86719 + 2.50921i) q^{61} +(-2.91384 - 0.855582i) q^{62} +(10.4535 + 11.4232i) q^{63} +(0.415415 - 0.909632i) q^{64} +(9.77489 - 3.91328i) q^{65} +(2.08695 + 0.582186i) q^{66} +(6.37707 - 1.22908i) q^{67} +(-3.31009 + 5.73324i) q^{68} +(6.44781 - 5.23695i) q^{69} +(-9.58080 - 16.5944i) q^{70} +(0.548659 + 0.633186i) q^{71} +(1.42905 - 2.63777i) q^{72} +(0.214787 - 1.49388i) q^{73} +(2.72181 - 0.259902i) q^{74} +(15.1606 + 1.24061i) q^{75} +(-2.59520 + 2.47452i) q^{76} +(0.307212 + 6.44918i) q^{77} +(-1.54364 + 4.66355i) q^{78} +(1.59555 + 1.52136i) q^{79} +(-2.43113 + 2.80568i) q^{80} +(4.81568 - 7.60324i) q^{81} +(5.41728 - 1.59066i) q^{82} +(0.855896 - 1.20194i) q^{83} +(8.80046 + 1.57279i) q^{84} +(17.7872 - 16.9601i) q^{85} +(1.00407 + 0.401968i) q^{86} +(1.67967 + 1.28445i) q^{87} +(1.16130 - 0.464915i) q^{88} +(-0.464649 - 0.298612i) q^{89} +(-7.84925 + 7.90123i) q^{90} -14.6387 q^{91} +(1.12045 - 4.66311i) q^{92} +(-5.02638 + 1.55016i) q^{93} +(5.46999 - 1.05425i) q^{94} +(11.8324 - 6.10003i) q^{95} +(-0.269704 - 1.71092i) q^{96} +(13.1646 - 1.25707i) q^{97} +(2.79515 + 19.4407i) q^{98} +(3.57073 - 1.15444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	−0.431117	−	1.67754i	−0.248905	−	0.968528i
$3$	−0.431117	−	1.67754i	−0.248905	−	0.968528i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	2.15343	+	3.02407i	0.963043	+	1.35240i	0.935707	+	0.352778i	$0.114763\pi$
$5$	2.15343	+	3.02407i	0.963043	+	1.35240i	0.0273357	+	0.999626i	$0.491298\pi$
$6$	−1.72628	−	0.141264i	−0.704751	−	0.0576708i
$7$	−1.21686	−	5.01596i	−0.459929	−	1.89585i	−0.444095	−	0.895980i	$-0.646475\pi$
$7$	−1.21686	−	5.01596i	−0.459929	−	1.89585i	−0.0158348	−	0.999875i	$-0.505041\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−2.62828	+	1.44643i	−0.876092	+	0.482143i
$10$	3.56206	−	1.04592i	1.12642	−	0.330748i
$11$	−1.22830	−	0.236735i	−0.370346	−	0.0713784i	0.000682423	−	1.00000i	$-0.499783\pi$
$11$	−1.22830	−	0.236735i	−0.370346	−	0.0713784i	−0.371029	+	0.928621i	$0.620995\pi$
$12$	−0.698106	+	1.58513i	−0.201526	+	0.457589i
$13$	0.668652	−	2.75622i	0.185451	−	0.764438i	−0.800766	−	0.598978i	$-0.795574\pi$
$13$	0.668652	−	2.75622i	0.185451	−	0.764438i	0.986216	−	0.165460i	$-0.0529110\pi$
$14$	−5.13808	−	0.490627i	−1.37321	−	0.131126i
$15$	4.14461	−	4.91619i	1.07013	−	1.26935i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−0.942149	−	6.55279i	−0.228505	−	1.58928i	−0.704413	−	0.709790i	$-0.748790\pi$
$17$	−0.942149	−	6.55279i	−0.228505	−	1.58928i	0.475909	−	0.879495i	$-0.342119\pi$
$18$	0.507252	+	2.95680i	0.119561	+	0.696926i
$19$	0.510319	−	3.54935i	0.117075	−	0.814277i	−0.843673	−	0.536857i	$-0.819612\pi$
$19$	0.510319	−	3.54935i	0.117075	−	0.814277i	0.960749	−	0.277420i	$-0.0894793\pi$
$20$	0.176645	−	3.70824i	0.0394991	−	0.829188i
$21$	−7.88986	+	4.20379i	−1.72171	+	0.917343i
$22$	−0.625453	+	1.08332i	−0.133347	+	0.230964i
$23$	2.00181	+	4.35807i	0.417407	+	0.908720i
$23$	2.00181	+	4.35807i	0.417407	+	0.908720i
$24$	1.26962	+	1.17816i	0.259161	+	0.240490i
$25$	−2.87239	+	8.29923i	−0.574478	+	1.65985i
$26$	−2.38594	−	1.53335i	−0.467921	−	0.300714i
$27$	3.55954	+	3.78546i	0.685033	+	0.728512i
$28$	−2.14415	+	4.69502i	−0.405205	+	0.887276i
$29$	−0.959618	+	0.754652i	−0.178197	+	0.140135i	−0.703273	−	0.710919i	$-0.748279\pi$
$29$	−0.959618	+	0.754652i	−0.178197	+	0.140135i	0.525077	+	0.851055i	$0.324037\pi$
$30$	−3.29023	−	5.52459i	−0.600711	−	1.00865i
$31$	−0.144500	−	3.03342i	−0.0259529	−	0.544818i	−0.973981	−	0.226631i	$-0.927229\pi$
$31$	−0.144500	−	3.03342i	−0.0259529	−	0.544818i	0.948028	−	0.318187i	$-0.103074\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	0.132407	+	2.16258i	0.0230492	+	0.376457i
$34$	−6.50054	−	1.25288i	−1.11483	−	0.214866i
$35$	12.5482	−	14.4814i	2.12103	−	2.44780i
$36$	2.96009	+	0.487722i	0.493348	+	0.0812870i
$37$	1.13582	+	2.48711i	0.186728	+	0.408878i	0.979725	−	0.200348i	$-0.0642073\pi$
$37$	1.13582	+	2.48711i	0.186728	+	0.408878i	−0.792996	+	0.609226i	$0.791480\pi$
$38$	−3.18723	−	1.64313i	−0.517037	−	0.266551i
$39$	−4.91194	+	0.0665624i	−0.786539	+	0.0106585i
$40$	−3.44651	−	1.37978i	−0.544942	−	0.218162i
$41$	3.27499	+	4.59908i	0.511468	+	0.718256i	0.986871	−	0.161512i	$-0.0516370\pi$
$41$	3.27499	+	4.59908i	0.511468	+	0.718256i	−0.475403	+	0.879768i	$0.657698\pi$
$42$	1.39207	+	8.83085i	0.214800	+	1.36263i
$43$	−0.0514617	+	1.08031i	−0.00784784	+	0.164746i	0.991541	+	0.129793i	$0.0414313\pi$
$43$	−0.0514617	+	1.08031i	−0.00784784	+	0.164746i	−0.999389	+	0.0349534i	$0.988872\pi$
$44$	0.819169	+	0.945371i	0.123494	+	0.142520i
$45$	−10.0339	−	4.83330i	−1.49577	−	0.720506i
$46$	4.77311	−	0.466330i	0.703756	−	0.0687567i
$47$	2.78533	+	4.82433i	0.406282	+	0.703701i	0.994470	−	0.105023i	$-0.0334917\pi$
$47$	2.78533	+	4.82433i	0.406282	+	0.703701i	−0.588188	+	0.808724i	$0.700158\pi$
$48$	1.52861	−	0.814459i	0.220636	−	0.117557i
$49$	−17.4573	+	8.99984i	−2.49389	+	1.28569i
$50$	6.90331	+	5.42882i	0.976275	+	0.767751i
$51$	−10.5864	+	4.40551i	−1.48239	+	0.616895i
$52$	−2.22938	+	1.75320i	−0.309159	+	0.243125i
$53$	7.49162	+	2.19974i	1.02905	+	0.302157i	0.752326	−	0.658791i	$-0.228932\pi$
$53$	7.49162	+	2.19974i	1.02905	+	0.302157i	0.276728	+	0.960948i	$0.410750\pi$
$54$	4.74147	−	2.12566i	0.645233	−	0.289266i
$55$	−1.92915	−	4.22426i	−0.260127	−	0.569599i
$56$	3.73552	+	3.56181i	0.499180	+	0.475967i
$57$	−6.17418	+	0.674102i	−0.817790	+	0.0892870i
$58$	0.399286	+	1.15366i	0.0524289	+	0.151483i
$59$	3.36911	−	13.8877i	0.438621	−	1.80802i	−0.137318	−	0.990527i	$-0.543848\pi$
$59$	3.36911	−	13.8877i	0.438621	−	1.80802i	0.575939	−	0.817493i	$-0.304637\pi$
$60$	−6.29687	+	1.30235i	−0.812923	+	0.168133i
$61$	4.86719	+	2.50921i	0.623180	+	0.321271i	0.740738	−	0.671795i	$-0.234476\pi$
$61$	4.86719	+	2.50921i	0.623180	+	0.321271i	−0.117558	+	0.993066i	$0.537507\pi$
$62$	−2.91384	−	0.855582i	−0.370059	−	0.108659i
$63$	10.4535	+	11.4232i	1.31701	+	1.43919i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	9.77489	−	3.91328i	1.21243	−	0.485382i
$66$	2.08695	+	0.582186i	0.256886	+	0.0716622i
$67$	6.37707	−	1.22908i	0.779083	−	0.150156i	0.215820	−	0.976433i	$-0.430758\pi$
$67$	6.37707	−	1.22908i	0.779083	−	0.150156i	0.563264	+	0.826277i	$0.309546\pi$
$68$	−3.31009	+	5.73324i	−0.401407	+	0.695257i
$69$	6.44781	−	5.23695i	0.776226	−	0.630455i
$70$	−9.58080	−	16.5944i	−1.14513	−	1.98341i
$71$	0.548659	+	0.633186i	0.0651138	+	0.0751453i	0.787372	−	0.616478i	$-0.211441\pi$
$71$	0.548659	+	0.633186i	0.0651138	+	0.0751453i	−0.722258	+	0.691624i	$0.756896\pi$
$72$	1.42905	−	2.63777i	0.168415	−	0.310864i
$73$	0.214787	−	1.49388i	0.0251390	−	0.174845i	−0.973384	−	0.229181i	$-0.926395\pi$
$73$	0.214787	−	1.49388i	0.0251390	−	0.174845i	0.998523	+	0.0543360i	$0.0173042\pi$
$74$	2.72181	−	0.259902i	0.316404	−	0.0302129i
$75$	15.1606	+	1.24061i	1.75060	+	0.143254i
$76$	−2.59520	+	2.47452i	−0.297690	+	0.283847i
$77$	0.307212	+	6.44918i	0.0350101	+	0.734952i
$78$	−1.54364	+	4.66355i	−0.174782	+	0.528043i
$79$	1.59555	+	1.52136i	0.179514	+	0.171166i	0.774508	−	0.632564i	$-0.217997\pi$
$79$	1.59555	+	1.52136i	0.179514	+	0.171166i	−0.594995	+	0.803730i	$0.702846\pi$
$80$	−2.43113	+	2.80568i	−0.271809	+	0.313684i
$81$	4.81568	−	7.60324i	0.535076	−	0.844804i
$82$	5.41728	−	1.59066i	0.598239	−	0.175659i
$83$	0.855896	−	1.20194i	0.0939468	−	0.131930i	−0.764927	−	0.644117i	$-0.777225\pi$
$83$	0.855896	−	1.20194i	0.0939468	−	0.131930i	0.858874	+	0.512187i	$0.171164\pi$
$84$	8.80046	+	1.57279i	0.960209	+	0.171605i
$85$	17.7872	−	16.9601i	1.92930	−	1.83958i
$86$	1.00407	+	0.401968i	0.108271	+	0.0433453i
$87$	1.67967	+	1.28445i	0.180079	+	0.137708i
$88$	1.16130	−	0.464915i	0.123795	−	0.0495601i
$89$	−0.464649	−	0.298612i	−0.0492527	−	0.0316528i	0.515783	−	0.856719i	$-0.327501\pi$
$89$	−0.464649	−	0.298612i	−0.0492527	−	0.0316528i	−0.565035	+	0.825067i	$0.691138\pi$
$90$	−7.84925	+	7.90123i	−0.827383	+	0.832863i
$91$	−14.6387			−1.53456
$92$	1.12045	−	4.66311i	0.116815	−	0.486163i
$93$	−5.02638	+	1.55016i	−0.521212	+	0.160744i
$94$	5.46999	−	1.05425i	0.564186	−	0.108738i
$95$	11.8324	−	6.10003i	1.21398	−	0.625850i
$96$	−0.269704	−	1.71092i	−0.0275266	−	0.174620i
$97$	13.1646	−	1.25707i	1.33666	−	0.127636i	0.597883	−	0.801583i	$-0.296009\pi$
$97$	13.1646	−	1.25707i	1.33666	−	0.127636i	0.738779	+	0.673948i	$0.235403\pi$
$98$	2.79515	+	19.4407i	0.282353	+	1.96381i
$99$	3.57073	−	1.15444i	0.358872	−	0.116026i
$100$	7.38809	−	4.74804i	0.738809	−	0.474804i
$101$	7.99526	−	11.2278i	0.795558	−	1.11720i	−0.195093	−	0.980785i	$-0.562501\pi$
$101$	7.99526	−	11.2278i	0.795558	−	1.11720i	0.990651	−	0.136420i	$-0.0435597\pi$
$102$	0.700741	+	11.4450i	0.0693837	+	1.13323i
$103$	5.73939	+	16.5829i	0.565519	+	1.63396i	0.757702	+	0.652600i	$0.226322\pi$
$103$	5.73939	+	16.5829i	0.565519	+	1.63396i	−0.192183	+	0.981359i	$0.561557\pi$
$104$	0.927620	+	2.68018i	0.0909606	+	0.262813i
$105$	−29.7028	−	14.8069i	−2.89870	−	1.44501i
$106$	4.52903	−	6.36013i	0.439898	−	0.617750i
$107$	−2.96493	+	1.90545i	−0.286631	+	0.184207i	−0.676053	−	0.736853i	$-0.736311\pi$
$107$	−2.96493	+	1.90545i	−0.286631	+	0.184207i	0.389422	+	0.921059i	$0.372675\pi$
$108$	−0.457970	−	5.17593i	−0.0440682	−	0.498054i
$109$	0.194710	+	1.35424i	0.0186499	+	0.129713i	0.997019	−	0.0771527i	$-0.0245829\pi$
$109$	0.194710	+	1.35424i	0.0186499	+	0.129713i	−0.978369	+	0.206865i	$0.933674\pi$
$110$	−4.62289	+	0.441432i	−0.440775	+	0.0420889i
$111$	3.68255	−	2.97762i	0.349532	−	0.282624i
$112$	4.58768	−	2.36511i	0.433495	−	0.223482i
$113$	−9.45890	+	1.82305i	−0.889818	+	0.171498i	−0.613619	−	0.789602i	$-0.710287\pi$
$113$	−9.45890	+	1.82305i	−0.889818	+	0.171498i	−0.276199	+	0.961100i	$0.589075\pi$
$114$	−1.38235	+	6.05508i	−0.129469	+	0.567111i
$115$	−8.86833	+	15.4384i	−0.826976	+	1.43964i
$116$	1.22081			0.113349
$117$	2.22928	+	8.21127i	0.206097	+	0.759132i
$118$	−12.0219	−	7.72602i	−1.10671	−	0.711238i
$119$	−31.7221	+	12.6996i	−2.90796	+	1.16417i
$120$	−0.828780	+	6.37651i	−0.0756569	+	0.582093i
$121$	−8.75937	−	3.50672i	−0.796306	−	0.318793i
$122$	3.96311	−	3.77882i	0.358803	−	0.342118i
$123$	6.30324	−	7.47667i	0.568344	−	0.674149i
$124$	−1.76155	+	2.47375i	−0.158192	+	0.222149i
$125$	−13.4726	+	3.95591i	−1.20503	+	0.353827i
$126$	14.2140	−	6.14237i	1.26628	−	0.547206i
$127$	8.45301	−	9.75529i	0.750083	−	0.865642i	−0.244493	−	0.969651i	$-0.578622\pi$
$127$	8.45301	−	9.75529i	0.750083	−	0.865642i	0.994576	+	0.104009i	$0.0331670\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	1.83446	−	0.379412i	0.161515	−	0.0334054i
$130$	−0.500995	−	10.5172i	−0.0439402	−	0.922418i
$131$	−5.51387	+	5.25747i	−0.481749	+	0.459347i	−0.891612	−	0.452800i	$-0.850425\pi$
$131$	−5.51387	+	5.25747i	−0.481749	+	0.459347i	0.409863	+	0.912147i	$0.365577\pi$
$132$	1.23274	−	1.78175i	0.107296	−	0.155082i
$133$	−18.4244	+	1.75932i	−1.59760	+	0.152552i
$134$	0.924254	−	6.42833i	0.0798434	−	0.555323i
$135$	−3.78227	+	18.9160i	−0.325526	+	1.62803i
$136$	4.33529	+	5.00319i	0.371748	+	0.429020i
$137$	4.71762	+	8.17116i	0.403054	+	0.698109i	0.994093	−	0.108533i	$-0.0346154\pi$
$137$	4.71762	+	8.17116i	0.403054	+	0.698109i	−0.591039	+	0.806643i	$0.701282\pi$
$138$	−2.84005	−	7.80603i	−0.241761	−	0.664493i
$139$	−6.76112	+	11.7106i	−0.573471	+	0.993280i	0.422735	+	0.906253i	$0.361070\pi$
$139$	−6.76112	+	11.7106i	−0.573471	+	0.993280i	−0.996206	+	0.0870270i	$0.972263\pi$
$140$	−18.8153	+	3.62636i	−1.59019	+	0.306483i
$141$	6.89221	−	6.75235i	0.580428	−	0.568650i
$142$	0.777810	−	0.311388i	0.0652723	−	0.0261311i
$143$	−1.47380	+	3.22717i	−0.123245	+	0.269870i
$144$	−2.02530	−	2.21318i	−0.168775	−	0.184432i
$145$	−4.34859	−	1.27686i	−0.361131	−	0.106038i
$146$	−1.34147	−	0.691575i	−0.111021	−	0.0572351i
$147$	22.6237	+	25.4053i	1.86597	+	2.09539i
$148$	0.644610	−	2.65712i	0.0529867	−	0.218414i
$149$	5.12622	+	14.8112i	0.419956	+	1.21338i	0.934514	+	0.355928i	$0.115835\pi$
$149$	5.12622	+	14.8112i	0.419956	+	1.21338i	−0.514557	+	0.857456i	$0.672044\pi$
$150$	6.13093	−	13.9210i	0.500589	−	1.13665i
$151$	−5.18996	−	4.94862i	−0.422353	−	0.402713i	0.448872	−	0.893596i	$-0.351826\pi$
$151$	−5.18996	−	4.94862i	−0.422353	−	0.402713i	−0.871226	+	0.490883i	$0.836674\pi$
$152$	1.48962	+	3.26180i	0.120824	+	0.264567i
$153$	11.9544	+	15.8598i	0.966454	+	1.28219i
$154$	6.19496	+	1.81900i	0.499204	+	0.146579i
$155$	8.86209	−	6.96923i	0.711821	−	0.559782i
$156$	3.90219	+	2.98404i	0.312425	+	0.238914i
$157$	−8.97857	−	7.06082i	−0.716568	−	0.563515i	0.191928	−	0.981409i	$-0.438526\pi$
$157$	−8.97857	−	7.06082i	−0.716568	−	0.563515i	−0.908496	+	0.417894i	$0.862768\pi$
$158$	1.95954	−	1.01021i	0.155892	−	0.0803681i
$159$	0.460386	−	13.5158i	0.0365110	−	1.07188i
$160$	1.85622	+	3.21507i	0.146747	+	0.254174i
$161$	19.4240	−	15.3442i	1.53082	−	1.20929i
$162$	−5.61001	−	7.03760i	−0.440764	−	0.552926i
$163$	−5.75177	−	6.63789i	−0.450513	−	0.519920i	0.484376	−	0.874860i	$-0.339047\pi$
$163$	−5.75177	−	6.63789i	−0.450513	−	0.519920i	−0.934889	+	0.354940i	$0.884501\pi$
$164$	0.268647	−	5.63959i	0.0209778	−	0.440378i
$165$	−6.25467	+	5.05738i	−0.486925	+	0.393716i
$166$	−0.855896	−	1.20194i	−0.0664304	−	0.0932885i
$167$	−16.9120	−	6.77052i	−1.30869	−	0.523919i	−0.390695	−	0.920520i	$-0.627765\pi$
$167$	−16.9120	−	6.77052i	−1.30869	−	0.523919i	−0.917991	+	0.396601i	$0.870190\pi$
$168$	4.36463	−	7.80204i	0.336739	−	0.601940i
$169$	4.40520	+	2.27104i	0.338862	+	0.174695i
$170$	−10.2097	−	22.3560i	−0.783046	−	1.71463i
$171$	3.79262	+	10.0668i	0.290029	+	0.769829i
$172$	0.708258	−	0.817373i	0.0540041	−	0.0623241i
$173$	−5.61917	−	1.08301i	−0.427218	−	0.0823395i	−0.0288899	−	0.999583i	$-0.509197\pi$
$173$	−5.61917	−	1.08301i	−0.427218	−	0.0823395i	−0.398328	+	0.917243i	$0.630409\pi$
$174$	1.76318	−	1.16718i	0.133666	−	0.0884838i
$175$	45.1239	+	4.30881i	3.41104	+	0.325715i
$176$	−0.0595205	−	1.24949i	−0.00448653	−	0.0941838i
$177$	−24.7496	+	0.335385i	−1.86029	+	0.0252091i
$178$	−0.434161	+	0.341428i	−0.0325417	+	0.0255911i
$179$	−4.78768	+	10.4836i	−0.357848	+	0.783578i	0.642010	+	0.766697i	$0.278101\pi$
$179$	−4.78768	+	10.4836i	−0.357848	+	0.783578i	−0.999858	+	0.0168809i	$0.994626\pi$
$180$	4.89944	+	10.0018i	0.365182	+	0.745489i
$181$	−0.500870	−	0.321890i	−0.0372294	−	0.0239259i	0.521894	−	0.853010i	$-0.325226\pi$
$181$	−0.500870	−	0.321890i	−0.0372294	−	0.0239259i	−0.559123	+	0.829085i	$0.688862\pi$
$182$	−4.78786	+	13.8336i	−0.354900	+	1.02542i
$183$	2.11097	−	9.24666i	0.156048	−	0.683533i
$184$	−4.04018	−	2.58398i	−0.297846	−	0.190493i
$185$	−5.07527	+	8.79062i	−0.373141	+	0.646300i
$186$	−0.179066	+	5.25694i	−0.0131297	+	0.385458i
$187$	−0.394036	+	8.27183i	−0.0288148	+	0.604896i
$188$	0.792787	−	5.51396i	0.0578200	−	0.402147i
$189$	14.6563	−	22.4609i	1.06609	−	1.63379i
$190$	−1.89453	−	13.1768i	−0.137444	−	0.955943i
$191$	−0.204251	−	0.841934i	−0.0147791	−	0.0609202i	0.963945	−	0.266103i	$-0.0857362\pi$
$191$	−0.204251	−	0.841934i	−0.0147791	−	0.0609202i	−0.978724	+	0.205183i	$0.934221\pi$
$192$	−1.70504	−	0.304718i	−0.123050	−	0.0219911i
$193$	0.932205	+	0.0890147i	0.0671016	+	0.00640742i	0.128553	−	0.991703i	$-0.458967\pi$
$193$	0.932205	+	0.0890147i	0.0671016	+	0.00640742i	−0.0614513	+	0.998110i	$0.519573\pi$
$194$	3.11779	−	12.8517i	0.223844	−	0.922698i
$195$	−10.7788	−	14.7107i	−0.771885	−	1.05345i
$196$	19.2857	+	3.71701i	1.37755	+	0.265501i
$197$	20.0389	−	5.88395i	1.42771	−	0.419214i	0.525607	−	0.850728i	$-0.323838\pi$
$197$	20.0389	−	5.88395i	1.42771	−	0.419214i	0.902107	+	0.431513i	$0.142020\pi$
$198$	0.0769224	−	3.75193i	0.00546664	−	0.266638i
$199$	−11.9916	+	7.70651i	−0.850059	+	0.546300i	−0.891593	−	0.452837i	$-0.850412\pi$
$199$	−11.9916	+	7.70651i	−0.850059	+	0.546300i	0.0415341	+	0.999137i	$0.486775\pi$
$200$	−2.07049	−	8.53469i	−0.146406	−	0.603493i
$201$	−4.81109	−	10.1679i	−0.339348	−	0.717189i
$202$	−7.99526	−	11.2278i	−0.562544	−	0.789983i
$203$	4.95302	+	3.89510i	0.347634	+	0.273382i
$204$	11.0448	+	3.08111i	0.773288	+	0.215721i
$205$	−6.85548	+	19.8076i	−0.478807	+	1.38342i
$206$	17.5480			1.22263
$207$	−11.5650	−	8.55873i	−0.803820	−	0.594873i
$208$	2.83617			0.196653
$209$	−1.46708	+	4.23886i	−0.101480	+	0.293208i
$210$	−23.7074	+	23.2263i	−1.63596	+	1.60277i
$211$	−11.5278	−	9.06556i	−0.793607	−	0.624099i	0.136812	−	0.990597i	$-0.456314\pi$
$211$	−11.5278	−	9.06556i	−0.793607	−	0.624099i	−0.930419	+	0.366498i	$0.880557\pi$
$212$	−4.52903	−	6.36013i	−0.311055	−	0.436815i
$213$	0.825658	−	1.19337i	0.0565732	−	0.0817686i
$214$	0.830914	+	3.42508i	0.0568001	+	0.234133i
$215$	−3.37776	+	2.17076i	−0.230362	+	0.148044i
$216$	−5.04105	−	1.26010i	−0.343000	−	0.0857389i
$217$	−15.0397	+	4.41605i	−1.02096	+	0.299781i
$218$	1.34344	+	0.258927i	0.0909893	+	0.0175367i
$219$	−2.59864	+	0.283722i	−0.175600	+	0.0191721i
$220$	−1.09485	+	4.51301i	−0.0738144	+	0.304267i
$221$	−18.6909	−	1.78476i	−1.25729	−	0.120056i
$222$	−1.60941	−	4.45390i	−0.108017	−	0.298926i
$223$	−2.77779	−	11.4502i	−0.186015	−	0.766764i	−0.986000	−	0.166744i	$-0.946675\pi$
$223$	−2.77779	−	11.4502i	−0.186015	−	0.766764i	0.799985	−	0.600019i	$-0.204841\pi$
$224$	−0.734551	−	5.10892i	−0.0490793	−	0.341354i
$225$	−4.45481	−	25.9674i	−0.296988	−	1.73116i
$226$	−1.37092	+	9.53493i	−0.0911920	+	0.634254i
$227$	−0.526795	+	11.0588i	−0.0349646	+	0.733997i	0.911522	+	0.411252i	$0.134909\pi$
$227$	−0.526795	+	11.0588i	−0.0349646	+	0.733997i	−0.946486	+	0.322745i	$0.895395\pi$
$228$	5.26994	+	3.28675i	0.349010	+	0.217670i
$229$	−7.78757	+	13.4885i	−0.514617	+	0.891343i	0.485239	+	0.874381i	$0.338733\pi$
$229$	−7.78757	+	13.4885i	−0.514617	+	0.891343i	−0.999856	+	0.0169612i	$0.994601\pi$
$230$	11.6888	+	13.4300i	0.770734	+	0.885547i
$231$	10.6863	−	3.29571i	0.703107	−	0.216842i
$232$	0.399286	−	1.15366i	0.0262144	−	0.0757416i
$233$	18.9605	+	12.1852i	1.24214	+	0.798276i	0.985737	−	0.168293i	$-0.0538256\pi$
$233$	18.9605	+	12.1852i	1.24214	+	0.798276i	0.256405	+	0.966569i	$0.417462\pi$
$234$	8.48878	+	0.578974i	0.554929	+	0.0378487i
$235$	−8.59110	+	18.8119i	−0.560421	+	1.22715i
$236$	−11.2331	+	8.83379i	−0.731211	+	0.575031i
$237$	1.86427	−	3.33248i	0.121097	−	0.216468i
$238$	1.62586	+	34.1310i	0.105389	+	2.21238i
$239$	0.455101	+	0.0434569i	0.0294381	+	0.00281099i	0.109765	−	0.993958i	$-0.464990\pi$
$239$	0.455101	+	0.0434569i	0.0294381	+	0.00281099i	−0.0803266	+	0.996769i	$0.525596\pi$
$240$	5.75474	+	2.86875i	0.371467	+	0.185177i
$241$	20.4379	+	3.93909i	1.31652	+	0.253739i	0.798690	−	0.601743i	$-0.205527\pi$
$241$	20.4379	+	3.93909i	1.31652	+	0.253739i	0.517833	+	0.855482i	$0.326739\pi$
$242$	−6.17877	+	7.13068i	−0.397186	+	0.458377i
$243$	−14.8309	−	4.80061i	−0.951399	−	0.307959i
$244$	−2.27478	−	4.98107i	−0.145628	−	0.318880i
$245$	−64.8091	−	33.4114i	−4.14050	−	2.13458i
$246$	−5.00387	−	8.40195i	−0.319035	−	0.535689i
$247$	−9.44156	−	3.77983i	−0.600752	−	0.240505i
$248$	1.76155	+	2.47375i	0.111859	+	0.157083i
$249$	−2.38529	−	0.917624i	−0.151162	−	0.0581521i
$250$	−0.668115	+	14.0255i	−0.0422553	+	0.887048i
$251$	4.76688	+	5.50127i	0.300883	+	0.347237i	0.885978	−	0.463727i	$-0.153488\pi$
$251$	4.76688	+	5.50127i	0.300883	+	0.347237i	−0.585095	+	0.810965i	$0.698943\pi$
$252$	−1.15561	−	15.4412i	−0.0727969	−	0.972703i
$253$	−1.42712	−	5.82691i	−0.0897221	−	0.366335i
$254$	−6.45405	−	11.1787i	−0.404963	−	0.701417i
$255$	−36.1196	−	22.5270i	−2.26190	−	1.41070i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	17.1296	+	13.4708i	1.06851	+	0.840287i	0.987687	−	0.156441i	$-0.0500021\pi$
$257$	17.1296	+	13.4708i	1.06851	+	0.840287i	0.0808248	+	0.996728i	$0.474245\pi$
$258$	0.241447	−	1.85766i	0.0150318	−	0.115653i
$259$	11.0931	−	8.72371i	0.689292	−	0.542065i
$260$	−10.1026	−	2.96639i	−0.626537	−	0.183968i
$261$	1.43059	−	3.37146i	0.0885514	−	0.208688i
$262$	3.16490	+	6.93016i	0.195528	+	0.428147i
$263$	−3.53184	−	3.36761i	−0.217783	−	0.207655i	0.573332	−	0.819323i	$-0.305651\pi$
$263$	−3.53184	−	3.36761i	−0.217783	−	0.207655i	−0.791115	+	0.611668i	$0.790499\pi$
$264$	−1.28057	−	1.74770i	−0.0788135	−	0.107563i
$265$	9.48052	+	27.3922i	0.582384	+	1.68269i
$266$	−4.36347	+	17.9865i	−0.267542	+	1.10282i
$267$	−0.300615	+	0.908204i	−0.0183974	+	0.0555812i
$268$	−5.77248	−	2.97592i	−0.352610	−	0.181783i
$269$	0.183980	+	0.0540214i	0.0112175	+	0.00329374i	0.287336	−	0.957830i	$-0.407230\pi$
$269$	0.183980	+	0.0540214i	0.0112175	+	0.00329374i	−0.276119	+	0.961123i	$0.589048\pi$
$270$	16.6386	+	9.76107i	1.01259	+	0.594040i
$271$	11.8606	−	25.9710i	0.720478	−	1.57763i	−0.0927554	−	0.995689i	$-0.529567\pi$
$271$	11.8606	−	25.9710i	0.720478	−	1.57763i	0.813233	−	0.581938i	$-0.197705\pi$
$272$	6.14596	−	2.46047i	0.372653	−	0.149188i
$273$	6.31101	+	24.5571i	0.381959	+	1.48626i
$274$	9.26474	−	1.78563i	0.559703	−	0.107874i
$275$	5.49288	−	9.51394i	0.331233	−	0.573712i
$276$	−8.30559	+	0.130750i	−0.499938	+	0.00787020i
$277$	−10.8325	−	18.7624i	−0.650861	−	1.12732i	−0.982914	−	0.184064i	$-0.941075\pi$
$277$	−10.8325	−	18.7624i	−0.650861	−	1.12732i	0.332053	−	0.943261i	$-0.392259\pi$
$278$	8.85518	+	10.2194i	0.531099	+	0.612920i
$279$	4.76741	+	7.76366i	0.285418	+	0.464798i
$280$	−2.72698	+	18.9666i	−0.162968	+	1.13347i
$281$	−23.1628	+	2.21178i	−1.38178	+	0.131944i	−0.759323	−	0.650713i	$-0.774470\pi$
$281$	−23.1628	+	2.21178i	−1.38178	+	0.131944i	−0.622453	+	0.782657i	$0.713864\pi$
$282$	−4.12676	−	8.72162i	−0.245745	−	0.519365i
$283$	4.49820	−	4.28903i	0.267390	−	0.254956i	−0.544507	−	0.838756i	$-0.683283\pi$
$283$	4.49820	−	4.28903i	0.267390	−	0.254956i	0.811897	+	0.583800i	$0.198435\pi$
$284$	−0.0398653	−	0.836876i	−0.00236557	−	0.0496595i
$285$	−15.3342	−	17.2195i	−0.908319	−	1.02000i
$286$	2.56765	+	2.44825i	0.151828	+	0.144768i
$287$	19.0836	−	22.0237i	1.12647	−	1.30002i
$288$	−2.75387	+	1.19005i	−0.162273	+	0.0701242i
$289$	−25.7400	+	7.55795i	−1.51412	+	0.444586i
$290$	−2.62892	+	3.69180i	−0.154375	+	0.216790i
$291$	−7.78425	−	21.5422i	−0.456321	−	1.26283i
$292$	−1.09229	+	1.04150i	−0.0639214	+	0.0609489i
$293$	−6.29108	−	2.51857i	−0.367529	−	0.147136i	0.180544	−	0.983567i	$-0.442214\pi$
$293$	−6.29108	−	2.51857i	−0.367529	−	0.147136i	−0.548073	+	0.836430i	$0.684638\pi$
$294$	31.4075	−	13.0702i	1.83172	−	0.762268i
$295$	49.2524	−	19.7177i	2.86758	−	1.14801i
$296$	−2.30015	−	1.47822i	−0.133693	−	0.0859196i
$297$	−3.47603	−	5.49235i	−0.201700	−	0.318698i
$298$	15.6733			0.907927
$299$	13.3503	−	2.60341i	0.772068	−	0.150559i
$300$	−11.1502	−	10.3469i	−0.643754	−	0.597376i
$301$	5.48144	−	1.05646i	0.315945	−	0.0608933i
$302$	−6.37392	+	3.28598i	−0.366778	+	0.189087i
$303$	−22.2819	−	8.57188i	−1.28006	−	0.492442i
$304$	3.56961	−	0.340857i	0.204731	−	0.0195495i
$305$	2.89312	+	20.1221i	0.165660	+	1.15219i
$306$	18.8974	−	6.10967i	1.08029	−	0.349266i
$307$	11.9474	−	7.67813i	0.681874	−	0.438214i	−0.153315	−	0.988177i	$-0.548995\pi$
$307$	11.9474	−	7.67813i	0.681874	−	0.438214i	0.835189	+	0.549964i	$0.185358\pi$
$308$	3.74513	−	5.25930i	0.213399	−	0.299677i
$309$	25.3441	−	16.7772i	1.44177	−	0.954422i
$310$	−3.68742	−	10.6541i	−0.209431	−	0.605112i
$311$	1.54677	+	4.46909i	0.0877091	+	0.253419i	0.980322	−	0.197405i	$-0.0632514\pi$
$311$	1.54677	+	4.46909i	0.0877091	+	0.253419i	−0.892613	+	0.450824i	$0.851130\pi$
$312$	4.09620	−	2.71159i	0.231901	−	0.153513i
$313$	5.68037	−	7.97697i	0.321074	−	0.450885i	−0.622221	−	0.782842i	$-0.713769\pi$
$313$	5.68037	−	7.97697i	0.321074	−	0.450885i	0.943295	+	0.331957i	$0.107709\pi$
$314$	−9.60908	+	6.17538i	−0.542272	+	0.348497i
$315$	−12.0338	+	56.2111i	−0.678028	+	3.16714i
$316$	−0.313749	−	2.18217i	−0.0176498	−	0.122757i
$317$	23.0473	−	2.20075i	1.29447	−	0.123607i	0.575011	−	0.818146i	$-0.304998\pi$
$317$	23.0473	−	2.20075i	1.29447	−	0.123607i	0.719455	+	0.694539i	$0.244392\pi$
$318$	−12.6219	−	4.85566i	−0.707801	−	0.272292i
$319$	1.35735	−	0.699764i	0.0759971	−	0.0391792i
$320$	3.64536	−	0.702585i	0.203782	−	0.0392757i
$321$	4.47469	+	4.15232i	0.249753	+	0.231760i
$322$	−8.14729	−	23.3742i	−0.454031	−	1.30260i
$323$	−23.7389			−1.32087
$324$	−8.48539	+	2.99969i	−0.471411	+	0.166650i
$325$	20.9539	+	13.4662i	1.16231	+	0.746972i
$326$	−8.15403	+	3.26438i	−0.451610	+	0.180797i
$327$	2.18785	−	0.910469i	0.120988	−	0.0503490i
$328$	−5.24155	−	2.09840i	−0.289416	−	0.115865i
$329$	20.8093	−	19.8416i	1.14725	−	1.09390i
$330$	2.73352	+	7.56477i	0.150476	+	0.416427i
$331$	4.87355	−	6.84395i	0.267875	−	0.376178i	−0.658626	−	0.752471i	$-0.728862\pi$
$331$	4.87355	−	6.84395i	0.267875	−	0.376178i	0.926501	+	0.376293i	$0.122801\pi$
$332$	−1.41577	+	0.415707i	−0.0777004	+	0.0228149i
$333$	−6.58269	−	4.89392i	−0.360729	−	0.268185i
$334$	−11.9295	+	13.7674i	−0.652754	+	0.753318i
$335$	17.4494	+	16.6380i	0.953362	+	0.909029i
$336$	−5.94540	−	6.67638i	−0.324348	−	0.364226i
$337$	0.286548	+	6.01539i	0.0156093	+	0.327679i	0.993143	+	0.116902i	$0.0372964\pi$
$337$	0.286548	+	6.01539i	0.0156093	+	0.327679i	−0.977534	+	0.210777i	$0.932401\pi$
$338$	3.58694	−	3.42014i	0.195104	−	0.186031i
$339$	7.13613	+	15.0817i	0.387581	+	0.819127i
$340$	−24.4657	+	2.33619i	−1.32684	+	0.126698i
$341$	−0.540629	+	3.76016i	−0.0292767	+	0.203624i
$342$	10.7536	−	0.291501i	0.581488	−	0.0157626i
$343$	42.7256	+	49.3080i	2.30697	+	2.66238i
$344$	−0.540770	−	0.936641i	−0.0291563	−	0.0505003i
$345$	29.7218	+	8.22122i	1.60017	+	0.442616i
$346$	−2.86129	+	4.95591i	−0.153824	+	0.266431i
$347$	−18.7688	+	3.61738i	−1.00756	+	0.194191i	−0.666225	−	0.745751i	$-0.732091\pi$
$347$	−18.7688	+	3.61738i	−1.00756	+	0.194191i	−0.341334	+	0.939942i	$0.610879\pi$
$348$	−0.526310	−	2.04795i	−0.0282132	−	0.109782i
$349$	−22.0830	+	8.84070i	−1.18208	+	0.473232i	−0.877649	−	0.479304i	$-0.840889\pi$
$349$	−22.0830	+	8.84070i	−1.18208	+	0.473232i	−0.304427	+	0.952536i	$0.598465\pi$
$350$	18.8304	−	41.2328i	1.00653	−	2.20399i
$351$	12.8136	−	7.27972i	0.683942	−	0.388562i
$352$	−1.20024	−	0.352421i	−0.0639727	−	0.0187841i
$353$	−15.3924	−	7.93535i	−0.819256	−	0.422356i	−0.00296440	−	0.999996i	$-0.500944\pi$
$353$	−15.3924	−	7.93535i	−0.819256	−	0.422356i	−0.816292	+	0.577640i	$0.803974\pi$
$354$	−7.77785	+	23.4981i	−0.413388	+	1.24891i
$355$	−0.733300	+	3.02270i	−0.0389195	+	0.160428i
$356$	0.180649	+	0.521952i	0.00957440	+	0.0276634i
$357$	34.9800	+	47.7400i	1.85134	+	2.52667i
$358$	8.34107	+	7.95319i	0.440839	+	0.420339i
$359$	−9.37760	−	20.5341i	−0.494931	−	1.08375i	−0.978084	−	0.208211i	$-0.933236\pi$
$359$	−9.37760	−	20.5341i	−0.494931	−	1.08375i	0.483153	−	0.875536i	$-0.339491\pi$
$360$	11.0541	−	1.35871i	0.582605	−	0.0716102i
$361$	5.89291	+	1.73031i	0.310153	+	0.0910692i
$362$	−0.468004	+	0.368043i	−0.0245978	+	0.0193439i
$363$	−2.10636	+	16.2060i	−0.110555	+	0.850594i
$364$	11.5068	+	9.04907i	0.603122	+	0.474300i
$365$	4.98012	−	2.56743i	0.260672	−	0.134386i
$366$	−8.04767	−	5.01916i	−0.420659	−	0.262356i
$367$	14.8836	+	25.7792i	0.776920	+	1.34566i	0.933709	+	0.358032i	$0.116552\pi$
$367$	14.8836	+	25.7792i	0.776920	+	1.34566i	−0.156789	+	0.987632i	$0.550114\pi$
$368$	−3.76327	+	2.97284i	−0.196174	+	0.154970i
$369$	−15.2598	−	7.35062i	−0.794396	−	0.382658i
$370$	6.64719	+	7.67127i	0.345571	+	0.398810i
$371$	1.91756	−	40.2545i	0.0995545	−	2.08991i
$372$	4.90925	+	1.88860i	0.254533	+	0.0979191i
$373$	−15.4054	−	21.6338i	−0.797661	−	1.12016i	−0.990308	−	0.138890i	$-0.955647\pi$
$373$	−15.4054	−	21.6338i	−0.797661	−	1.12016i	0.192647	−	0.981268i	$-0.438293\pi$
$374$	7.68801	+	3.07782i	0.397538	+	0.159150i
$375$	12.4445	+	20.8953i	0.642629	+	1.07903i
$376$	−4.95140	−	2.55262i	−0.255349	−	0.131641i
$377$	1.43834	+	3.14952i	0.0740781	+	0.162208i
$378$	−16.4319	−	21.1964i	−0.845168	−	1.09023i
$379$	−17.2142	+	19.8662i	−0.884232	+	1.02046i	0.115400	+	0.993319i	$0.463185\pi$
$379$	−17.2142	+	19.8662i	−0.884232	+	1.02046i	−0.999632	+	0.0271389i	$0.991360\pi$
$380$	−13.0717	−	2.51936i	−0.670564	−	0.129241i
$381$	−20.0091	−	9.97459i	−1.02510	−	0.511014i
$382$	−0.862432	−	0.0823523i	−0.0441259	−	0.00421351i
$383$	0.757008	+	15.8916i	0.0386813	+	0.812021i	0.931970	+	0.362536i	$0.118089\pi$
$383$	0.757008	+	15.8916i	0.0386813	+	0.812021i	−0.893288	+	0.449484i	$0.851608\pi$
$384$	−0.845621	+	1.51160i	−0.0431529	+	0.0771384i
$385$	−18.8412	+	14.8169i	−0.960236	+	0.755138i
$386$	0.389013	−	0.851820i	0.0198003	−	0.0433565i
$387$	−1.42734	−	2.91380i	−0.0725559	−	0.148117i
$388$	−11.1251	−	7.14969i	−0.564793	−	0.362971i
$389$	−3.07046	+	8.87152i	−0.155679	+	0.449804i	−0.995688	−	0.0927685i	$-0.970428\pi$
$389$	−3.07046	+	8.87152i	−0.155679	+	0.449804i	0.840009	+	0.542572i	$0.182550\pi$
$390$	−17.4270	+	5.37457i	−0.882451	+	0.272152i
$391$	26.6715	−	17.2234i	1.34884	−	0.871025i
$392$	9.82030	−	17.0093i	0.496000	−	0.859097i
$393$	11.1967	+	6.98316i	0.564800	+	0.352254i
$394$	0.993743	−	20.8612i	0.0500641	−	1.05097i
$395$	−1.16478	+	8.10119i	−0.0586062	+	0.407615i
$396$	−3.52042	−	1.29983i	−0.176908	−	0.0653188i
$397$	−2.54129	−	17.6751i	−0.127544	−	0.887086i	−0.948654	−	0.316316i	$-0.897554\pi$
$397$	−2.54129	−	17.6751i	−0.127544	−	0.887086i	0.821110	−	0.570770i	$-0.193355\pi$
$398$	3.36060	+	13.8526i	0.168452	+	0.694367i
$399$	10.8944	+	30.1492i	0.545401	+	1.50935i
$400$	−8.74248	−	0.834805i	−0.437124	−	0.0417403i
$401$	−0.365465	+	1.50647i	−0.0182504	+	0.0752293i	−0.980209	−	0.197968i	$-0.936566\pi$
$401$	−0.365465	+	1.50647i	−0.0182504	+	0.0752293i	0.961958	+	0.273197i	$0.0880811\pi$
$402$	−11.1822	+	1.22089i	−0.557719	+	0.0608923i
$403$	−8.45739	−	1.63003i	−0.421293	−	0.0811975i
$404$	−13.2252	+	3.88328i	−0.657981	+	0.193201i
$405$	33.3629	−	1.81009i	1.65782	−	0.0899440i
$406$	5.30085	−	3.40665i	0.263077	−	0.169069i
$407$	−0.806347	−	3.32381i	−0.0399691	−	0.164755i
$408$	6.52404	−	9.42958i	0.322988	−	0.466834i
$409$	0.535898	+	0.752564i	0.0264985	+	0.0372119i	0.827613	−	0.561300i	$-0.189698\pi$
$409$	0.535898	+	0.752564i	0.0264985	+	0.0372119i	−0.801114	+	0.598512i	$0.795759\pi$
$410$	16.4760	+	12.9569i	0.813691	+	0.639894i
$411$	11.6736	−	11.4367i	0.575816	−	0.564132i
$412$	5.73939	−	16.5829i	0.282759	−	0.816980i
$413$	−73.7597			−3.62948
$414$	−11.8705	+	8.12961i	−0.583405	+	0.399548i
$415$	5.47785			0.268897
$416$	0.927620	−	2.68018i	0.0454803	−	0.131407i
$417$	22.5598	+	6.29341i	1.10476	+	0.308190i
$418$	3.52589	+	2.77279i	0.172457	+	0.135621i
$419$	−9.19406	−	12.9112i	−0.449159	−	0.630756i	0.526467	−	0.850196i	$-0.323516\pi$
$419$	−9.19406	−	12.9112i	−0.449159	−	0.630756i	−0.975626	+	0.219440i	$0.929577\pi$
$420$	14.1950	+	30.0001i	0.692643	+	1.46385i
$421$	−8.33996	−	34.3778i	−0.406465	−	1.67547i	−0.695795	−	0.718241i	$-0.744948\pi$
$421$	−8.33996	−	34.3778i	−0.406465	−	1.67547i	0.289330	−	0.957229i	$-0.406567\pi$
$422$	−12.3373	+	7.92873i	−0.600572	+	0.385964i
$423$	−14.2987	−	8.65090i	−0.695225	−	0.420621i
$424$	−7.49162	+	2.19974i	−0.363825	+	0.106829i
$425$	57.0893	+	11.0031i	2.76924	+	0.533727i
$426$	−0.857692	−	1.17056i	−0.0415553	−	0.0567139i
$427$	6.66342	−	27.4670i	0.322465	−	1.32922i
$428$	3.50846	+	0.335018i	0.169588	+	0.0161937i
$429$	6.04909	+	1.08107i	0.292053	+	0.0521946i
$430$	0.946609	+	3.90197i	0.0456495	+	0.188170i
$431$	3.26482	+	22.7073i	0.157261	+	1.09377i	0.903652	+	0.428267i	$0.140876\pi$
$431$	3.26482	+	22.7073i	0.157261	+	1.09377i	−0.746391	+	0.665507i	$0.768215\pi$
$432$	−2.83956	+	4.35165i	−0.136618	+	0.209369i
$433$	−4.74858	+	33.0271i	−0.228202	+	1.58718i	0.477474	+	0.878646i	$0.341552\pi$
$433$	−4.74858	+	33.0271i	−0.228202	+	1.58718i	−0.705676	+	0.708534i	$0.749357\pi$
$434$	−0.745828	+	15.6568i	−0.0358009	+	0.751553i
$435$	−0.267236	+	7.84540i	−0.0128130	+	0.376158i
$436$	0.684083	−	1.18487i	0.0327616	−	0.0567448i
$437$	16.4899	−	4.88113i	0.788817	−	0.233496i
$438$	−0.581815	+	2.54851i	−0.0278002	+	0.121773i
$439$	1.37389	−	3.96958i	0.0655720	−	0.189458i	−0.907455	−	0.420149i	$-0.861978\pi$
$439$	1.37389	−	3.96958i	0.0655720	−	0.189458i	0.973027	+	0.230692i	$0.0740988\pi$
$440$	3.90671	+	2.51069i	0.186245	+	0.119693i
$441$	32.8649	−	48.9048i	1.56499	−	2.32880i
$442$	−7.79980	+	17.0792i	−0.370999	+	0.812374i
$443$	−5.96153	+	4.68820i	−0.283241	+	0.222743i	−0.749664	−	0.661819i	$-0.769785\pi$
$443$	−5.96153	+	4.68820i	−0.283241	+	0.222743i	0.466423	+	0.884562i	$0.345542\pi$
$444$	−4.73533	+	0.0641691i	−0.224729	+	0.00304533i
$445$	−0.0975664	−	2.04817i	−0.00462509	−	0.0970926i
$446$	−11.7290	−	1.11998i	−0.555384	−	0.0530327i
$447$	22.6364	−	14.9848i	1.07067	−	0.708757i
$448$	−5.06818	−	0.976811i	−0.239449	−	0.0461500i
$449$	−0.732203	+	0.845007i	−0.0345548	+	0.0398784i	−0.772764	−	0.634694i	$-0.781126\pi$
$449$	−0.732203	+	0.845007i	−0.0345548	+	0.0398784i	0.738209	+	0.674572i	$0.235672\pi$
$450$	−25.9962	−	4.28330i	−1.22547	−	0.201917i
$451$	−2.93391	−	6.42436i	−0.138152	−	0.302511i
$452$	8.56213	+	4.41409i	0.402729	+	0.207621i
$453$	−6.06403	+	10.8398i	−0.284913	+	0.509298i
$454$	10.2783	+	4.11479i	0.482383	+	0.193117i
$455$	−31.5235	−	44.2686i	−1.47784	−	2.07534i
$456$	4.82960	−	3.90511i	0.226167	−	0.182873i
$457$	−1.07714	+	22.6119i	−0.0503863	+	1.05774i	0.822176	+	0.569234i	$0.192760\pi$
$457$	−1.07714	+	22.6119i	−0.0503863	+	1.05774i	−0.872562	+	0.488504i	$0.837543\pi$
$458$	10.1995	+	11.7709i	0.476593	+	0.550018i
$459$	21.4517	−	26.8914i	1.00128	−	1.25518i
$460$	16.5144	−	6.65337i	0.769986	−	0.310215i
$461$	7.98570	+	13.8316i	0.371931	+	0.644204i	0.989863	−	0.142028i	$-0.0453624\pi$
$461$	7.98570	+	13.8316i	0.371931	+	0.644204i	−0.617931	+	0.786232i	$0.712029\pi$
$462$	0.380702	−	11.1765i	0.0177118	−	0.519977i
$463$	−22.8182	+	11.7636i	−1.06045	+	0.546700i	−0.897990	−	0.440016i	$-0.854973\pi$
$463$	−22.8182	+	11.7636i	−1.06045	+	0.546700i	−0.162459	+	0.986715i	$0.551943\pi$
$464$	−0.959618	−	0.754652i	−0.0445492	−	0.0350338i
$465$	−15.5118	−	11.8620i	−0.719340	−	0.550085i
$466$	17.7163	−	13.9323i	0.820694	−	0.645401i
$467$	−22.7589	−	6.68263i	−1.05316	−	0.309235i	−0.291066	−	0.956703i	$-0.594010\pi$
$467$	−22.7589	−	6.68263i	−1.05316	−	0.309235i	−0.762093	+	0.647468i	$0.775828\pi$
$468$	3.32354	−	7.83254i	0.153631	−	0.362059i
$469$	−13.9250	−	30.4915i	−0.642997	−	1.40797i
$470$	14.9674	+	14.2714i	0.690393	+	0.658289i
$471$	−7.97400	+	18.1059i	−0.367423	+	0.834278i
$472$	4.67396	+	13.5045i	0.215136	+	0.621596i
$473$	0.318959	−	1.31477i	0.0146658	−	0.0604531i
$474$	−2.53946	−	2.85168i	−0.116641	−	0.130982i
$475$	27.9910	+	14.4304i	1.28432	+	0.662111i
$476$	32.7856	+	9.62672i	1.50273	+	0.441240i
$477$	−22.8718	+	5.05459i	−1.04723	+	0.231434i
$478$	0.189916	−	0.415858i	0.00868655	−	0.0190209i
$479$	28.1252	−	11.2596i	1.28507	−	0.514466i	0.374275	−	0.927318i	$-0.377892\pi$
$479$	28.1252	−	11.2596i	1.28507	−	0.514466i	0.910798	+	0.412852i	$0.135467\pi$
$480$	4.59316	−	4.49996i	0.209648	−	0.205394i
$481$	7.61449	−	1.46757i	0.347191	−	0.0669156i
$482$	10.4070	−	18.0255i	0.474027	−	0.821040i
$483$	−34.1144	−	25.9693i	−1.55226	−	1.18165i
$484$	4.71762	+	8.17115i	0.214437	+	0.371416i
$485$	32.1505	+	37.1036i	1.45988	+	1.68479i
$486$	−9.38728	+	12.4450i	−0.425816	+	0.564518i
$487$	3.38139	−	23.5181i	0.153225	−	1.06571i	−0.757542	−	0.652786i	$-0.773600\pi$
$487$	3.38139	−	23.5181i	0.153225	−	1.06571i	0.910768	−	0.412920i	$-0.135491\pi$
$488$	−5.45112	+	0.520519i	−0.246761	+	0.0235628i
$489$	−8.65565	+	12.5105i	−0.391422	+	0.565745i
$490$	−52.7708	+	50.3169i	−2.38394	+	2.27308i
$491$	1.91045	+	40.1054i	0.0862176	+	1.80993i	0.465926	+	0.884824i	$0.345721\pi$
$491$	1.91045	+	40.1054i	0.0862176	+	1.80993i	−0.379708	+	0.925106i	$0.623976\pi$
$492$	−9.57645	+	1.98066i	−0.431740	+	0.0892948i
$493$	5.84918	+	5.57718i	0.263434	+	0.251184i
$494$	−6.65998	+	7.68602i	−0.299647	+	0.345811i
$495$	11.1804	+	8.31213i	0.502523	+	0.373602i
$496$	2.91384	−	0.855582i	0.130835	−	0.0384168i
$497$	2.50839	−	3.52255i	0.112517	−	0.158008i
$498$	−1.64731	+	1.95397i	−0.0738176	+	0.0875597i
$499$	6.33611	−	6.04147i	0.283643	−	0.270453i	−0.534878	−	0.844929i	$-0.679643\pi$
$499$	6.33611	−	6.04147i	0.283643	−	0.270453i	0.818522	+	0.574476i	$0.194794\pi$
$500$	13.0356	+	5.21865i	0.582968	+	0.233385i
$501$	−4.06680	+	31.2894i	−0.181691	+	1.39791i
$502$	6.75780	−	2.70541i	0.301615	−	0.120749i
$503$	−20.2989	−	13.0453i	−0.905085	−	0.581663i	0.00320949	−	0.999995i	$-0.498978\pi$
$503$	−20.2989	−	13.0453i	−0.905085	−	0.581663i	−0.908294	+	0.418332i	$0.862615\pi$
$504$	−14.9699	−	3.95826i	−0.666812	−	0.176315i
$505$	51.1708			2.27707
$506$	−5.97320	−	0.557169i	−0.265541	−	0.0247692i
$507$	1.91060	−	8.36899i	0.0848529	−	0.371680i
$508$	−12.6748	+	2.44287i	−0.562355	+	0.108385i
$509$	−0.305548	+	0.157521i	−0.0135432	+	0.00698198i	−0.464985	−	0.885319i	$-0.653940\pi$
$509$	−0.305548	+	0.157521i	−0.0135432	+	0.00698198i	0.451442	+	0.892301i	$0.350910\pi$
$510$	−33.1016	+	26.7652i	−1.46576	+	1.18518i
$511$	−7.75461	+	0.740475i	−0.343044	+	0.0327567i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	15.2524	−	10.7022i	0.673411	−	0.472516i
$514$	18.3325	−	11.7816i	0.808611	−	0.519663i
$515$	−37.7884	+	53.0664i	−1.66515	+	2.33838i
$516$	−1.67652	−	0.835747i	−0.0738045	−	0.0367917i
$517$	−2.27913	−	6.58511i	−0.100236	−	0.289613i
$518$	−4.61572	−	13.3362i	−0.202803	−	0.585961i
$519$	0.605732	+	9.89329i	0.0265887	+	0.434267i
$520$	−6.10749	+	8.57676i	−0.267831	+	0.376116i
$521$	24.9016	−	16.0033i	1.09096	−	0.701116i	0.133894	−	0.990996i	$-0.457252\pi$
$521$	24.9016	−	16.0033i	1.09096	−	0.701116i	0.957063	+	0.289880i	$0.0936154\pi$
$522$	−2.71813	−	2.45460i	−0.118969	−	0.107435i
$523$	−1.90784	−	13.2693i	−0.0834239	−	0.580226i	−0.988063	−	0.154048i	$-0.950769\pi$
$523$	−1.90784	−	13.2693i	−0.0834239	−	0.580226i	0.904639	−	0.426178i	$-0.140140\pi$
$524$	7.58415	−	0.724198i	0.331315	−	0.0316367i
$525$	−12.2255	−	77.5547i	−0.533563	−	3.38476i
$526$	−4.33754	+	2.23616i	−0.189126	+	0.0975012i
$527$	−19.7412	+	3.80481i	−0.859941	+	0.165740i
$528$	−2.07041	+	0.638523i	−0.0901029	+	0.0277882i
$529$	−14.9855	+	17.4481i	−0.651543	+	0.758612i
$530$	28.9864			1.25909
$531$	11.2326	+	41.3738i	0.487452	+	1.79547i
$532$	15.5701	+	10.0063i	0.675048	+	0.433827i
$533$	14.8659	−	5.95142i	0.643915	−	0.257785i
$534$	0.759932	+	0.581126i	0.0328855	+	0.0251478i
$535$	−12.1470	−	4.86292i	−0.525160	−	0.210242i
$536$	−4.70024	+	4.48167i	−0.203020	+	0.193579i
$537$	19.6506	+	3.51189i	0.847987	+	0.151549i
$538$	0.111224	−	0.156192i	0.00479521	−	0.00673394i
$539$	23.5733	−	6.92176i	1.01538	−	0.298141i
$540$	14.6662	−	12.5309i	0.631131	−	0.539245i
$541$	−10.5284	+	12.1504i	−0.452650	+	0.522386i	−0.935505	−	0.353314i	$-0.885055\pi$
$541$	−10.5284	+	12.1504i	−0.452650	+	0.522386i	0.482854	+	0.875701i	$0.339600\pi$
$542$	−20.6634	−	19.7025i	−0.887570	−	0.846296i
$543$	−0.324049	+	0.979001i	−0.0139063	+	0.0420130i
$544$	−0.315001	−	6.61268i	−0.0135055	−	0.283516i
$545$	−3.67602	+	3.50507i	−0.157463	+	0.150141i
$546$	25.2706	+	2.06793i	1.08148	+	0.0884991i
$547$	21.2591	−	2.03000i	0.908975	−	0.0867965i	0.369916	−	0.929065i	$-0.379386\pi$
$547$	21.2591	−	2.03000i	0.908975	−	0.0867965i	0.539058	+	0.842269i	$0.318780\pi$
$548$	1.34278	−	9.33921i	0.0573605	−	0.398951i
$549$	−16.4217	+	0.445148i	−0.700862	+	0.0189985i
$550$	−7.19414	−	8.30248i	−0.306759	−	0.354019i
$551$	2.18881	+	3.79113i	0.0932465	+	0.161508i
$552$	−2.59294	+	7.89156i	−0.110363	+	0.335887i
$553$	5.68950	−	9.85450i	0.241942	−	0.419056i
$554$	−21.2735	+	4.10012i	−0.903823	+	0.174198i
$555$	16.9347	+	4.72418i	0.718836	+	0.200530i
$556$	12.5536	−	5.02571i	0.532392	−	0.213137i
$557$	−0.541226	+	1.18512i	−0.0229325	+	0.0502151i	−0.920752	−	0.390149i	$-0.872423\pi$
$557$	−0.541226	+	1.18512i	−0.0229325	+	0.0502151i	0.897819	+	0.440364i	$0.145151\pi$
$558$	8.89593	−	1.96597i	0.376595	−	0.0832260i
$559$	2.94317	+	0.864194i	0.124483	+	0.0365515i
$560$	17.0315	+	8.78036i	0.719713	+	0.371038i
$561$	14.0462	−	2.90511i	0.593031	−	0.122654i
$562$	−5.48568	+	22.6123i	−0.231399	+	0.953841i
$563$	10.1261	+	29.2575i	0.426764	+	1.23305i	0.929567	+	0.368653i	$0.120181\pi$
$563$	10.1261	+	29.2575i	0.426764	+	1.23305i	−0.502803	+	0.864401i	$0.667698\pi$
$564$	−9.59166	+	1.04723i	−0.403882	+	0.0440962i
$565$	−25.8821	−	24.6785i	−1.08887	−	1.03823i
$566$	−2.58192	−	5.65361i	−0.108526	−	0.237639i
$567$	−43.9975	−	14.9032i	−1.84772	−	0.625875i
$568$	−0.803887	−	0.236043i	−0.0337304	−	0.00990413i
$569$	11.5483	−	9.08166i	0.484129	−	0.380723i	−0.346054	−	0.938215i	$-0.612479\pi$
$569$	11.5483	−	9.08166i	0.484129	−	0.380723i	0.830183	+	0.557492i	$0.188236\pi$
$570$	−21.2878	+	8.85887i	−0.891647	+	0.371057i
$571$	−37.1399	−	29.2071i	−1.55426	−	1.22228i	−0.870015	−	0.493025i	$-0.835891\pi$
$571$	−37.1399	−	29.2071i	−1.55426	−	1.22228i	−0.684241	−	0.729256i	$-0.739866\pi$
$572$	3.15339	−	1.62569i	0.131850	−	0.0679733i
$573$	−1.32432	+	0.705611i	−0.0553243	+	0.0294773i
$574$	−14.5707	−	25.2373i	−0.608171	−	1.05338i
$575$	−41.9186	+	4.09543i	−1.74813	+	0.170791i
$576$	0.223893	+	2.99163i	0.00932889	+	0.124651i
$577$	−6.76097	−	7.80258i	−0.281463	−	0.324825i	0.597360	−	0.801973i	$-0.296216\pi$
$577$	−6.76097	−	7.80258i	−0.281463	−	0.324825i	−0.878823	+	0.477147i	$0.841671\pi$
$578$	−1.27647	+	26.7963i	−0.0530940	+	1.11458i
$579$	−0.252563	−	1.60219i	−0.0104962	−	0.0665846i
$580$	2.62892	+	3.69180i	0.109160	+	0.153294i
$581$	−7.07038	−	2.83055i	−0.293329	−	0.117431i
$582$	−22.9034	+	0.310367i	−0.949375	+	0.0128651i
$583$	−8.68121	−	4.47547i	−0.359539	−	0.185355i
$584$	0.626962	+	1.37285i	0.0259439	+	0.0568091i
$585$	−20.0308	+	24.4239i	−0.828174	+	1.00980i
$586$	−4.43766	+	5.12134i	−0.183318	+	0.211560i
$587$	13.4907	+	2.60013i	0.556822	+	0.107319i	0.459896	−	0.887973i	$-0.347887\pi$
$587$	13.4907	+	2.60013i	0.556822	+	0.107319i	0.0969263	+	0.995292i	$0.469099\pi$
$588$	−2.07894	−	33.9549i	−0.0857342	−	1.40028i
$589$	−10.8404	−	1.03513i	−0.446671	−	0.0426519i
$590$	−2.52435	−	52.9926i	−0.103926	−	2.18167i
$591$	−18.5097	−	31.0794i	−0.761386	−	1.27844i
$592$	−2.14922	+	1.69017i	−0.0883324	+	0.0694654i
$593$	0.316328	−	0.692661i	0.0129900	−	0.0284442i	−0.903026	−	0.429586i	$-0.858659\pi$
$593$	0.316328	−	0.692661i	0.0129900	−	0.0284442i	0.916016	+	0.401142i	$0.131387\pi$
$594$	−6.32717	+	1.48848i	−0.259607	+	0.0610730i
$595$	−106.716	−	68.5820i	−4.37492	−	2.81159i
$596$	5.12622	−	14.8112i	0.209978	−	0.606692i
$597$	18.0977	+	16.7939i	0.740691	+	0.687329i
$598$	1.90624	−	13.4675i	0.0779518	−	0.550729i
$599$	7.71129	−	13.3564i	0.315075	−	0.545726i	−0.664379	−	0.747396i	$-0.731304\pi$
$599$	7.71129	−	13.3564i	0.315075	−	0.545726i	0.979453	+	0.201671i	$0.0646370\pi$
$600$	−13.4246	+	7.15278i	−0.548059	+	0.292011i
$601$	1.25815	−	26.4118i	0.0513210	−	1.07736i	−0.815505	−	0.578750i	$-0.803541\pi$
$601$	1.25815	−	26.4118i	0.0513210	−	1.07736i	0.866826	−	0.498611i	$-0.166156\pi$
$602$	0.794446	−	5.52549i	0.0323792	−	0.225202i
$603$	−14.9829	+	12.4543i	−0.610152	+	0.507180i
$604$	1.02055	+	7.09810i	0.0415257	+	0.288818i
$605$	−8.25811	−	34.0404i	−0.335740	−	1.38394i
$606$	−15.3881	+	18.2528i	−0.625100	+	0.741471i
$607$	−13.4961	−	1.28872i	−0.547788	−	0.0523074i	−0.182507	−	0.983205i	$-0.558421\pi$
$607$	−13.4961	−	1.28872i	−0.547788	−	0.0523074i	−0.365281	+	0.930897i	$0.619027\pi$
$608$	0.845396	−	3.48477i	0.0342853	−	0.141326i
$609$	4.39886	−	9.98814i	0.178251	−	0.404740i
$610$	19.9617	+	3.84730i	0.808224	+	0.155772i
$611$	15.1593	−	4.45118i	0.613281	−	0.180076i
$612$	0.407097	−	19.8563i	0.0164559	−	0.802645i
$613$	−3.40680	+	2.18942i	−0.137599	+	0.0884298i	−0.607629	−	0.794221i	$-0.707879\pi$
$613$	−3.40680	+	2.18942i	−0.137599	+	0.0884298i	0.470030	+	0.882650i	$0.344243\pi$
$614$	−3.34823	−	13.8016i	−0.135123	−	0.556986i
$615$	36.1835	+	2.96095i	1.45906	+	0.119397i
$616$	−3.74513	−	5.25930i	−0.150896	−	0.211903i
$617$	8.32554	+	6.54728i	0.335174	+	0.263583i	0.771533	−	0.636189i	$-0.219490\pi$
$617$	8.32554	+	6.54728i	0.335174	+	0.263583i	−0.436360	+	0.899772i	$0.643732\pi$
$618$	−7.56523	−	29.4375i	−0.304318	−	1.18415i
$619$	−3.73380	+	10.7881i	−0.150074	+	0.433611i	−0.994832	−	0.101538i	$-0.967623\pi$
$619$	−3.73380	+	10.7881i	−0.150074	+	0.433611i	0.844757	+	0.535149i	$0.179745\pi$
$620$	−11.2742			−0.452781
$621$	−9.37175	+	23.0905i	−0.376076	+	0.926589i
$622$	4.72919			0.189623
$623$	−0.932413	+	2.69403i	−0.0373564	+	0.107934i
$624$	−1.22272	−	4.75778i	−0.0489479	−	0.190464i
$625$	−6.45867	−	5.07915i	−0.258347	−	0.203166i
$626$	−5.68037	−	7.97697i	−0.227033	−	0.318824i
$627$	7.74333	+	0.633647i	0.309239	+	0.0253054i
$628$	2.69292	+	11.1004i	0.107459	+	0.442953i
$629$	15.2274	−	9.78605i	0.607156	−	0.390195i
$630$	49.1837	+	29.7568i	1.95953	+	1.18554i
$631$	−3.59972	+	1.05697i	−0.143303	+	0.0420774i	−0.352597	−	0.935775i	$-0.614701\pi$
$631$	−3.59972	+	1.05697i	−0.143303	+	0.0420774i	0.209295	+	0.977853i	$0.432883\pi$
$632$	−2.16477	−	0.417225i	−0.0861100	−	0.0165963i
$633$	−10.2380	+	23.2467i	−0.406924	+	0.923972i
$634$	5.45833	−	22.4995i	0.216778	−	0.893570i
$635$	47.7036	+	4.55514i	1.89306	+	0.180765i
$636$	−8.71682	+	10.3396i	−0.345645	+	0.409991i
$637$	13.1327	+	54.1338i	0.520337	+	2.14486i
$638$	−0.217331	−	1.51157i	−0.00860421	−	0.0598436i
$639$	−2.35789	−	0.870591i	−0.0932765	−	0.0344401i
$640$	0.528336	−	3.67466i	0.0208843	−	0.145254i
$641$	−1.00113	+	21.0164i	−0.0395424	+	0.830096i	0.888783	+	0.458328i	$0.151551\pi$
$641$	−1.00113	+	21.0164i	−0.0395424	+	0.830096i	−0.928326	+	0.371768i	$0.878752\pi$
$642$	5.38748	−	2.87050i	0.212627	−	0.113290i
$643$	22.7104	−	39.3356i	0.895611	−	1.55124i	0.0625640	−	0.998041i	$-0.480072\pi$
$643$	22.7104	−	39.3356i	0.895611	−	1.55124i	0.833047	−	0.553202i	$-0.186594\pi$
$644$	−24.7534	+	0.0542282i	−0.975421	+	0.00213689i
$645$	5.09774	+	4.73048i	0.200723	+	0.186263i
$646$	−7.76425	+	22.4333i	−0.305480	+	0.882627i
$647$	17.7753	+	11.4235i	0.698820	+	0.449104i	0.841211	−	0.540706i	$-0.181843\pi$
$647$	17.7753	+	11.4235i	0.698820	+	0.449104i	−0.142392	+	0.989810i	$0.545479\pi$
$648$	0.0594123	+	8.99980i	0.00233394	+	0.353546i
$649$	−7.42598	+	16.2606i	−0.291495	+	0.638285i
$650$	19.5789	−	15.3971i	0.767949	−	0.603922i
$651$	13.8919	+	23.3258i	0.544468	+	0.914211i
$652$	0.417921	+	8.77324i	0.0163671	+	0.343587i
$653$	9.18582	+	0.877140i	0.359469	+	0.0343251i	0.273228	−	0.961949i	$-0.411909\pi$
$653$	9.18582	+	0.877140i	0.359469	+	0.0343251i	0.0862406	+	0.996274i	$0.472515\pi$
$654$	−0.144819	−	2.36530i	−0.00566288	−	0.0924906i
$655$	−27.7727	−	5.35274i	−1.08517	−	0.209149i
$656$	−3.69733	+	4.26695i	−0.144357	+	0.166596i
$657$	1.59627	+	4.23700i	0.0622765	+	0.165301i
$658$	−11.9443	−	26.1544i	−0.465637	−	1.01960i
$659$	17.4331	+	8.98740i	0.679098	+	0.350099i	0.763022	−	0.646373i	$-0.223715\pi$
$659$	17.4331	+	8.98740i	0.679098	+	0.350099i	−0.0839236	+	0.996472i	$0.526745\pi$
$660$	8.04276	−	0.108989i	0.313064	−	0.00424238i
$661$	−4.90767	−	1.96474i	−0.190886	−	0.0764193i	0.274250	−	0.961658i	$-0.411570\pi$
$661$	−4.90767	−	1.96474i	−0.190886	−	0.0764193i	−0.465136	+	0.885239i	$0.653995\pi$
$662$	−4.87355	−	6.84395i	−0.189416	−	0.265998i
$663$	5.06394	+	32.1242i	0.196667	+	1.24760i
$664$	−0.0702089	+	1.47387i	−0.00272463	+	0.0571971i
$665$	−44.9959	−	51.9280i	−1.74487	−	2.01368i
$666$	−6.77775	+	4.62000i	−0.262632	+	0.179022i
$667$	−5.20980	−	2.67141i	−0.201724	−	0.103437i
$668$	9.10843	+	15.7763i	0.352416	+	0.610402i
$669$	−18.0106	+	9.59624i	−0.696332	+	0.371012i
$670$	21.4300	−	11.0479i	0.827914	−	0.426819i
$671$	−5.38435	−	4.23430i	−0.207861	−	0.163463i
$672$	−8.25373	+	3.43478i	−0.318395	+	0.132499i
$673$	11.1024	−	8.73101i	0.427965	−	0.336556i	−0.380831	−	0.924645i	$-0.624362\pi$
$673$	11.1024	−	8.73101i	0.427965	−	0.336556i	0.808796	+	0.588089i	$0.200120\pi$
$674$	5.77827	+	1.69665i	0.222571	+	0.0653526i
$675$	−41.6408	+	18.6681i	−1.60275	+	0.718535i
$676$	−2.05886	−	4.50828i	−0.0791869	−	0.173395i
$677$	21.8676	+	20.8507i	0.840441	+	0.801359i	0.982061	−	0.188562i	$-0.0603827\pi$
$677$	21.8676	+	20.8507i	0.840441	+	0.801359i	−0.141620	+	0.989921i	$0.545231\pi$
$678$	16.5862	−	1.81090i	0.636991	−	0.0695472i
$679$	−22.3248	−	64.5034i	−0.856749	−	2.47541i
$680$	−5.79425	+	23.8842i	−0.222199	+	0.915919i
$681$	18.7786	−	3.88390i	0.719599	−	0.148832i
$682$	3.37653	+	1.74072i	0.129294	+	0.0666557i
$683$	−24.8297	−	7.29065i	−0.950081	−	0.278969i	−0.230260	−	0.973129i	$-0.573958\pi$
$683$	−24.8297	−	7.29065i	−0.950081	−	0.278969i	−0.719820	+	0.694160i	$0.755776\pi$
$684$	3.24169	−	10.2575i	0.123949	−	0.392205i
$685$	−14.5511	+	31.8624i	−0.555968	+	1.21740i
$686$	60.5703	−	24.2487i	2.31258	−	0.925819i
$687$	25.9848	+	7.24885i	0.991381	+	0.276561i
$688$	−1.06199	+	0.204683i	−0.0404882	+	0.00780345i
$689$	11.0723	−	19.1777i	0.421819	−	0.730612i
$690$	17.4901	−	25.3982i	0.665837	−	0.966895i
$691$	8.84192	+	15.3147i	0.336363	+	0.582597i	0.983746	−	0.179568i	$-0.0574699\pi$
$691$	8.84192	+	15.3147i	0.336363	+	0.582597i	−0.647383	+	0.762165i	$0.724137\pi$
$692$	3.74750	+	4.32484i	0.142458	+	0.164406i
$693$	−10.1357	−	16.5059i	−0.385024	−	0.627006i
$694$	−2.72023	+	18.9196i	−0.103259	+	0.718179i
$695$	−49.9732	+	4.77187i	−1.89559	+	0.181007i
$696$	−2.10745	−	0.172456i	−0.0798828	−	0.00653692i
$697$	27.0513	−	25.7934i	1.02464	−	0.976993i
$698$	1.13183	+	23.7600i	0.0428403	+	0.899328i
$699$	12.2669	−	37.0602i	0.463977	−	1.40174i
$700$	−32.8062	−	31.2807i	−1.23996	−	1.18230i
$701$	−14.3960	+	16.6138i	−0.543729	+	0.627496i	−0.959410	−	0.282014i	$-0.908998\pi$
$701$	−14.3960	+	16.6138i	−0.543729	+	0.627496i	0.415682	+	0.909510i	$0.363543\pi$
$702$	−2.68840	−	14.4899i	−0.101467	−	0.546885i
$703$	9.40725	−	2.76222i	0.354801	−	0.104179i
$704$	−0.725596	+	1.01896i	−0.0273469	+	0.0384034i
$705$	35.2614	+	6.30179i	1.32802	+	0.237339i
$706$	−12.5333	+	11.9505i	−0.471696	+	0.449761i
$707$	−66.0471	−	26.4413i	−2.48396	−	0.994427i
$708$	19.6618	+	15.0355i	0.738936	+	0.565070i
$709$	−33.4816	+	13.4040i	−1.25743	+	0.503399i	−0.902175	−	0.431371i	$-0.858030\pi$
$709$	−33.4816	+	13.4040i	−1.25743	+	0.503399i	−0.355255	+	0.934770i	$0.615606\pi$
$710$	2.61662	+	1.68160i	0.0981999	+	0.0631092i
$711$	−6.39409	−	1.69069i	−0.239797	−	0.0634058i
$712$	0.552330			0.0206994
$713$	12.9306	−	6.70207i	0.484254	−	0.250995i
$714$	56.5552	−	17.4419i	2.11652	−	0.652746i
$715$	−12.9329	+	2.49261i	−0.483664	+	0.0932185i
$716$	10.2439	−	5.28108i	0.382831	−	0.197363i
$717$	−0.123301	−	0.782185i	−0.00460476	−	0.0292112i
$718$	−22.4718	+	2.14580i	−0.838641	+	0.0800805i
$719$	−0.903388	−	6.28320i	−0.0336907	−	0.234324i	0.966018	−	0.258476i	$-0.0832204\pi$
$719$	−0.903388	−	6.28320i	−0.0336907	−	0.234324i	−0.999708	+	0.0241525i	$0.992311\pi$
$720$	2.33148	−	10.8906i	0.0868890	−	0.405867i
$721$	76.1950	−	48.9676i	2.83765	−	1.82365i
$722$	3.56253	−	5.00287i	0.132584	−	0.186188i
$723$	−2.20315	−	35.9836i	−0.0819362	−	1.33825i
$724$	0.194731	+	0.562640i	0.00723714	+	0.0209103i
$725$	−3.50663	−	10.1317i	−0.130233	−	0.376284i
$726$	14.6258	+	7.29097i	0.542813	+	0.270593i
$727$	19.2069	−	26.9723i	0.712345	−	1.00035i	−0.286758	−	0.958003i	$-0.592578\pi$
$727$	19.2069	−	26.9723i	0.712345	−	1.00035i	0.999103	−	0.0423452i	$-0.0134829\pi$
$728$	12.3149	−	7.91430i	0.456420	−	0.293324i
$729$	−1.65939	+	26.9490i	−0.0614589	+	0.998110i
$730$	−0.797387	−	5.54595i	−0.0295126	−	0.205265i
$731$	7.12756	−	0.680599i	0.263622	−	0.0251729i
$732$	−7.37525	+	5.96345i	−0.272597	+	0.220416i
$733$	27.5760	−	14.2164i	1.01854	−	0.525096i	0.133719	−	0.991019i	$-0.457308\pi$
$733$	27.5760	−	14.2164i	1.01854	−	0.525096i	0.884825	+	0.465924i	$0.154278\pi$
$734$	29.2294	−	5.63350i	1.07888	−	0.207936i
$735$	−28.1087	+	123.124i	−1.03680	+	4.54150i
$736$	1.57849	+	4.52862i	0.0581838	+	0.166927i
$737$	−8.12392			−0.299249
$738$	−11.9373	+	12.0164i	−0.439420	+	0.442330i
$739$	−20.4016	−	13.1113i	−0.750483	−	0.482306i	0.108636	−	0.994082i	$-0.465352\pi$
$739$	−20.4016	−	13.1113i	−0.750483	−	0.482306i	−0.859119	+	0.511775i	$0.828988\pi$
$740$	9.42344	−	3.77257i	0.346412	−	0.138683i
$741$	−2.27040	+	17.4681i	−0.0834053	+	0.641708i
$742$	−37.4133	−	14.9780i	−1.37349	−	0.549861i
$743$	−24.6146	+	23.4700i	−0.903023	+	0.861031i	−0.990831	−	0.135107i	$-0.956862\pi$
$743$	−24.6146	+	23.4700i	−0.903023	+	0.861031i	0.0878082	+	0.996137i	$0.472014\pi$
$744$	3.39038	−	4.02155i	0.124297	−	0.147437i
$745$	−33.7512	+	47.3970i	−1.23655	+	1.73649i
$746$	−25.4826	+	7.48237i	−0.932985	+	0.273949i
$747$	−0.511013	+	4.39702i	−0.0186970	+	0.160879i
$748$	5.42304	−	6.25852i	0.198286	−	0.228834i
$749$	13.1656	+	12.5533i	0.481059	+	0.458689i
$750$	23.8163	−	4.92582i	0.869648	−	0.179866i
$751$	−0.147408	−	3.09448i	−0.00537900	−	0.112919i	−0.999960	−	0.00895373i	$-0.997150\pi$
$751$	−0.147408	−	3.09448i	−0.00537900	−	0.112919i	0.994581	−	0.103965i	$-0.0331531\pi$
$752$	−4.03168	+	3.84419i	−0.147020	+	0.140183i
$753$	7.17352	−	10.3683i	0.261418	−	0.377842i
$754$	3.44673	−	0.329123i	0.125523	−	0.0119860i
$755$	3.78875	−	26.3513i	0.137887	−	0.959022i
$756$	−25.4050	+	8.59554i	−0.923970	+	0.312617i
$757$	−13.7423	−	15.8595i	−0.499473	−	0.576423i	0.448899	−	0.893583i	$-0.351816\pi$
$757$	−13.7423	−	15.8595i	−0.499473	−	0.576423i	−0.948372	+	0.317160i	$0.897271\pi$
$758$	13.1434	+	22.7650i	0.477389	+	0.826862i
$759$	−9.15962	+	4.90613i	−0.332473	+	0.178081i
$760$	−6.65613	+	11.5288i	−0.241443	+	0.418192i
$761$	29.4743	−	5.68071i	1.06844	−	0.205926i	0.375431	−	0.926850i	$-0.377495\pi$
$761$	29.4743	−	5.68071i	1.06844	−	0.205926i	0.693013	+	0.720925i	$0.256283\pi$
$762$	−15.9703	+	15.6463i	−0.578544	+	0.566805i
$763$	6.55587	−	2.62458i	0.237339	−	0.0950160i
$764$	−0.359897	+	0.788064i	−0.0130206	+	0.0285112i
$765$	−22.2182	+	70.3038i	−0.803300	+	2.54184i
$766$	15.2651	+	4.48225i	0.551552	+	0.161950i
$767$	−36.0247	−	18.5720i	−1.30078	−	0.670597i
$768$	1.15188	+	1.29351i	0.0415651	+	0.0466754i
$769$	−4.59971	+	18.9603i	−0.165870	+	0.683725i	0.826762	+	0.562552i	$0.190181\pi$
$769$	−4.59971	+	18.9603i	−0.165870	+	0.683725i	−0.992631	+	0.121172i	$0.961335\pi$
$770$	7.83961	+	22.6511i	0.282520	+	0.816288i
$771$	15.2130	−	34.5430i	0.547883	−	1.24404i
$772$	−0.677737	−	0.646221i	−0.0243923	−	0.0232580i
$773$	9.88544	+	21.6461i	0.355554	+	0.778556i	0.999904	+	0.0138249i	$0.00440075\pi$
$773$	9.88544	+	21.6461i	0.355554	+	0.778556i	−0.644350	+	0.764731i	$0.722872\pi$
$774$	−3.22038	+	0.395830i	−0.115754	+	0.0142278i
$775$	25.5901	+	7.51393i	0.919223	+	0.269908i
$776$	−10.3951	+	8.17483i	−0.373164	+	0.293459i
$777$	−19.4168	−	14.8482i	−0.696573	−	0.532675i
$778$	7.37934	+	5.80318i	0.264562	+	0.208054i
$779$	17.9951	−	9.27709i	0.644740	−	0.332386i
$780$	−0.620841	+	18.2264i	−0.0222297	+	0.652609i
$781$	−0.524020	−	0.907629i	−0.0187509	−	0.0324775i
$782$	−7.55274	−	30.8378i	−0.270085	−	1.10276i
$783$	−6.27250	−	0.946383i	−0.224161	−	0.0338210i
$784$	−12.8619	−	14.8434i	−0.459352	−	0.530120i
$785$	2.01770	−	42.3568i	0.0720149	−	1.51178i
$786$	10.2612	−	8.29695i	0.366004	−	0.295942i
$787$	23.1727	+	32.5415i	0.826017	+	1.15998i	0.984976	+	0.172693i	$0.0552468\pi$
$787$	23.1727	+	32.5415i	0.826017	+	1.15998i	−0.158959	+	0.987285i	$0.550814\pi$
$788$	−19.3889	−	7.76213i	−0.690700	−	0.276514i
$789$	−4.12666	+	7.37664i	−0.146913	+	0.262615i
$790$	7.27467	+	3.75035i	0.258821	+	0.133432i
$791$	20.6545	+	45.2271i	0.734390	+	1.60809i
$792$	−2.37975	+	2.90166i	−0.0845609	+	0.103106i
$793$	10.1704	−	11.7373i	0.361161	−	0.416802i
$794$	−17.5341	−	3.37943i	−0.622263	−	0.119931i
$795$	41.8642	−	27.7132i	1.48477	−	0.982884i
$796$	14.1898	+	1.35497i	0.502946	+	0.0480255i
$797$	−1.14878	−	24.1158i	−0.0406918	−	0.854225i	−0.923291	−	0.384100i	$-0.874512\pi$
$797$	−1.14878	−	24.1158i	−0.0406918	−	0.854225i	0.882600	−	0.470125i	$-0.155791\pi$
$798$	32.0542	−	0.434371i	1.13471	−	0.0153766i
$799$	28.9886	−	22.7969i	1.02554	−	0.806497i
$800$	−3.64828	+	7.98861i	−0.128986	+	0.282440i
$801$	1.65315	+	0.112752i	0.0584111	+	0.00398391i
$802$	1.30408	+	0.838081i	0.0460487	+	0.0295937i
$803$	−0.617478	+	1.78408i	−0.0217903	+	0.0629590i
$804$	−2.50361	+	10.9665i	−0.0882956	+	0.386760i
$805$	88.2299	+	25.6968i	3.10970	+	0.905694i
$806$	−4.30652	+	7.45911i	−0.151691	+	0.262736i
$807$	0.0113062	−	0.331923i	0.000397997	−	0.0116842i
$808$	−0.655849	+	13.7680i	−0.0230727	+	0.484355i
$809$	1.08370	−	7.53731i	0.0381009	−	0.264998i	−0.961863	−	0.273533i	$-0.911808\pi$
$809$	1.08370	−	7.53731i	0.0381009	−	0.264998i	0.999964	+	0.00853523i	$0.00271688\pi$
$810$	9.20141	−	32.1200i	0.323305	−	1.12858i
$811$	7.50297	+	52.1843i	0.263465	+	1.83244i	0.506283	+	0.862367i	$0.331019\pi$
$811$	7.50297	+	52.1843i	0.263465	+	1.83244i	−0.242819	+	0.970072i	$0.578072\pi$
$812$	−1.48555	−	6.12351i	−0.0521325	−	0.214893i
$813$	−48.6807	−	8.70003i	−1.70731	−	0.305123i
$814$	−3.40473	−	0.325112i	−0.119336	−	0.0113952i
$815$	7.68742	−	31.6880i	0.269279	−	1.10998i
$816$	−6.77716	−	9.24934i	−0.237248	−	0.323792i
$817$	3.80815	+	0.733961i	0.133230	+	0.0256780i
$818$	0.886449	−	0.260285i	0.0309939	−	0.00910064i
$819$	38.4747	−	21.1739i	1.34441	−	0.739877i
$820$	17.6330	−	11.3321i	0.615772	−	0.395732i
$821$	−6.74530	−	27.8045i	−0.235413	−	0.970384i	−0.959732	−	0.280919i	$-0.909361\pi$
$821$	−6.74530	−	27.8045i	−0.235413	−	0.970384i	0.724319	−	0.689465i	$-0.242154\pi$
$822$	−6.98965	−	14.7721i	−0.243792	−	0.515238i
$823$	11.9879	+	16.8347i	0.417872	+	0.586819i	0.968834	−	0.247711i	$-0.0796784\pi$
$823$	11.9879	+	16.8347i	0.417872	+	0.586819i	−0.550962	+	0.834531i	$0.685739\pi$
$824$	−13.7937	−	10.8475i	−0.480525	−	0.377889i
$825$	−18.3281	−	5.11290i	−0.638102	−	0.178008i
$826$	−24.1244	+	69.7030i	−0.839396	+	2.42528i
$827$	−28.6509			−0.996289			−0.498145	−	0.867094i	$-0.665985\pi$
$827$	−28.6509			−0.996289			−0.498145	+	0.867094i	$0.665985\pi$
$828$	3.80002	+	13.8766i	0.132060	+	0.482245i
$829$	−41.7104			−1.44866			−0.724331	−	0.689453i	$-0.757851\pi$
$829$	−41.7104			−1.44866			−0.724331	+	0.689453i	$0.757851\pi$
$830$	1.79163	−	5.17658i	0.0621884	−	0.179682i
$831$	−26.8046	+	26.2607i	−0.929843	+	0.910974i
$832$	−2.22938	−	1.75320i	−0.0772898	−	0.0607814i
$833$	75.4214	+	105.915i	2.61320	+	3.66972i
$834$	13.3259	−	19.2607i	0.461437	−	0.666943i
$835$	−15.9442	−	65.7227i	−0.551771	−	2.27443i
$836$	3.77349	−	2.42508i	0.130509	−	0.0838730i
$837$	10.9685	−	11.3446i	0.379128	−	0.392125i
$838$	−15.2082	+	4.46554i	−0.525359	+	0.154259i
$839$	13.2971	+	2.56281i	0.459068	+	0.0884781i	0.413542	−	0.910485i	$-0.364291\pi$
$839$	13.2971	+	2.56281i	0.459068	+	0.0884781i	0.0455260	+	0.998963i	$0.485504\pi$
$840$	32.9928	−	3.60218i	1.13836	−	0.124287i
$841$	−6.48564	+	26.7342i	−0.223643	+	0.921868i
$842$	−35.2147	−	3.36260i	−1.21358	−	0.115883i
$843$	13.6962	+	37.9030i	0.471723	+	1.30545i
$844$	3.45750	+	14.2520i	0.119012	+	0.490575i
$845$	2.61851	+	18.2122i	0.0900796	+	0.626517i
$846$	−12.8517	+	10.6828i	−0.441852	+	0.367283i
$847$	−6.93066	+	48.2038i	−0.238140	+	1.65630i
$848$	−0.371515	+	7.79905i	−0.0127579	+	0.267821i
$849$	−9.13426	−	5.69684i	−0.313487	−	0.195515i
$850$	29.0700	−	50.3507i	0.997092	−	1.72701i
$851$	−8.56528	+	9.92873i	−0.293614	+	0.340352i
$852$	−1.38671	+	0.427667i	−0.0475078	+	0.0146516i
$853$	−14.6231	+	42.2506i	−0.500685	+	1.44663i	0.357801	+	0.933798i	$0.383527\pi$
$853$	−14.6231	+	42.2506i	−0.500685	+	1.44663i	−0.858486	+	0.512837i	$0.828595\pi$
$854$	−23.7769	−	15.2805i	−0.813630	−	0.522888i
$855$	−22.2756	+	33.1473i	−0.761809	+	1.13361i
$856$	1.46410	−	3.20593i	0.0500419	−	0.109576i
$857$	−32.7892	+	25.7857i	−1.12006	+	0.880822i	−0.993801	−	0.111175i	$-0.964539\pi$
$857$	−32.7892	+	25.7857i	−1.12006	+	0.880822i	−0.126256	+	0.991998i	$0.540296\pi$
$858$	3.00008	−	5.36281i	0.102421	−	0.183083i
$859$	0.120250	+	2.52437i	0.00410289	+	0.0861303i	0.999990	−	0.00447253i	$-0.00142366\pi$
$859$	0.120250	+	2.52437i	0.00410289	+	0.0861303i	−0.995887	+	0.0906028i	$0.971121\pi$
$860$	3.99697	+	0.381665i	0.136296	+	0.0130147i
$861$	−45.1728	−	22.5188i	−1.53949	−	0.767437i
$862$	22.5263	+	4.34158i	0.767248	+	0.147875i
$863$	−30.4503	+	35.1416i	−1.03654	+	1.19623i	−0.0563026	+	0.998414i	$0.517931\pi$
$863$	−30.4503	+	35.1416i	−1.03654	+	1.19623i	−0.980239	+	0.197819i	$0.936614\pi$
$864$	3.18359	+	4.10667i	0.108308	+	0.139712i
$865$	−8.82540	−	19.3249i	−0.300073	−	0.657068i
$866$	29.6575	+	15.2895i	1.00780	+	0.519559i
$867$	23.7757	+	39.9216i	0.807466	+	1.35581i
$868$	14.5518	+	5.82566i	0.493920	+	0.197736i
$869$	−1.59966	−	2.24641i	−0.0542647	−	0.0762041i
$870$	7.32651	+	2.81852i	0.248392	+	0.0955567i
$871$	0.876426	−	18.3984i	0.0296965	−	0.623407i
$872$	−0.895958	−	1.03399i	−0.0303410	−	0.0350153i
$873$	−32.7819	+	22.3456i	−1.10950	+	0.756284i
$874$	0.780639	−	17.1794i	0.0264055	−	0.581102i
$875$	36.2369	+	62.7642i	1.22503	+	2.12182i
$876$	2.21805	+	1.38335i	0.0749411	+	0.0467392i
$877$	−0.419608	+	0.216323i	−0.0141692	+	0.00730471i	−0.465297	−	0.885155i	$-0.654052\pi$
$877$	−0.419608	+	0.216323i	−0.0141692	+	0.00730471i	0.451127	+	0.892460i	$0.351022\pi$
$878$	−3.30191	−	2.59665i	−0.111434	−	0.0876326i
$879$	−1.51281	+	11.6393i	−0.0510258	+	0.392585i
$880$	3.65037	−	2.87068i	0.123054	−	0.0967706i
$881$	13.1748	+	3.86848i	0.443871	+	0.130332i	0.496028	−	0.868307i	$-0.334791\pi$
$881$	13.1748	+	3.86848i	0.443871	+	0.130332i	−0.0521568	+	0.998639i	$0.516610\pi$
$882$	−35.4660	−	47.0525i	−1.19420	−	1.58434i
$883$	−2.33687	−	5.11704i	−0.0786421	−	0.172202i	0.866227	−	0.499651i	$-0.166538\pi$
$883$	−2.33687	−	5.11704i	−0.0786421	−	0.172202i	−0.944869	+	0.327449i	$0.893811\pi$
$884$	13.5888	+	12.9569i	0.457040	+	0.435787i
$885$	−54.3107	−	74.1222i	−1.82563	−	2.49159i
$886$	2.48053	+	7.16702i	0.0833350	+	0.240781i
$887$	3.18557	−	13.1311i	0.106961	−	0.440899i	−0.892997	−	0.450062i	$-0.851402\pi$
$887$	3.18557	−	13.1311i	0.106961	−	0.440899i	0.999958	+	0.00916364i	$0.00291692\pi$
$888$	−1.48813	+	4.49588i	−0.0499385	+	0.150872i
$889$	−59.2183	−	30.5291i	−1.98612	−	1.02391i
$890$	−1.96743	−	0.577691i	−0.0659485	−	0.0193642i
$891$	−7.71506	+	8.19902i	−0.258464	+	0.274677i
$892$	−4.89456	+	10.7176i	−0.163882	+	0.358852i
$893$	18.5446	−	7.42416i	0.620573	−	0.248440i
$894$	−6.75700	−	26.2925i	−0.225988	−	0.879353i
$895$	−42.0129	+	8.09732i	−1.40434	+	0.270664i
$896$	−2.58073	+	4.46995i	−0.0862160	+	0.149331i
$897$	−10.1229	−	21.2733i	−0.337992	−	0.710295i
$898$	0.559053	+	0.968307i	0.0186558	+	0.0323128i
$899$	2.42784	+	2.80188i	0.0809730	+	0.0934478i
$900$	−12.5502	+	23.1655i	−0.418342	+	0.772184i
$901$	7.35620	−	51.1635i	0.245071	−	1.70450i
$902$	−7.03062	+	0.671342i	−0.234094	+	0.0223533i
$903$	−4.13539	−	8.73987i	−0.137617	−	0.290845i
$904$	6.97171	−	6.64752i	0.231876	−	0.221093i
$905$	−0.105172	−	2.20783i	−0.00349603	−	0.0733908i
$906$	8.26027	+	9.27586i	0.274429	+	0.308170i
$907$	35.7230	+	34.0618i	1.18616	+	1.13100i	0.988577	+	0.150716i	$0.0481581\pi$
$907$	35.7230	+	34.0618i	1.18616	+	1.13100i	0.197584	+	0.980286i	$0.436690\pi$
$908$	7.25017	−	8.36715i	0.240605	−	0.277673i
$909$	−4.77357	+	41.0743i	−0.158329	+	1.36235i
$910$	−52.1442	+	15.3109i	−1.72856	+	0.507552i
$911$	7.50021	−	10.5326i	0.248493	−	0.348960i	−0.671424	−	0.741074i	$-0.734317\pi$
$911$	7.50021	−	10.5326i	0.248493	−	0.348960i	0.919917	+	0.392114i	$0.128256\pi$
$912$	−2.11072	−	5.84121i	−0.0698929	−	0.193422i
$913$	−1.33584	+	1.27372i	−0.0442098	+	0.0421540i
$914$	21.0159	+	8.41351i	0.695145	+	0.278294i
$915$	32.5084	−	13.5283i	1.07469	−	0.447232i
$916$	14.4595	−	5.78869i	0.477754	−	0.191264i
$917$	33.0808	+	21.2598i	1.09243	+	0.702059i
$918$	−18.3962	−	29.0672i	−0.607165	−	0.959360i
$919$	37.9854			1.25302			0.626511	−	0.779412i	$-0.284482\pi$
$919$	37.9854			1.25302			0.626511	+	0.779412i	$0.284482\pi$
$920$	−0.886119	−	17.7822i	−0.0292145	−	0.586262i
$921$	−18.0311	−	16.7321i	−0.594144	−	0.551340i
$922$	15.6828	−	3.02261i	0.516485	−	0.0995443i
$923$	2.11206	−	1.08884i	0.0695194	−	0.0358397i
$924$	−10.4373	−	4.01523i	−0.343361	−	0.132092i
$925$	−23.9036	+	2.28252i	−0.785946	+	0.0750488i
$926$	3.65350	+	25.4107i	0.120062	+	0.835046i
$927$	−39.0707	−	35.2828i	−1.28325	−	1.15884i
$928$	−1.02701	+	0.660017i	−0.0337132	+	0.0216661i
$929$	−6.03503	+	8.47502i	−0.198003	+	0.278056i	−0.901625	−	0.432518i	$-0.857625\pi$
$929$	−6.03503	+	8.47502i	−0.198003	+	0.278056i	0.703622	+	0.710574i	$0.251565\pi$
$930$	−16.2830	+	10.7789i	−0.533939	+	0.353456i
$931$	23.0348	+	66.5547i	0.754935	+	2.18124i
$932$	−7.37157	−	21.2988i	−0.241464	−	0.697664i
$933$	6.83024	−	4.52146i	0.223612	−	0.148026i
$934$	−13.7588	+	19.3216i	−0.450202	+	0.632220i
$935$	−25.8631	+	16.6212i	−0.845814	+	0.543572i
$936$	−6.31474	−	5.70252i	−0.206404	−	0.186393i
$937$	1.98088	+	13.7773i	0.0647125	+	0.450085i	0.996256	+	0.0864547i	$0.0275538\pi$
$937$	1.98088	+	13.7773i	0.0647125	+	0.450085i	−0.931543	+	0.363630i	$0.881537\pi$
$938$	−33.3689	+	3.18635i	−1.08953	+	0.104038i
$939$	−15.8306	−	6.09005i	−0.516611	−	0.198741i
$940$	18.3818	−	9.47647i	0.599548	−	0.309088i
$941$	−14.7888	+	2.85031i	−0.482102	+	0.0929176i	−0.424511	−	0.905423i	$-0.639554\pi$
$941$	−14.7888	+	2.85031i	−0.482102	+	0.0929176i	−0.0575909	+	0.998340i	$0.518342\pi$
$942$	14.5021	+	13.4573i	0.472503	+	0.438463i
$943$	−13.4872	+	23.4791i	−0.439204	+	0.764586i
$944$	14.2905			0.465116
$945$	99.4844	−	4.04637i	3.23623	−	0.131628i
$946$	−1.13813	−	0.731435i	−0.0370040	−	0.0237810i
$947$	37.2549	−	14.9146i	1.21062	−	0.484660i	0.323515	−	0.946223i	$-0.395135\pi$
$947$	37.2549	−	14.9146i	1.21062	−	0.484660i	0.887108	+	0.461563i	$0.152711\pi$
$948$	−3.52542	+	1.46710i	−0.114500	+	0.0476491i
$949$	−3.97384	−	1.59089i	−0.128996	−	0.0516424i
$950$	22.7917	−	21.7318i	0.739460	−	0.705073i
$951$	−13.6279	−	37.7140i	−0.441916	−	1.22296i
$952$	19.8204	−	27.8338i	0.642382	−	0.902100i
$953$	2.61742	−	0.768545i	0.0847867	−	0.0248956i	−0.239064	−	0.971004i	$-0.576841\pi$
$953$	2.61742	−	0.768545i	0.0847867	−	0.0248956i	0.323851	+	0.946108i	$0.395022\pi$
$954$	−2.70406	+	23.2671i	−0.0875470	+	0.753300i
$955$	2.10623	−	2.43071i	0.0681558	−	0.0786560i
$956$	−0.330871	−	0.315484i	−0.0107011	−	0.0102035i
$957$	−1.75906	−	1.97533i	−0.0568623	−	0.0638534i
$958$	−1.44151	−	30.2610i	−0.0465730	−	0.977688i
$959$	35.2455	−	33.6066i	1.13814	−	1.08521i
$960$	−2.75019	−	5.81233i	−0.0887619	−	0.187592i
$961$	21.6789	−	2.07008i	0.699319	−	0.0667768i
$962$	1.10360	−	7.67570i	0.0355815	−	0.247474i
$963$	5.03657	−	9.29661i	0.162301	−	0.299579i
$964$	−13.6303	−	15.7302i	−0.439003	−	0.506636i
$965$	1.73825	+	3.01074i	0.0559562	+	0.0969190i
$966$	−35.6988	+	23.7444i	−1.14859	+	0.763964i
$967$	−17.4871	+	30.2885i	−0.562346	+	0.974011i	0.434945	+	0.900457i	$0.356768\pi$
$967$	−17.4871	+	30.2885i	−0.562346	+	0.974011i	−0.997291	+	0.0735546i	$0.976566\pi$
$968$	9.26473	−	1.78563i	0.297780	−	0.0573923i
$969$	10.2342	+	39.8230i	0.328771	+	1.27930i
$970$	45.5784	−	18.2468i	1.46343	−	0.585870i
$971$	11.1479	−	24.4106i	0.357754	−	0.783373i	−0.642105	−	0.766617i	$-0.721939\pi$
$971$	11.1479	−	24.4106i	0.357754	−	0.783373i	0.999860	−	0.0167564i	$-0.00533397\pi$
$972$	8.69029	+	12.9414i	0.278741	+	0.415094i
$973$	66.9672	+	19.6634i	2.14687	+	0.630378i
$974$	−21.1187	−	10.8874i	−0.676685	−	0.348856i
$975$	13.5566	−	40.9565i	0.434158	−	1.31166i
$976$	−1.29100	+	5.32156i	−0.0413238	+	0.170339i
$977$	1.18019	+	3.40994i	0.0377577	+	0.109094i	0.962304	−	0.271976i	$-0.0876771\pi$
$977$	1.18019	+	3.40994i	0.0377577	+	0.109094i	−0.924546	+	0.381069i	$0.875556\pi$
$978$	8.99147	+	12.2714i	0.287516	+	0.392396i
$979$	0.500037	+	0.476784i	0.0159812	+	0.0152381i
$980$	30.2898	+	66.3255i	0.967573	+	2.11869i
$981$	−2.47056	−	3.27768i	−0.0788791	−	0.104648i
$982$	38.5245	+	11.3118i	1.22937	+	0.360974i
$983$	−30.4654	+	23.9583i	−0.971696	+	0.764150i	−0.971790	−	0.235850i	$-0.924213\pi$
$983$	−30.4654	+	23.9583i	−0.971696	+	0.764150i	9.33827e−5		1.00000i	$0.499970\pi$
$984$	−1.26043	+	9.69757i	−0.0401811	+	0.309147i
$985$	60.9458	+	47.9283i	1.94190	+	1.52712i
$986$	7.18352	−	3.70336i	0.228770	−	0.117939i
$987$	−42.2563	−	26.3544i	−1.34503	−	0.838869i
$988$	5.08503	+	8.80754i	0.161776	+	0.280205i
$989$	−4.81110	+	1.93831i	−0.152984	+	0.0616348i
$990$	11.5117	−	7.84689i	0.365867	−	0.249391i
$991$	8.39983	+	9.69392i	0.266829	+	0.307937i	0.873314	−	0.487158i	$-0.161966\pi$
$991$	8.39983	+	9.69392i	0.266829	+	0.307937i	−0.606485	+	0.795095i	$0.707421\pi$
$992$	0.144500	−	3.03342i	0.00458787	−	0.0963111i
$993$	−13.5821	−	5.22504i	−0.431014	−	0.165812i
$994$	−2.50839	−	3.52255i	−0.0795614	−	0.111728i
$995$	−49.1280	−	19.6679i	−1.55746	−	0.623514i
$996$	1.30773	+	2.19579i	0.0414369	+	0.0695762i
$997$	20.7529	+	10.6989i	0.657251	+	0.338836i	0.754382	−	0.656435i	$-0.227937\pi$
$997$	20.7529	+	10.6989i	0.657251	+	0.338836i	−0.0971317	+	0.995272i	$0.530967\pi$
$998$	−3.63685	−	7.96360i	−0.115123	−	0.252083i
$999$	−5.37184	+	13.1526i	−0.169957	+	0.416129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.13.5	✓	240
9.7	even	3	inner	414.2.m.a.151.1	yes	240
23.16	even	11	inner	414.2.m.a.85.1	yes	240
207.16	even	33	inner	414.2.m.a.223.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.13.5	✓	240	1.1	even	1	trivial
414.2.m.a.85.1	yes	240	23.16	even	11	inner
414.2.m.a.151.1	yes	240	9.7	even	3	inner
414.2.m.a.223.5	yes	240	207.16	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.431117 - 1.67754i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(2.15343 + 3.02407i) q^{5} +(-1.72628 - 0.141264i) q^{6} +(-1.21686 - 5.01596i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.62828 + 1.44643i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.431117 - 1.67754i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(2.15343 + 3.02407i) q^{5} +(-1.72628 - 0.141264i) q^{6} +(-1.21686 - 5.01596i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.62828 + 1.44643i) q^{9} +(3.56206 - 1.04592i) q^{10} +(-1.22830 - 0.236735i) q^{11} +(-0.698106 + 1.58513i) q^{12} +(0.668652 - 2.75622i) q^{13} +(-5.13808 - 0.490627i) q^{14} +(4.14461 - 4.91619i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.942149 - 6.55279i) q^{17} +(0.507252 + 2.95680i) q^{18} +(0.510319 - 3.54935i) q^{19} +(0.176645 - 3.70824i) q^{20} +(-7.88986 + 4.20379i) q^{21} +(-0.625453 + 1.08332i) q^{22} +(2.00181 + 4.35807i) q^{23} +(1.26962 + 1.17816i) q^{24} +(-2.87239 + 8.29923i) q^{25} +(-2.38594 - 1.53335i) q^{26} +(3.55954 + 3.78546i) q^{27} +(-2.14415 + 4.69502i) q^{28} +(-0.959618 + 0.754652i) q^{29} +(-3.29023 - 5.52459i) q^{30} +(-0.144500 - 3.03342i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.132407 + 2.16258i) q^{33} +(-6.50054 - 1.25288i) q^{34} +(12.5482 - 14.4814i) q^{35} +(2.96009 + 0.487722i) q^{36} +(1.13582 + 2.48711i) q^{37} +(-3.18723 - 1.64313i) q^{38} +(-4.91194 + 0.0665624i) q^{39} +(-3.44651 - 1.37978i) q^{40} +(3.27499 + 4.59908i) q^{41} +(1.39207 + 8.83085i) q^{42} +(-0.0514617 + 1.08031i) q^{43} +(0.819169 + 0.945371i) q^{44} +(-10.0339 - 4.83330i) q^{45} +(4.77311 - 0.466330i) q^{46} +(2.78533 + 4.82433i) q^{47} +(1.52861 - 0.814459i) q^{48} +(-17.4573 + 8.99984i) q^{49} +(6.90331 + 5.42882i) q^{50} +(-10.5864 + 4.40551i) q^{51} +(-2.22938 + 1.75320i) q^{52} +(7.49162 + 2.19974i) q^{53} +(4.74147 - 2.12566i) q^{54} +(-1.92915 - 4.22426i) q^{55} +(3.73552 + 3.56181i) q^{56} +(-6.17418 + 0.674102i) q^{57} +(0.399286 + 1.15366i) q^{58} +(3.36911 - 13.8877i) q^{59} +(-6.29687 + 1.30235i) q^{60} +(4.86719 + 2.50921i) q^{61} +(-2.91384 - 0.855582i) q^{62} +(10.4535 + 11.4232i) q^{63} +(0.415415 - 0.909632i) q^{64} +(9.77489 - 3.91328i) q^{65} +(2.08695 + 0.582186i) q^{66} +(6.37707 - 1.22908i) q^{67} +(-3.31009 + 5.73324i) q^{68} +(6.44781 - 5.23695i) q^{69} +(-9.58080 - 16.5944i) q^{70} +(0.548659 + 0.633186i) q^{71} +(1.42905 - 2.63777i) q^{72} +(0.214787 - 1.49388i) q^{73} +(2.72181 - 0.259902i) q^{74} +(15.1606 + 1.24061i) q^{75} +(-2.59520 + 2.47452i) q^{76} +(0.307212 + 6.44918i) q^{77} +(-1.54364 + 4.66355i) q^{78} +(1.59555 + 1.52136i) q^{79} +(-2.43113 + 2.80568i) q^{80} +(4.81568 - 7.60324i) q^{81} +(5.41728 - 1.59066i) q^{82} +(0.855896 - 1.20194i) q^{83} +(8.80046 + 1.57279i) q^{84} +(17.7872 - 16.9601i) q^{85} +(1.00407 + 0.401968i) q^{86} +(1.67967 + 1.28445i) q^{87} +(1.16130 - 0.464915i) q^{88} +(-0.464649 - 0.298612i) q^{89} +(-7.84925 + 7.90123i) q^{90} -14.6387 q^{91} +(1.12045 - 4.66311i) q^{92} +(-5.02638 + 1.55016i) q^{93} +(5.46999 - 1.05425i) q^{94} +(11.8324 - 6.10003i) q^{95} +(-0.269704 - 1.71092i) q^{96} +(13.1646 - 1.25707i) q^{97} +(2.79515 + 19.4407i) q^{98} +(3.57073 - 1.15444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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