LMFDB - Embedded newform 690.2.n.a.659.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			659.17
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.804725 - 1.53376i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.14469 - 1.92086i) q^{5} +(1.40362 + 1.01481i) q^{6} +(-0.955977 - 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-1.70483 - 2.46851i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.804725 - 1.53376i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.14469 - 1.92086i) q^{5} +(1.40362 + 1.01481i) q^{6} +(-0.955977 - 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-1.70483 - 2.46851i) q^{9} +(1.73840 + 1.40640i) q^{10} +(-0.130034 - 0.904408i) q^{11} +(-1.20424 + 1.24491i) q^{12} +(2.47130 + 3.84542i) q^{13} +(0.744166 - 0.858813i) q^{14} +(-2.02498 - 3.30143i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.74601 - 5.94637i) q^{17} +(2.68601 - 1.33618i) q^{18} +(0.111059 - 0.378232i) q^{19} +(-1.63949 + 1.52055i) q^{20} +(-1.71159 + 0.971841i) q^{21} +0.913708 q^{22} +(1.02121 + 4.68584i) q^{23} +(-1.06086 - 1.36915i) q^{24} +(-2.37939 - 4.39756i) q^{25} +(-4.15798 + 1.89889i) q^{26} +(-5.15802 + 0.628334i) q^{27} +(0.744166 + 0.858813i) q^{28} +(-2.85664 - 9.72883i) q^{29} +(3.55602 - 1.53452i) q^{30} +(3.71757 - 8.14034i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-1.49179 - 0.528359i) q^{33} +(6.13433 - 0.881983i) q^{34} +(-2.27441 + 1.13304i) q^{35} +(0.940317 + 2.84882i) q^{36} +(-4.47941 + 5.16952i) q^{37} +(0.358577 + 0.163757i) q^{38} +(7.88666 - 0.695875i) q^{39} +(-1.27175 - 1.83920i) q^{40} +(-7.60595 + 6.59060i) q^{41} +(-0.718363 - 1.83248i) q^{42} +(1.93387 + 4.23459i) q^{43} +(-0.130034 + 0.904408i) q^{44} +(-6.69316 + 0.449078i) q^{45} +(-4.78348 + 0.343953i) q^{46} +8.91322 q^{47} +(1.50619 - 0.855213i) q^{48} +(-2.37146 - 5.19278i) q^{49} +(4.69142 - 1.72933i) q^{50} +(-10.5254 - 2.10723i) q^{51} +(-1.28782 - 4.38590i) q^{52} +(0.827835 - 1.28814i) q^{53} +(0.112124 - 5.19494i) q^{54} +(-1.88609 - 0.785485i) q^{55} +(-0.955977 + 0.614369i) q^{56} +(-0.490745 - 0.474711i) q^{57} +(10.0363 - 1.44301i) q^{58} +(-2.84841 - 4.43222i) q^{59} +(1.01283 + 3.73821i) q^{60} +(6.70797 + 3.06343i) q^{61} +(7.52841 + 4.83822i) q^{62} +(0.113207 + 3.40724i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(10.2154 - 0.345222i) q^{65} +(0.735284 - 1.40141i) q^{66} +(0.882061 - 6.13487i) q^{67} +6.19741i q^{68} +(8.00875 + 2.20452i) q^{69} +(-0.797822 - 2.41251i) q^{70} +(9.58910 + 1.37871i) q^{71} +(-2.95365 + 0.525316i) q^{72} +(1.47294 - 5.01637i) q^{73} +(-4.47941 - 5.16952i) q^{74} +(-8.65955 + 0.110587i) q^{75} +(-0.213121 + 0.331622i) q^{76} +(-0.431331 + 0.944482i) q^{77} +(-0.433598 + 7.90542i) q^{78} +(1.62557 + 2.52943i) q^{79} +(2.00146 - 0.997065i) q^{80} +(-3.18708 + 8.41680i) q^{81} +(-5.44107 - 8.46648i) q^{82} +(7.96766 + 6.90401i) q^{83} +(1.91606 - 0.450263i) q^{84} +(-13.4208 - 3.45288i) q^{85} +(-4.46670 + 1.31154i) q^{86} +(-17.2205 - 3.44763i) q^{87} +(-0.876696 - 0.257421i) q^{88} +(6.57963 + 14.4074i) q^{89} +(0.508028 - 6.68894i) q^{90} -5.19442i q^{91} +(0.340309 - 4.78374i) q^{92} +(-9.49370 - 12.2526i) q^{93} +(-1.26848 + 8.82250i) q^{94} +(-0.599403 - 0.646286i) q^{95} +(0.632155 + 1.61257i) q^{96} +(10.6822 + 12.3279i) q^{97} +(5.47742 - 1.60831i) q^{98} +(-2.01085 + 1.86286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	0.804725	−	1.53376i	0.464608	−	0.885516i
$3$	0.804725	−	1.53376i	0.464608	−	0.885516i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	1.14469	−	1.92086i	0.511919	−	0.859034i
$5$	1.14469	−	1.92086i	0.511919	−	0.859034i
$6$	1.40362	+	1.01481i	0.573027	+	0.414295i
$7$	−0.955977	−	0.614369i	−0.361325	−	0.232210i	0.347364	−	0.937730i	$-0.387077\pi$
$7$	−0.955977	−	0.614369i	−0.361325	−	0.232210i	−0.708689	+	0.705521i	$0.750713\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−1.70483	−	2.46851i	−0.568278	−	0.822836i
$10$	1.73840	+	1.40640i	0.549731	+	0.444743i
$11$	−0.130034	−	0.904408i	−0.0392068	−	0.272689i	0.960783	−	0.277303i	$-0.0894405\pi$
$11$	−0.130034	−	0.904408i	−0.0392068	−	0.272689i	−0.999989	+	0.00461363i	$0.998531\pi$
$12$	−1.20424	+	1.24491i	−0.347634	+	0.359376i
$13$	2.47130	+	3.84542i	0.685415	+	1.06653i	0.993352	+	0.115120i	$0.0367253\pi$
$13$	2.47130	+	3.84542i	0.685415	+	1.06653i	−0.307936	+	0.951407i	$0.599638\pi$
$14$	0.744166	−	0.858813i	0.198887	−	0.229527i
$15$	−2.02498	−	3.30143i	−0.522847	−	0.852427i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−1.74601	−	5.94637i	−0.423470	−	1.44221i	−0.844694	−	0.535250i	$-0.820217\pi$
$17$	−1.74601	−	5.94637i	−0.423470	−	1.44221i	0.421224	−	0.906957i	$-0.361601\pi$
$18$	2.68601	−	1.33618i	0.633098	−	0.314940i
$19$	0.111059	−	0.378232i	0.0254787	−	0.0867725i	−0.945772	−	0.324831i	$-0.894693\pi$
$19$	0.111059	−	0.378232i	0.0254787	−	0.0867725i	0.971251	+	0.238058i	$0.0765109\pi$
$20$	−1.63949	+	1.52055i	−0.366600	+	0.340006i
$21$	−1.71159	+	0.971841i	−0.373500	+	0.212073i
$22$	0.913708			0.194803
$23$	1.02121	+	4.68584i	0.212937	+	0.977066i
$23$	1.02121	+	4.68584i	0.212937	+	0.977066i
$24$	−1.06086	−	1.36915i	−0.216547	−	0.279477i
$25$	−2.37939	−	4.39756i	−0.475878	−	0.879511i
$26$	−4.15798	+	1.89889i	−0.815447	+	0.372402i
$27$	−5.15802	+	0.628334i	−0.992662	+	0.120923i
$28$	0.744166	+	0.858813i	0.140634	+	0.162300i
$29$	−2.85664	−	9.72883i	−0.530465	−	1.80660i	−0.588771	−	0.808300i	$-0.700388\pi$
$29$	−2.85664	−	9.72883i	−0.530465	−	1.80660i	0.0583057	−	0.998299i	$-0.481430\pi$
$30$	3.55602	−	1.53452i	0.649237	−	0.280164i
$31$	3.71757	−	8.14034i	0.667695	−	1.46205i	−0.207479	−	0.978239i	$-0.566526\pi$
$31$	3.71757	−	8.14034i	0.667695	−	1.46205i	0.875174	−	0.483808i	$-0.160747\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	−1.49179	−	0.528359i	−0.259687	−	0.0919754i
$34$	6.13433	−	0.881983i	1.05203	−	0.151259i
$35$	−2.27441	+	1.13304i	−0.384445	+	0.191518i
$36$	0.940317	+	2.84882i	0.156720	+	0.474804i
$37$	−4.47941	+	5.16952i	−0.736411	+	0.849864i	−0.993178	−	0.116610i	$-0.962797\pi$
$37$	−4.47941	+	5.16952i	−0.736411	+	0.849864i	0.256767	+	0.966473i	$0.417343\pi$
$38$	0.358577	+	0.163757i	0.0581689	+	0.0265648i
$39$	7.88666	−	0.695875i	1.26288	−	0.111429i
$40$	−1.27175	−	1.83920i	−0.201082	−	0.290802i
$41$	−7.60595	+	6.59060i	−1.18785	+	1.02928i	−0.188969	+	0.981983i	$0.560515\pi$
$41$	−7.60595	+	6.59060i	−1.18785	+	1.02928i	−0.998881	+	0.0472953i	$0.984940\pi$
$42$	−0.718363	−	1.83248i	−0.110846	−	0.282758i
$43$	1.93387	+	4.23459i	0.294913	+	0.645769i	0.997854	−	0.0654792i	$-0.0208576\pi$
$43$	1.93387	+	4.23459i	0.294913	+	0.645769i	−0.702941	+	0.711248i	$0.748130\pi$
$44$	−0.130034	+	0.904408i	−0.0196034	+	0.136345i
$45$	−6.69316	+	0.449078i	−0.997757	+	0.0669446i
$46$	−4.78348	+	0.343953i	−0.705286	+	0.0507130i
$47$	8.91322			1.30013			0.650063	−	0.759880i	$-0.274742\pi$
$47$	8.91322			1.30013			0.650063	+	0.759880i	$0.274742\pi$
$48$	1.50619	−	0.855213i	0.217400	−	0.123439i
$49$	−2.37146	−	5.19278i	−0.338780	−	0.741825i
$50$	4.69142	−	1.72933i	0.663467	−	0.244565i
$51$	−10.5254	−	2.10723i	−1.47385	−	0.295072i
$52$	−1.28782	−	4.38590i	−0.178588	−	0.608215i
$53$	0.827835	−	1.28814i	0.113712	−	0.176939i	−0.779733	−	0.626113i	$-0.784645\pi$
$53$	0.827835	−	1.28814i	0.113712	−	0.176939i	0.893445	+	0.449173i	$0.148281\pi$
$54$	0.112124	−	5.19494i	0.0152582	−	0.706942i
$55$	−1.88609	−	0.785485i	−0.254320	−	0.105915i
$56$	−0.955977	+	0.614369i	−0.127748	+	0.0820986i
$57$	−0.490745	−	0.474711i	−0.0650008	−	0.0628770i
$58$	10.0363	−	1.44301i	1.31784	−	0.189476i
$59$	−2.84841	−	4.43222i	−0.370832	−	0.577025i	0.604817	−	0.796365i	$-0.293246\pi$
$59$	−2.84841	−	4.43222i	−0.370832	−	0.577025i	−0.975649	+	0.219339i	$0.929610\pi$
$60$	1.01283	+	3.73821i	0.130756	+	0.482600i
$61$	6.70797	+	3.06343i	0.858868	+	0.392232i	0.795642	−	0.605768i	$-0.207134\pi$
$61$	6.70797	+	3.06343i	0.858868	+	0.392232i	0.0632259	+	0.997999i	$0.479861\pi$
$62$	7.52841	+	4.83822i	0.956110	+	0.614454i
$63$	0.113207	+	3.40724i	0.0142627	+	0.429272i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	10.2154	−	0.345222i	1.26706	−	0.0428195i
$66$	0.735284	−	1.40141i	0.0905072	−	0.172501i
$67$	0.882061	−	6.13487i	0.107761	−	0.749493i	−0.862259	−	0.506468i	$-0.830951\pi$
$67$	0.882061	−	6.13487i	0.107761	−	0.749493i	0.970020	−	0.243026i	$-0.0781399\pi$
$68$			6.19741i			0.751546i
$69$	8.00875	+	2.20452i	0.964140	+	0.265393i
$70$	−0.797822	−	2.41251i	−0.0953580	−	0.288350i
$71$	9.58910	+	1.37871i	1.13802	+	0.163622i	0.685458	−	0.728112i	$-0.259602\pi$
$71$	9.58910	+	1.37871i	1.13802	+	0.163622i	0.452559	+	0.891734i	$0.350511\pi$
$72$	−2.95365	+	0.525316i	−0.348091	+	0.0619091i
$73$	1.47294	−	5.01637i	0.172395	−	0.587122i	−0.827284	−	0.561784i	$-0.810115\pi$
$73$	1.47294	−	5.01637i	0.172395	−	0.587122i	0.999679	−	0.0253387i	$-0.00806644\pi$
$74$	−4.47941	−	5.16952i	−0.520721	−	0.600945i
$75$	−8.65955	+	0.110587i	−0.999918	+	0.0127694i
$76$	−0.213121	+	0.331622i	−0.0244466	+	0.0380397i
$77$	−0.431331	+	0.944482i	−0.0491547	+	0.107634i
$78$	−0.433598	+	7.90542i	−0.0490953	+	0.895113i
$79$	1.62557	+	2.52943i	0.182891	+	0.284584i	0.920578	−	0.390559i	$-0.127718\pi$
$79$	1.62557	+	2.52943i	0.182891	+	0.284584i	−0.737687	+	0.675143i	$0.764082\pi$
$80$	2.00146	−	0.997065i	0.223771	−	0.111475i
$81$	−3.18708	+	8.41680i	−0.354120	+	0.935200i
$82$	−5.44107	−	8.46648i	−0.600866	−	0.934966i
$83$	7.96766	+	6.90401i	0.874564	+	0.757814i	0.971391	−	0.237487i	$-0.0763238\pi$
$83$	7.96766	+	6.90401i	0.874564	+	0.757814i	−0.0968267	+	0.995301i	$0.530869\pi$
$84$	1.91606	−	0.450263i	0.209059	−	0.0491277i
$85$	−13.4208	−	3.45288i	−1.45569	−	0.374518i
$86$	−4.46670	+	1.31154i	−0.481657	+	0.141427i
$87$	−17.2205	−	3.44763i	−1.84623	−	0.369625i
$88$	−0.876696	−	0.257421i	−0.0934561	−	0.0274412i
$89$	6.57963	+	14.4074i	0.697439	+	1.52718i	0.843049	+	0.537837i	$0.180758\pi$
$89$	6.57963	+	14.4074i	0.697439	+	1.52718i	−0.145610	+	0.989342i	$0.546514\pi$
$90$	0.508028	−	6.68894i	0.0535509	−	0.705076i
$91$		−	5.19442i		−	0.544524i
$92$	0.340309	−	4.78374i	0.0354796	−	0.498740i
$93$	−9.49370	−	12.2526i	−0.984450	−	1.27053i
$94$	−1.26848	+	8.82250i	−0.130834	+	0.909971i
$95$	−0.599403	−	0.646286i	−0.0614974	−	0.0663075i
$96$	0.632155	+	1.61257i	0.0645190	+	0.164582i
$97$	10.6822	+	12.3279i	1.08461	+	1.25171i	0.965937	+	0.258778i	$0.0833200\pi$
$97$	10.6822	+	12.3279i	1.08461	+	1.25171i	0.118677	+	0.992933i	$0.462135\pi$
$98$	5.47742	−	1.60831i	0.553303	−	0.162464i
$99$	−2.01085	+	1.86286i	−0.202098	+	0.187224i
$100$	1.04407	+	4.88978i	0.104407	+	0.488978i
$101$	4.75115	+	4.11690i	0.472757	+	0.409647i	0.858384	−	0.513008i	$-0.171469\pi$
$101$	4.75115	+	4.11690i	0.472757	+	0.409647i	−0.385626	+	0.922655i	$0.626015\pi$
$102$	3.58370	−	10.1183i	0.354839	−	1.00186i
$103$	−0.422456	−	2.93825i	−0.0416259	−	0.289514i	−0.999992	−	0.00397239i	$-0.998736\pi$
$103$	−0.422456	−	2.93825i	−0.0416259	−	0.289514i	0.958366	−	0.285542i	$-0.0921735\pi$
$104$	4.52453	−	0.650529i	0.443667	−	0.0637897i
$105$	−0.0924690	+	4.40018i	−0.00902405	+	0.429414i
$106$	1.15721	+	1.00273i	0.112398	+	0.0973938i
$107$	14.2352	+	6.50102i	1.37617	+	0.628477i	0.959792	−	0.280713i	$-0.0905708\pi$
$107$	14.2352	+	6.50102i	1.37617	+	0.628477i	0.416381	+	0.909190i	$0.363298\pi$
$108$	5.12611	+	0.850301i	0.493260	+	0.0818202i
$109$	−1.71763	−	5.84972i	−0.164519	−	0.560301i	−0.999943	−	0.0106947i	$-0.996596\pi$
$109$	−1.71763	−	5.84972i	−0.164519	−	0.560301i	0.835423	−	0.549607i	$-0.185222\pi$
$110$	1.04591	−	1.75510i	0.0997234	−	0.167343i
$111$	4.32410	+	11.0304i	0.410426	+	1.04696i
$112$	−0.472066	−	1.03368i	−0.0446061	−	0.0976737i
$113$	−9.64896	−	1.38731i	−0.907698	−	0.130507i	−0.327376	−	0.944894i	$-0.606164\pi$
$113$	−9.64896	−	1.38731i	−0.907698	−	0.130507i	−0.580322	+	0.814387i	$0.697073\pi$
$114$	0.539719	−	0.418192i	0.0505494	−	0.0391673i
$115$	10.1698	+	3.40221i	0.948339	+	0.317258i
$116$			10.1396i			0.941434i
$117$	5.27929	−	12.6562i	0.488071	−	1.17007i
$118$	4.79247	−	2.18865i	0.441183	−	0.201482i
$119$	−1.98412	+	6.75729i	−0.181884	+	0.619440i
$120$	−3.84430	+	0.470518i	−0.350935	+	0.0429522i
$121$	9.75338	−	2.86385i	0.886671	−	0.260350i
$122$	−3.98689	+	6.20372i	−0.360956	+	0.561659i
$123$	3.98769	+	16.9693i	0.359557	+	1.53007i
$124$	−5.86038	+	6.76324i	−0.526277	+	0.607356i
$125$	−11.1707	−	0.463350i	−0.999141	−	0.0414433i
$126$	−3.38867	−	0.372846i	−0.301886	−	0.0332157i
$127$	14.7504	−	2.12078i	1.30888	−	0.188189i	0.547673	−	0.836693i	$-0.315514\pi$
$127$	14.7504	−	2.12078i	1.30888	−	0.188189i	0.761212	+	0.648504i	$0.224605\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	8.05107	+	0.441586i	0.708858	+	0.0388795i
$130$	−1.11209	+	10.1605i	−0.0975368	+	0.891136i
$131$	−0.345636	+	0.537820i	−0.0301983	+	0.0469895i	−0.856025	−	0.516935i	$-0.827073\pi$
$131$	−0.345636	+	0.537820i	−0.0301983	+	0.0469895i	0.825826	+	0.563925i	$0.190709\pi$
$132$	1.28250	+	0.927241i	0.111627	+	0.0807060i
$133$	−0.338544	+	0.293350i	−0.0293555	+	0.0254367i
$134$	5.94689	+	1.74617i	0.513733	+	0.150846i
$135$	−4.69737	+	10.6271i	−0.404286	+	0.914633i
$136$	−6.13433	−	0.881983i	−0.526014	−	0.0756295i
$137$			10.6373i			0.908803i	0.890797	+	0.454402i	$0.150147\pi$
$137$			10.6373i			0.908803i	−0.890797	+	0.454402i	$0.849853\pi$
$138$	−3.32185	+	7.61350i	−0.282774	+	0.648104i
$139$	−9.73039			−0.825321			−0.412661	−	0.910885i	$-0.635400\pi$
$139$	−9.73039			−0.825321			−0.412661	+	0.910885i	$0.635400\pi$
$140$	2.50149	−	0.446366i	0.211415	−	0.0377248i
$141$	7.17269	−	13.6707i	0.604050	−	1.15128i
$142$	−2.72934	+	9.29529i	−0.229041	+	0.780043i
$143$	3.15647	−	2.73510i	0.263958	−	0.228721i
$144$	−0.0996213	−	2.99835i	−0.00830177	−	0.249862i
$145$	−21.9577	−	5.64925i	−1.82348	−	0.469145i
$146$	4.75569	+	2.17185i	0.393584	+	0.179744i
$147$	−9.87285	−	0.541507i	−0.814299	−	0.0446628i
$148$	5.75439	−	3.69812i	0.473008	−	0.303984i
$149$	−1.24372	−	8.65025i	−0.101889	−	0.708656i	−0.975173	−	0.221444i	$-0.928923\pi$
$149$	−1.24372	−	8.65025i	−0.101889	−	0.708656i	0.873284	−	0.487212i	$-0.161986\pi$
$150$	1.12292	−	8.58714i	0.0916861	−	0.701137i
$151$	−1.99413	+	1.28155i	−0.162280	+	0.104291i	−0.619260	−	0.785186i	$-0.712567\pi$
$151$	−1.99413	+	1.28155i	−0.162280	+	0.104291i	0.456980	+	0.889477i	$0.348931\pi$
$152$	−0.297917	−	0.258146i	−0.0241642	−	0.0209384i
$153$	−11.7020	+	14.4476i	−0.946052	+	1.16802i
$154$	−0.873484	−	0.561354i	−0.0703874	−	0.0452352i
$155$	−11.3810	−	16.4590i	−0.914143	−	1.32202i
$156$	−7.76325	−	1.55424i	−0.621557	−	0.124439i
$157$	−17.4466	−	5.12278i	−1.39239	−	0.408843i	−0.502326	−	0.864678i	$-0.667522\pi$
$157$	−17.4466	−	5.12278i	−1.39239	−	0.408843i	−0.890064	+	0.455836i	$0.849340\pi$
$158$	−2.73503	+	1.24905i	−0.217587	+	0.0993688i
$159$	−1.30951	−	2.30630i	−0.103851	−	0.182901i
$160$	0.702078	+	2.12299i	0.0555041	+	0.167837i
$161$	1.90258	−	5.10696i	0.149945	−	0.402485i
$162$	−7.87756	−	4.35247i	−0.618920	−	0.341963i
$163$	15.4066	+	2.21514i	1.20674	+	0.173503i	0.716186	−	0.697909i	$-0.245886\pi$
$163$	15.4066	+	2.21514i	1.20674	+	0.173503i	0.490552	+	0.871412i	$0.336795\pi$
$164$	9.15464	−	4.18079i	0.714858	−	0.326465i
$165$	−2.72253	+	2.26070i	−0.211948	+	0.175996i
$166$	−7.96766	+	6.90401i	−0.618410	+	0.535855i
$167$	−6.41448	+	1.88346i	−0.496367	+	0.145747i	−0.520328	−	0.853966i	$-0.674190\pi$
$167$	−6.41448	+	1.88346i	−0.496367	+	0.145747i	0.0239611	+	0.999713i	$0.492372\pi$
$168$	0.172996	+	1.96064i	0.0133469	+	0.151266i
$169$	−3.27952	+	7.18116i	−0.252271	+	0.552397i
$170$	5.32771	−	12.7928i	0.408617	−	0.981161i
$171$	−1.12301	+	0.370673i	−0.0858785	+	0.0283461i
$172$	−0.662515	−	4.60789i	−0.0505163	−	0.351348i
$173$	2.76882	+	19.2576i	0.210510	+	1.46413i	0.771460	+	0.636278i	$0.219527\pi$
$173$	2.76882	+	19.2576i	0.210510	+	1.46413i	−0.560950	+	0.827850i	$0.689564\pi$
$174$	5.86327	−	16.5546i	0.444494	−	1.25500i
$175$	−0.427081	+	5.66579i	−0.0322843	+	0.428293i
$176$	0.379568	−	0.831138i	0.0286110	−	0.0626494i
$177$	−9.09014	+	0.802063i	−0.683257	+	0.0602867i
$178$	−15.1971	+	4.46227i	−1.13907	+	0.334462i
$179$	−3.40016	+	2.94626i	−0.254140	+	0.220214i	−0.772608	−	0.634883i	$-0.781048\pi$
$179$	−3.40016	+	2.94626i	−0.254140	+	0.220214i	0.518468	+	0.855097i	$0.326503\pi$
$180$	6.54856	+	1.45479i	0.488101	+	0.108434i
$181$	−13.5975	+	6.20977i	−1.01069	+	0.461569i	−0.850758	−	0.525558i	$-0.823856\pi$
$181$	−13.5975	+	6.20977i	−1.01069	+	0.461569i	−0.159937	+	0.987127i	$0.551129\pi$
$182$	5.14155	+	0.739244i	0.381117	+	0.0547964i
$183$	10.0966	−	7.82319i	0.746365	−	0.578307i
$184$	4.68662	+	1.01764i	0.345502	+	0.0750216i
$185$	4.80239	+	14.5218i	0.353079	+	1.06766i
$186$	13.4790	−	7.65334i	0.988326	−	0.561170i
$187$	−5.15090	+	2.35234i	−0.376671	+	0.172020i
$188$	−8.55217	−	2.51114i	−0.623731	−	0.183144i
$189$	5.31698	+	2.56826i	0.386754	+	0.186813i
$190$	0.725011	−	0.501326i	0.0525979	−	0.0363700i
$191$	−6.66753	−	4.28496i	−0.482445	−	0.310049i	0.276715	−	0.960952i	$-0.410754\pi$
$191$	−6.66753	−	4.28496i	−0.482445	−	0.310049i	−0.759161	+	0.650903i	$0.774390\pi$
$192$	−1.68612	+	0.396228i	−0.121685	+	0.0285953i
$193$	−5.97374	−	5.17628i	−0.429999	−	0.372597i	0.412802	−	0.910821i	$-0.364550\pi$
$193$	−5.97374	−	5.17628i	−0.429999	−	0.372597i	−0.842802	+	0.538224i	$0.819095\pi$
$194$	−13.7227	+	8.81903i	−0.985231	+	0.633170i
$195$	7.69107	−	15.9457i	0.550769	−	1.14190i
$196$	0.812427	+	5.65055i	0.0580305	+	0.403611i
$197$	4.26621	−	2.74173i	0.303955	−	0.195340i	−0.379768	−	0.925082i	$-0.623996\pi$
$197$	4.26621	−	2.74173i	0.303955	−	0.195340i	0.683723	+	0.729742i	$0.260360\pi$
$198$	−1.55772	−	2.25550i	−0.110702	−	0.160291i
$199$	−10.9150	−	4.98472i	−0.773745	−	0.353357i	−0.0109014	−	0.999941i	$-0.503470\pi$
$199$	−10.9150	−	4.98472i	−0.773745	−	0.353357i	−0.762844	+	0.646583i	$0.776197\pi$
$200$	−4.98859	+	0.337558i	−0.352747	+	0.0238690i
$201$	−8.69959	−	6.28975i	−0.613622	−	0.443645i
$202$	−4.75115	+	4.11690i	−0.334290	+	0.289664i
$203$	−3.24621	+	11.0556i	−0.227839	+	0.775949i
$204$	9.50533	+	4.98721i	0.665507	+	0.349175i
$205$	3.95317	+	22.1541i	0.276102	+	1.54731i
$206$	2.96846			0.206823
$207$	9.82605	−	10.5095i	0.682958	−	0.730458i
$208$			4.57106i			0.316946i
$209$	−0.356518	−	0.0512595i	−0.0246608	−	0.00354569i
$210$	−4.34223	−	0.717739i	−0.299643	−	0.0495287i
$211$	15.8447	+	4.65242i	1.09079	+	0.320286i	0.777188	−	0.629268i	$-0.216645\pi$
$211$	15.8447	+	4.65242i	1.09079	+	0.320286i	0.313605	+	0.949554i	$0.398463\pi$
$212$	−1.15721	+	1.00273i	−0.0794777	+	0.0688678i
$213$	9.83120	−	13.5979i	0.673622	−	0.931713i
$214$	−8.46074	+	13.1652i	−0.578364	+	0.899952i
$215$	10.3477	+	1.13258i	0.705708	+	0.0772413i
$216$	−1.57117	+	4.95292i	−0.106904	+	0.337004i
$217$	−8.55508	+	5.49802i	−0.580757	+	0.373230i
$218$	6.03462	−	0.867648i	0.408716	−	0.0587645i
$219$	−6.50860	−	6.29594i	−0.439810	−	0.425440i
$220$	1.58839	+	1.28504i	0.107089	+	0.0866374i
$221$	18.5514	−	21.4094i	1.24790	−	1.44015i
$222$	−11.5335	+	2.71030i	−0.774078	+	0.181903i
$223$	5.77324	−	8.98334i	0.386605	−	0.601569i	−0.592341	−	0.805687i	$-0.701796\pi$
$223$	5.77324	−	8.98334i	0.386605	−	0.601569i	0.978946	+	0.204118i	$0.0654327\pi$
$224$	1.09034	−	0.320153i	0.0728515	−	0.0213911i
$225$	−6.79894	+	13.3707i	−0.453263	+	0.891377i
$226$	2.74638	−	9.35332i	0.182687	−	0.622173i
$227$	−6.55117	+	2.99182i	−0.434817	+	0.198574i	−0.620784	−	0.783982i	$-0.713186\pi$
$227$	−6.55117	+	2.99182i	−0.434817	+	0.198574i	0.185967	+	0.982556i	$0.440458\pi$
$228$	0.337125	+	0.593741i	0.0223267	+	0.0393214i
$229$			14.7923i			0.977502i	0.872423	+	0.488751i	$0.162547\pi$
$229$			14.7923i			0.977502i	−0.872423	+	0.488751i	$0.837453\pi$
$230$	−4.81490	+	9.58211i	−0.317485	+	0.631825i
$231$	1.10151	+	1.42161i	0.0724738	+	0.0935348i
$232$	−10.0363	−	1.44301i	−0.658919	−	0.0947382i
$233$	−3.13206	−	6.85824i	−0.205188	−	0.449299i	0.778861	−	0.627196i	$-0.215798\pi$
$233$	−3.13206	−	6.85824i	−0.205188	−	0.449299i	−0.984049	+	0.177898i	$0.943070\pi$
$234$	11.7761	+	7.02673i	0.769827	+	0.459352i
$235$	10.2028	−	17.1210i	0.665559	−	1.11685i
$236$	1.48433	+	5.05517i	0.0966218	+	0.329064i
$237$	5.18768	−	0.457731i	0.336976	−	0.0297329i
$238$	−6.40614	−	2.92559i	−0.415249	−	0.189638i
$239$	12.4756	+	10.8101i	0.806976	+	0.699249i	0.957208	−	0.289402i	$-0.0934564\pi$
$239$	12.4756	+	10.8101i	0.806976	+	0.699249i	−0.150231	+	0.988651i	$0.548002\pi$
$240$	0.0813721	−	3.87213i	0.00525254	−	0.249945i
$241$	8.53816	−	1.22760i	0.549991	−	0.0790768i	0.138283	−	0.990393i	$-0.455842\pi$
$241$	8.53816	−	1.22760i	0.549991	−	0.0790768i	0.411708	+	0.911316i	$0.364932\pi$
$242$	1.44665	+	10.0617i	0.0929942	+	0.646789i
$243$	10.3446	+	11.6614i	0.663608	+	0.748081i
$244$	−5.57318	−	4.82919i	−0.356786	−	0.309157i
$245$	−12.6892	−	1.38886i	−0.810681	−	0.0887308i
$246$	−17.3641	+	1.53211i	−1.10709	+	0.0976838i
$247$	1.72892	−	0.507657i	0.110009	−	0.0323015i
$248$	−5.86038	−	6.76324i	−0.372134	−	0.429466i
$249$	17.0009	−	6.66463i	1.07739	−	0.422354i
$250$	2.04839	−	10.9911i	0.129552	−	0.695138i
$251$	3.58418	−	24.9285i	0.226231	−	1.57347i	−0.487544	−	0.873098i	$-0.662107\pi$
$251$	3.58418	−	24.9285i	0.226231	−	1.57347i	0.713776	−	0.700375i	$-0.246984\pi$
$252$	0.851308	−	3.30111i	0.0536274	−	0.207951i
$253$	4.10512	−	1.53291i	0.258087	−	0.0963733i
$254$			14.9021i			0.935038i
$255$	−16.0959	+	17.8056i	−1.00797	+	1.11503i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−12.4856	−	3.66611i	−0.778831	−	0.228686i	−0.131930	−	0.991259i	$-0.542117\pi$
$257$	−12.4856	−	3.66611i	−0.778831	−	0.228686i	−0.646902	+	0.762573i	$0.723936\pi$
$258$	−1.58288	+	7.90628i	−0.0985457	+	0.492224i
$259$	7.45821	−	2.18993i	0.463431	−	0.136076i
$260$	−9.89883	−	2.54676i	−0.613899	−	0.157944i
$261$	−19.1456	+	23.6377i	−1.18508	+	1.46314i
$262$	−0.483156	−	0.418657i	−0.0298495	−	0.0258647i
$263$	9.83503	+	15.3036i	0.606454	+	0.943661i	0.999706	+	0.0242305i	$0.00771358\pi$
$263$	9.83503	+	15.3036i	0.606454	+	0.943661i	−0.393252	+	0.919431i	$0.628650\pi$
$264$	−1.10032	+	1.13749i	−0.0677201	+	0.0700075i
$265$	−1.52672	−	3.06467i	−0.0937855	−	0.188261i
$266$	−0.242185	−	0.376847i	−0.0148493	−	0.0231059i
$267$	27.3922	+	1.50241i	1.67638	+	0.0919462i
$268$	−2.57472	+	5.63786i	−0.157276	+	0.344387i
$269$	5.64427	−	8.78265i	0.344137	−	0.535488i	−0.625440	−	0.780272i	$-0.715081\pi$
$269$	5.64427	−	8.78265i	0.344137	−	0.535488i	0.969578	+	0.244784i	$0.0787171\pi$
$270$	−9.85040	−	6.16195i	−0.599476	−	0.375004i
$271$	−0.564550	−	0.651525i	−0.0342939	−	0.0395773i	0.738343	−	0.674425i	$-0.235608\pi$
$271$	−0.564550	−	0.651525i	−0.0342939	−	0.0395773i	−0.772637	+	0.634848i	$0.781063\pi$
$272$	1.74601	−	5.94637i	0.105868	−	0.360552i
$273$	−7.96700	−	4.18008i	−0.482185	−	0.252990i
$274$	−10.5290	−	1.51384i	−0.636080	−	0.0914545i
$275$	−3.66778	+	2.72377i	−0.221176	+	0.164250i
$276$	−7.06325	−	4.37155i	−0.425158	−	0.263136i
$277$		−	13.4347i		−	0.807212i	−0.914933	−	0.403606i	$-0.867757\pi$
$277$		−	13.4347i		−	0.807212i	0.914933	−	0.403606i	$-0.132243\pi$
$278$	1.38478	−	9.63135i	0.0830536	−	0.577650i
$279$	−26.4323	+	4.70108i	−1.58246	+	0.281446i
$280$	0.0858227	+	2.53956i	0.00512889	+	0.151768i
$281$	−8.66510	−	10.0001i	−0.516917	−	0.596554i	0.435939	−	0.899976i	$-0.356416\pi$
$281$	−8.66510	−	10.0001i	−0.516917	−	0.596554i	−0.952856	+	0.303422i	$0.901871\pi$
$282$	12.5108	+	9.04523i	0.745007	+	0.538636i
$283$	25.3685	+	16.3033i	1.50800	+	0.969132i	0.993767	+	0.111481i	$0.0355594\pi$
$283$	25.3685	+	16.3033i	1.50800	+	0.969132i	0.514232	+	0.857651i	$0.328077\pi$
$284$	−8.81225	−	4.02442i	−0.522911	−	0.238805i
$285$	−1.47360	+	0.399257i	−0.0872886	+	0.0236500i
$286$	2.25805	+	3.51359i	0.133521	+	0.207763i
$287$	11.3202	−	1.62760i	0.668209	−	0.0960740i
$288$	2.98200	+	0.328102i	0.175716	+	0.0193336i
$289$	−18.0095	+	11.5740i	−1.05938	+	0.680822i
$290$	8.71665	−	20.9302i	0.511859	−	1.22906i
$291$	27.5043	−	6.46334i	1.61233	−	0.378888i
$292$	−2.82655	+	4.39820i	−0.165411	+	0.257385i
$293$	2.12053	+	7.22185i	0.123882	+	0.421905i	0.997957	−	0.0638867i	$-0.0203496\pi$
$293$	2.12053	+	7.22185i	0.123882	+	0.421905i	−0.874075	+	0.485791i	$0.838531\pi$
$294$	1.94105	−	9.69529i	0.113204	−	0.565441i
$295$	−11.7742	+	0.397901i	−0.685520	+	0.0231667i
$296$	2.84154	+	6.22212i	0.165161	+	0.361653i
$297$	1.23899	+	4.58325i	0.0718935	+	0.265947i
$298$	8.73920			0.506248
$299$	−15.4953	+	15.5071i	−0.896117	+	0.896800i
$300$	8.33993	+	2.33357i	0.481506	+	0.134729i
$301$	0.752864	−	5.23628i	0.0433943	−	0.301814i
$302$	−0.984710	−	2.15621i	−0.0566637	−	0.124076i
$303$	10.1377	−	3.97415i	0.582396	−	0.228309i
$304$	0.297917	−	0.258146i	0.0170867	−	0.0148057i
$305$	13.5629	−	9.37840i	0.776611	−	0.537005i
$306$	−12.6352	−	13.6390i	−0.722306	−	0.779691i
$307$	20.7597	+	9.48065i	1.18482	+	0.541090i	0.907649	−	0.419731i	$-0.137876\pi$
$307$	20.7597	+	9.48065i	1.18482	+	0.541090i	0.277172	+	0.960820i	$0.410603\pi$
$308$	0.679950	−	0.784704i	0.0387438	−	0.0447127i
$309$	−4.84653	−	1.71654i	−0.275709	−	0.0976503i
$310$	17.9112	−	8.92278i	1.01729	−	0.506780i
$311$	−7.18241	+	1.03267i	−0.407277	+	0.0585576i	−0.342909	−	0.939369i	$-0.611412\pi$
$311$	−7.18241	+	1.03267i	−0.407277	+	0.0585576i	−0.0643681	+	0.997926i	$0.520503\pi$
$312$	2.64325	−	7.46304i	0.149645	−	0.422511i
$313$	11.7474	−	13.5572i	0.664001	−	0.766298i	−0.319424	−	0.947612i	$-0.603489\pi$
$313$	11.7474	−	13.5572i	0.664001	−	0.766298i	0.983425	+	0.181313i	$0.0580349\pi$
$314$	7.55355	−	16.5400i	0.426271	−	0.933404i
$315$	6.67440	+	3.68276i	0.376060	+	0.207500i
$316$	−0.847098	−	2.88495i	−0.0476530	−	0.162291i
$317$	−8.78306	−	10.1362i	−0.493306	−	0.569305i	0.453440	−	0.891287i	$-0.350197\pi$
$317$	−8.78306	−	10.1362i	−0.493306	−	0.569305i	−0.946746	+	0.321982i	$0.895651\pi$
$318$	2.46918	−	0.967963i	0.138465	−	0.0542807i
$319$	−8.42737	+	3.84865i	−0.471842	+	0.215483i
$320$	−2.20130	+	0.392799i	−0.123056	+	0.0219581i
$321$	21.4265	−	16.6019i	1.19591	−	0.926628i
$322$	4.78421	+	2.61001i	0.266614	+	0.145450i
$323$	−2.44302			−0.135933
$324$	5.42927	−	7.17796i	0.301626	−	0.398775i
$325$	11.0303	−	20.0174i	0.611849	−	1.11037i
$326$	−4.38518	+	14.9345i	−0.242872	+	0.827148i
$327$	−10.3543	−	2.07298i	−0.572593	−	0.114636i
$328$	2.83539	+	9.65645i	0.156558	+	0.533188i
$329$	−8.52084	−	5.47601i	−0.469769	−	0.301902i
$330$	−1.85024	−	3.01655i	−0.101852	−	0.166055i
$331$	10.6386	−	12.2776i	0.584748	−	0.674836i	−0.383870	−	0.923387i	$-0.625409\pi$
$331$	10.6386	−	12.2776i	0.584748	−	0.674836i	0.968619	+	0.248551i	$0.0799545\pi$
$332$	−5.69983	−	8.86910i	−0.312819	−	0.486755i
$333$	20.3977	+	2.24430i	1.11779	+	0.122987i
$334$	−0.951414	−	6.61723i	−0.0520591	−	0.362079i
$335$	−10.7745	−	8.71681i	−0.588675	−	0.476250i
$336$	−1.96530	−	0.107793i	−0.107216	−	0.00588060i
$337$	0.990198	−	2.16823i	0.0539395	−	0.118111i	−0.880743	−	0.473594i	$-0.842956\pi$
$337$	0.990198	−	2.16823i	0.0539395	−	0.118111i	0.934683	+	0.355483i	$0.115684\pi$
$338$	−6.64134	−	4.26813i	−0.361241	−	0.232156i
$339$	−9.89257	+	13.6828i	−0.537290	+	0.743147i
$340$	11.9043	+	7.09409i	0.645604	+	0.384731i
$341$	−7.84559	−	2.30367i	−0.424863	−	0.124751i
$342$	−0.207080	−	1.16433i	−0.0111976	−	0.0629597i
$343$	−2.05528	+	14.2948i	−0.110975	+	0.771845i
$344$	4.65528			0.250996
$345$	13.4021	−	12.8602i	0.721543	−	0.692369i
$346$	−19.4556			−1.04594
$347$	−2.54956	+	17.7326i	−0.136867	+	0.951934i	0.799438	+	0.600748i	$0.205130\pi$
$347$	−2.54956	+	17.7326i	−0.136867	+	0.951934i	−0.936306	+	0.351186i	$0.885779\pi$
$348$	15.5516	+	8.15956i	0.833655	+	0.437398i
$349$	4.48842	+	1.31792i	0.240260	+	0.0705466i	0.399646	−	0.916670i	$-0.369133\pi$
$349$	4.48842	+	1.31792i	0.240260	+	0.0705466i	−0.159386	+	0.987216i	$0.550951\pi$
$350$	−5.54734	−	1.22906i	−0.296518	−	0.0656960i
$351$	−15.1632	−	18.2820i	−0.809353	−	0.975819i
$352$	0.768660	+	0.493988i	0.0409697	+	0.0263296i
$353$	−0.0845283	+	0.185091i	−0.00449899	+	0.00985141i	−0.911868	−	0.410483i	$-0.865360\pi$
$353$	−0.0845283	+	0.185091i	−0.00449899	+	0.00985141i	0.907369	+	0.420335i	$0.138087\pi$
$354$	0.499763	−	9.11176i	0.0265621	−	0.484285i
$355$	13.6248	−	16.8411i	0.723130	−	0.893834i
$356$	−2.25408	−	15.6775i	−0.119466	−	0.830904i
$357$	8.76739	+	8.48093i	0.464019	+	0.448858i
$358$	−2.43238	−	3.78485i	−0.128555	−	0.200036i
$359$	−17.1471	+	19.7888i	−0.904987	+	1.04441i	0.0938202	+	0.995589i	$0.470092\pi$
$359$	−17.1471	+	19.7888i	−0.904987	+	1.04441i	−0.998808	+	0.0488218i	$0.984453\pi$
$360$	−2.37194	+	6.27486i	−0.125012	+	0.330714i
$361$	15.8531	+	10.1882i	0.834373	+	0.536219i
$362$	−4.21144	−	14.3428i	−0.221348	−	0.753843i
$363$	3.45633	−	17.2639i	0.181410	−	0.906122i
$364$	−1.46344	+	4.98401i	−0.0767050	+	0.261233i
$365$	−7.94969	−	8.57148i	−0.416106	−	0.448652i
$366$	6.30666	+	11.1072i	0.329655	+	0.580584i
$367$	−11.5036			−0.600485			−0.300243	−	0.953863i	$-0.597068\pi$
$367$	−11.5036			−0.600485			−0.300243	+	0.953863i	$0.597068\pi$
$368$	−1.67426	+	4.49409i	−0.0872768	+	0.234271i
$369$	29.2358	+	7.53949i	1.52196	+	0.392490i
$370$	−15.0574	+	2.68684i	−0.782799	+	0.139682i
$371$	−1.58278	+	0.722833i	−0.0821740	+	0.0375276i
$372$	5.65718	+	14.4310i	0.293311	+	0.748210i
$373$	−1.82996	−	2.11188i	−0.0947515	−	0.109349i	0.706394	−	0.707819i	$-0.250321\pi$
$373$	−1.82996	−	2.11188i	−0.0947515	−	0.109349i	−0.801145	+	0.598470i	$0.795775\pi$
$374$	−1.59535	−	5.43325i	−0.0824933	−	0.280947i
$375$	−9.70004	+	16.7603i	−0.500908	+	0.865501i
$376$	3.70268	−	8.10775i	0.190951	−	0.418125i
$377$	30.3518	−	35.0279i	1.56320	−	1.80403i
$378$	−3.29880	+	4.89736i	−0.169672	+	0.251893i
$379$	0.210121	−	0.0302108i	0.0107932	−	0.00155183i	−0.136916	−	0.990583i	$-0.543719\pi$
$379$	0.210121	−	0.0302108i	0.0107932	−	0.00155183i	0.147709	+	0.989031i	$0.452810\pi$
$380$	0.393043	+	0.788978i	0.0201627	+	0.0404737i
$381$	8.61723	−	24.3302i	0.441474	−	1.24647i
$382$	5.19023	−	5.98985i	0.265555	−	0.306467i
$383$	−28.5118	−	13.0209i	−1.45689	−	0.665338i	−0.479644	−	0.877463i	$-0.659234\pi$
$383$	−28.5118	−	13.0209i	−1.45689	−	0.665338i	−0.977242	+	0.212125i	$0.931961\pi$
$384$	−0.152235	−	1.72535i	−0.00776871	−	0.0880463i
$385$	1.32048	+	1.90966i	0.0672978	+	0.0973253i
$386$	5.97374	−	5.17628i	0.304056	−	0.263466i
$387$	7.15619	−	11.9931i	0.363770	−	0.609641i
$388$	−6.77633	−	14.8381i	−0.344016	−	0.753290i
$389$	2.59557	−	18.0526i	0.131600	−	0.915301i	−0.811869	−	0.583840i	$-0.801549\pi$
$389$	2.59557	−	18.0526i	0.131600	−	0.915301i	0.943469	−	0.331461i	$-0.107541\pi$
$390$	14.6889	+	9.88210i	0.743799	+	0.500400i
$391$	26.0807	−	14.2540i	1.31896	−	0.720858i
$392$	−5.70866			−0.288331
$393$	0.546744	+	0.962919i	0.0275796	+	0.0485728i
$394$	2.10668	+	4.61298i	0.106133	+	0.232398i
$395$	6.71945	−	0.227080i	0.338092	−	0.0114256i
$396$	2.45423	−	1.22088i	0.123329	−	0.0613513i
$397$	−5.20139	−	17.7143i	−0.261050	−	0.889055i	−0.980832	−	0.194855i	$-0.937576\pi$
$397$	−5.20139	−	17.7143i	−0.261050	−	0.889055i	0.719782	−	0.694200i	$-0.244242\pi$
$398$	6.48735	−	10.0945i	0.325182	−	0.505992i
$399$	0.177494	+	0.755312i	0.00888579	+	0.0378129i
$400$	0.375828	−	4.98586i	0.0187914	−	0.249293i
$401$	−0.210668	+	0.135388i	−0.0105203	+	0.00676096i	−0.545890	−	0.837857i	$-0.683808\pi$
$401$	−0.210668	+	0.135388i	−0.0105203	+	0.00676096i	0.535370	+	0.844618i	$0.320172\pi$
$402$	7.46381	−	7.71592i	0.372261	−	0.384835i
$403$	40.4902	−	5.82162i	2.01696	−	0.289995i
$404$	−3.39883	−	5.28869i	−0.169098	−	0.263122i
$405$	12.5193	+	15.7565i	0.622088	+	0.782947i
$406$	−10.4811	−	4.78654i	−0.520166	−	0.237552i
$407$	5.25783	+	3.37900i	0.260621	+	0.167491i
$408$	−6.28920	+	8.69883i	−0.311362	+	0.430656i
$409$	−10.4300	−	12.0368i	−0.515728	−	0.595182i	0.436828	−	0.899545i	$-0.356102\pi$
$409$	−10.4300	−	12.0368i	−0.515728	−	0.595182i	−0.952556	+	0.304363i	$0.901556\pi$
$410$	−22.4912	+	0.760076i	−1.11076	+	0.0375375i
$411$	16.3150	+	8.56008i	0.804760	+	0.422237i
$412$	−0.422456	+	2.93825i	−0.0208129	+	0.144757i
$413$			5.98708i			0.294605i
$414$	9.00410	+	11.2217i	0.442527	+	0.551516i
$415$	22.3821	−	7.40181i	1.09869	−	0.363341i
$416$	−4.52453	−	0.650529i	−0.221833	−	0.0318948i
$417$	−7.83029	+	14.9241i	−0.383451	+	0.730835i
$418$	0.101476	−	0.345594i	0.00496333	−	0.0169036i
$419$	10.4325	+	12.0398i	0.509661	+	0.588180i	0.951012	−	0.309154i	$-0.100046\pi$
$419$	10.4325	+	12.0398i	0.509661	+	0.588180i	−0.441351	+	0.897335i	$0.645500\pi$
$420$	1.32840	−	4.19589i	0.0648192	−	0.204738i
$421$	10.0357	−	15.6159i	0.489111	−	0.761072i	−0.505711	−	0.862703i	$-0.668770\pi$
$421$	10.0357	−	15.6159i	0.489111	−	0.761072i	0.994822	+	0.101631i	$0.0324062\pi$
$422$	−6.86000	+	15.0213i	−0.333939	+	0.731225i
$423$	−15.1956	−	22.0024i	−0.738834	−	1.06979i
$424$	−0.827835	−	1.28814i	−0.0402032	−	0.0625575i
$425$	−21.9951	+	21.8269i	−1.06692	+	1.05876i
$426$	12.0604	+	11.6663i	0.584327	+	0.565235i
$427$	−4.53059	−	7.04974i	−0.219251	−	0.341161i
$428$	−11.8271	−	10.2482i	−0.571683	−	0.495366i
$429$	−1.65489	−	7.04227i	−0.0798989	−	0.340004i
$430$	−2.59369	+	10.0812i	−0.125079	+	0.486159i
$431$	−6.68325	+	1.96238i	−0.321921	+	0.0945244i	−0.438700	−	0.898633i	$-0.644561\pi$
$431$	−6.68325	+	1.96238i	−0.321921	+	0.0945244i	0.116780	+	0.993158i	$0.462743\pi$
$432$	−4.67891	−	2.26005i	−0.225114	−	0.108737i
$433$	−26.5442	−	7.79408i	−1.27563	−	0.374559i	−0.427341	−	0.904090i	$-0.640550\pi$
$433$	−26.5442	−	7.79408i	−1.27563	−	0.374559i	−0.848291	+	0.529531i	$0.822368\pi$
$434$	−4.22454	−	9.25045i	−0.202784	−	0.444036i
$435$	−26.3345	+	29.1317i	−1.26264	+	1.39676i
$436$			6.09668i			0.291978i
$437$	1.88575	+	0.134150i	0.0902078	+	0.00641726i
$438$	7.15813	−	5.54635i	0.342028	−	0.265015i
$439$	1.67590	−	11.6562i	0.0799864	−	0.556318i	−0.909941	−	0.414739i	$-0.863873\pi$
$439$	1.67590	−	11.6562i	0.0799864	−	0.556318i	0.989927	−	0.141579i	$-0.0452179\pi$
$440$	−1.49801	+	1.38934i	−0.0714149	+	0.0662343i
$441$	−8.77547	+	14.7068i	−0.417880	+	0.700324i
$442$	18.5514	+	21.4094i	0.882399	+	1.01834i
$443$	25.6971	−	7.54536i	1.22091	−	0.358491i	0.393097	−	0.919497i	$-0.371404\pi$
$443$	25.6971	−	7.54536i	1.22091	−	0.358491i	0.827812	+	0.561006i	$0.189586\pi$
$444$	−1.04133	−	11.8018i	−0.0494191	−	0.560090i
$445$	35.2061	+	3.85338i	1.66893	+	0.182668i
$446$	8.07029	+	6.99294i	0.382139	+	0.331125i
$447$	−14.2683	−	5.05351i	−0.674865	−	0.239023i
$448$	0.161723	+	1.12481i	0.00764068	+	0.0531421i
$449$	−20.2233	+	2.90767i	−0.954398	+	0.137222i	−0.601883	−	0.798585i	$-0.705583\pi$
$449$	−20.2233	+	2.90767i	−0.954398	+	0.137222i	−0.352515	+	0.935806i	$0.614673\pi$
$450$	−12.2670	−	8.63258i	−0.578270	−	0.406944i
$451$	6.94962	+	6.02188i	0.327245	+	0.283559i
$452$	8.86726	+	4.04954i	0.417081	+	0.190474i
$453$	0.360861	+	4.08981i	0.0169547	+	0.192156i
$454$	−2.02904	−	6.91027i	−0.0952275	−	0.324315i
$455$	−9.97775	−	5.94598i	−0.467764	−	0.278752i
$456$	−0.635675	+	0.249196i	−0.0297682	+	0.0116697i
$457$	4.15562	+	9.09955i	0.194392	+	0.425659i	0.981579	−	0.191055i	$-0.0611909\pi$
$457$	4.15562	+	9.09955i	0.194392	+	0.425659i	−0.787187	+	0.616714i	$0.788464\pi$
$458$	−14.6417	−	2.10516i	−0.684163	−	0.0983678i
$459$	12.7423	+	29.5744i	0.594759	+	1.38042i
$460$	−8.79934	−	6.12957i	−0.410271	−	0.285792i
$461$		−	17.0976i		−	0.796314i	−0.917317	−	0.398157i	$-0.869650\pi$
$461$		−	17.0976i		−	0.796314i	0.917317	−	0.398157i	$-0.130350\pi$
$462$	−1.56390	+	0.887978i	−0.0727591	+	0.0413125i
$463$	−7.29605	+	3.33199i	−0.339076	+	0.154851i	−0.577674	−	0.816268i	$-0.696039\pi$
$463$	−7.29605	+	3.33199i	−0.339076	+	0.154851i	0.238598	+	0.971118i	$0.423312\pi$
$464$	2.85664	−	9.72883i	0.132616	−	0.451650i
$465$	−34.4028	+	4.21068i	−1.59539	+	0.195266i
$466$	7.23417	−	2.12415i	0.335117	−	0.0983991i
$467$	−12.6660	+	19.7087i	−0.586113	+	0.912010i	0.413885	+	0.910329i	$0.364172\pi$
$467$	−12.6660	+	19.7087i	−0.586113	+	0.912010i	−0.999999	+	0.00168120i	$0.999465\pi$
$468$	−8.63112	+	10.6562i	−0.398974	+	0.492584i
$469$	−4.61230	+	5.32288i	−0.212976	+	0.245788i
$470$	15.4947	+	12.5356i	0.714719	+	0.578222i
$471$	−21.8968	+	22.6364i	−1.00895	+	1.04303i
$472$	−5.21496	+	0.749798i	−0.240038	+	0.0345122i
$473$	3.57832	−	2.29965i	0.164532	−	0.105738i
$474$	−0.285211	+	5.20002i	−0.0131002	+	0.238845i
$475$	−1.92755	+	0.411574i	−0.0884421	+	0.0188843i
$476$	3.80750	−	5.92458i	0.174516	−	0.271553i
$477$	−4.59110	+	0.152541i	−0.210212	+	0.00698438i
$478$	−12.4756	+	10.8101i	−0.570619	+	0.494444i
$479$	39.1601	+	11.4984i	1.78927	+	0.525377i	0.996458	−	0.0840904i	$-0.0267984\pi$
$479$	39.1601	+	11.4984i	1.78927	+	0.525377i	0.792811	+	0.609467i	$0.208617\pi$
$480$	3.82114	+	0.631605i	0.174410	+	0.0288287i
$481$	−30.9490	−	4.44979i	−1.41115	−	0.202893i
$482$			8.62596i			0.392902i
$483$	−6.30179	−	7.02780i	−0.286741	−	0.319776i
$484$	−10.1651			−0.462052
$485$	35.9080	−	6.40741i	1.63050	−	0.290945i
$486$	−13.0149	+	8.57974i	−0.590369	+	0.389185i
$487$	−3.42982	+	11.6809i	−0.155420	+	0.529312i	−0.999981	−	0.00614729i	$-0.998043\pi$
$487$	−3.42982	+	11.6809i	−0.155420	+	0.529312i	0.844561	+	0.535459i	$0.179861\pi$
$488$	5.57318	−	4.82919i	0.252286	−	0.218607i
$489$	15.7956	−	21.8474i	0.714300	−	0.987976i
$490$	3.18058	−	12.3624i	0.143684	−	0.558474i
$491$	−4.58738	−	2.09498i	−0.207025	−	0.0945453i	0.309204	−	0.950996i	$-0.399937\pi$
$491$	−4.58738	−	2.09498i	−0.207025	−	0.0945453i	−0.516229	+	0.856450i	$0.672665\pi$
$492$	0.954654	−	17.4054i	0.0430391	−	0.784696i
$493$	−52.8635	+	33.9733i	−2.38085	+	1.53008i
$494$	0.256439	+	1.78357i	0.0115377	+	0.0802467i
$495$	1.27649	+	5.99495i	0.0573739	+	0.269453i
$496$	7.52841	−	4.83822i	0.338036	−	0.217242i
$497$	−8.31993	−	7.20926i	−0.373200	−	0.323380i
$498$	4.17732	+	17.7763i	0.187190	+	0.796575i
$499$	−29.3886	−	18.8869i	−1.31562	−	0.845495i	−0.320796	−	0.947148i	$-0.603950\pi$
$499$	−29.3886	−	18.8869i	−1.31562	−	0.845495i	−0.994820	+	0.101653i	$0.967587\pi$
$500$	10.5877	+	3.59174i	0.473496	+	0.160628i
$501$	−2.27312	+	11.3539i	−0.101555	+	0.507256i
$502$	24.1647	+	7.09539i	1.07852	+	0.316683i
$503$	5.36550	−	2.45034i	0.239236	−	0.109255i	−0.292190	−	0.956360i	$-0.594384\pi$
$503$	5.36550	−	2.45034i	0.239236	−	0.109255i	0.531425	+	0.847105i	$0.321657\pi$
$504$	3.14636	+	1.31244i	0.140150	+	0.0584608i
$505$	13.3466	−	4.41374i	0.593914	−	0.196409i
$506$	0.933090	+	4.28149i	0.0414809	+	0.190336i
$507$	8.37505	+	10.8089i	0.371949	+	0.480038i
$508$	−14.7504	−	2.12078i	−0.654442	−	0.0940946i
$509$	5.65035	−	2.58043i	0.250447	−	0.114375i	−0.286236	−	0.958159i	$-0.592404\pi$
$509$	5.65035	−	2.58043i	0.250447	−	0.114375i	0.536683	+	0.843784i	$0.319677\pi$
$510$	−15.3337	−	18.4661i	−0.678987	−	0.817692i
$511$	−4.49000	+	3.89061i	−0.198626	+	0.172111i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−0.335189	+	2.02071i	−0.0147989	+	0.0892167i
$514$	5.40568	−	11.8368i	0.238434	−	0.522098i
$515$	−6.12754	−	2.55189i	−0.270012	−	0.112450i
$516$	−7.60054	−	2.69195i	−0.334595	−	0.118506i
$517$	−1.15902	−	8.06118i	−0.0509738	−	0.354530i
$518$	1.10622	+	7.69396i	0.0486047	+	0.338053i
$519$	31.7647	+	11.2504i	1.39431	+	0.493836i
$520$	3.92959	−	9.43563i	0.172324	−	0.413780i
$521$	−0.259221	+	0.567615i	−0.0113567	+	0.0248676i	−0.915225	−	0.402942i	$-0.867987\pi$
$521$	−0.259221	+	0.567615i	−0.0113567	+	0.0248676i	0.903869	+	0.427810i	$0.140715\pi$
$522$	−20.6724	−	22.3147i	−0.904806	−	0.976689i
$523$	−24.8294	+	7.29057i	−1.08571	+	0.318794i	−0.775162	−	0.631762i	$-0.782332\pi$
$523$	−24.8294	+	7.29057i	−1.08571	+	0.318794i	−0.310551	+	0.950557i	$0.600514\pi$
$524$	0.483156	−	0.418657i	0.0211068	−	0.0182891i
$525$	8.34627	+	5.21444i	0.364261	+	0.227577i
$526$	−16.5475	+	7.55700i	−0.721506	+	0.329501i
$527$	−54.8964	−	7.89291i	−2.39132	−	0.343820i
$528$	−0.969318	−	1.25100i	−0.0421841	−	0.0544429i
$529$	−20.9143	+	9.57048i	−0.909315	+	0.416108i
$530$	3.25075	−	1.07503i	0.141203	−	0.0466963i
$531$	−6.08490	+	14.5875i	−0.264062	+	0.633045i
$532$	0.407477	−	0.186089i	0.0176664	−	0.00806796i
$533$	−44.1402	−	12.9607i	−1.91192	−	0.561392i
$534$	−5.38544	+	26.8996i	−0.233051	+	1.16406i
$535$	28.7824	−	19.9023i	1.24437	−	0.860450i
$536$	−5.21405	−	3.35087i	−0.225213	−	0.144735i
$537$	1.78265	+	7.58596i	0.0769272	+	0.327358i
$538$	7.89000	+	6.83672i	0.340162	+	0.294752i
$539$	−4.38802	+	2.82001i	−0.189005	+	0.121466i
$540$	7.50109	−	8.87320i	0.322795	−	0.381842i
$541$	0.424572	+	2.95296i	0.0182538	+	0.126958i	0.996911	−	0.0785430i	$-0.0250268\pi$
$541$	0.424572	+	2.95296i	0.0182538	+	0.126958i	−0.978657	+	0.205501i	$0.934118\pi$
$542$	0.725237	−	0.466082i	0.0311516	−	0.0200199i
$543$	−1.41796	+	25.8525i	−0.0608505	+	1.10944i
$544$	5.63736	+	2.57450i	0.241700	+	0.110381i
$545$	−13.2026	−	3.39676i	−0.565538	−	0.145501i
$546$	5.27136	−	7.29102i	0.225593	−	0.312027i
$547$	−23.2611	+	20.1559i	−0.994575	+	0.861804i	−0.990406	−	0.138187i	$-0.955872\pi$
$547$	−23.2611	+	20.1559i	−0.994575	+	0.861804i	−0.00416877	+	0.999991i	$0.501327\pi$
$548$	2.99686	−	10.2064i	0.128020	−	0.435995i
$549$	−3.87388	−	21.7813i	−0.165333	−	0.929604i
$550$	−2.17407	−	4.01808i	−0.0927025	−	0.171332i
$551$	−3.99702			−0.170279
$552$	5.33226	−	6.36922i	0.226956	−	0.271092i
$553$		−	3.41678i		−	0.145296i
$554$	13.2979	+	1.91196i	0.564976	+	0.0812312i
$555$	26.1375	+	4.32034i	1.10948	+	0.183388i
$556$	9.33625	+	2.74137i	0.395945	+	0.116260i
$557$	8.80579	−	7.63026i	0.373113	−	0.323304i	−0.448039	−	0.894014i	$-0.647877\pi$
$557$	8.80579	−	7.63026i	0.373113	−	0.323304i	0.821152	+	0.570710i	$0.193332\pi$
$558$	−0.891515	−	26.8323i	−0.0377408	−	1.13590i
$559$	−11.5046	+	17.9015i	−0.486592	+	0.757152i
$560$	−2.52592	−	0.276467i	−0.106740	−	0.0116829i
$561$	−0.537140	+	9.79323i	−0.0226781	+	0.413471i
$562$	11.1314	−	7.15375i	0.469552	−	0.301763i
$563$	−8.52409	+	1.22558i	−0.359248	+	0.0516520i	−0.319576	−	0.947561i	$-0.603540\pi$
$563$	−8.52409	+	1.22558i	−0.359248	+	0.0516520i	−0.0396719	+	0.999213i	$0.512631\pi$
$564$	−10.7336	+	11.0962i	−0.451968	+	0.467234i
$565$	−13.7099	+	16.9463i	−0.576778	+	0.712934i
$566$	−19.7477	+	22.7900i	−0.830057	+	0.957937i
$567$	8.21780	−	6.08823i	0.345115	−	0.255682i
$568$	5.23757	−	8.14982i	0.219764	−	0.341959i
$569$	−2.26547	+	0.665201i	−0.0949733	+	0.0278867i	−0.328874	−	0.944374i	$-0.606669\pi$
$569$	−2.26547	+	0.665201i	−0.0949733	+	0.0278867i	0.233901	+	0.972261i	$0.424851\pi$
$570$	−0.185478	−	1.51542i	−0.00776882	−	0.0634741i
$571$	−3.60250	+	12.2690i	−0.150760	+	0.513441i	−0.999891	−	0.0147407i	$-0.995308\pi$
$571$	−3.60250	+	12.2690i	−0.150760	+	0.513441i	0.849132	+	0.528181i	$0.177126\pi$
$572$	−3.79918	+	1.73503i	−0.158852	+	0.0725451i
$573$	−11.9376	+	6.77817i	−0.498701	+	0.283162i
$574$			11.4366i			0.477354i
$575$	18.1764	−	15.6403i	0.758008	−	0.652245i
$576$	−0.749146	+	2.90496i	−0.0312144	+	0.121040i
$577$	−25.2836	−	3.63524i	−1.05257	−	0.151337i	−0.405755	−	0.913982i	$-0.632991\pi$
$577$	−25.2836	−	3.63524i	−1.05257	−	0.151337i	−0.646817	+	0.762645i	$0.723900\pi$
$578$	−8.89316	−	19.4733i	−0.369907	−	0.809983i
$579$	−12.7464	+	4.99680i	−0.529722	+	0.207660i
$580$	19.4766	+	11.6066i	0.808724	+	0.481938i
$581$	−3.37529	−	11.4952i	−0.140030	−	0.476900i
$582$	2.48328	+	28.1442i	0.102935	+	1.16661i
$583$	−1.27265	−	0.581199i	−0.0527077	−	0.0240708i
$584$	−3.95117	−	3.42371i	−0.163501	−	0.141674i
$585$	−18.2677	−	24.6282i	−0.755276	−	1.01825i
$586$	−7.45012	+	1.07117i	−0.307762	+	0.0442494i
$587$	3.99189	+	27.7642i	0.164763	+	1.14595i	0.889503	+	0.456929i	$0.151051\pi$
$587$	3.99189	+	27.7642i	0.164763	+	1.14595i	−0.724740	+	0.689022i	$0.758040\pi$
$588$	9.32037	+	3.30107i	0.384365	+	0.136134i
$589$	−2.66607	−	2.31016i	−0.109853	−	0.0951886i
$590$	1.28179	−	11.7110i	0.0527705	−	0.482133i
$591$	−0.772022	−	8.74968i	−0.0317568	−	0.359914i
$592$	−6.56318	+	1.92712i	−0.269745	+	0.0792043i
$593$	13.0277	+	15.0347i	0.534982	+	0.617402i	0.957318	−	0.289037i	$-0.0933351\pi$
$593$	13.0277	+	15.0347i	0.534982	+	0.617402i	−0.422336	+	0.906439i	$0.638790\pi$
$594$	−4.71293	+	0.574114i	−0.193374	+	0.0235562i
$595$	10.7086	+	11.5462i	0.439010	+	0.473348i
$596$	−1.24372	+	8.65025i	−0.0509447	+	0.354328i
$597$	−16.4289	+	12.7297i	−0.672392	+	0.520991i
$598$	−13.1441	−	17.5445i	−0.537501	−	0.717447i
$599$		−	27.6371i		−	1.12922i	−0.825357	−	0.564611i	$-0.809026\pi$
$599$		−	27.6371i		−	1.12922i	0.825357	−	0.564611i	$-0.190974\pi$
$600$	−3.49671	+	7.92294i	−0.142753	+	0.323453i
$601$	12.5572	+	27.4964i	0.512219	+	1.12160i	0.972302	+	0.233727i	$0.0750922\pi$
$601$	12.5572	+	27.4964i	0.512219	+	1.12160i	−0.460083	+	0.887876i	$0.652180\pi$
$602$	5.07584	+	1.49040i	0.206876	+	0.0607442i
$603$	−16.6477	+	8.28156i	−0.677949	+	0.337251i
$604$	2.27441	−	0.667826i	0.0925442	−	0.0271734i
$605$	5.66350	−	22.0131i	0.230254	−	0.894958i
$606$	2.49096	+	10.6001i	0.101188	+	0.430600i
$607$	−22.1014	−	19.1510i	−0.897069	−	0.777315i	0.0785212	−	0.996912i	$-0.474980\pi$
$607$	−22.1014	−	19.1510i	−0.897069	−	0.777315i	−0.975591	+	0.219597i	$0.929526\pi$
$608$	0.213121	+	0.331622i	0.00864319	+	0.0134491i
$609$	14.3443	+	13.8756i	0.581260	+	0.562268i
$610$	7.35273	+	14.7596i	0.297703	+	0.597597i
$611$	22.0272	+	34.2751i	0.891127	+	1.38662i
$612$	15.2984	−	10.5656i	0.618400	−	0.427087i
$613$	−0.700560	+	1.53401i	−0.0282953	+	0.0619581i	−0.923252	−	0.384195i	$-0.874479\pi$
$613$	−0.700560	+	1.53401i	−0.0282953	+	0.0619581i	0.894957	+	0.446153i	$0.147206\pi$
$614$	−12.3386	+	19.1992i	−0.497944	+	0.774816i
$615$	37.1603	+	11.7648i	1.49845	+	0.474401i
$616$	0.679950	+	0.784704i	0.0273960	+	0.0316166i
$617$	−8.90832	+	30.3390i	−0.358636	+	1.22140i	0.560731	+	0.827998i	$0.310520\pi$
$617$	−8.90832	+	30.3390i	−0.358636	+	1.22140i	−0.919366	+	0.393402i	$0.871298\pi$
$618$	2.38880	−	4.55291i	0.0960915	−	0.183145i
$619$	−11.5292	−	1.65765i	−0.463399	−	0.0666267i	−0.0933386	−	0.995634i	$-0.529754\pi$
$619$	−11.5292	−	1.65765i	−0.463399	−	0.0666267i	−0.370060	+	0.929008i	$0.620663\pi$
$620$	6.28293	+	18.9987i	0.252328	+	0.763007i
$621$	−8.21171	−	23.5280i	−0.329525	−	0.944147i
$622$		−	7.25627i		−	0.290950i
$623$	2.56147	−	17.8154i	0.102623	−	0.713761i
$624$	7.01090	+	3.67845i	0.280661	+	0.147256i
$625$	−13.6770	+	20.9270i	−0.547080	+	0.837080i
$626$	11.7474	+	13.5572i	0.469520	+	0.541855i
$627$	−0.365519	+	0.505563i	−0.0145974	+	0.0201902i
$628$	15.2966	+	9.83055i	0.610402	+	0.392282i
$629$	38.5610	+	17.6102i	1.53753	+	0.702165i
$630$	−4.59514	+	6.08236i	−0.183075	+	0.242327i
$631$	19.1110	+	29.7372i	0.760795	+	1.18382i	0.978185	+	0.207736i	$0.0666094\pi$
$631$	19.1110	+	29.7372i	0.760795	+	1.18382i	−0.217390	+	0.976085i	$0.569754\pi$
$632$	2.97614	−	0.427904i	0.118384	−	0.0170211i
$633$	19.8863	−	20.5580i	0.790410	−	0.817107i
$634$	11.2830	−	7.25113i	0.448104	−	0.287979i
$635$	12.8108	−	30.7610i	0.508382	−	1.22071i
$636$	0.606709	+	2.58181i	0.0240576	+	0.102375i
$637$	14.1078	−	21.9522i	0.558972	−	0.869777i
$638$	−2.61014	−	8.88931i	−0.103336	−	0.351931i
$639$	−12.9445	−	26.0213i	−0.512076	−	1.02939i
$640$	−0.0755234	−	2.23479i	−0.00298532	−	0.0883379i
$641$	8.89291	+	19.4728i	0.351249	+	0.769128i	0.999967	+	0.00809917i	$0.00257807\pi$
$641$	8.89291	+	19.4728i	0.351249	+	0.769128i	−0.648718	+	0.761029i	$0.724695\pi$
$642$	13.3836	+	23.5711i	0.528209	+	0.930276i
$643$	0.0334375			0.00131865			0.000659323	−	1.00000i	$-0.499790\pi$
$643$	0.0334375			0.00131865			0.000659323		1.00000i	$0.499790\pi$
$644$	−3.26431	+	4.36407i	−0.128632	+	0.171969i
$645$	10.0642	−	14.9595i	0.396276	−	0.589029i
$646$	0.347678	−	2.41815i	0.0136792	−	0.0951410i
$647$	−7.02734	−	15.3877i	−0.276273	−	0.604954i	0.719732	−	0.694252i	$-0.244265\pi$
$647$	−7.02734	−	15.3877i	−0.276273	−	0.604954i	−0.996005	+	0.0892983i	$0.971538\pi$
$648$	6.33223	+	6.39553i	0.248754	+	0.251240i
$649$	−3.63814	+	3.15247i	−0.142809	+	0.123745i
$650$	18.2439	+	13.7668i	0.715585	+	0.539977i
$651$	1.54814	+	17.5458i	0.0606766	+	0.687675i
$652$	−14.1585	−	6.46595i	−0.554488	−	0.253226i
$653$	5.93377	−	6.84794i	0.232206	−	0.267980i	−0.627674	−	0.778477i	$-0.715993\pi$
$653$	5.93377	−	6.84794i	0.232206	−	0.267980i	0.859880	+	0.510496i	$0.170538\pi$
$654$	3.52545	−	9.95388i	0.137856	−	0.389227i
$655$	0.637431	+	1.27955i	0.0249065	+	0.0499962i
$656$	−9.96168	+	1.43227i	−0.388938	+	0.0559209i
$657$	−14.8941	+	4.91612i	−0.581074	+	0.191796i
$658$	6.63291	−	7.65479i	0.258578	−	0.298415i
$659$	−8.20148	+	17.9587i	−0.319484	+	0.699573i	−0.999432	−	0.0336871i	$-0.989275\pi$
$659$	−8.20148	+	17.9587i	−0.319484	+	0.699573i	0.679948	+	0.733260i	$0.262002\pi$
$660$	3.24916	−	1.40210i	0.126473	−	0.0545768i
$661$	−6.37940	−	21.7262i	−0.248130	−	0.845053i	−0.985516	−	0.169582i	$-0.945758\pi$
$661$	−6.37940	−	21.7262i	−0.248130	−	0.845053i	0.737386	−	0.675471i	$-0.236060\pi$
$662$	10.6386	+	12.2776i	0.413480	+	0.477181i
$663$	−17.9081	−	45.6820i	−0.695495	−	1.77414i
$664$	9.59000	−	4.37960i	0.372164	−	0.169962i
$665$	0.175957	+	0.986089i	0.00682334	+	0.0382389i
$666$	−5.12435	+	19.8707i	−0.198564	+	0.769972i
$667$	42.6705	−	23.3210i	1.65221	−	0.902992i
$668$	6.68528			0.258661
$669$	−9.13241	−	16.0839i	−0.353079	−	0.621839i
$670$	10.1615	−	9.42433i	0.392571	−	0.364093i
$671$	1.89832	−	6.46509i	0.0732839	−	0.249582i
$672$	0.386387	−	1.92996i	0.0149052	−	0.0744497i
$673$	−11.5868	−	39.4612i	−0.446640	−	1.52112i	−0.808280	−	0.588798i	$-0.799601\pi$
$673$	−11.5868	−	39.4612i	−0.446640	−	1.52112i	0.361640	−	0.932318i	$-0.382217\pi$
$674$	2.00524	+	1.28869i	0.0772390	+	0.0496385i
$675$	15.0361	+	21.1876i	0.578739	+	0.815513i
$676$	5.16985	−	5.96632i	0.198840	−	0.229474i
$677$	3.54764	+	5.52023i	0.136347	+	0.212160i	0.902712	−	0.430245i	$-0.141573\pi$
$677$	3.54764	+	5.52023i	0.136347	+	0.212160i	−0.766365	+	0.642405i	$0.777937\pi$
$678$	−12.1357	−	11.7391i	−0.466067	−	0.450839i
$679$	−2.63805	−	18.3480i	−0.101239	−	0.704133i
$680$	−8.71604	+	10.7736i	−0.334245	+	0.413148i
$681$	−0.683162	+	12.4555i	−0.0261788	+	0.477297i
$682$	3.39677	−	7.43789i	0.130069	−	0.284812i
$683$	−12.3272	−	7.92223i	−0.471688	−	0.303136i	0.283116	−	0.959086i	$-0.408632\pi$
$683$	−12.3272	−	7.92223i	−0.471688	−	0.303136i	−0.754804	+	0.655950i	$0.772268\pi$
$684$	1.18195	−	0.0392707i	0.0451929	−	0.00150155i
$685$	20.4327	+	12.1763i	0.780692	+	0.465233i
$686$	−13.8568	−	4.06872i	−0.529054	−	0.155344i
$687$	22.6878	+	11.9037i	0.865594	+	0.454156i
$688$	−0.662515	+	4.60789i	−0.0252581	+	0.175674i
$689$	6.99926			0.266650
$690$	10.8220	+	15.0959i	0.411985	+	0.574689i
$691$	−12.8771			−0.489870			−0.244935	−	0.969540i	$-0.578767\pi$
$691$	−12.8771			−0.489870			−0.244935	+	0.969540i	$0.578767\pi$
$692$	2.76882	−	19.2576i	0.105255	−	0.732064i
$693$	3.06681	−	0.545443i	0.116499	−	0.0207196i
$694$	−17.1892	−	5.04721i	−0.652494	−	0.191590i
$695$	−11.1382	+	18.6907i	−0.422498	+	0.708979i
$696$	−10.2897	+	14.2321i	−0.390031	+	0.539467i
$697$	52.4702	+	33.7206i	1.98745	+	1.27726i
$698$	−1.94327	+	4.25518i	−0.0735540	+	0.161061i
$699$	−13.0393	−	0.715183i	−0.493193	−	0.0270507i
$700$	2.00602	−	5.31596i	0.0758204	−	0.200924i
$701$	5.60529	+	38.9857i	0.211709	+	1.47247i	0.767448	+	0.641112i	$0.221526\pi$
$701$	5.60529	+	38.9857i	0.211709	+	1.47247i	−0.555739	+	0.831357i	$0.687564\pi$
$702$	20.2538	−	12.4071i	0.764431	−	0.468276i
$703$	1.45780	+	2.26838i	0.0549820	+	0.0855536i
$704$	−0.598351	+	0.690534i	−0.0225512	+	0.0260255i
$705$	−18.0491	−	29.4264i	−0.679767	−	1.10826i
$706$	−0.171178	−	0.110009i	−0.00644235	−	0.00414025i
$707$	−2.01270	−	6.85462i	−0.0756954	−	0.257795i
$708$	8.94789	+	1.79142i	0.336282	+	0.0673255i
$709$	−12.9321	+	44.0427i	−0.485676	+	1.65406i	0.243627	+	0.969869i	$0.421663\pi$
$709$	−12.9321	+	44.0427i	−0.485676	+	1.65406i	−0.729303	+	0.684191i	$0.760155\pi$
$710$	14.7307	+	15.8829i	0.552833	+	0.596073i
$711$	3.47261	−	8.32500i	0.130233	−	0.312212i
$712$	15.8387			0.593580
$713$	41.9408	+	9.10693i	1.57069	+	0.341057i
$714$	−9.64233	+	7.47119i	−0.360855	+	0.279602i
$715$	−1.64057	−	9.19396i	−0.0613538	−	0.343835i
$716$	4.09249	−	1.86898i	0.152944	−	0.0698470i
$717$	26.6195	−	10.4353i	0.994124	−	0.389714i
$718$	−17.1471	−	19.7888i	−0.639923	−	0.738510i
$719$	−5.65708	−	19.2663i	−0.210974	−	0.718510i	−0.995185	−	0.0980161i	$-0.968750\pi$
$719$	−5.65708	−	19.2663i	−0.210974	−	0.718510i	0.784211	−	0.620494i	$-0.213068\pi$
$720$	−5.87343	−	3.24080i	−0.218890	−	0.120778i
$721$	−1.40131	+	3.06844i	−0.0521875	+	0.114275i
$722$	−12.3406	+	14.2418i	−0.459269	+	0.530025i
$723$	4.98802	−	14.0834i	0.185507	−	0.523766i
$724$	14.7962	−	2.12737i	0.549897	−	0.0790632i
$725$	−35.9860	+	35.7109i	−1.33649	+	1.32627i
$726$	16.5963	+	5.87807i	0.615948	+	0.218156i
$727$	2.30834	−	2.66397i	0.0856116	−	0.0988010i	−0.711327	−	0.702861i	$-0.751906\pi$
$727$	2.30834	−	2.66397i	0.0856116	−	0.0988010i	0.796939	+	0.604060i	$0.206451\pi$
$728$	−4.72501	−	2.15784i	−0.175121	−	0.0799749i
$729$	26.2104	−	6.48192i	0.970755	−	0.240071i
$730$	9.61559	−	6.64892i	0.355889	−	0.246088i
$731$	21.8039	−	18.8932i	0.806445	−	0.698789i
$732$	−11.8917	+	4.66175i	−0.439530	+	0.172303i
$733$	−18.1318	−	39.7032i	−0.669715	−	1.46647i	−0.873185	−	0.487389i	$-0.837949\pi$
$733$	−18.1318	−	39.7032i	−0.669715	−	1.46647i	0.203470	−	0.979081i	$-0.434778\pi$
$734$	1.63714	−	11.3866i	0.0604279	−	0.420285i
$735$	−12.3415	+	18.3445i	−0.455222	+	0.676646i
$736$	−4.21008	−	2.29679i	−0.155185	−	0.0846610i
$737$	−5.66312			−0.208604
$738$	−11.6234	+	27.8653i	−0.427865	+	1.02574i
$739$	13.1449	+	28.7834i	0.483544	+	1.05881i	0.981474	+	0.191596i	$0.0613665\pi$
$739$	13.1449	+	28.7834i	0.483544	+	1.05881i	−0.497930	+	0.867217i	$0.665906\pi$
$740$	−0.516599	−	15.2866i	−0.0189906	−	0.561945i
$741$	0.612683	−	3.06028i	0.0225075	−	0.112422i
$742$	−0.490222	−	1.66954i	−0.0179966	−	0.0612908i
$743$	0.127897	−	0.199011i	0.00469208	−	0.00730102i	−0.838900	−	0.544286i	$-0.816801\pi$
$743$	0.127897	−	0.199011i	0.00469208	−	0.00730102i	0.843592	+	0.536985i	$0.180437\pi$
$744$	−15.0892	+	3.54586i	−0.553196	+	0.129998i
$745$	−18.0396	−	7.51281i	−0.660919	−	0.275248i
$746$	2.35082	−	1.51078i	0.0860695	−	0.0553135i
$747$	3.45909	−	31.4384i	0.126561	−	1.15027i
$748$	5.60499	−	0.805875i	0.204939	−	0.0294657i
$749$	−9.61455	−	14.9605i	−0.351308	−	0.546646i
$750$	−15.2093	−	11.9866i	−0.555365	−	0.437687i
$751$	−12.8333	−	5.86078i	−0.468295	−	0.213863i	0.167269	−	0.985911i	$-0.446505\pi$
$751$	−12.8333	−	5.86078i	−0.468295	−	0.213863i	−0.635564	+	0.772048i	$0.719232\pi$
$752$	7.49828	+	4.81885i	0.273434	+	0.175725i
$753$	−35.3500	−	25.5579i	−1.28823	−	0.931380i
$754$	30.3518	+	35.0279i	1.10535	+	1.27564i
$755$	0.179022	+	5.29741i	0.00651529	+	0.192792i
$756$	−4.37805	−	3.96219i	−0.159228	−	0.144104i
$757$	−6.72746	+	46.7905i	−0.244514	+	1.70063i	0.384410	+	0.923162i	$0.374405\pi$
$757$	−6.72746	+	46.7905i	−0.244514	+	1.70063i	−0.628924	+	0.777467i	$0.716504\pi$
$758$			0.212282i			0.00771042i
$759$	0.952376	−	7.52984i	0.0345691	−	0.273316i
$760$	−0.836883	+	0.276759i	−0.0303569	+	0.0100391i
$761$	−0.151958	−	0.0218482i	−0.00550846	−	0.000791997i	0.139560	−	0.990214i	$-0.455431\pi$
$761$	−0.151958	−	0.0218482i	−0.00550846	−	0.000791997i	−0.145069	+	0.989422i	$0.546340\pi$
$762$	22.8562	+	11.9921i	0.827991	+	0.434426i
$763$	−1.95187	+	6.64746i	−0.0706625	+	0.240654i
$764$	5.19023	+	5.98985i	0.187776	+	0.216705i
$765$	14.3567	+	39.0159i	0.519068	+	1.41062i
$766$	16.9460	−	26.3686i	0.612285	−	0.952735i
$767$	10.0044	−	21.9067i	0.361240	−	0.791004i
$768$	1.72945	+	0.0948572i	0.0624062	+	0.00342286i
$769$	18.3873	+	28.6113i	0.663064	+	1.03175i	0.996048	+	0.0888156i	$0.0283082\pi$
$769$	18.3873	+	28.6113i	0.663064	+	1.03175i	−0.332984	+	0.942933i	$0.608055\pi$
$770$	−2.07815	+	1.03526i	−0.0748912	+	0.0373084i
$771$	−15.6704	+	16.1997i	−0.564356	+	0.583419i
$772$	4.27344	+	6.64960i	0.153804	+	0.239324i
$773$	−7.91290	−	6.85656i	−0.284607	−	0.246613i	0.500843	−	0.865538i	$-0.333023\pi$
$773$	−7.91290	−	6.85656i	−0.284607	−	0.246613i	−0.785451	+	0.618924i	$0.787569\pi$
$774$	10.8525	+	8.79014i	0.390087	+	0.315955i
$775$	−44.6431	+	3.02082i	−1.60363	+	0.108511i
$776$	15.6514	−	4.59567i	0.561853	−	0.164975i
$777$	2.64299	−	13.2014i	0.0948167	−	0.473597i
$778$	17.4994	+	5.13829i	0.627385	+	0.184217i
$779$	1.64807	+	3.60876i	0.0590481	+	0.129297i
$780$	−11.8720	+	13.1330i	−0.425084	+	0.470236i
$781$		−	8.85174i		−	0.316740i
$782$	10.3973	+	27.8438i	0.371806	+	0.995693i
$783$	20.8476	+	48.3866i	0.745032	+	1.72920i
$784$	0.812427	−	5.65055i	0.0290152	−	0.201805i
$785$	−29.8110	+	27.6485i	−1.06400	+	0.986816i
$786$	−1.03093	+	0.404141i	−0.0367720	+	0.0144152i
$787$	−16.1693	−	18.6604i	−0.576375	−	0.665172i	0.390446	−	0.920626i	$-0.372321\pi$
$787$	−16.1693	−	18.6604i	−0.576375	−	0.665172i	−0.966821	+	0.255454i	$0.917775\pi$
$788$	−4.86583	+	1.42874i	−0.173338	+	0.0508967i
$789$	31.3866	−	2.76937i	1.11739	−	0.0985923i
$790$	−0.731509	+	6.68337i	−0.0260259	+	0.237784i
$791$	8.37187	+	7.25427i	0.297669	+	0.257932i
$792$	0.859176	+	2.60299i	0.0305295	+	0.0924934i
$793$	4.79725	+	33.3656i	0.170355	+	1.18485i
$794$	18.2742	−	2.62744i	0.648528	−	0.0932442i
$795$	−5.92905	−	0.124598i	−0.210282	−	0.00441903i
$796$	9.06852	+	7.85792i	0.321425	+	0.278517i
$797$	−34.0423	−	15.5466i	−1.20584	−	0.550690i	−0.291866	−	0.956459i	$-0.594276\pi$
$797$	−34.0423	−	15.5466i	−1.20584	−	0.550690i	−0.913975	+	0.405770i	$0.867004\pi$
$798$	−0.772884	+	0.0681949i	−0.0273598	+	0.00241407i
$799$	−15.5626	−	53.0013i	−0.550565	−	1.87505i
$800$	4.88162	+	1.08156i	0.172591	+	0.0382391i
$801$	24.3476	−	40.8041i	0.860279	−	1.44174i
$802$	−0.104029	−	0.227791i	−0.00367339	−	0.00804359i
$803$	−4.72838	−	0.679839i	−0.166861	−	0.0239910i
$804$	6.57517	+	8.48593i	0.231888	+	0.299276i
$805$	−7.63189	−	9.50046i	−0.268989	−	0.334847i
$806$			40.9066i			1.44087i
$807$	−8.92839	−	15.7246i	−0.314294	−	0.553531i
$808$	5.71856	−	2.61158i	0.201178	−	0.0918751i
$809$	14.3704	−	48.9410i	0.505236	−	1.72067i	−0.172172	−	0.985067i	$-0.555079\pi$
$809$	14.3704	−	48.9410i	0.505236	−	1.72067i	0.677408	−	0.735608i	$-0.263103\pi$
$810$	−17.3778	+	10.1495i	−0.610594	+	0.356616i
$811$	15.6209	−	4.58672i	0.548526	−	0.161062i	0.00428497	−	0.999991i	$-0.498636\pi$
$811$	15.6209	−	4.58672i	0.548526	−	0.161062i	0.544241	+	0.838929i	$0.316818\pi$
$812$	6.22943	−	9.69319i	0.218610	−	0.340164i
$813$	−1.45359	+	0.341585i	−0.0509796	+	0.0119799i
$814$	−4.09288	+	4.72343i	−0.143455	+	0.165556i
$815$	21.8907	−	27.0583i	0.766797	−	0.947810i
$816$	−7.71524	−	7.46316i	−0.270087	−	0.261263i
$817$	1.81643	−	0.261164i	0.0635489	−	0.00913696i
$818$	13.3986	−	8.61078i	0.468472	−	0.301069i
$819$	−12.8225	+	8.85564i	−0.448054	+	0.309441i
$820$	2.44849	−	22.3705i	0.0855051	−	0.781210i
$821$	−17.1371	+	26.6659i	−0.598089	+	0.930645i	0.401799	+	0.915728i	$0.368385\pi$
$821$	−17.1371	+	26.6659i	−0.598089	+	0.930645i	−0.999889	+	0.0149175i	$0.995251\pi$
$822$	−10.7948	+	14.9307i	−0.376512	+	0.520769i
$823$	−31.0843	+	26.9347i	−1.08353	+	0.938883i	−0.998347	−	0.0574820i	$-0.981693\pi$
$823$	−31.0843	+	26.9347i	−1.08353	+	0.938883i	−0.0851826	+	0.996365i	$0.527147\pi$
$824$	−2.84822	−	0.836313i	−0.0992224	−	0.0291343i
$825$	1.22605	+	7.81738i	0.0426857	+	0.272166i
$826$	−5.92614	−	0.852050i	−0.206197	−	0.0296466i
$827$			2.35399i			0.0818562i	0.999162	+	0.0409281i	$0.0130315\pi$
$827$			2.35399i			0.0818562i	−0.999162	+	0.0409281i	$0.986969\pi$
$828$	−12.3889	+	7.31543i	−0.430543	+	0.254229i
$829$	6.73659			0.233971			0.116986	−	0.993134i	$-0.462677\pi$
$829$	6.73659			0.233971			0.116986	+	0.993134i	$0.462677\pi$
$830$	4.14117	+	23.2077i	0.143742	+	0.805550i
$831$	−20.6056	−	10.8112i	−0.714800	−	0.375038i
$832$	1.28782	−	4.38590i	0.0446470	−	0.152054i
$833$	−26.7376	+	23.1682i	−0.926402	+	0.802732i
$834$	−13.6578	−	9.87451i	−0.472931	−	0.341926i
$835$	−3.72470	+	14.4773i	−0.128899	+	0.501007i
$836$	0.327635	+	0.149626i	0.0113315	+	0.00517492i
$837$	−14.0604	+	44.3239i	−0.486000	+	1.53206i
$838$	−13.4019	+	8.61288i	−0.462961	+	0.297527i
$839$	−4.56948	−	31.7814i	−0.157756	−	1.09722i	−0.902756	−	0.430152i	$-0.858460\pi$
$839$	−4.56948	−	31.7814i	−0.157756	−	1.09722i	0.745000	−	0.667064i	$-0.232449\pi$
$840$	3.96413	+	1.91201i	0.136776	+	0.0659707i
$841$	−62.0934	+	39.9050i	−2.14115	+	1.37603i
$842$	14.0287	+	12.1559i	0.483461	+	0.418921i
$843$	−22.3107	+	5.24288i	−0.768422	+	0.180574i
$844$	−13.8921	−	8.92793i	−0.478187	−	0.307312i
$845$	10.0400	+	14.5197i	0.345385	+	0.499492i
$846$	23.9410	−	11.9096i	0.823107	−	0.409462i
$847$	−11.0835	−	3.25440i	−0.380833	−	0.111823i
$848$	1.39284	−	0.636088i	0.0478303	−	0.0218434i
$849$	45.4200	−	25.7894i	1.55881	−	0.885091i
$850$	−18.4745	−	24.8775i	−0.633671	−	0.853290i
$851$	−28.7980	−	15.7107i	−0.987183	−	0.538554i
$852$	−13.2639	+	10.2773i	−0.454415	+	0.352095i
$853$	−13.5062	−	1.94190i	−0.462443	−	0.0664893i	−0.0928442	−	0.995681i	$-0.529596\pi$
$853$	−13.5062	−	1.94190i	−0.462443	−	0.0664893i	−0.369599	+	0.929191i	$0.620505\pi$
$854$	7.62275	−	3.48119i	0.260845	−	0.119124i
$855$	−0.573480	+	2.58144i	−0.0196126	+	0.0882835i
$856$	11.8271	−	10.2482i	0.404241	−	0.350277i
$857$	53.4127	−	15.6834i	1.82454	−	0.535734i	0.824976	−	0.565168i	$-0.191189\pi$
$857$	53.4127	−	15.6834i	1.82454	−	0.535734i	0.999567	+	0.0294339i	$0.00937045\pi$
$858$	7.20611	−	0.635826i	0.246012	−	0.0217067i
$859$	−24.1175	+	52.8099i	−0.822878	+	1.80185i	−0.285890	+	0.958262i	$0.592289\pi$
$859$	−24.1175	+	52.8099i	−0.822878	+	1.80185i	−0.536988	+	0.843590i	$0.680438\pi$
$860$	−9.60948	−	4.00199i	−0.327680	−	0.136467i
$861$	6.61329	−	18.6722i	0.225380	−	0.636347i
$862$	−0.991279	−	6.89450i	−0.0337631	−	0.234827i
$863$	−4.34944	−	30.2510i	−0.148057	−	1.02976i	−0.919396	−	0.393333i	$-0.871322\pi$
$863$	−4.34944	−	30.2510i	−0.148057	−	1.02976i	0.771339	−	0.636424i	$-0.219587\pi$
$864$	2.90292	−	4.30964i	0.0987594	−	0.146617i
$865$	40.1605	+	16.7254i	1.36550	+	0.568680i
$866$	11.4924	−	25.1648i	0.390527	−	0.855134i
$867$	3.25903	+	36.9361i	0.110682	+	1.25441i
$868$	9.75751	−	2.86506i	0.331192	−	0.0972466i
$869$	2.07626	−	1.79909i	0.0704323	−	0.0610299i
$870$	−25.0874	−	30.2123i	−0.850541	−	1.02429i
$871$	25.7710	−	11.7692i	0.873216	−	0.398784i
$872$	−6.03462	−	0.867648i	−0.204358	−	0.0293823i
$873$	12.2202	−	47.3862i	0.413591	−	1.60378i
$874$	−0.401155	+	1.84747i	−0.0135693	+	0.0624915i
$875$	10.3943	+	7.30591i	0.351392	+	0.246985i
$876$	4.47118	+	7.87459i	0.151067	+	0.266058i
$877$	30.7409	−	14.0389i	1.03805	−	0.474060i	0.177868	−	0.984054i	$-0.443080\pi$
$877$	30.7409	−	14.0389i	1.03805	−	0.474060i	0.860178	+	0.509995i	$0.170353\pi$
$878$	11.2990	+	3.31769i	0.381323	+	0.111967i
$879$	12.7830	+	2.55923i	0.431160	+	0.0863206i
$880$	−1.16201	−	1.68049i	−0.0391714	−	0.0566492i
$881$	−0.650801	−	0.418244i	−0.0219260	−	0.0140910i	0.529632	−	0.848228i	$-0.322330\pi$
$881$	−0.650801	−	0.418244i	−0.0219260	−	0.0140910i	−0.551558	+	0.834137i	$0.685966\pi$
$882$	−13.3082	−	10.7791i	−0.448111	−	0.362953i
$883$	−18.4893	−	16.0211i	−0.622216	−	0.539153i	0.285693	−	0.958321i	$-0.407776\pi$
$883$	−18.4893	−	16.0211i	−0.622216	−	0.539153i	−0.907909	+	0.419168i	$0.862322\pi$
$884$	−23.8316	+	15.3157i	−0.801545	+	0.515122i
$885$	−8.86471	+	18.3790i	−0.297984	+	0.617803i
$886$	3.81148	+	26.5094i	0.128049	+	0.890601i
$887$	11.6648	−	7.49653i	0.391667	−	0.251709i	−0.329955	−	0.943997i	$-0.607034\pi$
$887$	11.6648	−	7.49653i	0.391667	−	0.251709i	0.721621	+	0.692288i	$0.243397\pi$
$888$	11.8299	+	0.648847i	0.396985	+	0.0217739i
$889$	−15.4040	−	7.03476i	−0.516632	−	0.235938i
$890$	−8.82452	+	34.2994i	−0.295798	+	1.14972i
$891$	8.02665	+	1.78795i	0.268903	+	0.0598984i
$892$	−8.07029	+	6.99294i	−0.270213	+	0.234141i
$893$	0.989894	−	3.37127i	0.0331255	−	0.112815i
$894$	7.03266	−	13.4038i	0.235207	−	0.448291i
$895$	1.76723	+	9.90377i	0.0590718	+	0.331047i
$896$	−1.13637			−0.0379635
$897$	11.3147	+	36.2450i	0.377787	+	1.21019i
$898$		−	20.4313i		−	0.681801i
$899$	−89.8157	−	12.9136i	−2.99552	−	0.430691i
$900$	10.2905	−	10.9136i	0.343016	−	0.363785i
$901$	−9.10515	−	2.67351i	−0.303337	−	0.0890676i
$902$	−6.94962	+	6.02188i	−0.231397	+	0.200507i
$903$	−7.42535	−	5.36848i	−0.247100	−	0.178652i
$904$	−5.27027	+	8.20070i	−0.175286	+	0.272751i
$905$	−3.63678	+	33.2271i	−0.120891	+	1.10451i
$906$	−4.09953	−	0.224852i	−0.136198	−	0.00747020i
$907$	19.1321	−	12.2955i	0.635272	−	0.408265i	−0.182986	−	0.983116i	$-0.558576\pi$
$907$	19.1321	−	12.2955i	0.635272	−	0.408265i	0.818258	+	0.574851i	$0.194940\pi$
$908$	7.12870	−	1.02495i	0.236574	−	0.0340142i
$909$	2.06267	−	18.7469i	0.0684145	−	0.621795i
$910$	7.30544	−	9.02999i	0.242173	−	0.299341i
$911$	10.0730	−	11.6248i	0.333732	−	0.385147i	−0.563937	−	0.825818i	$-0.690714\pi$
$911$	10.0730	−	11.6248i	0.333732	−	0.385147i	0.897669	+	0.440671i	$0.145259\pi$
$912$	−0.156193	−	0.664669i	−0.00517207	−	0.0220094i
$913$	5.20798	−	8.10377i	0.172359	−	0.268196i
$914$	−9.59833	+	2.81833i	−0.317485	+	0.0932219i
$915$	−3.46977	−	28.3493i	−0.114707	−	0.937199i
$916$	4.16747	−	14.1931i	0.137697	−	0.468953i
$917$	0.660840	−	0.301796i	0.0218229	−	0.00996617i
$918$	−31.0868	+	8.40370i	−1.02602	+	0.277363i
$919$		−	59.0770i		−	1.94877i	−0.224883	−	0.974386i	$-0.572200\pi$
$919$		−	59.0770i		−	1.94877i	0.224883	−	0.974386i	$-0.427800\pi$
$920$	7.31945	−	7.83745i	0.241315	−	0.258393i
$921$	31.2469	−	24.2111i	1.02962	−	0.797783i
$922$	16.9236	+	2.43324i	0.557348	+	0.0801345i
$923$	18.3959	+	40.2813i	0.605507	+	1.32588i
$924$	−0.656374	−	1.67435i	−0.0215931	−	0.0550821i
$925$	33.3915	+	7.39818i	1.09791	+	0.243251i
$926$	−2.25974	−	7.69597i	−0.0742597	−	0.252905i
$927$	−6.53288	+	6.05206i	−0.214568	+	0.198776i
$928$	9.22326	+	4.21212i	0.302768	+	0.138270i
$929$	26.3421	+	22.8255i	0.864255	+	0.748881i	0.969377	−	0.245578i	$-0.0789779\pi$
$929$	26.3421	+	22.8255i	0.864255	+	0.748881i	−0.105122	+	0.994459i	$0.533523\pi$
$930$	0.728202	−	34.6518i	0.0238787	−	1.13628i
$931$	−2.22745	+	0.320259i	−0.0730017	+	0.0104961i
$932$	1.07299	+	7.46284i	0.0351471	+	0.244453i
$933$	−4.19599	+	11.8471i	−0.137371	+	0.387857i
$934$	−17.7055	−	15.3419i	−0.579343	−	0.502004i
$935$	−1.37766	+	12.5868i	−0.0450542	+	0.411634i
$936$	−9.31942	−	10.0598i	−0.304615	−	0.328815i
$937$	−32.7334	+	9.61140i	−1.06935	+	0.313991i	−0.768612	−	0.639715i	$-0.779052\pi$
$937$	−32.7334	+	9.61140i	−1.06935	+	0.313991i	−0.300742	+	0.953706i	$0.597234\pi$
$938$	−4.61230	−	5.32288i	−0.150597	−	0.173798i
$939$	−11.3401	−	28.9275i	−0.370069	−	0.944013i
$940$	−14.6131	+	13.5530i	−0.476627	+	0.442051i
$941$	−1.68379	+	11.7110i	−0.0548901	+	0.381769i	0.943796	+	0.330528i	$0.107227\pi$
$941$	−1.68379	+	11.7110i	−0.0548901	+	0.381769i	−0.998686	+	0.0512410i	$0.983682\pi$
$942$	−19.2898	−	24.8955i	−0.628495	−	0.811138i
$943$	−38.6498	−	28.9099i	−1.25861	−	0.941436i
$944$		−	5.26859i		−	0.171478i
$945$	11.0195	−	7.27332i	0.358465	−	0.236601i
$946$	1.76699	+	3.86918i	0.0574499	+	0.125798i
$947$	−9.93189	−	2.91627i	−0.322743	−	0.0947659i	0.116348	−	0.993209i	$-0.462881\pi$
$947$	−9.93189	−	2.91627i	−0.322743	−	0.0947659i	−0.439091	+	0.898443i	$0.644699\pi$
$948$	−5.10650	−	1.02235i	−0.165851	−	0.0332043i
$949$	22.9301	−	6.73290i	0.744344	−	0.218559i
$950$	−0.133066	−	1.96650i	−0.00431722	−	0.0638018i
$951$	−22.6144	+	5.31425i	−0.733323	+	0.172326i
$952$	5.32242	+	4.61190i	0.172501	+	0.149473i
$953$	−6.10662	−	9.50209i	−0.197813	−	0.307803i	0.728150	−	0.685418i	$-0.240381\pi$
$953$	−6.10662	−	9.50209i	−0.197813	−	0.307803i	−0.925963	+	0.377615i	$0.876744\pi$
$954$	0.502393	−	4.56608i	0.0162656	−	0.147832i
$955$	−15.8630	+	7.90244i	−0.513315	+	0.255717i
$956$	−8.92464	−	13.8870i	−0.288644	−	0.449138i
$957$	−0.878813	+	16.0227i	−0.0284080	+	0.517939i
$958$	−16.9545	+	37.1251i	−0.547774	+	1.19946i
$959$	6.53521	−	10.1690i	0.211033	−	0.328374i
$960$	−1.16898	+	3.69235i	−0.0377287	+	0.119170i
$961$	−32.1441	−	37.0963i	−1.03691	−	1.19665i
$962$	8.80899	−	30.0007i	0.284013	−	0.967260i
$963$	−8.22091	−	46.2230i	−0.264915	−	1.48952i
$964$	−8.53816	−	1.22760i	−0.274995	−	0.0395384i
$965$	−16.7810	+	5.54950i	−0.540198	+	0.178645i
$966$	7.85311	−	5.23749i	0.252670	−	0.168513i
$967$			10.2820i			0.330648i	0.986239	+	0.165324i	$0.0528670\pi$
$967$			10.2820i			0.330648i	−0.986239	+	0.165324i	$0.947133\pi$
$968$	1.44665	−	10.0617i	0.0464971	−	0.323394i
$969$	−1.96596	+	3.74701i	−0.0631557	+	0.120371i
$970$	1.23195	+	36.4543i	0.0395556	+	1.17048i
$971$	4.37615	+	5.05034i	0.140437	+	0.162073i	0.821611	−	0.570049i	$-0.193076\pi$
$971$	4.37615	+	5.05034i	0.140437	+	0.162073i	−0.681174	+	0.732122i	$0.738530\pi$
$972$	−6.64019	−	14.1035i	−0.212984	−	0.452369i
$973$	9.30204	+	5.97806i	0.298210	+	0.191648i
$974$	−11.0739	−	5.05727i	−0.354830	−	0.162046i
$975$	−21.8256	−	33.0263i	−0.698979	−	1.05769i
$976$	3.98689	+	6.20372i	0.127617	+	0.198576i
$977$	−13.1747	+	1.89423i	−0.421495	+	0.0606018i	−0.349799	−	0.936825i	$-0.613750\pi$
$977$	−13.1747	+	1.89423i	−0.421495	+	0.0606018i	−0.0716956	+	0.997427i	$0.522841\pi$
$978$	19.3771	+	18.7440i	0.619612	+	0.599367i
$979$	12.1746	−	7.82412i	0.389101	−	0.250060i
$980$	11.7839	+	4.90755i	0.376422	+	0.156766i
$981$	−11.5118	+	14.2128i	−0.367544	+	0.453780i
$982$	2.72651	−	4.24254i	0.0870065	−	0.135385i
$983$	−10.7746	−	36.6949i	−0.343656	−	1.17039i	−0.932207	−	0.361925i	$-0.882120\pi$
$983$	−10.7746	−	36.6949i	−0.343656	−	1.17039i	0.588551	−	0.808460i	$-0.299699\pi$
$984$	17.0924	+	3.42198i	0.544885	+	0.109089i
$985$	−0.382998	−	11.3332i	−0.0122033	−	0.361106i
$986$	−26.1043	−	57.1603i	−0.831329	−	1.82036i
$987$	−15.2558	+	8.66223i	−0.485598	+	0.275722i
$988$	−1.80191			−0.0573265
$989$	−17.8677	+	13.3862i	−0.568161	+	0.425657i
$990$	−6.11559	+	0.410326i	−0.194366	+	0.0130410i
$991$	−0.955695	+	6.64700i	−0.0303587	+	0.211149i	−0.999354	−	0.0359285i	$-0.988561\pi$
$991$	−0.955695	+	6.64700i	−0.0303587	+	0.211149i	0.968996	+	0.247078i	$0.0794702\pi$
$992$	3.71757	+	8.14034i	0.118033	+	0.258456i
$993$	−10.2697	−	26.1971i	−0.325899	−	0.831338i
$994$	8.31993	−	7.20926i	0.263892	−	0.228664i
$995$	−22.0692	+	15.2603i	−0.699641	+	0.483783i
$996$	−18.1899	+	1.60497i	−0.576368	+	0.0508554i
$997$	3.18421	+	1.45418i	0.100845	+	0.0460544i	0.465199	−	0.885206i	$-0.345983\pi$
$997$	3.18421	+	1.45418i	0.100845	+	0.0460544i	−0.364354	+	0.931261i	$0.618710\pi$
$998$	22.8771	−	26.4016i	0.724163	−	0.835728i
$999$	19.8567	−	29.4791i	0.628239	−	0.932677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.659.17	yes	240
3.2	odd	2		690.2.n.b.659.24	yes	240
5.4	even	2		690.2.n.b.659.8	yes	240
15.14	odd	2	inner	690.2.n.a.659.1	yes	240
23.20	odd	22	inner	690.2.n.a.89.1	✓	240
69.20	even	22		690.2.n.b.89.8	yes	240
115.89	odd	22		690.2.n.b.89.24	yes	240
345.89	even	22	inner	690.2.n.a.89.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.1	✓	240	23.20	odd	22	inner
690.2.n.a.89.17	yes	240	345.89	even	22	inner
690.2.n.a.659.1	yes	240	15.14	odd	2	inner
690.2.n.a.659.17	yes	240	1.1	even	1	trivial
690.2.n.b.89.8	yes	240	69.20	even	22
690.2.n.b.89.24	yes	240	115.89	odd	22
690.2.n.b.659.8	yes	240	5.4	even	2
690.2.n.b.659.24	yes	240	3.2	odd	2

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.804725 - 1.53376i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.14469 - 1.92086i) q^{5} +(1.40362 + 1.01481i) q^{6} +(-0.955977 - 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-1.70483 - 2.46851i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.804725 - 1.53376i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.14469 - 1.92086i) q^{5} +(1.40362 + 1.01481i) q^{6} +(-0.955977 - 0.614369i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-1.70483 - 2.46851i) q^{9} +(1.73840 + 1.40640i) q^{10} +(-0.130034 - 0.904408i) q^{11} +(-1.20424 + 1.24491i) q^{12} +(2.47130 + 3.84542i) q^{13} +(0.744166 - 0.858813i) q^{14} +(-2.02498 - 3.30143i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.74601 - 5.94637i) q^{17} +(2.68601 - 1.33618i) q^{18} +(0.111059 - 0.378232i) q^{19} +(-1.63949 + 1.52055i) q^{20} +(-1.71159 + 0.971841i) q^{21} +0.913708 q^{22} +(1.02121 + 4.68584i) q^{23} +(-1.06086 - 1.36915i) q^{24} +(-2.37939 - 4.39756i) q^{25} +(-4.15798 + 1.89889i) q^{26} +(-5.15802 + 0.628334i) q^{27} +(0.744166 + 0.858813i) q^{28} +(-2.85664 - 9.72883i) q^{29} +(3.55602 - 1.53452i) q^{30} +(3.71757 - 8.14034i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-1.49179 - 0.528359i) q^{33} +(6.13433 - 0.881983i) q^{34} +(-2.27441 + 1.13304i) q^{35} +(0.940317 + 2.84882i) q^{36} +(-4.47941 + 5.16952i) q^{37} +(0.358577 + 0.163757i) q^{38} +(7.88666 - 0.695875i) q^{39} +(-1.27175 - 1.83920i) q^{40} +(-7.60595 + 6.59060i) q^{41} +(-0.718363 - 1.83248i) q^{42} +(1.93387 + 4.23459i) q^{43} +(-0.130034 + 0.904408i) q^{44} +(-6.69316 + 0.449078i) q^{45} +(-4.78348 + 0.343953i) q^{46} +8.91322 q^{47} +(1.50619 - 0.855213i) q^{48} +(-2.37146 - 5.19278i) q^{49} +(4.69142 - 1.72933i) q^{50} +(-10.5254 - 2.10723i) q^{51} +(-1.28782 - 4.38590i) q^{52} +(0.827835 - 1.28814i) q^{53} +(0.112124 - 5.19494i) q^{54} +(-1.88609 - 0.785485i) q^{55} +(-0.955977 + 0.614369i) q^{56} +(-0.490745 - 0.474711i) q^{57} +(10.0363 - 1.44301i) q^{58} +(-2.84841 - 4.43222i) q^{59} +(1.01283 + 3.73821i) q^{60} +(6.70797 + 3.06343i) q^{61} +(7.52841 + 4.83822i) q^{62} +(0.113207 + 3.40724i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(10.2154 - 0.345222i) q^{65} +(0.735284 - 1.40141i) q^{66} +(0.882061 - 6.13487i) q^{67} +6.19741i q^{68} +(8.00875 + 2.20452i) q^{69} +(-0.797822 - 2.41251i) q^{70} +(9.58910 + 1.37871i) q^{71} +(-2.95365 + 0.525316i) q^{72} +(1.47294 - 5.01637i) q^{73} +(-4.47941 - 5.16952i) q^{74} +(-8.65955 + 0.110587i) q^{75} +(-0.213121 + 0.331622i) q^{76} +(-0.431331 + 0.944482i) q^{77} +(-0.433598 + 7.90542i) q^{78} +(1.62557 + 2.52943i) q^{79} +(2.00146 - 0.997065i) q^{80} +(-3.18708 + 8.41680i) q^{81} +(-5.44107 - 8.46648i) q^{82} +(7.96766 + 6.90401i) q^{83} +(1.91606 - 0.450263i) q^{84} +(-13.4208 - 3.45288i) q^{85} +(-4.46670 + 1.31154i) q^{86} +(-17.2205 - 3.44763i) q^{87} +(-0.876696 - 0.257421i) q^{88} +(6.57963 + 14.4074i) q^{89} +(0.508028 - 6.68894i) q^{90} -5.19442i q^{91} +(0.340309 - 4.78374i) q^{92} +(-9.49370 - 12.2526i) q^{93} +(-1.26848 + 8.82250i) q^{94} +(-0.599403 - 0.646286i) q^{95} +(0.632155 + 1.61257i) q^{96} +(10.6822 + 12.3279i) q^{97} +(5.47742 - 1.60831i) q^{98} +(-2.01085 + 1.86286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Introduction

L-functions

Modular forms

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