LMFDB - Embedded newform 690.2.m.f.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, 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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + \cdots + 123904 $ x^20 - 6x^19 + 36x^18 - 172x^17 + 691x^16 - 2342x^15 + 7870x^14 - 23240x^13 + 63837x^12 - 154607x^11 + 334467x^10 - 664202x^9 + 1099560x^8 - 1331000x^7 + 1218096x^6 + 395648x^5 - 588544x^4 + 665984x^3 + 2323200x^2 + 991232*x + 123904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Root			$-0.626062 + 0.402346i$ of defining polynomial
Character	$\chi$	$=$	690.121
Dual form			690.2.m.f.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.565404 - 3.93247i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.565404 - 3.93247i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(0.826386 + 1.80953i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(-0.745933 - 5.18808i) q^{13} +(3.34222 + 2.14792i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.486585 + 0.561549i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-1.86505 - 2.15238i) q^{19} +(0.959493 + 0.281733i) q^{20} +(1.65041 - 3.61389i) q^{21} -1.98930 q^{22} +(-0.0381352 - 4.79568i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(5.02911 + 1.47668i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-3.34222 + 2.14792i) q^{28} +(6.71339 - 7.74767i) q^{29} +(0.142315 - 0.989821i) q^{30} +(0.449598 - 0.132014i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.283107 + 1.96905i) q^{33} +(-0.308668 - 0.675889i) q^{34} +(1.65041 + 3.61389i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(3.89255 + 2.50159i) q^{37} +(2.73264 - 0.802375i) q^{38} +(0.745933 - 5.18808i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(-5.61557 + 3.60891i) q^{41} +(2.60170 + 3.00252i) q^{42} +(8.69446 + 2.55292i) q^{43} +(0.826386 - 1.80953i) q^{44} -1.00000 q^{45} +(4.37815 + 1.95751i) q^{46} +6.95892 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-8.42819 - 2.47474i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-0.625081 + 0.401715i) q^{51} +(-3.43240 + 3.96121i) q^{52} +(0.148172 - 1.03056i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-1.67351 - 1.07550i) q^{55} +(-0.565404 - 3.93247i) q^{56} +(-1.18310 - 2.59063i) q^{57} +(4.25868 + 9.32521i) q^{58} +(0.178878 + 1.24412i) q^{59} +(0.841254 + 0.540641i) q^{60} +(-9.96393 + 2.92567i) q^{61} +(-0.0666856 + 0.463809i) q^{62} +(2.60170 - 3.00252i) q^{63} +(0.841254 - 0.540641i) q^{64} +(3.43240 + 3.96121i) q^{65} +(-1.90872 - 0.560451i) q^{66} +(0.997141 - 2.18343i) q^{67} +0.743035 q^{68} +(1.31451 - 4.61217i) q^{69} -3.97291 q^{70} +(-4.15549 + 9.09926i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-2.26325 - 2.61193i) q^{73} +(-3.89255 + 2.50159i) q^{74} +(0.654861 - 0.755750i) q^{75} +(-0.405313 + 2.81901i) q^{76} +(7.58318 - 2.22662i) q^{77} +(4.40937 + 2.83373i) q^{78} +(-0.734700 - 5.10995i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.949985 - 6.60729i) q^{82} +(4.51870 + 2.90399i) q^{83} +(-3.81198 + 1.11930i) q^{84} +(0.105745 - 0.735472i) q^{85} +(-5.93403 + 6.84823i) q^{86} +(8.62422 - 5.54245i) q^{87} +(1.30272 + 1.50341i) q^{88} +(12.3176 + 3.61676i) q^{89} +(0.415415 - 0.909632i) q^{90} -20.8237 q^{91} +(-3.59936 + 3.16932i) q^{92} +0.468578 q^{93} +(-2.89084 + 6.33006i) q^{94} +(2.73264 + 0.802375i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(-5.14661 + 3.30752i) q^{97} +(5.75230 - 6.63851i) q^{98} +(-0.283107 + 1.96905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	0.565404	−	3.93247i	0.213703	−	1.48633i	−0.546945	−	0.837169i	$-0.684209\pi$
$7$	0.565404	−	3.93247i	0.213703	−	1.48633i	0.760647	−	0.649165i	$-0.224882\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.142315	−	0.989821i	−0.0450039	−	0.313009i
$11$	0.826386	+	1.80953i	0.249165	+	0.545595i	0.992345	−	0.123496i	$-0.0394108\pi$
$11$	0.826386	+	1.80953i	0.249165	+	0.545595i	−0.743180	+	0.669091i	$0.766683\pi$
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	−0.745933	−	5.18808i	−0.206885	−	1.43891i	−0.783243	−	0.621716i	$-0.786436\pi$
$13$	−0.745933	−	5.18808i	−0.206885	−	1.43891i	0.576358	−	0.817197i	$-0.304473\pi$
$14$	3.34222	+	2.14792i	0.893247	+	0.574055i
$15$	−0.959493	+	0.281733i	−0.247740	+	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−0.486585	+	0.561549i	−0.118014	+	0.136196i	−0.811682	−	0.584099i	$-0.801448\pi$
$17$	−0.486585	+	0.561549i	−0.118014	+	0.136196i	0.693668	+	0.720295i	$0.255993\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	−1.86505	−	2.15238i	−0.427871	−	0.493789i	0.500348	−	0.865824i	$-0.333205\pi$
$19$	−1.86505	−	2.15238i	−0.427871	−	0.493789i	−0.928219	+	0.372035i	$0.878660\pi$
$20$	0.959493	+	0.281733i	0.214549	+	0.0629973i
$21$	1.65041	−	3.61389i	0.360148	−	0.788614i
$22$	−1.98930			−0.424121
$23$	−0.0381352	−	4.79568i	−0.00795175	−	0.999968i
$23$	−0.0381352	−	4.79568i	−0.00795175	−	0.999968i
$24$	1.00000			0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	5.02911	+	1.47668i	0.986290	+	0.289601i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−3.34222	+	2.14792i	−0.631621	+	0.405918i
$29$	6.71339	−	7.74767i	1.24665	−	1.43871i	0.391613	−	0.920130i	$-0.371917\pi$
$29$	6.71339	−	7.74767i	1.24665	−	1.43871i	0.855032	−	0.518576i	$-0.173538\pi$
$30$	0.142315	−	0.989821i	0.0259830	−	0.180716i
$31$	0.449598	−	0.132014i	0.0807501	−	0.0237104i	−0.241108	−	0.970498i	$-0.577511\pi$
$31$	0.449598	−	0.132014i	0.0807501	−	0.0237104i	0.321858	+	0.946788i	$0.395693\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.283107	+	1.96905i	0.0492827	+	0.342768i
$34$	−0.308668	−	0.675889i	−0.0529361	−	0.115914i
$35$	1.65041	+	3.61389i	0.278970	+	0.610858i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	3.89255	+	2.50159i	0.639931	+	0.411259i	0.819974	−	0.572400i	$-0.193988\pi$
$37$	3.89255	+	2.50159i	0.639931	+	0.411259i	−0.180044	+	0.983659i	$0.557624\pi$
$38$	2.73264	−	0.802375i	0.443293	−	0.130162i
$39$	0.745933	−	5.18808i	0.119445	−	0.830757i
$40$	−0.654861	+	0.755750i	−0.103543	+	0.119494i
$41$	−5.61557	+	3.60891i	−0.877004	+	0.563616i	−0.899888	−	0.436122i	$-0.856352\pi$
$41$	−5.61557	+	3.60891i	−0.877004	+	0.563616i	0.0228836	+	0.999738i	$0.492715\pi$
$42$	2.60170	+	3.00252i	0.401451	+	0.463300i
$43$	8.69446	+	2.55292i	1.32589	+	0.389317i	0.866616	−	0.498976i	$-0.166291\pi$
$43$	8.69446	+	2.55292i	1.32589	+	0.389317i	0.459276	+	0.888293i	$0.348109\pi$
$44$	0.826386	−	1.80953i	0.124582	−	0.272797i
$45$	−1.00000			−0.149071
$46$	4.37815	+	1.95751i	0.645522	+	0.288619i
$47$	6.95892			1.01506			0.507532	−	0.861633i	$-0.330558\pi$
$47$	6.95892			1.01506			0.507532	+	0.861633i	$0.330558\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−8.42819	−	2.47474i	−1.20403	−	0.353534i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	−0.625081	+	0.401715i	−0.0875289	+	0.0562514i
$52$	−3.43240	+	3.96121i	−0.475989	+	0.549320i
$53$	0.148172	−	1.03056i	0.0203530	−	0.141558i	−0.977111	−	0.212730i	$-0.931765\pi$
$53$	0.148172	−	1.03056i	0.0203530	−	0.141558i	0.997464	+	0.0711713i	$0.0226737\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	−1.67351	−	1.07550i	−0.225656	−	0.145020i
$56$	−0.565404	−	3.93247i	−0.0755553	−	0.525498i
$57$	−1.18310	−	2.59063i	−0.156706	−	0.343138i
$58$	4.25868	+	9.32521i	0.559192	+	1.22446i
$59$	0.178878	+	1.24412i	0.0232879	+	0.161971i	0.998147	−	0.0608522i	$-0.0193818\pi$
$59$	0.178878	+	1.24412i	0.0232879	+	0.161971i	−0.974859	+	0.222823i	$0.928473\pi$
$60$	0.841254	+	0.540641i	0.108605	+	0.0697964i
$61$	−9.96393	+	2.92567i	−1.27575	+	0.374594i	−0.848334	−	0.529461i	$-0.822394\pi$
$61$	−9.96393	+	2.92567i	−1.27575	+	0.374594i	−0.427416	+	0.904055i	$0.640576\pi$
$62$	−0.0666856	+	0.463809i	−0.00846909	+	0.0589038i
$63$	2.60170	−	3.00252i	0.327784	−	0.378282i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	3.43240	+	3.96121i	0.425737	+	0.491327i
$66$	−1.90872	−	0.560451i	−0.234947	−	0.0689868i
$67$	0.997141	−	2.18343i	0.121820	−	0.266749i	−0.838891	−	0.544300i	$-0.816795\pi$
$67$	0.997141	−	2.18343i	0.121820	−	0.266749i	0.960711	+	0.277551i	$0.0895227\pi$
$68$	0.743035			0.0901063
$69$	1.31451	−	4.61217i	0.158248	−	0.555239i
$70$	−3.97291			−0.474853
$71$	−4.15549	+	9.09926i	−0.493166	+	1.07988i	0.485464	+	0.874256i	$0.338651\pi$
$71$	−4.15549	+	9.09926i	−0.493166	+	1.07988i	−0.978630	+	0.205627i	$0.934077\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	−2.26325	−	2.61193i	−0.264894	−	0.305704i	0.607684	−	0.794179i	$-0.292099\pi$
$73$	−2.26325	−	2.61193i	−0.264894	−	0.305704i	−0.872578	+	0.488475i	$0.837553\pi$
$74$	−3.89255	+	2.50159i	−0.452499	+	0.290804i
$75$	0.654861	−	0.755750i	0.0756168	−	0.0872664i
$76$	−0.405313	+	2.81901i	−0.0464926	+	0.323363i
$77$	7.58318	−	2.22662i	0.864183	−	0.253747i
$78$	4.40937	+	2.83373i	0.499263	+	0.320857i
$79$	−0.734700	−	5.10995i	−0.0826603	−	0.574915i	−0.988492	−	0.151276i	$-0.951662\pi$
$79$	−0.734700	−	5.10995i	−0.0826603	−	0.574915i	0.905831	−	0.423639i	$-0.139247\pi$
$80$	−0.415415	−	0.909632i	−0.0464448	−	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.949985	−	6.60729i	−0.104908	−	0.729653i
$83$	4.51870	+	2.90399i	0.495992	+	0.318754i	0.764611	−	0.644492i	$-0.222931\pi$
$83$	4.51870	+	2.90399i	0.495992	+	0.318754i	−0.268620	+	0.963246i	$0.586567\pi$
$84$	−3.81198	+	1.11930i	−0.415921	+	0.122125i
$85$	0.105745	−	0.735472i	0.0114697	−	0.0797732i
$86$	−5.93403	+	6.84823i	−0.639883	+	0.738464i
$87$	8.62422	−	5.54245i	0.924613	−	0.594213i
$88$	1.30272	+	1.50341i	0.138870	+	0.160265i
$89$	12.3176	+	3.61676i	1.30566	+	0.383376i	0.859297	−	0.511477i	$-0.170901\pi$
$89$	12.3176	+	3.61676i	1.30566	+	0.383376i	0.446362	+	0.894853i	$0.352719\pi$
$90$	0.415415	−	0.909632i	0.0437886	−	0.0958836i
$91$	−20.8237			−2.18292
$92$	−3.59936	+	3.16932i	−0.375259	+	0.330425i
$93$	0.468578			0.0485893
$94$	−2.89084	+	6.33006i	−0.298167	+	0.652896i
$95$	2.73264	+	0.802375i	0.280363	+	0.0823220i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	−5.14661	+	3.30752i	−0.522559	+	0.335828i	−0.775183	−	0.631736i	$-0.782343\pi$
$97$	−5.14661	+	3.30752i	−0.522559	+	0.335828i	0.252625	+	0.967564i	$0.418706\pi$
$98$	5.75230	−	6.63851i	0.581070	−	0.670591i
$99$	−0.283107	+	1.96905i	−0.0284534	+	0.197897i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	−11.2231	−	7.21265i	−1.11674	−	0.717686i	−0.153989	−	0.988073i	$-0.549212\pi$
$101$	−11.2231	−	7.21265i	−1.11674	−	0.717686i	−0.962752	+	0.270387i	$0.912848\pi$
$102$	−0.105745	−	0.735472i	−0.0104703	−	0.0728226i
$103$	5.92127	+	12.9658i	0.583441	+	1.27756i	0.939326	+	0.343027i	$0.111452\pi$
$103$	5.92127	+	12.9658i	0.583441	+	1.27756i	−0.355885	+	0.934530i	$0.615821\pi$
$104$	−2.17737	−	4.76777i	−0.213508	−	0.467518i
$105$	0.565404	+	3.93247i	0.0551778	+	0.383770i
$106$	0.875878	+	0.562893i	0.0850728	+	0.0546730i
$107$	−16.8768	+	4.95546i	−1.63154	+	0.479063i	−0.964086	−	0.265591i	$-0.914433\pi$
$107$	−16.8768	+	4.95546i	−1.63154	+	0.479063i	−0.667452	+	0.744653i	$0.732615\pi$
$108$	0.142315	−	0.989821i	0.0136943	−	0.0952456i
$109$	10.0722	−	11.6239i	0.964739	−	1.11337i	−0.0287670	−	0.999586i	$-0.509158\pi$
$109$	10.0722	−	11.6239i	0.964739	−	1.11337i	0.993506	−	0.113782i	$-0.0362965\pi$
$110$	1.67351	−	1.07550i	0.159563	−	0.102545i
$111$	3.03009	+	3.49691i	0.287604	+	0.331912i
$112$	3.81198	+	1.11930i	0.360198	+	0.105764i
$113$	2.60976	−	5.71458i	0.245506	−	0.537583i	−0.746259	−	0.665656i	$-0.768152\pi$
$113$	2.60976	−	5.71458i	0.245506	−	0.537583i	0.991765	+	0.128073i	$0.0408792\pi$
$114$	2.84800			0.266740
$115$	2.62482	+	4.01377i	0.244766	+	0.374286i
$116$	−10.2516			−0.951840
$117$	2.17737	−	4.76777i	0.201298	−	0.440780i
$118$	−1.20600	−	0.354114i	−0.111021	−	0.0325988i
$119$	1.93316	+	2.23098i	0.177212	+	0.204514i
$120$	−0.841254	+	0.540641i	−0.0767956	+	0.0493535i
$121$	4.61197	−	5.32250i	0.419270	−	0.483863i
$122$	1.47788	−	10.2789i	0.133801	−	0.930606i
$123$	−6.40484	+	1.88063i	−0.577505	+	0.169571i
$124$	−0.394193	−	0.253333i	−0.0353996	−	0.0227499i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	1.65041	+	3.61389i	0.147030	+	0.321950i
$127$	−5.21818	−	11.4262i	−0.463039	−	1.01391i	−0.986784	−	0.162039i	$-0.948193\pi$
$127$	−5.21818	−	11.4262i	−0.463039	−	1.01391i	0.523746	−	0.851875i	$-0.324534\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	7.62303	+	4.89902i	0.671170	+	0.431335i
$130$	−5.02911	+	1.47668i	−0.441082	+	0.129513i
$131$	−0.385685	+	2.68250i	−0.0336974	+	0.234371i	−0.999709	−	0.0241285i	$-0.992319\pi$
$131$	−0.385685	+	2.68250i	−0.0336974	+	0.234371i	0.966011	+	0.258499i	$0.0832280\pi$
$132$	1.30272	−	1.50341i	0.113387	−	0.130855i
$133$	−9.51866	+	6.11727i	−0.825373	+	0.530435i
$134$	1.57189	+	1.81406i	0.135791	+	0.156711i
$135$	−0.959493	−	0.281733i	−0.0825800	−	0.0242477i
$136$	−0.308668	+	0.675889i	−0.0264681	+	0.0579570i
$137$	11.0078			0.940460			0.470230	−	0.882544i	$-0.344171\pi$
$137$	11.0078			0.940460			0.470230	+	0.882544i	$0.344171\pi$
$138$	3.64931	+	3.11168i	0.310650	+	0.264884i
$139$	−20.7883			−1.76324			−0.881620	−	0.471960i	$-0.843547\pi$
$139$	−20.7883			−1.76324			−0.881620	+	0.471960i	$0.843547\pi$
$140$	1.65041	−	3.61389i	0.139485	−	0.305429i
$141$	6.67704	+	1.96055i	0.562308	+	0.165108i
$142$	−6.55072	−	7.55994i	−0.549724	−	0.634416i
$143$	8.77157	−	5.63715i	0.733516	−	0.471402i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−1.45896	+	10.1473i	−0.121160	+	0.842686i
$146$	3.31609	−	0.973692i	0.274442	−	0.0805833i
$147$	−7.38958	−	4.74899i	−0.609482	−	0.391690i
$148$	−0.658502	−	4.57998i	−0.0541285	−	0.376472i
$149$	2.94223	+	6.44258i	0.241037	+	0.527797i	0.991029	−	0.133650i	$-0.0426699\pi$
$149$	2.94223	+	6.44258i	0.241037	+	0.527797i	−0.749992	+	0.661447i	$0.769943\pi$
$150$	0.415415	+	0.909632i	0.0339185	+	0.0742711i
$151$	1.70573	+	11.8636i	0.138811	+	0.965449i	0.933537	+	0.358481i	$0.116705\pi$
$151$	1.70573	+	11.8636i	0.138811	+	0.965449i	−0.794726	+	0.606968i	$0.792386\pi$
$152$	−2.39589	−	1.53975i	−0.194333	−	0.124890i
$153$	−0.712937	+	0.209337i	−0.0576376	+	0.0169239i
$154$	−1.12476	+	7.82287i	−0.0906357	+	0.630385i
$155$	−0.306854	+	0.354128i	−0.0246471	+	0.0284442i
$156$	−4.40937	+	2.83373i	−0.353032	+	0.226880i
$157$	8.89997	+	10.2711i	0.710295	+	0.819724i	0.990105	−	0.140331i	$-0.0448167\pi$
$157$	8.89997	+	10.2711i	0.710295	+	0.819724i	−0.279809	+	0.960056i	$0.590271\pi$
$158$	4.95338	+	1.45444i	0.394070	+	0.115709i
$159$	0.432513	−	0.947071i	0.0343005	−	0.0751076i
$160$	1.00000			0.0790569
$161$	−18.8804	−	2.56153i	−1.48799	−	0.201877i
$162$	−1.00000			−0.0785674
$163$	7.65864	−	16.7701i	0.599871	−	1.31353i	−0.329419	−	0.944184i	$-0.606853\pi$
$163$	7.65864	−	16.7701i	0.599871	−	1.31353i	0.929290	−	0.369351i	$-0.120420\pi$
$164$	6.40484	+	1.88063i	0.500134	+	0.146853i
$165$	−1.30272	−	1.50341i	−0.101416	−	0.117041i
$166$	−4.51870	+	2.90399i	−0.350719	+	0.225393i
$167$	−8.11968	+	9.37061i	−0.628320	+	0.725119i	−0.977265	−	0.212024i	$-0.931995\pi$
$167$	−8.11968	+	9.37061i	−0.628320	+	0.725119i	0.348945	+	0.937143i	$0.386540\pi$
$168$	0.565404	−	3.93247i	0.0436219	−	0.303397i
$169$	−13.8863	+	4.07739i	−1.06818	+	0.313645i
$170$	0.625081	+	0.401715i	0.0479415	+	0.0308102i
$171$	−0.405313	−	2.81901i	−0.0309951	−	0.215575i
$172$	−3.76429	−	8.24264i	−0.287024	−	0.628495i
$173$	1.70358	+	3.73032i	0.129521	+	0.283611i	0.963271	−	0.268531i	$-0.0865381\pi$
$173$	1.70358	+	3.73032i	0.129521	+	0.283611i	−0.833750	+	0.552142i	$0.813811\pi$
$174$	1.45896	+	10.1473i	0.110603	+	0.769264i
$175$	−3.34222	−	2.14792i	−0.252648	−	0.162367i
$176$	−1.90872	+	0.560451i	−0.143875	+	0.0422456i
$177$	−0.178878	+	1.24412i	−0.0134453	+	0.0935140i
$178$	−8.40682	+	9.70199i	−0.630118	+	0.727195i
$179$	−8.95564	+	5.75544i	−0.669376	+	0.430182i	−0.830701	−	0.556719i	$-0.812060\pi$
$179$	−8.95564	+	5.75544i	−0.669376	+	0.430182i	0.161324	+	0.986901i	$0.448423\pi$
$180$	0.654861	+	0.755750i	0.0488104	+	0.0563302i
$181$	−3.98886	−	1.17123i	−0.296489	−	0.0870571i	0.130105	−	0.991500i	$-0.458469\pi$
$181$	−3.98886	−	1.17123i	−0.296489	−	0.0870571i	−0.426594	+	0.904443i	$0.640287\pi$
$182$	8.65048	−	18.9419i	0.641216	−	1.40407i
$183$	−10.3846			−0.767650
$184$	−1.38769	−	4.59068i	−0.102302	−	0.338429i
$185$	−4.62708			−0.340190
$186$	−0.194654	+	0.426234i	−0.0142728	+	0.0312530i
$187$	−1.41825	−	0.416435i	−0.103713	−	0.0304528i
$188$	−4.55712	−	5.25920i	−0.332362	−	0.383567i
$189$	3.34222	−	2.14792i	0.243111	−	0.156238i
$190$	−1.86505	+	2.15238i	−0.135305	+	0.156150i
$191$	−2.66466	+	18.5331i	−0.192808	+	1.34101i	0.631724	+	0.775193i	$0.282348\pi$
$191$	−2.66466	+	18.5331i	−0.192808	+	1.34101i	−0.824532	+	0.565815i	$0.808561\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	−15.8221	−	10.1683i	−1.13890	−	0.731927i	−0.171502	−	0.985184i	$-0.554862\pi$
$193$	−15.8221	−	10.1683i	−1.13890	−	0.731927i	−0.967399	+	0.253256i	$0.918498\pi$
$194$	−0.870652	−	6.05551i	−0.0625091	−	0.434761i
$195$	2.17737	+	4.76777i	0.155925	+	0.341427i
$196$	3.64901	+	7.99021i	0.260643	+	0.570729i
$197$	−1.50370	−	10.4585i	−0.107134	−	0.745136i	−0.970595	−	0.240719i	$-0.922617\pi$
$197$	−1.50370	−	10.4585i	−0.107134	−	0.745136i	0.863460	−	0.504417i	$-0.168292\pi$
$198$	−1.67351	−	1.07550i	−0.118931	−	0.0764323i
$199$	−6.62081	+	1.94404i	−0.469337	+	0.137810i	−0.507845	−	0.861449i	$-0.669558\pi$
$199$	−6.62081	+	1.94404i	−0.469337	+	0.137810i	0.0385081	+	0.999258i	$0.487739\pi$
$200$	0.142315	−	0.989821i	0.0100632	−	0.0699909i
$201$	1.57189	−	1.81406i	0.110873	−	0.127954i
$202$	11.2231	−	7.21265i	0.789655	−	0.507480i
$203$	−26.6717	−	30.7808i	−1.87199	−	2.16039i
$204$	0.712937	+	0.209337i	0.0499156	+	0.0146565i
$205$	2.77299	−	6.07201i	0.193674	−	0.424087i
$206$	−14.2539			−0.993115
$207$	2.56066	−	4.05500i	0.177978	−	0.281842i
$208$	5.24143			0.363428
$209$	2.35355	−	5.15356i	0.162798	−	0.356479i
$210$	−3.81198	−	1.11930i	−0.263051	−	0.0772389i
$211$	−8.54259	−	9.85867i	−0.588096	−	0.678699i	0.381229	−	0.924481i	$-0.375501\pi$
$211$	−8.54259	−	9.85867i	−0.588096	−	0.678699i	−0.969325	+	0.245782i	$0.920955\pi$
$212$	−0.875878	+	0.562893i	−0.0601556	+	0.0386596i
$213$	−6.55072	+	7.55994i	−0.448848	+	0.517998i
$214$	2.50321	−	17.4102i	0.171116	−	1.19014i
$215$	−8.69446	+	2.55292i	−0.592957	+	0.174108i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−0.264936	−	1.84267i	−0.0179850	−	0.125089i
$218$	6.38934	+	13.9907i	0.432741	+	0.947570i
$219$	−1.43571	−	3.14377i	−0.0970163	−	0.212436i
$220$	0.283107	+	1.96905i	0.0190871	+	0.132754i
$221$	3.27632	+	2.10556i	0.220389	+	0.141635i
$222$	−4.43965	+	1.30360i	−0.297970	+	0.0874918i
$223$	−1.22871	+	8.54584i	−0.0822803	+	0.572272i	0.906421	+	0.422375i	$0.138803\pi$
$223$	−1.22871	+	8.54584i	−0.0822803	+	0.572272i	−0.988702	+	0.149897i	$0.952106\pi$
$224$	−2.60170	+	3.00252i	−0.173834	+	0.200615i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	4.11403	+	4.74785i	0.273661	+	0.315822i
$227$	−0.737579	−	0.216573i	−0.0489548	−	0.0143744i	0.257163	−	0.966368i	$-0.417212\pi$
$227$	−0.737579	−	0.216573i	−0.0489548	−	0.0143744i	−0.306118	+	0.951993i	$0.599030\pi$
$228$	−1.18310	+	2.59063i	−0.0783529	+	0.171569i
$229$	7.11582			0.470226			0.235113	−	0.971968i	$-0.424454\pi$
$229$	7.11582			0.470226			0.235113	+	0.971968i	$0.424454\pi$
$230$	−4.74144	+	0.720243i	−0.312641	+	0.0474914i
$231$	7.90332			0.520000
$232$	4.25868	−	9.32521i	0.279596	−	0.612230i
$233$	4.54752	+	1.33527i	0.297918	+	0.0874766i	0.427276	−	0.904121i	$-0.359473\pi$
$233$	4.54752	+	1.33527i	0.297918	+	0.0874766i	−0.129358	+	0.991598i	$0.541292\pi$
$234$	3.43240	+	3.96121i	0.224383	+	0.258952i
$235$	−5.85422	+	3.76228i	−0.381887	+	0.245424i
$236$	0.823105	−	0.949914i	0.0535796	−	0.0618341i
$237$	0.734700	−	5.10995i	0.0477239	−	0.331927i
$238$	−2.83243	+	0.831678i	−0.183599	+	0.0539097i
$239$	−14.0347	−	9.01954i	−0.907828	−	0.583426i	0.00127381	−	0.999999i	$-0.499595\pi$
$239$	−14.0347	−	9.01954i	−0.907828	−	0.583426i	−0.909102	+	0.416573i	$0.863231\pi$
$240$	−0.142315	−	0.989821i	−0.00918638	−	0.0638927i
$241$	12.3468	+	27.0357i	0.795328	+	1.74153i	0.660728	+	0.750626i	$0.270248\pi$
$241$	12.3468	+	27.0357i	0.795328	+	1.74153i	0.134600	+	0.990900i	$0.457025\pi$
$242$	2.92563	+	6.40624i	0.188067	+	0.411809i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	8.73606	+	5.61433i	0.559269	+	0.359420i
$245$	8.42819	−	2.47474i	0.538457	−	0.158105i
$246$	0.949985	−	6.60729i	0.0605688	−	0.421266i
$247$	−9.77550	+	11.2815i	−0.622000	+	0.717826i
$248$	0.394193	−	0.253333i	0.0250313	−	0.0160866i
$249$	3.51751	+	4.05942i	0.222913	+	0.257256i
$250$	−0.959493	−	0.281733i	−0.0606837	−	0.0178183i
$251$	−6.75551	+	14.7925i	−0.426404	+	0.933695i	0.567493	+	0.823379i	$0.307914\pi$
$251$	−6.75551	+	14.7925i	−0.426404	+	0.933695i	−0.993897	+	0.110316i	$0.964814\pi$
$252$	−3.97291			−0.250270
$253$	8.64643	−	4.03209i	0.543596	−	0.253495i
$254$	12.5614			0.788170
$255$	0.308668	−	0.675889i	0.0193295	−	0.0423258i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	16.8851	+	19.4864i	1.05326	+	1.21553i	0.975830	+	0.218532i	$0.0701268\pi$
$257$	16.8851	+	19.4864i	1.05326	+	1.21553i	0.0774327	+	0.996998i	$0.475328\pi$
$258$	−7.62303	+	4.89902i	−0.474589	+	0.305000i
$259$	12.0383	−	13.8929i	0.748023	−	0.863264i
$260$	0.745933	−	5.18808i	0.0462608	−	0.321751i
$261$	9.83637	−	2.88822i	0.608856	−	0.178776i
$262$	−2.27987	−	1.46518i	−0.140851	−	0.0905192i
$263$	1.65742	+	11.5276i	0.102201	+	0.710821i	0.974913	+	0.222586i	$0.0714499\pi$
$263$	1.65742	+	11.5276i	0.102201	+	0.710821i	−0.872712	+	0.488235i	$0.837641\pi$
$264$	0.826386	+	1.80953i	0.0508606	+	0.111369i
$265$	0.432513	+	0.947071i	0.0265691	+	0.0581781i
$266$	−1.61027	−	11.1997i	−0.0987321	−	0.686697i
$267$	10.7997	+	6.94052i	0.660928	+	0.424753i
$268$	−2.30312	+	0.676257i	−0.140685	+	0.0413090i
$269$	−0.516257	+	3.59064i	−0.0314767	+	0.218925i	−0.999489	−	0.0319792i	$-0.989819\pi$
$269$	−0.516257	+	3.59064i	−0.0314767	+	0.218925i	0.968012	+	0.250905i	$0.0807281\pi$
$270$	0.654861	−	0.755750i	0.0398536	−	0.0459935i
$271$	14.4230	−	9.26907i	0.876132	−	0.563056i	−0.0234905	−	0.999724i	$-0.507478\pi$
$271$	14.4230	−	9.26907i	0.876132	−	0.563056i	0.899623	+	0.436668i	$0.143842\pi$
$272$	−0.486585	−	0.561549i	−0.0295035	−	0.0340489i
$273$	−19.9802	−	5.86672i	−1.20926	−	0.355070i
$274$	−4.57280	+	10.0130i	−0.276253	+	0.604910i
$275$	1.98930			0.119959
$276$	−4.34646	+	2.02689i	−0.261626	+	0.122004i
$277$	28.5590			1.71594			0.857971	−	0.513699i	$-0.171725\pi$
$277$	28.5590			1.71594			0.857971	+	0.513699i	$0.171725\pi$
$278$	8.63577	−	18.9097i	0.517939	−	1.13413i
$279$	0.449598	+	0.132014i	0.0269167	+	0.00790346i
$280$	2.60170	+	3.00252i	0.155481	+	0.179435i
$281$	17.9585	−	11.5412i	1.07131	−	0.688492i	0.118779	−	0.992921i	$-0.462102\pi$
$281$	17.9585	−	11.5412i	1.07131	−	0.688492i	0.952535	+	0.304429i	$0.0984656\pi$
$282$	−4.55712	+	5.25920i	−0.271373	+	0.313181i
$283$	−1.96574	+	13.6720i	−0.116851	+	0.812719i	0.844137	+	0.536128i	$0.180114\pi$
$283$	−1.96574	+	13.6720i	−0.116851	+	0.812719i	−0.960988	+	0.276591i	$0.910795\pi$
$284$	9.59803	−	2.81824i	0.569538	−	0.167232i
$285$	2.39589	+	1.53975i	0.141920	+	0.0912067i
$286$	1.48389	+	10.3207i	0.0877440	+	0.610273i
$287$	11.0168	+	24.1235i	0.650304	+	1.42397i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	2.34078	+	16.2805i	0.137693	+	0.957675i
$290$	−8.62422	−	5.54245i	−0.506432	−	0.325464i
$291$	−5.86997	+	1.72358i	−0.344104	+	0.101038i
$292$	−0.491852	+	3.42091i	−0.0287835	+	0.200193i
$293$	0.803155	−	0.926891i	0.0469208	−	0.0541495i	−0.731804	−	0.681515i	$-0.761321\pi$
$293$	0.803155	−	0.926891i	0.0469208	−	0.0541495i	0.778725	+	0.627366i	$0.215867\pi$
$294$	7.38958	−	4.74899i	0.430969	−	0.276967i
$295$	−0.823105	−	0.949914i	−0.0479230	−	0.0553061i
$296$	4.43965	+	1.30360i	0.258049	+	0.0757702i
$297$	−0.826386	+	1.80953i	−0.0479518	+	0.105000i
$298$	−7.08263			−0.410285
$299$	−24.8519	+	3.77510i	−1.43722	+	0.218320i
$300$	−1.00000			−0.0577350
$301$	14.9552	−	32.7473i	0.862002	−	1.88752i
$302$	−11.5001	−	3.37674i	−0.661758	−	0.194310i
$303$	−8.73645	−	10.0824i	−0.501896	−	0.579219i
$304$	2.39589	−	1.53975i	0.137414	−	0.0883105i
$305$	6.80045	−	7.84814i	0.389393	−	0.449383i
$306$	0.105745	−	0.735472i	0.00604504	−	0.0420442i
$307$	8.95513	−	2.62946i	0.511096	−	0.150071i	−0.0160082	−	0.999872i	$-0.505096\pi$
$307$	8.95513	−	2.62946i	0.511096	−	0.150071i	0.527105	+	0.849800i	$0.323278\pi$
$308$	−6.64869	−	4.27286i	−0.378845	−	0.243469i
$309$	2.02854	+	14.1088i	0.115400	+	0.802621i
$310$	−0.194654	−	0.426234i	−0.0110556	−	0.0242085i
$311$	11.2086	+	24.5434i	0.635582	+	1.39173i	0.903626	+	0.428323i	$0.140895\pi$
$311$	11.2086	+	24.5434i	0.635582	+	1.39173i	−0.268044	+	0.963407i	$0.586377\pi$
$312$	−0.745933	−	5.18808i	−0.0422301	−	0.293717i
$313$	22.4097	+	14.4018i	1.26667	+	0.814041i	0.989183	−	0.146688i	$-0.0468614\pi$
$313$	22.4097	+	14.4018i	1.26667	+	0.814041i	0.277489	+	0.960729i	$0.410498\pi$
$314$	−13.0401	+	3.82892i	−0.735896	+	0.216079i
$315$	−0.565404	+	3.93247i	−0.0318569	+	0.221570i
$316$	−3.38072	+	3.90156i	−0.190180	+	0.219480i
$317$	−2.70066	+	1.73561i	−0.151684	+	0.0974817i	−0.614281	−	0.789087i	$-0.710554\pi$
$317$	−2.70066	+	1.73561i	−0.151684	+	0.0974817i	0.462597	+	0.886569i	$0.346918\pi$
$318$	0.681814	+	0.786855i	0.0382342	+	0.0441246i
$319$	19.5675	+	5.74554i	1.09557	+	0.321689i
$320$	−0.415415	+	0.909632i	−0.0232224	+	0.0508500i
$321$	−17.5892			−0.981736
$322$	10.1733	−	16.1101i	0.566934	−	0.897783i
$323$	2.11617			0.117747
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−5.02911	−	1.47668i	−0.278965	−	0.0819115i
$326$	12.0731	+	13.9331i	0.668667	+	0.771683i
$327$	12.9390	−	8.31539i	0.715529	−	0.459842i
$328$	−4.37135	+	5.04481i	−0.241367	+	0.278553i
$329$	3.93460	−	27.3658i	0.216922	−	1.50872i
$330$	1.90872	−	0.560451i	0.105072	−	0.0308518i
$331$	22.8779	+	14.7027i	1.25748	+	0.808136i	0.987938	−	0.154852i	$-0.0494900\pi$
$331$	22.8779	+	14.7027i	1.25748	+	0.808136i	0.269546	+	0.962988i	$0.413126\pi$
$332$	−0.764428	−	5.31671i	−0.0419534	−	0.291793i
$333$	1.92216	+	4.20894i	0.105334	+	0.230648i
$334$	−5.15077	−	11.2786i	−0.281838	−	0.617138i
$335$	0.341605	+	2.37592i	0.0186639	+	0.129810i
$336$	3.34222	+	2.14792i	0.182333	+	0.117178i
$337$	28.6934	−	8.42516i	1.56303	−	0.458948i	0.618069	−	0.786124i	$-0.287915\pi$
$337$	28.6934	−	8.42516i	1.56303	−	0.458948i	0.944963	+	0.327177i	$0.106097\pi$
$338$	2.05966	−	14.3252i	0.112031	−	0.779191i
$339$	4.11403	−	4.74785i	0.223444	−	0.257868i
$340$	−0.625081	+	0.401715i	−0.0338998	+	0.0217861i
$341$	0.610425	+	0.704468i	0.0330563	+	0.0381491i
$342$	2.73264	+	0.802375i	0.147764	+	0.0433875i
$343$	−2.94433	+	6.44719i	−0.158979	+	0.348116i
$344$	9.06151			0.488564
$345$	1.38769	+	4.59068i	0.0747107	+	0.247154i
$346$	−4.10091			−0.220466
$347$	5.89078	−	12.8990i	0.316234	−	0.692455i	−0.683047	−	0.730374i	$-0.739346\pi$
$347$	5.89078	−	12.8990i	0.316234	−	0.692455i	0.999281	+	0.0379192i	$0.0120730\pi$
$348$	−9.83637	−	2.88822i	−0.527285	−	0.154825i
$349$	−10.5336	−	12.1565i	−0.563853	−	0.650721i	0.400201	−	0.916427i	$-0.368940\pi$
$349$	−10.5336	−	12.1565i	−0.563853	−	0.650721i	−0.964054	+	0.265706i	$0.914395\pi$
$350$	3.34222	−	2.14792i	0.178649	−	0.114811i
$351$	3.43240	−	3.96121i	0.183208	−	0.211434i
$352$	0.283107	−	1.96905i	0.0150897	−	0.104951i
$353$	23.6033	−	6.93056i	1.25628	−	0.368876i	0.415170	−	0.909744i	$-0.363722\pi$
$353$	23.6033	−	6.93056i	1.25628	−	0.368876i	0.841108	+	0.540868i	$0.181904\pi$
$354$	−1.05738	−	0.679540i	−0.0561994	−	0.0361171i
$355$	−1.42361	−	9.90141i	−0.0755573	−	0.525512i
$356$	−5.33292	−	11.6775i	−0.282644	−	0.618905i
$357$	1.22631	+	2.68524i	0.0649032	+	0.142118i
$358$	−1.51503	−	10.5372i	−0.0800716	−	0.556910i
$359$	−14.6567	−	9.41928i	−0.773551	−	0.497131i	0.0933368	−	0.995635i	$-0.470247\pi$
$359$	−14.6567	−	9.41928i	−0.773551	−	0.497131i	−0.866888	+	0.498504i	$0.833883\pi$
$360$	−0.959493	+	0.281733i	−0.0505697	+	0.0148486i
$361$	1.54965	−	10.7780i	0.0815605	−	0.567266i
$362$	2.72242	−	3.14184i	0.143087	−	0.165132i
$363$	5.92467	−	3.80756i	0.310965	−	0.199845i
$364$	13.6366	+	15.7375i	0.714754	+	0.824870i
$365$	3.31609	+	0.973692i	0.173572	+	0.0509654i
$366$	4.31391	−	9.44614i	0.225492	−	0.493758i
$367$	2.03897			0.106433			0.0532167	−	0.998583i	$-0.483053\pi$
$367$	2.03897			0.106433			0.0532167	+	0.998583i	$0.483053\pi$
$368$	4.75229	+	0.644749i	0.247730	+	0.0336099i
$369$	−6.67524			−0.347499
$370$	1.92216	−	4.20894i	0.0999283	−	0.218812i
$371$	−3.96887	−	1.16537i	−0.206054	−	0.0605028i
$372$	−0.306854	−	0.354128i	−0.0159096	−	0.0183607i
$373$	−11.5604	+	7.42941i	−0.598574	+	0.384680i	−0.804557	−	0.593875i	$-0.797597\pi$
$373$	−11.5604	+	7.42941i	−0.598574	+	0.384680i	0.205983	+	0.978556i	$0.433961\pi$
$374$	0.967964	−	1.11709i	0.0500522	−	0.0577634i
$375$	−0.142315	+	0.989821i	−0.00734911	+	0.0511142i
$376$	6.67704	−	1.96055i	0.344342	−	0.101108i
$377$	−45.2032	−	29.0503i	−2.32808	−	1.49617i
$378$	0.565404	+	3.93247i	0.0290812	+	0.202264i
$379$	11.4696	+	25.1149i	0.589154	+	1.29007i	0.935952	+	0.352128i	$0.114542\pi$
$379$	11.4696	+	25.1149i	0.589154	+	1.29007i	−0.346797	+	0.937940i	$0.612731\pi$
$380$	−1.18310	−	2.59063i	−0.0606919	−	0.132897i
$381$	−1.78767	−	12.4335i	−0.0915851	−	0.636988i
$382$	−15.7514	−	10.1228i	−0.805910	−	0.517927i
$383$	4.50643	−	1.32321i	0.230268	−	0.0676128i	−0.164563	−	0.986367i	$-0.552621\pi$
$383$	4.50643	−	1.32321i	0.230268	−	0.0676128i	0.394831	+	0.918754i	$0.370803\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−5.17557	+	5.97293i	−0.263772	+	0.304409i
$386$	15.8221	−	10.1683i	0.805325	−	0.517551i
$387$	5.93403	+	6.84823i	0.301644	+	0.348115i
$388$	5.86997	+	1.72358i	0.298003	+	0.0875015i
$389$	−1.04315	+	2.28419i	−0.0528901	+	0.115813i	−0.934232	−	0.356666i	$-0.883913\pi$
$389$	−1.04315	+	2.28419i	−0.0528901	+	0.115813i	0.881342	+	0.472479i	$0.156641\pi$
$390$	−5.24143			−0.265410
$391$	2.71156	+	2.31209i	0.137130	+	0.116927i
$392$	−8.78401			−0.443659
$393$	−1.12581	+	2.46518i	−0.0567895	+	0.124352i
$394$	10.1380	+	2.97679i	0.510746	+	0.149969i
$395$	3.38072	+	3.90156i	0.170102	+	0.196309i
$396$	1.67351	−	1.07550i	0.0840969	−	0.0540458i
$397$	7.03196	−	8.11532i	0.352924	−	0.407296i	−0.551333	−	0.834286i	$-0.685880\pi$
$397$	7.03196	−	8.11532i	0.352924	−	0.407296i	0.904257	+	0.426990i	$0.140426\pi$
$398$	0.982018	−	6.83009i	0.0492241	−	0.342361i
$399$	−10.8565	+	3.18776i	−0.543506	+	0.159588i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	4.74290	+	32.9876i	0.236849	+	1.64732i	0.667360	+	0.744735i	$0.267424\pi$
$401$	4.74290	+	32.9876i	0.236849	+	1.64732i	−0.430511	+	0.902585i	$0.641667\pi$
$402$	0.997141	+	2.18343i	0.0497329	+	0.108900i
$403$	−1.02027	−	2.23407i	−0.0508231	−	0.111287i
$404$	1.89861	+	13.2051i	0.0944595	+	0.656980i
$405$	−0.841254	−	0.540641i	−0.0418022	−	0.0268647i
$406$	39.0790	−	11.4746i	1.93946	−	0.569476i
$407$	−1.30996	+	9.11097i	−0.0649323	+	0.451614i
$408$	−0.486585	+	0.561549i	−0.0240895	+	0.0278008i
$409$	8.83214	−	5.67607i	0.436721	−	0.280664i	−0.303750	−	0.952752i	$-0.598239\pi$
$409$	8.83214	−	5.67607i	0.436721	−	0.280664i	0.740471	+	0.672088i	$0.234602\pi$
$410$	4.37135	+	5.04481i	0.215886	+	0.249145i
$411$	10.5619	+	3.10125i	0.520980	+	0.152974i
$412$	5.92127	−	12.9658i	0.291720	−	0.638778i
$413$	4.99361			0.245720
$414$	2.62482	+	4.01377i	0.129003	+	0.197266i
$415$	−5.37139			−0.263671
$416$	−2.17737	+	4.76777i	−0.106754	+	0.233759i
$417$	−19.9462	−	5.85674i	−0.976771	−	0.286806i
$418$	3.71014	+	4.28173i	0.181469	+	0.209426i
$419$	−8.55875	+	5.50038i	−0.418122	+	0.268711i	−0.732742	−	0.680507i	$-0.761760\pi$
$419$	−8.55875	+	5.50038i	−0.418122	+	0.268711i	0.314619	+	0.949218i	$0.398123\pi$
$420$	2.60170	−	3.00252i	0.126950	−	0.146508i
$421$	4.70100	−	32.6962i	0.229113	−	1.59351i	−0.472747	−	0.881198i	$-0.656737\pi$
$421$	4.70100	−	32.6962i	0.229113	−	1.59351i	0.701859	−	0.712315i	$-0.252353\pi$
$422$	12.5165	−	3.67517i	0.609293	−	0.178905i
$423$	5.85422	+	3.76228i	0.284642	+	0.182928i
$424$	−0.148172	−	1.03056i	−0.00719588	−	0.0500485i
$425$	0.308668	+	0.675889i	0.0149726	+	0.0327854i
$426$	−4.15549	−	9.09926i	−0.201334	−	0.440860i
$427$	5.87148	+	40.8370i	0.284141	+	1.97624i
$428$	14.7970	+	9.50946i	0.715241	+	0.459657i
$429$	10.0044	−	2.93756i	0.483018	−	0.141827i
$430$	1.28959	−	8.96928i	0.0621894	−	0.432537i
$431$	−26.1054	+	30.1272i	−1.25745	+	1.45118i	−0.417351	+	0.908746i	$0.637041\pi$
$431$	−26.1054	+	30.1272i	−1.25745	+	1.45118i	−0.840101	+	0.542431i	$0.817504\pi$
$432$	−0.841254	+	0.540641i	−0.0404748	+	0.0260116i
$433$	−25.0079	−	28.8607i	−1.20180	−	1.38696i	−0.901311	−	0.433173i	$-0.857394\pi$
$433$	−25.0079	−	28.8607i	−1.20180	−	1.38696i	−0.300494	−	0.953784i	$-0.597152\pi$
$434$	1.78621	+	0.524479i	0.0857408	+	0.0251758i
$435$	−4.25868	+	9.32521i	−0.204188	+	0.447110i
$436$	−15.3806			−0.736598
$437$	−10.2510	+	9.02624i	−0.490371	+	0.431784i
$438$	3.45609			0.165138
$439$	8.59695	−	18.8247i	0.410310	−	0.898454i	−0.585810	−	0.810449i	$-0.699223\pi$
$439$	8.59695	−	18.8247i	0.410310	−	0.898454i	0.996120	−	0.0880054i	$-0.0280493\pi$
$440$	−1.90872	−	0.560451i	−0.0909948	−	0.0267185i
$441$	−5.75230	−	6.63851i	−0.273919	−	0.316119i
$442$	−3.27632	+	2.10556i	−0.155839	+	0.100151i
$443$	−5.54837	+	6.40316i	−0.263611	+	0.304223i	−0.872089	−	0.489348i	$-0.837235\pi$
$443$	−5.54837	+	6.40316i	−0.263611	+	0.304223i	0.608478	+	0.793571i	$0.291780\pi$
$444$	0.658502	−	4.57998i	0.0312511	−	0.217356i
$445$	−12.3176	+	3.61676i	−0.583908	+	0.171451i
$446$	−7.26315	−	4.66774i	−0.343920	−	0.221024i
$447$	1.00796	+	7.01053i	0.0476750	+	0.331587i
$448$	−1.65041	−	3.61389i	−0.0779744	−	0.170740i
$449$	−15.0737	−	33.0067i	−0.711370	−	1.55768i	−0.825617	−	0.564230i	$-0.809173\pi$
$449$	−15.0737	−	33.0067i	−0.711370	−	1.55768i	0.114248	−	0.993452i	$-0.463554\pi$
$450$	0.142315	+	0.989821i	0.00670879	+	0.0466606i
$451$	−11.1711	−	7.17920i	−0.526025	−	0.338056i
$452$	−6.02782	+	1.76993i	−0.283525	+	0.0832505i
$453$	−1.70573	+	11.8636i	−0.0801423	+	0.557402i
$454$	0.503403	−	0.580958i	0.0236259	−	0.0272657i
$455$	17.5180	−	11.2581i	0.821258	−	0.527790i
$456$	−1.86505	−	2.15238i	−0.0873387	−	0.100794i
$457$	−13.8020	−	4.05263i	−0.645630	−	0.189574i	−0.0575061	−	0.998345i	$-0.518315\pi$
$457$	−13.8020	−	4.05263i	−0.645630	−	0.189574i	−0.588123	+	0.808771i	$0.700133\pi$
$458$	−2.95602	+	6.47278i	−0.138126	+	0.302453i
$459$	−0.743035			−0.0346819
$460$	1.31451	−	4.61217i	0.0612893	−	0.215043i
$461$	−4.80918			−0.223986			−0.111993	−	0.993709i	$-0.535723\pi$
$461$	−4.80918			−0.223986			−0.111993	+	0.993709i	$0.535723\pi$
$462$	−3.28316	+	7.18911i	−0.152746	+	0.334468i
$463$	34.0139	+	9.98737i	1.58076	+	0.464153i	0.950110	−	0.311916i	$-0.100971\pi$
$463$	34.0139	+	9.98737i	1.58076	+	0.464153i	0.630649	+	0.776068i	$0.282789\pi$
$464$	6.71339	+	7.74767i	0.311661	+	0.359676i
$465$	−0.394193	+	0.253333i	−0.0182803	+	0.0117480i
$466$	−3.10371	+	3.58188i	−0.143777	+	0.165927i
$467$	3.51841	−	24.4711i	0.162813	−	1.13239i	−0.730487	−	0.682926i	$-0.760707\pi$
$467$	3.51841	−	24.4711i	0.162813	−	1.13239i	0.893300	−	0.449461i	$-0.148384\pi$
$468$	−5.02911	+	1.47668i	−0.232471	+	0.0682596i
$469$	−8.02251	−	5.15575i	−0.370445	−	0.238070i
$470$	−0.990358	−	6.88809i	−0.0456818	−	0.317724i
$471$	5.64575	+	12.3625i	0.260143	+	0.569633i
$472$	0.522142	+	1.14333i	0.0240335	+	0.0526261i
$473$	2.56538	+	17.8426i	0.117956	+	0.820404i
$474$	4.34297	+	2.79106i	0.199479	+	0.128198i
$475$	−2.73264	+	0.802375i	−0.125382	+	0.0368155i
$476$	0.420115	−	2.92196i	0.0192559	−	0.133928i
$477$	0.681814	−	0.786855i	0.0312181	−	0.0360276i
$478$	14.0347	−	9.01954i	0.641932	−	0.412544i
$479$	27.5989	+	31.8509i	1.26103	+	1.45530i	0.834671	+	0.550748i	$0.185658\pi$
$479$	27.5989	+	31.8509i	1.26103	+	1.45530i	0.426357	+	0.904555i	$0.359797\pi$
$480$	0.959493	+	0.281733i	0.0437947	+	0.0128593i
$481$	10.0749	−	22.0609i	0.459374	−	1.00589i
$482$	−29.7216			−1.35378
$483$	−17.3940	−	7.77700i	−0.791453	−	0.353866i
$484$	−7.04267			−0.320122
$485$	2.54142	−	5.56493i	0.115400	−	0.252691i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	12.7840	+	14.7535i	0.579298	+	0.668545i	0.967454	−	0.253049i	$-0.0814332\pi$
$487$	12.7840	+	14.7535i	0.579298	+	0.668545i	−0.388156	+	0.921594i	$0.626888\pi$
$488$	−8.73606	+	5.61433i	−0.395463	+	0.254149i
$489$	12.0731	−	13.9331i	0.545964	−	0.630076i
$490$	−1.25009	+	8.69460i	−0.0564735	+	0.392782i
$491$	−29.2270	+	8.58182i	−1.31900	+	0.387292i	−0.864130	−	0.503268i	$-0.832131\pi$
$491$	−29.2270	+	8.58182i	−1.31900	+	0.387292i	−0.454866	+	0.890560i	$0.650313\pi$
$492$	5.61557	+	3.60891i	0.253169	+	0.162702i
$493$	1.08406	+	7.53979i	0.0488235	+	0.339575i
$494$	−6.20115	−	13.5786i	−0.279003	−	0.610931i
$495$	−0.826386	−	1.80953i	−0.0371433	−	0.0813325i
$496$	0.0666856	+	0.463809i	0.00299427	+	0.0208256i
$497$	33.4330	+	21.4861i	1.49968	+	0.963784i
$498$	−5.15381	+	1.51329i	−0.230948	+	0.0678124i
$499$	0.559891	−	3.89413i	0.0250641	−	0.174325i	−0.973444	−	0.228924i	$-0.926479\pi$
$499$	0.559891	−	3.89413i	0.0250641	−	0.174325i	0.998508	+	0.0545995i	$0.0173882\pi$
$500$	0.654861	−	0.755750i	0.0292863	−	0.0337981i
$501$	−10.4308	+	6.70346i	−0.466013	+	0.299488i
$502$	−10.6494	−	12.2901i	−0.475306	−	0.548532i
$503$	−16.7227	−	4.91023i	−0.745629	−	0.218936i	−0.113219	−	0.993570i	$-0.536116\pi$
$503$	−16.7227	−	4.91023i	−0.745629	−	0.218936i	−0.632410	+	0.774634i	$0.717934\pi$
$504$	1.65041	−	3.61389i	0.0735149	−	0.160975i
$505$	13.3409			0.593664
$506$	0.0758625	+	9.54006i	0.00337250	+	0.424107i
$507$	−14.4726			−0.642749
$508$	−5.21818	+	11.4262i	−0.231519	+	0.506957i
$509$	16.0184	+	4.70344i	0.710005	+	0.208476i	0.616742	−	0.787165i	$-0.288452\pi$
$509$	16.0184	+	4.70344i	0.710005	+	0.208476i	0.0932627	+	0.995642i	$0.470270\pi$
$510$	0.486585	+	0.561549i	0.0215463	+	0.0248658i
$511$	−11.5510	+	7.42338i	−0.510987	+	0.328391i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	0.405313	−	2.81901i	0.0178950	−	0.124463i
$514$	−24.7398	+	7.26426i	−1.09123	+	0.320413i
$515$	−11.9911	−	7.70623i	−0.528392	−	0.339577i
$516$	−1.28959	−	8.96928i	−0.0567709	−	0.394850i
$517$	5.75076	+	12.5924i	0.252918	+	0.553813i
$518$	7.63656	+	16.7217i	0.335531	+	0.734711i
$519$	0.583620	+	4.05917i	0.0256181	+	0.178178i
$520$	4.40937	+	2.83373i	0.193364	+	0.124267i
$521$	29.6226	−	8.69799i	1.29779	−	0.381066i	0.441361	−	0.897329i	$-0.354496\pi$
$521$	29.6226	−	8.69799i	1.29779	−	0.381066i	0.856430	+	0.516264i	$0.172677\pi$
$522$	−1.45896	+	10.1473i	−0.0638569	+	0.444135i
$523$	2.31158	−	2.66770i	0.101078	−	0.116651i	−0.702956	−	0.711233i	$-0.748137\pi$
$523$	2.31158	−	2.66770i	0.101078	−	0.116651i	0.804035	+	0.594582i	$0.202683\pi$
$524$	2.27987	−	1.46518i	0.0995964	−	0.0640067i
$525$	−2.60170	−	3.00252i	−0.113548	−	0.131041i
$526$	−11.1744	−	3.28109i	−0.487226	−	0.143062i
$527$	−0.144635	+	0.316707i	−0.00630041	+	0.0137960i
$528$	−1.98930			−0.0865733
$529$	−22.9971	+	0.365769i	−0.999874	+	0.0159030i
$530$	−1.04116			−0.0452250
$531$	−0.522142	+	1.14333i	−0.0226590	+	0.0496163i
$532$	10.8565	+	3.18776i	0.470690	+	0.138207i
$533$	22.9121	+	26.4420i	0.992434	+	1.14533i
$534$	−10.7997	+	6.94052i	−0.467347	+	0.300346i
$535$	11.5185	−	13.2931i	0.497988	−	0.574709i
$536$	0.341605	−	2.37592i	0.0147551	−	0.102624i
$537$	−10.2144	+	2.99921i	−0.440783	+	0.129426i
$538$	−3.05170	−	1.96121i	−0.131568	−	0.0845538i
$539$	−2.48682	−	17.2962i	−0.107115	−	0.744999i
$540$	0.415415	+	0.909632i	0.0178766	+	0.0391443i
$541$	0.517617	+	1.13342i	0.0222541	+	0.0487296i	0.920433	−	0.390901i	$-0.127837\pi$
$541$	0.517617	+	1.13342i	0.0222541	+	0.0487296i	−0.898179	+	0.439631i	$0.855109\pi$
$542$	2.43993	+	16.9701i	0.104804	+	0.728928i
$543$	−3.49731	−	2.24758i	−0.150084	−	0.0964530i
$544$	0.712937	−	0.209337i	0.0305669	−	0.00897526i
$545$	−2.18889	+	15.2241i	−0.0937618	+	0.652128i
$546$	13.6366	−	15.7375i	0.583594	−	0.673503i
$547$	−10.9879	+	7.06147i	−0.469807	+	0.301927i	−0.754040	−	0.656828i	$-0.771898\pi$
$547$	−10.9879	+	7.06147i	−0.469807	+	0.301927i	0.284233	+	0.958755i	$0.408261\pi$
$548$	−7.20857	−	8.31914i	−0.307935	−	0.355376i
$549$	−9.96393	−	2.92567i	−0.425250	−	0.124865i
$550$	−0.826386	+	1.80953i	−0.0352372	+	0.0771588i
$551$	−29.1967			−1.24382
$552$	−0.0381352	−	4.79568i	−0.00162314	−	0.204118i
$553$	−20.5101			−0.872180
$554$	−11.8638	+	25.9781i	−0.504045	+	1.10371i
$555$	−4.43965	−	1.30360i	−0.188453	−	0.0553347i
$556$	13.6134	+	15.7107i	0.577338	+	0.666284i
$557$	−22.3640	+	14.3725i	−0.947593	+	0.608981i	−0.920538	−	0.390653i	$-0.872249\pi$
$557$	−22.3640	+	14.3725i	−0.947593	+	0.608981i	−0.0270550	+	0.999634i	$0.508613\pi$
$558$	−0.306854	+	0.354128i	−0.0129901	+	0.0149914i
$559$	6.75928	−	47.0118i	0.285887	−	1.98839i
$560$	−3.81198	+	1.11930i	−0.161085	+	0.0472990i
$561$	−1.24348	−	0.799133i	−0.0524996	−	0.0337394i
$562$	3.03804	+	21.1300i	0.128152	+	0.891316i
$563$	−5.37185	−	11.7627i	−0.226396	−	0.495739i	0.762011	−	0.647564i	$-0.224212\pi$
$563$	−5.37185	−	11.7627i	−0.226396	−	0.495739i	−0.988407	+	0.151825i	$0.951485\pi$
$564$	−2.89084	−	6.33006i	−0.121726	−	0.266544i
$565$	0.894065	+	6.21836i	0.0376136	+	0.261608i
$566$	−11.6199	−	7.46768i	−0.488422	−	0.313890i
$567$	3.81198	−	1.11930i	0.160088	−	0.0470061i
$568$	−1.42361	+	9.90141i	−0.0597333	+	0.415454i
$569$	−7.78401	+	8.98323i	−0.326323	+	0.376596i	−0.895077	−	0.445911i	$-0.852880\pi$
$569$	−7.78401	+	8.98323i	−0.326323	+	0.376596i	0.568755	+	0.822507i	$0.307425\pi$
$570$	−2.39589	+	1.53975i	−0.100353	+	0.0644929i
$571$	6.70799	+	7.74144i	0.280721	+	0.323969i	0.878546	−	0.477657i	$-0.158514\pi$
$571$	6.70799	+	7.74144i	0.280721	+	0.323969i	−0.597825	+	0.801626i	$0.703968\pi$
$572$	−10.0044	−	2.93756i	−0.418306	−	0.122826i
$573$	−7.77810	+	17.0317i	−0.324935	+	0.711508i
$574$	−26.5201			−1.10693
$575$	−4.37815	−	1.95751i	−0.182581	−	0.0816337i
$576$	1.00000			0.0416667
$577$	−3.15205	+	6.90204i	−0.131222	+	0.287336i	−0.963826	−	0.266533i	$-0.914122\pi$
$577$	−3.15205	+	6.90204i	−0.131222	+	0.287336i	0.832604	+	0.553869i	$0.186849\pi$
$578$	−15.7816	−	4.63391i	−0.656430	−	0.192745i
$579$	−12.3165	−	14.2140i	−0.511856	−	0.590713i
$580$	8.62422	−	5.54245i	0.358101	−	0.230138i
$581$	13.9748	−	16.1277i	0.579770	−	0.669091i
$582$	0.870652	−	6.05551i	0.0360897	−	0.251009i
$583$	1.98728	−	0.583519i	0.0823048	−	0.0241669i
$584$	−2.90744	−	1.86850i	−0.120311	−	0.0773191i
$585$	0.745933	+	5.18808i	0.0308405	+	0.214501i
$586$	0.509487	+	1.11562i	0.0210467	+	0.0460858i
$587$	4.58676	+	10.0436i	0.189316	+	0.414544i	0.980360	−	0.197215i	$-0.0631896\pi$
$587$	4.58676	+	10.0436i	0.189316	+	0.414544i	−0.791044	+	0.611759i	$0.790462\pi$
$588$	1.25009	+	8.69460i	0.0515530	+	0.358559i
$589$	−1.12266	−	0.721492i	−0.0462585	−	0.0297286i
$590$	1.20600	−	0.354114i	0.0496503	−	0.0145786i
$591$	1.50370	−	10.4585i	0.0618540	−	0.430204i
$592$	−3.03009	+	3.49691i	−0.124536	+	0.143722i
$593$	28.2209	−	18.1365i	1.15889	−	0.744776i	0.187503	−	0.982264i	$-0.439960\pi$
$593$	28.2209	−	18.1365i	1.15889	−	0.744776i	0.971390	+	0.237488i	$0.0763241\pi$
$594$	−1.30272	−	1.50341i	−0.0534511	−	0.0616859i
$595$	−2.83243	−	0.831678i	−0.116118	−	0.0340955i
$596$	2.94223	−	6.44258i	0.120518	−	0.263898i
$597$	−6.90032			−0.282411
$598$	6.88990	−	24.1743i	0.281749	−	0.988562i
$599$	−41.0360			−1.67669			−0.838344	−	0.545142i	$-0.816476\pi$
$599$	−41.0360			−1.67669			−0.838344	+	0.545142i	$0.816476\pi$
$600$	0.415415	−	0.909632i	0.0169592	−	0.0371356i
$601$	−3.23661	−	0.950355i	−0.132024	−	0.0387658i	0.215053	−	0.976602i	$-0.431008\pi$
$601$	−3.23661	−	0.950355i	−0.132024	−	0.0387658i	−0.347077	+	0.937837i	$0.612826\pi$
$602$	23.5753	+	27.2074i	0.960860	+	1.10889i
$603$	2.01930	−	1.29773i	0.0822324	−	0.0528475i
$604$	7.84892	−	9.05813i	0.319368	−	0.368570i
$605$	−1.00228	+	6.97099i	−0.0407484	+	0.283411i
$606$	12.8005	−	3.75857i	0.519986	−	0.152682i
$607$	32.4690	+	20.8666i	1.31788	+	0.846948i	0.995037	−	0.0995049i	$-0.0317259\pi$
$607$	32.4690	+	20.8666i	1.31788	+	0.846948i	0.322841	+	0.946453i	$0.395362\pi$
$608$	0.405313	+	2.81901i	0.0164376	+	0.114326i
$609$	−16.9194	−	37.0482i	−0.685607	−	1.50127i
$610$	4.31391	+	9.44614i	0.174665	+	0.382463i
$611$	−5.19089	−	36.1034i	−0.210001	−	1.46059i
$612$	0.625081	+	0.401715i	0.0252674	+	0.0162384i
$613$	−16.1841	+	4.75210i	−0.653672	+	0.191935i	−0.591720	−	0.806144i	$-0.701551\pi$
$613$	−16.1841	+	4.75210i	−0.653672	+	0.191935i	−0.0619520	+	0.998079i	$0.519733\pi$
$614$	−1.32825	+	9.23820i	−0.0536039	+	0.372823i
$615$	4.37135	−	5.04481i	0.176270	−	0.203426i
$616$	6.64869	−	4.27286i	0.267884	−	0.172158i
$617$	−15.7934	−	18.2266i	−0.635819	−	0.733774i	0.342811	−	0.939404i	$-0.388621\pi$
$617$	−15.7934	−	18.2266i	−0.635819	−	0.733774i	−0.978630	+	0.205630i	$0.934076\pi$
$618$	−13.6765	−	4.01578i	−0.550149	−	0.161538i
$619$	−1.97724	+	4.32955i	−0.0794720	+	0.174019i	−0.945197	−	0.326500i	$-0.894131\pi$
$619$	−1.97724	+	4.32955i	−0.0794720	+	0.174019i	0.865725	+	0.500520i	$0.166858\pi$
$620$	0.468578			0.0188186
$621$	3.59936	−	3.16932i	0.144437	−	0.127181i
$622$	−26.9817			−1.08187
$623$	21.1872	−	46.3935i	0.848848	−	1.85872i
$624$	5.02911	+	1.47668i	0.201326	+	0.0591145i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−22.4097	+	14.4018i	−0.895672	+	0.575614i
$627$	3.71014	−	4.28173i	0.148169	−	0.170996i
$628$	1.93415	−	13.4523i	0.0771809	−	0.536805i
$629$	−3.29882	+	0.968620i	−0.131532	+	0.0386214i
$630$	−3.34222	−	2.14792i	−0.133157	−	0.0855751i
$631$	−4.12398	−	28.6829i	−0.164173	−	1.14185i	−0.890661	−	0.454668i	$-0.849758\pi$
$631$	−4.12398	−	28.6829i	−0.164173	−	1.14185i	0.726488	−	0.687179i	$-0.241151\pi$
$632$	−2.14458	−	4.69598i	−0.0853068	−	0.186796i
$633$	−5.41904	−	11.8661i	−0.215388	−	0.471633i
$634$	−0.456871	−	3.17761i	−0.0181447	−	0.126199i
$635$	10.5673	+	6.79119i	0.419350	+	0.269500i
$636$	−0.998984	+	0.293328i	−0.0396123	+	0.0116312i
$637$	−6.55228	+	45.5721i	−0.259611	+	1.80563i
$638$	−13.3550	+	15.4125i	−0.528728	+	0.610185i
$639$	−8.41525	+	5.40815i	−0.332902	+	0.213943i
$640$	−0.654861	−	0.755750i	−0.0258856	−	0.0298736i
$641$	29.2146	+	8.57818i	1.15391	+	0.338818i	0.802062	−	0.597240i	$-0.203736\pi$
$641$	29.2146	+	8.57818i	1.15391	+	0.338818i	0.351845	+	0.936058i	$0.385554\pi$
$642$	7.30684	−	15.9997i	0.288378	−	0.631459i
$643$	−39.9951			−1.57725			−0.788627	−	0.614872i	$-0.789207\pi$
$643$	−39.9951			−1.57725			−0.788627	+	0.614872i	$0.789207\pi$
$644$	10.4282	+	15.9463i	0.410928	+	0.628373i
$645$	−9.06151			−0.356797
$646$	−0.879087	+	1.92493i	−0.0345872	+	0.0757355i
$647$	9.60803	+	2.82117i	0.377731	+	0.110912i	0.465086	−	0.885265i	$-0.346023\pi$
$647$	9.60803	+	2.82117i	0.377731	+	0.110912i	−0.0873553	+	0.996177i	$0.527842\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−2.10346	+	1.35181i	−0.0825680	+	0.0530632i
$650$	3.43240	−	3.96121i	0.134630	−	0.155371i
$651$	0.264936	−	1.84267i	0.0103837	−	0.0722199i
$652$	−17.6893	+	5.19406i	−0.692768	+	0.203415i
$653$	−2.54875	−	1.63798i	−0.0997404	−	0.0640993i	0.489820	−	0.871824i	$-0.337063\pi$
$653$	−2.54875	−	1.63798i	−0.0997404	−	0.0640993i	−0.589560	+	0.807724i	$0.700699\pi$
$654$	2.18889	+	15.2241i	0.0855924	+	0.595308i
$655$	−1.12581	−	2.46518i	−0.0439890	−	0.0963224i
$656$	−2.77299	−	6.07201i	−0.108267	−	0.237072i
$657$	−0.491852	−	3.42091i	−0.0191890	−	0.133462i
$658$	23.2583	+	14.9472i	0.906702	+	0.582702i
$659$	47.5205	−	13.9533i	1.85113	−	0.543542i	0.851313	−	0.524659i	$-0.175807\pi$
$659$	47.5205	−	13.9533i	1.85113	−	0.543542i	0.999822	−	0.0188833i	$-0.00601108\pi$
$660$	−0.283107	+	1.96905i	−0.0110199	+	0.0766453i
$661$	8.96906	−	10.3508i	0.348856	−	0.402601i	−0.554019	−	0.832504i	$-0.686907\pi$
$661$	8.96906	−	10.3508i	0.348856	−	0.402601i	0.902875	+	0.429903i	$0.141452\pi$
$662$	−22.8779	+	14.7027i	−0.889175	+	0.571438i
$663$	2.55040	+	2.94332i	0.0990492	+	0.114309i
$664$	5.15381	+	1.51329i	0.200007	+	0.0587272i
$665$	4.70036	−	10.2924i	0.182272	−	0.399120i
$666$	−4.62708			−0.179296
$667$	−37.4113	−	31.8998i	−1.44857	−	1.23517i
$668$	12.3991			0.479735
$669$	−3.58658	+	7.85351i	−0.138665	+	0.303634i
$670$	−2.30312	−	0.676257i	−0.0889772	−	0.0261261i
$671$	−13.5282	−	15.6123i	−0.522249	−	0.602707i
$672$	−3.34222	+	2.14792i	−0.128929	+	0.0828577i
$673$	−27.2401	+	31.4368i	−1.05003	+	1.21180i	−0.0733042	+	0.997310i	$0.523354\pi$
$673$	−27.2401	+	31.4368i	−1.05003	+	1.21180i	−0.976726	+	0.214490i	$0.931191\pi$
$674$	−4.25590	+	29.6004i	−0.163931	+	1.14017i
$675$	0.959493	−	0.281733i	0.0369309	−	0.0108439i
$676$	12.1751	+	7.82446i	0.468273	+	0.300941i
$677$	−1.53827	−	10.6989i	−0.0591204	−	0.411192i	−0.997794	−	0.0663849i	$-0.978853\pi$
$677$	−1.53827	−	10.6989i	−0.0591204	−	0.411192i	0.938674	−	0.344807i	$-0.112056\pi$
$678$	2.60976	+	5.71458i	0.100227	+	0.219467i
$679$	10.0968	+	22.1090i	0.387481	+	0.848464i
$680$	−0.105745	−	0.735472i	−0.00405513	−	0.0282041i
$681$	−0.646686	−	0.415600i	−0.0247811	−	0.0159258i
$682$	−0.894386	+	0.262615i	−0.0342478	+	0.0100561i
$683$	5.77812	−	40.1877i	0.221094	−	1.53774i	−0.512819	−	0.858497i	$-0.671399\pi$
$683$	5.77812	−	40.1877i	0.221094	−	1.53774i	0.733913	−	0.679244i	$-0.237692\pi$
$684$	−1.86505	+	2.15238i	−0.0713118	+	0.0822982i
$685$	−9.26035	+	5.95126i	−0.353820	+	0.227386i
$686$	−4.64145	−	5.35652i	−0.177211	−	0.204513i
$687$	6.82758	+	2.00476i	0.260488	+	0.0764863i
$688$	−3.76429	+	8.24264i	−0.143512	+	0.314248i
$689$	−5.45716			−0.207901
$690$	−4.75229	−	0.644749i	−0.180917	−	0.0245452i
$691$	11.5959			0.441129			0.220565	−	0.975372i	$-0.429210\pi$
$691$	11.5959			0.441129			0.220565	+	0.975372i	$0.429210\pi$
$692$	1.70358	−	3.73032i	0.0647604	−	0.141805i
$693$	7.58318	+	2.22662i	0.288061	+	0.0845824i
$694$	9.28623	+	10.7169i	0.352501	+	0.406807i
$695$	17.4882	−	11.2390i	0.663366	−	0.426320i
$696$	6.71339	−	7.74767i	0.254470	−	0.293675i
$697$	0.705872	−	4.90945i	0.0267368	−	0.185959i
$698$	15.4338	−	4.53176i	0.584176	−	0.171530i
$699$	3.98712	+	2.56237i	0.150807	+	0.0969176i
$700$	0.565404	+	3.93247i	0.0213703	+	0.148633i
$701$	−6.09880	−	13.3545i	−0.230348	−	0.504392i	0.758798	−	0.651326i	$-0.225787\pi$
$701$	−6.09880	−	13.3545i	−0.230348	−	0.504392i	−0.989146	+	0.146934i	$0.953060\pi$
$702$	2.17737	+	4.76777i	0.0821794	+	0.179948i
$703$	−1.87542	−	13.0438i	−0.0707327	−	0.491956i
$704$	1.67351	+	1.07550i	0.0630727	+	0.0405344i
$705$	−6.67704	+	1.96055i	−0.251472	+	0.0738388i
$706$	−3.50091	+	24.3494i	−0.131759	+	0.916401i
$707$	−34.7091	+	40.0565i	−1.30537	+	1.50648i
$708$	1.05738	−	0.679540i	0.0397390	−	0.0255387i
$709$	−2.14061	−	2.47040i	−0.0803923	−	0.0927777i	0.714128	−	0.700015i	$-0.246823\pi$
$709$	−2.14061	−	2.47040i	−0.0803923	−	0.0927777i	−0.794521	+	0.607237i	$0.792278\pi$
$710$	9.59803	+	2.81824i	0.360208	+	0.105766i
$711$	2.14458	−	4.69598i	0.0804280	−	0.176113i
$712$	12.8376			0.481108
$713$	−0.650241	−	2.15109i	−0.0243517	−	0.0805590i
$714$	−2.95201			−0.110476
$715$	−4.33144	+	9.48454i	−0.161987	+	0.354702i
$716$	10.2144	+	2.99921i	0.381729	+	0.112086i
$717$	−10.9251	−	12.6082i	−0.408005	−	0.470862i
$718$	14.6567	−	9.41928i	0.546983	−	0.351525i
$719$	−21.5981	+	24.9255i	−0.805472	+	0.929564i	−0.998668	−	0.0515963i	$-0.983569\pi$
$719$	−21.5981	+	24.9255i	−0.805472	+	0.929564i	0.193196	+	0.981160i	$0.438115\pi$
$720$	0.142315	−	0.989821i	0.00530376	−	0.0368885i
$721$	54.3355	−	15.9543i	2.02356	−	0.594170i
$722$	9.16031	+	5.88697i	0.340911	+	0.219090i
$723$	4.22983	+	29.4191i	0.157309	+	1.09411i
$724$	1.72699	+	3.78157i	0.0641829	+	0.140541i
$725$	−4.25868	−	9.32521i	−0.158163	−	0.346330i
$726$	1.00228	+	6.97099i	0.0371980	+	0.258718i
$727$	−9.11780	−	5.85965i	−0.338160	−	0.217322i	0.360528	−	0.932748i	$-0.382596\pi$
$727$	−9.11780	−	5.85965i	−0.338160	−	0.217322i	−0.698689	+	0.715426i	$0.746233\pi$
$728$	−19.9802	+	5.86672i	−0.740516	+	0.217435i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−2.26325	+	2.61193i	−0.0837668	+	0.0966720i
$731$	−5.66418	+	3.64015i	−0.209497	+	0.134636i
$732$	6.80045	+	7.84814i	0.251352	+	0.290076i
$733$	23.2138	+	6.81618i	0.857420	+	0.251761i	0.680756	−	0.732510i	$-0.261651\pi$
$733$	23.2138	+	6.81618i	0.857420	+	0.251761i	0.176664	+	0.984271i	$0.443469\pi$
$734$	−0.847019	+	1.85471i	−0.0312640	+	0.0684587i
$735$	8.78401			0.324003
$736$	−2.56066	+	4.05500i	−0.0943871	+	0.149469i
$737$	4.77502			0.175890
$738$	2.77299	−	6.07201i	0.102075	−	0.223514i
$739$	35.6078	+	10.4554i	1.30986	+	0.384608i	0.860822	−	0.508906i	$-0.169950\pi$
$739$	35.6078	+	10.4554i	1.30986	+	0.384608i	0.449034	+	0.893515i	$0.351768\pi$
$740$	3.03009	+	3.49691i	0.111388	+	0.128549i
$741$	−12.5579	+	8.07047i	−0.461326	+	0.296476i
$742$	2.70878	−	3.12610i	0.0994426	−	0.114763i
$743$	−0.177792	+	1.23657i	−0.00652254	+	0.0453653i	−0.992823	−	0.119595i	$-0.961840\pi$
$743$	−0.177792	+	1.23657i	−0.00652254	+	0.0453653i	0.986300	+	0.164960i	$0.0527495\pi$
$744$	0.449598	−	0.132014i	0.0164830	−	0.00483986i
$745$	−5.95828	−	3.82916i	−0.218295	−	0.140289i
$746$	−1.95567	−	13.6020i	−0.0716021	−	0.498004i
$747$	2.23136	+	4.88599i	0.0816410	+	0.178769i
$748$	0.614034	+	1.34455i	0.0224513	+	0.0491615i
$749$	9.94503	+	69.1692i	0.363383	+	2.52739i
$750$	−0.841254	−	0.540641i	−0.0307182	−	0.0197414i
$751$	17.1263	−	5.02874i	0.624948	−	0.183501i	0.0460999	−	0.998937i	$-0.485321\pi$
$751$	17.1263	−	5.02874i	0.624948	−	0.183501i	0.578848	+	0.815436i	$0.303503\pi$
$752$	−0.990358	+	6.88809i	−0.0361146	+	0.251183i
$753$	−10.6494	+	12.2901i	−0.388086	+	0.447875i
$754$	45.2032	−	29.0503i	1.64620	−	1.05795i
$755$	−7.84892	−	9.05813i	−0.285651	−	0.329659i
$756$	−3.81198	−	1.11930i	−0.138640	−	0.0407085i
$757$	−14.8546	+	32.5269i	−0.539898	+	1.18221i	0.421444	+	0.906854i	$0.361523\pi$
$757$	−14.8546	+	32.5269i	−0.539898	+	1.18221i	−0.961342	+	0.275357i	$0.911204\pi$
$758$	−27.6100			−1.00284
$759$	9.43216	−	1.43278i	0.342366	−	0.0520067i
$760$	2.84800			0.103308
$761$	−10.6114	+	23.2357i	−0.384662	+	0.842293i	0.613936	+	0.789356i	$0.289585\pi$
$761$	−10.6114	+	23.2357i	−0.384662	+	0.842293i	−0.998598	+	0.0529365i	$0.983142\pi$
$762$	12.0525	+	3.53895i	0.436618	+	0.128203i
$763$	−40.0158	−	46.1807i	−1.44867	−	1.67185i
$764$	15.7514	−	10.1228i	0.569865	−	0.366230i
$765$	0.486585	−	0.561549i	0.0175925	−	0.0203028i
$766$	−0.668407	+	4.64888i	−0.0241505	+	0.167971i
$767$	6.32117	−	1.85606i	0.228244	−	0.0670186i
$768$	−0.841254	−	0.540641i	−0.0303561	−	0.0195087i
$769$	3.05749	+	21.2653i	0.110256	+	0.766848i	0.967670	+	0.252220i	$0.0811607\pi$
$769$	3.05749	+	21.2653i	0.110256	+	0.766848i	−0.857414	+	0.514628i	$0.827930\pi$
$770$	−3.28316	−	7.18911i	−0.118317	−	0.259078i
$771$	10.7112	+	23.4542i	0.385753	+	0.844681i
$772$	2.67663	+	18.6164i	0.0963340	+	0.670017i
$773$	−8.70670	−	5.59545i	−0.313158	−	0.201255i	0.374615	−	0.927181i	$-0.377775\pi$
$773$	−8.70670	−	5.59545i	−0.313158	−	0.201255i	−0.687773	+	0.725926i	$0.741411\pi$
$774$	−8.69446	+	2.55292i	−0.312516	+	0.0917629i
$775$	0.0666856	−	0.463809i	0.00239542	−	0.0166605i
$776$	−4.00630	+	4.62351i	−0.143818	+	0.165974i
$777$	15.4647	−	9.93858i	0.554794	−	0.356545i
$778$	−1.64443	−	1.89777i	−0.0589557	−	0.0680385i
$779$	18.2410	+	5.35604i	0.653552	+	0.191900i
$780$	2.17737	−	4.76777i	0.0779623	−	0.170714i
$781$	−19.8995			−0.712058
$782$	−3.22957	+	1.50605i	−0.115489	+	0.0538562i
$783$	10.2516			0.366363
$784$	3.64901	−	7.99021i	0.130322	−	0.285365i
$785$	−13.0401	−	3.82892i	−0.465422	−	0.136660i
$786$	−1.77473	−	2.04814i	−0.0633024	−	0.0730548i
$787$	−18.4864	+	11.8805i	−0.658971	+	0.423495i	−0.826934	−	0.562298i	$-0.809917\pi$
$787$	−18.4864	+	11.8805i	−0.658971	+	0.423495i	0.167964	+	0.985793i	$0.446281\pi$
$788$	−6.91927	+	7.98527i	−0.246489	+	0.284463i
$789$	−1.65742	+	11.5276i	−0.0590056	+	0.410393i
$790$	−4.95338	+	1.45444i	−0.176233	+	0.0517468i
$791$	−20.9969	−	13.4939i	−0.746562	−	0.479786i
$792$	0.283107	+	1.96905i	0.0100598	+	0.0699673i
$793$	22.6110	+	49.5113i	0.802942	+	1.75820i
$794$	4.46077	+	9.76772i	0.158307	+	0.346643i
$795$	0.148172	+	1.03056i	0.00525513	+	0.0365502i
$796$	5.80492	+	3.73059i	0.205750	+	0.132227i
$797$	5.27084	−	1.54766i	0.186703	−	0.0548209i	−0.187045	−	0.982351i	$-0.559891\pi$
$797$	5.27084	−	1.54766i	0.186703	−	0.0548209i	0.373747	+	0.927531i	$0.378073\pi$
$798$	1.61027	−	11.1997i	0.0570030	−	0.396465i
$799$	−3.38610	+	3.90777i	−0.119792	+	0.138247i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	8.40682	+	9.70199i	0.297041	+	0.342803i
$802$	−31.9768	−	9.38924i	−1.12914	−	0.331546i
$803$	2.85606	−	6.25390i	0.100788	−	0.220695i
$804$	−2.40035			−0.0846538
$805$	17.2681	−	8.05264i	0.608620	−	0.283818i
$806$	2.45602			0.0865096
$807$	−1.50695	+	3.29975i	−0.0530470	+	0.116157i
$808$	−12.8005	−	3.75857i	−0.450321	−	0.132226i
$809$	1.71677	+	1.98125i	0.0603583	+	0.0696572i	0.785126	−	0.619336i	$-0.212598\pi$
$809$	1.71677	+	1.98125i	0.0603583	+	0.0696572i	−0.724767	+	0.688994i	$0.758053\pi$
$810$	0.841254	−	0.540641i	0.0295586	−	0.0189962i
$811$	22.6624	−	26.1538i	0.795784	−	0.918383i	−0.202359	−	0.979312i	$-0.564861\pi$
$811$	22.6624	−	26.1538i	0.795784	−	0.918383i	0.998142	+	0.0609283i	$0.0194061\pi$
$812$	−5.79631	+	40.3142i	−0.203411	+	1.41475i
$813$	16.4501	−	4.83019i	0.576931	−	0.169402i
$814$	−7.74346	−	4.97642i	−0.271408	−	0.174423i
$815$	2.62373	+	18.2485i	0.0919054	+	0.639216i
$816$	−0.308668	−	0.675889i	−0.0108055	−	0.0236608i
$817$	−10.7207	−	23.4751i	−0.375070	−	0.821288i
$818$	1.49413	+	10.3919i	0.0522411	+	0.363345i
$819$	−17.5180	−	11.2581i	−0.612129	−	0.393392i
$820$	−6.40484	+	1.88063i	−0.223667	+	0.0656745i
$821$	5.71231	−	39.7300i	0.199361	−	1.38659i	−0.606783	−	0.794867i	$-0.707540\pi$
$821$	5.71231	−	39.7300i	0.199361	−	1.38659i	0.806144	−	0.591719i	$-0.201550\pi$
$822$	−7.20857	+	8.31914i	−0.251428	+	0.290163i
$823$	9.97799	−	6.41246i	0.347811	−	0.223524i	−0.355057	−	0.934844i	$-0.615539\pi$
$823$	9.97799	−	6.41246i	0.347811	−	0.223524i	0.702868	+	0.711320i	$0.251902\pi$
$824$	9.33430	+	10.7724i	0.325176	+	0.375273i
$825$	1.90872	+	0.560451i	0.0664532	+	0.0195124i
$826$	−2.07442	+	4.54235i	−0.0721784	+	0.158049i
$827$	−43.1615			−1.50087			−0.750436	−	0.660943i	$-0.770156\pi$
$827$	−43.1615			−1.50087			−0.750436	+	0.660943i	$0.770156\pi$
$828$	−4.74144	+	0.720243i	−0.164776	+	0.0250302i
$829$	−34.5569			−1.20021			−0.600106	−	0.799920i	$-0.704875\pi$
$829$	−34.5569			−1.20021			−0.600106	+	0.799920i	$0.704875\pi$
$830$	2.23136	−	4.88599i	0.0774515	−	0.169595i
$831$	27.4021	+	8.04599i	0.950569	+	0.279112i
$832$	−3.43240	−	3.96121i	−0.118997	−	0.137330i
$833$	5.49072	−	3.52867i	0.190242	−	0.122261i
$834$	13.6134	−	15.7107i	0.471395	−	0.544019i
$835$	1.76457	−	12.2729i	0.0610656	−	0.424721i
$836$	−5.43605	+	1.59617i	−0.188010	+	0.0552046i
$837$	0.394193	+	0.253333i	0.0136253	+	0.00875645i
$838$	−1.44788	−	10.0703i	−0.0500163	−	0.347871i
$839$	2.29924	+	5.03463i	0.0793786	+	0.173815i	0.945160	−	0.326607i	$-0.105905\pi$
$839$	2.29924	+	5.03463i	0.0793786	+	0.173815i	−0.865782	+	0.500422i	$0.833178\pi$
$840$	1.65041	+	3.61389i	0.0569444	+	0.124691i
$841$	−10.8296	−	75.3214i	−0.373434	−	2.59729i
$842$	27.7886	+	17.8587i	0.957659	+	0.615450i
$843$	20.4826	−	6.01423i	0.705458	−	0.207141i
$844$	−1.85648	+	12.9121i	−0.0639027	+	0.444453i
$845$	9.47751	−	10.9376i	0.326036	−	0.376266i
$846$	−5.85422	+	3.76228i	−0.201272	+	0.129350i
$847$	−18.3229	−	21.1458i	−0.629584	−	0.726578i
$848$	0.998984	+	0.293328i	0.0343053	+	0.0100729i
$849$	−5.73798	+	12.5644i	−0.196927	+	0.431210i
$850$	−0.743035			−0.0254859
$851$	11.8484	−	18.7628i	0.406157	−	0.643181i
$852$	10.0032			0.342705
$853$	5.88694	−	12.8906i	0.201565	−	0.441365i	−0.781674	−	0.623687i	$-0.785634\pi$
$853$	5.88694	−	12.8906i	0.201565	−	0.441365i	0.983239	+	0.182322i	$0.0583612\pi$
$854$	−39.5858	−	11.6234i	−1.35460	−	0.397746i
$855$	1.86505	+	2.15238i	0.0637832	+	0.0736097i
$856$	−14.7970	+	9.50946i	−0.505751	+	0.325027i
$857$	−3.85574	+	4.44976i	−0.131710	+	0.152001i	−0.817773	−	0.575541i	$-0.804792\pi$
$857$	−3.85574	+	4.44976i	−0.131710	+	0.152001i	0.686064	+	0.727542i	$0.259337\pi$
$858$	−1.48389	+	10.3207i	−0.0506590	+	0.352341i
$859$	−41.6240	+	12.2219i	−1.42019	+	0.417006i	−0.899568	−	0.436780i	$-0.856119\pi$
$859$	−41.6240	+	12.2219i	−1.42019	+	0.417006i	−0.520624	+	0.853786i	$0.674301\pi$
$860$	7.62303	+	4.89902i	0.259943	+	0.167055i
$861$	3.77420	+	26.2502i	0.128625	+	0.894603i
$862$	−16.5601	−	36.2616i	−0.564039	−	1.23507i
$863$	−10.6667	−	23.3568i	−0.363099	−	0.795076i	−0.999714	−	0.0238944i	$-0.992393\pi$
$863$	−10.6667	−	23.3568i	−0.363099	−	0.795076i	0.636616	−	0.771181i	$-0.280334\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	−3.44990	−	2.21712i	−0.117300	−	0.0753843i
$866$	36.6413	−	10.7589i	1.24512	−	0.365601i
$867$	−2.34078	+	16.2805i	−0.0794971	+	0.552914i
$868$	−1.21910	+	1.40692i	−0.0413790	+	0.0477539i
$869$	8.63949	−	5.55226i	0.293074	−	0.188348i
$870$	−6.71339	−	7.74767i	−0.227605	−	0.262670i
$871$	−12.0716	−	3.54455i	−0.409032	−	0.120102i
$872$	6.38934	−	13.9907i	0.216370	−	0.473785i
$873$	−6.11778			−0.207056
$874$	−3.95214	−	13.0743i	−0.133683	−	0.442244i
$875$	3.97291			0.134309
$876$	−1.43571	+	3.14377i	−0.0485081	+	0.106218i
$877$	55.6247	+	16.3329i	1.87831	+	0.551522i	0.996854	+	0.0792581i	$0.0252551\pi$
$877$	55.6247	+	16.3329i	1.87831	+	0.551522i	0.881457	+	0.472264i	$0.156563\pi$
$878$	13.5522	+	15.6401i	0.457366	+	0.527829i
$879$	1.03176	−	0.663070i	0.0348003	−	0.0223648i
$880$	1.30272	−	1.50341i	0.0439146	−	0.0506801i
$881$	0.122535	−	0.852253i	0.00412832	−	0.0287131i	−0.987653	−	0.156656i	$-0.949928\pi$
$881$	0.122535	−	0.852253i	0.00412832	−	0.0287131i	0.991781	+	0.127943i	$0.0408376\pi$
$882$	8.42819	−	2.47474i	0.283792	−	0.0833288i
$883$	−7.56825	−	4.86382i	−0.254692	−	0.163680i	0.407065	−	0.913399i	$-0.366552\pi$
$883$	−7.56825	−	4.86382i	−0.254692	−	0.163680i	−0.661756	+	0.749719i	$0.730189\pi$
$884$	−0.554254	−	3.85492i	−0.0186416	−	0.129655i
$885$	−0.522142	−	1.14333i	−0.0175516	−	0.0384326i
$886$	−3.51964	−	7.70694i	−0.118245	−	0.258920i
$887$	−4.54661	−	31.6224i	−0.152660	−	1.06177i	−0.911737	−	0.410774i	$-0.865259\pi$
$887$	−4.54661	−	31.6224i	−0.152660	−	1.06177i	0.759077	−	0.651001i	$-0.225651\pi$
$888$	3.89255	+	2.50159i	0.130625	+	0.0839478i
$889$	−47.8837	+	14.0599i	−1.60597	+	0.471554i
$890$	1.82698	−	12.7069i	0.0612404	−	0.425936i
$891$	−1.30272	+	1.50341i	−0.0436426	+	0.0503663i
$892$	7.26315	−	4.66774i	0.243188	−	0.156288i
$893$	−12.9787	−	14.9782i	−0.434316	−	0.501227i
$894$	−6.79573	−	1.99541i	−0.227283	−	0.0667364i
$895$	4.42234	−	9.68357i	0.147823	−	0.323686i
$896$	3.97291			0.132726
$897$	−24.9088	−	3.37941i	−0.831681	−	0.112835i
$898$	36.2858			1.21087
$899$	1.99553	−	4.36959i	0.0665545	−	0.145734i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	0.506612	+	0.584661i	0.0168777	+	0.0194779i
$902$	11.1711	−	7.17920i	0.371956	−	0.239041i
$903$	23.5753	−	27.2074i	0.784538	−	0.905406i
$904$	0.894065	−	6.21836i	0.0297362	−	0.206819i
$905$	3.98886	−	1.17123i	0.132594	−	0.0389331i
$906$	−10.0830	−	6.47992i	−0.334984	−	0.215281i
$907$	−0.278247	−	1.93525i	−0.00923905	−	0.0642590i	0.984680	−	0.174369i	$-0.0557887\pi$
$907$	−0.278247	−	1.93525i	−0.00923905	−	0.0642590i	−0.993919	+	0.110110i	$0.964880\pi$
$908$	0.319337	+	0.699250i	0.0105976	+	0.0232054i
$909$	−5.54202	−	12.1353i	−0.183817	−	0.402504i
$910$	2.96352	+	20.6118i	0.0982398	+	0.683273i
$911$	33.6304	+	21.6129i	1.11422	+	0.716068i	0.962209	−	0.272310i	$-0.0877878\pi$
$911$	33.6304	+	21.6129i	1.11422	+	0.716068i	0.152014	+	0.988378i	$0.451424\pi$
$912$	2.73264	−	0.802375i	0.0904867	−	0.0265693i
$913$	−1.52068	+	10.5766i	−0.0503271	+	0.350033i
$914$	9.41995	−	10.8712i	0.311584	−	0.359587i
$915$	8.73606	−	5.61433i	0.288805	−	0.185604i
$916$	−4.65987	−	5.37778i	−0.153966	−	0.177687i
$917$	10.3308	+	3.03339i	0.341152	+	0.100171i
$918$	0.308668	−	0.675889i	0.0101876	−	0.0223077i
$919$	23.2591			0.767246			0.383623	−	0.923490i	$-0.374676\pi$
$919$	23.2591			0.767246			0.383623	+	0.923490i	$0.374676\pi$
$920$	3.64931	+	3.11168i	0.120314	+	0.102589i
$921$	9.33319			0.307539
$922$	1.99780	−	4.37458i	0.0657942	−	0.144069i
$923$	50.3074	+	14.7716i	1.65589	+	0.486212i
$924$	−5.17557	−	5.97293i	−0.170264	−	0.196495i
$925$	3.89255	−	2.50159i	0.127986	−	0.0822517i
$926$	−23.2147	+	26.7912i	−0.762883	+	0.880413i
$927$	−2.02854	+	14.1088i	−0.0666259	+	0.463394i
$928$	−9.83637	+	2.88822i	−0.322895	+	0.0948104i
$929$	−37.8783	−	24.3429i	−1.24275	−	0.798664i	−0.256919	−	0.966433i	$-0.582707\pi$
$929$	−37.8783	−	24.3429i	−1.24275	−	0.798664i	−0.985826	+	0.167769i	$0.946344\pi$
$930$	−0.0666856	−	0.463809i	−0.00218671	−	0.0152089i
$931$	10.3924	+	22.7561i	0.340597	+	0.745803i
$932$	−1.96886	−	4.31120i	−0.0644921	−	0.141218i
$933$	3.83990	+	26.7071i	0.125713	+	0.874350i
$934$	20.7981	+	13.3661i	0.680534	+	0.437353i
$935$	1.41825	−	0.416435i	0.0463817	−	0.0136189i
$936$	0.745933	−	5.18808i	0.0243816	−	0.169578i
$937$	−23.8927	+	27.5736i	−0.780540	+	0.900791i	−0.997148	−	0.0754673i	$-0.975955\pi$
$937$	−23.8927	+	27.5736i	−0.780540	+	0.900791i	0.216608	+	0.976259i	$0.430501\pi$
$938$	8.02251	−	5.15575i	0.261944	−	0.168341i
$939$	17.4445	+	20.1320i	0.569280	+	0.656984i
$940$	6.67704	+	1.96055i	0.217781	+	0.0639462i
$941$	8.30735	−	18.1906i	0.270812	−	0.592995i	−0.724547	−	0.689225i	$-0.757951\pi$
$941$	8.30735	−	18.1906i	0.270812	−	0.592995i	0.995359	+	0.0962298i	$0.0306784\pi$
$942$	−13.5906			−0.442807
$943$	17.5213	+	26.7928i	0.570572	+	0.872495i
$944$	−1.25692			−0.0409091
$945$	−1.65041	+	3.61389i	−0.0536877	+	0.117560i
$946$	−17.2959	−	5.07854i	−0.562338	−	0.165117i
$947$	−3.63154	−	4.19103i	−0.118009	−	0.136190i	0.693671	−	0.720292i	$-0.255992\pi$
$947$	−3.63154	−	4.19103i	−0.118009	−	0.136190i	−0.811680	+	0.584102i	$0.801447\pi$
$948$	−4.34297	+	2.79106i	−0.141053	+	0.0906494i
$949$	−11.8627	+	13.6903i	−0.385079	+	0.444405i
$950$	0.405313	−	2.81901i	0.0131501	−	0.0914609i
$951$	−3.08025	+	0.904442i	−0.0998839	+	0.0293285i
$952$	2.48339	+	1.59598i	0.0804871	+	0.0517259i
$953$	3.87139	+	26.9261i	0.125407	+	0.872223i	0.951271	+	0.308355i	$0.0997783\pi$
$953$	3.87139	+	26.9261i	0.125407	+	0.872223i	−0.825865	+	0.563868i	$0.809313\pi$
$954$	0.432513	+	0.947071i	0.0140031	+	0.0306626i
$955$	−7.77810	−	17.0317i	−0.251693	−	0.551132i
$956$	2.37425	+	16.5133i	0.0767886	+	0.534077i
$957$	17.1562	+	11.0256i	0.554581	+	0.356407i
$958$	−40.4376	+	11.8735i	−1.30648	+	0.383617i
$959$	6.22385	−	43.2878i	0.200979	−	1.39784i
$960$	−0.654861	+	0.755750i	−0.0211355	+	0.0243917i
$961$	−25.8941	+	16.6412i	−0.835295	+	0.536812i
$962$	15.8820	+	18.3288i	0.512057	+	0.590945i
$963$	−16.8768	−	4.95546i	−0.543846	−	0.159688i
$964$	12.3468	−	27.0357i	0.397664	−	0.870763i
$965$	18.8078			0.605444
$966$	14.2999	−	12.5914i	0.460093	−	0.405123i
$967$	6.02133			0.193633			0.0968165	−	0.995302i	$-0.469134\pi$
$967$	6.02133			0.193633			0.0968165	+	0.995302i	$0.469134\pi$
$968$	2.92563	−	6.40624i	0.0940334	−	0.205904i
$969$	2.03045	+	0.596193i	0.0652274	+	0.0191525i
$970$	4.00630	+	4.62351i	0.128634	+	0.148452i
$971$	−34.9999	+	22.4931i	−1.12320	+	0.721838i	−0.964130	−	0.265429i	$-0.914486\pi$
$971$	−34.9999	+	22.4931i	−1.12320	+	0.721838i	−0.159071	+	0.987267i	$0.550850\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−11.7538	+	81.7494i	−0.376809	+	2.62076i
$974$	−18.7309	+	5.49989i	−0.600177	+	0.176228i
$975$	−4.40937	−	2.83373i	−0.141213	−	0.0907520i
$976$	−1.47788	−	10.2789i	−0.0473058	−	0.329019i
$977$	−12.0751	−	26.4409i	−0.386318	−	0.845918i	−0.998476	−	0.0551829i	$-0.982426\pi$
$977$	−12.0751	−	26.4409i	−0.386318	−	0.845918i	0.612158	−	0.790735i	$-0.290301\pi$
$978$	7.65864	+	16.7701i	0.244896	+	0.536248i
$979$	3.63441	+	25.2779i	0.116156	+	0.807885i
$980$	−7.38958	−	4.74899i	−0.236051	−	0.151701i
$981$	14.7576	−	4.33322i	0.471174	−	0.138349i
$982$	4.33504	−	30.1508i	0.138337	−	0.962152i
$983$	16.4371	−	18.9695i	0.524263	−	0.605032i	−0.430430	−	0.902624i	$-0.641638\pi$
$983$	16.4371	−	18.9695i	0.524263	−	0.605032i	0.954693	+	0.297592i	$0.0961836\pi$
$984$	−5.61557	+	3.60891i	−0.179018	+	0.115048i
$985$	6.91927	+	7.98527i	0.220466	+	0.254432i
$986$	−7.30877	−	2.14605i	−0.232759	−	0.0683441i
$987$	11.4850	−	25.1487i	0.365573	−	0.800493i
$988$	14.9276			0.474910
$989$	11.9114	−	41.7932i	0.378762	−	1.32895i
$990$	1.98930			0.0632242
$991$	11.4756	−	25.1281i	0.364535	−	0.798220i	−0.635132	−	0.772404i	$-0.719054\pi$
$991$	11.4756	−	25.1281i	0.364535	−	0.798220i	0.999667	−	0.0258161i	$-0.00821843\pi$
$992$	−0.449598	−	0.132014i	−0.0142747	−	0.00419144i
$993$	17.8090	+	20.5526i	0.565150	+	0.652218i
$994$	−33.4330	+	21.4861i	−1.06043	+	0.681498i
$995$	4.51875	−	5.21491i	0.143254	−	0.165324i
$996$	0.764428	−	5.31671i	0.0242218	−	0.168467i
$997$	−1.11916	+	0.328616i	−0.0354443	+	0.0104074i	−0.299407	−	0.954126i	$-0.596789\pi$
$997$	−1.11916	+	0.328616i	−0.0354443	+	0.0104074i	0.263962	+	0.964533i	$0.414971\pi$
$998$	3.30963	+	2.12697i	0.104765	+	0.0673281i
$999$	0.658502	+	4.57998i	0.0208341	+	0.144904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.f.121.2	✓	20
23.4	even	11	inner	690.2.m.f.211.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.f.121.2	✓	20	1.1	even	1	trivial
690.2.m.f.211.2	yes	20	23.4	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.565404 - 3.93247i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.565404 - 3.93247i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(0.826386 + 1.80953i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(-0.745933 - 5.18808i) q^{13} +(3.34222 + 2.14792i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.486585 + 0.561549i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-1.86505 - 2.15238i) q^{19} +(0.959493 + 0.281733i) q^{20} +(1.65041 - 3.61389i) q^{21} -1.98930 q^{22} +(-0.0381352 - 4.79568i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(5.02911 + 1.47668i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-3.34222 + 2.14792i) q^{28} +(6.71339 - 7.74767i) q^{29} +(0.142315 - 0.989821i) q^{30} +(0.449598 - 0.132014i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.283107 + 1.96905i) q^{33} +(-0.308668 - 0.675889i) q^{34} +(1.65041 + 3.61389i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(3.89255 + 2.50159i) q^{37} +(2.73264 - 0.802375i) q^{38} +(0.745933 - 5.18808i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(-5.61557 + 3.60891i) q^{41} +(2.60170 + 3.00252i) q^{42} +(8.69446 + 2.55292i) q^{43} +(0.826386 - 1.80953i) q^{44} -1.00000 q^{45} +(4.37815 + 1.95751i) q^{46} +6.95892 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-8.42819 - 2.47474i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-0.625081 + 0.401715i) q^{51} +(-3.43240 + 3.96121i) q^{52} +(0.148172 - 1.03056i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-1.67351 - 1.07550i) q^{55} +(-0.565404 - 3.93247i) q^{56} +(-1.18310 - 2.59063i) q^{57} +(4.25868 + 9.32521i) q^{58} +(0.178878 + 1.24412i) q^{59} +(0.841254 + 0.540641i) q^{60} +(-9.96393 + 2.92567i) q^{61} +(-0.0666856 + 0.463809i) q^{62} +(2.60170 - 3.00252i) q^{63} +(0.841254 - 0.540641i) q^{64} +(3.43240 + 3.96121i) q^{65} +(-1.90872 - 0.560451i) q^{66} +(0.997141 - 2.18343i) q^{67} +0.743035 q^{68} +(1.31451 - 4.61217i) q^{69} -3.97291 q^{70} +(-4.15549 + 9.09926i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-2.26325 - 2.61193i) q^{73} +(-3.89255 + 2.50159i) q^{74} +(0.654861 - 0.755750i) q^{75} +(-0.405313 + 2.81901i) q^{76} +(7.58318 - 2.22662i) q^{77} +(4.40937 + 2.83373i) q^{78} +(-0.734700 - 5.10995i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.949985 - 6.60729i) q^{82} +(4.51870 + 2.90399i) q^{83} +(-3.81198 + 1.11930i) q^{84} +(0.105745 - 0.735472i) q^{85} +(-5.93403 + 6.84823i) q^{86} +(8.62422 - 5.54245i) q^{87} +(1.30272 + 1.50341i) q^{88} +(12.3176 + 3.61676i) q^{89} +(0.415415 - 0.909632i) q^{90} -20.8237 q^{91} +(-3.59936 + 3.16932i) q^{92} +0.468578 q^{93} +(-2.89084 + 6.33006i) q^{94} +(2.73264 + 0.802375i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(-5.14661 + 3.30752i) q^{97} +(5.75230 - 6.63851i) q^{98} +(-0.283107 + 1.96905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

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