LMFDB - Embedded newform 150.2.l.a.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	150.47
Dual form			150.2.l.a.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(1.61285 - 0.631448i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.55212 - 1.60963i) q^{5} +(-1.29484 - 1.15039i) q^{6} +(-2.97677 - 2.97677i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.20255 - 2.03686i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(1.61285 - 0.631448i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.55212 - 1.60963i) q^{5} +(-1.29484 - 1.15039i) q^{6} +(-2.97677 - 2.97677i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.20255 - 2.03686i) q^{9} +(-0.729547 + 2.11371i) q^{10} +(4.73921 + 1.53986i) q^{11} +(-0.437156 + 1.67598i) q^{12} +(1.57400 + 0.801995i) q^{13} +(-1.30090 + 4.00375i) q^{14} +(-3.51973 - 1.61601i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.223260 + 1.40961i) q^{17} +(-2.81479 - 1.03777i) q^{18} +(1.09331 + 1.50481i) q^{19} +(2.21453 - 0.309572i) q^{20} +(-6.68076 - 2.92140i) q^{21} +(-0.779529 - 4.92175i) q^{22} +(-1.86763 + 0.951606i) q^{23} +(1.69177 - 0.371369i) q^{24} +(-0.181847 + 4.99669i) q^{25} -1.76655i q^{26} +(2.26620 - 4.67593i) q^{27} +(4.15797 - 0.658557i) q^{28} +(4.57938 + 3.32712i) q^{29} +(0.158048 + 3.86976i) q^{30} +(-5.23835 + 3.80588i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.61596 - 0.509001i) q^{33} +(1.35733 - 0.441023i) q^{34} +(-0.171208 + 9.41183i) q^{35} +(0.353226 + 2.97913i) q^{36} +(1.16900 - 2.29429i) q^{37} +(0.844446 - 1.65732i) q^{38} +(3.04504 + 0.299594i) q^{39} +(-1.28121 - 1.83262i) q^{40} +(-3.58757 + 1.16567i) q^{41} +(0.430011 + 7.27889i) q^{42} +(6.26505 - 6.26505i) q^{43} +(-4.03141 + 2.92899i) q^{44} +(-6.69721 - 0.383852i) q^{45} +(1.69577 + 1.23205i) q^{46} +(4.62368 - 0.732319i) q^{47} +(-1.09894 - 1.33878i) q^{48} +10.7224i q^{49} +(4.53464 - 2.10642i) q^{50} +(0.530010 + 2.41446i) q^{51} +(-1.57400 + 0.801995i) q^{52} +(0.801081 + 5.05783i) q^{53} +(-5.19512 + 0.103626i) q^{54} +(-4.87721 - 10.0184i) q^{55} +(-2.47446 - 3.40580i) q^{56} +(2.71355 + 1.73666i) q^{57} +(0.885486 - 5.59074i) q^{58} +(-3.44032 - 10.5882i) q^{59} +(3.37623 - 1.89766i) q^{60} +(-2.99979 + 9.23241i) q^{61} +(5.76923 + 2.93957i) q^{62} +(-12.6197 - 0.493226i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-1.15212 - 3.77836i) q^{65} +(-4.36509 - 7.44580i) q^{66} +(-6.39326 - 1.01259i) q^{67} +(-1.00917 - 1.00917i) q^{68} +(-2.41131 + 2.71411i) q^{69} +(8.46373 - 4.12033i) q^{70} +(8.85681 - 12.1904i) q^{71} +(2.49407 - 1.66722i) q^{72} +(4.19747 + 8.23800i) q^{73} -2.57494 q^{74} +(2.86186 + 8.17372i) q^{75} -1.86005 q^{76} +(-9.52374 - 18.6914i) q^{77} +(-1.11548 - 2.84917i) q^{78} +(2.20434 - 3.03401i) q^{79} +(-1.05122 + 1.97356i) q^{80} +(0.702433 - 8.97255i) q^{81} +(2.66735 + 2.66735i) q^{82} +(-16.6646 - 2.63941i) q^{83} +(6.29032 - 3.68769i) q^{84} +(2.61548 - 1.82852i) q^{85} +(-8.42648 - 2.73793i) q^{86} +(9.48674 + 2.47449i) q^{87} +(4.43998 + 2.26228i) q^{88} +(0.351151 - 1.08073i) q^{89} +(2.69846 + 6.14153i) q^{90} +(-2.29810 - 7.07281i) q^{91} +(0.327901 - 2.07029i) q^{92} +(-6.04544 + 9.44605i) q^{93} +(-2.75161 - 3.78726i) q^{94} +(0.725250 - 4.09548i) q^{95} +(-0.693954 + 1.58696i) q^{96} +(0.549968 + 3.47236i) q^{97} +(9.55370 - 4.86785i) q^{98} +(13.5748 - 6.26147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	1.61285	−	0.631448i	0.931177	−	0.364566i
$3$	1.61285	−	0.631448i	0.931177	−	0.364566i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	−1.55212	−	1.60963i	−0.694129	−	0.719850i
$5$	−1.55212	−	1.60963i	−0.694129	−	0.719850i
$6$	−1.29484	−	1.15039i	−0.528617	−	0.469643i
$7$	−2.97677	−	2.97677i	−1.12511	−	1.12511i	−0.990960	−	0.134155i	$-0.957168\pi$
$7$	−2.97677	−	2.97677i	−1.12511	−	1.12511i	−0.134155	−	0.990960i	$-0.542832\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	2.20255	−	2.03686i	0.734183	−	0.678952i
$10$	−0.729547	+	2.11371i	−0.230703	+	0.668413i
$11$	4.73921	+	1.53986i	1.42893	+	0.464286i	0.918426	−	0.395592i	$-0.129461\pi$
$11$	4.73921	+	1.53986i	1.42893	+	0.464286i	0.510499	+	0.859878i	$0.329461\pi$
$12$	−0.437156	+	1.67598i	−0.126196	+	0.483813i
$13$	1.57400	+	0.801995i	0.436550	+	0.222433i	0.658432	−	0.752640i	$-0.271220\pi$
$13$	1.57400	+	0.801995i	0.436550	+	0.222433i	−0.221882	+	0.975074i	$0.571220\pi$
$14$	−1.30090	+	4.00375i	−0.347680	+	1.07005i
$15$	−3.51973	−	1.61601i	−0.908791	−	0.417252i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.223260	+	1.40961i	−0.0541486	+	0.341881i	0.945709	+	0.325014i	$0.105369\pi$
$17$	−0.223260	+	1.40961i	−0.0541486	+	0.341881i	−0.999858	+	0.0168665i	$0.994631\pi$
$18$	−2.81479	−	1.03777i	−0.663452	−	0.244605i
$19$	1.09331	+	1.50481i	0.250823	+	0.345228i	0.915799	−	0.401636i	$-0.131558\pi$
$19$	1.09331	+	1.50481i	0.250823	+	0.345228i	−0.664977	+	0.746864i	$0.731558\pi$
$20$	2.21453	−	0.309572i	0.495185	−	0.0692224i
$21$	−6.68076	−	2.92140i	−1.45786	−	0.637502i
$22$	−0.779529	−	4.92175i	−0.166196	−	1.04932i
$23$	−1.86763	+	0.951606i	−0.389428	+	0.198424i	−0.637731	−	0.770259i	$-0.720127\pi$
$23$	−1.86763	+	0.951606i	−0.389428	+	0.198424i	0.248303	+	0.968682i	$0.420127\pi$
$24$	1.69177	−	0.371369i	0.345331	−	0.0758053i
$25$	−0.181847	+	4.99669i	−0.0363693	+	0.999338i
$26$		−	1.76655i		−	0.346448i
$27$	2.26620	−	4.67593i	0.436131	−	0.899883i
$28$	4.15797	−	0.658557i	0.785782	−	0.124456i
$29$	4.57938	+	3.32712i	0.850370	+	0.617830i	0.925248	−	0.379363i	$-0.123857\pi$
$29$	4.57938	+	3.32712i	0.850370	+	0.617830i	−0.0748779	+	0.997193i	$0.523857\pi$
$30$	0.158048	+	3.86976i	0.0288555	+	0.706518i
$31$	−5.23835	+	3.80588i	−0.940835	+	0.683557i	−0.948622	−	0.316413i	$-0.897522\pi$
$31$	−5.23835	+	3.80588i	−0.940835	+	0.683557i	0.00778619	+	0.999970i	$0.497522\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	8.61596	−	0.509001i	1.49985	−	0.0886057i
$34$	1.35733	−	0.441023i	0.232780	−	0.0756348i
$35$	−0.171208	+	9.41183i	−0.0289394	+	1.59089i
$36$	0.353226	+	2.97913i	0.0588710	+	0.496522i
$37$	1.16900	−	2.29429i	0.192182	−	0.377178i	−0.774729	−	0.632294i	$-0.782114\pi$
$37$	1.16900	−	2.29429i	0.192182	−	0.377178i	0.966911	+	0.255116i	$0.0821135\pi$
$38$	0.844446	−	1.65732i	0.136987	−	0.268852i
$39$	3.04504	+	0.299594i	0.487597	+	0.0479734i
$40$	−1.28121	−	1.83262i	−0.202577	−	0.289763i
$41$	−3.58757	+	1.16567i	−0.560285	+	0.182048i	−0.575449	−	0.817837i	$-0.695173\pi$
$41$	−3.58757	+	1.16567i	−0.560285	+	0.182048i	0.0151644	+	0.999885i	$0.495173\pi$
$42$	0.430011	+	7.27889i	0.0663522	+	1.12316i
$43$	6.26505	−	6.26505i	0.955411	−	0.955411i	−0.0436361	−	0.999047i	$-0.513894\pi$
$43$	6.26505	−	6.26505i	0.955411	−	0.955411i	0.999047	+	0.0436361i	$0.0138942\pi$
$44$	−4.03141	+	2.92899i	−0.607758	+	0.441562i
$45$	−6.69721	−	0.383852i	−0.998362	−	0.0572212i
$46$	1.69577	+	1.23205i	0.250028	+	0.181656i
$47$	4.62368	−	0.732319i	0.674433	−	0.106820i	0.190182	−	0.981749i	$-0.439092\pi$
$47$	4.62368	−	0.732319i	0.674433	−	0.106820i	0.484251	+	0.874929i	$0.339092\pi$
$48$	−1.09894	−	1.33878i	−0.158618	−	0.193236i
$49$			10.7224i			1.53177i
$50$	4.53464	−	2.10642i	0.641295	−	0.297893i
$51$	0.530010	+	2.41446i	0.0742163	+	0.338092i
$52$	−1.57400	+	0.801995i	−0.218275	+	0.111217i
$53$	0.801081	+	5.05783i	0.110037	+	0.694746i	0.979605	+	0.200933i	$0.0643973\pi$
$53$	0.801081	+	5.05783i	0.110037	+	0.694746i	−0.869568	+	0.493813i	$0.835603\pi$
$54$	−5.19512	+	0.103626i	−0.706966	+	0.0141017i
$55$	−4.87721	−	10.0184i	−0.657643	−	1.35089i
$56$	−2.47446	−	3.40580i	−0.330663	−	0.455119i
$57$	2.71355	+	1.73666i	0.359419	+	0.230027i
$58$	0.885486	−	5.59074i	0.116270	−	0.734100i
$59$	−3.44032	−	10.5882i	−0.447892	−	1.37847i	−0.879281	−	0.476303i	$-0.841976\pi$
$59$	−3.44032	−	10.5882i	−0.447892	−	1.37847i	0.431389	−	0.902166i	$-0.358024\pi$
$60$	3.37623	−	1.89766i	0.435869	−	0.244986i
$61$	−2.99979	+	9.23241i	−0.384084	+	1.18209i	0.553058	+	0.833143i	$0.313461\pi$
$61$	−2.99979	+	9.23241i	−0.384084	+	1.18209i	−0.937142	+	0.348947i	$0.886539\pi$
$62$	5.76923	+	2.93957i	0.732693	+	0.373326i
$63$	−12.6197	−	0.493226i	−1.58994	−	0.0621407i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−1.15212	−	3.77836i	−0.142903	−	0.468648i
$66$	−4.36509	−	7.44580i	−0.537305	−	0.916514i
$67$	−6.39326	−	1.01259i	−0.781061	−	0.123708i	−0.246844	−	0.969055i	$-0.579393\pi$
$67$	−6.39326	−	1.01259i	−0.781061	−	0.123708i	−0.534217	+	0.845347i	$0.679393\pi$
$68$	−1.00917	−	1.00917i	−0.122380	−	0.122380i
$69$	−2.41131	+	2.71411i	−0.290288	+	0.326740i
$70$	8.46373	−	4.12033i	1.01161	−	0.492474i
$71$	8.85681	−	12.1904i	1.05111	−	1.44673i	0.163268	−	0.986582i	$-0.447797\pi$
$71$	8.85681	−	12.1904i	1.05111	−	1.44673i	0.887842	−	0.460147i	$-0.152203\pi$
$72$	2.49407	−	1.66722i	0.293928	−	0.196484i
$73$	4.19747	+	8.23800i	0.491277	+	0.964185i	0.994958	+	0.100295i	$0.0319786\pi$
$73$	4.19747	+	8.23800i	0.491277	+	0.964185i	−0.503681	+	0.863890i	$0.668021\pi$
$74$	−2.57494			−0.299330
$75$	2.86186	+	8.17372i	0.330459	+	0.943820i
$76$	−1.86005			−0.213363
$77$	−9.52374	−	18.6914i	−1.08533	−	2.13008i
$78$	−1.11548	−	2.84917i	−0.126303	−	0.322605i
$79$	2.20434	−	3.03401i	0.248007	−	0.341353i	−0.666805	−	0.745232i	$-0.732339\pi$
$79$	2.20434	−	3.03401i	0.248007	−	0.341353i	0.914812	+	0.403880i	$0.132339\pi$
$80$	−1.05122	+	1.97356i	−0.117530	+	0.220651i
$81$	0.702433	−	8.97255i	0.0780482	−	0.996950i
$82$	2.66735	+	2.66735i	0.294559	+	0.294559i
$83$	−16.6646	−	2.63941i	−1.82918	−	0.289713i	−0.855525	−	0.517761i	$-0.826766\pi$
$83$	−16.6646	−	2.63941i	−1.82918	−	0.289713i	−0.973650	+	0.228048i	$0.926766\pi$
$84$	6.29032	−	3.68769i	0.686330	−	0.402360i
$85$	2.61548	−	1.82852i	0.283689	−	0.198330i
$86$	−8.42648	−	2.73793i	−0.908650	−	0.295238i
$87$	9.48674	+	2.47449i	1.01709	+	0.265293i
$88$	4.43998	+	2.26228i	0.473303	+	0.241160i
$89$	0.351151	−	1.08073i	0.0372219	−	0.114557i	−0.930719	−	0.365735i	$-0.880818\pi$
$89$	0.351151	−	1.08073i	0.0372219	−	0.114557i	0.967941	+	0.251177i	$0.0808178\pi$
$90$	2.69846	+	6.14153i	0.284442	+	0.647374i
$91$	−2.29810	−	7.07281i	−0.240906	−	0.741432i
$92$	0.327901	−	2.07029i	0.0341860	−	0.215842i
$93$	−6.04544	+	9.44605i	−0.626883	+	0.979510i
$94$	−2.75161	−	3.78726i	−0.283807	−	0.390626i
$95$	0.725250	−	4.09548i	0.0744090	−	0.420187i
$96$	−0.693954	+	1.58696i	−0.0708264	+	0.161968i
$97$	0.549968	+	3.47236i	0.0558408	+	0.352565i	0.999750	+	0.0223598i	$0.00711793\pi$
$97$	0.549968	+	3.47236i	0.0558408	+	0.352565i	−0.943909	+	0.330205i	$0.892882\pi$
$98$	9.55370	−	4.86785i	0.965070	−	0.491728i
$99$	13.5748	−	6.26147i	1.36432	−	0.629301i
$100$	−3.93552	−	3.08410i	−0.393552	−	0.308410i
$101$			16.6740i			1.65912i	0.558415	+	0.829562i	$0.311410\pi$
$101$			16.6740i			1.65912i	−0.558415	+	0.829562i	$0.688590\pi$
$102$	1.91068	−	1.56838i	0.189186	−	0.155293i
$103$	−2.62027	+	0.415010i	−0.258183	+	0.0408921i	−0.284184	−	0.958770i	$-0.591723\pi$
$103$	−2.62027	+	0.415010i	−0.258183	+	0.0408921i	0.0260012	+	0.999662i	$0.491723\pi$
$104$	1.42917	+	1.03835i	0.140141	+	0.101819i
$105$	5.66695	+	15.2879i	0.553037	+	1.49195i
$106$	4.14287	−	3.00997i	0.402391	−	0.292355i
$107$	−8.35067	+	8.35067i	−0.807290	+	0.807290i	−0.984223	−	0.176933i	$-0.943382\pi$
$107$	−8.35067	+	8.35067i	−0.807290	+	0.807290i	0.176933	+	0.984223i	$0.443382\pi$
$108$	2.45087	+	4.58184i	0.235835	+	0.440888i
$109$	−12.6666	+	4.11563i	−1.21324	+	0.394206i	−0.844617	−	0.535372i	$-0.820172\pi$
$109$	−12.6666	+	4.11563i	−1.21324	+	0.394206i	−0.368625	+	0.929578i	$0.620172\pi$
$110$	−6.71230	+	8.89390i	−0.639992	+	0.848001i
$111$	0.436691	−	4.43849i	0.0414489	−	0.421283i
$112$	−1.91121	+	3.75095i	−0.180592	+	0.354432i
$113$	−0.679445	+	1.33349i	−0.0639168	+	0.125444i	−0.920755	−	0.390142i	$-0.872426\pi$
$113$	−0.679445	+	1.33349i	−0.0639168	+	0.125444i	0.856838	+	0.515586i	$0.172426\pi$
$114$	0.315452	−	3.20622i	0.0295448	−	0.300290i
$115$	4.43053	+	1.52920i	0.413149	+	0.142598i
$116$	−5.38339	+	1.74917i	−0.499835	+	0.162406i
$117$	5.10037	−	1.43959i	0.471529	−	0.133090i
$118$	−7.87230	+	7.87230i	−0.724704	+	0.724704i
$119$	4.86069	−	3.53149i	0.445578	−	0.323732i
$120$	−3.22360	−	2.14672i	−0.294273	−	0.195968i
$121$	11.1898	+	8.12983i	1.01725	+	0.739076i
$122$	9.58802	−	1.51859i	0.868058	−	0.137487i
$123$	−5.05015	+	4.14542i	−0.455356	+	0.373780i
$124$		−	6.47496i		−	0.581468i
$125$	8.32510	−	7.46276i	0.744619	−	0.667489i
$126$	5.28978	+	11.4682i	0.471251	+	1.02167i
$127$	1.38236	−	0.704349i	0.122665	−	0.0625009i	−0.391581	−	0.920144i	$-0.628072\pi$
$127$	1.38236	−	0.704349i	0.122665	−	0.0625009i	0.514246	+	0.857643i	$0.328072\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	6.14851	−	14.0606i	0.541347	−	1.23797i
$130$	−2.84349	+	2.74189i	−0.249391	+	0.240480i
$131$	3.74251	+	5.15112i	0.326984	+	0.450055i	0.940584	−	0.339562i	$-0.110279\pi$
$131$	3.74251	+	5.15112i	0.326984	+	0.450055i	−0.613599	+	0.789618i	$0.710279\pi$
$132$	−4.65255	+	7.26964i	−0.404952	+	0.632741i
$133$	1.22495	−	7.73403i	0.106217	−	0.670625i
$134$	2.00025	+	6.15614i	0.172795	+	0.531810i
$135$	−11.0440	+	3.60985i	−0.950513	+	0.310686i
$136$	−0.441023	+	1.35733i	−0.0378174	+	0.116390i
$137$	−3.66124	−	1.86549i	−0.312800	−	0.159380i	0.290542	−	0.956862i	$-0.406165\pi$
$137$	−3.66124	−	1.86549i	−0.312800	−	0.159380i	−0.603342	+	0.797483i	$0.706165\pi$
$138$	3.51300	+	0.916318i	0.299046	+	0.0780022i
$139$	−10.1584	−	3.30065i	−0.861621	−	0.279958i	−0.155316	−	0.987865i	$-0.549639\pi$
$139$	−10.1584	−	3.30065i	−0.861621	−	0.279958i	−0.706305	+	0.707907i	$0.749639\pi$
$140$	−7.51370	−	5.67064i	−0.635023	−	0.479257i
$141$	6.99487	−	4.10073i	0.589074	−	0.345344i
$142$	−14.8826	−	2.35717i	−1.24892	−	0.197809i
$143$	6.22457	+	6.22457i	0.520525	+	0.520525i
$144$	−2.61779	−	1.46532i	−0.218149	−	0.122110i
$145$	−1.75231	−	12.5352i	−0.145521	−	1.04099i
$146$	5.43450	−	7.47994i	0.449762	−	0.619045i
$147$	6.77062	+	17.2935i	0.558431	+	1.42635i
$148$	1.16900	+	2.29429i	0.0960909	+	0.188589i
$149$	−5.13270			−0.420487			−0.210244	−	0.977649i	$-0.567426\pi$
$149$	−5.13270			−0.420487			−0.210244	+	0.977649i	$0.567426\pi$
$150$	5.98358	−	6.26073i	0.488558	−	0.511186i
$151$	20.1314			1.63827			0.819136	−	0.573600i	$-0.194454\pi$
$151$	20.1314			1.63827			0.819136	+	0.573600i	$0.194454\pi$
$152$	0.844446	+	1.65732i	0.0684936	+	0.134426i
$153$	2.37943	+	3.55948i	0.192366	+	0.287767i
$154$	−12.3305	+	16.9714i	−0.993617	+	1.36760i
$155$	14.2566	+	2.52464i	1.14512	+	0.202784i
$156$	−2.03221	+	2.28740i	−0.162707	+	0.183138i
$157$	−7.13510	−	7.13510i	−0.569443	−	0.569443i	0.362529	−	0.931972i	$-0.381913\pi$
$157$	−7.13510	−	7.13510i	−0.569443	−	0.569443i	−0.931972	+	0.362529i	$0.881913\pi$
$158$	−3.70407	−	0.586667i	−0.294680	−	0.0466727i
$159$	4.48577	+	7.65166i	0.355745	+	0.606816i
$160$	2.23570	+	0.0406689i	0.176747	+	0.00321516i
$161$	8.39223	+	2.72680i	0.661401	+	0.214902i
$162$	−8.31350	+	3.44758i	−0.653170	+	0.270867i
$163$	−5.00771	−	2.55156i	−0.392234	−	0.199853i	0.246739	−	0.969082i	$-0.420641\pi$
$163$	−5.00771	−	2.55156i	−0.392234	−	0.199853i	−0.638974	+	0.769228i	$0.720641\pi$
$164$	1.16567	−	3.58757i	0.0910238	−	0.280143i
$165$	−14.1923	−	13.0785i	−1.10487	−	1.01816i
$166$	5.21383	+	16.0465i	0.404672	+	1.24545i
$167$	−2.62306	+	16.5614i	−0.202979	+	1.28156i	0.650130	+	0.759823i	$0.274714\pi$
$167$	−2.62306	+	16.5614i	−0.202979	+	1.28156i	−0.853109	+	0.521734i	$0.825286\pi$
$168$	−6.14150	−	3.93054i	−0.473827	−	0.303247i
$169$	−5.80692	−	7.99254i	−0.446686	−	0.614810i
$170$	−2.81662	−	1.50028i	−0.216025	−	0.115066i
$171$	5.47316	+	1.08751i	0.418543	+	0.0831637i
$172$	1.38603	+	8.75104i	0.105684	+	0.667260i
$173$	3.98829	−	2.03214i	0.303224	−	0.154500i	−0.295758	−	0.955263i	$-0.595572\pi$
$173$	3.98829	−	2.03214i	0.303224	−	0.154500i	0.598982	+	0.800763i	$0.295572\pi$
$174$	−2.10211	−	9.57614i	−0.159360	−	0.725966i
$175$	15.4153	−	14.3327i	1.16529	−	1.08345i
$176$		−	4.98310i		−	0.375615i
$177$	−12.2346	−	14.9048i	−0.919610	−	1.12031i
$178$	−1.12236	+	0.177764i	−0.0841243	+	0.0133240i
$179$	0.141142	+	0.102546i	0.0105495	+	0.00766463i	0.593047	−	0.805167i	$-0.297925\pi$
$179$	0.141142	+	0.102546i	0.0105495	+	0.00766463i	−0.582498	+	0.812832i	$0.697925\pi$
$180$	4.24707	−	5.19254i	0.316558	−	0.387029i
$181$	9.20445	−	6.68743i	0.684162	−	0.497072i	−0.190574	−	0.981673i	$-0.561035\pi$
$181$	9.20445	−	6.68743i	0.684162	−	0.497072i	0.874736	+	0.484600i	$0.161035\pi$
$182$	−5.25861	+	5.25861i	−0.389794	+	0.389794i
$183$	0.991580	+	16.7847i	0.0732997	+	1.24076i
$184$	−1.99350	+	0.647728i	−0.146963	+	0.0477511i
$185$	−5.50738	+	1.67935i	−0.404911	+	0.123468i
$186$	11.1611	+	1.09811i	0.818369	+	0.0805172i
$187$	−3.22868	+	6.33665i	−0.236105	+	0.463382i
$188$	−2.12527	+	4.17108i	−0.155001	+	0.304207i
$189$	−20.6652	+	7.17321i	−1.50317	+	0.521774i
$190$	−3.97836	+	1.21311i	−0.288620	+	0.0880081i
$191$	−17.5527	+	5.70322i	−1.27007	+	0.412671i	−0.865072	−	0.501647i	$-0.832728\pi$
$191$	−17.5527	+	5.70322i	−1.27007	+	0.412671i	−0.404998	+	0.914318i	$0.632728\pi$
$192$	1.72904	−	0.102145i	0.124782	−	0.00737171i
$193$	−3.31568	+	3.31568i	−0.238668	+	0.238668i	−0.816298	−	0.577630i	$-0.803977\pi$
$193$	−3.31568	+	3.31568i	−0.238668	+	0.238668i	0.577630	+	0.816298i	$0.303977\pi$
$194$	2.84422	−	2.06644i	0.204203	−	0.148362i
$195$	−4.24404	−	5.36641i	−0.303922	−	0.384297i
$196$	−8.67458	−	6.30245i	−0.619613	−	0.450175i
$197$	12.5246	−	1.98370i	0.892341	−	0.141333i	0.306607	−	0.951836i	$-0.400806\pi$
$197$	12.5246	−	1.98370i	0.892341	−	0.141333i	0.585734	+	0.810503i	$0.300806\pi$
$198$	−11.7418	−	9.25260i	−0.834457	−	0.657554i
$199$			1.62602i			0.115266i	0.998338	+	0.0576328i	$0.0183553\pi$
$199$			1.62602i			0.115266i	−0.998338	+	0.0576328i	$0.981645\pi$
$200$	−0.961263	+	4.90673i	−0.0679715	+	0.346958i
$201$	−10.9507	+	2.40385i	−0.772406	+	0.169555i
$202$	14.8566	−	7.56983i	1.04531	−	0.532612i
$203$	−3.72772	−	23.5359i	−0.261634	−	1.65189i
$204$	−2.26487	−	0.990397i	−0.158573	−	0.0693417i
$205$	7.44466	+	3.96542i	0.519957	+	0.276957i
$206$	1.55935	+	2.14627i	0.108645	+	0.149537i
$207$	−2.17526	+	5.90005i	−0.151191	+	0.410082i
$208$	0.276349	−	1.74480i	0.0191613	−	0.120980i
$209$	2.86422	+	8.81517i	0.198123	+	0.609758i
$210$	11.0489	−	11.9899i	0.762448	−	0.827380i
$211$	−3.73259	+	11.4877i	−0.256962	+	0.790848i	0.736475	+	0.676465i	$0.236489\pi$
$211$	−3.73259	+	11.4877i	−0.256962	+	0.790848i	−0.993437	+	0.114383i	$0.963511\pi$
$212$	−4.56273	−	2.32483i	−0.313370	−	0.159670i
$213$	6.58711	−	25.2538i	0.451341	−	1.73036i
$214$	11.2316	+	3.64938i	0.767778	+	0.249466i
$215$	−19.8086	−	0.360331i	−1.35093	−	0.0245744i
$216$	2.96978	−	4.26385i	0.202068	−	0.290118i
$217$	26.9226	+	4.26413i	1.82763	+	0.289468i
$218$	9.41758	+	9.41758i	0.637839	+	0.637839i
$219$	11.9717	+	10.6361i	0.808975	+	0.718724i
$220$	10.9718	+	1.94295i	0.739722	+	0.130994i
$221$	−1.48191	+	2.03968i	−0.0996842	+	0.137204i
$222$	−4.15298	+	1.62594i	−0.278730	+	0.109126i
$223$	2.82606	+	5.54645i	0.189247	+	0.371418i	0.966062	−	0.258311i	$-0.0831660\pi$
$223$	2.82606	+	5.54645i	0.189247	+	0.371418i	−0.776815	+	0.629729i	$0.783166\pi$
$224$	4.20979			0.281279
$225$	9.77702	+	11.3758i	0.651801	+	0.758390i
$226$	1.49661			0.0995528
$227$	4.15647	+	8.15754i	0.275875	+	0.541435i	0.986822	−	0.161811i	$-0.0517334\pi$
$227$	4.15647	+	8.15754i	0.275875	+	0.541435i	−0.710947	+	0.703246i	$0.751733\pi$
$228$	−2.99998	+	1.17452i	−0.198678	+	0.0777848i
$229$	10.8714	−	14.9632i	0.718400	−	0.988793i	−0.281175	−	0.959656i	$-0.590724\pi$
$229$	10.8714	−	14.9632i	0.718400	−	0.988793i	0.999575	−	0.0291365i	$-0.00927575\pi$
$230$	−0.648892	−	4.64187i	−0.0427866	−	0.306076i
$231$	−27.1630	−	24.1326i	−1.78719	−	1.58781i
$232$	4.00253	+	4.00253i	0.262779	+	0.262779i
$233$	13.6047	+	2.15478i	0.891276	+	0.141164i	0.585244	−	0.810857i	$-0.300999\pi$
$233$	13.6047	+	2.15478i	0.891276	+	0.141164i	0.306032	+	0.952021i	$0.400999\pi$
$234$	−3.59820	−	3.89090i	−0.235222	−	0.254356i
$235$	−8.35527	−	6.30579i	−0.545038	−	0.411344i
$236$	10.5882	+	3.44032i	0.689234	+	0.223946i
$237$	1.63944	−	6.28531i	0.106493	−	0.408275i
$238$	−5.35329	−	2.72764i	−0.347002	−	0.176806i
$239$	6.40747	−	19.7202i	0.414465	−	1.27559i	−0.498264	−	0.867025i	$-0.666029\pi$
$239$	6.40747	−	19.7202i	0.414465	−	1.27559i	0.912729	−	0.408566i	$-0.133971\pi$
$240$	−0.449261	+	3.84684i	−0.0289997	+	0.248312i
$241$	−1.92274	−	5.91757i	−0.123854	−	0.381184i	0.869836	−	0.493340i	$-0.164224\pi$
$241$	−1.92274	−	5.91757i	−0.123854	−	0.381184i	−0.993691	+	0.112156i	$0.964224\pi$
$242$	2.16369	−	13.6610i	0.139087	−	0.878163i
$243$	−4.53278	−	14.9149i	−0.290778	−	0.956791i
$244$	−5.70595	−	7.85356i	−0.365286	−	0.502773i
$245$	17.2591	−	16.6424i	1.10264	−	1.06324i
$246$	5.98631	+	2.61773i	0.381673	+	0.166900i
$247$	0.514023	+	3.24541i	0.0327065	+	0.206501i
$248$	−5.76923	+	2.93957i	−0.366346	+	0.186663i
$249$	−28.5441	+	6.26585i	−1.80891	+	0.397082i
$250$	−10.4289	−	4.02969i	−0.659580	−	0.254860i
$251$		−	3.76896i		−	0.237895i	−0.992901	−	0.118947i	$-0.962048\pi$
$251$		−	3.76896i		−	0.237895i	0.992901	−	0.118947i	$-0.0379520\pi$
$252$	7.81673	−	9.91968i	0.492408	−	0.624881i
$253$	−10.3164	+	1.63396i	−0.648589	+	0.102726i
$254$	−1.25516	−	0.911927i	−0.0787557	−	0.0572194i
$255$	3.06376	−	4.60066i	0.191860	−	0.288104i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−21.7693	+	21.7693i	−1.35793	+	1.35793i	−0.481471	+	0.876462i	$0.659897\pi$
$257$	−21.7693	+	21.7693i	−1.35793	+	1.35793i	−0.876462	+	0.481471i	$0.840103\pi$
$258$	−15.3195	+	0.905021i	−0.953749	+	0.0563441i
$259$	−10.3094	+	3.34973i	−0.640596	+	0.208142i
$260$	3.73396	+	1.28878i	0.231570	+	0.0799266i
$261$	16.8632	−	1.99941i	1.04380	−	0.123760i
$262$	2.89062	−	5.67316i	0.178583	−	0.350489i
$263$	2.51673	−	4.93937i	0.155188	−	0.304574i	−0.800302	−	0.599598i	$-0.795327\pi$
$263$	2.51673	−	4.93937i	0.155188	−	0.304574i	0.955490	+	0.295023i	$0.0953273\pi$
$264$	8.58951	+	0.845099i	0.528648	+	0.0520123i
$265$	6.89788	−	9.13980i	0.423733	−	0.561454i
$266$	−7.44718	+	2.41974i	−0.456616	+	0.148364i
$267$	−0.116073	−	1.96479i	−0.00710354	−	0.120243i
$268$	4.57707	−	4.57707i	0.279589	−	0.279589i
$269$	−2.80188	+	2.03568i	−0.170834	+	0.124118i	−0.669917	−	0.742436i	$-0.733670\pi$
$269$	−2.80188	+	2.03568i	−0.170834	+	0.124118i	0.499083	+	0.866554i	$0.333670\pi$
$270$	8.23025	+	8.20140i	0.500877	+	0.499122i
$271$	−3.81142	−	2.76916i	−0.231528	−	0.168215i	0.465973	−	0.884799i	$-0.345704\pi$
$271$	−3.81142	−	2.76916i	−0.231528	−	0.168215i	−0.697500	+	0.716584i	$0.745704\pi$
$272$	1.40961	−	0.223260i	0.0854701	−	0.0135371i
$273$	−8.17259	−	9.95623i	−0.494627	−	0.602579i
$274$			4.10910i			0.248240i
$275$	−8.55603	+	23.4004i	−0.515948	+	1.41109i
$276$	−0.778423	−	3.54611i	−0.0468556	−	0.213450i
$277$	−22.1735	+	11.2980i	−1.33228	+	0.678829i	−0.967644	−	0.252321i	$-0.918806\pi$
$277$	−22.1735	+	11.2980i	−1.33228	+	0.678829i	−0.364634	+	0.931151i	$0.618806\pi$
$278$	1.67090	+	10.5496i	0.100214	+	0.632725i
$279$	−3.78568	+	19.0524i	−0.226643	+	1.14064i
$280$	−1.64143	+	9.26917i	−0.0980945	+	0.553939i
$281$	5.67900	+	7.81648i	0.338781	+	0.466292i	0.944085	−	0.329702i	$-0.106948\pi$
$281$	5.67900	+	7.81648i	0.338781	+	0.466292i	−0.605304	+	0.795994i	$0.706948\pi$
$282$	−6.82938	−	4.37078i	−0.406684	−	0.260276i
$283$	−0.159612	+	1.00775i	−0.00948793	+	0.0599044i	−0.991978	−	0.126410i	$-0.959654\pi$
$283$	−0.159612	+	1.00775i	−0.00948793	+	0.0599044i	0.982490	+	0.186315i	$0.0596544\pi$
$284$	4.65630	+	14.3306i	0.276301	+	0.850366i
$285$	−1.41637	−	7.06334i	−0.0838983	−	0.418396i
$286$	2.72024	−	8.37203i	0.160851	−	0.495049i
$287$	14.1493	+	7.20945i	0.835210	+	0.425561i
$288$	−0.117162	+	2.99771i	−0.00690381	+	0.176642i
$289$	14.2308	+	4.62387i	0.837106	+	0.271992i
$290$	−10.3734	+	7.25219i	−0.609149	+	0.425863i
$291$	3.07963	+	5.25311i	0.180531	+	0.307943i
$292$	−9.13189	−	1.44635i	−0.534403	−	0.0846412i
$293$	−1.45604	−	1.45604i	−0.0850625	−	0.0850625i	0.663295	−	0.748358i	$-0.269157\pi$
$293$	−1.45604	−	1.45604i	−0.0850625	−	0.0850625i	−0.748358	+	0.663295i	$0.769157\pi$
$294$	12.3349	−	13.8838i	0.719384	−	0.809718i
$295$	−11.7034	+	21.9719i	−0.681397	+	1.27925i
$296$	1.51351	−	2.08317i	0.0879710	−	0.121082i
$297$	17.9403	−	18.6706i	1.04100	−	1.08338i
$298$	2.33020	+	4.57327i	0.134985	+	0.264922i
$299$	−3.70284			−0.214141
$300$	−8.29484	−	2.48910i	−0.478903	−	0.143708i
$301$	−37.2993			−2.14990
$302$	−9.13947	−	17.9372i	−0.525917	−	1.03217i
$303$	10.5288	+	26.8926i	0.604861	+	1.54494i
$304$	1.09331	−	1.50481i	0.0627057	−	0.0863069i
$305$	19.5169	−	9.50124i	1.11753	−	0.544040i
$306$	2.09128	−	3.73606i	0.119551	−	0.213576i
$307$	−11.9806	−	11.9806i	−0.683767	−	0.683767i	0.277080	−	0.960847i	$-0.410633\pi$
$307$	−11.9806	−	11.9806i	−0.683767	−	0.683767i	−0.960847	+	0.277080i	$0.910633\pi$
$308$	20.7196	+	3.28166i	1.18061	+	0.186990i
$309$	−3.96403	+	2.32391i	−0.225506	+	0.132203i
$310$	−4.22290	−	13.8489i	−0.239845	−	0.786565i
$311$	−3.64396	−	1.18399i	−0.206630	−	0.0671381i	0.203873	−	0.978997i	$-0.434647\pi$
$311$	−3.64396	−	1.18399i	−0.206630	−	0.0671381i	−0.410503	+	0.911859i	$0.634647\pi$
$312$	2.96069	+	0.772255i	0.167616	+	0.0437203i
$313$	20.3753	+	10.3817i	1.15168	+	0.586809i	0.922280	−	0.386523i	$-0.126324\pi$
$313$	20.3753	+	10.3817i	1.15168	+	0.586809i	0.229398	+	0.973333i	$0.426324\pi$
$314$	−3.11815	+	9.59669i	−0.175968	+	0.541573i
$315$	18.7935	+	21.0787i	1.05889	+	1.18765i
$316$	1.15889	+	3.56669i	0.0651926	+	0.200642i
$317$	−1.36994	+	8.64943i	−0.0769432	+	0.485800i	0.918883	+	0.394530i	$0.129093\pi$
$317$	−1.36994	+	8.64943i	−0.0769432	+	0.485800i	−0.995826	+	0.0912701i	$0.970907\pi$
$318$	4.78118	−	7.47063i	0.268115	−	0.418932i
$319$	16.5794	+	22.8195i	0.928266	+	1.27765i
$320$	−0.978749	−	2.01048i	−0.0547138	−	0.112390i
$321$	−8.19534	+	18.7414i	−0.457419	+	1.04604i
$322$	−1.38040	−	8.71548i	−0.0769265	−	0.485695i
$323$	−2.36529	+	1.20518i	−0.131608	+	0.0670578i
$324$	6.84606	+	5.84221i	0.380337	+	0.324567i
$325$	−4.29355	+	7.71897i	−0.238163	+	0.428172i
$326$			5.62029i			0.311279i
$327$	−17.8305	+	14.6362i	−0.986029	+	0.809383i
$328$	−3.72576	+	0.590102i	−0.205721	+	0.0325829i
$329$	−15.9436	−	11.5837i	−0.878999	−	0.638630i
$330$	−5.20987	+	18.5830i	−0.286794	+	1.02296i
$331$	4.85309	−	3.52598i	0.266750	−	0.193805i	−0.446367	−	0.894850i	$-0.647283\pi$
$331$	4.85309	−	3.52598i	0.266750	−	0.193805i	0.713118	+	0.701044i	$0.247283\pi$
$332$	11.9305	−	11.9305i	0.654773	−	0.654773i
$333$	−2.09836	−	7.43435i	−0.114989	−	0.407400i
$334$	15.9471	−	5.18154i	0.872588	−	0.283521i
$335$	8.29320	+	11.8625i	0.453106	+	0.648116i
$336$	−0.713952	+	7.25654i	−0.0389493	+	0.395877i
$337$	1.10341	−	2.16556i	0.0601063	−	0.117965i	−0.858999	−	0.511977i	$-0.828913\pi$
$337$	1.10341	−	2.16556i	0.0601063	−	0.117965i	0.919105	+	0.394012i	$0.128913\pi$
$338$	−4.48512	+	8.80254i	−0.243958	+	0.478795i
$339$	−0.253814	+	2.57974i	−0.0137853	+	0.140112i
$340$	−0.0580418	+	3.19074i	−0.00314776	+	0.173042i
$341$	−30.6862	+	9.97055i	−1.66175	+	0.539935i
$342$	−1.51579	−	5.37034i	−0.0819643	−	0.290394i
$343$	11.0807	−	11.0807i	0.598299	−	0.598299i
$344$	7.16799	−	5.20785i	0.386472	−	0.280788i
$345$	8.11137	−	0.331284i	0.436701	−	0.0178357i
$346$	−3.62129	−	2.63102i	−0.194682	−	0.141445i
$347$	22.4456	−	3.55504i	1.20494	−	0.190844i	0.478511	−	0.878082i	$-0.341177\pi$
$347$	22.4456	−	3.55504i	1.20494	−	0.190844i	0.726433	+	0.687237i	$0.241177\pi$
$348$	−7.57807	+	6.22047i	−0.406227	+	0.333452i
$349$		−	12.5328i		−	0.670865i	−0.942064	−	0.335432i	$-0.891118\pi$
$349$		−	12.5328i		−	0.670865i	0.942064	−	0.335432i	$-0.108882\pi$
$350$	−19.7690	−	7.22826i	−1.05670	−	0.386367i
$351$	7.31708	−	5.54245i	0.390557	−	0.295834i
$352$	−4.43998	+	2.26228i	−0.236651	+	0.120580i
$353$	−1.11770	−	7.05688i	−0.0594892	−	0.375600i	−0.999414	−	0.0342193i	$-0.989106\pi$
$353$	−1.11770	−	7.05688i	−0.0594892	−	0.375600i	0.939925	−	0.341381i	$-0.110894\pi$
$354$	−7.72587	+	17.6678i	−0.410625	+	0.939031i
$355$	−33.3689	+	4.66467i	−1.77104	+	0.247575i
$356$	0.667929	+	0.919325i	0.0354002	+	0.0487241i
$357$	5.60959	−	8.76503i	0.296891	−	0.463894i
$358$	0.0272918	−	0.172313i	0.00144241	−	0.00910704i
$359$	3.28973	+	10.1247i	0.173625	+	0.534363i	0.999568	−	0.0293907i	$-0.00935671\pi$
$359$	3.28973	+	10.1247i	0.173625	+	0.534363i	−0.825943	+	0.563754i	$0.809357\pi$
$360$	−6.55471	−	1.42680i	−0.345464	−	0.0751990i
$361$	4.80219	−	14.7796i	0.252747	−	0.777875i
$362$	−10.1373	−	5.16520i	−0.532803	−	0.271477i
$363$	23.1809	+	6.04643i	1.21668	+	0.317355i
$364$	7.07281	+	2.29810i	0.370716	+	0.120453i
$365$	6.74519	−	19.5427i	0.353059	−	1.02291i
$366$	14.5051	−	8.50359i	0.758193	−	0.444490i
$367$	4.14629	+	0.656708i	0.216435	+	0.0342799i	0.263710	−	0.964602i	$-0.415054\pi$
$367$	4.14629	+	0.656708i	0.216435	+	0.0342799i	−0.0472753	+	0.998882i	$0.515054\pi$
$368$	1.48216	+	1.48216i	0.0772630	+	0.0772630i
$369$	−5.52749	+	9.87483i	−0.287750	+	0.514063i
$370$	3.99661	+	4.14471i	0.207774	+	0.215473i
$371$	12.6714	−	17.4406i	0.657865	−	0.905473i
$372$	−4.08860	−	10.4431i	−0.211984	−	0.541450i
$373$	−2.06631	−	4.05536i	−0.106990	−	0.209979i	0.831305	−	0.555817i	$-0.187595\pi$
$373$	−2.06631	−	4.05536i	−0.106990	−	0.209979i	−0.938294	+	0.345838i	$0.887595\pi$
$374$	7.11179			0.367742
$375$	8.71476	−	17.2931i	0.450028	−	0.893014i
$376$	4.68132			0.241420
$377$	4.53964	+	8.90954i	0.233803	+	0.458864i
$378$	15.7732	+	15.1562i	0.811284	+	0.779552i
$379$	19.3891	−	26.6869i	0.995954	−	1.37081i	0.0681783	−	0.997673i	$-0.478281\pi$
$379$	19.3891	−	26.6869i	0.995954	−	1.37081i	0.927775	−	0.373139i	$-0.121719\pi$
$380$	2.88702	+	2.99400i	0.148101	+	0.153589i
$381$	1.78478	−	2.00890i	0.0914371	−	0.102919i
$382$	13.0504	+	13.0504i	0.667715	+	0.667715i
$383$	−16.8791	−	2.67339i	−0.862482	−	0.136604i	−0.290505	−	0.956873i	$-0.593823\pi$
$383$	−16.8791	−	2.67339i	−0.862482	−	0.136604i	−0.571977	+	0.820270i	$0.693823\pi$
$384$	−0.875978	−	1.49421i	−0.0447021	−	0.0762511i
$385$	−15.3043	+	44.3410i	−0.779980	+	2.25983i
$386$	4.45958	+	1.44901i	0.226987	+	0.0737525i
$387$	1.03807	−	26.5601i	0.0527679	−	1.35012i
$388$	−3.13246	−	1.59607i	−0.159027	−	0.0810281i
$389$	4.34112	−	13.3606i	0.220104	−	0.677409i	−0.778648	−	0.627461i	$-0.784094\pi$
$389$	4.34112	−	13.3606i	0.220104	−	0.677409i	0.998752	−	0.0499484i	$-0.0159057\pi$
$390$	−2.85476	+	6.21777i	−0.144556	+	0.314849i
$391$	−0.924425	−	2.84509i	−0.0467502	−	0.143882i
$392$	−1.67735	+	10.5904i	−0.0847189	+	0.534894i
$393$	9.28875	+	5.94477i	0.468556	+	0.299874i
$394$	−7.45354	−	10.2589i	−0.375504	−	0.516837i
$395$	−8.30504	+	1.16097i	−0.417872	+	0.0584147i
$396$	−2.91344	+	14.6627i	−0.146406	+	0.736826i
$397$	−0.577115	−	3.64376i	−0.0289646	−	0.182875i	0.968964	−	0.247200i	$-0.0795105\pi$
$397$	−0.577115	−	3.64376i	−0.0289646	−	0.182875i	−0.997929	+	0.0643251i	$0.979511\pi$
$398$	1.44880	−	0.738199i	0.0726216	−	0.0370026i
$399$	−2.90798	−	13.2473i	−0.145581	−	0.663194i
$400$	4.80833	−	1.37112i	0.240417	−	0.0685558i
$401$		−	29.3144i		−	1.46389i	−0.681364	−	0.731945i	$-0.738613\pi$
$401$		−	29.3144i		−	1.46389i	0.681364	−	0.731945i	$-0.261387\pi$
$402$	7.11338	+	8.66586i	0.354783	+	0.432214i
$403$	−11.2975	+	1.78935i	−0.562768	+	0.0891336i
$404$	−13.4895	−	9.80073i	−0.671130	−	0.487604i
$405$	−15.5328	+	12.7958i	−0.771830	+	0.635829i
$406$	−19.2783	+	14.0065i	−0.956764	+	0.695130i
$407$	9.07301	−	9.07301i	0.449732	−	0.449732i
$408$	0.145780	+	2.46765i	0.00721718	+	0.122167i
$409$	7.27469	−	2.36369i	0.359710	−	0.116877i	−0.123586	−	0.992334i	$-0.539439\pi$
$409$	7.27469	−	2.36369i	0.359710	−	0.116877i	0.483296	+	0.875457i	$0.339439\pi$
$410$	0.153411	−	8.43350i	0.00757643	−	0.416501i
$411$	−7.08297	−	0.696875i	−0.349377	−	0.0343743i
$412$	1.20440	−	2.36378i	0.0593368	−	0.116455i
$413$	−21.2777	+	41.7598i	−1.04701	+	2.05487i
$414$	6.24454	−	0.740395i	0.306902	−	0.0363884i
$415$	21.6169	+	30.9206i	1.06113	+	1.51783i
$416$	−1.68008	+	0.545893i	−0.0823729	+	0.0267646i
$417$	−18.4681	+	1.09103i	−0.904385	+	0.0534279i
$418$	6.55405	−	6.55405i	0.320569	−	0.320569i
$419$	−8.86483	+	6.44067i	−0.433075	+	0.314648i	−0.782877	−	0.622176i	$-0.786249\pi$
$419$	−8.86483	+	6.44067i	−0.433075	+	0.314648i	0.349802	+	0.936824i	$0.386249\pi$
$420$	−15.6992	−	4.40137i	−0.766040	−	0.214765i
$421$	−11.3681	−	8.25943i	−0.554048	−	0.402540i	0.275227	−	0.961379i	$-0.411247\pi$
$421$	−11.3681	−	8.25943i	−0.554048	−	0.402540i	−0.829276	+	0.558839i	$0.811247\pi$
$422$	11.9302	−	1.88956i	0.580753	−	0.0919823i
$423$	8.69225	−	11.0307i	0.422632	−	0.536333i
$424$			5.12087i			0.248692i
$425$	−7.00279	−	1.37190i	−0.339685	−	0.0665467i
$426$	−25.4918	+	5.59582i	−1.23508	+	0.271119i
$427$	36.4125	−	18.5531i	1.76213	−	0.897848i
$428$	−1.84743	−	11.6642i	−0.0892991	−	0.563812i
$429$	13.9698	+	6.10879i	0.674467	+	0.294935i
$430$	8.67184	+	17.8131i	0.418193	+	0.859026i
$431$	2.55158	+	3.51195i	0.122905	+	0.169164i	0.866036	−	0.499982i	$-0.166660\pi$
$431$	2.55158	+	3.51195i	0.122905	+	0.169164i	−0.743131	+	0.669146i	$0.766660\pi$
$432$	−5.14737	−	0.710346i	−0.247653	−	0.0341765i
$433$	1.22781	−	7.75206i	0.0590046	−	0.372540i	−0.940463	−	0.339897i	$-0.889608\pi$
$433$	1.22781	−	7.75206i	0.0590046	−	0.372540i	0.999467	−	0.0326428i	$-0.0103924\pi$
$434$	−8.42326	−	25.9241i	−0.404329	−	1.24440i
$435$	−10.7415	−	19.1109i	−0.515018	−	0.916297i
$436$	4.11563	−	12.6666i	0.197103	−	0.606621i
$437$	−3.47389	−	1.77004i	−0.166179	−	0.0846723i
$438$	4.04182	−	15.4956i	0.193126	−	0.740409i
$439$	−19.1294	−	6.21551i	−0.912994	−	0.296650i	−0.185405	−	0.982662i	$-0.559360\pi$
$439$	−19.1294	−	6.21551i	−0.912994	−	0.296650i	−0.727590	+	0.686012i	$0.759360\pi$
$440$	−3.24993	−	10.6581i	−0.154934	−	0.508104i
$441$	21.8399	+	23.6165i	1.04000	+	1.12460i
$442$	2.49014	+	0.394399i	0.118444	+	0.0187597i
$443$	−11.8995	−	11.8995i	−0.565363	−	0.565363i	0.365463	−	0.930826i	$-0.380911\pi$
$443$	−11.8995	−	11.8995i	−0.565363	−	0.565363i	−0.930826	+	0.365463i	$0.880911\pi$
$444$	3.33413	+	2.96217i	0.158231	+	0.140578i
$445$	−2.28461	+	1.11220i	−0.108301	+	0.0527233i
$446$	3.65892	−	5.03607i	0.173255	−	0.238465i
$447$	−8.27826	+	3.24103i	−0.391548	+	0.153296i
$448$	−1.91121	−	3.75095i	−0.0902960	−	0.177216i
$449$	3.55771			0.167899			0.0839495	−	0.996470i	$-0.473247\pi$
$449$	3.55771			0.167899			0.0839495	+	0.996470i	$0.473247\pi$
$450$	5.69728	−	13.8759i	0.268572	−	0.654117i
$451$	−18.7973			−0.885128
$452$	−0.679445	−	1.33349i	−0.0319584	−	0.0627219i
$453$	32.4689	−	12.7119i	1.52552	−	0.597259i
$454$	5.38142	−	7.40689i	0.252563	−	0.347623i
$455$	−7.81772	+	14.6769i	−0.366500	+	0.688066i
$456$	2.40847	+	2.13978i	0.112787	+	0.100204i
$457$	−13.4412	−	13.4412i	−0.628754	−	0.628754i	0.319001	−	0.947754i	$-0.396653\pi$
$457$	−13.4412	−	13.4412i	−0.628754	−	0.628754i	−0.947754	+	0.319001i	$0.896653\pi$
$458$	−18.2678	−	2.89333i	−0.853597	−	0.135196i
$459$	6.08528	+	4.23841i	0.284037	+	0.197832i
$460$	−3.84135	+	2.68553i	−0.179104	+	0.125214i
$461$	−30.4642	−	9.89843i	−1.41886	−	0.461016i	−0.503621	−	0.863925i	$-0.667999\pi$
$461$	−30.4642	−	9.89843i	−1.41886	−	0.461016i	−0.915240	+	0.402908i	$0.867999\pi$
$462$	−9.17058	+	35.1583i	−0.426654	+	1.63571i
$463$	2.76320	+	1.40792i	0.128417	+	0.0654317i	0.517019	−	0.855974i	$-0.327042\pi$
$463$	2.76320	+	1.40792i	0.128417	+	0.0654317i	−0.388602	+	0.921406i	$0.627042\pi$
$464$	1.74917	−	5.38339i	0.0812031	−	0.249918i
$465$	24.5879	−	4.93046i	1.14024	−	0.228645i
$466$	−4.25650	−	13.1002i	−0.197179	−	0.606853i
$467$	6.20197	−	39.1577i	0.286993	−	1.81200i	−0.249811	−	0.968295i	$-0.580368\pi$
$467$	6.20197	−	39.1577i	0.286993	−	1.81200i	0.536804	−	0.843707i	$-0.319632\pi$
$468$	−1.83327	+	4.97245i	−0.0847429	+	0.229852i
$469$	16.0170	+	22.0455i	0.739598	+	1.01797i
$470$	−1.82528	+	10.3074i	−0.0841941	+	0.475444i
$471$	−16.0133	−	7.00238i	−0.737852	−	0.322653i
$472$	−1.74160	−	10.9960i	−0.0801638	−	0.506134i
$473$	39.3387	−	20.0441i	1.80880	−	0.921628i
$474$	−6.34454	+	1.39272i	−0.291415	+	0.0639698i
$475$	−7.71790	+	5.18929i	−0.354122	+	0.238101i
$476$			6.00814i			0.275383i
$477$	12.0665	+	9.50842i	0.552486	+	0.435361i
$478$	−20.4797	+	3.24367i	−0.936721	+	0.148362i
$479$	10.9031	+	7.92157i	0.498176	+	0.361946i	0.808320	−	0.588744i	$-0.200377\pi$
$479$	10.9031	+	7.92157i	0.498176	+	0.361946i	−0.310144	+	0.950690i	$0.600377\pi$
$480$	3.63152	−	1.34613i	0.165755	−	0.0614423i
$481$	3.68001	−	2.67368i	0.167794	−	0.121910i
$482$	−4.39969	+	4.39969i	−0.200400	+	0.200400i
$483$	15.2572	−	0.901343i	0.694227	−	0.0410125i
$484$	−13.1543	+	4.27411i	−0.597925	+	0.194278i
$485$	4.73562	−	6.27477i	0.215033	−	0.284923i
$486$	−11.2314	+	10.8100i	−0.509468	+	0.490349i
$487$	0.947305	−	1.85919i	0.0429265	−	0.0842480i	−0.868547	−	0.495607i	$-0.834946\pi$
$487$	0.947305	−	1.85919i	0.0429265	−	0.0842480i	0.911473	+	0.411359i	$0.134946\pi$
$488$	−4.40713	+	8.64948i	−0.199501	+	0.391543i
$489$	−9.68785	−	0.953162i	−0.438100	−	0.0431035i
$490$	−22.6640	−	7.82247i	−1.02385	−	0.353383i
$491$	15.8067	−	5.13592i	0.713348	−	0.231781i	0.0702111	−	0.997532i	$-0.477633\pi$
$491$	15.8067	−	5.13592i	0.713348	−	0.231781i	0.643137	+	0.765751i	$0.277633\pi$
$492$	−0.385313	−	6.52227i	−0.0173712	−	0.294047i
$493$	−5.71233	+	5.71233i	−0.257270	+	0.257270i
$494$	2.65832	−	1.93138i	0.119604	−	0.0868970i
$495$	−31.1484	−	12.1319i	−1.40002	−	0.545290i
$496$	5.23835	+	3.80588i	0.235209	+	0.170889i
$497$	−62.6527	+	9.92321i	−2.81036	+	0.445117i
$498$	18.5416	+	22.5883i	0.830871	+	1.01221i
$499$			36.0457i			1.61363i	0.590806	+	0.806813i	$0.298810\pi$
$499$			36.0457i			1.61363i	−0.590806	+	0.806813i	$0.701190\pi$
$500$	1.14413	+	11.1216i	0.0511671	+	0.497375i
$501$	6.22704	+	28.3673i	0.278203	+	1.26736i
$502$	−3.35817	+	1.71107i	−0.149882	+	0.0763689i
$503$	−4.92776	−	31.1126i	−0.219718	−	1.38724i	−0.813007	−	0.582255i	$-0.802171\pi$
$503$	−4.92776	−	31.1126i	−0.219718	−	1.38724i	0.593289	−	0.804990i	$-0.297829\pi$
$504$	−12.3872	−	2.46132i	−0.551771	−	0.109636i
$505$	26.8390	−	25.8800i	1.19432	−	1.15165i
$506$	6.13944	+	8.45021i	0.272931	+	0.375658i
$507$	−14.4125	−	9.22397i	−0.640083	−	0.409651i
$508$	−0.242702	+	1.53236i	−0.0107682	+	0.0679876i
$509$	−0.189892	−	0.584428i	−0.00841683	−	0.0259043i	0.946760	−	0.321941i	$-0.104335\pi$
$509$	−0.189892	−	0.584428i	−0.00841683	−	0.0259043i	−0.955177	+	0.296036i	$0.904335\pi$
$510$	−5.49013	−	0.641176i	−0.243107	−	0.0283918i
$511$	12.0277	−	37.0176i	0.532076	−	1.63756i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	9.51406	−	1.70203i	0.420056	−	0.0751465i
$514$	29.2797	+	9.51354i	1.29147	+	0.419624i
$515$	4.73498	+	3.57353i	0.208648	+	0.157468i
$516$	7.76127	+	13.2389i	0.341671	+	0.582809i
$517$	23.0403	+	3.64922i	1.01331	+	0.160493i
$518$	7.66501	+	7.66501i	0.336781	+	0.336781i
$519$	5.14932	−	5.79592i	0.226030	−	0.254413i
$520$	−0.546873	−	3.91208i	−0.0239820	−	0.171556i
$521$	19.3712	−	26.6622i	0.848668	−	1.16809i	−0.135487	−	0.990779i	$-0.543260\pi$
$521$	19.3712	−	26.6622i	0.848668	−	1.16809i	0.984155	−	0.177312i	$-0.0567401\pi$
$522$	−9.43721	−	14.1175i	−0.413055	−	0.617905i
$523$	−18.1177	−	35.5580i	−0.792232	−	1.55484i	−0.831442	−	0.555612i	$-0.812484\pi$
$523$	−18.1177	−	35.5580i	−0.792232	−	1.55484i	0.0392100	−	0.999231i	$-0.487516\pi$
$524$	−6.36713			−0.278150
$525$	15.8122	−	32.8504i	0.690102	−	1.43371i
$526$	−5.54358			−0.241712
$527$	−4.19530	−	8.23373i	−0.182750	−	0.358667i
$528$	−3.14657	−	8.03698i	−0.136937	−	0.349765i
$529$	−10.9366	+	15.0529i	−0.475503	+	0.654474i
$530$	−11.2752	−	1.99667i	−0.489763	−	0.0867299i
$531$	−29.1442	−	16.3136i	−1.26475	−	0.707951i
$532$	5.53695	+	5.53695i	0.240057	+	0.240057i
$533$	−6.58172	−	1.04244i	−0.285086	−	0.0451532i
$534$	−1.69794	+	0.995416i	−0.0734771	+	0.0430759i
$535$	26.4028	+	0.480284i	1.14149	+	0.0207645i
$536$	−6.15614	−	2.00025i	−0.265905	−	0.0863977i
$537$	0.292393	+	0.0762667i	0.0126177	+	0.00329115i
$538$	3.08583	+	1.57231i	0.133040	+	0.0677872i
$539$	−16.5110	+	50.8156i	−0.711178	+	2.18878i
$540$	3.57105	−	11.0566i	0.153673	−	0.475799i
$541$	7.82078	+	24.0699i	0.336242	+	1.03485i	0.966107	+	0.258141i	$0.0831100\pi$
$541$	7.82078	+	24.0699i	0.336242	+	1.03485i	−0.629865	+	0.776704i	$0.716890\pi$
$542$	−0.736991	+	4.65318i	−0.0316565	+	0.199871i
$543$	10.6226	−	16.5979i	0.455860	−	0.712285i
$544$	−0.838876	−	1.15461i	−0.0359665	−	0.0495036i
$545$	26.2848	+	14.0007i	1.12592	+	0.599723i
$546$	−5.16079	+	11.8019i	−0.220861	+	0.505073i
$547$	6.44292	+	40.6790i	0.275479	+	1.73931i	0.605961	+	0.795495i	$0.292789\pi$
$547$	6.44292	+	40.6790i	0.275479	+	1.73931i	−0.330482	+	0.943812i	$0.607211\pi$
$548$	3.66124	−	1.86549i	0.156400	−	0.0796899i
$549$	12.1979	+	26.4450i	0.520594	+	1.12864i
$550$	24.7342	−	3.00006i	1.05467	−	0.127923i
$551$			10.5287i			0.448537i
$552$	−2.80621	+	2.30348i	−0.119440	+	0.0980425i
$553$	−15.5934	+	2.46975i	−0.663098	+	0.105024i
$554$	20.1331	+	14.6276i	0.855375	+	0.621466i
$555$	−7.82214	+	6.18616i	−0.332032	+	0.262588i
$556$	8.64122	−	6.27821i	0.366469	−	0.266256i
$557$	17.7694	−	17.7694i	0.752915	−	0.752915i	−0.222107	−	0.975022i	$-0.571293\pi$
$557$	17.7694	−	17.7694i	0.752915	−	0.752915i	0.975022	+	0.222107i	$0.0712934\pi$
$558$	18.6945	−	5.27655i	0.791400	−	0.223374i
$559$	14.8858	−	4.83667i	0.629600	−	0.204570i
$560$	9.00409	−	2.74559i	0.380492	−	0.116022i
$561$	−1.20611	+	12.2588i	−0.0509220	+	0.517566i
$562$	4.38632	−	8.60864i	0.185026	−	0.363133i
$563$	−4.70734	+	9.23868i	−0.198391	+	0.389364i	−0.968673	−	0.248339i	$-0.920115\pi$
$563$	−4.70734	+	9.23868i	−0.198391	+	0.389364i	0.770282	+	0.637703i	$0.220115\pi$
$564$	−0.793919	+	8.06931i	−0.0334300	+	0.339779i
$565$	3.20101	−	0.976072i	0.134667	−	0.0410637i
$566$	0.970373	−	0.315293i	0.0407878	−	0.0132528i
$567$	−28.8002	+	24.6183i	−1.20950	+	1.03387i
$568$	10.6548	−	10.6548i	0.447064	−	0.447064i
$569$	−15.6879	+	11.3979i	−0.657671	+	0.477826i	−0.865876	−	0.500259i	$-0.833238\pi$
$569$	−15.6879	+	11.3979i	−0.657671	+	0.477826i	0.208205	+	0.978085i	$0.433238\pi$
$570$	−5.65047	+	4.46868i	−0.236672	+	0.187172i
$571$	14.7088	+	10.6866i	0.615544	+	0.447219i	0.851362	−	0.524579i	$-0.175777\pi$
$571$	14.7088	+	10.6866i	0.615544	+	0.447219i	−0.235818	+	0.971797i	$0.575777\pi$
$572$	−8.69450	+	1.37707i	−0.363535	+	0.0575783i
$573$	−24.7086	+	20.2820i	−1.03221	+	0.847295i
$574$		−	15.8802i		−	0.662826i
$575$	−4.41526	−	9.50503i	−0.184129	−	0.396387i
$576$	2.72417	−	1.25654i	0.113507	−	0.0523559i
$577$	−5.29743	+	2.69918i	−0.220535	+	0.112368i	−0.560768	−	0.827973i	$-0.689494\pi$
$577$	−5.29743	+	2.69918i	−0.220535	+	0.112368i	0.340233	+	0.940341i	$0.389494\pi$
$578$	−2.34075	−	14.7789i	−0.0973625	−	0.614723i
$579$	−3.25401	+	7.44137i	−0.135232	+	0.309253i
$580$	11.1712	+	5.95037i	0.463858	+	0.247076i
$581$	41.7498	+	57.4636i	1.73207	+	2.38399i
$582$	3.28243	−	5.12883i	0.136061	−	0.212597i
$583$	−3.99187	+	25.2037i	−0.165326	+	1.04383i
$584$	2.85708	+	8.79320i	0.118227	+	0.363865i
$585$	−10.2336	−	5.97531i	−0.423107	−	0.247049i
$586$	−0.636311	+	1.95836i	−0.0262858	+	0.0808992i
$587$	23.3146	+	11.8794i	0.962295	+	0.490314i	0.863254	−	0.504770i	$-0.168423\pi$
$587$	23.3146	+	11.8794i	0.962295	+	0.490314i	0.0990406	+	0.995083i	$0.468423\pi$
$588$	−17.9704	−	4.68734i	−0.741088	−	0.193303i
$589$	−11.4543	−	3.72172i	−0.471966	−	0.153351i
$590$	24.8903	+	0.452771i	1.02472	+	0.0186403i
$591$	18.9476	−	11.1080i	0.779402	−	0.456923i
$592$	−2.54323	−	0.402809i	−0.104526	−	0.0165553i
$593$	23.6228	+	23.6228i	0.970072	+	0.970072i	0.999565	−	0.0294930i	$-0.00938927\pi$
$593$	23.6228	+	23.6228i	0.970072	+	0.970072i	−0.0294930	+	0.999565i	$0.509389\pi$
$594$	−24.7803	−	7.50867i	−1.01675	−	0.308084i
$595$	−13.2288	−	2.34262i	−0.542327	−	0.0960382i
$596$	3.01693	−	4.15244i	0.123578	−	0.170091i
$597$	1.02675	+	2.62253i	0.0420220	+	0.107333i
$598$	1.68106	+	3.29926i	0.0687435	+	0.134917i
$599$	7.73976			0.316238			0.158119	−	0.987420i	$-0.449457\pi$
$599$	7.73976			0.316238			0.158119	+	0.987420i	$0.449457\pi$
$600$	1.54797	+	8.52079i	0.0631957	+	0.347860i
$601$	−16.7407			−0.682866			−0.341433	−	0.939906i	$-0.610912\pi$
$601$	−16.7407			−0.682866			−0.341433	+	0.939906i	$0.610912\pi$
$602$	16.9335	+	33.2339i	0.690159	+	1.35451i
$603$	−16.1440	+	10.7919i	−0.657433	+	0.439479i
$604$	−11.8329	+	16.2867i	−0.481476	+	0.662695i
$605$	−4.28178	−	30.6299i	−0.174079	−	1.24528i
$606$	19.1815	−	21.5902i	0.779196	−	0.877041i
$607$	22.6982	+	22.6982i	0.921293	+	0.921293i	0.997121	−	0.0758281i	$-0.0241600\pi$
$607$	22.6982	+	22.6982i	0.921293	+	0.921293i	−0.0758281	+	0.997121i	$0.524160\pi$
$608$	−1.83715	−	0.290976i	−0.0745063	−	0.0118006i
$609$	−20.8739	−	35.6059i	−0.845853	−	1.44282i
$610$	−17.3261	−	13.0762i	−0.701515	−	0.529439i
$611$	7.86501	+	2.55550i	0.318184	+	0.103384i
$612$	−4.27828	−	0.167211i	−0.172939	−	0.00675909i
$613$	−38.6048	−	19.6701i	−1.55923	−	0.794470i	−0.559818	−	0.828616i	$-0.689129\pi$
$613$	−38.6048	−	19.6701i	−1.55923	−	0.794470i	−0.999417	+	0.0341460i	$0.989129\pi$
$614$	−5.23570	+	16.1138i	−0.211296	+	0.650301i
$615$	14.5110	+	1.69470i	0.585142	+	0.0683370i
$616$	−6.48251	−	19.9511i	−0.261188	−	0.803853i
$617$	−3.81403	+	24.0808i	−0.153547	+	0.969458i	0.783788	+	0.621028i	$0.213285\pi$
$617$	−3.81403	+	24.0808i	−0.153547	+	0.969458i	−0.937335	+	0.348429i	$0.886715\pi$
$618$	3.87025	+	2.47695i	0.155684	+	0.0996374i
$619$	−23.7633	−	32.7074i	−0.955130	−	1.31462i	−0.949211	−	0.314641i	$-0.898116\pi$
$619$	−23.7633	−	32.7074i	−0.955130	−	1.31462i	−0.00591868	−	0.999982i	$-0.501884\pi$
$620$	−10.4223	+	10.0499i	−0.418570	+	0.403614i
$621$	0.217209	+	10.8894i	0.00871630	+	0.436978i
$622$	0.599376	+	3.78431i	0.0240328	+	0.151737i
$623$	−4.26239	+	2.17180i	−0.170769	+	0.0870112i
$624$	−0.656040	−	2.98859i	−0.0262626	−	0.119639i
$625$	−24.9339	−	1.81726i	−0.997355	−	0.0726905i
$626$		−	22.8677i		−	0.913977i
$627$	10.1859	+	12.4089i	0.406785	+	0.495564i
$628$	9.96632	−	1.57851i	0.397700	−	0.0629894i
$629$	2.97306	+	2.16005i	0.118544	+	0.0861269i
$630$	10.2492	−	26.3146i	0.408339	−	1.04840i
$631$	−19.6592	+	14.2832i	−0.782619	+	0.568606i	−0.905764	−	0.423783i	$-0.860702\pi$
$631$	−19.6592	+	14.2832i	−0.782619	+	0.568606i	0.123145	+	0.992389i	$0.460702\pi$
$632$	2.65182	−	2.65182i	0.105484	−	0.105484i
$633$	1.23381	+	20.8849i	0.0490394	+	0.830100i
$634$	8.32864	−	2.70614i	0.330772	−	0.107474i
$635$	−3.27934	−	1.13187i	−0.130137	−	0.0449167i
$636$	−8.82699	−	0.868465i	−0.350013	−	0.0344369i
$637$	−8.59929	+	16.8771i	−0.340716	+	0.668693i
$638$	12.8055	−	25.1322i	0.506974	−	0.994992i
$639$	−5.32245	−	44.8899i	−0.210553	−	1.77582i
$640$	−1.34701	+	1.78481i	−0.0532453	+	0.0705509i
$641$	8.76326	−	2.84736i	0.346128	−	0.112464i	−0.130794	−	0.991410i	$-0.541753\pi$
$641$	8.76326	−	2.84736i	0.346128	−	0.112464i	0.476922	+	0.878946i	$0.341753\pi$
$642$	20.4193	−	1.20630i	0.805885	−	0.0476089i
$643$	−32.6751	+	32.6751i	−1.28858	+	1.28858i	−0.352932	+	0.935649i	$0.614815\pi$
$643$	−32.6751	+	32.6751i	−1.28858	+	1.28858i	−0.935649	+	0.352932i	$0.885185\pi$
$644$	−7.13886	+	5.18669i	−0.281311	+	0.204384i
$645$	−32.1757	+	11.9269i	−1.26692	+	0.469621i
$646$	2.14764	+	1.56035i	0.0844978	+	0.0613912i
$647$	−48.0211	+	7.60579i	−1.88790	+	0.299015i	−0.989988	−	0.141152i	$-0.954919\pi$
$647$	−48.0211	+	7.60579i	−1.88790	+	0.299015i	−0.897916	+	0.440167i	$0.854919\pi$
$648$	2.09740	−	8.75219i	0.0823937	−	0.343819i
$649$		−	55.4774i		−	2.17768i
$650$	8.82688	+	0.321240i	0.346219	+	0.0126001i
$651$	46.1147	−	10.1229i	1.80738	−	0.396746i
$652$	5.00771	−	2.55156i	0.196117	−	0.0999267i
$653$	3.10987	+	19.6349i	0.121699	+	0.768375i	0.970755	+	0.240073i	$0.0771712\pi$
$653$	3.10987	+	19.6349i	0.121699	+	0.768375i	−0.849056	+	0.528302i	$0.822829\pi$
$654$	21.1358	+	9.24240i	0.826476	+	0.361407i
$655$	2.48260	−	14.0192i	0.0970032	−	0.547777i
$656$	2.21724	+	3.05177i	0.0865688	+	0.119152i
$657$	26.0247	+	9.59494i	1.01532	+	0.374334i
$658$	−3.08291	+	19.4647i	−0.120184	+	0.758815i
$659$	−9.29483	−	28.6066i	−0.362075	−	1.11435i	−0.951792	−	0.306743i	$-0.900761\pi$
$659$	−9.29483	−	28.6066i	−0.362075	−	1.11435i	0.589717	−	0.807610i	$-0.299239\pi$
$660$	18.9228	−	3.79446i	0.736568	−	0.147699i
$661$	−4.51392	+	13.8924i	−0.175571	+	0.540352i	−0.999659	−	0.0261096i	$-0.991688\pi$
$661$	−4.51392	+	13.8924i	−0.175571	+	0.540352i	0.824088	+	0.566462i	$0.191688\pi$
$662$	−5.34493	−	2.72338i	−0.207736	−	0.105847i
$663$	−1.10215	+	4.22544i	−0.0428039	+	0.164102i
$664$	−16.0465	−	5.21383i	−0.622726	−	0.202336i
$665$	−14.3502	+	10.0324i	−0.556478	+	0.389041i
$666$	−5.67142	+	5.24478i	−0.219763	+	0.203231i
$667$	−11.7187	−	1.85606i	−0.453750	−	0.0718670i
$668$	−11.8566	−	11.8566i	−0.458747	−	0.458747i
$669$	8.06029	+	7.16107i	0.311629	+	0.276863i
$670$	6.80451	−	12.7747i	0.262881	−	0.493532i
$671$	−28.4333	+	39.1351i	−1.09766	+	1.51079i
$672$	6.78975	−	2.65826i	0.261920	−	0.102545i
$673$	15.3688	+	30.1630i	0.592425	+	1.16270i	0.971435	+	0.237306i	$0.0762645\pi$
$673$	15.3688	+	30.1630i	0.592425	+	1.16270i	−0.379010	+	0.925392i	$0.623736\pi$
$674$	−2.43046			−0.0936178
$675$	22.9521	+	12.1738i	0.883426	+	0.468571i
$676$	9.87932			0.379974
$677$	−3.49259	−	6.85459i	−0.134231	−	0.263443i	0.814101	−	0.580724i	$-0.197230\pi$
$677$	−3.49259	−	6.85459i	−0.134231	−	0.263443i	−0.948332	+	0.317280i	$0.897230\pi$
$678$	2.41380	−	0.945029i	0.0927013	−	0.0362936i
$679$	8.69931	−	11.9736i	0.333849	−	0.459503i
$680$	2.86932	−	1.39685i	0.110034	−	0.0535668i
$681$	11.8548	+	10.5323i	0.454278	+	0.403597i
$682$	22.8151	+	22.8151i	0.873634	+	0.873634i
$683$	2.86990	+	0.454547i	0.109814	+	0.0173928i	0.211099	−	0.977465i	$-0.432296\pi$
$683$	2.86990	+	0.454547i	0.109814	+	0.0173928i	−0.101286	+	0.994857i	$0.532296\pi$
$684$	−4.09685	+	3.78866i	−0.156647	+	0.144863i
$685$	2.67992	+	8.78872i	0.102394	+	0.335800i
$686$	−14.9035	−	4.84242i	−0.569016	−	0.184885i
$687$	8.08540	−	30.9980i	0.308477	−	1.18265i
$688$	−7.89443	−	4.02241i	−0.300972	−	0.153353i
$689$	−2.79545	+	8.60350i	−0.106498	+	0.327767i
$690$	−3.97766	−	7.07688i	−0.151427	−	0.269412i
$691$	−9.12811	−	28.0934i	−0.347249	−	1.06872i	−0.960368	−	0.278733i	$-0.910085\pi$
$691$	−9.12811	−	28.0934i	−0.347249	−	1.06872i	0.613119	−	0.789991i	$-0.289915\pi$
$692$	−0.700227	+	4.42106i	−0.0266186	+	0.168063i
$693$	−59.0481	−	21.7702i	−2.24305	−	0.826981i
$694$	−13.3577	−	18.3852i	−0.507050	−	0.697894i
$695$	10.4542	+	21.4743i	0.396549	+	0.814565i
$696$	8.98285	+	3.92808i	0.340494	+	0.148893i
$697$	−0.842182	−	5.31733i	−0.0318999	−	0.201408i
$698$	−11.1668	+	5.68977i	−0.422670	+	0.215361i
$699$	23.3030	−	5.11535i	0.881400	−	0.193480i
$700$	2.53449	+	20.8958i	0.0957949	+	0.789788i
$701$		−	41.1646i		−	1.55476i	−0.629028	−	0.777382i	$-0.716547\pi$
$701$		−	41.1646i		−	1.55476i	0.629028	−	0.777382i	$-0.283453\pi$
$702$	−8.26024	−	4.00335i	−0.311763	−	0.151097i
$703$	4.73055	−	0.749245i	0.178416	−	0.0282583i
$704$	4.03141	+	2.92899i	0.151940	+	0.110391i
$705$	−17.4576	−	4.89435i	−0.657489	−	0.184332i
$706$	−5.78030	+	4.19963i	−0.217544	+	0.158055i
$707$	49.6347	−	49.6347i	1.86671	−	1.86671i
$708$	19.2496	−	1.13720i	0.723443	−	0.0427385i
$709$	16.1533	−	5.24852i	0.606650	−	0.197112i	0.0104457	−	0.999945i	$-0.496675\pi$
$709$	16.1533	−	5.24852i	0.606650	−	0.197112i	0.596204	+	0.802833i	$0.296675\pi$
$710$	19.3054	+	27.6142i	0.724518	+	1.03634i
$711$	−1.32468	−	11.1725i	−0.0496795	−	0.419000i
$712$	0.515891	−	1.01249i	0.0193338	−	0.0379448i
$713$	6.16161	−	12.0928i	0.230754	−	0.452880i
$714$	−10.3564	−	1.01894i	−0.387578	−	0.0381328i
$715$	0.358003	−	19.6806i	0.0133886	−	0.736012i
$716$	−0.165923	+	0.0539115i	−0.00620082	+	0.00201477i
$717$	−2.11799	−	35.8516i	−0.0790976	−	1.33890i
$718$	7.52770	−	7.52770i	0.280931	−	0.280931i
$719$	17.4118	−	12.6504i	0.649349	−	0.471780i	−0.213700	−	0.976899i	$-0.568552\pi$
$719$	17.4118	−	12.6504i	0.649349	−	0.471780i	0.863049	+	0.505120i	$0.168552\pi$
$720$	1.70449	+	6.48804i	0.0635225	+	0.241795i
$721$	9.03534	+	6.56456i	0.336493	+	0.244477i
$722$	−15.3489	+	2.43102i	−0.571226	+	0.0904734i
$723$	−6.83771	−	8.33003i	−0.254297	−	0.309797i
$724$			11.3773i			0.422835i
$725$	−17.4573	+	22.2767i	−0.648349	+	0.827338i
$726$	−5.13651	−	23.3994i	−0.190634	−	0.868432i
$727$	−30.4534	+	15.5168i	−1.12945	+	0.575485i	−0.915884	−	0.401443i	$-0.868509\pi$
$727$	−30.4534	+	15.5168i	−1.12945	+	0.575485i	−0.213569	+	0.976928i	$0.568509\pi$
$728$	−1.16337	−	7.34523i	−0.0431174	−	0.272233i
$729$	−16.7286	−	21.1932i	−0.619579	−	0.784934i
$730$	−20.4750	+	2.86222i	−0.757813	+	0.105935i
$731$	7.43254	+	10.2300i	0.274902	+	0.378371i
$732$	−14.1619	−	9.06358i	−0.523440	−	0.335000i
$733$	2.91730	−	18.4191i	0.107753	−	0.680326i	−0.873387	−	0.487027i	$-0.838081\pi$
$733$	2.91730	−	18.4191i	0.107753	−	0.680326i	0.981140	−	0.193299i	$-0.0619186\pi$
$734$	−1.29725	−	3.99251i	−0.0478822	−	0.147366i
$735$	17.3275	−	37.7399i	0.639133	−	1.39206i
$736$	0.647728	−	1.99350i	0.0238756	−	0.0734815i
$737$	−28.7397	−	14.6436i	−1.05864	−	0.539405i
$738$	11.3080	+	0.441957i	0.416252	+	0.0162687i
$739$	−1.28835	−	0.418609i	−0.0473926	−	0.0153988i	0.285225	−	0.958461i	$-0.407932\pi$
$739$	−1.28835	−	0.418609i	−0.0473926	−	0.0153988i	−0.332617	+	0.943062i	$0.607932\pi$
$740$	1.87854	−	5.44266i	0.0690564	−	0.200076i
$741$	2.87835	+	4.90977i	0.105739	+	0.180365i
$742$	−21.2924	−	3.37239i	−0.781669	−	0.123804i
$743$	8.68111	+	8.68111i	0.318479	+	0.318479i	0.848183	−	0.529704i	$-0.177697\pi$
$743$	8.68111	+	8.68111i	0.318479	+	0.318479i	−0.529704	+	0.848183i	$0.677697\pi$
$744$	−7.44870	+	8.38404i	−0.273082	+	0.307374i
$745$	7.96657	+	8.26177i	0.291872	+	0.302688i
$746$	−2.67527	+	3.68219i	−0.0979486	+	0.134815i
$747$	−42.0806	+	28.1299i	−1.53965	+	1.02922i
$748$	−3.22868	−	6.33665i	−0.118052	−	0.231691i
$749$	49.7161			1.81659
$750$	−19.3647	+	0.0860167i	−0.707100	+	0.00314089i
$751$	40.0140			1.46013			0.730066	−	0.683377i	$-0.239489\pi$
$751$	40.0140			1.46013			0.730066	+	0.683377i	$0.239489\pi$
$752$	−2.12527	−	4.17108i	−0.0775007	−	0.152104i
$753$	−2.37990	−	6.07875i	−0.0867284	−	0.221522i
$754$	5.87750	−	8.08969i	0.214046	−	0.294609i
$755$	−31.2464	−	32.4042i	−1.13717	−	1.17931i
$756$	6.34343	−	20.9348i	0.230708	−	0.761391i
$757$	23.3400	+	23.3400i	0.848305	+	0.848305i	0.989922	−	0.141616i	$-0.0452299\pi$
$757$	23.3400	+	23.3400i	0.848305	+	0.848305i	−0.141616	+	0.989922i	$0.545230\pi$
$758$	−32.5807	−	5.16027i	−1.18338	−	0.187429i
$759$	−15.6071	+	9.14963i	−0.566501	+	0.332110i
$760$	1.35699	−	3.93160i	0.0492234	−	0.142614i
$761$	−6.88486	−	2.23703i	−0.249576	−	0.0810921i	0.181558	−	0.983380i	$-0.441886\pi$
$761$	−6.88486	−	2.23703i	−0.249576	−	0.0810921i	−0.431133	+	0.902288i	$0.641886\pi$
$762$	−2.60021	−	0.678231i	−0.0941958	−	0.0245697i
$763$	49.9570	+	25.4544i	1.80856	+	0.921509i
$764$	5.70322	−	17.5527i	0.206335	−	0.635035i
$765$	2.03630	−	9.35476i	0.0736227	−	0.338222i
$766$	5.28095	+	16.2531i	0.190808	+	0.587248i
$767$	3.07662	−	19.4250i	0.111090	−	0.701397i
$768$	−0.933665	+	1.45886i	−0.0336907	+	0.0526420i
$769$	−2.15066	−	2.96013i	−0.0775549	−	0.106745i	0.768477	−	0.639877i	$-0.221015\pi$
$769$	−2.15066	−	2.96013i	−0.0775549	−	0.106745i	−0.846032	+	0.533132i	$0.821015\pi$
$770$	46.4561	−	6.49415i	1.67416	−	0.234033i
$771$	−21.3644	+	48.8568i	−0.769420	+	1.75953i
$772$	−0.733534	−	4.63135i	−0.0264005	−	0.166686i
$773$	−29.4947	+	15.0283i	−1.06085	+	0.540531i	−0.895205	−	0.445655i	$-0.852971\pi$
$773$	−29.4947	+	15.0283i	−1.06085	+	0.540531i	−0.165646	+	0.986185i	$0.552971\pi$
$774$	−24.1365	+	11.1331i	−0.867568	+	0.400171i
$775$	−18.0643	−	26.8665i	−0.648887	−	0.965073i
$776$			3.51564i			0.126204i
$777$	−14.5123	+	11.9125i	−0.520626	+	0.427357i
$778$	−13.8752	+	2.19762i	−0.497450	+	0.0787884i
$779$	−5.67645	−	4.12419i	−0.203380	−	0.147764i
$780$	6.83610	−	0.279200i	0.244772	−	0.00999695i
$781$	60.7458	−	44.1344i	2.17366	−	1.57925i
$782$	−2.11531	+	2.11531i	−0.0756434	+	0.0756434i
$783$	25.9352	−	13.8730i	0.926848	−	0.495779i
$784$	10.1976	−	3.31339i	0.364199	−	0.118336i
$785$	−0.410371	+	22.5594i	−0.0146468	+	0.805181i
$786$	1.07982	−	10.9752i	0.0385160	−	0.391473i
$787$	−7.51367	+	14.7464i	−0.267833	+	0.525653i	−0.985277	−	0.170964i	$-0.945312\pi$
$787$	−7.51367	+	14.7464i	−0.267833	+	0.525653i	0.717444	+	0.696616i	$0.245312\pi$
$788$	−5.75693	+	11.2986i	−0.205082	+	0.402496i
$789$	0.940153	−	9.55563i	0.0334703	−	0.340189i
$790$	4.80484	+	6.87278i	0.170949	+	0.244522i
$791$	5.99204	−	1.94693i	0.213053	−	0.0692250i
$792$	14.3872	−	4.06081i	0.511227	−	0.144295i
$793$	−12.1260	+	12.1260i	−0.430608	+	0.430608i
$794$	−2.98461	+	2.16845i	−0.105920	+	0.0769552i
$795$	5.35391	−	19.0967i	0.189884	−	0.677292i
$796$	−1.31548	−	0.955752i	−0.0466260	−	0.0338757i
$797$	39.6609	−	6.28166i	1.40486	−	0.222508i	0.592456	−	0.805603i	$-0.298158\pi$
$797$	39.6609	−	6.28166i	1.40486	−	0.222508i	0.812404	+	0.583095i	$0.198158\pi$
$798$	−10.4832	+	8.60517i	−0.371102	+	0.304620i
$799$			6.68108i			0.236360i
$800$	−3.40461	−	3.66178i	−0.120371	−	0.129463i
$801$	−1.42787	−	3.09561i	−0.0504512	−	0.109378i
$802$	−26.1193	+	13.3084i	−0.922304	+	0.469937i
$803$	7.20730	+	45.5051i	0.254340	+	1.60584i
$804$	4.49193	−	10.2723i	0.158418	−	0.362276i
$805$	−8.63660	−	17.7408i	−0.304400	−	0.625279i
$806$	6.72327	+	9.25378i	0.236817	+	0.325951i
$807$	−3.23357	+	5.05249i	−0.113827	+	0.177856i
$808$	−2.60839	+	16.4687i	−0.0917627	+	0.579367i
$809$	−5.01595	−	15.4375i	−0.176351	−	0.542753i	0.823341	−	0.567546i	$-0.192107\pi$
$809$	−5.01595	−	15.4375i	−0.176351	−	0.542753i	−0.999693	+	0.0247932i	$0.992107\pi$
$810$	18.4529	+	8.03063i	0.648368	+	0.282168i
$811$	−12.6792	+	39.0226i	−0.445227	+	1.37027i	0.437007	+	0.899458i	$0.356039\pi$
$811$	−12.6792	+	39.0226i	−0.445227	+	1.37027i	−0.882234	+	0.470811i	$0.843961\pi$
$812$	21.2320	+	10.8183i	0.745098	+	0.379646i
$813$	−7.89582	−	2.05952i	−0.276919	−	0.0722305i
$814$	−12.2032	−	3.96505i	−0.427721	−	0.138975i
$815$	3.66550	+	12.0209i	0.128397	+	0.421074i
$816$	2.13251	−	1.25018i	0.0746527	−	0.0437650i
$817$	16.2774	+	2.57808i	0.569473	+	0.0901957i
$818$	−5.40870	−	5.40870i	−0.189111	−	0.189111i
$819$	−19.4680	−	10.8973i	−0.680266	−	0.380783i
$820$	−7.58395	+	3.69204i	−0.264843	+	0.128932i
$821$	−8.20025	+	11.2867i	−0.286191	+	0.393907i	−0.927772	−	0.373147i	$-0.878279\pi$
$821$	−8.20025	+	11.2867i	−0.286191	+	0.393907i	0.641582	+	0.767055i	$0.278279\pi$
$822$	2.59468	+	6.62735i	0.0904999	+	0.231155i
$823$	−7.77764	−	15.2645i	−0.271112	−	0.532086i	0.714805	−	0.699324i	$-0.246515\pi$
$823$	−7.77764	−	15.2645i	−0.271112	−	0.532086i	−0.985917	+	0.167237i	$0.946515\pi$
$824$	−2.65293			−0.0924192
$825$	0.976537	+	43.1439i	0.0339987	+	1.50208i
$826$	46.8681			1.63075
$827$	17.8399	+	35.0129i	0.620356	+	1.21752i	0.960798	+	0.277251i	$0.0894234\pi$
$827$	17.8399	+	35.0129i	0.620356	+	1.21752i	−0.340442	+	0.940266i	$0.610577\pi$
$828$	−3.49466	−	5.22779i	−0.121448	−	0.181678i
$829$	−16.9229	+	23.2923i	−0.587756	+	0.808977i	−0.994519	−	0.104557i	$-0.966657\pi$
$829$	−16.9229	+	23.2923i	−0.587756	+	0.808977i	0.406763	+	0.913534i	$0.366657\pi$
$830$	17.7365	−	33.2985i	0.615644	−	1.15581i
$831$	−28.6284	+	32.2233i	−0.993109	+	1.11781i
$832$	1.24914	+	1.24914i	0.0433060	+	0.0433060i
$833$	−15.1144	−	2.39388i	−0.523681	−	0.0829430i
$834$	9.35644	+	15.9599i	0.323987	+	0.552644i
$835$	30.7290	−	21.4830i	1.06342	−	0.743452i
$836$	−8.81517	−	2.86422i	−0.304879	−	0.0990613i
$837$	5.92488	+	33.1191i	0.204794	+	1.14476i
$838$	9.76323	+	4.97461i	0.337265	+	0.171845i
$839$	10.2985	−	31.6954i	0.355542	−	1.09425i	−0.600152	−	0.799886i	$-0.704893\pi$
$839$	10.2985	−	31.6954i	0.355542	−	1.09425i	0.955695	−	0.294360i	$-0.0951066\pi$
$840$	3.20562	+	15.9862i	0.110604	+	0.551577i
$841$	0.939554	+	2.89165i	0.0323984	+	0.0997121i
$842$	−2.19818	+	13.8788i	−0.0757544	+	0.478294i
$843$	14.0951	+	9.02079i	0.485460	+	0.310692i
$844$	−7.09981	−	9.77205i	−0.244385	−	0.336368i
$845$	−3.85203	+	21.7524i	−0.132514	+	0.748305i
$846$	−13.7747	−	2.73700i	−0.473583	−	0.0941000i
$847$	−9.10870	−	57.5100i	−0.312979	−	1.97607i
$848$	4.56273	−	2.32483i	0.156685	−	0.0798349i
$849$	0.378911	+	1.72613i	0.0130042	+	0.0592406i
$850$	1.95683	+	6.86236i	0.0671187	+	0.235377i
$851$			5.39730i			0.185017i
$852$	16.5589	+	20.1729i	0.567300	+	0.691112i
$853$	48.8210	−	7.73248i	1.67160	−	0.264755i	0.752445	−	0.658655i	$-0.228874\pi$
$853$	48.8210	−	7.73248i	1.67160	−	0.264755i	0.919153	+	0.393900i	$0.128874\pi$
$854$	−33.0619	−	24.0209i	−1.13135	−	0.821977i
$855$	−6.74451	−	10.4977i	−0.230657	−	0.359015i
$856$	−9.55419	+	6.94153i	−0.326556	+	0.237257i
$857$	5.79343	−	5.79343i	0.197900	−	0.197900i	−0.601199	−	0.799099i	$-0.705310\pi$
$857$	5.79343	−	5.79343i	0.197900	−	0.197900i	0.799099	+	0.601199i	$0.205310\pi$
$858$	−0.899173	−	15.2205i	−0.0306973	−	0.519619i
$859$	3.26295	−	1.06020i	0.111330	−	0.0361734i	−0.252822	−	0.967513i	$-0.581359\pi$
$859$	3.26295	−	1.06020i	0.111330	−	0.0361734i	0.364152	+	0.931339i	$0.381359\pi$
$860$	11.9347	−	15.8137i	0.406970	−	0.539241i
$861$	27.3731	+	2.69317i	0.932873	+	0.0917829i
$862$	1.97077	−	3.86786i	0.0671249	−	0.131740i
$863$	11.6022	−	22.7707i	0.394944	−	0.775122i	−0.604830	−	0.796354i	$-0.706759\pi$
$863$	11.6022	−	22.7707i	0.394944	−	0.775122i	0.999775	+	0.0212325i	$0.00675901\pi$
$864$	1.70393	+	4.90883i	0.0579690	+	0.167002i
$865$	−9.46131	−	3.26557i	−0.321694	−	0.111033i
$866$	−7.46455	+	2.42538i	−0.253656	+	0.0824177i
$867$	25.8718	−	1.52842i	0.878654	−	0.0519078i
$868$	−19.2745	+	19.2745i	−0.654219	+	0.654219i
$869$	15.1188	−	10.9844i	0.512869	−	0.372621i
$870$	−12.1514	+	18.2469i	−0.411970	+	0.618629i
$871$	−9.25092	−	6.72119i	−0.313455	−	0.227739i
$872$	−13.1545	+	2.08347i	−0.445468	+	0.0705551i
$873$	8.28403	+	6.52784i	0.280372	+	0.220934i
$874$			3.89884i			0.131880i
$875$	−46.9969	−	2.56698i	−1.58878	−	0.0867798i
$876$	−15.6416	+	3.43357i	−0.528482	+	0.116010i
$877$	26.8672	−	13.6895i	0.907241	−	0.462262i	0.0628704	−	0.998022i	$-0.479975\pi$
$877$	26.8672	−	13.6895i	0.907241	−	0.462262i	0.844371	+	0.535759i	$0.179975\pi$
$878$	3.14649	+	19.8662i	0.106189	+	0.670451i
$879$	−3.26777	−	1.42895i	−0.110219	−	0.0481973i
$880$	−8.02097	+	7.73437i	−0.270387	+	0.260726i
$881$	−29.7770	−	40.9845i	−1.00321	−	1.38080i	−0.923334	−	0.383997i	$-0.874547\pi$
$881$	−29.7770	−	40.9845i	−1.00321	−	1.38080i	−0.0798773	−	0.996805i	$-0.525453\pi$
$882$	11.1274	−	30.1812i	0.374678	−	1.01625i
$883$	1.76422	−	11.1388i	0.0593707	−	0.374852i	−0.940057	−	0.341018i	$-0.889228\pi$
$883$	1.76422	−	11.1388i	0.0593707	−	0.374852i	0.999427	−	0.0338339i	$-0.0107717\pi$
$884$	−0.779087	−	2.39778i	−0.0262035	−	0.0806462i
$885$	−5.00167	+	42.8273i	−0.168129	+	1.43962i
$886$	−5.20028	+	16.0048i	−0.174707	+	0.537692i
$887$	−16.7280	−	8.52333i	−0.561671	−	0.286186i	0.150015	−	0.988684i	$-0.452068\pi$
$887$	−16.7280	−	8.52333i	−0.561671	−	0.286186i	−0.711686	+	0.702498i	$0.752068\pi$
$888$	1.12565	−	4.31553i	0.0377743	−	0.144820i
$889$	−6.21167	−	2.01830i	−0.208333	−	0.0676914i
$890$	2.02817	+	1.53067i	0.0679844	+	0.0513083i
$891$	17.1455	−	41.4411i	0.574395	−	1.38833i
$892$	−6.14829	−	0.973793i	−0.205860	−	0.0326050i
$893$	6.15712	+	6.15712i	0.206040	+	0.206040i
$894$	6.64603	+	5.90458i	0.222277	+	0.197479i
$895$	−0.0540083	−	0.386351i	−0.00180530	−	0.0129143i
$896$	−2.47446	+	3.40580i	−0.0826657	+	0.113780i
$897$	−5.97212	+	2.33815i	−0.199403	+	0.0780686i
$898$	−1.61517	−	3.16995i	−0.0538989	−	0.105783i
$899$	−36.6510			−1.22238
$900$	−14.9500	+	1.22322i	−0.498335	+	0.0407739i
$901$	−7.30841			−0.243478
$902$	8.53377	+	16.7485i	0.284144	+	0.557663i
$903$	−60.1580	+	23.5525i	−2.00193	+	0.783780i
$904$	−0.879683	+	1.21078i	−0.0292578	+	0.0402699i
$905$	−25.0507	−	4.43612i	−0.832714	−	0.147461i
$906$	−26.0670	−	23.1589i	−0.866017	−	0.769402i
$907$	−29.1272	−	29.1272i	−0.967153	−	0.967153i	0.0323248	−	0.999477i	$-0.489709\pi$
$907$	−29.1272	−	29.1272i	−0.967153	−	0.967153i	−0.999477	+	0.0323248i	$0.989709\pi$
$908$	−9.04270	−	1.43222i	−0.300093	−	0.0475300i
$909$	33.9625	+	36.7253i	1.12647	+	1.21810i
$910$	16.6264	+	0.302446i	0.551161	+	0.0100260i
$911$	1.21439	+	0.394580i	0.0402346	+	0.0130730i	0.329065	−	0.944307i	$-0.393266\pi$
$911$	1.21439	+	0.394580i	0.0402346	+	0.0130730i	−0.288831	+	0.957380i	$0.593266\pi$
$912$	0.813132	−	3.11740i	0.0269255	−	0.103227i
$913$	−74.9126	−	38.1699i	−2.47925	−	1.26324i
$914$	−5.87403	+	18.0784i	−0.194296	+	0.597980i
$915$	25.4781	−	27.6479i	0.842282	−	0.914012i
$916$	5.71542	+	17.5902i	0.188843	+	0.581198i
$917$	4.19312	−	26.4743i	0.138469	−	0.874259i
$918$	1.01379	−	7.34623i	0.0334601	−	0.242462i
$919$	14.7998	+	20.3701i	0.488199	+	0.671949i	0.980055	−	0.198728i	$-0.0636811\pi$
$919$	14.7998	+	20.3701i	0.488199	+	0.671949i	−0.491855	+	0.870677i	$0.663681\pi$
$920$	4.13676	+	2.20346i	0.136385	+	0.0726459i
$921$	−26.8879	−	11.7577i	−0.885987	−	0.387430i
$922$	5.01091	+	31.6376i	0.165026	+	1.04193i
$923$	23.7173	−	12.0845i	0.780663	−	0.397768i
$924$	35.4897	−	7.79051i	1.16752	−	0.256289i
$925$	11.2513	+	6.25833i	0.369939	+	0.205772i
$926$		−	3.10121i		−	0.101912i
$927$	−4.92595	+	6.25119i	−0.161789	+	0.205316i
$928$	−5.59074	+	0.885486i	−0.183525	+	0.0290675i
$929$	24.8975	+	18.0891i	0.816859	+	0.593483i	0.915811	−	0.401609i	$-0.131549\pi$
$929$	24.8975	+	18.0891i	0.816859	+	0.593483i	−0.0989519	+	0.995092i	$0.531549\pi$
$930$	−15.5558	−	19.6696i	−0.510093	−	0.644993i
$931$	−16.1352	+	11.7229i	−0.528809	+	0.384202i
$932$	−9.73992	+	9.73992i	−0.319042	+	0.319042i
$933$	−6.62478	+	0.391369i	−0.216885	+	0.0128128i
$934$	−37.7054	+	12.2512i	−1.23376	+	0.400872i
$935$	15.2110	−	4.63824i	0.497453	−	0.151687i
$936$	5.26277	−	0.623990i	0.172019	−	0.0203958i
$937$	0.618103	−	1.21310i	0.0201925	−	0.0396301i	−0.880690	−	0.473693i	$-0.842921\pi$
$937$	0.618103	−	1.21310i	0.0201925	−	0.0396301i	0.900882	+	0.434063i	$0.142921\pi$
$938$	12.3711	−	24.2797i	0.403932	−	0.792762i
$939$	39.4177	+	3.87820i	1.28635	+	0.126560i
$940$	10.0126	−	3.05311i	0.326575	−	0.0995814i
$941$	−14.0374	+	4.56102i	−0.457606	+	0.148685i	−0.528744	−	0.848781i	$-0.677337\pi$
$941$	−14.0374	+	4.56102i	−0.457606	+	0.148685i	0.0711384	+	0.997466i	$0.477337\pi$
$942$	1.03070	+	17.4469i	0.0335821	+	0.568452i
$943$	5.59101	−	5.59101i	0.182068	−	0.182068i
$944$	−9.00688	+	6.54388i	−0.293149	+	0.212985i
$945$	43.6211	+	22.1297i	1.41899	+	0.719878i
$946$	−35.7188	−	25.9512i	−1.16132	−	0.843747i
$947$	−6.67988	+	1.05799i	−0.217067	+	0.0343800i	−0.264021	−	0.964517i	$-0.585049\pi$
$947$	−6.67988	+	1.05799i	−0.217067	+	0.0343800i	0.0469536	+	0.998897i	$0.485049\pi$
$948$	4.12129	+	5.02075i	0.133853	+	0.163066i
$949$			16.3330i			0.530191i
$950$	8.12755	+	4.52081i	0.263692	+	0.146675i
$951$	3.25217	+	14.8152i	0.105459	+	0.480417i
$952$	5.35329	−	2.72764i	0.173501	−	0.0884032i
$953$	2.66239	+	16.8097i	0.0862434	+	0.544519i	0.992544	+	0.121886i	$0.0388942\pi$
$953$	2.66239	+	16.8097i	0.0862434	+	0.544519i	−0.906301	+	0.422633i	$0.861106\pi$
$954$	2.99399	−	15.0681i	0.0969341	−	0.487846i
$955$	36.4240	+	19.4014i	1.17865	+	0.627814i
$956$	12.1877	+	16.7750i	0.394180	+	0.542542i
$957$	41.1493	+	26.3354i	1.33017	+	0.851303i
$958$	2.10827	−	13.3111i	0.0681150	−	0.430061i
$959$	5.34552	+	16.4518i	0.172616	+	0.531257i
$960$	−2.84809	−	2.62457i	−0.0919217	−	0.0847078i
$961$	3.37603	−	10.3904i	0.108904	−	0.335173i
$962$	−4.05296	−	2.06509i	−0.130673	−	0.0665811i
$963$	−1.38364	+	35.4019i	−0.0445870	+	1.14081i
$964$	5.91757	+	1.92274i	0.190592	+	0.0619271i
$965$	10.4834	+	0.190700i	0.337472	+	0.00613884i
$966$	−7.72973	−	13.1851i	−0.248700	−	0.424223i
$967$	38.7579	+	6.13865i	1.24637	+	0.197406i	0.744550	−	0.667566i	$-0.232664\pi$
$967$	38.7579	+	6.13865i	1.24637	+	0.197406i	0.501820	+	0.864972i	$0.332664\pi$
$968$	9.78020	+	9.78020i	0.314348	+	0.314348i
$969$	−3.05385	+	3.43732i	−0.0981037	+	0.110423i
$970$	−7.74079	−	1.37078i	−0.248542	−	0.0440131i
$971$	17.7969	−	24.4953i	0.571129	−	0.786091i	−0.421559	−	0.906801i	$-0.638517\pi$
$971$	17.7969	−	24.4953i	0.571129	−	0.786091i	0.992688	+	0.120710i	$0.0385171\pi$
$972$	14.7307	+	5.09966i	0.472487	+	0.163572i
$973$	20.4139	+	40.0644i	0.654438	+	1.28441i
$974$	−2.08662			−0.0668596
$975$	−2.05071	+	15.1607i	−0.0656753	+	0.485530i
$976$	9.70753			0.310731
$977$	19.1478	+	37.5797i	0.612593	+	1.20228i	0.963961	+	0.266044i	$0.0857167\pi$
$977$	19.1478	+	37.5797i	0.612593	+	1.20228i	−0.351368	+	0.936238i	$0.614283\pi$
$978$	3.54892	+	9.06466i	0.113482	+	0.289856i
$979$	3.32836	−	4.58109i	0.106375	−	0.146412i
$980$	3.31935	+	23.7451i	0.106033	+	0.758508i
$981$	−19.5159	+	34.8650i	−0.623094	+	1.11315i
$982$	−11.7522	−	11.7522i	−0.375029	−	0.375029i
$983$	−14.2241	−	2.25288i	−0.453679	−	0.0718557i	−0.0745867	−	0.997215i	$-0.523764\pi$
$983$	−14.2241	−	2.25288i	−0.453679	−	0.0718557i	−0.379092	+	0.925359i	$0.623764\pi$
$984$	−5.63646	+	3.30436i	−0.179684	+	0.105339i
$985$	−22.6327	−	17.0811i	−0.721138	−	0.544248i
$986$	7.68307	+	2.49638i	0.244679	+	0.0795009i
$987$	−33.0291	−	8.61519i	−1.05133	−	0.274224i
$988$	−2.92773	−	1.49175i	−0.0931434	−	0.0474589i
$989$	−5.73895	+	17.6627i	−0.182488	+	0.561640i
$990$	3.33145	+	33.2612i	0.105880	+	1.05711i
$991$	0.477429	+	1.46938i	0.0151660	+	0.0466762i	0.958353	−	0.285586i	$-0.0921882\pi$
$991$	0.477429	+	1.46938i	0.0151660	+	0.0466762i	−0.943187	+	0.332262i	$0.892188\pi$
$992$	1.01291	−	6.39524i	0.0321598	−	0.203049i
$993$	5.60082	−	8.75133i	0.177737	−	0.277715i
$994$	37.2854	+	51.3189i	1.18262	+	1.62774i
$995$	2.61730	−	2.52378i	0.0829741	−	0.0800093i
$996$	11.7086	−	26.7756i	0.371001	−	0.848417i
$997$	−7.78106	−	49.1277i	−0.246429	−	1.55589i	−0.731762	−	0.681560i	$-0.761302\pi$
$997$	−7.78106	−	49.1277i	−0.246429	−	1.55589i	0.485333	−	0.874329i	$-0.338698\pi$
$998$	32.1169	−	16.3644i	1.01664	−	0.518006i
$999$	−8.07873	−	10.6655i	−0.255600	−	0.337440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.47.5	✓	80
3.2	odd	2	inner	150.2.l.a.47.10	yes	80
5.2	odd	4		750.2.l.a.743.8		80
5.3	odd	4		750.2.l.c.743.3		80
5.4	even	2		750.2.l.b.257.6		80
15.2	even	4		750.2.l.a.743.3		80
15.8	even	4		750.2.l.c.743.8		80
15.14	odd	2		750.2.l.b.257.1		80
25.6	even	5		750.2.l.c.107.8		80
25.8	odd	20	inner	150.2.l.a.83.10	yes	80
25.17	odd	20		750.2.l.b.143.1		80
25.19	even	10		750.2.l.a.107.3		80
75.8	even	20	inner	150.2.l.a.83.5	yes	80
75.17	even	20		750.2.l.b.143.6		80
75.44	odd	10		750.2.l.a.107.8		80
75.56	odd	10		750.2.l.c.107.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.5	✓	80	1.1	even	1	trivial
150.2.l.a.47.10	yes	80	3.2	odd	2	inner
150.2.l.a.83.5	yes	80	75.8	even	20	inner
150.2.l.a.83.10	yes	80	25.8	odd	20	inner
750.2.l.a.107.3		80	25.19	even	10
750.2.l.a.107.8		80	75.44	odd	10
750.2.l.a.743.3		80	15.2	even	4
750.2.l.a.743.8		80	5.2	odd	4
750.2.l.b.143.1		80	25.17	odd	20
750.2.l.b.143.6		80	75.17	even	20
750.2.l.b.257.1		80	15.14	odd	2
750.2.l.b.257.6		80	5.4	even	2
750.2.l.c.107.3		80	75.56	odd	10
750.2.l.c.107.8		80	25.6	even	5
750.2.l.c.743.3		80	5.3	odd	4
750.2.l.c.743.8		80	15.8	even	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.61285 - 0.631448i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.55212 - 1.60963i) q^{5} +(-1.29484 - 1.15039i) q^{6} +(-2.97677 - 2.97677i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.20255 - 2.03686i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.61285 - 0.631448i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-1.55212 - 1.60963i) q^{5} +(-1.29484 - 1.15039i) q^{6} +(-2.97677 - 2.97677i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.20255 - 2.03686i) q^{9} +(-0.729547 + 2.11371i) q^{10} +(4.73921 + 1.53986i) q^{11} +(-0.437156 + 1.67598i) q^{12} +(1.57400 + 0.801995i) q^{13} +(-1.30090 + 4.00375i) q^{14} +(-3.51973 - 1.61601i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.223260 + 1.40961i) q^{17} +(-2.81479 - 1.03777i) q^{18} +(1.09331 + 1.50481i) q^{19} +(2.21453 - 0.309572i) q^{20} +(-6.68076 - 2.92140i) q^{21} +(-0.779529 - 4.92175i) q^{22} +(-1.86763 + 0.951606i) q^{23} +(1.69177 - 0.371369i) q^{24} +(-0.181847 + 4.99669i) q^{25} -1.76655i q^{26} +(2.26620 - 4.67593i) q^{27} +(4.15797 - 0.658557i) q^{28} +(4.57938 + 3.32712i) q^{29} +(0.158048 + 3.86976i) q^{30} +(-5.23835 + 3.80588i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.61596 - 0.509001i) q^{33} +(1.35733 - 0.441023i) q^{34} +(-0.171208 + 9.41183i) q^{35} +(0.353226 + 2.97913i) q^{36} +(1.16900 - 2.29429i) q^{37} +(0.844446 - 1.65732i) q^{38} +(3.04504 + 0.299594i) q^{39} +(-1.28121 - 1.83262i) q^{40} +(-3.58757 + 1.16567i) q^{41} +(0.430011 + 7.27889i) q^{42} +(6.26505 - 6.26505i) q^{43} +(-4.03141 + 2.92899i) q^{44} +(-6.69721 - 0.383852i) q^{45} +(1.69577 + 1.23205i) q^{46} +(4.62368 - 0.732319i) q^{47} +(-1.09894 - 1.33878i) q^{48} +10.7224i q^{49} +(4.53464 - 2.10642i) q^{50} +(0.530010 + 2.41446i) q^{51} +(-1.57400 + 0.801995i) q^{52} +(0.801081 + 5.05783i) q^{53} +(-5.19512 + 0.103626i) q^{54} +(-4.87721 - 10.0184i) q^{55} +(-2.47446 - 3.40580i) q^{56} +(2.71355 + 1.73666i) q^{57} +(0.885486 - 5.59074i) q^{58} +(-3.44032 - 10.5882i) q^{59} +(3.37623 - 1.89766i) q^{60} +(-2.99979 + 9.23241i) q^{61} +(5.76923 + 2.93957i) q^{62} +(-12.6197 - 0.493226i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-1.15212 - 3.77836i) q^{65} +(-4.36509 - 7.44580i) q^{66} +(-6.39326 - 1.01259i) q^{67} +(-1.00917 - 1.00917i) q^{68} +(-2.41131 + 2.71411i) q^{69} +(8.46373 - 4.12033i) q^{70} +(8.85681 - 12.1904i) q^{71} +(2.49407 - 1.66722i) q^{72} +(4.19747 + 8.23800i) q^{73} -2.57494 q^{74} +(2.86186 + 8.17372i) q^{75} -1.86005 q^{76} +(-9.52374 - 18.6914i) q^{77} +(-1.11548 - 2.84917i) q^{78} +(2.20434 - 3.03401i) q^{79} +(-1.05122 + 1.97356i) q^{80} +(0.702433 - 8.97255i) q^{81} +(2.66735 + 2.66735i) q^{82} +(-16.6646 - 2.63941i) q^{83} +(6.29032 - 3.68769i) q^{84} +(2.61548 - 1.82852i) q^{85} +(-8.42648 - 2.73793i) q^{86} +(9.48674 + 2.47449i) q^{87} +(4.43998 + 2.26228i) q^{88} +(0.351151 - 1.08073i) q^{89} +(2.69846 + 6.14153i) q^{90} +(-2.29810 - 7.07281i) q^{91} +(0.327901 - 2.07029i) q^{92} +(-6.04544 + 9.44605i) q^{93} +(-2.75161 - 3.78726i) q^{94} +(0.725250 - 4.09548i) q^{95} +(-0.693954 + 1.58696i) q^{96} +(0.549968 + 3.47236i) q^{97} +(9.55370 - 4.86785i) q^{98} +(13.5748 - 6.26147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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