LMFDB - Embedded newform 201.2.m.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(4,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.m (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	201.19
Dual form			201.2.m.a.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29041 - 0.665251i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.0624755 + 0.0877346i) q^{4} +(1.62071 + 1.87040i) q^{5} +(-1.42556 - 0.274754i) q^{6} +(0.228443 + 4.79562i) q^{7} +(0.390970 + 2.71926i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-1.29041 - 0.665251i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.0624755 + 0.0877346i) q^{4} +(1.62071 + 1.87040i) q^{5} +(-1.42556 - 0.274754i) q^{6} +(0.228443 + 4.79562i) q^{7} +(0.390970 + 2.71926i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.847092 - 3.49176i) q^{10} +(-5.54605 + 1.06891i) q^{11} +(0.0846625 + 0.0665793i) q^{12} +(6.20817 - 2.48538i) q^{13} +(2.89550 - 6.34027i) q^{14} +(2.08202 + 1.33803i) q^{15} +(1.37493 - 3.97260i) q^{16} +(-0.748151 + 1.05063i) q^{17} +(-1.44522 + 0.138002i) q^{18} +(-0.0188756 + 0.396247i) q^{19} +(-0.0628442 + 0.259047i) q^{20} +(1.57027 + 4.53700i) q^{21} +(7.86775 + 2.31018i) q^{22} +(-0.208809 - 0.199099i) q^{23} +(1.14124 + 2.49896i) q^{24} +(-0.160122 + 1.11368i) q^{25} +(-9.66446 - 0.922844i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.406469 + 0.319651i) q^{28} +(2.75195 - 4.76652i) q^{29} +(-1.79652 - 3.11167i) q^{30} +(1.92175 + 0.769353i) q^{31} +(-0.440483 + 0.419999i) q^{32} +(-5.02025 + 2.58812i) q^{33} +(1.66435 - 0.858033i) q^{34} +(-8.59950 + 8.19961i) q^{35} +(0.0999906 + 0.0400302i) q^{36} +(-3.28208 - 5.68473i) q^{37} +(0.287961 - 0.498763i) q^{38} +(5.25648 - 4.13375i) q^{39} +(-4.45246 + 5.13841i) q^{40} +(2.35465 + 0.224841i) q^{41} +(0.991955 - 6.89920i) q^{42} +(0.670915 + 1.46910i) q^{43} +(-0.440273 - 0.419799i) q^{44} +(2.37465 + 0.697260i) q^{45} +(0.136997 + 0.395828i) q^{46} +(0.595574 - 2.45499i) q^{47} +(0.200025 - 4.19905i) q^{48} +(-15.9775 + 1.52566i) q^{49} +(0.947496 - 1.33057i) q^{50} +(-0.421849 + 1.21885i) q^{51} +(0.605912 + 0.389396i) q^{52} +(-1.80067 + 3.94291i) q^{53} +(-1.34780 + 0.539577i) q^{54} +(-10.9879 - 8.64095i) q^{55} +(-12.9512 + 2.49614i) q^{56} +(0.0935248 + 0.385515i) q^{57} +(-6.72207 + 4.32001i) q^{58} +(-1.32279 - 9.20021i) q^{59} +(0.0126835 + 0.266259i) q^{60} +(-4.17435 - 0.804540i) q^{61} +(-1.96803 - 2.27122i) q^{62} +(2.78489 + 3.91082i) q^{63} +(-7.21925 + 2.11976i) q^{64} +(14.7103 + 7.58370i) q^{65} +8.19990 q^{66} +(7.19147 + 3.90931i) q^{67} -0.138918 q^{68} +(-0.256443 - 0.132206i) q^{69} +(16.5516 - 4.86000i) q^{70} +(6.32392 + 8.88070i) q^{71} +(1.79905 + 2.07621i) q^{72} +(-2.51218 - 0.484183i) q^{73} +(0.453447 + 9.51902i) q^{74} +(0.160122 + 1.11368i) q^{75} +(-0.0359439 + 0.0230997i) q^{76} +(-6.39306 - 26.3525i) q^{77} +(-9.53298 + 1.83733i) q^{78} +(10.7470 + 8.45150i) q^{79} +(9.65875 - 3.86678i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-2.88887 - 1.85657i) q^{82} +(3.69375 - 10.6724i) q^{83} +(-0.299948 + 0.421219i) q^{84} +(-3.17764 + 0.303428i) q^{85} +(0.111566 - 2.34206i) q^{86} +(1.29759 - 5.34876i) q^{87} +(-5.07499 - 14.6632i) q^{88} +(-0.278184 - 0.0816822i) q^{89} +(-2.60041 - 2.47948i) q^{90} +(13.3371 + 29.2042i) q^{91} +(0.00442241 - 0.0307585i) q^{92} +(2.06066 + 0.196769i) q^{93} +(-2.40172 + 2.77173i) q^{94} +(-0.771735 + 0.606899i) q^{95} +(-0.304313 + 0.527085i) q^{96} +(-0.0223946 - 0.0387886i) q^{97} +(21.6324 + 8.66029i) q^{98} +(-4.08773 + 3.89765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{2} + 10 q^{3} + 6 q^{4} - 2 q^{5} + 9 q^{6} + q^{7} - 45 q^{8} - 10 q^{9}+O(q^{10}) $ 100 * q + 2 * q^2 + 10 * q^3 + 6 * q^4 - 2 * q^5 + 9 * q^6 + q^7 - 45 * q^8 - 10 * q^9	\( 100 q + 2 q^{2} + 10 q^{3} + 6 q^{4} - 2 q^{5} + 9 q^{6} + q^{7} - 45 q^{8} - 10 q^{9} - 25 q^{10} + 9 q^{11} + 5 q^{12} - 3 q^{13} + 22 q^{14} - 9 q^{15} - 46 q^{17} + 2 q^{18} - 14 q^{19} - 16 q^{20} - q^{21} - 17 q^{22} + 12 q^{23} + 12 q^{24} - 44 q^{25} - 7 q^{26} + 10 q^{27} - 90 q^{28} + 43 q^{29} - 30 q^{30} - 10 q^{31} + 20 q^{32} - 42 q^{33} + 20 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} + 16 q^{38} + 3 q^{39} + 55 q^{40} - 48 q^{41} - 45 q^{43} - 147 q^{44} - 2 q^{45} + 47 q^{46} + 44 q^{47} - 64 q^{49} - 54 q^{50} + 24 q^{51} - 34 q^{52} + 68 q^{53} - 2 q^{54} - 17 q^{55} + 111 q^{56} + 3 q^{57} + 88 q^{58} - 2 q^{59} - 6 q^{60} + 21 q^{61} + 86 q^{62} + 23 q^{63} + 19 q^{64} + 6 q^{65} + 94 q^{66} + 20 q^{67} - 202 q^{68} + 21 q^{69} - 20 q^{70} + q^{71} + 32 q^{72} + 10 q^{73} + 67 q^{74} + 44 q^{75} - 90 q^{76} - 62 q^{77} + 51 q^{78} - 29 q^{79} + 199 q^{80} - 10 q^{81} - 36 q^{82} + 43 q^{83} - 75 q^{84} + 93 q^{85} - 83 q^{86} + 12 q^{87} + 54 q^{88} + 21 q^{89} - 25 q^{90} + 58 q^{91} - 192 q^{92} - q^{93} + 14 q^{94} - 109 q^{95} - 9 q^{96} - 35 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 100 * q + 2 * q^2 + 10 * q^3 + 6 * q^4 - 2 * q^5 + 9 * q^6 + q^7 - 45 * q^8 - 10 * q^9 - 25 * q^10 + 9 * q^11 + 5 * q^12 - 3 * q^13 + 22 * q^14 - 9 * q^15 - 46 * q^17 + 2 * q^18 - 14 * q^19 - 16 * q^20 - q^21 - 17 * q^22 + 12 * q^23 + 12 * q^24 - 44 * q^25 - 7 * q^26 + 10 * q^27 - 90 * q^28 + 43 * q^29 - 30 * q^30 - 10 * q^31 + 20 * q^32 - 42 * q^33 + 20 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 + 16 * q^38 + 3 * q^39 + 55 * q^40 - 48 * q^41 - 45 * q^43 - 147 * q^44 - 2 * q^45 + 47 * q^46 + 44 * q^47 - 64 * q^49 - 54 * q^50 + 24 * q^51 - 34 * q^52 + 68 * q^53 - 2 * q^54 - 17 * q^55 + 111 * q^56 + 3 * q^57 + 88 * q^58 - 2 * q^59 - 6 * q^60 + 21 * q^61 + 86 * q^62 + 23 * q^63 + 19 * q^64 + 6 * q^65 + 94 * q^66 + 20 * q^67 - 202 * q^68 + 21 * q^69 - 20 * q^70 + q^71 + 32 * q^72 + 10 * q^73 + 67 * q^74 + 44 * q^75 - 90 * q^76 - 62 * q^77 + 51 * q^78 - 29 * q^79 + 199 * q^80 - 10 * q^81 - 36 * q^82 + 43 * q^83 - 75 * q^84 + 93 * q^85 - 83 * q^86 + 12 * q^87 + 54 * q^88 + 21 * q^89 - 25 * q^90 + 58 * q^91 - 192 * q^92 - q^93 + 14 * q^94 - 109 * q^95 - 9 * q^96 - 35 * q^97 - 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{33}\right)$

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 $

$2$	−1.29041	−	0.665251i	−0.912455	−	0.470403i	−0.0629695	−	0.998015i	$-0.520057\pi$
$2$	−1.29041	−	0.665251i	−0.912455	−	0.470403i	−0.849485	+	0.527612i	$0.823087\pi$
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	0.0624755	+	0.0877346i	0.0312378	+	0.0438673i
$5$	1.62071	+	1.87040i	0.724806	+	0.836470i	0.991876	−	0.127207i	$-0.0406012\pi$
$5$	1.62071	+	1.87040i	0.724806	+	0.836470i	−0.267071	+	0.963677i	$0.586056\pi$
$6$	−1.42556	−	0.274754i	−0.581982	−	0.112168i
$7$	0.228443	+	4.79562i	0.0863435	+	1.81257i	0.463149	+	0.886281i	$0.346720\pi$
$7$	0.228443	+	4.79562i	0.0863435	+	1.81257i	−0.376805	+	0.926293i	$0.622977\pi$
$8$	0.390970	+	2.71926i	0.138229	+	0.961403i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	−0.847092	−	3.49176i	−0.267874	−	1.10419i
$11$	−5.54605	+	1.06891i	−1.67220	+	0.322289i	−0.935337	−	0.353757i	$-0.884904\pi$
$11$	−5.54605	+	1.06891i	−1.67220	+	0.322289i	−0.736859	+	0.676046i	$0.763692\pi$
$12$	0.0846625	+	0.0665793i	0.0244400	+	0.0192198i
$13$	6.20817	−	2.48538i	1.72184	−	0.689319i	0.721841	−	0.692059i	$-0.243296\pi$
$13$	6.20817	−	2.48538i	1.72184	−	0.689319i	0.999996	+	0.00273985i	$0.000872122\pi$
$14$	2.89550	−	6.34027i	0.773856	−	1.69451i
$15$	2.08202	+	1.33803i	0.537575	+	0.345478i
$16$	1.37493	−	3.97260i	0.343733	−	0.993151i
$17$	−0.748151	+	1.05063i	−0.181453	+	0.254815i	−0.895277	−	0.445510i	$-0.853022\pi$
$17$	−0.748151	+	1.05063i	−0.181453	+	0.254815i	0.713824	+	0.700325i	$0.246962\pi$
$18$	−1.44522	+	0.138002i	−0.340642	+	0.0325273i
$19$	−0.0188756	+	0.396247i	−0.00433036	+	0.0909054i	−0.999998	−	0.00207993i	$-0.999338\pi$
$19$	−0.0188756	+	0.396247i	−0.00433036	+	0.0909054i	0.995667	+	0.0929853i	$0.0296410\pi$
$20$	−0.0628442	+	0.259047i	−0.0140524	+	0.0579247i
$21$	1.57027	+	4.53700i	0.342661	+	0.990055i
$22$	7.86775	+	2.31018i	1.67741	+	0.492532i
$23$	−0.208809	−	0.199099i	−0.0435396	−	0.0415149i	0.667997	−	0.744164i	$-0.267152\pi$
$23$	−0.208809	−	0.199099i	−0.0435396	−	0.0415149i	−0.711537	+	0.702649i	$0.752000\pi$
$24$	1.14124	+	2.49896i	0.232954	+	0.510098i
$25$	−0.160122	+	1.11368i	−0.0320245	+	0.222735i
$26$	−9.66446	−	0.922844i	−1.89536	−	0.180985i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	−0.406469	+	0.319651i	−0.0768155	+	0.0604084i
$29$	2.75195	−	4.76652i	0.511025	−	0.885121i	−0.488894	−	0.872343i	$-0.662599\pi$
$29$	2.75195	−	4.76652i	0.511025	−	0.885121i	0.999918	−	0.0127773i	$-0.00406724\pi$
$30$	−1.79652	−	3.11167i	−0.327999	−	0.568110i
$31$	1.92175	+	0.769353i	0.345157	+	0.138180i	0.537763	−	0.843096i	$-0.319270\pi$
$31$	1.92175	+	0.769353i	0.345157	+	0.138180i	−0.192606	+	0.981276i	$0.561694\pi$
$32$	−0.440483	+	0.419999i	−0.0778671	+	0.0742461i
$33$	−5.02025	+	2.58812i	−0.873913	+	0.450533i
$34$	1.66435	−	0.858033i	0.285434	−	0.147151i
$35$	−8.59950	+	8.19961i	−1.45358	+	1.38599i
$36$	0.0999906	+	0.0400302i	0.0166651	+	0.00667170i
$37$	−3.28208	−	5.68473i	−0.539571	−	0.934564i	−0.998927	−	0.0463122i	$-0.985253\pi$
$37$	−3.28208	−	5.68473i	−0.539571	−	0.934564i	0.459356	−	0.888252i	$-0.348080\pi$
$38$	0.287961	−	0.498763i	0.0467134	−	0.0809101i
$39$	5.25648	−	4.13375i	0.841711	−	0.661929i
$40$	−4.45246	+	5.13841i	−0.703996	+	0.812455i
$41$	2.35465	+	0.224841i	0.367734	+	0.0351143i	0.277288	−	0.960787i	$-0.410565\pi$
$41$	2.35465	+	0.224841i	0.367734	+	0.0351143i	0.0904464	+	0.995901i	$0.471171\pi$
$42$	0.991955	−	6.89920i	0.153062	−	1.06457i
$43$	0.670915	+	1.46910i	0.102314	+	0.224035i	0.953865	−	0.300235i	$-0.0970652\pi$
$43$	0.670915	+	1.46910i	0.102314	+	0.224035i	−0.851552	+	0.524271i	$0.824338\pi$
$44$	−0.440273	−	0.419799i	−0.0663736	−	0.0632871i
$45$	2.37465	+	0.697260i	0.353992	+	0.103941i
$46$	0.136997	+	0.395828i	0.0201992	+	0.0583617i
$47$	0.595574	−	2.45499i	0.0868734	−	0.358097i	−0.911738	−	0.410772i	$-0.865259\pi$
$47$	0.595574	−	2.45499i	0.0868734	−	0.358097i	0.998612	+	0.0526744i	$0.0167745\pi$
$48$	0.200025	−	4.19905i	0.0288712	−	0.606081i
$49$	−15.9775	+	1.52566i	−2.28249	+	0.217952i
$50$	0.947496	−	1.33057i	0.133996	−	0.188171i
$51$	−0.421849	+	1.21885i	−0.0590706	+	0.170673i
$52$	0.605912	+	0.389396i	0.0840249	+	0.0539995i
$53$	−1.80067	+	3.94291i	−0.247340	+	0.541600i	−0.992058	−	0.125780i	$-0.959857\pi$
$53$	−1.80067	+	3.94291i	−0.247340	+	0.541600i	0.744718	+	0.667379i	$0.232584\pi$
$54$	−1.34780	+	0.539577i	−0.183412	+	0.0734272i
$55$	−10.9879	−	8.64095i	−1.48160	−	1.16515i
$56$	−12.9512	+	2.49614i	−1.73068	+	0.333561i
$57$	0.0935248	+	0.385515i	0.0123877	+	0.0510626i
$58$	−6.72207	+	4.32001i	−0.882650	+	0.567245i
$59$	−1.32279	−	9.20021i	−0.172213	−	1.19777i	−0.874196	−	0.485573i	$-0.838611\pi$
$59$	−1.32279	−	9.20021i	−0.172213	−	1.19777i	0.701984	−	0.712193i	$-0.252298\pi$
$60$	0.0126835	+	0.266259i	0.00163743	+	0.0343739i
$61$	−4.17435	−	0.804540i	−0.534471	−	0.103011i	−0.0851276	−	0.996370i	$-0.527130\pi$
$61$	−4.17435	−	0.804540i	−0.534471	−	0.103011i	−0.449343	+	0.893359i	$0.648342\pi$
$62$	−1.96803	−	2.27122i	−0.249940	−	0.288446i
$63$	2.78489	+	3.91082i	0.350863	+	0.492718i
$64$	−7.21925	+	2.11976i	−0.902406	+	0.264970i
$65$	14.7103	+	7.58370i	1.82459	+	0.940643i
$66$	8.19990			1.00934
$67$	7.19147	+	3.90931i	0.878578	+	0.477599i
$67$	7.19147	+	3.90931i	0.878578	+	0.477599i
$68$	−0.138918			−0.0168463
$69$	−0.256443	−	0.132206i	−0.0308721	−	0.0159157i
$70$	16.5516	−	4.86000i	1.97830	−	0.580881i
$71$	6.32392	+	8.88070i	0.750511	+	1.05395i	0.996411	+	0.0846501i	$0.0269772\pi$
$71$	6.32392	+	8.88070i	0.750511	+	1.05395i	−0.245900	+	0.969295i	$0.579083\pi$
$72$	1.79905	+	2.07621i	0.212020	+	0.244684i
$73$	−2.51218	−	0.484183i	−0.294028	−	0.0566693i	0.0401040	−	0.999196i	$-0.487231\pi$
$73$	−2.51218	−	0.484183i	−0.294028	−	0.0566693i	−0.334132	+	0.942526i	$0.608443\pi$
$74$	0.453447	+	9.51902i	0.0527121	+	1.10656i
$75$	0.160122	+	1.11368i	0.0184893	+	0.128596i
$76$	−0.0359439	+	0.0230997i	−0.00412304	+	0.00264972i
$77$	−6.39306	−	26.3525i	−0.728557	−	3.00315i
$78$	−9.53298	+	1.83733i	−1.07940	+	0.208037i
$79$	10.7470	+	8.45150i	1.20913	+	0.950868i	0.999637	−	0.0269425i	$-0.00857711\pi$
$79$	10.7470	+	8.45150i	1.20913	+	0.950868i	0.209490	+	0.977811i	$0.432820\pi$
$80$	9.65875	−	3.86678i	1.07988	−	0.432319i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−2.88887	−	1.85657i	−0.319023	−	0.205023i
$83$	3.69375	−	10.6724i	0.405442	−	1.17145i	−0.538868	−	0.842390i	$-0.681148\pi$
$83$	3.69375	−	10.6724i	0.405442	−	1.17145i	0.944310	−	0.329057i	$-0.106731\pi$
$84$	−0.299948	+	0.421219i	−0.0327271	+	0.0459587i
$85$	−3.17764	+	0.303428i	−0.344664	+	0.0329114i
$86$	0.111566	−	2.34206i	0.0120305	−	0.252551i
$87$	1.29759	−	5.34876i	0.139117	−	0.573447i
$88$	−5.07499	−	14.6632i	−0.540996	−	1.56311i
$89$	−0.278184	−	0.0816822i	−0.0294874	−	0.00865829i	0.266956	−	0.963709i	$-0.413982\pi$
$89$	−0.278184	−	0.0816822i	−0.0294874	−	0.00865829i	−0.296443	+	0.955051i	$0.595800\pi$
$90$	−2.60041	−	2.47948i	−0.274107	−	0.261361i
$91$	13.3371	+	29.2042i	1.39811	+	3.06144i
$92$	0.00442241	−	0.0307585i	0.000461068	−	0.00320680i
$93$	2.06066	+	0.196769i	0.213680	+	0.0204040i
$94$	−2.40172	+	2.77173i	−0.247718	+	0.285882i
$95$	−0.771735	+	0.606899i	−0.0791783	+	0.0622665i
$96$	−0.304313	+	0.527085i	−0.0310588	+	0.0537954i
$97$	−0.0223946	−	0.0387886i	−0.00227383	−	0.00393839i	0.864886	−	0.501968i	$-0.167390\pi$
$97$	−0.0223946	−	0.0387886i	−0.00227383	−	0.00393839i	−0.867160	+	0.498030i	$0.834057\pi$
$98$	21.6324	+	8.66029i	2.18520	+	0.874821i
$99$	−4.08773	+	3.89765i	−0.410833	+	0.391728i
$100$	−0.107712	+	0.0555292i	−0.0107712	+	0.00555292i
$101$	3.02248	−	1.55819i	0.300748	−	0.155046i	−0.301247	−	0.953546i	$-0.597403\pi$
$101$	3.02248	−	1.55819i	0.300748	−	0.155046i	0.601995	+	0.798500i	$0.294373\pi$
$102$	1.35520	−	1.29218i	0.134185	−	0.127945i
$103$	−14.2211	−	5.69326i	−1.40124	−	0.560973i	−0.456777	−	0.889581i	$-0.650996\pi$
$103$	−14.2211	−	5.69326i	−1.40124	−	0.560973i	−0.944467	+	0.328608i	$0.893421\pi$
$104$	9.18559	+	15.9099i	0.900722	+	1.56010i
$105$	−5.94107	+	10.2902i	−0.579789	+	1.00422i
$106$	4.94661	−	3.89006i	0.480457	−	0.377836i
$107$	5.03413	−	5.80970i	0.486668	−	0.561644i	−0.458304	−	0.888795i	$-0.651543\pi$
$107$	5.03413	−	5.80970i	0.486668	−	0.561644i	0.944972	+	0.327151i	$0.106089\pi$
$108$	0.107218	+	0.0102381i	0.0103171	+	0.000985161i
$109$	0.347644	−	2.41791i	0.0332982	−	0.231594i	−0.966376	−	0.257135i	$-0.917222\pi$
$109$	0.347644	−	2.41791i	0.0332982	−	0.231594i	0.999674	+	0.0255405i	$0.00813069\pi$
$110$	8.43041	+	18.4600i	0.803808	+	1.76009i
$111$	−4.75071	−	4.52979i	−0.450917	−	0.429949i
$112$	19.3652	+	5.68613i	1.82984	+	0.537289i
$113$	−0.00587780	−	0.0169828i	−0.000552937	−	0.00159761i	0.944724	−	0.327867i	$-0.106330\pi$
$113$	−0.00587780	−	0.0169828i	−0.000552937	−	0.00159761i	−0.945277	+	0.326269i	$0.894208\pi$
$114$	0.135779	−	0.559688i	0.0127168	−	0.0524196i
$115$	0.0339757	−	0.713238i	0.00316825	−	0.0665098i
$116$	0.590118	−	0.0563495i	0.0547911	−	0.00523192i
$117$	3.87895	−	5.44722i	0.358609	−	0.503596i
$118$	−4.41351	+	12.7520i	−0.406297	+	1.17392i
$119$	−5.20933	−	3.34784i	−0.477539	−	0.306896i
$120$	−2.82445	+	6.18468i	−0.257836	+	0.564581i
$121$	19.4040	−	7.76820i	1.76400	−	0.706200i
$122$	4.85139	+	3.81517i	0.439224	+	0.345409i
$123$	2.32261	−	0.447647i	0.209423	−	0.0403629i
$124$	0.0525635	+	0.216670i	0.00472034	+	0.0194575i
$125$	8.06755	−	5.18470i	0.721584	−	0.463734i
$126$	−0.991955	−	6.89920i	−0.0883704	−	0.614629i
$127$	−0.809478	−	16.9930i	−0.0718296	−	1.50789i	−0.691128	−	0.722733i	$-0.742886\pi$
$127$	−0.809478	−	16.9930i	−0.0718296	−	1.50789i	0.619298	−	0.785156i	$-0.287417\pi$
$128$	11.9212	+	2.29762i	1.05369	+	0.203083i
$129$	1.05763	+	1.22057i	0.0931192	+	0.107465i
$130$	−13.9372	−	19.5721i	−1.22238	−	1.71659i
$131$	−10.3996	+	3.05360i	−0.908617	+	0.266794i	−0.702459	−	0.711725i	$-0.747914\pi$
$131$	−10.3996	+	3.05360i	−0.908617	+	0.266794i	−0.206158	+	0.978519i	$0.566096\pi$
$132$	−0.540710	−	0.278755i	−0.0470628	−	0.0242625i
$133$	−1.90456			−0.165147
$134$	−6.67924	−	9.82873i	−0.576999	−	0.849073i
$135$	2.47490			0.213005
$136$	−3.14944	−	1.62365i	−0.270062	−	0.139227i
$137$	−12.3705	+	3.63230i	−1.05688	+	0.310329i	−0.763595	−	0.645696i	$-0.776568\pi$
$137$	−12.3705	+	3.63230i	−1.05688	+	0.310329i	−0.293288	+	0.956024i	$0.594749\pi$
$138$	0.242966	+	0.341198i	0.0206826	+	0.0290447i
$139$	−6.10725	−	7.04814i	−0.518010	−	0.597816i	0.435121	−	0.900372i	$-0.356705\pi$
$139$	−6.10725	−	7.04814i	−0.518010	−	0.597816i	−0.953132	+	0.302556i	$0.902160\pi$
$140$	−1.25665	−	0.242199i	−0.106206	−	0.0204695i
$141$	−0.120201	−	2.52334i	−0.0101228	−	0.212503i
$142$	−2.25253	−	15.6667i	−0.189028	−	1.31472i
$143$	−31.7742	+	20.4200i	−2.65709	+	1.70761i
$144$	−0.991086	−	4.08531i	−0.0825905	−	0.340443i
$145$	13.3754	−	2.57791i	1.11077	−	0.214083i
$146$	2.91963	+	2.29602i	0.241630	+	0.190020i
$147$	−14.9004	+	5.96523i	−1.22897	+	0.492004i
$148$	0.293698	−	0.643109i	0.0241418	−	0.0528632i
$149$	8.84819	+	5.68638i	0.724872	+	0.465847i	0.850328	−	0.526252i	$-0.176403\pi$
$149$	8.84819	+	5.68638i	0.724872	+	0.465847i	−0.125457	+	0.992099i	$0.540040\pi$
$150$	0.534250	−	1.54362i	0.0436214	−	0.126036i
$151$	−3.59464	+	5.04796i	−0.292527	+	0.410797i	−0.934518	−	0.355915i	$-0.884169\pi$
$151$	−3.59464	+	5.04796i	−0.292527	+	0.410797i	0.641991	+	0.766712i	$0.278109\pi$
$152$	−1.08488	+	0.103593i	−0.0879953	+	0.00840253i
$153$	−0.0613706	+	1.28833i	−0.00496152	+	0.104155i
$154$	−9.28140	+	38.2585i	−0.747917	+	3.08295i
$155$	1.67561	+	4.84135i	0.134588	+	0.388867i
$156$	0.691074	+	0.202918i	0.0553302	+	0.0162464i
$157$	−6.46694	−	6.16621i	−0.516118	−	0.492117i	0.386661	−	0.922222i	$-0.373628\pi$
$157$	−6.46694	−	6.16621i	−0.516118	−	0.492117i	−0.902779	+	0.430105i	$0.858477\pi$
$158$	−8.24557	−	18.0553i	−0.655983	−	1.43640i
$159$	−0.616880	+	4.29050i	−0.0489218	+	0.340259i
$160$	−1.49947	−	0.143182i	−0.118543	−	0.0113195i
$161$	0.907100	−	1.04685i	0.0714895	−	0.0825032i
$162$	−1.14119	+	0.897440i	−0.0896601	+	0.0705095i
$163$	−4.97225	+	8.61219i	−0.389457	+	0.674559i	−0.992377	−	0.123243i	$-0.960671\pi$
$163$	−4.97225	+	8.61219i	−0.389457	+	0.674559i	0.602920	+	0.797802i	$0.294004\pi$
$164$	0.127381	+	0.220631i	0.00994681	+	0.0172284i
$165$	−12.9772	−	5.19529i	−1.01027	−	0.404453i
$166$	−11.8663	+	11.3144i	−0.921000	+	0.878172i
$167$	17.7379	−	9.14450i	1.37260	−	0.707622i	0.395112	−	0.918633i	$-0.370706\pi$
$167$	17.7379	−	9.14450i	1.37260	−	0.707622i	0.977484	+	0.211010i	$0.0676754\pi$
$168$	−11.7234	+	6.04381i	−0.904476	+	0.466290i
$169$	22.9557	−	21.8883i	1.76583	−	1.68371i
$170$	4.30231	+	1.72238i	0.329972	+	0.132101i
$171$	0.198348	+	0.343549i	0.0151681	+	0.0262719i
$172$	−0.0869750	+	0.150645i	−0.00663178	+	0.0114866i
$173$	1.11823	−	0.879389i	0.0850177	−	0.0668587i	−0.574746	−	0.818332i	$-0.694899\pi$
$173$	1.11823	−	0.879389i	0.0850177	−	0.0668587i	0.659763	+	0.751474i	$0.270657\pi$
$174$	−5.23269	+	6.03884i	−0.396689	+	0.457803i
$175$	−5.37734	−	0.513474i	−0.406489	−	0.0388150i
$176$	−3.37907	+	23.5019i	−0.254707	+	1.77153i
$177$	−3.86121	−	8.45487i	−0.290226	−	0.635507i
$178$	0.304631	+	0.290465i	0.0228331	+	0.0217713i
$179$	−22.0902	−	6.48627i	−1.65110	−	0.484807i	−0.681975	−	0.731376i	$-0.738879\pi$
$179$	−22.0902	−	6.48627i	−1.65110	−	0.484807i	−0.969125	+	0.246569i	$0.920697\pi$
$180$	0.0871836	+	0.251900i	0.00649828	+	0.0187756i
$181$	−5.79746	+	23.8975i	−0.430922	+	1.77628i	0.179027	+	0.983844i	$0.442705\pi$
$181$	−5.79746	+	23.8975i	−0.430922	+	1.77628i	−0.609949	+	0.792441i	$0.708810\pi$
$182$	2.21782	−	46.5579i	0.164396	−	3.45110i
$183$	−4.23192	+	0.404100i	−0.312833	+	0.0298719i
$184$	0.459763	−	0.645646i	0.0338941	−	0.0475977i
$185$	5.31343	−	15.3522i	0.390651	−	1.12871i
$186$	−2.52818	−	1.62477i	−0.185375	−	0.119134i
$187$	3.02625	−	6.62656i	0.221301	−	0.484582i
$188$	0.252596	−	0.101124i	0.0184225	−	0.00737525i
$189$	3.77388	+	2.96782i	0.274510	+	0.215877i
$190$	1.39959	−	0.269749i	0.101537	−	0.0195697i
$191$	−0.785268	−	3.23692i	−0.0568200	−	0.234215i	0.936320	−	0.351149i	$-0.114209\pi$
$191$	−0.785268	−	3.23692i	−0.0568200	−	0.234215i	−0.993140	+	0.116933i	$0.962694\pi$
$192$	−6.32961	+	4.06779i	−0.456800	+	0.293568i
$193$	0.939330	+	6.53319i	0.0676145	+	0.470269i	0.995295	+	0.0968935i	$0.0308906\pi$
$193$	0.939330	+	6.53319i	0.0676145	+	0.470269i	−0.927680	+	0.373376i	$0.878200\pi$
$194$	0.00309400	+	0.0649511i	0.000222136	+	0.00466321i
$195$	16.2510	+	3.13213i	1.16376	+	0.224297i
$196$	−1.13205	−	1.30646i	−0.0808609	−	0.0933185i
$197$	−5.97705	−	8.39359i	−0.425847	−	0.598018i	0.544789	−	0.838573i	$-0.316610\pi$
$197$	−5.97705	−	8.39359i	−0.425847	−	0.598018i	−0.970635	+	0.240555i	$0.922670\pi$
$198$	7.86775	−	2.31018i	0.559137	−	0.164177i
$199$	−4.67401	−	2.40962i	−0.331332	−	0.170813i	0.284531	−	0.958667i	$-0.408162\pi$
$199$	−4.67401	−	2.40962i	−0.331332	−	0.170813i	−0.615863	+	0.787853i	$0.711192\pi$
$200$	−3.09098			−0.218565
$201$	8.00155	+	1.72489i	0.564386	+	0.121664i
$202$	−4.93681			−0.347353
$203$	23.4871	+	12.1084i	1.64847	+	0.849845i
$204$	−0.133291	+	0.0391377i	−0.00933221	+	0.00274018i
$205$	3.39566	+	4.76854i	0.237164	+	0.333050i
$206$	14.5635	+	16.8072i	1.01469	+	1.17101i
$207$	−0.283302	−	0.0546019i	−0.0196908	−	0.00379510i
$208$	−1.33761	−	28.0798i	−0.0927464	−	1.94699i
$209$	−0.318869	−	2.21778i	−0.0220566	−	0.153407i
$210$	14.5120	−	9.32627i	1.00142	−	0.643574i
$211$	−2.77444	−	11.4364i	−0.191000	−	0.787314i	−0.984011	−	0.178107i	$-0.943003\pi$
$211$	−2.77444	−	11.4364i	−0.191000	−	0.787314i	0.793011	−	0.609207i	$-0.208512\pi$
$212$	−0.458427	+	0.0883545i	−0.0314849	+	0.00606821i
$213$	8.56974	+	6.73932i	0.587189	+	0.461770i
$214$	−10.3610	+	4.14791i	−0.708262	+	0.283545i
$215$	−1.66045	+	3.63587i	−0.113242	+	0.247964i
$216$	2.31111	+	1.48526i	0.157251	+	0.101059i
$217$	−3.25051	+	9.39173i	−0.220659	+	0.637552i
$218$	−2.05712	+	2.88882i	−0.139326	+	0.195656i
$219$	−2.54683	+	0.243193i	−0.172099	+	0.0164334i
$220$	0.0716378	−	1.50386i	0.00482982	−	0.101390i
$221$	−2.03344	+	8.38193i	−0.136784	+	0.563830i
$222$	3.11690	+	9.00568i	0.209192	+	0.604422i
$223$	−1.72142	−	0.505456i	−0.115275	−	0.0338478i	0.223586	−	0.974684i	$-0.428224\pi$
$223$	−1.72142	−	0.505456i	−0.115275	−	0.0338478i	−0.338861	+	0.940836i	$0.610042\pi$
$224$	−2.11478	−	2.01644i	−0.141300	−	0.134729i
$225$	0.467395	+	1.02345i	0.0311597	+	0.0682302i
$226$	−0.00371306	+	0.0258249i	−0.000246989	+	0.00171785i
$227$	12.8636	+	1.22832i	0.853786	+	0.0815266i	0.512765	−	0.858529i	$-0.328621\pi$
$227$	12.8636	+	1.22832i	0.853786	+	0.0815266i	0.341021	+	0.940056i	$0.389227\pi$
$228$	−0.0279799	+	0.0322906i	−0.00185302	+	0.00213850i
$229$	18.1629	−	14.2835i	1.20024	−	0.943878i	0.200877	−	0.979616i	$-0.435621\pi$
$229$	18.1629	−	14.2835i	1.20024	−	0.943878i	0.999361	+	0.0357384i	$0.0113783\pi$
$230$	−0.518325	+	0.897765i	−0.0341773	+	0.0591969i
$231$	−13.5585	−	23.4839i	−0.892081	−	1.54513i
$232$	14.0373	+	5.61970i	0.921596	+	0.368951i
$233$	7.53608	−	7.18564i	0.493705	−	0.470747i	−0.401845	−	0.915708i	$-0.631631\pi$
$233$	7.53608	−	7.18564i	0.493705	−	0.470747i	0.895550	+	0.444961i	$0.146782\pi$
$234$	−8.62919	+	4.44866i	−0.564108	+	0.290818i
$235$	5.55708	−	2.86487i	0.362504	−	0.186884i
$236$	0.724535	−	0.690843i	0.0471632	−	0.0449700i
$237$	12.6927	+	5.08139i	0.824479	+	0.330072i
$238$	4.49501	+	7.78558i	0.291368	+	0.504664i
$239$	−11.2696	+	19.5195i	−0.728968	+	1.26261i	0.228352	+	0.973579i	$0.426666\pi$
$239$	−11.2696	+	19.5195i	−0.728968	+	1.26261i	−0.957320	+	0.289031i	$0.906667\pi$
$240$	8.17810	−	6.43133i	0.527894	−	0.415141i
$241$	−11.9896	+	13.8368i	−0.772320	+	0.891305i	−0.996530	−	0.0832358i	$-0.973475\pi$
$241$	−11.9896	+	13.8368i	−0.772320	+	0.891305i	0.224210	+	0.974541i	$0.428020\pi$
$242$	−30.2069	−	2.88441i	−1.94177	−	0.185417i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−0.190209	−	0.416499i	−0.0121769	−	0.0266636i
$245$	−28.7485	−	27.4116i	−1.83667	−	1.75127i
$246$	−3.29491	−	0.967473i	−0.210076	−	0.0616838i
$247$	0.867641	+	2.50688i	0.0552067	+	0.159509i
$248$	−1.34072	+	5.52653i	−0.0851359	+	0.350935i
$249$	0.537368	−	11.2807i	0.0340543	−	0.714888i
$250$	−13.8595	+	1.32343i	−0.876555	+	0.0837008i
$251$	−6.29788	+	8.84414i	−0.397519	+	0.558237i	−0.964022	−	0.265822i	$-0.914357\pi$
$251$	−6.29788	+	8.84414i	−0.397519	+	0.558237i	0.566503	+	0.824060i	$0.308296\pi$
$252$	−0.169127	+	0.488661i	−0.0106540	+	0.0307828i
$253$	1.37088	+	0.881012i	0.0861866	+	0.0553888i
$254$	−10.2601	+	22.4664i	−0.643774	+	1.40967i
$255$	−2.96344	+	1.18638i	−0.185578	+	0.0742942i
$256$	−2.02611	−	1.59335i	−0.126632	−	0.0995845i
$257$	6.11660	−	1.17888i	0.381543	−	0.0735364i	0.00512624	−	0.999987i	$-0.498368\pi$
$257$	6.11660	−	1.17888i	0.381543	−	0.0735364i	0.376417	+	0.926451i	$0.377156\pi$
$258$	−0.552788	−	2.27862i	−0.0344151	−	0.141861i
$259$	26.5120	−	17.0383i	1.64738	−	1.05871i
$260$	0.253682	+	1.76440i	0.0157327	+	0.109423i
$261$	−0.261886	−	5.49767i	−0.0162104	−	0.340297i
$262$	15.4511	+	2.97796i	0.954573	+	0.183979i
$263$	2.53490	+	2.92544i	0.156309	+	0.180390i	0.828503	−	0.559985i	$-0.189193\pi$
$263$	2.53490	+	2.92544i	0.156309	+	0.180390i	−0.672194	+	0.740375i	$0.734648\pi$
$264$	−9.00053	−	12.6395i	−0.553944	−	0.777906i
$265$	−10.2932	+	3.02235i	−0.632306	+	0.185662i
$266$	2.45766	+	1.26701i	0.150689	+	0.0776855i
$267$	−0.289928			−0.0177433
$268$	0.106309	+	0.875177i	0.00649384	+	0.0534599i
$269$	3.09969			0.188991			0.0944956	−	0.995525i	$-0.469876\pi$
$269$	3.09969			0.188991			0.0944956	+	0.995525i	$0.469876\pi$
$270$	−3.19363	−	1.64643i	−0.194358	−	0.100198i
$271$	−26.2427	+	7.70557i	−1.59413	+	0.468080i	−0.953906	−	0.300106i	$-0.902978\pi$
$271$	−26.2427	+	7.70557i	−1.59413	+	0.468080i	−0.640227	+	0.768185i	$0.721160\pi$
$272$	3.14509	+	4.41665i	0.190699	+	0.267799i
$273$	21.0247	+	24.2638i	1.27247	+	1.46851i
$274$	18.3794	+	3.54233i	1.11034	+	0.214000i
$275$	−0.302376	−	6.34766i	−0.0182340	−	0.382778i
$276$	−0.00442241	−	0.0307585i	−0.000266198	−	0.00185145i
$277$	−23.2269	+	14.9270i	−1.39557	+	0.896879i	−0.999770	−	0.0214579i	$-0.993169\pi$
$277$	−23.2269	+	14.9270i	−1.39557	+	0.896879i	−0.395801	+	0.918336i	$0.629533\pi$
$278$	3.19205	+	13.1578i	0.191447	+	0.789153i
$279$	2.03262	−	0.391756i	0.121690	−	0.0234538i
$280$	−25.6590	−	20.1785i	−1.53342	−	1.20589i
$281$	15.7973	−	6.32428i	0.942387	−	0.377275i	0.150961	−	0.988540i	$-0.451763\pi$
$281$	15.7973	−	6.32428i	0.942387	−	0.377275i	0.791426	+	0.611265i	$0.209339\pi$
$282$	−1.52354	+	3.33610i	−0.0907257	+	0.198662i
$283$	10.7920	+	6.93559i	0.641517	+	0.412278i	0.820558	−	0.571564i	$-0.193663\pi$
$283$	10.7920	+	6.93559i	0.641517	+	0.412278i	−0.179041	+	0.983842i	$0.557299\pi$
$284$	−0.384055	+	1.10965i	−0.0227894	+	0.0658458i
$285$	−0.569491	+	0.799738i	−0.0337337	+	0.0473724i
$286$	54.5860	−	5.21233i	3.22774	−	0.308212i
$287$	−0.540350	+	11.3433i	−0.0318959	+	0.669577i
$288$	−0.143489	+	0.591469i	−0.00845516	+	0.0348526i
$289$	5.01606	+	14.4930i	0.295062	+	0.852527i
$290$	−18.9747	−	5.57148i	−1.11423	−	0.327168i
$291$	−0.0324155	−	0.0309081i	−0.00190023	−	0.00181186i
$292$	−0.114470	−	0.250654i	−0.00669885	−	0.0146684i
$293$	1.21665	−	8.46199i	0.0710775	−	0.494355i	−0.922924	−	0.384983i	$-0.874207\pi$
$293$	1.21665	−	8.46199i	0.0710775	−	0.494355i	0.994001	−	0.109371i	$-0.0348837\pi$
$294$	23.1960	+	2.21495i	1.35282	+	0.129178i
$295$	15.0643	−	17.3851i	0.877075	−	1.01220i
$296$	14.1751	−	11.1474i	0.823909	−	0.647929i
$297$	−2.82406	+	4.89141i	−0.163869	+	0.283829i
$298$	−7.63488	−	13.2240i	−0.442277	−	0.766046i
$299$	−1.79115	−	0.717070i	−0.103585	−	0.0414692i
$300$	−0.0877041	+	0.0836257i	−0.00506360	+	0.00482813i
$301$	−6.89197	+	3.55306i	−0.397246	+	0.204795i
$302$	7.99670	−	4.12259i	0.460158	−	0.237228i
$303$	2.46105	−	2.34661i	0.141384	−	0.134809i
$304$	1.54818	+	0.619799i	0.0887943	+	0.0355479i
$305$	−5.26061	−	9.11165i	−0.301222	−	0.521732i
$306$	0.936254	−	1.62164i	0.0535221	−	0.0927029i
$307$	−1.57581	+	1.23923i	−0.0899361	+	0.0707265i	−0.662115	−	0.749403i	$-0.730341\pi$
$307$	−1.57581	+	1.23923i	−0.0899361	+	0.0707265i	0.572179	+	0.820129i	$0.306098\pi$
$308$	1.91262	−	2.20728i	0.108982	−	0.125771i
$309$	−15.2490	−	1.45610i	−0.867485	−	0.0828348i
$310$	1.05850	−	7.36201i	0.0601186	−	0.418134i
$311$	−8.07588	−	17.6837i	−0.457941	−	1.00275i	−0.987952	−	0.154761i	$-0.950539\pi$
$311$	−8.07588	−	17.6837i	−0.457941	−	1.00275i	0.530011	−	0.847991i	$-0.322188\pi$
$312$	13.2959	+	12.6776i	0.752729	+	0.717726i
$313$	−2.15244	−	0.632014i	−0.121663	−	0.0357235i	0.220334	−	0.975424i	$-0.429285\pi$
$313$	−2.15244	−	0.632014i	−0.121663	−	0.0357235i	−0.341997	+	0.939701i	$0.611103\pi$
$314$	4.24290	+	12.2590i	0.239441	+	0.691818i
$315$	−2.80132	+	11.5472i	−0.157836	+	0.650611i
$316$	−0.0700672	+	1.47089i	−0.00394159	+	0.0827441i
$317$	14.0938	−	1.34580i	0.791589	−	0.0755876i	0.308575	−	0.951200i	$-0.400148\pi$
$317$	14.0938	−	1.34580i	0.791589	−	0.0755876i	0.483014	+	0.875612i	$0.339542\pi$
$318$	3.65028	−	5.12610i	0.204698	−	0.287458i
$319$	−10.1675	+	29.3770i	−0.569269	+	1.64479i
$320$	−15.6652	−	10.0674i	−0.875709	−	0.562784i
$321$	3.19343	−	6.99264i	0.178240	−	0.390291i
$322$	−1.86694	+	0.747411i	−0.104041	+	0.0416516i
$323$	−0.402188	−	0.316284i	−0.0223783	−	0.0175985i
$324$	0.105759	−	0.0203835i	0.00587552	−	0.00113241i
$325$	1.77384	+	7.31185i	0.0983947	+	0.405589i
$326$	12.1455	−	7.80543i	0.672676	−	0.432303i
$327$	−0.347644	−	2.41791i	−0.0192247	−	0.133711i
$328$	0.309195	+	6.49080i	0.0170724	+	0.358394i
$329$	11.9092	+	2.29532i	0.656578	+	0.126545i
$330$	13.2897	+	15.3371i	0.731574	+	0.844281i
$331$	−1.36097	−	1.91121i	−0.0748056	−	0.105050i	0.775478	−	0.631375i	$-0.217509\pi$
$331$	−1.36097	−	1.91121i	−0.0748056	−	0.105050i	−0.850284	+	0.526325i	$0.823570\pi$
$332$	1.16711	−	0.342693i	0.0640533	−	0.0188077i
$333$	−5.83446	−	3.00787i	−0.319727	−	0.164831i
$334$	−28.9724			−1.58530
$335$	4.34332	+	19.7868i	0.237301	+	1.08107i
$336$	20.1827			1.10106
$337$	9.08022	+	4.68118i	0.494631	+	0.255000i	0.687447	−	0.726235i	$-0.258732\pi$
$337$	9.08022	+	4.68118i	0.494631	+	0.255000i	−0.192815	+	0.981235i	$0.561762\pi$
$338$	−44.1834	+	12.9734i	−2.40326	+	0.705661i
$339$	−0.0104243	−	0.0146389i	−0.000566171	−	0.000795076i
$340$	−0.225146	−	0.259832i	−0.0122103	−	0.0140914i
$341$	−11.4805	−	2.21268i	−0.621703	−	0.119824i
$342$	−0.0274035	−	0.575270i	−0.00148181	−	0.0311070i
$343$	−6.18361	−	43.0080i	−0.333884	−	2.32221i
$344$	−3.73255	+	2.39876i	−0.201246	+	0.129333i
$345$	−0.168343	−	0.693919i	−0.00906328	−	0.0373594i
$346$	−2.02799	+	0.390863i	−0.109025	+	0.0210129i
$347$	24.5070	+	19.2725i	1.31561	+	1.03460i	0.996210	+	0.0869816i	$0.0277221\pi$
$347$	24.5070	+	19.2725i	1.31561	+	1.03460i	0.319395	+	0.947622i	$0.396520\pi$
$348$	0.550339	−	0.220322i	0.0295013	−	0.0118105i
$349$	−12.5196	+	27.4141i	−0.670158	+	1.46744i	0.202586	+	0.979265i	$0.435066\pi$
$349$	−12.5196	+	27.4141i	−0.670158	+	1.46744i	−0.872744	+	0.488178i	$0.837662\pi$
$350$	6.59737	+	4.23987i	0.352644	+	0.226631i
$351$	2.18717	−	6.31940i	0.116742	−	0.337305i
$352$	1.99400	−	2.80017i	0.106280	−	0.149250i
$353$	−8.59910	+	0.821115i	−0.457684	+	0.0437035i	−0.321352	−	0.946960i	$-0.604137\pi$
$353$	−8.59910	+	0.821115i	−0.457684	+	0.0437035i	−0.136332	+	0.990663i	$0.543531\pi$
$354$	−0.642078	+	13.4789i	−0.0341261	+	0.716395i
$355$	−6.36123	+	26.2214i	−0.337619	+	1.39169i
$356$	−0.0102133	−	0.0295095i	−0.000541305	−	0.00156400i
$357$	−5.94151	−	1.74459i	−0.314458	−	0.0923333i
$358$	24.1903	+	23.0654i	1.27850	+	1.21905i
$359$	−9.27911	−	20.3184i	−0.489733	−	1.07237i	−0.979672	−	0.200608i	$-0.935708\pi$
$359$	−9.27911	−	20.3184i	−0.489733	−	1.07237i	0.489939	−	0.871757i	$-0.337019\pi$
$360$	−0.967612	+	6.72989i	−0.0509977	+	0.354696i
$361$	18.7573	+	1.79111i	0.987227	+	0.0942687i
$362$	23.3789	−	26.9807i	1.22877	−	1.41807i
$363$	16.4295	−	12.9203i	0.862324	−	0.678139i
$364$	−1.72898	+	2.99468i	−0.0906231	+	0.156964i
$365$	−3.16591	−	5.48351i	−0.165711	−	0.287020i
$366$	5.72973	+	2.29384i	0.299498	+	0.119901i
$367$	−14.3330	+	13.6665i	−0.748179	+	0.713387i	−0.964834	−	0.262861i	$-0.915334\pi$
$367$	−14.3330	+	13.6665i	−0.748179	+	0.713387i	0.216655	+	0.976248i	$0.430485\pi$
$368$	−1.07804	+	0.555767i	−0.0561966	+	0.0289714i
$369$	2.10241	−	1.08387i	0.109447	−	0.0564240i
$370$	−17.0695	+	16.2757i	−0.887402	+	0.846136i
$371$	−19.3200	−	7.73457i	−1.00305	−	0.401559i
$372$	0.111477	+	0.193084i	0.00577982	+	0.0100109i
$373$	5.03958	−	8.72881i	0.260940	−	0.451961i	−0.705552	−	0.708658i	$-0.749301\pi$
$373$	5.03958	−	8.72881i	0.260940	−	0.451961i	0.966492	+	0.256697i	$0.0826343\pi$
$374$	−8.31341	+	6.53774i	−0.429876	+	0.338058i
$375$	6.28006	−	7.24758i	0.324301	−	0.374263i
$376$	6.90861	+	0.659692i	0.356284	+	0.0340210i
$377$	5.23799	−	36.4310i	0.269770	−	1.87629i
$378$	−2.89550	−	6.34027i	−0.148929	−	0.326108i
$379$	0.0464316	+	0.0442725i	0.00238503	+	0.00227412i	0.691271	−	0.722596i	$-0.257051\pi$
$379$	0.0464316	+	0.0442725i	0.00238503	+	0.00227412i	−0.688886	+	0.724870i	$0.741900\pi$
$380$	−0.101461	−	0.0297915i	−0.00520482	−	0.00152827i
$381$	−5.56418	−	16.0767i	−0.285062	−	0.823632i
$382$	−1.14005	+	4.69934i	−0.0583299	+	0.240439i
$383$	−1.37177	+	28.7969i	−0.0700940	+	1.47145i	0.640558	+	0.767910i	$0.278703\pi$
$383$	−1.37177	+	28.7969i	−0.0700940	+	1.47145i	−0.710652	+	0.703544i	$0.751600\pi$
$384$	12.0856	−	1.15404i	0.616741	−	0.0588916i
$385$	38.9286	−	54.6676i	1.98398	−	2.78612i
$386$	3.13409	−	9.05535i	0.159521	−	0.460905i
$387$	1.35866	+	0.873160i	0.0690648	+	0.0443852i
$388$	0.00200399	−	0.00438812i	0.000101737	−	0.000222773i
$389$	−27.3398	+	10.9452i	−1.38618	+	0.554944i	−0.940361	−	0.340178i	$-0.889513\pi$
$389$	−27.3398	+	10.9452i	−1.38618	+	0.554944i	−0.445821	+	0.895122i	$0.647088\pi$
$390$	−18.8868	−	14.8527i	−0.956369	−	0.752097i
$391$	0.365399	−	0.0704250i	0.0184790	−	0.00356154i
$392$	−10.3954	−	42.8504i	−0.525046	−	2.16427i
$393$	−9.11804	+	5.85981i	−0.459944	+	0.295588i
$394$	2.12898	+	14.8074i	0.107256	+	0.745984i
$395$	1.61003	+	33.7986i	0.0810093	+	1.70059i
$396$	−0.597342	−	0.115128i	−0.0300176	−	0.00578541i
$397$	16.0193	+	18.4873i	0.803987	+	0.927851i	0.998593	−	0.0530306i	$-0.0168881\pi$
$397$	16.0193	+	18.4873i	0.803987	+	0.927851i	−0.194605	+	0.980882i	$0.562343\pi$
$398$	4.42837	+	6.21878i	0.221974	+	0.311719i
$399$	−1.82742	+	0.536578i	−0.0914852	+	0.0268625i
$400$	4.20404	+	2.16733i	0.210202	+	0.108367i
$401$	−34.4946			−1.72258			−0.861289	−	0.508115i	$-0.830343\pi$
$401$	−34.4946			−1.72258			−0.861289	+	0.508115i	$0.830343\pi$
$402$	−9.17776	−	7.54884i	−0.457745	−	0.376502i
$403$	13.8427			0.689553
$404$	0.325538	+	0.167827i	0.0161961	+	0.00834969i
$405$	2.37465	−	0.697260i	0.117997	−	0.0346471i
$406$	−22.2527	−	31.2496i	−1.10438	−	1.55089i
$407$	24.2791	+	28.0195i	1.20347	+	1.38888i
$408$	−3.47930	−	0.670581i	−0.172251	−	0.0331987i
$409$	−0.573291	−	12.0349i	−0.0283474	−	0.595086i	−0.967696	−	0.252121i	$-0.918872\pi$
$409$	−0.573291	−	12.0349i	−0.0283474	−	0.595086i	0.939348	−	0.342965i	$-0.111431\pi$
$410$	−1.20951	−	8.41233i	−0.0597334	−	0.415455i
$411$	−10.8461	+	6.97034i	−0.534997	+	0.343822i
$412$	−0.388973	−	1.60337i	−0.0191633	−	0.0789923i
$413$	43.8185	−	8.44533i	2.15617	−	0.415567i
$414$	0.329250	+	0.258925i	0.0161818	+	0.0127255i
$415$	25.9482	−	10.3881i	1.27375	−	0.509931i
$416$	−1.69074	+	3.70219i	−0.0828951	+	0.181515i
$417$	−7.84556	−	5.04203i	−0.384199	−	0.246909i
$418$	−1.06391	+	3.07397i	−0.0520376	+	0.150353i
$419$	−0.528463	+	0.742123i	−0.0258171	+	0.0362551i	−0.827283	−	0.561786i	$-0.810115\pi$
$419$	−0.528463	+	0.742123i	−0.0258171	+	0.0362551i	0.801466	+	0.598041i	$0.204054\pi$
$420$	−1.27398	+	0.121650i	−0.0621638	+	0.00593593i
$421$	0.707923	−	14.8611i	0.0345021	−	0.724287i	−0.913656	−	0.406488i	$-0.866753\pi$
$421$	0.707923	−	14.8611i	0.0345021	−	0.724287i	0.948158	−	0.317799i	$-0.102944\pi$
$422$	−4.02791	+	16.6033i	−0.196076	+	0.808236i
$423$	−0.826239	−	2.38726i	−0.0401731	−	0.116073i
$424$	−11.4258	−	3.35491i	−0.554885	−	0.162929i
$425$	−1.05027	−	1.00143i	−0.0509454	−	0.0485764i
$426$	−6.57511	−	14.3975i	−0.318565	−	0.697560i
$427$	2.90466	−	20.2024i	0.140567	−	0.977662i
$428$	0.824221	+	0.0787036i	0.0398402	+	0.00380428i
$429$	−24.7341	+	28.5447i	−1.19417	+	1.37815i
$430$	4.56142	−	3.58714i	0.219971	−	0.172987i
$431$	2.76353	−	4.78658i	0.133115	−	0.230561i	−0.791761	−	0.610831i	$-0.790835\pi$
$431$	2.76353	−	4.78658i	0.133115	−	0.230561i	0.924876	+	0.380270i	$0.124169\pi$
$432$	−2.10191	−	3.64061i	−0.101128	−	0.175159i
$433$	−1.44535	−	0.578633i	−0.0694593	−	0.0278073i	0.336673	−	0.941622i	$-0.390698\pi$
$433$	−1.44535	−	0.578633i	−0.0694593	−	0.0278073i	−0.406132	+	0.913814i	$0.633123\pi$
$434$	10.4423	−	9.95675i	0.501248	−	0.477939i
$435$	12.1074	−	6.24178i	0.580504	−	0.299271i
$436$	0.233854	−	0.120560i	0.0111996	−	0.00577378i
$437$	0.0828337	−	0.0789818i	0.00396247	−	0.00377821i
$438$	3.44823	+	1.38046i	0.164763	+	0.0659610i
$439$	3.73738	+	6.47333i	0.178375	+	0.308955i	0.941324	−	0.337504i	$-0.109583\pi$
$439$	3.73738	+	6.47333i	0.178375	+	0.308955i	−0.762949	+	0.646459i	$0.776249\pi$
$440$	19.2010	−	33.2572i	0.915374	−	1.58547i
$441$	−12.6163	+	9.92154i	−0.600774	+	0.472454i
$442$	8.20004	−	9.46335i	0.390036	−	0.450126i
$443$	−28.0865	−	2.68193i	−1.33443	−	0.127423i	−0.596670	−	0.802486i	$-0.703510\pi$
$443$	−28.0865	−	2.68193i	−1.33443	−	0.127423i	−0.737759	+	0.675064i	$0.764116\pi$
$444$	0.100616	−	0.699803i	0.00477504	−	0.0332112i
$445$	−0.298078	−	0.652700i	−0.0141303	−	0.0309409i
$446$	1.88508	+	1.79742i	0.0892612	+	0.0851104i
$447$	10.0918	+	2.96322i	0.477326	+	0.140156i
$448$	−11.8148	−	34.1365i	−0.558195	−	1.61280i
$449$	−6.99701	+	28.8421i	−0.330209	+	1.36114i	0.528611	+	0.848864i	$0.322713\pi$
$449$	−6.99701	+	28.8421i	−0.330209	+	1.36114i	−0.858820	+	0.512277i	$0.828802\pi$
$450$	0.0777229	−	1.63160i	0.00366389	−	0.0769145i
$451$	−13.2993	+	1.26993i	−0.626240	+	0.0597987i
$452$	0.00112276	−	0.00157669i	5.28101e−5	−	7.41615e-5i
$453$	−2.02685	+	5.85621i	−0.0952299	+	0.275149i
$454$	−15.7821	−	10.1425i	−0.740690	−	0.476013i
$455$	−33.0081	+	72.2776i	−1.54744	+	3.38843i
$456$	−1.01175	+	0.405043i	−0.0473795	+	0.0189679i
$457$	−13.8974	−	10.9291i	−0.650095	−	0.511240i	0.237784	−	0.971318i	$-0.423579\pi$
$457$	−13.8974	−	10.9291i	−0.650095	−	0.511240i	−0.887879	+	0.460078i	$0.847821\pi$
$458$	−32.9396	+	6.34859i	−1.53917	+	0.296650i
$459$	0.304079	+	1.25343i	0.0141932	+	0.0585052i
$460$	0.0646983	−	0.0415791i	0.00301657	−	0.00193863i
$461$	3.09287	+	21.5114i	0.144049	+	1.00189i	0.925724	+	0.378199i	$0.123457\pi$
$461$	3.09287	+	21.5114i	0.144049	+	1.00189i	−0.781675	+	0.623686i	$0.785634\pi$
$462$	1.87321	+	39.3236i	0.0871498	+	1.82950i
$463$	−10.0582	−	1.93857i	−0.467446	−	0.0900928i	−0.0499110	−	0.998754i	$-0.515894\pi$
$463$	−10.0582	−	1.93857i	−0.467446	−	0.0900928i	−0.417535	+	0.908661i	$0.637106\pi$
$464$	−15.1518	−	17.4861i	−0.703403	−	0.811770i
$465$	2.97170	+	4.17317i	0.137809	+	0.193526i
$466$	−14.5049	+	4.25901i	−0.671925	+	0.197295i
$467$	5.48071	+	2.82550i	0.253617	+	0.130749i	0.580348	−	0.814369i	$-0.302917\pi$
$467$	5.48071	+	2.82550i	0.253617	+	0.130749i	−0.326731	+	0.945118i	$0.605947\pi$
$468$	0.720249			0.0332935
$469$	−17.1047	+	35.3806i	−0.789823	+	1.63372i
$470$	−9.07675			−0.418679
$471$	−7.94220	−	4.09449i	−0.365957	−	0.188664i
$472$	24.5006	−	7.19402i	1.12773	−	0.331132i
$473$	−5.29126	−	7.43054i	−0.243293	−	0.341657i
$474$	−12.9983	−	15.0009i	−0.597033	−	0.689013i
$475$	−0.438269	−	0.0844694i	−0.0201092	−	0.00387572i
$476$	−0.0317349	−	0.666197i	−0.00145456	−	0.0305351i
$477$	0.616880	+	4.29050i	0.0282450	+	0.196448i
$478$	27.5277	−	17.6909i	1.25909	−	0.809165i
$479$	−3.45660	−	14.2483i	−0.157936	−	0.651021i	−0.994643	−	0.103370i	$-0.967037\pi$
$479$	−3.45660	−	14.2483i	−0.157936	−	0.651021i	0.836707	−	0.547651i	$-0.184478\pi$
$480$	−1.47907	+	0.285066i	−0.0675098	+	0.0130114i
$481$	−34.5044	−	27.1346i	−1.57327	−	1.23723i
$482$	24.6764	−	9.87895i	1.12398	−	0.449974i
$483$	0.575424	−	1.26000i	0.0261827	−	0.0573322i
$484$	1.89382	+	1.21708i	0.0860826	+	0.0553219i
$485$	0.0362551	−	0.104752i	0.00164626	−	0.00475655i
$486$	−0.842123	+	1.18260i	−0.0381995	+	0.0536437i
$487$	−31.4751	+	3.00551i	−1.42627	+	0.136193i	−0.779459	−	0.626454i	$-0.784506\pi$
$487$	−31.4751	+	3.00551i	−1.42627	+	0.136193i	−0.646816	+	0.762646i	$0.723900\pi$
$488$	0.555705	−	11.6657i	0.0251556	−	0.528081i
$489$	−2.34451	+	9.66418i	−0.106022	+	0.437029i
$490$	18.8616	+	54.4971i	0.852082	+	2.46193i
$491$	30.5453	+	8.96891i	1.37849	+	0.404761i	0.885243	−	0.465128i	$-0.153992\pi$
$491$	30.5453	+	8.96891i	1.37849	+	0.404761i	0.493247	+	0.869890i	$0.335810\pi$
$492$	0.184380	+	0.175806i	0.00831251	+	0.00792596i
$493$	2.94898	+	6.45736i	0.132815	+	0.290825i
$494$	0.548097	−	3.81210i	0.0246600	−	0.171514i
$495$	−13.9152	−	1.32874i	−0.625443	−	0.0597226i
$496$	5.69861	−	6.57655i	0.255875	−	0.295296i
$497$	−41.1438	+	32.3558i	−1.84555	+	1.45136i
$498$	−8.19794	+	14.1992i	−0.367358	+	0.636283i
$499$	−2.02558	−	3.50840i	−0.0906773	−	0.157058i	0.817119	−	0.576469i	$-0.195570\pi$
$499$	−2.02558	−	3.50840i	−0.0906773	−	0.157058i	−0.907796	+	0.419411i	$0.862237\pi$
$500$	0.958902	+	0.383886i	0.0428834	+	0.0171679i
$501$	14.4430	−	13.7714i	0.645267	−	0.615261i
$502$	14.0104	−	7.22286i	0.625315	−	0.322372i
$503$	16.0546	−	8.27671i	0.715838	−	0.369040i	−0.0615137	−	0.998106i	$-0.519593\pi$
$503$	16.0546	−	8.27671i	0.715838	−	0.369040i	0.777352	+	0.629066i	$0.216562\pi$
$504$	−9.54574	+	9.10184i	−0.425201	+	0.405428i
$505$	7.81303	+	3.12786i	0.347675	+	0.139188i
$506$	−1.18290	−	2.04884i	−0.0525863	−	0.0910822i
$507$	15.8592	−	27.4690i	0.704334	−	1.21994i
$508$	1.44030	−	1.13267i	0.0639032	−	0.0502540i
$509$	22.8501	−	26.3705i	1.01281	−	1.16885i	0.0272367	−	0.999629i	$-0.491329\pi$
$509$	22.8501	−	26.3705i	1.01281	−	1.16885i	0.985578	−	0.169222i	$-0.0541253\pi$
$510$	4.61328	+	0.440515i	0.204280	+	0.0195063i
$511$	1.74806	−	12.1581i	0.0773298	−	0.537841i
$512$	−8.53223	−	18.6830i	−0.377075	−	0.825679i
$513$	0.287103	+	0.273752i	0.0126759	+	0.0120865i
$514$	−8.67714	−	2.54784i	−0.382732	−	0.112380i
$515$	−12.3996	−	35.8263i	−0.546392	−	1.57870i
$516$	−0.0410103	+	0.169047i	−0.00180538	+	0.00744186i
$517$	−0.678912	+	14.2521i	−0.0298585	+	0.626807i
$518$	−45.5460	+	4.34912i	−2.00118	+	0.191089i
$519$	0.825185	−	1.15881i	0.0362216	−	0.0508661i
$520$	−14.8707	+	42.9662i	−0.652125	+	1.88419i
$521$	−9.41941	−	6.05349i	−0.412672	−	0.265208i	0.317791	−	0.948161i	$-0.397059\pi$
$521$	−9.41941	−	6.05349i	−0.412672	−	0.265208i	−0.730463	+	0.682953i	$0.760695\pi$
$522$	−3.31939	+	7.26845i	−0.145286	+	0.318131i
$523$	32.9207	−	13.1795i	1.43952	−	0.576298i	0.485021	−	0.874502i	$-0.338812\pi$
$523$	32.9207	−	13.1795i	1.43952	−	0.576298i	0.954502	+	0.298204i	$0.0963876\pi$
$524$	−0.917626	−	0.721629i	−0.0400867	−	0.0315245i
$525$	−5.30418	+	1.02230i	−0.231494	+	0.0446167i
$526$	−1.32491	−	5.46135i	−0.0577687	−	0.238126i
$527$	−2.24607	+	1.44346i	−0.0978401	+	0.0628780i
$528$	3.37907	+	23.5019i	0.147055	+	1.02279i
$529$	−1.09042	−	22.8908i	−0.0474097	−	0.995252i
$530$	15.2930	+	2.94749i	0.664286	+	0.128031i
$531$	−6.08681	−	7.02456i	−0.264145	−	0.304840i
$532$	−0.118989	−	0.167096i	−0.00515881	−	0.00724453i
$533$	15.1769	−	4.45633i	0.657383	−	0.193025i
$534$	0.374125	+	0.192875i	0.0161900	+	0.00834651i
$535$	19.0254			0.822538
$536$	−7.81879	+	21.0839i	−0.337720	+	0.910686i
$537$	−23.0228			−0.993507
$538$	−3.99985	−	2.06207i	−0.172446	−	0.0889020i
$539$	86.9810	−	25.5399i	3.74654	−	1.10008i
$540$	0.154621	+	0.217134i	0.00665381	+	0.00934397i
$541$	16.1874	+	18.6813i	0.695952	+	0.803171i	0.988200	−	0.153171i	$-0.0489486\pi$
$541$	16.1874	+	18.6813i	0.695952	+	0.803171i	−0.292248	+	0.956343i	$0.594403\pi$
$542$	38.9899	+	7.51469i	1.67476	+	0.322784i
$543$	1.17007	+	24.5628i	0.0502125	+	1.05409i
$544$	−0.111717	−	0.777008i	−0.00478982	−	0.0333139i
$545$	5.08591	−	3.26851i	0.217856	−	0.140008i
$546$	−10.9889	−	45.2968i	−0.470281	−	1.93852i
$547$	6.00679	−	1.15771i	0.256832	−	0.0495002i	−0.0592100	−	0.998246i	$-0.518858\pi$
$547$	6.00679	−	1.15771i	0.256832	−	0.0495002i	0.316042	+	0.948745i	$0.397646\pi$
$548$	−1.09153	−	0.858390i	−0.0466279	−	0.0366686i
$549$	−3.94665	+	1.58000i	−0.168439	+	0.0674328i
$550$	−3.83259	+	8.39221i	−0.163422	+	0.357845i
$551$	1.83678	+	1.18042i	0.0782493	+	0.0502878i
$552$	0.259239	−	0.749023i	0.0110340	−	0.0318805i
$553$	−38.0751	+	53.4690i	−1.61912	+	2.27373i
$554$	39.9024	−	3.81021i	1.69529	−	0.161881i
$555$	0.772999	−	16.2272i	0.0328120	−	0.688808i
$556$	0.236812	−	0.976153i	0.0100431	−	0.0413981i
$557$	5.21116	+	15.0567i	0.220804	+	0.637971i	0.999938	+	0.0111141i	$0.00353781\pi$
$557$	5.21116	+	15.0567i	0.220804	+	0.637971i	−0.779134	+	0.626857i	$0.784341\pi$
$558$	−2.88352	−	0.846679i	−0.122069	−	0.0358428i
$559$	7.81642	+	7.45294i	0.330599	+	0.315226i
$560$	20.7501	+	45.4363i	0.876851	+	1.92004i
$561$	1.03675	−	7.21073i	0.0437715	−	0.304437i
$562$	−24.5921	−	2.34827i	−1.03736	−	0.0990556i
$563$	14.0492	−	16.2137i	0.592104	−	0.683325i	−0.378058	−	0.925782i	$-0.623408\pi$
$563$	14.0492	−	16.2137i	0.592104	−	0.683325i	0.970162	+	0.242457i	$0.0779534\pi$
$564$	0.213874	−	0.168193i	0.00900574	−	0.00708219i
$565$	0.0222384	−	0.0385181i	0.000935578	−	0.00162047i
$566$	−9.31214	−	16.1291i	−0.391418	−	0.677957i
$567$	4.45715	+	1.78437i	0.187183	+	0.0749366i
$568$	−21.6765	+	20.6685i	−0.909524	+	0.867229i
$569$	−10.2231	+	5.27035i	−0.428573	+	0.220945i	−0.658997	−	0.752146i	$-0.729019\pi$
$569$	−10.2231	+	5.27035i	−0.428573	+	0.220945i	0.230424	+	0.973090i	$0.425989\pi$
$570$	1.26690	−	0.653133i	0.0530646	−	0.0273567i
$571$	−3.61901	+	3.45072i	−0.151451	+	0.144408i	−0.762017	−	0.647557i	$-0.775791\pi$
$571$	−3.61901	+	3.45072i	−0.151451	+	0.144408i	0.610566	+	0.791966i	$0.290942\pi$
$572$	−3.77665	−	1.51194i	−0.157910	−	0.0632175i
$573$	−1.66540	−	2.88456i	−0.0695733	−	0.120504i
$574$	8.24344	−	14.2781i	0.344074	−	0.595954i
$575$	0.255166	−	0.200665i	0.0106412	−	0.00836830i
$576$	−4.92719	+	5.68628i	−0.205299	+	0.236928i
$577$	15.9513	+	1.52316i	0.664061	+	0.0634102i	0.421643	−	0.906762i	$-0.361453\pi$
$577$	15.9513	+	1.52316i	0.664061	+	0.0634102i	0.242418	+	0.970172i	$0.422059\pi$
$578$	3.16869	−	22.0387i	0.131800	−	0.916690i
$579$	2.74189	+	6.00391i	0.113949	+	0.249514i
$580$	1.06181	+	1.01243i	0.0440892	+	0.0420390i
$581$	52.0245	+	15.2758i	2.15834	+	0.633746i
$582$	0.0212675	+	0.0614484i	0.000881566	+	0.00254712i
$583$	5.77195	−	23.7923i	0.239050	−	0.985377i
$584$	0.334431	−	7.02056i	0.0138388	−	0.290513i
$585$	16.4752	−	1.57319i	0.681165	−	0.0650434i
$586$	−7.19931	+	10.1100i	−0.297401	+	0.417641i
$587$	−5.66172	+	16.3585i	−0.233684	+	0.675186i	0.765800	+	0.643078i	$0.222343\pi$
$587$	−5.66172	+	16.3585i	−0.233684	+	0.675186i	−0.999484	+	0.0321073i	$0.989778\pi$
$588$	−1.45427	−	0.934602i	−0.0599731	−	0.0385423i
$589$	−0.341128	+	0.746967i	−0.0140559	+	0.0307782i
$590$	−31.0044	+	12.4123i	−1.27643	+	0.511006i
$591$	−8.09968	−	6.36966i	−0.333176	−	0.262013i
$592$	−27.0958	+	5.22230i	−1.11363	+	0.214635i
$593$	−1.13190	−	4.66574i	−0.0464814	−	0.191599i	0.943837	−	0.330410i	$-0.107187\pi$
$593$	−1.13190	−	4.66574i	−0.0464814	−	0.191599i	−0.990319	+	0.138811i	$0.955672\pi$
$594$	6.89820	−	4.43320i	0.283036	−	0.181896i
$595$	−2.18104	−	15.1694i	−0.0894138	−	0.621887i
$596$	0.0539025	+	1.13155i	0.00220793	+	0.0463502i
$597$	−5.16355	−	0.995192i	−0.211330	−	0.0407305i
$598$	1.83428	+	2.11688i	0.0750095	+	0.0865656i
$599$	−7.32306	−	10.2838i	−0.299212	−	0.420184i	0.637411	−	0.770524i	$-0.280006\pi$
$599$	−7.32306	−	10.2838i	−0.299212	−	0.420184i	−0.936623	+	0.350340i	$0.886066\pi$
$600$	−2.96577	+	0.870828i	−0.121077	+	0.0355514i
$601$	−15.0713	−	7.76982i	−0.614773	−	0.316938i	0.122566	−	0.992460i	$-0.460888\pi$
$601$	−15.0713	−	7.76982i	−0.614773	−	0.316938i	−0.737339	+	0.675523i	$0.763918\pi$
$602$	11.2571			0.458806
$603$	8.16339	−	0.599278i	0.332439	−	0.0244045i
$604$	−0.667458			−0.0271585
$605$	45.9781	+	23.7033i	1.86927	+	0.963678i
$606$	−4.73684	+	1.39086i	−0.192421	+	0.0564998i
$607$	−17.4875	−	24.5577i	−0.709794	−	0.996766i	−0.999217	−	0.0395647i	$-0.987403\pi$
$607$	−17.4875	−	24.5577i	−0.709794	−	0.996766i	0.289423	−	0.957201i	$-0.406537\pi$
$608$	−0.158109	−	0.182468i	−0.00641218	−	0.00740005i
$609$	25.9470	+	5.00088i	1.05143	+	0.202646i
$610$	0.726797	+	15.2574i	0.0294272	+	0.617752i
$611$	−2.40415	−	16.7212i	−0.0972615	−	0.676468i
$612$	−0.116865	+	0.0751046i	−0.00472399	+	0.00303592i
$613$	−0.547500	−	2.25683i	−0.0221133	−	0.0911524i	0.959686	−	0.281076i	$-0.0906912\pi$
$613$	−0.547500	−	2.25683i	−0.0221133	−	0.0911524i	−0.981799	+	0.189923i	$0.939176\pi$
$614$	2.85783	−	0.550801i	0.115333	−	0.0222285i
$615$	4.60157	+	3.61872i	0.185553	+	0.145921i
$616$	69.1599	−	27.6874i	2.78653	−	1.11556i
$617$	−6.14778	+	13.4618i	−0.247500	+	0.541950i	−0.992084	−	0.125579i	$-0.959921\pi$
$617$	−6.14778	+	13.4618i	−0.247500	+	0.541950i	0.744583	+	0.667530i	$0.232648\pi$
$618$	18.7087	+	12.0234i	0.752575	+	0.483651i
$619$	13.2533	−	38.2930i	0.532696	−	1.53912i	−0.282105	−	0.959384i	$-0.591033\pi$
$619$	13.2533	−	38.2930i	0.532696	−	1.53912i	0.814801	−	0.579741i	$-0.196846\pi$
$620$	−0.320069	+	0.449475i	−0.0128543	+	0.0180513i
$621$	−0.287209	+	0.0274252i	−0.0115253	+	0.00110053i
$622$	−1.34293	+	28.1917i	−0.0538468	+	1.13038i
$623$	0.328167	−	1.35272i	0.0131477	−	0.0541957i
$624$	−9.19443	−	26.5656i	−0.368072	−	1.06347i
$625$	28.1705	+	8.27159i	1.12682	+	0.330864i
$626$	2.35708	+	2.24747i	0.0942077	+	0.0898269i
$627$	−0.930775	−	2.03811i	−0.0371716	−	0.0813944i
$628$	0.136965	−	0.952611i	0.00546549	−	0.0380133i
$629$	8.42805	+	0.804781i	0.336048	+	0.0320887i
$630$	11.2966	−	13.0370i	0.450068	−	0.519406i
$631$	−17.0139	+	13.3799i	−0.677314	+	0.532645i	−0.896503	−	0.443037i	$-0.853901\pi$
$631$	−17.0139	+	13.3799i	−0.677314	+	0.532645i	0.219190	+	0.975682i	$0.429659\pi$
$632$	−18.7801	+	32.5280i	−0.747031	+	1.29390i
$633$	−5.88406	−	10.1915i	−0.233870	−	0.405075i
$634$	−19.0821	−	7.63931i	−0.757846	−	0.303396i
$635$	30.4719	−	29.0549i	1.20924	−	1.15301i
$636$	−0.414965	+	0.213929i	−0.0164544	+	0.00848285i
$637$	−95.3990	+	49.1816i	−3.77984	+	1.94865i
$638$	32.6632	−	31.1443i	1.29315	−	1.23301i
$639$	10.1213	+	4.05195i	0.400392	+	0.160293i
$640$	15.0234	+	26.0212i	0.593851	+	1.02858i
$641$	−13.0320	+	22.5721i	−0.514732	+	0.891543i	0.485121	+	0.874447i	$0.338775\pi$
$641$	−13.0320	+	22.5721i	−0.514732	+	0.891543i	−0.999854	+	0.0170959i	$0.994558\pi$
$642$	−8.77268	+	6.89891i	−0.346230	+	0.272278i
$643$	21.5107	−	24.8246i	0.848297	−	0.978987i	−0.151658	−	0.988433i	$-0.548461\pi$
$643$	21.5107	−	24.8246i	0.848297	−	0.978987i	0.999955	+	0.00944557i	$0.00300666\pi$
$644$	0.148516	+	0.0141816i	0.00585236	+	0.000558833i
$645$	−0.568844	+	3.95639i	−0.0223982	+	0.155783i
$646$	0.308578	+	0.675691i	0.0121408	+	0.0265847i
$647$	−2.36686	−	2.25680i	−0.0930510	−	0.0887240i	0.642126	−	0.766599i	$-0.278053\pi$
$647$	−2.36686	−	2.25680i	−0.0930510	−	0.0887240i	−0.735177	+	0.677875i	$0.762901\pi$
$648$	2.63594	+	0.773982i	0.103549	+	0.0304049i
$649$	17.1705	+	49.6109i	0.674001	+	1.94740i
$650$	2.57525	−	10.6153i	0.101009	−	0.416367i
$651$	−0.472885	+	9.92708i	−0.0185338	+	0.389073i
$652$	−1.06623	+	0.101813i	−0.0417568	+	0.00398729i
$653$	−5.47991	+	7.69546i	−0.214446	+	0.301147i	−0.907761	−	0.419487i	$-0.862210\pi$
$653$	−5.47991	+	7.69546i	−0.214446	+	0.301147i	0.693316	+	0.720634i	$0.256149\pi$
$654$	−1.15992	+	3.35136i	−0.0453564	+	0.131049i
$655$	−22.5662	−	14.5024i	−0.881736	−	0.566657i
$656$	4.13068	−	9.04494i	0.161276	−	0.353145i
$657$	−2.37515	+	0.950866i	−0.0926633	+	0.0370968i
$658$	−13.8408	−	10.8845i	−0.539571	−	0.424323i
$659$	−2.58016	+	0.497286i	−0.100509	+	0.0193715i	−0.239258	−	0.970956i	$-0.576904\pi$
$659$	−2.58016	+	0.497286i	−0.100509	+	0.0193715i	0.138749	+	0.990328i	$0.455692\pi$
$660$	−0.354951	−	1.46313i	−0.0138165	−	0.0569522i
$661$	16.4637	−	10.5806i	0.640362	−	0.411536i	−0.179771	−	0.983709i	$-0.557536\pi$
$661$	16.4637	−	10.5806i	0.640362	−	0.411536i	0.820133	+	0.572173i	$0.193899\pi$
$662$	0.484766	+	3.37162i	0.0188410	+	0.131042i
$663$	0.410397	+	8.61529i	0.0159385	+	0.334590i
$664$	30.4651	+	5.87167i	1.18228	+	0.227865i
$665$	−3.08675	−	3.56230i	−0.119699	−	0.138140i
$666$	5.52784	+	7.76276i	0.214199	+	0.300801i
$667$	−1.52364	+	0.447381i	−0.0589955	+	0.0173226i
$668$	1.91047	+	0.984916i	0.0739183	+	0.0381075i
$669$	−1.79410			−0.0693639
$670$	7.55856	−	28.4225i	0.292013	−	1.09806i
$671$	24.0111			0.926939
$672$	−2.59722	−	1.33896i	−0.100190	−	0.0516514i
$673$	−23.1393	+	6.79432i	−0.891955	+	0.261902i	−0.695427	−	0.718596i	$-0.744785\pi$
$673$	−23.1393	+	6.79432i	−0.891955	+	0.261902i	−0.196528	+	0.980498i	$0.562967\pi$
$674$	−8.60301	−	12.0812i	−0.331376	−	0.465352i
$675$	0.736802	+	0.850315i	0.0283595	+	0.0327286i
$676$	3.35453	+	0.646533i	0.129020	+	0.0248666i
$677$	0.268150	+	5.62915i	0.0103058	+	0.216346i	0.998146	+	0.0608709i	$0.0193878\pi$
$677$	0.268150	+	5.62915i	0.0103058	+	0.216346i	−0.987840	+	0.155475i	$0.950309\pi$
$678$	0.00371306	+	0.0258249i	0.000142599	+	0.000991799i
$679$	0.180899	−	0.116257i	0.00694228	−	0.00446153i
$680$	−2.06746	−	8.52220i	−0.0792836	−	0.326812i
$681$	12.6886	−	2.44552i	0.486227	−	0.0937126i
$682$	13.3425	+	10.4927i	0.510911	+	0.401785i
$683$	−16.3836	+	6.55899i	−0.626900	+	0.250973i	−0.663287	−	0.748365i	$-0.730839\pi$
$683$	−16.3836	+	6.55899i	−0.626900	+	0.250973i	0.0363875	+	0.999338i	$0.488415\pi$
$684$	−0.0177493	+	0.0388654i	−0.000678660	+	0.00148606i
$685$	−26.8429	−	17.2509i	−1.02562	−	0.659123i
$686$	−20.6317	+	59.6114i	−0.787722	+	2.27597i
$687$	13.4031	−	18.8220i	0.511359	−	0.718103i
$688$	6.75861	−	0.645369i	0.257670	−	0.0246045i
$689$	−1.37923	+	28.9536i	−0.0525444	+	1.10304i
$690$	−0.244399	+	1.00743i	−0.00930412	+	0.0383521i
$691$	12.0916	+	34.9364i	0.459986	+	1.32904i	0.901884	+	0.431978i	$0.142184\pi$
$691$	12.0916	+	34.9364i	0.459986	+	1.32904i	−0.441898	+	0.897065i	$0.645695\pi$
$692$	0.147015	+	0.0431675i	0.00558867	+	0.00164098i
$693$	−19.6254	−	18.7128i	−0.745509	−	0.710841i
$694$	−18.8029	−	41.1727i	−0.713750	−	1.56289i
$695$	3.28477	−	22.8461i	0.124598	−	0.866600i
$696$	15.0520	+	1.43729i	0.570544	+	0.0544803i
$697$	−1.99786	+	2.30565i	−0.0756742	+	0.0873327i
$698$	34.3926	−	27.0466i	1.30178	−	1.02373i
$699$	5.20639	−	9.01773i	0.196924	−	0.341082i
$700$	−0.290903	−	0.503858i	−0.0109951	−	0.0190441i
$701$	20.5527	+	8.22808i	0.776266	+	0.310770i	0.725755	−	0.687953i	$-0.241491\pi$
$701$	20.5527	+	8.22808i	0.776266	+	0.310770i	0.0505115	+	0.998723i	$0.483915\pi$
$702$	−7.02631	+	6.69958i	−0.265191	+	0.252859i
$703$	2.31451	−	1.19321i	0.0872935	−	0.0450029i
$704$	37.7725	−	19.4731i	1.42360	−	0.733918i
$705$	4.52485	−	4.31444i	0.170416	−	0.162491i
$706$	11.6426	+	4.66099i	0.438174	+	0.175418i
$707$	8.16297	+	14.1387i	0.307000	+	0.531740i
$708$	0.500553	−	0.866984i	0.0188119	−	0.0325832i
$709$	−2.64988	+	2.08389i	−0.0995183	+	0.0782620i	−0.666678	−	0.745346i	$-0.732285\pi$
$709$	−2.64988	+	2.08389i	−0.0995183	+	0.0782620i	0.567160	+	0.823608i	$0.308042\pi$
$710$	25.6524	−	29.6044i	0.962716	−	1.11103i
$711$	13.6101	+	1.29961i	0.510420	+	0.0487392i
$712$	0.113353	−	0.788389i	0.00424809	−	0.0295461i
$713$	−0.248101	−	0.543265i	−0.00929145	−	0.0203454i
$714$	6.50638	+	6.20382i	0.243495	+	0.232172i
$715$	−89.6905	−	26.3355i	−3.35424	−	0.984893i
$716$	−0.811027	−	2.34331i	−0.0303095	−	0.0875736i
$717$	−5.31380	+	21.9038i	−0.198448	+	0.818012i
$718$	−1.54302	+	32.3919i	−0.0575849	+	1.20886i
$719$	−45.4199	+	4.33708i	−1.69388	+	0.161746i	−0.896891	−	0.442251i	$-0.854180\pi$
$719$	−45.4199	+	4.33708i	−1.69388	+	0.161746i	−0.796987	+	0.603997i	$0.793574\pi$
$720$	6.03492	−	8.47486i	0.224908	−	0.315839i
$721$	24.0540	−	69.4994i	0.895817	−	2.58829i
$722$	−23.0130	−	14.7896i	−0.856456	−	0.550411i
$723$	−7.60570	+	16.6542i	−0.282859	+	0.619375i
$724$	−2.45883	+	0.984369i	−0.0913818	+	0.0365838i
$725$	4.86771	+	3.82801i	0.180782	+	0.142169i
$726$	−29.7959	+	5.74269i	−1.10583	+	0.213131i
$727$	3.78080	+	15.5847i	0.140222	+	0.578004i	0.997956	+	0.0639092i	$0.0203568\pi$
$727$	3.78080	+	15.5847i	0.140222	+	0.578004i	−0.857734	+	0.514095i	$0.828128\pi$
$728$	−74.1995	+	47.6851i	−2.75002	+	1.76733i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	0.437396	+	9.18208i	0.0161888	+	0.339844i
$731$	−2.04543	−	0.394223i	−0.0756528	−	0.0145809i
$732$	−0.299845	−	0.346040i	−0.0110826	−	0.0127900i
$733$	−2.98807	−	4.19615i	−0.110367	−	0.154988i	0.755698	−	0.654920i	$-0.227298\pi$
$733$	−2.98807	−	4.19615i	−0.110367	−	0.154988i	−0.866065	+	0.499932i	$0.833358\pi$
$734$	27.5871	−	8.10031i	1.01826	−	0.298988i
$735$	−35.3067	−	18.2019i	−1.30231	−	0.671387i
$736$	0.175598			0.00647262
$737$	−44.0630	−	13.9942i	−1.62308	−	0.515483i
$738$	−3.43401			−0.126408
$739$	11.9898	+	6.18116i	0.441051	+	0.227378i	0.664425	−	0.747355i	$-0.268677\pi$
$739$	11.9898	+	6.18116i	0.441051	+	0.227378i	−0.223374	+	0.974733i	$0.571707\pi$
$740$	1.67887	−	0.492962i	0.0617166	−	0.0181216i
$741$	1.53877	+	2.16090i	0.0565280	+	0.0793825i
$742$	19.7852	+	22.8334i	0.726339	+	0.838240i
$743$	−32.4212	−	6.24868i	−1.18942	−	0.229242i	−0.444117	−	0.895969i	$-0.646483\pi$
$743$	−32.4212	−	6.24868i	−1.18942	−	0.229242i	−0.745302	+	0.666727i	$0.767695\pi$
$744$	0.270590	+	5.68039i	0.00992033	+	0.208253i
$745$	3.70455	+	25.7657i	0.135724	+	0.943982i
$746$	−12.3100	+	7.91113i	−0.450699	+	0.289647i
$747$	−2.66255	−	10.9752i	−0.0974176	−	0.401561i
$748$	0.770445	−	0.148491i	0.0281702	−	0.00542937i
$749$	29.0111	+	22.8146i	1.06004	+	0.833626i
$750$	−12.9253	+	5.17450i	−0.471965	+	0.188946i
$751$	13.7804	−	30.1748i	0.502853	−	1.10110i	−0.472678	−	0.881235i	$-0.656713\pi$
$751$	13.7804	−	30.1748i	0.502853	−	1.10110i	0.975531	−	0.219860i	$-0.0705601\pi$
$752$	−8.93383	−	5.74143i	−0.325783	−	0.209368i
$753$	−3.55109	+	10.2602i	−0.129409	+	0.373903i
$754$	−30.9949	+	43.5262i	−1.12877	+	1.58513i
$755$	−15.2676	+	1.45788i	−0.555645	+	0.0530577i
$756$	−0.0246047	+	0.516516i	−0.000894864	+	0.0187855i
$757$	10.2136	−	42.1010i	0.371219	−	1.53019i	−0.413598	−	0.910460i	$-0.635728\pi$
$757$	10.2136	−	42.1010i	0.371219	−	1.53019i	0.784817	−	0.619727i	$-0.212757\pi$
$758$	−0.0304634	−	0.0880181i	−0.00110648	−	0.00319696i
$759$	1.56356	+	0.459103i	0.0567537	+	0.0166644i
$760$	−1.95204	−	1.86127i	−0.0708080	−	0.0675153i
$761$	10.4483	+	22.8786i	0.378751	+	0.829349i	0.998990	+	0.0449360i	$0.0143084\pi$
$761$	10.4483	+	22.8786i	0.378751	+	0.829349i	−0.620239	+	0.784413i	$0.712964\pi$
$762$	−3.51495	+	24.4470i	−0.127333	+	0.885621i
$763$	11.6748	+	1.11481i	0.422656	+	0.0403588i
$764$	0.234930	−	0.271123i	0.00849946	−	0.00980890i
$765$	−2.50916	+	1.97322i	−0.0907188	+	0.0713421i
$766$	20.9273	−	36.2471i	0.756134	−	1.30966i
$767$	−31.0781	−	53.8289i	−1.12217	−	1.94365i
$768$	−2.39294	−	0.957989i	−0.0863478	−	0.0345684i
$769$	−30.4521	+	29.0360i	−1.09813	+	1.04707i	−0.0994862	+	0.995039i	$0.531720\pi$
$769$	−30.4521	+	29.0360i	−1.09813	+	1.04707i	−0.998646	+	0.0520276i	$0.983432\pi$
$770$	−86.6013	+	44.6461i	−3.12089	+	1.60893i
$771$	5.53670	−	2.85437i	0.199400	−	0.102798i
$772$	−0.514501	+	0.490576i	−0.0185173	+	0.0176562i
$773$	11.0623	+	4.42867i	0.397882	+	0.159288i	0.561970	−	0.827158i	$-0.310044\pi$
$773$	11.0623	+	4.42867i	0.397882	+	0.159288i	−0.164088	+	0.986446i	$0.552468\pi$
$774$	−1.17236	−	2.03058i	−0.0421395	−	0.0729878i
$775$	−1.16452	+	2.01702i	−0.0418310	+	0.0724534i
$776$	0.0967206	−	0.0760619i	0.00347207	−	0.00273046i
$777$	20.6379	−	23.8174i	0.740380	−	0.854444i
$778$	42.5607	+	4.06406i	1.52588	+	0.145703i
$779$	−0.133538	+	0.928779i	−0.00478450	+	0.0332769i
$780$	0.740496	+	1.62146i	0.0265140	+	0.0580576i
$781$	−44.5655	−	42.4931i	−1.59468	−	1.52052i
$782$	−0.518364	−	0.152205i	−0.0185367	−	0.00544285i
$783$	−1.80015	−	5.20119i	−0.0643321	−	0.185875i
$784$	−15.9071	+	65.5698i	−0.568110	+	2.34178i
$785$	1.05225	−	22.0895i	0.0375564	−	0.788406i
$786$	15.6642	−	1.49575i	0.558724	−	0.0533517i
$787$	1.53459	−	2.15503i	0.0547021	−	0.0768184i	−0.786319	−	0.617821i	$-0.788016\pi$
$787$	1.53459	−	2.15503i	0.0547021	−	0.0768184i	0.841021	+	0.541003i	$0.181955\pi$
$788$	0.362989	−	1.04879i	0.0129309	−	0.0373615i
$789$	3.25641	+	2.09277i	0.115931	+	0.0745046i
$790$	20.4070	−	44.6850i	0.726047	−	1.58982i
$791$	0.0801002	−	0.0320673i	0.00284804	−	0.00114018i
$792$	−12.1969	−	9.59174i	−0.433398	−	0.340828i
$793$	−27.9147	+	5.38011i	−0.991279	+	0.191053i
$794$	−8.37276	−	34.5130i	−0.297138	−	1.22482i
$795$	−9.02475	+	5.79986i	−0.320075	+	0.205700i
$796$	−0.0806042	−	0.560614i	−0.00285694	−	0.0198705i
$797$	−2.40602	−	50.5087i	−0.0852258	−	1.78911i	−0.487032	−	0.873384i	$-0.661920\pi$
$797$	−2.40602	−	50.5087i	−0.0852258	−	1.78911i	0.401806	−	0.915725i	$-0.368383\pi$
$798$	2.71507	+	0.523286i	0.0961123	+	0.0185241i
$799$	2.13371	+	2.46243i	0.0754852	+	0.0871146i
$800$	−0.397212	−	0.557806i	−0.0140436	−	0.0197214i
$801$	−0.278184	+	0.0816822i	−0.00982915	+	0.00288610i
$802$	44.5120	+	22.9476i	1.57178	+	0.810306i
$803$	14.4502			0.509937
$804$	0.348568	+	0.809776i	0.0122931	+	0.0285586i
$805$	3.42818			0.120827
$806$	−17.8627	−	9.20885i	−0.629186	−	0.324368i
$807$	2.97413	−	0.873282i	0.104694	−	0.0307410i
$808$	5.41883	+	7.60969i	0.190634	+	0.267708i
$809$	−17.2113	−	19.8629i	−0.605118	−	0.698344i	0.367692	−	0.929948i	$-0.380148\pi$
$809$	−17.2113	−	19.8629i	−0.605118	−	0.698344i	−0.972810	+	0.231604i	$0.925603\pi$
$810$	−3.52811	−	0.679988i	−0.123965	−	0.0238923i
$811$	0.319267	+	6.70224i	0.0112110	+	0.235347i	0.997517	+	0.0704232i	$0.0224350\pi$
$811$	0.319267	+	6.70224i	0.0112110	+	0.235347i	−0.986306	+	0.164924i	$0.947262\pi$
$812$	0.405039	+	2.81711i	0.0142141	+	0.0988611i
$813$	−23.0088	+	14.7869i	−0.806955	+	0.518598i
$814$	−12.6898	−	52.3083i	−0.444779	−	1.83340i
$815$	−24.1669	+	4.65778i	−0.846529	+	0.163155i
$816$	4.26200	+	3.35168i	0.149200	+	0.117332i
$817$	−0.594790	+	0.238118i	−0.0208091	+	0.00833070i
$818$	−7.26642	+	15.9112i	−0.254064	+	0.556323i
$819$	27.0089	+	17.3576i	0.943768	+	0.606523i
$820$	−0.206220	+	0.595834i	−0.00720153	+	0.0208074i
$821$	6.93308	−	9.73615i	0.241966	−	0.339794i	−0.675678	−	0.737197i	$-0.736149\pi$
$821$	6.93308	−	9.73615i	0.241966	−	0.339794i	0.917644	+	0.397403i	$0.130088\pi$
$822$	18.6328	−	1.77922i	0.649895	−	0.0620575i
$823$	1.21154	−	25.4335i	0.0422318	−	0.886555i	−0.874005	−	0.485917i	$-0.838486\pi$
$823$	1.21154	−	25.4335i	0.0422318	−	0.886555i	0.916237	−	0.400637i	$-0.131211\pi$
$824$	9.92142	−	40.8967i	0.345629	−	1.42470i
$825$	−2.07847	−	6.00534i	−0.0723630	−	0.209079i
$826$	−62.1620	−	18.2524i	−2.16289	−	0.635082i
$827$	−10.6943	−	10.1970i	−0.371877	−	0.354584i	0.480977	−	0.876733i	$-0.340282\pi$
$827$	−10.6943	−	10.1970i	−0.371877	−	0.354584i	−0.852854	+	0.522149i	$0.825131\pi$
$828$	−0.0129089	−	0.0282666i	−0.000448617	−	0.000982334i
$829$	4.78810	−	33.3019i	0.166297	−	1.15662i	−0.720158	−	0.693810i	$-0.755931\pi$
$829$	4.78810	−	33.3019i	0.166297	−	1.15662i	0.886455	−	0.462814i	$-0.153160\pi$
$830$	−40.3944	−	3.85720i	−1.40211	−	0.133885i
$831$	−18.0806	+	20.8662i	−0.627210	+	0.723839i
$832$	−39.5499	+	31.1024i	−1.37115	+	1.07828i
$833$	10.3506	−	17.9278i	0.358629	−	0.621163i
$834$	6.76974	+	11.7255i	0.234417	+	0.406022i
$835$	45.8519	+	18.3563i	1.58677	+	0.635247i
$836$	0.174655	−	0.166533i	0.00604056	−	0.00575967i
$837$	1.83992	−	0.948543i	0.0635968	−	0.0327864i
$838$	1.17563	−	0.606079i	0.0406115	−	0.0209367i
$839$	−24.8375	+	23.6825i	−0.857487	+	0.817612i	−0.984699	−	0.174264i	$-0.944245\pi$
$839$	−24.8375	+	23.6825i	−0.857487	+	0.817612i	0.127212	+	0.991875i	$0.459397\pi$
$840$	−30.3046	−	12.1321i	−1.04561	−	0.418598i
$841$	−0.646477	−	1.11973i	−0.0222923	−	0.0386114i
$842$	−10.7999	+	18.7059i	−0.372189	+	0.644649i
$843$	13.3756	−	10.5187i	0.460681	−	0.362284i
$844$	0.830033	−	0.957909i	0.0285709	−	0.0329726i
$845$	78.1446	+	7.46191i	2.68826	+	0.256697i
$846$	−0.521943	+	3.63019i	−0.0179448	+	0.124809i
$847$	41.6861	+	91.2797i	1.43235	+	3.13641i
$848$	13.1878	+	12.5746i	0.452872	+	0.431812i
$849$	12.3088	+	3.61419i	0.422437	+	0.124039i
$850$	0.689070	+	1.99094i	0.0236349	+	0.0682886i
$851$	−0.446495	+	1.84048i	−0.0153057	+	0.0630908i
$852$	−0.0558723	+	1.17290i	−0.00191415	+	0.0401830i
$853$	−25.1386	+	2.40045i	−0.860730	+	0.0821897i	−0.516079	−	0.856541i	$-0.672609\pi$
$853$	−25.1386	+	2.40045i	−0.860730	+	0.0821897i	−0.344651	+	0.938731i	$0.612003\pi$
$854$	−17.1878	+	24.1369i	−0.588156	+	0.825949i
$855$	−0.321110	+	0.927787i	−0.0109817	+	0.0317297i
$856$	17.7663	+	11.4177i	0.607238	+	0.390248i
$857$	4.50827	−	9.87174i	0.154000	−	0.337212i	−0.816870	−	0.576823i	$-0.804292\pi$
$857$	4.50827	−	9.87174i	0.154000	−	0.337212i	0.970869	+	0.239610i	$0.0770197\pi$
$858$	50.9064	−	20.3798i	1.73792	−	0.695757i
$859$	−20.8695	−	16.4119i	−0.712056	−	0.559967i	0.195088	−	0.980786i	$-0.437501\pi$
$859$	−20.8695	−	16.4119i	−0.712056	−	0.559967i	−0.907145	+	0.420818i	$0.861743\pi$
$860$	−0.422729	+	0.0814743i	−0.0144149	+	0.00277825i
$861$	2.67733	+	11.0361i	0.0912431	+	0.376109i
$862$	−6.75035	+	4.33819i	−0.229918	+	0.147759i
$863$	−5.45666	−	37.9519i	−0.185747	−	1.29190i	−0.842871	−	0.538115i	$-0.819137\pi$
$863$	−5.45666	−	37.9519i	−0.185747	−	1.29190i	0.657125	−	0.753782i	$-0.271773\pi$
$864$	0.0289595	+	0.607936i	0.000985224	+	0.0206824i
$865$	3.45715	+	0.666311i	0.117547	+	0.0226553i
$866$	1.48016	+	1.70819i	0.0502978	+	0.0580468i
$867$	8.89601	+	12.4927i	0.302124	+	0.424274i
$868$	−1.02706	+	0.301571i	−0.0348606	+	0.0102360i
$869$	−68.6371	−	35.3849i	−2.32835	−	1.20035i
$870$	−19.7758			−0.670461
$871$	54.3620	+	6.39618i	1.84199	+	0.216726i
$872$	6.71085			0.227258
$873$	−0.0398102	−	0.0205236i	−0.00134737	−	0.000694619i
$874$	−0.159432	+	0.0468134i	−0.00539286	+	0.00158349i
$875$	26.7068	+	37.5045i	0.902856	+	1.26788i
$876$	−0.180451	−	0.208251i	−0.00609687	−	0.00703616i
$877$	32.0927	+	6.18536i	1.08369	+	0.208865i	0.699675	−	0.714461i	$-0.253328\pi$
$877$	32.0927	+	6.18536i	1.08369	+	0.208865i	0.384018	+	0.923326i	$0.374540\pi$
$878$	−0.516350	−	10.8395i	−0.0174260	−	0.365816i
$879$	−1.21665	−	8.46199i	−0.0410366	−	0.285416i
$880$	−49.4346	+	31.7697i	−1.66644	+	1.07096i
$881$	11.9533	+	49.2722i	0.402717	+	1.66002i	0.706827	+	0.707387i	$0.250126\pi$
$881$	11.9533	+	49.2722i	0.402717	+	1.66002i	−0.304109	+	0.952637i	$0.598359\pi$
$882$	22.8804	−	4.40984i	0.770423	−	0.148487i
$883$	−19.8641	−	15.6213i	−0.668481	−	0.525699i	0.225251	−	0.974301i	$-0.427680\pi$
$883$	−19.8641	−	15.6213i	−0.668481	−	0.525699i	−0.893732	+	0.448602i	$0.851922\pi$
$884$	−0.862425	+	0.345263i	−0.0290065	+	0.0116125i
$885$	9.55610	−	20.9249i	0.321225	−	0.703384i
$886$	34.4588	+	22.1453i	1.15767	+	0.743987i
$887$	−2.80338	+	8.09982i	−0.0941281	+	0.271965i	−0.982230	−	0.187681i	$-0.939903\pi$
$887$	−2.80338	+	8.09982i	−0.0941281	+	0.271965i	0.888102	+	0.459647i	$0.152024\pi$
$888$	10.4603	−	14.6894i	0.351024	−	0.492945i
$889$	81.3072	−	7.76390i	2.72696	−	0.260393i
$890$	−0.0495672	+	1.04054i	−0.00166150	+	0.0348791i
$891$	−1.33159	+	5.48891i	−0.0446101	+	0.183885i
$892$	−0.0632009	−	0.182607i	−0.00211612	−	0.00611414i
$893$	0.961542	+	0.282334i	0.0321768	+	0.00944795i
$894$	−11.0513	−	10.5373i	−0.369609	−	0.352422i
$895$	−23.6700	−	51.8300i	−0.791200	−	1.73249i
$896$	−8.29519	+	57.6943i	−0.277123	+	1.92743i
$897$	−1.92062	−	0.183397i	−0.0641277	−	0.00612345i
$898$	28.2162	−	32.5632i	0.941587	−	1.08665i
$899$	8.95570	−	7.04284i	0.298689	−	0.234892i
$900$	−0.0605914	+	0.104947i	−0.00201971	+	0.00349825i
$901$	−2.79537	−	4.84172i	−0.0931273	−	0.161301i
$902$	18.0063	+	7.20865i	0.599546	+	0.240022i
$903$	−5.61178	+	5.35082i	−0.186748	+	0.178064i
$904$	0.0438825	−	0.0226230i	0.00145951	−	0.000752430i
$905$	−54.0940	+	27.8874i	−1.79814	+	0.927008i
$906$	6.51131	−	6.20852i	0.216324	−	0.206264i
$907$	16.5511	+	6.62607i	0.549571	+	0.220015i	0.629794	−	0.776762i	$-0.283139\pi$
$907$	16.5511	+	6.62607i	0.549571	+	0.220015i	−0.0802236	+	0.996777i	$0.525563\pi$
$908$	0.695892	+	1.20532i	0.0230940	+	0.0400000i
$909$	1.70025	−	2.94491i	0.0563936	−	0.0976765i
$910$	90.6765	−	71.3088i	3.00590	−	2.36386i
$911$	−26.5240	+	30.6103i	−0.878778	+	1.01416i	0.120990	+	0.992654i	$0.461393\pi$
$911$	−26.5240	+	30.6103i	−0.878778	+	1.01416i	−0.999769	+	0.0215106i	$0.993152\pi$
$912$	1.66009	+	0.158519i	0.0549710	+	0.00524909i
$913$	−9.07786	+	63.1379i	−0.300433	+	2.08956i
$914$	10.6628	+	23.3482i	0.352693	+	0.772290i
$915$	−7.61457	−	7.26048i	−0.251730	−	0.240024i
$916$	2.38789	+	0.701148i	0.0788981	+	0.0231666i
$917$	−17.0196	−	49.1749i	−0.562037	−	1.62390i
$918$	0.441460	−	1.81972i	0.0145704	−	0.0600599i
$919$	1.98727	−	41.7179i	0.0655539	−	1.37615i	−0.691302	−	0.722565i	$-0.742963\pi$
$919$	1.98727	−	41.7179i	0.0655539	−	1.37615i	0.756856	−	0.653581i	$-0.226734\pi$
$920$	1.95276	−	0.186466i	0.0643807	−	0.00614761i
$921$	−1.16285	+	1.63299i	−0.0383170	+	0.0538088i
$922$	10.3194	−	29.8160i	0.339851	−	0.981936i
$923$	61.3319	+	39.4156i	2.01876	+	1.29738i
$924$	1.21328	−	2.65672i	0.0399141	−	0.0873996i
$925$	6.85648	−	2.74492i	0.225440	−	0.0902525i
$926$	11.6896	+	9.19279i	0.384143	+	0.302094i
$927$	−15.0415	+	2.89902i	−0.494029	+	0.0952162i
$928$	0.789749	+	3.25539i	0.0259248	+	0.106863i
$929$	6.45579	−	4.14888i	0.211808	−	0.136120i	−0.430436	−	0.902621i	$-0.641640\pi$
$929$	6.45579	−	4.14888i	0.211808	−	0.136120i	0.642243	+	0.766501i	$0.278004\pi$
$930$	−1.05850	−	7.36201i	−0.0347095	−	0.241410i
$931$	−0.302956	−	6.35983i	−0.00992898	−	0.208435i
$932$	1.10125	+	0.212249i	0.0360726	+	0.00695243i
$933$	−12.7308	−	14.6922i	−0.416789	−	0.481000i
$934$	−5.19268	−	7.29209i	−0.169910	−	0.238605i
$935$	17.2990	−	5.07945i	0.565739	−	0.166116i
$936$	16.3290	+	8.41816i	0.533729	+	0.275156i
$937$	−5.23902			−0.171151			−0.0855757	−	0.996332i	$-0.527273\pi$
$937$	−5.23902			−0.171151			−0.0855757	+	0.996332i	$0.527273\pi$
$938$	45.6090	−	34.2764i	1.48919	−	1.11916i
$939$	−2.24331			−0.0732077
$940$	0.598530	+	0.308564i	0.0195219	+	0.0100642i
$941$	−15.0964	+	4.43272i	−0.492130	+	0.144502i	−0.518376	−	0.855153i	$-0.673463\pi$
$941$	−15.0964	+	4.43272i	−0.492130	+	0.144502i	0.0262454	+	0.999656i	$0.491645\pi$
$942$	7.52480	+	10.5671i	0.245171	+	0.344295i
$943$	−0.446905	−	0.515755i	−0.0145532	−	0.0167953i
$944$	−38.3676	−	7.39474i	−1.24876	−	0.240678i
$945$	0.565375	+	11.8687i	0.0183916	+	0.386088i
$946$	1.88471	+	13.1084i	0.0612771	+	0.426192i
$947$	27.9196	−	17.9429i	0.907267	−	0.583065i	−0.00167031	−	0.999999i	$-0.500532\pi$
$947$	27.9196	−	17.9429i	0.907267	−	0.583065i	0.908937	+	0.416934i	$0.136895\pi$
$948$	0.347169	+	1.43105i	0.0112755	+	0.0464784i
$949$	−16.7994	+	3.23782i	−0.545332	+	0.105104i
$950$	0.509351	+	0.400558i	0.0165255	+	0.0129958i
$951$	13.1438	−	5.26198i	0.426217	−	0.170631i
$952$	7.06694	−	15.4744i	0.229041	−	0.501529i
$953$	22.6968	+	14.5863i	0.735221	+	0.472498i	0.853901	−	0.520435i	$-0.174230\pi$
$953$	22.6968	+	14.5863i	0.735221	+	0.472498i	−0.118681	+	0.992932i	$0.537866\pi$
$954$	2.05823	−	5.94686i	0.0666376	−	0.192537i
$955$	4.78165	−	6.71489i	0.154731	−	0.217289i
$956$	−2.41660	+	0.230758i	−0.0781586	+	0.00746324i
$957$	−1.47916	+	31.0515i	−0.0478146	+	1.00375i
$958$	−5.01827	+	20.6856i	−0.162133	+	0.668321i
$959$	−20.2451	−	58.4944i	−0.653748	−	1.88888i
$960$	−17.8669	−	5.24620i	−0.576652	−	0.169320i
$961$	−19.3345	−	18.4354i	−0.623695	−	0.594692i
$962$	26.4734	+	57.9687i	0.853538	+	1.86899i
$963$	1.09402	−	7.60908i	0.0352543	−	0.245199i
$964$	−1.96302	−	0.187446i	−0.0632247	−	0.00603723i
$965$	−10.6973	+	12.3454i	−0.344359	+	0.397411i
$966$	−1.58075	+	1.24311i	−0.0508598	+	0.0399966i
$967$	−22.9606	+	39.7690i	−0.738364	+	1.27888i	0.214868	+	0.976643i	$0.431068\pi$
$967$	−22.9606	+	39.7690i	−0.738364	+	1.27888i	−0.953232	+	0.302240i	$0.902266\pi$
$968$	28.7102	+	49.7274i	0.922779	+	1.59830i
$969$	−0.475004	−	0.190163i	−0.0152593	−	0.00610892i
$970$	−0.116470	+	0.111054i	−0.00373963	+	0.00356573i
$971$	−49.7458	+	25.6458i	−1.59642	+	0.823012i	−0.596630	+	0.802516i	$0.703494\pi$
$971$	−49.7458	+	25.6458i	−1.59642	+	0.823012i	−0.999790	+	0.0204953i	$0.993476\pi$
$972$	0.0957328	−	0.0493537i	0.00307063	−	0.00158302i
$973$	32.4050	−	30.8981i	1.03886	−	0.990549i
$974$	42.6151	+	17.0605i	1.36548	+	0.546654i
$975$	3.76197	+	6.51592i	0.120479	+	0.208677i
$976$	−8.93557	+	15.4769i	−0.286021	+	0.495402i
$977$	−14.4945	+	11.3986i	−0.463720	+	0.364674i	−0.822516	−	0.568743i	$-0.807430\pi$
$977$	−14.4945	+	11.3986i	−0.463720	+	0.364674i	0.358795	+	0.933416i	$0.383188\pi$
$978$	9.45446	−	10.9110i	0.302320	−	0.348896i
$979$	1.63013	+	0.155659i	0.0520993	+	0.00497488i
$980$	0.608872	−	4.23479i	0.0194497	−	0.135276i
$981$	−1.01477	−	2.22203i	−0.0323990	−	0.0709439i
$982$	−33.4493	−	31.8938i	−1.06741	−	1.01777i
$983$	−21.8535	−	6.41676i	−0.697017	−	0.204663i	−0.0860176	−	0.996294i	$-0.527414\pi$
$983$	−21.8535	−	6.41676i	−0.697017	−	0.204663i	−0.611000	+	0.791631i	$0.709232\pi$
$984$	2.12534	+	6.14076i	0.0677533	+	0.195760i
$985$	6.01231	−	24.7831i	0.191568	−	0.789655i
$986$	0.490384	−	10.2944i	0.0156170	−	0.327841i
$987$	12.0735	−	1.15288i	0.384304	−	0.0366966i
$988$	−0.165734	+	0.232741i	−0.00527271	+	0.00740448i
$989$	0.152403	−	0.440338i	0.00484612	−	0.0140019i
$990$	17.0723	+	10.9717i	0.542595	+	0.348704i
$991$	9.69812	−	21.2359i	0.308071	−	0.674581i	−0.690752	−	0.723092i	$-0.742720\pi$
$991$	9.69812	−	21.2359i	0.308071	−	0.674581i	0.998823	+	0.0485109i	$0.0154476\pi$
$992$	−1.16963	+	0.468247i	−0.0371356	+	0.0148669i
$993$	−1.84429	−	1.45037i	−0.0585268	−	0.0460260i
$994$	74.6169	−	14.3812i	2.36671	−	0.456145i
$995$	−3.06827	−	12.6476i	−0.0972708	−	0.400956i
$996$	1.02328	−	0.657624i	0.0324240	−	0.0208376i
$997$	2.05111	+	14.2658i	0.0649592	+	0.451801i	0.996178	+	0.0873416i	$0.0278372\pi$
$997$	2.05111	+	14.2658i	0.0649592	+	0.451801i	−0.931219	+	0.364460i	$0.881254\pi$
$998$	0.279850	+	5.87478i	0.00885850	+	0.185963i
$999$	−6.44554	−	1.24228i	−0.203928	−	0.0393039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.m.a.19.2	✓	100
3.2	odd	2		603.2.z.b.19.4		100
67.60	even	33	inner	201.2.m.a.127.2	yes	100
201.194	odd	66		603.2.z.b.127.4		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.m.a.19.2	✓	100	1.1	even	1	trivial
201.2.m.a.127.2	yes	100	67.60	even	33	inner
603.2.z.b.19.4		100	3.2	odd	2
603.2.z.b.127.4		100	201.194	odd	66

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29041 - 0.665251i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.0624755 + 0.0877346i) q^{4} +(1.62071 + 1.87040i) q^{5} +(-1.42556 - 0.274754i) q^{6} +(0.228443 + 4.79562i) q^{7} +(0.390970 + 2.71926i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-1.29041 - 0.665251i) q^{2} +(0.959493 - 0.281733i) q^{3} +(0.0624755 + 0.0877346i) q^{4} +(1.62071 + 1.87040i) q^{5} +(-1.42556 - 0.274754i) q^{6} +(0.228443 + 4.79562i) q^{7} +(0.390970 + 2.71926i) q^{8} +(0.841254 - 0.540641i) q^{9} +(-0.847092 - 3.49176i) q^{10} +(-5.54605 + 1.06891i) q^{11} +(0.0846625 + 0.0665793i) q^{12} +(6.20817 - 2.48538i) q^{13} +(2.89550 - 6.34027i) q^{14} +(2.08202 + 1.33803i) q^{15} +(1.37493 - 3.97260i) q^{16} +(-0.748151 + 1.05063i) q^{17} +(-1.44522 + 0.138002i) q^{18} +(-0.0188756 + 0.396247i) q^{19} +(-0.0628442 + 0.259047i) q^{20} +(1.57027 + 4.53700i) q^{21} +(7.86775 + 2.31018i) q^{22} +(-0.208809 - 0.199099i) q^{23} +(1.14124 + 2.49896i) q^{24} +(-0.160122 + 1.11368i) q^{25} +(-9.66446 - 0.922844i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-0.406469 + 0.319651i) q^{28} +(2.75195 - 4.76652i) q^{29} +(-1.79652 - 3.11167i) q^{30} +(1.92175 + 0.769353i) q^{31} +(-0.440483 + 0.419999i) q^{32} +(-5.02025 + 2.58812i) q^{33} +(1.66435 - 0.858033i) q^{34} +(-8.59950 + 8.19961i) q^{35} +(0.0999906 + 0.0400302i) q^{36} +(-3.28208 - 5.68473i) q^{37} +(0.287961 - 0.498763i) q^{38} +(5.25648 - 4.13375i) q^{39} +(-4.45246 + 5.13841i) q^{40} +(2.35465 + 0.224841i) q^{41} +(0.991955 - 6.89920i) q^{42} +(0.670915 + 1.46910i) q^{43} +(-0.440273 - 0.419799i) q^{44} +(2.37465 + 0.697260i) q^{45} +(0.136997 + 0.395828i) q^{46} +(0.595574 - 2.45499i) q^{47} +(0.200025 - 4.19905i) q^{48} +(-15.9775 + 1.52566i) q^{49} +(0.947496 - 1.33057i) q^{50} +(-0.421849 + 1.21885i) q^{51} +(0.605912 + 0.389396i) q^{52} +(-1.80067 + 3.94291i) q^{53} +(-1.34780 + 0.539577i) q^{54} +(-10.9879 - 8.64095i) q^{55} +(-12.9512 + 2.49614i) q^{56} +(0.0935248 + 0.385515i) q^{57} +(-6.72207 + 4.32001i) q^{58} +(-1.32279 - 9.20021i) q^{59} +(0.0126835 + 0.266259i) q^{60} +(-4.17435 - 0.804540i) q^{61} +(-1.96803 - 2.27122i) q^{62} +(2.78489 + 3.91082i) q^{63} +(-7.21925 + 2.11976i) q^{64} +(14.7103 + 7.58370i) q^{65} +8.19990 q^{66} +(7.19147 + 3.90931i) q^{67} -0.138918 q^{68} +(-0.256443 - 0.132206i) q^{69} +(16.5516 - 4.86000i) q^{70} +(6.32392 + 8.88070i) q^{71} +(1.79905 + 2.07621i) q^{72} +(-2.51218 - 0.484183i) q^{73} +(0.453447 + 9.51902i) q^{74} +(0.160122 + 1.11368i) q^{75} +(-0.0359439 + 0.0230997i) q^{76} +(-6.39306 - 26.3525i) q^{77} +(-9.53298 + 1.83733i) q^{78} +(10.7470 + 8.45150i) q^{79} +(9.65875 - 3.86678i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-2.88887 - 1.85657i) q^{82} +(3.69375 - 10.6724i) q^{83} +(-0.299948 + 0.421219i) q^{84} +(-3.17764 + 0.303428i) q^{85} +(0.111566 - 2.34206i) q^{86} +(1.29759 - 5.34876i) q^{87} +(-5.07499 - 14.6632i) q^{88} +(-0.278184 - 0.0816822i) q^{89} +(-2.60041 - 2.47948i) q^{90} +(13.3371 + 29.2042i) q^{91} +(0.00442241 - 0.0307585i) q^{92} +(2.06066 + 0.196769i) q^{93} +(-2.40172 + 2.77173i) q^{94} +(-0.771735 + 0.606899i) q^{95} +(-0.304313 + 0.527085i) q^{96} +(-0.0223946 - 0.0387886i) q^{97} +(21.6324 + 8.66029i) q^{98} +(-4.08773 + 3.89765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{2} + 10 q^{3} + 6 q^{4} - 2 q^{5} + 9 q^{6} + q^{7} - 45 q^{8} - 10 q^{9}+O(q^{10}) \) 100 * q + 2 * q^2 + 10 * q^3 + 6 * q^4 - 2 * q^5 + 9 * q^6 + q^7 - 45 * q^8 - 10 * q^9	\( 100 q + 2 q^{2} + 10 q^{3} + 6 q^{4} - 2 q^{5} + 9 q^{6} + q^{7} - 45 q^{8} - 10 q^{9} - 25 q^{10} + 9 q^{11} + 5 q^{12} - 3 q^{13} + 22 q^{14} - 9 q^{15} - 46 q^{17} + 2 q^{18} - 14 q^{19} - 16 q^{20} - q^{21} - 17 q^{22} + 12 q^{23} + 12 q^{24} - 44 q^{25} - 7 q^{26} + 10 q^{27} - 90 q^{28} + 43 q^{29} - 30 q^{30} - 10 q^{31} + 20 q^{32} - 42 q^{33} + 20 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} + 16 q^{38} + 3 q^{39} + 55 q^{40} - 48 q^{41} - 45 q^{43} - 147 q^{44} - 2 q^{45} + 47 q^{46} + 44 q^{47} - 64 q^{49} - 54 q^{50} + 24 q^{51} - 34 q^{52} + 68 q^{53} - 2 q^{54} - 17 q^{55} + 111 q^{56} + 3 q^{57} + 88 q^{58} - 2 q^{59} - 6 q^{60} + 21 q^{61} + 86 q^{62} + 23 q^{63} + 19 q^{64} + 6 q^{65} + 94 q^{66} + 20 q^{67} - 202 q^{68} + 21 q^{69} - 20 q^{70} + q^{71} + 32 q^{72} + 10 q^{73} + 67 q^{74} + 44 q^{75} - 90 q^{76} - 62 q^{77} + 51 q^{78} - 29 q^{79} + 199 q^{80} - 10 q^{81} - 36 q^{82} + 43 q^{83} - 75 q^{84} + 93 q^{85} - 83 q^{86} + 12 q^{87} + 54 q^{88} + 21 q^{89} - 25 q^{90} + 58 q^{91} - 192 q^{92} - q^{93} + 14 q^{94} - 109 q^{95} - 9 q^{96} - 35 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 100 * q + 2 * q^2 + 10 * q^3 + 6 * q^4 - 2 * q^5 + 9 * q^6 + q^7 - 45 * q^8 - 10 * q^9 - 25 * q^10 + 9 * q^11 + 5 * q^12 - 3 * q^13 + 22 * q^14 - 9 * q^15 - 46 * q^17 + 2 * q^18 - 14 * q^19 - 16 * q^20 - q^21 - 17 * q^22 + 12 * q^23 + 12 * q^24 - 44 * q^25 - 7 * q^26 + 10 * q^27 - 90 * q^28 + 43 * q^29 - 30 * q^30 - 10 * q^31 + 20 * q^32 - 42 * q^33 + 20 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 + 16 * q^38 + 3 * q^39 + 55 * q^40 - 48 * q^41 - 45 * q^43 - 147 * q^44 - 2 * q^45 + 47 * q^46 + 44 * q^47 - 64 * q^49 - 54 * q^50 + 24 * q^51 - 34 * q^52 + 68 * q^53 - 2 * q^54 - 17 * q^55 + 111 * q^56 + 3 * q^57 + 88 * q^58 - 2 * q^59 - 6 * q^60 + 21 * q^61 + 86 * q^62 + 23 * q^63 + 19 * q^64 + 6 * q^65 + 94 * q^66 + 20 * q^67 - 202 * q^68 + 21 * q^69 - 20 * q^70 + q^71 + 32 * q^72 + 10 * q^73 + 67 * q^74 + 44 * q^75 - 90 * q^76 - 62 * q^77 + 51 * q^78 - 29 * q^79 + 199 * q^80 - 10 * q^81 - 36 * q^82 + 43 * q^83 - 75 * q^84 + 93 * q^85 - 83 * q^86 + 12 * q^87 + 54 * q^88 + 21 * q^89 - 25 * q^90 + 58 * q^91 - 192 * q^92 - q^93 + 14 * q^94 - 109 * q^95 - 9 * q^96 - 35 * q^97 - 15 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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