LMFDB - Embedded newform 349.2.k.a.3.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(3,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(174))

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

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

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

chi := DirichletCharacter("349.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.k (of order $174$, degree $56$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$1624$
Relative dimension:	$29$ over $\Q(\zeta_{174})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{174}]$

Embedding invariants

Embedding label			3.12
Character	$\chi$	$=$	349.3
Dual form			349.2.k.a.233.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.787498 - 0.188310i) q^{2} +(-1.01339 + 0.184983i) q^{3} +(-1.19896 - 0.608175i) q^{4} +(-0.327670 - 2.57880i) q^{5} +(0.832873 + 0.0451571i) q^{6} +(3.73113 + 0.0673734i) q^{7} +(2.06390 + 1.75309i) q^{8} +(-1.81379 + 0.685000i) q^{9} +O(q^{10})$	\(q+(-0.787498 - 0.188310i) q^{2} +(-1.01339 + 0.184983i) q^{3} +(-1.19896 - 0.608175i) q^{4} +(-0.327670 - 2.57880i) q^{5} +(0.832873 + 0.0451571i) q^{6} +(3.73113 + 0.0673734i) q^{7} +(2.06390 + 1.75309i) q^{8} +(-1.81379 + 0.685000i) q^{9} +(-0.227573 + 2.09250i) q^{10} +(0.167615 - 0.761484i) q^{11} +(1.32751 + 0.394530i) q^{12} +(-3.56409 - 3.50032i) q^{13} +(-2.92557 - 0.755665i) q^{14} +(0.809090 + 2.55271i) q^{15} +(0.293077 + 0.400338i) q^{16} +(-0.508172 - 0.598266i) q^{17} +(1.55735 - 0.197882i) q^{18} +(-5.83322 - 0.848465i) q^{19} +(-1.17550 + 3.29115i) q^{20} +(-3.79354 + 0.621920i) q^{21} +(-0.275391 + 0.568103i) q^{22} +(-5.16451 + 5.25860i) q^{23} +(-2.41581 - 1.39477i) q^{24} +(-1.70173 + 0.439550i) q^{25} +(2.14757 + 3.42765i) q^{26} +(4.35938 - 2.62295i) q^{27} +(-4.43250 - 2.34996i) q^{28} +(-9.83667 + 2.92342i) q^{29} +(-0.156457 - 2.16261i) q^{30} +(3.29882 - 6.22224i) q^{31} +(-2.25055 - 5.36468i) q^{32} +(-0.0289977 + 0.802683i) q^{33} +(0.287525 + 0.566827i) q^{34} +(-1.04884 - 9.64392i) q^{35} +(2.59126 + 0.281816i) q^{36} +(-0.0829674 - 0.298821i) q^{37} +(4.43387 + 1.76661i) q^{38} +(4.25930 + 2.88788i) q^{39} +(3.84459 - 5.89681i) q^{40} +(-4.41372 + 5.19623i) q^{41} +(3.10452 + 0.224601i) q^{42} +(0.595700 + 0.544212i) q^{43} +(-0.664079 + 0.811048i) q^{44} +(2.36080 + 4.45295i) q^{45} +(5.05728 - 3.16861i) q^{46} +(1.06558 - 3.16254i) q^{47} +(-0.371056 - 0.351483i) q^{48} +(6.92139 + 0.250042i) q^{49} +(1.42288 - 0.0256930i) q^{50} +(0.625643 + 0.512272i) q^{51} +(2.14439 + 6.36433i) q^{52} +(1.30182 - 2.81384i) q^{53} +(-3.92693 + 1.24466i) q^{54} +(-2.01864 - 0.182730i) q^{55} +(7.58256 + 6.68006i) q^{56} +(6.06825 - 0.219221i) q^{57} +(8.29686 - 0.449843i) q^{58} +(0.261732 + 1.43384i) q^{59} +(0.582428 - 3.55266i) q^{60} +(-2.45093 - 2.58741i) q^{61} +(-3.76952 + 4.27880i) q^{62} +(-6.81365 + 2.43363i) q^{63} +(0.601543 + 3.66925i) q^{64} +(-7.85877 + 10.3380i) q^{65} +(0.173989 - 0.626651i) q^{66} +(-2.41504 + 6.06129i) q^{67} +(0.245426 + 1.02635i) q^{68} +(4.26089 - 6.28434i) q^{69} +(-0.990086 + 7.79207i) q^{70} +(1.28645 - 7.04750i) q^{71} +(-4.94434 - 1.76597i) q^{72} +(7.67452 - 4.24802i) q^{73} +(0.00906562 + 0.250945i) q^{74} +(1.64320 - 0.760223i) q^{75} +(6.47776 + 4.56489i) q^{76} +(0.676699 - 2.82991i) q^{77} +(-2.81037 - 3.07627i) q^{78} +(3.55002 + 7.67324i) q^{79} +(0.936360 - 0.886967i) q^{80} +(0.431864 - 0.380462i) q^{81} +(4.45430 - 3.26087i) q^{82} +(-10.4662 - 4.39068i) q^{83} +(4.92653 + 1.56148i) q^{84} +(-1.37630 + 1.50651i) q^{85} +(-0.366632 - 0.540741i) q^{86} +(9.42757 - 4.78216i) q^{87} +(1.68089 - 1.27778i) q^{88} +(10.9174 - 5.29227i) q^{89} +(-1.02059 - 3.95125i) q^{90} +(-13.0623 - 13.3003i) q^{91} +(9.39018 - 3.16392i) q^{92} +(-2.19197 + 6.91575i) q^{93} +(-1.43468 + 2.28983i) q^{94} +(-0.276647 + 15.3207i) q^{95} +(3.27305 + 5.02018i) q^{96} +(-4.63141 - 0.588482i) q^{97} +(-5.40349 - 1.50027i) q^{98} +(0.217598 + 1.49599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9}+O(q^{10}) $ 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9} - 58 q^{10} - 58 q^{11} - 57 q^{12} - 55 q^{13} - 48 q^{14} - 59 q^{15} - 29 q^{16} - 48 q^{17} + 43 q^{18} + 67 q^{19} - 58 q^{20} + 58 q^{21} - 55 q^{22} - 41 q^{23} - 39 q^{24} - 29 q^{25} - 112 q^{26} - 76 q^{27} - 58 q^{28} - 56 q^{29} - 67 q^{30} - 90 q^{31} - 67 q^{32} - 46 q^{33} + 5 q^{34} - 82 q^{36} + 45 q^{37} - 58 q^{38} - 58 q^{39} - 112 q^{40} + 10 q^{41} + 305 q^{42} - 13 q^{43} + 40 q^{44} - 56 q^{45} - 85 q^{46} - 58 q^{47} - 122 q^{48} - 93 q^{49} - 441 q^{50} - 160 q^{51} + 58 q^{52} - 58 q^{53} - 85 q^{54} + 34 q^{55} - 69 q^{56} - 29 q^{57} - 58 q^{58} - 40 q^{59} + 522 q^{60} + 87 q^{61} - 49 q^{62} - 37 q^{63} + 335 q^{64} - 58 q^{65} - 565 q^{66} - 116 q^{67} - 58 q^{68} + 16 q^{69} - 98 q^{70} - 34 q^{71} + 44 q^{72} - 52 q^{73} - 204 q^{74} - 95 q^{76} - 54 q^{77} + 439 q^{78} - 58 q^{79} - 192 q^{80} - 209 q^{81} - 79 q^{82} + 162 q^{83} + 330 q^{84} - 192 q^{85} + 126 q^{86} - 190 q^{87} - 8 q^{88} + 345 q^{89} - 46 q^{90} - 30 q^{91} + 62 q^{92} - 89 q^{93} - 87 q^{94} - 350 q^{95} + 990 q^{96} - 43 q^{97} - 464 q^{98} - 97 q^{99}+O(q^{100}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9 - 58 * q^10 - 58 * q^11 - 57 * q^12 - 55 * q^13 - 48 * q^14 - 59 * q^15 - 29 * q^16 - 48 * q^17 + 43 * q^18 + 67 * q^19 - 58 * q^20 + 58 * q^21 - 55 * q^22 - 41 * q^23 - 39 * q^24 - 29 * q^25 - 112 * q^26 - 76 * q^27 - 58 * q^28 - 56 * q^29 - 67 * q^30 - 90 * q^31 - 67 * q^32 - 46 * q^33 + 5 * q^34 - 82 * q^36 + 45 * q^37 - 58 * q^38 - 58 * q^39 - 112 * q^40 + 10 * q^41 + 305 * q^42 - 13 * q^43 + 40 * q^44 - 56 * q^45 - 85 * q^46 - 58 * q^47 - 122 * q^48 - 93 * q^49 - 441 * q^50 - 160 * q^51 + 58 * q^52 - 58 * q^53 - 85 * q^54 + 34 * q^55 - 69 * q^56 - 29 * q^57 - 58 * q^58 - 40 * q^59 + 522 * q^60 + 87 * q^61 - 49 * q^62 - 37 * q^63 + 335 * q^64 - 58 * q^65 - 565 * q^66 - 116 * q^67 - 58 * q^68 + 16 * q^69 - 98 * q^70 - 34 * q^71 + 44 * q^72 - 52 * q^73 - 204 * q^74 - 95 * q^76 - 54 * q^77 + 439 * q^78 - 58 * q^79 - 192 * q^80 - 209 * q^81 - 79 * q^82 + 162 * q^83 + 330 * q^84 - 192 * q^85 + 126 * q^86 - 190 * q^87 - 8 * q^88 + 345 * q^89 - 46 * q^90 - 30 * q^91 + 62 * q^92 - 89 * q^93 - 87 * q^94 - 350 * q^95 + 990 * q^96 - 43 * q^97 - 464 * q^98 - 97 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{174}\right)$

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 $

$2$	−0.787498	−	0.188310i	−0.556845	−	0.133155i	−0.0555883	−	0.998454i	$-0.517703\pi$
$2$	−0.787498	−	0.188310i	−0.556845	−	0.133155i	−0.501257	+	0.865299i	$0.667129\pi$
$3$	−1.01339	+	0.184983i	−0.585079	+	0.106800i	−0.463988	−	0.885842i	$-0.653582\pi$
$3$	−1.01339	+	0.184983i	−0.585079	+	0.106800i	−0.121091	+	0.992641i	$0.538639\pi$
$4$	−1.19896	−	0.608175i	−0.599479	−	0.304088i
$5$	−0.327670	−	2.57880i	−0.146539	−	1.15327i	−0.880487	−	0.474069i	$-0.842785\pi$
$5$	−0.327670	−	2.57880i	−0.146539	−	1.15327i	0.733949	−	0.679205i	$-0.237675\pi$
$6$	0.832873	+	0.0451571i	0.340019	+	0.0184353i
$7$	3.73113	+	0.0673734i	1.41024	+	0.0254648i	0.717918	−	0.696128i	$-0.245095\pi$
$7$	3.73113	+	0.0673734i	1.41024	+	0.0254648i	0.692318	+	0.721592i	$0.256589\pi$
$8$	2.06390	+	1.75309i	0.729697	+	0.619810i
$9$	−1.81379	+	0.685000i	−0.604597	+	0.228333i
$10$	−0.227573	+	2.09250i	−0.0719650	+	0.661707i
$11$	0.167615	−	0.761484i	0.0505379	−	0.229596i	−0.944581	−	0.328278i	$-0.893532\pi$
$11$	0.167615	−	0.761484i	0.0505379	−	0.229596i	0.995119	+	0.0986821i	$0.0314627\pi$
$12$	1.32751	+	0.394530i	0.383219	+	0.113891i
$13$	−3.56409	−	3.50032i	−0.988502	−	0.970814i	0.0110738	−	0.999939i	$-0.496475\pi$
$13$	−3.56409	−	3.50032i	−0.988502	−	0.970814i	−0.999576	+	0.0291251i	$0.990728\pi$
$14$	−2.92557	−	0.755665i	−0.781892	−	0.201960i
$15$	0.809090	+	2.55271i	0.208906	+	0.659106i
$16$	0.293077	+	0.400338i	0.0732694	+	0.100085i
$17$	−0.508172	−	0.598266i	−0.123250	−	0.145101i	0.697076	−	0.716997i	$-0.254484\pi$
$17$	−0.508172	−	0.598266i	−0.123250	−	0.145101i	−0.820326	+	0.571896i	$0.806208\pi$
$18$	1.55735	−	0.197882i	0.367070	−	0.0466411i
$19$	−5.83322	−	0.848465i	−1.33823	−	0.194651i	−0.563067	−	0.826411i	$-0.690379\pi$
$19$	−5.83322	−	0.848465i	−1.33823	−	0.194651i	−0.775164	+	0.631760i	$0.782333\pi$
$20$	−1.17550	+	3.29115i	−0.262850	+	0.735924i
$21$	−3.79354	+	0.621920i	−0.827819	+	0.135714i
$22$	−0.275391	+	0.568103i	−0.0587137	+	0.121120i
$23$	−5.16451	+	5.25860i	−1.07687	+	1.09649i	−0.0818718	+	0.996643i	$0.526090\pi$
$23$	−5.16451	+	5.25860i	−1.07687	+	1.09649i	−0.995002	+	0.0998520i	$0.968163\pi$
$24$	−2.41581	−	1.39477i	−0.493126	−	0.284706i
$25$	−1.70173	+	0.439550i	−0.340345	+	0.0879100i
$26$	2.14757	+	3.42765i	0.421173	+	0.672217i
$27$	4.35938	−	2.62295i	0.838964	−	0.504788i
$28$	−4.43250	−	2.34996i	−0.837663	−	0.444101i
$29$	−9.83667	+	2.92342i	−1.82662	+	0.542865i	−0.999808	−	0.0196068i	$-0.993759\pi$
$29$	−9.83667	+	2.92342i	−1.82662	+	0.542865i	−0.826816	+	0.562472i	$0.809851\pi$
$30$	−0.156457	−	2.16261i	−0.0285650	−	0.394837i
$31$	3.29882	−	6.22224i	0.592486	−	1.11755i	−0.388130	−	0.921605i	$-0.626879\pi$
$31$	3.29882	−	6.22224i	0.592486	−	1.11755i	0.980616	−	0.195942i	$-0.0627764\pi$
$32$	−2.25055	−	5.36468i	−0.397844	−	0.948351i
$33$	−0.0289977	+	0.802683i	−0.00504785	+	0.139729i
$34$	0.287525	+	0.566827i	0.0493101	+	0.0972100i
$35$	−1.04884	−	9.64392i	−0.177286	−	1.63012i
$36$	2.59126	+	0.281816i	0.431876	+	0.0469694i
$37$	−0.0829674	−	0.298821i	−0.0136398	−	0.0491259i	0.956417	−	0.292004i	$-0.0943222\pi$
$37$	−0.0829674	−	0.298821i	−0.0136398	−	0.0491259i	−0.970057	+	0.242878i	$0.921908\pi$
$38$	4.43387	+	1.76661i	0.719269	+	0.286583i
$39$	4.25930	+	2.88788i	0.682034	+	0.462431i
$40$	3.84459	−	5.89681i	0.607882	−	0.932367i
$41$	−4.41372	+	5.19623i	−0.689307	+	0.811515i	−0.989829	−	0.142260i	$-0.954563\pi$
$41$	−4.41372	+	5.19623i	−0.689307	+	0.811515i	0.300522	+	0.953775i	$0.402839\pi$
$42$	3.10452	+	0.224601i	0.479038	+	0.0346566i
$43$	0.595700	+	0.544212i	0.0908434	+	0.0829915i	0.718624	−	0.695399i	$-0.244772\pi$
$43$	0.595700	+	0.544212i	0.0908434	+	0.0829915i	−0.627781	+	0.778390i	$0.716037\pi$
$44$	−0.664079	+	0.811048i	−0.100114	+	0.122270i
$45$	2.36080	+	4.45295i	0.351928	+	0.663806i
$46$	5.05728	−	3.16861i	0.745656	−	0.467186i
$47$	1.06558	−	3.16254i	0.155431	−	0.461303i	−0.841440	−	0.540351i	$-0.818291\pi$
$47$	1.06558	−	3.16254i	0.155431	−	0.461303i	0.996871	+	0.0790478i	$0.0251880\pi$
$48$	−0.371056	−	0.351483i	−0.0535574	−	0.0507322i
$49$	6.92139	+	0.250042i	0.988770	+	0.0357203i
$50$	1.42288	−	0.0256930i	0.201225	−	0.00363354i
$51$	0.625643	+	0.512272i	0.0876076	+	0.0717324i
$52$	2.14439	+	6.36433i	0.297374	+	0.882573i
$53$	1.30182	−	2.81384i	0.178819	−	0.386510i	−0.797352	−	0.603515i	$-0.793767\pi$
$53$	1.30182	−	2.81384i	0.178819	−	0.386510i	0.976171	+	0.217004i	$0.0696286\pi$
$54$	−3.92693	+	1.24466i	−0.534388	+	0.169376i
$55$	−2.01864	−	0.182730i	−0.272193	−	0.0246394i
$56$	7.58256	+	6.68006i	1.01326	+	0.892661i
$57$	6.06825	−	0.219221i	0.803760	−	0.0290366i
$58$	8.29686	−	0.449843i	1.08943	−	0.0590673i
$59$	0.261732	+	1.43384i	0.0340746	+	0.186670i	0.996344	−	0.0854270i	$-0.0272254\pi$
$59$	0.261732	+	1.43384i	0.0340746	+	0.186670i	−0.962270	+	0.272097i	$0.912283\pi$
$60$	0.582428	−	3.55266i	0.0751912	−	0.458646i
$61$	−2.45093	−	2.58741i	−0.313809	−	0.331284i	0.549942	−	0.835203i	$-0.314650\pi$
$61$	−2.45093	−	2.58741i	−0.313809	−	0.331284i	−0.863751	+	0.503918i	$0.831891\pi$
$62$	−3.76952	+	4.27880i	−0.478730	+	0.543408i
$63$	−6.81365	+	2.43363i	−0.858439	+	0.306608i
$64$	0.601543	+	3.66925i	0.0751928	+	0.458656i
$65$	−7.85877	+	10.3380i	−0.974761	+	1.28228i
$66$	0.173989	−	0.626651i	0.0214165	−	0.0771354i
$67$	−2.41504	+	6.06129i	−0.295044	+	0.740505i	0.704482	+	0.709722i	$0.251179\pi$
$67$	−2.41504	+	6.06129i	−0.295044	+	0.740505i	−0.999526	+	0.0307830i	$0.990200\pi$
$68$	0.245426	+	1.02635i	0.0297623	+	0.124464i
$69$	4.26089	−	6.28434i	0.512951	−	0.756546i
$70$	−0.990086	+	7.79207i	−0.118338	+	0.931331i
$71$	1.28645	−	7.04750i	0.152673	−	0.836385i	−0.814095	−	0.580731i	$-0.802767\pi$
$71$	1.28645	−	7.04750i	0.152673	−	0.836385i	0.966768	−	0.255654i	$-0.0822907\pi$
$72$	−4.94434	−	1.76597i	−0.582696	−	0.208121i
$73$	7.67452	−	4.24802i	0.898234	−	0.497193i	0.0335093	−	0.999438i	$-0.489332\pi$
$73$	7.67452	−	4.24802i	0.898234	−	0.497193i	0.864725	+	0.502245i	$0.167493\pi$
$74$	0.00906562	+	0.250945i	0.00105386	+	0.0291717i
$75$	1.64320	−	0.760223i	0.189740	−	0.0877830i
$76$	6.47776	+	4.56489i	0.743050	+	0.523629i
$77$	0.676699	−	2.82991i	0.0771170	−	0.322498i
$78$	−2.81037	−	3.07627i	−0.318212	−	0.348318i
$79$	3.55002	+	7.67324i	0.399409	+	0.863307i	0.998058	+	0.0622961i	$0.0198423\pi$
$79$	3.55002	+	7.67324i	0.399409	+	0.863307i	−0.598649	+	0.801011i	$0.704296\pi$
$80$	0.936360	−	0.886967i	0.104688	−	0.0991659i
$81$	0.431864	−	0.380462i	0.0479848	−	0.0422735i
$82$	4.45430	−	3.26087i	0.491895	−	0.360103i
$83$	−10.4662	−	4.39068i	−1.14881	−	0.481940i	−0.271773	−	0.962361i	$-0.587610\pi$
$83$	−10.4662	−	4.39068i	−1.14881	−	0.481940i	−0.877038	+	0.480422i	$0.840484\pi$
$84$	4.92653	+	1.56148i	0.537529	+	0.170372i
$85$	−1.37630	+	1.50651i	−0.149280	+	0.163404i
$86$	−0.366632	−	0.540741i	−0.0395349	−	0.0583096i
$87$	9.42757	−	4.78216i	1.01074	−	0.512702i
$88$	1.68089	−	1.27778i	0.179183	−	0.136212i
$89$	10.9174	−	5.29227i	1.15724	−	0.560979i	0.244552	−	0.969636i	$-0.421359\pi$
$89$	10.9174	−	5.29227i	1.15724	−	0.560979i	0.912688	+	0.408657i	$0.134003\pi$
$90$	−1.02059	−	3.95125i	−0.107580	−	0.416498i
$91$	−13.0623	−	13.3003i	−1.36930	−	1.39425i
$92$	9.39018	−	3.16392i	0.978994	−	0.329861i
$93$	−2.19197	+	6.91575i	−0.227297	+	0.717130i
$94$	−1.43468	+	2.28983i	−0.147976	+	0.236178i
$95$	−0.276647	+	15.3207i	−0.0283834	+	1.57187i
$96$	3.27305	+	5.02018i	0.334054	+	0.512370i
$97$	−4.63141	−	0.588482i	−0.470249	−	0.0597513i	−0.112666	−	0.993633i	$-0.535939\pi$
$97$	−4.63141	−	0.588482i	−0.470249	−	0.0597513i	−0.357582	+	0.933882i	$0.616399\pi$
$98$	−5.40349	−	1.50027i	−0.545835	−	0.151550i
$99$	0.217598	+	1.49599i	0.0218694	+	0.150353i
$100$	2.30762	+	0.507945i	0.230762	+	0.0507945i
$101$	5.60438	−	2.23299i	0.557657	−	0.222191i	−0.0742440	−	0.997240i	$-0.523654\pi$
$101$	5.60438	−	2.23299i	0.557657	−	0.222191i	0.631901	+	0.775049i	$0.282275\pi$
$102$	−0.396227	−	0.521228i	−0.0392323	−	0.0516092i
$103$	8.55444	−	9.03081i	0.842894	−	0.889832i	−0.152242	−	0.988343i	$-0.548649\pi$
$103$	8.55444	−	9.03081i	0.842894	−	0.889832i	0.995136	+	0.0985110i	$0.0314080\pi$
$104$	−1.21955	−	13.4725i	−0.119587	−	1.32108i
$105$	2.84684	+	9.57900i	0.277823	+	0.934815i
$106$	−1.55505	+	1.97074i	−0.151040	+	0.191416i
$107$	−13.8142	−	10.9004i	−1.33547	−	1.05378i	−0.993472	−	0.114078i	$-0.963609\pi$
$107$	−13.8142	−	10.9004i	−1.33547	−	1.05378i	−0.341999	−	0.939700i	$-0.611104\pi$
$108$	−6.82193	+	0.493542i	−0.656441	+	0.0474911i
$109$	6.72304	−	9.18355i	0.643950	−	0.879625i	−0.354512	−	0.935051i	$-0.615353\pi$
$109$	6.72304	−	9.18355i	0.643950	−	0.879625i	0.998463	+	0.0554268i	$0.0176520\pi$
$110$	1.55526	+	0.524029i	0.148288	+	0.0499642i
$111$	0.139355	+	0.287474i	0.0132270	+	0.0272858i
$112$	1.06654	+	1.51346i	0.100778	+	0.143009i
$113$	−3.26178	+	10.9752i	−0.306842	+	1.03246i	0.654261	+	0.756269i	$0.272980\pi$
$113$	−3.26178	+	10.9752i	−0.306842	+	1.03246i	−0.961103	+	0.276189i	$0.910928\pi$
$114$	−4.82002	−	0.970074i	−0.451436	−	0.0908558i
$115$	15.2531	+	11.5951i	1.42236	+	1.08125i
$116$	13.5717	+	2.47737i	1.26010	+	0.230018i
$117$	8.86224	+	3.90744i	0.819314	+	0.361243i
$118$	0.0638927	−	1.17843i	0.00588180	−	0.108483i
$119$	−1.85575	−	2.26645i	−0.170116	−	0.207765i
$120$	−2.80524	+	6.68693i	−0.256083	+	0.610430i
$121$	9.43157	+	4.36351i	0.857415	+	0.396682i
$122$	1.44287	+	2.49912i	0.130631	+	0.226259i
$123$	3.51159	−	6.08225i	0.316629	−	0.548418i
$124$	−7.73936	+	5.45394i	−0.695015	+	0.489778i
$125$	−3.11982	−	7.83015i	−0.279045	−	0.700350i
$126$	5.82401	−	0.633399i	0.518844	−	0.0564276i
$127$	−2.99075	−	13.5871i	−0.265386	−	1.20566i	−0.901057	−	0.433701i	$-0.857207\pi$
$127$	−2.99075	−	13.5871i	−0.265386	−	1.20566i	0.635671	−	0.771960i	$-0.280724\pi$
$128$	−0.622332	+	8.60213i	−0.0550069	+	0.760328i
$129$	−0.704344	−	0.441302i	−0.0620140	−	0.0388545i
$130$	8.13552	−	6.66130i	0.713532	−	0.584234i
$131$	−4.62282	+	3.92666i	−0.403898	+	0.343074i	−0.826196	−	0.563383i	$-0.809499\pi$
$131$	−4.62282	+	3.92666i	−0.403898	+	0.343074i	0.422298	+	0.906457i	$0.361224\pi$
$132$	0.522939	−	0.944748i	0.0455160	−	0.0822297i
$133$	−21.7073	−	3.55874i	−1.88227	−	0.308582i
$134$	3.04324	−	4.31848i	0.262896	−	0.373060i
$135$	−8.19251	−	10.3825i	−0.705099	−	0.893584i
$136$		−	2.12563i		−	0.182271i
$137$	−6.90252	+	5.44656i	−0.589722	+	0.465331i	−0.868954	−	0.494892i	$-0.835208\pi$
$137$	−6.90252	+	5.44656i	−0.589722	+	0.465331i	0.279232	+	0.960224i	$0.409920\pi$
$138$	−4.53884	+	4.14654i	−0.386372	+	0.352977i
$139$	−1.23562	−	22.7898i	−0.104804	−	1.93300i	−0.303291	−	0.952898i	$-0.598086\pi$
$139$	−1.23562	−	22.7898i	−0.104804	−	1.93300i	0.198487	−	0.980104i	$-0.436397\pi$
$140$	−4.60768	+	12.2005i	−0.389420	+	1.03113i
$141$	−0.494832	+	3.40199i	−0.0416724	+	0.286499i
$142$	−2.34019	+	5.30764i	−0.196384	+	0.445407i
$143$	−3.26283	+	2.12729i	−0.272852	+	0.177893i
$144$	−0.805813	−	0.525372i	−0.0671511	−	0.0437810i
$145$	10.7621	+	24.4089i	0.893743	+	2.02705i
$146$	−6.84361	+	1.90012i	−0.566381	+	0.157255i
$147$	−7.06029	+	1.02695i	−0.582323	+	0.0847012i
$148$	−0.0822614	+	0.408733i	−0.00676185	+	0.0335976i
$149$	−1.21839	−	0.590624i	−0.0998147	−	0.0483858i	0.385627	−	0.922655i	$-0.373985\pi$
$149$	−1.21839	−	0.590624i	−0.0998147	−	0.0483858i	−0.485442	+	0.874269i	$0.661341\pi$
$150$	−1.43717	+	0.289244i	−0.117344	+	0.0236167i
$151$	1.54059	−	17.0190i	0.125372	−	1.38499i	−0.653082	−	0.757287i	$-0.726524\pi$
$151$	1.54059	−	17.0190i	0.125372	−	1.38499i	0.778453	−	0.627702i	$-0.216004\pi$
$152$	−10.5517	−	11.9773i	−0.855857	−	0.971486i
$153$	1.33153	+	0.737032i	0.107648	+	0.0595855i
$154$	−1.06580	+	2.10112i	−0.0858844	+	0.169313i
$155$	−17.1268	−	6.46815i	−1.37566	−	0.519535i
$156$	−3.35039	−	6.05285i	−0.268246	−	0.484616i
$157$	2.90056	+	8.12096i	0.231490	+	0.648124i	0.999966	+	0.00824508i	$0.00262452\pi$
$157$	2.90056	+	8.12096i	0.231490	+	0.648124i	−0.768476	+	0.639878i	$0.778985\pi$
$158$	−1.35069	−	6.71116i	−0.107455	−	0.533912i
$159$	−0.798735	+	3.09232i	−0.0633438	+	0.245237i
$160$	−13.0970	+	7.56156i	−1.03541	+	0.597794i
$161$	−19.6238	+	19.2726i	−1.54657	+	1.51889i
$162$	−0.411736	+	0.218289i	−0.0323491	+	0.0171504i
$163$	−4.53362	+	7.53493i	−0.355100	+	0.590181i	−0.981991	−	0.188926i	$-0.939500\pi$
$163$	−4.53362	+	7.53493i	−0.355100	+	0.590181i	0.626891	+	0.779107i	$0.284327\pi$
$164$	8.45208	−	3.54575i	0.659997	−	0.276876i
$165$	2.07946	−	0.188236i	0.161886	−	0.0146542i
$166$	7.41527	+	5.42853i	0.575537	+	0.421336i
$167$	0.112106	+	0.186322i	0.00867504	+	0.0144180i	0.861164	−	0.508327i	$-0.169736\pi$
$167$	0.112106	+	0.186322i	0.00867504	+	0.0144180i	−0.852489	+	0.522745i	$0.824908\pi$
$168$	−8.91976	−	5.36684i	−0.688174	−	0.414061i
$169$	0.215837	+	11.9530i	0.0166029	+	0.919465i
$170$	1.36752	−	0.927201i	0.104884	−	0.0711131i
$171$	11.1614	−	2.45682i	0.853536	−	0.187877i
$172$	−0.383243	−	1.01478i	−0.0292220	−	0.0773760i
$173$	6.17578	−	2.72296i	0.469536	−	0.207023i	−0.155162	−	0.987889i	$-0.549590\pi$
$173$	6.17578	−	2.72296i	0.469536	−	0.207023i	0.624698	+	0.780866i	$0.285222\pi$
$174$	−8.32471	+	1.99064i	−0.631095	+	0.150910i
$175$	−6.37898	+	1.52537i	−0.482206	+	0.115307i
$176$	0.353976	−	0.156071i	0.0266819	−	0.0117643i
$177$	−0.530470	−	1.40462i	−0.0398726	−	0.105577i
$178$	−9.59400	+	2.11180i	−0.719101	+	0.158286i
$179$	3.75628	−	2.54682i	0.280758	−	0.190358i	−0.412678	−	0.910877i	$-0.635407\pi$
$179$	3.75628	−	2.54682i	0.280758	−	0.190358i	0.693436	+	0.720519i	$0.256096\pi$
$180$	−0.122331	−	6.77468i	−0.00911801	−	0.504955i
$181$	20.6967	+	12.4528i	1.53837	+	0.925608i	0.996361	+	0.0852362i	$0.0271645\pi$
$181$	20.6967	+	12.4528i	1.53837	+	0.925608i	0.542011	+	0.840371i	$0.317663\pi$
$182$	7.78195	+	12.9337i	0.576836	+	0.958709i
$183$	2.96236	+	2.16867i	0.218984	+	0.160313i
$184$	−19.8778	+	1.79937i	−1.46541	+	0.132651i
$185$	−0.743415	+	0.311871i	−0.0546569	+	0.0229292i
$186$	3.02848	−	5.03337i	0.222059	−	0.369065i
$187$	−0.540748	+	0.286686i	−0.0395434	+	0.0209646i
$188$	−3.20096	+	3.14369i	−0.233454	+	0.229277i
$189$	16.4422	−	9.49289i	1.19599	−	0.690506i
$190$	3.10290	−	12.0129i	0.225108	−	0.871509i
$191$	−0.361548	−	1.79642i	−0.0261607	−	0.129985i	0.965105	−	0.261862i	$-0.0843364\pi$
$191$	−0.361548	−	1.79642i	−0.0261607	−	0.129985i	−0.991266	+	0.131877i	$0.957900\pi$
$192$	−1.28834	−	3.60709i	−0.0929781	−	0.260319i
$193$	−0.650316	−	1.17487i	−0.0468108	−	0.0845689i	0.850484	−	0.526002i	$-0.176309\pi$
$193$	−0.650316	−	1.17487i	−0.0468108	−	0.0845689i	−0.897294	+	0.441433i	$0.854470\pi$
$194$	3.53641	+	1.33557i	0.253899	+	0.0958882i
$195$	6.05161	−	11.9302i	0.433365	−	0.854337i
$196$	−8.14638	−	4.50921i	−0.581884	−	0.322086i
$197$	−5.07405	−	5.75957i	−0.361511	−	0.410352i	0.540998	−	0.841024i	$-0.318047\pi$
$197$	−5.07405	−	5.75957i	−0.361511	−	0.410352i	−0.902509	+	0.430672i	$0.858277\pi$
$198$	0.110352	−	1.21906i	0.00784235	−	0.0866351i
$199$	11.0572	−	2.22538i	0.783827	−	0.157753i	0.211062	−	0.977473i	$-0.432308\pi$
$199$	11.0572	−	2.22538i	0.783827	−	0.157753i	0.572765	+	0.819720i	$0.305871\pi$
$200$	−4.28275	−	2.07609i	−0.302836	−	0.146802i
$201$	1.32613	−	6.58917i	0.0935383	−	0.464764i
$202$	−4.83393	+	0.703114i	−0.340114	+	0.0494710i
$203$	−36.8989	+	10.2449i	−2.58980	+	0.719053i
$204$	−0.438569	−	0.994693i	−0.0307060	−	0.0696424i
$205$	14.8463	+	9.67945i	1.03691	+	0.676042i
$206$	−8.43719	+	5.50086i	−0.587847	+	0.383263i
$207$	5.76519	−	13.0757i	0.400708	−	0.908824i
$208$	0.356756	−	2.45271i	0.0247366	−	0.170065i
$209$	−1.62383	+	4.29968i	−0.112323	+	0.297415i
$210$	−0.438059	−	8.07953i	−0.0302290	−	0.557540i
$211$	10.3140	−	9.42249i	0.710042	−	0.648671i	−0.236359	−	0.971666i	$-0.575954\pi$
$211$	10.3140	−	9.42249i	0.710042	−	0.648671i	0.946401	+	0.322995i	$0.104690\pi$
$212$	−3.27213	+	2.58194i	−0.224731	+	0.177328i
$213$			7.37981i			0.505657i
$214$	8.82602	+	11.1854i	0.603334	+	0.764616i
$215$	1.20822	−	1.71451i	0.0823999	−	0.116929i
$216$	13.5956	+	2.22888i	0.925062	+	0.151656i
$217$	12.7276	−	22.9937i	0.864003	−	1.56092i
$218$	−7.02373	+	5.96601i	−0.475707	+	0.404069i
$219$	−6.99144	+	5.72454i	−0.472438	+	0.386828i
$220$	2.30913	+	1.44677i	0.155681	+	0.0975413i
$221$	−0.282950	+	3.91104i	−0.0190332	+	0.263085i
$222$	−0.0556074	−	0.252627i	−0.00373212	−	0.0169552i
$223$	−13.7120	+	1.49127i	−0.918221	+	0.0998626i	−0.555009	−	0.831844i	$-0.687285\pi$
$223$	−13.7120	+	1.49127i	−0.918221	+	0.0998626i	−0.363212	+	0.931707i	$0.618320\pi$
$224$	−8.03566	−	20.1680i	−0.536905	−	1.34753i
$225$	2.78548	−	1.96293i	0.185699	−	0.130862i
$226$	4.63537	−	8.02870i	0.308340	−	0.534061i
$227$	11.0723	+	19.1778i	0.734896	+	1.27288i	0.954769	+	0.297349i	$0.0961024\pi$
$227$	11.0723	+	19.1778i	0.734896	+	1.27288i	−0.219873	+	0.975529i	$0.570564\pi$
$228$	−7.40890	−	3.42772i	−0.490666	−	0.227006i
$229$	−11.2335	+	26.7775i	−0.742330	+	1.76951i	−0.111249	+	0.993793i	$0.535485\pi$
$229$	−11.2335	+	26.7775i	−0.742330	+	1.76951i	−0.631081	+	0.775717i	$0.717388\pi$
$230$	−9.82834	−	12.0035i	−0.648061	−	0.791485i
$231$	−0.162274	+	2.99297i	−0.0106768	+	0.196923i
$232$	−25.4269	−	11.2109i	−1.66936	−	0.736034i
$233$	−11.2146	−	2.04709i	−0.734690	−	0.134110i	−0.200762	−	0.979640i	$-0.564342\pi$
$233$	−11.2146	−	2.04709i	−0.734690	−	0.134110i	−0.533927	+	0.845530i	$0.679284\pi$
$234$	−6.24318	−	4.74594i	−0.408130	−	0.310252i
$235$	−8.50471	−	1.71165i	−0.554786	−	0.111656i
$236$	0.558220	−	1.87829i	0.0363370	−	0.122266i
$237$	−5.01696	−	7.11927i	−0.325887	−	0.462446i
$238$	1.03460	+	2.13428i	0.0670635	+	0.138345i
$239$	27.3105	+	9.20199i	1.76657	+	0.595227i	0.998956	−	0.0456826i	$-0.0145463\pi$
$239$	27.3105	+	9.20199i	1.76657	+	0.595227i	0.767616	+	0.640910i	$0.221443\pi$
$240$	−0.784821	+	1.07205i	−0.0506599	+	0.0692006i
$241$	−19.5395	+	1.41361i	−1.25865	+	0.0910589i	−0.685307	−	0.728255i	$-0.740332\pi$
$241$	−19.5395	+	1.41361i	−1.25865	+	0.0910589i	−0.573346	+	0.819314i	$0.694355\pi$
$242$	−6.60565	−	5.21231i	−0.424627	−	0.335060i
$243$	−9.82186	+	12.4474i	−0.630073	+	0.798502i
$244$	1.36496	+	4.59279i	0.0873825	+	0.294024i
$245$	−1.62313	−	17.9308i	−0.103698	−	1.14556i
$246$	−3.91072	+	4.12849i	−0.249338	+	0.263223i
$247$	17.8202	+	23.4421i	1.13387	+	1.49159i
$248$	17.7165	−	7.05892i	1.12500	−	0.448242i
$249$	11.4185	+	2.51339i	0.723616	+	0.159280i
$250$	0.982355	+	6.75372i	0.0621296	+	0.427143i
$251$	−14.1794	−	3.93690i	−0.894999	−	0.248495i	−0.210573	−	0.977578i	$-0.567533\pi$
$251$	−14.1794	−	3.93690i	−0.894999	−	0.248495i	−0.684425	+	0.729083i	$0.739947\pi$
$252$	9.64934	+	1.22608i	0.607852	+	0.0772355i
$253$	3.13869	+	4.81411i	0.197328	+	0.302661i
$254$	−0.203377	+	11.2630i	−0.0127610	+	0.706704i
$255$	1.11604	−	1.78127i	0.0698892	−	0.111547i
$256$	4.35680	−	13.7459i	0.272300	−	0.859117i
$257$	−0.279215	+	0.0940784i	−0.0174169	+	0.00586845i	−0.327997	−	0.944679i	$-0.606373\pi$
$257$	−0.279215	+	0.0940784i	−0.0174169	+	0.00586845i	0.310580	+	0.950547i	$0.399477\pi$
$258$	0.471567	+	0.480159i	0.0293585	+	0.0298934i
$259$	−0.289430	−	1.12053i	−0.0179843	−	0.0696265i
$260$	15.7097	−	7.61536i	0.974272	−	0.472284i
$261$	15.8391	−	12.0406i	0.980417	−	0.745294i
$262$	4.37989	−	2.22171i	0.270590	−	0.137258i
$263$	1.16530	+	1.71870i	0.0718558	+	0.105979i	0.861919	−	0.507046i	$-0.169263\pi$
$263$	1.16530	+	1.71870i	0.0718558	+	0.105979i	−0.790063	+	0.613025i	$0.789952\pi$
$264$	−1.46702	+	1.60582i	−0.0902890	+	0.0988313i
$265$	−7.68289	−	2.43512i	−0.471956	−	0.149588i
$266$	16.4243	+	6.89020i	1.00704	+	0.422465i
$267$	−10.0845	+	7.38264i	−0.617164	+	0.451810i
$268$	6.58186	−	5.79847i	0.402051	−	0.354198i
$269$	17.0114	−	16.1141i	1.03720	−	0.982491i	0.0373446	−	0.999302i	$-0.488110\pi$
$269$	17.0114	−	16.1141i	1.03720	−	0.982491i	0.999859	+	0.0168113i	$0.00535144\pi$
$270$	4.49646	+	9.71893i	0.273646	+	0.591475i
$271$	−6.91176	−	7.56568i	−0.419859	−	0.459583i	0.491692	−	0.870769i	$-0.336379\pi$
$271$	−6.91176	−	7.56568i	−0.419859	−	0.459583i	−0.911551	+	0.411187i	$0.865114\pi$
$272$	0.0905752	−	0.378779i	0.00549193	−	0.0229669i
$273$	15.6975	+	11.0620i	0.950054	+	0.669504i
$274$	6.46136	−	2.98934i	0.390345	−	0.180593i
$275$	0.0494749	+	1.36951i	0.00298345	+	0.0825847i
$276$	−8.93061	+	4.94329i	−0.537559	+	0.297551i
$277$	20.4873	+	7.31743i	1.23096	+	0.439662i	0.870062	−	0.492943i	$-0.164079\pi$
$277$	20.4873	+	7.31743i	1.23096	+	0.439662i	0.360900	+	0.932605i	$0.382470\pi$
$278$	−3.31848	+	18.1796i	−0.199029	+	1.09034i
$279$	−1.72114	+	13.5455i	−0.103042	+	0.810949i
$280$	14.7420	−	21.7428i	0.881000	−	1.29938i
$281$	5.87548	+	24.5708i	0.350502	+	1.46577i	0.814618	+	0.579998i	$0.196947\pi$
$281$	5.87548	+	24.5708i	0.350502	+	1.46577i	−0.464116	+	0.885774i	$0.653628\pi$
$282$	1.03031	−	2.58587i	0.0613538	−	0.153987i
$283$	5.78502	−	20.8358i	0.343884	−	1.23856i	−0.566247	−	0.824236i	$-0.691605\pi$
$283$	5.78502	−	20.8358i	0.343884	−	1.23856i	0.910131	−	0.414321i	$-0.135981\pi$
$284$	−5.82851	+	7.66728i	−0.345858	+	0.454969i
$285$	−2.55372	−	15.5770i	−0.151269	−	0.922700i
$286$	2.97006	−	1.06082i	0.175624	−	0.0627274i
$287$	−16.8183	+	19.0905i	−0.992751	+	1.12688i
$288$	7.75683	+	8.18879i	0.457076	+	0.482529i
$289$	2.65061	−	16.1680i	0.155918	−	0.951059i
$290$	−3.87869	−	21.2485i	−0.227765	−	1.24776i
$291$	4.80227	−	0.260371i	0.281514	−	0.0152632i
$292$	−11.7850	+	0.425743i	−0.689663	+	0.0249147i
$293$	−6.86409	−	6.04710i	−0.401004	−	0.353275i	0.436502	−	0.899703i	$-0.356217\pi$
$293$	−6.86409	−	6.04710i	−0.401004	−	0.353275i	−0.837506	+	0.546428i	$0.815987\pi$
$294$	5.75335	+	0.520803i	0.335542	+	0.0303738i
$295$	3.61182	−	1.14478i	0.210288	−	0.0666517i
$296$	0.352624	−	0.762185i	0.0204959	−	0.0443011i
$297$	−1.26664	−	3.75925i	−0.0734978	−	0.218134i
$298$	0.848262	+	0.694550i	0.0491385	+	0.0402342i
$299$	36.8136	−	0.664746i	2.12898	−	0.0384433i
$300$	−2.43247	−	0.0878754i	−0.140439	−	0.00507349i
$301$	2.18597	+	2.07066i	0.125997	+	0.119351i
$302$	−4.41806	+	13.1123i	−0.254231	+	0.754531i
$303$	−5.26634	+	3.29959i	−0.302543	+	0.189557i
$304$	−1.36991	−	2.58393i	−0.0785698	−	0.148198i
$305$	−5.86933	+	7.16827i	−0.336077	+	0.410454i
$306$	−0.909786	−	0.831151i	−0.0520090	−	0.0475137i
$307$	−25.1412	−	1.81888i	−1.43489	−	0.103809i	−0.667316	−	0.744774i	$-0.732557\pi$
$307$	−25.1412	−	1.81888i	−1.43489	−	0.103809i	−0.767570	+	0.640965i	$0.778534\pi$
$308$	−2.53241	+	2.98139i	−0.144298	+	0.169880i
$309$	−6.99841	+	10.7341i	−0.398125	+	0.610643i
$310$	12.2693	+	8.31880i	0.696850	+	0.472476i
$311$	−12.0919	−	4.81786i	−0.685670	−	0.273196i	0.00117534	−	0.999999i	$-0.499626\pi$
$311$	−12.0919	−	4.81786i	−0.685670	−	0.273196i	−0.686846	+	0.726803i	$0.741005\pi$
$312$	3.72805	+	13.4272i	0.211059	+	0.760166i
$313$	−4.09133	−	0.444959i	−0.231256	−	0.0251506i	−0.00824265	−	0.999966i	$-0.502624\pi$
$313$	−4.09133	−	0.444959i	−0.231256	−	0.0251506i	−0.223013	+	0.974815i	$0.571589\pi$
$314$	−0.754928	−	6.94144i	−0.0426030	−	0.391728i
$315$	8.50846	+	16.7736i	0.479398	+	0.945085i
$316$	0.410352	−	11.3589i	0.0230841	−	0.638990i
$317$	−4.30036	−	10.2509i	−0.241532	−	0.575746i	0.755291	−	0.655389i	$-0.227495\pi$
$317$	−4.30036	−	10.2509i	−0.241532	−	0.575746i	−0.996823	+	0.0796434i	$0.974622\pi$
$318$	1.21132	−	2.28478i	0.0679272	−	0.128124i
$319$	0.577358	+	7.98048i	0.0323259	+	0.446821i
$320$	9.26515	−	2.75356i	0.517937	−	0.153929i
$321$	16.0155	+	8.49089i	0.893899	+	0.473915i
$322$	19.0829	−	11.4818i	1.06345	−	0.639855i
$323$	2.45667	+	3.92098i	0.136693	+	0.218169i
$324$	−0.749174	+	0.193509i	−0.0416208	+	0.0107505i
$325$	7.60367	+	4.38998i	0.421776	+	0.243512i
$326$	4.98911	−	5.08002i	0.276321	−	0.281356i
$327$	−5.11424	+	10.5501i	−0.282818	+	0.583423i
$328$	−18.2189	+	2.98684i	−1.00597	+	0.164921i
$329$	4.18890	−	11.7281i	0.230942	−	0.646589i
$330$	−1.67302	−	0.243347i	−0.0920966	−	0.0133958i
$331$	32.4753	−	4.12641i	1.78500	−	0.226808i	0.837474	−	0.546478i	$-0.184032\pi$
$331$	32.4753	−	4.12641i	1.78500	−	0.226808i	0.947529	+	0.319669i	$0.103572\pi$
$332$	9.87819	+	11.6295i	0.542136	+	0.638252i
$333$	0.355178	+	0.485167i	0.0194636	+	0.0265870i
$334$	−0.0531971	−	0.167839i	−0.00291082	−	0.00918373i
$335$	16.4222	+	4.24180i	0.897241	+	0.231754i
$336$	−1.36078	−	1.33643i	−0.0742366	−	0.0729083i
$337$	−5.72524	−	1.70152i	−0.311874	−	0.0926875i	0.125149	−	0.992138i	$-0.460059\pi$
$337$	−5.72524	−	1.70152i	−0.311874	−	0.0926875i	−0.437023	+	0.899450i	$0.643967\pi$
$338$	2.08090	−	9.45364i	0.113186	−	0.514210i
$339$	1.27522	−	11.7255i	0.0692605	−	0.636840i
$340$	2.56634	−	0.969210i	0.139179	−	0.0525628i
$341$	−4.18520	−	3.55494i	−0.226641	−	0.192511i
$342$	−9.25224	−	0.167069i	−0.500304	−	0.00903403i
$343$	−0.276108	−	0.0149702i	−0.0149084	−	0.000808312i
$344$	0.275411	+	2.16751i	0.0148491	+	0.116864i
$345$	−17.6022	−	8.92879i	−0.947672	−	0.480710i
$346$	−5.37617	+	0.981362i	−0.289025	+	0.0527584i
$347$	28.0950	+	6.71819i	1.50822	+	0.360651i	0.900977	−	0.433866i	$-0.142851\pi$
$347$	28.0950	+	6.71819i	1.50822	+	0.360651i	0.607241	+	0.794518i	$0.292276\pi$
$348$	−14.2116			−0.761824
$349$	13.7012	+	12.6995i	0.733409	+	0.679787i
$349$	13.7012	+	12.6995i	0.733409	+	0.679787i
$350$	5.31067			0.283867
$351$	−24.7184	−	5.91077i	−1.31937	−	0.315494i
$352$	−4.46235	+	0.814553i	−0.237844	+	0.0434158i
$353$	14.3323	+	7.27009i	0.762829	+	0.386948i	0.790336	−	0.612674i	$-0.209906\pi$
$353$	14.3323	+	7.27009i	0.762829	+	0.386948i	−0.0275065	+	0.999622i	$0.508757\pi$
$354$	0.153241	+	1.20602i	0.00814468	+	0.0640995i
$355$	−18.5956	−	1.00823i	−0.986954	−	0.0535111i
$356$	−16.3081	−	0.294477i	−0.864328	−	0.0156072i
$357$	2.29985	+	1.95351i	0.121721	+	0.103391i
$358$	−3.43765	+	1.29827i	−0.181686	+	0.0686158i
$359$	3.49495	−	32.1355i	0.184456	−	1.69605i	−0.426584	−	0.904448i	$-0.640283\pi$
$359$	3.49495	−	32.1355i	0.184456	−	1.69605i	0.611040	−	0.791600i	$-0.290751\pi$
$360$	−2.93396	+	13.3291i	−0.154633	+	0.702506i
$361$	15.0938	+	4.48582i	0.794411	+	0.236096i
$362$	−13.9536	−	13.7039i	−0.733385	−	0.720262i
$363$	−10.3650	−	2.67724i	−0.544021	−	0.140519i
$364$	7.57223	+	23.8906i	0.396892	+	1.25221i
$365$	−13.4695	−	18.3991i	−0.705026	−	0.963053i
$366$	−1.92447	−	2.26566i	−0.100594	−	0.118428i
$367$	−6.84961	+	0.870333i	−0.357547	+	0.0454310i	−0.302759	−	0.953067i	$-0.597908\pi$
$367$	−6.84961	+	0.870333i	−0.357547	+	0.0454310i	−0.0547874	+	0.998498i	$0.517448\pi$
$368$	−3.61882	−	0.526372i	−0.188644	−	0.0274390i
$369$	4.44614	−	12.4483i	0.231457	−	0.648031i
$370$	0.644166	−	0.105606i	0.0334886	−	0.00549017i
$371$	5.04684	−	10.4111i	0.262019	−	0.540517i
$372$	6.83407	−	6.95859i	0.354330	−	0.360786i
$373$	−23.4849	−	13.5590i	−1.21600	−	0.702058i	−0.251940	−	0.967743i	$-0.581069\pi$
$373$	−23.4849	−	13.5590i	−1.21600	−	0.702058i	−0.964060	+	0.265685i	$0.914402\pi$
$374$	0.479823	−	0.123937i	0.0248111	−	0.00640861i
$375$	4.61002	+	7.35786i	0.238061	+	0.379958i
$376$	7.74346	−	4.65908i	0.399338	−	0.240274i
$377$	45.2917	+	24.0122i	2.33264	+	1.23669i
$378$	−14.7358	+	4.37941i	−0.757926	+	0.225252i
$379$	0.596913	+	8.25077i	0.0306614	+	0.423814i	0.989953	+	0.141397i	$0.0451593\pi$
$379$	0.596913	+	8.25077i	0.0306614	+	0.423814i	−0.959292	+	0.282417i	$0.908864\pi$
$380$	9.64937	−	18.2006i	0.495002	−	0.933673i
$381$	5.54416	+	13.2158i	0.284036	+	0.677064i
$382$	−0.0535662	+	1.48276i	−0.00274069	+	0.0758647i
$383$	−3.26417	−	6.43498i	−0.166791	−	0.328812i	0.793144	−	0.609034i	$-0.208443\pi$
$383$	−3.26417	−	6.43498i	−0.166791	−	0.328812i	−0.959935	+	0.280222i	$0.909592\pi$
$384$	−0.960581	−	8.83240i	−0.0490195	−	0.450726i
$385$	−7.51950	−	0.817794i	−0.383229	−	0.0416787i
$386$	0.290883	+	1.04767i	0.0148056	+	0.0533249i
$387$	−1.45326	−	0.579031i	−0.0738733	−	0.0294338i
$388$	5.19497	+	3.52228i	0.263735	+	0.178816i
$389$	−5.03426	+	7.72153i	−0.255247	+	0.391497i	−0.942117	−	0.335283i	$-0.891168\pi$
$389$	−5.03426	+	7.72153i	−0.255247	+	0.391497i	0.686870	+	0.726780i	$0.258984\pi$
$390$	−7.01220	+	8.25540i	−0.355076	+	0.418028i
$391$	5.77050	+	0.417475i	0.291827	+	0.0211126i
$392$	13.8467	+	12.6499i	0.699363	+	0.638915i
$393$	3.95834	−	4.83437i	0.199672	−	0.243862i
$394$	2.91122	+	5.49114i	0.146665	+	0.276639i
$395$	18.6245	−	11.6691i	0.937101	−	0.587136i
$396$	0.648933	−	1.92596i	0.0326101	−	0.0967834i
$397$	0.860925	+	0.815511i	0.0432086	+	0.0409293i	0.708999	−	0.705209i	$-0.249147\pi$
$397$	0.860925	+	0.815511i	0.0432086	+	0.0409293i	−0.665791	+	0.746139i	$0.731906\pi$
$398$	−9.12661	−	0.329708i	−0.457476	−	0.0165267i
$399$	22.6562	−	0.409106i	1.13423	−	0.0204809i
$400$	−0.674706	−	0.552444i	−0.0337353	−	0.0276222i
$401$	0.608730	+	1.80665i	0.0303985	+	0.0902197i	0.961778	−	0.273830i	$-0.0882905\pi$
$401$	0.608730	+	1.80665i	0.0303985	+	0.0902197i	−0.931380	+	0.364049i	$0.881394\pi$
$402$	−2.28513	+	4.93923i	−0.113972	+	0.246347i
$403$	−33.5371	+	10.6297i	−1.67060	+	0.529504i
$404$	−8.07746	−	0.731186i	−0.401869	−	0.0363778i
$405$	−1.12264	−	0.989024i	−0.0557846	−	0.0491450i
$406$	30.9870	−	1.11944i	1.53786	−	0.0555567i
$407$	−0.241454	+	0.0130913i	−0.0119684	+	0.000648910i
$408$	0.393205	+	2.15408i	0.0194665	+	0.106643i
$409$	1.24716	−	7.60737i	0.0616683	−	0.376160i	−0.937903	−	0.346897i	$-0.887235\pi$
$409$	1.24716	−	7.60737i	0.0616683	−	0.376160i	0.999572	−	0.0292636i	$-0.00931623\pi$
$410$	−9.86868	−	10.4182i	−0.487380	−	0.514520i
$411$	5.98740	−	6.79632i	0.295337	−	0.335238i
$412$	−15.7487	+	5.62496i	−0.775884	+	0.277122i
$413$	0.879953	+	5.36748i	0.0432997	+	0.264116i
$414$	−7.00235	+	9.21144i	−0.344147	+	0.452717i
$415$	−7.89323	+	28.4288i	−0.387463	+	1.39552i
$416$	−10.7569	+	26.9979i	−0.527402	+	1.32368i
$417$	5.46787	+	22.8663i	0.267763	+	1.11977i
$418$	2.08843	−	3.08021i	0.102149	−	0.150658i
$419$	0.118331	−	0.931277i	0.00578085	−	0.0454959i	−0.988873	−	0.148765i	$-0.952470\pi$
$419$	0.118331	−	0.931277i	0.00578085	−	0.0454959i	0.994654	+	0.103269i	$0.0329301\pi$
$420$	2.41247	−	13.2162i	0.117717	−	0.644884i
$421$	−31.1783	−	11.1359i	−1.51954	−	0.542732i	−0.561029	−	0.827796i	$-0.689594\pi$
$421$	−31.1783	−	11.1359i	−1.51954	−	0.542732i	−0.958509	+	0.285064i	$0.907985\pi$
$422$	−9.89656	+	5.47797i	−0.481757	+	0.266663i
$423$	0.233594	+	6.46610i	0.0113577	+	0.314393i
$424$	7.61972	−	3.52526i	0.370046	−	0.171202i
$425$	1.12774	+	0.794718i	0.0547033	+	0.0385495i
$426$	1.38969	−	5.81159i	0.0673307	−	0.281572i
$427$	−8.97042	−	9.81912i	−0.434109	−	0.475180i
$428$	9.93333	+	21.4705i	0.480146	+	1.03782i
$429$	2.91300	−	2.75934i	0.140641	−	0.133222i
$430$	−1.27433	+	1.12265i	−0.0614536	+	0.0541392i
$431$	5.43264	−	3.97709i	0.261681	−	0.191570i	−0.452045	−	0.891995i	$-0.649305\pi$
$431$	5.43264	−	3.97709i	0.261681	−	0.191570i	0.713726	+	0.700426i	$0.247006\pi$
$432$	2.32771	+	0.976500i	0.111992	+	0.0469819i
$433$	−22.3228	−	7.07528i	−1.07276	−	0.340016i	−0.286610	−	0.958047i	$-0.592528\pi$
$433$	−22.3228	−	7.07528i	−1.07276	−	0.340016i	−0.786154	+	0.618031i	$0.787931\pi$
$434$	−14.3529	+	15.7108i	−0.688960	+	0.754142i
$435$	−15.4214	−	22.7448i	−0.739399	−	1.09053i
$436$	−13.6458	+	6.92190i	−0.653518	+	0.331499i
$437$	34.5874	−	26.2927i	1.65454	−	1.25775i
$438$	6.58373	−	3.19150i	0.314583	−	0.152496i
$439$	0.396643	+	1.53561i	0.0189307	+	0.0732906i	0.976995	−	0.213264i	$-0.0684095\pi$
$439$	0.396643	+	1.53561i	0.0189307	+	0.0732906i	−0.958064	+	0.286555i	$0.907490\pi$
$440$	−3.84591	−	3.91599i	−0.183347	−	0.186687i
$441$	−12.7252	+	4.28763i	−0.605963	+	0.204173i
$442$	0.959309	−	3.02665i	0.0456297	−	0.143963i
$443$	18.3844	−	29.3425i	0.873469	−	1.39411i	−0.0451583	−	0.998980i	$-0.514379\pi$
$443$	18.3844	−	29.3425i	0.873469	−	1.39411i	0.918627	−	0.395126i	$-0.129299\pi$
$444$	0.00775410	−	0.429421i	0.000367993	−	0.0203794i
$445$	−17.2250	−	26.4196i	−0.816543	−	1.25241i
$446$	11.0790	+	1.40773i	0.524604	+	0.0666578i
$447$	1.34396	+	0.373148i	0.0635670	+	0.0176493i
$448$	1.99723	+	13.7310i	0.0943601	+	0.648728i
$449$	−3.82336	−	0.841584i	−0.180435	−	0.0397168i	0.123834	−	0.992303i	$-0.460481\pi$
$449$	−3.82336	−	0.841584i	−0.180435	−	0.0397168i	−0.304269	+	0.952586i	$0.598412\pi$
$450$	−2.56320	+	1.02127i	−0.120830	+	0.0481432i
$451$	3.21704	+	4.23195i	0.151485	+	0.199275i
$452$	10.5856	−	11.1750i	0.497903	−	0.525630i
$453$	1.58701	+	17.5318i	0.0745643	+	0.823718i
$454$	−5.10806	−	17.1875i	−0.239733	−	0.806650i
$455$	−30.0186	+	38.0431i	−1.40730	+	1.78349i
$456$	12.9085	+	10.1857i	0.604498	+	0.476991i
$457$	−35.0255	+	2.53397i	−1.63842	+	0.118534i	−0.860372	−	0.509666i	$-0.829769\pi$
$457$	−35.0255	+	2.53397i	−1.63842	+	0.118534i	−0.778052	+	0.628200i	$0.783792\pi$
$458$	13.8888	−	18.9719i	0.648982	−	0.886497i
$459$	−3.78454	−	1.27516i	−0.176647	−	0.0595194i
$460$	−11.2360	−	23.1787i	−0.523881	−	1.08071i
$461$	18.0054	+	25.5505i	0.838597	+	1.19000i	0.979792	+	0.200022i	$0.0641012\pi$
$461$	18.0054	+	25.5505i	0.838597	+	1.19000i	−0.141194	+	0.989982i	$0.545094\pi$
$462$	0.691395	−	2.32640i	0.0321666	−	0.108234i
$463$	1.65117	+	0.332313i	0.0767362	+	0.0154439i	0.235520	−	0.971869i	$-0.424321\pi$
$463$	1.65117	+	0.332313i	0.0767362	+	0.0154439i	−0.158784	+	0.987313i	$0.550757\pi$
$464$	−4.05326	−	3.08121i	−0.188168	−	0.143042i
$465$	18.5526	+	3.38657i	0.860356	+	0.157049i
$466$	8.44594	+	3.72389i	0.391251	+	0.172506i
$467$	−0.730005	+	13.4641i	−0.0337806	+	0.623046i	0.931805	+	0.362960i	$0.118234\pi$
$467$	−0.730005	+	13.4641i	−0.0337806	+	0.623046i	−0.965585	+	0.260086i	$0.916249\pi$
$468$	−8.24904	−	10.0746i	−0.381312	−	0.465701i
$469$	−9.41921	+	22.4528i	−0.434939	+	1.03677i
$470$	6.37512	+	2.94944i	0.294062	+	0.136048i
$471$	−4.44163	−	7.69312i	−0.204659	−	0.354480i
$472$	−1.97346	+	3.41813i	−0.0908358	+	0.157332i
$473$	0.514257	−	0.362398i	0.0236456	−	0.0166631i
$474$	2.61022	+	6.55115i	0.119891	+	0.300904i
$475$	10.2995	−	1.12014i	0.472572	−	0.0513953i
$476$	0.846568	+	3.84600i	0.0388024	+	0.176281i
$477$	−0.433749	+	5.99546i	−0.0198600	+	0.274513i
$478$	−19.7742	−	12.3894i	−0.904449	−	0.566677i
$479$	−8.03891	+	6.58220i	−0.367307	+	0.300748i	−0.799069	−	0.601239i	$-0.794674\pi$
$479$	−8.03891	+	6.58220i	−0.367307	+	0.300748i	0.431762	+	0.901988i	$0.357892\pi$
$480$	11.8736	−	10.0855i	0.541952	−	0.460338i
$481$	−0.750267	+	1.35544i	−0.0342092	+	0.0618028i
$482$	15.6535	+	2.56627i	0.712999	+	0.116890i
$483$	16.3213	−	23.1607i	0.742647	−	1.05385i
$484$	−8.65427	−	10.9677i	−0.393376	−	0.498532i
$485$			12.1363i			0.551082i
$486$	10.0787	−	7.95275i	0.457177	−	0.360744i
$487$	−9.86498	+	9.01232i	−0.447025	+	0.408387i	−0.866341	−	0.499453i	$-0.833534\pi$
$487$	−9.86498	+	9.01232i	−0.447025	+	0.408387i	0.419316	+	0.907840i	$0.362270\pi$
$488$	−0.522495	−	9.63685i	−0.0236522	−	0.436240i
$489$	3.20047	−	8.47444i	0.144730	−	0.383227i
$490$	−2.09834	+	14.4261i	−0.0947932	+	0.651705i
$491$	4.44916	−	10.0909i	0.200788	−	0.455395i	−0.785831	−	0.618442i	$-0.787764\pi$
$491$	4.44916	−	10.0909i	0.200788	−	0.455395i	0.986618	+	0.163047i	$0.0521321\pi$
$492$	−7.90932	+	5.15670i	−0.356580	+	0.232482i
$493$	6.74770	+	4.39935i	0.303901	+	0.198137i
$494$	−9.61901	−	21.8163i	−0.432780	−	0.981563i
$495$	3.78656	−	1.05133i	0.170193	−	0.0472539i
$496$	3.45781	−	0.502952i	0.155260	−	0.0225832i
$497$	5.27472	−	26.2085i	0.236603	−	1.17561i
$498$	−8.51872	−	4.12950i	−0.381733	−	0.185047i
$499$	−18.0397	+	3.63067i	−0.807569	+	0.162531i	−0.583575	−	0.812059i	$-0.698346\pi$
$499$	−18.0397	+	3.63067i	−0.807569	+	0.162531i	−0.223994	+	0.974590i	$0.571910\pi$
$500$	−1.02157	+	11.2854i	−0.0456862	+	0.504699i
$501$	−0.148073	−	0.168078i	−0.00661542	−	0.00750919i
$502$	10.4249	+	5.77043i	0.465287	+	0.257547i
$503$	−8.82391	+	17.3955i	−0.393439	+	0.775626i	−0.999809	−	0.0195566i	$-0.993775\pi$
$503$	−8.82391	+	17.3955i	−0.393439	+	0.775626i	0.606370	+	0.795183i	$0.292625\pi$
$504$	−18.3290	−	6.92218i	−0.816439	−	0.308338i
$505$	−7.59482	−	13.7209i	−0.337965	−	0.610572i
$506$	−1.56517	−	4.38215i	−0.0695803	−	0.194810i
$507$	−2.42983	−	12.0731i	−0.107913	−	0.536187i
$508$	−4.67756	+	18.1093i	−0.207533	+	0.803469i
$509$	−33.0985	+	19.1094i	−1.46706	+	0.847010i	−0.999321	−	0.0368546i	$-0.988266\pi$
$509$	−33.0985	+	19.1094i	−1.46706	+	0.847010i	−0.467743	+	0.883864i	$0.654933\pi$
$510$	−1.21431	+	1.19258i	−0.0537705	+	0.0528084i
$511$	28.9209	−	15.3329i	1.27938	−	0.678286i
$512$	2.87345	−	4.77571i	0.126990	−	0.211058i
$513$	−27.6547	+	11.6015i	−1.22099	+	0.512218i
$514$	0.237597	−	0.0215077i	0.0104799	−	0.000948662i
$515$	−26.0917	−	19.1011i	−1.14974	−	0.841693i
$516$	0.576089	+	0.957467i	0.0253609	+	0.0421501i
$517$	−2.22961	−	1.34151i	−0.0980583	−	0.0589997i
$518$	0.0169180	+	0.936919i	0.000743336	+	0.0411659i
$519$	−5.75475	+	3.90182i	−0.252606	+	0.171271i
$520$	−34.3432	+	7.55950i	−1.50605	+	0.331506i
$521$	−13.3369	−	35.3143i	−0.584299	−	1.54715i	−0.818229	−	0.574893i	$-0.805044\pi$
$521$	−13.3369	−	35.3143i	−0.584299	−	1.54715i	0.233930	−	0.972253i	$-0.424841\pi$
$522$	−14.7406	+	6.49927i	−0.645180	+	0.284465i
$523$	30.2590	−	7.23566i	1.32313	−	0.316393i	0.491093	−	0.871107i	$-0.336598\pi$
$523$	30.2590	−	7.23566i	1.32313	−	0.316393i	0.832041	+	0.554714i	$0.187172\pi$
$524$	7.93067	−	1.89641i	0.346453	−	0.0828452i
$525$	6.18220	−	2.72579i	0.269813	−	0.118963i
$526$	−0.594028	−	1.57291i	−0.0259008	−	0.0685820i
$527$	−5.39892	+	1.18839i	−0.235181	+	0.0517672i
$528$	−0.329844	+	0.223639i	−0.0143546	+	0.00973266i
$529$	−0.565547	−	31.3199i	−0.0245890	−	1.36174i
$530$	5.59170	+	3.36441i	0.242888	+	0.146141i
$531$	−1.45691	−	2.42140i	−0.0632243	−	0.105080i
$532$	23.8619	+	17.4686i	1.03454	+	0.757362i
$533$	33.9194	−	3.07044i	1.46921	−	0.132996i
$534$	9.33178	−	3.91479i	0.403826	−	0.169410i
$535$	−23.5833	+	39.1958i	−1.01960	+	1.69458i
$536$	−15.6104	+	8.27610i	−0.674265	+	0.357473i
$537$	−3.33545	+	3.27576i	−0.143935	+	0.141360i
$538$	−16.4309	+	9.48637i	−0.708385	+	0.408986i
$539$	1.35053	−	5.22862i	0.0581716	−	0.225212i
$540$	3.50809	+	17.4307i	0.150964	+	0.750097i
$541$	0.924498	+	2.58840i	0.0397473	+	0.111284i	0.959962	−	0.280129i	$-0.0903772\pi$
$541$	0.924498	+	2.58840i	0.0397473	+	0.111284i	−0.920215	+	0.391413i	$0.871986\pi$
$542$	4.01830	+	7.25951i	0.172601	+	0.311823i
$543$	−23.2773	−	8.79095i	−0.998923	−	0.377256i
$544$	−2.06584	+	4.07261i	−0.0885723	+	0.174612i
$545$	−25.8855	−	14.3282i	−1.10881	−	0.613752i
$546$	−10.2786	−	11.6673i	−0.439885	−	0.499315i
$547$	1.77989	−	19.6626i	0.0761027	−	0.840713i	−0.864818	−	0.502086i	$-0.832566\pi$
$547$	1.77989	−	19.6626i	0.0761027	−	0.840713i	0.940921	−	0.338627i	$-0.109962\pi$
$548$	11.5883	−	2.33226i	0.495028	−	0.0996290i
$549$	6.21785	+	3.01414i	0.265371	+	0.128640i
$550$	0.218931	−	1.08780i	0.00933525	−	0.0463841i
$551$	59.8598	−	8.70685i	2.55012	−	0.370924i
$552$	19.8110	−	5.50051i	0.843214	−	0.234117i
$553$	12.7286	+	28.8691i	0.541276	+	1.22764i
$554$	−14.7557	−	9.62041i	−0.626911	−	0.408732i
$555$	0.695676	−	0.453565i	0.0295298	−	0.0192528i
$556$	−12.3787	+	28.0754i	−0.524974	+	1.19066i
$557$	−0.431998	+	2.97000i	−0.0183043	+	0.125843i	−0.996736	−	0.0807266i	$-0.974276\pi$
$557$	−0.431998	+	2.97000i	−0.0183043	+	0.125843i	0.978432	+	0.206569i	$0.0662299\pi$
$558$	3.90615	−	10.3430i	0.165360	−	0.437852i
$559$	−0.218216	−	4.02476i	−0.00922956	−	0.170229i
$560$	3.55344	−	3.24631i	0.150160	−	0.137182i
$561$	0.494954	−	0.390553i	0.0208970	−	0.0164892i
$562$		−	20.4559i		−	0.862879i
$563$	−4.19452	−	5.31578i	−0.176778	−	0.224034i	0.688616	−	0.725127i	$-0.258219\pi$
$563$	−4.19452	−	5.31578i	−0.176778	−	0.224034i	−0.865393	+	0.501093i	$0.832931\pi$
$564$	2.66229	−	3.77789i	0.112102	−	0.159078i
$565$	29.3716	+	4.81523i	1.23567	+	0.202578i
$566$	−8.47926	+	15.3187i	−0.356410	+	0.643894i
$567$	1.63697	−	1.39046i	0.0687465	−	0.0583938i
$568$	15.0100	−	12.2901i	0.629805	−	0.515679i
$569$	−17.9346	−	11.2368i	−0.751857	−	0.471072i	0.0999073	−	0.994997i	$-0.468145\pi$
$569$	−17.9346	−	11.2368i	−0.751857	−	0.471072i	−0.851764	+	0.523925i	$0.824467\pi$
$570$	−0.922251	+	12.7477i	−0.0386288	+	0.533943i
$571$	9.46465	+	42.9983i	0.396083	+	1.79942i	0.577918	+	0.816095i	$0.303865\pi$
$571$	9.46465	+	42.9983i	0.396083	+	1.79942i	−0.181835	+	0.983329i	$0.558204\pi$
$572$	5.20577	−	0.566161i	0.217664	−	0.0236724i
$573$	0.698695	+	1.75359i	0.0291884	+	0.0732573i
$574$	16.8393	−	11.8667i	0.702858	−	0.495305i
$575$	6.47715	−	11.2188i	0.270116	−	0.467855i
$576$	−3.60451	−	6.24319i	−0.150188	−	0.260133i
$577$	−3.01988	−	1.39715i	−0.125719	−	0.0581640i	0.356021	−	0.934478i	$-0.384133\pi$
$577$	−3.01988	−	1.39715i	−0.125719	−	0.0581640i	−0.481740	+	0.876314i	$0.659995\pi$
$578$	−5.13194	+	12.2331i	−0.213461	+	0.508831i
$579$	0.876352	+	1.07030i	0.0364199	+	0.0444801i
$580$	1.94159	−	35.8105i	0.0806200	−	1.48695i
$581$	−38.7549	−	17.0874i	−1.60782	−	0.708903i
$582$	−3.83081	−	0.699272i	−0.158792	−	0.0289858i
$583$	−1.92449	−	1.46296i	−0.0797041	−	0.0605895i
$584$	23.2866	+	4.68664i	0.963604	+	0.193935i
$585$	7.17261	−	24.1343i	0.296551	−	0.997830i
$586$	4.26672	+	6.05465i	0.176257	+	0.250115i
$587$	−1.07672	−	2.22116i	−0.0444410	−	0.0916770i	0.876458	−	0.481478i	$-0.159900\pi$
$587$	−1.07672	−	2.22116i	−0.0444410	−	0.0916770i	−0.920899	+	0.389801i	$0.872544\pi$
$588$	9.08956	+	3.06263i	0.374847	+	0.126301i
$589$	−24.5221	+	33.4967i	−1.01041	+	1.38021i
$590$	−3.05987	+	0.221371i	−0.125973	+	0.00911368i
$591$	6.20739	+	4.89805i	0.255338	+	0.201479i
$592$	0.0953138	−	0.120793i	0.00391737	−	0.00496456i
$593$	1.51530	+	5.09867i	0.0622261	+	0.209377i	0.983942	−	0.178488i	$-0.0571206\pi$
$593$	1.51530	+	5.09867i	0.0622261	+	0.209377i	−0.921716	+	0.387865i	$0.873213\pi$
$594$	0.289572	+	3.19892i	0.0118813	+	0.131253i
$595$	−5.23664	+	5.52826i	−0.214681	+	0.226636i
$596$	1.10160	+	1.44913i	0.0451233	+	0.0593586i
$597$	−10.7936	+	4.30056i	−0.441753	+	0.176010i
$598$	−29.1158	−	6.40887i	−1.19063	−	0.262078i
$599$	2.23198	+	15.3449i	0.0911963	+	0.626977i	0.984218	+	0.176963i	$0.0566272\pi$
$599$	2.23198	+	15.3449i	0.0911963	+	0.626977i	−0.893021	+	0.450015i	$0.851419\pi$
$600$	4.72412	+	1.31165i	0.192861	+	0.0535477i
$601$	−20.7409	−	2.63540i	−0.846039	−	0.107500i	−0.309004	−	0.951061i	$-0.599996\pi$
$601$	−20.7409	−	2.63540i	−0.846039	−	0.107500i	−0.537035	+	0.843560i	$0.680456\pi$
$602$	−1.33152	−	2.04228i	−0.0542687	−	0.0832371i
$603$	0.228390	−	12.6482i	0.00930076	−	0.515075i
$604$	−12.1977	+	19.4682i	−0.496316	+	0.792148i
$605$	8.16217	−	25.7519i	0.331839	−	1.04696i
$606$	4.76857	−	1.60672i	0.193710	−	0.0652685i
$607$	1.86911	+	1.90316i	0.0758647	+	0.0772469i	0.750347	−	0.661044i	$-0.229886\pi$
$607$	1.86911	+	1.90316i	0.0758647	+	0.0772469i	−0.674483	+	0.738291i	$0.735633\pi$
$608$	8.57619	+	33.2029i	0.347810	+	1.34655i
$609$	35.4977	−	17.2077i	1.43844	−	0.697292i
$610$	5.97194	−	4.53975i	0.241797	−	0.183809i
$611$	−14.8677	+	7.54170i	−0.601484	+	0.305105i
$612$	−1.14820	−	1.69347i	−0.0464134	−	0.0684546i
$613$	−27.5905	+	30.2009i	−1.11437	+	1.21980i	−0.141136	+	0.989990i	$0.545075\pi$
$613$	−27.5905	+	30.2009i	−1.11437	+	1.21980i	−0.973235	+	0.229811i	$0.926189\pi$
$614$	19.4562	+	6.16670i	0.785186	+	0.248868i
$615$	−16.8356	−	7.06271i	−0.678875	−	0.284796i
$616$	6.35771	−	4.65432i	0.256160	−	0.187528i
$617$	13.7243	−	12.0908i	0.552519	−	0.486756i	−0.338348	−	0.941021i	$-0.609868\pi$
$617$	13.7243	−	12.0908i	0.552519	−	0.486756i	0.890867	+	0.454265i	$0.150098\pi$
$618$	7.53257	−	7.13523i	0.303004	−	0.287021i
$619$	9.52171	+	20.5808i	0.382710	+	0.827214i	0.999205	+	0.0398555i	$0.0126898\pi$
$619$	9.52171	+	20.5808i	0.382710	+	0.827214i	−0.616496	+	0.787358i	$0.711448\pi$
$620$	16.6006	+	18.1712i	0.666695	+	0.729771i
$621$	−8.72099	+	36.4705i	−0.349961	+	1.46351i
$622$	8.61511	+	6.07108i	0.345435	+	0.243428i
$623$	41.0908	−	19.0106i	1.64627	−	0.761644i
$624$	0.0921766	+	2.55153i	0.00369002	+	0.102143i
$625$	−26.8587	+	14.8669i	−1.07435	+	0.594677i
$626$	3.13812	+	1.12084i	0.125425	+	0.0447978i
$627$	0.850198	−	4.65762i	0.0339536	−	0.186007i
$628$	1.46132	−	11.5007i	0.0583130	−	0.458930i
$629$	−0.136613	+	0.201489i	−0.00544712	+	0.00803390i
$630$	−3.54176	−	14.8114i	−0.141107	−	0.590100i
$631$	−12.6304	+	31.6998i	−0.502807	+	1.26195i	0.430408	+	0.902634i	$0.358370\pi$
$631$	−12.6304	+	31.6998i	−0.502807	+	1.26195i	−0.933216	+	0.359317i	$0.883010\pi$
$632$	−6.12500	+	22.0603i	−0.243640	+	0.877510i
$633$	−8.70902	+	11.4565i	−0.346152	+	0.455356i
$634$	1.45618	+	8.88233i	0.0578325	+	0.352762i
$635$	−34.0585	+	12.1646i	−1.35157	+	0.482739i
$636$	2.83832	−	3.22179i	0.112547	−	0.127752i
$637$	−23.7933	−	25.1182i	−0.942723	−	0.995221i
$638$	1.04813	−	6.39333i	0.0414960	−	0.253114i
$639$	2.49420	+	13.6639i	0.0986690	+	0.540536i
$640$	22.3871	−	1.21379i	0.884927	−	0.0479794i
$641$	−39.3921	+	1.42308i	−1.55589	+	0.0562082i	−0.800608	−	0.599188i	$-0.795490\pi$
$641$	−39.3921	+	1.42308i	−1.55589	+	0.0562082i	−0.755285	+	0.655396i	$0.772502\pi$
$642$	−11.0133	−	9.70243i	−0.434659	−	0.382924i
$643$	32.0218	+	2.89867i	1.26282	+	0.114312i	0.701128	−	0.713035i	$-0.252680\pi$
$643$	32.0218	+	2.89867i	1.26282	+	0.114312i	0.561690	+	0.827348i	$0.310151\pi$
$644$	35.2492	−	11.1724i	1.38901	−	0.440253i
$645$	−0.907238	+	1.96096i	−0.0357225	+	0.0772128i
$646$	−1.19626	−	3.55038i	−0.0470663	−	0.139688i
$647$	−5.59262	−	4.57919i	−0.219869	−	0.180027i	0.517159	−	0.855889i	$-0.326990\pi$
$647$	−5.59262	−	4.57919i	−0.219869	−	0.180027i	−0.737028	+	0.675863i	$0.763771\pi$
$648$	1.55830	−	0.0281384i	0.0612160	−	0.00110538i
$649$	1.13572	+	0.0410288i	0.0445807	+	0.00161052i
$650$	−5.16120	−	4.88895i	−0.202439	−	0.191760i
$651$	−8.64449	+	25.6559i	−0.338804	+	1.00553i
$652$	10.0182	−	6.27683i	0.392342	−	0.245820i
$653$	−15.6243	−	29.4706i	−0.611426	−	1.15327i	−0.975104	−	0.221747i	$-0.928824\pi$
$653$	−15.6243	−	29.4706i	−0.611426	−	1.15327i	0.363678	−	0.931525i	$-0.381521\pi$
$654$	6.01414	−	7.34514i	0.235172	−	0.287218i
$655$	11.6408	+	10.6347i	0.454845	+	0.415531i
$656$	−3.37381	−	0.244083i	−0.131725	−	0.00952984i
$657$	−11.0101	+	12.9621i	−0.429544	+	0.505698i
$658$	−5.50726	+	8.44700i	−0.214695	+	0.329299i
$659$	6.80141	+	4.61147i	0.264945	+	0.179637i	0.686425	−	0.727200i	$-0.259179\pi$
$659$	6.80141	+	4.61147i	0.264945	+	0.179637i	−0.421480	+	0.906838i	$0.638489\pi$
$660$	−2.60767	−	1.03899i	−0.101503	−	0.0404426i
$661$	−4.36620	−	15.7256i	−0.169825	−	0.611656i	−0.998640	−	0.0521329i	$-0.983398\pi$
$661$	−4.36620	−	15.7256i	−0.169825	−	0.611656i	0.828815	−	0.559523i	$-0.189016\pi$
$662$	−26.3512	−	2.86587i	−1.02417	−	0.111385i
$663$	−0.436738	−	4.01574i	−0.0169615	−	0.155958i
$664$	−13.9038	−	27.4100i	−0.539573	−	1.06371i
$665$	−2.06442	+	57.1450i	−0.0800547	+	2.21599i
$666$	−0.188340	−	0.448951i	−0.00729804	−	0.0173965i
$667$	35.4285	−	66.8252i	1.37180	−	2.58748i
$668$	−0.0210942	−	0.291572i	−0.000816159	−	0.0112813i
$669$	13.6197	−	4.04770i	0.526566	−	0.156493i
$670$	−12.1337	−	6.43286i	−0.468765	−	0.248523i
$671$	−2.38109	+	1.43265i	−0.0919209	+	0.0553070i
$672$	11.8740	+	18.9515i	0.458048	+	0.731070i
$673$	44.3678	−	11.4601i	1.71025	−	0.441753i	0.737833	−	0.674984i	$-0.235849\pi$
$673$	44.3678	−	11.4601i	1.71025	−	0.441753i	0.972421	+	0.233231i	$0.0749298\pi$
$674$	4.18820	+	2.41806i	0.161323	+	0.0931401i
$675$	−6.26555	+	6.37971i	−0.241161	+	0.245555i
$676$	7.01077	−	14.4625i	0.269645	−	0.556249i
$677$	20.7748	−	3.40585i	0.798439	−	0.130897i	0.251267	−	0.967918i	$-0.419153\pi$
$677$	20.7748	−	3.40585i	0.798439	−	0.130897i	0.547172	+	0.837020i	$0.315704\pi$
$678$	−3.21225	+	8.99364i	−0.123366	+	0.345399i
$679$	−17.2408	−	2.50774i	−0.661640	−	0.0962382i
$680$	−5.48157	+	0.696506i	−0.210209	+	0.0267098i
$681$	−14.7681	−	17.3864i	−0.565915	−	0.666247i
$682$	2.62641	+	3.58762i	0.100570	+	0.137377i
$683$	−11.2586	−	35.5214i	−0.430800	−	1.35919i	−0.883878	−	0.467718i	$-0.845076\pi$
$683$	−11.2586	−	35.5214i	−0.430800	−	1.35919i	0.453077	−	0.891471i	$-0.350326\pi$
$684$	−14.8763	−	3.84249i	−0.568808	−	0.146921i
$685$	16.3074	+	16.0155i	0.623072	+	0.611923i
$686$	0.214616	+	0.0637828i	0.00819406	+	0.00243524i
$687$	6.43049	−	29.2140i	0.245338	−	1.11458i
$688$	−0.0432827	+	0.397978i	−0.00165014	+	0.0151728i
$689$	−14.4891	+	5.47200i	−0.551992	+	0.208467i
$690$	12.1803	+	10.3461i	0.463697	+	0.393868i
$691$	−8.87240	−	0.160210i	−0.337522	−	0.00609466i	−0.150966	−	0.988539i	$-0.548238\pi$
$691$	−8.87240	−	0.160210i	−0.337522	−	0.00609466i	−0.186556	+	0.982444i	$0.559733\pi$
$692$	−9.06054	−	0.491248i	−0.344430	−	0.0186745i
$693$	0.711096	+	5.59640i	0.0270123	+	0.212590i
$694$	−20.8596	−	10.5811i	−0.791821	−	0.401654i
$695$	−58.3653	+	10.6540i	−2.21392	+	0.404128i
$696$	27.8411	+	6.65747i	1.05531	+	0.252351i
$697$	5.35166			0.202709
$698$	−8.39824	−	12.5809i	−0.317878	−	0.476193i
$699$	11.7433			0.444174
$700$	8.57582	+	2.05069i	0.324135	+	0.0775086i
$701$	2.44939	−	0.447109i	0.0925121	−	0.0168871i	−0.133117	−	0.991100i	$-0.542499\pi$
$701$	2.44939	−	0.447109i	0.0925121	−	0.0168871i	0.225629	+	0.974213i	$0.427556\pi$
$702$	18.3526	+	9.30944i	0.692676	+	0.351362i
$703$	0.230427	+	1.81348i	0.00869072	+	0.0683969i
$704$	2.89490	+	0.156957i	0.109106	+	0.00591554i
$705$	8.93518	+	0.161343i	0.336518	+	0.00607654i
$706$	−9.91759	−	8.42408i	−0.373254	−	0.317044i
$707$	21.0611	−	7.95400i	0.792086	−	0.299141i
$708$	−0.218241	+	2.00669i	−0.00820201	+	0.0754162i
$709$	−5.40258	+	24.5442i	−0.202898	+	0.921776i	0.759579	+	0.650415i	$0.225405\pi$
$709$	−5.40258	+	24.5442i	−0.202898	+	0.921776i	−0.962478	+	0.271361i	$0.912526\pi$
$710$	14.4542	+	4.29571i	0.542455	+	0.161215i
$711$	−11.6952	−	11.4859i	−0.438603	−	0.430755i
$712$	31.8101	+	8.21645i	1.19214	+	0.307925i
$713$	15.6835	+	49.4820i	0.587352	+	1.85311i
$714$	−1.44326	−	1.97147i	−0.0540126	−	0.0737802i
$715$	6.55500	+	7.71714i	0.245143	+	0.288605i
$716$	−6.05254	+	0.769054i	−0.226194	+	0.0287409i
$717$	−29.3783	−	4.27320i	−1.09715	−	0.159585i
$718$	−8.80369	+	24.6485i	−0.328551	+	0.919874i
$719$	31.5480	−	5.17202i	1.17654	−	0.192884i	0.458376	−	0.888758i	$-0.348431\pi$
$719$	31.5480	−	5.17202i	1.17654	−	0.192884i	0.718164	+	0.695874i	$0.244983\pi$
$720$	−1.09079	+	2.25018i	−0.0406513	+	0.0838592i
$721$	32.5262	−	33.1188i	1.21134	−	1.23341i
$722$	−11.0416	−	6.37488i	−0.410927	−	0.237249i
$723$	19.5396	−	5.04701i	0.726686	−	0.187700i
$724$	−17.2410	−	27.5176i	−0.640755	−	1.02268i
$725$	15.4543	−	9.29856i	0.573959	−	0.345340i
$726$	7.65826	+	4.06015i	0.284225	+	0.150686i
$727$	30.1882	−	8.97180i	1.11962	−	0.332746i	0.328558	−	0.944484i	$-0.393437\pi$
$727$	30.1882	−	8.97180i	1.11962	−	0.332746i	0.791060	+	0.611738i	$0.209529\pi$
$728$	−3.64262	−	50.3497i	−0.135004	−	1.86609i
$729$	6.84201	−	12.9054i	0.253408	−	0.477978i
$730$	7.14247	+	17.0257i	0.264355	+	0.630149i
$731$	0.0228656	−	0.632940i	0.000845714	−	0.0234101i
$732$	−2.23282	−	4.40178i	−0.0825273	−	0.162694i
$733$	−3.92286	−	36.0701i	−0.144894	−	1.33228i	−0.810396	−	0.585882i	$-0.800748\pi$
$733$	−3.92286	−	36.0701i	−0.144894	−	1.33228i	0.665502	−	0.746396i	$-0.268217\pi$
$734$	5.55795	+	0.604463i	0.205147	+	0.0223111i
$735$	4.96174	+	17.8706i	0.183017	+	0.659166i
$736$	39.8337	+	15.8712i	1.46829	+	0.585020i
$737$	4.21078	+	2.85498i	0.155106	+	0.105165i
$738$	−5.84546	+	8.96574i	−0.215174	+	0.330033i
$739$	7.89766	−	9.29784i	0.290520	−	0.342027i	−0.597468	−	0.801893i	$-0.703827\pi$
$739$	7.89766	−	9.29784i	0.290520	−	0.342027i	0.887988	+	0.459866i	$0.152102\pi$
$740$	1.08100	+	0.0782060i	0.0397382	+	0.00287491i
$741$	−22.3952	−	20.4595i	−0.822707	−	0.751598i
$742$	−5.93489	+	7.24834i	−0.217877	+	0.266095i
$743$	−4.66460	−	8.79836i	−0.171127	−	0.322781i	0.783083	−	0.621918i	$-0.213646\pi$
$743$	−4.66460	−	8.79836i	−0.171127	−	0.322781i	−0.954210	+	0.299137i	$0.903301\pi$
$744$	−16.6479	+	10.4307i	−0.610343	+	0.382407i
$745$	−1.12387	+	3.33552i	−0.0411754	+	0.122204i
$746$	15.9410	+	15.1001i	0.583641	+	0.552854i
$747$	21.9910	+	0.794448i	0.804610	+	0.0290673i
$748$	0.822689	−	0.0148554i	0.0300805	−	0.000543166i
$749$	−50.8083	−	41.6014i	−1.85650	−	1.52008i
$750$	−2.24483	−	6.66241i	−0.0819694	−	0.243277i
$751$	2.74367	−	5.93035i	0.100118	−	0.216401i	−0.851044	−	0.525095i	$-0.824030\pi$
$751$	2.74367	−	5.93035i	0.100118	−	0.216401i	0.951161	+	0.308694i	$0.0998918\pi$
$752$	1.57838	−	0.500274i	0.0575577	−	0.0182431i
$753$	15.0975	+	1.36665i	0.550184	+	0.0498036i
$754$	−31.1454	−	27.4384i	−1.13425	−	0.999247i
$755$	−44.3935	+	1.60376i	−1.61564	+	0.0583667i
$756$	−25.4868	+	1.38185i	−0.926946	+	0.0502575i
$757$	8.98565	+	49.2259i	0.326589	+	1.78915i	0.572555	+	0.819867i	$0.305952\pi$
$757$	8.98565	+	49.2259i	0.326589	+	1.78915i	−0.245966	+	0.969279i	$0.579105\pi$
$758$	1.08363	−	6.60987i	0.0393593	−	0.240081i
$759$	−4.07124	−	4.29795i	−0.147776	−	0.156006i
$760$	−27.4295	+	31.1354i	−0.994974	+	1.12940i
$761$	10.3360	−	3.69169i	0.374678	−	0.133824i	−0.142297	−	0.989824i	$-0.545449\pi$
$761$	10.3360	−	3.69169i	0.374678	−	0.133824i	0.516975	+	0.856000i	$0.327058\pi$
$762$	−1.87736	−	11.4514i	−0.0680096	−	0.414840i
$763$	25.7033	−	33.8121i	0.930522	−	1.22408i
$764$	−0.659060	+	2.37372i	−0.0238440	+	0.0858782i
$765$	1.46435	−	3.67525i	0.0529438	−	0.132879i
$766$	1.35875	+	5.68221i	0.0490938	+	0.205307i
$767$	4.08605	−	6.02648i	0.147539	−	0.217604i
$768$	−1.87238	+	14.7358i	−0.0675636	+	0.531733i
$769$	−8.30598	+	45.5025i	−0.299521	+	1.64086i	0.393054	+	0.919516i	$0.371419\pi$
$769$	−8.30598	+	45.5025i	−0.299521	+	1.64086i	−0.692575	+	0.721346i	$0.743524\pi$
$770$	5.76759	+	2.06001i	0.207849	+	0.0742374i
$771$	0.265549	−	0.146988i	0.00956353	−	0.00529363i
$772$	0.0651757	+	1.80412i	0.00234573	+	0.0649318i
$773$	28.0292	−	12.9677i	1.00814	−	0.466416i	0.154899	−	0.987930i	$-0.450495\pi$
$773$	28.0292	−	12.9677i	1.00814	−	0.466416i	0.853243	+	0.521514i	$0.174633\pi$
$774$	1.03540	+	0.729649i	0.0372167	+	0.0262267i
$775$	−2.87870	+	12.0385i	−0.103406	+	0.432437i
$776$	−8.52709	−	9.33384i	−0.306105	−	0.335065i
$777$	0.500583	+	1.08199i	0.0179583	+	0.0388163i
$778$	5.41851	−	5.13268i	0.194263	−	0.184016i
$779$	30.1550	−	26.5659i	1.08042	−	0.951821i
$780$	−14.5113	+	10.6233i	−0.519586	+	0.380376i
$781$	−5.15093	−	2.16088i	−0.184315	−	0.0773223i
$782$	−4.46564	−	1.41540i	−0.159691	−	0.0506147i
$783$	−35.2138	+	38.5454i	−1.25844	+	1.37750i
$784$	1.92840	+	2.84418i	0.0688715	+	0.101578i
$785$	19.9919	−	10.1410i	0.713542	−	0.361947i
$786$	−4.02754	+	3.06166i	−0.143658	+	0.109206i
$787$	−3.07067	+	1.48853i	−0.109458	+	0.0530602i	−0.490127	−	0.871651i	$-0.663050\pi$
$787$	−3.07067	+	1.48853i	−0.109458	+	0.0530602i	0.380670	+	0.924711i	$0.375693\pi$
$788$	2.58074	+	9.99138i	0.0919351	+	0.355928i
$789$	−1.49883	−	1.52614i	−0.0533599	−	0.0543321i
$790$	−16.8642	+	5.68220i	−0.600000	+	0.202164i
$791$	−12.9096	+	40.7301i	−0.459011	+	1.44820i
$792$	−2.17350	+	3.46903i	−0.0772320	+	0.123267i
$793$	−0.321431	+	17.8008i	−0.0114144	+	0.632126i
$794$	−0.524408	−	0.804334i	−0.0186105	−	0.0285447i
$795$	8.23619	+	1.04652i	0.292108	+	0.0371161i
$796$	−14.6106	−	4.05661i	−0.517858	−	0.143783i
$797$	5.25366	+	36.1191i	0.186094	+	1.27940i	0.848073	+	0.529880i	$0.177763\pi$
$797$	5.25366	+	36.1191i	0.186094	+	1.27940i	−0.661979	+	0.749523i	$0.730283\pi$
$798$	−17.9188	−	3.94422i	−0.634317	−	0.139624i
$799$	−2.43354	+	0.969610i	−0.0860924	+	0.0343023i
$800$	6.18786	+	8.13999i	0.218774	+	0.287792i
$801$	−16.1766	+	17.0775i	−0.571573	+	0.603403i
$802$	−0.139164	−	1.53736i	−0.00491407	−	0.0542861i
$803$	−1.94843	−	6.55606i	−0.0687587	−	0.231358i
$804$	−5.59735	+	7.09362i	−0.197403	+	0.250173i
$805$	56.1303	+	44.2907i	1.97833	+	1.56104i
$806$	28.4121	−	2.05551i	1.00077	−	0.0724022i
$807$	−14.2583	+	19.4766i	−0.501916	+	0.685608i
$808$	15.4815	+	5.21632i	0.544637	+	0.183509i
$809$	22.1274	+	45.6466i	0.777959	+	1.60485i	0.796215	+	0.605014i	$0.206833\pi$
$809$	22.1274	+	45.6466i	0.777959	+	1.60485i	−0.0182553	+	0.999833i	$0.505811\pi$
$810$	0.697837	+	0.990258i	0.0245195	+	0.0347941i
$811$	14.2803	−	48.0502i	0.501449	−	1.68727i	−0.204383	−	0.978891i	$-0.565519\pi$
$811$	14.2803	−	48.0502i	0.501449	−	1.68727i	0.705832	−	0.708379i	$-0.250573\pi$
$812$	50.4709	+	10.1578i	1.77118	+	0.356468i
$813$	8.40380	+	6.38840i	0.294734	+	0.224051i
$814$	0.192610	+	0.0351589i	0.00675098	+	0.00123232i
$815$	20.9166	+	9.22232i	0.732677	+	0.323044i
$816$	−0.0217201	+	0.400604i	−0.000760357	+	0.0140240i
$817$	−3.01310	−	3.67993i	−0.105415	−	0.128745i
$818$	−2.41468	+	5.75593i	−0.0844273	+	0.201251i
$819$	32.8029	+	15.1763i	1.14623	+	0.530301i
$820$	−11.9133	−	20.6344i	−0.416030	−	0.720584i
$821$	−8.14366	+	14.1052i	−0.284216	+	0.492276i	−0.972419	−	0.233242i	$-0.925066\pi$
$821$	−8.14366	+	14.1052i	−0.284216	+	0.492276i	0.688203	+	0.725518i	$0.258400\pi$
$822$	−5.99488	+	4.22460i	−0.209095	+	0.147350i
$823$	−2.35386	−	5.90773i	−0.0820503	−	0.205931i	0.882228	−	0.470823i	$-0.156043\pi$
$823$	−2.35386	−	5.90773i	−0.0820503	−	0.205931i	−0.964278	+	0.264892i	$0.914664\pi$
$824$	33.4873	−	3.64196i	1.16658	−	0.126874i
$825$	−0.303473	−	1.37869i	−0.0105656	−	0.0479999i
$826$	0.317787	−	4.39258i	0.0110572	−	0.152837i
$827$	−35.1771	−	22.0400i	−1.22323	−	0.766407i	−0.244120	−	0.969745i	$-0.578499\pi$
$827$	−35.1771	−	22.0400i	−1.22323	−	0.766407i	−0.979109	+	0.203338i	$0.934821\pi$
$828$	−14.8645	+	12.1710i	−0.516578	+	0.422970i
$829$	17.2711	−	14.6702i	0.599850	−	0.509517i	−0.295228	−	0.955427i	$-0.595396\pi$
$829$	17.2711	−	14.6702i	0.599850	−	0.509517i	0.895078	+	0.445910i	$0.147120\pi$
$830$	11.5693	−	20.9013i	0.401577	−	0.725494i
$831$	−22.1151	−	3.62559i	−0.767165	−	0.125770i
$832$	10.6996	−	15.1831i	0.370941	−	0.526380i
$833$	−3.36766	−	4.26790i	−0.116683	−	0.147874i
$834$		−	19.0368i		−	0.659189i
$835$	0.443753	−	0.350152i	0.0153567	−	0.0121175i
$836$	4.56186	−	4.16757i	0.157775	−	0.144138i
$837$	−1.93981	−	35.7778i	−0.0670498	−	1.23666i
$838$	−0.268554	+	0.711096i	−0.00927704	+	0.0245644i
$839$	−2.29435	+	15.7737i	−0.0792097	+	0.544569i	0.911785	+	0.410668i	$0.134704\pi$
$839$	−2.29435	+	15.7737i	−0.0792097	+	0.544569i	−0.990995	+	0.133901i	$0.957250\pi$
$840$	−10.9173	+	24.7608i	−0.376681	+	0.854329i
$841$	63.9209	−	41.6750i	2.20417	−	1.43707i
$842$	22.4558	+	14.6407i	0.773879	+	0.504552i
$843$	−10.4993	−	23.8129i	−0.361615	−	0.820159i
$844$	−18.0965	+	5.02447i	−0.622908	+	0.172949i
$845$	30.7538	−	4.47326i	1.05796	−	0.153885i
$846$	1.03367	−	5.13603i	0.0355385	−	0.176580i
$847$	34.8965	+	16.9163i	1.19906	+	0.581250i
$848$	1.50802	−	0.303504i	0.0517856	−	0.0104224i
$849$	−2.00821	+	22.1848i	−0.0689214	+	0.761380i
$850$	−0.738437	−	0.838202i	−0.0253282	−	0.0287501i
$851$	1.99987	+	1.10697i	0.0685546	+	0.0379465i
$852$	4.48822	−	8.84808i	0.153764	−	0.303130i
$853$	8.01602	+	3.02735i	0.274463	+	0.103654i	0.486716	−	0.873560i	$-0.338195\pi$
$853$	8.01602	+	3.02735i	0.274463	+	0.103654i	−0.212252	+	0.977215i	$0.568080\pi$
$854$	5.21515	+	9.42175i	0.178459	+	0.322406i
$855$	−9.99291	−	27.9781i	−0.341750	−	0.956830i
$856$	−9.40179	−	46.7148i	−0.321347	−	1.59668i
$857$	3.66059	−	14.1720i	0.125043	−	0.484107i	−0.874957	−	0.484201i	$-0.839110\pi$
$857$	3.66059	−	14.1720i	0.125043	−	0.484107i	1.00000		9.37779e-5i	$2.98504e-5\pi$
$858$	−2.81359	+	1.62443i	−0.0960543	+	0.0554570i
$859$	−11.3995	+	11.1956i	−0.388948	+	0.381988i	−0.868636	−	0.495451i	$-0.835003\pi$
$859$	−11.3995	+	11.1956i	−0.388948	+	0.381988i	0.479688	+	0.877439i	$0.340750\pi$
$860$	−2.49133	+	1.32082i	−0.0849536	+	0.0450395i
$861$	13.5120	−	22.4571i	0.460488	−	0.765336i
$862$	−5.02711	+	2.10893i	−0.171224	+	0.0718305i
$863$	−49.2798	+	4.46089i	−1.67750	+	0.151850i	−0.887362	−	0.461074i	$-0.847464\pi$
$863$	−49.2798	+	4.46089i	−1.67750	+	0.151850i	−0.790141	+	0.612925i	$0.789993\pi$
$864$	−23.8823	−	17.4836i	−0.812493	−	0.594805i
$865$	−9.04558	−	15.0339i	−0.307559	−	0.511167i
$866$	16.2468	+	9.77536i	0.552088	+	0.332180i
$867$	0.304709	+	16.8748i	0.0103485	+	0.573097i
$868$	−29.2440	+	19.8279i	−0.992607	+	0.673004i
$869$	6.43809	−	1.41713i	0.218397	−	0.0480729i
$870$	7.86123	+	20.8155i	0.266521	+	0.705711i
$871$	29.8239	−	13.1496i	1.01054	−	0.445558i
$872$	29.9752	−	7.16780i	1.01509	−	0.242732i
$873$	8.80352	−	2.10513i	0.297954	−	0.0712480i
$874$	−32.1887	+	14.1923i	−1.08880	+	0.480061i
$875$	−11.1129	−	29.4255i	−0.375685	−	0.994765i
$876$	11.8640	−	2.61146i	0.400846	−	0.0882329i
$877$	16.1206	−	10.9300i	0.544353	−	0.369081i	−0.257800	−	0.966198i	$-0.582998\pi$
$877$	16.1206	−	10.9300i	0.544353	−	0.369081i	0.802154	+	0.597117i	$0.203687\pi$
$878$	−0.0231849	−	1.28398i	−0.000782454	−	0.0433322i
$879$	8.07458	+	4.85831i	0.272349	+	0.163867i
$880$	−0.518463	−	0.861692i	−0.0174774	−	0.0290476i
$881$	30.9965	+	22.6918i	1.04430	+	0.764505i	0.972497	−	0.232914i	$-0.0748260\pi$
$881$	30.9965	+	22.6918i	1.04430	+	0.764505i	0.0718026	+	0.997419i	$0.477125\pi$
$882$	10.8285	−	0.980213i	0.364614	−	0.0330055i
$883$	−25.9114	+	10.8702i	−0.871989	+	0.365810i	−0.776874	−	0.629657i	$-0.783196\pi$
$883$	−25.9114	+	10.8702i	−0.871989	+	0.365810i	−0.0951156	+	0.995466i	$0.530322\pi$
$884$	2.71784	−	4.51709i	0.0914109	−	0.151926i
$885$	−3.44840	+	1.82823i	−0.115917	+	0.0614552i
$886$	−20.0031	+	19.6452i	−0.672019	+	0.659994i
$887$	29.8283	−	17.2214i	1.00154	−	0.578237i	0.0928338	−	0.995682i	$-0.470407\pi$
$887$	29.8283	−	17.2214i	1.00154	−	0.578237i	0.908702	+	0.417444i	$0.137074\pi$
$888$	−0.216354	+	0.837618i	−0.00726036	+	0.0281086i
$889$	−10.2435	−	50.8968i	−0.343555	−	1.70702i
$890$	8.58958	+	24.0490i	0.287923	+	0.806125i
$891$	−0.217329	−	0.392628i	−0.00728079	−	0.0131535i
$892$	17.3470	+	6.55131i	0.580821	+	0.219354i
$893$	−8.89907	+	17.5436i	−0.297796	+	0.587076i
$894$	−0.988096	−	0.546934i	−0.0330469	−	0.0182922i
$895$	−7.79857	−	8.85218i	−0.260677	−	0.295896i
$896$	−2.90156	+	32.0538i	−0.0969343	+	1.07084i
$897$	−37.1834	+	7.48352i	−1.24152	+	0.249867i
$898$	2.85241	+	1.38272i	0.0951860	+	0.0461420i
$899$	−14.2592	+	70.8499i	−0.475572	+	2.36298i
$900$	−4.53348	+	0.659413i	−0.151116	+	0.0219804i
$901$	−2.34497	+	0.651078i	−0.0781223	+	0.0216906i
$902$	−1.73650	−	3.93845i	−0.0578190	−	0.131136i
$903$	−2.59827	−	1.69401i	−0.0864650	−	0.0563732i
$904$	−25.9724	+	16.9334i	−0.863830	+	0.563198i
$905$	25.3315	−	57.4530i	0.842048	−	1.90980i
$906$	2.05165	−	14.1051i	0.0681614	−	0.468612i
$907$	−18.9604	+	50.2046i	−0.629569	+	1.66702i	0.109996	+	0.993932i	$0.464916\pi$
$907$	−18.9604	+	50.2046i	−0.629569	+	1.66702i	−0.739565	+	0.673085i	$0.764969\pi$
$908$	−1.61177	−	29.7273i	−0.0534884	−	0.986536i
$909$	−8.63557	+	7.88918i	−0.286424	+	0.261667i
$910$	30.8035	−	24.3061i	1.02113	−	0.805738i
$911$			0.866142i			0.0286966i	0.999897	+	0.0143483i	$0.00456736\pi$
$911$			0.866142i			0.0286966i	−0.999897	+	0.0143483i	$0.995433\pi$
$912$	1.86623	+	2.36511i	0.0617971	+	0.0783165i
$913$	−5.09772	+	7.23387i	−0.168710	+	0.239406i
$914$	28.0597	+	4.60015i	0.928132	+	0.152159i
$915$	4.62189	−	8.34995i	0.152795	−	0.276041i
$916$	29.7539	−	25.2732i	0.983097	−	0.835050i
$917$	−17.5129	+	14.3394i	−0.578328	+	0.473530i
$918$	2.74019	+	1.71685i	0.0904398	+	0.0566645i
$919$	1.77354	−	24.5146i	0.0585038	−	0.808663i	−0.882510	−	0.470294i	$-0.844148\pi$
$919$	1.77354	−	24.5146i	0.0585038	−	0.808663i	0.941014	−	0.338369i	$-0.109875\pi$
$920$	11.1536	+	50.6713i	0.367723	+	1.67058i
$921$	25.8142	−	2.80747i	0.850608	−	0.0925092i
$922$	−9.36785	−	23.5115i	−0.308514	−	0.774311i
$923$	−29.2535	+	20.6150i	−0.962891	+	0.678551i
$924$	2.01481	−	3.48975i	0.0662823	−	0.114804i
$925$	0.272535	+	0.472044i	0.00896088	+	0.0155207i
$926$	−1.23771	−	0.572626i	−0.0406737	−	0.0188177i
$927$	−9.32985	+	22.2398i	−0.306433	+	0.730451i
$928$	37.8211	+	46.1914i	1.24154	+	1.51631i
$929$	0.611774	−	11.2835i	0.0200717	−	0.370200i	−0.971191	−	0.238301i	$-0.923410\pi$
$929$	0.611774	−	11.2835i	0.0200717	−	0.370200i	0.991263	−	0.131899i	$-0.0421076\pi$
$930$	−13.9724	−	6.16055i	−0.458173	−	0.202012i
$931$	−40.1618	−	7.33110i	−1.31625	−	0.240267i
$932$	12.2008	+	9.27479i	0.399650	+	0.303806i
$933$	13.1450	+	2.64556i	0.430348	+	0.0866118i
$934$	3.11031	−	10.4655i	0.101772	−	0.342442i
$935$	0.916493	+	1.30054i	0.0299725	+	0.0425322i
$936$	11.4406	+	23.6008i	0.373949	+	0.771417i
$937$	−36.4280	−	12.2740i	−1.19005	−	0.400975i	−0.346514	−	0.938045i	$-0.612635\pi$
$937$	−36.4280	−	12.2740i	−1.19005	−	0.400975i	−0.843538	+	0.537070i	$0.819531\pi$
$938$	11.6457	−	15.9078i	0.380245	−	0.519408i
$939$	4.22841	−	0.305910i	0.137989	−	0.00998299i
$940$	9.15580	+	7.22455i	0.298629	+	0.235639i
$941$	26.4543	−	33.5260i	0.862385	−	1.09292i	−0.132428	−	0.991193i	$-0.542277\pi$
$941$	26.4543	−	33.5260i	0.862385	−	1.09292i	0.994813	−	0.101723i	$-0.0324354\pi$
$942$	2.04908	+	6.89472i	0.0667626	+	0.224642i
$943$	−4.53025	−	50.0460i	−0.147525	−	1.62972i
$944$	−0.497313	+	0.525007i	−0.0161862	+	0.0170875i
$945$	−29.8679	−	39.2905i	−0.971602	−	1.27812i
$946$	−0.473219	+	0.188548i	−0.0153857	+	0.00613021i
$947$	−44.4441	−	9.78288i	−1.44424	−	0.317901i	−0.577388	−	0.816470i	$-0.695928\pi$
$947$	−44.4441	−	9.78288i	−1.44424	−	0.317901i	−0.866850	+	0.498569i	$0.833859\pi$
$948$	1.68536	+	11.5869i	0.0547379	+	0.376325i
$949$	−42.2221	−	11.7229i	−1.37059	−	0.380542i
$950$	−8.32174	−	1.05739i	−0.269993	−	0.0343062i
$951$	6.25416	+	9.59259i	0.202805	+	0.311061i
$952$	0.143211	−	7.93101i	0.00464149	−	0.257045i
$953$	9.63136	−	15.3722i	0.311990	−	0.497954i	−0.654013	−	0.756483i	$-0.726916\pi$
$953$	9.63136	−	15.3722i	0.311990	−	0.497954i	0.966003	+	0.258529i	$0.0832378\pi$
$954$	1.47058	−	4.63973i	0.0476118	−	0.150217i
$955$	−4.51415	+	1.52099i	−0.146074	+	0.0492182i
$956$	−27.1478	−	27.6424i	−0.878021	−	0.894019i
$957$	−2.06134	−	7.98051i	−0.0666336	−	0.257973i
$958$	7.57012	−	3.66966i	0.244579	−	0.118561i
$959$	−26.1212	+	19.8568i	−0.843497	+	0.641210i
$960$	−8.87981	+	4.50431i	−0.286595	+	0.145376i
$961$	−10.4372	−	15.3937i	−0.336684	−	0.496572i
$962$	0.846076	−	0.926123i	0.0272786	−	0.0298594i
$963$	32.5228	+	10.3082i	1.04803	+	0.332178i
$964$	24.2868	+	10.1886i	0.782225	+	0.328153i
$965$	−2.81666	+	2.06201i	−0.0906715	+	0.0663783i
$966$	−17.2144	+	15.1655i	−0.553864	+	0.487942i
$967$	−13.3646	+	12.6596i	−0.429776	+	0.407105i	−0.871772	−	0.489912i	$-0.837029\pi$
$967$	−13.3646	+	12.6596i	−0.429776	+	0.407105i	0.441996	+	0.897017i	$0.354270\pi$
$968$	11.8162	+	25.5402i	0.379785	+	0.820893i
$969$	−3.21487	−	3.51903i	−0.103276	−	0.113047i
$970$	2.28539	−	9.55732i	0.0733793	−	0.306867i
$971$	22.1073	+	15.5791i	0.709458	+	0.499956i	0.873701	−	0.486464i	$-0.161713\pi$
$971$	22.1073	+	15.5791i	0.709458	+	0.499956i	−0.164243	+	0.986420i	$0.552518\pi$
$972$	19.3462	−	8.95051i	0.620530	−	0.287088i
$973$	−3.07486	−	85.1149i	−0.0985754	−	2.72866i
$974$	9.46576	−	5.23951i	0.303302	−	0.167885i
$975$	−8.51753	−	3.04220i	−0.272779	−	0.0974284i
$976$	0.317529	−	1.73951i	0.0101639	−	0.0556805i
$977$	−2.75630	+	21.6924i	−0.0881819	+	0.694001i	0.885265	+	0.465087i	$0.153977\pi$
$977$	−2.75630	+	21.6924i	−0.0881819	+	0.694001i	−0.973447	+	0.228913i	$0.926483\pi$
$978$	−4.11618	+	6.07092i	−0.131621	+	0.194127i
$979$	−2.20006	−	9.20048i	−0.0703141	−	0.294049i
$980$	−8.95901	+	22.4854i	−0.286185	+	0.718270i
$981$	−5.90345	+	21.2623i	−0.188483	+	0.678854i
$982$	−5.40391	+	7.10873i	−0.172446	+	0.226849i
$983$	0.791005	+	4.82492i	0.0252292	+	0.153891i	0.996437	−	0.0843439i	$-0.0268794\pi$
$983$	0.791005	+	4.82492i	0.0252292	+	0.153891i	−0.971208	+	0.238235i	$0.923431\pi$
$984$	17.9103	−	6.39700i	0.570959	−	0.203929i
$985$	−13.1902	+	14.9722i	−0.420273	+	0.477054i
$986$	−4.48536	−	4.73514i	−0.142843	−	0.150797i
$987$	−2.07549	+	12.6599i	−0.0660636	+	0.402970i
$988$	−7.10879	−	38.9439i	−0.226161	−	1.23897i
$989$	−5.93829	+	0.321965i	−0.188827	+	0.0102379i
$990$	−3.17988	+	0.114876i	−0.101063	+	0.00365101i
$991$	−16.4424	−	14.4854i	−0.522309	−	0.460143i	0.358557	−	0.933508i	$-0.383269\pi$
$991$	−16.4424	−	14.4854i	−0.522309	−	0.460143i	−0.880866	+	0.473365i	$0.843039\pi$
$992$	−40.8045	−	3.69369i	−1.29554	−	0.117275i
$993$	−32.1467	+	10.1890i	−1.02014	+	0.323339i
$994$	−9.08914	+	19.6459i	−0.288290	+	0.623129i
$995$	−9.36193	−	27.7852i	−0.296793	−	0.880851i
$996$	−12.1617	−	9.95788i	−0.385357	−	0.315528i
$997$	−40.7540	+	0.735898i	−1.29069	+	0.0233061i	−0.659135	−	0.752025i	$-0.729077\pi$
$997$	−40.7540	+	0.735898i	−1.29069	+	0.0233061i	−0.631555	+	0.775331i	$0.717583\pi$
$998$	14.8899	+	0.537913i	0.471333	+	0.0170273i
$999$	−1.14548	−	1.08506i	−0.0362414	−	0.0343297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.k.a.3.12	✓	1624
349.233	even	174	inner	349.2.k.a.233.12	yes	1624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.k.a.3.12	✓	1624	1.1	even	1	trivial
349.2.k.a.233.12	yes	1624	349.233	even	174	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.k (of order \(174\), degree \(56\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.787498 - 0.188310i) q^{2} +(-1.01339 + 0.184983i) q^{3} +(-1.19896 - 0.608175i) q^{4} +(-0.327670 - 2.57880i) q^{5} +(0.832873 + 0.0451571i) q^{6} +(3.73113 + 0.0673734i) q^{7} +(2.06390 + 1.75309i) q^{8} +(-1.81379 + 0.685000i) q^{9} +O(q^{10})\)	\(q+(-0.787498 - 0.188310i) q^{2} +(-1.01339 + 0.184983i) q^{3} +(-1.19896 - 0.608175i) q^{4} +(-0.327670 - 2.57880i) q^{5} +(0.832873 + 0.0451571i) q^{6} +(3.73113 + 0.0673734i) q^{7} +(2.06390 + 1.75309i) q^{8} +(-1.81379 + 0.685000i) q^{9} +(-0.227573 + 2.09250i) q^{10} +(0.167615 - 0.761484i) q^{11} +(1.32751 + 0.394530i) q^{12} +(-3.56409 - 3.50032i) q^{13} +(-2.92557 - 0.755665i) q^{14} +(0.809090 + 2.55271i) q^{15} +(0.293077 + 0.400338i) q^{16} +(-0.508172 - 0.598266i) q^{17} +(1.55735 - 0.197882i) q^{18} +(-5.83322 - 0.848465i) q^{19} +(-1.17550 + 3.29115i) q^{20} +(-3.79354 + 0.621920i) q^{21} +(-0.275391 + 0.568103i) q^{22} +(-5.16451 + 5.25860i) q^{23} +(-2.41581 - 1.39477i) q^{24} +(-1.70173 + 0.439550i) q^{25} +(2.14757 + 3.42765i) q^{26} +(4.35938 - 2.62295i) q^{27} +(-4.43250 - 2.34996i) q^{28} +(-9.83667 + 2.92342i) q^{29} +(-0.156457 - 2.16261i) q^{30} +(3.29882 - 6.22224i) q^{31} +(-2.25055 - 5.36468i) q^{32} +(-0.0289977 + 0.802683i) q^{33} +(0.287525 + 0.566827i) q^{34} +(-1.04884 - 9.64392i) q^{35} +(2.59126 + 0.281816i) q^{36} +(-0.0829674 - 0.298821i) q^{37} +(4.43387 + 1.76661i) q^{38} +(4.25930 + 2.88788i) q^{39} +(3.84459 - 5.89681i) q^{40} +(-4.41372 + 5.19623i) q^{41} +(3.10452 + 0.224601i) q^{42} +(0.595700 + 0.544212i) q^{43} +(-0.664079 + 0.811048i) q^{44} +(2.36080 + 4.45295i) q^{45} +(5.05728 - 3.16861i) q^{46} +(1.06558 - 3.16254i) q^{47} +(-0.371056 - 0.351483i) q^{48} +(6.92139 + 0.250042i) q^{49} +(1.42288 - 0.0256930i) q^{50} +(0.625643 + 0.512272i) q^{51} +(2.14439 + 6.36433i) q^{52} +(1.30182 - 2.81384i) q^{53} +(-3.92693 + 1.24466i) q^{54} +(-2.01864 - 0.182730i) q^{55} +(7.58256 + 6.68006i) q^{56} +(6.06825 - 0.219221i) q^{57} +(8.29686 - 0.449843i) q^{58} +(0.261732 + 1.43384i) q^{59} +(0.582428 - 3.55266i) q^{60} +(-2.45093 - 2.58741i) q^{61} +(-3.76952 + 4.27880i) q^{62} +(-6.81365 + 2.43363i) q^{63} +(0.601543 + 3.66925i) q^{64} +(-7.85877 + 10.3380i) q^{65} +(0.173989 - 0.626651i) q^{66} +(-2.41504 + 6.06129i) q^{67} +(0.245426 + 1.02635i) q^{68} +(4.26089 - 6.28434i) q^{69} +(-0.990086 + 7.79207i) q^{70} +(1.28645 - 7.04750i) q^{71} +(-4.94434 - 1.76597i) q^{72} +(7.67452 - 4.24802i) q^{73} +(0.00906562 + 0.250945i) q^{74} +(1.64320 - 0.760223i) q^{75} +(6.47776 + 4.56489i) q^{76} +(0.676699 - 2.82991i) q^{77} +(-2.81037 - 3.07627i) q^{78} +(3.55002 + 7.67324i) q^{79} +(0.936360 - 0.886967i) q^{80} +(0.431864 - 0.380462i) q^{81} +(4.45430 - 3.26087i) q^{82} +(-10.4662 - 4.39068i) q^{83} +(4.92653 + 1.56148i) q^{84} +(-1.37630 + 1.50651i) q^{85} +(-0.366632 - 0.540741i) q^{86} +(9.42757 - 4.78216i) q^{87} +(1.68089 - 1.27778i) q^{88} +(10.9174 - 5.29227i) q^{89} +(-1.02059 - 3.95125i) q^{90} +(-13.0623 - 13.3003i) q^{91} +(9.39018 - 3.16392i) q^{92} +(-2.19197 + 6.91575i) q^{93} +(-1.43468 + 2.28983i) q^{94} +(-0.276647 + 15.3207i) q^{95} +(3.27305 + 5.02018i) q^{96} +(-4.63141 - 0.588482i) q^{97} +(-5.40349 - 1.50027i) q^{98} +(0.217598 + 1.49599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9}+O(q^{10}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9} - 58 q^{10} - 58 q^{11} - 57 q^{12} - 55 q^{13} - 48 q^{14} - 59 q^{15} - 29 q^{16} - 48 q^{17} + 43 q^{18} + 67 q^{19} - 58 q^{20} + 58 q^{21} - 55 q^{22} - 41 q^{23} - 39 q^{24} - 29 q^{25} - 112 q^{26} - 76 q^{27} - 58 q^{28} - 56 q^{29} - 67 q^{30} - 90 q^{31} - 67 q^{32} - 46 q^{33} + 5 q^{34} - 82 q^{36} + 45 q^{37} - 58 q^{38} - 58 q^{39} - 112 q^{40} + 10 q^{41} + 305 q^{42} - 13 q^{43} + 40 q^{44} - 56 q^{45} - 85 q^{46} - 58 q^{47} - 122 q^{48} - 93 q^{49} - 441 q^{50} - 160 q^{51} + 58 q^{52} - 58 q^{53} - 85 q^{54} + 34 q^{55} - 69 q^{56} - 29 q^{57} - 58 q^{58} - 40 q^{59} + 522 q^{60} + 87 q^{61} - 49 q^{62} - 37 q^{63} + 335 q^{64} - 58 q^{65} - 565 q^{66} - 116 q^{67} - 58 q^{68} + 16 q^{69} - 98 q^{70} - 34 q^{71} + 44 q^{72} - 52 q^{73} - 204 q^{74} - 95 q^{76} - 54 q^{77} + 439 q^{78} - 58 q^{79} - 192 q^{80} - 209 q^{81} - 79 q^{82} + 162 q^{83} + 330 q^{84} - 192 q^{85} + 126 q^{86} - 190 q^{87} - 8 q^{88} + 345 q^{89} - 46 q^{90} - 30 q^{91} + 62 q^{92} - 89 q^{93} - 87 q^{94} - 350 q^{95} + 990 q^{96} - 43 q^{97} - 464 q^{98} - 97 q^{99}+O(q^{100}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9 - 58 * q^10 - 58 * q^11 - 57 * q^12 - 55 * q^13 - 48 * q^14 - 59 * q^15 - 29 * q^16 - 48 * q^17 + 43 * q^18 + 67 * q^19 - 58 * q^20 + 58 * q^21 - 55 * q^22 - 41 * q^23 - 39 * q^24 - 29 * q^25 - 112 * q^26 - 76 * q^27 - 58 * q^28 - 56 * q^29 - 67 * q^30 - 90 * q^31 - 67 * q^32 - 46 * q^33 + 5 * q^34 - 82 * q^36 + 45 * q^37 - 58 * q^38 - 58 * q^39 - 112 * q^40 + 10 * q^41 + 305 * q^42 - 13 * q^43 + 40 * q^44 - 56 * q^45 - 85 * q^46 - 58 * q^47 - 122 * q^48 - 93 * q^49 - 441 * q^50 - 160 * q^51 + 58 * q^52 - 58 * q^53 - 85 * q^54 + 34 * q^55 - 69 * q^56 - 29 * q^57 - 58 * q^58 - 40 * q^59 + 522 * q^60 + 87 * q^61 - 49 * q^62 - 37 * q^63 + 335 * q^64 - 58 * q^65 - 565 * q^66 - 116 * q^67 - 58 * q^68 + 16 * q^69 - 98 * q^70 - 34 * q^71 + 44 * q^72 - 52 * q^73 - 204 * q^74 - 95 * q^76 - 54 * q^77 + 439 * q^78 - 58 * q^79 - 192 * q^80 - 209 * q^81 - 79 * q^82 + 162 * q^83 + 330 * q^84 - 192 * q^85 + 126 * q^86 - 190 * q^87 - 8 * q^88 + 345 * q^89 - 46 * q^90 - 30 * q^91 + 62 * q^92 - 89 * q^93 - 87 * q^94 - 350 * q^95 + 990 * q^96 - 43 * q^97 - 464 * q^98 - 97 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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