LMFDB - Embedded newform 429.2.f.a.131.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(131,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("429.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.f (of order $2$, degree $1$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	429.131
Dual form			429.2.f.a.131.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25502 q^{2} +(0.750108 + 1.56120i) q^{3} -0.424934 q^{4} +0.276238i q^{5} +(-0.941398 - 1.95933i) q^{6} -4.01346i q^{7} +3.04333 q^{8} +(-1.87468 + 2.34213i) q^{9} +O(q^{10})$	\(q-1.25502 q^{2} +(0.750108 + 1.56120i) q^{3} -0.424934 q^{4} +0.276238i q^{5} +(-0.941398 - 1.95933i) q^{6} -4.01346i q^{7} +3.04333 q^{8} +(-1.87468 + 2.34213i) q^{9} -0.346684i q^{10} +(-0.844765 - 3.20724i) q^{11} +(-0.318746 - 0.663406i) q^{12} -1.00000i q^{13} +5.03696i q^{14} +(-0.431263 + 0.207209i) q^{15} -2.96956 q^{16} -3.23251 q^{17} +(2.35275 - 2.93942i) q^{18} -4.68920i q^{19} -0.117383i q^{20} +(6.26580 - 3.01053i) q^{21} +(1.06019 + 4.02514i) q^{22} -3.58306i q^{23} +(2.28283 + 4.75124i) q^{24} +4.92369 q^{25} +1.25502i q^{26} +(-5.06274 - 1.16988i) q^{27} +1.70545i q^{28} +3.44536 q^{29} +(0.541242 - 0.260050i) q^{30} +5.10613 q^{31} -2.35981 q^{32} +(4.37347 - 3.72462i) q^{33} +4.05685 q^{34} +1.10867 q^{35} +(0.796613 - 0.995252i) q^{36} +8.11364 q^{37} +5.88502i q^{38} +(1.56120 - 0.750108i) q^{39} +0.840685i q^{40} -2.43779 q^{41} +(-7.86369 + 3.77826i) q^{42} +1.87809i q^{43} +(0.358969 + 1.36286i) q^{44} +(-0.646987 - 0.517857i) q^{45} +4.49680i q^{46} -4.55013i q^{47} +(-2.22749 - 4.63608i) q^{48} -9.10786 q^{49} -6.17931 q^{50} +(-2.42473 - 5.04659i) q^{51} +0.424934i q^{52} -2.85869i q^{53} +(6.35383 + 1.46822i) q^{54} +(0.885962 - 0.233357i) q^{55} -12.2143i q^{56} +(7.32077 - 3.51741i) q^{57} -4.32399 q^{58} +7.32158i q^{59} +(0.183258 - 0.0880500i) q^{60} -4.55291i q^{61} -6.40828 q^{62} +(9.40006 + 7.52393i) q^{63} +8.90073 q^{64} +0.276238 q^{65} +(-5.48877 + 4.67446i) q^{66} -12.6002 q^{67} +1.37360 q^{68} +(5.59387 - 2.68768i) q^{69} -1.39140 q^{70} -14.4052i q^{71} +(-5.70526 + 7.12789i) q^{72} +1.61376i q^{73} -10.1828 q^{74} +(3.69330 + 7.68686i) q^{75} +1.99260i q^{76} +(-12.8721 + 3.39043i) q^{77} +(-1.95933 + 0.941398i) q^{78} -0.650989i q^{79} -0.820308i q^{80} +(-1.97118 - 8.78148i) q^{81} +3.05947 q^{82} -5.36275 q^{83} +(-2.66255 + 1.27928i) q^{84} -0.892943i q^{85} -2.35703i q^{86} +(2.58440 + 5.37889i) q^{87} +(-2.57090 - 9.76069i) q^{88} +4.56861i q^{89} +(0.811980 + 0.649919i) q^{90} -4.01346 q^{91} +1.52256i q^{92} +(3.83015 + 7.97168i) q^{93} +5.71049i q^{94} +1.29534 q^{95} +(-1.77011 - 3.68413i) q^{96} +3.58425 q^{97} +11.4305 q^{98} +(9.09544 + 4.03398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	$ 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.25502			−0.887431			−0.443715	−	0.896168i	$-0.646340\pi$
$2$	−1.25502			−0.887431			−0.443715	+	0.896168i	$0.646340\pi$
$3$	0.750108	+	1.56120i	0.433075	+	0.901358i
$3$	0.750108	+	1.56120i	0.433075	+	0.901358i
$4$	−0.424934			−0.212467
$5$			0.276238i			0.123538i	0.998090	+	0.0617688i	$0.0196741\pi$
$5$			0.276238i			0.123538i	−0.998090	+	0.0617688i	$0.980326\pi$
$6$	−0.941398	−	1.95933i	−0.384324	−	0.799893i
$7$		−	4.01346i		−	1.51695i	−0.651705	−	0.758473i	$-0.725946\pi$
$7$		−	4.01346i		−	1.51695i	0.651705	−	0.758473i	$-0.274054\pi$
$8$	3.04333			1.07598
$9$	−1.87468	+	2.34213i	−0.624892	+	0.780711i
$10$		−	0.346684i		−	0.109631i
$11$	−0.844765	−	3.20724i	−0.254706	−	0.967018i
$11$	−0.844765	−	3.20724i	−0.254706	−	0.967018i
$12$	−0.318746	−	0.663406i	−0.0920141	−	0.191509i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$			5.03696i			1.34618i
$15$	−0.431263	+	0.207209i	−0.111352	+	0.0535011i
$16$	−2.96956			−0.742391
$17$	−3.23251			−0.783999			−0.391999	−	0.919966i	$-0.628216\pi$
$17$	−3.23251			−0.783999			−0.391999	+	0.919966i	$0.628216\pi$
$18$	2.35275	−	2.93942i	0.554548	−	0.692827i
$19$		−	4.68920i		−	1.07578i	−0.843016	−	0.537888i	$-0.819222\pi$
$19$		−	4.68920i		−	1.07578i	0.843016	−	0.537888i	$-0.180778\pi$
$20$		−	0.117383i		−	0.0262476i
$21$	6.26580	−	3.01053i	1.36731	−	0.656951i
$22$	1.06019	+	4.02514i	0.226034	+	0.858162i
$23$		−	3.58306i		−	0.747120i	−0.927606	−	0.373560i	$-0.878137\pi$
$23$		−	3.58306i		−	0.747120i	0.927606	−	0.373560i	$-0.121863\pi$
$24$	2.28283	+	4.75124i	0.465980	+	0.969843i
$25$	4.92369			0.984738
$26$			1.25502i			0.246129i
$27$	−5.06274	−	1.16988i	−0.974325	−	0.225144i
$28$			1.70545i			0.322301i
$29$	3.44536			0.639788			0.319894	−	0.947453i	$-0.396353\pi$
$29$	3.44536			0.639788			0.319894	+	0.947453i	$0.396353\pi$
$30$	0.541242	−	0.260050i	0.0988168	−	0.0474785i
$31$	5.10613			0.917088			0.458544	−	0.888672i	$-0.348371\pi$
$31$	5.10613			0.917088			0.458544	+	0.888672i	$0.348371\pi$
$32$	−2.35981			−0.417160
$33$	4.37347	−	3.72462i	0.761323	−	0.648373i
$34$	4.05685			0.695744
$35$	1.10867			0.187400
$36$	0.796613	−	0.995252i	0.132769	−	0.165875i
$37$	8.11364			1.33387			0.666937	−	0.745114i	$-0.267605\pi$
$37$	8.11364			1.33387			0.666937	+	0.745114i	$0.267605\pi$
$38$			5.88502i			0.954677i
$39$	1.56120	−	0.750108i	0.249992	−	0.120113i
$40$			0.840685i			0.132924i
$41$	−2.43779			−0.380719			−0.190360	−	0.981714i	$-0.560965\pi$
$41$	−2.43779			−0.380719			−0.190360	+	0.981714i	$0.560965\pi$
$42$	−7.86369	+	3.77826i	−1.21339	+	0.582999i
$43$			1.87809i			0.286406i	0.989693	+	0.143203i	$0.0457401\pi$
$43$			1.87809i			0.286406i	−0.989693	+	0.143203i	$0.954260\pi$
$44$	0.358969	+	1.36286i	0.0541167	+	0.205459i
$45$	−0.646987	−	0.517857i	−0.0964472	−	0.0771976i
$46$			4.49680i			0.663017i
$47$		−	4.55013i		−	0.663705i	−0.943331	−	0.331852i	$-0.892326\pi$
$47$		−	4.55013i		−	0.663705i	0.943331	−	0.331852i	$-0.107674\pi$
$48$	−2.22749	−	4.63608i	−0.321511	−	0.669160i
$49$	−9.10786			−1.30112
$50$	−6.17931			−0.873887
$51$	−2.42473	−	5.04659i	−0.339530	−	0.706663i
$52$			0.424934i			0.0589277i
$53$		−	2.85869i		−	0.392671i	−0.980537	−	0.196336i	$-0.937096\pi$
$53$		−	2.85869i		−	0.392671i	0.980537	−	0.196336i	$-0.0629042\pi$
$54$	6.35383	+	1.46822i	0.864646	+	0.199800i
$55$	0.885962	−	0.233357i	0.119463	−	0.0314658i
$56$		−	12.2143i		−	1.63220i
$57$	7.32077	−	3.51741i	0.969660	−	0.465892i
$58$	−4.32399			−0.567767
$59$			7.32158i			0.953189i	0.879123	+	0.476594i	$0.158129\pi$
$59$			7.32158i			0.953189i	−0.879123	+	0.476594i	$0.841871\pi$
$60$	0.183258	−	0.0880500i	0.0236585	−	0.0113672i
$61$		−	4.55291i		−	0.582940i	−0.956580	−	0.291470i	$-0.905856\pi$
$61$		−	4.55291i		−	0.582940i	0.956580	−	0.291470i	$-0.0941444\pi$
$62$	−6.40828			−0.813852
$63$	9.40006	+	7.52393i	1.18430	+	0.947927i
$64$	8.90073			1.11259
$65$	0.276238			0.0342632
$66$	−5.48877	+	4.67446i	−0.675621	+	0.575386i
$67$	−12.6002			−1.53936			−0.769679	−	0.638431i	$-0.779584\pi$
$67$	−12.6002			−1.53936			−0.769679	+	0.638431i	$0.779584\pi$
$68$	1.37360			0.166574
$69$	5.59387	−	2.68768i	0.673422	−	0.323559i
$70$	−1.39140			−0.166304
$71$		−	14.4052i		−	1.70959i	−0.518967	−	0.854794i	$-0.673683\pi$
$71$		−	14.4052i		−	1.70959i	0.518967	−	0.854794i	$-0.326317\pi$
$72$	−5.70526	+	7.12789i	−0.672371	+	0.840030i
$73$			1.61376i			0.188876i	0.995531	+	0.0944382i	$0.0301055\pi$
$73$			1.61376i			0.188876i	−0.995531	+	0.0944382i	$0.969895\pi$
$74$	−10.1828			−1.18372
$75$	3.69330	+	7.68686i	0.426466	+	0.887602i
$76$			1.99260i			0.228567i
$77$	−12.8721	+	3.39043i	−1.46691	+	0.386376i
$78$	−1.95933	+	0.941398i	−0.221850	+	0.106592i
$79$		−	0.650989i		−	0.0732420i	−0.999329	−	0.0366210i	$-0.988341\pi$
$79$		−	0.650989i		−	0.0732420i	0.999329	−	0.0366210i	$-0.0116594\pi$
$80$		−	0.820308i		−	0.0917132i
$81$	−1.97118	−	8.78148i	−0.219021	−	0.975720i
$82$	3.05947			0.337862
$83$	−5.36275			−0.588638			−0.294319	−	0.955707i	$-0.595093\pi$
$83$	−5.36275			−0.588638			−0.294319	+	0.955707i	$0.595093\pi$
$84$	−2.66255	+	1.27928i	−0.290508	+	0.139580i
$85$		−	0.892943i		−	0.0968533i
$86$		−	2.35703i		−	0.254165i
$87$	2.58440	+	5.37889i	0.277076	+	0.576678i
$88$	−2.57090	−	9.76069i	−0.274059	−	1.04049i
$89$			4.56861i			0.484272i	0.970242	+	0.242136i	$0.0778480\pi$
$89$			4.56861i			0.484272i	−0.970242	+	0.242136i	$0.922152\pi$
$90$	0.811980	+	0.649919i	0.0855902	+	0.0685075i
$91$	−4.01346			−0.420725
$92$			1.52256i			0.158738i
$93$	3.83015	+	7.97168i	0.397168	+	0.826625i
$94$			5.71049i			0.588992i
$95$	1.29534			0.132899
$96$	−1.77011	−	3.68413i	−0.180662	−	0.376010i
$97$	3.58425			0.363925			0.181963	−	0.983305i	$-0.441755\pi$
$97$	3.58425			0.363925			0.181963	+	0.983305i	$0.441755\pi$
$98$	11.4305			1.15466
$99$	9.09544	+	4.03398i	0.914126	+	0.405430i
$100$	−2.09224			−0.209224
$101$	−17.5276			−1.74406			−0.872030	−	0.489452i	$-0.837197\pi$
$101$	−17.5276			−1.74406			−0.872030	+	0.489452i	$0.837197\pi$
$102$	3.04308	+	6.33355i	0.301310	+	0.627115i
$103$	−4.73186			−0.466244			−0.233122	−	0.972448i	$-0.574894\pi$
$103$	−4.73186			−0.466244			−0.233122	+	0.972448i	$0.574894\pi$
$104$		−	3.04333i		−	0.298423i
$105$	0.831624	+	1.73086i	0.0811582	+	0.168914i
$106$			3.58770i			0.348468i
$107$	13.2712			1.28297			0.641487	−	0.767134i	$-0.278318\pi$
$107$	13.2712			1.28297			0.641487	+	0.767134i	$0.278318\pi$
$108$	2.15133	+	0.497123i	0.207012	+	0.0478357i
$109$			17.8365i			1.70843i	0.519920	+	0.854215i	$0.325962\pi$
$109$			17.8365i			1.70843i	−0.519920	+	0.854215i	$0.674038\pi$
$110$	−1.11190	+	0.292866i	−0.106015	+	0.0279237i
$111$	6.08611	+	12.6670i	0.577668	+	1.20230i
$112$			11.9182i			1.12617i
$113$			4.32519i			0.406880i	0.979087	+	0.203440i	$0.0652121\pi$
$113$			4.32519i			0.406880i	−0.979087	+	0.203440i	$0.934788\pi$
$114$	−9.18769	+	4.41441i	−0.860506	+	0.413447i
$115$	0.989779			0.0922974
$116$	−1.46405			−0.135934
$117$	2.34213	+	1.87468i	0.216530	+	0.173314i
$118$		−	9.18871i		−	0.845889i
$119$			12.9735i			1.18928i
$120$	−1.31248	+	0.630605i	−0.119812	+	0.0575661i
$121$	−9.57274	+	5.41873i	−0.870249	+	0.492611i
$122$			5.71397i			0.517319i
$123$	−1.82861	−	3.80587i	−0.164880	−	0.343164i
$124$	−2.16977			−0.194851
$125$			2.74130i			0.245190i
$126$	−11.7972	−	9.44266i	−1.05098	−	0.841219i
$127$			4.31858i			0.383212i	0.981472	+	0.191606i	$0.0613696\pi$
$127$			4.31858i			0.383212i	−0.981472	+	0.191606i	$0.938630\pi$
$128$	−6.45094			−0.570188
$129$	−2.93207	+	1.40877i	−0.258154	+	0.124035i
$130$	−0.346684			−0.0304062
$131$	10.5629			0.922881			0.461441	−	0.887171i	$-0.347333\pi$
$131$	10.5629			0.922881			0.461441	+	0.887171i	$0.347333\pi$
$132$	−1.85843	+	1.58272i	−0.161756	+	0.137758i
$133$	−18.8199			−1.63189
$134$	15.8134			1.36607
$135$	0.323167	−	1.39852i	0.0278138	−	0.120366i
$136$	−9.83760			−0.843567
$137$		−	8.01092i		−	0.684419i	−0.939624	−	0.342209i	$-0.888825\pi$
$137$		−	8.01092i		−	0.684419i	0.939624	−	0.342209i	$-0.111175\pi$
$138$	−7.02039	+	3.37309i	−0.597616	+	0.287136i
$139$		−	17.6480i		−	1.49688i	−0.663200	−	0.748442i	$-0.730802\pi$
$139$		−	17.6480i		−	1.49688i	0.663200	−	0.748442i	$-0.269198\pi$
$140$	−0.471112			−0.0398162
$141$	7.10365	−	3.41309i	0.598236	−	0.287434i
$142$			18.0788i			1.51714i
$143$	−3.20724	+	0.844765i	−0.268203	+	0.0706428i
$144$	5.56697	−	6.95512i	0.463914	−	0.579593i
$145$			0.951742i			0.0790378i
$146$		−	2.02530i		−	0.167615i
$147$	−6.83188	−	14.2192i	−0.563484	−	1.17278i
$148$	−3.44776			−0.283404
$149$	−17.1732			−1.40688			−0.703441	−	0.710753i	$-0.748354\pi$
$149$	−17.1732			−1.40688			−0.703441	+	0.710753i	$0.748354\pi$
$150$	−4.63515	−	9.64713i	−0.378459	−	0.787685i
$151$			4.33760i			0.352989i	0.984302	+	0.176494i	$0.0564758\pi$
$151$			4.33760i			0.352989i	−0.984302	+	0.176494i	$0.943524\pi$
$152$		−	14.2708i		−	1.15751i
$153$	6.05991	−	7.57097i	0.489914	−	0.612077i
$154$	16.1547	−	4.25505i	1.30178	−	0.342882i
$155$			1.41051i			0.113295i
$156$	−0.663406	+	0.318746i	−0.0531150	+	0.0255201i
$157$	−11.2494			−0.897797			−0.448898	−	0.893583i	$-0.648183\pi$
$157$	−11.2494			−0.897797			−0.448898	+	0.893583i	$0.648183\pi$
$158$			0.817002i			0.0649972i
$159$	4.46298	−	2.14433i	0.353937	−	0.170056i
$160$		−	0.651871i		−	0.0515349i
$161$	−14.3805			−1.13334
$162$	2.47387	+	11.0209i	0.194366	+	0.865884i
$163$	20.0403			1.56968			0.784840	−	0.619698i	$-0.212745\pi$
$163$	20.0403			1.56968			0.784840	+	0.619698i	$0.212745\pi$
$164$	1.03590			0.0808902
$165$	1.02888	+	1.20812i	0.0800984	+	0.0940519i
$166$	6.73033			0.522375
$167$	21.6905			1.67846			0.839231	−	0.543775i	$-0.183005\pi$
$167$	21.6905			1.67846			0.839231	+	0.543775i	$0.183005\pi$
$168$	19.0689	−	9.16204i	1.47120	−	0.706867i
$169$	−1.00000			−0.0769231
$170$			1.12066i			0.0859506i
$171$	10.9827	+	8.79073i	0.839871	+	0.672244i
$172$		−	0.798063i		−	0.0608517i
$173$	7.77467			0.591097			0.295549	−	0.955328i	$-0.404498\pi$
$173$	7.77467			0.591097			0.295549	+	0.955328i	$0.404498\pi$
$174$	−3.24346	−	6.75060i	−0.245886	−	0.511762i
$175$		−	19.7610i		−	1.49379i
$176$	2.50858	+	9.52410i	0.189092	+	0.717906i
$177$	−11.4304	+	5.49198i	−0.859164	+	0.412802i
$178$		−	5.73368i		−	0.429758i
$179$			6.18647i			0.462399i	0.972906	+	0.231199i	$0.0742650\pi$
$179$			6.18647i			0.462399i	−0.972906	+	0.231199i	$0.925735\pi$
$180$	0.274927	+	0.220055i	0.0204918	+	0.0164019i
$181$	16.1628			1.20137			0.600685	−	0.799486i	$-0.294894\pi$
$181$	16.1628			1.20137			0.600685	+	0.799486i	$0.294894\pi$
$182$	5.03696			0.373364
$183$	7.10799	−	3.41517i	0.525438	−	0.252457i
$184$		−	10.9044i		−	0.803886i
$185$			2.24130i			0.164784i
$186$	−4.80690	−	10.0046i	−0.352459	−	0.733572i
$187$	2.73071	+	10.3674i	0.199689	+	0.758141i
$188$			1.93350i			0.141015i
$189$	−4.69528	+	20.3191i	−0.341532	+	1.47800i
$190$	−1.62567			−0.117938
$191$			12.8976i			0.933237i	0.884459	+	0.466618i	$0.154528\pi$
$191$			12.8976i			0.933237i	−0.884459	+	0.466618i	$0.845472\pi$
$192$	6.67651	+	13.8958i	0.481836	+	1.00284i
$193$		−	24.2427i		−	1.74503i	−0.488590	−	0.872513i	$-0.662489\pi$
$193$		−	24.2427i		−	1.74503i	0.488590	−	0.872513i	$-0.337511\pi$
$194$	−4.49829			−0.322958
$195$	0.207209	+	0.431263i	0.0148385	+	0.0308834i
$196$	3.87024			0.276446
$197$	27.1562			1.93480			0.967400	−	0.253253i	$-0.0815003\pi$
$197$	27.1562			1.93480			0.967400	+	0.253253i	$0.0815003\pi$
$198$	−11.4149	−	5.06271i	−0.811224	−	0.359791i
$199$	−24.3970			−1.72946			−0.864728	−	0.502241i	$-0.832509\pi$
$199$	−24.3970			−1.72946			−0.864728	+	0.502241i	$0.832509\pi$
$200$	14.9844			1.05956
$201$	−9.45151	−	19.6714i	−0.666658	−	1.38751i
$202$	21.9974			1.54773
$203$		−	13.8278i		−	0.970523i
$204$	1.03035	+	2.14446i	0.0721390	+	0.150143i
$205$		−	0.673412i		−	0.0470331i
$206$	5.93856			0.413759
$207$	8.39201	+	6.71708i	0.583285	+	0.466869i
$208$			2.96956i			0.205902i
$209$	−15.0394	+	3.96127i	−1.04030	+	0.274007i
$210$	−1.04370	−	2.17225i	−0.0720222	−	0.149900i
$211$		−	4.66933i		−	0.321450i	−0.986999	−	0.160725i	$-0.948617\pi$
$211$		−	4.66933i		−	0.321450i	0.986999	−	0.160725i	$-0.0513833\pi$
$212$			1.21475i			0.0834296i
$213$	22.4894	−	10.8055i	1.54095	−	0.740380i
$214$	−16.6555			−1.13855
$215$	−0.518800			−0.0353819
$216$	−15.4076	−	3.56035i	−1.04835	−	0.242251i
$217$		−	20.4933i		−	1.39117i
$218$		−	22.3851i		−	1.51611i
$219$	−2.51940	+	1.21049i	−0.170245	+	0.0817977i
$220$	−0.376475	+	0.0991611i	−0.0253820	+	0.00668544i
$221$			3.23251i			0.217442i
$222$	−7.63817	−	15.8973i	−0.512640	−	1.06696i
$223$	24.0403			1.60986			0.804930	−	0.593370i	$-0.202203\pi$
$223$	24.0403			1.60986			0.804930	+	0.593370i	$0.202203\pi$
$224$			9.47101i			0.632809i
$225$	−9.23032	+	11.5319i	−0.615355	+	0.768797i
$226$		−	5.42818i		−	0.361077i
$227$	−9.86801			−0.654963			−0.327482	−	0.944858i	$-0.606200\pi$
$227$	−9.86801			−0.654963			−0.327482	+	0.944858i	$0.606200\pi$
$228$	−3.11084	+	1.49467i	−0.206021	+	0.0989866i
$229$	−6.04534			−0.399487			−0.199744	−	0.979848i	$-0.564011\pi$
$229$	−6.04534			−0.399487			−0.199744	+	0.979848i	$0.564011\pi$
$230$	−1.24219			−0.0819075
$231$	−14.9486	−	17.5527i	−0.983547	−	1.15488i
$232$	10.4854			0.688399
$233$	−0.355379			−0.0232817			−0.0116408	−	0.999932i	$-0.503705\pi$
$233$	−0.355379			−0.0232817			−0.0116408	+	0.999932i	$0.503705\pi$
$234$	−2.93942	−	2.35275i	−0.192156	−	0.153804i
$235$	1.25692			0.0819925
$236$		−	3.11119i		−	0.202521i
$237$	1.01632	−	0.488312i	0.0660173	−	0.0317193i
$238$		−	16.2820i		−	1.05541i
$239$	−6.87843			−0.444929			−0.222464	−	0.974941i	$-0.571410\pi$
$239$	−6.87843			−0.444929			−0.222464	+	0.974941i	$0.571410\pi$
$240$	1.28066	−	0.615319i	0.0826664	−	0.0397187i
$241$			13.7890i			0.888227i	0.895971	+	0.444113i	$0.146481\pi$
$241$			13.7890i			0.888227i	−0.895971	+	0.444113i	$0.853519\pi$
$242$	12.0139	−	6.80059i	0.772286	−	0.437158i
$243$	12.2310	−	9.66447i	0.784621	−	0.619976i
$244$			1.93468i			0.123855i
$245$		−	2.51594i		−	0.160738i
$246$	2.29493	+	4.77644i	0.146320	+	0.304534i
$247$	−4.68920			−0.298367
$248$	15.5397			0.986769
$249$	−4.02264	−	8.37231i	−0.254924	−	0.530573i
$250$		−	3.44038i		−	0.217589i
$251$			13.1445i			0.829672i	0.909896	+	0.414836i	$0.136161\pi$
$251$			13.1445i			0.829672i	−0.909896	+	0.414836i	$0.863839\pi$
$252$	−3.99440	−	3.19717i	−0.251624	−	0.201403i
$253$	−11.4917	+	3.02685i	−0.722479	+	0.190296i
$254$		−	5.41989i		−	0.340074i
$255$	1.39406	−	0.669804i	0.0872995	−	0.0419448i
$256$	−9.70543			−0.606589
$257$		−	23.9365i		−	1.49312i	−0.665318	−	0.746560i	$-0.731704\pi$
$257$		−	23.9365i		−	1.49312i	0.665318	−	0.746560i	$-0.268296\pi$
$258$	3.67979	−	1.76803i	0.229094	−	0.110073i
$259$		−	32.5638i		−	2.02341i
$260$	−0.117383			−0.00727979
$261$	−6.45894	+	8.06950i	−0.399798	+	0.499490i
$262$	−13.2566			−0.818993
$263$	15.3038			0.943674			0.471837	−	0.881686i	$-0.343591\pi$
$263$	15.3038			0.943674			0.471837	+	0.881686i	$0.343591\pi$
$264$	13.3099	−	11.3353i	0.819168	−	0.697637i
$265$	0.789680			0.0485096
$266$	23.6193			1.44819
$267$	−7.13250	+	3.42695i	−0.436502	+	0.209726i
$268$	5.35425			0.327063
$269$			0.373241i			0.0227569i	0.999935	+	0.0113785i	$0.00362196\pi$
$269$			0.373241i			0.0227569i	−0.999935	+	0.0113785i	$0.996378\pi$
$270$	−0.405580	+	1.75517i	−0.0246828	+	0.106816i
$271$			23.0569i			1.40061i	0.713846	+	0.700303i	$0.246952\pi$
$271$			23.0569i			1.40061i	−0.713846	+	0.700303i	$0.753048\pi$
$272$	9.59914			0.582034
$273$	−3.01053	−	6.26580i	−0.182206	−	0.379224i
$274$			10.0538i			0.607374i
$275$	−4.15936	−	15.7915i	−0.250819	−	0.952260i
$276$	−2.37702	+	1.14209i	−0.143080	+	0.0687456i
$277$			21.4561i			1.28917i	0.764532	+	0.644585i	$0.222970\pi$
$277$			21.4561i			1.28917i	−0.764532	+	0.644585i	$0.777030\pi$
$278$			22.1485i			1.32838i
$279$	−9.57234	+	11.9592i	−0.573081	+	0.715981i
$280$	3.37406			0.201638
$281$	−9.28215			−0.553727			−0.276863	−	0.960909i	$-0.589295\pi$
$281$	−9.28215			−0.553727			−0.276863	+	0.960909i	$0.589295\pi$
$282$	−8.91520	+	4.28348i	−0.530893	+	0.255078i
$283$			19.9371i			1.18514i	0.805521	+	0.592568i	$0.201886\pi$
$283$			19.9371i			1.18514i	−0.805521	+	0.592568i	$0.798114\pi$
$284$			6.12128i			0.363231i
$285$	0.971643	+	2.02228i	0.0575552	+	0.119789i
$286$	4.02514	−	1.06019i	0.238011	−	0.0626906i
$287$			9.78398i			0.577530i
$288$	4.42388	−	5.52700i	0.260680	−	0.325681i
$289$	−6.55088			−0.385346
$290$		−	1.19445i		−	0.0701406i
$291$	2.68857	+	5.59572i	0.157607	+	0.328027i
$292$		−	0.685741i		−	0.0401300i
$293$	−6.02612			−0.352050			−0.176025	−	0.984386i	$-0.556324\pi$
$293$	−6.02612			−0.352050			−0.176025	+	0.984386i	$0.556324\pi$
$294$	8.57412	+	17.8453i	0.500053	+	1.04076i
$295$	−2.02250			−0.117755
$296$	24.6925			1.43522
$297$	0.524733	+	17.2257i	0.0304481	+	0.999536i
$298$	21.5526			1.24851
$299$	−3.58306			−0.207214
$300$	−1.56941	−	3.26640i	−0.0906099	−	0.188586i
$301$	7.53763			0.434462
$302$		−	5.44376i		−	0.313253i
$303$	−13.1476	−	27.3640i	−0.755309	−	1.57202i
$304$			13.9249i			0.798647i
$305$	1.25769			0.0720150
$306$	−7.60528	+	9.50169i	−0.434765	+	0.543176i
$307$		−	21.8994i		−	1.24987i	−0.780678	−	0.624933i	$-0.785126\pi$
$307$		−	21.8994i		−	1.24987i	0.780678	−	0.624933i	$-0.214874\pi$
$308$	5.46980	−	1.44071i	0.311671	−	0.0820920i
$309$	−3.54940	−	7.38736i	−0.201919	−	0.420252i
$310$		−	1.77021i		−	0.100541i
$311$			19.6466i			1.11406i	0.830493	+	0.557029i	$0.188059\pi$
$311$			19.6466i			1.11406i	−0.830493	+	0.557029i	$0.811941\pi$
$312$	4.75124	−	2.28283i	0.268986	−	0.129240i
$313$	−0.393840			−0.0222612			−0.0111306	−	0.999938i	$-0.503543\pi$
$313$	−0.393840			−0.0222612			−0.0111306	+	0.999938i	$0.503543\pi$
$314$	14.1181			0.796732
$315$	−2.07840	+	2.59666i	−0.117105	+	0.146305i
$316$			0.276627i			0.0155615i
$317$			14.1737i			0.796075i	0.917369	+	0.398038i	$0.130309\pi$
$317$			14.1737i			0.796075i	−0.917369	+	0.398038i	$0.869691\pi$
$318$	−5.60111	+	2.69116i	−0.314095	+	0.150913i
$319$	−2.91052	−	11.0501i	−0.162958	−	0.618687i
$320$			2.45872i			0.137447i
$321$	9.95482	+	20.7189i	0.555624	+	1.15642i
$322$	18.0477			1.00576
$323$			15.1579i			0.843407i
$324$	0.837623	+	3.73155i	0.0465346	+	0.207308i
$325$		−	4.92369i		−	0.273117i
$326$	−25.1509			−1.39298
$327$	−27.8464	+	13.3793i	−1.53991	+	0.739879i
$328$	−7.41901			−0.409646
$329$	−18.2618			−1.00680
$330$	−1.29127	−	1.51621i	−0.0710818	−	0.0834646i
$331$	32.9921			1.81341			0.906706	−	0.421763i	$-0.138589\pi$
$331$	32.9921			1.81341			0.906706	+	0.421763i	$0.138589\pi$
$332$	2.27881			0.125066
$333$	−15.2104	+	19.0032i	−0.833527	+	1.04137i
$334$	−27.2220			−1.48952
$335$		−	3.48066i		−	0.190169i
$336$	−18.6067	+	8.93996i	−1.01508	+	0.487715i
$337$			29.0830i			1.58425i	0.610357	+	0.792126i	$0.291026\pi$
$337$			29.0830i			1.58425i	−0.610357	+	0.792126i	$0.708974\pi$
$338$	1.25502			0.0682639
$339$	−6.75247	+	3.24436i	−0.366744	+	0.176209i
$340$			0.379442i			0.0205781i
$341$	−4.31348	−	16.3766i	−0.233588	−	0.886841i
$342$	−13.7835	−	11.0325i	−0.745327	−	0.596570i
$343$			8.45981i			0.456787i
$344$			5.71565i			0.308167i
$345$	0.742441	+	1.54524i	0.0399717	+	0.0831930i
$346$	−9.75734			−0.524558
$347$	19.6725			1.05607			0.528037	−	0.849222i	$-0.322928\pi$
$347$	19.6725			1.05607			0.528037	+	0.849222i	$0.322928\pi$
$348$	−1.09820	−	2.28567i	−0.0588695	−	0.122525i
$349$			17.0495i			0.912638i	0.889816	+	0.456319i	$0.150832\pi$
$349$			17.0495i			0.912638i	−0.889816	+	0.456319i	$0.849168\pi$
$350$			24.8004i			1.32564i
$351$	−1.16988	+	5.06274i	−0.0624438	+	0.270229i
$352$	1.99349	+	7.56848i	0.106253	+	0.403401i
$353$		−	11.1193i		−	0.591819i	−0.955216	−	0.295910i	$-0.904377\pi$
$353$		−	11.1193i		−	0.591819i	0.955216	−	0.295910i	$-0.0956227\pi$
$354$	14.3454	−	6.89252i	0.762449	−	0.366334i
$355$	3.97928			0.211198
$356$		−	1.94136i		−	0.102892i
$357$	−20.2543	+	9.73156i	−1.07197	+	0.515049i
$358$		−	7.76413i		−	0.410347i
$359$	8.17358			0.431385			0.215693	−	0.976461i	$-0.430799\pi$
$359$	8.17358			0.431385			0.215693	+	0.976461i	$0.430799\pi$
$360$	−1.96900	−	1.57601i	−0.103775	−	0.0830631i
$361$	−2.98861			−0.157295
$362$	−20.2846			−1.06613
$363$	−15.6403	−	10.8803i	−0.820903	−	0.571068i
$364$	1.70545			0.0893901
$365$	−0.445783			−0.0233333
$366$	−8.92064	+	4.28610i	−0.466289	+	0.224038i
$367$	10.2181			0.533383			0.266691	−	0.963782i	$-0.414070\pi$
$367$	10.2181			0.533383			0.266691	+	0.963782i	$0.414070\pi$
$368$			10.6401i			0.554655i
$369$	4.57007	−	5.70964i	0.237908	−	0.297232i
$370$		−	2.81287i		−	0.146234i
$371$	−11.4732			−0.595661
$372$	−1.62756	−	3.38744i	−0.0843851	−	0.175630i
$373$			32.7288i			1.69463i	0.531089	+	0.847316i	$0.321783\pi$
$373$			32.7288i			1.69463i	−0.531089	+	0.847316i	$0.678217\pi$
$374$	−3.42709	−	13.0113i	−0.177211	−	0.672798i
$375$	−4.27972	+	2.05628i	−0.221004	+	0.106186i
$376$		−	13.8476i		−	0.714133i
$377$		−	3.44536i		−	0.177445i
$378$	5.89266	−	25.5008i	0.303086	−	1.31162i
$379$	16.5798			0.851647			0.425823	−	0.904806i	$-0.359985\pi$
$379$	16.5798			0.851647			0.425823	+	0.904806i	$0.359985\pi$
$380$	−0.550433			−0.0282366
$381$	−6.74215	+	3.23940i	−0.345411	+	0.165960i
$382$		−	16.1867i		−	0.828183i
$383$		−	36.8862i		−	1.88480i	−0.334495	−	0.942398i	$-0.608566\pi$
$383$		−	36.8862i		−	1.88480i	0.334495	−	0.942398i	$-0.391434\pi$
$384$	−4.83890	−	10.0712i	−0.246934	−	0.513943i
$385$	−0.936567	−	3.55577i	−0.0477319	−	0.181219i
$386$			30.4250i			1.54859i
$387$	−4.39873	−	3.52081i	−0.223600	−	0.178973i
$388$	−1.52307			−0.0773220
$389$			27.8356i			1.41132i	0.708550	+	0.705660i	$0.249350\pi$
$389$			27.8356i			1.41132i	−0.708550	+	0.705660i	$0.750650\pi$
$390$	−0.260050	−	0.541242i	−0.0131682	−	0.0274068i
$391$			11.5823i			0.585741i
$392$	−27.7182			−1.39998
$393$	7.92329	+	16.4907i	0.399677	+	0.831846i
$394$	−34.0815			−1.71700
$395$	0.179828			0.00904814
$396$	−3.86496	−	1.71417i	−0.194222	−	0.0861404i
$397$	33.7189			1.69230			0.846152	−	0.532942i	$-0.178913\pi$
$397$	33.7189			1.69230			0.846152	+	0.532942i	$0.178913\pi$
$398$	30.6186			1.53477
$399$	−14.1170	−	29.3816i	−0.706733	−	1.47092i
$400$	−14.6212			−0.731061
$401$		−	0.315205i		−	0.0157406i	−0.999969	−	0.00787030i	$-0.997495\pi$
$401$		−	0.315205i		−	0.0157406i	0.999969	−	0.00787030i	$-0.00250522\pi$
$402$	11.8618	+	24.6879i	0.591613	+	1.23132i
$403$		−	5.10613i		−	0.254355i
$404$	7.44806			0.370555
$405$	2.42578	−	0.544517i	0.120538	−	0.0270573i
$406$			17.3542i			0.861272i
$407$	−6.85412	−	26.0224i	−0.339746	−	1.28988i
$408$	−7.37926	−	15.3584i	−0.365328	−	0.760356i
$409$		−	6.16701i		−	0.304939i	−0.988308	−	0.152470i	$-0.951277\pi$
$409$		−	6.16701i		−	0.304939i	0.988308	−	0.152470i	$-0.0487226\pi$
$410$			0.845143i			0.0417386i
$411$	12.5066	−	6.00905i	0.616906	−	0.296405i
$412$	2.01072			0.0990613
$413$	29.3849			1.44594
$414$	−10.5321	−	8.43004i	−0.517625	−	0.414314i
$415$		−	1.48140i		−	0.0727189i
$416$			2.35981i			0.115699i
$417$	27.5520	−	13.2379i	1.34923	−	0.648264i
$418$	18.8747	−	4.97146i	0.923190	−	0.243162i
$419$		−	23.0586i		−	1.12648i	−0.826292	−	0.563242i	$-0.809554\pi$
$419$		−	23.0586i		−	1.12648i	0.826292	−	0.563242i	$-0.190446\pi$
$420$	−0.353385	−	0.735499i	−0.0172434	−	0.0358887i
$421$	17.1064			0.833714			0.416857	−	0.908972i	$-0.363132\pi$
$421$	17.1064			0.833714			0.416857	+	0.908972i	$0.363132\pi$
$422$			5.86009i			0.285265i
$423$	10.6570	+	8.53002i	0.518162	+	0.414744i
$424$		−	8.69994i		−	0.422506i
$425$	−15.9159			−0.772034
$426$	−28.2246	+	13.5611i	−1.36749	+	0.657036i
$427$	−18.2729			−0.884288
$428$	−5.63937			−0.272589
$429$	−3.72462	−	4.37347i	−0.179826	−	0.211153i
$430$	0.651103			0.0313990
$431$	−15.2351			−0.733849			−0.366924	−	0.930251i	$-0.619589\pi$
$431$	−15.2351			−0.733849			−0.366924	+	0.930251i	$0.619589\pi$
$432$	15.0341	+	3.47405i	0.723330	+	0.167145i
$433$	−22.5717			−1.08473			−0.542363	−	0.840144i	$-0.682470\pi$
$433$	−22.5717			−1.08473			−0.542363	+	0.840144i	$0.682470\pi$
$434$			25.7194i			1.23457i
$435$	−1.48586	+	0.713909i	−0.0712414	+	0.0342293i
$436$		−	7.57934i		−	0.362985i
$437$	−16.8017			−0.803734
$438$	3.16189	−	1.51919i	0.151081	−	0.0725898i
$439$			30.1701i			1.43994i	0.694005	+	0.719970i	$0.255844\pi$
$439$			30.1701i			1.43994i	−0.694005	+	0.719970i	$0.744156\pi$
$440$	2.69628	−	0.710182i	0.128540	−	0.0338566i
$441$	17.0743	−	21.3318i	0.813061	−	1.01580i
$442$		−	4.05685i		−	0.192965i
$443$			12.5040i			0.594083i	0.954864	+	0.297042i	$0.0960001\pi$
$443$			12.5040i			0.594083i	−0.954864	+	0.297042i	$0.904000\pi$
$444$	−2.58619	−	5.38264i	−0.122735	−	0.255449i
$445$	−1.26203			−0.0598258
$446$	−30.1710			−1.42864
$447$	−12.8818	−	26.8107i	−0.609286	−	1.26810i
$448$		−	35.7227i		−	1.68774i
$449$		−	16.4761i		−	0.777557i	−0.921331	−	0.388778i	$-0.872897\pi$
$449$		−	16.4761i		−	0.777557i	0.921331	−	0.388778i	$-0.127103\pi$
$450$	11.5842	−	14.4728i	0.546085	−	0.682254i
$451$	2.05936	+	7.81858i	0.0969716	+	0.368162i
$452$		−	1.83792i		−	0.0864484i
$453$	−6.77185	+	3.25367i	−0.318169	+	0.152871i
$454$	12.3845			0.581234
$455$		−	1.10867i		−	0.0519753i
$456$	22.2795	−	10.7046i	1.04333	−	0.501291i
$457$			33.5081i			1.56744i	0.621113	+	0.783721i	$0.286681\pi$
$457$			33.5081i			1.56744i	−0.621113	+	0.783721i	$0.713319\pi$
$458$	7.58700			0.354517
$459$	16.3654	+	3.78166i	0.763870	+	0.176513i
$460$	−0.420591			−0.0196101
$461$	29.7187			1.38414			0.692069	−	0.721832i	$-0.256700\pi$
$461$	29.7187			1.38414			0.692069	+	0.721832i	$0.256700\pi$
$462$	18.7608	+	22.0290i	0.872829	+	1.02488i
$463$	−14.5998			−0.678508			−0.339254	−	0.940695i	$-0.610175\pi$
$463$	−14.5998			−0.678508			−0.339254	+	0.940695i	$0.610175\pi$
$464$	−10.2312			−0.474973
$465$	−2.20208	+	1.05803i	−0.102119	+	0.0490652i
$466$	0.446007			0.0206609
$467$		−	8.63271i		−	0.399474i	−0.979850	−	0.199737i	$-0.935991\pi$
$467$		−	8.63271i		−	0.399474i	0.979850	−	0.199737i	$-0.0640088\pi$
$468$	−0.995252	−	0.796613i	−0.0460055	−	0.0368234i
$469$			50.5704i			2.33512i
$470$	−1.57746			−0.0727626
$471$	−8.43824	−	17.5625i	−0.388813	−	0.809236i
$472$			22.2820i			1.02561i
$473$	6.02347	−	1.58654i	0.276960	−	0.0729494i
$474$	−1.27550	+	0.612840i	−0.0585857	+	0.0281487i
$475$		−	23.0882i		−	1.05936i
$476$		−	5.51290i		−	0.252683i
$477$	6.69543	+	5.35911i	0.306563	+	0.245377i
$478$	8.63254			0.394843
$479$	−39.4948			−1.80456			−0.902281	−	0.431149i	$-0.858108\pi$
$479$	−39.4948			−1.80456			−0.902281	+	0.431149i	$0.858108\pi$
$480$	1.01770	−	0.488974i	0.0464514	−	0.0223185i
$481$		−	8.11364i		−	0.369950i
$482$		−	17.3054i		−	0.788240i
$483$	−10.7869	−	22.4508i	−0.490821	−	1.02154i
$484$	4.06778	−	2.30260i	0.184899	−	0.104664i
$485$			0.990106i			0.0449584i
$486$	−15.3501	+	12.1291i	−0.696296	+	0.550186i
$487$	−22.8082			−1.03354			−0.516769	−	0.856125i	$-0.672865\pi$
$487$	−22.8082			−1.03354			−0.516769	+	0.856125i	$0.672865\pi$
$488$		−	13.8560i		−	0.627232i
$489$	15.0324	+	31.2869i	0.679789	+	1.41484i
$490$			3.15755i			0.142643i
$491$	39.6986			1.79157			0.895786	−	0.444485i	$-0.146613\pi$
$491$	39.6986			1.79157			0.895786	+	0.444485i	$0.146613\pi$
$492$	0.777037	+	1.61724i	0.0350315	+	0.0729110i
$493$	−11.1372			−0.501593
$494$	5.88502			0.264780
$495$	−1.11434	+	2.51251i	−0.0500858	+	0.112929i
$496$	−15.1630			−0.680838
$497$	−57.8149			−2.59335
$498$	5.04848	+	10.5074i	0.226228	+	0.470847i
$499$	−10.5602			−0.472738			−0.236369	−	0.971663i	$-0.575957\pi$
$499$	−10.5602			−0.472738			−0.236369	+	0.971663i	$0.575957\pi$
$500$		−	1.16487i		−	0.0520947i
$501$	16.2702	+	33.8632i	0.726900	+	1.51290i
$502$		−	16.4965i		−	0.736276i
$503$	20.1722			0.899435			0.449717	−	0.893171i	$-0.351525\pi$
$503$	20.1722			0.899435			0.449717	+	0.893171i	$0.351525\pi$
$504$	28.6075	+	22.8978i	1.27428	+	1.01995i
$505$		−	4.84179i		−	0.215457i
$506$	14.4223	−	3.79874i	0.641150	−	0.168875i
$507$	−0.750108	−	1.56120i	−0.0333135	−	0.0693352i
$508$		−	1.83511i		−	0.0814198i
$509$		−	37.6995i		−	1.67100i	−0.549488	−	0.835501i	$-0.685177\pi$
$509$		−	37.6995i		−	1.67100i	0.549488	−	0.835501i	$-0.314823\pi$
$510$	−1.74957	+	0.840615i	−0.0774722	+	0.0372231i
$511$	6.47676			0.286515
$512$	25.0823			1.10849
$513$	−5.48582	+	23.7402i	−0.242205	+	1.04816i
$514$			30.0407i			1.32504i
$515$		−	1.30712i		−	0.0575986i
$516$	1.24593	−	0.598634i	0.0548492	−	0.0263534i
$517$	−14.5934	+	3.84379i	−0.641815	+	0.169050i
$518$			40.8681i			1.79564i
$519$	5.83184	+	12.1378i	0.255990	+	0.532790i
$520$	0.840685			0.0368665
$521$		−	16.5662i		−	0.725779i	−0.931832	−	0.362889i	$-0.881790\pi$
$521$		−	16.5662i		−	0.725779i	0.931832	−	0.362889i	$-0.118210\pi$
$522$	8.10607	−	10.1274i	0.354793	−	0.443262i
$523$		−	29.1262i		−	1.27360i	−0.771028	−	0.636801i	$-0.780257\pi$
$523$		−	29.1262i		−	1.27360i	0.771028	−	0.636801i	$-0.219743\pi$
$524$	−4.48852			−0.196082
$525$	30.8509	−	14.8229i	1.34644	−	0.646925i
$526$	−19.2066			−0.837445
$527$	−16.5056			−0.718996
$528$	−12.9873	+	11.0605i	−0.565199	+	0.481346i
$529$	10.1617			0.441812
$530$	−0.991061			−0.0430489
$531$	−17.1481	−	13.7256i	−0.744165	−	0.595640i
$532$	7.99722			0.346723
$533$			2.43779i			0.105592i
$534$	8.95141	−	4.30088i	0.387365	−	0.186117i
$535$			3.66601i			0.158495i
$536$	−38.3466			−1.65632
$537$	−9.65831	+	4.64052i	−0.416787	+	0.200253i
$538$		−	0.468424i		−	0.0201952i
$539$	7.69400	+	29.2111i	0.331404	+	1.25821i
$540$	−0.137325	+	0.594280i	−0.00590951	+	0.0255737i
$541$		−	15.0824i		−	0.648441i	−0.945981	−	0.324221i	$-0.894898\pi$
$541$		−	15.0824i		−	0.648441i	0.945981	−	0.324221i	$-0.105102\pi$
$542$		−	28.9368i		−	1.24294i
$543$	12.1238	+	25.2333i	0.520284	+	1.08286i
$544$	7.62811			0.327053
$545$	−4.92714			−0.211055
$546$	3.77826	+	7.86369i	0.161695	+	0.336535i
$547$		−	33.3769i		−	1.42709i	−0.700607	−	0.713547i	$-0.747087\pi$
$547$		−	33.3769i		−	1.42709i	0.700607	−	0.713547i	$-0.252913\pi$
$548$			3.40411i			0.145416i
$549$	10.6635	+	8.53522i	0.455108	+	0.364275i
$550$	5.22007	+	19.8185i	0.222585	+	0.845065i
$551$		−	16.1560i		−	0.688269i
$552$	17.0240	−	8.17951i	0.724589	−	0.348143i
$553$	−2.61272			−0.111104
$554$		−	26.9277i		−	1.14405i
$555$	−3.49911	+	1.68122i	−0.148529	+	0.0713637i
$556$			7.49923i			0.318038i
$557$	35.8341			1.51834			0.759170	−	0.650893i	$-0.225605\pi$
$557$	35.8341			1.51834			0.759170	+	0.650893i	$0.225605\pi$
$558$	12.0134	−	15.0091i	0.508570	−	0.635384i
$559$	1.87809			0.0794347
$560$	−3.29227			−0.139124
$561$	−14.1373	+	12.0399i	−0.596876	+	0.508324i
$562$	11.6493			0.491394
$563$	43.2613			1.82325			0.911623	−	0.411026i	$-0.134830\pi$
$563$	43.2613			1.82325			0.911623	+	0.411026i	$0.134830\pi$
$564$	−3.01858	+	1.45034i	−0.127105	+	0.0610702i
$565$	−1.19478			−0.0502649
$566$		−	25.0213i		−	1.05173i
$567$	−35.2441	+	7.91127i	−1.48011	+	0.332242i
$568$		−	43.8399i		−	1.83948i
$569$	0.782549			0.0328061			0.0164031	−	0.999865i	$-0.494779\pi$
$569$	0.782549			0.0328061			0.0164031	+	0.999865i	$0.494779\pi$
$570$	−1.21943	−	2.53799i	−0.0510762	−	0.106305i
$571$			4.73455i			0.198135i	0.995081	+	0.0990674i	$0.0315860\pi$
$571$			4.73455i			0.198135i	−0.995081	+	0.0990674i	$0.968414\pi$
$572$	1.36286	−	0.358969i	0.0569842	−	0.0150093i
$573$	−20.1357	+	9.67459i	−0.841180	+	0.404162i
$574$		−	12.2791i		−	0.512518i
$575$		−	17.6419i		−	0.735718i
$576$	−16.6860	+	20.8467i	−0.695249	+	0.868613i
$577$	35.9835			1.49801			0.749006	−	0.662564i	$-0.230532\pi$
$577$	35.9835			1.49801			0.749006	+	0.662564i	$0.230532\pi$
$578$	8.22147			0.341968
$579$	37.8476	−	18.1846i	1.57289	−	0.755728i
$580$		−	0.404427i		−	0.0167929i
$581$			21.5232i			0.892931i
$582$	−3.37420	−	7.02272i	−0.139865	−	0.291101i
$583$	−9.16850	+	2.41492i	−0.379720	+	0.100016i
$584$			4.91121i			0.203227i
$585$	−0.517857	+	0.646987i	−0.0214108	+	0.0267496i
$586$	7.56288			0.312420
$587$			45.0659i			1.86007i	0.367470	+	0.930035i	$0.380224\pi$
$587$			45.0659i			1.86007i	−0.367470	+	0.930035i	$0.619776\pi$
$588$	2.90310	+	6.04221i	0.119722	+	0.249176i
$589$		−	23.9437i		−	0.986582i
$590$	2.53827			0.104499
$591$	20.3701	+	42.3962i	0.837914	+	1.74395i
$592$	−24.0940			−0.990257
$593$	−39.4075			−1.61827			−0.809136	−	0.587621i	$-0.800065\pi$
$593$	−39.4075			−1.61827			−0.809136	+	0.587621i	$0.800065\pi$
$594$	−0.658548	−	21.6185i	−0.0270206	−	0.887019i
$595$	−3.58379			−0.146921
$596$	7.29747			0.298916
$597$	−18.3004	−	38.0885i	−0.748984	−	1.55886i
$598$	4.49680			0.183888
$599$			13.9146i			0.568537i	0.958745	+	0.284268i	$0.0917507\pi$
$599$			13.9146i			0.568537i	−0.958745	+	0.284268i	$0.908249\pi$
$600$	11.2399	+	23.3937i	0.458869	+	0.955042i
$601$			1.85713i			0.0757540i	0.999282	+	0.0378770i	$0.0120595\pi$
$601$			1.85713i			0.0757540i	−0.999282	+	0.0378770i	$0.987940\pi$
$602$	−9.45985			−0.385555
$603$	23.6213	−	29.5113i	0.961932	−	1.20179i
$604$		−	1.84319i		−	0.0749985i
$605$	−1.49686	−	2.64436i	−0.0608560	−	0.107508i
$606$	16.5004	+	34.3423i	0.670284	+	1.39506i
$607$			27.1986i			1.10396i	0.833858	+	0.551980i	$0.186127\pi$
$607$			27.1986i			1.10396i	−0.833858	+	0.551980i	$0.813873\pi$
$608$			11.0656i			0.448771i
$609$	21.5880	−	10.3724i	0.874789	−	0.420310i
$610$	−1.57842			−0.0639083
$611$	−4.55013			−0.184079
$612$	−2.57506	+	3.21716i	−0.104091	+	0.130046i
$613$		−	28.2085i		−	1.13933i	−0.821876	−	0.569666i	$-0.807073\pi$
$613$		−	28.2085i		−	1.13933i	0.821876	−	0.569666i	$-0.192927\pi$
$614$			27.4841i			1.10917i
$615$	1.05133	−	0.505132i	0.0423937	−	0.0203689i
$616$	−39.1741	+	10.3182i	−1.57837	+	0.415732i
$617$			20.5067i			0.825567i	0.910829	+	0.412783i	$0.135443\pi$
$617$			20.5067i			0.825567i	−0.910829	+	0.412783i	$0.864557\pi$
$618$	4.45456	+	9.27126i	0.179189	+	0.372945i
$619$	−20.7599			−0.834410			−0.417205	−	0.908812i	$-0.636990\pi$
$619$	−20.7599			−0.834410			−0.417205	+	0.908812i	$0.636990\pi$
$620$		−	0.599373i		−	0.0240714i
$621$	−4.19177	+	18.1401i	−0.168210	+	0.727938i
$622$		−	24.6568i		−	0.988649i
$623$	18.3359			0.734614
$624$	−4.63608	+	2.22749i	−0.185592	+	0.0891711i
$625$	23.8612			0.954448
$626$	0.494276			0.0197552
$627$	−17.4655	−	20.5081i	−0.697505	−	0.819013i
$628$	4.78023			0.190752
$629$	−26.2274			−1.04576
$630$	2.60843	−	3.25885i	0.103922	−	0.129836i
$631$	−10.0726			−0.400984			−0.200492	−	0.979695i	$-0.564254\pi$
$631$	−10.0726			−0.400984			−0.200492	+	0.979695i	$0.564254\pi$
$632$		−	1.98118i		−	0.0788070i
$633$	7.28975	−	3.50251i	0.289742	−	0.139212i
$634$		−	17.7882i		−	0.706461i
$635$	−1.19296			−0.0473411
$636$	−1.89647	+	0.911197i	−0.0751999	+	0.0361313i
$637$			9.10786i			0.360867i
$638$	3.65275	+	13.8681i	0.144614	+	0.549042i
$639$	33.7390	+	27.0052i	1.33470	+	1.06831i
$640$		−	1.78200i		−	0.0704396i
$641$			17.0114i			0.671908i	0.941878	+	0.335954i	$0.109059\pi$
$641$			17.0114i			0.671908i	−0.941878	+	0.335954i	$0.890941\pi$
$642$	−12.4935	−	26.0026i	−0.493078	−	1.02624i
$643$	6.55628			0.258554			0.129277	−	0.991608i	$-0.458734\pi$
$643$	6.55628			0.258554			0.129277	+	0.991608i	$0.458734\pi$
$644$	6.11075			0.240797
$645$	−0.389156	−	0.809949i	−0.0153230	−	0.0318917i
$646$		−	19.0234i		−	0.748466i
$647$		−	25.8217i		−	1.01516i	−0.861606	−	0.507578i	$-0.830541\pi$
$647$		−	25.8217i		−	1.01516i	0.861606	−	0.507578i	$-0.169459\pi$
$648$	−5.99897	−	26.7250i	−0.235662	−	1.04986i
$649$	23.4821	−	6.18502i	0.921751	−	0.242783i
$650$			6.17931i			0.242373i
$651$	31.9940	−	15.3722i	1.25394	−	0.602482i
$652$	−8.51581			−0.333505
$653$			4.98160i			0.194945i	0.995238	+	0.0974725i	$0.0310758\pi$
$653$			4.98160i			0.194945i	−0.995238	+	0.0974725i	$0.968924\pi$
$654$	34.9476	−	16.7913i	1.36656	−	0.656591i
$655$			2.91787i			0.114011i
$656$	7.23918			0.282642
$657$	−3.77964	−	3.02528i	−0.147458	−	0.118027i
$658$	22.9188			0.893469
$659$	−34.9099			−1.35989			−0.679947	−	0.733261i	$-0.737997\pi$
$659$	−34.9099			−1.35989			−0.679947	+	0.733261i	$0.737997\pi$
$660$	−0.437207	−	0.513371i	−0.0170183	−	0.0199829i
$661$	−2.09512			−0.0814907			−0.0407453	−	0.999170i	$-0.512973\pi$
$661$	−2.09512			−0.0814907			−0.0407453	+	0.999170i	$0.512973\pi$
$662$	−41.4057			−1.60928
$663$	−5.04659	+	2.42473i	−0.195993	+	0.0941688i
$664$	−16.3206			−0.633363
$665$		−	5.19878i		−	0.201600i
$666$	19.0894	−	23.8494i	0.739698	−	0.924145i
$667$		−	12.3449i		−	0.477998i
$668$	−9.21703			−0.356618
$669$	18.0329	+	37.5317i	0.697190	+	1.45106i
$670$			4.36828i			0.168761i
$671$	−14.6023	+	3.84614i	−0.563714	+	0.148479i
$672$	−14.7861	+	7.10428i	−0.570387	+	0.274054i
$673$		−	15.3076i		−	0.590063i	−0.955487	−	0.295032i	$-0.904670\pi$
$673$		−	15.3076i		−	0.590063i	0.955487	−	0.295032i	$-0.0953302\pi$
$674$		−	36.4996i		−	1.40591i
$675$	−24.9274	−	5.76015i	−0.959456	−	0.221708i
$676$	0.424934			0.0163436
$677$	−17.6334			−0.677705			−0.338853	−	0.940840i	$-0.610039\pi$
$677$	−17.6334			−0.677705			−0.338853	+	0.940840i	$0.610039\pi$
$678$	8.47447	−	4.07172i	0.325460	−	0.156374i
$679$		−	14.3852i		−	0.552054i
$680$		−	2.71752i		−	0.104212i
$681$	−7.40208	−	15.4059i	−0.283648	−	0.590356i
$682$	5.41349	+	20.5529i	0.207293	+	0.787010i
$683$			36.5198i			1.39739i	0.715419	+	0.698695i	$0.246236\pi$
$683$			36.5198i			1.39739i	−0.715419	+	0.698695i	$0.753764\pi$
$684$	−4.66694	−	3.73548i	−0.178445	−	0.142830i
$685$	2.21292			0.0845514
$686$		−	10.6172i		−	0.405367i
$687$	−4.53466	−	9.43797i	−0.173008	−	0.360081i
$688$		−	5.57710i		−	0.212625i
$689$	−2.85869			−0.108907
$690$	−0.931776	−	1.93930i	−0.0354721	−	0.0738280i
$691$	−13.6376			−0.518800			−0.259400	−	0.965770i	$-0.583525\pi$
$691$	−13.6376			−0.518800			−0.259400	+	0.965770i	$0.583525\pi$
$692$	−3.30372			−0.125589
$693$	16.1902	−	36.5042i	0.615015	−	1.38668i
$694$	−24.6893			−0.937192
$695$	4.87506			0.184921
$696$	7.86517	+	16.3698i	0.298129	+	0.620494i
$697$	7.88018			0.298483
$698$		−	21.3974i		−	0.809903i
$699$	−0.266573	−	0.554817i	−0.0100827	−	0.0209851i
$700$			8.39713i			0.317382i
$701$	11.8903			0.449091			0.224546	−	0.974464i	$-0.427910\pi$
$701$	11.8903			0.449091			0.224546	+	0.974464i	$0.427910\pi$
$702$	1.46822	−	6.35383i	0.0554146	−	0.239810i
$703$		−	38.0465i		−	1.43495i
$704$	−7.51903	−	28.5468i	−0.283384	−	1.07590i
$705$	0.942827	+	1.96230i	0.0355089	+	0.0739046i
$706$			13.9549i			0.525198i
$707$			70.3463i			2.64564i
$708$	4.85718	−	2.33373i	0.182544	−	0.0877068i
$709$	−13.9510			−0.523940			−0.261970	−	0.965076i	$-0.584372\pi$
$709$	−13.9510			−0.523940			−0.261970	+	0.965076i	$0.584372\pi$
$710$	−4.99406			−0.187424
$711$	1.52470	+	1.22039i	0.0571809	+	0.0457683i
$712$			13.9038i			0.521067i
$713$		−	18.2956i		−	0.685175i
$714$	25.4194	−	12.2133i	0.951299	−	0.457070i
$715$	−0.233357	−	0.885962i	−0.00872704	−	0.0331331i
$716$		−	2.62884i		−	0.0982444i
$717$	−5.15957	−	10.7386i	−0.192687	−	0.401040i
$718$	−10.2580			−0.382824
$719$			17.2475i			0.643223i	0.946872	+	0.321611i	$0.104224\pi$
$719$			17.2475i			0.643223i	−0.946872	+	0.321611i	$0.895776\pi$
$720$	1.92127	+	1.53781i	0.0716015	+	0.0573108i
$721$			18.9911i			0.707266i
$722$	3.75075			0.139589
$723$	−21.5273	+	10.3432i	−0.800610	+	0.384669i
$724$	−6.86811			−0.255251
$725$	16.9639			0.630024
$726$	19.6288	+	13.6550i	0.728494	+	0.506783i
$727$	−17.5778			−0.651924			−0.325962	−	0.945383i	$-0.605688\pi$
$727$	−17.5778			−0.651924			−0.325962	+	0.945383i	$0.605688\pi$
$728$	−12.2143			−0.452692
$729$	24.2627	+	11.8456i	0.898620	+	0.438728i
$730$	0.559464			0.0207067
$731$		−	6.07094i		−	0.224542i
$732$	−3.02042	+	1.45122i	−0.111638	+	0.0536387i
$733$			7.87654i			0.290927i	0.989364	+	0.145463i	$0.0464673\pi$
$733$			7.87654i			0.290927i	−0.989364	+	0.145463i	$0.953533\pi$
$734$	−12.8239			−0.473340
$735$	3.92788	−	1.88723i	0.144882	−	0.0696114i
$736$			8.45535i			0.311668i
$737$	10.6442	+	40.4118i	0.392084	+	1.48859i
$738$	−5.73551	+	7.16569i	−0.211127	+	0.263773i
$739$		−	21.4592i		−	0.789388i	−0.918813	−	0.394694i	$-0.870851\pi$
$739$		−	21.4592i		−	0.789388i	0.918813	−	0.394694i	$-0.129149\pi$
$740$		−	0.952404i		−	0.0350111i
$741$	−3.51741	−	7.32077i	−0.129215	−	0.268935i
$742$	14.3991			0.528608
$743$	7.20708			0.264402			0.132201	−	0.991223i	$-0.457796\pi$
$743$	7.20708			0.264402			0.132201	+	0.991223i	$0.457796\pi$
$744$	11.6564	+	24.2605i	0.427345	+	0.889432i
$745$		−	4.74389i		−	0.173803i
$746$		−	41.0751i		−	1.50387i
$747$	10.0534	−	12.5603i	0.367835	−	0.459556i
$748$	−1.16037	−	4.40547i	−0.0424274	−	0.161080i
$749$		−	53.2633i		−	1.94620i
$750$	5.37112	−	2.58066i	0.196125	−	0.0942323i
$751$	−6.03811			−0.220334			−0.110167	−	0.993913i	$-0.535139\pi$
$751$	−6.03811			−0.220334			−0.110167	+	0.993913i	$0.535139\pi$
$752$			13.5119i			0.492728i
$753$	−20.5211	+	9.85977i	−0.747831	+	0.359310i
$754$			4.32399i			0.157470i
$755$	−1.19821			−0.0436074
$756$	1.99518	−	8.63428i	0.0725642	−	0.314026i
$757$	−9.20995			−0.334741			−0.167371	−	0.985894i	$-0.553528\pi$
$757$	−9.20995			−0.334741			−0.167371	+	0.985894i	$0.553528\pi$
$758$	−20.8079			−0.755777
$759$	−13.3455	−	15.6704i	−0.484413	−	0.568799i
$760$	3.94214			0.142997
$761$	−7.10901			−0.257701			−0.128851	−	0.991664i	$-0.541129\pi$
$761$	−7.10901			−0.257701			−0.128851	+	0.991664i	$0.541129\pi$
$762$	8.46151	−	4.06550i	0.306528	−	0.147278i
$763$	71.5862			2.59159
$764$		−	5.48062i		−	0.198282i
$765$	2.09139	+	1.67398i	0.0756145	+	0.0605228i
$766$			46.2928i			1.67263i
$767$	7.32158			0.264367
$768$	−7.28012	−	15.1521i	−0.262699	−	0.546754i
$769$		−	37.3380i		−	1.34644i	−0.739442	−	0.673221i	$-0.764910\pi$
$769$		−	37.3380i		−	1.34644i	0.739442	−	0.673221i	$-0.235090\pi$
$770$	1.17541	+	4.46255i	0.0423587	+	0.160819i
$771$	37.3697	−	17.9550i	1.34584	−	0.646633i
$772$			10.3015i			0.370760i
$773$		−	16.2209i		−	0.583426i	−0.956506	−	0.291713i	$-0.905775\pi$
$773$		−	16.2209i		−	0.583426i	0.956506	−	0.291713i	$-0.0942252\pi$
$774$	5.52048	+	4.41867i	0.198430	+	0.158826i
$775$	25.1410			0.903092
$776$	10.9081			0.391576
$777$	50.8385	−	24.4264i	1.82382	−	0.876291i
$778$		−	34.9341i		−	1.25245i
$779$			11.4313i			0.409569i
$780$	−0.0880500	−	0.183258i	−0.00315269	−	0.00656169i
$781$	−46.2010	+	12.1691i	−1.65320	+	0.435443i
$782$		−	14.5360i		−	0.519805i
$783$	−17.4430	−	4.03068i	−0.623362	−	0.144045i
$784$	27.0464			0.965942
$785$		−	3.10750i		−	0.110912i
$786$	−9.94386	−	20.6961i	−0.354686	−	0.738206i
$787$		−	46.2361i		−	1.64814i	−0.566489	−	0.824070i	$-0.691698\pi$
$787$		−	46.2361i		−	1.64814i	0.566489	−	0.824070i	$-0.308302\pi$
$788$	−11.5396			−0.411081
$789$	11.4795	+	23.8923i	0.408682	+	0.850588i
$790$	−0.225687			−0.00802960
$791$	17.3590			0.617214
$792$	27.6804	+	12.2767i	0.983582	+	0.436234i
$793$	−4.55291			−0.161679
$794$	−42.3178			−1.50180
$795$	0.592345	+	1.23285i	0.0210083	+	0.0437245i
$796$	10.3671			0.367452
$797$			6.88317i			0.243814i	0.992542	+	0.121907i	$0.0389010\pi$
$797$			6.88317i			0.243814i	−0.992542	+	0.121907i	$0.961099\pi$
$798$	17.7170	+	36.8744i	0.627176	+	1.30534i
$799$			14.7083i			0.520344i
$800$	−11.6190			−0.410793
$801$	−10.7003	−	8.56466i	−0.378077	−	0.302617i
$802$			0.395588i			0.0139687i
$803$	5.17571	−	1.36325i	0.182647	−	0.0481080i
$804$	4.01626	+	8.35904i	0.141643	+	0.294800i
$805$		−	3.97244i		−	0.140010i
$806$			6.40828i			0.225722i
$807$	−0.582704	+	0.279971i	−0.0205121	+	0.00985546i
$808$	−53.3423			−1.87657
$809$	−16.3307			−0.574157			−0.287078	−	0.957907i	$-0.592684\pi$
$809$	−16.3307			−0.574157			−0.287078	+	0.957907i	$0.592684\pi$
$810$	−3.04440	+	0.683378i	−0.106969	+	0.0240114i
$811$			5.73092i			0.201240i	0.994925	+	0.100620i	$0.0320826\pi$
$811$			5.73092i			0.201240i	−0.994925	+	0.100620i	$0.967917\pi$
$812$			5.87591i			0.206204i
$813$	−35.9963	+	17.2952i	−1.26245	+	0.606568i
$814$	8.60204	+	32.6585i	0.301501	+	1.14468i
$815$			5.53591i			0.193914i
$816$	7.20040	+	14.9862i	0.252064	+	0.524620i
$817$	8.80673			0.308109
$818$			7.73970i			0.270612i
$819$	7.52393	−	9.40006i	0.262908	−	0.328465i
$820$			0.286155i			0.00999298i
$821$	0.753607			0.0263011			0.0131505	−	0.999914i	$-0.495814\pi$
$821$	0.753607			0.0263011			0.0131505	+	0.999914i	$0.495814\pi$
$822$	−15.6960	+	7.54146i	−0.547461	+	0.263039i
$823$	38.4171			1.33913			0.669567	−	0.742751i	$-0.266480\pi$
$823$	38.4171			1.33913			0.669567	+	0.742751i	$0.266480\pi$
$824$	−14.4006			−0.501669
$825$	21.5336	−	18.3389i	0.749704	−	0.638478i
$826$	−36.8785			−1.28317
$827$	26.1750			0.910195			0.455098	−	0.890442i	$-0.349604\pi$
$827$	26.1750			0.910195			0.455098	+	0.890442i	$0.349604\pi$
$828$	−3.56605	−	2.85431i	−0.123929	−	0.0991942i
$829$	−25.2266			−0.876156			−0.438078	−	0.898937i	$-0.644341\pi$
$829$	−25.2266			−0.876156			−0.438078	+	0.898937i	$0.644341\pi$
$830$			1.85918i			0.0645330i
$831$	−33.4972	+	16.0944i	−1.16200	+	0.558308i
$832$		−	8.90073i		−	0.308577i
$833$	29.4412			1.02008
$834$	−34.5782	+	16.6138i	−1.19735	+	0.575289i
$835$			5.99175i			0.207353i
$836$	6.39074	−	1.68328i	0.221028	−	0.0582174i
$837$	−25.8510	−	5.97359i	−0.893543	−	0.206477i
$838$			28.9389i			0.999677i
$839$		−	15.5895i		−	0.538209i	−0.963111	−	0.269105i	$-0.913272\pi$
$839$		−	15.5895i		−	0.538209i	0.963111	−	0.269105i	$-0.0867277\pi$
$840$	2.53091	+	5.26757i	0.0873246	+	0.181748i
$841$	−17.1295			−0.590671
$842$	−21.4688			−0.739863
$843$	−6.96262	−	14.4913i	−0.239805	−	0.499106i
$844$			1.98416i			0.0682975i
$845$		−	0.276238i		−	0.00950289i
$846$	−13.3747	−	10.7053i	−0.459833	−	0.368056i
$847$	21.7478	+	38.4198i	0.747265	+	1.32012i
$848$			8.48906i			0.291516i
$849$	−31.1257	+	14.9550i	−1.06823	+	0.513253i
$850$	19.9747			0.685126
$851$		−	29.0717i		−	0.996564i
$852$	−9.55652	+	4.59162i	−0.327401	+	0.157306i
$853$			23.1959i			0.794211i	0.917773	+	0.397106i	$0.129985\pi$
$853$			23.1959i			0.794211i	−0.917773	+	0.397106i	$0.870015\pi$
$854$	22.9328			0.784745
$855$	−2.42834	+	3.03385i	−0.0830474	+	0.103756i
$856$	40.3886			1.38045
$857$	−19.0865			−0.651981			−0.325990	−	0.945373i	$-0.605698\pi$
$857$	−19.0865			−0.651981			−0.325990	+	0.945373i	$0.605698\pi$
$858$	4.67446	+	5.48877i	0.159583	+	0.187384i
$859$	−9.16107			−0.312572			−0.156286	−	0.987712i	$-0.549952\pi$
$859$	−9.16107			−0.312572			−0.156286	+	0.987712i	$0.549952\pi$
$860$	0.220456			0.00751748
$861$	−15.2747	+	7.33904i	−0.520561	+	0.250114i
$862$	19.1203			0.651240
$863$			14.8799i			0.506516i	0.967399	+	0.253258i	$0.0815022\pi$
$863$			14.8799i			0.506516i	−0.967399	+	0.253258i	$0.918498\pi$
$864$	11.9471	+	2.76071i	0.406449	+	0.0939212i
$865$			2.14766i			0.0730227i
$866$	28.3278			0.962619
$867$	−4.91387	−	10.2272i	−0.166884	−	0.347335i
$868$			8.70828i			0.295578i
$869$	−2.08788	+	0.549933i	−0.0708264	+	0.0186552i
$870$	1.86477	−	0.895968i	0.0632218	−	0.0303762i
$871$			12.6002i			0.426941i
$872$			54.2825i			1.83824i
$873$	−6.71930	+	8.39479i	−0.227414	+	0.284120i
$874$	21.0864			0.713258
$875$	11.0021			0.371939
$876$	1.07058	−	0.514380i	0.0361715	−	0.0173793i
$877$		−	7.53362i		−	0.254392i	−0.991878	−	0.127196i	$-0.959402\pi$
$877$		−	7.53362i		−	0.254392i	0.991878	−	0.127196i	$-0.0405978\pi$
$878$		−	37.8640i		−	1.27785i
$879$	−4.52024	−	9.40796i	−0.152464	−	0.317323i
$880$	−2.63092	+	0.692967i	−0.0886883	+	0.0233599i
$881$		−	37.8885i		−	1.27650i	−0.769831	−	0.638248i	$-0.779660\pi$
$881$		−	37.8885i		−	1.27650i	0.769831	−	0.638248i	$-0.220340\pi$
$882$	−21.4285	+	26.7718i	−0.721535	+	0.901453i
$883$	−44.0403			−1.48207			−0.741037	−	0.671464i	$-0.765666\pi$
$883$	−44.0403			−1.48207			−0.741037	+	0.671464i	$0.765666\pi$
$884$		−	1.37360i		−	0.0461992i
$885$	−1.51710	−	3.15753i	−0.0509966	−	0.106139i
$886$		−	15.6927i		−	0.527208i
$887$	15.7836			0.529962			0.264981	−	0.964254i	$-0.414634\pi$
$887$	15.7836			0.529962			0.264981	+	0.964254i	$0.414634\pi$
$888$	18.5221	+	38.5499i	0.621559	+	1.29365i
$889$	17.3324			0.581311
$890$	1.58386			0.0530912
$891$	−26.4991	+	13.7403i	−0.887754	+	0.460319i
$892$	−10.2155			−0.342042
$893$	−21.3365			−0.713998
$894$	16.1668	+	33.6479i	0.540699	+	1.12535i
$895$	−1.70894			−0.0571236
$896$			25.8906i			0.864944i
$897$	−2.68768	−	5.59387i	−0.0897392	−	0.186774i
$898$			20.6778i			0.690027i
$899$	17.5925			0.586742
$900$	3.92228	−	4.90031i	0.130743	−	0.163344i
$901$			9.24074i			0.307854i
$902$	−2.58453	−	9.81244i	−0.0860555	−	0.326719i
$903$	5.65404	+	11.7677i	0.188155	+	0.391606i
$904$			13.1630i			0.437794i
$905$			4.46478i			0.148414i
$906$	8.49878	−	4.08341i	0.282353	−	0.135662i
$907$	35.0102			1.16250			0.581248	−	0.813727i	$-0.302565\pi$
$907$	35.0102			1.16250			0.581248	+	0.813727i	$0.302565\pi$
$908$	4.19325			0.139158
$909$	32.8585	−	41.0520i	1.08985	−	1.36161i
$910$			1.39140i			0.0461245i
$911$		−	3.52039i		−	0.116636i	−0.998298	−	0.0583179i	$-0.981426\pi$
$911$		−	3.52039i		−	0.116636i	0.998298	−	0.0583179i	$-0.0185737\pi$
$912$	−21.7395	+	10.4452i	−0.719867	+	0.345874i
$913$	4.53026	+	17.1996i	0.149930	+	0.569224i
$914$		−	42.0532i		−	1.39100i
$915$	0.943402	+	1.96350i	0.0311879	+	0.0649113i
$916$	2.56887			0.0848778
$917$		−	42.3936i		−	1.39996i
$918$	−20.5388	−	4.74605i	−0.677881	−	0.156643i
$919$			14.5017i			0.478368i	0.970974	+	0.239184i	$0.0768799\pi$
$919$			14.5017i			0.478368i	−0.970974	+	0.239184i	$0.923120\pi$
$920$	3.01223			0.0993102
$921$	34.1893	−	16.4269i	1.12658	−	0.541286i
$922$	−37.2974			−1.22833
$923$	−14.4052			−0.474154
$924$	6.35217	+	7.45875i	0.208971	+	0.245375i
$925$	39.9491			1.31352
$926$	18.3229			0.602129
$927$	8.87069	−	11.0826i	0.291352	−	0.364002i
$928$	−8.13041			−0.266894
$929$		−	14.8533i		−	0.487322i	−0.969860	−	0.243661i	$-0.921652\pi$
$929$		−	14.8533i		−	0.487322i	0.969860	−	0.243661i	$-0.0783484\pi$
$930$	2.76365	−	1.32785i	0.0906237	−	0.0435420i
$931$			42.7086i			1.39972i
$932$	0.151013			0.00494659
$933$	−30.6723	+	14.7371i	−1.00417	+	0.482471i
$934$			10.8342i			0.354506i
$935$	−2.86388	+	0.754327i	−0.0936589	+	0.0246691i
$936$	7.12789	+	5.70526i	0.232982	+	0.186482i
$937$		−	37.0494i		−	1.21035i	−0.796092	−	0.605175i	$-0.793103\pi$
$937$		−	37.0494i		−	1.21035i	0.796092	−	0.605175i	$-0.206897\pi$
$938$		−	63.4666i		−	2.07226i
$939$	−0.295423	−	0.614863i	−0.00964076	−	0.0200653i
$940$	−0.534108			−0.0174207
$941$	−27.9542			−0.911280			−0.455640	−	0.890164i	$-0.650589\pi$
$941$	−27.9542			−0.911280			−0.455640	+	0.890164i	$0.650589\pi$
$942$	10.5901	+	22.0412i	0.345045	+	0.718141i
$943$			8.73476i			0.284443i
$944$		−	21.7419i		−	0.707639i
$945$	−5.61292	−	1.29702i	−0.182588	−	0.0421920i
$946$	−7.55956	+	1.99114i	−0.245782	+	0.0647375i
$947$		−	38.6751i		−	1.25677i	−0.777901	−	0.628386i	$-0.783716\pi$
$947$		−	38.6751i		−	1.25677i	0.777901	−	0.628386i	$-0.216284\pi$
$948$	−0.431870	+	0.207500i	−0.0140265	+	0.00673930i
$949$	1.61376			0.0523849
$950$			28.9761i			0.940107i
$951$	−22.1280	+	10.6318i	−0.717548	+	0.344760i
$952$			39.4828i			1.27965i
$953$	31.5159			1.02090			0.510449	−	0.859908i	$-0.329479\pi$
$953$	31.5159			1.02090			0.510449	+	0.859908i	$0.329479\pi$
$954$	−8.40288	−	6.72578i	−0.272053	−	0.217755i
$955$	−3.56281			−0.115290
$956$	2.92288			0.0945326
$957$	15.0682	−	12.8327i	0.487085	−	0.414821i
$958$	49.5666			1.60142
$959$	−32.1515			−1.03823
$960$	−3.83855	+	1.84431i	−0.123889	+	0.0595248i
$961$	−4.92741			−0.158949
$962$			10.1828i			0.328305i
$963$	−24.8792	+	31.0829i	−0.801720	+	1.00163i
$964$		−	5.85941i		−	0.188719i
$965$	6.69676			0.215576
$966$	13.5378	+	28.1761i	0.435570	+	0.906550i
$967$		−	2.73150i		−	0.0878392i	−0.999035	−	0.0439196i	$-0.986015\pi$
$967$		−	2.73150i		−	0.0878392i	0.999035	−	0.0439196i	$-0.0139845\pi$
$968$	−29.1330	+	16.4910i	−0.936371	+	0.530040i
$969$	−23.6645	+	11.3701i	−0.760212	+	0.365259i
$970$		−	1.24260i		−	0.0398975i
$971$			27.1829i			0.872339i	0.899864	+	0.436170i	$0.143665\pi$
$971$			27.1829i			0.872339i	−0.899864	+	0.436170i	$0.856335\pi$
$972$	−5.19738	+	4.10676i	−0.166706	+	0.131724i
$973$	−70.8296			−2.27069
$974$	28.6246			0.917193
$975$	7.68686	−	3.69330i	0.246176	−	0.118280i
$976$			13.5202i			0.432769i
$977$			50.6238i			1.61960i	0.586707	+	0.809799i	$0.300424\pi$
$977$			50.6238i			1.61960i	−0.586707	+	0.809799i	$0.699576\pi$
$978$	−18.8659	−	39.2656i	−0.603266	−	1.25558i
$979$	14.6526	−	3.85940i	0.468300	−	0.123347i
$980$			1.06911i			0.0341514i
$981$	−41.7756	−	33.4377i	−1.33379	−	1.06758i
$982$	−49.8224			−1.58990
$983$		−	11.2155i		−	0.357720i	−0.983875	−	0.178860i	$-0.942759\pi$
$983$		−	11.2155i		−	0.357720i	0.983875	−	0.178860i	$-0.0572409\pi$
$984$	−5.56506	−	11.5825i	−0.177408	−	0.369238i
$985$			7.50159i			0.239021i
$986$	13.9773			0.445129
$987$	−13.6983	−	28.5102i	−0.436022	−	0.907491i
$988$	1.99260			0.0633930
$989$	6.72931			0.213979
$990$	1.39851	−	3.15324i	0.0444477	−	0.100217i
$991$	2.50086			0.0794426			0.0397213	−	0.999211i	$-0.487353\pi$
$991$	2.50086			0.0794426			0.0397213	+	0.999211i	$0.487353\pi$
$992$	−12.0495			−0.382572
$993$	24.7477	+	51.5072i	0.785344	+	1.63453i
$994$	72.5586			2.30142
$995$		−	6.73938i		−	0.213653i
$996$	1.70936	+	3.55768i	0.0541630	+	0.112729i
$997$		−	27.3234i		−	0.865340i	−0.901552	−	0.432670i	$-0.857571\pi$
$997$		−	27.3234i		−	0.865340i	0.901552	−	0.432670i	$-0.142429\pi$
$998$	13.2532			0.419522
$999$	−41.0773	−	9.49203i	−1.29963	−	0.300314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.f.a.131.16	yes	48
3.2	odd	2	inner	429.2.f.a.131.33	yes	48
11.10	odd	2	inner	429.2.f.a.131.34	yes	48
33.32	even	2	inner	429.2.f.a.131.15	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.f.a.131.15	✓	48	33.32	even	2	inner
429.2.f.a.131.16	yes	48	1.1	even	1	trivial
429.2.f.a.131.33	yes	48	3.2	odd	2	inner
429.2.f.a.131.34	yes	48	11.10	odd	2	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.25502 q^{2} +(0.750108 + 1.56120i) q^{3} -0.424934 q^{4} +0.276238i q^{5} +(-0.941398 - 1.95933i) q^{6} -4.01346i q^{7} +3.04333 q^{8} +(-1.87468 + 2.34213i) q^{9} +O(q^{10})\)	\(q-1.25502 q^{2} +(0.750108 + 1.56120i) q^{3} -0.424934 q^{4} +0.276238i q^{5} +(-0.941398 - 1.95933i) q^{6} -4.01346i q^{7} +3.04333 q^{8} +(-1.87468 + 2.34213i) q^{9} -0.346684i q^{10} +(-0.844765 - 3.20724i) q^{11} +(-0.318746 - 0.663406i) q^{12} -1.00000i q^{13} +5.03696i q^{14} +(-0.431263 + 0.207209i) q^{15} -2.96956 q^{16} -3.23251 q^{17} +(2.35275 - 2.93942i) q^{18} -4.68920i q^{19} -0.117383i q^{20} +(6.26580 - 3.01053i) q^{21} +(1.06019 + 4.02514i) q^{22} -3.58306i q^{23} +(2.28283 + 4.75124i) q^{24} +4.92369 q^{25} +1.25502i q^{26} +(-5.06274 - 1.16988i) q^{27} +1.70545i q^{28} +3.44536 q^{29} +(0.541242 - 0.260050i) q^{30} +5.10613 q^{31} -2.35981 q^{32} +(4.37347 - 3.72462i) q^{33} +4.05685 q^{34} +1.10867 q^{35} +(0.796613 - 0.995252i) q^{36} +8.11364 q^{37} +5.88502i q^{38} +(1.56120 - 0.750108i) q^{39} +0.840685i q^{40} -2.43779 q^{41} +(-7.86369 + 3.77826i) q^{42} +1.87809i q^{43} +(0.358969 + 1.36286i) q^{44} +(-0.646987 - 0.517857i) q^{45} +4.49680i q^{46} -4.55013i q^{47} +(-2.22749 - 4.63608i) q^{48} -9.10786 q^{49} -6.17931 q^{50} +(-2.42473 - 5.04659i) q^{51} +0.424934i q^{52} -2.85869i q^{53} +(6.35383 + 1.46822i) q^{54} +(0.885962 - 0.233357i) q^{55} -12.2143i q^{56} +(7.32077 - 3.51741i) q^{57} -4.32399 q^{58} +7.32158i q^{59} +(0.183258 - 0.0880500i) q^{60} -4.55291i q^{61} -6.40828 q^{62} +(9.40006 + 7.52393i) q^{63} +8.90073 q^{64} +0.276238 q^{65} +(-5.48877 + 4.67446i) q^{66} -12.6002 q^{67} +1.37360 q^{68} +(5.59387 - 2.68768i) q^{69} -1.39140 q^{70} -14.4052i q^{71} +(-5.70526 + 7.12789i) q^{72} +1.61376i q^{73} -10.1828 q^{74} +(3.69330 + 7.68686i) q^{75} +1.99260i q^{76} +(-12.8721 + 3.39043i) q^{77} +(-1.95933 + 0.941398i) q^{78} -0.650989i q^{79} -0.820308i q^{80} +(-1.97118 - 8.78148i) q^{81} +3.05947 q^{82} -5.36275 q^{83} +(-2.66255 + 1.27928i) q^{84} -0.892943i q^{85} -2.35703i q^{86} +(2.58440 + 5.37889i) q^{87} +(-2.57090 - 9.76069i) q^{88} +4.56861i q^{89} +(0.811980 + 0.649919i) q^{90} -4.01346 q^{91} +1.52256i q^{92} +(3.83015 + 7.97168i) q^{93} +5.71049i q^{94} +1.29534 q^{95} +(-1.77011 - 3.68413i) q^{96} +3.58425 q^{97} +11.4305 q^{98} +(9.09544 + 4.03398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9	\( 48 q - 6 q^{3} + 48 q^{4} + 14 q^{9} - 20 q^{12} - 6 q^{15} + 8 q^{16} - 4 q^{22} - 28 q^{25} - 12 q^{31} + 2 q^{33} - 16 q^{34} + 26 q^{36} + 20 q^{37} - 2 q^{42} - 50 q^{45} - 82 q^{48} - 56 q^{49} - 20 q^{55} - 80 q^{58} + 104 q^{60} + 16 q^{64} - 50 q^{66} + 60 q^{67} + 6 q^{69} + 80 q^{70} + 12 q^{75} + 10 q^{78} + 6 q^{81} - 8 q^{82} - 52 q^{88} - 8 q^{91} + 42 q^{93} - 92 q^{97} + 18 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 + 48 * q^4 + 14 * q^9 - 20 * q^12 - 6 * q^15 + 8 * q^16 - 4 * q^22 - 28 * q^25 - 12 * q^31 + 2 * q^33 - 16 * q^34 + 26 * q^36 + 20 * q^37 - 2 * q^42 - 50 * q^45 - 82 * q^48 - 56 * q^49 - 20 * q^55 - 80 * q^58 + 104 * q^60 + 16 * q^64 - 50 * q^66 + 60 * q^67 + 6 * q^69 + 80 * q^70 + 12 * q^75 + 10 * q^78 + 6 * q^81 - 8 * q^82 - 52 * q^88 - 8 * q^91 + 42 * q^93 - 92 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more