LMFDB - Embedded newform 234.2.z.a.227.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.7
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.73204 + 0.00498176i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.361873 - 1.35053i) q^{5} +(-0.453098 + 1.67174i) q^{6} +(-0.715284 - 0.715284i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99995 + 0.0172572i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.73204 + 0.00498176i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.361873 - 1.35053i) q^{5} +(-0.453098 + 1.67174i) q^{6} +(-0.715284 - 0.715284i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99995 + 0.0172572i) q^{9} +(1.21085 + 0.699086i) q^{10} +(5.61718 + 1.50512i) q^{11} +(-1.49750 - 0.870336i) q^{12} +(-0.218517 + 3.59892i) q^{13} +(0.876041 - 0.505782i) q^{14} +(0.633509 - 2.33737i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.67305 - 2.89781i) q^{17} +(-0.793114 + 2.89326i) q^{18} +(-7.07605 - 1.89602i) q^{19} +(-0.988657 + 0.988657i) q^{20} +(-1.23534 - 1.24247i) q^{21} +(-2.90767 + 5.03622i) q^{22} +0.580436 q^{23} +(1.22826 - 1.22122i) q^{24} +(2.63715 + 1.52256i) q^{25} +(-3.41974 - 1.14254i) q^{26} +(5.19596 + 0.0448353i) q^{27} +(0.261812 + 0.977097i) q^{28} +(-0.892249 + 0.515140i) q^{29} +(2.09377 + 1.21688i) q^{30} +(-8.52714 - 2.28484i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(9.72170 + 2.63491i) q^{33} +(3.23209 - 0.866036i) q^{34} +(-1.22486 + 0.707171i) q^{35} +(-2.58940 - 1.51492i) q^{36} +(-7.82443 + 2.09655i) q^{37} +(3.66283 - 6.34422i) q^{38} +(-0.396411 + 6.23240i) q^{39} +(-0.699086 - 1.21085i) q^{40} +(1.15731 + 1.15731i) q^{41} +(1.51986 - 0.871673i) q^{42} +8.38054i q^{43} +(-4.11206 - 4.11206i) q^{44} +(1.10891 - 4.04528i) q^{45} +(-0.150228 + 0.560658i) q^{46} +(-0.388741 - 1.45080i) q^{47} +(0.861707 + 1.50248i) q^{48} -5.97674i q^{49} +(-2.15322 + 2.15322i) q^{50} +(-2.88336 - 5.02747i) q^{51} +(1.98870 - 3.00750i) q^{52} -2.77082i q^{53} +(-1.38812 + 5.00731i) q^{54} +(4.06542 - 7.04151i) q^{55} -1.01156 q^{56} +(-12.2466 - 3.31924i) q^{57} +(-0.266656 - 0.995175i) q^{58} +(-3.10182 - 11.5761i) q^{59} +(-1.71732 + 1.70747i) q^{60} +2.82816 q^{61} +(4.41397 - 7.64523i) q^{62} +(-2.13347 - 2.15816i) q^{63} -1.00000i q^{64} +(4.78138 + 1.59747i) q^{65} +(-5.06129 + 8.70847i) q^{66} +(-0.802042 + 0.802042i) q^{67} +3.34611i q^{68} +(1.00534 + 0.00289159i) q^{69} +(-0.366058 - 1.36615i) q^{70} +(-2.71495 + 10.1323i) q^{71} +(2.13349 - 2.10908i) q^{72} +(0.788181 + 0.788181i) q^{73} -8.10045i q^{74} +(4.56007 + 2.65027i) q^{75} +(5.18003 + 5.18003i) q^{76} +(-2.94129 - 5.09447i) q^{77} +(-5.91744 - 1.99597i) q^{78} +(-0.827245 + 1.43283i) q^{79} +(1.35053 - 0.361873i) q^{80} +(8.99940 + 0.103542i) q^{81} +(-1.41741 + 0.818343i) q^{82} +(-15.7224 + 4.21280i) q^{83} +(0.448603 + 1.69368i) q^{84} +(-4.51902 + 1.21087i) q^{85} +(-8.09498 - 2.16904i) q^{86} +(-1.54798 + 0.887801i) q^{87} +(5.03622 - 2.90767i) q^{88} +(0.783797 + 2.92517i) q^{89} +(3.62043 + 2.11812i) q^{90} +(2.73056 - 2.41795i) q^{91} +(-0.502672 - 0.290218i) q^{92} +(-14.7580 - 3.99992i) q^{93} +1.50198 q^{94} +(-5.12127 + 8.87030i) q^{95} +(-1.67432 + 0.443474i) q^{96} +(8.70487 - 8.70487i) q^{97} +(5.77308 + 1.54689i) q^{98} +(16.8253 + 4.61222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.73204	+	0.00498176i	0.999996	+	0.00287622i
$3$	1.73204	+	0.00498176i	0.999996	+	0.00287622i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.361873	−	1.35053i	0.161835	−	0.603975i	−0.836588	−	0.547833i	$-0.815453\pi$
$5$	0.361873	−	1.35053i	0.161835	−	0.603975i	0.998423	−	0.0561429i	$-0.0178802\pi$
$6$	−0.453098	+	1.67174i	−0.184976	+	0.682483i
$7$	−0.715284	−	0.715284i	−0.270352	−	0.270352i	0.558890	−	0.829242i	$-0.311227\pi$
$7$	−0.715284	−	0.715284i	−0.270352	−	0.270352i	−0.829242	+	0.558890i	$0.811227\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.99995	+	0.0172572i	0.999983	+	0.00575242i
$10$	1.21085	+	0.699086i	0.382905	+	0.221070i
$11$	5.61718	+	1.50512i	1.69364	+	0.453810i	0.971326	−	0.237752i	$-0.0764106\pi$
$11$	5.61718	+	1.50512i	1.69364	+	0.453810i	0.722317	+	0.691562i	$0.243077\pi$
$12$	−1.49750	−	0.870336i	−0.432292	−	0.251244i
$13$	−0.218517	+	3.59892i	−0.0606058	+	0.998162i
$13$	−0.218517	+	3.59892i	−0.0606058	+	0.998162i
$14$	0.876041	−	0.505782i	0.234132	−	0.135176i
$15$	0.633509	−	2.33737i	0.163571	−	0.603507i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.67305	−	2.89781i	−0.405775	−	0.702823i	0.588636	−	0.808398i	$-0.299665\pi$
$17$	−1.67305	−	2.89781i	−0.405775	−	0.702823i	−0.994411	+	0.105575i	$0.966332\pi$
$18$	−0.793114	+	2.89326i	−0.186939	+	0.681949i
$19$	−7.07605	−	1.89602i	−1.62336	−	0.434977i	−0.671372	−	0.741120i	$-0.734295\pi$
$19$	−7.07605	−	1.89602i	−1.62336	−	0.434977i	−0.951986	+	0.306143i	$0.900961\pi$
$20$	−0.988657	+	0.988657i	−0.221070	+	0.221070i
$21$	−1.23534	−	1.24247i	−0.269573	−	0.271129i
$22$	−2.90767	+	5.03622i	−0.619916	+	1.07373i
$23$	0.580436			0.121029			0.0605146	−	0.998167i	$-0.480726\pi$
$23$	0.580436			0.121029			0.0605146	+	0.998167i	$0.480726\pi$
$24$	1.22826	−	1.22122i	0.250718	−	0.249280i
$25$	2.63715	+	1.52256i	0.527430	+	0.304512i
$26$	−3.41974	−	1.14254i	−0.670666	−	0.224071i
$27$	5.19596	+	0.0448353i	0.999963	+	0.00862856i
$28$	0.261812	+	0.977097i	0.0494779	+	0.184654i
$29$	−0.892249	+	0.515140i	−0.165687	+	0.0956592i	−0.580550	−	0.814224i	$-0.697163\pi$
$29$	−0.892249	+	0.515140i	−0.165687	+	0.0956592i	0.414864	+	0.909884i	$0.363829\pi$
$30$	2.09377	+	1.21688i	0.382268	+	0.222171i
$31$	−8.52714	−	2.28484i	−1.53152	−	0.410369i	−0.608005	−	0.793933i	$-0.708030\pi$
$31$	−8.52714	−	2.28484i	−1.53152	−	0.410369i	−0.923514	+	0.383564i	$0.874697\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	9.72170	+	2.63491i	1.69233	+	0.458680i
$34$	3.23209	−	0.866036i	0.554299	−	0.148524i
$35$	−1.22486	+	0.707171i	−0.207038	+	0.119534i
$36$	−2.58940	−	1.51492i	−0.431567	−	0.252487i
$37$	−7.82443	+	2.09655i	−1.28633	+	0.344671i	−0.836265	−	0.548326i	$-0.815265\pi$
$37$	−7.82443	+	2.09655i	−1.28633	+	0.344671i	−0.450064	+	0.892996i	$0.648599\pi$
$38$	3.66283	−	6.34422i	0.594190	−	1.02917i
$39$	−0.396411	+	6.23240i	−0.0634765	+	0.997983i
$40$	−0.699086	−	1.21085i	−0.110535	−	0.191453i
$41$	1.15731	+	1.15731i	0.180742	+	0.180742i	0.791679	−	0.610937i	$-0.209207\pi$
$41$	1.15731	+	1.15731i	0.180742	+	0.180742i	−0.610937	+	0.791679i	$0.709207\pi$
$42$	1.51986	−	0.871673i	0.234520	−	0.134502i
$43$			8.38054i			1.27802i	0.769198	+	0.639010i	$0.220656\pi$
$43$			8.38054i			1.27802i	−0.769198	+	0.639010i	$0.779344\pi$
$44$	−4.11206	−	4.11206i	−0.619916	−	0.619916i
$45$	1.10891	−	4.04528i	0.165306	−	0.603035i
$46$	−0.150228	+	0.560658i	−0.0221499	+	0.0826645i
$47$	−0.388741	−	1.45080i	−0.0567037	−	0.211621i	0.931761	−	0.363072i	$-0.118272\pi$
$47$	−0.388741	−	1.45080i	−0.0567037	−	0.211621i	−0.988465	+	0.151451i	$0.951605\pi$
$48$	0.861707	+	1.50248i	0.124377	+	0.216865i
$49$		−	5.97674i		−	0.853820i
$50$	−2.15322	+	2.15322i	−0.304512	+	0.304512i
$51$	−2.88336	−	5.02747i	−0.403752	−	0.703987i
$52$	1.98870	−	3.00750i	0.275784	−	0.417065i
$53$		−	2.77082i		−	0.380601i	−0.981726	−	0.190300i	$-0.939054\pi$
$53$		−	2.77082i		−	0.380601i	0.981726	−	0.190300i	$-0.0609462\pi$
$54$	−1.38812	+	5.00731i	−0.188899	+	0.681408i
$55$	4.06542	−	7.04151i	0.548180	−	0.949476i
$56$	−1.01156			−0.135176
$57$	−12.2466	−	3.31924i	−1.62210	−	0.439645i
$58$	−0.266656	−	0.995175i	−0.0350137	−	0.130673i
$59$	−3.10182	−	11.5761i	−0.403822	−	1.50708i	−0.806218	−	0.591619i	$-0.798489\pi$
$59$	−3.10182	−	11.5761i	−0.403822	−	1.50708i	0.402395	−	0.915466i	$-0.368178\pi$
$60$	−1.71732	+	1.70747i	−0.221705	+	0.220434i
$61$	2.82816			0.362108			0.181054	−	0.983473i	$-0.442049\pi$
$61$	2.82816			0.362108			0.181054	+	0.983473i	$0.442049\pi$
$62$	4.41397	−	7.64523i	0.560575	−	0.970945i
$63$	−2.13347	−	2.15816i	−0.268792	−	0.271903i
$64$		−	1.00000i		−	0.125000i
$65$	4.78138	+	1.59747i	0.593057	+	0.198142i
$66$	−5.06129	+	8.70847i	−0.623002	+	1.07194i
$67$	−0.802042	+	0.802042i	−0.0979851	+	0.0979851i	−0.754400	−	0.656415i	$-0.772072\pi$
$67$	−0.802042	+	0.802042i	−0.0979851	+	0.0979851i	0.656415	+	0.754400i	$0.272072\pi$
$68$			3.34611i			0.405775i
$69$	1.00534	+	0.00289159i	0.121029	+	0.000348107i
$70$	−0.366058	−	1.36615i	−0.0437524	−	0.163286i
$71$	−2.71495	+	10.1323i	−0.322205	+	1.20249i	0.594886	+	0.803810i	$0.297197\pi$
$71$	−2.71495	+	10.1323i	−0.322205	+	1.20249i	−0.917091	+	0.398677i	$0.869470\pi$
$72$	2.13349	−	2.10908i	0.251434	−	0.248558i
$73$	0.788181	+	0.788181i	0.0922496	+	0.0922496i	0.751726	−	0.659476i	$-0.229222\pi$
$73$	0.788181	+	0.788181i	0.0922496	+	0.0922496i	−0.659476	+	0.751726i	$0.729222\pi$
$74$		−	8.10045i		−	0.941658i
$75$	4.56007	+	2.65027i	0.526551	+	0.306027i
$76$	5.18003	+	5.18003i	0.594190	+	0.594190i
$77$	−2.94129	−	5.09447i	−0.335191	−	0.580568i
$78$	−5.91744	−	1.99597i	−0.670018	−	0.225999i
$79$	−0.827245	+	1.43283i	−0.0930723	+	0.161206i	−0.908802	−	0.417227i	$-0.863002\pi$
$79$	−0.827245	+	1.43283i	−0.0930723	+	0.161206i	0.815730	+	0.578433i	$0.196335\pi$
$80$	1.35053	−	0.361873i	0.150994	−	0.0404587i
$81$	8.99940	+	0.103542i	0.999934	+	0.0115046i
$82$	−1.41741	+	0.818343i	−0.156527	+	0.0903709i
$83$	−15.7224	+	4.21280i	−1.72576	+	0.462415i	−0.979198	−	0.202906i	$-0.934961\pi$
$83$	−15.7224	+	4.21280i	−1.72576	+	0.462415i	−0.746557	+	0.665321i	$0.768295\pi$
$84$	0.448603	+	1.69368i	0.0489466	+	0.184795i
$85$	−4.51902	+	1.21087i	−0.490156	+	0.131337i
$86$	−8.09498	−	2.16904i	−0.872904	−	0.233894i
$87$	−1.54798	+	0.887801i	−0.165961	+	0.0951822i
$88$	5.03622	−	2.90767i	0.536863	−	0.309958i
$89$	0.783797	+	2.92517i	0.0830824	+	0.310068i	0.994944	−	0.100430i	$-0.0320218\pi$
$89$	0.783797	+	2.92517i	0.0830824	+	0.310068i	−0.911862	+	0.410497i	$0.865355\pi$
$90$	3.62043	+	2.11812i	0.381627	+	0.223269i
$91$	2.73056	−	2.41795i	0.286240	−	0.253470i
$92$	−0.502672	−	0.290218i	−0.0524072	−	0.0302573i
$93$	−14.7580	−	3.99992i	−1.53033	−	0.414773i
$94$	1.50198			0.154917
$95$	−5.12127	+	8.87030i	−0.525431	+	0.910074i
$96$	−1.67432	+	0.443474i	−0.170884	+	0.0452619i
$97$	8.70487	−	8.70487i	0.883846	−	0.883846i	−0.110077	−	0.993923i	$-0.535110\pi$
$97$	8.70487	−	8.70487i	0.883846	−	0.883846i	0.993923	+	0.110077i	$0.0351099\pi$
$98$	5.77308	+	1.54689i	0.583170	+	0.156260i
$99$	16.8253	+	4.61222i	1.69100	+	0.463545i
$100$	−1.52256	−	2.63715i	−0.152256	−	0.263715i
$101$	5.09573	+	8.82607i	0.507044	+	0.878227i	0.999967	+	0.00815327i	$0.00259529\pi$
$101$	5.09573	+	8.82607i	0.507044	+	0.878227i	−0.492922	+	0.870073i	$0.664071\pi$
$102$	5.60244	−	1.48391i	0.554724	−	0.146929i
$103$	−8.54265	+	4.93210i	−0.841732	+	0.485974i	−0.857853	−	0.513896i	$-0.828202\pi$
$103$	−8.54265	+	4.93210i	−0.841732	+	0.485974i	0.0161205	+	0.999870i	$0.494868\pi$
$104$	2.39031	+	2.69934i	0.234389	+	0.264692i
$105$	−2.12503	+	1.21875i	−0.207381	+	0.118938i
$106$	2.67640	+	0.717140i	0.259955	+	0.0696548i
$107$	8.58323	+	4.95553i	0.829773	+	0.479069i	0.853775	−	0.520642i	$-0.174308\pi$
$107$	8.58323	+	4.95553i	0.829773	+	0.479069i	−0.0240022	+	0.999712i	$0.507641\pi$
$108$	−4.47741	−	2.63681i	−0.430839	−	0.253727i
$109$	6.99609	−	6.99609i	0.670103	−	0.670103i	−0.287636	−	0.957740i	$-0.592869\pi$
$109$	6.99609	−	6.99609i	0.670103	−	0.670103i	0.957740	+	0.287636i	$0.0928694\pi$
$110$	5.74937	+	5.74937i	0.548180	+	0.548180i
$111$	−13.5627	+	3.59234i	−1.28731	+	0.340970i
$112$	0.261812	−	0.977097i	0.0247389	−	0.0923269i
$113$	8.78784	+	5.07366i	0.826691	+	0.477290i	0.852718	−	0.522371i	$-0.174952\pi$
$113$	8.78784	+	5.07366i	0.826691	+	0.477290i	−0.0260276	+	0.999661i	$0.508286\pi$
$114$	6.37579	−	10.9702i	0.597148	−	1.02745i
$115$	0.210044	−	0.783896i	0.0195867	−	0.0730987i
$116$	1.03028			0.0956592
$117$	−0.717649	+	10.7928i	−0.0663467	+	0.997797i
$118$	11.9845			1.10326
$119$	−0.876052	+	3.26947i	−0.0803075	+	0.299712i
$120$	−1.20482	−	2.10073i	−0.109984	−	0.191770i
$121$	19.7610	+	11.4090i	1.79646	+	1.03718i
$122$	−0.731981	+	2.73179i	−0.0662704	+	0.247325i
$123$	1.99875	+	2.01028i	0.180221	+	0.181261i
$124$	6.24230	+	6.24230i	0.560575	+	0.560575i
$125$	7.95386	−	7.95386i	0.711415	−	0.711415i
$126$	2.63681	−	1.50220i	0.234905	−	0.133827i
$127$	−13.1106	−	7.56941i	−1.16338	−	0.671677i	−0.211267	−	0.977428i	$-0.567759\pi$
$127$	−13.1106	−	7.56941i	−1.16338	−	0.671677i	−0.952111	+	0.305752i	$0.901092\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−0.0417498	+	14.5155i	−0.00367587	+	1.27801i
$130$	−2.78055	+	4.20500i	−0.243870	+	0.368803i
$131$	3.29059	−	1.89982i	0.287500	−	0.165988i	−0.349314	−	0.937006i	$-0.613585\pi$
$131$	3.29059	−	1.89982i	0.287500	−	0.165988i	0.636814	+	0.771018i	$0.280252\pi$
$132$	−7.10178	−	7.14275i	−0.618131	−	0.621697i
$133$	3.70519	+	6.41758i	0.321281	+	0.556475i
$134$	−0.567130	−	0.982297i	−0.0489925	−	0.0848576i
$135$	1.94083	−	7.00107i	0.167040	−	0.602557i
$136$	−3.23209	−	0.866036i	−0.277149	−	0.0742620i
$137$	4.11536	−	4.11536i	0.351599	−	0.351599i	−0.509105	−	0.860704i	$-0.670024\pi$
$137$	4.11536	−	4.11536i	0.351599	−	0.351599i	0.860704	+	0.509105i	$0.170024\pi$
$138$	−0.262994	+	0.970336i	−0.0223876	+	0.0826004i
$139$	−1.13838	+	1.97173i	−0.0965559	+	0.167240i	−0.910257	−	0.414044i	$-0.864116\pi$
$139$	−1.13838	+	1.97173i	−0.0965559	+	0.167240i	0.813701	+	0.581284i	$0.197449\pi$
$140$	1.41434			0.119534
$141$	−0.666089	−	2.51479i	−0.0560948	−	0.211783i
$142$	−9.08440	−	5.24488i	−0.762346	−	0.440141i
$143$	−6.64426	+	19.8869i	−0.555621	+	1.66303i
$144$	1.48503	+	2.60666i	0.123752	+	0.217222i
$145$	0.372831	+	1.39143i	0.0309620	+	0.115552i
$146$	−0.965320	+	0.557328i	−0.0798905	+	0.0461248i
$147$	0.0297747	−	10.3520i	0.00245577	−	0.853816i
$148$	7.82443	+	2.09655i	0.643164	+	0.172335i
$149$	13.8851	−	3.72050i	1.13751	−	0.304795i	0.359561	−	0.933122i	$-0.382927\pi$
$149$	13.8851	−	3.72050i	1.13751	−	0.304795i	0.777949	+	0.628327i	$0.216260\pi$
$150$	−3.74020	+	3.71875i	−0.305386	+	0.303634i
$151$	−2.72013	+	0.728858i	−0.221361	+	0.0593136i	−0.367795	−	0.929907i	$-0.619887\pi$
$151$	−2.72013	+	0.728858i	−0.221361	+	0.0593136i	0.146434	+	0.989220i	$0.453221\pi$
$152$	−6.34422	+	3.66283i	−0.514584	+	0.297095i
$153$	−4.96907	−	8.72217i	−0.401725	−	0.705145i
$154$	5.68214	−	1.52252i	0.457880	−	0.122689i
$155$	−6.17149	+	10.6893i	−0.495706	+	0.858588i
$156$	3.45950	−	5.19921i	0.276982	−	0.416270i
$157$	3.93908	+	6.82268i	0.314372	+	0.544509i	0.979304	−	0.202395i	$-0.0648726\pi$
$157$	3.93908	+	6.82268i	0.314372	+	0.544509i	−0.664931	+	0.746904i	$0.731539\pi$
$158$	−1.16990	−	1.16990i	−0.0930723	−	0.0930723i
$159$	0.0138035	−	4.79918i	0.00109469	−	0.380599i
$160$			1.39817i			0.110535i
$161$	−0.415177	−	0.415177i	−0.0327205	−	0.0327205i
$162$	−2.42923	+	8.66596i	−0.190858	+	0.680862i
$163$	−1.79021	+	6.68116i	−0.140220	+	0.523309i	0.859701	+	0.510797i	$0.170650\pi$
$163$	−1.79021	+	6.68116i	−0.140220	+	0.523309i	−0.999922	+	0.0125123i	$0.996017\pi$
$164$	−0.423606	−	1.58092i	−0.0330780	−	0.123449i
$165$	7.07656	−	12.1759i	0.550909	−	0.947896i
$166$		−	16.2770i		−	1.26334i
$167$	−11.2080	+	11.2080i	−0.867298	+	0.867298i	−0.992173	−	0.124874i	$-0.960147\pi$
$167$	−11.2080	+	11.2080i	−0.867298	+	0.867298i	0.124874	+	0.992173i	$0.460147\pi$
$168$	−1.75207	−	0.00503937i	−0.135175	−	0.000388796i
$169$	−12.9045	−	1.57285i	−0.992654	−	0.120989i
$170$		−	4.67843i		−	0.358819i
$171$	−21.1951	−	5.81009i	−1.62083	−	0.444308i
$172$	4.19027	−	7.25776i	0.319505	−	0.553399i
$173$	−2.60453			−0.198018			−0.0990092	−	0.995087i	$-0.531567\pi$
$173$	−2.60453			−0.198018			−0.0990092	+	0.995087i	$0.531567\pi$
$174$	−0.456903	−	1.72501i	−0.0346377	−	0.130773i
$175$	−0.797249	−	2.97537i	−0.0602663	−	0.224917i
$176$	1.50512	+	5.61718i	0.113453	+	0.423411i
$177$	−5.31481	−	20.0658i	−0.399486	−	1.50824i
$178$	−3.02836			−0.226985
$179$	1.79612	−	3.11097i	0.134248	−	0.232525i	−0.791062	−	0.611736i	$-0.790471\pi$
$179$	1.79612	−	3.11097i	0.134248	−	0.232525i	0.925310	+	0.379211i	$0.123805\pi$
$180$	−2.98298	+	2.94886i	−0.222338	+	0.219795i
$181$		−	16.3443i		−	1.21486i	−0.794373	−	0.607430i	$-0.792201\pi$
$181$		−	16.3443i		−	1.21486i	0.794373	−	0.607430i	$-0.207799\pi$
$182$	1.62884	+	3.26333i	0.120738	+	0.241894i
$183$	4.89849	+	0.0140892i	0.362107	+	0.00104150i
$184$	0.410430	−	0.410430i	0.0302573	−	0.0302573i
$185$			11.3258i			0.832691i
$186$	7.68328	−	13.2199i	0.563365	−	0.969328i
$187$	−5.03629	−	18.7957i	−0.368290	−	1.37448i
$188$	−0.388741	+	1.45080i	−0.0283519	+	0.105811i
$189$	−3.68452	−	3.74866i	−0.268009	−	0.272675i
$190$	−7.24257	−	7.24257i	−0.525431	−	0.525431i
$191$		−	25.4377i		−	1.84061i	−0.391202	−	0.920305i	$-0.627941\pi$
$191$		−	25.4377i		−	1.84061i	0.391202	−	0.920305i	$-0.372059\pi$
$192$	0.00498176	−	1.73204i	0.000359527	−	0.124999i
$193$	8.92082	+	8.92082i	0.642134	+	0.642134i	0.951080	−	0.308945i	$-0.0999760\pi$
$193$	8.92082	+	8.92082i	0.642134	+	0.642134i	−0.308945	+	0.951080i	$0.599976\pi$
$194$	6.15527	+	10.6612i	0.441923	+	0.765433i
$195$	8.27360	+	2.79071i	0.592485	+	0.199847i
$196$	−2.98837	+	5.17601i	−0.213455	+	0.369715i
$197$	0.680083	−	0.182228i	0.0484539	−	0.0129832i	−0.234511	−	0.972114i	$-0.575349\pi$
$197$	0.680083	−	0.182228i	0.0484539	−	0.0129832i	0.282965	+	0.959130i	$0.408682\pi$
$198$	−8.80976	+	15.0582i	−0.626083	+	1.07014i
$199$	8.58639	−	4.95735i	0.608673	−	0.351418i	−0.163773	−	0.986498i	$-0.552366\pi$
$199$	8.58639	−	4.95735i	0.608673	−	0.351418i	0.772446	+	0.635081i	$0.219033\pi$
$200$	2.94136	−	0.788134i	0.207985	−	0.0557295i
$201$	−1.39317	+	1.38518i	−0.0982665	+	0.0977028i
$202$	−9.84420	+	2.63775i	−0.692635	+	0.185591i
$203$	1.00668	+	0.269740i	0.0706553	+	0.0189320i
$204$	−0.0166695	+	5.79560i	−0.00116710	+	0.405773i
$205$	1.98179	−	1.14418i	0.138414	−	0.0799133i
$206$	−2.55304	−	9.52809i	−0.177879	−	0.663853i
$207$	1.74128	+	0.0100167i	0.121027	+	0.000696210i
$208$	−3.22602	+	1.61022i	−0.223684	+	0.111649i
$209$	−36.8937	−	21.3006i	−2.55199	−	1.47339i
$210$	−0.627223	−	2.36805i	−0.0432825	−	0.163411i
$211$	−6.02887			−0.415045			−0.207522	−	0.978230i	$-0.566540\pi$
$211$	−6.02887			−0.415045			−0.207522	+	0.978230i	$0.566540\pi$
$212$	−1.38541	+	2.39960i	−0.0951502	+	0.164805i
$213$	−4.75289	+	17.5361i	−0.325663	+	1.20156i
$214$	−7.00818	+	7.00818i	−0.479069	+	0.479069i
$215$	11.3182	+	3.03269i	0.771893	+	0.206828i
$216$	3.70580	−	3.64239i	0.252148	−	0.247834i
$217$	4.46502	+	7.73364i	0.303105	+	0.524994i
$218$	4.94698	+	8.56842i	0.335052	+	0.580327i
$219$	1.36124	+	1.36909i	0.0919838	+	0.0925145i
$220$	−7.04151	+	4.06542i	−0.474738	+	0.274090i
$221$	10.7946	−	5.38797i	0.726123	−	0.362434i
$222$	0.0403545	−	14.0303i	0.00270842	−	0.941654i
$223$	28.1618	+	7.54594i	1.88586	+	0.505313i	0.999069	+	0.0431328i	$0.0137339\pi$
$223$	28.1618	+	7.54594i	1.88586	+	0.505313i	0.886786	+	0.462181i	$0.152933\pi$
$224$	0.876041	+	0.505782i	0.0585329	+	0.0337940i
$225$	7.88504	+	4.61311i	0.525669	+	0.307541i
$226$	−7.17524	+	7.17524i	−0.477290	+	0.477290i
$227$	10.2562	+	10.2562i	0.680729	+	0.680729i	0.960165	−	0.279435i	$-0.0901472\pi$
$227$	10.2562	+	10.2562i	0.680729	+	0.680729i	−0.279435	+	0.960165i	$0.590147\pi$
$228$	8.94623	+	8.99784i	0.592479	+	0.595897i
$229$	−2.55392	+	9.53135i	−0.168768	+	0.629849i	0.828762	+	0.559601i	$0.189046\pi$
$229$	−2.55392	+	9.53135i	−0.168768	+	0.629849i	−0.997530	+	0.0702479i	$0.977621\pi$
$230$	0.702822	+	0.405774i	0.0463427	+	0.0267560i
$231$	−5.06907	−	8.83849i	−0.333520	−	0.581530i
$232$	−0.266656	+	0.995175i	−0.0175068	+	0.0653364i
$233$	−2.06808			−0.135484			−0.0677421	−	0.997703i	$-0.521580\pi$
$233$	−2.06808			−0.135484			−0.0677421	+	0.997703i	$0.521580\pi$
$234$	−10.2393	−	3.48658i	−0.669365	−	0.227925i
$235$	−2.10003			−0.136991
$236$	−3.10182	+	11.5761i	−0.201911	+	0.753542i
$237$	−1.43996	+	2.47760i	−0.0935356	+	0.160938i
$238$	−2.93133	−	1.69240i	−0.190010	−	0.109702i
$239$	5.10931	−	19.0682i	0.330494	−	1.23342i	−0.578179	−	0.815910i	$-0.696236\pi$
$239$	5.10931	−	19.0682i	0.330494	−	1.23342i	0.908672	−	0.417510i	$-0.137097\pi$
$240$	2.34098	−	0.620053i	0.151110	−	0.0400242i
$241$	−7.17107	−	7.17107i	−0.461929	−	0.461929i	0.437358	−	0.899287i	$-0.355914\pi$
$241$	−7.17107	−	7.17107i	−0.461929	−	0.461929i	−0.899287	+	0.437358i	$0.855914\pi$
$242$	−16.1348	+	16.1348i	−1.03718	+	1.03718i
$243$	15.5868	+	0.224172i	0.999897	+	0.0143806i
$244$	−2.44926	−	1.41408i	−0.156797	−	0.0905271i
$245$	−8.07176	−	2.16282i	−0.515686	−	0.138178i
$246$	−2.45910	+	1.41034i	−0.156786	+	0.0899203i
$247$	8.36988	−	25.0519i	0.532563	−	1.59401i
$248$	−7.64523	+	4.41397i	−0.485472	+	0.280288i
$249$	−27.2528	+	7.21843i	−1.72708	+	0.457449i
$250$	5.62423	+	9.74145i	0.355707	+	0.616103i
$251$	4.78920	+	8.29514i	0.302292	+	0.523585i	0.976655	−	0.214815i	$-0.0689150\pi$
$251$	4.78920	+	8.29514i	0.302292	+	0.523585i	−0.674363	+	0.738400i	$0.735582\pi$
$252$	0.768562	+	2.93576i	0.0484148	+	0.184935i
$253$	3.26041	+	0.873624i	0.204980	+	0.0549243i
$254$	10.7048	−	10.7048i	0.671677	−	0.671677i
$255$	−7.83317	+	2.07476i	−0.490532	+	0.129927i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.77509			−0.360240			−0.180120	−	0.983645i	$-0.557649\pi$
$257$	−5.77509			−0.360240			−0.180120	+	0.983645i	$0.557649\pi$
$258$	−14.0101	−	3.79720i	−0.872228	−	0.236404i
$259$	7.09632	+	4.09706i	0.440944	+	0.254579i
$260$	−3.34206	−	3.77414i	−0.207266	−	0.234062i
$261$	−2.68559	+	1.53000i	−0.166234	+	0.0947045i
$262$	0.983420	+	3.67017i	0.0607559	+	0.226744i
$263$	−3.86009	+	2.22862i	−0.238023	+	0.137423i	−0.614268	−	0.789098i	$-0.710549\pi$
$263$	−3.86009	+	2.22862i	−0.238023	+	0.137423i	0.376245	+	0.926520i	$0.377215\pi$
$264$	8.73744	−	5.01111i	0.537753	−	0.308413i
$265$	−3.74207	−	1.00269i	−0.229874	−	0.0615945i
$266$	−7.15789	+	1.91795i	−0.438878	+	0.117597i
$267$	1.34300	+	5.07043i	0.0821902	+	0.310305i
$268$	1.09561	−	0.293568i	0.0669250	−	0.0179325i
$269$	11.4786	−	6.62715i	0.699860	−	0.404064i	−0.107435	−	0.994212i	$-0.534264\pi$
$269$	11.4786	−	6.62715i	0.699860	−	0.404064i	0.807295	+	0.590148i	$0.200931\pi$
$270$	6.26019	+	3.68671i	0.380983	+	0.224366i
$271$	−5.62562	+	1.50738i	−0.341732	+	0.0915668i	−0.425604	−	0.904910i	$-0.639938\pi$
$271$	−5.62562	+	1.50738i	−0.341732	+	0.0915668i	0.0838714	+	0.996477i	$0.473272\pi$
$272$	1.67305	−	2.89781i	0.101444	−	0.175706i
$273$	4.74149	−	4.17439i	0.286968	−	0.252646i
$274$	2.91000	+	5.04027i	0.175799	+	0.304494i
$275$	12.5217	+	12.5217i	0.755087	+	0.755087i
$276$	−0.869204	−	0.505174i	−0.0523199	−	0.0304079i
$277$			19.4395i			1.16800i	0.811752	+	0.584002i	$0.198514\pi$
$277$			19.4395i			1.16800i	−0.811752	+	0.584002i	$0.801486\pi$
$278$	−1.60991	−	1.60991i	−0.0965559	−	0.0965559i
$279$	−25.5416	−	7.00156i	−1.52913	−	0.419173i
$280$	−0.366058	+	1.36615i	−0.0218762	+	0.0816430i
$281$	−0.376063	−	1.40349i	−0.0224340	−	0.0837250i	0.953801	−	0.300438i	$-0.0971330\pi$
$281$	−0.376063	−	1.40349i	−0.0224340	−	0.0837250i	−0.976235	+	0.216713i	$0.930466\pi$
$282$	2.60150	+	0.00748250i	0.154917	+	0.000445577i
$283$		−	20.7333i		−	1.23247i	−0.787564	−	0.616233i	$-0.788658\pi$
$283$		−	20.7333i		−	1.23247i	0.787564	−	0.616233i	$-0.211342\pi$
$284$	7.41738	−	7.41738i	0.440141	−	0.440141i
$285$	−8.91446	+	15.3382i	−0.528047	+	0.908559i
$286$	−17.4896	−	11.5650i	−1.03418	−	0.683851i
$287$		−	1.65561i		−	0.0977278i
$288$	−2.90220	+	0.759775i	−0.171014	+	0.0447702i
$289$	2.90179	−	5.02604i	0.170693	−	0.295649i
$290$	−1.44051			−0.0845896
$291$	15.1206	−	15.0338i	0.886384	−	0.881300i
$292$	−0.288494	−	1.07667i	−0.0168828	−	0.0630076i
$293$	−6.14475	−	22.9325i	−0.358980	−	1.33973i	−0.875401	−	0.483398i	$-0.839402\pi$
$293$	−6.14475	−	22.9325i	−0.358980	−	1.33973i	0.516420	−	0.856335i	$-0.327264\pi$
$294$	9.99153	+	2.70805i	0.582718	+	0.157936i
$295$	−16.7564			−0.975595
$296$	−4.05022	+	7.01519i	−0.235414	+	0.407750i
$297$	29.1191	+	8.07238i	1.68966	+	0.468407i
$298$			14.3749i			0.832715i
$299$	−0.126835	+	2.08894i	−0.00733508	+	0.120807i
$300$	−2.62400	−	4.57524i	−0.151497	−	0.264152i
$301$	5.99447	−	5.99447i	0.345515	−	0.345515i
$302$		−	2.81609i		−	0.162048i
$303$	8.78206	+	15.3125i	0.504516	+	0.879681i
$304$	−1.89602	−	7.07605i	−0.108744	−	0.405839i
$305$	1.02343	−	3.81951i	0.0586017	−	0.218705i
$306$	9.71106	−	2.54229i	0.555144	−	0.145333i
$307$	14.7696	+	14.7696i	0.842947	+	0.842947i	0.989241	−	0.146294i	$-0.0467346\pi$
$307$	14.7696	+	14.7696i	0.842947	+	0.842947i	−0.146294	+	0.989241i	$0.546735\pi$
$308$			5.88258i			0.335191i
$309$	−14.8208	+	8.50006i	−0.843126	+	0.483551i
$310$	−8.72781	−	8.72781i	−0.495706	−	0.495706i
$311$	−14.0548	−	24.3437i	−0.796976	−	1.38040i	−0.921577	−	0.388195i	$-0.873099\pi$
$311$	−14.0548	−	24.3437i	−0.796976	−	1.38040i	0.124602	−	0.992207i	$-0.460235\pi$
$312$	4.12667	+	4.68728i	0.233627	+	0.265365i
$313$	8.76521	−	15.1818i	0.495439	−	0.858125i	−0.504547	−	0.863384i	$-0.668341\pi$
$313$	8.76521	−	15.1818i	0.495439	−	0.858125i	0.999986	+	0.00525876i	$0.00167392\pi$
$314$	−7.60971	+	2.03902i	−0.429441	+	0.115068i
$315$	−3.68671	+	2.10034i	−0.207723	+	0.118341i
$316$	1.43283	−	0.827245i	0.0806030	−	0.0465362i
$317$	21.3692	−	5.72585i	1.20021	−	0.321596i	0.397298	−	0.917690i	$-0.369948\pi$
$317$	21.3692	−	5.72585i	1.20021	−	0.321596i	0.802915	+	0.596094i	$0.203281\pi$
$318$	4.63207	+	1.25545i	0.259754	+	0.0704022i
$319$	−5.78727	+	1.55069i	−0.324025	+	0.0868222i
$320$	−1.35053	−	0.361873i	−0.0754969	−	0.0202293i
$321$	14.8418	+	8.62596i	0.828391	+	0.481454i
$322$	0.508485	−	0.293574i	0.0283368	−	0.0163603i
$323$	6.34429	+	23.6772i	0.353006	+	1.31744i
$324$	−7.74194	−	4.58937i	−0.430108	−	0.254965i
$325$	−6.05583	+	9.15819i	−0.335917	+	0.508005i
$326$	−5.99017	−	3.45843i	−0.331765	−	0.191544i
$327$	12.1524	−	12.0827i	0.672028	−	0.668173i
$328$	1.63669			0.0903709
$329$	−0.759675	+	1.31580i	−0.0418822	+	0.0725422i
$330$	9.92951	+	9.98679i	0.546602	+	0.549755i
$331$	16.0059	−	16.0059i	0.879762	−	0.879762i	−0.113748	−	0.993510i	$-0.536286\pi$
$331$	16.0059	−	16.0059i	0.879762	−	0.879762i	0.993510	+	0.113748i	$0.0362856\pi$
$332$	15.7224	+	4.21280i	0.862878	+	0.231207i
$333$	−23.5091	+	6.15452i	−1.28829	+	0.337266i
$334$	−7.92523	−	13.7269i	−0.433649	−	0.751102i
$335$	0.792945	+	1.37342i	0.0433232	+	0.0750380i
$336$	0.458338	−	1.69107i	0.0250044	−	0.0922554i
$337$	−26.9968	+	15.5866i	−1.47061	+	0.849058i	−0.999456	−	0.0329922i	$-0.989496\pi$
$337$	−26.9968	+	15.5866i	−1.47061	+	0.849058i	−0.471156	+	0.882050i	$0.656163\pi$
$338$	4.85919	−	12.0577i	0.264305	−	0.655853i
$339$	15.1956	+	8.83158i	0.825314	+	0.479666i
$340$	4.51902	+	1.21087i	0.245078	+	0.0656685i
$341$	−44.4595	−	25.6687i	−2.40762	−	1.39004i
$342$	11.0978	−	18.9691i	0.600101	−	1.02573i
$343$	−9.28206	+	9.28206i	−0.501184	+	0.501184i
$344$	5.92594	+	5.92594i	0.319505	+	0.319505i
$345$	0.367711	−	1.35670i	0.0197969	−	0.0730420i
$346$	0.674101	−	2.51578i	0.0362399	−	0.135249i
$347$	−17.6308	−	10.1791i	−0.946468	−	0.546444i	−0.0544863	−	0.998515i	$-0.517352\pi$
$347$	−17.6308	−	10.1791i	−0.946468	−	0.546444i	−0.891982	+	0.452071i	$0.850685\pi$
$348$	1.78449	+	0.00513261i	0.0956588	+	0.000275137i
$349$	−7.61062	+	28.4032i	−0.407387	+	1.52039i	0.392224	+	0.919870i	$0.371706\pi$
$349$	−7.61062	+	28.4032i	−0.407387	+	1.52039i	−0.799611	+	0.600519i	$0.794961\pi$
$350$	3.08033			0.164651
$351$	−1.29677	+	18.6901i	−0.0692163	+	0.997602i
$352$	−5.81533			−0.309958
$353$	−2.96995	+	11.0840i	−0.158075	+	0.589943i	0.840748	+	0.541427i	$0.182116\pi$
$353$	−2.96995	+	11.0840i	−0.158075	+	0.589943i	−0.998822	+	0.0485157i	$0.984551\pi$
$354$	20.7577	+	0.0597039i	1.10326	+	0.00317323i
$355$	12.7016	+	7.33325i	0.674129	+	0.389208i
$356$	0.783797	−	2.92517i	0.0415412	−	0.155034i
$357$	−1.53365	+	5.65850i	−0.0811692	+	0.299480i
$358$	2.54010	+	2.54010i	0.134248	+	0.134248i
$359$	25.9734	−	25.9734i	1.37083	−	1.37083i	0.511605	−	0.859221i	$-0.329051\pi$
$359$	25.9734	−	25.9734i	1.37083	−	1.37083i	0.859221	−	0.511605i	$-0.170949\pi$
$360$	−2.07633	−	3.64456i	−0.109432	−	0.192085i
$361$	30.0211	+	17.3327i	1.58006	+	0.912248i
$362$	15.7873	+	4.23021i	0.829765	+	0.222335i
$363$	34.1701	+	19.8594i	1.79347	+	1.04235i
$364$	−3.57371	+	0.728730i	−0.187313	+	0.0381958i
$365$	1.34968	−	0.779240i	0.0706457	−	0.0407873i
$366$	−1.28143	+	4.72793i	−0.0669815	+	0.247133i
$367$	2.78625	+	4.82592i	0.145441	+	0.251911i	0.929537	−	0.368728i	$-0.120207\pi$
$367$	2.78625	+	4.82592i	0.145441	+	0.251911i	−0.784096	+	0.620639i	$0.786873\pi$
$368$	0.290218	+	0.502672i	0.0151287	+	0.0262036i
$369$	3.45191	+	3.49185i	0.179699	+	0.181778i
$370$	−10.9399	−	2.93134i	−0.568738	−	0.152393i
$371$	−1.98192	+	1.98192i	−0.102896	+	0.102896i
$372$	10.7808	+	10.8430i	0.558960	+	0.562185i
$373$	−1.43922	+	2.49280i	−0.0745200	+	0.129072i	−0.900877	−	0.434074i	$-0.857076\pi$
$373$	−1.43922	+	2.49280i	−0.0745200	+	0.129072i	0.826357	+	0.563146i	$0.190409\pi$
$374$	19.4587			1.00619
$375$	13.8161	−	13.7368i	0.713458	−	0.709366i
$376$	−1.30075	−	0.750990i	−0.0670812	−	0.0387294i
$377$	−1.65898	−	3.32370i	−0.0854418	−	0.171179i
$378$	4.57455	−	2.58875i	0.235289	−	0.133151i
$379$	5.51954	+	20.5992i	0.283520	+	1.05811i	0.949914	+	0.312511i	$0.101170\pi$
$379$	5.51954	+	20.5992i	0.283520	+	1.05811i	−0.666394	+	0.745600i	$0.732163\pi$
$380$	8.87030	−	5.12127i	0.455037	−	0.262716i
$381$	−22.6704	−	13.1759i	−1.16144	−	0.675020i
$382$	24.5710	+	6.58377i	1.25716	+	0.336855i
$383$	12.5372	−	3.35934i	0.640623	−	0.171654i	0.0761376	−	0.997097i	$-0.475741\pi$
$383$	12.5372	−	3.35934i	0.640623	−	0.171654i	0.564486	+	0.825443i	$0.309075\pi$
$384$	1.67174	+	0.453098i	0.0853104	+	0.0231221i
$385$	−7.94461	+	2.12875i	−0.404895	+	0.108491i
$386$	−10.9257	+	6.30797i	−0.556105	+	0.321067i
$387$	−0.144625	+	25.1412i	−0.00735170	+	1.27800i
$388$	−11.8911	+	3.18620i	−0.603678	+	0.161755i
$389$	15.6511	−	27.1085i	0.793543	−	1.37446i	−0.130216	−	0.991486i	$-0.541567\pi$
$389$	15.6511	−	27.1085i	0.793543	−	1.37446i	0.923760	−	0.382972i	$-0.125099\pi$
$390$	−4.83698	+	7.26940i	−0.244930	+	0.368100i
$391$	−0.971100	−	1.68199i	−0.0491106	−	0.0850621i
$392$	−4.22619	−	4.22619i	−0.213455	−	0.213455i
$393$	5.70891	−	3.27418i	0.287976	−	0.165161i
$394$			0.704074i			0.0354707i
$395$	1.63572	+	1.63572i	0.0823021	+	0.0823021i
$396$	−12.2650	−	12.4069i	−0.616340	−	0.623472i
$397$	0.644906	−	2.40682i	0.0323669	−	0.120795i	−0.947852	−	0.318710i	$-0.896750\pi$
$397$	0.644906	−	2.40682i	0.0323669	−	0.120795i	0.980219	+	0.197915i	$0.0634170\pi$
$398$	2.56612	+	9.57687i	0.128628	+	0.480045i
$399$	6.38559	+	11.1340i	0.319679	+	0.557397i
$400$			3.04512i			0.152256i
$401$	14.5050	−	14.5050i	0.724345	−	0.724345i	−0.245142	−	0.969487i	$-0.578835\pi$
$401$	14.5050	−	14.5050i	0.724345	−	0.724345i	0.969487	+	0.245142i	$0.0788347\pi$
$402$	−0.977400	−	1.70421i	−0.0487483	−	0.0849981i
$403$	10.0863	−	30.1893i	0.502434	−	1.50383i
$404$		−	10.1915i		−	0.507044i
$405$	3.39648	−	12.1165i	0.168773	−	0.602074i
$406$	−0.521098	+	0.902568i	−0.0258617	+	0.0447937i
$407$	−47.1068			−2.33500
$408$	−5.59381	−	1.51611i	−0.276935	−	0.0750588i
$409$	−2.53544	−	9.46239i	−0.125369	−	0.467885i	0.874483	−	0.485056i	$-0.161201\pi$
$409$	−2.53544	−	9.46239i	−0.125369	−	0.467885i	−0.999853	+	0.0171708i	$0.994534\pi$
$410$	0.592273	+	2.21039i	0.0292503	+	0.109164i
$411$	7.14848	−	7.10748i	0.352609	−	0.350586i
$412$	9.86420			0.485974
$413$	−6.06155	+	10.4989i	−0.298269	+	0.516618i
$414$	−0.460351	+	1.67935i	−0.0226250	+	0.0825357i
$415$			22.7581i			1.11715i
$416$	−0.720398	−	3.53285i	−0.0353204	−	0.173212i
$417$	−1.98154	+	3.40945i	−0.0970365	+	0.166961i
$418$	30.1236	−	30.1236i	1.47339	−	1.47339i
$419$		−	1.73191i		−	0.0846094i	−0.999105	−	0.0423047i	$-0.986530\pi$
$419$		−	1.73191i		−	0.0846094i	0.999105	−	0.0423047i	$-0.0134700\pi$
$420$	2.44970	+	0.00704591i	0.119533	+	0.000343805i
$421$	0.920185	+	3.43418i	0.0448471	+	0.167372i	0.984717	−	0.174160i	$-0.0557210\pi$
$421$	0.920185	+	3.43418i	0.0448471	+	0.167372i	−0.939870	+	0.341532i	$0.889054\pi$
$422$	1.56039	−	5.82344i	0.0759584	−	0.283481i
$423$	−1.14117	−	4.35904i	−0.0554854	−	0.211944i
$424$	−1.95926	−	1.95926i	−0.0951502	−	0.0951502i
$425$		−	10.1893i		−	0.494253i
$426$	−15.7085	−	9.12962i	−0.761077	−	0.442332i
$427$	−2.02294	−	2.02294i	−0.0978967	−	0.0978967i
$428$	−4.95553	−	8.58323i	−0.239535	−	0.414886i
$429$	−11.6072	+	34.4119i	−0.560402	+	1.66142i
$430$	−5.85872	+	10.1476i	−0.282532	+	0.489360i
$431$	−14.3219	+	3.83753i	−0.689860	+	0.184847i	−0.586684	−	0.809816i	$-0.699567\pi$
$431$	−14.3219	+	3.83753i	−0.689860	+	0.184847i	−0.103176	+	0.994663i	$0.532900\pi$
$432$	2.55915	+	4.52225i	0.123127	+	0.217577i
$433$	−9.94854	+	5.74379i	−0.478096	+	0.276029i	−0.719623	−	0.694365i	$-0.755685\pi$
$433$	−9.94854	+	5.74379i	−0.478096	+	0.276029i	0.241527	+	0.970394i	$0.422352\pi$
$434$	−8.62576	+	2.31126i	−0.414050	+	0.110944i
$435$	0.638828	+	2.41187i	0.0306295	+	0.115640i
$436$	−9.55683	+	2.56075i	−0.457689	+	0.122637i
$437$	−4.10719	−	1.10052i	−0.196474	−	0.0526450i
$438$	−1.67475	+	0.960507i	−0.0800228	+	0.0458948i
$439$	−35.2492	+	20.3511i	−1.68235	+	0.971306i	−0.722259	+	0.691623i	$0.756896\pi$
$439$	−35.2492	+	20.3511i	−1.68235	+	0.971306i	−0.960092	+	0.279683i	$0.909771\pi$
$440$	−2.10441	−	7.85378i	−0.100324	−	0.374414i
$441$	0.103142	−	17.9299i	0.00491152	−	0.853805i
$442$	2.41053	+	11.8213i	0.114657	+	0.562281i
$443$	10.6734	+	6.16232i	0.507111	+	0.292780i	0.731645	−	0.681686i	$-0.238753\pi$
$443$	10.6734	+	6.16232i	0.507111	+	0.292780i	−0.224535	+	0.974466i	$0.572086\pi$
$444$	13.5418	+	3.67030i	0.642666	+	0.174185i
$445$	4.23417			0.200719
$446$	−14.5776	+	25.2492i	−0.690271	+	1.19558i
$447$	24.0681	−	6.37489i	1.13838	−	0.301522i
$448$	−0.715284	+	0.715284i	−0.0337940	+	0.0337940i
$449$	−27.3580	−	7.33055i	−1.29110	−	0.345950i	−0.453024	−	0.891498i	$-0.649655\pi$
$449$	−27.3580	−	7.33055i	−1.29110	−	0.345950i	−0.838080	+	0.545548i	$0.816322\pi$
$450$	−6.49672	+	6.42240i	−0.306258	+	0.302755i
$451$	4.75894	+	8.24272i	0.224090	+	0.388134i
$452$	−5.07366	−	8.78784i	−0.238645	−	0.413345i
$453$	−4.71502	+	1.24886i	−0.221531	+	0.0586767i
$454$	−12.5613	+	7.25224i	−0.589529	+	0.340365i
$455$	−2.27740	−	4.56269i	−0.106766	−	0.213902i
$456$	−11.0067	+	6.31258i	−0.515436	+	0.295614i
$457$	−29.0998	−	7.79727i	−1.36123	−	0.364741i	−0.496963	−	0.867772i	$-0.665551\pi$
$457$	−29.0998	−	7.79727i	−1.36123	−	0.364741i	−0.864268	+	0.503031i	$0.832218\pi$
$458$	−8.54557	−	4.93379i	−0.399308	−	0.230541i
$459$	−8.56319	−	15.1319i	−0.399696	−	0.706298i
$460$	−0.573852	+	0.573852i	−0.0267560	+	0.0267560i
$461$	20.1337	+	20.1337i	0.937718	+	0.937718i	0.998171	−	0.0604534i	$-0.0192547\pi$
$461$	20.1337	+	20.1337i	0.937718	+	0.937718i	−0.0604534	+	0.998171i	$0.519255\pi$
$462$	9.84930	−	2.60877i	0.458231	−	0.121371i
$463$	0.936943	−	3.49672i	0.0435434	−	0.162506i	−0.940731	−	0.339155i	$-0.889859\pi$
$463$	0.936943	−	3.49672i	0.0435434	−	0.162506i	0.984274	+	0.176649i	$0.0565256\pi$
$464$	−0.892249	−	0.515140i	−0.0414216	−	0.0239148i
$465$	−10.7425	+	18.4837i	−0.498174	+	0.857159i
$466$	0.535258	−	1.99761i	0.0247953	−	0.0925375i
$467$	36.6235			1.69473			0.847366	−	0.531010i	$-0.178187\pi$
$467$	36.6235			1.69473			0.847366	+	0.531010i	$0.178187\pi$
$468$	6.01791	−	8.98803i	0.278178	−	0.415472i
$469$	1.14738			0.0529809
$470$	0.543527	−	2.02847i	0.0250710	−	0.0935663i
$471$	6.78866	+	11.8368i	0.312805	+	0.545411i
$472$	−10.3789	−	5.99225i	−0.477727	−	0.275816i
$473$	−12.6137	+	47.0750i	−0.579979	+	2.16451i
$474$	−2.02049	−	2.03215i	−0.0928043	−	0.0933396i
$475$	−15.7738	−	15.7738i	−0.723751	−	0.723751i
$476$	2.39342	−	2.39342i	0.109702	−	0.109702i
$477$	0.0478167	−	8.31231i	0.00218937	−	0.380595i
$478$	17.0961	+	9.87043i	0.781957	+	0.451463i
$479$	−4.87703	−	1.30680i	−0.222837	−	0.0597091i	0.145673	−	0.989333i	$-0.453465\pi$
$479$	−4.87703	−	1.30680i	−0.222837	−	0.0597091i	−0.368510	+	0.929624i	$0.620132\pi$
$480$	−0.00696535	+	2.42169i	−0.000317923	+	0.110535i
$481$	−5.83555	−	28.6177i	−0.266078	−	1.30485i
$482$	8.78273	−	5.07071i	0.400043	−	0.230965i
$483$	−0.717036	−	0.721172i	−0.0326263	−	0.0328145i
$484$	−11.4090	−	19.7610i	−0.518592	−	0.898228i
$485$	−8.60613	−	14.9063i	−0.390784	−	0.676858i
$486$	−4.25071	+	14.9977i	−0.192816	+	0.680310i
$487$	−28.6137	−	7.66702i	−1.29661	−	0.347426i	−0.456443	−	0.889753i	$-0.650877\pi$
$487$	−28.6137	−	7.66702i	−1.29661	−	0.347426i	−0.840167	+	0.542327i	$0.817543\pi$
$488$	1.99981	−	1.99981i	0.0905271	−	0.0905271i
$489$	−3.13401	+	11.5632i	−0.141725	+	0.522904i
$490$	4.17825	−	7.23695i	0.188754	−	0.326932i
$491$	−1.97522			−0.0891403			−0.0445701	−	0.999006i	$-0.514192\pi$
$491$	−1.97522			−0.0891403			−0.0445701	+	0.999006i	$0.514192\pi$
$492$	−0.725828	−	2.74033i	−0.0327228	−	0.123544i
$493$	2.98556	+	1.72371i	0.134463	+	0.0776322i
$494$	22.0320	+	14.5686i	0.991264	+	0.655471i
$495$	12.3176	−	21.0540i	0.553633	−	0.946307i
$496$	−2.28484	−	8.52714i	−0.102592	−	0.382880i
$497$	9.18946	−	5.30554i	0.412204	−	0.237986i
$498$	0.0810881	−	28.1925i	0.00363365	−	1.26334i
$499$	−3.87214	−	1.03754i	−0.173341	−	0.0464465i	0.171105	−	0.985253i	$-0.445266\pi$
$499$	−3.87214	−	1.03754i	−0.173341	−	0.0464465i	−0.344445	+	0.938806i	$0.611933\pi$
$500$	−10.8652	+	2.91131i	−0.485905	+	0.130198i
$501$	−19.4685	+	19.3568i	−0.869789	+	0.864800i
$502$	−9.25203	+	2.47907i	−0.412938	+	0.110646i
$503$	−6.37037	+	3.67794i	−0.284041	+	0.163991i	−0.635251	−	0.772305i	$-0.719103\pi$
$503$	−6.37037	+	3.67794i	−0.284041	+	0.163991i	0.351211	+	0.936297i	$0.385770\pi$
$504$	−3.03464	−	0.0174568i	−0.135174	−	0.000777589i
$505$	13.7639	−	3.68802i	0.612485	−	0.164115i
$506$	−1.68771	+	2.92320i	−0.0750280	+	0.129952i
$507$	−22.3433	−	2.78854i	−0.992302	−	0.123843i
$508$	7.56941	+	13.1106i	0.335838	+	0.581689i
$509$	10.0747	+	10.0747i	0.446552	+	0.446552i	0.894207	−	0.447654i	$-0.147740\pi$
$509$	10.0747	+	10.0747i	0.446552	+	0.446552i	−0.447654	+	0.894207i	$0.647740\pi$
$510$	0.0233068	−	8.10325i	0.00103204	−	0.358818i
$511$		−	1.12755i		−	0.0498797i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−36.6819	−	10.1689i	−1.61954	−	0.448968i
$514$	1.49470	−	5.57831i	0.0659286	−	0.246049i
$515$	3.56959	+	13.3219i	0.157295	+	0.587033i
$516$	7.29389	−	12.5499i	0.321095	−	0.552478i
$517$		−	8.73451i		−	0.384143i
$518$	−5.79412	+	5.79412i	−0.254579	+	0.254579i
$519$	−4.51115	−	0.0129751i	−0.198018	−	0.000569544i
$520$	4.51053	−	2.25136i	0.197800	−	0.0987289i
$521$			28.5428i			1.25048i	0.780431	+	0.625242i	$0.215000\pi$
$521$			28.5428i			1.25048i	−0.780431	+	0.625242i	$0.785000\pi$
$522$	−0.782782	−	2.99008i	−0.0342614	−	0.130872i
$523$	7.95336	−	13.7756i	0.347776	−	0.602366i	−0.638078	−	0.769972i	$-0.720270\pi$
$523$	7.95336	−	13.7756i	0.347776	−	0.602366i	0.985854	+	0.167606i	$0.0536037\pi$
$524$	−3.79964			−0.165988
$525$	−1.36605	−	5.15745i	−0.0596192	−	0.225089i
$526$	−1.15362	−	4.30537i	−0.0503002	−	0.187723i
$527$	7.64532	+	28.5327i	0.333035	+	1.24290i
$528$	2.57895	+	9.73669i	0.112234	+	0.423735i
$529$	−22.6631			−0.985352
$530$	1.93704	−	3.35505i	0.0841396	−	0.145734i
$531$	−9.10553	−	34.7814i	−0.395146	−	1.50938i
$532$		−	7.41039i		−	0.321281i
$533$	−4.41797	+	3.91218i	−0.191364	+	0.169456i
$534$	−5.24525	−	0.0150866i	−0.226984	−	0.000652859i
$535$	9.79864	−	9.79864i	0.423632	−	0.423632i
$536$			1.13426i			0.0489925i
$537$	3.12646	−	5.37939i	0.134917	−	0.232138i
$538$	3.43046	+	12.8027i	0.147898	+	0.551962i
$539$	8.99570	−	33.5724i	0.387472	−	1.44607i
$540$	−5.18135	+	5.09269i	−0.222970	+	0.219155i
$541$	20.5826	+	20.5826i	0.884913	+	0.884913i	0.994029	−	0.109116i	$-0.0348019\pi$
$541$	20.5826	+	20.5826i	0.884913	+	0.884913i	−0.109116	+	0.994029i	$0.534802\pi$
$542$		−	5.82407i		−	0.250165i
$543$	0.0814232	−	28.3090i	0.00349420	−	1.21485i
$544$	2.36605	+	2.36605i	0.101444	+	0.101444i
$545$	−6.91673	−	11.9801i	−0.296280	−	0.513172i
$546$	2.80497	+	5.66034i	0.120042	+	0.242240i
$547$	−11.8581	+	20.5389i	−0.507017	+	0.878180i	0.492950	+	0.870058i	$0.335919\pi$
$547$	−11.8581	+	20.5389i	−0.507017	+	0.878180i	−0.999967	+	0.00812189i	$0.997415\pi$
$548$	−5.62169	+	1.50633i	−0.240147	+	0.0643471i
$549$	8.48433	+	0.0488062i	0.362102	+	0.00208300i
$550$	−15.3359	+	8.85418i	−0.653924	+	0.377543i
$551$	7.29032	−	1.95344i	0.310578	−	0.0832191i
$552$	0.712927	−	0.708838i	0.0303442	−	0.0301702i
$553$	1.61660	−	0.433166i	0.0687447	−	0.0184201i
$554$	−18.7771	−	5.03130i	−0.797762	−	0.213760i
$555$	−0.0564225	+	19.6168i	−0.00239500	+	0.832687i
$556$	1.97173	−	1.13838i	0.0836199	−	0.0482779i
$557$	−1.55296	−	5.79572i	−0.0658010	−	0.245573i	0.925189	−	0.379506i	$-0.123906\pi$
$557$	−1.55296	−	5.79572i	−0.0658010	−	0.245573i	−0.990990	+	0.133933i	$0.957239\pi$
$558$	13.3736	−	22.8591i	0.566151	−	0.967704i
$559$	−30.1609	−	1.83129i	−1.27567	−	0.0774555i
$560$	−1.22486	−	0.707171i	−0.0517596	−	0.0298834i
$561$	−8.62943	−	32.5800i	−0.364335	−	1.37553i
$562$	1.45300			0.0612909
$563$	17.1469	−	29.6993i	0.722656	−	1.25168i	−0.237275	−	0.971442i	$-0.576254\pi$
$563$	17.1469	−	29.6993i	0.722656	−	1.25168i	0.959932	−	0.280235i	$-0.0904123\pi$
$564$	−0.680544	+	2.51091i	−0.0286561	+	0.105729i
$565$	10.0322	−	10.0322i	0.422059	−	0.422059i
$566$	20.0268	+	5.36617i	0.841790	+	0.225557i
$567$	−6.36307	−	6.51119i	−0.267224	−	0.273444i
$568$	5.24488	+	9.08440i	0.220070	+	0.381173i
$569$	17.8407	+	30.9009i	0.747919	+	1.29543i	0.948818	+	0.315822i	$0.102280\pi$
$569$	17.8407	+	30.9009i	0.747919	+	1.29543i	−0.200899	+	0.979612i	$0.564386\pi$
$570$	−12.5084	−	12.5805i	−0.523918	−	0.526940i
$571$	25.3581	−	14.6405i	1.06121	−	0.612687i	0.135440	−	0.990786i	$-0.456755\pi$
$571$	25.3581	−	14.6405i	1.06121	−	0.612687i	0.925765	+	0.378099i	$0.123422\pi$
$572$	15.6975	−	13.9004i	0.656347	−	0.581206i
$573$	0.126725	−	44.0593i	0.00529400	−	1.84060i
$574$	1.59920	+	0.428504i	0.0667493	+	0.0178854i
$575$	1.53069	+	0.883747i	0.0638344	+	0.0368548i
$576$	0.0172572	−	2.99995i	0.000719052	−	0.124998i
$577$	−19.2968	+	19.2968i	−0.803337	+	0.803337i	−0.983616	−	0.180278i	$-0.942300\pi$
$577$	−19.2968	+	19.2968i	−0.803337	+	0.803337i	0.180278	+	0.983616i	$0.442300\pi$
$578$	4.10375	+	4.10375i	0.170693	+	0.170693i
$579$	15.4068	+	15.4957i	0.640285	+	0.643979i
$580$	0.372831	−	1.39143i	0.0154810	−	0.0577758i
$581$	14.2593	+	8.23262i	0.591576	+	0.341547i
$582$	10.6081	+	18.4964i	0.439719	+	0.766701i
$583$	4.17041	−	15.5642i	0.172721	−	0.644602i
$584$	1.11466			0.0461248
$585$	14.3163	+	4.87484i	0.591907	+	0.201550i
$586$	23.7415			0.980753
$587$	−5.15867	+	19.2524i	−0.212921	+	0.794633i	0.773967	+	0.633226i	$0.218270\pi$
$587$	−5.15867	+	19.2524i	−0.212921	+	0.794633i	−0.986888	+	0.161407i	$0.948397\pi$
$588$	−5.20177	+	8.95018i	−0.214517	+	0.369099i
$589$	56.0064	+	32.3353i	2.30770	+	1.33235i
$590$	4.33687	−	16.1854i	0.178546	−	0.666344i
$591$	1.17884	−	0.312238i	0.0484911	−	0.0128438i
$592$	−5.72788	−	5.72788i	−0.235414	−	0.235414i
$593$	3.24522	−	3.24522i	0.133265	−	0.133265i	−0.637328	−	0.770593i	$-0.719960\pi$
$593$	3.24522	−	3.24522i	0.133265	−	0.133265i	0.770593	+	0.637328i	$0.219960\pi$
$594$	−15.3339	+	26.0376i	−0.629158	+	1.06834i
$595$	4.09850	+	2.36627i	0.168022	+	0.0970075i
$596$	−13.8851	−	3.72050i	−0.568755	−	0.152397i
$597$	14.8967	−	8.54358i	0.609681	−	0.349665i
$598$	−1.98494	−	0.663172i	−0.0811701	−	0.0271191i
$599$	−36.4947	+	21.0702i	−1.49113	+	0.860906i	−0.999949	−	0.0101486i	$-0.996770\pi$
$599$	−36.4947	+	21.0702i	−1.49113	+	0.860906i	−0.491185	+	0.871055i	$0.663436\pi$
$600$	5.09848	−	1.35043i	0.208145	−	0.0551310i
$601$	−2.31955	−	4.01758i	−0.0946164	−	0.163880i	0.814832	−	0.579697i	$-0.196829\pi$
$601$	−2.31955	−	4.01758i	−0.0946164	−	0.163880i	−0.909448	+	0.415817i	$0.863496\pi$
$602$	4.23873	+	7.34169i	0.172758	+	0.299225i
$603$	−2.41993	+	2.39225i	−0.0985471	+	0.0974198i
$604$	2.72013	+	0.728858i	0.110681	+	0.0296568i
$605$	22.5592	−	22.5592i	0.917163	−	0.917163i
$606$	−17.0637	+	4.51965i	−0.693166	+	0.183598i
$607$	−5.75071	+	9.96053i	−0.233414	+	0.404285i	−0.958811	−	0.284046i	$-0.908323\pi$
$607$	−5.75071	+	9.96053i	−0.233414	+	0.404285i	0.725396	+	0.688331i	$0.241656\pi$
$608$	7.32567			0.297095
$609$	1.74228	+	0.472217i	0.0706006	+	0.0191352i
$610$	3.42448	+	1.97712i	0.138653	+	0.0800514i
$611$	5.30627	−	1.08202i	0.214669	−	0.0437740i
$612$	−0.0577446	+	10.0382i	−0.00233419	+	0.405768i
$613$	−3.05394	−	11.3975i	−0.123347	−	0.460339i	0.876428	−	0.481533i	$-0.159920\pi$
$613$	−3.05394	−	11.3975i	−0.123347	−	0.460339i	−0.999775	+	0.0211942i	$0.993253\pi$
$614$	−18.0890	+	10.4437i	−0.730014	+	0.421474i
$615$	3.43824	−	1.97190i	0.138643	−	0.0795149i
$616$	−5.68214	−	1.52252i	−0.228940	−	0.0613443i
$617$	−30.8124	+	8.25615i	−1.24046	+	0.332380i	−0.818644	−	0.574302i	$-0.805274\pi$
$617$	−30.8124	+	8.25615i	−1.24046	+	0.332380i	−0.421815	+	0.906682i	$0.638607\pi$
$618$	−4.37452	−	16.5158i	−0.175969	−	0.664362i
$619$	−22.3895	+	5.99924i	−0.899909	+	0.241130i	−0.678977	−	0.734160i	$-0.737576\pi$
$619$	−22.3895	+	5.99924i	−0.899909	+	0.241130i	−0.220932	+	0.975289i	$0.570910\pi$
$620$	10.6893	−	6.17149i	0.429294	−	0.247853i
$621$	3.01592	+	0.0260240i	0.121025	+	0.00104431i
$622$	27.1518	−	7.27531i	1.08869	−	0.291713i
$623$	1.53169	−	2.65297i	0.0613659	−	0.106289i
$624$	−5.59563	+	2.77290i	−0.224004	+	0.111005i
$625$	−0.250846	−	0.434477i	−0.0100338	−	0.0173791i
$626$	12.3959	+	12.3959i	0.495439	+	0.495439i
$627$	−63.7954	−	37.0773i	−2.54774	−	1.48073i
$628$		−	7.87815i		−	0.314372i
$629$	19.1661	+	19.1661i	0.764202	+	0.764202i
$630$	−1.07458	−	4.10470i	−0.0428123	−	0.163535i
$631$	6.12810	−	22.8704i	0.243956	−	0.910456i	−0.729949	−	0.683501i	$-0.760456\pi$
$631$	6.12810	−	22.8704i	0.243956	−	0.910456i	0.973905	−	0.226955i	$-0.0728770\pi$
$632$	0.428214	+	1.59811i	0.0170334	+	0.0635696i
$633$	−10.4423	−	0.0300344i	−0.415043	−	0.00119376i
$634$			22.1230i			0.878617i
$635$	−14.9671	+	14.9671i	−0.593951	+	0.593951i
$636$	−2.41154	+	4.14931i	−0.0956239	+	0.164531i
$637$	21.5098	+	1.30602i	0.852250	+	0.0517464i
$638$		−	5.99142i		−	0.237203i
$639$	−8.31957	+	30.3496i	−0.329117	+	1.20061i
$640$	0.699086	−	1.21085i	0.0276338	−	0.0478631i
$641$	−28.7047			−1.13377			−0.566884	−	0.823798i	$-0.691851\pi$
$641$	−28.7047			−1.13377			−0.566884	+	0.823798i	$0.691851\pi$
$642$	−12.1734	+	12.1036i	−0.480445	+	0.477690i
$643$	5.90865	+	22.0514i	0.233014	+	0.869621i	0.979034	+	0.203697i	$0.0652959\pi$
$643$	5.90865	+	22.0514i	0.233014	+	0.869621i	−0.746020	+	0.665924i	$0.768037\pi$
$644$	0.151965	+	0.567142i	0.00598827	+	0.0223485i
$645$	19.5885	+	5.30914i	0.771295	+	0.209047i
$646$	−24.5125			−0.964430
$647$	−18.5692	+	32.1627i	−0.730029	+	1.26445i	0.226841	+	0.973932i	$0.427160\pi$
$647$	−18.5692	+	32.1627i	−0.730029	+	1.26445i	−0.956870	+	0.290516i	$0.906173\pi$
$648$	6.43675	−	6.29032i	0.252860	−	0.247107i
$649$		−	69.6938i		−	2.73572i
$650$	−7.27876	−	8.21980i	−0.285497	−	0.322407i
$651$	7.69508	+	13.4172i	0.301594	+	0.525863i
$652$	4.89095	−	4.89095i	0.191544	−	0.191544i
$653$			44.4676i			1.74015i	0.492917	+	0.870076i	$0.335931\pi$
$653$			44.4676i			1.74015i	−0.492917	+	0.870076i	$0.664069\pi$
$654$	8.52570	+	14.8655i	0.333381	+	0.581288i
$655$	−1.37499	−	5.13153i	−0.0537253	−	0.200506i
$656$	−0.423606	+	1.58092i	−0.0165390	+	0.0617245i
$657$	2.35090	+	2.37810i	0.0917174	+	0.0927787i
$658$	−1.07434	−	1.07434i	−0.0418822	−	0.0418822i
$659$			0.414343i			0.0161405i	0.999967	+	0.00807026i	$0.00256887\pi$
$659$			0.414343i			0.0161405i	−0.999967	+	0.00807026i	$0.997431\pi$
$660$	−12.2164	+	7.00640i	−0.475525	+	0.272724i
$661$	−20.1566	−	20.1566i	−0.784000	−	0.784000i	0.196503	−	0.980503i	$-0.437042\pi$
$661$	−20.1566	−	20.1566i	−0.784000	−	0.784000i	−0.980503	+	0.196503i	$0.937042\pi$
$662$	11.3179	+	19.6031i	0.439881	+	0.761896i
$663$	18.7236	−	9.27842i	0.727163	−	0.360344i
$664$	−8.13850	+	14.0963i	−0.315835	+	0.547043i
$665$	10.0080	−	2.68162i	0.388092	−	0.103989i
$666$	0.139791	−	24.3009i	0.00541681	−	0.941642i
$667$	−0.517893	+	0.299006i	−0.0200529	+	0.0115776i
$668$	15.3104	−	4.10240i	0.592376	−	0.158727i
$669$	48.7399	+	13.2102i	1.88439	+	0.510735i
$670$	−1.53185	+	0.410458i	−0.0591806	+	0.0158574i
$671$	15.8863	+	4.25671i	0.613282	+	0.164328i
$672$	1.51482	+	0.880401i	0.0584355	+	0.0339622i
$673$	3.60027	−	2.07862i	0.138780	−	0.0801248i	−0.429002	−	0.903303i	$-0.641135\pi$
$673$	3.60027	−	2.07862i	0.138780	−	0.0801248i	0.567783	+	0.823179i	$0.307801\pi$
$674$	−8.06823	−	30.1111i	−0.310777	−	1.15983i
$675$	13.6342	+	8.02939i	0.524782	+	0.309051i
$676$	10.3892	+	7.81438i	0.399585	+	0.300553i
$677$	17.6062	+	10.1649i	0.676659	+	0.390669i	0.798595	−	0.601869i	$-0.205577\pi$
$677$	17.6062	+	10.1649i	0.676659	+	0.390669i	−0.121936	+	0.992538i	$0.538910\pi$
$678$	−12.4636	+	12.3921i	−0.478661	+	0.475915i
$679$	−12.4529			−0.477899
$680$	−2.33922	+	4.05164i	−0.0897048	+	0.155373i
$681$	17.7131	+	17.8153i	0.678769	+	0.682684i
$682$	36.3010	−	36.3010i	1.39004	−	1.39004i
$683$	−9.85750	−	2.64131i	−0.377187	−	0.101067i	0.0652445	−	0.997869i	$-0.479217\pi$
$683$	−9.85750	−	2.64131i	−0.377187	−	0.101067i	−0.442431	+	0.896802i	$0.645884\pi$
$684$	15.4504	+	15.6292i	0.590762	+	0.597598i
$685$	−4.06868	−	7.04716i	−0.155456	−	0.269258i
$686$	−6.56341	−	11.3682i	−0.250592	−	0.434038i
$687$	−4.47098	+	16.4960i	−0.170578	+	0.629361i
$688$	−7.25776	+	4.19027i	−0.276699	+	0.159753i
$689$	9.97196	+	0.605472i	0.379901	+	0.0230666i
$690$	1.21530	+	0.706320i	0.0462656	+	0.0268892i
$691$	40.8703	+	10.9512i	1.55478	+	0.416602i	0.931006	−	0.365004i	$-0.118932\pi$
$691$	40.8703	+	10.9512i	1.55478	+	0.416602i	0.623773	+	0.781606i	$0.285599\pi$
$692$	2.25559	+	1.30226i	0.0857445	+	0.0495046i
$693$	−8.73581	−	15.3339i	−0.331846	−	0.582487i
$694$	14.3954	−	14.3954i	0.546444	−	0.546444i
$695$	2.25093	+	2.25093i	0.0853826	+	0.0853826i
$696$	−0.466818	+	1.72236i	−0.0176947	+	0.0652858i
$697$	1.41743	−	5.28992i	0.0536890	−	0.200370i
$698$	−25.4656	−	14.7026i	−0.963888	−	0.556501i
$699$	−3.58200	−	0.0103027i	−0.135484	−	0.000389682i
$700$	−0.797249	+	2.97537i	−0.0301332	+	0.112458i
$701$	−16.7670			−0.633280			−0.316640	−	0.948546i	$-0.602555\pi$
$701$	−16.7670			−0.633280			−0.316640	+	0.948546i	$0.602555\pi$
$702$	−17.7176	−	6.08992i	−0.668707	−	0.229849i
$703$	59.3412			2.23810
$704$	1.50512	−	5.61718i	0.0567263	−	0.211705i
$705$	−3.63734	−	0.0104618i	−0.136990	−	0.000394015i
$706$	−9.93766	−	5.73751i	−0.374009	−	0.215934i
$707$	2.66825	−	9.95805i	0.100350	−	0.374511i
$708$	−5.43015	+	20.0349i	−0.204078	+	0.752959i
$709$	9.05848	+	9.05848i	0.340198	+	0.340198i	0.856442	−	0.516244i	$-0.172670\pi$
$709$	9.05848	+	9.05848i	0.340198	+	0.340198i	−0.516244	+	0.856442i	$0.672670\pi$
$710$	−10.3708	+	10.3708i	−0.389208	+	0.389208i
$711$	−2.50642	+	4.28414i	−0.0939981	+	0.160668i
$712$	2.62264	+	1.51418i	0.0982875	+	0.0567463i
$713$	−4.94946	−	1.32620i	−0.185359	−	0.0496667i
$714$	−5.06875	−	2.94592i	−0.189693	−	0.110248i
$715$	24.4535	+	16.1698i	0.914508	+	0.604717i
$716$	−3.11097	+	1.79612i	−0.116262	+	0.0671242i
$717$	8.94454	−	33.0015i	0.334040	−	1.23246i
$718$	18.3660	+	31.8108i	0.685413	+	1.18717i
$719$	−8.63433	−	14.9551i	−0.322006	−	0.557731i	0.658896	−	0.752234i	$-0.271024\pi$
$719$	−8.63433	−	14.9551i	−0.322006	−	0.557731i	−0.980902	+	0.194503i	$0.937690\pi$
$720$	4.05777	−	1.06230i	0.151224	−	0.0395894i
$721$	9.63828	+	2.58257i	0.358948	+	0.0961799i
$722$	−24.5122	+	24.5122i	−0.912248	+	0.912248i
$723$	−12.3849	−	12.4563i	−0.460599	−	0.463256i
$724$	−8.17213	+	14.1545i	−0.303715	+	0.526050i
$725$	−3.13732			−0.116517
$726$	−28.0266	+	27.8658i	−1.04016	+	1.03420i
$727$	12.1283	+	7.00226i	0.449813	+	0.259700i	0.707751	−	0.706462i	$-0.249710\pi$
$727$	12.1283	+	7.00226i	0.449813	+	0.259700i	−0.257938	+	0.966161i	$0.583043\pi$
$728$	0.221045	−	3.64054i	0.00819245	−	0.134928i
$729$	26.9960	+	0.465925i	0.999851	+	0.0172565i
$730$	0.403364	+	1.50538i	0.0149292	+	0.0557165i
$731$	24.2852	−	14.0211i	0.898222	−	0.518589i
$732$	−4.23517	−	2.46145i	−0.156536	−	0.0909777i
$733$	6.57489	+	1.76174i	0.242849	+	0.0650712i	0.378190	−	0.925728i	$-0.376546\pi$
$733$	6.57489	+	1.76174i	0.242849	+	0.0650712i	−0.135341	+	0.990799i	$0.543213\pi$
$734$	−5.38262	+	1.44227i	−0.198676	+	0.0532351i
$735$	−13.9699	−	3.78631i	−0.515286	−	0.139660i
$736$	−0.560658	+	0.150228i	−0.0206661	+	0.00553747i
$737$	−5.71238	+	3.29805i	−0.210418	+	0.121485i
$738$	−4.26629	+	2.43053i	−0.157044	+	0.0894690i
$739$	−17.1161	+	4.58625i	−0.629626	+	0.168708i	−0.559500	−	0.828830i	$-0.689007\pi$
$739$	−17.1161	+	4.58625i	−0.629626	+	0.168708i	−0.0701262	+	0.997538i	$0.522340\pi$
$740$	5.66291	−	9.80845i	0.208173	−	0.360566i
$741$	14.6218	−	43.3492i	0.537145	−	1.59247i
$742$	−1.40143	−	2.42735i	−0.0514481	−	0.0891108i
$743$	21.9872	+	21.9872i	0.806631	+	0.806631i	0.984122	−	0.177491i	$-0.0567982\pi$
$743$	21.9872	+	21.9872i	0.806631	+	0.806631i	−0.177491	+	0.984122i	$0.556798\pi$
$744$	−13.2639	+	7.60711i	−0.486276	+	0.278890i
$745$		−	20.0986i		−	0.736354i
$746$	−2.03537	−	2.03537i	−0.0745200	−	0.0745200i
$747$	−47.2391	+	12.3669i	−1.72839	+	0.452480i
$748$	−5.03629	+	18.7957i	−0.184145	+	0.687238i
$749$	−2.59484	−	9.68407i	−0.0948133	−	0.353848i
$750$	9.69288	+	16.9006i	0.353934	+	0.617124i
$751$		−	5.74389i		−	0.209598i	−0.994493	−	0.104799i	$-0.966580\pi$
$751$		−	5.74389i		−	0.209598i	0.994493	−	0.104799i	$-0.0334199\pi$
$752$	1.06206	−	1.06206i	0.0387294	−	0.0387294i
$753$	8.25378	+	14.3914i	0.300785	+	0.524452i
$754$	3.63983	−	0.742213i	0.132555	−	0.0270298i
$755$			3.93738i			0.143296i
$756$	1.31656	+	5.08869i	0.0478827	+	0.185074i
$757$	−13.1210	+	22.7262i	−0.476891	+	0.825999i	−0.999649	−	0.0264817i	$-0.991570\pi$
$757$	−13.1210	+	22.7262i	−0.476891	+	0.825999i	0.522759	+	0.852481i	$0.324903\pi$
$758$	−21.3259			−0.774591
$759$	5.64282	+	1.52940i	0.204821	+	0.0555136i
$760$	2.65097	+	9.89354i	0.0961606	+	0.358876i
$761$	−0.967626	−	3.61123i	−0.0350764	−	0.130907i	0.946167	−	0.323678i	$-0.104919\pi$
$761$	−0.967626	−	3.61123i	−0.0350764	−	0.130907i	−0.981244	+	0.192771i	$0.938253\pi$
$762$	18.5945	−	18.4878i	0.673606	−	0.669742i
$763$	−10.0084			−0.362328
$764$	−12.7189	+	22.0297i	−0.460152	+	0.797007i
$765$	−13.5777	+	3.55456i	−0.490904	+	0.128515i
$766$			12.9795i			0.468969i
$767$	42.3394	−	8.63362i	1.52879	−	0.311742i
$768$	−0.870336	+	1.49750i	−0.0314056	+	0.0540365i
$769$	34.6441	−	34.6441i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.73204 + 0.00498176i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.361873 - 1.35053i) q^{5} +(-0.453098 + 1.67174i) q^{6} +(-0.715284 - 0.715284i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99995 + 0.0172572i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.73204 + 0.00498176i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.361873 - 1.35053i) q^{5} +(-0.453098 + 1.67174i) q^{6} +(-0.715284 - 0.715284i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99995 + 0.0172572i) q^{9} +(1.21085 + 0.699086i) q^{10} +(5.61718 + 1.50512i) q^{11} +(-1.49750 - 0.870336i) q^{12} +(-0.218517 + 3.59892i) q^{13} +(0.876041 - 0.505782i) q^{14} +(0.633509 - 2.33737i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.67305 - 2.89781i) q^{17} +(-0.793114 + 2.89326i) q^{18} +(-7.07605 - 1.89602i) q^{19} +(-0.988657 + 0.988657i) q^{20} +(-1.23534 - 1.24247i) q^{21} +(-2.90767 + 5.03622i) q^{22} +0.580436 q^{23} +(1.22826 - 1.22122i) q^{24} +(2.63715 + 1.52256i) q^{25} +(-3.41974 - 1.14254i) q^{26} +(5.19596 + 0.0448353i) q^{27} +(0.261812 + 0.977097i) q^{28} +(-0.892249 + 0.515140i) q^{29} +(2.09377 + 1.21688i) q^{30} +(-8.52714 - 2.28484i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(9.72170 + 2.63491i) q^{33} +(3.23209 - 0.866036i) q^{34} +(-1.22486 + 0.707171i) q^{35} +(-2.58940 - 1.51492i) q^{36} +(-7.82443 + 2.09655i) q^{37} +(3.66283 - 6.34422i) q^{38} +(-0.396411 + 6.23240i) q^{39} +(-0.699086 - 1.21085i) q^{40} +(1.15731 + 1.15731i) q^{41} +(1.51986 - 0.871673i) q^{42} +8.38054i q^{43} +(-4.11206 - 4.11206i) q^{44} +(1.10891 - 4.04528i) q^{45} +(-0.150228 + 0.560658i) q^{46} +(-0.388741 - 1.45080i) q^{47} +(0.861707 + 1.50248i) q^{48} -5.97674i q^{49} +(-2.15322 + 2.15322i) q^{50} +(-2.88336 - 5.02747i) q^{51} +(1.98870 - 3.00750i) q^{52} -2.77082i q^{53} +(-1.38812 + 5.00731i) q^{54} +(4.06542 - 7.04151i) q^{55} -1.01156 q^{56} +(-12.2466 - 3.31924i) q^{57} +(-0.266656 - 0.995175i) q^{58} +(-3.10182 - 11.5761i) q^{59} +(-1.71732 + 1.70747i) q^{60} +2.82816 q^{61} +(4.41397 - 7.64523i) q^{62} +(-2.13347 - 2.15816i) q^{63} -1.00000i q^{64} +(4.78138 + 1.59747i) q^{65} +(-5.06129 + 8.70847i) q^{66} +(-0.802042 + 0.802042i) q^{67} +3.34611i q^{68} +(1.00534 + 0.00289159i) q^{69} +(-0.366058 - 1.36615i) q^{70} +(-2.71495 + 10.1323i) q^{71} +(2.13349 - 2.10908i) q^{72} +(0.788181 + 0.788181i) q^{73} -8.10045i q^{74} +(4.56007 + 2.65027i) q^{75} +(5.18003 + 5.18003i) q^{76} +(-2.94129 - 5.09447i) q^{77} +(-5.91744 - 1.99597i) q^{78} +(-0.827245 + 1.43283i) q^{79} +(1.35053 - 0.361873i) q^{80} +(8.99940 + 0.103542i) q^{81} +(-1.41741 + 0.818343i) q^{82} +(-15.7224 + 4.21280i) q^{83} +(0.448603 + 1.69368i) q^{84} +(-4.51902 + 1.21087i) q^{85} +(-8.09498 - 2.16904i) q^{86} +(-1.54798 + 0.887801i) q^{87} +(5.03622 - 2.90767i) q^{88} +(0.783797 + 2.92517i) q^{89} +(3.62043 + 2.11812i) q^{90} +(2.73056 - 2.41795i) q^{91} +(-0.502672 - 0.290218i) q^{92} +(-14.7580 - 3.99992i) q^{93} +1.50198 q^{94} +(-5.12127 + 8.87030i) q^{95} +(-1.67432 + 0.443474i) q^{96} +(8.70487 - 8.70487i) q^{97} +(5.77308 + 1.54689i) q^{98} +(16.8253 + 4.61222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more