LMFDB - Embedded newform 702.2.bc.a.305.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(305,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("702.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bc (of order $12$, degree $4$, not 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.10
Character	$\chi$	$=$	702.305
Dual form			702.2.bc.a.557.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.361873 + 1.35053i) q^{5} +(-0.715284 - 0.715284i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.21085 + 0.699086i) q^{10} +(-5.61718 - 1.50512i) q^{11} +(-0.218517 + 3.59892i) q^{13} +(-0.876041 + 0.505782i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.67305 + 2.89781i) q^{17} +(-7.07605 - 1.89602i) q^{19} +(0.988657 - 0.988657i) q^{20} +(-2.90767 + 5.03622i) q^{22} -0.580436 q^{23} +(2.63715 + 1.52256i) q^{25} +(3.41974 + 1.14254i) q^{26} +(0.261812 + 0.977097i) q^{28} +(0.892249 - 0.515140i) q^{29} +(-8.52714 - 2.28484i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.23209 - 0.866036i) q^{34} +(1.22486 - 0.707171i) q^{35} +(-7.82443 + 2.09655i) q^{37} +(-3.66283 + 6.34422i) q^{38} +(-0.699086 - 1.21085i) q^{40} +(-1.15731 - 1.15731i) q^{41} +8.38054i q^{43} +(4.11206 + 4.11206i) q^{44} +(-0.150228 + 0.560658i) q^{46} +(0.388741 + 1.45080i) q^{47} -5.97674i q^{49} +(2.15322 - 2.15322i) q^{50} +(1.98870 - 3.00750i) q^{52} +2.77082i q^{53} +(4.06542 - 7.04151i) q^{55} +1.01156 q^{56} +(-0.266656 - 0.995175i) q^{58} +(3.10182 + 11.5761i) q^{59} +2.82816 q^{61} +(-4.41397 + 7.64523i) q^{62} -1.00000i q^{64} +(-4.78138 - 1.59747i) q^{65} +(-0.802042 + 0.802042i) q^{67} -3.34611i q^{68} +(-0.366058 - 1.36615i) q^{70} +(2.71495 - 10.1323i) q^{71} +(0.788181 + 0.788181i) q^{73} +8.10045i q^{74} +(5.18003 + 5.18003i) q^{76} +(2.94129 + 5.09447i) q^{77} +(-0.827245 + 1.43283i) q^{79} +(-1.35053 + 0.361873i) q^{80} +(-1.41741 + 0.818343i) q^{82} +(15.7224 - 4.21280i) q^{83} +(-4.51902 + 1.21087i) q^{85} +(8.09498 + 2.16904i) q^{86} +(5.03622 - 2.90767i) q^{88} +(-0.783797 - 2.92517i) q^{89} +(2.73056 - 2.41795i) q^{91} +(0.502672 + 0.290218i) q^{92} +1.50198 q^{94} +(5.12127 - 8.87030i) q^{95} +(8.70487 - 8.70487i) q^{97} +(-5.77308 - 1.54689i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.361873	+	1.35053i	−0.161835	+	0.603975i	0.836588	+	0.547833i	$0.184547\pi$
$5$	−0.361873	+	1.35053i	−0.161835	+	0.603975i	−0.998423	+	0.0561429i	$0.982120\pi$
$6$		0			0
$7$	−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
$9$		0			0
$10$	1.21085	+	0.699086i	0.382905	+	0.221070i
$11$	−5.61718	−	1.50512i	−1.69364	−	0.453810i	−0.722317	−	0.691562i	$-0.756923\pi$
$11$	−5.61718	−	1.50512i	−1.69364	−	0.453810i	−0.971326	+	0.237752i	$0.923589\pi$
$12$		0			0
$13$	−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			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.67305	+	2.89781i	0.405775	+	0.702823i	0.994411	−	0.105575i	$-0.0336683\pi$
$17$	1.67305	+	2.89781i	0.405775	+	0.702823i	−0.588636	+	0.808398i	$0.700335\pi$
$18$		0			0
$19$	−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
$21$		0			0
$22$	−2.90767	+	5.03622i	−0.619916	+	1.07373i
$23$	−0.580436			−0.121029			−0.0605146	−	0.998167i	$-0.519274\pi$
$23$	−0.580436			−0.121029			−0.0605146	+	0.998167i	$0.519274\pi$
$24$		0			0
$25$	2.63715	+	1.52256i	0.527430	+	0.304512i
$26$	3.41974	+	1.14254i	0.670666	+	0.224071i
$27$		0			0
$28$	0.261812	+	0.977097i	0.0494779	+	0.184654i
$29$	0.892249	−	0.515140i	0.165687	−	0.0956592i	−0.414864	−	0.909884i	$-0.636171\pi$
$29$	0.892249	−	0.515140i	0.165687	−	0.0956592i	0.580550	+	0.814224i	$0.302837\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	3.23209	−	0.866036i	0.554299	−	0.148524i
$35$	1.22486	−	0.707171i	0.207038	−	0.119534i
$36$		0			0
$37$	−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			0
$40$	−0.699086	−	1.21085i	−0.110535	−	0.191453i
$41$	−1.15731	−	1.15731i	−0.180742	−	0.180742i	0.610937	−	0.791679i	$-0.290793\pi$
$41$	−1.15731	−	1.15731i	−0.180742	−	0.180742i	−0.791679	+	0.610937i	$0.790793\pi$
$42$		0			0
$43$			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
$45$		0			0
$46$	−0.150228	+	0.560658i	−0.0221499	+	0.0826645i
$47$	0.388741	+	1.45080i	0.0567037	+	0.211621i	0.988465	−	0.151451i	$-0.0483945\pi$
$47$	0.388741	+	1.45080i	0.0567037	+	0.211621i	−0.931761	+	0.363072i	$0.881728\pi$
$48$		0			0
$49$		−	5.97674i		−	0.853820i
$50$	2.15322	−	2.15322i	0.304512	−	0.304512i
$51$		0			0
$52$	1.98870	−	3.00750i	0.275784	−	0.417065i
$53$			2.77082i			0.380601i	0.981726	+	0.190300i	$0.0609462\pi$
$53$			2.77082i			0.380601i	−0.981726	+	0.190300i	$0.939054\pi$
$54$		0			0
$55$	4.06542	−	7.04151i	0.548180	−	0.949476i
$56$	1.01156			0.135176
$57$		0			0
$58$	−0.266656	−	0.995175i	−0.0350137	−	0.130673i
$59$	3.10182	+	11.5761i	0.403822	+	1.50708i	0.806218	+	0.591619i	$0.201511\pi$
$59$	3.10182	+	11.5761i	0.403822	+	1.50708i	−0.402395	+	0.915466i	$0.631822\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.78138	−	1.59747i	−0.593057	−	0.198142i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−0.366058	−	1.36615i	−0.0437524	−	0.163286i
$71$	2.71495	−	10.1323i	0.322205	−	1.20249i	−0.594886	−	0.803810i	$-0.702803\pi$
$71$	2.71495	−	10.1323i	0.322205	−	1.20249i	0.917091	−	0.398677i	$-0.130530\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	5.18003	+	5.18003i	0.594190	+	0.594190i
$77$	2.94129	+	5.09447i	0.335191	+	0.580568i
$78$		0			0
$79$	−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
$81$		0			0
$82$	−1.41741	+	0.818343i	−0.156527	+	0.0903709i
$83$	15.7224	−	4.21280i	1.72576	−	0.462415i	0.746557	−	0.665321i	$-0.231705\pi$
$83$	15.7224	−	4.21280i	1.72576	−	0.462415i	0.979198	+	0.202906i	$0.0650387\pi$
$84$		0			0
$85$	−4.51902	+	1.21087i	−0.490156	+	0.131337i
$86$	8.09498	+	2.16904i	0.872904	+	0.233894i
$87$		0			0
$88$	5.03622	−	2.90767i	0.536863	−	0.309958i
$89$	−0.783797	−	2.92517i	−0.0830824	−	0.310068i	0.911862	−	0.410497i	$-0.134645\pi$
$89$	−0.783797	−	2.92517i	−0.0830824	−	0.310068i	−0.994944	+	0.100430i	$0.967978\pi$
$90$		0			0
$91$	2.73056	−	2.41795i	0.286240	−	0.253470i
$92$	0.502672	+	0.290218i	0.0524072	+	0.0302573i
$93$		0			0
$94$	1.50198			0.154917
$95$	5.12127	−	8.87030i	0.525431	−	0.910074i
$96$		0			0
$97$	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
$99$		0			0
$100$	−1.52256	−	2.63715i	−0.152256	−	0.263715i
$101$	−5.09573	−	8.82607i	−0.507044	−	0.878227i	−0.999967	−	0.00815327i	$-0.997405\pi$
$101$	−5.09573	−	8.82607i	−0.507044	−	0.878227i	0.492922	−	0.870073i	$-0.335929\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	2.67640	+	0.717140i	0.259955	+	0.0696548i
$107$	−8.58323	−	4.95553i	−0.829773	−	0.479069i	0.0240022	−	0.999712i	$-0.492359\pi$
$107$	−8.58323	−	4.95553i	−0.829773	−	0.479069i	−0.853775	+	0.520642i	$0.825692\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	0.261812	−	0.977097i	0.0247389	−	0.0923269i
$113$	−8.78784	−	5.07366i	−0.826691	−	0.477290i	0.0260276	−	0.999661i	$-0.491714\pi$
$113$	−8.78784	−	5.07366i	−0.826691	−	0.477290i	−0.852718	+	0.522371i	$0.825048\pi$
$114$		0			0
$115$	0.210044	−	0.783896i	0.0195867	−	0.0730987i
$116$	−1.03028			−0.0956592
$117$		0			0
$118$	11.9845			1.10326
$119$	0.876052	−	3.26947i	0.0803075	−	0.299712i
$120$		0			0
$121$	19.7610	+	11.4090i	1.79646	+	1.03718i
$122$	0.731981	−	2.73179i	0.0662704	−	0.247325i
$123$		0			0
$124$	6.24230	+	6.24230i	0.560575	+	0.560575i
$125$	−7.95386	+	7.95386i	−0.711415	+	0.711415i
$126$		0			0
$127$	−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			0
$130$	−2.78055	+	4.20500i	−0.243870	+	0.368803i
$131$	−3.29059	+	1.89982i	−0.287500	+	0.165988i	−0.636814	−	0.771018i	$-0.719748\pi$
$131$	−3.29059	+	1.89982i	−0.287500	+	0.165988i	0.349314	+	0.937006i	$0.386415\pi$
$132$		0			0
$133$	3.70519	+	6.41758i	0.321281	+	0.556475i
$134$	0.567130	+	0.982297i	0.0489925	+	0.0848576i
$135$		0			0
$136$	−3.23209	−	0.866036i	−0.277149	−	0.0742620i
$137$	−4.11536	+	4.11536i	−0.351599	+	0.351599i	−0.860704	−	0.509105i	$-0.829976\pi$
$137$	−4.11536	+	4.11536i	−0.351599	+	0.351599i	0.509105	+	0.860704i	$0.329976\pi$
$138$		0			0
$139$	−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			0
$142$	−9.08440	−	5.24488i	−0.762346	−	0.440141i
$143$	6.64426	−	19.8869i	0.555621	−	1.66303i
$144$		0			0
$145$	0.372831	+	1.39143i	0.0309620	+	0.115552i
$146$	0.965320	−	0.557328i	0.0798905	−	0.0461248i
$147$		0			0
$148$	7.82443	+	2.09655i	0.643164	+	0.172335i
$149$	−13.8851	+	3.72050i	−1.13751	+	0.304795i	−0.777949	−	0.628327i	$-0.783740\pi$
$149$	−13.8851	+	3.72050i	−1.13751	+	0.304795i	−0.359561	+	0.933122i	$0.617073\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	5.68214	−	1.52252i	0.457880	−	0.122689i
$155$	6.17149	−	10.6893i	0.495706	−	0.858588i
$156$		0			0
$157$	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			0
$160$			1.39817i			0.110535i
$161$	0.415177	+	0.415177i	0.0327205	+	0.0327205i
$162$		0			0
$163$	−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
$165$		0			0
$166$		−	16.2770i		−	1.26334i
$167$	11.2080	−	11.2080i	0.867298	−	0.867298i	−0.124874	−	0.992173i	$-0.539853\pi$
$167$	11.2080	−	11.2080i	0.867298	−	0.867298i	0.992173	+	0.124874i	$0.0398528\pi$
$168$		0			0
$169$	−12.9045	−	1.57285i	−0.992654	−	0.120989i
$170$			4.67843i			0.358819i
$171$		0			0
$172$	4.19027	−	7.25776i	0.319505	−	0.553399i
$173$	2.60453			0.198018			0.0990092	−	0.995087i	$-0.468433\pi$
$173$	2.60453			0.198018			0.0990092	+	0.995087i	$0.468433\pi$
$174$		0			0
$175$	−0.797249	−	2.97537i	−0.0602663	−	0.224917i
$176$	−1.50512	−	5.61718i	−0.113453	−	0.423411i
$177$		0			0
$178$	−3.02836			−0.226985
$179$	−1.79612	+	3.11097i	−0.134248	+	0.232525i	−0.925310	−	0.379211i	$-0.876195\pi$
$179$	−1.79612	+	3.11097i	−0.134248	+	0.232525i	0.791062	+	0.611736i	$0.209529\pi$
$180$		0			0
$181$		−	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
$183$		0			0
$184$	0.410430	−	0.410430i	0.0302573	−	0.0302573i
$185$		−	11.3258i		−	0.832691i
$186$		0			0
$187$	−5.03629	−	18.7957i	−0.368290	−	1.37448i
$188$	0.388741	−	1.45080i	0.0283519	−	0.105811i
$189$		0			0
$190$	−7.24257	−	7.24257i	−0.525431	−	0.525431i
$191$			25.4377i			1.84061i	0.391202	+	0.920305i	$0.372059\pi$
$191$			25.4377i			1.84061i	−0.391202	+	0.920305i	$0.627941\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	−2.98837	+	5.17601i	−0.213455	+	0.369715i
$197$	−0.680083	+	0.182228i	−0.0484539	+	0.0129832i	−0.282965	−	0.959130i	$-0.591318\pi$
$197$	−0.680083	+	0.182228i	−0.0484539	+	0.0129832i	0.234511	+	0.972114i	$0.424651\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	−9.84420	+	2.63775i	−0.692635	+	0.185591i
$203$	−1.00668	−	0.269740i	−0.0706553	−	0.0189320i
$204$		0			0
$205$	1.98179	−	1.14418i	0.138414	−	0.0799133i
$206$	2.55304	+	9.52809i	0.177879	+	0.663853i
$207$		0			0
$208$	−3.22602	+	1.61022i	−0.223684	+	0.111649i
$209$	36.8937	+	21.3006i	2.55199	+	1.47339i
$210$		0			0
$211$	−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
$213$		0			0
$214$	−7.00818	+	7.00818i	−0.479069	+	0.479069i
$215$	−11.3182	−	3.03269i	−0.771893	−	0.206828i
$216$		0			0
$217$	4.46502	+	7.73364i	0.303105	+	0.524994i
$218$	−4.94698	−	8.56842i	−0.335052	−	0.580327i
$219$		0			0
$220$	−7.04151	+	4.06542i	−0.474738	+	0.274090i
$221$	−10.7946	+	5.38797i	−0.726123	+	0.362434i
$222$		0			0
$223$	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
$225$		0			0
$226$	−7.17524	+	7.17524i	−0.477290	+	0.477290i
$227$	−10.2562	−	10.2562i	−0.680729	−	0.680729i	0.279435	−	0.960165i	$-0.409853\pi$
$227$	−10.2562	−	10.2562i	−0.680729	−	0.680729i	−0.960165	+	0.279435i	$0.909853\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	−0.266656	+	0.995175i	−0.0175068	+	0.0653364i
$233$	2.06808			0.135484			0.0677421	−	0.997703i	$-0.478420\pi$
$233$	2.06808			0.135484			0.0677421	+	0.997703i	$0.478420\pi$
$234$		0			0
$235$	−2.10003			−0.136991
$236$	3.10182	−	11.5761i	0.201911	−	0.753542i
$237$		0			0
$238$	−2.93133	−	1.69240i	−0.190010	−	0.109702i
$239$	−5.10931	+	19.0682i	−0.330494	+	1.23342i	0.578179	+	0.815910i	$0.303764\pi$
$239$	−5.10931	+	19.0682i	−0.330494	+	1.23342i	−0.908672	+	0.417510i	$0.862903\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−2.44926	−	1.41408i	−0.156797	−	0.0905271i
$245$	8.07176	+	2.16282i	0.515686	+	0.138178i
$246$		0			0
$247$	8.36988	−	25.0519i	0.532563	−	1.59401i
$248$	7.64523	−	4.41397i	0.485472	−	0.280288i
$249$		0			0
$250$	5.62423	+	9.74145i	0.355707	+	0.616103i
$251$	−4.78920	−	8.29514i	−0.302292	−	0.523585i	0.674363	−	0.738400i	$-0.264418\pi$
$251$	−4.78920	−	8.29514i	−0.302292	−	0.523585i	−0.976655	+	0.214815i	$0.931085\pi$
$252$		0			0
$253$	3.26041	+	0.873624i	0.204980	+	0.0549243i
$254$	−10.7048	+	10.7048i	−0.671677	+	0.671677i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.77509			0.360240			0.180120	−	0.983645i	$-0.442351\pi$
$257$	5.77509			0.360240			0.180120	+	0.983645i	$0.442351\pi$
$258$		0			0
$259$	7.09632	+	4.09706i	0.440944	+	0.254579i
$260$	3.34206	+	3.77414i	0.207266	+	0.234062i
$261$		0			0
$262$	0.983420	+	3.67017i	0.0607559	+	0.226744i
$263$	3.86009	−	2.22862i	0.238023	−	0.137423i	−0.376245	−	0.926520i	$-0.622785\pi$
$263$	3.86009	−	2.22862i	0.238023	−	0.137423i	0.614268	+	0.789098i	$0.289451\pi$
$264$		0			0
$265$	−3.74207	−	1.00269i	−0.229874	−	0.0615945i
$266$	7.15789	−	1.91795i	0.438878	−	0.117597i
$267$		0			0
$268$	1.09561	−	0.293568i	0.0669250	−	0.0179325i
$269$	−11.4786	+	6.62715i	−0.699860	+	0.404064i	−0.807295	−	0.590148i	$-0.799069\pi$
$269$	−11.4786	+	6.62715i	−0.699860	+	0.404064i	0.107435	+	0.994212i	$0.465736\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	2.91000	+	5.04027i	0.175799	+	0.304494i
$275$	−12.5217	−	12.5217i	−0.755087	−	0.755087i
$276$		0			0
$277$			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
$279$		0			0
$280$	−0.366058	+	1.36615i	−0.0218762	+	0.0816430i
$281$	0.376063	+	1.40349i	0.0224340	+	0.0837250i	0.976235	−	0.216713i	$-0.0695337\pi$
$281$	0.376063	+	1.40349i	0.0224340	+	0.0837250i	−0.953801	+	0.300438i	$0.902867\pi$
$282$		0			0
$283$		−	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
$285$		0			0
$286$	−17.4896	−	11.5650i	−1.03418	−	0.683851i
$287$			1.65561i			0.0977278i
$288$		0			0
$289$	2.90179	−	5.02604i	0.170693	−	0.295649i
$290$	1.44051			0.0845896
$291$		0			0
$292$	−0.288494	−	1.07667i	−0.0168828	−	0.0630076i
$293$	6.14475	+	22.9325i	0.358980	+	1.33973i	0.875401	+	0.483398i	$0.160598\pi$
$293$	6.14475	+	22.9325i	0.358980	+	1.33973i	−0.516420	+	0.856335i	$0.672736\pi$
$294$		0			0
$295$	−16.7564			−0.975595
$296$	4.05022	−	7.01519i	0.235414	−	0.407750i
$297$		0			0
$298$			14.3749i			0.832715i
$299$	0.126835	−	2.08894i	0.00733508	−	0.120807i
$300$		0			0
$301$	5.99447	−	5.99447i	0.345515	−	0.345515i
$302$			2.81609i			0.162048i
$303$		0			0
$304$	−1.89602	−	7.07605i	−0.108744	−	0.405839i
$305$	−1.02343	+	3.81951i	−0.0586017	+	0.218705i
$306$		0			0
$307$	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
$309$		0			0
$310$	−8.72781	−	8.72781i	−0.495706	−	0.495706i
$311$	14.0548	+	24.3437i	0.796976	+	1.38040i	0.921577	+	0.388195i	$0.126901\pi$
$311$	14.0548	+	24.3437i	0.796976	+	1.38040i	−0.124602	+	0.992207i	$0.539765\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	1.43283	−	0.827245i	0.0806030	−	0.0465362i
$317$	−21.3692	+	5.72585i	−1.20021	+	0.321596i	−0.802915	−	0.596094i	$-0.796719\pi$
$317$	−21.3692	+	5.72585i	−1.20021	+	0.321596i	−0.397298	+	0.917690i	$0.630052\pi$
$318$		0			0
$319$	−5.78727	+	1.55069i	−0.324025	+	0.0868222i
$320$	1.35053	+	0.361873i	0.0754969	+	0.0202293i
$321$		0			0
$322$	0.508485	−	0.293574i	0.0283368	−	0.0163603i
$323$	−6.34429	−	23.6772i	−0.353006	−	1.31744i
$324$		0			0
$325$	−6.05583	+	9.15819i	−0.335917	+	0.508005i
$326$	5.99017	+	3.45843i	0.331765	+	0.191544i
$327$		0			0
$328$	1.63669			0.0903709
$329$	0.759675	−	1.31580i	0.0418822	−	0.0725422i
$330$		0			0
$331$	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
$333$		0			0
$334$	−7.92523	−	13.7269i	−0.433649	−	0.751102i
$335$	−0.792945	−	1.37342i	−0.0433232	−	0.0750380i
$336$		0			0
$337$	−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
$339$		0			0
$340$	4.51902	+	1.21087i	0.245078	+	0.0656685i
$341$	44.4595	+	25.6687i	2.40762	+	1.39004i
$342$		0			0
$343$	−9.28206	+	9.28206i	−0.501184	+	0.501184i
$344$	−5.92594	−	5.92594i	−0.319505	−	0.319505i
$345$		0			0
$346$	0.674101	−	2.51578i	0.0362399	−	0.135249i
$347$	17.6308	+	10.1791i	0.946468	+	0.546444i	0.891982	−	0.452071i	$-0.149315\pi$
$347$	17.6308	+	10.1791i	0.946468	+	0.546444i	0.0544863	+	0.998515i	$0.482648\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	−5.81533			−0.309958
$353$	2.96995	−	11.0840i	0.158075	−	0.589943i	−0.840748	−	0.541427i	$-0.817884\pi$
$353$	2.96995	−	11.0840i	0.158075	−	0.589943i	0.998822	−	0.0485157i	$-0.0154491\pi$
$354$		0			0
$355$	12.7016	+	7.33325i	0.674129	+	0.389208i
$356$	−0.783797	+	2.92517i	−0.0415412	+	0.155034i
$357$		0			0
$358$	2.54010	+	2.54010i	0.134248	+	0.134248i
$359$	−25.9734	+	25.9734i	−1.37083	+	1.37083i	−0.511605	+	0.859221i	$0.670949\pi$
$359$	−25.9734	+	25.9734i	−1.37083	+	1.37083i	−0.859221	+	0.511605i	$0.829051\pi$
$360$		0			0
$361$	30.0211	+	17.3327i	1.58006	+	0.912248i
$362$	−15.7873	−	4.23021i	−0.829765	−	0.222335i
$363$		0			0
$364$	−3.57371	+	0.728730i	−0.187313	+	0.0381958i
$365$	−1.34968	+	0.779240i	−0.0706457	+	0.0407873i
$366$		0			0
$367$	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
$369$		0			0
$370$	−10.9399	−	2.93134i	−0.568738	−	0.152393i
$371$	1.98192	−	1.98192i	0.102896	−	0.102896i
$372$		0			0
$373$	−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
$375$		0			0
$376$	−1.30075	−	0.750990i	−0.0670812	−	0.0387294i
$377$	1.65898	+	3.32370i	0.0854418	+	0.171179i
$378$		0			0
$379$	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
$381$		0			0
$382$	24.5710	+	6.58377i	1.25716	+	0.336855i
$383$	−12.5372	+	3.35934i	−0.640623	+	0.171654i	−0.564486	−	0.825443i	$-0.690925\pi$
$383$	−12.5372	+	3.35934i	−0.640623	+	0.171654i	−0.0761376	+	0.997097i	$0.524259\pi$
$384$		0			0
$385$	−7.94461	+	2.12875i	−0.404895	+	0.108491i
$386$	10.9257	−	6.30797i	0.556105	−	0.321067i
$387$		0			0
$388$	−11.8911	+	3.18620i	−0.603678	+	0.161755i
$389$	−15.6511	+	27.1085i	−0.793543	+	1.37446i	0.130216	+	0.991486i	$0.458433\pi$
$389$	−15.6511	+	27.1085i	−0.793543	+	1.37446i	−0.923760	+	0.382972i	$0.874901\pi$
$390$		0			0
$391$	−0.971100	−	1.68199i	−0.0491106	−	0.0850621i
$392$	4.22619	+	4.22619i	0.213455	+	0.213455i
$393$		0			0
$394$			0.704074i			0.0354707i
$395$	−1.63572	−	1.63572i	−0.0823021	−	0.0823021i
$396$		0			0
$397$	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
$399$		0			0
$400$			3.04512i			0.152256i
$401$	−14.5050	+	14.5050i	−0.724345	+	0.724345i	−0.969487	−	0.245142i	$-0.921165\pi$
$401$	−14.5050	+	14.5050i	−0.724345	+	0.724345i	0.245142	+	0.969487i	$0.421165\pi$
$402$		0			0
$403$	10.0863	−	30.1893i	0.502434	−	1.50383i
$404$			10.1915i			0.507044i
$405$		0			0
$406$	−0.521098	+	0.902568i	−0.0258617	+	0.0447937i
$407$	47.1068			2.33500
$408$		0			0
$409$	−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
$411$		0			0
$412$	9.86420			0.485974
$413$	6.06155	−	10.4989i	0.298269	−	0.516618i
$414$		0			0
$415$			22.7581i			1.11715i
$416$	0.720398	+	3.53285i	0.0353204	+	0.173212i
$417$		0			0
$418$	30.1236	−	30.1236i	1.47339	−	1.47339i
$419$			1.73191i			0.0846094i	0.999105	+	0.0423047i	$0.0134700\pi$
$419$			1.73191i			0.0846094i	−0.999105	+	0.0423047i	$0.986530\pi$
$420$		0			0
$421$	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
$423$		0			0
$424$	−1.95926	−	1.95926i	−0.0951502	−	0.0951502i
$425$			10.1893i			0.494253i
$426$		0			0
$427$	−2.02294	−	2.02294i	−0.0978967	−	0.0978967i
$428$	4.95553	+	8.58323i	0.239535	+	0.414886i
$429$		0			0
$430$	−5.85872	+	10.1476i	−0.282532	+	0.489360i
$431$	14.3219	−	3.83753i	0.689860	−	0.184847i	0.103176	−	0.994663i	$-0.467100\pi$
$431$	14.3219	−	3.83753i	0.689860	−	0.184847i	0.586684	+	0.809816i	$0.300433\pi$
$432$		0			0
$433$	−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			0
$436$	−9.55683	+	2.56075i	−0.457689	+	0.122637i
$437$	4.10719	+	1.10052i	0.196474	+	0.0526450i
$438$		0			0
$439$	−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			0
$442$	2.41053	+	11.8213i	0.114657	+	0.562281i
$443$	−10.6734	−	6.16232i	−0.507111	−	0.292780i	0.224535	−	0.974466i	$-0.427914\pi$
$443$	−10.6734	−	6.16232i	−0.507111	−	0.292780i	−0.731645	+	0.681686i	$0.761247\pi$
$444$		0			0
$445$	4.23417			0.200719
$446$	14.5776	−	25.2492i	0.690271	−	1.19558i
$447$		0			0
$448$	−0.715284	+	0.715284i	−0.0337940	+	0.0337940i
$449$	27.3580	+	7.33055i	1.29110	+	0.345950i	0.838080	−	0.545548i	$-0.183678\pi$
$449$	27.3580	+	7.33055i	1.29110	+	0.345950i	0.453024	+	0.891498i	$0.350345\pi$
$450$		0			0
$451$	4.75894	+	8.24272i	0.224090	+	0.388134i
$452$	5.07366	+	8.78784i	0.238645	+	0.413345i
$453$		0			0
$454$	−12.5613	+	7.25224i	−0.589529	+	0.340365i
$455$	2.27740	+	4.56269i	0.106766	+	0.213902i
$456$		0			0
$457$	−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
$459$		0			0
$460$	−0.573852	+	0.573852i	−0.0267560	+	0.0267560i
$461$	−20.1337	−	20.1337i	−0.937718	−	0.937718i	0.0604534	−	0.998171i	$-0.480745\pi$
$461$	−20.1337	−	20.1337i	−0.937718	−	0.937718i	−0.998171	+	0.0604534i	$0.980745\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	0.535258	−	1.99761i	0.0247953	−	0.0925375i
$467$	−36.6235			−1.69473			−0.847366	−	0.531010i	$-0.821813\pi$
$467$	−36.6235			−1.69473			−0.847366	+	0.531010i	$0.821813\pi$
$468$		0			0
$469$	1.14738			0.0529809
$470$	−0.543527	+	2.02847i	−0.0250710	+	0.0935663i
$471$		0			0
$472$	−10.3789	−	5.99225i	−0.477727	−	0.275816i
$473$	12.6137	−	47.0750i	0.579979	−	2.16451i
$474$		0			0
$475$	−15.7738	−	15.7738i	−0.723751	−	0.723751i
$476$	−2.39342	+	2.39342i	−0.109702	+	0.109702i
$477$		0			0
$478$	17.0961	+	9.87043i	0.781957	+	0.451463i
$479$	4.87703	+	1.30680i	0.222837	+	0.0597091i	0.368510	−	0.929624i	$-0.379868\pi$
$479$	4.87703	+	1.30680i	0.222837	+	0.0597091i	−0.145673	+	0.989333i	$0.546535\pi$
$480$		0			0
$481$	−5.83555	−	28.6177i	−0.266078	−	1.30485i
$482$	−8.78273	+	5.07071i	−0.400043	+	0.230965i
$483$		0			0
$484$	−11.4090	−	19.7610i	−0.518592	−	0.898228i
$485$	8.60613	+	14.9063i	0.390784	+	0.676858i
$486$		0			0
$487$	−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
$489$		0			0
$490$	4.17825	−	7.23695i	0.188754	−	0.326932i
$491$	1.97522			0.0891403			0.0445701	−	0.999006i	$-0.485808\pi$
$491$	1.97522			0.0891403			0.0445701	+	0.999006i	$0.485808\pi$
$492$		0			0
$493$	2.98556	+	1.72371i	0.134463	+	0.0776322i
$494$	−22.0320	−	14.5686i	−0.991264	−	0.655471i
$495$		0			0
$496$	−2.28484	−	8.52714i	−0.102592	−	0.382880i
$497$	−9.18946	+	5.30554i	−0.412204	+	0.237986i
$498$		0			0
$499$	−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
$501$		0			0
$502$	−9.25203	+	2.47907i	−0.412938	+	0.110646i
$503$	6.37037	−	3.67794i	0.284041	−	0.163991i	−0.351211	−	0.936297i	$-0.614230\pi$
$503$	6.37037	−	3.67794i	0.284041	−	0.163991i	0.635251	+	0.772305i	$0.280897\pi$
$504$		0			0
$505$	13.7639	−	3.68802i	0.612485	−	0.164115i
$506$	1.68771	−	2.92320i	0.0750280	−	0.129952i
$507$		0			0
$508$	7.56941	+	13.1106i	0.335838	+	0.581689i
$509$	−10.0747	−	10.0747i	−0.446552	−	0.446552i	0.447654	−	0.894207i	$-0.352260\pi$
$509$	−10.0747	−	10.0747i	−0.446552	−	0.446552i	−0.894207	+	0.447654i	$0.852260\pi$
$510$		0			0
$511$		−	1.12755i		−	0.0498797i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	1.49470	−	5.57831i	0.0659286	−	0.246049i
$515$	−3.56959	−	13.3219i	−0.157295	−	0.587033i
$516$		0			0
$517$		−	8.73451i		−	0.384143i
$518$	5.79412	−	5.79412i	0.254579	−	0.254579i
$519$		0			0
$520$	4.51053	−	2.25136i	0.197800	−	0.0987289i
$521$		−	28.5428i		−	1.25048i	−0.780431	−	0.625242i	$-0.785000\pi$
$521$		−	28.5428i		−	1.25048i	0.780431	−	0.625242i	$-0.215000\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	−1.15362	−	4.30537i	−0.0503002	−	0.187723i
$527$	−7.64532	−	28.5327i	−0.333035	−	1.24290i
$528$		0			0
$529$	−22.6631			−0.985352
$530$	−1.93704	+	3.35505i	−0.0841396	+	0.145734i
$531$		0			0
$532$		−	7.41039i		−	0.321281i
$533$	4.41797	−	3.91218i	0.191364	−	0.169456i
$534$		0			0
$535$	9.79864	−	9.79864i	0.423632	−	0.423632i
$536$		−	1.13426i		−	0.0489925i
$537$		0			0
$538$	3.43046	+	12.8027i	0.147898	+	0.551962i
$539$	−8.99570	+	33.5724i	−0.387472	+	1.44607i
$540$		0			0
$541$	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			0
$544$	2.36605	+	2.36605i	0.101444	+	0.101444i
$545$	6.91673	+	11.9801i	0.296280	+	0.513172i
$546$		0			0
$547$	−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
$549$		0			0
$550$	−15.3359	+	8.85418i	−0.653924	+	0.377543i
$551$	−7.29032	+	1.95344i	−0.310578	+	0.0832191i
$552$		0			0
$553$	1.61660	−	0.433166i	0.0687447	−	0.0184201i
$554$	18.7771	+	5.03130i	0.797762	+	0.213760i
$555$		0			0
$556$	1.97173	−	1.13838i	0.0836199	−	0.0482779i
$557$	1.55296	+	5.79572i	0.0658010	+	0.245573i	0.990990	−	0.133933i	$-0.0427607\pi$
$557$	1.55296	+	5.79572i	0.0658010	+	0.245573i	−0.925189	+	0.379506i	$0.876094\pi$
$558$		0			0
$559$	−30.1609	−	1.83129i	−1.27567	−	0.0774555i
$560$	1.22486	+	0.707171i	0.0517596	+	0.0298834i
$561$		0			0
$562$	1.45300			0.0612909
$563$	−17.1469	+	29.6993i	−0.722656	+	1.25168i	0.237275	+	0.971442i	$0.423746\pi$
$563$	−17.1469	+	29.6993i	−0.722656	+	1.25168i	−0.959932	+	0.280235i	$0.909588\pi$
$564$		0			0
$565$	10.0322	−	10.0322i	0.422059	−	0.422059i
$566$	−20.0268	−	5.36617i	−0.841790	−	0.225557i
$567$		0			0
$568$	5.24488	+	9.08440i	0.220070	+	0.381173i
$569$	−17.8407	−	30.9009i	−0.747919	−	1.29543i	−0.948818	−	0.315822i	$-0.897720\pi$
$569$	−17.8407	−	30.9009i	−0.747919	−	1.29543i	0.200899	−	0.979612i	$-0.435614\pi$
$570$		0			0
$571$	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			0
$574$	1.59920	+	0.428504i	0.0667493	+	0.0178854i
$575$	−1.53069	−	0.883747i	−0.0638344	−	0.0368548i
$576$		0			0
$577$	−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
$579$		0			0
$580$	0.372831	−	1.39143i	0.0154810	−	0.0577758i
$581$	−14.2593	−	8.23262i	−0.591576	−	0.341547i
$582$		0			0
$583$	4.17041	−	15.5642i	0.172721	−	0.644602i
$584$	−1.11466			−0.0461248
$585$		0			0
$586$	23.7415			0.980753
$587$	5.15867	−	19.2524i	0.212921	−	0.794633i	−0.773967	−	0.633226i	$-0.781730\pi$
$587$	5.15867	−	19.2524i	0.212921	−	0.794633i	0.986888	−	0.161407i	$-0.0516030\pi$
$588$		0			0
$589$	56.0064	+	32.3353i	2.30770	+	1.33235i
$590$	−4.33687	+	16.1854i	−0.178546	+	0.666344i
$591$		0			0
$592$	−5.72788	−	5.72788i	−0.235414	−	0.235414i
$593$	−3.24522	+	3.24522i	−0.133265	+	0.133265i	−0.770593	−	0.637328i	$-0.780040\pi$
$593$	−3.24522	+	3.24522i	−0.133265	+	0.133265i	0.637328	+	0.770593i	$0.280040\pi$
$594$		0			0
$595$	4.09850	+	2.36627i	0.168022	+	0.0970075i
$596$	13.8851	+	3.72050i	0.568755	+	0.152397i
$597$		0			0
$598$	−1.98494	−	0.663172i	−0.0811701	−	0.0271191i
$599$	36.4947	−	21.0702i	1.49113	−	0.860906i	0.491185	−	0.871055i	$-0.336564\pi$
$599$	36.4947	−	21.0702i	1.49113	−	0.860906i	0.999949	+	0.0101486i	$0.00323046\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	2.72013	+	0.728858i	0.110681	+	0.0296568i
$605$	−22.5592	+	22.5592i	−0.917163	+	0.917163i
$606$		0			0
$607$	−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
$609$		0			0
$610$	3.42448	+	1.97712i	0.138653	+	0.0800514i
$611$	−5.30627	+	1.08202i	−0.214669	+	0.0437740i
$612$		0			0
$613$	−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
$615$		0			0
$616$	−5.68214	−	1.52252i	−0.228940	−	0.0613443i
$617$	30.8124	−	8.25615i	1.24046	−	0.332380i	0.421815	−	0.906682i	$-0.361393\pi$
$617$	30.8124	−	8.25615i	1.24046	−	0.332380i	0.818644	+	0.574302i	$0.194726\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	27.1518	−	7.27531i	1.08869	−	0.291713i
$623$	−1.53169	+	2.65297i	−0.0613659	+	0.106289i
$624$		0			0
$625$	−0.250846	−	0.434477i	−0.0100338	−	0.0173791i
$626$	−12.3959	−	12.3959i	−0.495439	−	0.495439i
$627$		0			0
$628$		−	7.87815i		−	0.314372i
$629$	−19.1661	−	19.1661i	−0.764202	−	0.764202i
$630$		0			0
$631$	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
$633$		0			0
$634$			22.1230i			0.878617i
$635$	14.9671	−	14.9671i	0.593951	−	0.593951i
$636$		0			0
$637$	21.5098	+	1.30602i	0.852250	+	0.0517464i
$638$			5.99142i			0.237203i
$639$		0			0
$640$	0.699086	−	1.21085i	0.0276338	−	0.0478631i
$641$	28.7047			1.13377			0.566884	−	0.823798i	$-0.308149\pi$
$641$	28.7047			1.13377			0.566884	+	0.823798i	$0.308149\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	−24.5125			−0.964430
$647$	18.5692	−	32.1627i	0.730029	−	1.26445i	−0.226841	−	0.973932i	$-0.572840\pi$
$647$	18.5692	−	32.1627i	0.730029	−	1.26445i	0.956870	−	0.290516i	$-0.0938270\pi$
$648$		0			0
$649$		−	69.6938i		−	2.73572i
$650$	7.27876	+	8.21980i	0.285497	+	0.322407i
$651$		0			0
$652$	4.89095	−	4.89095i	0.191544	−	0.191544i
$653$		−	44.4676i		−	1.74015i	−0.492917	−	0.870076i	$-0.664069\pi$
$653$		−	44.4676i		−	1.74015i	0.492917	−	0.870076i	$-0.335931\pi$
$654$		0			0
$655$	−1.37499	−	5.13153i	−0.0537253	−	0.200506i
$656$	0.423606	−	1.58092i	0.0165390	−	0.0617245i
$657$		0			0
$658$	−1.07434	−	1.07434i	−0.0418822	−	0.0418822i
$659$		−	0.414343i		−	0.0161405i	−0.999967	−	0.00807026i	$-0.997431\pi$
$659$		−	0.414343i		−	0.0161405i	0.999967	−	0.00807026i	$-0.00256887\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	−8.13850	+	14.0963i	−0.315835	+	0.547043i
$665$	−10.0080	+	2.68162i	−0.388092	+	0.103989i
$666$		0			0
$667$	−0.517893	+	0.299006i	−0.0200529	+	0.0115776i
$668$	−15.3104	+	4.10240i	−0.592376	+	0.158727i
$669$		0			0
$670$	−1.53185	+	0.410458i	−0.0591806	+	0.0158574i
$671$	−15.8863	−	4.25671i	−0.613282	−	0.164328i
$672$		0			0
$673$	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
$675$		0			0
$676$	10.3892	+	7.81438i	0.399585	+	0.300553i
$677$	−17.6062	−	10.1649i	−0.676659	−	0.390669i	0.121936	−	0.992538i	$-0.461090\pi$
$677$	−17.6062	−	10.1649i	−0.676659	−	0.390669i	−0.798595	+	0.601869i	$0.794423\pi$
$678$		0			0
$679$	−12.4529			−0.477899
$680$	2.33922	−	4.05164i	0.0897048	−	0.155373i
$681$		0			0
$682$	36.3010	−	36.3010i	1.39004	−	1.39004i
$683$	9.85750	+	2.64131i	0.377187	+	0.101067i	0.442431	−	0.896802i	$-0.354116\pi$
$683$	9.85750	+	2.64131i	0.377187	+	0.101067i	−0.0652445	+	0.997869i	$0.520783\pi$
$684$		0			0
$685$	−4.06868	−	7.04716i	−0.155456	−	0.269258i
$686$	6.56341	+	11.3682i	0.250592	+	0.434038i
$687$		0			0
$688$	−7.25776	+	4.19027i	−0.276699	+	0.159753i
$689$	−9.97196	−	0.605472i	−0.379901	−	0.0230666i
$690$		0			0
$691$	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
$693$		0			0
$694$	14.3954	−	14.3954i	0.546444	−	0.546444i
$695$	−2.25093	−	2.25093i	−0.0853826	−	0.0853826i
$696$		0			0
$697$	1.41743	−	5.28992i	0.0536890	−	0.200370i
$698$	25.4656	+	14.7026i	0.963888	+	0.556501i
$699$		0			0
$700$	−0.797249	+	2.97537i	−0.0301332	+	0.112458i
$701$	16.7670			0.633280			0.316640	−	0.948546i	$-0.397445\pi$
$701$	16.7670			0.633280			0.316640	+	0.948546i	$0.397445\pi$
$702$		0			0
$703$	59.3412			2.23810
$704$	−1.50512	+	5.61718i	−0.0567263	+	0.211705i
$705$		0			0
$706$	−9.93766	−	5.73751i	−0.374009	−	0.215934i
$707$	−2.66825	+	9.95805i	−0.100350	+	0.374511i
$708$		0			0
$709$	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
$711$		0			0
$712$	2.62264	+	1.51418i	0.0982875	+	0.0567463i
$713$	4.94946	+	1.32620i	0.185359	+	0.0496667i
$714$		0			0
$715$	24.4535	+	16.1698i	0.914508	+	0.604717i
$716$	3.11097	−	1.79612i	0.116262	−	0.0671242i
$717$		0			0
$718$	18.3660	+	31.8108i	0.685413	+	1.18717i
$719$	8.63433	+	14.9551i	0.322006	+	0.557731i	0.980902	−	0.194503i	$-0.0623095\pi$
$719$	8.63433	+	14.9551i	0.322006	+	0.557731i	−0.658896	+	0.752234i	$0.728976\pi$
$720$		0			0
$721$	9.63828	+	2.58257i	0.358948	+	0.0961799i
$722$	24.5122	−	24.5122i	0.912248	−	0.912248i
$723$		0			0
$724$	−8.17213	+	14.1545i	−0.303715	+	0.526050i
$725$	3.13732			0.116517
$726$		0			0
$727$	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
$729$		0			0
$730$	0.403364	+	1.50538i	0.0149292	+	0.0557165i
$731$	−24.2852	+	14.0211i	−0.898222	+	0.518589i
$732$		0			0
$733$	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
$735$		0			0
$736$	−0.560658	+	0.150228i	−0.0206661	+	0.00553747i
$737$	5.71238	−	3.29805i	0.210418	−	0.121485i
$738$		0			0
$739$	−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
$741$		0			0
$742$	−1.40143	−	2.42735i	−0.0514481	−	0.0891108i
$743$	−21.9872	−	21.9872i	−0.806631	−	0.806631i	0.177491	−	0.984122i	$-0.443202\pi$
$743$	−21.9872	−	21.9872i	−0.806631	−	0.806631i	−0.984122	+	0.177491i	$0.943202\pi$
$744$		0			0
$745$		−	20.0986i		−	0.736354i
$746$	2.03537	+	2.03537i	0.0745200	+	0.0745200i
$747$		0			0
$748$	−5.03629	+	18.7957i	−0.184145	+	0.687238i
$749$	2.59484	+	9.68407i	0.0948133	+	0.353848i
$750$		0			0
$751$		−	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
$753$		0			0
$754$	3.63983	−	0.742213i	0.132555	−	0.0270298i
$755$		−	3.93738i		−	0.143296i
$756$		0			0
$757$	−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
$759$		0			0
$760$	2.65097	+	9.89354i	0.0961606	+	0.358876i
$761$	0.967626	+	3.61123i	0.0350764	+	0.130907i	0.981244	−	0.192771i	$-0.0617473\pi$
$761$	0.967626	+	3.61123i	0.0350764	+	0.130907i	−0.946167	+	0.323678i	$0.895081\pi$
$762$		0			0
$763$	−10.0084			−0.362328
$764$	12.7189	−	22.0297i	0.460152	−	0.797007i
$765$		0			0
$766$			12.9795i			0.468969i
$767$	−42.3394	+	8.63362i	−1.52879	+	0.311742i
$768$		0			0
$769$	34.6441	−	34.6441i	1.24930	−	1.24930i	0.293266	−	0.956031i	$-0.405258\pi$
$769$	34.6441	−	34.6441i	1.24930	−	1.24930i	0.956031	−	0.293266i	$-0.0947421\pi$
$770$			8.22486i			0.296403i
$771$		0			0
$772$	−3.26525	−	12.1861i	−0.117519	−	0.438586i
$773$	−1.60335	+	5.98377i	−0.0576683	+	0.215221i	−0.988747	−	0.149597i	$-0.952202\pi$
$773$	−1.60335	+	5.98377i	−0.0576683	+	0.215221i	0.931079	+	0.364818i	$0.118869\pi$
$774$		0			0
$775$	−19.0085	−	19.0085i	−0.682806	−	0.682806i
$776$			12.3105i			0.441923i
$777$		0			0
$778$	22.1340	+	22.1340i	0.793543	+	0.793543i
$779$	5.99491	+	10.3835i	0.214790	+	0.372027i
$780$		0			0
$781$	−30.5007	+	52.8288i	−1.09140	+	1.89036i
$782$	−1.87602	+	0.502678i	−0.0670864	+	0.0179757i
$783$		0			0
$784$	5.17601	−	2.98837i	0.184857	−	0.106727i
$785$	−10.6397	+	2.85089i	−0.379746	+	0.101753i
$786$		0			0
$787$	−19.0056	+	5.09254i	−0.677477	+	0.181529i	−0.581121	−	0.813817i	$-0.697386\pi$
$787$	−19.0056	+	5.09254i	−0.677477	+	0.181529i	−0.0963566	+	0.995347i	$0.530719\pi$
$788$	0.680083	+	0.182228i	0.0242270	+	0.00649159i
$789$		0			0
$790$	−2.00334	+	1.15663i	−0.0712757	+	0.0411511i
$791$	2.65669	+	9.91492i	0.0944612	+	0.352534i
$792$		0			0
$793$	−0.618001	+	10.1783i	−0.0219459	+	0.361443i
$794$	−2.15790	−	1.24586i	−0.0765809	−	0.0442140i
$795$		0			0
$796$	−9.91471			−0.351418
$797$	−2.20478	+	3.81880i	−0.0780974	+	0.135269i	−0.902429	−	0.430839i	$-0.858218\pi$
$797$	−2.20478	+	3.81880i	−0.0780974	+	0.135269i	0.824332	+	0.566107i	$0.191551\pi$
$798$		0			0
$799$	−3.55377	+	3.55377i	−0.125723	+	0.125723i
$800$	2.94136	+	0.788134i	0.103993	+	0.0278647i
$801$		0			0
$802$	10.2566	+	17.7649i	0.362172	+	0.627301i
$803$	−3.24105	−	5.61366i	−0.114374	−	0.198102i
$804$		0			0
$805$	−0.710950	+	0.410467i	−0.0250577	+	0.0144671i
$806$	−26.5501	−	17.5562i	−0.935186	−	0.618390i
$807$		0			0
$808$	9.84420	+	2.63775i	0.346318	+	0.0927956i
$809$	−17.1929	−	9.92632i	−0.604470	−	0.348991i	0.166328	−	0.986070i	$-0.446809\pi$
$809$	−17.1929	−	9.92632i	−0.604470	−	0.348991i	−0.770798	+	0.637080i	$0.780142\pi$
$810$		0			0
$811$	6.11440	−	6.11440i	0.214706	−	0.214706i	−0.591557	−	0.806263i	$-0.701487\pi$
$811$	6.11440	−	6.11440i	0.214706	−	0.214706i	0.806263	+	0.591557i	$0.201487\pi$
$812$	0.736944	+	0.736944i	0.0258617	+	0.0258617i
$813$		0			0
$814$	12.1921	−	45.5017i	0.427334	−	1.59483i
$815$	−8.37528	−	4.83547i	−0.293373	−	0.169379i
$816$		0			0
$817$	15.8897	−	59.3011i	0.555910	−	2.07468i
$818$	−9.79619			−0.342516
$819$		0			0
$820$	−2.28837			−0.0799133
$821$	−8.40409	+	31.3645i	−0.293305	+	1.09463i	0.649250	+	0.760575i	$0.275083\pi$
$821$	−8.40409	+	31.3645i	−0.293305	+	1.09463i	−0.942554	+	0.334053i	$0.891584\pi$
$822$		0			0
$823$	2.45985	+	1.42019i	0.0857448	+	0.0495048i	0.542259	−	0.840211i	$-0.317569\pi$
$823$	2.45985	+	1.42019i	0.0857448	+	0.0495048i	−0.456515	+	0.889716i	$0.650902\pi$
$824$	2.55304	−	9.52809i	0.0889395	−	0.331927i
$825$		0			0
$826$	−8.57233	−	8.57233i	−0.298269	−	0.298269i
$827$	0.354454	−	0.354454i	0.0123256	−	0.0123256i	−0.700917	−	0.713243i	$-0.747226\pi$
$827$	0.354454	−	0.354454i	0.0123256	−	0.0123256i	0.713243	+	0.700917i	$0.247226\pi$
$828$		0			0
$829$	−12.9034	−	7.44977i	−0.448153	−	0.258741i	0.258897	−	0.965905i	$-0.416641\pi$
$829$	−12.9034	−	7.44977i	−0.448153	−	0.258741i	−0.707050	+	0.707164i	$0.749974\pi$
$830$	21.9826	+	5.89022i	0.763027	+	0.204452i
$831$		0			0
$832$	3.59892	+	0.218517i	0.124770	+	0.00757573i
$833$	17.3195	−	9.99940i	0.600084	−	0.346459i
$834$		0			0
$835$	11.0808	+	19.1926i	0.383468	+	0.664186i
$836$	−21.3006	−	36.8937i	−0.736696	−	1.27600i
$837$		0			0
$838$	1.67290	+	0.448252i	0.0577893	+	0.0154846i
$839$	8.50311	−	8.50311i	0.293560	−	0.293560i	−0.544925	−	0.838485i	$-0.683442\pi$
$839$	8.50311	−	8.50311i	0.293560	−	0.293560i	0.838485	+	0.544925i	$0.183442\pi$
$840$		0			0
$841$	−13.9693	+	24.1955i	−0.481699	+	0.834327i
$842$	3.55532			0.122524
$843$		0			0
$844$	5.22116	+	3.01444i	0.179720	+	0.103761i
$845$	6.79398	−	16.8587i	0.233720	−	0.579958i
$846$		0			0
$847$	−5.97405	−	22.2955i	−0.205271	−	0.766081i
$848$	−2.39960	+	1.38541i	−0.0824025	+	0.0475751i
$849$		0			0
$850$	9.84209	+	2.63718i	0.337581	+	0.0904545i
$851$	4.54158	−	1.21691i	0.155683	−	0.0417152i
$852$		0			0
$853$	−11.7087	+	3.13735i	−0.400900	+	0.107421i	−0.453635	−	0.891188i	$-0.649873\pi$
$853$	−11.7087	+	3.13735i	−0.400900	+	0.107421i	0.0527349	+	0.998609i	$0.483206\pi$
$854$	−2.47758	+	1.43043i	−0.0847811	+	0.0489484i
$855$		0			0
$856$	9.57335	−	2.56517i	0.327211	−	0.0876758i
$857$	23.9473	−	41.4780i	0.818025	−	1.41686i	−0.0891105	−	0.996022i	$-0.528402\pi$
$857$	23.9473	−	41.4780i	0.818025	−	1.41686i	0.907135	−	0.420839i	$-0.138264\pi$
$858$		0			0
$859$	−26.9704	−	46.7142i	−0.920220	−	1.59387i	−0.799074	−	0.601232i	$-0.794677\pi$
$859$	−26.9704	−	46.7142i	−0.920220	−	1.59387i	−0.121145	−	0.992635i	$-0.538657\pi$
$860$	8.28548	+	8.28548i	0.282532	+	0.282532i
$861$		0			0
$862$		−	14.8271i		−	0.505012i
$863$	−23.3989	−	23.3989i	−0.796508	−	0.796508i	0.186035	−	0.982543i	$-0.440436\pi$
$863$	−23.3989	−	23.3989i	−0.796508	−	0.796508i	−0.982543	+	0.186035i	$0.940436\pi$
$864$		0			0
$865$	−0.942509	+	3.51749i	−0.0320463	+	0.119598i
$866$	2.97320	+	11.0962i	0.101034	+	0.377063i
$867$		0			0
$868$		−	8.93004i		−	0.303105i
$869$	6.80336	−	6.80336i	0.230788	−	0.230788i
$870$		0			0
$871$	−2.71123	−	3.06175i	−0.0918665	−	0.103743i
$872$			9.89396i			0.335052i
$873$		0			0
$874$	2.12604	−	3.68241i	0.0719144	−	0.124559i
$875$	11.3785			0.384665
$876$		0			0
$877$	2.46001	+	9.18088i	0.0830686	+	0.310016i	0.994941	−	0.100456i	$-0.0320303\pi$
$877$	2.46001	+	9.18088i	0.0830686	+	0.310016i	−0.911873	+	0.410473i	$0.865364\pi$
$878$	10.5345	+	39.3153i	0.355523	+	1.32683i
$879$		0			0
$880$	8.13083			0.274090
$881$	−12.5122	+	21.6718i	−0.421548	+	0.730143i	−0.996091	−	0.0883317i	$-0.971846\pi$
$881$	−12.5122	+	21.6718i	−0.421548	+	0.730143i	0.574543	+	0.818474i	$0.305180\pi$
$882$		0			0
$883$		−	36.5915i		−	1.23140i	−0.787980	−	0.615701i	$-0.788873\pi$
$883$		−	36.5915i		−	1.23140i	0.787980	−	0.615701i	$-0.211127\pi$
$884$	12.0424	+	0.731182i	0.405029	+	0.0245923i
$885$		0			0
$886$	−8.71483	+	8.71483i	−0.292780	+	0.292780i
$887$			48.8136i			1.63900i	0.573079	+	0.819500i	$0.305749\pi$
$887$			48.8136i			1.63900i	−0.573079	+	0.819500i	$0.694251\pi$
$888$		0			0
$889$	3.96353	+	14.7921i	0.132933	+	0.496111i
$890$	1.09588	−	4.08989i	0.0367341	−	0.137094i
$891$		0			0
$892$	−20.6159	−	20.6159i	−0.690271	−	0.690271i
$893$		−	11.0030i		−	0.368202i
$894$		0			0
$895$	−3.55149	−	3.55149i	−0.118713	−	0.118713i
$896$	0.505782	+	0.876041i	0.0168970	+	0.0292665i
$897$		0			0
$898$	14.1615	−	24.5285i	0.472577	−	0.818527i
$899$	−8.78535	+	2.35403i	−0.293008	+	0.0785112i
$900$		0			0
$901$	−8.02931	+	4.63572i	−0.267495	+	0.154438i
$902$	9.19356	−	2.46341i	0.306112	−	0.0820225i
$903$		0			0
$904$	9.80156	−	2.62632i	0.325995	−	0.0873501i
$905$	22.0734	+	5.91456i	0.733745	+	0.196606i
$906$		0			0
$907$	7.29873	−	4.21392i	0.242350	−	0.139921i	−0.373906	−	0.927467i	$-0.621982\pi$
$907$	7.29873	−	4.21392i	0.242350	−	0.139921i	0.616256	+	0.787546i	$0.288648\pi$
$908$	3.75404	+	14.0103i	0.124582	+	0.464947i
$909$		0			0
$910$	4.99666	−	1.01889i	0.165638	−	0.0337758i
$911$	−7.11409	−	4.10732i	−0.235700	−	0.136082i	0.377499	−	0.926010i	$-0.376784\pi$
$911$	−7.11409	−	4.10732i	−0.235700	−	0.136082i	−0.613199	+	0.789929i	$0.710118\pi$
$912$		0			0
$913$	−94.6562			−3.13266
$914$	−15.0632	+	26.0902i	−0.498245	+	0.862986i
$915$		0			0
$916$	6.97743	−	6.97743i	0.230541	−	0.230541i
$917$	3.71262	+	0.994793i	0.122601	+	0.0328510i
$918$		0			0
$919$	11.5951	+	20.0833i	0.382488	+	0.662488i	0.991417	−	0.130736i	$-0.0417341\pi$
$919$	11.5951	+	20.0833i	0.382488	+	0.662488i	−0.608929	+	0.793224i	$0.708401\pi$
$920$	0.405774	+	0.702822i	0.0133780	+	0.0231714i
$921$		0			0
$922$	−24.6586	+	14.2366i	−0.812087	+	0.468859i
$923$	35.8722	+	11.9850i	1.18075	+	0.394491i
$924$		0			0
$925$	−23.8263	−	6.38424i	−0.783404	−	0.209912i
$926$	−3.13507	−	1.81003i	−0.103025	−	0.0594814i
$927$		0			0
$928$	0.728518	−	0.728518i	0.0239148	−	0.0239148i
$929$	4.98880	+	4.98880i	0.163677	+	0.163677i	0.784194	−	0.620516i	$-0.213077\pi$
$929$	4.98880	+	4.98880i	0.163677	+	0.163677i	−0.620516	+	0.784194i	$0.713077\pi$
$930$		0			0
$931$	−11.3320	+	42.2917i	−0.371392	+	1.38605i
$932$	−1.79101	−	1.03404i	−0.0586664	−	0.0338711i
$933$		0			0
$934$	−9.47885	+	35.3755i	−0.310157	+	1.15752i
$935$	27.2066			0.889752
$936$		0			0
$937$	−46.7071			−1.52585			−0.762927	−	0.646484i	$-0.776239\pi$
$937$	−46.7071			−1.52585			−0.762927	+	0.646484i	$0.776239\pi$
$938$	0.296963	−	1.10828i	0.00969618	−	0.0361867i
$939$		0			0
$940$	1.81868	+	1.05001i	0.0593187	+	0.0342476i
$941$	−10.1255	+	37.7889i	−0.330082	+	1.23188i	0.579022	+	0.815312i	$0.303435\pi$
$941$	−10.1255	+	37.7889i	−0.330082	+	1.23188i	−0.909104	+	0.416570i	$0.863232\pi$
$942$		0			0
$943$	0.671745	+	0.671745i	0.0218750	+	0.0218750i
$944$	−8.47432	+	8.47432i	−0.275816	+	0.275816i
$945$		0			0
$946$	−42.2063	−	24.3678i	−1.37224	−	0.792266i
$947$	49.7829	+	13.3393i	1.61773	+	0.433469i	0.950333	−	0.311236i	$-0.100743\pi$
$947$	49.7829	+	13.3393i	1.61773	+	0.433469i	0.667394	+	0.744705i	$0.267410\pi$
$948$		0			0
$949$	−3.00883	+	2.66437i	−0.0976708	+	0.0864891i
$950$	−19.3189	+	11.1538i	−0.626787	+	0.361876i
$951$		0			0
$952$	1.69240	+	2.93133i	0.0548511	+	0.0950048i
$953$	16.8331	+	29.1557i	0.545276	+	0.944446i	0.998589	+	0.0530947i	$0.0169085\pi$
$953$	16.8331	+	29.1557i	0.545276	+	0.944446i	−0.453313	+	0.891351i	$0.649758\pi$
$954$		0			0
$955$	−34.3544	−	9.20524i	−1.11168	−	0.297875i
$956$	13.9589	−	13.9589i	0.451463	−	0.451463i
$957$		0			0
$958$	2.52454	−	4.37263i	0.0815641	−	0.141273i
$959$	5.88730			0.190111
$960$		0			0
$961$	40.6449	+	23.4663i	1.31112	+	0.756978i
$962$	−29.1529	−	1.77009i	−0.939927	−	0.0570699i
$963$		0			0
$964$	2.62479	+	9.79587i	0.0845389	+	0.315504i
$965$	−15.2760	+	8.81963i	−0.491753	+	0.283914i
$966$		0			0
$967$	41.2138	+	11.0432i	1.32535	+	0.355126i	0.850979	−	0.525200i	$-0.176010\pi$
$967$	41.2138	+	11.0432i	1.32535	+	0.355126i	0.474369	+	0.880326i	$0.342676\pi$
$968$	−22.0406	+	5.90575i	−0.708410	+	0.189818i
$969$		0			0
$970$	16.6258	−	4.45486i	0.533821	−	0.143037i
$971$	19.5275	−	11.2742i	0.626666	−	0.361806i	−0.152794	−	0.988258i	$-0.548827\pi$
$971$	19.5275	−	11.2742i	0.626666	−	0.361806i	0.779460	+	0.626452i	$0.215494\pi$
$972$		0			0
$973$	2.22461	−	0.596082i	0.0713177	−	0.0191095i
$974$	−14.8115	+	25.6543i	−0.474592	+	0.822018i
$975$		0			0
$976$	1.41408	+	2.44926i	0.0452635	+	0.0783987i
$977$	−16.8832	−	16.8832i	−0.540141	−	0.540141i	0.383429	−	0.923570i	$-0.374743\pi$
$977$	−16.8832	−	16.8832i	−0.540141	−	0.540141i	−0.923570	+	0.383429i	$0.874743\pi$
$978$		0			0
$979$			17.6109i			0.562847i
$980$	−5.90894	−	5.90894i	−0.188754	−	0.188754i
$981$		0			0
$982$	0.511224	−	1.90791i	0.0163138	−	0.0608839i
$983$	−6.76555	−	25.2494i	−0.215788	−	0.805330i	−0.985888	−	0.167407i	$-0.946461\pi$
$983$	−6.76555	−	25.2494i	−0.215788	−	0.805330i	0.770100	−	0.637923i	$-0.220206\pi$
$984$		0			0
$985$		−	0.984416i		−	0.0313661i
$986$	2.43770	−	2.43770i	0.0776322	−	0.0776322i
$987$		0			0
$988$	−19.7745	+	17.5106i	−0.629109	+	0.557087i
$989$		−	4.86436i		−	0.154678i
$990$		0			0
$991$	−5.16138	+	8.93977i	−0.163957	+	0.283981i	−0.936284	−	0.351243i	$-0.885759\pi$
$991$	−5.16138	+	8.93977i	−0.163957	+	0.283981i	0.772328	+	0.635224i	$0.219092\pi$
$992$	−8.82795			−0.280288
$993$		0			0
$994$	2.74635	+	10.2495i	0.0871089	+	0.325095i
$995$	3.58787	+	13.3901i	0.113743	+	0.424495i
$996$		0			0
$997$	34.0368			1.07796			0.538978	−	0.842320i	$-0.318811\pi$
$997$	34.0368			1.07796			0.538978	+	0.842320i	$0.318811\pi$
$998$	−2.00437	+	3.47166i	−0.0634471	+	0.109894i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.305.10		56
3.2	odd	2		234.2.z.a.227.7	yes	56
9.4	even	3		234.2.y.a.149.10	yes	56
9.5	odd	6		702.2.bb.a.71.3		56
13.11	odd	12		702.2.bb.a.89.3		56
39.11	even	12		234.2.y.a.11.10	✓	56
117.50	even	12	inner	702.2.bc.a.557.10		56
117.76	odd	12		234.2.z.a.167.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.10	✓	56	39.11	even	12
234.2.y.a.149.10	yes	56	9.4	even	3
234.2.z.a.167.7	yes	56	117.76	odd	12
234.2.z.a.227.7	yes	56	3.2	odd	2
702.2.bb.a.71.3		56	9.5	odd	6
702.2.bb.a.89.3		56	13.11	odd	12
702.2.bc.a.305.10		56	1.1	even	1	trivial
702.2.bc.a.557.10		56	117.50	even	12	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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.361873 + 1.35053i) q^{5} +(-0.715284 - 0.715284i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.21085 + 0.699086i) q^{10} +(-5.61718 - 1.50512i) q^{11} +(-0.218517 + 3.59892i) q^{13} +(-0.876041 + 0.505782i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.67305 + 2.89781i) q^{17} +(-7.07605 - 1.89602i) q^{19} +(0.988657 - 0.988657i) q^{20} +(-2.90767 + 5.03622i) q^{22} -0.580436 q^{23} +(2.63715 + 1.52256i) q^{25} +(3.41974 + 1.14254i) q^{26} +(0.261812 + 0.977097i) q^{28} +(0.892249 - 0.515140i) q^{29} +(-8.52714 - 2.28484i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.23209 - 0.866036i) q^{34} +(1.22486 - 0.707171i) q^{35} +(-7.82443 + 2.09655i) q^{37} +(-3.66283 + 6.34422i) q^{38} +(-0.699086 - 1.21085i) q^{40} +(-1.15731 - 1.15731i) q^{41} +8.38054i q^{43} +(4.11206 + 4.11206i) q^{44} +(-0.150228 + 0.560658i) q^{46} +(0.388741 + 1.45080i) q^{47} -5.97674i q^{49} +(2.15322 - 2.15322i) q^{50} +(1.98870 - 3.00750i) q^{52} +2.77082i q^{53} +(4.06542 - 7.04151i) q^{55} +1.01156 q^{56} +(-0.266656 - 0.995175i) q^{58} +(3.10182 + 11.5761i) q^{59} +2.82816 q^{61} +(-4.41397 + 7.64523i) q^{62} -1.00000i q^{64} +(-4.78138 - 1.59747i) q^{65} +(-0.802042 + 0.802042i) q^{67} -3.34611i q^{68} +(-0.366058 - 1.36615i) q^{70} +(2.71495 - 10.1323i) q^{71} +(0.788181 + 0.788181i) q^{73} +8.10045i q^{74} +(5.18003 + 5.18003i) q^{76} +(2.94129 + 5.09447i) q^{77} +(-0.827245 + 1.43283i) q^{79} +(-1.35053 + 0.361873i) q^{80} +(-1.41741 + 0.818343i) q^{82} +(15.7224 - 4.21280i) q^{83} +(-4.51902 + 1.21087i) q^{85} +(8.09498 + 2.16904i) q^{86} +(5.03622 - 2.90767i) q^{88} +(-0.783797 - 2.92517i) q^{89} +(2.73056 - 2.41795i) q^{91} +(0.502672 + 0.290218i) q^{92} +1.50198 q^{94} +(5.12127 - 8.87030i) q^{95} +(8.70487 - 8.70487i) q^{97} +(-5.77308 - 1.54689i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

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