LMFDB - Embedded newform 702.2.bb.a.89.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			89.3
Character	$\chi$	$=$	702.89
Dual form			702.2.bb.a.71.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.35053 - 0.361873i) q^{5} +(0.977097 + 0.261812i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.21085 - 0.699086i) q^{10} +(-4.11206 - 4.11206i) q^{11} +(3.22602 + 1.61022i) q^{13} +(-0.876041 + 0.505782i) q^{14} -1.00000 q^{16} +(-1.67305 + 2.89781i) q^{17} +(-7.07605 + 1.89602i) q^{19} +(-0.361873 + 1.35053i) q^{20} +5.81533 q^{22} +(-0.290218 + 0.502672i) q^{23} +(-2.63715 - 1.52256i) q^{25} +(-3.41974 + 1.14254i) q^{26} +(0.261812 - 0.977097i) q^{28} +1.03028i q^{29} +(2.28484 - 8.52714i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.866036 - 3.23209i) q^{34} +(-1.22486 - 0.707171i) q^{35} +(-7.82443 - 2.09655i) q^{37} +(3.66283 - 6.34422i) q^{38} +(-0.699086 - 1.21085i) q^{40} +(0.423606 + 1.58092i) q^{41} +(-7.25776 + 4.19027i) q^{43} +(-4.11206 + 4.11206i) q^{44} +(-0.150228 - 0.560658i) q^{46} +(1.45080 - 0.388741i) q^{47} +(-5.17601 - 2.98837i) q^{49} +(2.94136 - 0.788134i) q^{50} +(1.61022 - 3.22602i) q^{52} +2.77082i q^{53} +(4.06542 + 7.04151i) q^{55} +(0.505782 + 0.876041i) q^{56} +(-0.728518 - 0.728518i) q^{58} +(-8.47432 - 8.47432i) q^{59} +(-1.41408 - 2.44926i) q^{61} +(4.41397 + 7.64523i) q^{62} +1.00000i q^{64} +(-3.77414 - 3.34206i) q^{65} +(1.09561 - 0.293568i) q^{67} +(2.89781 + 1.67305i) q^{68} +(1.36615 - 0.366058i) q^{70} +(-2.71495 - 10.1323i) q^{71} +(0.788181 - 0.788181i) q^{73} +(7.01519 - 4.05022i) q^{74} +(1.89602 + 7.07605i) q^{76} +(-2.94129 - 5.09447i) q^{77} +(-0.827245 + 1.43283i) q^{79} +(1.35053 + 0.361873i) q^{80} +(-1.41741 - 0.818343i) q^{82} +(4.21280 + 15.7224i) q^{83} +(3.30815 - 3.30815i) q^{85} +(2.16904 - 8.09498i) q^{86} -5.81533i q^{88} +(0.783797 - 2.92517i) q^{89} +(2.73056 + 2.41795i) q^{91} +(0.502672 + 0.290218i) q^{92} +(-0.750990 + 1.30075i) q^{94} +10.2425 q^{95} +(3.18620 - 11.8911i) q^{97} +(5.77308 - 1.54689i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

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

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.35053	−	0.361873i	−0.603975	−	0.161835i	−0.0561429	−	0.998423i	$-0.517880\pi$
$5$	−1.35053	−	0.361873i	−0.603975	−	0.161835i	−0.547833	+	0.836588i	$0.684547\pi$
$6$		0			0
$7$	0.977097	+	0.261812i	0.369308	+	0.0989557i	0.438700	−	0.898634i	$-0.355439\pi$
$7$	0.977097	+	0.261812i	0.369308	+	0.0989557i	−0.0693918	+	0.997589i	$0.522106\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.21085	−	0.699086i	0.382905	−	0.221070i
$11$	−4.11206	−	4.11206i	−1.23983	−	1.23983i	−0.960069	−	0.279764i	$-0.909744\pi$
$11$	−4.11206	−	4.11206i	−1.23983	−	1.23983i	−0.279764	−	0.960069i	$-0.590256\pi$
$12$		0			0
$13$	3.22602	+	1.61022i	0.894736	+	0.446595i
$13$	3.22602	+	1.61022i	0.894736	+	0.446595i
$14$	−0.876041	+	0.505782i	−0.234132	+	0.135176i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.67305	+	2.89781i	−0.405775	+	0.702823i	−0.994411	−	0.105575i	$-0.966332\pi$
$17$	−1.67305	+	2.89781i	−0.405775	+	0.702823i	0.588636	+	0.808398i	$0.299665\pi$
$18$		0			0
$19$	−7.07605	+	1.89602i	−1.62336	+	0.434977i	−0.951986	−	0.306143i	$-0.900961\pi$
$19$	−7.07605	+	1.89602i	−1.62336	+	0.434977i	−0.671372	+	0.741120i	$0.734295\pi$
$20$	−0.361873	+	1.35053i	−0.0809174	+	0.301988i
$21$		0			0
$22$	5.81533			1.23983
$23$	−0.290218	+	0.502672i	−0.0605146	+	0.104814i	−0.894696	−	0.446676i	$-0.852608\pi$
$23$	−0.290218	+	0.502672i	−0.0605146	+	0.104814i	0.834181	+	0.551491i	$0.185941\pi$
$24$		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
$29$			1.03028i			0.191318i	0.995414	+	0.0956592i	$0.0304959\pi$
$29$			1.03028i			0.191318i	−0.995414	+	0.0956592i	$0.969504\pi$
$30$		0			0
$31$	2.28484	−	8.52714i	0.410369	−	1.53152i	−0.383564	−	0.923514i	$-0.625303\pi$
$31$	2.28484	−	8.52714i	0.410369	−	1.53152i	0.793933	−	0.608005i	$-0.208030\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−0.866036	−	3.23209i	−0.148524	−	0.554299i
$35$	−1.22486	−	0.707171i	−0.207038	−	0.119534i
$36$		0			0
$37$	−7.82443	−	2.09655i	−1.28633	−	0.344671i	−0.450064	−	0.892996i	$-0.648599\pi$
$37$	−7.82443	−	2.09655i	−1.28633	−	0.344671i	−0.836265	+	0.548326i	$0.815265\pi$
$38$	3.66283	−	6.34422i	0.594190	−	1.02917i
$39$		0			0
$40$	−0.699086	−	1.21085i	−0.110535	−	0.191453i
$41$	0.423606	+	1.58092i	0.0661561	+	0.246898i	0.991083	−	0.133248i	$-0.0425406\pi$
$41$	0.423606	+	1.58092i	0.0661561	+	0.246898i	−0.924927	+	0.380146i	$0.875874\pi$
$42$		0			0
$43$	−7.25776	+	4.19027i	−1.10680	+	0.639010i	−0.937998	−	0.346640i	$-0.887322\pi$
$43$	−7.25776	+	4.19027i	−1.10680	+	0.639010i	−0.168800	+	0.985650i	$0.553989\pi$
$44$	−4.11206	+	4.11206i	−0.619916	+	0.619916i
$45$		0			0
$46$	−0.150228	−	0.560658i	−0.0221499	−	0.0826645i
$47$	1.45080	−	0.388741i	0.211621	−	0.0567037i	−0.151451	−	0.988465i	$-0.548395\pi$
$47$	1.45080	−	0.388741i	0.211621	−	0.0567037i	0.363072	+	0.931761i	$0.381728\pi$
$48$		0			0
$49$	−5.17601	−	2.98837i	−0.739429	−	0.426910i
$50$	2.94136	−	0.788134i	0.415971	−	0.111459i
$51$		0			0
$52$	1.61022	−	3.22602i	0.223297	−	0.447368i
$53$			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
$56$	0.505782	+	0.876041i	0.0675880	+	0.117066i
$57$		0			0
$58$	−0.728518	−	0.728518i	−0.0956592	−	0.0956592i
$59$	−8.47432	−	8.47432i	−1.10326	−	1.10326i	−0.994014	−	0.109248i	$-0.965156\pi$
$59$	−8.47432	−	8.47432i	−1.10326	−	1.10326i	−0.109248	−	0.994014i	$-0.534844\pi$
$60$		0			0
$61$	−1.41408	−	2.44926i	−0.181054	−	0.313595i	0.761186	−	0.648534i	$-0.224618\pi$
$61$	−1.41408	−	2.44926i	−0.181054	−	0.313595i	−0.942240	+	0.334939i	$0.891284\pi$
$62$	4.41397	+	7.64523i	0.560575	+	0.970945i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−3.77414	−	3.34206i	−0.468124	−	0.414532i
$66$		0			0
$67$	1.09561	−	0.293568i	0.133850	−	0.0358650i	−0.191272	−	0.981537i	$-0.561261\pi$
$67$	1.09561	−	0.293568i	0.133850	−	0.0358650i	0.325122	+	0.945672i	$0.394595\pi$
$68$	2.89781	+	1.67305i	0.351411	+	0.202887i
$69$		0			0
$70$	1.36615	−	0.366058i	0.163286	−	0.0437524i
$71$	−2.71495	−	10.1323i	−0.322205	−	1.20249i	−0.917091	−	0.398677i	$-0.869470\pi$
$71$	−2.71495	−	10.1323i	−0.322205	−	1.20249i	0.594886	−	0.803810i	$-0.297197\pi$
$72$		0			0
$73$	0.788181	−	0.788181i	0.0922496	−	0.0922496i	−0.659476	−	0.751726i	$-0.729222\pi$
$73$	0.788181	−	0.788181i	0.0922496	−	0.0922496i	0.751726	+	0.659476i	$0.229222\pi$
$74$	7.01519	−	4.05022i	0.815500	−	0.470829i
$75$		0			0
$76$	1.89602	+	7.07605i	0.217489	+	0.811679i
$77$	−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
$83$	4.21280	+	15.7224i	0.462415	+	1.72576i	0.665321	+	0.746557i	$0.268295\pi$
$83$	4.21280	+	15.7224i	0.462415	+	1.72576i	−0.202906	+	0.979198i	$0.565039\pi$
$84$		0			0
$85$	3.30815	−	3.30815i	0.358819	−	0.358819i
$86$	2.16904	−	8.09498i	0.233894	−	0.872904i
$87$		0			0
$88$		−	5.81533i		−	0.619916i
$89$	0.783797	−	2.92517i	0.0830824	−	0.310068i	−0.911862	−	0.410497i	$-0.865355\pi$
$89$	0.783797	−	2.92517i	0.0830824	−	0.310068i	0.994944	+	0.100430i	$0.0320218\pi$
$90$		0			0
$91$	2.73056	+	2.41795i	0.286240	+	0.253470i
$92$	0.502672	+	0.290218i	0.0524072	+	0.0302573i
$93$		0			0
$94$	−0.750990	+	1.30075i	−0.0774587	+	0.134162i
$95$	10.2425			1.05086
$96$		0			0
$97$	3.18620	−	11.8911i	0.323510	−	1.20736i	−0.592291	−	0.805724i	$-0.701777\pi$
$97$	3.18620	−	11.8911i	0.323510	−	1.20736i	0.915801	−	0.401632i	$-0.131557\pi$
$98$	5.77308	−	1.54689i	0.583170	−	0.156260i
$99$		0			0
$100$	−1.52256	+	2.63715i	−0.152256	+	0.263715i
$101$	−10.1915			−1.01409			−0.507044	−	0.861920i	$-0.669262\pi$
$101$	−10.1915			−1.01409			−0.507044	+	0.861920i	$0.669262\pi$
$102$		0			0
$103$	8.54265	−	4.93210i	0.841732	−	0.485974i	−0.0161205	−	0.999870i	$-0.505132\pi$
$103$	8.54265	−	4.93210i	0.841732	−	0.485974i	0.857853	+	0.513896i	$0.171798\pi$
$104$	1.14254	+	3.41974i	0.112035	+	0.335333i
$105$		0			0
$106$	−1.95926	−	1.95926i	−0.190300	−	0.190300i
$107$	8.58323	−	4.95553i	0.829773	−	0.479069i	−0.0240022	−	0.999712i	$-0.507641\pi$
$107$	8.58323	−	4.95553i	0.829773	−	0.479069i	0.853775	+	0.520642i	$0.174308\pi$
$108$		0			0
$109$	6.99609	+	6.99609i	0.670103	+	0.670103i	0.957740	−	0.287636i	$-0.0928694\pi$
$109$	6.99609	+	6.99609i	0.670103	+	0.670103i	−0.287636	+	0.957740i	$0.592869\pi$
$110$	−7.85378	−	2.10441i	−0.748828	−	0.200648i
$111$		0			0
$112$	−0.977097	−	0.261812i	−0.0923269	−	0.0247389i
$113$			10.1473i			0.954580i	0.878746	+	0.477290i	$0.158381\pi$
$113$			10.1473i			0.954580i	−0.878746	+	0.477290i	$0.841619\pi$
$114$		0			0
$115$	0.573852	−	0.573852i	0.0535120	−	0.0535120i
$116$	1.03028			0.0956592
$117$		0			0
$118$	11.9845			1.10326
$119$	−2.39342	+	2.39342i	−0.219404	+	0.219404i
$120$		0			0
$121$			22.8181i			2.07437i
$122$	2.73179	+	0.731981i	0.247325	+	0.0662704i
$123$		0			0
$124$	−8.52714	−	2.28484i	−0.765760	−	0.205185i
$125$	7.95386	+	7.95386i	0.711415	+	0.711415i
$126$		0			0
$127$	−13.1106	+	7.56941i	−1.16338	+	0.671677i	−0.952111	−	0.305752i	$-0.901092\pi$
$127$	−13.1106	+	7.56941i	−1.16338	+	0.671677i	−0.211267	+	0.977428i	$0.567759\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	5.03191	−	0.305525i	0.441328	−	0.0267963i
$131$	−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
$133$	−7.41039			−0.642562
$134$	−0.567130	+	0.982297i	−0.0489925	+	0.0848576i
$135$		0			0
$136$	−3.23209	+	0.866036i	−0.277149	+	0.0742620i
$137$	1.50633	−	5.62169i	0.128694	−	0.480293i	−0.871250	−	0.490839i	$-0.836690\pi$
$137$	1.50633	−	5.62169i	0.128694	−	0.480293i	0.999944	+	0.0105460i	$0.00335697\pi$
$138$		0			0
$139$	2.27675			0.193112			0.0965559	−	0.995328i	$-0.469217\pi$
$139$	2.27675			0.193112			0.0965559	+	0.995328i	$0.469217\pi$
$140$	−0.707171	+	1.22486i	−0.0597668	+	0.103519i
$141$		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
$146$			1.11466i			0.0922496i
$147$		0			0
$148$	−2.09655	+	7.82443i	−0.172335	+	0.643164i
$149$	−10.1646	+	10.1646i	−0.832715	+	0.832715i	−0.987887	−	0.155172i	$-0.950407\pi$
$149$	−10.1646	+	10.1646i	−0.832715	+	0.832715i	0.155172	+	0.987887i	$0.450407\pi$
$150$		0			0
$151$	0.728858	+	2.72013i	0.0593136	+	0.221361i	0.989220	−	0.146434i	$-0.0467795\pi$
$151$	0.728858	+	2.72013i	0.0593136	+	0.221361i	−0.929907	+	0.367795i	$0.880113\pi$
$152$	−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	$0.731539\pi$
$158$	−0.428214	−	1.59811i	−0.0340668	−	0.127139i
$159$		0			0
$160$	−1.21085	+	0.699086i	−0.0957263	+	0.0552676i
$161$	−0.415177	+	0.415177i	−0.0327205	+	0.0327205i
$162$		0			0
$163$	−1.79021	−	6.68116i	−0.140220	−	0.523309i	−0.999922	−	0.0125123i	$-0.996017\pi$
$163$	−1.79021	−	6.68116i	−0.140220	−	0.523309i	0.859701	−	0.510797i	$-0.170650\pi$
$164$	1.58092	−	0.423606i	0.123449	−	0.0330780i
$165$		0			0
$166$	−14.0963	−	8.13850i	−1.09409	−	0.631670i
$167$	15.3104	−	4.10240i	1.18475	−	0.317453i	0.387942	−	0.921684i	$-0.373186\pi$
$167$	15.3104	−	4.10240i	1.18475	−	0.317453i	0.796809	+	0.604231i	$0.206519\pi$
$168$		0			0
$169$	7.81438	+	10.3892i	0.601106	+	0.799169i
$170$			4.67843i			0.358819i
$171$		0			0
$172$	4.19027	+	7.25776i	0.319505	+	0.553399i
$173$	1.30226	+	2.25559i	0.0990092	+	0.171489i	0.911275	−	0.411799i	$-0.135099\pi$
$173$	1.30226	+	2.25559i	0.0990092	+	0.171489i	−0.812266	+	0.583288i	$0.801766\pi$
$174$		0			0
$175$	−2.17812	−	2.17812i	−0.164651	−	0.164651i
$176$	4.11206	+	4.11206i	0.309958	+	0.309958i
$177$		0			0
$178$	1.51418	+	2.62264i	0.113493	+	0.196575i
$179$	1.79612	+	3.11097i	0.134248	+	0.232525i	0.925310	−	0.379211i	$-0.123805\pi$
$179$	1.79612	+	3.11097i	0.134248	+	0.232525i	−0.791062	+	0.611736i	$0.790471\pi$
$180$		0			0
$181$			16.3443i			1.21486i	0.794373	+	0.607430i	$0.207799\pi$
$181$			16.3443i			1.21486i	−0.794373	+	0.607430i	$0.792201\pi$
$182$	−3.64054	+	0.221045i	−0.269855	+	0.0163849i
$183$		0			0
$184$	−0.560658	+	0.150228i	−0.0413322	+	0.0110749i
$185$	9.80845	+	5.66291i	0.721131	+	0.416345i
$186$		0			0
$187$	18.7957	−	5.03629i	1.37448	−	0.368290i
$188$	−0.388741	−	1.45080i	−0.0283519	−	0.105811i
$189$		0			0
$190$	−7.24257	+	7.24257i	−0.525431	+	0.525431i
$191$	22.0297	−	12.7189i	1.59401	−	0.920305i	0.601406	−	0.798944i	$-0.294607\pi$
$191$	22.0297	−	12.7189i	1.59401	−	0.920305i	0.992608	−	0.121361i	$-0.0387259\pi$
$192$		0			0
$193$	3.26525	+	12.1861i	0.235038	+	0.877172i	0.978132	+	0.207985i	$0.0666906\pi$
$193$	3.26525	+	12.1861i	0.235038	+	0.877172i	−0.743094	+	0.669187i	$0.766643\pi$
$194$	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	$-0.408682\pi$
$197$	0.680083	+	0.182228i	0.0484539	+	0.0129832i	−0.234511	+	0.972114i	$0.575349\pi$
$198$		0			0
$199$	8.58639	+	4.95735i	0.608673	+	0.351418i	0.772446	−	0.635081i	$-0.219033\pi$
$199$	8.58639	+	4.95735i	0.608673	+	0.351418i	−0.163773	+	0.986498i	$0.552366\pi$
$200$	−0.788134	−	2.94136i	−0.0557295	−	0.207985i
$201$		0			0
$202$	7.20645	−	7.20645i	0.507044	−	0.507044i
$203$	−0.269740	+	1.00668i	−0.0189320	+	0.0706553i
$204$		0			0
$205$		−	2.28837i		−	0.159827i
$206$	−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
$211$	3.01444	−	5.22116i	0.207522	−	0.359439i	−0.743411	−	0.668835i	$-0.766793\pi$
$211$	3.01444	−	5.22116i	0.207522	−	0.359439i	0.950933	+	0.309396i	$0.100127\pi$
$212$	2.77082			0.190300
$213$		0			0
$214$	−2.56517	+	9.57335i	−0.175352	+	0.654421i
$215$	11.3182	−	3.03269i	0.771893	−	0.206828i
$216$		0			0
$217$	4.46502	−	7.73364i	0.303105	−	0.524994i
$218$	−9.89396			−0.670103
$219$		0			0
$220$	7.04151	−	4.06542i	0.474738	−	0.274090i
$221$	−10.0634	+	6.65441i	−0.676939	+	0.447624i
$222$		0			0
$223$	−20.6159	−	20.6159i	−1.38054	−	1.38054i	−0.843653	−	0.536889i	$-0.819599\pi$
$223$	−20.6159	−	20.6159i	−1.38054	−	1.38054i	−0.536889	−	0.843653i	$-0.680401\pi$
$224$	0.876041	−	0.505782i	0.0585329	−	0.0337940i
$225$		0			0
$226$	−7.17524	−	7.17524i	−0.477290	−	0.477290i
$227$	−14.0103	−	3.75404i	−0.929894	−	0.249164i	−0.238084	−	0.971244i	$-0.576519\pi$
$227$	−14.0103	−	3.75404i	−0.929894	−	0.249164i	−0.691809	+	0.722080i	$0.743186\pi$
$228$		0			0
$229$	9.53135	+	2.55392i	0.629849	+	0.168768i	0.559601	−	0.828762i	$-0.310954\pi$
$229$	9.53135	+	2.55392i	0.629849	+	0.168768i	0.0702479	+	0.997530i	$0.477621\pi$
$230$			0.811549i			0.0535120i
$231$		0			0
$232$	−0.728518	+	0.728518i	−0.0478296	+	0.0478296i
$233$	−2.06808			−0.135484			−0.0677421	−	0.997703i	$-0.521580\pi$
$233$	−2.06808			−0.135484			−0.0677421	+	0.997703i	$0.521580\pi$
$234$		0			0
$235$	−2.10003			−0.136991
$236$	−8.47432	+	8.47432i	−0.551631	+	0.551631i
$237$		0			0
$238$		−	3.38480i		−	0.219404i
$239$	−19.0682	−	5.10931i	−1.23342	−	0.330494i	−0.417510	−	0.908672i	$-0.637097\pi$
$239$	−19.0682	−	5.10931i	−1.23342	−	0.330494i	−0.815910	+	0.578179i	$0.803764\pi$
$240$		0			0
$241$	9.79587	+	2.62479i	0.631007	+	0.169078i	0.560127	−	0.828407i	$-0.310752\pi$
$241$	9.79587	+	2.62479i	0.631007	+	0.169078i	0.0708805	+	0.997485i	$0.477419\pi$
$242$	−16.1348	−	16.1348i	−1.03718	−	1.03718i
$243$		0			0
$244$	−2.44926	+	1.41408i	−0.156797	+	0.0905271i
$245$	5.90894	+	5.90894i	0.377508	+	0.377508i
$246$		0			0
$247$	−25.8805	−	5.27740i	−1.64674	−	0.335793i
$248$	7.64523	−	4.41397i	0.485472	−	0.280288i
$249$		0			0
$250$	−11.2485			−0.711415
$251$	4.78920	−	8.29514i	0.302292	−	0.523585i	−0.674363	−	0.738400i	$-0.735582\pi$
$251$	4.78920	−	8.29514i	0.302292	−	0.523585i	0.976655	+	0.214815i	$0.0689150\pi$
$252$		0			0
$253$	3.26041	−	0.873624i	0.204980	−	0.0549243i
$254$	3.91822	−	14.6230i	0.245851	−	0.917527i
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.88755	−	5.00138i	0.180120	−	0.311977i	−0.761801	−	0.647811i	$-0.775685\pi$
$257$	2.88755	−	5.00138i	0.180120	−	0.311977i	0.941921	+	0.335834i	$0.109018\pi$
$258$		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
$263$			4.45725i			0.274846i	0.990512	+	0.137423i	$0.0438819\pi$
$263$			4.45725i			0.274846i	−0.990512	+	0.137423i	$0.956118\pi$
$264$		0			0
$265$	1.00269	−	3.74207i	0.0615945	−	0.229874i
$266$	5.23994	−	5.23994i	0.321281	−	0.321281i
$267$		0			0
$268$	−0.293568	−	1.09561i	−0.0179325	−	0.0669250i
$269$	11.4786	+	6.62715i	0.699860	+	0.404064i	0.807295	−	0.590148i	$-0.200931\pi$
$269$	11.4786	+	6.62715i	0.699860	+	0.404064i	−0.107435	+	0.994212i	$0.534264\pi$
$270$		0			0
$271$	−5.62562	−	1.50738i	−0.341732	−	0.0915668i	0.0838714	−	0.996477i	$-0.473272\pi$
$271$	−5.62562	−	1.50738i	−0.341732	−	0.0915668i	−0.425604	+	0.904910i	$0.639938\pi$
$272$	1.67305	−	2.89781i	0.101444	−	0.175706i
$273$		0			0
$274$	2.91000	+	5.04027i	0.175799	+	0.304494i
$275$	4.58326	+	17.1050i	0.276381	+	1.03147i
$276$		0			0
$277$	−16.8351	+	9.71973i	−1.01152	+	0.584002i	−0.911637	−	0.410997i	$-0.865181\pi$
$277$	−16.8351	+	9.71973i	−1.01152	+	0.584002i	−0.0998845	+	0.994999i	$0.531847\pi$
$278$	−1.60991	+	1.60991i	−0.0965559	+	0.0965559i
$279$		0			0
$280$	−0.366058	−	1.36615i	−0.0218762	−	0.0816430i
$281$	1.40349	−	0.376063i	0.0837250	−	0.0224340i	−0.216713	−	0.976235i	$-0.569534\pi$
$281$	1.40349	−	0.376063i	0.0837250	−	0.0224340i	0.300438	+	0.953801i	$0.402867\pi$
$282$		0			0
$283$	−17.9556	−	10.3666i	−1.06735	−	0.616233i	−0.139892	−	0.990167i	$-0.544675\pi$
$283$	−17.9556	−	10.3666i	−1.06735	−	0.616233i	−0.927455	+	0.373934i	$0.878009\pi$
$284$	−10.1323	+	2.71495i	−0.601243	+	0.161103i
$285$		0			0
$286$	18.7604	+	9.36396i	1.10932	+	0.553703i
$287$			1.65561i			0.0977278i
$288$		0			0
$289$	2.90179	+	5.02604i	0.170693	+	0.295649i
$290$	0.720255	+	1.24752i	0.0422948	+	0.0732568i
$291$		0			0
$292$	−0.788181	−	0.788181i	−0.0461248	−	0.0461248i
$293$	−16.7878	−	16.7878i	−0.980753	−	0.980753i	0.0190656	−	0.999818i	$-0.493931\pi$
$293$	−16.7878	−	16.7878i	−0.980753	−	0.980753i	−0.999818	+	0.0190656i	$0.993931\pi$
$294$		0			0
$295$	8.37820	+	14.5115i	0.487797	+	0.844890i
$296$	−4.05022	−	7.01519i	−0.235414	−	0.407750i
$297$		0			0
$298$		−	14.3749i		−	0.832715i
$299$	−1.74566	+	1.15431i	−0.100954	+	0.0667557i
$300$		0			0
$301$	−8.18860	+	2.19413i	−0.471983	+	0.126467i
$302$	−2.43881	−	1.40805i	−0.140337	−	0.0810239i
$303$		0			0
$304$	7.07605	−	1.89602i	0.405839	−	0.108744i
$305$	1.02343	+	3.81951i	0.0586017	+	0.218705i
$306$		0			0
$307$	14.7696	−	14.7696i	0.842947	−	0.842947i	−0.146294	−	0.989241i	$-0.546735\pi$
$307$	14.7696	−	14.7696i	0.842947	−	0.842947i	0.989241	+	0.146294i	$0.0467346\pi$
$308$	−5.09447	+	2.94129i	−0.290284	+	0.167596i
$309$		0			0
$310$	−3.19460	−	11.9224i	−0.181441	−	0.677147i
$311$	−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	$-0.460235\pi$
$312$		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
$317$	−5.72585	−	21.3692i	−0.321596	−	1.20021i	−0.917690	−	0.397298i	$-0.869948\pi$
$317$	−5.72585	−	21.3692i	−0.321596	−	1.20021i	0.596094	−	0.802915i	$-0.296719\pi$
$318$		0			0
$319$	4.23658	−	4.23658i	0.237203	−	0.237203i
$320$	0.361873	−	1.35053i	0.0202293	−	0.0754969i
$321$		0			0
$322$		−	0.587148i		−	0.0327205i
$323$	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
$328$	−0.818343	+	1.41741i	−0.0451854	+	0.0782635i
$329$	1.51935			0.0837645
$330$		0			0
$331$	5.85855	−	21.8644i	0.322015	−	1.20178i	−0.595263	−	0.803531i	$-0.702952\pi$
$331$	5.85855	−	21.8644i	0.322015	−	1.20178i	0.917279	−	0.398246i	$-0.130381\pi$
$332$	15.7224	−	4.21280i	0.862878	−	0.231207i
$333$		0			0
$334$	−7.92523	+	13.7269i	−0.433649	+	0.751102i
$335$	−1.58589			−0.0866464
$336$		0			0
$337$	26.9968	−	15.5866i	1.47061	−	0.849058i	0.471156	−	0.882050i	$-0.343837\pi$
$337$	26.9968	−	15.5866i	1.47061	−	0.849058i	0.999456	+	0.0329922i	$0.0105036\pi$
$338$	−12.8719	−	1.82067i	−0.700138	−	0.0990314i
$339$		0			0
$340$	−3.30815	−	3.30815i	−0.179410	−	0.179410i
$341$	−44.4595	+	25.6687i	−2.40762	+	1.39004i
$342$		0			0
$343$	−9.28206	−	9.28206i	−0.501184	−	0.501184i
$344$	−8.09498	−	2.16904i	−0.436452	−	0.116947i
$345$		0			0
$346$	−2.51578	−	0.674101i	−0.135249	−	0.0362399i
$347$		−	20.3582i		−	1.09289i	−0.837496	−	0.546444i	$-0.815981\pi$
$347$		−	20.3582i		−	1.09289i	0.837496	−	0.546444i	$-0.184019\pi$
$348$		0			0
$349$	−20.7926	+	20.7926i	−1.11300	+	1.11300i	−0.120259	+	0.992743i	$0.538373\pi$
$349$	−20.7926	+	20.7926i	−1.11300	+	1.11300i	−0.992743	+	0.120259i	$0.961627\pi$
$350$	3.08033			0.164651
$351$		0			0
$352$	−5.81533			−0.309958
$353$	−8.11406	+	8.11406i	−0.431868	+	0.431868i	−0.889263	−	0.457395i	$-0.848782\pi$
$353$	−8.11406	+	8.11406i	−0.431868	+	0.431868i	0.457395	+	0.889263i	$0.348782\pi$
$354$		0			0
$355$			14.6665i			0.778417i
$356$	−2.92517	−	0.783797i	−0.155034	−	0.0415412i
$357$		0			0
$358$	−3.46984	−	0.929741i	−0.183387	−	0.0491383i
$359$	25.9734	+	25.9734i	1.37083	+	1.37083i	0.859221	+	0.511605i	$0.170949\pi$
$359$	25.9734	+	25.9734i	1.37083	+	1.37083i	0.511605	+	0.859221i	$0.329051\pi$
$360$		0			0
$361$	30.0211	−	17.3327i	1.58006	−	0.912248i
$362$	−11.5571	−	11.5571i	−0.607430	−	0.607430i
$363$		0			0
$364$	2.41795	−	2.73056i	0.126735	−	0.143120i
$365$	−1.34968	+	0.779240i	−0.0706457	+	0.0407873i
$366$		0			0
$367$	−5.57250			−0.290882			−0.145441	−	0.989367i	$-0.546460\pi$
$367$	−5.57250			−0.290882			−0.145441	+	0.989367i	$0.546460\pi$
$368$	0.290218	−	0.502672i	0.0151287	−	0.0262036i
$369$		0			0
$370$	−10.9399	+	2.93134i	−0.568738	+	0.152393i
$371$	−0.725434	+	2.70736i	−0.0376626	+	0.140559i
$372$		0			0
$373$	2.87844			0.149040			0.0745200	−	0.997220i	$-0.476258\pi$
$373$	2.87844			0.149040			0.0745200	+	0.997220i	$0.476258\pi$
$374$	−9.72936	+	16.8517i	−0.503093	+	0.871383i
$375$		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	−0.666394	−	0.745600i	$-0.732163\pi$
$379$	5.51954	−	20.5992i	0.283520	−	1.05811i	0.949914	−	0.312511i	$-0.101170\pi$
$380$		−	10.2425i		−	0.525431i
$381$		0			0
$382$	−6.58377	+	24.5710i	−0.336855	+	1.25716i
$383$	−9.17790	+	9.17790i	−0.468969	+	0.468969i	−0.901580	−	0.432612i	$-0.857592\pi$
$383$	−9.17790	+	9.17790i	−0.468969	+	0.468969i	0.432612	+	0.901580i	$0.357592\pi$
$384$		0			0
$385$	2.12875	+	7.94461i	0.108491	+	0.404895i
$386$	−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	$-0.541567\pi$
$389$	15.6511	−	27.1085i	0.793543	−	1.37446i	0.923760	−	0.382972i	$-0.125099\pi$
$390$		0			0
$391$	−0.971100	−	1.68199i	−0.0491106	−	0.0850621i
$392$	−1.54689	−	5.77308i	−0.0781299	−	0.291585i
$393$		0			0
$394$	−0.609746	+	0.352037i	−0.0307186	+	0.0177354i
$395$	1.63572	−	1.63572i	0.0823021	−	0.0823021i
$396$		0			0
$397$	0.644906	+	2.40682i	0.0323669	+	0.120795i	0.980219	−	0.197915i	$-0.0634170\pi$
$397$	0.644906	+	2.40682i	0.0323669	+	0.120795i	−0.947852	+	0.318710i	$0.896750\pi$
$398$	−9.57687	+	2.56612i	−0.480045	+	0.128628i
$399$		0			0
$400$	2.63715	+	1.52256i	0.131857	+	0.0761279i
$401$	−19.8142	+	5.30920i	−0.989473	+	0.265129i	−0.717029	−	0.697043i	$-0.754499\pi$
$401$	−19.8142	+	5.30920i	−0.989473	+	0.265129i	−0.272444	+	0.962172i	$0.587832\pi$
$402$		0			0
$403$	21.1015	−	23.8296i	1.05114	−	1.18704i
$404$			10.1915i			0.507044i
$405$		0			0
$406$	−0.521098	−	0.902568i	−0.0258617	−	0.0447937i
$407$	23.5534	+	40.7957i	1.16750	+	2.02217i
$408$		0			0
$409$	−6.92695	−	6.92695i	−0.342516	−	0.342516i	0.514797	−	0.857312i	$-0.327867\pi$
$409$	−6.92695	−	6.92695i	−0.342516	−	0.342516i	−0.857312	+	0.514797i	$0.827867\pi$
$410$	1.61812	+	1.61812i	0.0799133	+	0.0799133i
$411$		0			0
$412$	−4.93210	−	8.54265i	−0.242987	−	0.420866i
$413$	−6.06155	−	10.4989i	−0.298269	−	0.516618i
$414$		0			0
$415$		−	22.7581i		−	1.11715i
$416$	3.41974	−	1.14254i	0.167666	−	0.0560177i
$417$		0			0
$418$	−41.1496	+	11.0260i	−2.01269	+	0.539299i
$419$	−1.49988	−	0.865956i	−0.0732739	−	0.0423047i	0.462915	−	0.886402i	$-0.346803\pi$
$419$	−1.49988	−	0.865956i	−0.0732739	−	0.0423047i	−0.536189	+	0.844098i	$0.680137\pi$
$420$		0			0
$421$	−3.43418	+	0.920185i	−0.167372	+	0.0448471i	−0.341532	−	0.939870i	$-0.610946\pi$
$421$	−3.43418	+	0.920185i	−0.167372	+	0.0448471i	0.174160	+	0.984717i	$0.444279\pi$
$422$	1.56039	+	5.82344i	0.0759584	+	0.283481i
$423$		0			0
$424$	−1.95926	+	1.95926i	−0.0951502	+	0.0951502i
$425$	8.82418	−	5.09464i	0.428035	−	0.247126i
$426$		0			0
$427$	−0.740446	−	2.76338i	−0.0358327	−	0.133729i
$428$	−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	$-0.532900\pi$
$431$	−14.3219	−	3.83753i	−0.689860	−	0.184847i	−0.586684	+	0.809816i	$0.699567\pi$
$432$		0			0
$433$	−9.94854	−	5.74379i	−0.478096	−	0.276029i	0.241527	−	0.970394i	$-0.422352\pi$
$433$	−9.94854	−	5.74379i	−0.478096	−	0.276029i	−0.719623	+	0.694365i	$0.755685\pi$
$434$	2.31126	+	8.62576i	0.110944	+	0.414050i
$435$		0			0
$436$	6.99609	−	6.99609i	0.335052	−	0.335052i
$437$	1.10052	−	4.10719i	0.0526450	−	0.196474i
$438$		0			0
$439$			40.7022i			1.94261i	0.237834	+	0.971306i	$0.423563\pi$
$439$			40.7022i			1.94261i	−0.237834	+	0.971306i	$0.576437\pi$
$440$	−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
$445$	−2.11708	+	3.66690i	−0.100359	+	0.173828i
$446$	29.1553			1.38054
$447$		0			0
$448$	−0.261812	+	0.977097i	−0.0123695	+	0.0461635i
$449$	−27.3580	+	7.33055i	−1.29110	+	0.345950i	−0.838080	−	0.545548i	$-0.816322\pi$
$449$	−27.3580	+	7.33055i	−1.29110	+	0.345950i	−0.453024	+	0.891498i	$0.649655\pi$
$450$		0			0
$451$	4.75894	−	8.24272i	0.224090	−	0.388134i
$452$	10.1473			0.477290
$453$		0			0
$454$	12.5613	−	7.25224i	0.589529	−	0.340365i
$455$	−2.81271	−	4.25363i	−0.131862	−	0.199413i
$456$		0			0
$457$	21.3025	+	21.3025i	0.996490	+	0.996490i	0.999994	−	0.00350346i	$-0.00111519\pi$
$457$	21.3025	+	21.3025i	0.996490	+	0.996490i	−0.00350346	+	0.999994i	$0.501115\pi$
$458$	−8.54557	+	4.93379i	−0.399308	+	0.230541i
$459$		0			0
$460$	−0.573852	−	0.573852i	−0.0267560	−	0.0267560i
$461$	−27.5031	−	7.36943i	−1.28095	−	0.343228i	−0.446731	−	0.894668i	$-0.647412\pi$
$461$	−27.5031	−	7.36943i	−1.28095	−	0.343228i	−0.834215	+	0.551440i	$0.814079\pi$
$462$		0			0
$463$	−3.49672	−	0.936943i	−0.162506	−	0.0435434i	0.176649	−	0.984274i	$-0.443474\pi$
$463$	−3.49672	−	0.936943i	−0.162506	−	0.0435434i	−0.339155	+	0.940731i	$0.610141\pi$
$464$		−	1.03028i		−	0.0478296i
$465$		0			0
$466$	1.46235	−	1.46235i	0.0677421	−	0.0677421i
$467$	36.6235			1.69473			0.847366	−	0.531010i	$-0.178187\pi$
$467$	36.6235			1.69473			0.847366	+	0.531010i	$0.178187\pi$
$468$		0			0
$469$	1.14738			0.0529809
$470$	1.48494	−	1.48494i	0.0684953	−	0.0684953i
$471$		0			0
$472$		−	11.9845i		−	0.551631i
$473$	47.0750	+	12.6137i	2.16451	+	0.579979i
$474$		0			0
$475$	21.5474	+	5.77361i	0.988662	+	0.264911i
$476$	2.39342	+	2.39342i	0.109702	+	0.109702i
$477$		0			0
$478$	17.0961	−	9.87043i	0.781957	−	0.451463i
$479$	3.57024	+	3.57024i	0.163128	+	0.163128i	0.783951	−	0.620823i	$-0.213201\pi$
$479$	3.57024	+	3.57024i	0.163128	+	0.163128i	−0.620823	+	0.783951i	$0.713201\pi$
$480$		0			0
$481$	−21.8658	−	19.3626i	−0.996997	−	0.882857i
$482$	−8.78273	+	5.07071i	−0.400043	+	0.230965i
$483$		0			0
$484$	22.8181			1.03718
$485$	−8.60613	+	14.9063i	−0.390784	+	0.676858i
$486$		0			0
$487$	−28.6137	+	7.66702i	−1.29661	+	0.347426i	−0.840167	−	0.542327i	$-0.817543\pi$
$487$	−28.6137	+	7.66702i	−1.29661	+	0.347426i	−0.456443	+	0.889753i	$0.650877\pi$
$488$	0.731981	−	2.73179i	0.0331352	−	0.123662i
$489$		0			0
$490$	−8.35650			−0.377508
$491$	0.987608	−	1.71059i	0.0445701	−	0.0771978i	−0.842880	−	0.538102i	$-0.819142\pi$
$491$	0.987608	−	1.71059i	0.0445701	−	0.0771978i	0.887450	+	0.460904i	$0.152475\pi$
$492$		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
$497$		−	10.6111i		−	0.475972i
$498$		0			0
$499$	1.03754	−	3.87214i	0.0464465	−	0.173341i	−0.938806	−	0.344445i	$-0.888067\pi$
$499$	1.03754	−	3.87214i	0.0464465	−	0.173341i	0.985253	+	0.171105i	$0.0547336\pi$
$500$	7.95386	−	7.95386i	0.355707	−	0.355707i
$501$		0			0
$502$	2.47907	+	9.25203i	0.110646	+	0.412938i
$503$	−6.37037	−	3.67794i	−0.284041	−	0.163991i	0.351211	−	0.936297i	$-0.385770\pi$
$503$	−6.37037	−	3.67794i	−0.284041	−	0.163991i	−0.635251	+	0.772305i	$0.719103\pi$
$504$		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
$509$	3.68759	+	13.7623i	0.163449	+	0.610002i	0.998233	+	0.0594233i	$0.0189262\pi$
$509$	3.68759	+	13.7623i	0.163449	+	0.610002i	−0.834783	+	0.550579i	$0.814407\pi$
$510$		0			0
$511$	0.976484	−	0.563773i	0.0431971	−	0.0249399i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	1.49470	+	5.57831i	0.0659286	+	0.246049i
$515$	−13.3219	+	3.56959i	−0.587033	+	0.157295i
$516$		0			0
$517$	−7.56431	−	4.36726i	−0.332678	−	0.192072i
$518$	7.91492	−	2.12080i	0.347762	−	0.0931824i
$519$		0			0
$520$	−0.305525	−	5.03191i	−0.0133982	−	0.220664i
$521$		−	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	0.985854	−	0.167606i	$-0.0536037\pi$
$523$	7.95336	+	13.7756i	0.347776	+	0.602366i	−0.638078	+	0.769972i	$0.720270\pi$
$524$	1.89982	+	3.29059i	0.0829941	+	0.143750i
$525$		0			0
$526$	−3.15175	−	3.15175i	−0.137423	−	0.137423i
$527$	20.8874	+	20.8874i	0.909869	+	0.909869i
$528$		0			0
$529$	11.3315	+	19.6268i	0.492676	+	0.853340i
$530$	1.93704	+	3.35505i	0.0841396	+	0.145734i
$531$		0			0
$532$			7.41039i			0.321281i
$533$	−1.17907	+	5.78217i	−0.0510710	+	0.250453i
$534$		0			0
$535$	−13.3852	+	3.58655i	−0.578692	+	0.155060i
$536$	0.982297	+	0.567130i	0.0424288	+	0.0244963i
$537$		0			0
$538$	−12.8027	+	3.43046i	−0.551962	+	0.147898i
$539$	8.99570	+	33.5724i	0.387472	+	1.44607i
$540$		0			0
$541$	20.5826	−	20.5826i	0.884913	−	0.884913i	−0.109116	−	0.994029i	$-0.534802\pi$
$541$	20.5826	−	20.5826i	0.884913	−	0.884913i	0.994029	+	0.109116i	$0.0348019\pi$
$542$	5.04379	−	2.91204i	0.216649	−	0.125083i
$543$		0			0
$544$	0.866036	+	3.23209i	0.0371310	+	0.138575i
$545$	−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
$551$	−1.95344	−	7.29032i	−0.0832191	−	0.310578i
$552$		0			0
$553$	−1.18343	+	1.18343i	−0.0503246	+	0.0503246i
$554$	5.03130	−	18.7771i	0.213760	−	0.797762i
$555$		0			0
$556$		−	2.27675i		−	0.0965559i
$557$	−1.55296	+	5.79572i	−0.0658010	+	0.245573i	−0.990990	−	0.133933i	$-0.957239\pi$
$557$	−1.55296	+	5.79572i	−0.0658010	+	0.245573i	0.925189	+	0.379506i	$0.123906\pi$
$558$		0			0
$559$	−30.1609	+	1.83129i	−1.27567	+	0.0774555i
$560$	1.22486	+	0.707171i	0.0517596	+	0.0298834i
$561$		0			0
$562$	−0.726498	+	1.25833i	−0.0306455	+	0.0530795i
$563$	−34.2938			−1.44531			−0.722656	−	0.691208i	$-0.757079\pi$
$563$	−34.2938			−1.44531			−0.722656	+	0.691208i	$0.757079\pi$
$564$		0			0
$565$	3.67205	−	13.7043i	0.154484	−	0.576543i
$566$	20.0268	−	5.36617i	0.841790	−	0.225557i
$567$		0			0
$568$	5.24488	−	9.08440i	0.220070	−	0.381173i
$569$	−35.6813			−1.49584			−0.747919	−	0.663790i	$-0.768947\pi$
$569$	−35.6813			−1.49584			−0.747919	+	0.663790i	$0.768947\pi$
$570$		0			0
$571$	−25.3581	+	14.6405i	−1.06121	+	0.612687i	−0.925765	−	0.378099i	$-0.876578\pi$
$571$	−25.3581	+	14.6405i	−1.06121	+	0.612687i	−0.135440	+	0.990786i	$0.543245\pi$
$572$	−19.8869	+	6.64426i	−0.831513	+	0.277810i
$573$		0			0
$574$	−1.17070	−	1.17070i	−0.0488639	−	0.0488639i
$575$	1.53069	−	0.883747i	0.0638344	−	0.0368548i
$576$		0			0
$577$	−19.2968	−	19.2968i	−0.803337	−	0.803337i	0.180278	−	0.983616i	$-0.442300\pi$
$577$	−19.2968	−	19.2968i	−0.803337	−	0.803337i	−0.983616	+	0.180278i	$0.942300\pi$
$578$	−5.60582	−	1.50208i	−0.233171	−	0.0624781i
$579$		0			0
$580$	−1.39143	−	0.372831i	−0.0577758	−	0.0154810i
$581$			16.4652i			0.683094i
$582$		0			0
$583$	11.3938	−	11.3938i	0.471881	−	0.471881i
$584$	1.11466			0.0461248
$585$		0			0
$586$	23.7415			0.980753
$587$	−14.0938	+	14.0938i	−0.581712	+	0.581712i	−0.935373	−	0.353662i	$-0.884936\pi$
$587$	−14.0938	+	14.0938i	−0.581712	+	0.581712i	0.353662	+	0.935373i	$0.384936\pi$
$588$		0			0
$589$			64.6706i			2.66471i
$590$	−16.1854	−	4.33687i	−0.666344	−	0.178546i
$591$		0			0
$592$	7.82443	+	2.09655i	0.321582	+	0.0861677i
$593$	3.24522	+	3.24522i	0.133265	+	0.133265i	0.770593	−	0.637328i	$-0.219960\pi$
$593$	3.24522	+	3.24522i	0.133265	+	0.133265i	−0.637328	+	0.770593i	$0.719960\pi$
$594$		0			0
$595$	4.09850	−	2.36627i	0.168022	−	0.0970075i
$596$	10.1646	+	10.1646i	0.416358	+	0.416358i
$597$		0			0
$598$	0.418145	−	2.05059i	0.0170992	−	0.0838550i
$599$	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
$601$	4.63910			0.189233			0.0946164	−	0.995514i	$-0.469838\pi$
$601$	4.63910			0.189233			0.0946164	+	0.995514i	$0.469838\pi$
$602$	4.23873	−	7.34169i	0.172758	−	0.299225i
$603$		0			0
$604$	2.72013	−	0.728858i	0.110681	−	0.0296568i
$605$	8.25725	−	30.8165i	0.335705	−	1.25287i
$606$		0			0
$607$	11.5014			0.466829			0.233414	−	0.972377i	$-0.425010\pi$
$607$	11.5014			0.466829			0.233414	+	0.972377i	$0.425010\pi$
$608$	−3.66283	+	6.34422i	−0.148548	+	0.257292i
$609$		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	−0.999775	−	0.0211942i	$-0.993253\pi$
$613$	−3.05394	+	11.3975i	−0.123347	+	0.460339i	0.876428	+	0.481533i	$0.159920\pi$
$614$			20.8874i			0.842947i
$615$		0			0
$616$	1.52252	−	5.68214i	0.0613443	−	0.228940i
$617$	22.5562	−	22.5562i	0.908079	−	0.908079i	−0.0880383	−	0.996117i	$-0.528060\pi$
$617$	22.5562	−	22.5562i	0.908079	−	0.908079i	0.996117	+	0.0880383i	$0.0280598\pi$
$618$		0			0
$619$	5.99924	+	22.3895i	0.241130	+	0.899909i	0.975289	+	0.220932i	$0.0709097\pi$
$619$	5.99924	+	22.3895i	0.241130	+	0.899909i	−0.734160	+	0.678977i	$0.762424\pi$
$620$	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
$626$	4.53721	+	16.9331i	0.181343	+	0.676782i
$627$		0			0
$628$	6.82268	−	3.93908i	0.272255	−	0.157186i
$629$	19.1661	−	19.1661i	0.764202	−	0.764202i
$630$		0			0
$631$	6.12810	+	22.8704i	0.243956	+	0.910456i	0.973905	+	0.226955i	$0.0728770\pi$
$631$	6.12810	+	22.8704i	0.243956	+	0.910456i	−0.729949	+	0.683501i	$0.760456\pi$
$632$	−1.59811	+	0.428214i	−0.0635696	+	0.0170334i
$633$		0			0
$634$	19.1591	+	11.0615i	0.760904	+	0.439308i
$635$	20.4454	−	5.47834i	0.811353	−	0.217401i
$636$		0			0
$637$	−11.8860	−	17.9750i	−0.470939	−	0.712197i
$638$			5.99142i			0.237203i
$639$		0			0
$640$	0.699086	+	1.21085i	0.0276338	+	0.0478631i
$641$	14.3524	+	24.8590i	0.566884	+	0.981872i	0.996872	+	0.0790369i	$0.0251845\pi$
$641$	14.3524	+	24.8590i	0.566884	+	0.981872i	−0.429988	+	0.902835i	$0.641482\pi$
$642$		0			0
$643$	16.1427	+	16.1427i	0.636607	+	0.636607i	0.949717	−	0.313110i	$-0.101371\pi$
$643$	16.1427	+	16.1427i	0.636607	+	0.636607i	−0.313110	+	0.949717i	$0.601371\pi$
$644$	0.415177	+	0.415177i	0.0163603	+	0.0163603i
$645$		0			0
$646$	12.2562	+	21.2284i	0.482215	+	0.835221i
$647$	−18.5692	−	32.1627i	−0.730029	−	1.26445i	−0.956870	−	0.290516i	$-0.906173\pi$
$647$	−18.5692	−	32.1627i	−0.730029	−	1.26445i	0.226841	−	0.973932i	$-0.427160\pi$
$648$		0			0
$649$			69.6938i			2.73572i
$650$	10.7579	+	2.19370i	0.421961	+	0.0860439i
$651$		0			0
$652$	−6.68116	+	1.79021i	−0.261655	+	0.0701101i
$653$	38.5101	+	22.2338i	1.50702	+	0.870076i	0.999967	+	0.00815952i	$0.00259728\pi$
$653$	38.5101	+	22.2338i	1.50702	+	0.870076i	0.507050	+	0.861917i	$0.330736\pi$
$654$		0			0
$655$	5.13153	−	1.37499i	0.200506	−	0.0537253i
$656$	−0.423606	−	1.58092i	−0.0165390	−	0.0617245i
$657$		0			0
$658$	−1.07434	+	1.07434i	−0.0418822	+	0.0418822i
$659$	−0.358832	+	0.207172i	−0.0139781	+	0.00807026i	−0.506973	−	0.861962i	$-0.669236\pi$
$659$	−0.358832	+	0.207172i	−0.0139781	+	0.00807026i	0.492995	+	0.870032i	$0.335902\pi$
$660$		0			0
$661$	−7.37782	−	27.5344i	−0.286964	−	1.07096i	−0.947392	−	0.320075i	$-0.896292\pi$
$661$	−7.37782	−	27.5344i	−0.286964	−	1.07096i	0.660428	−	0.750889i	$-0.270375\pi$
$662$	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
$668$	−4.10240	−	15.3104i	−0.158727	−	0.592376i
$669$		0			0
$670$	1.12139	−	1.12139i	0.0433232	−	0.0433232i
$671$	−4.25671	+	15.8863i	−0.164328	+	0.613282i
$672$		0			0
$673$		−	4.15724i		−	0.160250i	−0.996785	−	0.0801248i	$-0.974468\pi$
$673$		−	4.15724i		−	0.160250i	0.996785	−	0.0801248i	$-0.0255319\pi$
$674$	−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
$679$	6.22646	−	10.7845i	0.238949	−	0.413873i
$680$	4.67843			0.179410
$681$		0			0
$682$	13.2871	−	49.5881i	0.508789	−	1.89883i
$683$	−9.85750	+	2.64131i	−0.377187	+	0.101067i	−0.442431	−	0.896802i	$-0.645884\pi$
$683$	−9.85750	+	2.64131i	−0.377187	+	0.101067i	0.0652445	+	0.997869i	$0.479217\pi$
$684$		0			0
$685$	−4.06868	+	7.04716i	−0.155456	+	0.269258i
$686$	13.1268			0.501184
$687$		0			0
$688$	7.25776	−	4.19027i	0.276699	−	0.159753i
$689$	−4.46162	+	8.93870i	−0.169974	+	0.340537i
$690$		0			0
$691$	−29.9191	−	29.9191i	−1.13818	−	1.13818i	−0.988777	−	0.149400i	$-0.952266\pi$
$691$	−29.9191	−	29.9191i	−1.13818	−	1.13818i	−0.149400	−	0.988777i	$-0.547734\pi$
$692$	2.25559	−	1.30226i	0.0857445	−	0.0495046i
$693$		0			0
$694$	14.3954	+	14.3954i	0.546444	+	0.546444i
$695$	−3.07483	−	0.823897i	−0.116635	−	0.0312522i
$696$		0			0
$697$	−5.28992	−	1.41743i	−0.200370	−	0.0536890i
$698$		−	29.4052i		−	1.11300i
$699$		0			0
$700$	−2.17812	+	2.17812i	−0.0823253	+	0.0823253i
$701$	−16.7670			−0.633280			−0.316640	−	0.948546i	$-0.602555\pi$
$701$	−16.7670			−0.633280			−0.316640	+	0.948546i	$0.602555\pi$
$702$		0			0
$703$	59.3412			2.23810
$704$	4.11206	−	4.11206i	0.154979	−	0.154979i
$705$		0			0
$706$		−	11.4750i		−	0.431868i
$707$	−9.95805	−	2.66825i	−0.374511	−	0.100350i
$708$		0			0
$709$	−12.3741	−	3.31563i	−0.464719	−	0.124521i	0.0188591	−	0.999822i	$-0.493997\pi$
$709$	−12.3741	−	3.31563i	−0.464719	−	0.124521i	−0.483579	+	0.875301i	$0.660663\pi$
$710$	−10.3708	−	10.3708i	−0.389208	−	0.389208i
$711$		0			0
$712$	2.62264	−	1.51418i	0.0982875	−	0.0567463i
$713$	3.62325	+	3.62325i	0.135692	+	0.135692i
$714$		0			0
$715$	1.77673	+	29.2622i	0.0664459	+	1.09435i
$716$	3.11097	−	1.79612i	0.116262	−	0.0671242i
$717$		0			0
$718$	−36.7320			−1.37083
$719$	−8.63433	+	14.9551i	−0.322006	+	0.557731i	−0.980902	−	0.194503i	$-0.937690\pi$
$719$	−8.63433	+	14.9551i	−0.322006	+	0.557731i	0.658896	+	0.752234i	$0.271024\pi$
$720$		0			0
$721$	9.63828	−	2.58257i	0.358948	−	0.0961799i
$722$	−8.97207	+	33.4842i	−0.333906	+	1.24615i
$723$		0			0
$724$	16.3443			0.607430
$725$	1.56866	−	2.71700i	0.0582586	−	0.100907i
$726$		0			0
$727$	−12.1283	−	7.00226i	−0.449813	−	0.259700i	0.257938	−	0.966161i	$-0.416957\pi$
$727$	−12.1283	−	7.00226i	−0.449813	−	0.259700i	−0.707751	+	0.706462i	$0.750290\pi$
$728$	0.221045	+	3.64054i	0.00819245	+	0.134928i
$729$		0			0
$730$	0.403364	−	1.50538i	0.0149292	−	0.0557165i
$731$		−	28.0422i		−	1.03718i
$732$		0			0
$733$	−1.76174	+	6.57489i	−0.0650712	+	0.242849i	−0.990799	−	0.135341i	$-0.956787\pi$
$733$	−1.76174	+	6.57489i	−0.0650712	+	0.242849i	0.925728	+	0.378190i	$0.123454\pi$
$734$	3.94035	−	3.94035i	0.145441	−	0.145441i
$735$		0			0
$736$	0.150228	+	0.560658i	0.00553747	+	0.0206661i
$737$	−5.71238	−	3.29805i	−0.210418	−	0.121485i
$738$		0			0
$739$	−17.1161	−	4.58625i	−0.629626	−	0.168708i	−0.0701262	−	0.997538i	$-0.522340\pi$
$739$	−17.1161	−	4.58625i	−0.629626	−	0.168708i	−0.559500	+	0.828830i	$0.689007\pi$
$740$	5.66291	−	9.80845i	0.208173	−	0.360566i
$741$		0			0
$742$	−1.40143	−	2.42735i	−0.0514481	−	0.0891108i
$743$	8.04786	+	30.0350i	0.295247	+	1.10188i	0.941021	+	0.338349i	$0.109868\pi$
$743$	8.04786	+	30.0350i	0.295247	+	1.10188i	−0.645773	+	0.763529i	$0.723465\pi$
$744$		0			0
$745$	17.4059	−	10.0493i	0.637702	−	0.368177i
$746$	−2.03537	+	2.03537i	−0.0745200	+	0.0745200i
$747$		0			0
$748$	−5.03629	−	18.7957i	−0.184145	−	0.687238i
$749$	9.68407	−	2.59484i	0.353848	−	0.0948133i
$750$		0			0
$751$	−4.97436	−	2.87195i	−0.181517	−	0.104799i	0.406488	−	0.913656i	$-0.366753\pi$
$751$	−4.97436	−	2.87195i	−0.181517	−	0.104799i	−0.588005	+	0.808857i	$0.700087\pi$
$752$	−1.45080	+	0.388741i	−0.0529053	+	0.0141759i
$753$		0			0
$754$	−1.17714	−	3.52329i	−0.0428689	−	0.128311i
$755$		−	3.93738i		−	0.143296i
$756$		0			0
$757$	−13.1210	−	22.7262i	−0.476891	−	0.825999i	0.522759	−	0.852481i	$-0.324903\pi$
$757$	−13.1210	−	22.7262i	−0.476891	−	0.825999i	−0.999649	+	0.0264817i	$0.991570\pi$
$758$	10.6629	+	18.4687i	0.387295	+	0.670815i
$759$		0			0
$760$	7.24257	+	7.24257i	0.262716	+	0.262716i
$761$	−2.64360	−	2.64360i	−0.0958306	−	0.0958306i	0.657566	−	0.753397i	$-0.271586\pi$
$761$	−2.64360	−	2.64360i	−0.0958306	−	0.0958306i	−0.753397	+	0.657566i	$0.771586\pi$
$762$		0			0
$763$	5.00419	+	8.66751i	0.181164	+	0.313785i
$764$	−12.7189	−	22.0297i	−0.460152	−	0.797007i
$765$		0			0
$766$		−	12.9795i		−	0.468969i
$767$	−13.6928	−	40.9838i	−0.494418	−	1.47984i
$768$		0			0
$769$	−47.3247	+	12.6806i	−1.70657	+	0.457274i	−0.974580	−	0.224040i	$-0.928075\pi$
$769$	−47.3247	+	12.6806i	−1.70657	+	0.457274i	−0.731991	+	0.681314i	$0.761409\pi$
$770$	−7.12294	−	4.11243i	−0.256693	−	0.148202i
$771$		0			0
$772$	12.1861	−	3.26525i	0.438586	−	0.117519i
$773$	1.60335	+	5.98377i	0.0576683	+	0.215221i	0.988747	−	0.149597i	$-0.0477977\pi$
$773$	1.60335	+	5.98377i	0.0576683	+	0.215221i	−0.931079	+	0.364818i	$0.881131\pi$
$774$		0			0
$775$	−19.0085	+	19.0085i	−0.682806	+	0.682806i
$776$	10.6612	−	6.15527i	0.382716	−	0.220961i
$777$		0			0
$778$	8.10162	+	30.2356i	0.290457	+	1.08400i
$779$	−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
$785$	−2.85089	−	10.6397i	−0.101753	−	0.379746i
$786$		0			0
$787$	13.9131	−	13.9131i	0.495948	−	0.495948i	−0.414226	−	0.910174i	$-0.635948\pi$
$787$	13.9131	−	13.9131i	0.495948	−	0.495948i	0.910174	+	0.414226i	$0.135948\pi$
$788$	0.182228	−	0.680083i	0.00649159	−	0.0242270i
$789$		0			0
$790$			2.31326i			0.0823021i
$791$	−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
$796$	4.95735	−	8.58639i	0.175709	−	0.304337i
$797$	−4.40957			−0.156195			−0.0780974	−	0.996946i	$-0.524885\pi$
$797$	−4.40957			−0.156195			−0.0780974	+	0.996946i	$0.524885\pi$
$798$		0			0
$799$	−1.30077	+	4.85454i	−0.0460179	+	0.171741i
$800$	−2.94136	+	0.788134i	−0.103993	+	0.0278647i
$801$		0			0
$802$	10.2566	−	17.7649i	0.362172	−	0.627301i
$803$	−6.48209			−0.228748
$804$		0			0
$805$	0.710950	−	0.410467i	0.0250577	−	0.0144671i
$806$	1.92906	+	31.7711i	0.0679482	+	1.11909i
$807$		0			0
$808$	−7.20645	−	7.20645i	−0.253522	−	0.253522i
$809$	17.1929	−	9.92632i	0.604470	−	0.348991i	−0.166328	−	0.986070i	$-0.553191\pi$
$809$	17.1929	−	9.92632i	0.604470	−	0.348991i	0.770798	+	0.637080i	$0.219858\pi$
$810$		0			0
$811$	6.11440	+	6.11440i	0.214706	+	0.214706i	0.806263	−	0.591557i	$-0.201487\pi$
$811$	6.11440	+	6.11440i	0.214706	+	0.214706i	−0.591557	+	0.806263i	$0.701487\pi$
$812$	1.00668	+	0.269740i	0.0353277	+	0.00946602i
$813$		0			0
$814$	−45.5017	−	12.1921i	−1.59483	−	0.427334i
$815$			9.67095i			0.338758i
$816$		0			0
$817$	43.4114	−	43.4114i	1.51877	−	1.51877i
$818$	9.79619			0.342516
$819$		0			0
$820$	−2.28837			−0.0799133
$821$	22.9604	−	22.9604i	0.801323	−	0.801323i	−0.181979	−	0.983302i	$-0.558250\pi$
$821$	22.9604	−	22.9604i	0.801323	−	0.801323i	0.983302	+	0.181979i	$0.0582504\pi$
$822$		0			0
$823$			2.84039i			0.0990096i	0.998774	+	0.0495048i	$0.0157643\pi$
$823$			2.84039i			0.0990096i	−0.998774	+	0.0495048i	$0.984236\pi$
$824$	9.52809	+	2.55304i	0.331927	+	0.0889395i
$825$		0			0
$826$	11.7100	+	3.13769i	0.407444	+	0.109174i
$827$	−0.354454	−	0.354454i	−0.0123256	−	0.0123256i	0.700917	−	0.713243i	$-0.252774\pi$
$827$	−0.354454	−	0.354454i	−0.0123256	−	0.0123256i	−0.713243	+	0.700917i	$0.752774\pi$
$828$		0			0
$829$	−12.9034	+	7.44977i	−0.448153	+	0.258741i	−0.707050	−	0.707164i	$-0.749974\pi$
$829$	−12.9034	+	7.44977i	−0.448153	+	0.258741i	0.258897	+	0.965905i	$0.416641\pi$
$830$	16.0924	+	16.0924i	0.558574	+	0.558574i
$831$		0			0
$832$	−1.61022	+	3.22602i	−0.0558243	+	0.111842i
$833$	17.3195	−	9.99940i	0.600084	−	0.346459i
$834$		0			0
$835$	−22.1617			−0.766936
$836$	21.3006	−	36.8937i	0.736696	−	1.27600i
$837$		0			0
$838$	1.67290	−	0.448252i	0.0577893	−	0.0154846i
$839$	−3.11235	+	11.6155i	−0.107450	+	0.401010i	−0.998612	−	0.0526764i	$-0.983225\pi$
$839$	−3.11235	+	11.6155i	−0.107450	+	0.401010i	0.891161	+	0.453687i	$0.149891\pi$
$840$		0			0
$841$	27.9385			0.963397
$842$	1.77766	−	3.07900i	0.0612622	−	0.106109i
$843$		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
$848$		−	2.77082i		−	0.0951502i
$849$		0			0
$850$	−2.63718	+	9.84209i	−0.0904545	+	0.337581i
$851$	3.32467	−	3.32467i	0.113968	−	0.113968i
$852$		0			0
$853$	3.13735	+	11.7087i	0.107421	+	0.400900i	0.998609	−	0.0527349i	$-0.0167938\pi$
$853$	3.13735	+	11.7087i	0.107421	+	0.400900i	−0.891188	+	0.453635i	$0.850127\pi$
$854$	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	$0.471598\pi$
$857$	−23.9473	+	41.4780i	−0.818025	+	1.41686i	−0.907135	+	0.420839i	$0.861736\pi$
$858$		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	$-0.538657\pi$
$860$	−3.03269	−	11.3182i	−0.103414	−	0.385946i
$861$		0			0
$862$	12.8406	−	7.41354i	0.437354	−	0.252506i
$863$	23.3989	−	23.3989i	0.796508	−	0.796508i	−0.186035	−	0.982543i	$-0.559564\pi$
$863$	23.3989	−	23.3989i	0.796508	−	0.796508i	0.982543	+	0.186035i	$0.0595639\pi$
$864$		0			0
$865$	−0.942509	−	3.51749i	−0.0320463	−	0.119598i
$866$	11.0962	−	2.97320i	0.377063	−	0.101034i
$867$		0			0
$868$	−7.73364	−	4.46502i	−0.262497	−	0.151553i
$869$	9.29356	−	2.49020i	0.315263	−	0.0844744i
$870$		0			0
$871$	4.00717	+	0.817118i	0.135778	+	0.0276870i
$872$			9.89396i			0.335052i
$873$		0			0
$874$	2.12604	+	3.68241i	0.0719144	+	0.124559i
$875$	5.68927	+	9.85410i	0.192332	+	0.333130i
$876$		0			0
$877$	6.72087	+	6.72087i	0.226948	+	0.226948i	0.811416	−	0.584469i	$-0.198697\pi$
$877$	6.72087	+	6.72087i	0.226948	+	0.226948i	−0.584469	+	0.811416i	$0.698697\pi$
$878$	−28.7808	−	28.7808i	−0.971306	−	0.971306i
$879$		0			0
$880$	−4.06542	−	7.04151i	−0.137045	−	0.237369i
$881$	12.5122	+	21.6718i	0.421548	+	0.730143i	0.996091	−	0.0883317i	$-0.0281536\pi$
$881$	12.5122	+	21.6718i	0.421548	+	0.730143i	−0.574543	+	0.818474i	$0.694820\pi$
$882$		0			0
$883$			36.5915i			1.23140i	0.787980	+	0.615701i	$0.211127\pi$
$883$			36.5915i			1.23140i	−0.787980	+	0.615701i	$0.788873\pi$
$884$	6.65441	+	10.0634i	0.223812	+	0.338469i
$885$		0			0
$886$	11.9047	−	3.18985i	0.399946	−	0.107165i
$887$	−42.2738	−	24.4068i	−1.41942	−	0.819500i	−0.423168	−	0.906051i	$-0.639082\pi$
$887$	−42.2738	−	24.4068i	−1.41942	−	0.819500i	−0.996247	+	0.0865513i	$0.972415\pi$
$888$		0			0
$889$	−14.7921	+	3.96353i	−0.496111	+	0.132933i
$890$	−1.09588	−	4.08989i	−0.0367341	−	0.137094i
$891$		0			0
$892$	−20.6159	+	20.6159i	−0.690271	+	0.690271i
$893$	−9.52888	+	5.50150i	−0.318872	+	0.184101i
$894$		0			0
$895$	−1.29994	−	4.85143i	−0.0434521	−	0.162165i
$896$	−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
$902$	2.46341	+	9.19356i	0.0820225	+	0.306112i
$903$		0			0
$904$	−7.17524	+	7.17524i	−0.238645	+	0.238645i
$905$	5.91456	−	22.0734i	0.196606	−	0.733745i
$906$		0			0
$907$		−	8.42784i		−	0.279842i	−0.990163	−	0.139921i	$-0.955315\pi$
$907$		−	8.42784i		−	0.279842i	0.990163	−	0.139921i	$-0.0446848\pi$
$908$	−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
$913$	47.3281	−	81.9746i	1.56633	−	2.71296i
$914$	−30.1263			−0.996490
$915$		0			0
$916$	2.55392	−	9.53135i	0.0843838	−	0.314925i
$917$	−3.71262	+	0.994793i	−0.122601	+	0.0328510i
$918$		0			0
$919$	11.5951	−	20.0833i	0.382488	−	0.662488i	−0.608929	−	0.793224i	$-0.708401\pi$
$919$	11.5951	−	20.0833i	0.382488	−	0.662488i	0.991417	+	0.130736i	$0.0417341\pi$
$920$	0.811549			0.0267560
$921$		0			0
$922$	24.6586	−	14.2366i	0.812087	−	0.468859i
$923$	7.55681	−	37.0588i	0.248735	−	1.21980i
$924$		0			0
$925$	17.4421	+	17.4421i	0.573491	+	0.573491i
$926$	3.13507	−	1.81003i	0.103025	−	0.0594814i
$927$		0			0
$928$	0.728518	+	0.728518i	0.0239148	+	0.0239148i
$929$	6.81483	+	1.82603i	0.223587	+	0.0599100i	0.368873	−	0.929480i	$-0.379744\pi$
$929$	6.81483	+	1.82603i	0.223587	+	0.0599100i	−0.145286	+	0.989390i	$0.546410\pi$
$930$		0			0
$931$	42.2917	+	11.3320i	1.38605	+	0.371392i
$932$			2.06808i			0.0677421i
$933$		0			0
$934$	−25.8967	+	25.8967i	−0.847366	+	0.847366i
$935$	−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	$0.776239\pi$
$938$	−0.811318	+	0.811318i	−0.0264905	+	0.0264905i
$939$		0			0
$940$			2.10003i			0.0684953i
$941$	−37.7889	−	10.1255i	−1.23188	−	0.330082i	−0.416570	−	0.909104i	$-0.636768\pi$
$941$	−37.7889	−	10.1255i	−1.23188	−	0.330082i	−0.815312	+	0.579022i	$0.803435\pi$
$942$		0			0
$943$	−0.917621	−	0.245876i	−0.0298819	−	0.00800682i
$944$	8.47432	+	8.47432i	0.275816	+	0.275816i
$945$		0			0
$946$	−42.2063	+	24.3678i	−1.37224	+	0.792266i
$947$	36.4436	+	36.4436i	1.18426	+	1.18426i	0.978630	+	0.205628i	$0.0659237\pi$
$947$	36.4436	+	36.4436i	1.18426	+	1.18426i	0.205628	+	0.978630i	$0.434076\pi$
$948$		0			0
$949$	3.81183	−	1.27354i	0.123737	−	0.0413409i
$950$	−19.3189	+	11.1538i	−0.626787	+	0.361876i
$951$		0			0
$952$	−3.38480			−0.109702
$953$	−16.8331	+	29.1557i	−0.545276	+	0.944446i	0.453313	+	0.891351i	$0.350242\pi$
$953$	−16.8331	+	29.1557i	−0.545276	+	0.944446i	−0.998589	+	0.0530947i	$0.983091\pi$
$954$		0			0
$955$	−34.3544	+	9.20524i	−1.11168	+	0.297875i
$956$	−5.10931	+	19.0682i	−0.165247	+	0.616710i
$957$		0			0
$958$	−5.04908			−0.163128
$959$	2.94365	−	5.09856i	0.0950555	−	0.164641i
$960$		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
$965$		−	17.6393i		−	0.567828i
$966$		0			0
$967$	−11.0432	+	41.2138i	−0.355126	+	1.32535i	0.525200	+	0.850979i	$0.323990\pi$
$967$	−11.0432	+	41.2138i	−0.355126	+	1.32535i	−0.880326	+	0.474369i	$0.842676\pi$
$968$	−16.1348	+	16.1348i	−0.518592	+	0.518592i
$969$		0			0
$970$	−4.45486	−	16.6258i	−0.143037	−	0.533821i
$971$	−19.5275	−	11.2742i	−0.626666	−	0.361806i	0.152794	−	0.988258i	$-0.451173\pi$
$971$	−19.5275	−	11.2742i	−0.626666	−	0.361806i	−0.779460	+	0.626452i	$0.784506\pi$
$972$		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
$977$	6.17968	+	23.0629i	0.197705	+	0.737847i	0.991550	+	0.129726i	$0.0414098\pi$
$977$	6.17968	+	23.0629i	0.197705	+	0.737847i	−0.793844	+	0.608121i	$0.791924\pi$
$978$		0			0
$979$	−15.2515	+	8.80546i	−0.487440	+	0.281424i
$980$	5.90894	−	5.90894i	0.188754	−	0.188754i
$981$		0			0
$982$	0.511224	+	1.90791i	0.0163138	+	0.0608839i
$983$	−25.2494	+	6.76555i	−0.805330	+	0.215788i	−0.637923	−	0.770100i	$-0.720206\pi$
$983$	−25.2494	+	6.76555i	−0.805330	+	0.215788i	−0.167407	+	0.985888i	$0.553539\pi$
$984$		0			0
$985$	−0.852530	−	0.492208i	−0.0271638	−	0.0156831i
$986$	3.32996	−	0.892260i	0.106048	−	0.0284154i
$987$		0			0
$988$	−5.27740	+	25.8805i	−0.167896	+	0.823368i
$989$		−	4.86436i		−	0.154678i
$990$		0			0
$991$	−5.16138	−	8.93977i	−0.163957	−	0.283981i	0.772328	−	0.635224i	$-0.219092\pi$
$991$	−5.16138	−	8.93977i	−0.163957	−	0.283981i	−0.936284	+	0.351243i	$0.885759\pi$
$992$	−4.41397	−	7.64523i	−0.140144	−	0.242736i
$993$		0			0
$994$	7.50316	+	7.50316i	0.237986	+	0.237986i
$995$	−9.80224	−	9.80224i	−0.310752	−	0.310752i
$996$		0			0
$997$	−17.0184	−	29.4767i	−0.538978	−	0.933537i	−0.998959	−	0.0456087i	$-0.985477\pi$
$997$	−17.0184	−	29.4767i	−0.538978	−	0.933537i	0.459981	−	0.887929i	$-0.347856\pi$
$998$	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.bb.a.89.3		56
3.2	odd	2		234.2.y.a.11.10	✓	56
9.4	even	3		234.2.z.a.167.7	yes	56
9.5	odd	6		702.2.bc.a.557.10		56
13.6	odd	12		702.2.bc.a.305.10		56
39.32	even	12		234.2.z.a.227.7	yes	56
117.32	even	12	inner	702.2.bb.a.71.3		56
117.58	odd	12		234.2.y.a.149.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.10	✓	56	3.2	odd	2
234.2.y.a.149.10	yes	56	117.58	odd	12
234.2.z.a.167.7	yes	56	9.4	even	3
234.2.z.a.227.7	yes	56	39.32	even	12
702.2.bb.a.71.3		56	117.32	even	12	inner
702.2.bb.a.89.3		56	1.1	even	1	trivial
702.2.bc.a.305.10		56	13.6	odd	12
702.2.bc.a.557.10		56	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.35053 - 0.361873i) q^{5} +(0.977097 + 0.261812i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.21085 - 0.699086i) q^{10} +(-4.11206 - 4.11206i) q^{11} +(3.22602 + 1.61022i) q^{13} +(-0.876041 + 0.505782i) q^{14} -1.00000 q^{16} +(-1.67305 + 2.89781i) q^{17} +(-7.07605 + 1.89602i) q^{19} +(-0.361873 + 1.35053i) q^{20} +5.81533 q^{22} +(-0.290218 + 0.502672i) q^{23} +(-2.63715 - 1.52256i) q^{25} +(-3.41974 + 1.14254i) q^{26} +(0.261812 - 0.977097i) q^{28} +1.03028i q^{29} +(2.28484 - 8.52714i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.866036 - 3.23209i) q^{34} +(-1.22486 - 0.707171i) q^{35} +(-7.82443 - 2.09655i) q^{37} +(3.66283 - 6.34422i) q^{38} +(-0.699086 - 1.21085i) q^{40} +(0.423606 + 1.58092i) q^{41} +(-7.25776 + 4.19027i) q^{43} +(-4.11206 + 4.11206i) q^{44} +(-0.150228 - 0.560658i) q^{46} +(1.45080 - 0.388741i) q^{47} +(-5.17601 - 2.98837i) q^{49} +(2.94136 - 0.788134i) q^{50} +(1.61022 - 3.22602i) q^{52} +2.77082i q^{53} +(4.06542 + 7.04151i) q^{55} +(0.505782 + 0.876041i) q^{56} +(-0.728518 - 0.728518i) q^{58} +(-8.47432 - 8.47432i) q^{59} +(-1.41408 - 2.44926i) q^{61} +(4.41397 + 7.64523i) q^{62} +1.00000i q^{64} +(-3.77414 - 3.34206i) q^{65} +(1.09561 - 0.293568i) q^{67} +(2.89781 + 1.67305i) q^{68} +(1.36615 - 0.366058i) q^{70} +(-2.71495 - 10.1323i) q^{71} +(0.788181 - 0.788181i) q^{73} +(7.01519 - 4.05022i) q^{74} +(1.89602 + 7.07605i) q^{76} +(-2.94129 - 5.09447i) q^{77} +(-0.827245 + 1.43283i) q^{79} +(1.35053 + 0.361873i) q^{80} +(-1.41741 - 0.818343i) q^{82} +(4.21280 + 15.7224i) q^{83} +(3.30815 - 3.30815i) q^{85} +(2.16904 - 8.09498i) q^{86} -5.81533i q^{88} +(0.783797 - 2.92517i) q^{89} +(2.73056 + 2.41795i) q^{91} +(0.502672 + 0.290218i) q^{92} +(-0.750990 + 1.30075i) q^{94} +10.2425 q^{95} +(3.18620 - 11.8911i) q^{97} +(5.77308 - 1.54689i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Introduction

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