LMFDB - Embedded newform 702.2.bb.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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([10, 5]))

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

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

chi := DirichletCharacter("702.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

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: 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			71.3
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.547833	−	0.836588i	$-0.684547\pi$
$5$	−1.35053	+	0.361873i	−0.603975	+	0.161835i	−0.0561429	+	0.998423i	$0.517880\pi$
$6$		0			0
$7$	0.977097	−	0.261812i	0.369308	−	0.0989557i	−0.0693918	−	0.997589i	$-0.522106\pi$
$7$	0.977097	−	0.261812i	0.369308	−	0.0989557i	0.438700	+	0.898634i	$0.355439\pi$
$8$	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	−0.279764	+	0.960069i	$0.590256\pi$
$11$	−4.11206	+	4.11206i	−1.23983	+	1.23983i	−0.960069	+	0.279764i	$0.909744\pi$
$12$		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	0.588636	−	0.808398i	$-0.299665\pi$
$17$	−1.67305	−	2.89781i	−0.405775	−	0.702823i	−0.994411	+	0.105575i	$0.966332\pi$
$18$		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	$0.900961\pi$
$20$	−0.361873	−	1.35053i	−0.0809174	−	0.301988i
$21$		0			0
$22$	5.81533			1.23983
$23$	−0.290218	−	0.502672i	−0.0605146	−	0.104814i	0.834181	−	0.551491i	$-0.185941\pi$
$23$	−0.290218	−	0.502672i	−0.0605146	−	0.104814i	−0.894696	+	0.446676i	$0.852608\pi$
$24$		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	$-0.969504\pi$
$29$		−	1.03028i		−	0.191318i	0.995414	−	0.0956592i	$-0.0304959\pi$
$30$		0			0
$31$	2.28484	+	8.52714i	0.410369	+	1.53152i	0.793933	+	0.608005i	$0.208030\pi$
$31$	2.28484	+	8.52714i	0.410369	+	1.53152i	−0.383564	+	0.923514i	$0.625303\pi$
$32$	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	−0.836265	−	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
$41$	0.423606	−	1.58092i	0.0661561	−	0.246898i	−0.924927	−	0.380146i	$-0.875874\pi$
$41$	0.423606	−	1.58092i	0.0661561	−	0.246898i	0.991083	+	0.133248i	$0.0425406\pi$
$42$		0			0
$43$	−7.25776	−	4.19027i	−1.10680	−	0.639010i	−0.168800	−	0.985650i	$-0.553989\pi$
$43$	−7.25776	−	4.19027i	−1.10680	−	0.639010i	−0.937998	+	0.346640i	$0.887322\pi$
$44$	−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	0.363072	−	0.931761i	$-0.381728\pi$
$47$	1.45080	+	0.388741i	0.211621	+	0.0567037i	−0.151451	+	0.988465i	$0.548395\pi$
$48$		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	$-0.939054\pi$
$53$		−	2.77082i		−	0.380601i	0.981726	−	0.190300i	$-0.0609462\pi$
$54$		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	−0.109248	+	0.994014i	$0.534844\pi$
$59$	−8.47432	+	8.47432i	−1.10326	+	1.10326i	−0.994014	+	0.109248i	$0.965156\pi$
$60$		0			0
$61$	−1.41408	+	2.44926i	−0.181054	+	0.313595i	−0.942240	−	0.334939i	$-0.891284\pi$
$61$	−1.41408	+	2.44926i	−0.181054	+	0.313595i	0.761186	+	0.648534i	$0.224618\pi$
$62$	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	0.325122	−	0.945672i	$-0.394595\pi$
$67$	1.09561	+	0.293568i	0.133850	+	0.0358650i	−0.191272	+	0.981537i	$0.561261\pi$
$68$	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	0.594886	+	0.803810i	$0.297197\pi$
$71$	−2.71495	+	10.1323i	−0.322205	+	1.20249i	−0.917091	+	0.398677i	$0.869470\pi$
$72$		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	$0.729222\pi$
$74$	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	0.815730	−	0.578433i	$-0.196335\pi$
$79$	−0.827245	−	1.43283i	−0.0930723	−	0.161206i	−0.908802	+	0.417227i	$0.863002\pi$
$80$	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	−0.202906	−	0.979198i	$-0.565039\pi$
$83$	4.21280	−	15.7224i	0.462415	−	1.72576i	0.665321	−	0.746557i	$-0.268295\pi$
$84$		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	0.994944	−	0.100430i	$-0.0320218\pi$
$89$	0.783797	+	2.92517i	0.0830824	+	0.310068i	−0.911862	+	0.410497i	$0.865355\pi$
$90$		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	0.915801	+	0.401632i	$0.131557\pi$
$97$	3.18620	+	11.8911i	0.323510	+	1.20736i	−0.592291	+	0.805724i	$0.701777\pi$
$98$	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	0.857853	−	0.513896i	$-0.171798\pi$
$103$	8.54265	+	4.93210i	0.841732	+	0.485974i	−0.0161205	+	0.999870i	$0.505132\pi$
$104$	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	0.853775	−	0.520642i	$-0.174308\pi$
$107$	8.58323	+	4.95553i	0.829773	+	0.479069i	−0.0240022	+	0.999712i	$0.507641\pi$
$108$		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	$0.0928694\pi$
$110$	−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	$-0.841619\pi$
$113$		−	10.1473i		−	0.954580i	0.878746	−	0.477290i	$-0.158381\pi$
$114$		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	−0.211267	−	0.977428i	$-0.567759\pi$
$127$	−13.1106	−	7.56941i	−1.16338	−	0.671677i	−0.952111	+	0.305752i	$0.901092\pi$
$128$	−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	0.349314	−	0.937006i	$-0.386415\pi$
$131$	−3.29059	−	1.89982i	−0.287500	−	0.165988i	−0.636814	+	0.771018i	$0.719748\pi$
$132$		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	0.999944	−	0.0105460i	$-0.00335697\pi$
$137$	1.50633	+	5.62169i	0.128694	+	0.480293i	−0.871250	+	0.490839i	$0.836690\pi$
$138$		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	0.155172	−	0.987887i	$-0.450407\pi$
$149$	−10.1646	−	10.1646i	−0.832715	−	0.832715i	−0.987887	+	0.155172i	$0.950407\pi$
$150$		0			0
$151$	0.728858	−	2.72013i	0.0593136	−	0.221361i	−0.929907	−	0.367795i	$-0.880113\pi$
$151$	0.728858	−	2.72013i	0.0593136	−	0.221361i	0.989220	+	0.146434i	$0.0467795\pi$
$152$	−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	−0.664931	−	0.746904i	$-0.731539\pi$
$157$	3.93908	−	6.82268i	0.314372	−	0.544509i	0.979304	+	0.202395i	$0.0648726\pi$
$158$	−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	0.859701	+	0.510797i	$0.170650\pi$
$163$	−1.79021	+	6.68116i	−0.140220	+	0.523309i	−0.999922	+	0.0125123i	$0.996017\pi$
$164$	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	0.796809	−	0.604231i	$-0.206519\pi$
$167$	15.3104	+	4.10240i	1.18475	+	0.317453i	0.387942	+	0.921684i	$0.373186\pi$
$168$		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	−0.812266	−	0.583288i	$-0.801766\pi$
$173$	1.30226	−	2.25559i	0.0990092	−	0.171489i	0.911275	+	0.411799i	$0.135099\pi$
$174$		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	−0.791062	−	0.611736i	$-0.790471\pi$
$179$	1.79612	−	3.11097i	0.134248	−	0.232525i	0.925310	+	0.379211i	$0.123805\pi$
$180$		0			0
$181$		−	16.3443i		−	1.21486i	−0.794373	−	0.607430i	$-0.792201\pi$
$181$		−	16.3443i		−	1.21486i	0.794373	−	0.607430i	$-0.207799\pi$
$182$	−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	0.992608	+	0.121361i	$0.0387259\pi$
$191$	22.0297	+	12.7189i	1.59401	+	0.920305i	0.601406	+	0.798944i	$0.294607\pi$
$192$		0			0
$193$	3.26525	−	12.1861i	0.235038	−	0.877172i	−0.743094	−	0.669187i	$-0.766643\pi$
$193$	3.26525	−	12.1861i	0.235038	−	0.877172i	0.978132	−	0.207985i	$-0.0666906\pi$
$194$	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	−0.234511	−	0.972114i	$-0.575349\pi$
$197$	0.680083	−	0.182228i	0.0484539	−	0.0129832i	0.282965	+	0.959130i	$0.408682\pi$
$198$		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	$0.219033\pi$
$200$	−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	0.950933	−	0.309396i	$-0.100127\pi$
$211$	3.01444	+	5.22116i	0.207522	+	0.359439i	−0.743411	+	0.668835i	$0.766793\pi$
$212$	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	−0.536889	+	0.843653i	$0.680401\pi$
$223$	−20.6159	+	20.6159i	−1.38054	+	1.38054i	−0.843653	+	0.536889i	$0.819599\pi$
$224$	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	−0.691809	−	0.722080i	$-0.743186\pi$
$227$	−14.0103	+	3.75404i	−0.929894	+	0.249164i	−0.238084	+	0.971244i	$0.576519\pi$
$228$		0			0
$229$	9.53135	−	2.55392i	0.629849	−	0.168768i	0.0702479	−	0.997530i	$-0.477621\pi$
$229$	9.53135	−	2.55392i	0.629849	−	0.168768i	0.559601	+	0.828762i	$0.310954\pi$
$230$		−	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	−0.815910	−	0.578179i	$-0.803764\pi$
$239$	−19.0682	+	5.10931i	−1.23342	+	0.330494i	−0.417510	+	0.908672i	$0.637097\pi$
$240$		0			0
$241$	9.79587	−	2.62479i	0.631007	−	0.169078i	0.0708805	−	0.997485i	$-0.477419\pi$
$241$	9.79587	−	2.62479i	0.631007	−	0.169078i	0.560127	+	0.828407i	$0.310752\pi$
$242$	−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	0.976655	−	0.214815i	$-0.0689150\pi$
$251$	4.78920	+	8.29514i	0.302292	+	0.523585i	−0.674363	+	0.738400i	$0.735582\pi$
$252$		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	0.941921	−	0.335834i	$-0.109018\pi$
$257$	2.88755	+	5.00138i	0.180120	+	0.311977i	−0.761801	+	0.647811i	$0.775685\pi$
$258$		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	$-0.956118\pi$
$263$		−	4.45725i		−	0.274846i	0.990512	−	0.137423i	$-0.0438819\pi$
$264$		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	−0.107435	−	0.994212i	$-0.534264\pi$
$269$	11.4786	−	6.62715i	0.699860	−	0.404064i	0.807295	+	0.590148i	$0.200931\pi$
$270$		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
$275$	4.58326	−	17.1050i	0.276381	−	1.03147i
$276$		0			0
$277$	−16.8351	−	9.71973i	−1.01152	−	0.584002i	−0.0998845	−	0.994999i	$-0.531847\pi$
$277$	−16.8351	−	9.71973i	−1.01152	−	0.584002i	−0.911637	+	0.410997i	$0.865181\pi$
$278$	−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	0.300438	−	0.953801i	$-0.402867\pi$
$281$	1.40349	+	0.376063i	0.0837250	+	0.0224340i	−0.216713	+	0.976235i	$0.569534\pi$
$282$		0			0
$283$	−17.9556	+	10.3666i	−1.06735	+	0.616233i	−0.927455	−	0.373934i	$-0.878009\pi$
$283$	−17.9556	+	10.3666i	−1.06735	+	0.616233i	−0.139892	+	0.990167i	$0.544675\pi$
$284$	−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	−0.999818	−	0.0190656i	$-0.993931\pi$
$293$	−16.7878	+	16.7878i	−0.980753	+	0.980753i	0.0190656	+	0.999818i	$0.493931\pi$
$294$		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	0.989241	−	0.146294i	$-0.0467346\pi$
$307$	14.7696	+	14.7696i	0.842947	+	0.842947i	−0.146294	+	0.989241i	$0.546735\pi$
$308$	−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	0.124602	+	0.992207i	$0.460235\pi$
$311$	−14.0548	+	24.3437i	−0.796976	+	1.38040i	−0.921577	+	0.388195i	$0.873099\pi$
$312$		0			0
$313$	8.76521	+	15.1818i	0.495439	+	0.858125i	0.999986	−	0.00525876i	$-0.00167392\pi$
$313$	8.76521	+	15.1818i	0.495439	+	0.858125i	−0.504547	+	0.863384i	$0.668341\pi$
$314$	−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	0.596094	+	0.802915i	$0.296719\pi$
$317$	−5.72585	+	21.3692i	−0.321596	+	1.20021i	−0.917690	+	0.397298i	$0.869948\pi$
$318$		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	0.917279	+	0.398246i	$0.130381\pi$
$331$	5.85855	+	21.8644i	0.322015	+	1.20178i	−0.595263	+	0.803531i	$0.702952\pi$
$332$	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	0.999456	−	0.0329922i	$-0.0105036\pi$
$337$	26.9968	+	15.5866i	1.47061	+	0.849058i	0.471156	+	0.882050i	$0.343837\pi$
$338$	−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	$0.184019\pi$
$347$			20.3582i			1.09289i	−0.837496	+	0.546444i	$0.815981\pi$
$348$		0			0
$349$	−20.7926	−	20.7926i	−1.11300	−	1.11300i	−0.992743	−	0.120259i	$-0.961627\pi$
$349$	−20.7926	−	20.7926i	−1.11300	−	1.11300i	−0.120259	−	0.992743i	$-0.538373\pi$
$350$	3.08033			0.164651
$351$		0			0
$352$	−5.81533			−0.309958
$353$	−8.11406	−	8.11406i	−0.431868	−	0.431868i	0.457395	−	0.889263i	$-0.348782\pi$
$353$	−8.11406	−	8.11406i	−0.431868	−	0.431868i	−0.889263	+	0.457395i	$0.848782\pi$
$354$		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	0.511605	−	0.859221i	$-0.329051\pi$
$359$	25.9734	−	25.9734i	1.37083	−	1.37083i	0.859221	−	0.511605i	$-0.170949\pi$
$360$		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	0.949914	+	0.312511i	$0.101170\pi$
$379$	5.51954	+	20.5992i	0.283520	+	1.05811i	−0.666394	+	0.745600i	$0.732163\pi$
$380$			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	0.432612	−	0.901580i	$-0.357592\pi$
$383$	−9.17790	−	9.17790i	−0.468969	−	0.468969i	−0.901580	+	0.432612i	$0.857592\pi$
$384$		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	0.923760	+	0.382972i	$0.125099\pi$
$389$	15.6511	+	27.1085i	0.793543	+	1.37446i	−0.130216	+	0.991486i	$0.541567\pi$
$390$		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	−0.947852	−	0.318710i	$-0.896750\pi$
$397$	0.644906	−	2.40682i	0.0323669	−	0.120795i	0.980219	+	0.197915i	$0.0634170\pi$
$398$	−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	−0.272444	−	0.962172i	$-0.587832\pi$
$401$	−19.8142	−	5.30920i	−0.989473	−	0.265129i	−0.717029	+	0.697043i	$0.754499\pi$
$402$		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	−0.857312	−	0.514797i	$-0.827867\pi$
$409$	−6.92695	+	6.92695i	−0.342516	+	0.342516i	0.514797	+	0.857312i	$0.327867\pi$
$410$	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	−0.536189	−	0.844098i	$-0.680137\pi$
$419$	−1.49988	+	0.865956i	−0.0732739	+	0.0423047i	0.462915	+	0.886402i	$0.346803\pi$
$420$		0			0
$421$	−3.43418	−	0.920185i	−0.167372	−	0.0448471i	0.174160	−	0.984717i	$-0.444279\pi$
$421$	−3.43418	−	0.920185i	−0.167372	−	0.0448471i	−0.341532	+	0.939870i	$0.610946\pi$
$422$	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	−0.586684	−	0.809816i	$-0.699567\pi$
$431$	−14.3219	+	3.83753i	−0.689860	+	0.184847i	−0.103176	+	0.994663i	$0.532900\pi$
$432$		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	$0.422352\pi$
$434$	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	$-0.576437\pi$
$439$		−	40.7022i		−	1.94261i	0.237834	−	0.971306i	$-0.423563\pi$
$440$	−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	−0.731645	−	0.681686i	$-0.761247\pi$
$443$	−10.6734	+	6.16232i	−0.507111	+	0.292780i	0.224535	+	0.974466i	$0.427914\pi$
$444$		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	−0.453024	−	0.891498i	$-0.649655\pi$
$449$	−27.3580	−	7.33055i	−1.29110	−	0.345950i	−0.838080	+	0.545548i	$0.816322\pi$
$450$		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	−0.00350346	−	0.999994i	$-0.501115\pi$
$457$	21.3025	−	21.3025i	0.996490	−	0.996490i	0.999994	+	0.00350346i	$0.00111519\pi$
$458$	−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	−0.834215	−	0.551440i	$-0.814079\pi$
$461$	−27.5031	+	7.36943i	−1.28095	+	0.343228i	−0.446731	+	0.894668i	$0.647412\pi$
$462$		0			0
$463$	−3.49672	+	0.936943i	−0.162506	+	0.0435434i	−0.339155	−	0.940731i	$-0.610141\pi$
$463$	−3.49672	+	0.936943i	−0.162506	+	0.0435434i	0.176649	+	0.984274i	$0.443474\pi$
$464$			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	−0.620823	−	0.783951i	$-0.713201\pi$
$479$	3.57024	−	3.57024i	0.163128	−	0.163128i	0.783951	+	0.620823i	$0.213201\pi$
$480$		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	−0.456443	−	0.889753i	$-0.650877\pi$
$487$	−28.6137	−	7.66702i	−1.29661	−	0.347426i	−0.840167	+	0.542327i	$0.817543\pi$
$488$	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	0.887450	−	0.460904i	$-0.152475\pi$
$491$	0.987608	+	1.71059i	0.0445701	+	0.0771978i	−0.842880	+	0.538102i	$0.819142\pi$
$492$		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	0.985253	−	0.171105i	$-0.0547336\pi$
$499$	1.03754	+	3.87214i	0.0464465	+	0.173341i	−0.938806	+	0.344445i	$0.888067\pi$
$500$	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	−0.635251	−	0.772305i	$-0.719103\pi$
$503$	−6.37037	+	3.67794i	−0.284041	+	0.163991i	0.351211	+	0.936297i	$0.385770\pi$
$504$		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	−0.834783	−	0.550579i	$-0.814407\pi$
$509$	3.68759	−	13.7623i	0.163449	−	0.610002i	0.998233	−	0.0594233i	$-0.0189262\pi$
$510$		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	$0.215000\pi$
$521$			28.5428i			1.25048i	−0.780431	+	0.625242i	$0.785000\pi$
$522$		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	$0.0536037\pi$
$524$	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	0.994029	−	0.109116i	$-0.0348019\pi$
$541$	20.5826	+	20.5826i	0.884913	+	0.884913i	−0.109116	+	0.994029i	$0.534802\pi$
$542$	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	−0.999967	−	0.00812189i	$-0.997415\pi$
$547$	−11.8581	−	20.5389i	−0.507017	−	0.878180i	0.492950	−	0.870058i	$-0.335919\pi$
$548$	−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	0.925189	−	0.379506i	$-0.123906\pi$
$557$	−1.55296	−	5.79572i	−0.0658010	−	0.245573i	−0.990990	+	0.133933i	$0.957239\pi$
$558$		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	−0.135440	−	0.990786i	$-0.543245\pi$
$571$	−25.3581	−	14.6405i	−1.06121	−	0.612687i	−0.925765	+	0.378099i	$0.876578\pi$
$572$	−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	−0.983616	−	0.180278i	$-0.942300\pi$
$577$	−19.2968	+	19.2968i	−0.803337	+	0.803337i	0.180278	+	0.983616i	$0.442300\pi$
$578$	−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	0.353662	−	0.935373i	$-0.384936\pi$
$587$	−14.0938	−	14.0938i	−0.581712	−	0.581712i	−0.935373	+	0.353662i	$0.884936\pi$
$588$		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	−0.637328	−	0.770593i	$-0.719960\pi$
$593$	3.24522	−	3.24522i	0.133265	−	0.133265i	0.770593	+	0.637328i	$0.219960\pi$
$594$		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	0.999949	−	0.0101486i	$-0.00323046\pi$
$599$	36.4947	+	21.0702i	1.49113	+	0.860906i	0.491185	+	0.871055i	$0.336564\pi$
$600$		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	0.876428	−	0.481533i	$-0.159920\pi$
$613$	−3.05394	−	11.3975i	−0.123347	−	0.460339i	−0.999775	+	0.0211942i	$0.993253\pi$
$614$		−	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	0.996117	−	0.0880383i	$-0.0280598\pi$
$617$	22.5562	+	22.5562i	0.908079	+	0.908079i	−0.0880383	+	0.996117i	$0.528060\pi$
$618$		0			0
$619$	5.99924	−	22.3895i	0.241130	−	0.899909i	−0.734160	−	0.678977i	$-0.762424\pi$
$619$	5.99924	−	22.3895i	0.241130	−	0.899909i	0.975289	−	0.220932i	$-0.0709097\pi$
$620$	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	−0.729949	−	0.683501i	$-0.760456\pi$
$631$	6.12810	−	22.8704i	0.243956	−	0.910456i	0.973905	−	0.226955i	$-0.0728770\pi$
$632$	−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	−0.429988	−	0.902835i	$-0.641482\pi$
$641$	14.3524	−	24.8590i	0.566884	−	0.981872i	0.996872	−	0.0790369i	$-0.0251845\pi$
$642$		0			0
$643$	16.1427	−	16.1427i	0.636607	−	0.636607i	−0.313110	−	0.949717i	$-0.601371\pi$
$643$	16.1427	−	16.1427i	0.636607	−	0.636607i	0.949717	+	0.313110i	$0.101371\pi$
$644$	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	0.226841	+	0.973932i	$0.427160\pi$
$647$	−18.5692	+	32.1627i	−0.730029	+	1.26445i	−0.956870	+	0.290516i	$0.906173\pi$
$648$		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	0.507050	−	0.861917i	$-0.330736\pi$
$653$	38.5101	−	22.2338i	1.50702	−	0.870076i	0.999967	−	0.00815952i	$-0.00259728\pi$
$654$		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	0.492995	−	0.870032i	$-0.335902\pi$
$659$	−0.358832	−	0.207172i	−0.0139781	−	0.00807026i	−0.506973	+	0.861962i	$0.669236\pi$
$660$		0			0
$661$	−7.37782	+	27.5344i	−0.286964	+	1.07096i	0.660428	+	0.750889i	$0.270375\pi$
$661$	−7.37782	+	27.5344i	−0.286964	+	1.07096i	−0.947392	+	0.320075i	$0.896292\pi$
$662$	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	$0.0255319\pi$
$673$			4.15724i			0.160250i	−0.996785	+	0.0801248i	$0.974468\pi$
$674$	−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	−0.798595	−	0.601869i	$-0.794423\pi$
$677$	−17.6062	+	10.1649i	−0.676659	+	0.390669i	0.121936	+	0.992538i	$0.461090\pi$
$678$		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	0.0652445	−	0.997869i	$-0.479217\pi$
$683$	−9.85750	−	2.64131i	−0.377187	−	0.101067i	−0.442431	+	0.896802i	$0.645884\pi$
$684$		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	−0.149400	+	0.988777i	$0.547734\pi$
$691$	−29.9191	+	29.9191i	−1.13818	+	1.13818i	−0.988777	+	0.149400i	$0.952266\pi$
$692$	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	−0.483579	−	0.875301i	$-0.660663\pi$
$709$	−12.3741	+	3.31563i	−0.464719	+	0.124521i	0.0188591	+	0.999822i	$0.493997\pi$
$710$	−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	0.658896	−	0.752234i	$-0.271024\pi$
$719$	−8.63433	−	14.9551i	−0.322006	−	0.557731i	−0.980902	+	0.194503i	$0.937690\pi$
$720$		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	−0.707751	−	0.706462i	$-0.750290\pi$
$727$	−12.1283	+	7.00226i	−0.449813	+	0.259700i	0.257938	+	0.966161i	$0.416957\pi$
$728$	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	0.925728	−	0.378190i	$-0.123454\pi$
$733$	−1.76174	−	6.57489i	−0.0650712	−	0.242849i	−0.990799	+	0.135341i	$0.956787\pi$
$734$	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	−0.559500	−	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
$743$	8.04786	−	30.0350i	0.295247	−	1.10188i	−0.645773	−	0.763529i	$-0.723465\pi$
$743$	8.04786	−	30.0350i	0.295247	−	1.10188i	0.941021	−	0.338349i	$-0.109868\pi$
$744$		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	−0.588005	−	0.808857i	$-0.700087\pi$
$751$	−4.97436	+	2.87195i	−0.181517	+	0.104799i	0.406488	+	0.913656i	$0.366753\pi$
$752$	−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	−0.999649	−	0.0264817i	$-0.991570\pi$
$757$	−13.1210	+	22.7262i	−0.476891	+	0.825999i	0.522759	+	0.852481i	$0.324903\pi$
$758$	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	−0.753397	−	0.657566i	$-0.771586\pi$
$761$	−2.64360	+	2.64360i	−0.0958306	+	0.0958306i	0.657566	+	0.753397i	$0.271586\pi$
$762$		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	−0.731991	−	0.681314i	$-0.761409\pi$
$769$	−47.3247	−	12.6806i	−1.70657	−	0.457274i	−0.974580	+	0.224040i	$0.928075\pi$
$770$	−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	−0.931079	−	0.364818i	$-0.881131\pi$
$773$	1.60335	−	5.98377i	0.0576683	−	0.215221i	0.988747	+	0.149597i	$0.0477977\pi$
$774$		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

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.bb (of order \(12\), degree \(4\), not minimal)

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

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