LMFDB - Embedded newform 702.2.bc.a.305.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(305,702)] 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("702.305"); 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([2, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage: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			305.3
Character	$\chi$	$=$	702.305
Dual form			702.2.bc.a.557.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.266463 + 0.994452i) q^{5} +(-0.248284 - 0.248284i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.891601 - 0.514766i) q^{10} +(-3.50922 - 0.940292i) q^{11} +(-3.13452 - 1.78180i) q^{13} +(0.304085 - 0.175564i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.67236 - 2.89660i) q^{17} +(-0.969723 - 0.259837i) q^{19} +(0.727989 - 0.727989i) q^{20} +(1.81650 - 3.14628i) q^{22} -1.47052 q^{23} +(3.41219 + 1.97003i) q^{25} +(2.53236 - 2.56655i) q^{26} +(0.0908784 + 0.339163i) q^{28} +(-5.04092 + 2.91038i) q^{29} +(-5.54424 - 1.48558i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.23074 - 0.865675i) q^{34} +(0.313065 - 0.180748i) q^{35} +(4.96682 - 1.33085i) q^{37} +(0.501966 - 0.869430i) q^{38} +(0.514766 + 0.891601i) q^{40} +(-6.60980 - 6.60980i) q^{41} -2.73886i q^{43} +(2.56893 + 2.56893i) q^{44} +(0.380599 - 1.42041i) q^{46} +(-2.19251 - 8.18256i) q^{47} -6.87671i q^{49} +(-2.78605 + 2.78605i) q^{50} +(1.82367 + 3.11034i) q^{52} +2.67501i q^{53} +(1.87015 - 3.23920i) q^{55} -0.351127 q^{56} +(-1.50652 - 5.62241i) q^{58} +(-1.25408 - 4.68030i) q^{59} +5.72649 q^{61} +(2.86991 - 4.97083i) q^{62} -1.00000i q^{64} +(2.60715 - 2.64234i) q^{65} +(-10.6589 + 10.6589i) q^{67} +3.34471i q^{68} +(0.0935622 + 0.349179i) q^{70} +(-1.53985 + 5.74681i) q^{71} +(2.47165 + 2.47165i) q^{73} +5.14203i q^{74} +(0.709887 + 0.709887i) q^{76} +(0.637824 + 1.10474i) q^{77} +(-1.76544 + 3.05783i) q^{79} +(-0.994452 + 0.266463i) q^{80} +(8.09532 - 4.67384i) q^{82} +(8.34680 - 2.23652i) q^{83} +(3.32615 - 0.891240i) q^{85} +(2.64553 + 0.708868i) q^{86} +(-3.14628 + 1.81650i) q^{88} +(-2.68520 - 10.0213i) q^{89} +(0.335858 + 1.22064i) q^{91} +(1.27351 + 0.735260i) q^{92} +8.47121 q^{94} +(0.516790 - 0.895107i) q^{95} +(-10.4441 + 10.4441i) q^{97} +(6.64239 + 1.77982i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) $ 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.266463	+	0.994452i	−0.119166	+	0.444732i	−0.999565	−	0.0295011i	$-0.990608\pi$
$5$	−0.266463	+	0.994452i	−0.119166	+	0.444732i	0.880399	+	0.474234i	$0.157275\pi$
$6$		0			0
$7$	−0.248284	−	0.248284i	−0.0938426	−	0.0938426i	0.658627	−	0.752470i	$-0.271138\pi$
$7$	−0.248284	−	0.248284i	−0.0938426	−	0.0938426i	−0.752470	+	0.658627i	$0.771138\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.891601	−	0.514766i	−0.281949	−	0.162783i
$11$	−3.50922	−	0.940292i	−1.05807	−	0.283509i	−0.312487	−	0.949922i	$-0.601162\pi$
$11$	−3.50922	−	0.940292i	−1.05807	−	0.283509i	−0.745582	+	0.666413i	$0.767829\pi$
$12$		0			0
$13$	−3.13452	−	1.78180i	−0.869358	−	0.494182i
$13$	−3.13452	−	1.78180i	−0.869358	−	0.494182i
$14$	0.304085	−	0.175564i	0.0812701	−	0.0469213i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.67236	−	2.89660i	−0.405606	−	0.702530i	0.588786	−	0.808289i	$-0.299606\pi$
$17$	−1.67236	−	2.89660i	−0.405606	−	0.702530i	−0.994392	+	0.105759i	$0.966273\pi$
$18$		0			0
$19$	−0.969723	−	0.259837i	−0.222470	−	0.0596106i	0.145862	−	0.989305i	$-0.453404\pi$
$19$	−0.969723	−	0.259837i	−0.222470	−	0.0596106i	−0.368332	+	0.929694i	$0.620071\pi$
$20$	0.727989	−	0.727989i	0.162783	−	0.162783i
$21$		0			0
$22$	1.81650	−	3.14628i	0.387280	−	0.670789i
$23$	−1.47052			−0.306625			−0.153312	−	0.988178i	$-0.548994\pi$
$23$	−1.47052			−0.306625			−0.153312	+	0.988178i	$0.548994\pi$
$24$		0			0
$25$	3.41219	+	1.97003i	0.682439	+	0.394006i
$26$	2.53236	−	2.56655i	0.496636	−	0.503341i
$27$		0			0
$28$	0.0908784	+	0.339163i	0.0171744	+	0.0640957i
$29$	−5.04092	+	2.91038i	−0.936075	+	0.540443i	−0.888728	−	0.458435i	$-0.848410\pi$
$29$	−5.04092	+	2.91038i	−0.936075	+	0.540443i	−0.0473474	+	0.998878i	$0.515077\pi$
$30$		0			0
$31$	−5.54424	−	1.48558i	−0.995775	−	0.266817i	−0.276101	−	0.961129i	$-0.589042\pi$
$31$	−5.54424	−	1.48558i	−0.995775	−	0.266817i	−0.719675	+	0.694312i	$0.755709\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	3.23074	−	0.865675i	0.554068	−	0.148462i
$35$	0.313065	−	0.180748i	0.0529177	−	0.0305520i
$36$		0			0
$37$	4.96682	−	1.33085i	0.816540	−	0.218791i	0.173707	−	0.984797i	$-0.444426\pi$
$37$	4.96682	−	1.33085i	0.816540	−	0.218791i	0.642833	+	0.766006i	$0.277759\pi$
$38$	0.501966	−	0.869430i	0.0814296	−	0.141040i
$39$		0			0
$40$	0.514766	+	0.891601i	0.0813917	+	0.140975i
$41$	−6.60980	−	6.60980i	−1.03228	−	1.03228i	−0.999461	−	0.0328164i	$-0.989552\pi$
$41$	−6.60980	−	6.60980i	−1.03228	−	1.03228i	−0.0328164	−	0.999461i	$-0.510448\pi$
$42$		0			0
$43$		−	2.73886i		−	0.417672i	−0.977951	−	0.208836i	$-0.933033\pi$
$43$		−	2.73886i		−	0.417672i	0.977951	−	0.208836i	$-0.0669674\pi$
$44$	2.56893	+	2.56893i	0.387280	+	0.387280i
$45$		0			0
$46$	0.380599	−	1.42041i	0.0561162	−	0.209429i
$47$	−2.19251	−	8.18256i	−0.319811	−	1.19355i	−0.919427	−	0.393262i	$-0.871347\pi$
$47$	−2.19251	−	8.18256i	−0.319811	−	1.19355i	0.599616	−	0.800288i	$-0.295320\pi$
$48$		0			0
$49$		−	6.87671i		−	0.982387i
$50$	−2.78605	+	2.78605i	−0.394006	+	0.394006i
$51$		0			0
$52$	1.82367	+	3.11034i	0.252898	+	0.431327i
$53$			2.67501i			0.367442i	0.982978	+	0.183721i	$0.0588142\pi$
$53$			2.67501i			0.367442i	−0.982978	+	0.183721i	$0.941186\pi$
$54$		0			0
$55$	1.87015	−	3.23920i	0.252171	−	0.436773i
$56$	−0.351127			−0.0469213
$57$		0			0
$58$	−1.50652	−	5.62241i	−0.197816	−	0.738259i
$59$	−1.25408	−	4.68030i	−0.163268	−	0.609323i	−0.998255	−	0.0590536i	$-0.981192\pi$
$59$	−1.25408	−	4.68030i	−0.163268	−	0.609323i	0.834987	−	0.550269i	$-0.185475\pi$
$60$		0			0
$61$	5.72649			0.733202			0.366601	−	0.930378i	$-0.380521\pi$
$61$	5.72649			0.733202			0.366601	+	0.930378i	$0.380521\pi$
$62$	2.86991	−	4.97083i	0.364479	−	0.631296i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.60715	−	2.64234i	0.323377	−	0.327742i
$66$		0			0
$67$	−10.6589	+	10.6589i	−1.30219	+	1.30219i	−0.375282	+	0.926911i	$0.622454\pi$
$67$	−10.6589	+	10.6589i	−1.30219	+	1.30219i	−0.926911	+	0.375282i	$0.877546\pi$
$68$			3.34471i			0.405606i
$69$		0			0
$70$	0.0935622	+	0.349179i	0.0111828	+	0.0417349i
$71$	−1.53985	+	5.74681i	−0.182747	+	0.682021i	0.812355	+	0.583164i	$0.198185\pi$
$71$	−1.53985	+	5.74681i	−0.182747	+	0.682021i	−0.995102	+	0.0988571i	$0.968481\pi$
$72$		0			0
$73$	2.47165	+	2.47165i	0.289285	+	0.289285i	0.836797	−	0.547513i	$-0.184425\pi$
$73$	2.47165	+	2.47165i	0.289285	+	0.289285i	−0.547513	+	0.836797i	$0.684425\pi$
$74$			5.14203i			0.597749i
$75$		0			0
$76$	0.709887	+	0.709887i	0.0814296	+	0.0814296i
$77$	0.637824	+	1.10474i	0.0726868	+	0.125897i
$78$		0			0
$79$	−1.76544	+	3.05783i	−0.198627	+	0.344033i	−0.948084	−	0.318021i	$-0.896982\pi$
$79$	−1.76544	+	3.05783i	−0.198627	+	0.344033i	0.749456	+	0.662054i	$0.230315\pi$
$80$	−0.994452	+	0.266463i	−0.111183	+	0.0297914i
$81$		0			0
$82$	8.09532	−	4.67384i	0.893979	−	0.516139i
$83$	8.34680	−	2.23652i	0.916181	−	0.245490i	0.230228	−	0.973137i	$-0.426053\pi$
$83$	8.34680	−	2.23652i	0.916181	−	0.245490i	0.685952	+	0.727647i	$0.259386\pi$
$84$		0			0
$85$	3.32615	−	0.891240i	0.360772	−	0.0966686i
$86$	2.64553	+	0.708868i	0.285275	+	0.0764392i
$87$		0			0
$88$	−3.14628	+	1.81650i	−0.335394	+	0.193640i
$89$	−2.68520	−	10.0213i	−0.284630	−	1.06225i	−0.949109	−	0.314947i	$-0.898013\pi$
$89$	−2.68520	−	10.0213i	−0.284630	−	1.06225i	0.664479	−	0.747307i	$-0.268653\pi$
$90$		0			0
$91$	0.335858	+	1.22064i	0.0352075	+	0.127958i
$92$	1.27351	+	0.735260i	0.132772	+	0.0766562i
$93$		0			0
$94$	8.47121			0.873739
$95$	0.516790	−	0.895107i	0.0530215	−	0.0918360i
$96$		0			0
$97$	−10.4441	+	10.4441i	−1.06044	+	1.06044i	−0.0623848	+	0.998052i	$0.519871\pi$
$97$	−10.4441	+	10.4441i	−1.06044	+	1.06044i	−0.998052	+	0.0623848i	$0.980129\pi$
$98$	6.64239	+	1.77982i	0.670983	+	0.179789i
$99$		0			0
$100$	−1.97003	−	3.41219i	−0.197003	−	0.341219i
$101$	8.67108	+	15.0187i	0.862804	+	1.49442i	0.869211	+	0.494442i	$0.164627\pi$
$101$	8.67108	+	15.0187i	0.862804	+	1.49442i	−0.00640634	+	0.999979i	$0.502039\pi$
$102$		0			0
$103$	−9.22402	+	5.32549i	−0.908870	+	0.524736i	−0.880067	−	0.474849i	$-0.842503\pi$
$103$	−9.22402	+	5.32549i	−0.908870	+	0.524736i	−0.0288023	+	0.999585i	$0.509169\pi$
$104$	−3.47636	+	0.956515i	−0.340885	+	0.0937940i
$105$		0			0
$106$	−2.58387	−	0.692345i	−0.250967	−	0.0672465i
$107$	0.693025	+	0.400118i	0.0669973	+	0.0386809i	0.533124	−	0.846037i	$-0.321018\pi$
$107$	0.693025	+	0.400118i	0.0669973	+	0.0386809i	−0.466127	+	0.884718i	$0.654351\pi$
$108$		0			0
$109$	5.83921	−	5.83921i	0.559294	−	0.559294i	−0.369812	−	0.929107i	$-0.620578\pi$
$109$	5.83921	−	5.83921i	0.559294	−	0.559294i	0.929107	+	0.369812i	$0.120578\pi$
$110$	2.64479	+	2.64479i	0.252171	+	0.252171i
$111$		0			0
$112$	0.0908784	−	0.339163i	0.00858720	−	0.0320479i
$113$	11.6846	+	6.74613i	1.09920	+	0.634623i	0.936010	−	0.351972i	$-0.114489\pi$
$113$	11.6846	+	6.74613i	1.09920	+	0.634623i	0.163188	+	0.986595i	$0.447822\pi$
$114$		0			0
$115$	0.391839	−	1.46236i	0.0365391	−	0.136366i
$116$	5.82075			0.540443
$117$		0			0
$118$	4.84540			0.446055
$119$	−0.303962	+	1.13440i	−0.0278641	+	0.103990i
$120$		0			0
$121$	1.90418	+	1.09938i	0.173107	+	0.0999436i
$122$	−1.48213	+	5.53137i	−0.134185	+	0.500787i
$123$		0			0
$124$	4.05867	+	4.05867i	0.364479	+	0.364479i
$125$	−6.50827	+	6.50827i	−0.582117	+	0.582117i
$126$		0			0
$127$	−16.2637	−	9.38987i	−1.44317	−	0.833216i	−0.445112	−	0.895475i	$-0.646836\pi$
$127$	−16.2637	−	9.38987i	−1.44317	−	0.833216i	−0.998060	+	0.0622590i	$0.980170\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	1.87753	+	3.20220i	0.164670	+	0.280851i
$131$	2.91497	−	1.68296i	0.254682	−	0.147041i	−0.367224	−	0.930133i	$-0.619692\pi$
$131$	2.91497	−	1.68296i	0.254682	−	0.147041i	0.621906	+	0.783092i	$0.286358\pi$
$132$		0			0
$133$	0.176254	+	0.305280i	0.0152831	+	0.0264712i
$134$	−7.53699	−	13.0544i	−0.651096	−	1.12773i
$135$		0			0
$136$	−3.23074	−	0.865675i	−0.277034	−	0.0742310i
$137$	−2.75305	+	2.75305i	−0.235209	+	0.235209i	−0.814863	−	0.579654i	$-0.803188\pi$
$137$	−2.75305	+	2.75305i	−0.235209	+	0.235209i	0.579654	+	0.814863i	$0.303188\pi$
$138$		0			0
$139$	−0.276245	+	0.478471i	−0.0234308	+	0.0405833i	−0.877503	−	0.479571i	$-0.840792\pi$
$139$	−0.276245	+	0.478471i	−0.0234308	+	0.0405833i	0.854072	+	0.520154i	$0.174126\pi$
$140$	−0.361497			−0.0305520
$141$		0			0
$142$	−5.15245	−	2.97477i	−0.432384	−	0.249637i
$143$	9.32429	+	9.20008i	0.779736	+	0.769350i
$144$		0			0
$145$	−1.55101	−	5.78846i	−0.128805	−	0.480705i
$146$	−3.02714	+	1.74772i	−0.250528	+	0.144642i
$147$		0			0
$148$	−4.96682	−	1.33085i	−0.408270	−	0.109396i
$149$	12.5052	−	3.35075i	1.02446	−	0.274504i	0.292803	−	0.956173i	$-0.405412\pi$
$149$	12.5052	−	3.35075i	1.02446	−	0.274504i	0.731661	+	0.681669i	$0.238745\pi$
$150$		0			0
$151$	−8.72875	+	2.33886i	−0.710336	+	0.190334i	−0.595856	−	0.803092i	$-0.703187\pi$
$151$	−8.72875	+	2.33886i	−0.710336	+	0.190334i	−0.114480	+	0.993426i	$0.536520\pi$
$152$	−0.869430	+	0.501966i	−0.0705201	+	0.0407148i
$153$		0			0
$154$	−1.23218	+	0.330162i	−0.0992920	+	0.0266052i
$155$	2.95467	−	5.11763i	0.237325	−	0.411058i
$156$		0			0
$157$	5.60064	+	9.70059i	0.446980	+	0.774191i	0.998188	−	0.0601763i	$-0.0191663\pi$
$157$	5.60064	+	9.70059i	0.446980	+	0.774191i	−0.551208	+	0.834368i	$0.685833\pi$
$158$	−2.49671	−	2.49671i	−0.198627	−	0.198627i
$159$		0			0
$160$		−	1.02953i		−	0.0813917i
$161$	0.365107	+	0.365107i	0.0287745	+	0.0287745i
$162$		0			0
$163$	−2.29883	+	8.57937i	−0.180059	+	0.671988i	0.815576	+	0.578650i	$0.196420\pi$
$163$	−2.29883	+	8.57937i	−0.180059	+	0.671988i	−0.995635	+	0.0933377i	$0.970246\pi$
$164$	2.41936	+	9.02916i	0.188920	+	0.705059i
$165$		0			0
$166$			8.64124i			0.670691i
$167$	6.56988	−	6.56988i	0.508392	−	0.508392i	−0.405640	−	0.914033i	$-0.632951\pi$
$167$	6.56988	−	6.56988i	0.508392	−	0.508392i	0.914033	+	0.405640i	$0.132951\pi$
$168$		0			0
$169$	6.65038	+	11.1702i	0.511568	+	0.859243i
$170$			3.44349i			0.264103i
$171$		0			0
$172$	−1.36943	+	2.37192i	−0.104418	+	0.180857i
$173$	−10.5884			−0.805023			−0.402512	−	0.915415i	$-0.631863\pi$
$173$	−10.5884			−0.805023			−0.402512	+	0.915415i	$0.631863\pi$
$174$		0			0
$175$	−0.358066	−	1.33632i	−0.0270673	−	0.101016i
$176$	−0.940292	−	3.50922i	−0.0708772	−	0.264517i
$177$		0			0
$178$	10.3748			0.777624
$179$	−12.5097	+	21.6674i	−0.935018	+	1.61950i	−0.160417	+	0.987049i	$0.551284\pi$
$179$	−12.5097	+	21.6674i	−0.935018	+	1.61950i	−0.774601	+	0.632450i	$0.782049\pi$
$180$		0			0
$181$			23.3875i			1.73838i	0.494482	+	0.869188i	$0.335358\pi$
$181$			23.3875i			1.73838i	−0.494482	+	0.869188i	$0.664642\pi$
$182$	−1.26598	+	0.00848836i	−0.0938405	+	0.000629199i
$183$		0			0
$184$	−1.03981	+	1.03981i	−0.0766562	+	0.0766562i
$185$			5.29389i			0.389214i
$186$		0			0
$187$	3.14500	+	11.7373i	0.229986	+	0.858318i
$188$	−2.19251	+	8.18256i	−0.159905	+	0.596775i
$189$		0			0
$190$	0.730852	+	0.730852i	0.0530215	+	0.0530215i
$191$		−	12.3120i		−	0.890865i	−0.895316	−	0.445432i	$-0.853050\pi$
$191$		−	12.3120i		−	0.890865i	0.895316	−	0.445432i	$-0.146950\pi$
$192$		0			0
$193$	−9.14996	−	9.14996i	−0.658629	−	0.658629i	0.296427	−	0.955056i	$-0.404205\pi$
$193$	−9.14996	−	9.14996i	−0.658629	−	0.658629i	−0.955056	+	0.296427i	$0.904205\pi$
$194$	−7.38509	−	12.7913i	−0.530218	−	0.918365i
$195$		0			0
$196$	−3.43835	+	5.95541i	−0.245597	+	0.425386i
$197$	−20.6372	+	5.52972i	−1.47034	+	0.393976i	−0.903048	−	0.429540i	$-0.858676\pi$
$197$	−20.6372	+	5.52972i	−1.47034	+	0.393976i	−0.567292	+	0.823517i	$0.692009\pi$
$198$		0			0
$199$	19.2376	−	11.1069i	1.36372	−	0.787344i	0.373603	−	0.927589i	$-0.378122\pi$
$199$	19.2376	−	11.1069i	1.36372	−	0.787344i	0.990117	+	0.140245i	$0.0447889\pi$
$200$	3.80581	−	1.01976i	0.269111	−	0.0721082i
$201$		0			0
$202$	−16.7512	+	4.48848i	−1.17861	+	0.315808i
$203$	1.97418	+	0.528980i	0.138560	+	0.0371271i
$204$		0			0
$205$	8.33440	−	4.81187i	0.582100	−	0.336075i
$206$	−2.75668	−	10.2881i	−0.192067	−	0.716803i
$207$		0			0
$208$	−0.0241746	−	3.60547i	−0.00167621	−	0.249994i
$209$	3.15865	+	1.82365i	0.218488	+	0.126144i
$210$		0			0
$211$	18.3511			1.26334			0.631670	−	0.775237i	$-0.282370\pi$
$211$	18.3511			1.26334			0.631670	+	0.775237i	$0.282370\pi$
$212$	1.33751	−	2.31663i	0.0918604	−	0.159107i
$213$		0			0
$214$	−0.565853	+	0.565853i	−0.0386809	+	0.0386809i
$215$	2.72366	+	0.729803i	0.185752	+	0.0497722i
$216$		0			0
$217$	1.00770	+	1.74539i	0.0684073	+	0.118485i
$218$	4.12894	+	7.15154i	0.279647	+	0.484363i
$219$		0			0
$220$	−3.23920	+	1.87015i	−0.218387	+	0.126086i
$221$	0.0808571	+	12.0593i	0.00543904	+	0.811193i
$222$		0			0
$223$	−24.4901	−	6.56211i	−1.63998	−	0.439432i	−0.683198	−	0.730233i	$-0.739411\pi$
$223$	−24.4901	−	6.56211i	−1.63998	−	0.439432i	−0.956783	+	0.290802i	$0.906078\pi$
$224$	0.304085	+	0.175564i	0.0203175	+	0.0117303i
$225$		0			0
$226$	−9.54047	+	9.54047i	−0.634623	+	0.634623i
$227$	−17.6248	−	17.6248i	−1.16980	−	1.16980i	−0.982257	−	0.187539i	$-0.939949\pi$
$227$	−17.6248	−	17.6248i	−1.16980	−	1.16980i	−0.187539	−	0.982257i	$-0.560051\pi$
$228$		0			0
$229$	0.401688	−	1.49912i	0.0265443	−	0.0990647i	−0.951383	−	0.308011i	$-0.900337\pi$
$229$	0.401688	−	1.49912i	0.0265443	−	0.0990647i	0.977927	+	0.208946i	$0.0670033\pi$
$230$	1.31112	+	0.756974i	0.0864525	+	0.0499134i
$231$		0			0
$232$	−1.50652	+	5.62241i	−0.0989080	+	0.369130i
$233$	9.96467			0.652807			0.326403	−	0.945231i	$-0.394163\pi$
$233$	9.96467			0.652807			0.326403	+	0.945231i	$0.394163\pi$
$234$		0			0
$235$	8.72139			0.568921
$236$	−1.25408	+	4.68030i	−0.0816338	+	0.304661i
$237$		0			0
$238$	−1.01708	−	0.587209i	−0.0659272	−	0.0380631i
$239$	0.0186887	−	0.0697473i	0.00120887	−	0.00451158i	−0.965319	−	0.261074i	$-0.915923\pi$
$239$	0.0186887	−	0.0697473i	0.00120887	−	0.00451158i	0.966528	+	0.256563i	$0.0825900\pi$
$240$		0			0
$241$	13.2296	+	13.2296i	0.852192	+	0.852192i	0.990403	−	0.138211i	$-0.0441351\pi$
$241$	13.2296	+	13.2296i	0.852192	+	0.852192i	−0.138211	+	0.990403i	$0.544135\pi$
$242$	−1.55476	+	1.55476i	−0.0999436	+	0.0999436i
$243$		0			0
$244$	−4.95929	−	2.86325i	−0.317486	−	0.183301i
$245$	6.83856	+	1.83239i	0.436899	+	0.117067i
$246$		0			0
$247$	2.57664	+	2.54231i	0.163947	+	0.161764i
$248$	−4.97083	+	2.86991i	−0.315648	+	0.182240i
$249$		0			0
$250$	−4.60204	−	7.97097i	−0.291059	−	0.504129i
$251$	−10.5789	−	18.3232i	−0.667735	−	1.15655i	−0.978536	−	0.206075i	$-0.933931\pi$
$251$	−10.5789	−	18.3232i	−0.667735	−	1.15655i	0.310802	−	0.950475i	$-0.399403\pi$
$252$		0			0
$253$	5.16037	+	1.38272i	0.324430	+	0.0869308i
$254$	13.2793	−	13.2793i	0.833216	−	0.833216i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.6439			0.913460			0.456730	−	0.889605i	$-0.349021\pi$
$257$	14.6439			0.913460			0.456730	+	0.889605i	$0.349021\pi$
$258$		0			0
$259$	−1.56361	−	0.902752i	−0.0971582	−	0.0560943i
$260$	−3.57903	+	0.984764i	−0.221962	+	0.0610724i
$261$		0			0
$262$	0.871165	+	3.25123i	0.0538207	+	0.200862i
$263$	−9.98128	+	5.76269i	−0.615472	+	0.355343i	−0.775104	−	0.631834i	$-0.782303\pi$
$263$	−9.98128	+	5.76269i	−0.615472	+	0.355343i	0.159632	+	0.987177i	$0.448969\pi$
$264$		0			0
$265$	−2.66017	−	0.712791i	−0.163413	−	0.0437864i
$266$	−0.340496	+	0.0912356i	−0.0208772	+	0.00559402i
$267$		0			0
$268$	14.5603	−	3.90143i	0.889414	−	0.238318i
$269$	17.7279	−	10.2352i	1.08089	−	0.624052i	0.149754	−	0.988723i	$-0.452152\pi$
$269$	17.7279	−	10.2352i	1.08089	−	0.624052i	0.931136	+	0.364671i	$0.118818\pi$
$270$		0			0
$271$	0.537040	−	0.143899i	0.0326229	−	0.00874127i	−0.242471	−	0.970159i	$-0.577958\pi$
$271$	0.537040	−	0.143899i	0.0326229	−	0.00874127i	0.275094	+	0.961417i	$0.411291\pi$
$272$	1.67236	−	2.89660i	0.101401	−	0.175632i
$273$		0			0
$274$	−1.94670	−	3.37178i	−0.117604	−	0.203697i
$275$	−10.1217	−	10.1217i	−0.610363	−	0.610363i
$276$		0			0
$277$		−	12.0749i		−	0.725509i	−0.931885	−	0.362754i	$-0.881836\pi$
$277$		−	12.0749i		−	0.725509i	0.931885	−	0.362754i	$-0.118164\pi$
$278$	−0.390670	−	0.390670i	−0.0234308	−	0.0234308i
$279$		0			0
$280$	0.0935622	−	0.349179i	0.00559141	−	0.0208674i
$281$	−3.77024	−	14.0707i	−0.224913	−	0.839388i	−0.982439	−	0.186583i	$-0.940259\pi$
$281$	−3.77024	−	14.0707i	−0.224913	−	0.839388i	0.757526	−	0.652805i	$-0.226408\pi$
$282$		0			0
$283$		−	13.3436i		−	0.793192i	−0.917993	−	0.396596i	$-0.870191\pi$
$283$		−	13.3436i		−	0.793192i	0.917993	−	0.396596i	$-0.129809\pi$
$284$	4.20696	−	4.20696i	0.249637	−	0.249637i
$285$		0			0
$286$	−11.2999	+	6.62541i	−0.668177	+	0.391769i
$287$			3.28222i			0.193743i
$288$		0			0
$289$	2.90646	−	5.03413i	0.170968	−	0.296125i
$290$	5.99265			0.351901
$291$		0			0
$292$	−0.904687	−	3.37634i	−0.0529428	−	0.197585i
$293$	5.46383	+	20.3913i	0.319200	+	1.19127i	0.920015	+	0.391883i	$0.128176\pi$
$293$	5.46383	+	20.3913i	0.319200	+	1.19127i	−0.600815	+	0.799388i	$0.705157\pi$
$294$		0			0
$295$	4.98850			0.290442
$296$	2.57101	−	4.45313i	0.149437	−	0.258833i
$297$		0			0
$298$			12.9463i			0.749960i
$299$	4.60937	+	2.62017i	0.266567	+	0.151528i
$300$		0			0
$301$	−0.680015	+	0.680015i	−0.0391954	+	0.0391954i
$302$		−	9.03667i		−	0.520002i
$303$		0			0
$304$	−0.259837	−	0.969723i	−0.0149027	−	0.0556174i
$305$	−1.52590	+	5.69472i	−0.0873726	+	0.326079i
$306$		0			0
$307$	−10.9437	−	10.9437i	−0.624590	−	0.624590i	0.322111	−	0.946702i	$-0.395607\pi$
$307$	−10.9437	−	10.9437i	−0.624590	−	0.624590i	−0.946702	+	0.322111i	$0.895607\pi$
$308$		−	1.27565i		−	0.0726868i
$309$		0			0
$310$	4.17853	+	4.17853i	0.237325	+	0.237325i
$311$	12.9553	+	22.4392i	0.734626	+	1.27241i	0.954887	+	0.296968i	$0.0959756\pi$
$311$	12.9553	+	22.4392i	0.734626	+	1.27241i	−0.220262	+	0.975441i	$0.570691\pi$
$312$		0			0
$313$	17.6482	−	30.5676i	0.997537	−	1.72779i	0.438028	−	0.898961i	$-0.355677\pi$
$313$	17.6482	−	30.5676i	0.997537	−	1.72779i	0.559509	−	0.828824i	$-0.310990\pi$
$314$	−10.8196	+	2.89910i	−0.610586	+	0.163606i
$315$		0			0
$316$	3.05783	−	1.76544i	0.172016	−	0.0993137i
$317$	12.2048	−	3.27025i	0.685487	−	0.183676i	0.100766	−	0.994910i	$-0.467871\pi$
$317$	12.2048	−	3.27025i	0.685487	−	0.183676i	0.584721	+	0.811234i	$0.301204\pi$
$318$		0			0
$319$	20.4263	−	5.47321i	1.14365	−	0.306441i
$320$	0.994452	+	0.266463i	0.0555916	+	0.0148957i
$321$		0			0
$322$	−0.447163	+	0.258170i	−0.0249194	+	0.0143872i
$323$	0.869078	+	3.24344i	0.0483568	+	0.180470i
$324$		0			0
$325$	−7.18538	−	12.2549i	−0.398573	−	0.679782i
$326$	−7.69205	−	4.44101i	−0.426023	−	0.245965i
$327$		0			0
$328$	−9.34767			−0.516139
$329$	−1.48724	+	2.57597i	−0.0819940	+	0.142018i
$330$		0			0
$331$	−7.04833	+	7.04833i	−0.387411	+	0.387411i	−0.873763	−	0.486352i	$-0.838327\pi$
$331$	−7.04833	+	7.04833i	−0.387411	+	0.387411i	0.486352	+	0.873763i	$0.338327\pi$
$332$	−8.34680	−	2.23652i	−0.458090	−	0.122745i
$333$		0			0
$334$	4.64560	+	8.04642i	0.254196	+	0.440281i
$335$	−7.75957	−	13.4400i	−0.423951	−	0.734304i
$336$		0			0
$337$	25.2475	−	14.5766i	1.37532	−	0.794040i	0.383727	−	0.923447i	$-0.374640\pi$
$337$	25.2475	−	14.5766i	1.37532	−	0.794040i	0.991592	+	0.129406i	$0.0413072\pi$
$338$	−12.5108	+	3.53273i	−0.680497	+	0.192155i
$339$		0			0
$340$	−3.32615	−	0.891240i	−0.180386	−	0.0483343i
$341$	18.0591	+	10.4264i	0.977954	+	0.564622i
$342$		0			0
$343$	−3.44537	+	3.44537i	−0.186032	+	0.186032i
$344$	−1.93666	−	1.93666i	−0.104418	−	0.104418i
$345$		0			0
$346$	2.74049	−	10.2276i	0.147329	−	0.549841i
$347$	−12.4232	−	7.17253i	−0.666912	−	0.385042i	0.127994	−	0.991775i	$-0.459146\pi$
$347$	−12.4232	−	7.17253i	−0.666912	−	0.385042i	−0.794906	+	0.606733i	$0.792480\pi$
$348$		0			0
$349$	6.84815	−	25.5577i	0.366573	−	1.36807i	−0.498702	−	0.866773i	$-0.666190\pi$
$349$	6.84815	−	25.5577i	0.366573	−	1.36807i	0.865276	−	0.501296i	$-0.167143\pi$
$350$	1.38346			0.0739492
$351$		0			0
$352$	3.63301			0.193640
$353$	−3.08503	+	11.5135i	−0.164200	+	0.612801i	0.833941	+	0.551853i	$0.186079\pi$
$353$	−3.08503	+	11.5135i	−0.164200	+	0.612801i	−0.998141	+	0.0609479i	$0.980588\pi$
$354$		0			0
$355$	−5.30461	−	3.06262i	−0.281540	−	0.162547i
$356$	−2.68520	+	10.0213i	−0.142315	+	0.531127i
$357$		0			0
$358$	−17.6914	−	17.6914i	−0.935018	−	0.935018i
$359$	13.9898	−	13.9898i	0.738351	−	0.738351i	−0.233907	−	0.972259i	$-0.575151\pi$
$359$	13.9898	−	13.9898i	0.738351	−	0.738351i	0.972259	+	0.233907i	$0.0751513\pi$
$360$		0			0
$361$	−15.5816	−	8.99606i	−0.820086	−	0.473477i
$362$	−22.5905	−	6.05312i	−1.18733	−	0.318145i
$363$		0			0
$364$	0.319460	−	1.22504i	0.0167443	−	0.0642094i
$365$	−3.11654	+	1.79934i	−0.163127	+	0.0941815i
$366$		0			0
$367$	−8.33971	−	14.4448i	−0.435329	−	0.754012i	0.561993	−	0.827142i	$-0.310035\pi$
$367$	−8.33971	−	14.4448i	−0.435329	−	0.754012i	−0.997322	+	0.0731295i	$0.976701\pi$
$368$	−0.735260	−	1.27351i	−0.0383281	−	0.0663862i
$369$		0			0
$370$	−5.11350	−	1.37016i	−0.265838	−	0.0712311i
$371$	0.664164	−	0.664164i	0.0344817	−	0.0344817i
$372$		0			0
$373$	0.266680	−	0.461903i	0.0138082	−	0.0239164i	−0.859039	−	0.511911i	$-0.828938\pi$
$373$	0.266680	−	0.461903i	0.0138082	−	0.0239164i	0.872847	+	0.487994i	$0.162271\pi$
$374$	−12.1514			−0.628332
$375$		0			0
$376$	−7.33629	−	4.23561i	−0.378340	−	0.218435i
$377$	20.9865	−	0.140715i	1.08086	−	0.00724717i
$378$		0			0
$379$	−8.93403	−	33.3422i	−0.458910	−	1.71268i	−0.676331	−	0.736598i	$-0.736431\pi$
$379$	−8.93403	−	33.3422i	−0.458910	−	1.71268i	0.217421	−	0.976078i	$-0.430236\pi$
$380$	−0.895107	+	0.516790i	−0.0459180	+	0.0265108i
$381$		0			0
$382$	11.8925	+	3.18658i	0.608472	+	0.163040i
$383$	−1.95166	+	0.522945i	−0.0997250	+	0.0267212i	−0.308336	−	0.951277i	$-0.599772\pi$
$383$	−1.95166	+	0.522945i	−0.0997250	+	0.0267212i	0.208611	+	0.977999i	$0.433106\pi$
$384$		0			0
$385$	−1.26857	+	0.339912i	−0.0646523	+	0.0173235i
$386$	11.2064	−	6.47000i	0.570389	−	0.329314i
$387$		0			0
$388$	14.2669	−	3.82280i	0.724292	−	0.194073i
$389$	0.968658	−	1.67777i	0.0491129	−	0.0850661i	−0.840424	−	0.541930i	$-0.817694\pi$
$389$	0.968658	−	1.67777i	0.0491129	−	0.0850661i	0.889537	+	0.456864i	$0.151027\pi$
$390$		0			0
$391$	2.45923	+	4.25951i	0.124369	+	0.215413i
$392$	−4.86257	−	4.86257i	−0.245597	−	0.245597i
$393$		0			0
$394$		−	21.3652i		−	1.07636i
$395$	−2.57044	−	2.57044i	−0.129333	−	0.129333i
$396$		0			0
$397$	−8.86089	+	33.0693i	−0.444716	+	1.65970i	0.271971	+	0.962305i	$0.412324\pi$
$397$	−8.86089	+	33.0693i	−0.444716	+	1.65970i	−0.716687	+	0.697395i	$0.754342\pi$
$398$	5.74933	+	21.4568i	0.288188	+	1.07553i
$399$		0			0
$400$			3.94006i			0.197003i
$401$	−6.35686	+	6.35686i	−0.317446	+	0.317446i	−0.847786	−	0.530339i	$-0.822065\pi$
$401$	−6.35686	+	6.35686i	−0.317446	+	0.317446i	0.530339	+	0.847786i	$0.322065\pi$
$402$		0			0
$403$	14.7315	+	14.5353i	0.733829	+	0.724054i
$404$		−	17.3422i		−	0.862804i
$405$		0			0
$406$	−1.02191	+	1.77000i	−0.0507166	+	0.0878438i
$407$	−18.6810			−0.925985
$408$		0			0
$409$	−3.81796	−	14.2488i	−0.188786	−	0.704558i	−0.993788	−	0.111287i	$-0.964503\pi$
$409$	−3.81796	−	14.2488i	−0.188786	−	0.704558i	0.805003	−	0.593271i	$-0.202164\pi$
$410$	2.49081	+	9.29581i	0.123012	+	0.459087i
$411$		0			0
$412$	10.6510			0.524736
$413$	−0.850676	+	1.47341i	−0.0418590	+	0.0725019i
$414$		0			0
$415$			8.89644i			0.436709i
$416$	3.48887	+	0.909813i	0.171056	+	0.0446073i
$417$		0			0
$418$	−2.57903	+	2.57903i	−0.126144	+	0.126144i
$419$		−	34.9519i		−	1.70751i	−0.520675	−	0.853755i	$-0.674320\pi$
$419$		−	34.9519i		−	1.70751i	0.520675	−	0.853755i	$-0.325680\pi$
$420$		0			0
$421$	−0.685052	−	2.55665i	−0.0333874	−	0.124603i	0.947221	−	0.320582i	$-0.103878\pi$
$421$	−0.685052	−	2.55665i	−0.0333874	−	0.124603i	−0.980608	+	0.195978i	$0.937212\pi$
$422$	−4.74961	+	17.7258i	−0.231207	+	0.862878i
$423$		0			0
$424$	1.89152	+	1.89152i	0.0918604	+	0.0918604i
$425$		−	13.1784i		−	0.639245i
$426$		0			0
$427$	−1.42180	−	1.42180i	−0.0688057	−	0.0688057i
$428$	−0.400118	−	0.693025i	−0.0193404	−	0.0334986i
$429$		0			0
$430$	−1.40987	+	2.44197i	−0.0679900	+	0.117762i
$431$	−14.1857	+	3.80104i	−0.683301	+	0.183090i	−0.583739	−	0.811942i	$-0.698411\pi$
$431$	−14.1857	+	3.80104i	−0.683301	+	0.183090i	−0.0995618	+	0.995031i	$0.531744\pi$
$432$		0			0
$433$	−13.2828	+	7.66884i	−0.638332	+	0.368541i	−0.783972	−	0.620797i	$-0.786809\pi$
$433$	−13.2828	+	7.66884i	−0.638332	+	0.368541i	0.145640	+	0.989338i	$0.453476\pi$
$434$	−1.94673	+	0.521626i	−0.0934462	+	0.0250388i
$435$		0			0
$436$	−7.97650	+	2.13730i	−0.382005	+	0.102358i
$437$	1.42600	+	0.382095i	0.0682147	+	0.0182781i
$438$		0			0
$439$	9.39837	−	5.42615i	0.448560	−	0.258976i	−0.258662	−	0.965968i	$-0.583282\pi$
$439$	9.39837	−	5.42615i	0.448560	−	0.258976i	0.707222	+	0.706992i	$0.249948\pi$
$440$	−0.968061	−	3.61285i	−0.0461505	−	0.172236i
$441$		0			0
$442$	−11.6693	−	3.04306i	−0.555051	−	0.144744i
$443$	−28.8694	−	16.6678i	−1.37163	−	0.791909i	−0.380494	−	0.924783i	$-0.624246\pi$
$443$	−28.8694	−	16.6678i	−1.37163	−	0.791909i	−0.991133	+	0.132874i	$0.957579\pi$
$444$		0			0
$445$	10.6812			0.506337
$446$	12.6770	−	21.9573i	0.600275	−	1.03971i
$447$		0			0
$448$	−0.248284	+	0.248284i	−0.0117303	+	0.0117303i
$449$	−17.6413	−	4.72697i	−0.832543	−	0.223079i	−0.182720	−	0.983165i	$-0.558490\pi$
$449$	−17.6413	−	4.72697i	−0.832543	−	0.223079i	−0.649823	+	0.760086i	$0.725157\pi$
$450$		0			0
$451$	16.9801	+	29.4104i	0.799561	+	1.38488i
$452$	−6.74613	−	11.6846i	−0.317311	−	0.549599i
$453$		0			0
$454$	21.5858	−	12.4626i	1.01307	−	0.584898i
$455$	−1.30337	+	0.00873905i	−0.0611027	+	0.000409693i
$456$		0			0
$457$	−6.16260	−	1.65126i	−0.288274	−	0.0772428i	0.111784	−	0.993733i	$-0.464343\pi$
$457$	−6.16260	−	1.65126i	−0.288274	−	0.0772428i	−0.400058	+	0.916490i	$0.631010\pi$
$458$	1.34408	+	0.776002i	0.0628045	+	0.0362602i
$459$		0			0
$460$	−1.07052	+	1.07052i	−0.0499134	+	0.0499134i
$461$	25.4639	+	25.4639i	1.18597	+	1.18597i	0.978171	+	0.207804i	$0.0666316\pi$
$461$	25.4639	+	25.4639i	1.18597	+	1.18597i	0.207804	+	0.978171i	$0.433368\pi$
$462$		0			0
$463$	−5.81062	+	21.6855i	−0.270042	+	1.00781i	0.689049	+	0.724715i	$0.258028\pi$
$463$	−5.81062	+	21.6855i	−0.270042	+	1.00781i	−0.959091	+	0.283097i	$0.908638\pi$
$464$	−5.04092	−	2.91038i	−0.234019	−	0.135111i
$465$		0			0
$466$	−2.57905	+	9.62513i	−0.119472	+	0.445875i
$467$	14.0000			0.647843			0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000			0.647843			0.323921	+	0.946084i	$0.394999\pi$
$468$		0			0
$469$	5.29288			0.244402
$470$	−2.25726	+	8.42422i	−0.104120	+	0.388580i
$471$		0			0
$472$	−4.19624	−	2.42270i	−0.193148	−	0.111514i
$473$	−2.57533	+	9.61125i	−0.118414	+	0.441926i
$474$		0			0
$475$	−2.79700	−	2.79700i	−0.128335	−	0.128335i
$476$	0.830439	−	0.830439i	0.0380631	−	0.0380631i
$477$		0			0
$478$	0.0625337	+	0.0361039i	0.00286023	+	0.00165135i
$479$	25.7135	+	6.88992i	1.17488	+	0.314809i	0.792894	−	0.609359i	$-0.208573\pi$
$479$	25.7135	+	6.88992i	1.17488	+	0.314809i	0.381987	+	0.924168i	$0.375240\pi$
$480$		0			0
$481$	−17.9399	−	4.67829i	−0.817988	−	0.213311i
$482$	−16.2029	+	9.35472i	−0.738020	+	0.426096i
$483$		0			0
$484$	−1.09938	−	1.90418i	−0.0499718	−	0.0865537i
$485$	−7.60319	−	13.1691i	−0.345243	−	0.597978i
$486$		0			0
$487$	−14.7534	−	3.95317i	−0.668542	−	0.179135i	−0.0914441	−	0.995810i	$-0.529148\pi$
$487$	−14.7534	−	3.95317i	−0.668542	−	0.179135i	−0.577098	+	0.816675i	$0.695815\pi$
$488$	4.04924	−	4.04924i	0.183301	−	0.183301i
$489$		0			0
$490$	−3.53990	+	6.13128i	−0.159916	+	0.276983i
$491$	1.87163			0.0844656			0.0422328	−	0.999108i	$-0.486553\pi$
$491$	1.87163			0.0844656			0.0422328	+	0.999108i	$0.486553\pi$
$492$		0			0
$493$	16.8604	+	9.73437i	0.759355	+	0.438414i
$494$	−3.12257	+	1.83084i	−0.140491	+	0.0823734i
$495$		0			0
$496$	−1.48558	−	5.54424i	−0.0667043	−	0.248944i
$497$	1.80916	−	1.04452i	0.0811521	−	0.0468532i
$498$		0			0
$499$	10.9455	+	2.93283i	0.489986	+	0.131291i	0.495349	−	0.868694i	$-0.335040\pi$
$499$	10.9455	+	2.93283i	0.489986	+	0.131291i	−0.00536247	+	0.999986i	$0.501707\pi$
$500$	8.89046	−	2.38219i	0.397594	−	0.106535i
$501$		0			0
$502$	20.4369	−	5.47604i	0.912142	−	0.244408i
$503$	0.311572	−	0.179886i	0.0138923	−	0.00802072i	−0.493038	−	0.870008i	$-0.664114\pi$
$503$	0.311572	−	0.179886i	0.0138923	−	0.00802072i	0.506930	+	0.861987i	$0.330780\pi$
$504$		0			0
$505$	−17.2459	+	4.62104i	−0.767434	+	0.205633i
$506$	−2.67121	+	4.62667i	−0.118750	+	0.205680i
$507$		0			0
$508$	9.38987	+	16.2637i	0.416608	+	0.721586i
$509$	−30.5184	−	30.5184i	−1.35270	−	1.35270i	−0.882623	−	0.470082i	$-0.844224\pi$
$509$	−30.5184	−	30.5184i	−1.35270	−	1.35270i	−0.470082	−	0.882623i	$-0.655776\pi$
$510$		0			0
$511$		−	1.22734i		−	0.0542945i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−3.79011	+	14.1449i	−0.167175	+	0.623905i
$515$	−2.83809	−	10.5919i	−0.125061	−	0.466734i
$516$		0			0
$517$			30.7760i			1.35353i
$518$	1.27668	−	1.27668i	0.0560943	−	0.0560943i
$519$		0			0
$520$	−0.0248886	−	3.71195i	−0.00109144	−	0.162780i
$521$		−	39.0644i		−	1.71144i	−0.517436	−	0.855722i	$-0.673113\pi$
$521$		−	39.0644i		−	1.71144i	0.517436	−	0.855722i	$-0.326887\pi$
$522$		0			0
$523$	−22.3670	+	38.7408i	−0.978041	+	1.69402i	−0.308529	+	0.951215i	$0.599837\pi$
$523$	−22.3670	+	38.7408i	−0.978041	+	1.69402i	−0.669512	+	0.742801i	$0.733497\pi$
$524$	−3.36592			−0.147041
$525$		0			0
$526$	−2.98299	−	11.1327i	−0.130065	−	0.485407i
$527$	4.96882	+	18.5439i	0.216445	+	0.807784i
$528$		0			0
$529$	−20.8376			−0.905981
$530$	1.37701	−	2.38505i	0.0598134	−	0.103600i
$531$		0			0
$532$		−	0.352507i		−	0.0152831i
$533$	8.94119	+	32.4959i	0.387286	+	1.40755i
$534$		0			0
$535$	−0.582564	+	0.582564i	−0.0251864	+	0.0251864i
$536$			15.0740i			0.651096i
$537$		0			0
$538$	5.29814	+	19.7729i	0.228419	+	0.852471i
$539$	−6.46612	+	24.1319i	−0.278515	+	1.03943i
$540$		0			0
$541$	20.3887	+	20.3887i	0.876580	+	0.876580i	0.993179	−	0.116599i	$-0.0371993\pi$
$541$	20.3887	+	20.3887i	0.876580	+	0.876580i	−0.116599	+	0.993179i	$0.537199\pi$
$542$			0.555985i			0.0238816i
$543$		0			0
$544$	2.36507	+	2.36507i	0.101401	+	0.101401i
$545$	4.25088	+	7.36274i	0.182088	+	0.315385i
$546$		0			0
$547$	9.46079	−	16.3866i	0.404514	−	0.700639i	−0.589751	−	0.807585i	$-0.700774\pi$
$547$	9.46079	−	16.3866i	0.404514	−	0.700639i	0.994265	+	0.106947i	$0.0341074\pi$
$548$	3.76073	−	1.00768i	0.160650	−	0.0430462i
$549$		0			0
$550$	12.3965	−	7.15714i	0.528590	−	0.305182i
$551$	5.64452	−	1.51244i	0.240465	−	0.0644323i
$552$		0			0
$553$	1.19754	−	0.320880i	0.0509246	−	0.0136452i
$554$	11.6634	+	3.12521i	0.495532	+	0.132777i
$555$		0			0
$556$	0.478471	−	0.276245i	0.0202917	−	0.0117154i
$557$	0.839623	+	3.13351i	0.0355760	+	0.132771i	0.981430	−	0.191821i	$-0.0614394\pi$
$557$	0.839623	+	3.13351i	0.0355760	+	0.132771i	−0.945854	+	0.324593i	$0.894773\pi$
$558$		0			0
$559$	−4.88009	+	8.58499i	−0.206406	+	0.363106i
$560$	0.313065	+	0.180748i	0.0132294	+	0.00763801i
$561$		0			0
$562$	14.5671			0.614475
$563$	−1.15338	+	1.99771i	−0.0486090	+	0.0841933i	−0.889306	−	0.457312i	$-0.848812\pi$
$563$	−1.15338	+	1.99771i	−0.0486090	+	0.0841933i	0.840697	+	0.541506i	$0.182145\pi$
$564$		0			0
$565$	−9.82222	+	9.82222i	−0.413224	+	0.413224i
$566$	12.8889	+	3.45357i	0.541761	+	0.145164i
$567$		0			0
$568$	2.97477	+	5.15245i	0.124818	+	0.216192i
$569$	−4.75114	−	8.22922i	−0.199178	−	0.344987i	0.749084	−	0.662475i	$-0.230494\pi$
$569$	−4.75114	−	8.22922i	−0.199178	−	0.344987i	−0.948262	+	0.317488i	$0.897161\pi$
$570$		0			0
$571$	22.0695	−	12.7418i	0.923578	−	0.533228i	0.0388033	−	0.999247i	$-0.487645\pi$
$571$	22.0695	−	12.7418i	0.923578	−	0.533228i	0.884775	+	0.466019i	$0.154312\pi$
$572$	−3.47503	−	12.6296i	−0.145298	−	0.528072i
$573$		0			0
$574$	−3.17038	−	0.849501i	−0.132329	−	0.0354575i
$575$	−5.01770	−	2.89697i	−0.209253	−	0.120812i
$576$		0			0
$577$	17.9008	−	17.9008i	0.745221	−	0.745221i	−0.228357	−	0.973577i	$-0.573335\pi$
$577$	17.9008	−	17.9008i	0.745221	−	0.745221i	0.973577	+	0.228357i	$0.0733353\pi$
$578$	4.11035	+	4.11035i	0.170968	+	0.170968i
$579$		0			0
$580$	−1.55101	+	5.78846i	−0.0644023	+	0.240353i
$581$	−2.62767	−	1.51709i	−0.109014	−	0.0629394i
$582$		0			0
$583$	2.51529	−	9.38721i	0.104173	−	0.388778i
$584$	3.49544			0.144642
$585$		0			0
$586$	−21.1106			−0.872071
$587$	−7.99701	+	29.8452i	−0.330072	+	1.23185i	0.579042	+	0.815298i	$0.303427\pi$
$587$	−7.99701	+	29.8452i	−0.330072	+	1.23185i	−0.909114	+	0.416547i	$0.863240\pi$
$588$		0			0
$589$	4.99037	+	2.88119i	0.205625	+	0.118718i
$590$	−1.29112	+	4.81852i	−0.0531545	+	0.198375i
$591$		0			0
$592$	3.63596	+	3.63596i	0.149437	+	0.149437i
$593$	1.91150	−	1.91150i	0.0784959	−	0.0784959i	−0.666769	−	0.745265i	$-0.732323\pi$
$593$	1.91150	−	1.91150i	0.0784959	−	0.0784959i	0.745265	+	0.666769i	$0.232323\pi$
$594$		0			0
$595$	−1.04711	−	0.604551i	−0.0429274	−	0.0247842i
$596$	−12.5052	−	3.35075i	−0.512232	−	0.137252i
$597$		0			0
$598$	−3.72388	+	3.77416i	−0.152281	+	0.154337i
$599$	24.8798	−	14.3643i	1.01656	−	0.586911i	0.103454	−	0.994634i	$-0.467011\pi$
$599$	24.8798	−	14.3643i	1.01656	−	0.586911i	0.913105	+	0.407723i	$0.133677\pi$
$600$		0			0
$601$	−15.4935	−	26.8355i	−0.631993	−	1.09464i	−0.987144	−	0.159835i	$-0.948904\pi$
$601$	−15.4935	−	26.8355i	−0.631993	−	1.09464i	0.355151	−	0.934809i	$-0.384430\pi$
$602$	−0.480843	−	0.832845i	−0.0195977	−	0.0339442i
$603$		0			0
$604$	8.72875	+	2.33886i	0.355168	+	0.0951670i
$605$	−1.60067	+	1.60067i	−0.0650766	+	0.0650766i
$606$		0			0
$607$	−5.03399	+	8.71913i	−0.204323	+	0.353899i	−0.949917	−	0.312502i	$-0.898833\pi$
$607$	−5.03399	+	8.71913i	−0.204323	+	0.353899i	0.745594	+	0.666401i	$0.232166\pi$
$608$	1.00393			0.0407148
$609$		0			0
$610$	−5.10575	−	2.94781i	−0.206726	−	0.119353i
$611$	−7.70722	+	29.5550i	−0.311801	+	1.19567i
$612$		0			0
$613$	−5.97413	−	22.2957i	−0.241293	−	0.900516i	−0.975211	−	0.221278i	$-0.928977\pi$
$613$	−5.97413	−	22.2957i	−0.241293	−	0.900516i	0.733918	−	0.679238i	$-0.237690\pi$
$614$	13.4032	−	7.73837i	0.540911	−	0.312295i
$615$		0			0
$616$	1.23218	+	0.330162i	0.0496460	+	0.0133026i
$617$	−25.3370	+	6.78904i	−1.02003	+	0.273316i	−0.729815	−	0.683645i	$-0.760394\pi$
$617$	−25.3370	+	6.78904i	−1.02003	+	0.273316i	−0.290216	+	0.956961i	$0.593727\pi$
$618$		0			0
$619$	−20.5005	+	5.49310i	−0.823985	+	0.220786i	−0.646088	−	0.763263i	$-0.723596\pi$
$619$	−20.5005	+	5.49310i	−0.823985	+	0.220786i	−0.177897	+	0.984049i	$0.556929\pi$
$620$	−5.11763	+	2.95467i	−0.205529	+	0.118662i
$621$		0			0
$622$	−25.0277	+	6.70614i	−1.00352	+	0.268892i
$623$	−1.82144	+	3.15482i	−0.0729743	+	0.126395i
$624$		0			0
$625$	5.11220	+	8.85460i	0.204488	+	0.354184i
$626$	24.9584	+	24.9584i	0.997537	+	0.997537i
$627$		0			0
$628$		−	11.2013i		−	0.446980i
$629$	−12.1612	−	12.1612i	−0.484900	−	0.484900i
$630$		0			0
$631$	2.60255	−	9.71284i	0.103606	−	0.386662i	−0.894578	−	0.446913i	$-0.852523\pi$
$631$	2.60255	−	9.71284i	0.103606	−	0.386662i	0.998183	+	0.0602509i	$0.0191901\pi$
$632$	0.913858	+	3.41056i	0.0363513	+	0.135665i
$633$		0			0
$634$			12.6353i			0.501811i
$635$	13.6714	−	13.6714i	0.542535	−	0.542535i
$636$		0			0
$637$	−12.2529	+	21.5552i	−0.485478	+	0.854046i
$638$			21.1468i			0.837212i
$639$		0			0
$640$	−0.514766	+	0.891601i	−0.0203479	+	0.0352436i
$641$	6.47708			0.255829			0.127915	−	0.991785i	$-0.459172\pi$
$641$	6.47708			0.255829			0.127915	+	0.991785i	$0.459172\pi$
$642$		0			0
$643$	−1.88381	−	7.03049i	−0.0742904	−	0.277255i	0.918781	−	0.394767i	$-0.129175\pi$
$643$	−1.88381	−	7.03049i	−0.0742904	−	0.277255i	−0.993071	+	0.117512i	$0.962508\pi$
$644$	−0.133638	−	0.498745i	−0.00526609	−	0.0196533i
$645$		0			0
$646$	−3.35786			−0.132113
$647$	−2.67717	+	4.63699i	−0.105250	+	0.182299i	−0.913840	−	0.406073i	$-0.866898\pi$
$647$	−2.67717	+	4.63699i	−0.105250	+	0.182299i	0.808590	+	0.588372i	$0.200231\pi$
$648$		0			0
$649$			17.6034i			0.690993i
$650$	13.6971	−	3.76873i	0.537244	−	0.147822i
$651$		0			0
$652$	6.28053	−	6.28053i	0.245965	−	0.245965i
$653$		−	13.5198i		−	0.529072i	−0.964376	−	0.264536i	$-0.914781\pi$
$653$		−	13.5198i		−	0.529072i	0.964376	−	0.264536i	$-0.0852189\pi$
$654$		0			0
$655$	0.896892	+	3.34725i	0.0350445	+	0.130788i
$656$	2.41936	−	9.02916i	0.0944600	−	0.352529i
$657$		0			0
$658$	−2.10327	−	2.10327i	−0.0819940	−	0.0819940i
$659$			25.9719i			1.01172i	0.862615	+	0.505861i	$0.168825\pi$
$659$			25.9719i			1.01172i	−0.862615	+	0.505861i	$0.831175\pi$
$660$		0			0
$661$	9.76168	+	9.76168i	0.379685	+	0.379685i	0.870989	−	0.491303i	$-0.163479\pi$
$661$	9.76168	+	9.76168i	0.379685	+	0.379685i	−0.491303	+	0.870989i	$0.663479\pi$
$662$	−4.98392	−	8.63240i	−0.193706	−	0.335508i
$663$		0			0
$664$	4.32062	−	7.48354i	0.167673	−	0.290418i
$665$	−0.350552	+	0.0939301i	−0.0135938	+	0.00364245i
$666$		0			0
$667$	7.41277	−	4.27977i	0.287024	−	0.165713i
$668$	−8.97462	+	2.40474i	−0.347238	+	0.0930422i
$669$		0			0
$670$	14.9903	−	4.01665i	0.579127	−	0.155177i
$671$	−20.0955	−	5.38458i	−0.775779	−	0.207869i
$672$		0			0
$673$	−24.4924	+	14.1407i	−0.944112	+	0.545083i	−0.891247	−	0.453518i	$-0.850169\pi$
$673$	−24.4924	+	14.1407i	−0.944112	+	0.545083i	−0.0528649	+	0.998602i	$0.516835\pi$
$674$	7.54543	+	28.1599i	0.290639	+	1.08468i
$675$		0			0
$676$	−0.174322	−	12.9988i	−0.00670468	−	0.499955i
$677$	34.1714	+	19.7289i	1.31331	+	0.758242i	0.982644	−	0.185504i	$-0.0593917\pi$
$677$	34.1714	+	19.7289i	1.31331	+	0.758242i	0.330671	+	0.943746i	$0.392725\pi$
$678$		0			0
$679$	5.18621			0.199028
$680$	1.72174	−	2.98215i	0.0660259	−	0.114360i
$681$		0			0
$682$	−14.7452	+	14.7452i	−0.564622	+	0.564622i
$683$	25.3130	+	6.78259i	0.968574	+	0.259529i	0.708226	−	0.705986i	$-0.249496\pi$
$683$	25.3130	+	6.78259i	0.968574	+	0.259529i	0.260348	+	0.965515i	$0.416163\pi$
$684$		0			0
$685$	−2.00419	−	3.47136i	−0.0765761	−	0.132634i
$686$	−2.43624	−	4.21970i	−0.0930162	−	0.161109i
$687$		0			0
$688$	2.37192	−	1.36943i	0.0904286	−	0.0522090i
$689$	4.76634	−	8.38488i	0.181583	−	0.319438i
$690$		0			0
$691$	−11.3975	−	3.05395i	−0.433581	−	0.116178i	0.0354255	−	0.999372i	$-0.488721\pi$
$691$	−11.3975	−	3.05395i	−0.433581	−	0.116178i	−0.469007	+	0.883195i	$0.655388\pi$
$692$	9.16985	+	5.29421i	0.348585	+	0.201256i
$693$		0			0
$694$	10.1435	−	10.1435i	0.385042	−	0.385042i
$695$	−0.402207	−	0.402207i	−0.0152566	−	0.0152566i
$696$		0			0
$697$	−8.09204	+	30.1999i	−0.306508	+	1.14390i
$698$	22.9144	+	13.2296i	0.867321	+	0.500748i
$699$		0			0
$700$	−0.358066	+	1.33632i	−0.0135336	+	0.0505082i
$701$	−32.2520			−1.21814			−0.609071	−	0.793115i	$-0.708458\pi$
$701$	−32.2520			−1.21814			−0.609071	+	0.793115i	$0.708458\pi$
$702$		0			0
$703$	−5.16224			−0.194698
$704$	−0.940292	+	3.50922i	−0.0354386	+	0.132259i
$705$		0			0
$706$	−10.3227	−	5.95982i	−0.388500	−	0.224301i
$707$	1.57603	−	5.88181i	0.0592726	−	0.221208i
$708$		0			0
$709$	9.57038	+	9.57038i	0.359423	+	0.359423i	0.863600	−	0.504177i	$-0.168204\pi$
$709$	9.57038	+	9.57038i	0.359423	+	0.359423i	−0.504177	+	0.863600i	$0.668204\pi$
$710$	4.33120	−	4.33120i	0.162547	−	0.162547i
$711$		0			0
$712$	−8.98484	−	5.18740i	−0.336721	−	0.194406i
$713$	8.15292	+	2.18457i	0.305329	+	0.0818127i
$714$		0			0
$715$	−11.6336	+	6.82108i	−0.435073	+	0.255094i
$716$	21.6674	−	12.5097i	0.809750	−	0.467509i
$717$		0			0
$718$	9.89226	+	17.1339i	0.369176	+	0.639431i
$719$	5.20762	+	9.01985i	0.194211	+	0.336384i	0.946642	−	0.322288i	$-0.104452\pi$
$719$	5.20762	+	9.01985i	0.194211	+	0.336384i	−0.752430	+	0.658672i	$0.771119\pi$
$720$		0			0
$721$	3.61241	+	0.967944i	0.134533	+	0.0360481i
$722$	12.7224	−	12.7224i	0.473477	−	0.473477i
$723$		0			0
$724$	11.6937	−	20.2541i	0.434594	−	0.752739i
$725$	−22.9341			−0.851752
$726$		0			0
$727$	−20.0010	−	11.5476i	−0.741796	−	0.428276i	0.0809260	−	0.996720i	$-0.474212\pi$
$727$	−20.0010	−	11.5476i	−0.741796	−	0.428276i	−0.822722	+	0.568444i	$0.807546\pi$
$728$	1.10061	+	0.625638i	0.0407914	+	0.0231877i
$729$		0			0
$730$	−0.931405	−	3.47605i	−0.0344728	−	0.128654i
$731$	−7.93338	+	4.58034i	−0.293427	+	0.169410i
$732$		0			0
$733$	−24.5643	−	6.58200i	−0.907305	−	0.243112i	−0.225154	−	0.974323i	$-0.572289\pi$
$733$	−24.5643	−	6.58200i	−0.907305	−	0.243112i	−0.682151	+	0.731212i	$0.738955\pi$
$734$	16.1111	−	4.31695i	0.594671	−	0.159342i
$735$		0			0
$736$	1.42041	−	0.380599i	0.0523571	−	0.0140290i
$737$	47.4269	−	27.3819i	1.74699	−	1.00863i
$738$		0			0
$739$	23.9997	−	6.43070i	0.882843	−	0.236557i	0.211209	−	0.977441i	$-0.432260\pi$
$739$	23.9997	−	6.43070i	0.882843	−	0.236557i	0.671633	+	0.740884i	$0.265593\pi$
$740$	2.64694	−	4.58464i	0.0973035	−	0.168535i
$741$		0			0
$742$	0.469635	+	0.813432i	0.0172408	+	0.0298620i
$743$	15.1274	+	15.1274i	0.554971	+	0.554971i	0.927871	−	0.372901i	$-0.121637\pi$
$743$	15.1274	+	15.1274i	0.554971	+	0.554971i	−0.372901	+	0.927871i	$0.621637\pi$
$744$		0			0
$745$			13.3286i			0.488324i
$746$	0.377142	+	0.377142i	0.0138082	+	0.0138082i
$747$		0			0
$748$	3.14500	−	11.7373i	0.114993	−	0.429159i
$749$	−0.0727242	−	0.271410i	−0.00265728	−	0.00991712i
$750$		0			0
$751$			42.6857i			1.55762i	0.627258	+	0.778812i	$0.284177\pi$
$751$			42.6857i			1.55762i	−0.627258	+	0.778812i	$0.715823\pi$
$752$	5.99005	−	5.99005i	0.218435	−	0.218435i
$753$		0			0
$754$	−5.29580	+	20.3079i	−0.192862	+	0.739569i
$755$		−	9.30355i		−	0.338591i
$756$		0			0
$757$	8.17298	−	14.1560i	0.297052	−	0.514509i	−0.678408	−	0.734685i	$-0.737330\pi$
$757$	8.17298	−	14.1560i	0.297052	−	0.514509i	0.975460	+	0.220176i	$0.0706632\pi$
$758$	34.5184			1.25377
$759$		0			0
$760$	−0.267510	−	0.998362i	−0.00970362	−	0.0362144i
$761$	−1.60666	−	5.99615i	−0.0582415	−	0.217360i	0.930672	−	0.365856i	$-0.119224\pi$
$761$	−1.60666	−	5.99615i	−0.0582415	−	0.217360i	−0.988913	+	0.148496i	$0.952557\pi$
$762$		0			0
$763$	−2.89957			−0.104971
$764$	−6.15600	+	10.6625i	−0.222716	+	0.385756i
$765$		0			0
$766$		−	2.02050i		−	0.0730038i
$767$	−4.40841	+	16.9050i	−0.159179	+	0.610404i
$768$		0			0
$769$	16.4608	−	16.4608i	0.593593	−	0.593593i	−0.345007	−	0.938600i	$-0.612124\pi$
$769$	16.4608	−	16.4608i	0.593593	−	0.593593i	0.938600	+	0.345007i	$0.112124\pi$
$770$		−	1.31332i		−	0.0473288i
$771$		0			0
$772$	3.34912	+	12.4991i	0.120537	+	0.449852i
$773$	−2.25389	+	8.41164i	−0.0810668	+	0.302546i	−0.994540	−	0.104353i	$-0.966723\pi$
$773$	−2.25389	+	8.41164i	−0.0810668	+	0.302546i	0.913474	+	0.406898i	$0.133390\pi$
$774$		0			0
$775$	−15.9914	−	15.9914i	−0.574428	−	0.574428i
$776$			14.7702i			0.530218i
$777$		0			0
$778$	1.36989	+	1.36989i	0.0491129	+	0.0491129i
$779$	4.69221	+	8.12715i	0.168116	+	0.291185i
$780$		0			0
$781$	10.8074	−	18.7189i	0.386718	−	0.669815i
$782$	−4.75087	+	1.27299i	−0.169891	+	0.0455221i
$783$		0			0
$784$	5.95541	−	3.43835i	0.212693	−	0.122798i
$785$	−11.1391	+	2.98472i	−0.397573	+	0.106529i
$786$		0			0
$787$	−7.48822	+	2.00646i	−0.266926	+	0.0715227i	−0.389800	−	0.920900i	$-0.627456\pi$
$787$	−7.48822	+	2.00646i	−0.266926	+	0.0715227i	0.122873	+	0.992422i	$0.460789\pi$
$788$	20.6372	+	5.52972i	0.735170	+	0.196988i
$789$		0			0
$790$	3.14813	−	1.81758i	0.112006	−	0.0646665i
$791$	−1.22615	−	4.57607i	−0.0435970	−	0.162706i
$792$		0			0
$793$	−17.9498	−	10.2035i	−0.637416	−	0.362336i
$794$	−29.6491	−	17.1179i	−1.05221	−	0.607493i
$795$		0			0
$796$	−22.2137			−0.787344
$797$	−9.36322	+	16.2176i	−0.331662	+	0.574456i	−0.982838	−	0.184471i	$-0.940943\pi$
$797$	−9.36322	+	16.2176i	−0.331662	+	0.574456i	0.651176	+	0.758927i	$0.274276\pi$
$798$		0			0
$799$	−20.0350	+	20.0350i	−0.708787	+	0.708787i
$800$	−3.80581	−	1.01976i	−0.134556	−	0.0360541i
$801$		0			0
$802$	−4.49498	−	7.78553i	−0.158723	−	0.274917i
$803$	−6.34949	−	10.9976i	−0.224069	−	0.388098i
$804$		0			0
$805$	−0.460369	+	0.265794i	−0.0162259	+	0.00936801i
$806$	−17.8528	+	10.4675i	−0.628838	+	0.368704i
$807$		0			0
$808$	16.7512	+	4.48848i	0.589306	+	0.157904i
$809$	8.00375	+	4.62097i	0.281397	+	0.162465i	0.634056	−	0.773287i	$-0.281389\pi$
$809$	8.00375	+	4.62097i	0.281397	+	0.162465i	−0.352659	+	0.935752i	$0.614722\pi$
$810$		0			0
$811$	27.8829	−	27.8829i	0.979100	−	0.979100i	−0.0206860	−	0.999786i	$-0.506585\pi$
$811$	27.8829	−	27.8829i	0.979100	−	0.979100i	0.999786	+	0.0206860i	$0.00658503\pi$
$812$	−1.44520	−	1.44520i	−0.0507166	−	0.0507166i
$813$		0			0
$814$	4.83501	−	18.0445i	0.169467	−	0.632459i
$815$	−7.91921	−	4.57216i	−0.277398	−	0.160156i
$816$		0			0
$817$	−0.711655	+	2.65593i	−0.0248977	+	0.0929194i
$818$	14.7515			0.515772
$819$		0			0
$820$	−9.62373			−0.336075
$821$	2.29371	−	8.56024i	0.0800510	−	0.298755i	−0.914280	−	0.405083i	$-0.867243\pi$
$821$	2.29371	−	8.56024i	0.0800510	−	0.298755i	0.994331	+	0.106328i	$0.0339094\pi$
$822$		0			0
$823$	−8.36300	−	4.82838i	−0.291516	−	0.168307i	0.347109	−	0.937825i	$-0.387163\pi$
$823$	−8.36300	−	4.82838i	−0.291516	−	0.168307i	−0.638625	+	0.769518i	$0.720497\pi$
$824$	−2.75668	+	10.2881i	−0.0960334	+	0.358401i
$825$		0			0
$826$	−1.20304	−	1.20304i	−0.0418590	−	0.0418590i
$827$	−16.2044	+	16.2044i	−0.563482	+	0.563482i	−0.930295	−	0.366813i	$-0.880449\pi$
$827$	−16.2044	+	16.2044i	−0.563482	+	0.563482i	0.366813	+	0.930295i	$0.380449\pi$
$828$		0			0
$829$	39.4372	+	22.7691i	1.36971	+	0.790802i	0.990891	−	0.134668i	$-0.0429969\pi$
$829$	39.4372	+	22.7691i	1.36971	+	0.790802i	0.378819	+	0.925471i	$0.376330\pi$
$830$	−8.59330	−	2.30257i	−0.298278	−	0.0799233i
$831$		0			0
$832$	−1.78180	+	3.13452i	−0.0617728	+	0.108670i
$833$	−19.9191	+	11.5003i	−0.690156	+	0.398462i
$834$		0			0
$835$	4.78280	+	8.28405i	0.165516	+	0.286681i
$836$	−1.82365	−	3.15865i	−0.0630721	−	0.109244i
$837$		0			0
$838$	33.7609	+	9.04621i	1.16625	+	0.312496i
$839$	22.5058	−	22.5058i	0.776987	−	0.776987i	−0.202330	−	0.979317i	$-0.564851\pi$
$839$	22.5058	−	22.5058i	0.776987	−	0.776987i	0.979317	+	0.202330i	$0.0648515\pi$
$840$		0			0
$841$	2.44058	−	4.22721i	0.0841579	−	0.145766i
$842$	2.64684			0.0912160
$843$		0			0
$844$	−15.8925	−	9.17554i	−0.547042	−	0.315835i
$845$	−12.8803	+	3.63706i	−0.443095	+	0.125119i
$846$		0			0
$847$	−0.199820	−	0.745737i	−0.00686588	−	0.0256238i
$848$	−2.31663	+	1.33751i	−0.0795534	+	0.0459302i
$849$		0			0
$850$	12.7293	+	3.41081i	0.436612	+	0.116990i
$851$	−7.30380	+	1.95705i	−0.250371	+	0.0670868i
$852$		0			0
$853$	1.99312	−	0.534054i	0.0682430	−	0.0182857i	−0.224536	−	0.974466i	$-0.572087\pi$
$853$	1.99312	−	0.534054i	0.0682430	−	0.0182857i	0.292779	+	0.956180i	$0.405420\pi$
$854$	1.74134	−	1.00536i	0.0595874	−	0.0344028i
$855$		0			0
$856$	0.772969	−	0.207116i	0.0264195	−	0.00707910i
$857$	7.56394	−	13.1011i	0.258379	−	0.447526i	−0.707429	−	0.706785i	$-0.750145\pi$
$857$	7.56394	−	13.1011i	0.258379	−	0.447526i	0.965808	+	0.259259i	$0.0834782\pi$
$858$		0			0
$859$	−15.4894	−	26.8284i	−0.528492	−	0.915375i	−0.999448	−	0.0332181i	$-0.989424\pi$
$859$	−15.4894	−	26.8284i	−0.528492	−	0.915375i	0.470956	−	0.882156i	$-0.343909\pi$
$860$	−1.99386	−	1.99386i	−0.0679900	−	0.0679900i
$861$		0			0
$862$		−	14.6861i		−	0.500211i
$863$	−14.4513	−	14.4513i	−0.491927	−	0.491927i	0.416986	−	0.908913i	$-0.363086\pi$
$863$	−14.4513	−	14.4513i	−0.491927	−	0.491927i	−0.908913	+	0.416986i	$0.863086\pi$
$864$		0			0
$865$	2.82142	−	10.5297i	0.0959312	−	0.358020i
$866$	−3.96968	−	14.8151i	−0.134895	−	0.503436i
$867$		0			0
$868$		−	2.01541i		−	0.0684073i
$869$	9.07056	−	9.07056i	0.307698	−	0.307698i
$870$		0			0
$871$	52.4025	−	14.4185i	1.77559	−	0.488552i
$872$		−	8.25788i		−	0.279647i
$873$		0			0
$874$	−0.738151	+	1.27851i	−0.0249683	+	0.0432464i
$875$	3.23180			0.109255
$876$		0			0
$877$	2.10830	+	7.86828i	0.0711922	+	0.265693i	0.992343	−	0.123513i	$-0.0394161\pi$
$877$	2.10830	+	7.86828i	0.0711922	+	0.265693i	−0.921151	+	0.389206i	$0.872749\pi$
$878$	2.80878	+	10.4825i	0.0947919	+	0.353768i
$879$		0			0
$880$	3.74030			0.126086
$881$	−7.84542	+	13.5887i	−0.264319	+	0.457814i	−0.967385	−	0.253311i	$-0.918481\pi$
$881$	−7.84542	+	13.5887i	−0.264319	+	0.457814i	0.703066	+	0.711125i	$0.251814\pi$
$882$		0			0
$883$			49.4553i			1.66430i	0.554549	+	0.832151i	$0.312891\pi$
$883$			49.4553i			1.66430i	−0.554549	+	0.832151i	$0.687109\pi$
$884$	5.95960	−	10.4840i	0.200443	−	0.352617i
$885$		0			0
$886$	23.5718	−	23.5718i	0.791909	−	0.791909i
$887$		−	26.5574i		−	0.891709i	−0.895105	−	0.445855i	$-0.852900\pi$
$887$		−	26.5574i		−	0.891709i	0.895105	−	0.445855i	$-0.147100\pi$
$888$		0			0
$889$	1.70667	+	6.36938i	0.0572399	+	0.213622i
$890$	−2.76450	+	10.3172i	−0.0926661	+	0.345835i
$891$		0			0
$892$	17.9280	+	17.9280i	0.600275	+	0.600275i
$893$			8.50452i			0.284593i
$894$		0			0
$895$	−18.2138	−	18.2138i	−0.608822	−	0.608822i
$896$	−0.175564	−	0.304085i	−0.00586516	−	0.0101588i
$897$		0			0
$898$	9.13180	−	15.8167i	0.304732	−	0.527811i
$899$	32.2717	−	8.64716i	1.07632	−	0.288399i
$900$		0			0
$901$	7.74846	−	4.47357i	0.258139	−	0.149036i
$902$	−32.8030	+	8.78954i	−1.09222	+	0.292660i
$903$		0			0
$904$	13.0325	−	3.49205i	0.433455	−	0.116144i
$905$	−23.2577	−	6.23188i	−0.773112	−	0.207155i
$906$		0			0
$907$	8.46275	−	4.88597i	0.281001	−	0.162236i	−0.352876	−	0.935670i	$-0.614796\pi$
$907$	8.46275	−	4.88597i	0.281001	−	0.162236i	0.633876	+	0.773434i	$0.281463\pi$
$908$	6.45111	+	24.0759i	0.214088	+	0.798986i
$909$		0			0
$910$	0.328895	−	1.26122i	0.0109027	−	0.0418089i
$911$	35.0988	+	20.2643i	1.16288	+	0.671387i	0.951992	−	0.306124i	$-0.0990323\pi$
$911$	35.0988	+	20.2643i	1.16288	+	0.671387i	0.210884	+	0.977511i	$0.432366\pi$
$912$		0			0
$913$	−31.3937			−1.03898
$914$	3.18999	−	5.52523i	0.105516	−	0.182758i
$915$		0			0
$916$	−1.09743	+	1.09743i	−0.0362602	+	0.0362602i
$917$	−1.14159	−	0.305889i	−0.0376988	−	0.0101014i
$918$		0			0
$919$	5.97895	+	10.3558i	0.197227	+	0.341608i	0.947628	−	0.319375i	$-0.103473\pi$
$919$	5.97895	+	10.3558i	0.197227	+	0.341608i	−0.750401	+	0.660983i	$0.770140\pi$
$920$	−0.756974	−	1.31112i	−0.0249567	−	0.0432263i
$921$		0			0
$922$	−31.1868	+	18.0057i	−1.02708	+	0.592987i
$923$	15.0664	−	15.2698i	0.495915	−	0.502610i
$924$		0			0
$925$	19.5696	+	5.24365i	0.643444	+	0.172410i
$926$	−19.4427	−	11.2253i	−0.638927	−	0.368885i
$927$		0			0
$928$	4.11589	−	4.11589i	0.135111	−	0.135111i
$929$	−13.1437	−	13.1437i	−0.431230	−	0.431230i	0.457817	−	0.889047i	$-0.348632\pi$
$929$	−13.1437	−	13.1437i	−0.431230	−	0.431230i	−0.889047	+	0.457817i	$0.848632\pi$
$930$		0			0
$931$	−1.78682	+	6.66851i	−0.0585607	+	0.218551i
$932$	−8.62965	−	4.98233i	−0.282674	−	0.163202i
$933$		0			0
$934$	−3.62347	+	13.5230i	−0.118563	+	0.442485i
$935$	−12.5102			−0.409128
$936$		0			0
$937$	−28.4270			−0.928669			−0.464335	−	0.885660i	$-0.653706\pi$
$937$	−28.4270			−0.928669			−0.464335	+	0.885660i	$0.653706\pi$
$938$	−1.36990	+	5.11253i	−0.0447287	+	0.166930i
$939$		0			0
$940$	−7.55295	−	4.36069i	−0.246350	−	0.142230i
$941$	−2.47011	+	9.21859i	−0.0805234	+	0.300518i	−0.994429	−	0.105410i	$-0.966385\pi$
$941$	−2.47011	+	9.21859i	−0.0805234	+	0.300518i	0.913905	+	0.405927i	$0.133051\pi$
$942$		0			0
$943$	9.71985	+	9.71985i	0.316522	+	0.316522i
$944$	3.42622	−	3.42622i	0.111514	−	0.111514i
$945$		0			0
$946$	−8.61721	−	4.97515i	−0.280170	−	0.161756i
$947$	−19.5132	−	5.22855i	−0.634094	−	0.169905i	−0.0725674	−	0.997364i	$-0.523119\pi$
$947$	−19.5132	−	5.22855i	−0.634094	−	0.169905i	−0.561527	+	0.827458i	$0.689786\pi$
$948$		0			0
$949$	−3.34344	−	12.1514i	−0.108533	−	0.394452i
$950$	3.42561	−	1.97778i	0.111141	−	0.0641675i
$951$		0			0
$952$	0.587209	+	1.01708i	0.0190316	+	0.0329636i
$953$	−28.6270	−	49.5834i	−0.927319	−	1.60616i	−0.787788	−	0.615947i	$-0.788774\pi$
$953$	−28.6270	−	49.5834i	−0.927319	−	1.60616i	−0.139532	−	0.990218i	$-0.544560\pi$
$954$		0			0
$955$	12.2437	+	3.28069i	0.396197	+	0.106161i
$956$	−0.0510586	+	0.0510586i	−0.00165135	+	0.00165135i
$957$		0			0
$958$	−13.3103	+	23.0541i	−0.430036	+	0.744845i
$959$	1.36708			0.0441452
$960$		0			0
$961$	1.68490	+	0.972775i	0.0543515	+	0.0313798i
$962$	9.16206	−	16.1178i	0.295397	−	0.519658i
$963$		0			0
$964$	−4.84236	−	18.0719i	−0.155962	−	0.582058i
$965$	11.5373	−	6.66108i	0.371400	−	0.214428i
$966$		0			0
$967$	−36.9339	−	9.89640i	−1.18771	−	0.318247i	−0.389732	−	0.920929i	$-0.627432\pi$
$967$	−36.9339	−	9.89640i	−1.18771	−	0.318247i	−0.797982	+	0.602682i	$0.794099\pi$
$968$	2.12384	−	0.569081i	0.0682627	−	0.0182909i
$969$		0			0
$970$	14.6882	−	3.93570i	0.471611	−	0.126368i
$971$	0.712957	−	0.411626i	0.0228799	−	0.0132097i	−0.488516	−	0.872555i	$-0.662462\pi$
$971$	0.712957	−	0.411626i	0.0228799	−	0.0132097i	0.511396	+	0.859345i	$0.329128\pi$
$972$		0			0
$973$	0.187384	−	0.0502094i	0.00600726	−	0.00160964i
$974$	7.63694	−	13.2276i	0.244703	−	0.423839i
$975$		0			0
$976$	2.86325	+	4.95929i	0.0916503	+	0.158743i
$977$	−2.22471	−	2.22471i	−0.0711749	−	0.0711749i	0.670623	−	0.741798i	$-0.266027\pi$
$977$	−2.22471	−	2.22471i	−0.0711749	−	0.0711749i	−0.741798	+	0.670623i	$0.766027\pi$
$978$		0			0
$979$			37.6917i			1.20463i
$980$	−5.00617	−	5.00617i	−0.159916	−	0.159916i
$981$		0			0
$982$	−0.484414	+	1.80786i	−0.0154583	+	0.0576911i
$983$	−13.4472	−	50.1857i	−0.428900	−	1.60068i	−0.755256	−	0.655429i	$-0.772488\pi$
$983$	−13.4472	−	50.1857i	−0.428900	−	1.60068i	0.326357	−	0.945247i	$-0.394179\pi$
$984$		0			0
$985$		−	21.9962i		−	0.700856i
$986$	−13.7665	+	13.7665i	−0.438414	+	0.438414i
$987$		0			0
$988$	−0.960276	−	3.49003i	−0.0305504	−	0.111033i
$989$			4.02754i			0.128068i
$990$		0			0
$991$	−20.4564	+	35.4315i	−0.649818	+	1.12552i	0.333348	+	0.942804i	$0.391822\pi$
$991$	−20.4564	+	35.4315i	−0.649818	+	1.12552i	−0.983166	+	0.182714i	$0.941512\pi$
$992$	5.73982			0.182240
$993$		0			0
$994$	0.540684	+	2.01786i	0.0171495	+	0.0640026i
$995$	5.91912	+	22.0905i	0.187649	+	0.700315i
$996$		0			0
$997$	30.9293			0.979542			0.489771	−	0.871851i	$-0.337080\pi$
$997$	30.9293			0.979542			0.489771	+	0.871851i	$0.337080\pi$
$998$	−5.66579	+	9.81344i	−0.179347	+	0.310639i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bc.a.305.3		56
3.2	odd	2		234.2.z.a.227.12	yes	56
9.4	even	3		234.2.y.a.149.5	yes	56
9.5	odd	6		702.2.bb.a.71.10		56
13.11	odd	12		702.2.bb.a.89.10		56
39.11	even	12		234.2.y.a.11.5	✓	56
117.50	even	12	inner	702.2.bc.a.557.3		56
117.76	odd	12		234.2.z.a.167.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.5	✓	56	39.11	even	12
234.2.y.a.149.5	yes	56	9.4	even	3
234.2.z.a.167.12	yes	56	117.76	odd	12
234.2.z.a.227.12	yes	56	3.2	odd	2
702.2.bb.a.71.10		56	9.5	odd	6
702.2.bb.a.89.10		56	13.11	odd	12
702.2.bc.a.305.3		56	1.1	even	1	trivial
702.2.bc.a.557.3		56	117.50	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.266463 + 0.994452i) q^{5} +(-0.248284 - 0.248284i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.891601 - 0.514766i) q^{10} +(-3.50922 - 0.940292i) q^{11} +(-3.13452 - 1.78180i) q^{13} +(0.304085 - 0.175564i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.67236 - 2.89660i) q^{17} +(-0.969723 - 0.259837i) q^{19} +(0.727989 - 0.727989i) q^{20} +(1.81650 - 3.14628i) q^{22} -1.47052 q^{23} +(3.41219 + 1.97003i) q^{25} +(2.53236 - 2.56655i) q^{26} +(0.0908784 + 0.339163i) q^{28} +(-5.04092 + 2.91038i) q^{29} +(-5.54424 - 1.48558i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.23074 - 0.865675i) q^{34} +(0.313065 - 0.180748i) q^{35} +(4.96682 - 1.33085i) q^{37} +(0.501966 - 0.869430i) q^{38} +(0.514766 + 0.891601i) q^{40} +(-6.60980 - 6.60980i) q^{41} -2.73886i q^{43} +(2.56893 + 2.56893i) q^{44} +(0.380599 - 1.42041i) q^{46} +(-2.19251 - 8.18256i) q^{47} -6.87671i q^{49} +(-2.78605 + 2.78605i) q^{50} +(1.82367 + 3.11034i) q^{52} +2.67501i q^{53} +(1.87015 - 3.23920i) q^{55} -0.351127 q^{56} +(-1.50652 - 5.62241i) q^{58} +(-1.25408 - 4.68030i) q^{59} +5.72649 q^{61} +(2.86991 - 4.97083i) q^{62} -1.00000i q^{64} +(2.60715 - 2.64234i) q^{65} +(-10.6589 + 10.6589i) q^{67} +3.34471i q^{68} +(0.0935622 + 0.349179i) q^{70} +(-1.53985 + 5.74681i) q^{71} +(2.47165 + 2.47165i) q^{73} +5.14203i q^{74} +(0.709887 + 0.709887i) q^{76} +(0.637824 + 1.10474i) q^{77} +(-1.76544 + 3.05783i) q^{79} +(-0.994452 + 0.266463i) q^{80} +(8.09532 - 4.67384i) q^{82} +(8.34680 - 2.23652i) q^{83} +(3.32615 - 0.891240i) q^{85} +(2.64553 + 0.708868i) q^{86} +(-3.14628 + 1.81650i) q^{88} +(-2.68520 - 10.0213i) q^{89} +(0.335858 + 1.22064i) q^{91} +(1.27351 + 0.735260i) q^{92} +8.47121 q^{94} +(0.516790 - 0.895107i) q^{95} +(-10.4441 + 10.4441i) q^{97} +(6.64239 + 1.77982i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 56 * q - 8 * q^7 + 24 * q^11 + 28 * q^16 - 8 * q^19 - 4 * q^28 - 4 * q^31 + 24 * q^35 - 4 * q^37 - 36 * q^38 + 48 * q^41 + 36 * q^47 + 24 * q^50 + 8 * q^52 + 36 * q^65 + 28 * q^67 + 24 * q^71 + 28 * q^73 + 4 * q^76 - 24 * q^77 - 24 * q^79 + 96 * q^83 - 72 * q^85 + 4 * q^91 + 24 * q^92 - 52 * q^97 - 48 * q^98

Introduction

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