LMFDB - Embedded newform 702.2.bb.a.197.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.7
Character	$\chi$	$=$	702.197
Dual form			702.2.bb.a.449.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.964970 - 3.60132i) q^{5} +(-0.861011 + 3.21334i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.22885 + 1.86418i) q^{10} +(-4.48313 + 4.48313i) q^{11} +(-0.905106 + 3.49010i) q^{13} +(2.88100 - 1.66335i) q^{14} -1.00000 q^{16} +(-1.38308 + 2.39556i) q^{17} +(0.703205 + 2.62440i) q^{19} +(3.60132 + 0.964970i) q^{20} +6.34010 q^{22} +(-0.0915043 + 0.158490i) q^{23} +(-7.70819 - 4.45033i) q^{25} +(3.10788 - 1.82787i) q^{26} +(-3.21334 - 0.861011i) q^{28} +0.948565i q^{29} +(2.14063 + 0.573581i) q^{31} +(0.707107 + 0.707107i) q^{32} +(2.67190 - 0.715935i) q^{34} +(10.7414 + 6.20155i) q^{35} +(1.96458 - 7.33191i) q^{37} +(1.35849 - 2.35297i) q^{38} +(-1.86418 - 3.22885i) q^{40} +(-2.27956 + 0.610806i) q^{41} +(-3.17570 + 1.83349i) q^{43} +(-4.48313 - 4.48313i) q^{44} +(0.176773 - 0.0473661i) q^{46} +(1.38011 + 5.15065i) q^{47} +(-3.52202 - 2.03344i) q^{49} +(2.30366 + 8.59737i) q^{50} +(-3.49010 - 0.905106i) q^{52} -3.43327i q^{53} +(11.8191 + 20.4712i) q^{55} +(1.66335 + 2.88100i) q^{56} +(0.670737 - 0.670737i) q^{58} +(-3.31440 + 3.31440i) q^{59} +(4.13990 + 7.17052i) q^{61} +(-1.10807 - 1.91924i) q^{62} -1.00000i q^{64} +(11.6955 + 6.62741i) q^{65} +(1.93297 + 7.21395i) q^{67} +(-2.39556 - 1.38308i) q^{68} +(-3.21016 - 11.9805i) q^{70} +(-11.7943 + 3.16027i) q^{71} +(2.16027 + 2.16027i) q^{73} +(-6.57361 + 3.79528i) q^{74} +(-2.62440 + 0.703205i) q^{76} +(-10.5458 - 18.2658i) q^{77} +(6.31331 - 10.9350i) q^{79} +(-0.964970 + 3.60132i) q^{80} +(2.04380 + 1.17999i) q^{82} +(-6.52658 + 1.74879i) q^{83} +(7.29255 + 7.29255i) q^{85} +(3.54203 + 0.949085i) q^{86} +6.34010i q^{88} +(-0.643808 - 0.172508i) q^{89} +(-10.4356 - 5.91342i) q^{91} +(-0.158490 - 0.0915043i) q^{92} +(2.66617 - 4.61795i) q^{94} +10.1298 q^{95} +(-5.65566 - 1.51543i) q^{97} +(1.05259 + 3.92830i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	0.964970	−	3.60132i	0.431548	−	1.61056i	−0.317648	−	0.948209i	$-0.602893\pi$
$5$	0.964970	−	3.60132i	0.431548	−	1.61056i	0.749195	−	0.662349i	$-0.230440\pi$
$6$		0			0
$7$	−0.861011	+	3.21334i	−0.325432	+	1.21453i	0.588446	+	0.808537i	$0.299740\pi$
$7$	−0.861011	+	3.21334i	−0.325432	+	1.21453i	−0.913877	+	0.405991i	$0.866927\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−3.22885	+	1.86418i	−1.02105	+	0.589505i
$11$	−4.48313	+	4.48313i	−1.35171	+	1.35171i	−0.467968	+	0.883745i	$0.655014\pi$
$11$	−4.48313	+	4.48313i	−1.35171	+	1.35171i	−0.883745	+	0.467968i	$0.844986\pi$
$12$		0			0
$13$	−0.905106	+	3.49010i	−0.251031	+	0.967979i
$13$	−0.905106	+	3.49010i	−0.251031	+	0.967979i
$14$	2.88100	−	1.66335i	0.769980	−	0.444548i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.38308	+	2.39556i	−0.335446	+	0.581010i	−0.983570	−	0.180525i	$-0.942220\pi$
$17$	−1.38308	+	2.39556i	−0.335446	+	0.581010i	0.648124	+	0.761534i	$0.275554\pi$
$18$		0			0
$19$	0.703205	+	2.62440i	0.161326	+	0.602078i	0.998480	+	0.0551104i	$0.0175511\pi$
$19$	0.703205	+	2.62440i	0.161326	+	0.602078i	−0.837154	+	0.546967i	$0.815782\pi$
$20$	3.60132	+	0.964970i	0.805279	+	0.215774i
$21$		0			0
$22$	6.34010			1.35171
$23$	−0.0915043	+	0.158490i	−0.0190800	+	0.0330475i	−0.875408	−	0.483385i	$-0.839407\pi$
$23$	−0.0915043	+	0.158490i	−0.0190800	+	0.0330475i	0.856328	+	0.516433i	$0.172740\pi$
$24$		0			0
$25$	−7.70819	−	4.45033i	−1.54164	−	0.890065i
$26$	3.10788	−	1.82787i	0.609505	−	0.358474i
$27$		0			0
$28$	−3.21334	−	0.861011i	−0.607264	−	0.162716i
$29$			0.948565i			0.176144i	0.996114	+	0.0880720i	$0.0280706\pi$
$29$			0.948565i			0.176144i	−0.996114	+	0.0880720i	$0.971929\pi$
$30$		0			0
$31$	2.14063	+	0.573581i	0.384469	+	0.103018i	0.445876	−	0.895095i	$-0.352892\pi$
$31$	2.14063	+	0.573581i	0.384469	+	0.103018i	−0.0614072	+	0.998113i	$0.519559\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	2.67190	−	0.715935i	0.458228	−	0.122782i
$35$	10.7414	+	6.20155i	1.81563	+	1.04825i
$36$		0			0
$37$	1.96458	−	7.33191i	0.322975	−	1.20536i	−0.593357	−	0.804939i	$-0.702198\pi$
$37$	1.96458	−	7.33191i	0.322975	−	1.20536i	0.916332	−	0.400419i	$-0.131136\pi$
$38$	1.35849	−	2.35297i	0.220376	−	0.381702i
$39$		0			0
$40$	−1.86418	−	3.22885i	−0.294753	−	0.510526i
$41$	−2.27956	+	0.610806i	−0.356007	+	0.0953919i	−0.432390	−	0.901687i	$-0.642330\pi$
$41$	−2.27956	+	0.610806i	−0.356007	+	0.0953919i	0.0763827	+	0.997079i	$0.475663\pi$
$42$		0			0
$43$	−3.17570	+	1.83349i	−0.484290	+	0.279605i	−0.722202	−	0.691682i	$-0.756870\pi$
$43$	−3.17570	+	1.83349i	−0.484290	+	0.279605i	0.237913	+	0.971287i	$0.423537\pi$
$44$	−4.48313	−	4.48313i	−0.675857	−	0.675857i
$45$		0			0
$46$	0.176773	−	0.0473661i	0.0260637	−	0.00698375i
$47$	1.38011	+	5.15065i	0.201310	+	0.751300i	0.990543	+	0.137205i	$0.0438120\pi$
$47$	1.38011	+	5.15065i	0.201310	+	0.751300i	−0.789232	+	0.614095i	$0.789521\pi$
$48$		0			0
$49$	−3.52202	−	2.03344i	−0.503146	−	0.290491i
$50$	2.30366	+	8.59737i	0.325786	+	1.21585i
$51$		0			0
$52$	−3.49010	−	0.905106i	−0.483990	−	0.125516i
$53$		−	3.43327i		−	0.471596i	−0.971802	−	0.235798i	$-0.924230\pi$
$53$		−	3.43327i		−	0.471596i	0.971802	−	0.235798i	$-0.0757704\pi$
$54$		0			0
$55$	11.8191	+	20.4712i	1.59368	+	2.76034i
$56$	1.66335	+	2.88100i	0.222274	+	0.384990i
$57$		0			0
$58$	0.670737	−	0.670737i	0.0880720	−	0.0880720i
$59$	−3.31440	+	3.31440i	−0.431498	+	0.431498i	−0.889138	−	0.457640i	$-0.848695\pi$
$59$	−3.31440	+	3.31440i	−0.431498	+	0.431498i	0.457640	+	0.889138i	$0.348695\pi$
$60$		0			0
$61$	4.13990	+	7.17052i	0.530060	+	0.918090i	0.999385	+	0.0350651i	$0.0111639\pi$
$61$	4.13990	+	7.17052i	0.530060	+	0.918090i	−0.469325	+	0.883025i	$0.655503\pi$
$62$	−1.10807	−	1.91924i	−0.140725	−	0.243744i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	11.6955	+	6.62741i	1.45065	+	0.822029i
$66$		0			0
$67$	1.93297	+	7.21395i	0.236150	+	0.881324i	0.977627	+	0.210346i	$0.0674589\pi$
$67$	1.93297	+	7.21395i	0.236150	+	0.881324i	−0.741477	+	0.670978i	$0.765874\pi$
$68$	−2.39556	−	1.38308i	−0.290505	−	0.167723i
$69$		0			0
$70$	−3.21016	−	11.9805i	−0.383687	−	1.43194i
$71$	−11.7943	+	3.16027i	−1.39972	+	0.375055i	−0.878245	−	0.478210i	$-0.841286\pi$
$71$	−11.7943	+	3.16027i	−1.39972	+	0.375055i	−0.521478	+	0.853265i	$0.674619\pi$
$72$		0			0
$73$	2.16027	+	2.16027i	0.252841	+	0.252841i	0.822134	−	0.569294i	$-0.192783\pi$
$73$	2.16027	+	2.16027i	0.252841	+	0.252841i	−0.569294	+	0.822134i	$0.692783\pi$
$74$	−6.57361	+	3.79528i	−0.764167	+	0.441192i
$75$		0			0
$76$	−2.62440	+	0.703205i	−0.301039	+	0.0806631i
$77$	−10.5458	−	18.2658i	−1.20180	−	2.08158i
$78$		0			0
$79$	6.31331	−	10.9350i	0.710302	−	1.23028i	−0.254441	−	0.967088i	$-0.581892\pi$
$79$	6.31331	−	10.9350i	0.710302	−	1.23028i	0.964744	−	0.263191i	$-0.0847751\pi$
$80$	−0.964970	+	3.60132i	−0.107887	+	0.402639i
$81$		0			0
$82$	2.04380	+	1.17999i	0.225700	+	0.130308i
$83$	−6.52658	+	1.74879i	−0.716385	+	0.191955i	−0.598558	−	0.801079i	$-0.704259\pi$
$83$	−6.52658	+	1.74879i	−0.716385	+	0.191955i	−0.117827	+	0.993034i	$0.537593\pi$
$84$		0			0
$85$	7.29255	+	7.29255i	0.790989	+	0.790989i
$86$	3.54203	+	0.949085i	0.381947	+	0.102342i
$87$		0			0
$88$			6.34010i			0.675857i
$89$	−0.643808	−	0.172508i	−0.0682435	−	0.0182858i	0.224536	−	0.974466i	$-0.427913\pi$
$89$	−0.643808	−	0.172508i	−0.0682435	−	0.0182858i	−0.292779	+	0.956180i	$0.594580\pi$
$90$		0			0
$91$	−10.4356	−	5.91342i	−1.09394	−	0.619895i
$92$	−0.158490	−	0.0915043i	−0.0165237	−	0.00953998i
$93$		0			0
$94$	2.66617	−	4.61795i	0.274995	−	0.476305i
$95$	10.1298			1.03930
$96$		0			0
$97$	−5.65566	−	1.51543i	−0.574246	−	0.153869i	−0.0400026	−	0.999200i	$-0.512737\pi$
$97$	−5.65566	−	1.51543i	−0.574246	−	0.153869i	−0.534243	+	0.845331i	$0.679403\pi$
$98$	1.05259	+	3.92830i	0.106327	+	0.396819i
$99$		0			0
$100$	4.45033	−	7.70819i	0.445033	−	0.770819i
$101$	9.35186			0.930545			0.465272	−	0.885168i	$-0.345956\pi$
$101$	9.35186			0.930545			0.465272	+	0.885168i	$0.345956\pi$
$102$		0			0
$103$	0.256212	−	0.147924i	0.0252453	−	0.0145754i	−0.487324	−	0.873221i	$-0.662027\pi$
$103$	0.256212	−	0.147924i	0.0252453	−	0.0145754i	0.512570	+	0.858646i	$0.328694\pi$
$104$	1.82787	+	3.10788i	0.179237	+	0.304753i
$105$		0			0
$106$	−2.42769	+	2.42769i	−0.235798	+	0.235798i
$107$	16.2026	−	9.35458i	1.56636	−	0.904341i	0.569777	−	0.821799i	$-0.307030\pi$
$107$	16.2026	−	9.35458i	1.56636	−	0.904341i	0.996588	−	0.0825417i	$-0.0263038\pi$
$108$		0			0
$109$	−7.95895	+	7.95895i	−0.762329	+	0.762329i	−0.976743	−	0.214414i	$-0.931216\pi$
$109$	−7.95895	+	7.95895i	−0.762329	+	0.762329i	0.214414	+	0.976743i	$0.431216\pi$
$110$	6.11801	−	22.8327i	0.583329	−	2.17701i
$111$		0			0
$112$	0.861011	−	3.21334i	0.0813579	−	0.303632i
$113$			6.98898i			0.657468i	0.944423	+	0.328734i	$0.106622\pi$
$113$			6.98898i			0.657468i	−0.944423	+	0.328734i	$0.893378\pi$
$114$		0			0
$115$	0.482474	+	0.482474i	0.0449910	+	0.0449910i
$116$	−0.948565			−0.0880720
$117$		0			0
$118$	4.68727			0.431498
$119$	−6.50691	−	6.50691i	−0.596487	−	0.596487i
$120$		0			0
$121$		−	29.1969i		−	2.65426i
$122$	2.14297	−	7.99767i	0.194015	−	0.724075i
$123$		0			0
$124$	−0.573581	+	2.14063i	−0.0515091	+	0.192234i
$125$	−10.2835	+	10.2835i	−0.919782	+	0.919782i
$126$		0			0
$127$	−1.39357	+	0.804578i	−0.123659	+	0.0713947i	−0.560554	−	0.828118i	$-0.689412\pi$
$127$	−1.39357	+	0.804578i	−0.123659	+	0.0713947i	0.436894	+	0.899513i	$0.356078\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−3.58371	−	12.9563i	−0.314313	−	1.13634i
$131$	−8.16562	+	4.71442i	−0.713434	+	0.411901i	−0.812331	−	0.583197i	$-0.801802\pi$
$131$	−8.16562	+	4.71442i	−0.713434	+	0.411901i	0.0988974	+	0.995098i	$0.468468\pi$
$132$		0			0
$133$	−9.03853			−0.783740
$134$	3.73421	−	6.46785i	0.322587	−	0.558737i
$135$		0			0
$136$	0.715935	+	2.67190i	0.0613909	+	0.229114i
$137$	−15.6755	−	4.20024i	−1.33925	−	0.358851i	−0.483093	−	0.875569i	$-0.660487\pi$
$137$	−15.6755	−	4.20024i	−1.33925	−	0.358851i	−0.856155	+	0.516718i	$0.827153\pi$
$138$		0			0
$139$	8.89419			0.754396			0.377198	−	0.926133i	$-0.376888\pi$
$139$	8.89419			0.754396			0.377198	+	0.926133i	$0.376888\pi$
$140$	−6.20155	+	10.7414i	−0.524127	+	0.907814i
$141$		0			0
$142$	10.5745	+	6.10517i	0.887389	+	0.512334i
$143$	−11.5888	−	19.7043i	−0.969108	−	1.64775i
$144$		0			0
$145$	3.41608	+	0.915337i	0.283690	+	0.0760146i
$146$		−	3.05508i		−	0.252841i
$147$		0			0
$148$	7.33191	+	1.96458i	0.602679	+	0.161487i
$149$	16.7277	+	16.7277i	1.37039	+	1.37039i	0.859862	+	0.510527i	$0.170550\pi$
$149$	16.7277	+	16.7277i	1.37039	+	1.37039i	0.510527	+	0.859862i	$0.329450\pi$
$150$		0			0
$151$	0.145209	−	0.0389086i	0.0118169	−	0.00316634i	−0.252906	−	0.967491i	$-0.581386\pi$
$151$	0.145209	−	0.0389086i	0.0118169	−	0.00316634i	0.264723	+	0.964325i	$0.414720\pi$
$152$	2.35297	+	1.35849i	0.190851	+	0.110188i
$153$		0			0
$154$	−5.45890	+	20.3729i	−0.439890	+	1.64169i
$155$	4.13129	−	7.15561i	0.331833	−	0.574752i
$156$		0			0
$157$	0.888484	+	1.53890i	0.0709087	+	0.122818i	0.899300	−	0.437333i	$-0.144077\pi$
$157$	0.888484	+	1.53890i	0.0709087	+	0.122818i	−0.828391	+	0.560150i	$0.810743\pi$
$158$	−12.1964	+	3.26801i	−0.970291	+	0.259989i
$159$		0			0
$160$	3.22885	−	1.86418i	0.255263	−	0.147376i
$161$	−0.430496	−	0.430496i	−0.0339278	−	0.0339278i
$162$		0			0
$163$	−5.77944	+	1.54860i	−0.452681	+	0.121295i	−0.477953	−	0.878385i	$-0.658621\pi$
$163$	−5.77944	+	1.54860i	−0.452681	+	0.121295i	0.0252727	+	0.999681i	$0.491955\pi$
$164$	−0.610806	−	2.27956i	−0.0476959	−	0.178004i
$165$		0			0
$166$	5.85157	+	3.37840i	0.454170	+	0.262215i
$167$	−4.60758	−	17.1957i	−0.356545	−	1.33064i	−0.878529	−	0.477689i	$-0.841475\pi$
$167$	−4.60758	−	17.1957i	−0.356545	−	1.33064i	0.521984	−	0.852955i	$-0.325192\pi$
$168$		0			0
$169$	−11.3616	−	6.31781i	−0.873967	−	0.485986i
$170$		−	10.3132i		−	0.790989i
$171$		0			0
$172$	−1.83349	−	3.17570i	−0.139802	−	0.242145i
$173$	−7.21223	−	12.4919i	−0.548335	−	0.949745i	−0.998389	−	0.0567432i	$-0.981928\pi$
$173$	−7.21223	−	12.4919i	−0.548335	−	0.949745i	0.450053	−	0.893002i	$-0.351405\pi$
$174$		0			0
$175$	20.9372	−	20.9372i	1.58271	−	1.58271i
$176$	4.48313	−	4.48313i	0.337928	−	0.337928i
$177$		0			0
$178$	0.333259	+	0.577222i	0.0249788	+	0.0432646i
$179$	7.51417	+	13.0149i	0.561636	+	0.972782i	0.997354	+	0.0726986i	$0.0231611\pi$
$179$	7.51417	+	13.0149i	0.561636	+	0.972782i	−0.435718	+	0.900083i	$0.643506\pi$
$180$		0			0
$181$			7.25012i			0.538897i	0.963015	+	0.269449i	$0.0868414\pi$
$181$			7.25012i			0.538897i	−0.963015	+	0.269449i	$0.913159\pi$
$182$	3.19763	+	11.5605i	0.237024	+	0.856919i
$183$		0			0
$184$	0.0473661	+	0.176773i	0.00349188	+	0.0130319i
$185$	−24.5088	−	14.1501i	−1.80192	−	1.04034i
$186$		0			0
$187$	−4.53910	−	16.9401i	−0.331932	−	1.23879i
$188$	−5.15065	+	1.38011i	−0.375650	+	0.100655i
$189$		0			0
$190$	−7.16289	−	7.16289i	−0.519650	−	0.519650i
$191$	2.75813	−	1.59241i	0.199571	−	0.115222i	−0.396884	−	0.917869i	$-0.629909\pi$
$191$	2.75813	−	1.59241i	0.199571	−	0.115222i	0.596455	+	0.802646i	$0.296575\pi$
$192$		0			0
$193$	−13.6996	+	3.67080i	−0.986119	+	0.264230i	−0.715620	−	0.698490i	$-0.753856\pi$
$193$	−13.6996	+	3.67080i	−0.986119	+	0.264230i	−0.270500	+	0.962720i	$0.587189\pi$
$194$	2.92759	+	5.07073i	0.210189	+	0.364057i
$195$		0			0
$196$	2.03344	−	3.52202i	0.145246	−	0.251573i
$197$	0.0907674	−	0.338748i	0.00646691	−	0.0241348i	−0.962617	−	0.270866i	$-0.912690\pi$
$197$	0.0907674	−	0.338748i	0.00646691	−	0.0241348i	0.969084	+	0.246731i	$0.0793566\pi$
$198$		0			0
$199$	−17.1252	−	9.88723i	−1.21397	−	0.700887i	−0.250350	−	0.968155i	$-0.580546\pi$
$199$	−17.1252	−	9.88723i	−1.21397	−	0.700887i	−0.963622	+	0.267268i	$0.913879\pi$
$200$	−8.59737	+	2.30366i	−0.607926	+	0.162893i
$201$		0			0
$202$	−6.61276	−	6.61276i	−0.465272	−	0.465272i
$203$	−3.04806	−	0.816725i	−0.213932	−	0.0573229i
$204$		0			0
$205$			8.79882i			0.614536i
$206$	−0.285767	−	0.0765711i	−0.0199103	−	0.00533496i
$207$		0			0
$208$	0.905106	−	3.49010i	0.0627578	−	0.241995i
$209$	−14.9181	−	8.61294i	−1.03190	−	0.595770i
$210$		0			0
$211$	4.63875	−	8.03456i	0.319345	−	0.553122i	−0.661007	−	0.750380i	$-0.729870\pi$
$211$	4.63875	−	8.03456i	0.319345	−	0.553122i	0.980352	+	0.197258i	$0.0632038\pi$
$212$	3.43327			0.235798
$213$		0			0
$214$	−18.0717	−	4.84229i	−1.23535	−	0.331012i
$215$	3.53853	+	13.2060i	0.241326	+	0.900639i
$216$		0			0
$217$	−3.68622	+	6.38472i	−0.250237	+	0.433423i
$218$	11.2557			0.762329
$219$		0			0
$220$	−20.4712	+	11.8191i	−1.38017	+	0.796842i
$221$	−7.10892	−	6.99532i	−0.478198	−	0.470556i
$222$		0			0
$223$	10.9424	−	10.9424i	0.732760	−	0.732760i	−0.238406	−	0.971166i	$-0.576625\pi$
$223$	10.9424	−	10.9424i	0.732760	−	0.732760i	0.971166	+	0.238406i	$0.0766248\pi$
$224$	−2.88100	+	1.66335i	−0.192495	+	0.111137i
$225$		0			0
$226$	4.94195	−	4.94195i	0.328734	−	0.328734i
$227$	−1.90344	+	7.10373i	−0.126336	+	0.471491i	−0.999884	−	0.0152467i	$-0.995147\pi$
$227$	−1.90344	+	7.10373i	−0.126336	+	0.471491i	0.873548	+	0.486738i	$0.161813\pi$
$228$		0			0
$229$	−6.40571	+	23.9064i	−0.423301	+	1.57978i	0.344304	+	0.938858i	$0.388115\pi$
$229$	−6.40571	+	23.9064i	−0.423301	+	1.57978i	−0.767605	+	0.640923i	$0.778552\pi$
$230$		−	0.682322i		−	0.0449910i
$231$		0			0
$232$	0.670737	+	0.670737i	0.0440360	+	0.0440360i
$233$	18.0279			1.18105			0.590525	−	0.807019i	$-0.298921\pi$
$233$	18.0279			1.18105			0.590525	+	0.807019i	$0.298921\pi$
$234$		0			0
$235$	19.8809			1.29689
$236$	−3.31440	−	3.31440i	−0.215749	−	0.215749i
$237$		0			0
$238$			9.20216i			0.596487i
$239$	−7.37545	+	27.5256i	−0.477078	+	1.78048i	0.136275	+	0.990671i	$0.456487\pi$
$239$	−7.37545	+	27.5256i	−0.477078	+	1.78048i	−0.613353	+	0.789809i	$0.710180\pi$
$240$		0			0
$241$	2.07549	−	7.74584i	0.133694	−	0.498954i	−0.866306	−	0.499514i	$-0.833512\pi$
$241$	2.07549	−	7.74584i	0.133694	−	0.498954i	1.00000		0.000560714i	$0.000178481\pi$
$242$	−20.6453	+	20.6453i	−1.32713	+	1.32713i
$243$		0			0
$244$	−7.17052	+	4.13990i	−0.459045	+	0.265030i
$245$	−10.7217	+	10.7217i	−0.684985	+	0.684985i
$246$		0			0
$247$	−9.79587	+	0.0788981i	−0.623296	+	0.00502017i
$248$	1.91924	−	1.10807i	0.121872	−	0.0703627i
$249$		0			0
$250$	14.5430			0.919782
$251$	3.03917	−	5.26399i	0.191830	−	0.332260i	−0.754026	−	0.656844i	$-0.771891\pi$
$251$	3.03917	−	5.26399i	0.191830	−	0.332260i	0.945857	+	0.324584i	$0.105224\pi$
$252$		0			0
$253$	−0.300306	−	1.12076i	−0.0188801	−	0.0704614i
$254$	1.55433	+	0.416480i	0.0975270	+	0.0261323i
$255$		0			0
$256$	1.00000			0.0625000
$257$	0.319391	−	0.553201i	0.0199230	−	0.0345077i	−0.855892	−	0.517155i	$-0.826991\pi$
$257$	0.319391	−	0.553201i	0.0199230	−	0.0345077i	0.875815	+	0.482647i	$0.160325\pi$
$258$		0			0
$259$	21.8684	+	12.6257i	1.35883	+	0.784524i
$260$	−6.62741	+	11.6955i	−0.411015	+	0.725327i
$261$		0			0
$262$	9.10757	+	2.44037i	0.562667	+	0.150766i
$263$			5.63477i			0.347455i	0.984794	+	0.173727i	$0.0555811\pi$
$263$			5.63477i			0.347455i	−0.984794	+	0.173727i	$0.944419\pi$
$264$		0			0
$265$	−12.3643	−	3.31300i	−0.759533	−	0.203516i
$266$	6.39121	+	6.39121i	0.391870	+	0.391870i
$267$		0			0
$268$	−7.21395	+	1.93297i	−0.440662	+	0.118075i
$269$	17.6754	+	10.2049i	1.07769	+	0.622202i	0.930271	−	0.366873i	$-0.119572\pi$
$269$	17.6754	+	10.2049i	1.07769	+	0.622202i	0.147415	+	0.989075i	$0.452905\pi$
$270$		0			0
$271$	5.54365	−	20.6892i	0.336753	−	1.25678i	−0.565204	−	0.824951i	$-0.691202\pi$
$271$	5.54365	−	20.6892i	0.336753	−	1.25678i	0.901956	−	0.431827i	$-0.142131\pi$
$272$	1.38308	−	2.39556i	0.0838615	−	0.145252i
$273$		0			0
$274$	8.11424	+	14.0543i	0.490199	+	0.849049i
$275$	54.5082	−	14.6054i	3.28697	−	0.880740i
$276$		0			0
$277$	−4.17616	+	2.41111i	−0.250921	+	0.144869i	−0.620186	−	0.784455i	$-0.712943\pi$
$277$	−4.17616	+	2.41111i	−0.250921	+	0.144869i	0.369265	+	0.929324i	$0.379610\pi$
$278$	−6.28914	−	6.28914i	−0.377198	−	0.377198i
$279$		0			0
$280$	11.9805	−	3.21016i	0.715970	−	0.191844i
$281$	0.975427	+	3.64034i	0.0581891	+	0.217165i	0.988898	−	0.148596i	$-0.0474755\pi$
$281$	0.975427	+	3.64034i	0.0581891	+	0.217165i	−0.930709	+	0.365761i	$0.880809\pi$
$282$		0			0
$283$	10.9117	+	6.29987i	0.648633	+	0.374489i	0.787932	−	0.615762i	$-0.211152\pi$
$283$	10.9117	+	6.29987i	0.648633	+	0.374489i	−0.139299	+	0.990250i	$0.544485\pi$
$284$	−3.16027	−	11.7943i	−0.187527	−	0.699861i
$285$		0			0
$286$	−5.73846	+	22.1276i	−0.339322	+	1.30843i
$287$		−	7.85090i		−	0.463424i
$288$		0			0
$289$	4.67418	+	8.09592i	0.274952	+	0.476231i
$290$	−1.76829	−	3.06278i	−0.103838	−	0.179852i
$291$		0			0
$292$	−2.16027	+	2.16027i	−0.126420	+	0.126420i
$293$	21.0170	−	21.0170i	1.22783	−	1.22783i	0.263045	−	0.964784i	$-0.415273\pi$
$293$	21.0170	−	21.0170i	1.22783	−	1.22783i	0.964784	−	0.263045i	$-0.0847267\pi$
$294$		0			0
$295$	8.73791	+	15.1345i	0.508741	+	0.881165i
$296$	−3.79528	−	6.57361i	−0.220596	−	0.382083i
$297$		0			0
$298$		−	23.6566i		−	1.37039i
$299$	−0.470325	−	0.462809i	−0.0271996	−	0.0267650i
$300$		0			0
$301$	−3.15731	−	11.7832i	−0.181984	−	0.679175i
$302$	−0.130191	−	0.0751656i	−0.00749163	−	0.00432530i
$303$		0			0
$304$	−0.703205	−	2.62440i	−0.0403315	−	0.150519i
$305$	29.8182	−	7.98976i	1.70738	−	0.457492i
$306$		0			0
$307$	−22.9539	−	22.9539i	−1.31005	−	1.31005i	−0.921376	−	0.388674i	$-0.872933\pi$
$307$	−22.9539	−	22.9539i	−1.31005	−	1.31005i	−0.388674	−	0.921376i	$-0.627067\pi$
$308$	18.2658	−	10.5458i	1.04079	−	0.600901i
$309$		0			0
$310$	−7.98104	+	2.13851i	−0.453293	+	0.121459i
$311$	11.8059	+	20.4483i	0.669449	+	1.15952i	0.978058	+	0.208331i	$0.0668030\pi$
$311$	11.8059	+	20.4483i	0.669449	+	1.15952i	−0.308610	+	0.951189i	$0.599864\pi$
$312$		0			0
$313$	8.71521	−	15.0952i	0.492613	−	0.853230i	−0.507351	−	0.861739i	$-0.669375\pi$
$313$	8.71521	−	15.0952i	0.492613	−	0.853230i	0.999964	+	0.00850920i	$0.00270860\pi$
$314$	0.459913	−	1.71642i	0.0259544	−	0.0968631i
$315$		0			0
$316$	10.9350	+	6.31331i	0.615140	+	0.355151i
$317$	−0.604929	+	0.162090i	−0.0339762	+	0.00910389i	−0.275767	−	0.961224i	$-0.588932\pi$
$317$	−0.604929	+	0.162090i	−0.0339762	+	0.00910389i	0.241791	+	0.970328i	$0.422265\pi$
$318$		0			0
$319$	−4.25254	−	4.25254i	−0.238096	−	0.238096i
$320$	−3.60132	−	0.964970i	−0.201320	−	0.0539435i
$321$		0			0
$322$			0.608813i			0.0339278i
$323$	−7.25949	−	1.94518i	−0.403929	−	0.108232i
$324$		0			0
$325$	22.5088	−	22.8743i	1.24856	−	1.26884i
$326$	5.18170	+	2.99166i	0.286988	+	0.165693i
$327$		0			0
$328$	−1.17999	+	2.04380i	−0.0651539	+	0.112850i
$329$	−17.7391			−0.977987
$330$		0			0
$331$	29.8637	+	8.00195i	1.64146	+	0.439827i	0.957203	−	0.289418i	$-0.0934616\pi$
$331$	29.8637	+	8.00195i	1.64146	+	0.439827i	0.684253	+	0.729244i	$0.260128\pi$
$332$	−1.74879	−	6.52658i	−0.0959774	−	0.358192i
$333$		0			0
$334$	−8.90116	+	15.4173i	−0.487050	+	0.843595i
$335$	27.8450			1.52133
$336$		0			0
$337$	7.79004	−	4.49758i	0.424350	−	0.244999i	−0.272586	−	0.962131i	$-0.587879\pi$
$337$	7.79004	−	4.49758i	0.424350	−	0.244999i	0.696937	+	0.717132i	$0.254546\pi$
$338$	3.56647	+	12.5012i	0.193991	+	0.679976i
$339$		0			0
$340$	−7.29255	+	7.29255i	−0.395494	+	0.395494i
$341$	−12.1682	+	7.02529i	−0.658943	+	0.380441i
$342$		0			0
$343$	−6.89966	+	6.89966i	−0.372547	+	0.372547i
$344$	−0.949085	+	3.54203i	−0.0511712	+	0.190974i
$345$		0			0
$346$	−3.73332	+	13.9330i	−0.200705	+	0.749040i
$347$			7.42847i			0.398781i	0.979920	+	0.199390i	$0.0638962\pi$
$347$			7.42847i			0.398781i	−0.979920	+	0.199390i	$0.936104\pi$
$348$		0			0
$349$	25.5197	+	25.5197i	1.36604	+	1.36604i	0.866011	+	0.500024i	$0.166676\pi$
$349$	25.5197	+	25.5197i	1.36604	+	1.36604i	0.500024	+	0.866011i	$0.333324\pi$
$350$	−29.6097			−1.58271
$351$		0			0
$352$	−6.34010			−0.337928
$353$	2.17346	+	2.17346i	0.115682	+	0.115682i	0.762578	−	0.646896i	$-0.223933\pi$
$353$	2.17346	+	2.17346i	0.115682	+	0.115682i	−0.646896	+	0.762578i	$0.723933\pi$
$354$		0			0
$355$			45.5245i			2.41619i
$356$	0.172508	−	0.643808i	0.00914289	−	0.0341217i
$357$		0			0
$358$	3.88962	−	14.5163i	0.205573	−	0.767209i
$359$	−9.73682	+	9.73682i	−0.513890	+	0.513890i	−0.915716	−	0.401826i	$-0.868376\pi$
$359$	−9.73682	+	9.73682i	−0.513890	+	0.513890i	0.401826	+	0.915716i	$0.368376\pi$
$360$		0			0
$361$	10.0615	−	5.80903i	0.529554	−	0.305738i
$362$	5.12661	−	5.12661i	0.269449	−	0.269449i
$363$		0			0
$364$	5.91342	−	10.4356i	0.309948	−	0.546972i
$365$	9.86442	−	5.69522i	0.516327	−	0.298102i
$366$		0			0
$367$	−15.8770			−0.828771			−0.414385	−	0.910102i	$-0.636003\pi$
$367$	−15.8770			−0.828771			−0.414385	+	0.910102i	$0.636003\pi$
$368$	0.0915043	−	0.158490i	0.00476999	−	0.00826187i
$369$		0			0
$370$	7.32466	+	27.3360i	0.380791	+	1.42113i
$371$	11.0323	+	2.95609i	0.572767	+	0.153472i
$372$		0			0
$373$	−0.725285			−0.0375538			−0.0187769	−	0.999824i	$-0.505977\pi$
$373$	−0.725285			−0.0375538			−0.0187769	+	0.999824i	$0.505977\pi$
$374$	−8.76886	+	15.1881i	−0.453427	+	0.785359i
$375$		0			0
$376$	4.61795	+	2.66617i	0.238153	+	0.137497i
$377$	−3.31058	−	0.858551i	−0.170504	−	0.0442176i
$378$		0			0
$379$	−2.92733	−	0.784375i	−0.150367	−	0.0402906i	0.182850	−	0.983141i	$-0.441468\pi$
$379$	−2.92733	−	0.784375i	−0.150367	−	0.0402906i	−0.333217	+	0.942850i	$0.608134\pi$
$380$			10.1298i			0.519650i
$381$		0			0
$382$	−3.07629	−	0.824290i	−0.157397	−	0.0421744i
$383$	−1.38928	−	1.38928i	−0.0709889	−	0.0709889i	0.670721	−	0.741710i	$-0.265985\pi$
$383$	−1.38928	−	1.38928i	−0.0709889	−	0.0709889i	−0.741710	+	0.670721i	$0.765985\pi$
$384$		0			0
$385$	−75.9574	+	20.3527i	−3.87115	+	1.03727i
$386$	12.2827	+	7.09144i	0.625175	+	0.360945i
$387$		0			0
$388$	1.51543	−	5.65566i	0.0769343	−	0.287123i
$389$	−11.5891	+	20.0729i	−0.587591	+	1.01774i	0.406956	+	0.913448i	$0.366590\pi$
$389$	−11.5891	+	20.0729i	−0.587591	+	1.01774i	−0.994547	+	0.104289i	$0.966743\pi$
$390$		0			0
$391$	−0.253115	−	0.438409i	−0.0128006	−	0.0221713i
$392$	−3.92830	+	1.05259i	−0.198409	+	0.0531636i
$393$		0			0
$394$	−0.303713	+	0.175349i	−0.0153009	+	0.00883396i
$395$	−33.2881	−	33.2881i	−1.67491	−	1.67491i
$396$		0			0
$397$	−3.81012	+	1.02092i	−0.191224	+	0.0512384i	−0.353160	−	0.935563i	$-0.614893\pi$
$397$	−3.81012	+	1.02092i	−0.191224	+	0.0512384i	0.161936	+	0.986801i	$0.448226\pi$
$398$	5.11801	+	19.1007i	0.256543	+	0.957430i
$399$		0			0
$400$	7.70819	+	4.45033i	0.385409	+	0.222516i
$401$	−5.75855	−	21.4912i	−0.287568	−	1.07322i	−0.946942	−	0.321404i	$-0.895845\pi$
$401$	−5.75855	−	21.4912i	−0.287568	−	1.07322i	0.659374	−	0.751815i	$-0.270821\pi$
$402$		0			0
$403$	−3.93935	+	6.95187i	−0.196233	+	0.346297i
$404$			9.35186i			0.465272i
$405$		0			0
$406$	1.57779	+	2.73282i	0.0783045	+	0.135627i
$407$	24.0624	+	41.6773i	1.19273	+	2.06587i
$408$		0			0
$409$	−19.9999	+	19.9999i	−0.988934	+	0.988934i	−0.999939	−	0.0110057i	$-0.996497\pi$
$409$	−19.9999	+	19.9999i	−0.988934	+	0.988934i	0.0110057	+	0.999939i	$0.496497\pi$
$410$	6.22171	−	6.22171i	0.307268	−	0.307268i
$411$		0			0
$412$	0.147924	+	0.256212i	0.00728769	+	0.0126227i
$413$	−7.79655	−	13.5040i	−0.383643	−	0.664490i
$414$		0			0
$415$			25.1918i			1.23662i
$416$	−3.10788	+	1.82787i	−0.152376	+	0.0896185i
$417$		0			0
$418$	4.45839	+	16.6389i	0.218067	+	0.813836i
$419$	9.72023	+	5.61198i	0.474864	+	0.274163i	0.718274	−	0.695761i	$-0.244933\pi$
$419$	9.72023	+	5.61198i	0.474864	+	0.274163i	−0.243409	+	0.969924i	$0.578266\pi$
$420$		0			0
$421$	−0.256866	−	0.958636i	−0.0125189	−	0.0467211i	0.959384	−	0.282104i	$-0.0910323\pi$
$421$	−0.256866	−	0.958636i	−0.0125189	−	0.0467211i	−0.971903	+	0.235383i	$0.924366\pi$
$422$	−8.96138	+	2.40120i	−0.436233	+	0.116888i
$423$		0			0
$424$	−2.42769	−	2.42769i	−0.117899	−	0.117899i
$425$	21.3221	−	12.3103i	1.03427	−	0.597138i
$426$		0			0
$427$	−26.6058	+	7.12900i	−1.28754	+	0.344996i
$428$	9.35458	+	16.2026i	0.452171	+	0.783182i
$429$		0			0
$430$	6.83591	−	11.8401i	0.329657	−	0.570982i
$431$	1.41740	−	5.28983i	0.0682740	−	0.254802i	−0.923350	−	0.383959i	$-0.874560\pi$
$431$	1.41740	−	5.28983i	0.0682740	−	0.254802i	0.991624	+	0.129157i	$0.0412271\pi$
$432$		0			0
$433$	−14.9131	−	8.61010i	−0.716680	−	0.413775i	0.0968497	−	0.995299i	$-0.469123\pi$
$433$	−14.9131	−	8.61010i	−0.716680	−	0.413775i	−0.813529	+	0.581524i	$0.802457\pi$
$434$	7.12122	−	1.90813i	0.341830	−	0.0915930i
$435$		0			0
$436$	−7.95895	−	7.95895i	−0.381165	−	0.381165i
$437$	−0.480287	−	0.128693i	−0.0229752	−	0.00615620i
$438$		0			0
$439$			5.14800i			0.245701i	0.992425	+	0.122850i	$0.0392035\pi$
$439$			5.14800i			0.245701i	−0.992425	+	0.122850i	$0.960796\pi$
$440$	22.8327	+	6.11801i	1.08851	+	0.291664i
$441$		0			0
$442$	0.0803264	+	9.97320i	0.00382074	+	0.474377i
$443$	−19.9015	−	11.4901i	−0.945547	−	0.545912i	−0.0538522	−	0.998549i	$-0.517150\pi$
$443$	−19.9015	−	11.4901i	−0.945547	−	0.545912i	−0.891695	+	0.452637i	$0.850483\pi$
$444$		0			0
$445$	−1.24251	+	2.15209i	−0.0589006	+	0.102019i
$446$	−15.4749			−0.732760
$447$		0			0
$448$	3.21334	+	0.861011i	0.151816	+	0.0406790i
$449$	4.11231	+	15.3473i	0.194072	+	0.724286i	0.992505	+	0.122203i	$0.0389958\pi$
$449$	4.11231	+	15.3473i	0.194072	+	0.724286i	−0.798433	+	0.602083i	$0.794338\pi$
$450$		0			0
$451$	7.48123	−	12.9579i	0.352277	−	0.610162i
$452$	−6.98898			−0.328734
$453$		0			0
$454$	6.36903	−	3.67716i	0.298913	−	0.172578i
$455$	−31.3661	+	31.8755i	−1.47047	+	1.49435i
$456$		0			0
$457$	18.3372	−	18.3372i	0.857780	−	0.857780i	−0.133296	−	0.991076i	$-0.542556\pi$
$457$	18.3372	−	18.3372i	0.857780	−	0.857780i	0.991076	+	0.133296i	$0.0425562\pi$
$458$	21.4339	−	12.3749i	1.00154	−	0.578240i
$459$		0			0
$460$	−0.482474	+	0.482474i	−0.0224955	+	0.0224955i
$461$	−0.435138	+	1.62396i	−0.0202664	+	0.0756352i	−0.975318	−	0.220803i	$-0.929132\pi$
$461$	−0.435138	+	1.62396i	−0.0202664	+	0.0756352i	0.955052	+	0.296438i	$0.0957989\pi$
$462$		0			0
$463$	4.49747	−	16.7848i	0.209015	−	0.780055i	−0.779173	−	0.626809i	$-0.784361\pi$
$463$	4.49747	−	16.7848i	0.209015	−	0.780055i	0.988188	−	0.153246i	$-0.0489727\pi$
$464$		−	0.948565i		−	0.0440360i
$465$		0			0
$466$	−12.7477	−	12.7477i	−0.590525	−	0.590525i
$467$	0.582570			0.0269581			0.0134791	−	0.999909i	$-0.495709\pi$
$467$	0.582570			0.0269581			0.0134791	+	0.999909i	$0.495709\pi$
$468$		0			0
$469$	−24.8452			−1.14724
$470$	−14.0579	−	14.0579i	−0.648444	−	0.648444i
$471$		0			0
$472$			4.68727i			0.215749i
$473$	6.01729	−	22.4568i	0.276675	−	1.03257i
$474$		0			0
$475$	6.25898	−	23.3588i	0.287182	−	1.07178i
$476$	6.50691	−	6.50691i	0.298244	−	0.298244i
$477$		0			0
$478$	24.6787	−	14.2483i	1.12878	−	0.651701i
$479$	−5.53126	+	5.53126i	−0.252730	+	0.252730i	−0.822089	−	0.569359i	$-0.807191\pi$
$479$	−5.53126	+	5.53126i	−0.252730	+	0.252730i	0.569359	+	0.822089i	$0.307191\pi$
$480$		0			0
$481$	23.8109	+	13.4927i	1.08569	+	0.615215i
$482$	−6.94473	+	4.00954i	−0.316324	+	0.182630i
$483$		0			0
$484$	29.1969			1.32713
$485$	−10.9151	+	18.9055i	−0.495629	+	0.858454i
$486$		0			0
$487$	1.40502	+	5.24359i	0.0636674	+	0.237610i	0.990425	−	0.138049i	$-0.0440831\pi$
$487$	1.40502	+	5.24359i	0.0636674	+	0.237610i	−0.926758	+	0.375659i	$0.877416\pi$
$488$	7.99767	+	2.14297i	0.362038	+	0.0970077i
$489$		0			0
$490$	15.1628			0.684985
$491$	−1.20154	+	2.08113i	−0.0542247	+	0.0939199i	−0.891864	−	0.452304i	$-0.850602\pi$
$491$	−1.20154	+	2.08113i	−0.0542247	+	0.0939199i	0.837639	+	0.546224i	$0.183935\pi$
$492$		0			0
$493$	−2.27235	−	1.31194i	−0.102341	−	0.0590868i
$494$	6.98252	+	6.87094i	0.314158	+	0.309138i
$495$		0			0
$496$	−2.14063	−	0.573581i	−0.0961172	−	0.0257545i
$497$		−	40.6200i		−	1.82206i
$498$		0			0
$499$	−6.02143	−	1.61344i	−0.269556	−	0.0722273i	0.121509	−	0.992590i	$-0.461227\pi$
$499$	−6.02143	−	1.61344i	−0.269556	−	0.0722273i	−0.391065	+	0.920363i	$0.627893\pi$
$500$	−10.2835	−	10.2835i	−0.459891	−	0.459891i
$501$		0			0
$502$	−5.87122	+	1.57319i	−0.262045	+	0.0702148i
$503$	11.8442	+	6.83823i	0.528105	+	0.304901i	0.740244	−	0.672338i	$-0.234710\pi$
$503$	11.8442	+	6.83823i	0.528105	+	0.304901i	−0.212140	+	0.977239i	$0.568043\pi$
$504$		0			0
$505$	9.02426	−	33.6790i	0.401574	−	1.49870i
$506$	−0.580146	+	1.00484i	−0.0257907	+	0.0446707i
$507$		0			0
$508$	−0.804578	−	1.39357i	−0.0356974	−	0.0618297i
$509$	−7.67175	+	2.05564i	−0.340044	+	0.0911146i	−0.424800	−	0.905287i	$-0.639656\pi$
$509$	−7.67175	+	2.05564i	−0.340044	+	0.0911146i	0.0847559	+	0.996402i	$0.472989\pi$
$510$		0			0
$511$	−8.80170	+	5.08166i	−0.389364	+	0.224799i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−0.617015	+	0.165329i	−0.0272154	+	0.00729234i
$515$	−0.285484	−	1.06544i	−0.0125799	−	0.0469490i
$516$		0			0
$517$	−29.2783	−	16.9038i	−1.28766	−	0.743429i
$518$	−6.53555	−	24.3910i	−0.287156	−	1.07168i
$519$		0			0
$520$	12.9563	−	3.58371i	0.568171	−	0.157156i
$521$		−	40.0151i		−	1.75309i	−0.481316	−	0.876547i	$-0.659841\pi$
$521$		−	40.0151i		−	1.75309i	0.481316	−	0.876547i	$-0.340159\pi$
$522$		0			0
$523$	5.07493	+	8.79004i	0.221911	+	0.384362i	0.955388	−	0.295353i	$-0.0954371\pi$
$523$	5.07493	+	8.79004i	0.221911	+	0.384362i	−0.733477	+	0.679714i	$0.762104\pi$
$524$	−4.71442	−	8.16562i	−0.205951	−	0.356717i
$525$		0			0
$526$	3.98438	−	3.98438i	0.173727	−	0.173727i
$527$	−4.33471	+	4.33471i	−0.188823	+	0.188823i
$528$		0			0
$529$	11.4833	+	19.8896i	0.499272	+	0.864764i
$530$	6.40023	+	11.0855i	0.278008	+	0.481525i
$531$		0			0
$532$		−	9.03853i		−	0.391870i
$533$	−0.0685312	−	8.50873i	−0.00296842	−	0.368554i
$534$		0			0
$535$	−18.0538	−	67.3776i	−0.780533	−	2.91299i
$536$	6.46785	+	3.73421i	0.279368	+	0.161293i
$537$		0			0
$538$	−5.28243	−	19.7143i	−0.227742	−	0.849944i
$539$	24.9058	−	6.67350i	1.07277	−	0.287448i
$540$		0			0
$541$	24.3541	+	24.3541i	1.04706	+	1.04706i	0.998836	+	0.0482280i	$0.0153574\pi$
$541$	24.3541	+	24.3541i	1.04706	+	1.04706i	0.0482280	+	0.998836i	$0.484643\pi$
$542$	−18.5494	+	10.7095i	−0.796766	+	0.460013i
$543$		0			0
$544$	−2.67190	+	0.715935i	−0.114557	+	0.0306954i
$545$	20.9826	+	36.3429i	0.898794	+	1.55676i
$546$		0			0
$547$	−3.38921	+	5.87029i	−0.144912	+	0.250996i	−0.929340	−	0.369224i	$-0.879623\pi$
$547$	−3.38921	+	5.87029i	−0.144912	+	0.250996i	0.784428	+	0.620220i	$0.212957\pi$
$548$	4.20024	−	15.6755i	0.179425	−	0.669624i
$549$		0			0
$550$	−48.8707	−	28.2155i	−2.08385	−	1.20311i
$551$	−2.48941	+	0.667035i	−0.106052	+	0.0284167i
$552$		0			0
$553$	29.7019	+	29.7019i	1.26305	+	1.26305i
$554$	4.65790	+	1.24808i	0.197895	+	0.0530259i
$555$		0			0
$556$			8.89419i			0.377198i
$557$	41.9906	+	11.2513i	1.77920	+	0.476734i	0.990437	−	0.137967i	$-0.0440568\pi$
$557$	41.9906	+	11.2513i	1.77920	+	0.476734i	0.788760	+	0.614701i	$0.210723\pi$
$558$		0			0
$559$	−3.52472	−	12.7430i	−0.149080	−	0.538972i
$560$	−10.7414	−	6.20155i	−0.453907	−	0.262063i
$561$		0			0
$562$	1.88438	−	3.26384i	0.0794878	−	0.137677i
$563$	−1.63879			−0.0690668			−0.0345334	−	0.999404i	$-0.510995\pi$
$563$	−1.63879			−0.0690668			−0.0345334	+	0.999404i	$0.510995\pi$
$564$		0			0
$565$	25.1695	+	6.74415i	1.05889	+	0.283729i
$566$	−3.26105	−	12.1704i	−0.137072	−	0.511561i
$567$		0			0
$568$	−6.10517	+	10.5745i	−0.256167	+	0.443694i
$569$	−3.08870			−0.129485			−0.0647424	−	0.997902i	$-0.520623\pi$
$569$	−3.08870			−0.129485			−0.0647424	+	0.997902i	$0.520623\pi$
$570$		0			0
$571$	5.59791	−	3.23195i	0.234265	−	0.135253i	−0.378273	−	0.925694i	$-0.623482\pi$
$571$	5.59791	−	3.23195i	0.234265	−	0.135253i	0.612538	+	0.790441i	$0.290149\pi$
$572$	19.7043	−	11.5888i	0.823876	−	0.484554i
$573$		0			0
$574$	−5.55143	+	5.55143i	−0.231712	+	0.231712i
$575$	1.41067	−	0.814448i	0.0588288	−	0.0339648i
$576$		0			0
$577$	32.0507	−	32.0507i	1.33429	−	1.33429i	0.432795	−	0.901492i	$-0.357527\pi$
$577$	32.0507	−	32.0507i	1.33429	−	1.33429i	0.901492	−	0.432795i	$-0.142473\pi$
$578$	2.41954	−	9.02983i	0.100639	−	0.375591i
$579$		0			0
$580$	−0.915337	+	3.41608i	−0.0380073	+	0.141845i
$581$		−	22.4778i		−	0.932537i
$582$		0			0
$583$	15.3918	+	15.3918i	0.637463	+	0.637463i
$584$	3.05508			0.126420
$585$		0			0
$586$	−29.7226			−1.22783
$587$	16.0190	+	16.0190i	0.661174	+	0.661174i	0.955657	−	0.294483i	$-0.0951473\pi$
$587$	16.0190	+	16.0190i	0.661174	+	0.661174i	−0.294483	+	0.955657i	$0.595147\pi$
$588$		0			0
$589$			6.02121i			0.248100i
$590$	4.52308	−	16.8803i	0.186212	−	0.694953i
$591$		0			0
$592$	−1.96458	+	7.33191i	−0.0807437	+	0.301340i
$593$	−14.2009	+	14.2009i	−0.583160	+	0.583160i	−0.935770	−	0.352610i	$-0.885294\pi$
$593$	−14.2009	+	14.2009i	−0.583160	+	0.583160i	0.352610	+	0.935770i	$0.385294\pi$
$594$		0			0
$595$	−29.7124	+	17.1545i	−1.21809	+	0.703265i
$596$	−16.7277	+	16.7277i	−0.685194	+	0.685194i
$597$		0			0
$598$	0.00531438	+	0.659826i	0.000217321	+	0.0269823i
$599$	8.75479	−	5.05458i	0.357711	−	0.206525i	−0.310365	−	0.950617i	$-0.600451\pi$
$599$	8.75479	−	5.05458i	0.357711	−	0.206525i	0.668076	+	0.744093i	$0.267118\pi$
$600$		0			0
$601$	−15.4541			−0.630387			−0.315194	−	0.949027i	$-0.602069\pi$
$601$	−15.4541			−0.630387			−0.315194	+	0.949027i	$0.602069\pi$
$602$	−6.09946	+	10.5646i	−0.248595	+	0.430580i
$603$		0			0
$604$	0.0389086	+	0.145209i	0.00158317	+	0.00590846i
$605$	−105.147	−	28.1741i	−4.27484	−	1.14544i
$606$		0			0
$607$	−28.3126			−1.14917			−0.574586	−	0.818444i	$-0.694837\pi$
$607$	−28.3126			−1.14917			−0.574586	+	0.818444i	$0.694837\pi$
$608$	−1.35849	+	2.35297i	−0.0550939	+	0.0954255i
$609$		0			0
$610$	−26.7342	−	15.4350i	−1.08244	−	0.624946i
$611$	−19.2254	+	0.154846i	−0.777778	+	0.00626440i
$612$		0			0
$613$	−10.9069	−	2.92249i	−0.440524	−	0.118038i	0.0317379	−	0.999496i	$-0.489896\pi$
$613$	−10.9069	−	2.92249i	−0.440524	−	0.118038i	−0.472262	+	0.881458i	$0.656562\pi$
$614$			32.4617i			1.31005i
$615$		0			0
$616$	−20.3729	−	5.45890i	−0.820847	−	0.219945i
$617$	−27.0649	−	27.0649i	−1.08959	−	1.08959i	−0.995570	−	0.0940202i	$-0.970028\pi$
$617$	−27.0649	−	27.0649i	−1.08959	−	1.08959i	−0.0940202	−	0.995570i	$-0.529972\pi$
$618$		0			0
$619$	25.4606	−	6.82214i	1.02335	−	0.274205i	0.292150	−	0.956372i	$-0.405629\pi$
$619$	25.4606	−	6.82214i	1.02335	−	0.274205i	0.731196	+	0.682168i	$0.238963\pi$
$620$	7.15561	+	4.13129i	0.287376	+	0.165917i
$621$		0			0
$622$	6.11116	−	22.8072i	0.245035	−	0.914484i
$623$	1.10865	−	1.92024i	0.0444172	−	0.0769328i
$624$		0			0
$625$	4.85917	+	8.41632i	0.194367	+	0.336653i
$626$	−16.8365	+	4.51132i	−0.672921	+	0.180309i
$627$		0			0
$628$	−1.53890	+	0.888484i	−0.0614088	+	0.0354544i
$629$	14.8469	+	14.8469i	0.591984	+	0.591984i
$630$		0			0
$631$	38.1709	−	10.2279i	1.51956	−	0.407165i	0.599963	−	0.800028i	$-0.295182\pi$
$631$	38.1709	−	10.2279i	1.51956	−	0.407165i	0.919597	+	0.392863i	$0.128515\pi$
$632$	−3.26801	−	12.1964i	−0.129994	−	0.485146i
$633$		0			0
$634$	0.542364	+	0.313134i	0.0215400	+	0.0124361i
$635$	1.55279	+	5.79508i	0.0616205	+	0.229971i
$636$		0			0
$637$	10.2847	−	10.4517i	0.407495	−	0.414112i
$638$			6.01399i			0.238096i
$639$		0			0
$640$	1.86418	+	3.22885i	0.0736881	+	0.127632i
$641$	16.8449	+	29.1763i	0.665335	+	1.15239i	0.979194	+	0.202925i	$0.0650448\pi$
$641$	16.8449	+	29.1763i	0.665335	+	1.15239i	−0.313859	+	0.949470i	$0.601622\pi$
$642$		0			0
$643$	16.2755	−	16.2755i	0.641844	−	0.641844i	−0.309165	−	0.951009i	$-0.600049\pi$
$643$	16.2755	−	16.2755i	0.641844	−	0.641844i	0.951009	+	0.309165i	$0.100049\pi$
$644$	0.430496	−	0.430496i	0.0169639	−	0.0169639i
$645$		0			0
$646$	3.75779	+	6.50868i	0.147848	+	0.256081i
$647$	3.32926	+	5.76644i	0.130887	+	0.226702i	0.924019	−	0.382348i	$-0.124884\pi$
$647$	3.32926	+	5.76644i	0.130887	+	0.226702i	−0.793132	+	0.609050i	$0.791551\pi$
$648$		0			0
$649$		−	29.7178i		−	1.16652i
$650$	−32.0907	+	0.258466i	−1.25870	+	0.0101379i
$651$		0			0
$652$	−1.54860	−	5.77944i	−0.0606477	−	0.226340i
$653$	−18.3358	−	10.5862i	−0.717536	−	0.414270i	0.0963092	−	0.995351i	$-0.469296\pi$
$653$	−18.3358	−	10.5862i	−0.717536	−	0.414270i	−0.813845	+	0.581082i	$0.802630\pi$
$654$		0			0
$655$	9.09855	+	33.9563i	0.355510	+	1.32678i
$656$	2.27956	−	0.610806i	0.0890018	−	0.0238480i
$657$		0			0
$658$	12.5434	+	12.5434i	0.488994	+	0.488994i
$659$	34.2945	−	19.7999i	1.33592	−	0.771296i	0.349723	−	0.936853i	$-0.386276\pi$
$659$	34.2945	−	19.7999i	1.33592	−	0.771296i	0.986200	+	0.165557i	$0.0529423\pi$
$660$		0			0
$661$	−24.0112	+	6.43378i	−0.933927	+	0.250245i	−0.693529	−	0.720429i	$-0.743945\pi$
$661$	−24.0112	+	6.43378i	−0.933927	+	0.250245i	−0.240399	+	0.970674i	$0.577278\pi$
$662$	−15.4586	−	26.7750i	−0.600815	−	1.04064i
$663$		0			0
$664$	−3.37840	+	5.85157i	−0.131108	+	0.227085i
$665$	−8.72191	+	32.5506i	−0.338221	+	1.26226i
$666$		0			0
$667$	−0.150338	−	0.0867978i	−0.00582112	−	0.00336082i
$668$	17.1957	−	4.60758i	0.665322	−	0.178273i
$669$		0			0
$670$	−19.6894	−	19.6894i	−0.760666	−	0.760666i
$671$	−50.7060	−	13.5866i	−1.95748	−	0.524506i
$672$		0			0
$673$			8.10263i			0.312334i	0.987731	+	0.156167i	$0.0499137\pi$
$673$			8.10263i			0.312334i	−0.987731	+	0.156167i	$0.950086\pi$
$674$	−8.68866	−	2.32812i	−0.334675	−	0.0896758i
$675$		0			0
$676$	6.31781	−	11.3616i	0.242993	−	0.436983i
$677$	1.64864	+	0.951842i	0.0633623	+	0.0365822i	0.531346	−	0.847155i	$-0.321686\pi$
$677$	1.64864	+	0.951842i	0.0633623	+	0.0365822i	−0.467984	+	0.883737i	$0.655020\pi$
$678$		0			0
$679$	9.73918	−	16.8688i	0.373755	−	0.647363i
$680$	10.3132			0.395494
$681$		0			0
$682$	13.5718	+	3.63656i	0.519692	+	0.139251i
$683$	1.49884	+	5.59375i	0.0573515	+	0.214039i	0.988655	−	0.150206i	$-0.0479938\pi$
$683$	1.49884	+	5.59375i	0.0573515	+	0.214039i	−0.931303	+	0.364245i	$0.881327\pi$
$684$		0			0
$685$	−30.2528	+	52.3993i	−1.15590	+	2.00208i
$686$	9.75759			0.372547
$687$		0			0
$688$	3.17570	−	1.83349i	0.121072	−	0.0699012i
$689$	11.9825	+	3.10747i	0.456495	+	0.118385i
$690$		0			0
$691$	−33.4689	+	33.4689i	−1.27322	+	1.27322i	−0.328828	+	0.944390i	$0.606654\pi$
$691$	−33.4689	+	33.4689i	−1.27322	+	1.27322i	−0.944390	+	0.328828i	$0.893346\pi$
$692$	12.4919	−	7.21223i	0.474872	−	0.274168i
$693$		0			0
$694$	5.25272	−	5.25272i	0.199390	−	0.199390i
$695$	8.58263	−	32.0308i	0.325558	−	1.21500i
$696$		0			0
$697$	1.68959	−	6.30562i	0.0639976	−	0.238842i
$698$		−	36.0902i		−	1.36604i
$699$		0			0
$700$	20.9372	+	20.9372i	0.791353	+	0.791353i
$701$	−28.7797			−1.08700			−0.543498	−	0.839411i	$-0.682900\pi$
$701$	−28.7797			−1.08700			−0.543498	+	0.839411i	$0.682900\pi$
$702$		0			0
$703$	20.6233			0.777824
$704$	4.48313	+	4.48313i	0.168964	+	0.168964i
$705$		0			0
$706$		−	3.07374i		−	0.115682i
$707$	−8.05205	+	30.0507i	−0.302829	+	1.13017i
$708$		0			0
$709$	8.40582	−	31.3709i	0.315687	−	1.17816i	−0.607661	−	0.794197i	$-0.707892\pi$
$709$	8.40582	−	31.3709i	0.315687	−	1.17816i	0.923348	−	0.383964i	$-0.125441\pi$
$710$	32.1907	−	32.1907i	1.20809	−	1.20809i
$711$		0			0
$712$	−0.577222	+	0.333259i	−0.0216323	+	0.0124894i
$713$	−0.286784	+	0.286784i	−0.0107401	+	0.0107401i
$714$		0			0
$715$	−82.1442	+	22.7211i	−3.07202	+	0.849721i
$716$	−13.0149	+	7.51417i	−0.486391	+	0.280818i
$717$		0			0
$718$	13.7699			0.513890
$719$	13.4021	−	23.2131i	0.499813	−	0.865701i	−0.500187	−	0.865917i	$-0.666735\pi$
$719$	13.4021	−	23.2131i	0.499813	−	0.865701i	1.00000		0.000215949i	$6.87386e-5\pi$
$720$		0			0
$721$	0.254728	+	0.950659i	0.00948658	+	0.0354044i
$722$	−11.2222	−	3.00697i	−0.417646	−	0.111908i
$723$		0			0
$724$	−7.25012			−0.269449
$725$	4.22142	−	7.31172i	0.156780	−	0.271550i
$726$		0			0
$727$	−2.56179	−	1.47905i	−0.0950116	−	0.0548550i	0.451741	−	0.892149i	$-0.350803\pi$
$727$	−2.56179	−	1.47905i	−0.0950116	−	0.0548550i	−0.546753	+	0.837294i	$0.684136\pi$
$728$	−11.5605	+	3.19763i	−0.428460	+	0.118512i
$729$		0			0
$730$	−11.0023	−	2.94806i	−0.407214	−	0.109113i
$731$		−	10.1435i		−	0.375169i
$732$		0			0
$733$	46.8751	+	12.5601i	1.73137	+	0.463920i	0.980498	−	0.196527i	$-0.0629663\pi$
$733$	46.8751	+	12.5601i	1.73137	+	0.463920i	0.750873	+	0.660447i	$0.229633\pi$
$734$	11.2267	+	11.2267i	0.414385	+	0.414385i
$735$		0			0
$736$	−0.176773	+	0.0473661i	−0.00651593	+	0.00174594i
$737$	−41.0068	−	23.6753i	−1.51050	−	0.872090i
$738$		0			0
$739$	−10.8543	+	40.5087i	−0.399281	+	1.49014i	0.415084	+	0.909783i	$0.363752\pi$
$739$	−10.8543	+	40.5087i	−0.399281	+	1.49014i	−0.814365	+	0.580354i	$0.802914\pi$
$740$	14.1501	−	24.5088i	0.520170	−	0.900960i
$741$		0			0
$742$	−5.71072	−	9.89126i	−0.209647	−	0.363119i
$743$	−39.4848	+	10.5799i	−1.44856	+	0.388140i	−0.895521	−	0.445018i	$-0.853197\pi$
$743$	−39.4848	+	10.5799i	−1.44856	+	0.388140i	−0.553035	+	0.833158i	$0.686530\pi$
$744$		0			0
$745$	76.3836	−	44.1001i	2.79848	−	1.61570i
$746$	0.512854	+	0.512854i	0.0187769	+	0.0187769i
$747$		0			0
$748$	16.9401	−	4.53910i	0.619393	−	0.165966i
$749$	16.1088	+	60.1188i	0.588602	+	2.19669i
$750$		0			0
$751$	22.8343	+	13.1834i	0.833234	+	0.481068i	0.854959	−	0.518696i	$-0.173582\pi$
$751$	22.8343	+	13.1834i	0.833234	+	0.481068i	−0.0217248	+	0.999764i	$0.506916\pi$
$752$	−1.38011	−	5.15065i	−0.0503276	−	0.187825i
$753$		0			0
$754$	1.73385	+	2.94802i	0.0631431	+	0.107361i
$755$		−	0.560489i		−	0.0203983i
$756$		0			0
$757$	−5.99038	−	10.3756i	−0.217724	−	0.377109i	0.736388	−	0.676560i	$-0.236530\pi$
$757$	−5.99038	−	10.3756i	−0.217724	−	0.377109i	−0.954112	+	0.299451i	$0.903197\pi$
$758$	1.51530	+	2.62457i	0.0550380	+	0.0953287i
$759$		0			0
$760$	7.16289	−	7.16289i	0.259825	−	0.259825i
$761$	8.76263	−	8.76263i	0.317645	−	0.317645i	−0.530217	−	0.847862i	$-0.677890\pi$
$761$	8.76263	−	8.76263i	0.317645	−	0.317645i	0.847862	+	0.530217i	$0.177890\pi$
$762$		0			0
$763$	−18.7220	−	32.4275i	−0.677784	−	1.17396i
$764$	1.59241	+	2.75813i	0.0576112	+	0.0997856i
$765$		0			0
$766$			1.96474i			0.0709889i
$767$	−8.56770	−	14.5675i	−0.309362	−	0.526001i
$768$		0			0
$769$	1.22527	+	4.57277i	0.0441843	+	0.164898i	0.984493	−	0.175425i	$-0.0561301\pi$
$769$	1.22527	+	4.57277i	0.0441843	+	0.164898i	−0.940308	+	0.340324i	$0.889463\pi$
$770$	68.1015	+	39.3184i	2.45421	+	1.41694i
$771$		0			0
$772$	−3.67080	−	13.6996i	−0.132115	−	0.493060i
$773$	−26.0869	+	6.98997i	−0.938281	+	0.251412i	−0.695382	−	0.718640i	$-0.744765\pi$
$773$	−26.0869	+	6.98997i	−0.938281	+	0.251412i	−0.242899	+	0.970052i	$0.578098\pi$
$774$		0			0
$775$	−13.9478	−	13.9478i	−0.501019	−	0.501019i
$776$	−5.07073	+	2.92759i	−0.182029	+	0.105094i
$777$		0			0
$778$	22.3884	−	5.99896i	0.802664	−	0.215073i
$779$	−3.20599	−	5.55294i	−0.114867	−	0.198955i
$780$		0			0
$781$	38.7074	−	67.0431i	1.38506	−	2.39899i
$782$	−0.131022	+	0.488982i	−0.00468534	+	0.0174859i
$783$		0			0
$784$	3.52202	+	2.03344i	0.125786	+	0.0726228i
$785$	6.39942	−	1.71472i	0.228405	−	0.0612010i
$786$		0			0
$787$	25.3004	+	25.3004i	0.901862	+	0.901862i	0.995597	−	0.0937351i	$-0.0298807\pi$
$787$	25.3004	+	25.3004i	0.901862	+	0.901862i	−0.0937351	+	0.995597i	$0.529881\pi$
$788$	0.338748	+	0.0907674i	0.0120674	+	0.00323345i
$789$		0			0
$790$			47.0765i			1.67491i
$791$	−22.4579	−	6.01759i	−0.798513	−	0.213961i
$792$		0			0
$793$	−28.7728	+	7.95858i	−1.02175	+	0.282617i
$794$	3.41606	+	1.97226i	0.121231	+	0.0699930i
$795$		0			0
$796$	9.88723	−	17.1252i	0.350444	−	0.606986i
$797$	−5.72377			−0.202746			−0.101373	−	0.994848i	$-0.532324\pi$
$797$	−5.72377			−0.202746			−0.101373	+	0.994848i	$0.532324\pi$
$798$		0			0
$799$	−14.2475	−	3.81761i	−0.504041	−	0.135057i
$800$	−2.30366	−	8.59737i	−0.0814466	−	0.303963i
$801$		0			0
$802$	−11.1247	+	19.2685i	−0.392825	+	0.680393i
$803$	−19.3695			−0.683536
$804$		0			0
$805$	−1.96577	+	1.13494i	−0.0692842	+	0.0400013i
$806$	7.70125	−	2.13017i	0.271265	−	0.0750320i
$807$		0			0
$808$	6.61276	−	6.61276i	0.232636	−	0.232636i
$809$	31.6723	−	18.2860i	1.11354	−	0.642903i	0.173796	−	0.984782i	$-0.444397\pi$
$809$	31.6723	−	18.2860i	1.11354	−	0.642903i	0.939744	+	0.341879i	$0.111063\pi$
$810$		0			0
$811$	13.4164	−	13.4164i	0.471115	−	0.471115i	−0.431160	−	0.902275i	$-0.641896\pi$
$811$	13.4164	−	13.4164i	0.471115	−	0.471115i	0.902275	+	0.431160i	$0.141896\pi$
$812$	0.816725	−	3.04806i	0.0286614	−	0.106966i
$813$		0			0
$814$	12.4556	−	46.4850i	0.436570	−	1.62930i
$815$			22.3079i			0.781413i
$816$		0			0
$817$	−7.04497	−	7.04497i	−0.246472	−	0.246472i
$818$	28.2842			0.988934
$819$		0			0
$820$	−8.79882			−0.307268
$821$	−2.17233	−	2.17233i	−0.0758148	−	0.0758148i	0.668183	−	0.743997i	$-0.267072\pi$
$821$	−2.17233	−	2.17233i	−0.0758148	−	0.0758148i	−0.743997	+	0.668183i	$0.767072\pi$
$822$		0			0
$823$			45.1543i			1.57398i	0.616965	+	0.786990i	$0.288362\pi$
$823$			45.1543i			1.57398i	−0.616965	+	0.786990i	$0.711638\pi$
$824$	0.0765711	−	0.285767i	0.00266748	−	0.00995517i
$825$		0			0
$826$	−4.03579	+	15.0618i	−0.140423	+	0.524066i
$827$	−9.71124	+	9.71124i	−0.337693	+	0.337693i	−0.855498	−	0.517806i	$-0.826749\pi$
$827$	−9.71124	+	9.71124i	−0.337693	+	0.337693i	0.517806	+	0.855498i	$0.326749\pi$
$828$		0			0
$829$	−11.7657	+	6.79293i	−0.408639	+	0.235928i	−0.690205	−	0.723614i	$-0.742480\pi$
$829$	−11.7657	+	6.79293i	−0.408639	+	0.235928i	0.281566	+	0.959542i	$0.409146\pi$
$830$	17.8133	−	17.8133i	0.618309	−	0.618309i
$831$		0			0
$832$	3.49010	+	0.905106i	0.120997	+	0.0313789i
$833$	9.74247	−	5.62482i	0.337557	−	0.194888i
$834$		0			0
$835$	−66.3734			−2.29695
$836$	8.61294	−	14.9181i	0.297885	−	0.515952i
$837$		0			0
$838$	−2.90497	−	10.8415i	−0.100351	−	0.374514i
$839$	42.9336	+	11.5040i	1.48223	+	0.397163i	0.907106	−	0.420901i	$-0.138286\pi$
$839$	42.9336	+	11.5040i	1.48223	+	0.397163i	0.575127	+	0.818064i	$0.304953\pi$
$840$		0			0
$841$	28.1002			0.968973
$842$	−0.496227	+	0.859490i	−0.0171011	+	0.0296200i
$843$		0			0
$844$	8.03456	+	4.63875i	0.276561	+	0.159672i
$845$	−33.7160	+	34.8201i	−1.15987	+	1.19785i
$846$		0			0
$847$	93.8193	+	25.1388i	3.22367	+	0.863780i
$848$			3.43327i			0.117899i
$849$		0			0
$850$	−23.7817	−	6.37228i	−0.815705	−	0.218568i
$851$	0.982268	+	0.982268i	0.0336717	+	0.0336717i
$852$		0			0
$853$	−15.3450	+	4.11168i	−0.525403	+	0.140781i	−0.511765	−	0.859126i	$-0.671008\pi$
$853$	−15.3450	+	4.11168i	−0.525403	+	0.140781i	−0.0136383	+	0.999907i	$0.504341\pi$
$854$	23.8541	+	13.7722i	0.816270	+	0.471274i
$855$		0			0
$856$	4.84229	−	18.0717i	0.165506	−	0.617676i
$857$	11.7570	−	20.3638i	0.401613	−	0.695614i	−0.592308	−	0.805712i	$-0.701783\pi$
$857$	11.7570	−	20.3638i	0.401613	−	0.695614i	0.993921	+	0.110098i	$0.0351164\pi$
$858$		0			0
$859$	−4.23525	−	7.33567i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$859$	−4.23525	−	7.33567i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$860$	−13.2060	+	3.53853i	−0.450320	+	0.120663i
$861$		0			0
$862$	−4.74273	+	2.73822i	−0.161538	+	0.0932640i
$863$	−4.48332	−	4.48332i	−0.152614	−	0.152614i	0.626670	−	0.779284i	$-0.284417\pi$
$863$	−4.48332	−	4.48332i	−0.152614	−	0.152614i	−0.779284	+	0.626670i	$0.784417\pi$
$864$		0			0
$865$	−51.9470	+	13.9192i	−1.76625	+	0.473266i
$866$	4.45692	+	16.6334i	0.151452	+	0.565227i
$867$		0			0
$868$	−6.38472	−	3.68622i	−0.216711	−	0.125118i
$869$	20.7195	+	77.3262i	0.702861	+	2.62311i
$870$		0			0
$871$	−26.9269	+	0.216875i	−0.912384	+	0.00734854i
$872$			11.2557i			0.381165i
$873$		0			0
$874$	0.248615	+	0.430614i	0.00840952	+	0.0145657i
$875$	−24.1901	−	41.8984i	−0.817774	−	1.41643i
$876$		0			0
$877$	−9.00681	+	9.00681i	−0.304138	+	0.304138i	−0.842630	−	0.538492i	$-0.818994\pi$
$877$	−9.00681	+	9.00681i	−0.304138	+	0.304138i	0.538492	+	0.842630i	$0.318994\pi$
$878$	3.64019	−	3.64019i	0.122850	−	0.122850i
$879$		0			0
$880$	−11.8191	−	20.4712i	−0.398421	−	0.690085i
$881$	28.5401	+	49.4329i	0.961541	+	1.66544i	0.718634	+	0.695389i	$0.244768\pi$
$881$	28.5401	+	49.4329i	0.961541	+	1.66544i	0.242907	+	0.970050i	$0.421899\pi$
$882$		0			0
$883$		−	35.3145i		−	1.18843i	−0.804307	−	0.594214i	$-0.797463\pi$
$883$		−	35.3145i		−	1.18843i	0.804307	−	0.594214i	$-0.202537\pi$
$884$	6.99532	−	7.10892i	0.235278	−	0.239099i
$885$		0			0
$886$	5.94772	+	22.1972i	0.199818	+	0.745729i
$887$	33.3408	+	19.2493i	1.11947	+	0.646328i	0.941267	−	0.337665i	$-0.109637\pi$
$887$	33.3408	+	19.2493i	1.11947	+	0.646328i	0.178207	+	0.983993i	$0.442970\pi$
$888$		0			0
$889$	−1.38550	−	5.17076i	−0.0464682	−	0.173422i
$890$	2.40035	−	0.643171i	0.0804598	−	0.0215591i
$891$		0			0
$892$	10.9424	+	10.9424i	0.366380	+	0.366380i
$893$	−12.5468	+	7.24393i	−0.419864	+	0.242409i
$894$		0			0
$895$	54.1219	−	14.5019i	1.80909	−	0.484745i
$896$	−1.66335	−	2.88100i	−0.0555685	−	0.0962474i
$897$		0			0
$898$	7.94437	−	13.7601i	0.265107	−	0.459179i
$899$	−0.544079	+	2.03053i	−0.0181460	+	0.0677219i
$900$		0			0
$901$	8.22462	+	4.74849i	0.274002	+	0.158195i
$902$	−14.4526	+	3.87257i	−0.481220	+	0.128942i
$903$		0			0
$904$	4.94195	+	4.94195i	0.164367	+	0.164367i
$905$	26.1100	+	6.99615i	0.867925	+	0.232560i
$906$		0			0
$907$		−	37.9356i		−	1.25963i	−0.776745	−	0.629815i	$-0.783131\pi$
$907$		−	37.9356i		−	1.25963i	0.776745	−	0.629815i	$-0.216869\pi$
$908$	−7.10373	−	1.90344i	−0.235746	−	0.0631678i
$909$		0			0
$910$	44.7186	−	0.360173i	1.48241	−	0.0119396i
$911$	36.1297	+	20.8595i	1.19703	+	0.691107i	0.959892	−	0.280369i	$-0.0904568\pi$
$911$	36.1297	+	20.8595i	1.19703	+	0.691107i	0.237140	+	0.971476i	$0.423790\pi$
$912$		0			0
$913$	21.4194	−	37.0995i	0.708879	−	1.22782i
$914$	−25.9328			−0.857780
$915$		0			0
$916$	−23.9064	−	6.40571i	−0.789891	−	0.211651i
$917$	−8.11834	−	30.2981i	−0.268091	−	1.00053i
$918$		0			0
$919$	−16.7214	+	28.9624i	−0.551590	+	0.955381i	0.446570	+	0.894748i	$0.352645\pi$
$919$	−16.7214	+	28.9624i	−0.551590	+	0.955381i	−0.998160	+	0.0606329i	$0.980688\pi$
$920$	0.682322			0.0224955
$921$		0			0
$922$	1.45600	−	0.840621i	0.0479508	−	0.0276844i
$923$	−0.354576	−	44.0236i	−0.0116710	−	1.44905i
$924$		0			0
$925$	−47.7727	+	47.7727i	−1.57076	+	1.57076i
$926$	−15.0488	+	8.68844i	−0.494535	+	0.285520i
$927$		0			0
$928$	−0.670737	+	0.670737i	−0.0220180	+	0.0220180i
$929$	−2.86847	+	10.7053i	−0.0941115	+	0.351229i	−0.996883	−	0.0788911i	$-0.974862\pi$
$929$	−2.86847	+	10.7053i	−0.0941115	+	0.351229i	0.902772	+	0.430120i	$0.141529\pi$
$930$		0			0
$931$	2.85985	−	10.6731i	0.0937277	−	0.349797i
$932$			18.0279i			0.590525i
$933$		0			0
$934$	−0.411940	−	0.411940i	−0.0134791	−	0.0134791i
$935$	−65.3869			−2.13838
$936$		0			0
$937$	−10.8175			−0.353392			−0.176696	−	0.984265i	$-0.556541\pi$
$937$	−10.8175			−0.353392			−0.176696	+	0.984265i	$0.556541\pi$
$938$	17.5682	+	17.5682i	0.573621	+	0.573621i
$939$		0			0
$940$			19.8809i			0.648444i
$941$	−3.40767	+	12.7176i	−0.111087	+	0.414582i	−0.998964	−	0.0454978i	$-0.985513\pi$
$941$	−3.40767	+	12.7176i	−0.111087	+	0.414582i	0.887877	+	0.460080i	$0.152179\pi$
$942$		0			0
$943$	0.111783	−	0.417179i	0.00364015	−	0.0135852i
$944$	3.31440	−	3.31440i	0.107875	−	0.107875i
$945$		0			0
$946$	−20.1342	+	11.6245i	−0.654621	+	0.377945i
$947$	35.8279	−	35.8279i	1.16425	−	1.16425i	0.180716	−	0.983535i	$-0.442159\pi$
$947$	35.8279	−	35.8279i	1.16425	−	1.16425i	0.983535	−	0.180716i	$-0.0578414\pi$
$948$		0			0
$949$	−9.49483	+	5.58428i	−0.308215	+	0.181273i
$950$	−20.9429	+	12.0914i	−0.679479	+	0.392297i
$951$		0			0
$952$	−9.20216			−0.298244
$953$	12.0254	−	20.8285i	0.389540	−	0.674702i	−0.602848	−	0.797856i	$-0.705967\pi$
$953$	12.0254	−	20.8285i	0.389540	−	0.674702i	0.992388	+	0.123154i	$0.0393008\pi$
$954$		0			0
$955$	−3.07325	−	11.4695i	−0.0994480	−	0.371145i
$956$	−27.5256	−	7.37545i	−0.890240	−	0.238539i
$957$		0			0
$958$	7.82238			0.252730
$959$	26.9936	−	46.7542i	0.871668	−	1.50977i
$960$		0			0
$961$	−22.5935	−	13.0443i	−0.728822	−	0.420785i
$962$	−7.29607	−	26.3777i	−0.235235	−	0.850450i
$963$		0			0
$964$	7.74584	+	2.07549i	0.249477	+	0.0668471i
$965$			52.8788i			1.70223i
$966$		0			0
$967$	31.8750	+	8.54089i	1.02503	+	0.274656i	0.731897	−	0.681415i	$-0.238635\pi$
$967$	31.8750	+	8.54089i	1.02503	+	0.274656i	0.293134	+	0.956071i	$0.405302\pi$
$968$	−20.6453	−	20.6453i	−0.663565	−	0.663565i
$969$		0			0
$970$	21.0863	−	5.65007i	0.677042	−	0.181413i
$971$	1.82907	+	1.05601i	0.0586976	+	0.0338891i	0.529062	−	0.848583i	$-0.322544\pi$
$971$	1.82907	+	1.05601i	0.0586976	+	0.0338891i	−0.470364	+	0.882472i	$0.655877\pi$
$972$		0			0
$973$	−7.65800	+	28.5800i	−0.245504	+	0.916234i
$974$	2.71428	−	4.70128i	0.0869712	−	0.150639i
$975$		0			0
$976$	−4.13990	−	7.17052i	−0.132515	−	0.229523i
$977$	39.4958	−	10.5829i	1.26358	−	0.338576i	0.436014	−	0.899940i	$-0.356390\pi$
$977$	39.4958	−	10.5829i	1.26358	−	0.338576i	0.827569	+	0.561364i	$0.189723\pi$
$978$		0			0
$979$	3.65965	−	2.11290i	0.116963	−	0.0675285i
$980$	−10.7217	−	10.7217i	−0.342492	−	0.342492i
$981$		0			0
$982$	2.32119	−	0.621962i	0.0740723	−	0.0198476i
$983$	−5.34955	−	19.9648i	−0.170624	−	0.636777i	−0.997256	−	0.0740342i	$-0.976413\pi$
$983$	−5.34955	−	19.9648i	−0.170624	−	0.636777i	0.826632	−	0.562743i	$-0.190254\pi$
$984$		0			0
$985$	−1.13235	−	0.653764i	−0.0360798	−	0.0208307i
$986$	0.679110	+	2.53447i	0.0216273	+	0.0807141i
$987$		0			0
$988$	−0.0788981	−	9.79587i	−0.00251008	−	0.311648i
$989$		−	0.671089i		−	0.0213394i
$990$		0			0
$991$	−13.1411	−	22.7610i	−0.417439	−	0.723026i	0.578242	−	0.815866i	$-0.303739\pi$
$991$	−13.1411	−	22.7610i	−0.417439	−	0.723026i	−0.995681	+	0.0928392i	$0.970406\pi$
$992$	1.10807	+	1.91924i	0.0351814	+	0.0609359i
$993$		0			0
$994$	−28.7227	+	28.7227i	−0.911028	+	0.911028i
$995$	−52.1324	+	52.1324i	−1.65271	+	1.65271i
$996$		0			0
$997$	28.7034	+	49.7157i	0.909045	+	1.57451i	0.815393	+	0.578908i	$0.196521\pi$
$997$	28.7034	+	49.7157i	0.909045	+	1.57451i	0.0936524	+	0.995605i	$0.470146\pi$
$998$	3.11692	+	5.39866i	0.0986644	+	0.170892i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.197.7		56
3.2	odd	2		234.2.y.a.119.10	yes	56
9.4	even	3		234.2.z.a.41.9	yes	56
9.5	odd	6		702.2.bc.a.665.7		56
13.7	odd	12		702.2.bc.a.683.7		56
39.20	even	12		234.2.z.a.137.9	yes	56
117.59	even	12	inner	702.2.bb.a.449.7		56
117.85	odd	12		234.2.y.a.59.10	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.10	✓	56	117.85	odd	12
234.2.y.a.119.10	yes	56	3.2	odd	2
234.2.z.a.41.9	yes	56	9.4	even	3
234.2.z.a.137.9	yes	56	39.20	even	12
702.2.bb.a.197.7		56	1.1	even	1	trivial
702.2.bb.a.449.7		56	117.59	even	12	inner
702.2.bc.a.665.7		56	9.5	odd	6
702.2.bc.a.683.7		56	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.964970 - 3.60132i) q^{5} +(-0.861011 + 3.21334i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.22885 + 1.86418i) q^{10} +(-4.48313 + 4.48313i) q^{11} +(-0.905106 + 3.49010i) q^{13} +(2.88100 - 1.66335i) q^{14} -1.00000 q^{16} +(-1.38308 + 2.39556i) q^{17} +(0.703205 + 2.62440i) q^{19} +(3.60132 + 0.964970i) q^{20} +6.34010 q^{22} +(-0.0915043 + 0.158490i) q^{23} +(-7.70819 - 4.45033i) q^{25} +(3.10788 - 1.82787i) q^{26} +(-3.21334 - 0.861011i) q^{28} +0.948565i q^{29} +(2.14063 + 0.573581i) q^{31} +(0.707107 + 0.707107i) q^{32} +(2.67190 - 0.715935i) q^{34} +(10.7414 + 6.20155i) q^{35} +(1.96458 - 7.33191i) q^{37} +(1.35849 - 2.35297i) q^{38} +(-1.86418 - 3.22885i) q^{40} +(-2.27956 + 0.610806i) q^{41} +(-3.17570 + 1.83349i) q^{43} +(-4.48313 - 4.48313i) q^{44} +(0.176773 - 0.0473661i) q^{46} +(1.38011 + 5.15065i) q^{47} +(-3.52202 - 2.03344i) q^{49} +(2.30366 + 8.59737i) q^{50} +(-3.49010 - 0.905106i) q^{52} -3.43327i q^{53} +(11.8191 + 20.4712i) q^{55} +(1.66335 + 2.88100i) q^{56} +(0.670737 - 0.670737i) q^{58} +(-3.31440 + 3.31440i) q^{59} +(4.13990 + 7.17052i) q^{61} +(-1.10807 - 1.91924i) q^{62} -1.00000i q^{64} +(11.6955 + 6.62741i) q^{65} +(1.93297 + 7.21395i) q^{67} +(-2.39556 - 1.38308i) q^{68} +(-3.21016 - 11.9805i) q^{70} +(-11.7943 + 3.16027i) q^{71} +(2.16027 + 2.16027i) q^{73} +(-6.57361 + 3.79528i) q^{74} +(-2.62440 + 0.703205i) q^{76} +(-10.5458 - 18.2658i) q^{77} +(6.31331 - 10.9350i) q^{79} +(-0.964970 + 3.60132i) q^{80} +(2.04380 + 1.17999i) q^{82} +(-6.52658 + 1.74879i) q^{83} +(7.29255 + 7.29255i) q^{85} +(3.54203 + 0.949085i) q^{86} +6.34010i q^{88} +(-0.643808 - 0.172508i) q^{89} +(-10.4356 - 5.91342i) q^{91} +(-0.158490 - 0.0915043i) q^{92} +(2.66617 - 4.61795i) q^{94} +10.1298 q^{95} +(-5.65566 - 1.51543i) q^{97} +(1.05259 + 3.92830i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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