LMFDB - Embedded newform 702.2.bc.a.683.7

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			683.7
Character	$\chi$	$=$	702.683
Dual form			702.2.bc.a.665.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(3.60132 + 0.964970i) q^{5} +(-2.35233 + 2.35233i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-3.22885 - 1.86418i) q^{10} +(1.64094 - 6.12407i) q^{11} +(3.47507 + 0.961205i) q^{13} +(2.88100 - 1.66335i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.38308 + 2.39556i) q^{17} +(0.703205 - 2.62440i) q^{19} +(2.63635 + 2.63635i) q^{20} +(-3.17005 + 5.49069i) q^{22} -0.183009 q^{23} +(7.70819 + 4.45033i) q^{25} +(-3.10788 - 1.82787i) q^{26} +(-3.21334 + 0.861011i) q^{28} +(0.821481 - 0.474282i) q^{29} +(-0.573581 + 2.14063i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.715935 - 2.67190i) q^{34} +(-10.7414 + 6.20155i) q^{35} +(1.96458 + 7.33191i) q^{37} +(-1.35849 + 2.35297i) q^{38} +(-1.86418 - 3.22885i) q^{40} +(-1.66875 + 1.66875i) q^{41} +3.66698i q^{43} +(4.48313 - 4.48313i) q^{44} +(0.176773 + 0.0473661i) q^{46} +(5.15065 - 1.38011i) q^{47} -4.06688i q^{49} +(-6.29371 - 6.29371i) q^{50} +(2.52889 + 2.56996i) q^{52} -3.43327i q^{53} +(11.8191 - 20.4712i) q^{55} +3.32669 q^{56} +(-0.916243 + 0.245507i) q^{58} +(-4.52756 + 1.21315i) q^{59} -8.27980 q^{61} +(1.10807 - 1.91924i) q^{62} +1.00000i q^{64} +(11.5873 + 6.81494i) q^{65} +(5.28097 + 5.28097i) q^{67} +2.76616i q^{68} +(11.9805 - 3.21016i) q^{70} +(11.7943 + 3.16027i) q^{71} +(2.16027 - 2.16027i) q^{73} -7.59055i q^{74} +(1.92119 - 1.92119i) q^{76} +(10.5458 + 18.2658i) q^{77} +(6.31331 - 10.9350i) q^{79} +(0.964970 + 3.60132i) q^{80} +(2.04380 - 1.17999i) q^{82} +(-1.74879 - 6.52658i) q^{83} +(2.66926 + 9.96181i) q^{85} +(0.949085 - 3.54203i) q^{86} +(-5.49069 + 3.17005i) q^{88} +(0.643808 - 0.172508i) q^{89} +(-10.4356 + 5.91342i) q^{91} +(-0.158490 - 0.0915043i) q^{92} -5.33235 q^{94} +(5.06492 - 8.77271i) q^{95} +(4.14023 + 4.14023i) q^{97} +(-1.05259 + 3.92830i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	3.60132	+	0.964970i	1.61056	+	0.431548i	0.948209	−	0.317648i	$-0.102893\pi$
$5$	3.60132	+	0.964970i	1.61056	+	0.431548i	0.662349	+	0.749195i	$0.269560\pi$
$6$		0			0
$7$	−2.35233	+	2.35233i	−0.889096	+	0.889096i	−0.994436	−	0.105340i	$-0.966407\pi$
$7$	−2.35233	+	2.35233i	−0.889096	+	0.889096i	0.105340	+	0.994436i	$0.466407\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−3.22885	−	1.86418i	−1.02105	−	0.589505i
$11$	1.64094	−	6.12407i	0.494762	−	1.84648i	−0.0366000	−	0.999330i	$-0.511653\pi$
$11$	1.64094	−	6.12407i	0.494762	−	1.84648i	0.531362	−	0.847145i	$-0.321681\pi$
$12$		0			0
$13$	3.47507	+	0.961205i	0.963810	+	0.266590i
$13$	3.47507	+	0.961205i	0.963810	+	0.266590i
$14$	2.88100	−	1.66335i	0.769980	−	0.444548i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.38308	+	2.39556i	0.335446	+	0.581010i	0.983570	−	0.180525i	$-0.0577797\pi$
$17$	1.38308	+	2.39556i	0.335446	+	0.581010i	−0.648124	+	0.761534i	$0.724446\pi$
$18$		0			0
$19$	0.703205	−	2.62440i	0.161326	−	0.602078i	−0.837154	−	0.546967i	$-0.815782\pi$
$19$	0.703205	−	2.62440i	0.161326	−	0.602078i	0.998480	−	0.0551104i	$-0.0175511\pi$
$20$	2.63635	+	2.63635i	0.589505	+	0.589505i
$21$		0			0
$22$	−3.17005	+	5.49069i	−0.675857	+	1.17062i
$23$	−0.183009			−0.0381599			−0.0190800	−	0.999818i	$-0.506074\pi$
$23$	−0.183009			−0.0381599			−0.0190800	+	0.999818i	$0.506074\pi$
$24$		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
$29$	0.821481	−	0.474282i	0.152545	−	0.0880720i	−0.421784	−	0.906696i	$-0.638596\pi$
$29$	0.821481	−	0.474282i	0.152545	−	0.0880720i	0.574330	+	0.818624i	$0.305263\pi$
$30$		0			0
$31$	−0.573581	+	2.14063i	−0.103018	+	0.384469i	−0.998113	−	0.0614072i	$-0.980441\pi$
$31$	−0.573581	+	2.14063i	−0.103018	+	0.384469i	0.895095	+	0.445876i	$0.147108\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$		0			0
$34$	−0.715935	−	2.67190i	−0.122782	−	0.458228i
$35$	−10.7414	+	6.20155i	−1.81563	+	1.04825i
$36$		0			0
$37$	1.96458	+	7.33191i	0.322975	+	1.20536i	0.916332	+	0.400419i	$0.131136\pi$
$37$	1.96458	+	7.33191i	0.322975	+	1.20536i	−0.593357	+	0.804939i	$0.702198\pi$
$38$	−1.35849	+	2.35297i	−0.220376	+	0.381702i
$39$		0			0
$40$	−1.86418	−	3.22885i	−0.294753	−	0.510526i
$41$	−1.66875	+	1.66875i	−0.260615	+	0.260615i	−0.825304	−	0.564689i	$-0.808996\pi$
$41$	−1.66875	+	1.66875i	−0.260615	+	0.260615i	0.564689	+	0.825304i	$0.308996\pi$
$42$		0			0
$43$			3.66698i			0.559209i	0.960115	+	0.279605i	$0.0902034\pi$
$43$			3.66698i			0.559209i	−0.960115	+	0.279605i	$0.909797\pi$
$44$	4.48313	−	4.48313i	0.675857	−	0.675857i
$45$		0			0
$46$	0.176773	+	0.0473661i	0.0260637	+	0.00698375i
$47$	5.15065	−	1.38011i	0.751300	−	0.201310i	0.137205	−	0.990543i	$-0.456188\pi$
$47$	5.15065	−	1.38011i	0.751300	−	0.201310i	0.614095	+	0.789232i	$0.289521\pi$
$48$		0			0
$49$		−	4.06688i		−	0.580983i
$50$	−6.29371	−	6.29371i	−0.890065	−	0.890065i
$51$		0			0
$52$	2.52889	+	2.56996i	0.350694	+	0.356389i
$53$		−	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
$56$	3.32669			0.444548
$57$		0			0
$58$	−0.916243	+	0.245507i	−0.120309	+	0.0322366i
$59$	−4.52756	+	1.21315i	−0.589438	+	0.157939i	−0.541196	−	0.840896i	$-0.682028\pi$
$59$	−4.52756	+	1.21315i	−0.589438	+	0.157939i	−0.0482414	+	0.998836i	$0.515362\pi$
$60$		0			0
$61$	−8.27980			−1.06012			−0.530060	−	0.847960i	$-0.677831\pi$
$61$	−8.27980			−1.06012			−0.530060	+	0.847960i	$0.677831\pi$
$62$	1.10807	−	1.91924i	0.140725	−	0.243744i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	11.5873	+	6.81494i	1.43723	+	0.845289i
$66$		0			0
$67$	5.28097	+	5.28097i	0.645174	+	0.645174i	0.951823	−	0.306649i	$-0.0992078\pi$
$67$	5.28097	+	5.28097i	0.645174	+	0.645174i	−0.306649	+	0.951823i	$0.599208\pi$
$68$			2.76616i			0.335446i
$69$		0			0
$70$	11.9805	−	3.21016i	1.43194	−	0.383687i
$71$	11.7943	+	3.16027i	1.39972	+	0.375055i	0.878245	−	0.478210i	$-0.158714\pi$
$71$	11.7943	+	3.16027i	1.39972	+	0.375055i	0.521478	+	0.853265i	$0.325381\pi$
$72$		0			0
$73$	2.16027	−	2.16027i	0.252841	−	0.252841i	−0.569294	−	0.822134i	$-0.692783\pi$
$73$	2.16027	−	2.16027i	0.252841	−	0.252841i	0.822134	+	0.569294i	$0.192783\pi$
$74$		−	7.59055i		−	0.882384i
$75$		0			0
$76$	1.92119	−	1.92119i	0.220376	−	0.220376i
$77$	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
$83$	−1.74879	−	6.52658i	−0.191955	−	0.716385i	−0.993034	−	0.117827i	$-0.962407\pi$
$83$	−1.74879	−	6.52658i	−0.191955	−	0.716385i	0.801079	−	0.598558i	$-0.204259\pi$
$84$		0			0
$85$	2.66926	+	9.96181i	0.289522	+	1.08051i
$86$	0.949085	−	3.54203i	0.102342	−	0.381947i
$87$		0			0
$88$	−5.49069	+	3.17005i	−0.585309	+	0.337928i
$89$	0.643808	−	0.172508i	0.0682435	−	0.0182858i	−0.224536	−	0.974466i	$-0.572087\pi$
$89$	0.643808	−	0.172508i	0.0682435	−	0.0182858i	0.292779	+	0.956180i	$0.405420\pi$
$90$		0			0
$91$	−10.4356	+	5.91342i	−1.09394	+	0.619895i
$92$	−0.158490	−	0.0915043i	−0.0165237	−	0.00953998i
$93$		0			0
$94$	−5.33235			−0.549990
$95$	5.06492	−	8.77271i	0.519650	−	0.900061i
$96$		0			0
$97$	4.14023	+	4.14023i	0.420377	+	0.420377i	0.885334	−	0.464957i	$-0.153930\pi$
$97$	4.14023	+	4.14023i	0.420377	+	0.420377i	−0.464957	+	0.885334i	$0.653930\pi$
$98$	−1.05259	+	3.92830i	−0.106327	+	0.396819i
$99$		0			0
$100$	4.45033	+	7.70819i	0.445033	+	0.770819i
$101$	4.67593	+	8.09895i	0.465272	+	0.805875i	0.999214	−	0.0396462i	$-0.0126231\pi$
$101$	4.67593	+	8.09895i	0.465272	+	0.805875i	−0.533942	+	0.845521i	$0.679290\pi$
$102$		0			0
$103$	−0.256212	+	0.147924i	−0.0252453	+	0.0145754i	−0.512570	−	0.858646i	$-0.671306\pi$
$103$	−0.256212	+	0.147924i	−0.0252453	+	0.0145754i	0.487324	+	0.873221i	$0.337973\pi$
$104$	−1.77757	−	3.13692i	−0.174305	−	0.307600i
$105$		0			0
$106$	−0.888596	+	3.31629i	−0.0863081	+	0.322106i
$107$	−16.2026	−	9.35458i	−1.56636	−	0.904341i	−0.996588	−	0.0825417i	$-0.973696\pi$
$107$	−16.2026	−	9.35458i	−1.56636	−	0.904341i	−0.569777	−	0.821799i	$-0.692970\pi$
$108$		0			0
$109$	−7.95895	−	7.95895i	−0.762329	−	0.762329i	0.214414	−	0.976743i	$-0.431216\pi$
$109$	−7.95895	−	7.95895i	−0.762329	−	0.762329i	−0.976743	+	0.214414i	$0.931216\pi$
$110$	−16.7147	+	16.7147i	−1.59368	+	1.59368i
$111$		0			0
$112$	−3.21334	−	0.861011i	−0.303632	−	0.0813579i
$113$	−6.05263	−	3.49449i	−0.569384	−	0.328734i	0.187519	−	0.982261i	$-0.439955\pi$
$113$	−6.05263	−	3.49449i	−0.569384	−	0.328734i	−0.756903	+	0.653527i	$0.773289\pi$
$114$		0			0
$115$	−0.659072	−	0.176598i	−0.0614588	−	0.0164678i
$116$	0.948565			0.0880720
$117$		0			0
$118$	4.68727			0.431498
$119$	−8.88860	−	2.38169i	−0.814817	−	0.218330i
$120$		0			0
$121$	−25.2852	−	14.5984i	−2.29866	−	1.32713i
$122$	7.99767	+	2.14297i	0.724075	+	0.194015i
$123$		0			0
$124$	−1.56705	+	1.56705i	−0.140725	+	0.140725i
$125$	10.2835	+	10.2835i	0.919782	+	0.919782i
$126$		0			0
$127$	−1.39357	−	0.804578i	−0.123659	−	0.0713947i	0.436894	−	0.899513i	$-0.356078\pi$
$127$	−1.39357	−	0.804578i	−0.123659	−	0.0713947i	−0.560554	+	0.828118i	$0.689412\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$		0			0
$130$	−9.42862	−	9.58173i	−0.826945	−	0.840374i
$131$	−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
$133$	4.51927	+	7.82760i	0.391870	+	0.678739i
$134$	−3.73421	−	6.46785i	−0.322587	−	0.558737i
$135$		0			0
$136$	0.715935	−	2.67190i	0.0613909	−	0.229114i
$137$	−11.4753	−	11.4753i	−0.980398	−	0.980398i	0.0194137	−	0.999812i	$-0.493820\pi$
$137$	−11.4753	−	11.4753i	−0.980398	−	0.980398i	−0.999812	+	0.0194137i	$0.993820\pi$
$138$		0			0
$139$	−4.44710	+	7.70260i	−0.377198	+	0.653326i	−0.990653	−	0.136403i	$-0.956446\pi$
$139$	−4.44710	+	7.70260i	−0.377198	+	0.653326i	0.613456	+	0.789729i	$0.289779\pi$
$140$	−12.4031			−1.04825
$141$		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
$146$	−2.64578	+	1.52754i	−0.218966	+	0.126420i
$147$		0			0
$148$	−1.96458	+	7.33191i	−0.161487	+	0.602679i
$149$	−6.12277	−	22.8505i	−0.501597	−	1.87199i	−0.489398	−	0.872060i	$-0.662784\pi$
$149$	−6.12277	−	22.8505i	−0.501597	−	1.87199i	−0.0121988	−	0.999926i	$-0.503883\pi$
$150$		0			0
$151$	−0.0389086	−	0.145209i	−0.00316634	−	0.0118169i	0.964325	−	0.264723i	$-0.0852804\pi$
$151$	−0.0389086	−	0.145209i	−0.00316634	−	0.0118169i	−0.967491	+	0.252906i	$0.918614\pi$
$152$	−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	$0.810743\pi$
$158$	−8.92836	+	8.92836i	−0.710302	+	0.710302i
$159$		0			0
$160$		−	3.72836i		−	0.294753i
$161$	0.430496	−	0.430496i	0.0339278	−	0.0339278i
$162$		0			0
$163$	−5.77944	−	1.54860i	−0.452681	−	0.121295i	0.0252727	−	0.999681i	$-0.491955\pi$
$163$	−5.77944	−	1.54860i	−0.452681	−	0.121295i	−0.477953	+	0.878385i	$0.658621\pi$
$164$	−2.27956	+	0.610806i	−0.178004	+	0.0476959i
$165$		0			0
$166$			6.75681i			0.524430i
$167$	12.5881	+	12.5881i	0.974099	+	0.974099i	0.999673	−	0.0255737i	$-0.00814124\pi$
$167$	12.5881	+	12.5881i	0.974099	+	0.974099i	−0.0255737	+	0.999673i	$0.508141\pi$
$168$		0			0
$169$	11.1522	+	6.68050i	0.857859	+	0.513885i
$170$		−	10.3132i		−	0.790989i
$171$		0			0
$172$	−1.83349	+	3.17570i	−0.139802	+	0.242145i
$173$	−14.4245			−1.09667			−0.548335	−	0.836258i	$-0.684738\pi$
$173$	−14.4245			−1.09667			−0.548335	+	0.836258i	$0.684738\pi$
$174$		0			0
$175$	−28.6008	+	7.66356i	−2.16202	+	0.579311i
$176$	6.12407	−	1.64094i	0.461619	−	0.123690i
$177$		0			0
$178$	−0.666519			−0.0499577
$179$	−7.51417	+	13.0149i	−0.561636	+	0.972782i	0.435718	+	0.900083i	$0.356494\pi$
$179$	−7.51417	+	13.0149i	−0.561636	+	0.972782i	−0.997354	+	0.0726986i	$0.976839\pi$
$180$		0			0
$181$		−	7.25012i		−	0.538897i	−0.963015	−	0.269449i	$-0.913159\pi$
$181$		−	7.25012i		−	0.538897i	0.963015	−	0.269449i	$-0.0868414\pi$
$182$	11.6105	−	3.01101i	0.860626	−	0.223191i
$183$		0			0
$184$	0.129407	+	0.129407i	0.00953998	+	0.00953998i
$185$			28.3003i			2.08068i
$186$		0			0
$187$	16.9401	−	4.53910i	1.23879	−	0.331932i
$188$	5.15065	+	1.38011i	0.375650	+	0.100655i
$189$		0			0
$190$	−7.16289	+	7.16289i	−0.519650	+	0.519650i
$191$			3.18481i			0.230445i	0.993340	+	0.115222i	$0.0367581\pi$
$191$			3.18481i			0.230445i	−0.993340	+	0.115222i	$0.963242\pi$
$192$		0			0
$193$	10.0288	−	10.0288i	0.721890	−	0.721890i	−0.247100	−	0.968990i	$-0.579478\pi$
$193$	10.0288	−	10.0288i	0.721890	−	0.721890i	0.968990	+	0.247100i	$0.0794777\pi$
$194$	−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	$-0.0873101\pi$
$197$	−0.0907674	−	0.338748i	−0.00646691	−	0.0241348i	−0.969084	+	0.246731i	$0.920643\pi$
$198$		0			0
$199$	−17.1252	+	9.88723i	−1.21397	+	0.700887i	−0.963622	−	0.267268i	$-0.913879\pi$
$199$	−17.1252	+	9.88723i	−1.21397	+	0.700887i	−0.250350	+	0.968155i	$0.580546\pi$
$200$	−2.30366	−	8.59737i	−0.162893	−	0.607926i
$201$		0			0
$202$	−2.42044	−	9.03320i	−0.170301	−	0.635574i
$203$	−0.816725	+	3.04806i	−0.0573229	+	0.213932i
$204$		0			0
$205$	−7.62000	+	4.39941i	−0.532204	+	0.307268i
$206$	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
$211$	−9.27751			−0.638690			−0.319345	−	0.947639i	$-0.603463\pi$
$211$	−9.27751			−0.638690			−0.319345	+	0.947639i	$0.603463\pi$
$212$	1.71664	−	2.97330i	0.117899	−	0.204207i
$213$		0			0
$214$	13.2294	+	13.2294i	0.904341	+	0.904341i
$215$	−3.53853	+	13.2060i	−0.241326	+	0.900639i
$216$		0			0
$217$	−3.68622	−	6.38472i	−0.250237	−	0.433423i
$218$	5.62783	+	9.74768i	0.381165	+	0.660196i
$219$		0			0
$220$	20.4712	−	11.8191i	1.38017	−	0.796842i
$221$	2.50367	+	9.65417i	0.168415	+	0.649409i
$222$		0			0
$223$	4.00521	−	14.9476i	0.268209	−	1.00097i	−0.692048	−	0.721851i	$-0.743291\pi$
$223$	4.00521	−	14.9476i	0.268209	−	1.00097i	0.960257	−	0.279117i	$-0.0900418\pi$
$224$	2.88100	+	1.66335i	0.192495	+	0.111137i
$225$		0			0
$226$	4.94195	+	4.94195i	0.328734	+	0.328734i
$227$	5.20029	−	5.20029i	0.345156	−	0.345156i	−0.513146	−	0.858301i	$-0.671520\pi$
$227$	5.20029	−	5.20029i	0.345156	−	0.345156i	0.858301	+	0.513146i	$0.171520\pi$
$228$		0			0
$229$	23.9064	+	6.40571i	1.57978	+	0.423301i	0.938858	−	0.344304i	$-0.111885\pi$
$229$	23.9064	+	6.40571i	1.57978	+	0.423301i	0.640923	+	0.767605i	$0.278552\pi$
$230$	0.590908	+	0.341161i	0.0389633	+	0.0224955i
$231$		0			0
$232$	−0.916243	−	0.245507i	−0.0601543	−	0.0161183i
$233$	−18.0279			−1.18105			−0.590525	−	0.807019i	$-0.701079\pi$
$233$	−18.0279			−1.18105			−0.590525	+	0.807019i	$0.701079\pi$
$234$		0			0
$235$	19.8809			1.29689
$236$	−4.52756	−	1.21315i	−0.294719	−	0.0789697i
$237$		0			0
$238$	7.96930	+	4.60108i	0.516573	+	0.298244i
$239$	−27.5256	−	7.37545i	−1.78048	−	0.477078i	−0.789809	−	0.613353i	$-0.789820\pi$
$239$	−27.5256	−	7.37545i	−1.78048	−	0.477078i	−0.990671	+	0.136275i	$0.956487\pi$
$240$		0			0
$241$	5.67035	−	5.67035i	0.365259	−	0.365259i	−0.500486	−	0.865745i	$-0.666845\pi$
$241$	5.67035	−	5.67035i	0.365259	−	0.365259i	0.865745	+	0.500486i	$0.166845\pi$
$242$	20.6453	+	20.6453i	1.32713	+	1.32713i
$243$		0			0
$244$	−7.17052	−	4.13990i	−0.459045	−	0.265030i
$245$	3.92442	−	14.6461i	0.250722	−	0.935706i
$246$		0			0
$247$	4.96626	−	8.44402i	0.315996	−	0.537280i
$248$	1.91924	−	1.10807i	0.121872	−	0.0703627i
$249$		0			0
$250$	−7.27151	−	12.5946i	−0.459891	−	0.796554i
$251$	−3.03917	−	5.26399i	−0.191830	−	0.332260i	0.754026	−	0.656844i	$-0.228109\pi$
$251$	−3.03917	−	5.26399i	−0.191830	−	0.332260i	−0.945857	+	0.324584i	$0.894776\pi$
$252$		0			0
$253$	−0.300306	+	1.12076i	−0.0188801	+	0.0704614i
$254$	1.13784	+	1.13784i	0.0713947	+	0.0713947i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.638781			0.0398461			0.0199230	−	0.999802i	$-0.493658\pi$
$257$	0.638781			0.0398461			0.0199230	+	0.999802i	$0.493658\pi$
$258$		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
$263$	4.87985	−	2.81738i	0.300905	−	0.173727i	−0.341945	−	0.939720i	$-0.611086\pi$
$263$	4.87985	−	2.81738i	0.300905	−	0.173727i	0.642849	+	0.765993i	$0.277752\pi$
$264$		0			0
$265$	3.31300	−	12.3643i	0.203516	−	0.759533i
$266$	−2.33934	−	8.73055i	−0.143434	−	0.535305i
$267$		0			0
$268$	1.93297	+	7.21395i	0.118075	+	0.440662i
$269$	−17.6754	+	10.2049i	−1.07769	+	0.622202i	−0.930271	−	0.366873i	$-0.880428\pi$
$269$	−17.6754	+	10.2049i	−1.07769	+	0.622202i	−0.147415	+	0.989075i	$0.547095\pi$
$270$		0			0
$271$	5.54365	+	20.6892i	0.336753	+	1.25678i	0.901956	+	0.431827i	$0.142131\pi$
$271$	5.54365	+	20.6892i	0.336753	+	1.25678i	−0.565204	+	0.824951i	$0.691202\pi$
$272$	−1.38308	+	2.39556i	−0.0838615	+	0.145252i
$273$		0			0
$274$	8.11424	+	14.0543i	0.490199	+	0.849049i
$275$	39.9027	−	39.9027i	2.40623	−	2.40623i
$276$		0			0
$277$			4.82222i			0.289739i	0.989451	+	0.144869i	$0.0462762\pi$
$277$			4.82222i			0.289739i	−0.989451	+	0.144869i	$0.953724\pi$
$278$	6.28914	−	6.28914i	0.377198	−	0.377198i
$279$		0			0
$280$	11.9805	+	3.21016i	0.715970	+	0.191844i
$281$	3.64034	−	0.975427i	0.217165	−	0.0581891i	−0.148596	−	0.988898i	$-0.547475\pi$
$281$	3.64034	−	0.975427i	0.217165	−	0.0581891i	0.365761	+	0.930709i	$0.380809\pi$
$282$		0			0
$283$			12.5997i			0.748977i	0.927232	+	0.374489i	$0.122182\pi$
$283$			12.5997i			0.748977i	−0.927232	+	0.374489i	$0.877818\pi$
$284$	8.63401	+	8.63401i	0.512334	+	0.512334i
$285$		0			0
$286$	−16.2938	+	16.0334i	−0.963473	+	0.948077i
$287$		−	7.85090i		−	0.463424i
$288$		0			0
$289$	4.67418	−	8.09592i	0.274952	−	0.476231i
$290$	−3.53659			−0.207676
$291$		0			0
$292$	2.95098	−	0.790714i	0.172693	−	0.0462730i
$293$	28.7098	−	7.69277i	1.67724	−	0.449416i	0.710195	−	0.704005i	$-0.248607\pi$
$293$	28.7098	−	7.69277i	1.67724	−	0.449416i	0.967050	+	0.254588i	$0.0819400\pi$
$294$		0			0
$295$	−17.4758			−1.01748
$296$	3.79528	−	6.57361i	0.220596	−	0.382083i
$297$		0			0
$298$			23.6566i			1.37039i
$299$	−0.635967	−	0.175909i	−0.0367789	−	0.0101731i
$300$		0			0
$301$	−8.62594	−	8.62594i	−0.497191	−	0.497191i
$302$			0.150331i			0.00865059i
$303$		0			0
$304$	2.62440	−	0.703205i	0.150519	−	0.0403315i
$305$	−29.8182	−	7.98976i	−1.70738	−	0.457492i
$306$		0			0
$307$	−22.9539	+	22.9539i	−1.31005	+	1.31005i	−0.388674	+	0.921376i	$0.627067\pi$
$307$	−22.9539	+	22.9539i	−1.31005	+	1.31005i	−0.921376	+	0.388674i	$0.872933\pi$
$308$			21.0916i			1.20180i
$309$		0			0
$310$	5.84253	−	5.84253i	0.331833	−	0.331833i
$311$	−11.8059	−	20.4483i	−0.669449	−	1.15952i	−0.978058	−	0.208331i	$-0.933197\pi$
$311$	−11.8059	−	20.4483i	−0.669449	−	1.15952i	0.308610	−	0.951189i	$-0.400136\pi$
$312$		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
$317$	−0.162090	−	0.604929i	−0.00910389	−	0.0339762i	0.961224	−	0.275767i	$-0.0889319\pi$
$317$	−0.162090	−	0.604929i	−0.00910389	−	0.0339762i	−0.970328	+	0.241791i	$0.922265\pi$
$318$		0			0
$319$	−1.55654	−	5.80907i	−0.0871493	−	0.325246i
$320$	−0.964970	+	3.60132i	−0.0539435	+	0.201320i
$321$		0			0
$322$	−0.527248	+	0.304407i	−0.0293824	+	0.0169639i
$323$	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
$328$	2.35997			0.130308
$329$	−8.86954	+	15.3625i	−0.488994	+	0.846962i
$330$		0			0
$331$	−21.8617	−	21.8617i	−1.20163	−	1.20163i	−0.973671	−	0.227958i	$-0.926795\pi$
$331$	−21.8617	−	21.8617i	−1.20163	−	1.20163i	−0.227958	−	0.973671i	$-0.573205\pi$
$332$	1.74879	−	6.52658i	0.0959774	−	0.358192i
$333$		0			0
$334$	−8.90116	−	15.4173i	−0.487050	−	0.843595i
$335$	13.9225	+	24.1144i	0.760666	+	1.31751i
$336$		0			0
$337$	−7.79004	+	4.49758i	−0.424350	+	0.244999i	−0.696937	−	0.717132i	$-0.745454\pi$
$337$	−7.79004	+	4.49758i	−0.424350	+	0.244999i	0.272586	+	0.962131i	$0.412121\pi$
$338$	−9.04313	−	9.33926i	−0.491881	−	0.507989i
$339$		0			0
$340$	−2.66926	+	9.96181i	−0.144761	+	0.540255i
$341$	12.1682	+	7.02529i	0.658943	+	0.380441i
$342$		0			0
$343$	−6.89966	−	6.89966i	−0.372547	−	0.372547i
$344$	2.59295	−	2.59295i	0.139802	−	0.139802i
$345$		0			0
$346$	13.9330	+	3.73332i	0.749040	+	0.200705i
$347$	−6.43324	−	3.71423i	−0.345354	−	0.199390i	0.317283	−	0.948331i	$-0.397230\pi$
$347$	−6.43324	−	3.71423i	−0.345354	−	0.199390i	−0.662637	+	0.748940i	$0.730563\pi$
$348$		0			0
$349$	−34.8605	−	9.34084i	−1.86604	−	0.500004i	−1.00000		2.82454e-5i	$-0.999991\pi$
$349$	−34.8605	−	9.34084i	−1.86604	−	0.500004i	−0.866040	−	0.499976i	$-0.833342\pi$
$350$	29.6097			1.58271
$351$		0			0
$352$	−6.34010			−0.337928
$353$	2.96901	+	0.795543i	0.158024	+	0.0423425i	0.336964	−	0.941518i	$-0.390600\pi$
$353$	2.96901	+	0.795543i	0.158024	+	0.0423425i	−0.178940	+	0.983860i	$0.557267\pi$
$354$		0			0
$355$	39.4254	+	22.7622i	2.09248	+	1.20809i
$356$	0.643808	+	0.172508i	0.0341217	+	0.00914289i
$357$		0			0
$358$	10.6266	−	10.6266i	0.561636	−	0.561636i
$359$	9.73682	+	9.73682i	0.513890	+	0.513890i	0.915716	−	0.401826i	$-0.131624\pi$
$359$	9.73682	+	9.73682i	0.513890	+	0.513890i	−0.401826	+	0.915716i	$0.631624\pi$
$360$		0			0
$361$	10.0615	+	5.80903i	0.529554	+	0.305738i
$362$	−1.87647	+	7.00308i	−0.0986250	+	0.368074i
$363$		0			0
$364$	−11.9942	−	0.0966037i	−0.628665	−	0.00506341i
$365$	9.86442	−	5.69522i	0.516327	−	0.298102i
$366$		0			0
$367$	7.93848	+	13.7499i	0.414385	+	0.717736i	0.995364	−	0.0961826i	$-0.0306633\pi$
$367$	7.93848	+	13.7499i	0.414385	+	0.717736i	−0.580978	+	0.813919i	$0.697330\pi$
$368$	−0.0915043	−	0.158490i	−0.00476999	−	0.00826187i
$369$		0			0
$370$	7.32466	−	27.3360i	0.380791	−	1.42113i
$371$	8.07618	+	8.07618i	0.419294	+	0.419294i
$372$		0			0
$373$	0.362643	−	0.628115i	0.0187769	−	0.0325226i	−0.856484	−	0.516173i	$-0.827356\pi$
$373$	0.362643	−	0.628115i	0.0187769	−	0.0325226i	0.875261	+	0.483651i	$0.160689\pi$
$374$	−17.5377			−0.906854
$375$		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	−0.333217	−	0.942850i	$-0.608134\pi$
$379$	−2.92733	+	0.784375i	−0.150367	+	0.0402906i	0.182850	+	0.983141i	$0.441468\pi$
$380$	8.77271	−	5.06492i	0.450030	−	0.259825i
$381$		0			0
$382$	0.824290	−	3.07629i	0.0421744	−	0.157397i
$383$	0.508512	+	1.89779i	0.0259837	+	0.0969727i	0.977700	−	0.210006i	$-0.0673485\pi$
$383$	0.508512	+	1.89779i	0.0259837	+	0.0969727i	−0.951716	+	0.306979i	$0.900682\pi$
$384$		0			0
$385$	20.3527	+	75.9574i	1.03727	+	3.87115i
$386$	−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	$-0.633410\pi$
$389$	11.5891	−	20.0729i	0.587591	−	1.01774i	0.994547	−	0.104289i	$-0.0332568\pi$
$390$		0			0
$391$	−0.253115	−	0.438409i	−0.0128006	−	0.0221713i
$392$	−2.87572	+	2.87572i	−0.145246	+	0.145246i
$393$		0			0
$394$			0.350698i			0.0176679i
$395$	33.2881	−	33.2881i	1.67491	−	1.67491i
$396$		0			0
$397$	−3.81012	−	1.02092i	−0.191224	−	0.0512384i	0.161936	−	0.986801i	$-0.448226\pi$
$397$	−3.81012	−	1.02092i	−0.191224	−	0.0512384i	−0.353160	+	0.935563i	$0.614893\pi$
$398$	19.1007	−	5.11801i	0.957430	−	0.256543i
$399$		0			0
$400$			8.90065i			0.445033i
$401$	15.7326	+	15.7326i	0.785651	+	0.785651i	0.980778	−	0.195127i	$-0.0625120\pi$
$401$	15.7326	+	15.7326i	0.785651	+	0.785651i	−0.195127	+	0.980778i	$0.562512\pi$
$402$		0			0
$403$	−4.05082	+	6.88751i	−0.201786	+	0.343091i
$404$			9.35186i			0.465272i
$405$		0			0
$406$	1.57779	−	2.73282i	0.0783045	−	0.135627i
$407$	48.1249			2.38546
$408$		0			0
$409$	27.3204	−	7.32049i	1.35091	−	0.361975i	0.490439	−	0.871476i	$-0.336837\pi$
$409$	27.3204	−	7.32049i	1.35091	−	0.361975i	0.860470	+	0.509501i	$0.170170\pi$
$410$	8.49901	−	2.27730i	0.419736	−	0.112468i
$411$		0			0
$412$	−0.295848			−0.0145754
$413$	7.79655	−	13.5040i	0.383643	−	0.664490i
$414$		0			0
$415$		−	25.1918i		−	1.23662i
$416$	0.0290390	−	3.60543i	0.00142375	−	0.176771i
$417$		0			0
$418$	12.1805	+	12.1805i	0.595770	+	0.595770i
$419$		−	11.2240i		−	0.548326i	−0.961683	−	0.274163i	$-0.911599\pi$
$419$		−	11.2240i		−	0.548326i	0.961683	−	0.274163i	$-0.0884008\pi$
$420$		0			0
$421$	0.958636	−	0.256866i	0.0467211	−	0.0125189i	−0.235383	−	0.971903i	$-0.575634\pi$
$421$	0.958636	−	0.256866i	0.0467211	−	0.0125189i	0.282104	+	0.959384i	$0.408968\pi$
$422$	8.96138	+	2.40120i	0.436233	+	0.116888i
$423$		0			0
$424$	−2.42769	+	2.42769i	−0.117899	+	0.117899i
$425$			24.6206i			1.19428i
$426$		0			0
$427$	19.4768	−	19.4768i	0.942548	−	0.942548i
$428$	−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	$-0.125440\pi$
$431$	−1.41740	−	5.28983i	−0.0682740	−	0.254802i	−0.991624	+	0.129157i	$0.958773\pi$
$432$		0			0
$433$	−14.9131	+	8.61010i	−0.716680	+	0.413775i	−0.813529	−	0.581524i	$-0.802457\pi$
$433$	−14.9131	+	8.61010i	−0.716680	+	0.413775i	0.0968497	+	0.995299i	$0.469123\pi$
$434$	1.90813	+	7.12122i	0.0915930	+	0.341830i
$435$		0			0
$436$	−2.91318	−	10.8721i	−0.139516	−	0.520681i
$437$	−0.128693	+	0.480287i	−0.00615620	+	0.0229752i
$438$		0			0
$439$	−4.45830	+	2.57400i	−0.212783	+	0.122850i	−0.602604	−	0.798040i	$-0.705870\pi$
$439$	−4.45830	+	2.57400i	−0.212783	+	0.122850i	0.389821	+	0.920891i	$0.372537\pi$
$440$	−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
$445$	2.48502			0.117801
$446$	−7.73747	+	13.4017i	−0.366380	+	0.634589i
$447$		0			0
$448$	−2.35233	−	2.35233i	−0.111137	−	0.111137i
$449$	−4.11231	+	15.3473i	−0.194072	+	0.724286i	0.798433	+	0.602083i	$0.205662\pi$
$449$	−4.11231	+	15.3473i	−0.194072	+	0.724286i	−0.992505	+	0.122203i	$0.961004\pi$
$450$		0			0
$451$	7.48123	+	12.9579i	0.352277	+	0.610162i
$452$	−3.49449	−	6.05263i	−0.164367	−	0.284692i
$453$		0			0
$454$	−6.36903	+	3.67716i	−0.298913	+	0.172578i
$455$	−43.2880	+	11.2261i	−2.02937	+	0.526288i
$456$		0			0
$457$	6.71190	−	25.0491i	0.313969	−	1.17175i	−0.610976	−	0.791649i	$-0.709223\pi$
$457$	6.71190	−	25.0491i	0.313969	−	1.17175i	0.924945	−	0.380100i	$-0.124111\pi$
$458$	−21.4339	−	12.3749i	−1.00154	−	0.578240i
$459$		0			0
$460$	−0.482474	−	0.482474i	−0.0224955	−	0.0224955i
$461$	1.18882	−	1.18882i	0.0553688	−	0.0553688i	−0.678880	−	0.734249i	$-0.737534\pi$
$461$	1.18882	−	1.18882i	0.0553688	−	0.0553688i	0.734249	+	0.678880i	$0.237534\pi$
$462$		0			0
$463$	−16.7848	−	4.49747i	−0.780055	−	0.209015i	−0.153246	−	0.988188i	$-0.548973\pi$
$463$	−16.7848	−	4.49747i	−0.780055	−	0.209015i	−0.626809	+	0.779173i	$0.715639\pi$
$464$	0.821481	+	0.474282i	0.0381363	+	0.0220180i
$465$		0			0
$466$	17.4137	+	4.66597i	0.806672	+	0.216147i
$467$	−0.582570			−0.0269581			−0.0134791	−	0.999909i	$-0.504291\pi$
$467$	−0.582570			−0.0269581			−0.0134791	+	0.999909i	$0.504291\pi$
$468$		0			0
$469$	−24.8452			−1.14724
$470$	−19.2035	−	5.14556i	−0.885791	−	0.237347i
$471$		0			0
$472$	4.05930	+	2.34364i	0.186844	+	0.107875i
$473$	22.4568	+	6.01729i	1.03257	+	0.276675i
$474$		0			0
$475$	17.0998	−	17.0998i	0.784595	−	0.784595i
$476$	−6.50691	−	6.50691i	−0.298244	−	0.298244i
$477$		0			0
$478$	24.6787	+	14.2483i	1.12878	+	0.651701i
$479$	2.02458	−	7.55584i	0.0925055	−	0.345235i	−0.904124	−	0.427270i	$-0.859475\pi$
$479$	2.02458	−	7.55584i	0.0925055	−	0.345235i	0.996629	+	0.0820351i	$0.0261420\pi$
$480$		0			0
$481$	−0.220422	+	27.3672i	−0.0100504	+	1.24784i
$482$	−6.94473	+	4.00954i	−0.316324	+	0.182630i
$483$		0			0
$484$	−14.5984	−	25.2852i	−0.663565	−	1.14933i
$485$	10.9151	+	18.9055i	0.495629	+	0.858454i
$486$		0			0
$487$	1.40502	−	5.24359i	0.0636674	−	0.237610i	−0.926758	−	0.375659i	$-0.877416\pi$
$487$	1.40502	−	5.24359i	0.0636674	−	0.237610i	0.990425	+	0.138049i	$0.0440831\pi$
$488$	5.85470	+	5.85470i	0.265030	+	0.265030i
$489$		0			0
$490$	−7.58139	+	13.1314i	−0.342492	+	0.593214i
$491$	−2.40308			−0.108449			−0.0542247	−	0.998529i	$-0.517269\pi$
$491$	−2.40308			−0.108449			−0.0542247	+	0.998529i	$0.517269\pi$
$492$		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
$497$	−35.1780	+	20.3100i	−1.57795	+	0.911028i
$498$		0			0
$499$	1.61344	−	6.02143i	0.0722273	−	0.269556i	−0.920363	−	0.391065i	$-0.872107\pi$
$499$	1.61344	−	6.02143i	0.0722273	−	0.269556i	0.992590	+	0.121509i	$0.0387734\pi$
$500$	3.76401	+	14.0475i	0.168332	+	0.628222i
$501$		0			0
$502$	1.57319	+	5.87122i	0.0702148	+	0.262045i
$503$	−11.8442	+	6.83823i	−0.528105	+	0.304901i	−0.740244	−	0.672338i	$-0.765290\pi$
$503$	−11.8442	+	6.83823i	−0.528105	+	0.304901i	0.212140	+	0.977239i	$0.431957\pi$
$504$		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
$509$	−5.61611	+	5.61611i	−0.248930	+	0.248930i	−0.820531	−	0.571602i	$-0.806322\pi$
$509$	−5.61611	+	5.61611i	−0.248930	+	0.248930i	0.571602	+	0.820531i	$0.306322\pi$
$510$		0			0
$511$			10.1633i			0.449599i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−0.617015	−	0.165329i	−0.0272154	−	0.00729234i
$515$	−1.06544	+	0.285484i	−0.0469490	+	0.0125799i
$516$		0			0
$517$		−	33.8076i		−	1.48686i
$518$	17.8555	+	17.8555i	0.784524	+	0.784524i
$519$		0			0
$520$	−3.37456	−	13.0123i	−0.147984	−	0.570629i
$521$		−	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	−0.733477	−	0.679714i	$-0.762104\pi$
$523$	5.07493	−	8.79004i	0.221911	−	0.384362i	0.955388	+	0.295353i	$0.0954371\pi$
$524$	−9.42885			−0.411901
$525$		0			0
$526$	−5.44277	+	1.45838i	−0.237316	+	0.0635886i
$527$	−5.92133	+	1.58662i	−0.257937	+	0.0691141i
$528$		0			0
$529$	−22.9665			−0.998544
$530$	−6.40023	+	11.0855i	−0.278008	+	0.481525i
$531$		0			0
$532$			9.03853i			0.391870i
$533$	−7.40304	+	4.19501i	−0.320661	+	0.181706i
$534$		0			0
$535$	−49.3238	−	49.3238i	−2.13245	−	2.13245i
$536$		−	7.46843i		−	0.322587i
$537$		0			0
$538$	19.7143	−	5.28243i	0.849944	−	0.227742i
$539$	−24.9058	−	6.67350i	−1.07277	−	0.287448i
$540$		0			0
$541$	24.3541	−	24.3541i	1.04706	−	1.04706i	0.0482280	−	0.998836i	$-0.484643\pi$
$541$	24.3541	−	24.3541i	1.04706	−	1.04706i	0.998836	−	0.0482280i	$-0.0153574\pi$
$542$		−	21.4190i		−	0.920026i
$543$		0			0
$544$	1.95597	−	1.95597i	0.0838615	−	0.0838615i
$545$	−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
$551$	−0.667035	−	2.48941i	−0.0284167	−	0.106052i
$552$		0			0
$553$	10.8717	+	40.5736i	0.462310	+	1.72536i
$554$	1.24808	−	4.65790i	0.0530259	−	0.197895i
$555$		0			0
$556$	−7.70260	+	4.44710i	−0.326663	+	0.188599i
$557$	−41.9906	+	11.2513i	−1.77920	+	0.476734i	−0.990437	−	0.137967i	$-0.955943\pi$
$557$	−41.9906	+	11.2513i	−1.77920	+	0.476734i	−0.788760	+	0.614701i	$0.789277\pi$
$558$		0			0
$559$	−3.52472	+	12.7430i	−0.149080	+	0.538972i
$560$	−10.7414	−	6.20155i	−0.453907	−	0.262063i
$561$		0			0
$562$	−3.76876			−0.158976
$563$	−0.819395	+	1.41923i	−0.0345334	+	0.0598136i	−0.882776	−	0.469795i	$-0.844328\pi$
$563$	−0.819395	+	1.41923i	−0.0345334	+	0.0598136i	0.848242	+	0.529609i	$0.177661\pi$
$564$		0			0
$565$	−18.4254	−	18.4254i	−0.775161	−	0.775161i
$566$	3.26105	−	12.1704i	0.137072	−	0.511561i
$567$		0			0
$568$	−6.10517	−	10.5745i	−0.256167	−	0.443694i
$569$	−1.54435	−	2.67489i	−0.0647424	−	0.112137i	0.831837	−	0.555020i	$-0.187289\pi$
$569$	−1.54435	−	2.67489i	−0.0647424	−	0.112137i	−0.896580	+	0.442882i	$0.853956\pi$
$570$		0			0
$571$	−5.59791	+	3.23195i	−0.234265	+	0.135253i	−0.612538	−	0.790441i	$-0.709851\pi$
$571$	−5.59791	+	3.23195i	−0.234265	+	0.135253i	0.378273	+	0.925694i	$0.376518\pi$
$572$	19.8884	−	11.2700i	0.831574	−	0.471221i
$573$		0			0
$574$	−2.03196	+	7.58339i	−0.0848125	+	0.316525i
$575$	−1.41067	−	0.814448i	−0.0588288	−	0.0339648i
$576$		0			0
$577$	32.0507	+	32.0507i	1.33429	+	1.33429i	0.901492	+	0.432795i	$0.142473\pi$
$577$	32.0507	+	32.0507i	1.33429	+	1.33429i	0.432795	+	0.901492i	$0.357527\pi$
$578$	−6.61029	+	6.61029i	−0.274952	+	0.274952i
$579$		0			0
$580$	3.41608	+	0.915337i	0.141845	+	0.0380073i
$581$	19.4664	+	11.2389i	0.807601	+	0.466269i
$582$		0			0
$583$	−21.0256	−	5.63379i	−0.870791	−	0.233328i
$584$	−3.05508			−0.126420
$585$		0			0
$586$	−29.7226			−1.22783
$587$	21.8823	+	5.86335i	0.903181	+	0.242007i	0.680382	−	0.732858i	$-0.261814\pi$
$587$	21.8823	+	5.86335i	0.903181	+	0.242007i	0.222799	+	0.974864i	$0.428481\pi$
$588$		0			0
$589$	5.21452	+	3.01060i	0.214861	+	0.124050i
$590$	16.8803	+	4.52308i	0.694953	+	0.186212i
$591$		0			0
$592$	−5.36733	+	5.36733i	−0.220596	+	0.220596i
$593$	14.2009	+	14.2009i	0.583160	+	0.583160i	0.935770	−	0.352610i	$-0.114706\pi$
$593$	14.2009	+	14.2009i	0.583160	+	0.583160i	−0.352610	+	0.935770i	$0.614706\pi$
$594$		0			0
$595$	−29.7124	−	17.1545i	−1.21809	−	0.703265i
$596$	6.12277	−	22.8505i	0.250799	−	0.935993i
$597$		0			0
$598$	0.568769	+	0.334515i	0.0232587	+	0.0136793i
$599$	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
$601$	7.72707	+	13.3837i	0.315194	+	0.545931i	0.979479	−	0.201548i	$-0.0645972\pi$
$601$	7.72707	+	13.3837i	0.315194	+	0.545931i	−0.664285	+	0.747479i	$0.731264\pi$
$602$	6.09946	+	10.5646i	0.248595	+	0.430580i
$603$		0			0
$604$	0.0389086	−	0.145209i	0.00158317	−	0.00590846i
$605$	−76.9730	−	76.9730i	−3.12940	−	3.12940i
$606$		0			0
$607$	14.1563	−	24.5194i	0.574586	−	0.995213i	−0.421500	−	0.906828i	$-0.638496\pi$
$607$	14.1563	−	24.5194i	0.574586	−	0.995213i	0.996086	−	0.0883842i	$-0.0281703\pi$
$608$	−2.71697			−0.110188
$609$		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	−0.472262	−	0.881458i	$-0.656562\pi$
$613$	−10.9069	+	2.92249i	−0.440524	+	0.118038i	0.0317379	+	0.999496i	$0.489896\pi$
$614$	28.1127	−	16.2309i	1.13454	−	0.655025i
$615$		0			0
$616$	5.45890	−	20.3729i	0.219945	−	0.820847i
$617$	9.90643	+	36.9713i	0.398818	+	1.48841i	0.815179	+	0.579209i	$0.196638\pi$
$617$	9.90643	+	36.9713i	0.398818	+	1.48841i	−0.416361	+	0.909199i	$0.636695\pi$
$618$		0			0
$619$	−6.82214	−	25.4606i	−0.274205	−	1.02335i	−0.956372	−	0.292150i	$-0.905629\pi$
$619$	−6.82214	−	25.4606i	−0.274205	−	1.02335i	0.682168	−	0.731196i	$-0.261037\pi$
$620$	−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
$626$	−12.3252	+	12.3252i	−0.492613	+	0.492613i
$627$		0			0
$628$			1.77697i			0.0709087i
$629$	−14.8469	+	14.8469i	−0.591984	+	0.591984i
$630$		0			0
$631$	38.1709	+	10.2279i	1.51956	+	0.407165i	0.919597	−	0.392863i	$-0.128515\pi$
$631$	38.1709	+	10.2279i	1.51956	+	0.407165i	0.599963	+	0.800028i	$0.295182\pi$
$632$	−12.1964	+	3.26801i	−0.485146	+	0.129994i
$633$		0			0
$634$			0.626268i			0.0248723i
$635$	−4.24229	−	4.24229i	−0.168350	−	0.168350i
$636$		0			0
$637$	3.90910	−	14.1327i	0.154884	−	0.559957i
$638$			6.01399i			0.238096i
$639$		0			0
$640$	1.86418	−	3.22885i	0.0736881	−	0.127632i
$641$	33.6899			1.33067			0.665335	−	0.746545i	$-0.268289\pi$
$641$	33.6899			1.33067			0.665335	+	0.746545i	$0.268289\pi$
$642$		0			0
$643$	−22.2328	+	5.95725i	−0.876775	+	0.234931i	−0.669015	−	0.743249i	$-0.733284\pi$
$643$	−22.2328	+	5.95725i	−0.876775	+	0.234931i	−0.207760	+	0.978180i	$0.566617\pi$
$644$	0.588069	−	0.157572i	0.0231731	−	0.00620923i
$645$		0			0
$646$	−7.51558			−0.295697
$647$	−3.32926	+	5.76644i	−0.130887	+	0.226702i	−0.924019	−	0.382348i	$-0.875116\pi$
$647$	−3.32926	+	5.76644i	−0.130887	+	0.226702i	0.793132	+	0.609050i	$0.208449\pi$
$648$		0			0
$649$			29.7178i			1.16652i
$650$	−15.8215	−	27.9206i	−0.620571	−	1.09514i
$651$		0			0
$652$	−4.23084	−	4.23084i	−0.165693	−	0.165693i
$653$			21.1724i			0.828539i	0.910154	+	0.414270i	$0.135963\pi$
$653$			21.1724i			0.828539i	−0.910154	+	0.414270i	$0.864037\pi$
$654$		0			0
$655$	−33.9563	+	9.09855i	−1.32678	+	0.355510i
$656$	−2.27956	−	0.610806i	−0.0890018	−	0.0238480i
$657$		0			0
$658$	12.5434	−	12.5434i	0.488994	−	0.488994i
$659$			39.5999i			1.54259i	0.636477	+	0.771296i	$0.280391\pi$
$659$			39.5999i			1.54259i	−0.636477	+	0.771296i	$0.719609\pi$
$660$		0			0
$661$	17.5774	−	17.5774i	0.683682	−	0.683682i	−0.277146	−	0.960828i	$-0.589388\pi$
$661$	17.5774	−	17.5774i	0.683682	−	0.683682i	0.960828	+	0.277146i	$0.0893884\pi$
$662$	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
$668$	4.60758	+	17.1957i	0.178273	+	0.665322i
$669$		0			0
$670$	−7.20681	−	26.8962i	−0.278423	−	1.03909i
$671$	−13.5866	+	50.7060i	−0.524506	+	1.95748i
$672$		0			0
$673$	−7.01709	+	4.05132i	−0.270489	+	0.156167i	−0.629110	−	0.777316i	$-0.716580\pi$
$673$	−7.01709	+	4.05132i	−0.270489	+	0.156167i	0.358621	+	0.933483i	$0.383247\pi$
$674$	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
$679$	−19.4784			−0.747511
$680$	5.15661	−	8.93152i	0.197747	−	0.342508i
$681$		0			0
$682$	−9.93526	−	9.93526i	−0.380441	−	0.380441i
$683$	−1.49884	+	5.59375i	−0.0573515	+	0.214039i	−0.988655	−	0.150206i	$-0.952006\pi$
$683$	−1.49884	+	5.59375i	−0.0573515	+	0.214039i	0.931303	+	0.364245i	$0.118673\pi$
$684$		0			0
$685$	−30.2528	−	52.3993i	−1.15590	−	2.00208i
$686$	4.87879	+	8.45032i	0.186273	+	0.322635i
$687$		0			0
$688$	−3.17570	+	1.83349i	−0.121072	+	0.0699012i
$689$	3.30008	−	11.9308i	0.125723	−	0.454529i
$690$		0			0
$691$	−12.2505	+	45.7194i	−0.466030	+	1.73925i	0.187421	+	0.982280i	$0.439987\pi$
$691$	−12.2505	+	45.7194i	−0.466030	+	1.73925i	−0.653451	+	0.756968i	$0.726680\pi$
$692$	−12.4919	−	7.21223i	−0.474872	−	0.274168i
$693$		0			0
$694$	5.25272	+	5.25272i	0.199390	+	0.199390i
$695$	−23.4482	+	23.4482i	−0.889440	+	0.889440i
$696$		0			0
$697$	−6.30562	−	1.68959i	−0.238842	−	0.0639976i
$698$	31.2551	+	18.0451i	1.18302	+	0.683018i
$699$		0			0
$700$	−28.6008	−	7.66356i	−1.08101	−	0.289655i
$701$	28.7797			1.08700			0.543498	−	0.839411i	$-0.317100\pi$
$701$	28.7797			1.08700			0.543498	+	0.839411i	$0.317100\pi$
$702$		0			0
$703$	20.6233			0.777824
$704$	6.12407	+	1.64094i	0.230809	+	0.0618452i
$705$		0			0
$706$	−2.66194	−	1.53687i	−0.100183	−	0.0578409i
$707$	−30.0507	−	8.05205i	−1.13017	−	0.302829i
$708$		0			0
$709$	22.9651	−	22.9651i	0.862473	−	0.862473i	−0.129152	−	0.991625i	$-0.541225\pi$
$709$	22.9651	−	22.9651i	0.862473	−	0.862473i	0.991625	+	0.129152i	$0.0412254\pi$
$710$	−32.1907	−	32.1907i	−1.20809	−	1.20809i
$711$		0			0
$712$	−0.577222	−	0.333259i	−0.0216323	−	0.0124894i
$713$	0.104970	−	0.391754i	0.00393117	−	0.0146713i
$714$		0			0
$715$	60.7491	−	59.7784i	2.27189	−	2.23558i
$716$	−13.0149	+	7.51417i	−0.486391	+	0.280818i
$717$		0			0
$718$	−6.88497	−	11.9251i	−0.256945	−	0.445042i
$719$	−13.4021	−	23.2131i	−0.499813	−	0.865701i	0.500187	−	0.865917i	$-0.333265\pi$
$719$	−13.4021	−	23.2131i	−0.499813	−	0.865701i	−1.00000		0.000215949i	$0.999931\pi$
$720$		0			0
$721$	0.254728	−	0.950659i	0.00948658	−	0.0354044i
$722$	−8.21520	−	8.21520i	−0.305738	−	0.305738i
$723$		0			0
$724$	3.62506	−	6.27879i	0.134724	−	0.233349i
$725$	8.44284			0.313559
$726$		0			0
$727$	2.56179	+	1.47905i	0.0950116	+	0.0548550i	0.546753	−	0.837294i	$-0.315864\pi$
$727$	2.56179	+	1.47905i	0.0950116	+	0.0548550i	−0.451741	+	0.892149i	$0.649197\pi$
$728$	11.5605	+	3.19763i	0.428460	+	0.118512i
$729$		0			0
$730$	−11.0023	+	2.94806i	−0.407214	+	0.109113i
$731$	−8.78449	+	5.07173i	−0.324906	+	0.187585i
$732$		0			0
$733$	−12.5601	+	46.8751i	−0.463920	+	1.73137i	0.196527	+	0.980498i	$0.437034\pi$
$733$	−12.5601	+	46.8751i	−0.463920	+	1.73137i	−0.660447	+	0.750873i	$0.729633\pi$
$734$	−4.10926	−	15.3360i	−0.151676	−	0.566061i
$735$		0			0
$736$	0.0473661	+	0.176773i	0.00174594	+	0.00651593i
$737$	41.0068	−	23.6753i	1.51050	−	0.872090i
$738$		0			0
$739$	−10.8543	−	40.5087i	−0.399281	−	1.49014i	−0.814365	−	0.580354i	$-0.802914\pi$
$739$	−10.8543	−	40.5087i	−0.399281	−	1.49014i	0.415084	−	0.909783i	$-0.363752\pi$
$740$	−14.1501	+	24.5088i	−0.520170	+	0.900960i
$741$		0			0
$742$	−5.71072	−	9.89126i	−0.209647	−	0.363119i
$743$	−28.9049	+	28.9049i	−1.06042	+	1.06042i	−0.0623634	+	0.998054i	$0.519864\pi$
$743$	−28.9049	+	28.9049i	−1.06042	+	1.06042i	−0.998054	+	0.0623634i	$0.980136\pi$
$744$		0			0
$745$		−	88.2002i		−	3.23140i
$746$	−0.512854	+	0.512854i	−0.0187769	+	0.0187769i
$747$		0			0
$748$	16.9401	+	4.53910i	0.619393	+	0.165966i
$749$	60.1188	−	16.1088i	2.19669	−	0.588602i
$750$		0			0
$751$			26.3667i			0.962135i	0.876683	+	0.481068i	$0.159751\pi$
$751$			26.3667i			0.962135i	−0.876683	+	0.481068i	$0.840249\pi$
$752$	3.77054	+	3.77054i	0.137497	+	0.137497i
$753$		0			0
$754$	−3.41999	−	0.0275454i	−0.124549	−	0.00100314i
$755$		−	0.560489i		−	0.0203983i
$756$		0			0
$757$	−5.99038	+	10.3756i	−0.217724	+	0.377109i	−0.954112	−	0.299451i	$-0.903197\pi$
$757$	−5.99038	+	10.3756i	−0.217724	+	0.377109i	0.736388	+	0.676560i	$0.236530\pi$
$758$	3.03059			0.110076
$759$		0			0
$760$	−9.78468	+	2.62180i	−0.354928	+	0.0951026i
$761$	11.9700	−	3.20735i	0.433911	−	0.116266i	−0.0352503	−	0.999379i	$-0.511223\pi$
$761$	11.9700	−	3.20735i	0.433911	−	0.116266i	0.469162	+	0.883112i	$0.344556\pi$
$762$		0			0
$763$	37.4441			1.35557
$764$	−1.59241	+	2.75813i	−0.0576112	+	0.0997856i
$765$		0			0
$766$		−	1.96474i		−	0.0709889i
$767$	−16.8996	−	0.136114i	−0.610211	−	0.00491478i
$768$		0			0
$769$	3.34750	+	3.34750i	0.120714	+	0.120714i	0.764883	−	0.644169i	$-0.222797\pi$
$769$	3.34750	+	3.34750i	0.120714	+	0.120714i	−0.644169	+	0.764883i	$0.722797\pi$
$770$		−	78.6369i		−	2.83388i
$771$		0			0
$772$	13.6996	−	3.67080i	0.493060	−	0.132115i
$773$	26.0869	+	6.98997i	0.938281	+	0.251412i	0.695382	−	0.718640i	$-0.255235\pi$
$773$	26.0869	+	6.98997i	0.938281	+	0.251412i	0.242899	+	0.970052i	$0.421902\pi$
$774$		0			0
$775$	−13.9478	+	13.9478i	−0.501019	+	0.501019i
$776$		−	5.85517i		−	0.210189i
$777$		0			0
$778$	−16.3895	+	16.3895i	−0.587591	+	0.587591i
$779$	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
$785$	1.71472	+	6.39942i	0.0612010	+	0.228405i
$786$		0			0
$787$	9.26059	+	34.5610i	0.330104	+	1.23197i	0.909080	+	0.416622i	$0.136786\pi$
$787$	9.26059	+	34.5610i	0.330104	+	1.23197i	−0.578976	+	0.815345i	$0.696547\pi$
$788$	0.0907674	−	0.338748i	0.00323345	−	0.0120674i
$789$		0			0
$790$	−40.7695	+	23.5383i	−1.45051	+	0.837454i
$791$	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
$796$	−19.7745			−0.700887
$797$	−2.86188	+	4.95693i	−0.101373	+	0.175583i	−0.912251	−	0.409633i	$-0.865657\pi$
$797$	−2.86188	+	4.95693i	−0.101373	+	0.175583i	0.810878	+	0.585216i	$0.198990\pi$
$798$		0			0
$799$	10.4299	+	10.4299i	0.368984	+	0.368984i
$800$	2.30366	−	8.59737i	0.0814466	−	0.303963i
$801$		0			0
$802$	−11.1247	−	19.2685i	−0.392825	−	0.680393i
$803$	−9.68477	−	16.7745i	−0.341768	−	0.591960i
$804$		0			0
$805$	1.96577	−	1.13494i	0.0692842	−	0.0400013i
$806$	5.69541	−	5.60440i	0.200612	−	0.197406i
$807$		0			0
$808$	2.42044	−	9.03320i	0.0851507	−	0.317787i
$809$	−31.6723	−	18.2860i	−1.11354	−	0.642903i	−0.173796	−	0.984782i	$-0.555603\pi$
$809$	−31.6723	−	18.2860i	−1.11354	−	0.642903i	−0.939744	+	0.341879i	$0.888937\pi$
$810$		0			0
$811$	13.4164	+	13.4164i	0.471115	+	0.471115i	0.902275	−	0.431160i	$-0.141896\pi$
$811$	13.4164	+	13.4164i	0.471115	+	0.471115i	−0.431160	+	0.902275i	$0.641896\pi$
$812$	−2.23133	+	2.23133i	−0.0783045	+	0.0783045i
$813$		0			0
$814$	−46.4850	−	12.4556i	−1.62930	−	0.436570i
$815$	−19.3192	−	11.1540i	−0.676724	−	0.390707i
$816$		0			0
$817$	9.62361	+	2.57864i	0.336687	+	0.0902151i
$818$	−28.2842			−0.988934
$819$		0			0
$820$	−8.79882			−0.307268
$821$	−2.96745	−	0.795127i	−0.103565	−	0.0277501i	0.206664	−	0.978412i	$-0.433739\pi$
$821$	−2.96745	−	0.795127i	−0.103565	−	0.0277501i	−0.310229	+	0.950662i	$0.600406\pi$
$822$		0			0
$823$	39.1048	+	22.5772i	1.36311	+	0.786990i	0.990036	−	0.140812i	$-0.0449714\pi$
$823$	39.1048	+	22.5772i	1.36311	+	0.786990i	0.373071	+	0.927803i	$0.378305\pi$
$824$	0.285767	+	0.0765711i	0.00995517	+	0.00266748i
$825$		0			0
$826$	−11.0260	+	11.0260i	−0.383643	+	0.383643i
$827$	9.71124	+	9.71124i	0.337693	+	0.337693i	0.855498	−	0.517806i	$-0.173251\pi$
$827$	9.71124	+	9.71124i	0.337693	+	0.337693i	−0.517806	+	0.855498i	$0.673251\pi$
$828$		0			0
$829$	−11.7657	−	6.79293i	−0.408639	−	0.235928i	0.281566	−	0.959542i	$-0.409146\pi$
$829$	−11.7657	−	6.79293i	−0.408639	−	0.235928i	−0.690205	+	0.723614i	$0.742480\pi$
$830$	−6.52012	+	24.3334i	−0.226317	+	0.844625i
$831$		0			0
$832$	−0.961205	+	3.47507i	−0.0333238	+	0.120476i
$833$	9.74247	−	5.62482i	0.337557	−	0.194888i
$834$		0			0
$835$	33.1867	+	57.4810i	1.14847	+	1.98921i
$836$	−8.61294	−	14.9181i	−0.297885	−	0.515952i
$837$		0			0
$838$	−2.90497	+	10.8415i	−0.100351	+	0.374514i
$839$	31.4296	+	31.4296i	1.08507	+	1.08507i	0.996028	+	0.0890420i	$0.0283805\pi$
$839$	31.4296	+	31.4296i	1.08507	+	1.08507i	0.0890420	+	0.996028i	$0.471619\pi$
$840$		0			0
$841$	−14.0501	+	24.3355i	−0.484487	+	0.839155i
$842$	−0.992453			−0.0342022
$843$		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
$848$	2.97330	−	1.71664i	0.102104	−	0.0589495i
$849$		0			0
$850$	6.37228	−	23.7817i	0.218568	−	0.815705i
$851$	−0.359535	−	1.34180i	−0.0123247	−	0.0459964i
$852$		0			0
$853$	4.11168	+	15.3450i	0.140781	+	0.525403i	0.999907	+	0.0136383i	$0.00434133\pi$
$853$	4.11168	+	15.3450i	0.140781	+	0.525403i	−0.859126	+	0.511765i	$0.828992\pi$
$854$	−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	−0.993921	−	0.110098i	$-0.964884\pi$
$857$	−11.7570	+	20.3638i	−0.401613	+	0.695614i	0.592308	+	0.805712i	$0.298217\pi$
$858$		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	$0.879492\pi$
$860$	−9.66743	+	9.66743i	−0.329657	+	0.329657i
$861$		0			0
$862$			5.47643i			0.186528i
$863$	4.48332	−	4.48332i	0.152614	−	0.152614i	−0.626670	−	0.779284i	$-0.715583\pi$
$863$	4.48332	−	4.48332i	0.152614	−	0.152614i	0.779284	+	0.626670i	$0.215583\pi$
$864$		0			0
$865$	−51.9470	−	13.9192i	−1.76625	−	0.473266i
$866$	16.6334	−	4.45692i	0.565227	−	0.151452i
$867$		0			0
$868$		−	7.37243i		−	0.250237i
$869$	−56.6067	−	56.6067i	−1.92025	−	1.92025i
$870$		0			0
$871$	13.2756	+	23.4278i	0.449828	+	0.793822i
$872$			11.2557i			0.381165i
$873$		0			0
$874$	0.248615	−	0.430614i	0.00840952	−	0.0145657i
$875$	−48.3802			−1.63555
$876$		0			0
$877$	12.3035	−	3.29672i	0.415461	−	0.111322i	−0.0450327	−	0.998986i	$-0.514339\pi$
$877$	12.3035	−	3.29672i	0.415461	−	0.111322i	0.460493	+	0.887663i	$0.347673\pi$
$878$	4.97259	−	1.33240i	0.167817	−	0.0449664i
$879$		0			0
$880$	23.6382			0.796842
$881$	−28.5401	+	49.4329i	−0.961541	+	1.66544i	−0.242907	+	0.970050i	$0.578101\pi$
$881$	−28.5401	+	49.4329i	−0.961541	+	1.66544i	−0.718634	+	0.695389i	$0.755232\pi$
$882$		0			0
$883$			35.3145i			1.18843i	0.804307	+	0.594214i	$0.202537\pi$
$883$			35.3145i			1.18843i	−0.804307	+	0.594214i	$0.797463\pi$
$884$	−2.65884	+	9.61259i	−0.0894266	+	0.323306i
$885$		0			0
$886$	16.2495	+	16.2495i	0.545912	+	0.545912i
$887$		−	38.4986i		−	1.29266i	−0.763059	−	0.646328i	$-0.776304\pi$
$887$		−	38.4986i		−	1.29266i	0.763059	−	0.646328i	$-0.223696\pi$
$888$		0			0
$889$	5.17076	−	1.38550i	0.173422	−	0.0464682i
$890$	−2.40035	−	0.643171i	−0.0804598	−	0.0215591i
$891$		0			0
$892$	10.9424	−	10.9424i	0.366380	−	0.366380i
$893$		−	14.4879i		−	0.484818i
$894$		0			0
$895$	−39.6199	+	39.6199i	−1.32435	+	1.32435i
$896$	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
$902$	−3.87257	−	14.4526i	−0.128942	−	0.481220i
$903$		0			0
$904$	1.80888	+	6.75083i	0.0601625	+	0.224529i
$905$	6.99615	−	26.1100i	0.232560	−	0.867925i
$906$		0			0
$907$	32.8532	−	18.9678i	1.09087	−	0.629815i	0.157064	−	0.987588i	$-0.449797\pi$
$907$	32.8532	−	18.9678i	1.09087	−	0.629815i	0.933809	+	0.357773i	$0.116464\pi$
$908$	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
$913$	−42.8388			−1.41776
$914$	−12.9664	+	22.4584i	−0.428890	+	0.742859i
$915$		0			0
$916$	17.5007	+	17.5007i	0.578240	+	0.578240i
$917$	8.11834	−	30.2981i	0.268091	−	1.00053i
$918$		0			0
$919$	−16.7214	−	28.9624i	−0.551590	−	0.955381i	−0.998160	−	0.0606329i	$-0.980688\pi$
$919$	−16.7214	−	28.9624i	−0.551590	−	0.955381i	0.446570	−	0.894748i	$-0.352645\pi$
$920$	0.341161	+	0.590908i	0.0112477	+	0.0194817i
$921$		0			0
$922$	−1.45600	+	0.840621i	−0.0479508	+	0.0276844i
$923$	37.9482	+	22.3188i	1.24908	+	0.734634i
$924$		0			0
$925$	−17.4860	+	65.2588i	−0.574937	+	2.14570i
$926$	15.0488	+	8.68844i	0.494535	+	0.285520i
$927$		0			0
$928$	−0.670737	−	0.670737i	−0.0220180	−	0.0220180i
$929$	7.83681	−	7.83681i	0.257117	−	0.257117i	−0.566763	−	0.823881i	$-0.691805\pi$
$929$	7.83681	−	7.83681i	0.257117	−	0.257117i	0.823881	+	0.566763i	$0.191805\pi$
$930$		0			0
$931$	−10.6731	−	2.85985i	−0.349797	−	0.0937277i
$932$	−15.6127	−	9.01397i	−0.511409	−	0.295262i
$933$		0			0
$934$	0.562720	+	0.150780i	0.0184128	+	0.00493368i
$935$	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	$0.556541\pi$
$938$	23.9986	+	6.43040i	0.783581	+	0.209960i
$939$		0			0
$940$	17.2174	+	9.94045i	0.561569	+	0.324222i
$941$	−12.7176	−	3.40767i	−0.414582	−	0.111087i	0.0454978	−	0.998964i	$-0.485513\pi$
$941$	−12.7176	−	3.40767i	−0.414582	−	0.111087i	−0.460080	+	0.887877i	$0.652179\pi$
$942$		0			0
$943$	0.305396	−	0.305396i	0.00994507	−	0.00994507i
$944$	−3.31440	−	3.31440i	−0.107875	−	0.107875i
$945$		0			0
$946$	−20.1342	−	11.6245i	−0.654621	−	0.377945i
$947$	−13.1139	+	48.9419i	−0.426146	+	1.59040i	0.335263	+	0.942125i	$0.391175\pi$
$947$	−13.1139	+	48.9419i	−0.426146	+	1.59040i	−0.761409	+	0.648272i	$0.775492\pi$
$948$		0			0
$949$	9.58355	−	5.43062i	0.311095	−	0.176285i
$950$	−20.9429	+	12.0914i	−0.679479	+	0.392297i
$951$		0			0
$952$	4.60108	+	7.96930i	0.149122	+	0.258287i
$953$	−12.0254	−	20.8285i	−0.389540	−	0.674702i	0.602848	−	0.797856i	$-0.294033\pi$
$953$	−12.0254	−	20.8285i	−0.389540	−	0.674702i	−0.992388	+	0.123154i	$0.960699\pi$
$954$		0			0
$955$	−3.07325	+	11.4695i	−0.0994480	+	0.371145i
$956$	−20.1501	−	20.1501i	−0.651701	−	0.651701i
$957$		0			0
$958$	−3.91119	+	6.77438i	−0.126365	+	0.218870i
$959$	53.9871			1.74334
$960$		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
$965$	45.7944	−	26.4394i	1.47417	−	0.851115i
$966$		0			0
$967$	−8.54089	+	31.8750i	−0.274656	+	1.02503i	0.681415	+	0.731897i	$0.261365\pi$
$967$	−8.54089	+	31.8750i	−0.274656	+	1.02503i	−0.956071	+	0.293134i	$0.905302\pi$
$968$	7.55670	+	28.2020i	0.242882	+	0.906446i
$969$		0			0
$970$	−5.65007	−	21.0863i	−0.181413	−	0.677042i
$971$	−1.82907	+	1.05601i	−0.0586976	+	0.0338891i	−0.529062	−	0.848583i	$-0.677456\pi$
$971$	−1.82907	+	1.05601i	−0.0586976	+	0.0338891i	0.470364	+	0.882472i	$0.344123\pi$
$972$		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
$977$	28.9129	−	28.9129i	0.925007	−	0.925007i	−0.0723711	−	0.997378i	$-0.523057\pi$
$977$	28.9129	−	28.9129i	0.925007	−	0.925007i	0.997378	+	0.0723711i	$0.0230566\pi$
$978$		0			0
$979$		−	4.22579i		−	0.135057i
$980$	10.7217	−	10.7217i	0.342492	−	0.342492i
$981$		0			0
$982$	2.32119	+	0.621962i	0.0740723	+	0.0198476i
$983$	−19.9648	+	5.34955i	−0.636777	+	0.170624i	−0.562743	−	0.826632i	$-0.690254\pi$
$983$	−19.9648	+	5.34955i	−0.636777	+	0.170624i	−0.0740342	+	0.997256i	$0.523587\pi$
$984$		0			0
$985$		−	1.30753i		−	0.0416613i
$986$	−1.85536	−	1.85536i	−0.0590868	−	0.0590868i
$987$		0			0
$988$	8.52292	−	4.82961i	0.271150	−	0.153650i
$989$		−	0.671089i		−	0.0213394i
$990$		0			0
$991$	−13.1411	+	22.7610i	−0.417439	+	0.723026i	−0.995681	−	0.0928392i	$-0.970406\pi$
$991$	−13.1411	+	22.7610i	−0.417439	+	0.723026i	0.578242	+	0.815866i	$0.303739\pi$
$992$	2.21615			0.0703627
$993$		0			0
$994$	39.2359	−	10.5132i	1.24449	−	0.333460i
$995$	−71.2141	+	19.0818i	−2.25764	+	0.604933i
$996$		0			0
$997$	−57.4068			−1.81809			−0.909045	−	0.416697i	$-0.863188\pi$
$997$	−57.4068			−1.81809			−0.909045	+	0.416697i	$0.863188\pi$
$998$	−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.bc.a.683.7		56
3.2	odd	2		234.2.z.a.137.9	yes	56
9.4	even	3		234.2.y.a.59.10	✓	56
9.5	odd	6		702.2.bb.a.449.7		56
13.2	odd	12		702.2.bb.a.197.7		56
39.2	even	12		234.2.y.a.119.10	yes	56
117.41	even	12	inner	702.2.bc.a.665.7		56
117.67	odd	12		234.2.z.a.41.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.10	✓	56	9.4	even	3
234.2.y.a.119.10	yes	56	39.2	even	12
234.2.z.a.41.9	yes	56	117.67	odd	12
234.2.z.a.137.9	yes	56	3.2	odd	2
702.2.bb.a.197.7		56	13.2	odd	12
702.2.bb.a.449.7		56	9.5	odd	6
702.2.bc.a.665.7		56	117.41	even	12	inner
702.2.bc.a.683.7		56	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(3.60132 + 0.964970i) q^{5} +(-2.35233 + 2.35233i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-3.22885 - 1.86418i) q^{10} +(1.64094 - 6.12407i) q^{11} +(3.47507 + 0.961205i) q^{13} +(2.88100 - 1.66335i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.38308 + 2.39556i) q^{17} +(0.703205 - 2.62440i) q^{19} +(2.63635 + 2.63635i) q^{20} +(-3.17005 + 5.49069i) q^{22} -0.183009 q^{23} +(7.70819 + 4.45033i) q^{25} +(-3.10788 - 1.82787i) q^{26} +(-3.21334 + 0.861011i) q^{28} +(0.821481 - 0.474282i) q^{29} +(-0.573581 + 2.14063i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.715935 - 2.67190i) q^{34} +(-10.7414 + 6.20155i) q^{35} +(1.96458 + 7.33191i) q^{37} +(-1.35849 + 2.35297i) q^{38} +(-1.86418 - 3.22885i) q^{40} +(-1.66875 + 1.66875i) q^{41} +3.66698i q^{43} +(4.48313 - 4.48313i) q^{44} +(0.176773 + 0.0473661i) q^{46} +(5.15065 - 1.38011i) q^{47} -4.06688i q^{49} +(-6.29371 - 6.29371i) q^{50} +(2.52889 + 2.56996i) q^{52} -3.43327i q^{53} +(11.8191 - 20.4712i) q^{55} +3.32669 q^{56} +(-0.916243 + 0.245507i) q^{58} +(-4.52756 + 1.21315i) q^{59} -8.27980 q^{61} +(1.10807 - 1.91924i) q^{62} +1.00000i q^{64} +(11.5873 + 6.81494i) q^{65} +(5.28097 + 5.28097i) q^{67} +2.76616i q^{68} +(11.9805 - 3.21016i) q^{70} +(11.7943 + 3.16027i) q^{71} +(2.16027 - 2.16027i) q^{73} -7.59055i q^{74} +(1.92119 - 1.92119i) q^{76} +(10.5458 + 18.2658i) q^{77} +(6.31331 - 10.9350i) q^{79} +(0.964970 + 3.60132i) q^{80} +(2.04380 - 1.17999i) q^{82} +(-1.74879 - 6.52658i) q^{83} +(2.66926 + 9.96181i) q^{85} +(0.949085 - 3.54203i) q^{86} +(-5.49069 + 3.17005i) q^{88} +(0.643808 - 0.172508i) q^{89} +(-10.4356 + 5.91342i) q^{91} +(-0.158490 - 0.0915043i) q^{92} -5.33235 q^{94} +(5.06492 - 8.77271i) q^{95} +(4.14023 + 4.14023i) q^{97} +(-1.05259 + 3.92830i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) \) 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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