LMFDB - Embedded newform 464.2.bl.c.367.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [464,2,Mod(15,464)] 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("464.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(464, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 0, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.bl (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			367.7
Character	$\chi$	$=$	464.367
Dual form			464.2.bl.c.287.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.432566 + 0.151361i) q^{3} +(-1.40256 - 0.320125i) q^{5} +(-0.759883 - 1.57791i) q^{7} +(-2.18129 - 1.73952i) q^{9} +(0.426306 - 3.78357i) q^{11} +(-3.71483 + 2.96248i) q^{13} +(-0.558244 - 0.350768i) q^{15} +(1.08583 - 1.08583i) q^{17} +(-1.57107 - 4.48986i) q^{19} +(-0.0898644 - 0.797568i) q^{21} +(-0.0809859 + 0.0184845i) q^{23} +(-2.64016 - 1.27143i) q^{25} +(-1.41172 - 2.24674i) q^{27} +(3.03315 + 4.44972i) q^{29} +(8.91399 - 5.60103i) q^{31} +(0.757091 - 1.57212i) q^{33} +(0.560651 + 2.45637i) q^{35} +(-5.41831 + 0.610497i) q^{37} +(-2.05531 + 0.719185i) q^{39} +(-0.943245 - 0.943245i) q^{41} +(0.824442 - 1.31209i) q^{43} +(2.50252 + 3.13806i) q^{45} +(-6.23817 - 0.702873i) q^{47} +(2.45204 - 3.07476i) q^{49} +(0.634047 - 0.305341i) q^{51} +(-1.20294 + 5.27045i) q^{53} +(-1.80913 + 5.17020i) q^{55} -2.17996i q^{57} +13.1391i q^{59} +(-0.0136381 + 0.0389754i) q^{61} +(-1.08729 + 4.76372i) q^{63} +(6.15862 - 2.96583i) q^{65} +(5.77933 - 7.24705i) q^{67} +(-0.0378296 - 0.00426237i) q^{69} +(-2.67627 - 3.35593i) q^{71} +(7.63754 - 12.1551i) q^{73} +(-0.949596 - 0.949596i) q^{75} +(-6.29408 + 2.20240i) q^{77} +(5.46954 - 0.616269i) q^{79} +(1.59189 + 6.97454i) q^{81} +(-5.03687 + 10.4592i) q^{83} +(-1.87054 + 1.17534i) q^{85} +(0.638524 + 2.38390i) q^{87} +(-2.84408 - 4.52633i) q^{89} +(7.49736 + 3.61054i) q^{91} +(4.70367 - 1.07358i) q^{93} +(0.766202 + 6.80023i) q^{95} +(3.29007 + 9.40249i) q^{97} +(-7.51150 + 7.51150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 4 q^{17} - 40 q^{21} - 28 q^{25} - 52 q^{29} - 84 q^{33} - 8 q^{37} + 4 q^{41} + 40 q^{45} - 28 q^{49} - 48 q^{53} - 4 q^{61} - 40 q^{65} + 24 q^{69} + 76 q^{73} + 156 q^{77} + 116 q^{81} + 152 q^{85}+ \cdots + 64 q^{97}+O(q^{100}) $ 120 * q + 4 * q^17 - 40 * q^21 - 28 * q^25 - 52 * q^29 - 84 * q^33 - 8 * q^37 + 4 * q^41 + 40 * q^45 - 28 * q^49 - 48 * q^53 - 4 * q^61 - 40 * q^65 + 24 * q^69 + 76 * q^73 + 156 * q^77 + 116 * q^81 + 152 * q^85 + 104 * q^89 + 112 * q^93 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{28}\right)$

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			0
$2$		0			0
$3$	0.432566	+	0.151361i	0.249742	+	0.0873885i	0.452247	−	0.891893i	$-0.350623\pi$
$3$	0.432566	+	0.151361i	0.249742	+	0.0873885i	−0.202505	+	0.979281i	$0.564908\pi$
$4$		0			0
$5$	−1.40256	−	0.320125i	−0.627243	−	0.143164i	−0.102928	−	0.994689i	$-0.532821\pi$
$5$	−1.40256	−	0.320125i	−0.627243	−	0.143164i	−0.524314	+	0.851525i	$0.675678\pi$
$6$		0			0
$7$	−0.759883	−	1.57791i	−0.287209	−	0.596395i	0.706586	−	0.707628i	$-0.250235\pi$
$7$	−0.759883	−	1.57791i	−0.287209	−	0.596395i	−0.993794	+	0.111232i	$0.964520\pi$
$8$		0			0
$9$	−2.18129	−	1.73952i	−0.727097	−	0.579841i
$10$		0			0
$11$	0.426306	−	3.78357i	0.128536	−	1.14079i	−0.749436	−	0.662077i	$-0.769675\pi$
$11$	0.426306	−	3.78357i	0.128536	−	1.14079i	0.877972	−	0.478712i	$-0.158896\pi$
$12$		0			0
$13$	−3.71483	+	2.96248i	−1.03031	+	0.821643i	−0.984158	−	0.177292i	$-0.943266\pi$
$13$	−3.71483	+	2.96248i	−1.03031	+	0.821643i	−0.0461492	+	0.998935i	$0.514695\pi$
$14$		0			0
$15$	−0.558244	−	0.350768i	−0.144138	−	0.0905679i
$16$		0			0
$17$	1.08583	−	1.08583i	0.263353	−	0.263353i	−0.563062	−	0.826415i	$-0.690377\pi$
$17$	1.08583	−	1.08583i	0.263353	−	0.263353i	0.826415	+	0.563062i	$0.190377\pi$
$18$		0			0
$19$	−1.57107	−	4.48986i	−0.360428	−	1.03005i	−0.971206	−	0.238243i	$-0.923429\pi$
$19$	−1.57107	−	4.48986i	−0.360428	−	1.03005i	0.610777	−	0.791802i	$-0.290857\pi$
$20$		0			0
$21$	−0.0898644	−	0.797568i	−0.0196100	−	0.174044i
$22$		0			0
$23$	−0.0809859	+	0.0184845i	−0.0168867	+	0.00385429i	−0.230956	−	0.972964i	$-0.574185\pi$
$23$	−0.0809859	+	0.0184845i	−0.0168867	+	0.00385429i	0.214069	+	0.976818i	$0.431328\pi$
$24$		0			0
$25$	−2.64016	−	1.27143i	−0.528031	−	0.254287i
$26$		0			0
$27$	−1.41172	−	2.24674i	−0.271686	−	0.432385i
$28$		0			0
$29$	3.03315	+	4.44972i	0.563243	+	0.826292i
$29$	3.03315	+	4.44972i	0.563243	+	0.826292i
$30$		0			0
$31$	8.91399	−	5.60103i	1.60100	−	1.00598i	0.627117	−	0.778925i	$-0.284235\pi$
$31$	8.91399	−	5.60103i	1.60100	−	1.00598i	0.973883	−	0.227050i	$-0.0729081\pi$
$32$		0			0
$33$	0.757091	−	1.57212i	0.131793	−	0.273670i
$34$		0			0
$35$	0.560651	+	2.45637i	0.0947673	+	0.415202i
$36$		0			0
$37$	−5.41831	+	0.610497i	−0.890764	+	0.100365i	−0.545471	−	0.838130i	$-0.683649\pi$
$37$	−5.41831	+	0.610497i	−0.890764	+	0.100365i	−0.345293	+	0.938495i	$0.612221\pi$
$38$		0			0
$39$	−2.05531	+	0.719185i	−0.329113	+	0.115162i
$40$		0			0
$41$	−0.943245	−	0.943245i	−0.147310	−	0.147310i	0.629605	−	0.776915i	$-0.283217\pi$
$41$	−0.943245	−	0.943245i	−0.147310	−	0.147310i	−0.776915	+	0.629605i	$0.783217\pi$
$42$		0			0
$43$	0.824442	−	1.31209i	0.125726	−	0.200092i	−0.777930	−	0.628351i	$-0.783730\pi$
$43$	0.824442	−	1.31209i	0.125726	−	0.200092i	0.903656	+	0.428259i	$0.140873\pi$
$44$		0			0
$45$	2.50252	+	3.13806i	0.373054	+	0.467795i
$46$		0			0
$47$	−6.23817	−	0.702873i	−0.909931	−	0.102525i	−0.355425	−	0.934705i	$-0.615664\pi$
$47$	−6.23817	−	0.702873i	−0.909931	−	0.102525i	−0.554505	+	0.832180i	$0.687093\pi$
$48$		0			0
$49$	2.45204	−	3.07476i	0.350291	−	0.439252i
$50$		0			0
$51$	0.634047	−	0.305341i	0.0887844	−	0.0427563i
$52$		0			0
$53$	−1.20294	+	5.27045i	−0.165237	+	0.723951i	0.822621	+	0.568591i	$0.192511\pi$
$53$	−1.20294	+	5.27045i	−0.165237	+	0.723951i	−0.987858	+	0.155361i	$0.950346\pi$
$54$		0			0
$55$	−1.80913	+	5.17020i	−0.243943	+	0.697150i
$56$		0			0
$57$		−	2.17996i		−	0.288743i
$58$		0			0
$59$			13.1391i			1.71056i	0.518166	+	0.855280i	$0.326615\pi$
$59$			13.1391i			1.71056i	−0.518166	+	0.855280i	$0.673385\pi$
$60$		0			0
$61$	−0.0136381	+	0.0389754i	−0.00174618	+	0.00499029i	−0.944753	−	0.327783i	$-0.893699\pi$
$61$	−0.0136381	+	0.0389754i	−0.00174618	+	0.00499029i	0.943007	+	0.332773i	$0.107984\pi$
$62$		0			0
$63$	−1.08729	+	4.76372i	−0.136985	+	0.600173i
$64$		0			0
$65$	6.15862	−	2.96583i	0.763883	−	0.367866i
$66$		0			0
$67$	5.77933	−	7.24705i	0.706058	−	0.885368i	−0.291402	−	0.956601i	$-0.594122\pi$
$67$	5.77933	−	7.24705i	0.706058	−	0.885368i	0.997460	+	0.0712324i	$0.0226932\pi$
$68$		0			0
$69$	−0.0378296	−	0.00426237i	−0.00455415	−	0.000513129i
$70$		0			0
$71$	−2.67627	−	3.35593i	−0.317615	−	0.398276i	0.597238	−	0.802064i	$-0.296265\pi$
$71$	−2.67627	−	3.35593i	−0.317615	−	0.398276i	−0.914853	+	0.403788i	$0.867693\pi$
$72$		0			0
$73$	7.63754	−	12.1551i	0.893907	−	1.42264i	−0.0123530	−	0.999924i	$-0.503932\pi$
$73$	7.63754	−	12.1551i	0.893907	−	1.42264i	0.906260	−	0.422721i	$-0.138925\pi$
$74$		0			0
$75$	−0.949596	−	0.949596i	−0.109650	−	0.109650i
$76$		0			0
$77$	−6.29408	+	2.20240i	−0.717278	+	0.250986i
$78$		0			0
$79$	5.46954	−	0.616269i	0.615371	−	0.0693357i	0.201223	−	0.979545i	$-0.435508\pi$
$79$	5.46954	−	0.616269i	0.615371	−	0.0693357i	0.414148	+	0.910210i	$0.364080\pi$
$80$		0			0
$81$	1.59189	+	6.97454i	0.176877	+	0.774948i
$82$		0			0
$83$	−5.03687	+	10.4592i	−0.552869	+	1.14804i	0.418003	+	0.908446i	$0.362730\pi$
$83$	−5.03687	+	10.4592i	−0.552869	+	1.14804i	−0.970872	+	0.239598i	$0.922984\pi$
$84$		0			0
$85$	−1.87054	+	1.17534i	−0.202889	+	0.127484i
$86$		0			0
$87$	0.638524	+	2.38390i	0.0684570	+	0.255581i
$88$		0			0
$89$	−2.84408	−	4.52633i	−0.301472	−	0.479790i	0.661294	−	0.750127i	$-0.270008\pi$
$89$	−2.84408	−	4.52633i	−0.301472	−	0.479790i	−0.962766	+	0.270337i	$0.912865\pi$
$90$		0			0
$91$	7.49736	+	3.61054i	0.785937	+	0.378487i
$92$		0			0
$93$	4.70367	−	1.07358i	0.487748	−	0.111325i
$94$		0			0
$95$	0.766202	+	6.80023i	0.0786106	+	0.697689i
$96$		0			0
$97$	3.29007	+	9.40249i	0.334056	+	0.954678i	0.981315	+	0.192408i	$0.0616297\pi$
$97$	3.29007	+	9.40249i	0.334056	+	0.954678i	−0.647259	+	0.762270i	$0.724085\pi$
$98$		0			0
$99$	−7.51150	+	7.51150i	−0.754934	+	0.754934i
$100$		0			0
$101$	−0.228340	−	0.143476i	−0.0227207	−	0.0142764i	0.520624	−	0.853786i	$-0.325699\pi$
$101$	−0.228340	−	0.143476i	−0.0227207	−	0.0142764i	−0.543345	+	0.839510i	$0.682842\pi$
$102$		0			0
$103$	−2.68985	+	2.14508i	−0.265039	+	0.211361i	−0.746988	−	0.664838i	$-0.768501\pi$
$103$	−2.68985	+	2.14508i	−0.265039	+	0.211361i	0.481949	+	0.876199i	$0.339929\pi$
$104$		0			0
$105$	−0.129281	+	1.14740i	−0.0126166	+	0.111975i
$106$		0			0
$107$	−4.09066	−	3.26220i	−0.395459	−	0.315368i	0.405491	−	0.914099i	$-0.367101\pi$
$107$	−4.09066	−	3.26220i	−0.395459	−	0.315368i	−0.800950	+	0.598731i	$0.795672\pi$
$108$		0			0
$109$	−3.26391	−	6.77757i	−0.312626	−	0.649174i	0.684156	−	0.729335i	$-0.260171\pi$
$109$	−3.26391	−	6.77757i	−0.312626	−	0.649174i	−0.996782	+	0.0801617i	$0.974456\pi$
$110$		0			0
$111$	−2.43618	−	0.556042i	−0.231232	−	0.0527772i
$112$		0			0
$113$	11.8580	+	4.14930i	1.11551	+	0.390333i	0.824201	−	0.566297i	$-0.191624\pi$
$113$	11.8580	+	4.14930i	1.11551	+	0.390333i	0.291306	+	0.956630i	$0.405910\pi$
$114$		0			0
$115$	0.119505			0.0111439
$116$		0			0
$117$	13.2564			1.22556
$118$		0			0
$119$	−2.53846	−	0.888244i	−0.232700	−	0.0814252i
$120$		0			0
$121$	−3.40944	−	0.778183i	−0.309949	−	0.0707439i
$122$		0			0
$123$	−0.265245	−	0.550787i	−0.0239163	−	0.0496627i
$124$		0			0
$125$	8.91977	+	7.11328i	0.797809	+	0.636231i
$126$		0			0
$127$	−0.182942	+	1.62365i	−0.0162335	+	0.144076i	−0.999214	−	0.0396319i	$-0.987381\pi$
$127$	−0.182942	+	1.62365i	−0.0162335	+	0.144076i	0.982981	+	0.183708i	$0.0588100\pi$
$128$		0			0
$129$	0.555225	−	0.442777i	0.0488849	−	0.0389844i
$130$		0			0
$131$	9.45394	+	5.94030i	0.825994	+	0.519007i	0.877450	−	0.479669i	$-0.159243\pi$
$131$	9.45394	+	5.94030i	0.825994	+	0.519007i	−0.0514555	+	0.998675i	$0.516386\pi$
$132$		0			0
$133$	−5.89078	+	5.89078i	−0.510796	+	0.510796i
$134$		0			0
$135$	1.26078	+	3.60311i	0.108511	+	0.310106i
$136$		0			0
$137$	−1.18476	−	10.5151i	−0.101221	−	0.898362i	−0.937008	−	0.349308i	$-0.886417\pi$
$137$	−1.18476	−	10.5151i	−0.101221	−	0.898362i	0.835787	−	0.549054i	$-0.185012\pi$
$138$		0			0
$139$	7.26661	−	1.65856i	0.616346	−	0.140677i	0.0970614	−	0.995278i	$-0.469056\pi$
$139$	7.26661	−	1.65856i	0.616346	−	0.140677i	0.519284	+	0.854602i	$0.326199\pi$
$140$		0			0
$141$	−2.59203	−	1.24826i	−0.218288	−	0.105122i
$142$		0			0
$143$	9.62508	+	15.3182i	0.804889	+	1.28097i
$144$		0			0
$145$	−2.82971	−	7.21197i	−0.234995	−	0.598921i
$146$		0			0
$147$	1.52607	−	0.958893i	0.125868	−	0.0790881i
$148$		0			0
$149$	0.710981	−	1.47637i	0.0582459	−	0.120949i	−0.869814	−	0.493380i	$-0.835761\pi$
$149$	0.710981	−	1.47637i	0.0582459	−	0.120949i	0.928060	+	0.372431i	$0.121476\pi$
$150$		0			0
$151$	−1.12982	−	4.95006i	−0.0919434	−	0.402830i	0.907924	−	0.419136i	$-0.137667\pi$
$151$	−1.12982	−	4.95006i	−0.0919434	−	0.402830i	−0.999867	+	0.0163053i	$0.994810\pi$
$152$		0			0
$153$	−4.25735	+	0.479688i	−0.344186	+	0.0387805i
$154$		0			0
$155$	−14.2954	+	5.00218i	−1.14824	+	0.401785i
$156$		0			0
$157$	−0.568619	−	0.568619i	−0.0453807	−	0.0453807i	0.684052	−	0.729433i	$-0.260216\pi$
$157$	−0.568619	−	0.568619i	−0.0453807	−	0.0453807i	−0.729433	+	0.684052i	$0.760216\pi$
$158$		0			0
$159$	−1.31809	+	2.09774i	−0.104532	+	0.166361i
$160$		0			0
$161$	0.0907068	+	0.113743i	0.00714869	+	0.00896418i
$162$		0			0
$163$	−10.7803	−	1.21464i	−0.844376	−	0.0951383i	−0.320831	−	0.947136i	$-0.603962\pi$
$163$	−10.7803	−	1.21464i	−0.844376	−	0.0951383i	−0.523545	+	0.851998i	$0.675391\pi$
$164$		0			0
$165$	−1.56514	+	1.96262i	−0.121846	+	0.152790i
$166$		0			0
$167$	18.7621	−	9.03536i	1.45186	−	0.699177i	0.468941	−	0.883230i	$-0.344636\pi$
$167$	18.7621	−	9.03536i	1.45186	−	0.699177i	0.982916	+	0.184052i	$0.0589216\pi$
$168$		0			0
$169$	2.13090	−	9.33610i	0.163916	−	0.718162i
$170$		0			0
$171$	−4.38325	+	12.5266i	−0.335196	+	0.957934i
$172$		0			0
$173$			21.8656i			1.66241i	0.555963	+	0.831207i	$0.312350\pi$
$173$			21.8656i			1.66241i	−0.555963	+	0.831207i	$0.687650\pi$
$174$		0			0
$175$			5.13208i			0.387949i
$176$		0			0
$177$	−1.98875	+	5.68351i	−0.149483	+	0.427199i
$178$		0			0
$179$	4.01881	−	17.6075i	0.300380	−	1.31605i	−0.569177	−	0.822215i	$-0.692738\pi$
$179$	4.01881	−	17.6075i	0.300380	−	1.31605i	0.869556	−	0.493834i	$-0.164405\pi$
$180$		0			0
$181$	−11.5651	+	5.56944i	−0.859624	+	0.413973i	−0.811141	−	0.584851i	$-0.801153\pi$
$181$	−11.5651	+	5.56944i	−0.859624	+	0.413973i	−0.0484831	+	0.998824i	$0.515439\pi$
$182$		0			0
$183$	−0.0117987	+	0.0147952i	−0.000872189	+	0.00109369i
$184$		0			0
$185$	7.79492	+	0.878277i	0.573094	+	0.0645722i
$186$		0			0
$187$	−3.64542	−	4.57122i	−0.266580	−	0.334281i
$188$		0			0
$189$	−2.47242	+	3.93483i	−0.179842	+	0.286217i
$190$		0			0
$191$	−18.6066	−	18.6066i	−1.34633	−	1.34633i	−0.889615	−	0.456712i	$-0.849027\pi$
$191$	−18.6066	−	18.6066i	−1.34633	−	1.34633i	−0.456712	−	0.889615i	$-0.650973\pi$
$192$		0			0
$193$	8.95458	−	3.13334i	0.644565	−	0.225543i	0.0118525	−	0.999930i	$-0.496227\pi$
$193$	8.95458	−	3.13334i	0.644565	−	0.225543i	0.632713	+	0.774387i	$0.281941\pi$
$194$		0			0
$195$	3.11292	−	0.350742i	0.222921	−	0.0251171i
$196$		0			0
$197$	−4.76847	−	20.8920i	−0.339739	−	1.48849i	−0.799616	−	0.600512i	$-0.794964\pi$
$197$	−4.76847	−	20.8920i	−0.339739	−	1.48849i	0.459877	−	0.887983i	$-0.347894\pi$
$198$		0			0
$199$	8.08434	−	16.7873i	0.573083	−	1.19002i	−0.389999	−	0.920815i	$-0.627525\pi$
$199$	8.08434	−	16.7873i	0.573083	−	1.19002i	0.963083	−	0.269205i	$-0.0867609\pi$
$200$		0			0
$201$	3.59686	−	2.26006i	0.253703	−	0.159412i
$202$		0			0
$203$	4.71642	−	8.16732i	0.331028	−	0.573233i
$204$		0			0
$205$	1.02100	+	1.62491i	0.0713097	+	0.113489i
$206$		0			0
$207$	0.208808	+	0.100557i	0.0145132	+	0.00698917i
$208$		0			0
$209$	−17.6575	+	4.03020i	−1.22139	+	0.278775i
$210$		0			0
$211$	−3.18695	−	28.2849i	−0.219398	−	1.94722i	−0.308576	−	0.951200i	$-0.599852\pi$
$211$	−3.18695	−	28.2849i	−0.219398	−	1.94722i	0.0891777	−	0.996016i	$-0.471576\pi$
$212$		0			0
$213$	−0.649703	−	1.85675i	−0.0445169	−	0.127222i
$214$		0			0
$215$	−1.57636	+	1.57636i	−0.107507	+	0.107507i
$216$		0			0
$217$	−15.6115	−	9.80938i	−1.05978	−	0.665904i
$218$		0			0
$219$	5.14355	−	4.10184i	0.347569	−	0.277177i
$220$		0			0
$221$	−0.816927	+	7.25043i	−0.0549525	+	0.487717i
$222$		0			0
$223$	−12.7030	−	10.1303i	−0.850654	−	0.678374i	0.0978284	−	0.995203i	$-0.468810\pi$
$223$	−12.7030	−	10.1303i	−0.850654	−	0.678374i	−0.948483	+	0.316829i	$0.897382\pi$
$224$		0			0
$225$	3.54727	+	7.36598i	0.236485	+	0.491065i
$226$		0			0
$227$	3.95262	+	0.902159i	0.262344	+	0.0598784i	0.351670	−	0.936124i	$-0.385614\pi$
$227$	3.95262	+	0.902159i	0.262344	+	0.0598784i	−0.0893254	+	0.996002i	$0.528471\pi$
$228$		0			0
$229$	−8.72689	−	3.05367i	−0.576689	−	0.201792i	0.0261459	−	0.999658i	$-0.491677\pi$
$229$	−8.72689	−	3.05367i	−0.576689	−	0.201792i	−0.602835	+	0.797866i	$0.705962\pi$
$230$		0			0
$231$	−3.05596			−0.201068
$232$		0			0
$233$	4.14230			0.271371			0.135685	−	0.990752i	$-0.456676\pi$
$233$	4.14230			0.271371			0.135685	+	0.990752i	$0.456676\pi$
$234$		0			0
$235$	8.52438	+	2.98281i	0.556069	+	0.194577i
$236$		0			0
$237$	2.45921	+	0.561300i	0.159743	+	0.0364603i
$238$		0			0
$239$	−7.03498	−	14.6083i	−0.455055	−	0.944931i	−0.994679	−	0.103025i	$-0.967148\pi$
$239$	−7.03498	−	14.6083i	−0.455055	−	0.944931i	0.539624	−	0.841906i	$-0.318566\pi$
$240$		0			0
$241$	−12.2308	−	9.75373i	−0.787855	−	0.628293i	0.144637	−	0.989485i	$-0.453799\pi$
$241$	−12.2308	−	9.75373i	−0.787855	−	0.628293i	−0.932492	+	0.361192i	$0.882370\pi$
$242$		0			0
$243$	−1.25835	+	11.1682i	−0.0807234	+	0.716440i
$244$		0			0
$245$	−4.42343	+	3.52757i	−0.282603	+	0.225368i
$246$		0			0
$247$	19.1374	+	12.0248i	1.21768	+	0.765120i
$248$		0			0
$249$	−3.76190	+	3.76190i	−0.238400	+	0.238400i
$250$		0			0
$251$	−0.681909	−	1.94878i	−0.0430417	−	0.123006i	0.920357	−	0.391080i	$-0.127899\pi$
$251$	−0.681909	−	1.94878i	−0.0430417	−	0.123006i	−0.963398	+	0.268074i	$0.913613\pi$
$252$		0			0
$253$	0.0354126	+	0.314296i	0.00222637	+	0.0197596i
$254$		0			0
$255$	−0.987035	+	0.225284i	−0.0618105	+	0.0141078i
$256$		0			0
$257$	1.11241	+	0.535706i	0.0693899	+	0.0334164i	0.468257	−	0.883592i	$-0.344882\pi$
$257$	1.11241	+	0.535706i	0.0693899	+	0.0334164i	−0.398867	+	0.917009i	$0.630596\pi$
$258$		0			0
$259$	5.08059	+	8.08571i	0.315693	+	0.502422i
$260$		0			0
$261$	1.12418	−	14.9824i	0.0695852	−	0.927385i
$262$		0			0
$263$	−15.5750	+	9.78644i	−0.960397	+	0.603457i	−0.918397	−	0.395660i	$-0.870516\pi$
$263$	−15.5750	+	9.78644i	−0.960397	+	0.603457i	−0.0420000	+	0.999118i	$0.513373\pi$
$264$		0			0
$265$	3.37440	−	7.00701i	0.207288	−	0.430437i
$266$		0			0
$267$	−0.545142	−	2.38842i	−0.0333621	−	0.146169i
$268$		0			0
$269$	8.55272	−	0.963660i	0.521468	−	0.0587554i	0.152693	−	0.988274i	$-0.451206\pi$
$269$	8.55272	−	0.963660i	0.521468	−	0.0587554i	0.368776	+	0.929518i	$0.379777\pi$
$270$		0			0
$271$	12.2308	−	4.27975i	0.742970	−	0.259976i	0.0678614	−	0.997695i	$-0.478382\pi$
$271$	12.2308	−	4.27975i	0.742970	−	0.259976i	0.675109	+	0.737718i	$0.264097\pi$
$272$		0			0
$273$	2.69661	+	2.69661i	0.163206	+	0.163206i
$274$		0			0
$275$	−5.93607	+	9.44720i	−0.357958	+	0.569687i
$276$		0			0
$277$	−8.40560	−	10.5403i	−0.505044	−	0.633305i	0.462315	−	0.886716i	$-0.347019\pi$
$277$	−8.40560	−	10.5403i	−0.505044	−	0.633305i	−0.967359	+	0.253411i	$0.918448\pi$
$278$		0			0
$279$	−29.1871	−	3.28860i	−1.74739	−	0.196883i
$280$		0			0
$281$	−18.6988	+	23.4476i	−1.11548	+	1.39877i	−0.208278	+	0.978070i	$0.566786\pi$
$281$	−18.6988	+	23.4476i	−1.11548	+	1.39877i	−0.907201	+	0.420697i	$0.861786\pi$
$282$		0			0
$283$	17.1237	−	8.24633i	1.01790	−	0.490193i	0.150922	−	0.988546i	$-0.451776\pi$
$283$	17.1237	−	8.24633i	1.01790	−	0.490193i	0.866975	+	0.498352i	$0.166061\pi$
$284$		0			0
$285$	−0.697859	+	3.05752i	−0.0413376	+	0.181112i
$286$		0			0
$287$	−0.771603	+	2.20512i	−0.0455463	+	0.130164i
$288$		0			0
$289$			14.6419i			0.861290i
$290$		0			0
$291$			4.56519i			0.267616i
$292$		0			0
$293$	8.09198	−	23.1256i	0.472739	−	1.35101i	−0.422880	−	0.906186i	$-0.638981\pi$
$293$	8.09198	−	23.1256i	0.472739	−	1.35101i	0.895618	−	0.444824i	$-0.146734\pi$
$294$		0			0
$295$	4.20613	−	18.4283i	0.244891	−	1.07294i
$296$		0			0
$297$	−9.10252	+	4.38354i	−0.528182	+	0.254359i
$298$		0			0
$299$	0.246089	−	0.308585i	0.0142317	−	0.0178460i
$300$		0			0
$301$	−2.69685	−	0.303862i	−0.155444	−	0.0175143i
$302$		0			0
$303$	−0.0770555	−	0.0966245i	−0.00442672	−	0.00555094i
$304$		0			0
$305$	0.0316052	−	0.0502994i	0.00180971	−	0.00288014i
$306$		0			0
$307$	−13.1481	−	13.1481i	−0.750403	−	0.750403i	0.224152	−	0.974554i	$-0.428039\pi$
$307$	−13.1481	−	13.1481i	−0.750403	−	0.750403i	−0.974554	+	0.224152i	$0.928039\pi$
$308$		0			0
$309$	−1.48822	+	0.520751i	−0.0846619	+	0.0296245i
$310$		0			0
$311$	23.0631	−	2.59859i	1.30779	−	0.147352i	0.569586	−	0.821932i	$-0.307104\pi$
$311$	23.0631	−	2.59859i	1.30779	−	0.147352i	0.738202	+	0.674580i	$0.235675\pi$
$312$		0			0
$313$	3.22110	+	14.1125i	0.182067	+	0.797688i	0.980645	+	0.195796i	$0.0627291\pi$
$313$	3.22110	+	14.1125i	0.182067	+	0.797688i	−0.798577	+	0.601892i	$0.794414\pi$
$314$		0			0
$315$	3.04997	−	6.33332i	0.171846	−	0.356842i
$316$		0			0
$317$	20.4130	−	12.8264i	1.14651	−	0.720401i	0.181702	−	0.983354i	$-0.441839\pi$
$317$	20.4130	−	12.8264i	1.14651	−	0.720401i	0.964809	+	0.262953i	$0.0846964\pi$
$318$		0			0
$319$	18.1289	−	9.57921i	1.01502	−	0.536333i
$320$		0			0
$321$	−1.27571	−	2.03028i	−0.0712033	−	0.113319i
$322$		0			0
$323$	−6.58116	−	3.16932i	−0.366185	−	0.176346i
$324$		0			0
$325$	13.5743	−	3.09825i	0.752967	−	0.171860i
$326$		0			0
$327$	−0.385992	−	3.42578i	−0.0213454	−	0.189446i
$328$		0			0
$329$	3.63121	+	10.3774i	0.200195	+	0.572124i
$330$		0			0
$331$	6.85391	−	6.85391i	0.376725	−	0.376725i	−0.493194	−	0.869919i	$-0.664171\pi$
$331$	6.85391	−	6.85391i	0.376725	−	0.376725i	0.869919	+	0.493194i	$0.164171\pi$
$332$		0			0
$333$	12.8809	+	8.09359i	0.705868	+	0.443526i
$334$		0			0
$335$	−10.4258	+	8.31430i	−0.569622	+	0.454259i
$336$		0			0
$337$	−3.82299	+	33.9299i	−0.208251	+	1.84828i	0.261151	+	0.965298i	$0.415898\pi$
$337$	−3.82299	+	33.9299i	−0.208251	+	1.84828i	−0.469403	+	0.882984i	$0.655531\pi$
$338$		0			0
$339$	4.50133	+	3.58969i	0.244478	+	0.194965i
$340$		0			0
$341$	−17.3918	−	36.1144i	−0.941819	−	1.95571i
$342$		0			0
$343$	−18.6671	−	4.26064i	−1.00793	−	0.230053i
$344$		0			0
$345$	0.0516937	+	0.0180884i	0.00278309	+	0.000973846i
$346$		0			0
$347$	−25.5757			−1.37298			−0.686488	−	0.727142i	$-0.740848\pi$
$347$	−25.5757			−1.37298			−0.686488	+	0.727142i	$0.740848\pi$
$348$		0			0
$349$	19.2209			1.02887			0.514436	−	0.857529i	$-0.328001\pi$
$349$	19.2209			1.02887			0.514436	+	0.857529i	$0.328001\pi$
$350$		0			0
$351$	11.9002	+	4.16406i	0.635186	+	0.222261i
$352$		0			0
$353$	10.7946	+	2.46379i	0.574537	+	0.131134i	0.499910	−	0.866077i	$-0.333366\pi$
$353$	10.7946	+	2.46379i	0.574537	+	0.131134i	0.0746269	+	0.997212i	$0.476223\pi$
$354$		0			0
$355$	2.67930	+	5.56363i	0.142203	+	0.295287i
$356$		0			0
$357$	−0.963603	−	0.768448i	−0.0509993	−	0.0406706i
$358$		0			0
$359$	−3.14032	+	27.8712i	−0.165740	+	1.47098i	0.585349	+	0.810782i	$0.300958\pi$
$359$	−3.14032	+	27.8712i	−0.165740	+	1.47098i	−0.751089	+	0.660201i	$0.770471\pi$
$360$		0			0
$361$	−2.83580	+	2.26148i	−0.149253	+	0.119025i
$362$		0			0
$363$	−1.35702	−	0.852674i	−0.0712252	−	0.0447538i
$364$		0			0
$365$	−14.6032	+	14.6032i	−0.764368	+	0.764368i
$366$		0			0
$367$	4.41972	+	12.6308i	0.230707	+	0.659324i	0.999796	+	0.0201820i	$0.00642458\pi$
$367$	4.41972	+	12.6308i	0.230707	+	0.659324i	−0.769089	+	0.639142i	$0.779290\pi$
$368$		0			0
$369$	0.416697	+	3.69829i	0.0216924	+	0.192525i
$370$		0			0
$371$	9.23040	−	2.10678i	0.479219	−	0.109379i
$372$		0			0
$373$	−13.3574	−	6.43257i	−0.691619	−	0.333066i	0.0548425	−	0.998495i	$-0.482534\pi$
$373$	−13.3574	−	6.43257i	−0.691619	−	0.333066i	−0.746461	+	0.665429i	$0.768249\pi$
$374$		0			0
$375$	2.78171	+	4.42707i	0.143647	+	0.228613i
$376$		0			0
$377$	−24.4498	−	7.54428i	−1.25923	−	0.388550i
$378$		0			0
$379$	12.5475	−	7.88414i	0.644524	−	0.404981i	−0.169730	−	0.985491i	$-0.554289\pi$
$379$	12.5475	−	7.88414i	0.644524	−	0.404981i	0.814254	+	0.580509i	$0.197147\pi$
$380$		0			0
$381$	−0.324893	+	0.674647i	−0.0166448	+	0.0345632i
$382$		0			0
$383$	7.78917	+	34.1266i	0.398008	+	1.74379i	0.635223	+	0.772329i	$0.280908\pi$
$383$	7.78917	+	34.1266i	0.398008	+	1.74379i	−0.237215	+	0.971457i	$0.576235\pi$
$384$		0			0
$385$	9.53285	−	1.07409i	0.485839	−	0.0547409i
$386$		0			0
$387$	−4.08076	+	1.42792i	−0.207437	+	0.0725852i
$388$		0			0
$389$	10.8190	+	10.8190i	0.548546	+	0.548546i	0.926020	−	0.377474i	$-0.123207\pi$
$389$	10.8190	+	10.8190i	0.548546	+	0.548546i	−0.377474	+	0.926020i	$0.623207\pi$
$390$		0			0
$391$	−0.0678661	+	0.108008i	−0.00343213	+	0.00546221i
$392$		0			0
$393$	3.19032	+	4.00053i	0.160930	+	0.201800i
$394$		0			0
$395$	−7.86862	−	0.886581i	−0.395913	−	0.0446087i
$396$		0			0
$397$	10.6098	−	13.3043i	0.532491	−	0.667723i	−0.440718	−	0.897646i	$-0.645276\pi$
$397$	10.6098	−	13.3043i	0.532491	−	0.667723i	0.973209	+	0.229923i	$0.0738475\pi$
$398$		0			0
$399$	−3.43979	+	1.65651i	−0.172205	+	0.0829295i
$400$		0			0
$401$	−1.37791	+	6.03701i	−0.0688094	+	0.301474i	−0.997609	−	0.0691083i	$-0.977985\pi$
$401$	−1.37791	+	6.03701i	−0.0688094	+	0.301474i	0.928800	+	0.370582i	$0.120842\pi$
$402$		0			0
$403$	−16.5210	+	47.2143i	−0.822970	+	2.35191i
$404$		0			0
$405$		−	10.2918i		−	0.511403i
$406$		0			0
$407$			20.7608i			1.02907i
$408$		0			0
$409$	9.09185	−	25.9830i	0.449563	−	1.28478i	−0.466776	−	0.884376i	$-0.654585\pi$
$409$	9.09185	−	25.9830i	0.449563	−	1.28478i	0.916339	−	0.400402i	$-0.131130\pi$
$410$		0			0
$411$	1.07909	−	4.72778i	0.0532273	−	0.233204i
$412$		0			0
$413$	20.7323	−	9.98415i	1.02017	−	0.491288i
$414$		0			0
$415$	10.4127	−	13.0572i	0.511142	−	0.640951i
$416$		0			0
$417$	3.39433	+	0.382449i	0.166221	+	0.0187286i
$418$		0			0
$419$	−15.2953	−	19.1797i	−0.747223	−	0.936988i	0.252307	−	0.967647i	$-0.418811\pi$
$419$	−15.2953	−	19.1797i	−0.747223	−	0.936988i	−0.999530	+	0.0306596i	$0.990239\pi$
$420$		0			0
$421$	1.62769	−	2.59045i	0.0793288	−	0.126251i	−0.804703	−	0.593677i	$-0.797676\pi$
$421$	1.62769	−	2.59045i	0.0793288	−	0.126251i	0.884032	+	0.467426i	$0.154819\pi$
$422$		0			0
$423$	12.3846	+	12.3846i	0.602160	+	0.602160i
$424$		0			0
$425$	−4.24733	+	1.48621i	−0.206026	+	0.0720916i
$426$		0			0
$427$	0.0718632	−	0.00809704i	0.00347771	−	0.000391843i
$428$		0			0
$429$	1.84489	+	8.08300i	0.0890723	+	0.390251i
$430$		0			0
$431$	5.79134	−	12.0258i	0.278959	−	0.579265i	−0.713666	−	0.700486i	$-0.752967\pi$
$431$	5.79134	−	12.0258i	0.278959	−	0.579265i	0.992626	+	0.121221i	$0.0386810\pi$
$432$		0			0
$433$	2.61507	−	1.64316i	0.125672	−	0.0789652i	−0.467729	−	0.883872i	$-0.654928\pi$
$433$	2.61507	−	1.64316i	0.125672	−	0.0789652i	0.593401	+	0.804907i	$0.297785\pi$
$434$		0			0
$435$	−0.132423	−	3.54796i	−0.00634918	−	0.170112i
$436$		0			0
$437$	0.210227	+	0.334575i	0.0100565	+	0.0160049i
$438$		0			0
$439$	6.87297	+	3.30985i	0.328029	+	0.157970i	0.590648	−	0.806929i	$-0.298872\pi$
$439$	6.87297	+	3.30985i	0.328029	+	0.157970i	−0.262619	+	0.964899i	$0.584586\pi$
$440$		0			0
$441$	−10.6972	+	2.44157i	−0.509392	+	0.116265i
$442$		0			0
$443$	2.65798	+	23.5902i	0.126285	+	1.12081i	0.883759	+	0.467942i	$0.155004\pi$
$443$	2.65798	+	23.5902i	0.126285	+	1.12081i	−0.757475	+	0.652864i	$0.773567\pi$
$444$		0			0
$445$	2.54000	+	7.25890i	0.120408	+	0.344105i
$446$		0			0
$447$	0.531011	−	0.531011i	0.0251160	−	0.0251160i
$448$		0			0
$449$	29.8537	+	18.7583i	1.40888	+	0.885259i	0.999631	−	0.0271624i	$-0.00864713\pi$
$449$	29.8537	+	18.7583i	1.40888	+	0.885259i	0.409251	+	0.912422i	$0.365790\pi$
$450$		0			0
$451$	−3.97094	+	3.16672i	−0.186984	+	0.149115i
$452$		0			0
$453$	0.260527	−	2.31224i	0.0122406	−	0.108638i
$454$		0			0
$455$	−9.35966	−	7.46408i	−0.438788	−	0.349921i
$456$		0			0
$457$	4.52794	+	9.40235i	0.211808	+	0.439824i	0.979622	−	0.200849i	$-0.0643700\pi$
$457$	4.52794	+	9.40235i	0.211808	+	0.439824i	−0.767814	+	0.640672i	$0.778656\pi$
$458$		0			0
$459$	−3.97247	−	0.906691i	−0.185419	−	0.0423207i
$460$		0			0
$461$	16.8980	+	5.91287i	0.787019	+	0.275390i	0.693717	−	0.720248i	$-0.255972\pi$
$461$	16.8980	+	5.91287i	0.787019	+	0.275390i	0.0933024	+	0.995638i	$0.470258\pi$
$462$		0			0
$463$	−37.5706			−1.74605			−0.873026	−	0.487673i	$-0.837846\pi$
$463$	−37.5706			−1.74605			−0.873026	+	0.487673i	$0.837846\pi$
$464$		0			0
$465$	−6.94084			−0.321874
$466$		0			0
$467$	26.7301	+	9.35328i	1.23692	+	0.432818i	0.867964	−	0.496628i	$-0.165429\pi$
$467$	26.7301	+	9.35328i	1.23692	+	0.432818i	0.368959	+	0.929446i	$0.379714\pi$
$468$		0			0
$469$	−15.8268	−	3.61237i	−0.730815	−	0.166804i
$470$		0			0
$471$	−0.159898	−	0.332032i	−0.00736772	−	0.0152992i
$472$		0			0
$473$	−4.61292	−	3.67868i	−0.212102	−	0.169146i
$474$		0			0
$475$	−1.56068	+	13.8515i	−0.0716091	+	0.635548i
$476$		0			0
$477$	11.7920	−	9.40383i	0.539920	−	0.430572i
$478$		0			0
$479$	16.8069	+	10.5605i	0.767926	+	0.482520i	0.858148	−	0.513402i	$-0.171615\pi$
$479$	16.8069	+	10.5605i	0.767926	+	0.482520i	−0.0902224	+	0.995922i	$0.528758\pi$
$480$		0			0
$481$	18.3195	−	18.3195i	0.835297	−	0.835297i
$482$		0			0
$483$	0.0220204	+	0.0629307i	0.00100196	+	0.00286345i
$484$		0			0
$485$	−1.60455	−	14.2408i	−0.0728588	−	0.646640i
$486$		0			0
$487$	−26.6204	+	6.07593i	−1.20628	+	0.275327i	−0.777969	−	0.628303i	$-0.783750\pi$
$487$	−26.6204	+	6.07593i	−1.20628	+	0.275327i	−0.428315	+	0.903629i	$0.640893\pi$
$488$		0			0
$489$	−4.47933	−	2.15713i	−0.202562	−	0.0975488i
$490$		0			0
$491$	8.46305	+	13.4689i	0.381932	+	0.607842i	0.981266	−	0.192658i	$-0.0617106\pi$
$491$	8.46305	+	13.4689i	0.381932	+	0.607842i	−0.599334	+	0.800499i	$0.704568\pi$
$492$		0			0
$493$	8.12514	+	1.53815i	0.365938	+	0.0692747i
$494$		0			0
$495$	12.9399	−	8.13069i	0.581606	−	0.365447i
$496$		0			0
$497$	−3.26172	+	6.77304i	−0.146308	+	0.303812i
$498$		0			0
$499$	7.68214	+	33.6576i	0.343900	+	1.50672i	0.790764	+	0.612121i	$0.209684\pi$
$499$	7.68214	+	33.6576i	0.343900	+	1.50672i	−0.446864	+	0.894602i	$0.647459\pi$
$500$		0			0
$501$	9.48346	−	1.06853i	0.423690	−	0.0477384i
$502$		0			0
$503$	−9.84059	+	3.44337i	−0.438770	+	0.153532i	−0.540619	−	0.841268i	$-0.681810\pi$
$503$	−9.84059	+	3.44337i	−0.438770	+	0.153532i	0.101849	+	0.994800i	$0.467524\pi$
$504$		0			0
$505$	0.274330	+	0.274330i	0.0122075	+	0.0122075i
$506$		0			0
$507$	2.33488	−	3.71594i	0.103696	−	0.165031i
$508$		0			0
$509$	−0.721266	−	0.904438i	−0.0319695	−	0.0400885i	0.765590	−	0.643329i	$-0.222447\pi$
$509$	−0.721266	−	0.904438i	−0.0319695	−	0.0400885i	−0.797559	+	0.603241i	$0.793876\pi$
$510$		0			0
$511$	−24.9833	−	2.81494i	−1.10520	−	0.124526i
$512$		0			0
$513$	−7.86964	+	9.86821i	−0.347453	+	0.435692i
$514$		0			0
$515$	4.45936	−	2.14752i	0.196503	−	0.0946309i
$516$		0			0
$517$	−5.31874	+	23.3029i	−0.233918	+	1.02486i
$518$		0			0
$519$	−3.30961	+	9.45833i	−0.145276	+	0.415175i
$520$		0			0
$521$		−	11.0638i		−	0.484713i	−0.970187	−	0.242357i	$-0.922080\pi$
$521$		−	11.0638i		−	0.484713i	0.970187	−	0.242357i	$-0.0779204\pi$
$522$		0			0
$523$			43.7439i			1.91279i	0.292083	+	0.956393i	$0.405652\pi$
$523$			43.7439i			1.91279i	−0.292083	+	0.956393i	$0.594348\pi$
$524$		0			0
$525$	−0.776798	+	2.21996i	−0.0339023	+	0.0968871i
$526$		0			0
$527$	3.59732	−	15.7609i	0.156702	−	0.686555i
$528$		0			0
$529$	−20.7161	+	9.97633i	−0.900699	+	0.433754i
$530$		0			0
$531$	22.8557	−	28.6601i	0.991852	−	1.24374i
$532$		0			0
$533$	6.29833	+	0.709652i	0.272811	+	0.0307384i
$534$		0			0
$535$	4.69308	+	5.88494i	0.202900	+	0.254428i
$536$		0			0
$537$	4.40350	−	7.00813i	0.190025	−	0.302423i
$538$		0			0
$539$	−10.5883	−	10.5883i	−0.456068	−	0.456068i
$540$		0			0
$541$	−14.8434	+	5.19393i	−0.638167	+	0.223304i	−0.629918	−	0.776662i	$-0.716912\pi$
$541$	−14.8434	+	5.19393i	−0.638167	+	0.223304i	−0.00824925	+	0.999966i	$0.502626\pi$
$542$		0			0
$543$	−5.84565	+	0.658646i	−0.250861	+	0.0282652i
$544$		0			0
$545$	2.40815	+	10.5508i	0.103154	+	0.451946i
$546$		0			0
$547$	18.4938	−	38.4027i	0.790736	−	1.64198i	0.0242625	−	0.999706i	$-0.492276\pi$
$547$	18.4938	−	38.4027i	0.790736	−	1.64198i	0.766474	−	0.642275i	$-0.222009\pi$
$548$		0			0
$549$	0.0975473	−	0.0612930i	0.00416322	−	0.00261592i
$550$		0			0
$551$	15.2133	−	20.6093i	0.648109	−	0.877984i
$552$		0			0
$553$	−5.12863	−	8.16216i	−0.218091	−	0.347090i
$554$		0			0
$555$	3.23888	+	1.55976i	0.137483	+	0.0662082i
$556$		0			0
$557$	29.5326	−	6.74062i	1.25134	−	0.285609i	0.455015	−	0.890484i	$-0.349634\pi$
$557$	29.5326	−	6.74062i	1.25134	−	0.285609i	0.796321	+	0.604874i	$0.206777\pi$
$558$		0			0
$559$	0.824381	+	7.31658i	0.0348676	+	0.309458i
$560$		0			0
$561$	−0.884981	−	2.52913i	−0.0373639	−	0.106780i
$562$		0			0
$563$	−7.89933	+	7.89933i	−0.332917	+	0.332917i	−0.853693	−	0.520776i	$-0.825643\pi$
$563$	−7.89933	+	7.89933i	−0.332917	+	0.332917i	0.520776	+	0.853693i	$0.325643\pi$
$564$		0			0
$565$	−15.3032	−	9.61567i	−0.643812	−	0.404534i
$566$		0			0
$567$	9.79556	−	7.81170i	0.411375	−	0.328061i
$568$		0			0
$569$	−0.179270	+	1.59106i	−0.00751537	+	0.0667008i	−0.996910	−	0.0785510i	$-0.974971\pi$
$569$	−0.179270	+	1.59106i	−0.00751537	+	0.0667008i	0.989395	+	0.145252i	$0.0463992\pi$
$570$		0			0
$571$	−26.3753	−	21.0336i	−1.10377	−	0.880227i	−0.110252	−	0.993904i	$-0.535166\pi$
$571$	−26.3753	−	21.0336i	−1.10377	−	0.880227i	−0.993518	+	0.113677i	$0.963737\pi$
$572$		0			0
$573$	−5.23226	−	10.8649i	−0.218581	−	0.453888i
$574$		0			0
$575$	0.237317	+	0.0541661i	0.00989682	+	0.00225888i
$576$		0			0
$577$	38.2220	+	13.3744i	1.59120	+	0.556785i	0.973313	−	0.229481i	$-0.0737028\pi$
$577$	38.2220	+	13.3744i	1.59120	+	0.556785i	0.617888	+	0.786266i	$0.287989\pi$
$578$		0			0
$579$	4.34771			0.180685
$580$		0			0
$581$	20.3311			0.843477
$582$		0			0
$583$	19.4283	+	6.79825i	0.804637	+	0.281555i
$584$		0			0
$585$	−18.5929	−	4.24370i	−0.768721	−	0.175455i
$586$		0			0
$587$	−5.07911	−	10.5469i	−0.209637	−	0.435316i	0.769464	−	0.638690i	$-0.220523\pi$
$587$	−5.07911	−	10.5469i	−0.209637	−	0.435316i	−0.979101	+	0.203374i	$0.934809\pi$
$588$		0			0
$589$	−39.1524	−	31.2230i	−1.61325	−	1.28652i
$590$		0			0
$591$	1.09957	−	9.75893i	0.0452302	−	0.401429i
$592$		0			0
$593$	−32.5216	+	25.9351i	−1.33550	+	1.06503i	−0.343454	+	0.939170i	$0.611597\pi$
$593$	−32.5216	+	25.9351i	−1.33550	+	1.06503i	−0.992048	+	0.125858i	$0.959832\pi$
$594$		0			0
$595$	3.27598	+	2.05843i	0.134302	+	0.0843876i
$596$		0			0
$597$	6.03796	−	6.03796i	0.247117	−	0.247117i
$598$		0			0
$599$	−12.0652	−	34.4804i	−0.492972	−	1.40883i	−0.874748	−	0.484578i	$-0.838973\pi$
$599$	−12.0652	−	34.4804i	−0.492972	−	1.40883i	0.381776	−	0.924255i	$-0.375312\pi$
$600$		0			0
$601$	−1.03049	−	9.14588i	−0.0420347	−	0.373068i	−0.997065	−	0.0765600i	$-0.975606\pi$
$601$	−1.03049	−	9.14588i	−0.0420347	−	0.373068i	0.955030	−	0.296508i	$-0.0958222\pi$
$602$		0			0
$603$	−25.2128	+	5.75466i	−1.02674	+	0.234348i
$604$		0			0
$605$	4.53282	+	2.18289i	0.184286	+	0.0887472i
$606$		0			0
$607$	−7.89925	−	12.5716i	−0.320621	−	0.510265i	0.647062	−	0.762438i	$-0.275998\pi$
$607$	−7.89925	−	12.5716i	−0.320621	−	0.510265i	−0.967682	+	0.252173i	$0.918855\pi$
$608$		0			0
$609$	3.27638	−	2.81902i	0.132766	−	0.114232i
$610$		0			0
$611$	25.2560	−	15.8694i	1.02175	−	0.642006i
$612$		0			0
$613$	−13.6167	+	28.2753i	−0.549972	+	1.14203i	0.421926	+	0.906630i	$0.361354\pi$
$613$	−13.6167	+	28.2753i	−0.549972	+	1.14203i	−0.971899	+	0.235399i	$0.924360\pi$
$614$		0			0
$615$	0.195701	+	0.857421i	0.00789142	+	0.0345746i
$616$		0			0
$617$	−40.2697	+	4.53731i	−1.62120	+	0.182665i	−0.875364	−	0.483465i	$-0.839378\pi$
$617$	−40.2697	+	4.53731i	−1.62120	+	0.182665i	−0.745835	+	0.666130i	$0.767949\pi$
$618$		0			0
$619$	−24.8603	+	8.69899i	−0.999220	+	0.349642i	−0.779827	−	0.625995i	$-0.784693\pi$
$619$	−24.8603	+	8.69899i	−0.999220	+	0.349642i	−0.219392	+	0.975637i	$0.570407\pi$
$620$		0			0
$621$	0.155859	+	0.155859i	0.00625442	+	0.00625442i
$622$		0			0
$623$	−4.98099	+	7.92720i	−0.199559	+	0.317597i
$624$		0			0
$625$	−1.09813	−	1.37701i	−0.0439251	−	0.0550804i
$626$		0			0
$627$	−8.24803	−	0.929330i	−0.329395	−	0.0371138i
$628$		0			0
$629$	−5.22048	+	6.54627i	−0.208154	+	0.261017i
$630$		0			0
$631$	23.5554	−	11.3437i	0.937724	−	0.451584i	0.0983583	−	0.995151i	$-0.468641\pi$
$631$	23.5554	−	11.3437i	0.937724	−	0.451584i	0.839366	+	0.543567i	$0.182927\pi$
$632$		0			0
$633$	2.90268	−	12.7175i	0.115371	−	0.505474i
$634$		0			0
$635$	0.776358	−	2.21870i	0.0308088	−	0.0880465i
$636$		0			0
$637$			18.6863i			0.740379i
$638$		0			0
$639$			11.9757i			0.473751i
$640$		0			0
$641$	−1.81274	+	5.18052i	−0.0715990	+	0.204618i	−0.974122	−	0.226024i	$-0.927427\pi$
$641$	−1.81274	+	5.18052i	−0.0715990	+	0.204618i	0.902523	+	0.430642i	$0.141713\pi$
$642$		0			0
$643$	0.651020	−	2.85231i	0.0256737	−	0.112484i	−0.960467	−	0.278392i	$-0.910198\pi$
$643$	0.651020	−	2.85231i	0.0256737	−	0.112484i	0.986141	+	0.165908i	$0.0530556\pi$
$644$		0			0
$645$	−0.920479	+	0.443279i	−0.0362438	+	0.0174541i
$646$		0			0
$647$	9.00278	−	11.2891i	0.353936	−	0.443822i	−0.572709	−	0.819759i	$-0.694108\pi$
$647$	9.00278	−	11.2891i	0.353936	−	0.443822i	0.926645	+	0.375937i	$0.122679\pi$
$648$		0			0
$649$	49.7125	+	5.60126i	1.95139	+	0.219869i
$650$		0			0
$651$	−5.26826	−	6.60618i	−0.206479	−	0.258917i
$652$		0			0
$653$	−10.6621	+	16.9687i	−0.417241	+	0.664036i	−0.987534	−	0.157406i	$-0.949687\pi$
$653$	−10.6621	+	16.9687i	−0.417241	+	0.664036i	0.570293	+	0.821442i	$0.306830\pi$
$654$		0			0
$655$	−11.3580	−	11.3580i	−0.443796	−	0.443796i
$656$		0			0
$657$	−37.8037	+	13.2281i	−1.47486	+	0.516077i
$658$		0			0
$659$	−10.9264	+	1.23111i	−0.425633	+	0.0479573i	−0.322183	−	0.946677i	$-0.604417\pi$
$659$	−10.9264	+	1.23111i	−0.425633	+	0.0479573i	−0.103450	+	0.994635i	$0.532988\pi$
$660$		0			0
$661$	−4.68713	−	20.5357i	−0.182308	−	0.798745i	−0.980528	−	0.196379i	$-0.937082\pi$
$661$	−4.68713	−	20.5357i	−0.182308	−	0.798745i	0.798220	−	0.602366i	$-0.205775\pi$
$662$		0			0
$663$	−1.45081	+	3.01264i	−0.0563448	+	0.117001i
$664$		0			0
$665$	10.1479	−	6.37638i	0.393520	−	0.247265i
$666$		0			0
$667$	−0.327894	−	0.304298i	−0.0126961	−	0.0117825i
$668$		0			0
$669$	−3.96154	−	6.30476i	−0.153162	−	0.243756i
$670$		0			0
$671$	0.141652	+	0.0682161i	0.00546842	+	0.00263345i
$672$		0			0
$673$	35.6655	−	8.14042i	1.37480	−	0.313790i	0.529606	−	0.848244i	$-0.322340\pi$
$673$	35.6655	−	8.14042i	1.37480	−	0.313790i	0.845198	+	0.534454i	$0.179483\pi$
$674$		0			0
$675$	0.870585	+	7.72665i	0.0335088	+	0.297399i
$676$		0			0
$677$	−0.529281	−	1.51260i	−0.0203419	−	0.0581338i	0.933265	−	0.359189i	$-0.116947\pi$
$677$	−0.529281	−	1.51260i	−0.0203419	−	0.0581338i	−0.953607	+	0.301056i	$0.902661\pi$
$678$		0			0
$679$	12.3362	−	12.3362i	0.473422	−	0.473422i
$680$		0			0
$681$	1.57322	+	0.988517i	0.0602857	+	0.0378800i
$682$		0			0
$683$	36.7312	−	29.2922i	1.40548	−	1.12083i	0.429478	−	0.903077i	$-0.358698\pi$
$683$	36.7312	−	29.2922i	1.40548	−	1.12083i	0.976003	−	0.217757i	$-0.0698739\pi$
$684$		0			0
$685$	−1.70443	+	15.1272i	−0.0651229	+	0.577982i
$686$		0			0
$687$	−3.31275	−	2.64183i	−0.126389	−	0.100792i
$688$		0			0
$689$	−11.1448	−	23.1425i	−0.424584	−	0.881659i
$690$		0			0
$691$	−3.15801	−	0.720796i	−0.120137	−	0.0274204i	0.162030	−	0.986786i	$-0.448196\pi$
$691$	−3.15801	−	0.720796i	−0.120137	−	0.0274204i	−0.282166	+	0.959365i	$0.591053\pi$
$692$		0			0
$693$	17.5603	+	6.14463i	0.667062	+	0.233415i
$694$		0			0
$695$	−10.7228			−0.406738
$696$		0			0
$697$	−2.04841			−0.0775892
$698$		0			0
$699$	1.79182	+	0.626983i	0.0677727	+	0.0237147i
$700$		0			0
$701$	−39.8431	−	9.09394i	−1.50485	−	0.343473i	−0.610928	−	0.791686i	$-0.709204\pi$
$701$	−39.8431	−	9.09394i	−1.50485	−	0.343473i	−0.893927	+	0.448213i	$0.852061\pi$
$702$		0			0
$703$	11.2536	+	23.3683i	0.424437	+	0.881353i
$704$		0			0
$705$	3.23587	+	2.58052i	0.121870	+	0.0971882i
$706$		0			0
$707$	−0.0528803	+	0.469326i	−0.00198877	+	0.0176508i
$708$		0			0
$709$	−16.3910	+	13.0713i	−0.615575	+	0.490905i	−0.880930	−	0.473246i	$-0.843082\pi$
$709$	−16.3910	+	13.0713i	−0.615575	+	0.490905i	0.265355	+	0.964151i	$0.414511\pi$
$710$		0			0
$711$	−13.0027	−	8.17012i	−0.487638	−	0.306403i
$712$		0			0
$713$	−0.618375	+	0.618375i	−0.0231583	+	0.0231583i
$714$		0			0
$715$	−8.59598	−	24.5659i	−0.321471	−	0.918713i
$716$		0			0
$717$	−0.831962	−	7.38387i	−0.0310702	−	0.275756i
$718$		0			0
$719$	38.1451	−	8.70637i	1.42257	−	0.324693i	0.559104	−	0.829097i	$-0.311145\pi$
$719$	38.1451	−	8.70637i	1.42257	−	0.324693i	0.863468	+	0.504404i	$0.168288\pi$
$720$		0			0
$721$	5.42873	+	2.61434i	0.202176	+	0.0973631i
$722$		0			0
$723$	−3.81429	−	6.07040i	−0.141855	−	0.225761i
$724$		0			0
$725$	−2.35049	−	15.6044i	−0.0872951	−	0.579533i
$726$		0			0
$727$	16.4781	−	10.3539i	0.611138	−	0.384004i	−0.190610	−	0.981666i	$-0.561046\pi$
$727$	16.4781	−	10.3539i	0.611138	−	0.384004i	0.801748	+	0.597662i	$0.203904\pi$
$728$		0			0
$729$	7.07713	−	14.6958i	0.262116	−	0.544289i
$730$		0			0
$731$	−0.529506	−	2.31992i	−0.0195845	−	0.0858052i
$732$		0			0
$733$	2.26595	−	0.255312i	0.0836949	−	0.00943015i	−0.0700177	−	0.997546i	$-0.522306\pi$
$733$	2.26595	−	0.255312i	0.0836949	−	0.00943015i	0.153713	+	0.988116i	$0.450877\pi$
$734$		0			0
$735$	−2.44736	+	0.856370i	−0.0902724	+	0.0315877i
$736$		0			0
$737$	−24.9560	−	24.9560i	−0.919264	−	0.919264i
$738$		0			0
$739$	2.62171	−	4.17243i	0.0964412	−	0.153485i	−0.795019	−	0.606585i	$-0.792539\pi$
$739$	2.62171	−	4.17243i	0.0964412	−	0.153485i	0.891460	+	0.453100i	$0.149682\pi$
$740$		0			0
$741$	6.45808	+	8.09817i	0.237243	+	0.297494i
$742$		0			0
$743$	−11.0494	−	1.24497i	−0.405364	−	0.0456736i	−0.0930715	−	0.995659i	$-0.529669\pi$
$743$	−11.0494	−	1.24497i	−0.405364	−	0.0456736i	−0.312293	+	0.949986i	$0.601097\pi$
$744$		0			0
$745$	−1.46981	+	1.84309i	−0.0538498	+	0.0675255i
$746$		0			0
$747$	29.1809	−	14.0528i	1.06767	−	0.514164i
$748$		0			0
$749$	−2.03904	+	8.93360i	−0.0745048	+	0.326427i
$750$		0			0
$751$	−8.63574	+	24.6795i	−0.315123	+	0.900569i	0.671993	+	0.740558i	$0.265439\pi$
$751$	−8.63574	+	24.6795i	−0.315123	+	0.900569i	−0.987115	+	0.160011i	$0.948847\pi$
$752$		0			0
$753$		−	0.946192i		−	0.0344811i
$754$		0			0
$755$			7.30443i			0.265835i
$756$		0			0
$757$	−9.04277	+	25.8428i	−0.328665	+	0.939271i	0.654421	+	0.756130i	$0.272912\pi$
$757$	−9.04277	+	25.8428i	−0.328665	+	0.939271i	−0.983087	+	0.183141i	$0.941373\pi$
$758$		0			0
$759$	−0.0322539	+	0.141314i	−0.00117074	+	0.00512936i
$760$		0			0
$761$	−13.6803	+	6.58807i	−0.495909	+	0.238817i	−0.665084	−	0.746769i	$-0.731604\pi$
$761$	−13.6803	+	6.58807i	−0.495909	+	0.238817i	0.169174	+	0.985586i	$0.445890\pi$
$762$		0			0
$763$	−8.21423	+	10.3003i	−0.297375	+	0.372897i
$764$		0			0
$765$	6.12473	+	0.690092i	0.221440	+	0.0249503i
$766$		0			0
$767$	−38.9241	−	48.8093i	−1.40547	−	1.76240i
$768$		0			0
$769$	26.3112	−	41.8740i	0.948806	−	1.51002i	0.0911209	−	0.995840i	$-0.470955\pi$
$769$	26.3112	−	41.8740i	0.948806	−	1.51002i	0.857685	−	0.514176i	$-0.171902\pi$
$770$		0			0
$771$	0.400103	+	0.400103i	0.0144094	+	0.0144094i
$772$		0			0
$773$	32.8501	−	11.4947i	1.18154	−	0.413437i	0.333180	−	0.942863i	$-0.391878\pi$
$773$	32.8501	−	11.4947i	1.18154	−	0.413437i	0.848356	+	0.529426i	$0.177593\pi$
$774$		0			0
$775$	−30.6557	+	3.45406i	−1.10118	+	0.124074i
$776$		0			0
$777$	0.973825	+	4.26661i	0.0349358	+	0.153064i
$778$		0			0
$779$	−2.75314	+	5.71695i	−0.0986413	+	0.204831i
$780$		0			0
$781$	−13.8383	+	8.69519i	−0.495174	+	0.311138i
$782$		0			0
$783$	5.71539	−	13.0965i	0.204251	−	0.468029i
$784$		0			0
$785$	0.615492	+	0.979549i	0.0219678	+	0.0349616i
$786$		0			0
$787$	23.6616	+	11.3948i	0.843445	+	0.406182i	0.805140	−	0.593084i	$-0.202090\pi$
$787$	23.6616	+	11.3948i	0.843445	+	0.406182i	0.0383047	+	0.999266i	$0.487804\pi$
$788$		0			0
$789$	−8.21851	+	1.87582i	−0.292587	+	0.0667810i
$790$		0			0
$791$	−2.46347	−	21.8639i	−0.0875909	−	0.777390i
$792$		0			0
$793$	−0.0648006	−	0.185190i	−0.00230114	−	0.00657627i
$794$		0			0
$795$	2.52024	−	2.52024i	0.0893837	−	0.0893837i
$796$		0			0
$797$	−29.0290	−	18.2401i	−1.02826	−	0.646099i	−0.0914045	−	0.995814i	$-0.529136\pi$
$797$	−29.0290	−	18.2401i	−1.02826	−	0.646099i	−0.936856	+	0.349715i	$0.886278\pi$
$798$		0			0
$799$	−7.53681	+	6.01041i	−0.266633	+	0.212633i
$800$		0			0
$801$	−1.66988	+	14.8206i	−0.0590023	+	0.523660i
$802$		0			0
$803$	−42.7337	−	34.0789i	−1.50804	−	1.20262i
$804$		0			0
$805$	−0.0908096	−	0.188568i	−0.00320062	−	0.00664615i
$806$		0			0
$807$	3.84547	+	0.877704i	0.135367	+	0.0308967i
$808$		0			0
$809$	−6.23425	−	2.18146i	−0.219184	−	0.0766960i	0.218453	−	0.975847i	$-0.429899\pi$
$809$	−6.23425	−	2.18146i	−0.219184	−	0.0766960i	−0.437637	+	0.899152i	$0.644185\pi$
$810$		0			0
$811$	−14.7209			−0.516920			−0.258460	−	0.966022i	$-0.583215\pi$
$811$	−14.7209			−0.516920			−0.258460	+	0.966022i	$0.583215\pi$
$812$		0			0
$813$	5.93843			0.208270
$814$		0			0
$815$	14.7311	+	5.15464i	0.516008	+	0.180559i
$816$		0			0
$817$	−7.18637	−	1.64024i	−0.251419	−	0.0573848i
$818$		0			0
$819$	−10.0733	−	20.9175i	−0.351990	−	0.730915i
$820$		0			0
$821$	11.7779	+	9.39260i	0.411053	+	0.327804i	0.807088	−	0.590432i	$-0.201043\pi$
$821$	11.7779	+	9.39260i	0.411053	+	0.327804i	−0.396035	+	0.918236i	$0.629614\pi$
$822$		0			0
$823$	−4.29781	+	38.1441i	−0.149812	+	1.32962i	0.663668	+	0.748028i	$0.268999\pi$
$823$	−4.29781	+	38.1441i	−0.149812	+	1.32962i	−0.813480	+	0.581593i	$0.802430\pi$
$824$		0			0
$825$	−3.99768	+	3.18804i	−0.139181	+	0.110993i
$826$		0			0
$827$	30.7298	+	19.3088i	1.06858	+	0.671432i	0.947027	−	0.321153i	$-0.104070\pi$
$827$	30.7298	+	19.3088i	1.06858	+	0.671432i	0.121551	+	0.992585i	$0.461213\pi$
$828$		0			0
$829$	−38.3923	+	38.3923i	−1.33342	+	1.33342i	−0.431130	+	0.902290i	$0.641885\pi$
$829$	−38.3923	+	38.3923i	−1.33342	+	1.33342i	−0.902290	+	0.431130i	$0.858115\pi$
$830$		0			0
$831$	−2.04058	−	5.83165i	−0.0707871	−	0.202298i
$832$		0			0
$833$	−0.676171	−	6.00118i	−0.0234279	−	0.207929i
$834$		0			0
$835$	−29.2074	+	6.66640i	−1.01076	+	0.230700i
$836$		0			0
$837$	−25.1681	−	12.1203i	−0.869937	−	0.418940i
$838$		0			0
$839$	16.8410	+	26.8024i	0.581417	+	0.925320i	0.999854	+	0.0170744i	$0.00543522\pi$
$839$	16.8410	+	26.8024i	0.581417	+	0.925320i	−0.418437	+	0.908246i	$0.637422\pi$
$840$		0			0
$841$	−10.5999	+	26.9934i	−0.365515	+	0.930805i
$842$		0			0
$843$	−11.6375	+	7.31235i	−0.400818	+	0.251851i
$844$		0			0
$845$	−5.97743	+	12.4123i	−0.205630	+	0.426995i
$846$		0			0
$847$	1.36287	+	5.97114i	0.0468289	+	0.205171i
$848$		0			0
$849$	8.65529	−	0.975217i	0.297049	−	0.0334694i
$850$		0			0
$851$	0.427522	−	0.149596i	0.0146553	−	0.00512810i
$852$		0			0
$853$	27.1825	+	27.1825i	0.930712	+	0.930712i	0.997750	−	0.0670381i	$-0.0213549\pi$
$853$	27.1825	+	27.1825i	0.930712	+	0.930712i	−0.0670381	+	0.997750i	$0.521355\pi$
$854$		0			0
$855$	10.1578	−	16.1661i	0.347391	−	0.552869i
$856$		0			0
$857$	−14.6725	−	18.3988i	−0.501204	−	0.628490i	0.465297	−	0.885155i	$-0.345948\pi$
$857$	−14.6725	−	18.3988i	−0.501204	−	0.628490i	−0.966500	+	0.256665i	$0.917376\pi$
$858$		0			0
$859$	−9.94804	−	1.12088i	−0.339423	−	0.0382438i	−0.0593919	−	0.998235i	$-0.518916\pi$
$859$	−9.94804	−	1.12088i	−0.339423	−	0.0382438i	−0.280031	+	0.959991i	$0.590345\pi$
$860$		0			0
$861$	−0.667538	+	0.837067i	−0.0227496	+	0.0285272i
$862$		0			0
$863$	40.3281	−	19.4210i	1.37278	−	0.661098i	0.405337	−	0.914168i	$-0.367154\pi$
$863$	40.3281	−	19.4210i	1.37278	−	0.661098i	0.967448	+	0.253069i	$0.0814401\pi$
$864$		0			0
$865$	6.99973	−	30.6678i	0.237998	−	1.04274i
$866$		0			0
$867$	−2.21622	+	6.33360i	−0.0752669	+	0.215100i
$868$		0			0
$869$		−	20.9571i		−	0.710920i
$870$		0			0
$871$			44.0427i			1.49233i
$872$		0			0
$873$	9.17923	−	26.2327i	0.310670	−	0.887843i
$874$		0			0
$875$	4.44616	−	19.4799i	0.150308	−	0.658540i
$876$		0			0
$877$	28.4878	−	13.7190i	0.961964	−	0.463257i	0.114099	−	0.993469i	$-0.463602\pi$
$877$	28.4878	−	13.7190i	0.961964	−	0.463257i	0.847865	+	0.530212i	$0.177888\pi$
$878$		0			0
$879$	7.00063	−	8.77851i	0.236125	−	0.296092i
$880$		0			0
$881$	−37.4369	−	4.21813i	−1.26128	−	0.142112i	−0.544114	−	0.839012i	$-0.683134\pi$
$881$	−37.4369	−	4.21813i	−1.26128	−	0.142112i	−0.717169	+	0.696899i	$0.754563\pi$
$882$		0			0
$883$	−9.87456	−	12.3823i	−0.332305	−	0.416698i	0.587406	−	0.809292i	$-0.300149\pi$
$883$	−9.87456	−	12.3823i	−0.332305	−	0.416698i	−0.919712	+	0.392594i	$0.871578\pi$
$884$		0			0
$885$	4.60876	−	7.33480i	0.154922	−	0.246557i
$886$		0			0
$887$	−20.0016	−	20.0016i	−0.671589	−	0.671589i	0.286493	−	0.958082i	$-0.407510\pi$
$887$	−20.0016	−	20.0016i	−0.671589	−	0.671589i	−0.958082	+	0.286493i	$0.907510\pi$
$888$		0			0
$889$	2.70100	−	0.945120i	0.0905886	−	0.0316983i
$890$		0			0
$891$	27.0673	−	3.04975i	0.906787	−	0.102170i
$892$		0			0
$893$	6.64480	+	29.1128i	0.222360	+	0.974222i
$894$		0			0
$895$	−11.2732	+	23.4091i	−0.376822	+	0.782479i
$896$		0			0
$897$	0.153157	−	0.0962352i	0.00511378	−	0.00321320i
$898$		0			0
$899$	51.9605	+	22.6759i	1.73298	+	0.756285i
$900$		0			0
$901$	4.41663	+	7.02902i	0.147139	+	0.234171i
$902$		0			0
$903$	−1.12057	−	0.539638i	−0.0372902	−	0.0179580i
$904$		0			0
$905$	18.0036	−	4.10920i	0.598459	−	0.136594i
$906$		0			0
$907$	−0.337976	−	2.99962i	−0.0112223	−	0.0996007i	0.986852	−	0.161624i	$-0.0516732\pi$
$907$	−0.337976	−	2.99962i	−0.0112223	−	0.0996007i	−0.998075	+	0.0620234i	$0.980245\pi$
$908$		0			0
$909$	0.248497	+	0.710165i	0.00824214	+	0.0235547i
$910$		0			0
$911$	−32.4573	+	32.4573i	−1.07536	+	1.07536i	−0.0784377	+	0.996919i	$0.524993\pi$
$911$	−32.4573	+	32.4573i	−1.07536	+	1.07536i	−0.996919	+	0.0784377i	$0.975007\pi$
$912$		0			0
$913$	37.4258	+	23.5162i	1.23861	+	0.778272i
$914$		0			0
$915$	0.0212847	−	0.0169740i	0.000703651	−	0.000561143i
$916$		0			0
$917$	2.18940	−	19.4314i	0.0723002	−	0.641682i
$918$		0			0
$919$	7.38174	+	5.88674i	0.243501	+	0.194186i	0.737634	−	0.675201i	$-0.235943\pi$
$919$	7.38174	+	5.88674i	0.243501	+	0.194186i	−0.494133	+	0.869386i	$0.664514\pi$
$920$		0			0
$921$	−3.69731	−	7.67754i	−0.121831	−	0.252984i
$922$		0			0
$923$	19.8837	+	4.53833i	0.654481	+	0.149381i
$924$		0			0
$925$	15.0814	+	5.27721i	0.495873	+	0.173513i
$926$		0			0
$927$	9.59877			0.315265
$928$		0			0
$929$	9.79335			0.321309			0.160655	−	0.987011i	$-0.448639\pi$
$929$	9.79335			0.321309			0.160655	+	0.987011i	$0.448639\pi$
$930$		0			0
$931$	−17.6576	−	6.17866i	−0.578704	−	0.202497i
$932$		0			0
$933$	10.3696	+	2.36680i	0.339486	+	0.0774856i
$934$		0			0
$935$	3.64956	+	7.57839i	0.119353	+	0.247840i
$936$		0			0
$937$	41.9509	+	33.4547i	1.37048	+	1.09292i	0.985441	+	0.170017i	$0.0543823\pi$
$937$	41.9509	+	33.4547i	1.37048	+	1.09292i	0.385036	+	0.922902i	$0.374189\pi$
$938$		0			0
$939$	−0.742757	+	6.59215i	−0.0242390	+	0.215127i
$940$		0			0
$941$	26.1237	−	20.8330i	0.851609	−	0.679135i	−0.0971043	−	0.995274i	$-0.530958\pi$
$941$	26.1237	−	20.8330i	0.851609	−	0.679135i	0.948713	+	0.316139i	$0.102387\pi$
$942$		0			0
$943$	0.0938250	+	0.0589541i	0.00305536	+	0.00191981i
$944$		0			0
$945$	4.72734	−	4.72734i	0.153780	−	0.153780i
$946$		0			0
$947$	9.14692	+	26.1404i	0.297235	+	0.849449i	0.991544	+	0.129772i	$0.0414245\pi$
$947$	9.14692	+	26.1404i	0.297235	+	0.849449i	−0.694309	+	0.719677i	$0.744290\pi$
$948$		0			0
$949$	7.63698	+	67.7801i	0.247907	+	2.20023i
$950$		0			0
$951$	10.7714	−	2.45850i	0.349287	−	0.0797224i
$952$		0			0
$953$	34.8106	+	16.7639i	1.12763	+	0.543036i	0.902240	−	0.431234i	$-0.141922\pi$
$953$	34.8106	+	16.7639i	1.12763	+	0.543036i	0.225385	+	0.974270i	$0.427636\pi$
$954$		0			0
$955$	20.1404	+	32.0533i	0.651728	+	1.03722i
$956$		0			0
$957$	9.29185	−	1.39963i	0.300363	−	0.0452436i
$958$		0			0
$959$	−15.6916	+	9.85966i	−0.506707	+	0.318385i
$960$		0			0
$961$	34.6373	−	71.9251i	1.11733	−	2.32016i
$962$		0			0
$963$	3.24827	+	14.2316i	0.104674	+	0.458607i
$964$		0			0
$965$	−13.5624	+	1.52811i	−0.436588	+	0.0491917i
$966$		0			0
$967$	−30.2664	+	10.5907i	−0.973301	+	0.340573i	−0.769647	−	0.638470i	$-0.779568\pi$
$967$	−30.2664	+	10.5907i	−0.973301	+	0.340573i	−0.203655	+	0.979043i	$0.565282\pi$
$968$		0			0
$969$	−2.36707	−	2.36707i	−0.0760413	−	0.0760413i
$970$		0			0
$971$	−2.59619	+	4.13181i	−0.0833156	+	0.132596i	−0.885782	−	0.464101i	$-0.846378\pi$
$971$	−2.59619	+	4.13181i	−0.0833156	+	0.132596i	0.802467	+	0.596697i	$0.203520\pi$
$972$		0			0
$973$	−8.13883	−	10.2058i	−0.260919	−	0.327182i
$974$		0			0
$975$	6.34074	+	0.714430i	0.203066	+	0.0228801i
$976$		0			0
$977$	−17.4337	+	21.8612i	−0.557754	+	0.699401i	−0.978141	−	0.207944i	$-0.933323\pi$
$977$	−17.4337	+	21.8612i	−0.557754	+	0.699401i	0.420387	+	0.907345i	$0.361894\pi$
$978$		0			0
$979$	−18.3381	+	8.83118i	−0.586089	+	0.282246i
$980$		0			0
$981$	−4.67020	+	20.4615i	−0.149108	+	0.653285i
$982$		0			0
$983$	−13.8491	+	39.5785i	−0.441718	+	1.26236i	0.480945	+	0.876751i	$0.340294\pi$
$983$	−13.8491	+	39.5785i	−0.441718	+	1.26236i	−0.922663	+	0.385607i	$0.873992\pi$
$984$		0			0
$985$			30.8288i			0.982286i
$986$		0			0
$987$			5.03853i			0.160378i
$988$		0			0
$989$	−0.0425148	+	0.121500i	−0.00135189	+	0.00386348i
$990$		0			0
$991$	1.15648	−	5.06685i	0.0367367	−	0.160954i	−0.953232	−	0.302238i	$-0.902266\pi$
$991$	1.15648	−	5.06685i	0.0367367	−	0.160954i	0.989969	+	0.141285i	$0.0451233\pi$
$992$		0			0
$993$	4.00218	−	1.92735i	0.127005	−	0.0611626i
$994$		0			0
$995$	−16.7128	+	20.9572i	−0.529830	+	0.664386i
$996$		0			0
$997$	7.97460	+	0.898522i	0.252558	+	0.0284565i	0.237336	−	0.971428i	$-0.423726\pi$
$997$	7.97460	+	0.898522i	0.252558	+	0.0284565i	0.0152224	+	0.999884i	$0.495154\pi$
$998$		0			0
$999$	9.02076	+	11.3117i	0.285404	+	0.357886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.bl.c.367.7	yes	120
4.3	odd	2	inner	464.2.bl.c.367.4	yes	120
29.26	odd	28	inner	464.2.bl.c.287.4	✓	120
116.55	even	28	inner	464.2.bl.c.287.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.2.bl.c.287.4	✓	120	29.26	odd	28	inner
464.2.bl.c.287.7	yes	120	116.55	even	28	inner
464.2.bl.c.367.4	yes	120	4.3	odd	2	inner
464.2.bl.c.367.7	yes	120	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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.bl (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.432566 + 0.151361i) q^{3} +(-1.40256 - 0.320125i) q^{5} +(-0.759883 - 1.57791i) q^{7} +(-2.18129 - 1.73952i) q^{9} +(0.426306 - 3.78357i) q^{11} +(-3.71483 + 2.96248i) q^{13} +(-0.558244 - 0.350768i) q^{15} +(1.08583 - 1.08583i) q^{17} +(-1.57107 - 4.48986i) q^{19} +(-0.0898644 - 0.797568i) q^{21} +(-0.0809859 + 0.0184845i) q^{23} +(-2.64016 - 1.27143i) q^{25} +(-1.41172 - 2.24674i) q^{27} +(3.03315 + 4.44972i) q^{29} +(8.91399 - 5.60103i) q^{31} +(0.757091 - 1.57212i) q^{33} +(0.560651 + 2.45637i) q^{35} +(-5.41831 + 0.610497i) q^{37} +(-2.05531 + 0.719185i) q^{39} +(-0.943245 - 0.943245i) q^{41} +(0.824442 - 1.31209i) q^{43} +(2.50252 + 3.13806i) q^{45} +(-6.23817 - 0.702873i) q^{47} +(2.45204 - 3.07476i) q^{49} +(0.634047 - 0.305341i) q^{51} +(-1.20294 + 5.27045i) q^{53} +(-1.80913 + 5.17020i) q^{55} -2.17996i q^{57} +13.1391i q^{59} +(-0.0136381 + 0.0389754i) q^{61} +(-1.08729 + 4.76372i) q^{63} +(6.15862 - 2.96583i) q^{65} +(5.77933 - 7.24705i) q^{67} +(-0.0378296 - 0.00426237i) q^{69} +(-2.67627 - 3.35593i) q^{71} +(7.63754 - 12.1551i) q^{73} +(-0.949596 - 0.949596i) q^{75} +(-6.29408 + 2.20240i) q^{77} +(5.46954 - 0.616269i) q^{79} +(1.59189 + 6.97454i) q^{81} +(-5.03687 + 10.4592i) q^{83} +(-1.87054 + 1.17534i) q^{85} +(0.638524 + 2.38390i) q^{87} +(-2.84408 - 4.52633i) q^{89} +(7.49736 + 3.61054i) q^{91} +(4.70367 - 1.07358i) q^{93} +(0.766202 + 6.80023i) q^{95} +(3.29007 + 9.40249i) q^{97} +(-7.51150 + 7.51150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 4 q^{17} - 40 q^{21} - 28 q^{25} - 52 q^{29} - 84 q^{33} - 8 q^{37} + 4 q^{41} + 40 q^{45} - 28 q^{49} - 48 q^{53} - 4 q^{61} - 40 q^{65} + 24 q^{69} + 76 q^{73} + 156 q^{77} + 116 q^{81} + 152 q^{85}+ \cdots + 64 q^{97}+O(q^{100}) \) 120 * q + 4 * q^17 - 40 * q^21 - 28 * q^25 - 52 * q^29 - 84 * q^33 - 8 * q^37 + 4 * q^41 + 40 * q^45 - 28 * q^49 - 48 * q^53 - 4 * q^61 - 40 * q^65 + 24 * q^69 + 76 * q^73 + 156 * q^77 + 116 * q^81 + 152 * q^85 + 104 * q^89 + 112 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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