LMFDB - Embedded newform 720.2.u.a.179.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			179.4
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.73123 - 1.41522i) q^{5} +3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +O(q^{10})$	\(q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.73123 - 1.41522i) q^{5} +3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +(-2.12547 + 2.34145i) q^{10} +(-0.761375 + 0.761375i) q^{11} +(-4.33164 + 4.33164i) q^{13} +(-0.795824 - 5.32284i) q^{14} +(3.31562 - 2.23755i) q^{16} -6.44408 q^{17} +(-2.98007 + 2.98007i) q^{19} +(2.48319 - 3.71937i) q^{20} +(0.905695 - 1.22413i) q^{22} -1.73120 q^{23} +(0.994326 - 4.90013i) q^{25} +(5.15271 - 6.96434i) q^{26} +(2.22619 + 7.27847i) q^{28} +(0.289500 - 0.289500i) q^{29} +3.89823i q^{31} +(-4.16955 + 3.82294i) q^{32} +(9.01313 - 1.34756i) q^{34} +(5.38582 + 6.58847i) q^{35} +(-1.64445 - 1.64445i) q^{37} +(3.54494 - 4.79130i) q^{38} +(-2.69538 + 5.72144i) q^{40} -2.59735 q^{41} +(7.61730 - 7.61730i) q^{43} +(-1.01078 + 1.90154i) q^{44} +(2.42137 - 0.362022i) q^{46} +5.14100i q^{47} -7.48300 q^{49} +(-0.366034 + 7.06159i) q^{50} +(-5.75057 + 10.8183i) q^{52} +(5.10351 - 5.10351i) q^{53} +(-0.240606 + 2.39563i) q^{55} +(-4.63574 - 9.71462i) q^{56} +(-0.344376 + 0.465454i) q^{58} +(-5.68382 + 5.68382i) q^{59} +(-0.647296 - 0.647296i) q^{61} +(-0.815183 - 5.45232i) q^{62} +(5.03237 - 6.21894i) q^{64} +(-1.36887 + 13.6293i) q^{65} +(9.09323 + 9.09323i) q^{67} +(-12.3246 + 3.76959i) q^{68} +(-8.91073 - 8.08881i) q^{70} +8.79742i q^{71} -12.1321 q^{73} +(2.64392 + 1.95616i) q^{74} +(-3.95625 + 7.44275i) q^{76} +(-2.89753 - 2.89753i) q^{77} -12.0907i q^{79} +(2.57349 - 8.56605i) q^{80} +(3.63283 - 0.543148i) q^{82} +(0.925156 - 0.925156i) q^{83} +(-11.1562 + 9.11977i) q^{85} +(-9.06116 + 12.2470i) q^{86} +(1.01610 - 2.87100i) q^{88} -13.2896 q^{89} +(-16.4847 - 16.4847i) q^{91} +(-3.31099 + 1.01270i) q^{92} +(-1.07507 - 7.19055i) q^{94} +(-0.941748 + 9.37663i) q^{95} +9.56150i q^{97} +(10.4662 - 1.56482i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.39867	+	0.209116i	−0.989007	+	0.147868i
$2$	−1.39867	+	0.209116i	−0.989007	+	0.147868i
$3$		0			0
$3$		0			0
$4$	1.91254	−	0.584968i	0.956270	−	0.292484i
$5$	1.73123	−	1.41522i	0.774230	−	0.632904i
$5$	1.73123	−	1.41522i	0.774230	−	0.632904i
$6$		0			0
$7$			3.80565i			1.43840i	0.694802	+	0.719201i	$0.255492\pi$
$7$			3.80565i			1.43840i	−0.694802	+	0.719201i	$0.744508\pi$
$8$	−2.55268	+	1.21812i	−0.902509	+	0.430670i
$9$		0			0
$10$	−2.12547	+	2.34145i	−0.672133	+	0.740430i
$11$	−0.761375	+	0.761375i	−0.229563	+	0.229563i	−0.812510	−	0.582947i	$-0.801900\pi$
$11$	−0.761375	+	0.761375i	−0.229563	+	0.229563i	0.582947	+	0.812510i	$0.301900\pi$
$12$		0			0
$13$	−4.33164	+	4.33164i	−1.20138	+	1.20138i	−0.227634	+	0.973747i	$0.573099\pi$
$13$	−4.33164	+	4.33164i	−1.20138	+	1.20138i	−0.973747	+	0.227634i	$0.926901\pi$
$14$	−0.795824	−	5.32284i	−0.212693	−	1.42259i
$15$		0			0
$16$	3.31562	−	2.23755i	0.828906	−	0.559388i
$17$	−6.44408			−1.56292			−0.781460	−	0.623955i	$-0.785525\pi$
$17$	−6.44408			−1.56292			−0.781460	+	0.623955i	$0.785525\pi$
$18$		0			0
$19$	−2.98007	+	2.98007i	−0.683674	+	0.683674i	−0.960826	−	0.277152i	$-0.910610\pi$
$19$	−2.98007	+	2.98007i	−0.683674	+	0.683674i	0.277152	+	0.960826i	$0.410610\pi$
$20$	2.48319	−	3.71937i	0.555259	−	0.831677i
$21$		0			0
$22$	0.905695	−	1.22413i	0.193095	−	0.260985i
$23$	−1.73120			−0.360980			−0.180490	−	0.983577i	$-0.557768\pi$
$23$	−1.73120			−0.360980			−0.180490	+	0.983577i	$0.557768\pi$
$24$		0			0
$25$	0.994326	−	4.90013i	0.198865	−	0.980027i
$26$	5.15271	−	6.96434i	1.01053	−	1.36582i
$27$		0			0
$28$	2.22619	+	7.27847i	0.420710	+	1.37550i
$29$	0.289500	−	0.289500i	0.0537589	−	0.0537589i	−0.679716	−	0.733475i	$-0.737897\pi$
$29$	0.289500	−	0.289500i	0.0537589	−	0.0537589i	0.733475	+	0.679716i	$0.237897\pi$
$30$		0			0
$31$			3.89823i			0.700142i	0.936723	+	0.350071i	$0.113843\pi$
$31$			3.89823i			0.700142i	−0.936723	+	0.350071i	$0.886157\pi$
$32$	−4.16955	+	3.82294i	−0.737079	+	0.675807i
$33$		0			0
$34$	9.01313	−	1.34756i	1.54574	−	0.231105i
$35$	5.38582	+	6.58847i	0.910370	+	1.11365i
$36$		0			0
$37$	−1.64445	−	1.64445i	−0.270346	−	0.270346i	0.558893	−	0.829239i	$-0.311226\pi$
$37$	−1.64445	−	1.64445i	−0.270346	−	0.270346i	−0.829239	+	0.558893i	$0.811226\pi$
$38$	3.54494	−	4.79130i	0.575066	−	0.777252i
$39$		0			0
$40$	−2.69538	+	5.72144i	−0.426177	+	0.904640i
$41$	−2.59735			−0.405638			−0.202819	−	0.979216i	$-0.565010\pi$
$41$	−2.59735			−0.405638			−0.202819	+	0.979216i	$0.565010\pi$
$42$		0			0
$43$	7.61730	−	7.61730i	1.16163	−	1.16163i	0.177507	−	0.984119i	$-0.443197\pi$
$43$	7.61730	−	7.61730i	1.16163	−	1.16163i	0.984119	−	0.177507i	$-0.0568034\pi$
$44$	−1.01078	+	1.90154i	−0.152381	+	0.286668i
$45$		0			0
$46$	2.42137	−	0.362022i	0.357012	−	0.0533773i
$47$			5.14100i			0.749892i	0.927047	+	0.374946i	$0.122339\pi$
$47$			5.14100i			0.749892i	−0.927047	+	0.374946i	$0.877661\pi$
$48$		0			0
$49$	−7.48300			−1.06900
$50$	−0.366034	+	7.06159i	−0.0517650	+	0.998659i
$51$		0			0
$52$	−5.75057	+	10.8183i	−0.797460	+	1.50023i
$53$	5.10351	−	5.10351i	0.701021	−	0.701021i	−0.263609	−	0.964630i	$-0.584913\pi$
$53$	5.10351	−	5.10351i	0.701021	−	0.701021i	0.964630	+	0.263609i	$0.0849128\pi$
$54$		0			0
$55$	−0.240606	+	2.39563i	−0.0324434	+	0.323026i
$56$	−4.63574	−	9.71462i	−0.619477	−	1.29817i
$57$		0			0
$58$	−0.344376	+	0.465454i	−0.0452187	+	0.0611171i
$59$	−5.68382	+	5.68382i	−0.739971	+	0.739971i	−0.972572	−	0.232601i	$-0.925276\pi$
$59$	−5.68382	+	5.68382i	−0.739971	+	0.739971i	0.232601	+	0.972572i	$0.425276\pi$
$60$		0			0
$61$	−0.647296	−	0.647296i	−0.0828778	−	0.0828778i	0.664453	−	0.747330i	$-0.268665\pi$
$61$	−0.647296	−	0.647296i	−0.0828778	−	0.0828778i	−0.747330	+	0.664453i	$0.768665\pi$
$62$	−0.815183	−	5.45232i	−0.103528	−	0.692446i
$63$		0			0
$64$	5.03237	−	6.21894i	0.629046	−	0.777368i
$65$	−1.36887	+	13.6293i	−0.169787	+	1.69050i
$66$		0			0
$67$	9.09323	+	9.09323i	1.11091	+	1.11091i	0.993027	+	0.117887i	$0.0376122\pi$
$67$	9.09323	+	9.09323i	1.11091	+	1.11091i	0.117887	+	0.993027i	$0.462388\pi$
$68$	−12.3246	+	3.76959i	−1.49457	+	0.457129i
$69$		0			0
$70$	−8.91073	−	8.08881i	−1.06504	−	0.966798i
$71$			8.79742i			1.04406i	0.852927	+	0.522031i	$0.174825\pi$
$71$			8.79742i			1.04406i	−0.852927	+	0.522031i	$0.825175\pi$
$72$		0			0
$73$	−12.1321			−1.41995			−0.709976	−	0.704225i	$-0.751294\pi$
$73$	−12.1321			−1.41995			−0.709976	+	0.704225i	$0.751294\pi$
$74$	2.64392	+	1.95616i	0.307350	+	0.227399i
$75$		0			0
$76$	−3.95625	+	7.44275i	−0.453814	+	0.853741i
$77$	−2.89753	−	2.89753i	−0.330204	−	0.330204i
$78$		0			0
$79$		−	12.0907i		−	1.36031i	−0.733068	−	0.680155i	$-0.761912\pi$
$79$		−	12.0907i		−	1.36031i	0.733068	−	0.680155i	$-0.238088\pi$
$80$	2.57349	−	8.56605i	0.287725	−	0.957713i
$81$		0			0
$82$	3.63283	−	0.543148i	0.401179	−	0.0599807i
$83$	0.925156	−	0.925156i	0.101549	−	0.101549i	−0.654507	−	0.756056i	$-0.727124\pi$
$83$	0.925156	−	0.925156i	0.101549	−	0.101549i	0.756056	+	0.654507i	$0.227124\pi$
$84$		0			0
$85$	−11.1562	+	9.11977i	−1.21006	+	0.989178i
$86$	−9.06116	+	12.2470i	−0.977090	+	1.32062i
$87$		0			0
$88$	1.01610	−	2.87100i	0.108317	−	0.306049i
$89$	−13.2896			−1.40870			−0.704349	−	0.709854i	$-0.748761\pi$
$89$	−13.2896			−1.40870			−0.704349	+	0.709854i	$0.748761\pi$
$90$		0			0
$91$	−16.4847	−	16.4847i	−1.72807	−	1.72807i
$92$	−3.31099	+	1.01270i	−0.345195	+	0.105581i
$93$		0			0
$94$	−1.07507	−	7.19055i	−0.110885	−	0.741649i
$95$	−0.941748	+	9.37663i	−0.0966213	+	0.962022i
$96$		0			0
$97$			9.56150i			0.970823i	0.874286	+	0.485411i	$0.161330\pi$
$97$			9.56150i			0.970823i	−0.874286	+	0.485411i	$0.838670\pi$
$98$	10.4662	−	1.56482i	1.05725	−	0.158070i
$99$		0			0
$100$	−0.964734	−	9.95336i	−0.0964734	−	0.995336i
$101$	11.7354	+	11.7354i	1.16771	+	1.16771i	0.982744	+	0.184969i	$0.0592184\pi$
$101$	11.7354	+	11.7354i	1.16771	+	1.16771i	0.184969	+	0.982744i	$0.440782\pi$
$102$		0			0
$103$		−	9.72480i		−	0.958213i	−0.877757	−	0.479107i	$-0.840961\pi$
$103$		−	9.72480i		−	0.958213i	0.877757	−	0.479107i	$-0.159039\pi$
$104$	5.78084	−	16.3338i	0.566858	−	1.60166i
$105$		0			0
$106$	−6.07088	+	8.20534i	−0.589656	+	0.796973i
$107$	8.15735	+	8.15735i	0.788601	+	0.788601i	0.981265	−	0.192664i	$-0.0617127\pi$
$107$	8.15735	+	8.15735i	0.788601	+	0.788601i	−0.192664	+	0.981265i	$0.561713\pi$
$108$		0			0
$109$	8.72633	+	8.72633i	0.835831	+	0.835831i	0.988307	−	0.152477i	$-0.0487249\pi$
$109$	8.72633	+	8.72633i	0.835831	+	0.835831i	−0.152477	+	0.988307i	$0.548725\pi$
$110$	−0.164437	−	3.40100i	−0.0156784	−	0.324273i
$111$		0			0
$112$	8.51535	+	12.6181i	0.804625	+	1.19230i
$113$	16.2773			1.53124			0.765619	−	0.643295i	$-0.222433\pi$
$113$	16.2773			1.53124			0.765619	+	0.643295i	$0.222433\pi$
$114$		0			0
$115$	−2.99711	+	2.45002i	−0.279482	+	0.228466i
$116$	0.384333	−	0.723030i	0.0356844	−	0.0671316i
$117$		0			0
$118$	6.76120	−	9.13836i	0.622419	−	0.841254i
$119$		−	24.5240i		−	2.24811i
$120$		0			0
$121$			9.84061i			0.894601i
$122$	1.04071	+	0.769992i	0.0942217	+	0.0697118i
$123$		0			0
$124$	2.28034	+	7.45552i	0.204781	+	0.669525i
$125$	−5.21334	−	9.89045i	−0.466295	−	0.884629i
$126$		0			0
$127$	8.61277			0.764260			0.382130	−	0.924109i	$-0.375191\pi$
$127$	8.61277			0.764260			0.382130	+	0.924109i	$0.375191\pi$
$128$	−5.73813	+	9.75058i	−0.507184	+	0.861838i
$129$		0			0
$130$	−0.935518	−	19.3491i	−0.0820503	−	1.69703i
$131$	7.09695	+	7.09695i	0.620064	+	0.620064i	0.945548	−	0.325484i	$-0.105527\pi$
$131$	7.09695	+	7.09695i	0.620064	+	0.620064i	−0.325484	+	0.945548i	$0.605527\pi$
$132$		0			0
$133$	−11.3411	−	11.3411i	−0.983398	−	0.983398i
$134$	−14.6199	−	10.8169i	−1.26297	−	0.934434i
$135$		0			0
$136$	16.4497	−	7.84967i	1.41055	−	0.673103i
$137$		−	9.30582i		−	0.795050i	−0.917591	−	0.397525i	$-0.869869\pi$
$137$		−	9.30582i		−	0.795050i	0.917591	−	0.397525i	$-0.130131\pi$
$138$		0			0
$139$	9.16328	+	9.16328i	0.777219	+	0.777219i	0.979357	−	0.202138i	$-0.0647889\pi$
$139$	9.16328	+	9.16328i	0.777219	+	0.777219i	−0.202138	+	0.979357i	$0.564789\pi$
$140$	14.1546	+	9.45018i	1.19629	+	0.798686i
$141$		0			0
$142$	−1.83968	−	12.3047i	−0.154383	−	1.03258i
$143$		−	6.59601i		−	0.551586i
$144$		0			0
$145$	0.0914866	−	0.910898i	0.00759755	−	0.0756460i
$146$	16.9687	−	2.53702i	1.40434	−	0.209965i
$147$		0			0
$148$	−4.10703	−	2.18313i	−0.337596	−	0.179452i
$149$	0.389077	+	0.389077i	0.0318744	+	0.0318744i	0.722864	−	0.690990i	$-0.242825\pi$
$149$	0.389077	+	0.389077i	0.0318744	+	0.0318744i	−0.690990	+	0.722864i	$0.742825\pi$
$150$		0			0
$151$	12.5843			1.02409			0.512047	−	0.858958i	$-0.328887\pi$
$151$	12.5843			1.02409			0.512047	+	0.858958i	$0.328887\pi$
$152$	3.97709	−	11.2372i	0.322584	−	0.911461i
$153$		0			0
$154$	4.65860	+	3.44676i	0.375401	+	0.277748i
$155$	5.51683	+	6.74873i	0.443123	+	0.542071i
$156$		0			0
$157$	−0.397418	+	0.397418i	−0.0317174	+	0.0317174i	−0.722788	−	0.691070i	$-0.757140\pi$
$157$	−0.397418	+	0.397418i	−0.0317174	+	0.0317174i	0.691070	+	0.722788i	$0.257140\pi$
$158$	2.52836	+	16.9109i	0.201146	+	1.34536i
$159$		0			0
$160$	−1.80816	+	12.5192i	−0.142948	+	0.989730i
$161$		−	6.58835i		−	0.519235i
$162$		0			0
$163$	−7.61573	−	7.61573i	−0.596510	−	0.596510i	0.342872	−	0.939382i	$-0.388600\pi$
$163$	−7.61573	−	7.61573i	−0.596510	−	0.596510i	−0.939382	+	0.342872i	$0.888600\pi$
$164$	−4.96754	+	1.51937i	−0.387899	+	0.118643i
$165$		0			0
$166$	−1.10052	+	1.48745i	−0.0854169	+	0.115449i
$167$	−2.33425			−0.180629			−0.0903147	−	0.995913i	$-0.528787\pi$
$167$	−2.33425			−0.180629			−0.0903147	+	0.995913i	$0.528787\pi$
$168$		0			0
$169$		−	24.5262i		−	1.88663i
$170$	13.6967	−	15.0885i	1.05049	−	1.15723i
$171$		0			0
$172$	10.1125	−	19.0243i	0.771072	−	1.45059i
$173$	−0.625160	−	0.625160i	−0.0475300	−	0.0475300i	0.682942	−	0.730472i	$-0.260700\pi$
$173$	−0.625160	−	0.625160i	−0.0475300	−	0.0475300i	−0.730472	+	0.682942i	$0.760700\pi$
$174$		0			0
$175$	18.6482	+	3.78406i	1.40967	+	0.286048i
$176$	−0.820818	+	4.22805i	−0.0618715	+	0.318701i
$177$		0			0
$178$	18.5878	−	2.77908i	1.39321	−	0.208301i
$179$	4.33232	+	4.33232i	0.323813	+	0.323813i	0.850228	−	0.526415i	$-0.176464\pi$
$179$	4.33232	+	4.33232i	0.323813	+	0.323813i	−0.526415	+	0.850228i	$0.676464\pi$
$180$		0			0
$181$	0.834317	−	0.834317i	0.0620143	−	0.0620143i	−0.675419	−	0.737434i	$-0.736037\pi$
$181$	0.834317	−	0.834317i	0.0620143	−	0.0620143i	0.737434	+	0.675419i	$0.236037\pi$
$182$	26.5039	+	19.6094i	1.96460	+	1.45355i
$183$		0			0
$184$	4.41920	−	2.10881i	0.325788	−	0.155464i
$185$	−5.17418	−	0.519672i	−0.380413	−	0.0382071i
$186$		0			0
$187$	4.90637	−	4.90637i	0.358789	−	0.358789i
$188$	3.00732	+	9.83238i	0.219332	+	0.717100i
$189$		0			0
$190$	−0.643614	−	13.3117i	−0.0466927	−	0.965733i
$191$	−18.1527			−1.31349			−0.656743	−	0.754114i	$-0.728066\pi$
$191$	−18.1527			−1.31349			−0.656743	+	0.754114i	$0.728066\pi$
$192$		0			0
$193$		−	15.2659i		−	1.09886i	−0.835538	−	0.549432i	$-0.814844\pi$
$193$		−	15.2659i		−	1.09886i	0.835538	−	0.549432i	$-0.185156\pi$
$194$	−1.99947	−	13.3734i	−0.143553	−	0.960151i
$195$		0			0
$196$	−14.3115	+	4.37732i	−1.02225	+	0.312665i
$197$	−0.287217	+	0.287217i	−0.0204633	+	0.0204633i	−0.717264	−	0.696801i	$-0.754606\pi$
$197$	−0.287217	+	0.287217i	−0.0204633	+	0.0204633i	0.696801	+	0.717264i	$0.254606\pi$
$198$		0			0
$199$	15.9569			1.13115			0.565576	−	0.824696i	$-0.308654\pi$
$199$	15.9569			1.13115			0.565576	+	0.824696i	$0.308654\pi$
$200$	3.43075	+	13.7197i	0.242591	+	0.970129i
$201$		0			0
$202$	−18.8679	−	13.9598i	−1.32754	−	0.982210i
$203$	1.10174	+	1.10174i	0.0773269	+	0.0773269i
$204$		0			0
$205$	−4.49661	+	3.67581i	−0.314057	+	0.256730i
$206$	2.03361	+	13.6018i	0.141689	+	0.947680i
$207$		0			0
$208$	−4.66982	+	24.0544i	−0.323794	+	1.66787i
$209$		−	4.53790i		−	0.313893i
$210$		0			0
$211$	−15.7303	+	15.7303i	−1.08292	+	1.08292i	−0.0866837	+	0.996236i	$0.527627\pi$
$211$	−15.7303	+	15.7303i	−1.08292	+	1.08292i	−0.996236	+	0.0866837i	$0.972373\pi$
$212$	6.77528	−	12.7461i	0.465328	−	0.875403i
$213$		0			0
$214$	−13.1153	−	9.70358i	−0.896540	−	0.663323i
$215$	2.40718	−	23.9674i	0.164169	−	1.63457i
$216$		0			0
$217$	−14.8353			−1.00709
$218$	−14.0300	−	10.3804i	−0.950235	−	0.703050i
$219$		0			0
$220$	0.941197	+	4.72248i	0.0634555	+	0.318390i
$221$	27.9135	−	27.9135i	1.87766	−	1.87766i
$222$		0			0
$223$	12.4886			0.836301			0.418150	−	0.908378i	$-0.362678\pi$
$223$	12.4886			0.836301			0.418150	+	0.908378i	$0.362678\pi$
$224$	−14.5488	−	15.8678i	−0.972082	−	1.06022i
$225$		0			0
$226$	−22.7665	+	3.40384i	−1.51440	+	0.226420i
$227$	−20.1265	+	20.1265i	−1.33584	+	1.33584i	−0.435800	+	0.900043i	$0.643535\pi$
$227$	−20.1265	+	20.1265i	−1.33584	+	1.33584i	−0.900043	+	0.435800i	$0.856465\pi$
$228$		0			0
$229$	5.05312	−	5.05312i	0.333920	−	0.333920i	−0.520153	−	0.854073i	$-0.674125\pi$
$229$	5.05312	−	5.05312i	0.333920	−	0.333920i	0.854073	+	0.520153i	$0.174125\pi$
$230$	3.67962	−	4.05351i	0.242627	−	0.267281i
$231$		0			0
$232$	−0.386356	+	1.09165i	−0.0253655	+	0.0716702i
$233$		−	12.6841i		−	0.830960i	−0.909602	−	0.415480i	$-0.863614\pi$
$233$		−	12.6841i		−	0.830960i	0.909602	−	0.415480i	$-0.136386\pi$
$234$		0			0
$235$	7.27563	+	8.90027i	0.474610	+	0.580589i
$236$	−7.54569	+	14.1954i	−0.491182	+	0.924042i
$237$		0			0
$238$	5.12836	+	34.3009i	0.332422	+	2.22339i
$239$	5.00305			0.323621			0.161810	−	0.986822i	$-0.448267\pi$
$239$	5.00305			0.323621			0.161810	+	0.986822i	$0.448267\pi$
$240$		0			0
$241$	−9.34398			−0.601898			−0.300949	−	0.953640i	$-0.597303\pi$
$241$	−9.34398			−0.601898			−0.300949	+	0.953640i	$0.597303\pi$
$242$	−2.05783	−	13.7637i	−0.132283	−	0.884767i
$243$		0			0
$244$	−1.61663	−	0.859333i	−0.103494	−	0.0550132i
$245$	−12.9548	+	10.5901i	−0.827652	+	0.676574i
$246$		0			0
$247$		−	25.8172i		−	1.64271i
$248$	−4.74851	−	9.95093i	−0.301531	−	0.631885i
$249$		0			0
$250$	9.35998	+	12.7433i	0.591977	+	0.805955i
$251$	−11.8770	+	11.8770i	−0.749672	+	0.749672i	−0.974418	−	0.224745i	$-0.927845\pi$
$251$	−11.8770	+	11.8770i	−0.749672	+	0.749672i	0.224745	+	0.974418i	$0.427845\pi$
$252$		0			0
$253$	1.31809	−	1.31809i	0.0828678	−	0.0828678i
$254$	−12.0464	+	1.80107i	−0.755859	+	0.113009i
$255$		0			0
$256$	5.98673	−	14.8378i	0.374170	−	0.927360i
$257$	4.63622			0.289199			0.144600	−	0.989490i	$-0.453811\pi$
$257$	4.63622			0.289199			0.144600	+	0.989490i	$0.453811\pi$
$258$		0			0
$259$	6.25821	−	6.25821i	0.388866	−	0.388866i
$260$	5.35469	+	26.8673i	0.332084	+	1.66624i
$261$		0			0
$262$	−11.4104	−	8.44219i	−0.704935	−	0.521560i
$263$	11.6055			0.715624			0.357812	−	0.933794i	$-0.383523\pi$
$263$	11.6055			0.715624			0.357812	+	0.933794i	$0.383523\pi$
$264$		0			0
$265$	1.61279	−	16.0579i	0.0990728	−	0.986430i
$266$	18.2340	+	13.4908i	1.11800	+	0.827175i
$267$		0			0
$268$	22.7104	+	12.0719i	1.38726	+	0.737410i
$269$	9.90154	−	9.90154i	0.603708	−	0.603708i	−0.337587	−	0.941294i	$-0.609611\pi$
$269$	9.90154	−	9.90154i	0.603708	−	0.603708i	0.941294	+	0.337587i	$0.109611\pi$
$270$		0			0
$271$		−	3.50755i		−	0.213068i	−0.994309	−	0.106534i	$-0.966025\pi$
$271$		−	3.50755i		−	0.213068i	0.994309	−	0.106534i	$-0.0339753\pi$
$272$	−21.3662	+	14.4190i	−1.29551	+	0.874279i
$273$		0			0
$274$	1.94600	+	13.0158i	0.117562	+	0.786310i
$275$	2.97379	+	4.48790i	0.179326	+	0.270630i
$276$		0			0
$277$	5.62344	+	5.62344i	0.337880	+	0.337880i	0.855569	−	0.517689i	$-0.173208\pi$
$277$	5.62344	+	5.62344i	0.337880	+	0.337880i	−0.517689	+	0.855569i	$0.673208\pi$
$278$	−14.7326	−	10.9002i	−0.883601	−	0.653750i
$279$		0			0
$280$	−21.7738	−	10.2577i	−1.30124	−	0.613014i
$281$	−24.9686			−1.48950			−0.744752	−	0.667341i	$-0.767432\pi$
$281$	−24.9686			−1.48950			−0.744752	+	0.667341i	$0.767432\pi$
$282$		0			0
$283$	−18.5071	+	18.5071i	−1.10014	+	1.10014i	−0.105742	+	0.994394i	$0.533722\pi$
$283$	−18.5071	+	18.5071i	−1.10014	+	1.10014i	−0.994394	+	0.105742i	$0.966278\pi$
$284$	5.14621	+	16.8254i	0.305371	+	0.998405i
$285$		0			0
$286$	1.37933	+	9.22562i	0.0815617	+	0.545523i
$287$		−	9.88461i		−	0.583470i
$288$		0			0
$289$	24.5262			1.44272
$290$	0.0625243	+	1.29317i	0.00367155	+	0.0759378i
$291$		0			0
$292$	−23.2031	+	7.09688i	−1.35786	+	0.415314i
$293$	3.44258	−	3.44258i	0.201118	−	0.201118i	−0.599361	−	0.800479i	$-0.704579\pi$
$293$	3.44258	−	3.44258i	0.201118	−	0.201118i	0.800479	+	0.599361i	$0.204579\pi$
$294$		0			0
$295$	−1.79618	+	17.8839i	−0.104577	+	1.04124i
$296$	6.20090	+	2.19462i	0.360420	+	0.127560i
$297$		0			0
$298$	−0.625552	−	0.462827i	−0.0362372	−	0.0268108i
$299$	7.49894	−	7.49894i	0.433675	−	0.433675i
$300$		0			0
$301$	28.9888	+	28.9888i	1.67089	+	1.67089i
$302$	−17.6012	+	2.63158i	−1.01284	+	0.151430i
$303$		0			0
$304$	−3.21273	+	16.5488i	−0.184263	+	0.949141i
$305$	−2.03668	−	0.204556i	−0.116620	−	0.0117128i
$306$		0			0
$307$	13.4561	+	13.4561i	0.767977	+	0.767977i	0.977750	−	0.209773i	$-0.0672724\pi$
$307$	13.4561	+	13.4561i	0.767977	+	0.767977i	−0.209773	+	0.977750i	$0.567272\pi$
$308$	−7.23661	−	3.84668i	−0.412344	−	0.219185i
$309$		0			0
$310$	−9.12749	−	8.28557i	−0.518406	−	0.470589i
$311$		−	10.6693i		−	0.604999i	−0.953150	−	0.302500i	$-0.902179\pi$
$311$		−	10.6693i		−	0.604999i	0.953150	−	0.302500i	$-0.0978211\pi$
$312$		0			0
$313$	−10.3187			−0.583250			−0.291625	−	0.956533i	$-0.594196\pi$
$313$	−10.3187			−0.583250			−0.291625	+	0.956533i	$0.594196\pi$
$314$	0.472749	−	0.638963i	0.0266788	−	0.0360587i
$315$		0			0
$316$	−7.07268	−	23.1240i	−0.397869	−	1.30082i
$317$	15.8698	+	15.8698i	0.891336	+	0.891336i	0.994649	−	0.103313i	$-0.0329444\pi$
$317$	15.8698	+	15.8698i	0.891336	+	0.891336i	−0.103313	+	0.994649i	$0.532944\pi$
$318$		0			0
$319$			0.440837i			0.0246821i
$320$	−0.0889531	−	17.8883i	−0.00497263	−	0.999988i
$321$		0			0
$322$	1.37773	+	9.21491i	0.0767780	+	0.513527i
$323$	19.2038	−	19.2038i	1.06853	−	1.06853i
$324$		0			0
$325$	16.9186	+	25.5327i	0.938473	+	1.41630i
$326$	12.2444	+	9.05929i	0.678157	+	0.501748i
$327$		0			0
$328$	6.63021	−	3.16388i	0.366092	−	0.174696i
$329$	−19.5649			−1.07865
$330$		0			0
$331$	−9.80202	−	9.80202i	−0.538768	−	0.538768i	0.384399	−	0.923167i	$-0.374409\pi$
$331$	−9.80202	−	9.80202i	−0.538768	−	0.538768i	−0.923167	+	0.384399i	$0.874409\pi$
$332$	1.22821	−	2.31058i	0.0674068	−	0.126810i
$333$		0			0
$334$	3.26484	−	0.488129i	0.178644	−	0.0267092i
$335$	28.6114	+	2.87360i	1.56321	+	0.157002i
$336$		0			0
$337$			13.6823i			0.745323i	0.927967	+	0.372662i	$0.121555\pi$
$337$			13.6823i			0.745323i	−0.927967	+	0.372662i	$0.878445\pi$
$338$	5.12884	+	34.3040i	0.278972	+	1.86589i
$339$		0			0
$340$	−16.0019	+	23.9680i	−0.867826	+	1.29985i
$341$	−2.96801	−	2.96801i	−0.160727	−	0.160727i
$342$		0			0
$343$		−	1.83811i		−	0.0992487i
$344$	−10.1658	+	28.7233i	−0.548101	+	1.54866i
$345$		0			0
$346$	1.00512	+	0.743660i	0.0540357	+	0.0399794i
$347$	−15.5812	−	15.5812i	−0.836445	−	0.836445i	0.151944	−	0.988389i	$-0.451447\pi$
$347$	−15.5812	−	15.5812i	−0.836445	−	0.836445i	−0.988389	+	0.151944i	$0.951447\pi$
$348$		0			0
$349$	−4.64370	−	4.64370i	−0.248572	−	0.248572i	0.571813	−	0.820384i	$-0.306240\pi$
$349$	−4.64370	−	4.64370i	−0.248572	−	0.248572i	−0.820384	+	0.571813i	$0.806240\pi$
$350$	−26.8740	−	1.39300i	−1.43647	−	0.0744589i
$351$		0			0
$352$	0.263896	−	6.08528i	0.0140657	−	0.324347i
$353$	−19.8254			−1.05520			−0.527601	−	0.849492i	$-0.676908\pi$
$353$	−19.8254			−1.05520			−0.527601	+	0.849492i	$0.676908\pi$
$354$		0			0
$355$	12.4502	+	15.2304i	0.660790	+	0.808344i
$356$	−25.4169	+	7.77401i	−1.34710	+	0.412022i
$357$		0			0
$358$	−6.96543	−	5.15352i	−0.368135	−	0.272372i
$359$		−	20.1443i		−	1.06318i	−0.847003	−	0.531589i	$-0.821595\pi$
$359$		−	20.1443i		−	1.06318i	0.847003	−	0.531589i	$-0.178405\pi$
$360$		0			0
$361$			1.23840i			0.0651788i
$362$	−0.992463	+	1.34140i	−0.0521627	+	0.0705025i
$363$		0			0
$364$	−41.1707	−	21.8847i	−2.15793	−	1.14707i
$365$	−21.0034	+	17.1695i	−1.09937	+	0.898694i
$366$		0			0
$367$	−36.1117			−1.88502			−0.942508	−	0.334183i	$-0.891540\pi$
$367$	−36.1117			−1.88502			−0.942508	+	0.334183i	$0.891540\pi$
$368$	−5.74001	+	3.87365i	−0.299219	+	0.201928i
$369$		0			0
$370$	7.34563	−	0.355157i	0.381881	−	0.0184637i
$371$	19.4222	+	19.4222i	1.00835	+	1.00835i
$372$		0			0
$373$	−1.62188	−	1.62188i	−0.0839777	−	0.0839777i	0.663870	−	0.747848i	$-0.268913\pi$
$373$	−1.62188	−	1.62188i	−0.0839777	−	0.0839777i	−0.747848	+	0.663870i	$0.768913\pi$
$374$	−5.83637	+	7.88838i	−0.301792	+	0.407898i
$375$		0			0
$376$	−6.26236	−	13.1233i	−0.322956	−	0.676785i
$377$			2.50802i			0.129170i
$378$		0			0
$379$	−10.9432	−	10.9432i	−0.562115	−	0.562115i	0.367793	−	0.929908i	$-0.380114\pi$
$379$	−10.9432	−	10.9432i	−0.562115	−	0.562115i	−0.929908	+	0.367793i	$0.880114\pi$
$380$	3.68390	+	18.4841i	0.188980	+	0.948213i
$381$		0			0
$382$	25.3896	−	3.79603i	1.29905	−	0.194222i
$383$			31.2822i			1.59845i	0.601035	+	0.799223i	$0.294755\pi$
$383$			31.2822i			1.59845i	−0.601035	+	0.799223i	$0.705245\pi$
$384$		0			0
$385$	−9.11693	−	0.915665i	−0.464642	−	0.0466666i
$386$	3.19235	+	21.3519i	0.162486	+	1.08678i
$387$		0			0
$388$	5.59317	+	18.2868i	0.283950	+	0.928369i
$389$	−4.10132	−	4.10132i	−0.207945	−	0.207945i	0.595448	−	0.803394i	$-0.296974\pi$
$389$	−4.10132	−	4.10132i	−0.207945	−	0.207945i	−0.803394	+	0.595448i	$0.796974\pi$
$390$		0			0
$391$	11.1560			0.564183
$392$	19.1017	−	9.11518i	0.964782	−	0.460386i
$393$		0			0
$394$	0.341659	−	0.461782i	0.0172125	−	0.0232643i
$395$	−17.1110	−	20.9318i	−0.860946	−	1.05319i
$396$		0			0
$397$	22.7531	−	22.7531i	1.14194	−	1.14194i	0.153849	−	0.988094i	$-0.450833\pi$
$397$	22.7531	−	22.7531i	1.14194	−	1.14194i	0.988094	−	0.153849i	$-0.0491670\pi$
$398$	−22.3183	+	3.33684i	−1.11872	+	0.167261i
$399$		0			0
$400$	−7.66749	−	18.4719i	−0.383375	−	0.923593i
$401$		−	21.2428i		−	1.06082i	−0.847743	−	0.530408i	$-0.822039\pi$
$401$		−	21.2428i		−	1.06082i	0.847743	−	0.530408i	$-0.177961\pi$
$402$		0			0
$403$	−16.8857	−	16.8857i	−0.841138	−	0.841138i
$404$	29.3092	+	15.5796i	1.45819	+	0.775112i
$405$		0			0
$406$	−1.77136	−	1.31057i	−0.0879110	−	0.0650427i
$407$	2.50409			0.124123
$408$		0			0
$409$			3.41459i			0.168841i	0.996430	+	0.0844204i	$0.0269039\pi$
$409$			3.41459i			0.168841i	−0.996430	+	0.0844204i	$0.973096\pi$
$410$	5.52060	−	6.08155i	0.272643	−	0.300346i
$411$		0			0
$412$	−5.68870	−	18.5991i	−0.280262	−	0.916311i
$413$	−21.6307	−	21.6307i	−1.06438	−	1.06438i
$414$		0			0
$415$	0.292364	−	2.91095i	0.0143516	−	0.142893i
$416$	1.50137	−	34.6206i	0.0736106	−	1.69741i
$417$		0			0
$418$	0.948949	+	6.34701i	0.0464146	+	0.310443i
$419$	−2.45392	−	2.45392i	−0.119882	−	0.119882i	0.644621	−	0.764503i	$-0.277015\pi$
$419$	−2.45392	−	2.45392i	−0.119882	−	0.119882i	−0.764503	+	0.644621i	$0.777015\pi$
$420$		0			0
$421$	16.7130	−	16.7130i	0.814540	−	0.814540i	−0.170770	−	0.985311i	$-0.554626\pi$
$421$	16.7130	−	16.7130i	0.814540	−	0.814540i	0.985311	+	0.170770i	$0.0546257\pi$
$422$	18.7120	−	25.2909i	0.910887	−	1.23114i
$423$		0			0
$424$	−6.81095	+	19.2443i	−0.330769	+	0.934587i
$425$	−6.40752	+	31.5769i	−0.310811	+	1.53170i
$426$		0			0
$427$	2.46339	−	2.46339i	0.119212	−	0.119212i
$428$	20.3731	+	10.8295i	0.984769	+	0.523462i
$429$		0			0
$430$	1.64513	+	34.0258i	0.0793352	+	1.64087i
$431$	−20.7930			−1.00156			−0.500782	−	0.865573i	$-0.666954\pi$
$431$	−20.7930			−1.00156			−0.500782	+	0.865573i	$0.666954\pi$
$432$		0			0
$433$		−	8.98760i		−	0.431916i	−0.976403	−	0.215958i	$-0.930712\pi$
$433$		−	8.98760i		−	0.431916i	0.976403	−	0.215958i	$-0.0692875\pi$
$434$	20.7497	−	3.10230i	0.996015	−	0.148915i
$435$		0			0
$436$	21.7941	+	11.5848i	1.04375	+	0.554813i
$437$	5.15910	−	5.15910i	0.246793	−	0.246793i
$438$		0			0
$439$	18.6849			0.891780			0.445890	−	0.895088i	$-0.352887\pi$
$439$	18.6849			0.891780			0.445890	+	0.895088i	$0.352887\pi$
$440$	−2.30397	−	6.40836i	−0.109837	−	0.305507i
$441$		0			0
$442$	−33.2045	+	44.8788i	−1.57938	+	2.13467i
$443$	−1.69635	−	1.69635i	−0.0805958	−	0.0805958i	0.665660	−	0.746255i	$-0.268150\pi$
$443$	−1.69635	−	1.69635i	−0.0805958	−	0.0805958i	−0.746255	+	0.665660i	$0.768150\pi$
$444$		0			0
$445$	−23.0074	+	18.8077i	−1.09066	+	0.891570i
$446$	−17.4674	+	2.61158i	−0.827108	+	0.123662i
$447$		0			0
$448$	23.6671	+	19.1515i	1.11817	+	0.904821i
$449$			20.9833i			0.990264i	0.868818	+	0.495132i	$0.164880\pi$
$449$			20.9833i			0.990264i	−0.868818	+	0.495132i	$0.835120\pi$
$450$		0			0
$451$	1.97756	−	1.97756i	0.0931196	−	0.0931196i
$452$	31.1309	−	9.52169i	1.46428	−	0.447863i
$453$		0			0
$454$	23.9415	−	32.3591i	1.12363	−	1.51869i
$455$	−51.8683	−	5.20943i	−2.43162	−	0.244222i
$456$		0			0
$457$	−0.679238			−0.0317734			−0.0158867	−	0.999874i	$-0.505057\pi$
$457$	−0.679238			−0.0317734			−0.0158867	+	0.999874i	$0.505057\pi$
$458$	−6.01094	+	8.12432i	−0.280873	+	0.379625i
$459$		0			0
$460$	−4.29891	+	6.43898i	−0.200438	+	0.300219i
$461$	30.3013	−	30.3013i	1.41127	−	1.41127i	0.660048	−	0.751223i	$-0.270536\pi$
$461$	30.3013	−	30.3013i	1.41127	−	1.41127i	0.751223	−	0.660048i	$-0.229464\pi$
$462$		0			0
$463$	−40.6442			−1.88889			−0.944447	−	0.328664i	$-0.893402\pi$
$463$	−40.6442			−1.88889			−0.944447	+	0.328664i	$0.893402\pi$
$464$	0.312102	−	1.60765i	0.0144890	−	0.0746331i
$465$		0			0
$466$	2.65244	+	17.7408i	0.122872	+	0.821825i
$467$	20.4572	−	20.4572i	0.946646	−	0.946646i	−0.0520011	−	0.998647i	$-0.516560\pi$
$467$	20.4572	−	20.4572i	0.946646	−	0.946646i	0.998647	+	0.0520011i	$0.0165599\pi$
$468$		0			0
$469$	−34.6057	+	34.6057i	−1.59794	+	1.59794i
$470$	−12.0374	−	10.9271i	−0.555243	−	0.504028i
$471$		0			0
$472$	7.58542	−	21.4326i	0.349147	−	0.986514i
$473$			11.5992i			0.533334i
$474$		0			0
$475$	11.6396	+	17.5659i	0.534060	+	0.805978i
$476$	−14.3457	−	46.9031i	−0.657536	−	2.14980i
$477$		0			0
$478$	−6.99760	+	1.04622i	−0.320063	+	0.0478530i
$479$	−20.9399			−0.956768			−0.478384	−	0.878151i	$-0.658777\pi$
$479$	−20.9399			−0.956768			−0.478384	+	0.878151i	$0.658777\pi$
$480$		0			0
$481$	14.2463			0.649577
$482$	13.0691	−	1.95398i	0.595282	−	0.0890013i
$483$		0			0
$484$	5.75645	+	18.8206i	0.261657	+	0.855481i
$485$	13.5316	+	16.5532i	0.614438	+	0.751641i
$486$		0			0
$487$			27.6996i			1.25519i	0.778540	+	0.627595i	$0.215961\pi$
$487$			27.6996i			1.25519i	−0.778540	+	0.627595i	$0.784039\pi$
$488$	2.44083	+	0.863857i	0.110491	+	0.0391050i
$489$		0			0
$490$	15.9049	−	17.5210i	0.718510	−	0.791519i
$491$	−12.9711	+	12.9711i	−0.585377	+	0.585377i	−0.936376	−	0.350999i	$-0.885842\pi$
$491$	−12.9711	+	12.9711i	−0.585377	+	0.585377i	0.350999	+	0.936376i	$0.385842\pi$
$492$		0			0
$493$	−1.86557	+	1.86557i	−0.0840208	+	0.0840208i
$494$	5.39879	+	36.1096i	0.242903	+	1.62465i
$495$		0			0
$496$	8.72248	+	12.9251i	0.391651	+	0.580352i
$497$	−33.4799			−1.50178
$498$		0			0
$499$	−8.96696	+	8.96696i	−0.401416	+	0.401416i	−0.878732	−	0.477316i	$-0.841610\pi$
$499$	−8.96696	+	8.96696i	−0.401416	+	0.401416i	0.477316	+	0.878732i	$0.341610\pi$
$500$	−15.7563	−	15.8663i	−0.704644	−	0.709561i
$501$		0			0
$502$	14.1283	−	19.0957i	0.630579	−	0.852283i
$503$	9.23509			0.411772			0.205886	−	0.978576i	$-0.433992\pi$
$503$	9.23509			0.411772			0.205886	+	0.978576i	$0.433992\pi$
$504$		0			0
$505$	36.9247	+	3.70856i	1.64313	+	0.165029i
$506$	−1.56794	+	2.11921i	−0.0697034	+	0.0942104i
$507$		0			0
$508$	16.4723	−	5.03820i	0.730839	−	0.223534i
$509$	−0.418802	+	0.418802i	−0.0185631	+	0.0185631i	−0.716327	−	0.697764i	$-0.754178\pi$
$509$	−0.418802	+	0.418802i	−0.0185631	+	0.0185631i	0.697764	+	0.716327i	$0.254178\pi$
$510$		0			0
$511$		−	46.1705i		−	2.04246i
$512$	−5.27062	+	22.0050i	−0.232931	+	0.972493i
$513$		0			0
$514$	−6.48452	+	0.969508i	−0.286020	+	0.0427632i
$515$	−13.7627	−	16.8359i	−0.606457	−	0.741878i
$516$		0			0
$517$	−3.91423	−	3.91423i	−0.172148	−	0.172148i
$518$	−7.44446	+	10.0618i	−0.327091	+	0.442092i
$519$		0			0
$520$	−13.1078	−	36.4587i	−0.574816	−	1.59882i
$521$	31.0344			1.35964			0.679821	−	0.733378i	$-0.262057\pi$
$521$	31.0344			1.35964			0.679821	+	0.733378i	$0.262057\pi$
$522$		0			0
$523$	12.5701	−	12.5701i	0.549653	−	0.549653i	−0.376687	−	0.926340i	$-0.622937\pi$
$523$	12.5701	−	12.5701i	0.549653	−	0.549653i	0.926340	+	0.376687i	$0.122937\pi$
$524$	17.7247	+	9.42172i	0.774307	+	0.411590i
$525$		0			0
$526$	−16.2322	+	2.42689i	−0.707757	+	0.105818i
$527$		−	25.1205i		−	1.09427i
$528$		0			0
$529$	−20.0029			−0.869693
$530$	1.10222	+	22.7970i	0.0478774	+	0.990236i
$531$		0			0
$532$	−28.3245	−	15.0561i	−1.22802	−	0.652766i
$533$	11.2508	−	11.2508i	0.487326	−	0.487326i
$534$		0			0
$535$	25.6667	+	2.57785i	1.10967	+	0.111450i
$536$	−34.2887	−	12.1355i	−1.48105	−	0.524173i
$537$		0			0
$538$	−11.7784	+	15.9195i	−0.507802	+	0.686340i
$539$	5.69737	−	5.69737i	0.245403	−	0.245403i
$540$		0			0
$541$	7.64792	+	7.64792i	0.328810	+	0.328810i	0.852134	−	0.523324i	$-0.175308\pi$
$541$	7.64792	+	7.64792i	0.328810	+	0.328810i	−0.523324	+	0.852134i	$0.675308\pi$
$542$	0.733485	+	4.90589i	0.0315059	+	0.210726i
$543$		0			0
$544$	26.8689	−	24.6354i	1.15200	−	1.05623i
$545$	27.4569	+	2.75766i	1.17613	+	0.118125i
$546$		0			0
$547$	5.50694	+	5.50694i	0.235460	+	0.235460i	0.814967	−	0.579507i	$-0.196755\pi$
$547$	5.50694	+	5.50694i	0.235460	+	0.235460i	−0.579507	+	0.814967i	$0.696755\pi$
$548$	−5.44361	−	17.7978i	−0.232540	−	0.760283i
$549$		0			0
$550$	−5.09783	−	5.65521i	−0.217372	−	0.241139i
$551$			1.72546i			0.0735071i
$552$		0			0
$553$	46.0130			1.95667
$554$	−9.04128	−	6.68937i	−0.384127	−	0.284204i
$555$		0			0
$556$	22.8854	+	12.1649i	0.970556	+	0.515907i
$557$	13.9022	+	13.9022i	0.589056	+	0.589056i	0.937376	−	0.348320i	$-0.113248\pi$
$557$	13.9022	+	13.9022i	0.589056	+	0.589056i	−0.348320	+	0.937376i	$0.613248\pi$
$558$		0			0
$559$			65.9908i			2.79111i
$560$	32.5994	+	9.79383i	1.37758	+	0.413865i
$561$		0			0
$562$	34.9228	−	5.22135i	1.47313	−	0.220249i
$563$	4.81937	−	4.81937i	0.203112	−	0.203112i	−0.598220	−	0.801332i	$-0.704125\pi$
$563$	4.81937	−	4.81937i	0.203112	−	0.203112i	0.801332	+	0.598220i	$0.204125\pi$
$564$		0			0
$565$	28.1797	−	23.0359i	1.18553	−	0.969126i
$566$	22.0152	−	29.7555i	0.925367	−	1.25072i
$567$		0			0
$568$	−10.7163	−	22.4570i	−0.449646	−	0.942275i
$569$	17.9682			0.753268			0.376634	−	0.926362i	$-0.377081\pi$
$569$	17.9682			0.753268			0.376634	+	0.926362i	$0.377081\pi$
$570$		0			0
$571$	3.94277	+	3.94277i	0.165000	+	0.165000i	0.784777	−	0.619778i	$-0.212777\pi$
$571$	3.94277	+	3.94277i	0.165000	+	0.165000i	−0.619778	+	0.784777i	$0.712777\pi$
$572$	−3.85846	−	12.6151i	−0.161330	−	0.527465i
$573$		0			0
$574$	2.06703	+	13.8253i	0.0862763	+	0.577056i
$575$	−1.72138	+	8.48312i	−0.0717865	+	0.353770i
$576$		0			0
$577$			16.1502i			0.672343i	0.941801	+	0.336172i	$0.109132\pi$
$577$			16.1502i			0.672343i	−0.941801	+	0.336172i	$0.890868\pi$
$578$	−34.3040	+	5.12884i	−1.42686	+	0.213331i
$579$		0			0
$580$	−0.357875	−	1.79565i	−0.0148599	−	0.0745602i
$581$	3.52082	+	3.52082i	0.146068	+	0.146068i
$582$		0			0
$583$			7.77137i			0.321857i
$584$	30.9693	−	14.7783i	1.28152	−	0.611532i
$585$		0			0
$586$	−4.09512	+	5.53492i	−0.169168	+	0.228645i
$587$	17.3882	+	17.3882i	0.717687	+	0.717687i	0.968131	−	0.250444i	$-0.0805767\pi$
$587$	17.3882	+	17.3882i	0.717687	+	0.717687i	−0.250444	+	0.968131i	$0.580577\pi$
$588$		0			0
$589$	−11.6170	−	11.6170i	−0.478669	−	0.478669i
$590$	−1.22755	−	25.3892i	−0.0505375	−	1.04526i
$591$		0			0
$592$	−9.13193	−	1.77284i	−0.375320	−	0.0728632i
$593$	18.7727			0.770904			0.385452	−	0.922728i	$-0.374045\pi$
$593$	18.7727			0.770904			0.385452	+	0.922728i	$0.374045\pi$
$594$		0			0
$595$	−34.7067	−	42.4566i	−1.42284	−	1.74055i
$596$	0.971723	+	0.516528i	0.0398033	+	0.0211578i
$597$		0			0
$598$	−8.92037	+	12.0567i	−0.364781	+	0.493034i
$599$			15.7898i			0.645154i	0.946543	+	0.322577i	$0.104549\pi$
$599$			15.7898i			0.645154i	−0.946543	+	0.322577i	$0.895451\pi$
$600$		0			0
$601$		−	19.1187i		−	0.779868i	−0.920843	−	0.389934i	$-0.872498\pi$
$601$		−	19.1187i		−	0.779868i	0.920843	−	0.389934i	$-0.127502\pi$
$602$	−46.6077	−	34.4836i	−1.89959	−	1.40545i
$603$		0			0
$604$	24.0679	−	7.36140i	0.979310	−	0.299531i
$605$	13.9266	+	17.0364i	0.566197	+	0.692628i
$606$		0			0
$607$	−20.4524			−0.830139			−0.415069	−	0.909790i	$-0.636243\pi$
$607$	−20.4524			−0.830139			−0.415069	+	0.909790i	$0.636243\pi$
$608$	1.03291	−	23.8182i	0.0418899	−	0.965954i
$609$		0			0
$610$	2.89142	−	0.139799i	0.117070	−	0.00566028i
$611$	−22.2690	−	22.2690i	−0.900907	−	0.900907i
$612$		0			0
$613$	−0.158629	−	0.158629i	−0.00640697	−	0.00640697i	0.703896	−	0.710303i	$-0.251442\pi$
$613$	−0.158629	−	0.158629i	−0.00640697	−	0.00640697i	−0.710303	+	0.703896i	$0.751442\pi$
$614$	−21.6344	−	16.0067i	−0.873094	−	0.645976i
$615$		0			0
$616$	10.9260	+	3.86693i	0.440222	+	0.155803i
$617$			28.8981i			1.16340i	0.813405	+	0.581698i	$0.197611\pi$
$617$			28.8981i			1.16340i	−0.813405	+	0.581698i	$0.802389\pi$
$618$		0			0
$619$	−13.3003	−	13.3003i	−0.534582	−	0.534582i	0.387350	−	0.921933i	$-0.373390\pi$
$619$	−13.3003	−	13.3003i	−0.534582	−	0.534582i	−0.921933	+	0.387350i	$0.873390\pi$
$620$	14.4990	+	9.68006i	0.582293	+	0.388760i
$621$		0			0
$622$	2.23112	+	14.9228i	0.0894597	+	0.598348i
$623$		−	50.5757i		−	2.02627i
$624$		0			0
$625$	−23.0226	−	9.74467i	−0.920905	−	0.389787i
$626$	14.4325	−	2.15782i	0.576838	−	0.0862437i
$627$		0			0
$628$	−0.527602	+	0.992556i	−0.0210536	+	0.0396073i
$629$	10.5970	+	10.5970i	0.422529	+	0.422529i
$630$		0			0
$631$	−40.6293			−1.61743			−0.808713	−	0.588203i	$-0.799836\pi$
$631$	−40.6293			−1.61743			−0.808713	+	0.588203i	$0.799836\pi$
$632$	14.7279	+	30.8637i	0.585845	+	1.22769i
$633$		0			0
$634$	−25.5152	−	18.8779i	−1.01334	−	0.749738i
$635$	14.9107	−	12.1889i	0.591713	−	0.483703i
$636$		0			0
$637$	32.4136	−	32.4136i	1.28428	−	1.28428i
$638$	−0.0921862	−	0.616584i	−0.00364969	−	0.0244108i
$639$		0			0
$640$	3.86516	+	25.0012i	0.152784	+	0.988260i
$641$		−	2.75673i		−	0.108884i	−0.998517	−	0.0544422i	$-0.982662\pi$
$641$		−	2.75673i		−	0.108884i	0.998517	−	0.0544422i	$-0.0173380\pi$
$642$		0			0
$643$	−14.9757	−	14.9757i	−0.590582	−	0.590582i	0.347206	−	0.937789i	$-0.387130\pi$
$643$	−14.9757	−	14.9757i	−0.590582	−	0.590582i	−0.937789	+	0.347206i	$0.887130\pi$
$644$	−3.85398	−	12.6005i	−0.151868	−	0.496529i
$645$		0			0
$646$	−22.8439	+	30.8756i	−0.898782	+	1.21478i
$647$	35.4556			1.39390			0.696952	−	0.717117i	$-0.254539\pi$
$647$	35.4556			1.39390			0.696952	+	0.717117i	$0.254539\pi$
$648$		0			0
$649$		−	8.65505i		−	0.339740i
$650$	−29.0027	−	32.1738i	−1.13758	−	1.26196i
$651$		0			0
$652$	−19.0203	−	10.1104i	−0.744894	−	0.395955i
$653$	24.6436	+	24.6436i	0.964380	+	0.964380i	0.999387	−	0.0350074i	$-0.0111455\pi$
$653$	24.6436	+	24.6436i	0.964380	+	0.964380i	−0.0350074	+	0.999387i	$0.511145\pi$
$654$		0			0
$655$	22.3302	+	2.24275i	0.872513	+	0.0876314i
$656$	−8.61184	+	5.81170i	−0.336236	+	0.226909i
$657$		0			0
$658$	27.3648	−	4.09133i	1.06679	−	0.159497i
$659$	27.1141	+	27.1141i	1.05621	+	1.05621i	0.998323	+	0.0578905i	$0.0184374\pi$
$659$	27.1141	+	27.1141i	1.05621	+	1.05621i	0.0578905	+	0.998323i	$0.481563\pi$
$660$		0			0
$661$	−20.5120	+	20.5120i	−0.797822	+	0.797822i	−0.982752	−	0.184929i	$-0.940794\pi$
$661$	−20.5120	+	20.5120i	−0.797822	+	0.797822i	0.184929	+	0.982752i	$0.440794\pi$
$662$	15.7595	+	11.6600i	0.612512	+	0.453179i
$663$		0			0
$664$	−1.23468	+	3.48858i	−0.0479148	+	0.135383i
$665$	−35.6842	−	3.58396i	−1.38377	−	0.138980i
$666$		0			0
$667$	−0.501183	+	0.501183i	−0.0194059	+	0.0194059i
$668$	−4.46434	+	1.36546i	−0.172731	+	0.0528313i
$669$		0			0
$670$	−40.6187	+	1.96389i	−1.56924	+	0.0758717i
$671$	0.985671			0.0380514
$672$		0			0
$673$		−	27.8896i		−	1.07506i	−0.843243	−	0.537532i	$-0.819357\pi$
$673$		−	27.8896i		−	1.07506i	0.843243	−	0.537532i	$-0.180643\pi$
$674$	−2.86120	−	19.1370i	−0.110209	−	0.737130i
$675$		0			0
$676$	−14.3471	−	46.9074i	−0.551810	−	1.80413i
$677$	−1.09939	+	1.09939i	−0.0422530	+	0.0422530i	−0.727918	−	0.685665i	$-0.759512\pi$
$677$	−1.09939	+	1.09939i	−0.0422530	+	0.0422530i	0.685665	+	0.727918i	$0.259512\pi$
$678$		0			0
$679$	−36.3877			−1.39643
$680$	17.3693	−	36.8695i	0.666081	−	1.41388i
$681$		0			0
$682$	4.77193	+	3.53060i	0.182726	+	0.135194i
$683$	16.3630	+	16.3630i	0.626115	+	0.626115i	0.947088	−	0.320974i	$-0.104010\pi$
$683$	16.3630	+	16.3630i	0.626115	+	0.626115i	−0.320974	+	0.947088i	$0.604010\pi$
$684$		0			0
$685$	−13.1698	−	16.1105i	−0.503190	−	0.615552i
$686$	0.384379	+	2.57091i	0.0146757	+	0.0981577i
$687$		0			0
$688$	8.21200	−	42.3002i	0.313079	−	1.61268i
$689$			44.2131i			1.68439i
$690$		0			0
$691$	−1.38110	+	1.38110i	−0.0525396	+	0.0525396i	−0.732888	−	0.680349i	$-0.761828\pi$
$691$	−1.38110	+	1.38110i	−0.0525396	+	0.0525396i	0.680349	+	0.732888i	$0.261828\pi$
$692$	−1.56134	−	0.829945i	−0.0593534	−	0.0315498i
$693$		0			0
$694$	25.0513	+	18.5347i	0.950934	+	0.703567i
$695$	28.8318	+	2.89574i	1.09365	+	0.109842i
$696$		0			0
$697$	16.7375			0.633980
$698$	7.46607	+	5.52392i	0.282595	+	0.209084i
$699$		0			0
$700$	37.8790	−	3.67144i	1.43169	−	0.138767i
$701$	−21.1577	+	21.1577i	−0.799115	+	0.799115i	−0.982956	−	0.183841i	$-0.941147\pi$
$701$	−21.1577	+	21.1577i	−0.799115	+	0.799115i	0.183841	+	0.982956i	$0.441147\pi$
$702$		0			0
$703$	9.80115			0.369657
$704$	0.903429	+	8.56647i	0.0340493	+	0.322861i
$705$		0			0
$706$	27.7292	−	4.14582i	1.04360	−	0.156030i
$707$	−44.6608	+	44.6608i	−1.67964	+	1.67964i
$708$		0			0
$709$	3.59943	−	3.59943i	0.135180	−	0.135180i	−0.636279	−	0.771459i	$-0.719527\pi$
$709$	3.59943	−	3.59943i	0.135180	−	0.135180i	0.771459	+	0.636279i	$0.219527\pi$
$710$	−20.5987	−	18.6987i	−0.773054	−	0.701748i
$711$		0			0
$712$	33.9242	−	16.1884i	1.27136	−	0.606684i
$713$		−	6.74861i		−	0.252738i
$714$		0			0
$715$	−9.33478	−	11.4192i	−0.349101	−	0.427055i
$716$	10.8200	+	5.75147i	0.404363	+	0.214942i
$717$		0			0
$718$	4.21251	+	28.1752i	0.157209	+	1.05149i
$719$	24.6502			0.919298			0.459649	−	0.888101i	$-0.347975\pi$
$719$	24.6502			0.919298			0.459649	+	0.888101i	$0.347975\pi$
$720$		0			0
$721$	37.0092			1.37830
$722$	−0.258969	−	1.73211i	−0.00963784	−	0.0644623i
$723$		0			0
$724$	1.10762	−	2.08371i	0.0411642	−	0.0774406i
$725$	−1.13073	−	1.70645i	−0.0419944	−	0.0633759i
$726$		0			0
$727$		−	47.1505i		−	1.74872i	−0.485281	−	0.874358i	$-0.661283\pi$
$727$		−	47.1505i		−	1.74872i	0.485281	−	0.874358i	$-0.338717\pi$
$728$	62.1606	+	21.9999i	2.30383	+	0.815370i
$729$		0			0
$730$	25.7864	−	28.4066i	0.954398	−	1.05138i
$731$	−49.0865	+	49.0865i	−1.81553	+	1.81553i
$732$		0			0
$733$	12.4236	−	12.4236i	0.458875	−	0.458875i	−0.439411	−	0.898286i	$-0.644813\pi$
$733$	12.4236	−	12.4236i	0.458875	−	0.458875i	0.898286	+	0.439411i	$0.144813\pi$
$734$	50.5083	−	7.55155i	1.86429	−	0.278733i
$735$		0			0
$736$	7.21832	−	6.61828i	0.266071	−	0.243953i
$737$	−13.8467			−0.510050
$738$		0			0
$739$	−10.3865	+	10.3865i	−0.382075	+	0.382075i	−0.871849	−	0.489774i	$-0.837079\pi$
$739$	−10.3865	+	10.3865i	−0.382075	+	0.382075i	0.489774	+	0.871849i	$0.337079\pi$
$740$	−10.1998	+	2.03284i	−0.374953	+	0.0747286i
$741$		0			0
$742$	−31.2267	−	23.1037i	−1.14637	−	0.848163i
$743$	−34.4041			−1.26216			−0.631082	−	0.775716i	$-0.717389\pi$
$743$	−34.4041			−1.26216			−0.631082	+	0.775716i	$0.717389\pi$
$744$		0			0
$745$	1.22421	+	0.122954i	0.0448516	+	0.00450470i
$746$	2.60763	+	1.92931i	0.0954721	+	0.0706370i
$747$		0			0
$748$	6.51356	−	12.2537i	0.238159	−	0.448040i
$749$	−31.0440	+	31.0440i	−1.13432	+	1.13432i
$750$		0			0
$751$			6.29639i			0.229759i	0.993379	+	0.114879i	$0.0366481\pi$
$751$			6.29639i			0.229759i	−0.993379	+	0.114879i	$0.963352\pi$
$752$	11.5033	+	17.0456i	0.419481	+	0.621590i
$753$		0			0
$754$	−0.524469	−	3.50789i	−0.0191000	−	0.127750i
$755$	21.7863	−	17.8095i	0.792884	−	0.648153i
$756$		0			0
$757$	−13.9886	−	13.9886i	−0.508425	−	0.508425i	0.405618	−	0.914043i	$-0.367056\pi$
$757$	−13.9886	−	13.9886i	−0.508425	−	0.508425i	−0.914043	+	0.405618i	$0.867056\pi$
$758$	17.5943	+	13.0175i	0.639054	+	0.472817i
$759$		0			0
$760$	−9.01787	−	25.0827i	−0.327113	−	0.909845i
$761$	45.7177			1.65726			0.828632	−	0.559793i	$-0.189119\pi$
$761$	45.7177			1.65726			0.828632	+	0.559793i	$0.189119\pi$
$762$		0			0
$763$	−33.2094	+	33.2094i	−1.20226	+	1.20226i
$764$	−34.7179	+	10.6188i	−1.25605	+	0.384174i
$765$		0			0
$766$	−6.54162	−	43.7534i	−0.236358	−	1.58087i
$767$		−	49.2406i		−	1.77797i
$768$		0			0
$769$	−34.9628			−1.26079			−0.630395	−	0.776274i	$-0.717107\pi$
$769$	−34.9628			−1.26079			−0.630395	+	0.776274i	$0.717107\pi$
$770$	12.9430	−	0.625788i	0.466434	−	0.0225518i
$771$		0			0
$772$	−8.93007	−	29.1967i	−0.321400	−	1.05081i
$773$	−30.9289	+	30.9289i	−1.11243	+	1.11243i	−0.119614	+	0.992820i	$0.538166\pi$
$773$	−30.9289	+	30.9289i	−1.11243	+	1.11243i	−0.992820	+	0.119614i	$0.961834\pi$
$774$		0			0
$775$	19.1018	+	3.87611i	0.686158	+	0.139234i
$776$	−11.6470	−	24.4075i	−0.418105	−	0.876177i
$777$		0			0
$778$	6.59404	+	4.87873i	0.236408	+	0.174911i
$779$	7.74028	−	7.74028i	0.277324	−	0.277324i
$780$		0			0
$781$	−6.69814	−	6.69814i	−0.239678	−	0.239678i
$782$	−15.6035	+	2.33290i	−0.557981	+	0.0834244i
$783$		0			0
$784$	−24.8108	+	16.7436i	−0.886100	+	0.597985i
$785$	−0.125590	+	1.25046i	−0.00448251	+	0.0446307i
$786$		0			0
$787$	12.2948	+	12.2948i	0.438261	+	0.438261i	0.891427	−	0.453165i	$-0.149705\pi$
$787$	12.2948	+	12.2948i	0.438261	+	0.438261i	−0.453165	+	0.891427i	$0.649705\pi$
$788$	−0.381301	+	0.717326i	−0.0135833	+	0.0255537i
$789$		0			0
$790$	28.3097	+	25.6985i	1.00721	+	0.914310i
$791$			61.9457i			2.20253i
$792$		0			0
$793$	5.60771			0.199136
$794$	−27.0659	+	36.5820i	−0.960534	+	1.29825i
$795$		0			0
$796$	30.5181	−	9.33426i	1.08169	−	0.330844i
$797$	12.8336	+	12.8336i	0.454588	+	0.454588i	0.896874	−	0.442286i	$-0.145832\pi$
$797$	12.8336	+	12.8336i	0.454588	+	0.454588i	−0.442286	+	0.896874i	$0.645832\pi$
$798$		0			0
$799$		−	33.1291i		−	1.17202i
$800$	14.5870	+	24.2326i	0.515730	+	0.856751i
$801$		0			0
$802$	4.44222	+	29.7116i	0.156860	+	1.04915i
$803$	9.23707	−	9.23707i	0.325969	−	0.325969i
$804$		0			0
$805$	−9.32394	−	11.4060i	−0.328626	−	0.402007i
$806$	27.1486	+	20.0864i	0.956268	+	0.707514i
$807$		0			0
$808$	−44.2518	−	15.6616i	−1.55677	−	0.550973i
$809$	−7.29119			−0.256345			−0.128172	−	0.991752i	$-0.540911\pi$
$809$	−7.29119			−0.256345			−0.128172	+	0.991752i	$0.540911\pi$
$810$		0			0
$811$	−2.59434	−	2.59434i	−0.0910995	−	0.0910995i	0.660088	−	0.751188i	$-0.270519\pi$
$811$	−2.59434	−	2.59434i	−0.0910995	−	0.0910995i	−0.751188	+	0.660088i	$0.770519\pi$
$812$	2.75160	+	1.46264i	0.0965623	+	0.0513285i
$813$		0			0
$814$	−3.50239	+	0.523646i	−0.122759	+	0.0183538i
$815$	−23.9625	−	2.40669i	−0.839369	−	0.0843026i
$816$		0			0
$817$			45.4001i			1.58835i
$818$	−0.714047	−	4.77588i	−0.0249661	−	0.166985i
$819$		0			0
$820$	−6.44972	+	9.66052i	−0.225234	+	0.337360i
$821$	−22.5527	−	22.5527i	−0.787094	−	0.787094i	0.193923	−	0.981017i	$-0.437879\pi$
$821$	−22.5527	−	22.5527i	−0.787094	−	0.787094i	−0.981017	+	0.193923i	$0.937879\pi$
$822$		0			0
$823$			15.9966i			0.557607i	0.960348	+	0.278803i	$0.0899378\pi$
$823$			15.9966i			0.557607i	−0.960348	+	0.278803i	$0.910062\pi$
$824$	11.8460	+	24.8243i	0.412674	+	0.864796i
$825$		0			0
$826$	34.7774	+	25.7308i	1.21006	+	0.895288i
$827$	−2.32558	−	2.32558i	−0.0808683	−	0.0808683i	0.665516	−	0.746384i	$-0.268212\pi$
$827$	−2.32558	−	2.32558i	−0.0808683	−	0.0808683i	−0.746384	+	0.665516i	$0.768212\pi$
$828$		0			0
$829$	−23.0734	−	23.0734i	−0.801371	−	0.801371i	0.181939	−	0.983310i	$-0.441763\pi$
$829$	−23.0734	−	23.0734i	−0.801371	−	0.801371i	−0.983310	+	0.181939i	$0.941763\pi$
$830$	0.199809	+	4.13259i	0.00693546	+	0.143444i
$831$		0			0
$832$	5.13982	+	48.7367i	0.178191	+	1.68964i
$833$	48.2211			1.67076
$834$		0			0
$835$	−4.04112	+	3.30346i	−0.139849	+	0.114321i
$836$	−2.65453	−	8.67892i	−0.0918088	−	0.300167i
$837$		0			0
$838$	3.94537	+	2.91906i	0.136291	+	0.100837i
$839$			51.5599i			1.78005i	0.455916	+	0.890023i	$0.349312\pi$
$839$			51.5599i			1.78005i	−0.455916	+	0.890023i	$0.650688\pi$
$840$		0			0
$841$			28.8324i			0.994220i
$842$	−19.8809	+	26.8708i	−0.685142	+	0.926030i
$843$		0			0
$844$	−20.8831	+	39.2866i	−0.718827	+	1.35230i
$845$	−34.7099	−	42.4606i	−1.19406	−	1.46069i
$846$		0			0
$847$	−37.4500			−1.28680
$848$	5.50195	−	28.3407i	0.188938	−	0.973223i
$849$		0			0
$850$	2.35875	−	45.5055i	0.0809046	−	1.56082i
$851$	2.84687	+	2.84687i	0.0975896	+	0.0975896i
$852$		0			0
$853$	14.7610	+	14.7610i	0.505408	+	0.505408i	0.913113	−	0.407706i	$-0.133671\pi$
$853$	14.7610	+	14.7610i	0.505408	+	0.505408i	−0.407706	+	0.913113i	$0.633671\pi$
$854$	−2.93032	+	3.96059i	−0.100274	+	0.135529i
$855$		0			0
$856$	−30.7597	−	10.8865i	−1.05135	−	0.372093i
$857$		−	38.9378i		−	1.33009i	−0.746803	−	0.665046i	$-0.768412\pi$
$857$		−	38.9378i		−	1.33009i	0.746803	−	0.665046i	$-0.231588\pi$
$858$		0			0
$859$	25.3522	+	25.3522i	0.865005	+	0.865005i	0.991914	−	0.126909i	$-0.0405056\pi$
$859$	25.3522	+	25.3522i	0.865005	+	0.865005i	−0.126909	+	0.991914i	$0.540506\pi$
$860$	−9.41635	−	47.2468i	−0.321095	−	1.61110i
$861$		0			0
$862$	29.0825	−	4.34816i	0.990554	−	0.148099i
$863$			12.4161i			0.422650i	0.977416	+	0.211325i	$0.0677779\pi$
$863$			12.4161i			0.422650i	−0.977416	+	0.211325i	$0.932222\pi$
$864$		0			0
$865$	−1.96703	−	0.197560i	−0.0668812	−	0.00671725i
$866$	1.87945	+	12.5707i	0.0638664	+	0.427168i
$867$		0			0
$868$	−28.3731	+	8.67818i	−0.963046	+	0.294557i
$869$	9.20556	+	9.20556i	0.312277	+	0.312277i
$870$		0			0
$871$	−78.7772			−2.66926
$872$	−32.9052	−	11.6458i	−1.11431	−	0.394377i
$873$		0			0
$874$	−6.13701	+	8.29471i	−0.207587	+	0.280573i
$875$	37.6396	−	19.8402i	1.27245	−	0.670720i
$876$		0			0
$877$	19.5580	−	19.5580i	0.660427	−	0.660427i	−0.295054	−	0.955481i	$-0.595337\pi$
$877$	19.5580	−	19.5580i	0.660427	−	0.660427i	0.955481	+	0.295054i	$0.0953375\pi$
$878$	−26.1339	+	3.90731i	−0.881977	+	0.131865i
$879$		0			0
$880$	4.56258	+	8.48137i	0.153805	+	0.285907i
$881$		−	18.4045i		−	0.620065i	−0.950726	−	0.310032i	$-0.899660\pi$
$881$		−	18.4045i		−	0.620065i	0.950726	−	0.310032i	$-0.100340\pi$
$882$		0			0
$883$	−14.8594	−	14.8594i	−0.500059	−	0.500059i	0.411398	−	0.911456i	$-0.365041\pi$
$883$	−14.8594	−	14.8594i	−0.500059	−	0.500059i	−0.911456	+	0.411398i	$0.865041\pi$
$884$	37.0571	−	69.7141i	1.24637	−	2.34474i
$885$		0			0
$886$	2.72736	+	2.01789i	0.0916274	+	0.0677924i
$887$	−21.5001			−0.721903			−0.360952	−	0.932585i	$-0.617548\pi$
$887$	−21.5001			−0.721903			−0.360952	+	0.932585i	$0.617548\pi$
$888$		0			0
$889$			32.7772i			1.09931i
$890$	28.2467	−	31.1169i	0.946832	−	1.04304i
$891$		0			0
$892$	23.8850	−	7.30546i	0.799730	−	0.244605i
$893$	−15.3205	−	15.3205i	−0.512682	−	0.512682i
$894$		0			0
$895$	13.6314	+	1.36908i	0.455648	+	0.0457633i
$896$	−37.1073	−	21.8373i	−1.23967	−	0.729534i
$897$		0			0
$898$	−4.38795	−	29.3487i	−0.146428	−	0.979378i
$899$	1.12854	+	1.12854i	0.0376389	+	0.0376389i
$900$		0			0
$901$	−32.8874	+	32.8874i	−1.09564	+	1.09564i
$902$	−2.35241	+	3.17949i	−0.0783266	+	0.105865i
$903$		0			0
$904$	−41.5507	+	19.8277i	−1.38196	+	0.659458i
$905$	0.263657	−	2.62513i	0.00876426	−	0.0872624i
$906$		0			0
$907$	−10.7338	+	10.7338i	−0.356409	+	0.356409i	−0.862487	−	0.506079i	$-0.831095\pi$
$907$	−10.7338	+	10.7338i	−0.356409	+	0.356409i	0.506079	+	0.862487i	$0.331095\pi$
$908$	−26.7194	+	50.2662i	−0.886715	+	1.66814i
$909$		0			0
$910$	73.6359	−	3.56026i	2.44101	−	0.118021i
$911$	13.7560			0.455757			0.227879	−	0.973690i	$-0.426821\pi$
$911$	13.7560			0.455757			0.227879	+	0.973690i	$0.426821\pi$
$912$		0			0
$913$			1.40878i			0.0466239i
$914$	0.950028	−	0.142040i	0.0314241	−	0.00469826i
$915$		0			0
$916$	6.70838	−	12.6202i	0.221651	−	0.416984i
$917$	−27.0085	+	27.0085i	−0.891901	+	0.891901i
$918$		0			0
$919$	18.2940			0.603463			0.301731	−	0.953393i	$-0.402435\pi$
$919$	18.2940			0.603463			0.301731	+	0.953393i	$0.402435\pi$
$920$	4.66625	−	9.90497i	0.153842	−	0.326557i
$921$		0			0
$922$	−36.0449	+	48.7179i	−1.18708	+	1.60444i
$923$	−38.1072	−	38.1072i	−1.25432	−	1.25432i
$924$		0			0
$925$	−9.69315	+	6.42291i	−0.318709	+	0.211184i
$926$	56.8477	−	8.49936i	1.86813	−	0.279306i
$927$		0			0
$928$	−0.100342	+	2.31383i	−0.00329390	+	0.0759551i
$929$		−	25.8063i		−	0.846678i	−0.905971	−	0.423339i	$-0.860858\pi$
$929$		−	25.8063i		−	0.846678i	0.905971	−	0.423339i	$-0.139142\pi$
$930$		0			0
$931$	22.2998	−	22.2998i	0.730847	−	0.730847i
$932$	−7.41977	−	24.2588i	−0.243043	−	0.794622i
$933$		0			0
$934$	−24.3349	+	32.8907i	−0.796261	+	1.07622i
$935$	1.55049	−	15.4376i	0.0507064	−	0.504865i
$936$		0			0
$937$	−33.2747			−1.08704			−0.543519	−	0.839397i	$-0.682909\pi$
$937$	−33.2747			−1.08704			−0.543519	+	0.839397i	$0.682909\pi$
$938$	41.1652	−	55.6384i	1.34409	−	1.81666i
$939$		0			0
$940$	19.1213	+	12.7661i	0.623669	+	0.416385i
$941$	−25.6703	+	25.6703i	−0.836826	+	0.836826i	−0.988440	−	0.151613i	$-0.951553\pi$
$941$	−25.6703	+	25.6703i	−0.836826	+	0.836826i	0.151613	+	0.988440i	$0.451553\pi$
$942$		0			0
$943$	4.49653			0.146427
$944$	−6.12757	+	31.5633i	−0.199436	+	1.02730i
$945$		0			0
$946$	−2.42559	−	16.2235i	−0.0788628	−	0.527471i
$947$	1.52610	−	1.52610i	0.0495917	−	0.0495917i	−0.681876	−	0.731468i	$-0.738836\pi$
$947$	1.52610	−	1.52610i	0.0495917	−	0.0495917i	0.731468	+	0.681876i	$0.238836\pi$
$948$		0			0
$949$	52.5518	−	52.5518i	1.70590	−	1.70590i
$950$	−19.9532	−	22.1348i	−0.647367	−	0.718148i
$951$		0			0
$952$	29.8731	+	62.6018i	0.968193	+	2.02894i
$953$			59.1008i			1.91446i	0.289325	+	0.957231i	$0.406569\pi$
$953$			59.1008i			1.91446i	−0.289325	+	0.957231i	$0.593431\pi$
$954$		0			0
$955$	−31.4266	+	25.6901i	−1.01694	+	0.831311i
$956$	9.56854	−	2.92663i	0.309469	−	0.0946539i
$957$		0			0
$958$	29.2879	−	4.37887i	0.946250	−	0.141475i
$959$	35.4147			1.14360
$960$		0			0
$961$	15.8038			0.509801
$962$	−19.9259	+	2.97914i	−0.642437	+	0.0960514i
$963$		0			0
$964$	−17.8707	+	5.46593i	−0.575578	+	0.176046i
$965$	−21.6046	−	26.4288i	−0.695475	−	0.850774i
$966$		0			0
$967$			20.7576i			0.667520i	0.942658	+	0.333760i	$0.108318\pi$
$967$			20.7576i			0.667520i	−0.942658	+	0.333760i	$0.891682\pi$
$968$	−11.9870	−	25.1200i	−0.385278	−	0.807386i
$969$		0			0
$970$	−22.3877	−	20.3227i	−0.718826	−	0.652523i
$971$	9.28924	−	9.28924i	0.298106	−	0.298106i	−0.542166	−	0.840272i	$-0.682396\pi$
$971$	9.28924	−	9.28924i	0.298106	−	0.298106i	0.840272	+	0.542166i	$0.182396\pi$
$972$		0			0
$973$	−34.8723	+	34.8723i	−1.11795	+	1.11795i
$974$	−5.79244	−	38.7426i	−0.185602	−	1.24139i
$975$		0			0
$976$	−3.59455	−	0.697832i	−0.115059	−	0.0223371i
$977$	1.97432			0.0631639			0.0315820	−	0.999501i	$-0.489945\pi$
$977$	1.97432			0.0631639			0.0315820	+	0.999501i	$0.489945\pi$
$978$		0			0
$979$	10.1184	−	10.1184i	0.323385	−	0.323385i
$980$	−18.5817	+	27.8321i	−0.593572	+	0.889063i
$981$		0			0
$982$	15.4298	−	20.8547i	0.492384	−	0.665500i
$983$	5.86679			0.187122			0.0935608	−	0.995614i	$-0.470175\pi$
$983$	5.86679			0.187122			0.0935608	+	0.995614i	$0.470175\pi$
$984$		0			0
$985$	−0.0907649	+	0.903712i	−0.00289201	+	0.0287947i
$986$	2.21919	−	2.99943i	0.0706733	−	0.0955212i
$987$		0			0
$988$	−15.1022	−	49.3764i	−0.480466	−	1.57087i
$989$	−13.1871	+	13.1871i	−0.419324	+	0.419324i
$990$		0			0
$991$			30.8789i			0.980900i	0.871469	+	0.490450i	$0.163168\pi$
$991$			30.8789i			0.980900i	−0.871469	+	0.490450i	$0.836832\pi$
$992$	−14.9027	−	16.2538i	−0.473161	−	0.516060i
$993$		0			0
$994$	46.8273	−	7.00120i	1.48527	−	0.222064i
$995$	27.6250	−	22.5824i	0.875772	−	0.715910i
$996$		0			0
$997$	28.6738	+	28.6738i	0.908108	+	0.908108i	0.996119	−	0.0880118i	$-0.0280513\pi$
$997$	28.6738	+	28.6738i	0.908108	+	0.908108i	−0.0880118	+	0.996119i	$0.528051\pi$
$998$	10.6667	−	14.4169i	0.337647	−	0.456360i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.179.4	yes	96
3.2	odd	2	inner	720.2.u.a.179.45	yes	96
4.3	odd	2		2880.2.u.a.2159.39		96
5.4	even	2	inner	720.2.u.a.179.46	yes	96
12.11	even	2		2880.2.u.a.2159.10		96
15.14	odd	2	inner	720.2.u.a.179.3	✓	96
16.5	even	4		2880.2.u.a.719.34		96
16.11	odd	4	inner	720.2.u.a.539.3	yes	96
20.19	odd	2		2880.2.u.a.2159.15		96
48.5	odd	4		2880.2.u.a.719.15		96
48.11	even	4	inner	720.2.u.a.539.46	yes	96
60.59	even	2		2880.2.u.a.2159.34		96
80.59	odd	4	inner	720.2.u.a.539.45	yes	96
80.69	even	4		2880.2.u.a.719.10		96
240.59	even	4	inner	720.2.u.a.539.4	yes	96
240.149	odd	4		2880.2.u.a.719.39		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.3	✓	96	15.14	odd	2	inner
720.2.u.a.179.4	yes	96	1.1	even	1	trivial
720.2.u.a.179.45	yes	96	3.2	odd	2	inner
720.2.u.a.179.46	yes	96	5.4	even	2	inner
720.2.u.a.539.3	yes	96	16.11	odd	4	inner
720.2.u.a.539.4	yes	96	240.59	even	4	inner
720.2.u.a.539.45	yes	96	80.59	odd	4	inner
720.2.u.a.539.46	yes	96	48.11	even	4	inner
2880.2.u.a.719.10		96	80.69	even	4
2880.2.u.a.719.15		96	48.5	odd	4
2880.2.u.a.719.34		96	16.5	even	4
2880.2.u.a.719.39		96	240.149	odd	4
2880.2.u.a.2159.10		96	12.11	even	2
2880.2.u.a.2159.15		96	20.19	odd	2
2880.2.u.a.2159.34		96	60.59	even	2
2880.2.u.a.2159.39		96	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.73123 - 1.41522i) q^{5} +3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +O(q^{10})\)	\(q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.73123 - 1.41522i) q^{5} +3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +(-2.12547 + 2.34145i) q^{10} +(-0.761375 + 0.761375i) q^{11} +(-4.33164 + 4.33164i) q^{13} +(-0.795824 - 5.32284i) q^{14} +(3.31562 - 2.23755i) q^{16} -6.44408 q^{17} +(-2.98007 + 2.98007i) q^{19} +(2.48319 - 3.71937i) q^{20} +(0.905695 - 1.22413i) q^{22} -1.73120 q^{23} +(0.994326 - 4.90013i) q^{25} +(5.15271 - 6.96434i) q^{26} +(2.22619 + 7.27847i) q^{28} +(0.289500 - 0.289500i) q^{29} +3.89823i q^{31} +(-4.16955 + 3.82294i) q^{32} +(9.01313 - 1.34756i) q^{34} +(5.38582 + 6.58847i) q^{35} +(-1.64445 - 1.64445i) q^{37} +(3.54494 - 4.79130i) q^{38} +(-2.69538 + 5.72144i) q^{40} -2.59735 q^{41} +(7.61730 - 7.61730i) q^{43} +(-1.01078 + 1.90154i) q^{44} +(2.42137 - 0.362022i) q^{46} +5.14100i q^{47} -7.48300 q^{49} +(-0.366034 + 7.06159i) q^{50} +(-5.75057 + 10.8183i) q^{52} +(5.10351 - 5.10351i) q^{53} +(-0.240606 + 2.39563i) q^{55} +(-4.63574 - 9.71462i) q^{56} +(-0.344376 + 0.465454i) q^{58} +(-5.68382 + 5.68382i) q^{59} +(-0.647296 - 0.647296i) q^{61} +(-0.815183 - 5.45232i) q^{62} +(5.03237 - 6.21894i) q^{64} +(-1.36887 + 13.6293i) q^{65} +(9.09323 + 9.09323i) q^{67} +(-12.3246 + 3.76959i) q^{68} +(-8.91073 - 8.08881i) q^{70} +8.79742i q^{71} -12.1321 q^{73} +(2.64392 + 1.95616i) q^{74} +(-3.95625 + 7.44275i) q^{76} +(-2.89753 - 2.89753i) q^{77} -12.0907i q^{79} +(2.57349 - 8.56605i) q^{80} +(3.63283 - 0.543148i) q^{82} +(0.925156 - 0.925156i) q^{83} +(-11.1562 + 9.11977i) q^{85} +(-9.06116 + 12.2470i) q^{86} +(1.01610 - 2.87100i) q^{88} -13.2896 q^{89} +(-16.4847 - 16.4847i) q^{91} +(-3.31099 + 1.01270i) q^{92} +(-1.07507 - 7.19055i) q^{94} +(-0.941748 + 9.37663i) q^{95} +9.56150i q^{97} +(10.4662 - 1.56482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more