LMFDB - Embedded newform 552.2.b.c.413.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(413,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("552.413");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.b (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			413.18
Character	$\chi$	$=$	552.413
Dual form			552.2.b.c.413.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02836 - 0.970807i) q^{2} +(1.71832 - 0.217636i) q^{3} +(0.115069 + 1.99669i) q^{4} +1.34112i q^{5} +(-1.97835 - 1.44435i) q^{6} -2.80797i q^{7} +(1.82006 - 2.16503i) q^{8} +(2.90527 - 0.747937i) q^{9} +O(q^{10})$	\(q+(-1.02836 - 0.970807i) q^{2} +(1.71832 - 0.217636i) q^{3} +(0.115069 + 1.99669i) q^{4} +1.34112i q^{5} +(-1.97835 - 1.44435i) q^{6} -2.80797i q^{7} +(1.82006 - 2.16503i) q^{8} +(2.90527 - 0.747937i) q^{9} +(1.30196 - 1.37916i) q^{10} -6.17378i q^{11} +(0.632276 + 3.40591i) q^{12} +4.84265i q^{13} +(-2.72599 + 2.88761i) q^{14} +(0.291875 + 2.30447i) q^{15} +(-3.97352 + 0.459514i) q^{16} -4.64639 q^{17} +(-3.71378 - 2.05130i) q^{18} +5.42593 q^{19} +(-2.67779 + 0.154321i) q^{20} +(-0.611113 - 4.82499i) q^{21} +(-5.99354 + 6.34890i) q^{22} +(3.02469 - 3.72173i) q^{23} +(2.65627 - 4.11634i) q^{24} +3.20141 q^{25} +(4.70128 - 4.98001i) q^{26} +(4.82941 - 1.91749i) q^{27} +(5.60663 - 0.323110i) q^{28} +1.97237 q^{29} +(1.93704 - 2.65319i) q^{30} -2.08414 q^{31} +(4.53233 + 3.38497i) q^{32} +(-1.34363 - 10.6085i) q^{33} +(4.77819 + 4.51075i) q^{34} +3.76581 q^{35} +(1.82770 + 5.71485i) q^{36} +6.74349 q^{37} +(-5.57983 - 5.26753i) q^{38} +(1.05393 + 8.32124i) q^{39} +(2.90356 + 2.44092i) q^{40} -6.56520i q^{41} +(-4.05569 + 5.55513i) q^{42} -8.76132 q^{43} +(12.3271 - 0.710411i) q^{44} +(1.00307 + 3.89631i) q^{45} +(-6.72356 + 0.890902i) q^{46} +1.29516i q^{47} +(-6.72778 + 1.65437i) q^{48} -0.884669 q^{49} +(-3.29221 - 3.10795i) q^{50} +(-7.98400 + 1.01122i) q^{51} +(-9.66925 + 0.557239i) q^{52} +8.64336i q^{53} +(-6.82791 - 2.71655i) q^{54} +8.27976 q^{55} +(-6.07934 - 5.11068i) q^{56} +(9.32350 - 1.18088i) q^{57} +(-2.02832 - 1.91479i) q^{58} -5.23804 q^{59} +(-4.56772 + 0.847956i) q^{60} -8.20972 q^{61} +(2.14326 + 2.02330i) q^{62} +(-2.10018 - 8.15790i) q^{63} +(-1.37473 - 7.88100i) q^{64} -6.49456 q^{65} +(-8.91710 + 12.2139i) q^{66} +1.61351 q^{67} +(-0.534656 - 9.27739i) q^{68} +(4.38742 - 7.05341i) q^{69} +(-3.87263 - 3.65587i) q^{70} +1.95795i q^{71} +(3.66847 - 7.65130i) q^{72} +8.57628 q^{73} +(-6.93477 - 6.54662i) q^{74} +(5.50105 - 0.696740i) q^{75} +(0.624357 + 10.8339i) q^{76} -17.3358 q^{77} +(6.99448 - 9.58043i) q^{78} +8.21280i q^{79} +(-0.616262 - 5.32895i) q^{80} +(7.88118 - 4.34592i) q^{81} +(-6.37354 + 6.75142i) q^{82} +10.6556i q^{83} +(9.56368 - 1.77541i) q^{84} -6.23135i q^{85} +(9.00984 + 8.50555i) q^{86} +(3.38917 - 0.429258i) q^{87} +(-13.3664 - 11.2367i) q^{88} -0.917940 q^{89} +(2.75104 - 4.98061i) q^{90} +13.5980 q^{91} +(7.77917 + 5.61111i) q^{92} +(-3.58123 + 0.453583i) q^{93} +(1.25735 - 1.33190i) q^{94} +7.27680i q^{95} +(8.52469 + 4.83008i) q^{96} +1.91006i q^{97} +(0.909762 + 0.858842i) q^{98} +(-4.61760 - 17.9365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) $ 80 * q - 12 * q^6 - 4 * q^9	$ 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) $ 80 * q - 12 * q^6 - 4 * q^9 + 16 * q^12 + 8 * q^16 + 20 * q^18 - 8 * q^24 - 144 * q^25 - 24 * q^31 + 40 * q^36 + 68 * q^39 - 24 * q^46 + 92 * q^48 - 160 * q^49 - 48 * q^52 - 32 * q^54 + 32 * q^55 - 40 * q^58 + 48 * q^64 + 72 * q^70 + 68 * q^72 - 8 * q^73 + 64 * q^78 + 12 * q^81 - 48 * q^82 + 92 * q^87 - 144 * q^94 + 68 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.02836	−	0.970807i	−0.727164	−	0.686464i
$2$	−1.02836	−	0.970807i	−0.727164	−	0.686464i
$3$	1.71832	−	0.217636i	0.992074	−	0.125652i
$3$	1.71832	−	0.217636i	0.992074	−	0.125652i
$4$	0.115069	+	1.99669i	0.0575346	+	0.998344i
$5$			1.34112i			0.599766i	0.953976	+	0.299883i	$0.0969476\pi$
$5$			1.34112i			0.599766i	−0.953976	+	0.299883i	$0.903052\pi$
$6$	−1.97835	−	1.44435i	−0.807656	−	0.589654i
$7$		−	2.80797i		−	1.06131i	−0.847588	−	0.530656i	$-0.821946\pi$
$7$		−	2.80797i		−	1.06131i	0.847588	−	0.530656i	$-0.178054\pi$
$8$	1.82006	−	2.16503i	0.643490	−	0.765455i
$9$	2.90527	−	0.747937i	0.968423	−	0.249312i
$10$	1.30196	−	1.37916i	0.411717	−	0.436128i
$11$		−	6.17378i		−	1.86146i	−0.365702	−	0.930732i	$-0.619171\pi$
$11$		−	6.17378i		−	1.86146i	0.365702	−	0.930732i	$-0.380829\pi$
$12$	0.632276	+	3.40591i	0.182522	+	0.983202i
$13$			4.84265i			1.34311i	0.740955	+	0.671555i	$0.234373\pi$
$13$			4.84265i			1.34311i	−0.740955	+	0.671555i	$0.765627\pi$
$14$	−2.72599	+	2.88761i	−0.728552	+	0.771747i
$15$	0.291875	+	2.30447i	0.0753618	+	0.595012i
$16$	−3.97352	+	0.459514i	−0.993380	+	0.114879i
$17$	−4.64639			−1.12692			−0.563458	−	0.826145i	$-0.690529\pi$
$17$	−4.64639			−1.12692			−0.563458	+	0.826145i	$0.690529\pi$
$18$	−3.71378	−	2.05130i	−0.875346	−	0.483497i
$19$	5.42593			1.24479			0.622396	−	0.782702i	$-0.286159\pi$
$19$	5.42593			1.24479			0.622396	+	0.782702i	$0.286159\pi$
$20$	−2.67779	+	0.154321i	−0.598772	+	0.0345072i
$21$	−0.611113	−	4.82499i	−0.133356	−	1.05290i
$22$	−5.99354	+	6.34890i	−1.27783	+	1.35359i
$23$	3.02469	−	3.72173i	0.630692	−	0.776033i
$23$	3.02469	−	3.72173i	0.630692	−	0.776033i
$24$	2.65627	−	4.11634i	0.542209	−	0.840244i
$25$	3.20141			0.640281
$26$	4.70128	−	4.98001i	0.921996	−	0.976660i
$27$	4.82941	−	1.91749i	0.929421	−	0.369021i
$28$	5.60663	−	0.323110i	1.05955	−	0.0610621i
$29$	1.97237			0.366260			0.183130	−	0.983089i	$-0.441377\pi$
$29$	1.97237			0.366260			0.183130	+	0.983089i	$0.441377\pi$
$30$	1.93704	−	2.65319i	0.353654	−	0.484404i
$31$	−2.08414			−0.374323			−0.187161	−	0.982329i	$-0.559929\pi$
$31$	−2.08414			−0.374323			−0.187161	+	0.982329i	$0.559929\pi$
$32$	4.53233	+	3.38497i	0.801210	+	0.598384i
$33$	−1.34363	−	10.6085i	−0.233897	−	1.84671i
$34$	4.77819	+	4.51075i	0.819452	+	0.773587i
$35$	3.76581			0.636538
$36$	1.82770	+	5.71485i	0.304617	+	0.952475i
$37$	6.74349			1.10862			0.554311	−	0.832309i	$-0.312982\pi$
$37$	6.74349			1.10862			0.554311	+	0.832309i	$0.312982\pi$
$38$	−5.57983	−	5.26753i	−0.905168	−	0.854505i
$39$	1.05393	+	8.32124i	0.168764	+	1.33246i
$40$	2.90356	+	2.44092i	0.459093	+	0.385943i
$41$		−	6.56520i		−	1.02531i	−0.858594	−	0.512656i	$-0.828662\pi$
$41$		−	6.56520i		−	1.02531i	0.858594	−	0.512656i	$-0.171338\pi$
$42$	−4.05569	+	5.55513i	−0.625806	+	0.857175i
$43$	−8.76132			−1.33609			−0.668045	−	0.744121i	$-0.732868\pi$
$43$	−8.76132			−1.33609			−0.668045	+	0.744121i	$0.732868\pi$
$44$	12.3271	−	0.710411i	1.85838	−	0.107098i
$45$	1.00307	+	3.89631i	0.149529	+	0.580827i
$46$	−6.72356	+	0.890902i	−0.991335	+	0.131356i
$47$			1.29516i			0.188919i	0.995529	+	0.0944595i	$0.0301123\pi$
$47$			1.29516i			0.188919i	−0.995529	+	0.0944595i	$0.969888\pi$
$48$	−6.72778	+	1.65437i	−0.971072	+	0.238788i
$49$	−0.884669			−0.126381
$50$	−3.29221	−	3.10795i	−0.465589	−	0.439530i
$51$	−7.98400	+	1.01122i	−1.11798	+	0.141599i
$52$	−9.66925	+	0.557239i	−1.34088	+	0.0772752i
$53$			8.64336i			1.18726i	0.804739	+	0.593628i	$0.202305\pi$
$53$			8.64336i			1.18726i	−0.804739	+	0.593628i	$0.797695\pi$
$54$	−6.82791	−	2.71655i	−0.929161	−	0.369676i
$55$	8.27976			1.11644
$56$	−6.07934	−	5.11068i	−0.812386	−	0.682943i
$57$	9.32350	−	1.18088i	1.23493	−	0.156411i
$58$	−2.02832	−	1.91479i	−0.266331	−	0.251424i
$59$	−5.23804			−0.681934			−0.340967	−	0.940075i	$-0.610754\pi$
$59$	−5.23804			−0.681934			−0.340967	+	0.940075i	$0.610754\pi$
$60$	−4.56772	+	0.847956i	−0.589691	+	0.109471i
$61$	−8.20972			−1.05115			−0.525573	−	0.850748i	$-0.676149\pi$
$61$	−8.20972			−1.05115			−0.525573	+	0.850748i	$0.676149\pi$
$62$	2.14326	+	2.02330i	0.272194	+	0.256959i
$63$	−2.10018	−	8.15790i	−0.264598	−	1.02780i
$64$	−1.37473	−	7.88100i	−0.171842	−	0.985125i
$65$	−6.49456			−0.805551
$66$	−8.91710	+	12.2139i	−1.09762	+	1.50342i
$67$	1.61351			0.197121			0.0985606	−	0.995131i	$-0.468576\pi$
$67$	1.61351			0.197121			0.0985606	+	0.995131i	$0.468576\pi$
$68$	−0.534656	−	9.27739i	−0.0648366	−	1.12505i
$69$	4.38742	−	7.05341i	0.528183	−	0.849131i
$70$	−3.87263	−	3.65587i	−0.462867	−	0.436960i
$71$			1.95795i			0.232365i	0.993228	+	0.116183i	$0.0370658\pi$
$71$			1.95795i			0.232365i	−0.993228	+	0.116183i	$0.962934\pi$
$72$	3.66847	−	7.65130i	0.432333	−	0.901714i
$73$	8.57628			1.00378			0.501889	−	0.864932i	$-0.332639\pi$
$73$	8.57628			1.00378			0.501889	+	0.864932i	$0.332639\pi$
$74$	−6.93477	−	6.54662i	−0.806150	−	0.761029i
$75$	5.50105	−	0.696740i	0.635207	−	0.0804526i
$76$	0.624357	+	10.8339i	0.0716186	+	1.24273i
$77$	−17.3358			−1.97559
$78$	6.99448	−	9.58043i	0.791969	−	1.08477i
$79$			8.21280i			0.924012i	0.886877	+	0.462006i	$0.152870\pi$
$79$			8.21280i			0.924012i	−0.886877	+	0.462006i	$0.847130\pi$
$80$	−0.616262	−	5.32895i	−0.0689002	−	0.595795i
$81$	7.88118	−	4.34592i	0.875687	−	0.482880i
$82$	−6.37354	+	6.75142i	−0.703840	+	0.745570i
$83$			10.6556i			1.16960i	0.811176	+	0.584802i	$0.198828\pi$
$83$			10.6556i			1.16960i	−0.811176	+	0.584802i	$0.801172\pi$
$84$	9.56368	−	1.77541i	1.04348	−	0.193713i
$85$		−	6.23135i		−	0.675885i
$86$	9.00984	+	8.50555i	0.971556	+	0.917177i
$87$	3.38917	−	0.429258i	0.363357	−	0.0460213i
$88$	−13.3664	−	11.2367i	−1.42487	−	1.19783i
$89$	−0.917940			−0.0973014			−0.0486507	−	0.998816i	$-0.515492\pi$
$89$	−0.917940			−0.0973014			−0.0486507	+	0.998816i	$0.515492\pi$
$90$	2.75104	−	4.98061i	0.289985	−	0.525003i
$91$	13.5980			1.42546
$92$	7.77917	+	5.61111i	0.811034	+	0.584998i
$93$	−3.58123	+	0.453583i	−0.371356	+	0.0470344i
$94$	1.25735	−	1.33190i	0.129686	−	0.137375i
$95$			7.27680i			0.746584i
$96$	8.52469	+	4.83008i	0.870048	+	0.492968i
$97$			1.91006i			0.193937i	0.995287	+	0.0969685i	$0.0309146\pi$
$97$			1.91006i			0.193937i	−0.995287	+	0.0969685i	$0.969085\pi$
$98$	0.909762	+	0.858842i	0.0918999	+	0.0867562i
$99$	−4.61760	−	17.9365i	−0.464086	−	1.80268i
$100$	0.368383	+	6.39221i	0.0368383	+	0.639221i
$101$	−16.1544			−1.60742			−0.803712	−	0.595019i	$-0.797145\pi$
$101$	−16.1544			−1.60742			−0.803712	+	0.595019i	$0.797145\pi$
$102$	9.19217	+	6.71102i	0.910160	+	0.664490i
$103$		−	9.72456i		−	0.958189i	−0.877763	−	0.479095i	$-0.840965\pi$
$103$		−	9.72456i		−	0.958189i	0.877763	−	0.479095i	$-0.159035\pi$
$104$	10.4845	+	8.81393i	1.02809	+	0.864277i
$105$	6.47088	−	0.819574i	0.631493	−	0.0799823i
$106$	8.39103	−	8.88853i	0.815009	−	0.863330i
$107$			2.49280i			0.240988i	0.992714	+	0.120494i	$0.0384479\pi$
$107$			2.49280i			0.240988i	−0.992714	+	0.120494i	$0.961552\pi$
$108$	4.38434	+	9.42219i	0.421883	+	0.906650i
$109$	−15.8055			−1.51389			−0.756945	−	0.653479i	$-0.773309\pi$
$109$	−15.8055			−1.51389			−0.756945	+	0.653479i	$0.773309\pi$
$110$	−8.51461	−	8.03804i	−0.811836	−	0.766397i
$111$	11.5875	−	1.46762i	1.09984	−	0.139301i
$112$	1.29030	+	11.1575i	0.121922	+	1.05428i
$113$	−3.53474			−0.332520			−0.166260	−	0.986082i	$-0.553169\pi$
$113$	−3.53474			−0.332520			−0.166260	+	0.986082i	$0.553169\pi$
$114$	−10.7344	−	7.83694i	−1.00536	−	0.733997i
$115$	4.99127	+	4.05646i	0.465438	+	0.378267i
$116$	0.226959	+	3.93821i	0.0210726	+	0.365653i
$117$	3.62200	+	14.0692i	0.334854	+	1.30070i
$118$	5.38661	+	5.08512i	0.495878	+	0.468123i
$119$			13.0469i			1.19601i
$120$	5.52049	+	3.56237i	0.503949	+	0.325198i
$121$	−27.1155			−2.46505
$122$	8.44259	+	7.97005i	0.764356	+	0.721574i
$123$	−1.42882	−	11.2811i	−0.128833	−	1.01719i
$124$	−0.239820	−	4.16137i	−0.0215365	−	0.373702i
$125$			10.9990i			0.983784i
$126$	−5.75999	+	10.4282i	−0.513140	+	0.929015i
$127$	−4.22479			−0.374890			−0.187445	−	0.982275i	$-0.560021\pi$
$127$	−4.22479			−0.374890			−0.187445	+	0.982275i	$0.560021\pi$
$128$	−6.23719	+	9.43914i	−0.551295	+	0.834310i
$129$	−15.0548	+	1.90678i	−1.32550	+	0.167882i
$130$	6.67878	+	6.30496i	0.585767	+	0.552981i
$131$	5.08510			0.444287			0.222143	−	0.975014i	$-0.428695\pi$
$131$	5.08510			0.444287			0.222143	+	0.975014i	$0.428695\pi$
$132$	21.0273	−	3.90353i	1.83019	−	0.339759i
$133$		−	15.2358i		−	1.32111i
$134$	−1.65927	−	1.56640i	−0.143339	−	0.135317i
$135$	2.57157	+	6.47681i	0.221326	+	0.557435i
$136$	−8.45673	+	10.0596i	−0.725158	+	0.862603i
$137$	20.5616			1.75670			0.878350	−	0.478018i	$-0.158645\pi$
$137$	20.5616			1.75670			0.878350	+	0.478018i	$0.158645\pi$
$138$	−11.3594	+	2.99414i	−0.966973	+	0.254878i
$139$			13.6067i			1.15410i	0.816707	+	0.577052i	$0.195797\pi$
$139$			13.6067i			1.15410i	−0.816707	+	0.577052i	$0.804203\pi$
$140$	0.433328	+	7.51914i	0.0366229	+	0.635483i
$141$	0.281874	+	2.22551i	0.0237380	+	0.187422i
$142$	1.90079	−	2.01348i	0.159510	−	0.168968i
$143$	29.8974			2.50015
$144$	−11.2005	+	4.30695i	−0.933371	+	0.358913i
$145$			2.64518i			0.219670i
$146$	−8.81955	−	8.32591i	−0.729911	−	0.689057i
$147$	−1.52015	+	0.192535i	−0.125380	+	0.0158801i
$148$	0.775967	+	13.4646i	0.0637841	+	1.10679i
$149$			14.0535i			1.15130i	0.817695	+	0.575652i	$0.195252\pi$
$149$			14.0535i			1.15130i	−0.817695	+	0.575652i	$0.804748\pi$
$150$	−6.33349	−	4.62395i	−0.517127	−	0.377544i
$151$	−5.49673			−0.447318			−0.223659	−	0.974667i	$-0.571800\pi$
$151$	−5.49673			−0.447318			−0.223659	+	0.974667i	$0.571800\pi$
$152$	9.87553	−	11.7473i	0.801012	−	0.952833i
$153$	−13.4990	+	3.47521i	−1.09133	+	0.280954i
$154$	17.8275	+	16.8297i	1.43658	+	1.35617i
$155$		−	2.79507i		−	0.224506i
$156$	−16.4936	+	3.06189i	−1.32055	+	0.245148i
$157$	15.7631			1.25803			0.629016	−	0.777392i	$-0.283458\pi$
$157$	15.7631			1.25803			0.629016	+	0.777392i	$0.283458\pi$
$158$	7.97304	−	8.44575i	0.634301	−	0.671908i
$159$	1.88110	+	14.8521i	0.149181	+	1.17785i
$160$	−4.53964	+	6.07838i	−0.358890	+	0.480538i
$161$	−10.4505	−	8.49323i	−0.823613	−	0.669360i
$162$	−12.3238	−	3.18191i	−0.968247	−	0.249995i
$163$			13.2932i			1.04120i	0.853800	+	0.520601i	$0.174292\pi$
$163$			13.2932i			1.04120i	−0.853800	+	0.520601i	$0.825708\pi$
$164$	13.1087	−	0.755452i	1.02361	−	0.0589909i
$165$	14.2273	−	1.80197i	1.10759	−	0.140283i
$166$	10.3445	−	10.9578i	0.802891	−	0.850493i
$167$			10.5750i			0.818318i	0.912463	+	0.409159i	$0.134178\pi$
$167$			10.5750i			0.818318i	−0.912463	+	0.409159i	$0.865822\pi$
$168$	−11.5585	−	7.45871i	−0.891760	−	0.575452i
$169$	−10.4512			−0.803942
$170$	−6.04944	+	6.40810i	−0.463971	+	0.491479i
$171$	15.7638	−	4.05825i	1.20549	−	0.310342i
$172$	−1.00816	−	17.4936i	−0.0768713	−	1.33388i
$173$	15.5116			1.17933			0.589664	−	0.807649i	$-0.299260\pi$
$173$	15.5116			1.17933			0.589664	+	0.807649i	$0.299260\pi$
$174$	−3.90203	−	2.84879i	−0.295812	−	0.215967i
$175$		−	8.98944i		−	0.679538i
$176$	2.83694	+	24.5316i	0.213842	+	1.84914i
$177$	−9.00064	+	1.13998i	−0.676530	+	0.0856864i
$178$	0.943977	+	0.891142i	0.0707541	+	0.0667939i
$179$	−9.95208			−0.743853			−0.371927	−	0.928262i	$-0.621303\pi$
$179$	−9.95208			−0.743853			−0.371927	+	0.928262i	$0.621303\pi$
$180$	−7.66428	+	2.45116i	−0.571262	+	0.182699i
$181$	−0.0303315			−0.00225452			−0.00112726	−	0.999999i	$-0.500359\pi$
$181$	−0.0303315			−0.00225452			−0.00112726	+	0.999999i	$0.500359\pi$
$182$	−13.9837	−	13.2010i	−1.03654	−	0.978525i
$183$	−14.1069	+	1.78673i	−1.04282	+	0.132079i
$184$	−2.55253	−	13.3223i	−0.188175	−	0.982136i
$185$			9.04381i			0.664914i
$186$	4.12315	+	3.01023i	0.302324	+	0.220721i
$187$			28.6858i			2.09771i
$188$	−2.58604	+	0.149033i	−0.188606	+	0.0108694i
$189$	−5.38424	−	13.5608i	−0.391646	−	0.986405i
$190$	7.06437	−	7.48321i	0.512503	−	0.542889i
$191$	−24.9085			−1.80232			−0.901158	−	0.433490i	$-0.857282\pi$
$191$	−24.9085			−1.80232			−0.901158	+	0.433490i	$0.857282\pi$
$192$	−4.07742	−	13.2429i	−0.294263	−	0.955725i
$193$	−4.83745			−0.348207			−0.174104	−	0.984727i	$-0.555703\pi$
$193$	−4.83745			−0.348207			−0.174104	+	0.984727i	$0.555703\pi$
$194$	1.85430	−	1.96424i	0.133131	−	0.141024i
$195$	−11.1597	+	1.41345i	−0.799166	+	0.101219i
$196$	−0.101798	−	1.76641i	−0.00727129	−	0.126172i
$197$	−11.5674			−0.824146			−0.412073	−	0.911151i	$-0.635195\pi$
$197$	−11.5674			−0.824146			−0.412073	+	0.911151i	$0.635195\pi$
$198$	−12.6643	+	22.9280i	−0.900012	+	1.62943i
$199$		−	4.84445i		−	0.343414i	−0.985148	−	0.171707i	$-0.945072\pi$
$199$		−	4.84445i		−	0.343414i	0.985148	−	0.171707i	$-0.0549283\pi$
$200$	5.82676	−	6.93115i	0.412014	−	0.490106i
$201$	2.77253	−	0.351157i	0.195559	−	0.0247687i
$202$	16.6126	+	15.6828i	1.16886	+	1.10344i
$203$		−	5.53835i		−	0.388716i
$204$	−2.93780	−	15.8252i	−0.205687	−	1.10798i
$205$	8.80470			0.614947
$206$	−9.44067	+	10.0004i	−0.657762	+	0.696761i
$207$	6.00393	−	13.0749i	0.417302	−	0.908768i
$208$	−2.22527	−	19.2424i	−0.154294	−	1.33422i
$209$		−	33.4985i		−	2.31714i
$210$	−7.45007	−	5.43915i	−0.514104	−	0.375337i
$211$		−	25.5581i		−	1.75949i	−0.475443	−	0.879747i	$-0.657712\pi$
$211$		−	25.5581i		−	1.75949i	0.475443	−	0.879747i	$-0.342288\pi$
$212$	−17.2581	+	0.994583i	−1.18529	+	0.0683083i
$213$	0.426119	+	3.36438i	0.0291972	+	0.230524i
$214$	2.42003	−	2.56351i	0.165430	−	0.175238i
$215$		−	11.7500i		−	0.801340i
$216$	4.63842	−	13.9458i	0.315604	−	0.948891i
$217$			5.85219i			0.397273i
$218$	16.2538	+	15.3441i	1.10085	+	1.03923i
$219$	14.7368	−	1.86650i	0.995822	−	0.126127i
$220$	0.952744	+	16.5321i	0.0642340	+	1.11459i
$221$		−	22.5008i		−	1.51357i
$222$	−13.3410	−	9.73996i	−0.895386	−	0.653703i
$223$	22.9173			1.53466			0.767328	−	0.641255i	$-0.221586\pi$
$223$	22.9173			1.53466			0.767328	+	0.641255i	$0.221586\pi$
$224$	9.50488	−	12.7266i	0.635071	−	0.850333i
$225$	9.30095	−	2.39445i	0.620063	−	0.159630i
$226$	3.63500	+	3.43155i	0.241797	+	0.228263i
$227$		−	2.32217i		−	0.154128i	−0.997026	−	0.0770640i	$-0.975445\pi$
$227$		−	2.32217i		−	0.154128i	0.997026	−	0.0770640i	$-0.0245546\pi$
$228$	3.43068	+	18.4802i	0.227203	+	1.22388i
$229$	−11.9304			−0.788385			−0.394192	−	0.919028i	$-0.628976\pi$
$229$	−11.9304			−0.788385			−0.394192	+	0.919028i	$0.628976\pi$
$230$	−1.19480	−	9.01708i	−0.0787830	−	0.594569i
$231$	−29.7884	+	3.77288i	−1.95993	+	0.248237i
$232$	3.58984	−	4.27025i	0.235685	−	0.280355i
$233$			27.4486i			1.79822i	0.437726	+	0.899109i	$0.355784\pi$
$233$			27.4486i			1.79822i	−0.437726	+	0.899109i	$0.644216\pi$
$234$	9.93374	−	17.9845i	0.649389	−	1.17569i
$235$	−1.73696			−0.113307
$236$	−0.602736	−	10.4587i	−0.0392348	−	0.680805i
$237$	1.78740	+	14.1122i	0.116104	+	0.916688i
$238$	12.6660	−	13.4170i	0.821016	−	0.869693i
$239$		−	7.36946i		−	0.476691i	−0.971180	−	0.238345i	$-0.923395\pi$
$239$		−	7.36946i		−	0.476691i	0.971180	−	0.238345i	$-0.0766050\pi$
$240$	−2.21871	−	9.02274i	−0.143217	−	0.582415i
$241$			24.7816i			1.59632i	0.602443	+	0.798162i	$0.294194\pi$
$241$			24.7816i			1.59632i	−0.602443	+	0.798162i	$0.705806\pi$
$242$	27.8847	+	26.3239i	1.79249	+	1.69217i
$243$	12.5966	−	9.18292i	0.808072	−	0.589084i
$244$	−0.944685	−	16.3922i	−0.0604773	−	1.04941i
$245$		−	1.18644i		−	0.0757991i
$246$	−9.48245	+	12.9882i	−0.604579	+	0.828100i
$247$			26.2759i			1.67189i
$248$	−3.79327	+	4.51223i	−0.240873	+	0.286527i
$249$	2.31904	+	18.3098i	0.146963	+	1.16033i
$250$	10.6779	−	11.3110i	0.675332	−	0.715372i
$251$			17.1403i			1.08189i	0.841059	+	0.540944i	$0.181933\pi$
$251$			17.1403i			1.08189i	−0.841059	+	0.540944i	$0.818067\pi$
$252$	16.0471	−	5.13213i	1.01087	−	0.323294i
$253$	−22.9771	−	18.6738i	−1.44456	−	1.17401i
$254$	4.34463	+	4.10146i	0.272606	+	0.257348i
$255$	−1.35616	−	10.7075i	−0.0849263	−	0.670528i
$256$	15.5777	−	3.65177i	0.973606	−	0.228236i
$257$			10.2467i			0.639171i	0.947557	+	0.319586i	$0.103544\pi$
$257$			10.2467i			0.639171i	−0.947557	+	0.319586i	$0.896456\pi$
$258$	17.3329	+	12.6544i	1.07910	+	0.787830i
$259$		−	18.9355i		−	1.17659i
$260$	−0.747323	−	12.9676i	−0.0463470	−	0.804216i
$261$	5.73027	−	1.47521i	0.354695	−	0.0913131i
$262$	−5.22933	−	4.93664i	−0.323069	−	0.304987i
$263$	0.385612			0.0237779			0.0118889	−	0.999929i	$-0.496216\pi$
$263$	0.385612			0.0237779			0.0118889	+	0.999929i	$0.496216\pi$
$264$	−25.4133	−	16.3992i	−1.56408	−	1.00930i
$265$	−11.5917			−0.712076
$266$	−14.7910	+	15.6680i	−0.906896	+	0.960665i
$267$	−1.57732	+	0.199776i	−0.0965302	+	0.0122261i
$268$	0.185665	+	3.22167i	0.0113413	+	0.196795i
$269$	7.40157			0.451282			0.225641	−	0.974211i	$-0.427552\pi$
$269$	7.40157			0.451282			0.225641	+	0.974211i	$0.427552\pi$
$270$	3.64321	−	9.15702i	0.221719	−	0.557279i
$271$	5.54348			0.336742			0.168371	−	0.985724i	$-0.446149\pi$
$271$	5.54348			0.336742			0.168371	+	0.985724i	$0.446149\pi$
$272$	18.4625	−	2.13508i	1.11945	−	0.129458i
$273$	23.3657	−	2.95941i	1.41416	−	0.179112i
$274$	−21.1449	−	19.9614i	−1.27741	−	1.20591i
$275$		−	19.7648i		−	1.19186i
$276$	14.5883	+	7.94867i	0.878113	+	0.478454i
$277$		−	9.38881i		−	0.564119i	−0.959397	−	0.282059i	$-0.908982\pi$
$277$		−	9.38881i		−	0.564119i	0.959397	−	0.282059i	$-0.0910175\pi$
$278$	13.2095	−	13.9926i	0.792251	−	0.839223i
$279$	−6.05499	+	1.55881i	−0.362503	+	0.0933232i
$280$	6.85401	−	8.15310i	0.409606	−	0.487241i
$281$	−7.05346			−0.420774			−0.210387	−	0.977618i	$-0.567472\pi$
$281$	−7.05346			−0.420774			−0.210387	+	0.977618i	$0.567472\pi$
$282$	1.87067	−	2.56228i	0.111397	−	0.152582i
$283$	−0.239678			−0.0142474			−0.00712370	−	0.999975i	$-0.502268\pi$
$283$	−0.239678			−0.0142474			−0.00712370	+	0.999975i	$0.502268\pi$
$284$	−3.90940	+	0.225299i	−0.231980	+	0.0133690i
$285$	1.58369	+	12.5039i	0.0938098	+	0.740667i
$286$	−30.7455	−	29.0246i	−1.81802	−	1.71626i
$287$	−18.4349			−1.08818
$288$	15.6994	+	6.44435i	0.925094	+	0.379737i
$289$	4.58894			0.269938
$290$	2.56796	−	2.72021i	0.150796	−	0.159736i
$291$	0.415697	+	3.28210i	0.0243686	+	0.192400i
$292$	0.986865	+	17.1241i	0.0577519	+	1.00212i
$293$		−	14.2081i		−	0.830048i	−0.909810	−	0.415024i	$-0.863773\pi$
$293$		−	14.2081i		−	0.830048i	0.909810	−	0.415024i	$-0.136227\pi$
$294$	1.75018	+	1.27777i	0.102073	+	0.0745212i
$295$		−	7.02482i		−	0.409001i
$296$	12.2736	−	14.5999i	0.713387	−	0.848600i
$297$	−11.8381	−	29.8157i	−0.686919	−	1.73008i
$298$	13.6432	−	14.4521i	0.790329	−	0.837187i
$299$	18.0230	+	14.6475i	1.04230	+	0.847088i
$300$	2.02417	+	10.9037i	0.116866	+	0.629526i
$301$			24.6015i			1.41801i
$302$	5.65265	+	5.33627i	0.325273	+	0.307068i
$303$	−27.7585	+	3.51578i	−1.59468	+	0.201976i
$304$	−21.5600	+	2.49329i	−1.23655	+	0.143000i
$305$		−	11.0102i		−	0.630442i
$306$	17.2557	+	9.53115i	0.986441	+	0.544860i
$307$		−	22.5656i		−	1.28789i	−0.765073	−	0.643943i	$-0.777297\pi$
$307$		−	22.5656i		−	1.28789i	0.765073	−	0.643943i	$-0.222703\pi$
$308$	−1.99481	−	34.6141i	−0.113665	−	1.97232i
$309$	−2.11641	−	16.7099i	−0.120398	−	0.950595i
$310$	−2.71348	+	2.87436i	−0.154115	+	0.163253i
$311$		−	14.2260i		−	0.806682i	−0.915050	−	0.403341i	$-0.867849\pi$
$311$		−	14.2260i		−	0.806682i	0.915050	−	0.403341i	$-0.132151\pi$
$312$	19.9340	+	12.8634i	1.12854	+	0.728246i
$313$			9.28451i			0.524792i	0.964960	+	0.262396i	$0.0845126\pi$
$313$			9.28451i			0.524792i	−0.964960	+	0.262396i	$0.915487\pi$
$314$	−16.2102	−	15.3029i	−0.914796	−	0.863594i
$315$	10.9407	−	2.81659i	0.616438	−	0.158697i
$316$	−16.3984	+	0.945039i	−0.922481	+	0.0531626i
$317$	−4.11851			−0.231319			−0.115659	−	0.993289i	$-0.536898\pi$
$317$	−4.11851			−0.231319			−0.115659	+	0.993289i	$0.536898\pi$
$318$	12.4840	−	17.0995i	0.700070	−	0.958895i
$319$		−	12.1770i		−	0.681780i
$320$	10.5693	−	1.84368i	0.590844	−	0.103065i
$321$	0.542523	+	4.28344i	0.0302807	+	0.239078i
$322$	2.50162	+	18.8795i	0.139410	+	1.05212i
$323$	−25.2110			−1.40278
$324$	9.58432	+	15.2362i	0.532462	+	0.846454i
$325$			15.5033i			0.859968i
$326$	12.9051	−	13.6702i	0.714747	−	0.757124i
$327$	−27.1589	+	3.43983i	−1.50189	+	0.190223i
$328$	−14.2139	−	11.9491i	−0.784830	−	0.659778i
$329$	3.63677			0.200502
$330$	−16.3802	−	11.9589i	−0.901701	−	0.658314i
$331$			23.4632i			1.28965i	0.764329	+	0.644827i	$0.223071\pi$
$331$			23.4632i			1.28965i	−0.764329	+	0.644827i	$0.776929\pi$
$332$	−21.2759	+	1.22613i	−1.16767	+	0.0672926i
$333$	19.5917	−	5.04370i	1.07362	−	0.276393i
$334$	10.2663	−	10.8750i	0.561746	−	0.595051i
$335$			2.16390i			0.118227i
$336$	4.64542	+	18.8914i	0.253429	+	1.03061i
$337$		−	7.32876i		−	0.399223i	−0.979875	−	0.199611i	$-0.936032\pi$
$337$		−	7.32876i		−	0.399223i	0.979875	−	0.199611i	$-0.0639680\pi$
$338$	10.7477	+	10.1461i	0.584598	+	0.551877i
$339$	−6.07382	+	0.769285i	−0.329885	+	0.0417818i
$340$	12.4421	−	0.717036i	0.674765	−	0.0388867i
$341$			12.8670i			0.696788i
$342$	−20.1507	−	11.1302i	−1.08962	−	0.601853i
$343$		−	17.1716i		−	0.927181i
$344$	−15.9462	+	18.9686i	−0.859760	+	1.02272i
$345$	9.45944	+	5.88404i	0.509279	+	0.316786i
$346$	−15.9516	−	15.0588i	−0.857565	−	0.809566i
$347$	−19.7499			−1.06023			−0.530115	−	0.847926i	$-0.677851\pi$
$347$	−19.7499			−1.06023			−0.530115	+	0.847926i	$0.677851\pi$
$348$	1.24708	+	6.71772i	0.0668507	+	0.360107i
$349$		−	33.5713i		−	1.79703i	−0.438945	−	0.898514i	$-0.644648\pi$
$349$		−	33.5713i		−	1.79703i	0.438945	−	0.898514i	$-0.355352\pi$
$350$	−8.72700	+	9.24442i	−0.466478	+	0.494135i
$351$	9.28572	+	23.3872i	0.495635	+	1.24831i
$352$	20.8980	−	27.9816i	1.11387	−	1.49142i
$353$		−	6.67543i		−	0.355297i	−0.984094	−	0.177649i	$-0.943151\pi$
$353$		−	6.67543i		−	0.355297i	0.984094	−	0.177649i	$-0.0568490\pi$
$354$	10.3626	+	7.56556i	0.550768	+	0.402105i
$355$	−2.62583			−0.139365
$356$	−0.105626	−	1.83284i	−0.00559819	−	0.0971402i
$357$	2.83947	+	22.4188i	0.150281	+	1.18653i
$358$	10.2344	+	9.66154i	0.540903	+	0.510628i
$359$	11.4626			0.604972			0.302486	−	0.953154i	$-0.402184\pi$
$359$	11.4626			0.604972			0.302486	+	0.953154i	$0.402184\pi$
$360$	10.2613	+	4.91984i	0.540817	+	0.259299i
$361$	10.4407			0.549509
$362$	0.0311918	+	0.0294460i	0.00163941	+	0.00154765i
$363$	−46.5932	+	5.90131i	−2.44551	+	0.309738i
$364$	1.56471	+	27.1509i	0.0820130	+	1.42310i
$365$			11.5018i			0.602031i
$366$	16.2417	+	11.8577i	0.848965	+	0.619812i
$367$			5.41598i			0.282712i	0.989959	+	0.141356i	$0.0451462\pi$
$367$			5.41598i			0.282712i	−0.989959	+	0.141356i	$0.954854\pi$
$368$	−10.3085	+	16.1782i	−0.537367	+	0.843349i
$369$	−4.91036	−	19.0737i	−0.255623	−	0.992936i
$370$	8.77979	−	9.30033i	0.456439	−	0.483501i
$371$	24.2702			1.26005
$372$	−1.31775	−	7.09839i	−0.0683223	−	0.368035i
$373$	13.1527			0.681018			0.340509	−	0.940241i	$-0.389401\pi$
$373$	13.1527			0.681018			0.340509	+	0.940241i	$0.389401\pi$
$374$	27.8483	−	29.4994i	1.44000	−	1.52538i
$375$	2.39378	+	18.8999i	0.123614	+	0.975987i
$376$	2.80407	+	2.35728i	0.144609	+	0.121567i
$377$			9.55150i			0.491927i
$378$	−7.62798	+	19.1725i	−0.392341	+	0.986129i
$379$	4.98683			0.256156			0.128078	−	0.991764i	$-0.459119\pi$
$379$	4.98683			0.256156			0.128078	+	0.991764i	$0.459119\pi$
$380$	−14.5295	+	0.837335i	−0.745347	+	0.0429544i
$381$	−7.25956	+	0.919465i	−0.371918	+	0.0471056i
$382$	25.6150	+	24.1813i	1.31058	+	1.23723i
$383$	6.42719			0.328414			0.164207	−	0.986426i	$-0.447494\pi$
$383$	6.42719			0.328414			0.164207	+	0.986426i	$0.447494\pi$
$384$	−8.66322	+	17.5769i	−0.442093	+	0.896969i
$385$		−	23.2493i		−	1.18489i
$386$	4.97467	+	4.69623i	0.253204	+	0.239032i
$387$	−25.4540	+	6.55292i	−1.29390	+	0.333103i
$388$	−3.81379	+	0.219789i	−0.193616	+	0.0111581i
$389$		−	14.3879i		−	0.729498i	−0.931106	−	0.364749i	$-0.881155\pi$
$389$		−	14.3879i		−	0.729498i	0.931106	−	0.364749i	$-0.118845\pi$
$390$	12.8485	+	9.38042i	0.650608	+	0.474996i
$391$	−14.0539	+	17.2926i	−0.710736	+	0.874524i
$392$	−1.61015	+	1.91534i	−0.0813250	+	0.0967391i
$393$	8.73784	−	1.10670i	0.440766	−	0.0558255i
$394$	11.8955	+	11.2297i	0.599289	+	0.565746i
$395$	−11.0143			−0.554190
$396$	35.2822	−	11.2838i	1.77300	−	0.567034i
$397$			5.15731i			0.258838i	0.991590	+	0.129419i	$0.0413112\pi$
$397$			5.15731i			0.258838i	−0.991590	+	0.129419i	$0.958689\pi$
$398$	−4.70303	+	4.98187i	−0.235741	+	0.249718i
$399$	−3.31586	−	26.1801i	−0.166000	−	1.31064i
$400$	−12.7208	+	1.47109i	−0.636042	+	0.0735545i
$401$	17.0512			0.851496			0.425748	−	0.904842i	$-0.360011\pi$
$401$	17.0512			0.851496			0.425748	+	0.904842i	$0.360011\pi$
$402$	−3.19207	−	2.33047i	−0.159206	−	0.116233i
$403$		−	10.0928i		−	0.502756i
$404$	−1.85887	−	32.2553i	−0.0924824	−	1.60476i
$405$	5.82838	+	10.5696i	0.289615	+	0.525207i
$406$	−5.37666	+	5.69544i	−0.266839	+	0.282660i
$407$		−	41.6328i		−	2.06366i
$408$	−12.3421	+	19.1261i	−0.611023	+	0.946883i
$409$	−0.175936			−0.00869950			−0.00434975	−	0.999991i	$-0.501385\pi$
$409$	−0.175936			−0.00869950			−0.00434975	+	0.999991i	$0.501385\pi$
$410$	−9.05445	−	8.54766i	−0.447167	−	0.422139i
$411$	35.3316	−	4.47495i	1.74278	−	0.220733i
$412$	19.4169	−	1.11900i	0.956602	−	0.0551290i
$413$			14.7082i			0.723744i
$414$	−18.8674	+	7.61711i	−0.927283	+	0.374361i
$415$	−14.2904			−0.701488
$416$	−16.3922	+	21.9485i	−0.803695	+	1.07611i
$417$	2.96130	+	23.3807i	0.145015	+	1.14496i
$418$	−32.5205	+	34.4486i	−1.59063	+	1.68494i
$419$			15.1092i			0.738133i	0.929403	+	0.369066i	$0.120323\pi$
$419$			15.1092i			0.738133i	−0.929403	+	0.369066i	$0.879677\pi$
$420$	2.38103	+	12.8260i	0.116182	+	0.625845i
$421$	−14.4108			−0.702337			−0.351169	−	0.936312i	$-0.614216\pi$
$421$	−14.4108			−0.702337			−0.351169	+	0.936312i	$0.614216\pi$
$422$	−24.8120	+	26.2831i	−1.20783	+	1.27944i
$423$	0.968700	+	3.76280i	0.0470998	+	0.182953i
$424$	18.7132	+	15.7315i	0.908791	+	0.763987i
$425$	−14.8750			−0.721543
$426$	2.82796	−	3.87349i	0.137015	−	0.187671i
$427$			23.0526i			1.11559i
$428$	−4.97735	+	0.286845i	−0.240589	+	0.0138652i
$429$	51.3735	−	6.50675i	2.48033	−	0.314149i
$430$	−11.4069	+	12.0832i	−0.550091	+	0.582706i
$431$	−14.2732			−0.687514			−0.343757	−	0.939059i	$-0.611700\pi$
$431$	−14.2732			−0.687514			−0.343757	+	0.939059i	$0.611700\pi$
$432$	−18.3087	+	9.83836i	−0.880875	+	0.473348i
$433$		−	14.5780i		−	0.700573i	−0.936643	−	0.350287i	$-0.886084\pi$
$433$		−	14.5780i		−	0.700573i	0.936643	−	0.350287i	$-0.113916\pi$
$434$	5.68135	−	6.01819i	0.272713	−	0.288882i
$435$	0.575685	+	4.54527i	0.0276020	+	0.217929i
$436$	−1.81872	−	31.5586i	−0.0871009	−	1.51138i
$437$	16.4118	−	20.1938i	0.785081	−	0.966001i
$438$	−16.9668	−	12.3872i	−0.810707	−	0.591881i
$439$	26.6570			1.27227			0.636134	−	0.771578i	$-0.280532\pi$
$439$	26.6570			1.27227			0.636134	+	0.771578i	$0.280532\pi$
$440$	15.0697	−	17.9259i	0.718419	−	0.854586i
$441$	−2.57020	+	0.661676i	−0.122391	+	0.0315084i
$442$	−21.8440	+	23.1391i	−1.03901	+	1.10061i
$443$	−18.0639			−0.858244			−0.429122	−	0.903247i	$-0.641177\pi$
$443$	−18.0639			−0.858244			−0.429122	+	0.903247i	$0.641177\pi$
$444$	4.26375	+	22.9677i	0.202349	+	1.09000i
$445$		−	1.23106i		−	0.0583580i
$446$	−23.5674	−	22.2483i	−1.11595	−	1.05349i
$447$	3.05853	+	24.1484i	0.144664	+	1.14218i
$448$	−22.1296	+	3.86021i	−1.04552	+	0.182378i
$449$			3.51992i			0.166115i	0.996545	+	0.0830577i	$0.0264686\pi$
$449$			3.51992i			0.166115i	−0.996545	+	0.0830577i	$0.973531\pi$
$450$	−11.8893	−	6.56705i	−0.560468	−	0.309574i
$451$	−40.5321			−1.90858
$452$	−0.406739	−	7.05777i	−0.0191314	−	0.331969i
$453$	−9.44517	+	1.19629i	−0.443773	+	0.0562064i
$454$	−2.25438	+	2.38804i	−0.105803	+	0.112076i
$455$			18.2365i			0.854940i
$456$	14.4127	−	22.3349i	0.674938	−	1.04593i
$457$			8.18565i			0.382908i	0.981502	+	0.191454i	$0.0613204\pi$
$457$			8.18565i			0.382908i	−0.981502	+	0.191454i	$0.938680\pi$
$458$	12.2688	+	11.5821i	0.573285	+	0.541198i
$459$	−22.4393	+	8.90940i	−1.04738	+	0.415855i
$460$	−7.52515	+	10.4328i	−0.350862	+	0.486431i
$461$	4.67228			0.217610			0.108805	−	0.994063i	$-0.465298\pi$
$461$	4.67228			0.217610			0.108805	+	0.994063i	$0.465298\pi$
$462$	34.2961	+	25.0389i	1.59560	+	1.16492i
$463$	34.0823			1.58394			0.791969	−	0.610562i	$-0.209056\pi$
$463$	34.0823			1.58394			0.791969	+	0.610562i	$0.209056\pi$
$464$	−7.83725	+	0.906332i	−0.363835	+	0.0420754i
$465$	−0.608308	−	4.80284i	−0.0282096	−	0.222726i
$466$	26.6473	−	28.2272i	1.23441	−	1.30760i
$467$			5.14166i			0.237928i	0.992899	+	0.118964i	$0.0379572\pi$
$467$			5.14166i			0.237928i	−0.992899	+	0.118964i	$0.962043\pi$
$468$	−27.6750	+	8.85092i	−1.27928	+	0.409134i
$469$		−	4.53067i		−	0.209207i
$470$	1.78623	+	1.68626i	0.0823928	+	0.0777812i
$471$	27.0861	−	3.43061i	1.24806	−	0.158074i
$472$	−9.53356	+	11.3405i	−0.438818	+	0.521990i
$473$			54.0905i			2.48708i
$474$	11.8622	−	16.2477i	0.544847	−	0.746284i
$475$	17.3706			0.797018
$476$	−26.0506	+	1.50130i	−1.19403	+	0.0688118i
$477$	6.46469	+	25.1113i	0.295998	+	1.14977i
$478$	−7.15432	+	7.57850i	−0.327231	+	0.346632i
$479$	−34.5989			−1.58086			−0.790432	−	0.612550i	$-0.790144\pi$
$479$	−34.5989			−1.58086			−0.790432	+	0.612550i	$0.790144\pi$
$480$	−6.47770	+	11.4326i	−0.295665	+	0.521825i
$481$			32.6563i			1.48900i
$482$	24.0582	−	25.4845i	1.09582	−	1.16079i
$483$	−19.8057	−	12.3197i	−0.901192	−	0.560567i
$484$	−3.12016	−	54.1412i	−0.141825	−	2.46096i
$485$	−2.56161			−0.116317
$486$	−21.8687	−	2.78546i	−0.991986	−	0.126351i
$487$	−15.8570			−0.718549			−0.359274	−	0.933232i	$-0.616976\pi$
$487$	−15.8570			−0.718549			−0.359274	+	0.933232i	$0.616976\pi$
$488$	−14.9422	+	17.7743i	−0.676402	+	0.804605i
$489$	2.89307	+	22.8420i	0.130829	+	1.03295i
$490$	−1.15181	+	1.22010i	−0.0520334	+	0.0551184i
$491$	22.7212			1.02540			0.512698	−	0.858569i	$-0.328646\pi$
$491$	22.7212			1.02540			0.512698	+	0.858569i	$0.328646\pi$
$492$	22.3605	−	4.15102i	1.00809	−	0.187142i
$493$	−9.16440			−0.412744
$494$	25.5088	−	27.0212i	1.14769	−	1.21574i
$495$	24.0549	−	6.19273i	1.08119	−	0.278343i
$496$	8.28137	−	0.957691i	0.371844	−	0.0430016i
$497$	5.49784			0.246612
$498$	15.3904	−	21.0804i	0.689661	−	0.944637i
$499$			3.47554i			0.155587i	0.996970	+	0.0777933i	$0.0247874\pi$
$499$			3.47554i			0.155587i	−0.996970	+	0.0777933i	$0.975213\pi$
$500$	−21.9616	+	1.26565i	−0.982155	+	0.0566016i
$501$	2.30150	+	18.1713i	0.102823	+	0.811832i
$502$	16.6399	−	17.6265i	0.742677	−	0.786710i
$503$	−16.9913			−0.757606			−0.378803	−	0.925477i	$-0.623664\pi$
$503$	−16.9913			−0.757606			−0.378803	+	0.925477i	$0.623664\pi$
$504$	−21.4846	−	10.3009i	−0.956999	−	0.458840i
$505$		−	21.6649i		−	0.964077i
$506$	5.50023	+	41.5098i	0.244515	+	1.84533i
$507$	−17.9586	+	2.27456i	−0.797570	+	0.101017i
$508$	−0.486143	−	8.43559i	−0.0215691	−	0.374269i
$509$	23.7927			1.05459			0.527295	−	0.849682i	$-0.323206\pi$
$509$	23.7927			1.05459			0.527295	+	0.849682i	$0.323206\pi$
$510$	−9.00026	+	12.3278i	−0.398538	+	0.545883i
$511$		−	24.0819i		−	1.06532i
$512$	−19.5647	−	11.3676i	−0.864647	−	0.502380i
$513$	26.2040	−	10.4041i	1.15694	−	0.459354i
$514$	9.94755	−	10.5373i	0.438768	−	0.464782i
$515$	13.0418			0.574689
$516$	−5.53958	−	29.8403i	−0.243866	−	1.31365i
$517$	7.99605			0.351666
$518$	−18.3827	+	19.4726i	−0.807689	+	0.855576i
$519$	26.6540	−	3.37589i	1.16998	−	0.148185i
$520$	−11.8205	+	14.0609i	−0.518364	+	0.616613i
$521$	40.4306			1.77130			0.885649	−	0.464355i	$-0.153714\pi$
$521$	40.4306			1.77130			0.885649	+	0.464355i	$0.153714\pi$
$522$	−7.32495	−	4.04593i	−0.320604	−	0.177085i
$523$	37.7446			1.65046			0.825228	−	0.564799i	$-0.191046\pi$
$523$	37.7446			1.65046			0.825228	+	0.564799i	$0.191046\pi$
$524$	0.585137	+	10.1533i	0.0255618	+	0.443551i
$525$	−1.95642	−	15.4468i	−0.0853853	−	0.674152i
$526$	−0.396550	−	0.374355i	−0.0172904	−	0.0163227i
$527$	9.68373			0.421830
$528$	10.2137	+	41.5358i	0.444496	+	1.80761i
$529$	−4.70248	−	22.5141i	−0.204456	−	0.978876i
$530$	11.9205	+	11.2533i	0.517796	+	0.488814i
$531$	−15.2179	+	3.91772i	−0.660401	+	0.170015i
$532$	30.4212	−	1.75317i	1.31892	−	0.0760096i
$533$	31.7930			1.37711
$534$	1.81600	+	1.32583i	0.0785861	+	0.0573741i
$535$	−3.34314			−0.144537
$536$	2.93669	−	3.49330i	0.126846	−	0.150887i
$537$	−17.1009	+	2.16593i	−0.737958	+	0.0934667i
$538$	−7.61152	−	7.18550i	−0.328156	−	0.309789i
$539$			5.46175i			0.235254i
$540$	−12.6362	+	5.87991i	−0.543778	+	0.253031i
$541$		−	1.12183i		−	0.0482313i	−0.999709	−	0.0241157i	$-0.992323\pi$
$541$		−	1.12183i		−	0.0482313i	0.999709	−	0.0241157i	$-0.00767700\pi$
$542$	−5.70072	−	5.38165i	−0.244867	−	0.231162i
$543$	−0.0521193	+	0.00660121i	−0.00223665	+	0.000283285i
$544$	−21.0590	−	15.7279i	−0.902895	−	0.674328i
$545$		−	21.1970i		−	0.907979i
$546$	−26.9015	−	19.6403i	−1.15128	−	0.840526i
$547$		−	24.3932i		−	1.04298i	−0.853258	−	0.521489i	$-0.825377\pi$
$547$		−	24.3932i		−	1.04298i	0.853258	−	0.521489i	$-0.174623\pi$
$548$	2.36601	+	41.0552i	0.101071	+	1.75379i
$549$	−23.8514	+	6.14035i	−1.01795	+	0.262064i
$550$	−19.1878	+	20.3254i	−0.818169	+	0.866678i
$551$	10.7019			0.455918
$552$	−7.28548	−	22.3366i	−0.310091	−	0.950707i
$553$	23.0612			0.980664
$554$	−9.11472	+	9.65512i	−0.387247	+	0.410207i
$555$	1.96825	+	15.5402i	0.0835478	+	0.659644i
$556$	−27.1683	+	1.56571i	−1.15219	+	0.0664009i
$557$		−	7.71934i		−	0.327079i	−0.986537	−	0.163540i	$-0.947709\pi$
$557$		−	7.71934i		−	0.327079i	0.986537	−	0.163540i	$-0.0522911\pi$
$558$	7.74004	+	4.27520i	0.327662	+	0.180984i
$559$		−	42.4280i		−	1.79451i
$560$	−14.9635	+	1.73044i	−0.632324	+	0.0731245i
$561$	6.24305	+	49.2914i	0.263582	+	2.08109i
$562$	7.25353	+	6.84754i	0.305972	+	0.288846i
$563$		−	2.37078i		−	0.0999163i	−0.998751	−	0.0499581i	$-0.984091\pi$
$563$		−	2.37078i		−	0.0999163i	0.998751	−	0.0499581i	$-0.0159088\pi$
$564$	−4.41121	+	0.818901i	−0.185745	+	0.0344819i
$565$		−	4.74050i		−	0.199434i
$566$	0.246477	+	0.232681i	0.0103602	+	0.00978032i
$567$	−12.2032	−	22.1301i	−0.512485	−	0.929376i
$568$	4.23902	+	3.56359i	0.177865	+	0.149525i
$569$	8.45368			0.354397			0.177198	−	0.984175i	$-0.443297\pi$
$569$	8.45368			0.354397			0.177198	+	0.984175i	$0.443297\pi$
$570$	10.5103	−	14.3960i	0.440226	−	0.602983i
$571$	11.0497			0.462416			0.231208	−	0.972904i	$-0.425732\pi$
$571$	11.0497			0.462416			0.231208	+	0.972904i	$0.425732\pi$
$572$	3.44027	+	59.6958i	0.143845	+	2.49601i
$573$	−42.8009	+	5.42098i	−1.78803	+	0.226465i
$574$	18.9578	+	17.8967i	0.791282	+	0.746993i
$575$	9.68327	−	11.9148i	0.403820	−	0.496880i
$576$	−9.88846	−	21.8682i	−0.412019	−	0.911175i
$577$	24.9723			1.03961			0.519804	−	0.854285i	$-0.326005\pi$
$577$	24.9723			1.03961			0.519804	+	0.854285i	$0.326005\pi$
$578$	−4.71911	−	4.45498i	−0.196289	−	0.185303i
$579$	−8.31231	+	1.05280i	−0.345448	+	0.0437530i
$580$	−5.28159	+	0.304378i	−0.219306	+	0.0126386i
$581$	29.9205			1.24131
$582$	2.75879	−	3.77875i	0.114356	−	0.156634i
$583$	53.3622			2.21003
$584$	15.6094	−	18.5679i	0.645921	−	0.768346i
$585$	−18.8684	+	4.85752i	−0.780114	+	0.200834i
$586$	−13.7933	+	14.6111i	−0.569798	+	0.603581i
$587$	−20.3561			−0.840187			−0.420093	−	0.907481i	$-0.638003\pi$
$587$	−20.3561			−0.840187			−0.420093	+	0.907481i	$0.638003\pi$
$588$	−0.559355	−	3.01310i	−0.0230674	−	0.124258i
$589$	−11.3084			−0.465954
$590$	−6.81974	+	7.22408i	−0.280764	+	0.297411i
$591$	−19.8766	+	2.51749i	−0.817614	+	0.103556i
$592$	−26.7954	+	3.09873i	−1.10128	+	0.127357i
$593$			7.15453i			0.293801i	0.989151	+	0.146901i	$0.0469298\pi$
$593$			7.15453i			0.293801i	−0.989151	+	0.146901i	$0.953070\pi$
$594$	−16.7714	+	42.1540i	−0.688138	+	1.72960i
$595$	−17.4974			−0.717324
$596$	−28.0604	+	1.61712i	−1.14940	+	0.0662398i
$597$	−1.05433	−	8.32433i	−0.0431507	−	0.340692i
$598$	−4.31432	−	32.5599i	−0.176426	−	1.33147i
$599$		−	29.8254i		−	1.21863i	−0.792927	−	0.609316i	$-0.791444\pi$
$599$		−	29.8254i		−	1.21863i	0.792927	−	0.609316i	$-0.208556\pi$
$600$	8.50380	−	13.1781i	0.347166	−	0.537992i
$601$	23.2672			0.949090			0.474545	−	0.880231i	$-0.342613\pi$
$601$	23.2672			0.949090			0.474545	+	0.880231i	$0.342613\pi$
$602$	23.8833	−	25.2993i	0.973410	−	1.03112i
$603$	4.68767	−	1.20680i	0.190897	−	0.0491448i
$604$	−0.632504	−	10.9753i	−0.0257362	−	0.446577i
$605$		−	36.3651i		−	1.47845i
$606$	31.9590	+	23.3326i	1.29825	+	0.947823i
$607$	−45.1275			−1.83167			−0.915833	−	0.401558i	$-0.868469\pi$
$607$	−45.1275			−1.83167			−0.915833	+	0.401558i	$0.868469\pi$
$608$	24.5921	+	18.3666i	0.997340	+	0.744864i
$609$	−1.20534	−	9.51667i	−0.0488429	−	0.385635i
$610$	−10.6888	+	11.3225i	−0.432775	+	0.458434i
$611$	−6.27202			−0.253739
$612$	−8.49222	−	26.5534i	−0.343278	−	1.07336i
$613$	−20.5759			−0.831054			−0.415527	−	0.909581i	$-0.636403\pi$
$613$	−20.5759			−0.831054			−0.415527	+	0.909581i	$0.636403\pi$
$614$	−21.9068	+	23.2057i	−0.884087	+	0.936504i
$615$	15.1293	−	1.91622i	0.610073	−	0.0772693i
$616$	−31.5522	+	37.5325i	−1.27127	+	1.51223i
$617$	24.4777			0.985434			0.492717	−	0.870189i	$-0.336004\pi$
$617$	24.4777			0.985434			0.492717	+	0.870189i	$0.336004\pi$
$618$	−14.0457	+	19.2385i	−0.565000	+	0.773887i
$619$	21.6956			0.872020			0.436010	−	0.899942i	$-0.356391\pi$
$619$	21.6956			0.872020			0.436010	+	0.899942i	$0.356391\pi$
$620$	5.58089	−	0.321627i	0.224134	−	0.0129168i
$621$	7.47113	−	23.7736i	0.299806	−	0.954000i
$622$	−13.8107	+	14.6295i	−0.553758	+	0.586590i
$623$			2.57754i			0.103267i
$624$	−8.01155	−	32.5803i	−0.320719	−	1.30426i
$625$	1.25603			0.0502412
$626$	9.01346	−	9.54787i	0.360251	−	0.381609i
$627$	−7.29046	−	57.5612i	−0.291153	−	2.29877i
$628$	1.81385	+	31.4740i	0.0723803	+	1.25595i
$629$	−31.3329			−1.24932
$630$	−13.9854	−	7.72481i	−0.557191	−	0.307764i
$631$		−	37.8901i		−	1.50838i	−0.656656	−	0.754190i	$-0.728030\pi$
$631$		−	37.8901i		−	1.50838i	0.656656	−	0.754190i	$-0.271970\pi$
$632$	17.7810	+	14.9478i	0.707289	+	0.594592i
$633$	−5.56236	−	43.9171i	−0.221084	−	1.74555i
$634$	4.23533	+	3.99828i	0.168207	+	0.158792i
$635$		−	5.66594i		−	0.224846i
$636$	−29.4385	+	5.46499i	−1.16731	+	0.216701i
$637$		−	4.28414i		−	0.169744i
$638$	−11.8215	+	12.5224i	−0.468017	+	0.495766i
$639$	1.46442	+	5.68836i	0.0579316	+	0.225028i
$640$	−12.6590	−	8.36481i	−0.500391	−	0.330648i
$641$	−20.7530			−0.819696			−0.409848	−	0.912154i	$-0.634418\pi$
$641$	−20.7530			−0.819696			−0.409848	+	0.912154i	$0.634418\pi$
$642$	3.60048	−	4.93163i	0.142100	−	0.194636i
$643$	−1.87244			−0.0738417			−0.0369209	−	0.999318i	$-0.511755\pi$
$643$	−1.87244			−0.0738417			−0.0369209	+	0.999318i	$0.511755\pi$
$644$	15.7558	−	21.8436i	0.620865	−	0.860760i
$645$	−2.55721	−	20.1902i	−0.100690	−	0.794989i
$646$	25.9261	+	24.4750i	1.02005	+	0.962955i
$647$			16.8036i			0.660617i	0.943873	+	0.330308i	$0.107153\pi$
$647$			16.8036i			0.660617i	−0.943873	+	0.330308i	$0.892847\pi$
$648$	4.93520	−	24.9729i	0.193873	−	0.981027i
$649$			32.3385i			1.26940i
$650$	15.0507	−	15.9430i	0.590337	−	0.625337i
$651$	1.27365	+	10.0560i	0.0499181	+	0.394124i
$652$	−26.5423	+	1.52963i	−1.03948	+	0.0599051i
$653$	−19.3214			−0.756106			−0.378053	−	0.925784i	$-0.623406\pi$
$653$	−19.3214			−0.756106			−0.378053	+	0.925784i	$0.623406\pi$
$654$	31.2687	+	22.8286i	1.22270	+	0.892670i
$655$			6.81971i			0.266468i
$656$	3.01680	+	26.0869i	0.117786	+	1.01852i
$657$	24.9164	−	6.41452i	0.972082	−	0.250254i
$658$	−3.73993	−	3.53060i	−0.145798	−	0.137637i
$659$		−	23.3970i		−	0.911419i	−0.890129	−	0.455709i	$-0.849386\pi$
$659$		−	23.3970i		−	0.911419i	0.890129	−	0.455709i	$-0.150614\pi$
$660$	5.23509	+	28.2001i	0.203776	+	1.09769i
$661$	23.4727			0.912984			0.456492	−	0.889728i	$-0.349106\pi$
$661$	23.4727			0.912984			0.456492	+	0.889728i	$0.349106\pi$
$662$	22.7782	−	24.1287i	0.885301	−	0.937790i
$663$	−4.89698	−	38.6637i	−0.190183	−	1.50157i
$664$	23.0697	+	19.3939i	0.895278	+	0.752628i
$665$	20.4330			0.792358
$666$	−25.0438	−	13.8329i	−0.970429	−	0.536015i
$667$	5.96581	−	7.34062i	0.230997	−	0.284230i
$668$	−21.1150	+	1.21686i	−0.816962	+	0.0470816i
$669$	39.3793	−	4.98762i	1.52249	−	0.192833i
$670$	2.10073	−	2.22528i	0.0811583	−	0.0859701i
$671$			50.6850i			1.95667i
$672$	13.5627	−	23.9370i	0.523192	−	0.923391i
$673$	−26.3870			−1.01714			−0.508572	−	0.861019i	$-0.669827\pi$
$673$	−26.3870			−1.01714			−0.508572	+	0.861019i	$0.669827\pi$
$674$	−7.11481	+	7.53664i	−0.274052	+	0.290301i
$675$	15.4609	−	6.13866i	0.595091	−	0.236277i
$676$	−1.20262	−	20.8679i	−0.0462545	−	0.802610i
$677$		−	19.2132i		−	0.738422i	−0.929346	−	0.369211i	$-0.879628\pi$
$677$		−	19.2132i		−	0.738422i	0.929346	−	0.369211i	$-0.120372\pi$
$678$	6.99293	+	5.10540i	0.268562	+	0.196072i
$679$	5.36337			0.205827
$680$	−13.4911	−	11.3415i	−0.517359	−	0.434925i
$681$	−0.505388	−	3.99024i	−0.0193665	−	0.152906i
$682$	12.4914	−	13.2320i	0.478320	−	0.506679i
$683$	−16.2143			−0.620422			−0.310211	−	0.950668i	$-0.600400\pi$
$683$	−16.2143			−0.620422			−0.310211	+	0.950668i	$0.600400\pi$
$684$	9.91698	+	31.0084i	0.379185	+	1.18563i
$685$			27.5756i			1.05361i
$686$	−16.6703	+	17.6587i	−0.636476	+	0.674213i
$687$	−20.5003	+	2.59649i	−0.782136	+	0.0990621i
$688$	34.8133	−	4.02595i	1.32724	−	0.153488i
$689$	−41.8567			−1.59461
$690$	−4.01550	−	15.2342i	−0.152867	−	0.579957i
$691$			10.2750i			0.390880i	0.980716	+	0.195440i	$0.0626134\pi$
$691$			10.2750i			0.390880i	−0.980716	+	0.195440i	$0.937387\pi$
$692$	1.78491	+	30.9719i	0.0678521	+	1.17737i
$693$	−50.3650	+	12.9660i	−1.91321	+	0.492539i
$694$	20.3101	+	19.1733i	0.770961	+	0.727810i
$695$	−18.2482			−0.692192
$696$	5.23915	−	8.11894i	0.198589	−	0.307748i
$697$			30.5045i			1.15544i
$698$	−32.5912	+	34.5235i	−1.23360	+	1.30673i
$699$	5.97379	+	47.1656i	0.225950	+	1.78397i
$700$	17.9491	−	1.03441i	0.678412	−	0.0390969i
$701$		−	37.9687i		−	1.43406i	−0.697044	−	0.717029i	$-0.745502\pi$
$701$		−	37.9687i		−	1.43406i	0.697044	−	0.717029i	$-0.254498\pi$
$702$	13.1553	−	33.0652i	0.496515	−	1.24796i
$703$	36.5897			1.38001
$704$	−48.6555	+	8.48731i	−1.83377	+	0.319877i
$705$	−2.98467	+	0.378025i	−0.112409	+	0.0142373i
$706$	−6.48055	+	6.86478i	−0.243899	+	0.258359i
$707$			45.3610i			1.70598i
$708$	−3.31189	−	17.8403i	−0.124468	−	0.670479i
$709$	−31.3658			−1.17797			−0.588983	−	0.808146i	$-0.700471\pi$
$709$	−31.3658			−1.17797			−0.588983	+	0.808146i	$0.700471\pi$
$710$	2.70032	+	2.54918i	0.101341	+	0.0956689i
$711$	6.14265	+	23.8604i	0.230367	+	0.894834i
$712$	−1.67071	+	1.98737i	−0.0626125	+	0.0744798i
$713$	−6.30388	+	7.75660i	−0.236082	+	0.290487i
$714$	18.8443	−	25.8113i	0.705230	−	0.965963i
$715$			40.0959i			1.49950i
$716$	−1.14518	−	19.8712i	−0.0427973	−	0.742621i
$717$	−1.60386	−	12.6631i	−0.0598972	−	0.472913i
$718$	−11.7877	−	11.1279i	−0.439914	−	0.415291i
$719$			13.6827i			0.510279i	0.966904	+	0.255140i	$0.0821214\pi$
$719$			13.6827i			0.510279i	−0.966904	+	0.255140i	$0.917879\pi$
$720$	−5.77613	−	15.0211i	−0.215264	−	0.559804i
$721$	−27.3062			−1.01694
$722$	−10.7368	−	10.1359i	−0.399583	−	0.377218i
$723$	5.39336	+	42.5828i	0.200581	+	1.58367i
$724$	−0.00349022	−	0.0605625i	−0.000129713	−	0.00225079i
$725$	6.31436			0.234509
$726$	53.6439	+	39.1643i	1.99091	+	1.45352i
$727$		−	7.42941i		−	0.275542i	−0.990464	−	0.137771i	$-0.956006\pi$
$727$		−	7.42941i		−	0.275542i	0.990464	−	0.137771i	$-0.0439937\pi$
$728$	24.7492	−	29.4401i	0.917267	−	1.09112i
$729$	19.6465	−	18.5207i	0.727647	−	0.685951i
$730$	11.1660	−	11.8280i	0.413273	−	0.437775i
$731$	40.7085			1.50566
$732$	−5.19081	−	27.9616i	−0.191858	−	1.03349i
$733$	22.0117			0.813021			0.406511	−	0.913646i	$-0.366745\pi$
$733$	22.0117			0.813021			0.406511	+	0.913646i	$0.366745\pi$
$734$	5.25787	−	5.56961i	0.194072	−	0.205578i
$735$	−0.258213	−	2.03869i	−0.00952431	−	0.0751984i
$736$	26.3068	−	6.62958i	0.969682	−	0.244370i
$737$		−	9.96143i		−	0.366934i
$738$	−13.4672	+	24.3817i	−0.495735	+	0.897503i
$739$		−	8.66574i		−	0.318774i	−0.987216	−	0.159387i	$-0.949048\pi$
$739$		−	8.66574i		−	0.318774i	0.987216	−	0.159387i	$-0.0509518\pi$
$740$	−18.0576	+	1.04066i	−0.663812	+	0.0382555i
$741$	5.71856	+	45.1504i	0.210077	+	1.65864i
$742$	−24.9587	−	23.5617i	−0.916262	−	0.864978i
$743$	45.6054			1.67310			0.836550	−	0.547891i	$-0.184569\pi$
$743$	45.6054			1.67310			0.836550	+	0.547891i	$0.184569\pi$
$744$	−5.53604	+	8.57902i	−0.202961	+	0.314522i
$745$	−18.8473			−0.690513
$746$	−13.5257	−	12.7687i	−0.495212	−	0.467495i
$747$	7.96971	+	30.9574i	0.291597	+	1.13267i
$748$	−57.2765	+	3.30085i	−2.09424	+	0.120691i
$749$	6.99970			0.255764
$750$	15.8865	−	21.7599i	0.580092	−	0.794559i
$751$			50.6579i			1.84853i	0.381748	+	0.924266i	$0.375322\pi$
$751$			50.6579i			1.84853i	−0.381748	+	0.924266i	$0.624678\pi$
$752$	−0.595146	−	5.14635i	−0.0217027	−	0.187668i
$753$	3.73035	+	29.4526i	0.135941	+	1.07331i
$754$	9.27266	−	9.82243i	0.337690	−	0.357712i
$755$		−	7.37176i		−	0.268286i
$756$	26.4572	−	12.3111i	0.962238	−	0.447749i
$757$	2.49892			0.0908248			0.0454124	−	0.998968i	$-0.485540\pi$
$757$	2.49892			0.0908248			0.0454124	+	0.998968i	$0.485540\pi$
$758$	−5.12828	−	4.84124i	−0.186267	−	0.175842i
$759$	−43.5462	−	27.0869i	−1.58063	−	0.983194i
$760$	15.7545	+	13.2442i	0.571476	+	0.480419i
$761$		−	35.7987i		−	1.29770i	−0.760916	−	0.648851i	$-0.775250\pi$
$761$		−	35.7987i		−	1.29770i	0.760916	−	0.648851i	$-0.224750\pi$
$762$	8.35810	+	6.10208i	0.302782	+	0.221055i
$763$			44.3812i			1.60671i
$764$	−2.86620	−	49.7345i	−0.103695	−	1.79933i
$765$	−4.66066	−	18.1038i	−0.168506	−	0.654543i
$766$	−6.60949	−	6.23956i	−0.238811	−	0.225444i
$767$		−	25.3660i		−	0.915912i
$768$	25.9728	−	9.66519i	0.937211	−	0.348763i
$769$		−	20.1663i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$769$		−	20.1663i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$770$	−22.5705	+	23.9087i	−0.813386	+	0.861611i
$771$	2.23005	+	17.6071i	0.0803131	+	0.634105i
$772$	−0.556641	−	9.65888i	−0.0200340	−	0.347631i
$773$			26.0350i			0.936415i	0.883619	+	0.468207i	$0.155100\pi$
$773$			26.0350i			0.936415i	−0.883619	+	0.468207i	$0.844900\pi$
$774$	32.5376	+	17.9721i	1.16954	+	0.645995i
$775$	−6.67218			−0.239672
$776$	4.13534	+	3.47643i	0.148450	+	0.124796i
$777$	−4.12104	−	32.5373i	−0.147841	−	1.16727i
$778$	−13.9679	+	14.7961i	−0.500774	+	0.530465i
$779$		−	35.6223i		−	1.27630i
$780$	−4.10635	−	22.1199i	−0.147031	−	0.792019i
$781$	12.0879			0.432540
$782$	31.2403	−	4.13948i	1.11715	−	0.148027i
$783$	9.52539	−	3.78200i	0.340410	−	0.135158i
$784$	3.51525	−	0.406518i	0.125545	−	0.0145185i
$785$			21.1402i			0.754525i
$786$	−10.0601	−	7.34466i	−0.358831	−	0.261975i
$787$	−8.07737			−0.287927			−0.143964	−	0.989583i	$-0.545985\pi$
$787$	−8.07737			−0.287927			−0.143964	+	0.989583i	$0.545985\pi$
$788$	−1.33105	−	23.0965i	−0.0474168	−	0.822780i
$789$	0.662607	−	0.0839230i	0.0235894	−	0.00298774i
$790$	11.3267	+	10.6928i	0.402987	+	0.380432i
$791$			9.92542i			0.352907i
$792$	−47.2374	−	22.6483i	−1.67851	−	0.804772i
$793$		−	39.7568i		−	1.41180i
$794$	5.00675	−	5.30360i	0.177683	−	0.188218i
$795$	−19.9184	+	2.52278i	−0.706432	+	0.0894737i
$796$	9.67286	−	0.557447i	0.342845	−	0.0197582i
$797$			37.2035i			1.31782i	0.752223	+	0.658908i	$0.228981\pi$
$797$			37.2035i			1.31782i	−0.752223	+	0.658908i	$0.771019\pi$
$798$	−22.0059	+	30.1417i	−0.778999	+	1.06700i
$799$		−	6.01783i		−	0.212896i
$800$	14.5098	+	10.8367i	0.512999	+	0.383134i
$801$	−2.66686	+	0.686561i	−0.0942289	+	0.0242584i
$802$	−17.5348	−	16.5534i	−0.619177	−	0.584521i
$803$		−	52.9480i		−	1.86850i
$804$	1.02018	+	5.49546i	0.0359791	+	0.193810i
$805$	11.3904	−	14.0153i	0.401459	−	0.493975i
$806$	−9.79812	+	10.3790i	−0.345124	+	0.365586i
$807$	12.7183	−	1.61085i	0.447705	−	0.0567045i
$808$	−29.4021	+	34.9748i	−1.03436	+	1.23041i
$809$			1.81783i			0.0639116i	0.999489	+	0.0319558i	$0.0101736\pi$
$809$			1.81783i			0.0639116i	−0.999489	+	0.0319558i	$0.989826\pi$
$810$	4.26732	−	16.5276i	0.149938	−	0.580721i
$811$		−	25.6084i		−	0.899233i	−0.893222	−	0.449617i	$-0.851561\pi$
$811$		−	25.6084i		−	0.899233i	0.893222	−	0.449617i	$-0.148439\pi$
$812$	11.0583	−	0.637293i	0.388072	−	0.0223646i
$813$	9.52549	−	1.20646i	0.334074	−	0.0423124i
$814$	−40.4174	+	42.8137i	−1.41663	+	1.50062i
$815$	−17.8277			−0.624477
$816$	31.2599	−	7.68686i	1.09432	−	0.269094i
$817$	−47.5383			−1.66315
$818$	0.180927	+	0.170800i	0.00632596	+	0.00597189i
$819$	39.5058	−	10.1704i	1.38045	−	0.355384i
$820$	1.01315	+	17.5802i	0.0353807	+	0.613928i
$821$	−5.10198			−0.178060			−0.0890301	−	0.996029i	$-0.528377\pi$
$821$	−5.10198			−0.178060			−0.0890301	+	0.996029i	$0.528377\pi$
$822$	−40.6780	−	29.6982i	−1.41881	−	1.03584i
$823$	−10.6288			−0.370498			−0.185249	−	0.982692i	$-0.559309\pi$
$823$	−10.6288			−0.370498			−0.185249	+	0.982692i	$0.559309\pi$
$824$	−21.0540	−	17.6993i	−0.733450	−	0.616585i
$825$	−4.30152	−	33.9623i	−0.149760	−	1.18241i
$826$	14.2788	−	15.1254i	0.496824	−	0.526281i
$827$			15.8531i			0.551267i	0.961263	+	0.275634i	$0.0888877\pi$
$827$			15.8531i			0.551267i	−0.961263	+	0.275634i	$0.911112\pi$
$828$	26.7973	+	10.4834i	0.931272	+	0.364325i
$829$		−	19.4000i		−	0.673791i	−0.941542	−	0.336896i	$-0.890623\pi$
$829$		−	19.4000i		−	0.673791i	0.941542	−	0.336896i	$-0.109377\pi$
$830$	14.6957	+	13.8732i	0.510097	+	0.481546i
$831$	−2.04334	−	16.1330i	−0.0708827	−	0.559648i
$832$	38.1649	−	6.65736i	1.32313	−	0.230802i
$833$	4.11052			0.142421
$834$	19.6528	−	26.9187i	0.680522	−	0.932119i
$835$	−14.1823			−0.490799
$836$	66.8859	−	3.85464i	2.31330	−	0.133315i
$837$	−10.0652	+	3.99631i	−0.347903	+	0.138133i
$838$	14.6681	−	15.5378i	0.506702	−	0.536744i
$839$	18.3937			0.635023			0.317511	−	0.948254i	$-0.397153\pi$
$839$	18.3937			0.635023			0.317511	+	0.948254i	$0.397153\pi$
$840$	10.0030	−	15.5013i	0.345136	−	0.534847i
$841$	−25.1098			−0.865854
$842$	14.8195	+	13.9901i	0.510714	+	0.482129i
$843$	−12.1201	+	1.53508i	−0.417439	+	0.0528711i
$844$	51.0316	−	2.94095i	1.75658	−	0.101232i
$845$		−	14.0163i		−	0.482177i
$846$	2.65677	−	4.80995i	0.0913417	−	0.165369i
$847$			76.1394i			2.61618i
$848$	−3.97174	−	34.3445i	−0.136390	−	1.17940i
$849$	−0.411845	+	0.0521625i	−0.0141345	+	0.00179021i
$850$	15.2969	+	14.4407i	0.524680	+	0.495313i
$851$	20.3970	−	25.0974i	0.699199	−	0.860328i
$852$	−6.66859	+	1.23796i	−0.228462	+	0.0424119i
$853$			33.2062i			1.13696i	0.822697	+	0.568479i	$0.192468\pi$
$853$			33.2062i			1.13696i	−0.822697	+	0.568479i	$0.807532\pi$
$854$	22.3796	−	23.7065i	0.765815	−	0.811219i
$855$	5.44259	+	21.1411i	0.186133	+	0.723009i
$856$	5.39700	+	4.53706i	0.184466	+	0.155074i
$857$			27.1763i			0.928324i	0.885750	+	0.464162i	$0.153645\pi$
$857$			27.1763i			0.928324i	−0.885750	+	0.464162i	$0.846355\pi$
$858$	−59.1475	−	43.1824i	−2.01926	−	1.47422i
$859$			1.63700i			0.0558536i	0.999610	+	0.0279268i	$0.00889053\pi$
$859$			1.63700i			0.0558536i	−0.999610	+	0.0279268i	$0.991109\pi$
$860$	23.4610	−	1.35206i	0.800013	−	0.0461048i
$861$	−31.6770	+	4.01208i	−1.07955	+	0.136731i
$862$	14.6780	+	13.8565i	0.499935	+	0.471953i
$863$		−	26.5108i		−	0.902440i	−0.892413	−	0.451220i	$-0.850989\pi$
$863$		−	26.5108i		−	0.902440i	0.892413	−	0.451220i	$-0.149011\pi$
$864$	28.3791	+	7.65674i	0.965477	+	0.260488i
$865$			20.8029i			0.707321i
$866$	−14.1524	+	14.9915i	−0.480918	+	0.509432i
$867$	7.88529	−	0.998718i	0.267798	−	0.0339182i
$868$	−11.6850	+	0.673407i	−0.396615	+	0.0228569i
$869$	50.7040			1.72001
$870$	3.82057	−	5.23308i	0.129529	−	0.177418i
$871$			7.81365i			0.264755i
$872$	−28.7670	+	34.2194i	−0.974172	+	1.15881i
$873$	1.42860	+	5.54923i	0.0483509	+	0.187813i
$874$	−36.4816	+	4.83397i	−1.23401	+	0.163511i
$875$	30.8849			1.04410
$876$	5.42258	+	29.2100i	0.183212	+	0.986916i
$877$			34.5725i			1.16743i	0.811958	+	0.583716i	$0.198402\pi$
$877$			34.5725i			1.16743i	−0.811958	+	0.583716i	$0.801598\pi$
$878$	−27.4131	−	25.8788i	−0.925148	−	0.873366i
$879$	−3.09220	−	24.4142i	−0.104297	−	0.823469i
$880$	−32.8998	+	3.80466i	−1.10905	+	0.128255i
$881$	−18.6056			−0.626839			−0.313420	−	0.949615i	$-0.601475\pi$
$881$	−18.6056			−0.626839			−0.313420	+	0.949615i	$0.601475\pi$
$882$	3.28546	+	1.81472i	0.110627	+	0.0611049i
$883$		−	13.2184i		−	0.444834i	−0.974952	−	0.222417i	$-0.928605\pi$
$883$		−	13.2184i		−	0.444834i	0.974952	−	0.222417i	$-0.0713946\pi$
$884$	44.9271	−	2.58915i	1.51106	−	0.0870826i
$885$	−1.52885	−	12.0709i	−0.0513918	−	0.405759i
$886$	18.5763	+	17.5366i	0.624084	+	0.589153i
$887$			4.96093i			0.166572i	0.996526	+	0.0832859i	$0.0265415\pi$
$887$			4.96093i			0.166572i	−0.996526	+	0.0832859i	$0.973459\pi$
$888$	17.9125	−	27.7585i	0.601105	−	0.931513i
$889$			11.8631i			0.397874i
$890$	−1.19513	+	1.26598i	−0.0400607	+	0.0424359i
$891$	−26.8307	−	48.6567i	−0.898863	−	1.63006i
$892$	2.63707	+	45.7587i	0.0882958	+	1.53211i
$893$			7.02746i			0.235165i
$894$	20.2981	−	27.8026i	0.678871	−	0.929858i
$895$		−	13.3469i		−	0.446138i
$896$	26.5048	+	17.5138i	0.885463	+	0.585096i
$897$	34.1572	+	21.2467i	1.14048	+	0.709407i
$898$	3.41716	−	3.61976i	0.114032	−	0.120793i
$899$	−4.11070			−0.137099
$900$	5.85122	+	18.2956i	0.195041	+	0.609852i
$901$		−	40.1604i		−	1.33794i
$902$	41.6818	+	39.3488i	1.38785	+	1.31017i
$903$	5.35416	+	42.2733i	0.178175	+	1.40677i
$904$	−6.43345	+	7.65282i	−0.213973	+	0.254529i
$905$		−	0.0406781i		−	0.00135218i
$906$	10.8744	+	7.93921i	0.361279	+	0.263763i
$907$	−3.89499			−0.129331			−0.0646655	−	0.997907i	$-0.520598\pi$
$907$	−3.89499			−0.129331			−0.0646655	+	0.997907i	$0.520598\pi$
$908$	4.63665	−	0.267210i	0.153873	−	0.00886768i
$909$	−46.9329	+	12.0825i	−1.55667	+	0.400750i
$910$	17.7041	−	18.7538i	0.586885	−	0.621681i
$911$	36.4367			1.20720			0.603600	−	0.797287i	$-0.293732\pi$
$911$	36.4367			1.20720			0.603600	+	0.797287i	$0.293732\pi$
$912$	−36.5045	+	8.97651i	−1.20878	+	0.297242i
$913$	65.7853			2.17717
$914$	7.94668	−	8.41783i	0.262853	−	0.278437i
$915$	−2.39621	−	18.9191i	−0.0792163	−	0.625445i
$916$	−1.37282	−	23.8213i	−0.0453594	−	0.787079i
$917$		−	14.2788i		−	0.471527i
$918$	31.7251	+	12.6222i	1.04709	+	0.416593i
$919$			2.53453i			0.0836063i	0.999126	+	0.0418032i	$0.0133102\pi$
$919$			2.53453i			0.0836063i	−0.999126	+	0.0418032i	$0.986690\pi$
$920$	17.8668	−	3.42324i	0.589051	−	0.112861i
$921$	−4.91108	−	38.7750i	−0.161825	−	1.27768i
$922$	−4.80481	−	4.53588i	−0.158238	−	0.149381i
$923$	−9.48164			−0.312092
$924$	−10.9610	−	59.0440i	−0.360590	−	1.94241i
$925$	21.5886			0.709830
$926$	−35.0490	−	33.0873i	−1.15178	−	1.08732i
$927$	−7.27336	−	28.2525i	−0.238888	−	0.927933i
$928$	8.93943	+	6.67641i	0.293451	+	0.219164i
$929$			55.4181i			1.81821i	0.416569	+	0.909104i	$0.363232\pi$
$929$			55.4181i			1.81821i	−0.416569	+	0.909104i	$0.636768\pi$
$930$	−4.03707	+	5.52962i	−0.132381	+	0.181324i
$931$	−4.80015			−0.157318
$932$	−54.8063	+	3.15849i	−1.79524	+	0.103460i
$933$	−3.09609	−	24.4449i	−0.101361	−	0.800289i
$934$	4.99156	−	5.28750i	0.163329	−	0.173012i
$935$	−38.4710			−1.25814
$936$	37.0525	+	17.7651i	1.21110	+	0.580671i
$937$		−	18.4826i		−	0.603800i	−0.953340	−	0.301900i	$-0.902379\pi$
$937$		−	18.4826i		−	0.603800i	0.953340	−	0.301900i	$-0.0976209\pi$
$938$	−4.39841	+	4.65918i	−0.143613	+	0.152128i
$939$	2.02064	+	15.9538i	0.0659411	+	0.520632i
$940$	−0.199871	−	3.46817i	−0.00651907	−	0.113119i
$941$			46.6958i			1.52224i	0.648610	+	0.761121i	$0.275350\pi$
$941$			46.6958i			1.52224i	−0.648610	+	0.761121i	$0.724650\pi$
$942$	−31.1849	−	22.7674i	−1.01606	−	0.741803i
$943$	−24.4339	−	19.8577i	−0.795676	−	0.646656i
$944$	20.8134	−	2.40695i	0.677420	−	0.0783396i
$945$	18.1867	−	7.22089i	0.591612	−	0.234896i
$946$	52.5114	−	55.6247i	1.70729	−	1.80852i
$947$	−22.2910			−0.724362			−0.362181	−	0.932108i	$-0.617968\pi$
$947$	−22.2910			−0.724362			−0.362181	+	0.932108i	$0.617968\pi$
$948$	−27.9720	+	5.19276i	−0.908490	+	0.168653i
$949$			41.5319i			1.34818i
$950$	−17.8633	−	16.8635i	−0.579562	−	0.547124i
$951$	−7.07694	+	0.896335i	−0.229485	+	0.0290657i
$952$	28.2470	+	23.7462i	0.915490	+	0.769619i
$953$	−29.3186			−0.949721			−0.474861	−	0.880061i	$-0.657501\pi$
$953$	−29.3186			−0.949721			−0.474861	+	0.880061i	$0.657501\pi$
$954$	17.7301	−	32.0995i	0.574034	−	1.03926i
$955$		−	33.4052i		−	1.08097i
$956$	14.7145	−	0.847997i	0.475901	−	0.0274262i
$957$	−2.65014	−	20.9240i	−0.0856670	−	0.676376i
$958$	35.5803	+	33.5888i	1.14955	+	1.08521i
$959$		−	57.7364i		−	1.86441i
$960$	17.7603	−	5.46830i	0.573211	−	0.176489i
$961$	−26.6564			−0.859883
$962$	31.7030	−	33.5826i	1.02215	−	1.08275i
$963$	1.86446	+	7.24226i	0.0600814	+	0.233379i
$964$	−49.4811	+	2.85160i	−1.59368	+	0.0918438i
$965$		−	6.48759i		−	0.208843i
$966$	8.40745	+	31.8967i	0.270505	+	1.02626i
$967$	−44.5365			−1.43220			−0.716098	−	0.698000i	$-0.754074\pi$
$967$	−44.5365			−1.43220			−0.716098	+	0.698000i	$0.754074\pi$
$968$	−49.3520	+	58.7060i	−1.58623	+	1.88688i
$969$	−43.3206	+	5.48681i	−1.39166	+	0.176262i
$970$	2.63427	+	2.48683i	0.0845813	+	0.0798472i
$971$		−	20.5639i		−	0.659926i	−0.943994	−	0.329963i	$-0.892964\pi$
$971$		−	20.5639i		−	0.659926i	0.943994	−	0.329963i	$-0.107036\pi$
$972$	19.7849	+	24.0948i	0.634601	+	0.772840i
$973$	38.2071			1.22486
$974$	16.3068	+	15.3941i	0.522503	+	0.493258i
$975$	3.37407	+	26.6397i	0.108057	+	0.853152i
$976$	32.6215	−	3.77248i	1.04419	−	0.120754i
$977$	−28.3080			−0.905655			−0.452827	−	0.891598i	$-0.649585\pi$
$977$	−28.3080			−0.905655			−0.452827	+	0.891598i	$0.649585\pi$
$978$	19.2000	−	26.2985i	0.613948	−	0.840933i
$979$			5.66715i			0.181123i
$980$	2.36896	−	0.136523i	0.0756736	−	0.00436107i
$981$	−45.9191	+	11.8215i	−1.46609	+	0.377431i
$982$	−23.3657	−	22.0579i	−0.745630	−	0.703897i
$983$	44.0813			1.40597			0.702987	−	0.711203i	$-0.251849\pi$
$983$	44.0813			1.40597			0.702987	+	0.711203i	$0.251849\pi$
$984$	−27.0246	−	17.4389i	−0.861512	−	0.555933i
$985$		−	15.5133i		−	0.494294i
$986$	9.42435	+	8.89686i	0.300132	+	0.283334i
$987$	6.24915	−	0.791491i	0.198913	−	0.0251935i
$988$	−52.4647	+	3.02354i	−1.66912	+	0.0961916i
$989$	−26.5003	+	32.6072i	−0.842661	+	1.03685i
$990$	−30.7492	−	16.9843i	−0.977273	−	0.539796i
$991$	−36.8884			−1.17180			−0.585900	−	0.810384i	$-0.699259\pi$
$991$	−36.8884			−1.17180			−0.585900	+	0.810384i	$0.699259\pi$
$992$	−9.44600	−	7.05475i	−0.299911	−	0.223989i
$993$	5.10643	+	40.3174i	0.162048	+	1.27943i
$994$	−5.65379	−	5.33734i	−0.179327	−	0.169290i
$995$	6.49698			0.205968
$996$	−36.2920	+	6.73728i	−1.14996	+	0.213479i
$997$		−	12.4632i		−	0.394713i	−0.980332	−	0.197357i	$-0.936764\pi$
$997$		−	12.4632i		−	0.394713i	0.980332	−	0.197357i	$-0.0632357\pi$
$998$	3.37408	−	3.57413i	0.106805	−	0.113137i
$999$	32.5671	−	12.9306i	1.03038	−	0.409105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.b.c.413.18	yes	80
3.2	odd	2	inner	552.2.b.c.413.63	yes	80
4.3	odd	2		2208.2.b.c.689.4		80
8.3	odd	2		2208.2.b.c.689.77		80
8.5	even	2	inner	552.2.b.c.413.61	yes	80
12.11	even	2		2208.2.b.c.689.79		80
23.22	odd	2	inner	552.2.b.c.413.17	✓	80
24.5	odd	2	inner	552.2.b.c.413.20	yes	80
24.11	even	2		2208.2.b.c.689.2		80
69.68	even	2	inner	552.2.b.c.413.64	yes	80
92.91	even	2		2208.2.b.c.689.3		80
184.45	odd	2	inner	552.2.b.c.413.62	yes	80
184.91	even	2		2208.2.b.c.689.78		80
276.275	odd	2		2208.2.b.c.689.80		80
552.275	odd	2		2208.2.b.c.689.1		80
552.413	even	2	inner	552.2.b.c.413.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.b.c.413.17	✓	80	23.22	odd	2	inner
552.2.b.c.413.18	yes	80	1.1	even	1	trivial
552.2.b.c.413.19	yes	80	552.413	even	2	inner
552.2.b.c.413.20	yes	80	24.5	odd	2	inner
552.2.b.c.413.61	yes	80	8.5	even	2	inner
552.2.b.c.413.62	yes	80	184.45	odd	2	inner
552.2.b.c.413.63	yes	80	3.2	odd	2	inner
552.2.b.c.413.64	yes	80	69.68	even	2	inner
2208.2.b.c.689.1		80	552.275	odd	2
2208.2.b.c.689.2		80	24.11	even	2
2208.2.b.c.689.3		80	92.91	even	2
2208.2.b.c.689.4		80	4.3	odd	2
2208.2.b.c.689.77		80	8.3	odd	2
2208.2.b.c.689.78		80	184.91	even	2
2208.2.b.c.689.79		80	12.11	even	2
2208.2.b.c.689.80		80	276.275	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02836 - 0.970807i) q^{2} +(1.71832 - 0.217636i) q^{3} +(0.115069 + 1.99669i) q^{4} +1.34112i q^{5} +(-1.97835 - 1.44435i) q^{6} -2.80797i q^{7} +(1.82006 - 2.16503i) q^{8} +(2.90527 - 0.747937i) q^{9} +O(q^{10})\)	\(q+(-1.02836 - 0.970807i) q^{2} +(1.71832 - 0.217636i) q^{3} +(0.115069 + 1.99669i) q^{4} +1.34112i q^{5} +(-1.97835 - 1.44435i) q^{6} -2.80797i q^{7} +(1.82006 - 2.16503i) q^{8} +(2.90527 - 0.747937i) q^{9} +(1.30196 - 1.37916i) q^{10} -6.17378i q^{11} +(0.632276 + 3.40591i) q^{12} +4.84265i q^{13} +(-2.72599 + 2.88761i) q^{14} +(0.291875 + 2.30447i) q^{15} +(-3.97352 + 0.459514i) q^{16} -4.64639 q^{17} +(-3.71378 - 2.05130i) q^{18} +5.42593 q^{19} +(-2.67779 + 0.154321i) q^{20} +(-0.611113 - 4.82499i) q^{21} +(-5.99354 + 6.34890i) q^{22} +(3.02469 - 3.72173i) q^{23} +(2.65627 - 4.11634i) q^{24} +3.20141 q^{25} +(4.70128 - 4.98001i) q^{26} +(4.82941 - 1.91749i) q^{27} +(5.60663 - 0.323110i) q^{28} +1.97237 q^{29} +(1.93704 - 2.65319i) q^{30} -2.08414 q^{31} +(4.53233 + 3.38497i) q^{32} +(-1.34363 - 10.6085i) q^{33} +(4.77819 + 4.51075i) q^{34} +3.76581 q^{35} +(1.82770 + 5.71485i) q^{36} +6.74349 q^{37} +(-5.57983 - 5.26753i) q^{38} +(1.05393 + 8.32124i) q^{39} +(2.90356 + 2.44092i) q^{40} -6.56520i q^{41} +(-4.05569 + 5.55513i) q^{42} -8.76132 q^{43} +(12.3271 - 0.710411i) q^{44} +(1.00307 + 3.89631i) q^{45} +(-6.72356 + 0.890902i) q^{46} +1.29516i q^{47} +(-6.72778 + 1.65437i) q^{48} -0.884669 q^{49} +(-3.29221 - 3.10795i) q^{50} +(-7.98400 + 1.01122i) q^{51} +(-9.66925 + 0.557239i) q^{52} +8.64336i q^{53} +(-6.82791 - 2.71655i) q^{54} +8.27976 q^{55} +(-6.07934 - 5.11068i) q^{56} +(9.32350 - 1.18088i) q^{57} +(-2.02832 - 1.91479i) q^{58} -5.23804 q^{59} +(-4.56772 + 0.847956i) q^{60} -8.20972 q^{61} +(2.14326 + 2.02330i) q^{62} +(-2.10018 - 8.15790i) q^{63} +(-1.37473 - 7.88100i) q^{64} -6.49456 q^{65} +(-8.91710 + 12.2139i) q^{66} +1.61351 q^{67} +(-0.534656 - 9.27739i) q^{68} +(4.38742 - 7.05341i) q^{69} +(-3.87263 - 3.65587i) q^{70} +1.95795i q^{71} +(3.66847 - 7.65130i) q^{72} +8.57628 q^{73} +(-6.93477 - 6.54662i) q^{74} +(5.50105 - 0.696740i) q^{75} +(0.624357 + 10.8339i) q^{76} -17.3358 q^{77} +(6.99448 - 9.58043i) q^{78} +8.21280i q^{79} +(-0.616262 - 5.32895i) q^{80} +(7.88118 - 4.34592i) q^{81} +(-6.37354 + 6.75142i) q^{82} +10.6556i q^{83} +(9.56368 - 1.77541i) q^{84} -6.23135i q^{85} +(9.00984 + 8.50555i) q^{86} +(3.38917 - 0.429258i) q^{87} +(-13.3664 - 11.2367i) q^{88} -0.917940 q^{89} +(2.75104 - 4.98061i) q^{90} +13.5980 q^{91} +(7.77917 + 5.61111i) q^{92} +(-3.58123 + 0.453583i) q^{93} +(1.25735 - 1.33190i) q^{94} +7.27680i q^{95} +(8.52469 + 4.83008i) q^{96} +1.91006i q^{97} +(0.909762 + 0.858842i) q^{98} +(-4.61760 - 17.9365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) \) 80 * q - 12 * q^6 - 4 * q^9	\( 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) \) 80 * q - 12 * q^6 - 4 * q^9 + 16 * q^12 + 8 * q^16 + 20 * q^18 - 8 * q^24 - 144 * q^25 - 24 * q^31 + 40 * q^36 + 68 * q^39 - 24 * q^46 + 92 * q^48 - 160 * q^49 - 48 * q^52 - 32 * q^54 + 32 * q^55 - 40 * q^58 + 48 * q^64 + 72 * q^70 + 68 * q^72 - 8 * q^73 + 64 * q^78 + 12 * q^81 - 48 * q^82 + 92 * q^87 - 144 * q^94 + 68 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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