LMFDB - Embedded newform 684.3.t.a.265.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (of order $6$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			265.15
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08441 + 2.79715i) q^{3} +(0.475788 - 0.824090i) q^{5} +(-4.90114 - 8.48903i) q^{7} +(-6.64810 - 6.06653i) q^{9} +O(q^{10})$	\(q+(-1.08441 + 2.79715i) q^{3} +(0.475788 - 0.824090i) q^{5} +(-4.90114 - 8.48903i) q^{7} +(-6.64810 - 6.06653i) q^{9} +(2.64648 + 4.58384i) q^{11} +(4.76077 + 2.74863i) q^{13} +(1.78915 + 2.22451i) q^{15} -12.9857 q^{17} +(13.7174 + 13.1466i) q^{19} +(29.0599 - 4.50362i) q^{21} +(-4.55328 + 7.88650i) q^{23} +(12.0473 + 20.8665i) q^{25} +(24.1783 - 12.0171i) q^{27} +(18.3181 - 10.5760i) q^{29} +(34.6062 + 19.9799i) q^{31} +(-15.6916 + 2.43183i) q^{33} -9.32763 q^{35} -4.32590i q^{37} +(-12.8510 + 10.3359i) q^{39} +(18.9804 + 10.9583i) q^{41} +(10.7335 + 18.5910i) q^{43} +(-8.16245 + 2.59224i) q^{45} +(29.0478 + 50.3123i) q^{47} +(-23.5424 + 40.7766i) q^{49} +(14.0819 - 36.3229i) q^{51} +56.0480i q^{53} +5.03667 q^{55} +(-51.6483 + 24.1132i) q^{57} +(-45.6289 - 26.3438i) q^{59} +(-48.1056 - 83.3214i) q^{61} +(-18.9157 + 86.1688i) q^{63} +(4.53023 - 2.61553i) q^{65} +(14.0526 + 8.11326i) q^{67} +(-17.1221 - 21.2884i) q^{69} +124.682i q^{71} -87.5546 q^{73} +(-71.4308 + 11.0701i) q^{75} +(25.9416 - 44.9321i) q^{77} +(73.4756 - 42.4212i) q^{79} +(7.39437 + 80.6618i) q^{81} +(50.1616 + 86.8825i) q^{83} +(-6.17844 + 10.7014i) q^{85} +(9.71817 + 62.7072i) q^{87} +21.8780i q^{89} -53.8857i q^{91} +(-93.4143 + 75.1323i) q^{93} +(17.3606 - 5.04936i) q^{95} +(15.1534 - 8.74883i) q^{97} +(10.2140 - 46.5288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.08441	+	2.79715i	−0.361471	+	0.932383i
$3$	−1.08441	+	2.79715i	−0.361471	+	0.932383i
$4$		0			0
$5$	0.475788	−	0.824090i	0.0951577	−	0.164818i	−0.814517	−	0.580140i	$-0.802998\pi$
$5$	0.475788	−	0.824090i	0.0951577	−	0.164818i	0.909674	+	0.415322i	$0.136331\pi$
$6$		0			0
$7$	−4.90114	−	8.48903i	−0.700163	−	1.21272i	−0.968409	−	0.249367i	$-0.919777\pi$
$7$	−4.90114	−	8.48903i	−0.700163	−	1.21272i	0.268246	−	0.963350i	$-0.413556\pi$
$8$		0			0
$9$	−6.64810	−	6.06653i	−0.738677	−	0.674059i
$10$		0			0
$11$	2.64648	+	4.58384i	0.240589	+	0.416713i	0.960882	−	0.276957i	$-0.0893259\pi$
$11$	2.64648	+	4.58384i	0.240589	+	0.416713i	−0.720293	+	0.693670i	$0.755993\pi$
$12$		0			0
$13$	4.76077	+	2.74863i	0.366213	+	0.211433i	0.671803	−	0.740730i	$-0.265520\pi$
$13$	4.76077	+	2.74863i	0.366213	+	0.211433i	−0.305590	+	0.952163i	$0.598854\pi$
$14$		0			0
$15$	1.78915	+	2.22451i	0.119277	+	0.148300i
$16$		0			0
$17$	−12.9857			−0.763864			−0.381932	−	0.924190i	$-0.624741\pi$
$17$	−12.9857			−0.763864			−0.381932	+	0.924190i	$0.624741\pi$
$18$		0			0
$19$	13.7174	+	13.1466i	0.721968	+	0.691927i
$19$	13.7174	+	13.1466i	0.721968	+	0.691927i
$20$		0			0
$21$	29.0599	−	4.50362i	1.38381	−	0.214458i
$22$		0			0
$23$	−4.55328	+	7.88650i	−0.197968	+	0.342891i	−0.947870	−	0.318658i	$-0.896768\pi$
$23$	−4.55328	+	7.88650i	−0.197968	+	0.342891i	0.749901	+	0.661550i	$0.230101\pi$
$24$		0			0
$25$	12.0473	+	20.8665i	0.481890	+	0.834658i
$26$		0			0
$27$	24.1783	−	12.0171i	0.895492	−	0.445078i
$28$		0			0
$29$	18.3181	−	10.5760i	0.631659	−	0.364689i	−0.149735	−	0.988726i	$-0.547842\pi$
$29$	18.3181	−	10.5760i	0.631659	−	0.364689i	0.781394	+	0.624038i	$0.214509\pi$
$30$		0			0
$31$	34.6062	+	19.9799i	1.11633	+	0.644514i	0.940462	−	0.339900i	$-0.110393\pi$
$31$	34.6062	+	19.9799i	1.11633	+	0.644514i	0.175869	+	0.984414i	$0.443727\pi$
$32$		0			0
$33$	−15.6916	+	2.43183i	−0.475503	+	0.0736919i
$34$		0			0
$35$	−9.32763			−0.266504
$36$		0			0
$37$		−	4.32590i		−	0.116916i	−0.998290	−	0.0584581i	$-0.981382\pi$
$37$		−	4.32590i		−	0.116916i	0.998290	−	0.0584581i	$-0.0186184\pi$
$38$		0			0
$39$	−12.8510	+	10.3359i	−0.329512	+	0.265024i
$40$		0			0
$41$	18.9804	+	10.9583i	0.462937	+	0.267277i	0.713278	−	0.700881i	$-0.247210\pi$
$41$	18.9804	+	10.9583i	0.462937	+	0.267277i	−0.250341	+	0.968158i	$0.580543\pi$
$42$		0			0
$43$	10.7335	+	18.5910i	0.249617	+	0.432349i	0.963420	−	0.267998i	$-0.0863620\pi$
$43$	10.7335	+	18.5910i	0.249617	+	0.432349i	−0.713803	+	0.700347i	$0.753029\pi$
$44$		0			0
$45$	−8.16245	+	2.59224i	−0.181388	+	0.0576054i
$46$		0			0
$47$	29.0478	+	50.3123i	0.618039	+	1.07047i	0.989843	+	0.142164i	$0.0454060\pi$
$47$	29.0478	+	50.3123i	0.618039	+	1.07047i	−0.371804	+	0.928311i	$0.621261\pi$
$48$		0			0
$49$	−23.5424	+	40.7766i	−0.480456	+	0.832175i
$50$		0			0
$51$	14.0819	−	36.3229i	0.276115	−	0.712214i
$52$		0			0
$53$			56.0480i			1.05751i	0.848775	+	0.528755i	$0.177341\pi$
$53$			56.0480i			1.05751i	−0.848775	+	0.528755i	$0.822659\pi$
$54$		0			0
$55$	5.03667			0.0915757
$56$		0			0
$57$	−51.6483	+	24.1132i	−0.906111	+	0.423039i
$58$		0			0
$59$	−45.6289	−	26.3438i	−0.773370	−	0.446506i	0.0607052	−	0.998156i	$-0.480665\pi$
$59$	−45.6289	−	26.3438i	−0.773370	−	0.446506i	−0.834076	+	0.551650i	$0.813998\pi$
$60$		0			0
$61$	−48.1056	−	83.3214i	−0.788617	−	1.36592i	−0.926814	−	0.375520i	$-0.877464\pi$
$61$	−48.1056	−	83.3214i	−0.788617	−	1.36592i	0.138197	−	0.990405i	$-0.455869\pi$
$62$		0			0
$63$	−18.9157	+	86.1688i	−0.300249	+	1.36776i
$64$		0			0
$65$	4.53023	−	2.61553i	0.0696959	−	0.0402390i
$66$		0			0
$67$	14.0526	+	8.11326i	0.209740	+	0.121093i	0.601190	−	0.799106i	$-0.294693\pi$
$67$	14.0526	+	8.11326i	0.209740	+	0.121093i	−0.391451	+	0.920199i	$0.628027\pi$
$68$		0			0
$69$	−17.1221	−	21.2884i	−0.248146	−	0.308528i
$70$		0			0
$71$			124.682i			1.75608i	0.478587	+	0.878040i	$0.341149\pi$
$71$			124.682i			1.75608i	−0.478587	+	0.878040i	$0.658851\pi$
$72$		0			0
$73$	−87.5546			−1.19938			−0.599689	−	0.800233i	$-0.704709\pi$
$73$	−87.5546			−1.19938			−0.599689	+	0.800233i	$0.704709\pi$
$74$		0			0
$75$	−71.4308	+	11.0701i	−0.952411	+	0.147602i
$76$		0			0
$77$	25.9416	−	44.9321i	0.336904	−	0.583534i
$78$		0			0
$79$	73.4756	−	42.4212i	0.930071	−	0.536977i	0.0432369	−	0.999065i	$-0.486233\pi$
$79$	73.4756	−	42.4212i	0.930071	−	0.536977i	0.886834	+	0.462088i	$0.152900\pi$
$80$		0			0
$81$	7.39437	+	80.6618i	0.0912885	+	0.995824i
$82$		0			0
$83$	50.1616	+	86.8825i	0.604357	+	1.04678i	0.992153	+	0.125032i	$0.0399033\pi$
$83$	50.1616	+	86.8825i	0.604357	+	1.04678i	−0.387796	+	0.921745i	$0.626763\pi$
$84$		0			0
$85$	−6.17844	+	10.7014i	−0.0726876	+	0.125899i
$86$		0			0
$87$	9.71817	+	62.7072i	0.111703	+	0.720773i
$88$		0			0
$89$			21.8780i			0.245820i	0.992418	+	0.122910i	$0.0392226\pi$
$89$			21.8780i			0.245820i	−0.992418	+	0.122910i	$0.960777\pi$
$90$		0			0
$91$		−	53.8857i		−	0.592150i
$92$		0			0
$93$	−93.4143	+	75.1323i	−1.00445	+	0.807875i
$94$		0			0
$95$	17.3606	−	5.04936i	0.182743	−	0.0531511i
$96$		0			0
$97$	15.1534	−	8.74883i	0.156221	−	0.0901942i	−0.419852	−	0.907593i	$-0.637918\pi$
$97$	15.1534	−	8.74883i	0.156221	−	0.0901942i	0.576073	+	0.817399i	$0.304585\pi$
$98$		0			0
$99$	10.2140	−	46.5288i	0.103171	−	0.469988i
$100$		0			0
$101$	49.0411	+	84.9417i	0.485555	+	0.841006i	0.999862	−	0.0165998i	$-0.00528411\pi$
$101$	49.0411	+	84.9417i	0.485555	+	0.841006i	−0.514307	+	0.857606i	$0.671951\pi$
$102$		0			0
$103$	113.316	+	65.4230i	1.10016	+	0.635175i	0.936262	−	0.351303i	$-0.114261\pi$
$103$	113.316	+	65.4230i	1.10016	+	0.635175i	0.163894	+	0.986478i	$0.447595\pi$
$104$		0			0
$105$	10.1150	−	26.0908i	0.0963333	−	0.248483i
$106$		0			0
$107$			30.4647i			0.284716i	0.989815	+	0.142358i	$0.0454685\pi$
$107$			30.4647i			0.284716i	−0.989815	+	0.142358i	$0.954531\pi$
$108$		0			0
$109$		−	115.441i		−	1.05909i	−0.848282	−	0.529545i	$-0.822363\pi$
$109$		−	115.441i		−	1.05909i	0.848282	−	0.529545i	$-0.177637\pi$
$110$		0			0
$111$	12.1002	+	4.69106i	0.109011	+	0.0422618i
$112$		0			0
$113$	104.334	+	60.2375i	0.923314	+	0.533075i	0.884691	−	0.466178i	$-0.154370\pi$
$113$	104.334	+	60.2375i	0.923314	+	0.533075i	0.0386230	+	0.999254i	$0.487703\pi$
$114$		0			0
$115$	4.33279	+	7.50461i	0.0376764	+	0.0652575i
$116$		0			0
$117$	−14.9754	−	47.1545i	−0.127995	−	0.403030i
$118$		0			0
$119$	63.6447	+	110.236i	0.534829	+	0.926352i
$120$		0			0
$121$	46.4922	−	80.5269i	0.384233	−	0.665512i
$122$		0			0
$123$	−51.2348	+	41.2077i	−0.416543	+	0.335022i
$124$		0			0
$125$	46.7172			0.373738
$126$		0			0
$127$			115.357i			0.908320i	0.890920	+	0.454160i	$0.150061\pi$
$127$			115.357i			0.908320i	−0.890920	+	0.454160i	$0.849939\pi$
$128$		0			0
$129$	−63.6414	+	9.86294i	−0.493344	+	0.0764569i
$130$		0			0
$131$	8.77227	−	15.1940i	0.0669639	−	0.115985i	−0.830600	−	0.556870i	$-0.812002\pi$
$131$	8.77227	−	15.1940i	0.0669639	−	0.115985i	0.897563	+	0.440885i	$0.145335\pi$
$132$		0			0
$133$	44.3710	−	180.881i	0.333617	−	1.36000i
$134$		0			0
$135$	1.60058	−	25.6427i	0.0118562	−	0.189946i
$136$		0			0
$137$	−121.610	−	210.634i	−0.887661	−	1.53747i	−0.842633	−	0.538489i	$-0.818995\pi$
$137$	−121.610	−	210.634i	−0.887661	−	1.53747i	−0.0450288	−	0.998986i	$-0.514338\pi$
$138$		0			0
$139$	45.0707	−	78.0648i	0.324250	−	0.561617i	−0.657110	−	0.753794i	$-0.728221\pi$
$139$	45.0707	−	78.0648i	0.324250	−	0.561617i	0.981360	+	0.192177i	$0.0615548\pi$
$140$		0			0
$141$	−172.231	+	26.6918i	−1.22150	+	0.189304i
$142$		0			0
$143$			29.0968i			0.203474i
$144$		0			0
$145$		−	20.1277i		−	0.138812i
$146$		0			0
$147$	−88.5285	−	110.070i	−0.602235	−	0.748777i
$148$		0			0
$149$	87.4603	−	151.486i	0.586982	−	1.01668i	−0.407644	−	0.913141i	$-0.633649\pi$
$149$	87.4603	−	151.486i	0.586982	−	1.01668i	0.994625	−	0.103541i	$-0.0330173\pi$
$150$		0			0
$151$	107.060	−	61.8113i	0.709008	−	0.409346i	−0.101686	−	0.994817i	$-0.532424\pi$
$151$	107.060	−	61.8113i	0.709008	−	0.409346i	0.810694	+	0.585471i	$0.199090\pi$
$152$		0			0
$153$	86.3301	+	78.7781i	0.564249	+	0.514890i
$154$		0			0
$155$	32.9305	−	19.0124i	0.212455	−	0.122661i
$156$		0			0
$157$	17.6742	−	30.6126i	0.112574	−	0.194985i	−0.804233	−	0.594314i	$-0.797424\pi$
$157$	17.6742	−	30.6126i	0.112574	−	0.194985i	0.916808	+	0.399329i	$0.130757\pi$
$158$		0			0
$159$	−156.775	−	60.7792i	−0.986004	−	0.382259i
$160$		0			0
$161$	89.2650			0.554441
$162$		0			0
$163$	−11.6784			−0.0716469			−0.0358234	−	0.999358i	$-0.511405\pi$
$163$	−11.6784			−0.0716469			−0.0358234	+	0.999358i	$0.511405\pi$
$164$		0			0
$165$	−5.46183	+	14.0883i	−0.0331020	+	0.0853837i
$166$		0			0
$167$	−171.137	−	98.8060i	−1.02477	−	0.591653i	−0.109290	−	0.994010i	$-0.534858\pi$
$167$	−171.137	−	98.8060i	−1.02477	−	0.591653i	−0.915483	+	0.402357i	$0.868191\pi$
$168$		0			0
$169$	−69.3901	−	120.187i	−0.410592	−	0.711166i
$170$		0			0
$171$	−11.4402	−	170.617i	−0.0669019	−	0.997760i
$172$		0			0
$173$	−208.068	+	120.128i	−1.20271	+	0.694383i	−0.961156	−	0.276006i	$-0.910989\pi$
$173$	−208.068	+	120.128i	−1.20271	+	0.694383i	−0.241550	+	0.970388i	$0.577656\pi$
$174$		0			0
$175$	118.091	−	204.539i	0.674803	−	1.16879i
$176$		0			0
$177$	123.168	−	99.0632i	0.695865	−	0.559679i
$178$		0			0
$179$			205.274i			1.14678i	0.819282	+	0.573391i	$0.194372\pi$
$179$			205.274i			1.14678i	−0.819282	+	0.573391i	$0.805628\pi$
$180$		0			0
$181$			287.302i			1.58730i	0.608372	+	0.793652i	$0.291823\pi$
$181$			287.302i			1.58730i	−0.608372	+	0.793652i	$0.708177\pi$
$182$		0			0
$183$	285.229	−	44.2038i	1.55863	−	0.241551i
$184$		0			0
$185$	−3.56493	−	2.05821i	−0.0192699	−	0.0111255i
$186$		0			0
$187$	−34.3664	−	59.5244i	−0.183778	−	0.318312i
$188$		0			0
$189$	−220.515	−	146.353i	−1.16674	−	0.774352i
$190$		0			0
$191$	131.570	+	227.887i	0.688850	+	1.19312i	0.972210	+	0.234110i	$0.0752175\pi$
$191$	131.570	+	227.887i	0.688850	+	1.19312i	−0.283360	+	0.959014i	$0.591449\pi$
$192$		0			0
$193$	80.1384	+	46.2679i	0.415225	+	0.239730i	0.693032	−	0.720907i	$-0.256274\pi$
$193$	80.1384	+	46.2679i	0.415225	+	0.239730i	−0.277807	+	0.960637i	$0.589608\pi$
$194$		0			0
$195$	2.40339	+	15.5081i	0.0123251	+	0.0795285i
$196$		0			0
$197$	39.4971			0.200493			0.100247	−	0.994963i	$-0.468037\pi$
$197$	39.4971			0.200493			0.100247	+	0.994963i	$0.468037\pi$
$198$		0			0
$199$	122.682			0.616494			0.308247	−	0.951306i	$-0.400258\pi$
$199$	122.682			0.616494			0.308247	+	0.951306i	$0.400258\pi$
$200$		0			0
$201$	−37.9328	+	30.5090i	−0.188720	+	0.151786i
$202$		0			0
$203$	−179.559	−	103.669i	−0.884529	−	0.510683i
$204$		0			0
$205$	18.0613	−	10.4277i	0.0881040	−	0.0508669i
$206$		0			0
$207$	78.1143	−	24.8076i	0.377364	−	0.119844i
$208$		0			0
$209$	−23.9591	+	97.6707i	−0.114637	+	0.467324i
$210$		0			0
$211$	−129.277	−	74.6381i	−0.612687	−	0.353735i	0.161329	−	0.986901i	$-0.448422\pi$
$211$	−129.277	−	74.6381i	−0.612687	−	0.353735i	−0.774017	+	0.633165i	$0.781755\pi$
$212$		0			0
$213$	−348.753	−	135.206i	−1.63734	−	0.634772i
$214$		0			0
$215$	20.4275			0.0950118
$216$		0			0
$217$		−	391.698i		−	1.80506i
$218$		0			0
$219$	94.9454	−	244.903i	0.433541	−	1.11828i
$220$		0			0
$221$	−61.8218	−	35.6929i	−0.279737	−	0.161506i
$222$		0			0
$223$	14.0759	−	8.12675i	0.0631209	−	0.0364428i	−0.468107	−	0.883672i	$-0.655064\pi$
$223$	14.0759	−	8.12675i	0.0631209	−	0.0364428i	0.531228	+	0.847229i	$0.321731\pi$
$224$		0			0
$225$	46.4957	−	211.807i	0.206648	−	0.941365i
$226$		0			0
$227$	99.4978	−	57.4451i	0.438316	−	0.253062i	−0.264567	−	0.964367i	$-0.585229\pi$
$227$	99.4978	−	57.4451i	0.438316	−	0.253062i	0.702883	+	0.711305i	$0.251896\pi$
$228$		0			0
$229$	83.5543	−	144.720i	0.364866	−	0.631966i	−0.623889	−	0.781513i	$-0.714448\pi$
$229$	83.5543	−	144.720i	0.364866	−	0.631966i	0.988755	+	0.149547i	$0.0477815\pi$
$230$		0			0
$231$	97.5505	+	121.288i	0.422297	+	0.525054i
$232$		0			0
$233$	27.4447			0.117788			0.0588941	−	0.998264i	$-0.481243\pi$
$233$	27.4447			0.117788			0.0588941	+	0.998264i	$0.481243\pi$
$234$		0			0
$235$	55.2825			0.235245
$236$		0			0
$237$	38.9804	+	251.524i	0.164474	+	1.06128i
$238$		0			0
$239$	12.0622	−	20.8923i	0.0504693	−	0.0874154i	−0.839687	−	0.543071i	$-0.817262\pi$
$239$	12.0622	−	20.8923i	0.0504693	−	0.0874154i	0.890156	+	0.455655i	$0.150595\pi$
$240$		0			0
$241$	−168.643	+	97.3663i	−0.699765	+	0.404010i	−0.807260	−	0.590196i	$-0.799050\pi$
$241$	−168.643	+	97.3663i	−0.699765	+	0.404010i	0.107495	+	0.994206i	$0.465717\pi$
$242$		0			0
$243$	−233.642	−	66.7875i	−0.961488	−	0.274846i
$244$		0			0
$245$	22.4024	+	38.8020i	0.0914383	+	0.158376i
$246$		0			0
$247$	29.1701	+	100.292i	0.118098	+	0.406040i
$248$		0			0
$249$	−297.419	+	46.0931i	−1.19446	+	0.185113i
$250$		0			0
$251$	317.823			1.26623			0.633113	−	0.774059i	$-0.281777\pi$
$251$	317.823			1.26623			0.633113	+	0.774059i	$0.281777\pi$
$252$		0			0
$253$	−48.2007			−0.190517
$254$		0			0
$255$	−23.2334	−	28.8867i	−0.0911112	−	0.113281i
$256$		0			0
$257$	−292.654	−	168.964i	−1.13873	−	0.657448i	−0.192616	−	0.981274i	$-0.561697\pi$
$257$	−292.654	−	168.964i	−1.13873	−	0.657448i	−0.946116	+	0.323827i	$0.895031\pi$
$258$		0			0
$259$	−36.7227	+	21.2019i	−0.141786	+	0.0818604i
$260$		0			0
$261$	−185.940	−	40.8174i	−0.712414	−	0.156388i
$262$		0			0
$263$	−49.8257	−	86.3006i	−0.189451	−	0.328139i	0.755616	−	0.655015i	$-0.227338\pi$
$263$	−49.8257	−	86.3006i	−0.189451	−	0.328139i	−0.945067	+	0.326876i	$0.894004\pi$
$264$		0			0
$265$	46.1886	+	26.6670i	0.174297	+	0.100630i
$266$		0			0
$267$	−61.1959	−	23.7247i	−0.229198	−	0.0888567i
$268$		0			0
$269$			469.942i			1.74700i	0.486826	+	0.873499i	$0.338154\pi$
$269$			469.942i			1.74700i	−0.486826	+	0.873499i	$0.661846\pi$
$270$		0			0
$271$	59.6791			0.220218			0.110109	−	0.993920i	$-0.464880\pi$
$271$	59.6791			0.220218			0.110109	+	0.993920i	$0.464880\pi$
$272$		0			0
$273$	150.726	+	58.4343i	0.552111	+	0.214045i
$274$		0			0
$275$	−63.7657	+	110.445i	−0.231875	+	0.401620i
$276$		0			0
$277$	−27.6801	−	47.9433i	−0.0999280	−	0.173080i	0.811727	−	0.584038i	$-0.198528\pi$
$277$	−27.6801	−	47.9433i	−0.0999280	−	0.173080i	−0.911655	+	0.410957i	$0.865195\pi$
$278$		0			0
$279$	−108.857	−	342.768i	−0.390168	−	1.22856i
$280$		0			0
$281$	−202.336	+	116.819i	−0.720057	+	0.415725i	−0.814774	−	0.579779i	$-0.803139\pi$
$281$	−202.336	+	116.819i	−0.720057	+	0.415725i	0.0947164	+	0.995504i	$0.469806\pi$
$282$		0			0
$283$	−67.7434	+	117.335i	−0.239376	+	0.414611i	−0.960535	−	0.278158i	$-0.910276\pi$
$283$	−67.7434	+	117.335i	−0.239376	+	0.414611i	0.721159	+	0.692769i	$0.243610\pi$
$284$		0			0
$285$	−4.70221	+	54.0357i	−0.0164990	+	0.189599i
$286$		0			0
$287$		−	214.834i		−	0.748549i
$288$		0			0
$289$	−120.372			−0.416511
$290$		0			0
$291$	8.03923	+	51.8738i	0.0276262	+	0.178260i
$292$		0			0
$293$	439.032	+	253.475i	1.49840	+	0.865103i	0.999998	−	0.00184097i	$-0.000586000\pi$
$293$	439.032	+	253.475i	1.49840	+	0.865103i	0.498405	+	0.866944i	$0.333919\pi$
$294$		0			0
$295$	−43.4194	+	25.0682i	−0.147184	+	0.0849769i
$296$		0			0
$297$	119.072	+	79.0265i	0.400916	+	0.266082i
$298$		0			0
$299$	−43.3542	+	25.0305i	−0.144997	+	0.0837141i
$300$		0			0
$301$	105.213	−	182.234i	0.349545	−	0.605430i
$302$		0			0
$303$	−290.775	+	45.0634i	−0.959655	+	0.148724i
$304$		0			0
$305$	−91.5524			−0.300172
$306$		0			0
$307$		−	386.556i		−	1.25914i	−0.776943	−	0.629571i	$-0.783231\pi$
$307$		−	386.556i		−	1.25914i	0.776943	−	0.629571i	$-0.216769\pi$
$308$		0			0
$309$	−305.879	+	246.016i	−0.989901	+	0.796169i
$310$		0			0
$311$	181.927	−	315.107i	0.584974	−	1.01320i	−0.409905	−	0.912128i	$-0.634438\pi$
$311$	181.927	−	315.107i	0.584974	−	1.01320i	0.994879	−	0.101076i	$-0.0322285\pi$
$312$		0			0
$313$	−43.7323	−	75.7466i	−0.139720	−	0.242002i	0.787671	−	0.616096i	$-0.211287\pi$
$313$	−43.7323	−	75.7466i	−0.139720	−	0.242002i	−0.927391	+	0.374095i	$0.877954\pi$
$314$		0			0
$315$	62.0109	+	56.5863i	0.196860	+	0.179639i
$316$		0			0
$317$	−52.2030	+	30.1394i	−0.164678	+	0.0950770i	−0.580074	−	0.814564i	$-0.696976\pi$
$317$	−52.2030	+	30.1394i	−0.164678	+	0.0950770i	0.415396	+	0.909641i	$0.363643\pi$
$318$		0			0
$319$	96.9572	+	55.9783i	0.303941	+	0.175480i
$320$		0			0
$321$	−85.2142	−	33.0363i	−0.265465	−	0.102917i
$322$		0			0
$323$	−178.130	−	170.718i	−0.551485	−	0.528538i
$324$		0			0
$325$			132.454i			0.407550i
$326$		0			0
$327$	322.905	+	125.186i	0.987479	+	0.382831i
$328$		0			0
$329$	284.735	−	493.176i	0.865456	−	1.49901i
$330$		0			0
$331$	380.837	−	219.876i	1.15057	−	0.664279i	0.201541	−	0.979480i	$-0.435405\pi$
$331$	380.837	−	219.876i	1.15057	−	0.664279i	0.949025	+	0.315201i	$0.102072\pi$
$332$		0			0
$333$	−26.2432	+	28.7590i	−0.0788085	+	0.0863634i
$334$		0			0
$335$	13.3721	−	7.72039i	0.0399167	−	0.0230459i
$336$		0			0
$337$	−373.851	−	215.843i	−1.10935	−	0.640484i	−0.170690	−	0.985325i	$-0.554600\pi$
$337$	−373.851	−	215.843i	−1.10935	−	0.640484i	−0.938661	+	0.344841i	$0.887933\pi$
$338$		0			0
$339$	−281.635	+	226.517i	−0.830782	+	0.668191i
$340$		0			0
$341$			211.506i			0.620253i
$342$		0			0
$343$	−18.7740			−0.0547347
$344$		0			0
$345$	−25.6901	+	3.98136i	−0.0744640	+	0.0115402i
$346$		0			0
$347$	−78.4364	+	135.856i	−0.226041	+	0.391515i	−0.956631	−	0.291301i	$-0.905912\pi$
$347$	−78.4364	+	135.856i	−0.226041	+	0.391515i	0.730590	+	0.682816i	$0.239245\pi$
$348$		0			0
$349$	−133.063	−	230.472i	−0.381269	−	0.660378i	0.609975	−	0.792421i	$-0.291180\pi$
$349$	−133.063	−	230.472i	−0.381269	−	0.660378i	−0.991244	+	0.132043i	$0.957846\pi$
$350$		0			0
$351$	148.138	+	9.24657i	0.422045	+	0.0263435i
$352$		0			0
$353$	260.748	+	451.629i	0.738663	+	1.27940i	0.953097	+	0.302664i	$0.0978760\pi$
$353$	260.748	+	451.629i	0.738663	+	1.27940i	−0.214434	+	0.976738i	$0.568791\pi$
$354$		0			0
$355$	102.749	+	59.3221i	0.289434	+	0.167105i
$356$		0			0
$357$	−377.363	+	58.4826i	−1.05704	+	0.163817i
$358$		0			0
$359$	−208.273			−0.580147			−0.290074	−	0.957004i	$-0.593680\pi$
$359$	−208.273			−0.580147			−0.290074	+	0.957004i	$0.593680\pi$
$360$		0			0
$361$	15.3336	+	360.674i	0.0424753	+	0.999098i
$362$		0			0
$363$	174.829	+	217.370i	0.481623	+	0.598816i
$364$		0			0
$365$	−41.6575	+	72.1529i	−0.114130	+	0.197679i
$366$		0			0
$367$	−42.8621	−	74.2394i	−0.116791	−	0.202287i	0.801704	−	0.597722i	$-0.203927\pi$
$367$	−42.8621	−	74.2394i	−0.116791	−	0.202287i	−0.918494	+	0.395435i	$0.870594\pi$
$368$		0			0
$369$	−59.7045	−	187.997i	−0.161801	−	0.509478i
$370$		0			0
$371$	475.793	−	274.699i	1.28246	−	0.740429i
$372$		0			0
$373$	176.192	+	101.725i	0.472366	+	0.272720i	0.717229	−	0.696837i	$-0.245410\pi$
$373$	176.192	+	101.725i	0.472366	+	0.272720i	−0.244864	+	0.969557i	$0.578743\pi$
$374$		0			0
$375$	−50.6607	+	130.675i	−0.135095	+	0.348467i
$376$		0			0
$377$	116.278			0.308429
$378$		0			0
$379$			1.90054i			0.00501462i	0.999997	+	0.00250731i	$0.000798102\pi$
$379$			1.90054i			0.00501462i	−0.999997	+	0.00250731i	$0.999202\pi$
$380$		0			0
$381$	−322.670	−	125.094i	−0.846902	−	0.328331i
$382$		0			0
$383$	482.284	+	278.447i	1.25923	+	0.727015i	0.972924	−	0.231124i	$-0.0742404\pi$
$383$	482.284	+	278.447i	1.25923	+	0.727015i	0.286303	+	0.958139i	$0.407574\pi$
$384$		0			0
$385$	−24.6854	−	42.7564i	−0.0641180	−	0.111056i
$386$		0			0
$387$	41.4255	−	188.710i	0.107043	−	0.487623i
$388$		0			0
$389$	83.8471	+	145.227i	0.215545	+	0.373335i	0.953441	−	0.301579i	$-0.0975138\pi$
$389$	83.8471	+	145.227i	0.215545	+	0.373335i	−0.737896	+	0.674915i	$0.764180\pi$
$390$		0			0
$391$	59.1274	−	102.412i	0.151221	−	0.261923i
$392$		0			0
$393$	32.9872	+	41.0139i	0.0839368	+	0.104361i
$394$		0			0
$395$		−	80.7340i		−	0.204390i
$396$		0			0
$397$	−383.975			−0.967192			−0.483596	−	0.875291i	$-0.660670\pi$
$397$	−383.975			−0.967192			−0.483596	+	0.875291i	$0.660670\pi$
$398$		0			0
$399$	457.834	+	320.262i	1.14745	+	0.802661i
$400$		0			0
$401$	−215.095	−	124.185i	−0.536397	−	0.309689i	0.207220	−	0.978294i	$-0.433558\pi$
$401$	−215.095	−	124.185i	−0.536397	−	0.309689i	−0.743618	+	0.668605i	$0.766892\pi$
$402$		0			0
$403$	109.835	+	190.239i	0.272543	+	0.472058i
$404$		0			0
$405$	69.9907	+	32.2843i	0.172817	+	0.0797144i
$406$		0			0
$407$	19.8293	−	11.4484i	0.0487205	−	0.0281288i
$408$		0			0
$409$	228.133	+	131.713i	0.557783	+	0.322036i	0.752255	−	0.658872i	$-0.228966\pi$
$409$	228.133	+	131.713i	0.557783	+	0.322036i	−0.194472	+	0.980908i	$0.562299\pi$
$410$		0			0
$411$	721.050	−	111.746i	1.75438	−	0.271888i
$412$		0			0
$413$			516.459i			1.25051i
$414$		0			0
$415$	95.4653			0.230037
$416$		0			0
$417$	169.484	+	210.724i	0.406436	+	0.505334i
$418$		0			0
$419$	150.379	−	260.464i	0.358900	−	0.621633i	−0.628878	−	0.777504i	$-0.716485\pi$
$419$	150.379	−	260.464i	0.358900	−	0.621633i	0.987777	+	0.155872i	$0.0498186\pi$
$420$		0			0
$421$	715.124	−	412.877i	1.69863	−	0.980705i	0.751570	−	0.659653i	$-0.229297\pi$
$421$	715.124	−	412.877i	1.69863	−	0.980705i	0.947061	−	0.321052i	$-0.104037\pi$
$422$		0			0
$423$	112.109	−	510.701i	0.265032	−	1.20733i
$424$		0			0
$425$	−156.442	−	270.965i	−0.368099	−	0.637565i
$426$		0			0
$427$	−471.545	+	816.740i	−1.10432	+	1.91274i
$428$		0			0
$429$	−81.3882	−	31.5530i	−0.189716	−	0.0735500i
$430$		0			0
$431$			26.4080i			0.0612715i	0.999531	+	0.0306358i	$0.00975319\pi$
$431$			26.4080i			0.0612715i	−0.999531	+	0.0306358i	$0.990247\pi$
$432$		0			0
$433$		−	317.690i		−	0.733695i	−0.930281	−	0.366847i	$-0.880437\pi$
$433$		−	317.690i		−	0.733695i	0.930281	−	0.366847i	$-0.119563\pi$
$434$		0			0
$435$	56.3002	+	21.8267i	0.129426	+	0.0501764i
$436$		0			0
$437$	−166.140	+	48.3221i	−0.380183	+	0.110577i
$438$		0			0
$439$	−391.143	+	225.826i	−0.890986	+	0.514411i	−0.874265	−	0.485449i	$-0.838656\pi$
$439$	−391.143	+	225.826i	−0.890986	+	0.514411i	−0.0167210	+	0.999860i	$0.505323\pi$
$440$		0			0
$441$	403.884	−	128.266i	0.915837	−	0.290853i
$442$		0			0
$443$	−116.360	−	201.542i	−0.262664	−	0.454947i	0.704285	−	0.709917i	$-0.251268\pi$
$443$	−116.360	−	201.542i	−0.262664	−	0.454947i	−0.966949	+	0.254970i	$0.917934\pi$
$444$		0			0
$445$	18.0294	+	10.4093i	0.0405155	+	0.0233916i
$446$		0			0
$447$	328.885	+	408.912i	0.735760	+	0.914793i
$448$		0			0
$449$		−	321.349i		−	0.715699i	−0.933779	−	0.357849i	$-0.883510\pi$
$449$		−	321.349i		−	0.715699i	0.933779	−	0.357849i	$-0.116490\pi$
$450$		0			0
$451$			116.004i			0.257216i
$452$		0			0
$453$	56.7978	+	366.492i	0.125382	+	0.809034i
$454$		0			0
$455$	−44.4066	−	25.6382i	−0.0975970	−	0.0563477i
$456$		0			0
$457$	110.763	+	191.848i	0.242371	+	0.419798i	0.961389	−	0.275193i	$-0.0887416\pi$
$457$	110.763	+	191.848i	0.242371	+	0.419798i	−0.719018	+	0.694991i	$0.755408\pi$
$458$		0			0
$459$	−313.972	+	156.050i	−0.684034	+	0.339979i
$460$		0			0
$461$	−6.96835	−	12.0695i	−0.0151157	−	0.0261812i	0.858369	−	0.513033i	$-0.171478\pi$
$461$	−6.96835	−	12.0695i	−0.0151157	−	0.0261812i	−0.873484	+	0.486852i	$0.838145\pi$
$462$		0			0
$463$	70.2174	−	121.620i	0.151657	−	0.262678i	−0.780179	−	0.625556i	$-0.784872\pi$
$463$	70.2174	−	121.620i	0.151657	−	0.262678i	0.931837	+	0.362877i	$0.118206\pi$
$464$		0			0
$465$	17.4704	+	112.729i	0.0375707	+	0.242428i
$466$		0			0
$467$	−923.044			−1.97654			−0.988270	−	0.152720i	$-0.951197\pi$
$467$	−923.044			−1.97654			−0.988270	+	0.152720i	$0.951197\pi$
$468$		0			0
$469$		−	159.057i		−	0.339140i
$470$		0			0
$471$	66.4618	+	82.6340i	0.141108	+	0.175444i
$472$		0			0
$473$	−56.8122	+	98.4016i	−0.120110	+	0.208037i
$474$		0			0
$475$	−109.066	+	444.614i	−0.229613	+	0.936029i
$476$		0			0
$477$	340.017	−	372.613i	0.712824	−	0.781158i
$478$		0			0
$479$	277.249	+	480.210i	0.578808	+	1.00253i	0.995616	+	0.0935308i	$0.0298154\pi$
$479$	277.249	+	480.210i	0.578808	+	1.00253i	−0.416808	+	0.908994i	$0.636851\pi$
$480$		0			0
$481$	11.8903	−	20.5946i	0.0247200	−	0.0428162i
$482$		0			0
$483$	−96.8001	+	249.688i	−0.200414	+	0.516951i
$484$		0			0
$485$		−	16.6504i		−	0.0343307i
$486$		0			0
$487$			810.285i			1.66383i	0.554903	+	0.831915i	$0.312755\pi$
$487$			810.285i			1.66383i	−0.554903	+	0.831915i	$0.687245\pi$
$488$		0			0
$489$	12.6643	−	32.6664i	0.0258983	−	0.0668024i
$490$		0			0
$491$	−424.393	+	735.070i	−0.864344	+	1.49709i	0.00335361	+	0.999994i	$0.498933\pi$
$491$	−424.393	+	735.070i	−0.864344	+	1.49709i	−0.867697	+	0.497093i	$0.834401\pi$
$492$		0			0
$493$	−237.873	+	137.336i	−0.482502	+	0.278573i
$494$		0			0
$495$	−33.4842	−	30.5551i	−0.0676449	−	0.0617275i
$496$		0			0
$497$	1058.43	−	611.083i	2.12963	−	1.22954i
$498$		0			0
$499$	43.9396	−	76.1056i	0.0880553	−	0.152516i	−0.818634	−	0.574316i	$-0.805268\pi$
$499$	43.9396	−	76.1056i	0.0880553	−	0.152516i	0.906689	+	0.421800i	$0.138601\pi$
$500$		0			0
$501$	461.959	−	371.550i	0.922073	−	0.741616i
$502$		0			0
$503$	−658.695			−1.30953			−0.654766	−	0.755831i	$-0.727233\pi$
$503$	−658.695			−1.30953			−0.654766	+	0.755831i	$0.727233\pi$
$504$		0			0
$505$	93.3327			0.184817
$506$		0			0
$507$	411.429	−	63.7619i	0.811497	−	0.125763i
$508$		0			0
$509$	−242.965	−	140.276i	−0.477338	−	0.275591i	0.241968	−	0.970284i	$-0.422207\pi$
$509$	−242.965	−	140.276i	−0.477338	−	0.275591i	−0.719306	+	0.694693i	$0.755540\pi$
$510$		0			0
$511$	429.118	+	743.254i	0.839761	+	1.45451i
$512$		0			0
$513$	489.647	+	153.019i	0.954477	+	0.298283i
$514$		0			0
$515$	107.829	−	62.2551i	0.209377	−	0.120884i
$516$		0			0
$517$	−153.749	+	266.302i	−0.297387	+	0.515090i
$518$		0			0
$519$	−110.385	−	712.267i	−0.212687	−	1.37238i
$520$		0			0
$521$			448.199i			0.860266i	0.902766	+	0.430133i	$0.141533\pi$
$521$			448.199i			0.860266i	−0.902766	+	0.430133i	$0.858467\pi$
$522$		0			0
$523$			223.570i			0.427477i	0.976891	+	0.213738i	$0.0685640\pi$
$523$			223.570i			0.427477i	−0.976891	+	0.213738i	$0.931436\pi$
$524$		0			0
$525$	444.067	+	552.122i	0.845842	+	1.05166i
$526$		0			0
$527$	−449.386	−	259.453i	−0.852725	−	0.492321i
$528$		0			0
$529$	223.035	+	386.309i	0.421617	+	0.730262i
$530$		0			0
$531$	143.529	+	451.945i	0.270300	+	0.851121i
$532$		0			0
$533$	60.2409	+	104.340i	0.113022	+	0.195760i
$534$		0			0
$535$	25.1056	+	14.4947i	0.0469264	+	0.0270930i
$536$		0			0
$537$	−574.182	−	222.602i	−1.06924	−	0.414528i
$538$		0			0
$539$	−249.218			−0.462371
$540$		0			0
$541$	−154.204			−0.285036			−0.142518	−	0.989792i	$-0.545520\pi$
$541$	−154.204			−0.285036			−0.142518	+	0.989792i	$0.545520\pi$
$542$		0			0
$543$	−803.627	−	311.554i	−1.47998	−	0.573764i
$544$		0			0
$545$	−95.1337	−	54.9254i	−0.174557	−	0.100781i
$546$		0			0
$547$	−472.268	+	272.664i	−0.863378	+	0.498472i	−0.865142	−	0.501527i	$-0.832772\pi$
$547$	−472.268	+	272.664i	−0.863378	+	0.498472i	0.00176382	+	0.999998i	$0.499439\pi$
$548$		0			0
$549$	−185.661	+	845.763i	−0.338181	+	1.54055i
$550$		0			0
$551$	390.315	+	95.7463i	0.708375	+	0.173768i
$552$		0			0
$553$	−720.229	−	415.824i	−1.30240	−	0.751942i
$554$		0			0
$555$	9.62299	−	7.73969i	0.0173387	−	0.0139454i
$556$		0			0
$557$	−556.533			−0.999161			−0.499580	−	0.866268i	$-0.666512\pi$
$557$	−556.533			−0.999161			−0.499580	+	0.866268i	$0.666512\pi$
$558$		0			0
$559$			118.010i			0.211109i
$560$		0			0
$561$	203.766	−	31.5790i	0.363219	−	0.0562906i
$562$		0			0
$563$	−823.656	−	475.538i	−1.46298	−	0.844651i	−0.463830	−	0.885924i	$-0.653525\pi$
$563$	−823.656	−	475.538i	−1.46298	−	0.844651i	−0.999148	+	0.0412738i	$0.986858\pi$
$564$		0			0
$565$	99.2823	−	57.3206i	0.175721	−	0.101452i
$566$		0			0
$567$	648.499	−	458.106i	1.14374	−	0.807947i
$568$		0			0
$569$	691.099	−	399.006i	1.21459	−	0.701241i	0.250831	−	0.968031i	$-0.419296\pi$
$569$	691.099	−	399.006i	1.21459	−	0.701241i	0.963755	+	0.266789i	$0.0859628\pi$
$570$		0			0
$571$	236.350	−	409.371i	0.413924	−	0.716937i	−0.581391	−	0.813624i	$-0.697491\pi$
$571$	236.350	−	409.371i	0.413924	−	0.716937i	0.995315	+	0.0966875i	$0.0308248\pi$
$572$		0			0
$573$	−780.110	+	120.899i	−1.36145	+	0.210993i
$574$		0			0
$575$	−219.418			−0.381596
$576$		0			0
$577$	649.275			1.12526			0.562630	−	0.826709i	$-0.309790\pi$
$577$	649.275			1.12526			0.562630	+	0.826709i	$0.309790\pi$
$578$		0			0
$579$	−216.321	+	173.986i	−0.373612	+	0.300493i
$580$		0			0
$581$	491.699	−	851.647i	0.846297	−	1.46583i
$582$		0			0
$583$	−256.915	+	148.330i	−0.440678	+	0.254426i
$584$		0			0
$585$	−45.9846	−	10.0945i	−0.0786062	−	0.0172556i
$586$		0			0
$587$	324.756	+	562.494i	0.553247	+	0.958252i	0.998038	+	0.0626177i	$0.0199449\pi$
$587$	324.756	+	562.494i	0.553247	+	0.958252i	−0.444790	+	0.895635i	$0.646722\pi$
$588$		0			0
$589$	212.039	+	729.027i	0.359999	+	1.23774i
$590$		0			0
$591$	−42.8312	+	110.479i	−0.0724725	+	0.186936i
$592$		0			0
$593$	−280.522			−0.473055			−0.236527	−	0.971625i	$-0.576009\pi$
$593$	−280.522			−0.473055			−0.236527	+	0.971625i	$0.576009\pi$
$594$		0			0
$595$	121.126			0.203573
$596$		0			0
$597$	−133.038	+	343.161i	−0.222845	+	0.574809i
$598$		0			0
$599$	−889.536	−	513.574i	−1.48504	−	0.857386i	−0.485180	−	0.874414i	$-0.661246\pi$
$599$	−889.536	−	513.574i	−1.48504	−	0.857386i	−0.999855	+	0.0170284i	$0.994579\pi$
$600$		0			0
$601$	−785.475	+	453.494i	−1.30695	+	0.754566i	−0.981586	−	0.191023i	$-0.938819\pi$
$601$	−785.475	+	453.494i	−1.30695	+	0.754566i	−0.325362	+	0.945590i	$0.605486\pi$
$602$		0			0
$603$	−44.2035	−	139.188i	−0.0733060	−	0.230826i
$604$		0			0
$605$	−44.2409	−	76.6276i	−0.0731255	−	0.126657i
$606$		0			0
$607$	−403.430	−	232.920i	−0.664629	−	0.383723i	0.129410	−	0.991591i	$-0.458692\pi$
$607$	−403.430	−	232.920i	−0.664629	−	0.383723i	−0.794038	+	0.607868i	$0.792025\pi$
$608$		0			0
$609$	484.693	−	389.835i	0.795884	−	0.640123i
$610$		0			0
$611$			319.367i			0.522695i
$612$		0			0
$613$	−1004.94			−1.63938			−0.819689	−	0.572809i	$-0.805854\pi$
$613$	−1004.94			−1.63938			−0.819689	+	0.572809i	$0.805854\pi$
$614$		0			0
$615$	9.58193	+	61.8282i	0.0155804	+	0.100534i
$616$		0			0
$617$	−90.5323	+	156.807i	−0.146730	+	0.254144i	−0.930017	−	0.367516i	$-0.880208\pi$
$617$	−90.5323	+	156.807i	−0.146730	+	0.254144i	0.783287	+	0.621660i	$0.213541\pi$
$618$		0			0
$619$	102.364	+	177.299i	0.165369	+	0.286428i	0.936786	−	0.349902i	$-0.113785\pi$
$619$	102.364	+	177.299i	0.165369	+	0.286428i	−0.771417	+	0.636330i	$0.780452\pi$
$620$		0			0
$621$	−15.3175	+	245.399i	−0.0246659	+	0.395168i
$622$		0			0
$623$	185.723	−	107.227i	0.298110	−	0.172114i
$624$		0			0
$625$	−278.954	+	483.162i	−0.446326	+	0.773059i
$626$		0			0
$627$	−247.218	−	172.933i	−0.394287	−	0.275810i
$628$		0			0
$629$			56.1748i			0.0893081i
$630$		0			0
$631$	937.909			1.48638			0.743192	−	0.669078i	$-0.233311\pi$
$631$	937.909			1.48638			0.743192	+	0.669078i	$0.233311\pi$
$632$		0			0
$633$	348.964	−	280.669i	0.551286	−	0.443395i
$634$		0			0
$635$	95.0642	+	54.8854i	0.149707	+	0.0864336i
$636$		0			0
$637$	−224.159	+	129.418i	−0.351899	+	0.203169i
$638$		0			0
$639$	756.386	−	828.896i	1.18370	−	1.29718i
$640$		0			0
$641$	260.151	−	150.198i	0.405852	−	0.234319i	−0.283154	−	0.959074i	$-0.591381\pi$
$641$	260.151	−	150.198i	0.405852	−	0.234319i	0.689006	+	0.724756i	$0.258047\pi$
$642$		0			0
$643$	−205.985	+	356.776i	−0.320350	+	0.554862i	−0.980560	−	0.196219i	$-0.937134\pi$
$643$	−205.985	+	356.776i	−0.320350	+	0.554862i	0.660210	+	0.751081i	$0.270467\pi$
$644$		0			0
$645$	−22.1519	+	57.1389i	−0.0343440	+	0.0885874i
$646$		0			0
$647$	−928.879			−1.43567			−0.717835	−	0.696213i	$-0.754867\pi$
$647$	−928.879			−1.43567			−0.717835	+	0.696213i	$0.754867\pi$
$648$		0			0
$649$		−	278.874i		−	0.429698i
$650$		0			0
$651$	1095.64	+	424.762i	1.68301	+	0.652476i
$652$		0			0
$653$	294.921	−	510.817i	0.451639	−	0.782263i	−0.546849	−	0.837232i	$-0.684173\pi$
$653$	294.921	−	510.817i	0.451639	−	0.782263i	0.998488	+	0.0549690i	$0.0175060\pi$
$654$		0			0
$655$	−8.34749	−	14.4583i	−0.0127443	−	0.0220737i
$656$		0			0
$657$	582.072	+	531.153i	0.885954	+	0.808452i
$658$		0			0
$659$	−112.152	+	64.7510i	−0.170185	+	0.0982564i	−0.582673	−	0.812707i	$-0.697993\pi$
$659$	−112.152	+	64.7510i	−0.170185	+	0.0982564i	0.412488	+	0.910963i	$0.364660\pi$
$660$		0			0
$661$	−316.637	−	182.810i	−0.479027	−	0.276566i	0.240984	−	0.970529i	$-0.422530\pi$
$661$	−316.637	−	182.810i	−0.479027	−	0.276566i	−0.720011	+	0.693963i	$0.755863\pi$
$662$		0			0
$663$	166.879	−	134.219i	0.251702	−	0.202442i
$664$		0			0
$665$	−127.951	−	122.627i	−0.192407	−	0.184401i
$666$		0			0
$667$			192.621i			0.288787i
$668$		0			0
$669$	7.46760	+	48.1853i	0.0111623	+	0.0720259i
$670$		0			0
$671$	254.622	−	441.017i	0.379466	−	0.657254i
$672$		0			0
$673$	1091.37	−	630.104i	1.62165	−	0.936262i	0.635176	−	0.772368i	$-0.280928\pi$
$673$	1091.37	−	630.104i	1.62165	−	0.936262i	0.986478	−	0.163894i	$-0.0524056\pi$
$674$		0			0
$675$	542.036	+	359.742i	0.803016	+	0.532951i
$676$		0			0
$677$	935.840	−	540.307i	1.38233	−	0.798091i	0.389898	−	0.920858i	$-0.372510\pi$
$677$	935.840	−	540.307i	1.38233	−	0.798091i	0.992435	+	0.122767i	$0.0391769\pi$
$678$		0			0
$679$	−148.538	−	85.7585i	−0.218760	−	0.126301i
$680$		0			0
$681$	52.7858	+	340.604i	0.0775121	+	0.500153i
$682$		0			0
$683$		−	191.836i		−	0.280873i	−0.990090	−	0.140437i	$-0.955149\pi$
$683$		−	191.836i		−	0.280873i	0.990090	−	0.140437i	$-0.0448506\pi$
$684$		0			0
$685$	−231.442			−0.337871
$686$		0			0
$687$	314.197	+	390.650i	0.457346	+	0.568632i
$688$		0			0
$689$	−154.055	+	266.831i	−0.223592	+	0.387273i
$690$		0			0
$691$	−266.760	−	462.041i	−0.386049	−	0.668656i	0.605865	−	0.795567i	$-0.292827\pi$
$691$	−266.760	−	462.041i	−0.386049	−	0.668656i	−0.991914	+	0.126911i	$0.959494\pi$
$692$		0			0
$693$	−445.044	+	141.338i	−0.642200	+	0.203951i
$694$		0			0
$695$	−42.8883	−	74.2847i	−0.0617097	−	0.106884i
$696$		0			0
$697$	−246.474	−	142.302i	−0.353621	−	0.204163i
$698$		0			0
$699$	−29.7613	+	76.7668i	−0.0425770	+	0.109824i
$700$		0			0
$701$	−671.660			−0.958145			−0.479073	−	0.877775i	$-0.659027\pi$
$701$	−671.660			−0.958145			−0.479073	+	0.877775i	$0.659027\pi$
$702$		0			0
$703$	56.8709	−	59.3401i	0.0808975	−	0.0844098i
$704$		0			0
$705$	−59.9491	+	154.633i	−0.0850341	+	0.219338i
$706$		0			0
$707$	480.715	−	832.622i	0.679936	−	1.17768i
$708$		0			0
$709$	−384.051	−	665.196i	−0.541680	−	0.938218i	−0.998808	−	0.0488166i	$-0.984455\pi$
$709$	−384.051	−	665.196i	−0.541680	−	0.938218i	0.457127	−	0.889401i	$-0.348878\pi$
$710$		0			0
$711$	−745.822	−	163.722i	−1.04898	−	0.230270i
$712$		0			0
$713$	−315.143	+	181.948i	−0.441996	+	0.255187i
$714$		0			0
$715$	23.9784	+	13.8439i	0.0335362	+	0.0193621i
$716$		0			0
$717$	45.3585	+	56.3956i	0.0632615	+	0.0786549i
$718$		0			0
$719$	585.045			0.813693			0.406846	−	0.913497i	$-0.366628\pi$
$719$	585.045			0.813693			0.406846	+	0.913497i	$0.366628\pi$
$720$		0			0
$721$		−	1282.59i		−	1.77890i
$722$		0			0
$723$	−89.4691	−	577.306i	−0.123747	−	0.798487i
$724$		0			0
$725$	441.366	+	254.823i	0.608781	+	0.351480i
$726$		0			0
$727$	701.841	+	1215.62i	0.965394	+	1.67211i	0.708553	+	0.705658i	$0.249348\pi$
$727$	701.841	+	1215.62i	0.965394	+	1.67211i	0.256841	+	0.966454i	$0.417318\pi$
$728$		0			0
$729$	440.179	−	581.105i	0.603812	−	0.797127i
$730$		0			0
$731$	−139.382	−	241.417i	−0.190673	−	0.330256i
$732$		0			0
$733$	−143.403	+	248.381i	−0.195639	+	0.338856i	−0.947110	−	0.320910i	$-0.896011\pi$
$733$	−143.403	+	248.381i	−0.195639	+	0.338856i	0.751471	+	0.659766i	$0.229345\pi$
$734$		0			0
$735$	−132.829	+	20.5853i	−0.180719	+	0.0280073i
$736$		0			0
$737$			85.8864i			0.116535i
$738$		0			0
$739$	195.178			0.264111			0.132055	−	0.991242i	$-0.457842\pi$
$739$	195.178			0.264111			0.132055	+	0.991242i	$0.457842\pi$
$740$		0			0
$741$	−312.164	−	27.1646i	−0.421274	−	0.0366594i
$742$		0			0
$743$	−263.691	−	152.242i	−0.354900	−	0.204902i	0.311941	−	0.950101i	$-0.399021\pi$
$743$	−263.691	−	152.242i	−0.354900	−	0.204902i	−0.666841	+	0.745200i	$0.732354\pi$
$744$		0			0
$745$	−83.2252	−	144.150i	−0.111712	−	0.193490i
$746$		0			0
$747$	193.596	−	881.910i	0.259165	−	1.18060i
$748$		0			0
$749$	258.615	−	149.312i	0.345281	−	0.199348i
$750$		0			0
$751$	−302.948	−	174.907i	−0.403393	−	0.232899i	0.284554	−	0.958660i	$-0.408155\pi$
$751$	−302.948	−	174.907i	−0.403393	−	0.232899i	−0.687947	+	0.725761i	$0.741488\pi$
$752$		0			0
$753$	−344.651	+	888.998i	−0.457704	+	1.18061i
$754$		0			0
$755$		−	117.636i		−	0.155810i
$756$		0			0
$757$	129.838			0.171516			0.0857582	−	0.996316i	$-0.472669\pi$
$757$	129.838			0.171516			0.0857582	+	0.996316i	$0.472669\pi$
$758$		0			0
$759$	52.2695	−	134.825i	0.0688662	−	0.177634i
$760$		0			0
$761$	695.841	−	1205.23i	0.914377	−	1.58375i	0.106567	−	0.994305i	$-0.466014\pi$
$761$	695.841	−	1205.23i	0.914377	−	1.58375i	0.807810	−	0.589443i	$-0.200653\pi$
$762$		0			0
$763$	−979.981	+	565.792i	−1.28438	+	0.741536i
$764$		0			0
$765$	105.995	−	33.6621i	0.138556	−	0.0440027i
$766$		0			0
$767$	−144.819	−	250.834i	−0.188812	−	0.327032i
$768$		0			0
$769$	11.4192	−	19.7787i	0.0148494	−	0.0257200i	−0.858505	−	0.512805i	$-0.828606\pi$
$769$	11.4192	−	19.7787i	0.0148494	−	0.0257200i	0.873355	+	0.487085i	$0.161940\pi$
$770$		0			0
$771$	789.976	−	635.371i	1.02461	−	0.824087i
$772$		0			0
$773$			732.644i			0.947793i	0.880581	+	0.473896i	$0.157153\pi$
$773$			732.644i			0.947793i	−0.880581	+	0.473896i	$0.842847\pi$
$774$		0			0
$775$			962.812i			1.24234i
$776$		0			0
$777$	−19.4822	−	125.710i	−0.0250736	−	0.161789i
$778$		0			0
$779$	116.297	+	399.848i	0.149290	+	0.513284i
$780$		0			0
$781$	−571.522	+	329.968i	−0.731782	+	0.422494i
$782$		0			0
$783$	315.808	−	475.839i	0.403331	−	0.607713i
$784$		0			0
$785$	−16.8183	−	29.1302i	−0.0214246	−	0.0371085i
$786$		0			0
$787$	−472.454	−	272.772i	−0.600323	−	0.346597i	0.168845	−	0.985643i	$-0.445996\pi$
$787$	−472.454	−	272.772i	−0.600323	−	0.346597i	−0.769169	+	0.639046i	$0.779329\pi$
$788$		0			0
$789$	295.427	−	45.7844i	0.374433	−	0.0580284i
$790$		0			0
$791$		−	1180.93i		−	1.49296i
$792$		0			0
$793$		−	528.898i		−	0.666959i
$794$		0			0
$795$	−124.679	+	100.278i	−0.156829	+	0.126136i
$796$		0			0
$797$	−203.065	−	117.239i	−0.254786	−	0.147101i	0.367168	−	0.930155i	$-0.380328\pi$
$797$	−203.065	−	117.239i	−0.254786	−	0.147101i	−0.621954	+	0.783054i	$0.713661\pi$
$798$		0			0
$799$	−377.206	−	653.340i	−0.472098	−	0.817697i
$800$		0			0
$801$	132.723	−	145.447i	0.165697	−	0.181581i
$802$		0			0
$803$	−231.712	−	401.337i	−0.288558	−	0.499797i
$804$		0			0
$805$	42.4712	−	73.5623i	0.0527593	−	0.0913818i
$806$		0			0
$807$	−1314.50	−	509.612i	−1.62887	−	0.631489i
$808$		0			0
$809$	−539.672			−0.667085			−0.333543	−	0.942735i	$-0.608244\pi$
$809$	−539.672			−0.667085			−0.333543	+	0.942735i	$0.608244\pi$
$810$		0			0
$811$			300.424i			0.370436i	0.982697	+	0.185218i	$0.0592992\pi$
$811$			300.424i			0.370436i	−0.982697	+	0.185218i	$0.940701\pi$
$812$		0			0
$813$	−64.7168	+	166.931i	−0.0796025	+	0.205328i
$814$		0			0
$815$	−5.55647	+	9.62408i	−0.00681775	+	0.0118087i
$816$		0			0
$817$	−97.1727	+	396.129i	−0.118938	+	0.484859i
$818$		0			0
$819$	−326.899	+	358.237i	−0.399144	+	0.437408i
$820$		0			0
$821$	−430.739	−	746.062i	−0.524652	−	0.908723i	−0.999588	−	0.0287032i	$-0.990862\pi$
$821$	−430.739	−	746.062i	−0.524652	−	0.908723i	0.474936	−	0.880020i	$-0.342471\pi$
$822$		0			0
$823$	711.781	−	1232.84i	0.864862	−	1.49798i	−0.00232210	−	0.999997i	$-0.500739\pi$
$823$	711.781	−	1232.84i	0.864862	−	1.49798i	0.867184	−	0.497988i	$-0.165928\pi$
$824$		0			0
$825$	−239.784	−	298.131i	−0.290647	−	0.361371i
$826$		0			0
$827$		−	910.950i		−	1.10151i	−0.834666	−	0.550756i	$-0.814340\pi$
$827$		−	910.950i		−	1.10151i	0.834666	−	0.550756i	$-0.185660\pi$
$828$		0			0
$829$		−	56.1843i		−	0.0677736i	−0.999426	−	0.0338868i	$-0.989211\pi$
$829$		−	56.1843i		−	0.0677736i	0.999426	−	0.0338868i	$-0.0107886\pi$
$830$		0			0
$831$	164.121	−	25.4350i	0.197498	−	0.0306077i
$832$		0			0
$833$	305.714	−	529.512i	0.367003	−	0.635669i
$834$		0			0
$835$	−162.850	+	94.0215i	−0.195030	+	0.112601i
$836$		0			0
$837$	1076.82	+	67.2138i	1.28652	+	0.0803032i
$838$		0			0
$839$	−830.398	+	479.431i	−0.989748	+	0.571431i	−0.905199	−	0.424988i	$-0.860278\pi$
$839$	−830.398	+	479.431i	−0.989748	+	0.571431i	−0.0845489	+	0.996419i	$0.526945\pi$
$840$		0			0
$841$	−196.798	+	340.864i	−0.234004	+	0.405308i
$842$		0			0
$843$	−107.344	−	692.644i	−0.127335	−	0.821642i
$844$		0			0
$845$	−132.060			−0.156284
$846$		0			0
$847$	−911.460			−1.07610
$848$		0			0
$849$	−254.742	−	316.728i	−0.300049	−	0.373060i
$850$		0			0
$851$	34.1162	+	19.6970i	0.0400896	+	0.0231457i
$852$		0			0
$853$	105.088	+	182.018i	0.123198	+	0.213386i	0.921027	−	0.389498i	$-0.127351\pi$
$853$	105.088	+	182.018i	0.123198	+	0.213386i	−0.797829	+	0.602884i	$0.794018\pi$
$854$		0			0
$855$	−146.047	−	71.7498i	−0.170815	−	0.0839179i
$856$		0			0
$857$	1099.75	−	634.940i	1.28325	−	0.740886i	0.305811	−	0.952092i	$-0.401072\pi$
$857$	1099.75	−	634.940i	1.28325	−	0.740886i	0.977442	+	0.211206i	$0.0677390\pi$
$858$		0			0
$859$	429.096	−	743.215i	0.499529	−	0.865210i	−0.500471	−	0.865754i	$-0.666840\pi$
$859$	429.096	−	743.215i	0.499529	−	0.865210i	1.00000		0.000543447i	$0.000172985\pi$
$860$		0			0
$861$	600.922	+	232.968i	0.697935	+	0.270579i
$862$		0			0
$863$			976.731i			1.13179i	0.824479	+	0.565893i	$0.191468\pi$
$863$			976.731i			1.13179i	−0.824479	+	0.565893i	$0.808532\pi$
$864$		0			0
$865$			228.622i			0.264303i
$866$		0			0
$867$	130.533	−	336.698i	0.150557	−	0.388348i
$868$		0			0
$869$	388.904	+	224.534i	0.447530	+	0.258382i
$870$		0			0
$871$	44.6007	+	77.2506i	0.0512063	+	0.0886919i
$872$		0			0
$873$	−153.817	−	33.7657i	−0.176193	−	0.0386777i
$874$		0			0
$875$	−228.968	−	396.583i	−0.261677	−	0.453238i
$876$		0			0
$877$	−618.005	−	356.805i	−0.704681	−	0.406848i	0.104408	−	0.994535i	$-0.466705\pi$
$877$	−618.005	−	356.805i	−0.704681	−	0.406848i	−0.809088	+	0.587687i	$0.800039\pi$
$878$		0			0
$879$	−1185.10	+	953.167i	−1.34824	+	1.08438i
$880$		0			0
$881$	1118.09			1.26912			0.634558	−	0.772875i	$-0.281182\pi$
$881$	1118.09			1.26912			0.634558	+	0.772875i	$0.281182\pi$
$882$		0			0
$883$	−259.973			−0.294420			−0.147210	−	0.989105i	$-0.547029\pi$
$883$	−259.973			−0.294420			−0.147210	+	0.989105i	$0.547029\pi$
$884$		0			0
$885$	−23.0349	−	148.635i	−0.0260282	−	0.167949i
$886$		0			0
$887$	−913.476	−	527.395i	−1.02985	−	0.594583i	−0.112907	−	0.993606i	$-0.536016\pi$
$887$	−913.476	−	527.395i	−1.02985	−	0.594583i	−0.916941	+	0.399022i	$0.869350\pi$
$888$		0			0
$889$	979.265	−	565.379i	1.10154	−	0.635972i
$890$		0			0
$891$	−350.172	+	247.365i	−0.393010	+	0.277626i
$892$		0			0
$893$	−262.976	+	1072.03i	−0.294486	+	1.20049i
$894$		0			0
$895$	169.164	+	97.6669i	0.189010	+	0.109125i
$896$		0			0
$897$	−23.0003	−	148.412i	−0.0256414	−	0.165453i
$898$		0			0
$899$	845.228			0.940187
$900$		0			0
$901$		−	727.822i		−	0.807794i
$902$		0			0
$903$	395.642	+	491.914i	0.438142	+	0.544755i
$904$		0			0
$905$	236.763	+	136.695i	0.261616	+	0.151044i
$906$		0			0
$907$	−488.484	+	282.026i	−0.538571	+	0.310944i	−0.744500	−	0.667623i	$-0.767312\pi$
$907$	−488.484	+	282.026i	−0.538571	+	0.310944i	0.205928	+	0.978567i	$0.433979\pi$
$908$		0			0
$909$	189.271	−	862.210i	0.208219	−	0.948525i
$910$		0			0
$911$	−477.954	+	275.947i	−0.524647	+	0.302905i	−0.738834	−	0.673887i	$-0.764623\pi$
$911$	−477.954	+	275.947i	−0.524647	+	0.302905i	0.214187	+	0.976793i	$0.431290\pi$
$912$		0			0
$913$	−265.504	+	459.866i	−0.290804	+	0.503687i
$914$		0			0
$915$	99.2806	−	256.086i	0.108503	−	0.279875i
$916$		0			0
$917$	−171.977			−0.187543
$918$		0			0
$919$	992.332			1.07979			0.539897	−	0.841731i	$-0.318463\pi$
$919$	992.332			1.07979			0.539897	+	0.841731i	$0.318463\pi$
$920$		0			0
$921$	1081.26	+	419.187i	1.17400	+	0.455143i
$922$		0			0
$923$	−342.704	+	593.580i	−0.371293	+	0.643099i
$924$		0			0
$925$	90.2662	−	52.1152i	0.0975851	−	0.0563408i
$926$		0			0
$927$	−356.445	−	1122.37i	−0.384514	−	1.21076i
$928$		0			0
$929$	720.122	+	1247.29i	0.775158	+	1.34261i	0.934706	+	0.355423i	$0.115663\pi$
$929$	720.122	+	1247.29i	0.775158	+	1.34261i	−0.159548	+	0.987190i	$0.551004\pi$
$930$		0			0
$931$	−859.013	+	249.846i	−0.922678	+	0.268363i
$932$		0			0
$933$	684.116	+	850.582i	0.733244	+	0.911664i
$934$		0			0
$935$	−65.4046			−0.0699514
$936$		0			0
$937$	1423.89			1.51963			0.759814	−	0.650141i	$-0.225290\pi$
$937$	1423.89			1.51963			0.759814	+	0.650141i	$0.225290\pi$
$938$		0			0
$939$	259.298	−	40.1852i	0.276143	−	0.0427958i
$940$		0			0
$941$	−209.478	−	120.942i	−0.222612	−	0.128525i	0.384547	−	0.923105i	$-0.374358\pi$
$941$	−209.478	−	120.942i	−0.222612	−	0.128525i	−0.607159	+	0.794580i	$0.707691\pi$
$942$		0			0
$943$	−172.846	+	99.7928i	−0.183294	+	0.105825i
$944$		0			0
$945$	−225.526	+	112.091i	−0.238652	+	0.118615i
$946$		0			0
$947$	−610.700	−	1057.76i	−0.644878	−	1.11696i	−0.984330	−	0.176338i	$-0.943575\pi$
$947$	−610.700	−	1057.76i	−0.644878	−	1.11696i	0.339452	−	0.940624i	$-0.389759\pi$
$948$		0			0
$949$	−416.827	−	240.655i	−0.439228	−	0.253588i
$950$		0			0
$951$	−27.6948	−	178.703i	−0.0291218	−	0.187911i
$952$		0			0
$953$		−	1357.25i		−	1.42419i	−0.702083	−	0.712095i	$-0.747747\pi$
$953$		−	1357.25i		−	1.42419i	0.702083	−	0.712095i	$-0.252253\pi$
$954$		0			0
$955$	250.399			0.262198
$956$		0			0
$957$	−261.721	+	210.500i	−0.273481	+	0.219958i
$958$		0			0
$959$	−1192.05	+	2064.69i	−1.24302	+	2.15297i
$960$		0			0
$961$	317.894	+	550.609i	0.330795	+	0.572954i
$962$		0			0
$963$	184.815	−	202.532i	0.191916	−	0.210314i
$964$		0			0
$965$	76.2578	−	44.0275i	0.0790237	−	0.0456243i
$966$		0			0
$967$	95.1010	−	164.720i	0.0983464	−	0.170341i	−0.812654	−	0.582747i	$-0.801978\pi$
$967$	95.1010	−	164.720i	0.0983464	−	0.170341i	0.911000	+	0.412406i	$0.135311\pi$
$968$		0			0
$969$	670.689	−	313.127i	0.692146	−	0.323145i
$970$		0			0
$971$		−	1797.35i		−	1.85103i	−0.378715	−	0.925513i	$-0.623634\pi$
$971$		−	1797.35i		−	1.85103i	0.378715	−	0.925513i	$-0.376366\pi$
$972$		0			0
$973$	−883.592			−0.908111
$974$		0			0
$975$	−370.493	−	143.635i	−0.379993	−	0.147317i
$976$		0			0
$977$	−538.681	−	311.007i	−0.551362	−	0.318329i	0.198309	−	0.980140i	$-0.436455\pi$
$977$	−538.681	−	311.007i	−0.551362	−	0.318329i	−0.749671	+	0.661811i	$0.769788\pi$
$978$		0			0
$979$	−100.285	+	57.8997i	−0.102436	+	0.0591416i
$980$		0			0
$981$	−700.326	+	767.462i	−0.713890	+	0.782326i
$982$		0			0
$983$	296.632	−	171.261i	0.301762	−	0.174223i	−0.341472	−	0.939892i	$-0.610925\pi$
$983$	296.632	−	171.261i	0.301762	−	0.174223i	0.643234	+	0.765669i	$0.277592\pi$
$984$		0			0
$985$	18.7923	−	32.5492i	0.0190785	−	0.0330449i
$986$		0			0
$987$	1070.72	+	1331.25i	1.08482	+	1.34879i
$988$		0			0
$989$	−195.491			−0.197665
$990$		0			0
$991$			311.427i			0.314255i	0.987578	+	0.157127i	$0.0502234\pi$
$991$			311.427i			0.314255i	−0.987578	+	0.157127i	$0.949777\pi$
$992$		0			0
$993$	202.043	+	1303.70i	0.203467	+	1.31289i
$994$		0			0
$995$	58.3708	−	101.101i	0.0586641	−	0.101609i
$996$		0			0
$997$	454.034	+	786.409i	0.455400	+	0.788776i	0.998711	−	0.0507556i	$-0.0161629\pi$
$997$	454.034	+	786.409i	0.455400	+	0.788776i	−0.543311	+	0.839531i	$0.682830\pi$
$998$		0			0
$999$	−51.9848	−	104.593i	−0.0520368	−	0.104698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.15	✓	80
3.2	odd	2		2052.3.t.a.37.17		80
9.2	odd	6		2052.3.t.a.721.18		80
9.7	even	3	inner	684.3.t.a.493.26	yes	80
19.18	odd	2	inner	684.3.t.a.265.26	yes	80
57.56	even	2		2052.3.t.a.37.18		80
171.56	even	6		2052.3.t.a.721.17		80
171.151	odd	6	inner	684.3.t.a.493.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.15	✓	80	1.1	even	1	trivial
684.3.t.a.265.26	yes	80	19.18	odd	2	inner
684.3.t.a.493.15	yes	80	171.151	odd	6	inner
684.3.t.a.493.26	yes	80	9.7	even	3	inner
2052.3.t.a.37.17		80	3.2	odd	2
2052.3.t.a.37.18		80	57.56	even	2
2052.3.t.a.721.17		80	171.56	even	6
2052.3.t.a.721.18		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08441 + 2.79715i) q^{3} +(0.475788 - 0.824090i) q^{5} +(-4.90114 - 8.48903i) q^{7} +(-6.64810 - 6.06653i) q^{9} +O(q^{10})\)	\(q+(-1.08441 + 2.79715i) q^{3} +(0.475788 - 0.824090i) q^{5} +(-4.90114 - 8.48903i) q^{7} +(-6.64810 - 6.06653i) q^{9} +(2.64648 + 4.58384i) q^{11} +(4.76077 + 2.74863i) q^{13} +(1.78915 + 2.22451i) q^{15} -12.9857 q^{17} +(13.7174 + 13.1466i) q^{19} +(29.0599 - 4.50362i) q^{21} +(-4.55328 + 7.88650i) q^{23} +(12.0473 + 20.8665i) q^{25} +(24.1783 - 12.0171i) q^{27} +(18.3181 - 10.5760i) q^{29} +(34.6062 + 19.9799i) q^{31} +(-15.6916 + 2.43183i) q^{33} -9.32763 q^{35} -4.32590i q^{37} +(-12.8510 + 10.3359i) q^{39} +(18.9804 + 10.9583i) q^{41} +(10.7335 + 18.5910i) q^{43} +(-8.16245 + 2.59224i) q^{45} +(29.0478 + 50.3123i) q^{47} +(-23.5424 + 40.7766i) q^{49} +(14.0819 - 36.3229i) q^{51} +56.0480i q^{53} +5.03667 q^{55} +(-51.6483 + 24.1132i) q^{57} +(-45.6289 - 26.3438i) q^{59} +(-48.1056 - 83.3214i) q^{61} +(-18.9157 + 86.1688i) q^{63} +(4.53023 - 2.61553i) q^{65} +(14.0526 + 8.11326i) q^{67} +(-17.1221 - 21.2884i) q^{69} +124.682i q^{71} -87.5546 q^{73} +(-71.4308 + 11.0701i) q^{75} +(25.9416 - 44.9321i) q^{77} +(73.4756 - 42.4212i) q^{79} +(7.39437 + 80.6618i) q^{81} +(50.1616 + 86.8825i) q^{83} +(-6.17844 + 10.7014i) q^{85} +(9.71817 + 62.7072i) q^{87} +21.8780i q^{89} -53.8857i q^{91} +(-93.4143 + 75.1323i) q^{93} +(17.3606 - 5.04936i) q^{95} +(15.1534 - 8.74883i) q^{97} +(10.2140 - 46.5288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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