LMFDB - Embedded newform 684.3.t.a.265.6

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			265.6
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.79131 - 1.09935i) q^{3} +(-2.57011 + 4.45156i) q^{5} +(-2.98315 - 5.16697i) q^{7} +(6.58286 + 6.13726i) q^{9} +O(q^{10})$	\(q+(-2.79131 - 1.09935i) q^{3} +(-2.57011 + 4.45156i) q^{5} +(-2.98315 - 5.16697i) q^{7} +(6.58286 + 6.13726i) q^{9} +(-7.15457 - 12.3921i) q^{11} +(8.81864 + 5.09144i) q^{13} +(12.0678 - 9.60024i) q^{15} -26.3424 q^{17} +(-1.92919 - 18.9018i) q^{19} +(2.64660 + 17.7022i) q^{21} +(-8.50256 + 14.7269i) q^{23} +(-0.710906 - 1.23133i) q^{25} +(-11.6278 - 24.3679i) q^{27} +(12.2060 - 7.04711i) q^{29} +(17.1984 + 9.92949i) q^{31} +(6.34741 + 42.4555i) q^{33} +30.6681 q^{35} +36.4359i q^{37} +(-19.0183 - 23.9066i) q^{39} +(66.2561 + 38.2530i) q^{41} +(37.4659 + 64.8928i) q^{43} +(-44.2390 + 13.5305i) q^{45} +(-31.4415 - 54.4582i) q^{47} +(6.70163 - 11.6076i) q^{49} +(73.5298 + 28.9595i) q^{51} +17.6577i q^{53} +73.5520 q^{55} +(-15.3947 + 54.8817i) q^{57} +(2.23351 + 1.28951i) q^{59} +(-14.8177 - 25.6651i) q^{61} +(12.0734 - 52.3218i) q^{63} +(-45.3297 + 26.1711i) q^{65} +(110.097 + 63.5645i) q^{67} +(39.9233 - 31.7600i) q^{69} -73.7076i q^{71} +101.243 q^{73} +(0.630703 + 4.21855i) q^{75} +(-42.6863 + 73.9348i) q^{77} +(-105.608 + 60.9727i) q^{79} +(5.66803 + 80.8014i) q^{81} +(70.4744 + 122.065i) q^{83} +(67.7027 - 117.265i) q^{85} +(-41.8179 + 6.25207i) q^{87} -53.5229i q^{89} -60.7542i q^{91} +(-37.0901 - 46.6234i) q^{93} +(89.1007 + 39.9918i) q^{95} +(91.5247 - 52.8418i) q^{97} +(28.9559 - 125.485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.79131	−	1.09935i	−0.930438	−	0.366450i
$3$	−2.79131	−	1.09935i	−0.930438	−	0.366450i
$4$		0			0
$5$	−2.57011	+	4.45156i	−0.514022	+	0.890311i	0.485846	+	0.874044i	$0.338512\pi$
$5$	−2.57011	+	4.45156i	−0.514022	+	0.890311i	−0.999868	+	0.0162670i	$0.994822\pi$
$6$		0			0
$7$	−2.98315	−	5.16697i	−0.426164	−	0.738138i	0.570364	−	0.821392i	$-0.306802\pi$
$7$	−2.98315	−	5.16697i	−0.426164	−	0.738138i	−0.996528	+	0.0832537i	$0.973469\pi$
$8$		0			0
$9$	6.58286	+	6.13726i	0.731429	+	0.681918i
$10$		0			0
$11$	−7.15457	−	12.3921i	−0.650415	−	1.12655i	−0.983022	−	0.183487i	$-0.941262\pi$
$11$	−7.15457	−	12.3921i	−0.650415	−	1.12655i	0.332607	−	0.943066i	$-0.392072\pi$
$12$		0			0
$13$	8.81864	+	5.09144i	0.678357	+	0.391650i	0.799236	−	0.601018i	$-0.205238\pi$
$13$	8.81864	+	5.09144i	0.678357	+	0.391650i	−0.120879	+	0.992667i	$0.538571\pi$
$14$		0			0
$15$	12.0678	−	9.60024i	0.804520	−	0.640016i
$16$		0			0
$17$	−26.3424			−1.54955			−0.774775	−	0.632236i	$-0.782137\pi$
$17$	−26.3424			−1.54955			−0.774775	+	0.632236i	$0.782137\pi$
$18$		0			0
$19$	−1.92919	−	18.9018i	−0.101536	−	0.994832i
$19$	−1.92919	−	18.9018i	−0.101536	−	0.994832i
$20$		0			0
$21$	2.64660	+	17.7022i	0.126029	+	0.842960i
$22$		0			0
$23$	−8.50256	+	14.7269i	−0.369676	+	0.640298i	−0.989515	−	0.144431i	$-0.953865\pi$
$23$	−8.50256	+	14.7269i	−0.369676	+	0.640298i	0.619838	+	0.784729i	$0.287198\pi$
$24$		0			0
$25$	−0.710906	−	1.23133i	−0.0284362	−	0.0492530i
$26$		0			0
$27$	−11.6278	−	24.3679i	−0.430660	−	0.902514i
$28$		0			0
$29$	12.2060	−	7.04711i	0.420895	−	0.243004i	−0.274565	−	0.961568i	$-0.588534\pi$
$29$	12.2060	−	7.04711i	0.420895	−	0.243004i	0.695460	+	0.718565i	$0.255201\pi$
$30$		0			0
$31$	17.1984	+	9.92949i	0.554787	+	0.320306i	0.751050	−	0.660245i	$-0.229548\pi$
$31$	17.1984	+	9.92949i	0.554787	+	0.320306i	−0.196264	+	0.980551i	$0.562881\pi$
$32$		0			0
$33$	6.34741	+	42.4555i	0.192346	+	1.28653i
$34$		0			0
$35$	30.6681			0.876231
$36$		0			0
$37$			36.4359i			0.984754i	0.870382	+	0.492377i	$0.163872\pi$
$37$			36.4359i			0.984754i	−0.870382	+	0.492377i	$0.836128\pi$
$38$		0			0
$39$	−19.0183	−	23.9066i	−0.487649	−	0.612989i
$40$		0			0
$41$	66.2561	+	38.2530i	1.61600	+	0.932999i	0.987940	+	0.154835i	$0.0494847\pi$
$41$	66.2561	+	38.2530i	1.61600	+	0.932999i	0.628062	+	0.778164i	$0.283849\pi$
$42$		0			0
$43$	37.4659	+	64.8928i	0.871299	+	1.50913i	0.860654	+	0.509191i	$0.170055\pi$
$43$	37.4659	+	64.8928i	0.871299	+	1.50913i	0.0106453	+	0.999943i	$0.496611\pi$
$44$		0			0
$45$	−44.2390	+	13.5305i	−0.983089	+	0.300679i
$46$		0			0
$47$	−31.4415	−	54.4582i	−0.668967	−	1.15869i	−0.978193	−	0.207697i	$-0.933403\pi$
$47$	−31.4415	−	54.4582i	−0.668967	−	1.15869i	0.309226	−	0.950989i	$-0.399930\pi$
$48$		0			0
$49$	6.70163	−	11.6076i	0.136768	−	0.236889i
$50$		0			0
$51$	73.5298	+	28.9595i	1.44176	+	0.567833i
$52$		0			0
$53$			17.6577i			0.333164i	0.986028	+	0.166582i	$0.0532731\pi$
$53$			17.6577i			0.333164i	−0.986028	+	0.166582i	$0.946727\pi$
$54$		0			0
$55$	73.5520			1.33731
$56$		0			0
$57$	−15.3947	+	54.8817i	−0.270083	+	0.962837i
$58$		0			0
$59$	2.23351	+	1.28951i	0.0378560	+	0.0218562i	0.518809	−	0.854890i	$-0.326376\pi$
$59$	2.23351	+	1.28951i	0.0378560	+	0.0218562i	−0.480953	+	0.876747i	$0.659709\pi$
$60$		0			0
$61$	−14.8177	−	25.6651i	−0.242914	−	0.420739i	0.718629	−	0.695393i	$-0.244770\pi$
$61$	−14.8177	−	25.6651i	−0.242914	−	0.420739i	−0.961543	+	0.274655i	$0.911437\pi$
$62$		0			0
$63$	12.0734	−	52.3218i	0.191641	−	0.830505i
$64$		0			0
$65$	−45.3297	+	26.1711i	−0.697380	+	0.402633i
$66$		0			0
$67$	110.097	+	63.5645i	1.64324	+	0.948724i	0.979672	+	0.200606i	$0.0642910\pi$
$67$	110.097	+	63.5645i	1.64324	+	0.948724i	0.663566	+	0.748118i	$0.269042\pi$
$68$		0			0
$69$	39.9233	−	31.7600i	0.578598	−	0.460290i
$70$		0			0
$71$		−	73.7076i		−	1.03814i	−0.854733	−	0.519068i	$-0.826279\pi$
$71$		−	73.7076i		−	1.03814i	0.854733	−	0.519068i	$-0.173721\pi$
$72$		0			0
$73$	101.243			1.38689			0.693445	−	0.720510i	$-0.256092\pi$
$73$	101.243			1.38689			0.693445	+	0.720510i	$0.256092\pi$
$74$		0			0
$75$	0.630703	+	4.21855i	0.00840938	+	0.0562473i
$76$		0			0
$77$	−42.6863	+	73.9348i	−0.554368	+	0.960193i
$78$		0			0
$79$	−105.608	+	60.9727i	−1.33681	+	0.771806i	−0.986333	−	0.164766i	$-0.947313\pi$
$79$	−105.608	+	60.9727i	−1.33681	+	0.771806i	−0.350475	+	0.936572i	$0.613980\pi$
$80$		0			0
$81$	5.66803	+	80.8014i	0.0699756	+	0.997549i
$82$		0			0
$83$	70.4744	+	122.065i	0.849089	+	1.47066i	0.882023	+	0.471207i	$0.156182\pi$
$83$	70.4744	+	122.065i	0.849089	+	1.47066i	−0.0329338	+	0.999458i	$0.510485\pi$
$84$		0			0
$85$	67.7027	−	117.265i	0.796503	−	1.37958i
$86$		0			0
$87$	−41.8179	+	6.25207i	−0.480665	+	0.0718629i
$88$		0			0
$89$		−	53.5229i		−	0.601381i	−0.953722	−	0.300690i	$-0.902783\pi$
$89$		−	53.5229i		−	0.601381i	0.953722	−	0.300690i	$-0.0972171\pi$
$90$		0			0
$91$		−	60.7542i		−	0.667628i
$92$		0			0
$93$	−37.0901	−	46.6234i	−0.398818	−	0.501327i
$94$		0			0
$95$	89.1007	+	39.9918i	0.937902	+	0.420966i
$96$		0			0
$97$	91.5247	−	52.8418i	0.943554	−	0.544761i	0.0524813	−	0.998622i	$-0.483287\pi$
$97$	91.5247	−	52.8418i	0.943554	−	0.544761i	0.891073	+	0.453861i	$0.149954\pi$
$98$		0			0
$99$	28.9559	−	125.485i	0.292484	−	1.26752i
$100$		0			0
$101$	54.3167	+	94.0792i	0.537789	+	0.931477i	0.999023	+	0.0441989i	$0.0140735\pi$
$101$	54.3167	+	94.0792i	0.537789	+	0.931477i	−0.461234	+	0.887279i	$0.652593\pi$
$102$		0			0
$103$	72.3244	+	41.7565i	0.702179	+	0.405403i	0.808159	−	0.588965i	$-0.200464\pi$
$103$	72.3244	+	41.7565i	0.702179	+	0.405403i	−0.105979	+	0.994368i	$0.533798\pi$
$104$		0			0
$105$	−85.6042	−	33.7150i	−0.815278	−	0.321095i
$106$		0			0
$107$			135.899i			1.27008i	0.772477	+	0.635042i	$0.219017\pi$
$107$			135.899i			1.27008i	−0.772477	+	0.635042i	$0.780983\pi$
$108$		0			0
$109$		−	70.8398i		−	0.649907i	−0.945730	−	0.324953i	$-0.894651\pi$
$109$		−	70.8398i		−	0.649907i	0.945730	−	0.324953i	$-0.105349\pi$
$110$		0			0
$111$	40.0558	−	101.704i	0.360863	−	0.916253i
$112$		0			0
$113$	−25.2841	−	14.5978i	−0.223753	−	0.129184i	0.383934	−	0.923361i	$-0.374569\pi$
$113$	−25.2841	−	14.5978i	−0.223753	−	0.129184i	−0.607687	+	0.794177i	$0.707902\pi$
$114$		0			0
$115$	−43.7050	−	75.6993i	−0.380043	−	0.658254i
$116$		0			0
$117$	26.8043	+	87.6386i	0.229097	+	0.749047i
$118$		0			0
$119$	78.5832	+	136.110i	0.660363	+	1.14378i
$120$		0			0
$121$	−41.8757	+	72.5308i	−0.346080	+	0.599428i
$122$		0			0
$123$	−142.888	−	179.615i	−1.16169	−	1.46028i
$124$		0			0
$125$	−121.197			−0.969576
$126$		0			0
$127$		−	127.478i		−	1.00377i	−0.864935	−	0.501884i	$-0.832641\pi$
$127$		−	127.478i		−	1.00377i	0.864935	−	0.501884i	$-0.167359\pi$
$128$		0			0
$129$	−33.2390	−	222.324i	−0.257667	−	1.72344i
$130$		0			0
$131$	−73.8810	+	127.966i	−0.563977	+	0.976837i	0.433167	+	0.901314i	$0.357396\pi$
$131$	−73.8810	+	127.966i	−0.563977	+	0.976837i	−0.997144	+	0.0755233i	$0.975937\pi$
$132$		0			0
$133$	−91.9100	+	66.3550i	−0.691052	+	0.498910i
$134$		0			0
$135$	138.360	+	10.8662i	1.02489	+	0.0804904i
$136$		0			0
$137$	28.6428	+	49.6108i	0.209071	+	0.362122i	0.951422	−	0.307889i	$-0.0996225\pi$
$137$	28.6428	+	49.6108i	0.209071	+	0.362122i	−0.742351	+	0.670011i	$0.766289\pi$
$138$		0			0
$139$	−41.6345	+	72.1131i	−0.299529	+	0.518799i	−0.976028	−	0.217644i	$-0.930163\pi$
$139$	−41.6345	+	72.1131i	−0.299529	+	0.518799i	0.676499	+	0.736443i	$0.263496\pi$
$140$		0			0
$141$	27.8943	+	186.575i	0.197832	+	1.32323i
$142$		0			0
$143$		−	145.708i		−	1.01894i
$144$		0			0
$145$			72.4473i			0.499637i
$146$		0			0
$147$	−31.4671	+	25.0329i	−0.214062	+	0.170292i
$148$		0			0
$149$	−105.987	+	183.575i	−0.711321	+	1.23204i	0.253040	+	0.967456i	$0.418569\pi$
$149$	−105.987	+	183.575i	−0.711321	+	1.23204i	−0.964361	+	0.264589i	$0.914764\pi$
$150$		0			0
$151$	−9.61410	+	5.55070i	−0.0636695	+	0.0367596i	−0.531497	−	0.847060i	$-0.678370\pi$
$151$	−9.61410	+	5.55070i	−0.0636695	+	0.0367596i	0.467827	+	0.883820i	$0.345037\pi$
$152$		0			0
$153$	−173.408	−	161.670i	−1.13339	−	1.05667i
$154$		0			0
$155$	−88.4034	+	51.0397i	−0.570344	+	0.329289i
$156$		0			0
$157$	113.617	−	196.790i	0.723673	−	1.25344i	−0.235844	−	0.971791i	$-0.575786\pi$
$157$	113.617	−	196.790i	0.723673	−	1.25344i	0.959518	−	0.281648i	$-0.0908812\pi$
$158$		0			0
$159$	19.4120	−	49.2882i	0.122088	−	0.309989i
$160$		0			0
$161$	101.458			0.630172
$162$		0			0
$163$	−59.5674			−0.365444			−0.182722	−	0.983165i	$-0.558491\pi$
$163$	−59.5674			−0.365444			−0.182722	+	0.983165i	$0.558491\pi$
$164$		0			0
$165$	−205.307	−	80.8594i	−1.24428	−	0.490057i
$166$		0			0
$167$	166.189	+	95.9494i	0.995145	+	0.574547i	0.906808	−	0.421543i	$-0.138511\pi$
$167$	166.189	+	95.9494i	0.995145	+	0.574547i	0.0883368	+	0.996091i	$0.471845\pi$
$168$		0			0
$169$	−32.6544	−	56.5591i	−0.193221	−	0.334669i
$170$		0			0
$171$	103.306	−	136.268i	0.604127	−	0.796888i
$172$		0			0
$173$	−193.610	+	111.781i	−1.11913	+	0.646131i	−0.941179	−	0.337909i	$-0.890281\pi$
$173$	−193.610	+	111.781i	−1.11913	+	0.646131i	−0.177952	+	0.984039i	$0.556947\pi$
$174$		0			0
$175$	−4.24148	+	7.34646i	−0.0242370	+	0.0419798i
$176$		0			0
$177$	−4.81678	−	6.05484i	−0.0272135	−	0.0342082i
$178$		0			0
$179$		−	253.993i		−	1.41896i	−0.704727	−	0.709479i	$-0.748931\pi$
$179$		−	253.993i		−	1.41896i	0.704727	−	0.709479i	$-0.251069\pi$
$180$		0			0
$181$			253.229i			1.39906i	0.714605	+	0.699528i	$0.246606\pi$
$181$			253.229i			1.39906i	−0.714605	+	0.699528i	$0.753394\pi$
$182$		0			0
$183$	13.1460	+	87.9291i	0.0718362	+	0.480487i
$184$		0			0
$185$	−162.197	−	93.6442i	−0.876738	−	0.506185i
$186$		0			0
$187$	188.468	+	326.437i	1.00785	+	1.74565i
$188$		0			0
$189$	−91.2206	+	132.774i	−0.482649	+	0.702506i
$190$		0			0
$191$	−96.3055	−	166.806i	−0.504217	−	0.873330i	−0.999988	−	0.00487650i	$-0.998448\pi$
$191$	−96.3055	−	166.806i	−0.504217	−	0.873330i	0.495771	−	0.868453i	$-0.334886\pi$
$192$		0			0
$193$	−153.709	−	88.7436i	−0.796417	−	0.459812i	0.0457997	−	0.998951i	$-0.485416\pi$
$193$	−153.709	−	88.7436i	−0.796417	−	0.459812i	−0.842217	+	0.539139i	$0.818750\pi$
$194$		0			0
$195$	155.301	−	23.2186i	0.796413	−	0.119070i
$196$		0			0
$197$	−96.0997			−0.487816			−0.243908	−	0.969798i	$-0.578429\pi$
$197$	−96.0997			−0.487816			−0.243908	+	0.969798i	$0.578429\pi$
$198$		0			0
$199$	200.310			1.00658			0.503292	−	0.864116i	$-0.332122\pi$
$199$	200.310			1.00658			0.503292	+	0.864116i	$0.332122\pi$
$200$		0			0
$201$	−237.435	−	298.463i	−1.18127	−	1.48489i
$202$		0			0
$203$	−72.8244	−	42.0452i	−0.358741	−	0.207119i
$204$		0			0
$205$	−340.570	+	196.628i	−1.66132	+	0.959163i
$206$		0			0
$207$	−146.354	+	44.7624i	−0.707023	+	0.216244i
$208$		0			0
$209$	−220.430	+	159.141i	−1.05469	+	0.761440i
$210$		0			0
$211$	−262.107	−	151.328i	−1.24221	−	0.717193i	−0.272670	−	0.962108i	$-0.587907\pi$
$211$	−262.107	−	151.328i	−1.24221	−	0.717193i	−0.969545	+	0.244915i	$0.921240\pi$
$212$		0			0
$213$	−81.0305	+	205.741i	−0.380425	+	0.965920i
$214$		0			0
$215$	−385.165			−1.79147
$216$		0			0
$217$		−	118.485i		−	0.546012i
$218$		0			0
$219$	−282.601	−	111.301i	−1.29041	−	0.508226i
$220$		0			0
$221$	−232.304	−	134.121i	−1.05115	−	0.606881i
$222$		0			0
$223$	289.182	−	166.959i	1.29678	−	0.748697i	0.316934	−	0.948448i	$-0.397347\pi$
$223$	289.182	−	166.959i	1.29678	−	0.748697i	0.979847	+	0.199751i	$0.0640132\pi$
$224$		0			0
$225$	2.87717	−	12.4687i	0.0127874	−	0.0554162i
$226$		0			0
$227$	249.817	−	144.232i	1.10051	−	0.635382i	0.164158	−	0.986434i	$-0.447509\pi$
$227$	249.817	−	144.232i	1.10051	−	0.635382i	0.936356	+	0.351052i	$0.114176\pi$
$228$		0			0
$229$	74.4581	−	128.965i	0.325144	−	0.563167i	−0.656397	−	0.754416i	$-0.727920\pi$
$229$	74.4581	−	128.965i	0.325144	−	0.563167i	0.981542	+	0.191249i	$0.0612538\pi$
$230$		0			0
$231$	200.431	−	159.448i	0.867667	−	0.690251i
$232$		0			0
$233$	181.587			0.779343			0.389671	−	0.920954i	$-0.372589\pi$
$233$	181.587			0.779343			0.389671	+	0.920954i	$0.372589\pi$
$234$		0			0
$235$	323.232			1.37545
$236$		0			0
$237$	361.815	−	54.0939i	1.52664	−	0.228244i
$238$		0			0
$239$	−67.7920	+	117.419i	−0.283649	+	0.491294i	−0.972281	−	0.233817i	$-0.924878\pi$
$239$	−67.7920	+	117.419i	−0.283649	+	0.491294i	0.688632	+	0.725111i	$0.258212\pi$
$240$		0			0
$241$	123.555	−	71.3346i	0.512677	−	0.295994i	−0.221256	−	0.975216i	$-0.571016\pi$
$241$	123.555	−	71.3346i	0.512677	−	0.295994i	0.733933	+	0.679221i	$0.237682\pi$
$242$		0			0
$243$	73.0079	−	231.773i	0.300444	−	0.953799i
$244$		0			0
$245$	34.4478	+	59.6654i	0.140603	+	0.243532i
$246$		0			0
$247$	79.2246	−	176.511i	0.320748	−	0.714618i
$248$		0			0
$249$	−62.5236	−	418.198i	−0.251099	−	1.67951i
$250$		0			0
$251$	144.400			0.575300			0.287650	−	0.957736i	$-0.407126\pi$
$251$	144.400			0.575300			0.287650	+	0.957736i	$0.407126\pi$
$252$		0			0
$253$	243.329			0.961773
$254$		0			0
$255$	−317.894	+	252.893i	−1.24664	+	0.991737i
$256$		0			0
$257$	89.6672	+	51.7694i	0.348900	+	0.201437i	0.664200	−	0.747554i	$-0.268772\pi$
$257$	89.6672	+	51.7694i	0.348900	+	0.201437i	−0.315301	+	0.948992i	$0.602105\pi$
$258$		0			0
$259$	188.263	−	108.694i	0.726885	−	0.419667i
$260$		0			0
$261$	123.600	+	28.5210i	0.473563	+	0.109276i
$262$		0			0
$263$	−14.8357	−	25.6962i	−0.0564096	−	0.0977043i	0.836442	−	0.548056i	$-0.184632\pi$
$263$	−14.8357	−	25.6962i	−0.0564096	−	0.0977043i	−0.892851	+	0.450352i	$0.851299\pi$
$264$		0			0
$265$	−78.6043	−	45.3822i	−0.296620	−	0.171254i
$266$		0			0
$267$	−58.8404	+	149.399i	−0.220376	+	0.559548i
$268$		0			0
$269$			159.003i			0.591088i	0.955329	+	0.295544i	$0.0955009\pi$
$269$			159.003i			0.591088i	−0.955329	+	0.295544i	$0.904499\pi$
$270$		0			0
$271$	94.5272			0.348809			0.174404	−	0.984674i	$-0.444200\pi$
$271$	94.5272			0.348809			0.174404	+	0.984674i	$0.444200\pi$
$272$		0			0
$273$	−66.7901	+	169.584i	−0.244652	+	0.621186i
$274$		0			0
$275$	−10.1724	+	17.6192i	−0.0369907	+	0.0640698i
$276$		0			0
$277$	76.2963	+	132.149i	0.275438	+	0.477072i	0.970245	−	0.242123i	$-0.0778438\pi$
$277$	76.2963	+	132.149i	0.275438	+	0.477072i	−0.694808	+	0.719196i	$0.744511\pi$
$278$		0			0
$279$	52.2746	+	170.915i	0.187364	+	0.612600i
$280$		0			0
$281$	397.350	−	229.410i	1.41406	−	0.816406i	0.418289	−	0.908314i	$-0.362630\pi$
$281$	397.350	−	229.410i	1.41406	−	0.816406i	0.995767	+	0.0919084i	$0.0292967\pi$
$282$		0			0
$283$	−128.040	+	221.772i	−0.452439	+	0.783647i	−0.998537	−	0.0540745i	$-0.982779\pi$
$283$	−128.040	+	221.772i	−0.452439	+	0.783647i	0.546098	+	0.837721i	$0.316112\pi$
$284$		0			0
$285$	−204.743	−	209.582i	−0.718396	−	0.735377i
$286$		0			0
$287$		−	456.457i		−	1.59044i
$288$		0			0
$289$	404.920			1.40111
$290$		0			0
$291$	−313.566	+	46.8803i	−1.07755	+	0.161101i
$292$		0			0
$293$	162.675	+	93.9204i	0.555204	+	0.320547i	0.751218	−	0.660054i	$-0.229466\pi$
$293$	162.675	+	93.9204i	0.555204	+	0.320547i	−0.196014	+	0.980601i	$0.562800\pi$
$294$		0			0
$295$	−11.4807	+	6.62838i	−0.0389176	+	0.0224691i
$296$		0			0
$297$	−218.777	+	318.434i	−0.736622	+	1.07217i
$298$		0			0
$299$	−149.962	+	86.5806i	−0.501545	+	0.289567i
$300$		0			0
$301$	223.533	−	387.170i	0.742633	−	1.28628i
$302$		0			0
$303$	−48.1888	−	322.318i	−0.159039	−	1.06375i
$304$		0			0
$305$	152.333			0.499451
$306$		0			0
$307$			173.787i			0.566082i	0.959108	+	0.283041i	$0.0913432\pi$
$307$			173.787i			0.566082i	−0.959108	+	0.283041i	$0.908657\pi$
$308$		0			0
$309$	−155.975	−	196.065i	−0.504774	−	0.634516i
$310$		0			0
$311$	−15.9734	+	27.6668i	−0.0513615	+	0.0889608i	−0.890563	−	0.454860i	$-0.849689\pi$
$311$	−15.9734	+	27.6668i	−0.0513615	+	0.0889608i	0.839202	+	0.543820i	$0.183023\pi$
$312$		0			0
$313$	−11.7047	−	20.2731i	−0.0373952	−	0.0647704i	0.846722	−	0.532035i	$-0.178573\pi$
$313$	−11.7047	−	20.2731i	−0.0373952	−	0.0647704i	−0.884117	+	0.467265i	$0.845239\pi$
$314$		0			0
$315$	201.884	+	188.218i	0.640900	+	0.597517i
$316$		0			0
$317$	−463.269	+	267.468i	−1.46142	+	0.843749i	−0.999077	−	0.0429549i	$-0.986323\pi$
$317$	−463.269	+	267.468i	−1.46142	+	0.843749i	−0.462338	+	0.886704i	$0.652989\pi$
$318$		0			0
$319$	−174.657	−	100.838i	−0.547513	−	0.316107i
$320$		0			0
$321$	149.401	−	379.337i	0.465423	−	1.18173i
$322$		0			0
$323$	50.8195	+	497.918i	0.157336	+	1.54154i
$324$		0			0
$325$		−	14.4782i		−	0.0445482i
$326$		0			0
$327$	−77.8778	+	197.736i	−0.238158	+	0.604698i
$328$		0			0
$329$	−187.589	+	324.914i	−0.570180	+	0.987581i
$330$		0			0
$331$	−210.125	+	121.316i	−0.634820	+	0.366513i	−0.782616	−	0.622504i	$-0.786115\pi$
$331$	−210.125	+	121.316i	−0.634820	+	0.366513i	0.147796	+	0.989018i	$0.452782\pi$
$332$		0			0
$333$	−223.617	+	239.852i	−0.671522	+	0.720278i
$334$		0			0
$335$	−565.922	+	326.735i	−1.68932	+	0.975329i
$336$		0			0
$337$	−238.386	−	137.632i	−0.707376	−	0.408404i	0.102713	−	0.994711i	$-0.467248\pi$
$337$	−238.386	−	137.632i	−0.707376	−	0.408404i	−0.810089	+	0.586307i	$0.800581\pi$
$338$		0			0
$339$	54.5278	+	68.5431i	0.160849	+	0.202192i
$340$		0			0
$341$		−	284.165i		−	0.833328i
$342$		0			0
$343$	−372.317			−1.08547
$344$		0			0
$345$	38.7743	+	259.347i	0.112389	+	0.751732i
$346$		0			0
$347$	225.264	−	390.168i	0.649175	−	1.12440i	−0.334145	−	0.942522i	$-0.608448\pi$
$347$	225.264	−	390.168i	0.649175	−	1.12440i	0.983320	−	0.181883i	$-0.0582191\pi$
$348$		0			0
$349$	−180.761	−	313.087i	−0.517939	−	0.897097i	−0.999783	−	0.0208397i	$-0.993366\pi$
$349$	−180.761	−	313.087i	−0.517939	−	0.897097i	0.481844	−	0.876257i	$-0.339967\pi$
$350$		0			0
$351$	21.5262	−	274.094i	0.0613283	−	0.780895i
$352$		0			0
$353$	89.1376	+	154.391i	0.252514	+	0.437368i	0.964217	−	0.265113i	$-0.0854091\pi$
$353$	89.1376	+	154.391i	0.252514	+	0.437368i	−0.711703	+	0.702481i	$0.752076\pi$
$354$		0			0
$355$	328.114	+	189.436i	0.924264	+	0.533624i
$356$		0			0
$357$	−69.7177	−	466.317i	−0.195288	−	1.30621i
$358$		0			0
$359$	−413.024			−1.15049			−0.575243	−	0.817983i	$-0.695092\pi$
$359$	−413.024			−1.15049			−0.575243	+	0.817983i	$0.695092\pi$
$360$		0			0
$361$	−353.556	+	72.9304i	−0.979381	+	0.202023i
$362$		0			0
$363$	196.625	−	156.420i	0.541666	−	0.430909i
$364$		0			0
$365$	−260.205	+	450.689i	−0.712891	+	1.23476i
$366$		0			0
$367$	88.1093	+	152.610i	0.240080	+	0.415830i	0.960737	−	0.277461i	$-0.0894931\pi$
$367$	88.1093	+	152.610i	0.240080	+	0.415830i	−0.720657	+	0.693292i	$0.756160\pi$
$368$		0			0
$369$	201.386	+	658.445i	0.545761	+	1.78440i
$370$		0			0
$371$	91.2368	−	52.6756i	0.245921	−	0.141983i
$372$		0			0
$373$	500.854	+	289.168i	1.34277	+	0.775250i	0.987213	−	0.159404i	$-0.0509572\pi$
$373$	500.854	+	289.168i	1.34277	+	0.775250i	0.355559	+	0.934654i	$0.384291\pi$
$374$		0			0
$375$	338.299	+	133.238i	0.902130	+	0.355301i
$376$		0			0
$377$	143.520			0.380689
$378$		0			0
$379$			364.316i			0.961256i	0.876924	+	0.480628i	$0.159591\pi$
$379$			364.316i			0.961256i	−0.876924	+	0.480628i	$0.840409\pi$
$380$		0			0
$381$	−140.143	+	355.832i	−0.367831	+	0.933943i
$382$		0			0
$383$	425.732	+	245.796i	1.11157	+	0.641766i	0.939236	−	0.343272i	$-0.111535\pi$
$383$	425.732	+	245.796i	1.11157	+	0.641766i	0.172336	+	0.985038i	$0.444869\pi$
$384$		0			0
$385$	−219.417	−	380.041i	−0.569914	−	0.987119i
$386$		0			0
$387$	−151.632	+	657.118i	−0.391813	+	1.69798i
$388$		0			0
$389$	66.0717	+	114.439i	0.169850	+	0.294189i	0.938367	−	0.345641i	$-0.112338\pi$
$389$	66.0717	+	114.439i	0.169850	+	0.294189i	−0.768517	+	0.639829i	$0.779005\pi$
$390$		0			0
$391$	223.978	−	387.940i	0.572833	−	0.992175i
$392$		0			0
$393$	346.904	−	275.971i	0.882708	−	0.702216i
$394$		0			0
$395$		−	626.826i		−	1.58690i
$396$		0			0
$397$	192.776			0.485583			0.242791	−	0.970079i	$-0.421937\pi$
$397$	192.776			0.485583			0.242791	+	0.970079i	$0.421937\pi$
$398$		0			0
$399$	329.497	−	84.1763i	0.825807	−	0.210968i
$400$		0			0
$401$	230.140	+	132.871i	0.573916	+	0.331350i	0.758712	−	0.651427i	$-0.225829\pi$
$401$	230.140	+	132.871i	0.573916	+	0.331350i	−0.184796	+	0.982777i	$0.559162\pi$
$402$		0			0
$403$	101.111	+	175.129i	0.250896	+	0.434564i
$404$		0			0
$405$	−374.260	−	182.437i	−0.924098	−	0.450461i
$406$		0			0
$407$	451.517	−	260.683i	1.10938	−	0.640499i
$408$		0			0
$409$	104.118	+	60.1127i	0.254568	+	0.146975i	0.621854	−	0.783133i	$-0.286380\pi$
$409$	104.118	+	60.1127i	0.254568	+	0.146975i	−0.367286	+	0.930108i	$0.619713\pi$
$410$		0			0
$411$	−25.4114	−	169.968i	−0.0618282	−	0.413547i
$412$		0			0
$413$		−	15.3873i		−	0.0372573i
$414$		0			0
$415$	−724.507			−1.74580
$416$		0			0
$417$	195.492	−	155.519i	0.468807	−	0.372948i
$418$		0			0
$419$	−73.0611	+	126.546i	−0.174370	+	0.302018i	−0.939943	−	0.341331i	$-0.889122\pi$
$419$	−73.0611	+	126.546i	−0.174370	+	0.302018i	0.765573	+	0.643349i	$0.222456\pi$
$420$		0			0
$421$	−112.380	+	64.8826i	−0.266936	+	0.154115i	−0.627494	−	0.778621i	$-0.715919\pi$
$421$	−112.380	+	64.8826i	−0.266936	+	0.154115i	0.360559	+	0.932737i	$0.382586\pi$
$422$		0			0
$423$	127.250	−	551.455i	0.300827	−	1.30368i
$424$		0			0
$425$	18.7269	+	32.4360i	0.0440634	+	0.0763200i
$426$		0			0
$427$	−88.4071	+	153.126i	−0.207042	+	0.358608i
$428$		0			0
$429$	−160.184	+	406.717i	−0.373390	+	0.948059i
$430$		0			0
$431$		−	13.7811i		−	0.0319747i	−0.999872	−	0.0159874i	$-0.994911\pi$
$431$		−	13.7811i		−	0.0319747i	0.999872	−	0.0159874i	$-0.00508915\pi$
$432$		0			0
$433$			148.036i			0.341884i	0.985281	+	0.170942i	$0.0546810\pi$
$433$			148.036i			0.341884i	−0.985281	+	0.170942i	$0.945319\pi$
$434$		0			0
$435$	79.6450	−	202.223i	0.183092	−	0.464881i
$436$		0			0
$437$	294.767	+	132.303i	0.674525	+	0.302752i
$438$		0			0
$439$	457.069	−	263.889i	1.04116	−	0.601114i	0.120998	−	0.992653i	$-0.461390\pi$
$439$	457.069	−	263.889i	1.04116	−	0.601114i	0.920162	+	0.391539i	$0.128057\pi$
$440$		0			0
$441$	115.354	−	35.2813i	0.261575	−	0.0800029i
$442$		0			0
$443$	−198.683	−	344.129i	−0.448495	−	0.776815i	0.549794	−	0.835300i	$-0.314706\pi$
$443$	−198.683	−	344.129i	−0.448495	−	0.776815i	−0.998288	+	0.0584852i	$0.981373\pi$
$444$		0			0
$445$	238.260	+	137.560i	0.535416	+	0.309123i
$446$		0			0
$447$	497.655	−	395.898i	1.11332	−	0.885677i
$448$		0			0
$449$		−	423.027i		−	0.942155i	−0.882092	−	0.471077i	$-0.843865\pi$
$449$		−	423.027i		−	0.942155i	0.882092	−	0.471077i	$-0.156135\pi$
$450$		0			0
$451$		−	1094.73i		−	2.42735i
$452$		0			0
$453$	32.9381	−	4.92449i	0.0727111	−	0.0108708i
$454$		0			0
$455$	270.451	+	156.145i	0.594397	+	0.343175i
$456$		0			0
$457$	179.595	+	311.067i	0.392986	+	0.680671i	0.992842	−	0.119437i	$-0.0381088\pi$
$457$	179.595	+	311.067i	0.392986	+	0.680671i	−0.599856	+	0.800108i	$0.704775\pi$
$458$		0			0
$459$	306.304	+	641.908i	0.667329	+	1.39849i
$460$		0			0
$461$	−176.128	−	305.062i	−0.382056	−	0.661740i	0.609300	−	0.792939i	$-0.291450\pi$
$461$	−176.128	−	305.062i	−0.382056	−	0.661740i	−0.991356	+	0.131200i	$0.958117\pi$
$462$		0			0
$463$	−438.766	+	759.965i	−0.947659	+	1.64139i	−0.197321	+	0.980339i	$0.563224\pi$
$463$	−438.766	+	759.965i	−0.947659	+	1.64139i	−0.750338	+	0.661054i	$0.770109\pi$
$464$		0			0
$465$	302.872	−	45.2815i	0.651338	−	0.0973797i
$466$		0			0
$467$	103.913			0.222513			0.111256	−	0.993792i	$-0.464513\pi$
$467$	103.913			0.222513			0.111256	+	0.993792i	$0.464513\pi$
$468$		0			0
$469$		−	758.490i		−	1.61725i
$470$		0			0
$471$	−533.481	+	424.398i	−1.13266	+	0.901057i
$472$		0			0
$473$	536.104	−	928.559i	1.13341	−	1.96313i
$474$		0			0
$475$	−21.9028	+	15.8129i	−0.0461111	+	0.0332902i
$476$		0			0
$477$	−108.370	+	116.238i	−0.227191	+	0.243686i
$478$		0			0
$479$	−50.6850	−	87.7889i	−0.105814	−	0.183275i	0.808256	−	0.588831i	$-0.200412\pi$
$479$	−50.6850	−	87.7889i	−0.105814	−	0.183275i	−0.914071	+	0.405555i	$0.867078\pi$
$480$		0			0
$481$	−185.511	+	321.315i	−0.385679	+	0.668015i
$482$		0			0
$483$	−283.200	−	111.538i	−0.586336	−	0.230927i
$484$		0			0
$485$			543.237i			1.12008i
$486$		0			0
$487$			606.006i			1.24436i	0.782872	+	0.622182i	$0.213754\pi$
$487$			606.006i			1.24436i	−0.782872	+	0.622182i	$0.786246\pi$
$488$		0			0
$489$	166.271	+	65.4855i	0.340023	+	0.133917i
$490$		0			0
$491$	118.627	−	205.469i	0.241604	−	0.418470i	−0.719568	−	0.694422i	$-0.755660\pi$
$491$	118.627	−	205.469i	0.241604	−	0.418470i	0.961171	+	0.275953i	$0.0889933\pi$
$492$		0			0
$493$	−321.534	+	185.638i	−0.652198	+	0.376547i
$494$		0			0
$495$	484.183	+	451.408i	0.978146	+	0.911935i
$496$		0			0
$497$	−380.845	+	219.881i	−0.766287	+	0.442416i
$498$		0			0
$499$	−58.8149	+	101.870i	−0.117866	+	0.204149i	−0.918922	−	0.394440i	$-0.870939\pi$
$499$	−58.8149	+	101.870i	−0.117866	+	0.204149i	0.801056	+	0.598589i	$0.204272\pi$
$500$		0			0
$501$	−358.404	−	450.525i	−0.715378	−	0.899251i
$502$		0			0
$503$	455.794			0.906151			0.453075	−	0.891472i	$-0.350327\pi$
$503$	455.794			0.906151			0.453075	+	0.891472i	$0.350327\pi$
$504$		0			0
$505$	−558.399			−1.10574
$506$		0			0
$507$	28.9704	+	193.773i	0.0571408	+	0.382195i
$508$		0			0
$509$	746.482	+	430.982i	1.46657	+	0.846722i	0.999301	−	0.0373950i	$-0.0119060\pi$
$509$	746.482	+	430.982i	1.46657	+	0.846722i	0.467265	+	0.884117i	$0.345239\pi$
$510$		0			0
$511$	−302.023	−	523.119i	−0.591043	−	1.02372i
$512$		0			0
$513$	−438.165	+	266.797i	−0.854122	+	0.520072i
$514$		0			0
$515$	−371.763	+	214.638i	−0.721870	+	0.416772i
$516$		0			0
$517$	−449.900	+	779.250i	−0.870213	+	1.50725i
$518$		0			0
$519$	663.311	−	99.1698i	1.27806	−	0.191079i
$520$		0			0
$521$		−	216.732i		−	0.415991i	−0.978130	−	0.207996i	$-0.933306\pi$
$521$		−	216.732i		−	0.415991i	0.978130	−	0.207996i	$-0.0666940\pi$
$522$		0			0
$523$			770.874i			1.47395i	0.675922	+	0.736973i	$0.263745\pi$
$523$			770.874i			1.47395i	−0.675922	+	0.736973i	$0.736255\pi$
$524$		0			0
$525$	19.9156	−	15.8434i	0.0379345	−	0.0301779i
$526$		0			0
$527$	−453.046	−	261.566i	−0.859670	−	0.496331i
$528$		0			0
$529$	119.913	+	207.695i	0.226679	+	0.392619i
$530$		0			0
$531$	6.78876	+	22.1963i	0.0127849	+	0.0418009i
$532$		0			0
$533$	389.526	+	674.678i	0.730817	+	1.26581i
$534$		0			0
$535$	−604.962	−	349.275i	−1.13077	−	0.652851i
$536$		0			0
$537$	−279.228	+	708.975i	−0.519977	+	1.32025i
$538$		0			0
$539$	−191.789			−0.355824
$540$		0			0
$541$	680.716			1.25825			0.629127	−	0.777302i	$-0.283412\pi$
$541$	680.716			1.25825			0.629127	+	0.777302i	$0.283412\pi$
$542$		0			0
$543$	278.388	−	706.842i	0.512684	−	1.30173i
$544$		0			0
$545$	315.348	+	182.066i	0.578619	+	0.334066i
$546$		0			0
$547$	653.970	−	377.570i	1.19556	−	0.690256i	0.235996	−	0.971754i	$-0.424165\pi$
$547$	653.970	−	377.570i	1.19556	−	0.690256i	0.959562	+	0.281498i	$0.0908314\pi$
$548$		0			0
$549$	59.9702	−	259.890i	0.109235	−	0.473388i
$550$		0			0
$551$	−156.751	−	217.119i	−0.284484	−	0.394046i
$552$		0			0
$553$	630.088	+	363.781i	1.13940	+	0.657833i
$554$		0			0
$555$	349.794	+	439.701i	0.630259	+	0.792254i
$556$		0			0
$557$	636.243			1.14227			0.571134	−	0.820857i	$-0.306504\pi$
$557$	636.243			1.14227			0.571134	+	0.820857i	$0.306504\pi$
$558$		0			0
$559$			763.021i			1.36498i
$560$		0			0
$561$	−167.206	−	1118.38i	−0.298049	−	1.99355i
$562$		0			0
$563$	782.036	+	451.509i	1.38905	+	0.801970i	0.993208	−	0.116348i	$-0.0371188\pi$
$563$	782.036	+	451.509i	1.38905	+	0.801970i	0.395844	+	0.918318i	$0.370452\pi$
$564$		0			0
$565$	129.966	−	75.0357i	0.230028	−	0.132807i
$566$		0			0
$567$	400.590	−	270.329i	0.706508	−	0.476771i
$568$		0			0
$569$	−346.924	+	200.297i	−0.609708	+	0.352015i	−0.772851	−	0.634587i	$-0.781170\pi$
$569$	−346.924	+	200.297i	−0.609708	+	0.352015i	0.163143	+	0.986602i	$0.447837\pi$
$570$		0			0
$571$	−282.611	+	489.497i	−0.494941	+	0.857262i	−0.999983	−	0.00583220i	$-0.998144\pi$
$571$	−282.611	+	489.497i	−0.494941	+	0.857262i	0.505042	+	0.863095i	$0.331477\pi$
$572$		0			0
$573$	85.4405	+	571.481i	0.149111	+	0.997349i
$574$		0			0
$575$	24.1781			0.0420488
$576$		0			0
$577$	−581.550			−1.00789			−0.503943	−	0.863737i	$-0.668118\pi$
$577$	−581.550			−1.00789			−0.503943	+	0.863737i	$0.668118\pi$
$578$		0			0
$579$	331.488	+	416.691i	0.572519	+	0.719673i
$580$		0			0
$581$	420.471	−	728.278i	0.723703	−	1.25349i
$582$		0			0
$583$	218.816	−	126.333i	0.375327	−	0.216695i
$584$		0			0
$585$	−459.018	−	105.920i	−0.784646	−	0.181059i
$586$		0			0
$587$	−209.501	−	362.867i	−0.356901	−	0.618171i	0.630540	−	0.776157i	$-0.282833\pi$
$587$	−209.501	−	362.867i	−0.356901	−	0.618171i	−0.987441	+	0.157985i	$0.949500\pi$
$588$		0			0
$589$	154.506	−	344.236i	0.262320	−	0.584442i
$590$		0			0
$591$	268.244	+	105.647i	0.453882	+	0.178760i
$592$		0			0
$593$	51.0813			0.0861405			0.0430702	−	0.999072i	$-0.486286\pi$
$593$	51.0813			0.0861405			0.0430702	+	0.999072i	$0.486286\pi$
$594$		0			0
$595$	−807.870			−1.35776
$596$		0			0
$597$	−559.129	−	220.211i	−0.936564	−	0.368863i
$598$		0			0
$599$	135.349	+	78.1439i	0.225959	+	0.130457i	0.608706	−	0.793396i	$-0.291689\pi$
$599$	135.349	+	78.1439i	0.225959	+	0.130457i	−0.382748	+	0.923853i	$0.625022\pi$
$600$		0			0
$601$	75.1499	−	43.3878i	0.125041	−	0.0721927i	−0.436175	−	0.899862i	$-0.643667\pi$
$601$	75.1499	−	43.3878i	0.125041	−	0.0721927i	0.561216	+	0.827669i	$0.310334\pi$
$602$		0			0
$603$	334.640	+	1094.13i	0.554959	+	1.81448i
$604$		0			0
$605$	−215.250	−	372.824i	−0.355785	−	0.616238i
$606$		0			0
$607$	−639.790	−	369.383i	−1.05402	−	0.608539i	−0.130248	−	0.991481i	$-0.541577\pi$
$607$	−639.790	−	369.383i	−1.05402	−	0.608539i	−0.923772	+	0.382943i	$0.874911\pi$
$608$		0			0
$609$	157.053	+	197.421i	0.257887	+	0.324172i
$610$		0			0
$611$		−	640.330i		−	1.04800i
$612$		0			0
$613$	59.5117			0.0970827			0.0485413	−	0.998821i	$-0.484543\pi$
$613$	59.5117			0.0970827			0.0485413	+	0.998821i	$0.484543\pi$
$614$		0			0
$615$	1166.80	−	174.445i	1.89724	−	0.283651i
$616$		0			0
$617$	240.931	−	417.305i	0.390488	−	0.676345i	−0.602026	−	0.798476i	$-0.705640\pi$
$617$	240.931	−	417.305i	0.390488	−	0.676345i	0.992514	+	0.122132i	$0.0389730\pi$
$618$		0			0
$619$	129.440	+	224.196i	0.209111	+	0.362191i	0.951435	−	0.307850i	$-0.0996096\pi$
$619$	129.440	+	224.196i	0.209111	+	0.362191i	−0.742324	+	0.670042i	$0.766276\pi$
$620$		0			0
$621$	457.729	+	35.9481i	0.737083	+	0.0578875i
$622$		0			0
$623$	−276.551	+	159.667i	−0.443902	+	0.256287i
$624$		0			0
$625$	329.262	−	570.298i	0.526819	−	0.912477i
$626$		0			0
$627$	790.241	−	201.882i	1.26035	−	0.321981i
$628$		0			0
$629$		−	959.808i		−	1.52593i
$630$		0			0
$631$	−1099.09			−1.74182			−0.870912	−	0.491439i	$-0.836471\pi$
$631$	−1099.09			−1.74182			−0.870912	+	0.491439i	$0.836471\pi$
$632$		0			0
$633$	565.261	+	710.551i	0.892988	+	1.12251i
$634$		0			0
$635$	567.478	+	327.633i	0.893665	+	0.515958i
$636$		0			0
$637$	118.198	−	68.2419i	0.185555	−	0.107130i
$638$		0			0
$639$	452.363	−	485.207i	0.707923	−	0.759322i
$640$		0			0
$641$	−228.042	+	131.660i	−0.355760	+	0.205398i	−0.667219	−	0.744861i	$-0.732516\pi$
$641$	−228.042	+	131.660i	−0.355760	+	0.205398i	0.311459	+	0.950260i	$0.399182\pi$
$642$		0			0
$643$	258.212	−	447.237i	0.401574	−	0.695547i	−0.592342	−	0.805687i	$-0.701797\pi$
$643$	258.212	−	447.237i	0.401574	−	0.695547i	0.993916	+	0.110140i	$0.0351299\pi$
$644$		0			0
$645$	1075.12	+	423.431i	1.66685	+	0.656483i
$646$		0			0
$647$	−461.747			−0.713673			−0.356837	−	0.934167i	$-0.616145\pi$
$647$	−461.747			−0.713673			−0.356837	+	0.934167i	$0.616145\pi$
$648$		0			0
$649$		−	36.9037i		−	0.0568624i
$650$		0			0
$651$	−130.256	+	330.728i	−0.200086	+	0.508030i
$652$		0			0
$653$	−407.268	+	705.409i	−0.623688	+	1.08026i	0.365105	+	0.930966i	$0.381033\pi$
$653$	−407.268	+	705.409i	−0.623688	+	1.08026i	−0.988793	+	0.149293i	$0.952300\pi$
$654$		0			0
$655$	−379.764	−	657.771i	−0.579793	−	1.00423i
$656$		0			0
$657$	666.468	+	621.355i	1.01441	+	0.945745i
$658$		0			0
$659$	−120.169	+	69.3797i	−0.182351	+	0.105280i	−0.588397	−	0.808572i	$-0.700241\pi$
$659$	−120.169	+	69.3797i	−0.182351	+	0.105280i	0.406046	+	0.913853i	$0.366907\pi$
$660$		0			0
$661$	722.602	+	417.195i	1.09320	+	0.631157i	0.934425	−	0.356159i	$-0.115914\pi$
$661$	722.602	+	417.195i	1.09320	+	0.631157i	0.158770	+	0.987316i	$0.449247\pi$
$662$		0			0
$663$	500.987	+	629.756i	0.755637	+	0.949858i
$664$		0			0
$665$	−59.1646	−	579.682i	−0.0889693	−	0.871702i
$666$		0			0
$667$			239.674i			0.359331i
$668$		0			0
$669$	−990.745	+	148.123i	−1.48093	+	0.221410i
$670$		0			0
$671$	−212.029	+	367.245i	−0.315989	+	0.547310i
$672$		0			0
$673$	−172.986	+	99.8738i	−0.257038	+	0.148401i	−0.622983	−	0.782236i	$-0.714079\pi$
$673$	−172.986	+	99.8738i	−0.257038	+	0.148401i	0.365945	+	0.930637i	$0.380746\pi$
$674$		0			0
$675$	−21.7385	+	31.6409i	−0.0322052	+	0.0468754i
$676$		0			0
$677$	−642.015	+	370.667i	−0.948323	+	0.547515i	−0.892560	−	0.450929i	$-0.851093\pi$
$677$	−642.015	+	370.667i	−0.948323	+	0.547515i	−0.0557636	+	0.998444i	$0.517759\pi$
$678$		0			0
$679$	−546.064	−	315.270i	−0.804218	−	0.464316i
$680$		0			0
$681$	−855.877	+	127.960i	−1.25679	+	0.187900i
$682$		0			0
$683$			453.789i			0.664405i	0.943208	+	0.332203i	$0.107792\pi$
$683$			453.789i			0.664405i	−0.943208	+	0.332203i	$0.892208\pi$
$684$		0			0
$685$	−294.460			−0.429869
$686$		0			0
$687$	−349.614	+	278.127i	−0.508899	+	0.404842i
$688$		0			0
$689$	−89.9032	+	155.717i	−0.130484	+	0.226004i
$690$		0			0
$691$	150.194	+	260.144i	0.217358	+	0.376475i	0.953999	−	0.299809i	$-0.0969229\pi$
$691$	150.194	+	260.144i	0.217358	+	0.376475i	−0.736642	+	0.676283i	$0.763590\pi$
$692$		0			0
$693$	−734.755	+	224.725i	−1.06025	+	0.324279i
$694$		0			0
$695$	−214.010	−	370.677i	−0.307928	−	0.533348i
$696$		0			0
$697$	−1745.34	−	1007.67i	−2.50408	−	1.44573i
$698$		0			0
$699$	−506.866	−	199.628i	−0.725130	−	0.285590i
$700$		0			0
$701$	919.752			1.31206			0.656029	−	0.754736i	$-0.272235\pi$
$701$	919.752			1.31206			0.656029	+	0.754736i	$0.272235\pi$
$702$		0			0
$703$	688.705	−	70.2918i	0.979665	−	0.0999884i
$704$		0			0
$705$	−902.241	−	355.345i	−1.27977	−	0.504036i
$706$		0			0
$707$	324.070	−	561.305i	0.458373	−	0.793925i
$708$		0			0
$709$	82.9247	+	143.630i	0.116960	+	0.202581i	0.918562	−	0.395278i	$-0.129352\pi$
$709$	82.9247	+	143.630i	0.116960	+	0.202581i	−0.801601	+	0.597859i	$0.796018\pi$
$710$		0			0
$711$	−1069.41	−	246.768i	−1.50409	−	0.347072i
$712$		0			0
$713$	−292.461	+	168.852i	−0.410183	+	0.236819i
$714$		0			0
$715$	648.629	+	374.486i	0.907173	+	0.523757i
$716$		0			0
$717$	318.314	−	253.227i	0.443952	−	0.353175i
$718$		0			0
$719$	−436.961			−0.607734			−0.303867	−	0.952714i	$-0.598278\pi$
$719$	−436.961			−0.607734			−0.303867	+	0.952714i	$0.598278\pi$
$720$		0			0
$721$		−	498.264i		−	0.691074i
$722$		0			0
$723$	−423.303	+	63.2868i	−0.585481	+	0.0875337i
$724$		0			0
$725$	−17.3546	−	10.0197i	−0.0239373	−	0.0138202i
$726$		0			0
$727$	−285.339	−	494.222i	−0.392489	−	0.679810i	0.600289	−	0.799783i	$-0.295052\pi$
$727$	−285.339	−	494.222i	−0.392489	−	0.679810i	−0.992777	+	0.119973i	$0.961719\pi$
$728$		0			0
$729$	−458.588	+	566.691i	−0.629064	+	0.777353i
$730$		0			0
$731$	−986.939	−	1709.43i	−1.35012	−	2.33848i
$732$		0			0
$733$	11.0987	−	19.2235i	0.0151415	−	0.0262258i	−0.858355	−	0.513056i	$-0.828513\pi$
$733$	11.0987	−	19.2235i	0.0151415	−	0.0262258i	0.873497	+	0.486830i	$0.161847\pi$
$734$		0			0
$735$	−30.5615	−	204.415i	−0.0415803	−	0.278116i
$736$		0			0
$737$		−	1819.11i		−	2.46826i
$738$		0			0
$739$	1263.61			1.70989			0.854944	−	0.518720i	$-0.173591\pi$
$739$	1263.61			1.70989			0.854944	+	0.518720i	$0.173591\pi$
$740$		0			0
$741$	−415.188	+	405.601i	−0.560307	+	0.547369i
$742$		0			0
$743$	−951.109	−	549.123i	−1.28009	−	0.739062i	−0.303227	−	0.952918i	$-0.598064\pi$
$743$	−951.109	−	549.123i	−1.28009	−	0.739062i	−0.976865	+	0.213857i	$0.931397\pi$
$744$		0			0
$745$	−544.795	−	943.613i	−0.731269	−	1.26659i
$746$		0			0
$747$	−285.223	+	1236.06i	−0.381825	+	1.65470i
$748$		0			0
$749$	702.186	−	405.407i	0.937498	−	0.541265i
$750$		0			0
$751$	401.859	+	232.014i	0.535099	+	0.308939i	0.743090	−	0.669191i	$-0.233359\pi$
$751$	401.859	+	232.014i	0.535099	+	0.308939i	−0.207991	+	0.978131i	$0.566693\pi$
$752$		0			0
$753$	−403.066	−	158.747i	−0.535281	−	0.210819i
$754$		0			0
$755$		−	57.0636i		−	0.0755809i
$756$		0			0
$757$	−1369.21			−1.80873			−0.904366	−	0.426758i	$-0.859656\pi$
$757$	−1369.21			−1.80873			−0.904366	+	0.426758i	$0.859656\pi$
$758$		0			0
$759$	−679.206	−	267.503i	−0.894870	−	0.352442i
$760$		0			0
$761$	383.669	−	664.534i	0.504164	−	0.873237i	−0.495825	−	0.868423i	$-0.665134\pi$
$761$	383.669	−	664.534i	0.504164	−	0.873237i	0.999988	−	0.00481460i	$-0.00153254\pi$
$762$		0			0
$763$	−366.027	+	211.326i	−0.479721	+	0.276967i
$764$		0			0
$765$	1165.36	−	356.426i	1.52335	−	0.465917i
$766$		0			0
$767$	13.1310	+	22.7435i	0.0171199	+	0.0296526i
$768$		0			0
$769$	193.135	−	334.520i	0.251151	−	0.435007i	−0.712692	−	0.701477i	$-0.752524\pi$
$769$	193.135	−	334.520i	0.251151	−	0.435007i	0.963843	+	0.266471i	$0.0858576\pi$
$770$		0			0
$771$	−193.377	−	243.080i	−0.250813	−	0.315279i
$772$		0			0
$773$			1151.51i			1.48966i	0.667254	+	0.744830i	$0.267470\pi$
$773$			1151.51i			1.48966i	−0.667254	+	0.744830i	$0.732530\pi$
$774$		0			0
$775$		−	28.2357i		−	0.0364332i
$776$		0			0
$777$	−644.994	+	96.4312i	−0.830108	+	0.124107i
$778$		0			0
$779$	595.229	−	1326.16i	0.764094	−	1.70238i
$780$		0			0
$781$	−913.390	+	527.346i	−1.16951	+	0.675219i
$782$		0			0
$783$	−313.652	−	215.491i	−0.400577	−	0.275212i
$784$		0			0
$785$	584.014	+	1011.54i	0.743967	+	1.28859i
$786$		0			0
$787$	−1198.19	−	691.776i	−1.52248	−	0.879003i	−0.999647	−	0.0265675i	$-0.991542\pi$
$787$	−1198.19	−	691.776i	−1.52248	−	0.879003i	−0.522832	−	0.852436i	$-0.675124\pi$
$788$		0			0
$789$	13.1620	+	88.0358i	0.0166819	+	0.111579i
$790$		0			0
$791$			174.189i			0.220214i
$792$		0			0
$793$		−	301.775i		−	0.380548i
$794$		0			0
$795$	169.518	+	213.090i	0.213230	+	0.268037i
$796$		0			0
$797$	55.3843	+	31.9762i	0.0694910	+	0.0401206i	0.534343	−	0.845268i	$-0.320559\pi$
$797$	55.3843	+	31.9762i	0.0694910	+	0.0401206i	−0.464852	+	0.885388i	$0.653892\pi$
$798$		0			0
$799$	828.243	+	1434.56i	1.03660	+	1.79544i
$800$		0			0
$801$	328.484	−	352.334i	0.410092	−	0.439867i
$802$		0			0
$803$	−724.350	−	1254.61i	−0.902054	−	1.56240i
$804$		0			0
$805$	−260.757	+	451.645i	−0.323922	+	0.561049i
$806$		0			0
$807$	174.800	−	443.826i	0.216604	−	0.549971i
$808$		0			0
$809$	−123.146			−0.152220			−0.0761100	−	0.997099i	$-0.524250\pi$
$809$	−123.146			−0.152220			−0.0761100	+	0.997099i	$0.524250\pi$
$810$		0			0
$811$		−	1052.82i		−	1.29817i	−0.760714	−	0.649087i	$-0.775151\pi$
$811$		−	1052.82i		−	1.29817i	0.760714	−	0.649087i	$-0.224849\pi$
$812$		0			0
$813$	−263.855	−	103.919i	−0.324545	−	0.127821i
$814$		0			0
$815$	153.095	−	265.168i	0.187846	−	0.325359i
$816$		0			0
$817$	1154.31	−	833.363i	1.41287	−	1.02003i
$818$		0			0
$819$	372.864	−	399.936i	0.455268	−	0.488322i
$820$		0			0
$821$	17.8687	+	30.9495i	0.0217645	+	0.0376973i	0.876703	−	0.481033i	$-0.159738\pi$
$821$	17.8687	+	30.9495i	0.0217645	+	0.0376973i	−0.854938	+	0.518730i	$0.826405\pi$
$822$		0			0
$823$	−751.435	+	1301.52i	−0.913044	+	1.58144i	−0.103305	+	0.994650i	$0.532942\pi$
$823$	−751.435	+	1301.52i	−0.913044	+	1.58144i	−0.809740	+	0.586789i	$0.800392\pi$
$824$		0			0
$825$	47.7642	−	37.9976i	0.0578959	−	0.0460577i
$826$		0			0
$827$			68.8878i			0.0832984i	0.999132	+	0.0416492i	$0.0132612\pi$
$827$			68.8878i			0.0832984i	−0.999132	+	0.0416492i	$0.986739\pi$
$828$		0			0
$829$			359.675i			0.433866i	0.976186	+	0.216933i	$0.0696054\pi$
$829$			359.675i			0.433866i	−0.976186	+	0.216933i	$0.930395\pi$
$830$		0			0
$831$	−67.6887	−	452.746i	−0.0814545	−	0.544820i
$832$		0			0
$833$	−176.537	+	305.771i	−0.211929	+	0.367072i
$834$		0			0
$835$	−854.248	+	493.201i	−1.02305	+	0.590659i
$836$		0			0
$837$	41.9811	−	534.547i	0.0501566	−	0.638646i
$838$		0			0
$839$	−737.543	+	425.820i	−0.879073	+	0.507533i	−0.870353	−	0.492429i	$-0.836109\pi$
$839$	−737.543	+	425.820i	−0.879073	+	0.507533i	−0.00872058	+	0.999962i	$0.502776\pi$
$840$		0			0
$841$	−321.176	+	556.294i	−0.381898	+	0.661467i
$842$		0			0
$843$	−1361.33	+	203.529i	−1.61486	+	0.241434i
$844$		0			0
$845$	335.701			0.397280
$846$		0			0
$847$	499.685			0.589947
$848$		0			0
$849$	601.205	−	478.274i	0.708133	−	0.563338i
$850$		0			0
$851$	−536.587	−	309.799i	−0.630537	−	0.364041i
$852$		0			0
$853$	−784.769	−	1359.26i	−0.920011	−	1.59351i	−0.799395	−	0.600806i	$-0.794846\pi$
$853$	−784.769	−	1359.26i	−0.920011	−	1.59351i	−0.120616	−	0.992699i	$-0.538487\pi$
$854$		0			0
$855$	341.097	+	810.094i	0.398944	+	0.947479i
$856$		0			0
$857$	274.425	−	158.440i	0.320216	−	0.184877i	−0.331273	−	0.943535i	$-0.607478\pi$
$857$	274.425	−	158.440i	0.320216	−	0.184877i	0.651489	+	0.758658i	$0.274145\pi$
$858$		0			0
$859$	−205.735	+	356.343i	−0.239505	+	0.414834i	−0.960572	−	0.278030i	$-0.910318\pi$
$859$	−205.735	+	356.343i	−0.239505	+	0.414834i	0.721068	+	0.692865i	$0.243652\pi$
$860$		0			0
$861$	−501.807	+	1274.12i	−0.582818	+	1.47981i
$862$		0			0
$863$		−	527.987i		−	0.611805i	−0.952063	−	0.305902i	$-0.901042\pi$
$863$		−	527.987i		−	0.611805i	0.952063	−	0.305902i	$-0.0989581\pi$
$864$		0			0
$865$		−	1149.15i		−	1.32850i
$866$		0			0
$867$	−1130.26	−	445.149i	−1.30364	−	0.513436i
$868$		0			0
$869$	1511.16	+	872.466i	1.73896	+	1.00399i
$870$		0			0
$871$	647.270	+	1121.10i	0.743134	+	1.28715i
$872$		0			0
$873$	926.798	+	213.861i	1.06162	+	0.244973i
$874$		0			0
$875$	361.549	+	626.221i	0.413199	+	0.715681i
$876$		0			0
$877$	1361.54	+	786.083i	1.55249	+	0.896332i	0.997938	+	0.0641853i	$0.0204449\pi$
$877$	1361.54	+	786.083i	1.55249	+	0.896332i	0.554555	+	0.832147i	$0.312888\pi$
$878$		0			0
$879$	−350.825	−	440.998i	−0.399118	−	0.501704i
$880$		0			0
$881$	503.960			0.572032			0.286016	−	0.958225i	$-0.407669\pi$
$881$	503.960			0.572032			0.286016	+	0.958225i	$0.407669\pi$
$882$		0			0
$883$	−1216.84			−1.37808			−0.689038	−	0.724725i	$-0.741967\pi$
$883$	−1216.84			−1.37808			−0.689038	+	0.724725i	$0.741967\pi$
$884$		0			0
$885$	39.3331	−	5.88059i	0.0444442	−	0.00664473i
$886$		0			0
$887$	119.522	+	69.0061i	0.134749	+	0.0777971i	0.565859	−	0.824502i	$-0.308545\pi$
$887$	119.522	+	69.0061i	0.134749	+	0.0777971i	−0.431110	+	0.902299i	$0.641878\pi$
$888$		0			0
$889$	−658.677	+	380.287i	−0.740919	+	0.427770i
$890$		0			0
$891$	960.745	−	648.338i	1.07828	−	0.727652i
$892$		0			0
$893$	−968.702	+	699.361i	−1.08477	+	0.783159i
$894$		0			0
$895$	1130.67	+	652.790i	1.26331	+	0.729374i
$896$		0			0
$897$	513.773	−	76.8128i	0.572768	−	0.0856330i
$898$		0			0
$899$	279.897			0.311342
$900$		0			0
$901$		−	465.146i		−	0.516255i
$902$		0			0
$903$	−1049.58	+	834.971i	−1.16233	+	0.924664i
$904$		0			0
$905$	−1127.26	−	650.826i	−1.24560	−	0.719145i
$906$		0			0
$907$	−854.842	+	493.543i	−0.942494	+	0.544149i	−0.890741	−	0.454511i	$-0.849814\pi$
$907$	−854.842	+	493.543i	−0.942494	+	0.544149i	−0.0517529	+	0.998660i	$0.516481\pi$
$908$		0			0
$909$	−219.830	+	952.666i	−0.241837	+	1.04804i
$910$		0			0
$911$	−437.883	+	252.812i	−0.480662	+	0.277510i	−0.720692	−	0.693255i	$-0.756176\pi$
$911$	−437.883	+	252.812i	−0.480662	+	0.277510i	0.240030	+	0.970765i	$0.422843\pi$
$912$		0			0
$913$	1008.43	−	1746.65i	1.10452	−	1.91309i
$914$		0			0
$915$	−425.208	−	167.467i	−0.464708	−	0.183024i
$916$		0			0
$917$	881.593			0.961388
$918$		0			0
$919$	−467.750			−0.508978			−0.254489	−	0.967076i	$-0.581907\pi$
$919$	−467.750			−0.508978			−0.254489	+	0.967076i	$0.581907\pi$
$920$		0			0
$921$	191.053	−	485.094i	0.207441	−	0.526704i
$922$		0			0
$923$	375.278	−	650.001i	0.406585	−	0.704226i
$924$		0			0
$925$	44.8645	−	25.9025i	0.0485021	−	0.0280027i
$926$		0			0
$927$	219.831	+	718.751i	0.237142	+	0.775352i
$928$		0			0
$929$	−134.469	−	232.908i	−0.144746	−	0.250708i	0.784532	−	0.620088i	$-0.212903\pi$
$929$	−134.469	−	232.908i	−0.144746	−	0.250708i	−0.929278	+	0.369380i	$0.879570\pi$
$930$		0			0
$931$	−232.333	−	104.280i	−0.249552	−	0.112008i
$932$		0			0
$933$	75.0023	−	59.6663i	0.0803884	−	0.0639510i
$934$		0			0
$935$	−1937.53			−2.07223
$936$		0			0
$937$	223.604			0.238638			0.119319	−	0.992856i	$-0.461929\pi$
$937$	223.604			0.238638			0.119319	+	0.992856i	$0.461929\pi$
$938$		0			0
$939$	10.3842	+	69.4562i	0.0110588	+	0.0739683i
$940$		0			0
$941$	−526.170	−	303.784i	−0.559160	−	0.322831i	0.193648	−	0.981071i	$-0.437968\pi$
$941$	−526.170	−	303.784i	−0.559160	−	0.322831i	−0.752808	+	0.658240i	$0.771301\pi$
$942$		0			0
$943$	−1126.69	+	650.496i	−1.19480	+	0.689816i
$944$		0			0
$945$	−356.603	−	747.316i	−0.377357	−	0.790811i
$946$		0			0
$947$	102.423	+	177.401i	0.108155	+	0.187329i	0.915023	−	0.403402i	$-0.132172\pi$
$947$	102.423	+	177.401i	0.108155	+	0.187329i	−0.806868	+	0.590732i	$0.798839\pi$
$948$		0			0
$949$	892.825	+	515.473i	0.940806	+	0.543175i
$950$		0			0
$951$	1587.17	−	237.293i	1.66895	−	0.249520i
$952$		0			0
$953$		−	1043.82i		−	1.09530i	−0.836708	−	0.547649i	$-0.815523\pi$
$953$		−	1043.82i		−	1.09530i	0.836708	−	0.547649i	$-0.184477\pi$
$954$		0			0
$955$	990.062			1.03671
$956$		0			0
$957$	376.665	+	473.479i	0.393589	+	0.494754i
$958$		0			0
$959$	170.891	−	295.993i	0.178198	−	0.308647i
$960$		0			0
$961$	−283.310	−	490.708i	−0.294808	−	0.510622i
$962$		0			0
$963$	−834.048	+	894.604i	−0.866094	+	0.928976i
$964$		0			0
$965$	790.095	−	456.161i	0.818751	−	0.472706i
$966$		0			0
$967$	−825.800	+	1430.33i	−0.853982	+	1.47914i	0.0236046	+	0.999721i	$0.492486\pi$
$967$	−825.800	+	1430.33i	−0.853982	+	1.47914i	−0.877586	+	0.479418i	$0.840848\pi$
$968$		0			0
$969$	405.534	−	1445.71i	0.418507	−	1.49197i
$970$		0			0
$971$			878.367i			0.904601i	0.891866	+	0.452300i	$0.149397\pi$
$971$			878.367i			0.904601i	−0.891866	+	0.452300i	$0.850603\pi$
$972$		0			0
$973$	496.808			0.510594
$974$		0			0
$975$	−15.9166	+	40.4131i	−0.0163247	+	0.0414493i
$976$		0			0
$977$	1525.97	+	881.019i	1.56189	+	0.901759i	0.997066	+	0.0765497i	$0.0243904\pi$
$977$	1525.97	+	881.019i	1.56189	+	0.901759i	0.564827	+	0.825209i	$0.308943\pi$
$978$		0			0
$979$	−663.260	+	382.933i	−0.677487	+	0.391147i
$980$		0			0
$981$	434.763	−	466.329i	0.443183	−	0.475360i
$982$		0			0
$983$	−587.396	+	339.133i	−0.597554	+	0.344998i	−0.768079	−	0.640355i	$-0.778787\pi$
$983$	−587.396	+	339.133i	−0.597554	+	0.344998i	0.170525	+	0.985353i	$0.445454\pi$
$984$		0			0
$985$	246.987	−	427.793i	0.250748	−	0.434308i
$986$		0			0
$987$	880.815	−	700.711i	0.892416	−	0.709940i
$988$		0			0
$989$	−1274.22			−1.28840
$990$		0			0
$991$		−	1571.57i		−	1.58584i	−0.609323	−	0.792922i	$-0.708559\pi$
$991$		−	1571.57i		−	1.58584i	0.609323	−	0.792922i	$-0.291441\pi$
$992$		0			0
$993$	719.894	−	107.629i	0.724969	−	0.108388i
$994$		0			0
$995$	−514.819	+	891.693i	−0.517406	+	0.896174i
$996$		0			0
$997$	−609.673	−	1055.98i	−0.611507	−	1.05916i	−0.990987	−	0.133962i	$-0.957230\pi$
$997$	−609.673	−	1055.98i	−0.611507	−	1.05916i	0.379479	−	0.925200i	$-0.376103\pi$
$998$		0			0
$999$	887.866	−	423.670i	0.888755	−	0.424094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.6	✓	80
3.2	odd	2		2052.3.t.a.37.31		80
9.2	odd	6		2052.3.t.a.721.32		80
9.7	even	3	inner	684.3.t.a.493.35	yes	80
19.18	odd	2	inner	684.3.t.a.265.35	yes	80
57.56	even	2		2052.3.t.a.37.32		80
171.56	even	6		2052.3.t.a.721.31		80
171.151	odd	6	inner	684.3.t.a.493.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.6	✓	80	1.1	even	1	trivial
684.3.t.a.265.35	yes	80	19.18	odd	2	inner
684.3.t.a.493.6	yes	80	171.151	odd	6	inner
684.3.t.a.493.35	yes	80	9.7	even	3	inner
2052.3.t.a.37.31		80	3.2	odd	2
2052.3.t.a.37.32		80	57.56	even	2
2052.3.t.a.721.31		80	171.56	even	6
2052.3.t.a.721.32		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)

\(f(q)\)	\(=\)	\(q+(-2.79131 - 1.09935i) q^{3} +(-2.57011 + 4.45156i) q^{5} +(-2.98315 - 5.16697i) q^{7} +(6.58286 + 6.13726i) q^{9} +O(q^{10})\)	\(q+(-2.79131 - 1.09935i) q^{3} +(-2.57011 + 4.45156i) q^{5} +(-2.98315 - 5.16697i) q^{7} +(6.58286 + 6.13726i) q^{9} +(-7.15457 - 12.3921i) q^{11} +(8.81864 + 5.09144i) q^{13} +(12.0678 - 9.60024i) q^{15} -26.3424 q^{17} +(-1.92919 - 18.9018i) q^{19} +(2.64660 + 17.7022i) q^{21} +(-8.50256 + 14.7269i) q^{23} +(-0.710906 - 1.23133i) q^{25} +(-11.6278 - 24.3679i) q^{27} +(12.2060 - 7.04711i) q^{29} +(17.1984 + 9.92949i) q^{31} +(6.34741 + 42.4555i) q^{33} +30.6681 q^{35} +36.4359i q^{37} +(-19.0183 - 23.9066i) q^{39} +(66.2561 + 38.2530i) q^{41} +(37.4659 + 64.8928i) q^{43} +(-44.2390 + 13.5305i) q^{45} +(-31.4415 - 54.4582i) q^{47} +(6.70163 - 11.6076i) q^{49} +(73.5298 + 28.9595i) q^{51} +17.6577i q^{53} +73.5520 q^{55} +(-15.3947 + 54.8817i) q^{57} +(2.23351 + 1.28951i) q^{59} +(-14.8177 - 25.6651i) q^{61} +(12.0734 - 52.3218i) q^{63} +(-45.3297 + 26.1711i) q^{65} +(110.097 + 63.5645i) q^{67} +(39.9233 - 31.7600i) q^{69} -73.7076i q^{71} +101.243 q^{73} +(0.630703 + 4.21855i) q^{75} +(-42.6863 + 73.9348i) q^{77} +(-105.608 + 60.9727i) q^{79} +(5.66803 + 80.8014i) q^{81} +(70.4744 + 122.065i) q^{83} +(67.7027 - 117.265i) q^{85} +(-41.8179 + 6.25207i) q^{87} -53.5229i q^{89} -60.7542i q^{91} +(-37.0901 - 46.6234i) q^{93} +(89.1007 + 39.9918i) q^{95} +(91.5247 - 52.8418i) q^{97} +(28.9559 - 125.485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 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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