LMFDB - Embedded newform 684.3.s.a.601.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (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			601.18
Character	$\chi$	$=$	684.601
Dual form			684.3.s.a.445.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.455700 - 2.96519i) q^{3} +(1.91242 - 3.31241i) q^{5} +(-3.97487 + 6.88467i) q^{7} +(-8.58467 + 2.70247i) q^{9} +O(q^{10})$	\(q+(-0.455700 - 2.96519i) q^{3} +(1.91242 - 3.31241i) q^{5} +(-3.97487 + 6.88467i) q^{7} +(-8.58467 + 2.70247i) q^{9} +(2.64440 - 4.58024i) q^{11} +14.2808i q^{13} +(-10.6934 - 4.16122i) q^{15} +(6.41269 + 11.1071i) q^{17} +(2.65616 + 18.8134i) q^{19} +(22.2257 + 8.64888i) q^{21} -18.5774 q^{23} +(5.18529 + 8.98119i) q^{25} +(11.9254 + 24.2237i) q^{27} +(24.1574 - 13.9473i) q^{29} +(-22.1365 + 12.7805i) q^{31} +(-14.7863 - 5.75394i) q^{33} +(15.2032 + 26.3328i) q^{35} +12.6278i q^{37} +(42.3453 - 6.50777i) q^{39} +(-29.4375 - 16.9957i) q^{41} +26.6270 q^{43} +(-7.46582 + 33.6042i) q^{45} +(-5.03379 - 8.71877i) q^{47} +(-7.09914 - 12.2961i) q^{49} +(30.0124 - 24.0763i) q^{51} +(26.8513 + 15.5026i) q^{53} +(-10.1144 - 17.5187i) q^{55} +(54.5749 - 16.4493i) q^{57} +(23.0876 + 13.3296i) q^{59} +(14.9942 + 25.9707i) q^{61} +(15.5173 - 69.8446i) q^{63} +(47.3040 + 27.3110i) q^{65} -48.5515i q^{67} +(8.46574 + 55.0856i) q^{69} +(38.6617 - 22.3213i) q^{71} +(-18.2629 - 31.6322i) q^{73} +(24.2680 - 19.4681i) q^{75} +(21.0223 + 36.4117i) q^{77} +2.68433i q^{79} +(66.3933 - 46.3997i) q^{81} +(-65.5498 + 113.536i) q^{83} +49.0551 q^{85} +(-52.3649 - 65.2755i) q^{87} +(133.364 + 76.9979i) q^{89} +(-98.3188 - 56.7644i) q^{91} +(47.9843 + 59.8148i) q^{93} +(67.3975 + 27.1809i) q^{95} +101.085i q^{97} +(-10.3234 + 46.4663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.455700	−	2.96519i	−0.151900	−	0.988396i
$3$	−0.455700	−	2.96519i	−0.151900	−	0.988396i
$4$		0			0
$5$	1.91242	−	3.31241i	0.382484	−	0.662482i	−0.608932	−	0.793222i	$-0.708402\pi$
$5$	1.91242	−	3.31241i	0.382484	−	0.662482i	0.991417	+	0.130740i	$0.0417353\pi$
$6$		0			0
$7$	−3.97487	+	6.88467i	−0.567838	+	0.983525i	0.428941	+	0.903332i	$0.358887\pi$
$7$	−3.97487	+	6.88467i	−0.567838	+	0.983525i	−0.996779	+	0.0801922i	$0.974447\pi$
$8$		0			0
$9$	−8.58467	+	2.70247i	−0.953853	+	0.300275i
$10$		0			0
$11$	2.64440	−	4.58024i	0.240400	−	0.416386i	−0.720428	−	0.693530i	$-0.756055\pi$
$11$	2.64440	−	4.58024i	0.240400	−	0.416386i	0.960828	+	0.277144i	$0.0893879\pi$
$12$		0			0
$13$			14.2808i			1.09852i	0.835650	+	0.549262i	$0.185091\pi$
$13$			14.2808i			1.09852i	−0.835650	+	0.549262i	$0.814909\pi$
$14$		0			0
$15$	−10.6934	−	4.16122i	−0.712894	−	0.277415i
$16$		0			0
$17$	6.41269	+	11.1071i	0.377217	+	0.653359i	0.990656	−	0.136383i	$-0.0435477\pi$
$17$	6.41269	+	11.1071i	0.377217	+	0.653359i	−0.613439	+	0.789742i	$0.710214\pi$
$18$		0			0
$19$	2.65616	+	18.8134i	0.139798	+	0.990180i
$19$	2.65616	+	18.8134i	0.139798	+	0.990180i
$20$		0			0
$21$	22.2257	+	8.64888i	1.05837	+	0.411851i
$22$		0			0
$23$	−18.5774			−0.807715			−0.403857	−	0.914822i	$-0.632331\pi$
$23$	−18.5774			−0.807715			−0.403857	+	0.914822i	$0.632331\pi$
$24$		0			0
$25$	5.18529	+	8.98119i	0.207412	+	0.359247i
$26$		0			0
$27$	11.9254	+	24.2237i	0.441680	+	0.897172i
$28$		0			0
$29$	24.1574	−	13.9473i	0.833014	−	0.480941i	−0.0218694	−	0.999761i	$-0.506962\pi$
$29$	24.1574	−	13.9473i	0.833014	−	0.480941i	0.854884	+	0.518820i	$0.173628\pi$
$30$		0			0
$31$	−22.1365	+	12.7805i	−0.714081	+	0.412275i	−0.812570	−	0.582863i	$-0.801932\pi$
$31$	−22.1365	+	12.7805i	−0.714081	+	0.412275i	0.0984892	+	0.995138i	$0.468599\pi$
$32$		0			0
$33$	−14.7863	−	5.75394i	−0.448071	−	0.174362i
$34$		0			0
$35$	15.2032	+	26.3328i	0.434378	+	0.752365i
$36$		0			0
$37$			12.6278i			0.341292i	0.985332	+	0.170646i	$0.0545855\pi$
$37$			12.6278i			0.341292i	−0.985332	+	0.170646i	$0.945415\pi$
$38$		0			0
$39$	42.3453	−	6.50777i	1.08578	−	0.166866i
$40$		0			0
$41$	−29.4375	−	16.9957i	−0.717988	−	0.414530i	0.0960240	−	0.995379i	$-0.469387\pi$
$41$	−29.4375	−	16.9957i	−0.717988	−	0.414530i	−0.814012	+	0.580849i	$0.802721\pi$
$42$		0			0
$43$	26.6270			0.619232			0.309616	−	0.950862i	$-0.399800\pi$
$43$	26.6270			0.619232			0.309616	+	0.950862i	$0.399800\pi$
$44$		0			0
$45$	−7.46582	+	33.6042i	−0.165907	+	0.746761i
$46$		0			0
$47$	−5.03379	−	8.71877i	−0.107102	−	0.185506i	0.807493	−	0.589877i	$-0.200824\pi$
$47$	−5.03379	−	8.71877i	−0.107102	−	0.185506i	−0.914595	+	0.404371i	$0.867490\pi$
$48$		0			0
$49$	−7.09914	−	12.2961i	−0.144880	−	0.250940i
$50$		0			0
$51$	30.0124	−	24.0763i	0.588478	−	0.472085i
$52$		0			0
$53$	26.8513	+	15.5026i	0.506628	+	0.292502i	0.731446	−	0.681899i	$-0.238846\pi$
$53$	26.8513	+	15.5026i	0.506628	+	0.292502i	−0.224818	+	0.974401i	$0.572179\pi$
$54$		0			0
$55$	−10.1144	−	17.5187i	−0.183899	−	0.318522i
$56$		0			0
$57$	54.5749	−	16.4493i	0.957455	−	0.288584i
$58$		0			0
$59$	23.0876	+	13.3296i	0.391315	+	0.225926i	0.682730	−	0.730671i	$-0.260793\pi$
$59$	23.0876	+	13.3296i	0.391315	+	0.225926i	−0.291415	+	0.956597i	$0.594126\pi$
$60$		0			0
$61$	14.9942	+	25.9707i	0.245806	+	0.425749i	0.962358	−	0.271785i	$-0.0876140\pi$
$61$	14.9942	+	25.9707i	0.245806	+	0.425749i	−0.716552	+	0.697534i	$0.754281\pi$
$62$		0			0
$63$	15.5173	−	69.8446i	0.246306	−	1.10865i
$64$		0			0
$65$	47.3040	+	27.3110i	0.727753	+	0.420168i
$66$		0			0
$67$		−	48.5515i		−	0.724649i	−0.932052	−	0.362324i	$-0.881983\pi$
$67$		−	48.5515i		−	0.724649i	0.932052	−	0.362324i	$-0.118017\pi$
$68$		0			0
$69$	8.46574	+	55.0856i	0.122692	+	0.798342i
$70$		0			0
$71$	38.6617	−	22.3213i	0.544531	−	0.314385i	−0.202382	−	0.979307i	$-0.564868\pi$
$71$	38.6617	−	22.3213i	0.544531	−	0.314385i	0.746913	+	0.664922i	$0.231535\pi$
$72$		0			0
$73$	−18.2629	−	31.6322i	−0.250176	−	0.433318i	0.713398	−	0.700759i	$-0.247155\pi$
$73$	−18.2629	−	31.6322i	−0.250176	−	0.433318i	−0.963574	+	0.267441i	$0.913822\pi$
$74$		0			0
$75$	24.2680	−	19.4681i	0.323573	−	0.259574i
$76$		0			0
$77$	21.0223	+	36.4117i	0.273017	+	0.472879i
$78$		0			0
$79$			2.68433i			0.0339789i	0.999856	+	0.0169894i	$0.00540817\pi$
$79$			2.68433i			0.0339789i	−0.999856	+	0.0169894i	$0.994592\pi$
$80$		0			0
$81$	66.3933	−	46.3997i	0.819670	−	0.572836i
$82$		0			0
$83$	−65.5498	+	113.536i	−0.789757	+	1.36790i	0.136359	+	0.990659i	$0.456460\pi$
$83$	−65.5498	+	113.536i	−0.789757	+	1.36790i	−0.926116	+	0.377239i	$0.876874\pi$
$84$		0			0
$85$	49.0551			0.577118
$86$		0			0
$87$	−52.3649	−	65.2755i	−0.601895	−	0.750293i
$88$		0			0
$89$	133.364	+	76.9979i	1.49847	+	0.865145i	0.999998	−	0.00175855i	$-0.000559765\pi$
$89$	133.364	+	76.9979i	1.49847	+	0.865145i	0.498476	+	0.866903i	$0.333893\pi$
$90$		0			0
$91$	−98.3188	−	56.7644i	−1.08043	−	0.623784i
$92$		0			0
$93$	47.9843	+	59.8148i	0.515960	+	0.643170i
$94$		0			0
$95$	67.3975	+	27.1809i	0.709447	+	0.286115i
$96$		0			0
$97$			101.085i			1.04212i	0.853521	+	0.521058i	$0.174463\pi$
$97$			101.085i			1.04212i	−0.853521	+	0.521058i	$0.825537\pi$
$98$		0			0
$99$	−10.3234	+	46.4663i	−0.104277	+	0.469357i
$100$		0			0
$101$	−3.74464	−	6.48591i	−0.0370757	−	0.0642169i	0.846892	−	0.531765i	$-0.178471\pi$
$101$	−3.74464	−	6.48591i	−0.0370757	−	0.0642169i	−0.883968	+	0.467548i	$0.845138\pi$
$102$		0			0
$103$	−57.6457	+	33.2818i	−0.559667	+	0.323124i	−0.753012	−	0.658007i	$-0.771400\pi$
$103$	−57.6457	+	33.2818i	−0.559667	+	0.323124i	0.193345	+	0.981131i	$0.438066\pi$
$104$		0			0
$105$	71.1535	−	57.0803i	0.677653	−	0.543622i
$106$		0			0
$107$			99.4176i			0.929137i	0.885537	+	0.464568i	$0.153790\pi$
$107$			99.4176i			0.929137i	−0.885537	+	0.464568i	$0.846210\pi$
$108$		0			0
$109$	74.6730	−	43.1125i	0.685073	−	0.395527i	−0.116691	−	0.993168i	$-0.537229\pi$
$109$	74.6730	−	43.1125i	0.685073	−	0.395527i	0.801764	+	0.597641i	$0.203895\pi$
$110$		0			0
$111$	37.4438	−	5.75450i	0.337332	−	0.0518423i
$112$		0			0
$113$	−128.680	+	74.2935i	−1.13876	+	0.657464i	−0.946124	−	0.323806i	$-0.895038\pi$
$113$	−128.680	+	74.2935i	−1.13876	+	0.657464i	−0.192638	+	0.981270i	$0.561704\pi$
$114$		0			0
$115$	−35.5279	+	61.5361i	−0.308938	+	0.535097i
$116$		0			0
$117$	−38.5935	−	122.596i	−0.329859	−	1.04783i
$118$		0			0
$119$	−101.958			−0.856793
$120$		0			0
$121$	46.5142	+	80.5650i	0.384415	+	0.665827i
$122$		0			0
$123$	−36.9809	+	95.0326i	−0.300658	+	0.772623i
$124$		0			0
$125$	135.287			1.08230
$126$		0			0
$127$	18.7261	+	10.8115i	0.147450	+	0.0851300i	0.571910	−	0.820317i	$-0.306203\pi$
$127$	18.7261	+	10.8115i	0.147450	+	0.0851300i	−0.424460	+	0.905447i	$0.639536\pi$
$128$		0			0
$129$	−12.1339	−	78.9540i	−0.0940613	−	0.612046i
$130$		0			0
$131$	−16.9934	+	29.4334i	−0.129721	+	0.224683i	−0.923568	−	0.383434i	$-0.874741\pi$
$131$	−16.9934	+	29.4334i	−0.129721	+	0.224683i	0.793848	+	0.608117i	$0.208075\pi$
$132$		0			0
$133$	−140.082	−	56.4941i	−1.05325	−	0.424768i
$134$		0			0
$135$	103.045	+	6.82410i	0.763297	+	0.0505489i
$136$		0			0
$137$	−5.49958	−	9.52556i	−0.0401429	−	0.0695296i	0.845256	−	0.534362i	$-0.179448\pi$
$137$	−5.49958	−	9.52556i	−0.0401429	−	0.0695296i	−0.885399	+	0.464832i	$0.846115\pi$
$138$		0			0
$139$	−206.386			−1.48479			−0.742394	−	0.669963i	$-0.766310\pi$
$139$	−206.386			−1.48479			−0.742394	+	0.669963i	$0.766310\pi$
$140$		0			0
$141$	−23.5589	+	18.8993i	−0.167084	+	0.134037i
$142$		0			0
$143$	65.4096	+	37.7643i	0.457410	+	0.264086i
$144$		0			0
$145$		−	106.692i		−	0.735809i
$146$		0			0
$147$	−33.2251	+	26.6536i	−0.226021	+	0.181317i
$148$		0			0
$149$	−31.0391	+	53.7613i	−0.208316	+	0.360814i	−0.951184	−	0.308624i	$-0.900132\pi$
$149$	−31.0391	+	53.7613i	−0.208316	+	0.360814i	0.742868	+	0.669438i	$0.233465\pi$
$150$		0			0
$151$	−181.343	−	104.699i	−1.20095	−	0.693369i	−0.240184	−	0.970727i	$-0.577208\pi$
$151$	−181.343	−	104.699i	−1.20095	−	0.693369i	−0.960766	+	0.277359i	$0.910541\pi$
$152$		0			0
$153$	−85.0675	−	78.0208i	−0.555997	−	0.509940i
$154$		0			0
$155$			97.7670i			0.630755i
$156$		0			0
$157$	94.4399	−	163.575i	0.601528	−	1.04188i	−0.391062	−	0.920364i	$-0.627892\pi$
$157$	94.4399	−	163.575i	0.601528	−	1.04188i	0.992590	−	0.121512i	$-0.0387744\pi$
$158$		0			0
$159$	33.7320	−	86.6836i	0.212151	−	0.545180i
$160$		0			0
$161$	73.8428	−	127.900i	0.458651	−	0.794407i
$162$		0			0
$163$	−319.340			−1.95914			−0.979571	−	0.201099i	$-0.935549\pi$
$163$	−319.340			−1.95914			−0.979571	+	0.201099i	$0.935549\pi$
$164$		0			0
$165$	−47.3371	+	37.9745i	−0.286892	+	0.230148i
$166$		0			0
$167$		−	251.049i		−	1.50329i	−0.659569	−	0.751644i	$-0.729261\pi$
$167$		−	251.049i		−	1.50329i	0.659569	−	0.751644i	$-0.270739\pi$
$168$		0			0
$169$	−34.9419			−0.206757
$170$		0			0
$171$	−73.6450	−	154.329i	−0.430672	−	0.902508i
$172$		0			0
$173$			114.034i			0.659158i	0.944128	+	0.329579i	$0.106907\pi$
$173$			114.034i			0.659158i	−0.944128	+	0.329579i	$0.893093\pi$
$174$		0			0
$175$	−82.4433			−0.471105
$176$		0			0
$177$	29.0038	−	74.5333i	0.163863	−	0.421092i
$178$		0			0
$179$			108.778i			0.607700i	0.952720	+	0.303850i	$0.0982721\pi$
$179$			108.778i			0.607700i	−0.952720	+	0.303850i	$0.901728\pi$
$180$		0			0
$181$	85.6045	+	49.4238i	0.472953	+	0.273060i	0.717475	−	0.696584i	$-0.245298\pi$
$181$	85.6045	+	49.4238i	0.472953	+	0.273060i	−0.244522	+	0.969644i	$0.578631\pi$
$182$		0			0
$183$	70.1751	−	56.2954i	0.383470	−	0.307625i
$184$		0			0
$185$	41.8285	+	24.1497i	0.226100	+	0.130539i
$186$		0			0
$187$	67.8310			0.362733
$188$		0			0
$189$	−214.174	−	14.1835i	−1.13319	−	0.0750451i
$190$		0			0
$191$	−41.6268	+	72.0997i	−0.217941	+	0.377485i	−0.954178	−	0.299238i	$-0.903267\pi$
$191$	−41.6268	+	72.0997i	−0.217941	+	0.377485i	0.736237	+	0.676724i	$0.236601\pi$
$192$		0			0
$193$	83.2933	+	48.0894i	0.431571	+	0.249168i	0.700016	−	0.714127i	$-0.253176\pi$
$193$	83.2933	+	48.0894i	0.431571	+	0.249168i	−0.268444	+	0.963295i	$0.586510\pi$
$194$		0			0
$195$	59.4257	−	152.711i	0.304747	−	0.783132i
$196$		0			0
$197$	174.092			0.883713			0.441857	−	0.897086i	$-0.354320\pi$
$197$	174.092			0.883713			0.441857	+	0.897086i	$0.354320\pi$
$198$		0			0
$199$	58.0248	−	100.502i	0.291582	−	0.505035i	−0.682602	−	0.730790i	$-0.739152\pi$
$199$	58.0248	−	100.502i	0.291582	−	0.505035i	0.974184	+	0.225756i	$0.0724851\pi$
$200$		0			0
$201$	−143.964	+	22.1249i	−0.716240	+	0.110074i
$202$		0			0
$203$			221.754i			1.09239i
$204$		0			0
$205$	−112.594	+	65.0060i	−0.549238	+	0.317103i
$206$		0			0
$207$	159.481	−	50.2050i	0.770441	−	0.242536i
$208$		0			0
$209$	93.1940	+	37.5845i	0.445904	+	0.179830i
$210$		0			0
$211$	56.3953	+	32.5598i	0.267276	+	0.154312i	0.627649	−	0.778496i	$-0.284017\pi$
$211$	56.3953	+	32.5598i	0.267276	+	0.154312i	−0.360373	+	0.932808i	$0.617351\pi$
$212$		0			0
$213$	−83.8050	−	104.467i	−0.393451	−	0.490457i
$214$		0			0
$215$	50.9220	−	88.1995i	0.236846	−	0.410230i
$216$		0			0
$217$		−	203.204i		−	0.936422i
$218$		0			0
$219$	−85.4731	+	68.5676i	−0.390288	+	0.313094i
$220$		0			0
$221$	−158.619	+	91.5785i	−0.717731	+	0.414382i
$222$		0			0
$223$			276.954i			1.24194i	0.783832	+	0.620972i	$0.213262\pi$
$223$			276.954i			1.24194i	−0.783832	+	0.620972i	$0.786738\pi$
$224$		0			0
$225$	−68.7854	−	63.0875i	−0.305713	−	0.280389i
$226$		0			0
$227$	−312.633	−	180.499i	−1.37724	−	0.795148i	−0.385411	−	0.922745i	$-0.625940\pi$
$227$	−312.633	−	180.499i	−1.37724	−	0.795148i	−0.991826	+	0.127597i	$0.959273\pi$
$228$		0			0
$229$	48.8659	+	84.6381i	0.213388	+	0.369599i	0.952773	−	0.303684i	$-0.0982168\pi$
$229$	48.8659	+	84.6381i	0.213388	+	0.369599i	−0.739385	+	0.673283i	$0.764883\pi$
$230$		0			0
$231$	98.3877	−	78.9279i	0.425921	−	0.341679i
$232$		0			0
$233$	−108.162	−	187.342i	−0.464216	−	0.804045i	0.534950	−	0.844884i	$-0.320330\pi$
$233$	−108.162	−	187.342i	−0.464216	−	0.804045i	−0.999166	+	0.0408387i	$0.986997\pi$
$234$		0			0
$235$	−38.5069			−0.163859
$236$		0			0
$237$	7.95955	−	1.22325i	0.0335846	−	0.00516139i
$238$		0			0
$239$	−95.2811	−	165.032i	−0.398666	−	0.690509i	0.594896	−	0.803803i	$-0.297193\pi$
$239$	−95.2811	−	165.032i	−0.398666	−	0.690509i	−0.993562	+	0.113294i	$0.963860\pi$
$240$		0			0
$241$	−339.264	+	195.874i	−1.40773	+	0.812756i	−0.995169	−	0.0981726i	$-0.968700\pi$
$241$	−339.264	+	195.874i	−1.40773	+	0.812756i	−0.412565	+	0.910928i	$0.635367\pi$
$242$		0			0
$243$	−167.839	−	175.724i	−0.690696	−	0.723145i
$244$		0			0
$245$	−54.3062			−0.221658
$246$		0			0
$247$	−268.671	+	37.9321i	−1.08774	+	0.153571i
$248$		0			0
$249$	366.525	+	142.629i	1.47199	+	0.572808i
$250$		0			0
$251$	−86.5365	+	149.886i	−0.344767	+	0.597154i	−0.985311	−	0.170767i	$-0.945375\pi$
$251$	−86.5365	+	149.886i	−0.344767	+	0.597154i	0.640545	+	0.767921i	$0.278709\pi$
$252$		0			0
$253$	−49.1263	+	85.0892i	−0.194175	+	0.336321i
$254$		0			0
$255$	−22.3544	−	145.457i	−0.0876643	−	0.570421i
$256$		0			0
$257$			271.345i			1.05582i	0.849301	+	0.527909i	$0.177024\pi$
$257$			271.345i			1.05582i	−0.849301	+	0.527909i	$0.822976\pi$
$258$		0			0
$259$	−86.9384	−	50.1939i	−0.335669	−	0.193799i
$260$		0			0
$261$	−169.691	+	185.018i	−0.650159	+	0.708880i
$262$		0			0
$263$	329.887			1.25432			0.627162	−	0.778889i	$-0.284216\pi$
$263$	329.887			1.25432			0.627162	+	0.778889i	$0.284216\pi$
$264$		0			0
$265$	102.702	−	59.2950i	0.387554	−	0.223755i
$266$		0			0
$267$	167.539	−	430.538i	0.627487	−	1.61250i
$268$		0			0
$269$	114.156	−	65.9081i	0.424373	−	0.245012i	−0.272574	−	0.962135i	$-0.587875\pi$
$269$	114.156	−	65.9081i	0.424373	−	0.245012i	0.696946	+	0.717123i	$0.254542\pi$
$270$		0			0
$271$	−229.959	−	398.301i	−0.848558	−	1.46975i	−0.882495	−	0.470322i	$-0.844138\pi$
$271$	−229.959	−	398.301i	−0.848558	−	1.46975i	0.0339369	−	0.999424i	$-0.489195\pi$
$272$		0			0
$273$	−123.513	+	317.401i	−0.452429	+	1.16264i
$274$		0			0
$275$	54.8480			0.199447
$276$		0			0
$277$	−143.132	+	247.912i	−0.516722	+	0.894989i	0.483089	+	0.875571i	$0.339515\pi$
$277$	−143.132	+	247.912i	−0.516722	+	0.894989i	−0.999811	+	0.0194182i	$0.993819\pi$
$278$		0			0
$279$	155.496	−	169.540i	0.557333	−	0.607670i
$280$		0			0
$281$	114.991	−	66.3903i	0.409222	−	0.236264i	−0.281234	−	0.959639i	$-0.590744\pi$
$281$	114.991	−	66.3903i	0.409222	−	0.236264i	0.690455	+	0.723375i	$0.257410\pi$
$282$		0			0
$283$	166.098	−	287.691i	0.586920	−	1.01658i	−0.407713	−	0.913110i	$-0.633674\pi$
$283$	166.098	−	287.691i	0.586920	−	1.01658i	0.994633	−	0.103465i	$-0.0329930\pi$
$284$		0			0
$285$	49.8835	−	212.232i	0.175030	−	0.744675i
$286$		0			0
$287$	234.020	−	135.112i	0.815401	−	0.470772i
$288$		0			0
$289$	62.2548	−	107.828i	0.215415	−	0.373109i
$290$		0			0
$291$	299.737	−	46.0646i	1.03002	−	0.158297i
$292$		0			0
$293$	113.130	−	65.3157i	0.386110	−	0.222921i	−0.294363	−	0.955694i	$-0.595108\pi$
$293$	113.130	−	65.3157i	0.386110	−	0.222921i	0.680473	+	0.732773i	$0.261774\pi$
$294$		0			0
$295$	88.3063	−	50.9837i	0.299343	−	0.172826i
$296$		0			0
$297$	142.486	+	9.43604i	0.479750	+	0.0317712i
$298$		0			0
$299$		−	265.301i		−	0.887295i
$300$		0			0
$301$	−105.839	+	183.318i	−0.351623	+	0.609030i
$302$		0			0
$303$	−17.5255	+	14.0592i	−0.0578400	+	0.0464000i
$304$		0			0
$305$	114.701			0.376068
$306$		0			0
$307$	−220.685	+	127.413i	−0.718844	+	0.415025i	−0.814327	−	0.580406i	$-0.802894\pi$
$307$	−220.685	+	127.413i	−0.718844	+	0.415025i	0.0954831	+	0.995431i	$0.469560\pi$
$308$		0			0
$309$	124.956	+	155.764i	0.404388	+	0.504090i
$310$		0			0
$311$	−55.6250	−	96.3453i	−0.178858	−	0.309792i	0.762631	−	0.646833i	$-0.223907\pi$
$311$	−55.6250	−	96.3453i	−0.178858	−	0.309792i	−0.941490	+	0.337042i	$0.890574\pi$
$312$		0			0
$313$	−181.922	−	315.098i	−0.581221	−	1.00670i	−0.995335	−	0.0964793i	$-0.969242\pi$
$313$	−181.922	−	315.098i	−0.581221	−	1.00670i	0.414114	−	0.910225i	$-0.364091\pi$
$314$		0			0
$315$	−201.679	−	184.972i	−0.640249	−	0.587213i
$316$		0			0
$317$	−271.069	+	156.502i	−0.855107	+	0.493696i	−0.862371	−	0.506277i	$-0.831021\pi$
$317$	−271.069	+	156.502i	−0.855107	+	0.493696i	0.00726361	+	0.999974i	$0.497688\pi$
$318$		0			0
$319$		−	147.529i		−	0.462474i
$320$		0			0
$321$	294.792	−	45.3046i	0.918355	−	0.141136i
$322$		0			0
$323$	−191.930	+	150.147i	−0.594209	+	0.464851i
$324$		0			0
$325$	−128.259	+	74.0502i	−0.394642	+	0.227847i
$326$		0			0
$327$	−161.865	−	201.773i	−0.495000	−	0.617043i
$328$		0			0
$329$	80.0345			0.243266
$330$		0			0
$331$	165.604	+	95.6114i	0.500313	+	0.288856i	0.728843	−	0.684681i	$-0.240058\pi$
$331$	165.604	+	95.6114i	0.500313	+	0.288856i	−0.228530	+	0.973537i	$0.573392\pi$
$332$		0			0
$333$	−34.1263	−	108.406i	−0.102481	−	0.325543i
$334$		0			0
$335$	−160.822	−	92.8509i	−0.480067	−	0.277167i
$336$		0			0
$337$	458.782	+	264.878i	1.36137	+	0.785989i	0.989807	−	0.142418i	$-0.0454877\pi$
$337$	458.782	+	264.878i	1.36137	+	0.785989i	0.371566	+	0.928407i	$0.378821\pi$
$338$		0			0
$339$	278.934	+	347.705i	0.822813	+	1.02568i
$340$		0			0
$341$			135.187i			0.396444i
$342$		0			0
$343$	−276.664			−0.806602
$344$		0			0
$345$	198.656	+	77.3048i	0.575815	+	0.224072i
$346$		0			0
$347$	31.6748	−	54.8624i	0.0912818	−	0.158105i	−0.816769	−	0.576965i	$-0.804237\pi$
$347$	31.6748	−	54.8624i	0.0912818	−	0.158105i	0.908051	+	0.418860i	$0.137570\pi$
$348$		0			0
$349$	171.227	−	296.574i	0.490623	−	0.849783i	−0.509319	−	0.860578i	$-0.670103\pi$
$349$	171.227	−	296.574i	0.490623	−	0.849783i	0.999942	+	0.0107945i	$0.00343607\pi$
$350$		0			0
$351$	−345.934	+	170.304i	−0.985566	+	0.485197i
$352$		0			0
$353$	−101.118	+	175.141i	−0.286453	+	0.496150i	−0.972960	−	0.230972i	$-0.925809\pi$
$353$	−101.118	+	175.141i	−0.286453	+	0.496150i	0.686508	+	0.727122i	$0.259143\pi$
$354$		0			0
$355$		−	170.751i		−	0.480989i
$356$		0			0
$357$	46.4624	+	302.326i	0.130147	+	0.846851i
$358$		0			0
$359$	−14.2795	−	24.7328i	−0.0397757	−	0.0688936i	0.845452	−	0.534051i	$-0.179331\pi$
$359$	−14.2795	−	24.7328i	−0.0397757	−	0.0688936i	−0.885228	+	0.465158i	$0.845998\pi$
$360$		0			0
$361$	−346.890	+	99.9427i	−0.960913	+	0.276850i
$362$		0			0
$363$	217.694	−	174.637i	0.599708	−	0.481094i
$364$		0			0
$365$	−139.705			−0.382754
$366$		0			0
$367$	219.299	+	379.836i	0.597544	+	1.03498i	0.993182	+	0.116570i	$0.0371900\pi$
$367$	219.299	+	379.836i	0.597544	+	1.03498i	−0.395639	+	0.918406i	$0.629477\pi$
$368$		0			0
$369$	298.642	+	66.3489i	0.809327	+	0.179807i
$370$		0			0
$371$	−213.461	+	123.242i	−0.575365	+	0.332187i
$372$		0			0
$373$	−209.926	+	121.201i	−0.562805	+	0.324936i	−0.754271	−	0.656564i	$-0.772009\pi$
$373$	−209.926	+	121.201i	−0.562805	+	0.324936i	0.191466	+	0.981499i	$0.438676\pi$
$374$		0			0
$375$	−61.6502	−	401.151i	−0.164401	−	1.06974i
$376$		0			0
$377$	199.179	+	344.988i	0.528326	+	0.915087i
$378$		0			0
$379$		−	93.9089i		−	0.247781i	−0.992296	−	0.123890i	$-0.960463\pi$
$379$		−	93.9089i		−	0.247781i	0.992296	−	0.123890i	$-0.0395371\pi$
$380$		0			0
$381$	23.5247	−	60.4532i	0.0617446	−	0.158670i
$382$		0			0
$383$	509.030	+	293.889i	1.32906	+	0.767334i	0.985154	−	0.171670i	$-0.0549164\pi$
$383$	509.030	+	293.889i	1.32906	+	0.767334i	0.343906	+	0.939004i	$0.388250\pi$
$384$		0			0
$385$	160.814			0.417699
$386$		0			0
$387$	−228.584	+	71.9586i	−0.590656	+	0.185940i
$388$		0			0
$389$	−121.984	−	211.283i	−0.313584	−	0.543143i	0.665552	−	0.746352i	$-0.268196\pi$
$389$	−121.984	−	211.283i	−0.313584	−	0.543143i	−0.979135	+	0.203209i	$0.934863\pi$
$390$		0			0
$391$	−119.131	−	206.342i	−0.304684	−	0.527728i
$392$		0			0
$393$	95.0195	+	36.9758i	0.241780	+	0.0940860i
$394$		0			0
$395$	8.89161	+	5.13357i	0.0225104	+	0.0129964i
$396$		0			0
$397$	187.117	+	324.096i	0.471327	+	0.816362i	0.999462	−	0.0327984i	$-0.0104419\pi$
$397$	187.117	+	324.096i	0.471327	+	0.816362i	−0.528135	+	0.849160i	$0.677109\pi$
$398$		0			0
$399$	−103.680	+	441.114i	−0.259850	+	1.10555i
$400$		0			0
$401$	−618.010	−	356.808i	−1.54117	−	0.889796i	−0.998765	−	0.0496804i	$-0.984180\pi$
$401$	−618.010	−	356.808i	−1.54117	−	0.889796i	−0.542407	−	0.840116i	$-0.682487\pi$
$402$		0			0
$403$	−182.516	−	316.128i	−0.452894	−	0.784436i
$404$		0			0
$405$	−26.7229	−	308.658i	−0.0659825	−	0.762118i
$406$		0			0
$407$	57.8385	+	33.3930i	0.142109	+	0.0820468i
$408$		0			0
$409$			254.901i			0.623230i	0.950208	+	0.311615i	$0.100870\pi$
$409$			254.901i			0.623230i	−0.950208	+	0.311615i	$0.899130\pi$
$410$		0			0
$411$	−25.7389	+	20.6481i	−0.0626251	+	0.0502387i
$412$		0			0
$413$	−183.540	+	105.967i	−0.444407	+	0.256578i
$414$		0			0
$415$	250.718	+	434.256i	0.604139	+	1.04640i
$416$		0			0
$417$	94.0499	+	611.972i	0.225539	+	1.46756i
$418$		0			0
$419$	40.7422	+	70.5676i	0.0972369	+	0.168419i	0.910540	−	0.413421i	$-0.135666\pi$
$419$	40.7422	+	70.5676i	0.0972369	+	0.168419i	−0.813303	+	0.581840i	$0.802333\pi$
$420$		0			0
$421$		−	555.712i		−	1.31998i	−0.751274	−	0.659991i	$-0.770560\pi$
$421$		−	555.712i		−	1.31998i	0.751274	−	0.659991i	$-0.229440\pi$
$422$		0			0
$423$	66.7757	+	61.2442i	0.157862	+	0.144785i
$424$		0			0
$425$	−66.5033	+	115.187i	−0.156478	+	0.271029i
$426$		0			0
$427$	−238.399			−0.558313
$428$		0			0
$429$	82.1710	−	211.161i	0.191541	−	0.492217i
$430$		0			0
$431$	−44.0582	−	25.4370i	−0.102223	−	0.0590186i	0.448017	−	0.894025i	$-0.352130\pi$
$431$	−44.0582	−	25.4370i	−0.102223	−	0.0590186i	−0.550240	+	0.835007i	$0.685464\pi$
$432$		0			0
$433$	587.106	+	338.966i	1.35590	+	0.782832i	0.989069	−	0.147454i	$-0.0471079\pi$
$433$	587.106	+	338.966i	1.35590	+	0.782832i	0.366835	+	0.930286i	$0.380441\pi$
$434$		0			0
$435$	−316.363	+	48.6197i	−0.727271	+	0.111769i
$436$		0			0
$437$	−49.3446	−	349.505i	−0.112917	−	0.799783i
$438$		0			0
$439$		−	281.489i		−	0.641204i	−0.947214	−	0.320602i	$-0.896115\pi$
$439$		−	281.489i		−	0.641204i	0.947214	−	0.320602i	$-0.103885\pi$
$440$		0			0
$441$	94.1736	+	86.3725i	0.213545	+	0.195856i
$442$		0			0
$443$	432.905	+	749.814i	0.977213	+	1.69258i	0.672429	+	0.740161i	$0.265251\pi$
$443$	432.905	+	749.814i	0.977213	+	1.69258i	0.304784	+	0.952421i	$0.401416\pi$
$444$		0			0
$445$	510.097	−	294.505i	1.14629	−	0.661809i
$446$		0			0
$447$	173.557	+	67.5377i	0.388270	+	0.151091i
$448$		0			0
$449$			615.442i			1.37070i	0.728216	+	0.685348i	$0.240350\pi$
$449$			615.442i			1.37070i	−0.728216	+	0.685348i	$0.759650\pi$
$450$		0			0
$451$	−155.689	+	89.8872i	−0.345209	+	0.199307i
$452$		0			0
$453$	−227.813	+	585.429i	−0.502899	+	1.29234i
$454$		0			0
$455$	−376.054	+	217.115i	−0.826492	+	0.477175i
$456$		0			0
$457$	333.190	−	577.102i	0.729081	−	1.26280i	−0.228191	−	0.973616i	$-0.573281\pi$
$457$	333.190	−	577.102i	0.729081	−	1.26280i	0.957272	−	0.289189i	$-0.0933855\pi$
$458$		0			0
$459$	−192.581	+	287.795i	−0.419566	+	0.627005i
$460$		0			0
$461$	−404.973			−0.878466			−0.439233	−	0.898373i	$-0.644750\pi$
$461$	−404.973			−0.878466			−0.439233	+	0.898373i	$0.644750\pi$
$462$		0			0
$463$	366.950	+	635.577i	0.792549	+	1.37274i	0.924384	+	0.381464i	$0.124580\pi$
$463$	366.950	+	635.577i	0.792549	+	1.37274i	−0.131835	+	0.991272i	$0.542087\pi$
$464$		0			0
$465$	289.897	−	44.5524i	0.623435	−	0.0958116i
$466$		0			0
$467$	840.548			1.79989			0.899944	−	0.436006i	$-0.143607\pi$
$467$	840.548			1.79989			0.899944	+	0.436006i	$0.143607\pi$
$468$		0			0
$469$	334.261	+	192.986i	0.712710	+	0.411483i
$470$		0			0
$471$	−528.066	−	205.491i	−1.12116	−	0.436286i
$472$		0			0
$473$	70.4125	−	121.958i	0.148864	−	0.257839i
$474$		0			0
$475$	−155.194	+	121.408i	−0.326724	+	0.255597i
$476$		0			0
$477$	−272.405	−	60.5199i	−0.571079	−	0.126876i
$478$		0			0
$479$	283.207	+	490.530i	0.591247	+	1.02407i	0.994065	+	0.108790i	$0.0346976\pi$
$479$	283.207	+	490.530i	0.591247	+	1.02407i	−0.402817	+	0.915280i	$0.631969\pi$
$480$		0			0
$481$	−180.336			−0.374918
$482$		0			0
$483$	−412.896	−	160.674i	−0.854858	−	0.332658i
$484$		0			0
$485$	334.836	+	193.318i	0.690383	+	0.398593i
$486$		0			0
$487$			374.070i			0.768111i	0.923310	+	0.384056i	$0.125473\pi$
$487$			374.070i			0.768111i	−0.923310	+	0.384056i	$0.874527\pi$
$488$		0			0
$489$	145.523	+	946.903i	0.297594	+	1.93641i
$490$		0			0
$491$	341.737	−	591.907i	0.696003	−	1.20551i	−0.273839	−	0.961776i	$-0.588293\pi$
$491$	341.737	−	591.907i	0.696003	−	1.20551i	0.969841	−	0.243737i	$-0.0783732\pi$
$492$		0			0
$493$	309.828	+	178.879i	0.628454	+	0.362838i
$494$		0			0
$495$	134.173	+	123.058i	0.271056	+	0.248603i
$496$		0			0
$497$			354.897i			0.714079i
$498$		0			0
$499$	107.071	−	185.452i	0.214570	−	0.371647i	−0.738569	−	0.674178i	$-0.764498\pi$
$499$	107.071	−	185.452i	0.214570	−	0.371647i	0.953140	+	0.302531i	$0.0978315\pi$
$500$		0			0
$501$	−744.408	+	114.403i	−1.48584	+	0.228350i
$502$		0			0
$503$	234.118	−	405.504i	0.465443	−	0.806171i	−0.533779	−	0.845624i	$-0.679228\pi$
$503$	234.118	−	405.504i	0.465443	−	0.806171i	0.999221	+	0.0394537i	$0.0125618\pi$
$504$		0			0
$505$	−28.6453			−0.0567234
$506$		0			0
$507$	15.9230	+	103.609i	0.0314064	+	0.204358i
$508$		0			0
$509$		−	882.494i		−	1.73378i	−0.498500	−	0.866890i	$-0.666116\pi$
$509$		−	882.494i		−	1.73378i	0.498500	−	0.866890i	$-0.333884\pi$
$510$		0			0
$511$	290.370			0.568239
$512$		0			0
$513$	−424.054	+	288.699i	−0.826616	+	0.562766i
$514$		0			0
$515$			254.595i			0.494360i
$516$		0			0
$517$	−53.2455			−0.102989
$518$		0			0
$519$	338.133	−	51.9654i	0.651509	−	0.100126i
$520$		0			0
$521$		−	309.176i		−	0.593429i	−0.954966	−	0.296714i	$-0.904109\pi$
$521$		−	309.176i		−	0.593429i	0.954966	−	0.296714i	$-0.0958909\pi$
$522$		0			0
$523$	580.689	+	335.261i	1.11030	+	0.641035i	0.938908	−	0.344168i	$-0.111839\pi$
$523$	580.689	+	335.261i	1.11030	+	0.641035i	0.171396	+	0.985202i	$0.445172\pi$
$524$		0			0
$525$	37.5694	+	244.460i	0.0715608	+	0.465638i
$526$		0			0
$527$	−283.909	−	163.915i	−0.538727	−	0.311034i
$528$		0			0
$529$	−183.879			−0.347597
$530$		0			0
$531$	−234.222	−	52.0369i	−0.441096	−	0.0979979i
$532$		0			0
$533$	242.713	−	420.392i	0.455372	−	0.788727i
$534$		0			0
$535$	329.312	+	190.128i	0.615536	+	0.355380i
$536$		0			0
$537$	322.548	−	49.5702i	0.600648	−	0.0923096i
$538$		0			0
$539$	−75.0920			−0.139317
$540$		0			0
$541$	448.760	−	777.276i	0.829502	−	1.43674i	−0.0689281	−	0.997622i	$-0.521958\pi$
$541$	448.760	−	777.276i	0.829502	−	1.43674i	0.898430	−	0.439117i	$-0.144709\pi$
$542$		0			0
$543$	107.541	−	276.356i	0.198049	−	0.508943i
$544$		0			0
$545$		−	329.797i		−	0.605132i
$546$		0			0
$547$	64.6950	−	37.3517i	0.118272	−	0.0682846i	−0.439697	−	0.898146i	$-0.644914\pi$
$547$	64.6950	−	37.3517i	0.118272	−	0.0682846i	0.557969	+	0.829862i	$0.311581\pi$
$548$		0			0
$549$	−198.905	−	182.428i	−0.362304	−	0.332292i
$550$		0			0
$551$	326.562	+	417.437i	0.592672	+	0.757600i
$552$		0			0
$553$	−18.4807	−	10.6699i	−0.0334191	−	0.0192945i
$554$		0			0
$555$	52.5471	−	135.034i	0.0946795	−	0.243305i
$556$		0			0
$557$	458.732	−	794.547i	0.823577	−	1.42648i	−0.0794258	−	0.996841i	$-0.525309\pi$
$557$	458.732	−	794.547i	0.823577	−	1.42648i	0.903002	−	0.429636i	$-0.141358\pi$
$558$		0			0
$559$			380.255i			0.680242i
$560$		0			0
$561$	−30.9106	−	201.132i	−0.0550991	−	0.358523i
$562$		0			0
$563$	−206.762	+	119.374i	−0.367251	+	0.212033i	−0.672257	−	0.740318i	$-0.734675\pi$
$563$	−206.762	+	119.374i	−0.367251	+	0.212033i	0.305006	+	0.952351i	$0.401342\pi$
$564$		0			0
$565$			568.322i			1.00588i
$566$		0			0
$567$	55.5421	+	641.529i	0.0979579	+	1.13144i
$568$		0			0
$569$	−321.105	−	185.390i	−0.564333	−	0.325818i	0.190550	−	0.981678i	$-0.438973\pi$
$569$	−321.105	−	185.390i	−0.564333	−	0.325818i	−0.754883	+	0.655860i	$0.772306\pi$
$570$		0			0
$571$	−187.660	−	325.036i	−0.328651	−	0.569240i	0.653593	−	0.756846i	$-0.273261\pi$
$571$	−187.660	−	325.036i	−0.328651	−	0.569240i	−0.982244	+	0.187606i	$0.939927\pi$
$572$		0			0
$573$	232.758	+	90.5753i	0.406210	+	0.158072i
$574$		0			0
$575$	−96.3294	−	166.847i	−0.167529	−	0.290169i
$576$		0			0
$577$	646.755			1.12089			0.560446	−	0.828191i	$-0.310630\pi$
$577$	646.755			1.12089			0.560446	+	0.828191i	$0.310630\pi$
$578$		0			0
$579$	104.637	−	268.895i	0.180721	−	0.464412i
$580$		0			0
$581$	−521.103	−	902.578i	−0.896908	−	1.55349i
$582$		0			0
$583$	142.011	−	81.9903i	0.243587	−	0.140635i
$584$		0			0
$585$	−479.896	−	106.618i	−0.820335	−	0.182253i
$586$		0			0
$587$	816.083			1.39026			0.695130	−	0.718884i	$-0.255347\pi$
$587$	816.083			1.39026			0.695130	+	0.718884i	$0.255347\pi$
$588$		0			0
$589$	−299.243	−	382.517i	−0.508053	−	0.649434i
$590$		0			0
$591$	−79.3335	−	516.214i	−0.134236	−	0.873459i
$592$		0			0
$593$	329.386	−	570.514i	0.555457	−	0.962080i	−0.442410	−	0.896813i	$-0.645877\pi$
$593$	329.386	−	570.514i	0.555457	−	0.962080i	0.997868	−	0.0652676i	$-0.0207901\pi$
$594$		0			0
$595$	−194.987	+	337.728i	−0.327710	+	0.567610i
$596$		0			0
$597$	−324.449	−	126.256i	−0.543465	−	0.211484i
$598$		0			0
$599$		−	831.970i		−	1.38893i	−0.719526	−	0.694466i	$-0.755641\pi$
$599$		−	831.970i		−	1.38893i	0.719526	−	0.694466i	$-0.244359\pi$
$600$		0			0
$601$	1026.61	+	592.713i	1.70817	+	0.986212i	0.936828	+	0.349791i	$0.113747\pi$
$601$	1026.61	+	592.713i	1.70817	+	0.986212i	0.771342	+	0.636421i	$0.219586\pi$
$602$		0			0
$603$	131.209	+	416.799i	0.217594	+	0.691208i
$604$		0			0
$605$	355.819			0.588131
$606$		0			0
$607$	−120.556	+	69.6030i	−0.198609	+	0.114667i	−0.596007	−	0.802979i	$-0.703247\pi$
$607$	−120.556	+	69.6030i	−0.198609	+	0.114667i	0.397397	+	0.917647i	$0.369913\pi$
$608$		0			0
$609$	657.544	−	101.054i	1.07971	−	0.165934i
$610$		0			0
$611$	124.511	−	71.8866i	0.203783	−	0.117654i
$612$		0			0
$613$	111.885	+	193.790i	0.182520	+	0.316134i	0.942738	−	0.333534i	$-0.108241\pi$
$613$	111.885	+	193.790i	0.182520	+	0.316134i	−0.760218	+	0.649668i	$0.774908\pi$
$614$		0			0
$615$	244.064	+	304.238i	0.396852	+	0.494697i
$616$		0			0
$617$	16.8135			0.0272504			0.0136252	−	0.999907i	$-0.495663\pi$
$617$	16.8135			0.0272504			0.0136252	+	0.999907i	$0.495663\pi$
$618$		0			0
$619$	288.780	−	500.182i	0.466527	−	0.808048i	−0.532742	−	0.846278i	$-0.678838\pi$
$619$	288.780	−	500.182i	0.466527	−	0.808048i	0.999269	+	0.0382294i	$0.0121718\pi$
$620$		0			0
$621$	−221.543	−	450.013i	−0.356752	−	0.724659i
$622$		0			0
$623$	−1060.21	+	612.113i	−1.70178	+	0.982524i
$624$		0			0
$625$	129.093	−	223.596i	0.206549	−	0.357754i
$626$		0			0
$627$	68.9765	−	293.465i	0.110010	−	0.468046i
$628$		0			0
$629$	−140.258	+	80.9783i	−0.222986	+	0.128741i
$630$		0			0
$631$	482.513	−	835.738i	0.764680	−	1.32447i	−0.175735	−	0.984438i	$-0.556230\pi$
$631$	482.513	−	835.738i	0.764680	−	1.32447i	0.940415	−	0.340028i	$-0.110437\pi$
$632$		0			0
$633$	70.8467	−	182.060i	0.111922	−	0.287615i
$634$		0			0
$635$	71.6244	−	41.3523i	0.112794	−	0.0651218i
$636$		0			0
$637$	175.598	−	101.382i	0.275664	−	0.159155i
$638$		0			0
$639$	−271.575	+	296.103i	−0.425000	+	0.463386i
$640$		0			0
$641$			476.248i			0.742976i	0.928438	+	0.371488i	$0.121152\pi$
$641$			476.248i			0.742976i	−0.928438	+	0.371488i	$0.878848\pi$
$642$		0			0
$643$	−326.068	+	564.766i	−0.507104	+	0.878330i	0.492862	+	0.870107i	$0.335951\pi$
$643$	−326.068	+	564.766i	−0.507104	+	0.878330i	−0.999966	+	0.00822274i	$0.997383\pi$
$644$		0			0
$645$	−284.733	−	110.801i	−0.441447	−	0.171784i
$646$		0			0
$647$	−55.1929			−0.0853059			−0.0426529	−	0.999090i	$-0.513581\pi$
$647$	−55.1929			−0.0853059			−0.0426529	+	0.999090i	$0.513581\pi$
$648$		0			0
$649$	122.106	−	70.4978i	0.188144	−	0.108625i
$650$		0			0
$651$	−602.537	+	92.5998i	−0.925555	+	0.142242i
$652$		0			0
$653$	−616.599	−	1067.98i	−0.944256	−	1.63550i	−0.757234	−	0.653144i	$-0.773450\pi$
$653$	−616.599	−	1067.98i	−0.944256	−	1.63550i	−0.187022	−	0.982356i	$-0.559884\pi$
$654$		0			0
$655$	64.9971	+	112.578i	0.0992322	+	0.171875i
$656$		0			0
$657$	242.266	+	222.197i	0.368746	+	0.338200i
$658$		0			0
$659$	−1046.04	+	603.931i	−1.58731	+	0.916436i	−0.593565	+	0.804786i	$0.702280\pi$
$659$	−1046.04	+	603.931i	−1.58731	+	0.916436i	−0.993748	+	0.111650i	$0.964387\pi$
$660$		0			0
$661$			934.971i			1.41448i	0.706974	+	0.707240i	$0.250060\pi$
$661$			934.971i			1.41448i	−0.706974	+	0.707240i	$0.749940\pi$
$662$		0			0
$663$	343.830	+	428.602i	0.518597	+	0.646458i
$664$		0			0
$665$	−455.028	+	355.969i	−0.684252	+	0.535292i
$666$		0			0
$667$	−448.783	+	259.105i	−0.672838	+	0.388463i
$668$		0			0
$669$	821.220	−	126.208i	1.22753	−	0.188651i
$670$		0			0
$671$	158.603			0.236368
$672$		0			0
$673$	−371.470	−	214.468i	−0.551961	−	0.318675i	0.197952	−	0.980212i	$-0.436571\pi$
$673$	−371.470	−	214.468i	−0.551961	−	0.318675i	−0.749913	+	0.661537i	$0.769904\pi$
$674$		0			0
$675$	−155.721	+	232.711i	−0.230697	+	0.344757i
$676$		0			0
$677$	−754.793	−	435.780i	−1.11491	−	0.643693i	−0.174813	−	0.984602i	$-0.555932\pi$
$677$	−754.793	−	435.780i	−1.11491	−	0.643693i	−0.940096	+	0.340909i	$0.889265\pi$
$678$		0			0
$679$	−695.939	−	401.801i	−1.02495	−	0.591753i
$680$		0			0
$681$	−392.745	+	1009.27i	−0.576719	+	1.48204i
$682$		0			0
$683$		−	20.0977i		−	0.0294257i	−0.999892	−	0.0147128i	$-0.995317\pi$
$683$		−	20.0977i		−	0.0294257i	0.999892	−	0.0147128i	$-0.00468341\pi$
$684$		0			0
$685$	−42.0701			−0.0614162
$686$		0			0
$687$	228.700	−	183.466i	0.332896	−	0.267054i
$688$		0			0
$689$	−221.390	+	383.458i	−0.321321	+	0.556543i
$690$		0			0
$691$	330.331	−	572.150i	0.478048	−	0.828004i	−0.521635	−	0.853169i	$-0.674678\pi$
$691$	330.331	−	572.150i	0.478048	−	0.828004i	0.999683	+	0.0251651i	$0.00801113\pi$
$692$		0			0
$693$	−278.871	−	255.771i	−0.402412	−	0.369077i
$694$		0			0
$695$	−394.696	+	683.634i	−0.567908	+	0.983646i
$696$		0			0
$697$		−	435.954i		−	0.625472i
$698$		0			0
$699$	−506.216	+	406.093i	−0.724200	+	0.580963i
$700$		0			0
$701$	−102.728	−	177.930i	−0.146545	−	0.253823i	0.783403	−	0.621514i	$-0.213482\pi$
$701$	−102.728	−	177.930i	−0.146545	−	0.253823i	−0.929948	+	0.367690i	$0.880149\pi$
$702$		0			0
$703$	−237.572	+	33.5414i	−0.337941	+	0.0477119i
$704$		0			0
$705$	17.5476	+	114.180i	0.0248902	+	0.161958i
$706$		0			0
$707$	59.5378			0.0842119
$708$		0			0
$709$	68.1450	+	118.031i	0.0961143	+	0.166475i	0.910073	−	0.414448i	$-0.136025\pi$
$709$	68.1450	+	118.031i	0.0961143	+	0.166475i	−0.813959	+	0.580923i	$0.802692\pi$
$710$		0			0
$711$	−7.25433	−	23.0441i	−0.0102030	−	0.0324109i
$712$		0			0
$713$	411.240	−	237.429i	0.576774	−	0.333000i
$714$		0			0
$715$	250.182	−	144.442i	0.349904	−	0.202017i
$716$		0			0
$717$	−445.930	+	357.731i	−0.621939	+	0.498928i
$718$		0			0
$719$	−59.4121	−	102.905i	−0.0826316	−	0.143122i	0.821748	−	0.569851i	$-0.192999\pi$
$719$	−59.4121	−	102.905i	−0.0826316	−	0.143122i	−0.904380	+	0.426729i	$0.859666\pi$
$720$		0			0
$721$		−	529.163i		−	0.733929i
$722$		0			0
$723$	735.406	+	916.721i	1.01716	+	1.26794i
$724$		0			0
$725$	250.526	+	144.641i	0.345554	+	0.199505i
$726$		0			0
$727$	−367.189			−0.505074			−0.252537	−	0.967587i	$-0.581265\pi$
$727$	−367.189			−0.505074			−0.252537	+	0.967587i	$0.581265\pi$
$728$		0			0
$729$	−444.571	+	577.752i	−0.609837	+	0.792527i
$730$		0			0
$731$	170.750	+	295.749i	0.233585	+	0.404581i
$732$		0			0
$733$	−8.02715	−	13.9034i	−0.0109511	−	0.0189678i	0.860498	−	0.509454i	$-0.170153\pi$
$733$	−8.02715	−	13.9034i	−0.0109511	−	0.0189678i	−0.871449	+	0.490486i	$0.836819\pi$
$734$		0			0
$735$	24.7473	+	161.028i	0.0336698	+	0.219086i
$736$		0			0
$737$	−222.378	−	128.390i	−0.301733	−	0.174206i
$738$		0			0
$739$	−290.683	−	503.478i	−0.393347	−	0.681296i	0.599542	−	0.800343i	$-0.295349\pi$
$739$	−290.683	−	503.478i	−0.393347	−	0.681296i	−0.992889	+	0.119047i	$0.962016\pi$
$740$		0			0
$741$	234.909	+	779.375i	0.317016	+	1.05179i
$742$		0			0
$743$	−673.469	−	388.827i	−0.906418	−	0.523321i	−0.0271413	−	0.999632i	$-0.508640\pi$
$743$	−673.469	−	388.827i	−0.906418	−	0.523321i	−0.879277	+	0.476311i	$0.841974\pi$
$744$		0			0
$745$	118.720	+	205.628i	0.159355	+	0.276011i
$746$		0			0
$747$	255.897	−	1151.81i	0.342566	−	1.54192i
$748$		0			0
$749$	−684.458	−	395.172i	−0.913829	−	0.527599i
$750$		0			0
$751$		−	746.926i		−	0.994575i	−0.867586	−	0.497287i	$-0.834329\pi$
$751$		−	746.926i		−	0.994575i	0.867586	−	0.497287i	$-0.165671\pi$
$752$		0			0
$753$	483.874	+	188.294i	0.642594	+	0.250058i
$754$		0			0
$755$	−693.610	+	400.456i	−0.918689	+	0.530405i
$756$		0			0
$757$	271.640	+	470.495i	0.358838	+	0.621526i	0.987767	−	0.155937i	$-0.0498397\pi$
$757$	271.640	+	470.495i	0.358838	+	0.621526i	−0.628929	+	0.777463i	$0.716506\pi$
$758$		0			0
$759$	274.692	+	106.893i	0.361913	+	0.140835i
$760$		0			0
$761$	−240.238	−	416.105i	−0.315688	−	0.546787i	0.663896	−	0.747825i	$-0.268902\pi$
$761$	−240.238	−	416.105i	−0.315688	−	0.546787i	−0.979583	+	0.201038i	$0.935569\pi$
$762$		0			0
$763$			685.465i			0.898382i
$764$		0			0
$765$	−421.122	+	132.570i	−0.550486	+	0.173294i
$766$		0			0
$767$	−190.358	+	329.709i	−0.248185	+	0.429869i
$768$		0			0
$769$	572.420			0.744369			0.372184	−	0.928159i	$-0.378609\pi$
$769$	572.420			0.744369			0.372184	+	0.928159i	$0.378609\pi$
$770$		0			0
$771$	804.590	−	123.652i	1.04357	−	0.160379i
$772$		0			0
$773$	159.458	+	92.0633i	0.206285	+	0.119099i	0.599584	−	0.800312i	$-0.295333\pi$
$773$	159.458	+	92.0633i	0.206285	+	0.119099i	−0.393299	+	0.919411i	$0.628666\pi$
$774$		0			0
$775$	−229.568	−	132.541i	−0.296217	−	0.171021i
$776$		0			0
$777$	−109.216	+	280.662i	−0.140562	+	0.361212i
$778$		0			0
$779$	241.558	−	598.963i	0.310087	−	0.768887i
$780$		0			0
$781$		−	236.106i		−	0.302313i
$782$		0			0
$783$	625.940	+	418.854i	0.799413	+	0.534935i
$784$		0			0
$785$	−361.218	−	625.647i	−0.460150	−	0.797003i
$786$		0			0
$787$	−320.809	+	185.219i	−0.407635	+	0.235348i	−0.689773	−	0.724026i	$-0.742290\pi$
$787$	−320.809	+	185.219i	−0.407635	+	0.235348i	0.282138	+	0.959374i	$0.408956\pi$
$788$		0			0
$789$	−150.330	−	978.178i	−0.190532	−	1.23977i
$790$		0			0
$791$		−	1181.23i		−	1.49333i
$792$		0			0
$793$	−370.883	+	214.129i	−0.467696	+	0.270024i
$794$		0			0
$795$	−222.622	−	277.510i	−0.280028	−	0.349069i
$796$		0			0
$797$	917.008	−	529.435i	1.15057	−	0.664285i	0.201548	−	0.979479i	$-0.435403\pi$
$797$	917.008	−	529.435i	1.15057	−	0.664285i	0.949027	+	0.315194i	$0.102070\pi$
$798$		0			0
$799$	64.5602	−	111.822i	0.0808013	−	0.139952i
$800$		0			0
$801$	−1352.97	−	300.589i	−1.68911	−	0.375267i
$802$		0			0
$803$	−193.178			−0.240570
$804$		0			0
$805$	−282.437	−	489.196i	−0.350854	−	0.607696i
$806$		0			0
$807$	−247.451	−	308.460i	−0.306631	−	0.382231i
$808$		0			0
$809$	−867.254			−1.07201			−0.536004	−	0.844216i	$-0.680067\pi$
$809$	−867.254			−1.07201			−0.536004	+	0.844216i	$0.680067\pi$
$810$		0			0
$811$	341.111	+	196.940i	0.420605	+	0.242837i	0.695336	−	0.718685i	$-0.255255\pi$
$811$	341.111	+	196.940i	0.420605	+	0.242837i	−0.274731	+	0.961521i	$0.588589\pi$
$812$		0			0
$813$	−1076.25	+	863.378i	−1.32379	+	1.06197i
$814$		0			0
$815$	−610.713	+	1057.79i	−0.749341	+	1.29790i
$816$		0			0
$817$	70.7254	+	500.944i	0.0865671	+	0.613151i
$818$		0			0
$819$	997.439	+	221.600i	1.21787	+	0.270574i
$820$		0			0
$821$	−715.769	−	1239.75i	−0.871826	−	1.51005i	−0.860106	−	0.510115i	$-0.829603\pi$
$821$	−715.769	−	1239.75i	−0.871826	−	1.51005i	−0.0117199	−	0.999931i	$-0.503731\pi$
$822$		0			0
$823$	564.047			0.685355			0.342678	−	0.939453i	$-0.388666\pi$
$823$	564.047			0.685355			0.342678	+	0.939453i	$0.388666\pi$
$824$		0			0
$825$	−24.9942	−	162.635i	−0.0302961	−	0.197133i
$826$		0			0
$827$	1306.09	+	754.071i	1.57931	+	0.911816i	0.994955	+	0.100318i	$0.0319859\pi$
$827$	1306.09	+	754.071i	1.57931	+	0.911816i	0.584355	+	0.811498i	$0.301347\pi$
$828$		0			0
$829$		−	26.6469i		−	0.0321435i	−0.999871	−	0.0160717i	$-0.994884\pi$
$829$		−	26.6469i		−	0.0321435i	0.999871	−	0.0160717i	$-0.00511601\pi$
$830$		0			0
$831$	800.331	+	311.440i	0.963094	+	0.374777i
$832$		0			0
$833$	91.0491	−	157.702i	0.109303	−	0.189318i
$834$		0			0
$835$	−831.578	−	480.112i	−0.995902	−	0.574984i
$836$		0			0
$837$	−573.577	−	383.815i	−0.685277	−	0.458560i
$838$		0			0
$839$			12.7710i			0.0152217i	0.999971	+	0.00761083i	$0.00242263\pi$
$839$			12.7710i			0.0152217i	−0.999971	+	0.00761083i	$0.997577\pi$
$840$		0			0
$841$	−31.4463	+	54.4666i	−0.0373915	+	0.0647640i
$842$		0			0
$843$	−249.261	−	310.717i	−0.295683	−	0.368585i
$844$		0			0
$845$	−66.8237	+	115.742i	−0.0790813	+	0.136973i
$846$		0			0
$847$	−739.552			−0.873143
$848$		0			0
$849$	−928.748	−	361.412i	−1.09393	−	0.425691i
$850$		0			0
$851$		−	234.592i		−	0.275667i
$852$		0			0
$853$	−317.139			−0.371793			−0.185896	−	0.982569i	$-0.559519\pi$
$853$	−317.139			−0.371793			−0.185896	+	0.982569i	$0.559519\pi$
$854$		0			0
$855$	−652.041	−	51.1995i	−0.762621	−	0.0598825i
$856$		0			0
$857$		−	784.517i		−	0.915422i	−0.889101	−	0.457711i	$-0.848669\pi$
$857$		−	784.517i		−	0.915422i	0.889101	−	0.457711i	$-0.151331\pi$
$858$		0			0
$859$	−1449.79			−1.68776			−0.843882	−	0.536529i	$-0.819735\pi$
$859$	−1449.79			−1.68776			−0.843882	+	0.536529i	$0.819735\pi$
$860$		0			0
$861$	−507.274	−	632.343i	−0.589169	−	0.734429i
$862$		0			0
$863$		−	1171.27i		−	1.35721i	−0.734504	−	0.678604i	$-0.762585\pi$
$863$		−	1171.27i		−	1.35721i	0.734504	−	0.678604i	$-0.237415\pi$
$864$		0			0
$865$	377.728	+	218.082i	0.436680	+	0.252117i
$866$		0			0
$867$	−348.101	−	135.460i	−0.401501	−	0.156240i
$868$		0			0
$869$	12.2949	+	7.09846i	0.0141483	+	0.00816854i
$870$		0			0
$871$	693.355			0.796045
$872$		0			0
$873$	−273.180	−	867.784i	−0.312921	−	0.994026i
$874$		0			0
$875$	−537.747	+	931.406i	−0.614568	+	1.06446i
$876$		0			0
$877$	44.1609	+	25.4963i	0.0503545	+	0.0290722i	0.524966	−	0.851123i	$-0.324078\pi$
$877$	44.1609	+	25.4963i	0.0503545	+	0.0290722i	−0.474611	+	0.880195i	$0.657411\pi$
$878$		0			0
$879$	−245.227	−	305.688i	−0.278984	−	0.347768i
$880$		0			0
$881$	−328.254			−0.372592			−0.186296	−	0.982494i	$-0.559648\pi$
$881$	−328.254			−0.372592			−0.186296	+	0.982494i	$0.559648\pi$
$882$		0			0
$883$	477.918	−	827.779i	0.541244	−	0.937462i	−0.457589	−	0.889164i	$-0.651287\pi$
$883$	477.918	−	827.779i	0.541244	−	0.937462i	0.998833	−	0.0482983i	$-0.0153798\pi$
$884$		0			0
$885$	−191.417	−	238.611i	−0.216291	−	0.269617i
$886$		0			0
$887$			126.546i			0.142667i	0.997453	+	0.0713335i	$0.0227255\pi$
$887$			126.546i			0.142667i	−0.997453	+	0.0713335i	$0.977275\pi$
$888$		0			0
$889$	−148.867	+	85.9487i	−0.167455	+	0.0966802i
$890$		0			0
$891$	−36.9511	−	426.797i	−0.0414715	−	0.479009i
$892$		0			0
$893$	150.659	−	117.861i	0.168712	−	0.131983i
$894$		0			0
$895$	360.318	+	208.030i	0.402590	+	0.232436i
$896$		0			0
$897$	−786.668	+	120.898i	−0.876998	+	0.134780i
$898$		0			0
$899$	−356.507	+	617.489i	−0.396560	+	0.686862i
$900$		0			0
$901$			397.653i			0.441347i
$902$		0			0
$903$	591.803	+	230.293i	0.655374	+	0.255032i
$904$		0			0
$905$	327.424	−	189.038i	0.361794	−	0.208882i
$906$		0			0
$907$			49.7158i			0.0548135i	0.999624	+	0.0274067i	$0.00872493\pi$
$907$			49.7158i			0.0548135i	−0.999624	+	0.0274067i	$0.991275\pi$
$908$		0			0
$909$	49.6745	+	45.5597i	0.0546475	+	0.0501206i
$910$		0			0
$911$	−135.218	−	78.0681i	−0.148428	−	0.0856950i	0.423947	−	0.905687i	$-0.360644\pi$
$911$	−135.218	−	78.0681i	−0.148428	−	0.0856950i	−0.572375	+	0.819992i	$0.693978\pi$
$912$		0			0
$913$	346.680	+	600.468i	0.379716	+	0.657687i
$914$		0			0
$915$	−52.2691	−	340.109i	−0.0571247	−	0.371704i
$916$		0			0
$917$	−135.093	−	233.988i	−0.147321	−	0.255167i
$918$		0			0
$919$	986.039			1.07295			0.536474	−	0.843917i	$-0.319756\pi$
$919$	986.039			1.07295			0.536474	+	0.843917i	$0.319756\pi$
$920$		0			0
$921$	478.368	+	596.311i	0.519401	+	0.647460i
$922$		0			0
$923$	318.767	+	552.121i	0.345360	+	0.598180i
$924$		0			0
$925$	−113.413	+	65.4789i	−0.122608	+	0.0707880i
$926$		0			0
$927$	404.927	−	441.499i	0.436814	−	0.476267i
$928$		0			0
$929$	1497.22			1.61164			0.805822	−	0.592158i	$-0.201724\pi$
$929$	1497.22			1.61164			0.805822	+	0.592158i	$0.201724\pi$
$930$		0			0
$931$	212.475	−	166.219i	0.228222	−	0.178538i
$932$		0			0
$933$	−260.333	+	208.843i	−0.279028	+	0.223840i
$934$		0			0
$935$	129.721	−	224.684i	0.138739	−	0.240304i
$936$		0			0
$937$	−195.810	+	339.153i	−0.208975	+	0.361956i	−0.951392	−	0.307982i	$-0.900346\pi$
$937$	−195.810	+	339.153i	−0.208975	+	0.361956i	0.742417	+	0.669938i	$0.233680\pi$
$938$		0			0
$939$	−851.424	+	683.024i	−0.906735	+	0.727395i
$940$		0			0
$941$			286.094i			0.304032i	0.988378	+	0.152016i	$0.0485765\pi$
$941$			286.094i			0.304032i	−0.988378	+	0.152016i	$0.951424\pi$
$942$		0			0
$943$	546.873	+	315.737i	0.579929	+	0.334822i
$944$		0			0
$945$	−456.572	+	682.306i	−0.483145	+	0.722017i
$946$		0			0
$947$	1277.25			1.34873			0.674366	−	0.738397i	$-0.264417\pi$
$947$	1277.25			1.34873			0.674366	+	0.738397i	$0.264417\pi$
$948$		0			0
$949$	451.734	−	260.809i	0.476011	−	0.274825i
$950$		0			0
$951$	587.583	+	732.452i	0.617858	+	0.770192i
$952$		0			0
$953$	−917.051	+	529.460i	−0.962278	+	0.555572i	−0.896873	−	0.442287i	$-0.854167\pi$
$953$	−917.051	+	529.460i	−0.962278	+	0.555572i	−0.0654048	+	0.997859i	$0.520834\pi$
$954$		0			0
$955$	159.216	+	275.770i	0.166718	+	0.288764i
$956$		0			0
$957$	−437.451	+	67.2290i	−0.457107	+	0.0702498i
$958$		0			0
$959$	87.4405			0.0911788
$960$		0			0
$961$	−153.817	+	266.418i	−0.160059	+	0.277230i
$962$		0			0
$963$	−268.673	−	853.468i	−0.278996	−	0.886260i
$964$		0			0
$965$	318.584	−	183.934i	0.330138	−	0.190606i
$966$		0			0
$967$	−869.770	+	1506.49i	−0.899452	+	1.55790i	−0.0712552	+	0.997458i	$0.522700\pi$
$967$	−869.770	+	1506.49i	−0.899452	+	1.55790i	−0.828196	+	0.560438i	$0.810633\pi$
$968$		0			0
$969$	532.676	+	500.685i	0.549717	+	0.516703i
$970$		0			0
$971$	1410.32	−	814.249i	1.45244	−	0.838567i	0.453821	−	0.891093i	$-0.350060\pi$
$971$	1410.32	−	814.249i	1.45244	−	0.838567i	0.998620	+	0.0525254i	$0.0167271\pi$
$972$		0			0
$973$	820.355	−	1420.90i	0.843119	−	1.46033i
$974$		0			0
$975$	278.020	+	346.566i	0.285149	+	0.355453i
$976$		0			0
$977$	1663.68	−	960.528i	1.70285	−	0.983141i	0.759999	−	0.649924i	$-0.225199\pi$
$977$	1663.68	−	960.528i	1.70285	−	0.983141i	0.942850	−	0.333217i	$-0.108134\pi$
$978$		0			0
$979$	705.338	−	407.227i	0.720468	−	0.415962i
$980$		0			0
$981$	−524.533	+	571.908i	−0.534692	+	0.582985i
$982$		0			0
$983$			129.779i			0.132023i	0.997819	+	0.0660117i	$0.0210275\pi$
$983$			129.779i			0.132023i	−0.997819	+	0.0660117i	$0.978973\pi$
$984$		0			0
$985$	332.936	−	576.663i	0.338006	−	0.585444i
$986$		0			0
$987$	−36.4717	−	237.317i	−0.0369521	−	0.240443i
$988$		0			0
$989$	−494.661			−0.500163
$990$		0			0
$991$	−880.021	+	508.080i	−0.888013	+	0.512695i	−0.873292	−	0.487197i	$-0.838019\pi$
$991$	−880.021	+	508.080i	−0.888013	+	0.512695i	−0.0147211	+	0.999892i	$0.504686\pi$
$992$		0			0
$993$	208.040	−	534.616i	0.209507	−	0.538385i
$994$		0			0
$995$	−221.936	−	384.404i	−0.223051	−	0.386336i
$996$		0			0
$997$	−889.798	−	1541.18i	−0.892475	−	1.54581i	−0.836898	−	0.547358i	$-0.815634\pi$
$997$	−889.798	−	1541.18i	−0.892475	−	1.54581i	−0.0555770	−	0.998454i	$-0.517700\pi$
$998$		0			0
$999$	−305.892	+	150.591i	−0.306198	+	0.150742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.601.18	yes	80
3.2	odd	2		2052.3.s.a.829.12		80
9.4	even	3		684.3.bl.a.373.33	yes	80
9.5	odd	6		2052.3.bl.a.145.29		80
19.8	odd	6		684.3.bl.a.673.33	yes	80
57.8	even	6		2052.3.bl.a.1585.29		80
171.103	odd	6	inner	684.3.s.a.445.18	✓	80
171.122	even	6		2052.3.s.a.901.12		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.18	✓	80	171.103	odd	6	inner
684.3.s.a.601.18	yes	80	1.1	even	1	trivial
684.3.bl.a.373.33	yes	80	9.4	even	3
684.3.bl.a.673.33	yes	80	19.8	odd	6
2052.3.s.a.829.12		80	3.2	odd	2
2052.3.s.a.901.12		80	171.122	even	6
2052.3.bl.a.145.29		80	9.5	odd	6
2052.3.bl.a.1585.29		80	57.8	even	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.455700 - 2.96519i) q^{3} +(1.91242 - 3.31241i) q^{5} +(-3.97487 + 6.88467i) q^{7} +(-8.58467 + 2.70247i) q^{9} +O(q^{10})\)	\(q+(-0.455700 - 2.96519i) q^{3} +(1.91242 - 3.31241i) q^{5} +(-3.97487 + 6.88467i) q^{7} +(-8.58467 + 2.70247i) q^{9} +(2.64440 - 4.58024i) q^{11} +14.2808i q^{13} +(-10.6934 - 4.16122i) q^{15} +(6.41269 + 11.1071i) q^{17} +(2.65616 + 18.8134i) q^{19} +(22.2257 + 8.64888i) q^{21} -18.5774 q^{23} +(5.18529 + 8.98119i) q^{25} +(11.9254 + 24.2237i) q^{27} +(24.1574 - 13.9473i) q^{29} +(-22.1365 + 12.7805i) q^{31} +(-14.7863 - 5.75394i) q^{33} +(15.2032 + 26.3328i) q^{35} +12.6278i q^{37} +(42.3453 - 6.50777i) q^{39} +(-29.4375 - 16.9957i) q^{41} +26.6270 q^{43} +(-7.46582 + 33.6042i) q^{45} +(-5.03379 - 8.71877i) q^{47} +(-7.09914 - 12.2961i) q^{49} +(30.0124 - 24.0763i) q^{51} +(26.8513 + 15.5026i) q^{53} +(-10.1144 - 17.5187i) q^{55} +(54.5749 - 16.4493i) q^{57} +(23.0876 + 13.3296i) q^{59} +(14.9942 + 25.9707i) q^{61} +(15.5173 - 69.8446i) q^{63} +(47.3040 + 27.3110i) q^{65} -48.5515i q^{67} +(8.46574 + 55.0856i) q^{69} +(38.6617 - 22.3213i) q^{71} +(-18.2629 - 31.6322i) q^{73} +(24.2680 - 19.4681i) q^{75} +(21.0223 + 36.4117i) q^{77} +2.68433i q^{79} +(66.3933 - 46.3997i) q^{81} +(-65.5498 + 113.536i) q^{83} +49.0551 q^{85} +(-52.3649 - 65.2755i) q^{87} +(133.364 + 76.9979i) q^{89} +(-98.3188 - 56.7644i) q^{91} +(47.9843 + 59.8148i) q^{93} +(67.3975 + 27.1809i) q^{95} +101.085i q^{97} +(-10.3234 + 46.4663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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