LMFDB - Embedded newform 684.3.bl.a.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(373,684)]

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, 5]))

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

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

chi := DirichletCharacter("684.373");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.bl (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			373.4
Character	$\chi$	$=$	684.373
Dual form			684.3.bl.a.673.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.85833 + 0.911006i) q^{3} +4.10591 q^{5} +(-6.48935 - 11.2399i) q^{7} +(7.34014 - 5.20792i) q^{9} +O(q^{10})$	\(q+(-2.85833 + 0.911006i) q^{3} +4.10591 q^{5} +(-6.48935 - 11.2399i) q^{7} +(7.34014 - 5.20792i) q^{9} +(-7.93892 - 13.7506i) q^{11} +(-0.338148 + 0.195230i) q^{13} +(-11.7360 + 3.74051i) q^{15} +(7.48023 + 12.9561i) q^{17} +(-9.33801 + 16.5469i) q^{19} +(28.7883 + 26.2155i) q^{21} +(9.34185 + 16.1806i) q^{23} -8.14153 q^{25} +(-16.2361 + 21.5729i) q^{27} +15.2452i q^{29} +(-12.7235 - 7.34592i) q^{31} +(35.2190 + 32.0714i) q^{33} +(-26.6447 - 46.1499i) q^{35} -35.7838i q^{37} +(0.788684 - 0.866087i) q^{39} -22.8900i q^{41} +(-8.04931 + 13.9418i) q^{43} +(30.1379 - 21.3832i) q^{45} -42.9710 q^{47} +(-59.7232 + 103.444i) q^{49} +(-33.1841 - 30.2184i) q^{51} +(17.6872 + 10.2117i) q^{53} +(-32.5965 - 56.4588i) q^{55} +(11.6168 - 55.8037i) q^{57} +69.4443i q^{59} -76.0888 q^{61} +(-106.169 - 48.7062i) q^{63} +(-1.38840 + 0.801596i) q^{65} +(-38.8408 + 22.4248i) q^{67} +(-41.4427 - 37.7389i) q^{69} +(20.3029 - 11.7219i) q^{71} +(33.0816 + 57.2991i) q^{73} +(23.2712 - 7.41698i) q^{75} +(-103.037 + 178.465i) q^{77} +(104.672 + 60.4325i) q^{79} +(26.7552 - 76.4536i) q^{81} +(-65.1021 - 112.760i) q^{83} +(30.7131 + 53.1967i) q^{85} +(-13.8885 - 43.5758i) q^{87} +(-113.522 - 65.5419i) q^{89} +(4.38872 + 2.53383i) q^{91} +(43.0602 + 9.40590i) q^{93} +(-38.3410 + 67.9402i) q^{95} +(124.988 + 72.1619i) q^{97} +(-129.885 - 59.5861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.85833	+	0.911006i	−0.952778	+	0.303669i
$3$	−2.85833	+	0.911006i	−0.952778	+	0.303669i
$4$		0			0
$5$	4.10591			0.821181			0.410591	−	0.911820i	$-0.365323\pi$
$5$	4.10591			0.821181			0.410591	+	0.911820i	$0.365323\pi$
$6$		0			0
$7$	−6.48935	−	11.2399i	−0.927049	−	1.60570i	−0.788231	−	0.615379i	$-0.789003\pi$
$7$	−6.48935	−	11.2399i	−0.927049	−	1.60570i	−0.138818	−	0.990318i	$-0.544330\pi$
$8$		0			0
$9$	7.34014	−	5.20792i	0.815571	−	0.578658i
$10$		0			0
$11$	−7.93892	−	13.7506i	−0.721720	−	1.25006i	−0.960310	−	0.278936i	$-0.910018\pi$
$11$	−7.93892	−	13.7506i	−0.721720	−	1.25006i	0.238590	−	0.971120i	$-0.423315\pi$
$12$		0			0
$13$	−0.338148	+	0.195230i	−0.0260114	+	0.0150177i	−0.512949	−	0.858419i	$-0.671447\pi$
$13$	−0.338148	+	0.195230i	−0.0260114	+	0.0150177i	0.486938	+	0.873437i	$0.338114\pi$
$14$		0			0
$15$	−11.7360	+	3.74051i	−0.782403	+	0.249367i
$16$		0			0
$17$	7.48023	+	12.9561i	0.440014	+	0.762126i	0.997690	−	0.0679325i	$-0.0216402\pi$
$17$	7.48023	+	12.9561i	0.440014	+	0.762126i	−0.557676	+	0.830059i	$0.688307\pi$
$18$		0			0
$19$	−9.33801	+	16.5469i	−0.491474	+	0.870892i
$19$	−9.33801	+	16.5469i	−0.491474	+	0.870892i
$20$		0			0
$21$	28.7883	+	26.2155i	1.37087	+	1.24836i
$22$		0			0
$23$	9.34185	+	16.1806i	0.406167	+	0.703503i	0.994457	−	0.105148i	$-0.0335317\pi$
$23$	9.34185	+	16.1806i	0.406167	+	0.703503i	−0.588289	+	0.808651i	$0.700198\pi$
$24$		0			0
$25$	−8.14153			−0.325661
$26$		0			0
$27$	−16.2361	+	21.5729i	−0.601337	+	0.798995i
$28$		0			0
$29$			15.2452i			0.525696i	0.964837	+	0.262848i	$0.0846618\pi$
$29$			15.2452i			0.525696i	−0.964837	+	0.262848i	$0.915338\pi$
$30$		0			0
$31$	−12.7235	−	7.34592i	−0.410436	−	0.236965i	0.280541	−	0.959842i	$-0.409486\pi$
$31$	−12.7235	−	7.34592i	−0.410436	−	0.236965i	−0.690977	+	0.722877i	$0.742819\pi$
$32$		0			0
$33$	35.2190	+	32.0714i	1.06724	+	0.971862i
$34$		0			0
$35$	−26.6447	−	46.1499i	−0.761276	−	1.31857i
$36$		0			0
$37$		−	35.7838i		−	0.967131i	−0.875308	−	0.483565i	$-0.839342\pi$
$37$		−	35.7838i		−	0.967131i	0.875308	−	0.483565i	$-0.160658\pi$
$38$		0			0
$39$	0.788684	−	0.866087i	0.0202227	−	0.0222074i
$40$		0			0
$41$		−	22.8900i		−	0.558293i	−0.960249	−	0.279146i	$-0.909949\pi$
$41$		−	22.8900i		−	0.558293i	0.960249	−	0.279146i	$-0.0900514\pi$
$42$		0			0
$43$	−8.04931	+	13.9418i	−0.187193	+	0.324228i	−0.944313	−	0.329047i	$-0.893272\pi$
$43$	−8.04931	+	13.9418i	−0.187193	+	0.324228i	0.757120	+	0.653276i	$0.226606\pi$
$44$		0			0
$45$	30.1379	−	21.3832i	0.669731	−	0.475183i
$46$		0			0
$47$	−42.9710			−0.914277			−0.457139	−	0.889395i	$-0.651126\pi$
$47$	−42.9710			−0.914277			−0.457139	+	0.889395i	$0.651126\pi$
$48$		0			0
$49$	−59.7232	+	103.444i	−1.21884	+	2.11110i
$50$		0			0
$51$	−33.1841	−	30.2184i	−0.650669	−	0.592518i
$52$		0			0
$53$	17.6872	+	10.2117i	0.333720	+	0.192674i	0.657492	−	0.753462i	$-0.271617\pi$
$53$	17.6872	+	10.2117i	0.333720	+	0.192674i	−0.323771	+	0.946135i	$0.604951\pi$
$54$		0			0
$55$	−32.5965	−	56.4588i	−0.592663	−	1.02652i
$56$		0			0
$57$	11.6168	−	55.8037i	0.203803	−	0.979012i
$58$		0			0
$59$			69.4443i			1.17702i	0.808489	+	0.588511i	$0.200286\pi$
$59$			69.4443i			1.17702i	−0.808489	+	0.588511i	$0.799714\pi$
$60$		0			0
$61$	−76.0888			−1.24736			−0.623679	−	0.781681i	$-0.714363\pi$
$61$	−76.0888			−1.24736			−0.623679	+	0.781681i	$0.714363\pi$
$62$		0			0
$63$	−106.169	−	48.7062i	−1.68522	−	0.773115i
$64$		0			0
$65$	−1.38840	+	0.801596i	−0.0213601	+	0.0123322i
$66$		0			0
$67$	−38.8408	+	22.4248i	−0.579714	+	0.334698i	−0.761020	−	0.648729i	$-0.775301\pi$
$67$	−38.8408	+	22.4248i	−0.579714	+	0.334698i	0.181306	+	0.983427i	$0.441968\pi$
$68$		0			0
$69$	−41.4427	−	37.7389i	−0.600619	−	0.546941i
$70$		0			0
$71$	20.3029	−	11.7219i	0.285957	−	0.165097i	−0.350160	−	0.936690i	$-0.613873\pi$
$71$	20.3029	−	11.7219i	0.285957	−	0.165097i	0.636117	+	0.771593i	$0.280540\pi$
$72$		0			0
$73$	33.0816	+	57.2991i	0.453173	+	0.784919i	0.998581	−	0.0532517i	$-0.0169586\pi$
$73$	33.0816	+	57.2991i	0.453173	+	0.784919i	−0.545408	+	0.838171i	$0.683625\pi$
$74$		0			0
$75$	23.2712	−	7.41698i	0.310283	−	0.0988931i
$76$		0			0
$77$	−103.037	+	178.465i	−1.33814	+	2.31773i
$78$		0			0
$79$	104.672	+	60.4325i	1.32496	+	0.764968i	0.984516	−	0.175296i	$-0.0560882\pi$
$79$	104.672	+	60.4325i	1.32496	+	0.764968i	0.340447	+	0.940264i	$0.389421\pi$
$80$		0			0
$81$	26.7552	−	76.4536i	0.330311	−	0.943872i
$82$		0			0
$83$	−65.1021	−	112.760i	−0.784363	−	1.35856i	−0.929379	−	0.369127i	$-0.879657\pi$
$83$	−65.1021	−	112.760i	−0.784363	−	1.35856i	0.145016	−	0.989429i	$-0.453677\pi$
$84$		0			0
$85$	30.7131	+	53.1967i	0.361331	+	0.625844i
$86$		0			0
$87$	−13.8885	−	43.5758i	−0.159637	−	0.500872i
$88$		0			0
$89$	−113.522	−	65.5419i	−1.27553	−	0.736426i	−0.299505	−	0.954095i	$-0.596821\pi$
$89$	−113.522	−	65.5419i	−1.27553	−	0.736426i	−0.976023	+	0.217669i	$0.930155\pi$
$90$		0			0
$91$	4.38872	+	2.53383i	0.0482277	+	0.0278443i
$92$		0			0
$93$	43.0602	+	9.40590i	0.463013	+	0.101139i
$94$		0			0
$95$	−38.3410	+	67.9402i	−0.403590	+	0.715160i
$96$		0			0
$97$	124.988	+	72.1619i	1.28854	+	0.743938i	0.978393	−	0.206752i	$-0.0662893\pi$
$97$	124.988	+	72.1619i	1.28854	+	0.743938i	0.310144	+	0.950689i	$0.399623\pi$
$98$		0			0
$99$	−129.885	−	59.5861i	−1.31197	−	0.601880i
$100$		0			0
$101$	−181.858			−1.80057			−0.900286	−	0.435299i	$-0.856643\pi$
$101$	−181.858			−1.80057			−0.900286	+	0.435299i	$0.856643\pi$
$102$		0			0
$103$	−123.209	−	71.1348i	−1.19621	−	0.690629i	−0.236498	−	0.971632i	$-0.576000\pi$
$103$	−123.209	−	71.1348i	−1.19621	−	0.690629i	−0.959707	+	0.281002i	$0.909333\pi$
$104$		0			0
$105$	118.202	+	107.638i	1.12573	+	1.02513i
$106$		0			0
$107$		−	7.60032i		−	0.0710310i	−0.999369	−	0.0355155i	$-0.988693\pi$
$107$		−	7.60032i		−	0.0710310i	0.999369	−	0.0355155i	$-0.0113073\pi$
$108$		0			0
$109$	−48.7475	+	28.1444i	−0.447225	+	0.258205i	−0.706657	−	0.707556i	$-0.749798\pi$
$109$	−48.7475	+	28.1444i	−0.447225	+	0.258205i	0.259433	+	0.965761i	$0.416464\pi$
$110$		0			0
$111$	32.5993	+	102.282i	0.293687	+	0.921461i
$112$		0			0
$113$	−42.3909	−	24.4744i	−0.375141	−	0.216588i	0.300561	−	0.953763i	$-0.402826\pi$
$113$	−42.3909	−	24.4744i	−0.375141	−	0.216588i	−0.675702	+	0.737175i	$0.736159\pi$
$114$		0			0
$115$	38.3568	+	66.4359i	0.333537	+	0.577703i
$116$		0			0
$117$	−1.46531	+	3.19406i	−0.0125240	+	0.0272997i
$118$		0			0
$119$	97.0837	−	168.154i	0.815829	−	1.41306i
$120$		0			0
$121$	−65.5530	+	113.541i	−0.541760	+	0.938356i
$122$		0			0
$123$	20.8529	+	65.4272i	0.169536	+	0.531929i
$124$		0			0
$125$	−136.076			−1.08861
$126$		0			0
$127$	198.477	+	114.591i	1.56281	+	0.902288i	0.996971	+	0.0777721i	$0.0247807\pi$
$127$	198.477	+	114.591i	1.56281	+	0.902288i	0.565838	+	0.824516i	$0.308553\pi$
$128$		0			0
$129$	10.3065	−	47.1833i	0.0798956	−	0.365762i
$130$		0			0
$131$	−64.5351			−0.492635			−0.246317	−	0.969189i	$-0.579221\pi$
$131$	−64.5351			−0.492635			−0.246317	+	0.969189i	$0.579221\pi$
$132$		0			0
$133$	246.583	−	2.42074i	1.85401	−	0.0182011i
$134$		0			0
$135$	−66.6639	+	88.5762i	−0.493807	+	0.656120i
$136$		0			0
$137$	−98.9698			−0.722407			−0.361204	−	0.932487i	$-0.617634\pi$
$137$	−98.9698			−0.722407			−0.361204	+	0.932487i	$0.617634\pi$
$138$		0			0
$139$	−61.8665	−	107.156i	−0.445083	−	0.770906i	0.552975	−	0.833198i	$-0.313493\pi$
$139$	−61.8665	−	107.156i	−0.445083	−	0.770906i	−0.998058	+	0.0622914i	$0.980159\pi$
$140$		0			0
$141$	122.825	−	39.1469i	0.871103	−	0.277637i
$142$		0			0
$143$	5.36906	+	3.09983i	0.0375459	+	0.0216771i
$144$		0			0
$145$			62.5953i			0.431692i
$146$		0			0
$147$	76.4711	−	350.085i	0.520211	−	2.38153i
$148$		0			0
$149$	152.679			1.02469			0.512345	−	0.858780i	$-0.328777\pi$
$149$	152.679			1.02469			0.512345	+	0.858780i	$0.328777\pi$
$150$		0			0
$151$	77.0133	−	44.4637i	0.510022	−	0.294461i	−0.222821	−	0.974859i	$-0.571526\pi$
$151$	77.0133	−	44.4637i	0.510022	−	0.294461i	0.732843	+	0.680398i	$0.238193\pi$
$152$		0			0
$153$	122.380	+	56.1434i	0.799872	+	0.366950i
$154$		0			0
$155$	−52.2416	−	30.1617i	−0.337042	−	0.194591i
$156$		0			0
$157$	191.195			1.21780			0.608901	−	0.793246i	$-0.291611\pi$
$157$	191.195			1.21780			0.608901	+	0.793246i	$0.291611\pi$
$158$		0			0
$159$	−59.8588	−	13.0753i	−0.376470	−	0.0822346i
$160$		0			0
$161$	121.245	−	210.002i	0.753074	−	1.30436i
$162$		0			0
$163$	13.9541			0.0856080			0.0428040	−	0.999083i	$-0.486371\pi$
$163$	13.9541			0.0856080			0.0428040	+	0.999083i	$0.486371\pi$
$164$		0			0
$165$	144.606	+	131.682i	0.876399	+	0.798075i
$166$		0			0
$167$	206.699	−	119.338i	1.23772	−	0.714596i	0.269089	−	0.963115i	$-0.413277\pi$
$167$	206.699	−	119.338i	1.23772	−	0.714596i	0.968627	+	0.248519i	$0.0799439\pi$
$168$		0			0
$169$	−84.4238	+	146.226i	−0.499549	+	0.865244i
$170$		0			0
$171$	17.6329	+	170.088i	0.103116	+	0.994669i
$172$		0			0
$173$	−122.600	−	70.7829i	−0.708668	−	0.409150i	0.101899	−	0.994795i	$-0.467508\pi$
$173$	−122.600	−	70.7829i	−0.708668	−	0.409150i	−0.810568	+	0.585645i	$0.800841\pi$
$174$		0			0
$175$	52.8332	+	91.5098i	0.301904	+	0.522913i
$176$		0			0
$177$	−63.2642	−	198.495i	−0.357425	−	1.12144i
$178$		0			0
$179$			253.540i			1.41643i	0.705998	+	0.708214i	$0.250499\pi$
$179$			253.540i			1.41643i	−0.705998	+	0.708214i	$0.749501\pi$
$180$		0			0
$181$	−200.068	−	115.509i	−1.10535	−	0.638173i	−0.167727	−	0.985833i	$-0.553643\pi$
$181$	−200.068	−	115.509i	−1.10535	−	0.638173i	−0.937620	+	0.347661i	$0.886976\pi$
$182$		0			0
$183$	217.487	−	69.3173i	1.18845	−	0.378783i
$184$		0			0
$185$		−	146.925i		−	0.794190i
$186$		0			0
$187$	118.770	−	205.716i	0.635134	−	1.10008i
$188$		0			0
$189$	347.838	+	42.4980i	1.84041	+	0.224857i
$190$		0			0
$191$	−135.073	−	233.954i	−0.707190	−	1.22489i	−0.965895	−	0.258933i	$-0.916629\pi$
$191$	−135.073	−	233.954i	−0.707190	−	1.22489i	0.258705	−	0.965956i	$-0.416704\pi$
$192$		0			0
$193$		−	25.0064i		−	0.129567i	−0.997899	−	0.0647835i	$-0.979364\pi$
$193$		−	25.0064i		−	0.129567i	0.997899	−	0.0647835i	$-0.0206357\pi$
$194$		0			0
$195$	3.23826	−	3.55607i	0.0166065	−	0.0182363i
$196$		0			0
$197$	243.933			1.23824			0.619119	−	0.785297i	$-0.287490\pi$
$197$	243.933			1.23824			0.619119	+	0.785297i	$0.287490\pi$
$198$		0			0
$199$	−86.3189	+	149.509i	−0.433763	+	0.751300i	−0.997194	−	0.0748635i	$-0.976148\pi$
$199$	−86.3189	+	149.509i	−0.433763	+	0.751300i	0.563431	+	0.826163i	$0.309481\pi$
$200$		0			0
$201$	90.5910	−	99.4817i	0.450701	−	0.494934i
$202$		0			0
$203$	171.354	−	98.9313i	0.844109	−	0.487346i
$204$		0			0
$205$		−	93.9842i		−	0.458459i
$206$		0			0
$207$	152.837	+	70.1159i	0.738345	+	0.338724i
$208$		0			0
$209$	301.665	−	2.96148i	1.44337	−	0.0141698i
$210$		0			0
$211$			80.3755i			0.380927i	0.981694	+	0.190463i	$0.0609990\pi$
$211$			80.3755i			0.380927i	−0.981694	+	0.190463i	$0.939001\pi$
$212$		0			0
$213$	−47.3538	+	52.0011i	−0.222318	+	0.244137i
$214$		0			0
$215$	−33.0497	+	57.2438i	−0.153720	+	0.266250i
$216$		0			0
$217$			190.681i			0.878714i
$218$		0			0
$219$	−146.758	−	133.642i	−0.670129	−	0.610239i
$220$		0			0
$221$	−5.05885	−	2.92073i	−0.0228907	−	0.0132160i
$222$		0			0
$223$	−112.933	−	65.2021i	−0.506428	−	0.292386i	0.224936	−	0.974373i	$-0.427783\pi$
$223$	−112.933	−	65.2021i	−0.506428	−	0.292386i	−0.731364	+	0.681987i	$0.761116\pi$
$224$		0			0
$225$	−59.7599	+	42.4004i	−0.265600	+	0.188446i
$226$		0			0
$227$	32.0290	−	18.4920i	0.141097	−	0.0814624i	−0.427790	−	0.903878i	$-0.640708\pi$
$227$	32.0290	−	18.4920i	0.141097	−	0.0814624i	0.568887	+	0.822416i	$0.307374\pi$
$228$		0			0
$229$	−79.1349	+	137.066i	−0.345567	+	0.598540i	−0.985457	−	0.169927i	$-0.945647\pi$
$229$	−79.1349	+	137.066i	−0.345567	+	0.598540i	0.639889	+	0.768467i	$0.278980\pi$
$230$		0			0
$231$	131.931	−	603.980i	0.571129	−	2.61463i
$232$		0			0
$233$	−125.476	−	217.331i	−0.538525	−	0.932753i	−0.998984	−	0.0450717i	$-0.985648\pi$
$233$	−125.476	−	217.331i	−0.538525	−	0.932753i	0.460459	−	0.887681i	$-0.347685\pi$
$234$		0			0
$235$	−176.435			−0.750787
$236$		0			0
$237$	−354.242	−	77.3792i	−1.49469	−	0.326494i
$238$		0			0
$239$	−87.5050	+	151.563i	−0.366130	+	0.634155i	−0.988957	−	0.148204i	$-0.952651\pi$
$239$	−87.5050	+	151.563i	−0.366130	+	0.634155i	0.622827	+	0.782360i	$0.285984\pi$
$240$		0			0
$241$			341.898i			1.41867i	0.704874	+	0.709333i	$0.251004\pi$
$241$			341.898i			1.41867i	−0.704874	+	0.709333i	$0.748996\pi$
$242$		0			0
$243$	−6.82548	+	242.904i	−0.0280884	+	0.999605i
$244$		0			0
$245$	−245.218	+	424.730i	−1.00089	+	1.73359i
$246$		0			0
$247$	−0.0728272	−	7.41838i	−0.000294847	−	0.0300339i
$248$		0			0
$249$	288.809	+	262.998i	1.15987	+	1.05622i
$250$		0			0
$251$	−138.459	+	239.818i	−0.551630	+	0.955451i	0.446527	+	0.894770i	$0.352661\pi$
$251$	−138.459	+	239.818i	−0.551630	+	0.955451i	−0.998157	+	0.0606811i	$0.980673\pi$
$252$		0			0
$253$	148.328	−	256.912i	0.586278	−	1.01546i
$254$		0			0
$255$	−136.251	−	124.074i	−0.534317	−	0.486565i
$256$		0			0
$257$	82.0790	−	47.3884i	0.319374	−	0.184390i	−0.331740	−	0.943371i	$-0.607636\pi$
$257$	82.0790	−	47.3884i	0.319374	−	0.184390i	0.651113	+	0.758980i	$0.274302\pi$
$258$		0			0
$259$	−402.206	+	232.214i	−1.55292	+	0.896578i
$260$		0			0
$261$	79.3957	+	111.902i	0.304198	+	0.428742i
$262$		0			0
$263$	−52.4275	+	90.8071i	−0.199344	+	0.345274i	−0.948316	−	0.317328i	$-0.897215\pi$
$263$	−52.4275	+	90.8071i	−0.199344	+	0.345274i	0.748972	+	0.662602i	$0.230548\pi$
$264$		0			0
$265$	72.6219	+	41.9283i	0.274045	+	0.158220i
$266$		0			0
$267$	384.193	+	83.9215i	1.43892	+	0.314313i
$268$		0			0
$269$	122.868	−	70.9381i	0.456760	−	0.263711i	−0.253921	−	0.967225i	$-0.581720\pi$
$269$	122.868	−	70.9381i	0.456760	−	0.263711i	0.710681	+	0.703514i	$0.248387\pi$
$270$		0			0
$271$	−48.7803	−	84.4900i	−0.180001	−	0.311771i	0.761879	−	0.647719i	$-0.224277\pi$
$271$	−48.7803	−	84.4900i	−0.180001	−	0.311771i	−0.941881	+	0.335948i	$0.890943\pi$
$272$		0			0
$273$	−14.8528	−	3.24437i	−0.0544057	−	0.0118842i
$274$		0			0
$275$	64.6350	+	111.951i	0.235036	+	0.407095i
$276$		0			0
$277$	85.1441	+	147.474i	0.307379	+	0.532397i	0.977788	−	0.209595i	$-0.0672146\pi$
$277$	85.1441	+	147.474i	0.307379	+	0.532397i	−0.670409	+	0.741992i	$0.733881\pi$
$278$		0			0
$279$	−131.649	+	12.3429i	−0.471861	+	0.0442399i
$280$		0			0
$281$		−	490.112i		−	1.74417i	−0.489354	−	0.872085i	$-0.662767\pi$
$281$		−	490.112i		−	1.74417i	0.489354	−	0.872085i	$-0.337233\pi$
$282$		0			0
$283$	−437.261			−1.54509			−0.772545	−	0.634960i	$-0.781017\pi$
$283$	−437.261			−1.54509			−0.772545	+	0.634960i	$0.781017\pi$
$284$		0			0
$285$	47.6974	−	229.125i	0.167359	−	0.803946i
$286$		0			0
$287$	−257.281	+	148.541i	−0.896449	+	0.517565i
$288$		0			0
$289$	32.5922	−	56.4514i	0.112776	−	0.195333i
$290$		0			0
$291$	−422.998	−	92.3979i	−1.45360	−	0.317519i
$292$		0			0
$293$	−232.886	−	134.457i	−0.794831	−	0.458896i	0.0468294	−	0.998903i	$-0.485088\pi$
$293$	−232.886	−	134.457i	−0.794831	−	0.458896i	−0.841661	+	0.540007i	$0.818422\pi$
$294$		0			0
$295$			285.132i			0.966549i
$296$		0			0
$297$	425.538	+	51.9911i	1.43279	+	0.175054i
$298$		0			0
$299$	−6.31786	−	3.64762i	−0.0211300	−	0.0121994i
$300$		0			0
$301$	208.939			0.694150
$302$		0			0
$303$	519.810	−	165.674i	1.71554	−	0.546777i
$304$		0			0
$305$	−312.413			−1.02431
$306$		0			0
$307$	222.433	−	128.422i	0.724536	−	0.418311i	−0.0918838	−	0.995770i	$-0.529289\pi$
$307$	222.433	−	128.422i	0.724536	−	0.418311i	0.816420	+	0.577459i	$0.195956\pi$
$308$		0			0
$309$	416.977	+	91.0828i	1.34944	+	0.294766i
$310$		0			0
$311$	77.6546	−	134.502i	0.249693	−	0.432482i	−0.713747	−	0.700403i	$-0.753004\pi$
$311$	77.6546	−	134.502i	0.249693	−	0.432482i	0.963441	+	0.267922i	$0.0863369\pi$
$312$		0			0
$313$	165.858			0.529897			0.264949	−	0.964263i	$-0.414645\pi$
$313$	165.858			0.529897			0.264949	+	0.964263i	$0.414645\pi$
$314$		0			0
$315$	−435.920	−	199.983i	−1.38387	−	0.634868i
$316$		0			0
$317$		−	277.809i		−	0.876368i	−0.898885	−	0.438184i	$-0.855622\pi$
$317$		−	277.809i		−	0.876368i	0.898885	−	0.438184i	$-0.144378\pi$
$318$		0			0
$319$	209.631	−	121.030i	0.657150	−	0.379406i
$320$		0			0
$321$	6.92394	+	21.7242i	0.0215699	+	0.0676768i
$322$		0			0
$323$	−284.235	+	2.79038i	−0.879985	+	0.00863893i
$324$		0			0
$325$	2.75304	−	1.58947i	0.00847090	−	0.00489067i
$326$		0			0
$327$	113.697	−	124.855i	0.347697	−	0.381821i
$328$		0			0
$329$	278.854	+	482.989i	0.847580	+	1.46805i
$330$		0			0
$331$	231.109	−	133.431i	0.698213	−	0.403113i	−0.108468	−	0.994100i	$-0.534595\pi$
$331$	231.109	−	133.431i	0.698213	−	0.403113i	0.806682	+	0.590986i	$0.201261\pi$
$332$		0			0
$333$	−186.359	−	262.658i	−0.559638	−	0.788763i
$334$		0			0
$335$	−159.477	+	92.0740i	−0.476050	+	0.274848i
$336$		0			0
$337$		−	392.322i		−	1.16416i	−0.813131	−	0.582080i	$-0.802239\pi$
$337$		−	392.322i		−	1.16416i	0.813131	−	0.582080i	$-0.197761\pi$
$338$		0			0
$339$	143.464	+	31.3376i	0.423197	+	0.0924414i
$340$		0			0
$341$			233.275i			0.684090i
$342$		0			0
$343$	914.303			2.66561
$344$		0			0
$345$	−170.160	−	154.953i	−0.493217	−	0.449138i
$346$		0			0
$347$	−468.496			−1.35013			−0.675067	−	0.737757i	$-0.735885\pi$
$347$	−468.496			−1.35013			−0.675067	+	0.737757i	$0.735885\pi$
$348$		0			0
$349$	−292.595	−	506.789i	−0.838380	−	1.45212i	−0.891248	−	0.453515i	$-0.850170\pi$
$349$	−292.595	−	506.789i	−0.838380	−	1.45212i	0.0528684	−	0.998601i	$-0.483164\pi$
$350$		0			0
$351$	1.27854	−	10.4646i	0.00364256	−	0.0298137i
$352$		0			0
$353$	−4.23602	−	7.33701i	−0.0120001	−	0.0207847i	0.859963	−	0.510356i	$-0.170486\pi$
$353$	−4.23602	−	7.33701i	−0.0120001	−	0.0207847i	−0.871963	+	0.489572i	$0.837153\pi$
$354$		0			0
$355$	83.3619	−	48.1290i	0.234822	−	0.135575i
$356$		0			0
$357$	−124.308	+	569.083i	−0.348202	+	1.59407i
$358$		0			0
$359$	−134.445	−	232.865i	−0.374498	−	0.648650i	0.615754	−	0.787939i	$-0.288852\pi$
$359$	−134.445	−	232.865i	−0.374498	−	0.648650i	−0.990252	+	0.139289i	$0.955518\pi$
$360$		0			0
$361$	−186.603	−	309.031i	−0.516906	−	0.856042i
$362$		0			0
$363$	83.9356	−	384.257i	0.231228	−	1.05856i
$364$		0			0
$365$	135.830	+	235.265i	0.372137	+	0.644561i
$366$		0			0
$367$	600.182			1.63537			0.817686	−	0.575664i	$-0.195256\pi$
$367$	600.182			1.63537			0.817686	+	0.575664i	$0.195256\pi$
$368$		0			0
$369$	−119.209	−	168.016i	−0.323060	−	0.455327i
$370$		0			0
$371$		−	265.069i		−	0.714472i
$372$		0			0
$373$	468.871	+	270.703i	1.25703	+	0.725745i	0.972495	−	0.232922i	$-0.0748286\pi$
$373$	468.871	+	270.703i	1.25703	+	0.725745i	0.284531	+	0.958667i	$0.408162\pi$
$374$		0			0
$375$	388.951	−	123.966i	1.03720	−	0.330576i
$376$		0			0
$377$	−2.97632	−	5.15513i	−0.00789474	−	0.0136741i
$378$		0			0
$379$			387.805i			1.02323i	0.859214	+	0.511617i	$0.170953\pi$
$379$			387.805i			1.02323i	−0.859214	+	0.511617i	$0.829047\pi$
$380$		0			0
$381$	−671.706	−	146.725i	−1.76301	−	0.385104i
$382$		0			0
$383$		−	96.4808i		−	0.251908i	−0.992036	−	0.125954i	$-0.959801\pi$
$383$		−	96.4808i		−	0.251908i	0.992036	−	0.125954i	$-0.0401992\pi$
$384$		0			0
$385$	−423.060	+	732.761i	−1.09886	+	1.90327i
$386$		0			0
$387$	13.5248	+	144.255i	0.0349478	+	0.372752i
$388$		0			0
$389$	346.622			0.891059			0.445530	−	0.895267i	$-0.353015\pi$
$389$	346.622			0.891059			0.445530	+	0.895267i	$0.353015\pi$
$390$		0			0
$391$	−139.758	+	242.069i	−0.357438	+	0.619102i
$392$		0			0
$393$	184.463	−	58.7919i	0.469371	−	0.149598i
$394$		0			0
$395$	429.774	+	248.130i	1.08804	+	0.628177i
$396$		0			0
$397$	42.6512	+	73.8740i	0.107434	+	0.186081i	0.914730	−	0.404066i	$-0.132403\pi$
$397$	42.6512	+	73.8740i	0.107434	+	0.186081i	−0.807296	+	0.590146i	$0.799070\pi$
$398$		0			0
$399$	−702.612	+	231.558i	−1.76093	+	0.580346i
$400$		0			0
$401$			482.699i			1.20374i	0.798594	+	0.601870i	$0.205577\pi$
$401$			482.699i			1.20374i	−0.798594	+	0.601870i	$0.794423\pi$
$402$		0			0
$403$	5.73657			0.0142347
$404$		0			0
$405$	109.854	−	313.912i	0.271245	−	0.775090i
$406$		0			0
$407$	−492.050	+	284.085i	−1.20897	+	0.697998i
$408$		0			0
$409$	−467.308	+	269.800i	−1.14256	+	0.659658i	−0.947064	−	0.321046i	$-0.895966\pi$
$409$	−467.308	+	269.800i	−1.14256	+	0.659658i	−0.195498	+	0.980704i	$0.562632\pi$
$410$		0			0
$411$	282.889	−	90.1621i	0.688293	−	0.219372i
$412$		0			0
$413$	780.546	−	450.648i	1.88994	−	1.09116i
$414$		0			0
$415$	−267.303	−	462.983i	−0.644104	−	1.11562i
$416$		0			0
$417$	274.455	+	249.927i	0.658165	+	0.599345i
$418$		0			0
$419$	−345.181	+	597.871i	−0.823820	+	1.42690i	0.0789970	+	0.996875i	$0.474828\pi$
$419$	−345.181	+	597.871i	−0.823820	+	1.42690i	−0.902817	+	0.430024i	$0.858505\pi$
$420$		0			0
$421$	−369.686	−	213.438i	−0.878115	−	0.506980i	−0.00807843	−	0.999967i	$-0.502571\pi$
$421$	−369.686	−	213.438i	−0.878115	−	0.506980i	−0.870036	+	0.492988i	$0.835905\pi$
$422$		0			0
$423$	−315.413	+	223.790i	−0.745658	+	0.529053i
$424$		0			0
$425$	−60.9005	−	105.483i	−0.143295	−	0.248195i
$426$		0			0
$427$	493.766	+	855.229i	1.15636	+	2.00288i
$428$		0			0
$429$	−18.1705	−	3.96910i	−0.0423556	−	0.00925197i
$430$		0			0
$431$	−132.173	−	76.3101i	−0.306666	−	0.177054i	0.338768	−	0.940870i	$-0.389990\pi$
$431$	−132.173	−	76.3101i	−0.306666	−	0.177054i	−0.645434	+	0.763816i	$0.723323\pi$
$432$		0			0
$433$	−272.158	−	157.131i	−0.628541	−	0.362889i	0.151646	−	0.988435i	$-0.451543\pi$
$433$	−272.158	−	157.131i	−0.628541	−	0.362889i	−0.780187	+	0.625546i	$0.784876\pi$
$434$		0			0
$435$	−57.0247	−	178.918i	−0.131091	−	0.411306i
$436$		0			0
$437$	−354.973	+	3.48482i	−0.812296	+	0.00797442i
$438$		0			0
$439$	−588.830	−	339.961i	−1.34130	−	0.774399i	−0.354301	−	0.935131i	$-0.615281\pi$
$439$	−588.830	−	339.961i	−1.34130	−	0.774399i	−0.986998	+	0.160732i	$0.948615\pi$
$440$		0			0
$441$	100.350	+	1070.32i	0.227550	+	2.42704i
$442$		0			0
$443$	102.921			0.232327			0.116164	−	0.993230i	$-0.462940\pi$
$443$	102.921			0.232327			0.116164	+	0.993230i	$0.462940\pi$
$444$		0			0
$445$	−466.111	−	269.109i	−1.04744	−	0.604739i
$446$		0			0
$447$	−436.407	+	139.091i	−0.976302	+	0.311166i
$448$		0			0
$449$		−	723.036i		−	1.61033i	−0.593053	−	0.805163i	$-0.702078\pi$
$449$		−	723.036i		−	1.61033i	0.593053	−	0.805163i	$-0.297922\pi$
$450$		0			0
$451$	−314.752	+	181.722i	−0.697897	+	0.402931i
$452$		0			0
$453$	−179.623	+	197.252i	−0.396519	+	0.435434i
$454$		0			0
$455$	18.0197	+	10.4037i	0.0396037	+	0.0228652i
$456$		0			0
$457$	68.0568	+	117.878i	0.148921	+	0.257938i	0.930829	−	0.365455i	$-0.119087\pi$
$457$	68.0568	+	117.878i	0.148921	+	0.257938i	−0.781908	+	0.623394i	$0.785753\pi$
$458$		0			0
$459$	−400.951	−	48.9872i	−0.873532	−	0.106726i
$460$		0			0
$461$	−396.670	+	687.052i	−0.860455	+	1.49035i	0.0110359	+	0.999939i	$0.496487\pi$
$461$	−396.670	+	687.052i	−0.860455	+	1.49035i	−0.871491	+	0.490412i	$0.836846\pi$
$462$		0			0
$463$	−13.1918	+	22.8488i	−0.0284919	+	0.0493495i	−0.879920	−	0.475122i	$-0.842404\pi$
$463$	−13.1918	+	22.8488i	−0.0284919	+	0.0493495i	0.851428	+	0.524472i	$0.175737\pi$
$464$		0			0
$465$	176.801	+	38.6197i	0.380218	+	0.0830532i
$466$		0			0
$467$	220.125			0.471361			0.235680	−	0.971831i	$-0.424268\pi$
$467$	220.125			0.471361			0.235680	+	0.971831i	$0.424268\pi$
$468$		0			0
$469$	504.103	+	291.044i	1.07485	+	0.620563i
$470$		0			0
$471$	−546.499	+	174.180i	−1.16029	+	0.369808i
$472$		0			0
$473$	255.612			0.540405
$474$		0			0
$475$	76.0257	−	134.717i	0.160054	−	0.283616i
$476$		0			0
$477$	183.008	−	17.1581i	0.383665	−	0.0359709i
$478$		0			0
$479$	235.625			0.491910			0.245955	−	0.969281i	$-0.420898\pi$
$479$	235.625			0.491910			0.245955	+	0.969281i	$0.420898\pi$
$480$		0			0
$481$	6.98607	+	12.1002i	0.0145241	+	0.0251564i
$482$		0			0
$483$	−155.245	+	710.712i	−0.321418	+	1.47145i
$484$		0			0
$485$	513.190	+	296.290i	1.05812	+	0.610908i
$486$		0			0
$487$		−	511.738i		−	1.05080i	−0.850856	−	0.525398i	$-0.823916\pi$
$487$		−	511.738i		−	1.05080i	0.850856	−	0.525398i	$-0.176084\pi$
$488$		0			0
$489$	−39.8855	+	12.7123i	−0.0815654	+	0.0259965i
$490$		0			0
$491$	59.0524			0.120270			0.0601348	−	0.998190i	$-0.480847\pi$
$491$	59.0524			0.120270			0.0601348	+	0.998190i	$0.480847\pi$
$492$		0			0
$493$	−197.519	+	114.038i	−0.400647	+	0.231314i
$494$		0			0
$495$	−533.295	−	244.655i	−1.07736	−	0.494253i
$496$		0			0
$497$	−263.505	−	152.135i	−0.530192	−	0.306106i
$498$		0			0
$499$	−274.421			−0.549943			−0.274971	−	0.961452i	$-0.588668\pi$
$499$	−274.421			−0.549943			−0.274971	+	0.961452i	$0.588668\pi$
$500$		0			0
$501$	−482.096	+	529.410i	−0.962268	+	1.05671i
$502$		0			0
$503$	301.952	−	522.996i	0.600302	−	1.03975i	−0.392473	−	0.919763i	$-0.628380\pi$
$503$	301.952	−	522.996i	0.600302	−	1.03975i	0.992775	−	0.119990i	$-0.0382863\pi$
$504$		0			0
$505$	−746.691			−1.47860
$506$		0			0
$507$	108.098	−	494.874i	0.213212	−	0.976083i
$508$		0			0
$509$	593.045	−	342.395i	1.16512	−	0.672682i	0.212593	−	0.977141i	$-0.431809\pi$
$509$	593.045	−	342.395i	1.16512	−	0.672682i	0.952525	+	0.304459i	$0.0984757\pi$
$510$		0			0
$511$	429.356	−	743.667i	0.840228	−	1.45532i
$512$		0			0
$513$	−205.352	−	470.106i	−0.400297	−	0.916386i
$514$		0			0
$515$	−505.885	−	292.073i	−0.982302	−	0.567132i
$516$		0			0
$517$	341.144	+	590.878i	0.659852	+	1.14290i
$518$		0			0
$519$	414.914	+	90.6322i	0.799450	+	0.174628i
$520$		0			0
$521$		−	868.338i		−	1.66668i	−0.552763	−	0.833338i	$-0.686427\pi$
$521$		−	868.338i		−	1.66668i	0.552763	−	0.833338i	$-0.313573\pi$
$522$		0			0
$523$	−746.158	−	430.795i	−1.42669	−	0.823699i	−0.429831	−	0.902909i	$-0.641427\pi$
$523$	−746.158	−	430.795i	−1.42669	−	0.823699i	−0.996858	+	0.0792098i	$0.974760\pi$
$524$		0			0
$525$	−234.381	−	213.434i	−0.446440	−	0.406541i
$526$		0			0
$527$		−	219.797i		−	0.417072i
$528$		0			0
$529$	89.9597	−	155.815i	0.170056	−	0.294546i
$530$		0			0
$531$	361.660	+	509.731i	0.681093	+	0.959945i
$532$		0			0
$533$	4.46881	+	7.74021i	0.00838426	+	0.0145220i
$534$		0			0
$535$		−	31.2062i		−	0.0583293i
$536$		0			0
$537$	−230.977	−	724.703i	−0.430125	−	1.34954i
$538$		0			0
$539$	1896.55			3.51865
$540$		0			0
$541$	−395.214	+	684.531i	−0.730526	+	1.26531i	0.226133	+	0.974096i	$0.427392\pi$
$541$	−395.214	+	684.531i	−0.730526	+	1.26531i	−0.956659	+	0.291211i	$0.905942\pi$
$542$		0			0
$543$	677.090	+	147.901i	1.24694	+	0.272377i
$544$		0			0
$545$	−200.153	+	115.558i	−0.367253	+	0.212033i
$546$		0			0
$547$		−	451.791i		−	0.825944i	−0.910744	−	0.412972i	$-0.864491\pi$
$547$		−	451.791i		−	0.825944i	0.910744	−	0.412972i	$-0.135509\pi$
$548$		0			0
$549$	−558.502	+	396.264i	−1.01731	+	0.721793i
$550$		0			0
$551$	−252.261	−	142.360i	−0.457825	−	0.258366i
$552$		0			0
$553$		−	1568.67i		−	2.83665i
$554$		0			0
$555$	133.850	+	419.961i	0.241171	+	0.756686i
$556$		0			0
$557$	−510.833	+	884.789i	−0.917115	+	1.58849i	−0.113341	+	0.993556i	$0.536155\pi$
$557$	−510.833	+	884.789i	−0.917115	+	1.58849i	−0.803775	+	0.594934i	$0.797178\pi$
$558$		0			0
$559$		−	6.28587i		−	0.0112448i
$560$		0			0
$561$	−152.076	+	696.204i	−0.271080	+	1.24101i
$562$		0			0
$563$	−264.370	−	152.634i	−0.469574	−	0.271109i	0.246487	−	0.969146i	$-0.420724\pi$
$563$	−264.370	−	152.634i	−0.469574	−	0.271109i	−0.716061	+	0.698037i	$0.754057\pi$
$564$		0			0
$565$	−174.053	−	100.490i	−0.308059	−	0.177858i
$566$		0			0
$567$	−1032.95	+	195.409i	−1.82179	+	0.344637i
$568$		0			0
$569$	576.757	−	332.991i	1.01363	−	0.585221i	0.101380	−	0.994848i	$-0.467674\pi$
$569$	576.757	−	332.991i	1.01363	−	0.585221i	0.912253	+	0.409626i	$0.134341\pi$
$570$		0			0
$571$	111.463	−	193.060i	0.195207	−	0.338108i	−0.751761	−	0.659435i	$-0.770795\pi$
$571$	111.463	−	193.060i	0.195207	−	0.338108i	0.946968	+	0.321327i	$0.104129\pi$
$572$		0			0
$573$	599.218	+	545.665i	1.04576	+	0.952295i
$574$		0			0
$575$	−76.0569	−	131.734i	−0.132273	−	0.229103i
$576$		0			0
$577$	−422.219			−0.731749			−0.365875	−	0.930664i	$-0.619230\pi$
$577$	−422.219			−0.731749			−0.365875	+	0.930664i	$0.619230\pi$
$578$		0			0
$579$	22.7810	+	71.4767i	0.0393455	+	0.123449i
$580$		0			0
$581$	−844.940	+	1463.48i	−1.45429	+	2.51890i
$582$		0			0
$583$		−	324.280i		−	0.556226i
$584$		0			0
$585$	−6.01643	+	13.1145i	−0.0102845	+	0.0224180i
$586$		0			0
$587$	24.2829	−	42.0591i	0.0413677	−	0.0716510i	−0.844600	−	0.535397i	$-0.820162\pi$
$587$	24.2829	−	42.0591i	0.0413677	−	0.0716510i	0.885968	+	0.463747i	$0.153495\pi$
$588$		0			0
$589$	240.365	−	141.939i	0.408090	−	0.240983i
$590$		0			0
$591$	−697.242	+	222.224i	−1.17977	+	0.376014i
$592$		0			0
$593$	545.462	−	944.768i	0.919835	−	1.59320i	0.120171	−	0.992753i	$-0.461656\pi$
$593$	545.462	−	944.768i	0.919835	−	1.59320i	0.799664	−	0.600448i	$-0.205011\pi$
$594$		0			0
$595$	398.616	−	690.424i	0.669944	−	1.16038i
$596$		0			0
$597$	110.525	−	505.983i	0.185134	−	0.847542i
$598$		0			0
$599$	−509.963	+	294.427i	−0.851358	+	0.491532i	−0.861109	−	0.508421i	$-0.830229\pi$
$599$	−509.963	+	294.427i	−0.851358	+	0.491532i	0.00975113	+	0.999952i	$0.496896\pi$
$600$		0			0
$601$	−838.716	+	484.233i	−1.39553	+	0.805712i	−0.993921	−	0.110097i	$-0.964884\pi$
$601$	−838.716	+	484.233i	−1.39553	+	0.805712i	−0.401613	+	0.915809i	$0.631550\pi$
$602$		0			0
$603$	−168.311	+	366.881i	−0.279122	+	0.608426i
$604$		0			0
$605$	−269.154	+	466.189i	−0.444883	+	0.770561i
$606$		0			0
$607$	−129.306	−	74.6547i	−0.213024	−	0.122990i	0.389692	−	0.920945i	$-0.372582\pi$
$607$	−129.306	−	74.6547i	−0.213024	−	0.122990i	−0.602716	+	0.797956i	$0.705915\pi$
$608$		0			0
$609$	−399.660	+	438.883i	−0.656256	+	0.720662i
$610$		0			0
$611$	14.5306	−	8.38923i	0.0237816	−	0.0137303i
$612$		0			0
$613$	480.397	+	832.071i	0.783681	+	1.35738i	0.929784	+	0.368106i	$0.119994\pi$
$613$	480.397	+	832.071i	0.783681	+	1.35738i	−0.146102	+	0.989269i	$0.546673\pi$
$614$		0			0
$615$	85.6202	+	268.638i	0.139220	+	0.436810i
$616$		0			0
$617$	−273.059	−	472.952i	−0.442559	−	0.766535i	0.555319	−	0.831637i	$-0.312596\pi$
$617$	−273.059	−	472.952i	−0.442559	−	0.766535i	−0.997879	+	0.0651021i	$0.979263\pi$
$618$		0			0
$619$	292.910	+	507.336i	0.473199	+	0.819605i	0.999529	−	0.0306750i	$-0.00976569\pi$
$619$	292.910	+	507.336i	0.473199	+	0.819605i	−0.526330	+	0.850280i	$0.676432\pi$
$620$		0			0
$621$	−500.736	−	61.1787i	−0.806339	−	0.0985165i
$622$		0			0
$623$			1701.30i			2.73081i
$624$		0			0
$625$	−355.177			−0.568284
$626$		0			0
$627$	−859.560	+	283.283i	−1.37091	+	0.451807i
$628$		0			0
$629$	463.621	−	267.671i	0.737076	−	0.425551i
$630$		0			0
$631$	174.403	−	302.075i	0.276392	−	0.478725i	−0.694093	−	0.719885i	$-0.744195\pi$
$631$	174.403	−	302.075i	0.276392	−	0.478725i	0.970485	+	0.241160i	$0.0775279\pi$
$632$		0			0
$633$	−73.2226	−	229.740i	−0.115676	−	0.362938i
$634$		0			0
$635$	814.927	+	470.498i	1.28335	+	0.740942i
$636$		0			0
$637$		−	46.6390i		−	0.0732167i
$638$		0			0
$639$	87.9795	−	191.776i	0.137683	−	0.300119i
$640$		0			0
$641$	−708.152	−	408.852i	−1.10476	−	0.637834i	−0.167294	−	0.985907i	$-0.553503\pi$
$641$	−708.152	−	408.852i	−1.10476	−	0.637834i	−0.937467	+	0.348073i	$0.886836\pi$
$642$		0			0
$643$	320.773			0.498869			0.249434	−	0.968392i	$-0.419755\pi$
$643$	320.773			0.498869			0.249434	+	0.968392i	$0.419755\pi$
$644$		0			0
$645$	42.3177	−	193.730i	0.0656088	−	0.300357i
$646$		0			0
$647$	−499.685			−0.772310			−0.386155	−	0.922434i	$-0.626197\pi$
$647$	−499.685			−0.772310			−0.386155	+	0.922434i	$0.626197\pi$
$648$		0			0
$649$	954.903	−	551.313i	1.47134	−	0.849481i
$650$		0			0
$651$	−173.712	−	545.030i	−0.266838	−	0.837219i
$652$		0			0
$653$	510.680	−	884.524i	0.782052	−	1.35455i	−0.148692	−	0.988884i	$-0.547506\pi$
$653$	510.680	−	884.524i	0.782052	−	1.35455i	0.930744	−	0.365671i	$-0.119160\pi$
$654$		0			0
$655$	−264.975			−0.404542
$656$		0			0
$657$	541.233	+	248.297i	0.823794	+	0.377925i
$658$		0			0
$659$		−	414.980i		−	0.629711i	−0.949140	−	0.314856i	$-0.898044\pi$
$659$		−	414.980i		−	0.629711i	0.949140	−	0.314856i	$-0.101956\pi$
$660$		0			0
$661$	240.026	−	138.579i	0.363125	−	0.209650i	−0.307326	−	0.951604i	$-0.599434\pi$
$661$	240.026	−	138.579i	0.363125	−	0.209650i	0.670451	+	0.741954i	$0.266101\pi$
$662$		0			0
$663$	17.1207	+	3.73977i	0.0258231	+	0.00564068i
$664$		0			0
$665$	1012.45	−	9.93934i	1.52248	−	0.0149464i
$666$		0			0
$667$	−246.676	+	142.418i	−0.369829	+	0.213521i
$668$		0			0
$669$	382.201	+	83.4864i	0.571302	+	0.124793i
$670$		0			0
$671$	604.063	+	1046.27i	0.900243	+	1.55927i
$672$		0			0
$673$	780.615	−	450.688i	1.15990	−	0.669670i	0.208622	−	0.977996i	$-0.433102\pi$
$673$	780.615	−	450.688i	1.15990	−	0.669670i	0.951281	+	0.308326i	$0.0997687\pi$
$674$		0			0
$675$	132.187	−	175.636i	0.195832	−	0.260202i
$676$		0			0
$677$	−341.330	+	197.067i	−0.504181	+	0.291089i	−0.730438	−	0.682979i	$-0.760684\pi$
$677$	−341.330	+	197.067i	−0.504181	+	0.291089i	0.226258	+	0.974067i	$0.427351\pi$
$678$		0			0
$679$		−	1873.14i		−	2.75867i
$680$		0			0
$681$	−74.7033	+	82.0348i	−0.109697	+	0.120462i
$682$		0			0
$683$			591.311i			0.865755i	0.901453	+	0.432878i	$0.142502\pi$
$683$			591.311i			0.865755i	−0.901453	+	0.432878i	$0.857498\pi$
$684$		0			0
$685$	−406.361			−0.593227
$686$		0			0
$687$	101.326	−	463.872i	0.147491	−	0.675214i
$688$		0			0
$689$	−7.97452			−0.0115740
$690$		0			0
$691$	−44.4269	−	76.9497i	−0.0642937	−	0.111360i	0.832087	−	0.554645i	$-0.187146\pi$
$691$	−44.4269	−	76.9497i	−0.0642937	−	0.111360i	−0.896380	+	0.443286i	$0.853813\pi$
$692$		0			0
$693$	173.127	+	1846.56i	0.249822	+	2.66460i
$694$		0			0
$695$	−254.018	−	439.973i	−0.365494	−	0.633054i
$696$		0			0
$697$	296.566	−	171.222i	0.425489	−	0.245656i
$698$		0			0
$699$	556.643	+	506.896i	0.796343	+	0.725173i
$700$		0			0
$701$	−545.551	−	944.922i	−0.778247	−	1.34796i	−0.932951	−	0.360003i	$-0.882776\pi$
$701$	−545.551	−	944.922i	−0.778247	−	1.34796i	0.154704	−	0.987961i	$-0.450558\pi$
$702$		0			0
$703$	592.113	+	334.150i	0.842266	+	0.475320i
$704$		0			0
$705$	504.310	−	160.733i	0.715333	−	0.227991i
$706$		0			0
$707$	1180.14	+	2044.06i	1.66922	+	2.89117i
$708$		0			0
$709$	−1018.89			−1.43708			−0.718541	−	0.695485i	$-0.755190\pi$
$709$	−1018.89			−1.43708			−0.718541	+	0.695485i	$0.755190\pi$
$710$		0			0
$711$	1083.03	−	101.541i	1.52326	−	0.142815i
$712$		0			0
$713$		−	274.498i		−	0.384990i
$714$		0			0
$715$	22.0449	+	12.7276i	0.0308320	+	0.0178009i
$716$		0			0
$717$	112.044	−	512.936i	0.156267	−	0.715391i
$718$		0			0
$719$	−162.296	−	281.105i	−0.225725	−	0.390967i	0.730812	−	0.682579i	$-0.239142\pi$
$719$	−162.296	−	281.105i	−0.225725	−	0.390967i	−0.956537	+	0.291612i	$0.905808\pi$
$720$		0			0
$721$			1846.47i			2.56099i
$722$		0			0
$723$	−311.471	−	977.259i	−0.430804	−	1.35167i
$724$		0			0
$725$		−	124.119i		−	0.171199i
$726$		0			0
$727$	−104.067	+	180.250i	−0.143146	+	0.247937i	−0.928680	−	0.370882i	$-0.879055\pi$
$727$	−104.067	+	180.250i	−0.143146	+	0.247937i	0.785534	+	0.618819i	$0.212389\pi$
$728$		0			0
$729$	−201.778	−	700.519i	−0.276787	−	0.960931i
$730$		0			0
$731$	−240.843			−0.329471
$732$		0			0
$733$	178.182	−	308.619i	0.243085	−	0.421036i	−0.718506	−	0.695521i	$-0.755174\pi$
$733$	178.182	−	308.619i	0.243085	−	0.421036i	0.961592	+	0.274484i	$0.0885072\pi$
$734$		0			0
$735$	313.983	−	1437.42i	0.427188	−	1.95567i
$736$		0			0
$737$	616.709	+	356.057i	0.836783	+	0.483117i
$738$		0			0
$739$	12.3234	+	21.3448i	0.0166758	+	0.0288833i	0.874243	−	0.485489i	$-0.161358\pi$
$739$	12.3234	+	21.3448i	0.0166758	+	0.0288833i	−0.857567	+	0.514372i	$0.828025\pi$
$740$		0			0
$741$	6.96635	+	21.1378i	0.00940128	+	0.0285261i
$742$		0			0
$743$			1103.97i			1.48583i	0.669385	+	0.742915i	$0.266558\pi$
$743$			1103.97i			1.48583i	−0.669385	+	0.742915i	$0.733442\pi$
$744$		0			0
$745$	626.885			0.841457
$746$		0			0
$747$	−1065.10	−	488.628i	−1.42584	−	0.654121i
$748$		0			0
$749$	−85.4266	+	49.3211i	−0.114054	+	0.0658493i
$750$		0			0
$751$	99.0385	−	57.1799i	0.131876	−	0.0761384i	−0.432611	−	0.901581i	$-0.642408\pi$
$751$	99.0385	−	57.1799i	0.131876	−	0.0761384i	0.564486	+	0.825442i	$0.309074\pi$
$752$		0			0
$753$	177.286	−	811.618i	0.235440	−	1.07785i
$754$		0			0
$755$	316.210	−	182.564i	0.418821	−	0.241806i
$756$		0			0
$757$	−463.471	−	802.756i	−0.612248	−	1.06044i	−0.990861	−	0.134889i	$-0.956932\pi$
$757$	−463.471	−	802.756i	−0.612248	−	1.06044i	0.378613	−	0.925555i	$-0.376401\pi$
$758$		0			0
$759$	−189.923	+	869.469i	−0.250228	+	1.14555i
$760$		0			0
$761$	291.762	−	505.347i	0.383393	−	0.664056i	−0.608152	−	0.793821i	$-0.708089\pi$
$761$	291.762	−	505.347i	0.383393	−	0.664056i	0.991545	+	0.129765i	$0.0414222\pi$
$762$		0			0
$763$	632.679	+	365.277i	0.829199	+	0.478738i
$764$		0			0
$765$	502.483	+	230.520i	0.656840	+	0.301333i
$766$		0			0
$767$	−13.5576	−	23.4825i	−0.0176762	−	0.0306160i
$768$		0			0
$769$	−445.185	−	771.083i	−0.578914	−	1.00271i	−0.995604	−	0.0936601i	$-0.970143\pi$
$769$	−445.185	−	771.083i	−0.578914	−	1.00271i	0.416690	−	0.909049i	$-0.363190\pi$
$770$		0			0
$771$	−191.438	+	210.226i	−0.248298	+	0.272667i
$772$		0			0
$773$	1247.51	+	720.250i	1.61385	+	0.931759i	0.988466	+	0.151445i	$0.0483928\pi$
$773$	1247.51	+	720.250i	1.61385	+	0.931759i	0.625388	+	0.780314i	$0.284941\pi$
$774$		0			0
$775$	103.589	+	59.8070i	0.133663	+	0.0771704i
$776$		0			0
$777$	938.090	−	1030.16i	1.20732	−	1.32581i
$778$		0			0
$779$	378.760	+	213.747i	0.486213	+	0.274387i
$780$		0			0
$781$	−322.367	−	186.118i	−0.412761	−	0.238308i
$782$		0			0
$783$	−328.883	−	247.523i	−0.420029	−	0.316121i
$784$		0			0
$785$	785.029			1.00004
$786$		0			0
$787$	885.613	+	511.309i	1.12530	+	0.649693i	0.942749	−	0.333503i	$-0.108231\pi$
$787$	885.613	+	511.309i	1.12530	+	0.649693i	0.182553	+	0.983196i	$0.441564\pi$
$788$		0			0
$789$	67.1295	−	307.319i	0.0850817	−	0.389504i
$790$		0			0
$791$			635.292i			0.803150i
$792$		0			0
$793$	25.7293	−	14.8548i	0.0324455	−	0.0187324i
$794$		0			0
$795$	−245.775	−	53.6860i	−0.309150	−	0.0675296i
$796$		0			0
$797$	−424.917	−	245.326i	−0.533146	−	0.307812i	0.209151	−	0.977883i	$-0.432930\pi$
$797$	−424.917	−	245.326i	−0.533146	−	0.307812i	−0.742297	+	0.670071i	$0.766263\pi$
$798$		0			0
$799$	−321.433	−	556.739i	−0.402294	−	0.696794i
$800$		0			0
$801$	−1174.60	+	110.126i	−1.46642	+	0.137486i
$802$		0			0
$803$	525.265	−	909.786i	0.654129	−	1.13298i
$804$		0			0
$805$	497.821	−	862.251i	0.618411	−	1.07112i
$806$		0			0
$807$	−286.574	+	314.699i	−0.355110	+	0.389961i
$808$		0			0
$809$	654.603			0.809151			0.404575	−	0.914505i	$-0.367419\pi$
$809$	654.603			0.809151			0.404575	+	0.914505i	$0.367419\pi$
$810$		0			0
$811$	−231.770	−	133.812i	−0.285783	−	0.164997i	0.350256	−	0.936654i	$-0.386095\pi$
$811$	−231.770	−	133.812i	−0.285783	−	0.164997i	−0.636038	+	0.771657i	$0.719428\pi$
$812$		0			0
$813$	216.401	+	197.061i	0.266176	+	0.242388i
$814$		0			0
$815$	57.2943			0.0702997
$816$		0			0
$817$	−155.530	−	263.380i	−0.190367	−	0.322375i
$818$		0			0
$819$	45.4098	−	4.25745i	0.0554454	−	0.00519835i
$820$		0			0
$821$	−781.628			−0.952043			−0.476022	−	0.879434i	$-0.657922\pi$
$821$	−781.628			−0.952043			−0.476022	+	0.879434i	$0.657922\pi$
$822$		0			0
$823$	−11.8416	−	20.5103i	−0.0143884	−	0.0249214i	0.858742	−	0.512409i	$-0.171247\pi$
$823$	−11.8416	−	20.5103i	−0.0143884	−	0.0249214i	−0.873130	+	0.487488i	$0.837913\pi$
$824$		0			0
$825$	−286.736	−	261.110i	−0.347559	−	0.316498i
$826$		0			0
$827$	215.842	+	124.616i	0.260994	+	0.150685i	0.624788	−	0.780794i	$-0.285185\pi$
$827$	215.842	+	124.616i	0.260994	+	0.150685i	−0.363794	+	0.931479i	$0.618519\pi$
$828$		0			0
$829$			1194.32i			1.44068i	0.693622	+	0.720339i	$0.256014\pi$
$829$			1194.32i			1.44068i	−0.693622	+	0.720339i	$0.743986\pi$
$830$		0			0
$831$	−377.720	−	343.963i	−0.454537	−	0.413914i
$832$		0			0
$833$	−1786.97			−2.14523
$834$		0			0
$835$	848.685	−	489.989i	1.01639	−	0.586813i
$836$		0			0
$837$	365.053	−	155.214i	0.436144	−	0.185440i
$838$		0			0
$839$	472.120	+	272.578i	0.562717	+	0.324885i	0.754235	−	0.656604i	$-0.228008\pi$
$839$	472.120	+	272.578i	0.562717	+	0.324885i	−0.191518	+	0.981489i	$0.561341\pi$
$840$		0			0
$841$	608.584			0.723644
$842$		0			0
$843$	446.495	+	1400.90i	0.529650	+	1.66181i
$844$		0			0
$845$	−346.636	+	600.391i	−0.410220	+	0.710522i
$846$		0			0
$847$	1701.58			2.00895
$848$		0			0
$849$	1249.84	−	398.347i	1.47213	−	0.469196i
$850$		0			0
$851$	579.002	−	334.287i	0.680379	−	0.392817i
$852$		0			0
$853$	−444.416	+	769.751i	−0.521003	+	0.902404i	0.478698	+	0.877979i	$0.341109\pi$
$853$	−444.416	+	769.751i	−0.521003	+	0.902404i	−0.999702	+	0.0244246i	$0.992225\pi$
$854$		0			0
$855$	72.3989	+	698.367i	0.0846770	+	0.816804i
$856$		0			0
$857$	156.953	+	90.6167i	0.183142	+	0.105737i	0.588768	−	0.808302i	$-0.299613\pi$
$857$	156.953	+	90.6167i	0.183142	+	0.105737i	−0.405626	+	0.914039i	$0.632946\pi$
$858$		0			0
$859$	−627.970	−	1087.68i	−0.731048	−	1.26621i	−0.956436	−	0.291943i	$-0.905698\pi$
$859$	−627.970	−	1087.68i	−0.731048	−	1.26621i	0.225388	−	0.974269i	$-0.427635\pi$
$860$		0			0
$861$	600.072	−	658.964i	0.696948	−	0.765348i
$862$		0			0
$863$		−	267.394i		−	0.309843i	−0.987927	−	0.154921i	$-0.950488\pi$
$863$		−	267.394i		−	0.309843i	0.987927	−	0.154921i	$-0.0495124\pi$
$864$		0			0
$865$	−503.383	−	290.628i	−0.581945	−	0.335986i
$866$		0			0
$867$	−41.7319	+	191.049i	−0.0481336	+	0.220356i
$868$		0			0
$869$		−	1919.07i		−	2.20837i
$870$		0			0
$871$	8.75597	−	15.1658i	0.0100528	−	0.0174119i
$872$		0			0
$873$	1293.24	−	121.250i	1.48138	−	0.138888i
$874$		0			0
$875$	883.045	+	1529.48i	1.00919	+	1.74797i
$876$		0			0
$877$			1250.37i			1.42574i	0.701298	+	0.712869i	$0.252604\pi$
$877$			1250.37i			1.42574i	−0.701298	+	0.712869i	$0.747396\pi$
$878$		0			0
$879$	788.155	+	172.161i	0.896650	+	0.195861i
$880$		0			0
$881$	596.782			0.677392			0.338696	−	0.940896i	$-0.390014\pi$
$881$	596.782			0.677392			0.338696	+	0.940896i	$0.390014\pi$
$882$		0			0
$883$	438.181	−	758.951i	0.496241	−	0.859514i	−0.503750	−	0.863850i	$-0.668047\pi$
$883$	438.181	−	758.951i	0.496241	−	0.859514i	0.999991	+	0.00433543i	$0.00138001\pi$
$884$		0			0
$885$	−259.757	−	815.002i	−0.293511	−	0.920907i
$886$		0			0
$887$	981.212	−	566.503i	1.10621	−	0.638673i	0.168368	−	0.985724i	$-0.446150\pi$
$887$	981.212	−	566.503i	1.10621	−	0.638673i	0.937846	+	0.347051i	$0.112817\pi$
$888$		0			0
$889$		−	2974.47i		−	3.34586i
$890$		0			0
$891$	−1263.69	+	239.059i	−1.41829	+	0.268305i
$892$		0			0
$893$	401.264	−	711.039i	0.449344	−	0.796237i
$894$		0			0
$895$			1041.01i			1.16314i
$896$		0			0
$897$	21.3815	+	4.67050i	0.0238367	+	0.00520680i
$898$		0			0
$899$	111.990	−	193.972i	0.124572	−	0.215765i
$900$		0			0
$901$			305.544i			0.339116i
$902$		0			0
$903$	−597.218	+	190.345i	−0.661371	+	0.210792i
$904$		0			0
$905$	−821.460	−	474.270i	−0.907691	−	0.524056i
$906$		0			0
$907$	−355.769	−	205.404i	−0.392249	−	0.226465i	0.290885	−	0.956758i	$-0.406050\pi$
$907$	−355.769	−	205.404i	−0.392249	−	0.226465i	−0.683134	+	0.730293i	$0.739383\pi$
$908$		0			0
$909$	−1334.86	+	947.100i	−1.46849	+	1.04191i
$910$		0			0
$911$	−822.448	+	474.840i	−0.902797	+	0.521230i	−0.878107	−	0.478465i	$-0.841193\pi$
$911$	−822.448	+	474.840i	−0.902797	+	0.521230i	−0.0246902	+	0.999695i	$0.507860\pi$
$912$		0			0
$913$	−1033.68	+	1790.39i	−1.13218	+	1.96100i
$914$		0			0
$915$	892.982	−	284.611i	0.975936	−	0.311050i
$916$		0			0
$917$	418.791	+	725.367i	0.456697	+	0.791022i
$918$		0			0
$919$	943.523			1.02668			0.513342	−	0.858184i	$-0.328407\pi$
$919$	943.523			1.02668			0.513342	+	0.858184i	$0.328407\pi$
$920$		0			0
$921$	−518.794	+	569.709i	−0.563294	+	0.618577i
$922$		0			0
$923$	−4.57693	+	7.92747i	−0.00495875	+	0.00858881i
$924$		0			0
$925$			291.335i			0.314957i
$926$		0			0
$927$	−1274.84	+	119.524i	−1.37523	+	0.128936i
$928$		0			0
$929$	81.0849	−	140.443i	0.0872819	−	0.151177i	−0.819079	−	0.573680i	$-0.805515\pi$
$929$	81.0849	−	140.443i	0.0872819	−	0.151177i	0.906361	+	0.422503i	$0.138849\pi$
$930$		0			0
$931$	−1153.98	−	1954.20i	−1.23951	−	2.09903i
$932$		0			0
$933$	−99.4309	+	455.195i	−0.106571	+	0.487883i
$934$		0			0
$935$	487.659	−	844.649i	0.521560	−	0.903368i
$936$		0			0
$937$	−118.230	+	204.780i	−0.126179	+	0.218548i	−0.922193	−	0.386730i	$-0.873605\pi$
$937$	−118.230	+	204.780i	−0.126179	+	0.218548i	0.796014	+	0.605278i	$0.206938\pi$
$938$		0			0
$939$	−474.077	+	151.098i	−0.504874	+	0.160913i
$940$		0			0
$941$	167.451	−	96.6779i	0.177950	−	0.102740i	−0.408379	−	0.912812i	$-0.633906\pi$
$941$	167.451	−	96.6779i	0.177950	−	0.102740i	0.586329	+	0.810073i	$0.300573\pi$
$942$		0			0
$943$	370.373	−	213.835i	0.392760	−	0.226760i
$944$		0			0
$945$	1428.19	+	174.493i	1.51131	+	0.184649i
$946$		0			0
$947$	−204.607	+	354.389i	−0.216058	+	0.374223i	−0.953599	−	0.301079i	$-0.902653\pi$
$947$	−204.607	+	354.389i	−0.216058	+	0.374223i	0.737542	+	0.675302i	$0.235987\pi$
$948$		0			0
$949$	−22.3730	−	12.9170i	−0.0235753	−	0.0136112i
$950$		0			0
$951$	253.085	+	794.070i	0.266126	+	0.834984i
$952$		0			0
$953$	−1046.85	+	604.399i	−1.09848	+	0.634207i	−0.935821	−	0.352476i	$-0.885340\pi$
$953$	−1046.85	+	604.399i	−1.09848	+	0.634207i	−0.162658	+	0.986683i	$0.552007\pi$
$954$		0			0
$955$	−554.598	−	960.593i	−0.580731	−	1.00586i
$956$		0			0
$957$	−488.935	+	536.920i	−0.510904	+	0.561045i
$958$		0			0
$959$	642.249	+	1112.41i	0.669707	+	1.15997i
$960$		0			0
$961$	−372.575	−	645.319i	−0.387695	−	0.671507i
$962$		0			0
$963$	−39.5818	−	55.7874i	−0.0411026	−	0.0579308i
$964$		0			0
$965$		−	102.674i		−	0.106398i
$966$		0			0
$967$	1179.86			1.22012			0.610061	−	0.792355i	$-0.291145\pi$
$967$	1179.86			1.22012			0.610061	+	0.792355i	$0.291145\pi$
$968$		0			0
$969$	809.897	−	266.916i	0.835807	−	0.275455i
$970$		0			0
$971$	927.828	−	535.682i	0.955538	−	0.551680i	0.0607413	−	0.998154i	$-0.480654\pi$
$971$	927.828	−	535.682i	0.955538	−	0.551680i	0.894797	+	0.446473i	$0.147320\pi$
$972$		0			0
$973$	−802.947	+	1390.74i	−0.825228	+	1.42934i
$974$		0			0
$975$	−6.42109	+	7.05127i	−0.00658574	+	0.00723207i
$976$		0			0
$977$	−489.309	−	282.503i	−0.500828	−	0.289153i	0.228228	−	0.973608i	$-0.426707\pi$
$977$	−489.309	−	282.503i	−0.500828	−	0.289153i	−0.729055	+	0.684455i	$0.760040\pi$
$978$		0			0
$979$			2081.33i			2.12597i
$980$		0			0
$981$	−211.240	+	460.457i	−0.215331	+	0.469375i
$982$		0			0
$983$	368.761	+	212.904i	0.375139	+	0.216586i	0.675701	−	0.737176i	$-0.263841\pi$
$983$	368.761	+	212.904i	0.375139	+	0.216586i	−0.300562	+	0.953762i	$0.597174\pi$
$984$		0			0
$985$	1001.57			1.01682
$986$		0			0
$987$	−1237.06	−	1126.51i	−1.25336	−	1.14134i
$988$		0			0
$989$	−300.782			−0.304127
$990$		0			0
$991$	−618.826	+	357.279i	−0.624446	+	0.360524i	−0.778598	−	0.627523i	$-0.784069\pi$
$991$	−618.826	+	357.279i	−0.624446	+	0.360524i	0.154152	+	0.988047i	$0.450735\pi$
$992$		0			0
$993$	−539.029	+	591.930i	−0.542829	+	0.596103i
$994$		0			0
$995$	−354.417	+	613.869i	−0.356198	+	0.616954i
$996$		0			0
$997$	−408.748			−0.409978			−0.204989	−	0.978764i	$-0.565716\pi$
$997$	−408.748			−0.409978			−0.204989	+	0.978764i	$0.565716\pi$
$998$		0			0
$999$	771.960	+	580.990i	0.772733	+	0.581572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.bl.a.373.4	yes	80
3.2	odd	2		2052.3.bl.a.145.12		80
9.2	odd	6		2052.3.s.a.829.29		80
9.7	even	3		684.3.s.a.601.10	yes	80
19.8	odd	6		684.3.s.a.445.10	✓	80
57.8	even	6		2052.3.s.a.901.29		80
171.65	even	6		2052.3.bl.a.1585.12		80
171.160	odd	6	inner	684.3.bl.a.673.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.10	✓	80	19.8	odd	6
684.3.s.a.601.10	yes	80	9.7	even	3
684.3.bl.a.373.4	yes	80	1.1	even	1	trivial
684.3.bl.a.673.4	yes	80	171.160	odd	6	inner
2052.3.s.a.829.29		80	9.2	odd	6
2052.3.s.a.901.29		80	57.8	even	6
2052.3.bl.a.145.12		80	3.2	odd	2
2052.3.bl.a.1585.12		80	171.65	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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.85833 + 0.911006i) q^{3} +4.10591 q^{5} +(-6.48935 - 11.2399i) q^{7} +(7.34014 - 5.20792i) q^{9} +O(q^{10})\)	\(q+(-2.85833 + 0.911006i) q^{3} +4.10591 q^{5} +(-6.48935 - 11.2399i) q^{7} +(7.34014 - 5.20792i) q^{9} +(-7.93892 - 13.7506i) q^{11} +(-0.338148 + 0.195230i) q^{13} +(-11.7360 + 3.74051i) q^{15} +(7.48023 + 12.9561i) q^{17} +(-9.33801 + 16.5469i) q^{19} +(28.7883 + 26.2155i) q^{21} +(9.34185 + 16.1806i) q^{23} -8.14153 q^{25} +(-16.2361 + 21.5729i) q^{27} +15.2452i q^{29} +(-12.7235 - 7.34592i) q^{31} +(35.2190 + 32.0714i) q^{33} +(-26.6447 - 46.1499i) q^{35} -35.7838i q^{37} +(0.788684 - 0.866087i) q^{39} -22.8900i q^{41} +(-8.04931 + 13.9418i) q^{43} +(30.1379 - 21.3832i) q^{45} -42.9710 q^{47} +(-59.7232 + 103.444i) q^{49} +(-33.1841 - 30.2184i) q^{51} +(17.6872 + 10.2117i) q^{53} +(-32.5965 - 56.4588i) q^{55} +(11.6168 - 55.8037i) q^{57} +69.4443i q^{59} -76.0888 q^{61} +(-106.169 - 48.7062i) q^{63} +(-1.38840 + 0.801596i) q^{65} +(-38.8408 + 22.4248i) q^{67} +(-41.4427 - 37.7389i) q^{69} +(20.3029 - 11.7219i) q^{71} +(33.0816 + 57.2991i) q^{73} +(23.2712 - 7.41698i) q^{75} +(-103.037 + 178.465i) q^{77} +(104.672 + 60.4325i) q^{79} +(26.7552 - 76.4536i) q^{81} +(-65.1021 - 112.760i) q^{83} +(30.7131 + 53.1967i) q^{85} +(-13.8885 - 43.5758i) q^{87} +(-113.522 - 65.5419i) q^{89} +(4.38872 + 2.53383i) q^{91} +(43.0602 + 9.40590i) q^{93} +(-38.3410 + 67.9402i) q^{95} +(124.988 + 72.1619i) q^{97} +(-129.885 - 59.5861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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