LMFDB - Embedded newform 684.3.be.a.425.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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, 1, 2]))

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

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (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			425.4
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82991 - 0.995790i) q^{3} +(-7.96394 - 4.59798i) q^{5} +(6.18838 - 10.7186i) q^{7} +(7.01680 + 5.63600i) q^{9} +O(q^{10})$	\(q+(-2.82991 - 0.995790i) q^{3} +(-7.96394 - 4.59798i) q^{5} +(6.18838 - 10.7186i) q^{7} +(7.01680 + 5.63600i) q^{9} +(10.7850 + 6.22670i) q^{11} +17.8022 q^{13} +(17.9586 + 20.9423i) q^{15} +(7.65677 - 4.42064i) q^{17} +(11.6858 - 14.9814i) q^{19} +(-28.1860 + 24.1703i) q^{21} -27.7422i q^{23} +(29.7829 + 51.5855i) q^{25} +(-14.2447 - 22.9366i) q^{27} +(11.6528 - 6.72777i) q^{29} +(-9.08468 - 15.7351i) q^{31} +(-24.3200 - 28.3606i) q^{33} +(-98.5679 + 56.9082i) q^{35} +20.0772 q^{37} +(-50.3786 - 17.7272i) q^{39} +(-54.0919 - 31.2300i) q^{41} +44.9257 q^{43} +(-29.9672 - 77.1479i) q^{45} +(-38.1600 + 22.0317i) q^{47} +(-52.0922 - 90.2263i) q^{49} +(-26.0700 + 4.88548i) q^{51} +(57.3275 + 33.0980i) q^{53} +(-57.2606 - 99.1782i) q^{55} +(-47.9881 + 30.7595i) q^{57} +(78.6137 + 45.3876i) q^{59} +(7.06171 + 12.2312i) q^{61} +(103.833 - 40.3326i) q^{63} +(-141.775 - 81.8541i) q^{65} +33.4118 q^{67} +(-27.6254 + 78.5079i) q^{69} +(1.24544 - 0.719053i) q^{71} +(-27.4552 - 47.5538i) q^{73} +(-32.9147 - 175.640i) q^{75} +(133.483 - 77.0665i) q^{77} +63.0803 q^{79} +(17.4711 + 79.0934i) q^{81} +(1.55636 + 0.898564i) q^{83} -81.3041 q^{85} +(-39.6760 + 7.43522i) q^{87} +(-103.627 - 59.8290i) q^{89} +(110.167 - 190.814i) q^{91} +(10.0400 + 53.5754i) q^{93} +(-161.949 + 65.5800i) q^{95} -139.746 q^{97} +(40.5823 + 104.476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.82991	−	0.995790i	−0.943304	−	0.331930i
$3$	−2.82991	−	0.995790i	−0.943304	−	0.331930i
$4$		0			0
$5$	−7.96394	−	4.59798i	−1.59279	−	0.919597i	−0.992826	−	0.119569i	$-0.961849\pi$
$5$	−7.96394	−	4.59798i	−1.59279	−	0.919597i	−0.599963	−	0.800028i	$-0.704818\pi$
$6$		0			0
$7$	6.18838	−	10.7186i	0.884055	−	1.53123i	0.0372614	−	0.999306i	$-0.488137\pi$
$7$	6.18838	−	10.7186i	0.884055	−	1.53123i	0.846793	−	0.531922i	$-0.178530\pi$
$8$		0			0
$9$	7.01680	+	5.63600i	0.779645	+	0.626222i
$10$		0			0
$11$	10.7850	+	6.22670i	0.980452	+	0.566064i	0.902406	−	0.430886i	$-0.141799\pi$
$11$	10.7850	+	6.22670i	0.980452	+	0.566064i	0.0780452	+	0.996950i	$0.475132\pi$
$12$		0			0
$13$	17.8022			1.36940			0.684699	−	0.728826i	$-0.259934\pi$
$13$	17.8022			1.36940			0.684699	+	0.728826i	$0.259934\pi$
$14$		0			0
$15$	17.9586	+	20.9423i	1.19724	+	1.39615i
$16$		0			0
$17$	7.65677	−	4.42064i	0.450398	−	0.260038i	−0.257600	−	0.966252i	$-0.582932\pi$
$17$	7.65677	−	4.42064i	0.450398	−	0.260038i	0.707998	+	0.706214i	$0.249598\pi$
$18$		0			0
$19$	11.6858	−	14.9814i	0.615041	−	0.788495i
$19$	11.6858	−	14.9814i	0.615041	−	0.788495i
$20$		0			0
$21$	−28.1860	+	24.1703i	−1.34219	+	1.15097i
$22$		0			0
$23$		−	27.7422i		−	1.20618i	−0.797673	−	0.603090i	$-0.793936\pi$
$23$		−	27.7422i		−	1.20618i	0.797673	−	0.603090i	$-0.206064\pi$
$24$		0			0
$25$	29.7829	+	51.5855i	1.19132	+	2.06342i
$26$		0			0
$27$	−14.2447	−	22.9366i	−0.527580	−	0.849505i
$28$		0			0
$29$	11.6528	−	6.72777i	0.401822	−	0.231992i	−0.285448	−	0.958394i	$-0.592142\pi$
$29$	11.6528	−	6.72777i	0.401822	−	0.231992i	0.687270	+	0.726402i	$0.258809\pi$
$30$		0			0
$31$	−9.08468	−	15.7351i	−0.293054	−	0.507585i	0.681476	−	0.731840i	$-0.261338\pi$
$31$	−9.08468	−	15.7351i	−0.293054	−	0.507585i	−0.974530	+	0.224256i	$0.928005\pi$
$32$		0			0
$33$	−24.3200	−	28.3606i	−0.736970	−	0.859412i
$34$		0			0
$35$	−98.5679	+	56.9082i	−2.81622	+	1.62595i
$36$		0			0
$37$	20.0772			0.542626			0.271313	−	0.962491i	$-0.412542\pi$
$37$	20.0772			0.542626			0.271313	+	0.962491i	$0.412542\pi$
$38$		0			0
$39$	−50.3786	−	17.7272i	−1.29176	−	0.454544i
$40$		0			0
$41$	−54.0919	−	31.2300i	−1.31931	−	0.761707i	−0.335696	−	0.941970i	$-0.608972\pi$
$41$	−54.0919	−	31.2300i	−1.31931	−	0.761707i	−0.983618	+	0.180264i	$0.942305\pi$
$42$		0			0
$43$	44.9257			1.04478			0.522392	−	0.852706i	$-0.325040\pi$
$43$	44.9257			1.04478			0.522392	+	0.852706i	$0.325040\pi$
$44$		0			0
$45$	−29.9672	−	77.1479i	−0.665938	−	1.71440i
$46$		0			0
$47$	−38.1600	+	22.0317i	−0.811915	+	0.468759i	−0.847620	−	0.530603i	$-0.821965\pi$
$47$	−38.1600	+	22.0317i	−0.811915	+	0.468759i	0.0357057	+	0.999362i	$0.488632\pi$
$48$		0			0
$49$	−52.0922	−	90.2263i	−1.06311	−	1.84135i
$50$		0			0
$51$	−26.0700	+	4.88548i	−0.511177	+	0.0957938i
$52$		0			0
$53$	57.3275	+	33.0980i	1.08165	+	0.624491i	0.931341	−	0.364147i	$-0.118640\pi$
$53$	57.3275	+	33.0980i	1.08165	+	0.624491i	0.150310	+	0.988639i	$0.451973\pi$
$54$		0			0
$55$	−57.2606	−	99.1782i	−1.04110	−	1.80324i
$56$		0			0
$57$	−47.9881	+	30.7595i	−0.841896	+	0.539640i
$58$		0			0
$59$	78.6137	+	45.3876i	1.33244	+	0.769282i	0.985672	−	0.168671i	$-0.0539475\pi$
$59$	78.6137	+	45.3876i	1.33244	+	0.769282i	0.346763	+	0.937953i	$0.387281\pi$
$60$		0			0
$61$	7.06171	+	12.2312i	0.115766	+	0.200512i	0.918086	−	0.396382i	$-0.129734\pi$
$61$	7.06171	+	12.2312i	0.115766	+	0.200512i	−0.802320	+	0.596894i	$0.796401\pi$
$62$		0			0
$63$	103.833	−	40.3326i	1.64814	−	0.640200i
$64$		0			0
$65$	−141.775	−	81.8541i	−2.18116	−	1.25929i
$66$		0			0
$67$	33.4118			0.498683			0.249342	−	0.968416i	$-0.419786\pi$
$67$	33.4118			0.498683			0.249342	+	0.968416i	$0.419786\pi$
$68$		0			0
$69$	−27.6254	+	78.5079i	−0.400368	+	1.13780i
$70$		0			0
$71$	1.24544	−	0.719053i	0.0175414	−	0.0101275i	−0.491204	−	0.871045i	$-0.663443\pi$
$71$	1.24544	−	0.719053i	0.0175414	−	0.0101275i	0.508745	+	0.860917i	$0.330110\pi$
$72$		0			0
$73$	−27.4552	−	47.5538i	−0.376099	−	0.651422i	0.614392	−	0.789001i	$-0.289401\pi$
$73$	−27.4552	−	47.5538i	−0.376099	−	0.651422i	−0.990491	+	0.137579i	$0.956068\pi$
$74$		0			0
$75$	−32.9147	−	175.640i	−0.438863	−	2.34187i
$76$		0			0
$77$	133.483	−	77.0665i	1.73355	−	1.00086i
$78$		0			0
$79$	63.0803			0.798485			0.399242	−	0.916845i	$-0.369273\pi$
$79$	63.0803			0.798485			0.399242	+	0.916845i	$0.369273\pi$
$80$		0			0
$81$	17.4711	+	79.0934i	0.215693	+	0.976461i
$82$		0			0
$83$	1.55636	+	0.898564i	0.0187513	+	0.0108261i	0.509346	−	0.860562i	$-0.329887\pi$
$83$	1.55636	+	0.898564i	0.0187513	+	0.0108261i	−0.490595	+	0.871388i	$0.663221\pi$
$84$		0			0
$85$	−81.3041			−0.956519
$86$		0			0
$87$	−39.6760	+	7.43522i	−0.456046	+	0.0854623i
$88$		0			0
$89$	−103.627	−	59.8290i	−1.16435	−	0.672236i	−0.212005	−	0.977269i	$-0.567999\pi$
$89$	−103.627	−	59.8290i	−1.16435	−	0.672236i	−0.952342	+	0.305033i	$0.901333\pi$
$90$		0			0
$91$	110.167	−	190.814i	1.21062	−	2.09686i
$92$		0			0
$93$	10.0400	+	53.5754i	0.107957	+	0.576080i
$94$		0			0
$95$	−161.949	+	65.5800i	−1.70473	+	0.690315i
$96$		0			0
$97$	−139.746			−1.44068			−0.720338	−	0.693623i	$-0.756013\pi$
$97$	−139.746			−1.44068			−0.720338	+	0.693623i	$0.756013\pi$
$98$		0			0
$99$	40.5823	+	104.476i	0.409923	+	1.05531i
$100$		0			0
$101$	−56.4621	+	32.5984i	−0.559031	+	0.322757i	−0.752757	−	0.658299i	$-0.771276\pi$
$101$	−56.4621	+	32.5984i	−0.559031	+	0.322757i	0.193725	+	0.981056i	$0.437943\pi$
$102$		0			0
$103$	68.2356	+	118.187i	0.662481	+	1.14745i	0.979962	+	0.199186i	$0.0638299\pi$
$103$	68.2356	+	118.187i	0.662481	+	1.14745i	−0.317481	+	0.948265i	$0.602837\pi$
$104$		0			0
$105$	335.607	−	62.8923i	3.19626	−	0.598974i
$106$		0			0
$107$			154.312i			1.44216i	0.692850	+	0.721082i	$0.256355\pi$
$107$			154.312i			1.44216i	−0.692850	+	0.721082i	$0.743645\pi$
$108$		0			0
$109$	9.60246	+	16.6319i	0.0880959	+	0.152587i	0.906706	−	0.421763i	$-0.138588\pi$
$109$	9.60246	+	16.6319i	0.0880959	+	0.152587i	−0.818610	+	0.574349i	$0.805255\pi$
$110$		0			0
$111$	−56.8166	−	19.9926i	−0.511861	−	0.180114i
$112$		0			0
$113$	47.2024	−	27.2523i	0.417721	−	0.241171i	−0.276381	−	0.961048i	$-0.589135\pi$
$113$	47.2024	−	27.2523i	0.417721	−	0.241171i	0.694102	+	0.719877i	$0.255802\pi$
$114$		0			0
$115$	−127.558	+	220.937i	−1.10920	+	1.92119i
$116$		0			0
$117$	124.914	+	100.333i	1.06764	+	0.857546i
$118$		0			0
$119$		−	109.426i		−	0.919550i
$120$		0			0
$121$	17.0437	+	29.5205i	0.140857	+	0.243971i
$122$		0			0
$123$	121.977	+	142.242i	0.991682	+	1.15644i
$124$		0			0
$125$		−	317.867i		−	2.54293i
$126$		0			0
$127$	25.6802	−	44.4795i	0.202207	−	0.350232i	−0.747033	−	0.664787i	$-0.768522\pi$
$127$	25.6802	−	44.4795i	0.202207	−	0.350232i	0.949239	+	0.314555i	$0.101855\pi$
$128$		0			0
$129$	−127.136	−	44.7366i	−0.985549	−	0.346795i
$130$		0			0
$131$	−44.4548	−	25.6660i	−0.339349	−	0.195923i	0.320635	−	0.947203i	$-0.396104\pi$
$131$	−44.4548	−	25.6660i	−0.339349	−	0.195923i	−0.659984	+	0.751279i	$0.729437\pi$
$132$		0			0
$133$	−88.2634	−	217.966i	−0.663635	−	1.63884i
$134$		0			0
$135$	7.98146	+	248.163i	0.0591219	+	1.83824i
$136$		0			0
$137$	25.4956	−	14.7199i	0.186099	−	0.107444i	−0.404056	−	0.914734i	$-0.632400\pi$
$137$	25.4956	−	14.7199i	0.186099	−	0.107444i	0.590155	+	0.807290i	$0.299067\pi$
$138$		0			0
$139$	−247.463			−1.78031			−0.890155	−	0.455658i	$-0.849404\pi$
$139$	−247.463			−1.78031			−0.890155	+	0.455658i	$0.849404\pi$
$140$		0			0
$141$	129.928	−	24.3484i	0.921478	−	0.172684i
$142$		0			0
$143$	191.996	+	110.849i	1.34263	+	0.775167i
$144$		0			0
$145$	−123.737			−0.853357
$146$		0			0
$147$	57.5698	+	307.205i	0.391631	+	2.08983i
$148$		0			0
$149$	−147.104	−	84.9307i	−0.987277	−	0.570005i	−0.0828180	−	0.996565i	$-0.526392\pi$
$149$	−147.104	−	84.9307i	−0.987277	−	0.570005i	−0.904459	+	0.426560i	$0.859725\pi$
$150$		0			0
$151$	38.4855	−	66.6589i	0.254871	−	0.441450i	−0.709989	−	0.704212i	$-0.751300\pi$
$151$	38.4855	−	66.6589i	0.254871	−	0.441450i	0.964861	+	0.262763i	$0.0846336\pi$
$152$		0			0
$153$	78.6408	+	12.1348i	0.513992	+	0.0793122i
$154$		0			0
$155$			167.085i			1.07797i
$156$		0			0
$157$	47.1518	−	81.6694i	0.300330	−	0.520187i	−0.675881	−	0.737011i	$-0.736236\pi$
$157$	47.1518	−	81.6694i	0.300330	−	0.520187i	0.976211	+	0.216824i	$0.0695698\pi$
$158$		0			0
$159$	−129.273	−	150.751i	−0.813038	−	0.948118i
$160$		0			0
$161$	−297.357	−	171.679i	−1.84694	−	1.06633i
$162$		0			0
$163$	−143.841			−0.882460			−0.441230	−	0.897394i	$-0.645458\pi$
$163$	−143.841			−0.882460			−0.441230	+	0.897394i	$0.645458\pi$
$164$		0			0
$165$	63.2817	+	337.685i	0.383526	+	2.04658i
$166$		0			0
$167$			45.2033i			0.270678i	0.990799	+	0.135339i	$0.0432124\pi$
$167$			45.2033i			0.270678i	−0.990799	+	0.135339i	$0.956788\pi$
$168$		0			0
$169$	147.917			0.875249
$170$		0			0
$171$	166.432	−	39.2605i	0.973287	−	0.229594i
$172$		0			0
$173$			115.631i			0.668389i	0.942504	+	0.334195i	$0.108464\pi$
$173$			115.631i			0.668389i	−0.942504	+	0.334195i	$0.891536\pi$
$174$		0			0
$175$	737.233			4.21276
$176$		0			0
$177$	−177.273	−	206.726i	−1.00154	−	1.16794i
$178$		0			0
$179$		−	60.2475i		−	0.336578i	−0.985738	−	0.168289i	$-0.946176\pi$
$179$		−	60.2475i		−	0.336578i	0.985738	−	0.168289i	$-0.0538243\pi$
$180$		0			0
$181$	160.641	−	278.238i	0.887518	−	1.53723i	0.0447187	−	0.999000i	$-0.485761\pi$
$181$	160.641	−	278.238i	0.887518	−	1.53723i	0.842800	−	0.538227i	$-0.180906\pi$
$182$		0			0
$183$	−7.80428	−	41.6453i	−0.0426463	−	0.227570i
$184$		0			0
$185$	−159.893	−	92.3144i	−0.864288	−	0.498997i
$186$		0			0
$187$	110.104			0.588792
$188$		0			0
$189$	−334.000	+	10.7422i	−1.76720	+	0.0568369i
$190$		0			0
$191$	252.708	+	145.901i	1.32308	+	0.763879i	0.984218	−	0.176958i	$-0.0566258\pi$
$191$	252.708	+	145.901i	1.32308	+	0.763879i	0.338859	+	0.940837i	$0.389959\pi$
$192$		0			0
$193$	−124.619	+	215.846i	−0.645692	+	1.11837i	0.338449	+	0.940985i	$0.390098\pi$
$193$	−124.619	+	215.846i	−0.645692	+	1.11837i	−0.984141	+	0.177387i	$0.943236\pi$
$194$		0			0
$195$	319.703	+	372.818i	1.63950	+	1.91189i
$196$		0			0
$197$		−	201.228i		−	1.02146i	−0.859741	−	0.510731i	$-0.829375\pi$
$197$		−	201.228i		−	1.02146i	0.859741	−	0.510731i	$-0.170625\pi$
$198$		0			0
$199$	39.8029	−	68.9406i	0.200015	−	0.346435i	−0.748518	−	0.663114i	$-0.769234\pi$
$199$	39.8029	−	68.9406i	0.200015	−	0.346435i	0.948533	+	0.316679i	$0.102568\pi$
$200$		0			0
$201$	−94.5524	−	33.2711i	−0.470410	−	0.165528i
$202$		0			0
$203$		−	166.536i		−	0.820375i
$204$		0			0
$205$	287.190	+	497.427i	1.40093	+	2.42648i
$206$		0			0
$207$	156.355	−	194.661i	0.755337	−	0.940393i
$208$		0			0
$209$	219.316	−	88.8100i	1.04936	−	0.424928i
$210$		0			0
$211$	−35.4495	+	61.4004i	−0.168007	+	0.290997i	−0.937719	−	0.347394i	$-0.887067\pi$
$211$	−35.4495	+	61.4004i	−0.168007	+	0.290997i	0.769712	+	0.638391i	$0.220400\pi$
$212$		0			0
$213$	−4.24050	+	0.794664i	−0.0199085	+	0.00373082i
$214$		0			0
$215$	−357.786	−	206.568i	−1.66412	−	0.960780i
$216$		0			0
$217$	−224.878			−1.03630
$218$		0			0
$219$	30.3422	+	161.913i	0.138549	+	0.739327i
$220$		0			0
$221$	136.307	−	78.6969i	0.616774	−	0.356095i
$222$		0			0
$223$	150.251			0.673770			0.336885	−	0.941546i	$-0.390627\pi$
$223$	150.251			0.673770			0.336885	+	0.941546i	$0.390627\pi$
$224$		0			0
$225$	−81.7549	+	529.822i	−0.363355	+	2.35477i
$226$		0			0
$227$	150.306	+	86.7791i	0.662140	+	0.382287i	0.793092	−	0.609102i	$-0.208470\pi$
$227$	150.306	+	86.7791i	0.662140	+	0.382287i	−0.130952	+	0.991389i	$0.541803\pi$
$228$		0			0
$229$	155.432	+	269.216i	0.678741	+	1.17561i	0.975360	+	0.220619i	$0.0708076\pi$
$229$	155.432	+	269.216i	0.678741	+	1.17561i	−0.296619	+	0.954996i	$0.595859\pi$
$230$		0			0
$231$	−454.487	+	85.1703i	−1.96748	+	0.368702i
$232$		0			0
$233$	−44.0235	+	25.4170i	−0.188942	+	0.109086i	−0.591487	−	0.806314i	$-0.701459\pi$
$233$	−44.0235	+	25.4170i	−0.188942	+	0.109086i	0.402545	+	0.915400i	$0.368126\pi$
$234$		0			0
$235$	405.205			1.72428
$236$		0			0
$237$	−178.512	−	62.8147i	−0.753214	−	0.265041i
$238$		0			0
$239$	−296.906	+	171.419i	−1.24228	+	0.717233i	−0.969559	−	0.244859i	$-0.921258\pi$
$239$	−296.906	+	171.419i	−1.24228	+	0.717233i	−0.272725	+	0.962092i	$0.587925\pi$
$240$		0			0
$241$	60.5248	+	104.832i	0.251140	+	0.434988i	0.963840	−	0.266482i	$-0.0858611\pi$
$241$	60.5248	+	104.832i	0.251140	+	0.434988i	−0.712700	+	0.701469i	$0.752528\pi$
$242$		0			0
$243$	29.3187	−	241.225i	0.120653	−	0.992695i
$244$		0			0
$245$			958.076i			3.91051i
$246$		0			0
$247$	208.032	−	266.701i	0.842236	−	1.07976i
$248$		0			0
$249$	−3.50958	−	4.09266i	−0.0140947	−	0.0164364i
$250$		0			0
$251$	−115.899	−	66.9141i	−0.461748	−	0.266590i	0.251031	−	0.967979i	$-0.419230\pi$
$251$	−115.899	−	66.9141i	−0.461748	−	0.266590i	−0.712779	+	0.701389i	$0.752564\pi$
$252$		0			0
$253$	172.742	−	299.198i	0.682776	−	1.18260i
$254$		0			0
$255$	230.084	+	80.9618i	0.902288	+	0.317497i
$256$		0			0
$257$			14.4882i			0.0563742i	0.999603	+	0.0281871i	$0.00897342\pi$
$257$			14.4882i			0.0563742i	−0.999603	+	0.0281871i	$0.991027\pi$
$258$		0			0
$259$	124.245	−	215.199i	0.479711	−	0.830884i
$260$		0			0
$261$	119.683	+	18.4679i	0.458557	+	0.0707583i
$262$		0			0
$263$		−	61.8637i		−	0.235223i	−0.993060	−	0.117612i	$-0.962476\pi$
$263$		−	61.8637i		−	0.235223i	0.993060	−	0.117612i	$-0.0375238\pi$
$264$		0			0
$265$	−304.369	−	527.182i	−1.14856	−	1.98937i
$266$		0			0
$267$	233.678	+	272.501i	0.875198	+	1.02060i
$268$		0			0
$269$	−224.517	+	129.625i	−0.834635	+	0.481877i	−0.855437	−	0.517907i	$-0.826711\pi$
$269$	−224.517	+	129.625i	−0.834635	+	0.481877i	0.0208021	+	0.999784i	$0.493378\pi$
$270$		0			0
$271$	73.8692	+	127.945i	0.272580	+	0.472123i	0.969522	−	0.245005i	$-0.0787897\pi$
$271$	73.8692	+	127.945i	0.272580	+	0.472123i	−0.696942	+	0.717128i	$0.745456\pi$
$272$		0			0
$273$	−501.773	+	430.285i	−1.83800	+	1.57613i
$274$		0			0
$275$			741.798i			2.69745i
$276$		0			0
$277$	163.842	−	283.783i	0.591488	−	1.02449i	−0.402545	−	0.915400i	$-0.631874\pi$
$277$	163.842	−	283.783i	0.591488	−	1.02449i	0.994032	−	0.109086i	$-0.0347925\pi$
$278$		0			0
$279$	24.9377	−	161.612i	0.0893824	−	0.579253i
$280$		0			0
$281$	171.739	−	99.1534i	0.611170	−	0.352859i	−0.162253	−	0.986749i	$-0.551876\pi$
$281$	171.739	−	99.1534i	0.611170	−	0.352859i	0.773423	+	0.633890i	$0.218543\pi$
$282$		0			0
$283$	−248.156	+	429.819i	−0.876877	+	1.51880i	−0.0221273	+	0.999755i	$0.507044\pi$
$283$	−248.156	+	429.819i	−0.876877	+	1.51880i	−0.854750	+	0.519040i	$0.826289\pi$
$284$		0			0
$285$	523.606	−	24.3181i	1.83721	−	0.0853268i
$286$		0			0
$287$	−669.483	+	386.526i	−2.33269	+	1.34678i
$288$		0			0
$289$	−105.416	+	182.586i	−0.364761	+	0.631784i
$290$		0			0
$291$	395.468	+	139.157i	1.35900	+	0.478204i
$292$		0			0
$293$	36.7454	−	21.2150i	0.125411	−	0.0724061i	−0.435982	−	0.899955i	$-0.643599\pi$
$293$	36.7454	−	21.2150i	0.125411	−	0.0724061i	0.561393	+	0.827549i	$0.310266\pi$
$294$		0			0
$295$	−417.383	−	722.929i	−1.41486	−	2.45061i
$296$		0			0
$297$	−10.8087	−	336.068i	−0.0363929	−	1.13154i
$298$		0			0
$299$		−	493.871i		−	1.65174i
$300$		0			0
$301$	278.017	−	481.540i	0.923646	−	1.59980i
$302$		0			0
$303$	192.244	−	36.0263i	0.634469	−	0.118899i
$304$		0			0
$305$		−	129.879i		−	0.425831i
$306$		0			0
$307$	152.789	+	264.639i	0.497685	+	0.862016i	0.999996	−	0.00267067i	$-0.000850100\pi$
$307$	152.789	+	264.639i	0.497685	+	0.862016i	−0.502311	+	0.864687i	$0.667517\pi$
$308$		0			0
$309$	−75.4108	−	402.408i	−0.244048	−	1.30229i
$310$		0			0
$311$	343.368	−	198.243i	1.10408	−	0.637438i	0.166787	−	0.985993i	$-0.446661\pi$
$311$	343.368	−	198.243i	1.10408	−	0.637438i	0.937288	+	0.348555i	$0.113327\pi$
$312$		0			0
$313$	−208.960	−	361.930i	−0.667605	−	1.15633i	−0.978572	−	0.205905i	$-0.933986\pi$
$313$	−208.960	−	361.930i	−0.667605	−	1.15633i	0.310967	−	0.950421i	$-0.399347\pi$
$314$		0			0
$315$	−1012.37	−	156.214i	−3.21386	−	0.495919i
$316$		0			0
$317$	−62.8907	+	36.3100i	−0.198394	+	0.114543i	−0.595906	−	0.803054i	$-0.703207\pi$
$317$	−62.8907	+	36.3100i	−0.198394	+	0.114543i	0.397512	+	0.917597i	$0.369874\pi$
$318$		0			0
$319$	167.567			0.525290
$320$		0			0
$321$	153.662	−	436.688i	0.478697	−	1.36040i
$322$		0			0
$323$	23.2480	−	166.368i	0.0719753	−	0.515071i
$324$		0			0
$325$	530.201	+	918.334i	1.63139	+	2.82564i
$326$		0			0
$327$	−10.6122	−	56.6290i	−0.0324532	−	0.173177i
$328$		0			0
$329$			545.362i			1.65763i
$330$		0			0
$331$	56.3494	−	97.6001i	0.170240	−	0.294864i	−0.768264	−	0.640133i	$-0.778879\pi$
$331$	56.3494	−	97.6001i	0.170240	−	0.294864i	0.938504	+	0.345269i	$0.112212\pi$
$332$		0			0
$333$	140.877	+	113.155i	0.423055	+	0.339804i
$334$		0			0
$335$	−266.090	−	153.627i	−0.794297	−	0.458588i
$336$		0			0
$337$	186.796	−	323.540i	0.554291	−	0.960061i	−0.443667	−	0.896192i	$-0.646323\pi$
$337$	186.796	−	323.540i	0.554291	−	0.960061i	0.997958	−	0.0638690i	$-0.0203440\pi$
$338$		0			0
$339$	−160.716	+	30.1180i	−0.474089	+	0.0888437i
$340$		0			0
$341$		−	226.270i		−	0.663550i
$342$		0			0
$343$	−683.003			−1.99126
$344$		0			0
$345$	580.985	−	498.211i	1.68401	−	1.44409i
$346$		0			0
$347$	−433.363	−	250.202i	−1.24888	−	0.721044i	−0.277997	−	0.960582i	$-0.589671\pi$
$347$	−433.363	−	250.202i	−1.24888	−	0.721044i	−0.970887	+	0.239538i	$0.923004\pi$
$348$		0			0
$349$	−286.909	+	496.940i	−0.822088	+	1.42390i	0.0820366	+	0.996629i	$0.473858\pi$
$349$	−286.909	+	496.940i	−0.822088	+	1.42390i	−0.904125	+	0.427269i	$0.859476\pi$
$350$		0			0
$351$	−253.586	−	408.322i	−0.722467	−	1.16331i
$352$		0			0
$353$	311.309	+	179.734i	0.881894	+	0.509162i	0.871282	−	0.490782i	$-0.163289\pi$
$353$	311.309	+	179.734i	0.881894	+	0.509162i	0.0106114	+	0.999944i	$0.496622\pi$
$354$		0			0
$355$	−13.2248			−0.0372529
$356$		0			0
$357$	−108.966	+	309.667i	−0.305226	+	0.867415i
$358$		0			0
$359$	66.6314	−	38.4697i	0.185603	−	0.107158i	−0.404320	−	0.914618i	$-0.632492\pi$
$359$	66.6314	−	38.4697i	0.185603	−	0.107158i	0.589922	+	0.807460i	$0.299158\pi$
$360$		0			0
$361$	−87.8848	−	350.139i	−0.243448	−	0.969914i
$362$		0			0
$363$	−18.8359	−	100.512i	−0.0518895	−	0.276894i
$364$		0			0
$365$			504.954i			1.38344i
$366$		0			0
$367$	334.880	+	580.030i	0.912481	+	1.58046i	0.810548	+	0.585672i	$0.199169\pi$
$367$	334.880	+	580.030i	0.912481	+	1.58046i	0.101932	+	0.994791i	$0.467497\pi$
$368$		0			0
$369$	−203.540	−	523.996i	−0.551600	−	1.42004i
$370$		0			0
$371$	709.529	−	409.647i	1.91248	−	1.10417i
$372$		0			0
$373$	11.4689	+	19.8647i	0.0307476	+	0.0532564i	0.880990	−	0.473135i	$-0.156878\pi$
$373$	11.4689	+	19.8647i	0.0307476	+	0.0532564i	−0.850242	+	0.526392i	$0.823545\pi$
$374$		0			0
$375$	−316.528	+	899.534i	−0.844075	+	2.39876i
$376$		0			0
$377$	207.446	−	119.769i	0.550254	−	0.317689i
$378$		0			0
$379$	3.99850			0.0105501			0.00527507	−	0.999986i	$-0.498321\pi$
$379$	3.99850			0.0105501			0.00527507	+	0.999986i	$0.498321\pi$
$380$		0			0
$381$	−116.965	+	100.301i	−0.306995	+	0.263257i
$382$		0			0
$383$	107.762	+	62.2167i	0.281364	+	0.162446i	0.634041	−	0.773300i	$-0.281395\pi$
$383$	107.762	+	62.2167i	0.281364	+	0.162446i	−0.352677	+	0.935745i	$0.614728\pi$
$384$		0			0
$385$	−1417.40			−3.68156
$386$		0			0
$387$	315.235	+	253.201i	0.814560	+	0.654266i
$388$		0			0
$389$	−498.942	+	288.064i	−1.28263	+	0.740526i	−0.977328	−	0.211731i	$-0.932090\pi$
$389$	−498.942	+	288.064i	−1.28263	+	0.740526i	−0.305300	+	0.952256i	$0.598757\pi$
$390$		0			0
$391$	−122.638	−	212.415i	−0.313652	−	0.543262i
$392$		0			0
$393$	100.245	+	116.900i	0.255077	+	0.297456i
$394$		0			0
$395$	−502.368	−	290.042i	−1.27182	−	0.734284i
$396$		0			0
$397$	43.2291	+	74.8750i	0.108889	+	0.188602i	0.915321	−	0.402726i	$-0.131937\pi$
$397$	43.2291	+	74.8750i	0.108889	+	0.188602i	−0.806431	+	0.591328i	$0.798604\pi$
$398$		0			0
$399$	32.7295	+	704.716i	0.0820289	+	1.76621i
$400$		0			0
$401$	−83.5216	−	48.2212i	−0.208283	−	0.120252i	0.392230	−	0.919867i	$-0.371704\pi$
$401$	−83.5216	−	48.2212i	−0.208283	−	0.120252i	−0.600513	+	0.799615i	$0.705037\pi$
$402$		0			0
$403$	−161.727	−	280.119i	−0.401308	−	0.695085i
$404$		0			0
$405$	224.531	−	710.227i	0.554398	−	1.75365i
$406$		0			0
$407$	216.531	+	125.014i	0.532018	+	0.307161i
$408$		0			0
$409$	−349.765			−0.855171			−0.427585	−	0.903975i	$-0.640636\pi$
$409$	−349.765			−0.855171			−0.427585	+	0.903975i	$0.640636\pi$
$410$		0			0
$411$	−86.8082	+	16.2677i	−0.211212	+	0.0395808i
$412$		0			0
$413$	972.983	−	561.752i	2.35589	−	1.36017i
$414$		0			0
$415$	−8.26317	−	14.3122i	−0.0199112	−	0.0344873i
$416$		0			0
$417$	700.299	+	246.421i	1.67937	+	0.590938i
$418$		0			0
$419$	536.131	−	309.536i	1.27955	−	0.738748i	0.302784	−	0.953059i	$-0.402084\pi$
$419$	536.131	−	309.536i	1.27955	−	0.738748i	0.976765	+	0.214311i	$0.0687506\pi$
$420$		0			0
$421$	−386.808			−0.918785			−0.459392	−	0.888233i	$-0.651933\pi$
$421$	−386.808			−0.918785			−0.459392	+	0.888233i	$0.651933\pi$
$422$		0			0
$423$	−391.932	−	60.4775i	−0.926552	−	0.142973i
$424$		0			0
$425$	456.082	+	263.319i	1.07313	+	0.619574i
$426$		0			0
$427$	174.802			0.409373
$428$		0			0
$429$	−432.949	−	504.880i	−1.00921	−	1.17688i
$430$		0			0
$431$	−73.4290	−	42.3942i	−0.170369	−	0.0983625i	0.412391	−	0.911007i	$-0.364694\pi$
$431$	−73.4290	−	42.3942i	−0.170369	−	0.0983625i	−0.582760	+	0.812644i	$0.698027\pi$
$432$		0			0
$433$	−113.236	+	196.131i	−0.261515	+	0.452958i	−0.966645	−	0.256121i	$-0.917556\pi$
$433$	−113.236	+	196.131i	−0.261515	+	0.452958i	0.705129	+	0.709079i	$0.250889\pi$
$434$		0			0
$435$	350.164	+	123.216i	0.804975	+	0.283255i
$436$		0			0
$437$	−415.616	−	324.189i	−0.951067	−	0.741851i
$438$		0			0
$439$	572.956			1.30514			0.652570	−	0.757728i	$-0.273691\pi$
$439$	572.956			1.30514			0.652570	+	0.757728i	$0.273691\pi$
$440$		0			0
$441$	142.994	−	926.691i	0.324250	−	2.10134i
$442$		0			0
$443$	458.388	−	264.651i	1.03474	−	0.597406i	0.116399	−	0.993203i	$-0.462865\pi$
$443$	458.388	−	264.651i	1.03474	−	0.597406i	0.918338	+	0.395797i	$0.129532\pi$
$444$		0			0
$445$	550.186	+	952.950i	1.23637	+	2.14146i
$446$		0			0
$447$	331.719	+	386.831i	0.742101	+	0.865395i
$448$		0			0
$449$			408.091i			0.908889i	0.890775	+	0.454445i	$0.150162\pi$
$449$			408.091i			0.908889i	−0.890775	+	0.454445i	$0.849838\pi$
$450$		0			0
$451$	−388.920	−	673.629i	−0.862350	−	1.49363i
$452$		0			0
$453$	−175.289	+	150.315i	−0.386951	+	0.331822i
$454$		0			0
$455$	−1754.72	+	1013.09i	−3.85653	+	2.22657i
$456$		0			0
$457$	−221.408	+	383.489i	−0.484481	+	0.839145i	−0.999841	−	0.0178284i	$-0.994325\pi$
$457$	−221.408	+	383.489i	−0.484481	+	0.839145i	0.515360	+	0.856974i	$0.327658\pi$
$458$		0			0
$459$	−210.463	−	112.650i	−0.458525	−	0.245425i
$460$		0			0
$461$		−	497.437i		−	1.07904i	−0.841973	−	0.539519i	$-0.818606\pi$
$461$		−	497.437i		−	1.07904i	0.841973	−	0.539519i	$-0.181394\pi$
$462$		0			0
$463$	−117.318	−	203.201i	−0.253387	−	0.438879i	0.711069	−	0.703122i	$-0.248211\pi$
$463$	−117.318	−	203.201i	−0.253387	−	0.438879i	−0.964456	+	0.264243i	$0.914878\pi$
$464$		0			0
$465$	166.381	−	472.835i	0.357809	−	1.01685i
$466$		0			0
$467$		−	117.467i		−	0.251536i	−0.992060	−	0.125768i	$-0.959861\pi$
$467$		−	117.467i		−	0.251536i	0.992060	−	0.125768i	$-0.0401395\pi$
$468$		0			0
$469$	206.765	−	358.127i	0.440863	−	0.763598i
$470$		0			0
$471$	−214.761	+	184.164i	−0.455968	+	0.391006i
$472$		0			0
$473$	484.522	+	279.739i	1.02436	+	0.591414i
$474$		0			0
$475$	1120.86	+	156.628i	2.35971	+	0.329742i
$476$		0			0
$477$	215.715	+	555.340i	0.452234	+	1.16424i
$478$		0			0
$479$	−246.127	+	142.102i	−0.513835	+	0.296663i	−0.734409	−	0.678707i	$-0.762540\pi$
$479$	−246.127	+	142.102i	−0.513835	+	0.296663i	0.220573	+	0.975370i	$0.429207\pi$
$480$		0			0
$481$	357.417			0.743070
$482$		0			0
$483$	670.538	+	781.942i	1.38828	+	1.61893i
$484$		0			0
$485$	1112.93	+	642.548i	2.29469	+	1.32484i
$486$		0			0
$487$	−956.196			−1.96344			−0.981721	−	0.190328i	$-0.939045\pi$
$487$	−956.196			−1.96344			−0.981721	+	0.190328i	$0.939045\pi$
$488$		0			0
$489$	407.057	+	143.235i	0.832428	+	0.292915i
$490$		0			0
$491$	−189.668	−	109.505i	−0.386290	−	0.223025i	0.294261	−	0.955725i	$-0.404926\pi$
$491$	−189.668	−	109.505i	−0.386290	−	0.223025i	−0.680551	+	0.732700i	$0.738260\pi$
$492$		0			0
$493$	59.4821	−	103.026i	0.120653	−	0.208978i
$494$		0			0
$495$	157.182	−	1018.63i	0.317539	−	2.05785i
$496$		0			0
$497$		−	17.7991i		−	0.0358131i
$498$		0			0
$499$	−412.896	+	715.157i	−0.827447	+	1.43318i	0.0725868	+	0.997362i	$0.476875\pi$
$499$	−412.896	+	715.157i	−0.827447	+	1.43318i	−0.900034	+	0.435819i	$0.856459\pi$
$500$		0			0
$501$	45.0130	−	127.921i	0.0898463	−	0.255332i
$502$		0			0
$503$	−98.1076	−	56.6425i	−0.195045	−	0.112609i	0.399297	−	0.916822i	$-0.369254\pi$
$503$	−98.1076	−	56.6425i	−0.195045	−	0.112609i	−0.594342	+	0.804212i	$0.702588\pi$
$504$		0			0
$505$	599.548			1.18722
$506$		0			0
$507$	−418.592	−	147.294i	−0.825626	−	0.290521i
$508$		0			0
$509$		−	583.639i		−	1.14664i	−0.819332	−	0.573319i	$-0.805655\pi$
$509$		−	583.639i		−	1.14664i	0.819332	−	0.573319i	$-0.194345\pi$
$510$		0			0
$511$	−679.613			−1.32997
$512$		0			0
$513$	−510.083	−	54.6275i	−0.994314	−	0.106486i
$514$		0			0
$515$		−	1254.98i		−	2.43686i
$516$		0			0
$517$	−548.739			−1.06139
$518$		0			0
$519$	115.145	−	327.227i	0.221858	−	0.630494i
$520$		0			0
$521$		−	502.648i		−	0.964775i	−0.875958	−	0.482387i	$-0.839770\pi$
$521$		−	502.648i		−	0.964775i	0.875958	−	0.482387i	$-0.160230\pi$
$522$		0			0
$523$	−141.139	+	244.460i	−0.269864	+	0.467419i	−0.968827	−	0.247740i	$-0.920312\pi$
$523$	−141.139	+	244.460i	−0.269864	+	0.467419i	0.698962	+	0.715158i	$0.253645\pi$
$524$		0			0
$525$	−2086.30	−	734.129i	−3.97391	−	1.39834i
$526$		0			0
$527$	−139.119	−	80.3202i	−0.263982	−	0.152410i
$528$		0			0
$529$	−240.628			−0.454872
$530$		0			0
$531$	295.812	+	761.543i	0.557085	+	1.43417i
$532$		0			0
$533$	−962.953	−	555.961i	−1.80667	−	1.04308i
$534$		0			0
$535$	709.522	−	1228.93i	1.32621	−	2.29706i
$536$		0			0
$537$	−59.9939	+	170.495i	−0.111720	+	0.317496i
$538$		0			0
$539$		−	1297.45i		−	2.40714i
$540$		0			0
$541$	−365.937	+	633.821i	−0.676408	+	1.17157i	0.299647	+	0.954050i	$0.403131\pi$
$541$	−365.937	+	633.821i	−0.676408	+	1.17157i	−0.976055	+	0.217524i	$0.930202\pi$
$542$		0			0
$543$	−731.666	+	627.425i	−1.34745	+	1.15548i
$544$		0			0
$545$		−	176.608i		−	0.324051i
$546$		0			0
$547$	−94.2521	−	163.249i	−0.172307	−	0.298445i	0.766919	−	0.641744i	$-0.221789\pi$
$547$	−94.2521	−	163.249i	−0.172307	−	0.298445i	−0.939226	+	0.343299i	$0.888456\pi$
$548$		0			0
$549$	−19.3846	+	125.624i	−0.0353089	+	0.228823i
$550$		0			0
$551$	35.3812	−	253.195i	0.0642127	−	0.459520i
$552$		0			0
$553$	390.365	−	676.132i	0.705904	−	1.22266i
$554$		0			0
$555$	360.558	+	420.462i	0.649654	+	0.757589i
$556$		0			0
$557$	−178.380	−	102.988i	−0.320251	−	0.184897i	0.331254	−	0.943542i	$-0.392528\pi$
$557$	−178.380	−	102.988i	−0.320251	−	0.184897i	−0.651504	+	0.758645i	$0.725862\pi$
$558$		0			0
$559$	799.775			1.43072
$560$		0			0
$561$	−311.585	−	109.640i	−0.555410	−	0.195438i
$562$		0			0
$563$	266.226	−	153.706i	0.472871	−	0.273012i	−0.244570	−	0.969632i	$-0.578647\pi$
$563$	266.226	−	153.706i	0.472871	−	0.273012i	0.717441	+	0.696619i	$0.245313\pi$
$564$		0			0
$565$	−501.223			−0.887121
$566$		0			0
$567$	955.887	+	302.194i	1.68587	+	0.532971i
$568$		0			0
$569$	866.808	+	500.452i	1.52339	+	0.879528i	0.999617	+	0.0276690i	$0.00880843\pi$
$569$	866.808	+	500.452i	1.52339	+	0.879528i	0.523771	+	0.851859i	$0.324525\pi$
$570$		0			0
$571$	61.3032	+	106.180i	0.107361	+	0.185955i	0.914700	−	0.404133i	$-0.132427\pi$
$571$	61.3032	+	106.180i	0.107361	+	0.185955i	−0.807339	+	0.590087i	$0.799093\pi$
$572$		0			0
$573$	−569.854	−	664.530i	−0.994510	−	1.15974i
$574$		0			0
$575$	1431.09	−	826.243i	2.48886	−	1.43694i
$576$		0			0
$577$	−888.963			−1.54066			−0.770332	−	0.637643i	$-0.779910\pi$
$577$	−888.963			−1.54066			−0.770332	+	0.637643i	$0.779910\pi$
$578$		0			0
$579$	567.596	−	486.730i	0.980305	−	0.840639i
$580$		0			0
$581$	19.2627	−	11.1213i	0.0331544	−	0.0191417i
$582$		0			0
$583$	412.184	+	713.923i	0.707004	+	1.22457i
$584$		0			0
$585$	−533.481	−	1373.40i	−0.911934	−	2.34769i
$586$		0			0
$587$			579.042i			0.986444i	0.869904	+	0.493222i	$0.164181\pi$
$587$			579.042i			0.986444i	−0.869904	+	0.493222i	$0.835819\pi$
$588$		0			0
$589$	−341.896	−	47.7761i	−0.580468	−	0.0811139i
$590$		0			0
$591$	−200.381	+	569.457i	−0.339054	+	0.963549i
$592$		0			0
$593$	−313.510	−	181.005i	−0.528684	−	0.305236i	0.211796	−	0.977314i	$-0.432069\pi$
$593$	−313.510	−	181.005i	−0.528684	−	0.305236i	−0.740481	+	0.672078i	$0.765402\pi$
$594$		0			0
$595$	−503.141	+	871.466i	−0.845615	+	1.46465i
$596$		0			0
$597$	−181.289	+	155.461i	−0.303667	+	0.260403i
$598$		0			0
$599$		−	63.5085i		−	0.106024i	−0.998594	−	0.0530121i	$-0.983118\pi$
$599$		−	63.5085i		−	0.106024i	0.998594	−	0.0530121i	$-0.0168822\pi$
$600$		0			0
$601$	360.114	−	623.737i	0.599192	−	1.03783i	−0.393748	−	0.919218i	$-0.628822\pi$
$601$	360.114	−	623.737i	0.599192	−	1.03783i	0.992941	−	0.118613i	$-0.0378448\pi$
$602$		0			0
$603$	234.444	+	188.309i	0.388796	+	0.312286i
$604$		0			0
$605$		−	313.467i		−	0.518127i
$606$		0			0
$607$	−229.939	−	398.266i	−0.378812	−	0.656122i	0.612078	−	0.790798i	$-0.290334\pi$
$607$	−229.939	−	398.266i	−0.378812	−	0.656122i	−0.990890	+	0.134676i	$0.957001\pi$
$608$		0			0
$609$	−165.835	+	471.283i	−0.272307	+	0.773863i
$610$		0			0
$611$	−679.330	+	392.212i	−1.11183	+	0.641918i
$612$		0			0
$613$	−0.881784	−	1.52730i	−0.00143847	−	0.00249151i	0.865305	−	0.501245i	$-0.167125\pi$
$613$	−0.881784	−	1.52730i	−0.00143847	−	0.00249151i	−0.866744	+	0.498754i	$0.833791\pi$
$614$		0			0
$615$	−317.389	−	1693.66i	−0.516079	−	2.75391i
$616$		0			0
$617$			132.098i			0.214098i	0.994254	+	0.107049i	$0.0341402\pi$
$617$			132.098i			0.214098i	−0.994254	+	0.107049i	$0.965860\pi$
$618$		0			0
$619$	99.4915	−	172.324i	0.160729	−	0.278392i	−0.774401	−	0.632695i	$-0.781949\pi$
$619$	99.4915	−	172.324i	0.160729	−	0.278392i	0.935130	+	0.354303i	$0.115282\pi$
$620$		0			0
$621$	−636.312	+	395.178i	−1.02466	+	0.636358i
$622$		0			0
$623$	−1282.57	+	740.490i	−2.05869	+	1.18859i
$624$		0			0
$625$	−716.972	+	1241.83i	−1.14716	+	1.98693i
$626$		0			0
$627$	−709.080	+	32.9322i	−1.13091	+	0.0525235i
$628$		0			0
$629$	153.726	−	88.7538i	0.244398	−	0.141103i
$630$		0			0
$631$	−472.474	+	818.349i	−0.748770	+	1.29691i	0.199642	+	0.979869i	$0.436022\pi$
$631$	−472.474	+	818.349i	−0.748770	+	1.29691i	−0.948412	+	0.317039i	$0.897311\pi$
$632$		0			0
$633$	161.461	−	138.457i	0.255073	−	0.218732i
$634$		0			0
$635$	−409.032	+	236.155i	−0.644144	+	0.371897i
$636$		0			0
$637$	−927.353	−	1606.22i	−1.45581	−	2.52154i
$638$		0			0
$639$	12.7916	+	1.97382i	0.0200181	+	0.00308892i
$640$		0			0
$641$		−	618.741i		−	0.965275i	−0.875820	−	0.482637i	$-0.839679\pi$
$641$		−	618.741i		−	0.965275i	0.875820	−	0.482637i	$-0.160321\pi$
$642$		0			0
$643$	−263.171	+	455.825i	−0.409286	+	0.708904i	−0.994810	−	0.101751i	$-0.967555\pi$
$643$	−263.171	+	455.825i	−0.409286	+	0.708904i	0.585524	+	0.810655i	$0.300889\pi$
$644$		0			0
$645$	806.804	+	940.848i	1.25086	+	1.45868i
$646$		0			0
$647$			35.6915i			0.0551646i	0.999620	+	0.0275823i	$0.00878084\pi$
$647$			35.6915i			0.0551646i	−0.999620	+	0.0275823i	$0.991219\pi$
$648$		0			0
$649$	565.231	+	979.008i	0.870926	+	1.50849i
$650$		0			0
$651$	636.385	+	223.931i	0.977549	+	0.343980i
$652$		0			0
$653$	−445.634	+	257.287i	−0.682441	+	0.394007i	−0.800774	−	0.598967i	$-0.795578\pi$
$653$	−445.634	+	257.287i	−0.682441	+	0.394007i	0.118333	+	0.992974i	$0.462245\pi$
$654$		0			0
$655$	236.023	+	408.805i	0.360341	+	0.624129i
$656$		0			0
$657$	75.3652	−	488.413i	0.114711	−	0.743399i
$658$		0			0
$659$	814.151	−	470.050i	1.23543	−	0.713278i	0.267276	−	0.963620i	$-0.413876\pi$
$659$	814.151	−	470.050i	1.23543	−	0.713278i	0.968158	+	0.250342i	$0.0805430\pi$
$660$		0			0
$661$	17.8706			0.0270357			0.0135178	−	0.999909i	$-0.495697\pi$
$661$	17.8706			0.0270357			0.0135178	+	0.999909i	$0.495697\pi$
$662$		0			0
$663$	−464.103	+	86.9722i	−0.700004	+	0.131180i
$664$		0			0
$665$	−299.279	+	2141.70i	−0.450043	+	3.22060i
$666$		0			0
$667$	−186.643	−	323.275i	−0.279825	−	0.484670i
$668$		0			0
$669$	−425.196	−	149.618i	−0.635570	−	0.223645i
$670$		0			0
$671$			175.885i			0.262123i
$672$		0			0
$673$	−197.191	+	341.544i	−0.293002	+	0.507495i	−0.974518	−	0.224308i	$-0.927988\pi$
$673$	−197.191	+	341.544i	−0.293002	+	0.507495i	0.681516	+	0.731803i	$0.261321\pi$
$674$		0			0
$675$	758.951	−	1417.94i	1.12437	−	2.10065i
$676$		0			0
$677$	−110.538	−	63.8192i	−0.163276	−	0.0942676i	0.416135	−	0.909303i	$-0.363384\pi$
$677$	−110.538	−	63.8192i	−0.163276	−	0.0942676i	−0.579412	+	0.815035i	$0.696718\pi$
$678$		0			0
$679$	−864.799	+	1497.88i	−1.27364	+	2.20600i
$680$		0			0
$681$	−338.938	−	395.250i	−0.497707	−	0.580397i
$682$		0			0
$683$			1227.28i			1.79690i	0.439079	+	0.898449i	$0.355305\pi$
$683$			1227.28i			1.79690i	−0.439079	+	0.898449i	$0.644695\pi$
$684$		0			0
$685$	−270.727			−0.395222
$686$		0			0
$687$	−171.776	−	916.634i	−0.250038	−	1.33426i
$688$		0			0
$689$	1020.55	+	589.217i	1.48121	+	0.855177i
$690$		0			0
$691$	565.702	−	979.824i	0.818671	−	1.41798i	−0.0879900	−	0.996121i	$-0.528044\pi$
$691$	565.702	−	979.824i	0.818671	−	1.41798i	0.906661	−	0.421859i	$-0.138622\pi$
$692$		0			0
$693$	1370.97	+	211.549i	1.97831	+	0.305266i
$694$		0			0
$695$	1970.78	+	1137.83i	2.83566	+	1.63717i
$696$		0			0
$697$	−552.226			−0.792289
$698$		0			0
$699$	149.893	−	28.0896i	0.214438	−	0.0401855i
$700$		0			0
$701$	477.157	−	275.487i	0.680681	−	0.392991i	−0.119431	−	0.992843i	$-0.538107\pi$
$701$	477.157	−	275.487i	0.680681	−	0.392991i	0.800111	+	0.599851i	$0.204774\pi$
$702$		0			0
$703$	234.617	−	300.784i	0.333737	−	0.427858i
$704$		0			0
$705$	−1146.70	−	403.499i	−1.62652	−	0.572340i
$706$		0			0
$707$			806.926i			1.14134i
$708$		0			0
$709$	527.847	+	914.258i	0.744495	+	1.28950i	0.950430	+	0.310937i	$0.100643\pi$
$709$	527.847	+	914.258i	0.744495	+	1.28950i	−0.205935	+	0.978566i	$0.566024\pi$
$710$		0			0
$711$	442.622	+	355.520i	0.622535	+	0.500028i
$712$		0			0
$713$	−436.526	+	252.029i	−0.612239	+	0.353476i
$714$		0			0
$715$	−1019.36	−	1765.59i	−1.42568	−	2.46935i
$716$		0			0
$717$	1010.91	−	189.444i	1.40992	−	0.264218i
$718$		0			0
$719$	579.398	−	334.516i	0.805839	−	0.465251i	−0.0396698	−	0.999213i	$-0.512631\pi$
$719$	579.398	−	334.516i	0.805839	−	0.465251i	0.845509	+	0.533961i	$0.179297\pi$
$720$		0			0
$721$	1689.07			2.34268
$722$		0			0
$723$	−66.8892	−	356.935i	−0.0925161	−	0.493687i
$724$		0			0
$725$	694.112	+	400.746i	0.957395	+	0.552753i
$726$		0			0
$727$	874.925			1.20347			0.601737	−	0.798695i	$-0.294476\pi$
$727$	874.925			1.20347			0.601737	+	0.798695i	$0.294476\pi$
$728$		0			0
$729$	−323.179	+	653.450i	−0.443318	+	0.896365i
$730$		0			0
$731$	343.986	−	198.600i	0.470569	−	0.271683i
$732$		0			0
$733$	105.584	+	182.878i	0.144044	+	0.249492i	0.929016	−	0.370040i	$-0.120656\pi$
$733$	105.584	+	182.878i	0.144044	+	0.249492i	−0.784972	+	0.619532i	$0.787323\pi$
$734$		0			0
$735$	954.042	−	2711.27i	1.29802	−	3.68880i
$736$		0			0
$737$	360.345	+	208.045i	0.488935	+	0.282287i
$738$		0			0
$739$	216.751	+	375.424i	0.293303	+	0.508016i	0.974589	−	0.224002i	$-0.0719122\pi$
$739$	216.751	+	375.424i	0.293303	+	0.508016i	−0.681286	+	0.732018i	$0.738579\pi$
$740$		0			0
$741$	−854.292	+	547.585i	−1.15289	+	0.738981i
$742$		0			0
$743$	1106.27	+	638.705i	1.48892	+	0.859629i	0.999920	−	0.0126534i	$-0.00402782\pi$
$743$	1106.27	+	638.705i	1.48892	+	0.859629i	0.489002	+	0.872283i	$0.337361\pi$
$744$		0			0
$745$	781.020	+	1352.77i	1.04835	+	1.81579i
$746$		0			0
$747$	5.85636	+	15.0767i	0.00783984	+	0.0201830i
$748$		0			0
$749$	1654.00	+	954.939i	2.20828	+	1.27495i
$750$		0			0
$751$	−182.090			−0.242464			−0.121232	−	0.992624i	$-0.538684\pi$
$751$	−182.090			−0.242464			−0.121232	+	0.992624i	$0.538684\pi$
$752$		0			0
$753$	261.351	+	304.772i	0.347079	+	0.404744i
$754$		0			0
$755$	−612.993	+	353.912i	−0.811912	+	0.468758i
$756$		0			0
$757$	−215.701	−	373.606i	−0.284942	−	0.493535i	0.687653	−	0.726040i	$-0.258641\pi$
$757$	−215.701	−	373.606i	−0.284942	−	0.493535i	−0.972595	+	0.232505i	$0.925308\pi$
$758$		0			0
$759$	−786.784	+	674.690i	−1.03661	+	0.888920i
$760$		0			0
$761$	493.184	−	284.740i	0.648074	−	0.374165i	−0.139644	−	0.990202i	$-0.544596\pi$
$761$	493.184	−	284.740i	0.648074	−	0.374165i	0.787718	+	0.616036i	$0.211263\pi$
$762$		0			0
$763$	237.695			0.311526
$764$		0			0
$765$	−570.495	−	458.230i	−0.745745	−	0.598993i
$766$		0			0
$767$	1399.49	+	807.998i	1.82463	+	1.05345i
$768$		0			0
$769$	−431.466			−0.561074			−0.280537	−	0.959843i	$-0.590512\pi$
$769$	−431.466			−0.561074			−0.280537	+	0.959843i	$0.590512\pi$
$770$		0			0
$771$	14.4272	−	41.0003i	0.0187123	−	0.0531780i
$772$		0			0
$773$	1155.50	+	667.130i	1.49483	+	0.863040i	0.999982	−	0.00594100i	$-0.00189109\pi$
$773$	1155.50	+	667.130i	1.49483	+	0.863040i	0.494846	+	0.868981i	$0.335224\pi$
$774$		0			0
$775$	541.137	−	937.276i	0.698241	−	1.20939i
$776$		0			0
$777$	−565.896	+	485.272i	−0.728308	+	0.624545i
$778$		0			0
$779$	−1099.98	+	445.426i	−1.41203	+	0.571792i
$780$		0			0
$781$	17.9093			0.0229313
$782$		0			0
$783$	−320.303	−	171.442i	−0.409072	−	0.218955i
$784$		0			0
$785$	−751.029	+	433.607i	−0.956725	+	0.552365i
$786$		0			0
$787$	−98.5362	−	170.670i	−0.125205	−	0.216861i	0.796608	−	0.604496i	$-0.206625\pi$
$787$	−98.5362	−	170.670i	−0.125205	−	0.216861i	−0.921813	+	0.387635i	$0.873292\pi$
$788$		0			0
$789$	−61.6032	+	175.069i	−0.0780776	+	0.221887i
$790$		0			0
$791$		−	674.592i		−	0.852834i
$792$		0			0
$793$	125.714	+	217.743i	0.158529	+	0.274581i
$794$		0			0
$795$	336.374	+	1794.97i	0.423112	+	2.25782i
$796$		0			0
$797$	327.725	−	189.212i	0.411198	−	0.237406i	−0.280106	−	0.959969i	$-0.590370\pi$
$797$	327.725	−	189.212i	0.411198	−	0.237406i	0.691305	+	0.722564i	$0.257036\pi$
$798$		0			0
$799$	−194.788	+	337.383i	−0.243790	+	0.422257i
$800$		0			0
$801$	−389.934	−	1003.85i	−0.486808	−	1.25324i
$802$		0			0
$803$		−	683.821i		−	0.851583i
$804$		0			0
$805$	1578.76	+	2734.49i	1.96119	+	3.39688i
$806$		0			0
$807$	764.442	−	143.255i	0.947264	−	0.177516i
$808$		0			0
$809$		−	396.303i		−	0.489867i	−0.969540	−	0.244934i	$-0.921234\pi$
$809$		−	396.303i		−	0.489867i	0.969540	−	0.244934i	$-0.0787662\pi$
$810$		0			0
$811$	−180.766	+	313.096i	−0.222893	+	0.386062i	−0.955685	−	0.294390i	$-0.904883\pi$
$811$	−180.766	+	313.096i	−0.222893	+	0.386062i	0.732792	+	0.680453i	$0.238217\pi$
$812$		0			0
$813$	−81.6368	−	435.632i	−0.100414	−	0.535833i
$814$		0			0
$815$	1145.54	+	661.379i	1.40557	+	0.811508i
$816$		0			0
$817$	524.992	−	673.050i	0.642585	−	0.823807i
$818$		0			0
$819$	1848.45	−	718.007i	2.25695	−	0.876688i
$820$		0			0
$821$	−319.776	+	184.623i	−0.389496	+	0.224876i	−0.681942	−	0.731406i	$-0.738864\pi$
$821$	−319.776	+	184.623i	−0.389496	+	0.224876i	0.292446	+	0.956282i	$0.405531\pi$
$822$		0			0
$823$	−1184.13			−1.43880			−0.719398	−	0.694598i	$-0.755582\pi$
$823$	−1184.13			−1.43880			−0.719398	+	0.694598i	$0.755582\pi$
$824$		0			0
$825$	738.675	−	2099.22i	0.895363	−	2.54451i
$826$		0			0
$827$	241.191	+	139.252i	0.291646	+	0.168382i	0.638684	−	0.769469i	$-0.279479\pi$
$827$	241.191	+	139.252i	0.291646	+	0.168382i	−0.347038	+	0.937851i	$0.612813\pi$
$828$		0			0
$829$	451.640			0.544800			0.272400	−	0.962184i	$-0.412183\pi$
$829$	451.640			0.544800			0.272400	+	0.962184i	$0.412183\pi$
$830$		0			0
$831$	−746.247	+	639.928i	−0.898011	+	0.770070i
$832$		0			0
$833$	−797.716	−	460.561i	−0.957642	−	0.552895i
$834$		0			0
$835$	207.844	−	359.997i	0.248915	−	0.431134i
$836$		0			0
$837$	−231.503	+	432.514i	−0.276586	+	0.516743i
$838$		0			0
$839$			328.398i			0.391415i	0.980662	+	0.195708i	$0.0627004\pi$
$839$			328.398i			0.391415i	−0.980662	+	0.195708i	$0.937300\pi$
$840$		0			0
$841$	−329.974	+	571.532i	−0.392359	+	0.679586i
$842$		0			0
$843$	−584.742	+	109.580i	−0.693644	+	0.129988i
$844$		0			0
$845$	−1178.00	−	680.120i	−1.39409	−	0.804876i
$846$		0			0
$847$	421.892			0.498101
$848$		0			0
$849$	1130.27	−	969.239i	1.33130	−	1.14162i
$850$		0			0
$851$		−	556.984i		−	0.654505i
$852$		0			0
$853$	689.106			0.807862			0.403931	−	0.914790i	$-0.367644\pi$
$853$	689.106			0.807862			0.403931	+	0.914790i	$0.367644\pi$
$854$		0			0
$855$	−1505.97	−	452.583i	−1.76137	−	0.529337i
$856$		0			0
$857$			948.075i			1.10627i	0.833091	+	0.553136i	$0.186569\pi$
$857$			948.075i			1.10627i	−0.833091	+	0.553136i	$0.813431\pi$
$858$		0			0
$859$	−329.056			−0.383068			−0.191534	−	0.981486i	$-0.561346\pi$
$859$	−329.056			−0.383068			−0.191534	+	0.981486i	$0.561346\pi$
$860$		0			0
$861$	2279.48	−	427.171i	2.64748	−	0.496133i
$862$		0			0
$863$			105.449i			0.122189i	0.998132	+	0.0610947i	$0.0194592\pi$
$863$			105.449i			0.122189i	−0.998132	+	0.0610947i	$0.980541\pi$
$864$		0			0
$865$	531.671	−	920.882i	0.614649	−	1.06460i
$866$		0			0
$867$	480.135	−	411.729i	0.553789	−	0.474890i
$868$		0			0
$869$	680.319	+	392.782i	0.782876	+	0.451993i
$870$		0			0
$871$	594.802			0.682896
$872$		0			0
$873$	−980.568	−	787.606i	−1.12322	−	0.902183i
$874$		0			0
$875$	−3407.08	−	1967.08i	−3.89381	−	2.24809i
$876$		0			0
$877$	513.138	−	888.781i	0.585106	−	1.01343i	−0.409757	−	0.912195i	$-0.634386\pi$
$877$	513.138	−	888.781i	0.585106	−	1.01343i	0.994862	−	0.101238i	$-0.0322803\pi$
$878$		0			0
$879$	−125.112	+	23.4458i	−0.142334	+	0.0266733i
$880$		0			0
$881$		−	97.5037i		−	0.110674i	−0.998468	−	0.0553369i	$-0.982377\pi$
$881$		−	97.5037i		−	0.110674i	0.998468	−	0.0553369i	$-0.0176233\pi$
$882$		0			0
$883$	−548.561	+	950.135i	−0.621246	+	1.07603i	0.368007	+	0.929823i	$0.380040\pi$
$883$	−548.561	+	950.135i	−0.621246	+	1.07603i	−0.989254	+	0.146208i	$0.953293\pi$
$884$		0			0
$885$	461.273	+	2461.45i	0.521212	+	2.78130i
$886$		0			0
$887$		−	149.842i		−	0.168931i	−0.996426	−	0.0844657i	$-0.973082\pi$
$887$		−	149.842i		−	0.168931i	0.996426	−	0.0844657i	$-0.0269183\pi$
$888$		0			0
$889$	−317.838	−	550.512i	−0.357523	−	0.619248i
$890$		0			0
$891$	−304.066	+	961.807i	−0.341263	+	1.07947i
$892$		0			0
$893$	−115.864	+	829.148i	−0.129747	+	0.928497i
$894$		0			0
$895$	−277.017	+	479.808i	−0.309517	+	0.536098i
$896$		0			0
$897$	−491.791	+	1397.61i	−0.548262	+	1.55809i
$898$		0			0
$899$	−211.725	−	122.239i	−0.235511	−	0.135973i
$900$		0			0
$901$	585.258			0.649565
$902$		0			0
$903$	−1266.28	+	1085.87i	−1.40230	+	1.20251i
$904$		0			0
$905$	−2558.67	+	1477.25i	−2.82726	+	1.63232i
$906$		0			0
$907$	−443.001			−0.488424			−0.244212	−	0.969722i	$-0.578529\pi$
$907$	−443.001			−0.488424			−0.244212	+	0.969722i	$0.578529\pi$
$908$		0			0
$909$	−579.908	−	89.4836i	−0.637963	−	0.0984418i
$910$		0			0
$911$	434.611	+	250.923i	0.477070	+	0.275437i	0.719195	−	0.694808i	$-0.244511\pi$
$911$	434.611	+	250.923i	0.477070	+	0.275437i	−0.242124	+	0.970245i	$0.577844\pi$
$912$		0			0
$913$	11.1902	+	19.3820i	0.0122565	+	0.0212289i
$914$		0			0
$915$	−129.332	+	367.545i	−0.141346	+	0.401688i
$916$		0			0
$917$	−550.206	+	317.662i	−0.600007	+	0.346414i
$918$		0			0
$919$	552.796			0.601519			0.300759	−	0.953700i	$-0.402760\pi$
$919$	552.796			0.601519			0.300759	+	0.953700i	$0.402760\pi$
$920$		0			0
$921$	−168.856	−	901.051i	−0.183340	−	0.978340i
$922$		0			0
$923$	22.1715	−	12.8007i	0.0240211	−	0.0138686i
$924$		0			0
$925$	597.956	+	1035.69i	0.646439	+	1.11967i
$926$		0			0
$927$	−187.308	+	1213.87i	−0.202059	+	1.30946i
$928$		0			0
$929$			54.4095i			0.0585678i	0.999571	+	0.0292839i	$0.00932269\pi$
$929$			54.4095i			0.0585678i	−0.999571	+	0.0292839i	$0.990677\pi$
$930$		0			0
$931$	−1960.45	−	273.951i	−2.10575	−	0.294255i
$932$		0			0
$933$	−1169.11	+	219.089i	−1.25306	+	0.234822i
$934$		0			0
$935$	−876.862	−	506.257i	−0.937821	−	0.541451i
$936$		0			0
$937$	−9.02057	+	15.6241i	−0.00962708	+	0.0166746i	−0.870799	−	0.491640i	$-0.836398\pi$
$937$	−9.02057	+	15.6241i	−0.00962708	+	0.0166746i	0.861172	+	0.508314i	$0.169731\pi$
$938$		0			0
$939$	230.933	+	1232.31i	0.245935	+	1.31236i
$940$		0			0
$941$			96.4734i			0.102522i	0.998685	+	0.0512611i	$0.0163241\pi$
$941$			96.4734i			0.102522i	−0.998685	+	0.0512611i	$0.983676\pi$
$942$		0			0
$943$	−866.387	+	1500.63i	−0.918756	+	1.59133i
$944$		0			0
$945$	2709.35	+	1450.18i	2.86704	+	1.53458i
$946$		0			0
$947$			269.920i			0.285026i	0.989793	+	0.142513i	$0.0455183\pi$
$947$			269.920i			0.285026i	−0.989793	+	0.142513i	$0.954482\pi$
$948$		0			0
$949$	−488.762	−	846.560i	−0.515028	−	0.892055i
$950$		0			0
$951$	214.132	−	40.1281i	0.225166	−	0.0421957i
$952$		0			0
$953$	1360.20	−	785.311i	1.42728	−	0.824041i	0.430376	−	0.902650i	$-0.358381\pi$
$953$	1360.20	−	785.311i	1.42728	−	0.824041i	0.996906	+	0.0786088i	$0.0250478\pi$
$954$		0			0
$955$	−1341.70	−	2323.89i	−1.40492	−	2.43340i
$956$		0			0
$957$	−474.201	−	166.862i	−0.495508	−	0.174359i
$958$		0			0
$959$		−	364.369i		−	0.379947i
$960$		0			0
$961$	315.437	−	546.353i	0.328239	−	0.568526i
$962$		0			0
$963$	−869.699	+	1082.77i	−0.903114	+	1.12438i
$964$		0			0
$965$	1984.91	−	1145.99i	2.05690	−	1.18755i
$966$		0			0
$967$	765.770	−	1326.35i	0.791903	−	1.37162i	−0.132885	−	0.991131i	$-0.542424\pi$
$967$	765.770	−	1326.35i	0.791903	−	1.37162i	0.924787	−	0.380484i	$-0.124243\pi$
$968$		0			0
$969$	−231.457	+	447.656i	−0.238862	+	0.461977i
$970$		0			0
$971$	−700.095	+	404.200i	−0.721004	+	0.416272i	−0.815122	−	0.579289i	$-0.803330\pi$
$971$	−700.095	+	404.200i	−0.721004	+	0.416272i	0.0941179	+	0.995561i	$0.469997\pi$
$972$		0			0
$973$	−1531.40	+	2652.46i	−1.57389	+	2.72606i
$974$		0			0
$975$	−585.953	−	3126.77i	−0.600977	−	3.20695i
$976$		0			0
$977$	1047.31	−	604.662i	1.07196	−	0.618897i	0.143244	−	0.989687i	$-0.454246\pi$
$977$	1047.31	−	604.662i	1.07196	−	0.618897i	0.928717	+	0.370790i	$0.120913\pi$
$978$		0			0
$979$	−745.075	−	1290.51i	−0.761057	−	1.31819i
$980$		0			0
$981$	−26.3590	+	170.822i	−0.0268695	+	0.174131i
$982$		0			0
$983$		−	1914.47i		−	1.94758i	−0.227451	−	0.973789i	$-0.573039\pi$
$983$		−	1914.47i		−	1.94758i	0.227451	−	0.973789i	$-0.426961\pi$
$984$		0			0
$985$	−925.243	+	1602.57i	−0.939333	+	1.62697i
$986$		0			0
$987$	543.066	−	1543.33i	0.550219	−	1.56365i
$988$		0			0
$989$		−	1246.34i		−	1.26020i
$990$		0			0
$991$	−315.732	−	546.864i	−0.318599	−	0.551830i	0.661597	−	0.749860i	$-0.269879\pi$
$991$	−315.732	−	546.864i	−0.318599	−	0.551830i	−0.980196	+	0.198029i	$0.936546\pi$
$992$		0			0
$993$	−256.653	+	220.087i	−0.258462	+	0.221639i
$994$		0			0
$995$	−633.976	+	366.026i	−0.637162	+	0.367866i
$996$		0			0
$997$	433.993	+	751.698i	0.435299	+	0.753960i	0.997320	−	0.0731629i	$-0.0233093\pi$
$997$	433.993	+	751.698i	0.435299	+	0.753960i	−0.562021	+	0.827123i	$0.689976\pi$
$998$		0			0
$999$	−285.992	−	460.502i	−0.286279	−	0.460963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.4	yes	80
3.2	odd	2		2052.3.be.a.197.40		80
9.4	even	3		2052.3.m.a.881.40		80
9.5	odd	6		684.3.m.a.653.22	yes	80
19.11	even	3		684.3.m.a.353.22	✓	80
57.11	odd	6		2052.3.m.a.1493.1		80
171.49	even	3		2052.3.be.a.125.40		80
171.68	odd	6	inner	684.3.be.a.581.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.22	✓	80	19.11	even	3
684.3.m.a.653.22	yes	80	9.5	odd	6
684.3.be.a.425.4	yes	80	1.1	even	1	trivial
684.3.be.a.581.4	yes	80	171.68	odd	6	inner
2052.3.m.a.881.40		80	9.4	even	3
2052.3.m.a.1493.1		80	57.11	odd	6
2052.3.be.a.125.40		80	171.49	even	3
2052.3.be.a.197.40		80	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.82991 - 0.995790i) q^{3} +(-7.96394 - 4.59798i) q^{5} +(6.18838 - 10.7186i) q^{7} +(7.01680 + 5.63600i) q^{9} +O(q^{10})\)	\(q+(-2.82991 - 0.995790i) q^{3} +(-7.96394 - 4.59798i) q^{5} +(6.18838 - 10.7186i) q^{7} +(7.01680 + 5.63600i) q^{9} +(10.7850 + 6.22670i) q^{11} +17.8022 q^{13} +(17.9586 + 20.9423i) q^{15} +(7.65677 - 4.42064i) q^{17} +(11.6858 - 14.9814i) q^{19} +(-28.1860 + 24.1703i) q^{21} -27.7422i q^{23} +(29.7829 + 51.5855i) q^{25} +(-14.2447 - 22.9366i) q^{27} +(11.6528 - 6.72777i) q^{29} +(-9.08468 - 15.7351i) q^{31} +(-24.3200 - 28.3606i) q^{33} +(-98.5679 + 56.9082i) q^{35} +20.0772 q^{37} +(-50.3786 - 17.7272i) q^{39} +(-54.0919 - 31.2300i) q^{41} +44.9257 q^{43} +(-29.9672 - 77.1479i) q^{45} +(-38.1600 + 22.0317i) q^{47} +(-52.0922 - 90.2263i) q^{49} +(-26.0700 + 4.88548i) q^{51} +(57.3275 + 33.0980i) q^{53} +(-57.2606 - 99.1782i) q^{55} +(-47.9881 + 30.7595i) q^{57} +(78.6137 + 45.3876i) q^{59} +(7.06171 + 12.2312i) q^{61} +(103.833 - 40.3326i) q^{63} +(-141.775 - 81.8541i) q^{65} +33.4118 q^{67} +(-27.6254 + 78.5079i) q^{69} +(1.24544 - 0.719053i) q^{71} +(-27.4552 - 47.5538i) q^{73} +(-32.9147 - 175.640i) q^{75} +(133.483 - 77.0665i) q^{77} +63.0803 q^{79} +(17.4711 + 79.0934i) q^{81} +(1.55636 + 0.898564i) q^{83} -81.3041 q^{85} +(-39.6760 + 7.43522i) q^{87} +(-103.627 - 59.8290i) q^{89} +(110.167 - 190.814i) q^{91} +(10.0400 + 53.5754i) q^{93} +(-161.949 + 65.5800i) q^{95} -139.746 q^{97} +(40.5823 + 104.476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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