LMFDB - Embedded newform 684.3.m.a.353.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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			353.11
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79577 + 2.40317i) q^{3} -4.55087i q^{5} +(5.85150 - 10.1351i) q^{7} +(-2.55043 - 8.63107i) q^{9} +O(q^{10})$	\(q+(-1.79577 + 2.40317i) q^{3} -4.55087i q^{5} +(5.85150 - 10.1351i) q^{7} +(-2.55043 - 8.63107i) q^{9} +(14.0645 + 8.12016i) q^{11} +(-3.63225 + 6.29124i) q^{13} +(10.9365 + 8.17232i) q^{15} +(-19.6143 - 11.3243i) q^{17} +(-13.5931 - 13.2751i) q^{19} +(13.8484 + 32.2624i) q^{21} +(-33.4828 - 19.3313i) q^{23} +4.28954 q^{25} +(25.3219 + 9.37031i) q^{27} +25.8349i q^{29} +(14.0349 + 24.3091i) q^{31} +(-44.7708 + 19.2175i) q^{33} +(-46.1236 - 26.6295i) q^{35} -47.8191 q^{37} +(-8.59622 - 20.0265i) q^{39} -8.35430i q^{41} +(-39.1823 - 67.8657i) q^{43} +(-39.2789 + 11.6067i) q^{45} +16.4142i q^{47} +(-43.9802 - 76.1759i) q^{49} +(62.4370 - 26.8006i) q^{51} +(43.6381 - 25.1945i) q^{53} +(36.9538 - 64.0059i) q^{55} +(56.3123 - 8.82731i) q^{57} +74.9477i q^{59} +62.3287 q^{61} +(-102.401 - 24.6559i) q^{63} +(28.6306 + 16.5299i) q^{65} +(28.5642 - 49.4746i) q^{67} +(106.584 - 45.7502i) q^{69} +(-73.0839 - 42.1950i) q^{71} +(28.4345 - 49.2501i) q^{73} +(-7.70302 + 10.3085i) q^{75} +(164.597 - 95.0303i) q^{77} +(-59.5243 - 103.099i) q^{79} +(-67.9907 + 44.0258i) q^{81} +(-71.4114 - 41.2294i) q^{83} +(-51.5356 + 89.2622i) q^{85} +(-62.0856 - 46.3935i) q^{87} +(123.100 - 71.0719i) q^{89} +(42.5082 + 73.6264i) q^{91} +(-83.6224 - 9.92542i) q^{93} +(-60.4134 + 61.8603i) q^{95} +(-59.2528 - 102.629i) q^{97} +(34.2151 - 142.102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.79577	+	2.40317i	−0.598590	+	0.801056i
$3$	−1.79577	+	2.40317i	−0.598590	+	0.801056i
$4$		0			0
$5$		−	4.55087i		−	0.910175i	−0.890447	−	0.455087i	$-0.849608\pi$
$5$		−	4.55087i		−	0.910175i	0.890447	−	0.455087i	$-0.150392\pi$
$6$		0			0
$7$	5.85150	−	10.1351i	0.835929	−	1.44787i	−0.0573428	−	0.998355i	$-0.518263\pi$
$7$	5.85150	−	10.1351i	0.835929	−	1.44787i	0.893272	−	0.449517i	$-0.148404\pi$
$8$		0			0
$9$	−2.55043	−	8.63107i	−0.283381	−	0.959008i
$10$		0			0
$11$	14.0645	+	8.12016i	1.27859	+	0.738197i	0.976590	−	0.215110i	$-0.0690110\pi$
$11$	14.0645	+	8.12016i	1.27859	+	0.738197i	0.302004	+	0.953307i	$0.402344\pi$
$12$		0			0
$13$	−3.63225	+	6.29124i	−0.279404	+	0.483941i	−0.971237	−	0.238116i	$-0.923470\pi$
$13$	−3.63225	+	6.29124i	−0.279404	+	0.483941i	0.691833	+	0.722058i	$0.256803\pi$
$14$		0			0
$15$	10.9365	+	8.17232i	0.729101	+	0.544821i
$16$		0			0
$17$	−19.6143	−	11.3243i	−1.15378	−	0.666137i	−0.203976	−	0.978976i	$-0.565387\pi$
$17$	−19.6143	−	11.3243i	−1.15378	−	0.666137i	−0.949806	+	0.312839i	$0.898720\pi$
$18$		0			0
$19$	−13.5931	−	13.2751i	−0.715424	−	0.698691i
$19$	−13.5931	−	13.2751i	−0.715424	−	0.698691i
$20$		0			0
$21$	13.8484	+	32.2624i	0.659447	+	1.53631i
$22$		0			0
$23$	−33.4828	−	19.3313i	−1.45577	−	0.840491i	−0.456974	−	0.889480i	$-0.651067\pi$
$23$	−33.4828	−	19.3313i	−1.45577	−	0.840491i	−0.998799	+	0.0489892i	$0.984400\pi$
$24$		0			0
$25$	4.28954			0.171582
$26$		0			0
$27$	25.3219	+	9.37031i	0.937847	+	0.347048i
$28$		0			0
$29$			25.8349i			0.890858i	0.895317	+	0.445429i	$0.146949\pi$
$29$			25.8349i			0.890858i	−0.895317	+	0.445429i	$0.853051\pi$
$30$		0			0
$31$	14.0349	+	24.3091i	0.452738	+	0.784166i	0.998555	−	0.0537388i	$-0.0171138\pi$
$31$	14.0349	+	24.3091i	0.452738	+	0.784166i	−0.545817	+	0.837905i	$0.683780\pi$
$32$		0			0
$33$	−44.7708	+	19.2175i	−1.35669	+	0.582348i
$34$		0			0
$35$	−46.1236	−	26.6295i	−1.31782	−	0.760842i
$36$		0			0
$37$	−47.8191			−1.29241			−0.646204	−	0.763164i	$-0.723645\pi$
$37$	−47.8191			−1.29241			−0.646204	+	0.763164i	$0.723645\pi$
$38$		0			0
$39$	−8.59622	−	20.0265i	−0.220416	−	0.513500i
$40$		0			0
$41$		−	8.35430i		−	0.203763i	−0.994797	−	0.101882i	$-0.967514\pi$
$41$		−	8.35430i		−	0.203763i	0.994797	−	0.101882i	$-0.0324863\pi$
$42$		0			0
$43$	−39.1823	−	67.8657i	−0.911216	−	1.57827i	−0.812349	−	0.583172i	$-0.801812\pi$
$43$	−39.1823	−	67.8657i	−0.911216	−	1.57827i	−0.0988670	−	0.995101i	$-0.531522\pi$
$44$		0			0
$45$	−39.2789	+	11.6067i	−0.872865	+	0.257926i
$46$		0			0
$47$			16.4142i			0.349239i	0.984636	+	0.174619i	$0.0558695\pi$
$47$			16.4142i			0.349239i	−0.984636	+	0.174619i	$0.944131\pi$
$48$		0			0
$49$	−43.9802	−	76.1759i	−0.897555	−	1.55461i
$50$		0			0
$51$	62.4370	−	26.8006i	1.22426	−	0.525502i
$52$		0			0
$53$	43.6381	−	25.1945i	0.823360	−	0.475367i	−0.0282138	−	0.999602i	$-0.508982\pi$
$53$	43.6381	−	25.1945i	0.823360	−	0.475367i	0.851574	+	0.524235i	$0.175649\pi$
$54$		0			0
$55$	36.9538	−	64.0059i	0.671888	−	1.16374i
$56$		0			0
$57$	56.3123	−	8.82731i	0.987936	−	0.154865i
$58$		0			0
$59$			74.9477i			1.27030i	0.772389	+	0.635150i	$0.219062\pi$
$59$			74.9477i			1.27030i	−0.772389	+	0.635150i	$0.780938\pi$
$60$		0			0
$61$	62.3287			1.02178			0.510891	−	0.859645i	$-0.329315\pi$
$61$	62.3287			1.02178			0.510891	+	0.859645i	$0.329315\pi$
$62$		0			0
$63$	−102.401	−	24.6559i	−1.62541	−	0.391364i
$64$		0			0
$65$	28.6306	+	16.5299i	0.440471	+	0.254306i
$66$		0			0
$67$	28.5642	−	49.4746i	0.426331	−	0.738427i	−0.570213	−	0.821497i	$-0.693139\pi$
$67$	28.5642	−	49.4746i	0.426331	−	0.738427i	0.996544	+	0.0830700i	$0.0264725\pi$
$68$		0			0
$69$	106.584	−	45.7502i	1.54469	−	0.663046i
$70$		0			0
$71$	−73.0839	−	42.1950i	−1.02935	−	0.594296i	−0.112552	−	0.993646i	$-0.535902\pi$
$71$	−73.0839	−	42.1950i	−1.02935	−	0.594296i	−0.916799	+	0.399350i	$0.869236\pi$
$72$		0			0
$73$	28.4345	−	49.2501i	0.389514	−	0.674658i	−0.602870	−	0.797839i	$-0.705976\pi$
$73$	28.4345	−	49.2501i	0.389514	−	0.674658i	0.992384	+	0.123181i	$0.0393096\pi$
$74$		0			0
$75$	−7.70302	+	10.3085i	−0.102707	+	0.137446i
$76$		0			0
$77$	164.597	−	95.0303i	2.13763	−	1.23416i
$78$		0			0
$79$	−59.5243	−	103.099i	−0.753472	−	1.30505i	−0.946131	−	0.323785i	$-0.895044\pi$
$79$	−59.5243	−	103.099i	−0.753472	−	1.30505i	0.192659	−	0.981266i	$-0.438289\pi$
$80$		0			0
$81$	−67.9907	+	44.0258i	−0.839391	+	0.543528i
$82$		0			0
$83$	−71.4114	−	41.2294i	−0.860379	−	0.496740i	0.00376048	−	0.999993i	$-0.498803\pi$
$83$	−71.4114	−	41.2294i	−0.860379	−	0.496740i	−0.864139	+	0.503253i	$0.832136\pi$
$84$		0			0
$85$	−51.5356	+	89.2622i	−0.606301	+	1.05014i
$86$		0			0
$87$	−62.0856	−	46.3935i	−0.713627	−	0.533259i
$88$		0			0
$89$	123.100	−	71.0719i	1.38315	−	0.798560i	0.390616	−	0.920554i	$-0.372262\pi$
$89$	123.100	−	71.0719i	1.38315	−	0.798560i	0.992531	+	0.121993i	$0.0389286\pi$
$90$		0			0
$91$	42.5082	+	73.6264i	0.467123	+	0.809081i
$92$		0			0
$93$	−83.6224	−	9.92542i	−0.899165	−	0.106725i
$94$		0			0
$95$	−60.4134	+	61.8603i	−0.635931	+	0.651161i
$96$		0			0
$97$	−59.2528	−	102.629i	−0.610854	−	1.05803i	−0.991097	−	0.133143i	$-0.957493\pi$
$97$	−59.2528	−	102.629i	−0.610854	−	1.05803i	0.380243	−	0.924887i	$-0.375840\pi$
$98$		0			0
$99$	34.2151	−	142.102i	0.345607	−	1.43537i
$100$		0			0
$101$			90.1148i			0.892226i	0.894977	+	0.446113i	$0.147192\pi$
$101$			90.1148i			0.892226i	−0.894977	+	0.446113i	$0.852808\pi$
$102$		0			0
$103$	−43.0937	−	74.6404i	−0.418385	−	0.724664i	0.577392	−	0.816467i	$-0.304070\pi$
$103$	−43.0937	−	74.6404i	−0.418385	−	0.724664i	−0.995777	+	0.0918028i	$0.970737\pi$
$104$		0			0
$105$	146.822	−	63.0223i	1.39831	−	0.600212i
$106$		0			0
$107$			116.854i			1.09209i	0.837756	+	0.546045i	$0.183867\pi$
$107$			116.854i			1.09209i	−0.837756	+	0.546045i	$0.816133\pi$
$108$		0			0
$109$	−59.8897	+	103.732i	−0.549447	+	0.951670i	0.448865	+	0.893599i	$0.351828\pi$
$109$	−59.8897	+	103.732i	−0.549447	+	0.951670i	−0.998312	+	0.0580708i	$0.981505\pi$
$110$		0			0
$111$	85.8721	−	114.917i	0.773623	−	1.03529i
$112$		0			0
$113$	−121.648	+	70.2335i	−1.07653	+	0.621535i	−0.929958	−	0.367665i	$-0.880157\pi$
$113$	−121.648	+	70.2335i	−1.07653	+	0.621535i	−0.146572	+	0.989200i	$0.546824\pi$
$114$		0			0
$115$	−87.9743	+	152.376i	−0.764994	+	1.32501i
$116$		0			0
$117$	63.5639	+	15.3049i	0.543281	+	0.130811i
$118$		0			0
$119$	−229.546	+	132.529i	−1.92896	+	1.11369i
$120$		0			0
$121$	71.3740	+	123.623i	0.589868	+	1.02168i
$122$		0			0
$123$	20.0768	+	15.0024i	0.163226	+	0.121971i
$124$		0			0
$125$		−	133.293i		−	1.06634i
$126$		0			0
$127$	−35.1261	−	60.8401i	−0.276583	−	0.479056i	0.693950	−	0.720023i	$-0.255869\pi$
$127$	−35.1261	−	60.8401i	−0.276583	−	0.479056i	−0.970533	+	0.240967i	$0.922535\pi$
$128$		0			0
$129$	233.455	+	27.7096i	1.80973	+	0.214803i
$130$		0			0
$131$		−	2.59427i		−	0.0198036i	−0.999951	−	0.00990178i	$-0.996848\pi$
$131$		−	2.59427i		−	0.0198036i	0.999951	−	0.00990178i	$-0.00315189\pi$
$132$		0			0
$133$	−214.085	+	60.0875i	−1.60966	+	0.451786i
$134$		0			0
$135$	42.6431	−	115.237i	0.315875	−	0.853605i
$136$		0			0
$137$			148.184i			1.08164i	0.841139	+	0.540819i	$0.181886\pi$
$137$			148.184i			1.08164i	−0.841139	+	0.540819i	$0.818114\pi$
$138$		0			0
$139$	66.7195	−	115.561i	0.479996	−	0.831378i	−0.519741	−	0.854324i	$-0.673971\pi$
$139$	66.7195	−	115.561i	0.479996	−	0.831378i	0.999737	+	0.0229465i	$0.00730472\pi$
$140$		0			0
$141$	−39.4461	−	29.4761i	−0.279760	−	0.209051i
$142$		0			0
$143$	−102.172	+	58.9889i	−0.714488	+	0.412510i
$144$		0			0
$145$	117.571			0.810837
$146$		0			0
$147$	262.042	+	31.1026i	1.78260	+	0.211582i
$148$		0			0
$149$		−	122.448i		−	0.821797i	−0.911681	−	0.410899i	$-0.865215\pi$
$149$		−	122.448i		−	0.821797i	0.911681	−	0.410899i	$-0.134785\pi$
$150$		0			0
$151$	−36.8974	+	63.9082i	−0.244354	+	0.423233i	−0.961950	−	0.273226i	$-0.911909\pi$
$151$	−36.8974	+	63.9082i	−0.244354	+	0.423233i	0.717596	+	0.696460i	$0.245243\pi$
$152$		0			0
$153$	−47.7162	+	198.174i	−0.311871	+	1.29526i
$154$		0			0
$155$	110.628	−	63.8710i	0.713728	−	0.412071i
$156$		0			0
$157$	292.029			1.86005			0.930027	−	0.367491i	$-0.119783\pi$
$157$	292.029			1.86005			0.930027	+	0.367491i	$0.119783\pi$
$158$		0			0
$159$	−17.8174	+	150.113i	−0.112059	+	0.944107i
$160$		0			0
$161$	−391.849	+	226.234i	−2.43385	+	1.40518i
$162$		0			0
$163$	39.5636			0.242722			0.121361	−	0.992608i	$-0.461274\pi$
$163$	39.5636			0.242722			0.121361	+	0.992608i	$0.461274\pi$
$164$		0			0
$165$	87.4564	+	203.746i	0.530039	+	1.23483i
$166$		0			0
$167$	−2.36252	−	1.36400i	−0.0141468	−	0.00816766i	0.492910	−	0.870080i	$-0.335933\pi$
$167$	−2.36252	−	1.36400i	−0.0141468	−	0.00816766i	−0.507057	+	0.861913i	$0.669267\pi$
$168$		0			0
$169$	58.1135	+	100.656i	0.343867	+	0.595595i
$170$		0			0
$171$	−79.9105	+	151.180i	−0.467313	+	0.884092i
$172$		0			0
$173$	−103.541	+	59.7794i	−0.598503	+	0.345546i	−0.768452	−	0.639907i	$-0.778973\pi$
$173$	−103.541	+	59.7794i	−0.598503	+	0.345546i	0.169949	+	0.985453i	$0.445640\pi$
$174$		0			0
$175$	25.1002	−	43.4749i	0.143430	−	0.248428i
$176$		0			0
$177$	−180.112	−	134.589i	−1.01758	−	0.760388i
$178$		0			0
$179$		−	16.1873i		−	0.0904318i	−0.998977	−	0.0452159i	$-0.985602\pi$
$179$		−	16.1873i		−	0.0904318i	0.998977	−	0.0452159i	$-0.0143976\pi$
$180$		0			0
$181$	−171.692	−	297.380i	−0.948576	−	1.64298i	−0.748429	−	0.663215i	$-0.769191\pi$
$181$	−171.692	−	297.380i	−0.948576	−	1.64298i	−0.200147	−	0.979766i	$-0.564142\pi$
$182$		0			0
$183$	−111.928	+	149.786i	−0.611629	+	0.818505i
$184$		0			0
$185$			217.619i			1.17632i
$186$		0			0
$187$	−183.911	−	318.543i	−0.983480	−	1.70344i
$188$		0			0
$189$	243.140	−	201.809i	1.28646	−	1.06777i
$190$		0			0
$191$	−10.9165	−	6.30263i	−0.0571543	−	0.0329981i	0.471151	−	0.882053i	$-0.343839\pi$
$191$	−10.9165	−	6.30263i	−0.0571543	−	0.0329981i	−0.528305	+	0.849055i	$0.677172\pi$
$192$		0			0
$193$	137.420			0.712022			0.356011	−	0.934482i	$-0.384137\pi$
$193$	137.420			0.712022			0.356011	+	0.934482i	$0.384137\pi$
$194$		0			0
$195$	−91.1382	+	39.1203i	−0.467375	+	0.200617i
$196$		0			0
$197$			191.963i			0.974429i	0.873282	+	0.487215i	$0.161987\pi$
$197$			191.963i			0.974429i	−0.873282	+	0.487215i	$0.838013\pi$
$198$		0			0
$199$	−64.5484	−	111.801i	−0.324364	−	0.561815i	0.657019	−	0.753874i	$-0.271817\pi$
$199$	−64.5484	−	111.801i	−0.324364	−	0.561815i	−0.981383	+	0.192059i	$0.938484\pi$
$200$		0			0
$201$	67.6011	+	157.490i	0.336324	+	0.783530i
$202$		0			0
$203$	261.839	+	151.173i	1.28985	+	0.744694i
$204$		0			0
$205$	−38.0194			−0.185460
$206$		0			0
$207$	−81.4544	+	338.295i	−0.393499	+	1.63428i
$208$		0			0
$209$	−83.3837	−	297.086i	−0.398965	−	1.42147i
$210$		0			0
$211$	156.934			0.743765			0.371882	−	0.928280i	$-0.378712\pi$
$211$	156.934			0.743765			0.371882	+	0.928280i	$0.378712\pi$
$212$		0			0
$213$	232.643	−	99.8603i	1.09222	−	0.468828i
$214$		0			0
$215$	−308.848	+	178.314i	−1.43650	+	0.829366i
$216$		0			0
$217$	328.501			1.51383
$218$		0			0
$219$	67.2943	+	156.775i	0.307280	+	0.715866i
$220$		0			0
$221$	142.488	−	82.2655i	0.644742	−	0.372242i
$222$		0			0
$223$	−50.3370	−	87.1863i	−0.225727	−	0.390970i	0.730811	−	0.682580i	$-0.239142\pi$
$223$	−50.3370	−	87.1863i	−0.225727	−	0.390970i	−0.956537	+	0.291610i	$0.905809\pi$
$224$		0			0
$225$	−10.9401	−	37.0233i	−0.0486229	−	0.164548i
$226$		0			0
$227$	−27.5603	−	15.9119i	−0.121411	−	0.0700967i	0.438065	−	0.898943i	$-0.355664\pi$
$227$	−27.5603	−	15.9119i	−0.121411	−	0.0700967i	−0.559476	+	0.828847i	$0.688997\pi$
$228$		0			0
$229$	−77.4200	−	134.095i	−0.338078	−	0.585569i	0.645993	−	0.763344i	$-0.276444\pi$
$229$	−77.4200	−	134.095i	−0.338078	−	0.585569i	−0.984071	+	0.177774i	$0.943110\pi$
$230$		0			0
$231$	−67.2051	+	566.207i	−0.290931	+	2.45111i
$232$		0			0
$233$	334.241	+	192.974i	1.43451	+	0.828215i	0.997460	−	0.0712220i	$-0.0226899\pi$
$233$	334.241	+	192.974i	1.43451	+	0.828215i	0.437050	+	0.899437i	$0.356023\pi$
$234$		0			0
$235$	74.6990			0.317868
$236$		0			0
$237$	354.656	+	42.0953i	1.49644	+	0.177617i
$238$		0			0
$239$	19.8128	−	11.4390i	0.0828990	−	0.0478617i	−0.457978	−	0.888964i	$-0.651426\pi$
$239$	19.8128	−	11.4390i	0.0828990	−	0.0478617i	0.540876	+	0.841102i	$0.318093\pi$
$240$		0			0
$241$	206.571			0.857143			0.428571	−	0.903508i	$-0.359017\pi$
$241$	206.571			0.857143			0.428571	+	0.903508i	$0.359017\pi$
$242$		0			0
$243$	16.2942	−	242.453i	0.0670544	−	0.997749i
$244$		0			0
$245$	−346.667	+	200.148i	−1.41497	+	0.816932i
$246$		0			0
$247$	132.890	−	37.2986i	0.538018	−	0.151006i
$248$		0			0
$249$	227.320	−	97.5751i	0.912930	−	0.391868i
$250$		0			0
$251$	−170.812	+	98.6182i	−0.680525	+	0.392901i	−0.800053	−	0.599930i	$-0.795195\pi$
$251$	−170.812	+	98.6182i	−0.680525	+	0.392901i	0.119528	+	0.992831i	$0.461862\pi$
$252$		0			0
$253$	−313.946	−	543.771i	−1.24089	−	2.14929i
$254$		0			0
$255$	−121.966	−	284.143i	−0.478298	−	1.11429i
$256$		0			0
$257$	175.563	+	101.361i	0.683125	+	0.394403i	0.801032	−	0.598622i	$-0.204285\pi$
$257$	175.563	+	101.361i	0.683125	+	0.394403i	−0.117906	+	0.993025i	$0.537618\pi$
$258$		0			0
$259$	−279.814	+	484.652i	−1.08036	+	1.87124i
$260$		0			0
$261$	222.983	−	65.8900i	0.854340	−	0.252452i
$262$		0			0
$263$	179.210	−	103.467i	0.681405	−	0.393409i	−0.118979	−	0.992897i	$-0.537962\pi$
$263$	179.210	−	103.467i	0.681405	−	0.393409i	0.800384	+	0.599487i	$0.204629\pi$
$264$		0			0
$265$	−114.657	−	198.591i	−0.432667	−	0.749402i
$266$		0			0
$267$	−50.2618	+	423.459i	−0.188246	+	1.58599i
$268$		0			0
$269$	54.5399	+	31.4886i	0.202751	+	0.117058i	0.597938	−	0.801542i	$-0.295987\pi$
$269$	54.5399	+	31.4886i	0.202751	+	0.117058i	−0.395187	+	0.918601i	$0.629320\pi$
$270$		0			0
$271$	−101.148	+	175.193i	−0.373239	+	0.646469i	−0.990062	−	0.140633i	$-0.955086\pi$
$271$	−101.148	+	175.193i	−0.373239	+	0.646469i	0.616823	+	0.787102i	$0.288420\pi$
$272$		0			0
$273$	−253.272	−	30.0617i	−0.927735	−	0.110116i
$274$		0			0
$275$	60.3303	+	34.8317i	0.219383	+	0.126661i
$276$		0			0
$277$	−48.8226	+	84.5632i	−0.176255	+	0.305282i	−0.940595	−	0.339531i	$-0.889732\pi$
$277$	−48.8226	+	84.5632i	−0.176255	+	0.305282i	0.764340	+	0.644813i	$0.223065\pi$
$278$		0			0
$279$	174.019	−	183.135i	0.623724	−	0.656397i
$280$		0			0
$281$			228.082i			0.811679i	0.913944	+	0.405840i	$0.133021\pi$
$281$			228.082i			0.811679i	−0.913944	+	0.405840i	$0.866979\pi$
$282$		0			0
$283$	206.080			0.728199			0.364099	−	0.931360i	$-0.381377\pi$
$283$	206.080			0.728199			0.364099	+	0.931360i	$0.381377\pi$
$284$		0			0
$285$	−40.1720	−	256.270i	−0.140954	−	0.899194i
$286$		0			0
$287$	−84.6716	−	48.8852i	−0.295023	−	0.170332i
$288$		0			0
$289$	111.981	+	193.956i	0.387476	+	0.671128i
$290$		0			0
$291$	353.039	+	41.9034i	1.21319	+	0.143998i
$292$		0			0
$293$	218.824	−	126.338i	0.746840	−	0.431189i	−0.0777107	−	0.996976i	$-0.524761\pi$
$293$	218.824	−	126.338i	0.746840	−	0.431189i	0.824551	+	0.565787i	$0.191428\pi$
$294$		0			0
$295$	341.078			1.15619
$296$		0			0
$297$	280.052	+	337.407i	0.942936	+	1.13605i
$298$		0			0
$299$	243.236	−	140.432i	0.813497	−	0.469673i
$300$		0			0
$301$	−917.101			−3.04685
$302$		0			0
$303$	−216.561	−	161.825i	−0.714723	−	0.534077i
$304$		0			0
$305$		−	283.650i		−	0.930001i
$306$		0			0
$307$	261.675	−	453.234i	0.852361	−	1.47633i	−0.0267099	−	0.999643i	$-0.508503\pi$
$307$	261.675	−	453.234i	0.852361	−	1.47633i	0.879071	−	0.476690i	$-0.158164\pi$
$308$		0			0
$309$	256.760	+	30.4757i	0.830937	+	0.0986268i
$310$		0			0
$311$	332.891	−	192.195i	1.07039	−	0.617989i	0.142101	−	0.989852i	$-0.454614\pi$
$311$	332.891	−	192.195i	1.07039	−	0.617989i	0.928287	+	0.371863i	$0.121281\pi$
$312$		0			0
$313$	220.518			0.704531			0.352265	−	0.935900i	$-0.385411\pi$
$313$	220.518			0.704531			0.352265	+	0.935900i	$0.385411\pi$
$314$		0			0
$315$	−112.206	+	466.012i	−0.356209	+	1.47940i
$316$		0			0
$317$		−	192.289i		−	0.606590i	−0.952897	−	0.303295i	$-0.901913\pi$
$317$		−	192.289i		−	0.606590i	0.952897	−	0.303295i	$-0.0980867\pi$
$318$		0			0
$319$	−209.784	+	363.356i	−0.657629	+	1.13905i
$320$		0			0
$321$	−280.819	−	209.842i	−0.874825	−	0.653714i
$322$		0			0
$323$	116.286	+	414.314i	0.360020	+	1.28271i
$324$		0			0
$325$	−15.5807	+	26.9865i	−0.0479405	+	0.0830354i
$326$		0			0
$327$	−141.737	−	330.204i	−0.433447	−	1.00980i
$328$		0			0
$329$	166.360	+	96.0478i	0.505653	+	0.291939i
$330$		0			0
$331$	140.614	−	243.551i	0.424817	−	0.735804i	−0.571586	−	0.820542i	$-0.693672\pi$
$331$	140.614	−	243.551i	0.424817	−	0.735804i	0.996403	+	0.0847374i	$0.0270051\pi$
$332$		0			0
$333$	121.959	+	412.730i	0.366244	+	1.23943i
$334$		0			0
$335$	−225.153	−	129.992i	−0.672098	−	0.388036i
$336$		0			0
$337$	−498.307			−1.47866			−0.739328	−	0.673346i	$-0.764857\pi$
$337$	−498.307			−1.47866			−0.739328	+	0.673346i	$0.764857\pi$
$338$		0			0
$339$	49.6689	−	418.464i	0.146516	−	1.23441i
$340$		0			0
$341$			455.862i			1.33684i
$342$		0			0
$343$	−455.953			−1.32931
$344$		0			0
$345$	−208.203	−	485.049i	−0.603488	−	1.40594i
$346$		0			0
$347$		−	156.769i		−	0.451783i	−0.974153	−	0.225891i	$-0.927471\pi$
$347$		−	156.769i		−	0.451783i	0.974153	−	0.225891i	$-0.0725294\pi$
$348$		0			0
$349$	−27.3145	+	47.3101i	−0.0782651	+	0.135559i	−0.902501	−	0.430687i	$-0.858271\pi$
$349$	−27.3145	+	47.3101i	−0.0782651	+	0.135559i	0.824236	+	0.566246i	$0.191605\pi$
$350$		0			0
$351$	−150.926	+	125.271i	−0.429989	+	0.356897i
$352$		0			0
$353$	22.4457	+	12.9590i	0.0635854	+	0.0367111i	0.531456	−	0.847086i	$-0.321645\pi$
$353$	22.4457	+	12.9590i	0.0635854	+	0.0367111i	−0.467870	+	0.883797i	$0.654979\pi$
$354$		0			0
$355$	−192.024	+	332.596i	−0.540913	+	0.936889i
$356$		0			0
$357$	93.7238	−	789.629i	0.262532	−	2.21185i
$358$		0			0
$359$	−551.226	−	318.250i	−1.53545	−	0.886491i	−0.999097	−	0.0424966i	$-0.986469\pi$
$359$	−551.226	−	318.250i	−1.53545	−	0.886491i	−0.536351	−	0.843995i	$-0.680198\pi$
$360$		0			0
$361$	8.54208	+	360.899i	0.0236623	+	0.999720i
$362$		0			0
$363$	−425.259	−	50.4755i	−1.17151	−	0.139051i
$364$		0			0
$365$	−224.131	−	129.402i	−0.614057	−	0.354526i
$366$		0			0
$367$	199.085			0.542466			0.271233	−	0.962514i	$-0.412569\pi$
$367$	199.085			0.542466			0.271233	+	0.962514i	$0.412569\pi$
$368$		0			0
$369$	−72.1065	+	21.3070i	−0.195411	+	0.0577426i
$370$		0			0
$371$		−	589.702i		−	1.58949i
$372$		0			0
$373$	225.834	+	391.156i	0.605453	+	1.04867i	0.991980	+	0.126397i	$0.0403412\pi$
$373$	225.834	+	391.156i	0.605453	+	1.04867i	−0.386527	+	0.922278i	$0.626325\pi$
$374$		0			0
$375$	320.325	+	239.364i	0.854201	+	0.638303i
$376$		0			0
$377$	−162.533	−	93.8388i	−0.431123	−	0.248909i
$378$		0			0
$379$	−98.6773			−0.260362			−0.130181	−	0.991490i	$-0.541556\pi$
$379$	−98.6773			−0.260362			−0.130181	+	0.991490i	$0.541556\pi$
$380$		0			0
$381$	209.287	+	24.8410i	0.549310	+	0.0651995i
$382$		0			0
$383$			395.105i			1.03161i	0.856707	+	0.515803i	$0.172506\pi$
$383$			395.105i			1.03161i	−0.856707	+	0.515803i	$0.827494\pi$
$384$		0			0
$385$	−432.471	−	749.062i	−1.12330	−	1.94561i
$386$		0			0
$387$	−485.822	+	511.271i	−1.25535	+	1.32111i
$388$		0			0
$389$		−	251.142i		−	0.645610i	−0.946466	−	0.322805i	$-0.895374\pi$
$389$		−	251.142i		−	0.645610i	0.946466	−	0.322805i	$-0.104626\pi$
$390$		0			0
$391$	437.828	+	758.340i	1.11976	+	1.93949i
$392$		0			0
$393$	6.23446	+	4.65870i	0.0158638	+	0.0118542i
$394$		0			0
$395$	−469.191	+	270.887i	−1.18782	+	0.685791i
$396$		0			0
$397$	157.630	−	273.022i	0.397052	−	0.687714i	−0.596309	−	0.802755i	$-0.703367\pi$
$397$	157.630	−	273.022i	0.397052	−	0.687714i	0.993361	+	0.115041i	$0.0367000\pi$
$398$		0			0
$399$	240.046	−	622.384i	0.601619	−	1.55986i
$400$		0			0
$401$			278.610i			0.694788i	0.937719	+	0.347394i	$0.112933\pi$
$401$			278.610i			0.694788i	−0.937719	+	0.347394i	$0.887067\pi$
$402$		0			0
$403$	−203.913			−0.505987
$404$		0			0
$405$	200.356	+	309.417i	0.494706	+	0.763993i
$406$		0			0
$407$	−672.554	−	388.299i	−1.65247	−	0.954052i
$408$		0			0
$409$	100.271	−	173.675i	0.245161	−	0.424632i	−0.717016	−	0.697057i	$-0.754492\pi$
$409$	100.271	−	173.675i	0.245161	−	0.424632i	0.962177	+	0.272425i	$0.0878257\pi$
$410$		0			0
$411$	−356.112	−	266.105i	−0.866452	−	0.647457i
$412$		0			0
$413$	759.602	+	438.557i	1.83923	+	1.06188i
$414$		0			0
$415$	−187.630	+	324.984i	−0.452120	+	0.783095i
$416$		0			0
$417$	157.901	+	367.860i	0.378659	+	0.882158i
$418$		0			0
$419$	452.302	−	261.137i	1.07948	−	0.623238i	0.148723	−	0.988879i	$-0.452484\pi$
$419$	452.302	−	261.137i	1.07948	−	0.623238i	0.930756	+	0.365641i	$0.119150\pi$
$420$		0			0
$421$	129.320	+	223.990i	0.307174	+	0.532042i	0.977743	−	0.209806i	$-0.0672832\pi$
$421$	129.320	+	223.990i	0.307174	+	0.532042i	−0.670569	+	0.741847i	$0.733950\pi$
$422$		0			0
$423$	141.672	−	41.8632i	0.334922	−	0.0989674i
$424$		0			0
$425$	−84.1363	−	48.5761i	−0.197968	−	0.114297i
$426$		0			0
$427$	364.717	−	631.708i	0.854138	−	1.47941i
$428$		0			0
$429$	41.7167	−	351.466i	0.0972418	−	0.819269i
$430$		0			0
$431$	263.486	−	152.124i	0.611336	−	0.352955i	−0.162152	−	0.986766i	$-0.551843\pi$
$431$	263.486	−	152.124i	0.611336	−	0.352955i	0.773488	+	0.633811i	$0.218510\pi$
$432$		0			0
$433$	398.394	+	690.039i	0.920079	+	1.59362i	0.799290	+	0.600945i	$0.205209\pi$
$433$	398.394	+	690.039i	0.920079	+	1.59362i	0.120789	+	0.992678i	$0.461458\pi$
$434$		0			0
$435$	−211.131	+	282.544i	−0.485359	+	0.649526i
$436$		0			0
$437$	198.508	+	707.259i	0.454251	+	1.61844i
$438$		0			0
$439$	251.837	+	436.195i	0.573662	+	0.993611i	0.996186	+	0.0872592i	$0.0278108\pi$
$439$	251.837	+	436.195i	0.573662	+	0.993611i	−0.422524	+	0.906352i	$0.638856\pi$
$440$		0			0
$441$	−545.311	+	573.877i	−1.23653	+	1.30131i
$442$		0			0
$443$			337.606i			0.762091i	0.924556	+	0.381045i	$0.124436\pi$
$443$			337.606i			0.762091i	−0.924556	+	0.381045i	$0.875564\pi$
$444$		0			0
$445$	−323.439	−	560.213i	−0.726830	−	1.25891i
$446$		0			0
$447$	294.262	+	219.888i	0.658305	+	0.491919i
$448$		0			0
$449$			771.592i			1.71847i	0.511584	+	0.859233i	$0.329059\pi$
$449$			771.592i			1.71847i	−0.511584	+	0.859233i	$0.670941\pi$
$450$		0			0
$451$	67.8382	−	117.499i	0.150417	−	0.260531i
$452$		0			0
$453$	−87.3229	−	203.435i	−0.192766	−	0.449084i
$454$		0			0
$455$	335.065	−	193.450i	0.736406	−	0.425164i
$456$		0			0
$457$	174.821	−	302.800i	0.382542	−	0.662581i	−0.608883	−	0.793260i	$-0.708382\pi$
$457$	174.821	−	302.800i	0.382542	−	0.662581i	0.991425	+	0.130678i	$0.0417155\pi$
$458$		0			0
$459$	−390.559	−	470.545i	−0.850890	−	1.02515i
$460$		0			0
$461$	255.613	−	147.578i	0.554474	−	0.320126i	−0.196450	−	0.980514i	$-0.562941\pi$
$461$	255.613	−	147.578i	0.554474	−	0.320126i	0.750925	+	0.660388i	$0.229608\pi$
$462$		0			0
$463$	78.9995	+	136.831i	0.170625	+	0.295532i	0.938639	−	0.344902i	$-0.112088\pi$
$463$	78.9995	+	136.831i	0.170625	+	0.295532i	−0.768013	+	0.640434i	$0.778755\pi$
$464$		0			0
$465$	−45.1694	+	380.555i	−0.0971384	+	0.818398i
$466$		0			0
$467$		−	666.947i		−	1.42815i	−0.700068	−	0.714076i	$-0.746847\pi$
$467$		−	666.947i		−	1.42815i	0.700068	−	0.714076i	$-0.253153\pi$
$468$		0			0
$469$	−334.287	−	579.002i	−0.712765	−	1.23455i
$470$		0			0
$471$	−524.416	+	701.793i	−1.11341	+	1.49001i
$472$		0			0
$473$		−	1272.67i		−	2.69063i
$474$		0			0
$475$	−58.3079	−	56.9442i	−0.122753	−	0.119882i
$476$		0			0
$477$	−328.751	−	312.387i	−0.689205	−	0.654899i
$478$		0			0
$479$		−	193.176i		−	0.403290i	−0.979459	−	0.201645i	$-0.935371\pi$
$479$		−	193.176i		−	0.403290i	0.979459	−	0.201645i	$-0.0646287\pi$
$480$		0			0
$481$	173.691	−	300.842i	0.361104	−	0.625450i
$482$		0			0
$483$	159.992	−	1347.94i	0.331246	−	2.79077i
$484$		0			0
$485$	−467.051	+	269.652i	−0.962992	+	0.555984i
$486$		0			0
$487$	−550.037			−1.12944			−0.564720	−	0.825282i	$-0.691016\pi$
$487$	−550.037			−1.12944			−0.564720	+	0.825282i	$0.691016\pi$
$488$		0			0
$489$	−71.0471	+	95.0780i	−0.145291	+	0.194433i
$490$		0			0
$491$			255.091i			0.519534i	0.965671	+	0.259767i	$0.0836458\pi$
$491$			255.091i			0.519534i	−0.965671	+	0.259767i	$0.916354\pi$
$492$		0			0
$493$	292.563	−	506.733i	0.593433	−	1.02786i
$494$		0			0
$495$	−646.687	−	155.709i	−1.30644	−	0.314563i
$496$		0			0
$497$	−855.301	+	493.808i	−1.72093	+	0.993578i
$498$		0			0
$499$	485.339			0.972622			0.486311	−	0.873786i	$-0.338342\pi$
$499$	485.339			0.972622			0.486311	+	0.873786i	$0.338342\pi$
$500$		0			0
$501$	7.52046	−	3.22809i	0.0150109	−	0.00644330i
$502$		0			0
$503$	−172.886	+	99.8159i	−0.343710	+	0.198441i	−0.661912	−	0.749582i	$-0.730255\pi$
$503$	−172.886	+	99.8159i	−0.343710	+	0.198441i	0.318201	+	0.948023i	$0.396921\pi$
$504$		0			0
$505$	410.101			0.812082
$506$		0			0
$507$	−346.251	−	41.0977i	−0.682940	−	0.0810605i
$508$		0			0
$509$	−178.301	−	102.942i	−0.350298	−	0.202244i	0.314519	−	0.949251i	$-0.398157\pi$
$509$	−178.301	−	102.942i	−0.350298	−	0.202244i	−0.664816	+	0.747007i	$0.731490\pi$
$510$		0			0
$511$	−332.770	−	576.374i	−0.651212	−	1.12793i
$512$		0			0
$513$	−219.809	−	463.522i	−0.428479	−	0.903552i
$514$		0			0
$515$	−339.679	+	196.114i	−0.659571	+	0.380804i
$516$		0			0
$517$	−133.286	+	230.858i	−0.257807	+	0.446534i
$518$		0			0
$519$	42.2758	−	356.176i	0.0814563	−	0.686274i
$520$		0			0
$521$		−	570.510i		−	1.09503i	−0.836796	−	0.547514i	$-0.815574\pi$
$521$		−	570.510i		−	1.09503i	0.836796	−	0.547514i	$-0.184426\pi$
$522$		0			0
$523$	−466.633	−	808.231i	−0.892223	−	1.54538i	−0.837205	−	0.546890i	$-0.815812\pi$
$523$	−466.633	−	808.231i	−0.892223	−	1.54538i	−0.0550183	−	0.998485i	$-0.517522\pi$
$524$		0			0
$525$	59.4032	+	138.391i	0.113149	+	0.263602i
$526$		0			0
$527$		−	635.742i		−	1.20634i
$528$		0			0
$529$	482.898	+	836.403i	0.912850	+	1.58110i
$530$		0			0
$531$	646.879	−	191.148i	1.21823	−	0.359978i
$532$		0			0
$533$	52.5589	+	30.3449i	0.0986095	+	0.0569322i
$534$		0			0
$535$	531.786			0.993993
$536$		0			0
$537$	38.9008	+	29.0686i	0.0724409	+	0.0541316i
$538$		0			0
$539$		−	1428.50i		−	2.65029i
$540$		0			0
$541$	77.8507	+	134.841i	0.143901	+	0.249245i	0.928963	−	0.370174i	$-0.120702\pi$
$541$	77.8507	+	134.841i	0.143901	+	0.249245i	−0.785061	+	0.619418i	$0.787368\pi$
$542$		0			0
$543$	1022.97	+	121.420i	1.88393	+	0.223610i
$544$		0			0
$545$	472.072	+	272.551i	0.866186	+	0.500093i
$546$		0			0
$547$	34.1225			0.0623811			0.0311906	−	0.999513i	$-0.490070\pi$
$547$	34.1225			0.0623811			0.0311906	+	0.999513i	$0.490070\pi$
$548$		0			0
$549$	−158.965	−	537.963i	−0.289553	−	0.979897i
$550$		0			0
$551$	342.961	−	351.175i	0.622435	−	0.637341i
$552$		0			0
$553$	−1393.23			−2.51939
$554$		0			0
$555$	−522.975	−	390.793i	−0.942297	−	0.704132i
$556$		0			0
$557$	34.3037	−	19.8053i	0.0615865	−	0.0355570i	−0.468891	−	0.883256i	$-0.655346\pi$
$557$	34.3037	−	19.8053i	0.0615865	−	0.0355570i	0.530477	+	0.847699i	$0.322013\pi$
$558$		0			0
$559$	569.279			1.01839
$560$		0			0
$561$	1095.77	+	130.061i	1.95325	+	0.231838i
$562$		0			0
$563$	31.8404	−	18.3831i	0.0565549	−	0.0326520i	−0.471456	−	0.881890i	$-0.656271\pi$
$563$	31.8404	−	18.3831i	0.0565549	−	0.0326520i	0.528011	+	0.849238i	$0.322938\pi$
$564$		0			0
$565$	319.624	+	553.605i	0.565706	+	0.979831i
$566$		0			0
$567$	48.3582	+	946.709i	0.0852878	+	1.66968i
$568$		0			0
$569$	−13.7340	−	7.92934i	−0.0241371	−	0.0139356i	0.487883	−	0.872909i	$-0.337769\pi$
$569$	−13.7340	−	7.92934i	−0.0241371	−	0.0139356i	−0.512020	+	0.858974i	$0.671103\pi$
$570$		0			0
$571$	445.433	+	771.512i	0.780093	+	1.35116i	0.931887	+	0.362748i	$0.118161\pi$
$571$	445.433	+	771.512i	0.780093	+	1.35116i	−0.151794	+	0.988412i	$0.548505\pi$
$572$		0			0
$573$	34.7497	−	14.9160i	0.0606453	−	0.0260315i
$574$		0			0
$575$	−143.626	−	82.9223i	−0.249784	−	0.144213i
$576$		0			0
$577$	420.790			0.729272			0.364636	−	0.931150i	$-0.381193\pi$
$577$	420.790			0.729272			0.364636	+	0.931150i	$0.381193\pi$
$578$		0			0
$579$	−246.775	+	330.244i	−0.426209	+	0.570370i
$580$		0			0
$581$	−835.728	+	482.508i	−1.43843	+	0.830478i
$582$		0			0
$583$	818.332			1.40366
$584$		0			0
$585$	69.6505	−	289.271i	0.119061	−	0.494481i
$586$		0			0
$587$	562.001	−	324.471i	0.957412	−	0.552762i	0.0620362	−	0.998074i	$-0.480241\pi$
$587$	562.001	−	324.471i	0.957412	−	0.552762i	0.895375	+	0.445312i	$0.146907\pi$
$588$		0			0
$589$	131.930	−	516.750i	0.223990	−	0.877335i
$590$		0			0
$591$	−461.318	−	344.721i	−0.780572	−	0.583283i
$592$		0			0
$593$	104.519	−	60.3443i	0.176255	−	0.101761i	−0.409277	−	0.912410i	$-0.634219\pi$
$593$	104.519	−	60.3443i	0.176255	−	0.101761i	0.585532	+	0.810649i	$0.300886\pi$
$594$		0			0
$595$	603.121	+	1044.64i	1.01365	+	1.75569i
$596$		0			0
$597$	384.591	+	45.6484i	0.644206	+	0.0764630i
$598$		0			0
$599$	−417.863	−	241.253i	−0.697601	−	0.402760i	0.108852	−	0.994058i	$-0.465282\pi$
$599$	−417.863	−	241.253i	−0.697601	−	0.402760i	−0.806453	+	0.591298i	$0.798616\pi$
$600$		0			0
$601$	−191.870	+	332.329i	−0.319251	+	0.552960i	−0.980332	−	0.197355i	$-0.936765\pi$
$601$	−191.870	+	332.329i	−0.319251	+	0.552960i	0.661081	+	0.750315i	$0.270098\pi$
$602$		0			0
$603$	−499.870	−	120.358i	−0.828971	−	0.199599i
$604$		0			0
$605$	562.595	−	324.814i	0.929909	−	0.536883i
$606$		0			0
$607$	−131.396	−	227.585i	−0.216468	−	0.374934i	0.737258	−	0.675612i	$-0.236120\pi$
$607$	−131.396	−	227.585i	−0.216468	−	0.374934i	−0.953726	+	0.300678i	$0.902787\pi$
$608$		0			0
$609$	−833.497	+	357.772i	−1.36863	+	0.587474i
$610$		0			0
$611$	−103.266	−	59.6205i	−0.169011	−	0.0975786i
$612$		0			0
$613$	−416.617	+	721.601i	−0.679636	+	1.17716i	0.295455	+	0.955357i	$0.404529\pi$
$613$	−416.617	+	721.601i	−0.679636	+	1.17716i	−0.975091	+	0.221807i	$0.928805\pi$
$614$		0			0
$615$	68.2740	−	91.3669i	0.111015	−	0.148564i
$616$		0			0
$617$	−1031.09	−	595.298i	−1.67113	−	0.964826i	−0.967008	−	0.254745i	$-0.918008\pi$
$617$	−1031.09	−	595.298i	−1.67113	−	0.964826i	−0.704120	−	0.710081i	$-0.748658\pi$
$618$		0			0
$619$	−515.688	+	893.198i	−0.833099	+	1.44297i	0.0624707	+	0.998047i	$0.480102\pi$
$619$	−515.688	+	893.198i	−0.833099	+	1.44297i	−0.895569	+	0.444922i	$0.853231\pi$
$620$		0			0
$621$	−666.707	−	803.249i	−1.07360	−	1.29348i
$622$		0			0
$623$		−	1663.51i		−	2.67016i
$624$		0			0
$625$	−499.361			−0.798978
$626$		0			0
$627$	863.686	+	333.113i	1.37749	+	0.531281i
$628$		0			0
$629$	937.939	+	541.519i	1.49116	+	0.860921i
$630$		0			0
$631$	121.585	+	210.592i	0.192686	+	0.333743i	0.946140	−	0.323759i	$-0.104947\pi$
$631$	121.585	+	210.592i	0.192686	+	0.333743i	−0.753453	+	0.657502i	$0.771613\pi$
$632$		0			0
$633$	−281.818	+	377.140i	−0.445210	+	0.595797i
$634$		0			0
$635$	−276.876	+	159.854i	−0.436025	+	0.251739i
$636$		0			0
$637$	638.988			1.00312
$638$		0			0
$639$	−177.793	+	738.407i	−0.278236	+	1.15557i
$640$		0			0
$641$	502.684	−	290.225i	0.784219	−	0.452769i	−0.0537045	−	0.998557i	$-0.517103\pi$
$641$	502.684	−	290.225i	0.784219	−	0.452769i	0.837923	+	0.545788i	$0.183770\pi$
$642$		0			0
$643$	−783.487			−1.21849			−0.609244	−	0.792983i	$-0.708527\pi$
$643$	−783.487			−1.21849			−0.609244	+	0.792983i	$0.708527\pi$
$644$		0			0
$645$	126.103	−	1062.42i	0.195508	−	1.64717i
$646$		0			0
$647$			642.116i			0.992452i	0.868193	+	0.496226i	$0.165281\pi$
$647$			642.116i			0.992452i	−0.868193	+	0.496226i	$0.834719\pi$
$648$		0			0
$649$	−608.587	+	1054.10i	−0.937731	+	1.62420i
$650$		0			0
$651$	−589.912	+	789.442i	−0.906162	+	1.21266i
$652$		0			0
$653$	546.629	−	315.597i	0.837104	−	0.483302i	−0.0191745	−	0.999816i	$-0.506104\pi$
$653$	546.629	−	315.597i	0.837104	−	0.483302i	0.856279	+	0.516514i	$0.172770\pi$
$654$		0			0
$655$	−11.8062			−0.0180247
$656$		0			0
$657$	−497.601	−	119.812i	−0.757383	−	0.182362i
$658$		0			0
$659$			170.496i			0.258720i	0.991598	+	0.129360i	$0.0412923\pi$
$659$			170.496i			0.258720i	−0.991598	+	0.129360i	$0.958708\pi$
$660$		0			0
$661$	594.727	−	1030.10i	0.899738	−	1.55839i	0.0719098	−	0.997411i	$-0.477091\pi$
$661$	594.727	−	1030.10i	0.899738	−	1.55839i	0.827828	−	0.560981i	$-0.189576\pi$
$662$		0			0
$663$	−58.1779	+	490.153i	−0.0877495	+	0.739295i
$664$		0			0
$665$	273.451	+	974.272i	0.411204	+	1.46507i
$666$		0			0
$667$	499.422	−	865.024i	0.748758	−	1.29689i
$668$		0			0
$669$	299.917	+	35.5982i	0.448306	+	0.0532110i
$670$		0			0
$671$	876.624	+	506.119i	1.30644	+	0.754276i
$672$		0			0
$673$	−50.1653	+	86.8888i	−0.0745398	+	0.129107i	−0.900886	−	0.434056i	$-0.857082\pi$
$673$	−50.1653	+	86.8888i	−0.0745398	+	0.129107i	0.826346	+	0.563162i	$0.190415\pi$
$674$		0			0
$675$	108.619	+	40.1943i	0.160917	+	0.0595471i
$676$		0			0
$677$	301.480	+	174.060i	0.445318	+	0.257105i	0.705851	−	0.708360i	$-0.250565\pi$
$677$	301.480	+	174.060i	0.445318	+	0.257105i	−0.260533	+	0.965465i	$0.583898\pi$
$678$		0			0
$679$	−1386.87			−2.04252
$680$		0			0
$681$	87.7310	−	37.6578i	0.128827	−	0.0552978i
$682$		0			0
$683$			50.5434i			0.0740021i	0.999315	+	0.0370010i	$0.0117805\pi$
$683$			50.5434i			0.0740021i	−0.999315	+	0.0370010i	$0.988220\pi$
$684$		0			0
$685$	674.368			0.984479
$686$		0			0
$687$	461.282	+	54.7511i	0.671444	+	0.0796960i
$688$		0			0
$689$			366.050i			0.531277i
$690$		0			0
$691$	203.726	−	352.863i	0.294827	−	0.510656i	−0.680117	−	0.733103i	$-0.738071\pi$
$691$	203.726	−	352.863i	0.294827	−	0.510656i	0.974945	+	0.222447i	$0.0714045\pi$
$692$		0			0
$693$	−1240.01	−	1178.28i	−1.78933	−	1.70026i
$694$		0			0
$695$	−525.906	−	303.632i	−0.756699	−	0.436880i
$696$		0			0
$697$	−94.6068	+	163.864i	−0.135734	+	0.235099i
$698$		0			0
$699$	−1063.97	+	456.700i	−1.52213	+	0.653362i
$700$		0			0
$701$	−106.817	−	61.6711i	−0.152379	−	0.0879758i	0.421872	−	0.906655i	$-0.361373\pi$
$701$	−106.817	−	61.6711i	−0.152379	−	0.0879758i	−0.574251	+	0.818680i	$0.694706\pi$
$702$		0			0
$703$	650.008	+	634.805i	0.924620	+	0.902994i
$704$		0			0
$705$	−134.142	+	179.514i	−0.190273	+	0.254630i
$706$		0			0
$707$	913.323	+	527.307i	1.29183	+	0.745837i
$708$		0			0
$709$	−230.842			−0.325588			−0.162794	−	0.986660i	$-0.552051\pi$
$709$	−230.842			−0.325588			−0.162794	+	0.986660i	$0.552051\pi$
$710$		0			0
$711$	−738.043	+	776.704i	−1.03803	+	1.09241i
$712$		0			0
$713$		−	1085.25i		−	1.52209i
$714$		0			0
$715$	268.451	+	464.971i	0.375456	+	0.650309i
$716$		0			0
$717$	−8.08959	+	68.1553i	−0.0112826	+	0.0950562i
$718$		0			0
$719$	524.661	+	302.913i	0.729710	+	0.421298i	0.818316	−	0.574769i	$-0.194908\pi$
$719$	524.661	+	302.913i	0.729710	+	0.421298i	−0.0886062	+	0.996067i	$0.528241\pi$
$720$		0			0
$721$	−1008.65			−1.39896
$722$		0			0
$723$	−370.955	+	496.426i	−0.513077	+	0.686619i
$724$		0			0
$725$			110.820i			0.152855i
$726$		0			0
$727$	−277.882	−	481.306i	−0.382231	−	0.662044i	0.609150	−	0.793055i	$-0.291511\pi$
$727$	−277.882	−	481.306i	−0.382231	−	0.662044i	−0.991381	+	0.131012i	$0.958177\pi$
$728$		0			0
$729$	553.395	+	474.548i	0.759115	+	0.650957i
$730$		0			0
$731$			1774.85i			2.42798i
$732$		0			0
$733$	−42.5759	−	73.7436i	−0.0580844	−	0.100605i	0.835521	−	0.549458i	$-0.185166\pi$
$733$	−42.5759	−	73.7436i	−0.0580844	−	0.100605i	−0.893605	+	0.448853i	$0.851833\pi$
$734$		0			0
$735$	141.544	−	1192.52i	0.192577	−	1.62247i
$736$		0			0
$737$	803.484	−	463.892i	1.09021	−	0.629432i
$738$		0			0
$739$	−294.756	+	510.533i	−0.398859	+	0.690843i	−0.993585	−	0.113085i	$-0.963927\pi$
$739$	−294.756	+	510.533i	−0.398859	+	0.690843i	0.594727	+	0.803928i	$0.297260\pi$
$740$		0			0
$741$	−149.006	+	386.337i	−0.201087	+	0.521373i
$742$		0			0
$743$		−	1406.01i		−	1.89234i	−0.323672	−	0.946169i	$-0.604917\pi$
$743$		−	1406.01i		−	1.89234i	0.323672	−	0.946169i	$-0.395083\pi$
$744$		0			0
$745$	−557.245			−0.747979
$746$		0			0
$747$	−173.724	+	721.509i	−0.232563	+	0.965876i
$748$		0			0
$749$	1184.32	+	683.770i	1.58121	+	0.912910i
$750$		0			0
$751$	−4.98872	+	8.64072i	−0.00664277	+	0.0115056i	−0.869328	−	0.494236i	$-0.835448\pi$
$751$	−4.98872	+	8.64072i	−0.00664277	+	0.0115056i	0.862685	+	0.505742i	$0.168781\pi$
$752$		0			0
$753$	69.7425	−	587.585i	0.0926195	−	0.780325i
$754$		0			0
$755$	290.838	+	167.916i	0.385216	+	0.222405i
$756$		0			0
$757$	−546.784	+	947.058i	−0.722304	+	1.25107i	0.237770	+	0.971322i	$0.423584\pi$
$757$	−546.784	+	947.058i	−0.722304	+	1.25107i	−0.960074	+	0.279746i	$0.909750\pi$
$758$		0			0
$759$	1870.55	+	222.022i	2.46449	+	0.292519i
$760$		0			0
$761$	864.824	−	499.306i	1.13643	−	0.656118i	0.190886	−	0.981612i	$-0.438864\pi$
$761$	864.824	−	499.306i	1.13643	−	0.656118i	0.945544	+	0.325494i	$0.105530\pi$
$762$		0			0
$763$	700.890	+	1213.98i	0.918597	+	1.59106i
$764$		0			0
$765$	901.866	+	217.150i	1.17891	+	0.283857i
$766$		0			0
$767$	−471.514	−	272.229i	−0.614751	−	0.354926i
$768$		0			0
$769$	−13.8515	+	23.9914i	−0.0180123	+	0.0311982i	−0.874891	−	0.484320i	$-0.839067\pi$
$769$	−13.8515	+	23.9914i	−0.0180123	+	0.0311982i	0.856879	+	0.515518i	$0.172400\pi$
$770$		0			0
$771$	−558.860	+	239.886i	−0.724850	+	0.311136i
$772$		0			0
$773$	258.082	−	149.004i	0.333870	−	0.192760i	−0.323688	−	0.946164i	$-0.604923\pi$
$773$	258.082	−	149.004i	0.333870	−	0.192760i	0.657558	+	0.753404i	$0.271589\pi$
$774$		0			0
$775$	60.2032	+	104.275i	0.0776815	+	0.134548i
$776$		0			0
$777$	−662.218	−	1542.76i	−0.852275	−	1.98554i
$778$		0			0
$779$	−110.904	+	113.560i	−0.142368	+	0.145777i
$780$		0			0
$781$	−685.260	−	1186.91i	−0.877414	−	1.51973i
$782$		0			0
$783$	−242.081	+	654.188i	−0.309171	+	0.835489i
$784$		0			0
$785$		−	1328.99i		−	1.69297i
$786$		0			0
$787$	200.548	+	347.359i	0.254825	+	0.441370i	0.964848	−	0.262808i	$-0.0846487\pi$
$787$	200.548	+	347.359i	0.254825	+	0.441370i	−0.710023	+	0.704179i	$0.751315\pi$
$788$		0			0
$789$	−73.1713	+	616.473i	−0.0927392	+	0.781334i
$790$		0			0
$791$			1643.89i			2.07824i
$792$		0			0
$793$	−226.393	+	392.125i	−0.285490	+	0.494483i
$794$		0			0
$795$	683.146	+	81.0849i	0.859303	+	0.101994i
$796$		0			0
$797$	−876.314	+	505.940i	−1.09952	+	0.634806i	−0.936094	−	0.351750i	$-0.885587\pi$
$797$	−876.314	+	505.940i	−1.09952	+	0.634806i	−0.163422	+	0.986556i	$0.552253\pi$
$798$		0			0
$799$	185.880	−	321.953i	0.232641	−	0.402945i
$800$		0			0
$801$	−927.384	−	881.222i	−1.15778	−	1.10015i
$802$		0			0
$803$	799.837	−	461.786i	0.996061	−	0.575076i
$804$		0			0
$805$	1029.56	+	1783.26i	1.27896	+	2.21523i
$806$		0			0
$807$	−173.614	+	74.5222i	−0.215135	+	0.0923448i
$808$		0			0
$809$			1149.91i			1.42139i	0.703499	+	0.710696i	$0.251620\pi$
$809$			1149.91i			1.42139i	−0.703499	+	0.710696i	$0.748380\pi$
$810$		0			0
$811$	433.837	+	751.428i	0.534941	+	0.926545i	0.999166	+	0.0408280i	$0.0129996\pi$
$811$	433.837	+	751.428i	0.534941	+	0.926545i	−0.464225	+	0.885717i	$0.653667\pi$
$812$		0			0
$813$	−239.380	−	557.682i	−0.294441	−	0.685955i
$814$		0			0
$815$		−	180.049i		−	0.220919i
$816$		0			0
$817$	−368.319	+	1442.65i	−0.450819	+	1.76579i
$818$		0			0
$819$	527.061	−	554.670i	0.643542	−	0.677253i
$820$		0			0
$821$		−	182.423i		−	0.222197i	−0.993809	−	0.111098i	$-0.964563\pi$
$821$		−	182.423i		−	0.222197i	0.993809	−	0.111098i	$-0.0354368\pi$
$822$		0			0
$823$	807.006	−	1397.77i	0.980566	−	1.69839i	0.320377	−	0.947290i	$-0.396191\pi$
$823$	807.006	−	1397.77i	0.980566	−	1.69839i	0.660189	−	0.751099i	$-0.270476\pi$
$824$		0			0
$825$	−192.046	+	82.4341i	−0.232783	+	0.0999202i
$826$		0			0
$827$	1058.90	−	611.359i	1.28042	−	0.739249i	0.303492	−	0.952834i	$-0.401847\pi$
$827$	1058.90	−	611.359i	1.28042	−	0.739249i	0.976924	+	0.213585i	$0.0685140\pi$
$828$		0			0
$829$	−281.377			−0.339417			−0.169708	−	0.985494i	$-0.554283\pi$
$829$	−281.377			−0.339417			−0.169708	+	0.985494i	$0.554283\pi$
$830$		0			0
$831$	−115.545	−	269.185i	−0.139044	−	0.323929i
$832$		0			0
$833$			1992.18i			2.39158i
$834$		0			0
$835$	−6.20739	+	10.7515i	−0.00743400	+	0.0128761i
$836$		0			0
$837$	127.606	+	747.064i	0.152456	+	0.892550i
$838$		0			0
$839$	1101.13	−	635.736i	1.31243	−	0.757731i	0.329930	−	0.944005i	$-0.392975\pi$
$839$	1101.13	−	635.736i	1.31243	−	0.757731i	0.982498	+	0.186275i	$0.0596414\pi$
$840$		0			0
$841$	173.558			0.206371
$842$		0			0
$843$	−548.119	−	409.582i	−0.650200	−	0.485863i
$844$		0			0
$845$	458.071	−	264.467i	0.542096	−	0.312979i
$846$		0			0
$847$	1670.58			1.97235
$848$		0			0
$849$	−370.073	+	495.245i	−0.435892	+	0.583328i
$850$		0			0
$851$	1601.12	+	924.406i	1.88145	+	1.08626i
$852$		0			0
$853$	224.714	+	389.217i	0.263440	+	0.456292i	0.967154	−	0.254192i	$-0.0818095\pi$
$853$	224.714	+	389.217i	0.263440	+	0.456292i	−0.703714	+	0.710484i	$0.748476\pi$
$854$		0			0
$855$	688.000	+	363.662i	0.804679	+	0.425336i
$856$		0			0
$857$	−614.928	+	355.029i	−0.717535	+	0.414269i	−0.813845	−	0.581082i	$-0.802629\pi$
$857$	−614.928	+	355.029i	−0.717535	+	0.414269i	0.0963097	+	0.995351i	$0.469296\pi$
$858$		0			0
$859$	86.8406	−	150.412i	0.101095	−	0.175102i	−0.811041	−	0.584989i	$-0.801099\pi$
$859$	86.8406	−	150.412i	0.101095	−	0.175102i	0.912136	+	0.409888i	$0.134432\pi$
$860$		0			0
$861$	269.530	−	115.694i	0.313043	−	0.134371i
$862$		0			0
$863$		−	560.406i		−	0.649370i	−0.945822	−	0.324685i	$-0.894742\pi$
$863$		−	560.406i		−	0.649370i	0.945822	−	0.324685i	$-0.105258\pi$
$864$		0			0
$865$	272.049	+	471.202i	0.314507	+	0.544742i
$866$		0			0
$867$	−667.200	−	79.1923i	−0.769550	−	0.0913406i
$868$		0			0
$869$		−	1933.39i		−	2.22484i
$870$		0			0
$871$	207.504	+	359.408i	0.238237	+	0.412639i
$872$		0			0
$873$	−734.677	+	773.162i	−0.841554	+	0.885638i
$874$		0			0
$875$	−1350.94	−	779.965i	−1.54393	−	0.891388i
$876$		0			0
$877$	1372.57			1.56507			0.782537	−	0.622604i	$-0.213925\pi$
$877$	1372.57			1.56507			0.782537	+	0.622604i	$0.213925\pi$
$878$		0			0
$879$	−89.3460	+	752.746i	−0.101645	+	0.856366i
$880$		0			0
$881$		−	105.391i		−	0.119627i	−0.998210	−	0.0598135i	$-0.980949\pi$
$881$		−	105.391i		−	0.119627i	0.998210	−	0.0598135i	$-0.0190506\pi$
$882$		0			0
$883$	−439.165	−	760.656i	−0.497356	−	0.861446i	0.502640	−	0.864496i	$-0.332362\pi$
$883$	−439.165	−	760.656i	−0.497356	−	0.861446i	−0.999995	+	0.00305054i	$0.999029\pi$
$884$		0			0
$885$	−612.497	+	819.666i	−0.692086	+	0.926177i
$886$		0			0
$887$	−998.562	−	576.520i	−1.12577	−	0.649966i	−0.182906	−	0.983130i	$-0.558550\pi$
$887$	−998.562	−	576.520i	−1.12577	−	0.649966i	−0.942869	+	0.333164i	$0.891884\pi$
$888$		0			0
$889$	−822.161			−0.924815
$890$		0			0
$891$	−1313.75	+	67.1069i	−1.47447	+	0.0753164i
$892$		0			0
$893$	217.901	−	223.119i	0.244010	−	0.249854i
$894$		0			0
$895$	−73.6664			−0.0823088
$896$		0			0
$897$	−99.3131	+	836.719i	−0.110717	+	0.932798i
$898$		0			0
$899$	−628.024	+	362.590i	−0.698581	+	0.403326i
$900$		0			0
$901$	−1141.24			−1.26664
$902$		0			0
$903$	1646.90	−	2203.95i	1.82381	−	2.44069i
$904$		0			0
$905$	−1353.34	+	781.350i	−1.49540	+	0.863370i
$906$		0			0
$907$	−540.908	−	936.880i	−0.596370	−	1.03294i	−0.993352	−	0.115117i	$-0.963276\pi$
$907$	−540.908	−	936.880i	−0.596370	−	1.03294i	0.396982	−	0.917827i	$-0.370058\pi$
$908$		0			0
$909$	777.787	−	229.831i	0.855651	−	0.252839i
$910$		0			0
$911$	−348.268	−	201.073i	−0.382292	−	0.220716i	0.296523	−	0.955026i	$-0.404173\pi$
$911$	−348.268	−	201.073i	−0.382292	−	0.220716i	−0.678815	+	0.734309i	$0.737506\pi$
$912$		0			0
$913$	−669.579	−	1159.74i	−0.733383	−	1.27026i
$914$		0			0
$915$	681.659	+	509.370i	0.744982	+	0.556689i
$916$		0			0
$917$	−26.2931	−	15.1804i	−0.0286730	−	0.0165544i
$918$		0			0
$919$	−761.698			−0.828834			−0.414417	−	0.910087i	$-0.636014\pi$
$919$	−761.698			−0.828834			−0.414417	+	0.910087i	$0.636014\pi$
$920$		0			0
$921$	619.290	+	1442.75i	0.672410	+	1.56651i
$922$		0			0
$923$	530.918	−	306.526i	0.575209	−	0.332097i
$924$		0			0
$925$	−205.122			−0.221753
$926$		0			0
$927$	−534.319	+	562.309i	−0.576396	+	0.606590i
$928$		0			0
$929$	−912.960	+	527.098i	−0.982734	+	0.567382i	−0.903095	−	0.429442i	$-0.858710\pi$
$929$	−912.960	+	527.098i	−0.982734	+	0.567382i	−0.0796399	+	0.996824i	$0.525377\pi$
$930$		0			0
$931$	−413.420	+	1619.31i	−0.444060	+	1.73932i
$932$		0			0
$933$	−135.919	+	1145.13i	−0.145680	+	1.22736i
$934$		0			0
$935$	−1449.65	+	836.954i	−1.55043	+	0.895138i
$936$		0			0
$937$	−77.1282	−	133.590i	−0.0823140	−	0.142572i	0.821929	−	0.569589i	$-0.192898\pi$
$937$	−77.1282	−	133.590i	−0.0823140	−	0.142572i	−0.904244	+	0.427017i	$0.859564\pi$
$938$		0			0
$939$	−396.000	+	529.942i	−0.421725	+	0.564368i
$940$		0			0
$941$	304.283	+	175.678i	0.323362	+	0.186693i	0.652890	−	0.757453i	$-0.273556\pi$
$941$	304.283	+	175.678i	0.323362	+	0.186693i	−0.329528	+	0.944146i	$0.606890\pi$
$942$		0			0
$943$	−161.499	+	279.725i	−0.171261	+	0.296633i
$944$		0			0
$945$	−918.409	−	1106.50i	−0.971861	−	1.17090i
$946$		0			0
$947$	860.990	−	497.093i	0.909176	−	0.524913i	0.0290101	−	0.999579i	$-0.490764\pi$
$947$	860.990	−	497.093i	0.909176	−	0.524913i	0.880166	+	0.474666i	$0.157431\pi$
$948$		0			0
$949$	206.563	+	357.777i	0.217663	+	0.377004i
$950$		0			0
$951$	462.102	+	345.307i	0.485912	+	0.363098i
$952$		0			0
$953$	−941.583	−	543.623i	−0.988020	−	0.570433i	−0.0833378	−	0.996521i	$-0.526558\pi$
$953$	−941.583	−	543.623i	−0.988020	−	0.570433i	−0.904682	+	0.426088i	$0.859891\pi$
$954$		0			0
$955$	−28.6825	+	49.6795i	−0.0300340	+	0.0520204i
$956$		0			0
$957$	−496.482	−	1156.65i	−0.518790	−	1.20862i
$958$		0			0
$959$	1501.86	+	867.101i	1.56607	+	0.904172i
$960$		0			0
$961$	86.5438	−	149.898i	0.0900560	−	0.155981i
$962$		0			0
$963$	1008.57	−	298.026i	1.04732	−	0.309477i
$964$		0			0
$965$		−	625.383i		−	0.648065i
$966$		0			0
$967$	623.082			0.644345			0.322173	−	0.946681i	$-0.395587\pi$
$967$	623.082			0.644345			0.322173	+	0.946681i	$0.395587\pi$
$968$		0			0
$969$	−1204.49	−	464.557i	−1.24302	−	0.479419i
$970$		0			0
$971$	−614.569	−	354.822i	−0.632924	−	0.365419i	0.148960	−	0.988843i	$-0.452408\pi$
$971$	−614.569	−	354.822i	−0.632924	−	0.365419i	−0.781884	+	0.623424i	$0.785741\pi$
$972$		0			0
$973$	−780.818	−	1352.42i	−0.802485	−	1.38995i
$974$		0			0
$975$	−36.8738	−	85.9045i	−0.0378193	−	0.0881072i
$976$		0			0
$977$	486.933	−	281.131i	0.498396	−	0.287749i	−0.229655	−	0.973272i	$-0.573760\pi$
$977$	486.933	−	281.131i	0.498396	−	0.287749i	0.728051	+	0.685523i	$0.240426\pi$
$978$		0			0
$979$	2308.46			2.35798
$980$		0			0
$981$	1048.06	+	252.351i	1.06836	+	0.257239i
$982$		0			0
$983$	−522.063	+	301.413i	−0.531092	+	0.306626i	−0.741461	−	0.670996i	$-0.765867\pi$
$983$	−522.063	+	301.413i	−0.531092	+	0.306626i	0.210369	+	0.977622i	$0.432533\pi$
$984$		0			0
$985$	873.598			0.886901
$986$		0			0
$987$	−529.563	+	227.310i	−0.536538	+	0.230304i
$988$		0			0
$989$			3029.78i			3.06348i
$990$		0			0
$991$	−476.739	+	825.736i	−0.481068	+	0.833235i	−0.999764	−	0.0217240i	$-0.993085\pi$
$991$	−476.739	+	825.736i	−0.481068	+	0.833235i	0.518696	+	0.854959i	$0.326418\pi$
$992$		0			0
$993$	332.783	+	775.282i	0.335129	+	0.780747i
$994$		0			0
$995$	−508.793	+	293.752i	−0.511350	+	0.295228i
$996$		0			0
$997$	399.603			0.400805			0.200403	−	0.979714i	$-0.435775\pi$
$997$	399.603			0.400805			0.200403	+	0.979714i	$0.435775\pi$
$998$		0			0
$999$	−1210.87	−	448.080i	−1.21208	−	0.448529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.11	✓	80
3.2	odd	2		2052.3.m.a.1493.29		80
9.4	even	3		2052.3.be.a.125.12		80
9.5	odd	6		684.3.be.a.581.15	yes	80
19.7	even	3		684.3.be.a.425.15	yes	80
57.26	odd	6		2052.3.be.a.197.12		80
171.121	even	3		2052.3.m.a.881.12		80
171.140	odd	6	inner	684.3.m.a.653.11	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.11	✓	80	1.1	even	1	trivial
684.3.m.a.653.11	yes	80	171.140	odd	6	inner
684.3.be.a.425.15	yes	80	19.7	even	3
684.3.be.a.581.15	yes	80	9.5	odd	6
2052.3.m.a.881.12		80	171.121	even	3
2052.3.m.a.1493.29		80	3.2	odd	2
2052.3.be.a.125.12		80	9.4	even	3
2052.3.be.a.197.12		80	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.79577 + 2.40317i) q^{3} -4.55087i q^{5} +(5.85150 - 10.1351i) q^{7} +(-2.55043 - 8.63107i) q^{9} +O(q^{10})\)	\(q+(-1.79577 + 2.40317i) q^{3} -4.55087i q^{5} +(5.85150 - 10.1351i) q^{7} +(-2.55043 - 8.63107i) q^{9} +(14.0645 + 8.12016i) q^{11} +(-3.63225 + 6.29124i) q^{13} +(10.9365 + 8.17232i) q^{15} +(-19.6143 - 11.3243i) q^{17} +(-13.5931 - 13.2751i) q^{19} +(13.8484 + 32.2624i) q^{21} +(-33.4828 - 19.3313i) q^{23} +4.28954 q^{25} +(25.3219 + 9.37031i) q^{27} +25.8349i q^{29} +(14.0349 + 24.3091i) q^{31} +(-44.7708 + 19.2175i) q^{33} +(-46.1236 - 26.6295i) q^{35} -47.8191 q^{37} +(-8.59622 - 20.0265i) q^{39} -8.35430i q^{41} +(-39.1823 - 67.8657i) q^{43} +(-39.2789 + 11.6067i) q^{45} +16.4142i q^{47} +(-43.9802 - 76.1759i) q^{49} +(62.4370 - 26.8006i) q^{51} +(43.6381 - 25.1945i) q^{53} +(36.9538 - 64.0059i) q^{55} +(56.3123 - 8.82731i) q^{57} +74.9477i q^{59} +62.3287 q^{61} +(-102.401 - 24.6559i) q^{63} +(28.6306 + 16.5299i) q^{65} +(28.5642 - 49.4746i) q^{67} +(106.584 - 45.7502i) q^{69} +(-73.0839 - 42.1950i) q^{71} +(28.4345 - 49.2501i) q^{73} +(-7.70302 + 10.3085i) q^{75} +(164.597 - 95.0303i) q^{77} +(-59.5243 - 103.099i) q^{79} +(-67.9907 + 44.0258i) q^{81} +(-71.4114 - 41.2294i) q^{83} +(-51.5356 + 89.2622i) q^{85} +(-62.0856 - 46.3935i) q^{87} +(123.100 - 71.0719i) q^{89} +(42.5082 + 73.6264i) q^{91} +(-83.6224 - 9.92542i) q^{93} +(-60.4134 + 61.8603i) q^{95} +(-59.2528 - 102.629i) q^{97} +(34.2151 - 142.102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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