LMFDB - Embedded newform 684.3.be.a.425.15

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			425.15
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18332 - 2.75677i) q^{3} +(3.94117 + 2.27544i) q^{5} +(5.85150 - 10.1351i) q^{7} +(-6.19951 + 6.52427i) q^{9} +O(q^{10})$	\(q+(-1.18332 - 2.75677i) q^{3} +(3.94117 + 2.27544i) q^{5} +(5.85150 - 10.1351i) q^{7} +(-6.19951 + 6.52427i) q^{9} +(14.0645 + 8.12016i) q^{11} +7.26450 q^{13} +(1.60918 - 13.5575i) q^{15} +(19.6143 - 11.3243i) q^{17} +(-13.5931 + 13.2751i) q^{19} +(-34.8643 - 4.13816i) q^{21} +38.6626i q^{23} +(-2.14477 - 3.71485i) q^{25} +(25.3219 + 9.37031i) q^{27} +(22.3737 - 12.9174i) q^{29} +(14.0349 + 24.3091i) q^{31} +(5.74255 - 48.3814i) q^{33} +(46.1236 - 26.6295i) q^{35} -47.8191 q^{37} +(-8.59622 - 20.0265i) q^{39} +(7.23503 + 4.17715i) q^{41} +78.3646 q^{43} +(-39.2789 + 11.6067i) q^{45} +(14.2151 - 8.20711i) q^{47} +(-43.9802 - 76.1759i) q^{49} +(-54.4285 - 40.6717i) q^{51} +(-43.6381 - 25.1945i) q^{53} +(36.9538 + 64.0059i) q^{55} +(52.6813 + 21.7641i) q^{57} +(-64.9066 - 37.4738i) q^{59} +(-31.1644 - 53.9783i) q^{61} +(29.8476 + 101.009i) q^{63} +(28.6306 + 16.5299i) q^{65} -57.1284 q^{67} +(106.584 - 45.7502i) q^{69} +(73.0839 - 42.1950i) q^{71} +(28.4345 + 49.2501i) q^{73} +(-7.70302 + 10.3085i) q^{75} +(164.597 - 95.0303i) q^{77} +119.049 q^{79} +(-4.13211 - 80.8945i) q^{81} +(-71.4114 - 41.2294i) q^{83} +103.071 q^{85} +(-62.0856 - 46.3935i) q^{87} +(-123.100 - 71.0719i) q^{89} +(42.5082 - 73.6264i) q^{91} +(50.4068 - 67.4564i) q^{93} +(-83.7793 + 21.3894i) q^{95} +118.506 q^{97} +(-140.171 + 41.4197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.18332	−	2.75677i	−0.394440	−	0.918922i
$3$	−1.18332	−	2.75677i	−0.394440	−	0.918922i
$4$		0			0
$5$	3.94117	+	2.27544i	0.788235	+	0.455087i	0.839341	−	0.543606i	$-0.182941\pi$
$5$	3.94117	+	2.27544i	0.788235	+	0.455087i	−0.0511060	+	0.998693i	$0.516275\pi$
$6$		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
$9$	−6.19951	+	6.52427i	−0.688835	+	0.724919i
$10$		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
$13$	7.26450			0.558808			0.279404	−	0.960174i	$-0.409863\pi$
$13$	7.26450			0.558808			0.279404	+	0.960174i	$0.409863\pi$
$14$		0			0
$15$	1.60918	−	13.5575i	0.107279	−	0.903831i
$16$		0			0
$17$	19.6143	−	11.3243i	1.15378	−	0.666137i	0.203976	−	0.978976i	$-0.434613\pi$
$17$	19.6143	−	11.3243i	1.15378	−	0.666137i	0.949806	+	0.312839i	$0.101280\pi$
$18$		0			0
$19$	−13.5931	+	13.2751i	−0.715424	+	0.698691i
$19$	−13.5931	+	13.2751i	−0.715424	+	0.698691i
$20$		0			0
$21$	−34.8643	−	4.13816i	−1.66020	−	0.197055i
$22$		0			0
$23$			38.6626i			1.68098i	0.541826	+	0.840491i	$0.317733\pi$
$23$			38.6626i			1.68098i	−0.541826	+	0.840491i	$0.682267\pi$
$24$		0			0
$25$	−2.14477	−	3.71485i	−0.0857908	−	0.148594i
$26$		0			0
$27$	25.3219	+	9.37031i	0.937847	+	0.347048i
$28$		0			0
$29$	22.3737	−	12.9174i	0.771506	−	0.445429i	−0.0619056	−	0.998082i	$-0.519718\pi$
$29$	22.3737	−	12.9174i	0.771506	−	0.445429i	0.833412	+	0.552653i	$0.186384\pi$
$30$		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
$33$	5.74255	−	48.3814i	0.174017	−	1.46610i
$34$		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
$41$	7.23503	+	4.17715i	0.176464	+	0.101882i	0.585630	−	0.810578i	$-0.300847\pi$
$41$	7.23503	+	4.17715i	0.176464	+	0.101882i	−0.409166	+	0.912460i	$0.634180\pi$
$42$		0			0
$43$	78.3646			1.82243			0.911216	−	0.411929i	$-0.135145\pi$
$43$	78.3646			1.82243			0.911216	+	0.411929i	$0.135145\pi$
$44$		0			0
$45$	−39.2789	+	11.6067i	−0.872865	+	0.257926i
$46$		0			0
$47$	14.2151	−	8.20711i	0.302449	−	0.174619i	−0.341093	−	0.940029i	$-0.610797\pi$
$47$	14.2151	−	8.20711i	0.302449	−	0.174619i	0.643543	+	0.765410i	$0.277464\pi$
$48$		0			0
$49$	−43.9802	−	76.1759i	−0.897555	−	1.55461i
$50$		0			0
$51$	−54.4285	−	40.6717i	−1.06723	−	0.797485i
$52$		0			0
$53$	−43.6381	−	25.1945i	−0.823360	−	0.475367i	0.0282138	−	0.999602i	$-0.491018\pi$
$53$	−43.6381	−	25.1945i	−0.823360	−	0.475367i	−0.851574	+	0.524235i	$0.824351\pi$
$54$		0			0
$55$	36.9538	+	64.0059i	0.671888	+	1.16374i
$56$		0			0
$57$	52.6813	+	21.7641i	0.924234	+	0.381827i
$58$		0			0
$59$	−64.9066	−	37.4738i	−1.10011	−	0.635150i	−0.163861	−	0.986483i	$-0.552395\pi$
$59$	−64.9066	−	37.4738i	−1.10011	−	0.635150i	−0.936250	+	0.351334i	$0.885728\pi$
$60$		0			0
$61$	−31.1644	−	53.9783i	−0.510891	−	0.884890i	−0.999920	−	0.0126221i	$-0.995982\pi$
$61$	−31.1644	−	53.9783i	−0.510891	−	0.884890i	0.489029	−	0.872267i	$-0.337351\pi$
$62$		0			0
$63$	29.8476	+	101.009i	0.473772	+	1.60332i
$64$		0			0
$65$	28.6306	+	16.5299i	0.440471	+	0.254306i
$66$		0			0
$67$	−57.1284			−0.852662			−0.426331	−	0.904567i	$-0.640194\pi$
$67$	−57.1284			−0.852662			−0.426331	+	0.904567i	$0.640194\pi$
$68$		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	$-0.464098\pi$
$71$	73.0839	−	42.1950i	1.02935	−	0.594296i	0.916799	+	0.399350i	$0.130764\pi$
$72$		0			0
$73$	28.4345	+	49.2501i	0.389514	+	0.674658i	0.992384	−	0.123181i	$-0.0393096\pi$
$73$	28.4345	+	49.2501i	0.389514	+	0.674658i	−0.602870	+	0.797839i	$0.705976\pi$
$74$		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
$79$	119.049			1.50694			0.753472	−	0.657480i	$-0.228378\pi$
$79$	119.049			1.50694			0.753472	+	0.657480i	$0.228378\pi$
$80$		0			0
$81$	−4.13211	−	80.8945i	−0.0510138	−	0.998698i
$82$		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
$85$	103.071			1.21260
$86$		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	$-0.627738\pi$
$89$	−123.100	−	71.0719i	−1.38315	−	0.798560i	−0.992531	+	0.121993i	$0.961071\pi$
$90$		0			0
$91$	42.5082	−	73.6264i	0.467123	−	0.809081i
$92$		0			0
$93$	50.4068	−	67.4564i	0.542009	−	0.725337i
$94$		0			0
$95$	−83.7793	+	21.3894i	−0.881887	+	0.225152i
$96$		0			0
$97$	118.506			1.22171			0.610854	−	0.791743i	$-0.290826\pi$
$97$	118.506			1.22171			0.610854	+	0.791743i	$0.290826\pi$
$98$		0			0
$99$	−140.171	+	41.4197i	−1.41587	+	0.418381i
$100$		0			0
$101$	78.0417	−	45.0574i	0.772690	−	0.446113i	−0.0611432	−	0.998129i	$-0.519475\pi$
$101$	78.0417	−	45.0574i	0.772690	−	0.446113i	0.833833	+	0.552016i	$0.186141\pi$
$102$		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
$105$	−127.990	−	95.6407i	−1.21895	−	0.910864i
$106$		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	−0.998312	−	0.0580708i	$-0.981505\pi$
$109$	−59.8897	−	103.732i	−0.549447	−	0.951670i	0.448865	−	0.893599i	$-0.351828\pi$
$110$		0			0
$111$	56.5853	+	131.826i	0.509777	+	1.18762i
$112$		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
$117$	−45.0363	+	47.3955i	−0.384926	+	0.405090i
$118$		0			0
$119$		−	265.057i		−	2.22737i
$120$		0			0
$121$	71.3740	+	123.623i	0.589868	+	1.02168i
$122$		0			0
$123$	2.95407	−	24.8882i	0.0240168	−	0.202343i
$124$		0			0
$125$		−	133.293i		−	1.06634i
$126$		0			0
$127$	−35.1261	+	60.8401i	−0.276583	+	0.479056i	−0.970533	−	0.240967i	$-0.922535\pi$
$127$	−35.1261	+	60.8401i	−0.276583	+	0.479056i	0.693950	+	0.720023i	$0.255869\pi$
$128$		0			0
$129$	−92.7303	−	216.033i	−0.718840	−	1.67467i
$130$		0			0
$131$	2.24670	+	1.29713i	0.0171504	+	0.00990178i	0.508551	−	0.861032i	$-0.330181\pi$
$131$	2.24670	+	1.29713i	0.0171504	+	0.00990178i	−0.491400	+	0.870934i	$0.663515\pi$
$132$		0			0
$133$	55.0050	+	215.446i	0.413571	+	1.61990i
$134$		0			0
$135$	78.4763	+	94.5484i	0.581306	+	0.700358i
$136$		0			0
$137$	128.331	−	74.0922i	0.936726	−	0.540819i	0.0477932	−	0.998857i	$-0.484781\pi$
$137$	128.331	−	74.0922i	0.936726	−	0.540819i	0.888932	+	0.458038i	$0.151448\pi$
$138$		0			0
$139$	−133.439			−0.959992			−0.479996	−	0.877271i	$-0.659362\pi$
$139$	−133.439			−0.959992			−0.479996	+	0.877271i	$0.659362\pi$
$140$		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
$147$	−157.956	+	211.383i	−1.07453	+	1.43798i
$148$		0			0
$149$	106.043	+	61.2239i	0.711697	+	0.410899i	0.811689	−	0.584090i	$-0.198548\pi$
$149$	106.043	+	61.2239i	0.711697	+	0.410899i	−0.0999919	+	0.994988i	$0.531882\pi$
$150$		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
$155$			127.742i			0.824142i
$156$		0			0
$157$	−146.014	+	252.904i	−0.930027	+	1.61085i	−0.146757	+	0.989173i	$0.546884\pi$
$157$	−146.014	+	252.904i	−0.930027	+	1.61085i	−0.783270	+	0.621682i	$0.786450\pi$
$158$		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
$165$	132.721	−	177.613i	0.804371	−	1.07644i
$166$		0			0
$167$			2.72800i			0.0163353i	0.999967	+	0.00816766i	$0.00259988\pi$
$167$			2.72800i			0.0163353i	−0.999967	+	0.00816766i	$0.997400\pi$
$168$		0			0
$169$	−116.227			−0.687734
$170$		0			0
$171$	−2.34019	−	170.984i	−0.0136853	−	0.999906i
$172$		0			0
$173$		−	119.559i		−	0.691092i	−0.938402	−	0.345546i	$-0.887694\pi$
$173$		−	119.559i		−	0.691092i	0.938402	−	0.345546i	$-0.112306\pi$
$174$		0			0
$175$	−50.2005			−0.286860
$176$		0			0
$177$	−26.5014	+	223.276i	−0.149725	+	1.26145i
$178$		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	−0.200147	+	0.979766i	$0.564142\pi$
$181$	−171.692	+	297.380i	−0.948576	+	1.64298i	−0.748429	+	0.663215i	$0.769191\pi$
$182$		0			0
$183$	−111.928	+	149.786i	−0.611629	+	0.818505i
$184$		0			0
$185$	−188.463	−	108.809i	−1.01872	−	0.588159i
$186$		0			0
$187$	367.821			1.96696
$188$		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
$193$	−68.7102	+	119.009i	−0.356011	+	0.616629i	−0.987290	−	0.158926i	$-0.949197\pi$
$193$	−68.7102	+	119.009i	−0.356011	+	0.616629i	0.631279	+	0.775556i	$0.282530\pi$
$194$		0			0
$195$	11.6899	−	98.4881i	0.0599482	−	0.505067i
$196$		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	−0.981383	−	0.192059i	$-0.938484\pi$
$199$	−64.5484	+	111.801i	−0.324364	+	0.561815i	0.657019	+	0.753874i	$0.271817\pi$
$200$		0			0
$201$	67.6011	+	157.490i	0.336324	+	0.783530i
$202$		0			0
$203$		−	302.346i		−	1.48939i
$204$		0			0
$205$	19.0097	+	32.9257i	0.0927302	+	0.160613i
$206$		0			0
$207$	−252.245	−	239.689i	−1.21857	−	1.15792i
$208$		0			0
$209$	−298.976	+	76.3307i	−1.43051	+	0.365218i
$210$		0			0
$211$	−78.4672	+	135.909i	−0.371882	+	0.644119i	−0.989855	−	0.142080i	$-0.954621\pi$
$211$	−78.4672	+	135.909i	−0.371882	+	0.644119i	0.617973	+	0.786200i	$0.287954\pi$
$212$		0			0
$213$	−202.803	−	151.545i	−0.952128	−	0.711479i
$214$		0			0
$215$	308.848	+	178.314i	1.43650	+	0.829366i
$216$		0			0
$217$	328.501			1.51383
$218$		0			0
$219$	102.124	−	136.666i	0.466318	−	0.624045i
$220$		0			0
$221$	142.488	−	82.2655i	0.644742	−	0.372242i
$222$		0			0
$223$	100.674			0.451453			0.225727	−	0.974191i	$-0.427524\pi$
$223$	100.674			0.451453			0.225727	+	0.974191i	$0.427524\pi$
$224$		0			0
$225$	37.5332	+	9.03720i	0.166814	+	0.0401653i
$226$		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
$231$	−456.747	−	341.305i	−1.97726	−	1.47751i
$232$		0			0
$233$	−334.241	+	192.974i	−1.43451	+	0.828215i	−0.997460	−	0.0712220i	$-0.977310\pi$
$233$	−334.241	+	192.974i	−1.43451	+	0.828215i	−0.437050	+	0.899437i	$0.643977\pi$
$234$		0			0
$235$	74.6990			0.317868
$236$		0			0
$237$	−140.872	−	328.189i	−0.594398	−	1.38476i
$238$		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
$241$	−103.286	−	178.896i	−0.428571	−	0.742307i	0.568175	−	0.822908i	$-0.307650\pi$
$241$	−103.286	−	178.896i	−0.428571	−	0.742307i	−0.996747	+	0.0806002i	$0.974316\pi$
$242$		0			0
$243$	−218.118	+	107.115i	−0.897603	+	0.440804i
$244$		0			0
$245$		−	400.297i		−	1.63386i
$246$		0			0
$247$	−98.7467	+	96.4371i	−0.399784	+	0.390434i
$248$		0			0
$249$	−29.1573	+	245.652i	−0.117098	+	0.986555i
$250$		0			0
$251$	170.812	+	98.6182i	0.680525	+	0.392901i	0.800053	−	0.599930i	$-0.204805\pi$
$251$	170.812	+	98.6182i	0.680525	+	0.392901i	−0.119528	+	0.992831i	$0.538138\pi$
$252$		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
$257$		−	202.723i		−	0.788805i	−0.918938	−	0.394403i	$-0.870952\pi$
$257$		−	202.723i		−	0.788805i	0.918938	−	0.394403i	$-0.129048\pi$
$258$		0			0
$259$	−279.814	+	484.652i	−1.08036	+	1.87124i
$260$		0			0
$261$	−54.4290	+	226.054i	−0.208540	+	0.866106i
$262$		0			0
$263$			206.933i			0.786819i	0.919363	+	0.393409i	$0.128704\pi$
$263$			206.933i			0.786819i	−0.919363	+	0.393409i	$0.871296\pi$
$264$		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	$-0.704013\pi$
$269$	−54.5399	+	31.4886i	−0.202751	+	0.117058i	0.395187	+	0.918601i	$0.370680\pi$
$270$		0			0
$271$	−101.148	−	175.193i	−0.373239	−	0.646469i	0.616823	−	0.787102i	$-0.288420\pi$
$271$	−101.148	−	175.193i	−0.373239	−	0.646469i	−0.990062	+	0.140633i	$0.955086\pi$
$272$		0			0
$273$	−253.272	−	30.0617i	−0.927735	−	0.110116i
$274$		0			0
$275$		−	69.6635i		−	0.253322i
$276$		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
$279$	−245.609	−	59.1374i	−0.880318	−	0.211962i
$280$		0			0
$281$	197.525	−	114.041i	0.702935	−	0.405840i	−0.105505	−	0.994419i	$-0.533646\pi$
$281$	197.525	−	114.041i	0.702935	−	0.405840i	0.808440	+	0.588579i	$0.200313\pi$
$282$		0			0
$283$	−103.040	+	178.471i	−0.364099	+	0.630639i	−0.988631	−	0.150361i	$-0.951957\pi$
$283$	−103.040	+	178.471i	−0.364099	+	0.630639i	0.624532	+	0.780999i	$0.285290\pi$
$284$		0			0
$285$	158.103	+	205.649i	0.554748	+	0.721577i
$286$		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
$291$	−140.230	−	326.692i	−0.481890	−	1.12265i
$292$		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
$295$	−170.539	−	295.382i	−0.578097	−	1.00129i
$296$		0			0
$297$	280.052	+	337.407i	0.942936	+	1.13605i
$298$		0			0
$299$			280.864i			0.939345i
$300$		0			0
$301$	458.551	−	794.233i	1.52342	−	2.63865i
$302$		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	0.879071	+	0.476690i	$0.158164\pi$
$307$	261.675	+	453.234i	0.852361	+	1.47633i	−0.0267099	+	0.999643i	$0.508503\pi$
$308$		0			0
$309$	−154.773	+	207.123i	−0.500882	+	0.670300i
$310$		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
$313$	−110.259	−	190.974i	−0.352265	−	0.610141i	0.634381	−	0.773021i	$-0.281255\pi$
$313$	−110.259	−	190.974i	−0.352265	−	0.610141i	−0.986646	+	0.162879i	$0.947922\pi$
$314$		0			0
$315$	−112.206	+	466.012i	−0.356209	+	1.47940i
$316$		0			0
$317$	−166.527	+	96.1444i	−0.525322	+	0.303295i	−0.739109	−	0.673585i	$-0.764753\pi$
$317$	−166.527	+	96.1444i	−0.525322	+	0.303295i	0.213787	+	0.976880i	$0.431420\pi$
$318$		0			0
$319$	419.567			1.31526
$320$		0			0
$321$	322.138	−	138.275i	1.00355	−	0.430764i
$322$		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
$327$	−215.096	+	287.850i	−0.657787	+	0.880275i
$328$		0			0
$329$		−	192.096i		−	0.583877i
$330$		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
$333$	296.455	−	311.985i	0.890256	−	0.936891i
$334$		0			0
$335$	−225.153	−	129.992i	−0.672098	−	0.388036i
$336$		0			0
$337$	249.153	−	431.546i	0.739328	−	1.28055i	−0.213471	−	0.976949i	$-0.568477\pi$
$337$	249.153	−	431.546i	0.739328	−	1.28055i	0.952798	−	0.303604i	$-0.0981899\pi$
$338$		0			0
$339$	337.566	+	252.246i	0.995769	+	0.744089i
$340$		0			0
$341$			455.862i			1.33684i
$342$		0			0
$343$	−455.953			−1.32931
$344$		0			0
$345$	524.166	+	62.2151i	1.51932	+	0.180334i
$346$		0			0
$347$	135.766	+	78.3843i	0.391255	+	0.225891i	0.682704	−	0.730695i	$-0.260804\pi$
$347$	135.766	+	78.3843i	0.391255	+	0.225891i	−0.291449	+	0.956586i	$0.594137\pi$
$348$		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
$351$	183.951	+	68.0706i	0.524076	+	0.193933i
$352$		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
$355$	384.048			1.08183
$356$		0			0
$357$	−730.701	+	313.647i	−2.04678	+	0.878564i
$358$		0			0
$359$	551.226	−	318.250i	1.53545	−	0.886491i	0.536351	−	0.843995i	$-0.319802\pi$
$359$	551.226	−	318.250i	1.53545	−	0.886491i	0.999097	−	0.0424966i	$-0.0135312\pi$
$360$		0			0
$361$	8.54208	−	360.899i	0.0236623	−	0.999720i
$362$		0			0
$363$	256.343	−	343.048i	0.706178	−	0.945035i
$364$		0			0
$365$			258.804i			0.709052i
$366$		0			0
$367$	−99.5425	−	172.413i	−0.271233	−	0.469789i	0.697945	−	0.716152i	$-0.254098\pi$
$367$	−99.5425	−	172.413i	−0.271233	−	0.469789i	−0.969178	+	0.246362i	$0.920765\pi$
$368$		0			0
$369$	−72.1065	+	21.3070i	−0.195411	+	0.0577426i
$370$		0			0
$371$	−510.697	+	294.851i	−1.37654	+	0.794746i
$372$		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
$375$	−367.458	+	157.728i	−0.979887	+	0.420609i
$376$		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
$383$	−342.171	−	197.553i	−0.893397	−	0.515803i	−0.0183451	−	0.999832i	$-0.505840\pi$
$383$	−342.171	−	197.553i	−0.893397	−	0.515803i	−0.875052	+	0.484029i	$0.839173\pi$
$384$		0			0
$385$	864.942			2.24660
$386$		0			0
$387$	−485.822	+	511.271i	−1.25535	+	1.32111i
$388$		0			0
$389$	−217.495	+	125.571i	−0.559114	+	0.322805i	−0.752790	−	0.658261i	$-0.771292\pi$
$389$	−217.495	+	125.571i	−0.559114	+	0.322805i	0.193676	+	0.981066i	$0.437959\pi$
$390$		0			0
$391$	437.828	+	758.340i	1.11976	+	1.93949i
$392$		0			0
$393$	0.917328	−	7.72855i	0.00233417	−	0.0196655i
$394$		0			0
$395$	469.191	+	270.887i	1.18782	+	0.685791i
$396$		0			0
$397$	157.630	+	273.022i	0.397052	+	0.687714i	0.993361	−	0.115041i	$-0.0367000\pi$
$397$	157.630	+	273.022i	0.397052	+	0.687714i	−0.596309	+	0.802755i	$0.703367\pi$
$398$		0			0
$399$	528.847	−	406.578i	1.32543	−	1.01899i
$400$		0			0
$401$	−241.283	−	139.305i	−0.601704	−	0.347394i	0.168008	−	0.985786i	$-0.446267\pi$
$401$	−241.283	−	139.305i	−0.601704	−	0.347394i	−0.769712	+	0.638392i	$0.779600\pi$
$402$		0			0
$403$	101.956	+	176.594i	0.252994	+	0.438198i
$404$		0			0
$405$	167.785	−	328.222i	0.414284	−	0.810424i
$406$		0			0
$407$	−672.554	−	388.299i	−1.65247	−	0.954052i
$408$		0			0
$409$	−200.542			−0.490323			−0.245161	−	0.969482i	$-0.578841\pi$
$409$	−200.542			−0.490323			−0.245161	+	0.969482i	$0.578841\pi$
$410$		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
$421$	−258.641			−0.614349			−0.307174	−	0.951653i	$-0.599383\pi$
$421$	−258.641			−0.614349			−0.307174	+	0.951653i	$0.599383\pi$
$422$		0			0
$423$	−34.5815	+	143.623i	−0.0817529	+	0.339535i
$424$		0			0
$425$	−84.1363	−	48.5761i	−0.197968	−	0.114297i
$426$		0			0
$427$	−729.433			−1.70828
$428$		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	$-0.448157\pi$
$431$	−263.486	−	152.124i	−0.611336	−	0.352955i	−0.773488	+	0.633811i	$0.781490\pi$
$432$		0			0
$433$	398.394	−	690.039i	0.920079	−	1.59362i	0.120789	−	0.992678i	$-0.461458\pi$
$433$	398.394	−	690.039i	0.920079	−	1.59362i	0.799290	−	0.600945i	$-0.205209\pi$
$434$		0			0
$435$	−139.124	−	324.117i	−0.319826	−	0.745096i
$436$		0			0
$437$	−513.251	−	525.542i	−1.17449	−	1.20261i
$438$		0			0
$439$	−503.675			−1.14732			−0.573662	−	0.819092i	$-0.694478\pi$
$439$	−503.675			−1.14732			−0.573662	+	0.819092i	$0.694478\pi$
$440$		0			0
$441$	769.647	+	185.315i	1.74523	+	0.420215i
$442$		0			0
$443$	292.376	−	168.803i	0.659990	−	0.381045i	−0.132283	−	0.991212i	$-0.542231\pi$
$443$	292.376	−	168.803i	0.659990	−	0.381045i	0.792273	+	0.610167i	$0.208897\pi$
$444$		0			0
$445$	−323.439	−	560.213i	−0.726830	−	1.25891i
$446$		0			0
$447$	43.2973	−	364.783i	0.0968620	−	0.816069i
$448$		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
$453$	219.842	+	26.0937i	0.485301	+	0.0576021i
$454$		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
$459$	602.783	−	102.961i	1.31325	−	0.224316i
$460$		0			0
$461$			295.156i			0.640252i	0.947375	+	0.320126i	$0.103725\pi$
$461$			295.156i			0.640252i	−0.947375	+	0.320126i	$0.896275\pi$
$462$		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
$465$	352.155	−	151.160i	0.757322	−	0.325074i
$466$		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
$471$	869.979	+	103.261i	1.84709	+	0.219237i
$472$		0			0
$473$	1102.16	+	636.333i	2.33015	+	1.34531i
$474$		0			0
$475$	78.4690	+	22.0241i	0.165198	+	0.0463664i
$476$		0			0
$477$	434.910	−	128.513i	0.911761	−	0.269420i
$478$		0			0
$479$	−167.295	+	96.5879i	−0.349259	+	0.201645i	−0.664359	−	0.747414i	$-0.731295\pi$
$479$	−167.295	+	96.5879i	−0.349259	+	0.201645i	0.315100	+	0.949059i	$0.397962\pi$
$480$		0			0
$481$	−347.382			−0.722208
$482$		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
$489$	−46.8164	−	109.068i	−0.0957390	−	0.223042i
$490$		0			0
$491$	−220.915	−	127.546i	−0.449930	−	0.259767i	0.257871	−	0.966179i	$-0.416979\pi$
$491$	−220.915	−	127.546i	−0.449930	−	0.259767i	−0.707801	+	0.706412i	$0.750312\pi$
$492$		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
$497$		−	987.617i		−	1.98716i
$498$		0			0
$499$	−242.669	+	420.316i	−0.486311	+	0.842316i	−0.999876	−	0.0157350i	$-0.994991\pi$
$499$	−242.669	+	420.316i	−0.486311	+	0.842316i	0.513565	+	0.858051i	$0.328325\pi$
$500$		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	$-0.269745\pi$
$503$	172.886	+	99.8159i	0.343710	+	0.198441i	−0.318201	+	0.948023i	$0.603079\pi$
$504$		0			0
$505$	410.101			0.812082
$506$		0			0
$507$	137.534	+	320.411i	0.271270	+	0.631974i
$508$		0			0
$509$			205.885i			0.404489i	0.979335	+	0.202244i	$0.0648235\pi$
$509$			205.885i			0.404489i	−0.979335	+	0.202244i	$0.935176\pi$
$510$		0			0
$511$	665.539			1.30242
$512$		0			0
$513$	−468.594	+	208.780i	−0.913438	+	0.406979i
$514$		0			0
$515$		−	392.228i		−	0.761607i
$516$		0			0
$517$	266.572			0.515613
$518$		0			0
$519$	−329.596	+	141.476i	−0.635059	+	0.272594i
$520$		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	−0.0550183	+	0.998485i	$0.517522\pi$
$523$	−466.633	+	808.231i	−0.892223	+	1.54538i	−0.837205	+	0.546890i	$0.815812\pi$
$524$		0			0
$525$	59.4032	+	138.391i	0.113149	+	0.263602i
$526$		0			0
$527$	550.569	+	317.871i	1.04472	+	0.603171i
$528$		0			0
$529$	−965.795			−1.82570
$530$		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
$535$	−265.893	+	460.540i	−0.496997	+	0.860823i
$536$		0			0
$537$	−44.6246	+	19.1547i	−0.0830998	+	0.0356699i
$538$		0			0
$539$		−	1428.50i		−	2.65029i
$540$		0			0
$541$	77.8507	−	134.841i	0.143901	−	0.249245i	−0.785061	−	0.619418i	$-0.787368\pi$
$541$	77.8507	−	134.841i	0.143901	−	0.249245i	0.928963	+	0.370174i	$0.120702\pi$
$542$		0			0
$543$	1022.97	+	121.420i	1.88393	+	0.223610i
$544$		0			0
$545$		−	545.101i		−	1.00019i
$546$		0			0
$547$	−17.0612	−	29.5509i	−0.0311906	−	0.0540237i	0.850009	−	0.526769i	$-0.176597\pi$
$547$	−17.0612	−	29.5509i	−0.0311906	−	0.0540237i	−0.881199	+	0.472745i	$0.843263\pi$
$548$		0			0
$549$	545.372	+	131.314i	0.993392	+	0.239188i
$550$		0			0
$551$	−132.646	+	472.601i	−0.240736	+	0.857715i
$552$		0			0
$553$	696.613	−	1206.57i	1.25970	−	2.18186i
$554$		0			0
$555$	−76.9497	+	648.306i	−0.138648	+	1.16812i
$556$		0			0
$557$	−34.3037	−	19.8053i	−0.0615865	−	0.0355570i	0.468891	−	0.883256i	$-0.344654\pi$
$557$	−34.3037	−	19.8053i	−0.0615865	−	0.0355570i	−0.530477	+	0.847699i	$0.677987\pi$
$558$		0			0
$559$	569.279			1.01839
$560$		0			0
$561$	−435.250	−	1014.00i	−0.775847	−	1.80748i
$562$		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
$565$	−639.248			−1.13141
$566$		0			0
$567$	−844.053	−	431.475i	−1.48863	−	0.760979i
$568$		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
$573$	−4.45720	+	37.5522i	−0.00777870	+	0.0655361i
$574$		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
$579$	409.387	+	48.5916i	0.707059	+	0.0839233i
$580$		0			0
$581$	−835.728	+	482.508i	−1.43843	+	0.830478i
$582$		0			0
$583$	−409.166	−	708.696i	−0.701829	−	1.21560i
$584$		0			0
$585$	−285.342	+	84.3166i	−0.487763	+	0.144131i
$586$		0			0
$587$			648.942i			1.10552i	0.833339	+	0.552762i	$0.186426\pi$
$587$			648.942i			1.10552i	−0.833339	+	0.552762i	$0.813574\pi$
$588$		0			0
$589$	−513.484	−	144.120i	−0.871789	−	0.244687i
$590$		0			0
$591$	529.196	−	227.153i	0.895424	−	0.384354i
$592$		0			0
$593$	−104.519	−	60.3443i	−0.176255	−	0.101761i	0.409277	−	0.912410i	$-0.365781\pi$
$593$	−104.519	−	60.3443i	−0.176255	−	0.101761i	−0.585532	+	0.810649i	$0.699114\pi$
$594$		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
$599$			482.506i			0.805520i	0.915306	+	0.402760i	$0.131949\pi$
$599$			482.506i			0.805520i	−0.915306	+	0.402760i	$0.868051\pi$
$600$		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
$603$	354.168	−	372.721i	0.587343	−	0.618111i
$604$		0			0
$605$			649.629i			1.07377i
$606$		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	−0.975091	−	0.221807i	$-0.928805\pi$
$613$	−416.617	−	721.601i	−0.679636	−	1.17716i	0.295455	−	0.955357i	$-0.404529\pi$
$614$		0			0
$615$	68.2740	−	91.3669i	0.111015	−	0.148564i
$616$		0			0
$617$			1190.60i			1.92965i	0.262888	+	0.964826i	$0.415325\pi$
$617$			1190.60i			1.92965i	−0.262888	+	0.964826i	$0.584675\pi$
$618$		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
$621$	−362.280	+	979.009i	−0.583382	+	1.57650i
$622$		0			0
$623$	−1440.64	+	831.755i	−2.31243	+	1.33508i
$624$		0			0
$625$	249.681	−	432.460i	0.399489	−	0.691935i
$626$		0			0
$627$	564.210	+	733.883i	0.899856	+	1.17047i
$628$		0			0
$629$	−937.939	+	541.519i	−1.49116	+	0.860921i
$630$		0			0
$631$	121.585	−	210.592i	0.192686	−	0.333743i	−0.753453	−	0.657502i	$-0.771613\pi$
$631$	121.585	−	210.592i	0.192686	−	0.333743i	0.946140	+	0.323759i	$0.104947\pi$
$632$		0			0
$633$	467.521	+	55.4917i	0.738580	+	0.0876647i
$634$		0			0
$635$	−276.876	+	159.854i	−0.436025	+	0.251739i
$636$		0			0
$637$	−319.494	−	553.380i	−0.501560	−	0.868728i
$638$		0			0
$639$	−177.793	+	738.407i	−0.278236	+	1.15557i
$640$		0			0
$641$			580.450i			0.905538i	0.891628	+	0.452769i	$0.149564\pi$
$641$			580.450i			0.905538i	−0.891628	+	0.452769i	$0.850436\pi$
$642$		0			0
$643$	391.744	−	678.520i	0.609244	−	1.05524i	−0.382122	−	0.924112i	$-0.624807\pi$
$643$	391.744	−	678.520i	0.609244	−	1.05524i	0.991365	−	0.131129i	$-0.0418601\pi$
$644$		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
$651$	−388.721	−	905.600i	−0.597114	−	1.39109i
$652$		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
$655$	5.90309	+	10.2245i	0.00901235	+	0.0156099i
$656$		0			0
$657$	−497.601	−	119.812i	−0.757383	−	0.182362i
$658$		0			0
$659$	147.654	−	85.2482i	0.224058	−	0.129360i	−0.383770	−	0.923429i	$-0.625374\pi$
$659$	147.654	−	85.2482i	0.224058	−	0.129360i	0.607828	+	0.794069i	$0.292041\pi$
$660$		0			0
$661$	−1189.45			−1.79948			−0.899738	−	0.436430i	$-0.856243\pi$
$661$	−1189.45			−1.79948			−0.899738	+	0.436430i	$0.856243\pi$
$662$		0			0
$663$	−395.396	−	295.460i	−0.596373	−	0.445641i
$664$		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
$669$	−119.130	−	277.535i	−0.178071	−	0.414850i
$670$		0			0
$671$		−	1012.24i		−	1.50855i
$672$		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
$675$	−19.5003	−	114.164i	−0.0288893	−	0.169132i
$676$		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
$679$	693.436	−	1201.07i	1.02126	−	1.76888i
$680$		0			0
$681$	−11.2529	+	94.8062i	−0.0165240	+	0.139216i
$682$		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
$687$	−278.057	+	372.106i	−0.404741	+	0.541639i
$688$		0			0
$689$	−317.009	−	183.025i	−0.460100	−	0.265639i
$690$		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
$693$	−400.420	+	1663.02i	−0.577806	+	2.39974i
$694$		0			0
$695$	−525.906	−	303.632i	−0.756699	−	0.436880i
$696$		0			0
$697$	189.214			0.271468
$698$		0			0
$699$	927.498	+	693.074i	1.32689	+	0.991522i
$700$		0			0
$701$	106.817	−	61.6711i	0.152379	−	0.0879758i	−0.421872	−	0.906655i	$-0.638627\pi$
$701$	106.817	−	61.6711i	0.152379	−	0.0879758i	0.574251	+	0.818680i	$0.305294\pi$
$702$		0			0
$703$	650.008	−	634.805i	0.924620	−	0.902994i
$704$		0			0
$705$	−88.3928	−	205.928i	−0.125380	−	0.292096i
$706$		0			0
$707$		−	1054.61i		−	1.49167i
$708$		0			0
$709$	115.421	+	199.915i	0.162794	+	0.281967i	0.935870	−	0.352347i	$-0.114616\pi$
$709$	115.421	+	199.915i	0.162794	+	0.281967i	−0.773076	+	0.634314i	$0.781283\pi$
$710$		0			0
$711$	−738.043	+	776.704i	−1.03803	+	1.09241i
$712$		0			0
$713$	−939.854	+	542.625i	−1.31817	+	0.761045i
$714$		0			0
$715$	268.451	+	464.971i	0.375456	+	0.650309i
$716$		0			0
$717$	−54.9794	−	41.0834i	−0.0766798	−	0.0572991i
$718$		0			0
$719$	−524.661	+	302.913i	−0.729710	+	0.421298i	−0.818316	−	0.574769i	$-0.805092\pi$
$719$	−524.661	+	302.913i	−0.729710	+	0.421298i	0.0886062	+	0.996067i	$0.471759\pi$
$720$		0			0
$721$	−1008.65			−1.39896
$722$		0			0
$723$	−370.955	+	496.426i	−0.513077	+	0.686619i
$724$		0			0
$725$	−95.9727	−	55.4099i	−0.132376	−	0.0764274i
$726$		0			0
$727$	555.764			0.764462			0.382231	−	0.924067i	$-0.375156\pi$
$727$	555.764			0.764462			0.382231	+	0.924067i	$0.375156\pi$
$728$		0			0
$729$	553.395	+	474.548i	0.759115	+	0.650957i
$730$		0			0
$731$	1537.07	−	887.426i	2.10269	−	1.21399i
$732$		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
$735$	−1103.52	+	473.679i	−1.50139	+	0.644461i
$736$		0			0
$737$	−803.484	−	463.892i	−1.09021	−	0.629432i
$738$		0			0
$739$	−294.756	−	510.533i	−0.398859	−	0.690843i	0.594727	−	0.803928i	$-0.297260\pi$
$739$	−294.756	−	510.533i	−0.398859	−	0.690843i	−0.993585	+	0.113085i	$0.963927\pi$
$740$		0			0
$741$	382.703	+	158.106i	0.516469	+	0.213368i
$742$		0			0
$743$	1217.64	+	703.004i	1.63881	+	0.946169i	0.981243	+	0.192777i	$0.0617493\pi$
$743$	1217.64	+	703.004i	1.63881	+	0.946169i	0.657571	+	0.753393i	$0.271584\pi$
$744$		0			0
$745$	278.622	+	482.588i	0.373990	+	0.647769i
$746$		0			0
$747$	711.708	−	210.305i	0.952754	−	0.281533i
$748$		0			0
$749$	1184.32	+	683.770i	1.58121	+	0.912910i
$750$		0			0
$751$	9.97744			0.0132855			0.00664277	−	0.999978i	$-0.497886\pi$
$751$	9.97744			0.0132855			0.00664277	+	0.999978i	$0.497886\pi$
$752$		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	−0.960074	−	0.279746i	$-0.909750\pi$
$757$	−546.784	−	947.058i	−0.722304	−	1.25107i	0.237770	−	0.971322i	$-0.423584\pi$
$758$		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
$763$	−1401.78			−1.83719
$764$		0			0
$765$	−638.991	+	672.464i	−0.835282	+	0.879038i
$766$		0			0
$767$	−471.514	−	272.229i	−0.614751	−	0.354926i
$768$		0			0
$769$	27.7029			0.0360246			0.0180123	−	0.999838i	$-0.494266\pi$
$769$	27.7029			0.0360246			0.0180123	+	0.999838i	$0.494266\pi$
$770$		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	$-0.395077\pi$
$773$	−258.082	−	149.004i	−0.333870	−	0.192760i	−0.657558	+	0.753404i	$0.728411\pi$
$774$		0			0
$775$	60.2032	−	104.275i	0.0776815	−	0.134548i
$776$		0			0
$777$	1667.18	+	197.883i	2.14566	+	0.254676i
$778$		0			0
$779$	−153.798	+	39.2658i	−0.197431	+	0.0504054i
$780$		0			0
$781$	1370.52			1.75483
$782$		0			0
$783$	687.584	−	117.446i	0.878140	−	0.149995i
$784$		0			0
$785$	−1150.94	+	664.493i	−1.46616	+	0.846487i
$786$		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
$789$	570.467	−	244.868i	0.723025	−	0.310353i
$790$		0			0
$791$			1643.89i			2.07824i
$792$		0			0
$793$	−226.393	−	392.125i	−0.285490	−	0.494483i
$794$		0			0
$795$	−411.794	+	551.079i	−0.517980	+	0.693181i
$796$		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
$801$	1226.85	−	362.527i	1.53165	−	0.452593i
$802$		0			0
$803$			923.572i			1.15015i
$804$		0			0
$805$	1029.56	+	1783.26i	1.27896	+	2.21523i
$806$		0			0
$807$	151.345	+	113.093i	0.187540	+	0.140140i
$808$		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	−0.464225	−	0.885717i	$-0.653667\pi$
$811$	433.837	−	751.428i	0.534941	−	0.926545i	0.999166	−	0.0408280i	$-0.0129996\pi$
$812$		0			0
$813$	−363.276	+	486.150i	−0.446834	+	0.597971i
$814$		0			0
$815$	155.927	+	90.0245i	0.191322	+	0.110460i
$816$		0			0
$817$	−1065.21	+	1040.30i	−1.30381	+	1.27332i
$818$		0			0
$819$	216.828	+	733.783i	0.264747	+	0.895950i
$820$		0			0
$821$	−157.983	+	91.2117i	−0.192428	+	0.111098i	−0.593119	−	0.805115i	$-0.702103\pi$
$821$	−157.983	+	91.2117i	−0.192428	+	0.111098i	0.400691	+	0.916213i	$0.368770\pi$
$822$		0			0
$823$	−1614.01			−1.96113			−0.980566	−	0.196191i	$-0.937143\pi$
$823$	−1614.01			−1.96113			−0.980566	+	0.196191i	$0.937143\pi$
$824$		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	$-0.598153\pi$
$827$	−1058.90	−	611.359i	−1.28042	−	0.739249i	−0.976924	+	0.213585i	$0.931486\pi$
$828$		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
$831$	290.893	+	34.5271i	0.350052	+	0.0415489i
$832$		0			0
$833$	−1725.28	−	996.091i	−2.07117	−	1.19579i
$834$		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
$839$			1271.47i			1.51546i	0.652567	+	0.757731i	$0.273692\pi$
$839$			1271.47i			1.51546i	−0.652567	+	0.757731i	$0.726308\pi$
$840$		0			0
$841$	−86.7792	+	150.306i	−0.103186	+	0.178723i
$842$		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
$849$	613.931	+	72.8696i	0.723123	+	0.0858299i
$850$		0			0
$851$		−	1848.81i		−	2.17252i
$852$		0			0
$853$	−449.429			−0.526880			−0.263440	−	0.964676i	$-0.584857\pi$
$853$	−449.429			−0.526880			−0.263440	+	0.964676i	$0.584857\pi$
$854$		0			0
$855$	379.840	−	679.202i	0.444258	−	0.794389i
$856$		0			0
$857$		−	710.057i		−	0.828538i	−0.910154	−	0.414269i	$-0.864037\pi$
$857$		−	710.057i		−	0.828538i	0.910154	−	0.414269i	$-0.135963\pi$
$858$		0			0
$859$	−173.681			−0.202190			−0.101095	−	0.994877i	$-0.532235\pi$
$859$	−173.681			−0.202190			−0.101095	+	0.994877i	$0.532235\pi$
$860$		0			0
$861$	−234.959	−	175.573i	−0.272890	−	0.203918i
$862$		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
$869$	1674.36	+	966.693i	1.92677	+	1.11242i
$870$		0			0
$871$	−415.009			−0.476474
$872$		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
$877$	−686.285	+	1188.68i	−0.782537	+	1.35539i	0.147923	+	0.988999i	$0.452741\pi$
$877$	−686.285	+	1188.68i	−0.782537	+	1.35539i	−0.930460	+	0.366395i	$0.880592\pi$
$878$		0			0
$879$	−607.224	−	453.749i	−0.690812	−	0.516210i
$880$		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	−0.999995	−	0.00305054i	$-0.999029\pi$
$883$	−439.165	+	760.656i	−0.497356	+	0.861446i	0.502640	+	0.864496i	$0.332362\pi$
$884$		0			0
$885$	−612.497	+	819.666i	−0.692086	+	0.926177i
$886$		0			0
$887$			1153.04i			1.29993i	0.759963	+	0.649966i	$0.225217\pi$
$887$			1153.04i			1.29993i	−0.759963	+	0.649966i	$0.774783\pi$
$888$		0			0
$889$	411.080	+	712.012i	0.462408	+	0.800914i
$890$		0			0
$891$	598.760	−	1171.30i	0.672009	−	1.31459i
$892$		0			0
$893$	−84.2766	+	300.267i	−0.0943746	+	0.336245i
$894$		0			0
$895$	36.8332	−	63.7969i	0.0411544	−	0.0712815i
$896$		0			0
$897$	774.277	−	332.352i	0.863185	−	0.370515i
$898$		0			0
$899$	628.024	+	362.590i	0.698581	+	0.403326i
$900$		0			0
$901$	−1141.24			−1.26664
$902$		0			0
$903$	−2732.13	−	324.285i	−3.02561	−	0.359120i
$904$		0			0
$905$	−1353.34	+	781.350i	−1.49540	+	0.863370i
$906$		0			0
$907$	1081.82			1.19274			0.596370	−	0.802709i	$-0.296609\pi$
$907$	1081.82			1.19274			0.596370	+	0.802709i	$0.296609\pi$
$908$		0			0
$909$	−189.854	+	788.499i	−0.208860	+	0.867435i
$910$		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
$915$	−781.957	+	335.649i	−0.854598	+	0.366829i
$916$		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
$921$	939.816	−	1257.70i	1.02043	−	1.36558i
$922$		0			0
$923$	530.918	−	306.526i	0.575209	−	0.332097i
$924$		0			0
$925$	102.561	+	177.641i	0.110877	+	0.192044i
$926$		0			0
$927$	754.134	+	181.580i	0.813521	+	0.195879i
$928$		0			0
$929$		−	1054.20i		−	1.13476i	−0.823455	−	0.567382i	$-0.807956\pi$
$929$		−	1054.20i		−	1.13476i	0.823455	−	0.567382i	$-0.192044\pi$
$930$		0			0
$931$	1609.07	+	451.621i	1.72832	+	0.485092i
$932$		0			0
$933$	−923.751	−	690.274i	−0.990087	−	0.739844i
$934$		0			0
$935$	1449.65	+	836.954i	1.55043	+	0.895138i
$936$		0			0
$937$	−77.1282	+	133.590i	−0.0823140	+	0.142572i	−0.904244	−	0.427017i	$-0.859564\pi$
$937$	−77.1282	+	133.590i	−0.0823140	+	0.142572i	0.821929	+	0.569589i	$0.192898\pi$
$938$		0			0
$939$	−396.000	+	529.942i	−0.421725	+	0.564368i
$940$		0			0
$941$		−	351.356i		−	0.373386i	−0.982418	−	0.186693i	$-0.940223\pi$
$941$		−	351.356i		−	0.373386i	0.982418	−	0.186693i	$-0.0597769\pi$
$942$		0			0
$943$	−161.499	+	279.725i	−0.171261	+	0.296633i
$944$		0			0
$945$	1417.46	−	242.116i	1.49996	−	0.256207i
$946$		0			0
$947$			994.185i			1.04983i	0.851156	+	0.524913i	$0.175902\pi$
$947$			994.185i			1.04983i	−0.851156	+	0.524913i	$0.824098\pi$
$948$		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	$-0.473442\pi$
$953$	941.583	−	543.623i	0.988020	−	0.570433i	0.904682	+	0.426088i	$0.140109\pi$
$954$		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
$959$		−	1734.20i		−	1.80834i
$960$		0			0
$961$	86.5438	−	149.898i	0.0900560	−	0.155981i
$962$		0			0
$963$	−762.384	−	724.436i	−0.791676	−	0.752270i
$964$		0			0
$965$	−541.597	+	312.691i	−0.561241	+	0.324032i
$966$		0			0
$967$	−311.541	+	539.605i	−0.322173	+	0.558019i	−0.980936	−	0.194331i	$-0.937747\pi$
$967$	−311.541	+	539.605i	−0.322173	+	0.558019i	0.658763	+	0.752350i	$0.271080\pi$
$968$		0			0
$969$	1279.77	−	169.692i	1.32071	−	0.175121i
$970$		0			0
$971$	614.569	−	354.822i	0.632924	−	0.365419i	−0.148960	−	0.988843i	$-0.547592\pi$
$971$	614.569	−	354.822i	0.632924	−	0.365419i	0.781884	+	0.623424i	$0.214259\pi$
$972$		0			0
$973$	−780.818	+	1352.42i	−0.802485	+	1.38995i
$974$		0			0
$975$	−55.9586	+	74.8859i	−0.0573934	+	0.0768061i
$976$		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
$979$	−1154.23	−	1999.19i	−1.17899	−	2.04207i
$980$		0			0
$981$	1048.06	+	252.351i	1.06836	+	0.257239i
$982$		0			0
$983$		−	602.827i		−	0.613252i	−0.951830	−	0.306626i	$-0.900800\pi$
$983$		−	602.827i		−	0.613252i	0.951830	−	0.306626i	$-0.0992001\pi$
$984$		0			0
$985$	−436.799	+	756.558i	−0.443451	+	0.768079i
$986$		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	0.518696	−	0.854959i	$-0.326418\pi$
$991$	−476.739	−	825.736i	−0.481068	−	0.833235i	−0.999764	+	0.0217240i	$0.993085\pi$
$992$		0			0
$993$	−837.805	−	99.4420i	−0.843711	−	0.100143i
$994$		0			0
$995$	−508.793	+	293.752i	−0.511350	+	0.295228i
$996$		0			0
$997$	−199.801	−	346.066i	−0.200403	−	0.347108i	0.748256	−	0.663411i	$-0.230892\pi$
$997$	−199.801	−	346.066i	−0.200403	−	0.347108i	−0.948658	+	0.316303i	$0.897558\pi$
$998$		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.be.a.425.15	yes	80
3.2	odd	2		2052.3.be.a.197.12		80
9.4	even	3		2052.3.m.a.881.12		80
9.5	odd	6		684.3.m.a.653.11	yes	80
19.11	even	3		684.3.m.a.353.11	✓	80
57.11	odd	6		2052.3.m.a.1493.29		80
171.49	even	3		2052.3.be.a.125.12		80
171.68	odd	6	inner	684.3.be.a.581.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.11	✓	80	19.11	even	3
684.3.m.a.653.11	yes	80	9.5	odd	6
684.3.be.a.425.15	yes	80	1.1	even	1	trivial
684.3.be.a.581.15	yes	80	171.68	odd	6	inner
2052.3.m.a.881.12		80	9.4	even	3
2052.3.m.a.1493.29		80	57.11	odd	6
2052.3.be.a.125.12		80	171.49	even	3
2052.3.be.a.197.12		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)

\(f(q)\)	\(=\)	\(q+(-1.18332 - 2.75677i) q^{3} +(3.94117 + 2.27544i) q^{5} +(5.85150 - 10.1351i) q^{7} +(-6.19951 + 6.52427i) q^{9} +O(q^{10})\)	\(q+(-1.18332 - 2.75677i) q^{3} +(3.94117 + 2.27544i) q^{5} +(5.85150 - 10.1351i) q^{7} +(-6.19951 + 6.52427i) q^{9} +(14.0645 + 8.12016i) q^{11} +7.26450 q^{13} +(1.60918 - 13.5575i) q^{15} +(19.6143 - 11.3243i) q^{17} +(-13.5931 + 13.2751i) q^{19} +(-34.8643 - 4.13816i) q^{21} +38.6626i q^{23} +(-2.14477 - 3.71485i) q^{25} +(25.3219 + 9.37031i) q^{27} +(22.3737 - 12.9174i) q^{29} +(14.0349 + 24.3091i) q^{31} +(5.74255 - 48.3814i) q^{33} +(46.1236 - 26.6295i) q^{35} -47.8191 q^{37} +(-8.59622 - 20.0265i) q^{39} +(7.23503 + 4.17715i) q^{41} +78.3646 q^{43} +(-39.2789 + 11.6067i) q^{45} +(14.2151 - 8.20711i) q^{47} +(-43.9802 - 76.1759i) q^{49} +(-54.4285 - 40.6717i) q^{51} +(-43.6381 - 25.1945i) q^{53} +(36.9538 + 64.0059i) q^{55} +(52.6813 + 21.7641i) q^{57} +(-64.9066 - 37.4738i) q^{59} +(-31.1644 - 53.9783i) q^{61} +(29.8476 + 101.009i) q^{63} +(28.6306 + 16.5299i) q^{65} -57.1284 q^{67} +(106.584 - 45.7502i) q^{69} +(73.0839 - 42.1950i) q^{71} +(28.4345 + 49.2501i) q^{73} +(-7.70302 + 10.3085i) q^{75} +(164.597 - 95.0303i) q^{77} +119.049 q^{79} +(-4.13211 - 80.8945i) q^{81} +(-71.4114 - 41.2294i) q^{83} +103.071 q^{85} +(-62.0856 - 46.3935i) q^{87} +(-123.100 - 71.0719i) q^{89} +(42.5082 - 73.6264i) q^{91} +(50.4068 - 67.4564i) q^{93} +(-83.7793 + 21.3894i) q^{95} +118.506 q^{97} +(-140.171 + 41.4197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 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

Properties

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