LMFDB - Embedded newform 345.3.d.a.229.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,3,Mod(229,345)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("345.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	345.d (of order $2$, degree $1$, 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:	$9.40056912043$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.11
Character	$\chi$	$=$	345.229
Dual form			345.3.d.a.229.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58060i q^{2} -1.73205i q^{3} -2.65950 q^{4} +(-2.43175 + 4.36882i) q^{5} -4.46973 q^{6} +10.6156 q^{7} -3.45929i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.58060i q^{2} -1.73205i q^{3} -2.65950 q^{4} +(-2.43175 + 4.36882i) q^{5} -4.46973 q^{6} +10.6156 q^{7} -3.45929i q^{8} -3.00000 q^{9} +(11.2742 + 6.27538i) q^{10} -13.4737i q^{11} +4.60639i q^{12} -9.14733i q^{13} -27.3947i q^{14} +(7.56702 + 4.21191i) q^{15} -19.5651 q^{16} -13.0172 q^{17} +7.74180i q^{18} -2.02864i q^{19} +(6.46724 - 11.6189i) q^{20} -18.3868i q^{21} -34.7702 q^{22} +(18.2865 - 13.9500i) q^{23} -5.99167 q^{24} +(-13.1732 - 21.2478i) q^{25} -23.6056 q^{26} +5.19615i q^{27} -28.2322 q^{28} -51.3184 q^{29} +(10.8693 - 19.5275i) q^{30} +40.4219 q^{31} +36.6524i q^{32} -23.3371 q^{33} +33.5921i q^{34} +(-25.8145 + 46.3777i) q^{35} +7.97850 q^{36} -21.4236 q^{37} -5.23511 q^{38} -15.8436 q^{39} +(15.1130 + 8.41214i) q^{40} +63.6968 q^{41} -47.4490 q^{42} +52.8262 q^{43} +35.8332i q^{44} +(7.29525 - 13.1065i) q^{45} +(-35.9995 - 47.1902i) q^{46} -26.1636i q^{47} +33.8877i q^{48} +63.6913 q^{49} +(-54.8320 + 33.9947i) q^{50} +22.5464i q^{51} +24.3273i q^{52} -34.9955 q^{53} +13.4092 q^{54} +(58.8640 + 32.7646i) q^{55} -36.7225i q^{56} -3.51371 q^{57} +132.432i q^{58} -43.6117 q^{59} +(-20.1245 - 11.2016i) q^{60} +37.0162i q^{61} -104.313i q^{62} -31.8469 q^{63} +16.3251 q^{64} +(39.9630 + 22.2440i) q^{65} +60.2237i q^{66} -11.7715 q^{67} +34.6192 q^{68} +(-24.1622 - 31.6732i) q^{69} +(119.682 + 66.6170i) q^{70} -28.0198 q^{71} +10.3779i q^{72} -69.7792i q^{73} +55.2858i q^{74} +(-36.8022 + 22.8166i) q^{75} +5.39517i q^{76} -143.031i q^{77} +40.8861i q^{78} +88.5264i q^{79} +(47.5773 - 85.4762i) q^{80} +9.00000 q^{81} -164.376i q^{82} -17.5856 q^{83} +48.8997i q^{84} +(31.6545 - 56.8696i) q^{85} -136.323i q^{86} +88.8861i q^{87} -46.6094 q^{88} +4.49467i q^{89} +(-33.8225 - 18.8261i) q^{90} -97.1045i q^{91} +(-48.6330 + 37.1002i) q^{92} -70.0128i q^{93} -67.5179 q^{94} +(8.86276 + 4.93314i) q^{95} +63.4839 q^{96} -48.1339 q^{97} -164.362i q^{98} +40.4210i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9}+O(q^{10}) $ 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9	$ 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9} + 148 q^{16} - 12 q^{24} - 64 q^{25} + 136 q^{26} + 76 q^{29} - 68 q^{31} - 108 q^{35} + 276 q^{36} + 48 q^{39} + 20 q^{41} + 344 q^{46} + 412 q^{49} - 352 q^{50} - 36 q^{54} - 184 q^{55} - 396 q^{59} - 684 q^{64} - 144 q^{69} + 600 q^{70} + 156 q^{71} - 120 q^{75} + 432 q^{81} - 76 q^{85} + 112 q^{95} + 516 q^{96}+O(q^{100}) $ 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9 + 148 * q^16 - 12 * q^24 - 64 * q^25 + 136 * q^26 + 76 * q^29 - 68 * q^31 - 108 * q^35 + 276 * q^36 + 48 * q^39 + 20 * q^41 + 344 * q^46 + 412 * q^49 - 352 * q^50 - 36 * q^54 - 184 * q^55 - 396 * q^59 - 684 * q^64 - 144 * q^69 + 600 * q^70 + 156 * q^71 - 120 * q^75 + 432 * q^81 - 76 * q^85 + 112 * q^95 + 516 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	2.58060i		−	1.29030i	−0.764056	−	0.645150i	$-0.776795\pi$
$2$		−	2.58060i		−	1.29030i	0.764056	−	0.645150i	$-0.223205\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−2.65950			−0.664875
$5$	−2.43175	+	4.36882i	−0.486350	+	0.873764i
$5$	−2.43175	+	4.36882i	−0.486350	+	0.873764i
$6$	−4.46973			−0.744955
$7$	10.6156			1.51652			0.758258	−	0.651954i	$-0.226051\pi$
$7$	10.6156			1.51652			0.758258	+	0.651954i	$0.226051\pi$
$8$		−	3.45929i		−	0.432412i
$9$	−3.00000			−0.333333
$10$	11.2742	+	6.27538i	1.12742	+	0.627538i
$11$		−	13.4737i		−	1.22488i	−0.790517	−	0.612440i	$-0.790188\pi$
$11$		−	13.4737i		−	1.22488i	0.790517	−	0.612440i	$-0.209812\pi$
$12$			4.60639i			0.383866i
$13$		−	9.14733i		−	0.703640i	−0.936068	−	0.351820i	$-0.885563\pi$
$13$		−	9.14733i		−	0.703640i	0.936068	−	0.351820i	$-0.114437\pi$
$14$		−	27.3947i		−	1.95676i
$15$	7.56702	+	4.21191i	0.504468	+	0.280794i
$16$	−19.5651			−1.22282
$17$	−13.0172			−0.765715			−0.382858	−	0.923807i	$-0.625060\pi$
$17$	−13.0172			−0.765715			−0.382858	+	0.923807i	$0.625060\pi$
$18$			7.74180i			0.430100i
$19$		−	2.02864i		−	0.106770i	−0.998574	−	0.0533852i	$-0.982999\pi$
$19$		−	2.02864i		−	0.106770i	0.998574	−	0.0533852i	$-0.0170011\pi$
$20$	6.46724	−	11.6189i	0.323362	−	0.580944i
$21$		−	18.3868i		−	0.875561i
$22$	−34.7702			−1.58046
$23$	18.2865	−	13.9500i	0.795065	−	0.606524i
$23$	18.2865	−	13.9500i	0.795065	−	0.606524i
$24$	−5.99167			−0.249653
$25$	−13.1732	−	21.2478i	−0.526927	−	0.849910i
$26$	−23.6056			−0.907908
$27$			5.19615i			0.192450i
$28$	−28.2322			−1.00829
$29$	−51.3184			−1.76960			−0.884801	−	0.465970i	$-0.845706\pi$
$29$	−51.3184			−1.76960			−0.884801	+	0.465970i	$0.845706\pi$
$30$	10.8693	−	19.5275i	0.362309	−	0.650915i
$31$	40.4219			1.30393			0.651966	−	0.758248i	$-0.273944\pi$
$31$	40.4219			1.30393			0.651966	+	0.758248i	$0.273944\pi$
$32$			36.6524i			1.14539i
$33$	−23.3371			−0.707184
$34$			33.5921i			0.988003i
$35$	−25.8145	+	46.3777i	−0.737558	+	1.32508i
$36$	7.97850			0.221625
$37$	−21.4236			−0.579017			−0.289508	−	0.957175i	$-0.593492\pi$
$37$	−21.4236			−0.579017			−0.289508	+	0.957175i	$0.593492\pi$
$38$	−5.23511			−0.137766
$39$	−15.8436			−0.406247
$40$	15.1130	+	8.41214i	0.377826	+	0.210303i
$41$	63.6968			1.55358			0.776790	−	0.629760i	$-0.216847\pi$
$41$	63.6968			1.55358			0.776790	+	0.629760i	$0.216847\pi$
$42$	−47.4490			−1.12974
$43$	52.8262			1.22852			0.614258	−	0.789105i	$-0.289455\pi$
$43$	52.8262			1.22852			0.614258	+	0.789105i	$0.289455\pi$
$44$			35.8332i			0.814392i
$45$	7.29525	−	13.1065i	0.162117	−	0.291255i
$46$	−35.9995	−	47.1902i	−0.782598	−	1.02587i
$47$		−	26.1636i		−	0.556673i	−0.960484	−	0.278337i	$-0.910217\pi$
$47$		−	26.1636i		−	0.556673i	0.960484	−	0.278337i	$-0.0897831\pi$
$48$			33.8877i			0.705993i
$49$	63.6913			1.29982
$50$	−54.8320	+	33.9947i	−1.09664	+	0.679895i
$51$			22.5464i			0.442086i
$52$			24.3273i			0.467833i
$53$	−34.9955			−0.660292			−0.330146	−	0.943930i	$-0.607098\pi$
$53$	−34.9955			−0.660292			−0.330146	+	0.943930i	$0.607098\pi$
$54$	13.4092			0.248318
$55$	58.8640	+	32.7646i	1.07026	+	0.595720i
$56$		−	36.7225i		−	0.655759i
$57$	−3.51371			−0.0616440
$58$			132.432i			2.28332i
$59$	−43.6117			−0.739181			−0.369590	−	0.929195i	$-0.620502\pi$
$59$	−43.6117			−0.739181			−0.369590	+	0.929195i	$0.620502\pi$
$60$	−20.1245	−	11.2016i	−0.335408	−	0.186693i
$61$			37.0162i			0.606824i	0.952860	+	0.303412i	$0.0981258\pi$
$61$			37.0162i			0.606824i	−0.952860	+	0.303412i	$0.901874\pi$
$62$		−	104.313i		−	1.68247i
$63$	−31.8469			−0.505506
$64$	16.3251			0.255079
$65$	39.9630	+	22.2440i	0.614816	+	0.342216i
$66$			60.2237i			0.912480i
$67$	−11.7715			−0.175694			−0.0878471	−	0.996134i	$-0.527999\pi$
$67$	−11.7715			−0.175694			−0.0878471	+	0.996134i	$0.527999\pi$
$68$	34.6192			0.509105
$69$	−24.1622	−	31.6732i	−0.350177	−	0.459031i
$70$	119.682	+	66.6170i	1.70975	+	0.951671i
$71$	−28.0198			−0.394645			−0.197323	−	0.980339i	$-0.563225\pi$
$71$	−28.0198			−0.394645			−0.197323	+	0.980339i	$0.563225\pi$
$72$			10.3779i			0.144137i
$73$		−	69.7792i		−	0.955880i	−0.878393	−	0.477940i	$-0.841384\pi$
$73$		−	69.7792i		−	0.955880i	0.878393	−	0.477940i	$-0.158616\pi$
$74$			55.2858i			0.747106i
$75$	−36.8022	+	22.8166i	−0.490696	+	0.304222i
$76$			5.39517i			0.0709890i
$77$		−	143.031i		−	1.85755i
$78$			40.8861i			0.524181i
$79$			88.5264i			1.12059i	0.828294	+	0.560294i	$0.189312\pi$
$79$			88.5264i			1.12059i	−0.828294	+	0.560294i	$0.810688\pi$
$80$	47.5773	−	85.4762i	0.594717	−	1.06845i
$81$	9.00000			0.111111
$82$		−	164.376i		−	2.00458i
$83$	−17.5856			−0.211875			−0.105937	−	0.994373i	$-0.533784\pi$
$83$	−17.5856			−0.211875			−0.105937	+	0.994373i	$0.533784\pi$
$84$			48.8997i			0.582139i
$85$	31.6545	−	56.8696i	0.372406	−	0.669055i
$86$		−	136.323i		−	1.58515i
$87$			88.8861i			1.02168i
$88$	−46.6094			−0.529652
$89$			4.49467i			0.0505020i	0.999681	+	0.0252510i	$0.00803849\pi$
$89$			4.49467i			0.0505020i	−0.999681	+	0.0252510i	$0.991962\pi$
$90$	−33.8225	−	18.8261i	−0.375806	−	0.209179i
$91$		−	97.1045i		−	1.06708i
$92$	−48.6330	+	37.1002i	−0.528619	+	0.403263i
$93$		−	70.0128i		−	0.752826i
$94$	−67.5179			−0.718276
$95$	8.86276	+	4.93314i	0.0932922	+	0.0519278i
$96$	63.4839			0.661290
$97$	−48.1339			−0.496226			−0.248113	−	0.968731i	$-0.579810\pi$
$97$	−48.1339			−0.496226			−0.248113	+	0.968731i	$0.579810\pi$
$98$		−	164.362i		−	1.67716i
$99$			40.4210i			0.408293i
$100$	35.0341	+	56.5084i	0.350341	+	0.565084i
$101$	−33.3210			−0.329911			−0.164956	−	0.986301i	$-0.552748\pi$
$101$	−33.3210			−0.329911			−0.164956	+	0.986301i	$0.552748\pi$
$102$	58.1832			0.570424
$103$	184.252			1.78885			0.894427	−	0.447214i	$-0.147584\pi$
$103$	184.252			1.78885			0.894427	+	0.447214i	$0.147584\pi$
$104$	−31.6433			−0.304262
$105$	80.3286	+	44.7121i	0.765034	+	0.425829i
$106$			90.3093i			0.851975i
$107$	151.494			1.41583			0.707915	−	0.706298i	$-0.249636\pi$
$107$	151.494			1.41583			0.707915	+	0.706298i	$0.249636\pi$
$108$		−	13.8192i		−	0.127955i
$109$			171.048i			1.56925i	0.619973	+	0.784623i	$0.287143\pi$
$109$			171.048i			1.56925i	−0.619973	+	0.784623i	$0.712857\pi$
$110$	84.5524	−	151.905i	0.768658	−	1.38095i
$111$			37.1068i			0.334296i
$112$	−207.695			−1.85442
$113$	99.3326			0.879050			0.439525	−	0.898230i	$-0.355147\pi$
$113$	99.3326			0.879050			0.439525	+	0.898230i	$0.355147\pi$
$114$			9.06747i			0.0795392i
$115$	16.4771	+	113.813i	0.143279	+	0.989682i
$116$	136.481			1.17656
$117$			27.4420i			0.234547i
$118$			112.544i			0.953766i
$119$	−138.185			−1.16122
$120$	14.5702	−	26.1765i	0.121419	−	0.218138i
$121$	−60.5398			−0.500329
$122$	95.5241			0.782985
$123$		−	110.326i		−	0.896960i
$124$	−107.502			−0.866953
$125$	124.862	−	5.88204i	0.998892	−	0.0470563i
$126$			82.1840i			0.652254i
$127$		−	192.285i		−	1.51405i	−0.653384	−	0.757027i	$-0.726651\pi$
$127$		−	192.285i		−	1.51405i	0.653384	−	0.757027i	$-0.273349\pi$
$128$			104.481i			0.816260i
$129$		−	91.4976i		−	0.709284i
$130$	57.4029	−	103.129i	0.441561	−	0.793297i
$131$	214.023			1.63376			0.816882	−	0.576805i	$-0.195701\pi$
$131$	214.023			1.63376			0.816882	+	0.576805i	$0.195701\pi$
$132$	62.0650			0.470189
$133$		−	21.5353i		−	0.161919i
$134$			30.3776i			0.226698i
$135$	−22.7011	−	12.6357i	−0.168156	−	0.0935981i
$136$			45.0302i			0.331104i
$137$	30.3537			0.221560			0.110780	−	0.993845i	$-0.464665\pi$
$137$	30.3537			0.221560			0.110780	+	0.993845i	$0.464665\pi$
$138$	−81.7358	+	62.3530i	−0.592288	+	0.451833i
$139$	180.271			1.29692			0.648458	−	0.761250i	$-0.275414\pi$
$139$	180.271			1.29692			0.648458	+	0.761250i	$0.275414\pi$
$140$	68.6538	−	123.342i	0.490384	−	0.881012i
$141$	−45.3168			−0.321396
$142$			72.3080i			0.509211i
$143$	−123.248			−0.861875
$144$	58.6952			0.407605
$145$	124.794	−	224.201i	0.860646	−	1.54621i
$146$	−180.072			−1.23337
$147$		−	110.317i		−	0.750453i
$148$	56.9762			0.384974
$149$			198.850i			1.33456i	0.744806	+	0.667281i	$0.232542\pi$
$149$			198.850i			1.33456i	−0.744806	+	0.667281i	$0.767458\pi$
$150$	58.8806	+	94.9718i	0.392537	+	0.633145i
$151$	92.0109			0.609344			0.304672	−	0.952457i	$-0.401453\pi$
$151$	92.0109			0.609344			0.304672	+	0.952457i	$0.401453\pi$
$152$	−7.01766			−0.0461688
$153$	39.0515			0.255238
$154$	−369.107			−2.39680
$155$	−98.2960	+	176.596i	−0.634168	+	1.13933i
$156$	42.1362			0.270104
$157$	−175.725			−1.11927			−0.559633	−	0.828741i	$-0.689058\pi$
$157$	−175.725			−1.11927			−0.559633	+	0.828741i	$0.689058\pi$
$158$	228.451			1.44589
$159$			60.6139i			0.381220i
$160$	−160.128	−	89.1296i	−1.00080	−	0.557060i
$161$	194.123	−	148.088i	1.20573	−	0.919804i
$162$		−	23.2254i		−	0.143367i
$163$			142.565i			0.874634i	0.899308	+	0.437317i	$0.144071\pi$
$163$			142.565i			0.874634i	−0.899308	+	0.437317i	$0.855929\pi$
$164$	−169.402			−1.03294
$165$	56.7500	−	101.956i	0.343939	−	0.617912i
$166$			45.3814i			0.273382i
$167$			101.828i			0.609748i	0.952393	+	0.304874i	$0.0986144\pi$
$167$			101.828i			0.609748i	−0.952393	+	0.304874i	$0.901386\pi$
$168$	−63.6053			−0.378603
$169$	85.3264			0.504890
$170$	−146.758	−	81.6876i	−0.863281	−	0.480515i
$171$			6.08592i			0.0355902i
$172$	−140.491			−0.816810
$173$		−	167.636i		−	0.968996i	−0.874792	−	0.484498i	$-0.839002\pi$
$173$		−	167.636i		−	0.968996i	0.874792	−	0.484498i	$-0.160998\pi$
$174$	229.380			1.31827
$175$	−139.841	−	225.558i	−0.799094	−	1.28890i
$176$			263.613i			1.49780i
$177$			75.5376i			0.426766i
$178$	11.5990			0.0651627
$179$	284.226			1.58786			0.793928	−	0.608012i	$-0.208033\pi$
$179$	284.226			1.58786			0.793928	+	0.608012i	$0.208033\pi$
$180$	−19.4017	+	34.8566i	−0.107787	+	0.193648i
$181$			132.900i			0.734253i	0.930171	+	0.367126i	$0.119658\pi$
$181$			132.900i			0.734253i	−0.930171	+	0.367126i	$0.880342\pi$
$182$	−250.588			−1.37686
$183$	64.1140			0.350350
$184$	−48.2573	−	63.2584i	−0.262268	−	0.343795i
$185$	52.0969	−	93.5960i	0.281605	−	0.505924i
$186$	−180.675			−0.971372
$187$			175.389i			0.937909i
$188$			69.5823i			0.370118i
$189$			55.1604i			0.291854i
$190$	12.7305	−	22.8712i	0.0670025	−	0.120375i
$191$		−	238.599i		−	1.24921i	−0.780941	−	0.624605i	$-0.785260\pi$
$191$		−	238.599i		−	1.24921i	0.780941	−	0.624605i	$-0.214740\pi$
$192$		−	28.2759i		−	0.147270i
$193$		−	256.081i		−	1.32684i	−0.748245	−	0.663422i	$-0.769103\pi$
$193$		−	256.081i		−	1.32684i	0.748245	−	0.663422i	$-0.230897\pi$
$194$			124.214i			0.640281i
$195$	38.5278	−	69.2180i	0.197578	−	0.354964i
$196$	−169.387			−0.864220
$197$			370.200i			1.87919i	0.342293	+	0.939593i	$0.388796\pi$
$197$			370.200i			1.87919i	−0.342293	+	0.939593i	$0.611204\pi$
$198$	104.311			0.526821
$199$			134.362i			0.675184i	0.941293	+	0.337592i	$0.109612\pi$
$199$			134.362i			0.675184i	−0.941293	+	0.337592i	$0.890388\pi$
$200$	−73.5022	+	45.5699i	−0.367511	+	0.227849i
$201$			20.3889i			0.101437i
$202$			85.9883i			0.425685i
$203$	−544.777			−2.68363
$204$		−	59.9621i		−	0.293932i
$205$	−154.895	+	278.280i	−0.755583	+	1.35746i
$206$		−	475.481i		−	2.30816i
$207$	−54.8595	+	41.8501i	−0.265022	+	0.202175i
$208$			178.968i			0.860423i
$209$	−27.3332			−0.130781
$210$	115.384	−	207.296i	0.549448	−	0.987124i
$211$	−163.472			−0.774749			−0.387375	−	0.921922i	$-0.626618\pi$
$211$	−163.472			−0.774749			−0.387375	+	0.921922i	$0.626618\pi$
$212$	93.0705			0.439012
$213$			48.5317i			0.227849i
$214$		−	390.945i		−	1.82685i
$215$	−128.460	+	230.788i	−0.597489	+	1.07343i
$216$	17.9750			0.0832176
$217$	429.104			1.97744
$218$	441.406			2.02480
$219$	−120.861			−0.551877
$220$	−156.549	−	87.1375i	−0.711586	−	0.396079i
$221$			119.072i			0.538788i
$222$	95.7579			0.431342
$223$			164.137i			0.736041i	0.929818	+	0.368021i	$0.119964\pi$
$223$			164.137i			0.736041i	−0.929818	+	0.368021i	$0.880036\pi$
$224$			389.088i			1.73700i
$225$	39.5196	+	63.7433i	0.175642	+	0.283303i
$226$		−	256.338i		−	1.13424i
$227$	−182.685			−0.804778			−0.402389	−	0.915469i	$-0.631820\pi$
$227$	−182.685			−0.804778			−0.402389	+	0.915469i	$0.631820\pi$
$228$	9.34470			0.0409855
$229$		−	122.957i		−	0.536929i	−0.963290	−	0.268464i	$-0.913484\pi$
$229$		−	122.957i		−	0.536929i	0.963290	−	0.268464i	$-0.0865162\pi$
$230$	293.707	−	42.5207i	1.27699	−	0.184873i
$231$	−247.738			−1.07246
$232$			177.526i			0.765196i
$233$			251.816i			1.08075i	0.841423	+	0.540377i	$0.181718\pi$
$233$			251.816i			1.08075i	−0.841423	+	0.540377i	$0.818282\pi$
$234$	70.8168			0.302636
$235$	114.304	+	63.6235i	0.486401	+	0.270738i
$236$	115.985			0.491463
$237$	153.332			0.646971
$238$			356.601i			1.49832i
$239$	−62.1918			−0.260217			−0.130108	−	0.991500i	$-0.541533\pi$
$239$	−62.1918			−0.260217			−0.130108	+	0.991500i	$0.541533\pi$
$240$	−148.049	−	82.4064i	−0.616872	−	0.343360i
$241$			177.949i			0.738376i	0.929355	+	0.369188i	$0.120364\pi$
$241$			177.949i			0.738376i	−0.929355	+	0.369188i	$0.879636\pi$
$242$			156.229i			0.645575i
$243$		−	15.5885i		−	0.0641500i
$244$		−	98.4447i		−	0.403462i
$245$	−154.881	+	278.256i	−0.632169	+	1.13574i
$246$	−284.707			−1.15735
$247$	−18.5566			−0.0751280
$248$		−	139.831i		−	0.563836i
$249$			30.4592i			0.122326i
$250$	−15.1792	−	322.218i	−0.0607168	−	1.28887i
$251$		−	405.598i		−	1.61593i	−0.589232	−	0.807964i	$-0.700569\pi$
$251$		−	405.598i		−	1.61593i	0.589232	−	0.807964i	$-0.299431\pi$
$252$	84.6967			0.336098
$253$	−187.958	−	246.386i	−0.742918	−	0.973859i
$254$	−496.210			−1.95358
$255$	−98.5011	−	54.8272i	−0.386279	−	0.215009i
$256$	334.925			1.30830
$257$			17.7678i			0.0691355i	0.999402	+	0.0345677i	$0.0110054\pi$
$257$			17.7678i			0.0691355i	−0.999402	+	0.0345677i	$0.988995\pi$
$258$	−236.119			−0.915189
$259$	−227.425			−0.878089
$260$	−106.282	−	59.1580i	−0.408776	−	0.227531i
$261$	153.955			0.589867
$262$		−	552.308i		−	2.10805i
$263$	−500.613			−1.90347			−0.951736	−	0.306917i	$-0.900703\pi$
$263$	−500.613			−1.90347			−0.951736	+	0.306917i	$0.900703\pi$
$264$			80.7298i			0.305795i
$265$	85.1002	−	152.889i	0.321133	−	0.576939i
$266$	−55.5739			−0.208924
$267$	7.78500			0.0291573
$268$	31.3064			0.116815
$269$	−14.9568			−0.0556014			−0.0278007	−	0.999613i	$-0.508850\pi$
$269$	−14.9568			−0.0556014			−0.0278007	+	0.999613i	$0.508850\pi$
$270$	−32.6078	+	58.5824i	−0.120770	+	0.216972i
$271$	−325.447			−1.20091			−0.600456	−	0.799658i	$-0.705014\pi$
$271$	−325.447			−1.20091			−0.600456	+	0.799658i	$0.705014\pi$
$272$	254.682			0.936329
$273$	−168.190			−0.616080
$274$		−	78.3309i		−	0.285879i
$275$	−286.285	+	177.491i	−1.04104	+	0.645422i
$276$	64.2594	+	84.2348i	0.232824	+	0.305198i
$277$			205.553i			0.742069i	0.928619	+	0.371034i	$0.120997\pi$
$277$			205.553i			0.742069i	−0.928619	+	0.371034i	$0.879003\pi$
$278$		−	465.209i		−	1.67341i
$279$	−121.266			−0.434644
$280$	160.434	+	89.3000i	0.572979	+	0.318929i
$281$		−	26.9247i		−	0.0958174i	−0.998852	−	0.0479087i	$-0.984744\pi$
$281$		−	26.9247i		−	0.0958174i	0.998852	−	0.0479087i	$-0.0152557\pi$
$282$			116.944i			0.414697i
$283$	−337.272			−1.19178			−0.595888	−	0.803068i	$-0.703200\pi$
$283$	−337.272			−1.19178			−0.595888	+	0.803068i	$0.703200\pi$
$284$	74.5187			0.262390
$285$	8.54445	−	15.3507i	0.0299805	−	0.0538623i
$286$			318.054i			1.11208i
$287$	676.181			2.35603
$288$		−	109.957i		−	0.381796i
$289$	−119.554			−0.413680
$290$	−578.573	−	322.043i	−1.99508	−	1.11049i
$291$			83.3704i			0.286496i
$292$			185.578i			0.635541i
$293$	334.610			1.14201			0.571007	−	0.820945i	$-0.306553\pi$
$293$	334.610			1.14201			0.571007	+	0.820945i	$0.306553\pi$
$294$	−284.683			−0.968310
$295$	106.053	−	190.532i	0.359501	−	0.645870i
$296$			74.1106i			0.250374i
$297$	70.0112			0.235728
$298$	513.152			1.72199
$299$	−127.606	−	167.273i	−0.426775	−	0.559440i
$300$	97.8755	−	60.6808i	0.326252	−	0.202269i
$301$	560.783			1.86307
$302$		−	237.443i		−	0.786237i
$303$			57.7137i			0.190474i
$304$			39.6904i			0.130561i
$305$	−161.717	−	90.0142i	−0.530221	−	0.295129i
$306$		−	100.776i		−	0.329334i
$307$		−	364.819i		−	1.18833i	−0.804341	−	0.594167i	$-0.797482\pi$
$307$		−	364.819i		−	1.18833i	0.804341	−	0.594167i	$-0.202518\pi$
$308$			380.392i			1.23504i
$309$		−	319.134i		−	1.03280i
$310$	455.724	+	253.663i	1.47008	+	0.818267i
$311$	506.422			1.62837			0.814183	−	0.580608i	$-0.197185\pi$
$311$	506.422			1.62837			0.814183	+	0.580608i	$0.197185\pi$
$312$			54.8078i			0.175666i
$313$	6.68609			0.0213613			0.0106807	−	0.999943i	$-0.496600\pi$
$313$	6.68609			0.0213613			0.0106807	+	0.999943i	$0.496600\pi$
$314$			453.475i			1.44419i
$315$	77.4436	−	139.133i	0.245853	−	0.441693i
$316$		−	235.436i		−	0.745051i
$317$			263.373i			0.830830i	0.909632	+	0.415415i	$0.136364\pi$
$317$			263.373i			0.830830i	−0.909632	+	0.415415i	$0.863636\pi$
$318$	156.420			0.491888
$319$			691.448i			2.16755i
$320$	−39.6985	+	71.3213i	−0.124058	+	0.222879i
$321$		−	262.395i		−	0.817430i
$322$	−382.157	−	500.953i	−1.18682	−	1.55575i
$323$			26.4071i			0.0817558i
$324$	−23.9355			−0.0738750
$325$	−194.360	+	120.499i	−0.598031	+	0.370767i
$326$	367.904			1.12854
$327$	296.263			0.906004
$328$		−	220.346i		−	0.671786i
$329$		−	277.743i		−	0.844205i
$330$	−263.107	−	146.449i	−0.797292	−	0.443785i
$331$	96.9434			0.292880			0.146440	−	0.989220i	$-0.453218\pi$
$331$	96.9434			0.292880			0.146440	+	0.989220i	$0.453218\pi$
$332$	46.7689			0.140870
$333$	64.2709			0.193006
$334$	262.777			0.786758
$335$	28.6254	−	51.4276i	0.0854489	−	0.153515i
$336$			359.739i			1.07065i
$337$	105.897			0.314235			0.157117	−	0.987580i	$-0.449780\pi$
$337$	105.897			0.314235			0.157117	+	0.987580i	$0.449780\pi$
$338$		−	220.193i		−	0.651460i
$339$		−	172.049i		−	0.507519i
$340$	−84.1851	+	151.245i	−0.247603	+	0.444838i
$341$		−	544.632i		−	1.59716i
$342$	15.7053			0.0459220
$343$	155.958			0.454687
$344$		−	182.741i		−	0.531225i
$345$	197.131	−	28.5391i	0.571393	−	0.0827220i
$346$	−432.602			−1.25030
$347$			126.018i			0.363163i	0.983376	+	0.181582i	$0.0581216\pi$
$347$			126.018i			0.363163i	−0.983376	+	0.181582i	$0.941878\pi$
$348$		−	236.393i		−	0.679290i
$349$	101.758			0.291570			0.145785	−	0.989316i	$-0.453429\pi$
$349$	101.758			0.291570			0.145785	+	0.989316i	$0.453429\pi$
$350$	−582.075	+	360.875i	−1.66307	+	1.03107i
$351$	47.5309			0.135416
$352$	493.843			1.40296
$353$			360.000i			1.01983i	0.860225	+	0.509915i	$0.170323\pi$
$353$			360.000i			1.01983i	−0.860225	+	0.509915i	$0.829677\pi$
$354$	194.933			0.550657
$355$	68.1372	−	122.414i	0.191936	−	0.344827i
$356$		−	11.9536i		−	0.0335775i
$357$			239.344i			0.670431i
$358$		−	733.474i		−	2.04881i
$359$			12.9291i			0.0360143i	0.999838	+	0.0180072i	$0.00573217\pi$
$359$			12.9291i			0.0360143i	−0.999838	+	0.0180072i	$0.994268\pi$
$360$	−45.3391	−	25.2364i	−0.125942	−	0.0701011i
$361$	356.885			0.988600
$362$	342.961			0.947407
$363$			104.858i			0.288865i
$364$			258.250i			0.709477i
$365$	304.853	+	169.686i	0.835213	+	0.464892i
$366$		−	165.453i		−	0.452056i
$367$	57.3171			0.156177			0.0780887	−	0.996946i	$-0.475118\pi$
$367$	57.3171			0.156177			0.0780887	+	0.996946i	$0.475118\pi$
$368$	−357.776	+	272.934i	−0.972219	+	0.741667i
$369$	−191.090			−0.517860
$370$	−241.534	−	134.441i	−0.652794	−	0.363355i
$371$	−371.499			−1.00134
$372$			186.199i			0.500535i
$373$	−187.359			−0.502302			−0.251151	−	0.967948i	$-0.580809\pi$
$373$	−187.359			−0.502302			−0.251151	+	0.967948i	$0.580809\pi$
$374$	452.609			1.21018
$375$	−10.1880	−	216.267i	−0.0271680	−	0.576711i
$376$	−90.5077			−0.240712
$377$			469.426i			1.24516i
$378$	142.347			0.376579
$379$		−	698.849i		−	1.84393i	−0.387273	−	0.921965i	$-0.626583\pi$
$379$		−	698.849i		−	1.84393i	0.387273	−	0.921965i	$-0.373417\pi$
$380$	−23.5705	−	13.1197i	−0.0620277	−	0.0345255i
$381$	−333.047			−0.874139
$382$	−615.729			−1.61186
$383$	−468.292			−1.22269			−0.611347	−	0.791363i	$-0.709372\pi$
$383$	−468.292			−1.22269			−0.611347	+	0.791363i	$0.709372\pi$
$384$	180.967			0.471268
$385$	624.878	+	347.816i	1.62306	+	0.903419i
$386$	−660.843			−1.71203
$387$	−158.479			−0.409505
$388$	128.012			0.329928
$389$			389.288i			1.00074i	0.865812	+	0.500370i	$0.166803\pi$
$389$			389.288i			1.00074i	−0.865812	+	0.500370i	$0.833197\pi$
$390$	−178.624	−	99.4248i	−0.458010	−	0.254935i
$391$	−238.038	+	181.590i	−0.608794	+	0.464425i
$392$		−	220.327i		−	0.562059i
$393$		−	370.699i		−	0.943254i
$394$	955.338			2.42472
$395$	−386.756	−	215.274i	−0.979129	−	0.544998i
$396$		−	107.500i		−	0.271464i
$397$		−	505.144i		−	1.27240i	−0.771522	−	0.636202i	$-0.780504\pi$
$397$		−	505.144i		−	1.27240i	0.771522	−	0.636202i	$-0.219496\pi$
$398$	346.734			0.871190
$399$	−37.3002			−0.0934841
$400$	257.734	+	415.714i	0.644335	+	1.03928i
$401$			338.290i			0.843615i	0.906685	+	0.421808i	$0.138604\pi$
$401$			338.290i			0.843615i	−0.906685	+	0.421808i	$0.861396\pi$
$402$	52.6155			0.130884
$403$		−	369.752i		−	0.917500i
$404$	88.6173			0.219350
$405$	−21.8858	+	39.3194i	−0.0540389	+	0.0970849i
$406$			1405.85i			3.46269i
$407$			288.655i			0.709226i
$408$	77.9945			0.191163
$409$	43.8096			0.107114			0.0535569	−	0.998565i	$-0.482944\pi$
$409$	43.8096			0.107114			0.0535569	+	0.998565i	$0.482944\pi$
$410$	718.129	+	399.721i	1.75153	+	0.974930i
$411$		−	52.5742i		−	0.127918i
$412$	−490.018			−1.18936
$413$	−462.965			−1.12098
$414$	107.999	+	141.570i	0.260866	+	0.341958i
$415$	42.7638	−	76.8284i	0.103045	−	0.185129i
$416$	335.272			0.805942
$417$		−	312.239i		−	0.748775i
$418$			70.5361i			0.168747i
$419$			681.962i			1.62759i	0.581149	+	0.813797i	$0.302603\pi$
$419$			681.962i			1.62759i	−0.581149	+	0.813797i	$0.697397\pi$
$420$	−213.634	−	118.912i	−0.508652	−	0.283123i
$421$		−	10.1887i		−	0.0242012i	−0.999927	−	0.0121006i	$-0.996148\pi$
$421$		−	10.1887i		−	0.0242012i	0.999927	−	0.0121006i	$-0.00385183\pi$
$422$			421.856i			0.999659i
$423$			78.4909i			0.185558i
$424$			121.060i			0.285518i
$425$	171.477	+	276.586i	0.403476	+	0.650789i
$426$	125.241			0.293993
$427$			392.950i			0.920258i
$428$	−402.898			−0.941350
$429$			213.472i			0.497603i
$430$	595.572	+	331.504i	1.38505	+	0.770940i
$431$			370.468i			0.859555i	0.902935	+	0.429778i	$0.141408\pi$
$431$			370.468i			0.859555i	−0.902935	+	0.429778i	$0.858592\pi$
$432$		−	101.663i		−	0.235331i
$433$	−192.856			−0.445395			−0.222698	−	0.974888i	$-0.571486\pi$
$433$	−192.856			−0.445395			−0.222698	+	0.974888i	$0.571486\pi$
$434$		−	1107.35i		−	2.55149i
$435$	−388.328	−	216.149i	−0.892707	−	0.496894i
$436$		−	454.902i		−	1.04335i
$437$	−28.2996	−	37.0967i	−0.0647588	−	0.0848895i
$438$			311.894i			0.712088i
$439$	−290.524			−0.661785			−0.330892	−	0.943668i	$-0.607350\pi$
$439$	−290.524			−0.661785			−0.330892	+	0.943668i	$0.607350\pi$
$440$	113.342	−	203.628i	0.257596	−	0.462791i
$441$	−191.074			−0.433274
$442$	307.278			0.695199
$443$			664.358i			1.49968i	0.661619	+	0.749840i	$0.269870\pi$
$443$			664.358i			1.49968i	−0.661619	+	0.749840i	$0.730130\pi$
$444$		−	98.6856i		−	0.222265i
$445$	−19.6364	−	10.9299i	−0.0441268	−	0.0245616i
$446$	423.573			0.949715
$447$	344.418			0.770510
$448$	173.301			0.386832
$449$	308.857			0.687877			0.343939	−	0.938992i	$-0.388239\pi$
$449$	308.857			0.687877			0.343939	+	0.938992i	$0.388239\pi$
$450$	164.496	−	101.984i	0.365547	−	0.226632i
$451$		−	858.229i		−	1.90295i
$452$	−264.175			−0.584458
$453$		−	159.368i		−	0.351805i
$454$			471.436i			1.03841i
$455$	424.232	+	236.134i	0.932378	+	0.518976i
$456$			12.1549i			0.0266556i
$457$	−171.251			−0.374729			−0.187364	−	0.982291i	$-0.559994\pi$
$457$	−171.251			−0.374729			−0.187364	+	0.982291i	$0.559994\pi$
$458$	−317.302			−0.692800
$459$		−	67.6392i		−	0.147362i
$460$	−43.8207	−	302.687i	−0.0952625	−	0.658015i
$461$	480.333			1.04194			0.520968	−	0.853576i	$-0.325571\pi$
$461$	480.333			1.04194			0.520968	+	0.853576i	$0.325571\pi$
$462$			639.312i			1.38379i
$463$		−	404.452i		−	0.873547i	−0.899571	−	0.436774i	$-0.856121\pi$
$463$		−	404.452i		−	0.873547i	0.899571	−	0.436774i	$-0.143879\pi$
$464$	1004.05			2.16390
$465$	305.873	+	170.254i	0.657792	+	0.366137i
$466$	649.836			1.39450
$467$	−466.580			−0.999101			−0.499550	−	0.866285i	$-0.666501\pi$
$467$	−466.580			−0.999101			−0.499550	+	0.866285i	$0.666501\pi$
$468$		−	72.9820i		−	0.155944i
$469$	−124.962			−0.266443
$470$	164.187	−	294.974i	0.349333	−	0.627604i
$471$			304.364i			0.646208i
$472$			150.866i			0.319630i
$473$		−	711.763i		−	1.50478i
$474$		−	395.689i		−	0.834787i
$475$	−43.1040	+	26.7236i	−0.0907453	+	0.0562603i
$476$	367.504			0.772067
$477$	104.986			0.220097
$478$			160.492i			0.335758i
$479$		−	595.025i		−	1.24222i	−0.783722	−	0.621111i	$-0.786681\pi$
$479$		−	595.025i		−	1.24222i	0.783722	−	0.621111i	$-0.213319\pi$
$480$	−154.377	+	277.350i	−0.321619	+	0.577812i
$481$			195.969i			0.407420i
$482$	459.214			0.952727
$483$	−256.497	−	336.230i	−0.531049	−	0.696129i
$484$	161.006			0.332656
$485$	117.050	−	210.288i	0.241339	−	0.433584i
$486$	−40.2276			−0.0827728
$487$		−	341.495i		−	0.701222i	−0.936521	−	0.350611i	$-0.885974\pi$
$487$		−	341.495i		−	0.701222i	0.936521	−	0.350611i	$-0.114026\pi$
$488$	128.050			0.262398
$489$	246.930			0.504970
$490$	718.068	+	399.687i	1.46544	+	0.815688i
$491$	−431.266			−0.878342			−0.439171	−	0.898404i	$-0.644728\pi$
$491$	−431.266			−0.878342			−0.439171	+	0.898404i	$0.644728\pi$
$492$			293.412i			0.596366i
$493$	668.020			1.35501
$494$			47.8872i			0.0969377i
$495$	−176.592	−	98.2938i	−0.356752	−	0.198573i
$496$	−790.857			−1.59447
$497$	−297.448			−0.598486
$498$	78.6030			0.157837
$499$	−37.2477			−0.0746447			−0.0373223	−	0.999303i	$-0.511883\pi$
$499$	−37.2477			−0.0746447			−0.0373223	+	0.999303i	$0.511883\pi$
$500$	−332.069	+	15.6433i	−0.664139	+	0.0312866i
$501$	176.371			0.352038
$502$	−1046.69			−2.08503
$503$	617.073			1.22678			0.613392	−	0.789778i	$-0.289804\pi$
$503$	617.073			1.22678			0.613392	+	0.789778i	$0.289804\pi$
$504$			110.168i			0.218586i
$505$	81.0284	−	145.574i	0.160452	−	0.288265i
$506$	−635.825	+	485.046i	−1.25657	+	0.958588i
$507$		−	147.790i		−	0.291498i
$508$			511.382i			1.00666i
$509$	52.9763			0.104079			0.0520396	−	0.998645i	$-0.483428\pi$
$509$	52.9763			0.104079			0.0520396	+	0.998645i	$0.483428\pi$
$510$	−141.487	+	254.192i	−0.277426	+	0.498416i
$511$		−	740.749i		−	1.44961i
$512$		−	446.382i		−	0.871840i
$513$	10.5411			0.0205480
$514$	45.8516			0.0892055
$515$	−448.055	+	804.964i	−0.870009	+	1.56304i
$516$			243.338i			0.471585i
$517$	−352.520			−0.681858
$518$			586.893i			1.13300i
$519$	−290.355			−0.559450
$520$	76.9485	−	138.244i	0.147978	−	0.265853i
$521$			882.216i			1.69331i	0.532139	+	0.846657i	$0.321388\pi$
$521$			882.216i			1.69331i	−0.532139	+	0.846657i	$0.678612\pi$
$522$		−	397.297i		−	0.761106i
$523$	−73.6435			−0.140810			−0.0704049	−	0.997518i	$-0.522429\pi$
$523$	−73.6435			−0.140810			−0.0704049	+	0.997518i	$0.522429\pi$
$524$	−569.195			−1.08625
$525$	−390.678	+	242.213i	−0.744149	+	0.461357i
$526$			1291.88i			2.45605i
$527$	−526.179			−0.998442
$528$	456.591			0.864756
$529$	139.792	−	510.195i	0.264258	−	0.964452i
$530$	−394.545	−	219.610i	−0.744425	−	0.414358i
$531$	130.835			0.246394
$532$			57.2730i			0.107656i
$533$		−	582.655i		−	1.09316i
$534$		−	20.0900i		−	0.0376217i
$535$	−368.395	+	661.849i	−0.688589	+	1.23710i
$536$			40.7211i			0.0759722i
$537$		−	492.294i		−	0.916749i
$538$			38.5975i			0.0717425i
$539$		−	858.156i		−	1.59213i
$540$	60.3735	+	33.6048i	0.111803	+	0.0622311i
$541$	−748.687			−1.38389			−0.691947	−	0.721948i	$-0.743247\pi$
$541$	−748.687			−1.38389			−0.691947	+	0.721948i	$0.743247\pi$
$542$			839.849i			1.54954i
$543$	230.189			0.423921
$544$		−	477.111i		−	0.877042i
$545$	−747.277	−	415.945i	−1.37115	−	0.763203i
$546$			434.031i			0.794929i
$547$		−	852.140i		−	1.55784i	−0.627121	−	0.778922i	$-0.715767\pi$
$547$		−	852.140i		−	1.55784i	0.627121	−	0.778922i	$-0.284233\pi$
$548$	−80.7258			−0.147310
$549$		−	111.049i		−	0.202275i
$550$	458.034	+	738.788i	0.832789	+	1.34325i
$551$			104.107i			0.188941i
$552$	−109.567	+	83.5841i	−0.198490	+	0.151420i
$553$			939.762i			1.69939i
$554$	530.451			0.957492
$555$	−162.113	−	90.2345i	−0.292095	−	0.162585i
$556$	−479.432			−0.862288
$557$	−649.327			−1.16576			−0.582878	−	0.812559i	$-0.698074\pi$
$557$	−649.327			−1.16576			−0.582878	+	0.812559i	$0.698074\pi$
$558$			312.939i			0.560822i
$559$		−	483.218i		−	0.864433i
$560$	505.063	−	907.383i	0.901898	−	1.62033i
$561$	303.783			0.541502
$562$	−69.4819			−0.123633
$563$	856.934			1.52209			0.761043	−	0.648701i	$-0.224688\pi$
$563$	856.934			1.52209			0.761043	+	0.648701i	$0.224688\pi$
$564$	120.520			0.213688
$565$	−241.552	+	433.966i	−0.427526	+	0.768082i
$566$			870.365i			1.53775i
$567$	95.5406			0.168502
$568$			96.9287i			0.170649i
$569$		−	1107.99i		−	1.94727i	−0.228118	−	0.973633i	$-0.573257\pi$
$569$		−	1107.99i		−	1.94727i	0.228118	−	0.973633i	$-0.426743\pi$
$570$	−39.6142	−	22.0498i	−0.0694985	−	0.0386839i
$571$		−	1008.38i		−	1.76599i	−0.469380	−	0.882996i	$-0.655523\pi$
$571$		−	1008.38i		−	1.76599i	0.469380	−	0.882996i	$-0.344477\pi$
$572$	327.778			0.573039
$573$	−413.266			−0.721232
$574$		−	1744.95i		−	3.03999i
$575$	−537.299	−	204.781i	−0.934433	−	0.356140i
$576$	−48.9752			−0.0850264
$577$			156.252i			0.270801i	0.990791	+	0.135400i	$0.0432321\pi$
$577$			156.252i			0.270801i	−0.990791	+	0.135400i	$0.956768\pi$
$578$			308.520i			0.533771i
$579$	−443.545			−0.766054
$580$	−331.889	+	596.263i	−0.572222	+	1.02804i
$581$	−186.682			−0.321312
$582$	215.146			0.369666
$583$			471.517i			0.808778i
$584$	−241.387			−0.413333
$585$	−119.889	−	66.7320i	−0.204939	−	0.114072i
$586$		−	863.496i		−	1.47354i
$587$		−	1037.14i		−	1.76684i	−0.468580	−	0.883421i	$-0.655234\pi$
$587$		−	1037.14i		−	1.76684i	0.468580	−	0.883421i	$-0.344766\pi$
$588$			293.387i			0.498958i
$589$		−	82.0015i		−	0.139222i
$590$	−491.686	−	273.680i	−0.833366	−	0.463864i
$591$	641.205			1.08495
$592$	419.154			0.708031
$593$		−	813.942i		−	1.37258i	−0.727326	−	0.686292i	$-0.759237\pi$
$593$		−	813.942i		−	1.37258i	0.727326	−	0.686292i	$-0.240763\pi$
$594$		−	180.671i		−	0.304160i
$595$	336.032	−	603.706i	0.564759	−	1.01463i
$596$		−	528.841i		−	0.887317i
$597$	232.721			0.389818
$598$	−431.664	+	329.299i	−0.721846	+	0.550668i
$599$	261.803			0.437067			0.218533	−	0.975829i	$-0.429873\pi$
$599$	261.803			0.437067			0.218533	+	0.975829i	$0.429873\pi$
$600$	78.9294	+	127.310i	0.131549	+	0.212183i
$601$	−964.285			−1.60447			−0.802234	−	0.597010i	$-0.796355\pi$
$601$	−964.285			−1.60447			−0.802234	+	0.597010i	$0.796355\pi$
$602$		−	1447.16i		−	2.40391i
$603$	35.3145			0.0585647
$604$	−244.703			−0.405138
$605$	147.218	−	264.488i	0.243335	−	0.437170i
$606$	148.936			0.245769
$607$			185.360i			0.305371i	0.988275	+	0.152686i	$0.0487922\pi$
$607$			185.360i			0.305371i	−0.988275	+	0.152686i	$0.951208\pi$
$608$	74.3546			0.122294
$609$			943.581i			1.54939i
$610$	−232.291	+	417.328i	−0.380805	+	0.684144i
$611$	−239.327			−0.391698
$612$	−103.857			−0.169702
$613$	−453.609			−0.739982			−0.369991	−	0.929035i	$-0.620639\pi$
$613$	−453.609			−0.739982			−0.369991	+	0.929035i	$0.620639\pi$
$614$	−941.452			−1.53331
$615$	481.995	+	268.285i	0.783731	+	0.436236i
$616$	−494.787			−0.803226
$617$	754.085			1.22218			0.611090	−	0.791561i	$-0.290732\pi$
$617$	754.085			1.22218			0.611090	+	0.791561i	$0.290732\pi$
$618$	−823.557			−1.33262
$619$			732.503i			1.18337i	0.806171	+	0.591683i	$0.201536\pi$
$619$			732.503i			1.18337i	−0.806171	+	0.591683i	$0.798464\pi$
$620$	261.418	−	469.658i	0.421642	−	0.757512i
$621$	72.4866	+	95.0195i	0.116726	+	0.153010i
$622$		−	1306.87i		−	2.10108i
$623$			47.7137i			0.0765871i
$624$	309.982			0.496765
$625$	−277.934	+	559.801i	−0.444695	+	0.895682i
$626$		−	17.2541i		−	0.0275625i
$627$			47.3425i			0.0755064i
$628$	467.340			0.744172
$629$	278.875			0.443362
$630$	−359.047	−	199.851i	−0.569916	−	0.317224i
$631$		−	481.418i		−	0.762944i	−0.924380	−	0.381472i	$-0.875417\pi$
$631$		−	481.418i		−	0.762944i	0.924380	−	0.381472i	$-0.124583\pi$
$632$	306.239			0.484555
$633$			283.142i			0.447302i
$634$	679.661			1.07202
$635$	840.058	+	467.589i	1.32293	+	0.736360i
$636$		−	161.203i		−	0.253464i
$637$		−	582.605i		−	0.914608i
$638$	1784.35			2.79679
$639$	84.0594			0.131548
$640$	−456.460	−	254.072i	−0.713218	−	0.396988i
$641$			75.5576i			0.117875i	0.998262	+	0.0589373i	$0.0187712\pi$
$641$			75.5576i			0.117875i	−0.998262	+	0.0589373i	$0.981229\pi$
$642$	−677.137			−1.05473
$643$	758.077			1.17897			0.589485	−	0.807780i	$-0.299331\pi$
$643$	758.077			1.17897			0.589485	+	0.807780i	$0.299331\pi$
$644$	−516.269	+	393.841i	−0.801660	+	0.611555i
$645$	399.737	+	222.499i	0.619747	+	0.344960i
$646$	68.1462			0.105490
$647$			376.751i			0.582304i	0.956677	+	0.291152i	$0.0940386\pi$
$647$			376.751i			0.582304i	−0.956677	+	0.291152i	$0.905961\pi$
$648$		−	31.1336i		−	0.0480457i
$649$			587.609i			0.905407i
$650$	310.961	+	501.566i	0.478401	+	0.771640i
$651$		−	743.229i		−	1.14167i
$652$		−	379.153i		−	0.581522i
$653$		−	533.952i		−	0.817690i	−0.912604	−	0.408845i	$-0.865932\pi$
$653$		−	533.952i		−	0.817690i	0.912604	−	0.408845i	$-0.134068\pi$
$654$		−	764.538i		−	1.16902i
$655$	−520.451	+	935.028i	−0.794581	+	1.42752i
$656$	−1246.23			−1.89974
$657$			209.338i			0.318627i
$658$	−716.745			−1.08928
$659$			242.254i			0.367609i	0.982963	+	0.183804i	$0.0588413\pi$
$659$			242.254i			0.367609i	−0.982963	+	0.183804i	$0.941159\pi$
$660$	−150.927	+	271.151i	−0.228677	+	0.410835i
$661$		−	405.408i		−	0.613326i	−0.951818	−	0.306663i	$-0.900788\pi$
$661$		−	405.408i		−	0.613326i	0.951818	−	0.306663i	$-0.0992124\pi$
$662$		−	250.172i		−	0.377904i
$663$	206.239			0.311070
$664$			60.8338i			0.0916171i
$665$	94.0837	+	52.3684i	0.141479	+	0.0787494i
$666$		−	165.857i		−	0.249035i
$667$	−938.435	+	715.895i	−1.40695	+	1.07331i
$668$		−	270.812i		−	0.405406i
$669$	284.294			0.424954
$670$	−132.714	−	73.8707i	−0.198081	−	0.110255i
$671$	498.745			0.743286
$672$	673.921			1.00286
$673$			317.299i			0.471470i	0.971817	+	0.235735i	$0.0757497\pi$
$673$			317.299i			0.471470i	−0.971817	+	0.235735i	$0.924250\pi$
$674$		−	273.278i		−	0.405457i
$675$	110.407	−	68.4499i	0.163565	−	0.101407i
$676$	−226.926			−0.335689
$677$	179.625			0.265325			0.132663	−	0.991161i	$-0.457647\pi$
$677$	179.625			0.265325			0.132663	+	0.991161i	$0.457647\pi$
$678$	−443.990			−0.654853
$679$	−510.971			−0.752535
$680$	−196.729	−	109.502i	−0.289307	−	0.161033i
$681$			316.419i			0.464639i
$682$	−1405.48			−2.06082
$683$			857.322i			1.25523i	0.778524	+	0.627615i	$0.215969\pi$
$683$			857.322i			1.25523i	−0.778524	+	0.627615i	$0.784031\pi$
$684$		−	16.1855i		−	0.0236630i
$685$	−73.8127	+	132.610i	−0.107756	+	0.193591i
$686$		−	402.465i		−	0.586683i
$687$	−212.967			−0.309996
$688$	−1033.55			−1.50225
$689$			320.115i			0.464608i
$690$	−73.6480	−	508.716i	−0.106736	−	0.737269i
$691$	−798.856			−1.15609			−0.578043	−	0.816006i	$-0.696184\pi$
$691$	−798.856			−1.15609			−0.578043	+	0.816006i	$0.696184\pi$
$692$			445.829i			0.644261i
$693$			429.094i			0.619183i
$694$	325.201			0.468589
$695$	−438.375	+	787.573i	−0.630755	+	1.13320i
$696$	307.483			0.441786
$697$	−829.151			−1.18960
$698$		−	262.596i		−	0.376212i
$699$	436.158			0.623974
$700$	371.909	+	599.872i	0.531298	+	0.856960i
$701$		−	559.422i		−	0.798034i	−0.916943	−	0.399017i	$-0.869351\pi$
$701$		−	559.422i		−	0.798034i	0.916943	−	0.399017i	$-0.130649\pi$
$702$		−	122.658i		−	0.174727i
$703$			43.4608i			0.0618219i
$704$		−	219.959i		−	0.312441i
$705$	110.199	−	197.981i	0.156311	−	0.280824i
$706$	929.017			1.31589
$707$	−353.723			−0.500316
$708$		−	200.892i		−	0.283746i
$709$			256.572i			0.361879i	0.983494	+	0.180939i	$0.0579138\pi$
$709$			256.572i			0.361879i	−0.983494	+	0.180939i	$0.942086\pi$
$710$	−315.901	−	175.835i	−0.444930	−	0.247655i
$711$		−	265.579i		−	0.373529i
$712$	15.5484			0.0218376
$713$	739.176	−	563.888i	1.03671	−	0.790866i
$714$	617.651			0.865057
$715$	299.708	−	538.449i	0.419173	−	0.753075i
$716$	−755.900			−1.05573
$717$			107.719i			0.150236i
$718$	33.3650			0.0464693
$719$	402.827			0.560260			0.280130	−	0.959962i	$-0.409622\pi$
$719$	402.827			0.560260			0.280130	+	0.959962i	$0.409622\pi$
$720$	−142.732	+	256.429i	−0.198239	+	0.356151i
$721$	1955.95			2.71283
$722$		−	920.977i		−	1.27559i
$723$	308.216			0.426302
$724$		−	353.447i		−	0.488187i
$725$	676.027	+	1090.40i	0.932451	+	1.50400i
$726$	270.597			0.372723
$727$	268.778			0.369709			0.184854	−	0.982766i	$-0.440819\pi$
$727$	268.778			0.369709			0.184854	+	0.982766i	$0.440819\pi$
$728$	−335.913			−0.461419
$729$	−27.0000			−0.0370370
$730$	437.891	−	786.704i	0.599850	−	1.07768i
$731$	−687.647			−0.940694
$732$	−170.511			−0.232939
$733$	494.812			0.675051			0.337525	−	0.941316i	$-0.390410\pi$
$733$	494.812			0.675051			0.337525	+	0.941316i	$0.390410\pi$
$734$		−	147.913i		−	0.201516i
$735$	481.954	+	268.263i	0.655719	+	0.364983i
$736$	511.303	+	670.245i	0.694706	+	0.910659i
$737$			158.606i			0.215204i
$738$			493.128i			0.668195i
$739$	−1179.17			−1.59562			−0.797812	−	0.602906i	$-0.794010\pi$
$739$	−1179.17			−1.59562			−0.797812	+	0.602906i	$0.794010\pi$
$740$	−138.552	+	248.919i	−0.187232	+	0.336376i
$741$			32.1410i			0.0433752i
$742$			958.690i			1.29203i
$743$	1032.15			1.38917			0.694586	−	0.719410i	$-0.255588\pi$
$743$	1032.15			1.38917			0.694586	+	0.719410i	$0.255588\pi$
$744$	−242.195			−0.325531
$745$	−868.739	−	483.553i	−1.16609	−	0.649064i
$746$			483.498i			0.648120i
$747$	52.7568			0.0706249
$748$		−	466.447i		−	0.623592i
$749$	1608.20			2.14713
$750$	−558.098	+	26.2911i	−0.744130	+	0.0350548i
$751$		−	64.1267i		−	0.0853884i	−0.999088	−	0.0426942i	$-0.986406\pi$
$751$		−	64.1267i		−	0.0853884i	0.999088	−	0.0426942i	$-0.0135941\pi$
$752$			511.893i			0.680709i
$753$	−702.516			−0.932957
$754$	1211.40			1.60663
$755$	−223.748	+	401.979i	−0.296354	+	0.532423i
$756$		−	146.699i		−	0.194046i
$757$	−425.583			−0.562197			−0.281099	−	0.959679i	$-0.590699\pi$
$757$	−425.583			−0.562197			−0.281099	+	0.959679i	$0.590699\pi$
$758$	−1803.45			−2.37922
$759$	−426.754	+	325.553i	−0.562258	+	0.428924i
$760$	17.0652	−	30.6589i	0.0224542	−	0.0403406i
$761$	−95.1552			−0.125040			−0.0625199	−	0.998044i	$-0.519914\pi$
$761$	−95.1552			−0.125040			−0.0625199	+	0.998044i	$0.519914\pi$
$762$			859.462i			1.12790i
$763$			1815.78i			2.37979i
$764$			634.554i			0.830569i
$765$	−94.9634	+	170.609i	−0.124135	+	0.223018i
$766$			1208.47i			1.57764i
$767$			398.930i			0.520118i
$768$		−	580.107i		−	0.755347i
$769$			693.573i			0.901916i	0.892545	+	0.450958i	$0.148918\pi$
$769$			693.573i			0.901916i	−0.892545	+	0.450958i	$0.851082\pi$
$770$	897.576	−	1612.56i	1.16568	−	2.09424i
$771$	30.7748			0.0399154
$772$			681.048i			0.882186i
$773$	−729.623			−0.943885			−0.471942	−	0.881629i	$-0.656447\pi$
$773$	−729.623			−0.943885			−0.471942	+	0.881629i	$0.656447\pi$
$774$			408.970i			0.528385i
$775$	−532.485	−	858.875i	−0.687078	−	1.10823i
$776$			166.509i			0.214574i
$777$			393.912i			0.506965i
$778$	1004.60			1.29125
$779$		−	129.218i		−	0.165876i
$780$	−102.465	+	184.085i	−0.131365	+	0.236007i
$781$			377.530i			0.483393i
$782$	468.611	+	614.282i	0.599247	+	0.785527i
$783$		−	266.658i		−	0.340560i
$784$	−1246.12			−1.58944
$785$	427.319	−	767.710i	0.544355	−	0.977974i
$786$	−956.626			−1.21708
$787$	−647.561			−0.822823			−0.411411	−	0.911450i	$-0.634964\pi$
$787$	−647.561			−0.822823			−0.411411	+	0.911450i	$0.634964\pi$
$788$		−	984.547i		−	1.24942i
$789$			867.088i			1.09897i
$790$	−555.536	+	998.063i	−0.703211	+	1.26337i
$791$	1054.48			1.33309
$792$	139.828			0.176551
$793$	338.600			0.426986
$794$	−1303.58			−1.64178
$795$	−264.811	−	147.398i	−0.333096	−	0.185406i
$796$		−	357.335i		−	0.448913i
$797$	−743.005			−0.932252			−0.466126	−	0.884718i	$-0.654351\pi$
$797$	−743.005			−0.932252			−0.466126	+	0.884718i	$0.654351\pi$
$798$			96.2568i			0.120623i
$799$			340.576i			0.426253i
$800$	778.782	−	482.829i	0.973478	−	0.603537i
$801$		−	13.4840i		−	0.0168340i
$802$	872.991			1.08852
$803$	−940.182			−1.17084
$804$		−	54.2242i		−	0.0674430i
$805$	174.914	+	1208.20i	0.217285	+	1.50087i
$806$	−954.184			−1.18385
$807$			25.9059i			0.0321015i
$808$			115.267i			0.142657i
$809$	−424.936			−0.525260			−0.262630	−	0.964897i	$-0.584590\pi$
$809$	−424.936			−0.525260			−0.262630	+	0.964897i	$0.584590\pi$
$810$	101.468	+	56.4784i	0.125269	+	0.0697264i
$811$	1497.39			1.84634			0.923172	−	0.384386i	$-0.125587\pi$
$811$	1497.39			1.84634			0.923172	+	0.384386i	$0.125587\pi$
$812$	1448.83			1.78428
$813$			563.691i			0.693347i
$814$	744.903			0.915114
$815$	−622.842	−	346.683i	−0.764223	−	0.425378i
$816$		−	441.121i		−	0.540590i
$817$		−	107.165i		−	0.131169i
$818$		−	113.055i		−	0.138209i
$819$			291.314i			0.355694i
$820$	411.942	−	740.085i	0.502369	−	0.902543i
$821$	87.1968			0.106208			0.0531040	−	0.998589i	$-0.483089\pi$
$821$	87.1968			0.106208			0.0531040	+	0.998589i	$0.483089\pi$
$822$	−135.673			−0.165052
$823$			758.712i			0.921885i	0.887430	+	0.460943i	$0.152489\pi$
$823$			758.712i			0.921885i	−0.887430	+	0.460943i	$0.847511\pi$
$824$		−	637.382i		−	0.773521i
$825$	307.424	+	495.861i	0.372635	+	0.601043i
$826$			1194.73i			1.44640i
$827$	410.049			0.495828			0.247914	−	0.968782i	$-0.420255\pi$
$827$	410.049			0.495828			0.247914	+	0.968782i	$0.420255\pi$
$828$	145.899	−	111.301i	0.176206	−	0.134421i
$829$	855.758			1.03228			0.516139	−	0.856505i	$-0.327369\pi$
$829$	855.758			1.03228			0.516139	+	0.856505i	$0.327369\pi$
$830$	−198.263	−	110.356i	−0.238872	−	0.132959i
$831$	356.028			0.428434
$832$		−	149.331i		−	0.179484i
$833$	−829.081			−0.995295
$834$	−805.765			−0.966145
$835$	−444.868	−	247.620i	−0.532776	−	0.296551i
$836$	72.6927			0.0869530
$837$			210.038i			0.250942i
$838$	1759.87			2.10009
$839$		−	445.714i		−	0.531244i	−0.964077	−	0.265622i	$-0.914423\pi$
$839$		−	445.714i		−	0.531244i	0.964077	−	0.265622i	$-0.0855773\pi$
$840$	154.672	−	277.880i	0.184134	−	0.330810i
$841$	1792.58			2.13149
$842$	−26.2930			−0.0312268
$843$	−46.6349			−0.0553202
$844$	434.754			0.515111
$845$	−207.493	+	372.776i	−0.245553	+	0.441155i
$846$	202.554			0.239425
$847$	−642.667			−0.758757
$848$	684.688			0.807416
$849$			584.173i			0.688072i
$850$	713.757	−	442.515i	0.839714	−	0.520606i
$851$	−391.763	+	298.861i	−0.460356	+	0.351188i
$852$		−	129.070i		−	0.151491i
$853$		−	298.157i		−	0.349540i	−0.984609	−	0.174770i	$-0.944082\pi$
$853$		−	298.157i		−	0.349540i	0.984609	−	0.174770i	$-0.0559182\pi$
$854$	1014.05			1.18741
$855$	−26.5883	−	14.7994i	−0.0310974	−	0.0173093i
$856$		−	524.061i		−	0.612221i
$857$		−	646.703i		−	0.754612i	−0.926089	−	0.377306i	$-0.876850\pi$
$857$		−	646.703i		−	0.754612i	0.926089	−	0.377306i	$-0.123150\pi$
$858$	550.886			0.642058
$859$	−787.813			−0.917128			−0.458564	−	0.888661i	$-0.651636\pi$
$859$	−787.813			−0.917128			−0.458564	+	0.888661i	$0.651636\pi$
$860$	341.640	−	613.781i	0.397255	−	0.713699i
$861$		−	1171.18i		−	1.36025i
$862$	956.031			1.10908
$863$		−	496.242i		−	0.575020i	−0.957778	−	0.287510i	$-0.907173\pi$
$863$		−	496.242i		−	0.575020i	0.957778	−	0.287510i	$-0.0928275\pi$
$864$	−190.452			−0.220430
$865$	732.373	+	407.650i	0.846674	+	0.471271i
$866$			497.685i			0.574693i
$867$			207.073i			0.238838i
$868$	−1141.20			−1.31475
$869$	1192.78			1.37258
$870$	−557.794	+	1002.12i	−0.641143	+	1.15186i
$871$			107.678i			0.123626i
$872$	591.704			0.678560
$873$	144.402			0.165409
$874$	−95.7318	+	73.0300i	−0.109533	+	0.0835584i
$875$	1325.48	−	62.4415i	1.51484	−	0.0713617i
$876$	321.430			0.366930
$877$		−	240.800i		−	0.274573i	−0.990531	−	0.137286i	$-0.956162\pi$
$877$		−	240.800i		−	0.274573i	0.990531	−	0.137286i	$-0.0438380\pi$
$878$			749.725i			0.853901i
$879$		−	579.562i		−	0.659343i
$880$	−1151.68	−	641.041i	−1.30873	−	0.728456i
$881$		−	1293.36i		−	1.46806i	−0.679119	−	0.734028i	$-0.737638\pi$
$881$		−	1293.36i		−	1.46806i	0.679119	−	0.734028i	$-0.262362\pi$
$882$			493.086i			0.559054i
$883$		−	1090.85i		−	1.23539i	−0.786416	−	0.617697i	$-0.788066\pi$
$883$		−	1090.85i		−	1.23539i	0.786416	−	0.617697i	$-0.211934\pi$
$884$		−	316.673i		−	0.358227i
$885$	−330.010	−	183.689i	−0.372893	−	0.207558i
$886$	1714.44			1.93504
$887$		−	792.287i		−	0.893221i	−0.894729	−	0.446610i	$-0.852631\pi$
$887$		−	792.287i		−	0.893221i	0.894729	−	0.446610i	$-0.147369\pi$
$888$	128.363			0.144553
$889$		−	2041.22i		−	2.29609i
$890$	−28.2058	+	50.6738i	−0.0316919	+	0.0569368i
$891$		−	121.263i		−	0.136098i
$892$		−	436.523i		−	0.489376i
$893$	−53.0766			−0.0594363
$894$		−	888.805i		−	0.994189i
$895$	−691.167	+	1241.73i	−0.772254	+	1.38741i
$896$			1109.13i			1.23787i
$897$	−289.725	+	221.019i	−0.322993	+	0.246398i
$898$		−	797.036i		−	0.887568i
$899$	−2074.39			−2.30744
$900$	−105.102	−	169.525i	−0.116780	−	0.188361i
$901$	455.542			0.505596
$902$	−2214.75			−2.45537
$903$		−	971.304i		−	1.07564i
$904$		−	343.621i		−	0.380111i
$905$	−580.615	−	323.179i	−0.641564	−	0.357104i
$906$	−411.264			−0.453934
$907$	1063.38			1.17242			0.586209	−	0.810160i	$-0.300620\pi$
$907$	1063.38			1.17242			0.586209	+	0.810160i	$0.300620\pi$
$908$	485.850			0.535077
$909$	99.9631			0.109970
$910$	609.367	−	1094.77i	0.669634	−	1.20305i
$911$			1010.83i			1.10958i	0.831990	+	0.554791i	$0.187202\pi$
$911$			1010.83i			1.10958i	−0.831990	+	0.554791i	$0.812798\pi$
$912$	68.7459			0.0753792
$913$			236.943i			0.259521i
$914$			441.930i			0.483512i
$915$	−155.909	+	280.103i	−0.170393	+	0.306123i
$916$			327.004i			0.356991i
$917$	2271.99			2.47763
$918$	−174.550			−0.190141
$919$			1124.67i			1.22379i	0.790938	+	0.611896i	$0.209593\pi$
$919$			1124.67i			1.22379i	−0.790938	+	0.611896i	$0.790407\pi$
$920$	393.714	−	56.9989i	0.427950	−	0.0619554i
$921$	−631.885			−0.686085
$922$		−	1239.55i		−	1.34441i
$923$			256.306i			0.277688i
$924$	658.858			0.713050
$925$	282.217	+	455.204i	0.305100	+	0.492112i
$926$	−1043.73			−1.12714
$927$	−552.756			−0.596285
$928$		−	1880.95i		−	2.02688i
$929$	−150.276			−0.161761			−0.0808805	−	0.996724i	$-0.525773\pi$
$929$	−150.276			−0.161761			−0.0808805	+	0.996724i	$0.525773\pi$
$930$	439.357	−	789.337i	0.472427	−	0.848750i
$931$		−	129.207i		−	0.138783i
$932$		−	669.704i		−	0.718567i
$933$		−	877.148i		−	0.940138i
$934$			1204.06i			1.28914i
$935$	−766.243	−	426.502i	−0.819511	−	0.456152i
$936$	94.9298			0.101421
$937$	−569.216			−0.607488			−0.303744	−	0.952754i	$-0.598237\pi$
$937$	−569.216			−0.607488			−0.303744	+	0.952754i	$0.598237\pi$
$938$			322.477i			0.343792i
$939$		−	11.5806i		−	0.0123330i
$940$	−303.992	−	169.207i	−0.323396	−	0.180007i
$941$			210.336i			0.223524i	0.993735	+	0.111762i	$0.0356494\pi$
$941$			210.336i			0.223524i	−0.993735	+	0.111762i	$0.964351\pi$
$942$	785.442			0.833803
$943$	1164.79	−	888.573i	1.23520	−	0.942283i
$944$	853.265			0.903882
$945$	−240.986	−	134.136i	−0.255011	−	0.141943i
$946$	−1836.78			−1.94162
$947$			697.227i			0.736248i	0.929777	+	0.368124i	$0.120000\pi$
$947$			697.227i			0.736248i	−0.929777	+	0.368124i	$0.880000\pi$
$948$	−407.787			−0.430155
$949$	−638.293			−0.672596
$950$	68.9630	+	111.234i	0.0725927	+	0.117089i
$951$	456.176			0.479680
$952$			478.023i			0.502125i
$953$	−1347.25			−1.41370			−0.706849	−	0.707364i	$-0.749884\pi$
$953$	−1347.25			−1.41370			−0.706849	+	0.707364i	$0.749884\pi$
$954$		−	270.928i		−	0.283992i
$955$	1042.40	+	580.213i	1.09151	+	0.607553i
$956$	165.399			0.173012
$957$	1197.62			1.25143
$958$	−1535.52			−1.60284
$959$	322.224			0.336000
$960$	123.532	+	68.7598i	0.128679	+	0.0716248i
$961$	672.932			0.700241
$962$	505.717			0.525694
$963$	−454.481			−0.471943
$964$		−	473.255i		−	0.490928i
$965$	1118.77	+	622.725i	1.15935	+	0.645311i
$966$	−867.676	+	661.915i	−0.898215	+	0.685213i
$967$		−	140.056i		−	0.144835i	−0.997374	−	0.0724176i	$-0.976929\pi$
$967$		−	140.056i		−	0.144835i	0.997374	−	0.0724176i	$-0.0230714\pi$
$968$			209.425i			0.216348i
$969$	45.7385			0.0472017
$970$	−542.671	−	302.058i	−0.559454	−	0.311400i
$971$			1550.06i			1.59635i	0.602426	+	0.798175i	$0.294201\pi$
$971$			1550.06i			1.59635i	−0.602426	+	0.798175i	$0.705799\pi$
$972$			41.4575i			0.0426518i
$973$	1913.69			1.96680
$974$	−881.262			−0.904787
$975$	208.711	+	336.642i	0.214063	+	0.345274i
$976$		−	724.225i		−	0.742034i
$977$	1464.91			1.49940			0.749698	−	0.661780i	$-0.230199\pi$
$977$	1464.91			1.49940			0.749698	+	0.661780i	$0.230199\pi$
$978$		−	637.229i		−	0.651563i
$979$	60.5598			0.0618588
$980$	411.907	−	740.022i	0.420314	−	0.755125i
$981$		−	513.143i		−	0.523082i
$982$			1112.92i			1.13332i
$983$	931.060			0.947162			0.473581	−	0.880750i	$-0.342961\pi$
$983$	931.060			0.947162			0.473581	+	0.880750i	$0.342961\pi$
$984$	−381.650			−0.387856
$985$	−1617.34	−	900.233i	−1.64197	−	0.913942i
$986$		−	1723.89i		−	1.74837i
$987$	−481.066			−0.487402
$988$	49.3514			0.0499508
$989$	966.006	−	736.928i	0.976750	−	0.745124i
$990$	−253.657	+	455.714i	−0.256219	+	0.460317i
$991$	−900.153			−0.908328			−0.454164	−	0.890918i	$-0.650062\pi$
$991$	−900.153			−0.908328			−0.454164	+	0.890918i	$0.650062\pi$
$992$			1481.56i			1.49351i
$993$		−	167.911i		−	0.169095i
$994$			767.594i			0.772227i
$995$	−587.002	−	326.734i	−0.589951	−	0.328376i
$996$		−	81.0062i		−	0.0813315i
$997$		−	293.925i		−	0.294809i	−0.989076	−	0.147405i	$-0.952908\pi$
$997$		−	293.925i		−	0.294809i	0.989076	−	0.147405i	$-0.0470919\pi$
$998$			96.1214i			0.0963141i
$999$		−	111.320i		−	0.111432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.3.d.a.229.11	✓	48
5.4	even	2	inner	345.3.d.a.229.38	yes	48
23.22	odd	2	inner	345.3.d.a.229.12	yes	48
115.114	odd	2	inner	345.3.d.a.229.37	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.3.d.a.229.11	✓	48	1.1	even	1	trivial
345.3.d.a.229.12	yes	48	23.22	odd	2	inner
345.3.d.a.229.37	yes	48	115.114	odd	2	inner
345.3.d.a.229.38	yes	48	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	345.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.58060i q^{2} -1.73205i q^{3} -2.65950 q^{4} +(-2.43175 + 4.36882i) q^{5} -4.46973 q^{6} +10.6156 q^{7} -3.45929i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.58060i q^{2} -1.73205i q^{3} -2.65950 q^{4} +(-2.43175 + 4.36882i) q^{5} -4.46973 q^{6} +10.6156 q^{7} -3.45929i q^{8} -3.00000 q^{9} +(11.2742 + 6.27538i) q^{10} -13.4737i q^{11} +4.60639i q^{12} -9.14733i q^{13} -27.3947i q^{14} +(7.56702 + 4.21191i) q^{15} -19.5651 q^{16} -13.0172 q^{17} +7.74180i q^{18} -2.02864i q^{19} +(6.46724 - 11.6189i) q^{20} -18.3868i q^{21} -34.7702 q^{22} +(18.2865 - 13.9500i) q^{23} -5.99167 q^{24} +(-13.1732 - 21.2478i) q^{25} -23.6056 q^{26} +5.19615i q^{27} -28.2322 q^{28} -51.3184 q^{29} +(10.8693 - 19.5275i) q^{30} +40.4219 q^{31} +36.6524i q^{32} -23.3371 q^{33} +33.5921i q^{34} +(-25.8145 + 46.3777i) q^{35} +7.97850 q^{36} -21.4236 q^{37} -5.23511 q^{38} -15.8436 q^{39} +(15.1130 + 8.41214i) q^{40} +63.6968 q^{41} -47.4490 q^{42} +52.8262 q^{43} +35.8332i q^{44} +(7.29525 - 13.1065i) q^{45} +(-35.9995 - 47.1902i) q^{46} -26.1636i q^{47} +33.8877i q^{48} +63.6913 q^{49} +(-54.8320 + 33.9947i) q^{50} +22.5464i q^{51} +24.3273i q^{52} -34.9955 q^{53} +13.4092 q^{54} +(58.8640 + 32.7646i) q^{55} -36.7225i q^{56} -3.51371 q^{57} +132.432i q^{58} -43.6117 q^{59} +(-20.1245 - 11.2016i) q^{60} +37.0162i q^{61} -104.313i q^{62} -31.8469 q^{63} +16.3251 q^{64} +(39.9630 + 22.2440i) q^{65} +60.2237i q^{66} -11.7715 q^{67} +34.6192 q^{68} +(-24.1622 - 31.6732i) q^{69} +(119.682 + 66.6170i) q^{70} -28.0198 q^{71} +10.3779i q^{72} -69.7792i q^{73} +55.2858i q^{74} +(-36.8022 + 22.8166i) q^{75} +5.39517i q^{76} -143.031i q^{77} +40.8861i q^{78} +88.5264i q^{79} +(47.5773 - 85.4762i) q^{80} +9.00000 q^{81} -164.376i q^{82} -17.5856 q^{83} +48.8997i q^{84} +(31.6545 - 56.8696i) q^{85} -136.323i q^{86} +88.8861i q^{87} -46.6094 q^{88} +4.49467i q^{89} +(-33.8225 - 18.8261i) q^{90} -97.1045i q^{91} +(-48.6330 + 37.1002i) q^{92} -70.0128i q^{93} -67.5179 q^{94} +(8.86276 + 4.93314i) q^{95} +63.4839 q^{96} -48.1339 q^{97} -164.362i q^{98} +40.4210i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9}+O(q^{10}) \) 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9	\( 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9} + 148 q^{16} - 12 q^{24} - 64 q^{25} + 136 q^{26} + 76 q^{29} - 68 q^{31} - 108 q^{35} + 276 q^{36} + 48 q^{39} + 20 q^{41} + 344 q^{46} + 412 q^{49} - 352 q^{50} - 36 q^{54} - 184 q^{55} - 396 q^{59} - 684 q^{64} - 144 q^{69} + 600 q^{70} + 156 q^{71} - 120 q^{75} + 432 q^{81} - 76 q^{85} + 112 q^{95} + 516 q^{96}+O(q^{100}) \) 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9 + 148 * q^16 - 12 * q^24 - 64 * q^25 + 136 * q^26 + 76 * q^29 - 68 * q^31 - 108 * q^35 + 276 * q^36 + 48 * q^39 + 20 * q^41 + 344 * q^46 + 412 * q^49 - 352 * q^50 - 36 * q^54 - 184 * q^55 - 396 * q^59 - 684 * q^64 - 144 * q^69 + 600 * q^70 + 156 * q^71 - 120 * q^75 + 432 * q^81 - 76 * q^85 + 112 * q^95 + 516 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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