LMFDB - Embedded newform 483.3.f.a.22.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(22,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.f (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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.8
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.23657 q^{2} -1.73205 q^{3} +6.47539 q^{4} -4.61855i q^{5} +5.60591 q^{6} +2.64575i q^{7} -8.01179 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.23657 q^{2} -1.73205 q^{3} +6.47539 q^{4} -4.61855i q^{5} +5.60591 q^{6} +2.64575i q^{7} -8.01179 q^{8} +3.00000 q^{9} +14.9483i q^{10} +2.93058i q^{11} -11.2157 q^{12} -15.4536 q^{13} -8.56316i q^{14} +7.99957i q^{15} +0.0291511 q^{16} -24.9051i q^{17} -9.70971 q^{18} +15.1966i q^{19} -29.9070i q^{20} -4.58258i q^{21} -9.48503i q^{22} +(19.6279 - 11.9895i) q^{23} +13.8768 q^{24} +3.66895 q^{25} +50.0166 q^{26} -5.19615 q^{27} +17.1323i q^{28} -2.82436 q^{29} -25.8912i q^{30} -9.30833 q^{31} +31.9528 q^{32} -5.07591i q^{33} +80.6071i q^{34} +12.2195 q^{35} +19.4262 q^{36} -30.8753i q^{37} -49.1850i q^{38} +26.7664 q^{39} +37.0029i q^{40} -74.7145 q^{41} +14.8318i q^{42} -2.66427i q^{43} +18.9766i q^{44} -13.8557i q^{45} +(-63.5270 + 38.8047i) q^{46} +53.7831 q^{47} -0.0504912 q^{48} -7.00000 q^{49} -11.8748 q^{50} +43.1369i q^{51} -100.068 q^{52} +1.59067i q^{53} +16.8177 q^{54} +13.5350 q^{55} -21.1972i q^{56} -26.3214i q^{57} +9.14123 q^{58} -94.3907 q^{59} +51.8004i q^{60} +115.051i q^{61} +30.1271 q^{62} +7.93725i q^{63} -103.534 q^{64} +71.3732i q^{65} +16.4285i q^{66} +112.901i q^{67} -161.270i q^{68} +(-33.9965 + 20.7663i) q^{69} -39.5494 q^{70} -15.5639 q^{71} -24.0354 q^{72} -65.7091 q^{73} +99.9301i q^{74} -6.35481 q^{75} +98.4043i q^{76} -7.75358 q^{77} -86.6313 q^{78} -5.83968i q^{79} -0.134636i q^{80} +9.00000 q^{81} +241.819 q^{82} +54.9299i q^{83} -29.6740i q^{84} -115.025 q^{85} +8.62308i q^{86} +4.89193 q^{87} -23.4792i q^{88} +172.575i q^{89} +44.8448i q^{90} -40.8863i q^{91} +(127.098 - 77.6364i) q^{92} +16.1225 q^{93} -174.073 q^{94} +70.1866 q^{95} -55.3439 q^{96} +1.81335i q^{97} +22.6560 q^{98} +8.79173i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	−3.23657			−1.61829			−0.809143	−	0.587612i	$-0.800068\pi$
$2$	−3.23657			−1.61829			−0.809143	+	0.587612i	$0.800068\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	6.47539			1.61885
$5$		−	4.61855i		−	0.923711i	−0.886955	−	0.461855i	$-0.847184\pi$
$5$		−	4.61855i		−	0.923711i	0.886955	−	0.461855i	$-0.152816\pi$
$6$	5.60591			0.934318
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−8.01179			−1.00147
$9$	3.00000			0.333333
$10$			14.9483i			1.49483i
$11$			2.93058i			0.266416i	0.991088	+	0.133208i	$0.0425279\pi$
$11$			2.93058i			0.266416i	−0.991088	+	0.133208i	$0.957472\pi$
$12$	−11.2157			−0.934643
$13$	−15.4536			−1.18874			−0.594368	−	0.804193i	$-0.702598\pi$
$13$	−15.4536			−1.18874			−0.594368	+	0.804193i	$0.702598\pi$
$14$		−	8.56316i		−	0.611654i
$15$			7.99957i			0.533305i
$16$	0.0291511			0.00182195
$17$		−	24.9051i		−	1.46500i	−0.680764	−	0.732502i	$-0.738352\pi$
$17$		−	24.9051i		−	1.46500i	0.680764	−	0.732502i	$-0.261648\pi$
$18$	−9.70971			−0.539429
$19$			15.1966i			0.799824i	0.916554	+	0.399912i	$0.130959\pi$
$19$			15.1966i			0.799824i	−0.916554	+	0.399912i	$0.869041\pi$
$20$		−	29.9070i		−	1.49535i
$21$		−	4.58258i		−	0.218218i
$22$		−	9.48503i		−	0.431138i
$23$	19.6279	−	11.9895i	0.853385	−	0.521281i
$23$	19.6279	−	11.9895i	0.853385	−	0.521281i
$24$	13.8768			0.578201
$25$	3.66895			0.146758
$26$	50.0166			1.92372
$27$	−5.19615			−0.192450
$28$			17.1323i			0.611867i
$29$	−2.82436			−0.0973916			−0.0486958	−	0.998814i	$-0.515506\pi$
$29$	−2.82436			−0.0973916			−0.0486958	+	0.998814i	$0.515506\pi$
$30$		−	25.8912i		−	0.863039i
$31$	−9.30833			−0.300269			−0.150134	−	0.988666i	$-0.547971\pi$
$31$	−9.30833			−0.300269			−0.150134	+	0.988666i	$0.547971\pi$
$32$	31.9528			0.998525
$33$		−	5.07591i		−	0.153815i
$34$			80.6071i			2.37080i
$35$	12.2195			0.349130
$36$	19.4262			0.539616
$37$		−	30.8753i		−	0.834468i	−0.908799	−	0.417234i	$-0.863000\pi$
$37$		−	30.8753i		−	0.834468i	0.908799	−	0.417234i	$-0.137000\pi$
$38$		−	49.1850i		−	1.29434i
$39$	26.7664			0.686317
$40$			37.0029i			0.925072i
$41$	−74.7145			−1.82231			−0.911153	−	0.412068i	$-0.864807\pi$
$41$	−74.7145			−1.82231			−0.911153	+	0.412068i	$0.864807\pi$
$42$			14.8318i			0.353139i
$43$		−	2.66427i		−	0.0619597i	−0.999520	−	0.0309798i	$-0.990137\pi$
$43$		−	2.66427i		−	0.0619597i	0.999520	−	0.0309798i	$-0.00986276\pi$
$44$			18.9766i			0.431287i
$45$		−	13.8557i		−	0.307904i
$46$	−63.5270	+	38.8047i	−1.38102	+	0.843581i
$47$	53.7831			1.14432			0.572161	−	0.820141i	$-0.306105\pi$
$47$	53.7831			1.14432			0.572161	+	0.820141i	$0.306105\pi$
$48$	−0.0504912			−0.00105190
$49$	−7.00000			−0.142857
$50$	−11.8748			−0.237496
$51$			43.1369i			0.845821i
$52$	−100.068			−1.92438
$53$			1.59067i			0.0300127i	0.999887	+	0.0150063i	$0.00477684\pi$
$53$			1.59067i			0.0300127i	−0.999887	+	0.0150063i	$0.995223\pi$
$54$	16.8177			0.311439
$55$	13.5350			0.246092
$56$		−	21.1972i		−	0.378521i
$57$		−	26.3214i		−	0.461778i
$58$	9.14123			0.157607
$59$	−94.3907			−1.59984			−0.799921	−	0.600105i	$-0.795125\pi$
$59$	−94.3907			−1.59984			−0.799921	+	0.600105i	$0.795125\pi$
$60$			51.8004i			0.863340i
$61$			115.051i			1.88609i	0.332668	+	0.943044i	$0.392051\pi$
$61$			115.051i			1.88609i	−0.332668	+	0.943044i	$0.607949\pi$
$62$	30.1271			0.485920
$63$			7.93725i			0.125988i
$64$	−103.534			−1.61772
$65$			71.3732i			1.09805i
$66$			16.4285i			0.248917i
$67$			112.901i			1.68509i	0.538629	+	0.842543i	$0.318942\pi$
$67$			112.901i			1.68509i	−0.538629	+	0.842543i	$0.681058\pi$
$68$		−	161.270i		−	2.37162i
$69$	−33.9965	+	20.7663i	−0.492702	+	0.300962i
$70$	−39.5494			−0.564992
$71$	−15.5639			−0.219210			−0.109605	−	0.993975i	$-0.534959\pi$
$71$	−15.5639			−0.219210			−0.109605	+	0.993975i	$0.534959\pi$
$72$	−24.0354			−0.333825
$73$	−65.7091			−0.900125			−0.450062	−	0.892997i	$-0.648598\pi$
$73$	−65.7091			−0.900125			−0.450062	+	0.892997i	$0.648598\pi$
$74$			99.9301i			1.35041i
$75$	−6.35481			−0.0847308
$76$			98.4043i			1.29479i
$77$	−7.75358			−0.100696
$78$	−86.6313			−1.11066
$79$		−	5.83968i		−	0.0739200i	−0.999317	−	0.0369600i	$-0.988233\pi$
$79$		−	5.83968i		−	0.0739200i	0.999317	−	0.0369600i	$-0.0117674\pi$
$80$		−	0.134636i		−	0.00168295i
$81$	9.00000			0.111111
$82$	241.819			2.94901
$83$			54.9299i			0.661805i	0.943665	+	0.330903i	$0.107353\pi$
$83$			54.9299i			0.661805i	−0.943665	+	0.330903i	$0.892647\pi$
$84$		−	29.6740i		−	0.353262i
$85$	−115.025			−1.35324
$86$			8.62308i			0.100268i
$87$	4.89193			0.0562291
$88$		−	23.4792i		−	0.266809i
$89$			172.575i			1.93904i	0.245013	+	0.969520i	$0.421208\pi$
$89$			172.575i			1.93904i	−0.245013	+	0.969520i	$0.578792\pi$
$90$			44.8448i			0.498276i
$91$		−	40.8863i		−	0.449300i
$92$	127.098	−	77.6364i	1.38150	−	0.843874i
$93$	16.1225			0.173360
$94$	−174.073			−1.85184
$95$	70.1866			0.738806
$96$	−55.3439			−0.576499
$97$			1.81335i			0.0186943i	0.999956	+	0.00934717i	$0.00297534\pi$
$97$			1.81335i			0.0186943i	−0.999956	+	0.00934717i	$0.997025\pi$
$98$	22.6560			0.231184
$99$			8.79173i			0.0888054i
$100$	23.7579			0.237579
$101$	−33.3132			−0.329834			−0.164917	−	0.986307i	$-0.552736\pi$
$101$	−33.3132			−0.329834			−0.164917	+	0.986307i	$0.552736\pi$
$102$		−	139.616i		−	1.36878i
$103$			112.394i			1.09120i	0.838045	+	0.545601i	$0.183699\pi$
$103$			112.394i			1.09120i	−0.838045	+	0.545601i	$0.816301\pi$
$104$	123.811			1.19049
$105$	−21.1649			−0.201570
$106$		−	5.14832i		−	0.0485691i
$107$		−	33.4623i		−	0.312731i	−0.987699	−	0.156366i	$-0.950022\pi$
$107$		−	33.4623i		−	0.312731i	0.987699	−	0.156366i	$-0.0499778\pi$
$108$	−33.6471			−0.311548
$109$		−	37.1568i		−	0.340888i	−0.985367	−	0.170444i	$-0.945480\pi$
$109$		−	37.1568i		−	0.340888i	0.985367	−	0.170444i	$-0.0545202\pi$
$110$	−43.8071			−0.398246
$111$			53.4776i			0.481780i
$112$			0.0771266i			0.000688631i
$113$			88.0058i			0.778812i	0.921066	+	0.389406i	$0.127320\pi$
$113$			88.0058i			0.778812i	−0.921066	+	0.389406i	$0.872680\pi$
$114$			85.1910i			0.747289i
$115$	−55.3740	−	90.6524i	−0.481513	−	0.788281i
$116$	−18.2888			−0.157662
$117$	−46.3607			−0.396246
$118$	305.502			2.58900
$119$	65.8927			0.553720
$120$		−	64.0909i		−	0.534091i
$121$	112.412			0.929022
$122$		−	372.372i		−	3.05223i
$123$	129.409			1.05211
$124$	−60.2751			−0.486089
$125$		−	132.409i		−	1.05927i
$126$		−	25.6895i		−	0.203885i
$127$	−55.0491			−0.433457			−0.216729	−	0.976232i	$-0.569539\pi$
$127$	−55.0491			−0.433457			−0.216729	+	0.976232i	$0.569539\pi$
$128$	207.284			1.61941
$129$			4.61464i			0.0357724i
$130$		−	231.004i		−	1.77696i
$131$	−153.904			−1.17484			−0.587418	−	0.809284i	$-0.699856\pi$
$131$	−153.904			−1.17484			−0.587418	+	0.809284i	$0.699856\pi$
$132$		−	32.8685i		−	0.249004i
$133$	−40.2066			−0.302305
$134$		−	365.411i		−	2.72695i
$135$			23.9987i			0.177768i
$136$			199.534i			1.46716i
$137$		−	159.358i		−	1.16319i	−0.813477	−	0.581597i	$-0.802428\pi$
$137$		−	159.358i		−	1.16319i	0.813477	−	0.581597i	$-0.197572\pi$
$138$	110.032	−	67.2118i	0.797333	−	0.487042i
$139$	70.0443			0.503916			0.251958	−	0.967738i	$-0.418926\pi$
$139$	70.0443			0.503916			0.251958	+	0.967738i	$0.418926\pi$
$140$	79.1264			0.565188
$141$	−93.1551			−0.660674
$142$	50.3737			0.354744
$143$		−	45.2879i		−	0.316699i
$144$	0.0874534			0.000607315
$145$			13.0444i			0.0899617i
$146$	212.672			1.45666
$147$	12.1244			0.0824786
$148$		−	199.930i		−	1.35088i
$149$			267.897i			1.79796i	0.437985	+	0.898982i	$0.355692\pi$
$149$			267.897i			1.79796i	−0.437985	+	0.898982i	$0.644308\pi$
$150$	20.5678			0.137119
$151$	−3.63835			−0.0240950			−0.0120475	−	0.999927i	$-0.503835\pi$
$151$	−3.63835			−0.0240950			−0.0120475	+	0.999927i	$0.503835\pi$
$152$		−	121.752i		−	0.801002i
$153$		−	74.7153i		−	0.488335i
$154$	25.0950			0.162955
$155$			42.9910i			0.277361i
$156$	173.323			1.11104
$157$			278.943i			1.77671i	0.459158	+	0.888354i	$0.348151\pi$
$157$			278.943i			1.77671i	−0.459158	+	0.888354i	$0.651849\pi$
$158$			18.9005i			0.119624i
$159$		−	2.75512i		−	0.0173278i
$160$		−	147.576i		−	0.922349i
$161$	31.7211	+	51.9304i	0.197026	+	0.322549i
$162$	−29.1291			−0.179810
$163$	174.779			1.07226			0.536132	−	0.844134i	$-0.319885\pi$
$163$	174.779			1.07226			0.536132	+	0.844134i	$0.319885\pi$
$164$	−483.806			−2.95004
$165$	−23.4434			−0.142081
$166$		−	177.784i		−	1.07099i
$167$	−283.198			−1.69580			−0.847898	−	0.530159i	$-0.822132\pi$
$167$	−283.198			−1.69580			−0.847898	+	0.530159i	$0.822132\pi$
$168$			36.7146i			0.218539i
$169$	69.8130			0.413095
$170$	372.288			2.18993
$171$			45.5899i			0.266608i
$172$		−	17.2522i		−	0.100303i
$173$	31.0358			0.179398			0.0896990	−	0.995969i	$-0.471410\pi$
$173$	31.0358			0.179398			0.0896990	+	0.995969i	$0.471410\pi$
$174$	−15.8331			−0.0909947
$175$			9.70713i			0.0554693i
$176$			0.0854297i			0.000485396i
$177$	163.489			0.923669
$178$		−	558.550i		−	3.13792i
$179$	−33.6434			−0.187952			−0.0939759	−	0.995574i	$-0.529958\pi$
$179$	−33.6434			−0.187952			−0.0939759	+	0.995574i	$0.529958\pi$
$180$		−	89.7209i		−	0.498449i
$181$			45.3731i			0.250680i	0.992114	+	0.125340i	$0.0400022\pi$
$181$			45.3731i			0.250680i	−0.992114	+	0.125340i	$0.959998\pi$
$182$			132.331i			0.727096i
$183$		−	199.275i		−	1.08893i
$184$	−157.254	+	96.0570i	−0.854643	+	0.522049i
$185$	−142.599			−0.770807
$186$	−52.1816			−0.280546
$187$	72.9863			0.390301
$188$	348.267			1.85248
$189$		−	13.7477i		−	0.0727393i
$190$	−227.164			−1.19560
$191$		−	48.8754i		−	0.255892i	−0.991781	−	0.127946i	$-0.959162\pi$
$191$		−	48.8754i		−	0.255892i	0.991781	−	0.127946i	$-0.0408385\pi$
$192$	179.326			0.933992
$193$	−234.618			−1.21564			−0.607818	−	0.794076i	$-0.707955\pi$
$193$	−234.618			−1.21564			−0.607818	+	0.794076i	$0.707955\pi$
$194$		−	5.86904i		−	0.0302528i
$195$		−	123.622i		−	0.633959i
$196$	−45.3278			−0.231264
$197$	−141.358			−0.717554			−0.358777	−	0.933423i	$-0.616806\pi$
$197$	−141.358			−0.717554			−0.358777	+	0.933423i	$0.616806\pi$
$198$		−	28.4551i		−	0.143713i
$199$		−	145.768i		−	0.732504i	−0.930516	−	0.366252i	$-0.880641\pi$
$199$		−	145.768i		−	0.732504i	0.930516	−	0.366252i	$-0.119359\pi$
$200$	−29.3949			−0.146974
$201$		−	195.550i		−	0.972885i
$202$	107.821			0.533765
$203$		−	7.47254i		−	0.0368106i
$204$			279.328i			1.36926i
$205$			345.073i			1.68328i
$206$		−	363.771i		−	1.76588i
$207$	58.8836	−	35.9684i	0.284462	−	0.173760i
$208$	−0.450489			−0.00216581
$209$	−44.5350			−0.213086
$210$	68.5016			0.326198
$211$	80.5589			0.381796			0.190898	−	0.981610i	$-0.438860\pi$
$211$	80.5589			0.381796			0.190898	+	0.981610i	$0.438860\pi$
$212$			10.3002i			0.0485860i
$213$	26.9575			0.126561
$214$			108.303i			0.506089i
$215$	−12.3051			−0.0572328
$216$	41.6305			0.192734
$217$		−	24.6275i		−	0.113491i
$218$			120.261i			0.551654i
$219$	113.812			0.519687
$220$	87.6447			0.398385
$221$			384.873i			1.74150i
$222$		−	173.084i		−	0.779658i
$223$	150.489			0.674837			0.337419	−	0.941355i	$-0.390446\pi$
$223$	150.489			0.674837			0.337419	+	0.941355i	$0.390446\pi$
$224$			84.5392i			0.377407i
$225$	11.0069			0.0489193
$226$		−	284.837i		−	1.26034i
$227$			132.755i			0.584825i	0.956292	+	0.292412i	$0.0944580\pi$
$227$			132.755i			0.584825i	−0.956292	+	0.292412i	$0.905542\pi$
$228$		−	170.441i		−	0.747549i
$229$		−	12.1580i		−	0.0530918i	−0.999648	−	0.0265459i	$-0.991549\pi$
$229$		−	12.1580i		−	0.0530918i	0.999648	−	0.0265459i	$-0.00845082\pi$
$230$	179.222	+	293.403i	0.779225	+	1.27566i
$231$	13.4296			0.0581368
$232$	22.6281			0.0975351
$233$	−134.094			−0.575509			−0.287755	−	0.957704i	$-0.592909\pi$
$233$	−134.094			−0.575509			−0.287755	+	0.957704i	$0.592909\pi$
$234$	150.050			0.641238
$235$		−	248.400i		−	1.05702i
$236$	−611.217			−2.58990
$237$			10.1146i			0.0426777i
$238$	−213.266			−0.896077
$239$	−92.0888			−0.385309			−0.192654	−	0.981267i	$-0.561710\pi$
$239$	−92.0888			−0.385309			−0.192654	+	0.981267i	$0.561710\pi$
$240$			0.233197i			0.000971652i
$241$			223.750i			0.928422i	0.885725	+	0.464211i	$0.153662\pi$
$241$			223.750i			0.928422i	−0.885725	+	0.464211i	$0.846338\pi$
$242$	−363.829			−1.50342
$243$	−15.5885			−0.0641500
$244$			745.003i			3.05329i
$245$			32.3299i			0.131959i
$246$	−418.843			−1.70261
$247$		−	234.843i		−	0.950780i
$248$	74.5763			0.300711
$249$		−	95.1413i		−	0.382094i
$250$			428.552i			1.71421i
$251$			129.429i			0.515653i	0.966191	+	0.257827i	$0.0830063\pi$
$251$			129.429i			0.515653i	−0.966191	+	0.257827i	$0.916994\pi$
$252$			51.3968i			0.203956i
$253$	35.1360	+	57.5210i	0.138878	+	0.227356i
$254$	178.170			0.701458
$255$	199.230			0.781294
$256$	−256.754			−1.00295
$257$	233.113			0.907053			0.453527	−	0.891243i	$-0.350166\pi$
$257$	233.113			0.907053			0.453527	+	0.891243i	$0.350166\pi$
$258$		−	14.9356i		−	0.0578900i
$259$	81.6884			0.315399
$260$			462.170i			1.77758i
$261$	−8.47307			−0.0324639
$262$	498.120			1.90122
$263$			146.687i			0.557747i	0.960328	+	0.278873i	$0.0899610\pi$
$263$			146.687i			0.557747i	−0.960328	+	0.278873i	$0.910039\pi$
$264$			40.6671i			0.154042i
$265$	7.34660			0.0277230
$266$	130.131			0.489216
$267$		−	298.908i		−	1.11951i
$268$			731.077i			2.72790i
$269$	104.745			0.389386			0.194693	−	0.980864i	$-0.437629\pi$
$269$	104.745			0.389386			0.194693	+	0.980864i	$0.437629\pi$
$270$		−	77.6736i		−	0.287680i
$271$	263.606			0.972717			0.486358	−	0.873759i	$-0.338325\pi$
$271$	263.606			0.972717			0.486358	+	0.873759i	$0.338325\pi$
$272$		−	0.726011i		−	0.00266916i
$273$			70.8172i			0.259404i
$274$			515.772i			1.88238i
$275$			10.7521i			0.0390987i
$276$	−220.140	+	134.470i	−0.797610	+	0.487211i
$277$	−380.816			−1.37479			−0.687394	−	0.726284i	$-0.741246\pi$
$277$	−380.816			−1.37479			−0.687394	+	0.726284i	$0.741246\pi$
$278$	−226.703			−0.815480
$279$	−27.9250			−0.100090
$280$	−97.9004			−0.349644
$281$		−	47.2087i		−	0.168003i	−0.996466	−	0.0840013i	$-0.973230\pi$
$281$		−	47.2087i		−	0.168003i	0.996466	−	0.0840013i	$-0.0267700\pi$
$282$	301.503			1.06916
$283$		−	59.5032i		−	0.210259i	−0.994459	−	0.105129i	$-0.966474\pi$
$283$		−	59.5032i		−	0.210259i	0.994459	−	0.105129i	$-0.0335257\pi$
$284$	−100.782			−0.354868
$285$	−121.567			−0.426550
$286$			146.578i			0.512509i
$287$		−	197.676i		−	0.688767i
$288$	95.8584			0.332842
$289$	−331.263			−1.14624
$290$		−	42.2193i		−	0.145584i
$291$		−	3.14082i		−	0.0107932i
$292$	−425.492			−1.45717
$293$		−	205.325i		−	0.700768i	−0.936606	−	0.350384i	$-0.886051\pi$
$293$		−	205.325i		−	0.700768i	0.936606	−	0.350384i	$-0.113949\pi$
$294$	−39.2413			−0.133474
$295$			435.949i			1.47779i
$296$			247.366i			0.835697i
$297$		−	15.2277i		−	0.0512718i
$298$		−	867.067i		−	2.90962i
$299$	−303.321	+	185.280i	−1.01445	+	0.619665i
$300$	−41.1499			−0.137166
$301$	7.04898			0.0234185
$302$	11.7758			0.0389926
$303$	57.7001			0.190430
$304$			0.442999i			0.00145724i
$305$	531.371			1.74220
$306$			241.821i			0.790265i
$307$	−188.680			−0.614591			−0.307296	−	0.951614i	$-0.599424\pi$
$307$	−188.680			−0.614591			−0.307296	+	0.951614i	$0.599424\pi$
$308$	−50.2075			−0.163011
$309$		−	194.672i		−	0.630006i
$310$		−	139.143i		−	0.448850i
$311$	−451.261			−1.45100			−0.725500	−	0.688222i	$-0.758391\pi$
$311$	−451.261			−1.45100			−0.725500	+	0.688222i	$0.758391\pi$
$312$	−214.447			−0.687329
$313$		−	620.664i		−	1.98295i	−0.130287	−	0.991476i	$-0.541590\pi$
$313$		−	620.664i		−	1.98295i	0.130287	−	0.991476i	$-0.458410\pi$
$314$		−	902.820i		−	2.87522i
$315$	36.6586			0.116377
$316$		−	37.8142i		−	0.119665i
$317$	−240.848			−0.759771			−0.379886	−	0.925033i	$-0.624037\pi$
$317$	−240.848			−0.759771			−0.379886	+	0.925033i	$0.624037\pi$
$318$			8.91715i			0.0280414i
$319$		−	8.27700i		−	0.0259467i
$320$			478.178i			1.49431i
$321$			57.9583i			0.180556i
$322$	−102.668	−	168.077i	−0.318844	−	0.521977i
$323$	378.474			1.17175
$324$	58.2785			0.179872
$325$	−56.6984			−0.174457
$326$	−565.685			−1.73523
$327$			64.3575i			0.196812i
$328$	598.597			1.82499
$329$			142.297i			0.432513i
$330$	75.8761			0.229928
$331$	−399.744			−1.20769			−0.603843	−	0.797103i	$-0.706365\pi$
$331$	−399.744			−1.20769			−0.603843	+	0.797103i	$0.706365\pi$
$332$			355.692i			1.07136i
$333$		−	92.6259i		−	0.278156i
$334$	916.591			2.74428
$335$	521.438			1.55653
$336$		−	0.133587i		−	0.000397581i
$337$		−	380.934i		−	1.13037i	−0.824965	−	0.565184i	$-0.808805\pi$
$337$		−	380.934i		−	1.13037i	0.824965	−	0.565184i	$-0.191195\pi$
$338$	−225.955			−0.668505
$339$		−	152.430i		−	0.449647i
$340$	−744.835			−2.19069
$341$		−	27.2788i		−	0.0799964i
$342$		−	147.555i		−	0.431448i
$343$		−	18.5203i		−	0.0539949i
$344$			21.3455i			0.0620510i
$345$	95.9105	+	157.014i	0.278001	+	0.455114i
$346$	−100.450			−0.290317
$347$	475.546			1.37045			0.685225	−	0.728331i	$-0.259704\pi$
$347$	475.546			1.37045			0.685225	+	0.728331i	$0.259704\pi$
$348$	31.6772			0.0910263
$349$	−167.751			−0.480663			−0.240331	−	0.970691i	$-0.577256\pi$
$349$	−167.751			−0.480663			−0.240331	+	0.970691i	$0.577256\pi$
$350$		−	31.4178i		−	0.0897652i
$351$	80.2991			0.228772
$352$			93.6402i			0.266023i
$353$	−398.591			−1.12915			−0.564576	−	0.825381i	$-0.690960\pi$
$353$	−398.591			−1.12915			−0.564576	+	0.825381i	$0.690960\pi$
$354$	−529.145			−1.49476
$355$			71.8828i			0.202487i
$356$			1117.49i			3.13901i
$357$	−114.129			−0.319690
$358$	108.889			0.304160
$359$		−	371.041i		−	1.03354i	−0.856124	−	0.516770i	$-0.827134\pi$
$359$		−	371.041i		−	1.03354i	0.856124	−	0.516770i	$-0.172866\pi$
$360$			111.009i			0.308357i
$361$	130.062			0.360282
$362$		−	146.853i		−	0.405672i
$363$	−194.703			−0.536371
$364$		−	264.755i		−	0.727349i
$365$			303.481i			0.831455i
$366$			644.967i			1.76221i
$367$			513.182i			1.39832i	0.714967	+	0.699158i	$0.246442\pi$
$367$			513.182i			1.39832i	−0.714967	+	0.699158i	$0.753558\pi$
$368$	0.572174	−	0.349506i	0.00155482	−	0.000949745i
$369$	−224.144			−0.607435
$370$	461.533			1.24739
$371$	−4.20852			−0.0113437
$372$	104.399			0.280644
$373$		−	463.384i		−	1.24232i	−0.783685	−	0.621158i	$-0.786662\pi$
$373$		−	463.384i		−	1.24232i	0.783685	−	0.621158i	$-0.213338\pi$
$374$	−236.225			−0.631619
$375$			229.339i			0.611572i
$376$	−430.899			−1.14601
$377$	43.6464			0.115773
$378$			44.4955i			0.117713i
$379$		−	404.771i		−	1.06800i	−0.845485	−	0.533998i	$-0.820689\pi$
$379$		−	404.771i		−	1.06800i	0.845485	−	0.533998i	$-0.179311\pi$
$380$	454.486			1.19601
$381$	95.3478			0.250257
$382$			158.189i			0.414107i
$383$		−	550.465i		−	1.43725i	−0.695400	−	0.718623i	$-0.744773\pi$
$383$		−	550.465i		−	1.43725i	0.695400	−	0.718623i	$-0.255227\pi$
$384$	−359.027			−0.934966
$385$			35.8103i			0.0930139i
$386$	759.357			1.96725
$387$		−	7.99280i		−	0.0206532i
$388$			11.7422i			0.0302633i
$389$			642.282i			1.65111i	0.564322	+	0.825555i	$0.309138\pi$
$389$			642.282i			1.65111i	−0.564322	+	0.825555i	$0.690862\pi$
$390$			400.111i			1.02593i
$391$	−298.598	−	488.834i	−0.763679	−	1.25021i
$392$	56.0825			0.143068
$393$	266.569			0.678292
$394$	457.516			1.16121
$395$	−26.9709			−0.0682807
$396$			56.9299i			0.143762i
$397$	29.4833			0.0742652			0.0371326	−	0.999310i	$-0.488178\pi$
$397$	29.4833			0.0742652			0.0371326	+	0.999310i	$0.488178\pi$
$398$			471.789i			1.18540i
$399$	69.6398			0.174536
$400$	0.106954			0.000267385
$401$			463.906i			1.15687i	0.815727	+	0.578437i	$0.196337\pi$
$401$			463.906i			1.15687i	−0.815727	+	0.578437i	$0.803663\pi$
$402$			632.911i			1.57441i
$403$	143.847			0.356940
$404$	−215.716			−0.533951
$405$		−	41.5670i		−	0.102635i
$406$			24.1854i			0.0595700i
$407$	90.4825			0.222316
$408$		−	345.604i		−	0.847067i
$409$	372.076			0.909721			0.454860	−	0.890563i	$-0.349689\pi$
$409$	372.076			0.909721			0.454860	+	0.890563i	$0.349689\pi$
$410$		−	1116.85i		−	2.72403i
$411$			276.016i			0.671571i
$412$			727.795i			1.76649i
$413$		−	249.734i		−	0.604684i
$414$	−190.581	+	116.414i	−0.460340	+	0.281194i
$415$	253.697			0.611317
$416$	−493.785			−1.18698
$417$	−121.320			−0.290936
$418$	144.141			0.344834
$419$			398.036i			0.949966i	0.879995	+	0.474983i	$0.157546\pi$
$419$			398.036i			0.949966i	−0.879995	+	0.474983i	$0.842454\pi$
$420$	−137.051			−0.326312
$421$			419.454i			0.996328i	0.867083	+	0.498164i	$0.165992\pi$
$421$			419.454i			0.996328i	−0.867083	+	0.498164i	$0.834008\pi$
$422$	−260.735			−0.617854
$423$	161.349			0.381441
$424$		−	12.7441i		−	0.0300569i
$425$		−	91.3755i		−	0.215001i
$426$	−87.2498			−0.204812
$427$	−304.397			−0.712874
$428$		−	216.681i		−	0.506265i
$429$			78.4410i			0.182846i
$430$	39.8262			0.0926190
$431$		−	269.366i		−	0.624979i	−0.949921	−	0.312490i	$-0.898837\pi$
$431$		−	269.366i		−	0.624979i	0.949921	−	0.312490i	$-0.101163\pi$
$432$	−0.151474			−0.000350634
$433$		−	358.912i		−	0.828896i	−0.910073	−	0.414448i	$-0.863975\pi$
$433$		−	358.912i		−	0.828896i	0.910073	−	0.414448i	$-0.136025\pi$
$434$			79.7087i			0.183661i
$435$		−	22.5936i		−	0.0519394i
$436$		−	240.605i		−	0.551846i
$437$	182.200	+	298.278i	0.416933	+	0.682558i
$438$	−368.359			−0.841003
$439$	−222.724			−0.507345			−0.253672	−	0.967290i	$-0.581638\pi$
$439$	−222.724			−0.507345			−0.253672	+	0.967290i	$0.581638\pi$
$440$	−108.440			−0.246454
$441$	−21.0000			−0.0476190
$442$		−	1245.67i		−	2.81825i
$443$	123.225			0.278160			0.139080	−	0.990281i	$-0.455586\pi$
$443$	123.225			0.278160			0.139080	+	0.990281i	$0.455586\pi$
$444$			346.288i			0.779929i
$445$	797.045			1.79111
$446$	−487.068			−1.09208
$447$		−	464.011i		−	1.03806i
$448$		−	273.926i		−	0.611441i
$449$	−462.304			−1.02963			−0.514815	−	0.857301i	$-0.672139\pi$
$449$	−462.304			−1.02963			−0.514815	+	0.857301i	$0.672139\pi$
$450$	−35.6245			−0.0791655
$451$		−	218.957i		−	0.485492i
$452$			569.872i			1.26078i
$453$	6.30180			0.0139113
$454$		−	429.672i		−	0.946413i
$455$	−188.836			−0.415024
$456$			210.881i			0.462459i
$457$			710.676i			1.55509i	0.628828	+	0.777545i	$0.283535\pi$
$457$			710.676i			1.55509i	−0.628828	+	0.777545i	$0.716465\pi$
$458$			39.3503i			0.0859178i
$459$			129.411i			0.281940i
$460$	−358.568	−	587.010i	−0.779496	−	1.27611i
$461$	326.628			0.708521			0.354261	−	0.935147i	$-0.384733\pi$
$461$	326.628			0.708521			0.354261	+	0.935147i	$0.384733\pi$
$462$	−43.4658			−0.0940819
$463$	16.6115			0.0358779			0.0179390	−	0.999839i	$-0.494290\pi$
$463$	16.6115			0.0358779			0.0179390	+	0.999839i	$0.494290\pi$
$464$	−0.0823332			−0.000177442
$465$		−	74.4626i		−	0.160135i
$466$	434.004			0.931338
$467$		−	523.319i		−	1.12060i	−0.828291	−	0.560299i	$-0.810686\pi$
$467$		−	523.319i		−	1.12060i	0.828291	−	0.560299i	$-0.189314\pi$
$468$	−300.204			−0.641461
$469$	−298.707			−0.636902
$470$			803.965i			1.71056i
$471$		−	483.144i		−	1.02578i
$472$	756.238			1.60220
$473$	7.80784			0.0165071
$474$		−	32.7367i		−	0.0690647i
$475$			55.7557i			0.117381i
$476$	426.681			0.896388
$477$			4.77201i			0.0100042i
$478$	298.052			0.623540
$479$		−	861.906i		−	1.79939i	−0.436523	−	0.899693i	$-0.643790\pi$
$479$		−	861.906i		−	1.79939i	0.436523	−	0.899693i	$-0.356210\pi$
$480$			255.609i			0.532518i
$481$			477.134i			0.991962i
$482$		−	724.182i		−	1.50245i
$483$	−54.9426	−	89.9462i	−0.113753	−	0.186224i
$484$	727.910			1.50395
$485$	8.37506			0.0172682
$486$	50.4532			0.103813
$487$	−25.7518			−0.0528785			−0.0264393	−	0.999650i	$-0.508417\pi$
$487$	−25.7518			−0.0528785			−0.0264393	+	0.999650i	$0.508417\pi$
$488$		−	921.767i		−	1.88887i
$489$	−302.726			−0.619072
$490$		−	104.638i		−	0.213547i
$491$	694.469			1.41440			0.707199	−	0.707015i	$-0.249959\pi$
$491$	694.469			1.41440			0.707199	+	0.707015i	$0.249959\pi$
$492$	837.977			1.70320
$493$			70.3408i			0.142679i
$494$			760.085i			1.53863i
$495$	40.6051			0.0820305
$496$	−0.271348			−0.000547073
$497$		−	41.1782i		−	0.0828536i
$498$			307.932i			0.618337i
$499$	807.321			1.61788			0.808939	−	0.587893i	$-0.200042\pi$
$499$	807.321			1.61788			0.808939	+	0.587893i	$0.200042\pi$
$500$		−	857.401i		−	1.71480i
$501$	490.513			0.979069
$502$		−	418.906i		−	0.834474i
$503$		−	375.920i		−	0.747355i	−0.927559	−	0.373678i	$-0.878097\pi$
$503$		−	375.920i		−	0.747355i	0.927559	−	0.373678i	$-0.121903\pi$
$504$		−	63.5916i		−	0.126174i
$505$			153.859i			0.304671i
$506$	−113.720	−	186.171i	−0.224744	−	0.367926i
$507$	−120.920			−0.238500
$508$	−356.464			−0.701702
$509$	402.707			0.791173			0.395587	−	0.918429i	$-0.370541\pi$
$509$	402.707			0.791173			0.395587	+	0.918429i	$0.370541\pi$
$510$	−644.822			−1.26436
$511$		−	173.850i		−	0.340215i
$512$	1.86567			0.00364389
$513$		−	78.9641i		−	0.153926i
$514$	−754.486			−1.46787
$515$	519.097			1.00796
$516$			29.8816i			0.0579101i
$517$			157.616i			0.304866i
$518$	−264.390			−0.510406
$519$	−53.7557			−0.103575
$520$		−	571.827i		−	1.09967i
$521$		−	690.363i		−	1.32507i	−0.749030	−	0.662537i	$-0.769480\pi$
$521$		−	690.363i		−	1.32507i	0.749030	−	0.662537i	$-0.230520\pi$
$522$	27.4237			0.0525358
$523$		−	274.655i		−	0.525152i	−0.964911	−	0.262576i	$-0.915428\pi$
$523$		−	274.655i		−	0.525152i	0.964911	−	0.262576i	$-0.0845721\pi$
$524$	−996.586			−1.90188
$525$		−	16.8132i		−	0.0320252i
$526$		−	474.764i		−	0.902594i
$527$			231.825i			0.439895i
$528$		−	0.147969i		−	0.000280243i
$529$	241.506	−	470.655i	0.456533	−	0.889706i
$530$	−23.7778			−0.0448638
$531$	−283.172			−0.533281
$532$	−260.353			−0.489386
$533$	1154.61			2.16624
$534$			967.437i			1.81168i
$535$	−154.547			−0.288873
$536$		−	904.537i		−	1.68757i
$537$	58.2720			0.108514
$538$	−339.014			−0.630138
$539$		−	20.5140i		−	0.0380595i
$540$			155.401i			0.287780i
$541$	582.111			1.07599			0.537995	−	0.842948i	$-0.319182\pi$
$541$	582.111			1.07599			0.537995	+	0.842948i	$0.319182\pi$
$542$	−853.181			−1.57413
$543$		−	78.5885i		−	0.144730i
$544$		−	795.787i		−	1.46284i
$545$	−171.611			−0.314882
$546$		−	229.205i		−	0.419789i
$547$	−523.370			−0.956800			−0.478400	−	0.878142i	$-0.658783\pi$
$547$	−523.370			−0.956800			−0.478400	+	0.878142i	$0.658783\pi$
$548$		−	1031.90i		−	1.88304i
$549$			345.154i			0.628696i
$550$		−	34.8001i		−	0.0632729i
$551$		−	42.9208i		−	0.0778961i
$552$	272.372	−	166.376i	0.493428	−	0.301405i
$553$	15.4503			0.0279391
$554$	1232.54			2.22480
$555$	246.989			0.445026
$556$	453.565			0.815764
$557$			424.538i			0.762187i	0.924537	+	0.381093i	$0.124452\pi$
$557$			424.538i			0.762187i	−0.924537	+	0.381093i	$0.875548\pi$
$558$	90.3812			0.161973
$559$			41.1724i			0.0736537i
$560$	0.356214			0.000636096
$561$	−126.416			−0.225340
$562$			152.794i			0.271876i
$563$		−	746.148i		−	1.32531i	−0.748926	−	0.662654i	$-0.769430\pi$
$563$		−	746.148i		−	1.32531i	0.748926	−	0.662654i	$-0.230570\pi$
$564$	−603.216			−1.06953
$565$	406.460			0.719397
$566$			192.586i			0.340259i
$567$			23.8118i			0.0419961i
$568$	124.695			0.219533
$569$			292.834i			0.514647i	0.966325	+	0.257324i	$0.0828407\pi$
$569$			292.834i			0.514647i	−0.966325	+	0.257324i	$0.917159\pi$
$570$	393.459			0.690279
$571$			959.451i			1.68030i	0.542355	+	0.840150i	$0.317533\pi$
$571$			959.451i			1.68030i	−0.542355	+	0.840150i	$0.682467\pi$
$572$		−	293.257i		−	0.512687i
$573$			84.6548i			0.147740i
$574$			639.793i			1.11462i
$575$	72.0136	−	43.9887i	0.125241	−	0.0765021i
$576$	−310.602			−0.539240
$577$	93.9124			0.162760			0.0813799	−	0.996683i	$-0.474067\pi$
$577$	93.9124			0.162760			0.0813799	+	0.996683i	$0.474067\pi$
$578$	1072.16			1.85494
$579$	406.370			0.701848
$580$			84.4679i			0.145634i
$581$	−145.331			−0.250139
$582$			10.1655i			0.0174665i
$583$	−4.66159			−0.00799586
$584$	526.448			0.901451
$585$			214.120i			0.366016i
$586$			664.549i			1.13404i
$587$	−530.842			−0.904330			−0.452165	−	0.891934i	$-0.649348\pi$
$587$	−530.842			−0.904330			−0.452165	+	0.891934i	$0.649348\pi$
$588$	78.5100			0.133520
$589$		−	141.455i		−	0.240162i
$590$		−	1410.98i		−	2.39149i
$591$	244.840			0.414280
$592$		−	0.900050i		−	0.00152035i
$593$	−836.235			−1.41018			−0.705089	−	0.709119i	$-0.749093\pi$
$593$	−836.235			−1.41018			−0.705089	+	0.709119i	$0.749093\pi$
$594$			49.2856i			0.0829725i
$595$		−	304.329i		−	0.511477i
$596$			1734.74i			2.91063i
$597$			252.478i			0.422911i
$598$	981.719	−	599.672i	1.64167	−	1.00280i
$599$	133.373			0.222659			0.111329	−	0.993784i	$-0.464489\pi$
$599$	133.373			0.222659			0.111329	+	0.993784i	$0.464489\pi$
$600$	50.9134			0.0848556
$601$	−873.614			−1.45360			−0.726800	−	0.686849i	$-0.758993\pi$
$601$	−873.614			−1.45360			−0.726800	+	0.686849i	$0.758993\pi$
$602$	−22.8145			−0.0378979
$603$			338.702i			0.561695i
$604$	−23.5597			−0.0390062
$605$		−	519.180i		−	0.858148i
$606$	−186.751			−0.308169
$607$	−1197.84			−1.97337			−0.986687	−	0.162630i	$-0.948002\pi$
$607$	−1197.84			−1.97337			−0.986687	+	0.162630i	$0.948002\pi$
$608$			485.576i			0.798644i
$609$			12.9428i			0.0212526i
$610$	−1719.82			−2.81938
$611$	−831.142			−1.36030
$612$		−	483.811i		−	0.790540i
$613$			439.201i			0.716478i	0.933630	+	0.358239i	$0.116623\pi$
$613$			439.201i			0.716478i	−0.933630	+	0.358239i	$0.883377\pi$
$614$	610.675			0.994584
$615$		−	597.684i		−	0.971845i
$616$	62.1201			0.100844
$617$		−	126.704i		−	0.205355i	−0.994715	−	0.102677i	$-0.967259\pi$
$617$		−	126.704i		−	0.205355i	0.994715	−	0.102677i	$-0.0327410\pi$
$618$			630.070i			1.01953i
$619$			610.765i			0.986697i	0.869832	+	0.493348i	$0.164227\pi$
$619$			610.765i			0.986697i	−0.869832	+	0.493348i	$0.835773\pi$
$620$			278.384i			0.449006i
$621$	−101.989	+	62.2990i	−0.164234	+	0.100321i
$622$	1460.54			2.34813
$623$	−456.589			−0.732888
$624$	0.780270			0.00125043
$625$	−519.815			−0.831704
$626$			2008.82i			3.20898i
$627$	77.1368			0.123025
$628$			1806.27i			2.87622i
$629$	−768.952			−1.22250
$630$	−118.648			−0.188331
$631$			943.021i			1.49449i	0.664551	+	0.747243i	$0.268623\pi$
$631$			943.021i			1.49449i	−0.664551	+	0.747243i	$0.731377\pi$
$632$			46.7863i			0.0740289i
$633$	−139.532			−0.220430
$634$	779.520			1.22953
$635$			254.247i			0.400389i
$636$		−	17.8405i		−	0.0280511i
$637$	108.175			0.169820
$638$			26.7891i			0.0419892i
$639$	−46.6917			−0.0730700
$640$		−	957.354i		−	1.49587i
$641$		−	977.288i		−	1.52463i	−0.647206	−	0.762315i	$-0.724063\pi$
$641$		−	977.288i		−	1.52463i	0.647206	−	0.762315i	$-0.275937\pi$
$642$		−	187.586i		−	0.292190i
$643$		−	855.465i		−	1.33043i	−0.746653	−	0.665214i	$-0.768340\pi$
$643$		−	855.465i		−	1.33043i	0.746653	−	0.665214i	$-0.231660\pi$
$644$	205.407	+	336.270i	0.318955	+	0.522158i
$645$	21.3130			0.0330434
$646$	−1224.96			−1.89622
$647$	−357.779			−0.552982			−0.276491	−	0.961017i	$-0.589172\pi$
$647$	−357.779			−0.552982			−0.276491	+	0.961017i	$0.589172\pi$
$648$	−72.1061			−0.111275
$649$		−	276.619i		−	0.426224i
$650$	183.508			0.282321
$651$			42.6561i			0.0655240i
$652$	1131.76			1.73583
$653$	520.581			0.797215			0.398607	−	0.917122i	$-0.369494\pi$
$653$	520.581			0.797215			0.398607	+	0.917122i	$0.369494\pi$
$654$		−	208.298i		−	0.318498i
$655$			710.812i			1.08521i
$656$	−2.17801			−0.00332014
$657$	−197.127			−0.300042
$658$		−	460.554i		−	0.699929i
$659$		−	636.441i		−	0.965768i	−0.875684	−	0.482884i	$-0.839589\pi$
$659$		−	636.441i		−	0.965768i	0.875684	−	0.482884i	$-0.160411\pi$
$660$	−151.805			−0.230008
$661$			1033.29i			1.56322i	0.623766	+	0.781611i	$0.285602\pi$
$661$			1033.29i			1.56322i	−0.623766	+	0.781611i	$0.714398\pi$
$662$	1293.80			1.95438
$663$		−	666.619i		−	1.00546i
$664$		−	440.086i		−	0.662781i
$665$			185.696i			0.279242i
$666$			299.790i			0.450136i
$667$	−55.4361	+	33.8625i	−0.0831126	+	0.0507684i
$668$	−1833.82			−2.74524
$669$	−260.654			−0.389618
$670$	−1687.67			−2.51891
$671$	−337.167			−0.502484
$672$		−	146.426i		−	0.217896i
$673$	−468.106			−0.695552			−0.347776	−	0.937578i	$-0.613063\pi$
$673$	−468.106			−0.695552			−0.347776	+	0.937578i	$0.613063\pi$
$674$			1232.92i			1.82926i
$675$	−19.0644			−0.0282436
$676$	452.067			0.668738
$677$			722.201i			1.06677i	0.845874	+	0.533383i	$0.179080\pi$
$677$			722.201i			1.06677i	−0.845874	+	0.533383i	$0.820920\pi$
$678$			493.352i			0.727658i
$679$	−4.79768			−0.00706580
$680$	921.560			1.35524
$681$		−	229.939i		−	0.337649i
$682$			88.2897i			0.129457i
$683$	551.975			0.808163			0.404081	−	0.914723i	$-0.367591\pi$
$683$	551.975			0.808163			0.404081	+	0.914723i	$0.367591\pi$
$684$			295.213i			0.431598i
$685$	−736.002			−1.07446
$686$			59.9421i			0.0873792i
$687$			21.0583i			0.0306526i
$688$		−	0.0776663i		−	0.000112887i
$689$		−	24.5816i		−	0.0356772i
$690$	−310.421	−	508.189i	−0.449886	−	0.736505i
$691$	−736.563			−1.06594			−0.532969	−	0.846135i	$-0.678924\pi$
$691$	−736.563			−1.06594			−0.532969	+	0.846135i	$0.678924\pi$
$692$	200.969			0.290418
$693$	−23.2607			−0.0335653
$694$	−1539.14			−2.21778
$695$		−	323.504i		−	0.465473i
$696$	−39.1931			−0.0563119
$697$			1860.77i			2.66969i
$698$	542.939			0.777849
$699$	232.257			0.332270
$700$			62.8575i			0.0897964i
$701$			327.666i			0.467427i	0.972306	+	0.233713i	$0.0750877\pi$
$701$			327.666i			0.467427i	−0.972306	+	0.233713i	$0.924912\pi$
$702$	−259.894			−0.370219
$703$	469.201			0.667427
$704$		−	303.415i		−	0.430987i
$705$			430.242i			0.610272i
$706$	1290.07			1.82729
$707$		−	88.1384i		−	0.124665i
$708$	1058.66			1.49528
$709$		−	434.190i		−	0.612398i	−0.951967	−	0.306199i	$-0.900943\pi$
$709$		−	434.190i		−	0.612398i	0.951967	−	0.306199i	$-0.0990574\pi$
$710$		−	232.654i		−	0.327681i
$711$		−	17.5190i		−	0.0246400i
$712$		−	1382.63i		−	1.94190i
$713$	−182.703	+	111.602i	−0.256245	+	0.156524i
$714$	369.388			0.517350
$715$	−209.165			−0.292538
$716$	−217.854			−0.304265
$717$	159.503			0.222458
$718$			1200.90i			1.67256i
$719$	936.978			1.30317			0.651584	−	0.758577i	$-0.274105\pi$
$719$	936.978			1.30317			0.651584	+	0.758577i	$0.274105\pi$
$720$		−	0.403908i		−	0.000560984i
$721$	−297.366			−0.412436
$722$	−420.954			−0.583039
$723$		−	387.546i		−	0.536025i
$724$			293.809i			0.405813i
$725$	−10.3624			−0.0142930
$726$	630.169			0.868002
$727$			815.192i			1.12131i	0.828050	+	0.560655i	$0.189451\pi$
$727$			815.192i			1.12131i	−0.828050	+	0.560655i	$0.810549\pi$
$728$			327.573i			0.449962i
$729$	27.0000			0.0370370
$730$		−	982.238i		−	1.34553i
$731$	−66.3538			−0.0907712
$732$		−	1290.38i		−	1.76282i
$733$		−	476.591i		−	0.650192i	−0.945681	−	0.325096i	$-0.894603\pi$
$733$		−	476.591i		−	0.650192i	0.945681	−	0.325096i	$-0.105397\pi$
$734$		−	1660.95i		−	2.26287i
$735$		−	55.9970i		−	0.0761864i
$736$	627.165	−	383.097i	0.852127	−	0.520512i
$737$	−330.864			−0.448934
$738$	725.457			0.983004
$739$	858.892			1.16224			0.581118	−	0.813820i	$-0.302616\pi$
$739$	858.892			1.16224			0.581118	+	0.813820i	$0.302616\pi$
$740$	−923.386			−1.24782
$741$			406.759i			0.548933i
$742$	13.6212			0.0183574
$743$			94.2457i			0.126845i	0.997987	+	0.0634224i	$0.0202015\pi$
$743$			94.2457i			0.126845i	−0.997987	+	0.0634224i	$0.979798\pi$
$744$	−129.170			−0.173616
$745$	1237.30			1.66080
$746$			1499.78i			2.01042i
$747$			164.790i			0.220602i
$748$	472.615			0.631838
$749$	88.5328			0.118201
$750$		−	742.273i		−	0.989697i
$751$			383.210i			0.510266i	0.966906	+	0.255133i	$0.0821193\pi$
$751$			383.210i			0.510266i	−0.966906	+	0.255133i	$0.917881\pi$
$752$	1.56784			0.00208489
$753$		−	224.178i		−	0.297713i
$754$	−141.265			−0.187354
$755$			16.8039i			0.0222568i
$756$		−	89.0219i		−	0.117754i
$757$			184.528i			0.243763i	0.992545	+	0.121881i	$0.0388927\pi$
$757$			184.528i			0.243763i	−0.992545	+	0.121881i	$0.961107\pi$
$758$			1310.07i			1.72832i
$759$	−60.8574	−	99.6293i	−0.0801810	−	0.131264i
$760$	−562.320			−0.739895
$761$	−244.980			−0.321919			−0.160960	−	0.986961i	$-0.551459\pi$
$761$	−244.980			−0.321919			−0.160960	+	0.986961i	$0.551459\pi$
$762$	−308.600			−0.404987
$763$	98.3077			0.128844
$764$		−	316.488i		−	0.414251i
$765$	−345.076			−0.451080
$766$			1781.62i			2.32588i
$767$	1458.67			1.90179
$768$	444.711			0.579051
$769$		−	51.1696i		−	0.0665405i	−0.999446	−	0.0332702i	$-0.989408\pi$
$769$		−	51.1696i		−	0.0665405i	0.999446	−	0.0332702i	$-0.0105922\pi$
$770$		−	115.903i		−	0.150523i
$771$	−403.763			−0.523688
$772$	−1519.24			−1.96793
$773$			1041.81i			1.34775i	0.738843	+	0.673877i	$0.235372\pi$
$773$			1041.81i			1.34775i	−0.738843	+	0.673877i	$0.764628\pi$
$774$			25.8693i			0.0334228i
$775$	−34.1518			−0.0440668
$776$		−	14.5282i		−	0.0187219i
$777$	−141.488			−0.182096
$778$		−	2078.79i		−	2.67197i
$779$		−	1135.41i		−	1.45752i
$780$		−	800.501i		−	1.02628i
$781$		−	45.6112i		−	0.0584011i
$782$	966.435	+	1582.14i	1.23585	+	2.02320i
$783$	14.6758			0.0187430
$784$	−0.204058			−0.000260278
$785$	1288.31			1.64117
$786$	−862.769			−1.09767
$787$			437.311i			0.555668i	0.960629	+	0.277834i	$0.0896166\pi$
$787$			437.311i			0.555668i	−0.960629	+	0.277834i	$0.910383\pi$
$788$	−915.350			−1.16161
$789$		−	254.070i		−	0.322015i
$790$	87.2932			0.110498
$791$	−232.841			−0.294363
$792$		−	70.4375i		−	0.0889363i
$793$		−	1777.95i		−	2.24206i
$794$	−95.4248			−0.120182
$795$	−12.7247			−0.0160059
$796$		−	943.907i		−	1.18581i
$797$		−	1171.76i		−	1.47022i	−0.677950	−	0.735108i	$-0.737131\pi$
$797$		−	1171.76i		−	1.47022i	0.677950	−	0.735108i	$-0.262869\pi$
$798$	−225.394			−0.282449
$799$		−	1339.47i		−	1.67644i
$800$	117.233			0.146542
$801$			517.724i			0.646347i
$802$		−	1501.47i		−	1.87215i
$803$		−	192.566i		−	0.239808i
$804$		−	1266.26i		−	1.57495i
$805$	239.844	−	146.506i	0.297942	−	0.181995i
$806$	−465.571			−0.577631
$807$	−181.423			−0.224812
$808$	266.898			0.330320
$809$	−1573.47			−1.94496			−0.972479	−	0.232989i	$-0.925149\pi$
$809$	−1573.47			−1.94496			−0.972479	+	0.232989i	$0.925149\pi$
$810$			134.535i			0.166092i
$811$	580.336			0.715581			0.357791	−	0.933802i	$-0.383530\pi$
$811$	580.336			0.715581			0.357791	+	0.933802i	$0.383530\pi$
$812$		−	48.3877i		−	0.0595907i
$813$	−456.579			−0.561598
$814$	−292.853			−0.359770
$815$		−	807.227i		−	0.990463i
$816$			1.25749i			0.00154104i
$817$	40.4879			0.0495568
$818$	−1204.25			−1.47219
$819$		−	122.659i		−	0.149767i
$820$			2234.49i			2.72498i
$821$	−1540.41			−1.87626			−0.938132	−	0.346279i	$-0.887445\pi$
$821$	−1540.41			−1.87626			−0.938132	+	0.346279i	$0.887445\pi$
$822$		−	893.344i		−	1.08679i
$823$	1594.60			1.93754			0.968772	−	0.247951i	$-0.0797574\pi$
$823$	1594.60			1.93754			0.968772	+	0.247951i	$0.0797574\pi$
$824$		−	900.476i		−	1.09281i
$825$		−	18.6233i		−	0.0225737i
$826$			808.283i			0.978551i
$827$			805.566i			0.974082i	0.873379	+	0.487041i	$0.161924\pi$
$827$			805.566i			0.974082i	−0.873379	+	0.487041i	$0.838076\pi$
$828$	381.294	−	232.909i	0.460501	−	0.281291i
$829$	−513.777			−0.619756			−0.309878	−	0.950776i	$-0.600288\pi$
$829$	−513.777			−0.619756			−0.309878	+	0.950776i	$0.600288\pi$
$830$	−821.107			−0.989286
$831$	659.594			0.793735
$832$	1599.97			1.92304
$833$			174.336i			0.209286i
$834$	392.662			0.470818
$835$			1307.97i			1.56643i
$836$	−288.381			−0.344954
$837$	48.3675			0.0577867
$838$		−	1288.27i		−	1.53732i
$839$			957.631i			1.14140i	0.821160	+	0.570698i	$0.193327\pi$
$839$			957.631i			1.14140i	−0.821160	+	0.570698i	$0.806673\pi$
$840$	169.569			0.201867
$841$	−833.023			−0.990515
$842$		−	1357.59i		−	1.61234i
$843$			81.7679i			0.0969963i
$844$	521.650			0.618069
$845$		−	322.435i		−	0.381580i
$846$	−522.219			−0.617280
$847$			297.413i			0.351137i
$848$			0.0463699i			5.46814e-5i
$849$			103.063i			0.121393i
$850$			295.743i			0.347933i
$851$	−370.178	−	606.016i	−0.434992	−	0.712122i
$852$	174.560			0.204883
$853$	−694.747			−0.814474			−0.407237	−	0.913322i	$-0.633508\pi$
$853$	−694.747			−0.814474			−0.407237	+	0.913322i	$0.633508\pi$
$854$	985.203			1.15363
$855$	210.560			0.246269
$856$			268.093i			0.313192i
$857$	−198.585			−0.231721			−0.115861	−	0.993265i	$-0.536963\pi$
$857$	−198.585			−0.231721			−0.115861	+	0.993265i	$0.536963\pi$
$858$		−	253.880i		−	0.295897i
$859$	−384.669			−0.447811			−0.223905	−	0.974611i	$-0.571881\pi$
$859$	−384.669			−0.447811			−0.223905	+	0.974611i	$0.571881\pi$
$860$	−79.6801			−0.0926513
$861$			342.385i			0.397660i
$862$			871.822i			1.01139i
$863$	987.992			1.14483			0.572417	−	0.819963i	$-0.306006\pi$
$863$	987.992			1.14483			0.572417	+	0.819963i	$0.306006\pi$
$864$	−166.032			−0.192166
$865$		−	143.341i		−	0.165712i
$866$			1161.64i			1.34139i
$867$	573.765			0.661782
$868$		−	159.473i		−	0.183725i
$869$	17.1136			0.0196935
$870$			73.1259i			0.0840528i
$871$		−	1744.72i		−	2.00312i
$872$			297.693i			0.341390i
$873$			5.44005i			0.00623145i
$874$	−589.702	−	965.397i	−0.674716	−	1.10457i
$875$	350.322			0.400368
$876$	736.974			0.841295
$877$	391.192			0.446057			0.223028	−	0.974812i	$-0.428406\pi$
$877$	391.192			0.446057			0.223028	+	0.974812i	$0.428406\pi$
$878$	720.863			0.821029
$879$			355.633i			0.404589i
$880$	0.394562			0.000448365
$881$		−	300.919i		−	0.341565i	−0.985309	−	0.170783i	$-0.945370\pi$
$881$		−	300.919i		−	0.341565i	0.985309	−	0.170783i	$-0.0546296\pi$
$882$	67.9680			0.0770612
$883$	1588.28			1.79873			0.899366	−	0.437196i	$-0.144028\pi$
$883$	1588.28			1.79873			0.899366	+	0.437196i	$0.144028\pi$
$884$			2492.20i			2.81923i
$885$		−	755.085i		−	0.853204i
$886$	−398.826			−0.450142
$887$	800.034			0.901955			0.450978	−	0.892535i	$-0.351075\pi$
$887$	800.034			0.901955			0.450978	+	0.892535i	$0.351075\pi$
$888$		−	428.451i		−	0.482490i
$889$		−	145.646i		−	0.163831i
$890$	−2579.69			−2.89853
$891$			26.3752i			0.0296018i
$892$	974.474			1.09246
$893$			817.323i			0.915256i
$894$			1501.80i			1.67987i
$895$			155.384i			0.173613i
$896$			548.423i			0.612079i
$897$	525.367	−	320.914i	0.585693	−	0.357764i
$898$	1496.28			1.66623
$899$	26.2900			0.0292436
$900$	71.2737			0.0791930
$901$	39.6158			0.0439687
$902$			708.669i			0.785665i
$903$	−12.2092			−0.0135207
$904$		−	705.084i		−	0.779960i
$905$	209.558			0.231556
$906$	−20.3962			−0.0225124
$907$		−	579.539i		−	0.638963i	−0.947593	−	0.319481i	$-0.896491\pi$
$907$		−	579.539i		−	0.638963i	0.947593	−	0.319481i	$-0.103509\pi$
$908$			859.642i			0.946743i
$909$	−99.9396			−0.109945
$910$	611.180			0.671627
$911$			841.706i			0.923936i	0.886896	+	0.461968i	$0.152857\pi$
$911$			841.706i			0.923936i	−0.886896	+	0.461968i	$0.847143\pi$
$912$		−	0.767298i		−	0.000841335i
$913$	−160.976			−0.176316
$914$		−	2300.15i		−	2.51658i
$915$	−920.362			−1.00586
$916$		−	78.7280i		−	0.0859476i
$917$		−	407.190i		−	0.444046i
$918$		−	418.847i		−	0.456260i
$919$		−	583.667i		−	0.635111i	−0.948240	−	0.317556i	$-0.897138\pi$
$919$		−	583.667i		−	0.635111i	0.948240	−	0.317556i	$-0.102862\pi$
$920$	443.644	+	726.288i	0.482222	+	0.789443i
$921$	326.803			0.354834
$922$	−1057.16			−1.14659
$923$	240.518			0.260583
$924$	86.9619			0.0941146
$925$		−	113.280i		−	0.122465i
$926$	−53.7643			−0.0580608
$927$			337.182i			0.363734i
$928$	−90.2461			−0.0972480
$929$	1686.54			1.81543			0.907715	−	0.419587i	$-0.137825\pi$
$929$	1686.54			1.81543			0.907715	+	0.419587i	$0.137825\pi$
$930$			241.004i			0.259144i
$931$		−	106.377i		−	0.114261i
$932$	−868.309			−0.931662
$933$	781.607			0.837735
$934$			1693.76i			1.81345i
$935$		−	337.091i		−	0.360525i
$936$	371.432			0.396829
$937$		−	1127.48i		−	1.20328i	−0.798766	−	0.601642i	$-0.794513\pi$
$937$		−	1127.48i		−	1.20328i	0.798766	−	0.601642i	$-0.205487\pi$
$938$	966.787			1.03069
$939$			1075.02i			1.14486i
$940$		−	1608.49i		−	1.71116i
$941$			1038.28i			1.10338i	0.834048	+	0.551692i	$0.186018\pi$
$941$			1038.28i			1.10338i	−0.834048	+	0.551692i	$0.813982\pi$
$942$			1563.73i			1.66001i
$943$	−1466.49	+	895.787i	−1.55513	+	0.949933i
$944$	−2.75160			−0.00291483
$945$	−63.4946			−0.0671901
$946$	−25.2706			−0.0267131
$947$	−1646.42			−1.73857			−0.869284	−	0.494312i	$-0.835420\pi$
$947$	−1646.42			−1.73857			−0.869284	+	0.494312i	$0.835420\pi$
$948$			65.4962i			0.0690888i
$949$	1015.44			1.07001
$950$		−	180.457i		−	0.189955i
$951$	417.160			0.438654
$952$	−527.918			−0.554536
$953$			1388.86i			1.45735i	0.684858	+	0.728676i	$0.259864\pi$
$953$			1388.86i			1.45735i	−0.684858	+	0.728676i	$0.740136\pi$
$954$		−	15.4450i		−	0.0161897i
$955$	−225.734			−0.236371
$956$	−596.312			−0.623757
$957$			14.3362i			0.0149803i
$958$			2789.62i			2.91192i
$959$	421.621			0.439646
$960$		−	828.229i		−	0.862738i
$961$	−874.355			−0.909839
$962$		−	1544.28i		−	1.60528i
$963$		−	100.387i		−	0.104244i
$964$			1448.87i			1.50297i
$965$			1083.60i			1.12290i
$966$	177.826	+	291.117i	0.184084	+	0.301364i
$967$	−1907.18			−1.97227			−0.986133	−	0.165960i	$-0.946928\pi$
$967$	−1907.18			−1.97227			−0.986133	+	0.165960i	$0.946928\pi$
$968$	−900.619			−0.930391
$969$	−655.536			−0.676508
$970$	−27.1065			−0.0279448
$971$			1252.06i			1.28946i	0.764412	+	0.644728i	$0.223029\pi$
$971$			1252.06i			1.28946i	−0.764412	+	0.644728i	$0.776971\pi$
$972$	−100.941			−0.103849
$973$			185.320i			0.190462i
$974$	83.3476			0.0855725
$975$	98.2045			0.100723
$976$			3.35388i			0.00343635i
$977$		−	379.765i		−	0.388705i	−0.980932	−	0.194353i	$-0.937739\pi$
$977$		−	379.765i		−	0.388705i	0.980932	−	0.194353i	$-0.0622606\pi$
$978$	979.796			1.00184
$979$	−505.743			−0.516592
$980$			209.349i			0.213621i
$981$		−	111.470i		−	0.113629i
$982$	−2247.70			−2.28890
$983$		−	824.188i		−	0.838442i	−0.907884	−	0.419221i	$-0.862303\pi$
$983$		−	824.188i		−	0.838442i	0.907884	−	0.419221i	$-0.137697\pi$
$984$	−1036.80			−1.05366
$985$			652.870i			0.662813i
$986$		−	227.663i		−	0.230896i
$987$		−	246.465i		−	0.249711i
$988$		−	1520.70i		−	1.53917i
$989$	−31.9431	−	52.2938i	−0.0322984	−	0.0528755i
$990$	−131.421			−0.132749
$991$	−213.523			−0.215462			−0.107731	−	0.994180i	$-0.534359\pi$
$991$	−213.523			−0.215462			−0.107731	+	0.994180i	$0.534359\pi$
$992$	−297.427			−0.299826
$993$	692.377			0.697258
$994$			133.276i			0.134081i
$995$	−673.239			−0.676622
$996$		−	616.077i		−	0.618552i
$997$	−257.640			−0.258415			−0.129207	−	0.991618i	$-0.541243\pi$
$997$	−257.640			−0.258415			−0.129207	+	0.991618i	$0.541243\pi$
$998$	−2612.95			−2.61819
$999$			160.433i			0.160593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.8	yes	48
23.22	odd	2	inner	483.3.f.a.22.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.7	✓	48	23.22	odd	2	inner
483.3.f.a.22.8	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.23657 q^{2} -1.73205 q^{3} +6.47539 q^{4} -4.61855i q^{5} +5.60591 q^{6} +2.64575i q^{7} -8.01179 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.23657 q^{2} -1.73205 q^{3} +6.47539 q^{4} -4.61855i q^{5} +5.60591 q^{6} +2.64575i q^{7} -8.01179 q^{8} +3.00000 q^{9} +14.9483i q^{10} +2.93058i q^{11} -11.2157 q^{12} -15.4536 q^{13} -8.56316i q^{14} +7.99957i q^{15} +0.0291511 q^{16} -24.9051i q^{17} -9.70971 q^{18} +15.1966i q^{19} -29.9070i q^{20} -4.58258i q^{21} -9.48503i q^{22} +(19.6279 - 11.9895i) q^{23} +13.8768 q^{24} +3.66895 q^{25} +50.0166 q^{26} -5.19615 q^{27} +17.1323i q^{28} -2.82436 q^{29} -25.8912i q^{30} -9.30833 q^{31} +31.9528 q^{32} -5.07591i q^{33} +80.6071i q^{34} +12.2195 q^{35} +19.4262 q^{36} -30.8753i q^{37} -49.1850i q^{38} +26.7664 q^{39} +37.0029i q^{40} -74.7145 q^{41} +14.8318i q^{42} -2.66427i q^{43} +18.9766i q^{44} -13.8557i q^{45} +(-63.5270 + 38.8047i) q^{46} +53.7831 q^{47} -0.0504912 q^{48} -7.00000 q^{49} -11.8748 q^{50} +43.1369i q^{51} -100.068 q^{52} +1.59067i q^{53} +16.8177 q^{54} +13.5350 q^{55} -21.1972i q^{56} -26.3214i q^{57} +9.14123 q^{58} -94.3907 q^{59} +51.8004i q^{60} +115.051i q^{61} +30.1271 q^{62} +7.93725i q^{63} -103.534 q^{64} +71.3732i q^{65} +16.4285i q^{66} +112.901i q^{67} -161.270i q^{68} +(-33.9965 + 20.7663i) q^{69} -39.5494 q^{70} -15.5639 q^{71} -24.0354 q^{72} -65.7091 q^{73} +99.9301i q^{74} -6.35481 q^{75} +98.4043i q^{76} -7.75358 q^{77} -86.6313 q^{78} -5.83968i q^{79} -0.134636i q^{80} +9.00000 q^{81} +241.819 q^{82} +54.9299i q^{83} -29.6740i q^{84} -115.025 q^{85} +8.62308i q^{86} +4.89193 q^{87} -23.4792i q^{88} +172.575i q^{89} +44.8448i q^{90} -40.8863i q^{91} +(127.098 - 77.6364i) q^{92} +16.1225 q^{93} -174.073 q^{94} +70.1866 q^{95} -55.3439 q^{96} +1.81335i q^{97} +22.6560 q^{98} +8.79173i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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