LMFDB - Embedded newform 483.3.f.a.22.33

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			22.33
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68447 q^{2} +1.73205 q^{3} -1.16256 q^{4} -5.25050i q^{5} +2.91759 q^{6} -2.64575i q^{7} -8.69618 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.68447 q^{2} +1.73205 q^{3} -1.16256 q^{4} -5.25050i q^{5} +2.91759 q^{6} -2.64575i q^{7} -8.69618 q^{8} +3.00000 q^{9} -8.84432i q^{10} -5.14913i q^{11} -2.01361 q^{12} -16.5713 q^{13} -4.45669i q^{14} -9.09413i q^{15} -9.99824 q^{16} +5.08838i q^{17} +5.05341 q^{18} -18.9229i q^{19} +6.10400i q^{20} -4.58258i q^{21} -8.67356i q^{22} +(-18.6091 - 13.5167i) q^{23} -15.0622 q^{24} -2.56774 q^{25} -27.9140 q^{26} +5.19615 q^{27} +3.07583i q^{28} -25.1762 q^{29} -15.3188i q^{30} +30.8557 q^{31} +17.9430 q^{32} -8.91855i q^{33} +8.57123i q^{34} -13.8915 q^{35} -3.48767 q^{36} +5.29777i q^{37} -31.8750i q^{38} -28.7024 q^{39} +45.6593i q^{40} +8.11734 q^{41} -7.71922i q^{42} -66.5183i q^{43} +5.98615i q^{44} -15.7515i q^{45} +(-31.3465 - 22.7686i) q^{46} -1.22703 q^{47} -17.3175 q^{48} -7.00000 q^{49} -4.32529 q^{50} +8.81333i q^{51} +19.2651 q^{52} +4.56136i q^{53} +8.75277 q^{54} -27.0355 q^{55} +23.0079i q^{56} -32.7753i q^{57} -42.4085 q^{58} +48.1727 q^{59} +10.5724i q^{60} -23.5877i q^{61} +51.9756 q^{62} -7.93725i q^{63} +70.2174 q^{64} +87.0079i q^{65} -15.0230i q^{66} +54.7641i q^{67} -5.91552i q^{68} +(-32.2319 - 23.4117i) q^{69} -23.3999 q^{70} +74.8749 q^{71} -26.0885 q^{72} +75.3872 q^{73} +8.92393i q^{74} -4.44746 q^{75} +21.9989i q^{76} -13.6233 q^{77} -48.3484 q^{78} -146.653i q^{79} +52.4958i q^{80} +9.00000 q^{81} +13.6734 q^{82} +37.6892i q^{83} +5.32750i q^{84} +26.7165 q^{85} -112.048i q^{86} -43.6064 q^{87} +44.7777i q^{88} -91.4505i q^{89} -26.5329i q^{90} +43.8437i q^{91} +(21.6341 + 15.7140i) q^{92} +53.4437 q^{93} -2.06689 q^{94} -99.3544 q^{95} +31.0781 q^{96} +183.683i q^{97} -11.7913 q^{98} -15.4474i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.68447			0.842236			0.421118	−	0.907006i	$-0.361638\pi$
$2$	1.68447			0.842236			0.421118	+	0.907006i	$0.361638\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−1.16256			−0.290639
$5$		−	5.25050i		−	1.05010i	−0.851071	−	0.525050i	$-0.824047\pi$
$5$		−	5.25050i		−	1.05010i	0.851071	−	0.525050i	$-0.175953\pi$
$6$	2.91759			0.486265
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−8.69618			−1.08702
$9$	3.00000			0.333333
$10$		−	8.84432i		−	0.884432i
$11$		−	5.14913i		−	0.468102i	−0.972224	−	0.234051i	$-0.924802\pi$
$11$		−	5.14913i		−	0.468102i	0.972224	−	0.234051i	$-0.0751983\pi$
$12$	−2.01361			−0.167800
$13$	−16.5713			−1.27472			−0.637360	−	0.770567i	$-0.719973\pi$
$13$	−16.5713			−1.27472			−0.637360	+	0.770567i	$0.719973\pi$
$14$		−	4.45669i		−	0.318335i
$15$		−	9.09413i		−	0.606275i
$16$	−9.99824			−0.624890
$17$			5.08838i			0.299316i	0.988738	+	0.149658i	$0.0478173\pi$
$17$			5.08838i			0.299316i	−0.988738	+	0.149658i	$0.952183\pi$
$18$	5.05341			0.280745
$19$		−	18.9229i		−	0.995940i	−0.867194	−	0.497970i	$-0.834079\pi$
$19$		−	18.9229i		−	0.995940i	0.867194	−	0.497970i	$-0.165921\pi$
$20$			6.10400i			0.305200i
$21$		−	4.58258i		−	0.218218i
$22$		−	8.67356i		−	0.394253i
$23$	−18.6091	−	13.5167i	−0.809090	−	0.587685i
$23$	−18.6091	−	13.5167i	−0.809090	−	0.587685i
$24$	−15.0622			−0.627593
$25$	−2.56774			−0.102710
$26$	−27.9140			−1.07361
$27$	5.19615			0.192450
$28$			3.07583i			0.109851i
$29$	−25.1762			−0.868144			−0.434072	−	0.900878i	$-0.642924\pi$
$29$	−25.1762			−0.868144			−0.434072	+	0.900878i	$0.642924\pi$
$30$		−	15.3188i		−	0.510627i
$31$	30.8557			0.995346			0.497673	−	0.867365i	$-0.334188\pi$
$31$	30.8557			0.995346			0.497673	+	0.867365i	$0.334188\pi$
$32$	17.9430			0.560718
$33$		−	8.91855i		−	0.270259i
$34$			8.57123i			0.252095i
$35$	−13.8915			−0.396900
$36$	−3.48767			−0.0968796
$37$			5.29777i			0.143183i	0.997434	+	0.0715914i	$0.0228078\pi$
$37$			5.29777i			0.143183i	−0.997434	+	0.0715914i	$0.977192\pi$
$38$		−	31.8750i		−	0.838816i
$39$	−28.7024			−0.735959
$40$			45.6593i			1.14148i
$41$	8.11734			0.197984			0.0989919	−	0.995088i	$-0.468438\pi$
$41$	8.11734			0.197984			0.0989919	+	0.995088i	$0.468438\pi$
$42$		−	7.71922i		−	0.183791i
$43$		−	66.5183i		−	1.54694i	−0.633835	−	0.773468i	$-0.718520\pi$
$43$		−	66.5183i		−	1.54694i	0.633835	−	0.773468i	$-0.281480\pi$
$44$			5.98615i			0.136049i
$45$		−	15.7515i		−	0.350033i
$46$	−31.3465	−	22.7686i	−0.681445	−	0.494969i
$47$	−1.22703			−0.0261070			−0.0130535	−	0.999915i	$-0.504155\pi$
$47$	−1.22703			−0.0261070			−0.0130535	+	0.999915i	$0.504155\pi$
$48$	−17.3175			−0.360780
$49$	−7.00000			−0.142857
$50$	−4.32529			−0.0865058
$51$			8.81333i			0.172810i
$52$	19.2651			0.370483
$53$			4.56136i			0.0860634i	0.999074	+	0.0430317i	$0.0137016\pi$
$53$			4.56136i			0.0860634i	−0.999074	+	0.0430317i	$0.986298\pi$
$54$	8.75277			0.162088
$55$	−27.0355			−0.491554
$56$			23.0079i			0.410856i
$57$		−	32.7753i		−	0.575006i
$58$	−42.4085			−0.731182
$59$	48.1727			0.816486			0.408243	−	0.912873i	$-0.366142\pi$
$59$	48.1727			0.816486			0.408243	+	0.912873i	$0.366142\pi$
$60$			10.5724i			0.176207i
$61$		−	23.5877i		−	0.386683i	−0.981131	−	0.193342i	$-0.938067\pi$
$61$		−	23.5877i		−	0.386683i	0.981131	−	0.193342i	$-0.0619326\pi$
$62$	51.9756			0.838316
$63$		−	7.93725i		−	0.125988i
$64$	70.2174			1.09715
$65$			87.0079i			1.33858i
$66$		−	15.0230i		−	0.227622i
$67$			54.7641i			0.817374i	0.912675	+	0.408687i	$0.134013\pi$
$67$			54.7641i			0.817374i	−0.912675	+	0.408687i	$0.865987\pi$
$68$		−	5.91552i		−	0.0869930i
$69$	−32.2319	−	23.4117i	−0.467128	−	0.339300i
$70$	−23.3999			−0.334284
$71$	74.8749			1.05458			0.527288	−	0.849687i	$-0.323209\pi$
$71$	74.8749			1.05458			0.527288	+	0.849687i	$0.323209\pi$
$72$	−26.0885			−0.362341
$73$	75.3872			1.03270			0.516351	−	0.856377i	$-0.327290\pi$
$73$	75.3872			1.03270			0.516351	+	0.856377i	$0.327290\pi$
$74$			8.92393i			0.120594i
$75$	−4.44746			−0.0592995
$76$			21.9989i			0.289459i
$77$	−13.6233			−0.176926
$78$	−48.3484			−0.619851
$79$		−	146.653i		−	1.85637i	−0.372118	−	0.928185i	$-0.621368\pi$
$79$		−	146.653i		−	1.85637i	0.372118	−	0.928185i	$-0.378632\pi$
$80$			52.4958i			0.656197i
$81$	9.00000			0.111111
$82$	13.6734			0.166749
$83$			37.6892i			0.454087i	0.973885	+	0.227043i	$0.0729059\pi$
$83$			37.6892i			0.454087i	−0.973885	+	0.227043i	$0.927094\pi$
$84$			5.32750i			0.0634226i
$85$	26.7165			0.314312
$86$		−	112.048i		−	1.30289i
$87$	−43.6064			−0.501223
$88$			44.7777i			0.508838i
$89$		−	91.4505i		−	1.02753i	−0.857930	−	0.513767i	$-0.828250\pi$
$89$		−	91.4505i		−	1.02753i	0.857930	−	0.513767i	$-0.171750\pi$
$90$		−	26.5329i		−	0.294811i
$91$			43.8437i			0.481799i
$92$	21.6341	+	15.7140i	0.235153	+	0.170804i
$93$	53.4437			0.574664
$94$	−2.06689			−0.0219882
$95$	−99.3544			−1.04584
$96$	31.0781			0.323730
$97$			183.683i			1.89364i	0.321763	+	0.946820i	$0.395725\pi$
$97$			183.683i			1.89364i	−0.321763	+	0.946820i	$0.604275\pi$
$98$	−11.7913			−0.120319
$99$		−	15.4474i		−	0.156034i
$100$	2.98514			0.0298514
$101$	−53.7540			−0.532217			−0.266109	−	0.963943i	$-0.585738\pi$
$101$	−53.7540			−0.532217			−0.266109	+	0.963943i	$0.585738\pi$
$102$			14.8458i			0.145547i
$103$			116.847i			1.13444i	0.823567	+	0.567219i	$0.191981\pi$
$103$			116.847i			1.13444i	−0.823567	+	0.567219i	$0.808019\pi$
$104$	144.107			1.38565
$105$	−24.0608			−0.229151
$106$			7.68348i			0.0724857i
$107$			84.4162i			0.788936i	0.918910	+	0.394468i	$0.129071\pi$
$107$			84.4162i			0.788936i	−0.918910	+	0.394468i	$0.870929\pi$
$108$	−6.04082			−0.0559335
$109$			95.5159i			0.876292i	0.898904	+	0.438146i	$0.144365\pi$
$109$			95.5159i			0.876292i	−0.898904	+	0.438146i	$0.855635\pi$
$110$	−45.5405			−0.414005
$111$			9.17600i			0.0826667i
$112$			26.4529i			0.236186i
$113$		−	85.6225i		−	0.757721i	−0.925454	−	0.378861i	$-0.876316\pi$
$113$		−	85.6225i		−	0.757721i	0.925454	−	0.378861i	$-0.123684\pi$
$114$		−	55.2091i		−	0.484291i
$115$	−70.9697	+	97.7069i	−0.617128	+	0.849625i
$116$	29.2687			0.252316
$117$	−49.7140			−0.424906
$118$	81.1455			0.687674
$119$	13.4626			0.113131
$120$			79.0842i			0.659035i
$121$	94.4865			0.780880
$122$		−	39.7328i		−	0.325678i
$123$	14.0596			0.114306
$124$	−35.8715			−0.289286
$125$		−	117.781i		−	0.942244i
$126$		−	13.3701i		−	0.106112i
$127$	124.224			0.978142			0.489071	−	0.872244i	$-0.337336\pi$
$127$	124.224			0.978142			0.489071	+	0.872244i	$0.337336\pi$
$128$	46.5073			0.363338
$129$		−	115.213i		−	0.893124i
$130$			146.562i			1.12740i
$131$	−242.980			−1.85481			−0.927406	−	0.374057i	$-0.877966\pi$
$131$	−242.980			−1.85481			−0.927406	+	0.374057i	$0.877966\pi$
$132$			10.3683i			0.0785478i
$133$	−50.0652			−0.376430
$134$			92.2485i			0.688422i
$135$		−	27.2824i		−	0.202092i
$136$		−	44.2494i		−	0.325363i
$137$		−	92.4830i		−	0.675058i	−0.941315	−	0.337529i	$-0.890409\pi$
$137$		−	92.4830i		−	0.675058i	0.941315	−	0.337529i	$-0.109591\pi$
$138$	−54.2936	−	39.4363i	−0.393432	−	0.285771i
$139$	−144.896			−1.04241			−0.521207	−	0.853430i	$-0.674518\pi$
$139$	−144.896			−1.04241			−0.521207	+	0.853430i	$0.674518\pi$
$140$	16.1497			0.115355
$141$	−2.12527			−0.0150729
$142$	126.125			0.888202
$143$			85.3280i			0.596699i
$144$	−29.9947			−0.208297
$145$			132.187i			0.911638i
$146$	126.988			0.869778
$147$	−12.1244			−0.0824786
$148$		−	6.15895i		−	0.0416145i
$149$		−	163.154i		−	1.09499i	−0.836809	−	0.547495i	$-0.815581\pi$
$149$		−	163.154i		−	1.09499i	0.836809	−	0.547495i	$-0.184419\pi$
$150$	−7.49162			−0.0499442
$151$	1.18704			0.00786118			0.00393059	−	0.999992i	$-0.498749\pi$
$151$	1.18704			0.00786118			0.00393059	+	0.999992i	$0.498749\pi$
$152$			164.556i			1.08261i
$153$			15.2651i			0.0997721i
$154$	−22.9481			−0.149013
$155$		−	162.008i		−	1.04521i
$156$	33.3682			0.213898
$157$		−	5.58203i		−	0.0355543i	−0.999842	−	0.0177772i	$-0.994341\pi$
$157$		−	5.58203i		−	0.0355543i	0.999842	−	0.0177772i	$-0.00565894\pi$
$158$		−	247.033i		−	1.56350i
$159$			7.90051i			0.0496887i
$160$		−	94.2095i		−	0.588809i
$161$	−35.7620	+	49.2350i	−0.222124	+	0.305807i
$162$	15.1602			0.0935818
$163$	262.382			1.60971			0.804853	−	0.593474i	$-0.202244\pi$
$163$	262.382			1.60971			0.804853	+	0.593474i	$0.202244\pi$
$164$	−9.43686			−0.0575418
$165$	−46.8268			−0.283799
$166$			63.4864i			0.382448i
$167$	11.9270			0.0714192			0.0357096	−	0.999362i	$-0.488631\pi$
$167$	11.9270			0.0714192			0.0357096	+	0.999362i	$0.488631\pi$
$168$			39.8509i			0.237208i
$169$	105.610			0.624909
$170$	45.0032			0.264725
$171$		−	56.7686i		−	0.331980i
$172$			77.3312i			0.449600i
$173$	−114.243			−0.660366			−0.330183	−	0.943917i	$-0.607110\pi$
$173$	−114.243			−0.660366			−0.330183	+	0.943917i	$0.607110\pi$
$174$	−73.4538			−0.422148
$175$			6.79361i			0.0388206i
$176$			51.4822i			0.292513i
$177$	83.4376			0.471399
$178$		−	154.046i		−	0.865425i
$179$	−144.217			−0.805684			−0.402842	−	0.915269i	$-0.631978\pi$
$179$	−144.217			−0.805684			−0.402842	+	0.915269i	$0.631978\pi$
$180$			18.3120i			0.101733i
$181$		−	146.232i		−	0.807912i	−0.914778	−	0.403956i	$-0.867635\pi$
$181$		−	146.232i		−	0.807912i	0.914778	−	0.403956i	$-0.132365\pi$
$182$			73.8534i			0.405788i
$183$		−	40.8551i		−	0.223252i
$184$	161.828	+	117.544i	0.879499	+	0.638826i
$185$	27.8159			0.150356
$186$	90.0244			0.484002
$187$	26.2007			0.140111
$188$	1.42649			0.00758770
$189$		−	13.7477i		−	0.0727393i
$190$	−167.360			−0.880840
$191$		−	29.9731i		−	0.156927i	−0.996917	−	0.0784637i	$-0.974999\pi$
$191$		−	29.9731i		−	0.156927i	0.996917	−	0.0784637i	$-0.0250015\pi$
$192$	121.620			0.633438
$193$	228.897			1.18600			0.592998	−	0.805204i	$-0.297944\pi$
$193$	228.897			1.18600			0.592998	+	0.805204i	$0.297944\pi$
$194$			309.409i			1.59489i
$195$			150.702i			0.772831i
$196$	8.13789			0.0415198
$197$	157.964			0.801848			0.400924	−	0.916111i	$-0.368689\pi$
$197$	157.964			0.801848			0.400924	+	0.916111i	$0.368689\pi$
$198$		−	26.0207i		−	0.131418i
$199$			230.897i			1.16029i	0.814514	+	0.580144i	$0.197004\pi$
$199$			230.897i			1.16029i	−0.814514	+	0.580144i	$0.802996\pi$
$200$	22.3296			0.111648
$201$			94.8542i			0.471911i
$202$	−90.5470			−0.448253
$203$			66.6099i			0.328128i
$204$		−	10.2460i		−	0.0502254i
$205$		−	42.6201i		−	0.207903i
$206$			196.826i			0.955465i
$207$	−55.8272	−	40.5502i	−0.269697	−	0.195895i
$208$	165.684			0.796559
$209$	−97.4361			−0.466202
$210$	−40.5297			−0.192999
$211$	134.996			0.639791			0.319895	−	0.947453i	$-0.396352\pi$
$211$	134.996			0.639791			0.319895	+	0.947453i	$0.396352\pi$
$212$		−	5.30283i		−	0.0250134i
$213$	129.687			0.608860
$214$			142.197i			0.664470i
$215$	−349.254			−1.62444
$216$	−45.1867			−0.209198
$217$		−	81.6366i		−	0.376206i
$218$			160.894i			0.738045i
$219$	130.574			0.596231
$220$	31.4303			0.142865
$221$		−	84.3213i		−	0.381544i
$222$			15.4567i			0.0696248i
$223$	−220.660			−0.989508			−0.494754	−	0.869033i	$-0.664742\pi$
$223$	−220.660			−0.989508			−0.494754	+	0.869033i	$0.664742\pi$
$224$		−	47.4726i		−	0.211931i
$225$	−7.70323			−0.0342366
$226$		−	144.229i		−	0.638180i
$227$			14.3023i			0.0630058i	0.999504	+	0.0315029i	$0.0100293\pi$
$227$			14.3023i			0.0630058i	−0.999504	+	0.0315029i	$0.989971\pi$
$228$			38.1032i			0.167119i
$229$			223.592i			0.976386i	0.872736	+	0.488193i	$0.162344\pi$
$229$			223.592i			0.976386i	−0.872736	+	0.488193i	$0.837656\pi$
$230$	−119.546	+	164.585i	−0.519767	+	0.715585i
$231$	−23.5963			−0.102148
$232$	218.936			0.943692
$233$	−111.662			−0.479235			−0.239618	−	0.970867i	$-0.577022\pi$
$233$	−111.662			−0.479235			−0.239618	+	0.970867i	$0.577022\pi$
$234$	−83.7419			−0.357871
$235$			6.44250i			0.0274149i
$236$	−56.0034			−0.237303
$237$		−	254.011i		−	1.07178i
$238$	22.6773			0.0952829
$239$	213.969			0.895267			0.447633	−	0.894217i	$-0.352267\pi$
$239$	213.969			0.895267			0.447633	+	0.894217i	$0.352267\pi$
$240$			90.9253i			0.378856i
$241$		−	74.8861i		−	0.310731i	−0.987857	−	0.155365i	$-0.950344\pi$
$241$		−	74.8861i		−	0.310731i	0.987857	−	0.155365i	$-0.0496555\pi$
$242$	159.160			0.657685
$243$	15.5885			0.0641500
$244$			27.4220i			0.112385i
$245$			36.7535i			0.150014i
$246$	23.6831			0.0962726
$247$			313.577i			1.26954i
$248$	−268.327			−1.08196
$249$			65.2796i			0.262167i
$250$		−	198.398i		−	0.793592i
$251$		−	349.225i		−	1.39133i	−0.718365	−	0.695667i	$-0.755109\pi$
$251$		−	349.225i		−	1.39133i	0.718365	−	0.695667i	$-0.244891\pi$
$252$			9.22750i			0.0366171i
$253$	−69.5994	+	95.8204i	−0.275097	+	0.378737i
$254$	209.252			0.823826
$255$	46.2744			0.181468
$256$	−202.529			−0.791130
$257$	195.195			0.759512			0.379756	−	0.925087i	$-0.376008\pi$
$257$	195.195			0.759512			0.379756	+	0.925087i	$0.376008\pi$
$258$		−	194.073i		−	0.752221i
$259$	14.0166			0.0541180
$260$		−	101.151i		−	0.389044i
$261$	−75.5285			−0.289381
$262$	−409.293			−1.56219
$263$		−	435.152i		−	1.65457i	−0.561782	−	0.827285i	$-0.689884\pi$
$263$		−	435.152i		−	1.65457i	0.561782	−	0.827285i	$-0.310116\pi$
$264$			77.5573i			0.293778i
$265$	23.9494			0.0903751
$266$	−84.3333			−0.317043
$267$		−	158.397i		−	0.593247i
$268$		−	63.6663i		−	0.237561i
$269$	73.7768			0.274263			0.137132	−	0.990553i	$-0.456212\pi$
$269$	73.7768			0.274263			0.137132	+	0.990553i	$0.456212\pi$
$270$		−	45.9564i		−	0.170209i
$271$	23.2898			0.0859403			0.0429702	−	0.999076i	$-0.486318\pi$
$271$	23.2898			0.0859403			0.0429702	+	0.999076i	$0.486318\pi$
$272$		−	50.8748i		−	0.187040i
$273$			75.9395i			0.278167i
$274$		−	155.785i		−	0.568558i
$275$			13.2216i			0.0480787i
$276$	37.4713	+	27.2174i	0.135766	+	0.0986138i
$277$	−455.498			−1.64440			−0.822199	−	0.569200i	$-0.807253\pi$
$277$	−455.498			−1.64440			−0.822199	+	0.569200i	$0.807253\pi$
$278$	−244.072			−0.877958
$279$	92.5672			0.331782
$280$	120.803			0.431440
$281$		−	516.616i		−	1.83849i	−0.393685	−	0.919245i	$-0.628800\pi$
$281$		−	516.616i		−	1.83849i	0.393685	−	0.919245i	$-0.371200\pi$
$282$	−3.57996			−0.0126949
$283$			163.090i			0.576288i	0.957587	+	0.288144i	$0.0930383\pi$
$283$			163.090i			0.576288i	−0.957587	+	0.288144i	$0.906962\pi$
$284$	−87.0463			−0.306501
$285$	−172.087			−0.603814
$286$			143.733i			0.502561i
$287$		−	21.4765i		−	0.0748309i
$288$	53.8289			0.186906
$289$	263.108			0.910410
$290$			222.666i			0.767814i
$291$			318.149i			1.09329i
$292$	−87.6418			−0.300143
$293$		−	213.461i		−	0.728535i	−0.931294	−	0.364268i	$-0.881319\pi$
$293$		−	213.461i		−	0.728535i	0.931294	−	0.364268i	$-0.118681\pi$
$294$	−20.4231			−0.0694664
$295$		−	252.931i		−	0.857392i
$296$		−	46.0703i		−	0.155643i
$297$		−	26.7556i		−	0.0900863i
$298$		−	274.828i		−	0.922240i
$299$	308.377	+	223.991i	1.03136	+	0.749133i
$300$	5.17042			0.0172347
$301$	−175.991			−0.584687
$302$	1.99953			0.00662097
$303$	−93.1046			−0.307276
$304$			189.195i			0.622353i
$305$	−123.847			−0.406056
$306$			25.7137i			0.0840316i
$307$	525.773			1.71262			0.856308	−	0.516465i	$-0.172753\pi$
$307$	525.773			1.71262			0.856308	+	0.516465i	$0.172753\pi$
$308$	15.8379			0.0514216
$309$			202.385i			0.654968i
$310$		−	272.898i		−	0.880316i
$311$	−521.619			−1.67723			−0.838616	−	0.544723i	$-0.816635\pi$
$311$	−521.619			−1.67723			−0.838616	+	0.544723i	$0.816635\pi$
$312$	249.601			0.800004
$313$		−	357.981i		−	1.14371i	−0.820355	−	0.571854i	$-0.806224\pi$
$313$		−	357.981i		−	1.14371i	0.820355	−	0.571854i	$-0.193776\pi$
$314$		−	9.40277i		−	0.0299451i
$315$	−41.6745			−0.132300
$316$			170.493i			0.539534i
$317$	−511.318			−1.61299			−0.806495	−	0.591241i	$-0.798638\pi$
$317$	−511.318			−1.61299			−0.806495	+	0.591241i	$0.798638\pi$
$318$			13.3082i			0.0418496i
$319$			129.635i			0.406380i
$320$		−	368.676i		−	1.15211i
$321$			146.213i			0.455492i
$322$	−60.2400	+	82.9349i	−0.187081	+	0.257562i
$323$	96.2866			0.298101
$324$	−10.4630			−0.0322932
$325$	42.5510			0.130926
$326$	441.975			1.35575
$327$			165.438i			0.505928i
$328$	−70.5898			−0.215213
$329$			3.24641i			0.00986750i
$330$	−78.8785			−0.239026
$331$	20.6921			0.0625139			0.0312570	−	0.999511i	$-0.490049\pi$
$331$	20.6921			0.0625139			0.0312570	+	0.999511i	$0.490049\pi$
$332$		−	43.8158i		−	0.131975i
$333$			15.8933i			0.0477276i
$334$	20.0907			0.0601518
$335$	287.539			0.858325
$336$			45.8177i			0.136362i
$337$			45.6668i			0.135510i	0.997702	+	0.0677549i	$0.0215836\pi$
$337$			45.6668i			0.135510i	−0.997702	+	0.0677549i	$0.978416\pi$
$338$	177.896			0.526321
$339$		−	148.303i		−	0.437471i
$340$	−31.0594			−0.0913513
$341$		−	158.880i		−	0.465924i
$342$		−	95.6250i		−	0.279605i
$343$			18.5203i			0.0539949i
$344$			578.455i			1.68155i
$345$	−122.923	+	169.233i	−0.356299	+	0.490531i
$346$	−192.439			−0.556183
$347$	−221.394			−0.638023			−0.319012	−	0.947751i	$-0.603351\pi$
$347$	−221.394			−0.638023			−0.319012	+	0.947751i	$0.603351\pi$
$348$	50.6949			0.145675
$349$	−396.851			−1.13711			−0.568555	−	0.822645i	$-0.692497\pi$
$349$	−396.851			−1.13711			−0.568555	+	0.822645i	$0.692497\pi$
$350$			11.4436i			0.0326961i
$351$	−86.1073			−0.245320
$352$		−	92.3906i		−	0.262473i
$353$	113.672			0.322017			0.161008	−	0.986953i	$-0.448525\pi$
$353$	113.672			0.322017			0.161008	+	0.986953i	$0.448525\pi$
$354$	140.548			0.397029
$355$		−	393.131i		−	1.10741i
$356$			106.316i			0.298641i
$357$	23.3179			0.0653162
$358$	−242.930			−0.678576
$359$		−	533.662i		−	1.48652i	−0.669001	−	0.743262i	$-0.733278\pi$
$359$		−	533.662i		−	1.48652i	0.669001	−	0.743262i	$-0.266722\pi$
$360$			136.978i			0.380494i
$361$	2.92568			0.00810438
$362$		−	246.324i		−	0.680453i
$363$	163.655			0.450841
$364$		−	50.9707i		−	0.140029i
$365$		−	395.821i		−	1.08444i
$366$		−	68.8192i		−	0.188031i
$367$		−	141.823i		−	0.386438i	−0.981156	−	0.193219i	$-0.938107\pi$
$367$		−	141.823i		−	0.386438i	0.981156	−	0.193219i	$-0.0618928\pi$
$368$	186.058	+	135.144i	0.505592	+	0.367238i
$369$	24.3520			0.0659946
$370$	46.8551			0.126635
$371$	12.0682			0.0325289
$372$	−62.1313			−0.167020
$373$		−	352.593i		−	0.945288i	−0.881253	−	0.472644i	$-0.843300\pi$
$373$		−	352.593i		−	0.945288i	0.881253	−	0.472644i	$-0.156700\pi$
$374$	44.1343			0.118006
$375$		−	204.002i		−	0.544005i
$376$	10.6704			0.0283788
$377$	417.203			1.10664
$378$		−	23.1577i		−	0.0612636i
$379$		−	324.988i		−	0.857488i	−0.903426	−	0.428744i	$-0.858956\pi$
$379$		−	324.988i		−	0.857488i	0.903426	−	0.428744i	$-0.141044\pi$
$380$	115.505			0.303961
$381$	215.162			0.564730
$382$		−	50.4889i		−	0.132170i
$383$			321.831i			0.840289i	0.907457	+	0.420144i	$0.138021\pi$
$383$			321.831i			0.840289i	−0.907457	+	0.420144i	$0.861979\pi$
$384$	80.5530			0.209774
$385$			71.5292i			0.185790i
$386$	385.571			0.998889
$387$		−	199.555i		−	0.515646i
$388$		−	213.542i		−	0.550366i
$389$			247.566i			0.636417i	0.948021	+	0.318209i	$0.103081\pi$
$389$			247.566i			0.636417i	−0.948021	+	0.318209i	$0.896919\pi$
$390$			253.853i			0.650906i
$391$	68.7783	−	94.6900i	0.175904	−	0.242174i
$392$	60.8732			0.155289
$393$	−420.854			−1.07088
$394$	266.086			0.675345
$395$	−770.003			−1.94937
$396$			17.9584i			0.0453496i
$397$	−354.672			−0.893381			−0.446690	−	0.894689i	$-0.647397\pi$
$397$	−354.672			−0.893381			−0.446690	+	0.894689i	$0.647397\pi$
$398$			388.940i			0.977237i
$399$	−86.7154			−0.217332
$400$	25.6729			0.0641823
$401$			42.3965i			0.105727i	0.998602	+	0.0528634i	$0.0168348\pi$
$401$			42.3965i			0.105727i	−0.998602	+	0.0528634i	$0.983165\pi$
$402$			159.779i			0.397461i
$403$	−511.321			−1.26879
$404$	62.4920			0.154683
$405$		−	47.2545i		−	0.116678i
$406$			112.202i			0.276361i
$407$	27.2789			0.0670242
$408$		−	76.6423i		−	0.187849i
$409$	−136.489			−0.333714			−0.166857	−	0.985981i	$-0.553362\pi$
$409$	−136.489			−0.333714			−0.166857	+	0.985981i	$0.553362\pi$
$410$		−	71.7923i		−	0.175103i
$411$		−	160.185i		−	0.389745i
$412$		−	135.841i		−	0.329712i
$413$		−	127.453i		−	0.308603i
$414$	−94.0394	−	68.3057i	−0.227148	−	0.164990i
$415$	197.887			0.476836
$416$	−297.339			−0.714757
$417$	−250.966			−0.601838
$418$	−164.128			−0.392652
$419$			31.6805i			0.0756098i	0.999285	+	0.0378049i	$0.0120365\pi$
$419$			31.6805i			0.0756098i	−0.999285	+	0.0378049i	$0.987963\pi$
$420$	27.9720			0.0666001
$421$			266.709i			0.633513i	0.948507	+	0.316757i	$0.102594\pi$
$421$			266.709i			0.633513i	−0.948507	+	0.316757i	$0.897406\pi$
$422$	227.397			0.538855
$423$	−3.68108			−0.00870232
$424$		−	39.6664i		−	0.0935528i
$425$		−	13.0656i		−	0.0307427i
$426$	218.454			0.512804
$427$	−62.4071			−0.146153
$428$		−	98.1385i		−	0.229296i
$429$			147.792i			0.344504i
$430$	−588.309			−1.36816
$431$			302.414i			0.701656i	0.936440	+	0.350828i	$0.114100\pi$
$431$			302.414i			0.701656i	−0.936440	+	0.350828i	$0.885900\pi$
$432$	−51.9524			−0.120260
$433$			61.2371i			0.141425i	0.997497	+	0.0707125i	$0.0225273\pi$
$433$			61.2371i			0.141425i	−0.997497	+	0.0707125i	$0.977473\pi$
$434$		−	137.515i		−	0.316854i
$435$			228.955i			0.526334i
$436$		−	111.043i		−	0.254685i
$437$	−255.775	+	352.137i	−0.585298	+	0.805805i
$438$	219.949			0.502167
$439$	33.6468			0.0766442			0.0383221	−	0.999265i	$-0.487799\pi$
$439$	33.6468			0.0766442			0.0383221	+	0.999265i	$0.487799\pi$
$440$	235.105			0.534330
$441$	−21.0000			−0.0476190
$442$		−	142.037i		−	0.321350i
$443$	−397.241			−0.896706			−0.448353	−	0.893857i	$-0.647989\pi$
$443$	−397.241			−0.896706			−0.448353	+	0.893857i	$0.647989\pi$
$444$		−	10.6676i		−	0.0240261i
$445$	−480.161			−1.07901
$446$	−371.696			−0.833399
$447$		−	282.590i		−	0.632193i
$448$		−	185.778i		−	0.414682i
$449$	235.474			0.524441			0.262221	−	0.965008i	$-0.415545\pi$
$449$	235.474			0.524441			0.262221	+	0.965008i	$0.415545\pi$
$450$	−12.9759			−0.0288353
$451$		−	41.7972i		−	0.0926767i
$452$			99.5409i			0.220223i
$453$	2.05601			0.00453866
$454$			24.0918i			0.0530657i
$455$	230.201			0.505937
$456$			285.020i			0.625044i
$457$		−	403.103i		−	0.882063i	−0.897492	−	0.441032i	$-0.854613\pi$
$457$		−	403.103i		−	0.882063i	0.897492	−	0.441032i	$-0.145387\pi$
$458$			376.635i			0.822347i
$459$			26.4400i			0.0576035i
$460$	82.5062	−	113.590i	0.179361	−	0.246934i
$461$	160.805			0.348818			0.174409	−	0.984673i	$-0.444199\pi$
$461$	160.805			0.348818			0.174409	+	0.984673i	$0.444199\pi$
$462$	−39.7472			−0.0860330
$463$	−127.190			−0.274708			−0.137354	−	0.990522i	$-0.543860\pi$
$463$	−127.190			−0.274708			−0.137354	+	0.990522i	$0.543860\pi$
$464$	251.717			0.542494
$465$		−	280.606i		−	0.603454i
$466$	−188.091			−0.403629
$467$			711.620i			1.52381i	0.647688	+	0.761906i	$0.275736\pi$
$467$			711.620i			1.52381i	−0.647688	+	0.761906i	$0.724264\pi$
$468$	57.7954			0.123494
$469$	144.892			0.308938
$470$			10.8522i			0.0230898i
$471$		−	9.66835i		−	0.0205273i
$472$	−418.918			−0.887539
$473$	−342.511			−0.724125
$474$		−	427.874i		−	0.902688i
$475$			48.5890i			0.102293i
$476$	−15.6510			−0.0328803
$477$			13.6841i			0.0286878i
$478$	360.424			0.754026
$479$			692.110i			1.44491i	0.691420	+	0.722453i	$0.256986\pi$
$479$			692.110i			1.44491i	−0.691420	+	0.722453i	$0.743014\pi$
$480$		−	163.176i		−	0.339949i
$481$		−	87.7911i		−	0.182518i
$482$		−	126.144i		−	0.261709i
$483$	−61.9415	+	85.2775i	−0.128243	+	0.176558i
$484$	−109.846			−0.226954
$485$	964.428			1.98851
$486$	26.2583			0.0540294
$487$	440.516			0.904549			0.452275	−	0.891879i	$-0.350613\pi$
$487$	440.516			0.904549			0.452275	+	0.891879i	$0.350613\pi$
$488$			205.123i			0.420333i
$489$	454.459			0.929364
$490$			61.9102i			0.126347i
$491$	215.624			0.439152			0.219576	−	0.975595i	$-0.429533\pi$
$491$	215.624			0.439152			0.219576	+	0.975595i	$0.429533\pi$
$492$	−16.3451			−0.0332218
$493$		−	128.106i		−	0.259850i
$494$			528.212i			1.06925i
$495$	−81.1064			−0.163851
$496$	−308.503			−0.621982
$497$		−	198.100i		−	0.398592i
$498$			109.962i			0.220807i
$499$	213.342			0.427540			0.213770	−	0.976884i	$-0.431426\pi$
$499$	213.342			0.427540			0.213770	+	0.976884i	$0.431426\pi$
$500$			136.926i			0.273853i
$501$	20.6582			0.0412339
$502$		−	588.259i		−	1.17183i
$503$		−	961.743i		−	1.91201i	−0.293344	−	0.956007i	$-0.594768\pi$
$503$		−	961.743i		−	1.91201i	0.293344	−	0.956007i	$-0.405232\pi$
$504$			69.0238i			0.136952i
$505$			282.235i			0.558881i
$506$	−117.238	+	161.407i	−0.231696	+	0.318986i
$507$	182.921			0.360791
$508$	−144.417			−0.284286
$509$	52.3238			0.102797			0.0513987	−	0.998678i	$-0.483632\pi$
$509$	52.3238			0.102797			0.0513987	+	0.998678i	$0.483632\pi$
$510$	77.9479			0.152839
$511$		−	199.456i		−	0.390325i
$512$	−527.184			−1.02966
$513$		−	98.3260i		−	0.191669i
$514$	328.800			0.639688
$515$	613.506			1.19127
$516$			133.942i			0.259577i
$517$			6.31812i			0.0122207i
$518$	23.6105			0.0455801
$519$	−197.875			−0.381262
$520$		−	756.636i		−	1.45507i
$521$			303.600i			0.582725i	0.956613	+	0.291363i	$0.0941086\pi$
$521$			303.600i			0.582725i	−0.956613	+	0.291363i	$0.905891\pi$
$522$	−127.226			−0.243727
$523$			874.667i			1.67240i	0.548421	+	0.836202i	$0.315229\pi$
$523$			874.667i			1.67240i	−0.548421	+	0.836202i	$0.684771\pi$
$524$	282.478			0.539080
$525$			11.7669i			0.0224131i
$526$		−	733.001i		−	1.39354i
$527$			157.006i			0.297923i
$528$			89.1698i			0.168882i
$529$	163.595	+	503.068i	0.309253	+	0.950980i
$530$	40.3421			0.0761172
$531$	144.518			0.272162
$532$	58.2035			0.109405
$533$	−134.515			−0.252374
$534$		−	266.815i		−	0.499654i
$535$	443.227			0.828462
$536$		−	476.238i		−	0.888504i
$537$	−249.792			−0.465162
$538$	124.275			0.230994
$539$			36.0439i			0.0668718i
$540$			31.7173i			0.0587358i
$541$	199.085			0.367995			0.183998	−	0.982927i	$-0.441096\pi$
$541$	199.085			0.367995			0.183998	+	0.982927i	$0.441096\pi$
$542$	39.2311			0.0723820
$543$		−	253.282i		−	0.466448i
$544$			91.3005i			0.167832i
$545$	501.506			0.920195
$546$			127.918i			0.234282i
$547$	907.883			1.65975			0.829875	−	0.557950i	$-0.188412\pi$
$547$	907.883			1.65975			0.829875	+	0.557950i	$0.188412\pi$
$548$			107.517i			0.196198i
$549$		−	70.7630i		−	0.128894i
$550$			22.2715i			0.0404936i
$551$			476.405i			0.864619i
$552$	280.294	+	203.592i	0.507779	+	0.368827i
$553$	−388.008			−0.701642
$554$	−767.274			−1.38497
$555$	48.1786			0.0868082
$556$	168.449			0.302966
$557$			978.009i			1.75585i	0.478798	+	0.877925i	$0.341073\pi$
$557$			978.009i			1.75585i	−0.478798	+	0.877925i	$0.658927\pi$
$558$	155.927			0.279439
$559$			1102.30i			1.97191i
$560$	138.891			0.248019
$561$	45.3809			0.0808929
$562$		−	870.225i		−	1.54844i
$563$			833.089i			1.47973i	0.672754	+	0.739866i	$0.265111\pi$
$563$			833.089i			1.47973i	−0.672754	+	0.739866i	$0.734889\pi$
$564$	2.47075			0.00438076
$565$	−449.561			−0.795683
$566$			274.720i			0.485371i
$567$		−	23.8118i		−	0.0419961i
$568$	−651.126			−1.14635
$569$			410.801i			0.721971i	0.932571	+	0.360985i	$0.117560\pi$
$569$			410.801i			0.721971i	−0.932571	+	0.360985i	$0.882440\pi$
$570$	−289.875			−0.508553
$571$			19.5907i			0.0343095i	0.999853	+	0.0171547i	$0.00546079\pi$
$571$			19.5907i			0.0343095i	−0.999853	+	0.0171547i	$0.994539\pi$
$572$		−	99.1985i		−	0.173424i
$573$		−	51.9150i		−	0.0906021i
$574$		−	36.1765i		−	0.0630252i
$575$	47.7833	+	34.7075i	0.0831014	+	0.0603609i
$576$	210.652			0.365715
$577$	405.304			0.702433			0.351216	−	0.936294i	$-0.385768\pi$
$577$	405.304			0.702433			0.351216	+	0.936294i	$0.385768\pi$
$578$	443.199			0.766780
$579$	396.462			0.684736
$580$		−	153.675i		−	0.264957i
$581$	99.7163			0.171629
$582$			535.912i			0.920811i
$583$	23.4870			0.0402865
$584$	−655.581			−1.12257
$585$			261.024i			0.446194i
$586$		−	359.569i		−	0.613599i
$587$	732.080			1.24715			0.623577	−	0.781762i	$-0.285679\pi$
$587$	732.080			1.24715			0.623577	+	0.781762i	$0.285679\pi$
$588$	14.0952			0.0239715
$589$		−	583.879i		−	0.991305i
$590$		−	426.055i		−	0.722126i
$591$	273.602			0.462947
$592$		−	52.9683i		−	0.0894735i
$593$	−216.408			−0.364938			−0.182469	−	0.983212i	$-0.558409\pi$
$593$	−216.408			−0.364938			−0.182469	+	0.983212i	$0.558409\pi$
$594$		−	45.0691i		−	0.0758739i
$595$		−	70.6853i		−	0.118799i
$596$			189.675i			0.318247i
$597$			399.926i			0.669893i
$598$	519.453	+	377.306i	0.868650	+	0.630947i
$599$	311.243			0.519604			0.259802	−	0.965662i	$-0.416343\pi$
$599$	311.243			0.519604			0.259802	+	0.965662i	$0.416343\pi$
$600$	38.6759			0.0644599
$601$	−534.655			−0.889609			−0.444805	−	0.895628i	$-0.646727\pi$
$601$	−534.655			−0.889609			−0.444805	+	0.895628i	$0.646727\pi$
$602$	−296.451			−0.492444
$603$			164.292i			0.272458i
$604$	−1.38000			−0.00228477
$605$		−	496.101i		−	0.820002i
$606$	−156.832			−0.258799
$607$	655.735			1.08029			0.540144	−	0.841573i	$-0.318370\pi$
$607$	655.735			1.08029			0.540144	+	0.841573i	$0.318370\pi$
$608$		−	339.532i		−	0.558441i
$609$			115.372i			0.189445i
$610$	−208.617			−0.341995
$611$	20.3335			0.0332790
$612$		−	17.7466i		−	0.0289977i
$613$		−	236.244i		−	0.385389i	−0.981259	−	0.192695i	$-0.938277\pi$
$613$		−	236.244i		−	0.385389i	0.981259	−	0.192695i	$-0.0617227\pi$
$614$	885.650			1.44243
$615$		−	73.8202i		−	0.120033i
$616$	118.471			0.192323
$617$		−	541.746i		−	0.878032i	−0.898479	−	0.439016i	$-0.855327\pi$
$617$		−	541.746i		−	0.878032i	0.898479	−	0.439016i	$-0.144673\pi$
$618$			340.912i			0.551638i
$619$			258.742i			0.418000i	0.977916	+	0.209000i	$0.0670208\pi$
$619$			258.742i			0.418000i	−0.977916	+	0.209000i	$0.932979\pi$
$620$			188.343i			0.303780i
$621$	−96.6956	−	70.2351i	−0.155709	−	0.113100i
$622$	−878.652			−1.41262
$623$	−241.955			−0.388371
$624$	286.974			0.459894
$625$	−682.600			−1.09216
$626$		−	603.009i		−	0.963273i
$627$	−168.764			−0.269162
$628$			6.48942i			0.0103335i
$629$	−26.9570			−0.0428570
$630$	−70.1996			−0.111428
$631$			543.128i			0.860742i	0.902652	+	0.430371i	$0.141617\pi$
$631$			543.128i			0.860742i	−0.902652	+	0.430371i	$0.858383\pi$
$632$			1275.32i			2.01792i
$633$	233.820			0.369383
$634$	−861.300			−1.35852
$635$		−	652.238i		−	1.02715i
$636$		−	9.18478i		−	0.0144415i
$637$	115.999			0.182103
$638$			218.367i			0.342268i
$639$	224.625			0.351525
$640$		−	244.187i		−	0.381542i
$641$		−	244.642i		−	0.381656i	−0.981623	−	0.190828i	$-0.938883\pi$
$641$		−	244.642i		−	0.381656i	0.981623	−	0.190828i	$-0.0611173\pi$
$642$			246.292i			0.383632i
$643$			857.395i			1.33343i	0.745313	+	0.666714i	$0.232300\pi$
$643$			857.395i			1.33343i	−0.745313	+	0.666714i	$0.767700\pi$
$644$	41.5753	−	57.2384i	0.0645579	−	0.0888795i
$645$	−604.926			−0.937870
$646$	162.192			0.251071
$647$	592.573			0.915879			0.457939	−	0.888983i	$-0.348588\pi$
$647$	592.573			0.915879			0.457939	+	0.888983i	$0.348588\pi$
$648$	−78.2656			−0.120780
$649$		−	248.047i		−	0.382199i
$650$	71.6759			0.110271
$651$		−	141.399i		−	0.217202i
$652$	−305.034			−0.467843
$653$	−819.934			−1.25564			−0.627821	−	0.778358i	$-0.716053\pi$
$653$	−819.934			−1.25564			−0.627821	+	0.778358i	$0.716053\pi$
$654$			278.676i			0.426110i
$655$			1275.77i			1.94774i
$656$	−81.1591			−0.123718
$657$	226.162			0.344234
$658$			5.46848i			0.00831076i
$659$			1158.93i			1.75861i	0.476257	+	0.879306i	$0.341993\pi$
$659$			1158.93i			1.75861i	−0.476257	+	0.879306i	$0.658007\pi$
$660$	54.4388			0.0824830
$661$			268.191i			0.405735i	0.979206	+	0.202867i	$0.0650260\pi$
$661$			268.191i			0.405735i	−0.979206	+	0.202867i	$0.934974\pi$
$662$	34.8553			0.0526515
$663$		−	146.049i		−	0.220285i
$664$		−	327.752i		−	0.493602i
$665$			262.867i			0.395289i
$666$			26.7718i			0.0401979i
$667$	468.505	+	340.300i	0.702407	+	0.510195i
$668$	−13.8658			−0.0207572
$669$	−382.195			−0.571293
$670$	484.351			0.722912
$671$	−121.456			−0.181007
$672$		−	82.2250i		−	0.122359i
$673$	1060.41			1.57564			0.787822	−	0.615902i	$-0.211208\pi$
$673$	1060.41			1.57564			0.787822	+	0.615902i	$0.211208\pi$
$674$			76.9244i			0.114131i
$675$	−13.3424			−0.0197665
$676$	−122.777			−0.181623
$677$			537.261i			0.793590i	0.917907	+	0.396795i	$0.129878\pi$
$677$			537.261i			0.793590i	−0.917907	+	0.396795i	$0.870122\pi$
$678$		−	249.811i		−	0.368453i
$679$	485.980			0.715729
$680$	−232.332			−0.341664
$681$			24.7723i			0.0363764i
$682$		−	267.629i		−	0.392418i
$683$	903.944			1.32349			0.661745	−	0.749729i	$-0.269816\pi$
$683$	903.944			1.32349			0.661745	+	0.749729i	$0.269816\pi$
$684$			65.9966i			0.0964863i
$685$	−485.582			−0.708878
$686$			31.1968i			0.0454765i
$687$			387.273i			0.563717i
$688$			665.066i			0.966665i
$689$		−	75.5879i		−	0.109707i
$690$	−207.060	+	285.069i	−0.300088	+	0.413143i
$691$	662.843			0.959251			0.479626	−	0.877473i	$-0.340772\pi$
$691$	662.843			0.959251			0.479626	+	0.877473i	$0.340772\pi$
$692$	132.814			0.191928
$693$	−40.8699			−0.0589754
$694$	−372.932			−0.537366
$695$			760.774i			1.09464i
$696$	379.209			0.544841
$697$			41.3041i			0.0592598i
$698$	−668.485			−0.957715
$699$	−193.404			−0.276687
$700$		−	7.89795i		−	0.0112828i
$701$			355.080i			0.506533i	0.967397	+	0.253267i	$0.0815050\pi$
$701$			355.080i			0.506533i	−0.967397	+	0.253267i	$0.918495\pi$
$702$	−145.045			−0.206617
$703$	100.249			0.142601
$704$		−	361.558i		−	0.513577i
$705$			11.1587i			0.0158280i
$706$	191.477			0.271214
$707$			142.220i			0.201159i
$708$	−97.0008			−0.137007
$709$		−	525.671i		−	0.741427i	−0.928747	−	0.370713i	$-0.879113\pi$
$709$		−	525.671i		−	0.741427i	0.928747	−	0.370713i	$-0.120887\pi$
$710$		−	662.217i		−	0.932701i
$711$		−	439.960i		−	0.618790i
$712$			795.270i			1.11695i
$713$	−574.197	−	417.069i	−0.805325	−	0.584950i
$714$	39.2783			0.0550116
$715$	448.014			0.626594
$716$	167.661			0.234163
$717$	370.605			0.516883
$718$		−	898.938i		−	1.25200i
$719$	795.818			1.10684			0.553420	−	0.832902i	$-0.313322\pi$
$719$	795.818			1.10684			0.553420	+	0.832902i	$0.313322\pi$
$720$			157.487i			0.218732i
$721$	309.149			0.428778
$722$	4.92822			0.00682580
$723$		−	129.707i		−	0.179401i
$724$			170.003i			0.234811i
$725$	64.6460			0.0891668
$726$	275.673			0.379715
$727$			988.298i			1.35942i	0.733481	+	0.679710i	$0.237894\pi$
$727$			988.298i			1.35942i	−0.733481	+	0.679710i	$0.762106\pi$
$728$		−	381.272i		−	0.523726i
$729$	27.0000			0.0370370
$730$		−	666.748i		−	0.913354i
$731$	338.470			0.463023
$732$			47.4963i			0.0648856i
$733$		−	647.186i		−	0.882927i	−0.897279	−	0.441464i	$-0.854459\pi$
$733$		−	647.186i		−	0.882927i	0.897279	−	0.441464i	$-0.145541\pi$
$734$		−	238.897i		−	0.325472i
$735$			63.6589i			0.0866108i
$736$	−333.902	−	242.530i	−0.453671	−	0.329525i
$737$	281.987			0.382615
$738$	41.0203			0.0555830
$739$	−1318.38			−1.78400			−0.892002	−	0.452032i	$-0.850699\pi$
$739$	−1318.38			−1.78400			−0.892002	+	0.452032i	$0.850699\pi$
$740$	−32.3375			−0.0436994
$741$			543.132i			0.732971i
$742$	20.3286			0.0273970
$743$		−	787.954i		−	1.06050i	−0.847840	−	0.530252i	$-0.822097\pi$
$743$		−	787.954i		−	1.06050i	0.847840	−	0.530252i	$-0.177903\pi$
$744$	−464.756			−0.624672
$745$	−856.638			−1.14985
$746$		−	593.932i		−	0.796156i
$747$			113.068i			0.151362i
$748$	−30.4598			−0.0407216
$749$	223.344			0.298190
$750$		−	343.635i		−	0.458181i
$751$			814.508i			1.08457i	0.840196	+	0.542283i	$0.182440\pi$
$751$			814.508i			1.08457i	−0.840196	+	0.542283i	$0.817560\pi$
$752$	12.2681			0.0163140
$753$		−	604.875i		−	0.803287i
$754$	702.767			0.932051
$755$		−	6.23254i		−	0.00825503i
$756$			15.9825i			0.0211409i
$757$			504.937i			0.667024i	0.942746	+	0.333512i	$0.108234\pi$
$757$			504.937i			0.667024i	−0.942746	+	0.333512i	$0.891766\pi$
$758$		−	547.433i		−	0.722207i
$759$	−120.550	+	165.966i	−0.158827	+	0.218664i
$760$	864.004			1.13685
$761$	78.0448			0.102556			0.0512778	−	0.998684i	$-0.483671\pi$
$761$	78.0448			0.102556			0.0512778	+	0.998684i	$0.483671\pi$
$762$	362.435			0.475636
$763$	252.711			0.331207
$764$			34.8454i			0.0456092i
$765$	80.1496			0.104771
$766$			542.114i			0.707721i
$767$	−798.287			−1.04079
$768$	−350.791			−0.456759
$769$		−	1503.86i		−	1.95561i	−0.209519	−	0.977804i	$-0.567190\pi$
$769$		−	1503.86i		−	1.95561i	0.209519	−	0.977804i	$-0.432810\pi$
$770$			120.489i			0.156479i
$771$	338.087			0.438505
$772$	−266.106			−0.344697
$773$		−	843.814i		−	1.09161i	−0.837912	−	0.545805i	$-0.816224\pi$
$773$		−	843.814i		−	1.09161i	0.837912	−	0.545805i	$-0.183776\pi$
$774$		−	336.144i		−	0.434295i
$775$	−79.2296			−0.102232
$776$		−	1597.34i		−	2.05843i
$777$	24.2774			0.0312451
$778$			417.018i			0.536013i
$779$		−	153.603i		−	0.197180i
$780$		−	175.200i		−	0.224615i
$781$		−	385.540i		−	0.493650i
$782$	115.855	−	159.503i	0.148152	−	0.203967i
$783$	−130.819			−0.167074
$784$	69.9877			0.0892700
$785$	−29.3084			−0.0373356
$786$	−708.917			−0.901930
$787$		−	740.405i		−	0.940794i	−0.882455	−	0.470397i	$-0.844111\pi$
$787$		−	740.405i		−	0.940794i	0.882455	−	0.470397i	$-0.155889\pi$
$788$	−183.642			−0.233048
$789$		−	753.705i		−	0.955266i
$790$	−1297.05			−1.64183
$791$	−226.536			−0.286392
$792$			134.333i			0.169613i
$793$			390.880i			0.492913i
$794$	−597.435			−0.752437
$795$	41.4816			0.0521781
$796$		−	268.431i		−	0.337225i
$797$		−	352.346i		−	0.442090i	−0.975264	−	0.221045i	$-0.929053\pi$
$797$		−	352.346i		−	0.442090i	0.975264	−	0.221045i	$-0.0709468\pi$
$798$	−146.070			−0.183045
$799$		−	6.24358i		−	0.00781424i
$800$	−46.0729			−0.0575911
$801$		−	274.351i		−	0.342511i
$802$			71.4157i			0.0890470i
$803$		−	388.178i		−	0.483410i
$804$		−	110.273i		−	0.137156i
$805$	258.508	+	187.768i	0.321128	+	0.233252i
$806$	−861.306			−1.06862
$807$	127.785			0.158346
$808$	467.454			0.578532
$809$	632.768			0.782161			0.391080	−	0.920357i	$-0.372101\pi$
$809$	632.768			0.782161			0.391080	+	0.920357i	$0.372101\pi$
$810$		−	79.5988i		−	0.0982702i
$811$	−151.871			−0.187264			−0.0936322	−	0.995607i	$-0.529848\pi$
$811$	−151.871			−0.187264			−0.0936322	+	0.995607i	$0.529848\pi$
$812$		−	77.4377i		−	0.0953666i
$813$	40.3392			0.0496177
$814$	45.9505			0.0564502
$815$		−	1377.64i		−	1.69035i
$816$		−	88.1178i		−	0.107987i
$817$	−1258.72			−1.54066
$818$	−229.912			−0.281066
$819$			131.531i			0.160600i
$820$			49.5482i			0.0604247i
$821$	−1433.18			−1.74565			−0.872827	−	0.488029i	$-0.837716\pi$
$821$	−1433.18			−1.74565			−0.872827	+	0.488029i	$0.837716\pi$
$822$		−	269.827i		−	0.328257i
$823$	336.220			0.408530			0.204265	−	0.978916i	$-0.434520\pi$
$823$	336.220			0.408530			0.204265	+	0.978916i	$0.434520\pi$
$824$		−	1016.12i		−	1.23316i
$825$			22.9005i			0.0277582i
$826$		−	214.691i		−	0.259916i
$827$			419.306i			0.507021i	0.967333	+	0.253510i	$0.0815852\pi$
$827$			419.306i			0.507021i	−0.967333	+	0.253510i	$0.918415\pi$
$828$	64.9022	+	47.1419i	0.0783844	+	0.0569347i
$829$	−362.274			−0.437001			−0.218501	−	0.975837i	$-0.570117\pi$
$829$	−362.274			−0.437001			−0.218501	+	0.975837i	$0.570117\pi$
$830$	333.335			0.401609
$831$	−788.947			−0.949394
$832$	−1163.60			−1.39855
$833$		−	35.6186i		−	0.0427595i
$834$	−422.746			−0.506889
$835$		−	62.6227i		−	0.0749973i
$836$	113.275			0.135496
$837$	160.331			0.191555
$838$			53.3649i			0.0636813i
$839$			1338.76i			1.59566i	0.602881	+	0.797831i	$0.294019\pi$
$839$			1338.76i			1.59566i	−0.602881	+	0.797831i	$0.705981\pi$
$840$	209.237			0.249092
$841$	−207.160			−0.246326
$842$			449.264i			0.533567i
$843$		−	894.805i		−	1.06145i
$844$	−156.940			−0.185948
$845$		−	554.503i		−	0.656217i
$846$	−6.20068			−0.00732940
$847$		−	249.988i		−	0.295145i
$848$		−	45.6056i		−	0.0537801i
$849$			282.480i			0.332720i
$850$		−	22.0087i		−	0.0258926i
$851$	71.6086	−	98.5865i	0.0841464	−	0.115848i
$852$	−150.769			−0.176958
$853$	−264.897			−0.310548			−0.155274	−	0.987871i	$-0.549626\pi$
$853$	−264.897			−0.310548			−0.155274	+	0.987871i	$0.549626\pi$
$854$	−105.123			−0.123095
$855$	−298.063			−0.348612
$856$		−	734.098i		−	0.857591i
$857$	1437.97			1.67791			0.838955	−	0.544201i	$-0.183167\pi$
$857$	1437.97			1.67791			0.838955	+	0.544201i	$0.183167\pi$
$858$			248.952i			0.290154i
$859$	1291.10			1.50303			0.751514	−	0.659717i	$-0.229324\pi$
$859$	1291.10			1.50303			0.751514	+	0.659717i	$0.229324\pi$
$860$	406.027			0.472125
$861$		−	37.1983i		−	0.0432036i
$862$			509.407i			0.590960i
$863$	−668.654			−0.774802			−0.387401	−	0.921911i	$-0.626627\pi$
$863$	−668.654			−0.774802			−0.387401	+	0.921911i	$0.626627\pi$
$864$	93.2344			0.107910
$865$			599.834i			0.693450i
$866$			103.152i			0.119113i
$867$	455.717			0.525625
$868$			94.9071i			0.109340i
$869$	−755.136			−0.868971
$870$			385.669i			0.443298i
$871$		−	907.515i		−	1.04192i
$872$		−	830.623i		−	0.952549i
$873$			551.049i			0.631213i
$874$	−430.846	+	593.164i	−0.492959	+	0.678678i
$875$	−311.618			−0.356135
$876$	−151.800			−0.173288
$877$	1574.53			1.79536			0.897678	−	0.440652i	$-0.145253\pi$
$877$	1574.53			1.79536			0.897678	+	0.440652i	$0.145253\pi$
$878$	56.6771			0.0645525
$879$		−	369.725i		−	0.420620i
$880$	270.307			0.307167
$881$		−	774.263i		−	0.878845i	−0.898280	−	0.439423i	$-0.855183\pi$
$881$		−	774.263i		−	0.878845i	0.898280	−	0.439423i	$-0.144817\pi$
$882$	−35.3739			−0.0401065
$883$	953.790			1.08017			0.540085	−	0.841610i	$-0.318392\pi$
$883$	953.790			1.08017			0.540085	+	0.841610i	$0.318392\pi$
$884$			98.0282i			0.110892i
$885$		−	438.089i		−	0.495016i
$886$	−669.140			−0.755238
$887$	−787.369			−0.887676			−0.443838	−	0.896107i	$-0.646383\pi$
$887$	−787.369			−0.887676			−0.443838	+	0.896107i	$0.646383\pi$
$888$		−	79.7961i		−	0.0898605i
$889$		−	328.666i		−	0.369703i
$890$	−808.817			−0.908783
$891$		−	46.3421i		−	0.0520114i
$892$	256.530			0.287589
$893$			23.2189i			0.0260010i
$894$		−	476.015i		−	0.532456i
$895$			757.214i			0.846049i
$896$		−	123.047i		−	0.137329i
$897$	534.125	+	387.963i	0.595457	+	0.432512i
$898$	396.650			0.441703
$899$	−776.829			−0.864104
$900$	8.95543			0.00995048
$901$	−23.2099			−0.0257602
$902$		−	70.4062i		−	0.0780557i
$903$	−304.825			−0.337569
$904$			744.588i			0.823660i
$905$	−767.792			−0.848389
$906$	3.46329			0.00382262
$907$		−	1172.23i		−	1.29243i	−0.763157	−	0.646213i	$-0.776352\pi$
$907$		−	1172.23i		−	1.29243i	0.763157	−	0.646213i	$-0.223648\pi$
$908$		−	16.6272i		−	0.0183119i
$909$	−161.262			−0.177406
$910$	387.767			0.426118
$911$			623.175i			0.684056i	0.939690	+	0.342028i	$0.111114\pi$
$911$			623.175i			0.684056i	−0.939690	+	0.342028i	$0.888886\pi$
$912$			327.696i			0.359316i
$913$	194.066			0.212559
$914$		−	679.015i		−	0.742905i
$915$	−214.509			−0.234437
$916$		−	259.939i		−	0.283776i
$917$			642.865i			0.701053i
$918$			44.5374i			0.0485157i
$919$		−	255.066i		−	0.277548i	−0.990324	−	0.138774i	$-0.955684\pi$
$919$		−	255.066i		−	0.277548i	0.990324	−	0.138774i	$-0.0443161\pi$
$920$	617.165	−	849.677i	0.670831	−	0.923562i
$921$	910.666			0.988779
$922$	270.872			0.293787
$923$	−1240.78			−1.34429
$924$	27.4320			0.0296883
$925$		−	13.6033i		−	0.0147063i
$926$	−214.248			−0.231369
$927$			350.542i			0.378146i
$928$	−451.735			−0.486783
$929$	−844.115			−0.908628			−0.454314	−	0.890842i	$-0.650116\pi$
$929$	−844.115			−0.908628			−0.454314	+	0.890842i	$0.650116\pi$
$930$		−	472.673i		−	0.508251i
$931$			132.460i			0.142277i
$932$	129.813			0.139284
$933$	−903.471			−0.968350
$934$			1198.70i			1.28341i
$935$		−	137.567i		−	0.147130i
$936$	432.322			0.461883
$937$			652.990i			0.696894i	0.937328	+	0.348447i	$0.113291\pi$
$937$			652.990i			0.696894i	−0.937328	+	0.348447i	$0.886709\pi$
$938$	244.067			0.260199
$939$		−	620.041i		−	0.660321i
$940$		−	7.48977i		−	0.00796784i
$941$		−	839.486i		−	0.892121i	−0.895003	−	0.446061i	$-0.852827\pi$
$941$		−	839.486i		−	0.892121i	0.895003	−	0.446061i	$-0.147173\pi$
$942$		−	16.2861i		−	0.0172888i
$943$	−151.056	−	109.720i	−0.160187	−	0.116352i
$944$	−481.642			−0.510214
$945$	−72.1824			−0.0763835
$946$	−576.950			−0.609884
$947$	−1324.96			−1.39911			−0.699554	−	0.714580i	$-0.746618\pi$
$947$	−1324.96			−1.39911			−0.699554	+	0.714580i	$0.746618\pi$
$948$			295.302i			0.311500i
$949$	−1249.27			−1.31640
$950$			81.8468i			0.0861546i
$951$	−885.628			−0.931260
$952$	−117.073			−0.122976
$953$		−	1532.23i		−	1.60780i	−0.594767	−	0.803898i	$-0.702756\pi$
$953$		−	1532.23i		−	1.60780i	0.594767	−	0.803898i	$-0.297244\pi$
$954$			23.0504i			0.0241619i
$955$	−157.374			−0.164789
$956$	−248.751			−0.260199
$957$			224.535i			0.234624i
$958$			1165.84i			1.21695i
$959$	−244.687			−0.255148
$960$		−	638.566i		−	0.665173i
$961$	−8.92325			−0.00928538
$962$		−	147.882i		−	0.153723i
$963$			253.248i			0.262979i
$964$			87.0593i			0.0903105i
$965$		−	1201.83i		−	1.24542i
$966$	−104.339	+	143.647i	−0.108011	+	0.148703i
$967$	−58.0750			−0.0600568			−0.0300284	−	0.999549i	$-0.509560\pi$
$967$	−58.0750			−0.0600568			−0.0300284	+	0.999549i	$0.509560\pi$
$968$	−821.671			−0.848834
$969$	166.773			0.172109
$970$	1624.55			1.67480
$971$			1678.36i			1.72848i	0.503077	+	0.864241i	$0.332201\pi$
$971$			1678.36i			1.72848i	−0.503077	+	0.864241i	$0.667799\pi$
$972$	−18.1225			−0.0186445
$973$			383.358i			0.393995i
$974$	742.036			0.761844
$975$	73.7004			0.0755902
$976$			235.835i			0.241635i
$977$			973.492i			0.996409i	0.867059	+	0.498205i	$0.166007\pi$
$977$			973.492i			0.996409i	−0.867059	+	0.498205i	$0.833993\pi$
$978$	765.524			0.782744
$979$	−470.890			−0.480991
$980$		−	42.7280i		−	0.0436000i
$981$			286.548i			0.292097i
$982$	363.212			0.369869
$983$		−	1120.94i		−	1.14032i	−0.821533	−	0.570161i	$-0.806881\pi$
$983$		−	1120.94i		−	1.14032i	0.821533	−	0.570161i	$-0.193119\pi$
$984$	−122.265			−0.124253
$985$		−	829.390i		−	0.842020i
$986$		−	215.791i		−	0.218855i
$987$			5.62294i			0.00569701i
$988$		−	364.551i		−	0.368979i
$989$	−899.111	+	1237.84i	−0.909111	+	1.25161i
$990$	−136.621			−0.138002
$991$	1314.51			1.32644			0.663222	−	0.748422i	$-0.269188\pi$
$991$	1314.51			1.32644			0.663222	+	0.748422i	$0.269188\pi$
$992$	553.643			0.558108
$993$	35.8398			0.0360924
$994$		−	333.694i		−	0.335709i
$995$	1212.33			1.21842
$996$		−	75.8912i		−	0.0761960i
$997$	1273.17			1.27700			0.638501	−	0.769621i	$-0.279555\pi$
$997$	1273.17			1.27700			0.638501	+	0.769621i	$0.279555\pi$
$998$	359.369			0.360089
$999$			27.5280i			0.0275556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.33	✓	48
23.22	odd	2	inner	483.3.f.a.22.34	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.33	✓	48	1.1	even	1	trivial
483.3.f.a.22.34	yes	48	23.22	odd	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.68447 q^{2} +1.73205 q^{3} -1.16256 q^{4} -5.25050i q^{5} +2.91759 q^{6} -2.64575i q^{7} -8.69618 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.68447 q^{2} +1.73205 q^{3} -1.16256 q^{4} -5.25050i q^{5} +2.91759 q^{6} -2.64575i q^{7} -8.69618 q^{8} +3.00000 q^{9} -8.84432i q^{10} -5.14913i q^{11} -2.01361 q^{12} -16.5713 q^{13} -4.45669i q^{14} -9.09413i q^{15} -9.99824 q^{16} +5.08838i q^{17} +5.05341 q^{18} -18.9229i q^{19} +6.10400i q^{20} -4.58258i q^{21} -8.67356i q^{22} +(-18.6091 - 13.5167i) q^{23} -15.0622 q^{24} -2.56774 q^{25} -27.9140 q^{26} +5.19615 q^{27} +3.07583i q^{28} -25.1762 q^{29} -15.3188i q^{30} +30.8557 q^{31} +17.9430 q^{32} -8.91855i q^{33} +8.57123i q^{34} -13.8915 q^{35} -3.48767 q^{36} +5.29777i q^{37} -31.8750i q^{38} -28.7024 q^{39} +45.6593i q^{40} +8.11734 q^{41} -7.71922i q^{42} -66.5183i q^{43} +5.98615i q^{44} -15.7515i q^{45} +(-31.3465 - 22.7686i) q^{46} -1.22703 q^{47} -17.3175 q^{48} -7.00000 q^{49} -4.32529 q^{50} +8.81333i q^{51} +19.2651 q^{52} +4.56136i q^{53} +8.75277 q^{54} -27.0355 q^{55} +23.0079i q^{56} -32.7753i q^{57} -42.4085 q^{58} +48.1727 q^{59} +10.5724i q^{60} -23.5877i q^{61} +51.9756 q^{62} -7.93725i q^{63} +70.2174 q^{64} +87.0079i q^{65} -15.0230i q^{66} +54.7641i q^{67} -5.91552i q^{68} +(-32.2319 - 23.4117i) q^{69} -23.3999 q^{70} +74.8749 q^{71} -26.0885 q^{72} +75.3872 q^{73} +8.92393i q^{74} -4.44746 q^{75} +21.9989i q^{76} -13.6233 q^{77} -48.3484 q^{78} -146.653i q^{79} +52.4958i q^{80} +9.00000 q^{81} +13.6734 q^{82} +37.6892i q^{83} +5.32750i q^{84} +26.7165 q^{85} -112.048i q^{86} -43.6064 q^{87} +44.7777i q^{88} -91.4505i q^{89} -26.5329i q^{90} +43.8437i q^{91} +(21.6341 + 15.7140i) q^{92} +53.4437 q^{93} -2.06689 q^{94} -99.3544 q^{95} +31.0781 q^{96} +183.683i q^{97} -11.7913 q^{98} -15.4474i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more