LMFDB - Embedded newform 483.3.f.a.22.10

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			22.10
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.89983 q^{2} +1.73205 q^{3} +4.40899 q^{4} +7.66563i q^{5} -5.02265 q^{6} +2.64575i q^{7} -1.18601 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.89983 q^{2} +1.73205 q^{3} +4.40899 q^{4} +7.66563i q^{5} -5.02265 q^{6} +2.64575i q^{7} -1.18601 q^{8} +3.00000 q^{9} -22.2290i q^{10} -21.3601i q^{11} +7.63660 q^{12} -24.5575 q^{13} -7.67222i q^{14} +13.2773i q^{15} -14.1967 q^{16} -23.1246i q^{17} -8.69948 q^{18} -14.5030i q^{19} +33.7977i q^{20} +4.58258i q^{21} +61.9405i q^{22} +(19.0162 - 12.9377i) q^{23} -2.05424 q^{24} -33.7618 q^{25} +71.2125 q^{26} +5.19615 q^{27} +11.6651i q^{28} +20.1704 q^{29} -38.5017i q^{30} +48.4690 q^{31} +45.9122 q^{32} -36.9967i q^{33} +67.0573i q^{34} -20.2813 q^{35} +13.2270 q^{36} +36.8319i q^{37} +42.0562i q^{38} -42.5348 q^{39} -9.09154i q^{40} -15.4070 q^{41} -13.2887i q^{42} -55.7126i q^{43} -94.1765i q^{44} +22.9969i q^{45} +(-55.1437 + 37.5170i) q^{46} -60.0964 q^{47} -24.5895 q^{48} -7.00000 q^{49} +97.9035 q^{50} -40.0530i q^{51} -108.274 q^{52} -14.8057i q^{53} -15.0679 q^{54} +163.738 q^{55} -3.13790i q^{56} -25.1199i q^{57} -58.4906 q^{58} +95.6217 q^{59} +58.5393i q^{60} +24.7832i q^{61} -140.552 q^{62} +7.93725i q^{63} -76.3503 q^{64} -188.249i q^{65} +107.284i q^{66} -28.9116i q^{67} -101.956i q^{68} +(32.9371 - 22.4087i) q^{69} +58.8124 q^{70} +38.7353 q^{71} -3.55804 q^{72} -71.3117 q^{73} -106.806i q^{74} -58.4772 q^{75} -63.9436i q^{76} +56.5135 q^{77} +123.344 q^{78} +13.8494i q^{79} -108.827i q^{80} +9.00000 q^{81} +44.6777 q^{82} -9.87591i q^{83} +20.2046i q^{84} +177.265 q^{85} +161.557i q^{86} +34.9361 q^{87} +25.3333i q^{88} -17.9357i q^{89} -66.6870i q^{90} -64.9730i q^{91} +(83.8424 - 57.0421i) q^{92} +83.9507 q^{93} +174.269 q^{94} +111.175 q^{95} +79.5222 q^{96} +43.6587i q^{97} +20.2988 q^{98} -64.0802i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.89983			−1.44991			−0.724957	−	0.688794i	$-0.758140\pi$
$2$	−2.89983			−1.44991			−0.724957	+	0.688794i	$0.758140\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	4.40899			1.10225
$5$			7.66563i			1.53313i	0.642169	+	0.766563i	$0.278035\pi$
$5$			7.66563i			1.53313i	−0.642169	+	0.766563i	$0.721965\pi$
$6$	−5.02265			−0.837108
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−1.18601			−0.148252
$9$	3.00000			0.333333
$10$		−	22.2290i		−	2.22290i
$11$		−	21.3601i		−	1.94183i	−0.239434	−	0.970913i	$-0.576962\pi$
$11$		−	21.3601i		−	1.94183i	0.239434	−	0.970913i	$-0.423038\pi$
$12$	7.63660			0.636384
$13$	−24.5575			−1.88904			−0.944519	−	0.328458i	$-0.893471\pi$
$13$	−24.5575			−1.88904			−0.944519	+	0.328458i	$0.893471\pi$
$14$		−	7.67222i		−	0.548016i
$15$			13.2773i			0.885150i
$16$	−14.1967			−0.887297
$17$		−	23.1246i		−	1.36027i	−0.733087	−	0.680135i	$-0.761921\pi$
$17$		−	23.1246i		−	1.36027i	0.733087	−	0.680135i	$-0.238079\pi$
$18$	−8.69948			−0.483304
$19$		−	14.5030i		−	0.763316i	−0.924304	−	0.381658i	$-0.875353\pi$
$19$		−	14.5030i		−	0.763316i	0.924304	−	0.381658i	$-0.124647\pi$
$20$			33.7977i			1.68989i
$21$			4.58258i			0.218218i
$22$			61.9405i			2.81548i
$23$	19.0162	−	12.9377i	0.826792	−	0.562508i
$23$	19.0162	−	12.9377i	0.826792	−	0.562508i
$24$	−2.05424			−0.0855932
$25$	−33.7618			−1.35047
$26$	71.2125			2.73894
$27$	5.19615			0.192450
$28$			11.6651i			0.416611i
$29$	20.1704			0.695531			0.347765	−	0.937582i	$-0.386941\pi$
$29$	20.1704			0.695531			0.347765	+	0.937582i	$0.386941\pi$
$30$		−	38.5017i		−	1.28339i
$31$	48.4690			1.56352			0.781758	−	0.623582i	$-0.214323\pi$
$31$	48.4690			1.56352			0.781758	+	0.623582i	$0.214323\pi$
$32$	45.9122			1.43475
$33$		−	36.9967i		−	1.12111i
$34$			67.0573i			1.97227i
$35$	−20.2813			−0.579467
$36$	13.2270			0.367416
$37$			36.8319i			0.995457i	0.867333	+	0.497729i	$0.165832\pi$
$37$			36.8319i			0.995457i	−0.867333	+	0.497729i	$0.834168\pi$
$38$			42.0562i			1.10674i
$39$	−42.5348			−1.09064
$40$		−	9.09154i		−	0.227288i
$41$	−15.4070			−0.375781			−0.187890	−	0.982190i	$-0.560165\pi$
$41$	−15.4070			−0.375781			−0.187890	+	0.982190i	$0.560165\pi$
$42$		−	13.2887i		−	0.316397i
$43$		−	55.7126i		−	1.29564i	−0.761792	−	0.647821i	$-0.775680\pi$
$43$		−	55.7126i		−	1.29564i	0.761792	−	0.647821i	$-0.224320\pi$
$44$		−	94.1765i		−	2.14037i
$45$			22.9969i			0.511042i
$46$	−55.1437	+	37.5170i	−1.19878	+	0.815587i
$47$	−60.0964			−1.27865			−0.639324	−	0.768938i	$-0.720786\pi$
$47$	−60.0964			−1.27865			−0.639324	+	0.768938i	$0.720786\pi$
$48$	−24.5895			−0.512281
$49$	−7.00000			−0.142857
$50$	97.9035			1.95807
$51$		−	40.0530i		−	0.785352i
$52$	−108.274			−2.08219
$53$		−	14.8057i		−	0.279353i	−0.990197	−	0.139677i	$-0.955394\pi$
$53$		−	14.8057i		−	0.279353i	0.990197	−	0.139677i	$-0.0446063\pi$
$54$	−15.0679			−0.279036
$55$	163.738			2.97706
$56$		−	3.13790i		−	0.0560339i
$57$		−	25.1199i		−	0.440701i
$58$	−58.4906			−1.00846
$59$	95.6217			1.62071			0.810353	−	0.585942i	$-0.199275\pi$
$59$	95.6217			1.62071			0.810353	+	0.585942i	$0.199275\pi$
$60$			58.5393i			0.975656i
$61$			24.7832i			0.406281i	0.979150	+	0.203141i	$0.0651149\pi$
$61$			24.7832i			0.406281i	−0.979150	+	0.203141i	$0.934885\pi$
$62$	−140.552			−2.26696
$63$			7.93725i			0.125988i
$64$	−76.3503			−1.19297
$65$		−	188.249i		−	2.89613i
$66$			107.284i			1.62552i
$67$		−	28.9116i		−	0.431517i	−0.976447	−	0.215758i	$-0.930778\pi$
$67$		−	28.9116i		−	0.431517i	0.976447	−	0.215758i	$-0.0692223\pi$
$68$		−	101.956i		−	1.49936i
$69$	32.9371	−	22.4087i	0.477349	−	0.324764i
$70$	58.8124			0.840177
$71$	38.7353			0.545567			0.272784	−	0.962075i	$-0.412056\pi$
$71$	38.7353			0.545567			0.272784	+	0.962075i	$0.412056\pi$
$72$	−3.55804			−0.0494172
$73$	−71.3117			−0.976873			−0.488437	−	0.872599i	$-0.662433\pi$
$73$	−71.3117			−0.976873			−0.488437	+	0.872599i	$0.662433\pi$
$74$		−	106.806i		−	1.44333i
$75$	−58.4772			−0.779696
$76$		−	63.9436i		−	0.841364i
$77$	56.5135			0.733941
$78$	123.344			1.58133
$79$			13.8494i			0.175309i	0.996151	+	0.0876545i	$0.0279372\pi$
$79$			13.8494i			0.175309i	−0.996151	+	0.0876545i	$0.972063\pi$
$80$		−	108.827i		−	1.36034i
$81$	9.00000			0.111111
$82$	44.6777			0.544850
$83$		−	9.87591i		−	0.118987i	−0.998229	−	0.0594934i	$-0.981051\pi$
$83$		−	9.87591i		−	0.118987i	0.998229	−	0.0594934i	$-0.0189485\pi$
$84$			20.2046i			0.240530i
$85$	177.265			2.08546
$86$			161.557i			1.87857i
$87$	34.9361			0.401565
$88$			25.3333i			0.287879i
$89$		−	17.9357i		−	0.201525i	−0.994911	−	0.100763i	$-0.967872\pi$
$89$		−	17.9357i		−	0.201525i	0.994911	−	0.100763i	$-0.0321282\pi$
$90$		−	66.6870i		−	0.740966i
$91$		−	64.9730i		−	0.713989i
$92$	83.8424	−	57.0421i	0.911331	−	0.620023i
$93$	83.9507			0.902696
$94$	174.269			1.85393
$95$	111.175			1.17026
$96$	79.5222			0.828356
$97$			43.6587i			0.450089i	0.974348	+	0.225045i	$0.0722528\pi$
$97$			43.6587i			0.450089i	−0.974348	+	0.225045i	$0.927747\pi$
$98$	20.2988			0.207130
$99$		−	64.0802i		−	0.647275i
$100$	−148.856			−1.48856
$101$	−30.6066			−0.303036			−0.151518	−	0.988454i	$-0.548416\pi$
$101$	−30.6066			−0.303036			−0.151518	+	0.988454i	$0.548416\pi$
$102$			116.147i			1.13869i
$103$		−	50.1044i		−	0.486450i	−0.969970	−	0.243225i	$-0.921795\pi$
$103$		−	50.1044i		−	0.486450i	0.969970	−	0.243225i	$-0.0782054\pi$
$104$	29.1255			0.280053
$105$	−35.1283			−0.334555
$106$			42.9340i			0.405038i
$107$		−	78.8462i		−	0.736881i	−0.929651	−	0.368440i	$-0.879892\pi$
$107$		−	78.8462i		−	0.736881i	0.929651	−	0.368440i	$-0.120108\pi$
$108$	22.9098			0.212128
$109$		−	149.793i		−	1.37425i	−0.726539	−	0.687125i	$-0.758872\pi$
$109$		−	149.793i		−	1.37425i	0.726539	−	0.687125i	$-0.241128\pi$
$110$	−474.813			−4.31648
$111$			63.7947i			0.574727i
$112$		−	37.5611i		−	0.335367i
$113$			49.6484i			0.439366i	0.975571	+	0.219683i	$0.0705024\pi$
$113$			49.6484i			0.439366i	−0.975571	+	0.219683i	$0.929498\pi$
$114$			72.8434i			0.638978i
$115$	99.1754	+	145.771i	0.862395	+	1.26758i
$116$	88.9311			0.766648
$117$	−73.6725			−0.629679
$118$	−277.286			−2.34988
$119$	61.1819			0.514134
$120$		−	15.7470i		−	0.131225i
$121$	−335.253			−2.77069
$122$		−	71.8669i		−	0.589073i
$123$	−26.6857			−0.216957
$124$	213.699			1.72338
$125$		−	67.1650i		−	0.537320i
$126$		−	23.0167i		−	0.182672i
$127$	−22.9804			−0.180948			−0.0904740	−	0.995899i	$-0.528838\pi$
$127$	−22.9804			−0.180948			−0.0904740	+	0.995899i	$0.528838\pi$
$128$	37.7540			0.294953
$129$		−	96.4971i		−	0.748039i
$130$			545.888i			4.19914i
$131$	112.596			0.859509			0.429755	−	0.902946i	$-0.358600\pi$
$131$	112.596			0.859509			0.429755	+	0.902946i	$0.358600\pi$
$132$		−	163.118i		−	1.23575i
$133$	38.3713			0.288506
$134$			83.8387i			0.625662i
$135$			39.8318i			0.295050i
$136$			27.4261i			0.201662i
$137$		−	66.0321i		−	0.481986i	−0.970527	−	0.240993i	$-0.922527\pi$
$137$		−	66.0321i		−	0.481986i	0.970527	−	0.240993i	$-0.0774731\pi$
$138$	−95.5118	+	64.9814i	−0.692114	+	0.470879i
$139$	−173.970			−1.25159			−0.625793	−	0.779989i	$-0.715224\pi$
$139$	−173.970			−1.25159			−0.625793	+	0.779989i	$0.715224\pi$
$140$	−89.4203			−0.638717
$141$	−104.090			−0.738228
$142$	−112.326			−0.791025
$143$			524.550i			3.66818i
$144$	−42.5902			−0.295766
$145$			154.619i			1.06634i
$146$	206.792			1.41638
$147$	−12.1244			−0.0824786
$148$			162.392i			1.09724i
$149$		−	147.220i		−	0.988054i	−0.869446	−	0.494027i	$-0.835524\pi$
$149$		−	147.220i		−	0.988054i	0.869446	−	0.494027i	$-0.164476\pi$
$150$	169.574			1.13049
$151$	−0.584214			−0.00386897			−0.00193448	−	0.999998i	$-0.500616\pi$
$151$	−0.584214			−0.00386897			−0.00193448	+	0.999998i	$0.500616\pi$
$152$			17.2008i			0.113163i
$153$		−	69.3738i		−	0.453423i
$154$	−163.879			−1.06415
$155$			371.545i			2.39707i
$156$	−187.536			−1.20215
$157$		−	0.0946435i		−	0.000602825i	−1.00000		0.000301412i	$-0.999904\pi$
$157$		−	0.0946435i		−	0.000602825i	1.00000		0.000301412i	$-9.59425e-5\pi$
$158$		−	40.1609i		−	0.254183i
$159$		−	25.6443i		−	0.161285i
$160$			351.945i			2.19966i
$161$	34.2299	+	50.3122i	0.212608	+	0.312498i
$162$	−26.0984			−0.161101
$163$	31.6600			0.194233			0.0971167	−	0.995273i	$-0.469038\pi$
$163$	31.6600			0.194233			0.0971167	+	0.995273i	$0.469038\pi$
$164$	−67.9294			−0.414204
$165$	283.603			1.71881
$166$			28.6384i			0.172521i
$167$	129.452			0.775159			0.387579	−	0.921836i	$-0.373311\pi$
$167$	129.452			0.775159			0.387579	+	0.921836i	$0.373311\pi$
$168$		−	5.43500i		−	0.0323512i
$169$	434.070			2.56846
$170$	−514.036			−3.02374
$171$		−	43.5090i		−	0.254439i
$172$		−	245.637i		−	1.42812i
$173$	−191.724			−1.10823			−0.554117	−	0.832439i	$-0.686944\pi$
$173$	−191.724			−1.10823			−0.554117	+	0.832439i	$0.686944\pi$
$174$	−101.309			−0.582234
$175$		−	89.3254i		−	0.510431i
$176$			303.244i			1.72297i
$177$	165.622			0.935715
$178$			52.0105i			0.292194i
$179$	82.4216			0.460456			0.230228	−	0.973137i	$-0.426053\pi$
$179$	82.4216			0.460456			0.230228	+	0.973137i	$0.426053\pi$
$180$			101.393i			0.563295i
$181$		−	198.224i		−	1.09516i	−0.836752	−	0.547581i	$-0.815549\pi$
$181$		−	198.224i		−	1.09516i	0.836752	−	0.547581i	$-0.184451\pi$
$182$			188.410i			1.03522i
$183$			42.9257i			0.234567i
$184$	−22.5535	+	15.3443i	−0.122573	+	0.0833927i
$185$	−282.340			−1.52616
$186$	−243.443			−1.30883
$187$	−493.943			−2.64141
$188$	−264.965			−1.40939
$189$			13.7477i			0.0727393i
$190$	−322.387			−1.69677
$191$		−	291.406i		−	1.52569i	−0.646583	−	0.762843i	$-0.723803\pi$
$191$		−	291.406i		−	1.52569i	0.646583	−	0.762843i	$-0.276197\pi$
$192$	−132.243			−0.688764
$193$	−141.629			−0.733827			−0.366913	−	0.930255i	$-0.619585\pi$
$193$	−141.629			−0.733827			−0.366913	+	0.930255i	$0.619585\pi$
$194$		−	126.603i		−	0.652590i
$195$		−	326.056i		−	1.67208i
$196$	−30.8630			−0.157464
$197$	225.553			1.14494			0.572470	−	0.819926i	$-0.305985\pi$
$197$	225.553			1.14494			0.572470	+	0.819926i	$0.305985\pi$
$198$			185.822i			0.938493i
$199$		−	76.0047i		−	0.381933i	−0.981597	−	0.190967i	$-0.938838\pi$
$199$		−	76.0047i		−	0.381933i	0.981597	−	0.190967i	$-0.0611622\pi$
$200$	40.0420			0.200210
$201$		−	50.0764i		−	0.249136i
$202$	88.7540			0.439376
$203$			53.3658i			0.262886i
$204$		−	176.593i		−	0.865654i
$205$		−	118.104i		−	0.576119i
$206$			145.294i			0.705311i
$207$	57.0487	−	38.8130i	0.275597	−	0.187503i
$208$	348.636			1.67614
$209$	−309.785			−1.48223
$210$	101.866			0.485076
$211$	64.3162			0.304816			0.152408	−	0.988318i	$-0.451297\pi$
$211$	64.3162			0.304816			0.152408	+	0.988318i	$0.451297\pi$
$212$		−	65.2783i		−	0.307917i
$213$	67.0915			0.314983
$214$			228.640i			1.06841i
$215$	427.072			1.98638
$216$	−6.16271			−0.0285311
$217$			128.237i			0.590953i
$218$			434.375i			1.99254i
$219$	−123.516			−0.563998
$220$	721.922			3.28146
$221$			567.882i			2.56960i
$222$		−	184.994i		−	0.833305i
$223$	−206.293			−0.925080			−0.462540	−	0.886598i	$-0.653062\pi$
$223$	−206.293			−0.925080			−0.462540	+	0.886598i	$0.653062\pi$
$224$			121.472i			0.542286i
$225$	−101.286			−0.450158
$226$		−	143.972i		−	0.637043i
$227$		−	295.776i		−	1.30298i	−0.758659	−	0.651488i	$-0.774145\pi$
$227$		−	295.776i		−	1.30298i	0.758659	−	0.651488i	$-0.225855\pi$
$228$		−	110.754i		−	0.485762i
$229$			35.2342i			0.153861i	0.997036	+	0.0769305i	$0.0245120\pi$
$229$			35.2342i			0.153861i	−0.997036	+	0.0769305i	$0.975488\pi$
$230$	−287.591	−	422.711i	−1.25040	−	1.83788i
$231$	97.8842			0.423741
$232$	−23.9224			−0.103114
$233$	99.8965			0.428740			0.214370	−	0.976752i	$-0.431230\pi$
$233$	99.8965			0.428740			0.214370	+	0.976752i	$0.431230\pi$
$234$	213.637			0.912980
$235$		−	460.677i		−	1.96033i
$236$	421.596			1.78642
$237$			23.9879i			0.101215i
$238$	−177.417			−0.745449
$239$	−352.484			−1.47483			−0.737415	−	0.675440i	$-0.763954\pi$
$239$	−352.484			−1.47483			−0.737415	+	0.675440i	$0.763954\pi$
$240$		−	188.494i		−	0.785391i
$241$			263.827i			1.09472i	0.836898	+	0.547359i	$0.184367\pi$
$241$			263.827i			1.09472i	−0.836898	+	0.547359i	$0.815633\pi$
$242$	972.175			4.01725
$243$	15.5885			0.0641500
$244$			109.269i			0.447823i
$245$		−	53.6594i		−	0.219018i
$246$	77.3840			0.314569
$247$			356.157i			1.44193i
$248$	−57.4849			−0.231794
$249$		−	17.1056i		−	0.0686971i
$250$			194.767i			0.779067i
$251$		−	167.791i		−	0.668492i	−0.942486	−	0.334246i	$-0.891518\pi$
$251$		−	167.791i		−	0.668492i	0.942486	−	0.334246i	$-0.108482\pi$
$252$			34.9953i			0.138870i
$253$	−276.350	−	406.188i	−1.09229	−	1.60549i
$254$	66.6391			0.262359
$255$	307.031			1.20404
$256$	195.921			0.765317
$257$	−70.2520			−0.273354			−0.136677	−	0.990616i	$-0.543642\pi$
$257$	−70.2520			−0.273354			−0.136677	+	0.990616i	$0.543642\pi$
$258$			279.825i			1.08459i
$259$	−97.4481			−0.376247
$260$		−	829.987i		−	3.19226i
$261$	60.5112			0.231844
$262$	−326.508			−1.24621
$263$		−	35.7078i		−	0.135771i	−0.997693	−	0.0678855i	$-0.978375\pi$
$263$		−	35.7078i		−	0.135771i	0.997693	−	0.0678855i	$-0.0216253\pi$
$264$			43.8786i			0.166207i
$265$	113.495			0.428283
$266$	−111.270			−0.418309
$267$		−	31.0656i		−	0.116351i
$268$		−	127.471i		−	0.475639i
$269$	−61.0645			−0.227006			−0.113503	−	0.993538i	$-0.536207\pi$
$269$	−61.0645			−0.227006			−0.113503	+	0.993538i	$0.536207\pi$
$270$		−	115.505i		−	0.427797i
$271$	79.3467			0.292792			0.146396	−	0.989226i	$-0.453233\pi$
$271$	79.3467			0.292792			0.146396	+	0.989226i	$0.453233\pi$
$272$			328.294i			1.20696i
$273$		−	112.537i		−	0.412222i
$274$			191.482i			0.698838i
$275$			721.155i			2.62238i
$276$	145.219	−	98.7999i	0.526157	−	0.357971i
$277$	−9.47197			−0.0341948			−0.0170974	−	0.999854i	$-0.505443\pi$
$277$	−9.47197			−0.0341948			−0.0170974	+	0.999854i	$0.505443\pi$
$278$	504.484			1.81469
$279$	145.407			0.521172
$280$	24.0539			0.0859070
$281$		−	200.842i		−	0.714741i	−0.933963	−	0.357371i	$-0.883673\pi$
$281$		−	200.842i		−	0.714741i	0.933963	−	0.357371i	$-0.116327\pi$
$282$	301.843			1.07037
$283$		−	323.221i		−	1.14212i	−0.820907	−	0.571062i	$-0.806532\pi$
$283$		−	323.221i		−	1.14212i	0.820907	−	0.571062i	$-0.193468\pi$
$284$	170.784			0.601351
$285$	192.560			0.675649
$286$		−	1521.10i		−	5.31854i
$287$		−	40.7631i		−	0.142032i
$288$	137.736			0.478252
$289$	−245.747			−0.850335
$290$		−	448.367i		−	1.54609i
$291$			75.6190i			0.259859i
$292$	−314.413			−1.07676
$293$			312.073i			1.06510i	0.846400	+	0.532548i	$0.178765\pi$
$293$			312.073i			1.06510i	−0.846400	+	0.532548i	$0.821235\pi$
$294$	35.1585			0.119587
$295$			733.000i			2.48475i
$296$		−	43.6831i		−	0.147578i
$297$		−	110.990i		−	0.373704i
$298$			426.913i			1.43259i
$299$	−466.991	+	317.717i	−1.56184	+	1.06260i
$300$	−257.826			−0.859419
$301$	147.402			0.489707
$302$	1.69412			0.00560966
$303$	−53.0123			−0.174958
$304$			205.895i			0.677287i
$305$	−189.979			−0.622880
$306$			201.172i			0.657425i
$307$	256.912			0.836847			0.418423	−	0.908252i	$-0.362583\pi$
$307$	256.912			0.836847			0.418423	+	0.908252i	$0.362583\pi$
$308$	249.168			0.808985
$309$		−	86.7833i		−	0.280852i
$310$		−	1077.42i		−	3.47554i
$311$	−302.391			−0.972319			−0.486160	−	0.873870i	$-0.661603\pi$
$311$	−302.391			−0.972319			−0.486160	+	0.873870i	$0.661603\pi$
$312$	50.4469			0.161689
$313$			443.127i			1.41574i	0.706343	+	0.707870i	$0.250344\pi$
$313$			443.127i			1.41574i	−0.706343	+	0.707870i	$0.749656\pi$
$314$			0.274450i			0.000874043i
$315$	−60.8440			−0.193156
$316$			61.0620i			0.193234i
$317$	29.6095			0.0934053			0.0467027	−	0.998909i	$-0.485129\pi$
$317$	29.6095			0.0934053			0.0467027	+	0.998909i	$0.485129\pi$
$318$			74.3639i			0.233849i
$319$		−	430.841i		−	1.35060i
$320$		−	585.273i		−	1.82898i
$321$		−	136.566i		−	0.425438i
$322$	−99.2607	−	145.897i	−0.308263	−	0.453095i
$323$	−335.376			−1.03832
$324$	39.6810			0.122472
$325$	829.106			2.55110
$326$	−91.8086			−0.281622
$327$		−	259.450i		−	0.793424i
$328$	18.2729			0.0557101
$329$		−	159.000i		−	0.483283i
$330$	−822.400			−2.49212
$331$	166.644			0.503455			0.251728	−	0.967798i	$-0.419001\pi$
$331$	166.644			0.503455			0.251728	+	0.967798i	$0.419001\pi$
$332$		−	43.5428i		−	0.131153i
$333$			110.496i			0.331819i
$334$	−375.387			−1.12391
$335$	221.626			0.661569
$336$		−	65.0577i		−	0.193624i
$337$		−	373.572i		−	1.10852i	−0.832342	−	0.554262i	$-0.813001\pi$
$337$		−	373.572i		−	1.10852i	0.832342	−	0.554262i	$-0.186999\pi$
$338$	−1258.73			−3.72405
$339$			85.9936i			0.253668i
$340$	781.558			2.29870
$341$		−	1035.30i		−	3.03607i
$342$			126.169i			0.368914i
$343$		−	18.5203i		−	0.0539949i
$344$			66.0759i			0.192081i
$345$	171.777	+	252.483i	0.497904	+	0.731835i
$346$	555.967			1.60684
$347$	247.289			0.712648			0.356324	−	0.934362i	$-0.384030\pi$
$347$	247.289			0.712648			0.356324	+	0.934362i	$0.384030\pi$
$348$	154.033			0.442624
$349$	427.280			1.22430			0.612149	−	0.790743i	$-0.290305\pi$
$349$	427.280			1.22430			0.612149	+	0.790743i	$0.290305\pi$
$350$			259.028i			0.740081i
$351$	−127.604			−0.363545
$352$		−	980.687i		−	2.78604i
$353$	−461.657			−1.30781			−0.653906	−	0.756576i	$-0.726871\pi$
$353$	−461.657			−1.30781			−0.653906	+	0.756576i	$0.726871\pi$
$354$	−480.274			−1.35671
$355$			296.930i			0.836423i
$356$		−	79.0785i		−	0.222131i
$357$	105.970			0.296835
$358$	−239.008			−0.667621
$359$		−	280.808i		−	0.782195i	−0.920349	−	0.391097i	$-0.872096\pi$
$359$		−	280.808i		−	0.782195i	0.920349	−	0.391097i	$-0.127904\pi$
$360$		−	27.2746i		−	0.0757628i
$361$	150.663			0.417349
$362$			574.816i			1.58789i
$363$	−580.675			−1.59966
$364$		−	286.466i		−	0.786993i
$365$		−	546.649i		−	1.49767i
$366$		−	124.477i		−	0.340101i
$367$			712.423i			1.94121i	0.240681	+	0.970604i	$0.422629\pi$
$367$			712.423i			1.94121i	−0.240681	+	0.970604i	$0.577371\pi$
$368$	−269.968	+	183.673i	−0.733610	+	0.499111i
$369$	−46.2210			−0.125260
$370$	818.736			2.21280
$371$	39.1722			0.105586
$372$	370.138			0.994996
$373$			601.055i			1.61141i	0.592319	+	0.805704i	$0.298213\pi$
$373$			601.055i			1.61141i	−0.592319	+	0.805704i	$0.701787\pi$
$374$	1432.35			3.82981
$375$		−	116.333i		−	0.310222i
$376$	71.2752			0.189562
$377$	−495.334			−1.31388
$378$		−	39.8660i		−	0.105466i
$379$		−	495.803i		−	1.30819i	−0.756414	−	0.654093i	$-0.773050\pi$
$379$		−	495.803i		−	1.30819i	0.756414	−	0.654093i	$-0.226950\pi$
$380$	490.168			1.28992
$381$	−39.8032			−0.104470
$382$			845.027i			2.21211i
$383$			189.048i			0.493599i	0.969067	+	0.246799i	$0.0793789\pi$
$383$			189.048i			0.493599i	−0.969067	+	0.246799i	$0.920621\pi$
$384$	65.3919			0.170291
$385$			433.211i			1.12522i
$386$	410.698			1.06399
$387$		−	167.138i		−	0.431881i
$388$			192.491i			0.496110i
$389$		−	187.187i		−	0.481201i	−0.970624	−	0.240601i	$-0.922656\pi$
$389$		−	187.187i		−	0.481201i	0.970624	−	0.240601i	$-0.0773444\pi$
$390$			945.506i			2.42437i
$391$	−299.178	−	439.742i	−0.765162	−	1.12466i
$392$	8.30210			0.0211788
$393$	195.021			0.496238
$394$	−654.065			−1.66006
$395$	−106.164			−0.268771
$396$		−	282.529i		−	0.713458i
$397$	739.527			1.86279			0.931394	−	0.364012i	$-0.118593\pi$
$397$	739.527			1.86279			0.931394	+	0.364012i	$0.118593\pi$
$398$			220.401i			0.553770i
$399$	66.4611			0.166569
$400$	479.308			1.19827
$401$			270.705i			0.675076i	0.941312	+	0.337538i	$0.109594\pi$
$401$			270.705i			0.675076i	−0.941312	+	0.337538i	$0.890406\pi$
$402$			145.213i			0.361226i
$403$	−1190.28			−2.95354
$404$	−134.945			−0.334021
$405$			68.9906i			0.170347i
$406$		−	154.752i		−	0.381162i
$407$	786.733			1.93300
$408$			47.5034i			0.116430i
$409$	−135.282			−0.330764			−0.165382	−	0.986230i	$-0.552886\pi$
$409$	−135.282			−0.330764			−0.165382	+	0.986230i	$0.552886\pi$
$410$			342.482i			0.835323i
$411$		−	114.371i		−	0.278275i
$412$		−	220.910i		−	0.536189i
$413$			252.991i			0.612570i
$414$	−165.431	+	112.551i	−0.399592	+	0.271862i
$415$	75.7050			0.182422
$416$	−1127.49			−2.71031
$417$	−301.326			−0.722603
$418$	898.323			2.14910
$419$			482.244i			1.15094i	0.817823	+	0.575470i	$0.195181\pi$
$419$			482.244i			1.15094i	−0.817823	+	0.575470i	$0.804819\pi$
$420$	−154.881			−0.368763
$421$		−	267.087i		−	0.634410i	−0.948357	−	0.317205i	$-0.897256\pi$
$421$		−	267.087i		−	0.634410i	0.948357	−	0.317205i	$-0.102744\pi$
$422$	−186.506			−0.441957
$423$	−180.289			−0.426216
$424$			17.5598i			0.0414146i
$425$			780.729i			1.83701i
$426$	−194.554			−0.456699
$427$	−65.5701			−0.153560
$428$		−	347.633i		−	0.812226i
$429$			908.547i			2.11782i
$430$	−1238.44			−2.88008
$431$		−	147.922i		−	0.343207i	−0.985166	−	0.171603i	$-0.945105\pi$
$431$		−	147.922i		−	0.343207i	0.985166	−	0.171603i	$-0.0548947\pi$
$432$	−73.7684			−0.170760
$433$			459.179i			1.06046i	0.847854	+	0.530230i	$0.177894\pi$
$433$			459.179i			1.06046i	−0.847854	+	0.530230i	$0.822106\pi$
$434$		−	371.865i		−	0.856831i
$435$			267.807i			0.615649i
$436$		−	660.438i		−	1.51477i
$437$	−187.635	−	275.792i	−0.429371	−	0.631103i
$438$	358.174			0.817748
$439$	496.750			1.13155			0.565775	−	0.824560i	$-0.308577\pi$
$439$	496.750			1.13155			0.565775	+	0.824560i	$0.308577\pi$
$440$	−194.196			−0.441354
$441$	−21.0000			−0.0476190
$442$		−	1646.76i		−	3.72570i
$443$	−658.279			−1.48596			−0.742979	−	0.669315i	$-0.766588\pi$
$443$	−658.279			−1.48596			−0.742979	+	0.669315i	$0.766588\pi$
$444$			281.271i			0.633493i
$445$	137.489			0.308963
$446$	598.214			1.34129
$447$		−	254.993i		−	0.570453i
$448$		−	202.004i		−	0.450902i
$449$	773.252			1.72216			0.861082	−	0.508465i	$-0.169787\pi$
$449$	773.252			1.72216			0.861082	+	0.508465i	$0.169787\pi$
$450$	293.710			0.652690
$451$			329.095i			0.729701i
$452$			218.900i			0.484291i
$453$	−1.01189			−0.00223375
$454$			857.698i			1.88920i
$455$	498.059			1.09463
$456$			29.7926i			0.0653346i
$457$		−	175.394i		−	0.383795i	−0.981415	−	0.191898i	$-0.938536\pi$
$457$		−	175.394i		−	0.383795i	0.981415	−	0.191898i	$-0.0614642\pi$
$458$		−	102.173i		−	0.223085i
$459$		−	120.159i		−	0.261784i
$460$	437.264	+	642.705i	0.950573	+	1.39718i
$461$	−216.139			−0.468848			−0.234424	−	0.972134i	$-0.575320\pi$
$461$	−216.139			−0.468848			−0.234424	+	0.972134i	$0.575320\pi$
$462$	−283.847			−0.614388
$463$	−581.314			−1.25554			−0.627769	−	0.778400i	$-0.716032\pi$
$463$	−581.314			−1.25554			−0.627769	+	0.778400i	$0.716032\pi$
$464$	−286.354			−0.617142
$465$			643.535i			1.38395i
$466$	−289.683			−0.621636
$467$		−	557.888i		−	1.19462i	−0.802010	−	0.597311i	$-0.796236\pi$
$467$		−	557.888i		−	1.19462i	0.802010	−	0.597311i	$-0.203764\pi$
$468$	−324.821			−0.694063
$469$	76.4930			0.163098
$470$			1335.88i			2.84230i
$471$		−	0.163927i		−	0.000348041i
$472$	−113.409			−0.240273
$473$	−1190.03			−2.51591
$474$		−	69.5607i		−	0.146753i
$475$			489.648i			1.03084i
$476$	269.751			0.566703
$477$		−	44.4172i		−	0.0931177i
$478$	1022.14			2.13838
$479$			816.324i			1.70423i	0.523359	+	0.852113i	$0.324679\pi$
$479$			816.324i			1.70423i	−0.523359	+	0.852113i	$0.675321\pi$
$480$			609.587i			1.26997i
$481$		−	904.499i		−	1.88046i
$482$		−	765.052i		−	1.58725i
$483$	59.2879	+	87.1433i	0.122749	+	0.180421i
$484$	−1478.13			−3.05398
$485$	−334.671			−0.690043
$486$	−45.2038			−0.0930120
$487$	−169.233			−0.347501			−0.173751	−	0.984790i	$-0.555589\pi$
$487$	−169.233			−0.347501			−0.173751	+	0.984790i	$0.555589\pi$
$488$		−	29.3932i		−	0.0602319i
$489$	54.8368			0.112141
$490$			155.603i			0.317557i
$491$	−260.741			−0.531041			−0.265521	−	0.964105i	$-0.585544\pi$
$491$	−260.741			−0.531041			−0.265521	+	0.964105i	$0.585544\pi$
$492$	−117.657			−0.239141
$493$		−	466.432i		−	0.946109i
$494$		−	1032.79i		−	2.09068i
$495$	491.215			0.992354
$496$	−688.102			−1.38730
$497$			102.484i			0.206205i
$498$			49.6032i			0.0996048i
$499$	386.813			0.775176			0.387588	−	0.921833i	$-0.373308\pi$
$499$	386.813			0.775176			0.387588	+	0.921833i	$0.373308\pi$
$500$		−	296.130i		−	0.592260i
$501$	224.217			0.447538
$502$			486.566i			0.969255i
$503$			81.2567i			0.161544i	0.996733	+	0.0807720i	$0.0257386\pi$
$503$			81.2567i			0.161544i	−0.996733	+	0.0807720i	$0.974261\pi$
$504$		−	9.41369i		−	0.0186780i
$505$		−	234.619i		−	0.464592i
$506$	801.366	+	1177.87i	1.58373	+	2.32782i
$507$	751.831			1.48290
$508$	−101.320			−0.199450
$509$	366.298			0.719643			0.359821	−	0.933021i	$-0.382838\pi$
$509$	366.298			0.719643			0.359821	+	0.933021i	$0.382838\pi$
$510$	−890.337			−1.74576
$511$		−	188.673i		−	0.369223i
$512$	−719.153			−1.40460
$513$		−	75.3598i		−	0.146900i
$514$	203.719			0.396340
$515$	384.081			0.745789
$516$		−	425.455i		−	0.824525i
$517$			1283.66i			2.48291i
$518$	282.583			0.545526
$519$	−332.076			−0.639839
$520$			223.265i			0.429356i
$521$		−	207.640i		−	0.398541i	−0.979945	−	0.199270i	$-0.936143\pi$
$521$		−	207.640i		−	0.398541i	0.979945	−	0.199270i	$-0.0638572\pi$
$522$	−175.472			−0.336153
$523$			954.258i			1.82458i	0.409540	+	0.912292i	$0.365689\pi$
$523$			954.258i			1.82458i	−0.409540	+	0.912292i	$0.634311\pi$
$524$	496.434			0.947393
$525$		−	154.716i		−	0.294697i
$526$			103.546i			0.196856i
$527$		−	1120.83i		−	2.12680i
$528$			525.233i			0.994760i
$529$	194.233	−	492.051i	0.367171	−	0.930154i
$530$	−329.116			−0.620974
$531$	286.865			0.540236
$532$	169.179			0.318006
$533$	378.357			0.709864
$534$			90.0848i			0.168698i
$535$	604.406			1.12973
$536$			34.2896i			0.0639731i
$537$	142.758			0.265844
$538$	177.076			0.329138
$539$			149.521i			0.277404i
$540$			175.618i			0.325219i
$541$	−962.141			−1.77845			−0.889225	−	0.457471i	$-0.848756\pi$
$541$	−962.141			−1.77845			−0.889225	+	0.457471i	$0.848756\pi$
$542$	−230.092			−0.424523
$543$		−	343.335i		−	0.632292i
$544$		−	1061.70i		−	1.95165i
$545$	1148.26			2.10690
$546$			326.336i			0.597686i
$547$	−948.368			−1.73376			−0.866881	−	0.498514i	$-0.833879\pi$
$547$	−948.368			−1.73376			−0.866881	+	0.498514i	$0.833879\pi$
$548$		−	291.135i		−	0.531269i
$549$			74.3495i			0.135427i
$550$		−	2091.23i		−	3.80223i
$551$		−	292.531i		−	0.530909i
$552$	−39.0638	+	26.5770i	−0.0707678	+	0.0481468i
$553$	−36.6421			−0.0662606
$554$	27.4671			0.0495795
$555$	−489.027			−0.881129
$556$	−767.035			−1.37956
$557$			488.802i			0.877561i	0.898594	+	0.438781i	$0.144589\pi$
$557$			488.802i			0.877561i	−0.898594	+	0.438781i	$0.855411\pi$
$558$	−421.655			−0.755654
$559$			1368.16i			2.44752i
$560$	287.929			0.514159
$561$	−855.535			−1.52502
$562$			582.408i			1.03631i
$563$			634.765i			1.12747i	0.825956	+	0.563734i	$0.190636\pi$
$563$			634.765i			1.12747i	−0.825956	+	0.563734i	$0.809364\pi$
$564$	−458.933			−0.813710
$565$	−380.586			−0.673604
$566$			937.285i			1.65598i
$567$			23.8118i			0.0419961i
$568$	−45.9406			−0.0808813
$569$		−	82.6433i		−	0.145243i	−0.997360	−	0.0726215i	$-0.976863\pi$
$569$		−	82.6433i		−	0.145243i	0.997360	−	0.0726215i	$-0.0231365\pi$
$570$	−558.391			−0.979633
$571$			7.06853i			0.0123792i	0.999981	+	0.00618960i	$0.00197022\pi$
$571$			7.06853i			0.0123792i	−0.999981	+	0.00618960i	$0.998030\pi$
$572$			2312.74i			4.04325i
$573$		−	504.730i		−	0.880856i
$574$			118.206i			0.205934i
$575$	−642.023	+	436.800i	−1.11656	+	0.759652i
$576$	−229.051			−0.397658
$577$	120.115			0.208171			0.104086	−	0.994568i	$-0.466808\pi$
$577$	120.115			0.208171			0.104086	+	0.994568i	$0.466808\pi$
$578$	712.623			1.23291
$579$	−245.308			−0.423675
$580$			681.713i			1.17537i
$581$	26.1292			0.0449728
$582$		−	219.282i		−	0.376773i
$583$	−316.251			−0.542455
$584$	84.5767			0.144823
$585$		−	564.746i		−	0.965377i
$586$		−	904.958i		−	1.54430i
$587$	1063.93			1.81249			0.906247	−	0.422750i	$-0.138935\pi$
$587$	1063.93			1.81249			0.906247	+	0.422750i	$0.138935\pi$
$588$	−53.4562			−0.0909119
$589$		−	702.946i		−	1.19346i
$590$		−	2125.57i		−	3.60267i
$591$	390.669			0.661031
$592$		−	522.893i		−	0.883266i
$593$	358.957			0.605323			0.302661	−	0.953098i	$-0.402125\pi$
$593$	358.957			0.605323			0.302661	+	0.953098i	$0.402125\pi$
$594$			321.852i			0.541839i
$595$			468.998i			0.788232i
$596$		−	649.093i		−	1.08908i
$597$		−	131.644i		−	0.220509i
$598$	1354.19	−	921.323i	2.26453	−	1.54067i
$599$	−690.887			−1.15340			−0.576700	−	0.816956i	$-0.695660\pi$
$599$	−690.887			−1.15340			−0.576700	+	0.816956i	$0.695660\pi$
$600$	69.3548			0.115591
$601$	280.146			0.466133			0.233066	−	0.972461i	$-0.425124\pi$
$601$	280.146			0.466133			0.233066	+	0.972461i	$0.425124\pi$
$602$	−427.439			−0.710032
$603$		−	86.7349i		−	0.143839i
$604$	−2.57580			−0.00426456
$605$		−	2569.92i		−	4.24781i
$606$	153.726			0.253674
$607$	−972.078			−1.60145			−0.800723	−	0.599035i	$-0.795551\pi$
$607$	−972.078			−1.60145			−0.800723	+	0.599035i	$0.795551\pi$
$608$		−	665.864i		−	1.09517i
$609$			92.4323i			0.151777i
$610$	550.905			0.903123
$611$	1475.82			2.41541
$612$		−	305.869i		−	0.499785i
$613$			1043.54i			1.70234i	0.524886	+	0.851172i	$0.324108\pi$
$613$			1043.54i			1.70234i	−0.524886	+	0.851172i	$0.675892\pi$
$614$	−745.000			−1.21335
$615$		−	204.563i		−	0.332622i
$616$	−67.0257			−0.108808
$617$		−	101.207i		−	0.164031i	−0.996631	−	0.0820156i	$-0.973864\pi$
$617$		−	101.207i		−	0.164031i	0.996631	−	0.0820156i	$-0.0261357\pi$
$618$			251.657i			0.407211i
$619$		−	225.172i		−	0.363767i	−0.983320	−	0.181884i	$-0.941781\pi$
$619$		−	225.172i		−	0.363767i	0.983320	−	0.181884i	$-0.0582194\pi$
$620$			1638.14i			2.64216i
$621$	98.8112	−	67.2261i	0.159116	−	0.108255i
$622$	876.882			1.40978
$623$	47.4535			0.0761693
$624$	603.856			0.967718
$625$	−329.184			−0.526695
$626$		−	1284.99i		−	2.05270i
$627$	−536.564			−0.855763
$628$		−	0.417282i		−	0.000664463i
$629$	851.723			1.35409
$630$	176.437			0.280059
$631$		−	238.722i		−	0.378324i	−0.981946	−	0.189162i	$-0.939423\pi$
$631$		−	238.722i		−	0.378324i	0.981946	−	0.189162i	$-0.0605771\pi$
$632$		−	16.4256i		−	0.0259899i
$633$	111.399			0.175986
$634$	−85.8624			−0.135430
$635$		−	176.159i		−	0.277416i
$636$		−	113.065i		−	0.177776i
$637$	171.902			0.269862
$638$			1249.36i			1.95825i
$639$	116.206			0.181856
$640$			289.408i			0.452201i
$641$		−	13.4831i		−	0.0210345i	−0.999945	−	0.0105172i	$-0.996652\pi$
$641$		−	13.4831i		−	0.0210345i	0.999945	−	0.0105172i	$-0.00334781\pi$
$642$			396.017i			0.616849i
$643$		−	135.190i		−	0.210249i	−0.994459	−	0.105124i	$-0.966476\pi$
$643$		−	135.190i		−	0.210249i	0.994459	−	0.105124i	$-0.0335241\pi$
$644$	150.919	+	221.826i	0.234347	+	0.344451i
$645$	739.711			1.14684
$646$	972.532			1.50547
$647$	−1028.55			−1.58971			−0.794857	−	0.606796i	$-0.792454\pi$
$647$	−1028.55			−1.58971			−0.794857	+	0.606796i	$0.792454\pi$
$648$	−10.6741			−0.0164724
$649$		−	2042.49i		−	3.14713i
$650$	−2404.26			−3.69887
$651$			222.113i			0.341187i
$652$	139.589			0.214093
$653$	217.516			0.333103			0.166552	−	0.986033i	$-0.446737\pi$
$653$	217.516			0.333103			0.166552	+	0.986033i	$0.446737\pi$
$654$			752.359i			1.15040i
$655$			863.117i			1.31774i
$656$	218.729			0.333429
$657$	−213.935			−0.325624
$658$			461.073i			0.700719i
$659$			793.296i			1.20379i	0.798576	+	0.601894i	$0.205587\pi$
$659$			793.296i			1.20379i	−0.798576	+	0.601894i	$0.794413\pi$
$660$	1250.41			1.89455
$661$			179.910i			0.272179i	0.990697	+	0.136089i	$0.0434534\pi$
$661$			179.910i			0.272179i	−0.990697	+	0.136089i	$0.956547\pi$
$662$	−483.238			−0.729967
$663$			983.600i			1.48356i
$664$			11.7130i			0.0176400i
$665$			294.140i			0.442316i
$666$		−	320.418i		−	0.481109i
$667$	383.564	−	260.958i	0.575059	−	0.391241i
$668$	570.751			0.854418
$669$	−357.310			−0.534095
$670$	−642.676			−0.959218
$671$	529.370			0.788928
$672$			210.396i			0.313089i
$673$	253.556			0.376754			0.188377	−	0.982097i	$-0.439677\pi$
$673$	253.556			0.376754			0.188377	+	0.982097i	$0.439677\pi$
$674$			1083.30i			1.60726i
$675$	−175.432			−0.259899
$676$	1913.81			2.83108
$677$		−	566.422i		−	0.836665i	−0.908294	−	0.418332i	$-0.862615\pi$
$677$		−	566.422i		−	0.836665i	0.908294	−	0.418332i	$-0.137385\pi$
$678$		−	249.366i		−	0.367797i
$679$	−115.510			−0.170118
$680$	−210.238			−0.309174
$681$		−	512.298i		−	0.752274i
$682$			3002.19i			4.40204i
$683$	943.122			1.38085			0.690426	−	0.723403i	$-0.257423\pi$
$683$	943.122			1.38085			0.690426	+	0.723403i	$0.257423\pi$
$684$		−	191.831i		−	0.280455i
$685$	506.177			0.738945
$686$			53.7055i			0.0782880i
$687$			61.0274i			0.0888317i
$688$			790.938i			1.14962i
$689$			363.591i			0.527709i
$690$	−498.123	−	732.158i	−0.721917	−	1.06110i
$691$	444.301			0.642983			0.321492	−	0.946912i	$-0.395816\pi$
$691$	444.301			0.642983			0.321492	+	0.946912i	$0.395816\pi$
$692$	−845.312			−1.22155
$693$	169.540			0.244647
$694$	−717.095			−1.03328
$695$		−	1333.59i		−	1.91884i
$696$	−41.4347			−0.0595327
$697$			356.281i			0.511163i
$698$	−1239.04			−1.77513
$699$	173.026			0.247533
$700$		−	393.835i		−	0.562622i
$701$			201.877i			0.287984i	0.989579	+	0.143992i	$0.0459939\pi$
$701$			201.877i			0.287984i	−0.989579	+	0.143992i	$0.954006\pi$
$702$	370.031			0.527109
$703$	534.173			0.759848
$704$			1630.85i			2.31655i
$705$		−	797.916i		−	1.13180i
$706$	1338.73			1.89621
$707$		−	80.9776i		−	0.114537i
$708$	730.225			1.03139
$709$			848.778i			1.19715i	0.801067	+	0.598574i	$0.204266\pi$
$709$			848.778i			1.19715i	−0.801067	+	0.598574i	$0.795734\pi$
$710$		−	861.046i		−	1.21274i
$711$			41.5483i			0.0584364i
$712$			21.2720i			0.0298764i
$713$	921.697	−	627.076i	1.29270	−	0.879489i
$714$	−307.295			−0.430385
$715$	−4021.00			−5.62378
$716$	363.397			0.507537
$717$	−610.521			−0.851493
$718$			814.295i			1.13411i
$719$	−173.366			−0.241121			−0.120561	−	0.992706i	$-0.538469\pi$
$719$	−173.366			−0.241121			−0.120561	+	0.992706i	$0.538469\pi$
$720$		−	326.481i		−	0.453446i
$721$	132.564			0.183861
$722$	−436.897			−0.605120
$723$			456.962i			0.632036i
$724$		−	873.970i		−	1.20714i
$725$	−680.989			−0.939296
$726$	1683.86			2.31936
$727$		−	249.279i		−	0.342887i	−0.985194	−	0.171443i	$-0.945157\pi$
$727$		−	249.279i		−	0.342887i	0.985194	−	0.171443i	$-0.0548431\pi$
$728$			77.0589i			0.105850i
$729$	27.0000			0.0370370
$730$			1585.19i			2.17149i
$731$	−1288.33			−1.76242
$732$			189.259i			0.258551i
$733$		−	331.771i		−	0.452621i	−0.974055	−	0.226310i	$-0.927334\pi$
$733$		−	331.771i		−	0.452621i	0.974055	−	0.226310i	$-0.0726663\pi$
$734$		−	2065.90i		−	2.81458i
$735$		−	92.9408i		−	0.126450i
$736$	873.076	−	593.996i	1.18624	−	0.807060i
$737$	−617.554			−0.837930
$738$	134.033			0.181617
$739$	671.110			0.908132			0.454066	−	0.890968i	$-0.349973\pi$
$739$	671.110			0.908132			0.454066	+	0.890968i	$0.349973\pi$
$740$	−1244.83			−1.68221
$741$			616.882i			0.832500i
$742$	−113.593			−0.153090
$743$		−	1176.40i		−	1.58331i	−0.610967	−	0.791656i	$-0.709219\pi$
$743$		−	1176.40i		−	1.58331i	0.610967	−	0.791656i	$-0.290781\pi$
$744$	−99.5667			−0.133826
$745$	1128.53			1.51481
$746$		−	1742.96i		−	2.33640i
$747$		−	29.6277i		−	0.0396623i
$748$	−2177.79			−2.91149
$749$	208.608			0.278515
$750$			337.346i			0.449795i
$751$			626.464i			0.834173i	0.908867	+	0.417087i	$0.136949\pi$
$751$			626.464i			0.834173i	−0.908867	+	0.417087i	$0.863051\pi$
$752$	853.174			1.13454
$753$		−	290.623i		−	0.385954i
$754$	1436.38			1.90502
$755$		−	4.47836i		−	0.00593161i
$756$			60.6137i			0.0801768i
$757$			589.991i			0.779380i	0.920946	+	0.389690i	$0.127418\pi$
$757$			589.991i			0.779380i	−0.920946	+	0.389690i	$0.872582\pi$
$758$			1437.74i			1.89676i
$759$	−478.652	−	703.538i	−0.630635	−	0.926928i
$760$	−131.855			−0.173493
$761$	−371.524			−0.488205			−0.244103	−	0.969749i	$-0.578493\pi$
$761$	−371.524			−0.488205			−0.244103	+	0.969749i	$0.578493\pi$
$762$	115.422			0.151473
$763$	396.316			0.519418
$764$		−	1284.81i		−	1.68169i
$765$	531.794			0.695155
$766$		−	548.208i		−	0.715676i
$767$	−2348.23			−3.06158
$768$	339.345			0.441856
$769$		−	1242.64i		−	1.61591i	−0.589241	−	0.807957i	$-0.700573\pi$
$769$		−	1242.64i		−	1.61591i	0.589241	−	0.807957i	$-0.299427\pi$
$770$		−	1256.24i		−	1.63148i
$771$	−121.680			−0.157821
$772$	−624.440			−0.808860
$773$			1144.15i			1.48014i	0.672531	+	0.740069i	$0.265207\pi$
$773$			1144.15i			1.48014i	−0.672531	+	0.740069i	$0.734793\pi$
$774$			484.671i			0.626190i
$775$	−1636.40			−2.11149
$776$		−	51.7798i		−	0.0667265i
$777$	−168.785			−0.217227
$778$			542.811i			0.697700i
$779$			223.448i			0.286839i
$780$		−	1437.58i		−	1.84305i
$781$		−	827.389i		−	1.05940i
$782$	867.566	+	1275.18i	1.10942	+	1.63066i
$783$	104.808			0.133855
$784$	99.3772			0.126757
$785$	0.725501			0.000924206
$786$	−565.528			−0.719502
$787$		−	637.991i		−	0.810662i	−0.914170	−	0.405331i	$-0.867156\pi$
$787$		−	637.991i		−	0.810662i	0.914170	−	0.405331i	$-0.132844\pi$
$788$	994.462			1.26201
$789$		−	61.8477i		−	0.0783874i
$790$	307.859			0.389694
$791$	−131.357			−0.166065
$792$			76.0000i			0.0959596i
$793$		−	608.612i		−	0.767481i
$794$	−2144.50			−2.70088
$795$	196.579			0.247270
$796$		−	335.104i		−	0.420986i
$797$			43.4552i			0.0545235i	0.999628	+	0.0272617i	$0.00867875\pi$
$797$			43.4552i			0.0545235i	−0.999628	+	0.0272617i	$0.991321\pi$
$798$	−192.726			−0.241511
$799$			1389.71i			1.73931i
$800$	−1550.08			−1.93760
$801$		−	53.8072i		−	0.0671750i
$802$		−	784.998i		−	0.978801i
$803$			1523.22i			1.89692i
$804$		−	220.787i		−	0.274610i
$805$	−385.674	+	262.393i	−0.479099	+	0.325955i
$806$	3451.60			4.28238
$807$	−105.767			−0.131062
$808$	36.2999			0.0449256
$809$	749.812			0.926839			0.463419	−	0.886139i	$-0.346622\pi$
$809$	749.812			0.926839			0.463419	+	0.886139i	$0.346622\pi$
$810$		−	200.061i		−	0.246989i
$811$	826.180			1.01872			0.509359	−	0.860554i	$-0.329883\pi$
$811$	826.180			1.01872			0.509359	+	0.860554i	$0.329883\pi$
$812$			235.290i			0.289766i
$813$	137.433			0.169044
$814$	−2281.39			−2.80269
$815$			242.694i			0.297784i
$816$			568.622i			0.696840i
$817$	−808.000			−0.988984
$818$	392.295			0.479579
$819$		−	194.919i		−	0.237996i
$820$		−	520.722i		−	0.635026i
$821$	1165.81			1.41999			0.709994	−	0.704208i	$-0.248698\pi$
$821$	1165.81			1.41999			0.709994	+	0.704208i	$0.248698\pi$
$822$			331.656i			0.403474i
$823$	−1628.15			−1.97831			−0.989154	−	0.146880i	$-0.953077\pi$
$823$	−1628.15			−1.97831			−0.989154	+	0.146880i	$0.953077\pi$
$824$			59.4245i			0.0721171i
$825$			1249.08i			1.51403i
$826$		−	733.631i		−	0.888173i
$827$		−	79.7286i		−	0.0964070i	−0.998838	−	0.0482035i	$-0.984650\pi$
$827$		−	79.7286i		−	0.0964070i	0.998838	−	0.0482035i	$-0.0153496\pi$
$828$	251.527	−	171.126i	0.303777	−	0.206674i
$829$	−610.542			−0.736480			−0.368240	−	0.929731i	$-0.620040\pi$
$829$	−610.542			−0.736480			−0.368240	+	0.929731i	$0.620040\pi$
$830$	−219.531			−0.264496
$831$	−16.4059			−0.0197424
$832$	1874.97			2.25357
$833$			161.872i			0.194324i
$834$	873.792			1.04771
$835$			992.327i			1.18842i
$836$	−1365.84			−1.63378
$837$	251.852			0.300899
$838$		−	1398.42i		−	1.66876i
$839$			1565.02i			1.86534i	0.360731	+	0.932670i	$0.382527\pi$
$839$			1565.02i			1.86534i	−0.360731	+	0.932670i	$0.617473\pi$
$840$	41.6627			0.0495984
$841$	−434.156			−0.516237
$842$			774.505i			0.919840i
$843$		−	347.869i		−	0.412656i
$844$	283.570			0.335983
$845$			3327.42i			3.93777i
$846$	522.808			0.617976
$847$		−	886.996i		−	1.04722i
$848$			210.193i			0.247869i
$849$		−	559.835i		−	0.659406i
$850$		−	2263.98i		−	2.66350i
$851$	476.519	+	700.404i	0.559952	+	0.823036i
$852$	295.806			0.347190
$853$	689.669			0.808522			0.404261	−	0.914644i	$-0.367529\pi$
$853$	689.669			0.808522			0.404261	+	0.914644i	$0.367529\pi$
$854$	190.142			0.222649
$855$	333.524			0.390086
$856$			93.5127i			0.109244i
$857$	621.263			0.724928			0.362464	−	0.931998i	$-0.381936\pi$
$857$	621.263			0.724928			0.362464	+	0.931998i	$0.381936\pi$
$858$		−	2634.63i		−	3.07066i
$859$	4.73275			0.00550961			0.00275480	−	0.999996i	$-0.499123\pi$
$859$	4.73275			0.00550961			0.00275480	+	0.999996i	$0.499123\pi$
$860$	1882.96			2.18949
$861$		−	70.6038i		−	0.0820021i
$862$			428.948i			0.497620i
$863$	−1550.97			−1.79719			−0.898594	−	0.438780i	$-0.855411\pi$
$863$	−1550.97			−1.79719			−0.898594	+	0.438780i	$0.855411\pi$
$864$	238.567			0.276119
$865$		−	1469.69i		−	1.69906i
$866$		−	1331.54i		−	1.53757i
$867$	−425.646			−0.490941
$868$			565.396i			0.651378i
$869$	295.825			0.340420
$870$		−	776.595i		−	0.892638i
$871$			709.997i			0.815151i
$872$			177.657i			0.203735i
$873$			130.976i			0.150030i
$874$	544.109	+	799.750i	0.622550	+	0.915045i
$875$	177.702			0.203088
$876$	−544.579			−0.621666
$877$	1095.15			1.24875			0.624374	−	0.781125i	$-0.285354\pi$
$877$	1095.15			1.24875			0.624374	+	0.781125i	$0.285354\pi$
$878$	−1440.49			−1.64065
$879$			540.526i			0.614933i
$880$	−2324.55			−2.64154
$881$			129.206i			0.146659i	0.997308	+	0.0733294i	$0.0233624\pi$
$881$			129.206i			0.146659i	−0.997308	+	0.0733294i	$0.976638\pi$
$882$	60.8964			0.0690435
$883$	697.948			0.790428			0.395214	−	0.918589i	$-0.370670\pi$
$883$	697.948			0.790428			0.395214	+	0.918589i	$0.370670\pi$
$884$			2503.79i			2.83234i
$885$			1269.59i			1.43457i
$886$	1908.90			2.15451
$887$	0.0283614			3.19745e−5			1.59873e−5	−	1.00000i	$-0.499995\pi$
$887$	0.0283614			3.19745e−5			1.59873e−5		1.00000i	$0.499995\pi$
$888$		−	75.6614i		−	0.0852043i
$889$		−	60.8004i		−	0.0683919i
$890$	−398.693			−0.447970
$891$		−	192.241i		−	0.215758i
$892$	−909.544			−1.01967
$893$			871.579i			0.976012i
$894$			739.435i			0.827108i
$895$			631.813i			0.705937i
$896$			99.8878i			0.111482i
$897$	−808.851	+	550.302i	−0.901729	+	0.613491i
$898$	−2242.30			−2.49699
$899$	977.638			1.08747
$900$	−446.567			−0.496186
$901$	−342.376			−0.379996
$902$		−	954.318i		−	1.05800i
$903$	255.307			0.282732
$904$		−	58.8837i		−	0.0651368i
$905$	1519.51			1.67902
$906$	2.93430			0.00323874
$907$			1681.53i			1.85395i	0.375128	+	0.926973i	$0.377599\pi$
$907$			1681.53i			1.85395i	−0.375128	+	0.926973i	$0.622401\pi$
$908$		−	1304.07i		−	1.43620i
$909$	−91.8199			−0.101012
$910$	−1444.28			−1.58713
$911$		−	953.486i		−	1.04664i	−0.852137	−	0.523318i	$-0.824694\pi$
$911$		−	953.486i		−	1.04664i	0.852137	−	0.523318i	$-0.175306\pi$
$912$			356.621i			0.391032i
$913$	−210.950			−0.231052
$914$			508.614i			0.556470i
$915$	−329.052			−0.359620
$916$			155.347i			0.169593i
$917$			297.900i			0.324864i
$918$			348.440i			0.379564i
$919$			838.425i			0.912323i	0.889897	+	0.456162i	$0.150776\pi$
$919$			838.425i			0.912323i	−0.889897	+	0.456162i	$0.849224\pi$
$920$	−117.623	−	172.887i	−0.127851	−	0.187920i
$921$	444.984			0.483154
$922$	626.766			0.679790
$923$	−951.241			−1.03060
$924$	431.571			0.467068
$925$		−	1243.51i		−	1.34434i
$926$	1685.71			1.82042
$927$		−	150.313i		−	0.162150i
$928$	926.066			0.997916
$929$	865.148			0.931268			0.465634	−	0.884977i	$-0.345826\pi$
$929$	865.148			0.931268			0.465634	+	0.884977i	$0.345826\pi$
$930$		−	1866.14i		−	2.00660i
$931$			101.521i			0.109045i
$932$	440.443			0.472579
$933$	−523.757			−0.561369
$934$			1617.78i			1.73210i
$935$		−	3786.38i		−	4.04961i
$936$	87.3765			0.0933510
$937$		−	838.545i		−	0.894925i	−0.894303	−	0.447462i	$-0.852328\pi$
$937$		−	838.545i		−	0.894925i	0.894303	−	0.447462i	$-0.147672\pi$
$938$	−221.816			−0.236478
$939$			767.518i			0.817378i
$940$		−	2031.12i		−	2.16077i
$941$		−	1547.90i		−	1.64496i	−0.568797	−	0.822478i	$-0.692591\pi$
$941$		−	1547.90i		−	1.64496i	0.568797	−	0.822478i	$-0.307409\pi$
$942$			0.475361i			0.000504629i
$943$	−292.983	+	199.331i	−0.310693	+	0.211380i
$944$	−1357.52			−1.43805
$945$	−105.385			−0.111518
$946$	3450.87			3.64785
$947$	380.381			0.401669			0.200835	−	0.979625i	$-0.435635\pi$
$947$	380.381			0.401669			0.200835	+	0.979625i	$0.435635\pi$
$948$			105.763i			0.111564i
$949$	1751.24			1.84535
$950$		−	1419.89i		−	1.49463i
$951$	51.2851			0.0539276
$952$	−72.5626			−0.0762212
$953$			1420.93i			1.49101i	0.666501	+	0.745504i	$0.267791\pi$
$953$			1420.93i			1.49101i	−0.666501	+	0.745504i	$0.732209\pi$
$954$			128.802i			0.135013i
$955$	2233.81			2.33907
$956$	−1554.10			−1.62563
$957$		−	746.239i		−	0.779769i
$958$		−	2367.20i		−	2.47098i
$959$	174.705			0.182174
$960$		−	1013.72i		−	1.05596i
$961$	1388.24			1.44458
$962$			2622.89i			2.72650i
$963$		−	236.539i		−	0.245627i
$964$			1163.21i			1.20665i
$965$		−	1085.67i		−	1.12505i
$966$	−171.925	−	252.700i	−0.177976	−	0.261595i
$967$	850.587			0.879614			0.439807	−	0.898092i	$-0.355047\pi$
$967$	850.587			0.879614			0.439807	+	0.898092i	$0.355047\pi$
$968$	397.615			0.410759
$969$	−580.888			−0.599472
$970$	970.488			1.00050
$971$			833.166i			0.858050i	0.903293	+	0.429025i	$0.141143\pi$
$971$			833.166i			0.858050i	−0.903293	+	0.429025i	$0.858857\pi$
$972$	68.7294			0.0707093
$973$		−	460.282i		−	0.473055i
$974$	490.746			0.503846
$975$	1436.05			1.47288
$976$		−	351.840i		−	0.360492i
$977$		−	1594.94i		−	1.63249i	−0.577705	−	0.816245i	$-0.696052\pi$
$977$		−	1594.94i		−	1.63249i	0.577705	−	0.816245i	$-0.303948\pi$
$978$	−159.017			−0.162594
$979$	−383.109			−0.391326
$980$		−	236.584i		−	0.241412i
$981$		−	449.380i		−	0.458084i
$982$	756.105			0.769964
$983$		−	290.884i		−	0.295915i	−0.988994	−	0.147957i	$-0.952730\pi$
$983$		−	290.884i		−	0.295915i	0.988994	−	0.147957i	$-0.0472698\pi$
$984$	31.6496			0.0321643
$985$			1729.01i			1.75534i
$986$			1352.57i			1.37178i
$987$		−	275.397i		−	0.279024i
$988$			1570.30i			1.58937i
$989$	−720.792	−	1059.44i	−0.728809	−	1.07123i
$990$	−1424.44			−1.43883
$991$	717.180			0.723693			0.361847	−	0.932238i	$-0.382146\pi$
$991$	717.180			0.723693			0.361847	+	0.932238i	$0.382146\pi$
$992$	2225.32			2.24326
$993$	288.635			0.290670
$994$		−	297.186i		−	0.298980i
$995$	582.624			0.585552
$996$		−	75.4184i		−	0.0757213i
$997$	−561.555			−0.563245			−0.281622	−	0.959525i	$-0.590873\pi$
$997$	−561.555			−0.563245			−0.281622	+	0.959525i	$0.590873\pi$
$998$	−1121.69			−1.12394
$999$			191.384i			0.191576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.10	yes	48
23.22	odd	2	inner	483.3.f.a.22.9	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.9	✓	48	23.22	odd	2	inner
483.3.f.a.22.10	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)

\(f(q)\)	\(=\)	\(q-2.89983 q^{2} +1.73205 q^{3} +4.40899 q^{4} +7.66563i q^{5} -5.02265 q^{6} +2.64575i q^{7} -1.18601 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.89983 q^{2} +1.73205 q^{3} +4.40899 q^{4} +7.66563i q^{5} -5.02265 q^{6} +2.64575i q^{7} -1.18601 q^{8} +3.00000 q^{9} -22.2290i q^{10} -21.3601i q^{11} +7.63660 q^{12} -24.5575 q^{13} -7.67222i q^{14} +13.2773i q^{15} -14.1967 q^{16} -23.1246i q^{17} -8.69948 q^{18} -14.5030i q^{19} +33.7977i q^{20} +4.58258i q^{21} +61.9405i q^{22} +(19.0162 - 12.9377i) q^{23} -2.05424 q^{24} -33.7618 q^{25} +71.2125 q^{26} +5.19615 q^{27} +11.6651i q^{28} +20.1704 q^{29} -38.5017i q^{30} +48.4690 q^{31} +45.9122 q^{32} -36.9967i q^{33} +67.0573i q^{34} -20.2813 q^{35} +13.2270 q^{36} +36.8319i q^{37} +42.0562i q^{38} -42.5348 q^{39} -9.09154i q^{40} -15.4070 q^{41} -13.2887i q^{42} -55.7126i q^{43} -94.1765i q^{44} +22.9969i q^{45} +(-55.1437 + 37.5170i) q^{46} -60.0964 q^{47} -24.5895 q^{48} -7.00000 q^{49} +97.9035 q^{50} -40.0530i q^{51} -108.274 q^{52} -14.8057i q^{53} -15.0679 q^{54} +163.738 q^{55} -3.13790i q^{56} -25.1199i q^{57} -58.4906 q^{58} +95.6217 q^{59} +58.5393i q^{60} +24.7832i q^{61} -140.552 q^{62} +7.93725i q^{63} -76.3503 q^{64} -188.249i q^{65} +107.284i q^{66} -28.9116i q^{67} -101.956i q^{68} +(32.9371 - 22.4087i) q^{69} +58.8124 q^{70} +38.7353 q^{71} -3.55804 q^{72} -71.3117 q^{73} -106.806i q^{74} -58.4772 q^{75} -63.9436i q^{76} +56.5135 q^{77} +123.344 q^{78} +13.8494i q^{79} -108.827i q^{80} +9.00000 q^{81} +44.6777 q^{82} -9.87591i q^{83} +20.2046i q^{84} +177.265 q^{85} +161.557i q^{86} +34.9361 q^{87} +25.3333i q^{88} -17.9357i q^{89} -66.6870i q^{90} -64.9730i q^{91} +(83.8424 - 57.0421i) q^{92} +83.9507 q^{93} +174.269 q^{94} +111.175 q^{95} +79.5222 q^{96} +43.6587i q^{97} +20.2988 q^{98} -64.0802i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 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

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