LMFDB - Embedded newform 483.3.f.a.22.5

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			22.5
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.28216 q^{2} +1.73205 q^{3} +6.77257 q^{4} +2.78765i q^{5} -5.68487 q^{6} +2.64575i q^{7} -9.10001 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.28216 q^{2} +1.73205 q^{3} +6.77257 q^{4} +2.78765i q^{5} -5.68487 q^{6} +2.64575i q^{7} -9.10001 q^{8} +3.00000 q^{9} -9.14952i q^{10} +7.34623i q^{11} +11.7304 q^{12} +3.74384 q^{13} -8.68378i q^{14} +4.82836i q^{15} +2.77741 q^{16} +19.4029i q^{17} -9.84648 q^{18} -7.40141i q^{19} +18.8796i q^{20} +4.58258i q^{21} -24.1115i q^{22} +(-19.1329 + 12.7646i) q^{23} -15.7617 q^{24} +17.2290 q^{25} -12.2879 q^{26} +5.19615 q^{27} +17.9185i q^{28} -40.6316 q^{29} -15.8474i q^{30} +8.80682 q^{31} +27.2841 q^{32} +12.7240i q^{33} -63.6834i q^{34} -7.37544 q^{35} +20.3177 q^{36} -22.4788i q^{37} +24.2926i q^{38} +6.48451 q^{39} -25.3677i q^{40} -0.856967 q^{41} -15.0407i q^{42} -40.9123i q^{43} +49.7528i q^{44} +8.36296i q^{45} +(62.7971 - 41.8953i) q^{46} +16.9402 q^{47} +4.81062 q^{48} -7.00000 q^{49} -56.5483 q^{50} +33.6068i q^{51} +25.3554 q^{52} +34.8928i q^{53} -17.0546 q^{54} -20.4787 q^{55} -24.0764i q^{56} -12.8196i q^{57} +133.359 q^{58} -27.4908 q^{59} +32.7004i q^{60} +94.2762i q^{61} -28.9054 q^{62} +7.93725i q^{63} -100.661 q^{64} +10.4365i q^{65} -41.7623i q^{66} +61.9795i q^{67} +131.407i q^{68} +(-33.1391 + 22.1089i) q^{69} +24.2074 q^{70} -77.3081 q^{71} -27.3000 q^{72} -132.608 q^{73} +73.7790i q^{74} +29.8415 q^{75} -50.1265i q^{76} -19.4363 q^{77} -21.2832 q^{78} +124.048i q^{79} +7.74246i q^{80} +9.00000 q^{81} +2.81270 q^{82} +59.1946i q^{83} +31.0358i q^{84} -54.0885 q^{85} +134.281i q^{86} -70.3760 q^{87} -66.8508i q^{88} +66.6559i q^{89} -27.4486i q^{90} +9.90526i q^{91} +(-129.579 + 86.4489i) q^{92} +15.2539 q^{93} -55.6003 q^{94} +20.6325 q^{95} +47.2575 q^{96} +7.24707i q^{97} +22.9751 q^{98} +22.0387i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.28216			−1.64108			−0.820540	−	0.571589i	$-0.806327\pi$
$2$	−3.28216			−1.64108			−0.820540	+	0.571589i	$0.806327\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	6.77257			1.69314
$5$			2.78765i			0.557530i	0.960359	+	0.278765i	$0.0899251\pi$
$5$			2.78765i			0.557530i	−0.960359	+	0.278765i	$0.910075\pi$
$6$	−5.68487			−0.947478
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−9.10001			−1.13750
$9$	3.00000			0.333333
$10$		−	9.14952i		−	0.914952i
$11$			7.34623i			0.667839i	0.942602	+	0.333919i	$0.108371\pi$
$11$			7.34623i			0.667839i	−0.942602	+	0.333919i	$0.891629\pi$
$12$	11.7304			0.977536
$13$	3.74384			0.287987			0.143994	−	0.989579i	$-0.454006\pi$
$13$	3.74384			0.287987			0.143994	+	0.989579i	$0.454006\pi$
$14$		−	8.68378i		−	0.620270i
$15$			4.82836i			0.321890i
$16$	2.77741			0.173588
$17$			19.4029i			1.14135i	0.821177	+	0.570673i	$0.193318\pi$
$17$			19.4029i			1.14135i	−0.821177	+	0.570673i	$0.806682\pi$
$18$	−9.84648			−0.547027
$19$		−	7.40141i		−	0.389548i	−0.980848	−	0.194774i	$-0.937603\pi$
$19$		−	7.40141i		−	0.389548i	0.980848	−	0.194774i	$-0.0623973\pi$
$20$			18.8796i			0.943978i
$21$			4.58258i			0.218218i
$22$		−	24.1115i		−	1.09598i
$23$	−19.1329	+	12.7646i	−0.831863	+	0.554981i
$23$	−19.1329	+	12.7646i	−0.831863	+	0.554981i
$24$	−15.7617			−0.656737
$25$	17.2290			0.689160
$26$	−12.2879			−0.472610
$27$	5.19615			0.192450
$28$			17.9185i			0.639948i
$29$	−40.6316			−1.40109			−0.700544	−	0.713609i	$-0.747059\pi$
$29$	−40.6316			−1.40109			−0.700544	+	0.713609i	$0.747059\pi$
$30$		−	15.8474i		−	0.528248i
$31$	8.80682			0.284091			0.142045	−	0.989860i	$-0.454632\pi$
$31$	8.80682			0.284091			0.142045	+	0.989860i	$0.454632\pi$
$32$	27.2841			0.852629
$33$			12.7240i			0.385577i
$34$		−	63.6834i		−	1.87304i
$35$	−7.37544			−0.210727
$36$	20.3177			0.564381
$37$		−	22.4788i		−	0.607535i	−0.952746	−	0.303767i	$-0.901755\pi$
$37$		−	22.4788i		−	0.607535i	0.952746	−	0.303767i	$-0.0982446\pi$
$38$			24.2926i			0.639279i
$39$	6.48451			0.166270
$40$		−	25.3677i		−	0.634192i
$41$	−0.856967			−0.0209016			−0.0104508	−	0.999945i	$-0.503327\pi$
$41$	−0.856967			−0.0209016			−0.0104508	+	0.999945i	$0.503327\pi$
$42$		−	15.0407i		−	0.358113i
$43$		−	40.9123i		−	0.951448i	−0.879595	−	0.475724i	$-0.842186\pi$
$43$		−	40.9123i		−	0.951448i	0.879595	−	0.475724i	$-0.157814\pi$
$44$			49.7528i			1.13075i
$45$			8.36296i			0.185843i
$46$	62.7971	−	41.8953i	1.36515	−	0.910768i
$47$	16.9402			0.360429			0.180214	−	0.983627i	$-0.442321\pi$
$47$	16.9402			0.360429			0.180214	+	0.983627i	$0.442321\pi$
$48$	4.81062			0.100221
$49$	−7.00000			−0.142857
$50$	−56.5483			−1.13097
$51$			33.6068i			0.658957i
$52$	25.3554			0.487604
$53$			34.8928i			0.658354i	0.944268	+	0.329177i	$0.106771\pi$
$53$			34.8928i			0.658354i	−0.944268	+	0.329177i	$0.893229\pi$
$54$	−17.0546			−0.315826
$55$	−20.4787			−0.372341
$56$		−	24.0764i		−	0.429935i
$57$		−	12.8196i		−	0.224905i
$58$	133.359			2.29930
$59$	−27.4908			−0.465945			−0.232973	−	0.972483i	$-0.574845\pi$
$59$	−27.4908			−0.465945			−0.232973	+	0.972483i	$0.574845\pi$
$60$			32.7004i			0.545006i
$61$			94.2762i			1.54551i	0.634704	+	0.772756i	$0.281122\pi$
$61$			94.2762i			1.54551i	−0.634704	+	0.772756i	$0.718878\pi$
$62$	−28.9054			−0.466216
$63$			7.93725i			0.125988i
$64$	−100.661			−1.57282
$65$			10.4365i			0.160562i
$66$		−	41.7623i		−	0.632762i
$67$			61.9795i			0.925067i	0.886602	+	0.462533i	$0.153059\pi$
$67$			61.9795i			0.925067i	−0.886602	+	0.462533i	$0.846941\pi$
$68$			131.407i			1.93246i
$69$	−33.1391	+	22.1089i	−0.480276	+	0.320418i
$70$	24.2074			0.345819
$71$	−77.3081			−1.08885			−0.544423	−	0.838811i	$-0.683251\pi$
$71$	−77.3081			−1.08885			−0.544423	+	0.838811i	$0.683251\pi$
$72$	−27.3000			−0.379167
$73$	−132.608			−1.81654			−0.908272	−	0.418379i	$-0.862598\pi$
$73$	−132.608			−1.81654			−0.908272	+	0.418379i	$0.862598\pi$
$74$			73.7790i			0.997013i
$75$	29.8415			0.397887
$76$		−	50.1265i		−	0.659560i
$77$	−19.4363			−0.252419
$78$	−21.2832			−0.272862
$79$			124.048i			1.57023i	0.619351	+	0.785114i	$0.287396\pi$
$79$			124.048i			1.57023i	−0.619351	+	0.785114i	$0.712604\pi$
$80$			7.74246i			0.0967808i
$81$	9.00000			0.111111
$82$	2.81270			0.0343012
$83$			59.1946i			0.713188i	0.934259	+	0.356594i	$0.116062\pi$
$83$			59.1946i			0.713188i	−0.934259	+	0.356594i	$0.883938\pi$
$84$			31.0358i			0.369474i
$85$	−54.0885			−0.636335
$86$			134.281i			1.56140i
$87$	−70.3760			−0.808919
$88$		−	66.8508i		−	0.759668i
$89$			66.6559i			0.748943i	0.927238	+	0.374471i	$0.122176\pi$
$89$			66.6559i			0.748943i	−0.927238	+	0.374471i	$0.877824\pi$
$90$		−	27.4486i		−	0.304984i
$91$			9.90526i			0.108849i
$92$	−129.579	+	86.4489i	−1.40846	+	0.939662i
$93$	15.2539			0.164020
$94$	−55.6003			−0.591492
$95$	20.6325			0.217185
$96$	47.2575			0.492266
$97$			7.24707i			0.0747120i	0.999302	+	0.0373560i	$0.0118936\pi$
$97$			7.24707i			0.0747120i	−0.999302	+	0.0373560i	$0.988106\pi$
$98$	22.9751			0.234440
$99$			22.0387i			0.222613i
$100$	116.685			1.16685
$101$	20.6541			0.204496			0.102248	−	0.994759i	$-0.467396\pi$
$101$	20.6541			0.204496			0.102248	+	0.994759i	$0.467396\pi$
$102$		−	110.303i		−	1.08140i
$103$		−	117.447i		−	1.14026i	−0.821553	−	0.570132i	$-0.806892\pi$
$103$		−	117.447i		−	1.14026i	0.821553	−	0.570132i	$-0.193108\pi$
$104$	−34.0689			−0.327586
$105$	−12.7746			−0.121663
$106$		−	114.524i		−	1.08041i
$107$			85.9178i			0.802970i	0.915866	+	0.401485i	$0.131506\pi$
$107$			85.9178i			0.802970i	−0.915866	+	0.401485i	$0.868494\pi$
$108$	35.1913			0.325845
$109$			191.485i			1.75674i	0.477977	+	0.878372i	$0.341370\pi$
$109$			191.485i			1.75674i	−0.477977	+	0.878372i	$0.658630\pi$
$110$	67.2144			0.611040
$111$		−	38.9344i		−	0.350760i
$112$			7.34834i			0.0656102i
$113$		−	133.624i		−	1.18251i	−0.806483	−	0.591257i	$-0.798632\pi$
$113$		−	133.624i		−	1.18251i	0.806483	−	0.591257i	$-0.201368\pi$
$114$			42.0760i			0.369088i
$115$	−35.5832	−	53.3357i	−0.309419	−	0.463789i
$116$	−275.180			−2.37224
$117$	11.2315			0.0959958
$118$	90.2291			0.764654
$119$	−51.3352			−0.431388
$120$		−	43.9381i		−	0.366151i
$121$	67.0329			0.553991
$122$		−	309.429i		−	2.53631i
$123$	−1.48431			−0.0120676
$124$	59.6448			0.481006
$125$			117.720i			0.941758i
$126$		−	26.0513i		−	0.206757i
$127$	−5.96059			−0.0469337			−0.0234669	−	0.999725i	$-0.507470\pi$
$127$	−5.96059			−0.0469337			−0.0234669	+	0.999725i	$0.507470\pi$
$128$	221.247			1.72849
$129$		−	70.8621i		−	0.549319i
$130$		−	34.2543i		−	0.263495i
$131$	67.0342			0.511711			0.255856	−	0.966715i	$-0.417643\pi$
$131$	67.0342			0.511711			0.255856	+	0.966715i	$0.417643\pi$
$132$			86.1744i			0.652837i
$133$	19.5823			0.147235
$134$		−	203.427i		−	1.51811i
$135$			14.4851i			0.107297i
$136$		−	176.567i		−	1.29828i
$137$			2.58095i			0.0188391i	0.999956	+	0.00941953i	$0.00299837\pi$
$137$			2.58095i			0.0188391i	−0.999956	+	0.00941953i	$0.997002\pi$
$138$	108.768	−	72.5648i	0.788172	−	0.525832i
$139$	22.8055			0.164069			0.0820343	−	0.996630i	$-0.473858\pi$
$139$	22.8055			0.164069			0.0820343	+	0.996630i	$0.473858\pi$
$140$	−49.9506			−0.356790
$141$	29.3412			0.208094
$142$	253.738			1.78688
$143$			27.5031i			0.192329i
$144$	8.33224			0.0578628
$145$		−	113.267i		−	0.781150i
$146$	435.240			2.98109
$147$	−12.1244			−0.0824786
$148$		−	152.239i		−	1.02864i
$149$		−	131.419i		−	0.882006i	−0.897506	−	0.441003i	$-0.854623\pi$
$149$		−	131.419i		−	0.882006i	0.897506	−	0.441003i	$-0.145377\pi$
$150$	−97.9445			−0.652964
$151$	−99.7634			−0.660685			−0.330342	−	0.943861i	$-0.607164\pi$
$151$	−99.7634			−0.660685			−0.330342	+	0.943861i	$0.607164\pi$
$152$			67.3529i			0.443111i
$153$			58.2087i			0.380449i
$154$	63.7930			0.414240
$155$			24.5503i			0.158389i
$156$	43.9168			0.281518
$157$		−	31.6630i		−	0.201675i	−0.994903	−	0.100838i	$-0.967848\pi$
$157$		−	31.6630i		−	0.201675i	0.994903	−	0.100838i	$-0.0321523\pi$
$158$		−	407.145i		−	2.57687i
$159$			60.4361i			0.380101i
$160$			76.0587i			0.475367i
$161$	−33.7719	−	50.6208i	−0.209763	−	0.314415i
$162$	−29.5394			−0.182342
$163$	105.168			0.645201			0.322601	−	0.946535i	$-0.395443\pi$
$163$	105.168			0.645201			0.322601	+	0.946535i	$0.395443\pi$
$164$	−5.80387			−0.0353894
$165$	−35.4702			−0.214971
$166$		−	194.286i		−	1.17040i
$167$	69.6119			0.416837			0.208419	−	0.978040i	$-0.433168\pi$
$167$	69.6119			0.416837			0.208419	+	0.978040i	$0.433168\pi$
$168$		−	41.7015i		−	0.248223i
$169$	−154.984			−0.917063
$170$	177.527			1.04428
$171$		−	22.2042i		−	0.129849i
$172$		−	277.081i		−	1.61094i
$173$	93.3923			0.539840			0.269920	−	0.962883i	$-0.413003\pi$
$173$	93.3923			0.539840			0.269920	+	0.962883i	$0.413003\pi$
$174$	230.985			1.32750
$175$			45.5836i			0.260478i
$176$			20.4035i			0.115929i
$177$	−47.6154			−0.269014
$178$		−	218.775i		−	1.22907i
$179$	−18.6887			−0.104406			−0.0522032	−	0.998636i	$-0.516624\pi$
$179$	−18.6887			−0.104406			−0.0522032	+	0.998636i	$0.516624\pi$
$180$			56.6387i			0.314659i
$181$		−	141.499i		−	0.781761i	−0.920441	−	0.390881i	$-0.872171\pi$
$181$		−	141.499i		−	0.781761i	0.920441	−	0.390881i	$-0.127829\pi$
$182$		−	32.5106i		−	0.178630i
$183$			163.291i			0.892301i
$184$	174.109	−	116.158i	0.946246	−	0.631292i
$185$	62.6630			0.338719
$186$	−50.0656			−0.269170
$187$	−142.538			−0.762235
$188$	114.728			0.610257
$189$			13.7477i			0.0727393i
$190$	−67.7193			−0.356417
$191$		−	289.469i		−	1.51554i	−0.652519	−	0.757772i	$-0.726288\pi$
$191$		−	289.469i		−	1.51554i	0.652519	−	0.757772i	$-0.273712\pi$
$192$	−174.349			−0.908069
$193$	157.578			0.816465			0.408233	−	0.912878i	$-0.366145\pi$
$193$	157.578			0.816465			0.408233	+	0.912878i	$0.366145\pi$
$194$		−	23.7860i		−	0.122608i
$195$			18.0766i			0.0927004i
$196$	−47.4080			−0.241877
$197$	−7.97780			−0.0404964			−0.0202482	−	0.999795i	$-0.506446\pi$
$197$	−7.97780			−0.0404964			−0.0202482	+	0.999795i	$0.506446\pi$
$198$		−	72.3345i		−	0.365326i
$199$			299.579i			1.50542i	0.658350	+	0.752712i	$0.271255\pi$
$199$			299.579i			1.50542i	−0.658350	+	0.752712i	$0.728745\pi$
$200$	−156.784			−0.783920
$201$			107.352i			0.534088i
$202$	−67.7900			−0.335594
$203$		−	107.501i		−	0.529562i
$204$			227.604i			1.11571i
$205$		−	2.38893i		−	0.0116533i
$206$			385.480i			1.87126i
$207$	−57.3986	+	38.2937i	−0.277288	+	0.184994i
$208$	10.3982			0.0499912
$209$	54.3724			0.260155
$210$	41.9284			0.199659
$211$	141.461			0.670433			0.335216	−	0.942141i	$-0.391191\pi$
$211$	141.461			0.670433			0.335216	+	0.942141i	$0.391191\pi$
$212$			236.314i			1.11469i
$213$	−133.902			−0.628646
$214$		−	281.996i		−	1.31774i
$215$	114.049			0.530461
$216$	−47.2850			−0.218912
$217$			23.3006i			0.107376i
$218$		−	628.485i		−	2.88296i
$219$	−229.683			−1.04878
$220$	−138.694			−0.630425
$221$			72.6412i			0.328693i
$222$			127.789i			0.575626i
$223$	142.812			0.640412			0.320206	−	0.947348i	$-0.396248\pi$
$223$	142.812			0.640412			0.320206	+	0.947348i	$0.396248\pi$
$224$			72.1870i			0.322264i
$225$	51.6870			0.229720
$226$			438.576i			1.94060i
$227$		−	220.920i		−	0.973218i	−0.873620	−	0.486609i	$-0.838234\pi$
$227$		−	220.920i		−	0.973218i	0.873620	−	0.486609i	$-0.161766\pi$
$228$		−	86.8217i		−	0.380797i
$229$			342.678i			1.49641i	0.663468	+	0.748205i	$0.269084\pi$
$229$			342.678i			1.49641i	−0.663468	+	0.748205i	$0.730916\pi$
$230$	116.790	+	175.056i	0.507781	+	0.761115i
$231$	−33.6646			−0.145734
$232$	369.748			1.59374
$233$	−57.8140			−0.248129			−0.124064	−	0.992274i	$-0.539593\pi$
$233$	−57.8140			−0.248129			−0.124064	+	0.992274i	$0.539593\pi$
$234$	−36.8636			−0.157537
$235$			47.2233i			0.200950i
$236$	−186.183			−0.788912
$237$			214.857i			0.906572i
$238$	168.490			0.707943
$239$	−369.300			−1.54519			−0.772595	−	0.634899i	$-0.781042\pi$
$239$	−369.300			−1.54519			−0.772595	+	0.634899i	$0.781042\pi$
$240$			13.4103i			0.0558764i
$241$			37.1026i			0.153953i	0.997033	+	0.0769763i	$0.0245266\pi$
$241$			37.1026i			0.153953i	−0.997033	+	0.0769763i	$0.975473\pi$
$242$	−220.013			−0.909144
$243$	15.5885			0.0641500
$244$			638.492i			2.61677i
$245$		−	19.5136i		−	0.0796472i
$246$	4.87174			0.0198038
$247$		−	27.7096i		−	0.112185i
$248$	−80.1421			−0.323154
$249$			102.528i			0.411759i
$250$		−	386.375i		−	1.54550i
$251$		−	196.331i		−	0.782196i	−0.920349	−	0.391098i	$-0.872095\pi$
$251$		−	196.331i		−	0.782196i	0.920349	−	0.391098i	$-0.127905\pi$
$252$			53.7556i			0.213316i
$253$	−93.7714	−	140.554i	−0.370638	−	0.555551i
$254$	19.5636			0.0770220
$255$	−93.6841			−0.367388
$256$	−323.527			−1.26378
$257$	319.634			1.24371			0.621856	−	0.783131i	$-0.286379\pi$
$257$	319.634			1.24371			0.621856	+	0.783131i	$0.286379\pi$
$258$			232.581i			0.901476i
$259$	59.4733			0.229627
$260$			70.6820i			0.271854i
$261$	−121.895			−0.467030
$262$	−220.017			−0.839759
$263$		−	208.330i		−	0.792131i	−0.918222	−	0.396065i	$-0.870375\pi$
$263$		−	208.330i		−	0.792131i	0.918222	−	0.396065i	$-0.129625\pi$
$264$		−	115.789i		−	0.438594i
$265$	−97.2690			−0.367053
$266$	−64.2722			−0.241625
$267$			115.451i			0.432402i
$268$			419.760i			1.56627i
$269$	−17.4800			−0.0649815			−0.0324908	−	0.999472i	$-0.510344\pi$
$269$	−17.4800			−0.0649815			−0.0324908	+	0.999472i	$0.510344\pi$
$270$		−	47.5423i		−	0.176083i
$271$	−76.9658			−0.284007			−0.142003	−	0.989866i	$-0.545354\pi$
$271$	−76.9658			−0.284007			−0.142003	+	0.989866i	$0.545354\pi$
$272$			53.8898i			0.198124i
$273$			17.1564i			0.0628440i
$274$		−	8.47109i		−	0.0309164i
$275$			126.568i			0.460248i
$276$	−224.437	+	149.734i	−0.813176	+	0.542514i
$277$	326.944			1.18031			0.590153	−	0.807292i	$-0.299068\pi$
$277$	326.944			1.18031			0.590153	+	0.807292i	$0.299068\pi$
$278$	−74.8514			−0.269250
$279$	26.4204			0.0946969
$280$	67.1165			0.239702
$281$			195.830i			0.696903i	0.937327	+	0.348452i	$0.113292\pi$
$281$			195.830i			0.696903i	−0.937327	+	0.348452i	$0.886708\pi$
$282$	−96.3025			−0.341498
$283$		−	359.211i		−	1.26930i	−0.772802	−	0.634648i	$-0.781145\pi$
$283$		−	359.211i		−	1.26930i	0.772802	−	0.634648i	$-0.218855\pi$
$284$	−523.575			−1.84357
$285$	35.7366			0.125392
$286$		−	90.2694i		−	0.315627i
$287$		−	2.26732i		−	0.00790007i
$288$	81.8524			0.284210
$289$	−87.4721			−0.302672
$290$			371.759i			1.28193i
$291$			12.5523i			0.0431350i
$292$	−898.095			−3.07567
$293$		−	59.6930i		−	0.203730i	−0.994798	−	0.101865i	$-0.967519\pi$
$293$		−	59.6930i		−	0.203730i	0.994798	−	0.101865i	$-0.0324810\pi$
$294$	39.7941			0.135354
$295$		−	76.6347i		−	0.259779i
$296$			204.557i			0.691072i
$297$			38.1721i			0.128526i
$298$			431.338i			1.44744i
$299$	−71.6303	+	47.7884i	−0.239566	+	0.159827i
$300$	202.104			0.673679
$301$	108.244			0.359614
$302$	327.439			1.08424
$303$	35.7739			0.118066
$304$		−	20.5568i		−	0.0676209i
$305$	−262.809			−0.861670
$306$		−	191.050i		−	0.624347i
$307$	168.152			0.547727			0.273864	−	0.961769i	$-0.411698\pi$
$307$	168.152			0.547727			0.273864	+	0.961769i	$0.411698\pi$
$308$	−131.634			−0.427382
$309$		−	203.424i		−	0.658331i
$310$		−	80.5781i		−	0.259929i
$311$	495.245			1.59243			0.796214	−	0.605015i	$-0.206833\pi$
$311$	495.245			1.59243			0.796214	+	0.605015i	$0.206833\pi$
$312$	−59.0092			−0.189132
$313$		−	370.674i		−	1.18426i	−0.805842	−	0.592130i	$-0.798287\pi$
$313$		−	370.674i		−	1.18426i	0.805842	−	0.592130i	$-0.201713\pi$
$314$			103.923i			0.330965i
$315$	−22.1263			−0.0702422
$316$			840.124i			2.65862i
$317$	275.198			0.868131			0.434066	−	0.900881i	$-0.357079\pi$
$317$	275.198			0.868131			0.434066	+	0.900881i	$0.357079\pi$
$318$		−	198.361i		−	0.623776i
$319$		−	298.489i		−	0.935702i
$320$		−	280.607i		−	0.876896i
$321$			148.814i			0.463595i
$322$	110.845	+	166.145i	0.344238	+	0.515980i
$323$	143.609			0.444609
$324$	60.9531			0.188127
$325$	64.5025			0.198469
$326$	−345.177			−1.05883
$327$			331.662i			1.01426i
$328$	7.79841			0.0237756
$329$			44.8194i			0.136229i
$330$	116.419			0.352784
$331$	83.7782			0.253106			0.126553	−	0.991960i	$-0.459609\pi$
$331$	83.7782			0.253106			0.126553	+	0.991960i	$0.459609\pi$
$332$			400.900i			1.20753i
$333$		−	67.4364i		−	0.202512i
$334$	−228.477			−0.684064
$335$	−172.777			−0.515753
$336$			12.7277i			0.0378801i
$337$			519.798i			1.54243i	0.636576	+	0.771214i	$0.280350\pi$
$337$			519.798i			1.54243i	−0.636576	+	0.771214i	$0.719650\pi$
$338$	508.681			1.50497
$339$		−	231.444i		−	0.682725i
$340$	−366.318			−1.07741
$341$			64.6969i			0.189727i
$342$			72.8778i			0.213093i
$343$		−	18.5203i		−	0.0539949i
$344$			372.302i			1.08227i
$345$	−61.6318	−	92.3802i	−0.178643	−	0.267769i
$346$	−306.528			−0.885920
$347$	47.0383			0.135557			0.0677785	−	0.997700i	$-0.478409\pi$
$347$	47.0383			0.135557			0.0677785	+	0.997700i	$0.478409\pi$
$348$	−476.626			−1.36961
$349$	−149.404			−0.428092			−0.214046	−	0.976824i	$-0.568664\pi$
$349$	−149.404			−0.428092			−0.214046	+	0.976824i	$0.568664\pi$
$350$		−	149.613i		−	0.427465i
$351$	19.4535			0.0554232
$352$			200.435i			0.569419i
$353$	311.382			0.882102			0.441051	−	0.897482i	$-0.354606\pi$
$353$	311.382			0.882102			0.441051	+	0.897482i	$0.354606\pi$
$354$	156.281			0.441473
$355$		−	215.508i		−	0.607065i
$356$			451.432i			1.26807i
$357$	−88.9152			−0.249062
$358$	61.3394			0.171339
$359$			309.900i			0.863230i	0.902058	+	0.431615i	$0.142056\pi$
$359$			309.900i			0.863230i	−0.902058	+	0.431615i	$0.857944\pi$
$360$		−	76.1030i		−	0.211397i
$361$	306.219			0.848253
$362$			464.422i			1.28293i
$363$	116.104			0.319847
$364$			67.0840i			0.184297i
$365$		−	369.664i		−	1.01278i
$366$		−	535.947i		−	1.46434i
$367$		−	60.4009i		−	0.164580i	−0.996608	−	0.0822900i	$-0.973777\pi$
$367$		−	60.4009i		−	0.164580i	0.996608	−	0.0822900i	$-0.0262234\pi$
$368$	−53.1398	+	35.4525i	−0.144402	+	0.0963382i
$369$	−2.57090			−0.00696721
$370$	−205.670			−0.555865
$371$	−92.3176			−0.248835
$372$	103.308			0.277709
$373$		−	160.463i		−	0.430196i	−0.976592	−	0.215098i	$-0.930993\pi$
$373$		−	160.463i		−	0.430196i	0.976592	−	0.215098i	$-0.0690070\pi$
$374$	467.833			1.25089
$375$			203.897i			0.543724i
$376$	−154.156			−0.409988
$377$	−152.118			−0.403496
$378$		−	45.1222i		−	0.119371i
$379$			190.016i			0.501362i	0.968070	+	0.250681i	$0.0806546\pi$
$379$			190.016i			0.501362i	−0.968070	+	0.250681i	$0.919345\pi$
$380$	139.735			0.367725
$381$	−10.3240			−0.0270972
$382$			950.083i			2.48713i
$383$		−	513.529i		−	1.34081i	−0.741997	−	0.670404i	$-0.766121\pi$
$383$		−	513.529i		−	1.34081i	0.741997	−	0.670404i	$-0.233879\pi$
$384$	383.212			0.997947
$385$		−	54.1816i		−	0.140731i
$386$	−517.195			−1.33988
$387$		−	122.737i		−	0.317149i
$388$			49.0812i			0.126498i
$389$		−	390.284i		−	1.00330i	−0.865070	−	0.501651i	$-0.832726\pi$
$389$		−	390.284i		−	1.00330i	0.865070	−	0.501651i	$-0.167274\pi$
$390$		−	59.3302i		−	0.152129i
$391$	−247.669	−	371.233i	−0.633425	−	0.949444i
$392$	63.7001			0.162500
$393$	116.107			0.295437
$394$	26.1844			0.0664579
$395$	−345.803			−0.875450
$396$			149.258i			0.376915i
$397$	−552.158			−1.39082			−0.695412	−	0.718611i	$-0.744778\pi$
$397$	−552.158			−1.39082			−0.695412	+	0.718611i	$0.744778\pi$
$398$		−	983.267i		−	2.47052i
$399$	33.9175			0.0850063
$400$	47.8520			0.119630
$401$		−	41.0185i		−	0.102291i	−0.998691	−	0.0511453i	$-0.983713\pi$
$401$		−	41.0185i		−	0.102291i	0.998691	−	0.0511453i	$-0.0162871\pi$
$402$		−	352.345i		−	0.876480i
$403$	32.9713			0.0818146
$404$	139.881			0.346241
$405$			25.0889i			0.0619478i
$406$			352.836i			0.869053i
$407$	165.134			0.405735
$408$		−	305.822i		−	0.749564i
$409$	−211.284			−0.516586			−0.258293	−	0.966067i	$-0.583160\pi$
$409$	−211.284			−0.516586			−0.258293	+	0.966067i	$0.583160\pi$
$410$			7.84083i			0.0191240i
$411$			4.47034i			0.0108767i
$412$		−	795.419i		−	1.93063i
$413$		−	72.7338i		−	0.176111i
$414$	188.391	−	125.686i	0.455051	−	0.303589i
$415$	−165.014			−0.397624
$416$	102.147			0.245546
$417$	39.5004			0.0947251
$418$	−178.459			−0.426935
$419$			48.5428i			0.115854i	0.998321	+	0.0579270i	$0.0184491\pi$
$419$			48.5428i			0.115854i	−0.998321	+	0.0579270i	$0.981551\pi$
$420$	−86.5170			−0.205993
$421$			190.130i			0.451616i	0.974172	+	0.225808i	$0.0725022\pi$
$421$			190.130i			0.451616i	−0.974172	+	0.225808i	$0.927498\pi$
$422$	−464.299			−1.10023
$423$	50.8205			0.120143
$424$		−	317.525i		−	0.748879i
$425$			334.292i			0.786570i
$426$	439.486			1.03166
$427$	−249.431			−0.584148
$428$			581.884i			1.35954i
$429$			47.6367i			0.111041i
$430$	−374.328			−0.870529
$431$			528.069i			1.22522i	0.790386	+	0.612609i	$0.209880\pi$
$431$			528.069i			1.22522i	−0.790386	+	0.612609i	$0.790120\pi$
$432$	14.4319			0.0334071
$433$			570.370i			1.31725i	0.752471	+	0.658625i	$0.228862\pi$
$433$			570.370i			1.31725i	−0.752471	+	0.658625i	$0.771138\pi$
$434$		−	76.4764i		−	0.176213i
$435$		−	196.184i		−	0.450997i
$436$			1296.85i			2.97442i
$437$	94.4757	+	141.610i	0.216192	+	0.324050i
$438$	753.858			1.72114
$439$	477.624			1.08798			0.543991	−	0.839091i	$-0.316913\pi$
$439$	477.624			1.08798			0.543991	+	0.839091i	$0.316913\pi$
$440$	186.357			0.423538
$441$	−21.0000			−0.0476190
$442$		−	238.420i		−	0.539412i
$443$	665.292			1.50179			0.750894	−	0.660423i	$-0.229623\pi$
$443$	665.292			1.50179			0.750894	+	0.660423i	$0.229623\pi$
$444$		−	263.686i		−	0.593887i
$445$	−185.814			−0.417558
$446$	−468.731			−1.05097
$447$		−	227.624i		−	0.509227i
$448$		−	266.323i		−	0.594470i
$449$	576.679			1.28436			0.642181	−	0.766553i	$-0.278030\pi$
$449$	576.679			1.28436			0.642181	+	0.766553i	$0.278030\pi$
$450$	−169.645			−0.376989
$451$		−	6.29547i		−	0.0139589i
$452$		−	904.978i		−	2.00216i
$453$	−172.795			−0.381446
$454$			725.096i			1.59713i
$455$	−27.6124			−0.0606866
$456$			116.659i			0.255830i
$457$		−	505.790i		−	1.10676i	−0.832928	−	0.553381i	$-0.813337\pi$
$457$		−	505.790i		−	1.10676i	0.832928	−	0.553381i	$-0.186663\pi$
$458$		−	1124.72i		−	2.45573i
$459$			100.820i			0.219652i
$460$	−240.989	−	361.220i	−0.523890	−	0.785261i
$461$	−723.295			−1.56897			−0.784485	−	0.620148i	$-0.787073\pi$
$461$	−723.295			−1.56897			−0.784485	+	0.620148i	$0.787073\pi$
$462$	110.493			0.239162
$463$	622.083			1.34359			0.671796	−	0.740737i	$-0.265523\pi$
$463$	622.083			1.34359			0.671796	+	0.740737i	$0.265523\pi$
$464$	−112.851			−0.243213
$465$			42.5224i			0.0914461i
$466$	189.755			0.407199
$467$		−	401.686i		−	0.860140i	−0.902795	−	0.430070i	$-0.858489\pi$
$467$		−	401.686i		−	0.860140i	0.902795	−	0.430070i	$-0.141511\pi$
$468$	76.0662			0.162535
$469$	−163.982			−0.349642
$470$		−	154.994i		−	0.329775i
$471$		−	54.8420i		−	0.116437i
$472$	250.166			0.530014
$473$	300.551			0.635414
$474$		−	705.196i		−	1.48776i
$475$		−	127.519i		−	0.268461i
$476$	−347.671			−0.730402
$477$			104.678i			0.219451i
$478$	1212.10			2.53578
$479$			52.7804i			0.110189i	0.998481	+	0.0550944i	$0.0175460\pi$
$479$			52.7804i			0.110189i	−0.998481	+	0.0550944i	$0.982454\pi$
$480$			131.738i			0.274453i
$481$		−	84.1569i		−	0.174962i
$482$		−	121.777i		−	0.252649i
$483$	−58.4946	−	87.6777i	−0.121107	−	0.181527i
$484$	453.985			0.937986
$485$	−20.2023			−0.0416542
$486$	−51.1638			−0.105275
$487$	629.626			1.29287			0.646434	−	0.762970i	$-0.276260\pi$
$487$	629.626			1.29287			0.646434	+	0.762970i	$0.276260\pi$
$488$		−	857.914i		−	1.75802i
$489$	182.156			0.372507
$490$			64.0466i			0.130707i
$491$	25.7496			0.0524432			0.0262216	−	0.999656i	$-0.491652\pi$
$491$	25.7496			0.0524432			0.0262216	+	0.999656i	$0.491652\pi$
$492$	−10.0526			−0.0204321
$493$		−	788.370i		−	1.59913i
$494$			90.9475i			0.184104i
$495$	−61.4362			−0.124114
$496$	24.4602			0.0493148
$497$		−	204.538i		−	0.411545i
$498$		−	336.514i		−	0.675730i
$499$	262.836			0.526725			0.263363	−	0.964697i	$-0.415168\pi$
$499$	262.836			0.526725			0.263363	+	0.964697i	$0.415168\pi$
$500$			797.265i			1.59453i
$501$	120.571			0.240661
$502$			644.390i			1.28365i
$503$		−	757.291i		−	1.50555i	−0.658279	−	0.752774i	$-0.728715\pi$
$503$		−	757.291i		−	1.50555i	0.658279	−	0.752774i	$-0.271285\pi$
$504$		−	72.2291i		−	0.143312i
$505$			57.5764i			0.114013i
$506$	307.773	+	461.322i	0.608246	+	0.911703i
$507$	−268.440			−0.529467
$508$	−40.3685			−0.0794655
$509$	−460.495			−0.904706			−0.452353	−	0.891839i	$-0.649415\pi$
$509$	−460.495			−0.904706			−0.452353	+	0.891839i	$0.649415\pi$
$510$	307.486			0.602914
$511$		−	350.847i		−	0.686589i
$512$	176.877			0.345463
$513$		−	38.4588i		−	0.0749685i
$514$	−1049.09			−2.04103
$515$	327.402			0.635732
$516$		−	479.919i		−	0.930075i
$517$			124.446i			0.240708i
$518$	−195.201			−0.376835
$519$	161.760			0.311677
$520$		−	94.9724i		−	0.182639i
$521$		−	292.391i		−	0.561211i	−0.959823	−	0.280606i	$-0.909465\pi$
$521$		−	292.391i		−	0.561211i	0.959823	−	0.280606i	$-0.0905353\pi$
$522$	400.078			0.766433
$523$			128.901i			0.246465i	0.992378	+	0.123233i	$0.0393262\pi$
$523$			128.901i			0.246465i	−0.992378	+	0.123233i	$0.960674\pi$
$524$	453.994			0.866400
$525$			78.9532i			0.150387i
$526$			683.773i			1.29995i
$527$			170.878i			0.324246i
$528$			35.3399i			0.0669316i
$529$	203.132	−	488.445i	0.383992	−	0.923336i
$530$	319.252			0.602363
$531$	−82.4723			−0.155315
$532$	132.622			0.249290
$533$	−3.20834			−0.00601940
$534$		−	378.930i		−	0.709607i
$535$	−239.509			−0.447680
$536$		−	564.014i		−	1.05226i
$537$	−32.3698			−0.0602790
$538$	57.3722			0.106640
$539$		−	51.4236i		−	0.0954056i
$540$			98.1011i			0.181669i
$541$	−890.548			−1.64612			−0.823058	−	0.567958i	$-0.807734\pi$
$541$	−890.548			−1.64612			−0.823058	+	0.567958i	$0.807734\pi$
$542$	252.614			0.466078
$543$		−	245.083i		−	0.451350i
$544$			529.391i			0.973145i
$545$	−533.794			−0.979439
$546$		−	56.3101i		−	0.103132i
$547$	451.013			0.824522			0.412261	−	0.911066i	$-0.364739\pi$
$547$	451.013			0.824522			0.412261	+	0.911066i	$0.364739\pi$
$548$			17.4797i			0.0318972i
$549$			282.829i			0.515170i
$550$		−	415.417i		−	0.755303i
$551$			300.731i			0.545791i
$552$	301.566	−	201.191i	0.546315	−	0.364476i
$553$	−328.200			−0.593490
$554$	−1073.08			−1.93697
$555$	108.536			0.195560
$556$	154.452			0.277792
$557$			798.237i			1.43310i	0.697536	+	0.716550i	$0.254280\pi$
$557$			798.237i			1.43310i	−0.697536	+	0.716550i	$0.745720\pi$
$558$	−86.7161			−0.155405
$559$		−	153.169i		−	0.274005i
$560$	−20.4846			−0.0365797
$561$	−246.883			−0.440077
$562$		−	642.745i		−	1.14367i
$563$			743.196i			1.32006i	0.751238	+	0.660032i	$0.229457\pi$
$563$			743.196i			1.32006i	−0.751238	+	0.660032i	$0.770543\pi$
$564$	198.715			0.352332
$565$	372.498			0.659288
$566$			1178.99i			2.08301i
$567$			23.8118i			0.0419961i
$568$	703.505			1.23856
$569$			1101.92i			1.93658i	0.249824	+	0.968291i	$0.419627\pi$
$569$			1101.92i			1.93658i	−0.249824	+	0.968291i	$0.580373\pi$
$570$	−117.293			−0.205778
$571$			713.916i			1.25029i	0.780509	+	0.625145i	$0.214960\pi$
$571$			713.916i			1.25029i	−0.780509	+	0.625145i	$0.785040\pi$
$572$			186.266i			0.325641i
$573$		−	501.375i		−	0.875000i
$574$			7.44171i			0.0129646i
$575$	−329.640	+	219.921i	−0.573287	+	0.382470i
$576$	−301.982			−0.524274
$577$	−606.046			−1.05034			−0.525170	−	0.850997i	$-0.675998\pi$
$577$	−606.046			−1.05034			−0.525170	+	0.850997i	$0.675998\pi$
$578$	287.097			0.496708
$579$	272.933			0.471386
$580$		−	767.107i		−	1.32260i
$581$	−156.614			−0.269560
$582$		−	41.1986i		−	0.0707880i
$583$	−256.330			−0.439675
$584$	1206.73			2.06632
$585$			31.3095i			0.0535206i
$586$			195.922i			0.334338i
$587$	−1038.80			−1.76967			−0.884835	−	0.465905i	$-0.845729\pi$
$587$	−1038.80			−1.76967			−0.884835	+	0.465905i	$0.845729\pi$
$588$	−82.1130			−0.139648
$589$		−	65.1828i		−	0.110667i
$590$			251.527i			0.426318i
$591$	−13.8180			−0.0233806
$592$		−	62.4329i		−	0.105461i
$593$	−623.644			−1.05168			−0.525838	−	0.850585i	$-0.676248\pi$
$593$	−623.644			−1.05168			−0.525838	+	0.850585i	$0.676248\pi$
$594$		−	125.287i		−	0.210921i
$595$		−	143.105i		−	0.240512i
$596$		−	890.044i		−	1.49336i
$597$			518.887i			0.869157i
$598$	235.102	−	156.849i	0.393147	−	0.262290i
$599$	932.541			1.55683			0.778415	−	0.627750i	$-0.216024\pi$
$599$	932.541			1.55683			0.778415	+	0.627750i	$0.216024\pi$
$600$	−271.558			−0.452597
$601$	−321.981			−0.535742			−0.267871	−	0.963455i	$-0.586320\pi$
$601$	−321.981			−0.535742			−0.267871	+	0.963455i	$0.586320\pi$
$602$	−355.273			−0.590154
$603$			185.938i			0.308356i
$604$	−675.654			−1.11863
$605$			186.865i			0.308867i
$606$	−117.416			−0.193755
$607$	1116.54			1.83944			0.919722	−	0.392571i	$-0.128414\pi$
$607$	1116.54			1.83944			0.919722	+	0.392571i	$0.128414\pi$
$608$		−	201.941i		−	0.332140i
$609$		−	186.197i		−	0.305743i
$610$	862.582			1.41407
$611$	63.4212			0.103799
$612$			394.222i			0.644154i
$613$			984.755i			1.60645i	0.595675	+	0.803226i	$0.296885\pi$
$613$			984.755i			1.60645i	−0.595675	+	0.803226i	$0.703115\pi$
$614$	−551.903			−0.898864
$615$		−	4.13774i		−	0.00672803i
$616$	176.870			0.287127
$617$			308.789i			0.500469i	0.968185	+	0.250235i	$0.0805077\pi$
$617$			308.789i			0.500469i	−0.968185	+	0.250235i	$0.919492\pi$
$618$			667.671i			1.08037i
$619$		−	889.616i		−	1.43718i	−0.695432	−	0.718591i	$-0.744787\pi$
$619$		−	889.616i		−	1.43718i	0.695432	−	0.718591i	$-0.255213\pi$
$620$			166.269i			0.268176i
$621$	−99.4172	+	66.3266i	−0.160092	+	0.106806i
$622$	−1625.47			−2.61330
$623$	−176.355			−0.283074
$624$	18.0102			0.0288625
$625$	102.563			0.164101
$626$			1216.61i			1.94347i
$627$	94.1758			0.150201
$628$		−	214.440i		−	0.341465i
$629$	436.153			0.693408
$630$	72.6221			0.115273
$631$			55.1014i			0.0873240i	0.999046	+	0.0436620i	$0.0139025\pi$
$631$			55.1014i			0.0873240i	−0.999046	+	0.0436620i	$0.986098\pi$
$632$		−	1128.84i		−	1.78614i
$633$	245.018			0.387075
$634$	−903.242			−1.42467
$635$		−	16.6160i		−	0.0261670i
$636$			409.307i			0.643565i
$637$	−26.2068			−0.0411411
$638$			979.688i			1.53556i
$639$	−231.924			−0.362949
$640$			616.761i			0.963689i
$641$			146.120i			0.227957i	0.993483	+	0.113978i	$0.0363595\pi$
$641$			146.120i			0.227957i	−0.993483	+	0.113978i	$0.963641\pi$
$642$		−	488.431i		−	0.760796i
$643$		−	1114.71i		−	1.73360i	−0.498653	−	0.866802i	$-0.666172\pi$
$643$		−	1114.71i		−	1.73360i	0.498653	−	0.866802i	$-0.333828\pi$
$644$	−228.722	−	342.833i	−0.355159	−	0.532349i
$645$	197.539			0.306262
$646$	−471.347			−0.729639
$647$	−362.955			−0.560981			−0.280491	−	0.959857i	$-0.590497\pi$
$647$	−362.955			−0.560981			−0.280491	+	0.959857i	$0.590497\pi$
$648$	−81.9001			−0.126389
$649$		−	201.954i		−	0.311176i
$650$	−211.708			−0.325704
$651$			40.3579i			0.0619937i
$652$	712.256			1.09242
$653$	−231.202			−0.354061			−0.177030	−	0.984205i	$-0.556649\pi$
$653$	−231.202			−0.354061			−0.177030	+	0.984205i	$0.556649\pi$
$654$		−	1088.57i		−	1.66448i
$655$			186.868i			0.285295i
$656$	−2.38015			−0.00362828
$657$	−397.823			−0.605515
$658$		−	147.105i		−	0.223563i
$659$		−	348.022i		−	0.528107i	−0.964508	−	0.264053i	$-0.914941\pi$
$659$		−	348.022i		−	0.528107i	0.964508	−	0.264053i	$-0.0850595\pi$
$660$	−240.224			−0.363976
$661$			1125.69i			1.70302i	0.524340	+	0.851509i	$0.324312\pi$
$661$			1125.69i			1.70302i	−0.524340	+	0.851509i	$0.675688\pi$
$662$	−274.973			−0.415368
$663$			125.818i			0.189771i
$664$		−	538.672i		−	0.811253i
$665$			54.5886i			0.0820881i
$666$			221.337i			0.332338i
$667$	777.398	−	518.644i	1.16551	−	0.777578i
$668$	471.451			0.705765
$669$	247.357			0.369742
$670$	567.082			0.846392
$671$	−692.574			−1.03215
$672$			125.032i			0.186059i
$673$	971.764			1.44393			0.721964	−	0.691930i	$-0.243239\pi$
$673$	971.764			1.44393			0.721964	+	0.691930i	$0.243239\pi$
$674$		−	1706.06i		−	2.53125i
$675$	89.5245			0.132629
$676$	−1049.64			−1.55272
$677$			432.134i			0.638307i	0.947703	+	0.319154i	$0.103399\pi$
$677$			432.134i			0.638307i	−0.947703	+	0.319154i	$0.896601\pi$
$678$			759.635i			1.12041i
$679$	−19.1739			−0.0282385
$680$	492.206			0.723833
$681$		−	382.645i		−	0.561888i
$682$		−	212.345i		−	0.311357i
$683$	924.855			1.35411			0.677054	−	0.735934i	$-0.263257\pi$
$683$	924.855			1.35411			0.677054	+	0.735934i	$0.263257\pi$
$684$		−	150.380i		−	0.219853i
$685$	−7.19479			−0.0105033
$686$			60.7864i			0.0886100i
$687$			593.535i			0.863952i
$688$		−	113.630i		−	0.165160i
$689$			130.633i			0.189598i
$690$	202.285	+	303.207i	0.293167	+	0.439430i
$691$	604.638			0.875019			0.437510	−	0.899214i	$-0.355861\pi$
$691$	604.638			0.875019			0.437510	+	0.899214i	$0.355861\pi$
$692$	632.506			0.914026
$693$	−58.3089			−0.0841398
$694$	−154.387			−0.222460
$695$			63.5739i			0.0914733i
$696$	640.422			0.920147
$697$		−	16.6276i		−	0.0238560i
$698$	490.368			0.702533
$699$	−100.137			−0.143257
$700$			308.718i			0.441026i
$701$			711.153i			1.01448i	0.861804	+	0.507242i	$0.169335\pi$
$701$			711.153i			1.01448i	−0.861804	+	0.507242i	$0.830665\pi$
$702$	−63.8496			−0.0909539
$703$	−166.375			−0.236664
$704$		−	739.475i		−	1.05039i
$705$			81.7931i			0.116019i
$706$	−1022.01			−1.44760
$707$			54.6456i			0.0772922i
$708$	−322.479			−0.455478
$709$		−	331.156i		−	0.467075i	−0.972348	−	0.233537i	$-0.924970\pi$
$709$		−	331.156i		−	0.467075i	0.972348	−	0.233537i	$-0.0750301\pi$
$710$			707.332i			0.996242i
$711$			372.144i			0.523409i
$712$		−	606.570i		−	0.851924i
$713$	−168.499	+	112.415i	−0.236325	+	0.157665i
$714$	291.834			0.408731
$715$	−76.6690			−0.107229
$716$	−126.571			−0.176775
$717$	−639.647			−0.892116
$718$		−	1017.14i		−	1.41663i
$719$	−576.485			−0.801787			−0.400894	−	0.916125i	$-0.631300\pi$
$719$	−576.485			−0.801787			−0.400894	+	0.916125i	$0.631300\pi$
$720$			23.2274i			0.0322603i
$721$	310.736			0.430979
$722$	−1005.06			−1.39205
$723$			64.2636i			0.0888846i
$724$		−	958.310i		−	1.32363i
$725$	−700.041			−0.965574
$726$	−381.073			−0.524894
$727$		−	1023.00i		−	1.40715i	−0.710621	−	0.703575i	$-0.751586\pi$
$727$		−	1023.00i		−	1.40715i	0.710621	−	0.703575i	$-0.248414\pi$
$728$		−	90.1380i		−	0.123816i
$729$	27.0000			0.0370370
$730$			1213.30i			1.66205i
$731$	793.816			1.08593
$732$			1105.90i			1.51079i
$733$			1229.83i			1.67780i	0.544284	+	0.838901i	$0.316801\pi$
$733$			1229.83i			1.67780i	−0.544284	+	0.838901i	$0.683199\pi$
$734$			198.245i			0.270089i
$735$		−	33.7985i		−	0.0459843i
$736$	−522.023	+	348.270i	−0.709271	+	0.473193i
$737$	−455.315			−0.617796
$738$	8.43810			0.0114337
$739$	293.034			0.396527			0.198264	−	0.980149i	$-0.436470\pi$
$739$	293.034			0.396527			0.198264	+	0.980149i	$0.436470\pi$
$740$	424.390			0.573500
$741$		−	47.9945i		−	0.0647699i
$742$	303.001			0.408357
$743$		−	1145.14i		−	1.54124i	−0.637294	−	0.770621i	$-0.719946\pi$
$743$		−	1145.14i		−	1.54124i	0.637294	−	0.770621i	$-0.280054\pi$
$744$	−138.810			−0.186573
$745$	366.350			0.491745
$746$			526.665i			0.705985i
$747$			177.584i			0.237729i
$748$	−965.349			−1.29057
$749$	−227.317			−0.303494
$750$		−	669.221i		−	0.892295i
$751$		−	909.316i		−	1.21081i	−0.795919	−	0.605404i	$-0.793012\pi$
$751$		−	909.316i		−	1.21081i	0.795919	−	0.605404i	$-0.206988\pi$
$752$	47.0498			0.0625662
$753$		−	340.056i		−	0.451601i
$754$	499.275			0.662169
$755$		−	278.106i		−	0.368352i
$756$			93.1074i			0.123158i
$757$			703.956i			0.929929i	0.885329	+	0.464964i	$0.153933\pi$
$757$			703.956i			0.929929i	−0.885329	+	0.464964i	$0.846067\pi$
$758$		−	623.664i		−	0.822775i
$759$	−162.417	−	243.447i	−0.213988	−	0.320747i
$760$	−187.756			−0.247048
$761$	261.889			0.344138			0.172069	−	0.985085i	$-0.444955\pi$
$761$	261.889			0.344138			0.172069	+	0.985085i	$0.444955\pi$
$762$	33.8851			0.0444687
$763$	−506.622			−0.663987
$764$		−	1960.45i		−	2.56603i
$765$	−162.266			−0.212112
$766$			1685.48i			2.20037i
$767$	−102.921			−0.134186
$768$	−560.365			−0.729642
$769$		−	438.046i		−	0.569631i	−0.958582	−	0.284816i	$-0.908068\pi$
$769$		−	438.046i		−	0.569631i	0.958582	−	0.284816i	$-0.0919324\pi$
$770$			177.833i			0.230952i
$771$	553.623			0.718058
$772$	1067.21			1.38239
$773$		−	837.173i		−	1.08302i	−0.840695	−	0.541509i	$-0.817853\pi$
$773$		−	837.173i		−	1.08302i	0.840695	−	0.541509i	$-0.182147\pi$
$774$			402.842i			0.520467i
$775$	151.733			0.195784
$776$		−	65.9484i		−	0.0849850i
$777$	103.011			0.132575
$778$			1280.98i			1.64650i
$779$			6.34276i			0.00814218i
$780$			122.425i			0.156955i
$781$		−	567.923i		−	0.727174i
$782$	812.890	+	1218.44i	1.03950	+	1.55811i
$783$	−211.128			−0.269640
$784$	−19.4419			−0.0247983
$785$	88.2656			0.112440
$786$	−381.080			−0.484835
$787$		−	1233.03i		−	1.56675i	−0.621549	−	0.783375i	$-0.713497\pi$
$787$		−	1233.03i		−	1.56675i	0.621549	−	0.783375i	$-0.286503\pi$
$788$	−54.0302			−0.0685662
$789$		−	360.839i		−	0.457337i
$790$	1134.98			1.43668
$791$	353.536			0.446948
$792$		−	200.552i		−	0.253223i
$793$			352.954i			0.445088i
$794$	1812.27			2.28245
$795$	−168.475			−0.211918
$796$			2028.92i			2.54890i
$797$		−	324.595i		−	0.407271i	−0.979047	−	0.203635i	$-0.934724\pi$
$797$		−	324.595i		−	0.407271i	0.979047	−	0.203635i	$-0.0652757\pi$
$798$	−111.323			−0.139502
$799$			328.688i			0.411374i
$800$	470.078			0.587598
$801$			199.968i			0.249648i
$802$			134.629i			0.167867i
$803$		−	974.167i		−	1.21316i
$804$			727.046i			0.904286i
$805$	141.113	−	94.1442i	0.175296	−	0.116949i
$806$	−108.217			−0.134264
$807$	−30.2763			−0.0375171
$808$	−187.952			−0.232614
$809$	821.535			1.01549			0.507747	−	0.861506i	$-0.330478\pi$
$809$	821.535			1.01549			0.507747	+	0.861506i	$0.330478\pi$
$810$		−	82.3457i		−	0.101661i
$811$	−286.315			−0.353040			−0.176520	−	0.984297i	$-0.556484\pi$
$811$	−286.315			−0.353040			−0.176520	+	0.984297i	$0.556484\pi$
$812$		−	728.058i		−	0.896623i
$813$	−133.309			−0.163971
$814$	−541.997			−0.665844
$815$			293.171i			0.359719i
$816$			93.3399i			0.114387i
$817$	−302.808			−0.370634
$818$	693.467			0.847759
$819$			29.7158i			0.0362830i
$820$		−	16.1792i		−	0.0197307i
$821$	−347.091			−0.422766			−0.211383	−	0.977403i	$-0.567797\pi$
$821$	−347.091			−0.422766			−0.211383	+	0.977403i	$0.567797\pi$
$822$		−	14.6724i		−	0.0178496i
$823$	−627.377			−0.762305			−0.381153	−	0.924512i	$-0.624473\pi$
$823$	−627.377			−0.762305			−0.381153	+	0.924512i	$0.624473\pi$
$824$			1068.77i			1.29705i
$825$			219.222i			0.265724i
$826$			238.724i			0.289012i
$827$		−	434.650i		−	0.525574i	−0.964854	−	0.262787i	$-0.915358\pi$
$827$		−	434.650i		−	0.525574i	0.964854	−	0.262787i	$-0.0846417\pi$
$828$	−388.736	+	259.347i	−0.469488	+	0.313221i
$829$	−200.868			−0.242301			−0.121151	−	0.992634i	$-0.538658\pi$
$829$	−200.868			−0.242301			−0.121151	+	0.992634i	$0.538658\pi$
$830$	541.602			0.652533
$831$	566.284			0.681449
$832$	−376.856			−0.452953
$833$		−	135.820i		−	0.163049i
$834$	−129.646			−0.155451
$835$			194.054i			0.232400i
$836$	368.241			0.440480
$837$	45.7616			0.0546733
$838$		−	159.325i		−	0.190126i
$839$			1097.49i			1.30809i	0.756454	+	0.654046i	$0.226930\pi$
$839$			1097.49i			1.30809i	−0.756454	+	0.654046i	$0.773070\pi$
$840$	116.249			0.138392
$841$	809.925			0.963050
$842$		−	624.038i		−	0.741138i
$843$			339.187i			0.402357i
$844$	958.057			1.13514
$845$		−	432.041i		−	0.511291i
$846$	−166.801			−0.197164
$847$			177.352i			0.209389i
$848$			96.9117i			0.114283i
$849$		−	622.171i		−	0.732828i
$850$		−	1097.20i		−	1.29082i
$851$	286.932	+	430.083i	0.337170	+	0.505386i
$852$	−906.858			−1.06439
$853$	424.358			0.497488			0.248744	−	0.968569i	$-0.419982\pi$
$853$	424.358			0.497488			0.248744	+	0.968569i	$0.419982\pi$
$854$	818.673			0.958634
$855$	61.8976			0.0723949
$856$		−	781.853i		−	0.913379i
$857$	1606.59			1.87467			0.937335	−	0.348430i	$-0.113285\pi$
$857$	1606.59			1.87467			0.937335	+	0.348430i	$0.113285\pi$
$858$		−	156.351i		−	0.182228i
$859$	1235.99			1.43887			0.719436	−	0.694559i	$-0.244400\pi$
$859$	1235.99			1.43887			0.719436	+	0.694559i	$0.244400\pi$
$860$	772.406			0.898146
$861$		−	3.92712i		−	0.00456111i
$862$		−	1733.21i		−	2.01068i
$863$	−307.747			−0.356601			−0.178300	−	0.983976i	$-0.557060\pi$
$863$	−307.747			−0.356601			−0.178300	+	0.983976i	$0.557060\pi$
$864$	141.773			0.164089
$865$			260.345i			0.300977i
$866$		−	1872.04i		−	2.16171i
$867$	−151.506			−0.174748
$868$			157.805i			0.181803i
$869$	−911.285			−1.04866
$870$			643.906i			0.740122i
$871$			232.041i			0.266408i
$872$		−	1742.52i		−	1.99830i
$873$			21.7412i			0.0249040i
$874$	−310.084	−	464.787i	−0.354788	−	0.531792i
$875$	−311.457			−0.355951
$876$	−1555.55			−1.77574
$877$	−104.777			−0.119472			−0.0597362	−	0.998214i	$-0.519026\pi$
$877$	−104.777			−0.119472			−0.0597362	+	0.998214i	$0.519026\pi$
$878$	−1567.64			−1.78546
$879$		−	103.391i		−	0.117624i
$880$	−56.8779			−0.0646340
$881$		−	1184.55i		−	1.34455i	−0.740301	−	0.672276i	$-0.765317\pi$
$881$		−	1184.55i		−	1.34455i	0.740301	−	0.672276i	$-0.234683\pi$
$882$	68.9253			0.0781466
$883$	−898.241			−1.01726			−0.508630	−	0.860985i	$-0.669848\pi$
$883$	−898.241			−1.01726			−0.508630	+	0.860985i	$0.669848\pi$
$884$			491.968i			0.556525i
$885$		−	132.735i		−	0.149983i
$886$	−2183.59			−2.46455
$887$	−1301.00			−1.46675			−0.733373	−	0.679827i	$-0.762055\pi$
$887$	−1301.00			−1.46675			−0.733373	+	0.679827i	$0.762055\pi$
$888$			354.303i			0.398990i
$889$		−	15.7702i		−	0.0177393i
$890$	609.870			0.685247
$891$			66.1160i			0.0742043i
$892$	967.203			1.08431
$893$		−	125.381i		−	0.140404i
$894$			747.099i			0.835681i
$895$		−	52.0977i		−	0.0582097i
$896$			585.365i			0.653310i
$897$	−124.067	+	82.7720i	−0.138314	+	0.0922764i
$898$	−1892.75			−2.10774
$899$	−357.835			−0.398037
$900$	350.054			0.388948
$901$	−677.021			−0.751411
$902$			20.6627i			0.0229077i
$903$	187.484			0.207623
$904$			1215.98i			1.34511i
$905$	394.449			0.435856
$906$	567.141			0.625984
$907$		−	886.325i		−	0.977205i	−0.872506	−	0.488603i	$-0.837507\pi$
$907$		−	886.325i		−	0.977205i	0.872506	−	0.488603i	$-0.162493\pi$
$908$		−	1496.20i		−	1.64780i
$909$	61.9622			0.0681653
$910$	90.6283			0.0995916
$911$		−	1148.22i		−	1.26039i	−0.776437	−	0.630195i	$-0.782975\pi$
$911$		−	1148.22i		−	1.26039i	0.776437	−	0.630195i	$-0.217025\pi$
$912$		−	35.6054i		−	0.0390410i
$913$	−434.857			−0.476295
$914$			1660.08i			1.81628i
$915$	−455.199			−0.497485
$916$			2320.81i			2.53363i
$917$			177.356i			0.193409i
$918$		−	330.909i		−	0.360467i
$919$		−	180.919i		−	0.196865i	−0.995144	−	0.0984324i	$-0.968617\pi$
$919$		−	180.919i		−	0.196865i	0.995144	−	0.0984324i	$-0.0313828\pi$
$920$	323.807	+	485.356i	0.351964	+	0.527561i
$921$	291.248			0.316231
$922$	2373.97			2.57480
$923$	−289.429			−0.313574
$924$	−227.996			−0.246749
$925$		−	387.287i		−	0.418688i
$926$	−2041.77			−2.20494
$927$		−	352.341i		−	0.380088i
$928$	−1108.60			−1.19461
$929$	1319.40			1.42024			0.710118	−	0.704083i	$-0.248642\pi$
$929$	1319.40			1.42024			0.710118	+	0.704083i	$0.248642\pi$
$930$		−	139.565i		−	0.150070i
$931$			51.8098i			0.0556497i
$932$	−391.549			−0.420117
$933$	857.790			0.919389
$934$			1318.40i			1.41156i
$935$		−	397.347i		−	0.424970i
$936$	−102.207			−0.109195
$937$			539.214i			0.575469i	0.957710	+	0.287734i	$0.0929020\pi$
$937$			539.214i			0.575469i	−0.957710	+	0.287734i	$0.907098\pi$
$938$	538.216			0.573791
$939$		−	642.026i		−	0.683733i
$940$			319.823i			0.340237i
$941$			1615.46i			1.71674i	0.513028	+	0.858372i	$0.328524\pi$
$941$			1615.46i			1.71674i	−0.513028	+	0.858372i	$0.671476\pi$
$942$			180.000i			0.191083i
$943$	16.3962	−	10.9388i	0.0173873	−	0.0116000i
$944$	−76.3532			−0.0808827
$945$	−38.3239			−0.0405544
$946$	−986.456			−1.04276
$947$	678.516			0.716490			0.358245	−	0.933628i	$-0.383375\pi$
$947$	678.516			0.716490			0.358245	+	0.933628i	$0.383375\pi$
$948$			1455.14i			1.53495i
$949$	−496.462			−0.523142
$950$			418.537i			0.440565i
$951$	476.656			0.501216
$952$	467.151			0.490705
$953$			613.791i			0.644062i	0.946729	+	0.322031i	$0.104366\pi$
$953$			613.791i			0.644062i	−0.946729	+	0.322031i	$0.895634\pi$
$954$		−	343.571i		−	0.360137i
$955$	806.939			0.844962
$956$	−2501.11			−2.61623
$957$		−	516.998i		−	0.540228i
$958$		−	173.234i		−	0.180829i
$959$	−6.82855			−0.00712049
$960$		−	486.025i		−	0.506276i
$961$	−883.440			−0.919292
$962$			276.216i			0.287127i
$963$			257.753i			0.267657i
$964$			251.280i			0.260664i
$965$			439.272i			0.455204i
$966$	191.988	+	287.772i	0.198746	+	0.297901i
$967$	1383.87			1.43110			0.715549	−	0.698562i	$-0.246176\pi$
$967$	1383.87			1.43110			0.715549	+	0.698562i	$0.246176\pi$
$968$	−610.001			−0.630166
$969$	248.738			0.256695
$970$	66.3072			0.0683579
$971$		−	1031.26i		−	1.06206i	−0.847353	−	0.531030i	$-0.821805\pi$
$971$		−	1031.26i		−	1.06206i	0.847353	−	0.531030i	$-0.178195\pi$
$972$	105.574			0.108615
$973$			60.3378i			0.0620121i
$974$	−2066.53			−2.12170
$975$	111.722			0.114586
$976$			261.844i			0.268283i
$977$			991.160i			1.01449i	0.861801	+	0.507247i	$0.169337\pi$
$977$			991.160i			1.01449i	−0.861801	+	0.507247i	$0.830663\pi$
$978$	−597.865			−0.611314
$979$	−489.670			−0.500173
$980$		−	132.157i		−	0.134854i
$981$			574.455i			0.585582i
$982$	−84.5143			−0.0860634
$983$			1914.93i			1.94804i	0.226453	+	0.974022i	$0.427287\pi$
$983$			1914.93i			1.94804i	−0.226453	+	0.974022i	$0.572713\pi$
$984$	13.5072			0.0137269
$985$		−	22.2393i		−	0.0225780i
$986$			2587.56i			2.62430i
$987$			77.6295i			0.0786520i
$988$		−	187.666i		−	0.189945i
$989$	522.227	+	782.768i	0.528035	+	0.791475i
$990$	201.643			0.203680
$991$	−51.8628			−0.0523338			−0.0261669	−	0.999658i	$-0.508330\pi$
$991$	−51.8628			−0.0523338			−0.0261669	+	0.999658i	$0.508330\pi$
$992$	240.286			0.242224
$993$	145.108			0.146131
$994$			671.326i			0.675379i
$995$	−835.123			−0.839320
$996$			694.379i			0.697167i
$997$	−625.045			−0.626926			−0.313463	−	0.949600i	$-0.601489\pi$
$997$	−625.045			−0.626926			−0.313463	+	0.949600i	$0.601489\pi$
$998$	−862.669			−0.864398
$999$		−	116.803i		−	0.116920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.5	✓	48
23.22	odd	2	inner	483.3.f.a.22.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.5	✓	48	1.1	even	1	trivial
483.3.f.a.22.6	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)

\(f(q)\)	\(=\)	\(q-3.28216 q^{2} +1.73205 q^{3} +6.77257 q^{4} +2.78765i q^{5} -5.68487 q^{6} +2.64575i q^{7} -9.10001 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.28216 q^{2} +1.73205 q^{3} +6.77257 q^{4} +2.78765i q^{5} -5.68487 q^{6} +2.64575i q^{7} -9.10001 q^{8} +3.00000 q^{9} -9.14952i q^{10} +7.34623i q^{11} +11.7304 q^{12} +3.74384 q^{13} -8.68378i q^{14} +4.82836i q^{15} +2.77741 q^{16} +19.4029i q^{17} -9.84648 q^{18} -7.40141i q^{19} +18.8796i q^{20} +4.58258i q^{21} -24.1115i q^{22} +(-19.1329 + 12.7646i) q^{23} -15.7617 q^{24} +17.2290 q^{25} -12.2879 q^{26} +5.19615 q^{27} +17.9185i q^{28} -40.6316 q^{29} -15.8474i q^{30} +8.80682 q^{31} +27.2841 q^{32} +12.7240i q^{33} -63.6834i q^{34} -7.37544 q^{35} +20.3177 q^{36} -22.4788i q^{37} +24.2926i q^{38} +6.48451 q^{39} -25.3677i q^{40} -0.856967 q^{41} -15.0407i q^{42} -40.9123i q^{43} +49.7528i q^{44} +8.36296i q^{45} +(62.7971 - 41.8953i) q^{46} +16.9402 q^{47} +4.81062 q^{48} -7.00000 q^{49} -56.5483 q^{50} +33.6068i q^{51} +25.3554 q^{52} +34.8928i q^{53} -17.0546 q^{54} -20.4787 q^{55} -24.0764i q^{56} -12.8196i q^{57} +133.359 q^{58} -27.4908 q^{59} +32.7004i q^{60} +94.2762i q^{61} -28.9054 q^{62} +7.93725i q^{63} -100.661 q^{64} +10.4365i q^{65} -41.7623i q^{66} +61.9795i q^{67} +131.407i q^{68} +(-33.1391 + 22.1089i) q^{69} +24.2074 q^{70} -77.3081 q^{71} -27.3000 q^{72} -132.608 q^{73} +73.7790i q^{74} +29.8415 q^{75} -50.1265i q^{76} -19.4363 q^{77} -21.2832 q^{78} +124.048i q^{79} +7.74246i q^{80} +9.00000 q^{81} +2.81270 q^{82} +59.1946i q^{83} +31.0358i q^{84} -54.0885 q^{85} +134.281i q^{86} -70.3760 q^{87} -66.8508i q^{88} +66.6559i q^{89} -27.4486i q^{90} +9.90526i q^{91} +(-129.579 + 86.4489i) q^{92} +15.2539 q^{93} -55.6003 q^{94} +20.6325 q^{95} +47.2575 q^{96} +7.24707i q^{97} +22.9751 q^{98} +22.0387i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 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

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