LMFDB - Embedded newform 483.3.f.a.22.3

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			22.3
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.83573 q^{2} +1.73205 q^{3} +10.7128 q^{4} -8.86189i q^{5} -6.64368 q^{6} +2.64575i q^{7} -25.7486 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.83573 q^{2} +1.73205 q^{3} +10.7128 q^{4} -8.86189i q^{5} -6.64368 q^{6} +2.64575i q^{7} -25.7486 q^{8} +3.00000 q^{9} +33.9918i q^{10} -2.29410i q^{11} +18.5552 q^{12} +15.0567 q^{13} -10.1484i q^{14} -15.3492i q^{15} +55.9134 q^{16} -7.09765i q^{17} -11.5072 q^{18} -22.0994i q^{19} -94.9359i q^{20} +4.58258i q^{21} +8.79953i q^{22} +(22.1641 + 6.14418i) q^{23} -44.5979 q^{24} -53.5331 q^{25} -57.7536 q^{26} +5.19615 q^{27} +28.3435i q^{28} +39.3447 q^{29} +58.8756i q^{30} +6.20172 q^{31} -111.474 q^{32} -3.97349i q^{33} +27.2247i q^{34} +23.4464 q^{35} +32.1385 q^{36} +33.2177i q^{37} +84.7673i q^{38} +26.0790 q^{39} +228.181i q^{40} -6.76874 q^{41} -17.5775i q^{42} -68.6344i q^{43} -24.5762i q^{44} -26.5857i q^{45} +(-85.0157 - 23.5674i) q^{46} -56.9055 q^{47} +96.8448 q^{48} -7.00000 q^{49} +205.339 q^{50} -12.2935i q^{51} +161.300 q^{52} +6.03878i q^{53} -19.9310 q^{54} -20.3300 q^{55} -68.1244i q^{56} -38.2772i q^{57} -150.916 q^{58} -103.615 q^{59} -164.434i q^{60} -30.0632i q^{61} -23.7881 q^{62} +7.93725i q^{63} +203.932 q^{64} -133.431i q^{65} +15.2412i q^{66} +129.206i q^{67} -76.0359i q^{68} +(38.3894 + 10.6420i) q^{69} -89.9339 q^{70} +25.8589 q^{71} -77.2458 q^{72} +0.973133 q^{73} -127.414i q^{74} -92.7221 q^{75} -236.747i q^{76} +6.06961 q^{77} -100.032 q^{78} -78.4213i q^{79} -495.498i q^{80} +9.00000 q^{81} +25.9630 q^{82} -71.3251i q^{83} +49.0923i q^{84} -62.8986 q^{85} +263.263i q^{86} +68.1470 q^{87} +59.0697i q^{88} -150.485i q^{89} +101.975i q^{90} +39.8364i q^{91} +(237.441 + 65.8216i) q^{92} +10.7417 q^{93} +218.274 q^{94} -195.842 q^{95} -193.079 q^{96} -164.879i q^{97} +26.8501 q^{98} -6.88229i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.83573			−1.91787			−0.958933	−	0.283634i	$-0.908460\pi$
$2$	−3.83573			−1.91787			−0.958933	+	0.283634i	$0.908460\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	10.7128			2.67821
$5$		−	8.86189i		−	1.77238i	−0.463324	−	0.886189i	$-0.653343\pi$
$5$		−	8.86189i		−	1.77238i	0.463324	−	0.886189i	$-0.346657\pi$
$6$	−6.64368			−1.10728
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−25.7486			−3.21857
$9$	3.00000			0.333333
$10$			33.9918i			3.39918i
$11$		−	2.29410i		−	0.208554i	−0.994548	−	0.104277i	$-0.966747\pi$
$11$		−	2.29410i		−	0.208554i	0.994548	−	0.104277i	$-0.0332529\pi$
$12$	18.5552			1.54626
$13$	15.0567			1.15821			0.579105	−	0.815253i	$-0.303402\pi$
$13$	15.0567			1.15821			0.579105	+	0.815253i	$0.303402\pi$
$14$		−	10.1484i		−	0.724885i
$15$		−	15.3492i		−	1.02328i
$16$	55.9134			3.49459
$17$		−	7.09765i		−	0.417509i	−0.977968	−	0.208754i	$-0.933059\pi$
$17$		−	7.09765i		−	0.417509i	0.977968	−	0.208754i	$-0.0669409\pi$
$18$	−11.5072			−0.639288
$19$		−	22.0994i		−	1.16313i	−0.813502	−	0.581563i	$-0.802442\pi$
$19$		−	22.0994i		−	1.16313i	0.813502	−	0.581563i	$-0.197558\pi$
$20$		−	94.9359i		−	4.74680i
$21$			4.58258i			0.218218i
$22$			8.79953i			0.399979i
$23$	22.1641	+	6.14418i	0.963658	+	0.267138i
$23$	22.1641	+	6.14418i	0.963658	+	0.267138i
$24$	−44.5979			−1.85825
$25$	−53.5331			−2.14132
$26$	−57.7536			−2.22129
$27$	5.19615			0.192450
$28$			28.3435i			1.01227i
$29$	39.3447			1.35671			0.678356	−	0.734733i	$-0.262693\pi$
$29$	39.3447			1.35671			0.678356	+	0.734733i	$0.262693\pi$
$30$			58.8756i			1.96252i
$31$	6.20172			0.200055			0.100028	−	0.994985i	$-0.468107\pi$
$31$	6.20172			0.200055			0.100028	+	0.994985i	$0.468107\pi$
$32$	−111.474			−3.48357
$33$		−	3.97349i		−	0.120409i
$34$			27.2247i			0.800725i
$35$	23.4464			0.669896
$36$	32.1385			0.892736
$37$			33.2177i			0.897776i	0.893588	+	0.448888i	$0.148180\pi$
$37$			33.2177i			0.897776i	−0.893588	+	0.448888i	$0.851820\pi$
$38$			84.7673i			2.23072i
$39$	26.0790			0.668693
$40$			228.181i			5.70453i
$41$	−6.76874			−0.165091			−0.0825456	−	0.996587i	$-0.526305\pi$
$41$	−6.76874			−0.165091			−0.0825456	+	0.996587i	$0.526305\pi$
$42$		−	17.5775i		−	0.418513i
$43$		−	68.6344i		−	1.59615i	−0.602559	−	0.798074i	$-0.705852\pi$
$43$		−	68.6344i		−	1.59615i	0.602559	−	0.798074i	$-0.294148\pi$
$44$		−	24.5762i		−	0.558551i
$45$		−	26.5857i		−	0.590793i
$46$	−85.0157	−	23.5674i	−1.84817	−	0.512336i
$47$	−56.9055			−1.21076			−0.605378	−	0.795938i	$-0.706978\pi$
$47$	−56.9055			−1.21076			−0.605378	+	0.795938i	$0.706978\pi$
$48$	96.8448			2.01760
$49$	−7.00000			−0.142857
$50$	205.339			4.10677
$51$		−	12.2935i		−	0.241049i
$52$	161.300			3.10193
$53$			6.03878i			0.113939i	0.998376	+	0.0569696i	$0.0181438\pi$
$53$			6.03878i			0.113939i	−0.998376	+	0.0569696i	$0.981856\pi$
$54$	−19.9310			−0.369093
$55$	−20.3300			−0.369637
$56$		−	68.1244i		−	1.21651i
$57$		−	38.2772i		−	0.671531i
$58$	−150.916			−2.60199
$59$	−103.615			−1.75618			−0.878092	−	0.478492i	$-0.841183\pi$
$59$	−103.615			−1.75618			−0.878092	+	0.478492i	$0.841183\pi$
$60$		−	164.434i		−	2.74056i
$61$		−	30.0632i		−	0.492839i	−0.969163	−	0.246420i	$-0.920746\pi$
$61$		−	30.0632i		−	0.492839i	0.969163	−	0.246420i	$-0.0792541\pi$
$62$	−23.7881			−0.383679
$63$			7.93725i			0.125988i
$64$	203.932			3.18643
$65$		−	133.431i		−	2.05279i
$66$			15.2412i			0.230928i
$67$			129.206i			1.92844i	0.265100	+	0.964221i	$0.414595\pi$
$67$			129.206i			1.92844i	−0.265100	+	0.964221i	$0.585405\pi$
$68$		−	76.0359i		−	1.11817i
$69$	38.3894	+	10.6420i	0.556368	+	0.154232i
$70$	−89.9339			−1.28477
$71$	25.8589			0.364210			0.182105	−	0.983279i	$-0.441709\pi$
$71$	25.8589			0.364210			0.182105	+	0.983279i	$0.441709\pi$
$72$	−77.2458			−1.07286
$73$	0.973133			0.0133306			0.00666529	−	0.999978i	$-0.497878\pi$
$73$	0.973133			0.0133306			0.00666529	+	0.999978i	$0.497878\pi$
$74$		−	127.414i		−	1.72181i
$75$	−92.7221			−1.23629
$76$		−	236.747i		−	3.11509i
$77$	6.06961			0.0788260
$78$	−100.032			−1.28246
$79$		−	78.4213i		−	0.992675i	−0.868130	−	0.496338i	$-0.834678\pi$
$79$		−	78.4213i		−	0.992675i	0.868130	−	0.496338i	$-0.165322\pi$
$80$		−	495.498i		−	6.19373i
$81$	9.00000			0.111111
$82$	25.9630			0.316623
$83$		−	71.3251i		−	0.859339i	−0.902986	−	0.429669i	$-0.858630\pi$
$83$		−	71.3251i		−	0.859339i	0.902986	−	0.429669i	$-0.141370\pi$
$84$			49.0923i			0.584433i
$85$	−62.8986			−0.739983
$86$			263.263i			3.06120i
$87$	68.1470			0.783298
$88$			59.0697i			0.671247i
$89$		−	150.485i		−	1.69084i	−0.534101	−	0.845421i	$-0.679350\pi$
$89$		−	150.485i		−	1.69084i	0.534101	−	0.845421i	$-0.320650\pi$
$90$			101.975i			1.13306i
$91$			39.8364i			0.437762i
$92$	237.441	+	65.8216i	2.58088	+	0.715452i
$93$	10.7417			0.115502
$94$	218.274			2.32206
$95$	−195.842			−2.06150
$96$	−193.079			−2.01124
$97$		−	164.879i		−	1.69978i	−0.526961	−	0.849889i	$-0.676669\pi$
$97$		−	164.879i		−	1.69978i	0.526961	−	0.849889i	$-0.323331\pi$
$98$	26.8501			0.273981
$99$		−	6.88229i		−	0.0695180i
$100$	−573.491			−5.73491
$101$	−4.46324			−0.0441905			−0.0220953	−	0.999756i	$-0.507034\pi$
$101$	−4.46324			−0.0441905			−0.0220953	+	0.999756i	$0.507034\pi$
$102$			47.1545i			0.462299i
$103$		−	17.4220i		−	0.169146i	−0.996417	−	0.0845730i	$-0.973047\pi$
$103$		−	17.4220i		−	0.169146i	0.996417	−	0.0845730i	$-0.0269526\pi$
$104$	−387.690			−3.72779
$105$	40.6103			0.386765
$106$		−	23.1631i		−	0.218520i
$107$			174.982i			1.63535i	0.575681	+	0.817674i	$0.304737\pi$
$107$			174.982i			1.63535i	−0.575681	+	0.817674i	$0.695263\pi$
$108$	55.6655			0.515421
$109$		−	126.918i		−	1.16439i	−0.813051	−	0.582193i	$-0.802195\pi$
$109$		−	126.918i		−	1.16439i	0.813051	−	0.582193i	$-0.197805\pi$
$110$	77.9805			0.708913
$111$			57.5347i			0.518331i
$112$			147.933i			1.32083i
$113$		−	28.0406i		−	0.248147i	−0.992273	−	0.124073i	$-0.960404\pi$
$113$		−	28.0406i		−	0.248147i	0.992273	−	0.124073i	$-0.0395958\pi$
$114$			146.821i			1.28791i
$115$	54.4491	−	196.416i	0.473470	−	1.70797i
$116$	421.493			3.63356
$117$	45.1702			0.386070
$118$	397.439			3.36812
$119$	18.7786			0.157803
$120$			395.222i			3.29351i
$121$	115.737			0.956505
$122$			115.314i			0.945199i
$123$	−11.7238			−0.0953154
$124$	66.4379			0.535790
$125$			252.857i			2.02286i
$126$		−	30.4452i		−	0.241628i
$127$	136.369			1.07377			0.536886	−	0.843655i	$-0.319600\pi$
$127$	136.369			1.07377			0.536886	+	0.843655i	$0.319600\pi$
$128$	−336.330			−2.62758
$129$		−	118.878i		−	0.921536i
$130$			511.806i			3.93697i
$131$	−109.648			−0.837005			−0.418502	−	0.908216i	$-0.637445\pi$
$131$	−109.648			−0.837005			−0.418502	+	0.908216i	$0.637445\pi$
$132$		−	42.5673i		−	0.322480i
$133$	58.4695			0.439620
$134$		−	495.598i		−	3.69849i
$135$		−	46.0477i		−	0.341094i
$136$			182.754i			1.34378i
$137$			265.750i			1.93978i	0.243537	+	0.969892i	$0.421692\pi$
$137$			265.750i			1.93978i	−0.243537	+	0.969892i	$0.578308\pi$
$138$	−147.251	−	40.8200i	−1.06704	−	0.295797i
$139$	−202.123			−1.45412			−0.727061	−	0.686573i	$-0.759114\pi$
$139$	−202.123			−1.45412			−0.727061	+	0.686573i	$0.759114\pi$
$140$	251.177			1.79412
$141$	−98.5632			−0.699030
$142$	−99.1878			−0.698505
$143$		−	34.5416i		−	0.241549i
$144$	167.740			1.16486
$145$		−	348.668i		−	2.40461i
$146$	−3.73267			−0.0255663
$147$	−12.1244			−0.0824786
$148$			355.856i			2.40443i
$149$		−	99.4774i		−	0.667634i	−0.942638	−	0.333817i	$-0.891663\pi$
$149$		−	99.4774i		−	0.667634i	0.942638	−	0.333817i	$-0.108337\pi$
$150$	355.657			2.37105
$151$	−40.4629			−0.267966			−0.133983	−	0.990984i	$-0.542777\pi$
$151$	−40.4629			−0.267966			−0.133983	+	0.990984i	$0.542777\pi$
$152$			569.028i			3.74361i
$153$		−	21.2929i		−	0.139170i
$154$	−23.2814			−0.151178
$155$		−	54.9589i		−	0.354574i
$156$	279.380			1.79090
$157$			154.947i			0.986925i	0.869767	+	0.493462i	$0.164269\pi$
$157$			154.947i			0.986925i	−0.869767	+	0.493462i	$0.835731\pi$
$158$			300.803i			1.90382i
$159$			10.4595i			0.0657829i
$160$			987.872i			6.17420i
$161$	−16.2560	+	58.6408i	−0.100969	+	0.364229i
$162$	−34.5216			−0.213096
$163$	−157.550			−0.966562			−0.483281	−	0.875465i	$-0.660555\pi$
$163$	−157.550			−0.966562			−0.483281	+	0.875465i	$0.660555\pi$
$164$	−72.5123			−0.442148
$165$	−35.2126			−0.213410
$166$			273.584i			1.64810i
$167$	−57.3615			−0.343482			−0.171741	−	0.985142i	$-0.554939\pi$
$167$	−57.3615			−0.343482			−0.171741	+	0.985142i	$0.554939\pi$
$168$		−	117.995i		−	0.702351i
$169$	57.7051			0.341450
$170$	241.262			1.41919
$171$		−	66.2981i		−	0.387708i
$172$		−	735.268i		−	4.27481i
$173$	268.463			1.55181			0.775903	−	0.630852i	$-0.217294\pi$
$173$	268.463			1.55181			0.775903	+	0.630852i	$0.217294\pi$
$174$	−261.393			−1.50226
$175$		−	141.635i		−	0.809344i
$176$		−	128.271i		−	0.728810i
$177$	−179.466			−1.01393
$178$			577.219i			3.24281i
$179$	−90.7832			−0.507169			−0.253584	−	0.967313i	$-0.581610\pi$
$179$	−90.7832			−0.507169			−0.253584	+	0.967313i	$0.581610\pi$
$180$		−	284.808i		−	1.58227i
$181$		−	0.138624i		−	0.000765878i	−1.00000		0.000382939i	$-0.999878\pi$
$181$		−	0.138624i		−	0.000765878i	1.00000		0.000382939i	$-0.000121893\pi$
$182$		−	152.802i		−	0.839569i
$183$		−	52.0710i		−	0.284541i
$184$	−570.695	−	158.204i	−3.10161	−	0.859805i
$185$	294.372			1.59120
$186$	−41.2022			−0.221517
$187$	−16.2827			−0.0870731
$188$	−609.619			−3.24265
$189$			13.7477i			0.0727393i
$190$	751.198			3.95367
$191$			147.161i			0.770475i	0.922818	+	0.385237i	$0.125880\pi$
$191$			147.161i			0.770475i	−0.922818	+	0.385237i	$0.874120\pi$
$192$	353.220			1.83969
$193$	103.961			0.538659			0.269329	−	0.963048i	$-0.413198\pi$
$193$	103.961			0.538659			0.269329	+	0.963048i	$0.413198\pi$
$194$			632.430i			3.25995i
$195$		−	231.109i		−	1.18518i
$196$	−74.9898			−0.382601
$197$	−104.624			−0.531089			−0.265544	−	0.964099i	$-0.585552\pi$
$197$	−104.624			−0.531089			−0.265544	+	0.964099i	$0.585552\pi$
$198$			26.3986i			0.133326i
$199$		−	67.7199i		−	0.340301i	−0.985418	−	0.170151i	$-0.945575\pi$
$199$		−	67.7199i		−	0.340301i	0.985418	−	0.170151i	$-0.0544254\pi$
$200$	1378.40			6.89201
$201$			223.791i			1.11339i
$202$	17.1198			0.0847514
$203$			104.096i			0.512789i
$204$		−	131.698i		−	0.645578i
$205$			59.9838i			0.292604i
$206$			66.8262i			0.324399i
$207$	66.4924	+	18.4326i	0.321219	+	0.0890462i
$208$	841.872			4.04746
$209$	−50.6981			−0.242575
$210$	−155.770			−0.741762
$211$	205.955			0.976089			0.488045	−	0.872819i	$-0.337710\pi$
$211$	205.955			0.976089			0.488045	+	0.872819i	$0.337710\pi$
$212$			64.6924i			0.305153i
$213$	44.7889			0.210277
$214$		−	671.185i		−	3.13638i
$215$	−608.230			−2.82898
$216$	−133.794			−0.619415
$217$			16.4082i			0.0756138i
$218$			486.823i			2.23313i
$219$	1.68552			0.00769642
$220$	−217.792			−0.989964
$221$		−	106.867i		−	0.483562i
$222$		−	220.688i		−	0.994089i
$223$	−222.235			−0.996569			−0.498285	−	0.867013i	$-0.666037\pi$
$223$	−222.235			−0.996569			−0.498285	+	0.867013i	$0.666037\pi$
$224$		−	294.933i		−	1.31667i
$225$	−160.599			−0.713775
$226$			107.556i			0.475912i
$227$		−	122.880i		−	0.541323i	−0.962675	−	0.270662i	$-0.912758\pi$
$227$		−	122.880i		−	0.541323i	0.962675	−	0.270662i	$-0.0872424\pi$
$228$		−	410.058i		−	1.79850i
$229$		−	46.7869i		−	0.204309i	−0.994769	−	0.102155i	$-0.967426\pi$
$229$		−	46.7869i		−	0.204309i	0.994769	−	0.102155i	$-0.0325737\pi$
$230$	−208.852	+	753.399i	−0.908052	+	3.27565i
$231$	10.5129			0.0455102
$232$	−1013.07			−4.36668
$233$	370.382			1.58962			0.794812	−	0.606856i	$-0.207569\pi$
$233$	370.382			1.58962			0.794812	+	0.606856i	$0.207569\pi$
$234$	−173.261			−0.740430
$235$			504.290i			2.14592i
$236$	−1110.01			−4.70342
$237$		−	135.830i		−	0.573121i
$238$	−72.0297			−0.302646
$239$	244.361			1.02243			0.511216	−	0.859452i	$-0.329195\pi$
$239$	244.361			1.02243			0.511216	+	0.859452i	$0.329195\pi$
$240$		−	858.228i		−	3.57595i
$241$		−	144.596i		−	0.599984i	−0.953942	−	0.299992i	$-0.903016\pi$
$241$		−	144.596i		−	0.599984i	0.953942	−	0.299992i	$-0.0969840\pi$
$242$	−443.936			−1.83445
$243$	15.5885			0.0641500
$244$		−	322.062i		−	1.31993i
$245$			62.0332i			0.253197i
$246$	44.9693			0.182802
$247$		−	332.744i		−	1.34714i
$248$	−159.685			−0.643893
$249$		−	123.539i		−	0.496140i
$250$		−	969.892i		−	3.87957i
$251$		−	164.873i		−	0.656866i	−0.944527	−	0.328433i	$-0.893479\pi$
$251$		−	164.873i		−	0.656866i	0.944527	−	0.328433i	$-0.106521\pi$
$252$			85.0304i			0.337422i
$253$	14.0953	−	50.8466i	0.0557128	−	0.200975i
$254$	−523.075			−2.05935
$255$	−108.943			−0.427229
$256$	474.344			1.85291
$257$	70.0744			0.272663			0.136332	−	0.990663i	$-0.456469\pi$
$257$	70.0744			0.272663			0.136332	+	0.990663i	$0.456469\pi$
$258$			455.985i			1.76738i
$259$	−87.8858			−0.339327
$260$		−	1429.42i		−	5.49779i
$261$	118.034			0.452238
$262$	420.579			1.60526
$263$		−	37.4693i		−	0.142469i	−0.997460	−	0.0712344i	$-0.977306\pi$
$263$		−	37.4693i		−	0.142469i	0.997460	−	0.0712344i	$-0.0226938\pi$
$264$			102.312i			0.387545i
$265$	53.5150			0.201943
$266$	−224.273			−0.843132
$267$		−	260.647i		−	0.976208i
$268$			1384.16i			5.16477i
$269$	−231.229			−0.859586			−0.429793	−	0.902927i	$-0.641414\pi$
$269$	−231.229			−0.859586			−0.429793	+	0.902927i	$0.641414\pi$
$270$			176.627i			0.654173i
$271$	48.6653			0.179577			0.0897884	−	0.995961i	$-0.471381\pi$
$271$	48.6653			0.179577			0.0897884	+	0.995961i	$0.471381\pi$
$272$		−	396.853i		−	1.45902i
$273$			68.9986i			0.252742i
$274$		−	1019.35i		−	3.72024i
$275$			122.810i			0.446582i
$276$	411.259	+	114.006i	1.49007	+	0.413066i
$277$	−12.4790			−0.0450504			−0.0225252	−	0.999746i	$-0.507171\pi$
$277$	−12.4790			−0.0450504			−0.0225252	+	0.999746i	$0.507171\pi$
$278$	775.289			2.78881
$279$	18.6051			0.0666851
$280$	−603.711			−2.15611
$281$			265.717i			0.945613i	0.881166	+	0.472807i	$0.156759\pi$
$281$			265.717i			0.945613i	−0.881166	+	0.472807i	$0.843241\pi$
$282$	378.062			1.34064
$283$			463.763i			1.63874i	0.573266	+	0.819370i	$0.305676\pi$
$283$			463.763i			1.63874i	−0.573266	+	0.819370i	$0.694324\pi$
$284$	277.022			0.975429
$285$	−339.209			−1.19021
$286$			132.492i			0.463259i
$287$		−	17.9084i		−	0.0623986i
$288$	−334.423			−1.16119
$289$	238.623			0.825687
$290$			1337.40i			4.61171i
$291$		−	285.578i		−	0.981368i
$292$	10.4250			0.0357021
$293$			299.454i			1.02203i	0.859572	+	0.511014i	$0.170730\pi$
$293$			299.454i			1.02203i	−0.859572	+	0.511014i	$0.829270\pi$
$294$	46.5058			0.158183
$295$			918.223i			3.11262i
$296$		−	855.309i		−	2.88956i
$297$		−	11.9205i		−	0.0401363i
$298$			381.569i			1.28043i
$299$	333.719	+	92.5113i	1.11612	+	0.309402i
$300$	−993.315			−3.31105
$301$	181.589			0.603287
$302$	155.205			0.513923
$303$	−7.73056			−0.0255134
$304$		−	1235.65i		−	4.06464i
$305$	−266.417			−0.873497
$306$			81.6740i			0.266908i
$307$	562.045			1.83077			0.915383	−	0.402583i	$-0.131888\pi$
$307$	562.045			1.83077			0.915383	+	0.402583i	$0.131888\pi$
$308$	65.0226			0.211112
$309$		−	30.1759i		−	0.0976565i
$310$			210.808i			0.680025i
$311$	153.549			0.493726			0.246863	−	0.969050i	$-0.420600\pi$
$311$	153.549			0.493726			0.246863	+	0.969050i	$0.420600\pi$
$312$	−671.498			−2.15224
$313$			360.712i			1.15243i	0.817297	+	0.576217i	$0.195472\pi$
$313$			360.712i			1.15243i	−0.817297	+	0.576217i	$0.804528\pi$
$314$		−	594.336i		−	1.89279i
$315$	70.3391			0.223299
$316$		−	840.114i		−	2.65859i
$317$	168.048			0.530119			0.265059	−	0.964232i	$-0.414608\pi$
$317$	168.048			0.530119			0.265059	+	0.964232i	$0.414608\pi$
$318$		−	40.1197i		−	0.126163i
$319$		−	90.2604i		−	0.282948i
$320$		−	1807.22i		−	5.64756i
$321$			303.078i			0.944169i
$322$	62.3536	−	224.930i	0.193645	−	0.698541i
$323$	−156.854			−0.485615
$324$	96.4155			0.297579
$325$	−806.033			−2.48010
$326$	604.318			1.85374
$327$		−	219.828i		−	0.672258i
$328$	174.285			0.531358
$329$		−	150.558i		−	0.457622i
$330$	135.066			0.409291
$331$	546.021			1.64961			0.824805	−	0.565417i	$-0.191285\pi$
$331$	546.021			1.64961			0.824805	+	0.565417i	$0.191285\pi$
$332$		−	764.094i		−	2.30149i
$333$			99.6531i			0.299259i
$334$	220.023			0.658752
$335$	1145.01			3.41793
$336$			256.227i			0.762581i
$337$			283.226i			0.840434i	0.907424	+	0.420217i	$0.138046\pi$
$337$			283.226i			0.840434i	−0.907424	+	0.420217i	$0.861954\pi$
$338$	−221.341			−0.654855
$339$		−	48.5677i		−	0.143268i
$340$	−673.821			−1.98183
$341$		−	14.2273i		−	0.0417224i
$342$			254.302i			0.743572i
$343$		−	18.5203i		−	0.0539949i
$344$			1767.24i			5.13732i
$345$	94.3086	−	340.203i	0.273358	−	0.986095i
$346$	−1029.75			−2.97616
$347$	123.133			0.354850			0.177425	−	0.984134i	$-0.443223\pi$
$347$	123.133			0.354850			0.177425	+	0.984134i	$0.443223\pi$
$348$	730.047			2.09784
$349$	−330.667			−0.947470			−0.473735	−	0.880667i	$-0.657095\pi$
$349$	−330.667			−0.947470			−0.473735	+	0.880667i	$0.657095\pi$
$350$			543.275i			1.55221i
$351$	78.2371			0.222898
$352$			255.733i			0.726513i
$353$	−2.49981			−0.00708161			−0.00354080	−	0.999994i	$-0.501127\pi$
$353$	−2.49981			−0.00708161			−0.00354080	+	0.999994i	$0.501127\pi$
$354$	688.384			1.94459
$355$		−	229.159i		−	0.645518i
$356$		−	1612.12i		−	4.52842i
$357$	32.5255			0.0911078
$358$	348.220			0.972681
$359$			142.325i			0.396449i	0.980157	+	0.198224i	$0.0635175\pi$
$359$			142.325i			0.396449i	−0.980157	+	0.198224i	$0.936483\pi$
$360$			684.544i			1.90151i
$361$	−127.383			−0.352860
$362$			0.531724i			0.00146885i
$363$	200.463			0.552239
$364$			426.760i			1.17242i
$365$		−	8.62379i		−	0.0236268i
$366$			199.730i			0.545711i
$367$		−	35.9679i		−	0.0980053i	−0.998799	−	0.0490027i	$-0.984396\pi$
$367$		−	35.9679i		−	0.0980053i	0.998799	−	0.0490027i	$-0.0156043\pi$
$368$	1239.27	+	343.542i	3.36759	+	0.933538i
$369$	−20.3062			−0.0550304
$370$	−1129.13			−3.05170
$371$	−15.9771			−0.0430650
$372$	115.074			0.309338
$373$		−	422.662i		−	1.13314i	−0.824013	−	0.566571i	$-0.808270\pi$
$373$		−	422.662i		−	1.13314i	0.824013	−	0.566571i	$-0.191730\pi$
$374$	62.4559			0.166995
$375$			437.962i			1.16790i
$376$	1465.24			3.89691
$377$	592.402			1.57136
$378$		−	52.7326i		−	0.139504i
$379$			533.484i			1.40761i	0.710394	+	0.703805i	$0.248517\pi$
$379$			533.484i			1.40761i	−0.710394	+	0.703805i	$0.751483\pi$
$380$	−2098.02			−5.52112
$381$	236.198			0.619943
$382$		−	564.469i		−	1.47767i
$383$			447.089i			1.16734i	0.811993	+	0.583668i	$0.198383\pi$
$383$			447.089i			1.16734i	−0.811993	+	0.583668i	$0.801617\pi$
$384$	−582.540			−1.51703
$385$		−	53.7882i		−	0.139710i
$386$	−398.767			−1.03308
$387$		−	205.903i		−	0.532049i
$388$		−	1766.32i		−	4.55236i
$389$		−	384.353i		−	0.988055i	−0.869446	−	0.494027i	$-0.835524\pi$
$389$		−	384.353i		−	0.988055i	0.869446	−	0.494027i	$-0.164476\pi$
$390$			886.473i			2.27301i
$391$	43.6092	−	157.313i	0.111533	−	0.402335i
$392$	180.240			0.459796
$393$	−189.915			−0.483245
$394$	401.311			1.01856
$395$	−694.961			−1.75940
$396$		−	73.7287i		−	0.186184i
$397$	−427.857			−1.07772			−0.538862	−	0.842394i	$-0.681146\pi$
$397$	−427.857			−1.07772			−0.538862	+	0.842394i	$0.681146\pi$
$398$			259.755i			0.652652i
$399$	101.272			0.253815
$400$	−2993.22			−7.48304
$401$			52.0462i			0.129791i	0.997892	+	0.0648955i	$0.0206714\pi$
$401$			52.0462i			0.129791i	−0.997892	+	0.0648955i	$0.979329\pi$
$402$		−	858.401i		−	2.13533i
$403$	93.3775			0.231706
$404$	−47.8139			−0.118351
$405$		−	79.7570i		−	0.196931i
$406$		−	399.285i		−	0.983461i
$407$	76.2046			0.187235
$408$			316.540i			0.775833i
$409$	409.460			1.00112			0.500562	−	0.865701i	$-0.333127\pi$
$409$	409.460			1.00112			0.500562	+	0.865701i	$0.333127\pi$
$410$		−	230.082i		−	0.561175i
$411$			460.293i			1.11993i
$412$		−	186.639i		−	0.453008i
$413$		−	274.139i		−	0.663775i
$414$	−255.047	−	70.7023i	−0.616055	−	0.170779i
$415$	−632.076			−1.52307
$416$	−1678.44			−4.03470
$417$	−350.087			−0.839537
$418$	194.464			0.465225
$419$			718.694i			1.71526i	0.514266	+	0.857631i	$0.328064\pi$
$419$			718.694i			1.71526i	−0.514266	+	0.857631i	$0.671936\pi$
$420$	435.051			1.03584
$421$			320.503i			0.761290i	0.924721	+	0.380645i	$0.124298\pi$
$421$			320.503i			0.761290i	−0.924721	+	0.380645i	$0.875702\pi$
$422$	−789.987			−1.87201
$423$	−170.716			−0.403585
$424$		−	155.490i		−	0.366722i
$425$			379.959i			0.894021i
$426$	−171.798			−0.403282
$427$	79.5397			0.186276
$428$			1874.56i			4.37980i
$429$		−	59.8277i		−	0.139459i
$430$	2333.01			5.42560
$431$			420.620i			0.975918i	0.872867	+	0.487959i	$0.162258\pi$
$431$			420.620i			0.975918i	−0.872867	+	0.487959i	$0.837742\pi$
$432$	290.534			0.672533
$433$		−	317.443i		−	0.733125i	−0.930393	−	0.366562i	$-0.880535\pi$
$433$		−	317.443i		−	0.733125i	0.930393	−	0.366562i	$-0.119465\pi$
$434$		−	62.9374i		−	0.145017i
$435$		−	603.911i		−	1.38830i
$436$		−	1359.65i		−	3.11847i
$437$	135.783	−	489.814i	0.310716	−	1.12086i
$438$	−6.46518			−0.0147607
$439$	151.755			0.345684			0.172842	−	0.984950i	$-0.444705\pi$
$439$	151.755			0.345684			0.172842	+	0.984950i	$0.444705\pi$
$440$	523.470			1.18970
$441$	−21.0000			−0.0476190
$442$			409.914i			0.927408i
$443$	−170.396			−0.384641			−0.192320	−	0.981332i	$-0.561601\pi$
$443$	−170.396			−0.384641			−0.192320	+	0.981332i	$0.561601\pi$
$444$			616.360i			1.38820i
$445$	−1333.58			−2.99681
$446$	852.433			1.91129
$447$		−	172.300i		−	0.385458i
$448$			539.552i			1.20436i
$449$	632.355			1.40836			0.704181	−	0.710020i	$-0.251314\pi$
$449$	632.355			1.40836			0.704181	+	0.710020i	$0.251314\pi$
$450$	616.016			1.36892
$451$			15.5281i			0.0344304i
$452$		−	300.394i		−	0.664588i
$453$	−70.0838			−0.154710
$454$			471.336i			1.03818i
$455$	353.025			0.775880
$456$			985.586i			2.16137i
$457$		−	228.388i		−	0.499756i	−0.968277	−	0.249878i	$-0.919609\pi$
$457$		−	228.388i		−	0.499756i	0.968277	−	0.249878i	$-0.0803905\pi$
$458$			179.462i			0.391838i
$459$		−	36.8804i		−	0.0803496i
$460$	583.304	−	2104.17i	1.26805	−	4.57429i
$461$	577.925			1.25363			0.626817	−	0.779167i	$-0.284357\pi$
$461$	577.925			1.25363			0.626817	+	0.779167i	$0.284357\pi$
$462$	−40.3245			−0.0872825
$463$	−175.547			−0.379151			−0.189576	−	0.981866i	$-0.560711\pi$
$463$	−175.547			−0.379151			−0.189576	+	0.981866i	$0.560711\pi$
$464$	2199.89			4.74115
$465$		−	95.1916i		−	0.204713i
$466$	−1420.69			−3.04868
$467$			789.029i			1.68957i	0.535107	+	0.844784i	$0.320271\pi$
$467$			789.029i			1.68957i	−0.535107	+	0.844784i	$0.679729\pi$
$468$	483.900			1.03398
$469$	−341.846			−0.728883
$470$		−	1934.32i		−	4.11558i
$471$			268.376i			0.569801i
$472$	2667.94			5.65241
$473$	−157.454			−0.332883
$474$			521.006i			1.09917i
$475$			1183.05i			2.49063i
$476$	201.172			0.422630
$477$			18.1163i			0.0379798i
$478$	−937.303			−1.96089
$479$		−	441.484i		−	0.921680i	−0.887483	−	0.460840i	$-0.847548\pi$
$479$		−	441.484i		−	0.921680i	0.887483	−	0.460840i	$-0.152452\pi$
$480$			1711.05i			3.56468i
$481$			500.150i			1.03981i
$482$			554.632i			1.15069i
$483$	−28.1562	+	101.569i	−0.0582944	+	0.210287i
$484$	1239.87			2.56172
$485$	−1461.14			−3.01265
$486$	−59.7931			−0.123031
$487$	−516.547			−1.06067			−0.530335	−	0.847788i	$-0.677934\pi$
$487$	−516.547			−1.06067			−0.530335	+	0.847788i	$0.677934\pi$
$488$			774.085i			1.58624i
$489$	−272.884			−0.558045
$490$		−	237.943i		−	0.485597i
$491$	−23.6429			−0.0481525			−0.0240763	−	0.999710i	$-0.507664\pi$
$491$	−23.6429			−0.0481525			−0.0240763	+	0.999710i	$0.507664\pi$
$492$	−125.595			−0.255274
$493$		−	279.254i		−	0.566439i
$494$			1276.32i			2.58364i
$495$	−60.9901			−0.123212
$496$	346.759			0.699111
$497$			68.4162i			0.137658i
$498$			473.861i			0.951529i
$499$	88.3199			0.176994			0.0884969	−	0.996076i	$-0.471794\pi$
$499$	88.3199			0.176994			0.0884969	+	0.996076i	$0.471794\pi$
$500$			2708.82i			5.41763i
$501$	−99.3530			−0.198309
$502$			632.410i			1.25978i
$503$		−	579.131i		−	1.15135i	−0.817677	−	0.575677i	$-0.804739\pi$
$503$		−	579.131i		−	1.15135i	0.817677	−	0.575677i	$-0.195261\pi$
$504$		−	204.373i		−	0.405502i
$505$			39.5528i			0.0783223i
$506$	−54.0659	+	195.034i	−0.106850	+	0.385443i
$507$	99.9481			0.197136
$508$	1460.90			2.87578
$509$	−345.867			−0.679502			−0.339751	−	0.940515i	$-0.610343\pi$
$509$	−345.867			−0.679502			−0.339751	+	0.940515i	$0.610343\pi$
$510$	417.878			0.819368
$511$			2.57467i			0.00503849i
$512$	−474.136			−0.926047
$513$		−	114.832i		−	0.223844i
$514$	−268.787			−0.522931
$515$	−154.392			−0.299791
$516$		−	1273.52i		−	2.46807i
$517$			130.547i			0.252508i
$518$	337.106			0.650784
$519$	464.991			0.895936
$520$			3435.66i			6.60704i
$521$		−	441.530i		−	0.847466i	−0.905787	−	0.423733i	$-0.860719\pi$
$521$		−	441.530i		−	0.847466i	0.905787	−	0.423733i	$-0.139281\pi$
$522$	−452.747			−0.867331
$523$			62.9887i			0.120437i	0.998185	+	0.0602187i	$0.0191798\pi$
$523$			62.9887i			0.120437i	−0.998185	+	0.0602187i	$0.980820\pi$
$524$	−1174.64			−2.24167
$525$		−	245.319i		−	0.467275i
$526$			143.722i			0.273236i
$527$		−	44.0176i		−	0.0835248i
$528$		−	222.171i		−	0.420779i
$529$	453.498	+	272.361i	0.857274	+	0.514860i
$530$	−205.269			−0.387300
$531$	−310.844			−0.585395
$532$	626.373			1.17739
$533$	−101.915			−0.191210
$534$			999.773i			1.87223i
$535$	1550.67			2.89846
$536$		−	3326.86i		−	6.20684i
$537$	−157.241			−0.292814
$538$	886.931			1.64857
$539$			16.0587i			0.0297934i
$540$		−	493.301i		−	0.913521i
$541$	−618.050			−1.14242			−0.571211	−	0.820803i	$-0.693526\pi$
$541$	−618.050			−1.14242			−0.571211	+	0.820803i	$0.693526\pi$
$542$	−186.667			−0.344404
$543$		−	0.240104i		−	0.000442180i
$544$			791.205i			1.45442i
$545$	−1124.73			−2.06373
$546$		−	264.660i		−	0.484725i
$547$	−315.255			−0.576334			−0.288167	−	0.957580i	$-0.593046\pi$
$547$	−315.255			−0.576334			−0.288167	+	0.957580i	$0.593046\pi$
$548$			2846.94i			5.19514i
$549$		−	90.1896i		−	0.164280i
$550$		−	471.066i		−	0.856484i
$551$		−	869.493i		−	1.57803i
$552$	−988.474	−	274.018i	−1.79071	−	0.496409i
$553$	207.483			0.375196
$554$	47.8659			0.0864006
$555$	509.867			0.918679
$556$	−2165.31			−3.89444
$557$		−	210.920i		−	0.378671i	−0.981912	−	0.189335i	$-0.939367\pi$
$557$		−	210.920i		−	0.378671i	0.981912	−	0.189335i	$-0.0606333\pi$
$558$	−71.3643			−0.127893
$559$		−	1033.41i		−	1.84867i
$560$	1310.96			2.34101
$561$	−28.2024			−0.0502717
$562$		−	1019.22i		−	1.81356i
$563$			548.549i			0.974332i	0.873309	+	0.487166i	$0.161969\pi$
$563$			548.549i			0.974332i	−0.873309	+	0.487166i	$0.838031\pi$
$564$	−1055.89			−1.87215
$565$	−248.493			−0.439810
$566$		−	1778.87i		−	3.14288i
$567$			23.8118i			0.0419961i
$568$	−665.830			−1.17224
$569$			569.440i			1.00077i	0.865802	+	0.500386i	$0.166809\pi$
$569$			569.440i			1.00077i	−0.865802	+	0.500386i	$0.833191\pi$
$570$	1301.11			2.28266
$571$			124.187i			0.217490i	0.994070	+	0.108745i	$0.0346832\pi$
$571$			124.187i			0.217490i	−0.994070	+	0.108745i	$0.965317\pi$
$572$		−	370.038i		−	0.646919i
$573$			254.890i			0.444834i
$574$			68.6918i			0.119672i
$575$	−1186.52	−	328.917i	−2.06350	−	0.572030i
$576$	611.795			1.06214
$577$	880.984			1.52684			0.763418	−	0.645905i	$-0.223520\pi$
$577$	880.984			1.52684			0.763418	+	0.645905i	$0.223520\pi$
$578$	−915.295			−1.58356
$579$	180.066			0.310995
$580$		−	3735.22i		−	6.44004i
$581$	188.709			0.324800
$582$			1095.40i			1.88213i
$583$	13.8535			0.0237625
$584$	−25.0568			−0.0429055
$585$		−	400.293i		−	0.684262i
$586$		−	1148.63i		−	1.96011i
$587$	740.530			1.26155			0.630775	−	0.775965i	$-0.282737\pi$
$587$	740.530			1.26155			0.630775	+	0.775965i	$0.282737\pi$
$588$	−129.886			−0.220895
$589$		−	137.054i		−	0.232689i
$590$		−	3522.06i		−	5.96959i
$591$	−181.215			−0.306624
$592$			1857.31i			3.13735i
$593$	602.557			1.01612			0.508059	−	0.861323i	$-0.330363\pi$
$593$	602.557			1.01612			0.508059	+	0.861323i	$0.330363\pi$
$594$			45.7237i			0.0769759i
$595$		−	166.414i		−	0.279687i
$596$		−	1065.68i		−	1.78806i
$597$		−	117.294i		−	0.196473i
$598$	−1280.06	−	354.848i	−2.14056	−	0.593392i
$599$	643.607			1.07447			0.537235	−	0.843433i	$-0.319469\pi$
$599$	643.607			1.07447			0.537235	+	0.843433i	$0.319469\pi$
$600$	2387.46			3.97911
$601$	177.729			0.295723			0.147861	−	0.989008i	$-0.452761\pi$
$601$	177.729			0.295723			0.147861	+	0.989008i	$0.452761\pi$
$602$	−696.528			−1.15702
$603$			387.617i			0.642814i
$604$	−433.472			−0.717669
$605$		−	1025.65i		−	1.69529i
$606$	29.6523			0.0489313
$607$	−388.983			−0.640829			−0.320414	−	0.947277i	$-0.603822\pi$
$607$	−388.983			−0.640829			−0.320414	+	0.947277i	$0.603822\pi$
$608$			2463.51i			4.05183i
$609$			180.300i			0.296059i
$610$	1021.90			1.67525
$611$	−856.810			−1.40231
$612$		−	228.108i		−	0.372725i
$613$			217.931i			0.355515i	0.984074	+	0.177758i	$0.0568843\pi$
$613$			217.931i			0.355515i	−0.984074	+	0.177758i	$0.943116\pi$
$614$	−2155.85			−3.51116
$615$			103.895i			0.168935i
$616$	−156.284			−0.253708
$617$		−	907.090i		−	1.47016i	−0.677979	−	0.735081i	$-0.737144\pi$
$617$		−	907.090i		−	1.47016i	0.677979	−	0.735081i	$-0.262856\pi$
$618$			115.746i			0.187292i
$619$			974.089i			1.57365i	0.617177	+	0.786824i	$0.288276\pi$
$619$			974.089i			1.57365i	−0.617177	+	0.786824i	$0.711724\pi$
$620$		−	588.765i		−	0.949622i
$621$	115.168	+	31.9261i	0.185456	+	0.0514108i
$622$	−588.971			−0.946899
$623$	398.146			0.639078
$624$	1458.17			2.33680
$625$	902.466			1.44394
$626$		−	1383.59i		−	2.21021i
$627$	−87.8117			−0.140050
$628$			1659.92i			2.64319i
$629$	235.767			0.374829
$630$	−269.802			−0.428257
$631$		−	217.964i		−	0.345426i	−0.984972	−	0.172713i	$-0.944747\pi$
$631$		−	217.964i		−	0.345426i	0.984972	−	0.172713i	$-0.0552533\pi$
$632$			2019.24i			3.19500i
$633$	356.724			0.563545
$634$	−644.585			−1.01670
$635$		−	1208.49i		−	1.90313i
$636$			112.051i			0.176180i
$637$	−105.397			−0.165459
$638$			346.215i			0.542656i
$639$	77.5767			0.121403
$640$			2980.52i			4.65706i
$641$		−	776.091i		−	1.21075i	−0.795940	−	0.605375i	$-0.793023\pi$
$641$		−	776.091i		−	1.21075i	0.795940	−	0.605375i	$-0.206977\pi$
$642$		−	1162.53i		−	1.81079i
$643$		−	405.054i		−	0.629945i	−0.949101	−	0.314972i	$-0.898005\pi$
$643$		−	405.054i		−	0.629945i	0.949101	−	0.314972i	$-0.101995\pi$
$644$	−174.148	+	628.209i	−0.270415	+	0.975479i
$645$	−1053.49			−1.63331
$646$	601.648			0.931344
$647$	65.6081			0.101404			0.0507018	−	0.998714i	$-0.483854\pi$
$647$	65.6081			0.101404			0.0507018	+	0.998714i	$0.483854\pi$
$648$	−231.737			−0.357619
$649$			237.702i			0.366259i
$650$	3091.73			4.75650
$651$			28.4198i			0.0436557i
$652$	−1687.80			−2.58865
$653$	1053.55			1.61340			0.806701	−	0.590960i	$-0.201251\pi$
$653$	1053.55			1.61340			0.806701	+	0.590960i	$0.201251\pi$
$654$			843.203i			1.28930i
$655$			971.685i			1.48349i
$656$	−378.463			−0.576925
$657$	2.91940			0.00444353
$658$			577.499i			0.877658i
$659$		−	932.060i		−	1.41436i	−0.707036	−	0.707178i	$-0.749968\pi$
$659$		−	932.060i		−	1.41436i	0.707036	−	0.707178i	$-0.250032\pi$
$660$	−377.227			−0.571556
$661$			573.064i			0.866965i	0.901162	+	0.433483i	$0.142715\pi$
$661$			573.064i			0.866965i	−0.901162	+	0.433483i	$0.857285\pi$
$662$	−2094.39			−3.16373
$663$		−	185.100i		−	0.279185i
$664$			1836.52i			2.76585i
$665$		−	518.150i		−	0.779173i
$666$		−	382.242i		−	0.573938i
$667$	872.041	+	241.741i	1.30741	+	0.362430i
$668$	−614.504			−0.919915
$669$	−384.922			−0.575370
$670$	−4391.93			−6.55513
$671$	−68.9678			−0.102784
$672$		−	510.839i		−	0.760177i
$673$	−754.416			−1.12098			−0.560488	−	0.828163i	$-0.689386\pi$
$673$	−754.416			−1.12098			−0.560488	+	0.828163i	$0.689386\pi$
$674$		−	1086.38i		−	1.61184i
$675$	−278.166			−0.412098
$676$	618.184			0.914474
$677$		−	437.536i		−	0.646286i	−0.946350	−	0.323143i	$-0.895261\pi$
$677$		−	437.536i		−	0.646286i	0.946350	−	0.323143i	$-0.104739\pi$
$678$			186.293i			0.274768i
$679$	436.228			0.642456
$680$	1619.55			2.38169
$681$		−	212.835i		−	0.312533i
$682$			54.5722i			0.0800179i
$683$	−89.0019			−0.130310			−0.0651551	−	0.997875i	$-0.520754\pi$
$683$	−89.0019			−0.130310			−0.0651551	+	0.997875i	$0.520754\pi$
$684$		−	710.241i		−	1.03836i
$685$	2355.05			3.43803
$686$			71.0387i			0.103555i
$687$		−	81.0372i		−	0.117958i
$688$		−	3837.58i		−	5.57788i
$689$			90.9243i			0.131966i
$690$	−361.742	+	1304.93i	−0.524264	+	1.89120i
$691$	1196.81			1.73199			0.865995	−	0.500053i	$-0.166686\pi$
$691$	1196.81			1.73199			0.865995	+	0.500053i	$0.166686\pi$
$692$	2875.99			4.15606
$693$	18.2088			0.0262753
$694$	−472.305			−0.680554
$695$			1791.19i			2.57725i
$696$	−1754.69			−2.52110
$697$			48.0421i			0.0689269i
$698$	1268.35			1.81712
$699$	641.521			0.917770
$700$		−	1517.31i		−	2.16759i
$701$			906.332i			1.29291i	0.762951	+	0.646456i	$0.223750\pi$
$701$			906.332i			1.29291i	−0.762951	+	0.646456i	$0.776250\pi$
$702$	−300.096			−0.427488
$703$	734.091			1.04423
$704$		−	467.839i		−	0.664543i
$705$			873.456i			1.23894i
$706$	9.58859			0.0135816
$707$		−	11.8086i		−	0.0167024i
$708$	−1922.59			−2.71552
$709$		−	1293.05i		−	1.82377i	−0.410447	−	0.911885i	$-0.634627\pi$
$709$		−	1293.05i		−	1.82377i	0.410447	−	0.911885i	$-0.365373\pi$
$710$			878.991i			1.23802i
$711$		−	235.264i		−	0.330892i
$712$			3874.77i			5.44210i
$713$	137.456	+	38.1045i	0.192785	+	0.0534425i
$714$	−124.759			−0.174733
$715$	−306.104			−0.428117
$716$	−972.545			−1.35830
$717$	423.246			0.590301
$718$		−	545.921i		−	0.760336i
$719$	−149.666			−0.208159			−0.104079	−	0.994569i	$-0.533190\pi$
$719$	−149.666			−0.208159			−0.104079	+	0.994569i	$0.533190\pi$
$720$		−	1486.49i		−	2.06458i
$721$	46.0944			0.0639312
$722$	488.605			0.676739
$723$		−	250.448i		−	0.346401i
$724$		−	1.48505i		−	0.00205118i
$725$	−2106.24			−2.90516
$726$	−768.920			−1.05912
$727$		−	1022.15i		−	1.40599i	−0.711195	−	0.702995i	$-0.751846\pi$
$727$		−	1022.15i		−	1.40599i	0.711195	−	0.702995i	$-0.248154\pi$
$728$		−	1025.73i		−	1.40897i
$729$	27.0000			0.0370370
$730$			33.0785i			0.0453131i
$731$	−487.142			−0.666405
$732$		−	557.827i		−	0.762059i
$733$			913.532i			1.24629i	0.782105	+	0.623146i	$0.214146\pi$
$733$			913.532i			1.24629i	−0.782105	+	0.623146i	$0.785854\pi$
$734$			137.963i			0.187961i
$735$			107.445i			0.146183i
$736$	−2470.73	−	684.918i	−3.35697	−	0.930596i
$737$	296.410			0.402185
$738$	77.8891			0.105541
$739$	127.300			0.172260			0.0861300	−	0.996284i	$-0.472550\pi$
$739$	127.300			0.172260			0.0861300	+	0.996284i	$0.472550\pi$
$740$	3153.55			4.26156
$741$		−	576.330i		−	0.777773i
$742$	61.2839			0.0825929
$743$			344.634i			0.463841i	0.972735	+	0.231920i	$0.0745009\pi$
$743$			344.634i			0.463841i	−0.972735	+	0.231920i	$0.925499\pi$
$744$	−276.583			−0.371752
$745$	−881.558			−1.18330
$746$			1621.22i			2.17321i
$747$		−	213.975i		−	0.286446i
$748$	−174.433			−0.233200
$749$	−462.960			−0.618104
$750$		−	1679.90i		−	2.23987i
$751$			588.204i			0.783228i	0.920130	+	0.391614i	$0.128083\pi$
$751$			588.204i			0.783228i	−0.920130	+	0.391614i	$0.871917\pi$
$752$	−3181.78			−4.23109
$753$		−	285.569i		−	0.379242i
$754$	−2272.29			−3.01365
$755$			358.578i			0.474938i
$756$			147.277i			0.194811i
$757$		−	6.00617i		−	0.00793417i	−0.999992	−	0.00396709i	$-0.998737\pi$
$757$		−	6.00617i		−	0.00793417i	0.999992	−	0.00396709i	$-0.00126277\pi$
$758$		−	2046.30i		−	2.69960i
$759$	24.4139	−	88.0690i	0.0321658	−	0.116033i
$760$	5042.66			6.63508
$761$	659.193			0.866219			0.433109	−	0.901341i	$-0.357416\pi$
$761$	659.193			0.866219			0.433109	+	0.901341i	$0.357416\pi$
$762$	−905.993			−1.18897
$763$	335.794			0.440096
$764$			1576.51i			2.06349i
$765$	−188.696			−0.246661
$766$		−	1714.91i		−	2.23879i
$767$	−1560.10			−2.03403
$768$	821.588			1.06978
$769$		−	299.704i		−	0.389732i	−0.980830	−	0.194866i	$-0.937573\pi$
$769$		−	299.704i		−	0.389732i	0.980830	−	0.194866i	$-0.0624272\pi$
$770$			206.317i			0.267944i
$771$	121.372			0.157422
$772$	1113.72			1.44264
$773$			374.493i			0.484468i	0.970218	+	0.242234i	$0.0778801\pi$
$773$			374.493i			0.484468i	−0.970218	+	0.242234i	$0.922120\pi$
$774$			789.789i			1.02040i
$775$	−331.997			−0.428383
$776$			4245.39i			5.47087i
$777$	−152.223			−0.195911
$778$			1474.28i			1.89496i
$779$			149.585i			0.192022i
$780$		−	2475.84i		−	3.17415i
$781$		−	59.3228i		−	0.0759575i
$782$	−167.273	+	603.411i	−0.213904	+	0.771625i
$783$	204.441			0.261099
$784$	−391.394			−0.499227
$785$	1373.13			1.74920
$786$	728.464			0.926799
$787$			62.4755i			0.0793843i	0.999212	+	0.0396922i	$0.0126377\pi$
$787$			62.4755i			0.0793843i	−0.999212	+	0.0396922i	$0.987362\pi$
$788$	−1120.82			−1.42237
$789$		−	64.8987i		−	0.0822544i
$790$	2665.68			3.37428
$791$	74.1884			0.0937906
$792$			177.209i			0.223749i
$793$		−	452.653i		−	0.570811i
$794$	1641.14			2.06693
$795$	92.6907			0.116592
$796$		−	725.472i		−	0.911397i
$797$		−	1170.64i		−	1.46881i	−0.678714	−	0.734403i	$-0.737462\pi$
$797$		−	1170.64i		−	1.46881i	0.678714	−	0.734403i	$-0.262538\pi$
$798$	−388.452			−0.486782
$799$			403.895i			0.505501i
$800$	5967.56			7.45945
$801$		−	451.455i		−	0.563614i
$802$		−	199.635i		−	0.248922i
$803$		−	2.23246i		−	0.00278015i
$804$			2397.43i			2.98188i
$805$	519.668	+	144.059i	0.645551	+	0.178955i
$806$	−358.171			−0.444381
$807$	−400.500			−0.496282
$808$	114.922			0.142230
$809$	−694.362			−0.858297			−0.429148	−	0.903234i	$-0.641186\pi$
$809$	−694.362			−0.858297			−0.429148	+	0.903234i	$0.641186\pi$
$810$			305.926i			0.377687i
$811$	236.981			0.292208			0.146104	−	0.989269i	$-0.453327\pi$
$811$	236.981			0.292208			0.146104	+	0.989269i	$0.453327\pi$
$812$			1115.16i			1.37336i
$813$	84.2908			0.103679
$814$	−292.300			−0.359091
$815$			1396.19i			1.71311i
$816$		−	687.370i		−	0.842365i
$817$	−1516.78			−1.85652
$818$	−1570.58			−1.92002
$819$			119.509i			0.145921i
$820$			642.596i			0.783654i
$821$	−824.059			−1.00373			−0.501863	−	0.864947i	$-0.667352\pi$
$821$	−824.059			−1.00373			−0.501863	+	0.864947i	$0.667352\pi$
$822$		−	1765.56i		−	2.14788i
$823$	1023.22			1.24328			0.621639	−	0.783304i	$-0.286467\pi$
$823$	1023.22			1.24328			0.621639	+	0.783304i	$0.286467\pi$
$824$			448.593i			0.544409i
$825$			212.713i			0.257834i
$826$			1051.52i			1.27303i
$827$			789.533i			0.954696i	0.878714	+	0.477348i	$0.158402\pi$
$827$			789.533i			0.954696i	−0.878714	+	0.477348i	$0.841598\pi$
$828$	712.322	+	197.465i	0.860292	+	0.238484i
$829$	−270.227			−0.325968			−0.162984	−	0.986629i	$-0.552112\pi$
$829$	−270.227			−0.325968			−0.162984	+	0.986629i	$0.552112\pi$
$830$	2424.47			2.92105
$831$	−21.6142			−0.0260099
$832$	3070.54			3.69056
$833$			49.6835i			0.0596441i
$834$	1342.84			1.61012
$835$			508.331i			0.608780i
$836$	−543.120			−0.649665
$837$	32.2251			0.0385007
$838$		−	2756.72i		−	3.28964i
$839$			164.321i			0.195853i	0.995194	+	0.0979266i	$0.0312210\pi$
$839$			164.321i			0.195853i	−0.995194	+	0.0979266i	$0.968779\pi$
$840$	−1045.66			−1.24483
$841$	707.003			0.840669
$842$		−	1229.36i		−	1.46005i
$843$			460.236i			0.545950i
$844$	2206.36			2.61417
$845$		−	511.376i		−	0.605179i
$846$	654.822			0.774022
$847$			306.212i			0.361525i
$848$			337.649i			0.398171i
$849$			803.261i			0.946127i
$850$		−	1457.42i		−	1.71461i
$851$	−204.096	+	736.242i	−0.239830	+	0.865149i
$852$	479.816			0.563164
$853$	−1240.03			−1.45373			−0.726863	−	0.686782i	$-0.759023\pi$
$853$	−1240.03			−1.45373			−0.726863	+	0.686782i	$0.759023\pi$
$854$	−305.093			−0.357252
$855$	−587.527			−0.687166
$856$		−	4505.55i		−	5.26349i
$857$	−723.177			−0.843847			−0.421924	−	0.906631i	$-0.638645\pi$
$857$	−723.177			−0.843847			−0.421924	+	0.906631i	$0.638645\pi$
$858$			229.483i			0.267463i
$859$	−825.639			−0.961163			−0.480582	−	0.876950i	$-0.659574\pi$
$859$	−825.639			−0.961163			−0.480582	+	0.876950i	$0.659574\pi$
$860$	−6515.87			−7.57659
$861$		−	31.0182i		−	0.0360258i
$862$		−	1613.39i		−	1.87168i
$863$	1375.42			1.59377			0.796885	−	0.604131i	$-0.206480\pi$
$863$	1375.42			1.59377			0.796885	+	0.604131i	$0.206480\pi$
$864$	−579.237			−0.670413
$865$		−	2379.09i		−	2.75039i
$866$			1217.63i			1.40603i
$867$	413.308			0.476710
$868$			175.778i			0.202509i
$869$	−179.906			−0.207027
$870$			2316.44i			2.66257i
$871$			1945.41i			2.23354i
$872$			3267.96i			3.74766i
$873$		−	494.636i		−	0.566593i
$874$	−520.826	+	1878.79i	−0.595910	+	2.14965i
$875$	−668.997			−0.764568
$876$	18.0566			0.0206126
$877$	755.845			0.861853			0.430927	−	0.902387i	$-0.358187\pi$
$877$	755.845			0.861853			0.430927	+	0.902387i	$0.358187\pi$
$878$	−582.093			−0.662976
$879$			518.670i			0.590068i
$880$	−1136.72			−1.29173
$881$		−	297.426i		−	0.337601i	−0.985650	−	0.168800i	$-0.946011\pi$
$881$		−	297.426i		−	0.337601i	0.985650	−	0.168800i	$-0.0539893\pi$
$882$	80.5503			0.0913269
$883$	−1449.28			−1.64131			−0.820656	−	0.571422i	$-0.806392\pi$
$883$	−1449.28			−1.64131			−0.820656	+	0.571422i	$0.806392\pi$
$884$		−	1144.85i		−	1.29508i
$885$			1590.41i			1.79707i
$886$	653.592			0.737689
$887$	−473.042			−0.533306			−0.266653	−	0.963793i	$-0.585918\pi$
$887$	−473.042			−0.533306			−0.266653	+	0.963793i	$0.585918\pi$
$888$		−	1481.44i		−	1.66829i
$889$			360.799i			0.405848i
$890$	5115.25			5.74748
$891$		−	20.6469i		−	0.0231727i
$892$	−2380.77			−2.66902
$893$			1257.58i			1.40826i
$894$			660.896i			0.739257i
$895$			804.511i			0.898895i
$896$		−	889.845i		−	0.993131i
$897$	578.019	+	160.234i	0.644391	+	0.178634i
$898$	−2425.54			−2.70105
$899$	244.004			0.271418
$900$	−1720.47			−1.91164
$901$	42.8611			0.0475706
$902$		−	59.5617i		−	0.0660329i
$903$	314.522			0.348308
$904$			722.006i			0.798679i
$905$	−1.22847			−0.00135743
$906$	268.823			0.296714
$907$			1059.09i			1.16768i	0.811867	+	0.583842i	$0.198451\pi$
$907$			1059.09i			1.16768i	−0.811867	+	0.583842i	$0.801549\pi$
$908$		−	1316.40i		−	1.44978i
$909$	−13.3897			−0.0147302
$910$	−1354.11			−1.48803
$911$		−	867.979i		−	0.952776i	−0.879235	−	0.476388i	$-0.841946\pi$
$911$		−	867.979i		−	0.952776i	0.879235	−	0.476388i	$-0.158054\pi$
$912$		−	2140.21i		−	2.34672i
$913$	−163.627			−0.179219
$914$			876.037i			0.958465i
$915$	−461.447			−0.504314
$916$		−	501.220i		−	0.547183i
$917$		−	290.100i		−	0.316358i
$918$			141.463i			0.154100i
$919$			948.695i			1.03231i	0.856494	+	0.516156i	$0.172638\pi$
$919$			948.695i			1.03231i	−0.856494	+	0.516156i	$0.827362\pi$
$920$	−1401.99	+	5057.44i	−1.52390	+	5.49722i
$921$	973.491			1.05699
$922$	−2216.76			−2.40430
$923$	389.350			0.421831
$924$	112.623			0.121886
$925$		−	1778.25i		−	1.92243i
$926$	673.351			0.727161
$927$		−	52.2661i		−	0.0563820i
$928$	−4385.92			−4.72620
$929$	1409.26			1.51696			0.758481	−	0.651696i	$-0.225942\pi$
$929$	1409.26			1.51696			0.758481	+	0.651696i	$0.225942\pi$
$930$			365.129i			0.392612i
$931$			154.696i			0.166161i
$932$	3967.84			4.25734
$933$	265.954			0.285053
$934$		−	3026.50i		−	3.24037i
$935$			144.295i			0.154326i
$936$	−1163.07			−1.24260
$937$			1265.88i			1.35099i	0.737364	+	0.675495i	$0.236070\pi$
$937$			1265.88i			1.35099i	−0.737364	+	0.675495i	$0.763930\pi$
$938$	1311.23			1.39790
$939$			624.772i			0.665358i
$940$			5402.37i			5.74721i
$941$			388.953i			0.413340i	0.978411	+	0.206670i	$0.0662627\pi$
$941$			388.953i			0.413340i	−0.978411	+	0.206670i	$0.933737\pi$
$942$		−	1029.42i		−	1.09280i
$943$	−150.023	−	41.5884i	−0.159091	−	0.0441022i
$944$	−5793.45			−6.13713
$945$	121.831			0.128922
$946$	603.950			0.638425
$947$	−1096.67			−1.15805			−0.579026	−	0.815309i	$-0.696567\pi$
$947$	−1096.67			−1.15805			−0.579026	+	0.815309i	$0.696567\pi$
$948$		−	1455.12i		−	1.53494i
$949$	14.6522			0.0154396
$950$		−	4537.85i		−	4.77669i
$951$	291.067			0.306064
$952$	−483.523			−0.507902
$953$			336.869i			0.353483i	0.984257	+	0.176741i	$0.0565556\pi$
$953$			336.869i			0.353483i	−0.984257	+	0.176741i	$0.943444\pi$
$954$		−	69.4894i		−	0.0728401i
$955$	1304.12			1.36557
$956$	2617.80			2.73828
$957$		−	156.336i		−	0.163360i
$958$			1693.42i			1.76766i
$959$	−703.109			−0.733169
$960$		−	3130.20i		−	3.26062i
$961$	−922.539			−0.959978
$962$		−	1918.44i		−	1.99422i
$963$			524.947i			0.545116i
$964$		−	1549.03i		−	1.60688i
$965$		−	921.292i		−	0.954707i
$966$	108.000	−	389.591i	0.111801	−	0.403303i
$967$	−320.761			−0.331707			−0.165854	−	0.986150i	$-0.553038\pi$
$967$	−320.761			−0.331707			−0.165854	+	0.986150i	$0.553038\pi$
$968$	−2980.07			−3.07858
$969$	−271.678			−0.280370
$970$	5604.52			5.77786
$971$		−	928.767i		−	0.956505i	−0.878222	−	0.478253i	$-0.841270\pi$
$971$		−	928.767i		−	0.956505i	0.878222	−	0.478253i	$-0.158730\pi$
$972$	166.996			0.171807
$973$		−	534.767i		−	0.549606i
$974$	1981.33			2.03422
$975$	−1396.09			−1.43189
$976$		−	1680.93i		−	1.72227i
$977$		−	712.142i		−	0.728907i	−0.931222	−	0.364453i	$-0.881256\pi$
$977$		−	712.142i		−	0.728907i	0.931222	−	0.364453i	$-0.118744\pi$
$978$	1046.71			1.07026
$979$	−345.227			−0.352632
$980$			664.551i			0.678114i
$981$		−	380.754i		−	0.388129i
$982$	90.6877			0.0923500
$983$		−	1597.38i		−	1.62500i	−0.582961	−	0.812500i	$-0.698106\pi$
$983$		−	1597.38i		−	1.62500i	0.582961	−	0.812500i	$-0.301894\pi$
$984$	301.871			0.306780
$985$			927.171i			0.941290i
$986$			1071.14i			1.08635i
$987$		−	260.774i		−	0.264208i
$988$		−	3564.63i		−	3.60793i
$989$	421.702	−	1521.22i	0.426393	−	1.53814i
$990$	233.941			0.236304
$991$	−1771.78			−1.78788			−0.893938	−	0.448191i	$-0.852068\pi$
$991$	−1771.78			−1.78788			−0.893938	+	0.448191i	$0.852068\pi$
$992$	−691.331			−0.696907
$993$	945.736			0.952403
$994$		−	262.426i		−	0.264010i
$995$	−600.126			−0.603142
$996$		−	1323.45i		−	1.32876i
$997$	124.674			0.125049			0.0625244	−	0.998043i	$-0.480085\pi$
$997$	124.674			0.125049			0.0625244	+	0.998043i	$0.480085\pi$
$998$	−338.771			−0.339450
$999$			172.604i			0.172777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.3	✓	48
23.22	odd	2	inner	483.3.f.a.22.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.3	✓	48	1.1	even	1	trivial
483.3.f.a.22.4	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)

\(f(q)\)	\(=\)	\(q-3.83573 q^{2} +1.73205 q^{3} +10.7128 q^{4} -8.86189i q^{5} -6.64368 q^{6} +2.64575i q^{7} -25.7486 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.83573 q^{2} +1.73205 q^{3} +10.7128 q^{4} -8.86189i q^{5} -6.64368 q^{6} +2.64575i q^{7} -25.7486 q^{8} +3.00000 q^{9} +33.9918i q^{10} -2.29410i q^{11} +18.5552 q^{12} +15.0567 q^{13} -10.1484i q^{14} -15.3492i q^{15} +55.9134 q^{16} -7.09765i q^{17} -11.5072 q^{18} -22.0994i q^{19} -94.9359i q^{20} +4.58258i q^{21} +8.79953i q^{22} +(22.1641 + 6.14418i) q^{23} -44.5979 q^{24} -53.5331 q^{25} -57.7536 q^{26} +5.19615 q^{27} +28.3435i q^{28} +39.3447 q^{29} +58.8756i q^{30} +6.20172 q^{31} -111.474 q^{32} -3.97349i q^{33} +27.2247i q^{34} +23.4464 q^{35} +32.1385 q^{36} +33.2177i q^{37} +84.7673i q^{38} +26.0790 q^{39} +228.181i q^{40} -6.76874 q^{41} -17.5775i q^{42} -68.6344i q^{43} -24.5762i q^{44} -26.5857i q^{45} +(-85.0157 - 23.5674i) q^{46} -56.9055 q^{47} +96.8448 q^{48} -7.00000 q^{49} +205.339 q^{50} -12.2935i q^{51} +161.300 q^{52} +6.03878i q^{53} -19.9310 q^{54} -20.3300 q^{55} -68.1244i q^{56} -38.2772i q^{57} -150.916 q^{58} -103.615 q^{59} -164.434i q^{60} -30.0632i q^{61} -23.7881 q^{62} +7.93725i q^{63} +203.932 q^{64} -133.431i q^{65} +15.2412i q^{66} +129.206i q^{67} -76.0359i q^{68} +(38.3894 + 10.6420i) q^{69} -89.9339 q^{70} +25.8589 q^{71} -77.2458 q^{72} +0.973133 q^{73} -127.414i q^{74} -92.7221 q^{75} -236.747i q^{76} +6.06961 q^{77} -100.032 q^{78} -78.4213i q^{79} -495.498i q^{80} +9.00000 q^{81} +25.9630 q^{82} -71.3251i q^{83} +49.0923i q^{84} -62.8986 q^{85} +263.263i q^{86} +68.1470 q^{87} +59.0697i q^{88} -150.485i q^{89} +101.975i q^{90} +39.8364i q^{91} +(237.441 + 65.8216i) q^{92} +10.7417 q^{93} +218.274 q^{94} -195.842 q^{95} -193.079 q^{96} -164.879i q^{97} +26.8501 q^{98} -6.88229i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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