LMFDB - Embedded newform 483.3.f.a.22.31

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			22.31
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.48387 q^{2} -1.73205 q^{3} -1.79814 q^{4} -9.06666i q^{5} -2.57013 q^{6} -2.64575i q^{7} -8.60366 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.48387 q^{2} -1.73205 q^{3} -1.79814 q^{4} -9.06666i q^{5} -2.57013 q^{6} -2.64575i q^{7} -8.60366 q^{8} +3.00000 q^{9} -13.4537i q^{10} +9.31172i q^{11} +3.11448 q^{12} -2.55999 q^{13} -3.92594i q^{14} +15.7039i q^{15} -5.57411 q^{16} -19.3198i q^{17} +4.45160 q^{18} +32.4413i q^{19} +16.3031i q^{20} +4.58258i q^{21} +13.8173i q^{22} +(-13.7461 + 18.4403i) q^{23} +14.9020 q^{24} -57.2042 q^{25} -3.79868 q^{26} -5.19615 q^{27} +4.75744i q^{28} -43.8708 q^{29} +23.3025i q^{30} +38.5233 q^{31} +26.1434 q^{32} -16.1284i q^{33} -28.6680i q^{34} -23.9881 q^{35} -5.39443 q^{36} +23.6310i q^{37} +48.1385i q^{38} +4.43403 q^{39} +78.0065i q^{40} +4.56089 q^{41} +6.79993i q^{42} -8.34483i q^{43} -16.7438i q^{44} -27.2000i q^{45} +(-20.3973 + 27.3629i) q^{46} -52.7999 q^{47} +9.65464 q^{48} -7.00000 q^{49} -84.8834 q^{50} +33.4629i q^{51} +4.60323 q^{52} -84.5305i q^{53} -7.71039 q^{54} +84.4262 q^{55} +22.7632i q^{56} -56.1899i q^{57} -65.0984 q^{58} -71.9676 q^{59} -28.2379i q^{60} -4.54423i q^{61} +57.1634 q^{62} -7.93725i q^{63} +61.0898 q^{64} +23.2105i q^{65} -23.9323i q^{66} +17.3246i q^{67} +34.7398i q^{68} +(23.8089 - 31.9396i) q^{69} -35.5951 q^{70} -7.16233 q^{71} -25.8110 q^{72} -105.118 q^{73} +35.0653i q^{74} +99.0807 q^{75} -58.3341i q^{76} +24.6365 q^{77} +6.57950 q^{78} +24.4448i q^{79} +50.5385i q^{80} +9.00000 q^{81} +6.76775 q^{82} -50.7216i q^{83} -8.24013i q^{84} -175.166 q^{85} -12.3826i q^{86} +75.9865 q^{87} -80.1149i q^{88} +139.070i q^{89} -40.3611i q^{90} +6.77309i q^{91} +(24.7174 - 33.1583i) q^{92} -66.7243 q^{93} -78.3479 q^{94} +294.134 q^{95} -45.2818 q^{96} -87.9243i q^{97} -10.3871 q^{98} +27.9352i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.48387			0.741933			0.370966	−	0.928646i	$-0.379027\pi$
$2$	1.48387			0.741933			0.370966	+	0.928646i	$0.379027\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−1.79814			−0.449536
$5$		−	9.06666i		−	1.81333i	−0.421850	−	0.906666i	$-0.638619\pi$
$5$		−	9.06666i		−	1.81333i	0.421850	−	0.906666i	$-0.361381\pi$
$6$	−2.57013			−0.428355
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−8.60366			−1.07546
$9$	3.00000			0.333333
$10$		−	13.4537i		−	1.34537i
$11$			9.31172i			0.846520i	0.906008	+	0.423260i	$0.139114\pi$
$11$			9.31172i			0.846520i	−0.906008	+	0.423260i	$0.860886\pi$
$12$	3.11448			0.259540
$13$	−2.55999			−0.196922			−0.0984611	−	0.995141i	$-0.531392\pi$
$13$	−2.55999			−0.196922			−0.0984611	+	0.995141i	$0.531392\pi$
$14$		−	3.92594i		−	0.280424i
$15$			15.7039i			1.04693i
$16$	−5.57411			−0.348382
$17$		−	19.3198i		−	1.13646i	−0.822870	−	0.568229i	$-0.807629\pi$
$17$		−	19.3198i		−	1.13646i	0.822870	−	0.568229i	$-0.192371\pi$
$18$	4.45160			0.247311
$19$			32.4413i			1.70744i	0.520736	+	0.853718i	$0.325658\pi$
$19$			32.4413i			1.70744i	−0.520736	+	0.853718i	$0.674342\pi$
$20$			16.3031i			0.815157i
$21$			4.58258i			0.218218i
$22$			13.8173i			0.628061i
$23$	−13.7461	+	18.4403i	−0.597656	+	0.801753i
$23$	−13.7461	+	18.4403i	−0.597656	+	0.801753i
$24$	14.9020			0.620916
$25$	−57.2042			−2.28817
$26$	−3.79868			−0.146103
$27$	−5.19615			−0.192450
$28$			4.75744i			0.169909i
$29$	−43.8708			−1.51279			−0.756393	−	0.654117i	$-0.773040\pi$
$29$	−43.8708			−1.51279			−0.756393	+	0.654117i	$0.773040\pi$
$30$			23.3025i			0.776750i
$31$	38.5233			1.24269			0.621343	−	0.783539i	$-0.286587\pi$
$31$	38.5233			1.24269			0.621343	+	0.783539i	$0.286587\pi$
$32$	26.1434			0.816982
$33$		−	16.1284i		−	0.488739i
$34$		−	28.6680i		−	0.843176i
$35$	−23.9881			−0.685375
$36$	−5.39443			−0.149845
$37$			23.6310i			0.638677i	0.947641	+	0.319338i	$0.103461\pi$
$37$			23.6310i			0.638677i	−0.947641	+	0.319338i	$0.896539\pi$
$38$			48.1385i			1.26680i
$39$	4.43403			0.113693
$40$			78.0065i			1.95016i
$41$	4.56089			0.111241			0.0556206	−	0.998452i	$-0.482286\pi$
$41$	4.56089			0.111241			0.0556206	+	0.998452i	$0.482286\pi$
$42$			6.79993i			0.161903i
$43$		−	8.34483i		−	0.194066i	−0.995281	−	0.0970329i	$-0.969065\pi$
$43$		−	8.34483i		−	0.194066i	0.995281	−	0.0970329i	$-0.0309352\pi$
$44$		−	16.7438i		−	0.380541i
$45$		−	27.2000i		−	0.604444i
$46$	−20.3973	+	27.3629i	−0.443420	+	0.594847i
$47$	−52.7999			−1.12340			−0.561701	−	0.827340i	$-0.689853\pi$
$47$	−52.7999			−1.12340			−0.561701	+	0.827340i	$0.689853\pi$
$48$	9.65464			0.201138
$49$	−7.00000			−0.142857
$50$	−84.8834			−1.69767
$51$			33.4629i			0.656135i
$52$	4.60323			0.0885236
$53$		−	84.5305i		−	1.59492i	−0.603375	−	0.797458i	$-0.706178\pi$
$53$		−	84.5305i		−	1.59492i	0.603375	−	0.797458i	$-0.293822\pi$
$54$	−7.71039			−0.142785
$55$	84.4262			1.53502
$56$			22.7632i			0.406485i
$57$		−	56.1899i		−	0.985788i
$58$	−65.0984			−1.12239
$59$	−71.9676			−1.21979			−0.609895	−	0.792483i	$-0.708788\pi$
$59$	−71.9676			−1.21979			−0.609895	+	0.792483i	$0.708788\pi$
$60$		−	28.2379i		−	0.470631i
$61$		−	4.54423i		−	0.0744955i	−0.999306	−	0.0372477i	$-0.988141\pi$
$61$		−	4.54423i		−	0.0744955i	0.999306	−	0.0372477i	$-0.0118591\pi$
$62$	57.1634			0.921990
$63$		−	7.93725i		−	0.125988i
$64$	61.0898			0.954528
$65$			23.2105i			0.357085i
$66$		−	23.9323i		−	0.362611i
$67$			17.3246i			0.258576i	0.991607	+	0.129288i	$0.0412692\pi$
$67$			17.3246i			0.258576i	−0.991607	+	0.129288i	$0.958731\pi$
$68$			34.7398i			0.510879i
$69$	23.8089	−	31.9396i	0.345057	−	0.462892i
$70$	−35.5951			−0.508502
$71$	−7.16233			−0.100878			−0.0504390	−	0.998727i	$-0.516062\pi$
$71$	−7.16233			−0.100878			−0.0504390	+	0.998727i	$0.516062\pi$
$72$	−25.8110			−0.358486
$73$	−105.118			−1.43997			−0.719986	−	0.693988i	$-0.755852\pi$
$73$	−105.118			−1.43997			−0.719986	+	0.693988i	$0.755852\pi$
$74$			35.0653i			0.473855i
$75$	99.0807			1.32108
$76$		−	58.3341i		−	0.767554i
$77$	24.6365			0.319955
$78$	6.57950			0.0843526
$79$			24.4448i			0.309427i	0.987959	+	0.154714i	$0.0494455\pi$
$79$			24.4448i			0.309427i	−0.987959	+	0.154714i	$0.950555\pi$
$80$			50.5385i			0.631731i
$81$	9.00000			0.111111
$82$	6.76775			0.0825335
$83$		−	50.7216i		−	0.611103i	−0.952175	−	0.305552i	$-0.901159\pi$
$83$		−	50.7216i		−	0.611103i	0.952175	−	0.305552i	$-0.0988409\pi$
$84$		−	8.24013i		−	0.0980968i
$85$	−175.166			−2.06078
$86$		−	12.3826i		−	0.143984i
$87$	75.9865			0.873407
$88$		−	80.1149i		−	0.910397i
$89$			139.070i			1.56258i	0.624166	+	0.781292i	$0.285439\pi$
$89$			139.070i			1.56258i	−0.624166	+	0.781292i	$0.714561\pi$
$90$		−	40.3611i		−	0.448457i
$91$			6.77309i			0.0744296i
$92$	24.7174	−	33.1583i	0.268668	−	0.360417i
$93$	−66.7243			−0.717465
$94$	−78.3479			−0.833489
$95$	294.134			3.09615
$96$	−45.2818			−0.471685
$97$		−	87.9243i		−	0.906436i	−0.891400	−	0.453218i	$-0.850276\pi$
$97$		−	87.9243i		−	0.906436i	0.891400	−	0.453218i	$-0.149724\pi$
$98$	−10.3871			−0.105990
$99$			27.9352i			0.282173i
$100$	102.861			1.02861
$101$	81.4044			0.805984			0.402992	−	0.915203i	$-0.367970\pi$
$101$	81.4044			0.805984			0.402992	+	0.915203i	$0.367970\pi$
$102$			49.6544i			0.486808i
$103$		−	33.0355i		−	0.320733i	−0.987058	−	0.160366i	$-0.948732\pi$
$103$		−	33.0355i		−	0.320733i	0.987058	−	0.160366i	$-0.0512676\pi$
$104$	22.0253			0.211782
$105$	41.5486			0.395701
$106$		−	125.432i		−	1.18332i
$107$		−	111.869i		−	1.04550i	−0.852485	−	0.522752i	$-0.824905\pi$
$107$		−	111.869i		−	1.04550i	0.852485	−	0.522752i	$-0.175095\pi$
$108$	9.34343			0.0865132
$109$			71.4959i			0.655926i	0.944691	+	0.327963i	$0.106362\pi$
$109$			71.4959i			0.655926i	−0.944691	+	0.327963i	$0.893638\pi$
$110$	125.277			1.13888
$111$		−	40.9302i		−	0.368740i
$112$			14.7477i			0.131676i
$113$			49.1628i			0.435069i	0.976053	+	0.217535i	$0.0698015\pi$
$113$			49.1628i			0.435069i	−0.976053	+	0.217535i	$0.930198\pi$
$114$		−	83.3783i		−	0.731389i
$115$	167.192	+	124.631i	1.45384	+	1.08375i
$116$	78.8860			0.680052
$117$	−7.67996			−0.0656407
$118$	−106.790			−0.905002
$119$	−51.1154			−0.429541
$120$		−	135.111i		−	1.12593i
$121$	34.2919			0.283404
$122$		−	6.74302i		−	0.0552706i
$123$	−7.89969			−0.0642252
$124$	−69.2704			−0.558632
$125$			291.985i			2.33588i
$126$		−	11.7778i		−	0.0934747i
$127$	−38.1027			−0.300021			−0.150011	−	0.988684i	$-0.547931\pi$
$127$	−38.1027			−0.300021			−0.150011	+	0.988684i	$0.547931\pi$
$128$	−13.9247			−0.108787
$129$			14.4537i			0.112044i
$130$			34.4413i			0.264933i
$131$	229.827			1.75440			0.877202	−	0.480122i	$-0.159408\pi$
$131$	229.827			1.75440			0.877202	+	0.480122i	$0.159408\pi$
$132$			29.0011i			0.219706i
$133$	85.8315			0.645350
$134$			25.7074i			0.191846i
$135$			47.1117i			0.348976i
$136$			166.221i			1.22221i
$137$		−	132.544i		−	0.967472i	−0.875214	−	0.483736i	$-0.839279\pi$
$137$		−	132.544i		−	0.967472i	0.875214	−	0.483736i	$-0.160721\pi$
$138$	35.3292	−	47.3940i	0.256009	−	0.343435i
$139$	−122.541			−0.881590			−0.440795	−	0.897608i	$-0.645303\pi$
$139$	−122.541			−0.881590			−0.440795	+	0.897608i	$0.645303\pi$
$140$	43.1341			0.308101
$141$	91.4521			0.648596
$142$	−10.6279			−0.0748446
$143$		−	23.8379i		−	0.166699i
$144$	−16.7223			−0.116127
$145$			397.761i			2.74318i
$146$	−155.981			−1.06836
$147$	12.1244			0.0824786
$148$		−	42.4920i		−	0.287108i
$149$		−	281.158i		−	1.88696i	−0.331423	−	0.943482i	$-0.607529\pi$
$149$		−	281.158i		−	1.88696i	0.331423	−	0.943482i	$-0.392471\pi$
$150$	147.022			0.980149
$151$	−155.004			−1.02651			−0.513257	−	0.858235i	$-0.671561\pi$
$151$	−155.004			−1.02651			−0.513257	+	0.858235i	$0.671561\pi$
$152$		−	279.114i		−	1.83628i
$153$		−	57.9594i		−	0.378820i
$154$	36.5572			0.237385
$155$		−	349.277i		−	2.25340i
$156$	−7.97302			−0.0511091
$157$		−	86.4632i		−	0.550721i	−0.961341	−	0.275361i	$-0.911203\pi$
$157$		−	86.4632i		−	0.550721i	0.961341	−	0.275361i	$-0.0887972\pi$
$158$			36.2727i			0.229574i
$159$			146.411i			0.920825i
$160$		−	237.034i		−	1.48146i
$161$	48.7885	+	36.3687i	0.303034	+	0.225893i
$162$	13.3548			0.0824370
$163$	−238.744			−1.46469			−0.732344	−	0.680935i	$-0.761574\pi$
$163$	−238.744			−1.46469			−0.732344	+	0.680935i	$0.761574\pi$
$164$	−8.20114			−0.0500069
$165$	−146.230			−0.886245
$166$		−	75.2640i		−	0.453398i
$167$	−176.325			−1.05584			−0.527920	−	0.849294i	$-0.677028\pi$
$167$	−176.325			−1.05584			−0.527920	+	0.849294i	$0.677028\pi$
$168$		−	39.4269i		−	0.234684i
$169$	−162.446			−0.961222
$170$	−259.923			−1.52896
$171$			97.3238i			0.569145i
$172$			15.0052i			0.0872395i
$173$	17.5784			0.101609			0.0508046	−	0.998709i	$-0.483821\pi$
$173$	17.5784			0.101609			0.0508046	+	0.998709i	$0.483821\pi$
$174$	112.754			0.648010
$175$			151.348i			0.864847i
$176$		−	51.9045i		−	0.294912i
$177$	124.651			0.704246
$178$			206.361i			1.15933i
$179$	−198.134			−1.10689			−0.553447	−	0.832884i	$-0.686688\pi$
$179$	−198.134			−1.10689			−0.553447	+	0.832884i	$0.686688\pi$
$180$			48.9094i			0.271719i
$181$			196.005i			1.08290i	0.840733	+	0.541450i	$0.182125\pi$
$181$			196.005i			1.08290i	−0.840733	+	0.541450i	$0.817875\pi$
$182$			10.0504i			0.0552217i
$183$			7.87083i			0.0430100i
$184$	118.267	−	158.654i	0.642754	−	0.862251i
$185$	214.254			1.15813
$186$	−99.0098			−0.532311
$187$	179.901			0.962035
$188$	94.9418			0.505009
$189$			13.7477i			0.0727393i
$190$	436.455			2.29713
$191$		−	130.232i		−	0.681845i	−0.940091	−	0.340922i	$-0.889261\pi$
$191$		−	130.232i		−	0.681845i	0.940091	−	0.340922i	$-0.110739\pi$
$192$	−105.811			−0.551097
$193$	−136.522			−0.707369			−0.353685	−	0.935365i	$-0.615071\pi$
$193$	−136.522			−0.707369			−0.353685	+	0.935365i	$0.615071\pi$
$194$		−	130.468i		−	0.672514i
$195$		−	40.2018i		−	0.206163i
$196$	12.5870			0.0642194
$197$	−324.986			−1.64968			−0.824838	−	0.565369i	$-0.808734\pi$
$197$	−324.986			−1.64968			−0.824838	+	0.565369i	$0.808734\pi$
$198$			41.4520i			0.209354i
$199$		−	77.3532i		−	0.388710i	−0.980931	−	0.194355i	$-0.937739\pi$
$199$		−	77.3532i		−	0.388710i	0.980931	−	0.194355i	$-0.0622613\pi$
$200$	492.166			2.46083
$201$		−	30.0071i		−	0.149289i
$202$	120.793			0.597986
$203$			116.071i			0.571779i
$204$		−	60.1710i		−	0.294956i
$205$		−	41.3520i		−	0.201717i
$206$		−	49.0202i		−	0.237962i
$207$	−41.2383	+	55.3209i	−0.199219	+	0.267251i
$208$	14.2696			0.0686041
$209$	−302.084			−1.44538
$210$	61.6526			0.293584
$211$	−316.333			−1.49921			−0.749603	−	0.661887i	$-0.769756\pi$
$211$	−316.333			−1.49921			−0.749603	+	0.661887i	$0.769756\pi$
$212$			151.998i			0.716972i
$213$	12.4055			0.0582419
$214$		−	165.998i		−	0.775693i
$215$	−75.6597			−0.351905
$216$	44.7060			0.206972
$217$		−	101.923i		−	0.469691i
$218$			106.090i			0.486653i
$219$	182.070			0.831368
$220$	−151.810			−0.690047
$221$			49.4585i			0.223794i
$222$		−	60.7348i		−	0.273580i
$223$	81.6517			0.366151			0.183076	−	0.983099i	$-0.441395\pi$
$223$	81.6517			0.366151			0.183076	+	0.983099i	$0.441395\pi$
$224$		−	69.1690i		−	0.308790i
$225$	−171.613			−0.762723
$226$			72.9510i			0.322792i
$227$		−	132.661i		−	0.584411i	−0.956356	−	0.292205i	$-0.905611\pi$
$227$		−	132.661i		−	0.584411i	0.956356	−	0.292205i	$-0.0943891\pi$
$228$			101.038i			0.443147i
$229$			89.4015i			0.390400i	0.980764	+	0.195200i	$0.0625355\pi$
$229$			89.4015i			0.390400i	−0.980764	+	0.195200i	$0.937464\pi$
$230$	248.090	+	184.936i	1.07865	+	0.804068i
$231$	−42.6717			−0.184726
$232$	377.450			1.62694
$233$	274.436			1.17784			0.588919	−	0.808192i	$-0.299554\pi$
$233$	274.436			1.17784			0.588919	+	0.808192i	$0.299554\pi$
$234$	−11.3960			−0.0487010
$235$			478.718i			2.03710i
$236$	129.408			0.548339
$237$		−	42.3396i		−	0.178648i
$238$	−75.8483			−0.318691
$239$	233.100			0.975312			0.487656	−	0.873036i	$-0.337852\pi$
$239$	233.100			0.975312			0.487656	+	0.873036i	$0.337852\pi$
$240$		−	87.5353i		−	0.364730i
$241$		−	333.262i		−	1.38283i	−0.722459	−	0.691414i	$-0.756988\pi$
$241$		−	333.262i		−	1.38283i	0.722459	−	0.691414i	$-0.243012\pi$
$242$	50.8845			0.210267
$243$	−15.5885			−0.0641500
$244$			8.17117i			0.0334884i
$245$			63.4666i			0.259047i
$246$	−11.7221			−0.0476507
$247$		−	83.0493i		−	0.336232i
$248$	−331.441			−1.33646
$249$			87.8524i			0.352821i
$250$			433.266i			1.73306i
$251$		−	85.5025i		−	0.340648i	−0.985388	−	0.170324i	$-0.945519\pi$
$251$		−	85.5025i		−	0.340648i	0.985388	−	0.170324i	$-0.0544814\pi$
$252$			14.2723i			0.0566362i
$253$	−171.711	−	128.000i	−0.678700	−	0.505928i
$254$	−56.5393			−0.222595
$255$	303.396			1.18979
$256$	−265.022			−1.03524
$257$	208.375			0.810797			0.405399	−	0.914140i	$-0.367133\pi$
$257$	208.375			0.810797			0.405399	+	0.914140i	$0.367133\pi$
$258$			21.4473i			0.0831290i
$259$	62.5218			0.241397
$260$		−	41.7359i		−	0.160523i
$261$	−131.612			−0.504262
$262$	341.032			1.30165
$263$			200.384i			0.761916i	0.924592	+	0.380958i	$0.124406\pi$
$263$			200.384i			0.761916i	−0.924592	+	0.380958i	$0.875594\pi$
$264$			138.763i			0.525618i
$265$	−766.409			−2.89211
$266$	127.362			0.478806
$267$		−	240.876i		−	0.902158i
$268$		−	31.1521i		−	0.116239i
$269$	61.1837			0.227449			0.113724	−	0.993512i	$-0.463722\pi$
$269$	61.1837			0.227449			0.113724	+	0.993512i	$0.463722\pi$
$270$			69.9075i			0.258917i
$271$	452.523			1.66982			0.834912	−	0.550383i	$-0.185518\pi$
$271$	452.523			1.66982			0.834912	+	0.550383i	$0.185518\pi$
$272$			107.691i			0.395921i
$273$		−	11.7313i		−	0.0429719i
$274$		−	196.677i		−	0.717799i
$275$		−	532.670i		−	1.93698i
$276$	−42.8119	+	57.4319i	−0.155115	+	0.208087i
$277$	−16.0791			−0.0580472			−0.0290236	−	0.999579i	$-0.509240\pi$
$277$	−16.0791			−0.0580472			−0.0290236	+	0.999579i	$0.509240\pi$
$278$	−181.834			−0.654080
$279$	115.570			0.414229
$280$	206.386			0.737092
$281$		−	284.692i		−	1.01314i	−0.862199	−	0.506569i	$-0.830914\pi$
$281$		−	284.692i		−	1.01314i	0.862199	−	0.506569i	$-0.169086\pi$
$282$	135.703			0.481215
$283$			231.088i			0.816564i	0.912856	+	0.408282i	$0.133872\pi$
$283$			231.088i			0.816564i	−0.912856	+	0.408282i	$0.866128\pi$
$284$	12.8789			0.0453482
$285$	−509.455			−1.78756
$286$		−	35.3722i		−	0.123679i
$287$		−	12.0670i		−	0.0420452i
$288$	78.4303			0.272327
$289$	−84.2546			−0.291538
$290$			590.224i			2.03526i
$291$			152.289i			0.523331i
$292$	189.017			0.647319
$293$			358.614i			1.22394i	0.790881	+	0.611970i	$0.209623\pi$
$293$			358.614i			1.22394i	−0.790881	+	0.611970i	$0.790377\pi$
$294$	17.9909			0.0611936
$295$			652.505i			2.21188i
$296$		−	203.313i		−	0.686870i
$297$		−	48.3851i		−	0.162913i
$298$		−	417.200i		−	1.40000i
$299$	35.1898	−	47.2070i	0.117692	−	0.157883i
$300$	−178.161			−0.593871
$301$	−22.0783			−0.0733500
$302$	−230.004			−0.761604
$303$	−140.997			−0.465335
$304$		−	180.831i		−	0.594839i
$305$	−41.2009			−0.135085
$306$		−	86.0039i		−	0.281059i
$307$	−285.732			−0.930723			−0.465361	−	0.885121i	$-0.654076\pi$
$307$	−285.732			−0.930723			−0.465361	+	0.885121i	$0.654076\pi$
$308$	−44.3000			−0.143831
$309$			57.2191i			0.185175i
$310$		−	518.280i		−	1.67187i
$311$	−426.887			−1.37263			−0.686314	−	0.727305i	$-0.740772\pi$
$311$	−426.887			−1.37263			−0.686314	+	0.727305i	$0.740772\pi$
$312$	−38.1489			−0.122272
$313$		−	9.41955i		−	0.0300944i	−0.999887	−	0.0150472i	$-0.995210\pi$
$313$		−	9.41955i		−	0.0300944i	0.999887	−	0.0150472i	$-0.00478986\pi$
$314$		−	128.300i		−	0.408598i
$315$	−71.9643			−0.228458
$316$		−	43.9552i		−	0.139099i
$317$	305.261			0.962967			0.481484	−	0.876455i	$-0.340098\pi$
$317$	305.261			0.962967			0.481484	+	0.876455i	$0.340098\pi$
$318$			217.254i			0.683190i
$319$		−	408.513i		−	1.28060i
$320$		−	553.880i		−	1.73087i
$321$			193.763i			0.603622i
$322$	72.3955	+	53.9663i	0.224831	+	0.167597i
$323$	626.759			1.94043
$324$	−16.1833			−0.0499484
$325$	146.442			0.450591
$326$	−354.264			−1.08670
$327$		−	123.835i		−	0.378699i
$328$	−39.2404			−0.119635
$329$			139.695i			0.424606i
$330$	−216.986			−0.657534
$331$	−254.788			−0.769752			−0.384876	−	0.922968i	$-0.625756\pi$
$331$	−254.788			−0.769752			−0.384876	+	0.922968i	$0.625756\pi$
$332$			91.2047i			0.274713i
$333$			70.8931i			0.212892i
$334$	−261.643			−0.783362
$335$	157.076			0.468884
$336$		−	25.5438i		−	0.0760231i
$337$		−	229.517i		−	0.681060i	−0.940234	−	0.340530i	$-0.889393\pi$
$337$		−	229.517i		−	0.681060i	0.940234	−	0.340530i	$-0.110607\pi$
$338$	−241.049			−0.713162
$339$		−	85.1525i		−	0.251187i
$340$	314.974			0.926393
$341$			358.718i			1.05196i
$342$			144.415i			0.422267i
$343$			18.5203i			0.0539949i
$344$			71.7961i			0.208710i
$345$	−289.585	−	215.867i	−0.839377	−	0.625702i
$346$	26.0840			0.0753872
$347$	516.762			1.48923			0.744614	−	0.667495i	$-0.232634\pi$
$347$	516.762			1.48923			0.744614	+	0.667495i	$0.232634\pi$
$348$	−136.635			−0.392628
$349$	49.8612			0.142869			0.0714343	−	0.997445i	$-0.477242\pi$
$349$	49.8612			0.142869			0.0714343	+	0.997445i	$0.477242\pi$
$350$			224.580i			0.641658i
$351$	13.3021			0.0378977
$352$			243.440i			0.691592i
$353$	−572.786			−1.62262			−0.811312	−	0.584613i	$-0.801246\pi$
$353$	−572.786			−1.62262			−0.811312	+	0.584613i	$0.801246\pi$
$354$	184.966			0.522503
$355$			64.9384i			0.182925i
$356$		−	250.068i		−	0.702437i
$357$	88.5344			0.247996
$358$	−294.004			−0.821241
$359$			279.721i			0.779168i	0.920991	+	0.389584i	$0.127381\pi$
$359$			279.721i			0.779168i	−0.920991	+	0.389584i	$0.872619\pi$
$360$			234.019i			0.650054i
$361$	−691.436			−1.91534
$362$			290.845i			0.803440i
$363$	−59.3952			−0.163623
$364$		−	12.1790i		−	0.0334588i
$365$			953.069i			2.61115i
$366$			11.6793i			0.0319105i
$367$		−	294.499i		−	0.802448i	−0.915980	−	0.401224i	$-0.868585\pi$
$367$		−	294.499i		−	0.802448i	0.915980	−	0.401224i	$-0.131415\pi$
$368$	76.6221	−	102.788i	0.208212	−	0.279316i
$369$	13.6827			0.0370804
$370$	317.925			0.859256
$371$	−223.647			−0.602821
$372$	119.980			0.322526
$373$			456.957i			1.22509i	0.790437	+	0.612543i	$0.209854\pi$
$373$			456.957i			1.22509i	−0.790437	+	0.612543i	$0.790146\pi$
$374$	266.948			0.713765
$375$		−	505.733i		−	1.34862i
$376$	454.273			1.20817
$377$	112.309			0.297901
$378$			20.3998i			0.0539677i
$379$			293.440i			0.774248i	0.922028	+	0.387124i	$0.126531\pi$
$379$			293.440i			0.774248i	−0.922028	+	0.387124i	$0.873469\pi$
$380$	−528.895			−1.39183
$381$	65.9958			0.173217
$382$		−	193.247i		−	0.505883i
$383$		−	440.359i		−	1.14976i	−0.818237	−	0.574881i	$-0.805048\pi$
$383$		−	440.359i		−	1.14976i	0.818237	−	0.574881i	$-0.194952\pi$
$384$	24.1184			0.0628083
$385$		−	223.371i		−	0.580183i
$386$	−202.581			−0.524820
$387$		−	25.0345i		−	0.0646886i
$388$			158.100i			0.407475i
$389$			584.329i			1.50213i	0.660227	+	0.751066i	$0.270460\pi$
$389$			584.329i			1.50213i	−0.660227	+	0.751066i	$0.729540\pi$
$390$		−	59.6541i		−	0.152959i
$391$	356.263	+	265.572i	0.911159	+	0.679211i
$392$	60.2257			0.153637
$393$	−398.072			−1.01291
$394$	−482.236			−1.22395
$395$	221.632			0.561094
$396$		−	50.2314i		−	0.126847i
$397$	−551.294			−1.38865			−0.694325	−	0.719662i	$-0.744297\pi$
$397$	−551.294			−1.38865			−0.694325	+	0.719662i	$0.744297\pi$
$398$		−	114.782i		−	0.288396i
$399$	−148.665			−0.372593
$400$	318.863			0.797156
$401$		−	508.714i		−	1.26861i	−0.773081	−	0.634307i	$-0.781286\pi$
$401$		−	508.714i		−	1.26861i	0.773081	−	0.634307i	$-0.218714\pi$
$402$		−	44.5265i		−	0.110762i
$403$	−98.6191			−0.244712
$404$	−146.377			−0.362319
$405$		−	81.5999i		−	0.201481i
$406$			172.234i			0.424222i
$407$	−220.046			−0.540653
$408$		−	287.903i		−	0.705645i
$409$	435.452			1.06467			0.532337	−	0.846532i	$-0.321314\pi$
$409$	435.452			1.06467			0.532337	+	0.846532i	$0.321314\pi$
$410$		−	61.3608i		−	0.149661i
$411$			229.572i			0.558570i
$412$			59.4025i			0.144181i
$413$			190.408i			0.461037i
$414$	−61.1920	+	82.0888i	−0.147807	+	0.198282i
$415$	−459.875			−1.10813
$416$	−66.9269			−0.160882
$417$	212.247			0.508986
$418$	−448.252			−1.07237
$419$		−	314.132i		−	0.749719i	−0.927082	−	0.374860i	$-0.877691\pi$
$419$		−	314.132i		−	0.749719i	0.927082	−	0.374860i	$-0.122309\pi$
$420$	−74.7104			−0.177882
$421$			104.191i			0.247485i	0.992314	+	0.123743i	$0.0394897\pi$
$421$			104.191i			0.247485i	−0.992314	+	0.123743i	$0.960510\pi$
$422$	−469.395			−1.11231
$423$	−158.400			−0.374467
$424$			727.272i			1.71526i
$425$			1105.17i			2.60041i
$426$	18.4081			0.0432116
$427$	−12.0229			−0.0281566
$428$			201.156i			0.469991i
$429$			41.2884i			0.0962435i
$430$	−112.269			−0.261090
$431$			407.846i			0.946279i	0.880987	+	0.473140i	$0.156879\pi$
$431$			407.846i			0.946279i	−0.880987	+	0.473140i	$0.843121\pi$
$432$	28.9639			0.0670461
$433$		−	688.964i		−	1.59114i	−0.605861	−	0.795570i	$-0.707171\pi$
$433$		−	688.964i		−	1.59114i	0.605861	−	0.795570i	$-0.292829\pi$
$434$		−	151.240i		−	0.348479i
$435$		−	688.943i		−	1.58378i
$436$		−	128.560i		−	0.294862i
$437$	−598.227	−	445.941i	−1.36894	−	1.02046i
$438$	270.167			0.616819
$439$	763.289			1.73870			0.869349	−	0.494198i	$-0.164538\pi$
$439$	763.289			1.73870			0.869349	+	0.494198i	$0.164538\pi$
$440$	−726.374			−1.65085
$441$	−21.0000			−0.0476190
$442$			73.3897i			0.166040i
$443$	−288.564			−0.651386			−0.325693	−	0.945475i	$-0.605598\pi$
$443$	−288.564			−0.651386			−0.325693	+	0.945475i	$0.605598\pi$
$444$			73.5983i			0.165762i
$445$	1260.90			2.83348
$446$	121.160			0.271660
$447$			486.979i			1.08944i
$448$		−	161.628i		−	0.360778i
$449$	622.375			1.38613			0.693067	−	0.720873i	$-0.256259\pi$
$449$	622.375			1.38613			0.693067	+	0.720873i	$0.256259\pi$
$450$	−254.650			−0.565889
$451$			42.4697i			0.0941679i
$452$		−	88.4018i		−	0.195579i
$453$	268.474			0.592658
$454$		−	196.851i		−	0.433594i
$455$	61.4093			0.134965
$456$			483.439i			1.06017i
$457$			361.025i			0.789988i	0.918684	+	0.394994i	$0.129253\pi$
$457$			361.025i			0.789988i	−0.918684	+	0.394994i	$0.870747\pi$
$458$			132.660i			0.289650i
$459$			100.389i			0.218712i
$460$	−300.635	−	224.104i	−0.653555	−	0.487184i
$461$	609.759			1.32269			0.661344	−	0.750083i	$-0.269986\pi$
$461$	609.759			1.32269			0.661344	+	0.750083i	$0.269986\pi$
$462$	−63.3190			−0.137054
$463$	450.168			0.972285			0.486143	−	0.873880i	$-0.338404\pi$
$463$	450.168			0.972285			0.486143	+	0.873880i	$0.338404\pi$
$464$	244.541			0.527027
$465$			604.966i			1.30100i
$466$	407.226			0.873876
$467$			796.388i			1.70533i	0.522459	+	0.852664i	$0.325015\pi$
$467$			796.388i			1.70533i	−0.522459	+	0.852664i	$0.674985\pi$
$468$	13.8097			0.0295079
$469$	45.8366			0.0977326
$470$			710.354i			1.51139i
$471$			149.759i			0.317959i
$472$	619.185			1.31183
$473$	77.7047			0.164281
$474$		−	62.8262i		−	0.132545i
$475$		−	1855.78i		−	3.90690i
$476$	91.9128			0.193094
$477$		−	253.592i		−	0.531639i
$478$	345.888			0.723616
$479$			489.890i			1.02273i	0.859362	+	0.511367i	$0.170861\pi$
$479$			489.890i			1.02273i	−0.859362	+	0.511367i	$0.829139\pi$
$480$			410.554i			0.855321i
$481$		−	60.4952i		−	0.125770i
$482$		−	494.515i		−	1.02597i
$483$	−84.5041	−	62.9925i	−0.174957	−	0.130419i
$484$	−61.6617			−0.127400
$485$	−797.179			−1.64367
$486$	−23.1312			−0.0475950
$487$	301.771			0.619653			0.309827	−	0.950793i	$-0.399729\pi$
$487$	301.771			0.619653			0.309827	+	0.950793i	$0.399729\pi$
$488$			39.0970i			0.0801168i
$489$	413.517			0.845638
$490$			94.1759i			0.192196i
$491$	−458.635			−0.934083			−0.467042	−	0.884235i	$-0.654680\pi$
$491$	−458.635			−0.934083			−0.467042	+	0.884235i	$0.654680\pi$
$492$	14.2048			0.0288715
$493$			847.575i			1.71922i
$494$		−	123.234i		−	0.249461i
$495$	253.278			0.511674
$496$	−214.733			−0.432929
$497$			18.9497i			0.0381283i
$498$			130.361i			0.261769i
$499$	−66.2550			−0.132776			−0.0663878	−	0.997794i	$-0.521147\pi$
$499$	−66.2550			−0.132776			−0.0663878	+	0.997794i	$0.521147\pi$
$500$		−	525.031i		−	1.05006i
$501$	305.404			0.609589
$502$		−	126.874i		−	0.252738i
$503$		−	568.366i		−	1.12995i	−0.825108	−	0.564976i	$-0.808886\pi$
$503$		−	568.366i		−	1.12995i	0.825108	−	0.564976i	$-0.191114\pi$
$504$			68.2895i			0.135495i
$505$		−	738.066i		−	1.46152i
$506$	−254.796	−	189.934i	−0.503550	−	0.375364i
$507$	281.366			0.554962
$508$	68.5141			0.134870
$509$	26.9621			0.0529707			0.0264854	−	0.999649i	$-0.491568\pi$
$509$	26.9621			0.0529707			0.0264854	+	0.999649i	$0.491568\pi$
$510$	450.199			0.882744
$511$			278.116i			0.544258i
$512$	−337.557			−0.659292
$513$		−	168.570i		−	0.328596i
$514$	309.200			0.601557
$515$	−299.521			−0.581595
$516$		−	25.9898i		−	0.0503678i
$517$		−	491.658i		−	0.950982i
$518$	92.7740			0.179100
$519$	−30.4467			−0.0586641
$520$		−	199.696i		−	0.384030i
$521$		−	541.033i		−	1.03845i	−0.854637	−	0.519226i	$-0.826220\pi$
$521$		−	541.033i		−	1.03845i	0.854637	−	0.519226i	$-0.173780\pi$
$522$	−195.295			−0.374129
$523$			329.954i			0.630886i	0.948944	+	0.315443i	$0.102153\pi$
$523$			329.954i			0.630886i	−0.948944	+	0.315443i	$0.897847\pi$
$524$	−413.262			−0.788667
$525$		−	262.143i		−	0.499320i
$526$			297.343i			0.565291i
$527$		−	744.262i		−	1.41226i
$528$			89.9013i			0.170268i
$529$	−151.090	−	506.964i	−0.285615	−	0.958344i
$530$	−1137.25			−2.14575
$531$	−215.903			−0.406596
$532$	−154.337			−0.290108
$533$	−11.6758			−0.0219059
$534$		−	357.428i		−	0.669341i
$535$	−1014.28			−1.89584
$536$		−	149.055i		−	0.278088i
$537$	343.178			0.639066
$538$	90.7884			0.168752
$539$		−	65.1820i		−	0.120931i
$540$		−	84.7136i		−	0.156877i
$541$	−127.946			−0.236500			−0.118250	−	0.992984i	$-0.537728\pi$
$541$	−127.946			−0.236500			−0.118250	+	0.992984i	$0.537728\pi$
$542$	671.483			1.23890
$543$		−	339.491i		−	0.625213i
$544$		−	505.086i		−	0.928467i
$545$	648.229			1.18941
$546$		−	17.4077i		−	0.0318823i
$547$	238.199			0.435465			0.217733	−	0.976008i	$-0.430134\pi$
$547$	238.199			0.435465			0.217733	+	0.976008i	$0.430134\pi$
$548$			238.333i			0.434914i
$549$		−	13.6327i		−	0.0248318i
$550$		−	790.411i		−	1.43711i
$551$		−	1423.22i		−	2.58298i
$552$	−204.844	+	274.797i	−0.371094	+	0.497821i
$553$	64.6747			0.116952
$554$	−23.8592			−0.0430671
$555$	−371.100			−0.668648
$556$	220.346			0.396306
$557$			893.790i			1.60465i	0.596887	+	0.802325i	$0.296404\pi$
$557$			893.790i			1.60465i	−0.596887	+	0.802325i	$0.703596\pi$
$558$	171.490			0.307330
$559$			21.3627i			0.0382158i
$560$	133.712			0.238772
$561$	−311.597			−0.555431
$562$		−	422.444i		−	0.751680i
$563$		−	924.676i		−	1.64241i	−0.570635	−	0.821204i	$-0.693303\pi$
$563$		−	924.676i		−	1.64241i	0.570635	−	0.821204i	$-0.306697\pi$
$564$	−164.444			−0.291567
$565$	445.743			0.788925
$566$			342.903i			0.605836i
$567$		−	23.8118i		−	0.0419961i
$568$	61.6223			0.108490
$569$		−	848.850i		−	1.49183i	−0.666042	−	0.745914i	$-0.732013\pi$
$569$		−	848.850i		−	1.49183i	0.666042	−	0.745914i	$-0.267987\pi$
$570$	−755.962			−1.32625
$571$			119.725i			0.209676i	0.994489	+	0.104838i	$0.0334324\pi$
$571$			119.725i			0.209676i	−0.994489	+	0.104838i	$0.966568\pi$
$572$			42.8640i			0.0749370i
$573$			225.569i			0.393663i
$574$		−	17.9058i		−	0.0311947i
$575$	786.334	−	1054.86i	1.36754	−	1.83455i
$576$	183.269			0.318176
$577$	908.395			1.57434			0.787171	−	0.616735i	$-0.211545\pi$
$577$	908.395			1.57434			0.787171	+	0.616735i	$0.211545\pi$
$578$	−125.022			−0.216302
$579$	236.463			0.408400
$580$		−	715.232i		−	1.23316i
$581$	−134.197			−0.230975
$582$			225.977i			0.388276i
$583$	787.125			1.35013
$584$	904.400			1.54863
$585$			69.6316i			0.119028i
$586$			532.135i			0.908081i
$587$	705.171			1.20131			0.600656	−	0.799507i	$-0.294906\pi$
$587$	705.171			1.20131			0.600656	+	0.799507i	$0.294906\pi$
$588$	−21.8013			−0.0370771
$589$			1249.74i			2.12181i
$590$			968.230i			1.64107i
$591$	562.893			0.952441
$592$		−	131.722i		−	0.222503i
$593$	−704.621			−1.18823			−0.594116	−	0.804380i	$-0.702498\pi$
$593$	−704.621			−1.18823			−0.594116	+	0.804380i	$0.702498\pi$
$594$		−	71.7970i		−	0.120870i
$595$			463.446i			0.778900i
$596$			505.562i			0.848258i
$597$			133.980i			0.224422i
$598$	52.2169	−	70.0488i	0.0873193	−	0.117138i
$599$	−719.086			−1.20048			−0.600239	−	0.799821i	$-0.704928\pi$
$599$	−719.086			−1.20048			−0.600239	+	0.799821i	$0.704928\pi$
$600$	−852.457			−1.42076
$601$	−226.459			−0.376803			−0.188401	−	0.982092i	$-0.560331\pi$
$601$	−226.459			−0.376803			−0.188401	+	0.982092i	$0.560331\pi$
$602$	−32.7613			−0.0544207
$603$			51.9738i			0.0861921i
$604$	278.719			0.461455
$605$		−	310.912i		−	0.513905i
$606$	−209.220			−0.345247
$607$	1076.48			1.77343			0.886717	−	0.462312i	$-0.152980\pi$
$607$	1076.48			1.77343			0.886717	+	0.462312i	$0.152980\pi$
$608$			848.126i			1.39494i
$609$		−	201.041i		−	0.330117i
$610$	−61.1366			−0.100224
$611$	135.167			0.221223
$612$			104.219i			0.170293i
$613$			983.519i			1.60443i	0.597032	+	0.802217i	$0.296347\pi$
$613$			983.519i			1.60443i	−0.597032	+	0.802217i	$0.703653\pi$
$614$	−423.988			−0.690534
$615$			71.6238i			0.116461i
$616$	−211.964			−0.344098
$617$			140.967i			0.228472i	0.993454	+	0.114236i	$0.0364420\pi$
$617$			140.967i			0.228472i	−0.993454	+	0.114236i	$0.963558\pi$
$618$			84.9055i			0.137387i
$619$		−	102.165i		−	0.165049i	−0.996589	−	0.0825246i	$-0.973702\pi$
$619$		−	102.165i		−	0.165049i	0.996589	−	0.0825246i	$-0.0262983\pi$
$620$			628.051i			1.01298i
$621$	71.4268	−	95.8187i	0.115019	−	0.154297i
$622$	−633.443			−1.01840
$623$	367.945			0.590601
$624$	−24.7158			−0.0396086
$625$	1217.22			1.94755
$626$		−	13.9773i		−	0.0223280i
$627$	523.225			0.834490
$628$			155.473i			0.247569i
$629$	456.547			0.725830
$630$	−106.785			−0.169501
$631$		−	666.393i		−	1.05609i	−0.849216	−	0.528045i	$-0.822925\pi$
$631$		−	666.393i		−	1.05609i	0.849216	−	0.528045i	$-0.177075\pi$
$632$		−	210.314i		−	0.332776i
$633$	547.904			0.865567
$634$	452.966			0.714457
$635$			345.464i			0.544038i
$636$		−	263.268i		−	0.413944i
$637$	17.9199			0.0281317
$638$		−	606.178i		−	0.950122i
$639$	−21.4870			−0.0336260
$640$			126.251i			0.197267i
$641$			818.588i			1.27705i	0.769602	+	0.638524i	$0.220455\pi$
$641$			818.588i			1.27705i	−0.769602	+	0.638524i	$0.779545\pi$
$642$			287.518i			0.447847i
$643$			680.177i			1.05782i	0.848679	+	0.528909i	$0.177399\pi$
$643$			680.177i			1.05782i	−0.848679	+	0.528909i	$0.822601\pi$
$644$	−87.7287	−	65.3962i	−0.136225	−	0.101547i
$645$	131.046			0.203173
$646$	930.026			1.43967
$647$	822.754			1.27164			0.635822	−	0.771836i	$-0.280661\pi$
$647$	822.754			1.27164			0.635822	+	0.771836i	$0.280661\pi$
$648$	−77.4330			−0.119495
$649$		−	670.142i		−	1.03258i
$650$	217.301			0.334308
$651$			176.536i			0.271176i
$652$	429.296			0.658430
$653$	227.439			0.348299			0.174149	−	0.984719i	$-0.444282\pi$
$653$	227.439			0.348299			0.174149	+	0.984719i	$0.444282\pi$
$654$		−	183.754i		−	0.280969i
$655$		−	2083.76i		−	3.18131i
$656$	−25.4229			−0.0387544
$657$	−315.354			−0.479991
$658$			207.289i			0.315029i
$659$		−	593.207i		−	0.900162i	−0.892988	−	0.450081i	$-0.851395\pi$
$659$		−	593.207i		−	0.900162i	0.892988	−	0.450081i	$-0.148605\pi$
$660$	262.943			0.398399
$661$			523.089i			0.791360i	0.918388	+	0.395680i	$0.129491\pi$
$661$			523.089i			0.791360i	−0.918388	+	0.395680i	$0.870509\pi$
$662$	−378.071			−0.571104
$663$		−	85.6646i		−	0.129207i
$664$			436.391i			0.657216i
$665$		−	778.205i		−	1.17023i
$666$			105.196i			0.157952i
$667$	603.052	−	808.991i	0.904126	−	1.21288i
$668$	317.058			0.474638
$669$	−141.425			−0.211398
$670$	233.080			0.347881
$671$	42.3146			0.0630619
$672$			119.804i			0.178280i
$673$	−712.720			−1.05902			−0.529510	−	0.848304i	$-0.677624\pi$
$673$	−712.720			−1.05902			−0.529510	+	0.848304i	$0.677624\pi$
$674$		−	340.573i		−	0.505301i
$675$	297.242			0.440359
$676$	292.102			0.432104
$677$		−	590.156i		−	0.871722i	−0.900014	−	0.435861i	$-0.856444\pi$
$677$		−	590.156i		−	0.871722i	0.900014	−	0.435861i	$-0.143556\pi$
$678$		−	126.355i		−	0.186364i
$679$	−232.626			−0.342600
$680$	1507.07			2.21628
$681$			229.776i			0.337410i
$682$			532.289i			0.780483i
$683$	−1079.06			−1.57989			−0.789944	−	0.613179i	$-0.789890\pi$
$683$	−1079.06			−1.57989			−0.789944	+	0.613179i	$0.789890\pi$
$684$		−	175.002i		−	0.255851i
$685$	−1201.73			−1.75435
$686$			27.4816i			0.0400606i
$687$		−	154.848i		−	0.225397i
$688$			46.5150i			0.0676089i
$689$			216.397i			0.314074i
$690$	−429.705	−	320.318i	−0.622761	−	0.464229i
$691$	585.637			0.847522			0.423761	−	0.905774i	$-0.360710\pi$
$691$	585.637			0.847522			0.423761	+	0.905774i	$0.360710\pi$
$692$	−31.6085			−0.0456770
$693$	73.9095			0.106652
$694$	766.805			1.10491
$695$			1111.04i			1.59861i
$696$	−653.762			−0.939313
$697$		−	88.1155i		−	0.126421i
$698$	73.9872			0.105999
$699$	−475.337			−0.680025
$700$		−	272.146i		−	0.388780i
$701$			808.408i			1.15322i	0.817019	+	0.576611i	$0.195625\pi$
$701$			808.408i			1.15322i	−0.817019	+	0.576611i	$0.804375\pi$
$702$	19.7385			0.0281175
$703$	−766.621			−1.09050
$704$			568.851i			0.808027i
$705$		−	829.165i		−	1.17612i
$706$	−849.938			−1.20388
$707$		−	215.376i		−	0.304633i
$708$	−224.141			−0.316584
$709$		−	264.882i		−	0.373599i	−0.982398	−	0.186799i	$-0.940189\pi$
$709$		−	264.882i		−	0.373599i	0.982398	−	0.186799i	$-0.0598115\pi$
$710$			96.3598i			0.135718i
$711$			73.3343i			0.103142i
$712$		−	1196.51i		−	1.68049i
$713$	−529.544	+	710.381i	−0.742699	+	0.996327i
$714$	131.373			0.183996
$715$	−216.130			−0.302280
$716$	356.274			0.497589
$717$	−403.740			−0.563097
$718$			415.069i			0.578090i
$719$	630.432			0.876818			0.438409	−	0.898776i	$-0.355542\pi$
$719$	630.432			0.876818			0.438409	+	0.898776i	$0.355542\pi$
$720$			151.616i			0.210577i
$721$	−87.4036			−0.121226
$722$	−1026.00			−1.42105
$723$			577.226i			0.798376i
$724$		−	352.445i		−	0.486803i
$725$	2509.60			3.46151
$726$	−88.1345			−0.121397
$727$		−	686.738i		−	0.944619i	−0.881433	−	0.472309i	$-0.843421\pi$
$727$		−	686.738i		−	0.944619i	0.881433	−	0.472309i	$-0.156579\pi$
$728$		−	58.2734i		−	0.0800459i
$729$	27.0000			0.0370370
$730$			1414.23i			1.93730i
$731$	−161.220			−0.220548
$732$		−	14.1529i		−	0.0193345i
$733$			1193.52i			1.62827i	0.580679	+	0.814133i	$0.302787\pi$
$733$			1193.52i			1.62827i	−0.580679	+	0.814133i	$0.697213\pi$
$734$		−	436.996i		−	0.595363i
$735$		−	109.927i		−	0.149561i
$736$	−359.370	+	482.093i	−0.488274	+	0.655018i
$737$	−161.322			−0.218890
$738$	20.3032			0.0275112
$739$	208.477			0.282107			0.141054	−	0.990002i	$-0.454951\pi$
$739$	208.477			0.282107			0.141054	+	0.990002i	$0.454951\pi$
$740$	−385.260			−0.520622
$741$			143.846i			0.194124i
$742$	−331.862			−0.447253
$743$		−	1007.95i		−	1.35660i	−0.734785	−	0.678300i	$-0.762717\pi$
$743$		−	1007.95i		−	1.35660i	0.734785	−	0.678300i	$-0.237283\pi$
$744$	574.073			0.771604
$745$	−2549.16			−3.42169
$746$			678.063i			0.908932i
$747$		−	152.165i		−	0.203701i
$748$	−323.487			−0.432469
$749$	−295.977			−0.395163
$750$		−	750.439i		−	1.00059i
$751$			370.056i			0.492751i	0.969174	+	0.246376i	$0.0792397\pi$
$751$			370.056i			0.492751i	−0.969174	+	0.246376i	$0.920760\pi$
$752$	294.312			0.391373
$753$			148.095i			0.196673i
$754$	166.651			0.221023
$755$			1405.36i			1.86141i
$756$		−	24.7204i		−	0.0326989i
$757$		−	377.374i		−	0.498513i	−0.968437	−	0.249257i	$-0.919814\pi$
$757$		−	377.374i		−	0.498513i	0.968437	−	0.249257i	$-0.0801863\pi$
$758$			435.426i			0.574440i
$759$	297.412	+	221.702i	0.391847	+	0.292097i
$760$	−2530.63			−3.32978
$761$	−326.135			−0.428561			−0.214281	−	0.976772i	$-0.568741\pi$
$761$	−326.135			−0.428561			−0.214281	+	0.976772i	$0.568741\pi$
$762$	97.9289			0.128516
$763$	189.160			0.247917
$764$			234.177i			0.306514i
$765$	−525.498			−0.686925
$766$		−	653.434i		−	0.853047i
$767$	184.236			0.240204
$768$	459.031			0.597696
$769$		−	779.728i		−	1.01395i	−0.861961	−	0.506975i	$-0.830764\pi$
$769$		−	779.728i		−	1.01395i	0.861961	−	0.506975i	$-0.169236\pi$
$770$		−	331.452i		−	0.430457i
$771$	−360.916			−0.468114
$772$	245.487			0.317988
$773$		−	742.483i		−	0.960522i	−0.877126	−	0.480261i	$-0.840542\pi$
$773$		−	742.483i		−	0.960522i	0.877126	−	0.480261i	$-0.159458\pi$
$774$		−	37.1478i		−	0.0479946i
$775$	−2203.70			−2.84348
$776$			756.471i			0.974834i
$777$	−108.291			−0.139371
$778$			867.066i			1.11448i
$779$			147.961i			0.189937i
$780$			72.2886i			0.0926777i
$781$		−	66.6936i		−	0.0853952i
$782$	528.647	+	394.072i	0.676019	+	0.503929i
$783$	227.959			0.291136
$784$	39.0187			0.0497688
$785$	−783.932			−0.998640
$786$	−590.685			−0.751508
$787$		−	1269.92i		−	1.61362i	−0.590810	−	0.806811i	$-0.701192\pi$
$787$		−	1269.92i		−	1.61362i	0.590810	−	0.806811i	$-0.298808\pi$
$788$	584.372			0.741589
$789$		−	347.075i		−	0.439893i
$790$	328.872			0.416294
$791$	130.073			0.164441
$792$		−	240.345i		−	0.303466i
$793$			11.6332i			0.0146698i
$794$	−818.046			−1.03028
$795$	1327.46			1.66976
$796$			139.092i			0.174739i
$797$		−	209.738i		−	0.263159i	−0.991306	−	0.131579i	$-0.957995\pi$
$797$		−	209.738i		−	0.263159i	0.991306	−	0.131579i	$-0.0420049\pi$
$798$	−220.598			−0.276439
$799$			1020.08i			1.27670i
$800$	−1495.52			−1.86939
$801$			417.210i			0.520861i
$802$		−	754.863i		−	0.941226i
$803$		−	978.829i		−	1.21897i
$804$			53.9571i			0.0671108i
$805$	329.743	−	442.348i	0.409618	−	0.549501i
$806$	−146.338			−0.181560
$807$	−105.973			−0.131318
$808$	−700.376			−0.866802
$809$	−1059.61			−1.30978			−0.654891	−	0.755723i	$-0.727286\pi$
$809$	−1059.61			−1.30978			−0.654891	+	0.755723i	$0.727286\pi$
$810$		−	121.083i		−	0.149486i
$811$	−573.545			−0.707208			−0.353604	−	0.935395i	$-0.615044\pi$
$811$	−573.545			−0.707208			−0.353604	+	0.935395i	$0.615044\pi$
$812$		−	208.713i		−	0.257035i
$813$	−783.792			−0.964074
$814$	−326.518			−0.401128
$815$			2164.61i			2.65596i
$816$		−	186.526i		−	0.228585i
$817$	270.717			0.331355
$818$	646.152			0.789917
$819$			20.3193i			0.0248099i
$820$			74.3569i			0.0906791i
$821$	−1216.78			−1.48207			−0.741033	−	0.671468i	$-0.765664\pi$
$821$	−1216.78			−1.48207			−0.741033	+	0.671468i	$0.765664\pi$
$822$			340.655i			0.414422i
$823$	−1062.39			−1.29087			−0.645437	−	0.763814i	$-0.723325\pi$
$823$	−1062.39			−1.29087			−0.645437	+	0.763814i	$0.723325\pi$
$824$			284.226i			0.344935i
$825$			922.611i			1.11832i
$826$			282.540i			0.342058i
$827$		−	886.803i		−	1.07231i	−0.844118	−	0.536157i	$-0.819876\pi$
$827$		−	886.803i		−	1.07231i	0.844118	−	0.536157i	$-0.180124\pi$
$828$	74.1523	−	99.4750i	0.0895559	−	0.120139i
$829$	124.420			0.150085			0.0750425	−	0.997180i	$-0.476091\pi$
$829$	124.420			0.150085			0.0750425	+	0.997180i	$0.476091\pi$
$830$	−682.393			−0.822160
$831$	27.8498			0.0335136
$832$	−156.389			−0.187968
$833$			135.239i			0.162351i
$834$	314.946			0.377633
$835$			1598.68i			1.91459i
$836$	543.191			0.649749
$837$	−200.173			−0.239155
$838$		−	466.130i		−	0.556241i
$839$		−	99.1985i		−	0.118234i	−0.998251	−	0.0591171i	$-0.981171\pi$
$839$		−	99.1985i		−	0.118234i	0.998251	−	0.0591171i	$-0.0188285\pi$
$840$	−357.471			−0.425560
$841$	1083.65			1.28852
$842$			154.606i			0.183617i
$843$			493.101i			0.584935i
$844$	568.811			0.673947
$845$			1472.85i			1.74301i
$846$	−235.044			−0.277830
$847$		−	90.7277i		−	0.107117i
$848$			471.182i			0.555639i
$849$		−	400.256i		−	0.471444i
$850$			1639.93i			1.92933i
$851$	−435.764	−	324.834i	−0.512061	−	0.381709i
$852$	−22.3069			−0.0261818
$853$	141.064			0.165374			0.0826869	−	0.996576i	$-0.473650\pi$
$853$	141.064			0.165374			0.0826869	+	0.996576i	$0.473650\pi$
$854$	−17.8403			−0.0208903
$855$	882.402			1.03205
$856$			962.482i			1.12440i
$857$	−112.754			−0.131569			−0.0657843	−	0.997834i	$-0.520955\pi$
$857$	−112.754			−0.131569			−0.0657843	+	0.997834i	$0.520955\pi$
$858$			61.2665i			0.0714062i
$859$	217.574			0.253288			0.126644	−	0.991948i	$-0.459579\pi$
$859$	217.574			0.253288			0.126644	+	0.991948i	$0.459579\pi$
$860$	136.047			0.158194
$861$			20.9006i			0.0242748i
$862$			605.189i			0.702075i
$863$	1094.08			1.26776			0.633882	−	0.773430i	$-0.281461\pi$
$863$	1094.08			1.26776			0.633882	+	0.773430i	$0.281461\pi$
$864$	−135.845			−0.157228
$865$		−	159.377i		−	0.184251i
$866$		−	1022.33i		−	1.18052i
$867$	145.933			0.168320
$868$			183.272i			0.211143i
$869$	−227.623			−0.261936
$870$		−	1022.30i		−	1.17506i
$871$		−	44.3508i		−	0.0509194i
$872$		−	615.127i		−	0.705421i
$873$		−	263.773i		−	0.302145i
$874$	−887.689	−	661.716i	−1.01566	−	0.757112i
$875$	772.519			0.882879
$876$	−327.387			−0.373730
$877$	756.394			0.862479			0.431239	−	0.902238i	$-0.358076\pi$
$877$	756.394			0.862479			0.431239	+	0.902238i	$0.358076\pi$
$878$	1132.62			1.29000
$879$		−	621.138i		−	0.706642i
$880$	−470.600			−0.534773
$881$		−	441.745i		−	0.501413i	−0.968063	−	0.250707i	$-0.919337\pi$
$881$		−	441.745i		−	0.501413i	0.968063	−	0.250707i	$-0.0806630\pi$
$882$	−31.1612			−0.0353301
$883$	898.298			1.01732			0.508662	−	0.860966i	$-0.330140\pi$
$883$	898.298			1.01732			0.508662	+	0.860966i	$0.330140\pi$
$884$		−	88.9334i		−	0.100603i
$885$		−	1130.17i		−	1.27703i
$886$	−428.190			−0.483285
$887$	372.711			0.420193			0.210097	−	0.977681i	$-0.432622\pi$
$887$	372.711			0.420193			0.210097	+	0.977681i	$0.432622\pi$
$888$			352.149i			0.396565i
$889$			100.810i			0.113397i
$890$	1871.00			2.10225
$891$			83.8055i			0.0940578i
$892$	−146.822			−0.164598
$893$		−	1712.90i		−	1.91814i
$894$			722.612i			0.808291i
$895$			1796.41i			2.00717i
$896$			36.8414i			0.0411177i
$897$	−60.9505	+	81.7649i	−0.0679493	+	0.0911537i
$898$	923.520			1.02842
$899$	−1690.05			−1.87992
$900$	308.584			0.342871
$901$	−1633.11			−1.81256
$902$			63.0194i			0.0698663i
$903$	38.2408			0.0423486
$904$		−	422.981i		−	0.467899i
$905$	1777.11			1.96366
$906$	398.379			0.439712
$907$			1498.21i			1.65183i	0.563793	+	0.825916i	$0.309342\pi$
$907$			1498.21i			1.65183i	−0.563793	+	0.825916i	$0.690658\pi$
$908$			238.544i			0.262714i
$909$	244.213			0.268661
$910$	91.1231			0.100135
$911$			411.409i			0.451601i	0.974174	+	0.225801i	$0.0724998\pi$
$911$			411.409i			0.451601i	−0.974174	+	0.225801i	$0.927500\pi$
$912$			313.209i			0.343431i
$913$	472.305			0.517311
$914$			535.712i			0.586118i
$915$	71.3621			0.0779914
$916$		−	160.757i		−	0.175499i
$917$		−	608.065i		−	0.663102i
$918$			148.963i			0.162269i
$919$			1393.48i			1.51630i	0.652081	+	0.758150i	$0.273896\pi$
$919$			1393.48i			1.51630i	−0.652081	+	0.758150i	$0.726104\pi$
$920$	−1438.46	−	1072.28i	−1.56355	−	1.16553i
$921$	494.902			0.537353
$922$	904.800			0.981345
$923$	18.3355			0.0198651
$924$	76.7298			0.0830409
$925$		−	1351.80i		−	1.46140i
$926$	667.989			0.721370
$927$		−	99.1064i		−	0.106911i
$928$	−1146.93			−1.23592
$929$	−1582.75			−1.70371			−0.851855	−	0.523777i	$-0.824522\pi$
$929$	−1582.75			−1.70371			−0.851855	+	0.523777i	$0.824522\pi$
$930$			897.688i			0.965256i
$931$		−	227.089i		−	0.243919i
$932$	−493.476			−0.529480
$933$	739.390			0.792487
$934$			1181.73i			1.26524i
$935$		−	1631.10i		−	1.74449i
$936$	66.0758			0.0705938
$937$			1656.90i			1.76830i	0.467201	+	0.884151i	$0.345262\pi$
$937$			1656.90i			1.76830i	−0.467201	+	0.884151i	$0.654738\pi$
$938$	68.0154			0.0725110
$939$			16.3151i			0.0173750i
$940$		−	860.804i		−	0.915749i
$941$			283.541i			0.301318i	0.988586	+	0.150659i	$0.0481396\pi$
$941$			283.541i			0.301318i	−0.988586	+	0.150659i	$0.951860\pi$
$942$			222.222i			0.235904i
$943$	−62.6944	+	84.1042i	−0.0664840	+	0.0891880i
$944$	401.155			0.424952
$945$	124.646			0.131900
$946$	115.303			0.121885
$947$	354.428			0.374264			0.187132	−	0.982335i	$-0.440081\pi$
$947$	354.428			0.374264			0.187132	+	0.982335i	$0.440081\pi$
$948$			76.1326i			0.0803086i
$949$	269.101			0.283562
$950$		−	2753.73i		−	2.89866i
$951$	−528.727			−0.555969
$952$	439.780			0.461953
$953$		−	911.432i		−	0.956382i	−0.878256	−	0.478191i	$-0.841293\pi$
$953$		−	911.432i		−	0.956382i	0.878256	−	0.478191i	$-0.158707\pi$
$954$		−	376.296i		−	0.394440i
$955$	−1180.77			−1.23641
$956$	−419.146			−0.438438
$957$			707.565i			0.739357i
$958$			726.931i			0.758800i
$959$	−350.678			−0.365670
$960$			959.348i			0.999321i
$961$	523.043			0.544269
$962$		−	89.7667i		−	0.0933126i
$963$		−	335.607i		−	0.348501i
$964$			599.252i			0.621631i
$965$			1237.80i			1.28269i
$966$	−125.393	−	93.4724i	−0.129806	−	0.0967623i
$967$	−531.759			−0.549905			−0.274953	−	0.961458i	$-0.588662\pi$
$967$	−531.759			−0.549905			−0.274953	+	0.961458i	$0.588662\pi$
$968$	−295.036			−0.304789
$969$	−1085.58			−1.12031
$970$	−1182.91			−1.21949
$971$		−	133.687i		−	0.137680i	−0.997628	−	0.0688400i	$-0.978070\pi$
$971$		−	133.687i		−	0.137680i	0.997628	−	0.0688400i	$-0.0219298\pi$
$972$	28.0303			0.0288377
$973$			324.213i			0.333210i
$974$	447.788			0.459741
$975$	−253.645			−0.260149
$976$			25.3300i			0.0259529i
$977$		−	1020.19i		−	1.04420i	−0.852883	−	0.522102i	$-0.825148\pi$
$977$		−	1020.19i		−	1.04420i	0.852883	−	0.522102i	$-0.174852\pi$
$978$	613.603			0.627406
$979$	−1294.98			−1.32276
$980$		−	114.122i		−	0.116451i
$981$			214.488i			0.218642i
$982$	−680.552			−0.693027
$983$		−	1553.40i		−	1.58026i	−0.612939	−	0.790130i	$-0.710013\pi$
$983$		−	1553.40i		−	1.58026i	0.612939	−	0.790130i	$-0.289987\pi$
$984$	67.9663			0.0690715
$985$			2946.54i			2.99141i
$986$			1257.69i			1.27554i
$987$		−	241.959i		−	0.245146i
$988$			149.335i			0.151148i
$989$	153.881	+	114.709i	0.155593	+	0.115985i
$990$	375.831			0.379627
$991$	−645.590			−0.651453			−0.325727	−	0.945464i	$-0.605609\pi$
$991$	−645.590			−0.651453			−0.325727	+	0.945464i	$0.605609\pi$
$992$	1007.13			1.01525
$993$	441.305			0.444416
$994$			28.1189i			0.0282886i
$995$	−701.335			−0.704859
$996$		−	157.971i		−	0.158606i
$997$	−327.689			−0.328675			−0.164337	−	0.986404i	$-0.552549\pi$
$997$	−327.689			−0.328675			−0.164337	+	0.986404i	$0.552549\pi$
$998$	−98.3135			−0.0985106
$999$		−	122.790i		−	0.122913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.31	✓	48
23.22	odd	2	inner	483.3.f.a.22.32	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.31	✓	48	1.1	even	1	trivial
483.3.f.a.22.32	yes	48	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.48387 q^{2} -1.73205 q^{3} -1.79814 q^{4} -9.06666i q^{5} -2.57013 q^{6} -2.64575i q^{7} -8.60366 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.48387 q^{2} -1.73205 q^{3} -1.79814 q^{4} -9.06666i q^{5} -2.57013 q^{6} -2.64575i q^{7} -8.60366 q^{8} +3.00000 q^{9} -13.4537i q^{10} +9.31172i q^{11} +3.11448 q^{12} -2.55999 q^{13} -3.92594i q^{14} +15.7039i q^{15} -5.57411 q^{16} -19.3198i q^{17} +4.45160 q^{18} +32.4413i q^{19} +16.3031i q^{20} +4.58258i q^{21} +13.8173i q^{22} +(-13.7461 + 18.4403i) q^{23} +14.9020 q^{24} -57.2042 q^{25} -3.79868 q^{26} -5.19615 q^{27} +4.75744i q^{28} -43.8708 q^{29} +23.3025i q^{30} +38.5233 q^{31} +26.1434 q^{32} -16.1284i q^{33} -28.6680i q^{34} -23.9881 q^{35} -5.39443 q^{36} +23.6310i q^{37} +48.1385i q^{38} +4.43403 q^{39} +78.0065i q^{40} +4.56089 q^{41} +6.79993i q^{42} -8.34483i q^{43} -16.7438i q^{44} -27.2000i q^{45} +(-20.3973 + 27.3629i) q^{46} -52.7999 q^{47} +9.65464 q^{48} -7.00000 q^{49} -84.8834 q^{50} +33.4629i q^{51} +4.60323 q^{52} -84.5305i q^{53} -7.71039 q^{54} +84.4262 q^{55} +22.7632i q^{56} -56.1899i q^{57} -65.0984 q^{58} -71.9676 q^{59} -28.2379i q^{60} -4.54423i q^{61} +57.1634 q^{62} -7.93725i q^{63} +61.0898 q^{64} +23.2105i q^{65} -23.9323i q^{66} +17.3246i q^{67} +34.7398i q^{68} +(23.8089 - 31.9396i) q^{69} -35.5951 q^{70} -7.16233 q^{71} -25.8110 q^{72} -105.118 q^{73} +35.0653i q^{74} +99.0807 q^{75} -58.3341i q^{76} +24.6365 q^{77} +6.57950 q^{78} +24.4448i q^{79} +50.5385i q^{80} +9.00000 q^{81} +6.76775 q^{82} -50.7216i q^{83} -8.24013i q^{84} -175.166 q^{85} -12.3826i q^{86} +75.9865 q^{87} -80.1149i q^{88} +139.070i q^{89} -40.3611i q^{90} +6.77309i q^{91} +(24.7174 - 33.1583i) q^{92} -66.7243 q^{93} -78.3479 q^{94} +294.134 q^{95} -45.2818 q^{96} -87.9243i q^{97} -10.3871 q^{98} +27.9352i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

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Database

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