LMFDB - Embedded newform 483.3.f.a.22.2

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			22.2
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.89548 q^{2} -1.73205 q^{3} +11.1748 q^{4} -5.58204i q^{5} +6.74717 q^{6} -2.64575i q^{7} -27.9492 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.89548 q^{2} -1.73205 q^{3} +11.1748 q^{4} -5.58204i q^{5} +6.74717 q^{6} -2.64575i q^{7} -27.9492 q^{8} +3.00000 q^{9} +21.7447i q^{10} +2.39573i q^{11} -19.3553 q^{12} +3.11386 q^{13} +10.3065i q^{14} +9.66838i q^{15} +64.1766 q^{16} +21.5972i q^{17} -11.6864 q^{18} +28.1601i q^{19} -62.3781i q^{20} +4.58258i q^{21} -9.33253i q^{22} +(-12.2020 - 19.4964i) q^{23} +48.4095 q^{24} -6.15917 q^{25} -12.1300 q^{26} -5.19615 q^{27} -29.5657i q^{28} -26.5764 q^{29} -37.6630i q^{30} -10.2295 q^{31} -138.202 q^{32} -4.14953i q^{33} -84.1314i q^{34} -14.7687 q^{35} +33.5243 q^{36} +23.1532i q^{37} -109.697i q^{38} -5.39336 q^{39} +156.014i q^{40} +43.5431 q^{41} -17.8513i q^{42} -37.6961i q^{43} +26.7718i q^{44} -16.7461i q^{45} +(47.5326 + 75.9481i) q^{46} -31.7454 q^{47} -111.157 q^{48} -7.00000 q^{49} +23.9929 q^{50} -37.4074i q^{51} +34.7967 q^{52} +76.1649i q^{53} +20.2415 q^{54} +13.3731 q^{55} +73.9467i q^{56} -48.7747i q^{57} +103.528 q^{58} +80.8498 q^{59} +108.042i q^{60} +58.9379i q^{61} +39.8488 q^{62} -7.93725i q^{63} +281.657 q^{64} -17.3817i q^{65} +16.1644i q^{66} -11.9484i q^{67} +241.344i q^{68} +(21.1345 + 33.7688i) q^{69} +57.5312 q^{70} +105.964 q^{71} -83.8477 q^{72} -15.6066 q^{73} -90.1930i q^{74} +10.6680 q^{75} +314.683i q^{76} +6.33851 q^{77} +21.0097 q^{78} +118.357i q^{79} -358.236i q^{80} +9.00000 q^{81} -169.621 q^{82} -52.9699i q^{83} +51.2093i q^{84} +120.556 q^{85} +146.844i q^{86} +46.0317 q^{87} -66.9588i q^{88} +6.05127i q^{89} +65.2342i q^{90} -8.23850i q^{91} +(-136.355 - 217.869i) q^{92} +17.7180 q^{93} +123.664 q^{94} +157.191 q^{95} +239.373 q^{96} -46.7582i q^{97} +27.2684 q^{98} +7.18719i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.89548			−1.94774			−0.973871	−	0.227104i	$-0.927074\pi$
$2$	−3.89548			−1.94774			−0.973871	+	0.227104i	$0.927074\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	11.1748			2.79370
$5$		−	5.58204i		−	1.11641i	−0.829704	−	0.558204i	$-0.811491\pi$
$5$		−	5.58204i		−	1.11641i	0.829704	−	0.558204i	$-0.188509\pi$
$6$	6.74717			1.12453
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−27.9492			−3.49365
$9$	3.00000			0.333333
$10$			21.7447i			2.17447i
$11$			2.39573i			0.217794i	0.994053	+	0.108897i	$0.0347318\pi$
$11$			2.39573i			0.217794i	−0.994053	+	0.108897i	$0.965268\pi$
$12$	−19.3553			−1.61294
$13$	3.11386			0.239528			0.119764	−	0.992802i	$-0.461786\pi$
$13$	3.11386			0.239528			0.119764	+	0.992802i	$0.461786\pi$
$14$			10.3065i			0.736177i
$15$			9.66838i			0.644558i
$16$	64.1766			4.01104
$17$			21.5972i			1.27042i	0.772339	+	0.635211i	$0.219087\pi$
$17$			21.5972i			1.27042i	−0.772339	+	0.635211i	$0.780913\pi$
$18$	−11.6864			−0.649247
$19$			28.1601i			1.48211i	0.671444	+	0.741055i	$0.265674\pi$
$19$			28.1601i			1.48211i	−0.671444	+	0.741055i	$0.734326\pi$
$20$		−	62.3781i		−	3.11890i
$21$			4.58258i			0.218218i
$22$		−	9.33253i		−	0.424206i
$23$	−12.2020	−	19.4964i	−0.530521	−	0.847672i
$23$	−12.2020	−	19.4964i	−0.530521	−	0.847672i
$24$	48.4095			2.01706
$25$	−6.15917			−0.246367
$26$	−12.1300			−0.466538
$27$	−5.19615			−0.192450
$28$		−	29.5657i		−	1.05592i
$29$	−26.5764			−0.916427			−0.458214	−	0.888842i	$-0.651511\pi$
$29$	−26.5764			−0.916427			−0.458214	+	0.888842i	$0.651511\pi$
$30$		−	37.6630i		−	1.25543i
$31$	−10.2295			−0.329983			−0.164992	−	0.986295i	$-0.552760\pi$
$31$	−10.2295			−0.329983			−0.164992	+	0.986295i	$0.552760\pi$
$32$	−138.202			−4.31881
$33$		−	4.14953i		−	0.125743i
$34$		−	84.1314i		−	2.47445i
$35$	−14.7687			−0.421963
$36$	33.5243			0.931232
$37$			23.1532i			0.625763i	0.949792	+	0.312881i	$0.101294\pi$
$37$			23.1532i			0.625763i	−0.949792	+	0.312881i	$0.898706\pi$
$38$		−	109.697i		−	2.88677i
$39$	−5.39336			−0.138291
$40$			156.014i			3.90034i
$41$	43.5431			1.06203			0.531013	−	0.847363i	$-0.321811\pi$
$41$	43.5431			1.06203			0.531013	+	0.847363i	$0.321811\pi$
$42$		−	17.8513i		−	0.425032i
$43$		−	37.6961i		−	0.876653i	−0.898816	−	0.438326i	$-0.855571\pi$
$43$		−	37.6961i		−	0.876653i	0.898816	−	0.438326i	$-0.144429\pi$
$44$			26.7718i			0.608449i
$45$		−	16.7461i		−	0.372136i
$46$	47.5326	+	75.9481i	1.03332	+	1.65104i
$47$	−31.7454			−0.675435			−0.337717	−	0.941248i	$-0.609655\pi$
$47$	−31.7454			−0.675435			−0.337717	+	0.941248i	$0.609655\pi$
$48$	−111.157			−2.31577
$49$	−7.00000			−0.142857
$50$	23.9929			0.479858
$51$		−	37.4074i		−	0.733478i
$52$	34.7967			0.669167
$53$			76.1649i			1.43707i	0.695489	+	0.718537i	$0.255188\pi$
$53$			76.1649i			1.43707i	−0.695489	+	0.718537i	$0.744812\pi$
$54$	20.2415			0.374843
$55$	13.3731			0.243147
$56$			73.9467i			1.32048i
$57$		−	48.7747i		−	0.855696i
$58$	103.528			1.78496
$59$	80.8498			1.37034			0.685168	−	0.728385i	$-0.259729\pi$
$59$	80.8498			1.37034			0.685168	+	0.728385i	$0.259729\pi$
$60$			108.042i			1.80070i
$61$			58.9379i			0.966196i	0.875566	+	0.483098i	$0.160489\pi$
$61$			58.9379i			0.966196i	−0.875566	+	0.483098i	$0.839511\pi$
$62$	39.8488			0.642722
$63$		−	7.93725i		−	0.125988i
$64$	281.657			4.40089
$65$		−	17.3817i		−	0.267411i
$66$			16.1644i			0.244915i
$67$		−	11.9484i		−	0.178334i	−0.996017	−	0.0891669i	$-0.971580\pi$
$67$		−	11.9484i		−	0.178334i	0.996017	−	0.0891669i	$-0.0284204\pi$
$68$			241.344i			3.54917i
$69$	21.1345	+	33.7688i	0.306297	+	0.489403i
$70$	57.5312			0.821874
$71$	105.964			1.49246			0.746229	−	0.665690i	$-0.231863\pi$
$71$	105.964			1.49246			0.746229	+	0.665690i	$0.231863\pi$
$72$	−83.8477			−1.16455
$73$	−15.6066			−0.213788			−0.106894	−	0.994270i	$-0.534091\pi$
$73$	−15.6066			−0.213788			−0.106894	+	0.994270i	$0.534091\pi$
$74$		−	90.1930i		−	1.21882i
$75$	10.6680			0.142240
$76$			314.683i			4.14056i
$77$	6.33851			0.0823183
$78$	21.0097			0.269356
$79$			118.357i			1.49819i	0.662461	+	0.749096i	$0.269512\pi$
$79$			118.357i			1.49819i	−0.662461	+	0.749096i	$0.730488\pi$
$80$		−	358.236i		−	4.47795i
$81$	9.00000			0.111111
$82$	−169.621			−2.06855
$83$		−	52.9699i		−	0.638192i	−0.947722	−	0.319096i	$-0.896621\pi$
$83$		−	52.9699i		−	0.638192i	0.947722	−	0.319096i	$-0.103379\pi$
$84$			51.2093i			0.609634i
$85$	120.556			1.41831
$86$			146.844i			1.70749i
$87$	46.0317			0.529099
$88$		−	66.9588i		−	0.760896i
$89$			6.05127i			0.0679918i	0.999422	+	0.0339959i	$0.0108233\pi$
$89$			6.05127i			0.0679918i	−0.999422	+	0.0339959i	$0.989177\pi$
$90$			65.2342i			0.724825i
$91$		−	8.23850i		−	0.0905329i
$92$	−136.355	−	217.869i	−1.48212	−	2.36814i
$93$	17.7180			0.190516
$94$	123.664			1.31557
$95$	157.191			1.65464
$96$	239.373			2.49347
$97$		−	46.7582i		−	0.482044i	−0.970520	−	0.241022i	$-0.922517\pi$
$97$		−	46.7582i		−	0.482044i	0.970520	−	0.241022i	$-0.0774825\pi$
$98$	27.2684			0.278249
$99$			7.18719i			0.0725979i
$100$	−68.8273			−0.688273
$101$	131.523			1.30221			0.651105	−	0.758987i	$-0.274306\pi$
$101$	131.523			1.30221			0.651105	+	0.758987i	$0.274306\pi$
$102$			145.720i			1.42863i
$103$		−	141.443i		−	1.37323i	−0.727019	−	0.686617i	$-0.759095\pi$
$103$		−	141.443i		−	1.37323i	0.727019	−	0.686617i	$-0.240905\pi$
$104$	−87.0300			−0.836827
$105$	25.5801			0.243620
$106$		−	296.699i		−	2.79905i
$107$			140.823i			1.31610i	0.752973	+	0.658052i	$0.228619\pi$
$107$			140.823i			1.31610i	−0.752973	+	0.658052i	$0.771381\pi$
$108$	−58.0659			−0.537647
$109$			61.9580i			0.568422i	0.958762	+	0.284211i	$0.0917317\pi$
$109$			61.9580i			0.568422i	−0.958762	+	0.284211i	$0.908268\pi$
$110$	−52.0945			−0.473587
$111$		−	40.1026i		−	0.361284i
$112$		−	169.795i		−	1.51603i
$113$			195.137i			1.72688i	0.504452	+	0.863440i	$0.331695\pi$
$113$			195.137i			1.72688i	−0.504452	+	0.863440i	$0.668305\pi$
$114$			190.001i			1.66668i
$115$	−108.830	+	68.1120i	−0.946347	+	0.592278i
$116$	−296.985			−2.56022
$117$	9.34158			0.0798425
$118$	−314.949			−2.66906
$119$	57.1408			0.480174
$120$		−	270.224i		−	2.25186i
$121$	115.260			0.952566
$122$		−	229.592i		−	1.88190i
$123$	−75.4189			−0.613161
$124$	−114.312			−0.921873
$125$		−	105.170i		−	0.841362i
$126$			30.9194i			0.245392i
$127$	−124.857			−0.983130			−0.491565	−	0.870841i	$-0.663575\pi$
$127$	−124.857			−0.983130			−0.491565	+	0.870841i	$0.663575\pi$
$128$	−544.381			−4.25298
$129$			65.2915i			0.506136i
$130$			67.7100i			0.520846i
$131$	−243.837			−1.86135			−0.930674	−	0.365849i	$-0.880779\pi$
$131$	−243.837			−1.86135			−0.930674	+	0.365849i	$0.880779\pi$
$132$		−	46.3701i		−	0.351288i
$133$	74.5046			0.560185
$134$			46.5446i			0.347348i
$135$			29.0051i			0.214853i
$136$		−	603.624i		−	4.43841i
$137$			207.001i			1.51095i	0.655175	+	0.755477i	$0.272595\pi$
$137$			207.001i			1.51095i	−0.655175	+	0.755477i	$0.727405\pi$
$138$	−82.3290	−	131.546i	−0.596587	−	0.953231i
$139$	182.843			1.31542			0.657708	−	0.753273i	$-0.271526\pi$
$139$	182.843			1.31542			0.657708	+	0.753273i	$0.271526\pi$
$140$	−165.037			−1.17883
$141$	54.9847			0.389962
$142$	−412.783			−2.90692
$143$			7.45997i			0.0521676i
$144$	192.530			1.33701
$145$			148.350i			1.02311i
$146$	60.7951			0.416405
$147$	12.1244			0.0824786
$148$			258.732i			1.74819i
$149$			155.134i			1.04117i	0.853811	+	0.520583i	$0.174285\pi$
$149$			155.134i			1.04117i	−0.853811	+	0.520583i	$0.825715\pi$
$150$	−41.5570			−0.277046
$151$	84.9068			0.562296			0.281148	−	0.959664i	$-0.409285\pi$
$151$	84.9068			0.562296			0.281148	+	0.959664i	$0.409285\pi$
$152$		−	787.053i		−	5.17798i
$153$			64.7915i			0.423474i
$154$	−24.6915			−0.160335
$155$			57.1014i			0.368396i
$156$	−60.2696			−0.386344
$157$		−	237.995i		−	1.51589i	−0.652316	−	0.757947i	$-0.726202\pi$
$157$		−	237.995i		−	1.51589i	0.652316	−	0.757947i	$-0.273798\pi$
$158$		−	461.058i		−	2.91809i
$159$		−	131.921i		−	0.829695i
$160$			771.449i			4.82155i
$161$	−51.5827	+	32.2834i	−0.320390	+	0.200518i
$162$	−35.0593			−0.216416
$163$	252.259			1.54760			0.773800	−	0.633430i	$-0.218354\pi$
$163$	252.259			1.54760			0.773800	+	0.633430i	$0.218354\pi$
$164$	486.585			2.96698
$165$	−23.1628			−0.140381
$166$			206.343i			1.24303i
$167$	130.396			0.780812			0.390406	−	0.920643i	$-0.372335\pi$
$167$	130.396			0.780812			0.390406	+	0.920643i	$0.372335\pi$
$168$		−	128.079i		−	0.762378i
$169$	−159.304			−0.942627
$170$	−469.625			−2.76250
$171$			84.4803i			0.494037i
$172$		−	421.245i		−	2.44910i
$173$	310.218			1.79317			0.896584	−	0.442874i	$-0.146041\pi$
$173$	310.218			1.79317			0.896584	+	0.442874i	$0.146041\pi$
$174$	−179.315			−1.03055
$175$			16.2956i			0.0931178i
$176$			153.750i			0.873579i
$177$	−140.036			−0.791164
$178$		−	23.5726i		−	0.132430i
$179$	34.5495			0.193014			0.0965069	−	0.995332i	$-0.469233\pi$
$179$	34.5495			0.193014			0.0965069	+	0.995332i	$0.469233\pi$
$180$		−	187.134i		−	1.03963i
$181$		−	83.8097i		−	0.463037i	−0.972831	−	0.231518i	$-0.925631\pi$
$181$		−	83.8097i		−	0.463037i	0.972831	−	0.231518i	$-0.0743694\pi$
$182$			32.0929i			0.176335i
$183$		−	102.084i		−	0.557833i
$184$	341.036	+	544.911i	1.85346	+	2.96147i
$185$	129.242			0.698607
$186$	−69.0201			−0.371076
$187$	−51.7410			−0.276690
$188$	−354.748			−1.88696
$189$			13.7477i			0.0727393i
$190$	−612.334			−3.22281
$191$		−	157.259i		−	0.823347i	−0.911331	−	0.411673i	$-0.864944\pi$
$191$		−	157.259i		−	0.823347i	0.911331	−	0.411673i	$-0.135056\pi$
$192$	−487.844			−2.54085
$193$	20.9082			0.108333			0.0541663	−	0.998532i	$-0.482750\pi$
$193$	20.9082			0.108333			0.0541663	+	0.998532i	$0.482750\pi$
$194$			182.146i			0.938896i
$195$			30.1060i			0.154390i
$196$	−78.2235			−0.399099
$197$	333.061			1.69066			0.845332	−	0.534242i	$-0.179403\pi$
$197$	333.061			1.69066			0.845332	+	0.534242i	$0.179403\pi$
$198$		−	27.9976i		−	0.141402i
$199$		−	276.096i		−	1.38742i	−0.720256	−	0.693708i	$-0.755976\pi$
$199$		−	276.096i		−	1.38742i	0.720256	−	0.693708i	$-0.244024\pi$
$200$	172.144			0.860720
$201$			20.6952i			0.102961i
$202$	−512.347			−2.53637
$203$			70.3145i			0.346377i
$204$		−	418.020i		−	2.04912i
$205$		−	243.059i		−	1.18566i
$206$			550.989i			2.67471i
$207$	−36.6060	−	58.4893i	−0.176840	−	0.282557i
$208$	199.837			0.960754
$209$	−67.4640			−0.322794
$210$	−99.6469			−0.474509
$211$	−128.933			−0.611059			−0.305529	−	0.952183i	$-0.598833\pi$
$211$	−128.933			−0.611059			−0.305529	+	0.952183i	$0.598833\pi$
$212$			851.126i			4.01475i
$213$	−183.536			−0.861671
$214$		−	548.574i		−	2.56343i
$215$	−210.421			−0.978702
$216$	145.228			0.672354
$217$			27.0647i			0.124722i
$218$		−	241.356i		−	1.10714i
$219$	27.0313			0.123431
$220$	149.441			0.679278
$221$			67.2506i			0.304301i
$222$			156.219i			0.703688i
$223$	−38.4977			−0.172635			−0.0863176	−	0.996268i	$-0.527510\pi$
$223$	−38.4977			−0.172635			−0.0863176	+	0.996268i	$0.527510\pi$
$224$			365.648i			1.63236i
$225$	−18.4775			−0.0821222
$226$		−	760.154i		−	3.36351i
$227$			33.7442i			0.148653i	0.997234	+	0.0743265i	$0.0236807\pi$
$227$			33.7442i			0.148653i	−0.997234	+	0.0743265i	$0.976319\pi$
$228$		−	545.047i		−	2.39056i
$229$			251.499i			1.09825i	0.835741	+	0.549124i	$0.185038\pi$
$229$			251.499i			1.09825i	−0.835741	+	0.549124i	$0.814962\pi$
$230$	423.945	−	265.329i	1.84324	−	1.15360i
$231$	−10.9786			−0.0475265
$232$	742.790			3.20168
$233$	−263.749			−1.13197			−0.565986	−	0.824415i	$-0.691504\pi$
$233$	−263.749			−1.13197			−0.565986	+	0.824415i	$0.691504\pi$
$234$	−36.3899			−0.155513
$235$			177.204i			0.754060i
$236$	903.479			3.82830
$237$		−	205.001i		−	0.864982i
$238$	−222.591			−0.935255
$239$	224.446			0.939105			0.469553	−	0.882905i	$-0.344415\pi$
$239$	224.446			0.939105			0.469553	+	0.882905i	$0.344415\pi$
$240$			620.484i			2.58535i
$241$			233.230i			0.967760i	0.875134	+	0.483880i	$0.160773\pi$
$241$			233.230i			0.967760i	−0.875134	+	0.483880i	$0.839227\pi$
$242$	−448.995			−1.85535
$243$	−15.5885			−0.0641500
$244$			658.619i			2.69926i
$245$			39.0743i			0.159487i
$246$	293.793			1.19428
$247$			87.6865i			0.355006i
$248$	285.906			1.15285
$249$			91.7466i			0.368460i
$250$			409.689i			1.63876i
$251$		−	41.8187i		−	0.166608i	−0.996524	−	0.0833042i	$-0.973453\pi$
$251$		−	41.8187i		−	0.166608i	0.996524	−	0.0833042i	$-0.0265473\pi$
$252$		−	88.6971i		−	0.351973i
$253$	46.7082	−	29.2327i	0.184618	−	0.115544i
$254$	486.380			1.91488
$255$	−208.810			−0.818861
$256$	993.999			3.88281
$257$	272.834			1.06161			0.530806	−	0.847493i	$-0.321889\pi$
$257$	272.834			1.06161			0.530806	+	0.847493i	$0.321889\pi$
$258$		−	254.342i		−	0.985821i
$259$	61.2577			0.236516
$260$		−	194.237i		−	0.747064i
$261$	−79.7292			−0.305476
$262$	949.861			3.62543
$263$			390.161i			1.48350i	0.670676	+	0.741751i	$0.266004\pi$
$263$			390.161i			1.48350i	−0.670676	+	0.741751i	$0.733996\pi$
$264$			115.976i			0.439303i
$265$	425.155			1.60436
$266$	−290.231			−1.09110
$267$		−	10.4811i		−	0.0392551i
$268$		−	133.520i		−	0.498210i
$269$	−202.017			−0.750992			−0.375496	−	0.926824i	$-0.622528\pi$
$269$	−202.017			−0.750992			−0.375496	+	0.926824i	$0.622528\pi$
$270$		−	112.989i		−	0.418478i
$271$	−210.812			−0.777906			−0.388953	−	0.921258i	$-0.627163\pi$
$271$	−210.812			−0.777906			−0.388953	+	0.921258i	$0.627163\pi$
$272$			1386.03i			5.09571i
$273$			14.2695i			0.0522692i
$274$		−	806.367i		−	2.94295i
$275$		−	14.7557i		−	0.0536571i
$276$	236.173	+	377.359i	0.855700	+	1.36724i
$277$	−228.883			−0.826294			−0.413147	−	0.910664i	$-0.635570\pi$
$277$	−228.883			−0.826294			−0.413147	+	0.910664i	$0.635570\pi$
$278$	−712.261			−2.56209
$279$	−30.6884			−0.109994
$280$	412.774			1.47419
$281$		−	185.090i		−	0.658685i	−0.944211	−	0.329342i	$-0.893173\pi$
$281$		−	185.090i		−	0.658685i	0.944211	−	0.329342i	$-0.106827\pi$
$282$	−214.192			−0.759546
$283$		−	186.339i		−	0.658442i	−0.944253	−	0.329221i	$-0.893214\pi$
$283$		−	186.339i		−	0.658442i	0.944253	−	0.329221i	$-0.106786\pi$
$284$	1184.13			4.16947
$285$	−272.262			−0.955306
$286$		−	29.0602i		−	0.101609i
$287$		−	115.204i		−	0.401408i
$288$	−414.606			−1.43960
$289$	−177.438			−0.613972
$290$		−	577.897i		−	1.99275i
$291$			80.9876i			0.278308i
$292$	−174.400			−0.597260
$293$		−	287.630i		−	0.981671i	−0.871252	−	0.490836i	$-0.836692\pi$
$293$		−	287.630i		−	0.981671i	0.871252	−	0.490836i	$-0.163308\pi$
$294$	−47.2302			−0.160647
$295$		−	451.307i		−	1.52985i
$296$		−	647.115i		−	2.18620i
$297$		−	12.4486i		−	0.0419144i
$298$		−	604.320i		−	2.02792i
$299$	−37.9953	−	60.7092i	−0.127075	−	0.203041i
$300$	119.212			0.397375
$301$	−99.7344			−0.331344
$302$	−330.753			−1.09521
$303$	−227.805			−0.751832
$304$			1807.22i			5.94480i
$305$	328.994			1.07867
$306$		−	252.394i		−	0.824818i
$307$	106.999			0.348530			0.174265	−	0.984699i	$-0.444245\pi$
$307$	106.999			0.348530			0.174265	+	0.984699i	$0.444245\pi$
$308$	70.8314			0.229972
$309$			244.987i			0.792837i
$310$		−	222.437i		−	0.717540i
$311$	−439.744			−1.41397			−0.706985	−	0.707229i	$-0.749945\pi$
$311$	−439.744			−1.41397			−0.706985	+	0.707229i	$0.749945\pi$
$312$	150.740			0.483142
$313$			396.790i			1.26770i	0.773456	+	0.633850i	$0.218526\pi$
$313$			396.790i			1.26770i	−0.773456	+	0.633850i	$0.781474\pi$
$314$			927.107i			2.95257i
$315$	−44.3061			−0.140654
$316$			1322.62i			4.18549i
$317$	495.819			1.56410			0.782050	−	0.623216i	$-0.214174\pi$
$317$	495.819			1.56410			0.782050	+	0.623216i	$0.214174\pi$
$318$			513.898i			1.61603i
$319$		−	63.6699i		−	0.199592i
$320$		−	1572.22i		−	4.91318i
$321$		−	243.913i		−	0.759853i
$322$	200.940	−	125.760i	0.624036	−	0.390558i
$323$	−608.178			−1.88290
$324$	100.573			0.310411
$325$	−19.1788			−0.0590116
$326$	−982.669			−3.01432
$327$		−	107.314i		−	0.328179i
$328$	−1217.00			−3.71035
$329$			83.9905i			0.255290i
$330$	90.2304			0.273425
$331$	−136.372			−0.412001			−0.206001	−	0.978552i	$-0.566045\pi$
$331$	−136.372			−0.412001			−0.206001	+	0.978552i	$0.566045\pi$
$332$		−	591.927i		−	1.78291i
$333$			69.4597i			0.208588i
$334$	−507.954			−1.52082
$335$	−66.6962			−0.199093
$336$			294.094i			0.875280i
$337$			414.570i			1.23018i	0.788458	+	0.615089i	$0.210880\pi$
$337$			414.570i			1.23018i	−0.788458	+	0.615089i	$0.789120\pi$
$338$	620.565			1.83599
$339$		−	337.988i		−	0.997014i
$340$	1347.19			3.96232
$341$		−	24.5071i		−	0.0718683i
$342$		−	329.091i		−	0.962255i
$343$			18.5203i			0.0539949i
$344$			1053.58i			3.06272i
$345$	188.499	−	117.973i	0.546374	−	0.341952i
$346$	−1208.45			−3.49263
$347$	−311.459			−0.897577			−0.448788	−	0.893638i	$-0.648144\pi$
$347$	−311.459			−0.897577			−0.448788	+	0.893638i	$0.648144\pi$
$348$	514.394			1.47814
$349$	154.371			0.442323			0.221161	−	0.975237i	$-0.429015\pi$
$349$	154.371			0.442323			0.221161	+	0.975237i	$0.429015\pi$
$350$		−	63.4793i		−	0.181369i
$351$	−16.1801			−0.0460971
$352$		−	331.095i		−	0.940610i
$353$	−263.060			−0.745212			−0.372606	−	0.927990i	$-0.621536\pi$
$353$	−263.060			−0.745212			−0.372606	+	0.927990i	$0.621536\pi$
$354$	545.508			1.54098
$355$		−	591.498i		−	1.66619i
$356$			67.6216i			0.189948i
$357$	−98.9707			−0.277229
$358$	−134.587			−0.375941
$359$		−	313.582i		−	0.873487i	−0.899586	−	0.436743i	$-0.856132\pi$
$359$		−	313.582i		−	0.873487i	0.899586	−	0.436743i	$-0.143868\pi$
$360$			468.041i			1.30011i
$361$	−431.990			−1.19665
$362$			326.479i			0.901876i
$363$	−199.637			−0.549964
$364$		−	92.0634i		−	0.252921i
$365$			87.1164i			0.238675i
$366$			397.665i			1.08652i
$367$			518.592i			1.41306i	0.707685	+	0.706528i	$0.249740\pi$
$367$			518.592i			1.41306i	−0.707685	+	0.706528i	$0.750260\pi$
$368$	−783.083	−	1251.22i	−2.12794	−	3.40004i
$369$	130.629			0.354009
$370$	−503.461			−1.36070
$371$	201.513			0.543163
$372$	197.995			0.532243
$373$			271.102i			0.726814i	0.931630	+	0.363407i	$0.118387\pi$
$373$			271.102i			0.726814i	−0.931630	+	0.363407i	$0.881613\pi$
$374$	201.556			0.538920
$375$			182.160i			0.485761i
$376$	887.260			2.35973
$377$	−82.7551			−0.219510
$378$		−	53.5540i		−	0.141677i
$379$		−	91.5954i		−	0.241676i	−0.992672	−	0.120838i	$-0.961442\pi$
$379$		−	91.5954i		−	0.241676i	0.992672	−	0.120838i	$-0.0385582\pi$
$380$	1756.57			4.62256
$381$	216.260			0.567610
$382$			612.601i			1.60367i
$383$			444.007i			1.15929i	0.814870	+	0.579644i	$0.196808\pi$
$383$			444.007i			1.15929i	−0.814870	+	0.579644i	$0.803192\pi$
$384$	942.895			2.45546
$385$		−	35.3818i		−	0.0919008i
$386$	−81.4474			−0.211004
$387$		−	113.088i		−	0.292218i
$388$		−	522.513i		−	1.34668i
$389$		−	293.326i		−	0.754051i	−0.926203	−	0.377026i	$-0.876947\pi$
$389$		−	293.326i		−	0.754051i	0.926203	−	0.377026i	$-0.123053\pi$
$390$		−	117.277i		−	0.300711i
$391$	421.068	−	263.529i	1.07690	−	0.673986i
$392$	195.645			0.499093
$393$	422.337			1.07465
$394$	−1297.43			−3.29297
$395$	660.675			1.67259
$396$			80.3153i			0.202816i
$397$	389.331			0.980683			0.490342	−	0.871530i	$-0.336872\pi$
$397$	389.331			0.980683			0.490342	+	0.871530i	$0.336872\pi$
$398$			1075.53i			2.70233i
$399$	−129.046			−0.323423
$400$	−395.274			−0.988186
$401$		−	660.220i		−	1.64644i	−0.567726	−	0.823218i	$-0.692177\pi$
$401$		−	660.220i		−	1.64644i	0.567726	−	0.823218i	$-0.307823\pi$
$402$		−	80.6177i		−	0.200541i
$403$	−31.8532			−0.0790401
$404$	1469.74			3.63798
$405$		−	50.2384i		−	0.124045i
$406$		−	273.909i		−	0.674653i
$407$	−55.4689			−0.136287
$408$			1045.51i			2.56252i
$409$	−705.366			−1.72461			−0.862306	−	0.506388i	$-0.830980\pi$
$409$	−705.366			−1.72461			−0.862306	+	0.506388i	$0.830980\pi$
$410$			946.833i			2.30935i
$411$		−	358.536i		−	0.872349i
$412$		−	1580.60i		−	3.83640i
$413$		−	213.909i		−	0.517938i
$414$	142.598	+	227.844i	0.344439	+	0.550348i
$415$	−295.680			−0.712482
$416$	−430.341			−1.03447
$417$	−316.693			−0.759456
$418$	262.805			0.628720
$419$			391.119i			0.933458i	0.884400	+	0.466729i	$0.154568\pi$
$419$			391.119i			0.933458i	−0.884400	+	0.466729i	$0.845432\pi$
$420$	285.852			0.680601
$421$			624.843i			1.48419i	0.670296	+	0.742094i	$0.266167\pi$
$421$			624.843i			1.48419i	−0.670296	+	0.742094i	$0.733833\pi$
$422$	502.258			1.19018
$423$	−95.2363			−0.225145
$424$		−	2128.75i		−	5.02064i
$425$		−	133.021i		−	0.312990i
$426$	714.961			1.67831
$427$	155.935			0.365188
$428$			1573.67i			3.67679i
$429$		−	12.9210i		−	0.0301190i
$430$	819.691			1.90626
$431$			319.684i			0.741726i	0.928688	+	0.370863i	$0.120938\pi$
$431$			319.684i			0.741726i	−0.928688	+	0.370863i	$0.879062\pi$
$432$	−333.471			−0.771925
$433$		−	250.183i		−	0.577789i	−0.957361	−	0.288895i	$-0.906712\pi$
$433$		−	250.183i		−	0.577789i	0.957361	−	0.288895i	$-0.0932877\pi$
$434$		−	105.430i		−	0.242926i
$435$		−	256.951i		−	0.590691i
$436$			692.367i			1.58800i
$437$	549.022	−	343.609i	1.25634	−	0.786291i
$438$	−105.300			−0.240411
$439$	−244.377			−0.556668			−0.278334	−	0.960484i	$-0.589782\pi$
$439$	−244.377			−0.556668			−0.278334	+	0.960484i	$0.589782\pi$
$440$	−373.767			−0.849470
$441$	−21.0000			−0.0476190
$442$		−	261.973i		−	0.592700i
$443$	−718.170			−1.62115			−0.810576	−	0.585634i	$-0.800846\pi$
$443$	−718.170			−1.62115			−0.810576	+	0.585634i	$0.800846\pi$
$444$		−	448.137i		−	1.00932i
$445$	33.7784			0.0759066
$446$	149.967			0.336249
$447$		−	268.699i		−	0.601117i
$448$		−	745.193i		−	1.66338i
$449$	263.218			0.586233			0.293116	−	0.956077i	$-0.405308\pi$
$449$	263.218			0.586233			0.293116	+	0.956077i	$0.405308\pi$
$450$	71.9788			0.159953
$451$			104.318i			0.231303i
$452$			2180.62i			4.82438i
$453$	−147.063			−0.324642
$454$		−	131.450i		−	0.289538i
$455$	−45.9876			−0.101072
$456$			1363.22i			2.98951i
$457$			661.998i			1.44857i	0.689499	+	0.724286i	$0.257831\pi$
$457$			661.998i			1.44857i	−0.689499	+	0.724286i	$0.742169\pi$
$458$		−	979.708i		−	2.13910i
$459$		−	112.222i		−	0.244493i
$460$	−1216.15	+	761.137i	−2.64381	+	1.65465i
$461$	299.234			0.649098			0.324549	−	0.945869i	$-0.394788\pi$
$461$	299.234			0.649098			0.324549	+	0.945869i	$0.394788\pi$
$462$	42.7670			0.0925693
$463$	−131.514			−0.284047			−0.142024	−	0.989863i	$-0.545361\pi$
$463$	−131.514			−0.284047			−0.142024	+	0.989863i	$0.545361\pi$
$464$	−1705.58			−3.67582
$465$		−	98.9025i		−	0.212694i
$466$	1027.43			2.20479
$467$			397.109i			0.850341i	0.905113	+	0.425170i	$0.139786\pi$
$467$			397.109i			0.850341i	−0.905113	+	0.425170i	$0.860214\pi$
$468$	104.390			0.223056
$469$	−31.6124			−0.0674038
$470$		−	690.296i		−	1.46871i
$471$			412.220i			0.875202i
$472$	−2259.69			−4.78748
$473$	90.3096			0.190929
$474$			798.577i			1.68476i
$475$		−	173.443i		−	0.365142i
$476$	638.535			1.34146
$477$			228.495i			0.479024i
$478$	−874.326			−1.82913
$479$		−	631.433i		−	1.31823i	−0.752041	−	0.659116i	$-0.770930\pi$
$479$		−	631.433i		−	1.31823i	0.752041	−	0.659116i	$-0.229070\pi$
$480$		−	1336.19i		−	2.78373i
$481$			72.0959i			0.149887i
$482$		−	908.544i		−	1.88495i
$483$	89.3439	−	55.9166i	0.184977	−	0.115769i
$484$	1288.01			2.66118
$485$	−261.006			−0.538157
$486$	60.7246			0.124948
$487$	−656.345			−1.34773			−0.673865	−	0.738854i	$-0.735367\pi$
$487$	−656.345			−1.34773			−0.673865	+	0.738854i	$0.735367\pi$
$488$		−	1647.27i		−	3.37555i
$489$	−436.925			−0.893507
$490$		−	152.213i		−	0.310639i
$491$	−126.007			−0.256633			−0.128317	−	0.991733i	$-0.540957\pi$
$491$	−126.007			−0.256633			−0.128317	+	0.991733i	$0.540957\pi$
$492$	−842.789			−1.71299
$493$		−	573.975i		−	1.16425i
$494$		−	341.581i		−	0.691460i
$495$	40.1192			0.0810489
$496$	−656.494			−1.32358
$497$		−	280.356i		−	0.564096i
$498$		−	357.397i		−	0.717665i
$499$	241.457			0.483882			0.241941	−	0.970291i	$-0.422216\pi$
$499$	241.457			0.483882			0.241941	+	0.970291i	$0.422216\pi$
$500$		−	1175.25i		−	2.35051i
$501$	−225.852			−0.450802
$502$			162.904i			0.324510i
$503$		−	571.589i		−	1.13636i	−0.822905	−	0.568180i	$-0.807648\pi$
$503$		−	571.589i		−	1.13636i	0.822905	−	0.568180i	$-0.192352\pi$
$504$			221.840i			0.440159i
$505$		−	734.168i		−	1.45380i
$506$	−181.951	+	113.875i	−0.359587	+	0.225050i
$507$	275.922			0.544226
$508$	−1395.26			−2.74657
$509$	173.270			0.340413			0.170206	−	0.985408i	$-0.445557\pi$
$509$	173.270			0.340413			0.170206	+	0.985408i	$0.445557\pi$
$510$	813.414			1.59493
$511$			41.2911i			0.0808044i
$512$	−1694.58			−3.30973
$513$		−	146.324i		−	0.285232i
$514$	−1062.82			−2.06775
$515$	−789.541			−1.53309
$516$			729.618i			1.41399i
$517$		−	76.0535i		−	0.147105i
$518$	−238.628			−0.460672
$519$	−537.313			−1.03529
$520$			485.805i			0.934240i
$521$			580.938i			1.11504i	0.830162	+	0.557522i	$0.188248\pi$
$521$			580.938i			1.11504i	−0.830162	+	0.557522i	$0.811752\pi$
$522$	310.584			0.594988
$523$			298.842i			0.571399i	0.958319	+	0.285699i	$0.0922259\pi$
$523$			298.842i			0.571399i	−0.958319	+	0.285699i	$0.907774\pi$
$524$	−2724.82			−5.20004
$525$		−	28.2248i		−	0.0537616i
$526$		−	1519.86i		−	2.88948i
$527$		−	220.928i		−	0.419218i
$528$		−	266.303i		−	0.504361i
$529$	−231.223	+	475.791i	−0.437094	+	0.899416i
$530$	−1656.19			−3.12488
$531$	242.549			0.456779
$532$	832.572			1.56499
$533$	135.587			0.254385
$534$			40.8290i			0.0764588i
$535$	786.080			1.46931
$536$			333.948i			0.623036i
$537$	−59.8414			−0.111437
$538$	786.953			1.46274
$539$		−	16.7701i		−	0.0311134i
$540$			324.126i			0.600233i
$541$	696.281			1.28703			0.643513	−	0.765435i	$-0.277476\pi$
$541$	696.281			1.28703			0.643513	+	0.765435i	$0.277476\pi$
$542$	821.216			1.51516
$543$			145.163i			0.267334i
$544$		−	2984.77i		−	5.48671i
$545$	345.852			0.634591
$546$		−	55.5866i		−	0.101807i
$547$	525.802			0.961247			0.480623	−	0.876927i	$-0.340410\pi$
$547$	525.802			0.961247			0.480623	+	0.876927i	$0.340410\pi$
$548$			2313.19i			4.22114i
$549$			176.814i			0.322065i
$550$			57.4806i			0.104510i
$551$		−	748.393i		−	1.35825i
$552$	−590.692	−	943.813i	−1.07009	−	1.70981i
$553$	313.144			0.566264
$554$	891.611			1.60941
$555$	−223.854			−0.403341
$556$	2043.23			3.67487
$557$			79.5046i			0.142737i	0.997450	+	0.0713686i	$0.0227367\pi$
$557$			79.5046i			0.142737i	−0.997450	+	0.0713686i	$0.977263\pi$
$558$	119.546			0.214241
$559$		−	117.380i		−	0.209983i
$560$	−947.804			−1.69251
$561$	89.6181			0.159747
$562$			721.017i			1.28295i
$563$			577.470i			1.02570i	0.858478	+	0.512851i	$0.171411\pi$
$563$			577.470i			1.02570i	−0.858478	+	0.512851i	$0.828589\pi$
$564$	614.442			1.08944
$565$	1089.26			1.92790
$566$			725.880i			1.28247i
$567$		−	23.8118i		−	0.0419961i
$568$	−2961.63			−5.21413
$569$		−	532.318i		−	0.935533i	−0.883852	−	0.467767i	$-0.845059\pi$
$569$		−	532.318i		−	0.935533i	0.883852	−	0.467767i	$-0.154941\pi$
$570$	1060.59			1.86069
$571$			300.680i			0.526585i	0.964716	+	0.263293i	$0.0848085\pi$
$571$			300.680i			0.526585i	−0.964716	+	0.263293i	$0.915192\pi$
$572$			83.3635i			0.145740i
$573$			272.381i			0.475360i
$574$			448.776i			0.781840i
$575$	75.1541	+	120.082i	0.130703	+	0.208838i
$576$	844.970			1.46696
$577$	−7.55944			−0.0131013			−0.00655064	−	0.999979i	$-0.502085\pi$
$577$	−7.55944			−0.0131013			−0.00655064	+	0.999979i	$0.502085\pi$
$578$	691.206			1.19586
$579$	−36.2140			−0.0625458
$580$			1657.78i			2.85825i
$581$	−140.145			−0.241214
$582$		−	315.486i		−	0.542072i
$583$	−182.471			−0.312986
$584$	436.191			0.746903
$585$		−	52.1451i		−	0.0891368i
$586$			1120.46i			1.91204i
$587$	−363.672			−0.619543			−0.309772	−	0.950811i	$-0.600253\pi$
$587$	−363.672			−0.619543			−0.309772	+	0.950811i	$0.600253\pi$
$588$	135.487			0.230420
$589$		−	288.063i		−	0.489071i
$590$			1758.06i			2.97976i
$591$	−576.878			−0.976105
$592$			1485.90i			2.50996i
$593$	455.135			0.767512			0.383756	−	0.923435i	$-0.374630\pi$
$593$	455.135			0.767512			0.383756	+	0.923435i	$0.374630\pi$
$594$			48.4932i			0.0816384i
$595$		−	318.962i		−	0.536070i
$596$			1733.58i			2.90870i
$597$			478.212i			0.801025i
$598$	148.010	+	236.492i	0.247508	+	0.395471i
$599$	−893.265			−1.49126			−0.745630	−	0.666360i	$-0.767851\pi$
$599$	−893.265			−1.49126			−0.745630	+	0.666360i	$0.767851\pi$
$600$	−298.162			−0.496937
$601$	476.950			0.793594			0.396797	−	0.917906i	$-0.370122\pi$
$601$	476.950			0.793594			0.396797	+	0.917906i	$0.370122\pi$
$602$	388.514			0.645371
$603$		−	35.8451i		−	0.0594446i
$604$	948.815			1.57089
$605$		−	643.389i		−	1.06345i
$606$	887.410			1.46437
$607$	375.828			0.619157			0.309579	−	0.950874i	$-0.399812\pi$
$607$	375.828			0.619157			0.309579	+	0.950874i	$0.399812\pi$
$608$		−	3891.78i		−	6.40095i
$609$		−	121.788i		−	0.199981i
$610$	−1281.59			−2.10097
$611$	−98.8508			−0.161785
$612$			724.031i			1.18306i
$613$		−	176.512i		−	0.287947i	−0.989582	−	0.143974i	$-0.954012\pi$
$613$		−	176.512i		−	0.287947i	0.989582	−	0.143974i	$-0.0459881\pi$
$614$	−416.811			−0.678845
$615$			420.991i			0.684538i
$616$	−177.156			−0.287592
$617$		−	97.9061i		−	0.158681i	−0.996848	−	0.0793404i	$-0.974719\pi$
$617$		−	97.9061i		−	0.158681i	0.996848	−	0.0793404i	$-0.0252814\pi$
$618$		−	954.342i		−	1.54424i
$619$		−	199.557i		−	0.322387i	−0.986923	−	0.161193i	$-0.948466\pi$
$619$		−	199.557i		−	0.322387i	0.986923	−	0.161193i	$-0.0515343\pi$
$620$			638.095i			1.02919i
$621$	63.4034	+	101.307i	0.102099	+	0.163134i
$622$	1713.02			2.75405
$623$	16.0102			0.0256985
$624$	−346.128			−0.554692
$625$	−741.044			−1.18567
$626$		−	1545.69i		−	2.46915i
$627$	116.851			0.186365
$628$		−	2659.55i		−	4.23495i
$629$	−500.044			−0.794983
$630$	172.593			0.273958
$631$			846.206i			1.34106i	0.741884	+	0.670528i	$0.233932\pi$
$631$			846.206i			1.34106i	−0.741884	+	0.670528i	$0.766068\pi$
$632$		−	3307.99i		−	5.23417i
$633$	223.319			0.352795
$634$	−1931.46			−3.04646
$635$			696.959i			1.09757i
$636$		−	1474.19i		−	2.31791i
$637$	−21.7970			−0.0342182
$638$			248.025i			0.388754i
$639$	317.893			0.497486
$640$			3038.76i			4.74806i
$641$			1184.11i			1.84728i	0.383255	+	0.923642i	$0.374803\pi$
$641$			1184.11i			1.84728i	−0.383255	+	0.923642i	$0.625197\pi$
$642$			950.158i			1.48000i
$643$		−	668.278i		−	1.03931i	−0.854375	−	0.519656i	$-0.826060\pi$
$643$		−	668.278i		−	1.03931i	0.854375	−	0.519656i	$-0.173940\pi$
$644$	−576.426	+	360.760i	−0.895071	+	0.560187i
$645$	364.460			0.565054
$646$	2369.15			3.66741
$647$	−299.560			−0.462998			−0.231499	−	0.972835i	$-0.574363\pi$
$647$	−299.560			−0.462998			−0.231499	+	0.972835i	$0.574363\pi$
$648$	−251.543			−0.388184
$649$			193.694i			0.298451i
$650$	74.7106			0.114939
$651$		−	46.8774i		−	0.0720083i
$652$	2818.94			4.32352
$653$	132.906			0.203531			0.101766	−	0.994808i	$-0.467551\pi$
$653$	132.906			0.203531			0.101766	+	0.994808i	$0.467551\pi$
$654$			418.042i			0.639207i
$655$			1361.11i			2.07802i
$656$	2794.45			4.25983
$657$	−46.8197			−0.0712628
$658$		−	327.183i		−	0.497239i
$659$		−	29.8198i		−	0.0452500i	−0.999744	−	0.0226250i	$-0.992798\pi$
$659$		−	29.8198i		−	0.0452500i	0.999744	−	0.0226250i	$-0.00720238\pi$
$660$	−258.840			−0.392181
$661$			536.340i			0.811406i	0.914005	+	0.405703i	$0.132973\pi$
$661$			536.340i			0.811406i	−0.914005	+	0.405703i	$0.867027\pi$
$662$	531.236			0.802472
$663$		−	116.481i		−	0.175688i
$664$			1480.47i			2.22962i
$665$		−	415.888i		−	0.625395i
$666$		−	270.579i		−	0.406275i
$667$	324.285	+	518.145i	0.486184	+	0.776829i
$668$	1457.14			2.18135
$669$	66.6799			0.0996710
$670$	259.814			0.387782
$671$	−141.199			−0.210431
$672$		−	633.321i		−	0.942442i
$673$	−153.495			−0.228076			−0.114038	−	0.993476i	$-0.536379\pi$
$673$	−153.495			−0.228076			−0.114038	+	0.993476i	$0.536379\pi$
$674$		−	1614.95i		−	2.39607i
$675$	32.0040			0.0474133
$676$	−1780.19			−2.63341
$677$			899.450i			1.32858i	0.747474	+	0.664291i	$0.231266\pi$
$677$			899.450i			1.32858i	−0.747474	+	0.664291i	$0.768734\pi$
$678$			1316.63i			1.94193i
$679$	−123.711			−0.182195
$680$	−3369.46			−4.95508
$681$		−	58.4467i		−	0.0858248i
$682$			95.4669i			0.139981i
$683$	−731.776			−1.07141			−0.535707	−	0.844404i	$-0.679955\pi$
$683$	−731.776			−1.07141			−0.535707	+	0.844404i	$0.679955\pi$
$684$			944.048i			1.38019i
$685$	1155.49			1.68684
$686$		−	72.1453i		−	0.105168i
$687$		−	435.608i		−	0.634073i
$688$		−	2419.21i		−	3.51629i
$689$			237.167i			0.344219i
$690$	−734.294	+	459.563i	−1.06419	+	0.666034i
$691$	87.6166			0.126797			0.0633984	−	0.997988i	$-0.479806\pi$
$691$	87.6166			0.126797			0.0633984	+	0.997988i	$0.479806\pi$
$692$	3466.62			5.00956
$693$	19.0155			0.0274394
$694$	1213.28			1.74825
$695$		−	1020.64i		−	1.46854i
$696$	−1286.55			−1.84849
$697$			940.408i			1.34922i
$698$	−601.348			−0.861530
$699$	456.827			0.653544
$700$			182.100i			0.260143i
$701$			397.477i			0.567014i	0.958970	+	0.283507i	$0.0914980\pi$
$701$			397.477i			0.567014i	−0.958970	+	0.283507i	$0.908502\pi$
$702$	63.0292			0.0897852
$703$	−651.997			−0.927449
$704$			674.774i			0.958485i
$705$		−	306.927i		−	0.435357i
$706$	1024.74			1.45148
$707$		−	347.978i		−	0.492189i
$708$	−1564.87			−2.21027
$709$		−	61.1930i		−	0.0863089i	−0.999068	−	0.0431545i	$-0.986259\pi$
$709$		−	61.1930i		−	0.0863089i	0.999068	−	0.0431545i	$-0.0137408\pi$
$710$			2304.17i			3.24531i
$711$			355.072i			0.499398i
$712$		−	169.128i		−	0.237540i
$713$	124.820	+	199.439i	0.175063	+	0.279717i
$714$	385.539			0.539970
$715$	41.6418			0.0582403
$716$	386.083			0.539222
$717$	−388.752			−0.542193
$718$			1221.55i			1.70133i
$719$	−1328.79			−1.84810			−0.924051	−	0.382269i	$-0.875143\pi$
$719$	−1328.79			−1.84810			−0.924051	+	0.382269i	$0.875143\pi$
$720$		−	1074.71i		−	1.49265i
$721$	−374.223			−0.519034
$722$	1682.81			2.33076
$723$		−	403.967i		−	0.558737i
$724$		−	936.555i		−	1.29358i
$725$	163.688			0.225777
$726$	777.682			1.07119
$727$		−	158.956i		−	0.218647i	−0.994006	−	0.109323i	$-0.965132\pi$
$727$		−	158.956i		−	0.218647i	0.994006	−	0.109323i	$-0.0348684\pi$
$728$			230.260i			0.316291i
$729$	27.0000			0.0370370
$730$		−	339.360i		−	0.464877i
$731$	814.128			1.11372
$732$		−	1140.76i		−	1.55842i
$733$		−	981.315i		−	1.33877i	−0.742918	−	0.669383i	$-0.766559\pi$
$733$		−	981.315i		−	1.33877i	0.742918	−	0.669383i	$-0.233441\pi$
$734$		−	2020.16i		−	2.75227i
$735$		−	67.6786i		−	0.0920798i
$736$	1686.34	+	2694.45i	2.29122	+	3.66093i
$737$	28.6251			0.0388400
$738$	−508.864			−0.689518
$739$	1204.10			1.62936			0.814681	−	0.579909i	$-0.196912\pi$
$739$	1204.10			1.62936			0.814681	+	0.579909i	$0.196912\pi$
$740$	1444.25			1.95169
$741$		−	151.878i		−	0.204963i
$742$	−784.992			−1.05794
$743$			871.920i			1.17351i	0.809764	+	0.586756i	$0.199595\pi$
$743$			871.920i			1.17351i	−0.809764	+	0.586756i	$0.800405\pi$
$744$	−495.204			−0.665597
$745$	865.962			1.16237
$746$		−	1056.07i		−	1.41565i
$747$		−	158.910i		−	0.212731i
$748$	−578.195			−0.772987
$749$	372.583			0.497440
$750$		−	709.602i		−	0.946136i
$751$			251.990i			0.335539i	0.985826	+	0.167770i	$0.0536565\pi$
$751$			251.990i			0.335539i	−0.985826	+	0.167770i	$0.946344\pi$
$752$	−2037.31			−2.70919
$753$			72.4322i			0.0961914i
$754$	322.371			0.427548
$755$		−	473.953i		−	0.627752i
$756$			153.628i			0.203211i
$757$		−	638.815i		−	0.843877i	−0.906625	−	0.421938i	$-0.861350\pi$
$757$		−	638.815i		−	0.843877i	0.906625	−	0.421938i	$-0.138650\pi$
$758$			356.808i			0.470723i
$759$	−80.9010	+	50.6325i	−0.106589	+	0.0667095i
$760$	−4393.36			−5.78074
$761$	−558.838			−0.734347			−0.367174	−	0.930152i	$-0.619675\pi$
$761$	−558.838			−0.734347			−0.367174	+	0.930152i	$0.619675\pi$
$762$	−842.435			−1.10556
$763$	163.926			0.214843
$764$		−	1757.34i		−	2.30018i
$765$	361.669			0.472770
$766$		−	1729.62i		−	2.25799i
$767$	251.755			0.328233
$768$	−1721.66			−2.24174
$769$		−	334.303i		−	0.434724i	−0.976091	−	0.217362i	$-0.930255\pi$
$769$		−	334.303i		−	0.434724i	0.976091	−	0.217362i	$-0.0697452\pi$
$770$			137.829i			0.178999i
$771$	−472.563			−0.612922
$772$	233.644			0.302648
$773$			272.063i			0.351957i	0.984394	+	0.175978i	$0.0563089\pi$
$773$			272.063i			0.351957i	−0.984394	+	0.175978i	$0.943691\pi$
$774$			440.533i			0.569164i
$775$	63.0051			0.0812969
$776$			1306.86i			1.68409i
$777$	−106.101			−0.136553
$778$			1142.65i			1.46870i
$779$			1226.18i			1.57404i
$780$			336.428i			0.431317i
$781$			253.862i			0.325048i
$782$	−1640.26	+	1026.57i	−2.09752	+	1.31275i
$783$	138.095			0.176366
$784$	−449.236			−0.573005
$785$	−1328.50			−1.69236
$786$	−1645.21			−2.09314
$787$			874.132i			1.11071i	0.831612	+	0.555357i	$0.187418\pi$
$787$			874.132i			1.11071i	−0.831612	+	0.555357i	$0.812582\pi$
$788$	3721.88			4.72320
$789$		−	675.778i		−	0.856500i
$790$	−2573.65			−3.25778
$791$	516.285			0.652699
$792$		−	200.877i		−	0.253632i
$793$			183.524i			0.231431i
$794$	−1516.63			−1.91012
$795$	−736.391			−0.926278
$796$		−	3085.31i		−	3.87602i
$797$			278.982i			0.350040i	0.984565	+	0.175020i	$0.0559989\pi$
$797$			278.982i			0.350040i	−0.984565	+	0.175020i	$0.944001\pi$
$798$	502.695			0.629944
$799$		−	685.611i		−	0.858087i
$800$	851.209			1.06401
$801$			18.1538i			0.0226639i
$802$			2571.88i			3.20683i
$803$		−	37.3891i		−	0.0465618i
$804$			231.264i			0.287642i
$805$	180.207	+	287.937i	0.223860	+	0.357686i
$806$	124.083			0.153950
$807$	349.904			0.433586
$808$	−3675.97			−4.54947
$809$	−204.255			−0.252478			−0.126239	−	0.992000i	$-0.540291\pi$
$809$	−204.255			−0.252478			−0.126239	+	0.992000i	$0.540291\pi$
$810$			195.703i			0.241608i
$811$	−1370.95			−1.69045			−0.845223	−	0.534414i	$-0.820532\pi$
$811$	−1370.95			−1.69045			−0.845223	+	0.534414i	$0.820532\pi$
$812$			785.749i			0.967672i
$813$	365.138			0.449124
$814$	216.078			0.265452
$815$		−	1408.12i		−	1.72775i
$816$		−	2400.68i		−	2.94201i
$817$	1061.52			1.29930
$818$	2747.74			3.35910
$819$		−	24.7155i		−	0.0301776i
$820$		−	2716.13i		−	3.31236i
$821$	210.370			0.256236			0.128118	−	0.991759i	$-0.459106\pi$
$821$	210.370			0.256236			0.128118	+	0.991759i	$0.459106\pi$
$822$			1396.67i			1.69911i
$823$	75.5676			0.0918197			0.0459098	−	0.998946i	$-0.485381\pi$
$823$	75.5676			0.0918197			0.0459098	+	0.998946i	$0.485381\pi$
$824$			3953.23i			4.79761i
$825$			25.5576i			0.0309789i
$826$			833.277i			1.00881i
$827$			382.070i			0.461995i	0.972954	+	0.230997i	$0.0741989\pi$
$827$			382.070i			0.461995i	−0.972954	+	0.230997i	$0.925801\pi$
$828$	−409.064	−	653.606i	−0.494038	−	0.789379i
$829$	−408.973			−0.493333			−0.246667	−	0.969100i	$-0.579335\pi$
$829$	−408.973			−0.493333			−0.246667	+	0.969100i	$0.579335\pi$
$830$	1151.82			1.38773
$831$	396.438			0.477061
$832$	877.039			1.05413
$833$		−	151.180i		−	0.181489i
$834$	1233.67			1.47922
$835$		−	727.873i		−	0.871705i
$836$	−753.895			−0.901789
$837$	53.1539			0.0635053
$838$		−	1523.60i		−	1.81813i
$839$		−	527.188i		−	0.628353i	−0.949365	−	0.314177i	$-0.898272\pi$
$839$		−	527.188i		−	0.628353i	0.949365	−	0.314177i	$-0.101728\pi$
$840$	−714.945			−0.851125
$841$	−134.696			−0.160161
$842$		−	2434.07i		−	2.89081i
$843$			320.586i			0.380292i
$844$	−1440.80			−1.70711
$845$			889.241i			1.05236i
$846$	370.991			0.438524
$847$		−	304.951i		−	0.360036i
$848$			4888.01i			5.76416i
$849$			322.749i			0.380151i
$850$			518.179i			0.609623i
$851$	451.406	−	282.515i	0.530441	−	0.331981i
$852$	−2050.97			−2.40725
$853$	−180.416			−0.211508			−0.105754	−	0.994392i	$-0.533726\pi$
$853$	−180.416			−0.211508			−0.105754	+	0.994392i	$0.533726\pi$
$854$	−607.443			−0.711291
$855$	471.572			0.551546
$856$		−	3935.90i		−	4.59801i
$857$	234.585			0.273728			0.136864	−	0.990590i	$-0.456298\pi$
$857$	234.585			0.273728			0.136864	+	0.990590i	$0.456298\pi$
$858$			50.3337i			0.0586640i
$859$	490.292			0.570771			0.285386	−	0.958413i	$-0.407878\pi$
$859$	490.292			0.570771			0.285386	+	0.958413i	$0.407878\pi$
$860$	−2351.41			−2.73420
$861$			199.540i			0.231753i
$862$		−	1245.32i		−	1.44469i
$863$	1107.20			1.28297			0.641483	−	0.767137i	$-0.278320\pi$
$863$	1107.20			1.28297			0.641483	+	0.767137i	$0.278320\pi$
$864$	718.118			0.831155
$865$		−	1731.65i		−	2.00191i
$866$			974.582i			1.12538i
$867$	307.331			0.354477
$868$			302.442i			0.348435i
$869$	−283.552			−0.326297
$870$			1000.95i			1.15051i
$871$		−	37.2055i		−	0.0427159i
$872$		−	1731.68i		−	1.98587i
$873$		−	140.275i		−	0.160681i
$874$	−2138.70	+	1338.52i	−2.44703	+	1.53149i
$875$	−278.254			−0.318005
$876$	302.069			0.344828
$877$	1145.09			1.30569			0.652846	−	0.757491i	$-0.273575\pi$
$877$	1145.09			1.30569			0.652846	+	0.757491i	$0.273575\pi$
$878$	951.968			1.08425
$879$			498.189i			0.566768i
$880$	858.238			0.975270
$881$		−	7.28773i		−	0.00827211i	−0.999991	−	0.00413605i	$-0.998683\pi$
$881$		−	7.28773i		−	0.00827211i	0.999991	−	0.00413605i	$-0.00131655\pi$
$882$	81.8051			0.0927496
$883$	−192.661			−0.218189			−0.109094	−	0.994031i	$-0.534795\pi$
$883$	−192.661			−0.218189			−0.109094	+	0.994031i	$0.534795\pi$
$884$			751.510i			0.850125i
$885$			781.686i			0.883262i
$886$	2797.62			3.15758
$887$	−668.445			−0.753603			−0.376801	−	0.926294i	$-0.622976\pi$
$887$	−668.445			−0.753603			−0.376801	+	0.926294i	$0.622976\pi$
$888$			1120.84i			1.26220i
$889$			330.342i			0.371588i
$890$	−131.583			−0.147846
$891$			21.5616i			0.0241993i
$892$	−430.203			−0.482290
$893$		−	893.954i		−	1.00107i
$894$			1046.71i			1.17082i
$895$		−	192.857i		−	0.215482i
$896$			1440.30i			1.60747i
$897$	65.8098	+	105.151i	0.0733665	+	0.117226i
$898$	−1025.36			−1.14183
$899$	271.863			0.302406
$900$	−206.482			−0.229424
$901$	−1644.95			−1.82569
$902$		−	406.367i		−	0.450518i
$903$	172.745			0.191301
$904$		−	5453.94i		−	6.03312i
$905$	−467.829			−0.516938
$906$	572.881			0.632319
$907$			1515.42i			1.67080i	0.549643	+	0.835400i	$0.314764\pi$
$907$			1515.42i			1.67080i	−0.549643	+	0.835400i	$0.685236\pi$
$908$			377.084i			0.415291i
$909$	394.570			0.434070
$910$	179.144			0.196861
$911$		−	1779.53i		−	1.95338i	−0.214650	−	0.976691i	$-0.568861\pi$
$911$		−	1779.53i		−	1.95338i	0.214650	−	0.976691i	$-0.431139\pi$
$912$		−	3130.20i		−	3.43223i
$913$	126.902			0.138994
$914$		−	2578.80i		−	2.82144i
$915$	−569.834			−0.622770
$916$			2810.44i			3.06817i
$917$			645.131i			0.703524i
$918$			437.160i			0.476209i
$919$			205.108i			0.223186i	0.993754	+	0.111593i	$0.0355953\pi$
$919$			205.108i			0.223186i	−0.993754	+	0.111593i	$0.964405\pi$
$920$	3041.71	−	1903.68i	3.30621	−	2.06922i
$921$	−185.327			−0.201224
$922$	−1165.66			−1.26427
$923$	329.958			0.357485
$924$	−122.684			−0.132775
$925$		−	142.605i		−	0.154167i
$926$	512.310			0.553251
$927$		−	424.330i		−	0.457745i
$928$	3672.91			3.95788
$929$	−1670.04			−1.79768			−0.898840	−	0.438277i	$-0.855589\pi$
$929$	−1670.04			−1.79768			−0.898840	+	0.438277i	$0.855589\pi$
$930$			385.273i			0.414272i
$931$		−	197.121i		−	0.211730i
$932$	−2947.34			−3.16238
$933$	761.660			0.816355
$934$		−	1546.93i		−	1.65624i
$935$			288.820i			0.308899i
$936$	−261.090			−0.278942
$937$		−	204.266i		−	0.218000i	−0.994042	−	0.109000i	$-0.965235\pi$
$937$		−	204.266i		−	0.218000i	0.994042	−	0.109000i	$-0.0347649\pi$
$938$	123.146			0.131285
$939$		−	687.261i		−	0.731907i
$940$			1980.22i			2.10662i
$941$		−	286.609i		−	0.304579i	−0.988336	−	0.152289i	$-0.951335\pi$
$941$		−	286.609i		−	0.304579i	0.988336	−	0.152289i	$-0.0486646\pi$
$942$		−	1605.80i		−	1.70467i
$943$	−531.313	−	848.936i	−0.563428	−	0.900250i
$944$	5188.67			5.49647
$945$	76.7404			0.0812067
$946$	−351.800			−0.371881
$947$	277.717			0.293260			0.146630	−	0.989191i	$-0.453157\pi$
$947$	277.717			0.293260			0.146630	+	0.989191i	$0.453157\pi$
$948$		−	2290.84i		−	2.41650i
$949$	−48.5966			−0.0512082
$950$			675.643i			0.711203i
$951$	−858.784			−0.903033
$952$	−1597.04			−1.67756
$953$		−	70.9750i		−	0.0744754i	−0.999306	−	0.0372377i	$-0.988144\pi$
$953$		−	70.9750i		−	0.0744754i	0.999306	−	0.0372377i	$-0.0118559\pi$
$954$		−	890.097i		−	0.933016i
$955$	−877.827			−0.919191
$956$	2508.14			2.62357
$957$			110.279i			0.115235i
$958$			2459.74i			2.56758i
$959$	547.672			0.571087
$960$			2723.16i			2.83663i
$961$	−856.358			−0.891111
$962$		−	280.848i		−	0.291942i
$963$			422.469i			0.438701i
$964$			2606.30i			2.70363i
$965$		−	116.710i		−	0.120943i
$966$	−348.038	+	217.822i	−0.360287	+	0.225489i
$967$	1717.45			1.77606			0.888030	−	0.459786i	$-0.152074\pi$
$967$	1717.45			1.77606			0.888030	+	0.459786i	$0.152074\pi$
$968$	−3221.44			−3.32794
$969$	1053.40			1.08710
$970$	1016.75			1.04819
$971$		−	1438.59i		−	1.48156i	−0.671750	−	0.740778i	$-0.734457\pi$
$971$		−	1438.59i		−	1.48156i	0.671750	−	0.740778i	$-0.265543\pi$
$972$	−174.198			−0.179216
$973$		−	483.757i		−	0.497180i
$974$	2556.78			2.62503
$975$	33.2186			0.0340704
$976$			3782.44i			3.87545i
$977$			496.158i			0.507838i	0.967226	+	0.253919i	$0.0817196\pi$
$977$			496.158i			0.507838i	−0.967226	+	0.253919i	$0.918280\pi$
$978$	1702.03			1.74032
$979$	−14.4972			−0.0148082
$980$			436.647i			0.445558i
$981$			185.874i			0.189474i
$982$	490.858			0.499855
$983$			719.595i			0.732039i	0.930607	+	0.366020i	$0.119280\pi$
$983$			719.595i			0.732039i	−0.930607	+	0.366020i	$0.880720\pi$
$984$	2107.90			2.14217
$985$		−	1859.16i		−	1.88747i
$986$			2235.91i			2.26766i
$987$		−	145.476i		−	0.147392i
$988$			979.878i			0.991779i
$989$	−734.939	+	459.967i	−0.743113	+	0.465083i
$990$	−156.284			−0.157862
$991$	293.225			0.295888			0.147944	−	0.988996i	$-0.452735\pi$
$991$	293.225			0.295888			0.147944	+	0.988996i	$0.452735\pi$
$992$	1413.73			1.42514
$993$	236.204			0.237869
$994$			1092.12i			1.09871i
$995$	−1541.18			−1.54892
$996$			1025.25i			1.02937i
$997$	562.161			0.563853			0.281926	−	0.959436i	$-0.409027\pi$
$997$	562.161			0.563853			0.281926	+	0.959436i	$0.409027\pi$
$998$	−940.592			−0.942477
$999$		−	120.308i		−	0.120428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.2	yes	48
23.22	odd	2	inner	483.3.f.a.22.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.1	✓	48	23.22	odd	2	inner
483.3.f.a.22.2	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.89548 q^{2} -1.73205 q^{3} +11.1748 q^{4} -5.58204i q^{5} +6.74717 q^{6} -2.64575i q^{7} -27.9492 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.89548 q^{2} -1.73205 q^{3} +11.1748 q^{4} -5.58204i q^{5} +6.74717 q^{6} -2.64575i q^{7} -27.9492 q^{8} +3.00000 q^{9} +21.7447i q^{10} +2.39573i q^{11} -19.3553 q^{12} +3.11386 q^{13} +10.3065i q^{14} +9.66838i q^{15} +64.1766 q^{16} +21.5972i q^{17} -11.6864 q^{18} +28.1601i q^{19} -62.3781i q^{20} +4.58258i q^{21} -9.33253i q^{22} +(-12.2020 - 19.4964i) q^{23} +48.4095 q^{24} -6.15917 q^{25} -12.1300 q^{26} -5.19615 q^{27} -29.5657i q^{28} -26.5764 q^{29} -37.6630i q^{30} -10.2295 q^{31} -138.202 q^{32} -4.14953i q^{33} -84.1314i q^{34} -14.7687 q^{35} +33.5243 q^{36} +23.1532i q^{37} -109.697i q^{38} -5.39336 q^{39} +156.014i q^{40} +43.5431 q^{41} -17.8513i q^{42} -37.6961i q^{43} +26.7718i q^{44} -16.7461i q^{45} +(47.5326 + 75.9481i) q^{46} -31.7454 q^{47} -111.157 q^{48} -7.00000 q^{49} +23.9929 q^{50} -37.4074i q^{51} +34.7967 q^{52} +76.1649i q^{53} +20.2415 q^{54} +13.3731 q^{55} +73.9467i q^{56} -48.7747i q^{57} +103.528 q^{58} +80.8498 q^{59} +108.042i q^{60} +58.9379i q^{61} +39.8488 q^{62} -7.93725i q^{63} +281.657 q^{64} -17.3817i q^{65} +16.1644i q^{66} -11.9484i q^{67} +241.344i q^{68} +(21.1345 + 33.7688i) q^{69} +57.5312 q^{70} +105.964 q^{71} -83.8477 q^{72} -15.6066 q^{73} -90.1930i q^{74} +10.6680 q^{75} +314.683i q^{76} +6.33851 q^{77} +21.0097 q^{78} +118.357i q^{79} -358.236i q^{80} +9.00000 q^{81} -169.621 q^{82} -52.9699i q^{83} +51.2093i q^{84} +120.556 q^{85} +146.844i q^{86} +46.0317 q^{87} -66.9588i q^{88} +6.05127i q^{89} +65.2342i q^{90} -8.23850i q^{91} +(-136.355 - 217.869i) q^{92} +17.7180 q^{93} +123.664 q^{94} +157.191 q^{95} +239.373 q^{96} -46.7582i q^{97} +27.2684 q^{98} +7.18719i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 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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