LMFDB - Embedded newform 483.3.f.a.22.19

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			22.19
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.876983 q^{2} +1.73205 q^{3} -3.23090 q^{4} +8.50705i q^{5} -1.51898 q^{6} +2.64575i q^{7} +6.34138 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-0.876983 q^{2} +1.73205 q^{3} -3.23090 q^{4} +8.50705i q^{5} -1.51898 q^{6} +2.64575i q^{7} +6.34138 q^{8} +3.00000 q^{9} -7.46053i q^{10} -12.5240i q^{11} -5.59608 q^{12} +23.0788 q^{13} -2.32028i q^{14} +14.7346i q^{15} +7.36233 q^{16} +13.0806i q^{17} -2.63095 q^{18} +23.2463i q^{19} -27.4854i q^{20} +4.58258i q^{21} +10.9834i q^{22} +(-19.0867 + 12.8334i) q^{23} +10.9836 q^{24} -47.3698 q^{25} -20.2397 q^{26} +5.19615 q^{27} -8.54816i q^{28} -13.6391 q^{29} -12.9220i q^{30} -23.6204 q^{31} -31.8221 q^{32} -21.6923i q^{33} -11.4714i q^{34} -22.5075 q^{35} -9.69270 q^{36} +38.3359i q^{37} -20.3866i q^{38} +39.9737 q^{39} +53.9464i q^{40} -27.0412 q^{41} -4.01884i q^{42} -5.04663i q^{43} +40.4639i q^{44} +25.5211i q^{45} +(16.7387 - 11.2547i) q^{46} -21.8114 q^{47} +12.7519 q^{48} -7.00000 q^{49} +41.5425 q^{50} +22.6562i q^{51} -74.5654 q^{52} +55.7900i q^{53} -4.55694 q^{54} +106.543 q^{55} +16.7777i q^{56} +40.2637i q^{57} +11.9613 q^{58} +50.7804 q^{59} -47.6061i q^{60} -68.5432i q^{61} +20.7146 q^{62} +7.93725i q^{63} -1.54183 q^{64} +196.333i q^{65} +19.0238i q^{66} -34.3720i q^{67} -42.2620i q^{68} +(-33.0592 + 22.2281i) q^{69} +19.7387 q^{70} -103.295 q^{71} +19.0241 q^{72} +128.233 q^{73} -33.6199i q^{74} -82.0470 q^{75} -75.1064i q^{76} +33.1355 q^{77} -35.0562 q^{78} -130.267i q^{79} +62.6316i q^{80} +9.00000 q^{81} +23.7147 q^{82} +39.2795i q^{83} -14.8058i q^{84} -111.277 q^{85} +4.42581i q^{86} -23.6237 q^{87} -79.4196i q^{88} +5.35404i q^{89} -22.3816i q^{90} +61.0608i q^{91} +(61.6674 - 41.4635i) q^{92} -40.9117 q^{93} +19.1282 q^{94} -197.757 q^{95} -55.1176 q^{96} +142.335i q^{97} +6.13888 q^{98} -37.5721i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.876983			−0.438491			−0.219246	−	0.975670i	$-0.570360\pi$
$2$	−0.876983			−0.438491			−0.219246	+	0.975670i	$0.570360\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−3.23090			−0.807725
$5$			8.50705i			1.70141i	0.525644	+	0.850705i	$0.323824\pi$
$5$			8.50705i			1.70141i	−0.525644	+	0.850705i	$0.676176\pi$
$6$	−1.51898			−0.253163
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	6.34138			0.792672
$9$	3.00000			0.333333
$10$		−	7.46053i		−	0.746053i
$11$		−	12.5240i		−	1.13855i	−0.822148	−	0.569275i	$-0.807224\pi$
$11$		−	12.5240i		−	1.13855i	0.822148	−	0.569275i	$-0.192776\pi$
$12$	−5.59608			−0.466340
$13$	23.0788			1.77529			0.887647	−	0.460525i	$-0.152339\pi$
$13$	23.0788			1.77529			0.887647	+	0.460525i	$0.152339\pi$
$14$		−	2.32028i		−	0.165734i
$15$			14.7346i			0.982309i
$16$	7.36233			0.460145
$17$			13.0806i			0.769445i	0.923032	+	0.384723i	$0.125703\pi$
$17$			13.0806i			0.769445i	−0.923032	+	0.384723i	$0.874297\pi$
$18$	−2.63095			−0.146164
$19$			23.2463i			1.22349i	0.791056	+	0.611744i	$0.209532\pi$
$19$			23.2463i			1.22349i	−0.791056	+	0.611744i	$0.790468\pi$
$20$		−	27.4854i		−	1.37427i
$21$			4.58258i			0.218218i
$22$			10.9834i			0.499244i
$23$	−19.0867	+	12.8334i	−0.829858	+	0.557974i
$23$	−19.0867	+	12.8334i	−0.829858	+	0.557974i
$24$	10.9836			0.457649
$25$	−47.3698			−1.89479
$26$	−20.2397			−0.778451
$27$	5.19615			0.192450
$28$		−	8.54816i		−	0.305291i
$29$	−13.6391			−0.470315			−0.235158	−	0.971957i	$-0.575561\pi$
$29$	−13.6391			−0.470315			−0.235158	+	0.971957i	$0.575561\pi$
$30$		−	12.9220i		−	0.430734i
$31$	−23.6204			−0.761947			−0.380973	−	0.924586i	$-0.624411\pi$
$31$	−23.6204			−0.761947			−0.380973	+	0.924586i	$0.624411\pi$
$32$	−31.8221			−0.994442
$33$		−	21.6923i		−	0.657342i
$34$		−	11.4714i		−	0.337395i
$35$	−22.5075			−0.643072
$36$	−9.69270			−0.269242
$37$			38.3359i			1.03610i	0.855349	+	0.518052i	$0.173343\pi$
$37$			38.3359i			1.03610i	−0.855349	+	0.518052i	$0.826657\pi$
$38$		−	20.3866i		−	0.536489i
$39$	39.9737			1.02497
$40$			53.9464i			1.34866i
$41$	−27.0412			−0.659542			−0.329771	−	0.944061i	$-0.606972\pi$
$41$	−27.0412			−0.659542			−0.329771	+	0.944061i	$0.606972\pi$
$42$		−	4.01884i		−	0.0956867i
$43$		−	5.04663i		−	0.117363i	−0.998277	−	0.0586817i	$-0.981310\pi$
$43$		−	5.04663i		−	0.117363i	0.998277	−	0.0586817i	$-0.0186897\pi$
$44$			40.4639i			0.919635i
$45$			25.5211i			0.567136i
$46$	16.7387	−	11.2547i	0.363886	−	0.244667i
$47$	−21.8114			−0.464071			−0.232036	−	0.972707i	$-0.574539\pi$
$47$	−21.8114			−0.464071			−0.232036	+	0.972707i	$0.574539\pi$
$48$	12.7519			0.265665
$49$	−7.00000			−0.142857
$50$	41.5425			0.830851
$51$			22.6562i			0.444239i
$52$	−74.5654			−1.43395
$53$			55.7900i			1.05264i	0.850286	+	0.526321i	$0.176429\pi$
$53$			55.7900i			1.05264i	−0.850286	+	0.526321i	$0.823571\pi$
$54$	−4.55694			−0.0843877
$55$	106.543			1.93714
$56$			16.7777i			0.299602i
$57$			40.2637i			0.706381i
$58$	11.9613			0.206229
$59$	50.7804			0.860685			0.430342	−	0.902666i	$-0.358393\pi$
$59$	50.7804			0.860685			0.430342	+	0.902666i	$0.358393\pi$
$60$		−	47.6061i		−	0.793436i
$61$		−	68.5432i		−	1.12366i	−0.827253	−	0.561830i	$-0.810098\pi$
$61$		−	68.5432i		−	1.12366i	0.827253	−	0.561830i	$-0.189902\pi$
$62$	20.7146			0.334107
$63$			7.93725i			0.125988i
$64$	−1.54183			−0.0240911
$65$			196.333i			3.02050i
$66$			19.0238i			0.288239i
$67$		−	34.3720i		−	0.513015i	−0.966542	−	0.256508i	$-0.917428\pi$
$67$		−	34.3720i		−	0.513015i	0.966542	−	0.256508i	$-0.0825719\pi$
$68$		−	42.2620i		−	0.621500i
$69$	−33.0592	+	22.2281i	−0.479119	+	0.322146i
$70$	19.7387			0.281982
$71$	−103.295			−1.45486			−0.727431	−	0.686181i	$-0.759286\pi$
$71$	−103.295			−1.45486			−0.727431	+	0.686181i	$0.759286\pi$
$72$	19.0241			0.264224
$73$	128.233			1.75662			0.878308	−	0.478096i	$-0.158673\pi$
$73$	128.233			1.75662			0.878308	+	0.478096i	$0.158673\pi$
$74$		−	33.6199i		−	0.454323i
$75$	−82.0470			−1.09396
$76$		−	75.1064i		−	0.988242i
$77$	33.1355			0.430331
$78$	−35.0562			−0.449439
$79$		−	130.267i		−	1.64894i	−0.565903	−	0.824472i	$-0.691472\pi$
$79$		−	130.267i		−	1.64894i	0.565903	−	0.824472i	$-0.308528\pi$
$80$			62.6316i			0.782896i
$81$	9.00000			0.111111
$82$	23.7147			0.289204
$83$			39.2795i			0.473247i	0.971601	+	0.236624i	$0.0760409\pi$
$83$			39.2795i			0.473247i	−0.971601	+	0.236624i	$0.923959\pi$
$84$		−	14.8058i		−	0.176260i
$85$	−111.277			−1.30914
$86$			4.42581i			0.0514629i
$87$	−23.6237			−0.271537
$88$		−	79.4196i		−	0.902496i
$89$			5.35404i			0.0601578i	0.999548	+	0.0300789i	$0.00957586\pi$
$89$			5.35404i			0.0601578i	−0.999548	+	0.0300789i	$0.990424\pi$
$90$		−	22.3816i		−	0.248684i
$91$			61.0608i			0.670998i
$92$	61.6674	−	41.4635i	0.670298	−	0.450690i
$93$	−40.9117			−0.439910
$94$	19.1282			0.203491
$95$	−197.757			−2.08165
$96$	−55.1176			−0.574141
$97$			142.335i			1.46737i	0.679487	+	0.733687i	$0.262202\pi$
$97$			142.335i			1.46737i	−0.679487	+	0.733687i	$0.737798\pi$
$98$	6.13888			0.0626416
$99$		−	37.5721i		−	0.379516i
$100$	153.047			1.53047
$101$	83.7772			0.829477			0.414738	−	0.909941i	$-0.363873\pi$
$101$	83.7772			0.829477			0.414738	+	0.909941i	$0.363873\pi$
$102$		−	19.8691i		−	0.194795i
$103$			45.4480i			0.441243i	0.975360	+	0.220621i	$0.0708085\pi$
$103$			45.4480i			0.441243i	−0.975360	+	0.220621i	$0.929192\pi$
$104$	146.351			1.40723
$105$	−38.9842			−0.371278
$106$		−	48.9269i		−	0.461574i
$107$			93.2200i			0.871215i	0.900137	+	0.435607i	$0.143466\pi$
$107$			93.2200i			0.871215i	−0.900137	+	0.435607i	$0.856534\pi$
$108$	−16.7883			−0.155447
$109$		−	121.762i		−	1.11708i	−0.829476	−	0.558542i	$-0.811361\pi$
$109$		−	121.762i		−	1.11708i	0.829476	−	0.558542i	$-0.188639\pi$
$110$	−93.4360			−0.849418
$111$			66.3997i			0.598195i
$112$			19.4789i			0.173919i
$113$			139.100i			1.23098i	0.788146	+	0.615488i	$0.211041\pi$
$113$			139.100i			1.23098i	−0.788146	+	0.615488i	$0.788959\pi$
$114$		−	35.3106i		−	0.309742i
$115$	−109.174	−	162.372i	−0.949342	−	1.41193i
$116$	44.0667			0.379886
$117$	69.2365			0.591765
$118$	−44.5336			−0.377403
$119$	−34.6079			−0.290823
$120$			93.4379i			0.778649i
$121$	−35.8516			−0.296294
$122$			60.1113i			0.492715i
$123$	−46.8368			−0.380787
$124$	76.3150			0.615444
$125$		−	190.301i		−	1.52241i
$126$		−	6.96084i		−	0.0552447i
$127$	−202.970			−1.59819			−0.799096	−	0.601204i	$-0.794688\pi$
$127$	−202.970			−1.59819			−0.799096	+	0.601204i	$0.794688\pi$
$128$	128.641			1.00501
$129$		−	8.74102i		−	0.0677598i
$130$		−	172.180i		−	1.32446i
$131$	−28.7014			−0.219095			−0.109547	−	0.993982i	$-0.534940\pi$
$131$	−28.7014			−0.219095			−0.109547	+	0.993982i	$0.534940\pi$
$132$			70.0856i			0.530951i
$133$	−61.5039			−0.462435
$134$			30.1437i			0.224953i
$135$			44.2039i			0.327436i
$136$			82.9488i			0.609918i
$137$			156.835i			1.14478i	0.819982	+	0.572389i	$0.193983\pi$
$137$			156.835i			1.14478i	−0.819982	+	0.572389i	$0.806017\pi$
$138$	28.9924	−	19.4937i	0.210090	−	0.141258i
$139$	159.986			1.15098			0.575488	−	0.817810i	$-0.304812\pi$
$139$	159.986			1.15098			0.575488	+	0.817810i	$0.304812\pi$
$140$	72.7196			0.519426
$141$	−37.7784			−0.267932
$142$	90.5881			0.637944
$143$		−	289.040i		−	2.02126i
$144$	22.0870			0.153382
$145$		−	116.029i		−	0.800199i
$146$	−112.458			−0.770261
$147$	−12.1244			−0.0824786
$148$		−	123.859i		−	0.836888i
$149$		−	248.689i		−	1.66905i	−0.550970	−	0.834525i	$-0.685742\pi$
$149$		−	248.689i		−	1.66905i	0.550970	−	0.834525i	$-0.314258\pi$
$150$	71.9538			0.479692
$151$	127.529			0.844560			0.422280	−	0.906465i	$-0.361230\pi$
$151$	127.529			0.844560			0.422280	+	0.906465i	$0.361230\pi$
$152$			147.413i			0.969825i
$153$			39.2417i			0.256482i
$154$	−29.0593			−0.188696
$155$		−	200.939i		−	1.29638i
$156$	−129.151			−0.827891
$157$		−	30.5819i		−	0.194789i	−0.995246	−	0.0973946i	$-0.968949\pi$
$157$		−	30.5819i		−	0.194789i	0.995246	−	0.0973946i	$-0.0310509\pi$
$158$			114.242i			0.723048i
$159$			96.6311i			0.607743i
$160$		−	270.712i		−	1.69195i
$161$	−33.9540	−	50.4988i	−0.210894	−	0.313657i
$162$	−7.89285			−0.0487213
$163$	272.859			1.67398			0.836990	−	0.547218i	$-0.184313\pi$
$163$	272.859			1.67398			0.836990	+	0.547218i	$0.184313\pi$
$164$	87.3676			0.532729
$165$	184.537			1.11841
$166$		−	34.4475i		−	0.207515i
$167$	−87.5074			−0.523996			−0.261998	−	0.965068i	$-0.584381\pi$
$167$	−87.5074			−0.523996			−0.261998	+	0.965068i	$0.584381\pi$
$168$			29.0598i			0.172975i
$169$	363.632			2.15167
$170$	97.5880			0.574047
$171$			69.7388i			0.407829i
$172$			16.3052i			0.0947974i
$173$	255.005			1.47402			0.737008	−	0.675884i	$-0.236238\pi$
$173$	255.005			1.47402			0.737008	+	0.675884i	$0.236238\pi$
$174$	20.7176			0.119067
$175$		−	125.329i		−	0.716165i
$176$		−	92.2061i		−	0.523898i
$177$	87.9543			0.496917
$178$		−	4.69541i		−	0.0263787i
$179$	−341.018			−1.90513			−0.952564	−	0.304337i	$-0.901565\pi$
$179$	−341.018			−1.90513			−0.952564	+	0.304337i	$0.901565\pi$
$180$		−	82.4563i		−	0.458090i
$181$			292.617i			1.61667i	0.588725	+	0.808334i	$0.299630\pi$
$181$			292.617i			1.61667i	−0.588725	+	0.808334i	$0.700370\pi$
$182$		−	53.5493i		−	0.294227i
$183$		−	118.720i		−	0.648745i
$184$	−121.036	+	81.3814i	−0.657806	+	0.442290i
$185$	−326.125			−1.76284
$186$	35.8788			0.192897
$187$	163.822			0.876051
$188$	70.4703			0.374842
$189$			13.7477i			0.0727393i
$190$	173.430			0.912787
$191$			115.651i			0.605504i	0.953069	+	0.302752i	$0.0979054\pi$
$191$			115.651i			0.605504i	−0.953069	+	0.302752i	$0.902095\pi$
$192$	−2.67053			−0.0139090
$193$	−134.250			−0.695598			−0.347799	−	0.937569i	$-0.613071\pi$
$193$	−134.250			−0.695598			−0.347799	+	0.937569i	$0.613071\pi$
$194$		−	124.826i		−	0.643431i
$195$			340.058i			1.74389i
$196$	22.6163			0.115389
$197$	186.004			0.944182			0.472091	−	0.881550i	$-0.343499\pi$
$197$	186.004			0.944182			0.472091	+	0.881550i	$0.343499\pi$
$198$			32.9501i			0.166415i
$199$			51.5488i			0.259039i	0.991577	+	0.129520i	$0.0413435\pi$
$199$			51.5488i			0.259039i	−0.991577	+	0.129520i	$0.958656\pi$
$200$	−300.390			−1.50195
$201$		−	59.5341i		−	0.296190i
$202$	−73.4711			−0.363719
$203$		−	36.0858i		−	0.177763i
$204$		−	73.2000i		−	0.358823i
$205$		−	230.041i		−	1.12215i
$206$		−	39.8571i		−	0.193481i
$207$	−57.2602	+	38.5002i	−0.276619	+	0.185991i
$208$	169.914			0.816893
$209$	291.137			1.39300
$210$	34.1885			0.162802
$211$	348.367			1.65103			0.825513	−	0.564382i	$-0.190886\pi$
$211$	348.367			1.65103			0.825513	+	0.564382i	$0.190886\pi$
$212$		−	180.252i		−	0.850245i
$213$	−178.912			−0.839964
$214$		−	81.7523i		−	0.382020i
$215$	42.9319			0.199683
$216$	32.9508			0.152550
$217$		−	62.4936i		−	0.287989i
$218$			106.783i			0.489832i
$219$	222.106			1.01418
$220$	−344.229			−1.56468
$221$			301.884i			1.36599i
$222$		−	58.2314i		−	0.262303i
$223$	−238.570			−1.06982			−0.534911	−	0.844909i	$-0.679655\pi$
$223$	−238.570			−1.06982			−0.534911	+	0.844909i	$0.679655\pi$
$224$		−	84.1935i		−	0.375864i
$225$	−142.109			−0.631598
$226$		−	121.989i		−	0.539773i
$227$		−	119.769i		−	0.527615i	−0.964575	−	0.263807i	$-0.915022\pi$
$227$		−	119.769i		−	0.527615i	0.964575	−	0.263807i	$-0.0849783\pi$
$228$		−	130.088i		−	0.570562i
$229$		−	224.050i		−	0.978382i	−0.872177	−	0.489191i	$-0.837292\pi$
$229$		−	224.050i		−	0.978382i	0.872177	−	0.489191i	$-0.162708\pi$
$230$	95.7440	+	142.397i	0.416278	+	0.619119i
$231$	57.3924			0.248452
$232$	−86.4910			−0.372806
$233$	352.648			1.51351			0.756756	−	0.653697i	$-0.226783\pi$
$233$	352.648			1.51351			0.756756	+	0.653697i	$0.226783\pi$
$234$	−60.7192			−0.259484
$235$		−	185.550i		−	0.789575i
$236$	−164.066			−0.695197
$237$		−	225.628i		−	0.952018i
$238$	30.3506			0.127523
$239$	−365.595			−1.52969			−0.764844	−	0.644216i	$-0.777184\pi$
$239$	−365.595			−1.52969			−0.764844	+	0.644216i	$0.777184\pi$
$240$			108.481i			0.452005i
$241$		−	91.4962i		−	0.379652i	−0.981818	−	0.189826i	$-0.939208\pi$
$241$		−	91.4962i		−	0.379652i	0.981818	−	0.189826i	$-0.0607924\pi$
$242$	31.4412			0.129922
$243$	15.5885			0.0641500
$244$			221.456i			0.907608i
$245$		−	59.5493i		−	0.243058i
$246$	41.0751			0.166972
$247$			536.496i			2.17205i
$248$	−149.786			−0.603974
$249$			68.0342i			0.273230i
$250$			166.891i			0.667563i
$251$		−	219.581i		−	0.874826i	−0.899261	−	0.437413i	$-0.855895\pi$
$251$		−	219.581i		−	0.874826i	0.899261	−	0.437413i	$-0.144105\pi$
$252$		−	25.6445i		−	0.101764i
$253$	160.726	+	239.043i	0.635281	+	0.944834i
$254$	178.001			0.700793
$255$	−192.737			−0.755833
$256$	−106.648			−0.416595
$257$	−358.124			−1.39348			−0.696740	−	0.717324i	$-0.745367\pi$
$257$	−358.124			−1.39348			−0.696740	+	0.717324i	$0.745367\pi$
$258$			7.66572i			0.0297121i
$259$	−101.427			−0.391611
$260$		−	634.331i		−	2.43973i
$261$	−40.9174			−0.156772
$262$	25.1706			0.0960711
$263$		−	12.2132i		−	0.0464378i	−0.999730	−	0.0232189i	$-0.992609\pi$
$263$		−	12.2132i		−	0.0464378i	0.999730	−	0.0232189i	$-0.00739148\pi$
$264$		−	137.559i		−	0.521056i
$265$	−474.608			−1.79097
$266$	53.9378			0.202774
$267$			9.27348i			0.0347321i
$268$			111.053i			0.414376i
$269$	76.6918			0.285100			0.142550	−	0.989788i	$-0.454470\pi$
$269$	76.6918			0.285100			0.142550	+	0.989788i	$0.454470\pi$
$270$		−	38.7661i		−	0.143578i
$271$	182.371			0.672955			0.336477	−	0.941692i	$-0.390764\pi$
$271$	182.371			0.672955			0.336477	+	0.941692i	$0.390764\pi$
$272$			96.3034i			0.354057i
$273$			105.760i			0.387401i
$274$		−	137.541i		−	0.501975i
$275$			593.262i			2.15731i
$276$	106.811	−	71.8168i	0.386996	−	0.260206i
$277$	−267.169			−0.964510			−0.482255	−	0.876031i	$-0.660182\pi$
$277$	−267.169			−0.964510			−0.482255	+	0.876031i	$0.660182\pi$
$278$	−140.305			−0.504693
$279$	−70.8611			−0.253982
$280$	−142.729			−0.509745
$281$		−	307.421i		−	1.09402i	−0.837125	−	0.547012i	$-0.815765\pi$
$281$		−	307.421i		−	1.09402i	0.837125	−	0.547012i	$-0.184235\pi$
$282$	33.1310			0.117486
$283$		−	135.101i		−	0.477389i	−0.971095	−	0.238694i	$-0.923281\pi$
$283$		−	135.101i		−	0.477389i	0.971095	−	0.238694i	$-0.0767194\pi$
$284$	333.736			1.17513
$285$	−342.525			−1.20184
$286$			253.483i			0.886305i
$287$		−	71.5444i		−	0.249284i
$288$	−95.4664			−0.331481
$289$	117.899			0.407954
$290$			101.755i			0.350880i
$291$			246.532i			0.847189i
$292$	−414.308			−1.41886
$293$			430.595i			1.46961i	0.678280	+	0.734803i	$0.262726\pi$
$293$			430.595i			1.46961i	−0.678280	+	0.734803i	$0.737274\pi$
$294$	10.6329			0.0361662
$295$			431.991i			1.46438i
$296$			243.102i			0.821291i
$297$		−	65.0768i		−	0.219114i
$298$			218.096i			0.731864i
$299$	−440.499	+	296.180i	−1.47324	+	0.990568i
$300$	265.086			0.883619
$301$	13.3521			0.0443592
$302$	−111.840			−0.370333
$303$	145.106			0.478899
$304$			171.147i			0.562982i
$305$	583.101			1.91181
$306$		−	34.4143i		−	0.112465i
$307$	197.821			0.644368			0.322184	−	0.946677i	$-0.395583\pi$
$307$	197.821			0.644368			0.322184	+	0.946677i	$0.395583\pi$
$308$	−107.057			−0.347589
$309$			78.7182i			0.254752i
$310$			176.220i			0.568453i
$311$	113.735			0.365707			0.182853	−	0.983140i	$-0.441467\pi$
$311$	113.735			0.365707			0.182853	+	0.983140i	$0.441467\pi$
$312$	253.488			0.812462
$313$			360.036i			1.15027i	0.818057	+	0.575137i	$0.195051\pi$
$313$			360.036i			1.15027i	−0.818057	+	0.575137i	$0.804949\pi$
$314$			26.8198i			0.0854134i
$315$	−67.5226			−0.214357
$316$			420.878i			1.33189i
$317$	379.702			1.19780			0.598899	−	0.800824i	$-0.295605\pi$
$317$	379.702			1.19780			0.598899	+	0.800824i	$0.295605\pi$
$318$		−	84.7438i		−	0.266490i
$319$			170.817i			0.535477i
$320$		−	13.1164i		−	0.0409888i
$321$			161.462i			0.502996i
$322$	29.7771	+	44.2866i	0.0924754	+	0.137536i
$323$	−304.074			−0.941407
$324$	−29.0781			−0.0897473
$325$	−1093.24			−3.36381
$326$	−239.292			−0.734026
$327$		−	210.898i		−	0.644949i
$328$	−171.479			−0.522801
$329$		−	57.7074i		−	0.175402i
$330$	−161.836			−0.490412
$331$	406.011			1.22662			0.613309	−	0.789843i	$-0.289838\pi$
$331$	406.011			1.22662			0.613309	+	0.789843i	$0.289838\pi$
$332$		−	126.908i		−	0.382254i
$333$			115.008i			0.345368i
$334$	76.7425			0.229768
$335$	292.405			0.872849
$336$			33.7384i			0.100412i
$337$			471.913i			1.40034i	0.713978	+	0.700168i	$0.246892\pi$
$337$			471.913i			1.40034i	−0.713978	+	0.700168i	$0.753108\pi$
$338$	−318.899			−0.943488
$339$			240.929i			0.710705i
$340$	359.525			1.05743
$341$			295.822i			0.867514i
$342$		−	61.1597i		−	0.178830i
$343$		−	18.5203i		−	0.0539949i
$344$		−	32.0026i		−	0.0930307i
$345$	−189.096	−	281.236i	−0.548103	−	0.815177i
$346$	−223.635			−0.646343
$347$	372.428			1.07328			0.536639	−	0.843812i	$-0.319694\pi$
$347$	372.428			1.07328			0.536639	+	0.843812i	$0.319694\pi$
$348$	76.3258			0.219327
$349$	33.8607			0.0970222			0.0485111	−	0.998823i	$-0.484552\pi$
$349$	33.8607			0.0970222			0.0485111	+	0.998823i	$0.484552\pi$
$350$			109.911i			0.314032i
$351$	119.921			0.341655
$352$			398.542i			1.13222i
$353$	128.147			0.363023			0.181512	−	0.983389i	$-0.441901\pi$
$353$	128.147			0.363023			0.181512	+	0.983389i	$0.441901\pi$
$354$	−77.1344			−0.217894
$355$		−	878.736i		−	2.47531i
$356$		−	17.2984i		−	0.0485910i
$357$	−59.9427			−0.167907
$358$	299.067			0.835383
$359$		−	495.508i		−	1.38025i	−0.723692	−	0.690123i	$-0.757556\pi$
$359$		−	495.508i		−	1.38025i	0.723692	−	0.690123i	$-0.242444\pi$
$360$			161.839i			0.449553i
$361$	−179.389			−0.496923
$362$		−	256.620i		−	0.708895i
$363$	−62.0967			−0.171065
$364$		−	197.281i		−	0.541982i
$365$			1090.88i			2.98872i
$366$			104.116i			0.284469i
$367$		−	551.754i		−	1.50342i	−0.659495	−	0.751709i	$-0.729230\pi$
$367$		−	551.754i		−	1.50342i	0.659495	−	0.751709i	$-0.270770\pi$
$368$	−140.523	+	94.4837i	−0.381855	+	0.256749i
$369$	−81.1237			−0.219847
$370$	286.006			0.772989
$371$	−147.606			−0.397861
$372$	132.182			0.355327
$373$		−	351.979i		−	0.943643i	−0.881694	−	0.471821i	$-0.843597\pi$
$373$		−	351.979i		−	0.943643i	0.881694	−	0.471821i	$-0.156403\pi$
$374$	−143.669			−0.384141
$375$		−	329.611i		−	0.878963i
$376$	−138.314			−0.367856
$377$	−314.775			−0.834948
$378$		−	12.0565i		−	0.0318956i
$379$		−	42.9132i		−	0.113227i	−0.998396	−	0.0566137i	$-0.981970\pi$
$379$		−	42.9132i		−	0.113227i	0.998396	−	0.0566137i	$-0.0180303\pi$
$380$	638.934			1.68140
$381$	−351.555			−0.922716
$382$		−	101.424i		−	0.265508i
$383$			57.1916i			0.149325i	0.997209	+	0.0746626i	$0.0237880\pi$
$383$			57.1916i			0.149325i	−0.997209	+	0.0746626i	$0.976212\pi$
$384$	222.812			0.580240
$385$			281.885i			0.732169i
$386$	117.735			0.305014
$387$		−	15.1399i		−	0.0391211i
$388$		−	459.871i		−	1.18524i
$389$		−	360.807i		−	0.927524i	−0.885960	−	0.463762i	$-0.846499\pi$
$389$		−	360.807i		−	0.927524i	0.885960	−	0.463762i	$-0.153501\pi$
$390$		−	298.225i		−	0.764680i
$391$	−167.868	−	249.665i	−0.429330	−	0.638530i
$392$	−44.3896			−0.113239
$393$	−49.7123			−0.126494
$394$	−163.122			−0.414016
$395$	1108.18			2.80553
$396$			121.392i			0.306545i
$397$	130.989			0.329948			0.164974	−	0.986298i	$-0.447246\pi$
$397$	130.989			0.329948			0.164974	+	0.986298i	$0.447246\pi$
$398$		−	45.2074i		−	0.113587i
$399$	−106.528			−0.266987
$400$	−348.752			−0.871880
$401$			439.104i			1.09502i	0.836799	+	0.547511i	$0.184425\pi$
$401$			439.104i			1.09502i	−0.836799	+	0.547511i	$0.815575\pi$
$402$			52.2104i			0.129877i
$403$	−545.130			−1.35268
$404$	−270.676			−0.669989
$405$			76.5634i			0.189045i
$406$			31.6466i			0.0779473i
$407$	480.120			1.17966
$408$			143.672i			0.352136i
$409$	349.213			0.853822			0.426911	−	0.904294i	$-0.359602\pi$
$409$	349.213			0.853822			0.426911	+	0.904294i	$0.359602\pi$
$410$			201.742i			0.492054i
$411$			271.645i			0.660938i
$412$		−	146.838i		−	0.356403i
$413$			134.352i			0.325308i
$414$	50.2162	−	33.7640i	0.121295	−	0.0815556i
$415$	−334.153			−0.805188
$416$	−734.417			−1.76543
$417$	277.103			0.664516
$418$	−255.322			−0.610819
$419$			286.780i			0.684438i	0.939620	+	0.342219i	$0.111178\pi$
$419$			286.780i			0.684438i	−0.939620	+	0.342219i	$0.888822\pi$
$420$	125.954			0.299891
$421$		−	242.493i		−	0.575993i	−0.957631	−	0.287997i	$-0.907011\pi$
$421$		−	242.493i		−	0.575993i	0.957631	−	0.287997i	$-0.0929892\pi$
$422$	−305.512			−0.723961
$423$	−65.4341			−0.154690
$424$			353.785i			0.834400i
$425$		−	619.624i		−	1.45794i
$426$	156.903			0.368317
$427$	181.348			0.424703
$428$		−	301.185i		−	0.703702i
$429$		−	500.632i		−	1.16697i
$430$	−37.6505			−0.0875594
$431$		−	332.399i		−	0.771227i	−0.922660	−	0.385614i	$-0.873990\pi$
$431$		−	332.399i		−	0.771227i	0.922660	−	0.385614i	$-0.126010\pi$
$432$	38.2558			0.0885550
$433$		−	478.058i		−	1.10406i	−0.833824	−	0.552030i	$-0.813854\pi$
$433$		−	478.058i		−	1.10406i	0.833824	−	0.552030i	$-0.186146\pi$
$434$			54.8058i			0.126281i
$435$		−	200.968i		−	0.461995i
$436$			393.401i			0.902297i
$437$	−298.329	−	443.696i	−0.682675	−	1.01532i
$438$	−194.783			−0.444710
$439$	−63.2723			−0.144128			−0.0720641	−	0.997400i	$-0.522959\pi$
$439$	−63.2723			−0.144128			−0.0720641	+	0.997400i	$0.522959\pi$
$440$	675.627			1.53551
$441$	−21.0000			−0.0476190
$442$		−	264.747i		−	0.598975i
$443$	228.582			0.515987			0.257993	−	0.966147i	$-0.416939\pi$
$443$	228.582			0.515987			0.257993	+	0.966147i	$0.416939\pi$
$444$		−	214.531i		−	0.483177i
$445$	−45.5471			−0.102353
$446$	209.222			0.469108
$447$		−	430.741i		−	0.963627i
$448$		−	4.07930i		−	0.00910558i
$449$	−100.730			−0.224343			−0.112171	−	0.993689i	$-0.535781\pi$
$449$	−100.730			−0.224343			−0.112171	+	0.993689i	$0.535781\pi$
$450$	124.628			0.276950
$451$			338.666i			0.750921i
$452$		−	449.419i		−	0.994291i
$453$	220.886			0.487607
$454$			105.035i			0.231354i
$455$	−519.447			−1.14164
$456$			255.327i			0.559929i
$457$			15.9353i			0.0348695i	0.999848	+	0.0174347i	$0.00554993\pi$
$457$			15.9353i			0.0348695i	−0.999848	+	0.0174347i	$0.994450\pi$
$458$			196.488i			0.429012i
$459$			67.9686i			0.148080i
$460$	352.732	+	524.607i	0.766808	+	1.14045i
$461$	166.928			0.362100			0.181050	−	0.983474i	$-0.442050\pi$
$461$	166.928			0.362100			0.181050	+	0.983474i	$0.442050\pi$
$462$	−50.3321			−0.108944
$463$	540.984			1.16843			0.584216	−	0.811598i	$-0.301402\pi$
$463$	540.984			1.16843			0.584216	+	0.811598i	$0.301402\pi$
$464$	−100.416			−0.216413
$465$		−	348.037i		−	0.748467i
$466$	−309.267			−0.663662
$467$		−	177.590i		−	0.380279i	−0.981757	−	0.190139i	$-0.939106\pi$
$467$		−	177.590i		−	0.380279i	0.981757	−	0.190139i	$-0.0608940\pi$
$468$	−223.696			−0.477983
$469$	90.9399			0.193902
$470$			162.724i			0.346222i
$471$		−	52.9694i		−	0.112462i
$472$	322.018			0.682241
$473$	−63.2042			−0.133624
$474$			197.872i			0.417452i
$475$		−	1101.17i		−	2.31826i
$476$	111.815			0.234905
$477$			167.370i			0.350881i
$478$	320.621			0.670755
$479$			67.8651i			0.141681i	0.997488	+	0.0708404i	$0.0225681\pi$
$479$			67.8651i			0.141681i	−0.997488	+	0.0708404i	$0.977432\pi$
$480$		−	468.888i		−	0.976849i
$481$			884.746i			1.83939i
$482$			80.2406i			0.166474i
$483$	−58.8100	−	87.4664i	−0.121760	−	0.181090i
$484$	115.833			0.239324
$485$	−1210.85			−2.49660
$486$	−13.6708			−0.0281292
$487$	−406.664			−0.835039			−0.417520	−	0.908668i	$-0.637100\pi$
$487$	−406.664			−0.835039			−0.417520	+	0.908668i	$0.637100\pi$
$488$		−	434.659i		−	0.890694i
$489$	472.605			0.966473
$490$			52.2237i			0.106579i
$491$	−23.5446			−0.0479524			−0.0239762	−	0.999713i	$-0.507633\pi$
$491$	−23.5446			−0.0479524			−0.0239762	+	0.999713i	$0.507633\pi$
$492$	151.325			0.307571
$493$		−	178.408i		−	0.361882i
$494$		−	470.498i		−	0.952425i
$495$	319.628			0.645713
$496$	−173.901			−0.350606
$497$		−	273.293i		−	0.549886i
$498$		−	59.6648i		−	0.119809i
$499$	485.859			0.973665			0.486832	−	0.873495i	$-0.338152\pi$
$499$	485.859			0.973665			0.486832	+	0.873495i	$0.338152\pi$
$500$			614.844i			1.22969i
$501$	−151.567			−0.302529
$502$			192.569i			0.383604i
$503$		−	19.6069i		−	0.0389799i	−0.999810	−	0.0194900i	$-0.993796\pi$
$503$		−	19.6069i		−	0.0389799i	0.999810	−	0.0194900i	$-0.00620424\pi$
$504$			50.3331i			0.0998673i
$505$			712.696i			1.41128i
$506$	−140.954	−	209.637i	−0.278565	−	0.414302i
$507$	629.829			1.24227
$508$	655.777			1.29090
$509$	−271.092			−0.532597			−0.266299	−	0.963891i	$-0.585801\pi$
$509$	−271.092			−0.532597			−0.266299	+	0.963891i	$0.585801\pi$
$510$	169.027			0.331426
$511$			339.272i			0.663938i
$512$	−421.034			−0.822332
$513$			120.791i			0.235460i
$514$	314.069			0.611029
$515$	−386.628			−0.750734
$516$			28.2414i			0.0547313i
$517$			273.166i			0.528368i
$518$	88.9499			0.171718
$519$	441.681			0.851023
$520$			1245.02i			2.39427i
$521$			262.852i			0.504514i	0.967660	+	0.252257i	$0.0811729\pi$
$521$			262.852i			0.504514i	−0.967660	+	0.252257i	$0.918827\pi$
$522$	35.8839			0.0687431
$523$			699.055i			1.33662i	0.743881	+	0.668312i	$0.232983\pi$
$523$			699.055i			1.33662i	−0.743881	+	0.668312i	$0.767017\pi$
$524$	92.7314			0.176968
$525$		−	217.076i		−	0.413478i
$526$			10.7107i			0.0203626i
$527$		−	308.968i		−	0.586276i
$528$		−	159.706i		−	0.302473i
$529$	199.608	−	489.896i	0.377330	−	0.926079i
$530$	416.223			0.785327
$531$	152.341			0.286895
$532$	198.713			0.373520
$533$	−624.080			−1.17088
$534$		−	8.13268i		−	0.0152297i
$535$	−793.027			−1.48229
$536$		−	217.966i		−	0.406653i
$537$	−590.661			−1.09993
$538$	−67.2574			−0.125014
$539$			87.6683i			0.162650i
$540$		−	142.818i		−	0.264479i
$541$	−128.516			−0.237553			−0.118777	−	0.992921i	$-0.537897\pi$
$541$	−128.516			−0.237553			−0.118777	+	0.992921i	$0.537897\pi$
$542$	−159.936			−0.295085
$543$			506.827i			0.933383i
$544$		−	416.252i		−	0.765168i
$545$	1035.84			1.90062
$546$		−	92.7501i		−	0.169872i
$547$	827.377			1.51257			0.756286	−	0.654241i	$-0.227012\pi$
$547$	827.377			1.51257			0.756286	+	0.654241i	$0.227012\pi$
$548$		−	506.717i		−	0.924666i
$549$		−	205.630i		−	0.374553i
$550$		−	520.280i		−	0.945964i
$551$		−	317.059i		−	0.575425i
$552$	−209.641	+	140.957i	−0.379784	+	0.255356i
$553$	344.653			0.623242
$554$	234.303			0.422929
$555$	−564.865			−1.01777
$556$	−516.898			−0.929672
$557$			9.93497i			0.0178366i	0.999960	+	0.00891828i	$0.00283882\pi$
$557$			9.93497i			0.0178366i	−0.999960	+	0.00891828i	$0.997161\pi$
$558$	62.1439			0.111369
$559$		−	116.470i		−	0.208355i
$560$	−165.708			−0.295907
$561$	283.747			0.505788
$562$			269.603i			0.479720i
$563$			30.4387i			0.0540651i	0.999635	+	0.0270326i	$0.00860578\pi$
$563$			30.4387i			0.0540651i	−0.999635	+	0.0270326i	$0.991394\pi$
$564$	122.058			0.216415
$565$	−1183.33			−2.09439
$566$			118.481i			0.209331i
$567$			23.8118i			0.0419961i
$568$	−655.033			−1.15323
$569$			575.238i			1.01096i	0.862837	+	0.505481i	$0.168685\pi$
$569$			575.238i			1.01096i	−0.862837	+	0.505481i	$0.831315\pi$
$570$	300.389			0.526998
$571$			501.266i			0.877875i	0.898518	+	0.438937i	$0.144645\pi$
$571$			501.266i			0.877875i	−0.898518	+	0.438937i	$0.855355\pi$
$572$			933.860i			1.63262i
$573$			200.314i			0.349588i
$574$			62.7432i			0.109309i
$575$	904.136	−	607.916i	1.57241	−	1.05725i
$576$	−4.62549			−0.00803036
$577$	152.556			0.264396			0.132198	−	0.991223i	$-0.457797\pi$
$577$	152.556			0.264396			0.132198	+	0.991223i	$0.457797\pi$
$578$	−103.395			−0.178884
$579$	−232.529			−0.401604
$580$			374.878i			0.646341i
$581$	−103.924			−0.178871
$582$		−	216.204i		−	0.371485i
$583$	698.716			1.19848
$584$	813.173			1.39242
$585$			588.998i			1.00683i
$586$		−	377.624i		−	0.644410i
$587$	−636.140			−1.08371			−0.541857	−	0.840471i	$-0.682278\pi$
$587$	−636.140			−1.08371			−0.541857	+	0.840471i	$0.682278\pi$
$588$	39.1726			0.0666201
$589$		−	549.085i		−	0.932233i
$590$		−	378.849i		−	0.642117i
$591$	322.168			0.545124
$592$			282.241i			0.476759i
$593$	396.439			0.668531			0.334266	−	0.942479i	$-0.391512\pi$
$593$	396.439			0.668531			0.334266	+	0.942479i	$0.391512\pi$
$594$			57.0713i			0.0960796i
$595$		−	294.411i		−	0.494809i
$596$			803.488i			1.34813i
$597$			89.2852i			0.149556i
$598$	386.310	−	259.745i	0.646004	−	0.434355i
$599$	654.905			1.09333			0.546665	−	0.837351i	$-0.315897\pi$
$599$	654.905			1.09333			0.546665	+	0.837351i	$0.315897\pi$
$600$	−520.291			−0.867151
$601$	232.243			0.386428			0.193214	−	0.981157i	$-0.438109\pi$
$601$	232.243			0.386428			0.193214	+	0.981157i	$0.438109\pi$
$602$	−11.7096			−0.0194511
$603$		−	103.116i		−	0.171005i
$604$	−412.032			−0.682173
$605$		−	304.991i		−	0.504117i
$606$	−127.256			−0.209993
$607$	590.271			0.972439			0.486220	−	0.873837i	$-0.338375\pi$
$607$	590.271			0.972439			0.486220	+	0.873837i	$0.338375\pi$
$608$		−	739.746i		−	1.21669i
$609$		−	62.5024i		−	0.102631i
$610$	−511.369			−0.838310
$611$	−503.380			−0.823863
$612$		−	126.786i		−	0.207167i
$613$		−	677.917i		−	1.10590i	−0.833214	−	0.552950i	$-0.813502\pi$
$613$		−	677.917i		−	1.10590i	0.833214	−	0.552950i	$-0.186498\pi$
$614$	−173.486			−0.282550
$615$		−	398.443i		−	0.647875i
$616$	210.125			0.341111
$617$			700.862i			1.13592i	0.823057	+	0.567959i	$0.192267\pi$
$617$			700.862i			1.13592i	−0.823057	+	0.567959i	$0.807733\pi$
$618$		−	69.0345i		−	0.111706i
$619$		−	821.711i		−	1.32748i	−0.747963	−	0.663741i	$-0.768968\pi$
$619$		−	821.711i		−	1.32748i	0.747963	−	0.663741i	$-0.231032\pi$
$620$			649.215i			1.04712i
$621$	−99.1776	+	66.6843i	−0.159706	+	0.107382i
$622$	−99.7435			−0.160359
$623$	−14.1655			−0.0227375
$624$	294.299			0.471633
$625$	434.655			0.695448
$626$		−	315.745i		−	0.504385i
$627$	504.264			0.804250
$628$			98.8071i			0.157336i
$629$	−501.455			−0.797225
$630$	59.2162			0.0939939
$631$			473.991i			0.751174i	0.926787	+	0.375587i	$0.122559\pi$
$631$			473.991i			0.751174i	−0.926787	+	0.375587i	$0.877441\pi$
$632$		−	826.069i		−	1.30707i
$633$	603.389			0.953221
$634$	−332.992			−0.525224
$635$		−	1726.68i		−	2.71918i
$636$		−	312.206i		−	0.490889i
$637$	−161.552			−0.253613
$638$		−	149.804i		−	0.234802i
$639$	−309.885			−0.484954
$640$			1094.35i			1.70993i
$641$		−	865.776i		−	1.35066i	−0.737514	−	0.675332i	$-0.764000\pi$
$641$		−	865.776i		−	1.35066i	0.737514	−	0.675332i	$-0.236000\pi$
$642$		−	141.599i		−	0.220559i
$643$		−	875.488i		−	1.36157i	−0.732484	−	0.680784i	$-0.761639\pi$
$643$		−	875.488i		−	1.36157i	0.732484	−	0.680784i	$-0.238361\pi$
$644$	109.702	+	163.157i	0.170345	+	0.253349i
$645$	74.3602			0.115287
$646$	266.668			0.412799
$647$	421.449			0.651389			0.325694	−	0.945475i	$-0.394402\pi$
$647$	421.449			0.651389			0.325694	+	0.945475i	$0.394402\pi$
$648$	57.0724			0.0880747
$649$		−	635.976i		−	0.979932i
$650$	958.752			1.47500
$651$		−	108.242i		−	0.166270i
$652$	−881.580			−1.35212
$653$	292.745			0.448307			0.224154	−	0.974554i	$-0.428038\pi$
$653$	292.745			0.448307			0.224154	+	0.974554i	$0.428038\pi$
$654$			184.954i			0.282805i
$655$		−	244.164i		−	0.372770i
$656$	−199.086			−0.303485
$657$	384.699			0.585538
$658$			50.6084i			0.0769125i
$659$			148.383i			0.225164i	0.993642	+	0.112582i	$0.0359121\pi$
$659$			148.383i			0.225164i	−0.993642	+	0.112582i	$0.964088\pi$
$660$	−596.221			−0.903366
$661$			929.771i			1.40661i	0.710887	+	0.703306i	$0.248294\pi$
$661$			929.771i			1.40661i	−0.710887	+	0.703306i	$0.751706\pi$
$662$	−356.064			−0.537861
$663$			522.878i			0.788655i
$664$			249.086i			0.375130i
$665$		−	523.216i		−	0.786791i
$666$		−	100.860i		−	0.151441i
$667$	260.327	−	175.037i	0.390295	−	0.262424i
$668$	282.728			0.423245
$669$	−413.216			−0.617662
$670$	−256.434			−0.382737
$671$	−858.438			−1.27934
$672$		−	145.827i		−	0.217005i
$673$	38.3818			0.0570308			0.0285154	−	0.999593i	$-0.490922\pi$
$673$	38.3818			0.0570308			0.0285154	+	0.999593i	$0.490922\pi$
$674$		−	413.860i		−	0.614036i
$675$	−246.141			−0.364653
$676$	−1174.86			−1.73796
$677$		−	849.717i		−	1.25512i	−0.778568	−	0.627561i	$-0.784053\pi$
$677$		−	849.717i		−	1.25512i	0.778568	−	0.627561i	$-0.215947\pi$
$678$		−	211.291i		−	0.311638i
$679$	−376.584			−0.554615
$680$	−705.649			−1.03772
$681$		−	207.445i		−	0.304618i
$682$		−	259.431i		−	0.380397i
$683$	626.374			0.917092			0.458546	−	0.888671i	$-0.348370\pi$
$683$	626.374			0.917092			0.458546	+	0.888671i	$0.348370\pi$
$684$		−	225.319i		−	0.329414i
$685$	−1334.20			−1.94774
$686$			16.2420i			0.0236763i
$687$		−	388.065i		−	0.564869i
$688$		−	37.1549i		−	0.0540042i
$689$			1287.57i			1.86875i
$690$	165.834	+	246.639i	0.240338	+	0.357448i
$691$	−839.803			−1.21535			−0.607673	−	0.794188i	$-0.707897\pi$
$691$	−839.803			−1.21535			−0.607673	+	0.794188i	$0.707897\pi$
$692$	−823.895			−1.19060
$693$	99.4065			0.143444
$694$	−326.613			−0.470624
$695$			1361.01i			1.95828i
$696$	−149.807			−0.215240
$697$		−	353.715i		−	0.507482i
$698$	−29.6953			−0.0425434
$699$	610.805			0.873827
$700$			404.925i			0.578464i
$701$			60.0039i			0.0855976i	0.999084	+	0.0427988i	$0.0136274\pi$
$701$			60.0039i			0.0855976i	−0.999084	+	0.0427988i	$0.986373\pi$
$702$	−105.169			−0.149813
$703$	−891.166			−1.26766
$704$			19.3099i			0.0274289i
$705$		−	321.382i		−	0.455861i
$706$	−112.383			−0.159183
$707$			221.654i			0.313513i
$708$	−284.171			−0.401372
$709$		−	513.355i		−	0.724056i	−0.932167	−	0.362028i	$-0.882085\pi$
$709$		−	513.355i		−	0.724056i	0.932167	−	0.362028i	$-0.117915\pi$
$710$			770.637i			1.08540i
$711$		−	390.800i		−	0.549648i
$712$			33.9520i			0.0476854i
$713$	450.836	−	303.130i	0.632308	−	0.425147i
$714$	52.5687			0.0736256
$715$	2458.88			3.43899
$716$	1101.80			1.53882
$717$	−633.230			−0.883166
$718$			434.552i			0.605226i
$719$	715.154			0.994651			0.497326	−	0.867564i	$-0.334315\pi$
$719$	715.154			0.994651			0.497326	+	0.867564i	$0.334315\pi$
$720$			187.895i			0.260965i
$721$	−120.244			−0.166774
$722$	157.321			0.217896
$723$		−	158.476i		−	0.219192i
$724$		−	945.416i		−	1.30582i
$725$	646.084			0.891150
$726$	54.4578			0.0750107
$727$			740.130i			1.01806i	0.860749	+	0.509030i	$0.169996\pi$
$727$			740.130i			1.01806i	−0.860749	+	0.509030i	$0.830004\pi$
$728$			387.210i			0.531881i
$729$	27.0000			0.0370370
$730$		−	956.686i		−	1.31053i
$731$	66.0128			0.0903047
$732$			383.574i			0.524008i
$733$			762.622i			1.04041i	0.854041	+	0.520206i	$0.174145\pi$
$733$			762.622i			1.04041i	−0.854041	+	0.520206i	$0.825855\pi$
$734$			483.879i			0.659236i
$735$		−	103.142i		−	0.140330i
$736$	607.381	−	408.386i	0.825246	−	0.554873i
$737$	−430.477			−0.584093
$738$	71.1441			0.0964012
$739$	389.726			0.527369			0.263685	−	0.964609i	$-0.415062\pi$
$739$	389.726			0.527369			0.263685	+	0.964609i	$0.415062\pi$
$740$	1053.68			1.42389
$741$			929.239i			1.25403i
$742$	129.448			0.174459
$743$		−	1256.31i		−	1.69086i	−0.534084	−	0.845432i	$-0.679343\pi$
$743$		−	1256.31i		−	1.69086i	0.534084	−	0.845432i	$-0.320657\pi$
$744$	−259.436			−0.348705
$745$	2115.60			2.83974
$746$			308.679i			0.413779i
$747$			117.839i			0.157749i
$748$	−529.291			−0.707608
$749$	−246.637			−0.329288
$750$			289.063i			0.385418i
$751$			1129.63i			1.50417i	0.659066	+	0.752085i	$0.270952\pi$
$751$			1129.63i			1.50417i	−0.659066	+	0.752085i	$0.729048\pi$
$752$	−160.582			−0.213540
$753$		−	380.326i		−	0.505081i
$754$	276.053			0.366118
$755$			1084.89i			1.43694i
$756$		−	44.4175i		−	0.0587534i
$757$		−	288.263i		−	0.380796i	−0.981707	−	0.190398i	$-0.939022\pi$
$757$		−	288.263i		−	0.380796i	0.981707	−	0.190398i	$-0.0609779\pi$
$758$			37.6341i			0.0496492i
$759$	278.386	+	414.035i	0.366780	+	0.545500i
$760$	−1254.05			−1.65007
$761$	−550.487			−0.723374			−0.361687	−	0.932300i	$-0.617799\pi$
$761$	−550.487			−0.723374			−0.361687	+	0.932300i	$0.617799\pi$
$762$	308.308			0.404603
$763$	322.152			0.422218
$764$		−	373.658i		−	0.489081i
$765$	−333.831			−0.436380
$766$		−	50.1560i		−	0.0654778i
$767$	1171.95			1.52797
$768$	−184.720			−0.240521
$769$		−	544.260i		−	0.707750i	−0.935293	−	0.353875i	$-0.884864\pi$
$769$		−	544.260i		−	0.707750i	0.935293	−	0.353875i	$-0.115136\pi$
$770$		−	247.208i		−	0.321050i
$771$	−620.289			−0.804526
$772$	433.750			0.561852
$773$			291.565i			0.377187i	0.982055	+	0.188593i	$0.0603928\pi$
$773$			291.565i			0.377187i	−0.982055	+	0.188593i	$0.939607\pi$
$774$			13.2774i			0.0171543i
$775$	1118.89			1.44373
$776$			902.602i			1.16315i
$777$	−175.677			−0.226096
$778$			316.421i			0.406711i
$779$		−	628.608i		−	0.806942i
$780$		−	1098.69i		−	1.40858i
$781$			1293.67i			1.65643i
$782$	147.218	+	218.952i	0.188258	+	0.279990i
$783$	−70.8711			−0.0905122
$784$	−51.5363			−0.0657350
$785$	260.162			0.331416
$786$	43.5968			0.0554667
$787$			1263.89i			1.60595i	0.596009	+	0.802977i	$0.296752\pi$
$787$			1263.89i			1.60595i	−0.596009	+	0.802977i	$0.703248\pi$
$788$	−600.960			−0.762640
$789$		−	21.1538i		−	0.0268109i
$790$	−971.858			−1.23020
$791$	−368.025			−0.465265
$792$		−	238.259i		−	0.300832i
$793$		−	1581.90i		−	1.99483i
$794$	−114.876			−0.144679
$795$	−822.045			−1.03402
$796$		−	166.549i		−	0.209233i
$797$			1323.97i			1.66120i	0.556872	+	0.830598i	$0.312001\pi$
$797$			1323.97i			1.66120i	−0.556872	+	0.830598i	$0.687999\pi$
$798$	93.4231			0.117071
$799$		−	285.305i		−	0.357077i
$800$	1507.41			1.88426
$801$			16.0621i			0.0200526i
$802$		−	385.086i		−	0.480158i
$803$		−	1605.99i		−	1.99999i
$804$			192.349i			0.239240i
$805$	429.595	−	288.848i	0.533659	−	0.358818i
$806$	478.070			0.593138
$807$	132.834			0.164602
$808$	531.263			0.657503
$809$	−1225.98			−1.51543			−0.757713	−	0.652588i	$-0.773683\pi$
$809$	−1225.98			−1.51543			−0.757713	+	0.652588i	$0.773683\pi$
$810$		−	67.1448i		−	0.0828948i
$811$	−496.612			−0.612345			−0.306172	−	0.951976i	$-0.599048\pi$
$811$	−496.612			−0.612345			−0.306172	+	0.951976i	$0.599048\pi$
$812$			116.590i			0.143583i
$813$	315.875			0.388531
$814$	−421.057			−0.517269
$815$			2321.22i			2.84813i
$816$			166.802i			0.204415i
$817$	117.315			0.143593
$818$	−306.254			−0.374394
$819$			183.182i			0.223666i
$820$			743.240i			0.906390i
$821$	987.326			1.20259			0.601295	−	0.799027i	$-0.294652\pi$
$821$	987.326			1.20259			0.601295	+	0.799027i	$0.294652\pi$
$822$		−	238.228i		−	0.289816i
$823$	710.196			0.862936			0.431468	−	0.902128i	$-0.357996\pi$
$823$	710.196			0.862936			0.431468	+	0.902128i	$0.357996\pi$
$824$			288.203i			0.349761i
$825$			1027.56i			1.24553i
$826$		−	117.825i		−	0.142645i
$827$		−	1078.33i		−	1.30391i	−0.758258	−	0.651954i	$-0.773949\pi$
$827$		−	1078.33i		−	1.30391i	0.758258	−	0.651954i	$-0.226051\pi$
$828$	185.002	−	124.390i	0.223433	−	0.150230i
$829$	−946.344			−1.14155			−0.570774	−	0.821107i	$-0.693357\pi$
$829$	−946.344			−1.14155			−0.570774	+	0.821107i	$0.693357\pi$
$830$	293.046			0.353068
$831$	−462.751			−0.556860
$832$	−35.5836			−0.0427688
$833$		−	91.5640i		−	0.109921i
$834$	−243.015			−0.291385
$835$		−	744.429i		−	0.891532i
$836$	−940.636			−1.12516
$837$	−122.735			−0.146637
$838$		−	251.501i		−	0.300120i
$839$			274.185i			0.326800i	0.986560	+	0.163400i	$0.0522461\pi$
$839$			274.185i			0.326800i	−0.986560	+	0.163400i	$0.947754\pi$
$840$	−247.213			−0.294302
$841$	−654.974			−0.778803
$842$			212.662i			0.252568i
$843$		−	532.469i		−	0.631635i
$844$	−1125.54			−1.33358
$845$			3093.43i			3.66087i
$846$	57.3846			0.0678304
$847$		−	94.8543i		−	0.111989i
$848$			410.744i			0.484368i
$849$		−	234.002i		−	0.275621i
$850$			543.400i			0.639294i
$851$	−491.980	−	731.707i	−0.578119	−	0.859820i
$852$	578.048			0.678460
$853$	−1427.43			−1.67343			−0.836713	−	0.547642i	$-0.815525\pi$
$853$	−1427.43			−1.67343			−0.836713	+	0.547642i	$0.815525\pi$
$854$	−159.039			−0.186229
$855$	−593.271			−0.693885
$856$			591.143i			0.690588i
$857$	−220.849			−0.257700			−0.128850	−	0.991664i	$-0.541129\pi$
$857$	−220.849			−0.257700			−0.128850	+	0.991664i	$0.541129\pi$
$858$			439.046i			0.511708i
$859$	369.199			0.429800			0.214900	−	0.976636i	$-0.431057\pi$
$859$	369.199			0.429800			0.214900	+	0.976636i	$0.431057\pi$
$860$	−138.709			−0.161289
$861$		−	123.919i		−	0.143924i
$862$			291.508i			0.338177i
$863$	−1632.21			−1.89132			−0.945661	−	0.325155i	$-0.894583\pi$
$863$	−1632.21			−1.89132			−0.945661	+	0.325155i	$0.894583\pi$
$864$	−165.353			−0.191380
$865$			2169.34i			2.50790i
$866$			419.248i			0.484121i
$867$	204.207			0.235533
$868$			201.911i			0.232616i
$869$	−1631.46			−1.87740
$870$			176.245i			0.202581i
$871$		−	793.266i		−	0.910753i
$872$		−	772.140i		−	0.885481i
$873$			427.006i			0.489125i
$874$	261.629	+	389.113i	0.299347	+	0.445210i
$875$	503.490			0.575417
$876$	−717.602			−0.819181
$877$	206.417			0.235367			0.117683	−	0.993051i	$-0.462453\pi$
$877$	206.417			0.235367			0.117683	+	0.993051i	$0.462453\pi$
$878$	55.4887			0.0631990
$879$			745.812i			0.848478i
$880$	784.401			0.891365
$881$			55.8054i			0.0633432i	0.999498	+	0.0316716i	$0.0100831\pi$
$881$			55.8054i			0.0633432i	−0.999498	+	0.0316716i	$0.989917\pi$
$882$	18.4166			0.0208805
$883$	630.662			0.714226			0.357113	−	0.934061i	$-0.383761\pi$
$883$	630.662			0.714226			0.357113	+	0.934061i	$0.383761\pi$
$884$		−	975.357i		−	1.10335i
$885$			748.231i			0.845459i
$886$	−200.463			−0.226256
$887$	1456.52			1.64207			0.821035	−	0.570877i	$-0.193397\pi$
$887$	1456.52			1.64207			0.821035	+	0.570877i	$0.193397\pi$
$888$			421.065i			0.474173i
$889$		−	537.009i		−	0.604059i
$890$	39.9440			0.0448809
$891$		−	112.716i		−	0.126505i
$892$	770.797			0.864122
$893$		−	507.033i		−	0.567786i
$894$			377.753i			0.422542i
$895$		−	2901.06i		−	3.24140i
$896$			340.351i			0.379856i
$897$	−762.967	+	512.998i	−0.850577	+	0.571905i
$898$	88.3384			0.0983724
$899$	322.161			0.358355
$900$	459.142			0.510157
$901$	−729.765			−0.809950
$902$		−	297.004i		−	0.329273i
$903$	23.1266			0.0256108
$904$			882.088i			0.975761i
$905$	−2489.30			−2.75061
$906$	−193.713			−0.213812
$907$		−	457.001i		−	0.503860i	−0.967746	−	0.251930i	$-0.918935\pi$
$907$		−	457.001i		−	0.503860i	0.967746	−	0.251930i	$-0.0810652\pi$
$908$			386.960i			0.426168i
$909$	251.331			0.276492
$910$	455.546			0.500600
$911$		−	262.220i		−	0.287837i	−0.989590	−	0.143919i	$-0.954030\pi$
$911$		−	262.220i		−	0.287837i	0.989590	−	0.143919i	$-0.0459703\pi$
$912$			296.435i			0.325038i
$913$	491.938			0.538815
$914$		−	13.9750i		−	0.0152900i
$915$	1009.96			1.10378
$916$			723.882i			0.790264i
$917$		−	75.9368i		−	0.0828100i
$918$		−	59.6073i		−	0.0649317i
$919$		−	847.074i		−	0.921735i	−0.887469	−	0.460867i	$-0.847538\pi$
$919$		−	847.074i		−	0.921735i	0.887469	−	0.460867i	$-0.152462\pi$
$920$	−692.316	−	1029.66i	−0.752517	−	1.11920i
$921$	342.636			0.372026
$922$	−146.393			−0.158778
$923$	−2383.93			−2.58281
$924$	−185.429			−0.200681
$925$		−	1815.96i		−	1.96320i
$926$	−474.433			−0.512347
$927$			136.344i			0.147081i
$928$	434.027			0.467701
$929$	−909.557			−0.979071			−0.489535	−	0.871983i	$-0.662834\pi$
$929$	−909.557			−0.979071			−0.489535	+	0.871983i	$0.662834\pi$
$930$			305.223i			0.328197i
$931$		−	162.724i		−	0.174784i
$932$	−1139.37			−1.22250
$933$	196.994			0.211141
$934$			155.744i			0.166749i
$935$			1393.64i			1.49052i
$936$	439.054			0.469075
$937$		−	646.176i		−	0.689622i	−0.938672	−	0.344811i	$-0.887943\pi$
$937$		−	646.176i		−	0.689622i	0.938672	−	0.344811i	$-0.112057\pi$
$938$	−79.7527			−0.0850242
$939$			623.600i			0.664111i
$940$			599.494i			0.637760i
$941$		−	891.060i		−	0.946929i	−0.880813	−	0.473464i	$-0.843003\pi$
$941$		−	891.060i		−	0.946929i	0.880813	−	0.473464i	$-0.156997\pi$
$942$			46.4533i			0.0493135i
$943$	516.129	−	347.031i	0.547327	−	0.368008i
$944$	373.862			0.396040
$945$	−116.953			−0.123759
$946$	55.4290			0.0585930
$947$	−210.772			−0.222568			−0.111284	−	0.993789i	$-0.535496\pi$
$947$	−210.772			−0.222568			−0.111284	+	0.993789i	$0.535496\pi$
$948$			728.983i			0.768969i
$949$	2959.46			3.11851
$950$			965.709i			1.01654i
$951$	657.663			0.691549
$952$	−219.462			−0.230527
$953$			922.418i			0.967910i	0.875093	+	0.483955i	$0.160800\pi$
$953$			922.418i			0.967910i	−0.875093	+	0.483955i	$0.839200\pi$
$954$		−	146.781i		−	0.153858i
$955$	−983.851			−1.03021
$956$	1181.20			1.23557
$957$			295.864i			0.309158i
$958$		−	59.5166i		−	0.0621259i
$959$	−414.945			−0.432685
$960$		−	22.7183i		−	0.0236649i
$961$	−403.079			−0.419437
$962$		−	775.907i		−	0.806556i
$963$			279.660i			0.290405i
$964$			295.615i			0.306655i
$965$		−	1142.07i		−	1.18350i
$966$	51.5754	+	76.7066i	0.0533907	+	0.0794064i
$967$	170.846			0.176676			0.0883381	−	0.996091i	$-0.471844\pi$
$967$	170.846			0.176676			0.0883381	+	0.996091i	$0.471844\pi$
$968$	−227.348			−0.234864
$969$	−526.672			−0.543521
$970$	1061.90			1.09474
$971$		−	1022.83i		−	1.05338i	−0.850059	−	0.526688i	$-0.823434\pi$
$971$		−	1022.83i		−	1.05338i	0.850059	−	0.526688i	$-0.176566\pi$
$972$	−50.3648			−0.0518156
$973$			423.282i			0.435028i
$974$	356.637			0.366157
$975$	−1893.55			−1.94210
$976$		−	504.638i		−	0.517047i
$977$		−	1778.11i		−	1.81997i	−0.414645	−	0.909983i	$-0.636094\pi$
$977$		−	1778.11i		−	1.81997i	0.414645	−	0.909983i	$-0.363906\pi$
$978$	−414.467			−0.423790
$979$	67.0543			0.0684926
$980$			192.398i			0.196324i
$981$		−	365.286i		−	0.372361i
$982$	20.6482			0.0210267
$983$		−	1436.39i		−	1.46123i	−0.682787	−	0.730617i	$-0.739232\pi$
$983$		−	1436.39i		−	1.46123i	0.682787	−	0.730617i	$-0.260768\pi$
$984$	−297.010			−0.301839
$985$			1582.34i			1.60644i
$986$			156.461i			0.158682i
$987$		−	99.9522i		−	0.101269i
$988$		−	1733.37i		−	1.75442i
$989$	64.7654	+	96.3237i	0.0654858	+	0.0973950i
$990$	−280.308			−0.283139
$991$	−576.904			−0.582143			−0.291072	−	0.956701i	$-0.594012\pi$
$991$	−576.904			−0.582143			−0.291072	+	0.956701i	$0.594012\pi$
$992$	751.650			0.757712
$993$	703.231			0.708188
$994$			239.673i			0.241120i
$995$	−438.528			−0.440732
$996$		−	219.812i		−	0.220694i
$997$	590.258			0.592035			0.296017	−	0.955183i	$-0.404341\pi$
$997$	590.258			0.592035			0.296017	+	0.955183i	$0.404341\pi$
$998$	−426.090			−0.426944
$999$			199.199i			0.199398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.19	✓	48
23.22	odd	2	inner	483.3.f.a.22.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.19	✓	48	1.1	even	1	trivial
483.3.f.a.22.20	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)

\(f(q)\)	\(=\)	\(q-0.876983 q^{2} +1.73205 q^{3} -3.23090 q^{4} +8.50705i q^{5} -1.51898 q^{6} +2.64575i q^{7} +6.34138 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-0.876983 q^{2} +1.73205 q^{3} -3.23090 q^{4} +8.50705i q^{5} -1.51898 q^{6} +2.64575i q^{7} +6.34138 q^{8} +3.00000 q^{9} -7.46053i q^{10} -12.5240i q^{11} -5.59608 q^{12} +23.0788 q^{13} -2.32028i q^{14} +14.7346i q^{15} +7.36233 q^{16} +13.0806i q^{17} -2.63095 q^{18} +23.2463i q^{19} -27.4854i q^{20} +4.58258i q^{21} +10.9834i q^{22} +(-19.0867 + 12.8334i) q^{23} +10.9836 q^{24} -47.3698 q^{25} -20.2397 q^{26} +5.19615 q^{27} -8.54816i q^{28} -13.6391 q^{29} -12.9220i q^{30} -23.6204 q^{31} -31.8221 q^{32} -21.6923i q^{33} -11.4714i q^{34} -22.5075 q^{35} -9.69270 q^{36} +38.3359i q^{37} -20.3866i q^{38} +39.9737 q^{39} +53.9464i q^{40} -27.0412 q^{41} -4.01884i q^{42} -5.04663i q^{43} +40.4639i q^{44} +25.5211i q^{45} +(16.7387 - 11.2547i) q^{46} -21.8114 q^{47} +12.7519 q^{48} -7.00000 q^{49} +41.5425 q^{50} +22.6562i q^{51} -74.5654 q^{52} +55.7900i q^{53} -4.55694 q^{54} +106.543 q^{55} +16.7777i q^{56} +40.2637i q^{57} +11.9613 q^{58} +50.7804 q^{59} -47.6061i q^{60} -68.5432i q^{61} +20.7146 q^{62} +7.93725i q^{63} -1.54183 q^{64} +196.333i q^{65} +19.0238i q^{66} -34.3720i q^{67} -42.2620i q^{68} +(-33.0592 + 22.2281i) q^{69} +19.7387 q^{70} -103.295 q^{71} +19.0241 q^{72} +128.233 q^{73} -33.6199i q^{74} -82.0470 q^{75} -75.1064i q^{76} +33.1355 q^{77} -35.0562 q^{78} -130.267i q^{79} +62.6316i q^{80} +9.00000 q^{81} +23.7147 q^{82} +39.2795i q^{83} -14.8058i q^{84} -111.277 q^{85} +4.42581i q^{86} -23.6237 q^{87} -79.4196i q^{88} +5.35404i q^{89} -22.3816i q^{90} +61.0608i q^{91} +(61.6674 - 41.4635i) q^{92} -40.9117 q^{93} +19.1282 q^{94} -197.757 q^{95} -55.1176 q^{96} +142.335i q^{97} +6.13888 q^{98} -37.5721i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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