LMFDB - Embedded newform 483.3.f.a.22.11

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			22.11
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.49369 q^{2} +1.73205 q^{3} +2.21850 q^{4} +2.66866i q^{5} -4.31920 q^{6} -2.64575i q^{7} +4.44250 q^{8} +3.00000 q^{9} -6.65481i q^{10} +5.14993i q^{11} +3.84256 q^{12} +6.24116 q^{13} +6.59769i q^{14} +4.62225i q^{15} -19.9523 q^{16} -11.3967i q^{17} -7.48108 q^{18} -9.41543i q^{19} +5.92043i q^{20} -4.58258i q^{21} -12.8423i q^{22} +(10.8890 + 20.2590i) q^{23} +7.69464 q^{24} +17.8783 q^{25} -15.5635 q^{26} +5.19615 q^{27} -5.86961i q^{28} +27.6168 q^{29} -11.5265i q^{30} -52.6391 q^{31} +31.9848 q^{32} +8.91994i q^{33} +28.4198i q^{34} +7.06060 q^{35} +6.65551 q^{36} +49.4855i q^{37} +23.4792i q^{38} +10.8100 q^{39} +11.8555i q^{40} +15.3168 q^{41} +11.4275i q^{42} -68.2674i q^{43} +11.4251i q^{44} +8.00597i q^{45} +(-27.1539 - 50.5198i) q^{46} +46.0234 q^{47} -34.5583 q^{48} -7.00000 q^{49} -44.5829 q^{50} -19.7396i q^{51} +13.8461 q^{52} +95.2919i q^{53} -12.9576 q^{54} -13.7434 q^{55} -11.7538i q^{56} -16.3080i q^{57} -68.8679 q^{58} +78.9912 q^{59} +10.2545i q^{60} -57.0256i q^{61} +131.266 q^{62} -7.93725i q^{63} +0.0487738 q^{64} +16.6555i q^{65} -22.2436i q^{66} +93.3931i q^{67} -25.2836i q^{68} +(18.8604 + 35.0897i) q^{69} -17.6070 q^{70} +117.690 q^{71} +13.3275 q^{72} +120.277 q^{73} -123.402i q^{74} +30.9661 q^{75} -20.8882i q^{76} +13.6254 q^{77} -26.9569 q^{78} +97.4970i q^{79} -53.2457i q^{80} +9.00000 q^{81} -38.1955 q^{82} +32.6207i q^{83} -10.1665i q^{84} +30.4138 q^{85} +170.238i q^{86} +47.8338 q^{87} +22.8786i q^{88} +140.985i q^{89} -19.9644i q^{90} -16.5126i q^{91} +(24.1574 + 44.9448i) q^{92} -91.1736 q^{93} -114.768 q^{94} +25.1265 q^{95} +55.3993 q^{96} -74.2797i q^{97} +17.4559 q^{98} +15.4498i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 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}+ \cdots - 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

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 $

$2$	−2.49369			−1.24685			−0.623423	−	0.781885i	$-0.714259\pi$
$2$	−2.49369			−1.24685			−0.623423	+	0.781885i	$0.714259\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	2.21850			0.554626
$5$			2.66866i			0.533731i	0.963734	+	0.266866i	$0.0859880\pi$
$5$			2.66866i			0.533731i	−0.963734	+	0.266866i	$0.914012\pi$
$6$	−4.31920			−0.719867
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	4.44250			0.555313
$9$	3.00000			0.333333
$10$		−	6.65481i		−	0.665481i
$11$			5.14993i			0.468175i	0.972215	+	0.234088i	$0.0752103\pi$
$11$			5.14993i			0.468175i	−0.972215	+	0.234088i	$0.924790\pi$
$12$	3.84256			0.320214
$13$	6.24116			0.480090			0.240045	−	0.970762i	$-0.422838\pi$
$13$	6.24116			0.480090			0.240045	+	0.970762i	$0.422838\pi$
$14$			6.59769i			0.471264i
$15$			4.62225i			0.308150i
$16$	−19.9523			−1.24702
$17$		−	11.3967i		−	0.670393i	−0.942148	−	0.335197i	$-0.891197\pi$
$17$		−	11.3967i		−	0.670393i	0.942148	−	0.335197i	$-0.108803\pi$
$18$	−7.48108			−0.415615
$19$		−	9.41543i		−	0.495549i	−0.968818	−	0.247774i	$-0.920301\pi$
$19$		−	9.41543i		−	0.495549i	0.968818	−	0.247774i	$-0.0796992\pi$
$20$			5.92043i			0.296021i
$21$		−	4.58258i		−	0.218218i
$22$		−	12.8423i		−	0.583743i
$23$	10.8890	+	20.2590i	0.473437	+	0.880828i
$23$	10.8890	+	20.2590i	0.473437	+	0.880828i
$24$	7.69464			0.320610
$25$	17.8783			0.715131
$26$	−15.5635			−0.598598
$27$	5.19615			0.192450
$28$		−	5.86961i		−	0.209629i
$29$	27.6168			0.952305			0.476152	−	0.879363i	$-0.342031\pi$
$29$	27.6168			0.952305			0.476152	+	0.879363i	$0.342031\pi$
$30$		−	11.5265i		−	0.384216i
$31$	−52.6391			−1.69804			−0.849018	−	0.528364i	$-0.822806\pi$
$31$	−52.6391			−1.69804			−0.849018	+	0.528364i	$0.822806\pi$
$32$	31.9848			0.999525
$33$			8.91994i			0.270301i
$34$			28.4198i			0.835878i
$35$	7.06060			0.201731
$36$	6.65551			0.184875
$37$			49.4855i			1.33745i	0.743511	+	0.668723i	$0.233159\pi$
$37$			49.4855i			1.33745i	−0.743511	+	0.668723i	$0.766841\pi$
$38$			23.4792i			0.617873i
$39$	10.8100			0.277180
$40$			11.8555i			0.296388i
$41$	15.3168			0.373581			0.186791	−	0.982400i	$-0.440191\pi$
$41$	15.3168			0.373581			0.186791	+	0.982400i	$0.440191\pi$
$42$			11.4275i			0.272084i
$43$		−	68.2674i		−	1.58761i	−0.608171	−	0.793806i	$-0.708096\pi$
$43$		−	68.2674i		−	1.58761i	0.608171	−	0.793806i	$-0.291904\pi$
$44$			11.4251i			0.259662i
$45$			8.00597i			0.177910i
$46$	−27.1539	−	50.5198i	−0.590303	−	1.09826i
$47$	46.0234			0.979221			0.489610	−	0.871941i	$-0.337139\pi$
$47$	46.0234			0.979221			0.489610	+	0.871941i	$0.337139\pi$
$48$	−34.5583			−0.719965
$49$	−7.00000			−0.142857
$50$	−44.5829			−0.891659
$51$		−	19.7396i		−	0.387052i
$52$	13.8461			0.266270
$53$			95.2919i			1.79796i	0.437989	+	0.898980i	$0.355691\pi$
$53$			95.2919i			1.79796i	−0.437989	+	0.898980i	$0.644309\pi$
$54$	−12.9576			−0.239956
$55$	−13.7434			−0.249880
$56$		−	11.7538i		−	0.209889i
$57$		−	16.3080i		−	0.286105i
$58$	−68.8679			−1.18738
$59$	78.9912			1.33883			0.669417	−	0.742887i	$-0.266544\pi$
$59$	78.9912			1.33883			0.669417	+	0.742887i	$0.266544\pi$
$60$			10.2545i			0.170908i
$61$		−	57.0256i		−	0.934846i	−0.884034	−	0.467423i	$-0.845183\pi$
$61$		−	57.0256i		−	0.934846i	0.884034	−	0.467423i	$-0.154817\pi$
$62$	131.266			2.11719
$63$		−	7.93725i		−	0.125988i
$64$	0.0487738			0.000762091
$65$			16.6555i			0.256239i
$66$		−	22.2436i		−	0.337024i
$67$			93.3931i			1.39393i	0.717107	+	0.696963i	$0.245466\pi$
$67$			93.3931i			1.39393i	−0.717107	+	0.696963i	$0.754534\pi$
$68$		−	25.2836i		−	0.371818i
$69$	18.8604	+	35.0897i	0.273339	+	0.508546i
$70$	−17.6070			−0.251528
$71$	117.690			1.65761			0.828803	−	0.559541i	$-0.189022\pi$
$71$	117.690			1.65761			0.828803	+	0.559541i	$0.189022\pi$
$72$	13.3275			0.185104
$73$	120.277			1.64763			0.823814	−	0.566860i	$-0.191842\pi$
$73$	120.277			1.64763			0.823814	+	0.566860i	$0.191842\pi$
$74$		−	123.402i		−	1.66759i
$75$	30.9661			0.412881
$76$		−	20.8882i		−	0.274844i
$77$	13.6254			0.176954
$78$	−26.9569			−0.345601
$79$			97.4970i			1.23414i	0.786909	+	0.617069i	$0.211680\pi$
$79$			97.4970i			1.23414i	−0.786909	+	0.617069i	$0.788320\pi$
$80$		−	53.2457i		−	0.665571i
$81$	9.00000			0.111111
$82$	−38.1955			−0.465799
$83$			32.6207i			0.393020i	0.980502	+	0.196510i	$0.0629608\pi$
$83$			32.6207i			0.393020i	−0.980502	+	0.196510i	$0.937039\pi$
$84$		−	10.1665i		−	0.121029i
$85$	30.4138			0.357810
$86$			170.238i			1.97951i
$87$	47.8338			0.549813
$88$			22.8786i			0.259984i
$89$			140.985i			1.58410i	0.610455	+	0.792051i	$0.290987\pi$
$89$			140.985i			1.58410i	−0.610455	+	0.792051i	$0.709013\pi$
$90$		−	19.9644i		−	0.221827i
$91$		−	16.5126i		−	0.181457i
$92$	24.1574	+	44.9448i	0.262580	+	0.488530i
$93$	−91.1736			−0.980362
$94$	−114.768			−1.22094
$95$	25.1265			0.264490
$96$	55.3993			0.577076
$97$		−	74.2797i		−	0.765770i	−0.923796	−	0.382885i	$-0.874931\pi$
$97$		−	74.2797i		−	0.765770i	0.923796	−	0.382885i	$-0.125069\pi$
$98$	17.4559			0.178121
$99$			15.4498i			0.156058i
$100$	39.6630			0.396630
$101$	69.5857			0.688967			0.344484	−	0.938792i	$-0.388054\pi$
$101$	69.5857			0.688967			0.344484	+	0.938792i	$0.388054\pi$
$102$			49.2246i			0.482594i
$103$			90.5965i			0.879577i	0.898101	+	0.439789i	$0.144947\pi$
$103$			90.5965i			0.879577i	−0.898101	+	0.439789i	$0.855053\pi$
$104$	27.7264			0.266600
$105$	12.2293			0.116470
$106$		−	237.629i		−	2.24178i
$107$		−	14.2065i		−	0.132771i	−0.997794	−	0.0663855i	$-0.978853\pi$
$107$		−	14.2065i		−	0.132771i	0.997794	−	0.0663855i	$-0.0211467\pi$
$108$	11.5277			0.106738
$109$		−	126.930i		−	1.16450i	−0.813010	−	0.582250i	$-0.802173\pi$
$109$		−	126.930i		−	1.16450i	0.813010	−	0.582250i	$-0.197827\pi$
$110$	34.2718			0.311562
$111$			85.7115i			0.772175i
$112$			52.7887i			0.471328i
$113$		−	103.390i		−	0.914958i	−0.889220	−	0.457479i	$-0.848752\pi$
$113$		−	103.390i		−	0.914958i	0.889220	−	0.457479i	$-0.151248\pi$
$114$			40.6671i			0.356729i
$115$	−54.0644	+	29.0591i	−0.470125	+	0.252688i
$116$	61.2681			0.528173
$117$	18.7235			0.160030
$118$	−196.980			−1.66932
$119$	−30.1528			−0.253385
$120$			20.5343i			0.171120i
$121$	94.4782			0.780812
$122$			142.204i			1.16561i
$123$	26.5295			0.215687
$124$	−116.780			−0.941775
$125$			114.427i			0.915419i
$126$			19.7931i			0.157088i
$127$	88.5042			0.696884			0.348442	−	0.937330i	$-0.386711\pi$
$127$	88.5042			0.696884			0.348442	+	0.937330i	$0.386711\pi$
$128$	−128.061			−1.00047
$129$		−	118.243i		−	0.916609i
$130$		−	41.5337i		−	0.319490i
$131$	−207.393			−1.58315			−0.791574	−	0.611073i	$-0.790738\pi$
$131$	−207.393			−1.58315			−0.791574	+	0.611073i	$0.790738\pi$
$132$			19.7889i			0.149916i
$133$	−24.9109			−0.187300
$134$		−	232.894i		−	1.73801i
$135$			13.8667i			0.102717i
$136$		−	50.6298i		−	0.372278i
$137$		−	157.449i		−	1.14926i	−0.818413	−	0.574630i	$-0.805146\pi$
$137$		−	157.449i		−	1.14926i	0.818413	−	0.574630i	$-0.194854\pi$
$138$	−47.0320	−	87.5029i	−0.340812	−	0.634079i
$139$	115.205			0.828812			0.414406	−	0.910092i	$-0.363989\pi$
$139$	115.205			0.828812			0.414406	+	0.910092i	$0.363989\pi$
$140$	15.6640			0.111886
$141$	79.7148			0.565353
$142$	−293.483			−2.06678
$143$			32.1416i			0.224766i
$144$	−59.8568			−0.415672
$145$			73.6998i			0.508275i
$146$	−299.934			−2.05434
$147$	−12.1244			−0.0824786
$148$			109.784i			0.741783i
$149$			4.64544i			0.0311775i	0.999878	+	0.0155887i	$0.00496225\pi$
$149$			4.64544i			0.0311775i	−0.999878	+	0.0155887i	$0.995038\pi$
$150$	−77.2199			−0.514799
$151$	−221.430			−1.46643			−0.733214	−	0.679998i	$-0.761980\pi$
$151$	−221.430			−1.46643			−0.733214	+	0.679998i	$0.761980\pi$
$152$		−	41.8281i		−	0.275185i
$153$		−	34.1901i		−	0.223464i
$154$	−33.9777			−0.220634
$155$		−	140.476i		−	0.906295i
$156$	23.9821			0.153731
$157$		−	208.739i		−	1.32955i	−0.747044	−	0.664775i	$-0.768528\pi$
$157$		−	208.739i		−	1.32955i	0.747044	−	0.664775i	$-0.231472\pi$
$158$		−	243.127i		−	1.53878i
$159$			165.050i			1.03805i
$160$			85.3564i			0.533477i
$161$	53.6004	−	28.8097i	0.332922	−	0.178942i
$162$	−22.4432			−0.138538
$163$	−101.699			−0.623923			−0.311961	−	0.950095i	$-0.600986\pi$
$163$	−101.699			−0.623923			−0.311961	+	0.950095i	$0.600986\pi$
$164$	33.9805			0.207198
$165$	−23.8043			−0.144268
$166$		−	81.3459i		−	0.490036i
$167$	−212.169			−1.27047			−0.635236	−	0.772318i	$-0.719097\pi$
$167$	−212.169			−1.27047			−0.635236	+	0.772318i	$0.719097\pi$
$168$		−	20.3581i		−	0.121179i
$169$	−130.048			−0.769514
$170$	−75.8428			−0.446134
$171$		−	28.2463i		−	0.165183i
$172$		−	151.451i		−	0.880532i
$173$	−198.776			−1.14900			−0.574498	−	0.818506i	$-0.694803\pi$
$173$	−198.776			−1.14900			−0.574498	+	0.818506i	$0.694803\pi$
$174$	−119.283			−0.685533
$175$		−	47.3015i		−	0.270294i
$176$		−	102.753i		−	0.583822i
$177$	136.817			0.772976
$178$		−	351.573i		−	1.97513i
$179$	−40.3609			−0.225480			−0.112740	−	0.993625i	$-0.535963\pi$
$179$	−40.3609			−0.225480			−0.112740	+	0.993625i	$0.535963\pi$
$180$			17.7613i			0.0986738i
$181$			268.080i			1.48111i	0.671998	+	0.740553i	$0.265437\pi$
$181$			268.080i			1.48111i	−0.671998	+	0.740553i	$0.734563\pi$
$182$			41.1773i			0.226249i
$183$		−	98.7713i		−	0.539734i
$184$	48.3746	+	90.0008i	0.262906	+	0.489135i
$185$	−132.060			−0.713837
$186$	227.359			1.22236
$187$	58.6921			0.313862
$188$	102.103			0.543101
$189$		−	13.7477i		−	0.0727393i
$190$	−62.6579			−0.329778
$191$			146.577i			0.767420i	0.923454	+	0.383710i	$0.125354\pi$
$191$			146.577i			0.767420i	−0.923454	+	0.383710i	$0.874646\pi$
$192$	0.0844787			0.000439993
$193$	87.5334			0.453541			0.226771	−	0.973948i	$-0.427183\pi$
$193$	87.5334			0.453541			0.226771	+	0.973948i	$0.427183\pi$
$194$			185.231i			0.954797i
$195$			28.8482i			0.147939i
$196$	−15.5295			−0.0792323
$197$	59.4002			0.301524			0.150762	−	0.988570i	$-0.451827\pi$
$197$	59.4002			0.301524			0.150762	+	0.988570i	$0.451827\pi$
$198$		−	38.5270i		−	0.194581i
$199$		−	393.816i		−	1.97897i	−0.144624	−	0.989487i	$-0.546197\pi$
$199$		−	393.816i		−	1.97897i	0.144624	−	0.989487i	$-0.453803\pi$
$200$	79.4243			0.397121
$201$			161.762i			0.804784i
$202$	−173.525			−0.859036
$203$		−	73.0673i		−	0.359937i
$204$		−	43.7925i		−	0.214669i
$205$			40.8754i			0.199392i
$206$		−	225.920i		−	1.09670i
$207$	32.6671	+	60.7771i	0.157812	+	0.293609i
$208$	−124.525			−0.598679
$209$	48.4888			0.232004
$210$	−30.4962			−0.145220
$211$	−138.956			−0.658560			−0.329280	−	0.944232i	$-0.606806\pi$
$211$	−138.956			−0.658560			−0.329280	+	0.944232i	$0.606806\pi$
$212$			211.406i			0.997196i
$213$	203.845			0.957019
$214$			35.4266i			0.165545i
$215$	182.182			0.847358
$216$	23.0839			0.106870
$217$			139.270i			0.641797i
$218$			316.526i			1.45195i
$219$	208.326			0.951259
$220$	−30.4898			−0.138590
$221$		−	71.1286i		−	0.321849i
$222$		−	213.738i		−	0.962784i
$223$	−72.6245			−0.325671			−0.162835	−	0.986653i	$-0.552064\pi$
$223$	−72.6245			−0.325671			−0.162835	+	0.986653i	$0.552064\pi$
$224$		−	84.6238i		−	0.377785i
$225$	53.6348			0.238377
$226$			257.824i			1.14081i
$227$			295.613i			1.30226i	0.758967	+	0.651130i	$0.225705\pi$
$227$			295.613i			1.30226i	−0.758967	+	0.651130i	$0.774295\pi$
$228$		−	36.1794i		−	0.158681i
$229$		−	244.457i		−	1.06750i	−0.845642	−	0.533750i	$-0.820782\pi$
$229$		−	244.457i		−	1.06750i	0.845642	−	0.533750i	$-0.179218\pi$
$230$	134.820	−	72.4645i	0.586174	−	0.315063i
$231$	23.5999			0.102164
$232$	122.688			0.528827
$233$	−374.035			−1.60530			−0.802650	−	0.596451i	$-0.796577\pi$
$233$	−374.035			−1.60530			−0.802650	+	0.596451i	$0.796577\pi$
$234$	−46.6906			−0.199533
$235$			122.821i			0.522640i
$236$	175.242			0.742553
$237$			168.870i			0.712530i
$238$	75.1918			0.315932
$239$	45.5079			0.190409			0.0952047	−	0.995458i	$-0.469649\pi$
$239$	45.5079			0.190409			0.0952047	+	0.995458i	$0.469649\pi$
$240$		−	92.2243i		−	0.384268i
$241$			266.574i			1.10612i	0.833143	+	0.553058i	$0.186539\pi$
$241$			266.574i			1.10612i	−0.833143	+	0.553058i	$0.813461\pi$
$242$	−235.600			−0.973552
$243$	15.5885			0.0641500
$244$		−	126.512i		−	0.518490i
$245$		−	18.6806i		−	0.0762473i
$246$	−66.1565			−0.268929
$247$		−	58.7632i		−	0.237908i
$248$	−233.849			−0.942941
$249$			56.5007i			0.226910i
$250$		−	285.347i		−	1.14139i
$251$		−	6.34778i		−	0.0252899i	−0.999920	−	0.0126450i	$-0.995975\pi$
$251$		−	6.34778i		−	0.0252899i	0.999920	−	0.0126450i	$-0.00402513\pi$
$252$		−	17.6088i		−	0.0698763i
$253$	−104.333	+	56.0778i	−0.412382	+	0.221652i
$254$	−220.702			−0.868907
$255$	52.6783			0.206582
$256$	319.149			1.24668
$257$	125.676			0.489013			0.244506	−	0.969648i	$-0.421374\pi$
$257$	125.676			0.489013			0.244506	+	0.969648i	$0.421374\pi$
$258$			294.861i			1.14287i
$259$	130.926			0.505507
$260$			36.9503i			0.142117i
$261$	82.8505			0.317435
$262$	517.173			1.97394
$263$		−	344.866i		−	1.31128i	−0.755074	−	0.655639i	$-0.772399\pi$
$263$		−	344.866i		−	1.31128i	0.755074	−	0.655639i	$-0.227601\pi$
$264$			39.6269i			0.150102i
$265$	−254.301			−0.959627
$266$	62.1201			0.233534
$267$			244.193i			0.914581i
$268$			207.193i			0.773108i
$269$	135.450			0.503533			0.251766	−	0.967788i	$-0.418989\pi$
$269$	135.450			0.503533			0.251766	+	0.967788i	$0.418989\pi$
$270$		−	34.5794i		−	0.128072i
$271$	361.853			1.33525			0.667626	−	0.744497i	$-0.267311\pi$
$271$	361.853			1.33525			0.667626	+	0.744497i	$0.267311\pi$
$272$			227.390i			0.835991i
$273$		−	28.6006i		−	0.104764i
$274$			392.629i			1.43295i
$275$			92.0719i			0.334807i
$276$	41.8419	+	77.8466i	0.151601	+	0.282053i
$277$	86.5619			0.312498			0.156249	−	0.987718i	$-0.450060\pi$
$277$	86.5619			0.312498			0.156249	+	0.987718i	$0.450060\pi$
$278$	−287.286			−1.03340
$279$	−157.917			−0.566012
$280$	31.3667			0.112024
$281$		−	281.370i		−	1.00132i	−0.865645	−	0.500658i	$-0.833091\pi$
$281$		−	281.370i		−	1.00132i	0.865645	−	0.500658i	$-0.166909\pi$
$282$	−198.784			−0.704909
$283$		−	68.6536i		−	0.242592i	−0.992616	−	0.121296i	$-0.961295\pi$
$283$		−	68.6536i		−	0.242592i	0.992616	−	0.121296i	$-0.0387050\pi$
$284$	261.096			0.919352
$285$	43.5204			0.152703
$286$		−	80.1512i		−	0.280249i
$287$		−	40.5245i		−	0.141201i
$288$	95.9544			0.333175
$289$	159.116			0.550573
$290$		−	183.785i		−	0.633741i
$291$		−	128.656i		−	0.442117i
$292$	266.835			0.913818
$293$		−	340.957i		−	1.16368i	−0.813305	−	0.581838i	$-0.802334\pi$
$293$		−	340.957i		−	1.16368i	0.813305	−	0.581838i	$-0.197666\pi$
$294$	30.2344			0.102838
$295$			210.800i			0.714578i
$296$			219.840i			0.742701i
$297$			26.7598i			0.0901004i
$298$		−	11.5843i		−	0.0388735i
$299$	67.9603	+	126.440i	0.227292	+	0.422876i
$300$	68.6984			0.228995
$301$	−180.618			−0.600061
$302$	552.180			1.82841
$303$	120.526			0.397775
$304$			187.859i			0.617957i
$305$	152.182			0.498956
$306$			85.2595i			0.278626i
$307$	270.059			0.879671			0.439836	−	0.898078i	$-0.355037\pi$
$307$	270.059			0.879671			0.439836	+	0.898078i	$0.355037\pi$
$308$	30.2281			0.0981432
$309$			156.918i			0.507824i
$310$			350.303i			1.13001i
$311$	210.711			0.677527			0.338763	−	0.940872i	$-0.389991\pi$
$311$	210.711			0.677527			0.338763	+	0.940872i	$0.389991\pi$
$312$	48.0235			0.153921
$313$		−	301.021i		−	0.961727i	−0.876795	−	0.480864i	$-0.840323\pi$
$313$		−	301.021i		−	0.961727i	0.876795	−	0.480864i	$-0.159677\pi$
$314$			520.532i			1.65774i
$315$	21.1818			0.0672438
$316$			216.297i			0.684486i
$317$	205.023			0.646759			0.323380	−	0.946269i	$-0.395181\pi$
$317$	205.023			0.646759			0.323380	+	0.946269i	$0.395181\pi$
$318$		−	411.585i		−	1.29429i
$319$			142.225i			0.445846i
$320$			0.130161i			0.000406752i
$321$		−	24.6064i		−	0.0766554i
$322$	−133.663	+	71.8426i	−0.415102	+	0.223114i
$323$	−107.305			−0.332213
$324$	19.9665			0.0616251
$325$	111.581			0.343327
$326$	253.607			0.777936
$327$		−	219.850i		−	0.672324i
$328$	68.0451			0.207455
$329$		−	121.766i		−	0.370111i
$330$	59.3605			0.179880
$331$	−482.620			−1.45807			−0.729033	−	0.684478i	$-0.760030\pi$
$331$	−482.620			−1.45807			−0.729033	+	0.684478i	$0.760030\pi$
$332$			72.3691i			0.217979i
$333$			148.457i			0.445816i
$334$	529.084			1.58408
$335$	−249.234			−0.743982
$336$			91.4327i			0.272121i
$337$		−	72.6179i		−	0.215483i	−0.994179	−	0.107742i	$-0.965638\pi$
$337$		−	72.6179i		−	0.215483i	0.994179	−	0.107742i	$-0.0343620\pi$
$338$	324.299			0.959466
$339$		−	179.077i		−	0.528251i
$340$	67.4732			0.198451
$341$		−	271.088i		−	0.794979i
$342$			70.4376i			0.205958i
$343$			18.5203i			0.0539949i
$344$		−	303.278i		−	0.881622i
$345$	−93.6423	+	50.3319i	−0.271427	+	0.145889i
$346$	495.688			1.43262
$347$	−392.651			−1.13156			−0.565779	−	0.824557i	$-0.691425\pi$
$347$	−392.651			−1.13156			−0.565779	+	0.824557i	$0.691425\pi$
$348$	106.119			0.304941
$349$	−4.12922			−0.0118316			−0.00591579	−	0.999983i	$-0.501883\pi$
$349$	−4.12922			−0.0118316			−0.00591579	+	0.999983i	$0.501883\pi$
$350$			117.955i			0.337015i
$351$	32.4300			0.0923933
$352$			164.719i			0.467953i
$353$	−462.131			−1.30915			−0.654577	−	0.755996i	$-0.727153\pi$
$353$	−462.131			−1.30915			−0.654577	+	0.755996i	$0.727153\pi$
$354$	−341.179			−0.963783
$355$			314.074i			0.884716i
$356$			312.776i			0.878584i
$357$	−52.2262			−0.146292
$358$	100.648			0.281139
$359$		−	160.266i		−	0.446424i	−0.974770	−	0.223212i	$-0.928346\pi$
$359$		−	160.266i		−	0.446424i	0.974770	−	0.223212i	$-0.0716542\pi$
$360$			35.5665i			0.0987959i
$361$	272.350			0.754431
$362$		−	668.510i		−	1.84671i
$363$	163.641			0.450802
$364$		−	36.6332i		−	0.100641i
$365$			320.978i			0.879390i
$366$			246.305i			0.672965i
$367$		−	360.101i		−	0.981203i	−0.871384	−	0.490601i	$-0.836777\pi$
$367$		−	360.101i		−	0.981203i	0.871384	−	0.490601i	$-0.163223\pi$
$368$	−217.261	−	404.214i	−0.590383	−	1.09841i
$369$	45.9505			0.124527
$370$	329.317			0.890045
$371$	252.119			0.679565
$372$	−202.269			−0.543734
$373$			375.533i			1.00679i	0.864057	+	0.503395i	$0.167916\pi$
$373$			375.533i			1.00679i	−0.864057	+	0.503395i	$0.832084\pi$
$374$	−146.360			−0.391337
$375$			198.194i			0.528517i
$376$	204.459			0.543774
$377$	172.361			0.457192
$378$			34.2826i			0.0906947i
$379$		−	139.156i		−	0.367167i	−0.983004	−	0.183583i	$-0.941230\pi$
$379$		−	139.156i		−	0.367167i	0.983004	−	0.183583i	$-0.0587697\pi$
$380$	55.7433			0.146693
$381$	153.294			0.402346
$382$		−	365.519i		−	0.956855i
$383$		−	160.388i		−	0.418767i	−0.977834	−	0.209383i	$-0.932854\pi$
$383$		−	160.388i		−	0.418767i	0.977834	−	0.209383i	$-0.0671457\pi$
$384$	−221.808			−0.577624
$385$			36.3616i			0.0944457i
$386$	−218.281			−0.565496
$387$		−	204.802i		−	0.529204i
$388$		−	164.790i		−	0.424716i
$389$			670.351i			1.72327i	0.507532	+	0.861633i	$0.330558\pi$
$389$			670.351i			1.72327i	−0.507532	+	0.861633i	$0.669442\pi$
$390$		−	71.9386i		−	0.184458i
$391$	230.886	−	124.099i	0.590501	−	0.317389i
$392$	−31.0975			−0.0793304
$393$	−359.214			−0.914031
$394$	−148.126			−0.375954
$395$	−260.186			−0.658698
$396$			34.2754i			0.0865541i
$397$	−256.252			−0.645472			−0.322736	−	0.946489i	$-0.604603\pi$
$397$	−256.252			−0.645472			−0.322736	+	0.946489i	$0.604603\pi$
$398$			982.055i			2.46748i
$399$	−43.1469			−0.108138
$400$	−356.712			−0.891780
$401$			509.697i			1.27106i	0.772075	+	0.635532i	$0.219219\pi$
$401$			509.697i			1.27106i	−0.772075	+	0.635532i	$0.780781\pi$
$402$		−	403.384i		−	1.00344i
$403$	−328.529			−0.815209
$404$	154.376			0.382119
$405$			24.0179i			0.0593035i
$406$			182.207i			0.448787i
$407$	−254.847			−0.626160
$408$		−	87.6934i		−	0.214935i
$409$	409.626			1.00153			0.500766	−	0.865583i	$-0.333052\pi$
$409$	409.626			1.00153			0.500766	+	0.865583i	$0.333052\pi$
$410$		−	101.931i		−	0.248611i
$411$		−	272.709i		−	0.663526i
$412$			200.989i			0.487837i
$413$		−	208.991i		−	0.506032i
$414$	−81.4618	−	151.559i	−0.196768	−	0.366086i
$415$	−87.0533			−0.209767
$416$	199.622			0.479861
$417$	199.541			0.478515
$418$	−120.916			−0.289273
$419$		−	256.628i		−	0.612476i	−0.951955	−	0.306238i	$-0.900930\pi$
$419$		−	256.628i		−	0.612476i	0.951955	−	0.306238i	$-0.0990704\pi$
$420$	27.1308			0.0645971
$421$			481.447i			1.14358i	0.820400	+	0.571790i	$0.193751\pi$
$421$			481.447i			1.14358i	−0.820400	+	0.571790i	$0.806249\pi$
$422$	346.514			0.821124
$423$	138.070			0.326407
$424$			423.334i			0.998430i
$425$		−	203.753i		−	0.479419i
$426$	−508.327			−1.19326
$427$	−150.876			−0.353339
$428$		−	31.5172i		−	0.0736383i
$429$			55.6708i			0.129769i
$430$	−454.306			−1.05653
$431$		−	412.625i		−	0.957367i	−0.877988	−	0.478684i	$-0.841114\pi$
$431$		−	412.625i		−	0.957367i	0.877988	−	0.478684i	$-0.158886\pi$
$432$	−103.675			−0.239988
$433$		−	291.701i		−	0.673674i	−0.941563	−	0.336837i	$-0.890643\pi$
$433$		−	291.701i		−	0.673674i	0.941563	−	0.336837i	$-0.109357\pi$
$434$		−	347.297i		−	0.800223i
$435$			127.652i			0.293453i
$436$		−	281.596i		−	0.645862i
$437$	190.748	−	102.525i	0.436493	−	0.234611i
$438$	−519.500			−1.18607
$439$	−408.934			−0.931513			−0.465757	−	0.884913i	$-0.654218\pi$
$439$	−408.934			−0.931513			−0.465757	+	0.884913i	$0.654218\pi$
$440$	−61.0550			−0.138761
$441$	−21.0000			−0.0476190
$442$			177.373i			0.401296i
$443$	−608.745			−1.37414			−0.687071	−	0.726591i	$-0.741104\pi$
$443$	−608.745			−1.37414			−0.687071	+	0.726591i	$0.741104\pi$
$444$			190.151i			0.428269i
$445$	−376.240			−0.845484
$446$	181.103			0.406061
$447$			8.04614i			0.0180003i
$448$		−	0.129043i		−	0.000288043i
$449$	104.386			0.232486			0.116243	−	0.993221i	$-0.462915\pi$
$449$	104.386			0.232486			0.116243	+	0.993221i	$0.462915\pi$
$450$	−133.749			−0.297220
$451$			78.8807i			0.174902i
$452$		−	229.372i		−	0.507460i
$453$	−383.529			−0.846642
$454$		−	737.168i		−	1.62372i
$455$	44.0664			0.0968491
$456$		−	72.4483i		−	0.158878i
$457$		−	329.999i		−	0.722098i	−0.932547	−	0.361049i	$-0.882419\pi$
$457$		−	329.999i		−	0.722098i	0.932547	−	0.361049i	$-0.117581\pi$
$458$			609.602i			1.33101i
$459$		−	59.2189i		−	0.129017i
$460$	−119.942	+	64.4678i	−0.260744	+	0.140147i
$461$	−96.9709			−0.210349			−0.105175	−	0.994454i	$-0.533540\pi$
$461$	−96.9709			−0.210349			−0.105175	+	0.994454i	$0.533540\pi$
$462$	−58.8510			−0.127383
$463$	−445.155			−0.961459			−0.480729	−	0.876869i	$-0.659628\pi$
$463$	−445.155			−0.961459			−0.480729	+	0.876869i	$0.659628\pi$
$464$	−551.018			−1.18754
$465$		−	243.311i		−	0.523250i
$466$	932.728			2.00156
$467$			494.092i			1.05801i	0.848618	+	0.529006i	$0.177435\pi$
$467$			494.092i			1.05801i	−0.848618	+	0.529006i	$0.822565\pi$
$468$	41.5382			0.0887567
$469$	247.095			0.526855
$470$		−	306.277i		−	0.651652i
$471$		−	361.547i		−	0.767616i
$472$	350.919			0.743472
$473$	351.572			0.743281
$474$		−	421.109i		−	0.888416i
$475$		−	168.332i		−	0.354382i
$476$	−66.8941			−0.140534
$477$			285.876i			0.599320i
$478$	−113.483			−0.237411
$479$			362.166i			0.756088i	0.925788	+	0.378044i	$0.123403\pi$
$479$			362.166i			0.756088i	−0.925788	+	0.378044i	$0.876597\pi$
$480$			147.842i			0.308003i
$481$			308.847i			0.642094i
$482$		−	664.754i		−	1.37916i
$483$	92.8386	−	49.8999i	0.192212	−	0.103312i
$484$	209.600			0.433059
$485$	198.227			0.408715
$486$	−38.8728			−0.0799852
$487$	−121.978			−0.250468			−0.125234	−	0.992127i	$-0.539968\pi$
$487$	−121.978			−0.250468			−0.125234	+	0.992127i	$0.539968\pi$
$488$		−	253.336i		−	0.519132i
$489$	−176.149			−0.360222
$490$			46.5837i			0.0950687i
$491$	54.4849			0.110967			0.0554836	−	0.998460i	$-0.482330\pi$
$491$	54.4849			0.110967			0.0554836	+	0.998460i	$0.482330\pi$
$492$	58.8559			0.119626
$493$		−	314.741i		−	0.638419i
$494$			146.537i			0.296635i
$495$	−41.2302			−0.0832933
$496$	1050.27			2.11748
$497$		−	311.379i		−	0.626516i
$498$		−	140.895i		−	0.282922i
$499$	−146.517			−0.293621			−0.146811	−	0.989165i	$-0.546901\pi$
$499$	−146.517			−0.293621			−0.146811	+	0.989165i	$0.546901\pi$
$500$			253.858i			0.507715i
$501$	−367.487			−0.733507
$502$			15.8294i			0.0315327i
$503$		−	655.135i		−	1.30246i	−0.758882	−	0.651228i	$-0.774254\pi$
$503$		−	655.135i		−	1.30246i	0.758882	−	0.651228i	$-0.225746\pi$
$504$		−	35.2613i		−	0.0699628i
$505$			185.700i			0.367723i
$506$	260.174	−	139.841i	0.514177	−	0.276365i
$507$	−225.250			−0.444279
$508$	196.347			0.386510
$509$	5.65935			0.0111186			0.00555928	−	0.999985i	$-0.498230\pi$
$509$	5.65935			0.0111186			0.00555928	+	0.999985i	$0.498230\pi$
$510$	−131.364			−0.257576
$511$		−	318.223i		−	0.622745i
$512$	−283.617			−0.553939
$513$		−	48.9240i		−	0.0953684i
$514$	−313.398			−0.609724
$515$	−241.771			−0.469458
$516$		−	262.322i		−	0.508375i
$517$			237.017i			0.458447i
$518$	−326.490			−0.630290
$519$	−344.291			−0.663374
$520$			73.9922i			0.142293i
$521$			722.523i			1.38680i	0.720553	+	0.693400i	$0.243888\pi$
$521$			722.523i			1.38680i	−0.720553	+	0.693400i	$0.756112\pi$
$522$	−206.604			−0.395793
$523$		−	718.409i		−	1.37363i	−0.726832	−	0.686815i	$-0.759008\pi$
$523$		−	718.409i		−	1.37363i	0.726832	−	0.686815i	$-0.240992\pi$
$524$	−460.101			−0.878056
$525$		−	81.9286i		−	0.156054i
$526$			859.990i			1.63496i
$527$			599.912i			1.13835i
$528$		−	177.973i		−	0.337070i
$529$	−291.857	+	441.203i	−0.551715	+	0.834033i
$530$	634.149			1.19651
$531$	236.974			0.446278
$532$	−55.2649			−0.103881
$533$	95.5949			0.179353
$534$		−	608.943i		−	1.14034i
$535$	37.9122			0.0708640
$536$			414.899i			0.774065i
$537$	−69.9071			−0.130181
$538$	−337.772			−0.627828
$539$		−	36.0495i		−	0.0668822i
$540$			30.7634i			0.0569693i
$541$	894.865			1.65410			0.827048	−	0.562132i	$-0.190019\pi$
$541$	894.865			1.65410			0.827048	+	0.562132i	$0.190019\pi$
$542$	−902.351			−1.66485
$543$			464.329i			0.855117i
$544$		−	364.521i		−	0.670075i
$545$	338.734			0.621530
$546$			71.3211i			0.130625i
$547$	−828.170			−1.51402			−0.757011	−	0.653402i	$-0.773341\pi$
$547$	−828.170			−1.51402			−0.757011	+	0.653402i	$0.773341\pi$
$548$		−	349.301i		−	0.637410i
$549$		−	171.077i		−	0.311615i
$550$		−	229.599i		−	0.417453i
$551$		−	260.024i		−	0.471914i
$552$	83.7873	+	155.886i	0.151789	+	0.282402i
$553$	257.953			0.466461
$554$	−215.859			−0.389637
$555$	−228.734			−0.412134
$556$	255.583			0.459681
$557$			1087.71i			1.95279i	0.215988	+	0.976396i	$0.430703\pi$
$557$			1087.71i			1.95279i	−0.215988	+	0.976396i	$0.569297\pi$
$558$	393.797			0.705730
$559$		−	426.068i		−	0.762196i
$560$	−140.875			−0.251562
$561$	101.658			0.181208
$562$			701.650i			1.24849i
$563$		−	188.523i		−	0.334855i	−0.985884	−	0.167428i	$-0.946454\pi$
$563$		−	188.523i		−	0.334855i	0.985884	−	0.167428i	$-0.0535460\pi$
$564$	176.848			0.313560
$565$	275.913			0.488342
$566$			171.201i			0.302475i
$567$		−	23.8118i		−	0.0419961i
$568$	522.838			0.920490
$569$		−	765.885i		−	1.34602i	−0.739634	−	0.673010i	$-0.765001\pi$
$569$		−	765.885i		−	1.34602i	0.739634	−	0.673010i	$-0.234999\pi$
$570$	−108.527			−0.190398
$571$		−	206.350i		−	0.361384i	−0.983540	−	0.180692i	$-0.942166\pi$
$571$		−	206.350i		−	0.361384i	0.983540	−	0.180692i	$-0.0578338\pi$
$572$			71.3062i			0.124661i
$573$			253.879i			0.443070i
$574$			101.056i			0.176055i
$575$	194.677	+	362.197i	0.338569	+	0.629907i
$576$	0.146321			0.000254030
$577$	−269.172			−0.466503			−0.233251	−	0.972416i	$-0.574936\pi$
$577$	−269.172			−0.466503			−0.233251	+	0.972416i	$0.574936\pi$
$578$	−396.785			−0.686480
$579$	151.612			0.261852
$580$			163.503i			0.281902i
$581$	86.3062			0.148548
$582$			320.829i			0.551253i
$583$	−490.747			−0.841761
$584$	534.330			0.914949
$585$			49.9666i			0.0854129i
$586$			850.243i			1.45093i
$587$	239.644			0.408251			0.204126	−	0.978945i	$-0.434565\pi$
$587$	239.644			0.408251			0.204126	+	0.978945i	$0.434565\pi$
$588$	−26.8979			−0.0457448
$589$			495.620i			0.841460i
$590$		−	525.671i		−	0.890969i
$591$	102.884			0.174085
$592$		−	987.348i		−	1.66782i
$593$	−3.82945			−0.00645775			−0.00322887	−	0.999995i	$-0.501028\pi$
$593$	−3.82945			−0.00645775			−0.00322887	+	0.999995i	$0.501028\pi$
$594$		−	66.7308i		−	0.112341i
$595$		−	80.4674i		−	0.135239i
$596$			10.3059i			0.0172918i
$597$		−	682.109i		−	1.14256i
$598$	−169.472	−	315.302i	−0.283398	−	0.527262i
$599$	737.444			1.23112			0.615562	−	0.788088i	$-0.288929\pi$
$599$	737.444			1.23112			0.615562	+	0.788088i	$0.288929\pi$
$600$	137.567			0.229278
$601$	41.7430			0.0694558			0.0347279	−	0.999397i	$-0.488944\pi$
$601$	41.7430			0.0694558			0.0347279	+	0.999397i	$0.488944\pi$
$602$	450.407			0.748184
$603$			280.179i			0.464642i
$604$	−491.245			−0.813319
$605$			252.130i			0.416744i
$606$	−300.555			−0.495965
$607$	226.628			0.373357			0.186679	−	0.982421i	$-0.440228\pi$
$607$	226.628			0.373357			0.186679	+	0.982421i	$0.440228\pi$
$608$		−	301.151i		−	0.495313i
$609$		−	126.556i		−	0.207810i
$610$	−379.494			−0.622122
$611$	287.239			0.470114
$612$		−	75.8508i		−	0.123939i
$613$			412.370i			0.672708i	0.941736	+	0.336354i	$0.109194\pi$
$613$			412.370i			0.672708i	−0.941736	+	0.336354i	$0.890806\pi$
$614$	−673.445			−1.09682
$615$			70.7982i			0.115119i
$616$	60.5310			0.0982647
$617$		−	215.207i		−	0.348797i	−0.984675	−	0.174398i	$-0.944202\pi$
$617$		−	215.207i		−	0.348797i	0.984675	−	0.174398i	$-0.0557980\pi$
$618$		−	391.305i		−	0.633179i
$619$		−	605.499i		−	0.978189i	−0.872231	−	0.489095i	$-0.837327\pi$
$619$		−	605.499i		−	0.978189i	0.872231	−	0.489095i	$-0.162673\pi$
$620$		−	311.646i		−	0.502655i
$621$	56.5812	+	105.269i	0.0911130	+	0.169515i
$622$	−525.448			−0.844772
$623$	373.011			0.598734
$624$	−215.684			−0.345648
$625$	141.590			0.226544
$626$			750.653i			1.19913i
$627$	83.9851			0.133947
$628$		−	463.089i		−	0.737403i
$629$	563.971			0.896615
$630$	−52.8209			−0.0838427
$631$			1029.64i			1.63176i	0.578224	+	0.815878i	$0.303746\pi$
$631$			1029.64i			1.63176i	−0.578224	+	0.815878i	$0.696254\pi$
$632$			433.130i			0.685333i
$633$	−240.679			−0.380220
$634$	−511.264			−0.806409
$635$			236.187i			0.371949i
$636$			366.165i			0.575731i
$637$	−43.6881			−0.0685842
$638$		−	354.665i		−	0.555901i
$639$	353.070			0.552535
$640$		−	341.750i		−	0.533985i
$641$			140.851i			0.219737i	0.993946	+	0.109868i	$0.0350430\pi$
$641$			140.851i			0.219737i	−0.993946	+	0.109868i	$0.964957\pi$
$642$			61.3607i			0.0955775i
$643$		−	847.482i		−	1.31801i	−0.752138	−	0.659006i	$-0.770977\pi$
$643$		−	847.482i		−	1.31801i	0.752138	−	0.659006i	$-0.229023\pi$
$644$	118.913	−	63.9145i	0.184647	−	0.0992461i
$645$	315.549			0.489223
$646$	267.585			0.414218
$647$	−468.639			−0.724325			−0.362163	−	0.932115i	$-0.617962\pi$
$647$	−468.639			−0.724325			−0.362163	+	0.932115i	$0.617962\pi$
$648$	39.9825			0.0617014
$649$			406.799i			0.626809i
$650$	−278.249			−0.428076
$651$			241.223i			0.370542i
$652$	−225.621			−0.346044
$653$	−82.0353			−0.125628			−0.0628142	−	0.998025i	$-0.520008\pi$
$653$	−82.0353			−0.125628			−0.0628142	+	0.998025i	$0.520008\pi$
$654$			548.238i			0.838285i
$655$		−	553.459i		−	0.844976i
$656$	−305.605			−0.465862
$657$	360.831			0.549209
$658$			303.648i			0.461471i
$659$		−	217.649i		−	0.330272i	−0.986271	−	0.165136i	$-0.947194\pi$
$659$		−	217.649i		−	0.330272i	0.986271	−	0.165136i	$-0.0528063\pi$
$660$	−52.8098			−0.0800149
$661$		−	957.496i		−	1.44856i	−0.689508	−	0.724278i	$-0.742173\pi$
$661$		−	957.496i		−	1.44856i	0.689508	−	0.724278i	$-0.257827\pi$
$662$	1203.51			1.81799
$663$		−	123.198i		−	0.185820i
$664$			144.917i			0.218249i
$665$		−	66.4786i		−	0.0999678i
$666$		−	370.205i		−	0.555864i
$667$	300.721	+	559.491i	0.450856	+	0.838817i
$668$	−470.697			−0.704637
$669$	−125.789			−0.188026
$670$	621.513			0.927632
$671$	293.678			0.437672
$672$		−	146.573i		−	0.218114i
$673$	−722.505			−1.07356			−0.536780	−	0.843722i	$-0.680359\pi$
$673$	−722.505			−1.07356			−0.536780	+	0.843722i	$0.680359\pi$
$674$			181.087i			0.268675i
$675$	92.8983			0.137627
$676$	−288.512			−0.426793
$677$		−	695.664i		−	1.02757i	−0.857919	−	0.513784i	$-0.828243\pi$
$677$		−	695.664i		−	1.02757i	0.857919	−	0.513784i	$-0.171757\pi$
$678$			446.564i			0.658648i
$679$	−196.526			−0.289434
$680$	135.114			0.198696
$681$			512.017i			0.751860i
$682$			676.010i			0.991217i
$683$	−610.279			−0.893527			−0.446763	−	0.894652i	$-0.647423\pi$
$683$	−610.279			−0.893527			−0.446763	+	0.894652i	$0.647423\pi$
$684$		−	62.6645i		−	0.0916148i
$685$	420.176			0.613396
$686$		−	46.1838i		−	0.0673234i
$687$		−	423.413i		−	0.616321i
$688$			1362.09i			1.97978i
$689$			594.732i			0.863182i
$690$	233.515	−	125.512i	0.338428	−	0.181902i
$691$	−951.249			−1.37663			−0.688313	−	0.725413i	$-0.741649\pi$
$691$	−951.249			−1.37663			−0.688313	+	0.725413i	$0.741649\pi$
$692$	−440.987			−0.637264
$693$	40.8763			0.0589846
$694$	979.150			1.41088
$695$			307.442i			0.442363i
$696$	212.502			0.305318
$697$		−	174.561i		−	0.250447i
$698$	10.2970			0.0147522
$699$	−647.847			−0.926820
$700$		−	104.939i		−	0.149912i
$701$		−	757.495i		−	1.08059i	−0.841475	−	0.540296i	$-0.818312\pi$
$701$		−	757.495i		−	1.08059i	0.841475	−	0.540296i	$-0.181688\pi$
$702$	−80.8706			−0.115200
$703$	465.927			0.662770
$704$			0.251182i			0.000356792i
$705$			212.731i			0.301747i
$706$	1152.41			1.63231
$707$		−	184.106i		−	0.260405i
$708$	303.529			0.428713
$709$		−	1172.53i		−	1.65379i	−0.562359	−	0.826893i	$-0.690106\pi$
$709$		−	1172.53i		−	1.65379i	0.562359	−	0.826893i	$-0.309894\pi$
$710$		−	783.204i		−	1.10310i
$711$			292.491i			0.411380i
$712$			626.326i			0.879672i
$713$	−573.190	−	1066.42i	−0.803913	−	1.49568i
$714$	130.236			0.182403
$715$	−85.7748			−0.119965
$716$	−89.5408			−0.125057
$717$	78.8219			0.109933
$718$			399.654i			0.556622i
$719$	−181.032			−0.251784			−0.125892	−	0.992044i	$-0.540179\pi$
$719$	−181.032			−0.251784			−0.125892	+	0.992044i	$0.540179\pi$
$720$		−	159.737i		−	0.221857i
$721$	239.696			0.332449
$722$	−679.157			−0.940660
$723$			461.720i			0.638616i
$724$			594.737i			0.821461i
$725$	493.742			0.681023
$726$	−408.071			−0.562081
$727$		−	835.202i		−	1.14883i	−0.818563	−	0.574417i	$-0.805229\pi$
$727$		−	835.202i		−	1.14883i	0.818563	−	0.574417i	$-0.194771\pi$
$728$		−	73.3571i		−	0.100765i
$729$	27.0000			0.0370370
$730$		−	800.419i		−	1.09646i
$731$	−778.022			−1.06433
$732$		−	219.124i		−	0.299350i
$733$			777.897i			1.06125i	0.847606	+	0.530625i	$0.178043\pi$
$733$			777.897i			1.06125i	−0.847606	+	0.530625i	$0.821957\pi$
$734$			897.982i			1.22341i
$735$		−	32.3557i		−	0.0440214i
$736$	348.284	+	647.981i	0.473212	+	0.880409i
$737$	−480.968			−0.652602
$738$	−114.586			−0.155266
$739$	−44.8546			−0.0606963			−0.0303482	−	0.999539i	$-0.509662\pi$
$739$	−44.8546			−0.0606963			−0.0303482	+	0.999539i	$0.509662\pi$
$740$	−292.975			−0.395913
$741$		−	101.781i		−	0.137356i
$742$	−628.706			−0.847313
$743$			896.506i			1.20660i	0.797513	+	0.603301i	$0.206148\pi$
$743$			896.506i			1.20660i	−0.797513	+	0.603301i	$0.793852\pi$
$744$	−405.039			−0.544407
$745$	−12.3971			−0.0166404
$746$		−	936.463i		−	1.25531i
$747$			97.8620i			0.131007i
$748$	130.209			0.174076
$749$	−37.5869			−0.0501827
$750$		−	494.235i		−	0.658980i
$751$		−	484.548i		−	0.645204i	−0.946535	−	0.322602i	$-0.895443\pi$
$751$		−	484.548i		−	0.645204i	0.946535	−	0.322602i	$-0.104557\pi$
$752$	−918.270			−1.22110
$753$		−	10.9947i		−	0.0146012i
$754$	−429.816			−0.570048
$755$		−	590.922i		−	0.782678i
$756$		−	30.4994i		−	0.0403431i
$757$			1187.18i			1.56827i	0.620588	+	0.784137i	$0.286894\pi$
$757$			1187.18i			1.56827i	−0.620588	+	0.784137i	$0.713106\pi$
$758$			347.013i			0.457800i
$759$	−180.709	+	97.1297i	−0.238089	+	0.127971i
$760$	111.625			0.146875
$761$	1485.05			1.95144			0.975720	−	0.219023i	$-0.0702871\pi$
$761$	1485.05			1.95144			0.975720	+	0.219023i	$0.0702871\pi$
$762$	−382.268			−0.501664
$763$	−335.826			−0.440139
$764$			325.182i			0.425631i
$765$	91.2415			0.119270
$766$			399.958i			0.522138i
$767$	492.997			0.642760
$768$	552.783			0.719769
$769$		−	523.256i		−	0.680437i	−0.940346	−	0.340219i	$-0.889499\pi$
$769$		−	523.256i		−	0.680437i	0.940346	−	0.340219i	$-0.110501\pi$
$770$		−	90.6747i		−	0.117759i
$771$	217.678			0.282332
$772$	194.193			0.251546
$773$			1040.51i			1.34607i	0.739611	+	0.673035i	$0.235010\pi$
$773$			1040.51i			1.34607i	−0.739611	+	0.673035i	$0.764990\pi$
$774$			510.713i			0.659836i
$775$	−941.097			−1.21432
$776$		−	329.988i		−	0.425242i
$777$	226.771			0.291855
$778$		−	1671.65i		−	2.14865i
$779$		−	144.215i		−	0.185128i
$780$			63.9999i			0.0820511i
$781$			606.095i			0.776050i
$782$	−575.759	+	309.465i	−0.736264	+	0.395735i
$783$	143.501			0.183271
$784$	139.666			0.178145
$785$	557.053			0.709622
$786$	895.770			1.13966
$787$		−	234.535i		−	0.298011i	−0.988836	−	0.149006i	$-0.952393\pi$
$787$		−	234.535i		−	0.298011i	0.988836	−	0.149006i	$-0.0476072\pi$
$788$	131.780			0.167233
$789$		−	597.326i		−	0.757067i
$790$	648.824			0.821296
$791$	−273.545			−0.345822
$792$			68.6357i			0.0866613i
$793$		−	355.906i		−	0.448810i
$794$	639.015			0.804805
$795$	−440.463			−0.554041
$796$		−	873.682i		−	1.09759i
$797$		−	188.839i		−	0.236937i	−0.992958	−	0.118469i	$-0.962202\pi$
$797$		−	188.839i		−	0.236937i	0.992958	−	0.118469i	$-0.0377985\pi$
$798$	107.595			0.134831
$799$		−	524.514i		−	0.656463i
$800$	571.833			0.714791
$801$			422.955i			0.528034i
$802$		−	1271.03i		−	1.58482i
$803$			619.417i			0.771379i
$804$			358.869i			0.446354i
$805$	76.8832	+	143.041i	0.0955071	+	0.177691i
$806$	819.251			1.01644
$807$	234.607			0.290715
$808$	309.135			0.382592
$809$	−1146.29			−1.41692			−0.708460	−	0.705751i	$-0.750610\pi$
$809$	−1146.29			−1.41692			−0.708460	+	0.705751i	$0.750610\pi$
$810$		−	59.8933i		−	0.0739423i
$811$	222.648			0.274535			0.137267	−	0.990534i	$-0.456168\pi$
$811$	222.648			0.274535			0.137267	+	0.990534i	$0.456168\pi$
$812$		−	162.100i		−	0.199631i
$813$	626.748			0.770908
$814$	635.510			0.780725
$815$		−	271.401i		−	0.333007i
$816$			393.850i			0.482660i
$817$	−642.766			−0.786740
$818$	−1021.48			−1.24876
$819$		−	49.5377i		−	0.0604856i
$820$			90.6822i			0.110588i
$821$	364.296			0.443722			0.221861	−	0.975078i	$-0.428787\pi$
$821$	364.296			0.443722			0.221861	+	0.975078i	$0.428787\pi$
$822$			680.053i			0.827315i
$823$	−1065.20			−1.29429			−0.647147	−	0.762365i	$-0.724038\pi$
$823$	−1065.20			−1.29429			−0.647147	+	0.762365i	$0.724038\pi$
$824$			402.475i			0.488441i
$825$			159.473i			0.193301i
$826$			521.160i			0.630944i
$827$			95.8650i			0.115919i	0.998319	+	0.0579595i	$0.0184594\pi$
$827$			95.8650i			0.115919i	−0.998319	+	0.0579595i	$0.981541\pi$
$828$	72.4722	+	134.834i	0.0875268	+	0.162843i
$829$	527.103			0.635830			0.317915	−	0.948119i	$-0.397017\pi$
$829$	527.103			0.635830			0.317915	+	0.948119i	$0.397017\pi$
$830$	217.084			0.261547
$831$	149.930			0.180421
$832$	0.304405			0.000365872
$833$			79.7768i			0.0957705i
$834$	−497.593			−0.596635
$835$		−	566.205i		−	0.678090i
$836$	107.573			0.128675
$837$	−273.521			−0.326787
$838$			639.950i			0.763664i
$839$		−	33.3890i		−	0.0397961i	−0.999802	−	0.0198981i	$-0.993666\pi$
$839$		−	33.3890i		−	0.0397961i	0.999802	−	0.0198981i	$-0.00633417\pi$
$840$	54.3288			0.0646771
$841$	−78.3101			−0.0931155
$842$		−	1200.58i		−	1.42587i
$843$		−	487.347i		−	0.578110i
$844$	−308.275			−0.365255
$845$		−	347.053i		−	0.410714i
$846$	−344.304			−0.406979
$847$		−	249.966i		−	0.295119i
$848$		−	1901.29i		−	2.24209i
$849$		−	118.911i		−	0.140061i
$850$			508.098i			0.597762i
$851$	−1002.53	+	538.850i	−1.17806	+	0.633197i
$852$	452.231			0.530788
$853$	40.2346			0.0471684			0.0235842	−	0.999722i	$-0.492492\pi$
$853$	40.2346			0.0471684			0.0235842	+	0.999722i	$0.492492\pi$
$854$	376.237			0.440559
$855$	75.3796			0.0881633
$856$		−	63.1124i		−	0.0737294i
$857$	521.982			0.609080			0.304540	−	0.952499i	$-0.401497\pi$
$857$	521.982			0.609080			0.304540	+	0.952499i	$0.401497\pi$
$858$		−	138.826i		−	0.161802i
$859$	−695.237			−0.809356			−0.404678	−	0.914459i	$-0.632616\pi$
$859$	−695.237			−0.809356			−0.404678	+	0.914459i	$0.632616\pi$
$860$	404.172			0.469967
$861$		−	70.1906i		−	0.0815222i
$862$			1028.96i			1.19369i
$863$	−1373.70			−1.59178			−0.795889	−	0.605443i	$-0.792996\pi$
$863$	−1373.70			−1.59178			−0.795889	+	0.605443i	$0.792996\pi$
$864$	166.198			0.192359
$865$		−	530.466i		−	0.613255i
$866$			727.412i			0.839968i
$867$	275.596			0.317873
$868$			308.971i			0.355958i
$869$	−502.103			−0.577793
$870$		−	318.325i		−	0.365890i
$871$			582.882i			0.669210i
$872$		−	563.889i		−	0.646661i
$873$		−	222.839i		−	0.255257i
$874$	−475.666	+	255.666i	−0.544240	+	0.292524i
$875$	302.746			0.345996
$876$	462.171			0.527593
$877$	−361.480			−0.412178			−0.206089	−	0.978533i	$-0.566074\pi$
$877$	−361.480			−0.412178			−0.206089	+	0.978533i	$0.566074\pi$
$878$	1019.76			1.16145
$879$		−	590.555i		−	0.671849i
$880$	274.212			0.311604
$881$			1338.45i			1.51924i	0.650369	+	0.759619i	$0.274614\pi$
$881$			1338.45i			1.51924i	−0.650369	+	0.759619i	$0.725386\pi$
$882$	52.3676			0.0593736
$883$	−1310.05			−1.48364			−0.741819	−	0.670601i	$-0.766036\pi$
$883$	−1310.05			−1.48364			−0.741819	+	0.670601i	$0.766036\pi$
$884$		−	157.799i		−	0.178506i
$885$			365.117i			0.412562i
$886$	1518.02			1.71334
$887$	447.735			0.504774			0.252387	−	0.967626i	$-0.418784\pi$
$887$	447.735			0.504774			0.252387	+	0.967626i	$0.418784\pi$
$888$			380.773i			0.428799i
$889$		−	234.160i		−	0.263397i
$890$	938.228			1.05419
$891$			46.3494i			0.0520195i
$892$	−161.118			−0.180625
$893$		−	433.330i		−	0.485252i
$894$		−	20.0646i		−	0.0224436i
$895$		−	107.709i		−	0.120346i
$896$			338.817i			0.378144i
$897$	117.711	+	219.000i	0.131227	+	0.244148i
$898$	−260.307			−0.289874
$899$	−1453.73			−1.61705
$900$	118.989			0.132210
$901$	1086.01			1.20534
$902$		−	196.704i		−	0.218076i
$903$	−312.840			−0.346446
$904$		−	459.312i		−	0.508088i
$905$	−715.414			−0.790513
$906$	956.403			1.05563
$907$			968.975i			1.06833i	0.845380	+	0.534165i	$0.179374\pi$
$907$			968.975i			1.06833i	−0.845380	+	0.534165i	$0.820626\pi$
$908$			655.819i			0.722267i
$909$	208.757			0.229656
$910$	−109.888			−0.120756
$911$		−	591.354i		−	0.649127i	−0.945864	−	0.324563i	$-0.894783\pi$
$911$		−	591.354i		−	0.649127i	0.945864	−	0.324563i	$-0.105217\pi$
$912$			325.381i			0.356778i
$913$	−167.994			−0.184002
$914$			822.916i			0.900345i
$915$	263.586			0.288073
$916$		−	542.330i		−	0.592063i
$917$			548.709i			0.598374i
$918$			147.674i			0.160865i
$919$			1600.58i			1.74165i	0.491593	+	0.870825i	$0.336415\pi$
$919$			1600.58i			1.74165i	−0.491593	+	0.870825i	$0.663585\pi$
$920$	−240.181	+	129.095i	−0.261067	+	0.140321i
$921$	467.756			0.507879
$922$	241.816			0.262273
$923$	734.523			0.795799
$924$	52.3566			0.0566630
$925$			884.716i			0.956450i
$926$	1110.08			1.19879
$927$			271.789i			0.293192i
$928$	883.319			0.951852
$929$	711.120			0.765469			0.382734	−	0.923858i	$-0.374982\pi$
$929$	711.120			0.765469			0.382734	+	0.923858i	$0.374982\pi$
$930$			606.743i			0.652412i
$931$			65.9080i			0.0707927i
$932$	−829.798			−0.890341
$933$	364.962			0.391170
$934$		−	1232.11i		−	1.31918i
$935$			156.629i			0.167518i
$936$	83.1792			0.0888666
$937$		−	1164.04i		−	1.24231i	−0.783689	−	0.621154i	$-0.786664\pi$
$937$		−	1164.04i		−	1.24231i	0.783689	−	0.621154i	$-0.213336\pi$
$938$	−616.179			−0.656907
$939$		−	521.383i		−	0.555254i
$940$			272.478i			0.289870i
$941$			1445.44i			1.53607i	0.640410	+	0.768033i	$0.278764\pi$
$941$			1445.44i			1.53607i	−0.640410	+	0.768033i	$0.721236\pi$
$942$			901.587i			0.957099i
$943$	166.786	+	310.304i	0.176867	+	0.329061i
$944$	−1576.05			−1.66955
$945$	36.6879			0.0388232
$946$	−876.713			−0.926758
$947$	732.422			0.773413			0.386706	−	0.922203i	$-0.373613\pi$
$947$	732.422			0.773413			0.386706	+	0.922203i	$0.373613\pi$
$948$			374.638i			0.395188i
$949$	750.668			0.791009
$950$			419.767i			0.441860i
$951$	355.110			0.373407
$952$	−133.954			−0.140708
$953$		−	562.719i		−	0.590471i	−0.955424	−	0.295236i	$-0.904602\pi$
$953$		−	562.719i		−	0.590471i	0.955424	−	0.295236i	$-0.0953982\pi$
$954$		−	712.886i		−	0.747260i
$955$	−391.164			−0.409596
$956$	100.959			0.105606
$957$			246.341i			0.257409i
$958$		−	903.132i		−	0.942726i
$959$	−416.570			−0.434380
$960$			0.225445i			0.000234838i
$961$	1809.88			1.88333
$962$		−	770.170i		−	0.800593i
$963$		−	42.6195i		−	0.0442570i
$964$			591.396i			0.613481i
$965$			233.597i			0.242069i
$966$	−231.511	+	124.435i	−0.239659	+	0.128815i
$967$	465.518			0.481404			0.240702	−	0.970599i	$-0.422622\pi$
$967$	465.518			0.481404			0.240702	+	0.970599i	$0.422622\pi$
$968$	419.720			0.433595
$969$	−185.857			−0.191803
$970$	−494.317			−0.509605
$971$		−	1455.59i		−	1.49906i	−0.661969	−	0.749531i	$-0.730279\pi$
$971$		−	1455.59i		−	1.49906i	0.661969	−	0.749531i	$-0.269721\pi$
$972$	34.5831			0.0355793
$973$		−	304.804i		−	0.313262i
$974$	304.176			0.312296
$975$	193.264			0.198220
$976$			1137.79i			1.16577i
$977$		−	66.0078i		−	0.0675618i	−0.999429	−	0.0337809i	$-0.989245\pi$
$977$		−	66.0078i		−	0.0675618i	0.999429	−	0.0337809i	$-0.0107548\pi$
$978$	439.260			0.449142
$979$	−726.063			−0.741637
$980$		−	41.4430i		−	0.0422888i
$981$		−	380.791i		−	0.388166i
$982$	−135.869			−0.138359
$983$		−	423.670i		−	0.430997i	−0.976504	−	0.215498i	$-0.930862\pi$
$983$		−	423.670i		−	0.430997i	0.976504	−	0.215498i	$-0.0691376\pi$
$984$	117.858			0.119774
$985$			158.519i			0.160933i
$986$			784.866i			0.796010i
$987$		−	210.906i		−	0.213683i
$988$		−	130.367i		−	0.131950i
$989$	1383.03	−	743.366i	1.39841	−	0.751634i
$990$	102.815			0.103854
$991$	754.405			0.761256			0.380628	−	0.924728i	$-0.375708\pi$
$991$	754.405			0.761256			0.380628	+	0.924728i	$0.375708\pi$
$992$	−1683.65			−1.69723
$993$	−835.922			−0.841815
$994$			776.482i			0.781169i
$995$	1050.96			1.05624
$996$			125.347i			0.125850i
$997$	−1021.22			−1.02429			−0.512144	−	0.858899i	$-0.671149\pi$
$997$	−1021.22			−1.02429			−0.512144	+	0.858899i	$0.671149\pi$
$998$	365.368			0.366100
$999$			257.134i			0.257392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.11	✓	48
23.22	odd	2	inner	483.3.f.a.22.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.11	✓	48	1.1	even	1	trivial
483.3.f.a.22.12	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)

\(f(q)\)	\(=\)	\(q-2.49369 q^{2} +1.73205 q^{3} +2.21850 q^{4} +2.66866i q^{5} -4.31920 q^{6} -2.64575i q^{7} +4.44250 q^{8} +3.00000 q^{9} -6.65481i q^{10} +5.14993i q^{11} +3.84256 q^{12} +6.24116 q^{13} +6.59769i q^{14} +4.62225i q^{15} -19.9523 q^{16} -11.3967i q^{17} -7.48108 q^{18} -9.41543i q^{19} +5.92043i q^{20} -4.58258i q^{21} -12.8423i q^{22} +(10.8890 + 20.2590i) q^{23} +7.69464 q^{24} +17.8783 q^{25} -15.5635 q^{26} +5.19615 q^{27} -5.86961i q^{28} +27.6168 q^{29} -11.5265i q^{30} -52.6391 q^{31} +31.9848 q^{32} +8.91994i q^{33} +28.4198i q^{34} +7.06060 q^{35} +6.65551 q^{36} +49.4855i q^{37} +23.4792i q^{38} +10.8100 q^{39} +11.8555i q^{40} +15.3168 q^{41} +11.4275i q^{42} -68.2674i q^{43} +11.4251i q^{44} +8.00597i q^{45} +(-27.1539 - 50.5198i) q^{46} +46.0234 q^{47} -34.5583 q^{48} -7.00000 q^{49} -44.5829 q^{50} -19.7396i q^{51} +13.8461 q^{52} +95.2919i q^{53} -12.9576 q^{54} -13.7434 q^{55} -11.7538i q^{56} -16.3080i q^{57} -68.8679 q^{58} +78.9912 q^{59} +10.2545i q^{60} -57.0256i q^{61} +131.266 q^{62} -7.93725i q^{63} +0.0487738 q^{64} +16.6555i q^{65} -22.2436i q^{66} +93.3931i q^{67} -25.2836i q^{68} +(18.8604 + 35.0897i) q^{69} -17.6070 q^{70} +117.690 q^{71} +13.3275 q^{72} +120.277 q^{73} -123.402i q^{74} +30.9661 q^{75} -20.8882i q^{76} +13.6254 q^{77} -26.9569 q^{78} +97.4970i q^{79} -53.2457i q^{80} +9.00000 q^{81} -38.1955 q^{82} +32.6207i q^{83} -10.1665i q^{84} +30.4138 q^{85} +170.238i q^{86} +47.8338 q^{87} +22.8786i q^{88} +140.985i q^{89} -19.9644i q^{90} -16.5126i q^{91} +(24.1574 + 44.9448i) q^{92} -91.1736 q^{93} -114.768 q^{94} +25.1265 q^{95} +55.3993 q^{96} -74.2797i q^{97} +17.4559 q^{98} +15.4498i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36}+ \cdots - 28 q^{98}+O(q^{100}) \) 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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