LMFDB - Embedded newform 547.3.b.b.546.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,3,Mod(546,547)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("547.546");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	547.b (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:	$14.9046704605$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			546.9
Character	$\chi$	$=$	547.546
Dual form			547.3.b.b.546.80

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.42438i q^{2} +4.48969i q^{3} -7.72636 q^{4} +7.63002i q^{5} +15.3744 q^{6} +10.8574i q^{7} +12.7605i q^{8} -11.1573 q^{9} +O(q^{10})$	\(q-3.42438i q^{2} +4.48969i q^{3} -7.72636 q^{4} +7.63002i q^{5} +15.3744 q^{6} +10.8574i q^{7} +12.7605i q^{8} -11.1573 q^{9} +26.1281 q^{10} -5.76209 q^{11} -34.6890i q^{12} +6.53683 q^{13} +37.1799 q^{14} -34.2564 q^{15} +12.7912 q^{16} -17.5280i q^{17} +38.2069i q^{18} +25.4773 q^{19} -58.9523i q^{20} -48.7464 q^{21} +19.7316i q^{22} +23.4417i q^{23} -57.2905 q^{24} -33.2172 q^{25} -22.3846i q^{26} -9.68572i q^{27} -83.8883i q^{28} -42.3678 q^{29} +117.307i q^{30} -2.41221i q^{31} +7.23999i q^{32} -25.8700i q^{33} -60.0223 q^{34} -82.8423 q^{35} +86.2055 q^{36} -9.97535i q^{37} -87.2438i q^{38} +29.3484i q^{39} -97.3625 q^{40} -56.0380i q^{41} +166.926i q^{42} +27.7638i q^{43} +44.5200 q^{44} -85.1306i q^{45} +80.2733 q^{46} -5.88515 q^{47} +57.4285i q^{48} -68.8835 q^{49} +113.748i q^{50} +78.6951 q^{51} -50.5059 q^{52} +22.5976 q^{53} -33.1676 q^{54} -43.9649i q^{55} -138.546 q^{56} +114.385i q^{57} +145.083i q^{58} +97.5650i q^{59} +264.677 q^{60} -73.3324i q^{61} -8.26031 q^{62} -121.140i q^{63} +75.9572 q^{64} +49.8762i q^{65} -88.5887 q^{66} -79.4893 q^{67} +135.427i q^{68} -105.246 q^{69} +283.683i q^{70} -9.75447i q^{71} -142.373i q^{72} +102.536 q^{73} -34.1594 q^{74} -149.135i q^{75} -196.847 q^{76} -62.5615i q^{77} +100.500 q^{78} -107.073i q^{79} +97.5970i q^{80} -56.9300 q^{81} -191.895 q^{82} -120.146i q^{83} +376.633 q^{84} +133.739 q^{85} +95.0737 q^{86} -190.218i q^{87} -73.5270i q^{88} +139.959i q^{89} -291.519 q^{90} +70.9731i q^{91} -181.119i q^{92} +10.8301 q^{93} +20.1530i q^{94} +194.392i q^{95} -32.5053 q^{96} +103.867 q^{97} +235.883i q^{98} +64.2896 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) $ 88 * q - 192 * q^4 - 306 * q^9	$ 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) $ 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$		−	3.42438i		−	1.71219i	−0.516820	−	0.856094i	$-0.672884\pi$
$2$		−	3.42438i		−	1.71219i	0.516820	−	0.856094i	$-0.327116\pi$
$3$			4.48969i			1.49656i	0.663381	+	0.748282i	$0.269121\pi$
$3$			4.48969i			1.49656i	−0.663381	+	0.748282i	$0.730879\pi$
$4$	−7.72636			−1.93159
$5$			7.63002i			1.52600i	0.646396	+	0.763002i	$0.276275\pi$
$5$			7.63002i			1.52600i	−0.646396	+	0.763002i	$0.723725\pi$
$6$	15.3744			2.56240
$7$			10.8574i			1.55106i	0.631311	+	0.775530i	$0.282517\pi$
$7$			10.8574i			1.55106i	−0.631311	+	0.775530i	$0.717483\pi$
$8$			12.7605i			1.59506i
$9$	−11.1573			−1.23970
$10$	26.1281			2.61281
$11$	−5.76209			−0.523827			−0.261913	−	0.965091i	$-0.584353\pi$
$11$	−5.76209			−0.523827			−0.261913	+	0.965091i	$0.584353\pi$
$12$		−	34.6890i		−	2.89075i
$13$	6.53683			0.502833			0.251417	−	0.967879i	$-0.419104\pi$
$13$	6.53683			0.502833			0.251417	+	0.967879i	$0.419104\pi$
$14$	37.1799			2.65571
$15$	−34.2564			−2.28376
$16$	12.7912			0.799449
$17$		−	17.5280i		−	1.03106i	−0.856873	−	0.515528i	$-0.827596\pi$
$17$		−	17.5280i		−	1.03106i	0.856873	−	0.515528i	$-0.172404\pi$
$18$			38.2069i			2.12260i
$19$	25.4773			1.34091			0.670455	−	0.741951i	$-0.266099\pi$
$19$	25.4773			1.34091			0.670455	+	0.741951i	$0.266099\pi$
$20$		−	58.9523i		−	2.94761i
$21$	−48.7464			−2.32126
$22$			19.7316i			0.896890i
$23$			23.4417i			1.01921i	0.860410	+	0.509603i	$0.170208\pi$
$23$			23.4417i			1.01921i	−0.860410	+	0.509603i	$0.829792\pi$
$24$	−57.2905			−2.38710
$25$	−33.2172			−1.32869
$26$		−	22.3846i		−	0.860946i
$27$		−	9.68572i		−	0.358730i
$28$		−	83.8883i		−	2.99601i
$29$	−42.3678			−1.46096			−0.730480	−	0.682935i	$-0.760703\pi$
$29$	−42.3678			−1.46096			−0.730480	+	0.682935i	$0.760703\pi$
$30$			117.307i			3.91023i
$31$		−	2.41221i		−	0.0778131i	−0.999243	−	0.0389066i	$-0.987613\pi$
$31$		−	2.41221i		−	0.0778131i	0.999243	−	0.0389066i	$-0.0123875\pi$
$32$			7.23999i			0.226250i
$33$		−	25.8700i		−	0.783940i
$34$	−60.0223			−1.76536
$35$	−82.8423			−2.36692
$36$	86.2055			2.39460
$37$		−	9.97535i		−	0.269604i	−0.990873	−	0.134802i	$-0.956960\pi$
$37$		−	9.97535i		−	0.269604i	0.990873	−	0.134802i	$-0.0430399\pi$
$38$		−	87.2438i		−	2.29589i
$39$			29.3484i			0.752522i
$40$	−97.3625			−2.43406
$41$		−	56.0380i		−	1.36678i	−0.730053	−	0.683391i	$-0.760505\pi$
$41$		−	56.0380i		−	1.36678i	0.730053	−	0.683391i	$-0.239495\pi$
$42$			166.926i			3.97443i
$43$			27.7638i			0.645669i	0.946455	+	0.322835i	$0.104636\pi$
$43$			27.7638i			0.645669i	−0.946455	+	0.322835i	$0.895364\pi$
$44$	44.5200			1.01182
$45$		−	85.1306i		−	1.89179i
$46$	80.2733			1.74507
$47$	−5.88515			−0.125216			−0.0626080	−	0.998038i	$-0.519942\pi$
$47$	−5.88515			−0.125216			−0.0626080	+	0.998038i	$0.519942\pi$
$48$			57.4285i			1.19643i
$49$	−68.8835			−1.40579
$50$			113.748i			2.27496i
$51$	78.6951			1.54304
$52$	−50.5059			−0.971268
$53$	22.5976			0.426369			0.213185	−	0.977012i	$-0.431616\pi$
$53$	22.5976			0.426369			0.213185	+	0.977012i	$0.431616\pi$
$54$	−33.1676			−0.614214
$55$		−	43.9649i		−	0.799362i
$56$	−138.546			−2.47403
$57$			114.385i			2.00676i
$58$			145.083i			2.50144i
$59$			97.5650i			1.65364i	0.562464	+	0.826822i	$0.309854\pi$
$59$			97.5650i			1.65364i	−0.562464	+	0.826822i	$0.690146\pi$
$60$	264.677			4.41129
$61$		−	73.3324i		−	1.20217i	−0.799185	−	0.601085i	$-0.794735\pi$
$61$		−	73.3324i		−	1.20217i	0.799185	−	0.601085i	$-0.205265\pi$
$62$	−8.26031			−0.133231
$63$		−	121.140i		−	1.92285i
$64$	75.9572			1.18683
$65$			49.8762i			0.767326i
$66$	−88.5887			−1.34225
$67$	−79.4893			−1.18641			−0.593204	−	0.805052i	$-0.702137\pi$
$67$	−79.4893			−1.18641			−0.593204	+	0.805052i	$0.702137\pi$
$68$			135.427i			1.99158i
$69$	−105.246			−1.52531
$70$			283.683i			4.05262i
$71$		−	9.75447i		−	0.137387i	−0.997638	−	0.0686934i	$-0.978117\pi$
$71$		−	9.75447i		−	0.137387i	0.997638	−	0.0686934i	$-0.0218830\pi$
$72$		−	142.373i		−	1.97740i
$73$	102.536			1.40460			0.702301	−	0.711880i	$-0.252156\pi$
$73$	102.536			1.40460			0.702301	+	0.711880i	$0.252156\pi$
$74$	−34.1594			−0.461613
$75$		−	149.135i		−	1.98847i
$76$	−196.847			−2.59009
$77$		−	62.5615i		−	0.812487i
$78$	100.500			1.28846
$79$		−	107.073i		−	1.35535i	−0.735359	−	0.677677i	$-0.762987\pi$
$79$		−	107.073i		−	1.35535i	0.735359	−	0.677677i	$-0.237013\pi$
$80$			97.5970i			1.21996i
$81$	−56.9300			−0.702840
$82$	−191.895			−2.34019
$83$		−	120.146i		−	1.44755i	−0.690037	−	0.723774i	$-0.742406\pi$
$83$		−	120.146i		−	1.44755i	0.690037	−	0.723774i	$-0.257594\pi$
$84$	376.633			4.48372
$85$	133.739			1.57340
$86$	95.0737			1.10551
$87$		−	190.218i		−	2.18642i
$88$		−	73.5270i		−	0.835534i
$89$			139.959i			1.57257i	0.617863	+	0.786285i	$0.287998\pi$
$89$			139.959i			1.57257i	−0.617863	+	0.786285i	$0.712002\pi$
$90$	−291.519			−3.23910
$91$			70.9731i			0.779925i
$92$		−	181.119i		−	1.96869i
$93$	10.8301			0.116452
$94$			20.1530i			0.214393i
$95$			194.392i			2.04623i
$96$	−32.5053			−0.338597
$97$	103.867			1.07079			0.535397	−	0.844601i	$-0.320162\pi$
$97$	103.867			1.07079			0.535397	+	0.844601i	$0.320162\pi$
$98$			235.883i			2.40697i
$99$	64.2896			0.649389
$100$	256.648			2.56648
$101$			119.526i			1.18343i	0.806148	+	0.591714i	$0.201548\pi$
$101$			119.526i			1.18343i	−0.806148	+	0.591714i	$0.798452\pi$
$102$		−	269.482i		−	2.64198i
$103$			30.3738i			0.294892i	0.989070	+	0.147446i	$0.0471052\pi$
$103$			30.3738i			0.294892i	−0.989070	+	0.147446i	$0.952895\pi$
$104$			83.4130i			0.802048i
$105$		−	371.936i		−	3.54225i
$106$		−	77.3826i		−	0.730024i
$107$			42.5360i			0.397533i	0.980047	+	0.198767i	$0.0636935\pi$
$107$			42.5360i			0.397533i	−0.980047	+	0.198767i	$0.936306\pi$
$108$			74.8354i			0.692920i
$109$		−	35.9402i		−	0.329727i	−0.986316	−	0.164863i	$-0.947282\pi$
$109$		−	35.9402i		−	0.329727i	0.986316	−	0.164863i	$-0.0527183\pi$
$110$	−150.552			−1.36866
$111$	44.7863			0.403480
$112$			138.879i			1.23999i
$113$	164.538			1.45609			0.728045	−	0.685530i	$-0.240429\pi$
$113$	164.538			1.45609			0.728045	+	0.685530i	$0.240429\pi$
$114$	391.698			3.43594
$115$	−178.861			−1.55531
$116$	327.349			2.82197
$117$	−72.9336			−0.623364
$118$	334.099			2.83135
$119$	190.308			1.59923
$120$		−	437.128i		−	3.64273i
$121$	−87.7983			−0.725606
$122$	−251.118			−2.05834
$123$	251.593			2.04548
$124$			18.6376i			0.150303i
$125$		−	62.6974i		−	0.501579i
$126$	−414.828			−3.29229
$127$	62.0815			0.488830			0.244415	−	0.969671i	$-0.421404\pi$
$127$	62.0815			0.488830			0.244415	+	0.969671i	$0.421404\pi$
$128$		−	231.146i		−	1.80583i
$129$	−124.651			−0.966285
$130$	170.795			1.31381
$131$	−168.998			−1.29006			−0.645029	−	0.764158i	$-0.723155\pi$
$131$	−168.998			−1.29006			−0.645029	+	0.764158i	$0.723155\pi$
$132$			199.881i			1.51425i
$133$			276.617i			2.07983i
$134$			272.201i			2.03135i
$135$	73.9022			0.547424
$136$	223.665			1.64459
$137$	−256.786			−1.87435			−0.937174	−	0.348864i	$-0.886568\pi$
$137$	−256.786			−1.87435			−0.937174	+	0.348864i	$0.886568\pi$
$138$			360.402i			2.61161i
$139$	214.455			1.54284			0.771421	−	0.636325i	$-0.219546\pi$
$139$	214.455			1.54284			0.771421	+	0.636325i	$0.219546\pi$
$140$	640.069			4.57192
$141$		−	26.4225i		−	0.187394i
$142$	−33.4030			−0.235232
$143$	−37.6659			−0.263398
$144$	−142.715			−0.991079
$145$		−	323.267i		−	2.22943i
$146$		−	351.122i		−	2.40494i
$147$		−	309.266i		−	2.10385i
$148$			77.0732i			0.520765i
$149$	−120.198			−0.806699			−0.403349	−	0.915046i	$-0.632154\pi$
$149$	−120.198			−0.806699			−0.403349	+	0.915046i	$0.632154\pi$
$150$	−510.694			−3.40463
$151$			148.695i			0.984738i	0.870387	+	0.492369i	$0.163869\pi$
$151$			148.695i			0.984738i	−0.870387	+	0.492369i	$0.836131\pi$
$152$			325.102i			2.13883i
$153$			195.565i			1.27820i
$154$	−214.234			−1.39113
$155$	18.4052			0.118743
$156$		−	226.756i		−	1.45356i
$157$	−102.736			−0.654372			−0.327186	−	0.944960i	$-0.606100\pi$
$157$	−102.736			−0.654372			−0.327186	+	0.944960i	$0.606100\pi$
$158$	−366.658			−2.32062
$159$			101.456i			0.638089i
$160$	−55.2412			−0.345258
$161$	−254.517			−1.58085
$162$			194.950i			1.20339i
$163$			289.944i			1.77880i	0.457132	+	0.889399i	$0.348877\pi$
$163$			289.944i			1.77880i	−0.457132	+	0.889399i	$0.651123\pi$
$164$			432.970i			2.64006i
$165$	197.389			1.19630
$166$	−411.427			−2.47847
$167$	178.169			1.06688			0.533439	−	0.845839i	$-0.320899\pi$
$167$	178.169			1.06688			0.533439	+	0.845839i	$0.320899\pi$
$168$		−	622.027i		−	3.70254i
$169$	−126.270			−0.747159
$170$		−	457.972i		−	2.69395i
$171$	−284.258			−1.66233
$172$		−	214.513i		−	1.24717i
$173$			234.467i			1.35530i	0.735383	+	0.677651i	$0.237002\pi$
$173$			234.467i			1.35530i	−0.735383	+	0.677651i	$0.762998\pi$
$174$	−651.380			−3.74356
$175$		−	360.653i		−	2.06087i
$176$	−73.7040			−0.418773
$177$	−438.037			−2.47478
$178$	479.272			2.69254
$179$	−207.199			−1.15754			−0.578769	−	0.815491i	$-0.696467\pi$
$179$	−207.199			−1.15754			−0.578769	+	0.815491i	$0.696467\pi$
$180$			657.750i			3.65416i
$181$	275.735			1.52340			0.761700	−	0.647930i	$-0.224365\pi$
$181$	275.735			1.52340			0.761700	+	0.647930i	$0.224365\pi$
$182$	243.039			1.33538
$183$	329.240			1.79912
$184$	−299.127			−1.62569
$185$	76.1122			0.411417
$186$		−	37.0862i		−	0.199388i
$187$			100.998i			0.540095i
$188$	45.4708			0.241866
$189$	105.162			0.556412
$190$	665.672			3.50354
$191$	18.1998			0.0952871			0.0476436	−	0.998864i	$-0.484829\pi$
$191$	18.1998			0.0952871			0.0476436	+	0.998864i	$0.484829\pi$
$192$			341.024i			1.77617i
$193$	133.326			0.690807			0.345404	−	0.938454i	$-0.387742\pi$
$193$	133.326			0.690807			0.345404	+	0.938454i	$0.387742\pi$
$194$		−	355.680i		−	1.83340i
$195$	−223.929			−1.14835
$196$	532.219			2.71540
$197$		−	17.1856i		−	0.0872365i	−0.999048	−	0.0436182i	$-0.986111\pi$
$197$		−	17.1856i		−	0.0872365i	0.999048	−	0.0436182i	$-0.0138885\pi$
$198$		−	220.152i		−	1.11188i
$199$	−49.8109			−0.250306			−0.125153	−	0.992137i	$-0.539942\pi$
$199$	−49.8109			−0.250306			−0.125153	+	0.992137i	$0.539942\pi$
$200$		−	423.867i		−	2.11933i
$201$		−	356.882i		−	1.77553i
$202$	409.303			2.02625
$203$		−	460.005i		−	2.26603i
$204$	−608.027			−2.98052
$205$	427.571			2.08571
$206$	104.011			0.504910
$207$		−	261.547i		−	1.26351i
$208$	83.6139			0.401990
$209$	−146.802			−0.702404
$210$	−1273.65			−6.06500
$211$			225.495i			1.06870i	0.845264	+	0.534349i	$0.179443\pi$
$211$			225.495i			1.06870i	−0.845264	+	0.534349i	$0.820557\pi$
$212$	−174.597			−0.823570
$213$	43.7945			0.205608
$214$	145.659			0.680651
$215$	−211.838			−0.985294
$216$	123.594			0.572196
$217$	26.1903			0.120693
$218$	−123.073			−0.564554
$219$			460.355i			2.10208i
$220$			339.689i			1.54404i
$221$		−	114.577i		−	0.518450i
$222$		−	153.365i		−	0.690834i
$223$		−	12.4060i		−	0.0556325i	−0.999613	−	0.0278162i	$-0.991145\pi$
$223$		−	12.4060i		−	0.0556325i	0.999613	−	0.0278162i	$-0.00885533\pi$
$224$	−78.6076			−0.350927
$225$	370.615			1.64718
$226$		−	563.441i		−	2.49310i
$227$	−71.0247			−0.312884			−0.156442	−	0.987687i	$-0.550002\pi$
$227$	−71.0247			−0.312884			−0.156442	+	0.987687i	$0.550002\pi$
$228$		−	883.780i		−	3.87623i
$229$			284.294i			1.24146i	0.784026	+	0.620728i	$0.213163\pi$
$229$			284.294i			1.24146i	−0.784026	+	0.620728i	$0.786837\pi$
$230$			612.487i			2.66299i
$231$	280.882			1.21594
$232$		−	540.633i		−	2.33031i
$233$	−336.290			−1.44330			−0.721652	−	0.692256i	$-0.756617\pi$
$233$	−336.290			−1.44330			−0.721652	+	0.692256i	$0.756617\pi$
$234$			249.752i			1.06732i
$235$		−	44.9038i		−	0.191080i
$236$		−	753.822i		−	3.19416i
$237$	480.725			2.02837
$238$		−	651.688i		−	2.73818i
$239$	18.3550			0.0767990			0.0383995	−	0.999262i	$-0.487774\pi$
$239$	18.3550			0.0767990			0.0383995	+	0.999262i	$0.487774\pi$
$240$	−438.180			−1.82575
$241$		−	236.332i		−	0.980629i	−0.871546	−	0.490314i	$-0.836882\pi$
$241$		−	236.332i		−	0.980629i	0.871546	−	0.490314i	$-0.163118\pi$
$242$			300.654i			1.24237i
$243$		−	342.770i		−	1.41057i
$244$			566.592i			2.32210i
$245$		−	525.583i		−	2.14524i
$246$		−	861.551i		−	3.50224i
$247$	166.541			0.674254
$248$	30.7809			0.124116
$249$	539.421			2.16635
$250$	−214.700			−0.858798
$251$		−	93.3726i		−	0.372002i	−0.982550	−	0.186001i	$-0.940447\pi$
$251$		−	93.3726i		−	0.372002i	0.982550	−	0.186001i	$-0.0595528\pi$
$252$			935.969i			3.71416i
$253$		−	135.073i		−	0.533887i
$254$		−	212.590i		−	0.836970i
$255$			600.445i			2.35469i
$256$	−487.703			−1.90509
$257$			228.190i			0.887897i	0.896052	+	0.443949i	$0.146423\pi$
$257$			228.190i			0.887897i	−0.896052	+	0.443949i	$0.853577\pi$
$258$			426.851i			1.65446i
$259$	108.307			0.418172
$260$		−	385.361i		−	1.48216i
$261$	472.711			1.81116
$262$			578.711i			2.20882i
$263$	489.301			1.86046			0.930230	−	0.366978i	$-0.119608\pi$
$263$	489.301			1.86046			0.930230	+	0.366978i	$0.119608\pi$
$264$	330.113			1.25043
$265$			172.420i			0.650641i
$266$	947.242			3.56106
$267$	−628.372			−2.35345
$268$	614.163			2.29165
$269$	−149.254			−0.554847			−0.277423	−	0.960748i	$-0.589480\pi$
$269$	−149.254			−0.554847			−0.277423	+	0.960748i	$0.589480\pi$
$270$		−	253.069i		−	0.937293i
$271$			35.8215i			0.132183i	0.997814	+	0.0660914i	$0.0210529\pi$
$271$			35.8215i			0.132183i	−0.997814	+	0.0660914i	$0.978947\pi$
$272$		−	224.203i		−	0.824277i
$273$	−318.647			−1.16721
$274$			879.331i			3.20924i
$275$	191.401			0.696002
$276$	813.169			2.94627
$277$	−138.817			−0.501144			−0.250572	−	0.968098i	$-0.580619\pi$
$277$	−138.817			−0.501144			−0.250572	+	0.968098i	$0.580619\pi$
$278$		−	734.375i		−	2.64164i
$279$			26.9138i			0.0964651i
$280$		−	1057.11i		−	3.77538i
$281$		−	108.226i		−	0.385147i	−0.981283	−	0.192574i	$-0.938317\pi$
$281$		−	108.226i		−	0.385147i	0.981283	−	0.192574i	$-0.0616835\pi$
$282$	−90.4807			−0.320853
$283$			392.389i			1.38653i	0.720681	+	0.693267i	$0.243829\pi$
$283$			392.389i			1.38653i	−0.720681	+	0.693267i	$0.756171\pi$
$284$			75.3665i			0.265375i
$285$	−872.760			−3.06232
$286$			128.982i			0.450986i
$287$	608.428			2.11996
$288$		−	80.7789i		−	0.280482i
$289$	−18.2294			−0.0630775
$290$	−1106.99			−3.81720
$291$			466.330i			1.60251i
$292$	−792.230			−2.71312
$293$	335.288			1.14433			0.572164	−	0.820139i	$-0.306104\pi$
$293$	335.288			1.14433			0.572164	+	0.820139i	$0.306104\pi$
$294$	−1059.04			−3.60219
$295$	−744.423			−2.52347
$296$	127.290			0.430034
$297$			55.8100i			0.187913i
$298$			411.604i			1.38122i
$299$			153.235i			0.512491i
$300$			1152.27i			3.84090i
$301$	−301.443			−1.00147
$302$	509.189			1.68606
$303$	−536.635			−1.77107
$304$	325.885			1.07199
$305$	559.528			1.83452
$306$	669.689			2.18853
$307$		−	77.6171i		−	0.252824i	−0.991978	−	0.126412i	$-0.959654\pi$
$307$		−	77.6171i		−	0.252824i	0.991978	−	0.126412i	$-0.0403462\pi$
$308$			483.372i			1.56939i
$309$	−136.369			−0.441324
$310$		−	63.0263i		−	0.203311i
$311$	−335.941			−1.08020			−0.540098	−	0.841602i	$-0.681613\pi$
$311$	−335.941			−1.08020			−0.540098	+	0.841602i	$0.681613\pi$
$312$	−374.499			−1.20032
$313$	−553.023			−1.76685			−0.883423	−	0.468576i	$-0.844767\pi$
$313$	−553.023			−1.76685			−0.883423	+	0.468576i	$0.844767\pi$
$314$			351.808i			1.12041i
$315$	924.299			2.93428
$316$			827.285i			2.61799i
$317$	130.901			0.412938			0.206469	−	0.978453i	$-0.433803\pi$
$317$	130.901			0.412938			0.206469	+	0.978453i	$0.433803\pi$
$318$	347.424			1.09253
$319$	244.127			0.765289
$320$			579.555i			1.81111i
$321$	−190.974			−0.594933
$322$			871.561i			2.70671i
$323$		−	446.565i		−	1.38255i
$324$	439.862			1.35760
$325$	−217.135			−0.668109
$326$	992.878			3.04564
$327$	161.360			0.493457
$328$	715.071			2.18009
$329$		−	63.8976i		−	0.194217i
$330$		−	675.934i		−	2.04828i
$331$			457.276i			1.38150i	0.723094	+	0.690750i	$0.242719\pi$
$331$			457.276i			1.38150i	−0.723094	+	0.690750i	$0.757281\pi$
$332$			928.295i			2.79607i
$333$			111.298i			0.334229i
$334$		−	610.116i		−	1.82670i
$335$		−	606.505i		−	1.81046i
$336$	−623.525			−1.85573
$337$		−	31.4149i		−	0.0932194i	−0.998913	−	0.0466097i	$-0.985158\pi$
$337$		−	31.4149i		−	0.0932194i	0.998913	−	0.0466097i	$-0.0148417\pi$
$338$			432.395i			1.27928i
$339$			738.725i			2.17913i
$340$	−1033.31			−3.03916
$341$			13.8994i			0.0407606i
$342$			973.407i			2.84622i
$343$		−	215.884i		−	0.629398i
$344$	−354.279			−1.02988
$345$		−	803.030i		−	2.32762i
$346$	802.905			2.32053
$347$	128.618			0.370657			0.185329	−	0.982677i	$-0.440665\pi$
$347$	128.618			0.370657			0.185329	+	0.982677i	$0.440665\pi$
$348$			1469.70i			4.22326i
$349$	249.103			0.713763			0.356882	−	0.934150i	$-0.383840\pi$
$349$	249.103			0.713763			0.356882	+	0.934150i	$0.383840\pi$
$350$	−1235.01			−3.52861
$351$		−	63.3139i		−	0.180382i
$352$		−	41.7175i		−	0.118516i
$353$	127.079			0.359998			0.179999	−	0.983667i	$-0.442391\pi$
$353$	127.079			0.359998			0.179999	+	0.983667i	$0.442391\pi$
$354$			1500.00i			4.23730i
$355$	74.4268			0.209653
$356$		−	1081.37i		−	3.03756i
$357$			854.426i			2.39335i
$358$			709.529i			1.98192i
$359$		−	425.481i		−	1.18518i	−0.805502	−	0.592592i	$-0.798104\pi$
$359$		−	425.481i		−	1.18518i	0.805502	−	0.592592i	$-0.201896\pi$
$360$	1086.31			3.01752
$361$	288.091			0.798037
$362$		−	944.222i		−	2.60835i
$363$		−	394.187i		−	1.08591i
$364$		−	548.364i		−	1.50649i
$365$			782.351i			2.14343i
$366$		−	1127.44i		−	3.08044i
$367$	98.4348			0.268215			0.134107	−	0.990967i	$-0.457183\pi$
$367$	98.4348			0.268215			0.134107	+	0.990967i	$0.457183\pi$
$368$			299.848i			0.814803i
$369$			625.234i			1.69440i
$370$		−	260.637i		−	0.704424i
$371$			245.351i			0.661324i
$372$	−83.6770			−0.224938
$373$			90.9841i			0.243925i	0.992535	+	0.121963i	$0.0389188\pi$
$373$			90.9841i			0.243925i	−0.992535	+	0.121963i	$0.961081\pi$
$374$	345.854			0.924744
$375$	281.492			0.750645
$376$		−	75.0972i		−	0.199727i
$377$	−276.951			−0.734619
$378$		−	360.114i		−	0.952683i
$379$	372.012			0.981562			0.490781	−	0.871283i	$-0.336712\pi$
$379$	372.012			0.981562			0.490781	+	0.871283i	$0.336712\pi$
$380$		−	1501.94i		−	3.95248i
$381$			278.727i			0.731566i
$382$		−	62.3231i		−	0.163150i
$383$	636.063			1.66074			0.830370	−	0.557213i	$-0.188129\pi$
$383$	636.063			1.66074			0.830370	+	0.557213i	$0.188129\pi$
$384$	1037.77			2.70254
$385$	477.345			1.23986
$386$		−	456.558i		−	1.18279i
$387$		−	309.770i		−	0.800438i
$388$	−802.513			−2.06833
$389$		−	3.96814i		−	0.0102009i	−0.999987	−	0.00510044i	$-0.998376\pi$
$389$		−	3.96814i		−	0.0102009i	0.999987	−	0.00510044i	$-0.00162353\pi$
$390$			766.816i			1.96619i
$391$	410.886			1.05086
$392$		−	878.985i		−	2.24231i
$393$		−	758.747i		−	1.93065i
$394$	−58.8499			−0.149365
$395$	816.969			2.06828
$396$	−496.724			−1.25435
$397$			50.9260i			0.128277i	0.997941	+	0.0641385i	$0.0204299\pi$
$397$			50.9260i			0.128277i	−0.997941	+	0.0641385i	$0.979570\pi$
$398$			170.571i			0.428571i
$399$	−1241.93			−3.11260
$400$	−424.887			−1.06222
$401$	59.4856			0.148343			0.0741716	−	0.997245i	$-0.476369\pi$
$401$	59.4856			0.148343			0.0741716	+	0.997245i	$0.476369\pi$
$402$	−1222.10			−3.04005
$403$		−	15.7682i		−	0.0391270i
$404$		−	923.502i		−	2.28590i
$405$		−	434.377i		−	1.07254i
$406$	−1575.23			−3.87988
$407$			57.4789i			0.141226i
$408$			1004.19i			2.46124i
$409$	444.130			1.08589			0.542946	−	0.839768i	$-0.317309\pi$
$409$	444.130			1.08589			0.542946	+	0.839768i	$0.317309\pi$
$410$		−	1464.17i		−	3.57113i
$411$		−	1152.89i		−	2.80508i
$412$		−	234.679i		−	0.569610i
$413$	−1059.30			−2.56490
$414$	−895.636			−2.16337
$415$	916.720			2.20896
$416$			47.3266i			0.113766i
$417$			962.836i			2.30896i
$418$			502.707i			1.20265i
$419$	−321.018			−0.766152			−0.383076	−	0.923717i	$-0.625135\pi$
$419$	−321.018			−0.766152			−0.383076	+	0.923717i	$0.625135\pi$
$420$			2873.71i			6.84218i
$421$			121.349i			0.288239i	0.989560	+	0.144119i	$0.0460349\pi$
$421$			121.349i			0.288239i	−0.989560	+	0.144119i	$0.953965\pi$
$422$	772.181			1.82981
$423$	65.6626			0.155231
$424$			288.355i			0.680083i
$425$			582.230i			1.36995i
$426$		−	149.969i		−	0.352040i
$427$	796.200			1.86464
$428$		−	328.649i		−	0.767871i
$429$		−	169.108i		−	0.394191i
$430$			725.414i			1.68701i
$431$		−	421.947i		−	0.978995i	−0.872005	−	0.489498i	$-0.837180\pi$
$431$		−	421.947i		−	0.978995i	0.872005	−	0.489498i	$-0.162820\pi$
$432$		−	123.892i		−	0.286787i
$433$			578.984i			1.33714i	0.743647	+	0.668572i	$0.233094\pi$
$433$			578.984i			1.33714i	−0.743647	+	0.668572i	$0.766906\pi$
$434$		−	89.6856i		−	0.206649i
$435$	1451.37			3.33648
$436$			277.687i			0.636897i
$437$			597.231i			1.36666i
$438$	1576.43			3.59915
$439$	745.262			1.69763			0.848817	−	0.528686i	$-0.177315\pi$
$439$	745.262			1.69763			0.848817	+	0.528686i	$0.177315\pi$
$440$	561.012			1.27503
$441$	768.556			1.74276
$442$	−392.356			−0.887684
$443$	−107.231			−0.242057			−0.121029	−	0.992649i	$-0.538619\pi$
$443$	−107.231			−0.242057			−0.121029	+	0.992649i	$0.538619\pi$
$444$	−346.035			−0.779357
$445$	−1067.89			−2.39975
$446$	−42.4830			−0.0952533
$447$		−	539.652i		−	1.20728i
$448$			824.699i			1.84085i
$449$	−794.747			−1.77004			−0.885019	−	0.465555i	$-0.845855\pi$
$449$	−794.747			−1.77004			−0.885019	+	0.465555i	$0.845855\pi$
$450$		−	1269.13i		−	2.82028i
$451$			322.896i			0.715957i
$452$	−1271.28			−2.81257
$453$	−667.597			−1.47372
$454$			243.215i			0.535716i
$455$	−541.526			−1.19017
$456$	−1459.61			−3.20089
$457$			139.856i			0.306030i	0.988224	+	0.153015i	$0.0488982\pi$
$457$			139.856i			0.306030i	−0.988224	+	0.153015i	$0.951102\pi$
$458$	973.529			2.12561
$459$	−169.771			−0.369871
$460$	1381.94			3.00422
$461$		−	531.671i		−	1.15330i	−0.816992	−	0.576650i	$-0.804360\pi$
$461$		−	531.671i		−	1.15330i	0.816992	−	0.576650i	$-0.195640\pi$
$462$		−	961.845i		−	2.08191i
$463$		−	317.457i		−	0.685653i	−0.939399	−	0.342827i	$-0.888616\pi$
$463$		−	317.457i		−	0.685653i	0.939399	−	0.342827i	$-0.111384\pi$
$464$	−541.935			−1.16796
$465$			82.6336i			0.177707i
$466$			1151.58i			2.47121i
$467$	−404.802			−0.866813			−0.433406	−	0.901199i	$-0.642689\pi$
$467$	−404.802			−0.866813			−0.433406	+	0.901199i	$0.642689\pi$
$468$	563.511			1.20408
$469$		−	863.048i		−	1.84019i
$470$	−153.768			−0.327165
$471$		−	461.255i		−	0.979310i
$472$	−1244.97			−2.63766
$473$		−	159.978i		−	0.338219i
$474$		−	1646.18i		−	3.47296i
$475$	−846.284			−1.78165
$476$	−1470.39			−3.08906
$477$	−252.128			−0.528571
$478$		−	62.8543i		−	0.131494i
$479$	372.322			0.777290			0.388645	−	0.921388i	$-0.372943\pi$
$479$	372.322			0.777290			0.388645	+	0.921388i	$0.372943\pi$
$480$		−	248.016i		−	0.516700i
$481$		−	65.2072i		−	0.135566i
$482$	−809.288			−1.67902
$483$		−	1142.70i		−	2.36584i
$484$	678.361			1.40157
$485$			792.507i			1.63403i
$486$	−1173.77			−2.41517
$487$		−	767.235i		−	1.57543i	−0.616039	−	0.787716i	$-0.711263\pi$
$487$		−	767.235i		−	1.57543i	0.616039	−	0.787716i	$-0.288737\pi$
$488$	935.755			1.91753
$489$	−1301.76			−2.66208
$490$	−1799.79			−3.67305
$491$			518.128i			1.05525i	0.849477	+	0.527625i	$0.176917\pi$
$491$			518.128i			1.05525i	−0.849477	+	0.527625i	$0.823083\pi$
$492$	−1943.90			−3.95102
$493$			742.621i			1.50633i
$494$		−	570.298i		−	1.15445i
$495$			490.531i			0.990971i
$496$		−	30.8550i		−	0.0622076i
$497$	105.908			0.213095
$498$		−	1847.18i		−	3.70920i
$499$	−293.179			−0.587533			−0.293766	−	0.955877i	$-0.594909\pi$
$499$	−293.179			−0.587533			−0.293766	+	0.955877i	$0.594909\pi$
$500$			484.423i			0.968845i
$501$			799.922i			1.59665i
$502$	−319.743			−0.636938
$503$		−	468.222i		−	0.930859i	−0.885085	−	0.465429i	$-0.845900\pi$
$503$		−	468.222i		−	0.930859i	0.885085	−	0.465429i	$-0.154100\pi$
$504$	1545.80			3.06706
$505$	−911.987			−1.80591
$506$	−462.542			−0.914116
$507$		−	566.912i		−	1.11817i
$508$	−479.664			−0.944220
$509$	−65.6515			−0.128981			−0.0644907	−	0.997918i	$-0.520542\pi$
$509$	−65.6515			−0.128981			−0.0644907	+	0.997918i	$0.520542\pi$
$510$	2056.15			4.03167
$511$			1113.28i			2.17862i
$512$			745.494i			1.45604i
$513$		−	246.766i		−	0.481025i
$514$	781.407			1.52025
$515$	−231.753			−0.450006
$516$	963.097			1.86647
$517$	33.9108			0.0655915
$518$		−	370.883i		−	0.715990i
$519$	−1052.69			−2.02830
$520$	−636.443			−1.22393
$521$	−871.540			−1.67282			−0.836411	−	0.548103i	$-0.815350\pi$
$521$	−871.540			−1.67282			−0.836411	+	0.548103i	$0.815350\pi$
$522$		−	1618.74i		−	3.10104i
$523$		−	837.631i		−	1.60159i	−0.598939	−	0.800795i	$-0.704411\pi$
$523$		−	837.631i		−	1.60159i	0.598939	−	0.800795i	$-0.295589\pi$
$524$	1305.74			2.49186
$525$	1619.22			3.08423
$526$		−	1675.55i		−	3.18546i
$527$	−42.2811			−0.0802297
$528$		−	330.908i		−	0.626720i
$529$	−20.5147			−0.0387802
$530$	590.431			1.11402
$531$		−	1088.56i		−	2.05003i
$532$		−	2137.25i		−	4.01738i
$533$		−	366.311i		−	0.687263i
$534$			2151.78i			4.02955i
$535$	−324.551			−0.606637
$536$		−	1014.32i		−	1.89239i
$537$		−	930.261i		−	1.73233i
$538$			511.101i			0.950002i
$539$	396.913			0.736388
$540$	−570.995			−1.05740
$541$			749.802i			1.38596i	0.720959	+	0.692978i	$0.243702\pi$
$541$			749.802i			1.38596i	−0.720959	+	0.692978i	$0.756298\pi$
$542$	122.666			0.226322
$543$			1237.97i			2.27986i
$544$	126.902			0.233276
$545$	274.224			0.503164
$546$			1091.17i			1.99848i
$547$	270.845	+	475.239i	0.495146	+	0.868810i
$547$	270.845	+	475.239i	0.495146	+	0.868810i
$548$	1984.02			3.62047
$549$			818.193i			1.49033i
$550$		−	655.428i		−	1.19169i
$551$	−1079.42			−1.95901
$552$		−	1342.99i		−	2.43295i
$553$	1162.54			2.10224
$554$			475.361i			0.858052i
$555$			341.720i			0.615712i
$556$	−1656.96			−2.98014
$557$	506.611			0.909536			0.454768	−	0.890610i	$-0.349722\pi$
$557$	506.611			0.909536			0.454768	+	0.890610i	$0.349722\pi$
$558$	92.1629			0.165167
$559$			181.487i			0.324664i
$560$	−1059.65			−1.89223
$561$	−453.449			−0.808286
$562$	−370.608			−0.659445
$563$	−1058.54			−1.88017			−0.940084	−	0.340942i	$-0.889254\pi$
$563$	−1058.54			−1.88017			−0.940084	+	0.340942i	$0.889254\pi$
$564$			204.150i			0.361968i
$565$			1255.43i			2.22200i
$566$	1343.69			2.37401
$567$		−	618.113i		−	1.09015i
$568$	124.471			0.219140
$569$		−	538.550i		−	0.946484i	−0.880932	−	0.473242i	$-0.843084\pi$
$569$		−	538.550i		−	0.946484i	0.880932	−	0.473242i	$-0.156916\pi$
$570$			2988.66i			5.24326i
$571$	−42.2394			−0.0739745			−0.0369872	−	0.999316i	$-0.511776\pi$
$571$	−42.2394			−0.0739745			−0.0369872	+	0.999316i	$0.511776\pi$
$572$	291.020			0.508776
$573$			81.7117i			0.142603i
$574$		−	2083.49i		−	3.62977i
$575$		−	778.669i		−	1.35421i
$576$	−847.479			−1.47132
$577$			4.26992i			0.00740020i	0.999993	+	0.00370010i	$0.00117778\pi$
$577$			4.26992i			0.00740020i	−0.999993	+	0.00370010i	$0.998822\pi$
$578$			62.4243i			0.108001i
$579$			598.592i			1.03384i
$580$			2497.68i			4.30634i
$581$	1304.48			2.24523
$582$	1596.89			2.74380
$583$	−130.209			−0.223344
$584$			1308.41i			2.24042i
$585$		−	556.485i		−	0.951256i
$586$		−	1148.15i		−	1.95930i
$587$	711.060			1.21135			0.605673	−	0.795714i	$-0.292904\pi$
$587$	711.060			1.21135			0.605673	+	0.795714i	$0.292904\pi$
$588$			2389.50i			4.06377i
$589$		−	61.4564i		−	0.104340i
$590$			2549.18i			4.32065i
$591$	77.1580			0.130555
$592$		−	127.597i		−	0.215535i
$593$	−594.701			−1.00287			−0.501434	−	0.865196i	$-0.667194\pi$
$593$	−594.701			−1.00287			−0.501434	+	0.865196i	$0.667194\pi$
$594$	191.115			0.321742
$595$			1452.06i			2.44043i
$596$	928.694			1.55821
$597$		−	223.635i		−	0.374599i
$598$	524.733			0.877481
$599$	−156.779			−0.261734			−0.130867	−	0.991400i	$-0.541776\pi$
$599$	−156.779			−0.261734			−0.130867	+	0.991400i	$0.541776\pi$
$600$	1903.03			3.17172
$601$	335.957			0.558997			0.279498	−	0.960146i	$-0.409832\pi$
$601$	335.957			0.558997			0.279498	+	0.960146i	$0.409832\pi$
$602$			1032.25i			1.71471i
$603$	886.888			1.47079
$604$		−	1148.87i		−	1.90211i
$605$		−	669.903i		−	1.10728i
$606$			1837.64i			3.03241i
$607$	−13.8608			−0.0228349			−0.0114175	−	0.999935i	$-0.503634\pi$
$607$	−13.8608			−0.0228349			−0.0114175	+	0.999935i	$0.503634\pi$
$608$			184.455i			0.303380i
$609$	2065.28			3.39127
$610$		−	1916.03i		−	3.14104i
$611$	−38.4703			−0.0629628
$612$		−	1511.01i		−	2.46896i
$613$	−978.023			−1.59547			−0.797735	−	0.603008i	$-0.793969\pi$
$613$	−978.023			−1.59547			−0.797735	+	0.603008i	$0.793969\pi$
$614$	−265.790			−0.432883
$615$			1919.66i			3.12140i
$616$	798.313			1.29596
$617$		−	596.213i		−	0.966310i	−0.875535	−	0.483155i	$-0.839491\pi$
$617$		−	596.213i		−	0.966310i	0.875535	−	0.483155i	$-0.160509\pi$
$618$			466.979i			0.755630i
$619$		−	476.044i		−	0.769053i	−0.923114	−	0.384527i	$-0.874365\pi$
$619$		−	476.044i		−	0.769053i	0.923114	−	0.384527i	$-0.125635\pi$
$620$	−142.205			−0.229363
$621$	227.050			0.365620
$622$			1150.39i			1.84950i
$623$	−1519.59			−2.43915
$624$			375.400i			0.601603i
$625$	−352.048			−0.563276
$626$			1893.76i			3.02517i
$627$		−	659.098i		−	1.05119i
$628$	793.779			1.26398
$629$	−174.848			−0.277977
$630$		−	3165.15i		−	5.02404i
$631$	1.38768			0.00219918			0.00109959	−	0.999999i	$-0.499650\pi$
$631$	1.38768			0.00219918			0.00109959	+	0.999999i	$0.499650\pi$
$632$	1366.30			2.16187
$633$	−1012.40			−1.59938
$634$		−	448.255i		−	0.707027i
$635$			473.683i			0.745957i
$636$		−	783.886i		−	1.23253i
$637$	−450.280			−0.706876
$638$		−	835.984i		−	1.31032i
$639$			108.834i			0.170319i
$640$	1763.65			2.75570
$641$			989.614i			1.54386i	0.635708	+	0.771930i	$0.280708\pi$
$641$			989.614i			1.54386i	−0.635708	+	0.771930i	$0.719292\pi$
$642$			653.966i			1.01864i
$643$	390.139			0.606749			0.303374	−	0.952871i	$-0.401887\pi$
$643$	390.139			0.606749			0.303374	+	0.952871i	$0.401887\pi$
$644$	1966.49			3.05355
$645$		−	951.088i		−	1.47456i
$646$	−1529.21			−2.36719
$647$	252.919			0.390911			0.195455	−	0.980713i	$-0.437382\pi$
$647$	252.919			0.390911			0.195455	+	0.980713i	$0.437382\pi$
$648$		−	726.453i		−	1.12107i
$649$		−	562.179i		−	0.866223i
$650$			743.553i			1.14393i
$651$			117.587i			0.180624i
$652$		−	2240.21i		−	3.43591i
$653$		−	668.540i		−	1.02380i	−0.859046	−	0.511899i	$-0.828942\pi$
$653$		−	668.540i		−	1.02380i	0.859046	−	0.511899i	$-0.171058\pi$
$654$		−	552.559i		−	0.844891i
$655$		−	1289.45i		−	1.96863i
$656$		−	716.793i		−	1.09267i
$657$	−1144.03			−1.74129
$658$	−218.809			−0.332537
$659$			381.194i			0.578443i	0.957262	+	0.289221i	$0.0933964\pi$
$659$			381.194i			0.578443i	−0.957262	+	0.289221i	$0.906604\pi$
$660$	−1525.10			−2.31075
$661$	−135.591			−0.205129			−0.102565	−	0.994726i	$-0.532705\pi$
$661$	−135.591			−0.205129			−0.102565	+	0.994726i	$0.532705\pi$
$662$	1565.89			2.36539
$663$	514.417			0.775893
$664$	1533.12			2.30892
$665$	−2110.60			−3.17383
$666$	381.127			0.572263
$667$		−	993.175i		−	1.48902i
$668$	−1376.59			−2.06077
$669$	55.6993			0.0832576
$670$	−2076.90			−3.09985
$671$			422.548i			0.629729i
$672$		−	352.924i		−	0.525184i
$673$	150.940			0.224279			0.112139	−	0.993692i	$-0.464230\pi$
$673$	150.940			0.224279			0.112139	+	0.993692i	$0.464230\pi$
$674$	−107.577			−0.159609
$675$			321.733i			0.476641i
$676$	975.606			1.44320
$677$	−208.448			−0.307899			−0.153949	−	0.988079i	$-0.549199\pi$
$677$	−208.448			−0.307899			−0.153949	+	0.988079i	$0.549199\pi$
$678$	2529.67			3.73108
$679$			1127.73i			1.66086i
$680$			1706.57i			2.50966i
$681$		−	318.879i		−	0.468251i
$682$	47.5967			0.0697898
$683$	−288.388			−0.422238			−0.211119	−	0.977460i	$-0.567711\pi$
$683$	−288.388			−0.422238			−0.211119	+	0.977460i	$0.567711\pi$
$684$	2196.28			3.21094
$685$		−	1959.28i		−	2.86026i
$686$	−739.267			−1.07765
$687$	−1276.39			−1.85792
$688$			355.132i			0.516180i
$689$	147.717			0.214393
$690$	−2749.88			−3.98533
$691$	835.332			1.20887			0.604437	−	0.796653i	$-0.293398\pi$
$691$	835.332			1.20887			0.604437	+	0.796653i	$0.293398\pi$
$692$		−	1811.58i		−	2.61789i
$693$			698.019i			1.00724i
$694$		−	440.437i		−	0.634635i
$695$			1636.30i			2.35438i
$696$	2427.27			3.48746
$697$	−982.232			−1.40923
$698$		−	853.024i		−	1.22210i
$699$		−	1509.84i		−	2.16000i
$700$			2786.53i			3.98076i
$701$	857.407			1.22312			0.611560	−	0.791198i	$-0.290542\pi$
$701$	857.407			1.22312			0.611560	+	0.791198i	$0.290542\pi$
$702$	−216.811			−0.308847
$703$		−	254.145i		−	0.361515i
$704$	−437.672			−0.621694
$705$	201.604			0.285964
$706$		−	435.167i		−	0.616384i
$707$	−1297.75			−1.83557
$708$	3384.43			4.78027
$709$			651.750i			0.919253i	0.888112	+	0.459626i	$0.152017\pi$
$709$			651.750i			0.919253i	−0.888112	+	0.459626i	$0.847983\pi$
$710$		−	254.865i		−	0.358965i
$711$			1194.65i			1.68024i
$712$	−1785.94			−2.50834
$713$	56.5463			0.0793076
$714$	2925.88			4.09787
$715$		−	287.391i		−	0.401946i
$716$	1600.90			2.23589
$717$			82.4081i			0.114935i
$718$	−1457.01			−2.02926
$719$			1131.03i			1.57306i	0.617554	+	0.786528i	$0.288124\pi$
$719$			1131.03i			1.57306i	−0.617554	+	0.786528i	$0.711876\pi$
$720$		−	1088.92i		−	1.51239i
$721$	−329.781			−0.457394
$722$		−	986.533i		−	1.36639i
$723$	1061.06			1.46757
$724$	−2130.43			−2.94258
$725$	1407.34			1.94116
$726$	−1349.85			−1.85929
$727$			365.216i			0.502361i	0.967940	+	0.251180i	$0.0808187\pi$
$727$			365.216i			0.502361i	−0.967940	+	0.251180i	$0.919181\pi$
$728$	−905.650			−1.24402
$729$	1026.56			1.40818
$730$	2679.07			3.66995
$731$	486.642			0.665722
$732$	−2543.82			−3.47517
$733$			25.1976i			0.0343760i	0.999852	+	0.0171880i	$0.00547138\pi$
$733$			25.1976i			0.0343760i	−0.999852	+	0.0171880i	$0.994529\pi$
$734$		−	337.078i		−	0.459234i
$735$	2359.70			3.21048
$736$	−169.718			−0.230595
$737$	458.025			0.621472
$738$	2141.04			2.90114
$739$			214.196i			0.289845i	0.989443	+	0.144923i	$0.0462934\pi$
$739$			214.196i			0.289845i	−0.989443	+	0.144923i	$0.953707\pi$
$740$	−588.070			−0.794689
$741$			747.716i			1.00906i
$742$	840.175			1.13231
$743$	−1223.40			−1.64657			−0.823287	−	0.567625i	$-0.807862\pi$
$743$	−1223.40			−1.64657			−0.823287	+	0.567625i	$0.807862\pi$
$744$			138.197i			0.185748i
$745$		−	917.114i		−	1.23103i
$746$	311.564			0.417646
$747$			1340.51i			1.79453i
$748$		−	780.345i		−	1.04324i
$749$	−461.831			−0.616597
$750$		−	963.935i		−	1.28525i
$751$	959.508			1.27764			0.638820	−	0.769356i	$-0.279423\pi$
$751$	959.508			1.27764			0.638820	+	0.769356i	$0.279423\pi$
$752$	−75.2781			−0.100104
$753$	419.214			0.556725
$754$			948.386i			1.25781i
$755$	−1134.55			−1.50271
$756$	−812.519			−1.07476
$757$	−1070.78			−1.41451			−0.707256	−	0.706958i	$-0.750067\pi$
$757$	−1070.78			−1.41451			−0.707256	+	0.706958i	$0.750067\pi$
$758$		−	1273.91i		−	1.68062i
$759$	606.438			0.798996
$760$	−2480.53			−3.26386
$761$	−1040.16			−1.36684			−0.683418	−	0.730027i	$-0.739507\pi$
$761$	−1040.16			−1.36684			−0.683418	+	0.730027i	$0.739507\pi$
$762$	954.465			1.25258
$763$	390.218			0.511426
$764$	−140.618			−0.184056
$765$	−1492.17			−1.95054
$766$		−	2178.12i		−	2.84350i
$767$			637.766i			0.831507i
$768$		−	2189.63i		−	2.85109i
$769$			1421.89i			1.84902i	0.381162	+	0.924508i	$0.375524\pi$
$769$			1421.89i			1.84902i	−0.381162	+	0.924508i	$0.624476\pi$
$770$		−	1634.61i		−	2.12287i
$771$	−1024.50			−1.32879
$772$	−1030.12			−1.33436
$773$			70.2537i			0.0908845i	0.998967	+	0.0454422i	$0.0144697\pi$
$773$			70.2537i			0.0908845i	−0.998967	+	0.0454422i	$0.985530\pi$
$774$	−1060.77			−1.37050
$775$			80.1268i			0.103389i
$776$			1325.39i			1.70798i
$777$			486.263i			0.625821i
$778$	−13.5884			−0.0174658
$779$		−	1427.70i		−	1.83273i
$780$	1730.15			2.21814
$781$			56.2061i			0.0719669i
$782$		−	1407.03i		−	1.79927i
$783$			410.363i			0.524090i
$784$	−881.102			−1.12385
$785$		−	783.881i		−	0.998575i
$786$	−2598.24			−3.30564
$787$	445.181			0.565668			0.282834	−	0.959169i	$-0.408725\pi$
$787$	445.181			0.565668			0.282834	+	0.959169i	$0.408725\pi$
$788$			132.782i			0.168505i
$789$			2196.81i			2.78430i
$790$		−	2797.61i		−	3.54128i
$791$			1786.46i			2.25848i
$792$			820.364i			1.03581i
$793$		−	479.362i		−	0.604491i
$794$	174.390			0.219634
$795$	−774.112			−0.973726
$796$	384.857			0.483488
$797$	1370.31			1.71933			0.859667	−	0.510855i	$-0.170671\pi$
$797$	1370.31			1.71933			0.859667	+	0.510855i	$0.170671\pi$
$798$			4252.82i			5.32935i
$799$			103.155i			0.129105i
$800$		−	240.492i		−	0.300615i
$801$		−	1561.57i		−	1.94952i
$802$		−	203.701i		−	0.253992i
$803$	−590.822			−0.735768
$804$			2757.40i			3.42960i
$805$		−	1941.97i		−	2.41238i
$806$	−53.9962			−0.0669929
$807$		−	670.103i		−	0.830364i
$808$	−1525.21			−1.88763
$809$			1120.64i			1.38521i	0.721316	+	0.692607i	$0.243538\pi$
$809$			1120.64i			1.38521i	−0.721316	+	0.692607i	$0.756462\pi$
$810$	−1487.47			−1.83638
$811$	771.896			0.951783			0.475891	−	0.879504i	$-0.342126\pi$
$811$	771.896			0.951783			0.475891	+	0.879504i	$0.342126\pi$
$812$			3554.16i			4.37705i
$813$	−160.828			−0.197820
$814$	196.830			0.241805
$815$	−2212.28			−2.71445
$816$	1006.60			1.23358
$817$			707.345i			0.865784i
$818$		−	1520.87i		−	1.85925i
$819$		−	791.870i		−	0.966875i
$820$	−3303.57			−4.02874
$821$			924.046i			1.12551i	0.826623	+	0.562756i	$0.190259\pi$
$821$			924.046i			1.12551i	−0.826623	+	0.562756i	$0.809741\pi$
$822$	−3947.92			−4.80283
$823$	−1310.16			−1.59194			−0.795968	−	0.605338i	$-0.793038\pi$
$823$	−1310.16			−1.59194			−0.795968	+	0.605338i	$0.793038\pi$
$824$	−387.584			−0.470369
$825$			859.330i			1.04161i
$826$			3627.46i			4.39159i
$827$		−	1585.63i		−	1.91733i	−0.284542	−	0.958664i	$-0.591841\pi$
$827$		−	1585.63i		−	1.91733i	0.284542	−	0.958664i	$-0.408159\pi$
$828$			2020.81i			2.44059i
$829$	1587.08			1.91445			0.957223	−	0.289350i	$-0.0934391\pi$
$829$	1587.08			1.91445			0.957223	+	0.289350i	$0.0934391\pi$
$830$		−	3139.19i		−	3.78216i
$831$		−	623.244i		−	0.749993i
$832$	496.520			0.596778
$833$			1207.39i			1.44944i
$834$	3297.12			3.95338
$835$			1359.43i			1.62806i
$836$	1134.25			1.35676
$837$	−23.3640			−0.0279139
$838$			1099.29i			1.31180i
$839$	967.544			1.15321			0.576606	−	0.817023i	$-0.304377\pi$
$839$	967.544			1.15321			0.576606	+	0.817023i	$0.304377\pi$
$840$	4746.08			5.65009
$841$	954.032			1.13440
$842$	415.543			0.493519
$843$	485.903			0.576398
$844$		−	1742.26i		−	2.06429i
$845$		−	963.441i		−	1.14017i
$846$		−	224.853i		−	0.265784i
$847$		−	953.262i		−	1.12546i
$848$	289.050			0.340861
$849$	−1761.71			−2.07504
$850$	1993.77			2.34562
$851$	233.840			0.274782
$852$	−338.372			−0.397151
$853$	−229.925			−0.269548			−0.134774	−	0.990876i	$-0.543031\pi$
$853$	−229.925			−0.269548			−0.134774	+	0.990876i	$0.543031\pi$
$854$		−	2726.49i		−	3.19261i
$855$		−	2168.90i		−	2.53672i
$856$	−542.779			−0.634088
$857$			1089.75i			1.27158i	0.771861	+	0.635792i	$0.219326\pi$
$857$			1089.75i			1.27158i	−0.771861	+	0.635792i	$0.780674\pi$
$858$	−579.090			−0.674930
$859$	849.928			0.989439			0.494719	−	0.869053i	$-0.335271\pi$
$859$	849.928			0.989439			0.494719	+	0.869053i	$0.335271\pi$
$860$	1636.74			1.90318
$861$			2731.65i			3.17265i
$862$	−1444.91			−1.67622
$863$			144.438i			0.167367i	0.996492	+	0.0836837i	$0.0266685\pi$
$863$			144.438i			0.167367i	−0.996492	+	0.0836837i	$0.973331\pi$
$864$	70.1245			0.0811626
$865$	−1788.99			−2.06820
$866$	1982.66			2.28944
$867$		−	81.8443i		−	0.0943995i
$868$	−202.356			−0.233129
$869$			616.965i			0.709971i
$870$		−	4970.04i		−	5.71269i
$871$	−519.608			−0.596565
$872$	458.613			0.525933
$873$	−1158.88			−1.32747
$874$	2045.15			2.33998
$875$	680.732			0.777979
$876$		−	3556.87i		−	4.06035i
$877$		−	1141.41i		−	1.30149i	−0.759296	−	0.650746i	$-0.774456\pi$
$877$		−	1141.41i		−	1.30149i	0.759296	−	0.650746i	$-0.225544\pi$
$878$		−	2552.06i		−	2.90667i
$879$			1505.34i			1.71256i
$880$		−	562.363i		−	0.639049i
$881$			783.117i			0.888895i	0.895805	+	0.444448i	$0.146600\pi$
$881$			783.117i			0.888895i	−0.895805	+	0.444448i	$0.853400\pi$
$882$		−	2631.82i		−	2.98393i
$883$	−497.346			−0.563246			−0.281623	−	0.959525i	$-0.590873\pi$
$883$	−497.346			−0.563246			−0.281623	+	0.959525i	$0.590873\pi$
$884$			885.266i			1.00143i
$885$		−	3342.23i		−	3.77653i
$886$			367.201i			0.414448i
$887$	−1712.59			−1.93077			−0.965383	−	0.260837i	$-0.916002\pi$
$887$	−1712.59			−1.93077			−0.965383	+	0.260837i	$0.916002\pi$
$888$			571.493i			0.643573i
$889$			674.044i			0.758205i
$890$			3656.85i			4.10882i
$891$	328.036			0.368166
$892$			95.8536i			0.107459i
$893$	−149.938			−0.167903
$894$	−1847.97			−2.06708
$895$		−	1580.94i		−	1.76641i
$896$	2509.65			2.80095
$897$	−687.976			−0.766975
$898$			2721.51i			3.03064i
$899$			102.200i			0.113682i
$900$	−2863.51			−3.18167
$901$		−	396.089i		−	0.439611i
$902$	1105.72			1.22585
$903$		−	1353.39i		−	1.49877i
$904$			2099.58i			2.32255i
$905$			2103.87i			2.32471i
$906$			2286.10i			2.52329i
$907$	−782.063			−0.862253			−0.431126	−	0.902292i	$-0.641884\pi$
$907$	−782.063			−0.862253			−0.431126	+	0.902292i	$0.641884\pi$
$908$	548.762			0.604364
$909$		−	1333.59i		−	1.46710i
$910$			1854.39i			2.03779i
$911$		−	596.039i		−	0.654269i	−0.944978	−	0.327134i	$-0.893917\pi$
$911$		−	596.039i		−	0.654269i	0.944978	−	0.327134i	$-0.106083\pi$
$912$			1463.12i			1.60430i
$913$			692.295i			0.758264i
$914$	478.918			0.523980
$915$			2512.11i			2.74547i
$916$		−	2196.55i		−	2.39799i
$917$		−	1834.88i		−	2.00096i
$918$			581.360i			0.633289i
$919$	−171.093			−0.186173			−0.0930866	−	0.995658i	$-0.529673\pi$
$919$	−171.093			−0.186173			−0.0930866	+	0.995658i	$0.529673\pi$
$920$		−	2282.35i		−	2.48081i
$921$	348.477			0.378368
$922$	−1820.64			−1.97467
$923$		−	63.7633i		−	0.0690827i
$924$	−2170.19			−2.34869
$925$			331.353i			0.358220i
$926$	−1087.09			−1.17397
$927$		−	338.891i		−	0.365578i
$928$		−	306.742i		−	0.330541i
$929$		−	1368.72i		−	1.47332i	−0.676262	−	0.736661i	$-0.736401\pi$
$929$		−	1368.72i		−	1.47332i	0.676262	−	0.736661i	$-0.263599\pi$
$930$	282.969			0.304267
$931$	−1754.96			−1.88503
$932$	2598.30			2.78787
$933$		−	1508.27i		−	1.61658i
$934$			1386.19i			1.48415i
$935$	−770.615			−0.824187
$936$		−	930.666i		−	0.994301i
$937$		−	853.847i		−	0.911257i	−0.890170	−	0.455628i	$-0.849415\pi$
$937$		−	853.847i		−	0.911257i	0.890170	−	0.455628i	$-0.150585\pi$
$938$	−2955.40			−3.15075
$939$		−	2482.90i		−	2.64420i
$940$			346.943i			0.369088i
$941$	1520.48			1.61581			0.807907	−	0.589310i	$-0.200600\pi$
$941$	1520.48			1.61581			0.807907	+	0.589310i	$0.200600\pi$
$942$	−1579.51			−1.67676
$943$	1313.63			1.39303
$944$			1247.97i			1.32200i
$945$			802.387i			0.849087i
$946$	−547.823			−0.579095
$947$	1516.24			1.60109			0.800547	−	0.599270i	$-0.204542\pi$
$947$	1516.24			1.60109			0.800547	+	0.599270i	$0.204542\pi$
$948$	−3714.25			−3.91799
$949$	670.261			0.706281
$950$			2897.99i			3.05052i
$951$			587.706i			0.617988i
$952$			2428.42i			2.55086i
$953$	1507.29			1.58163			0.790814	−	0.612057i	$-0.209658\pi$
$953$	1507.29			1.58163			0.790814	+	0.612057i	$0.209658\pi$
$954$			863.383i			0.905013i
$955$			138.865i			0.145409i
$956$	−141.817			−0.148344
$957$			1096.06i			1.14530i
$958$		−	1274.97i		−	1.33087i
$959$		−	2788.03i		−	2.90722i
$960$	−2602.02			−2.71044
$961$	955.181			0.993945
$962$	−223.294			−0.232115
$963$		−	474.588i		−	0.492823i
$964$			1825.98i			1.89417i
$965$			1017.28i			1.05417i
$966$	−3913.04			−4.05077
$967$		−	753.197i		−	0.778901i	−0.921047	−	0.389451i	$-0.872665\pi$
$967$		−	753.197i		−	0.778901i	0.921047	−	0.389451i	$-0.127335\pi$
$968$		−	1120.35i		−	1.15738i
$969$	2004.94			2.06908
$970$	2713.84			2.79778
$971$			492.191i			0.506890i	0.967350	+	0.253445i	$0.0815638\pi$
$971$			492.191i			0.506890i	−0.967350	+	0.253445i	$0.918436\pi$
$972$			2648.36i			2.72465i
$973$			2328.43i			2.39304i
$974$	−2627.30			−2.69744
$975$		−	974.870i		−	0.999867i
$976$		−	938.008i		−	0.961074i
$977$			217.449i			0.222568i	0.993789	+	0.111284i	$0.0354964\pi$
$977$			217.449i			0.222568i	−0.993789	+	0.111284i	$0.964504\pi$
$978$			4457.71i			4.55799i
$979$		−	806.456i		−	0.823755i
$980$			4060.84i			4.14371i
$981$			400.996i			0.408763i
$982$	1774.27			1.80679
$983$			1126.32i			1.14580i	0.819627	+	0.572898i	$0.194181\pi$
$983$			1126.32i			1.14580i	−0.819627	+	0.572898i	$0.805819\pi$
$984$			3210.45i			3.26265i
$985$	131.126			0.133123
$986$	2543.02			2.57912
$987$	286.880			0.290659
$988$	−1286.75			−1.30238
$989$	−650.831			−0.658070
$990$	1679.76			1.69673
$991$	−73.6532			−0.0743221			−0.0371611	−	0.999309i	$-0.511831\pi$
$991$	−73.6532			−0.0743221			−0.0371611	+	0.999309i	$0.511831\pi$
$992$	17.4643			0.0176052
$993$	−2053.03			−2.06750
$994$		−	362.670i		−	0.364859i
$995$		−	380.058i		−	0.381968i
$996$	−4167.76			−4.18449
$997$		−	299.679i		−	0.300581i	−0.988642	−	0.150290i	$-0.951979\pi$
$997$		−	299.679i		−	0.300581i	0.988642	−	0.150290i	$-0.0480209\pi$
$998$			1003.96i			1.00597i
$999$	−96.6185			−0.0967152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.3.b.b.546.9	✓	88
547.546	odd	2	inner	547.3.b.b.546.80	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.3.b.b.546.9	✓	88	1.1	even	1	trivial
547.3.b.b.546.80	yes	88	547.546	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	547.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.42438i q^{2} +4.48969i q^{3} -7.72636 q^{4} +7.63002i q^{5} +15.3744 q^{6} +10.8574i q^{7} +12.7605i q^{8} -11.1573 q^{9} +O(q^{10})\)	\(q-3.42438i q^{2} +4.48969i q^{3} -7.72636 q^{4} +7.63002i q^{5} +15.3744 q^{6} +10.8574i q^{7} +12.7605i q^{8} -11.1573 q^{9} +26.1281 q^{10} -5.76209 q^{11} -34.6890i q^{12} +6.53683 q^{13} +37.1799 q^{14} -34.2564 q^{15} +12.7912 q^{16} -17.5280i q^{17} +38.2069i q^{18} +25.4773 q^{19} -58.9523i q^{20} -48.7464 q^{21} +19.7316i q^{22} +23.4417i q^{23} -57.2905 q^{24} -33.2172 q^{25} -22.3846i q^{26} -9.68572i q^{27} -83.8883i q^{28} -42.3678 q^{29} +117.307i q^{30} -2.41221i q^{31} +7.23999i q^{32} -25.8700i q^{33} -60.0223 q^{34} -82.8423 q^{35} +86.2055 q^{36} -9.97535i q^{37} -87.2438i q^{38} +29.3484i q^{39} -97.3625 q^{40} -56.0380i q^{41} +166.926i q^{42} +27.7638i q^{43} +44.5200 q^{44} -85.1306i q^{45} +80.2733 q^{46} -5.88515 q^{47} +57.4285i q^{48} -68.8835 q^{49} +113.748i q^{50} +78.6951 q^{51} -50.5059 q^{52} +22.5976 q^{53} -33.1676 q^{54} -43.9649i q^{55} -138.546 q^{56} +114.385i q^{57} +145.083i q^{58} +97.5650i q^{59} +264.677 q^{60} -73.3324i q^{61} -8.26031 q^{62} -121.140i q^{63} +75.9572 q^{64} +49.8762i q^{65} -88.5887 q^{66} -79.4893 q^{67} +135.427i q^{68} -105.246 q^{69} +283.683i q^{70} -9.75447i q^{71} -142.373i q^{72} +102.536 q^{73} -34.1594 q^{74} -149.135i q^{75} -196.847 q^{76} -62.5615i q^{77} +100.500 q^{78} -107.073i q^{79} +97.5970i q^{80} -56.9300 q^{81} -191.895 q^{82} -120.146i q^{83} +376.633 q^{84} +133.739 q^{85} +95.0737 q^{86} -190.218i q^{87} -73.5270i q^{88} +139.959i q^{89} -291.519 q^{90} +70.9731i q^{91} -181.119i q^{92} +10.8301 q^{93} +20.1530i q^{94} +194.392i q^{95} -32.5053 q^{96} +103.867 q^{97} +235.883i q^{98} +64.2896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) \) 88 * q - 192 * q^4 - 306 * q^9	\( 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) \) 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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