LMFDB - Embedded newform 201.3.b.a.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(133,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("201.133");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			133.1
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.81177i q^{2} -1.73205i q^{3} -10.5296 q^{4} -6.86815i q^{5} -6.60217 q^{6} +3.56836i q^{7} +24.8892i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.81177i q^{2} -1.73205i q^{3} -10.5296 q^{4} -6.86815i q^{5} -6.60217 q^{6} +3.56836i q^{7} +24.8892i q^{8} -3.00000 q^{9} -26.1798 q^{10} +4.73705i q^{11} +18.2377i q^{12} -20.4000i q^{13} +13.6017 q^{14} -11.8960 q^{15} +52.7535 q^{16} +20.9109 q^{17} +11.4353i q^{18} -13.7121 q^{19} +72.3186i q^{20} +6.18058 q^{21} +18.0565 q^{22} -26.1433 q^{23} +43.1094 q^{24} -22.1714 q^{25} -77.7601 q^{26} +5.19615i q^{27} -37.5733i q^{28} +47.0962 q^{29} +45.3447i q^{30} -1.48280i q^{31} -101.527i q^{32} +8.20481 q^{33} -79.7074i q^{34} +24.5080 q^{35} +31.5887 q^{36} -52.3505 q^{37} +52.2674i q^{38} -35.3338 q^{39} +170.943 q^{40} +17.3762i q^{41} -23.5589i q^{42} -28.1041i q^{43} -49.8791i q^{44} +20.6044i q^{45} +99.6522i q^{46} -75.7613 q^{47} -91.3718i q^{48} +36.2668 q^{49} +84.5123i q^{50} -36.2187i q^{51} +214.803i q^{52} -97.4461i q^{53} +19.8065 q^{54} +32.5347 q^{55} -88.8135 q^{56} +23.7501i q^{57} -179.520i q^{58} -15.2818 q^{59} +125.260 q^{60} +37.9436i q^{61} -5.65209 q^{62} -10.7051i q^{63} -175.985 q^{64} -140.110 q^{65} -31.2748i q^{66} +(-66.9280 - 3.10603i) q^{67} -220.183 q^{68} +45.2815i q^{69} -93.4188i q^{70} +4.45453 q^{71} -74.6676i q^{72} -3.98095 q^{73} +199.548i q^{74} +38.4020i q^{75} +144.383 q^{76} -16.9035 q^{77} +134.684i q^{78} -55.5165i q^{79} -362.319i q^{80} +9.00000 q^{81} +66.2340 q^{82} +99.4756 q^{83} -65.0788 q^{84} -143.619i q^{85} -107.126 q^{86} -81.5730i q^{87} -117.901 q^{88} +91.0204 q^{89} +78.5393 q^{90} +72.7945 q^{91} +275.278 q^{92} -2.56828 q^{93} +288.784i q^{94} +94.1769i q^{95} -175.851 q^{96} -36.9594i q^{97} -138.241i q^{98} -14.2111i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) $ 22 * q - 52 * q^4 - 66 * q^9	$ 22 q - 52 q^{4} - 66 q^{9} - 36 q^{10} + 72 q^{14} + 12 q^{15} + 116 q^{16} - 14 q^{17} - 26 q^{19} + 48 q^{21} + 32 q^{22} - 82 q^{23} + 36 q^{24} - 62 q^{25} - 100 q^{26} + 102 q^{29} + 36 q^{33} - 180 q^{35} + 156 q^{36} + 106 q^{37} - 72 q^{39} + 76 q^{40} + 154 q^{47} + 146 q^{49} - 224 q^{55} - 452 q^{56} + 370 q^{59} - 24 q^{60} - 300 q^{62} + 148 q^{64} - 284 q^{65} - 134 q^{67} - 116 q^{68} + 160 q^{71} + 218 q^{73} + 480 q^{76} - 396 q^{77} + 198 q^{81} - 68 q^{82} + 128 q^{83} + 20 q^{86} - 856 q^{88} - 118 q^{89} + 108 q^{90} - 400 q^{91} + 804 q^{92} - 72 q^{93} - 144 q^{96}+O(q^{100}) $ 22 * q - 52 * q^4 - 66 * q^9 - 36 * q^10 + 72 * q^14 + 12 * q^15 + 116 * q^16 - 14 * q^17 - 26 * q^19 + 48 * q^21 + 32 * q^22 - 82 * q^23 + 36 * q^24 - 62 * q^25 - 100 * q^26 + 102 * q^29 + 36 * q^33 - 180 * q^35 + 156 * q^36 + 106 * q^37 - 72 * q^39 + 76 * q^40 + 154 * q^47 + 146 * q^49 - 224 * q^55 - 452 * q^56 + 370 * q^59 - 24 * q^60 - 300 * q^62 + 148 * q^64 - 284 * q^65 - 134 * q^67 - 116 * q^68 + 160 * q^71 + 218 * q^73 + 480 * q^76 - 396 * q^77 + 198 * q^81 - 68 * q^82 + 128 * q^83 + 20 * q^86 - 856 * q^88 - 118 * q^89 + 108 * q^90 - 400 * q^91 + 804 * q^92 - 72 * q^93 - 144 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	3.81177i		−	1.90588i	−0.303153	−	0.952942i	$-0.598039\pi$
$2$		−	3.81177i		−	1.90588i	0.303153	−	0.952942i	$-0.401961\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−10.5296			−2.63239
$5$		−	6.86815i		−	1.37363i	−0.726833	−	0.686815i	$-0.759008\pi$
$5$		−	6.86815i		−	1.37363i	0.726833	−	0.686815i	$-0.240992\pi$
$6$	−6.60217			−1.10036
$7$			3.56836i			0.509765i	0.966972	+	0.254883i	$0.0820368\pi$
$7$			3.56836i			0.509765i	−0.966972	+	0.254883i	$0.917963\pi$
$8$			24.8892i			3.11115i
$9$	−3.00000			−0.333333
$10$	−26.1798			−2.61798
$11$			4.73705i			0.430641i	0.976543	+	0.215320i	$0.0690796\pi$
$11$			4.73705i			0.430641i	−0.976543	+	0.215320i	$0.930920\pi$
$12$			18.2377i			1.51981i
$13$		−	20.4000i		−	1.56923i	−0.619983	−	0.784615i	$-0.712860\pi$
$13$		−	20.4000i		−	1.56923i	0.619983	−	0.784615i	$-0.287140\pi$
$14$	13.6017			0.971553
$15$	−11.8960			−0.793065
$16$	52.7535			3.29710
$17$	20.9109			1.23005			0.615026	−	0.788507i	$-0.289146\pi$
$17$	20.9109			1.23005			0.615026	+	0.788507i	$0.289146\pi$
$18$			11.4353i			0.635295i
$19$	−13.7121			−0.721691			−0.360845	−	0.932626i	$-0.617512\pi$
$19$	−13.7121			−0.721691			−0.360845	+	0.932626i	$0.617512\pi$
$20$			72.3186i			3.61593i
$21$	6.18058			0.294313
$22$	18.0565			0.820751
$23$	−26.1433			−1.13666			−0.568332	−	0.822799i	$-0.692411\pi$
$23$	−26.1433			−1.13666			−0.568332	+	0.822799i	$0.692411\pi$
$24$	43.1094			1.79622
$25$	−22.1714			−0.886857
$26$	−77.7601			−2.99077
$27$			5.19615i			0.192450i
$28$		−	37.5733i		−	1.34190i
$29$	47.0962			1.62401			0.812003	−	0.583653i	$-0.198377\pi$
$29$	47.0962			1.62401			0.812003	+	0.583653i	$0.198377\pi$
$30$			45.3447i			1.51149i
$31$		−	1.48280i		−	0.0478322i	−0.999714	−	0.0239161i	$-0.992387\pi$
$31$		−	1.48280i		−	0.0478322i	0.999714	−	0.0239161i	$-0.00761346\pi$
$32$		−	101.527i		−	3.17273i
$33$	8.20481			0.248630
$34$		−	79.7074i		−	2.34434i
$35$	24.5080			0.700228
$36$	31.5887			0.877464
$37$	−52.3505			−1.41488			−0.707439	−	0.706775i	$-0.750150\pi$
$37$	−52.3505			−1.41488			−0.707439	+	0.706775i	$0.750150\pi$
$38$			52.2674i			1.37546i
$39$	−35.3338			−0.905996
$40$	170.943			4.27357
$41$			17.3762i			0.423810i	0.977290	+	0.211905i	$0.0679667\pi$
$41$			17.3762i			0.423810i	−0.977290	+	0.211905i	$0.932033\pi$
$42$		−	23.5589i		−	0.560927i
$43$		−	28.1041i		−	0.653584i	−0.945096	−	0.326792i	$-0.894032\pi$
$43$		−	28.1041i		−	0.653584i	0.945096	−	0.326792i	$-0.105968\pi$
$44$		−	49.8791i		−	1.13362i
$45$			20.6044i			0.457876i
$46$			99.6522i			2.16635i
$47$	−75.7613			−1.61194			−0.805971	−	0.591955i	$-0.798356\pi$
$47$	−75.7613			−1.61194			−0.805971	+	0.591955i	$0.798356\pi$
$48$		−	91.3718i		−	1.90358i
$49$	36.2668			0.740139
$50$			84.5123i			1.69025i
$51$		−	36.2187i		−	0.710171i
$52$			214.803i			4.13083i
$53$		−	97.4461i		−	1.83861i	−0.393551	−	0.919303i	$-0.628754\pi$
$53$		−	97.4461i		−	1.83861i	0.393551	−	0.919303i	$-0.371246\pi$
$54$	19.8065			0.366787
$55$	32.5347			0.591541
$56$	−88.8135			−1.58596
$57$			23.7501i			0.416668i
$58$		−	179.520i		−	3.09517i
$59$	−15.2818			−0.259013			−0.129507	−	0.991579i	$-0.541339\pi$
$59$	−15.2818			−0.259013			−0.129507	+	0.991579i	$0.541339\pi$
$60$	125.260			2.08766
$61$			37.9436i			0.622026i	0.950406	+	0.311013i	$0.100668\pi$
$61$			37.9436i			0.622026i	−0.950406	+	0.311013i	$0.899332\pi$
$62$	−5.65209			−0.0911627
$63$		−	10.7051i		−	0.169922i
$64$	−175.985			−2.74976
$65$	−140.110			−2.15554
$66$		−	31.2748i		−	0.473861i
$67$	−66.9280	−	3.10603i	−0.998925	−	0.0463586i
$67$	−66.9280	−	3.10603i	−0.998925	−	0.0463586i
$68$	−220.183			−3.23798
$69$			45.2815i			0.656254i
$70$		−	93.4188i		−	1.33455i
$71$	4.45453			0.0627399			0.0313700	−	0.999508i	$-0.490013\pi$
$71$	4.45453			0.0627399			0.0313700	+	0.999508i	$0.490013\pi$
$72$		−	74.6676i		−	1.03705i
$73$	−3.98095			−0.0545335			−0.0272668	−	0.999628i	$-0.508680\pi$
$73$	−3.98095			−0.0545335			−0.0272668	+	0.999628i	$0.508680\pi$
$74$			199.548i			2.69659i
$75$			38.4020i			0.512027i
$76$	144.383			1.89977
$77$	−16.9035			−0.219526
$78$			134.684i			1.72672i
$79$		−	55.5165i		−	0.702741i	−0.936237	−	0.351370i	$-0.885716\pi$
$79$		−	55.5165i		−	0.702741i	0.936237	−	0.351370i	$-0.114284\pi$
$80$		−	362.319i		−	4.52899i
$81$	9.00000			0.111111
$82$	66.2340			0.807732
$83$	99.4756			1.19850			0.599250	−	0.800562i	$-0.295465\pi$
$83$	99.4756			1.19850			0.599250	+	0.800562i	$0.295465\pi$
$84$	−65.0788			−0.774748
$85$		−	143.619i		−	1.68964i
$86$	−107.126			−1.24565
$87$		−	81.5730i		−	0.937620i
$88$	−117.901			−1.33979
$89$	91.0204			1.02270			0.511351	−	0.859372i	$-0.329145\pi$
$89$	91.0204			1.02270			0.511351	+	0.859372i	$0.329145\pi$
$90$	78.5393			0.872659
$91$	72.7945			0.799939
$92$	275.278			2.99215
$93$	−2.56828			−0.0276160
$94$			288.784i			3.07217i
$95$			94.1769i			0.991335i
$96$	−175.851			−1.83178
$97$		−	36.9594i		−	0.381025i	−0.981685	−	0.190512i	$-0.938985\pi$
$97$		−	36.9594i		−	0.381025i	0.981685	−	0.190512i	$-0.0610150\pi$
$98$		−	138.241i		−	1.41062i
$99$		−	14.2111i		−	0.143547i
$100$	233.456			2.33456
$101$			123.065i			1.21847i	0.792991	+	0.609233i	$0.208523\pi$
$101$			123.065i			1.21847i	−0.792991	+	0.609233i	$0.791477\pi$
$102$	−138.057			−1.35350
$103$	−123.585			−1.19986			−0.599929	−	0.800053i	$-0.704805\pi$
$103$	−123.585			−1.19986			−0.599929	+	0.800053i	$0.704805\pi$
$104$	507.740			4.88211
$105$		−	42.4491i		−	0.404277i
$106$	−371.442			−3.50417
$107$	191.553			1.79022			0.895110	−	0.445846i	$-0.147097\pi$
$107$	191.553			1.79022			0.895110	+	0.445846i	$0.147097\pi$
$108$		−	54.7132i		−	0.506604i
$109$		−	206.243i		−	1.89214i	−0.323964	−	0.946070i	$-0.605016\pi$
$109$		−	206.243i		−	1.89214i	0.323964	−	0.946070i	$-0.394984\pi$
$110$		−	124.015i		−	1.12741i
$111$			90.6737i			0.816880i
$112$			188.243i			1.68075i
$113$		−	190.368i		−	1.68468i	−0.538949	−	0.842338i	$-0.681178\pi$
$113$		−	190.368i		−	1.68468i	0.538949	−	0.842338i	$-0.318822\pi$
$114$	90.5298			0.794121
$115$			179.556i			1.56136i
$116$	−495.903			−4.27502
$117$			61.2000i			0.523077i
$118$			58.2506i			0.493649i
$119$			74.6175i			0.627038i
$120$		−	296.081i		−	2.46734i
$121$	98.5604			0.814549
$122$	144.632			1.18551
$123$	30.0964			0.244687
$124$			15.6132i			0.125913i
$125$		−	19.4270i		−	0.155416i
$126$	−40.8052			−0.323851
$127$	142.751			1.12402			0.562012	−	0.827129i	$-0.310027\pi$
$127$	142.751			1.12402			0.562012	+	0.827129i	$0.310027\pi$
$128$			264.703i			2.06800i
$129$	−48.6777			−0.377347
$130$			534.067i			4.10821i
$131$	194.707			1.48631			0.743157	−	0.669117i	$-0.233327\pi$
$131$	194.707			1.48631			0.743157	+	0.669117i	$0.233327\pi$
$132$	−86.3931			−0.654493
$133$		−	48.9298i		−	0.367893i
$134$	−11.8394	+	255.114i	−0.0883541	+	1.90383i
$135$	35.6879			0.264355
$136$			520.455i			3.82688i
$137$			81.0556i			0.591647i	0.955243	+	0.295823i	$0.0955940\pi$
$137$			81.0556i			0.591647i	−0.955243	+	0.295823i	$0.904406\pi$
$138$	172.603			1.25074
$139$		−	59.5255i		−	0.428241i	−0.976807	−	0.214120i	$-0.931312\pi$
$139$		−	59.5255i		−	0.428241i	0.976807	−	0.214120i	$-0.0686885\pi$
$140$	−258.059			−1.84328
$141$			131.222i			0.930655i
$142$		−	16.9796i		−	0.119575i
$143$	96.6358			0.675775
$144$	−158.261			−1.09903
$145$		−	323.463i		−	2.23078i
$146$			15.1744i			0.103935i
$147$		−	62.8160i		−	0.427320i
$148$	551.228			3.72451
$149$	80.5042			0.540297			0.270148	−	0.962819i	$-0.412927\pi$
$149$	80.5042			0.540297			0.270148	+	0.962819i	$0.412927\pi$
$150$	146.380			0.975864
$151$	−134.851			−0.893055			−0.446528	−	0.894770i	$-0.647340\pi$
$151$	−134.851			−0.893055			−0.446528	+	0.894770i	$0.647340\pi$
$152$		−	341.284i		−	2.24529i
$153$	−62.7326			−0.410017
$154$			64.4321i			0.418390i
$155$	−10.1841			−0.0657038
$156$	372.050			2.38494
$157$	85.2821			0.543198			0.271599	−	0.962411i	$-0.412448\pi$
$157$	85.2821			0.543198			0.271599	+	0.962411i	$0.412448\pi$
$158$	−211.616			−1.33934
$159$	−168.782			−1.06152
$160$	−697.305			−4.35816
$161$		−	93.2886i		−	0.579432i
$162$		−	34.3059i		−	0.211765i
$163$	93.3113			0.572462			0.286231	−	0.958161i	$-0.407598\pi$
$163$	93.3113			0.572462			0.286231	+	0.958161i	$0.407598\pi$
$164$		−	182.964i		−	1.11563i
$165$		−	56.3518i		−	0.341526i
$166$		−	379.178i		−	2.28420i
$167$	−57.3975			−0.343698			−0.171849	−	0.985123i	$-0.554974\pi$
$167$	−57.3975			−0.343698			−0.171849	+	0.985123i	$0.554974\pi$
$168$			153.830i			0.915652i
$169$	−247.160			−1.46249
$170$	−547.442			−3.22025
$171$	41.1364			0.240564
$172$			295.924i			1.72049i
$173$	37.5170			0.216861			0.108431	−	0.994104i	$-0.465417\pi$
$173$	37.5170			0.216861			0.108431	+	0.994104i	$0.465417\pi$
$174$	−310.937			−1.78700
$175$		−	79.1156i		−	0.452089i
$176$			249.896i			1.41986i
$177$			26.4688i			0.149541i
$178$		−	346.949i		−	1.94915i
$179$			100.834i			0.563318i	0.959515	+	0.281659i	$0.0908846\pi$
$179$			100.834i			0.563318i	−0.959515	+	0.281659i	$0.909115\pi$
$180$		−	216.956i		−	1.20531i
$181$	65.9459			0.364342			0.182171	−	0.983267i	$-0.441688\pi$
$181$	65.9459			0.364342			0.182171	+	0.983267i	$0.441688\pi$
$182$		−	277.476i		−	1.52459i
$183$	65.7203			0.359127
$184$		−	650.686i		−	3.53633i
$185$			359.551i			1.94352i
$186$			9.78970i			0.0526328i
$187$			99.0558i			0.529710i
$188$	797.733			4.24326
$189$	−18.5417			−0.0981044
$190$	358.980			1.88937
$191$			26.0981i			0.136639i	0.997663	+	0.0683197i	$0.0217638\pi$
$191$			26.0981i			0.136639i	−0.997663	+	0.0683197i	$0.978236\pi$
$192$			304.815i			1.58758i
$193$	−167.154			−0.866081			−0.433041	−	0.901374i	$-0.642559\pi$
$193$	−167.154			−0.866081			−0.433041	+	0.901374i	$0.642559\pi$
$194$	−140.881			−0.726189
$195$			242.678i			1.24450i
$196$	−381.874			−1.94834
$197$			182.043i			0.924076i	0.886860	+	0.462038i	$0.152882\pi$
$197$			182.043i			0.924076i	−0.886860	+	0.462038i	$0.847118\pi$
$198$	−54.1696			−0.273584
$199$	−73.3895			−0.368792			−0.184396	−	0.982852i	$-0.559033\pi$
$199$	−73.3895			−0.368792			−0.184396	+	0.982852i	$0.559033\pi$
$200$		−	551.829i		−	2.75915i
$201$	−5.37979	+	115.923i	−0.0267651	+	0.576730i
$202$	469.096			2.32225
$203$			168.056i			0.827862i
$204$			381.367i			1.86945i
$205$	119.342			0.582157
$206$			471.079i			2.28679i
$207$	78.4299			0.378888
$208$		−	1076.17i		−	5.17391i
$209$		−	64.9550i		−	0.310789i
$210$	−161.806			−0.770505
$211$	−17.0566			−0.0808371			−0.0404186	−	0.999183i	$-0.512869\pi$
$211$	−17.0566			−0.0808371			−0.0404186	+	0.999183i	$0.512869\pi$
$212$			1026.07i			4.83993i
$213$		−	7.71548i		−	0.0362229i
$214$		−	730.157i		−	3.41195i
$215$	−193.023			−0.897782
$216$	−129.328			−0.598741
$217$	5.29116			0.0243832
$218$	−786.151			−3.60620
$219$			6.89520i			0.0314849i
$220$	−342.577			−1.55717
$221$		−	426.582i		−	1.93024i
$222$	345.627			1.55688
$223$	−34.0734			−0.152796			−0.0763978	−	0.997077i	$-0.524342\pi$
$223$	−34.0734			−0.152796			−0.0763978	+	0.997077i	$0.524342\pi$
$224$	362.286			1.61735
$225$	66.5143			0.295619
$226$	−725.640			−3.21080
$227$	164.490			0.724626			0.362313	−	0.932057i	$-0.381987\pi$
$227$	164.490			0.724626			0.362313	+	0.932057i	$0.381987\pi$
$228$		−	250.078i		−	1.09683i
$229$			153.676i			0.671073i	0.942027	+	0.335536i	$0.108918\pi$
$229$			153.676i			0.671073i	−0.942027	+	0.335536i	$0.891082\pi$
$230$	684.426			2.97576
$231$			29.2777i			0.126743i
$232$			1172.19i			5.05253i
$233$			165.804i			0.711605i	0.934561	+	0.355802i	$0.115792\pi$
$233$			165.804i			0.711605i	−0.934561	+	0.355802i	$0.884208\pi$
$234$	233.280			0.996924
$235$			520.339i			2.21421i
$236$	160.911			0.681825
$237$	−96.1574			−0.405727
$238$	284.424			1.19506
$239$		−	220.906i		−	0.924293i	−0.886804	−	0.462146i	$-0.847080\pi$
$239$		−	220.906i		−	0.924293i	0.886804	−	0.462146i	$-0.152920\pi$
$240$	−627.555			−2.61481
$241$	114.292			0.474239			0.237120	−	0.971480i	$-0.423797\pi$
$241$	114.292			0.474239			0.237120	+	0.971480i	$0.423797\pi$
$242$		−	375.689i		−	1.55243i
$243$		−	15.5885i		−	0.0641500i
$244$		−	399.530i		−	1.63742i
$245$		−	249.086i		−	1.01668i
$246$		−	114.721i		−	0.466344i
$247$			279.727i			1.13250i
$248$	36.9057			0.148813
$249$		−	172.297i		−	0.691955i
$250$	−74.0513			−0.296205
$251$		−	341.575i		−	1.36086i	−0.732814	−	0.680428i	$-0.761794\pi$
$251$		−	341.575i		−	1.36086i	0.732814	−	0.680428i	$-0.238206\pi$
$252$			112.720i			0.447301i
$253$		−	123.842i		−	0.489494i
$254$		−	544.134i		−	2.14226i
$255$	−248.755			−0.975511
$256$	305.048			1.19160
$257$	−227.753			−0.886199			−0.443100	−	0.896472i	$-0.646121\pi$
$257$	−227.753			−0.886199			−0.443100	+	0.896472i	$0.646121\pi$
$258$			185.548i			0.719179i
$259$		−	186.805i		−	0.721256i
$260$	1475.30			5.67423
$261$	−141.289			−0.541335
$262$		−	742.179i		−	2.83274i
$263$	369.137			1.40356			0.701781	−	0.712392i	$-0.252388\pi$
$263$	369.137			1.40356			0.701781	+	0.712392i	$0.252388\pi$
$264$			204.211i			0.773527i
$265$	−669.274			−2.52556
$266$	−186.509			−0.701161
$267$		−	157.652i		−	0.590457i
$268$	704.723	+	32.7051i	2.62956	+	0.122034i
$269$	−453.706			−1.68664			−0.843319	−	0.537414i	$-0.819401\pi$
$269$	−453.706			−1.68664			−0.843319	+	0.537414i	$0.819401\pi$
$270$		−	136.034i		−	0.503830i
$271$			82.3059i			0.303712i	0.988403	+	0.151856i	$0.0485250\pi$
$271$			82.3059i			0.303712i	−0.988403	+	0.151856i	$0.951475\pi$
$272$	1103.12			4.05560
$273$		−	126.084i		−	0.461845i
$274$	308.965			1.12761
$275$		−	105.027i		−	0.381917i
$276$		−	476.795i		−	1.72752i
$277$	202.154			0.729796			0.364898	−	0.931047i	$-0.381104\pi$
$277$	202.154			0.729796			0.364898	+	0.931047i	$0.381104\pi$
$278$	−226.897			−0.816177
$279$			4.44840i			0.0159441i
$280$			609.984i			2.17852i
$281$			448.411i			1.59577i	0.602812	+	0.797884i	$0.294047\pi$
$281$			448.411i			1.59577i	−0.602812	+	0.797884i	$0.705953\pi$
$282$	500.189			1.77372
$283$	40.4553			0.142952			0.0714758	−	0.997442i	$-0.477229\pi$
$283$	40.4553			0.142952			0.0714758	+	0.997442i	$0.477229\pi$
$284$	−46.9043			−0.165156
$285$	163.119			0.572348
$286$		−	368.353i		−	1.28795i
$287$	−62.0045			−0.216043
$288$			304.582i			1.05758i
$289$	148.265			0.513028
$290$	−1232.97			−4.25161
$291$	−64.0156			−0.219985
$292$	41.9177			0.143554
$293$	205.481			0.701301			0.350651	−	0.936506i	$-0.385960\pi$
$293$	205.481			0.701301			0.350651	+	0.936506i	$0.385960\pi$
$294$	−239.440			−0.814422
$295$			104.958i			0.355788i
$296$		−	1302.96i		−	4.40190i
$297$	−24.6144			−0.0828768
$298$		−	306.863i		−	1.02974i
$299$			533.323i			1.78369i
$300$		−	404.357i		−	1.34786i
$301$	100.285			0.333174
$302$			514.022i			1.70206i
$303$	213.155			0.703482
$304$	−723.363			−2.37948
$305$	260.602			0.854434
$306$			239.122i			0.781445i
$307$	−126.169			−0.410975			−0.205487	−	0.978660i	$-0.565878\pi$
$307$	−126.169			−0.410975			−0.205487	+	0.978660i	$0.565878\pi$
$308$	177.986			0.577878
$309$			214.056i			0.692739i
$310$			38.8193i			0.125224i
$311$		−	30.6995i		−	0.0987122i	−0.998781	−	0.0493561i	$-0.984283\pi$
$311$		−	30.6995i		−	0.0987122i	0.998781	−	0.0493561i	$-0.0157169\pi$
$312$		−	879.431i		−	2.81869i
$313$		−	176.622i		−	0.564289i	−0.959372	−	0.282144i	$-0.908954\pi$
$313$		−	176.622i		−	0.564289i	0.959372	−	0.282144i	$-0.0910457\pi$
$314$		−	325.075i		−	1.03527i
$315$	−73.5240			−0.233409
$316$			584.565i			1.84989i
$317$	−267.128			−0.842675			−0.421337	−	0.906904i	$-0.638439\pi$
$317$	−267.128			−0.842675			−0.421337	+	0.906904i	$0.638439\pi$
$318$			643.356i			2.02313i
$319$			223.097i			0.699363i
$320$			1208.69i			3.77715i
$321$		−	331.780i		−	1.03358i
$322$	−355.594			−1.10433
$323$	−286.733			−0.887717
$324$	−94.7661			−0.292488
$325$			452.297i			1.39168i
$326$		−	355.681i		−	1.09105i
$327$	−357.224			−1.09243
$328$	−432.479			−1.31853
$329$		−	270.343i		−	0.821712i
$330$	−214.800			−0.650909
$331$			409.730i			1.23786i	0.785448	+	0.618928i	$0.212433\pi$
$331$			409.730i			1.23786i	−0.785448	+	0.618928i	$0.787567\pi$
$332$	−1047.43			−3.15492
$333$	157.051			0.471626
$334$			218.786i			0.655048i
$335$	−21.3326	+	459.671i	−0.0636795	+	1.37215i
$336$	326.047			0.970379
$337$		−	174.324i		−	0.517283i	−0.965973	−	0.258641i	$-0.916725\pi$
$337$		−	174.324i		−	0.517283i	0.965973	−	0.258641i	$-0.0832748\pi$
$338$			942.117i			2.78733i
$339$	−329.728			−0.972649
$340$			1512.25i			4.44778i
$341$	7.02409			0.0205985
$342$		−	156.802i		−	0.458486i
$343$			304.262i			0.887063i
$344$	699.489			2.03340
$345$	311.000			0.901449
$346$		−	143.006i		−	0.413312i
$347$		−	384.451i		−	1.10793i	−0.832540	−	0.553964i	$-0.813114\pi$
$347$		−	384.451i		−	1.10793i	0.832540	−	0.553964i	$-0.186886\pi$
$348$			858.928i			2.46818i
$349$	−266.361			−0.763213			−0.381606	−	0.924325i	$-0.624629\pi$
$349$	−266.361			−0.763213			−0.381606	+	0.924325i	$0.624629\pi$
$350$	−301.570			−0.861629
$351$	106.002			0.301999
$352$	480.940			1.36631
$353$			202.859i			0.574671i	0.957830	+	0.287335i	$0.0927694\pi$
$353$			202.859i			0.574671i	−0.957830	+	0.287335i	$0.907231\pi$
$354$	100.893			0.285009
$355$		−	30.5944i		−	0.0861814i
$356$	−958.406			−2.69215
$357$	129.241			0.362020
$358$	384.355			1.07362
$359$	159.406			0.444026			0.222013	−	0.975044i	$-0.428737\pi$
$359$	159.406			0.444026			0.222013	+	0.975044i	$0.428737\pi$
$360$	−512.828			−1.42452
$361$	−172.978			−0.479163
$362$		−	251.370i		−	0.694393i
$363$		−	170.712i		−	0.470280i
$364$	−766.495			−2.10575
$365$			27.3417i			0.0749088i
$366$		−	250.510i		−	0.684454i
$367$			393.231i			1.07147i	0.844385	+	0.535737i	$0.179966\pi$
$367$			393.231i			1.07147i	−0.844385	+	0.535737i	$0.820034\pi$
$368$	−1379.15			−3.74769
$369$		−	52.1286i		−	0.141270i
$370$	1370.52			3.70412
$371$	347.722			0.937257
$372$	27.0429			0.0726960
$373$		−	258.827i		−	0.693907i	−0.937882	−	0.346954i	$-0.887216\pi$
$373$		−	258.827i		−	0.693907i	0.937882	−	0.346954i	$-0.112784\pi$
$374$	377.578			1.00957
$375$	−33.6486			−0.0897296
$376$		−	1885.64i		−	5.01499i
$377$		−	960.762i		−	2.54844i
$378$			70.6767i			0.186976i
$379$			397.095i			1.04774i	0.851797	+	0.523871i	$0.175513\pi$
$379$			397.095i			1.04774i	−0.851797	+	0.523871i	$0.824487\pi$
$380$		−	991.642i		−	2.60958i
$381$		−	247.252i		−	0.648955i
$382$	99.4799			0.260419
$383$			377.209i			0.984880i	0.870346	+	0.492440i	$0.163895\pi$
$383$			377.209i			0.984880i	−0.870346	+	0.492440i	$0.836105\pi$
$384$	458.480			1.19396
$385$			116.096i			0.301547i
$386$			637.151i			1.65065i
$387$			84.3123i			0.217861i
$388$			389.167i			1.00301i
$389$	411.731			1.05844			0.529218	−	0.848486i	$-0.322485\pi$
$389$	411.731			1.05844			0.529218	+	0.848486i	$0.322485\pi$
$390$	925.032			2.37188
$391$	−546.679			−1.39816
$392$			902.652i			2.30268i
$393$		−	337.243i		−	0.858124i
$394$	693.906			1.76118
$395$	−381.295			−0.965305
$396$			149.637i			0.377872i
$397$	98.5479			0.248232			0.124116	−	0.992268i	$-0.460391\pi$
$397$	98.5479			0.248232			0.124116	+	0.992268i	$0.460391\pi$
$398$			279.744i			0.702874i
$399$	−84.7488			−0.212403
$400$	−1169.62			−2.92405
$401$		−	329.491i		−	0.821674i	−0.911709	−	0.410837i	$-0.865236\pi$
$401$		−	329.491i		−	0.821674i	0.911709	−	0.410837i	$-0.134764\pi$
$402$	441.870	+	20.5065i	1.09918	+	0.0510113i
$403$	−30.2491			−0.0750598
$404$		−	1295.82i		−	3.20748i
$405$		−	61.8133i		−	0.152625i
$406$	640.590			1.57781
$407$		−	247.987i		−	0.609304i
$408$	901.455			2.20945
$409$			661.143i			1.61649i	0.588849	+	0.808243i	$0.299581\pi$
$409$			661.143i			1.61649i	−0.588849	+	0.808243i	$0.700419\pi$
$410$		−	454.905i		−	1.10952i
$411$	140.392			0.341587
$412$	1301.30			3.15850
$413$		−	54.5309i		−	0.132036i
$414$		−	298.956i		−	0.722117i
$415$		−	683.213i		−	1.64630i
$416$	−2071.16			−4.97875
$417$	−103.101			−0.247245
$418$	−247.593			−0.592328
$419$	110.362			0.263393			0.131696	−	0.991290i	$-0.457958\pi$
$419$	110.362			0.263393			0.131696	+	0.991290i	$0.457958\pi$
$420$			446.971i			1.06422i
$421$	688.611			1.63565			0.817827	−	0.575463i	$-0.195178\pi$
$421$	688.611			1.63565			0.817827	+	0.575463i	$0.195178\pi$
$422$			65.0159i			0.154066i
$423$	227.284			0.537314
$424$	2425.36			5.72018
$425$	−463.624			−1.09088
$426$	−29.4096			−0.0690366
$427$	−135.396			−0.317087
$428$	−2016.98			−4.71256
$429$		−	167.378i		−	0.390159i
$430$			735.759i			1.71107i
$431$	60.6255			0.140662			0.0703312	−	0.997524i	$-0.477594\pi$
$431$	60.6255			0.140662			0.0703312	+	0.997524i	$0.477594\pi$
$432$			274.115i			0.634527i
$433$			207.487i			0.479185i	0.970874	+	0.239593i	$0.0770139\pi$
$433$			207.487i			0.479185i	−0.970874	+	0.239593i	$0.922986\pi$
$434$		−	20.1687i		−	0.0464716i
$435$	−560.255			−1.28794
$436$			2171.65i			4.98085i
$437$	358.480			0.820321
$438$	26.2829			0.0600066
$439$	−483.919			−1.10232			−0.551161	−	0.834399i	$-0.685815\pi$
$439$	−483.919			−1.10232			−0.551161	+	0.834399i	$0.685815\pi$
$440$			809.763i			1.84037i
$441$	−108.800			−0.246713
$442$	−1626.03			−3.67880
$443$		−	55.2890i		−	0.124806i	−0.998051	−	0.0624030i	$-0.980124\pi$
$443$		−	55.2890i		−	0.124806i	0.998051	−	0.0624030i	$-0.0198764\pi$
$444$		−	954.755i		−	2.15035i
$445$		−	625.142i		−	1.40481i
$446$			129.880i			0.291210i
$447$		−	139.437i		−	0.311941i
$448$		−	627.977i		−	1.40173i
$449$	408.732			0.910315			0.455158	−	0.890411i	$-0.349583\pi$
$449$	408.732			0.910315			0.455158	+	0.890411i	$0.349583\pi$
$450$		−	253.537i		−	0.563416i
$451$	−82.3118			−0.182510
$452$			2004.50i			4.43473i
$453$			233.569i			0.515606i
$454$		−	626.998i		−	1.38105i
$455$		−	499.963i		−	1.09882i
$456$	−591.121			−1.29632
$457$	685.666			1.50036			0.750182	−	0.661231i	$-0.229966\pi$
$457$	685.666			1.50036			0.750182	+	0.661231i	$0.229966\pi$
$458$	585.776			1.27899
$459$			108.656i			0.236724i
$460$		−	1890.65i		−	4.11010i
$461$	84.2748			0.182809			0.0914044	−	0.995814i	$-0.470864\pi$
$461$	84.2748			0.182809			0.0914044	+	0.995814i	$0.470864\pi$
$462$	111.600			0.241558
$463$		−	692.880i		−	1.49650i	−0.663416	−	0.748251i	$-0.730894\pi$
$463$		−	692.880i		−	1.49650i	0.663416	−	0.748251i	$-0.269106\pi$
$464$	2484.49			5.35451
$465$			17.6393i			0.0379341i
$466$	632.006			1.35624
$467$	375.239			0.803509			0.401754	−	0.915747i	$-0.368401\pi$
$467$	375.239			0.803509			0.401754	+	0.915747i	$0.368401\pi$
$468$		−	644.410i		−	1.37694i
$469$	11.0834	−	238.823i	0.0236320	−	0.509217i
$470$	1983.41			4.22003
$471$		−	147.713i		−	0.313615i
$472$		−	380.352i		−	0.805829i
$473$	133.130			0.281460
$474$			366.530i			0.773269i
$475$	304.017			0.640037
$476$		−	785.690i		−	1.65061i
$477$			292.338i			0.612869i
$478$	−842.042			−1.76159
$479$	489.168			1.02123			0.510614	−	0.859810i	$-0.329418\pi$
$479$	489.168			1.02123			0.510614	+	0.859810i	$0.329418\pi$
$480$			1207.77i			2.51618i
$481$			1067.95i			2.22027i
$482$		−	435.653i		−	0.903845i
$483$	−161.581			−0.334535
$484$	−1037.80			−2.14421
$485$	−253.843			−0.523387
$486$	−59.4196			−0.122262
$487$		−	261.143i		−	0.536228i	−0.963387	−	0.268114i	$-0.913600\pi$
$487$		−	261.143i		−	0.536228i	0.963387	−	0.268114i	$-0.0864004\pi$
$488$	−944.386			−1.93522
$489$		−	161.620i		−	0.330511i
$490$	−949.457			−1.93767
$491$	594.659			1.21112			0.605559	−	0.795800i	$-0.292950\pi$
$491$	594.659			1.21112			0.605559	+	0.795800i	$0.292950\pi$
$492$	−316.903			−0.644111
$493$	984.823			1.99761
$494$	1066.26			2.15841
$495$	−97.6042			−0.197180
$496$		−	78.2229i		−	0.157708i
$497$			15.8954i			0.0319826i
$498$	−656.755			−1.31879
$499$			917.470i			1.83862i	0.393538	+	0.919309i	$0.371251\pi$
$499$			917.470i			1.83862i	−0.393538	+	0.919309i	$0.628749\pi$
$500$			204.558i			0.409116i
$501$			99.4154i			0.198434i
$502$	−1302.00			−2.59363
$503$		−	82.4709i		−	0.163958i	−0.996634	−	0.0819791i	$-0.973876\pi$
$503$		−	82.4709i		−	0.163958i	0.996634	−	0.0819791i	$-0.0261241\pi$
$504$	266.441			0.528652
$505$	845.229			1.67372
$506$	−472.057			−0.932919
$507$			428.094i			0.844367i
$508$	−1503.11			−2.95887
$509$	512.212			1.00631			0.503156	−	0.864196i	$-0.332172\pi$
$509$	512.212			1.00631			0.503156	+	0.864196i	$0.332172\pi$
$510$			948.198i			1.85921i
$511$		−	14.2054i		−	0.0277993i
$512$		−	103.960i		−	0.203046i
$513$		−	71.2503i		−	0.138889i
$514$			868.142i			1.68899i
$515$			848.803i			1.64816i
$516$	512.556			0.993325
$517$		−	358.885i		−	0.694168i
$518$	−712.058			−1.37463
$519$		−	64.9813i		−	0.125205i
$520$		−	3487.23i		−	6.70621i
$521$		−	505.807i		−	0.970838i	−0.874282	−	0.485419i	$-0.838667\pi$
$521$		−	505.807i		−	0.970838i	0.874282	−	0.485419i	$-0.161333\pi$
$522$			538.559i			1.03172i
$523$	−36.6151			−0.0700097			−0.0350048	−	0.999387i	$-0.511145\pi$
$523$	−36.6151			−0.0700097			−0.0350048	+	0.999387i	$0.511145\pi$
$524$	−2050.18			−3.91256
$525$	−137.032			−0.261014
$526$		−	1407.06i		−	2.67503i
$527$		−	31.0066i		−	0.0588361i
$528$	432.833			0.819759
$529$	154.472			0.292007
$530$			2551.12i			4.81343i
$531$	45.8454			0.0863378
$532$			515.209i			0.968438i
$533$	354.474			0.665055
$534$	−600.933			−1.12534
$535$		−	1315.62i		−	2.45910i
$536$	77.3065	−	1665.78i	0.144229	−	3.10780i
$537$	174.649			0.325232
$538$			1729.42i			3.21453i
$539$			171.798i			0.318734i
$540$	−375.779			−0.695886
$541$		−	70.9784i		−	0.131199i	−0.997846	−	0.0655993i	$-0.979104\pi$
$541$		−	70.9784i		−	0.131199i	0.997846	−	0.0655993i	$-0.0208959\pi$
$542$	313.731			0.578839
$543$		−	114.222i		−	0.210353i
$544$		−	2123.03i		−	3.90263i
$545$	−1416.51			−2.59910
$546$	−480.602			−0.880223
$547$		−	46.0516i		−	0.0841894i	−0.999114	−	0.0420947i	$-0.986597\pi$
$547$		−	46.0516i		−	0.0841894i	0.999114	−	0.0420947i	$-0.0134031\pi$
$548$		−	853.481i		−	1.55745i
$549$		−	113.831i		−	0.207342i
$550$	−400.339			−0.727889
$551$	−645.789			−1.17203
$552$	−1127.02			−2.04170
$553$	198.103			0.358233
$554$		−	770.562i		−	1.39091i
$555$	622.760			1.12209
$556$			626.778i			1.12730i
$557$	−52.4981			−0.0942515			−0.0471258	−	0.998889i	$-0.515006\pi$
$557$	−52.4981			−0.0942515			−0.0471258	+	0.998889i	$0.515006\pi$
$558$	16.9563			0.0303876
$559$	−573.324			−1.02562
$560$	1292.88			2.30872
$561$	171.570			0.305828
$562$	1709.24			3.04135
$563$		−	419.406i		−	0.744948i	−0.928043	−	0.372474i	$-0.878510\pi$
$563$		−	419.406i		−	0.744948i	0.928043	−	0.372474i	$-0.121490\pi$
$564$		−	1381.71i		−	2.44985i
$565$	−1307.48			−2.31412
$566$		−	154.206i		−	0.272449i
$567$			32.1152i			0.0566406i
$568$			110.870i			0.195193i
$569$	−555.462			−0.976207			−0.488103	−	0.872786i	$-0.662311\pi$
$569$	−555.462			−0.976207			−0.488103	+	0.872786i	$0.662311\pi$
$570$		−	621.772i		−	1.09083i
$571$	−162.102			−0.283891			−0.141945	−	0.989874i	$-0.545336\pi$
$571$	−162.102			−0.283891			−0.141945	+	0.989874i	$0.545336\pi$
$572$	−1017.53			−1.77890
$573$	45.2033			0.0788887
$574$			236.347i			0.411754i
$575$	579.634			1.00806
$576$	527.955			0.916588
$577$		−	72.0181i		−	0.124815i	−0.998051	−	0.0624074i	$-0.980122\pi$
$577$		−	72.0181i		−	0.124815i	0.998051	−	0.0624074i	$-0.0198778\pi$
$578$		−	565.151i		−	0.977771i
$579$			289.519i			0.500032i
$580$			3405.93i			5.87229i
$581$			354.964i			0.610954i
$582$			244.013i			0.419266i
$583$	461.607			0.791778
$584$		−	99.0826i		−	0.169662i
$585$	420.331			0.718514
$586$		−	783.247i		−	1.33660i
$587$			731.896i			1.24684i	0.781887	+	0.623421i	$0.214258\pi$
$587$			731.896i			1.24684i	−0.781887	+	0.623421i	$0.785742\pi$
$588$			661.425i			1.12487i
$589$			20.3323i			0.0345201i
$590$	400.074			0.678091
$591$	315.308			0.533516
$592$	−2761.67			−4.66499
$593$		−	526.043i		−	0.887087i	−0.896253	−	0.443544i	$-0.853721\pi$
$593$		−	526.043i		−	0.887087i	0.896253	−	0.443544i	$-0.146279\pi$
$594$			93.8244i			0.157954i
$595$	512.484			0.861317
$596$	−847.675			−1.42227
$597$			127.114i			0.212922i
$598$	2032.90			3.39951
$599$		−	1070.39i		−	1.78697i	−0.449095	−	0.893484i	$-0.648253\pi$
$599$		−	1070.39i		−	1.78697i	0.449095	−	0.893484i	$-0.351747\pi$
$600$	−955.796			−1.59299
$601$	−14.9915			−0.0249442			−0.0124721	−	0.999922i	$-0.503970\pi$
$601$	−14.9915			−0.0249442			−0.0124721	+	0.999922i	$0.503970\pi$
$602$		−	382.265i		−	0.634992i
$603$	200.784	+	9.31808i	0.332975	+	0.0154529i
$604$	1419.93			2.35087
$605$		−	676.927i		−	1.11889i
$606$		−	812.497i		−	1.34075i
$607$	964.158			1.58840			0.794200	−	0.607657i	$-0.207890\pi$
$607$	964.158			1.58840			0.794200	+	0.607657i	$0.207890\pi$
$608$			1392.16i			2.28973i
$609$	291.082			0.477966
$610$		−	993.355i		−	1.62845i
$611$			1545.53i			2.52951i
$612$	660.548			1.07933
$613$	−1151.75			−1.87887			−0.939436	−	0.342723i	$-0.888651\pi$
$613$	−1151.75			−1.87887			−0.939436	+	0.342723i	$0.888651\pi$
$614$			480.928i			0.783270i
$615$		−	206.707i		−	0.336109i
$616$		−	420.714i		−	0.682977i
$617$	59.0411			0.0956906			0.0478453	−	0.998855i	$-0.484765\pi$
$617$	59.0411			0.0956906			0.0478453	+	0.998855i	$0.484765\pi$
$618$	815.932			1.32028
$619$	−732.815			−1.18387			−0.591935	−	0.805986i	$-0.701636\pi$
$619$	−732.815			−1.18387			−0.591935	+	0.805986i	$0.701636\pi$
$620$	107.234			0.172958
$621$		−	135.845i		−	0.218751i
$622$	−117.019			−0.188134
$623$			324.793i			0.521338i
$624$	−1863.99			−2.98716
$625$	−687.713			−1.10034
$626$	−673.243			−1.07547
$627$	−112.505			−0.179434
$628$	−897.983			−1.42991
$629$	−1094.69			−1.74037
$630$			280.256i			0.444851i
$631$			696.223i			1.10336i	0.834054	+	0.551682i	$0.186014\pi$
$631$			696.223i			1.10336i	−0.834054	+	0.551682i	$0.813986\pi$
$632$	1381.76			2.18633
$633$			29.5430i			0.0466713i
$634$			1018.23i			1.60604i
$635$		−	980.435i		−	1.54399i
$636$	1777.20			2.79434
$637$		−	739.843i		−	1.16145i
$638$	850.393			1.33290
$639$	−13.3636			−0.0209133
$640$	1818.02			2.84066
$641$			819.690i			1.27877i	0.768888	+	0.639384i	$0.220810\pi$
$641$			819.690i			1.27877i	−0.768888	+	0.639384i	$0.779190\pi$
$642$	−1264.67			−1.96989
$643$	919.457			1.42995			0.714974	−	0.699151i	$-0.246438\pi$
$643$	919.457			1.42995			0.714974	+	0.699151i	$0.246438\pi$
$644$			982.289i			1.52529i
$645$			334.326i			0.518335i
$646$			1092.96i			1.69189i
$647$			43.3362i			0.0669802i	0.999439	+	0.0334901i	$0.0106622\pi$
$647$			43.3362i			0.0669802i	−0.999439	+	0.0334901i	$0.989338\pi$
$648$			224.003i			0.345683i
$649$		−	72.3906i		−	0.111542i
$650$	1724.05			2.65239
$651$		−	9.16455i		−	0.0140777i
$652$	−982.528			−1.50694
$653$			337.755i			0.517236i	0.965980	+	0.258618i	$0.0832672\pi$
$653$			337.755i			0.517236i	−0.965980	+	0.258618i	$0.916733\pi$
$654$			1361.65i			2.08204i
$655$		−	1337.28i		−	2.04165i
$656$			916.656i			1.39734i
$657$	11.9428			0.0181778
$658$	−1030.49			−1.56609
$659$	−998.483			−1.51515			−0.757574	−	0.652749i	$-0.773616\pi$
$659$	−998.483			−1.51515			−0.757574	+	0.652749i	$0.773616\pi$
$660$			593.360i			0.899031i
$661$		−	123.559i		−	0.186927i	−0.995623	−	0.0934634i	$-0.970206\pi$
$661$		−	123.559i		−	0.186927i	0.995623	−	0.0934634i	$-0.0297938\pi$
$662$	1561.80			2.35921
$663$	−738.862			−1.11442
$664$			2475.87i			3.72872i
$665$	−336.057			−0.505348
$666$		−	598.644i		−	0.898864i
$667$	−1231.25			−1.84595
$668$	604.371			0.904747
$669$			59.0169i			0.0882165i
$670$	1752.16	+	81.3151i	2.61516	+	0.121366i
$671$	−179.741			−0.267870
$672$		−	627.498i		−	0.933777i
$673$		−	8.52334i		−	0.0126647i	−0.999980	−	0.00633235i	$-0.997984\pi$
$673$		−	8.52334i		−	0.0126647i	0.999980	−	0.00633235i	$-0.00201566\pi$
$674$	−664.483			−0.985880
$675$		−	115.206i		−	0.170676i
$676$	2602.49			3.84984
$677$			408.308i			0.603113i	0.953448	+	0.301557i	$0.0975062\pi$
$677$			408.308i			0.603113i	−0.953448	+	0.301557i	$0.902494\pi$
$678$			1256.85i			1.85375i
$679$	131.884			0.194233
$680$	3574.56			5.25671
$681$		−	284.905i		−	0.418363i
$682$		−	26.7742i		−	0.0392583i
$683$		−	663.289i		−	0.971140i	−0.874198	−	0.485570i	$-0.838612\pi$
$683$		−	663.289i		−	0.971140i	0.874198	−	0.485570i	$-0.161388\pi$
$684$	−433.148			−0.633258
$685$	556.702			0.812703
$686$	1159.78			1.69064
$687$	266.174			0.387444
$688$		−	1482.59i		−	2.15493i
$689$	−1987.90			−2.88520
$690$		−	1185.46i		−	1.71806i
$691$	349.342			0.505560			0.252780	−	0.967524i	$-0.418655\pi$
$691$	349.342			0.505560			0.252780	+	0.967524i	$0.418655\pi$
$692$	−395.038			−0.570864
$693$	50.7104			0.0731752
$694$	−1465.44			−2.11158
$695$	−408.830			−0.588244
$696$	2030.29			2.91708
$697$			363.351i			0.521308i
$698$			1015.31i			1.45459i
$699$	287.181			0.410845
$700$			833.053i			1.19008i
$701$		−	355.517i		−	0.507157i	−0.967315	−	0.253579i	$-0.918392\pi$
$701$		−	355.517i		−	0.507157i	0.967315	−	0.253579i	$-0.0816076\pi$
$702$		−	404.053i		−	0.575574i
$703$	717.836			1.02110
$704$		−	833.648i		−	1.18416i
$705$	901.254			1.27837
$706$	773.250			1.09526
$707$	−439.140			−0.621132
$708$		−	278.705i		−	0.393652i
$709$	150.250			0.211918			0.105959	−	0.994371i	$-0.466209\pi$
$709$	150.250			0.211918			0.105959	+	0.994371i	$0.466209\pi$
$710$	−116.619			−0.164252
$711$			166.550i			0.234247i
$712$			2265.43i			3.18178i
$713$			38.7653i			0.0543692i
$714$		−	492.638i		−	0.689969i
$715$		−	663.709i		−	0.928264i
$716$		−	1061.74i		−	1.48287i
$717$	−382.620			−0.533641
$718$		−	607.617i		−	0.846263i
$719$	1169.15			1.62608			0.813041	−	0.582206i	$-0.197810\pi$
$719$	1169.15			1.62608			0.813041	+	0.582206i	$0.197810\pi$
$720$			1086.96i			1.50966i
$721$		−	440.997i		−	0.611646i
$722$			659.351i			0.913228i
$723$		−	197.959i		−	0.273802i
$724$	−694.382			−0.959091
$725$	−1044.19			−1.44026
$726$	−650.713			−0.896299
$727$		−	1170.34i		−	1.60982i	−0.593398	−	0.804909i	$-0.702214\pi$
$727$		−	1170.34i		−	1.60982i	0.593398	−	0.804909i	$-0.297786\pi$
$728$			1811.80i			2.48873i
$729$	−27.0000			−0.0370370
$730$	104.220			0.142768
$731$		−	587.682i		−	0.803942i
$732$	−692.006			−0.945363
$733$			726.905i			0.991685i	0.868413	+	0.495842i	$0.165141\pi$
$733$			726.905i			0.991685i	−0.868413	+	0.495842i	$0.834859\pi$
$734$	1498.90			2.04210
$735$	−431.429			−0.586979
$736$			2654.26i			3.60633i
$737$	14.7134	−	317.041i	0.0199639	−	0.430178i
$738$	−198.702			−0.269244
$739$		−	395.402i		−	0.535049i	−0.963551	−	0.267525i	$-0.913794\pi$
$739$		−	395.402i		−	0.535049i	0.963551	−	0.267525i	$-0.0862057\pi$
$740$		−	3785.91i		−	5.11610i
$741$	484.502			0.653849
$742$		−	1325.44i		−	1.78630i
$743$	764.338			1.02872			0.514360	−	0.857575i	$-0.328030\pi$
$743$	764.338			1.02872			0.514360	+	0.857575i	$0.328030\pi$
$744$		−	63.9225i		−	0.0859174i
$745$		−	552.915i		−	0.742168i
$746$	−986.589			−1.32251
$747$	−298.427			−0.399500
$748$		−	1043.02i		−	1.39441i
$749$			683.531i			0.912592i
$750$			128.261i			0.171014i
$751$	−760.762			−1.01300			−0.506499	−	0.862241i	$-0.669061\pi$
$751$	−760.762			−1.01300			−0.506499	+	0.862241i	$0.669061\pi$
$752$	−3996.68			−5.31473
$753$	−591.625			−0.785691
$754$	−3662.20			−4.85703
$755$			926.179i			1.22673i
$756$	195.236			0.258249
$757$			574.422i			0.758814i	0.925230	+	0.379407i	$0.123872\pi$
$757$			574.422i			0.758814i	−0.925230	+	0.379407i	$0.876128\pi$
$758$	1513.63			1.99688
$759$	−214.501			−0.282610
$760$	−2343.99			−3.08419
$761$	−393.692			−0.517335			−0.258668	−	0.965966i	$-0.583283\pi$
$761$	−393.692			−0.517335			−0.258668	+	0.965966i	$0.583283\pi$
$762$	−942.467			−1.23683
$763$	735.949			0.964547
$764$		−	274.802i		−	0.359688i
$765$			430.857i			0.563212i
$766$	1437.83			1.87707
$767$			311.749i			0.406452i
$768$		−	528.359i		−	0.687968i
$769$			1306.03i			1.69835i	0.528109	+	0.849177i	$0.322901\pi$
$769$			1306.03i			1.69835i	−0.528109	+	0.849177i	$0.677099\pi$
$770$	442.529			0.574713
$771$			394.480i			0.511647i
$772$	1760.06			2.27987
$773$	−1227.66			−1.58818			−0.794088	−	0.607803i	$-0.792051\pi$
$773$	−1227.66			−1.58818			−0.794088	+	0.607803i	$0.792051\pi$
$774$	321.379			0.415218
$775$			32.8758i			0.0424204i
$776$	919.890			1.18543
$777$	−323.556			−0.416417
$778$		−	1569.42i		−	2.01726i
$779$		−	238.264i		−	0.305859i
$780$		−	2555.29i		−	3.27602i
$781$			21.1013i			0.0270184i
$782$			2083.81i			2.66472i
$783$			244.719i			0.312540i
$784$	1913.20			2.44031
$785$		−	585.730i		−	0.746152i
$786$	−1285.49			−1.63548
$787$		−	778.633i		−	0.989368i	−0.869073	−	0.494684i	$-0.835284\pi$
$787$		−	778.633i		−	0.989368i	0.869073	−	0.494684i	$-0.164716\pi$
$788$		−	1916.83i		−	2.43253i
$789$		−	639.364i		−	0.810347i
$790$			1453.41i			1.83976i
$791$	679.303			0.858790
$792$	353.704			0.446596
$793$	774.050			0.976103
$794$		−	375.642i		−	0.473100i
$795$			1159.22i			1.45813i
$796$	772.760			0.970804
$797$	−259.996			−0.326218			−0.163109	−	0.986608i	$-0.552152\pi$
$797$	−259.996			−0.326218			−0.163109	+	0.986608i	$0.552152\pi$
$798$			323.043i			0.404815i
$799$	−1584.23			−1.98277
$800$			2251.01i			2.81376i
$801$	−273.061			−0.340901
$802$	−1255.94			−1.56602
$803$		−	18.8579i		−	0.0234843i
$804$	56.6469	−	1220.62i	0.0704564	−	1.51818i
$805$	−640.720			−0.795925
$806$			115.303i			0.143055i
$807$			785.841i			0.973781i
$808$	−3062.99			−3.79083
$809$			1045.99i			1.29294i	0.762939	+	0.646470i	$0.223755\pi$
$809$			1045.99i			1.29294i	−0.762939	+	0.646470i	$0.776245\pi$
$810$	−235.618			−0.290886
$811$			945.162i			1.16543i	0.812677	+	0.582714i	$0.198009\pi$
$811$			945.162i			1.16543i	−0.812677	+	0.582714i	$0.801991\pi$
$812$		−	1769.56i		−	2.17926i
$813$	142.558			0.175348
$814$	−945.267			−1.16126
$815$		−	640.876i		−	0.786351i
$816$		−	1910.67i		−	2.34150i
$817$			385.367i			0.471685i
$818$	2520.12			3.08083
$819$	−218.383			−0.266646
$820$	−1256.62			−1.53247
$821$	812.585			0.989750			0.494875	−	0.868964i	$-0.335214\pi$
$821$	812.585			0.989750			0.494875	+	0.868964i	$0.335214\pi$
$822$		−	535.143i		−	0.651026i
$823$	−113.983			−0.138497			−0.0692487	−	0.997599i	$-0.522060\pi$
$823$	−113.983			−0.138497			−0.0692487	+	0.997599i	$0.522060\pi$
$824$		−	3075.94i		−	3.73294i
$825$	−181.912			−0.220500
$826$	−207.859			−0.251645
$827$	55.7448			0.0674060			0.0337030	−	0.999432i	$-0.489270\pi$
$827$	55.7448			0.0674060			0.0337030	+	0.999432i	$0.489270\pi$
$828$	−825.833			−0.997383
$829$	−1042.05			−1.25699			−0.628497	−	0.777812i	$-0.716330\pi$
$829$	−1042.05			−1.25699			−0.628497	+	0.777812i	$0.716330\pi$
$830$	−2604.25			−3.13765
$831$		−	350.140i		−	0.421348i
$832$			3590.09i			4.31501i
$833$	758.371			0.910410
$834$			392.998i			0.471220i
$835$			394.214i			0.472113i
$836$			683.948i			0.818119i
$837$	7.70485			0.00920532
$838$		−	420.673i		−	0.501996i
$839$	−964.339			−1.14939			−0.574695	−	0.818367i	$-0.694879\pi$
$839$	−964.339			−1.14939			−0.574695	+	0.818367i	$0.694879\pi$
$840$	1056.52			1.25777
$841$	1377.05			1.63740
$842$		−	2624.82i		−	3.11737i
$843$	776.670			0.921317
$844$	179.599			0.212795
$845$			1697.53i			2.00891i
$846$		−	866.353i		−	1.02406i
$847$			351.699i			0.415229i
$848$		−	5140.63i		−	6.06206i
$849$		−	70.0706i		−	0.0825331i
$850$			1767.23i			2.07909i
$851$	1368.61			1.60824
$852$			81.2407i			0.0953529i
$853$	489.142			0.573437			0.286719	−	0.958015i	$-0.407436\pi$
$853$	489.142			0.573437			0.286719	+	0.958015i	$0.407436\pi$
$854$			516.099i			0.604332i
$855$		−	282.531i		−	0.330445i
$856$			4767.61i			5.56964i
$857$			289.386i			0.337673i	0.985644	+	0.168836i	$0.0540010\pi$
$857$			289.386i			0.337673i	−0.985644	+	0.168836i	$0.945999\pi$
$858$	−638.006			−0.743597
$859$	207.535			0.241601			0.120801	−	0.992677i	$-0.461454\pi$
$859$	207.535			0.241601			0.120801	+	0.992677i	$0.461454\pi$
$860$	2032.45			2.36331
$861$			107.395i			0.124733i
$862$		−	231.090i		−	0.268086i
$863$	−618.704			−0.716923			−0.358461	−	0.933545i	$-0.616699\pi$
$863$	−618.704			−0.716923			−0.358461	+	0.933545i	$0.616699\pi$
$864$	527.552			0.610593
$865$		−	257.672i		−	0.297887i
$866$	790.893			0.913271
$867$		−	256.802i		−	0.296197i
$868$	−55.7136			−0.0641862
$869$	262.984			0.302629
$870$			2135.56i			2.45467i
$871$	−63.3629	+	1365.33i	−0.0727473	+	1.56754i
$872$	5133.23			5.88673
$873$			110.878i			0.127008i
$874$		−	1366.44i		−	1.56344i
$875$	69.3225			0.0792258
$876$		−	72.6035i		−	0.0828807i
$877$	−566.683			−0.646161			−0.323080	−	0.946372i	$-0.604718\pi$
$877$	−566.683			−0.646161			−0.323080	+	0.946372i	$0.604718\pi$
$878$			1844.59i			2.10090i
$879$		−	355.904i		−	0.404897i
$880$	1716.32			1.95037
$881$	−160.966			−0.182708			−0.0913541	−	0.995818i	$-0.529119\pi$
$881$	−160.966			−0.182708			−0.0913541	+	0.995818i	$0.529119\pi$
$882$			414.722i			0.470206i
$883$		−	1173.83i		−	1.32936i	−0.747126	−	0.664682i	$-0.768567\pi$
$883$		−	1173.83i		−	1.32936i	0.747126	−	0.664682i	$-0.231433\pi$
$884$			4491.73i			5.08114i
$885$	181.792			0.205415
$886$	−210.749			−0.237866
$887$	729.417			0.822342			0.411171	−	0.911558i	$-0.365120\pi$
$887$	729.417			0.822342			0.411171	+	0.911558i	$0.365120\pi$
$888$	−2256.80			−2.54144
$889$			509.387i			0.572988i
$890$	−2382.89			−2.67741
$891$			42.6334i			0.0478490i
$892$	358.778			0.402218
$893$	1038.85			1.16332
$894$	−531.503			−0.594522
$895$	692.542			0.773790
$896$	−944.556			−1.05419
$897$	923.743			1.02981
$898$		−	1557.99i		−	1.73495i
$899$		−	69.8342i		−	0.0776798i
$900$	−700.367			−0.778185
$901$		−	2037.68i		−	2.26158i
$902$			313.754i			0.347842i
$903$		−	173.700i		−	0.192358i
$904$	4738.12			5.24128
$905$		−	452.926i		−	0.500471i
$906$	890.312			0.982684
$907$	−1272.88			−1.40340			−0.701700	−	0.712473i	$-0.747575\pi$
$907$	−1272.88			−1.40340			−0.701700	+	0.712473i	$0.747575\pi$
$908$	−1732.01			−1.90750
$909$		−	369.195i		−	0.406155i
$910$	−1905.74			−2.09422
$911$	1634.42			1.79409			0.897045	−	0.441939i	$-0.145709\pi$
$911$	1634.42			1.79409			0.897045	+	0.441939i	$0.145709\pi$
$912$			1252.90i			1.37380i
$913$			471.220i			0.516123i
$914$		−	2613.60i		−	2.85952i
$915$		−	451.376i		−	0.493307i
$916$		−	1618.14i		−	1.76653i
$917$			694.785i			0.757672i
$918$	414.172			0.451168
$919$		−	986.056i		−	1.07297i	−0.843911	−	0.536483i	$-0.819753\pi$
$919$		−	986.056i		−	1.07297i	0.843911	−	0.536483i	$-0.180247\pi$
$920$	−4469.00			−4.85761
$921$			218.531i			0.237276i
$922$		−	321.236i		−	0.348412i
$923$		−	90.8725i		−	0.0984534i
$924$		−	308.281i		−	0.333638i
$925$	1160.69			1.25479
$926$	−2641.10			−2.85216
$927$	370.756			0.399953
$928$		−	4781.56i		−	5.15254i
$929$		−	456.780i		−	0.491691i	−0.969309	−	0.245845i	$-0.920934\pi$
$929$		−	456.780i		−	0.491691i	0.969309	−	0.245845i	$-0.0790655\pi$
$930$	67.2371			0.0722979
$931$	−497.295			−0.534152
$932$		−	1745.84i		−	1.87322i
$933$	−53.1731			−0.0569915
$934$		−	1430.32i		−	1.53139i
$935$	680.330			0.727626
$936$	−1523.22			−1.62737
$937$			1491.05i			1.59130i	0.605756	+	0.795651i	$0.292871\pi$
$937$			1491.05i			1.59130i	−0.605756	+	0.795651i	$0.707129\pi$
$938$	−910.337	−	42.2474i	−0.970509	−	0.0450398i
$939$	−305.919			−0.325792
$940$		−	5478.95i		−	5.82867i
$941$		−	1061.49i		−	1.12804i	−0.825760	−	0.564021i	$-0.809254\pi$
$941$		−	1061.49i		−	1.12804i	0.825760	−	0.564021i	$-0.190746\pi$
$942$	−563.047			−0.597715
$943$		−	454.271i		−	0.481729i
$944$	−806.169			−0.853992
$945$			127.347i			0.134759i
$946$		−	507.462i		−	0.536430i
$947$	−1292.53			−1.36487			−0.682434	−	0.730947i	$-0.739079\pi$
$947$	−1292.53			−1.36487			−0.682434	+	0.730947i	$0.739079\pi$
$948$	1012.50			1.06803
$949$			81.2113i			0.0855757i
$950$		−	1158.84i		−	1.21984i
$951$			462.679i			0.486518i
$952$	−1857.17			−1.95081
$953$	−309.563			−0.324830			−0.162415	−	0.986723i	$-0.551928\pi$
$953$	−309.563			−0.324830			−0.162415	+	0.986723i	$0.551928\pi$
$954$	1114.33			1.16806
$955$	179.246			0.187692
$956$			2326.04i			2.43310i
$957$	386.415			0.403777
$958$		−	1864.59i		−	1.94634i
$959$	−289.235			−0.301601
$960$	2093.51			2.18074
$961$	958.801			0.997712
$962$	4070.78			4.23158
$963$	−574.660			−0.596740
$964$	−1203.44			−1.24838
$965$			1148.04i			1.18967i
$966$			615.908i			0.637586i
$967$	1336.51			1.38212			0.691061	−	0.722796i	$-0.257144\pi$
$967$	1336.51			1.38212			0.691061	+	0.722796i	$0.257144\pi$
$968$			2453.09i			2.53418i
$969$			496.635i			0.512524i
$970$			967.589i			0.997515i
$971$	345.205			0.355515			0.177757	−	0.984074i	$-0.443116\pi$
$971$	345.205			0.355515			0.177757	+	0.984074i	$0.443116\pi$
$972$			164.140i			0.168868i
$973$	212.408			0.218302
$974$	−995.417			−1.02199
$975$	783.402			0.803489
$976$			2001.66i			2.05088i
$977$	−1271.71			−1.30165			−0.650823	−	0.759230i	$-0.725576\pi$
$977$	−1271.71			−1.30165			−0.650823	+	0.759230i	$0.725576\pi$
$978$	−616.058			−0.629916
$979$			431.168i			0.440417i
$980$			2622.77i			2.67629i
$981$			618.729i			0.630713i
$982$		−	2266.70i		−	2.30825i
$983$		−	463.327i		−	0.471340i	−0.971833	−	0.235670i	$-0.924272\pi$
$983$		−	463.327i		−	0.471340i	0.971833	−	0.235670i	$-0.0757285\pi$
$984$			749.076i			0.761256i
$985$	1250.30			1.26934
$986$		−	3753.91i		−	3.80722i
$987$	−468.248			−0.474416
$988$		−	2945.41i		−	2.98118i
$989$			734.734i			0.742906i
$990$			372.044i			0.375802i
$991$		−	143.769i		−	0.145074i	−0.997366	−	0.0725372i	$-0.976890\pi$
$991$		−	143.769i		−	0.145074i	0.997366	−	0.0725372i	$-0.0231096\pi$
$992$	−150.545			−0.151759
$993$	709.674			0.714677
$994$	60.5894			0.0609552
$995$			504.050i			0.506583i
$996$			1814.21i			1.82150i
$997$	−1017.62			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$997$	−1017.62			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$998$	3497.18			3.50419
$999$		−	272.021i		−	0.272293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.1	✓	22
3.2	odd	2		603.3.b.e.334.22		22
67.66	odd	2	inner	201.3.b.a.133.22	yes	22
201.200	even	2		603.3.b.e.334.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.1	✓	22	1.1	even	1	trivial
201.3.b.a.133.22	yes	22	67.66	odd	2	inner
603.3.b.e.334.1		22	201.200	even	2
603.3.b.e.334.22		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.81177i q^{2} -1.73205i q^{3} -10.5296 q^{4} -6.86815i q^{5} -6.60217 q^{6} +3.56836i q^{7} +24.8892i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.81177i q^{2} -1.73205i q^{3} -10.5296 q^{4} -6.86815i q^{5} -6.60217 q^{6} +3.56836i q^{7} +24.8892i q^{8} -3.00000 q^{9} -26.1798 q^{10} +4.73705i q^{11} +18.2377i q^{12} -20.4000i q^{13} +13.6017 q^{14} -11.8960 q^{15} +52.7535 q^{16} +20.9109 q^{17} +11.4353i q^{18} -13.7121 q^{19} +72.3186i q^{20} +6.18058 q^{21} +18.0565 q^{22} -26.1433 q^{23} +43.1094 q^{24} -22.1714 q^{25} -77.7601 q^{26} +5.19615i q^{27} -37.5733i q^{28} +47.0962 q^{29} +45.3447i q^{30} -1.48280i q^{31} -101.527i q^{32} +8.20481 q^{33} -79.7074i q^{34} +24.5080 q^{35} +31.5887 q^{36} -52.3505 q^{37} +52.2674i q^{38} -35.3338 q^{39} +170.943 q^{40} +17.3762i q^{41} -23.5589i q^{42} -28.1041i q^{43} -49.8791i q^{44} +20.6044i q^{45} +99.6522i q^{46} -75.7613 q^{47} -91.3718i q^{48} +36.2668 q^{49} +84.5123i q^{50} -36.2187i q^{51} +214.803i q^{52} -97.4461i q^{53} +19.8065 q^{54} +32.5347 q^{55} -88.8135 q^{56} +23.7501i q^{57} -179.520i q^{58} -15.2818 q^{59} +125.260 q^{60} +37.9436i q^{61} -5.65209 q^{62} -10.7051i q^{63} -175.985 q^{64} -140.110 q^{65} -31.2748i q^{66} +(-66.9280 - 3.10603i) q^{67} -220.183 q^{68} +45.2815i q^{69} -93.4188i q^{70} +4.45453 q^{71} -74.6676i q^{72} -3.98095 q^{73} +199.548i q^{74} +38.4020i q^{75} +144.383 q^{76} -16.9035 q^{77} +134.684i q^{78} -55.5165i q^{79} -362.319i q^{80} +9.00000 q^{81} +66.2340 q^{82} +99.4756 q^{83} -65.0788 q^{84} -143.619i q^{85} -107.126 q^{86} -81.5730i q^{87} -117.901 q^{88} +91.0204 q^{89} +78.5393 q^{90} +72.7945 q^{91} +275.278 q^{92} -2.56828 q^{93} +288.784i q^{94} +94.1769i q^{95} -175.851 q^{96} -36.9594i q^{97} -138.241i q^{98} -14.2111i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 22 * q - 52 * q^4 - 66 * q^9	\( 22 q - 52 q^{4} - 66 q^{9} - 36 q^{10} + 72 q^{14} + 12 q^{15} + 116 q^{16} - 14 q^{17} - 26 q^{19} + 48 q^{21} + 32 q^{22} - 82 q^{23} + 36 q^{24} - 62 q^{25} - 100 q^{26} + 102 q^{29} + 36 q^{33} - 180 q^{35} + 156 q^{36} + 106 q^{37} - 72 q^{39} + 76 q^{40} + 154 q^{47} + 146 q^{49} - 224 q^{55} - 452 q^{56} + 370 q^{59} - 24 q^{60} - 300 q^{62} + 148 q^{64} - 284 q^{65} - 134 q^{67} - 116 q^{68} + 160 q^{71} + 218 q^{73} + 480 q^{76} - 396 q^{77} + 198 q^{81} - 68 q^{82} + 128 q^{83} + 20 q^{86} - 856 q^{88} - 118 q^{89} + 108 q^{90} - 400 q^{91} + 804 q^{92} - 72 q^{93} - 144 q^{96}+O(q^{100}) \) 22 * q - 52 * q^4 - 66 * q^9 - 36 * q^10 + 72 * q^14 + 12 * q^15 + 116 * q^16 - 14 * q^17 - 26 * q^19 + 48 * q^21 + 32 * q^22 - 82 * q^23 + 36 * q^24 - 62 * q^25 - 100 * q^26 + 102 * q^29 + 36 * q^33 - 180 * q^35 + 156 * q^36 + 106 * q^37 - 72 * q^39 + 76 * q^40 + 154 * q^47 + 146 * q^49 - 224 * q^55 - 452 * q^56 + 370 * q^59 - 24 * q^60 - 300 * q^62 + 148 * q^64 - 284 * q^65 - 134 * q^67 - 116 * q^68 + 160 * q^71 + 218 * q^73 + 480 * q^76 - 396 * q^77 + 198 * q^81 - 68 * q^82 + 128 * q^83 + 20 * q^86 - 856 * q^88 - 118 * q^89 + 108 * q^90 - 400 * q^91 + 804 * q^92 - 72 * q^93 - 144 * q^96

Introduction

L-functions

Modular forms

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Database

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