LMFDB - Embedded newform 201.3.b.a.133.17

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			133.17
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74898i q^{2} +1.73205i q^{3} -3.55688 q^{4} +0.569953i q^{5} -4.76137 q^{6} +7.88425i q^{7} +1.21813i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+2.74898i q^{2} +1.73205i q^{3} -3.55688 q^{4} +0.569953i q^{5} -4.76137 q^{6} +7.88425i q^{7} +1.21813i q^{8} -3.00000 q^{9} -1.56679 q^{10} -7.66550i q^{11} -6.16069i q^{12} +2.48603i q^{13} -21.6736 q^{14} -0.987188 q^{15} -17.5761 q^{16} -20.2672 q^{17} -8.24693i q^{18} +13.9464 q^{19} -2.02725i q^{20} -13.6559 q^{21} +21.0723 q^{22} +10.7451 q^{23} -2.10987 q^{24} +24.6752 q^{25} -6.83403 q^{26} -5.19615i q^{27} -28.0433i q^{28} -27.0033 q^{29} -2.71376i q^{30} +2.26181i q^{31} -43.4439i q^{32} +13.2770 q^{33} -55.7141i q^{34} -4.49365 q^{35} +10.6706 q^{36} +53.4007 q^{37} +38.3385i q^{38} -4.30592 q^{39} -0.694279 q^{40} +16.0040i q^{41} -37.5398i q^{42} +44.5642i q^{43} +27.2653i q^{44} -1.70986i q^{45} +29.5381i q^{46} -2.48918 q^{47} -30.4428i q^{48} -13.1614 q^{49} +67.8314i q^{50} -35.1039i q^{51} -8.84249i q^{52} +86.0954i q^{53} +14.2841 q^{54} +4.36898 q^{55} -9.60406 q^{56} +24.1559i q^{57} -74.2314i q^{58} -16.5679 q^{59} +3.51131 q^{60} +97.3961i q^{61} -6.21766 q^{62} -23.6527i q^{63} +49.1217 q^{64} -1.41692 q^{65} +36.4983i q^{66} +(-28.4570 - 60.6564i) q^{67} +72.0880 q^{68} +18.6111i q^{69} -12.3530i q^{70} +11.6370 q^{71} -3.65440i q^{72} +58.7294 q^{73} +146.797i q^{74} +42.7386i q^{75} -49.6058 q^{76} +60.4367 q^{77} -11.8369i q^{78} +0.870913i q^{79} -10.0176i q^{80} +9.00000 q^{81} -43.9946 q^{82} +47.5818 q^{83} +48.5724 q^{84} -11.5514i q^{85} -122.506 q^{86} -46.7711i q^{87} +9.33760 q^{88} +47.1427 q^{89} +4.70037 q^{90} -19.6004 q^{91} -38.2191 q^{92} -3.91757 q^{93} -6.84271i q^{94} +7.94882i q^{95} +75.2470 q^{96} +21.2215i q^{97} -36.1803i q^{98} +22.9965i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.74898i			1.37449i	0.726426	+	0.687244i	$0.241180\pi$
$2$			2.74898i			1.37449i	−0.726426	+	0.687244i	$0.758820\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.55688			−0.889219
$5$			0.569953i			0.113991i	0.998374	+	0.0569953i	$0.0181520\pi$
$5$			0.569953i			0.113991i	−0.998374	+	0.0569953i	$0.981848\pi$
$6$	−4.76137			−0.793561
$7$			7.88425i			1.12632i	0.826347	+	0.563161i	$0.190415\pi$
$7$			7.88425i			1.12632i	−0.826347	+	0.563161i	$0.809585\pi$
$8$			1.21813i			0.152267i
$9$	−3.00000			−0.333333
$10$	−1.56679			−0.156679
$11$		−	7.66550i		−	0.696864i	−0.937334	−	0.348432i	$-0.886714\pi$
$11$		−	7.66550i		−	0.696864i	0.937334	−	0.348432i	$-0.113286\pi$
$12$		−	6.16069i		−	0.513391i
$13$			2.48603i			0.191233i	0.995418	+	0.0956164i	$0.0304822\pi$
$13$			2.48603i			0.191233i	−0.995418	+	0.0956164i	$0.969518\pi$
$14$	−21.6736			−1.54812
$15$	−0.987188			−0.0658125
$16$	−17.5761			−1.09851
$17$	−20.2672			−1.19219			−0.596095	−	0.802914i	$-0.703282\pi$
$17$	−20.2672			−1.19219			−0.596095	+	0.802914i	$0.703282\pi$
$18$		−	8.24693i		−	0.458163i
$19$	13.9464			0.734023			0.367012	−	0.930216i	$-0.380381\pi$
$19$	13.9464			0.734023			0.367012	+	0.930216i	$0.380381\pi$
$20$		−	2.02725i		−	0.101363i
$21$	−13.6559			−0.650282
$22$	21.0723			0.957832
$23$	10.7451			0.467179			0.233589	−	0.972335i	$-0.424953\pi$
$23$	10.7451			0.467179			0.233589	+	0.972335i	$0.424953\pi$
$24$	−2.10987			−0.0879111
$25$	24.6752			0.987006
$26$	−6.83403			−0.262847
$27$		−	5.19615i		−	0.192450i
$28$		−	28.0433i		−	1.00155i
$29$	−27.0033			−0.931148			−0.465574	−	0.885009i	$-0.654152\pi$
$29$	−27.0033			−0.931148			−0.465574	+	0.885009i	$0.654152\pi$
$30$		−	2.71376i		−	0.0904586i
$31$			2.26181i			0.0729616i	0.999334	+	0.0364808i	$0.0116148\pi$
$31$			2.26181i			0.0729616i	−0.999334	+	0.0364808i	$0.988385\pi$
$32$		−	43.4439i		−	1.35762i
$33$	13.2770			0.402335
$34$		−	55.7141i		−	1.63865i
$35$	−4.49365			−0.128390
$36$	10.6706			0.296406
$37$	53.4007			1.44326			0.721632	−	0.692277i	$-0.243392\pi$
$37$	53.4007			1.44326			0.721632	+	0.692277i	$0.243392\pi$
$38$			38.3385i			1.00891i
$39$	−4.30592			−0.110408
$40$	−0.694279			−0.0173570
$41$			16.0040i			0.390341i	0.980769	+	0.195170i	$0.0625260\pi$
$41$			16.0040i			0.390341i	−0.980769	+	0.195170i	$0.937474\pi$
$42$		−	37.5398i		−	0.893805i
$43$			44.5642i			1.03638i	0.855267	+	0.518188i	$0.173393\pi$
$43$			44.5642i			1.03638i	−0.855267	+	0.518188i	$0.826607\pi$
$44$			27.2653i			0.619665i
$45$		−	1.70986i		−	0.0379969i
$46$			29.5381i			0.642132i
$47$	−2.48918			−0.0529613			−0.0264807	−	0.999649i	$-0.508430\pi$
$47$	−2.48918			−0.0529613			−0.0264807	+	0.999649i	$0.508430\pi$
$48$		−	30.4428i		−	0.634224i
$49$	−13.1614			−0.268599
$50$			67.8314i			1.35663i
$51$		−	35.1039i		−	0.688311i
$52$		−	8.84249i		−	0.170048i
$53$			86.0954i			1.62444i	0.583350	+	0.812221i	$0.301742\pi$
$53$			86.0954i			1.62444i	−0.583350	+	0.812221i	$0.698258\pi$
$54$	14.2841			0.264520
$55$	4.36898			0.0794360
$56$	−9.60406			−0.171501
$57$			24.1559i			0.423789i
$58$		−	74.2314i		−	1.27985i
$59$	−16.5679			−0.280811			−0.140406	−	0.990094i	$-0.544841\pi$
$59$	−16.5679			−0.280811			−0.140406	+	0.990094i	$0.544841\pi$
$60$	3.51131			0.0585218
$61$			97.3961i			1.59666i	0.602222	+	0.798329i	$0.294282\pi$
$61$			97.3961i			1.59666i	−0.602222	+	0.798329i	$0.705718\pi$
$62$	−6.21766			−0.100285
$63$		−	23.6527i		−	0.375440i
$64$	49.1217			0.767526
$65$	−1.41692			−0.0217987
$66$			36.4983i			0.553004i
$67$	−28.4570	−	60.6564i	−0.424731	−	0.905320i
$67$	−28.4570	−	60.6564i	−0.424731	−	0.905320i
$68$	72.0880			1.06012
$69$			18.6111i			0.269726i
$70$		−	12.3530i		−	0.176471i
$71$	11.6370			0.163902			0.0819509	−	0.996636i	$-0.473885\pi$
$71$	11.6370			0.163902			0.0819509	+	0.996636i	$0.473885\pi$
$72$		−	3.65440i		−	0.0507555i
$73$	58.7294			0.804512			0.402256	−	0.915527i	$-0.368226\pi$
$73$	58.7294			0.804512			0.402256	+	0.915527i	$0.368226\pi$
$74$			146.797i			1.98375i
$75$			42.7386i			0.569848i
$76$	−49.6058			−0.652708
$77$	60.4367			0.784893
$78$		−	11.8369i		−	0.151755i
$79$			0.870913i			0.0110242i	0.999985	+	0.00551211i	$0.00175457\pi$
$79$			0.870913i			0.0110242i	−0.999985	+	0.00551211i	$0.998245\pi$
$80$		−	10.0176i		−	0.125220i
$81$	9.00000			0.111111
$82$	−43.9946			−0.536519
$83$	47.5818			0.573274			0.286637	−	0.958039i	$-0.407463\pi$
$83$	47.5818			0.573274			0.286637	+	0.958039i	$0.407463\pi$
$84$	48.5724			0.578243
$85$		−	11.5514i		−	0.135898i
$86$	−122.506			−1.42449
$87$		−	46.7711i		−	0.537598i
$88$	9.33760			0.106109
$89$	47.1427			0.529694			0.264847	−	0.964290i	$-0.414679\pi$
$89$	47.1427			0.529694			0.264847	+	0.964290i	$0.414679\pi$
$90$	4.70037			0.0522263
$91$	−19.6004			−0.215390
$92$	−38.2191			−0.415425
$93$	−3.91757			−0.0421244
$94$		−	6.84271i		−	0.0727948i
$95$			7.94882i			0.0836718i
$96$	75.2470			0.783823
$97$			21.2215i			0.218778i	0.993999	+	0.109389i	$0.0348895\pi$
$97$			21.2215i			0.218778i	−0.993999	+	0.109389i	$0.965111\pi$
$98$		−	36.1803i		−	0.369187i
$99$			22.9965i			0.232288i
$100$	−87.7665			−0.877665
$101$		−	59.1548i		−	0.585691i	−0.956160	−	0.292845i	$-0.905398\pi$
$101$		−	59.1548i		−	0.585691i	0.956160	−	0.292845i	$-0.0946021\pi$
$102$	96.4997			0.946076
$103$	89.1395			0.865432			0.432716	−	0.901530i	$-0.357555\pi$
$103$	89.1395			0.865432			0.432716	+	0.901530i	$0.357555\pi$
$104$	−3.02831			−0.0291184
$105$		−	7.78324i		−	0.0741261i
$106$	−236.674			−2.23278
$107$	176.991			1.65412			0.827061	−	0.562113i	$-0.190011\pi$
$107$	176.991			1.65412			0.827061	+	0.562113i	$0.190011\pi$
$108$			18.4821i			0.171130i
$109$			16.6150i			0.152431i	0.997091	+	0.0762154i	$0.0242837\pi$
$109$			16.6150i			0.152431i	−0.997091	+	0.0762154i	$0.975716\pi$
$110$			12.0102i			0.109184i
$111$			92.4928i			0.833268i
$112$		−	138.575i		−	1.23727i
$113$		−	109.236i		−	0.966686i	−0.875431	−	0.483343i	$-0.839422\pi$
$113$		−	109.236i		−	0.966686i	0.875431	−	0.483343i	$-0.160578\pi$
$114$	−66.4042			−0.582493
$115$			6.12421i			0.0532540i
$116$	96.0474			0.827995
$117$		−	7.45808i		−	0.0637443i
$118$		−	45.5447i		−	0.385972i
$119$		−	159.792i		−	1.34279i
$120$		−	1.20253i		−	0.0100210i
$121$	62.2401			0.514381
$122$	−267.740			−2.19459
$123$	−27.7197			−0.225363
$124$		−	8.04498i		−	0.0648788i
$125$			28.3125i			0.226500i
$126$	65.0209			0.516039
$127$	−82.6343			−0.650664			−0.325332	−	0.945600i	$-0.605476\pi$
$127$	−82.6343			−0.650664			−0.325332	+	0.945600i	$0.605476\pi$
$128$		−	38.7411i		−	0.302664i
$129$	−77.1874			−0.598352
$130$		−	3.89508i		−	0.0299621i
$131$	−159.802			−1.21986			−0.609930	−	0.792455i	$-0.708802\pi$
$131$	−159.802			−1.21986			−0.609930	+	0.792455i	$0.708802\pi$
$132$	−47.2248			−0.357764
$133$			109.957i			0.826746i
$134$	166.743	−	78.2276i	1.24435	−	0.583788i
$135$	2.96156			0.0219375
$136$		−	24.6882i		−	0.181531i
$137$		−	160.701i		−	1.17300i	−0.809949	−	0.586500i	$-0.800505\pi$
$137$		−	160.701i		−	1.17300i	0.809949	−	0.586500i	$-0.199495\pi$
$138$	−51.1615			−0.370735
$139$		−	262.704i		−	1.88996i	−0.327135	−	0.944978i	$-0.606083\pi$
$139$		−	262.704i		−	1.88996i	0.327135	−	0.944978i	$-0.393917\pi$
$140$	15.9834			0.114167
$141$		−	4.31139i		−	0.0305772i
$142$			31.9899i			0.225281i
$143$	19.0566			0.133263
$144$	52.7284			0.366169
$145$		−	15.3906i		−	0.106142i
$146$			161.446i			1.10579i
$147$		−	22.7962i		−	0.155076i
$148$	−189.940			−1.28338
$149$	−66.1688			−0.444086			−0.222043	−	0.975037i	$-0.571272\pi$
$149$	−66.1688			−0.444086			−0.222043	+	0.975037i	$0.571272\pi$
$150$	−117.488			−0.783250
$151$	−223.415			−1.47957			−0.739784	−	0.672844i	$-0.765072\pi$
$151$	−223.415			−1.47957			−0.739784	+	0.672844i	$0.765072\pi$
$152$			16.9886i			0.111767i
$153$	60.8017			0.397397
$154$			166.139i			1.07883i
$155$	−1.28912			−0.00831694
$156$	15.3156			0.0981772
$157$	26.1291			0.166427			0.0832137	−	0.996532i	$-0.473482\pi$
$157$	26.1291			0.166427			0.0832137	+	0.996532i	$0.473482\pi$
$158$	−2.39412			−0.0151527
$159$	−149.122			−0.937872
$160$	24.7610			0.154756
$161$			84.7172i			0.526193i
$162$			24.7408i			0.152721i
$163$	123.266			0.756230			0.378115	−	0.925759i	$-0.376572\pi$
$163$	123.266			0.756230			0.378115	+	0.925759i	$0.376572\pi$
$164$		−	56.9242i		−	0.347099i
$165$			7.56729i			0.0458624i
$166$			130.801i			0.787959i
$167$	39.3704			0.235751			0.117875	−	0.993028i	$-0.462392\pi$
$167$	39.3704			0.235751			0.117875	+	0.993028i	$0.462392\pi$
$168$		−	16.6347i		−	0.0990162i
$169$	162.820			0.963430
$170$	31.7545			0.186791
$171$	−41.8393			−0.244674
$172$		−	158.509i		−	0.921566i
$173$	−25.7219			−0.148681			−0.0743407	−	0.997233i	$-0.523685\pi$
$173$	−25.7219			−0.148681			−0.0743407	+	0.997233i	$0.523685\pi$
$174$	128.573			0.738923
$175$			194.545i			1.11169i
$176$			134.730i			0.765511i
$177$		−	28.6964i		−	0.162126i
$178$			129.594i			0.728058i
$179$			65.9386i			0.368372i	0.982891	+	0.184186i	$0.0589649\pi$
$179$			65.9386i			0.368372i	−0.982891	+	0.184186i	$0.941035\pi$
$180$			6.08176i			0.0337876i
$181$	172.993			0.955764			0.477882	−	0.878424i	$-0.341405\pi$
$181$	172.993			0.955764			0.477882	+	0.878424i	$0.341405\pi$
$182$		−	53.8812i		−	0.296050i
$183$	−168.695			−0.921830
$184$			13.0890i			0.0711357i
$185$			30.4359i			0.164519i
$186$		−	10.7693i		−	0.0578995i
$187$			155.358i			0.830794i
$188$	8.85372			0.0470943
$189$	40.9678			0.216761
$190$	−21.8511			−0.115006
$191$		−	126.533i		−	0.662475i	−0.943547	−	0.331237i	$-0.892534\pi$
$191$		−	126.533i		−	0.662475i	0.943547	−	0.331237i	$-0.107466\pi$
$192$			85.0812i			0.443131i
$193$	142.998			0.740920			0.370460	−	0.928848i	$-0.379200\pi$
$193$	142.998			0.740920			0.370460	+	0.928848i	$0.379200\pi$
$194$	−58.3374			−0.300708
$195$		−	2.45418i		−	0.0125855i
$196$	46.8134			0.238844
$197$		−	204.717i		−	1.03917i	−0.854418	−	0.519586i	$-0.826086\pi$
$197$		−	204.717i		−	1.03917i	0.854418	−	0.519586i	$-0.173914\pi$
$198$	−63.2169			−0.319277
$199$	−156.942			−0.788654			−0.394327	−	0.918970i	$-0.629022\pi$
$199$	−156.942			−0.788654			−0.394327	+	0.918970i	$0.629022\pi$
$200$			30.0576i			0.150288i
$201$	105.060	−	49.2889i	0.522687	−	0.245219i
$202$	162.615			0.805025
$203$		−	212.901i		−	1.04877i
$204$			124.860i			0.612060i
$205$	−9.12152			−0.0444952
$206$			245.043i			1.18953i
$207$	−32.2353			−0.155726
$208$		−	43.6947i		−	0.210071i
$209$		−	106.906i		−	0.511514i
$210$	21.3959			0.101885
$211$	−139.667			−0.661927			−0.330963	−	0.943644i	$-0.607374\pi$
$211$	−139.667			−0.661927			−0.330963	+	0.943644i	$0.607374\pi$
$212$		−	306.231i		−	1.44449i
$213$			20.1559i			0.0946288i
$214$			486.544i			2.27357i
$215$	−25.3995			−0.118137
$216$	6.32960			0.0293037
$217$	−17.8327			−0.0821781
$218$	−45.6741			−0.209514
$219$			101.722i			0.464485i
$220$	−15.5399			−0.0706360
$221$		−	50.3848i		−	0.227986i
$222$	−254.261			−1.14532
$223$	245.031			1.09879			0.549397	−	0.835562i	$-0.314858\pi$
$223$	245.031			1.09879			0.549397	+	0.835562i	$0.314858\pi$
$224$	342.522			1.52912
$225$	−74.0255			−0.329002
$226$	300.286			1.32870
$227$	−380.340			−1.67551			−0.837754	−	0.546048i	$-0.816132\pi$
$227$	−380.340			−1.67551			−0.837754	+	0.546048i	$0.816132\pi$
$228$		−	85.9198i		−	0.376841i
$229$			249.057i			1.08758i	0.839220	+	0.543792i	$0.183012\pi$
$229$			249.057i			1.08758i	−0.839220	+	0.543792i	$0.816988\pi$
$230$	−16.8353			−0.0731971
$231$			104.679i			0.453158i
$232$		−	32.8936i		−	0.141783i
$233$			318.190i			1.36562i	0.730594	+	0.682812i	$0.239243\pi$
$233$			318.190i			1.36562i	−0.730594	+	0.682812i	$0.760757\pi$
$234$	20.5021			0.0876158
$235$		−	1.41872i		−	0.00603710i
$236$	58.9298			0.249703
$237$	−1.50847			−0.00636483
$238$	439.264			1.84565
$239$		−	370.783i		−	1.55139i	−0.631106	−	0.775696i	$-0.717399\pi$
$239$		−	370.783i		−	1.55139i	0.631106	−	0.775696i	$-0.282601\pi$
$240$	17.3509			0.0722956
$241$	−161.802			−0.671379			−0.335690	−	0.941973i	$-0.608969\pi$
$241$	−161.802			−0.671379			−0.335690	+	0.941973i	$0.608969\pi$
$242$			171.097i			0.707011i
$243$			15.5885i			0.0641500i
$244$		−	346.426i		−	1.41978i
$245$		−	7.50137i		−	0.0306178i
$246$		−	76.2008i		−	0.309759i
$247$			34.6712i			0.140369i
$248$	−2.75518			−0.0111096
$249$			82.4141i			0.330980i
$250$	−77.8305			−0.311322
$251$		−	267.332i		−	1.06507i	−0.846409	−	0.532534i	$-0.821240\pi$
$251$		−	267.332i		−	1.06507i	0.846409	−	0.532534i	$-0.178760\pi$
$252$			84.1299i			0.333849i
$253$		−	82.3667i		−	0.325560i
$254$		−	227.160i		−	0.894330i
$255$	20.0076			0.0784610
$256$	302.985			1.18354
$257$	44.1237			0.171688			0.0858439	−	0.996309i	$-0.472641\pi$
$257$	44.1237			0.171688			0.0858439	+	0.996309i	$0.472641\pi$
$258$		−	212.187i		−	0.822428i
$259$			421.025i			1.62558i
$260$	5.03981			0.0193839
$261$	81.0099			0.310383
$262$		−	439.291i		−	1.67668i
$263$	245.272			0.932593			0.466297	−	0.884628i	$-0.345588\pi$
$263$	245.272			0.932593			0.466297	+	0.884628i	$0.345588\pi$
$264$			16.1732i			0.0612621i
$265$	−49.0704			−0.185171
$266$	−302.270			−1.13635
$267$			81.6536i			0.305819i
$268$	101.218	+	215.747i	0.377679	+	0.805028i
$269$	476.179			1.77018			0.885091	−	0.465417i	$-0.154096\pi$
$269$	476.179			1.77018			0.885091	+	0.465417i	$0.154096\pi$
$270$			8.14127i			0.0301529i
$271$		−	205.041i		−	0.756610i	−0.925681	−	0.378305i	$-0.876507\pi$
$271$		−	205.041i		−	0.756610i	0.925681	−	0.378305i	$-0.123493\pi$
$272$	356.219			1.30963
$273$		−	33.9490i		−	0.124355i
$274$	441.763			1.61227
$275$		−	189.147i		−	0.687809i
$276$		−	66.1974i		−	0.239845i
$277$	−97.1261			−0.350636			−0.175318	−	0.984512i	$-0.556095\pi$
$277$	−97.1261			−0.350636			−0.175318	+	0.984512i	$0.556095\pi$
$278$	722.167			2.59772
$279$		−	6.78542i		−	0.0243205i
$280$		−	5.47387i		−	0.0195495i
$281$			266.692i			0.949083i	0.880233	+	0.474542i	$0.157386\pi$
$281$			266.692i			0.949083i	−0.880233	+	0.474542i	$0.842614\pi$
$282$	11.8519			0.0420281
$283$	−371.871			−1.31403			−0.657017	−	0.753876i	$-0.728182\pi$
$283$	−371.871			−1.31403			−0.657017	+	0.753876i	$0.728182\pi$
$284$	−41.3915			−0.145745
$285$	−13.7678			−0.0483079
$286$			52.3863i			0.183169i
$287$	−126.179			−0.439649
$288$			130.332i			0.452540i
$289$	121.760			0.421316
$290$	42.3084			0.145891
$291$	−36.7567			−0.126312
$292$	−208.893			−0.715388
$293$	−47.4151			−0.161826			−0.0809131	−	0.996721i	$-0.525784\pi$
$293$	−47.4151			−0.161826			−0.0809131	+	0.996721i	$0.525784\pi$
$294$	62.6662			0.213150
$295$		−	9.44290i		−	0.0320098i
$296$			65.0492i			0.219761i
$297$	−39.8311			−0.134112
$298$		−	181.896i		−	0.610391i
$299$			26.7126i			0.0893399i
$300$		−	152.016i		−	0.506720i
$301$	−351.355			−1.16729
$302$		−	614.162i		−	2.03365i
$303$	102.459			0.338149
$304$	−245.125			−0.806331
$305$	−55.5112			−0.182004
$306$			167.142i			0.546217i
$307$	−566.002			−1.84366			−0.921828	−	0.387600i	$-0.873304\pi$
$307$	−566.002			−1.84366			−0.921828	+	0.387600i	$0.873304\pi$
$308$	−214.966			−0.697942
$309$			154.394i			0.499658i
$310$		−	3.54378i		−	0.0114315i
$311$			506.695i			1.62924i	0.579992	+	0.814622i	$0.303055\pi$
$311$			506.695i			1.62924i	−0.579992	+	0.814622i	$0.696945\pi$
$312$		−	5.24519i		−	0.0168115i
$313$		−	5.30641i		−	0.0169534i	−0.999964	−	0.00847670i	$-0.997302\pi$
$313$		−	5.30641i		−	0.0169534i	0.999964	−	0.00847670i	$-0.00269825\pi$
$314$			71.8283i			0.228753i
$315$	13.4810			0.0427967
$316$		−	3.09773i		−	0.00980294i
$317$	−238.172			−0.751332			−0.375666	−	0.926755i	$-0.622586\pi$
$317$	−238.172			−0.751332			−0.375666	+	0.926755i	$0.622586\pi$
$318$		−	409.932i		−	1.28909i
$319$			206.994i			0.648883i
$320$			27.9971i			0.0874908i
$321$			306.557i			0.955007i
$322$	−232.886			−0.723247
$323$	−282.656			−0.875095
$324$	−32.0119			−0.0988022
$325$			61.3431i			0.188748i
$326$			338.854i			1.03943i
$327$	−28.7779			−0.0880059
$328$	−19.4950			−0.0594359
$329$		−	19.6253i		−	0.0596515i
$330$	−20.8023			−0.0630373
$331$		−	542.655i		−	1.63944i	−0.572763	−	0.819721i	$-0.694128\pi$
$331$		−	542.655i		−	1.63944i	0.572763	−	0.819721i	$-0.305872\pi$
$332$	−169.243			−0.509767
$333$	−160.202			−0.481088
$334$			108.228i			0.324037i
$335$	34.5713	−	16.2191i	0.103198	−	0.0484154i
$336$	240.018			0.714340
$337$		−	289.660i		−	0.859525i	−0.902942	−	0.429763i	$-0.858597\pi$
$337$		−	289.660i		−	0.859525i	0.902942	−	0.429763i	$-0.141403\pi$
$338$			447.588i			1.32422i
$339$	189.201			0.558116
$340$			41.0868i			0.120844i
$341$	17.3379			0.0508443
$342$		−	115.015i		−	0.336302i
$343$			282.561i			0.823792i
$344$	−54.2851			−0.157806
$345$	−10.6074			−0.0307462
$346$		−	70.7088i		−	0.204361i
$347$		−	239.781i		−	0.691012i	−0.938416	−	0.345506i	$-0.887707\pi$
$347$		−	239.781i		−	0.691012i	0.938416	−	0.345506i	$-0.112293\pi$
$348$			166.359i			0.478043i
$349$	−412.299			−1.18137			−0.590686	−	0.806901i	$-0.701143\pi$
$349$	−412.299			−1.18137			−0.590686	+	0.806901i	$0.701143\pi$
$350$	−534.800			−1.52800
$351$	12.9178			0.0368028
$352$	−333.019			−0.946077
$353$			587.877i			1.66537i	0.553744	+	0.832687i	$0.313199\pi$
$353$			587.877i			1.66537i	−0.553744	+	0.832687i	$0.686801\pi$
$354$	78.8857			0.222841
$355$			6.63257i			0.0186833i
$356$	−167.681			−0.471014
$357$	276.768			0.775259
$358$	−181.264			−0.506323
$359$	398.306			1.10949			0.554744	−	0.832021i	$-0.312816\pi$
$359$	398.306			1.10949			0.554744	+	0.832021i	$0.312816\pi$
$360$	2.08284			0.00578566
$361$	−166.497			−0.461210
$362$			475.555i			1.31369i
$363$			107.803i			0.296978i
$364$	69.7164			0.191529
$365$			33.4730i			0.0917068i
$366$		−	463.739i		−	1.26705i
$367$		−	362.107i		−	0.986667i	−0.869840	−	0.493333i	$-0.835778\pi$
$367$		−	362.107i		−	0.986667i	0.869840	−	0.493333i	$-0.164222\pi$
$368$	−188.858			−0.513200
$369$		−	48.0119i		−	0.130114i
$370$	−83.6677			−0.226129
$371$	−678.798			−1.82964
$372$	13.9343			0.0374578
$373$		−	412.876i		−	1.10691i	−0.832881	−	0.553453i	$-0.813310\pi$
$373$		−	412.876i		−	1.10691i	0.832881	−	0.553453i	$-0.186690\pi$
$374$	−427.077			−1.14192
$375$	−49.0387			−0.130770
$376$		−	3.03215i		−	0.00806424i
$377$		−	67.1309i		−	0.178066i
$378$			112.619i			0.297935i
$379$		−	287.294i		−	0.758031i	−0.925390	−	0.379015i	$-0.876263\pi$
$379$		−	287.294i		−	0.758031i	0.925390	−	0.379015i	$-0.123737\pi$
$380$		−	28.2730i		−	0.0744026i
$381$		−	143.127i		−	0.375661i
$382$	347.835			0.910564
$383$			496.866i			1.29730i	0.761087	+	0.648650i	$0.224666\pi$
$383$			496.866i			1.29730i	−0.761087	+	0.648650i	$0.775334\pi$
$384$	67.1015			0.174743
$385$			34.4461i			0.0894704i
$386$			393.097i			1.01839i
$387$		−	133.693i		−	0.345459i
$388$		−	75.4823i		−	0.194542i
$389$	546.907			1.40593			0.702966	−	0.711224i	$-0.251859\pi$
$389$	546.907			1.40593			0.702966	+	0.711224i	$0.251859\pi$
$390$	6.74647			0.0172986
$391$	−217.774			−0.556966
$392$		−	16.0323i		−	0.0408987i
$393$		−	276.785i		−	0.704286i
$394$	562.762			1.42833
$395$	−0.496380			−0.00125666
$396$		−	81.7958i		−	0.206555i
$397$	354.047			0.891806			0.445903	−	0.895081i	$-0.352883\pi$
$397$	354.047			0.891806			0.445903	+	0.895081i	$0.352883\pi$
$398$		−	431.430i		−	1.08400i
$399$	−190.452			−0.477322
$400$	−433.694			−1.08423
$401$			374.785i			0.934627i	0.884092	+	0.467313i	$0.154778\pi$
$401$			374.785i			0.934627i	−0.884092	+	0.467313i	$0.845222\pi$
$402$	135.494	+	288.808i	0.337050	+	0.718427i
$403$	−5.62291			−0.0139526
$404$			210.406i			0.520808i
$405$			5.12958i			0.0126656i
$406$	585.259			1.44152
$407$		−	409.343i		−	1.00576i
$408$	42.7612			0.104807
$409$			329.904i			0.806611i	0.915065	+	0.403305i	$0.132139\pi$
$409$			329.904i			0.806611i	−0.915065	+	0.403305i	$0.867861\pi$
$410$		−	25.0748i		−	0.0611582i
$411$	278.342			0.677232
$412$	−317.058			−0.769559
$413$		−	130.625i		−	0.316283i
$414$		−	88.6142i		−	0.214044i
$415$			27.1194i			0.0653479i
$416$	108.003			0.259622
$417$	455.016			1.09117
$418$	293.884			0.703071
$419$	97.9544			0.233781			0.116891	−	0.993145i	$-0.462707\pi$
$419$	97.9544			0.233781			0.116891	+	0.993145i	$0.462707\pi$
$420$			27.6840i			0.0659143i
$421$	167.697			0.398331			0.199165	−	0.979966i	$-0.436177\pi$
$421$	167.697			0.398331			0.199165	+	0.979966i	$0.436177\pi$
$422$		−	383.940i		−	0.909811i
$423$	7.46755			0.0176538
$424$	−104.876			−0.247348
$425$	−500.097			−1.17670
$426$	−55.4082			−0.130066
$427$	−767.895			−1.79835
$428$	−629.535			−1.47088
$429$			33.0071i			0.0769395i
$430$		−	69.8227i		−	0.162378i
$431$	715.507			1.66011			0.830055	−	0.557682i	$-0.188309\pi$
$431$	715.507			1.66011			0.830055	+	0.557682i	$0.188309\pi$
$432$			91.3283i			0.211408i
$433$		−	676.116i		−	1.56147i	−0.624863	−	0.780735i	$-0.714845\pi$
$433$		−	676.116i		−	1.56147i	0.624863	−	0.780735i	$-0.285155\pi$
$434$		−	49.0216i		−	0.112953i
$435$	26.6573			0.0612812
$436$		−	59.0974i		−	0.135544i
$437$	149.856			0.342920
$438$	−279.632			−0.638430
$439$	98.1589			0.223597			0.111798	−	0.993731i	$-0.464339\pi$
$439$	98.1589			0.223597			0.111798	+	0.993731i	$0.464339\pi$
$440$			5.32199i			0.0120954i
$441$	39.4841			0.0895332
$442$	138.507			0.313364
$443$		−	639.852i		−	1.44436i	−0.691705	−	0.722180i	$-0.743140\pi$
$443$		−	639.852i		−	1.44436i	0.691705	−	0.722180i	$-0.256860\pi$
$444$		−	328.986i		−	0.740959i
$445$			26.8692i			0.0603801i
$446$			673.584i			1.51028i
$447$		−	114.608i		−	0.256393i
$448$			387.288i			0.864481i
$449$	692.760			1.54290			0.771448	−	0.636292i	$-0.219533\pi$
$449$	692.760			1.54290			0.771448	+	0.636292i	$0.219533\pi$
$450$		−	203.494i		−	0.452210i
$451$	122.678			0.272014
$452$			388.537i			0.859596i
$453$		−	386.966i		−	0.854229i
$454$		−	1045.55i		−	2.30297i
$455$		−	11.1713i		−	0.0245524i
$456$	−29.4251			−0.0645288
$457$	203.608			0.445532			0.222766	−	0.974872i	$-0.428491\pi$
$457$	203.608			0.445532			0.222766	+	0.974872i	$0.428491\pi$
$458$	−684.651			−1.49487
$459$			105.312i			0.229437i
$460$		−	21.7831i		−	0.0473545i
$461$	686.706			1.48960			0.744800	−	0.667288i	$-0.232545\pi$
$461$	686.706			1.48960			0.744800	+	0.667288i	$0.232545\pi$
$462$	−287.762			−0.622860
$463$			185.724i			0.401131i	0.979680	+	0.200566i	$0.0642780\pi$
$463$			185.724i			0.401131i	−0.979680	+	0.200566i	$0.935722\pi$
$464$	474.613			1.02287
$465$		−	2.23283i		−	0.00480178i
$466$	−874.698			−1.87704
$467$	−170.511			−0.365121			−0.182560	−	0.983195i	$-0.558439\pi$
$467$	−170.511			−0.365121			−0.182560	+	0.983195i	$0.558439\pi$
$468$			26.5275i			0.0566826i
$469$	478.230	−	224.362i	1.01968	−	0.478384i
$470$	3.90002			0.00829792
$471$			45.2569i			0.0960869i
$472$		−	20.1818i		−	0.0427581i
$473$	341.607			0.722213
$474$		−	4.14674i		−	0.00874839i
$475$	344.131			0.724486
$476$			568.360i			1.19403i
$477$		−	258.286i		−	0.541481i
$478$	1019.27			2.13237
$479$	−301.488			−0.629411			−0.314705	−	0.949189i	$-0.601906\pi$
$479$	−301.488			−0.629411			−0.314705	+	0.949189i	$0.601906\pi$
$480$			42.8873i			0.0893485i
$481$			132.756i			0.275999i
$482$		−	444.791i		−	0.922803i
$483$	−146.734			−0.303798
$484$	−221.380			−0.457397
$485$	−12.0953			−0.0249387
$486$	−42.8523			−0.0881735
$487$			4.00063i			0.00821484i	0.999992	+	0.00410742i	$0.00130744\pi$
$487$			4.00063i			0.00821484i	−0.999992	+	0.00410742i	$0.998693\pi$
$488$	−118.641			−0.243118
$489$			213.502i			0.436610i
$490$	20.6211			0.0420839
$491$	−111.462			−0.227010			−0.113505	−	0.993537i	$-0.536208\pi$
$491$	−111.462			−0.227010			−0.113505	+	0.993537i	$0.536208\pi$
$492$	98.5956			0.200397
$493$	547.282			1.11010
$494$	−95.3104			−0.192936
$495$	−13.1069			−0.0264787
$496$		−	39.7538i		−	0.0801489i
$497$			91.7493i			0.184606i
$498$	−226.554			−0.454929
$499$			378.376i			0.758269i	0.925342	+	0.379134i	$0.123778\pi$
$499$			378.376i			0.758269i	−0.925342	+	0.379134i	$0.876222\pi$
$500$		−	100.704i		−	0.201408i
$501$			68.1915i			0.136111i
$502$	734.889			1.46392
$503$		−	569.920i		−	1.13304i	−0.824048	−	0.566520i	$-0.808289\pi$
$503$		−	569.920i		−	1.13304i	0.824048	−	0.566520i	$-0.191711\pi$
$504$	28.8122			0.0571670
$505$	33.7154			0.0667633
$506$	226.424			0.447479
$507$			282.012i			0.556237i
$508$	293.920			0.578583
$509$	388.882			0.764011			0.382005	−	0.924160i	$-0.375234\pi$
$509$	388.882			0.764011			0.382005	+	0.924160i	$0.375234\pi$
$510$			55.0003i			0.107844i
$511$			463.037i			0.906139i
$512$			677.935i			1.32409i
$513$		−	72.4678i		−	0.141263i
$514$			121.295i			0.235983i
$515$			50.8054i			0.0986512i
$516$	274.546			0.532066
$517$			19.0808i			0.0369068i
$518$	−1157.39			−2.23434
$519$		−	44.5516i		−	0.0858412i
$520$		−	1.72599i		−	0.00331922i
$521$			327.448i			0.628500i	0.949340	+	0.314250i	$0.101753\pi$
$521$			327.448i			0.628500i	−0.949340	+	0.314250i	$0.898247\pi$
$522$			222.694i			0.426617i
$523$	84.4454			0.161464			0.0807318	−	0.996736i	$-0.474274\pi$
$523$	84.4454			0.161464			0.0807318	+	0.996736i	$0.474274\pi$
$524$	568.395			1.08472
$525$	−336.962			−0.641832
$526$			674.247i			1.28184i
$527$		−	45.8406i		−	0.0869840i
$528$	−233.359			−0.441968
$529$	−413.543			−0.781744
$530$		−	134.893i		−	0.254516i
$531$	49.7036			0.0936037
$532$		−	391.104i		−	0.735159i
$533$	−39.7863			−0.0746459
$534$	−224.464			−0.420345
$535$			100.877i			0.188554i
$536$	73.8876	−	34.6644i	0.137850	−	0.0646723i
$537$	−114.209			−0.212680
$538$			1309.01i			2.43310i
$539$			100.889i			0.187177i
$540$	−10.5339			−0.0195073
$541$		−	922.374i		−	1.70494i	−0.522774	−	0.852471i	$-0.675103\pi$
$541$		−	922.374i		−	1.70494i	0.522774	−	0.852471i	$-0.324897\pi$
$542$	563.654			1.03995
$543$			299.633i			0.551810i
$544$			880.486i			1.61854i
$545$	−9.46975			−0.0173757
$546$	93.3250			0.170925
$547$			534.420i			0.977002i	0.872563	+	0.488501i	$0.162456\pi$
$547$			534.420i			0.977002i	−0.872563	+	0.488501i	$0.837544\pi$
$548$			571.594i			1.04305i
$549$		−	292.188i		−	0.532219i
$550$	519.962			0.945386
$551$	−376.600			−0.683484
$552$	−22.6708			−0.0410702
$553$	−6.86649			−0.0124168
$554$		−	266.997i		−	0.481945i
$555$	−52.7166			−0.0949848
$556$			934.405i			1.68059i
$557$	−464.750			−0.834380			−0.417190	−	0.908819i	$-0.636985\pi$
$557$	−464.750			−0.834380			−0.417190	+	0.908819i	$0.636985\pi$
$558$	18.6530			0.0334283
$559$	−110.788			−0.198189
$560$	78.9810			0.141038
$561$	−269.089			−0.479659
$562$	−733.131			−1.30450
$563$			217.206i			0.385801i	0.981218	+	0.192901i	$0.0617895\pi$
$563$			217.206i			0.385801i	−0.981218	+	0.192901i	$0.938211\pi$
$564$			15.3351i			0.0271899i
$565$	62.2591			0.110193
$566$		−	1022.27i		−	1.80612i
$567$			70.9582i			0.125147i
$568$			14.1755i			0.0249568i
$569$	−724.367			−1.27305			−0.636527	−	0.771255i	$-0.719629\pi$
$569$	−724.367			−1.27305			−0.636527	+	0.771255i	$0.719629\pi$
$570$		−	37.8473i		−	0.0663987i
$571$	1046.86			1.83339			0.916694	−	0.399589i	$-0.130847\pi$
$571$	1046.86			1.83339			0.916694	+	0.399589i	$0.130847\pi$
$572$	−67.7821			−0.118500
$573$	219.161			0.382480
$574$		−	346.864i		−	0.604293i
$575$	265.137			0.461108
$576$	−147.365			−0.255842
$577$			658.286i			1.14088i	0.821341	+	0.570438i	$0.193227\pi$
$577$			658.286i			1.14088i	−0.821341	+	0.570438i	$0.806773\pi$
$578$			334.716i			0.579094i
$579$			247.679i			0.427771i
$580$			54.7425i			0.0943837i
$581$			375.147i			0.645691i
$582$		−	101.043i		−	0.173614i
$583$	659.965			1.13201
$584$			71.5401i			0.122500i
$585$	4.25076			0.00726625
$586$		−	130.343i		−	0.222428i
$587$		−	124.272i		−	0.211706i	−0.994382	−	0.105853i	$-0.966243\pi$
$587$		−	124.272i		−	0.211706i	0.994382	−	0.105853i	$-0.0337574\pi$
$588$			81.0832i			0.137897i
$589$			31.5442i			0.0535555i
$590$	25.9583			0.0439972
$591$	354.580			0.599966
$592$	−938.578			−1.58544
$593$			375.306i			0.632894i	0.948610	+	0.316447i	$0.102490\pi$
$593$			375.306i			0.632894i	−0.948610	+	0.316447i	$0.897510\pi$
$594$		−	109.495i		−	0.184335i
$595$	91.0739			0.153065
$596$	235.354			0.394890
$597$		−	271.832i		−	0.455329i
$598$	−73.4324			−0.122797
$599$			230.090i			0.384124i	0.981383	+	0.192062i	$0.0615174\pi$
$599$			230.090i			0.384124i	−0.981383	+	0.192062i	$0.938483\pi$
$600$	−52.0613			−0.0867688
$601$	−646.953			−1.07646			−0.538230	−	0.842798i	$-0.680907\pi$
$601$	−646.953			−1.07646			−0.538230	+	0.842798i	$0.680907\pi$
$602$		−	965.867i		−	1.60443i
$603$	85.3709	+	181.969i	0.141577	+	0.301773i
$604$	794.659			1.31566
$605$			35.4739i			0.0586346i
$606$			281.658i			0.464782i
$607$	−50.8358			−0.0837493			−0.0418746	−	0.999123i	$-0.513333\pi$
$607$	−50.8358			−0.0837493			−0.0418746	+	0.999123i	$0.513333\pi$
$608$		−	605.887i		−	0.996525i
$609$	368.755			0.605509
$610$		−	152.599i		−	0.250162i
$611$		−	6.18817i		−	0.0101279i
$612$	−216.264			−0.353373
$613$	938.869			1.53160			0.765799	−	0.643080i	$-0.222344\pi$
$613$	938.869			1.53160			0.765799	+	0.643080i	$0.222344\pi$
$614$		−	1555.93i		−	2.53408i
$615$		−	15.7989i		−	0.0256893i
$616$			73.6199i			0.119513i
$617$	−224.273			−0.363489			−0.181745	−	0.983346i	$-0.558174\pi$
$617$	−224.273			−0.363489			−0.181745	+	0.983346i	$0.558174\pi$
$618$	−424.426			−0.686774
$619$	37.1650			0.0600403			0.0300202	−	0.999549i	$-0.490443\pi$
$619$	37.1650			0.0600403			0.0300202	+	0.999549i	$0.490443\pi$
$620$	4.58526			0.00739558
$621$		−	55.8333i		−	0.0899086i
$622$	−1392.89			−2.23938
$623$			371.685i			0.596605i
$624$	75.6815			0.121284
$625$	600.742			0.961187
$626$	14.5872			0.0233023
$627$	185.167			0.295323
$628$	−92.9380			−0.147990
$629$	−1082.28			−1.72064
$630$			37.0589i			0.0588236i
$631$		−	1227.72i		−	1.94567i	−0.231495	−	0.972836i	$-0.574362\pi$
$631$		−	1227.72i		−	1.94567i	0.231495	−	0.972836i	$-0.425638\pi$
$632$	−1.06089			−0.00167862
$633$		−	241.909i		−	0.382164i
$634$		−	654.730i		−	1.03270i
$635$		−	47.0977i		−	0.0741696i
$636$	530.407			0.833974
$637$		−	32.7195i		−	0.0513650i
$638$	−569.021			−0.891883
$639$	−34.9111			−0.0546340
$640$	22.0806			0.0345009
$641$			57.1741i			0.0891952i	0.999005	+	0.0445976i	$0.0142006\pi$
$641$			57.1741i			0.0891952i	−0.999005	+	0.0445976i	$0.985799\pi$
$642$	−842.719			−1.31265
$643$	−275.272			−0.428106			−0.214053	−	0.976822i	$-0.568667\pi$
$643$	−275.272			−0.428106			−0.214053	+	0.976822i	$0.568667\pi$
$644$		−	301.329i		−	0.467902i
$645$		−	43.9932i		−	0.0682066i
$646$		−	777.014i		−	1.20281i
$647$			367.872i			0.568582i	0.958738	+	0.284291i	$0.0917581\pi$
$647$			367.872i			0.568582i	−0.958738	+	0.284291i	$0.908242\pi$
$648$			10.9632i			0.0169185i
$649$			127.001i			0.195687i
$650$	−168.631			−0.259432
$651$		−	30.8871i		−	0.0474456i
$652$	−438.441			−0.672455
$653$			74.3838i			0.113911i	0.998377	+	0.0569554i	$0.0181393\pi$
$653$			74.3838i			0.113911i	−0.998377	+	0.0569554i	$0.981861\pi$
$654$		−	79.1099i		−	0.120963i
$655$		−	91.0795i		−	0.139053i
$656$		−	281.288i		−	0.428793i
$657$	−176.188			−0.268171
$658$	53.9496			0.0819903
$659$	392.769			0.596008			0.298004	−	0.954565i	$-0.403679\pi$
$659$	392.769			0.596008			0.298004	+	0.954565i	$0.403679\pi$
$660$		−	26.9159i		−	0.0407817i
$661$		−	874.976i		−	1.32371i	−0.749630	−	0.661857i	$-0.769768\pi$
$661$		−	874.976i		−	1.32371i	0.749630	−	0.661857i	$-0.230232\pi$
$662$	1491.75			2.25340
$663$	87.2691			0.131628
$664$			57.9609i			0.0872905i
$665$	−62.6705			−0.0942413
$666$		−	440.392i		−	0.661250i
$667$	−290.153			−0.435013
$668$	−140.036			−0.209634
$669$			424.406i			0.634388i
$670$	44.5861	+	95.0358i	0.0665464	+	0.141844i
$671$	746.590			1.11265
$672$			593.266i			0.882836i
$673$			306.819i			0.455897i	0.973673	+	0.227949i	$0.0732019\pi$
$673$			306.819i			0.455897i	−0.973673	+	0.227949i	$0.926798\pi$
$674$	796.269			1.18141
$675$		−	128.216i		−	0.189949i
$676$	−579.130			−0.856701
$677$			1146.56i			1.69359i	0.531919	+	0.846795i	$0.321471\pi$
$677$			1146.56i			1.69359i	−0.531919	+	0.846795i	$0.678529\pi$
$678$			520.111i			0.767125i
$679$	−167.316			−0.246415
$680$	14.0711			0.0206928
$681$		−	658.769i		−	0.967355i
$682$			47.6615i			0.0698849i
$683$		−	873.552i		−	1.27899i	−0.768794	−	0.639496i	$-0.779143\pi$
$683$		−	873.552i		−	1.27899i	0.768794	−	0.639496i	$-0.220857\pi$
$684$	148.817			0.217569
$685$	91.5920			0.133711
$686$	−776.753			−1.13229
$687$	−431.379			−0.627917
$688$		−	783.266i		−	1.13847i
$689$	−214.035			−0.310646
$690$		−	29.1596i		−	0.0422603i
$691$	−1221.90			−1.76831			−0.884155	−	0.467193i	$-0.845265\pi$
$691$	−1221.90			−1.76831			−0.884155	+	0.467193i	$0.845265\pi$
$692$	91.4895			0.132210
$693$	−181.310			−0.261631
$694$	659.153			0.949789
$695$	149.729			0.215437
$696$	56.9734			0.0818583
$697$		−	324.356i		−	0.465360i
$698$		−	1133.40i		−	1.62378i
$699$	−551.122			−0.788444
$700$		−	691.973i		−	0.988533i
$701$		−	986.573i		−	1.40738i	−0.710507	−	0.703690i	$-0.751534\pi$
$701$		−	986.573i		−	1.40738i	0.710507	−	0.703690i	$-0.248466\pi$
$702$			35.5107i			0.0505850i
$703$	744.750			1.05939
$704$		−	376.542i		−	0.534861i
$705$	2.45729			0.00348552
$706$	−1616.06			−2.28904
$707$	466.391			0.659676
$708$			102.069i			0.144166i
$709$	−667.190			−0.941029			−0.470515	−	0.882392i	$-0.655932\pi$
$709$	−667.190			−0.941029			−0.470515	+	0.882392i	$0.655932\pi$
$710$	−18.2328			−0.0256800
$711$		−	2.61274i		−	0.00367474i
$712$			57.4261i			0.0806547i
$713$			24.3034i			0.0340861i
$714$			760.828i			1.06559i
$715$			10.8614i			0.0151908i
$716$		−	234.536i		−	0.327564i
$717$	642.215			0.895697
$718$			1094.93i			1.52498i
$719$	−1269.51			−1.76566			−0.882828	−	0.469696i	$-0.844364\pi$
$719$	−1269.51			−1.76566			−0.882828	+	0.469696i	$0.844364\pi$
$720$			30.0527i			0.0417399i
$721$			702.798i			0.974755i
$722$		−	457.696i		−	0.633928i
$723$		−	280.250i		−	0.387621i
$724$	−615.316			−0.849884
$725$	−666.310			−0.919049
$726$	−296.348			−0.408193
$727$			1025.15i			1.41011i	0.709154	+	0.705053i	$0.249077\pi$
$727$			1025.15i			1.41011i	−0.709154	+	0.705053i	$0.750923\pi$
$728$		−	23.8759i		−	0.0327966i
$729$	−27.0000			−0.0370370
$730$	−92.0165			−0.126050
$731$		−	903.192i		−	1.23556i
$732$	600.027			0.819710
$733$			990.219i			1.35091i	0.737400	+	0.675456i	$0.236053\pi$
$733$			990.219i			1.35091i	−0.737400	+	0.675456i	$0.763947\pi$
$734$	995.423			1.35616
$735$	12.9928			0.0176772
$736$		−	466.809i		−	0.634252i
$737$	−464.962	+	218.137i	−0.630884	+	0.295980i
$738$	131.984			0.178840
$739$			868.581i			1.17535i	0.809099	+	0.587673i	$0.199956\pi$
$739$			868.581i			1.17535i	−0.809099	+	0.587673i	$0.800044\pi$
$740$		−	108.257i		−	0.146293i
$741$	−60.0523			−0.0810423
$742$		−	1866.00i		−	2.51482i
$743$	902.496			1.21466			0.607332	−	0.794448i	$-0.292240\pi$
$743$	902.496			1.21466			0.607332	+	0.794448i	$0.292240\pi$
$744$		−	4.77212i		−	0.00641413i
$745$		−	37.7131i		−	0.0506216i
$746$	1134.99			1.52143
$747$	−142.745			−0.191091
$748$		−	552.591i		−	0.738758i
$749$			1395.44i			1.86307i
$750$		−	134.806i		−	0.179742i
$751$	135.482			0.180403			0.0902013	−	0.995924i	$-0.471249\pi$
$751$	135.482			0.180403			0.0902013	+	0.995924i	$0.471249\pi$
$752$	43.7502			0.0581785
$753$	463.032			0.614917
$754$	184.541			0.244750
$755$		−	127.336i		−	0.168657i
$756$	−145.717			−0.192748
$757$			230.766i			0.304843i	0.988316	+	0.152422i	$0.0487072\pi$
$757$			230.766i			0.304843i	−0.988316	+	0.152422i	$0.951293\pi$
$758$	789.764			1.04190
$759$	142.663			0.187962
$760$	−9.68272			−0.0127404
$761$	814.913			1.07085			0.535423	−	0.844584i	$-0.320152\pi$
$761$	814.913			1.07085			0.535423	+	0.844584i	$0.320152\pi$
$762$	393.452			0.516342
$763$	−130.996			−0.171686
$764$			450.061i			0.589085i
$765$			34.6541i			0.0452995i
$766$	−1365.87			−1.78312
$767$		−	41.1881i		−	0.0537003i
$768$			524.785i			0.683314i
$769$			218.493i			0.284127i	0.989858	+	0.142063i	$0.0453736\pi$
$769$			218.493i			0.284127i	−0.989858	+	0.142063i	$0.954626\pi$
$770$	−94.6916			−0.122976
$771$			76.4246i			0.0991239i
$772$	−508.625			−0.658841
$773$	−604.826			−0.782440			−0.391220	−	0.920297i	$-0.627947\pi$
$773$	−604.826			−0.782440			−0.391220	+	0.920297i	$0.627947\pi$
$774$	367.518			0.474829
$775$			55.8105i			0.0720135i
$776$	−25.8506			−0.0333126
$777$	−729.236			−0.938528
$778$			1503.44i			1.93244i
$779$			223.198i			0.286519i
$780$			8.72920i			0.0111913i
$781$		−	89.2037i		−	0.114217i
$782$		−	598.655i		−	0.765543i
$783$			140.313i			0.179199i
$784$	231.326			0.295059
$785$			14.8924i			0.0189712i
$786$	760.875			0.968034
$787$			276.416i			0.351228i	0.984459	+	0.175614i	$0.0561911\pi$
$787$			276.416i			0.351228i	−0.984459	+	0.175614i	$0.943809\pi$
$788$			728.153i			0.924052i
$789$			424.824i			0.538433i
$790$		−	1.36454i		−	0.00172726i
$791$	861.240			1.08880
$792$	−28.0128			−0.0353697
$793$	−242.129			−0.305333
$794$			973.267i			1.22578i
$795$		−	84.9924i		−	0.106909i
$796$	558.224			0.701286
$797$	174.907			0.219456			0.109728	−	0.993962i	$-0.465002\pi$
$797$	174.907			0.219456			0.109728	+	0.993962i	$0.465002\pi$
$798$		−	523.547i		−	0.656074i
$799$	50.4488			0.0631400
$800$		−	1071.98i		−	1.33998i
$801$	−141.428			−0.176565
$802$	−1030.28			−1.28463
$803$		−	450.190i		−	0.560635i
$804$	−373.686	+	175.315i	−0.464783	+	0.218053i
$805$	−48.2848			−0.0599811
$806$		−	15.4573i		−	0.0191777i
$807$			824.767i			1.02202i
$808$	72.0583			0.0891811
$809$			1472.15i			1.81972i	0.414914	+	0.909861i	$0.363812\pi$
$809$			1472.15i			1.81972i	−0.414914	+	0.909861i	$0.636188\pi$
$810$	−14.1011			−0.0174088
$811$		−	1613.40i		−	1.98940i	−0.102817	−	0.994700i	$-0.532786\pi$
$811$		−	1613.40i		−	1.98940i	0.102817	−	0.994700i	$-0.467214\pi$
$812$			757.262i			0.932588i
$813$	355.142			0.436829
$814$	1125.28			1.38240
$815$			70.2556i			0.0862032i
$816$			616.990i			0.756115i
$817$			621.512i			0.760725i
$818$	−906.898			−1.10868
$819$	58.8013			0.0717965
$820$	32.4441			0.0395660
$821$	−1127.80			−1.37369			−0.686846	−	0.726803i	$-0.741005\pi$
$821$	−1127.80			−1.37369			−0.686846	+	0.726803i	$0.741005\pi$
$822$			765.156i			0.930847i
$823$	943.059			1.14588			0.572940	−	0.819597i	$-0.305803\pi$
$823$	943.059			1.14588			0.572940	+	0.819597i	$0.305803\pi$
$824$			108.584i			0.131776i
$825$	327.613			0.397107
$826$	359.085			0.434728
$827$	−1495.74			−1.80863			−0.904317	−	0.426862i	$-0.859619\pi$
$827$	−1495.74			−1.80863			−0.904317	+	0.426862i	$0.859619\pi$
$828$	114.657			0.138475
$829$	−1563.72			−1.88627			−0.943136	−	0.332408i	$-0.892139\pi$
$829$	−1563.72			−1.88627			−0.943136	+	0.332408i	$0.892139\pi$
$830$	−74.5506			−0.0898200
$831$		−	168.227i		−	0.202440i
$832$			122.118i			0.146776i
$833$	266.745			0.320222
$834$			1250.83i			1.49980i
$835$			22.4393i			0.0268734i
$836$			380.253i			0.454849i
$837$	11.7527			0.0140415
$838$			269.274i			0.321330i
$839$	173.696			0.207027			0.103514	−	0.994628i	$-0.466991\pi$
$839$	173.696			0.207027			0.103514	+	0.994628i	$0.466991\pi$
$840$	9.48101			0.0112869
$841$	−111.822			−0.132964
$842$			460.996i			0.547501i
$843$	−461.925			−0.547953
$844$	496.777			0.588598
$845$			92.7996i			0.109822i
$846$			20.5281i			0.0242649i
$847$			490.716i			0.579358i
$848$		−	1513.22i		−	1.78446i
$849$		−	644.100i		−	0.758658i
$850$		−	1374.76i		−	1.61736i
$851$	573.797			0.674262
$852$		−	71.6922i		−	0.0841458i
$853$	−1099.40			−1.28886			−0.644432	−	0.764661i	$-0.722906\pi$
$853$	−1099.40			−1.28886			−0.644432	+	0.764661i	$0.722906\pi$
$854$		−	2110.93i		−	2.47181i
$855$		−	23.8465i		−	0.0278906i
$856$			215.598i			0.251867i
$857$		−	311.790i		−	0.363815i	−0.983316	−	0.181908i	$-0.941773\pi$
$857$		−	311.790i		−	0.363815i	0.983316	−	0.181908i	$-0.0582272\pi$
$858$	−90.7357			−0.105753
$859$	−177.750			−0.206927			−0.103464	−	0.994633i	$-0.532993\pi$
$859$	−177.750			−0.206927			−0.103464	+	0.994633i	$0.532993\pi$
$860$	90.3429			0.105050
$861$		−	218.549i		−	0.253832i
$862$			1966.91i			2.28180i
$863$	1016.84			1.17826			0.589132	−	0.808037i	$-0.299470\pi$
$863$	1016.84			1.17826			0.589132	+	0.808037i	$0.299470\pi$
$864$	−225.741			−0.261274
$865$		−	14.6603i		−	0.0169483i
$866$	1858.63			2.14622
$867$			210.895i			0.243247i
$868$	63.4286			0.0730744
$869$	6.67598			0.00768238
$870$			73.2804i			0.0842303i
$871$	150.793	−	70.7448i	0.173127	−	0.0812225i
$872$	−20.2392			−0.0232101
$873$		−	63.6645i		−	0.0729261i
$874$			411.951i			0.471340i
$875$	−223.223			−0.255112
$876$		−	361.814i		−	0.413029i
$877$	972.570			1.10897			0.554487	−	0.832193i	$-0.312915\pi$
$877$	972.570			1.10897			0.554487	+	0.832193i	$0.312915\pi$
$878$			269.837i			0.307331i
$879$		−	82.1254i		−	0.0934304i
$880$	−76.7897			−0.0872611
$881$	−1759.81			−1.99752			−0.998760	−	0.0497933i	$-0.984144\pi$
$881$	−1759.81			−1.99752			−0.998760	+	0.0497933i	$0.984144\pi$
$882$			108.541i			0.123062i
$883$		−	852.460i		−	0.965414i	−0.875782	−	0.482707i	$-0.839654\pi$
$883$		−	852.460i		−	0.965414i	0.875782	−	0.482707i	$-0.160346\pi$
$884$			179.213i			0.202729i
$885$	16.3556			0.0184809
$886$	1758.94			1.98526
$887$	615.947			0.694416			0.347208	−	0.937788i	$-0.387130\pi$
$887$	615.947			0.694416			0.347208	+	0.937788i	$0.387130\pi$
$888$	−112.668			−0.126879
$889$		−	651.509i		−	0.732856i
$890$	−73.8627			−0.0829918
$891$		−	68.9895i		−	0.0774293i
$892$	−871.545			−0.977068
$893$	−34.7152			−0.0388749
$894$	315.054			0.352409
$895$	−37.5819			−0.0419910
$896$	305.444			0.340897
$897$	−46.2676			−0.0515804
$898$			1904.38i			2.12069i
$899$		−	61.0763i		−	0.0679380i
$900$	263.300			0.292555
$901$		−	1744.91i		−	1.93664i
$902$			337.240i			0.373881i
$903$		−	608.565i		−	0.673937i
$904$	133.063			0.147194
$905$			98.5981i			0.108948i
$906$	1063.76			1.17413
$907$	684.121			0.754267			0.377134	−	0.926159i	$-0.376910\pi$
$907$	684.121			0.754267			0.377134	+	0.926159i	$0.376910\pi$
$908$	1352.82			1.48989
$909$			177.464i			0.195230i
$910$	30.7098			0.0337470
$911$	1629.77			1.78899			0.894494	−	0.447080i	$-0.147536\pi$
$911$	1629.77			1.78899			0.894494	+	0.447080i	$0.147536\pi$
$912$		−	424.568i		−	0.465535i
$913$		−	364.738i		−	0.399494i
$914$			559.714i			0.612379i
$915$		−	96.1482i		−	0.105080i
$916$		−	885.864i		−	0.967101i
$917$		−	1259.92i		−	1.37395i
$918$	−289.499			−0.315359
$919$			808.557i			0.879823i	0.898041	+	0.439911i	$0.144990\pi$
$919$			808.557i			0.879823i	−0.898041	+	0.439911i	$0.855010\pi$
$920$	−7.46010			−0.00810881
$921$		−	980.344i		−	1.06443i
$922$			1887.74i			2.04744i
$923$			28.9300i			0.0313434i
$924$		−	372.332i		−	0.402957i
$925$	1317.67			1.42451
$926$	−510.551			−0.551351
$927$	−267.419			−0.288477
$928$			1173.13i			1.26415i
$929$		−	1280.47i		−	1.37834i	−0.724602	−	0.689168i	$-0.757976\pi$
$929$		−	1280.47i		−	1.37834i	0.724602	−	0.689168i	$-0.242024\pi$
$930$	6.13800			0.00660000
$931$	−183.554			−0.197158
$932$		−	1131.76i		−	1.21434i
$933$	−877.621			−0.940644
$934$		−	468.732i		−	0.501855i
$935$	−88.5471			−0.0947027
$936$	9.08493			0.00970612
$937$		−	1227.06i		−	1.30957i	−0.755817	−	0.654783i	$-0.772760\pi$
$937$		−	1227.06i		−	1.30957i	0.755817	−	0.654783i	$-0.227240\pi$
$938$	616.766	+	1314.64i	0.657533	+	1.40154i
$939$	9.19098			0.00978805
$940$			5.04621i			0.00536830i
$941$			1238.95i			1.31664i	0.752740	+	0.658318i	$0.228732\pi$
$941$			1238.95i			1.31664i	−0.752740	+	0.658318i	$0.771268\pi$
$942$	−124.410			−0.132070
$943$			171.964i			0.182359i
$944$	291.199			0.308473
$945$			23.3497i			0.0247087i
$946$			939.070i			0.992674i
$947$	−1435.26			−1.51558			−0.757791	−	0.652498i	$-0.773721\pi$
$947$	−1435.26			−1.51558			−0.757791	+	0.652498i	$0.773721\pi$
$948$	5.36543			0.00565973
$949$			146.003i			0.153849i
$950$			946.007i			0.995797i
$951$		−	412.526i		−	0.433782i
$952$	194.648			0.204462
$953$	−1395.06			−1.46386			−0.731930	−	0.681380i	$-0.761380\pi$
$953$	−1395.06			−1.46386			−0.731930	+	0.681380i	$0.761380\pi$
$954$	710.023			0.744259
$955$	72.1177			0.0755159
$956$			1318.83i			1.37953i
$957$	−358.524			−0.374633
$958$		−	828.783i		−	0.865118i
$959$	1267.01			1.32117
$960$	−48.4923			−0.0505128
$961$	955.884			0.994677
$962$	−364.942			−0.379358
$963$	−530.973			−0.551374
$964$	575.511			0.597003
$965$			81.5020i			0.0844580i
$966$		−	403.370i		−	0.417567i
$967$	1076.27			1.11300			0.556502	−	0.830847i	$-0.312143\pi$
$967$	1076.27			1.11300			0.556502	+	0.830847i	$0.312143\pi$
$968$			75.8167i			0.0783230i
$969$		−	489.574i		−	0.505236i
$970$		−	33.2496i		−	0.0342779i
$971$	−803.586			−0.827586			−0.413793	−	0.910371i	$-0.635796\pi$
$971$	−803.586			−0.827586			−0.413793	+	0.910371i	$0.635796\pi$
$972$		−	55.4462i		−	0.0570435i
$973$	2071.22			2.12870
$974$	−10.9976			−0.0112912
$975$	−106.249			−0.108974
$976$		−	1711.85i		−	1.75394i
$977$	239.306			0.244940			0.122470	−	0.992472i	$-0.460919\pi$
$977$	239.306			0.244940			0.122470	+	0.992472i	$0.460919\pi$
$978$	−586.913			−0.600115
$979$		−	361.373i		−	0.369124i
$980$			26.6815i			0.0272260i
$981$		−	49.8449i		−	0.0508103i
$982$		−	306.406i		−	0.312022i
$983$		−	277.162i		−	0.281955i	−0.990013	−	0.140977i	$-0.954975\pi$
$983$		−	277.162i		−	0.281955i	0.990013	−	0.140977i	$-0.0450245\pi$
$984$		−	33.7663i		−	0.0343153i
$985$	116.679			0.118456
$986$			1504.47i			1.52583i
$987$	33.9921			0.0344398
$988$		−	123.321i		−	0.124819i
$989$			478.847i			0.484173i
$990$		−	36.0307i		−	0.0363946i
$991$		−	1263.41i		−	1.27489i	−0.770497	−	0.637443i	$-0.779992\pi$
$991$		−	1263.41i		−	1.27489i	0.770497	−	0.637443i	$-0.220008\pi$
$992$	98.2617			0.0990541
$993$	939.907			0.946532
$994$	−252.217			−0.253739
$995$		−	89.4497i		−	0.0898992i
$996$		−	293.137i		−	0.294314i
$997$	−1289.01			−1.29289			−0.646446	−	0.762960i	$-0.723746\pi$
$997$	−1289.01			−1.29289			−0.646446	+	0.762960i	$0.723746\pi$
$998$	−1040.15			−1.04223
$999$		−	277.478i		−	0.277756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.17	yes	22
3.2	odd	2		603.3.b.e.334.6		22
67.66	odd	2	inner	201.3.b.a.133.6	✓	22
201.200	even	2		603.3.b.e.334.17		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.6	✓	22	67.66	odd	2	inner
201.3.b.a.133.17	yes	22	1.1	even	1	trivial
603.3.b.e.334.6		22	3.2	odd	2
603.3.b.e.334.17		22	201.200	even	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)

\(f(q)\)	\(=\)	\(q+2.74898i q^{2} +1.73205i q^{3} -3.55688 q^{4} +0.569953i q^{5} -4.76137 q^{6} +7.88425i q^{7} +1.21813i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+2.74898i q^{2} +1.73205i q^{3} -3.55688 q^{4} +0.569953i q^{5} -4.76137 q^{6} +7.88425i q^{7} +1.21813i q^{8} -3.00000 q^{9} -1.56679 q^{10} -7.66550i q^{11} -6.16069i q^{12} +2.48603i q^{13} -21.6736 q^{14} -0.987188 q^{15} -17.5761 q^{16} -20.2672 q^{17} -8.24693i q^{18} +13.9464 q^{19} -2.02725i q^{20} -13.6559 q^{21} +21.0723 q^{22} +10.7451 q^{23} -2.10987 q^{24} +24.6752 q^{25} -6.83403 q^{26} -5.19615i q^{27} -28.0433i q^{28} -27.0033 q^{29} -2.71376i q^{30} +2.26181i q^{31} -43.4439i q^{32} +13.2770 q^{33} -55.7141i q^{34} -4.49365 q^{35} +10.6706 q^{36} +53.4007 q^{37} +38.3385i q^{38} -4.30592 q^{39} -0.694279 q^{40} +16.0040i q^{41} -37.5398i q^{42} +44.5642i q^{43} +27.2653i q^{44} -1.70986i q^{45} +29.5381i q^{46} -2.48918 q^{47} -30.4428i q^{48} -13.1614 q^{49} +67.8314i q^{50} -35.1039i q^{51} -8.84249i q^{52} +86.0954i q^{53} +14.2841 q^{54} +4.36898 q^{55} -9.60406 q^{56} +24.1559i q^{57} -74.2314i q^{58} -16.5679 q^{59} +3.51131 q^{60} +97.3961i q^{61} -6.21766 q^{62} -23.6527i q^{63} +49.1217 q^{64} -1.41692 q^{65} +36.4983i q^{66} +(-28.4570 - 60.6564i) q^{67} +72.0880 q^{68} +18.6111i q^{69} -12.3530i q^{70} +11.6370 q^{71} -3.65440i q^{72} +58.7294 q^{73} +146.797i q^{74} +42.7386i q^{75} -49.6058 q^{76} +60.4367 q^{77} -11.8369i q^{78} +0.870913i q^{79} -10.0176i q^{80} +9.00000 q^{81} -43.9946 q^{82} +47.5818 q^{83} +48.5724 q^{84} -11.5514i q^{85} -122.506 q^{86} -46.7711i q^{87} +9.33760 q^{88} +47.1427 q^{89} +4.70037 q^{90} -19.6004 q^{91} -38.2191 q^{92} -3.91757 q^{93} -6.84271i q^{94} +7.94882i q^{95} +75.2470 q^{96} +21.2215i q^{97} -36.1803i q^{98} +22.9965i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 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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