LMFDB - Embedded newform 201.3.b.a.133.7

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			133.7
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70381i q^{2} -1.73205i q^{3} +1.09704 q^{4} +1.67394i q^{5} -2.95108 q^{6} +0.231323i q^{7} -8.68437i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.70381i q^{2} -1.73205i q^{3} +1.09704 q^{4} +1.67394i q^{5} -2.95108 q^{6} +0.231323i q^{7} -8.68437i q^{8} -3.00000 q^{9} +2.85207 q^{10} -17.0699i q^{11} -1.90013i q^{12} -6.17688i q^{13} +0.394131 q^{14} +2.89935 q^{15} -10.4084 q^{16} +15.1276 q^{17} +5.11142i q^{18} -6.48191 q^{19} +1.83638i q^{20} +0.400664 q^{21} -29.0839 q^{22} -37.1566 q^{23} -15.0418 q^{24} +22.1979 q^{25} -10.5242 q^{26} +5.19615i q^{27} +0.253771i q^{28} +24.7322 q^{29} -4.93994i q^{30} +48.8900i q^{31} -17.0037i q^{32} -29.5660 q^{33} -25.7745i q^{34} -0.387222 q^{35} -3.29112 q^{36} -20.6311 q^{37} +11.0439i q^{38} -10.6987 q^{39} +14.5371 q^{40} -75.9269i q^{41} -0.682654i q^{42} +60.0149i q^{43} -18.7264i q^{44} -5.02182i q^{45} +63.3077i q^{46} +71.6202 q^{47} +18.0278i q^{48} +48.9465 q^{49} -37.8210i q^{50} -26.2017i q^{51} -6.77627i q^{52} +88.0248i q^{53} +8.85325 q^{54} +28.5740 q^{55} +2.00890 q^{56} +11.2270i q^{57} -42.1390i q^{58} -7.13740 q^{59} +3.18070 q^{60} -41.0621i q^{61} +83.2991 q^{62} -0.693970i q^{63} -70.6044 q^{64} +10.3397 q^{65} +50.3747i q^{66} +(49.0877 + 45.6004i) q^{67} +16.5955 q^{68} +64.3571i q^{69} +0.659752i q^{70} -0.114820 q^{71} +26.0531i q^{72} +58.1017 q^{73} +35.1514i q^{74} -38.4479i q^{75} -7.11090 q^{76} +3.94867 q^{77} +18.2285i q^{78} -24.2814i q^{79} -17.4230i q^{80} +9.00000 q^{81} -129.365 q^{82} -3.41432 q^{83} +0.439544 q^{84} +25.3227i q^{85} +102.254 q^{86} -42.8375i q^{87} -148.242 q^{88} +147.335 q^{89} -8.55622 q^{90} +1.42886 q^{91} -40.7622 q^{92} +84.6799 q^{93} -122.027i q^{94} -10.8503i q^{95} -29.4512 q^{96} +50.6774i q^{97} -83.3954i q^{98} +51.2097i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.70381i		−	0.851904i	−0.904746	−	0.425952i	$-0.859939\pi$
$2$		−	1.70381i		−	0.851904i	0.904746	−	0.425952i	$-0.140061\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	1.09704			0.274260
$5$			1.67394i			0.334788i	0.985890	+	0.167394i	$0.0535352\pi$
$5$			1.67394i			0.334788i	−0.985890	+	0.167394i	$0.946465\pi$
$6$	−2.95108			−0.491847
$7$			0.231323i			0.0330462i	0.999863	+	0.0165231i	$0.00525971\pi$
$7$			0.231323i			0.0330462i	−0.999863	+	0.0165231i	$0.994740\pi$
$8$		−	8.68437i		−	1.08555i
$9$	−3.00000			−0.333333
$10$	2.85207			0.285207
$11$		−	17.0699i		−	1.55181i	−0.630850	−	0.775905i	$-0.717293\pi$
$11$		−	17.0699i		−	1.55181i	0.630850	−	0.775905i	$-0.282707\pi$
$12$		−	1.90013i		−	0.158344i
$13$		−	6.17688i		−	0.475145i	−0.971370	−	0.237572i	$-0.923648\pi$
$13$		−	6.17688i		−	0.475145i	0.971370	−	0.237572i	$-0.0763517\pi$
$14$	0.394131			0.0281522
$15$	2.89935			0.193290
$16$	−10.4084			−0.650522
$17$	15.1276			0.889858			0.444929	−	0.895566i	$-0.353229\pi$
$17$	15.1276			0.889858			0.444929	+	0.895566i	$0.353229\pi$
$18$			5.11142i			0.283968i
$19$	−6.48191			−0.341153			−0.170576	−	0.985344i	$-0.554563\pi$
$19$	−6.48191			−0.341153			−0.170576	+	0.985344i	$0.554563\pi$
$20$			1.83638i			0.0918189i
$21$	0.400664			0.0190792
$22$	−29.0839			−1.32199
$23$	−37.1566			−1.61550			−0.807752	−	0.589522i	$-0.799316\pi$
$23$	−37.1566			−1.61550			−0.807752	+	0.589522i	$0.799316\pi$
$24$	−15.0418			−0.626741
$25$	22.1979			0.887917
$26$	−10.5242			−0.404777
$27$			5.19615i			0.192450i
$28$			0.253771i			0.00906324i
$29$	24.7322			0.852836			0.426418	−	0.904526i	$-0.359775\pi$
$29$	24.7322			0.852836			0.426418	+	0.904526i	$0.359775\pi$
$30$		−	4.93994i		−	0.164665i
$31$			48.8900i			1.57710i	0.614974	+	0.788548i	$0.289167\pi$
$31$			48.8900i			1.57710i	−0.614974	+	0.788548i	$0.710833\pi$
$32$		−	17.0037i		−	0.531365i
$33$	−29.5660			−0.895938
$34$		−	25.7745i		−	0.758074i
$35$	−0.387222			−0.0110635
$36$	−3.29112			−0.0914199
$37$	−20.6311			−0.557596			−0.278798	−	0.960350i	$-0.589936\pi$
$37$	−20.6311			−0.557596			−0.278798	+	0.960350i	$0.589936\pi$
$38$			11.0439i			0.290629i
$39$	−10.6987			−0.274325
$40$	14.5371			0.363428
$41$		−	75.9269i		−	1.85187i	−0.377677	−	0.925937i	$-0.623277\pi$
$41$		−	75.9269i		−	1.85187i	0.377677	−	0.925937i	$-0.376723\pi$
$42$		−	0.682654i		−	0.0162537i
$43$			60.0149i			1.39569i	0.716247	+	0.697847i	$0.245859\pi$
$43$			60.0149i			1.39569i	−0.716247	+	0.697847i	$0.754141\pi$
$44$		−	18.7264i		−	0.425599i
$45$		−	5.02182i		−	0.111596i
$46$			63.3077i			1.37626i
$47$	71.6202			1.52383			0.761917	−	0.647675i	$-0.224258\pi$
$47$	71.6202			1.52383			0.761917	+	0.647675i	$0.224258\pi$
$48$			18.0278i			0.375579i
$49$	48.9465			0.998908
$50$		−	37.8210i		−	0.756420i
$51$		−	26.2017i		−	0.513760i
$52$		−	6.77627i		−	0.130313i
$53$			88.0248i			1.66085i	0.557133	+	0.830423i	$0.311901\pi$
$53$			88.0248i			1.66085i	−0.557133	+	0.830423i	$0.688099\pi$
$54$	8.85325			0.163949
$55$	28.5740			0.519528
$56$	2.00890			0.0358732
$57$			11.2270i			0.196965i
$58$		−	42.1390i		−	0.726534i
$59$	−7.13740			−0.120973			−0.0604865	−	0.998169i	$-0.519265\pi$
$59$	−7.13740			−0.120973			−0.0604865	+	0.998169i	$0.519265\pi$
$60$	3.18070			0.0530117
$61$		−	41.0621i		−	0.673149i	−0.941657	−	0.336575i	$-0.890732\pi$
$61$		−	41.0621i		−	0.673149i	0.941657	−	0.336575i	$-0.109268\pi$
$62$	83.2991			1.34353
$63$		−	0.693970i		−	0.0110154i
$64$	−70.6044			−1.10319
$65$	10.3397			0.159073
$66$			50.3747i			0.763253i
$67$	49.0877	+	45.6004i	0.732652	+	0.680604i
$67$	49.0877	+	45.6004i	0.732652	+	0.680604i
$68$	16.5955			0.244052
$69$			64.3571i			0.932712i
$70$			0.659752i			0.00942503i
$71$	−0.114820			−0.00161719			−0.000808594	−	1.00000i	$-0.500257\pi$
$71$	−0.114820			−0.00161719			−0.000808594		1.00000i	$0.500257\pi$
$72$			26.0531i			0.361849i
$73$	58.1017			0.795913			0.397957	−	0.917404i	$-0.369719\pi$
$73$	58.1017			0.795913			0.397957	+	0.917404i	$0.369719\pi$
$74$			35.1514i			0.475018i
$75$		−	38.4479i		−	0.512639i
$76$	−7.11090			−0.0935645
$77$	3.94867			0.0512814
$78$			18.2285i			0.233698i
$79$		−	24.2814i		−	0.307360i	−0.988121	−	0.153680i	$-0.950888\pi$
$79$		−	24.2814i		−	0.307360i	0.988121	−	0.153680i	$-0.0491125\pi$
$80$		−	17.4230i		−	0.217787i
$81$	9.00000			0.111111
$82$	−129.365			−1.57762
$83$	−3.41432			−0.0411363			−0.0205682	−	0.999788i	$-0.506548\pi$
$83$	−3.41432			−0.0411363			−0.0205682	+	0.999788i	$0.506548\pi$
$84$	0.439544			0.00523267
$85$			25.3227i			0.297914i
$86$	102.254			1.18900
$87$		−	42.8375i		−	0.492385i
$88$	−148.242			−1.68456
$89$	147.335			1.65545			0.827727	−	0.561131i	$-0.189634\pi$
$89$	147.335			1.65545			0.827727	+	0.561131i	$0.189634\pi$
$90$	−8.55622			−0.0950692
$91$	1.42886			0.0157017
$92$	−40.7622			−0.443068
$93$	84.6799			0.910536
$94$		−	122.027i		−	1.29816i
$95$		−	10.8503i		−	0.114214i
$96$	−29.4512			−0.306783
$97$			50.6774i			0.522447i	0.965278	+	0.261224i	$0.0841260\pi$
$97$			50.6774i			0.522447i	−0.965278	+	0.261224i	$0.915874\pi$
$98$		−	83.3954i		−	0.850974i
$99$			51.2097i			0.517270i
$100$	24.3520			0.243520
$101$			112.488i			1.11374i	0.830599	+	0.556871i	$0.187998\pi$
$101$			112.488i			1.11374i	−0.830599	+	0.556871i	$0.812002\pi$
$102$	−44.6427			−0.437674
$103$	−40.4944			−0.393149			−0.196575	−	0.980489i	$-0.562982\pi$
$103$	−40.4944			−0.393149			−0.196575	+	0.980489i	$0.562982\pi$
$104$	−53.6423			−0.515792
$105$			0.670688i			0.00638751i
$106$	149.977			1.41488
$107$	−185.218			−1.73101			−0.865503	−	0.500904i	$-0.833001\pi$
$107$	−185.218			−1.73101			−0.865503	+	0.500904i	$0.833001\pi$
$108$			5.70038i			0.0527813i
$109$			12.9245i			0.118573i	0.998241	+	0.0592867i	$0.0188826\pi$
$109$			12.9245i			0.118573i	−0.998241	+	0.0592867i	$0.981117\pi$
$110$		−	48.6847i		−	0.442588i
$111$			35.7340i			0.321928i
$112$		−	2.40770i		−	0.0214973i
$113$		−	43.2302i		−	0.382568i	−0.981535	−	0.191284i	$-0.938735\pi$
$113$		−	43.2302i		−	0.382568i	0.981535	−	0.191284i	$-0.0612651\pi$
$114$	19.1286			0.167795
$115$		−	62.1980i		−	0.540852i
$116$	27.1322			0.233898
$117$			18.5306i			0.158382i
$118$			12.1608i			0.103057i
$119$			3.49937i			0.0294064i
$120$		−	25.1791i		−	0.209825i
$121$	−170.382			−1.40812
$122$	−69.9620			−0.573459
$123$	−131.509			−1.06918
$124$			53.6342i			0.432534i
$125$			79.0066i			0.632052i
$126$	−1.18239			−0.00938407
$127$	−24.6588			−0.194164			−0.0970820	−	0.995276i	$-0.530951\pi$
$127$	−24.6588			−0.194164			−0.0970820	+	0.995276i	$0.530951\pi$
$128$			52.2816i			0.408450i
$129$	103.949			0.805805
$130$		−	17.6169i		−	0.135515i
$131$	2.21761			0.0169283			0.00846415	−	0.999964i	$-0.497306\pi$
$131$	2.21761			0.0169283			0.00846415	+	0.999964i	$0.497306\pi$
$132$	−32.4350			−0.245720
$133$		−	1.49942i		−	0.0112738i
$134$	77.6944	−	83.6360i	0.579809	−	0.624149i
$135$	−8.69805			−0.0644300
$136$		−	131.374i		−	0.965983i
$137$			35.0283i			0.255681i	0.991795	+	0.127841i	$0.0408046\pi$
$137$			35.0283i			0.255681i	−0.991795	+	0.127841i	$0.959195\pi$
$138$	109.652			0.794581
$139$		−	115.954i		−	0.834201i	−0.908860	−	0.417100i	$-0.863046\pi$
$139$		−	115.954i		−	0.834201i	0.908860	−	0.417100i	$-0.136954\pi$
$140$	−0.424797			−0.00303427
$141$		−	124.050i		−	0.879786i
$142$			0.195632i			0.00137769i
$143$	−105.439			−0.737334
$144$	31.2251			0.216841
$145$			41.4003i			0.285519i
$146$		−	98.9941i		−	0.678042i
$147$		−	84.7778i		−	0.576720i
$148$	−22.6331			−0.152926
$149$	−173.698			−1.16576			−0.582879	−	0.812559i	$-0.698074\pi$
$149$	−173.698			−1.16576			−0.582879	+	0.812559i	$0.698074\pi$
$150$	−65.5079			−0.436719
$151$	90.1841			0.597246			0.298623	−	0.954371i	$-0.403473\pi$
$151$	90.1841			0.597246			0.298623	+	0.954371i	$0.403473\pi$
$152$			56.2913i			0.370337i
$153$	−45.3828			−0.296619
$154$		−	6.72778i		−	0.0436869i
$155$	−81.8389			−0.527993
$156$	−11.7369			−0.0752362
$157$	−187.743			−1.19581			−0.597907	−	0.801566i	$-0.704001\pi$
$157$	−187.743			−1.19581			−0.597907	+	0.801566i	$0.704001\pi$
$158$	−41.3709			−0.261841
$159$	152.463			0.958890
$160$	28.4631			0.177895
$161$		−	8.59520i		−	0.0533863i
$162$		−	15.3343i		−	0.0946560i
$163$	138.325			0.848620			0.424310	−	0.905517i	$-0.360517\pi$
$163$	138.325			0.848620			0.424310	+	0.905517i	$0.360517\pi$
$164$		−	83.2947i		−	0.507895i
$165$		−	49.4917i		−	0.299950i
$166$			5.81734i			0.0350442i
$167$	−193.082			−1.15618			−0.578088	−	0.815974i	$-0.696201\pi$
$167$	−193.082			−1.15618			−0.578088	+	0.815974i	$0.696201\pi$
$168$		−	3.47952i		−	0.0207114i
$169$	130.846			0.774238
$170$	43.1450			0.253794
$171$	19.4457			0.113718
$172$			65.8386i			0.382783i
$173$	−51.0583			−0.295135			−0.147567	−	0.989052i	$-0.547144\pi$
$173$	−51.0583			−0.295135			−0.147567	+	0.989052i	$0.547144\pi$
$174$	−72.9868			−0.419465
$175$			5.13490i			0.0293423i
$176$			177.670i			1.00949i
$177$			12.3623i			0.0698437i
$178$		−	251.031i		−	1.41029i
$179$			241.268i			1.34787i	0.738792	+	0.673933i	$0.235396\pi$
$179$			241.268i			1.34787i	−0.738792	+	0.673933i	$0.764604\pi$
$180$		−	5.50914i		−	0.0306063i
$181$	87.5484			0.483693			0.241846	−	0.970315i	$-0.422247\pi$
$181$	87.5484			0.483693			0.241846	+	0.970315i	$0.422247\pi$
$182$		−	2.43450i		−	0.0133764i
$183$	−71.1217			−0.388643
$184$			322.682i			1.75371i
$185$		−	34.5352i		−	0.186677i
$186$		−	144.278i		−	0.775690i
$187$		−	258.227i		−	1.38089i
$188$	78.5701			0.417926
$189$	−1.20199			−0.00635975
$190$	−18.4869			−0.0972994
$191$		−	52.2618i		−	0.273622i	−0.990597	−	0.136811i	$-0.956315\pi$
$191$		−	52.2618i		−	0.273622i	0.990597	−	0.136811i	$-0.0436853\pi$
$192$			122.290i			0.636929i
$193$	321.010			1.66327			0.831633	−	0.555326i	$-0.187406\pi$
$193$	321.010			1.66327			0.831633	+	0.555326i	$0.187406\pi$
$194$	86.3445			0.445075
$195$		−	17.9089i		−	0.0918407i
$196$	53.6962			0.273960
$197$		−	16.7115i		−	0.0848302i	−0.999100	−	0.0424151i	$-0.986495\pi$
$197$		−	16.7115i		−	0.0848302i	0.999100	−	0.0424151i	$-0.0135052\pi$
$198$	87.2516			0.440664
$199$	−269.230			−1.35291			−0.676456	−	0.736483i	$-0.736485\pi$
$199$	−269.230			−1.35291			−0.676456	+	0.736483i	$0.736485\pi$
$200$		−	192.775i		−	0.963875i
$201$	78.9823	−	85.0224i	0.392947	−	0.422997i
$202$	191.658			0.948802
$203$			5.72114i			0.0281830i
$204$		−	28.7443i		−	0.140904i
$205$	127.097			0.619986
$206$			68.9946i			0.334925i
$207$	111.470			0.538502
$208$			64.2911i			0.309092i
$209$			110.646i			0.529405i
$210$	1.14272			0.00544154
$211$	263.342			1.24806			0.624032	−	0.781399i	$-0.285493\pi$
$211$	263.342			1.24806			0.624032	+	0.781399i	$0.285493\pi$
$212$			96.5666i			0.455503i
$213$			0.198875i			0.000933684i
$214$			315.575i			1.47465i
$215$	−100.461			−0.467262
$216$	45.1253			0.208914
$217$	−11.3094			−0.0521170
$218$	22.0209			0.101013
$219$		−	100.635i		−	0.459521i
$220$	31.3468			0.142486
$221$		−	93.4413i		−	0.422811i
$222$	60.8839			0.274252
$223$	−215.722			−0.967363			−0.483682	−	0.875244i	$-0.660701\pi$
$223$	−215.722			−0.967363			−0.483682	+	0.875244i	$0.660701\pi$
$224$	3.93335			0.0175596
$225$	−66.5938			−0.295972
$226$	−73.6559			−0.325911
$227$	−240.463			−1.05931			−0.529655	−	0.848213i	$-0.677679\pi$
$227$	−240.463			−1.05931			−0.529655	+	0.848213i	$0.677679\pi$
$228$			12.3164i			0.0540195i
$229$		−	103.066i		−	0.450068i	−0.974351	−	0.225034i	$-0.927751\pi$
$229$		−	103.066i		−	0.450068i	0.974351	−	0.225034i	$-0.0722494\pi$
$230$	−105.973			−0.460754
$231$		−	6.83930i		−	0.0296074i
$232$		−	214.784i		−	0.925793i
$233$			358.956i			1.54059i	0.637691	+	0.770293i	$0.279890\pi$
$233$			358.956i			1.54059i	−0.637691	+	0.770293i	$0.720110\pi$
$234$	31.5726			0.134926
$235$			119.888i			0.510162i
$236$	−7.83001			−0.0331780
$237$	−42.0567			−0.177454
$238$	5.96225			0.0250515
$239$			134.112i			0.561139i	0.959834	+	0.280570i	$0.0905234\pi$
$239$			134.112i			0.561139i	−0.959834	+	0.280570i	$0.909477\pi$
$240$	−30.1775			−0.125739
$241$	212.437			0.881482			0.440741	−	0.897634i	$-0.354716\pi$
$241$	212.437			0.881482			0.440741	+	0.897634i	$0.354716\pi$
$242$			290.298i			1.19958i
$243$		−	15.5885i		−	0.0641500i
$244$		−	45.0467i		−	0.184618i
$245$			81.9336i			0.334423i
$246$			224.066i			0.910839i
$247$			40.0379i			0.162097i
$248$	424.579			1.71201
$249$			5.91377i			0.0237501i
$250$	134.612			0.538448
$251$		−	51.4667i		−	0.205047i	−0.994731	−	0.102523i	$-0.967308\pi$
$251$		−	51.4667i		−	0.205047i	0.994731	−	0.102523i	$-0.0326916\pi$
$252$		−	0.761312i		−	0.00302108i
$253$			634.260i			2.50696i
$254$			42.0139i			0.165409i
$255$	43.8602			0.172001
$256$	−193.340			−0.755233
$257$	−191.569			−0.745404			−0.372702	−	0.927951i	$-0.621569\pi$
$257$	−191.569			−0.745404			−0.372702	+	0.927951i	$0.621569\pi$
$258$		−	177.109i		−	0.686468i
$259$		−	4.77245i		−	0.0184264i
$260$	11.3431			0.0436273
$261$	−74.1967			−0.284279
$262$		−	3.77838i		−	0.0144213i
$263$	−28.6536			−0.108949			−0.0544746	−	0.998515i	$-0.517348\pi$
$263$	−28.6536			−0.108949			−0.0544746	+	0.998515i	$0.517348\pi$
$264$			256.762i			0.972583i
$265$	−147.348			−0.556032
$266$	−2.55472			−0.00960420
$267$		−	255.192i		−	0.955777i
$268$	53.8511	+	50.0254i	0.200937	+	0.186662i
$269$	453.835			1.68712			0.843560	−	0.537035i	$-0.180456\pi$
$269$	453.835			1.68712			0.843560	+	0.537035i	$0.180456\pi$
$270$			14.8198i			0.0548882i
$271$		−	276.240i		−	1.01934i	−0.860371	−	0.509668i	$-0.829768\pi$
$271$		−	276.240i		−	1.01934i	0.860371	−	0.509668i	$-0.170232\pi$
$272$	−157.453			−0.578872
$273$		−	2.47485i		−	0.00906540i
$274$	59.6816			0.217816
$275$		−	378.917i		−	1.37788i
$276$			70.6023i			0.255805i
$277$	162.470			0.586535			0.293267	−	0.956030i	$-0.405257\pi$
$277$	162.470			0.586535			0.293267	+	0.956030i	$0.405257\pi$
$278$	−197.563			−0.710659
$279$		−	146.670i		−	0.525698i
$280$			3.36278i			0.0120099i
$281$		−	282.632i		−	1.00581i	−0.864342	−	0.502904i	$-0.832265\pi$
$281$		−	282.632i		−	1.00581i	0.864342	−	0.502904i	$-0.167735\pi$
$282$	−211.357			−0.749493
$283$	143.894			0.508461			0.254231	−	0.967144i	$-0.418178\pi$
$283$	143.894			0.508461			0.254231	+	0.967144i	$0.418178\pi$
$284$	−0.125962			−0.000443529
$285$	−18.7933			−0.0659415
$286$			179.647i			0.628138i
$287$	17.5637			0.0611974
$288$			51.0110i			0.177122i
$289$	−60.1561			−0.208153
$290$	70.5382			0.243235
$291$	87.7758			0.301635
$292$	63.7398			0.218287
$293$	−301.398			−1.02866			−0.514332	−	0.857591i	$-0.671960\pi$
$293$	−301.398			−1.02866			−0.514332	+	0.857591i	$0.671960\pi$
$294$	−144.445			−0.491310
$295$		−	11.9476i		−	0.0405003i
$296$			179.168i			0.605297i
$297$	88.6979			0.298646
$298$			295.948i			0.993114i
$299$			229.512i			0.767598i
$300$		−	42.1789i		−	0.140596i
$301$	−13.8828			−0.0461224
$302$		−	153.656i		−	0.508796i
$303$	194.835			0.643020
$304$	67.4659			0.221927
$305$	68.7356			0.225363
$306$			77.3235i			0.252691i
$307$	−386.892			−1.26023			−0.630117	−	0.776500i	$-0.716993\pi$
$307$	−386.892			−1.26023			−0.630117	+	0.776500i	$0.716993\pi$
$308$	4.33185			0.0140644
$309$			70.1383i			0.226985i
$310$			139.438i			0.449799i
$311$		−	63.0030i		−	0.202582i	−0.994857	−	0.101291i	$-0.967703\pi$
$311$		−	63.0030i		−	0.202582i	0.994857	−	0.101291i	$-0.0322973\pi$
$312$			92.9112i			0.297792i
$313$		−	436.775i		−	1.39545i	−0.716368	−	0.697723i	$-0.754197\pi$
$313$		−	436.775i		−	1.39545i	0.716368	−	0.697723i	$-0.245803\pi$
$314$			319.878i			1.01872i
$315$	1.16167			0.00368783
$316$		−	26.6377i		−	0.0842964i
$317$	−351.024			−1.10733			−0.553665	−	0.832739i	$-0.686771\pi$
$317$	−351.024			−1.10733			−0.553665	+	0.832739i	$0.686771\pi$
$318$		−	259.768i		−	0.816882i
$319$		−	422.177i		−	1.32344i
$320$		−	118.188i		−	0.369336i
$321$			320.806i			0.999396i
$322$	−14.6446			−0.0454800
$323$	−98.0556			−0.303578
$324$	9.87335			0.0304733
$325$		−	137.114i		−	0.421889i
$326$		−	235.679i		−	0.722943i
$327$	22.3859			0.0684584
$328$	−659.377			−2.01030
$329$			16.5674i			0.0503569i
$330$	−84.3243			−0.255528
$331$		−	313.995i		−	0.948625i	−0.880357	−	0.474313i	$-0.842697\pi$
$331$		−	313.995i		−	0.948625i	0.880357	−	0.474313i	$-0.157303\pi$
$332$	−3.74564			−0.0112820
$333$	61.8932			0.185865
$334$			328.974i			0.984952i
$335$	−76.3325	+	82.1699i	−0.227858	+	0.245283i
$336$	−4.17025			−0.0124115
$337$		−	380.856i		−	1.13014i	−0.825045	−	0.565068i	$-0.808850\pi$
$337$		−	380.856i		−	1.13014i	0.825045	−	0.565068i	$-0.191150\pi$
$338$		−	222.937i		−	0.659576i
$339$	−74.8768			−0.220876
$340$			27.7800i			0.0817058i
$341$	834.547			2.44735
$342$		−	33.1318i		−	0.0968765i
$343$			22.6573i			0.0660563i
$344$	521.192			1.51509
$345$	−107.730			−0.312261
$346$			86.9935i			0.251426i
$347$		−	433.957i		−	1.25060i	−0.780386	−	0.625298i	$-0.784977\pi$
$347$		−	433.957i		−	1.25060i	0.780386	−	0.625298i	$-0.215023\pi$
$348$		−	46.9944i		−	0.135041i
$349$	−85.7727			−0.245767			−0.122884	−	0.992421i	$-0.539214\pi$
$349$	−85.7727			−0.245767			−0.122884	+	0.992421i	$0.539214\pi$
$350$	8.74888			0.0249968
$351$	32.0960			0.0914416
$352$	−290.251			−0.824577
$353$		−	420.236i		−	1.19047i	−0.803551	−	0.595235i	$-0.797059\pi$
$353$		−	420.236i		−	1.19047i	0.803551	−	0.595235i	$-0.202941\pi$
$354$	21.0631			0.0595002
$355$		−	0.192203i		−	0.000541416i
$356$	161.633			0.454024
$357$	6.06108			0.0169778
$358$	411.074			1.14825
$359$	274.258			0.763951			0.381975	−	0.924172i	$-0.375244\pi$
$359$	274.258			0.763951			0.381975	+	0.924172i	$0.375244\pi$
$360$	−43.6114			−0.121143
$361$	−318.985			−0.883615
$362$		−	149.166i		−	0.412060i
$363$			295.110i			0.812976i
$364$	1.56751			0.00430635
$365$			97.2588i			0.266462i
$366$			121.178i			0.331086i
$367$		−	530.883i		−	1.44655i	−0.690561	−	0.723274i	$-0.742636\pi$
$367$		−	530.883i		−	1.44655i	0.690561	−	0.723274i	$-0.257364\pi$
$368$	386.739			1.05092
$369$			227.781i			0.617292i
$370$	−58.8413			−0.159031
$371$	−20.3622			−0.0548847
$372$	92.8971			0.249723
$373$			374.144i			1.00307i	0.865138	+	0.501533i	$0.167230\pi$
$373$			374.144i			1.00307i	−0.865138	+	0.501533i	$0.832770\pi$
$374$	−439.969			−1.17639
$375$	136.843			0.364916
$376$		−	621.977i		−	1.65419i
$377$		−	152.768i		−	0.405220i
$378$			2.04796i			0.00541789i
$379$		−	567.960i		−	1.49857i	−0.662245	−	0.749287i	$-0.730396\pi$
$379$		−	567.960i		−	1.49857i	0.662245	−	0.749287i	$-0.269604\pi$
$380$		−	11.9032i		−	0.0313243i
$381$			42.7103i			0.112101i
$382$	−89.0441			−0.233100
$383$			300.925i			0.785706i	0.919601	+	0.392853i	$0.128512\pi$
$383$			300.925i			0.785706i	−0.919601	+	0.392853i	$0.871488\pi$
$384$	90.5545			0.235819
$385$			6.60984i			0.0171684i
$386$		−	546.940i		−	1.41694i
$387$		−	180.045i		−	0.465232i
$388$			55.5950i			0.143286i
$389$	−330.666			−0.850042			−0.425021	−	0.905184i	$-0.639733\pi$
$389$	−330.666			−0.850042			−0.425021	+	0.905184i	$0.639733\pi$
$390$	−30.5134			−0.0782395
$391$	−562.090			−1.43757
$392$		−	425.070i		−	1.08436i
$393$		−	3.84101i		−	0.00977356i
$394$	−28.4733			−0.0722671
$395$	40.6457			0.102900
$396$			56.1791i			0.141866i
$397$	−240.588			−0.606016			−0.303008	−	0.952988i	$-0.597991\pi$
$397$	−240.588			−0.606016			−0.303008	+	0.952988i	$0.597991\pi$
$398$			458.716i			1.15255i
$399$	−2.59707			−0.00650894
$400$	−231.044			−0.577609
$401$			484.141i			1.20733i	0.797237	+	0.603667i	$0.206294\pi$
$401$			484.141i			1.20733i	−0.797237	+	0.603667i	$0.793706\pi$
$402$	−144.862	−	134.571i	−0.360353	−	0.334753i
$403$	301.987			0.749348
$404$			123.404i			0.305455i
$405$			15.0655i			0.0371987i
$406$	9.74773			0.0240092
$407$			352.170i			0.865283i
$408$	−227.546			−0.557710
$409$			734.714i			1.79637i	0.439621	+	0.898183i	$0.355113\pi$
$409$			734.714i			1.79637i	−0.439621	+	0.898183i	$0.644887\pi$
$410$		−	216.549i		−	0.528168i
$411$	60.6709			0.147618
$412$	−44.4239			−0.107825
$413$		−	1.65105i		−	0.00399770i
$414$		−	189.923i		−	0.458752i
$415$		−	5.71536i		−	0.0137720i
$416$	−105.030			−0.252475
$417$	−200.838			−0.481626
$418$	188.519			0.451002
$419$	−241.523			−0.576428			−0.288214	−	0.957566i	$-0.593061\pi$
$419$	−241.523			−0.576428			−0.288214	+	0.957566i	$0.593061\pi$
$420$			0.735771i			0.00175183i
$421$	−294.060			−0.698481			−0.349240	−	0.937033i	$-0.613560\pi$
$421$	−294.060			−0.698481			−0.349240	+	0.937033i	$0.613560\pi$
$422$		−	448.683i		−	1.06323i
$423$	−214.861			−0.507945
$424$	764.441			1.80293
$425$	335.801			0.790120
$426$	0.338844			0.000795409
$427$	9.49863			0.0222450
$428$	−203.191			−0.474745
$429$			182.625i			0.425700i
$430$			171.167i			0.398062i
$431$	197.718			0.458743			0.229372	−	0.973339i	$-0.426333\pi$
$431$	197.718			0.458743			0.229372	+	0.973339i	$0.426333\pi$
$432$		−	54.0834i		−	0.125193i
$433$			665.304i			1.53650i	0.640150	+	0.768250i	$0.278872\pi$
$433$			665.304i			1.53650i	−0.640150	+	0.768250i	$0.721128\pi$
$434$			19.2690i			0.0443987i
$435$	71.7074			0.164845
$436$			14.1787i			0.0325199i
$437$	240.846			0.551134
$438$	−171.463			−0.391468
$439$	404.469			0.921342			0.460671	−	0.887571i	$-0.347609\pi$
$439$	404.469			0.921342			0.460671	+	0.887571i	$0.347609\pi$
$440$		−	248.148i		−	0.563972i
$441$	−146.839			−0.332969
$442$	−159.206			−0.360195
$443$		−	380.196i		−	0.858230i	−0.903250	−	0.429115i	$-0.858826\pi$
$443$		−	380.196i		−	0.858230i	0.903250	−	0.429115i	$-0.141174\pi$
$444$			39.2016i			0.0882919i
$445$			246.631i			0.554227i
$446$			367.549i			0.824100i
$447$			300.854i			0.673051i
$448$		−	16.3325i		−	0.0364564i
$449$	−651.148			−1.45022			−0.725109	−	0.688634i	$-0.758211\pi$
$449$	−651.148			−1.45022			−0.725109	+	0.688634i	$0.758211\pi$
$450$			113.463i			0.252140i
$451$	−1296.06			−2.87376
$452$		−	47.4251i		−	0.104923i
$453$		−	156.204i		−	0.344820i
$454$			409.703i			0.902430i
$455$			2.39182i			0.00525675i
$456$	97.4994			0.213814
$457$	46.6687			0.102120			0.0510599	−	0.998696i	$-0.483740\pi$
$457$	46.6687			0.102120			0.0510599	+	0.998696i	$0.483740\pi$
$458$	−175.604			−0.383415
$459$			78.6052i			0.171253i
$460$		−	68.2336i		−	0.148334i
$461$	555.103			1.20413			0.602064	−	0.798448i	$-0.294345\pi$
$461$	555.103			1.20413			0.602064	+	0.798448i	$0.294345\pi$
$462$	−11.6529			−0.0252226
$463$			257.300i			0.555724i	0.960621	+	0.277862i	$0.0896257\pi$
$463$			257.300i			0.555724i	−0.960621	+	0.277862i	$0.910374\pi$
$464$	−257.422			−0.554788
$465$			141.749i			0.304837i
$466$	611.593			1.31243
$467$	−662.936			−1.41956			−0.709782	−	0.704422i	$-0.751206\pi$
$467$	−662.936			−1.41956			−0.709782	+	0.704422i	$0.751206\pi$
$468$			20.3288i			0.0434377i
$469$	−10.5485	+	11.3551i	−0.0224914	+	0.0242114i
$470$	204.266			0.434609
$471$			325.180i			0.690403i
$472$			61.9839i			0.131322i
$473$	1024.45			2.16585
$474$			71.6565i			0.151174i
$475$	−143.885			−0.302915
$476$			3.83894i			0.00806500i
$477$		−	264.075i		−	0.553615i
$478$	228.502			0.478037
$479$	801.249			1.67275			0.836377	−	0.548155i	$-0.184670\pi$
$479$	801.249			1.67275			0.836377	+	0.548155i	$0.184670\pi$
$480$		−	49.2996i		−	0.102708i
$481$			127.436i			0.264939i
$482$		−	361.952i		−	0.750938i
$483$	−14.8873			−0.0308226
$484$	−186.916			−0.386189
$485$	−84.8309			−0.174909
$486$	−26.5597			−0.0546497
$487$			910.081i			1.86875i	0.356292	+	0.934375i	$0.384041\pi$
$487$			910.081i			1.86875i	−0.356292	+	0.934375i	$0.615959\pi$
$488$	−356.599			−0.730735
$489$		−	239.586i		−	0.489951i
$490$	139.599			0.284896
$491$	−304.380			−0.619918			−0.309959	−	0.950750i	$-0.600315\pi$
$491$	−304.380			−0.619918			−0.309959	+	0.950750i	$0.600315\pi$
$492$	−144.271			−0.293233
$493$	374.139			0.758903
$494$	68.2170			0.138091
$495$	−85.7221			−0.173176
$496$		−	508.864i		−	1.02594i
$497$		−	0.0265606i		−	5.34419e-5i
$498$	10.0759			0.0202328
$499$			536.431i			1.07501i	0.843260	+	0.537506i	$0.180633\pi$
$499$			536.431i			1.07501i	−0.843260	+	0.537506i	$0.819367\pi$
$500$			86.6732i			0.173346i
$501$			334.427i			0.667519i
$502$	−87.6894			−0.174680
$503$			382.936i			0.761305i	0.924718	+	0.380652i	$0.124301\pi$
$503$			382.936i			0.761305i	−0.924718	+	0.380652i	$0.875699\pi$
$504$	−6.02670			−0.0119577
$505$	−188.298			−0.372868
$506$	1080.66			2.13569
$507$		−	226.632i		−	0.447006i
$508$	−27.0517			−0.0532513
$509$	817.957			1.60699			0.803494	−	0.595313i	$-0.202972\pi$
$509$	817.957			1.60699			0.803494	+	0.595313i	$0.202972\pi$
$510$		−	74.7293i		−	0.146528i
$511$			13.4403i			0.0263019i
$512$			538.540i			1.05184i
$513$		−	33.6810i		−	0.0656549i
$514$			326.396i			0.635013i
$515$		−	67.7852i		−	0.131622i
$516$	114.036			0.221000
$517$		−	1222.55i		−	2.36470i
$518$	−8.13133			−0.0156976
$519$			88.4355i			0.170396i
$520$		−	89.7941i		−	0.172681i
$521$		−	18.2212i		−	0.0349734i	−0.999847	−	0.0174867i	$-0.994434\pi$
$521$		−	18.2212i		−	0.0349734i	0.999847	−	0.0174867i	$-0.00556648\pi$
$522$			126.417i			0.242178i
$523$	984.652			1.88270			0.941350	−	0.337431i	$-0.109558\pi$
$523$	984.652			1.88270			0.941350	+	0.337431i	$0.109558\pi$
$524$	2.43280			0.00464275
$525$	8.89391			0.0169408
$526$			48.8203i			0.0928142i
$527$			739.587i			1.40339i
$528$	307.733			0.582827
$529$	851.614			1.60986
$530$			251.053i			0.473686i
$531$	21.4122			0.0403243
$532$		−	1.64492i		−	0.00309195i
$533$	−468.991			−0.879908
$534$	−434.799			−0.814230
$535$		−	310.043i		−	0.579520i
$536$	396.011	−	426.296i	0.738827	−	0.795328i
$537$	417.889			0.778191
$538$		−	773.248i		−	1.43726i
$539$		−	835.512i		−	1.55012i
$540$	−9.54210			−0.0176706
$541$			489.235i			0.904317i	0.891938	+	0.452158i	$0.149346\pi$
$541$			489.235i			0.904317i	−0.891938	+	0.452158i	$0.850654\pi$
$542$	−470.660			−0.868376
$543$		−	151.638i		−	0.279260i
$544$		−	257.224i		−	0.472839i
$545$	−21.6349			−0.0396970
$546$	−4.21667			−0.00772285
$547$			854.458i			1.56208i	0.624481	+	0.781040i	$0.285310\pi$
$547$			854.458i			1.56208i	−0.624481	+	0.781040i	$0.714690\pi$
$548$			38.4275i			0.0701231i
$549$			123.186i			0.224383i
$550$	−645.601			−1.17382
$551$	−160.312			−0.290947
$552$	558.902			1.01250
$553$	5.61686			0.0101571
$554$		−	276.818i		−	0.499671i
$555$	−59.8167			−0.107778
$556$		−	127.206i		−	0.228788i
$557$	273.710			0.491401			0.245700	−	0.969346i	$-0.420982\pi$
$557$	273.710			0.491401			0.245700	+	0.969346i	$0.420982\pi$
$558$	−249.897			−0.447845
$559$	370.705			0.663157
$560$	4.03034			0.00719704
$561$	−447.262			−0.797258
$562$	−481.551			−0.856852
$563$		−	290.462i		−	0.515918i	−0.966156	−	0.257959i	$-0.916950\pi$
$563$		−	290.462i		−	0.515918i	0.966156	−	0.257959i	$-0.0830500\pi$
$564$		−	136.087i		−	0.241290i
$565$	72.3647			0.128079
$566$		−	245.169i		−	0.433160i
$567$			2.08191i			0.00367180i
$568$			0.997143i			0.00175553i
$569$	−19.6804			−0.0345877			−0.0172939	−	0.999850i	$-0.505505\pi$
$569$	−19.6804			−0.0345877			−0.0172939	+	0.999850i	$0.505505\pi$
$570$			32.0202i			0.0561758i
$571$	137.587			0.240959			0.120479	−	0.992716i	$-0.461557\pi$
$571$	137.587			0.240959			0.120479	+	0.992716i	$0.461557\pi$
$572$	−115.670			−0.202221
$573$	−90.5202			−0.157976
$574$		−	29.9251i		−	0.0521343i
$575$	−824.800			−1.43443
$576$	211.813			0.367731
$577$			573.203i			0.993419i	0.867917	+	0.496710i	$0.165459\pi$
$577$			573.203i			0.993419i	−0.867917	+	0.496710i	$0.834541\pi$
$578$			102.494i			0.177326i
$579$		−	556.006i		−	0.960287i
$580$			45.4177i			0.0783064i
$581$		−	0.789811i		−	0.00135940i
$582$		−	149.553i		−	0.256964i
$583$	1502.58			2.57732
$584$		−	504.577i		−	0.864001i
$585$	−31.0192			−0.0530243
$586$			513.525i			0.876322i
$587$			492.232i			0.838556i	0.907858	+	0.419278i	$0.137717\pi$
$587$			492.232i			0.838556i	−0.907858	+	0.419278i	$0.862283\pi$
$588$		−	93.0045i		−	0.158171i
$589$		−	316.900i		−	0.538031i
$590$	−20.3564			−0.0345024
$591$	−28.9452			−0.0489767
$592$	214.735			0.362729
$593$		−	509.030i		−	0.858399i	−0.903210	−	0.429199i	$-0.858796\pi$
$593$		−	509.030i		−	0.858399i	0.903210	−	0.429199i	$-0.141204\pi$
$594$		−	151.124i		−	0.254418i
$595$	−5.85773			−0.00984493
$596$	−190.553			−0.319720
$597$			466.319i			0.781105i
$598$	391.044			0.653920
$599$			823.261i			1.37439i	0.726472	+	0.687196i	$0.241159\pi$
$599$			823.261i			1.37439i	−0.726472	+	0.687196i	$0.758841\pi$
$600$	−333.896			−0.556494
$601$	−623.647			−1.03768			−0.518841	−	0.854871i	$-0.673636\pi$
$601$	−623.647			−1.03768			−0.518841	+	0.854871i	$0.673636\pi$
$602$			23.6537i			0.0392919i
$603$	−147.263	−	136.801i	−0.244217	−	0.226868i
$604$	98.9355			0.163800
$605$		−	285.209i		−	0.471421i
$606$		−	331.961i		−	0.547791i
$607$	432.911			0.713198			0.356599	−	0.934258i	$-0.383936\pi$
$607$	432.911			0.713198			0.356599	+	0.934258i	$0.383936\pi$
$608$			110.216i			0.181277i
$609$	9.90931			0.0162715
$610$		−	117.112i		−	0.191987i
$611$		−	442.389i		−	0.724041i
$612$	−49.7866			−0.0813507
$613$	−770.350			−1.25669			−0.628344	−	0.777935i	$-0.716267\pi$
$613$	−770.350			−1.25669			−0.628344	+	0.777935i	$0.716267\pi$
$614$			659.190i			1.07360i
$615$		−	220.139i		−	0.357949i
$616$		−	34.2917i		−	0.0556684i
$617$	483.310			0.783322			0.391661	−	0.920110i	$-0.371901\pi$
$617$	483.310			0.783322			0.391661	+	0.920110i	$0.371901\pi$
$618$	119.502			0.193369
$619$	−134.893			−0.217920			−0.108960	−	0.994046i	$-0.534752\pi$
$619$	−134.893			−0.217920			−0.108960	+	0.994046i	$0.534752\pi$
$620$	−89.7805			−0.144807
$621$		−	193.071i		−	0.310904i
$622$	−107.345			−0.172580
$623$			34.0821i			0.0547065i
$624$	111.355			0.178454
$625$	422.696			0.676313
$626$	−744.180			−1.18879
$627$	191.644			0.305652
$628$	−205.961			−0.327963
$629$	−312.098			−0.496181
$630$		−	1.97926i		−	0.00314168i
$631$		−	173.864i		−	0.275536i	−0.990464	−	0.137768i	$-0.956007\pi$
$631$		−	173.864i		−	0.275536i	0.990464	−	0.137768i	$-0.0439929\pi$
$632$	−210.869			−0.333653
$633$		−	456.121i		−	0.720570i
$634$			598.077i			0.943339i
$635$		−	41.2774i		−	0.0650038i
$636$	167.258			0.262985
$637$		−	302.337i		−	0.474626i
$638$	−719.309			−1.12744
$639$	0.344461			0.000539063
$640$	−87.5164			−0.136744
$641$			232.442i			0.362623i	0.983426	+	0.181312i	$0.0580343\pi$
$641$			232.442i			0.362623i	−0.983426	+	0.181312i	$0.941966\pi$
$642$	546.592			0.851390
$643$	−353.105			−0.549152			−0.274576	−	0.961565i	$-0.588538\pi$
$643$	−353.105			−0.549152			−0.274576	+	0.961565i	$0.588538\pi$
$644$		−	9.42926i		−	0.0146417i
$645$			174.004i			0.269774i
$646$			167.068i			0.258619i
$647$		−	577.481i		−	0.892552i	−0.894895	−	0.446276i	$-0.852750\pi$
$647$		−	577.481i		−	0.892552i	0.894895	−	0.446276i	$-0.147250\pi$
$648$		−	78.1594i		−	0.120616i
$649$			121.835i			0.187727i
$650$	−233.616			−0.359409
$651$			19.5884i			0.0300898i
$652$	151.748			0.232742
$653$			806.229i			1.23465i	0.786707	+	0.617327i	$0.211784\pi$
$653$			806.229i			1.23465i	−0.786707	+	0.617327i	$0.788216\pi$
$654$		−	38.1413i		−	0.0583200i
$655$			3.71214i			0.00566740i
$656$			790.273i			1.20469i
$657$	−174.305			−0.265304
$658$	28.2277			0.0428993
$659$	−361.778			−0.548980			−0.274490	−	0.961590i	$-0.588509\pi$
$659$	−361.778			−0.548980			−0.274490	+	0.961590i	$0.588509\pi$
$660$		−	54.2943i		−	0.0822641i
$661$		−	359.179i		−	0.543388i	−0.962384	−	0.271694i	$-0.912416\pi$
$661$		−	359.179i		−	0.543388i	0.962384	−	0.271694i	$-0.0875838\pi$
$662$	−534.987			−0.808137
$663$	−161.845			−0.244110
$664$			29.6512i			0.0446554i
$665$	2.50994			0.00377434
$666$		−	105.454i		−	0.158339i
$667$	−918.966			−1.37776
$668$	−211.818			−0.317093
$669$			373.641i			0.558507i
$670$	140.002	+	130.056i	0.208958	+	0.194113i
$671$	−700.927			−1.04460
$672$		−	6.81276i		−	0.0101380i
$673$			334.337i			0.496786i	0.968659	+	0.248393i	$0.0799024\pi$
$673$			334.337i			0.496786i	−0.968659	+	0.248393i	$0.920098\pi$
$674$	−648.905			−0.962767
$675$			115.344i			0.170880i
$676$	143.543			0.212342
$677$		−	389.269i		−	0.574991i	−0.957782	−	0.287495i	$-0.907177\pi$
$677$		−	389.269i		−	0.574991i	0.957782	−	0.287495i	$-0.0928226\pi$
$678$			127.576i			0.188165i
$679$	−11.7229			−0.0172649
$680$	219.912			0.323400
$681$			416.495i			0.611593i
$682$		−	1421.91i		−	2.08491i
$683$			1043.09i			1.52722i	0.645679	+	0.763609i	$0.276574\pi$
$683$			1043.09i			1.52722i	−0.645679	+	0.763609i	$0.723426\pi$
$684$	21.3327			0.0311882
$685$	−58.6354			−0.0855991
$686$	38.6037			0.0562736
$687$	−178.515			−0.259847
$688$		−	624.656i		−	0.907930i
$689$	543.719			0.789142
$690$			183.551i			0.266016i
$691$	54.0222			0.0781797			0.0390899	−	0.999236i	$-0.487554\pi$
$691$	54.0222			0.0781797			0.0390899	+	0.999236i	$0.487554\pi$
$692$	−56.0129			−0.0809435
$693$	−11.8460			−0.0170938
$694$	−739.379			−1.06539
$695$	194.100			0.279281
$696$	−372.017			−0.534507
$697$		−	1148.59i		−	1.64791i
$698$			146.140i			0.209370i
$699$	621.731			0.889457
$700$			5.63318i			0.00804740i
$701$		−	129.689i		−	0.185006i	−0.995712	−	0.0925031i	$-0.970513\pi$
$701$		−	129.689i		−	0.185006i	0.995712	−	0.0925031i	$-0.0294868\pi$
$702$		−	54.6854i		−	0.0778995i
$703$	133.729			0.190226
$704$			1205.21i			1.71195i
$705$	207.652			0.294542
$706$	−716.002			−1.01417
$707$	−26.0211			−0.0368050
$708$			13.5620i			0.0191553i
$709$	−1319.24			−1.86071			−0.930355	−	0.366661i	$-0.880501\pi$
$709$	−1319.24			−1.86071			−0.930355	+	0.366661i	$0.880501\pi$
$710$	−0.327476			−0.000461234
$711$			72.8443i			0.102453i
$712$		−	1279.52i		−	1.79707i
$713$		−	1816.59i		−	2.54781i
$714$		−	10.3269i		−	0.0144635i
$715$		−	176.498i		−	0.246851i
$716$			264.680i			0.369665i
$717$	232.289			0.323974
$718$		−	467.284i		−	0.650813i
$719$	−321.289			−0.446855			−0.223427	−	0.974721i	$-0.571725\pi$
$719$	−321.289			−0.446855			−0.223427	+	0.974721i	$0.571725\pi$
$720$			52.2689i			0.0725957i
$721$		−	9.36730i		−	0.0129921i
$722$			543.489i			0.752755i
$723$		−	367.952i		−	0.508924i
$724$	96.0440			0.132657
$725$	549.004			0.757247
$726$	502.811			0.692577
$727$		−	1195.43i		−	1.64433i	−0.569251	−	0.822164i	$-0.692767\pi$
$727$		−	1195.43i		−	1.64433i	0.569251	−	0.822164i	$-0.307233\pi$
$728$		−	12.4087i		−	0.0170450i
$729$	−27.0000			−0.0370370
$730$	165.710			0.227000
$731$			907.880i			1.24197i
$732$	−78.0232			−0.106589
$733$			1030.45i			1.40579i	0.711292	+	0.702897i	$0.248110\pi$
$733$			1030.45i			1.40579i	−0.711292	+	0.702897i	$0.751890\pi$
$734$	−904.522			−1.23232
$735$	141.913			0.193079
$736$			631.799i			0.858422i
$737$	778.396	−	837.922i	1.05617	−	1.13694i
$738$	388.094			0.525873
$739$		−	941.580i		−	1.27413i	−0.770811	−	0.637064i	$-0.780149\pi$
$739$		−	941.580i		−	1.27413i	0.770811	−	0.637064i	$-0.219851\pi$
$740$		−	37.8864i		−	0.0511979i
$741$	69.3478			0.0935867
$742$			34.6933i			0.0467565i
$743$	906.786			1.22044			0.610219	−	0.792233i	$-0.291081\pi$
$743$	906.786			1.22044			0.610219	+	0.792233i	$0.291081\pi$
$744$		−	735.392i		−	0.988430i
$745$		−	290.760i		−	0.390282i
$746$	637.469			0.854516
$747$	10.2429			0.0137121
$748$		−	283.285i		−	0.378723i
$749$		−	42.8452i		−	0.0572032i
$750$		−	233.155i		−	0.310873i
$751$	308.426			0.410687			0.205344	−	0.978690i	$-0.434169\pi$
$751$	308.426			0.410687			0.205344	+	0.978690i	$0.434169\pi$
$752$	−745.448			−0.991287
$753$	−89.1430			−0.118384
$754$	−260.287			−0.345209
$755$			150.963i			0.199951i
$756$	−1.31863			−0.00174422
$757$		−	529.766i		−	0.699823i	−0.936783	−	0.349911i	$-0.886212\pi$
$757$		−	529.766i		−	0.699823i	0.936783	−	0.349911i	$-0.113788\pi$
$758$	−967.694			−1.27664
$759$	1098.57			1.44739
$760$	−94.2283			−0.123985
$761$	221.065			0.290492			0.145246	−	0.989396i	$-0.453603\pi$
$761$	221.065			0.290492			0.145246	+	0.989396i	$0.453603\pi$
$762$	72.7702			0.0954989
$763$	−2.98974			−0.00391840
$764$		−	57.3333i		−	0.0750435i
$765$		−	75.9681i		−	0.0993047i
$766$	512.719			0.669346
$767$			44.0869i			0.0574796i
$768$			334.874i			0.436034i
$769$			1095.22i			1.42421i	0.702071	+	0.712107i	$0.252259\pi$
$769$			1095.22i			1.42421i	−0.702071	+	0.712107i	$0.747741\pi$
$770$	11.2619			0.0146259
$771$			331.807i			0.430359i
$772$	352.161			0.456167
$773$	−1130.88			−1.46298			−0.731491	−	0.681852i	$-0.761175\pi$
$773$	−1130.88			−1.46298			−0.731491	+	0.681852i	$0.761175\pi$
$774$	−306.761			−0.396333
$775$			1085.26i			1.40033i
$776$	440.101			0.567141
$777$	−8.26612			−0.0106385
$778$			563.392i			0.724154i
$779$			492.151i			0.631772i
$780$		−	19.6468i		−	0.0251882i
$781$			1.95997i			0.00250957i
$782$			957.693i			1.22467i
$783$			128.512i			0.164128i
$784$	−509.452			−0.649812
$785$		−	314.270i		−	0.400344i
$786$	−6.54434			−0.00832613
$787$			158.947i			0.201965i	0.994888	+	0.100983i	$0.0321987\pi$
$787$			158.947i			0.201965i	−0.994888	+	0.100983i	$0.967801\pi$
$788$		−	18.3332i		−	0.0232655i
$789$			49.6295i			0.0629018i
$790$		−	69.2524i		−	0.0876613i
$791$	10.0001			0.0126424
$792$	444.725			0.561521
$793$	−253.636			−0.319843
$794$			409.916i			0.516267i
$795$			255.215i			0.321025i
$796$	−295.355			−0.371049
$797$	−297.783			−0.373630			−0.186815	−	0.982395i	$-0.559816\pi$
$797$	−297.783			−0.373630			−0.186815	+	0.982395i	$0.559816\pi$
$798$			4.42490i			0.00554499i
$799$	1083.44			1.35600
$800$		−	377.446i		−	0.471808i
$801$	−442.006			−0.551818
$802$	824.883			1.02853
$803$		−	991.791i		−	1.23511i
$804$	86.6466	−	93.2728i	0.107769	−	0.116011i
$805$	14.3879			0.0178731
$806$		−	514.528i		−	0.638373i
$807$		−	786.066i		−	0.974059i
$808$	976.888			1.20902
$809$			300.512i			0.371461i	0.982601	+	0.185731i	$0.0594652\pi$
$809$			300.512i			0.371461i	−0.982601	+	0.185731i	$0.940535\pi$
$810$	25.6687			0.0316897
$811$		−	488.597i		−	0.602463i	−0.953551	−	0.301231i	$-0.902602\pi$
$811$		−	488.597i		−	0.602463i	0.953551	−	0.301231i	$-0.0973976\pi$
$812$			6.27632i			0.00772945i
$813$	−478.462			−0.588514
$814$	600.031			0.737138
$815$			231.548i			0.284108i
$816$			272.717i			0.334212i
$817$		−	389.011i		−	0.476145i
$818$	1251.81			1.53033
$819$	−4.28657			−0.00523391
$820$	139.430			0.170037
$821$	−1059.77			−1.29083			−0.645414	−	0.763833i	$-0.723315\pi$
$821$	−1059.77			−1.29083			−0.645414	+	0.763833i	$0.723315\pi$
$822$		−	103.372i		−	0.125756i
$823$	−700.469			−0.851116			−0.425558	−	0.904931i	$-0.639922\pi$
$823$	−700.469			−0.851116			−0.425558	+	0.904931i	$0.639922\pi$
$824$			351.668i			0.426782i
$825$	−656.303			−0.795519
$826$	−2.81307			−0.00340565
$827$	−124.290			−0.150290			−0.0751449	−	0.997173i	$-0.523942\pi$
$827$	−124.290			−0.150290			−0.0751449	+	0.997173i	$0.523942\pi$
$828$	122.287			0.147689
$829$	404.979			0.488515			0.244258	−	0.969710i	$-0.421456\pi$
$829$	404.979			0.488515			0.244258	+	0.969710i	$0.421456\pi$
$830$	−9.73788			−0.0117324
$831$		−	281.407i		−	0.338636i
$832$			436.115i			0.524176i
$833$	740.442			0.888886
$834$			342.190i			0.410299i
$835$		−	323.207i		−	0.387074i
$836$			121.382i			0.145194i
$837$	−254.040			−0.303512
$838$			411.509i			0.491061i
$839$	862.599			1.02813			0.514064	−	0.857752i	$-0.328139\pi$
$839$	862.599			1.02813			0.514064	+	0.857752i	$0.328139\pi$
$840$	5.82451			0.00693394
$841$	−229.317			−0.272672
$842$			501.022i			0.595038i
$843$	−489.533			−0.580704
$844$	288.896			0.342294
$845$			219.029i			0.259206i
$846$			366.081i			0.432720i
$847$		−	39.4133i		−	0.0465329i
$848$		−	916.193i		−	1.08042i
$849$		−	249.233i		−	0.293560i
$850$		−	572.140i		−	0.673106i
$851$	766.580			0.900799
$852$			0.218173i			0.000256072i
$853$	618.299			0.724852			0.362426	−	0.932013i	$-0.381949\pi$
$853$	618.299			0.724852			0.362426	+	0.932013i	$0.381949\pi$
$854$		−	16.1838i		−	0.0189506i
$855$			32.5510i			0.0380713i
$856$			1608.50i			1.87909i
$857$		−	36.4038i		−	0.0424782i	−0.999774	−	0.0212391i	$-0.993239\pi$
$857$		−	36.4038i		−	0.0424782i	0.999774	−	0.0212391i	$-0.00676112\pi$
$858$	311.158			0.362656
$859$	794.284			0.924661			0.462330	−	0.886708i	$-0.347013\pi$
$859$	794.284			0.924661			0.462330	+	0.886708i	$0.347013\pi$
$860$	−110.210			−0.128151
$861$		−	30.4212i		−	0.0353324i
$862$		−	336.874i		−	0.390805i
$863$	756.374			0.876447			0.438223	−	0.898866i	$-0.355608\pi$
$863$	756.374			0.876447			0.438223	+	0.898866i	$0.355608\pi$
$864$	88.3536			0.102261
$865$		−	85.4686i		−	0.0988076i
$866$	1133.55			1.30895
$867$			104.193i			0.120177i
$868$	−12.4068			−0.0142936
$869$	−414.482			−0.476964
$870$		−	122.176i		−	0.140432i
$871$	281.668	−	303.209i	0.323385	−	0.348116i
$872$	112.241			0.128717
$873$		−	152.032i		−	0.174149i
$874$		−	410.355i		−	0.469513i
$875$	−18.2761			−0.0208869
$876$		−	110.401i		−	0.126028i
$877$	791.856			0.902914			0.451457	−	0.892293i	$-0.350904\pi$
$877$	791.856			0.902914			0.451457	+	0.892293i	$0.350904\pi$
$878$		−	689.138i		−	0.784895i
$879$			522.037i			0.593899i
$880$	−297.409			−0.337964
$881$	73.4812			0.0834066			0.0417033	−	0.999130i	$-0.486722\pi$
$881$	73.4812			0.0834066			0.0417033	+	0.999130i	$0.486722\pi$
$882$			250.186i			0.283658i
$883$			549.406i			0.622204i	0.950376	+	0.311102i	$0.100698\pi$
$883$			549.406i			0.622204i	−0.950376	+	0.311102i	$0.899302\pi$
$884$		−	102.509i		−	0.115960i
$885$	−20.6938			−0.0233829
$886$	−647.781			−0.731129
$887$	−724.671			−0.816991			−0.408495	−	0.912760i	$-0.633946\pi$
$887$	−724.671			−0.816991			−0.408495	+	0.912760i	$0.633946\pi$
$888$	310.328			0.349468
$889$		−	5.70416i		−	0.00641638i
$890$	420.212			0.472148
$891$		−	153.629i		−	0.172423i
$892$	−236.655			−0.265309
$893$	−464.235			−0.519860
$894$	512.597			0.573375
$895$	−403.869			−0.451250
$896$	−12.0940			−0.0134977
$897$	397.526			0.443173
$898$			1109.43i			1.23545i
$899$			1209.16i			1.34500i
$900$	−73.0559			−0.0811733
$901$			1331.60i			1.47792i
$902$			2208.25i			2.44817i
$903$			24.0458i			0.0266288i
$904$	−375.427			−0.415295
$905$			146.551i			0.161935i
$906$	−266.141			−0.293754
$907$	−1074.27			−1.18442			−0.592210	−	0.805784i	$-0.701744\pi$
$907$	−1074.27			−1.18442			−0.592210	+	0.805784i	$0.701744\pi$
$908$	−263.798			−0.290526
$909$		−	337.464i		−	0.371248i
$910$	4.07521			0.00447825
$911$	−660.946			−0.725516			−0.362758	−	0.931883i	$-0.618165\pi$
$911$	−660.946			−0.725516			−0.362758	+	0.931883i	$0.618165\pi$
$912$		−	116.854i		−	0.128130i
$913$			58.2821i			0.0638358i
$914$		−	79.5146i		−	0.0869962i
$915$		−	119.054i		−	0.130113i
$916$		−	113.067i		−	0.123436i
$917$			0.512985i			0.000559416i
$918$	133.928			0.145891
$919$			889.031i			0.967390i	0.875237	+	0.483695i	$0.160706\pi$
$919$			889.031i			0.967390i	−0.875237	+	0.483695i	$0.839294\pi$
$920$	−540.151			−0.587120
$921$			670.117i			0.727597i
$922$		−	945.789i		−	1.02580i
$923$			0.709231i			0.000768398i
$924$		−	7.50298i		−	0.00812010i
$925$	−457.967			−0.495099
$926$	438.390			0.473423
$927$	121.483			0.131050
$928$		−	420.539i		−	0.453167i
$929$		−	1414.83i		−	1.52296i	−0.648187	−	0.761481i	$-0.724472\pi$
$929$		−	1414.83i		−	1.52296i	0.648187	−	0.761481i	$-0.275528\pi$
$930$	241.513			0.259692
$931$	−317.266			−0.340780
$932$			393.789i			0.422520i
$933$	−109.124			−0.116961
$934$			1129.52i			1.20933i
$935$	432.256			0.462306
$936$	160.927			0.171931
$937$		−	226.058i		−	0.241257i	−0.992698	−	0.120629i	$-0.961509\pi$
$937$		−	226.058i		−	0.241257i	0.992698	−	0.120629i	$-0.0384910\pi$
$938$	19.3470	+	17.9725i	0.0206258	+	0.0191605i
$939$	−756.516			−0.805661
$940$			131.522i			0.139917i
$941$		−	1255.25i		−	1.33395i	−0.745079	−	0.666976i	$-0.767588\pi$
$941$		−	1255.25i		−	1.33395i	0.745079	−	0.666976i	$-0.232412\pi$
$942$	554.044			0.588157
$943$			2821.18i			2.99171i
$944$	74.2886			0.0786955
$945$		−	2.01206i		−	0.00212917i
$946$		−	1745.46i		−	1.84510i
$947$	581.882			0.614448			0.307224	−	0.951637i	$-0.400600\pi$
$947$	581.882			0.614448			0.307224	+	0.951637i	$0.400600\pi$
$948$	−46.1378			−0.0486685
$949$		−	358.887i		−	0.378174i
$950$			245.152i			0.258055i
$951$			607.991i			0.639318i
$952$	30.3898			0.0319221
$953$	−679.604			−0.713121			−0.356561	−	0.934272i	$-0.616051\pi$
$953$	−679.604			−0.713121			−0.356561	+	0.934272i	$0.616051\pi$
$954$	−449.932			−0.471627
$955$	87.4833			0.0916055
$956$			147.126i			0.153898i
$957$	−731.232			−0.764088
$958$		−	1365.17i		−	1.42503i
$959$	−8.10288			−0.00844930
$960$	−204.707			−0.213236
$961$	−1429.23			−1.48723
$962$	217.126			0.225702
$963$	555.653			0.577002
$964$	233.052			0.241755
$965$			537.352i			0.556842i
$966$			25.3651i			0.0262579i
$967$	4.27980			0.00442585			0.00221293	−	0.999998i	$-0.499296\pi$
$967$	4.27980			0.00442585			0.00221293	+	0.999998i	$0.499296\pi$
$968$			1479.66i			1.52858i
$969$			169.837i			0.175271i
$970$			144.536i			0.149006i
$971$	−1474.24			−1.51827			−0.759134	−	0.650934i	$-0.774378\pi$
$971$	−1474.24			−1.51827			−0.759134	+	0.650934i	$0.774378\pi$
$972$		−	17.1011i		−	0.0175938i
$973$	26.8229			0.0275672
$974$	1550.60			1.59199
$975$	−237.488			−0.243578
$976$			427.389i			0.437898i
$977$	1233.46			1.26250			0.631248	−	0.775581i	$-0.282543\pi$
$977$	1233.46			1.26250			0.631248	+	0.775581i	$0.282543\pi$
$978$	−408.208			−0.417391
$979$		−	2515.00i		−	2.56895i
$980$			89.8843i			0.0917187i
$981$		−	38.7735i		−	0.0395245i
$982$			518.605i			0.528111i
$983$			290.584i			0.295609i	0.989017	+	0.147805i	$0.0472207\pi$
$983$			290.584i			0.295609i	−0.989017	+	0.147805i	$0.952779\pi$
$984$			1142.07i			1.16065i
$985$	27.9741			0.0284001
$986$		−	637.461i		−	0.646512i
$987$	28.6956			0.0290736
$988$			43.9232i			0.0444567i
$989$		−	2229.95i		−	2.25475i
$990$			146.054i			0.147529i
$991$			1401.68i			1.41441i	0.707010	+	0.707203i	$0.250044\pi$
$991$			1401.68i			1.41441i	−0.707010	+	0.707203i	$0.749956\pi$
$992$	831.309			0.838013
$993$	−543.855			−0.547689
$994$	−0.0452542			−4.55274e−5
$995$		−	450.675i		−	0.452939i
$996$			6.48763i			0.00651369i
$997$	1450.74			1.45510			0.727550	−	0.686054i	$-0.240659\pi$
$997$	1450.74			1.45510			0.727550	+	0.686054i	$0.240659\pi$
$998$	913.975			0.915807
$999$		−	107.202i		−	0.107309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.7	✓	22
3.2	odd	2		603.3.b.e.334.16		22
67.66	odd	2	inner	201.3.b.a.133.16	yes	22
201.200	even	2		603.3.b.e.334.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.7	✓	22	1.1	even	1	trivial
201.3.b.a.133.16	yes	22	67.66	odd	2	inner
603.3.b.e.334.7		22	201.200	even	2
603.3.b.e.334.16		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)

\(f(q)\)	\(=\)	\(q-1.70381i q^{2} -1.73205i q^{3} +1.09704 q^{4} +1.67394i q^{5} -2.95108 q^{6} +0.231323i q^{7} -8.68437i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.70381i q^{2} -1.73205i q^{3} +1.09704 q^{4} +1.67394i q^{5} -2.95108 q^{6} +0.231323i q^{7} -8.68437i q^{8} -3.00000 q^{9} +2.85207 q^{10} -17.0699i q^{11} -1.90013i q^{12} -6.17688i q^{13} +0.394131 q^{14} +2.89935 q^{15} -10.4084 q^{16} +15.1276 q^{17} +5.11142i q^{18} -6.48191 q^{19} +1.83638i q^{20} +0.400664 q^{21} -29.0839 q^{22} -37.1566 q^{23} -15.0418 q^{24} +22.1979 q^{25} -10.5242 q^{26} +5.19615i q^{27} +0.253771i q^{28} +24.7322 q^{29} -4.93994i q^{30} +48.8900i q^{31} -17.0037i q^{32} -29.5660 q^{33} -25.7745i q^{34} -0.387222 q^{35} -3.29112 q^{36} -20.6311 q^{37} +11.0439i q^{38} -10.6987 q^{39} +14.5371 q^{40} -75.9269i q^{41} -0.682654i q^{42} +60.0149i q^{43} -18.7264i q^{44} -5.02182i q^{45} +63.3077i q^{46} +71.6202 q^{47} +18.0278i q^{48} +48.9465 q^{49} -37.8210i q^{50} -26.2017i q^{51} -6.77627i q^{52} +88.0248i q^{53} +8.85325 q^{54} +28.5740 q^{55} +2.00890 q^{56} +11.2270i q^{57} -42.1390i q^{58} -7.13740 q^{59} +3.18070 q^{60} -41.0621i q^{61} +83.2991 q^{62} -0.693970i q^{63} -70.6044 q^{64} +10.3397 q^{65} +50.3747i q^{66} +(49.0877 + 45.6004i) q^{67} +16.5955 q^{68} +64.3571i q^{69} +0.659752i q^{70} -0.114820 q^{71} +26.0531i q^{72} +58.1017 q^{73} +35.1514i q^{74} -38.4479i q^{75} -7.11090 q^{76} +3.94867 q^{77} +18.2285i q^{78} -24.2814i q^{79} -17.4230i q^{80} +9.00000 q^{81} -129.365 q^{82} -3.41432 q^{83} +0.439544 q^{84} +25.3227i q^{85} +102.254 q^{86} -42.8375i q^{87} -148.242 q^{88} +147.335 q^{89} -8.55622 q^{90} +1.42886 q^{91} -40.7622 q^{92} +84.6799 q^{93} -122.027i q^{94} -10.8503i q^{95} -29.4512 q^{96} +50.6774i q^{97} -83.3954i q^{98} +51.2097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 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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