LMFDB - Embedded newform 201.3.b.a.133.2

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			133.2
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.60849i q^{2} +1.73205i q^{3} -9.02122 q^{4} +2.97147i q^{5} +6.25009 q^{6} +2.36023i q^{7} +18.1190i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.60849i q^{2} +1.73205i q^{3} -9.02122 q^{4} +2.97147i q^{5} +6.25009 q^{6} +2.36023i q^{7} +18.1190i q^{8} -3.00000 q^{9} +10.7225 q^{10} +15.8430i q^{11} -15.6252i q^{12} +6.13135i q^{13} +8.51687 q^{14} -5.14674 q^{15} +29.2976 q^{16} +11.1919 q^{17} +10.8255i q^{18} +18.6522 q^{19} -26.8063i q^{20} -4.08804 q^{21} +57.1694 q^{22} -24.0263 q^{23} -31.3831 q^{24} +16.1704 q^{25} +22.1249 q^{26} -5.19615i q^{27} -21.2922i q^{28} -48.8475 q^{29} +18.5720i q^{30} +34.1879i q^{31} -33.2439i q^{32} -27.4409 q^{33} -40.3858i q^{34} -7.01336 q^{35} +27.0637 q^{36} -21.5831 q^{37} -67.3062i q^{38} -10.6198 q^{39} -53.8403 q^{40} +0.389551i q^{41} +14.7517i q^{42} +6.25093i q^{43} -142.923i q^{44} -8.91442i q^{45} +86.6989i q^{46} -9.41744 q^{47} +50.7449i q^{48} +43.4293 q^{49} -58.3506i q^{50} +19.3849i q^{51} -55.3123i q^{52} +52.4024i q^{53} -18.7503 q^{54} -47.0771 q^{55} -42.7651 q^{56} +32.3065i q^{57} +176.266i q^{58} +70.4686 q^{59} +46.4299 q^{60} -43.4575i q^{61} +123.367 q^{62} -7.08069i q^{63} -2.77008 q^{64} -18.2191 q^{65} +99.0203i q^{66} +(4.99504 + 66.8135i) q^{67} -100.964 q^{68} -41.6148i q^{69} +25.3077i q^{70} +8.27674 q^{71} -54.3571i q^{72} +28.8865 q^{73} +77.8826i q^{74} +28.0079i q^{75} -168.265 q^{76} -37.3932 q^{77} +38.3215i q^{78} -107.776i q^{79} +87.0569i q^{80} +9.00000 q^{81} +1.40569 q^{82} -151.065 q^{83} +36.8791 q^{84} +33.2564i q^{85} +22.5565 q^{86} -84.6064i q^{87} -287.060 q^{88} -99.8011 q^{89} -32.1676 q^{90} -14.4714 q^{91} +216.747 q^{92} -59.2152 q^{93} +33.9828i q^{94} +55.4244i q^{95} +57.5801 q^{96} -164.777i q^{97} -156.714i q^{98} -47.5290i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) $ 22 * q - 52 * q^4 - 66 * q^9	$ 22 q - 52 q^{4} - 66 q^{9} - 36 q^{10} + 72 q^{14} + 12 q^{15} + 116 q^{16} - 14 q^{17} - 26 q^{19} + 48 q^{21} + 32 q^{22} - 82 q^{23} + 36 q^{24} - 62 q^{25} - 100 q^{26} + 102 q^{29} + 36 q^{33} - 180 q^{35} + 156 q^{36} + 106 q^{37} - 72 q^{39} + 76 q^{40} + 154 q^{47} + 146 q^{49} - 224 q^{55} - 452 q^{56} + 370 q^{59} - 24 q^{60} - 300 q^{62} + 148 q^{64} - 284 q^{65} - 134 q^{67} - 116 q^{68} + 160 q^{71} + 218 q^{73} + 480 q^{76} - 396 q^{77} + 198 q^{81} - 68 q^{82} + 128 q^{83} + 20 q^{86} - 856 q^{88} - 118 q^{89} + 108 q^{90} - 400 q^{91} + 804 q^{92} - 72 q^{93} - 144 q^{96}+O(q^{100}) $ 22 * q - 52 * q^4 - 66 * q^9 - 36 * q^10 + 72 * q^14 + 12 * q^15 + 116 * q^16 - 14 * q^17 - 26 * q^19 + 48 * q^21 + 32 * q^22 - 82 * q^23 + 36 * q^24 - 62 * q^25 - 100 * q^26 + 102 * q^29 + 36 * q^33 - 180 * q^35 + 156 * q^36 + 106 * q^37 - 72 * q^39 + 76 * q^40 + 154 * q^47 + 146 * q^49 - 224 * q^55 - 452 * q^56 + 370 * q^59 - 24 * q^60 - 300 * q^62 + 148 * q^64 - 284 * q^65 - 134 * q^67 - 116 * q^68 + 160 * q^71 + 218 * q^73 + 480 * q^76 - 396 * q^77 + 198 * q^81 - 68 * q^82 + 128 * q^83 + 20 * q^86 - 856 * q^88 - 118 * q^89 + 108 * q^90 - 400 * q^91 + 804 * q^92 - 72 * q^93 - 144 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	3.60849i		−	1.80425i	−0.431478	−	0.902123i	$-0.642008\pi$
$2$		−	3.60849i		−	1.80425i	0.431478	−	0.902123i	$-0.357992\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−9.02122			−2.25531
$5$			2.97147i			0.594295i	0.954832	+	0.297147i	$0.0960352\pi$
$5$			2.97147i			0.594295i	−0.954832	+	0.297147i	$0.903965\pi$
$6$	6.25009			1.04168
$7$			2.36023i			0.337176i	0.985687	+	0.168588i	$0.0539207\pi$
$7$			2.36023i			0.337176i	−0.985687	+	0.168588i	$0.946079\pi$
$8$			18.1190i			2.26488i
$9$	−3.00000			−0.333333
$10$	10.7225			1.07225
$11$			15.8430i			1.44027i	0.693832	+	0.720137i	$0.255921\pi$
$11$			15.8430i			1.44027i	−0.693832	+	0.720137i	$0.744079\pi$
$12$		−	15.6252i		−	1.30210i
$13$			6.13135i			0.471642i	0.971796	+	0.235821i	$0.0757779\pi$
$13$			6.13135i			0.471642i	−0.971796	+	0.235821i	$0.924222\pi$
$14$	8.51687			0.608348
$15$	−5.14674			−0.343116
$16$	29.2976			1.83110
$17$	11.1919			0.658346			0.329173	−	0.944270i	$-0.393230\pi$
$17$	11.1919			0.658346			0.329173	+	0.944270i	$0.393230\pi$
$18$			10.8255i			0.601416i
$19$	18.6522			0.981693			0.490846	−	0.871246i	$-0.336688\pi$
$19$	18.6522			0.981693			0.490846	+	0.871246i	$0.336688\pi$
$20$		−	26.8063i		−	1.34032i
$21$	−4.08804			−0.194668
$22$	57.1694			2.59861
$23$	−24.0263			−1.04462			−0.522312	−	0.852755i	$-0.674930\pi$
$23$	−24.0263			−1.04462			−0.522312	+	0.852755i	$0.674930\pi$
$24$	−31.3831			−1.30763
$25$	16.1704			0.646814
$26$	22.1249			0.850959
$27$		−	5.19615i		−	0.192450i
$28$		−	21.2922i		−	0.760434i
$29$	−48.8475			−1.68440			−0.842199	−	0.539167i	$-0.818739\pi$
$29$	−48.8475			−1.68440			−0.842199	+	0.539167i	$0.818739\pi$
$30$			18.5720i			0.619066i
$31$			34.1879i			1.10284i	0.834229	+	0.551418i	$0.185913\pi$
$31$			34.1879i			1.10284i	−0.834229	+	0.551418i	$0.814087\pi$
$32$		−	33.2439i		−	1.03887i
$33$	−27.4409			−0.831543
$34$		−	40.3858i		−	1.18782i
$35$	−7.01336			−0.200382
$36$	27.0637			0.751769
$37$	−21.5831			−0.583328			−0.291664	−	0.956521i	$-0.594209\pi$
$37$	−21.5831			−0.583328			−0.291664	+	0.956521i	$0.594209\pi$
$38$		−	67.3062i		−	1.77122i
$39$	−10.6198			−0.272303
$40$	−53.8403			−1.34601
$41$			0.389551i			0.00950125i	0.999989	+	0.00475062i	$0.00151218\pi$
$41$			0.389551i			0.00950125i	−0.999989	+	0.00475062i	$0.998488\pi$
$42$			14.7517i			0.351230i
$43$			6.25093i			0.145371i	0.997355	+	0.0726853i	$0.0231569\pi$
$43$			6.25093i			0.145371i	−0.997355	+	0.0726853i	$0.976843\pi$
$44$		−	142.923i		−	3.24826i
$45$		−	8.91442i		−	0.198098i
$46$			86.6989i			1.88476i
$47$	−9.41744			−0.200371			−0.100186	−	0.994969i	$-0.531944\pi$
$47$	−9.41744			−0.200371			−0.100186	+	0.994969i	$0.531944\pi$
$48$			50.7449i			1.05719i
$49$	43.4293			0.886313
$50$		−	58.3506i		−	1.16701i
$51$			19.3849i			0.380096i
$52$		−	55.3123i		−	1.06370i
$53$			52.4024i			0.988724i	0.869256	+	0.494362i	$0.164598\pi$
$53$			52.4024i			0.988724i	−0.869256	+	0.494362i	$0.835402\pi$
$54$	−18.7503			−0.347227
$55$	−47.0771			−0.855947
$56$	−42.7651			−0.763663
$57$			32.3065i			0.566781i
$58$			176.266i			3.03907i
$59$	70.4686			1.19438			0.597192	−	0.802099i	$-0.296283\pi$
$59$	70.4686			1.19438			0.597192	+	0.802099i	$0.296283\pi$
$60$	46.4299			0.773832
$61$		−	43.4575i		−	0.712418i	−0.934406	−	0.356209i	$-0.884069\pi$
$61$		−	43.4575i		−	0.712418i	0.934406	−	0.356209i	$-0.115931\pi$
$62$	123.367			1.98979
$63$		−	7.08069i		−	0.112392i
$64$	−2.77008			−0.0432824
$65$	−18.2191			−0.280294
$66$			99.0203i			1.50031i
$67$	4.99504	+	66.8135i	0.0745528	+	0.997217i
$67$	4.99504	+	66.8135i	0.0745528	+	0.997217i
$68$	−100.964			−1.48477
$69$		−	41.6148i		−	0.603113i
$70$			25.3077i			0.361538i
$71$	8.27674			0.116574			0.0582869	−	0.998300i	$-0.481436\pi$
$71$	8.27674			0.116574			0.0582869	+	0.998300i	$0.481436\pi$
$72$		−	54.3571i		−	0.754960i
$73$	28.8865			0.395706			0.197853	−	0.980232i	$-0.436603\pi$
$73$	28.8865			0.395706			0.197853	+	0.980232i	$0.436603\pi$
$74$			77.8826i			1.05247i
$75$			28.0079i			0.373438i
$76$	−168.265			−2.21402
$77$	−37.3932			−0.485625
$78$			38.3215i			0.491301i
$79$		−	107.776i		−	1.36425i	−0.731234	−	0.682127i	$-0.761055\pi$
$79$		−	107.776i		−	1.36425i	0.731234	−	0.682127i	$-0.238945\pi$
$80$			87.0569i			1.08821i
$81$	9.00000			0.111111
$82$	1.40569			0.0171426
$83$	−151.065			−1.82006			−0.910028	−	0.414547i	$-0.863940\pi$
$83$	−151.065			−1.82006			−0.910028	+	0.414547i	$0.863940\pi$
$84$	36.8791			0.439037
$85$			33.2564i			0.391251i
$86$	22.5565			0.262284
$87$		−	84.6064i		−	0.972487i
$88$	−287.060			−3.26205
$89$	−99.8011			−1.12136			−0.560680	−	0.828032i	$-0.689460\pi$
$89$	−99.8011			−1.12136			−0.560680	+	0.828032i	$0.689460\pi$
$90$	−32.1676			−0.357418
$91$	−14.4714			−0.159026
$92$	216.747			2.35594
$93$	−59.2152			−0.636723
$94$			33.9828i			0.361519i
$95$			55.4244i			0.583415i
$96$	57.5801			0.599793
$97$		−	164.777i		−	1.69873i	−0.527808	−	0.849364i	$-0.676986\pi$
$97$		−	164.777i		−	1.69873i	0.527808	−	0.849364i	$-0.323014\pi$
$98$		−	156.714i		−	1.59913i
$99$		−	47.5290i		−	0.480091i
$100$	−145.876			−1.45876
$101$		−	4.40247i		−	0.0435889i	−0.999762	−	0.0217944i	$-0.993062\pi$
$101$		−	4.40247i		−	0.0435889i	0.999762	−	0.0217944i	$-0.00693793\pi$
$102$	69.9503			0.685787
$103$	128.008			1.24280			0.621400	−	0.783494i	$-0.286564\pi$
$103$	128.008			1.24280			0.621400	+	0.783494i	$0.286564\pi$
$104$	−111.094			−1.06821
$105$		−	12.1475i		−	0.115690i
$106$	189.094			1.78390
$107$	123.563			1.15480			0.577399	−	0.816462i	$-0.304068\pi$
$107$	123.563			1.15480			0.577399	+	0.816462i	$0.304068\pi$
$108$			46.8756i			0.434034i
$109$			120.209i			1.10283i	0.834230	+	0.551417i	$0.185913\pi$
$109$			120.209i			1.10283i	−0.834230	+	0.551417i	$0.814087\pi$
$110$			169.877i			1.54434i
$111$		−	37.3831i		−	0.336785i
$112$			69.1490i			0.617402i
$113$		−	40.1395i		−	0.355217i	−0.984101	−	0.177609i	$-0.943164\pi$
$113$		−	40.1395i		−	0.355217i	0.984101	−	0.177609i	$-0.0568361\pi$
$114$	116.578			1.02261
$115$		−	71.3936i		−	0.620814i
$116$	440.664			3.79883
$117$		−	18.3940i		−	0.157214i
$118$		−	254.285i		−	2.15496i
$119$			26.4154i			0.221978i
$120$		−	93.2541i		−	0.777117i
$121$	−130.001			−1.07439
$122$	−156.816			−1.28538
$123$	−0.674722			−0.00548555
$124$		−	308.417i		−	2.48723i
$125$			122.337i			0.978693i
$126$	−25.5506			−0.202783
$127$	76.4030			0.601598			0.300799	−	0.953687i	$-0.402747\pi$
$127$	76.4030			0.601598			0.300799	+	0.953687i	$0.402747\pi$
$128$		−	122.980i		−	0.960780i
$129$	−10.8269			−0.0839297
$130$			65.7436i			0.505720i
$131$	157.248			1.20036			0.600182	−	0.799863i	$-0.295095\pi$
$131$	157.248			1.20036			0.600182	+	0.799863i	$0.295095\pi$
$132$	247.551			1.87538
$133$			44.0234i			0.331003i
$134$	241.096	−	18.0246i	1.79923	−	0.134512i
$135$	15.4402			0.114372
$136$			202.786i			1.49107i
$137$		−	175.324i		−	1.27974i	−0.768483	−	0.639870i	$-0.778988\pi$
$137$		−	175.324i		−	1.27974i	0.768483	−	0.639870i	$-0.221012\pi$
$138$	−150.167			−1.08817
$139$		−	163.159i		−	1.17381i	−0.809656	−	0.586904i	$-0.800346\pi$
$139$		−	163.159i		−	1.17381i	0.809656	−	0.586904i	$-0.199654\pi$
$140$	63.2691			0.451922
$141$		−	16.3115i		−	0.115684i
$142$		−	29.8666i		−	0.210328i
$143$	−97.1390			−0.679294
$144$	−87.8927			−0.610366
$145$		−	145.149i		−	1.00103i
$146$		−	104.237i		−	0.713951i
$147$			75.2218i			0.511713i
$148$	194.706			1.31558
$149$	−141.991			−0.952962			−0.476481	−	0.879185i	$-0.658088\pi$
$149$	−141.991			−0.952962			−0.476481	+	0.879185i	$0.658088\pi$
$150$	101.066			0.673775
$151$	195.386			1.29394			0.646972	−	0.762514i	$-0.276035\pi$
$151$	195.386			1.29394			0.646972	+	0.762514i	$0.276035\pi$
$152$			337.960i			2.22342i
$153$	−33.5756			−0.219449
$154$			134.933i			0.876188i
$155$	−101.589			−0.655410
$156$	95.8036			0.614126
$157$	−134.827			−0.858770			−0.429385	−	0.903122i	$-0.641270\pi$
$157$	−134.827			−0.858770			−0.429385	+	0.903122i	$0.641270\pi$
$158$	−388.909			−2.46145
$159$	−90.7636			−0.570840
$160$	98.7833			0.617396
$161$		−	56.7077i		−	0.352221i
$162$		−	32.4764i		−	0.200472i
$163$	−101.761			−0.624302			−0.312151	−	0.950033i	$-0.601049\pi$
$163$	−101.761			−0.624302			−0.312151	+	0.950033i	$0.601049\pi$
$164$		−	3.51423i		−	0.0214282i
$165$		−	81.5399i		−	0.494181i
$166$			545.116i			3.28383i
$167$	−96.7190			−0.579156			−0.289578	−	0.957154i	$-0.593515\pi$
$167$	−96.7190			−0.579156			−0.289578	+	0.957154i	$0.593515\pi$
$168$		−	74.0713i		−	0.440901i
$169$	131.407			0.777554
$170$	120.005			0.705914
$171$	−55.9565			−0.327231
$172$		−	56.3911i		−	0.327855i
$173$	118.163			0.683022			0.341511	−	0.939878i	$-0.389061\pi$
$173$	118.163			0.683022			0.341511	+	0.939878i	$0.389061\pi$
$174$	−305.302			−1.75461
$175$			38.1657i			0.218090i
$176$			464.162i			2.63728i
$177$			122.055i			0.689577i
$178$			360.132i			2.02321i
$179$			347.775i			1.94288i	0.237289	+	0.971439i	$0.423741\pi$
$179$			347.775i			1.94288i	−0.237289	+	0.971439i	$0.576259\pi$
$180$			80.4190i			0.446772i
$181$	63.4458			0.350529			0.175265	−	0.984521i	$-0.443922\pi$
$181$	63.4458			0.350529			0.175265	+	0.984521i	$0.443922\pi$
$182$			52.2199i			0.286923i
$183$	75.2706			0.411315
$184$		−	435.334i		−	2.36595i
$185$		−	64.1337i		−	0.346669i
$186$			213.678i			1.14881i
$187$			177.313i			0.948198i
$188$	84.9568			0.451898
$189$	12.2641			0.0648895
$190$	199.999			1.05262
$191$		−	144.754i		−	0.757874i	−0.925422	−	0.378937i	$-0.876290\pi$
$191$		−	144.754i		−	0.757874i	0.925422	−	0.378937i	$-0.123710\pi$
$192$		−	4.79791i		−	0.0249891i
$193$	54.9019			0.284466			0.142233	−	0.989833i	$-0.454572\pi$
$193$	54.9019			0.284466			0.142233	+	0.989833i	$0.454572\pi$
$194$	−594.595			−3.06492
$195$		−	31.5565i		−	0.161828i
$196$	−391.786			−1.99891
$197$		−	353.502i		−	1.79443i	−0.441599	−	0.897213i	$-0.645588\pi$
$197$		−	353.502i		−	1.79443i	0.441599	−	0.897213i	$-0.354412\pi$
$198$	−171.508			−0.866203
$199$	337.128			1.69411			0.847054	−	0.531506i	$-0.178374\pi$
$199$	337.128			1.69411			0.847054	+	0.531506i	$0.178374\pi$
$200$			292.991i			1.46496i
$201$	−115.724	+	8.65166i	−0.575744	+	0.0430431i
$202$	−15.8863			−0.0786450
$203$		−	115.291i		−	0.567938i
$204$		−	174.876i		−	0.857233i
$205$	−1.15754			−0.00564654
$206$		−	461.917i		−	2.24232i
$207$	72.0790			0.348208
$208$			179.634i			0.863623i
$209$			295.507i			1.41391i
$210$	−43.8341			−0.208734
$211$	188.825			0.894906			0.447453	−	0.894307i	$-0.352331\pi$
$211$	188.825			0.894906			0.447453	+	0.894307i	$0.352331\pi$
$212$		−	472.734i		−	2.22988i
$213$			14.3357i			0.0673039i
$214$		−	445.878i		−	2.08354i
$215$	−18.5745			−0.0863929
$216$	94.1493			0.435877
$217$	−80.6914			−0.371850
$218$	433.773			1.98978
$219$			50.0330i			0.228461i
$220$	424.693			1.93042
$221$			68.6213i			0.310504i
$222$	−134.897			−0.607642
$223$	63.1454			0.283163			0.141582	−	0.989927i	$-0.454781\pi$
$223$	63.1454			0.283163			0.141582	+	0.989927i	$0.454781\pi$
$224$	78.4632			0.350282
$225$	−48.5111			−0.215605
$226$	−144.843			−0.640899
$227$	329.878			1.45321			0.726604	−	0.687056i	$-0.241097\pi$
$227$	329.878			1.45321			0.726604	+	0.687056i	$0.241097\pi$
$228$		−	291.444i		−	1.27826i
$229$			418.648i			1.82816i	0.405540	+	0.914078i	$0.367084\pi$
$229$			418.648i			1.82816i	−0.405540	+	0.914078i	$0.632916\pi$
$230$	−257.623			−1.12010
$231$		−	64.7668i		−	0.280376i
$232$		−	885.071i		−	3.81496i
$233$		−	105.371i		−	0.452234i	−0.974100	−	0.226117i	$-0.927397\pi$
$233$		−	105.371i		−	0.452234i	0.974100	−	0.226117i	$-0.0726032\pi$
$234$	−66.3748			−0.283653
$235$		−	27.9837i		−	0.119079i
$236$	−635.713			−2.69370
$237$	186.673			0.787652
$238$	95.3198			0.400503
$239$			418.156i			1.74961i	0.484478	+	0.874804i	$0.339010\pi$
$239$			418.156i			1.74961i	−0.484478	+	0.874804i	$0.660990\pi$
$240$	−150.787			−0.628279
$241$	−441.059			−1.83012			−0.915059	−	0.403319i	$-0.867856\pi$
$241$	−441.059			−1.83012			−0.915059	+	0.403319i	$0.867856\pi$
$242$			469.108i			1.93846i
$243$			15.5885i			0.0641500i
$244$			392.040i			1.60672i
$245$			129.049i			0.526731i
$246$			2.43473i			0.00989728i
$247$			114.363i			0.463008i
$248$	−619.453			−2.49779
$249$		−	261.652i		−	1.05081i
$250$	441.451			1.76580
$251$			363.132i			1.44674i	0.690460	+	0.723370i	$0.257408\pi$
$251$			363.132i			1.44674i	−0.690460	+	0.723370i	$0.742592\pi$
$252$			63.8765i			0.253478i
$253$		−	380.650i		−	1.50454i
$254$		−	275.700i		−	1.08543i
$255$	−57.6017			−0.225889
$256$	−454.852			−1.77677
$257$	71.6198			0.278676			0.139338	−	0.990245i	$-0.455502\pi$
$257$	71.6198			0.278676			0.139338	+	0.990245i	$0.455502\pi$
$258$			39.0689i			0.151430i
$259$		−	50.9412i		−	0.196684i
$260$	164.359			0.632149
$261$	146.543			0.561466
$262$		−	567.428i		−	2.16575i
$263$	61.3793			0.233381			0.116691	−	0.993168i	$-0.462771\pi$
$263$	61.3793			0.233381			0.116691	+	0.993168i	$0.462771\pi$
$264$		−	497.203i		−	1.88335i
$265$	−155.712			−0.587593
$266$	158.858			0.597211
$267$		−	172.861i		−	0.647418i
$268$	−45.0613	−	602.740i	−0.168139	−	2.24903i
$269$	35.7989			0.133081			0.0665407	−	0.997784i	$-0.478804\pi$
$269$	35.7989			0.133081			0.0665407	+	0.997784i	$0.478804\pi$
$270$		−	55.7159i		−	0.206355i
$271$		−	283.858i		−	1.04745i	−0.851889	−	0.523723i	$-0.824543\pi$
$271$		−	283.858i		−	1.04745i	0.851889	−	0.523723i	$-0.175457\pi$
$272$	327.895			1.20550
$273$		−	25.0652i		−	0.0918138i
$274$	−632.657			−2.30897
$275$			256.187i			0.931590i
$276$			375.417i			1.36021i
$277$	−13.8610			−0.0500397			−0.0250199	−	0.999687i	$-0.507965\pi$
$277$	−13.8610			−0.0500397			−0.0250199	+	0.999687i	$0.507965\pi$
$278$	−588.760			−2.11784
$279$		−	102.564i		−	0.367612i
$280$		−	127.075i		−	0.453841i
$281$			406.473i			1.44652i	0.690573	+	0.723262i	$0.257358\pi$
$281$			406.473i			1.44652i	−0.690573	+	0.723262i	$0.742642\pi$
$282$	−58.8599			−0.208723
$283$	276.670			0.977632			0.488816	−	0.872387i	$-0.337429\pi$
$283$	276.670			0.977632			0.488816	+	0.872387i	$0.337429\pi$
$284$	−74.6663			−0.262909
$285$	−95.9979			−0.336835
$286$			350.526i			1.22561i
$287$	−0.919430			−0.00320359
$288$			99.7317i			0.346291i
$289$	−163.742			−0.566581
$290$	−523.770			−1.80610
$291$	285.401			0.980761
$292$	−260.592			−0.892438
$293$	525.614			1.79390			0.896952	−	0.442128i	$-0.145776\pi$
$293$	525.614			1.79390			0.896952	+	0.442128i	$0.145776\pi$
$294$	271.437			0.923256
$295$			209.396i			0.709815i
$296$		−	391.066i		−	1.32117i
$297$	82.3227			0.277181
$298$			512.375i			1.71938i
$299$		−	147.314i		−	0.492688i
$300$		−	252.665i		−	0.842217i
$301$	−14.7536			−0.0490154
$302$		−	705.047i		−	2.33459i
$303$	7.62531			0.0251660
$304$	546.463			1.79758
$305$	129.133			0.423386
$306$			121.157i			0.395939i
$307$	33.6318			0.109550			0.0547748	−	0.998499i	$-0.482556\pi$
$307$	33.6318			0.109550			0.0547748	+	0.998499i	$0.482556\pi$
$308$	337.332			1.09523
$309$			221.717i			0.717531i
$310$			366.581i			1.18252i
$311$			303.906i			0.977188i	0.872511	+	0.488594i	$0.162490\pi$
$311$			303.906i			0.977188i	−0.872511	+	0.488594i	$0.837510\pi$
$312$		−	192.421i		−	0.616733i
$313$			233.282i			0.745311i	0.927970	+	0.372655i	$0.121553\pi$
$313$			233.282i			0.745311i	−0.927970	+	0.372655i	$0.878447\pi$
$314$			486.522i			1.54943i
$315$	21.0401			0.0667939
$316$			972.271i			3.07681i
$317$	−288.242			−0.909282			−0.454641	−	0.890675i	$-0.650232\pi$
$317$	−288.242			−0.909282			−0.454641	+	0.890675i	$0.650232\pi$
$318$			327.520i			1.02994i
$319$		−	773.892i		−	2.42599i
$320$		−	8.23120i		−	0.0257225i
$321$			214.018i			0.666723i
$322$	−204.629			−0.635494
$323$	208.753			0.646293
$324$	−81.1910			−0.250590
$325$			99.1460i			0.305065i
$326$			367.204i			1.12639i
$327$	−208.208			−0.636722
$328$	−7.05830			−0.0215192
$329$		−	22.2273i		−	0.0675602i
$330$	−294.236			−0.891625
$331$			104.615i			0.316058i	0.987434	+	0.158029i	$0.0505140\pi$
$331$			104.615i			0.316058i	−0.987434	+	0.158029i	$0.949486\pi$
$332$	1362.79			4.10478
$333$	64.7494			0.194443
$334$			349.010i			1.04494i
$335$	−198.535	+	14.8426i	−0.592641	+	0.0443063i
$336$	−119.770			−0.356457
$337$			52.9250i			0.157047i	0.996912	+	0.0785237i	$0.0250206\pi$
$337$			52.9250i			0.157047i	−0.996912	+	0.0785237i	$0.974979\pi$
$338$		−	474.180i		−	1.40290i
$339$	69.5237			0.205085
$340$		−	300.013i		−	0.882391i
$341$	−541.640			−1.58839
$342$			201.919i			0.590405i
$343$			218.154i			0.636019i
$344$	−113.261			−0.329247
$345$	123.657			0.358427
$346$		−	426.390i		−	1.23234i
$347$		−	466.498i		−	1.34438i	−0.740381	−	0.672188i	$-0.765355\pi$
$347$		−	466.498i		−	1.34438i	0.740381	−	0.672188i	$-0.234645\pi$
$348$			763.253i			2.19326i
$349$	−299.605			−0.858466			−0.429233	−	0.903194i	$-0.641216\pi$
$349$	−299.605			−0.858466			−0.429233	+	0.903194i	$0.641216\pi$
$350$	137.721			0.393488
$351$	31.8594			0.0907676
$352$	526.684			1.49626
$353$			87.4000i			0.247592i	0.992308	+	0.123796i	$0.0395069\pi$
$353$			87.4000i			0.247592i	−0.992308	+	0.123796i	$0.960493\pi$
$354$	440.435			1.24417
$355$			24.5941i			0.0692792i
$356$	900.328			2.52901
$357$	−45.7528			−0.128159
$358$	1254.94			3.50543
$359$	239.534			0.667226			0.333613	−	0.942710i	$-0.391732\pi$
$359$	239.534			0.667226			0.333613	+	0.942710i	$0.391732\pi$
$360$	161.521			0.448669
$361$	−13.0967			−0.0362790
$362$		−	228.944i		−	0.632442i
$363$		−	225.169i		−	0.620299i
$364$	130.550			0.358653
$365$			85.8356i			0.235166i
$366$		−	271.613i		−	0.742113i
$367$			568.059i			1.54784i	0.633281	+	0.773922i	$0.281708\pi$
$367$			568.059i			1.54784i	−0.633281	+	0.773922i	$0.718292\pi$
$368$	−703.913			−1.91281
$369$		−	1.16865i		−	0.00316708i
$370$	−231.426			−0.625476
$371$	−123.682			−0.333374
$372$	534.194			1.43600
$373$		−	410.940i		−	1.10171i	−0.834599	−	0.550857i	$-0.814301\pi$
$373$		−	410.940i		−	1.10171i	0.834599	−	0.550857i	$-0.185699\pi$
$374$	639.833			1.71078
$375$	−211.893			−0.565048
$376$		−	170.635i		−	0.453817i
$377$		−	299.501i		−	0.794433i
$378$		−	44.2550i		−	0.117077i
$379$			7.13671i			0.0188304i	0.999956	+	0.00941518i	$0.00299699\pi$
$379$			7.13671i			0.0188304i	−0.999956	+	0.00941518i	$0.997003\pi$
$380$		−	499.996i		−	1.31578i
$381$			132.334i			0.347333i
$382$	−522.344			−1.36739
$383$		−	167.336i		−	0.436908i	−0.975847	−	0.218454i	$-0.929899\pi$
$383$		−	167.336i		−	0.436908i	0.975847	−	0.218454i	$-0.0701014\pi$
$384$	213.007			0.554706
$385$		−	111.113i		−	0.288605i
$386$		−	198.113i		−	0.513247i
$387$		−	18.7528i		−	0.0484569i
$388$			1486.49i			3.83115i
$389$	45.1800			0.116144			0.0580720	−	0.998312i	$-0.481505\pi$
$389$	45.1800			0.116144			0.0580720	+	0.998312i	$0.481505\pi$
$390$	−113.871			−0.291978
$391$	−268.900			−0.687723
$392$			786.898i			2.00739i
$393$			272.361i			0.693031i
$394$	−1275.61			−3.23759
$395$	320.253			0.810768
$396$			428.770i			1.08275i
$397$	−581.782			−1.46545			−0.732723	−	0.680527i	$-0.761751\pi$
$397$	−581.782			−1.46545			−0.732723	+	0.680527i	$0.761751\pi$
$398$		−	1216.52i		−	3.05659i
$399$	−76.2507			−0.191105
$400$	473.752			1.18438
$401$		−	212.836i		−	0.530762i	−0.964144	−	0.265381i	$-0.914502\pi$
$401$		−	212.836i		−	0.530762i	0.964144	−	0.265381i	$-0.0854978\pi$
$402$	31.2195	+	417.591i	0.0776603	+	1.03878i
$403$	−209.618			−0.520144
$404$			39.7157i			0.0983062i
$405$			26.7433i			0.0660327i
$406$	−416.028			−1.02470
$407$		−	341.942i		−	0.840152i
$408$	−351.236			−0.860872
$409$			251.833i			0.615729i	0.951430	+	0.307865i	$0.0996144\pi$
$409$			251.833i			0.615729i	−0.951430	+	0.307865i	$0.900386\pi$
$410$			4.17698i			0.0101877i
$411$	303.671			0.738858
$412$	−1154.79			−2.80289
$413$			166.322i			0.402717i
$414$		−	260.097i		−	0.628253i
$415$		−	448.884i		−	1.08165i
$416$	203.830			0.489976
$417$	282.600			0.677699
$418$	1066.33			2.55104
$419$	663.724			1.58407			0.792034	−	0.610478i	$-0.209022\pi$
$419$	663.724			1.58407			0.792034	+	0.610478i	$0.209022\pi$
$420$			109.585i			0.260917i
$421$	−87.6371			−0.208164			−0.104082	−	0.994569i	$-0.533190\pi$
$421$	−87.6371			−0.208164			−0.104082	+	0.994569i	$0.533190\pi$
$422$		−	681.375i		−	1.61463i
$423$	28.2523			0.0667903
$424$	−949.481			−2.23934
$425$	180.977			0.425827
$426$	51.7304			0.121433
$427$	102.570			0.240210
$428$	−1114.69			−2.60442
$429$		−	168.250i		−	0.392191i
$430$			67.0259i			0.155874i
$431$	579.504			1.34456			0.672279	−	0.740298i	$-0.265316\pi$
$431$	579.504			1.34456			0.672279	+	0.740298i	$0.265316\pi$
$432$		−	152.235i		−	0.352395i
$433$			305.597i			0.705766i	0.935667	+	0.352883i	$0.114799\pi$
$433$			305.597i			0.705766i	−0.935667	+	0.352883i	$0.885201\pi$
$434$			291.174i			0.670908i
$435$	251.406			0.577944
$436$		−	1084.43i		−	2.48723i
$437$	−448.143			−1.02550
$438$	180.544			0.412200
$439$	−236.016			−0.537622			−0.268811	−	0.963193i	$-0.586631\pi$
$439$	−236.016			−0.537622			−0.268811	+	0.963193i	$0.586631\pi$
$440$		−	852.992i		−	1.93862i
$441$	−130.288			−0.295438
$442$	247.619			0.560225
$443$		−	201.911i		−	0.455781i	−0.973687	−	0.227890i	$-0.926817\pi$
$443$		−	201.911i		−	0.455781i	0.973687	−	0.227890i	$-0.0731828\pi$
$444$			337.241i			0.759552i
$445$		−	296.556i		−	0.666419i
$446$		−	227.860i		−	0.510896i
$447$		−	245.936i		−	0.550193i
$448$		−	6.53801i		−	0.0145938i
$449$	−851.236			−1.89585			−0.947925	−	0.318495i	$-0.896823\pi$
$449$	−851.236			−1.89585			−0.947925	+	0.318495i	$0.896823\pi$
$450$			175.052i			0.389004i
$451$	−6.17166			−0.0136844
$452$			362.108i			0.801123i
$453$			338.418i			0.747059i
$454$		−	1190.36i		−	2.62195i
$455$		−	43.0013i		−	0.0945084i
$456$	−585.363			−1.28369
$457$	770.581			1.68617			0.843086	−	0.537778i	$-0.180736\pi$
$457$	770.581			1.68617			0.843086	+	0.537778i	$0.180736\pi$
$458$	1510.69			3.29844
$459$		−	58.1547i		−	0.126699i
$460$			644.058i			1.40013i
$461$	−277.269			−0.601452			−0.300726	−	0.953711i	$-0.597229\pi$
$461$	−277.269			−0.601452			−0.300726	+	0.953711i	$0.597229\pi$
$462$	−233.711			−0.505867
$463$		−	737.848i		−	1.59362i	−0.604227	−	0.796812i	$-0.706518\pi$
$463$		−	737.848i		−	1.59362i	0.604227	−	0.796812i	$-0.293482\pi$
$464$	−1431.11			−3.08430
$465$		−	175.956i		−	0.378401i
$466$	−380.229			−0.815942
$467$	32.5786			0.0697614			0.0348807	−	0.999391i	$-0.488895\pi$
$467$	32.5786			0.0697614			0.0348807	+	0.999391i	$0.488895\pi$
$468$			165.937i			0.354566i
$469$	−157.695	+	11.7894i	−0.336237	+	0.0251374i
$470$	−100.979			−0.214849
$471$		−	233.527i		−	0.495811i
$472$			1276.82i			2.70514i
$473$	−99.0336			−0.209373
$474$		−	673.610i		−	1.42112i
$475$	301.612			0.634973
$476$		−	238.299i		−	0.500629i
$477$		−	157.207i		−	0.329575i
$478$	1508.91			3.15672
$479$	−670.882			−1.40059			−0.700294	−	0.713854i	$-0.746948\pi$
$479$	−670.882			−1.40059			−0.700294	+	0.713854i	$0.746948\pi$
$480$			171.098i			0.356454i
$481$		−	132.334i		−	0.275122i
$482$			1591.56i			3.30199i
$483$	98.2205			0.203355
$484$	1172.77			2.42308
$485$	489.629			1.00954
$486$	56.2508			0.115742
$487$			105.072i			0.215754i	0.994164	+	0.107877i	$0.0344053\pi$
$487$			105.072i			0.215754i	−0.994164	+	0.107877i	$0.965595\pi$
$488$	787.408			1.61354
$489$		−	176.256i		−	0.360441i
$490$	465.673			0.950352
$491$	317.794			0.647238			0.323619	−	0.946187i	$-0.395100\pi$
$491$	317.794			0.647238			0.323619	+	0.946187i	$0.395100\pi$
$492$	6.08682			0.0123716
$493$	−546.696			−1.10892
$494$	412.678			0.835380
$495$	141.231			0.285316
$496$			1001.62i			2.01940i
$497$			19.5350i			0.0393058i
$498$	−944.168			−1.89592
$499$		−	206.847i		−	0.414523i	−0.978286	−	0.207262i	$-0.933545\pi$
$499$		−	206.847i		−	0.414523i	0.978286	−	0.207262i	$-0.0664551\pi$
$500$		−	1103.63i		−	2.20725i
$501$		−	167.522i		−	0.334376i
$502$	1310.36			2.61028
$503$			6.80129i			0.0135214i	0.999977	+	0.00676072i	$0.00215202\pi$
$503$			6.80129i			0.0135214i	−0.999977	+	0.00676072i	$0.997848\pi$
$504$	128.295			0.254554
$505$	13.0818			0.0259046
$506$	−1373.57			−2.71457
$507$			227.603i			0.448921i
$508$	−689.249			−1.35679
$509$	574.618			1.12892			0.564458	−	0.825462i	$-0.309085\pi$
$509$	574.618			1.12892			0.564458	+	0.825462i	$0.309085\pi$
$510$			207.855i			0.407560i
$511$			68.1789i			0.133422i
$512$			1149.41i			2.24494i
$513$		−	96.9195i		−	0.188927i
$514$		−	258.440i		−	0.502801i
$515$			380.373i			0.738589i
$516$	97.6722			0.189287
$517$		−	149.201i		−	0.288589i
$518$	−183.821			−0.354866
$519$			204.664i			0.394343i
$520$		−	330.113i		−	0.634833i
$521$		−	857.653i		−	1.64617i	−0.567920	−	0.823084i	$-0.692252\pi$
$521$		−	857.653i		−	1.64617i	0.567920	−	0.823084i	$-0.307748\pi$
$522$		−	528.798i		−	1.01302i
$523$	−317.203			−0.606507			−0.303253	−	0.952910i	$-0.598073\pi$
$523$	−317.203			−0.606507			−0.303253	+	0.952910i	$0.598073\pi$
$524$	−1418.57			−2.70719
$525$	−66.1050			−0.125914
$526$		−	221.487i		−	0.421078i
$527$			382.627i			0.726048i
$528$	−803.952			−1.52264
$529$	48.2647			0.0912376
$530$			561.887i			1.06016i
$531$	−211.406			−0.398128
$532$		−	397.145i		−	0.746513i
$533$	−2.38847			−0.00448119
$534$	−623.766			−1.16810
$535$			367.165i			0.686290i
$536$	−1210.60	+	90.5053i	−2.25858	+	0.168853i
$537$	−602.364			−1.12172
$538$		−	129.180i		−	0.240112i
$539$			688.051i			1.27653i
$540$	−139.290			−0.257944
$541$			908.084i			1.67853i	0.543723	+	0.839265i	$0.317014\pi$
$541$			908.084i			1.67853i	−0.543723	+	0.839265i	$0.682986\pi$
$542$	−1024.30			−1.88985
$543$			109.891i			0.202378i
$544$		−	372.062i		−	0.683937i
$545$	−357.198			−0.655408
$546$	−90.4475			−0.165655
$547$		−	914.375i		−	1.67162i	−0.549020	−	0.835809i	$-0.684999\pi$
$547$		−	914.375i		−	1.67162i	0.549020	−	0.835809i	$-0.315001\pi$
$548$			1581.64i			2.88621i
$549$			130.372i			0.237473i
$550$	924.449			1.68082
$551$	−911.112			−1.65356
$552$	754.021			1.36598
$553$	254.376			0.459993
$554$			50.0173i			0.0902840i
$555$	111.083			0.200149
$556$			1471.90i			2.64730i
$557$	−119.832			−0.215139			−0.107569	−	0.994198i	$-0.534307\pi$
$557$	−119.832			−0.215139			−0.107569	+	0.994198i	$0.534307\pi$
$558$	−370.101			−0.663263
$559$	−38.3266			−0.0685629
$560$	−205.474			−0.366918
$561$	−307.115			−0.547443
$562$	1466.76			2.60989
$563$		−	460.684i		−	0.818266i	−0.912475	−	0.409133i	$-0.865831\pi$
$563$		−	460.684i		−	0.818266i	0.912475	−	0.409133i	$-0.134169\pi$
$564$			147.150i			0.260903i
$565$	119.274			0.211104
$566$		−	998.361i		−	1.76389i
$567$			21.2421i			0.0374640i
$568$			149.967i			0.264026i
$569$	251.776			0.442488			0.221244	−	0.975219i	$-0.428988\pi$
$569$	251.776			0.442488			0.221244	+	0.975219i	$0.428988\pi$
$570$			346.408i			0.607733i
$571$	−846.245			−1.48204			−0.741021	−	0.671482i	$-0.765658\pi$
$571$	−846.245			−1.48204			−0.741021	+	0.671482i	$0.765658\pi$
$572$	876.313			1.53202
$573$	250.721			0.437559
$574$			3.31776i			0.00578006i
$575$	−388.514			−0.675677
$576$	8.31023			0.0144275
$577$		−	151.839i		−	0.263152i	−0.991306	−	0.131576i	$-0.957996\pi$
$577$		−	151.839i		−	0.263152i	0.991306	−	0.131576i	$-0.0420037\pi$
$578$			590.861i			1.02225i
$579$			95.0929i			0.164236i
$580$			1309.42i			2.25762i
$581$		−	356.547i		−	0.613678i
$582$		−	1029.87i		−	1.76953i
$583$	−830.212			−1.42403
$584$			523.397i			0.896227i
$585$	54.6574			0.0934314
$586$		−	1896.67i		−	3.23665i
$587$			1082.40i			1.84395i	0.387247	+	0.921976i	$0.373426\pi$
$587$			1082.40i			1.84395i	−0.387247	+	0.921976i	$0.626574\pi$
$588$		−	678.592i		−	1.15407i
$589$			637.679i			1.08265i
$590$	755.602			1.28068
$591$	612.283			1.03601
$592$	−632.333			−1.06813
$593$		−	1013.99i		−	1.70993i	−0.518685	−	0.854965i	$-0.673578\pi$
$593$		−	1013.99i		−	1.70993i	0.518685	−	0.854965i	$-0.326422\pi$
$594$		−	297.061i		−	0.500103i
$595$	−78.4926			−0.131920
$596$	1280.94			2.14922
$597$			583.922i			0.978094i
$598$	−531.581			−0.888931
$599$			500.517i			0.835587i	0.908542	+	0.417794i	$0.137196\pi$
$599$			500.517i			0.835587i	−0.908542	+	0.417794i	$0.862804\pi$
$600$	−507.476			−0.845793
$601$	−85.5431			−0.142335			−0.0711673	−	0.997464i	$-0.522672\pi$
$601$	−85.5431			−0.142335			−0.0711673	+	0.997464i	$0.522672\pi$
$602$			53.2384i			0.0884359i
$603$	−14.9851	−	200.441i	−0.0248509	−	0.332406i
$604$	−1762.62			−2.91824
$605$		−	386.295i		−	0.638504i
$606$		−	27.5159i		−	0.0454057i
$607$	−693.676			−1.14279			−0.571397	−	0.820674i	$-0.693598\pi$
$607$	−693.676			−1.14279			−0.571397	+	0.820674i	$0.693598\pi$
$608$		−	620.071i		−	1.01985i
$609$	199.691			0.327899
$610$		−	465.975i		−	0.763893i
$611$		−	57.7416i		−	0.0945034i
$612$	302.893			0.494924
$613$	259.288			0.422982			0.211491	−	0.977380i	$-0.432168\pi$
$613$	259.288			0.422982			0.211491	+	0.977380i	$0.432168\pi$
$614$		−	121.360i		−	0.197655i
$615$		−	2.00492i		−	0.00326003i
$616$		−	677.528i		−	1.09988i
$617$	488.735			0.792115			0.396058	−	0.918226i	$-0.370378\pi$
$617$	488.735			0.792115			0.396058	+	0.918226i	$0.370378\pi$
$618$	800.064			1.29460
$619$	−336.022			−0.542847			−0.271423	−	0.962460i	$-0.587494\pi$
$619$	−336.022			−0.542847			−0.271423	+	0.962460i	$0.587494\pi$
$620$	916.453			1.47815
$621$			124.844i			0.201038i
$622$	1096.64			1.76309
$623$		−	235.554i		−	0.378096i
$624$	−311.135			−0.498613
$625$	40.7390			0.0651824
$626$	841.797			1.34472
$627$	−511.832			−0.816320
$628$	1216.30			1.93679
$629$	−241.556			−0.384031
$630$		−	75.9230i		−	0.120513i
$631$		−	256.515i		−	0.406522i	−0.979125	−	0.203261i	$-0.934846\pi$
$631$		−	256.515i		−	0.406522i	0.979125	−	0.203261i	$-0.0651539\pi$
$632$	1952.80			3.08987
$633$			327.055i			0.516674i
$634$			1040.12i			1.64057i
$635$			227.029i			0.357527i
$636$	818.799			1.28742
$637$			266.280i			0.418022i
$638$	−2792.58			−4.37709
$639$	−24.8302			−0.0388579
$640$	365.431			0.570986
$641$		−	829.680i		−	1.29435i	−0.762340	−	0.647177i	$-0.775950\pi$
$641$		−	829.680i		−	1.29435i	0.762340	−	0.647177i	$-0.224050\pi$
$642$	772.283			1.20293
$643$	79.0785			0.122984			0.0614918	−	0.998108i	$-0.480414\pi$
$643$	79.0785			0.122984			0.0614918	+	0.998108i	$0.480414\pi$
$644$			511.572i			0.794367i
$645$		−	32.1719i		−	0.0498790i
$646$		−	753.283i		−	1.16607i
$647$			223.614i			0.345617i	0.984955	+	0.172808i	$0.0552842\pi$
$647$			223.614i			0.345617i	−0.984955	+	0.172808i	$0.944716\pi$
$648$			163.071i			0.251653i
$649$			1116.44i			1.72024i
$650$	357.768			0.550412
$651$		−	139.762i		−	0.214687i
$652$	918.010			1.40799
$653$		−	372.193i		−	0.569974i	−0.958531	−	0.284987i	$-0.908011\pi$
$653$		−	372.193i		−	0.569974i	0.958531	−	0.284987i	$-0.0919893\pi$
$654$			751.317i			1.14880i
$655$			467.257i			0.713370i
$656$			11.4129i			0.0173977i
$657$	−86.6596			−0.131902
$658$	−80.2071			−0.121895
$659$	668.818			1.01490			0.507449	−	0.861682i	$-0.330588\pi$
$659$	668.818			1.01490			0.507449	+	0.861682i	$0.330588\pi$
$660$			735.590i			1.11453i
$661$		−	793.338i		−	1.20021i	−0.799922	−	0.600104i	$-0.795126\pi$
$661$		−	793.338i		−	1.20021i	0.799922	−	0.600104i	$-0.204874\pi$
$662$	377.503			0.570247
$663$	−118.856			−0.179269
$664$		−	2737.15i		−	4.12221i
$665$	−130.814			−0.196713
$666$		−	233.648i		−	0.350823i
$667$	1173.63			1.75956
$668$	872.524			1.30617
$669$			109.371i			0.163484i
$670$	53.5595	+	716.411i	0.0799395	+	1.06927i
$671$	688.498			1.02608
$672$			135.902i			0.202236i
$673$		−	99.4781i		−	0.147813i	−0.997265	−	0.0739065i	$-0.976453\pi$
$673$		−	99.4781i		−	0.147813i	0.997265	−	0.0739065i	$-0.0235466\pi$
$674$	190.979			0.283352
$675$		−	84.0236i		−	0.124479i
$676$	−1185.45			−1.75362
$677$			15.3218i			0.0226319i	0.999936	+	0.0113159i	$0.00360206\pi$
$677$			15.3218i			0.0226319i	−0.999936	+	0.0113159i	$0.996398\pi$
$678$		−	250.876i		−	0.370023i
$679$	388.911			0.572770
$680$	−602.574			−0.886138
$681$			571.366i			0.839010i
$682$			1954.50i			2.86584i
$683$		−	539.003i		−	0.789170i	−0.918859	−	0.394585i	$-0.870888\pi$
$683$		−	539.003i		−	0.789170i	0.918859	−	0.394585i	$-0.129112\pi$
$684$	504.796			0.738006
$685$	520.972			0.760543
$686$	787.209			1.14753
$687$	−725.119			−1.05549
$688$			183.137i			0.266188i
$689$	−321.297			−0.466324
$690$		−	446.217i		−	0.646691i
$691$	291.850			0.422359			0.211179	−	0.977447i	$-0.432270\pi$
$691$	291.850			0.422359			0.211179	+	0.977447i	$0.432270\pi$
$692$	−1065.97			−1.54042
$693$	112.179			0.161875
$694$	−1683.36			−2.42559
$695$	484.824			0.697588
$696$	1532.99			2.20257
$697$			4.35981i			0.00625510i
$698$			1081.12i			1.54888i
$699$	182.507			0.261097
$700$		−	344.302i		−	0.491859i
$701$			299.568i			0.427344i	0.976905	+	0.213672i	$0.0685424\pi$
$701$			299.568i			0.427344i	−0.976905	+	0.213672i	$0.931458\pi$
$702$		−	114.964i		−	0.163767i
$703$	−402.572			−0.572649
$704$		−	43.8864i		−	0.0623386i
$705$	48.4691			0.0687505
$706$	315.382			0.446717
$707$	10.3908			0.0146971
$708$		−	1101.09i		−	1.55521i
$709$	1098.15			1.54887			0.774435	−	0.632654i	$-0.218034\pi$
$709$	1098.15			1.54887			0.774435	+	0.632654i	$0.218034\pi$
$710$	88.7476			0.124997
$711$			323.328i			0.454751i
$712$		−	1808.30i		−	2.53975i
$713$		−	821.411i		−	1.15205i
$714$			165.099i			0.231231i
$715$		−	288.646i		−	0.403701i
$716$		−	3137.36i		−	4.38178i
$717$	−724.268			−1.01014
$718$		−	864.357i		−	1.20384i
$719$	−495.307			−0.688883			−0.344442	−	0.938808i	$-0.611932\pi$
$719$	−495.307			−0.688883			−0.344442	+	0.938808i	$0.611932\pi$
$720$		−	261.171i		−	0.362737i
$721$			302.129i			0.419042i
$722$			47.2594i			0.0654562i
$723$		−	763.936i		−	1.05662i
$724$	−572.359			−0.790551
$725$	−789.882			−1.08949
$726$	−812.519			−1.11917
$727$		−	620.704i		−	0.853789i	−0.904301	−	0.426894i	$-0.859608\pi$
$727$		−	620.704i		−	0.853789i	0.904301	−	0.426894i	$-0.140392\pi$
$728$		−	262.208i		−	0.360176i
$729$	−27.0000			−0.0370370
$730$	309.737			0.424297
$731$			69.9597i			0.0957041i
$732$	−679.033			−0.927640
$733$			408.888i			0.557828i	0.960316	+	0.278914i	$0.0899744\pi$
$733$			408.888i			0.557828i	−0.960316	+	0.278914i	$0.910026\pi$
$734$	2049.84			2.79269
$735$	−223.519			−0.304108
$736$			798.729i			1.08523i
$737$	−1058.53	+	79.1365i	−1.43627	+	0.107376i
$738$	−4.21708			−0.00571420
$739$			1049.98i			1.42082i	0.703790	+	0.710408i	$0.251490\pi$
$739$			1049.98i			1.42082i	−0.703790	+	0.710408i	$0.748510\pi$
$740$			578.564i			0.781844i
$741$	−198.082			−0.267318
$742$			446.304i			0.601488i
$743$	−1284.78			−1.72918			−0.864592	−	0.502474i	$-0.832423\pi$
$743$	−1284.78			−1.72918			−0.864592	+	0.502474i	$0.832423\pi$
$744$		−	1072.92i		−	1.44210i
$745$		−	421.924i		−	0.566340i
$746$	−1482.87			−1.98777
$747$	453.194			0.606685
$748$		−	1599.58i		−	2.13848i
$749$			291.638i			0.389370i
$750$			764.615i			1.01949i
$751$	567.716			0.755946			0.377973	−	0.925817i	$-0.376621\pi$
$751$	567.716			0.755946			0.377973	+	0.925817i	$0.376621\pi$
$752$	−275.908			−0.366899
$753$	−628.963			−0.835276
$754$	−1080.75			−1.43335
$755$			580.583i			0.768984i
$756$	−110.637			−0.146346
$757$		−	140.695i		−	0.185858i	−0.995673	−	0.0929291i	$-0.970377\pi$
$757$		−	140.695i		−	0.185858i	0.995673	−	0.0929291i	$-0.0296230\pi$
$758$	25.7528			0.0339746
$759$	659.304			0.868649
$760$	−1004.24			−1.32137
$761$	949.280			1.24741			0.623705	−	0.781660i	$-0.285627\pi$
$761$	949.280			1.24741			0.623705	+	0.781660i	$0.285627\pi$
$762$	477.526			0.626674
$763$	−283.721			−0.371849
$764$			1305.86i			1.70924i
$765$		−	99.7691i		−	0.130417i
$766$	−603.831			−0.788290
$767$			432.067i			0.563321i
$768$		−	787.827i		−	1.02582i
$769$			405.144i			0.526845i	0.964681	+	0.263423i	$0.0848514\pi$
$769$			405.144i			0.526845i	−0.964681	+	0.263423i	$0.915149\pi$
$770$	−400.950			−0.520714
$771$			124.049i			0.160894i
$772$	−495.282			−0.641558
$773$	−818.026			−1.05825			−0.529124	−	0.848544i	$-0.677479\pi$
$773$	−818.026			−1.05825			−0.529124	+	0.848544i	$0.677479\pi$
$774$	−67.6694			−0.0874281
$775$			552.831i			0.713330i
$776$	2985.60			3.84742
$777$	88.2327			0.113556
$778$		−	163.032i		−	0.209552i
$779$			7.26597i			0.00932731i
$780$			284.678i			0.364972i
$781$			131.128i			0.167898i
$782$			970.323i			1.24082i
$783$			253.819i			0.324162i
$784$	1272.37			1.62293
$785$		−	400.634i		−	0.510362i
$786$	982.813			1.25040
$787$			563.328i			0.715791i	0.933762	+	0.357896i	$0.116506\pi$
$787$			563.328i			0.715791i	−0.933762	+	0.357896i	$0.883494\pi$
$788$			3189.02i			4.04698i
$789$			106.312i			0.134743i
$790$		−	1155.63i		−	1.46283i
$791$	94.7385			0.119771
$792$	861.181			1.08735
$793$	266.453			0.336006
$794$			2099.36i			2.64403i
$795$		−	269.702i		−	0.339247i
$796$	−3041.30			−3.82073
$797$	960.318			1.20492			0.602458	−	0.798151i	$-0.294188\pi$
$797$	960.318			1.20492			0.602458	+	0.798151i	$0.294188\pi$
$798$			275.150i			0.344800i
$799$	−105.399			−0.131913
$800$		−	537.565i		−	0.671957i
$801$	299.403			0.373787
$802$	−768.016			−0.957626
$803$			457.650i			0.569925i
$804$	1043.98	−	78.0485i	1.29848	−	0.0970753i
$805$	168.505			0.209323
$806$			756.405i			0.938468i
$807$			62.0055i			0.0768346i
$808$	79.7686			0.0987236
$809$			336.288i			0.415684i	0.978162	+	0.207842i	$0.0666440\pi$
$809$			336.288i			0.415684i	−0.978162	+	0.207842i	$0.933356\pi$
$810$	96.5029			0.119139
$811$			869.657i			1.07233i	0.844114	+	0.536164i	$0.180127\pi$
$811$			869.657i			1.07233i	−0.844114	+	0.536164i	$0.819873\pi$
$812$			1040.07i			1.28087i
$813$	491.656			0.604743
$814$	−1233.90			−1.51584
$815$		−	302.381i		−	0.371019i
$816$			567.931i			0.695993i
$817$			116.593i			0.142709i
$818$	908.739			1.11093
$819$	43.4142			0.0530087
$820$	10.4424			0.0127347
$821$	937.379			1.14175			0.570876	−	0.821036i	$-0.306604\pi$
$821$	937.379			1.14175			0.570876	+	0.821036i	$0.306604\pi$
$822$		−	1095.79i		−	1.33308i
$823$	20.5973			0.0250271			0.0125135	−	0.999922i	$-0.496017\pi$
$823$	20.5973			0.0250271			0.0125135	+	0.999922i	$0.496017\pi$
$824$			2319.39i			2.81479i
$825$	−443.729			−0.537853
$826$	600.172			0.726601
$827$	−179.654			−0.217236			−0.108618	−	0.994084i	$-0.534642\pi$
$827$	−179.654			−0.217236			−0.108618	+	0.994084i	$0.534642\pi$
$828$	−650.241			−0.785315
$829$	−543.735			−0.655893			−0.327947	−	0.944696i	$-0.606357\pi$
$829$	−543.735			−0.655893			−0.327947	+	0.944696i	$0.606357\pi$
$830$	−1619.80			−1.95156
$831$		−	24.0080i		−	0.0288905i
$832$		−	16.9843i		−	0.0204138i
$833$	486.056			0.583500
$834$		−	1019.76i		−	1.22274i
$835$		−	287.398i		−	0.344189i
$836$		−	2665.83i		−	3.18879i
$837$	177.646			0.212241
$838$		−	2395.04i		−	2.85805i
$839$	−1185.21			−1.41264			−0.706320	−	0.707892i	$-0.749646\pi$
$839$	−1185.21			−1.41264			−0.706320	+	0.707892i	$0.749646\pi$
$840$	220.101			0.262025
$841$	1545.08			1.83720
$842$			316.238i			0.375580i
$843$	−704.033			−0.835151
$844$	−1703.43			−2.01829
$845$			390.471i			0.462096i
$846$		−	101.948i		−	0.120506i
$847$		−	306.833i		−	0.362258i
$848$			1535.26i			1.81045i
$849$			479.206i			0.564436i
$850$		−	653.053i		−	0.768297i
$851$	518.564			0.609358
$852$		−	129.326i		−	0.151791i
$853$	804.681			0.943354			0.471677	−	0.881771i	$-0.343649\pi$
$853$	804.681			0.943354			0.471677	+	0.881771i	$0.343649\pi$
$854$		−	370.122i		−	0.433398i
$855$		−	166.273i		−	0.194472i
$856$			2238.85i			2.61548i
$857$		−	1332.39i		−	1.55472i	−0.629057	−	0.777359i	$-0.716559\pi$
$857$		−	1332.39i		−	1.55472i	0.629057	−	0.777359i	$-0.283441\pi$
$858$	−607.128			−0.707609
$859$	491.404			0.572065			0.286033	−	0.958220i	$-0.407663\pi$
$859$	491.404			0.572065			0.286033	+	0.958220i	$0.407663\pi$
$860$	167.565			0.194842
$861$		−	1.59250i		−	0.00184959i
$862$		−	2091.14i		−	2.42591i
$863$	334.079			0.387113			0.193557	−	0.981089i	$-0.437998\pi$
$863$	334.079			0.387113			0.193557	+	0.981089i	$0.437998\pi$
$864$	−172.740			−0.199931
$865$			351.118i			0.405916i
$866$	1102.74			1.27338
$867$		−	283.609i		−	0.327116i
$868$	727.935			0.838635
$869$	1707.50			1.96490
$870$		−	907.196i		−	1.04275i
$871$	−409.657	+	30.6263i	−0.470330	+	0.0351622i
$872$	−2178.07			−2.49779
$873$			494.330i			0.566243i
$874$			1617.12i			1.85025i
$875$	−288.742			−0.329991
$876$		−	451.358i		−	0.515249i
$877$	35.5034			0.0404828			0.0202414	−	0.999795i	$-0.493557\pi$
$877$	35.5034			0.0404828			0.0202414	+	0.999795i	$0.493557\pi$
$878$			851.662i			0.970003i
$879$			910.390i			1.03571i
$880$	−1379.24			−1.56732
$881$	526.017			0.597069			0.298534	−	0.954399i	$-0.403502\pi$
$881$	526.017			0.597069			0.298534	+	0.954399i	$0.403502\pi$
$882$			470.143i			0.533042i
$883$			410.389i			0.464767i	0.972624	+	0.232383i	$0.0746524\pi$
$883$			410.389i			0.464767i	−0.972624	+	0.232383i	$0.925348\pi$
$884$		−	619.048i		−	0.700281i
$885$	−362.684			−0.409812
$886$	−728.594			−0.822341
$887$	−904.878			−1.02016			−0.510078	−	0.860128i	$-0.670383\pi$
$887$	−904.878			−1.02016			−0.510078	+	0.860128i	$0.670383\pi$
$888$	677.346			0.762777
$889$			180.329i			0.202844i
$890$	−1070.12			−1.20238
$891$			142.587i			0.160030i
$892$	−569.649			−0.638619
$893$	−175.656			−0.196703
$894$	−887.459			−0.992684
$895$	−1033.40			−1.15464
$896$	290.260			0.323951
$897$	255.155			0.284454
$898$			3071.68i			3.42058i
$899$		−	1670.00i		−	1.85762i
$900$	437.629			0.486254
$901$			586.481i			0.650922i
$902$			22.2704i			0.0246900i
$903$		−	25.5540i		−	0.0282991i
$904$	727.290			0.804525
$905$			188.528i			0.208318i
$906$	1221.18			1.34788
$907$	1713.99			1.88974			0.944870	−	0.327446i	$-0.106188\pi$
$907$	1713.99			1.88974			0.944870	+	0.327446i	$0.106188\pi$
$908$	−2975.91			−3.27743
$909$			13.2074i			0.0145296i
$910$	−155.170			−0.170516
$911$	−511.518			−0.561491			−0.280745	−	0.959782i	$-0.590582\pi$
$911$	−511.518			−0.561491			−0.280745	+	0.959782i	$0.590582\pi$
$912$			946.502i			1.03783i
$913$		−	2393.32i		−	2.62138i
$914$		−	2780.64i		−	3.04227i
$915$			223.664i			0.244442i
$916$		−	3776.71i		−	4.12305i
$917$			371.141i			0.404734i
$918$	−209.851			−0.228596
$919$			1276.12i			1.38860i	0.719686	+	0.694300i	$0.244286\pi$
$919$			1276.12i			1.38860i	−0.719686	+	0.694300i	$0.755714\pi$
$920$	1293.58			1.40607
$921$			58.2519i			0.0632485i
$922$			1000.52i			1.08517i
$923$			50.7476i			0.0549811i
$924$			584.276i			0.632333i
$925$	−349.007			−0.377305
$926$	−2662.52			−2.87529
$927$	−384.025			−0.414267
$928$			1623.88i			1.74987i
$929$		−	434.296i		−	0.467488i	−0.972298	−	0.233744i	$-0.924902\pi$
$929$		−	434.296i		−	0.467488i	0.972298	−	0.233744i	$-0.0750978\pi$
$930$	−634.938			−0.682729
$931$	810.051			0.870087
$932$			950.571i			1.01993i
$933$	−526.380			−0.564180
$934$		−	117.560i		−	0.125867i
$935$	−526.881			−0.563509
$936$	333.283			0.356071
$937$		−	347.495i		−	0.370859i	−0.982658	−	0.185430i	$-0.940632\pi$
$937$		−	347.495i		−	0.370859i	0.982658	−	0.185430i	$-0.0593677\pi$
$938$	42.5421	+	569.042i	0.0453540	+	0.606655i
$939$	−404.057			−0.430305
$940$			252.447i			0.268560i
$941$		−	867.740i		−	0.922147i	−0.887362	−	0.461074i	$-0.847464\pi$
$941$		−	867.740i		−	0.922147i	0.887362	−	0.461074i	$-0.152536\pi$
$942$	−842.681			−0.894566
$943$		−	9.35948i		−	0.00992522i
$944$	2064.56			2.18703
$945$			36.4425i			0.0385635i
$946$			357.362i			0.377761i
$947$	−578.592			−0.610973			−0.305487	−	0.952196i	$-0.598819\pi$
$947$	−578.592			−0.610973			−0.305487	+	0.952196i	$0.598819\pi$
$948$	−1684.02			−1.77640
$949$			177.113i			0.186632i
$950$		−	1088.37i		−	1.14565i
$951$		−	499.250i		−	0.524974i
$952$	−478.622			−0.502754
$953$	−1480.69			−1.55372			−0.776858	−	0.629675i	$-0.783188\pi$
$953$	−1480.69			−1.55372			−0.776858	+	0.629675i	$0.783188\pi$
$954$	−567.281			−0.594634
$955$	430.132			0.450400
$956$		−	3772.28i		−	3.94590i
$957$	1340.42			1.40065
$958$			2420.87i			2.52701i
$959$	413.806			0.431497
$960$	14.2569			0.0148509
$961$	−207.815			−0.216248
$962$	−477.525			−0.496388
$963$	−370.690			−0.384933
$964$	3978.89			4.12748
$965$			163.140i			0.169057i
$966$		−	354.428i		−	0.366903i
$967$	−1441.67			−1.49087			−0.745435	−	0.666579i	$-0.767758\pi$
$967$	−1441.67			−1.49087			−0.745435	+	0.666579i	$0.767758\pi$
$968$		−	2355.50i		−	2.43337i
$969$			361.570i			0.373138i
$970$		−	1766.82i		−	1.82147i
$971$	−89.6857			−0.0923643			−0.0461821	−	0.998933i	$-0.514705\pi$
$971$	−89.6857			−0.0923643			−0.0461821	+	0.998933i	$0.514705\pi$
$972$		−	140.627i		−	0.144678i
$973$	385.094			0.395780
$974$	379.153			0.389274
$975$	−171.726			−0.176129
$976$		−	1273.20i		−	1.30451i
$977$	1064.93			1.09000			0.545001	−	0.838435i	$-0.316529\pi$
$977$	1064.93			1.09000			0.545001	+	0.838435i	$0.316529\pi$
$978$	−636.017			−0.650324
$979$		−	1581.15i		−	1.61507i
$980$		−	1164.18i		−	1.18794i
$981$		−	360.627i		−	0.367611i
$982$		−	1146.76i		−	1.16778i
$983$		−	900.359i		−	0.915930i	−0.888970	−	0.457965i	$-0.848579\pi$
$983$		−	900.359i		−	0.915930i	0.888970	−	0.457965i	$-0.151421\pi$
$984$		−	12.2253i		−	0.0124241i
$985$	1050.42			1.06642
$986$			1972.75i			2.00076i
$987$	38.4988			0.0390059
$988$		−	1031.69i		−	1.04422i
$989$		−	150.187i		−	0.151857i
$990$		−	509.632i		−	0.514780i
$991$		−	1145.15i		−	1.15555i	−0.816197	−	0.577774i	$-0.803921\pi$
$991$		−	1145.15i		−	1.15555i	0.816197	−	0.577774i	$-0.196079\pi$
$992$	1136.54			1.14571
$993$	−181.199			−0.182476
$994$	70.4919			0.0709174
$995$			1001.77i			1.00680i
$996$			2360.42i			2.36990i
$997$	1769.81			1.77513			0.887566	−	0.460680i	$-0.152395\pi$
$997$	1769.81			1.77513			0.887566	+	0.460680i	$0.152395\pi$
$998$	−746.406			−0.747902
$999$			112.149i			0.112262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.2	✓	22
3.2	odd	2		603.3.b.e.334.21		22
67.66	odd	2	inner	201.3.b.a.133.21	yes	22
201.200	even	2		603.3.b.e.334.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.2	✓	22	1.1	even	1	trivial
201.3.b.a.133.21	yes	22	67.66	odd	2	inner
603.3.b.e.334.2		22	201.200	even	2
603.3.b.e.334.21		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-3.60849i q^{2} +1.73205i q^{3} -9.02122 q^{4} +2.97147i q^{5} +6.25009 q^{6} +2.36023i q^{7} +18.1190i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.60849i q^{2} +1.73205i q^{3} -9.02122 q^{4} +2.97147i q^{5} +6.25009 q^{6} +2.36023i q^{7} +18.1190i q^{8} -3.00000 q^{9} +10.7225 q^{10} +15.8430i q^{11} -15.6252i q^{12} +6.13135i q^{13} +8.51687 q^{14} -5.14674 q^{15} +29.2976 q^{16} +11.1919 q^{17} +10.8255i q^{18} +18.6522 q^{19} -26.8063i q^{20} -4.08804 q^{21} +57.1694 q^{22} -24.0263 q^{23} -31.3831 q^{24} +16.1704 q^{25} +22.1249 q^{26} -5.19615i q^{27} -21.2922i q^{28} -48.8475 q^{29} +18.5720i q^{30} +34.1879i q^{31} -33.2439i q^{32} -27.4409 q^{33} -40.3858i q^{34} -7.01336 q^{35} +27.0637 q^{36} -21.5831 q^{37} -67.3062i q^{38} -10.6198 q^{39} -53.8403 q^{40} +0.389551i q^{41} +14.7517i q^{42} +6.25093i q^{43} -142.923i q^{44} -8.91442i q^{45} +86.6989i q^{46} -9.41744 q^{47} +50.7449i q^{48} +43.4293 q^{49} -58.3506i q^{50} +19.3849i q^{51} -55.3123i q^{52} +52.4024i q^{53} -18.7503 q^{54} -47.0771 q^{55} -42.7651 q^{56} +32.3065i q^{57} +176.266i q^{58} +70.4686 q^{59} +46.4299 q^{60} -43.4575i q^{61} +123.367 q^{62} -7.08069i q^{63} -2.77008 q^{64} -18.2191 q^{65} +99.0203i q^{66} +(4.99504 + 66.8135i) q^{67} -100.964 q^{68} -41.6148i q^{69} +25.3077i q^{70} +8.27674 q^{71} -54.3571i q^{72} +28.8865 q^{73} +77.8826i q^{74} +28.0079i q^{75} -168.265 q^{76} -37.3932 q^{77} +38.3215i q^{78} -107.776i q^{79} +87.0569i q^{80} +9.00000 q^{81} +1.40569 q^{82} -151.065 q^{83} +36.8791 q^{84} +33.2564i q^{85} +22.5565 q^{86} -84.6064i q^{87} -287.060 q^{88} -99.8011 q^{89} -32.1676 q^{90} -14.4714 q^{91} +216.747 q^{92} -59.2152 q^{93} +33.9828i q^{94} +55.4244i q^{95} +57.5801 q^{96} -164.777i q^{97} -156.714i q^{98} -47.5290i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 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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