LMFDB - Embedded newform 201.5.b.a.133.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,5,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, 5, names="a")

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

chi := DirichletCharacter("201.133");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 5 $
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:	$20.7773625799$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			133.19
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12514i q^{2} +5.19615i q^{3} +11.4838 q^{4} +15.4974i q^{5} +11.0426 q^{6} -14.1489i q^{7} -58.4069i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-2.12514i q^{2} +5.19615i q^{3} +11.4838 q^{4} +15.4974i q^{5} +11.0426 q^{6} -14.1489i q^{7} -58.4069i q^{8} -27.0000 q^{9} +32.9341 q^{10} -140.860i q^{11} +59.6714i q^{12} -150.360i q^{13} -30.0685 q^{14} -80.5267 q^{15} +59.6171 q^{16} -16.5440 q^{17} +57.3789i q^{18} +424.932 q^{19} +177.968i q^{20} +73.5199 q^{21} -299.347 q^{22} +299.979 q^{23} +303.491 q^{24} +384.832 q^{25} -319.537 q^{26} -140.296i q^{27} -162.483i q^{28} +484.514 q^{29} +171.131i q^{30} +1371.90i q^{31} -1061.21i q^{32} +731.929 q^{33} +35.1583i q^{34} +219.271 q^{35} -310.062 q^{36} +130.564 q^{37} -903.042i q^{38} +781.294 q^{39} +905.154 q^{40} +262.092i q^{41} -156.240i q^{42} -1704.94i q^{43} -1617.60i q^{44} -418.429i q^{45} -637.499i q^{46} -143.673 q^{47} +309.779i q^{48} +2200.81 q^{49} -817.822i q^{50} -85.9649i q^{51} -1726.70i q^{52} -1870.47i q^{53} -298.149 q^{54} +2182.96 q^{55} -826.395 q^{56} +2208.01i q^{57} -1029.66i q^{58} -2584.22 q^{59} -924.750 q^{60} -825.751i q^{61} +2915.48 q^{62} +382.021i q^{63} -1301.34 q^{64} +2330.19 q^{65} -1555.45i q^{66} +(3178.50 - 3169.90i) q^{67} -189.987 q^{68} +1558.74i q^{69} -465.982i q^{70} -7307.13 q^{71} +1576.99i q^{72} +3028.62 q^{73} -277.468i q^{74} +1999.64i q^{75} +4879.82 q^{76} -1993.01 q^{77} -1660.36i q^{78} -3784.46i q^{79} +923.908i q^{80} +729.000 q^{81} +556.983 q^{82} -5513.48 q^{83} +844.286 q^{84} -256.388i q^{85} -3623.25 q^{86} +2517.61i q^{87} -8227.19 q^{88} -3433.53 q^{89} -889.222 q^{90} -2127.43 q^{91} +3444.89 q^{92} -7128.59 q^{93} +305.325i q^{94} +6585.33i q^{95} +5514.19 q^{96} +15620.0i q^{97} -4677.03i q^{98} +3803.21i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) $ 46 * q - 396 * q^4 - 1242 * q^9	$ 46 q - 396 q^{4} - 1242 q^{9} + 396 q^{10} + 792 q^{14} - 252 q^{15} + 3396 q^{16} + 462 q^{17} - 590 q^{19} - 936 q^{21} + 3184 q^{22} - 1446 q^{23} - 1404 q^{24} - 6278 q^{25} + 2700 q^{26} - 1014 q^{29} + 540 q^{33} + 9924 q^{35} + 10692 q^{36} - 386 q^{37} + 4968 q^{39} - 9988 q^{40} - 2754 q^{47} - 19062 q^{49} - 2320 q^{55} - 3396 q^{56} - 7098 q^{59} + 72 q^{60} - 21180 q^{62} - 75644 q^{64} + 18396 q^{65} + 8574 q^{67} + 9084 q^{68} - 23040 q^{71} - 22338 q^{73} + 28016 q^{76} + 45084 q^{77} + 33534 q^{81} + 17564 q^{82} + 35856 q^{83} + 40176 q^{84} + 31764 q^{86} - 19448 q^{88} - 14538 q^{89} - 10692 q^{90} + 13792 q^{91} - 67692 q^{92} + 22464 q^{93} + 22464 q^{96}+O(q^{100}) $ 46 * q - 396 * q^4 - 1242 * q^9 + 396 * q^10 + 792 * q^14 - 252 * q^15 + 3396 * q^16 + 462 * q^17 - 590 * q^19 - 936 * q^21 + 3184 * q^22 - 1446 * q^23 - 1404 * q^24 - 6278 * q^25 + 2700 * q^26 - 1014 * q^29 + 540 * q^33 + 9924 * q^35 + 10692 * q^36 - 386 * q^37 + 4968 * q^39 - 9988 * q^40 - 2754 * q^47 - 19062 * q^49 - 2320 * q^55 - 3396 * q^56 - 7098 * q^59 + 72 * q^60 - 21180 * q^62 - 75644 * q^64 + 18396 * q^65 + 8574 * q^67 + 9084 * q^68 - 23040 * q^71 - 22338 * q^73 + 28016 * q^76 + 45084 * q^77 + 33534 * q^81 + 17564 * q^82 + 35856 * q^83 + 40176 * q^84 + 31764 * q^86 - 19448 * q^88 - 14538 * q^89 - 10692 * q^90 + 13792 * q^91 - 67692 * q^92 + 22464 * q^93 + 22464 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	2.12514i		−	0.531286i	−0.964071	−	0.265643i	$-0.914416\pi$
$2$		−	2.12514i		−	0.531286i	0.964071	−	0.265643i	$-0.0855842\pi$
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	11.4838			0.717735
$5$			15.4974i			0.619895i	0.950754	+	0.309947i	$0.100311\pi$
$5$			15.4974i			0.619895i	−0.950754	+	0.309947i	$0.899689\pi$
$6$	11.0426			0.306738
$7$		−	14.1489i		−	0.288753i	−0.989523	−	0.144377i	$-0.953882\pi$
$7$		−	14.1489i		−	0.288753i	0.989523	−	0.144377i	$-0.0461177\pi$
$8$		−	58.4069i		−	0.912609i
$9$	−27.0000			−0.333333
$10$	32.9341			0.329341
$11$		−	140.860i		−	1.16413i	−0.813142	−	0.582065i	$-0.802245\pi$
$11$		−	140.860i		−	1.16413i	0.813142	−	0.582065i	$-0.197755\pi$
$12$			59.6714i			0.414385i
$13$		−	150.360i		−	0.889705i	−0.895604	−	0.444852i	$-0.853256\pi$
$13$		−	150.360i		−	0.889705i	0.895604	−	0.444852i	$-0.146744\pi$
$14$	−30.0685			−0.153411
$15$	−80.5267			−0.357896
$16$	59.6171			0.232879
$17$	−16.5440			−0.0572455			−0.0286228	−	0.999590i	$-0.509112\pi$
$17$	−16.5440			−0.0572455			−0.0286228	+	0.999590i	$0.509112\pi$
$18$			57.3789i			0.177095i
$19$	424.932			1.17710			0.588549	−	0.808462i	$-0.299699\pi$
$19$	424.932			1.17710			0.588549	+	0.808462i	$0.299699\pi$
$20$			177.968i			0.444920i
$21$	73.5199			0.166712
$22$	−299.347			−0.618486
$23$	299.979			0.567069			0.283534	−	0.958962i	$-0.408493\pi$
$23$	299.979			0.567069			0.283534	+	0.958962i	$0.408493\pi$
$24$	303.491			0.526895
$25$	384.832			0.615730
$26$	−319.537			−0.472687
$27$		−	140.296i		−	0.192450i
$28$		−	162.483i		−	0.207249i
$29$	484.514			0.576117			0.288058	−	0.957613i	$-0.406990\pi$
$29$	484.514			0.576117			0.288058	+	0.957613i	$0.406990\pi$
$30$			171.131i			0.190145i
$31$			1371.90i			1.42757i	0.700363	+	0.713787i	$0.253021\pi$
$31$			1371.90i			1.42757i	−0.700363	+	0.713787i	$0.746979\pi$
$32$		−	1061.21i		−	1.03633i
$33$	731.929			0.672111
$34$			35.1583i			0.0304137i
$35$	219.271			0.178997
$36$	−310.062			−0.239245
$37$	130.564			0.0953720			0.0476860	−	0.998862i	$-0.484815\pi$
$37$	130.564			0.0953720			0.0476860	+	0.998862i	$0.484815\pi$
$38$		−	903.042i		−	0.625376i
$39$	781.294			0.513671
$40$	905.154			0.565721
$41$			262.092i			0.155914i	0.996957	+	0.0779571i	$0.0248397\pi$
$41$			262.092i			0.155914i	−0.996957	+	0.0779571i	$0.975160\pi$
$42$		−	156.240i		−	0.0885717i
$43$		−	1704.94i		−	0.922088i	−0.887377	−	0.461044i	$-0.847475\pi$
$43$		−	1704.94i		−	0.922088i	0.887377	−	0.461044i	$-0.152525\pi$
$44$		−	1617.60i		−	0.835538i
$45$		−	418.429i		−	0.206632i
$46$		−	637.499i		−	0.301276i
$47$	−143.673			−0.0650397			−0.0325199	−	0.999471i	$-0.510353\pi$
$47$	−143.673			−0.0650397			−0.0325199	+	0.999471i	$0.510353\pi$
$48$			309.779i			0.134453i
$49$	2200.81			0.916621
$50$		−	817.822i		−	0.327129i
$51$		−	85.9649i		−	0.0330507i
$52$		−	1726.70i		−	0.638572i
$53$		−	1870.47i		−	0.665884i	−0.942947	−	0.332942i	$-0.891959\pi$
$53$		−	1870.47i		−	0.665884i	0.942947	−	0.332942i	$-0.108041\pi$
$54$	−298.149			−0.102246
$55$	2182.96			0.721638
$56$	−826.395			−0.263519
$57$			2208.01i			0.679598i
$58$		−	1029.66i		−	0.306083i
$59$	−2584.22			−0.742378			−0.371189	−	0.928557i	$-0.621050\pi$
$59$	−2584.22			−0.742378			−0.371189	+	0.928557i	$0.621050\pi$
$60$	−924.750			−0.256875
$61$		−	825.751i		−	0.221916i	−0.993825	−	0.110958i	$-0.964608\pi$
$61$		−	825.751i		−	0.221916i	0.993825	−	0.110958i	$-0.0353920\pi$
$62$	2915.48			0.758449
$63$			382.021i			0.0962511i
$64$	−1301.34			−0.317710
$65$	2330.19			0.551523
$66$		−	1555.45i		−	0.357083i
$67$	3178.50	−	3169.90i	0.708065	−	0.706148i
$67$	3178.50	−	3169.90i	0.708065	−	0.706148i
$68$	−189.987			−0.0410871
$69$			1558.74i			0.327397i
$70$		−	465.982i		−	0.0950984i
$71$	−7307.13			−1.44954			−0.724770	−	0.688991i	$-0.758054\pi$
$71$	−7307.13			−1.44954			−0.724770	+	0.688991i	$0.758054\pi$
$72$			1576.99i			0.304203i
$73$	3028.62			0.568328			0.284164	−	0.958776i	$-0.408284\pi$
$73$	3028.62			0.568328			0.284164	+	0.958776i	$0.408284\pi$
$74$		−	277.468i		−	0.0506698i
$75$			1999.64i			0.355492i
$76$	4879.82			0.844845
$77$	−1993.01			−0.336147
$78$		−	1660.36i		−	0.272906i
$79$		−	3784.46i		−	0.606387i	−0.952929	−	0.303193i	$-0.901947\pi$
$79$		−	3784.46i		−	0.606387i	0.952929	−	0.303193i	$-0.0980528\pi$
$80$			923.908i			0.144361i
$81$	729.000			0.111111
$82$	556.983			0.0828350
$83$	−5513.48			−0.800330			−0.400165	−	0.916443i	$-0.631047\pi$
$83$	−5513.48			−0.800330			−0.400165	+	0.916443i	$0.631047\pi$
$84$	844.286			0.119655
$85$		−	256.388i		−	0.0354862i
$86$	−3623.25			−0.489893
$87$			2517.61i			0.332621i
$88$	−8227.19			−1.06240
$89$	−3433.53			−0.433472			−0.216736	−	0.976230i	$-0.569541\pi$
$89$	−3433.53			−0.433472			−0.216736	+	0.976230i	$0.569541\pi$
$90$	−889.222			−0.109780
$91$	−2127.43			−0.256905
$92$	3444.89			0.407005
$93$	−7128.59			−0.824210
$94$			305.325i			0.0345547i
$95$			6585.33i			0.729677i
$96$	5514.19			0.598328
$97$			15620.0i			1.66012i	0.557677	+	0.830058i	$0.311693\pi$
$97$			15620.0i			1.66012i	−0.557677	+	0.830058i	$0.688307\pi$
$98$		−	4677.03i		−	0.486988i
$99$			3803.21i			0.388043i
$100$	4419.31			0.441931
$101$		−	5735.86i		−	0.562284i	−0.959666	−	0.281142i	$-0.909287\pi$
$101$		−	5735.86i		−	0.562284i	0.959666	−	0.281142i	$-0.0907131\pi$
$102$	−182.688			−0.0175594
$103$	334.874			0.0315650			0.0157825	−	0.999875i	$-0.494976\pi$
$103$	334.874			0.0315650			0.0157825	+	0.999875i	$0.494976\pi$
$104$	−8782.07			−0.811952
$105$			1139.37i			0.103344i
$106$	−3975.01			−0.353775
$107$	9001.56			0.786231			0.393115	−	0.919489i	$-0.371397\pi$
$107$	9001.56			0.786231			0.393115	+	0.919489i	$0.371397\pi$
$108$		−	1611.13i		−	0.138128i
$109$			11734.2i			0.987641i	0.869564	+	0.493821i	$0.164400\pi$
$109$			11734.2i			0.987641i	−0.869564	+	0.493821i	$0.835600\pi$
$110$		−	4639.10i		−	0.383396i
$111$			678.432i			0.0550630i
$112$		−	843.517i		−	0.0672447i
$113$			13824.1i			1.08263i	0.840820	+	0.541315i	$0.182073\pi$
$113$			13824.1i			1.08263i	−0.840820	+	0.541315i	$0.817927\pi$
$114$	4692.35			0.361061
$115$			4648.89i			0.351523i
$116$	5564.05			0.413499
$117$			4059.72i			0.296568i
$118$			5491.84i			0.394415i
$119$			234.079i			0.0165298i
$120$			4703.32i			0.326619i
$121$	−5200.48			−0.355200
$122$	−1754.84			−0.117901
$123$	−1361.87			−0.0900171
$124$			15754.6i			1.02462i
$125$			15649.7i			1.00158i
$126$	811.849			0.0511369
$127$	7383.88			0.457802			0.228901	−	0.973450i	$-0.426487\pi$
$127$	7383.88			0.457802			0.228901	+	0.973450i	$0.426487\pi$
$128$		−	14213.8i		−	0.867539i
$129$	8859.14			0.532368
$130$		−	4951.98i		−	0.293016i
$131$	−17395.1			−1.01364			−0.506820	−	0.862052i	$-0.669179\pi$
$131$	−17395.1			−1.01364			−0.506820	+	0.862052i	$0.669179\pi$
$132$	8405.30			0.482398
$133$		−	6012.33i		−	0.339891i
$134$	−6736.49	−	6754.77i	−0.375166	−	0.376185i
$135$	2174.22			0.119299
$136$			966.282i			0.0522427i
$137$		−	22301.9i		−	1.18823i	−0.804379	−	0.594116i	$-0.797502\pi$
$137$		−	22301.9i		−	1.18823i	0.804379	−	0.594116i	$-0.202498\pi$
$138$	3312.54			0.173942
$139$			9089.71i			0.470458i	0.971940	+	0.235229i	$0.0755840\pi$
$139$			9089.71i			0.470458i	−0.971940	+	0.235229i	$0.924416\pi$
$140$	2518.06			0.128472
$141$		−	746.546i		−	0.0375507i
$142$			15528.7i			0.770120i
$143$	−21179.7			−1.03573
$144$	−1609.66			−0.0776264
$145$			7508.70i			0.357132i
$146$		−	6436.26i		−	0.301945i
$147$			11435.7i			0.529212i
$148$	1499.37			0.0684518
$149$	−24244.5			−1.09205			−0.546023	−	0.837770i	$-0.683859\pi$
$149$	−24244.5			−1.09205			−0.546023	+	0.837770i	$0.683859\pi$
$150$	4249.53			0.188868
$151$	11350.1			0.497789			0.248895	−	0.968531i	$-0.419933\pi$
$151$	11350.1			0.497789			0.248895	+	0.968531i	$0.419933\pi$
$152$		−	24819.0i		−	1.07423i
$153$	446.687			0.0190818
$154$			4235.44i			0.178590i
$155$	−21260.8			−0.884945
$156$	8972.19			0.368680
$157$	−48092.3			−1.95109			−0.975543	−	0.219811i	$-0.929456\pi$
$157$	−48092.3			−1.95109			−0.975543	+	0.219811i	$0.929456\pi$
$158$	−8042.52			−0.322165
$159$	9719.23			0.384448
$160$	16445.9			0.642418
$161$		−	4244.38i		−	0.163743i
$162$		−	1549.23i		−	0.0590318i
$163$	−6024.40			−0.226746			−0.113373	−	0.993553i	$-0.536165\pi$
$163$	−6024.40			−0.226746			−0.113373	+	0.993553i	$0.536165\pi$
$164$			3009.80i			0.111905i
$165$			11343.0i			0.416638i
$166$			11716.9i			0.425204i
$167$	−20922.7			−0.750212			−0.375106	−	0.926982i	$-0.622394\pi$
$167$	−20922.7			−0.750212			−0.375106	+	0.926982i	$0.622394\pi$
$168$		−	4294.07i		−	0.152143i
$169$	5952.85			0.208426
$170$	−544.861			−0.0188533
$171$	−11473.2			−0.392366
$172$		−	19579.1i		−	0.661815i
$173$	12837.1			0.428919			0.214460	−	0.976733i	$-0.431201\pi$
$173$	12837.1			0.428919			0.214460	+	0.976733i	$0.431201\pi$
$174$	5350.28			0.176717
$175$		−	5444.95i		−	0.177794i
$176$		−	8397.65i		−	0.271102i
$177$		−	13428.0i		−	0.428612i
$178$			7296.75i			0.230298i
$179$		−	41654.8i		−	1.30005i	−0.759914	−	0.650023i	$-0.774759\pi$
$179$		−	41654.8i		−	1.30005i	0.759914	−	0.650023i	$-0.225241\pi$
$180$		−	4805.14i		−	0.148307i
$181$	14895.1			0.454659			0.227330	−	0.973818i	$-0.427001\pi$
$181$	14895.1			0.454659			0.227330	+	0.973818i	$0.427001\pi$
$182$			4521.10i			0.136490i
$183$	4290.73			0.128123
$184$		−	17520.9i		−	0.517512i
$185$			2023.40i			0.0591206i
$186$			15149.3i			0.437891i
$187$			2330.38i			0.0666413i
$188$	−1649.90			−0.0466813
$189$	−1985.04			−0.0555706
$190$	13994.8			0.387667
$191$			15093.0i			0.413721i	0.978370	+	0.206861i	$0.0663247\pi$
$191$			15093.0i			0.413721i	−0.978370	+	0.206861i	$0.933675\pi$
$192$		−	6761.97i		−	0.183430i
$193$	−12827.9			−0.344381			−0.172191	−	0.985064i	$-0.555085\pi$
$193$	−12827.9			−0.344381			−0.172191	+	0.985064i	$0.555085\pi$
$194$	33194.8			0.881996
$195$			12108.0i			0.318422i
$196$	25273.6			0.657892
$197$		−	4298.33i		−	0.110756i	−0.998465	−	0.0553780i	$-0.982364\pi$
$197$		−	4298.33i		−	0.110756i	0.998465	−	0.0553780i	$-0.0176364\pi$
$198$	8082.38			0.206162
$199$	−28040.0			−0.708062			−0.354031	−	0.935234i	$-0.615189\pi$
$199$	−28040.0			−0.708062			−0.354031	+	0.935234i	$0.615189\pi$
$200$		−	22476.8i		−	0.561921i
$201$	16471.3	+	16516.0i	0.407695	+	0.408801i
$202$	−12189.5			−0.298733
$203$		−	6855.35i		−	0.166356i
$204$		−	987.201i		−	0.0237217i
$205$	−4061.73			−0.0966504
$206$		−	711.654i		−	0.0167701i
$207$	−8099.44			−0.189023
$208$		−	8964.03i		−	0.207194i
$209$		−	59855.9i		−	1.37030i
$210$	2421.32			0.0549051
$211$	37744.4			0.847788			0.423894	−	0.905712i	$-0.360663\pi$
$211$	37744.4			0.847788			0.423894	+	0.905712i	$0.360663\pi$
$212$		−	21480.0i		−	0.477928i
$213$		−	37969.0i		−	0.836893i
$214$		−	19129.6i		−	0.417713i
$215$	26422.1			0.571598
$216$	−8194.27			−0.175632
$217$	19410.9			0.412217
$218$	24936.8			0.524720
$219$			15737.2i			0.328125i
$220$	25068.6			0.517945
$221$			2487.55i			0.0509316i
$222$	1441.76			0.0292542
$223$	67793.9			1.36327			0.681634	−	0.731694i	$-0.261270\pi$
$223$	67793.9			1.36327			0.681634	+	0.731694i	$0.261270\pi$
$224$	−15014.9			−0.299245
$225$	−10390.5			−0.205243
$226$	29378.2			0.575186
$227$	76608.7			1.48671			0.743355	−	0.668897i	$-0.233233\pi$
$227$	76608.7			1.48671			0.743355	+	0.668897i	$0.233233\pi$
$228$			25356.3i			0.487771i
$229$			59548.7i			1.13554i	0.823188	+	0.567769i	$0.192193\pi$
$229$			59548.7i			1.13554i	−0.823188	+	0.567769i	$0.807807\pi$
$230$	9879.56			0.186759
$231$		−	10356.0i		−	0.194074i
$232$		−	28299.0i		−	0.525769i
$233$			14026.3i			0.258364i	0.991621	+	0.129182i	$0.0412351\pi$
$233$			14026.3i			0.258364i	−0.991621	+	0.129182i	$0.958765\pi$
$234$	8627.49			0.157562
$235$		−	2226.55i		−	0.0403178i
$236$	−29676.6			−0.532831
$237$	19664.6			0.350097
$238$	497.452			0.00878207
$239$			65173.6i			1.14097i	0.821306	+	0.570487i	$0.193246\pi$
$239$			65173.6i			1.14097i	−0.821306	+	0.570487i	$0.806754\pi$
$240$	−4800.77			−0.0833466
$241$	−38443.3			−0.661891			−0.330946	−	0.943650i	$-0.607368\pi$
$241$	−38443.3			−0.661891			−0.330946	+	0.943650i	$0.607368\pi$
$242$			11051.8i			0.188713i
$243$			3788.00i			0.0641500i
$244$		−	9482.73i		−	0.159277i
$245$			34106.7i			0.568209i
$246$			2894.17i			0.0478248i
$247$		−	63892.9i		−	1.04727i
$248$	80128.4			1.30282
$249$		−	28648.9i		−	0.462071i
$250$	33257.9			0.532127
$251$			70298.9i			1.11584i	0.829895	+	0.557919i	$0.188400\pi$
$251$			70298.9i			1.11584i	−0.829895	+	0.557919i	$0.811600\pi$
$252$			4387.04i			0.0690828i
$253$		−	42255.0i		−	0.660142i
$254$		−	15691.8i		−	0.243224i
$255$	1332.23			0.0204880
$256$	−51027.7			−0.778622
$257$	−72587.0			−1.09899			−0.549494	−	0.835498i	$-0.685179\pi$
$257$	−72587.0			−1.09899			−0.549494	+	0.835498i	$0.685179\pi$
$258$		−	18826.9i		−	0.282840i
$259$		−	1847.34i		−	0.0275390i
$260$	26759.3			0.395848
$261$	−13081.9			−0.192039
$262$			36967.0i			0.538532i
$263$	92314.3			1.33462			0.667310	−	0.744780i	$-0.267446\pi$
$263$	92314.3			1.33462			0.667310	+	0.744780i	$0.267446\pi$
$264$		−	42749.7i		−	0.613374i
$265$	28987.3			0.412778
$266$	−12777.1			−0.180579
$267$		−	17841.2i		−	0.250265i
$268$	36501.2	−	36402.3i	0.508203	−	0.506827i
$269$	−50428.2			−0.696898			−0.348449	−	0.937328i	$-0.613292\pi$
$269$	−50428.2			−0.696898			−0.348449	+	0.937328i	$0.613292\pi$
$270$		−	4620.53i		−	0.0633818i
$271$			38723.3i			0.527270i	0.964622	+	0.263635i	$0.0849215\pi$
$271$			38723.3i			0.527270i	−0.964622	+	0.263635i	$0.915079\pi$
$272$	−986.302			−0.0133313
$273$		−	11054.5i		−	0.148324i
$274$	−47394.8			−0.631291
$275$		−	54207.3i		−	0.716791i
$276$			17900.2i			0.234985i
$277$	−148103.			−1.93021			−0.965104	−	0.261866i	$-0.915662\pi$
$277$	−148103.			−1.93021			−0.965104	+	0.261866i	$0.915662\pi$
$278$	19316.9			0.249948
$279$		−	37041.2i		−	0.475858i
$280$		−	12807.0i		−	0.163354i
$281$			68162.1i			0.863238i	0.902056	+	0.431619i	$0.142058\pi$
$281$			68162.1i			0.863238i	−0.902056	+	0.431619i	$0.857942\pi$
$282$	−1586.52			−0.0199502
$283$	−115931.			−1.44752			−0.723762	−	0.690049i	$-0.757589\pi$
$283$	−115931.			−1.44752			−0.723762	+	0.690049i	$0.757589\pi$
$284$	−83913.4			−1.04039
$285$	−34218.4			−0.421279
$286$			45009.9i			0.550270i
$287$	3708.32			0.0450208
$288$			28652.6i			0.345445i
$289$	−83247.3			−0.996723
$290$	15957.1			0.189739
$291$	−81164.1			−0.958469
$292$	34780.0			0.407909
$293$	41226.8			0.480225			0.240112	−	0.970745i	$-0.422816\pi$
$293$	41226.8			0.480225			0.240112	+	0.970745i	$0.422816\pi$
$294$	24302.6			0.281163
$295$		−	40048.6i		−	0.460197i
$296$		−	7625.86i		−	0.0870373i
$297$	−19762.1			−0.224037
$298$			51523.1i			0.580188i
$299$		−	45104.9i		−	0.504524i
$300$			22963.4i			0.255149i
$301$	−24123.1			−0.266256
$302$		−	24120.6i		−	0.264469i
$303$	29804.4			0.324635
$304$	25333.2			0.274122
$305$	12797.0			0.137565
$306$		−	949.274i		−	0.0101379i
$307$	155765.			1.65269			0.826347	−	0.563161i	$-0.190415\pi$
$307$	155765.			1.65269			0.826347	+	0.563161i	$0.190415\pi$
$308$	−22887.3			−0.241264
$309$			1740.05i			0.0182241i
$310$			45182.3i			0.470159i
$311$			111773.i			1.15562i	0.816170	+	0.577812i	$0.196093\pi$
$311$			111773.i			1.15562i	−0.816170	+	0.577812i	$0.803907\pi$
$312$		−	45633.0i		−	0.468781i
$313$			100869.i			1.02960i	0.857309	+	0.514802i	$0.172134\pi$
$313$			100869.i			1.02960i	−0.857309	+	0.514802i	$0.827866\pi$
$314$			102203.i			1.03658i
$315$	−5920.32			−0.0596656
$316$		−	43459.8i		−	0.435225i
$317$	8327.17			0.0828665			0.0414332	−	0.999141i	$-0.486808\pi$
$317$	8327.17			0.0828665			0.0414332	+	0.999141i	$0.486808\pi$
$318$		−	20654.8i		−	0.204252i
$319$		−	68248.6i		−	0.670675i
$320$		−	20167.4i		−	0.196947i
$321$			46773.5i			0.453931i
$322$	−9019.92			−0.0869944
$323$	−7030.06			−0.0673836
$324$	8371.66			0.0797484
$325$		−	57863.3i		−	0.547818i
$326$			12802.7i			0.120467i
$327$	−60972.5			−0.570215
$328$	15308.0			0.142289
$329$			2032.81i			0.0187804i
$330$	24105.4			0.221354
$331$		−	80650.1i		−	0.736121i	−0.929802	−	0.368060i	$-0.880022\pi$
$331$		−	80650.1i		−	0.736121i	0.929802	−	0.368060i	$-0.119978\pi$
$332$	−63315.5			−0.574425
$333$	−3525.23			−0.0317907
$334$			44463.7i			0.398577i
$335$	49125.1	+	49258.4i	0.437737	+	0.438926i
$336$	4383.04			0.0388237
$337$		−	66001.8i		−	0.581161i	−0.956851	−	0.290580i	$-0.906152\pi$
$337$		−	66001.8i		−	0.581161i	0.956851	−	0.290580i	$-0.0938483\pi$
$338$		−	12650.7i		−	0.110734i
$339$	−71832.2			−0.625057
$340$		−	2944.30i		−	0.0254697i
$341$	193245.			1.66188
$342$			24382.1i			0.208459i
$343$		−	65110.6i		−	0.553431i
$344$	−99580.4			−0.841506
$345$	−24156.3			−0.202952
$346$		−	27280.7i		−	0.227879i
$347$			203672.i			1.69151i	0.533575	+	0.845753i	$0.320848\pi$
$347$			203672.i			1.69151i	−0.533575	+	0.845753i	$0.679152\pi$
$348$			28911.6i			0.238734i
$349$	−7050.26			−0.0578834			−0.0289417	−	0.999581i	$-0.509214\pi$
$349$	−7050.26			−0.0578834			−0.0289417	+	0.999581i	$0.509214\pi$
$350$	−11571.3			−0.0944596
$351$	−21094.9			−0.171224
$352$	−149481.			−1.20643
$353$			109841.i			0.881485i	0.897634	+	0.440742i	$0.145285\pi$
$353$			109841.i			0.881485i	−0.897634	+	0.440742i	$0.854715\pi$
$354$	−28536.4			−0.227716
$355$		−	113241.i		−	0.898563i
$356$	−39429.9			−0.311118
$357$	−1216.31			−0.00954351
$358$	−88522.4			−0.690697
$359$	−43382.7			−0.336610			−0.168305	−	0.985735i	$-0.553829\pi$
$359$	−43382.7			−0.336610			−0.168305	+	0.985735i	$0.553829\pi$
$360$	−24439.2			−0.188574
$361$	50246.5			0.385560
$362$		−	31654.2i		−	0.241554i
$363$		−	27022.5i		−	0.205075i
$364$	−24430.9			−0.184390
$365$			46935.7i			0.352304i
$366$		−	9118.41i		−	0.0680702i
$367$			38775.9i			0.287892i	0.989586	+	0.143946i	$0.0459792\pi$
$367$			38775.9i			0.287892i	−0.989586	+	0.143946i	$0.954021\pi$
$368$	17883.9			0.132059
$369$		−	7076.48i		−	0.0519714i
$370$	4300.02			0.0314099
$371$	−26465.1			−0.192276
$372$	−81863.1			−0.591564
$373$		−	30028.9i		−	0.215835i	−0.994160	−	0.107918i	$-0.965582\pi$
$373$		−	30028.9i		−	0.215835i	0.994160	−	0.107918i	$-0.0344183\pi$
$374$	4952.39			0.0354056
$375$	−81318.4			−0.578264
$376$			8391.49i			0.0593558i
$377$		−	72851.6i		−	0.512574i
$378$			4218.49i			0.0295239i
$379$			181900.i			1.26635i	0.774008	+	0.633176i	$0.218249\pi$
$379$			181900.i			1.26635i	−0.774008	+	0.633176i	$0.781751\pi$
$380$			75624.4i			0.523715i
$381$			38367.8i			0.264312i
$382$	32074.7			0.219804
$383$			12019.6i			0.0819393i	0.999160	+	0.0409696i	$0.0130447\pi$
$383$			12019.6i			0.0819393i	−0.999160	+	0.0409696i	$0.986955\pi$
$384$	73856.9			0.500874
$385$		−	30886.5i		−	0.208376i
$386$			27261.1i			0.182965i
$387$			46033.4i			0.307363i
$388$			179377.i			1.19152i
$389$	−174841.			−1.15543			−0.577717	−	0.816237i	$-0.696056\pi$
$389$	−174841.			−1.15543			−0.577717	+	0.816237i	$0.696056\pi$
$390$	25731.2			0.169173
$391$	−4962.84			−0.0324621
$392$		−	128542.i		−	0.836517i
$393$		−	90387.4i		−	0.585225i
$394$	−9134.57			−0.0588431
$395$	58649.2			0.375896
$396$			43675.2i			0.278513i
$397$	86945.2			0.551652			0.275826	−	0.961208i	$-0.411049\pi$
$397$	86945.2			0.551652			0.275826	+	0.961208i	$0.411049\pi$
$398$			59589.0i			0.376183i
$399$	31241.0			0.196236
$400$	22942.5			0.143391
$401$			232697.i			1.44711i	0.690265	+	0.723557i	$0.257494\pi$
$401$			232697.i			1.44711i	−0.690265	+	0.723557i	$0.742506\pi$
$402$	35098.8	−	35003.8i	0.217190	−	0.216602i
$403$	206279.			1.27012
$404$		−	65869.2i		−	0.403571i
$405$			11297.6i			0.0688772i
$406$	−14568.6			−0.0883824
$407$		−	18391.2i		−	0.111025i
$408$	−5020.95			−0.0301624
$409$			3891.81i			0.0232651i	0.999932	+	0.0116326i	$0.00370284\pi$
$409$			3891.81i			0.0232651i	−0.999932	+	0.0116326i	$0.996297\pi$
$410$			8631.77i			0.0513490i
$411$	115884.			0.686026
$412$	3845.61			0.0226553
$413$			36563.9i			0.214364i
$414$			17212.5i			0.100425i
$415$		−	85444.4i		−	0.496121i
$416$	−159563.			−0.922031
$417$	−47231.5			−0.271619
$418$	−127202.			−0.728019
$419$	135557.			0.772136			0.386068	−	0.922470i	$-0.373833\pi$
$419$	135557.			0.772136			0.386068	+	0.922470i	$0.373833\pi$
$420$			13084.2i			0.0741735i
$421$	−22225.5			−0.125397			−0.0626984	−	0.998033i	$-0.519971\pi$
$421$	−22225.5			−0.125397			−0.0626984	+	0.998033i	$0.519971\pi$
$422$		−	80212.2i		−	0.450418i
$423$	3879.16			0.0216799
$424$	−109248.			−0.607691
$425$	−6366.64			−0.0352478
$426$	−80689.5			−0.444629
$427$	−11683.5			−0.0640791
$428$	103372.			0.564306
$429$		−	110053.i		−	0.597980i
$430$		−	56150.8i		−	0.303682i
$431$	272418.			1.46650			0.733248	−	0.679961i	$-0.238003\pi$
$431$	272418.			1.46650			0.733248	+	0.679961i	$0.238003\pi$
$432$		−	8364.05i		−	0.0448176i
$433$		−	87474.9i		−	0.466560i	−0.972410	−	0.233280i	$-0.925054\pi$
$433$		−	87474.9i		−	0.466560i	0.972410	−	0.233280i	$-0.0749459\pi$
$434$		−	41250.9i		−	0.219005i
$435$	−39016.3			−0.206190
$436$			134752.i			0.708865i
$437$	127471.			0.667495
$438$	33443.8			0.174328
$439$	−297017.			−1.54118			−0.770588	−	0.637334i	$-0.780037\pi$
$439$	−297017.			−1.54118			−0.770588	+	0.637334i	$0.780037\pi$
$440$		−	127500.i		−	0.658573i
$441$	−59421.8			−0.305540
$442$	5286.40			0.0270592
$443$			28301.2i			0.144211i	0.997397	+	0.0721054i	$0.0229718\pi$
$443$			28301.2i			0.144211i	−0.997397	+	0.0721054i	$0.977028\pi$
$444$			7790.95i			0.0395207i
$445$		−	53210.7i		−	0.268707i
$446$		−	144072.i		−	0.724285i
$447$		−	125978.i		−	0.630493i
$448$			18412.6i			0.0917400i
$449$	158078.			0.784111			0.392056	−	0.919942i	$-0.371764\pi$
$449$	158078.			0.784111			0.392056	+	0.919942i	$0.371764\pi$
$450$			22081.2i			0.109043i
$451$	36918.2			0.181505
$452$			158753.i			0.777042i
$453$			58976.8i			0.287399i
$454$		−	162804.i		−	0.789868i
$455$		−	32969.6i		−	0.159254i
$456$	128963.			0.620207
$457$	69237.7			0.331521			0.165760	−	0.986166i	$-0.446992\pi$
$457$	69237.7			0.331521			0.165760	+	0.986166i	$0.446992\pi$
$458$	126550.			0.603295
$459$			2321.05i			0.0110169i
$460$			53386.8i			0.252300i
$461$	116050.			0.546063			0.273032	−	0.962005i	$-0.411974\pi$
$461$	116050.			0.546063			0.273032	+	0.962005i	$0.411974\pi$
$462$	−22008.0			−0.103109
$463$		−	44612.1i		−	0.208109i	−0.994572	−	0.104054i	$-0.966818\pi$
$463$		−	44612.1i		−	0.208109i	0.994572	−	0.104054i	$-0.0331816\pi$
$464$	28885.3			0.134166
$465$		−	110474.i		−	0.510923i
$466$	29807.9			0.137265
$467$	280077.			1.28423			0.642117	−	0.766607i	$-0.278056\pi$
$467$	280077.			1.28423			0.642117	+	0.766607i	$0.278056\pi$
$468$			46620.9i			0.212857i
$469$	−44850.6	−	44972.4i	−0.203903	−	0.204456i
$470$	−4731.74			−0.0214203
$471$		−	249895.i		−	1.12646i
$472$			150936.i			0.677501i
$473$	−240158.			−1.07343
$474$		−	41790.1i		−	0.186002i
$475$	163527.			0.724775
$476$			2688.11i			0.0118640i
$477$			50502.6i			0.221961i
$478$	138503.			0.606184
$479$	408350.			1.77976			0.889880	−	0.456195i	$-0.150788\pi$
$479$	408350.			1.77976			0.889880	+	0.456195i	$0.150788\pi$
$480$			85455.4i			0.370900i
$481$		−	19631.6i		−	0.0848529i
$482$			81697.6i			0.351654i
$483$	22054.5			0.0945371
$484$	−59721.1			−0.254939
$485$	−242069.			−1.02910
$486$	8050.03			0.0340820
$487$		−	231180.i		−	0.974748i	−0.873193	−	0.487374i	$-0.837955\pi$
$487$		−	231180.i		−	0.974748i	0.873193	−	0.487374i	$-0.162045\pi$
$488$	−48229.6			−0.202523
$489$		−	31303.7i		−	0.130912i
$490$	72481.7			0.301881
$491$	−68575.7			−0.284451			−0.142225	−	0.989834i	$-0.545426\pi$
$491$	−68575.7			−0.284451			−0.142225	+	0.989834i	$0.545426\pi$
$492$	−15639.4			−0.0646085
$493$	−8015.78			−0.0329801
$494$	−135782.			−0.556399
$495$	−58939.8			−0.240546
$496$			81788.5i			0.332452i
$497$			103388.i			0.418560i
$498$	−60883.0			−0.245492
$499$		−	332977.i		−	1.33725i	−0.743599	−	0.668626i	$-0.766883\pi$
$499$		−	332977.i		−	1.33725i	0.743599	−	0.668626i	$-0.233117\pi$
$500$			179718.i			0.718871i
$501$		−	108717.i		−	0.433135i
$502$	149395.			0.592829
$503$		−	377517.i		−	1.49211i	−0.665886	−	0.746054i	$-0.731946\pi$
$503$		−	377517.i		−	1.49211i	0.665886	−	0.746054i	$-0.268054\pi$
$504$	22312.7			0.0878396
$505$	88890.7			0.348557
$506$	−89798.0			−0.350724
$507$			30931.9i			0.120335i
$508$	84794.8			0.328580
$509$	145831.			0.562879			0.281439	−	0.959579i	$-0.409188\pi$
$509$	145831.			0.562879			0.281439	+	0.959579i	$0.409188\pi$
$510$		−	2831.18i		−	0.0108850i
$511$		−	42851.7i		−	0.164107i
$512$		−	118979.i		−	0.453868i
$513$		−	59616.4i		−	0.226533i
$514$			154258.i			0.583877i
$515$			5189.66i			0.0195670i
$516$	101736.			0.382099
$517$			20237.7i			0.0757147i
$518$	−3925.87			−0.0146311
$519$			66703.6i			0.247637i
$520$		−	136099.i		−	0.503325i
$521$		−	58647.2i		−	0.216059i	−0.994148	−	0.108029i	$-0.965546\pi$
$521$		−	58647.2i		−	0.216059i	0.994148	−	0.108029i	$-0.0344541\pi$
$522$			27800.9i			0.102028i
$523$	−40466.9			−0.147944			−0.0739718	−	0.997260i	$-0.523567\pi$
$523$	−40466.9			−0.147944			−0.0739718	+	0.997260i	$0.523567\pi$
$524$	−199761.			−0.727525
$525$	28292.8			0.102650
$526$		−	196181.i		−	0.709065i
$527$		−	22696.6i		−	0.0817222i
$528$	43635.5			0.156521
$529$	−189853.			−0.678433
$530$		−	61602.2i		−	0.219303i
$531$	69773.9			0.247459
$532$		−	69044.2i		−	0.243952i
$533$	39408.1			0.138718
$534$	−37915.0			−0.132962
$535$			139500.i			0.487380i
$536$	−185144.	−	185647.i	−0.644436	−	0.646186i
$537$	216445.			0.750582
$538$			107167.i			0.370252i
$539$		−	310005.i		−	1.06707i
$540$	24968.2			0.0856250
$541$			134100.i			0.458180i	0.973405	+	0.229090i	$0.0735750\pi$
$541$			134100.i			0.458180i	−0.973405	+	0.229090i	$0.926425\pi$
$542$	82292.5			0.280131
$543$			77397.2i			0.262498i
$544$			17556.5i			0.0593255i
$545$	−181849.			−0.612234
$546$	−23492.3			−0.0788026
$547$		−	66785.3i		−	0.223206i	−0.993753	−	0.111603i	$-0.964401\pi$
$547$		−	66785.3i		−	0.223206i	0.993753	−	0.111603i	$-0.0355985\pi$
$548$		−	256110.i		−	0.852836i
$549$			22295.3i			0.0739721i
$550$	−115198.			−0.380821
$551$	205886.			0.678146
$552$	91041.1			0.298786
$553$	−53546.0			−0.175096
$554$			314740.i			1.02549i
$555$	−10513.9			−0.0341333
$556$			104384.i			0.337664i
$557$	452469.			1.45841			0.729203	−	0.684297i	$-0.239891\pi$
$557$	452469.			1.45841			0.729203	+	0.684297i	$0.239891\pi$
$558$	−78718.0			−0.252816
$559$	−256355.			−0.820386
$560$	13072.3			0.0416846
$561$	−12109.0			−0.0384753
$562$	144854.			0.458626
$563$		−	27935.4i		−	0.0881328i	−0.999029	−	0.0440664i	$-0.985969\pi$
$563$		−	27935.4i		−	0.0881328i	0.999029	−	0.0440664i	$-0.0140313\pi$
$564$		−	8573.15i		−	0.0269515i
$565$	−214237.			−0.671117
$566$			246370.i			0.769050i
$567$		−	10314.6i		−	0.0320837i
$568$			426787.i			1.32286i
$569$	−216711.			−0.669355			−0.334677	−	0.942333i	$-0.608627\pi$
$569$	−216711.			−0.669355			−0.334677	+	0.942333i	$0.608627\pi$
$570$			72719.0i			0.223820i
$571$	531562.			1.63035			0.815177	−	0.579212i	$-0.196640\pi$
$571$	531562.			1.63035			0.815177	+	0.579212i	$0.196640\pi$
$572$	−243223.			−0.743381
$573$	−78425.4			−0.238862
$574$		−	7880.70i		−	0.0239189i
$575$	115441.			0.349161
$576$	35136.2			0.105903
$577$			50781.4i			0.152529i	0.997088	+	0.0762646i	$0.0242994\pi$
$577$			50781.4i			0.152529i	−0.997088	+	0.0762646i	$0.975701\pi$
$578$			176912.i			0.529545i
$579$		−	66655.5i		−	0.198829i
$580$			86228.1i			0.256326i
$581$			78009.7i			0.231098i
$582$			172485.i			0.509221i
$583$	−263474.			−0.775175
$584$		−	176893.i		−	0.518661i
$585$	−62915.0			−0.183841
$586$		−	87612.9i		−	0.255137i
$587$		−	421224.i		−	1.22247i	−0.791450	−	0.611234i	$-0.790674\pi$
$587$		−	421224.i		−	1.22247i	0.791450	−	0.611234i	$-0.209326\pi$
$588$			131325.i			0.379834i
$589$			582964.i			1.68039i
$590$	−85109.0			−0.244496
$591$	22334.8			0.0639450
$592$	7783.86			0.0222102
$593$			290492.i			0.826084i	0.910712	+	0.413042i	$0.135534\pi$
$593$			290492.i			0.826084i	−0.910712	+	0.413042i	$0.864466\pi$
$594$			41997.3i			0.119028i
$595$	−3627.61			−0.0102468
$596$	−278418.			−0.783800
$597$		−	145700.i		−	0.408800i
$598$	−95854.4			−0.268046
$599$		−	217774.i		−	0.606948i	−0.952840	−	0.303474i	$-0.901853\pi$
$599$		−	217774.i		−	0.606948i	0.952840	−	0.303474i	$-0.0981466\pi$
$600$	116793.			0.324425
$601$	−407897.			−1.12928			−0.564640	−	0.825337i	$-0.690985\pi$
$601$	−407897.			−1.12928			−0.564640	+	0.825337i	$0.690985\pi$
$602$			51265.0i			0.141458i
$603$	−85819.6	+	85587.2i	−0.236022	+	0.235383i
$604$	130342.			0.357281
$605$		−	80593.7i		−	0.220186i
$606$		−	63338.6i		−	0.172474i
$607$	−41137.9			−0.111651			−0.0558257	−	0.998441i	$-0.517779\pi$
$607$	−41137.9			−0.111651			−0.0558257	+	0.998441i	$0.517779\pi$
$608$		−	450941.i		−	1.21987i
$609$	35621.5			0.0960455
$610$		−	27195.4i		−	0.0730862i
$611$			21602.6i			0.0578661i
$612$	5129.65			0.0136957
$613$	438257.			1.16629			0.583147	−	0.812367i	$-0.301821\pi$
$613$	438257.			1.16629			0.583147	+	0.812367i	$0.301821\pi$
$614$		−	331022.i		−	0.878053i
$615$		−	21105.4i		−	0.0558011i
$616$			116406.i			0.306770i
$617$	−585250.			−1.53734			−0.768672	−	0.639643i	$-0.779082\pi$
$617$	−585250.			−1.53734			−0.768672	+	0.639643i	$0.779082\pi$
$618$	3697.86			0.00968220
$619$	−8773.65			−0.0228981			−0.0114490	−	0.999934i	$-0.503644\pi$
$619$	−8773.65			−0.0228981			−0.0114490	+	0.999934i	$0.503644\pi$
$620$	−244154.			−0.635156
$621$		−	42085.9i		−	0.109132i
$622$	237534.			0.613967
$623$			48580.8i			0.125167i
$624$	46578.5			0.119623
$625$	−2009.97			−0.00514553
$626$	214362.			0.547014
$627$	311020.			0.791141
$628$	−552281.			−1.40036
$629$	−2160.05			−0.00545962
$630$			12581.5i			0.0316995i
$631$			451397.i			1.13370i	0.823819	+	0.566852i	$0.191839\pi$
$631$			451397.i			1.13370i	−0.823819	+	0.566852i	$0.808161\pi$
$632$	−221039.			−0.553394
$633$			196125.i			0.489470i
$634$		−	17696.4i		−	0.0440258i
$635$			114431.i			0.283789i
$636$	111613.			0.275932
$637$		−	330914.i		−	0.815522i
$638$	−145038.			−0.356320
$639$	197293.			0.483180
$640$	220276.			0.537783
$641$		−	102606.i		−	0.249722i	−0.992174	−	0.124861i	$-0.960152\pi$
$641$		−	102606.i		−	0.249722i	0.992174	−	0.124861i	$-0.0398484\pi$
$642$	99400.3			0.241167
$643$	−65402.1			−0.158187			−0.0790933	−	0.996867i	$-0.525202\pi$
$643$	−65402.1			−0.158187			−0.0790933	+	0.996867i	$0.525202\pi$
$644$		−	48741.5i		−	0.117524i
$645$			137293.i			0.330012i
$646$			14939.9i			0.0358000i
$647$		−	613675.i		−	1.46599i	−0.680236	−	0.732993i	$-0.738123\pi$
$647$		−	613675.i		−	1.46599i	0.680236	−	0.732993i	$-0.261877\pi$
$648$		−	42578.7i		−	0.101401i
$649$			364013.i			0.864225i
$650$	−122968.			−0.291048
$651$			100862.i			0.237993i
$652$	−69182.8			−0.162743
$653$			234715.i			0.550446i	0.961380	+	0.275223i	$0.0887516\pi$
$653$			234715.i			0.550446i	−0.961380	+	0.275223i	$0.911248\pi$
$654$			129575.i			0.302947i
$655$		−	269578.i		−	0.628350i
$656$			15625.2i			0.0363092i
$657$	−81772.8			−0.189443
$658$	4320.02			0.00997779
$659$	−396983.			−0.914115			−0.457057	−	0.889437i	$-0.651097\pi$
$659$	−396983.			−0.914115			−0.457057	+	0.889437i	$0.651097\pi$
$660$			130260.i			0.299036i
$661$			812230.i			1.85899i	0.368839	+	0.929493i	$0.379755\pi$
$661$			812230.i			1.85899i	−0.368839	+	0.929493i	$0.620245\pi$
$662$	−171393.			−0.391091
$663$	−12925.7			−0.0294054
$664$			322025.i			0.730388i
$665$	93175.4			0.210697
$666$			7491.63i			0.0168899i
$667$	145344.			0.326698
$668$	−240271.			−0.538454
$669$			352268.i			0.787083i
$670$	104681.	−	104398.i	0.233195	−	0.232564i
$671$	−116315.			−0.258340
$672$		−	78019.8i		−	0.172769i
$673$		−	726158.i		−	1.60325i	−0.597828	−	0.801624i	$-0.703969\pi$
$673$		−	726158.i		−	1.60325i	0.597828	−	0.801624i	$-0.296031\pi$
$674$	−140263.			−0.308762
$675$		−	53990.4i		−	0.118497i
$676$	68361.2			0.149595
$677$			315755.i			0.688927i	0.938800	+	0.344463i	$0.111939\pi$
$677$			315755.i			0.688927i	−0.938800	+	0.344463i	$0.888061\pi$
$678$			152654.i			0.332084i
$679$	221007.			0.479364
$680$	−14974.8			−0.0323850
$681$			398070.i			0.858352i
$682$		−	410674.i		−	0.882934i
$683$			777091.i			1.66583i	0.553402	+	0.832914i	$0.313329\pi$
$683$			777091.i			1.66583i	−0.553402	+	0.832914i	$0.686671\pi$
$684$	−131755.			−0.281615
$685$	345621.			0.736579
$686$	−138369.			−0.294030
$687$	−309424.			−0.655603
$688$		−	101644.i		−	0.214735i
$689$	−281244.			−0.592440
$690$			51335.7i			0.107825i
$691$	451443.			0.945467			0.472734	−	0.881205i	$-0.343267\pi$
$691$	451443.			0.945467			0.472734	+	0.881205i	$0.343267\pi$
$692$	147418.			0.307850
$693$	53811.4			0.112049
$694$	432833.			0.898673
$695$	−140867.			−0.291634
$696$	147046.			0.303553
$697$		−	4336.04i		−	0.00892539i
$698$			14982.8i			0.0307526i
$699$	−72882.8			−0.149166
$700$		−	62528.5i		−	0.127609i
$701$			233441.i			0.475052i	0.971381	+	0.237526i	$0.0763365\pi$
$701$			233441.i			0.475052i	−0.971381	+	0.237526i	$0.923663\pi$
$702$			44829.8i			0.0909687i
$703$	55481.0			0.112262
$704$			183307.i			0.369856i
$705$	11569.5			0.0232775
$706$	233428.			0.468320
$707$	−81156.2			−0.162361
$708$		−	154204.i		−	0.307630i
$709$	−488380.			−0.971551			−0.485775	−	0.874084i	$-0.661463\pi$
$709$	−488380.			−0.971551			−0.485775	+	0.874084i	$0.661463\pi$
$710$	−240654.			−0.477394
$711$			102180.i			0.202129i
$712$			200542.i			0.395590i
$713$			411541.i			0.809532i
$714$			2584.83i			0.00507033i
$715$		−	328229.i		−	0.642045i
$716$		−	478354.i		−	0.933090i
$717$	−338652.			−0.658742
$718$			92194.4i			0.178836i
$719$	−993249.			−1.92132			−0.960662	−	0.277722i	$-0.910421\pi$
$719$	−993249.			−1.92132			−0.960662	+	0.277722i	$0.910421\pi$
$720$		−	24945.5i		−	0.0481202i
$721$		−	4738.10i		−	0.00911451i
$722$		−	106781.i		−	0.204843i
$723$		−	199757.i		−	0.382143i
$724$	171052.			0.326325
$725$	186456.			0.354733
$726$	−57426.7			−0.108953
$727$		−	920535.i		−	1.74169i	−0.491555	−	0.870846i	$-0.663571\pi$
$727$		−	920535.i		−	1.74169i	0.491555	−	0.870846i	$-0.336429\pi$
$728$			124257.i			0.234454i
$729$	−19683.0			−0.0370370
$730$	99745.1			0.187174
$731$			28206.5i			0.0527854i
$732$	49273.7			0.0919587
$733$			982506.i			1.82864i	0.404998	+	0.914318i	$0.367272\pi$
$733$			982506.i			1.82864i	−0.404998	+	0.914318i	$0.632728\pi$
$734$	82404.3			0.152953
$735$	−177224.			−0.328056
$736$		−	318340.i		−	0.587672i
$737$	−446511.	−	447723.i	−0.822048	−	0.824280i
$738$	−15038.5			−0.0276117
$739$			579821.i			1.06171i	0.847463	+	0.530854i	$0.178129\pi$
$739$			579821.i			1.06171i	−0.847463	+	0.530854i	$0.821871\pi$
$740$			23236.3i			0.0424329i
$741$	331997.			0.604641
$742$			56242.1i			0.102154i
$743$	−155032.			−0.280830			−0.140415	−	0.990093i	$-0.544844\pi$
$743$	−155032.			−0.280830			−0.140415	+	0.990093i	$0.544844\pi$
$744$			416359.i			0.752181i
$745$		−	375726.i		−	0.676953i
$746$	−63815.8			−0.114670
$747$	148864.			0.266777
$748$			26761.5i			0.0478308i
$749$		−	127362.i		−	0.227027i
$750$			172813.i			0.307224i
$751$	−505893.			−0.896972			−0.448486	−	0.893790i	$-0.648037\pi$
$751$	−505893.			−0.896972			−0.448486	+	0.893790i	$0.648037\pi$
$752$	−8565.35			−0.0151464
$753$	−365284.			−0.644230
$754$	−154820.			−0.272323
$755$			175897.i			0.308577i
$756$	−22795.7			−0.0398850
$757$		−	136453.i		−	0.238117i	−0.992887	−	0.119059i	$-0.962012\pi$
$757$		−	136453.i		−	0.238117i	0.992887	−	0.119059i	$-0.0379877\pi$
$758$	386564.			0.672795
$759$	219564.			0.381133
$760$	384629.			0.665909
$761$	1.05549e6			1.82258			0.911288	−	0.411769i	$-0.135089\pi$
$761$	1.05549e6			1.82258			0.911288	+	0.411769i	$0.135089\pi$
$762$	81537.0			0.140425
$763$	166026.			0.285185
$764$			173324.i			0.296942i
$765$			6922.47i			0.0118287i
$766$	25543.4			0.0435332
$767$			388563.i			0.660497i
$768$		−	265148.i		−	0.449537i
$769$			566817.i			0.958495i	0.877680	+	0.479248i	$0.159090\pi$
$769$			566817.i			0.958495i	−0.877680	+	0.479248i	$0.840910\pi$
$770$	−65638.2			−0.110707
$771$		−	377173.i		−	0.634501i
$772$	−147312.			−0.247175
$773$	7846.42			0.0131314			0.00656572	−	0.999978i	$-0.497910\pi$
$773$	7846.42			0.0131314			0.00656572	+	0.999978i	$0.497910\pi$
$774$	97827.6			0.163298
$775$			527950.i			0.879000i
$776$	912319.			1.51504
$777$	9599.07			0.0158996
$778$			371563.i			0.613866i
$779$			111371.i			0.183526i
$780$			139045.i			0.228543i
$781$			1.02928e6i			1.68745i
$782$			10546.8i			0.0172467i
$783$		−	67975.5i		−	0.110874i
$784$	131206.			0.213462
$785$		−	745304.i		−	1.20947i
$786$	−192086.			−0.310922
$787$		−	913395.i		−	1.47472i	−0.675501	−	0.737359i	$-0.736072\pi$
$787$		−	913395.i		−	1.47472i	0.675501	−	0.737359i	$-0.263928\pi$
$788$		−	49361.0i		−	0.0794935i
$789$			479679.i			0.770543i
$790$		−	124638.i		−	0.199708i
$791$	195596.			0.312613
$792$	222134.			0.354132
$793$	−124160.			−0.197440
$794$		−	184771.i		−	0.293085i
$795$			150623.i			0.238317i
$796$	−322004.			−0.508201
$797$	454024.			0.714763			0.357381	−	0.933959i	$-0.383670\pi$
$797$	454024.			0.714763			0.357381	+	0.933959i	$0.383670\pi$
$798$		−	66391.6i		−	0.104258i
$799$	2376.92			0.00372323
$800$		−	408386.i		−	0.638102i
$801$	92705.4			0.144491
$802$	494515.			0.768831
$803$		−	426611.i		−	0.661609i
$804$	189152.	+	189666.i	0.292617	+	0.293411i
$805$	65776.8			0.101503
$806$		−	438372.i		−	0.674796i
$807$		−	262033.i		−	0.402354i
$808$	−335014.			−0.513145
$809$			356194.i			0.544238i	0.962264	+	0.272119i	$0.0877245\pi$
$809$			356194.i			0.544238i	−0.962264	+	0.272119i	$0.912276\pi$
$810$	24009.0			0.0365935
$811$		−	755132.i		−	1.14810i	−0.818819	−	0.574052i	$-0.805371\pi$
$811$		−	755132.i		−	1.14810i	0.818819	−	0.574052i	$-0.194629\pi$
$812$		−	78725.2i		−	0.119399i
$813$	−201212.			−0.304420
$814$	−39084.0			−0.0589862
$815$		−	93362.4i		−	0.140558i
$816$		−	5124.98i		−	0.00769683i
$817$		−	724485.i		−	1.08539i
$818$	8270.66			0.0123604
$819$	57440.7			0.0856351
$820$	−46644.0			−0.0693694
$821$	−670094.			−0.994145			−0.497072	−	0.867709i	$-0.665592\pi$
$821$	−670094.			−0.994145			−0.497072	+	0.867709i	$0.665592\pi$
$822$		−	246271.i		−	0.364476i
$823$	−859989.			−1.26968			−0.634838	−	0.772645i	$-0.718933\pi$
$823$	−859989.			−1.26968			−0.634838	+	0.772645i	$0.718933\pi$
$824$		−	19558.9i		−	0.0288065i
$825$	281669.			0.413839
$826$	77703.6			0.113889
$827$	94985.9			0.138883			0.0694413	−	0.997586i	$-0.477878\pi$
$827$	94985.9			0.138883			0.0694413	+	0.997586i	$0.477878\pi$
$828$	−93012.1			−0.135668
$829$	−168723.			−0.245508			−0.122754	−	0.992437i	$-0.539173\pi$
$829$	−168723.			−0.245508			−0.122754	+	0.992437i	$0.539173\pi$
$830$	−181582.			−0.263582
$831$		−	769566.i		−	1.11441i
$832$			195670.i			0.282668i
$833$	−36410.1			−0.0524725
$834$			100374.i			0.144307i
$835$		−	324246.i		−	0.465052i
$836$		−	687371.i		−	0.983510i
$837$	192472.			0.274737
$838$		−	288078.i		−	0.410225i
$839$	644294.			0.915293			0.457647	−	0.889134i	$-0.348693\pi$
$839$	644294.			0.915293			0.457647	+	0.889134i	$0.348693\pi$
$840$	66546.9			0.0943125
$841$	−472527.			−0.668089
$842$			47232.3i			0.0666216i
$843$	−354181.			−0.498391
$844$	433447.			0.608487
$845$			92253.5i			0.129202i
$846$		−	8243.78i		−	0.0115182i
$847$			73581.2i			0.102565i
$848$		−	111512.i		−	0.155070i
$849$		−	602394.i		−	0.835729i
$850$			13530.0i			0.0187267i
$851$	39166.6			0.0540824
$852$		−	436027.i		−	0.600667i
$853$	−1.02820e6			−1.41313			−0.706563	−	0.707651i	$-0.749755\pi$
$853$	−1.02820e6			−1.41313			−0.706563	+	0.707651i	$0.749755\pi$
$854$			24829.1i			0.0340443i
$855$		−	177804.i		−	0.243226i
$856$		−	525754.i		−	0.717521i
$857$		−	774855.i		−	1.05502i	−0.849550	−	0.527508i	$-0.823126\pi$
$857$		−	774855.i		−	1.05502i	0.849550	−	0.527508i	$-0.176874\pi$
$858$	−233878.			−0.317698
$859$	529398.			0.717457			0.358728	−	0.933442i	$-0.383210\pi$
$859$	529398.			0.717457			0.358728	+	0.933442i	$0.383210\pi$
$860$	303425.			0.410256
$861$			19269.0i			0.0259928i
$862$		−	578927.i		−	0.779129i
$863$	228380.			0.306646			0.153323	−	0.988176i	$-0.451003\pi$
$863$	228380.			0.306646			0.153323	+	0.988176i	$0.451003\pi$
$864$	−148883.			−0.199443
$865$			198942.i			0.265885i
$866$	−185897.			−0.247877
$867$		−	432566.i		−	0.575458i
$868$	222910.			0.295862
$869$	−533078.			−0.705913
$870$			82915.3i			0.109546i
$871$	−476626.	−	477920.i	−0.628263	−	0.629968i
$872$	685357.			0.901330
$873$		−	421741.i		−	0.553372i
$874$		−	270894.i		−	0.354631i
$875$	221427.			0.289210
$876$			180722.i			0.235507i
$877$	431604.			0.561159			0.280580	−	0.959831i	$-0.409473\pi$
$877$	431604.			0.561159			0.280580	+	0.959831i	$0.409473\pi$
$878$			631204.i			0.818805i
$879$			214221.i			0.277258i
$880$	130141.			0.168055
$881$	−124451.			−0.160341			−0.0801707	−	0.996781i	$-0.525547\pi$
$881$	−124451.			−0.160341			−0.0801707	+	0.996781i	$0.525547\pi$
$882$			126280.i			0.162329i
$883$		−	719279.i		−	0.922520i	−0.887265	−	0.461260i	$-0.847398\pi$
$883$		−	719279.i		−	0.922520i	0.887265	−	0.461260i	$-0.152602\pi$
$884$			28566.4i			0.0365554i
$885$	208099.			0.265695
$886$	60144.1			0.0766171
$887$	1.00728e6			1.28027			0.640137	−	0.768261i	$-0.278878\pi$
$887$	1.00728e6			1.28027			0.640137	+	0.768261i	$0.278878\pi$
$888$	39625.1			0.0502510
$889$		−	104474.i		−	0.132192i
$890$	−113080.			−0.142760
$891$		−	102687.i		−	0.129348i
$892$	778530.			0.978465
$893$	−61051.2			−0.0765581
$894$	−267722.			−0.334972
$895$	645540.			0.805892
$896$	−201109.			−0.250505
$897$	234372.			0.291287
$898$		−	335938.i		−	0.416587i
$899$			664704.i			0.822449i
$900$	−119322.			−0.147310
$901$			30944.9i			0.0381189i
$902$		−	78456.5i		−	0.0964308i
$903$		−	125347.i		−	0.153723i
$904$	807424.			0.988018
$905$			230835.i			0.281841i
$906$	125334.			0.152691
$907$	−758683.			−0.922244			−0.461122	−	0.887337i	$-0.652553\pi$
$907$	−758683.			−0.922244			−0.461122	+	0.887337i	$0.652553\pi$
$908$	879756.			1.06706
$909$			154868.i			0.187428i
$910$	−70065.1			−0.0846095
$911$	778125.			0.937590			0.468795	−	0.883307i	$-0.344688\pi$
$911$	778125.			0.937590			0.468795	+	0.883307i	$0.344688\pi$
$912$			131635.i			0.158264i
$913$			776627.i			0.931689i
$914$		−	147140.i		−	0.176132i
$915$			66495.0i			0.0794231i
$916$			683843.i			0.815015i
$917$			246121.i			0.292692i
$918$	4932.57			0.00585313
$919$			775730.i			0.918501i	0.888307	+	0.459251i	$0.151882\pi$
$919$			775730.i			0.918501i	−0.888307	+	0.459251i	$0.848118\pi$
$920$	271527.			0.320803
$921$			809377.i			0.954183i
$922$		−	246623.i		−	0.290116i
$923$			1.09870e6i			1.28966i
$924$		−	118926.i		−	0.139294i
$925$	50245.2			0.0587234
$926$	−94807.1			−0.110565
$927$	−9041.58			−0.0105217
$928$		−	514169.i		−	0.597049i
$929$			855651.i			0.991437i	0.868483	+	0.495719i	$0.165095\pi$
$929$			855651.i			0.991437i	−0.868483	+	0.495719i	$0.834905\pi$
$930$	−234774.			−0.271446
$931$	935195.			1.07895
$932$			161075.i			0.185437i
$933$	−580791.			−0.667200
$934$		−	595205.i		−	0.682296i
$935$	−36114.7			−0.0413106
$936$	237116.			0.270651
$937$			715631.i			0.815098i	0.913183	+	0.407549i	$0.133616\pi$
$937$			715631.i			0.815098i	−0.913183	+	0.407549i	$0.866384\pi$
$938$	−95572.7	+	95314.0i	−0.108625	+	0.108331i
$939$	−524132.			−0.594442
$940$		−	25569.2i		−	0.0289375i
$941$		−	248323.i		−	0.280438i	−0.990121	−	0.140219i	$-0.955219\pi$
$941$		−	248323.i		−	0.280438i	0.990121	−	0.140219i	$-0.0447807\pi$
$942$	−531063.			−0.598472
$943$			78622.1i			0.0884141i
$944$	−154064.			−0.172885
$945$		−	30762.9i		−	0.0344479i
$946$			510370.i			0.570299i
$947$	720175.			0.803042			0.401521	−	0.915850i	$-0.368482\pi$
$947$	720175.			0.803042			0.401521	+	0.915850i	$0.368482\pi$
$948$	225824.			0.251277
$949$		−	455384.i		−	0.505644i
$950$		−	347519.i		−	0.385063i
$951$			43269.3i			0.0478430i
$952$	13671.8			0.0150853
$953$	−611406.			−0.673200			−0.336600	−	0.941648i	$-0.609277\pi$
$953$	−611406.			−0.673200			−0.336600	+	0.941648i	$0.609277\pi$
$954$	107325.			0.117925
$955$	−233901.			−0.256464
$956$			748438.i			0.818918i
$957$	354630.			0.387214
$958$		−	867802.i		−	0.945561i
$959$	−315548.			−0.343106
$960$	104793.			0.113707
$961$	−958583.			−1.03797
$962$	−41720.1			−0.0450811
$963$	−243042.			−0.262077
$964$	−441474.			−0.475063
$965$		−	198798.i		−	0.213480i
$966$		−	46868.9i		−	0.0502262i
$967$	383409.			0.410024			0.205012	−	0.978759i	$-0.434277\pi$
$967$	383409.			0.410024			0.205012	+	0.978759i	$0.434277\pi$
$968$			303744.i			0.324158i
$969$		−	36529.3i		−	0.0389039i
$970$			514432.i			0.546745i
$971$	1.20186e6			1.27472			0.637362	−	0.770565i	$-0.280026\pi$
$971$	1.20186e6			1.27472			0.637362	+	0.770565i	$0.280026\pi$
$972$			43500.4i			0.0460427i
$973$	128610.			0.135846
$974$	−491291.			−0.517870
$975$	300666.			0.316283
$976$		−	49228.9i		−	0.0516797i
$977$	−1.37174e6			−1.43709			−0.718544	−	0.695481i	$-0.755191\pi$
$977$	−1.37174e6			−1.43709			−0.718544	+	0.695481i	$0.755191\pi$
$978$	−66524.9			−0.0695515
$979$			483647.i			0.504618i
$980$			391674.i			0.407824i
$981$		−	316823.i		−	0.329214i
$982$			145733.i			0.151125i
$983$			941199.i			0.974035i	0.873392	+	0.487018i	$0.161915\pi$
$983$			941199.i			0.974035i	−0.873392	+	0.487018i	$0.838085\pi$
$984$			79542.6i			0.0821504i
$985$	66612.8			0.0686570
$986$			17034.7i			0.0175219i
$987$	−10562.8			−0.0108429
$988$		−	733731.i		−	0.751662i
$989$		−	511447.i		−	0.522887i
$990$			125256.i			0.127799i
$991$			1.19282e6i			1.21459i	0.794478	+	0.607293i	$0.207745\pi$
$991$			1.19282e6i			1.21459i	−0.794478	+	0.607293i	$0.792255\pi$
$992$	1.45587e6			1.47944
$993$	419070.			0.425000
$994$	219714.			0.222375
$995$		−	434546.i		−	0.438924i
$996$		−	328997.i		−	0.331645i
$997$	249912.			0.251418			0.125709	−	0.992067i	$-0.459879\pi$
$997$	249912.			0.251418			0.125709	+	0.992067i	$0.459879\pi$
$998$	−707624.			−0.710463
$999$		−	18317.7i		−	0.0183543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.19	✓	46
67.66	odd	2	inner	201.5.b.a.133.28	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.19	✓	46	1.1	even	1	trivial
201.5.b.a.133.28	yes	46	67.66	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	201.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.12514i q^{2} +5.19615i q^{3} +11.4838 q^{4} +15.4974i q^{5} +11.0426 q^{6} -14.1489i q^{7} -58.4069i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-2.12514i q^{2} +5.19615i q^{3} +11.4838 q^{4} +15.4974i q^{5} +11.0426 q^{6} -14.1489i q^{7} -58.4069i q^{8} -27.0000 q^{9} +32.9341 q^{10} -140.860i q^{11} +59.6714i q^{12} -150.360i q^{13} -30.0685 q^{14} -80.5267 q^{15} +59.6171 q^{16} -16.5440 q^{17} +57.3789i q^{18} +424.932 q^{19} +177.968i q^{20} +73.5199 q^{21} -299.347 q^{22} +299.979 q^{23} +303.491 q^{24} +384.832 q^{25} -319.537 q^{26} -140.296i q^{27} -162.483i q^{28} +484.514 q^{29} +171.131i q^{30} +1371.90i q^{31} -1061.21i q^{32} +731.929 q^{33} +35.1583i q^{34} +219.271 q^{35} -310.062 q^{36} +130.564 q^{37} -903.042i q^{38} +781.294 q^{39} +905.154 q^{40} +262.092i q^{41} -156.240i q^{42} -1704.94i q^{43} -1617.60i q^{44} -418.429i q^{45} -637.499i q^{46} -143.673 q^{47} +309.779i q^{48} +2200.81 q^{49} -817.822i q^{50} -85.9649i q^{51} -1726.70i q^{52} -1870.47i q^{53} -298.149 q^{54} +2182.96 q^{55} -826.395 q^{56} +2208.01i q^{57} -1029.66i q^{58} -2584.22 q^{59} -924.750 q^{60} -825.751i q^{61} +2915.48 q^{62} +382.021i q^{63} -1301.34 q^{64} +2330.19 q^{65} -1555.45i q^{66} +(3178.50 - 3169.90i) q^{67} -189.987 q^{68} +1558.74i q^{69} -465.982i q^{70} -7307.13 q^{71} +1576.99i q^{72} +3028.62 q^{73} -277.468i q^{74} +1999.64i q^{75} +4879.82 q^{76} -1993.01 q^{77} -1660.36i q^{78} -3784.46i q^{79} +923.908i q^{80} +729.000 q^{81} +556.983 q^{82} -5513.48 q^{83} +844.286 q^{84} -256.388i q^{85} -3623.25 q^{86} +2517.61i q^{87} -8227.19 q^{88} -3433.53 q^{89} -889.222 q^{90} -2127.43 q^{91} +3444.89 q^{92} -7128.59 q^{93} +305.325i q^{94} +6585.33i q^{95} +5514.19 q^{96} +15620.0i q^{97} -4677.03i q^{98} +3803.21i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 46 * q - 396 * q^4 - 1242 * q^9	\( 46 q - 396 q^{4} - 1242 q^{9} + 396 q^{10} + 792 q^{14} - 252 q^{15} + 3396 q^{16} + 462 q^{17} - 590 q^{19} - 936 q^{21} + 3184 q^{22} - 1446 q^{23} - 1404 q^{24} - 6278 q^{25} + 2700 q^{26} - 1014 q^{29} + 540 q^{33} + 9924 q^{35} + 10692 q^{36} - 386 q^{37} + 4968 q^{39} - 9988 q^{40} - 2754 q^{47} - 19062 q^{49} - 2320 q^{55} - 3396 q^{56} - 7098 q^{59} + 72 q^{60} - 21180 q^{62} - 75644 q^{64} + 18396 q^{65} + 8574 q^{67} + 9084 q^{68} - 23040 q^{71} - 22338 q^{73} + 28016 q^{76} + 45084 q^{77} + 33534 q^{81} + 17564 q^{82} + 35856 q^{83} + 40176 q^{84} + 31764 q^{86} - 19448 q^{88} - 14538 q^{89} - 10692 q^{90} + 13792 q^{91} - 67692 q^{92} + 22464 q^{93} + 22464 q^{96}+O(q^{100}) \) 46 * q - 396 * q^4 - 1242 * q^9 + 396 * q^10 + 792 * q^14 - 252 * q^15 + 3396 * q^16 + 462 * q^17 - 590 * q^19 - 936 * q^21 + 3184 * q^22 - 1446 * q^23 - 1404 * q^24 - 6278 * q^25 + 2700 * q^26 - 1014 * q^29 + 540 * q^33 + 9924 * q^35 + 10692 * q^36 - 386 * q^37 + 4968 * q^39 - 9988 * q^40 - 2754 * q^47 - 19062 * q^49 - 2320 * q^55 - 3396 * q^56 - 7098 * q^59 + 72 * q^60 - 21180 * q^62 - 75644 * q^64 + 18396 * q^65 + 8574 * q^67 + 9084 * q^68 - 23040 * q^71 - 22338 * q^73 + 28016 * q^76 + 45084 * q^77 + 33534 * q^81 + 17564 * q^82 + 35856 * q^83 + 40176 * q^84 + 31764 * q^86 - 19448 * q^88 - 14538 * q^89 - 10692 * q^90 + 13792 * q^91 - 67692 * q^92 + 22464 * q^93 + 22464 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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