LMFDB - Embedded newform 201.5.b.a.133.12

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			133.12
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.92431i q^{2} -5.19615i q^{3} -8.24886 q^{4} +24.9820i q^{5} -25.5875 q^{6} +17.9795i q^{7} -38.1691i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-4.92431i q^{2} -5.19615i q^{3} -8.24886 q^{4} +24.9820i q^{5} -25.5875 q^{6} +17.9795i q^{7} -38.1691i q^{8} -27.0000 q^{9} +123.019 q^{10} +173.423i q^{11} +42.8623i q^{12} -5.35667i q^{13} +88.5365 q^{14} +129.810 q^{15} -319.938 q^{16} +135.856 q^{17} +132.956i q^{18} +482.464 q^{19} -206.073i q^{20} +93.4240 q^{21} +853.987 q^{22} +748.805 q^{23} -198.332 q^{24} +0.898843 q^{25} -26.3779 q^{26} +140.296i q^{27} -148.310i q^{28} +861.691 q^{29} -639.227i q^{30} +1131.75i q^{31} +964.770i q^{32} +901.130 q^{33} -668.999i q^{34} -449.163 q^{35} +222.719 q^{36} -1716.64 q^{37} -2375.80i q^{38} -27.8341 q^{39} +953.540 q^{40} -2678.37i q^{41} -460.049i q^{42} +820.561i q^{43} -1430.54i q^{44} -674.514i q^{45} -3687.35i q^{46} -3747.85 q^{47} +1662.45i q^{48} +2077.74 q^{49} -4.42618i q^{50} -705.931i q^{51} +44.1864i q^{52} +1512.84i q^{53} +690.862 q^{54} -4332.45 q^{55} +686.259 q^{56} -2506.96i q^{57} -4243.24i q^{58} +6209.98 q^{59} -1070.79 q^{60} +4907.24i q^{61} +5573.09 q^{62} -485.446i q^{63} -368.179 q^{64} +133.820 q^{65} -4437.45i q^{66} +(-3365.02 + 2971.15i) q^{67} -1120.66 q^{68} -3890.91i q^{69} +2211.82i q^{70} +5439.27 q^{71} +1030.56i q^{72} -4422.45 q^{73} +8453.29i q^{74} -4.67052i q^{75} -3979.77 q^{76} -3118.05 q^{77} +137.064i q^{78} -5870.90i q^{79} -7992.70i q^{80} +729.000 q^{81} -13189.1 q^{82} +11825.2 q^{83} -770.641 q^{84} +3393.97i q^{85} +4040.70 q^{86} -4477.48i q^{87} +6619.38 q^{88} +2552.17 q^{89} -3321.52 q^{90} +96.3101 q^{91} -6176.79 q^{92} +5880.74 q^{93} +18455.6i q^{94} +12052.9i q^{95} +5013.09 q^{96} +12696.1i q^{97} -10231.4i q^{98} -4682.41i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	4.92431i		−	1.23108i	−0.788106	−	0.615539i	$-0.788938\pi$
$2$		−	4.92431i		−	1.23108i	0.788106	−	0.615539i	$-0.211062\pi$
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−8.24886			−0.515553
$5$			24.9820i			0.999281i	0.866233	+	0.499640i	$0.166534\pi$
$5$			24.9820i			0.999281i	−0.866233	+	0.499640i	$0.833466\pi$
$6$	−25.5875			−0.710763
$7$			17.9795i			0.366928i	0.983026	+	0.183464i	$0.0587311\pi$
$7$			17.9795i			0.366928i	−0.983026	+	0.183464i	$0.941269\pi$
$8$		−	38.1691i		−	0.596392i
$9$	−27.0000			−0.333333
$10$	123.019			1.23019
$11$			173.423i			1.43324i	0.697461	+	0.716622i	$0.254313\pi$
$11$			173.423i			1.43324i	−0.697461	+	0.716622i	$0.745687\pi$
$12$			42.8623i			0.297655i
$13$		−	5.35667i		−	0.0316963i	−0.999874	−	0.0158481i	$-0.994955\pi$
$13$		−	5.35667i		−	0.0316963i	0.999874	−	0.0158481i	$-0.00504483\pi$
$14$	88.5365			0.451717
$15$	129.810			0.576935
$16$	−319.938			−1.24976
$17$	135.856			0.470091			0.235046	−	0.971984i	$-0.424476\pi$
$17$	135.856			0.470091			0.235046	+	0.971984i	$0.424476\pi$
$18$			132.956i			0.410359i
$19$	482.464			1.33646			0.668232	−	0.743953i	$-0.267051\pi$
$19$	482.464			1.33646			0.668232	+	0.743953i	$0.267051\pi$
$20$		−	206.073i		−	0.515183i
$21$	93.4240			0.211846
$22$	853.987			1.76444
$23$	748.805			1.41551			0.707755	−	0.706458i	$-0.249708\pi$
$23$	748.805			1.41551			0.707755	+	0.706458i	$0.249708\pi$
$24$	−198.332			−0.344327
$25$	0.898843			0.00143815
$26$	−26.3779			−0.0390206
$27$			140.296i			0.192450i
$28$		−	148.310i		−	0.189171i
$29$	861.691			1.02460			0.512302	−	0.858806i	$-0.328793\pi$
$29$	861.691			1.02460			0.512302	+	0.858806i	$0.328793\pi$
$30$		−	639.227i		−	0.710252i
$31$			1131.75i			1.17768i	0.808250	+	0.588839i	$0.200415\pi$
$31$			1131.75i			1.17768i	−0.808250	+	0.588839i	$0.799585\pi$
$32$			964.770i			0.942158i
$33$	901.130			0.827484
$34$		−	668.999i		−	0.578719i
$35$	−449.163			−0.366664
$36$	222.719			0.171851
$37$	−1716.64			−1.25394			−0.626970	−	0.779044i	$-0.715705\pi$
$37$	−1716.64			−1.25394			−0.626970	+	0.779044i	$0.715705\pi$
$38$		−	2375.80i		−	1.64529i
$39$	−27.8341			−0.0182999
$40$	953.540			0.595963
$41$		−	2678.37i		−	1.59332i	−0.604429	−	0.796659i	$-0.706599\pi$
$41$		−	2678.37i		−	1.59332i	0.604429	−	0.796659i	$-0.293401\pi$
$42$		−	460.049i		−	0.260799i
$43$			820.561i			0.443786i	0.975071	+	0.221893i	$0.0712236\pi$
$43$			820.561i			0.443786i	−0.975071	+	0.221893i	$0.928776\pi$
$44$		−	1430.54i		−	0.738914i
$45$		−	674.514i		−	0.333094i
$46$		−	3687.35i		−	1.74260i
$47$	−3747.85			−1.69663			−0.848313	−	0.529496i	$-0.822381\pi$
$47$	−3747.85			−1.69663			−0.848313	+	0.529496i	$0.822381\pi$
$48$			1662.45i			0.721548i
$49$	2077.74			0.865364
$50$		−	4.42618i		−	0.00177047i
$51$		−	705.931i		−	0.271407i
$52$			44.1864i			0.0163411i
$53$			1512.84i			0.538568i	0.963061	+	0.269284i	$0.0867870\pi$
$53$			1512.84i			0.538568i	−0.963061	+	0.269284i	$0.913213\pi$
$54$	690.862			0.236921
$55$	−4332.45			−1.43221
$56$	686.259			0.218833
$57$		−	2506.96i		−	0.771608i
$58$		−	4243.24i		−	1.26137i
$59$	6209.98			1.78397			0.891983	−	0.452070i	$-0.149314\pi$
$59$	6209.98			1.78397			0.891983	+	0.452070i	$0.149314\pi$
$60$	−1070.79			−0.297441
$61$			4907.24i			1.31880i	0.751794	+	0.659398i	$0.229189\pi$
$61$			4907.24i			1.31880i	−0.751794	+	0.659398i	$0.770811\pi$
$62$	5573.09			1.44981
$63$		−	485.446i		−	0.122309i
$64$	−368.179			−0.0898875
$65$	133.820			0.0316735
$66$		−	4437.45i		−	1.01870i
$67$	−3365.02	+	2971.15i	−0.749615	+	0.661874i
$67$	−3365.02	+	2971.15i	−0.749615	+	0.661874i
$68$	−1120.66			−0.242357
$69$		−	3890.91i		−	0.817245i
$70$			2211.82i			0.451392i
$71$	5439.27			1.07901			0.539503	−	0.841984i	$-0.318612\pi$
$71$	5439.27			1.07901			0.539503	+	0.841984i	$0.318612\pi$
$72$			1030.56i			0.198797i
$73$	−4422.45			−0.829883			−0.414942	−	0.909848i	$-0.636198\pi$
$73$	−4422.45			−0.829883			−0.414942	+	0.909848i	$0.636198\pi$
$74$			8453.29i			1.54370i
$75$		−	4.67052i		−	0.000830315i
$76$	−3979.77			−0.689019
$77$	−3118.05			−0.525898
$78$			137.064i			0.0225286i
$79$		−	5870.90i		−	0.940698i	−0.882481	−	0.470349i	$-0.844128\pi$
$79$		−	5870.90i		−	0.940698i	0.882481	−	0.470349i	$-0.155872\pi$
$80$		−	7992.70i		−	1.24886i
$81$	729.000			0.111111
$82$	−13189.1			−1.96150
$83$	11825.2			1.71654			0.858269	−	0.513199i	$-0.171540\pi$
$83$	11825.2			1.71654			0.858269	+	0.513199i	$0.171540\pi$
$84$	−770.641			−0.109218
$85$			3393.97i			0.469753i
$86$	4040.70			0.546336
$87$		−	4477.48i		−	0.591555i
$88$	6619.38			0.854775
$89$	2552.17			0.322203			0.161101	−	0.986938i	$-0.448495\pi$
$89$	2552.17			0.322203			0.161101	+	0.986938i	$0.448495\pi$
$90$	−3321.52			−0.410064
$91$	96.3101			0.0116303
$92$	−6176.79			−0.729771
$93$	5880.74			0.679933
$94$			18455.6i			2.08868i
$95$			12052.9i			1.33550i
$96$	5013.09			0.543955
$97$			12696.1i			1.34936i	0.738110	+	0.674681i	$0.235719\pi$
$97$			12696.1i			1.34936i	−0.738110	+	0.674681i	$0.764281\pi$
$98$		−	10231.4i		−	1.06533i
$99$		−	4682.41i		−	0.477748i
$100$	−7.41442			−0.000741442
$101$		−	10582.0i		−	1.03735i	−0.854971	−	0.518675i	$-0.826425\pi$
$101$		−	10582.0i		−	1.03735i	0.854971	−	0.518675i	$-0.173575\pi$
$102$	−3476.22			−0.334124
$103$	−11880.7			−1.11987			−0.559936	−	0.828536i	$-0.689174\pi$
$103$	−11880.7			−1.11987			−0.559936	+	0.828536i	$0.689174\pi$
$104$	−204.459			−0.0189034
$105$			2333.92i			0.211694i
$106$	7449.69			0.663019
$107$	20.3048			0.00177350			0.000886748	−	1.00000i	$-0.499718\pi$
$107$	20.3048			0.00177350			0.000886748		1.00000i	$0.499718\pi$
$108$		−	1157.28i		−	0.0992183i
$109$		−	6082.27i		−	0.511933i	−0.966686	−	0.255966i	$-0.917606\pi$
$109$		−	6082.27i		−	0.511933i	0.966686	−	0.255966i	$-0.0823936\pi$
$110$			21334.3i			1.76317i
$111$			8919.94i			0.723962i
$112$		−	5752.32i		−	0.458571i
$113$			21783.3i			1.70595i	0.521949	+	0.852976i	$0.325205\pi$
$113$			21783.3i			1.70595i	−0.521949	+	0.852976i	$0.674795\pi$
$114$	−12345.0			−0.949910
$115$			18706.7i			1.41449i
$116$	−7107.97			−0.528238
$117$			144.630i			0.0105654i
$118$		−	30579.9i		−	2.19620i
$119$			2442.63i			0.172490i
$120$		−	4954.74i		−	0.344079i
$121$	−15434.4			−1.05419
$122$	24164.8			1.62354
$123$	−13917.2			−0.919902
$124$		−	9335.63i		−	0.607156i
$125$			15636.2i			1.00072i
$126$	−2390.49			−0.150572
$127$	16891.0			1.04725			0.523623	−	0.851950i	$-0.324580\pi$
$127$	16891.0			1.04725			0.523623	+	0.851950i	$0.324580\pi$
$128$			17249.4i			1.05282i
$129$	4263.76			0.256220
$130$		−	658.974i		−	0.0389925i
$131$	−18583.3			−1.08288			−0.541440	−	0.840739i	$-0.682121\pi$
$131$	−18583.3			−1.08288			−0.541440	+	0.840739i	$0.682121\pi$
$132$	−7433.29			−0.426612
$133$			8674.44i			0.490386i
$134$	14630.9	+	16570.4i	0.814819	+	0.922835i
$135$	−3504.88			−0.192312
$136$		−	5185.51i		−	0.280358i
$137$			4412.36i			0.235087i	0.993068	+	0.117544i	$0.0375020\pi$
$137$			4412.36i			0.235087i	−0.993068	+	0.117544i	$0.962498\pi$
$138$	−19160.0			−1.00609
$139$		−	21795.1i		−	1.12805i	−0.825757	−	0.564026i	$-0.809252\pi$
$139$		−	21795.1i		−	1.12805i	0.825757	−	0.564026i	$-0.190748\pi$
$140$	3705.08			0.189035
$141$			19474.4i			0.979547i
$142$		−	26784.6i		−	1.32834i
$143$	928.968			0.0454285
$144$	8638.33			0.416586
$145$			21526.8i			1.02387i
$146$			21777.5i			1.02165i
$147$		−	10796.2i		−	0.499618i
$148$	14160.3			0.646473
$149$	19415.7			0.874543			0.437272	−	0.899330i	$-0.355945\pi$
$149$	19415.7			0.874543			0.437272	+	0.899330i	$0.355945\pi$
$150$	−22.9991			−0.00102218
$151$	−386.093			−0.0169331			−0.00846657	−	0.999964i	$-0.502695\pi$
$151$	−386.093			−0.0169331			−0.00846657	+	0.999964i	$0.502695\pi$
$152$		−	18415.2i		−	0.797056i
$153$	−3668.12			−0.156697
$154$			15354.2i			0.647421i
$155$	−28273.4			−1.17683
$156$	229.599			0.00943456
$157$	5251.77			0.213062			0.106531	−	0.994309i	$-0.466026\pi$
$157$	5251.77			0.213062			0.106531	+	0.994309i	$0.466026\pi$
$158$	−28910.1			−1.15807
$159$	7860.93			0.310942
$160$	−24101.9			−0.941481
$161$			13463.1i			0.519390i
$162$		−	3589.82i		−	0.136786i
$163$	−19016.0			−0.715722			−0.357861	−	0.933775i	$-0.616494\pi$
$163$	−19016.0			−0.715722			−0.357861	+	0.933775i	$0.616494\pi$
$164$			22093.5i			0.821440i
$165$			22512.1i			0.826889i
$166$		−	58231.2i		−	2.11319i
$167$	−26038.2			−0.933636			−0.466818	−	0.884353i	$-0.654600\pi$
$167$	−26038.2			−0.933636			−0.466818	+	0.884353i	$0.654600\pi$
$168$		−	3565.91i		−	0.126343i
$169$	28532.3			0.998995
$170$	16713.0			0.578303
$171$	−13026.5			−0.445488
$172$		−	6768.69i		−	0.228796i
$173$	5559.50			0.185756			0.0928782	−	0.995677i	$-0.470393\pi$
$173$	5559.50			0.185756			0.0928782	+	0.995677i	$0.470393\pi$
$174$	−22048.5			−0.728251
$175$			16.1607i			0.000527697i
$176$		−	55484.5i		−	1.79121i
$177$		−	32268.0i		−	1.02997i
$178$		−	12567.7i		−	0.396657i
$179$		−	1454.35i		−	0.0453902i	−0.999742	−	0.0226951i	$-0.992775\pi$
$179$		−	1454.35i		−	0.0453902i	0.999742	−	0.0226951i	$-0.00722470\pi$
$180$			5563.97i			0.171728i
$181$	17804.8			0.543476			0.271738	−	0.962371i	$-0.412402\pi$
$181$	17804.8			0.543476			0.271738	+	0.962371i	$0.412402\pi$
$182$		−	474.261i		−	0.0143177i
$183$	25498.8			0.761407
$184$		−	28581.2i		−	0.844199i
$185$		−	42885.2i		−	1.25304i
$186$		−	28958.6i		−	0.837051i
$187$			23560.6i			0.673756i
$188$	30915.4			0.874701
$189$	−2522.45			−0.0706153
$190$	59352.3			1.64411
$191$		−	62017.5i		−	1.69999i	−0.526788	−	0.849997i	$-0.676604\pi$
$191$		−	62017.5i		−	1.69999i	0.526788	−	0.849997i	$-0.323396\pi$
$192$			1913.12i			0.0518966i
$193$	−64298.6			−1.72618			−0.863092	−	0.505047i	$-0.831475\pi$
$193$	−64298.6			−1.72618			−0.863092	+	0.505047i	$0.831475\pi$
$194$	62519.8			1.66117
$195$		−	695.352i		−	0.0182867i
$196$	−17139.0			−0.446141
$197$		−	8560.18i		−	0.220572i	−0.993900	−	0.110286i	$-0.964823\pi$
$197$		−	8560.18i		−	0.220572i	0.993900	−	0.110286i	$-0.0351767\pi$
$198$	−23057.7			−0.588145
$199$	−43233.6			−1.09173			−0.545865	−	0.837873i	$-0.683799\pi$
$199$	−43233.6			−1.09173			−0.545865	+	0.837873i	$0.683799\pi$
$200$		−	34.3080i		−	0.000857700i
$201$	15438.6	+	17485.2i	0.382133	+	0.432790i
$202$	−52109.2			−1.27706
$203$			15492.8i			0.375956i
$204$			5823.12i			0.139925i
$205$	66911.0			1.59217
$206$			58504.3i			1.37865i
$207$	−20217.7			−0.471837
$208$			1713.80i			0.0396127i
$209$			83670.1i			1.91548i
$210$	11493.0			0.260611
$211$	23953.3			0.538023			0.269012	−	0.963137i	$-0.413303\pi$
$211$	23953.3			0.538023			0.269012	+	0.963137i	$0.413303\pi$
$212$		−	12479.2i		−	0.277661i
$213$		−	28263.3i		−	0.622964i
$214$		−	99.9869i		−	0.00218331i
$215$	−20499.3			−0.443467
$216$	5354.97			0.114776
$217$	−20348.2			−0.432123
$218$	−29951.0			−0.630229
$219$			22979.7i			0.479133i
$220$	35737.7			0.738383
$221$		−	727.738i		−	0.0149001i
$222$	43924.6			0.891254
$223$	−31362.5			−0.630669			−0.315334	−	0.948981i	$-0.602117\pi$
$223$	−31362.5			−0.630669			−0.315334	+	0.948981i	$0.602117\pi$
$224$	−17346.1			−0.345704
$225$	−24.2688			−0.000479383
$226$	107268.			2.10016
$227$	21492.0			0.417085			0.208543	−	0.978013i	$-0.433128\pi$
$227$	21492.0			0.417085			0.208543	+	0.978013i	$0.433128\pi$
$228$			20679.5i			0.397805i
$229$			24063.1i			0.458860i	0.973325	+	0.229430i	$0.0736863\pi$
$229$			24063.1i			0.458860i	−0.973325	+	0.229430i	$0.926314\pi$
$230$	92117.5			1.74135
$231$			16201.8i			0.303627i
$232$		−	32890.0i		−	0.611065i
$233$		−	50191.8i		−	0.924530i	−0.886742	−	0.462265i	$-0.847037\pi$
$233$		−	50191.8i		−	0.924530i	0.886742	−	0.462265i	$-0.152963\pi$
$234$	712.204			0.0130069
$235$		−	93628.7i		−	1.69540i
$236$	−51225.2			−0.919729
$237$	−30506.1			−0.543112
$238$	12028.3			0.212348
$239$		−	85186.9i		−	1.49134i	−0.666315	−	0.745671i	$-0.732129\pi$
$239$		−	85186.9i		−	1.49134i	0.666315	−	0.745671i	$-0.267871\pi$
$240$	−41531.3			−0.721029
$241$	−16761.2			−0.288583			−0.144291	−	0.989535i	$-0.546090\pi$
$241$	−16761.2			−0.288583			−0.144291	+	0.989535i	$0.546090\pi$
$242$			76003.9i			1.29779i
$243$		−	3788.00i		−	0.0641500i
$244$		−	40479.1i		−	0.679910i
$245$			51906.1i			0.864741i
$246$			68532.7i			1.13247i
$247$		−	2584.40i		−	0.0423610i
$248$	43197.8			0.702357
$249$		−	61445.7i		−	0.991044i
$250$	76997.6			1.23196
$251$			48671.0i			0.772543i	0.922385	+	0.386272i	$0.126237\pi$
$251$			48671.0i			0.772543i	−0.922385	+	0.386272i	$0.873763\pi$
$252$			4004.37i			0.0630570i
$253$			129860.i			2.02877i
$254$		−	83176.8i		−	1.28924i
$255$	17635.6			0.271212
$256$	79050.3			1.20621
$257$	96593.9			1.46246			0.731229	−	0.682132i	$-0.238947\pi$
$257$	96593.9			1.46246			0.731229	+	0.682132i	$0.238947\pi$
$258$		−	20996.1i		−	0.315427i
$259$		−	30864.3i		−	0.460105i
$260$	−1103.87			−0.0163294
$261$	−23265.7			−0.341534
$262$			91510.1i			1.33311i
$263$	30643.3			0.443020			0.221510	−	0.975158i	$-0.428901\pi$
$263$	30643.3			0.443020			0.221510	+	0.975158i	$0.428901\pi$
$264$		−	34395.3i		−	0.493505i
$265$	−37793.7			−0.538181
$266$	42715.7			0.603704
$267$		−	13261.5i		−	0.186024i
$268$	27757.6	−	24508.6i	0.386467	−	0.341232i
$269$	−60863.6			−0.841111			−0.420555	−	0.907267i	$-0.638165\pi$
$269$	−60863.6			−0.841111			−0.420555	+	0.907267i	$0.638165\pi$
$270$			17259.1i			0.236751i
$271$		−	116336.i		−	1.58407i	−0.610474	−	0.792037i	$-0.709021\pi$
$271$		−	116336.i		−	1.58407i	0.610474	−	0.792037i	$-0.290979\pi$
$272$	−43465.6			−0.587500
$273$		−	500.442i		−	0.00671473i
$274$	21727.8			0.289411
$275$			155.880i			0.00206122i
$276$			32095.5i			0.421334i
$277$	−70926.4			−0.924375			−0.462188	−	0.886782i	$-0.652935\pi$
$277$	−70926.4			−0.924375			−0.462188	+	0.886782i	$0.652935\pi$
$278$	−107326.			−1.38872
$279$		−	30557.2i		−	0.392559i
$280$			17144.1i			0.218675i
$281$		−	37074.1i		−	0.469524i	−0.972053	−	0.234762i	$-0.924569\pi$
$281$		−	37074.1i		−	0.469524i	0.972053	−	0.234762i	$-0.0754311\pi$
$282$	95897.9			1.20590
$283$	−52519.6			−0.655766			−0.327883	−	0.944718i	$-0.606335\pi$
$283$	−52519.6			−0.655766			−0.327883	+	0.944718i	$0.606335\pi$
$284$	−44867.7			−0.556285
$285$	62628.8			0.771053
$286$		−	4574.53i		−	0.0559261i
$287$	48155.6			0.584633
$288$		−	26048.8i		−	0.314053i
$289$	−65064.0			−0.779014
$290$	106005.			1.26046
$291$	65971.1			0.779054
$292$	36480.1			0.427849
$293$	−43110.1			−0.502162			−0.251081	−	0.967966i	$-0.580786\pi$
$293$	−43110.1			−0.502162			−0.251081	+	0.967966i	$0.580786\pi$
$294$	−53164.1			−0.615069
$295$			155138.i			1.78268i
$296$			65522.7i			0.747839i
$297$	−24330.5			−0.275828
$298$		−	95609.1i		−	1.07663i
$299$		−	4011.10i		−	0.0448664i
$300$			38.5265i			0.000428072i
$301$	−14753.3			−0.162838
$302$			1901.24i			0.0208460i
$303$	−54985.8			−0.598915
$304$	−154359.			−1.67026
$305$	−122593.			−1.31785
$306$			18063.0i			0.192906i
$307$	−12863.9			−0.136489			−0.0682443	−	0.997669i	$-0.521740\pi$
$307$	−12863.9			−0.136489			−0.0682443	+	0.997669i	$0.521740\pi$
$308$	25720.3			0.271128
$309$			61734.0i			0.646558i
$310$			139227.i			1.44877i
$311$		−	73161.8i		−	0.756421i	−0.925720	−	0.378211i	$-0.876540\pi$
$311$		−	73161.8i		−	0.756421i	0.925720	−	0.378211i	$-0.123460\pi$
$312$			1062.40i			0.0109139i
$313$			76436.7i			0.780213i	0.920770	+	0.390107i	$0.127562\pi$
$313$			76436.7i			0.780213i	−0.920770	+	0.390107i	$0.872438\pi$
$314$		−	25861.4i		−	0.262296i
$315$	12127.4			0.122221
$316$			48428.2i			0.484980i
$317$	−130744.			−1.30108			−0.650541	−	0.759471i	$-0.725458\pi$
$317$	−130744.			−1.30108			−0.650541	+	0.759471i	$0.725458\pi$
$318$		−	38709.7i		−	0.382794i
$319$			149437.i			1.46851i
$320$		−	9197.86i		−	0.0898229i
$321$		−	105.507i		−	0.00102393i
$322$	66296.6			0.639410
$323$	65545.8			0.628261
$324$	−6013.42			−0.0572837
$325$		−	4.81481i		−	4.55840e-5i
$326$			93640.8i			0.881109i
$327$	−31604.4			−0.295564
$328$	−102231.			−0.950241
$329$		−	67384.3i		−	0.622539i
$330$	110856.			1.01797
$331$			4552.78i			0.0415548i	0.999784	+	0.0207774i	$0.00661412\pi$
$331$			4552.78i			0.0415548i	−0.999784	+	0.0207774i	$0.993386\pi$
$332$	−97544.7			−0.884967
$333$	46349.4			0.417980
$334$			128220.i			1.14938i
$335$	−74225.4	−	84065.0i	−0.661398	−	0.749076i
$336$	−29889.9			−0.264756
$337$		−	126344.i		−	1.11249i	−0.831019	−	0.556244i	$-0.812242\pi$
$337$		−	126344.i		−	1.11249i	0.831019	−	0.556244i	$-0.187758\pi$
$338$		−	140502.i		−	1.22984i
$339$	113189.			0.984932
$340$		−	27996.3i		−	0.242183i
$341$	−196271.			−1.68790
$342$			64146.7i			0.548431i
$343$			80525.3i			0.684454i
$344$	31320.0			0.264671
$345$	97202.7			0.816658
$346$		−	27376.7i		−	0.228681i
$347$		−	54477.4i		−	0.452436i	−0.974077	−	0.226218i	$-0.927364\pi$
$347$		−	54477.4i		−	0.452436i	0.974077	−	0.226218i	$-0.0726362\pi$
$348$			36934.1i			0.304978i
$349$	158383.			1.30034			0.650170	−	0.759788i	$-0.274698\pi$
$349$	158383.			1.30034			0.650170	+	0.759788i	$0.274698\pi$
$350$	79.5804			0.000649636
$351$	751.520			0.00609995
$352$	−167313.			−1.35034
$353$		−	35006.6i		−	0.280931i	−0.990086	−	0.140466i	$-0.955140\pi$
$353$		−	35006.6i		−	0.280931i	0.990086	−	0.140466i	$-0.0448600\pi$
$354$	−158898.			−1.26798
$355$			135884.i			1.07823i
$356$	−21052.5			−0.166113
$357$	12692.3			0.0995869
$358$	−7161.66			−0.0558789
$359$	−242305.			−1.88007			−0.940035	−	0.341077i	$-0.889208\pi$
$359$	−242305.			−1.88007			−0.940035	+	0.341077i	$0.889208\pi$
$360$	−25745.6			−0.198654
$361$	102450.			0.786138
$362$		−	87676.5i		−	0.669062i
$363$			80199.5i			0.608637i
$364$	−794.448			−0.00599602
$365$		−	110482.i		−	0.829286i
$366$		−	125564.i		−	0.937351i
$367$			110007.i			0.816751i	0.912814	+	0.408375i	$0.133905\pi$
$367$			110007.i			0.816751i	−0.912814	+	0.408375i	$0.866095\pi$
$368$	−239571.			−1.76905
$369$			72315.9i			0.531106i
$370$	−211180.			−1.54259
$371$	−27200.0			−0.197616
$372$	−48509.4			−0.350542
$373$		−	154900.i		−	1.11336i	−0.830728	−	0.556679i	$-0.812075\pi$
$373$		−	154900.i		−	1.11336i	0.830728	−	0.556679i	$-0.187925\pi$
$374$	116020.			0.829446
$375$	81248.2			0.577765
$376$			143052.i			1.01185i
$377$		−	4615.80i		−	0.0324761i
$378$			12421.3i			0.0869330i
$379$		−	56316.9i		−	0.392067i	−0.980597	−	0.196033i	$-0.937194\pi$
$379$		−	56316.9i		−	0.392067i	0.980597	−	0.196033i	$-0.0628061\pi$
$380$		−	99422.8i		−	0.688523i
$381$		−	87768.4i		−	0.604628i
$382$	−305393.			−2.09282
$383$		−	189787.i		−	1.29380i	−0.762573	−	0.646902i	$-0.776064\pi$
$383$		−	189787.i		−	1.29380i	0.762573	−	0.646902i	$-0.223936\pi$
$384$	89630.3			0.607844
$385$		−	77895.1i		−	0.525519i
$386$			316626.i			2.12507i
$387$		−	22155.2i		−	0.147929i
$388$		−	104729.i		−	0.695668i
$389$	143598.			0.948965			0.474482	−	0.880265i	$-0.342635\pi$
$389$	143598.			0.948965			0.474482	+	0.880265i	$0.342635\pi$
$390$	−3424.13			−0.0225124
$391$	101730.			0.665419
$392$		−	79305.3i		−	0.516096i
$393$			96561.7i			0.625201i
$394$	−42153.0			−0.271541
$395$	146667.			0.940021
$396$			38624.5i			0.246305i
$397$	−50070.9			−0.317691			−0.158845	−	0.987303i	$-0.550777\pi$
$397$	−50070.9			−0.317691			−0.158845	+	0.987303i	$0.550777\pi$
$398$			212896.i			1.34400i
$399$	45073.7			0.283125
$400$	−287.574			−0.00179734
$401$			271893.i			1.69087i	0.534080	+	0.845434i	$0.320658\pi$
$401$			271893.i			1.69087i	−0.534080	+	0.845434i	$0.679342\pi$
$402$	86102.4	−	76024.3i	0.532799	−	0.470436i
$403$	6062.41			0.0373280
$404$			87289.5i			0.534810i
$405$			18211.9i			0.111031i
$406$	76291.2			0.462831
$407$		−	297705.i		−	1.79720i
$408$	−26944.7			−0.161865
$409$			4933.87i			0.0294945i	0.999891	+	0.0147473i	$0.00469437\pi$
$409$			4933.87i			0.0294945i	−0.999891	+	0.0147473i	$0.995306\pi$
$410$		−	329491.i		−	1.96009i
$411$	22927.3			0.135728
$412$	98002.3			0.577353
$413$			111652.i			0.654587i
$414$			99558.5i			0.580868i
$415$			295418.i			1.71530i
$416$	5167.96			0.0298629
$417$	−113251.			−0.651281
$418$	412018.			2.35811
$419$	−33507.8			−0.190862			−0.0954308	−	0.995436i	$-0.530423\pi$
$419$	−33507.8			−0.190862			−0.0954308	+	0.995436i	$0.530423\pi$
$420$		−	19252.2i		−	0.109139i
$421$	−19217.5			−0.108426			−0.0542129	−	0.998529i	$-0.517265\pi$
$421$	−19217.5			−0.108426			−0.0542129	+	0.998529i	$0.517265\pi$
$422$		−	117954.i		−	0.662349i
$423$	101192.			0.565542
$424$	57743.6			0.321197
$425$	122.114			0.000676061
$426$	−139177.			−0.766917
$427$	−88229.5			−0.483903
$428$	−167.491			−0.000914332
$429$		−	4827.06i		−	0.0262282i
$430$			100945.i			0.545943i
$431$	309047.			1.66368			0.831840	−	0.555016i	$-0.187288\pi$
$431$	309047.			1.66368			0.831840	+	0.555016i	$0.187288\pi$
$432$		−	44886.1i		−	0.240516i
$433$			269917.i			1.43964i	0.694159	+	0.719822i	$0.255776\pi$
$433$			269917.i			1.43964i	−0.694159	+	0.719822i	$0.744224\pi$
$434$			100201.i			0.531977i
$435$	111856.			0.591130
$436$			50171.8i			0.263929i
$437$	361271.			1.89178
$438$	113159.			0.589851
$439$	287298.			1.49075			0.745374	−	0.666646i	$-0.232271\pi$
$439$	287298.			1.49075			0.745374	+	0.666646i	$0.232271\pi$
$440$			165365.i			0.854160i
$441$	−56098.9			−0.288455
$442$	−3583.61			−0.0183432
$443$			159388.i			0.812171i	0.913835	+	0.406086i	$0.133107\pi$
$443$			159388.i			0.812171i	−0.913835	+	0.406086i	$0.866893\pi$
$444$		−	73579.3i		−	0.373241i
$445$			63758.3i			0.321971i
$446$			154439.i			0.776402i
$447$		−	100887.i		−	0.504918i
$448$		−	6619.67i		−	0.0329822i
$449$	−230738.			−1.14453			−0.572264	−	0.820069i	$-0.693935\pi$
$449$	−230738.			−1.14453			−0.572264	+	0.820069i	$0.693935\pi$
$450$			119.507i			0.000590158i
$451$	464489.			2.28361
$452$		−	179687.i		−	0.879510i
$453$			2006.20i			0.00977635i
$454$		−	105833.i		−	0.513464i
$455$			2406.02i			0.0116219i
$456$	−95688.1			−0.460181
$457$	91261.3			0.436973			0.218486	−	0.975840i	$-0.429888\pi$
$457$	91261.3			0.436973			0.218486	+	0.975840i	$0.429888\pi$
$458$	118494.			0.564893
$459$			19060.1i			0.0904691i
$460$		−	154309.i		−	0.729246i
$461$	206952.			0.973795			0.486897	−	0.873459i	$-0.338129\pi$
$461$	206952.			0.973795			0.486897	+	0.873459i	$0.338129\pi$
$462$	79782.9			0.373789
$463$		−	221619.i		−	1.03382i	−0.856040	−	0.516909i	$-0.827082\pi$
$463$		−	221619.i		−	1.03382i	0.856040	−	0.516909i	$-0.172918\pi$
$464$	−275688.			−1.28051
$465$			146913.i			0.679444i
$466$	−247160.			−1.13817
$467$	310465.			1.42357			0.711786	−	0.702397i	$-0.247887\pi$
$467$	310465.			1.42357			0.711786	+	0.702397i	$0.247887\pi$
$468$		−	1193.03i		−	0.00544704i
$469$	−53419.7	−	60501.3i	−0.242860	−	0.275055i
$470$	−461057.			−2.08718
$471$		−	27289.0i		−	0.123012i
$472$		−	237029.i		−	1.06394i
$473$	−142304.			−0.636055
$474$			150221.i			0.668614i
$475$	433.659			0.00192203
$476$		−	20148.9i		−	0.0889276i
$477$		−	40846.6i		−	0.179523i
$478$	−419487.			−1.83596
$479$	−314496.			−1.37071			−0.685353	−	0.728211i	$-0.740352\pi$
$479$	−314496.			−1.37071			−0.685353	+	0.728211i	$0.740352\pi$
$480$			125237.i			0.543564i
$481$			9195.49i			0.0397452i
$482$			82537.3i			0.355268i
$483$	69956.4			0.299870
$484$	127316.			0.543492
$485$	−317175.			−1.34839
$486$	−18653.3			−0.0789737
$487$		−	38902.8i		−	0.164030i	−0.996631	−	0.0820150i	$-0.973864\pi$
$487$		−	38902.8i		−	0.164030i	0.996631	−	0.0820150i	$-0.0261355\pi$
$488$	187305.			0.786518
$489$			98810.1i			0.413222i
$490$	255602.			1.06456
$491$	45700.5			0.189565			0.0947824	−	0.995498i	$-0.469784\pi$
$491$	45700.5			0.189565			0.0947824	+	0.995498i	$0.469784\pi$
$492$	114801.			0.474259
$493$	117066.			0.481657
$494$	−12726.4			−0.0521497
$495$	116976.			0.477405
$496$		−	362090.i		−	1.47181i
$497$			97795.1i			0.395917i
$498$	−302578.			−1.22005
$499$			109736.i			0.440704i	0.975420	+	0.220352i	$0.0707206\pi$
$499$			109736.i			0.440704i	−0.975420	+	0.220352i	$0.929279\pi$
$500$		−	128981.i		−	0.515924i
$501$			135298.i			0.539035i
$502$	239671.			0.951061
$503$		−	416659.i		−	1.64682i	−0.567450	−	0.823408i	$-0.692070\pi$
$503$		−	416659.i		−	1.64682i	0.567450	−	0.823408i	$-0.307930\pi$
$504$	−18529.0			−0.0729442
$505$	264360.			1.03660
$506$	639470.			2.49758
$507$		−	148258.i		−	0.576770i
$508$	−139332.			−0.539912
$509$	−181078.			−0.698924			−0.349462	−	0.936951i	$-0.613636\pi$
$509$	−181078.			−0.698924			−0.349462	+	0.936951i	$0.613636\pi$
$510$		−	86843.1i		−	0.333883i
$511$		−	79513.2i		−	0.304507i
$512$		−	113279.i		−	0.432125i
$513$			67687.8i			0.257203i
$514$		−	475659.i		−	1.80040i
$515$		−	296804.i		−	1.11907i
$516$	−35171.1			−0.132095
$517$		−	649961.i		−	2.43168i
$518$	−151986.			−0.566426
$519$		−	28888.0i		−	0.107246i
$520$		−	5107.80i		−	0.0188898i
$521$		−	219184.i		−	0.807482i	−0.914873	−	0.403741i	$-0.867710\pi$
$521$		−	219184.i		−	0.807482i	0.914873	−	0.403741i	$-0.132290\pi$
$522$			114567.i			0.420456i
$523$	−124276.			−0.454343			−0.227171	−	0.973855i	$-0.572948\pi$
$523$	−124276.			−0.454343			−0.227171	+	0.973855i	$0.572948\pi$
$524$	153291.			0.558283
$525$	83.9735			0.000304666
$526$		−	150897.i		−	0.545393i
$527$			153755.i			0.553616i
$528$	−288306.			−1.03416
$529$	280868.			1.00367
$530$			186108.i			0.662542i
$531$	−167670.			−0.594655
$532$		−	71554.2i		−	0.252820i
$533$	−14347.1			−0.0505022
$534$	−65303.6			−0.229010
$535$			507.254i			0.00177222i
$536$	113406.	+	128440.i	0.394736	+	0.447064i
$537$	−7557.01			−0.0262061
$538$			299711.i			1.03547i
$539$			360327.i			1.24028i
$540$	28911.2			0.0991469
$541$		−	188570.i		−	0.644286i	−0.946691	−	0.322143i	$-0.895597\pi$
$541$		−	188570.i		−	0.644286i	0.946691	−	0.322143i	$-0.104403\pi$
$542$	−572874.			−1.95012
$543$		−	92516.6i		−	0.313776i
$544$			131070.i			0.442900i
$545$	151947.			0.511564
$546$	−2464.33			−0.00826636
$547$		−	479551.i		−	1.60273i	−0.598176	−	0.801365i	$-0.704108\pi$
$547$		−	479551.i		−	1.60273i	0.598176	−	0.801365i	$-0.295892\pi$
$548$		−	36396.9i		−	0.121200i
$549$		−	132495.i		−	0.439598i
$550$	767.600			0.00253752
$551$	415735.			1.36935
$552$	−148512.			−0.487398
$553$	105556.			0.345168
$554$			349264.i			1.13798i
$555$	−222838.			−0.723442
$556$			179784.i			0.581571i
$557$	−496811.			−1.60133			−0.800665	−	0.599112i	$-0.795520\pi$
$557$	−496811.			−1.60133			−0.800665	+	0.599112i	$0.795520\pi$
$558$	−150473.			−0.483271
$559$	4395.48			0.0140664
$560$	143704.			0.458241
$561$	122424.			0.388993
$562$	−182565.			−0.578021
$563$			152188.i			0.480135i	0.970756	+	0.240067i	$0.0771696\pi$
$563$			152188.i			0.480135i	−0.970756	+	0.240067i	$0.922830\pi$
$564$		−	160641.i		−	0.505009i
$565$	−544191.			−1.70473
$566$			258623.i			0.807299i
$567$			13107.0i			0.0407698i
$568$		−	207612.i		−	0.643510i
$569$	102592.			0.316877			0.158439	−	0.987369i	$-0.449354\pi$
$569$	102592.			0.316877			0.158439	+	0.987369i	$0.449354\pi$
$570$		−	308404.i		−	0.949227i
$571$	−258790.			−0.793735			−0.396867	−	0.917876i	$-0.629903\pi$
$571$	−258790.			−0.793735			−0.396867	+	0.917876i	$0.629903\pi$
$572$	−7662.92			−0.0234208
$573$	−322252.			−0.981492
$574$		−	237133.i		−	0.719729i
$575$	673.058			0.00203571
$576$	9940.84			0.0299625
$577$		−	334969.i		−	1.00613i	−0.864249	−	0.503064i	$-0.832206\pi$
$577$		−	334969.i		−	1.00613i	0.864249	−	0.503064i	$-0.167794\pi$
$578$			320396.i			0.959027i
$579$			334105.i			0.996613i
$580$		−	177571.i		−	0.527858i
$581$			212611.i			0.629846i
$582$		−	324862.i		−	0.959077i
$583$	−262360.			−0.771900
$584$			168801.i			0.494935i
$585$	−3613.15			−0.0105578
$586$			212288.i			0.618201i
$587$		−	657461.i		−	1.90807i	−0.299697	−	0.954034i	$-0.596886\pi$
$587$		−	657461.i		−	1.90807i	0.299697	−	0.954034i	$-0.403114\pi$
$588$			89056.7i			0.257580i
$589$			546028.i			1.57393i
$590$	763947.			2.19462
$591$	−44480.0			−0.127347
$592$	549220.			1.56712
$593$			176065.i			0.500683i	0.968158	+	0.250342i	$0.0805429\pi$
$593$			176065.i			0.500683i	−0.968158	+	0.250342i	$0.919457\pi$
$594$			119811.i			0.339566i
$595$	−61021.7			−0.172366
$596$	−160158.			−0.450874
$597$			224648.i			0.630310i
$598$	−19751.9			−0.0552341
$599$		−	594559.i		−	1.65707i	−0.559935	−	0.828536i	$-0.689174\pi$
$599$		−	594559.i		−	1.65707i	0.559935	−	0.828536i	$-0.310826\pi$
$600$	−178.269			−0.000495193
$601$	393181.			1.08854			0.544269	−	0.838911i	$-0.316807\pi$
$601$	393181.			1.08854			0.544269	+	0.838911i	$0.316807\pi$
$602$			72649.6i			0.200466i
$603$	90855.6	−	80221.1i	0.249872	−	0.220625i
$604$	3184.82			0.00872994
$605$		−	385583.i		−	1.05343i
$606$			270767.i			0.737311i
$607$	25254.6			0.0685431			0.0342715	−	0.999413i	$-0.489089\pi$
$607$	25254.6			0.0685431			0.0342715	+	0.999413i	$0.489089\pi$
$608$			465467.i			1.25916i
$609$	80502.7			0.217058
$610$			603685.i			1.62237i
$611$			20076.0i			0.0537767i
$612$	30257.8			0.0807857
$613$	−203866.			−0.542531			−0.271266	−	0.962505i	$-0.587442\pi$
$613$	−203866.			−0.542531			−0.271266	+	0.962505i	$0.587442\pi$
$614$			63346.0i			0.168028i
$615$		−	347680.i		−	0.919241i
$616$			119013.i			0.313641i
$617$	−164578.			−0.432316			−0.216158	−	0.976358i	$-0.569353\pi$
$617$	−164578.			−0.432316			−0.216158	+	0.976358i	$0.569353\pi$
$618$	303997.			0.795963
$619$	−147024.			−0.383712			−0.191856	−	0.981423i	$-0.561451\pi$
$619$	−147024.			−0.383712			−0.191856	+	0.981423i	$0.561451\pi$
$620$	233223.			0.606719
$621$			105054.i			0.272415i
$622$	−360272.			−0.931214
$623$			45886.6i			0.118225i
$624$	8905.18			0.0228704
$625$	−390062.			−0.998560
$626$	376398.			0.960504
$627$	434763.			1.10590
$628$	−43321.1			−0.109845
$629$	−233217.			−0.589466
$630$		−	59719.2i		−	0.150464i
$631$			264972.i			0.665490i	0.943017	+	0.332745i	$0.107975\pi$
$631$			264972.i			0.665490i	−0.943017	+	0.332745i	$0.892025\pi$
$632$	−224087.			−0.561024
$633$		−	124465.i		−	0.310628i
$634$			643826.i			1.60173i
$635$			421972.i			1.04649i
$636$	−64843.7			−0.160307
$637$		−	11129.8i		−	0.0274288i
$638$	735874.			1.80785
$639$	−146860.			−0.359668
$640$	−430924.			−1.05206
$641$		−	11897.4i		−	0.0289559i	−0.999895	−	0.0144779i	$-0.995391\pi$
$641$		−	11897.4i		−	0.0289559i	0.999895	−	0.0144779i	$-0.00460863\pi$
$642$	−519.547			−0.00126054
$643$	478390.			1.15707			0.578536	−	0.815657i	$-0.303624\pi$
$643$	478390.			1.15707			0.578536	+	0.815657i	$0.303624\pi$
$644$		−	111055.i		−	0.267773i
$645$			106517.i			0.256036i
$646$		−	322768.i		−	0.773438i
$647$			124174.i			0.296635i	0.988940	+	0.148317i	$0.0473857\pi$
$647$			124174.i			0.296635i	−0.988940	+	0.148317i	$0.952614\pi$
$648$		−	27825.2i		−	0.0662657i
$649$			1.07695e6i			2.55686i
$650$	−23.7096			−5.61174e−5
$651$			105733.i			0.249486i
$652$	156860.			0.368993
$653$		−	396475.i		−	0.929800i	−0.885363	−	0.464900i	$-0.846090\pi$
$653$		−	396475.i		−	0.929800i	0.885363	−	0.464900i	$-0.153910\pi$
$654$			155630.i			0.363863i
$655$		−	464249.i		−	1.08210i
$656$			856912.i			1.99126i
$657$	119406.			0.276628
$658$	−331821.			−0.766394
$659$	185626.			0.427432			0.213716	−	0.976896i	$-0.431443\pi$
$659$	185626.			0.427432			0.213716	+	0.976896i	$0.431443\pi$
$660$		−	185699.i		−	0.426306i
$661$			337245.i			0.771867i	0.922527	+	0.385934i	$0.126121\pi$
$661$			337245.i			0.771867i	−0.922527	+	0.385934i	$0.873879\pi$
$662$	22419.3			0.0511572
$663$	−3781.44			−0.00860260
$664$		−	451358.i		−	1.02373i
$665$	−216705.			−0.490033
$666$		−	228239.i		−	0.514566i
$667$	645239.			1.45034
$668$	214785.			0.481339
$669$			162964.i			0.364117i
$670$	−413962.	+	365509.i	−0.922171	+	0.814233i
$671$	−851026.			−1.89016
$672$			90132.7i			0.199592i
$673$			100968.i			0.222922i	0.993769	+	0.111461i	$0.0355530\pi$
$673$			100968.i			0.222922i	−0.993769	+	0.111461i	$0.964447\pi$
$674$	−622158.			−1.36956
$675$			126.104i			0.000276772i
$676$	−235359.			−0.515036
$677$			663775.i			1.44825i	0.689669	+	0.724125i	$0.257756\pi$
$677$			663775.i			1.44825i	−0.689669	+	0.724125i	$0.742244\pi$
$678$		−	557380.i		−	1.21253i
$679$	−228270.			−0.495118
$680$	129545.			0.280157
$681$		−	111676.i		−	0.240804i
$682$			966499.i			2.07794i
$683$			495831.i			1.06290i	0.847090	+	0.531450i	$0.178353\pi$
$683$			495831.i			1.06290i	−0.847090	+	0.531450i	$0.821647\pi$
$684$	107454.			0.229673
$685$	−110230.			−0.234918
$686$	396532.			0.842616
$687$	125036.			0.264923
$688$		−	262529.i		−	0.554626i
$689$	8103.77			0.0170706
$690$		−	478656.i		−	1.00537i
$691$	610472.			1.27853			0.639263	−	0.768988i	$-0.279239\pi$
$691$	610472.			1.27853			0.639263	+	0.768988i	$0.279239\pi$
$692$	−45859.5			−0.0957673
$693$	84187.3			0.175299
$694$	−268264.			−0.556984
$695$	544485.			1.12724
$696$	−170901.			−0.352798
$697$		−	363873.i		−	0.749005i
$698$		−	779926.i		−	1.60082i
$699$	−260804.			−0.533778
$700$		−	133.307i		−	0.000272056i
$701$			227204.i			0.462359i	0.972911	+	0.231179i	$0.0742585\pi$
$701$			227204.i			0.462359i	−0.972911	+	0.231179i	$0.925742\pi$
$702$		−	3700.72i		−	0.00750952i
$703$	−828218.			−1.67585
$704$		−	63850.6i		−	0.128831i
$705$	−486509.			−0.978843
$706$	−172383.			−0.345848
$707$	190259.			0.380633
$708$			266174.i			0.531006i
$709$	−360589.			−0.717332			−0.358666	−	0.933466i	$-0.616768\pi$
$709$	−360589.			−0.717332			−0.358666	+	0.933466i	$0.616768\pi$
$710$	669134.			1.32738
$711$			158514.i			0.313566i
$712$		−	97413.9i		−	0.192159i
$713$			847459.i			1.66702i
$714$		−	62500.6i		−	0.122599i
$715$			23207.5i			0.0453959i
$716$			11996.7i			0.0234011i
$717$	−442644.			−0.861026
$718$			1.19319e6i			2.31451i
$719$	−385332.			−0.745380			−0.372690	−	0.927956i	$-0.621565\pi$
$719$	−385332.			−0.745380			−0.372690	+	0.927956i	$0.621565\pi$
$720$			215803.i			0.416286i
$721$		−	213609.i		−	0.410912i
$722$		−	504497.i		−	0.967798i
$723$			87093.6i			0.166613i
$724$	−146869.			−0.280191
$725$	774.525			0.00147353
$726$	394928.			0.749280
$727$			281282.i			0.532199i	0.963946	+	0.266099i	$0.0857349\pi$
$727$			281282.i			0.532199i	−0.963946	+	0.266099i	$0.914265\pi$
$728$		−	3676.07i		−	0.00693618i
$729$	−19683.0			−0.0370370
$730$	−544046.			−1.02092
$731$			111478.i			0.208620i
$732$	−210336.			−0.392546
$733$		−	873170.i		−	1.62514i	−0.582864	−	0.812570i	$-0.698068\pi$
$733$		−	873170.i		−	1.62514i	0.582864	−	0.812570i	$-0.301932\pi$
$734$	541710.			1.00548
$735$	269712.			0.499259
$736$			722425.i			1.33364i
$737$	−515265.	−	583571.i	−0.948628	−	1.07438i
$738$	356106.			0.653833
$739$		−	1.05931e6i		−	1.93969i	−0.243718	−	0.969846i	$-0.578367\pi$
$739$		−	1.05931e6i		−	1.93969i	0.243718	−	0.969846i	$-0.421633\pi$
$740$			353754.i			0.646008i
$741$	−13428.9			−0.0244571
$742$			133941.i			0.243280i
$743$	659842.			1.19526			0.597630	−	0.801772i	$-0.296109\pi$
$743$	659842.			1.19526			0.597630	+	0.801772i	$0.296109\pi$
$744$		−	224462.i		−	0.405506i
$745$			485044.i			0.873914i
$746$	−762778.			−1.37063
$747$	−319281.			−0.572180
$748$		−	194348.i		−	0.347357i
$749$			365.069i			0.000650745i
$750$		−	400091.i		−	0.711273i
$751$	648233.			1.14935			0.574674	−	0.818382i	$-0.305129\pi$
$751$	648233.			1.14935			0.574674	+	0.818382i	$0.305129\pi$
$752$	1.19908e6			2.12037
$753$	252902.			0.446028
$754$	−22729.6			−0.0399806
$755$		−	9645.37i		−	0.0169210i
$756$	20807.3			0.0364060
$757$		−	1.01395e6i		−	1.76940i	−0.466164	−	0.884699i	$-0.654364\pi$
$757$		−	1.01395e6i		−	1.76940i	0.466164	−	0.884699i	$-0.345636\pi$
$758$	−277322.			−0.482665
$759$	674771.			1.17131
$760$	460049.			0.796483
$761$	−236398.			−0.408201			−0.204101	−	0.978950i	$-0.565427\pi$
$761$	−236398.			−0.408201			−0.204101	+	0.978950i	$0.565427\pi$
$762$	−432199.			−0.744345
$763$	109356.			0.187842
$764$			511573.i			0.876438i
$765$		−	91637.1i		−	0.156584i
$766$	−934570.			−1.59277
$767$		−	33264.8i		−	0.0565451i
$768$		−	410758.i		−	0.696407i
$769$		−	229496.i		−	0.388080i	−0.980994	−	0.194040i	$-0.937841\pi$
$769$		−	229496.i		−	0.388080i	0.980994	−	0.194040i	$-0.0621592\pi$
$770$	−383580.			−0.646955
$771$		−	501917.i		−	0.844351i
$772$	530390.			0.889940
$773$	933143.			1.56167			0.780835	−	0.624737i	$-0.214794\pi$
$773$	933143.			1.56167			0.780835	+	0.624737i	$0.214794\pi$
$774$	−109099.			−0.182112
$775$			1017.26i			0.00169368i
$776$	484600.			0.804748
$777$	−160376.			−0.265642
$778$		−	707123.i		−	1.16825i
$779$		−	1.29222e6i		−	2.12941i
$780$			5735.85i			0.00942777i
$781$			943292.i			1.54648i
$782$		−	500950.i		−	0.819183i
$783$			120892.i			0.197185i
$784$	−664748.			−1.08150
$785$			131200.i			0.212909i
$786$	475500.			0.769672
$787$			966665.i			1.56073i	0.625327	+	0.780363i	$0.284966\pi$
$787$			966665.i			1.56073i	−0.625327	+	0.780363i	$0.715034\pi$
$788$			70611.7i			0.113717i
$789$		−	159227.i		−	0.255778i
$790$		−	722233.i		−	1.15724i
$791$	−391652.			−0.625962
$792$	−178723.			−0.284925
$793$	26286.5			0.0418009
$794$			246565.i			0.391102i
$795$			196382.i			0.310719i
$796$	356628.			0.562845
$797$	−992640.			−1.56270			−0.781349	−	0.624094i	$-0.785468\pi$
$797$	−992640.			−1.56270			−0.781349	+	0.624094i	$0.785468\pi$
$798$		−	221957.i		−	0.348549i
$799$	−509169.			−0.797569
$800$			867.177i			0.00135496i
$801$	−68908.6			−0.107401
$802$	1.33889e6			2.08159
$803$		−	766952.i		−	1.18943i
$804$	−127350.	−	144233.i	−0.197010	−	0.223127i
$805$	−336336.			−0.519017
$806$		−	29853.2i		−	0.0459537i
$807$			316257.i			0.485615i
$808$	−403906.			−0.618667
$809$			169217.i			0.258552i	0.991609	+	0.129276i	$0.0412653\pi$
$809$			169217.i			0.258552i	−0.991609	+	0.129276i	$0.958735\pi$
$810$	89681.0			0.136688
$811$		−	560746.i		−	0.852558i	−0.904592	−	0.426279i	$-0.859824\pi$
$811$		−	560746.i		−	0.852558i	0.904592	−	0.426279i	$-0.140176\pi$
$812$		−	127797.i		−	0.193825i
$813$	−604499.			−0.914565
$814$	−1.46599e6			−2.21250
$815$		−	475058.i		−	0.715207i
$816$			225854.i			0.339194i
$817$			395891.i			0.593105i
$818$	24295.9			0.0363100
$819$	−2600.37			−0.00387675
$820$	−551939.			−0.820850
$821$	−340701.			−0.505461			−0.252730	−	0.967537i	$-0.581329\pi$
$821$	−340701.			−0.505461			−0.252730	+	0.967537i	$0.581329\pi$
$822$		−	112901.i		−	0.167092i
$823$	−491653.			−0.725871			−0.362936	−	0.931814i	$-0.618225\pi$
$823$	−491653.			−0.725871			−0.362936	+	0.931814i	$0.618225\pi$
$824$			453476.i			0.667882i
$825$	809.975			0.00119005
$826$	549810.			0.805847
$827$	349917.			0.511628			0.255814	−	0.966726i	$-0.417657\pi$
$827$	349917.			0.511628			0.255814	+	0.966726i	$0.417657\pi$
$828$	166773.			0.243257
$829$	809510.			1.17791			0.588956	−	0.808165i	$-0.299539\pi$
$829$	809510.			1.17791			0.588956	+	0.808165i	$0.299539\pi$
$830$	1.45473e6			2.11167
$831$			368544.i			0.533688i
$832$			1972.22i			0.00284910i
$833$	282274.			0.406800
$834$			557681.i			0.801777i
$835$		−	650486.i		−	0.932964i
$836$		−	690183.i		−	0.987533i
$837$	−158780.			−0.226644
$838$			165003.i			0.234965i
$839$	−584420.			−0.830235			−0.415117	−	0.909768i	$-0.636259\pi$
$839$	−584420.			−0.830235			−0.415117	+	0.909768i	$0.636259\pi$
$840$	89083.6			0.126252
$841$	35231.2			0.0498121
$842$			94633.0i			0.133481i
$843$	−192643.			−0.271080
$844$	−197588.			−0.277380
$845$			712795.i			0.998277i
$846$		−	498300.i		−	0.696226i
$847$		−	277502.i		−	0.386812i
$848$		−	484014.i		−	0.673080i
$849$			272900.i			0.378607i
$850$		−	601.325i		−	0.000832284i
$851$	−1.28543e6			−1.77496
$852$			233139.i			0.321171i
$853$	170655.			0.234542			0.117271	−	0.993100i	$-0.462585\pi$
$853$	170655.			0.234542			0.117271	+	0.993100i	$0.462585\pi$
$854$			434470.i			0.595722i
$855$		−	325429.i		−	0.445168i
$856$		−	775.013i		−	0.00105770i
$857$			1.06994e6i			1.45679i	0.685156	+	0.728397i	$0.259734\pi$
$857$			1.06994e6i			1.45679i	−0.685156	+	0.728397i	$0.740266\pi$
$858$	−23770.0			−0.0322889
$859$	648235.			0.878509			0.439255	−	0.898363i	$-0.355243\pi$
$859$	648235.			0.878509			0.439255	+	0.898363i	$0.355243\pi$
$860$	169096.			0.228631
$861$		−	250224.i		−	0.337538i
$862$		−	1.52184e6i		−	2.04812i
$863$	−1.02864e6			−1.38115			−0.690576	−	0.723260i	$-0.742643\pi$
$863$	−1.02864e6			−1.38115			−0.690576	+	0.723260i	$0.742643\pi$
$864$	−135354.			−0.181318
$865$			138888.i			0.185623i
$866$	1.32916e6			1.77231
$867$			338083.i			0.449764i
$868$	167850.			0.222783
$869$	1.01815e6			1.34825
$870$		−	550816.i		−	0.727727i
$871$	15915.5	+	18025.3i	0.0209790	+	0.0237600i
$872$	−232155.			−0.305312
$873$		−	342796.i		−	0.449787i
$874$		−	1.77901e6i		−	2.32893i
$875$	−281131.			−0.367191
$876$		−	189556.i		−	0.247019i
$877$	−976035.			−1.26901			−0.634507	−	0.772917i	$-0.718797\pi$
$877$	−976035.			−1.26901			−0.634507	+	0.772917i	$0.718797\pi$
$878$		−	1.41475e6i		−	1.83523i
$879$			224007.i			0.289924i
$880$	1.38611e6			1.78992
$881$	1.11235e6			1.43315			0.716573	−	0.697512i	$-0.245710\pi$
$881$	1.11235e6			1.43315			0.716573	+	0.697512i	$0.245710\pi$
$882$			276249.i			0.355110i
$883$		−	209127.i		−	0.268218i	−0.990967	−	0.134109i	$-0.957183\pi$
$883$		−	209127.i		−	0.268218i	0.990967	−	0.134109i	$-0.0428173\pi$
$884$			6003.01i			0.00768182i
$885$	806120.			1.02923
$886$	784876.			0.999847
$887$	659151.			0.837795			0.418898	−	0.908033i	$-0.362417\pi$
$887$	659151.			0.837795			0.418898	+	0.908033i	$0.362417\pi$
$888$	340466.			0.431765
$889$			303692.i			0.384264i
$890$	313966.			0.396372
$891$			126425.i			0.159249i
$892$	258705.			0.325143
$893$	−1.80820e6			−2.26748
$894$	−496800.			−0.621593
$895$	36332.5			0.0453576
$896$	−310134.			−0.386308
$897$	−20842.3			−0.0259036
$898$			1.13623e6i			1.40900i
$899$			975218.i			1.20665i
$900$	200.189			0.000247147
$901$			205529.i			0.253176i
$902$		−	2.28729e6i		−	2.81131i
$903$			76660.1i			0.0940144i
$904$	831449.			1.01742
$905$			444800.i			0.543085i
$906$	9879.13			0.0120355
$907$	1.19999e6			1.45869			0.729343	−	0.684148i	$-0.239826\pi$
$907$	1.19999e6			1.45869			0.729343	+	0.684148i	$0.239826\pi$
$908$	−177284.			−0.215030
$909$			285714.i			0.345784i
$910$	11848.0			0.0143074
$911$	−842256.			−1.01486			−0.507432	−	0.861692i	$-0.669405\pi$
$911$	−842256.			−1.01486			−0.507432	+	0.861692i	$0.669405\pi$
$912$			802070.i			0.964324i
$913$			2.05076e6i			2.46022i
$914$		−	449399.i		−	0.537948i
$915$			637010.i			0.760859i
$916$		−	198493.i		−	0.236567i
$917$		−	334118.i		−	0.397339i
$918$	93858.0			0.111375
$919$			985723.i			1.16714i	0.812062	+	0.583571i	$0.198345\pi$
$919$			985723.i			1.16714i	−0.812062	+	0.583571i	$0.801655\pi$
$920$	714016.			0.843591
$921$			66842.9i			0.0788018i
$922$		−	1.01910e6i		−	1.19882i
$923$		−	29136.4i		−	0.0342005i
$924$		−	133647.i		−	0.156536i
$925$	−1542.99			−0.00180335
$926$	−1.09132e6			−1.27271
$927$	320779.			0.373290
$928$			831334.i			0.965339i
$929$		−	718636.i		−	0.832679i	−0.909209	−	0.416339i	$-0.863313\pi$
$929$		−	718636.i		−	0.832679i	0.909209	−	0.416339i	$-0.136687\pi$
$930$	723444.			0.836448
$931$	1.00243e6			1.15653
$932$			414025.i			0.476645i
$933$	−380160.			−0.436720
$934$		−	1.52883e6i		−	1.75253i
$935$	−588591.			−0.673271
$936$	5520.40			0.00630113
$937$		−	172001.i		−	0.195908i	−0.995191	−	0.0979541i	$-0.968770\pi$
$937$		−	172001.i		−	0.195908i	0.995191	−	0.0979541i	$-0.0312298\pi$
$938$	−297927.	+	263056.i	−0.338614	+	0.298980i
$939$	397177.			0.450456
$940$			772330.i			0.874072i
$941$			664755.i			0.750727i	0.926878	+	0.375364i	$0.122482\pi$
$941$			664755.i			0.750727i	−0.926878	+	0.375364i	$0.877518\pi$
$942$	−134380.			−0.151437
$943$		−	2.00557e6i		−	2.25536i
$944$	−1.98681e6			−2.22952
$945$		−	63015.9i		−	0.0705645i
$946$			700749.i			0.783033i
$947$	532317.			0.593568			0.296784	−	0.954945i	$-0.404086\pi$
$947$	532317.			0.593568			0.296784	+	0.954945i	$0.404086\pi$
$948$	251640.			0.280003
$949$			23689.6i			0.0263042i
$950$		−	2135.47i		−	0.00236617i
$951$			679368.i			0.751180i
$952$	93232.7			0.102871
$953$	1.23655e6			1.36153			0.680763	−	0.732503i	$-0.261648\pi$
$953$	1.23655e6			1.36153			0.680763	+	0.732503i	$0.261648\pi$
$954$	−201141.			−0.221006
$955$	1.54932e6			1.69877
$956$			702694.i			0.768866i
$957$	776496.			0.847843
$958$			1.54868e6i			1.68745i
$959$	−79331.8			−0.0862601
$960$	−47793.5			−0.0518593
$961$	−357334.			−0.386926
$962$	45281.5			0.0489295
$963$	−548.228			−0.000591165
$964$	138261.			0.148780
$965$		−	1.60631e6i		−	1.72494i
$966$		−	344487.i		−	0.369164i
$967$	282095.			0.301677			0.150838	−	0.988558i	$-0.451803\pi$
$967$	282095.			0.301677			0.150838	+	0.988558i	$0.451803\pi$
$968$			589117.i			0.628711i
$969$		−	340586.i		−	0.362726i
$970$			1.56187e6i			1.65997i
$971$	553504.			0.587060			0.293530	−	0.955950i	$-0.405170\pi$
$971$	553504.			0.587060			0.293530	+	0.955950i	$0.405170\pi$
$972$			31246.6i			0.0330728i
$973$	391864.			0.413913
$974$	−191570.			−0.201934
$975$	−25.0185			−2.63179e−5
$976$		−	1.57001e6i		−	1.64818i
$977$	1.44241e6			1.51112			0.755562	−	0.655077i	$-0.227364\pi$
$977$	1.44241e6			1.51112			0.755562	+	0.655077i	$0.227364\pi$
$978$	486572.			0.508709
$979$			442604.i			0.461796i
$980$		−	428166.i		−	0.445820i
$981$			164221.i			0.170644i
$982$		−	225044.i		−	0.233369i
$983$			1.35825e6i			1.40564i	0.711368	+	0.702820i	$0.248076\pi$
$983$			1.35825e6i			1.40564i	−0.711368	+	0.702820i	$0.751924\pi$
$984$			531207.i			0.548622i
$985$	213851.			0.220413
$986$		−	576471.i		−	0.592958i
$987$	−350139.			−0.359423
$988$			21318.3i			0.0218393i
$989$			614440.i			0.628184i
$990$		−	576027.i		−	0.587722i
$991$		−	208295.i		−	0.212095i	−0.994361	−	0.106048i	$-0.966180\pi$
$991$		−	208295.i		−	0.212095i	0.994361	−	0.106048i	$-0.0338196\pi$
$992$	−1.09188e6			−1.10956
$993$	23656.9			0.0239917
$994$	481574.			0.487405
$995$		−	1.08006e6i		−	1.09094i
$996$			506857.i			0.510936i
$997$	19481.9			0.0195993			0.00979966	−	0.999952i	$-0.496881\pi$
$997$	19481.9			0.0195993			0.00979966	+	0.999952i	$0.496881\pi$
$998$	540373.			0.542541
$999$		−	240838.i		−	0.241321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.12	✓	46
67.66	odd	2	inner	201.5.b.a.133.35	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.12	✓	46	1.1	even	1	trivial
201.5.b.a.133.35	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)

\(f(q)\)	\(=\)	\(q-4.92431i q^{2} -5.19615i q^{3} -8.24886 q^{4} +24.9820i q^{5} -25.5875 q^{6} +17.9795i q^{7} -38.1691i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-4.92431i q^{2} -5.19615i q^{3} -8.24886 q^{4} +24.9820i q^{5} -25.5875 q^{6} +17.9795i q^{7} -38.1691i q^{8} -27.0000 q^{9} +123.019 q^{10} +173.423i q^{11} +42.8623i q^{12} -5.35667i q^{13} +88.5365 q^{14} +129.810 q^{15} -319.938 q^{16} +135.856 q^{17} +132.956i q^{18} +482.464 q^{19} -206.073i q^{20} +93.4240 q^{21} +853.987 q^{22} +748.805 q^{23} -198.332 q^{24} +0.898843 q^{25} -26.3779 q^{26} +140.296i q^{27} -148.310i q^{28} +861.691 q^{29} -639.227i q^{30} +1131.75i q^{31} +964.770i q^{32} +901.130 q^{33} -668.999i q^{34} -449.163 q^{35} +222.719 q^{36} -1716.64 q^{37} -2375.80i q^{38} -27.8341 q^{39} +953.540 q^{40} -2678.37i q^{41} -460.049i q^{42} +820.561i q^{43} -1430.54i q^{44} -674.514i q^{45} -3687.35i q^{46} -3747.85 q^{47} +1662.45i q^{48} +2077.74 q^{49} -4.42618i q^{50} -705.931i q^{51} +44.1864i q^{52} +1512.84i q^{53} +690.862 q^{54} -4332.45 q^{55} +686.259 q^{56} -2506.96i q^{57} -4243.24i q^{58} +6209.98 q^{59} -1070.79 q^{60} +4907.24i q^{61} +5573.09 q^{62} -485.446i q^{63} -368.179 q^{64} +133.820 q^{65} -4437.45i q^{66} +(-3365.02 + 2971.15i) q^{67} -1120.66 q^{68} -3890.91i q^{69} +2211.82i q^{70} +5439.27 q^{71} +1030.56i q^{72} -4422.45 q^{73} +8453.29i q^{74} -4.67052i q^{75} -3979.77 q^{76} -3118.05 q^{77} +137.064i q^{78} -5870.90i q^{79} -7992.70i q^{80} +729.000 q^{81} -13189.1 q^{82} +11825.2 q^{83} -770.641 q^{84} +3393.97i q^{85} +4040.70 q^{86} -4477.48i q^{87} +6619.38 q^{88} +2552.17 q^{89} -3321.52 q^{90} +96.3101 q^{91} -6176.79 q^{92} +5880.74 q^{93} +18455.6i q^{94} +12052.9i q^{95} +5013.09 q^{96} +12696.1i q^{97} -10231.4i q^{98} -4682.41i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 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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