LMFDB - Embedded newform 201.5.b.a.133.20

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			133.20
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.39569i q^{2} -5.19615i q^{3} +14.0521 q^{4} -17.8182i q^{5} -7.25221 q^{6} -70.8079i q^{7} -41.9433i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-1.39569i q^{2} -5.19615i q^{3} +14.0521 q^{4} -17.8182i q^{5} -7.25221 q^{6} -70.8079i q^{7} -41.9433i q^{8} -27.0000 q^{9} -24.8687 q^{10} -59.5504i q^{11} -73.0166i q^{12} +138.470i q^{13} -98.8259 q^{14} -92.5860 q^{15} +166.293 q^{16} -130.643 q^{17} +37.6836i q^{18} -343.962 q^{19} -250.382i q^{20} -367.929 q^{21} -83.1139 q^{22} +731.541 q^{23} -217.944 q^{24} +307.512 q^{25} +193.261 q^{26} +140.296i q^{27} -994.997i q^{28} -368.058 q^{29} +129.221i q^{30} +574.950i q^{31} -903.187i q^{32} -309.433 q^{33} +182.336i q^{34} -1261.67 q^{35} -379.405 q^{36} -425.221 q^{37} +480.064i q^{38} +719.509 q^{39} -747.354 q^{40} -2266.40i q^{41} +513.514i q^{42} +3233.83i q^{43} -836.805i q^{44} +481.091i q^{45} -1021.00i q^{46} -2958.96 q^{47} -864.084i q^{48} -2612.76 q^{49} -429.191i q^{50} +678.839i q^{51} +1945.78i q^{52} -1575.15i q^{53} +195.810 q^{54} -1061.08 q^{55} -2969.92 q^{56} +1787.28i q^{57} +513.695i q^{58} -3488.61 q^{59} -1301.02 q^{60} -3764.53i q^{61} +802.451 q^{62} +1911.81i q^{63} +1400.12 q^{64} +2467.28 q^{65} +431.872i q^{66} +(-1398.17 - 4265.71i) q^{67} -1835.80 q^{68} -3801.20i q^{69} +1760.90i q^{70} +2995.55 q^{71} +1132.47i q^{72} +8192.86 q^{73} +593.477i q^{74} -1597.88i q^{75} -4833.37 q^{76} -4216.64 q^{77} -1004.21i q^{78} +2426.32i q^{79} -2963.04i q^{80} +729.000 q^{81} -3163.19 q^{82} +6692.92 q^{83} -5170.15 q^{84} +2327.81i q^{85} +4513.43 q^{86} +1912.49i q^{87} -2497.74 q^{88} +6225.82 q^{89} +671.454 q^{90} +9804.74 q^{91} +10279.7 q^{92} +2987.53 q^{93} +4129.78i q^{94} +6128.78i q^{95} -4693.09 q^{96} +8167.16i q^{97} +3646.61i q^{98} +1607.86i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.39569i		−	0.348922i	−0.984664	−	0.174461i	$-0.944182\pi$
$2$		−	1.39569i		−	0.348922i	0.984664	−	0.174461i	$-0.0558183\pi$
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	14.0521			0.878253
$5$		−	17.8182i		−	0.712728i	−0.934347	−	0.356364i	$-0.884016\pi$
$5$		−	17.8182i		−	0.712728i	0.934347	−	0.356364i	$-0.115984\pi$
$6$	−7.25221			−0.201450
$7$		−	70.8079i		−	1.44506i	−0.691340	−	0.722530i	$-0.742979\pi$
$7$		−	70.8079i		−	1.44506i	0.691340	−	0.722530i	$-0.257021\pi$
$8$		−	41.9433i		−	0.655364i
$9$	−27.0000			−0.333333
$10$	−24.8687			−0.248687
$11$		−	59.5504i		−	0.492152i	−0.969251	−	0.246076i	$-0.920859\pi$
$11$		−	59.5504i		−	0.492152i	0.969251	−	0.246076i	$-0.0791413\pi$
$12$		−	73.0166i		−	0.507060i
$13$			138.470i			0.819347i	0.912232	+	0.409673i	$0.134357\pi$
$13$			138.470i			0.819347i	−0.912232	+	0.409673i	$0.865643\pi$
$14$	−98.8259			−0.504214
$15$	−92.5860			−0.411493
$16$	166.293			0.649582
$17$	−130.643			−0.452050			−0.226025	−	0.974121i	$-0.572573\pi$
$17$	−130.643			−0.452050			−0.226025	+	0.974121i	$0.572573\pi$
$18$			37.6836i			0.116307i
$19$	−343.962			−0.952803			−0.476402	−	0.879228i	$-0.658059\pi$
$19$	−343.962			−0.952803			−0.476402	+	0.879228i	$0.658059\pi$
$20$		−	250.382i		−	0.625955i
$21$	−367.929			−0.834306
$22$	−83.1139			−0.171723
$23$	731.541			1.38288			0.691438	−	0.722436i	$-0.256978\pi$
$23$	731.541			1.38288			0.691438	+	0.722436i	$0.256978\pi$
$24$	−217.944			−0.378375
$25$	307.512			0.492020
$26$	193.261			0.285888
$27$			140.296i			0.192450i
$28$		−	994.997i		−	1.26913i
$29$	−368.058			−0.437644			−0.218822	−	0.975765i	$-0.570221\pi$
$29$	−368.058			−0.437644			−0.218822	+	0.975765i	$0.570221\pi$
$30$			129.221i			0.143579i
$31$			574.950i			0.598283i	0.954209	+	0.299141i	$0.0967003\pi$
$31$			574.950i			0.598283i	−0.954209	+	0.299141i	$0.903300\pi$
$32$		−	903.187i		−	0.882018i
$33$	−309.433			−0.284144
$34$			182.336i			0.157730i
$35$	−1261.67			−1.02993
$36$	−379.405			−0.292751
$37$	−425.221			−0.310607			−0.155304	−	0.987867i	$-0.549636\pi$
$37$	−425.221			−0.310607			−0.155304	+	0.987867i	$0.549636\pi$
$38$			480.064i			0.332454i
$39$	719.509			0.473050
$40$	−747.354			−0.467096
$41$		−	2266.40i		−	1.34825i	−0.738619	−	0.674123i	$-0.764522\pi$
$41$		−	2266.40i		−	1.34825i	0.738619	−	0.674123i	$-0.235478\pi$
$42$			513.514i			0.291108i
$43$			3233.83i			1.74896i	0.485059	+	0.874482i	$0.338798\pi$
$43$			3233.83i			1.74896i	−0.485059	+	0.874482i	$0.661202\pi$
$44$		−	836.805i		−	0.432234i
$45$			481.091i			0.237576i
$46$		−	1021.00i		−	0.482516i
$47$	−2958.96			−1.33950			−0.669750	−	0.742586i	$-0.733599\pi$
$47$	−2958.96			−1.33950			−0.669750	+	0.742586i	$0.733599\pi$
$48$		−	864.084i		−	0.375036i
$49$	−2612.76			−1.08820
$50$		−	429.191i		−	0.171677i
$51$			678.839i			0.260991i
$52$			1945.78i			0.719594i
$53$		−	1575.15i		−	0.560752i	−0.959890	−	0.280376i	$-0.909541\pi$
$53$		−	1575.15i		−	0.560752i	0.959890	−	0.280376i	$-0.0904592\pi$
$54$	195.810			0.0671501
$55$	−1061.08			−0.350770
$56$	−2969.92			−0.947041
$57$			1787.28i			0.550101i
$58$			513.695i			0.152704i
$59$	−3488.61			−1.00219			−0.501093	−	0.865393i	$-0.667069\pi$
$59$	−3488.61			−1.00219			−0.501093	+	0.865393i	$0.667069\pi$
$60$	−1301.02			−0.361395
$61$		−	3764.53i		−	1.01170i	−0.862622	−	0.505850i	$-0.831179\pi$
$61$		−	3764.53i		−	1.01170i	0.862622	−	0.505850i	$-0.168821\pi$
$62$	802.451			0.208754
$63$			1911.81i			0.481687i
$64$	1400.12			0.341826
$65$	2467.28			0.583971
$66$			431.872i			0.0991443i
$67$	−1398.17	−	4265.71i	−0.311466	−	0.950257i
$67$	−1398.17	−	4265.71i	−0.311466	−	0.950257i
$68$	−1835.80			−0.397015
$69$		−	3801.20i		−	0.798404i
$70$			1760.90i			0.359367i
$71$	2995.55			0.594236			0.297118	−	0.954841i	$-0.403974\pi$
$71$	2995.55			0.594236			0.297118	+	0.954841i	$0.403974\pi$
$72$			1132.47i			0.218455i
$73$	8192.86			1.53741			0.768705	−	0.639604i	$-0.220902\pi$
$73$	8192.86			1.53741			0.768705	+	0.639604i	$0.220902\pi$
$74$			593.477i			0.108378i
$75$		−	1597.88i		−	0.284068i
$76$	−4833.37			−0.836803
$77$	−4216.64			−0.711189
$78$		−	1004.21i		−	0.165058i
$79$			2426.32i			0.388770i	0.980925	+	0.194385i	$0.0622712\pi$
$79$			2426.32i			0.388770i	−0.980925	+	0.194385i	$0.937729\pi$
$80$		−	2963.04i		−	0.462975i
$81$	729.000			0.111111
$82$	−3163.19			−0.470433
$83$	6692.92			0.971538			0.485769	−	0.874087i	$-0.338540\pi$
$83$	6692.92			0.971538			0.485769	+	0.874087i	$0.338540\pi$
$84$	−5170.15			−0.732732
$85$			2327.81i			0.322189i
$86$	4513.43			0.610252
$87$			1912.49i			0.252674i
$88$	−2497.74			−0.322539
$89$	6225.82			0.785989			0.392994	−	0.919541i	$-0.371439\pi$
$89$	6225.82			0.785989			0.392994	+	0.919541i	$0.371439\pi$
$90$	671.454			0.0828955
$91$	9804.74			1.18400
$92$	10279.7			1.21452
$93$	2987.53			0.345419
$94$			4129.78i			0.467382i
$95$			6128.78i			0.679089i
$96$	−4693.09			−0.509233
$97$			8167.16i			0.868016i	0.900909	+	0.434008i	$0.142901\pi$
$97$			8167.16i			0.868016i	−0.900909	+	0.434008i	$0.857099\pi$
$98$			3646.61i			0.379697i
$99$			1607.86i			0.164051i
$100$	4321.18			0.432118
$101$		−	17668.8i		−	1.73206i	−0.499990	−	0.866031i	$-0.666663\pi$
$101$		−	17668.8i		−	1.73206i	0.499990	−	0.866031i	$-0.333337\pi$
$102$	947.448			0.0910657
$103$	−6248.19			−0.588952			−0.294476	−	0.955659i	$-0.595145\pi$
$103$	−6248.19			−0.588952			−0.294476	+	0.955659i	$0.595145\pi$
$104$	5807.87			0.536971
$105$			6555.82i			0.594633i
$106$	−2198.42			−0.195659
$107$	1612.55			0.140846			0.0704230	−	0.997517i	$-0.477565\pi$
$107$	1612.55			0.140846			0.0704230	+	0.997517i	$0.477565\pi$
$108$			1971.45i			0.169020i
$109$			6508.84i			0.547836i	0.961753	+	0.273918i	$0.0883197\pi$
$109$			6508.84i			0.547836i	−0.961753	+	0.273918i	$0.911680\pi$
$110$			1480.94i			0.122392i
$111$			2209.51i			0.179329i
$112$		−	11774.9i		−	0.938685i
$113$		−	12048.3i		−	0.943559i	−0.881716	−	0.471780i	$-0.843612\pi$
$113$		−	12048.3i		−	0.943559i	0.881716	−	0.471780i	$-0.156388\pi$
$114$	2494.49			0.191943
$115$		−	13034.7i		−	0.985614i
$116$	−5171.97			−0.384362
$117$		−	3738.68i		−	0.273116i
$118$			4869.02i			0.349685i
$119$			9250.53i			0.653240i
$120$			3883.37i			0.269678i
$121$	11094.7			0.757786
$122$	−5254.12			−0.353004
$123$	−11776.6			−0.778410
$124$			8079.23i			0.525444i
$125$		−	16615.7i		−	1.06340i
$126$	2668.30			0.168071
$127$	19847.9			1.23057			0.615287	−	0.788303i	$-0.289040\pi$
$127$	19847.9			1.23057			0.615287	+	0.788303i	$0.289040\pi$
$128$		−	16405.1i		−	1.00129i
$129$	16803.5			1.00976
$130$		−	3443.55i		−	0.203760i
$131$	14150.4			0.824567			0.412284	−	0.911056i	$-0.364731\pi$
$131$	14150.4			0.824567			0.412284	+	0.911056i	$0.364731\pi$
$132$	−4348.17			−0.249551
$133$			24355.2i			1.37686i
$134$	−5953.60	+	1951.41i	−0.331566	+	0.108677i
$135$	2499.82			0.137164
$136$			5479.58i			0.296258i
$137$			12782.1i			0.681024i	0.940240	+	0.340512i	$0.110600\pi$
$137$			12782.1i			0.681024i	−0.940240	+	0.340512i	$0.889400\pi$
$138$	−5305.29			−0.278581
$139$			18261.4i			0.945156i	0.881289	+	0.472578i	$0.156677\pi$
$139$			18261.4i			0.945156i	−0.881289	+	0.472578i	$0.843323\pi$
$140$	−17729.0			−0.904543
$141$			15375.2i			0.773361i
$142$		−	4180.85i		−	0.207342i
$143$	8245.92			0.403243
$144$	−4489.91			−0.216527
$145$			6558.13i			0.311921i
$146$		−	11434.7i		−	0.536437i
$147$			13576.3i			0.628271i
$148$	−5975.23			−0.272792
$149$	22548.6			1.01566			0.507828	−	0.861459i	$-0.330449\pi$
$149$	22548.6			1.01566			0.507828	+	0.861459i	$0.330449\pi$
$150$	−2230.14			−0.0991175
$151$	23149.7			1.01529			0.507646	−	0.861566i	$-0.330516\pi$
$151$	23149.7			1.01529			0.507646	+	0.861566i	$0.330516\pi$
$152$			14426.9i			0.624433i
$153$	3527.35			0.150683
$154$			5885.12i			0.248150i
$155$	10244.6			0.426413
$156$	10110.6			0.415458
$157$	−20900.2			−0.847914			−0.423957	−	0.905682i	$-0.639359\pi$
$157$	−20900.2			−0.847914			−0.423957	+	0.905682i	$0.639359\pi$
$158$	3386.38			0.135651
$159$	−8184.73			−0.323750
$160$	−16093.1			−0.628639
$161$		−	51798.9i		−	1.99834i
$162$		−	1017.46i		−	0.0387691i
$163$	−17548.9			−0.660502			−0.330251	−	0.943893i	$-0.607133\pi$
$163$	−17548.9			−0.660502			−0.330251	+	0.943893i	$0.607133\pi$
$164$		−	31847.6i		−	1.18410i
$165$			5513.54i			0.202517i
$166$		−	9341.24i		−	0.338991i
$167$	29872.8			1.07113			0.535567	−	0.844493i	$-0.320098\pi$
$167$	29872.8			1.07113			0.535567	+	0.844493i	$0.320098\pi$
$168$			15432.2i			0.546774i
$169$	9387.18			0.328671
$170$	3248.90			0.112419
$171$	9286.97			0.317601
$172$			45442.0i			1.53603i
$173$	−15791.3			−0.527624			−0.263812	−	0.964574i	$-0.584980\pi$
$173$	−15791.3			−0.527624			−0.263812	+	0.964574i	$0.584980\pi$
$174$	2669.24			0.0881635
$175$		−	21774.3i		−	0.710998i
$176$		−	9902.82i		−	0.319693i
$177$			18127.4i			0.578613i
$178$		−	8689.31i		−	0.274249i
$179$		−	50797.1i		−	1.58538i	−0.609625	−	0.792690i	$-0.708680\pi$
$179$		−	50797.1i		−	1.58538i	0.609625	−	0.792690i	$-0.291320\pi$
$180$			6760.32i			0.208652i
$181$	25169.1			0.768264			0.384132	−	0.923278i	$-0.374501\pi$
$181$	25169.1			0.768264			0.384132	+	0.923278i	$0.374501\pi$
$182$		−	13684.4i		−	0.413126i
$183$	−19561.1			−0.584105
$184$		−	30683.3i		−	0.906288i
$185$			7576.67i			0.221378i
$186$		−	4169.66i		−	0.120524i
$187$			7779.82i			0.222478i
$188$	−41579.4			−1.17642
$189$	9934.08			0.278102
$190$	8553.87			0.236949
$191$			10861.1i			0.297719i	0.988858	+	0.148860i	$0.0475602\pi$
$191$			10861.1i			0.297719i	−0.988858	+	0.148860i	$0.952440\pi$
$192$		−	7275.24i		−	0.197353i
$193$	−8537.40			−0.229198			−0.114599	−	0.993412i	$-0.536558\pi$
$193$	−8537.40			−0.229198			−0.114599	+	0.993412i	$0.536558\pi$
$194$	11398.8			0.302870
$195$		−	12820.3i		−	0.337156i
$196$	−36714.7			−0.955713
$197$			45225.9i			1.16535i	0.812706	+	0.582673i	$0.197993\pi$
$197$			45225.9i			1.16535i	−0.812706	+	0.582673i	$0.802007\pi$
$198$	2244.07			0.0572410
$199$	−33559.2			−0.847433			−0.423717	−	0.905795i	$-0.639275\pi$
$199$	−33559.2			−0.847433			−0.423717	+	0.905795i	$0.639275\pi$
$200$		−	12898.1i		−	0.322452i
$201$	−22165.3	+	7265.11i	−0.548631	+	0.179825i
$202$	−24660.1			−0.604355
$203$			26061.4i			0.632421i
$204$			9539.07i			0.229217i
$205$	−40383.2			−0.960932
$206$			8720.53i			0.205498i
$207$	−19751.6			−0.460959
$208$			23026.5i			0.532233i
$209$			20483.1i			0.468924i
$210$	9149.89			0.207481
$211$	−54076.4			−1.21463			−0.607314	−	0.794462i	$-0.707753\pi$
$211$	−54076.4			−1.21463			−0.607314	+	0.794462i	$0.707753\pi$
$212$		−	22134.1i		−	0.492482i
$213$		−	15565.3i		−	0.343083i
$214$		−	2250.61i		−	0.0491443i
$215$	57621.0			1.24653
$216$	5884.49			0.126125
$217$	40711.0			0.864555
$218$	9084.32			0.191152
$219$		−	42571.3i		−	0.887624i
$220$	−14910.4			−0.308065
$221$		−	18090.0i		−	0.370386i
$222$	3083.80			0.0625720
$223$	−91119.0			−1.83231			−0.916156	−	0.400822i	$-0.868725\pi$
$223$	−91119.0			−1.83231			−0.916156	+	0.400822i	$0.868725\pi$
$224$	−63952.8			−1.27457
$225$	−8302.83			−0.164007
$226$	−16815.7			−0.329229
$227$	−15182.1			−0.294632			−0.147316	−	0.989089i	$-0.547063\pi$
$227$	−15182.1			−0.294632			−0.147316	+	0.989089i	$0.547063\pi$
$228$			25114.9i			0.483128i
$229$		−	56463.8i		−	1.07671i	−0.842718	−	0.538355i	$-0.819046\pi$
$229$		−	56463.8i		−	1.07671i	0.842718	−	0.538355i	$-0.180954\pi$
$230$	−18192.4			−0.343903
$231$			21910.3i			0.410605i
$232$			15437.6i			0.286816i
$233$			63893.1i			1.17691i	0.808531	+	0.588453i	$0.200263\pi$
$233$			63893.1i			1.17691i	−0.808531	+	0.588453i	$0.799737\pi$
$234$	−5218.03			−0.0952961
$235$			52723.3i			0.954699i
$236$	−49022.1			−0.880173
$237$	12607.5			0.224457
$238$	12910.9			0.227930
$239$		−	42186.9i		−	0.738554i	−0.929319	−	0.369277i	$-0.879605\pi$
$239$		−	42186.9i		−	0.738554i	0.929319	−	0.369277i	$-0.120395\pi$
$240$	−15396.4			−0.267299
$241$	109240.			1.88083			0.940413	−	0.340035i	$-0.110439\pi$
$241$	109240.			1.88083			0.940413	+	0.340035i	$0.110439\pi$
$242$		−	15484.8i		−	0.264409i
$243$		−	3788.00i		−	0.0641500i
$244$		−	52899.4i		−	0.888528i
$245$			46554.7i			0.775589i
$246$			16436.4i			0.271605i
$247$		−	47628.3i		−	0.780676i
$248$	24115.3			0.392093
$249$		−	34777.5i		−	0.560918i
$250$	−23190.3			−0.371045
$251$			42810.9i			0.679527i	0.940511	+	0.339764i	$0.110347\pi$
$251$			42810.9i			0.679527i	−0.940511	+	0.339764i	$0.889653\pi$
$252$			26864.9i			0.423043i
$253$		−	43563.6i		−	0.680585i
$254$		−	27701.6i		−	0.429375i
$255$	12095.7			0.186016
$256$	−494.526			−0.00754588
$257$	−82044.4			−1.24217			−0.621087	−	0.783742i	$-0.713309\pi$
$257$	−82044.4			−1.24217			−0.621087	+	0.783742i	$0.713309\pi$
$258$		−	23452.4i		−	0.352329i
$259$			30109.0i			0.448846i
$260$	34670.3			0.512874
$261$	9937.57			0.145881
$262$		−	19749.6i		−	0.287710i
$263$	31303.1			0.452560			0.226280	−	0.974062i	$-0.427344\pi$
$263$	31303.1			0.452560			0.226280	+	0.974062i	$0.427344\pi$
$264$			12978.7i			0.186218i
$265$	−28066.4			−0.399663
$266$	33992.3			0.480416
$267$		−	32350.3i		−	0.453791i
$268$	−19647.2	−	59941.9i	−0.273546	−	0.834567i
$269$	16380.0			0.226365			0.113183	−	0.993574i	$-0.463895\pi$
$269$	16380.0			0.226365			0.113183	+	0.993574i	$0.463895\pi$
$270$		−	3488.98i		−	0.0478597i
$271$		−	24676.9i		−	0.336010i	−0.985786	−	0.168005i	$-0.946267\pi$
$271$		−	24676.9i		−	0.336010i	0.985786	−	0.168005i	$-0.0537325\pi$
$272$	−21724.9			−0.293644
$273$		−	50946.9i		−	0.683586i
$274$	17839.9			0.237624
$275$		−	18312.5i		−	0.242148i
$276$		−	53414.7i		−	0.701201i
$277$	87950.4			1.14625			0.573123	−	0.819469i	$-0.305732\pi$
$277$	87950.4			1.14625			0.573123	+	0.819469i	$0.305732\pi$
$278$	25487.2			0.329786
$279$		−	15523.6i		−	0.199428i
$280$			52918.6i			0.674982i
$281$			18033.9i			0.228390i	0.993458	+	0.114195i	$0.0364289\pi$
$281$			18033.9i			0.228390i	−0.993458	+	0.114195i	$0.963571\pi$
$282$	21459.0			0.269843
$283$	44618.5			0.557112			0.278556	−	0.960420i	$-0.410144\pi$
$283$	44618.5			0.557112			0.278556	+	0.960420i	$0.410144\pi$
$284$	42093.6			0.521890
$285$	31846.1			0.392072
$286$		−	11508.7i		−	0.140701i
$287$	−160479.			−1.94830
$288$			24386.0i			0.294006i
$289$	−66453.5			−0.795651
$290$	9153.11			0.108836
$291$	42437.8			0.501149
$292$	115126.			1.35024
$293$	21766.2			0.253541			0.126770	−	0.991932i	$-0.459539\pi$
$293$	21766.2			0.253541			0.126770	+	0.991932i	$0.459539\pi$
$294$	18948.3			0.219218
$295$			62160.7i			0.714286i
$296$			17835.2i			0.203561i
$297$	8354.69			0.0947147
$298$		−	31470.8i		−	0.354385i
$299$			101296.i			1.13305i
$300$		−	22453.5i		−	0.249483i
$301$	228981.			2.52736
$302$		−	32309.7i		−	0.354258i
$303$	−91809.6			−1.00001
$304$	−57198.5			−0.618924
$305$	−67077.2			−0.721066
$306$		−	4923.08i		−	0.0525768i
$307$	170870.			1.81296			0.906482	−	0.422245i	$-0.138758\pi$
$307$	170870.			1.81296			0.906482	+	0.422245i	$0.138758\pi$
$308$	−59252.5			−0.624604
$309$			32466.5i			0.340031i
$310$		−	14298.2i		−	0.148785i
$311$			41798.6i			0.432156i	0.976376	+	0.216078i	$0.0693265\pi$
$311$			41798.6i			0.432156i	−0.976376	+	0.216078i	$0.930673\pi$
$312$		−	30178.6i		−	0.310020i
$313$			7509.24i			0.0766491i	0.999265	+	0.0383246i	$0.0122021\pi$
$313$			7509.24i			0.0766491i	−0.999265	+	0.0383246i	$0.987798\pi$
$314$			29170.2i			0.295856i
$315$	34065.1			0.343311
$316$			34094.7i			0.341439i
$317$	−145232.			−1.44526			−0.722629	−	0.691236i	$-0.757066\pi$
$317$	−145232.			−1.44526			−0.722629	+	0.691236i	$0.757066\pi$
$318$			11423.3i			0.112964i
$319$			21918.0i			0.215387i
$320$		−	24947.6i		−	0.243629i
$321$		−	8379.03i		−	0.0813175i
$322$	−72295.2			−0.697265
$323$	44936.1			0.430715
$324$	10243.9			0.0975837
$325$			42581.1i			0.403135i
$326$			24492.8i			0.230464i
$327$	33820.9			0.316293
$328$	−95060.4			−0.883592
$329$			209518.i			1.93566i
$330$	7695.18			0.0706628
$331$		−	29396.8i		−	0.268314i	−0.990960	−	0.134157i	$-0.957167\pi$
$331$		−	29396.8i		−	0.268314i	0.990960	−	0.134157i	$-0.0428327\pi$
$332$	94049.3			0.853256
$333$	11481.0			0.103536
$334$		−	41693.2i		−	0.373742i
$335$	−76007.1	+	24912.9i	−0.677275	+	0.221990i
$336$	−61184.0			−0.541950
$337$			103530.i			0.911602i	0.890082	+	0.455801i	$0.150647\pi$
$337$			103530.i			0.911602i	−0.890082	+	0.455801i	$0.849353\pi$
$338$		−	13101.6i		−	0.114681i
$339$	−62604.8			−0.544764
$340$			32710.6i			0.282963i
$341$	34238.5			0.294446
$342$		−	12961.7i		−	0.110818i
$343$			14994.5i			0.127451i
$344$	135638.			1.14621
$345$	−67730.5			−0.569044
$346$			22039.7i			0.184100i
$347$			129199.i			1.07300i	0.843901	+	0.536499i	$0.180254\pi$
$347$			129199.i			1.07300i	−0.843901	+	0.536499i	$0.819746\pi$
$348$			26874.4i			0.221911i
$349$	145192.			1.19204			0.596021	−	0.802969i	$-0.296748\pi$
$349$	145192.			1.19204			0.596021	+	0.802969i	$0.296748\pi$
$350$	−30390.2			−0.248083
$351$	−19426.7			−0.157683
$352$	−53785.1			−0.434087
$353$		−	77909.8i		−	0.625234i	−0.949879	−	0.312617i	$-0.898794\pi$
$353$		−	77909.8i		−	0.625234i	0.949879	−	0.312617i	$-0.101206\pi$
$354$	25300.1			0.201891
$355$		−	53375.2i		−	0.423529i
$356$	87485.5			0.690297
$357$	48067.2			0.377148
$358$	−70897.0			−0.553174
$359$	222649.			1.72755			0.863776	−	0.503875i	$-0.168093\pi$
$359$	222649.			1.72755			0.863776	+	0.503875i	$0.168093\pi$
$360$	20178.6			0.155699
$361$	−12011.1			−0.0921658
$362$		−	35128.3i		−	0.268065i
$363$		−	57650.0i		−	0.437508i
$364$	137777.			1.03986
$365$		−	145982.i		−	1.09575i
$366$			27301.2i			0.203807i
$367$		−	118056.i		−	0.876506i	−0.898852	−	0.438253i	$-0.855597\pi$
$367$		−	118056.i		−	0.876506i	0.898852	−	0.438253i	$-0.144403\pi$
$368$	121650.			0.898291
$369$			61192.8i			0.449415i
$370$	10574.7			0.0772438
$371$	−111533.			−0.810320
$372$	41980.9			0.303365
$373$		−	198954.i		−	1.43000i	−0.699126	−	0.714999i	$-0.746427\pi$
$373$		−	198954.i		−	1.43000i	0.699126	−	0.714999i	$-0.253573\pi$
$374$	10858.2			0.0776274
$375$	−86337.6			−0.613956
$376$			124108.i			0.877861i
$377$		−	50964.9i		−	0.358582i
$378$		−	13864.9i		−	0.0970360i
$379$		−	22396.5i		−	0.155920i	−0.996956	−	0.0779599i	$-0.975159\pi$
$379$		−	22396.5i		−	0.155920i	0.996956	−	0.0779599i	$-0.0248406\pi$
$380$			86121.9i			0.596412i
$381$		−	103133.i		−	0.710473i
$382$	15158.7			0.103881
$383$			261718.i			1.78417i	0.451867	+	0.892085i	$0.350758\pi$
$383$			261718.i			1.78417i	−0.451867	+	0.892085i	$0.649242\pi$
$384$	−85243.5			−0.578094
$385$			75132.9i			0.506884i
$386$			11915.6i			0.0799723i
$387$		−	87313.5i		−	0.582988i
$388$			114765.i			0.762338i
$389$	68503.0			0.452700			0.226350	−	0.974046i	$-0.427321\pi$
$389$	68503.0			0.452700			0.226350	+	0.974046i	$0.427321\pi$
$390$	−17893.2			−0.117641
$391$	−95570.4			−0.625129
$392$			109588.i			0.713166i
$393$		−	73527.6i		−	0.476064i
$394$	63121.4			0.406616
$395$	43232.5			0.277087
$396$			22593.7i			0.144078i
$397$	−87000.0			−0.551999			−0.275999	−	0.961158i	$-0.589009\pi$
$397$	−87000.0			−0.551999			−0.275999	+	0.961158i	$0.589009\pi$
$398$			46838.2i			0.295688i
$399$	126554.			0.794929
$400$	51137.1			0.319607
$401$		−	70431.2i		−	0.438002i	−0.975725	−	0.219001i	$-0.929720\pi$
$401$		−	70431.2i		−	0.438002i	0.975725	−	0.219001i	$-0.0702798\pi$
$402$	10139.8	+	30935.8i	0.0627449	+	0.191430i
$403$	−79613.1			−0.490201
$404$		−	248282.i		−	1.52119i
$405$		−	12989.5i		−	0.0791919i
$406$	36373.7			0.220666
$407$			25322.1i			0.152866i
$408$	28472.7			0.171044
$409$		−	223560.i		−	1.33643i	−0.743966	−	0.668217i	$-0.767058\pi$
$409$		−	223560.i		−	1.33643i	0.743966	−	0.668217i	$-0.232942\pi$
$410$			56362.3i			0.335291i
$411$	66417.9			0.393189
$412$	−87799.9			−0.517249
$413$			247021.i			1.44822i
$414$			27567.1i			0.160839i
$415$		−	119256.i		−	0.692442i
$416$	125064.			0.722679
$417$	94888.8			0.545686
$418$	28588.0			0.163618
$419$	−44453.5			−0.253208			−0.126604	−	0.991953i	$-0.540408\pi$
$419$	−44453.5			−0.253208			−0.126604	+	0.991953i	$0.540408\pi$
$420$			92122.8i			0.522238i
$421$	291673.			1.64563			0.822816	−	0.568308i	$-0.192402\pi$
$421$	291673.			1.64563			0.822816	+	0.568308i	$0.192402\pi$
$422$			75473.9i			0.423811i
$423$	79891.8			0.446500
$424$	−66067.1			−0.367497
$425$	−40174.2			−0.222418
$426$	−21724.3			−0.119709
$427$	−266559.			−1.46197
$428$	22659.6			0.123698
$429$		−	42847.1i		−	0.232813i
$430$		−	80421.1i		−	0.434944i
$431$	−245656.			−1.32243			−0.661216	−	0.750196i	$-0.729959\pi$
$431$	−245656.			−1.32243			−0.661216	+	0.750196i	$0.729959\pi$
$432$			23330.3i			0.125012i
$433$			80516.6i			0.429447i	0.976675	+	0.214724i	$0.0688851\pi$
$433$			80516.6i			0.429447i	−0.976675	+	0.214724i	$0.931115\pi$
$434$		−	56819.9i		−	0.301662i
$435$	34077.0			0.180087
$436$			91462.5i			0.481139i
$437$	−251622.			−1.31761
$438$	−59416.3			−0.309712
$439$	−40821.9			−0.211819			−0.105909	−	0.994376i	$-0.533775\pi$
$439$	−40821.9			−0.211819			−0.105909	+	0.994376i	$0.533775\pi$
$440$			44505.2i			0.229882i
$441$	70544.6			0.362733
$442$	−25248.0			−0.129236
$443$		−	33574.1i		−	0.171079i	−0.996335	−	0.0855395i	$-0.972739\pi$
$443$		−	33574.1i		−	0.171079i	0.996335	−	0.0855395i	$-0.0272614\pi$
$444$			31048.2i			0.157496i
$445$		−	110933.i		−	0.560196i
$446$			127174.i			0.639334i
$447$		−	117166.i		−	0.586389i
$448$		−	99139.6i		−	0.493959i
$449$	154970.			0.768694			0.384347	−	0.923189i	$-0.374427\pi$
$449$	154970.			0.768694			0.384347	+	0.923189i	$0.374427\pi$
$450$			11588.2i			0.0572255i
$451$	−134965.			−0.663542
$452$		−	169303.i		−	0.828684i
$453$		−	120289.i		−	0.586179i
$454$			21189.5i			0.102804i
$455$		−	174703.i		−	0.843873i
$456$	74964.4			0.360517
$457$	108340.			0.518749			0.259374	−	0.965777i	$-0.416484\pi$
$457$	108340.			0.518749			0.259374	+	0.965777i	$0.416484\pi$
$458$	−78805.9			−0.375688
$459$		−	18328.6i		−	0.0869971i
$460$		−	183165.i		−	0.865618i
$461$	−295826.			−1.39199			−0.695993	−	0.718048i	$-0.745036\pi$
$461$	−295826.			−1.39199			−0.695993	+	0.718048i	$0.745036\pi$
$462$	30580.0			0.143269
$463$		−	88576.0i		−	0.413194i	−0.978426	−	0.206597i	$-0.933761\pi$
$463$		−	88576.0i		−	0.413194i	0.978426	−	0.206597i	$-0.0662389\pi$
$464$	−61205.5			−0.284285
$465$		−	53232.3i		−	0.246190i
$466$	89174.9			0.410649
$467$	−194332.			−0.891066			−0.445533	−	0.895265i	$-0.646986\pi$
$467$	−194332.			−0.891066			−0.445533	+	0.895265i	$0.646986\pi$
$468$		−	52536.1i		−	0.239865i
$469$	−302046.	+	99001.5i	−1.37318	+	0.450087i
$470$	73585.3			0.333116
$471$			108601.i			0.489543i
$472$			146324.i			0.656797i
$473$	192576.			0.860756
$474$		−	17596.2i		−	0.0783179i
$475$	−105773.			−0.468798
$476$			129989.i			0.573710i
$477$			42529.1i			0.186917i
$478$	−58879.9			−0.257698
$479$	−118184.			−0.515098			−0.257549	−	0.966265i	$-0.582915\pi$
$479$	−118184.			−0.515098			−0.257549	+	0.966265i	$0.582915\pi$
$480$			83622.4i			0.362945i
$481$		−	58880.2i		−	0.254495i
$482$		−	152465.i		−	0.656262i
$483$	−269155.			−1.15374
$484$	155904.			0.665528
$485$	145524.			0.618659
$486$	−5286.86			−0.0223834
$487$		−	232509.i		−	0.980353i	−0.871623	−	0.490177i	$-0.836932\pi$
$487$		−	232509.i		−	0.980353i	0.871623	−	0.490177i	$-0.163068\pi$
$488$	−157897.			−0.663032
$489$			91186.7i			0.381341i
$490$	64975.9			0.270620
$491$	−365485.			−1.51603			−0.758013	−	0.652239i	$-0.773830\pi$
$491$	−365485.			−1.51603			−0.758013	+	0.652239i	$0.773830\pi$
$492$	−165485.			−0.683641
$493$	48084.1			0.197837
$494$	−66474.3			−0.272395
$495$	28649.2			0.116923
$496$			95610.1i			0.388634i
$497$		−	212108.i		−	0.858707i
$498$	−48538.5			−0.195717
$499$			291909.i			1.17232i	0.810195	+	0.586160i	$0.199361\pi$
$499$			291909.i			1.17232i	−0.810195	+	0.586160i	$0.800639\pi$
$500$		−	233484.i		−	0.933937i
$501$		−	155224.i		−	0.618419i
$502$	59750.7			0.237102
$503$			152671.i			0.603420i	0.953400	+	0.301710i	$0.0975574\pi$
$503$			152671.i			0.603420i	−0.953400	+	0.301710i	$0.902443\pi$
$504$	80187.8			0.315680
$505$	−314825.			−1.23449
$506$	−60801.2			−0.237471
$507$		−	48777.2i		−	0.189758i
$508$	278904.			1.08076
$509$	−382834.			−1.47766			−0.738831	−	0.673890i	$-0.764622\pi$
$509$	−382834.			−1.47766			−0.738831	+	0.673890i	$0.764622\pi$
$510$		−	16881.8i		−	0.0649050i
$511$		−	580119.i		−	2.22165i
$512$		−	261792.i		−	0.998656i
$513$		−	48256.5i		−	0.183367i
$514$			114508.i			0.433422i
$515$			111331.i			0.419762i
$516$	236123.			0.886829
$517$			176207.i			0.659238i
$518$	42022.9			0.156612
$519$			82053.8i			0.304624i
$520$		−	103486.i		−	0.382714i
$521$			413835.i			1.52459i	0.647232	+	0.762293i	$0.275927\pi$
$521$			413835.i			1.52459i	−0.647232	+	0.762293i	$0.724073\pi$
$522$		−	13869.8i		−	0.0509012i
$523$	−282316.			−1.03213			−0.516063	−	0.856551i	$-0.672603\pi$
$523$	−282316.			−1.03213			−0.516063	+	0.856551i	$0.672603\pi$
$524$	198842.			0.724179
$525$	−113143.			−0.410495
$526$		−	43689.4i		−	0.157908i
$527$		−	75112.9i		−	0.270454i
$528$	−51456.5			−0.184575
$529$	255312.			0.912346
$530$			39171.9i			0.139451i
$531$	94192.5			0.334062
$532$			342241.i			1.20923i
$533$	313828.			1.10468
$534$	−45151.0			−0.158338
$535$		−	28732.6i		−	0.100385i
$536$	−178918.	+	58643.9i	−0.622765	+	0.204124i
$537$	−263950.			−0.915319
$538$		−	22861.4i		−	0.0789839i
$539$			155591.i			0.535559i
$540$	35127.6			0.120465
$541$			212679.i			0.726656i	0.931661	+	0.363328i	$0.118360\pi$
$541$			212679.i			0.726656i	−0.931661	+	0.363328i	$0.881640\pi$
$542$	−34441.3			−0.117242
$543$		−	130783.i		−	0.443558i
$544$			117995.i			0.398717i
$545$	115976.			0.390458
$546$	−71106.1			−0.238518
$547$		−	215883.i		−	0.721512i	−0.932660	−	0.360756i	$-0.882519\pi$
$547$		−	215883.i		−	0.721512i	0.932660	−	0.360756i	$-0.117481\pi$
$548$			179615.i			0.598111i
$549$			101642.i			0.337233i
$550$	−25558.5			−0.0844910
$551$	126598.			0.416988
$552$	−159435.			−0.523245
$553$	171802.			0.561796
$554$		−	122751.i		−	0.399951i
$555$	39369.6			0.127813
$556$			256610.i			0.830087i
$557$	505452.			1.62918			0.814591	−	0.580036i	$-0.196962\pi$
$557$	505452.			1.62918			0.814591	+	0.580036i	$0.196962\pi$
$558$	−21666.2			−0.0695848
$559$	−447787.			−1.43301
$560$	−209807.			−0.669026
$561$	40425.1			0.128447
$562$	25169.7			0.0796904
$563$			530528.i			1.67375i	0.547391	+	0.836877i	$0.315621\pi$
$563$			530528.i			1.67375i	−0.547391	+	0.836877i	$0.684379\pi$
$564$			216053.i			0.679207i
$565$	−214679.			−0.672501
$566$		−	62273.6i		−	0.194389i
$567$		−	51619.0i		−	0.160562i
$568$		−	125643.i		−	0.389441i
$569$	120559.			0.372369			0.186184	−	0.982515i	$-0.440388\pi$
$569$	120559.			0.372369			0.186184	+	0.982515i	$0.440388\pi$
$570$		−	44447.2i		−	0.136803i
$571$	−214441.			−0.657712			−0.328856	−	0.944380i	$-0.606663\pi$
$571$	−214441.			−0.657712			−0.328856	+	0.944380i	$0.606663\pi$
$572$	115872.			0.354150
$573$	56435.9			0.171888
$574$			223979.i			0.679804i
$575$	224958.			0.680402
$576$	−37803.2			−0.113942
$577$			140796.i			0.422902i	0.977389	+	0.211451i	$0.0678189\pi$
$577$			140796.i			0.422902i	−0.977389	+	0.211451i	$0.932181\pi$
$578$			92748.5i			0.277620i
$579$			44361.6i			0.132328i
$580$			92155.2i			0.273945i
$581$		−	473912.i		−	1.40393i
$582$		−	59230.0i		−	0.174862i
$583$	−93801.0			−0.275975
$584$		−	343636.i		−	1.00756i
$585$	−66616.5			−0.194657
$586$		−	30378.9i		−	0.0884660i
$587$			613767.i			1.78126i	0.454728	+	0.890630i	$0.349736\pi$
$587$			613767.i			1.78126i	−0.454728	+	0.890630i	$0.650264\pi$
$588$			190775.i			0.551781i
$589$		−	197761.i		−	0.570046i
$590$	86757.0			0.249230
$591$	235001.			0.672813
$592$	−70711.3			−0.201765
$593$		−	106350.i		−	0.302433i	−0.988501	−	0.151217i	$-0.951681\pi$
$593$		−	106350.i		−	0.302433i	0.988501	−	0.151217i	$-0.0483191\pi$
$594$		−	11660.6i		−	0.0330481i
$595$	164828.			0.465582
$596$	316854.			0.892003
$597$			174379.i			0.489266i
$598$	141378.			0.395348
$599$		−	524988.i		−	1.46317i	−0.681749	−	0.731586i	$-0.738780\pi$
$599$		−	524988.i		−	1.46317i	0.681749	−	0.731586i	$-0.261220\pi$
$600$	−67020.4			−0.186168
$601$	−203049.			−0.562148			−0.281074	−	0.959686i	$-0.590691\pi$
$601$	−203049.			−0.562148			−0.281074	+	0.959686i	$0.590691\pi$
$602$		−	319586.i		−	0.881851i
$603$	37750.6	+	115174.i	0.103822	+	0.316752i
$604$	325300.			0.891683
$605$		−	197688.i		−	0.540095i
$606$			128138.i			0.348925i
$607$	−193655.			−0.525596			−0.262798	−	0.964851i	$-0.584645\pi$
$607$	−193655.			−0.525596			−0.262798	+	0.964851i	$0.584645\pi$
$608$			310662.i			0.840390i
$609$	135419.			0.365128
$610$			93618.9i			0.251596i
$611$		−	409726.i		−	1.09752i
$612$	49566.5			0.132338
$613$	631844.			1.68147			0.840734	−	0.541448i	$-0.182124\pi$
$613$	631844.			1.68147			0.840734	+	0.541448i	$0.182124\pi$
$614$		−	238481.i		−	0.632583i
$615$			209837.i			0.554794i
$616$			176860.i			0.466088i
$617$	62057.8			0.163014			0.0815072	−	0.996673i	$-0.474027\pi$
$617$	62057.8			0.163014			0.0815072	+	0.996673i	$0.474027\pi$
$618$	45313.2			0.118645
$619$	−117811.			−0.307471			−0.153735	−	0.988112i	$-0.549130\pi$
$619$	−117811.			−0.307471			−0.153735	+	0.988112i	$0.549130\pi$
$620$	143957.			0.374498
$621$			102632.i			0.266135i
$622$	58337.8			0.150789
$623$		−	440837.i		−	1.13580i
$624$	119649.			0.307285
$625$	−103866.			−0.265897
$626$	10480.6			0.0267446
$627$	106433.			0.270734
$628$	−293691.			−0.744683
$629$	55552.0			0.140410
$630$		−	47544.2i		−	0.119789i
$631$			381563.i			0.958314i	0.877729	+	0.479157i	$0.159058\pi$
$631$			381563.i			0.958314i	−0.877729	+	0.479157i	$0.840942\pi$
$632$	101768.			0.254786
$633$			280989.i			0.701266i
$634$			202699.i			0.504283i
$635$		−	353654.i		−	0.877064i
$636$	−115012.			−0.284335
$637$		−	361788.i		−	0.891611i
$638$	30590.7			0.0751534
$639$	−80879.7			−0.198079
$640$	−292309.			−0.713646
$641$		−	97686.1i		−	0.237748i	−0.992909	−	0.118874i	$-0.962072\pi$
$641$		−	97686.1i		−	0.237748i	0.992909	−	0.118874i	$-0.0379284\pi$
$642$	−11694.5			−0.0283735
$643$	34731.4			0.0840040			0.0420020	−	0.999118i	$-0.486626\pi$
$643$	34731.4			0.0840040			0.0420020	+	0.999118i	$0.486626\pi$
$644$		−	727881.i		−	1.75505i
$645$		−	299408.i		−	0.719687i
$646$		−	62716.8i		−	0.150286i
$647$			244694.i			0.584541i	0.956336	+	0.292270i	$0.0944107\pi$
$647$			244694.i			0.584541i	−0.956336	+	0.292270i	$0.905589\pi$
$648$		−	30576.7i		−	0.0728183i
$649$			207748.i			0.493228i
$650$	59430.0			0.140663
$651$		−	211541.i		−	0.499151i
$652$	−246598.			−0.580088
$653$			162834.i			0.381872i	0.981602	+	0.190936i	$0.0611523\pi$
$653$			162834.i			0.381872i	−0.981602	+	0.190936i	$0.938848\pi$
$654$		−	47203.5i		−	0.110362i
$655$		−	252134.i		−	0.587692i
$656$		−	376887.i		−	0.875796i
$657$	−221207.			−0.512470
$658$	292422.			0.675395
$659$	−57824.1			−0.133149			−0.0665745	−	0.997781i	$-0.521207\pi$
$659$	−57824.1			−0.133149			−0.0665745	+	0.997781i	$0.521207\pi$
$660$			77476.5i			0.177862i
$661$		−	265938.i		−	0.608665i	−0.952566	−	0.304332i	$-0.901567\pi$
$661$		−	265938.i		−	0.608665i	0.952566	−	0.304332i	$-0.0984334\pi$
$662$	−41028.8			−0.0936209
$663$	−93998.5			−0.213842
$664$		−	280724.i		−	0.636711i
$665$	433966.			0.981324
$666$		−	16023.9i		−	0.0361259i
$667$	−269250.			−0.605207
$668$	419775.			0.940726
$669$			473468.i			1.05789i
$670$	34770.6	+	106082.i	0.0774574	+	0.236316i
$671$	−224179.			−0.497910
$672$			332308.i			0.735873i
$673$			450494.i			0.994625i	0.867572	+	0.497312i	$0.165680\pi$
$673$			450494.i			0.994625i	−0.867572	+	0.497312i	$0.834320\pi$
$674$	144495.			0.318078
$675$			43142.8i			0.0946892i
$676$	131909.			0.288656
$677$			494277.i			1.07843i	0.842168	+	0.539216i	$0.181279\pi$
$677$			494277.i			1.07843i	−0.842168	+	0.539216i	$0.818721\pi$
$678$			87376.9i			0.190080i
$679$	578300.			1.25434
$680$	97636.2			0.211151
$681$			78888.5i			0.170106i
$682$		−	47786.3i		−	0.102739i
$683$		−	367898.i		−	0.788652i	−0.918971	−	0.394326i	$-0.870978\pi$
$683$		−	367898.i		−	0.788652i	0.918971	−	0.394326i	$-0.129022\pi$
$684$	130501.			0.278934
$685$	227754.			0.485384
$686$	20927.7			0.0444706
$687$	−293394.			−0.621639
$688$			537764.i			1.13609i
$689$	218111.			0.459450
$690$			94530.7i			0.198552i
$691$	348001.			0.728826			0.364413	−	0.931237i	$-0.381270\pi$
$691$	348001.			0.728826			0.364413	+	0.931237i	$0.381270\pi$
$692$	−221900.			−0.463387
$693$	113849.			0.237063
$694$	180321.			0.374393
$695$	325384.			0.673639
$696$	80216.0			0.165593
$697$			296088.i			0.609475i
$698$		−	202643.i		−	0.415930i
$699$	331998.			0.679487
$700$		−	305974.i		−	0.624436i
$701$			601662.i			1.22438i	0.790710	+	0.612191i	$0.209712\pi$
$701$			601662.i			1.22438i	−0.790710	+	0.612191i	$0.790288\pi$
$702$			27113.7i			0.0550192i
$703$	146260.			0.295948
$704$		−	83377.7i		−	0.168230i
$705$	273958.			0.551196
$706$	−108738.			−0.218158
$707$	−1.25109e6			−2.50293
$708$			254726.i			0.508168i
$709$	743249.			1.47857			0.739284	−	0.673393i	$-0.235164\pi$
$709$	743249.			1.47857			0.739284	+	0.673393i	$0.235164\pi$
$710$	−74495.2			−0.147779
$711$		−	65510.5i		−	0.129590i
$712$		−	261132.i		−	0.515109i
$713$			420600.i			0.827351i
$714$		−	67086.8i		−	0.131595i
$715$		−	146927.i		−	0.287403i
$716$		−	713804.i		−	1.39236i
$717$	−219210.			−0.426404
$718$		−	310748.i		−	0.602782i
$719$	720218.			1.39318			0.696589	−	0.717471i	$-0.254700\pi$
$719$	720218.			1.39318			0.696589	+	0.717471i	$0.254700\pi$
$720$			80002.1i			0.154325i
$721$			442421.i			0.851070i
$722$			16763.8i			0.0321587i
$723$		−	567629.i		−	1.08590i
$724$	353678.			0.674731
$725$	−113182.			−0.215329
$726$	−80461.5			−0.152656
$727$			495258.i			0.937050i	0.883450	+	0.468525i	$0.155214\pi$
$727$			495258.i			0.937050i	−0.883450	+	0.468525i	$0.844786\pi$
$728$		−	411244.i		−	0.775955i
$729$	−19683.0			−0.0370370
$730$	−203745.			−0.382333
$731$		−	422476.i		−	0.790619i
$732$	−274873.			−0.512992
$733$			1.01917e6i			1.89687i	0.316975	+	0.948434i	$0.397333\pi$
$733$			1.01917e6i			1.89687i	−0.316975	+	0.948434i	$0.602667\pi$
$734$	−164769.			−0.305833
$735$	241905.			0.447786
$736$		−	660718.i		−	1.21972i
$737$	−254025.	+	83261.6i	−0.467671	+	0.153289i
$738$	85406.2			0.156811
$739$			760989.i			1.39344i	0.717342	+	0.696722i	$0.245359\pi$
$739$			760989.i			1.39344i	−0.717342	+	0.696722i	$0.754641\pi$
$740$			106468.i			0.194426i
$741$	−247484.			−0.450724
$742$			155666.i			0.282739i
$743$	339475.			0.614937			0.307469	−	0.951558i	$-0.400518\pi$
$743$	339475.			0.614937			0.307469	+	0.951558i	$0.400518\pi$
$744$		−	125307.i		−	0.226375i
$745$		−	401775.i		−	0.723886i
$746$	−277678.			−0.498958
$747$	−180709.			−0.323846
$748$			109322.i			0.195392i
$749$		−	114181.i		−	0.203531i
$750$			120500.i			0.214223i
$751$	−587651.			−1.04193			−0.520966	−	0.853577i	$-0.674428\pi$
$751$	−587651.			−1.04193			−0.520966	+	0.853577i	$0.674428\pi$
$752$	−492054.			−0.870115
$753$	222452.			0.392325
$754$	−71131.1			−0.125117
$755$		−	412485.i		−	0.723626i
$756$	139594.			0.244244
$757$			710036.i			1.23905i	0.784977	+	0.619525i	$0.212675\pi$
$757$			710036.i			1.23905i	−0.784977	+	0.619525i	$0.787325\pi$
$758$	−31258.5			−0.0544039
$759$	−226363.			−0.392936
$760$	257061.			0.445051
$761$	981461.			1.69474			0.847371	−	0.531001i	$-0.178184\pi$
$761$	981461.			1.69474			0.847371	+	0.531001i	$0.178184\pi$
$762$	−143941.			−0.247900
$763$	460877.			0.791656
$764$			152621.i			0.261473i
$765$		−	62851.0i		−	0.107396i
$766$	365277.			0.622537
$767$		−	483066.i		−	0.821138i
$768$			2569.63i			0.00435661i
$769$			479442.i			0.810744i	0.914152	+	0.405372i	$0.132858\pi$
$769$			479442.i			0.810744i	−0.914152	+	0.405372i	$0.867142\pi$
$770$	104862.			0.176863
$771$			426315.i			0.717170i
$772$	−119968.			−0.201294
$773$	94191.4			0.157635			0.0788175	−	0.996889i	$-0.474886\pi$
$773$	94191.4			0.157635			0.0788175	+	0.996889i	$0.474886\pi$
$774$	−121862.			−0.203417
$775$			176804.i			0.294367i
$776$	342558.			0.568867
$777$	156451.			0.259141
$778$		−	95608.9i		−	0.157957i
$779$			779556.i			1.28461i
$780$		−	180152.i		−	0.296108i
$781$		−	178386.i		−	0.292455i
$782$			133387.i			0.218122i
$783$		−	51637.1i		−	0.0842245i
$784$	−434484.			−0.706874
$785$			372404.i			0.604332i
$786$	−102622.			−0.166109
$787$		−	837770.i		−	1.35262i	−0.736618	−	0.676309i	$-0.763578\pi$
$787$		−	837770.i		−	1.35262i	0.736618	−	0.676309i	$-0.236422\pi$
$788$			635517.i			1.02347i
$789$		−	162656.i		−	0.261286i
$790$		−	60339.2i		−	0.0966819i
$791$	−853116.			−1.36350
$792$	67439.0			0.107513
$793$	521273.			0.828932
$794$			121425.i			0.192605i
$795$			145837.i			0.230746i
$796$	−471576.			−0.744261
$797$	−768349.			−1.20960			−0.604800	−	0.796377i	$-0.706747\pi$
$797$	−768349.			−1.20960			−0.604800	+	0.796377i	$0.706747\pi$
$798$		−	176629.i		−	0.277369i
$799$	386566.			0.605522
$800$		−	277741.i		−	0.433970i
$801$	−168097.			−0.261996
$802$	−98300.0			−0.152829
$803$		−	487888.i		−	0.756640i
$804$	−311467.	+	102090.i	−0.481837	+	0.157932i
$805$	−922963.			−1.42427
$806$			111115.i			0.171042i
$807$		−	85113.1i		−	0.130692i
$808$	−741087.			−1.13513
$809$			706252.i			1.07910i	0.841953	+	0.539551i	$0.181406\pi$
$809$			706252.i			1.07910i	−0.841953	+	0.539551i	$0.818594\pi$
$810$	−18129.2			−0.0276318
$811$		−	792209.i		−	1.20448i	−0.798316	−	0.602238i	$-0.794276\pi$
$811$		−	792209.i		−	1.20448i	0.798316	−	0.602238i	$-0.205724\pi$
$812$			366217.i			0.555426i
$813$	−128225.			−0.193996
$814$	35341.8			0.0533384
$815$			312689.i			0.470758i
$816$			112886.i			0.169535i
$817$		−	1.11232e6i		−	1.66642i
$818$	−312020.			−0.466312
$819$	−264728.			−0.394668
$820$	−567466.			−0.843941
$821$	−113194.			−0.167934			−0.0839668	−	0.996469i	$-0.526759\pi$
$821$	−113194.			−0.167934			−0.0839668	+	0.996469i	$0.526759\pi$
$822$		−	92698.8i		−	0.137192i
$823$	−311534.			−0.459945			−0.229972	−	0.973197i	$-0.573864\pi$
$823$	−311534.			−0.459945			−0.229972	+	0.973197i	$0.573864\pi$
$824$			262070.i			0.385978i
$825$	−95154.4			−0.139804
$826$	344765.			0.505316
$827$	−395367.			−0.578081			−0.289041	−	0.957317i	$-0.593336\pi$
$827$	−395367.			−0.578081			−0.289041	+	0.957317i	$0.593336\pi$
$828$	−277551.			−0.404838
$829$	723804.			1.05320			0.526601	−	0.850113i	$-0.323466\pi$
$829$	723804.			1.05320			0.526601	+	0.850113i	$0.323466\pi$
$830$	−166444.			−0.241608
$831$		−	457003.i		−	0.661786i
$832$			193874.i			0.280074i
$833$	341338.			0.491920
$834$		−	132435.i		−	0.190402i
$835$		−	532280.i		−	0.763426i
$836$			287829.i			0.411834i
$837$	−80663.2			−0.115140
$838$			62043.3i			0.0883500i
$839$	10424.2			0.0148088			0.00740440	−	0.999973i	$-0.497643\pi$
$839$	10424.2			0.0148088			0.00740440	+	0.999973i	$0.497643\pi$
$840$	274973.			0.389701
$841$	−571814.			−0.808468
$842$		−	407085.i		−	0.574197i
$843$	93707.0			0.131861
$844$	−759885.			−1.06675
$845$		−	167262.i		−	0.234253i
$846$		−	111504.i		−	0.155794i
$847$		−	785596.i		−	1.09505i
$848$		−	261937.i		−	0.364254i
$849$		−	231845.i		−	0.321649i
$850$			56070.7i			0.0776064i
$851$	−311067.			−0.429531
$852$		−	218725.i		−	0.301313i
$853$	99450.3			0.136681			0.0683405	−	0.997662i	$-0.478230\pi$
$853$	99450.3			0.136681			0.0683405	+	0.997662i	$0.478230\pi$
$854$			372033.i			0.510113i
$855$		−	165477.i		−	0.226363i
$856$		−	67635.5i		−	0.0923054i
$857$			60546.7i			0.0824383i	0.999150	+	0.0412192i	$0.0131242\pi$
$857$			60546.7i			0.0824383i	−0.999150	+	0.0412192i	$0.986876\pi$
$858$	−59801.2			−0.0812335
$859$	−78165.5			−0.105932			−0.0529662	−	0.998596i	$-0.516868\pi$
$859$	−78165.5			−0.105932			−0.0529662	+	0.998596i	$0.516868\pi$
$860$	809694.			1.09477
$861$			833874.i			1.12485i
$862$			342860.i			0.461426i
$863$	−208906.			−0.280498			−0.140249	−	0.990116i	$-0.544790\pi$
$863$	−208906.			−0.280498			−0.140249	+	0.990116i	$0.544790\pi$
$864$	126714.			0.169744
$865$			281372.i			0.376052i
$866$	112376.			0.149844
$867$			345303.i			0.459369i
$868$	572073.			0.759298
$869$	144488.			0.191334
$870$		−	47561.0i		−	0.0628365i
$871$	590670.	−	193604.i	0.778590	−	0.255198i
$872$	273002.			0.359032
$873$		−	220513.i		−	0.289339i
$874$			351187.i			0.459743i
$875$	−1.17652e6			−1.53668
$876$		−	598215.i		−	0.779559i
$877$	−599006.			−0.778811			−0.389405	−	0.921066i	$-0.627320\pi$
$877$	−599006.			−0.778811			−0.389405	+	0.921066i	$0.627320\pi$
$878$			56974.7i			0.0739082i
$879$		−	113101.i		−	0.146382i
$880$	−176450.			−0.227854
$881$	451584.			0.581818			0.290909	−	0.956751i	$-0.406042\pi$
$881$	451584.			0.581818			0.290909	+	0.956751i	$0.406042\pi$
$882$		−	98458.4i		−	0.126566i
$883$			597836.i			0.766762i	0.923590	+	0.383381i	$0.125240\pi$
$883$			597836.i			0.766762i	−0.923590	+	0.383381i	$0.874760\pi$
$884$		−	254202.i		−	0.325293i
$885$	322997.			0.412393
$886$	−46859.0			−0.0596933
$887$	−544652.			−0.692264			−0.346132	−	0.938186i	$-0.612505\pi$
$887$	−544652.			−0.692264			−0.346132	+	0.938186i	$0.612505\pi$
$888$	92674.4			0.117526
$889$		−	1.40539e6i		−	1.77825i
$890$	−154828.			−0.195465
$891$		−	43412.3i		−	0.0546836i
$892$	−1.28041e6			−1.60923
$893$	1.01777e6			1.27628
$894$	−163527.			−0.204604
$895$	−905113.			−1.12994
$896$	−1.16161e6			−1.44692
$897$	526351.			0.654169
$898$		−	216289.i		−	0.268215i
$899$		−	211615.i		−	0.261835i
$900$	−116672.			−0.144039
$901$			205782.i			0.253488i
$902$			188369.i			0.231525i
$903$		−	1.18982e6i		−	1.45917i
$904$	−505346.			−0.618375
$905$		−	448468.i		−	0.547563i
$906$	−167886.			−0.204531
$907$	1.25923e6			1.53071			0.765353	−	0.643611i	$-0.222565\pi$
$907$	1.25923e6			1.53071			0.765353	+	0.643611i	$0.222565\pi$
$908$	−213340.			−0.258762
$909$			477057.i			0.577354i
$910$	−243831.			−0.294446
$911$	1.13579e6			1.36855			0.684277	−	0.729222i	$-0.260118\pi$
$911$	1.13579e6			1.36855			0.684277	+	0.729222i	$0.260118\pi$
$912$			297212.i			0.357336i
$913$		−	398566.i		−	0.478144i
$914$		−	151209.i		−	0.181003i
$915$			348543.i			0.416308i
$916$		−	793432.i		−	0.945625i
$917$		−	1.00196e6i		−	1.19155i
$918$	−25581.1			−0.0303552
$919$			103665.i			0.122745i	0.998115	+	0.0613723i	$0.0195477\pi$
$919$			103665.i			0.122745i	−0.998115	+	0.0613723i	$0.980452\pi$
$920$	−546720.			−0.645936
$921$		−	887867.i		−	1.04672i
$922$			412882.i			0.485695i
$923$			414792.i			0.486886i
$924$			307885.i			0.360615i
$925$	−130761.			−0.152825
$926$	−123625.			−0.144173
$927$	168701.			0.196317
$928$			332425.i			0.386010i
$929$		−	376440.i		−	0.436178i	−0.975929	−	0.218089i	$-0.930018\pi$
$929$		−	376440.i		−	0.436178i	0.975929	−	0.218089i	$-0.0699823\pi$
$930$	−74295.8			−0.0859010
$931$	898691.			1.03684
$932$			897829.i			1.03362i
$933$	217192.			0.249505
$934$			271227.i			0.310913i
$935$	138622.			0.158566
$936$	−156813.			−0.178990
$937$			735181.i			0.837365i	0.908133	+	0.418683i	$0.137508\pi$
$937$			735181.i			0.837365i	−0.908133	+	0.418683i	$0.862492\pi$
$938$	138175.	+	421562.i	0.157045	+	0.479133i
$939$	39019.1			0.0442534
$940$			740870.i			0.838467i
$941$		−	115602.i		−	0.130553i	−0.997867	−	0.0652763i	$-0.979207\pi$
$941$		−	115602.i		−	0.130553i	0.997867	−	0.0652763i	$-0.0207929\pi$
$942$	151573.			0.170813
$943$		−	1.65797e6i		−	1.86446i
$944$	−580131.			−0.651002
$945$		−	177007.i		−	0.198211i
$946$		−	268776.i		−	0.300337i
$947$	−1.34934e6			−1.50460			−0.752298	−	0.658823i	$-0.771055\pi$
$947$	−1.34934e6			−1.50460			−0.752298	+	0.658823i	$0.771055\pi$
$948$	177161.			0.197130
$949$			1.13446e6i			1.25967i
$950$			147626.i			0.163574i
$951$			754650.i			0.834420i
$952$	387998.			0.428110
$953$	−301926.			−0.332441			−0.166220	−	0.986089i	$-0.553156\pi$
$953$	−301926.			−0.332441			−0.166220	+	0.986089i	$0.553156\pi$
$954$	59357.4			0.0652196
$955$	193525.			0.212193
$956$		−	592813.i		−	0.648637i
$957$	113889.			0.124354
$958$			164949.i			0.179729i
$959$	905076.			0.984120
$960$	−129632.			−0.140659
$961$	592954.			0.642057
$962$	−82178.5			−0.0887990
$963$	−43538.7			−0.0469487
$964$	1.53505e6			1.65184
$965$			152121.i			0.163356i
$966$			375657.i			0.402566i
$967$	−1.54796e6			−1.65541			−0.827705	−	0.561163i	$-0.810354\pi$
$967$	−1.54796e6			−1.65541			−0.827705	+	0.561163i	$0.810354\pi$
$968$		−	465351.i		−	0.496626i
$969$		−	233495.i		−	0.248673i
$970$		−	203106.i		−	0.215864i
$971$	−610630.			−0.647649			−0.323824	−	0.946117i	$-0.604969\pi$
$971$	−610630.			−0.647649			−0.323824	+	0.946117i	$0.604969\pi$
$972$		−	53229.1i		−	0.0563400i
$973$	1.29305e6			1.36581
$974$	−324511.			−0.342067
$975$	221258.			0.232750
$976$		−	626015.i		−	0.657182i
$977$	141369.			0.148104			0.0740519	−	0.997254i	$-0.476407\pi$
$977$	141369.			0.148104			0.0740519	+	0.997254i	$0.476407\pi$
$978$	127268.			0.133058
$979$		−	370750.i		−	0.386826i
$980$			654189.i			0.681163i
$981$		−	175739.i		−	0.182612i
$982$			510104.i			0.528976i
$983$			1.33430e6i			1.38085i	0.723403	+	0.690426i	$0.242577\pi$
$983$			1.33430e6i			1.38085i	−0.723403	+	0.690426i	$0.757423\pi$
$984$			493948.i			0.510142i
$985$	805844.			0.830575
$986$		−	67110.4i		−	0.0690297i
$987$	1.08869e6			1.11755
$988$		−	669275.i		−	0.685631i
$989$			2.36568e6i			2.41860i
$990$		−	39985.3i		−	0.0407972i
$991$			1.05187e6i			1.07106i	0.844516	+	0.535530i	$0.179888\pi$
$991$			1.05187e6i			1.07106i	−0.844516	+	0.535530i	$0.820112\pi$
$992$	519287.			0.527696
$993$	−152750.			−0.154911
$994$	−296037.			−0.299622
$995$			597964.i			0.603989i
$996$		−	488695.i		−	0.492628i
$997$	−1.77074e6			−1.78141			−0.890704	−	0.454584i	$-0.849788\pi$
$997$	−1.77074e6			−1.78141			−0.890704	+	0.454584i	$0.849788\pi$
$998$	407414.			0.409049
$999$		−	59656.9i		−	0.0597764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.20	✓	46
67.66	odd	2	inner	201.5.b.a.133.27	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.20	✓	46	1.1	even	1	trivial
201.5.b.a.133.27	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)

\(f(q)\)	\(=\)	\(q-1.39569i q^{2} -5.19615i q^{3} +14.0521 q^{4} -17.8182i q^{5} -7.25221 q^{6} -70.8079i q^{7} -41.9433i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-1.39569i q^{2} -5.19615i q^{3} +14.0521 q^{4} -17.8182i q^{5} -7.25221 q^{6} -70.8079i q^{7} -41.9433i q^{8} -27.0000 q^{9} -24.8687 q^{10} -59.5504i q^{11} -73.0166i q^{12} +138.470i q^{13} -98.8259 q^{14} -92.5860 q^{15} +166.293 q^{16} -130.643 q^{17} +37.6836i q^{18} -343.962 q^{19} -250.382i q^{20} -367.929 q^{21} -83.1139 q^{22} +731.541 q^{23} -217.944 q^{24} +307.512 q^{25} +193.261 q^{26} +140.296i q^{27} -994.997i q^{28} -368.058 q^{29} +129.221i q^{30} +574.950i q^{31} -903.187i q^{32} -309.433 q^{33} +182.336i q^{34} -1261.67 q^{35} -379.405 q^{36} -425.221 q^{37} +480.064i q^{38} +719.509 q^{39} -747.354 q^{40} -2266.40i q^{41} +513.514i q^{42} +3233.83i q^{43} -836.805i q^{44} +481.091i q^{45} -1021.00i q^{46} -2958.96 q^{47} -864.084i q^{48} -2612.76 q^{49} -429.191i q^{50} +678.839i q^{51} +1945.78i q^{52} -1575.15i q^{53} +195.810 q^{54} -1061.08 q^{55} -2969.92 q^{56} +1787.28i q^{57} +513.695i q^{58} -3488.61 q^{59} -1301.02 q^{60} -3764.53i q^{61} +802.451 q^{62} +1911.81i q^{63} +1400.12 q^{64} +2467.28 q^{65} +431.872i q^{66} +(-1398.17 - 4265.71i) q^{67} -1835.80 q^{68} -3801.20i q^{69} +1760.90i q^{70} +2995.55 q^{71} +1132.47i q^{72} +8192.86 q^{73} +593.477i q^{74} -1597.88i q^{75} -4833.37 q^{76} -4216.64 q^{77} -1004.21i q^{78} +2426.32i q^{79} -2963.04i q^{80} +729.000 q^{81} -3163.19 q^{82} +6692.92 q^{83} -5170.15 q^{84} +2327.81i q^{85} +4513.43 q^{86} +1912.49i q^{87} -2497.74 q^{88} +6225.82 q^{89} +671.454 q^{90} +9804.74 q^{91} +10279.7 q^{92} +2987.53 q^{93} +4129.78i q^{94} +6128.78i q^{95} -4693.09 q^{96} +8167.16i q^{97} +3646.61i q^{98} +1607.86i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 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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