LMFDB - Embedded newform 201.5.b.a.133.11

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			133.11
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.02761i q^{2} +5.19615i q^{3} -9.27688 q^{4} +18.9854i q^{5} +26.1242 q^{6} +67.2401i q^{7} -33.8013i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-5.02761i q^{2} +5.19615i q^{3} -9.27688 q^{4} +18.9854i q^{5} +26.1242 q^{6} +67.2401i q^{7} -33.8013i q^{8} -27.0000 q^{9} +95.4513 q^{10} -151.013i q^{11} -48.2041i q^{12} +106.995i q^{13} +338.057 q^{14} -98.6511 q^{15} -318.370 q^{16} -455.598 q^{17} +135.746i q^{18} -124.150 q^{19} -176.125i q^{20} -349.390 q^{21} -759.233 q^{22} -232.829 q^{23} +175.636 q^{24} +264.554 q^{25} +537.929 q^{26} -140.296i q^{27} -623.778i q^{28} -1382.72 q^{29} +495.979i q^{30} +69.5323i q^{31} +1059.82i q^{32} +784.685 q^{33} +2290.57i q^{34} -1276.58 q^{35} +250.476 q^{36} -939.304 q^{37} +624.176i q^{38} -555.962 q^{39} +641.731 q^{40} -923.217i q^{41} +1756.60i q^{42} +540.259i q^{43} +1400.93i q^{44} -512.606i q^{45} +1170.57i q^{46} -472.100 q^{47} -1654.30i q^{48} -2120.23 q^{49} -1330.08i q^{50} -2367.36i q^{51} -992.578i q^{52} +3555.91i q^{53} -705.354 q^{54} +2867.04 q^{55} +2272.80 q^{56} -645.101i q^{57} +6951.77i q^{58} +5522.44 q^{59} +915.174 q^{60} +1462.21i q^{61} +349.581 q^{62} -1815.48i q^{63} +234.442 q^{64} -2031.34 q^{65} -3945.09i q^{66} +(-4013.44 + 2010.83i) q^{67} +4226.53 q^{68} -1209.81i q^{69} +6418.15i q^{70} +5194.64 q^{71} +912.634i q^{72} -7423.88 q^{73} +4722.46i q^{74} +1374.66i q^{75} +1151.72 q^{76} +10154.1 q^{77} +2795.16i q^{78} +3858.59i q^{79} -6044.38i q^{80} +729.000 q^{81} -4641.58 q^{82} -7915.12 q^{83} +3241.24 q^{84} -8649.72i q^{85} +2716.21 q^{86} -7184.81i q^{87} -5104.42 q^{88} +6463.07 q^{89} -2577.18 q^{90} -7194.35 q^{91} +2159.92 q^{92} -361.300 q^{93} +2373.53i q^{94} -2357.03i q^{95} -5506.98 q^{96} +4144.74i q^{97} +10659.7i q^{98} +4077.34i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	5.02761i		−	1.25690i	−0.777849	−	0.628451i	$-0.783689\pi$
$2$		−	5.02761i		−	1.25690i	0.777849	−	0.628451i	$-0.216311\pi$
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	−9.27688			−0.579805
$5$			18.9854i			0.759416i	0.925106	+	0.379708i	$0.123976\pi$
$5$			18.9854i			0.759416i	−0.925106	+	0.379708i	$0.876024\pi$
$6$	26.1242			0.725673
$7$			67.2401i			1.37225i	0.727485	+	0.686123i	$0.240689\pi$
$7$			67.2401i			1.37225i	−0.727485	+	0.686123i	$0.759311\pi$
$8$		−	33.8013i		−	0.528145i
$9$	−27.0000			−0.333333
$10$	95.4513			0.954513
$11$		−	151.013i		−	1.24804i	−0.781409	−	0.624019i	$-0.785499\pi$
$11$		−	151.013i		−	1.24804i	0.781409	−	0.624019i	$-0.214501\pi$
$12$		−	48.2041i		−	0.334750i
$13$			106.995i			0.633106i	0.948575	+	0.316553i	$0.102525\pi$
$13$			106.995i			0.633106i	−0.948575	+	0.316553i	$0.897475\pi$
$14$	338.057			1.72478
$15$	−98.6511			−0.438449
$16$	−318.370			−1.24363
$17$	−455.598			−1.57646			−0.788232	−	0.615378i	$-0.789003\pi$
$17$	−455.598			−1.57646			−0.788232	+	0.615378i	$0.789003\pi$
$18$			135.746i			0.418968i
$19$	−124.150			−0.343905			−0.171952	−	0.985105i	$-0.555008\pi$
$19$	−124.150			−0.343905			−0.171952	+	0.985105i	$0.555008\pi$
$20$		−	176.125i		−	0.440313i
$21$	−349.390			−0.792267
$22$	−759.233			−1.56866
$23$	−232.829			−0.440130			−0.220065	−	0.975485i	$-0.570627\pi$
$23$	−232.829			−0.440130			−0.220065	+	0.975485i	$0.570627\pi$
$24$	175.636			0.304924
$25$	264.554			0.423287
$26$	537.929			0.795753
$27$		−	140.296i		−	0.192450i
$28$		−	623.778i		−	0.795635i
$29$	−1382.72			−1.64414			−0.822068	−	0.569390i	$-0.807179\pi$
$29$	−1382.72			−1.64414			−0.822068	+	0.569390i	$0.807179\pi$
$30$			495.979i			0.551088i
$31$			69.5323i			0.0723541i	0.999345	+	0.0361770i	$0.0115180\pi$
$31$			69.5323i			0.0723541i	−0.999345	+	0.0361770i	$0.988482\pi$
$32$			1059.82i			1.03498i
$33$	784.685			0.720555
$34$			2290.57i			1.98146i
$35$	−1276.58			−1.04211
$36$	250.476			0.193268
$37$	−939.304			−0.686124			−0.343062	−	0.939313i	$-0.611464\pi$
$37$	−939.304			−0.686124			−0.343062	+	0.939313i	$0.611464\pi$
$38$			624.176i			0.432255i
$39$	−555.962			−0.365524
$40$	641.731			0.401082
$41$		−	923.217i		−	0.549207i	−0.961558	−	0.274603i	$-0.911453\pi$
$41$		−	923.217i		−	0.549207i	0.961558	−	0.274603i	$-0.0885466\pi$
$42$			1756.60i			0.995803i
$43$			540.259i			0.292190i	0.989271	+	0.146095i	$0.0466705\pi$
$43$			540.259i			0.292190i	−0.989271	+	0.146095i	$0.953329\pi$
$44$			1400.93i			0.723618i
$45$		−	512.606i		−	0.253139i
$46$			1170.57i			0.553201i
$47$	−472.100			−0.213716			−0.106858	−	0.994274i	$-0.534079\pi$
$47$	−472.100			−0.213716			−0.106858	+	0.994274i	$0.534079\pi$
$48$		−	1654.30i		−	0.718011i
$49$	−2120.23			−0.883061
$50$		−	1330.08i		−	0.532030i
$51$		−	2367.36i		−	0.910172i
$52$		−	992.578i		−	0.367078i
$53$			3555.91i			1.26590i	0.774193	+	0.632949i	$0.218156\pi$
$53$			3555.91i			1.26590i	−0.774193	+	0.632949i	$0.781844\pi$
$54$	−705.354			−0.241891
$55$	2867.04			0.947781
$56$	2272.80			0.724745
$57$		−	645.101i		−	0.198554i
$58$			6951.77i			2.06652i
$59$	5522.44			1.58645			0.793226	−	0.608927i	$-0.208400\pi$
$59$	5522.44			1.58645			0.793226	+	0.608927i	$0.208400\pi$
$60$	915.174			0.254215
$61$			1462.21i			0.392962i	0.980508	+	0.196481i	$0.0629514\pi$
$61$			1462.21i			0.392962i	−0.980508	+	0.196481i	$0.937049\pi$
$62$	349.581			0.0909420
$63$		−	1815.48i		−	0.457416i
$64$	234.442			0.0572367
$65$	−2031.34			−0.480791
$66$		−	3945.09i		−	0.905668i
$67$	−4013.44	+	2010.83i	−0.894061	+	0.447945i
$67$	−4013.44	+	2010.83i	−0.894061	+	0.447945i
$68$	4226.53			0.914041
$69$		−	1209.81i		−	0.254109i
$70$			6418.15i			1.30983i
$71$	5194.64			1.03048			0.515239	−	0.857047i	$-0.327703\pi$
$71$	5194.64			1.03048			0.515239	+	0.857047i	$0.327703\pi$
$72$			912.634i			0.176048i
$73$	−7423.88			−1.39311			−0.696555	−	0.717504i	$-0.745285\pi$
$73$	−7423.88			−1.39311			−0.696555	+	0.717504i	$0.745285\pi$
$74$			4722.46i			0.862391i
$75$			1374.66i			0.244385i
$76$	1151.72			0.199398
$77$	10154.1			1.71262
$78$			2795.16i			0.459428i
$79$			3858.59i			0.618265i	0.951019	+	0.309133i	$0.100039\pi$
$79$			3858.59i			0.618265i	−0.951019	+	0.309133i	$0.899961\pi$
$80$		−	6044.38i		−	0.944434i
$81$	729.000			0.111111
$82$	−4641.58			−0.690300
$83$	−7915.12			−1.14895			−0.574475	−	0.818522i	$-0.694794\pi$
$83$	−7915.12			−1.14895			−0.574475	+	0.818522i	$0.694794\pi$
$84$	3241.24			0.459360
$85$		−	8649.72i		−	1.19719i
$86$	2716.21			0.367254
$87$		−	7184.81i		−	0.949242i
$88$	−5104.42			−0.659145
$89$	6463.07			0.815941			0.407971	−	0.912995i	$-0.366237\pi$
$89$	6463.07			0.815941			0.407971	+	0.912995i	$0.366237\pi$
$90$	−2577.18			−0.318171
$91$	−7194.35			−0.868777
$92$	2159.92			0.255190
$93$	−361.300			−0.0417736
$94$			2373.53i			0.268621i
$95$		−	2357.03i		−	0.261167i
$96$	−5506.98			−0.597545
$97$			4144.74i			0.440509i	0.975442	+	0.220254i	$0.0706887\pi$
$97$			4144.74i			0.440509i	−0.975442	+	0.220254i	$0.929311\pi$
$98$			10659.7i			1.10992i
$99$			4077.34i			0.416013i
$100$	−2454.24			−0.245424
$101$		−	9623.54i		−	0.943392i	−0.881761	−	0.471696i	$-0.843642\pi$
$101$		−	9623.54i		−	0.943392i	0.881761	−	0.471696i	$-0.156358\pi$
$102$	−11902.2			−1.14400
$103$	345.346			0.0325522			0.0162761	−	0.999868i	$-0.494819\pi$
$103$	345.346			0.0325522			0.0162761	+	0.999868i	$0.494819\pi$
$104$	3616.56			0.334371
$105$		−	6633.31i		−	0.601661i
$106$	17877.7			1.59111
$107$	−10339.7			−0.903114			−0.451557	−	0.892242i	$-0.649131\pi$
$107$	−10339.7			−0.903114			−0.451557	+	0.892242i	$0.649131\pi$
$108$			1301.51i			0.111583i
$109$		−	659.405i		−	0.0555008i	−0.999615	−	0.0277504i	$-0.991166\pi$
$109$		−	659.405i		−	0.0555008i	0.999615	−	0.0277504i	$-0.00883436\pi$
$110$		−	14414.3i		−	1.19127i
$111$		−	4880.77i		−	0.396134i
$112$		−	21407.2i		−	1.70657i
$113$		−	16793.0i		−	1.31513i	−0.753396	−	0.657567i	$-0.771586\pi$
$113$		−	16793.0i		−	1.31513i	0.753396	−	0.657567i	$-0.228414\pi$
$114$	−3243.32			−0.249563
$115$		−	4420.35i		−	0.334242i
$116$	12827.3			0.953277
$117$		−	2888.86i		−	0.211035i
$118$		−	27764.7i		−	1.99402i
$119$		−	30634.5i		−	2.16330i
$120$			3334.53i			0.231565i
$121$	−8163.81			−0.557599
$122$	7351.43			0.493915
$123$	4797.18			0.317085
$124$		−	645.042i		−	0.0419512i
$125$			16888.6i			1.08087i
$126$	−9127.54			−0.574927
$127$	−16543.5			−1.02570			−0.512850	−	0.858478i	$-0.671410\pi$
$127$	−16543.5			−1.02570			−0.512850	+	0.858478i	$0.671410\pi$
$128$			15778.4i			0.963038i
$129$	−2807.27			−0.168696
$130$			10212.8i			0.604308i
$131$	−9862.04			−0.574677			−0.287339	−	0.957829i	$-0.592771\pi$
$131$	−9862.04			−0.574677			−0.287339	+	0.957829i	$0.592771\pi$
$132$	−7279.42			−0.417781
$133$		−	8347.83i		−	0.471922i
$134$	10109.7	+	20178.0i	0.563024	+	1.12375i
$135$	2663.58			0.146150
$136$			15399.8i			0.832601i
$137$			24653.1i			1.31350i	0.754109	+	0.656749i	$0.228069\pi$
$137$			24653.1i			1.31350i	−0.754109	+	0.656749i	$0.771931\pi$
$138$	−6082.48			−0.319391
$139$			1425.09i			0.0737585i	0.999320	+	0.0368792i	$0.0117417\pi$
$139$			1425.09i			0.0737585i	−0.999320	+	0.0368792i	$0.988258\pi$
$140$	11842.7			0.604218
$141$		−	2453.10i		−	0.123389i
$142$		−	26116.6i		−	1.29521i
$143$	16157.6			0.790140
$144$	8595.98			0.414544
$145$		−	26251.5i		−	1.24858i
$146$			37324.4i			1.75100i
$147$		−	11017.0i		−	0.509835i
$148$	8713.81			0.397818
$149$	9792.36			0.441077			0.220539	−	0.975378i	$-0.429218\pi$
$149$	9792.36			0.441077			0.220539	+	0.975378i	$0.429218\pi$
$150$	6911.28			0.307168
$151$	443.516			0.0194516			0.00972580	−	0.999953i	$-0.496904\pi$
$151$	443.516			0.0194516			0.00972580	+	0.999953i	$0.496904\pi$
$152$			4196.41i			0.181632i
$153$	12301.2			0.525488
$154$		−	51050.9i		−	2.15259i
$155$	−1320.10			−0.0549469
$156$	5157.59			0.211932
$157$	−3074.36			−0.124725			−0.0623627	−	0.998054i	$-0.519864\pi$
$157$	−3074.36			−0.124725			−0.0623627	+	0.998054i	$0.519864\pi$
$158$	19399.5			0.777099
$159$	−18477.0			−0.730867
$160$	−20121.1			−0.785980
$161$		−	15655.4i		−	0.603967i
$162$		−	3665.13i		−	0.139656i
$163$	42746.6			1.60889			0.804446	−	0.594026i	$-0.202462\pi$
$163$	42746.6			1.60889			0.804446	+	0.594026i	$0.202462\pi$
$164$			8564.57i			0.318433i
$165$			14897.6i			0.547201i
$166$			39794.2i			1.44412i
$167$	−2527.85			−0.0906398			−0.0453199	−	0.998973i	$-0.514431\pi$
$167$	−2527.85			−0.0906398			−0.0453199	+	0.998973i	$0.514431\pi$
$168$			11809.8i			0.418432i
$169$	17113.1			0.599177
$170$	−43487.4			−1.50476
$171$	3352.04			0.114635
$172$		−	5011.92i		−	0.169413i
$173$	34112.4			1.13978			0.569889	−	0.821722i	$-0.306986\pi$
$173$	34112.4			1.13978			0.569889	+	0.821722i	$0.306986\pi$
$174$	−36122.4			−1.19310
$175$			17788.6i			0.580854i
$176$			48077.8i			1.55210i
$177$			28695.4i			0.915939i
$178$		−	32493.8i		−	1.02556i
$179$		−	47940.4i		−	1.49622i	−0.663574	−	0.748111i	$-0.730961\pi$
$179$		−	47940.4i		−	1.49622i	0.663574	−	0.748111i	$-0.269039\pi$
$180$			4755.38i			0.146771i
$181$	63592.3			1.94110			0.970549	−	0.240904i	$-0.0774441\pi$
$181$	63592.3			1.94110			0.970549	+	0.240904i	$0.0774441\pi$
$182$			36170.4i			1.09197i
$183$	−7597.88			−0.226877
$184$			7869.91i			0.232452i
$185$		−	17833.1i		−	0.521054i
$186$			1816.48i			0.0525054i
$187$			68801.1i			1.96749i
$188$	4379.61			0.123914
$189$	9433.52			0.264089
$190$	−11850.2			−0.328262
$191$			65669.0i			1.80009i	0.435798	+	0.900045i	$0.356466\pi$
$191$			65669.0i			1.80009i	−0.435798	+	0.900045i	$0.643534\pi$
$192$			1218.19i			0.0330457i
$193$	4154.95			0.111545			0.0557726	−	0.998443i	$-0.482238\pi$
$193$	4154.95			0.111545			0.0557726	+	0.998443i	$0.482238\pi$
$194$	20838.2			0.553676
$195$		−	10555.2i		−	0.277585i
$196$	19669.1			0.512003
$197$			55597.6i			1.43260i	0.697795	+	0.716298i	$0.254165\pi$
$197$			55597.6i			1.43260i	−0.697795	+	0.716298i	$0.745835\pi$
$198$	20499.3			0.522888
$199$	33970.0			0.857806			0.428903	−	0.903350i	$-0.358900\pi$
$199$	33970.0			0.857806			0.428903	+	0.903350i	$0.358900\pi$
$200$		−	8942.26i		−	0.223557i
$201$	−10448.6	−	20854.4i	−0.258621	−	0.516186i
$202$	−48383.4			−1.18575
$203$		−	92974.1i		−	2.25616i
$204$			21961.7i			0.527722i
$205$	17527.7			0.417077
$206$		−	1736.27i		−	0.0409149i
$207$	6286.38			0.146710
$208$		−	34063.9i		−	0.787350i
$209$			18748.2i			0.429206i
$210$	−33349.7			−0.756229
$211$	−46910.8			−1.05368			−0.526839	−	0.849965i	$-0.676623\pi$
$211$	−46910.8			−1.05368			−0.526839	+	0.849965i	$0.676623\pi$
$212$		−	32987.7i		−	0.733974i
$213$			26992.1i			0.594947i
$214$			51984.2i			1.13513i
$215$	−10257.0			−0.221894
$216$	−4742.19			−0.101641
$217$	−4675.35			−0.0992876
$218$	−3315.23			−0.0697591
$219$		−	38575.6i		−	0.804312i
$220$	−26597.1			−0.549528
$221$		−	48746.7i		−	0.998069i
$222$	−24538.6			−0.497902
$223$	−56948.5			−1.14518			−0.572588	−	0.819843i	$-0.694061\pi$
$223$	−56948.5			−1.14518			−0.572588	+	0.819843i	$0.694061\pi$
$224$	−71262.3			−1.42025
$225$	−7142.96			−0.141096
$226$	−84428.4			−1.65300
$227$	71484.1			1.38726			0.693630	−	0.720331i	$-0.256010\pi$
$227$	71484.1			1.38726			0.693630	+	0.720331i	$0.256010\pi$
$228$			5984.52i			0.115122i
$229$		−	77696.7i		−	1.48160i	−0.671725	−	0.740801i	$-0.734446\pi$
$229$		−	77696.7i		−	1.48160i	0.671725	−	0.740801i	$-0.265554\pi$
$230$	−22223.8			−0.420110
$231$			52762.3i			0.988779i
$232$			46737.6i			0.868341i
$233$		−	4361.24i		−	0.0803338i	−0.999193	−	0.0401669i	$-0.987211\pi$
$233$		−	4361.24i		−	0.0803338i	0.999193	−	0.0401669i	$-0.0127890\pi$
$234$	−14524.1			−0.265251
$235$		−	8963.01i		−	0.162300i
$236$	−51231.0			−0.919833
$237$	−20049.8			−0.356956
$238$	−154018.			−2.71906
$239$			74265.5i			1.30014i	0.759873	+	0.650072i	$0.225261\pi$
$239$			74265.5i			1.30014i	−0.759873	+	0.650072i	$0.774739\pi$
$240$	31407.5			0.545269
$241$	−40151.3			−0.691298			−0.345649	−	0.938364i	$-0.612341\pi$
$241$	−40151.3			−0.691298			−0.345649	+	0.938364i	$0.612341\pi$
$242$			41044.5i			0.700848i
$243$			3788.00i			0.0641500i
$244$		−	13564.8i		−	0.227841i
$245$		−	40253.4i		−	0.670611i
$246$		−	24118.3i		−	0.398545i
$247$		−	13283.4i		−	0.217728i
$248$	2350.28			0.0382134
$249$		−	41128.2i		−	0.663347i
$250$	84909.1			1.35855
$251$			4427.98i			0.0702842i	0.999382	+	0.0351421i	$0.0111884\pi$
$251$			4427.98i			0.0702842i	−0.999382	+	0.0351421i	$0.988812\pi$
$252$			16842.0i			0.265212i
$253$			35160.1i			0.549299i
$254$			83174.4i			1.28921i
$255$	44945.3			0.691200
$256$	83078.8			1.26768
$257$	−128538.			−1.94611			−0.973054	−	0.230578i	$-0.925938\pi$
$257$	−128538.			−1.94611			−0.973054	+	0.230578i	$0.925938\pi$
$258$			14113.9i			0.212034i
$259$		−	63158.9i		−	0.941532i
$260$	18844.5			0.278765
$261$	37333.4			0.548045
$262$			49582.5i			0.722314i
$263$	63327.3			0.915544			0.457772	−	0.889070i	$-0.348648\pi$
$263$	63327.3			0.915544			0.457772	+	0.889070i	$0.348648\pi$
$264$		−	26523.3i		−	0.380557i
$265$	−67510.4			−0.961344
$266$	−41969.7			−0.593161
$267$			33583.1i			0.471084i
$268$	37232.2	−	18654.2i	0.518381	−	0.259721i
$269$	−59575.1			−0.823304			−0.411652	−	0.911341i	$-0.635048\pi$
$269$	−59575.1			−0.823304			−0.411652	+	0.911341i	$0.635048\pi$
$270$		−	13391.4i		−	0.183696i
$271$			65599.3i			0.893224i	0.894728	+	0.446612i	$0.147370\pi$
$271$			65599.3i			0.893224i	−0.894728	+	0.446612i	$0.852630\pi$
$272$	145049.			1.96054
$273$		−	37382.9i		−	0.501589i
$274$	123946.			1.65094
$275$		−	39951.0i		−	0.528278i
$276$			11223.3i			0.147334i
$277$	106391.			1.38658			0.693292	−	0.720656i	$-0.256159\pi$
$277$	106391.			1.38658			0.693292	+	0.720656i	$0.256159\pi$
$278$	7164.78			0.0927072
$279$		−	1877.37i		−	0.0241180i
$280$			43150.0i			0.550383i
$281$			26539.3i			0.336107i	0.985778	+	0.168054i	$0.0537481\pi$
$281$			26539.3i			0.336107i	−0.985778	+	0.168054i	$0.946252\pi$
$282$	−12333.2			−0.155088
$283$	−97919.4			−1.22263			−0.611316	−	0.791386i	$-0.709360\pi$
$283$	−97919.4			−1.22263			−0.611316	+	0.791386i	$0.709360\pi$
$284$	−48190.0			−0.597476
$285$	12247.5			0.150785
$286$		−	81234.0i		−	0.993130i
$287$	62077.2			0.753647
$288$		−	28615.1i		−	0.344993i
$289$	124049.			1.48524
$290$	−131982.			−1.56935
$291$	−21536.7			−0.254328
$292$	68870.4			0.807731
$293$	120981.			1.40923			0.704615	−	0.709590i	$-0.251120\pi$
$293$	120981.			1.40923			0.704615	+	0.709590i	$0.251120\pi$
$294$	−55389.4			−0.640814
$295$			104846.i			1.20478i
$296$			31749.7i			0.362373i
$297$	−21186.5			−0.240185
$298$		−	49232.2i		−	0.554391i
$299$		−	24911.5i		−	0.278649i
$300$		−	12752.6i		−	0.141695i
$301$	−36327.1			−0.400957
$302$		−	2229.83i		−	0.0244488i
$303$	50005.4			0.544667
$304$	39525.5			0.427691
$305$	−27760.7			−0.298422
$306$		−	61845.4i		−	0.660487i
$307$	−7739.25			−0.0821150			−0.0410575	−	0.999157i	$-0.513073\pi$
$307$	−7739.25			−0.0821150			−0.0410575	+	0.999157i	$0.513073\pi$
$308$	−94198.3			−0.992983
$309$			1794.47i			0.0187940i
$310$			6636.94i			0.0690629i
$311$		−	145710.i		−	1.50650i	−0.657736	−	0.753248i	$-0.728486\pi$
$311$		−	145710.i		−	1.50650i	0.657736	−	0.753248i	$-0.271514\pi$
$312$			18792.2i			0.193049i
$313$		−	95579.0i		−	0.975605i	−0.872954	−	0.487802i	$-0.837799\pi$
$313$		−	95579.0i		−	0.975605i	0.872954	−	0.487802i	$-0.162201\pi$
$314$			15456.7i			0.156768i
$315$	34467.7			0.347369
$316$		−	35795.7i		−	0.358473i
$317$	−71022.9			−0.706773			−0.353386	−	0.935477i	$-0.614970\pi$
$317$	−71022.9			−0.706773			−0.353386	+	0.935477i	$0.614970\pi$
$318$			92895.4i			0.918628i
$319$			208808.i			2.05194i
$320$			4450.97i			0.0434665i
$321$		−	53726.9i		−	0.521413i
$322$	−78709.4			−0.759128
$323$	56562.4			0.542154
$324$	−6762.84			−0.0644227
$325$			28305.9i			0.267985i
$326$		−	214913.i		−	2.02222i
$327$	3426.37			0.0320434
$328$	−31205.9			−0.290061
$329$		−	31744.0i		−	0.293272i
$330$	74899.1			0.687779
$331$		−	20488.9i		−	0.187009i	−0.995619	−	0.0935044i	$-0.970193\pi$
$331$		−	20488.9i		−	0.187009i	0.995619	−	0.0935044i	$-0.0298069\pi$
$332$	73427.6			0.666167
$333$	25361.2			0.228708
$334$			12709.1i			0.113925i
$335$	−38176.4	−	76196.8i	−0.340177	−	0.678965i
$336$	111235.			0.985288
$337$		−	49364.4i		−	0.434665i	−0.976098	−	0.217332i	$-0.930264\pi$
$337$		−	49364.4i		−	0.434665i	0.976098	−	0.217332i	$-0.0697355\pi$
$338$		−	86038.0i		−	0.753107i
$339$	87258.7			0.759293
$340$			80242.4i			0.694138i
$341$	10500.2			0.0903006
$342$		−	16852.8i		−	0.144085i
$343$			18879.1i			0.160469i
$344$	18261.4			0.154319
$345$	22968.8			0.192975
$346$		−	171504.i		−	1.43259i
$347$			122510.i			1.01745i	0.860930	+	0.508724i	$0.169883\pi$
$347$			122510.i			1.01745i	−0.860930	+	0.508724i	$0.830117\pi$
$348$			66652.6i			0.550375i
$349$	156144.			1.28196			0.640982	−	0.767556i	$-0.278527\pi$
$349$	156144.			1.28196			0.640982	+	0.767556i	$0.278527\pi$
$350$	89434.4			0.730077
$351$	15011.0			0.121841
$352$	160046.			1.29169
$353$			78772.5i			0.632157i	0.948733	+	0.316079i	$0.102366\pi$
$353$			78772.5i			0.632157i	−0.948733	+	0.316079i	$0.897634\pi$
$354$	144270.			1.15125
$355$			98622.4i			0.782562i
$356$	−59957.1			−0.473087
$357$	159181.			1.24898
$358$	−241026.			−1.88060
$359$	−156631.			−1.21532			−0.607659	−	0.794198i	$-0.707891\pi$
$359$	−156631.			−1.21532			−0.607659	+	0.794198i	$0.707891\pi$
$360$	−17326.7			−0.133694
$361$	−114908.			−0.881729
$362$		−	319717.i		−	2.43977i
$363$		−	42420.4i		−	0.321930i
$364$	66741.0			0.503721
$365$		−	140945.i		−	1.05795i
$366$			38199.2i			0.285162i
$367$			20791.9i			0.154370i	0.997017	+	0.0771850i	$0.0245932\pi$
$367$			20791.9i			0.154370i	−0.997017	+	0.0771850i	$0.975407\pi$
$368$	74125.6			0.547360
$369$			24926.9i			0.183069i
$370$	−89657.8			−0.654914
$371$	−239100.			−1.73712
$372$	3351.74			0.0242206
$373$			169032.i			1.21493i	0.794346	+	0.607465i	$0.207814\pi$
$373$			169032.i			1.21493i	−0.794346	+	0.607465i	$0.792186\pi$
$374$	345905.			2.47294
$375$	−87755.5			−0.624039
$376$			15957.6i			0.112873i
$377$		−	147944.i		−	1.04091i
$378$		−	47428.1i		−	0.331934i
$379$			226193.i			1.57471i	0.616501	+	0.787354i	$0.288550\pi$
$379$			226193.i			1.57471i	−0.616501	+	0.787354i	$0.711450\pi$
$380$			21865.9i			0.151426i
$381$		−	85962.6i		−	0.592188i
$382$	330158.			2.26254
$383$		−	246228.i		−	1.67857i	−0.543692	−	0.839285i	$-0.682974\pi$
$383$		−	246228.i		−	1.67857i	0.543692	−	0.839285i	$-0.317026\pi$
$384$	−81987.0			−0.556010
$385$			192780.i			1.30059i
$386$		−	20889.5i		−	0.140201i
$387$		−	14587.0i		−	0.0973967i
$388$		−	38450.3i		−	0.255409i
$389$	−175811.			−1.16184			−0.580919	−	0.813961i	$-0.697307\pi$
$389$	−175811.			−1.16184			−0.580919	+	0.813961i	$0.697307\pi$
$390$	−53067.3			−0.348897
$391$	106076.			0.693850
$392$			71666.4i			0.466384i
$393$		−	51244.6i		−	0.331790i
$394$	279523.			1.80063
$395$	−73257.0			−0.469521
$396$		−	37825.0i		−	0.241206i
$397$	116777.			0.740928			0.370464	−	0.928847i	$-0.379199\pi$
$397$	116777.			0.740928			0.370464	+	0.928847i	$0.379199\pi$
$398$		−	170788.i		−	1.07818i
$399$	43376.6			0.272464
$400$	−84226.0			−0.526413
$401$		−	65272.5i		−	0.405921i	−0.979187	−	0.202960i	$-0.934944\pi$
$401$		−	65272.5i		−	0.405921i	0.979187	−	0.202960i	$-0.0650563\pi$
$402$	−104848.	+	52531.3i	−0.648796	+	0.325062i
$403$	−7439.60			−0.0458078
$404$			89276.4i			0.546983i
$405$			13840.4i			0.0843796i
$406$	−467437.			−2.83577
$407$			141847.i			0.856309i
$408$	−80019.7			−0.480703
$409$		−	287332.i		−	1.71766i	−0.512259	−	0.858831i	$-0.671191\pi$
$409$		−	287332.i		−	1.71766i	0.512259	−	0.858831i	$-0.328809\pi$
$410$		−	88122.2i		−	0.524225i
$411$	−128101.			−0.758349
$412$	−3203.73			−0.0188739
$413$			371329.i			2.17700i
$414$		−	31605.5i		−	0.184400i
$415$		−	150272.i		−	0.872532i
$416$	−113395.			−0.655251
$417$	−7404.97			−0.0425845
$418$	94258.5			0.539471
$419$	−79986.7			−0.455606			−0.227803	−	0.973707i	$-0.573154\pi$
$419$	−79986.7			−0.455606			−0.227803	+	0.973707i	$0.573154\pi$
$420$			61536.4i			0.348846i
$421$	−198813.			−1.12171			−0.560854	−	0.827915i	$-0.689527\pi$
$421$	−198813.			−1.12171			−0.560854	+	0.827915i	$0.689527\pi$
$422$			235849.i			1.32437i
$423$	12746.7			0.0712388
$424$	120194.			0.668577
$425$	−120530.			−0.667296
$426$	135706.			0.747790
$427$	−98319.3			−0.539241
$428$	95920.6			0.523630
$429$			83957.2i			0.456188i
$430$			51568.4i			0.278899i
$431$	−365888.			−1.96967			−0.984836	−	0.173487i	$-0.944496\pi$
$431$	−365888.			−1.96967			−0.984836	+	0.173487i	$0.944496\pi$
$432$			44666.0i			0.239337i
$433$			24034.1i			0.128189i	0.997944	+	0.0640946i	$0.0204159\pi$
$433$			24034.1i			0.128189i	−0.997944	+	0.0640946i	$0.979584\pi$
$434$			23505.9i			0.124795i
$435$	136407.			0.720870
$436$			6117.22i			0.0321796i
$437$	28905.6			0.151363
$438$	−193943.			−1.01094
$439$	−97415.6			−0.505475			−0.252737	−	0.967535i	$-0.581331\pi$
$439$	−97415.6			−0.505475			−0.252737	+	0.967535i	$0.581331\pi$
$440$		−	96909.4i		−	0.500565i
$441$	57246.2			0.294354
$442$	−245079.			−1.25448
$443$		−	244543.i		−	1.24608i	−0.782188	−	0.623042i	$-0.785896\pi$
$443$		−	244543.i		−	1.24608i	0.782188	−	0.623042i	$-0.214104\pi$
$444$			45278.3i			0.229680i
$445$			122704.i			0.619639i
$446$			286315.i			1.43938i
$447$			50882.6i			0.254656i
$448$			15763.9i			0.0785429i
$449$	−76739.1			−0.380648			−0.190324	−	0.981721i	$-0.560954\pi$
$449$	−76739.1			−0.380648			−0.190324	+	0.981721i	$0.560954\pi$
$450$			35912.0i			0.177343i
$451$	−139417.			−0.685431
$452$			155786.i			0.762521i
$453$			2304.58i			0.0112304i
$454$		−	359395.i		−	1.74365i
$455$		−	136588.i		−	0.659764i
$456$	−21805.2			−0.104865
$457$	220481.			1.05569			0.527847	−	0.849339i	$-0.322999\pi$
$457$	220481.			1.05569			0.527847	+	0.849339i	$0.322999\pi$
$458$	−390629.			−1.86223
$459$			63918.7i			0.303391i
$460$			41007.1i			0.193795i
$461$	5115.66			0.0240713			0.0120357	−	0.999928i	$-0.496169\pi$
$461$	5115.66			0.0240713			0.0120357	+	0.999928i	$0.496169\pi$
$462$	265268.			1.24280
$463$			31656.2i			0.147672i	0.997270	+	0.0738358i	$0.0235241\pi$
$463$			31656.2i			0.147672i	−0.997270	+	0.0738358i	$0.976476\pi$
$464$	440215.			2.04470
$465$		−	6859.43i		−	0.0317236i
$466$	−21926.6			−0.100972
$467$	−200992.			−0.921604			−0.460802	−	0.887503i	$-0.652438\pi$
$467$	−200992.			−0.921604			−0.460802	+	0.887503i	$0.652438\pi$
$468$			26799.6i			0.122359i
$469$	−135208.	−	269864.i	−0.614692	−	1.22687i
$470$	−45062.5			−0.203995
$471$		−	15974.8i		−	0.0720102i
$472$		−	186665.i		−	0.837876i
$473$	81586.0			0.364664
$474$			100803.i			0.448658i
$475$	−32844.3			−0.145570
$476$			284192.i			1.25429i
$477$		−	96009.5i		−	0.421966i
$478$	373378.			1.63415
$479$	331616.			1.44532			0.722661	−	0.691203i	$-0.242919\pi$
$479$	331616.			1.44532			0.722661	+	0.691203i	$0.242919\pi$
$480$		−	104552.i		−	0.453786i
$481$		−	100501.i		−	0.434389i
$482$			201865.i			0.868895i
$483$	81348.0			0.348701
$484$	75734.6			0.323299
$485$	−78689.7			−0.334529
$486$	19044.6			0.0806304
$487$			119702.i			0.504713i	0.967634	+	0.252357i	$0.0812056\pi$
$487$			119702.i			0.504713i	−0.967634	+	0.252357i	$0.918794\pi$
$488$	49424.6			0.207541
$489$			222118.i			0.928894i
$490$	−202379.			−0.842893
$491$	−304188.			−1.26177			−0.630883	−	0.775878i	$-0.717307\pi$
$491$	−304188.			−1.26177			−0.630883	+	0.775878i	$0.717307\pi$
$492$	−44502.8			−0.183847
$493$	629964.			2.59192
$494$	−66783.7			−0.273663
$495$	−77410.0			−0.315927
$496$		−	22137.0i		−	0.0899818i
$497$			349288.i			1.41407i
$498$	−206777.			−0.833763
$499$			178024.i			0.714953i	0.933922	+	0.357477i	$0.116363\pi$
$499$			178024.i			0.714953i	−0.933922	+	0.357477i	$0.883637\pi$
$500$		−	156673.i		−	0.626692i
$501$		−	13135.1i		−	0.0523309i
$502$	22262.1			0.0883404
$503$			219743.i			0.868520i	0.900787	+	0.434260i	$0.142990\pi$
$503$			219743.i			0.868520i	−0.900787	+	0.434260i	$0.857010\pi$
$504$	−61365.6			−0.241582
$505$	182707.			0.716427
$506$	176771.			0.690416
$507$			88922.2i			0.345935i
$508$	153472.			0.594706
$509$	182492.			0.704381			0.352190	−	0.935928i	$-0.385437\pi$
$509$	182492.			0.704381			0.352190	+	0.935928i	$0.385437\pi$
$510$		−	225967.i		−	0.868771i
$511$		−	499182.i		−	1.91169i
$512$		−	165233.i		−	0.630315i
$513$			17417.7i			0.0661845i
$514$			646241.i			2.44607i
$515$			6556.54i			0.0247207i
$516$	26042.7			0.0978107
$517$			71293.0i			0.266726i
$518$	−317538.			−1.18341
$519$			177253.i			0.658051i
$520$			68661.9i			0.253927i
$521$			212512.i			0.782902i	0.920199	+	0.391451i	$0.128027\pi$
$521$			212512.i			0.782902i	−0.920199	+	0.391451i	$0.871973\pi$
$522$		−	187698.i		−	0.688839i
$523$	−472326.			−1.72679			−0.863393	−	0.504532i	$-0.831665\pi$
$523$	−472326.			−1.72679			−0.863393	+	0.504532i	$0.831665\pi$
$524$	91488.9			0.333201
$525$	−92432.5			−0.335356
$526$		−	318385.i		−	1.15075i
$527$		−	31678.8i		−	0.114064i
$528$	−249820.			−0.896105
$529$	−225632.			−0.806285
$530$			339416.i			1.20832i
$531$	−149106.			−0.528818
$532$			77441.8i			0.273623i
$533$	98779.5			0.347706
$534$	168843.			0.592107
$535$		−	196304.i		−	0.685839i
$536$	67968.5	+	135659.i	0.236580	+	0.472193i
$537$	249106.			0.863844
$538$			299521.i			1.03481i
$539$			320181.i			1.10209i
$540$	−24709.7			−0.0847383
$541$			224930.i			0.768517i	0.923226	+	0.384258i	$0.125543\pi$
$541$			224930.i			0.768517i	−0.923226	+	0.384258i	$0.874457\pi$
$542$	329808.			1.12270
$543$			330435.i			1.12069i
$544$		−	482851.i		−	1.63161i
$545$	12519.1			0.0421482
$546$	−187947.			−0.630448
$547$			570141.i			1.90549i	0.303765	+	0.952747i	$0.401756\pi$
$547$			570141.i			1.90549i	−0.303765	+	0.952747i	$0.598244\pi$
$548$		−	228703.i		−	0.761573i
$549$		−	39479.7i		−	0.130987i
$550$	−200858.			−0.663994
$551$	171664.			0.565426
$552$	−40893.2			−0.134206
$553$	−259452.			−0.848412
$554$		−	534894.i		−	1.74280i
$555$	92663.4			0.300831
$556$		−	13220.4i		−	0.0427655i
$557$	−337945.			−1.08927			−0.544635	−	0.838673i	$-0.683332\pi$
$557$	−337945.			−1.08927			−0.544635	+	0.838673i	$0.683332\pi$
$558$	−9438.69			−0.0303140
$559$	−57805.0			−0.184987
$560$	406424.			1.29600
$561$	−357501.			−1.13593
$562$	133430.			0.422454
$563$			530964.i			1.67513i	0.546339	+	0.837564i	$0.316021\pi$
$563$			530964.i			1.67513i	−0.546339	+	0.837564i	$0.683979\pi$
$564$			22757.1i			0.0715417i
$565$	318821.			0.998735
$566$			492301.i			1.53673i
$567$			49018.0i			0.152472i
$568$		−	175585.i		−	0.544241i
$569$	385897.			1.19192			0.595960	−	0.803014i	$-0.296772\pi$
$569$	385897.			1.19192			0.595960	+	0.803014i	$0.296772\pi$
$570$		−	61575.7i		−	0.189522i
$571$	−218959.			−0.671569			−0.335784	−	0.941939i	$-0.609001\pi$
$571$	−218959.			−0.671569			−0.335784	+	0.941939i	$0.609001\pi$
$572$	−149892.			−0.458127
$573$	−341226.			−1.03928
$574$		−	312100.i		−	0.947261i
$575$	−61595.9			−0.186301
$576$	−6329.93			−0.0190789
$577$		−	333856.i		−	1.00278i	−0.865220	−	0.501392i	$-0.832821\pi$
$577$		−	333856.i		−	1.00278i	0.865220	−	0.501392i	$-0.167179\pi$
$578$		−	623669.i		−	1.86680i
$579$			21589.7i			0.0644006i
$580$			243532.i			0.723934i
$581$		−	532214.i		−	1.57664i
$582$			108278.i			0.319665i
$583$	536987.			1.57989
$584$			250936.i			0.735763i
$585$	54846.2			0.160264
$586$		−	608245.i		−	1.77126i
$587$			465863.i			1.35202i	0.736894	+	0.676008i	$0.236292\pi$
$587$			465863.i			1.35202i	−0.736894	+	0.676008i	$0.763708\pi$
$588$			102204.i			0.295605i
$589$		−	8632.41i		−	0.0248829i
$590$	527124.			1.51429
$591$	−288894.			−0.827110
$592$	299046.			0.853285
$593$		−	306311.i		−	0.871070i	−0.900172	−	0.435535i	$-0.856559\pi$
$593$		−	306311.i		−	0.871070i	0.900172	−	0.435535i	$-0.143441\pi$
$594$			106517.i			0.301889i
$595$	581608.			1.64284
$596$	−90842.5			−0.255739
$597$			176513.i			0.495255i
$598$	−125245.			−0.350235
$599$		−	154619.i		−	0.430932i	−0.976511	−	0.215466i	$-0.930873\pi$
$599$		−	154619.i		−	0.430932i	0.976511	−	0.215466i	$-0.0691271\pi$
$600$	46465.4			0.129070
$601$	−257817.			−0.713778			−0.356889	−	0.934147i	$-0.616163\pi$
$601$	−257817.			−0.713778			−0.356889	+	0.934147i	$0.616163\pi$
$602$			182638.i			0.503964i
$603$	108363.	−	54292.3i	0.298020	−	0.149315i
$604$	−4114.44			−0.0112781
$605$		−	154993.i		−	0.423450i
$606$		−	251408.i		−	0.684594i
$607$	87115.8			0.236439			0.118220	−	0.992987i	$-0.462281\pi$
$607$	87115.8			0.236439			0.118220	+	0.992987i	$0.462281\pi$
$608$		−	131576.i		−	0.355934i
$609$	483107.			1.30259
$610$			139570.i			0.375087i
$611$		−	50512.3i		−	0.135305i
$612$	−114116.			−0.304680
$613$	−88057.5			−0.234339			−0.117170	−	0.993112i	$-0.537382\pi$
$613$	−88057.5			−0.234339			−0.117170	+	0.993112i	$0.537382\pi$
$614$			38910.0i			0.103211i
$615$			91076.3i			0.240799i
$616$		−	343221.i		−	0.904509i
$617$	125552.			0.329801			0.164901	−	0.986310i	$-0.447270\pi$
$617$	125552.			0.329801			0.164901	+	0.986310i	$0.447270\pi$
$618$	9021.90			0.0236222
$619$	−201541.			−0.525997			−0.262998	−	0.964796i	$-0.584711\pi$
$619$	−201541.			−0.525997			−0.262998	+	0.964796i	$0.584711\pi$
$620$	12246.4			0.0318585
$621$			32665.0i			0.0847031i
$622$	−732573.			−1.89352
$623$			434577.i			1.11967i
$624$	177001.			0.454577
$625$	−155290.			−0.397542
$626$	−480534.			−1.22624
$627$	−97418.3			−0.247802
$628$	28520.4			0.0723164
$629$	427945.			1.08165
$630$		−	173290.i		−	0.436609i
$631$			710589.i			1.78468i	0.451365	+	0.892339i	$0.350937\pi$
$631$			710589.i			1.78468i	−0.451365	+	0.892339i	$0.649063\pi$
$632$	130425.			0.326533
$633$		−	243756.i		−	0.608341i
$634$			357075.i			0.888344i
$635$		−	314085.i		−	0.778933i
$636$	171409.			0.423760
$637$		−	226854.i		−	0.559071i
$638$	1.04980e6			2.57909
$639$	−140255.			−0.343493
$640$	−299560.			−0.731347
$641$		−	498293.i		−	1.21274i	−0.795182	−	0.606371i	$-0.792625\pi$
$641$		−	498293.i		−	1.21274i	0.795182	−	0.606371i	$-0.207375\pi$
$642$	−270118.			−0.655365
$643$	311261.			0.752841			0.376420	−	0.926449i	$-0.377155\pi$
$643$	311261.			0.752841			0.376420	+	0.926449i	$0.377155\pi$
$644$			145234.i			0.350183i
$645$		−	53297.2i		−	0.128110i
$646$		−	284374.i		−	0.681435i
$647$			169232.i			0.404273i	0.979357	+	0.202137i	$0.0647885\pi$
$647$			169232.i			0.404273i	−0.979357	+	0.202137i	$0.935211\pi$
$648$		−	24641.1i		−	0.0586827i
$649$		−	833958.i		−	1.97995i
$650$	142311.			0.336831
$651$		−	24293.9i		−	0.0573237i
$652$	−396555.			−0.932843
$653$		−	630869.i		−	1.47949i	−0.672886	−	0.739746i	$-0.734946\pi$
$653$		−	630869.i		−	1.47949i	0.672886	−	0.739746i	$-0.265054\pi$
$654$		−	17226.5i		−	0.0402755i
$655$		−	187235.i		−	0.436419i
$656$			293924.i			0.683011i
$657$	200445.			0.464370
$658$	−159597.			−0.368614
$659$	−782530.			−1.80190			−0.900949	−	0.433926i	$-0.857128\pi$
$659$	−782530.			−1.80190			−0.900949	+	0.433926i	$0.857128\pi$
$660$		−	138203.i		−	0.317270i
$661$		−	306143.i		−	0.700682i	−0.936622	−	0.350341i	$-0.886066\pi$
$661$		−	306143.i		−	0.700682i	0.936622	−	0.350341i	$-0.113934\pi$
$662$	−103010.			−0.235052
$663$	253295.			0.576235
$664$			267541.i			0.606812i
$665$	158487.			0.358386
$666$		−	127506.i		−	0.287464i
$667$	321937.			0.723634
$668$	23450.6			0.0525534
$669$		−	295913.i		−	0.661168i
$670$	−383088.	+	191936.i	−0.853392	+	0.427570i
$671$	220812.			0.490432
$672$		−	370290.i		−	0.819980i
$673$			73255.4i			0.161737i	0.996725	+	0.0808685i	$0.0257694\pi$
$673$			73255.4i			0.161737i	−0.996725	+	0.0808685i	$0.974231\pi$
$674$	−248185.			−0.546331
$675$		−	37115.9i		−	0.0814616i
$676$	−158756.			−0.347406
$677$		−	787993.i		−	1.71927i	−0.510905	−	0.859637i	$-0.670689\pi$
$677$		−	787993.i		−	1.71927i	0.510905	−	0.859637i	$-0.329311\pi$
$678$		−	438703.i		−	0.954358i
$679$	−278693.			−0.604486
$680$	−292371.			−0.632291
$681$			371443.i			0.800935i
$682$		−	52791.2i		−	0.113499i
$683$		−	348687.i		−	0.747470i	−0.927535	−	0.373735i	$-0.878077\pi$
$683$		−	348687.i		−	0.747470i	0.927535	−	0.373735i	$-0.121923\pi$
$684$	−31096.5			−0.0664659
$685$	−468048.			−0.997492
$686$	94916.6			0.201695
$687$	403724.			0.855403
$688$		−	172002.i		−	0.363377i
$689$	−380464.			−0.801447
$690$		−	115478.i		−	0.242551i
$691$	846698.			1.77326			0.886630	−	0.462479i	$-0.153040\pi$
$691$	846698.			1.77326			0.886630	+	0.462479i	$0.153040\pi$
$692$	−316457.			−0.660849
$693$	−274161.			−0.570872
$694$	615932.			1.27883
$695$	−27055.9			−0.0560134
$696$	−242856.			−0.501337
$697$			420616.i			0.865805i
$698$		−	785033.i		−	1.61130i
$699$	22661.7			0.0463807
$700$		−	165023.i		−	0.336782i
$701$			731336.i			1.48827i	0.668031	+	0.744133i	$0.267137\pi$
$701$			731336.i			1.48827i	−0.668031	+	0.744133i	$0.732863\pi$
$702$		−	75469.3i		−	0.153143i
$703$	116614.			0.235961
$704$		−	35403.7i		−	0.0714336i
$705$	46573.1			0.0937038
$706$	396038.			0.794561
$707$	647088.			1.29457
$708$		−	266204.i		−	0.531066i
$709$	−349966.			−0.696198			−0.348099	−	0.937458i	$-0.613173\pi$
$709$	−349966.			−0.696198			−0.348099	+	0.937458i	$0.613173\pi$
$710$	495835.			0.983604
$711$		−	104182.i		−	0.206088i
$712$		−	218460.i		−	0.430935i
$713$		−	16189.1i		−	0.0318452i
$714$		−	800302.i		−	1.56985i
$715$			306758.i			0.600045i
$716$			444737.i			0.867516i
$717$	−385895.			−0.750638
$718$			787482.i			1.52754i
$719$	−886462.			−1.71476			−0.857378	−	0.514688i	$-0.827908\pi$
$719$	−886462.			−1.71476			−0.857378	+	0.514688i	$0.827908\pi$
$720$			163198.i			0.314811i
$721$			23221.1i			0.0446696i
$722$			577712.i			1.10825i
$723$		−	208632.i		−	0.399121i
$724$	−589938.			−1.12546
$725$	−365804.			−0.695940
$726$	−213273.			−0.404635
$727$			581750.i			1.10070i	0.834935	+	0.550348i	$0.185505\pi$
$727$			581750.i			1.10070i	−0.834935	+	0.550348i	$0.814495\pi$
$728$			243178.i			0.458840i
$729$	−19683.0			−0.0370370
$730$	−708619.			−1.32974
$731$		−	246141.i		−	0.460627i
$732$	70484.6			0.131544
$733$			652553.i			1.21453i	0.794500	+	0.607264i	$0.207733\pi$
$733$			652553.i			1.21453i	−0.794500	+	0.607264i	$0.792267\pi$
$734$	104534.			0.194028
$735$	209163.			0.387177
$736$		−	246756.i		−	0.455526i
$737$	303660.	+	606080.i	0.559053	+	1.11582i
$738$	125323.			0.230100
$739$		−	15794.9i		−	0.0289220i	−0.999895	−	0.0144610i	$-0.995397\pi$
$739$		−	15794.9i		−	0.0289220i	0.999895	−	0.0144610i	$-0.00460324\pi$
$740$			165435.i			0.302110i
$741$	69022.5			0.125705
$742$			1.20210e6i			2.18340i
$743$	275475.			0.499005			0.249503	−	0.968374i	$-0.419733\pi$
$743$	275475.			0.499005			0.249503	+	0.968374i	$0.419733\pi$
$744$			12212.4i			0.0220625i
$745$			185912.i			0.334961i
$746$	849828.			1.52705
$747$	213708.			0.382984
$748$		−	638259.i		−	1.14076i
$749$		−	695246.i		−	1.23929i
$750$			441200.i			0.784356i
$751$	395216.			0.700736			0.350368	−	0.936612i	$-0.386056\pi$
$751$	395216.			0.700736			0.350368	+	0.936612i	$0.386056\pi$
$752$	150302.			0.265784
$753$	−23008.4			−0.0405786
$754$	−743804.			−1.30832
$755$			8420.34i			0.0147719i
$756$	−87513.6			−0.153120
$757$		−	935128.i		−	1.63185i	−0.578161	−	0.815923i	$-0.696229\pi$
$757$		−	935128.i		−	1.63185i	0.578161	−	0.815923i	$-0.303771\pi$
$758$	1.13721e6			1.97925
$759$	−182697.			−0.317138
$760$	−79670.7			−0.137934
$761$	−61376.1			−0.105982			−0.0529908	−	0.998595i	$-0.516875\pi$
$761$	−61376.1			−0.105982			−0.0529908	+	0.998595i	$0.516875\pi$
$762$	−432187.			−0.744323
$763$	44338.5			0.0761608
$764$		−	609204.i		−	1.04370i
$765$			233542.i			0.399064i
$766$	−1.23794e6			−2.10980
$767$			590873.i			1.00439i
$768$			431690.i			0.731896i
$769$		−	360240.i		−	0.609171i	−0.952485	−	0.304585i	$-0.901482\pi$
$769$		−	360240.i		−	0.609171i	0.952485	−	0.304585i	$-0.0985179\pi$
$770$	969222.			1.63471
$771$		−	667905.i		−	1.12359i
$772$	−38544.9			−0.0646744
$773$	−529295.			−0.885806			−0.442903	−	0.896569i	$-0.646051\pi$
$773$	−529295.			−0.885806			−0.442903	+	0.896569i	$0.646051\pi$
$774$	−73337.8			−0.122418
$775$			18395.0i			0.0306265i
$776$	140098.			0.232652
$777$	328183.			0.543594
$778$			883907.i			1.46032i
$779$			114617.i			0.188875i
$780$			97918.9i			0.160945i
$781$		−	784456.i		−	1.28608i
$782$		−	533311.i		−	0.872102i
$783$			193990.i			0.316414i
$784$	675016.			1.09820
$785$		−	58367.9i		−	0.0947185i
$786$	−257638.			−0.417028
$787$		−	234605.i		−	0.378781i	−0.981902	−	0.189391i	$-0.939349\pi$
$787$		−	234605.i		−	0.378781i	0.981902	−	0.189391i	$-0.0606513\pi$
$788$		−	515772.i		−	0.830626i
$789$			329058.i			0.528590i
$790$			368308.i			0.590142i
$791$	1.12916e6			1.80469
$792$	137819.			0.219715
$793$	−156449.			−0.248787
$794$		−	587109.i		−	0.931275i
$795$		−	350794.i		−	0.555032i
$796$	−315135.			−0.497360
$797$	118490.			0.186537			0.0932687	−	0.995641i	$-0.470268\pi$
$797$	118490.			0.186537			0.0932687	+	0.995641i	$0.470268\pi$
$798$		−	218081.i		−	0.342461i
$799$	215088.			0.336916
$800$			280379.i			0.438093i
$801$	−174503.			−0.271980
$802$	−328165.			−0.510203
$803$			1.12110e6i			1.73865i
$804$	96930.0	+	193464.i	0.149950	+	0.299287i
$805$	297225.			0.458663
$806$			37403.4i			0.0575759i
$807$		−	309561.i		−	0.475335i
$808$	−325288.			−0.498247
$809$		−	563185.i		−	0.860506i	−0.902708	−	0.430253i	$-0.858424\pi$
$809$		−	563185.i		−	0.860506i	0.902708	−	0.430253i	$-0.141576\pi$
$810$	69584.0			0.106057
$811$		−	398470.i		−	0.605835i	−0.953017	−	0.302917i	$-0.902039\pi$
$811$		−	398470.i		−	0.605835i	0.953017	−	0.302917i	$-0.0979606\pi$
$812$			862509.i			1.30813i
$813$	−340864.			−0.515703
$814$	713150.			1.07630
$815$			811562.i			1.22182i
$816$			753695.i			1.13192i
$817$		−	67073.0i		−	0.100486i
$818$	−1.44459e6			−2.15893
$819$	194247.			0.289592
$820$	−162602.			−0.241823
$821$	−987726.			−1.46538			−0.732690	−	0.680562i	$-0.761736\pi$
$821$	−987726.			−1.46538			−0.732690	+	0.680562i	$0.761736\pi$
$822$			644042.i			0.953171i
$823$	−761513.			−1.12429			−0.562144	−	0.827039i	$-0.690023\pi$
$823$	−761513.			−1.12429			−0.562144	+	0.827039i	$0.690023\pi$
$824$		−	11673.1i		−	0.0171923i
$825$	207592.			0.305001
$826$	1.86690e6			2.73628
$827$	−637910.			−0.932714			−0.466357	−	0.884597i	$-0.654434\pi$
$827$	−637910.			−0.932714			−0.466357	+	0.884597i	$0.654434\pi$
$828$	−58318.0			−0.0850632
$829$	−402389.			−0.585513			−0.292757	−	0.956187i	$-0.594573\pi$
$829$	−402389.			−0.585513			−0.292757	+	0.956187i	$0.594573\pi$
$830$	−755509.			−1.09669
$831$			552825.i			0.800545i
$832$			25084.1i			0.0362369i
$833$	965972.			1.39211
$834$			37229.3i			0.0535245i
$835$		−	47992.3i		−	0.0688333i
$836$		−	173924.i		−	0.248856i
$837$	9755.11			0.0139245
$838$			402142.i			0.572653i
$839$	920528.			1.30772			0.653858	−	0.756617i	$-0.273149\pi$
$839$	920528.			1.30772			0.653858	+	0.756617i	$0.273149\pi$
$840$	−224214.			−0.317764
$841$	1.20463e6			1.70318
$842$			999553.i			1.40988i
$843$	−137902.			−0.194051
$844$	435185.			0.610927
$845$			324899.i			0.455025i
$846$		−	64085.4i		−	0.0895403i
$847$		−	548935.i		−	0.765164i
$848$		−	1.13209e6i		−	1.57431i
$849$		−	508804.i		−	0.705887i
$850$			605980.i			0.838727i
$851$	218697.			0.301984
$852$		−	250403.i		−	0.344953i
$853$	−484273.			−0.665568			−0.332784	−	0.943003i	$-0.607988\pi$
$853$	−484273.			−0.665568			−0.332784	+	0.943003i	$0.607988\pi$
$854$			494311.i			0.677773i
$855$			63639.9i			0.0870557i
$856$			349497.i			0.476975i
$857$		−	634502.i		−	0.863915i	−0.901894	−	0.431958i	$-0.857823\pi$
$857$		−	634502.i		−	0.863915i	0.901894	−	0.431958i	$-0.142177\pi$
$858$	422104.			0.573384
$859$	954995.			1.29424			0.647120	−	0.762388i	$-0.275973\pi$
$859$	954995.			1.29424			0.647120	+	0.762388i	$0.275973\pi$
$860$	95153.3			0.128655
$861$			322562.i			0.435119i
$862$			1.83954e6i			2.47569i
$863$	178910.			0.240223			0.120111	−	0.992760i	$-0.461675\pi$
$863$	178910.			0.240223			0.120111	+	0.992760i	$0.461675\pi$
$864$	148688.			0.199182
$865$			647639.i			0.865567i
$866$	120834.			0.161121
$867$			644576.i			0.857504i
$868$	43372.7			0.0575674
$869$	582696.			0.771618
$870$		−	685799.i		−	0.906063i
$871$	−215148.	−	429418.i	−0.283597	−	0.566035i
$872$	−22288.7			−0.0293125
$873$		−	111908.i		−	0.146836i
$874$		−	145326.i		−	0.190249i
$875$	−1.13559e6			−1.48322
$876$			357861.i			0.466344i
$877$	1.04987e6			1.36501			0.682505	−	0.730881i	$-0.260891\pi$
$877$	1.04987e6			1.36501			0.682505	+	0.730881i	$0.260891\pi$
$878$			489768.i			0.635333i
$879$			628635.i			0.813619i
$880$	−912777.			−1.17869
$881$	995577.			1.28269			0.641347	−	0.767251i	$-0.278376\pi$
$881$	995577.			1.28269			0.641347	+	0.767251i	$0.278376\pi$
$882$		−	287812.i		−	0.369974i
$883$			1.54982e6i			1.98774i	0.110568	+	0.993869i	$0.464733\pi$
$883$			1.54982e6i			1.98774i	−0.110568	+	0.993869i	$0.535267\pi$
$884$			452217.i			0.578685i
$885$	−544795.			−0.695579
$886$	−1.22947e6			−1.56621
$887$	−583903.			−0.742152			−0.371076	−	0.928602i	$-0.621011\pi$
$887$	−583903.			−0.742152			−0.371076	+	0.928602i	$0.621011\pi$
$888$	−164976.			−0.209216
$889$		−	1.11239e6i		−	1.40751i
$890$	616908.			0.778826
$891$		−	110088.i		−	0.138671i
$892$	528304.			0.663979
$893$	58611.0			0.0734981
$894$	255818.			0.320078
$895$	910169.			1.13626
$896$	−1.06094e6			−1.32153
$897$	129444.			0.160878
$898$			385814.i			0.478438i
$899$		−	96143.5i		−	0.118960i
$900$	66264.4			0.0818079
$901$		−	1.62007e6i		−	1.99564i
$902$			700936.i			0.861520i
$903$		−	188761.i		−	0.231492i
$904$	−567623.			−0.694581
$905$			1.20733e6i			1.47410i
$906$	11586.5			0.0141155
$907$	−398599.			−0.484531			−0.242266	−	0.970210i	$-0.577891\pi$
$907$	−398599.			−0.484531			−0.242266	+	0.970210i	$0.577891\pi$
$908$	−663150.			−0.804340
$909$			259836.i			0.314464i
$910$	−686709.			−0.829259
$911$	−683325.			−0.823361			−0.411681	−	0.911328i	$-0.635058\pi$
$911$	−683325.			−0.823361			−0.411681	+	0.911328i	$0.635058\pi$
$912$			205380.i			0.246927i
$913$			1.19528e6i			1.43393i
$914$		−	1.10849e6i		−	1.32691i
$915$		−	144249.i		−	0.172294i
$916$			720782.i			0.859040i
$917$		−	663124.i		−	0.788599i
$918$	321358.			0.381333
$919$		−	784151.i		−	0.928472i	−0.885711	−	0.464236i	$-0.846329\pi$
$919$		−	784151.i		−	0.928472i	0.885711	−	0.464236i	$-0.153671\pi$
$920$	−149413.			−0.176528
$921$		−	40214.3i		−	0.0474091i
$922$		−	25719.5i		−	0.0302553i
$923$			555800.i			0.652402i
$924$		−	489469.i		−	0.573299i
$925$	−248497.			−0.290427
$926$	159155.			0.185609
$927$	−9324.35			−0.0108507
$928$		−	1.46543e6i		−	1.70165i
$929$		−	1.00451e6i		−	1.16392i	−0.813218	−	0.581959i	$-0.802287\pi$
$929$		−	1.00451e6i		−	1.16392i	0.813218	−	0.581959i	$-0.197713\pi$
$930$	−34486.6			−0.0398735
$931$	263226.			0.303689
$932$			40458.7i			0.0465779i
$933$	757131.			0.869776
$934$			1.01051e6i			1.15837i
$935$	−1.30622e6			−1.49414
$936$	−97647.2			−0.111457
$937$			335172.i			0.381758i	0.981614	+	0.190879i	$0.0611338\pi$
$937$			335172.i			0.381758i	−0.981614	+	0.190879i	$0.938866\pi$
$938$	−1.35677e6	+	679774.i	−1.54206	+	0.772608i
$939$	496643.			0.563266
$940$			83148.7i			0.0941022i
$941$		−	100686.i		−	0.113707i	−0.998383	−	0.0568536i	$-0.981893\pi$
$941$		−	100686.i		−	0.113707i	0.998383	−	0.0568536i	$-0.0181068\pi$
$942$	−80315.2			−0.0905099
$943$			214952.i			0.241723i
$944$	−1.75818e6			−1.97296
$945$			179099.i			0.200554i
$946$		−	410183.i		−	0.458348i
$947$	31380.8			0.0349916			0.0174958	−	0.999847i	$-0.494431\pi$
$947$	31380.8			0.0349916			0.0174958	+	0.999847i	$0.494431\pi$
$948$	186000.			0.206965
$949$		−	794317.i		−	0.881986i
$950$			165128.i			0.182968i
$951$		−	369046.i		−	0.408055i
$952$	−1.03548e6			−1.14253
$953$	909435.			1.00135			0.500675	−	0.865635i	$-0.333085\pi$
$953$	909435.			1.00135			0.500675	+	0.865635i	$0.333085\pi$
$954$	−482698.			−0.530370
$955$	−1.24675e6			−1.36702
$956$		−	688952.i		−	0.753829i
$957$	−1.08500e6			−1.18469
$958$		−	1.66724e6i		−	1.81663i
$959$	−1.65767e6			−1.80244
$960$	−23127.9			−0.0250954
$961$	918686.			0.994765
$962$	−505279.			−0.545985
$963$	279173.			0.301038
$964$	372479.			0.400818
$965$			78883.4i			0.0847092i
$966$		−	408986.i		−	0.438283i
$967$	−99880.4			−0.106814			−0.0534069	−	0.998573i	$-0.517008\pi$
$967$	−99880.4			−0.106814			−0.0534069	+	0.998573i	$0.517008\pi$
$968$			275947.i			0.294493i
$969$			293907.i			0.313013i
$970$			395621.i			0.420471i
$971$	−1.05668e6			−1.12074			−0.560369	−	0.828243i	$-0.689341\pi$
$971$	−1.05668e6			−1.12074			−0.560369	+	0.828243i	$0.689341\pi$
$972$		−	35140.8i		−	0.0371945i
$973$	−95823.0			−0.101215
$974$	601817.			0.634376
$975$	−147082.			−0.154721
$976$		−	465524.i		−	0.488700i
$977$	−800011.			−0.838121			−0.419060	−	0.907958i	$-0.637640\pi$
$977$	−800011.			−0.838121			−0.419060	+	0.907958i	$0.637640\pi$
$978$	1.11672e6			1.16753
$979$		−	976005.i		−	1.01833i
$980$			373426.i			0.388823i
$981$			17803.9i			0.0185003i
$982$			1.52934e6i			1.58592i
$983$		−	930594.i		−	0.963060i	−0.876430	−	0.481530i	$-0.840081\pi$
$983$		−	930594.i		−	0.963060i	0.876430	−	0.481530i	$-0.159919\pi$
$984$		−	162151.i		−	0.167467i
$985$	−1.05554e6			−1.08794
$986$		−	3.16721e6i		−	3.25779i
$987$	164947.			0.169320
$988$			123228.i			0.126240i
$989$		−	125788.i		−	0.128602i
$990$			389187.i			0.397089i
$991$		−	1.11869e6i		−	1.13910i	−0.821956	−	0.569551i	$-0.807117\pi$
$991$		−	1.11869e6i		−	1.13910i	0.821956	−	0.569551i	$-0.192883\pi$
$992$	−73691.6			−0.0748849
$993$	106463.			0.107970
$994$	1.75608e6			1.77735
$995$			644934.i			0.651432i
$996$			381541.i			0.384612i
$997$	605125.			0.608772			0.304386	−	0.952549i	$-0.401549\pi$
$997$	605125.			0.608772			0.304386	+	0.952549i	$0.401549\pi$
$998$	895036.			0.898627
$999$			131781.i			0.132045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.11	✓	46
67.66	odd	2	inner	201.5.b.a.133.36	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.11	✓	46	1.1	even	1	trivial
201.5.b.a.133.36	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)

\(f(q)\)	\(=\)	\(q-5.02761i q^{2} +5.19615i q^{3} -9.27688 q^{4} +18.9854i q^{5} +26.1242 q^{6} +67.2401i q^{7} -33.8013i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-5.02761i q^{2} +5.19615i q^{3} -9.27688 q^{4} +18.9854i q^{5} +26.1242 q^{6} +67.2401i q^{7} -33.8013i q^{8} -27.0000 q^{9} +95.4513 q^{10} -151.013i q^{11} -48.2041i q^{12} +106.995i q^{13} +338.057 q^{14} -98.6511 q^{15} -318.370 q^{16} -455.598 q^{17} +135.746i q^{18} -124.150 q^{19} -176.125i q^{20} -349.390 q^{21} -759.233 q^{22} -232.829 q^{23} +175.636 q^{24} +264.554 q^{25} +537.929 q^{26} -140.296i q^{27} -623.778i q^{28} -1382.72 q^{29} +495.979i q^{30} +69.5323i q^{31} +1059.82i q^{32} +784.685 q^{33} +2290.57i q^{34} -1276.58 q^{35} +250.476 q^{36} -939.304 q^{37} +624.176i q^{38} -555.962 q^{39} +641.731 q^{40} -923.217i q^{41} +1756.60i q^{42} +540.259i q^{43} +1400.93i q^{44} -512.606i q^{45} +1170.57i q^{46} -472.100 q^{47} -1654.30i q^{48} -2120.23 q^{49} -1330.08i q^{50} -2367.36i q^{51} -992.578i q^{52} +3555.91i q^{53} -705.354 q^{54} +2867.04 q^{55} +2272.80 q^{56} -645.101i q^{57} +6951.77i q^{58} +5522.44 q^{59} +915.174 q^{60} +1462.21i q^{61} +349.581 q^{62} -1815.48i q^{63} +234.442 q^{64} -2031.34 q^{65} -3945.09i q^{66} +(-4013.44 + 2010.83i) q^{67} +4226.53 q^{68} -1209.81i q^{69} +6418.15i q^{70} +5194.64 q^{71} +912.634i q^{72} -7423.88 q^{73} +4722.46i q^{74} +1374.66i q^{75} +1151.72 q^{76} +10154.1 q^{77} +2795.16i q^{78} +3858.59i q^{79} -6044.38i q^{80} +729.000 q^{81} -4641.58 q^{82} -7915.12 q^{83} +3241.24 q^{84} -8649.72i q^{85} +2716.21 q^{86} -7184.81i q^{87} -5104.42 q^{88} +6463.07 q^{89} -2577.18 q^{90} -7194.35 q^{91} +2159.92 q^{92} -361.300 q^{93} +2373.53i q^{94} -2357.03i q^{95} -5506.98 q^{96} +4144.74i q^{97} +10659.7i q^{98} +4077.34i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 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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