LMFDB - Embedded newform 201.5.b.a.133.8

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			133.8
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.58118i q^{2} +5.19615i q^{3} -15.1496 q^{4} +19.0393i q^{5} +29.0007 q^{6} -39.7168i q^{7} -4.74646i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-5.58118i q^{2} +5.19615i q^{3} -15.1496 q^{4} +19.0393i q^{5} +29.0007 q^{6} -39.7168i q^{7} -4.74646i q^{8} -27.0000 q^{9} +106.262 q^{10} +26.8068i q^{11} -78.7194i q^{12} +248.217i q^{13} -221.666 q^{14} -98.9310 q^{15} -268.884 q^{16} +281.691 q^{17} +150.692i q^{18} +293.597 q^{19} -288.437i q^{20} +206.374 q^{21} +149.614 q^{22} +651.048 q^{23} +24.6633 q^{24} +262.506 q^{25} +1385.34 q^{26} -140.296i q^{27} +601.691i q^{28} +34.6831 q^{29} +552.151i q^{30} -1293.25i q^{31} +1424.75i q^{32} -139.292 q^{33} -1572.17i q^{34} +756.178 q^{35} +409.038 q^{36} +2474.30 q^{37} -1638.62i q^{38} -1289.77 q^{39} +90.3692 q^{40} +380.745i q^{41} -1151.81i q^{42} +1340.43i q^{43} -406.111i q^{44} -514.060i q^{45} -3633.62i q^{46} -1219.96 q^{47} -1397.16i q^{48} +823.579 q^{49} -1465.09i q^{50} +1463.71i q^{51} -3760.38i q^{52} +2848.73i q^{53} -783.018 q^{54} -510.382 q^{55} -188.514 q^{56} +1525.58i q^{57} -193.573i q^{58} -5207.23 q^{59} +1498.76 q^{60} -112.559i q^{61} -7217.84 q^{62} +1072.35i q^{63} +3649.62 q^{64} -4725.87 q^{65} +777.415i q^{66} +(3389.04 - 2943.72i) q^{67} -4267.50 q^{68} +3382.95i q^{69} -4220.37i q^{70} +8426.67 q^{71} +128.154i q^{72} +8335.83 q^{73} -13809.5i q^{74} +1364.02i q^{75} -4447.87 q^{76} +1064.68 q^{77} +7198.46i q^{78} -4895.95i q^{79} -5119.35i q^{80} +729.000 q^{81} +2125.01 q^{82} -3332.63 q^{83} -3126.48 q^{84} +5363.20i q^{85} +7481.21 q^{86} +180.219i q^{87} +127.237 q^{88} -4743.25 q^{89} -2869.06 q^{90} +9858.38 q^{91} -9863.10 q^{92} +6719.91 q^{93} +6808.80i q^{94} +5589.88i q^{95} -7403.19 q^{96} -8426.37i q^{97} -4596.54i q^{98} -723.784i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	5.58118i		−	1.39529i	−0.716441	−	0.697647i	$-0.754230\pi$
$2$		−	5.58118i		−	1.39529i	0.716441	−	0.697647i	$-0.245770\pi$
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	−15.1496			−0.946847
$5$			19.0393i			0.761571i	0.924663	+	0.380785i	$0.124346\pi$
$5$			19.0393i			0.761571i	−0.924663	+	0.380785i	$0.875654\pi$
$6$	29.0007			0.805574
$7$		−	39.7168i		−	0.810546i	−0.914196	−	0.405273i	$-0.867176\pi$
$7$		−	39.7168i		−	0.810546i	0.914196	−	0.405273i	$-0.132824\pi$
$8$		−	4.74646i		−	0.0741635i
$9$	−27.0000			−0.333333
$10$	106.262			1.06262
$11$			26.8068i			0.221544i	0.993846	+	0.110772i	$0.0353323\pi$
$11$			26.8068i			0.221544i	−0.993846	+	0.110772i	$0.964668\pi$
$12$		−	78.7194i		−	0.546663i
$13$			248.217i			1.46874i	0.678749	+	0.734370i	$0.262522\pi$
$13$			248.217i			1.46874i	−0.678749	+	0.734370i	$0.737478\pi$
$14$	−221.666			−1.13095
$15$	−98.9310			−0.439693
$16$	−268.884			−1.05033
$17$	281.691			0.974710			0.487355	−	0.873204i	$-0.337962\pi$
$17$	281.691			0.974710			0.487355	+	0.873204i	$0.337962\pi$
$18$			150.692i			0.465098i
$19$	293.597			0.813289			0.406645	−	0.913586i	$-0.366699\pi$
$19$	293.597			0.813289			0.406645	+	0.913586i	$0.366699\pi$
$20$		−	288.437i		−	0.721091i
$21$	206.374			0.467969
$22$	149.614			0.309119
$23$	651.048			1.23072			0.615358	−	0.788248i	$-0.289012\pi$
$23$	651.048			1.23072			0.615358	+	0.788248i	$0.289012\pi$
$24$	24.6633			0.0428183
$25$	262.506			0.420010
$26$	1385.34			2.04933
$27$		−	140.296i		−	0.192450i
$28$			601.691i			0.767464i
$29$	34.6831			0.0412404			0.0206202	−	0.999787i	$-0.493436\pi$
$29$	34.6831			0.0412404			0.0206202	+	0.999787i	$0.493436\pi$
$30$			552.151i			0.613502i
$31$		−	1293.25i		−	1.34573i	−0.739765	−	0.672865i	$-0.765063\pi$
$31$		−	1293.25i		−	1.34573i	0.739765	−	0.672865i	$-0.234937\pi$
$32$			1424.75i			1.39135i
$33$	−139.292			−0.127908
$34$		−	1572.17i		−	1.36001i
$35$	756.178			0.617288
$36$	409.038			0.315616
$37$	2474.30			1.80738			0.903688	−	0.428191i	$-0.140849\pi$
$37$	2474.30			1.80738			0.903688	+	0.428191i	$0.140849\pi$
$38$		−	1638.62i		−	1.13478i
$39$	−1289.77			−0.847978
$40$	90.3692			0.0564807
$41$			380.745i			0.226499i	0.993567	+	0.113250i	$0.0361260\pi$
$41$			380.745i			0.226499i	−0.993567	+	0.113250i	$0.963874\pi$
$42$		−	1151.81i		−	0.652955i
$43$			1340.43i			0.724951i	0.931993	+	0.362476i	$0.118068\pi$
$43$			1340.43i			0.724951i	−0.931993	+	0.362476i	$0.881932\pi$
$44$		−	406.111i		−	0.209768i
$45$		−	514.060i		−	0.253857i
$46$		−	3633.62i		−	1.71721i
$47$	−1219.96			−0.552267			−0.276133	−	0.961119i	$-0.589053\pi$
$47$	−1219.96			−0.552267			−0.276133	+	0.961119i	$0.589053\pi$
$48$		−	1397.16i		−	0.606407i
$49$	823.579			0.343015
$50$		−	1465.09i		−	0.586038i
$51$			1463.71i			0.562749i
$52$		−	3760.38i		−	1.39067i
$53$			2848.73i			1.01414i	0.861904	+	0.507072i	$0.169272\pi$
$53$			2848.73i			1.01414i	−0.861904	+	0.507072i	$0.830728\pi$
$54$	−783.018			−0.268525
$55$	−510.382			−0.168721
$56$	−188.514			−0.0601129
$57$			1525.58i			0.469553i
$58$		−	193.573i		−	0.0575425i
$59$	−5207.23			−1.49590			−0.747950	−	0.663755i	$-0.768962\pi$
$59$	−5207.23			−1.49590			−0.747950	+	0.663755i	$0.768962\pi$
$60$	1498.76			0.416322
$61$		−	112.559i		−	0.0302497i	−0.999886	−	0.0151249i	$-0.995185\pi$
$61$		−	112.559i		−	0.0302497i	0.999886	−	0.0151249i	$-0.00481458\pi$
$62$	−7217.84			−1.87769
$63$			1072.35i			0.270182i
$64$	3649.62			0.891020
$65$	−4725.87			−1.11855
$66$			777.415i			0.178470i
$67$	3389.04	−	2943.72i	0.754966	−	0.655763i
$67$	3389.04	−	2943.72i	0.754966	−	0.655763i
$68$	−4267.50			−0.922902
$69$			3382.95i			0.710554i
$70$		−	4220.37i		−	0.861299i
$71$	8426.67			1.67163			0.835813	−	0.549014i	$-0.184996\pi$
$71$	8426.67			1.67163			0.835813	+	0.549014i	$0.184996\pi$
$72$			128.154i			0.0247212i
$73$	8335.83			1.56424			0.782120	−	0.623128i	$-0.214138\pi$
$73$	8335.83			1.56424			0.782120	+	0.623128i	$0.214138\pi$
$74$		−	13809.5i		−	2.52182i
$75$			1364.02i			0.242493i
$76$	−4447.87			−0.770061
$77$	1064.68			0.179571
$78$			7198.46i			1.18318i
$79$		−	4895.95i		−	0.784481i	−0.919863	−	0.392241i	$-0.871700\pi$
$79$		−	4895.95i		−	0.784481i	0.919863	−	0.392241i	$-0.128300\pi$
$80$		−	5119.35i		−	0.799899i
$81$	729.000			0.111111
$82$	2125.01			0.316033
$83$	−3332.63			−0.483762			−0.241881	−	0.970306i	$-0.577764\pi$
$83$	−3332.63			−0.483762			−0.241881	+	0.970306i	$0.577764\pi$
$84$	−3126.48			−0.443095
$85$			5363.20i			0.742311i
$86$	7481.21			1.01152
$87$			180.219i			0.0238101i
$88$	127.237			0.0164305
$89$	−4743.25			−0.598819			−0.299410	−	0.954125i	$-0.596790\pi$
$89$	−4743.25			−0.598819			−0.299410	+	0.954125i	$0.596790\pi$
$90$	−2869.06			−0.354205
$91$	9858.38			1.19048
$92$	−9863.10			−1.16530
$93$	6719.91			0.776958
$94$			6808.80i			0.770575i
$95$			5589.88i			0.619377i
$96$	−7403.19			−0.803298
$97$		−	8426.37i		−	0.895565i	−0.894143	−	0.447782i	$-0.852214\pi$
$97$		−	8426.37i		−	0.895565i	0.894143	−	0.447782i	$-0.147786\pi$
$98$		−	4596.54i		−	0.478607i
$99$		−	723.784i		−	0.0738479i
$100$	−3976.85			−0.397685
$101$			19178.6i			1.88007i	0.341080	+	0.940034i	$0.389207\pi$
$101$			19178.6i			1.88007i	−0.341080	+	0.940034i	$0.610793\pi$
$102$	8169.23			0.785201
$103$	−12686.6			−1.19583			−0.597916	−	0.801559i	$-0.704005\pi$
$103$	−12686.6			−1.19583			−0.597916	+	0.801559i	$0.704005\pi$
$104$	1178.15			0.108927
$105$			3929.22i			0.356392i
$106$	15899.3			1.41503
$107$	−17787.3			−1.55361			−0.776804	−	0.629743i	$-0.783160\pi$
$107$	−17787.3			−1.55361			−0.776804	+	0.629743i	$0.783160\pi$
$108$			2125.42i			0.182221i
$109$			3266.92i			0.274970i	0.990504	+	0.137485i	$0.0439019\pi$
$109$			3266.92i			0.274970i	−0.990504	+	0.137485i	$0.956098\pi$
$110$			2848.53i			0.235416i
$111$			12856.8i			1.04349i
$112$			10679.2i			0.851339i
$113$		−	913.142i		−	0.0715124i	−0.999361	−	0.0357562i	$-0.988616\pi$
$113$		−	913.142i		−	0.0715124i	0.999361	−	0.0357562i	$-0.0113840\pi$
$114$	8514.52			0.655164
$115$			12395.5i			0.937277i
$116$	−525.434			−0.0390483
$117$		−	6701.86i		−	0.489580i
$118$			29062.5i			2.08722i
$119$		−	11187.9i		−	0.790048i
$120$			469.572i			0.0326092i
$121$	13922.4			0.950918
$122$	−628.213			−0.0422073
$123$	−1978.41			−0.130769
$124$			19592.1i			1.27420i
$125$			16897.5i			1.08144i
$126$	5984.99			0.376984
$127$	−4217.65			−0.261495			−0.130747	−	0.991416i	$-0.541738\pi$
$127$	−4217.65			−0.261495			−0.130747	+	0.991416i	$0.541738\pi$
$128$			2426.76i			0.148117i
$129$	−6965.10			−0.418551
$130$			26375.9i			1.56071i
$131$	6789.04			0.395609			0.197804	−	0.980242i	$-0.436619\pi$
$131$	6789.04			0.395609			0.197804	+	0.980242i	$0.436619\pi$
$132$	2110.22			0.121110
$133$		−	11660.7i		−	0.659208i
$134$	−16429.4	−	18914.9i	−0.914983	−	1.05340i
$135$	2671.14			0.146564
$136$		−	1337.04i		−	0.0722879i
$137$			19610.9i			1.04486i	0.852683	+	0.522428i	$0.174974\pi$
$137$			19610.9i			1.04486i	−0.852683	+	0.522428i	$0.825026\pi$
$138$	18880.8			0.991432
$139$			22232.8i			1.15071i	0.817905	+	0.575354i	$0.195136\pi$
$139$			22232.8i			1.15071i	−0.817905	+	0.575354i	$0.804864\pi$
$140$	−11455.8			−0.584478
$141$		−	6339.09i		−	0.318851i
$142$		−	47030.8i		−	2.33241i
$143$	−6653.90			−0.325390
$144$	7259.86			0.350109
$145$			660.342i			0.0314075i
$146$		−	46523.8i		−	2.18258i
$147$			4279.44i			0.198040i
$148$	−37484.5			−1.71131
$149$	−11795.3			−0.531296			−0.265648	−	0.964070i	$-0.585586\pi$
$149$	−11795.3			−0.531296			−0.265648	+	0.964070i	$0.585586\pi$
$150$	7612.85			0.338349
$151$	−28968.3			−1.27048			−0.635242	−	0.772313i	$-0.719100\pi$
$151$	−28968.3			−1.27048			−0.635242	+	0.772313i	$0.719100\pi$
$152$		−	1393.55i		−	0.0603163i
$153$	−7605.66			−0.324903
$154$		−	5942.17i		−	0.250555i
$155$	24622.5			1.02487
$156$	19539.5			0.802905
$157$	13648.8			0.553727			0.276863	−	0.960909i	$-0.410705\pi$
$157$	13648.8			0.553727			0.276863	+	0.960909i	$0.410705\pi$
$158$	−27325.2			−1.09458
$159$	−14802.4			−0.585516
$160$	−27126.1			−1.05961
$161$		−	25857.5i		−	0.997552i
$162$		−	4068.68i		−	0.155033i
$163$	19157.2			0.721035			0.360517	−	0.932753i	$-0.382600\pi$
$163$	19157.2			0.721035			0.360517	+	0.932753i	$0.382600\pi$
$164$		−	5768.12i		−	0.214460i
$165$		−	2652.02i		−	0.0974113i
$166$			18600.0i			0.674990i
$167$	−5192.63			−0.186189			−0.0930946	−	0.995657i	$-0.529676\pi$
$167$	−5192.63			−0.186189			−0.0930946	+	0.995657i	$0.529676\pi$
$168$		−	979.548i		−	0.0347062i
$169$	−33050.7			−1.15720
$170$	29933.0			1.03574
$171$	−7927.13			−0.271096
$172$		−	20307.0i		−	0.686418i
$173$	−3875.09			−0.129476			−0.0647381	−	0.997902i	$-0.520621\pi$
$173$	−3875.09			−0.129476			−0.0647381	+	0.997902i	$0.520621\pi$
$174$	1005.83			0.0332222
$175$		−	10425.9i		−	0.340437i
$176$		−	7207.91i		−	0.232693i
$177$		−	27057.6i		−	0.863659i
$178$			26472.9i			0.835529i
$179$		−	21813.1i		−	0.680786i	−0.940283	−	0.340393i	$-0.889440\pi$
$179$		−	21813.1i		−	0.680786i	0.940283	−	0.340393i	$-0.110560\pi$
$180$			7787.79i			0.240364i
$181$	−40254.4			−1.22873			−0.614365	−	0.789022i	$-0.710588\pi$
$181$	−40254.4			−1.22873			−0.614365	+	0.789022i	$0.710588\pi$
$182$		−	55021.4i		−	1.66107i
$183$	584.875			0.0174647
$184$		−	3090.18i		−	0.0912741i
$185$			47108.8i			1.37645i
$186$		−	37505.0i		−	1.08408i
$187$			7551.24i			0.215941i
$188$	18481.8			0.522913
$189$	−5572.11			−0.155990
$190$	31198.1			0.864214
$191$			2499.34i			0.0685108i	0.999413	+	0.0342554i	$0.0109060\pi$
$191$			2499.34i			0.0685108i	−0.999413	+	0.0342554i	$0.989094\pi$
$192$			18964.0i			0.514431i
$193$	−12974.6			−0.348322			−0.174161	−	0.984717i	$-0.555721\pi$
$193$	−12974.6			−0.348322			−0.174161	+	0.984717i	$0.555721\pi$
$194$	−47029.1			−1.24958
$195$		−	24556.4i		−	0.645795i
$196$	−12476.9			−0.324783
$197$		−	72382.7i		−	1.86510i	−0.361039	−	0.932551i	$-0.617578\pi$
$197$		−	72382.7i		−	1.86510i	0.361039	−	0.932551i	$-0.382422\pi$
$198$	−4039.57			−0.103040
$199$	44732.1			1.12957			0.564785	−	0.825238i	$-0.308959\pi$
$199$	44732.1			1.12957			0.564785	+	0.825238i	$0.308959\pi$
$200$		−	1245.98i		−	0.0311494i
$201$	15296.0	+	17610.0i	0.378605	+	0.435880i
$202$	107039.			2.62325
$203$		−	1377.50i		−	0.0334272i
$204$		−	22174.6i		−	0.532838i
$205$	−7249.11			−0.172495
$206$			70806.1i			1.66854i
$207$	−17578.3			−0.410238
$208$		−	66741.6i		−	1.54266i
$209$			7870.41i			0.180179i
$210$	21929.7			0.497271
$211$	53606.1			1.20406			0.602031	−	0.798473i	$-0.294358\pi$
$211$	53606.1			1.20406			0.602031	+	0.798473i	$0.294358\pi$
$212$		−	43157.0i		−	0.960240i
$213$			43786.3i			0.965114i
$214$			99273.8i			2.16774i
$215$	−25520.9			−0.552102
$216$	−665.910			−0.0142728
$217$	−51363.6			−1.09078
$218$	18233.2			0.383664
$219$			43314.3i			0.903114i
$220$	7732.06			0.159753
$221$			69920.6i			1.43160i
$222$	71756.3			1.45597
$223$	−51547.8			−1.03657			−0.518287	−	0.855207i	$-0.673430\pi$
$223$	−51547.8			−1.03657			−0.518287	+	0.855207i	$0.673430\pi$
$224$	56586.3			1.12776
$225$	−7087.67			−0.140003
$226$	−5096.41			−0.0997809
$227$	20921.7			0.406018			0.203009	−	0.979177i	$-0.434928\pi$
$227$	20921.7			0.406018			0.203009	+	0.979177i	$0.434928\pi$
$228$		−	23111.8i		−	0.444595i
$229$		−	4877.50i		−	0.0930092i	−0.998918	−	0.0465046i	$-0.985192\pi$
$229$		−	4877.50i		−	0.0930092i	0.998918	−	0.0465046i	$-0.0148082\pi$
$230$	69181.4			1.30778
$231$			5532.24i			0.103676i
$232$		−	164.622i		−	0.00305853i
$233$		−	3831.75i		−	0.0705805i	−0.999377	−	0.0352903i	$-0.988764\pi$
$233$		−	3831.75i		−	0.0705805i	0.999377	−	0.0352903i	$-0.0112356\pi$
$234$	−37404.3			−0.683108
$235$		−	23227.1i		−	0.420590i
$236$	78887.3			1.41639
$237$	25440.1			0.452920
$238$	−62441.5			−1.10235
$239$		−	103193.i		−	1.80656i	−0.429049	−	0.903281i	$-0.641151\pi$
$239$		−	103193.i		−	1.80656i	0.429049	−	0.903281i	$-0.358849\pi$
$240$	26600.9			0.461822
$241$	15128.9			0.260479			0.130240	−	0.991483i	$-0.458425\pi$
$241$	15128.9			0.260479			0.130240	+	0.991483i	$0.458425\pi$
$242$		−	77703.4i		−	1.32681i
$243$			3788.00i			0.0641500i
$244$			1705.22i			0.0286419i
$245$			15680.3i			0.261230i
$246$			11041.9i			0.182462i
$247$			72875.9i			1.19451i
$248$	−6138.35			−0.0998040
$249$		−	17316.9i		−	0.279300i
$250$	94307.8			1.50892
$251$			47377.8i			0.752016i	0.926616	+	0.376008i	$0.122703\pi$
$251$			47377.8i			0.752016i	−0.926616	+	0.376008i	$0.877297\pi$
$252$		−	16245.7i		−	0.255821i
$253$			17452.5i			0.272657i
$254$			23539.5i			0.364862i
$255$	−27868.0			−0.428573
$256$	71938.0			1.09769
$257$	−40018.5			−0.605892			−0.302946	−	0.953008i	$-0.597970\pi$
$257$	−40018.5			−0.605892			−0.302946	+	0.953008i	$0.597970\pi$
$258$			38873.5i			0.584002i
$259$		−	98271.1i		−	1.46496i
$260$	71594.9			1.05910
$261$	−936.445			−0.0137468
$262$		−	37890.9i		−	0.551991i
$263$	34610.0			0.500368			0.250184	−	0.968198i	$-0.419509\pi$
$263$	34610.0			0.500368			0.250184	+	0.968198i	$0.419509\pi$
$264$			661.145i			0.00948613i
$265$	−54237.8			−0.772343
$266$	−65080.7			−0.919790
$267$		−	24646.6i		−	0.345728i
$268$	−51342.5	+	44596.1i	−0.714838	+	0.620908i
$269$	−84311.8			−1.16515			−0.582577	−	0.812775i	$-0.697956\pi$
$269$	−84311.8			−1.16515			−0.582577	+	0.812775i	$0.697956\pi$
$270$		−	14908.1i		−	0.204501i
$271$		−	11770.7i		−	0.160274i	−0.996784	−	0.0801370i	$-0.974464\pi$
$271$		−	11770.7i		−	0.160274i	0.996784	−	0.0801370i	$-0.0255358\pi$
$272$	−75742.2			−1.02376
$273$			51225.6i			0.687325i
$274$	109452.			1.45788
$275$			7036.95i			0.0930506i
$276$		−	51250.2i		−	0.672786i
$277$	117997.			1.53784			0.768922	−	0.639343i	$-0.220793\pi$
$277$	117997.			1.53784			0.768922	+	0.639343i	$0.220793\pi$
$278$	124085.			1.60558
$279$			34917.7i			0.448577i
$280$		−	3589.17i		−	0.0457802i
$281$		−	8816.43i		−	0.111656i	−0.998440	−	0.0558278i	$-0.982220\pi$
$281$		−	8816.43i		−	0.111656i	0.998440	−	0.0558278i	$-0.0177798\pi$
$282$	−35379.6			−0.444892
$283$	66984.1			0.836371			0.418186	−	0.908362i	$-0.362666\pi$
$283$	66984.1			0.836371			0.418186	+	0.908362i	$0.362666\pi$
$284$	−127660.			−1.58278
$285$	−29045.9			−0.357598
$286$			37136.6i			0.454015i
$287$	15122.0			0.183588
$288$		−	38468.1i		−	0.463784i
$289$	−4171.07			−0.0499403
$290$	3685.49			0.0438227
$291$	43784.7			0.517055
$292$	−126284.			−1.48110
$293$	−92863.8			−1.08171			−0.540856	−	0.841115i	$-0.681899\pi$
$293$	−92863.8			−1.08171			−0.540856	+	0.841115i	$0.681899\pi$
$294$	23884.3			0.276324
$295$		−	99141.9i		−	1.13923i
$296$		−	11744.2i		−	0.134041i
$297$	3760.89			0.0426361
$298$			65831.7i			0.741315i
$299$			161601.i			1.80760i
$300$		−	20664.3i		−	0.229604i
$301$	53237.7			0.587606
$302$			161677.i			1.77270i
$303$	−99654.8			−1.08546
$304$	−78943.6			−0.854220
$305$	2143.05			0.0230373
$306$			42448.6i			0.453336i
$307$	−107275.			−1.13821			−0.569104	−	0.822266i	$-0.692710\pi$
$307$	−107275.			−1.13821			−0.569104	+	0.822266i	$0.692710\pi$
$308$	−16129.4			−0.170027
$309$		−	65921.5i		−	0.690414i
$310$		−	137422.i		−	1.42999i
$311$		−	27028.1i		−	0.279444i	−0.990191	−	0.139722i	$-0.955379\pi$
$311$		−	27028.1i		−	0.279444i	0.990191	−	0.139722i	$-0.0446209\pi$
$312$			6121.86i			0.0628889i
$313$		−	161111.i		−	1.64451i	−0.569117	−	0.822257i	$-0.692715\pi$
$313$		−	161111.i		−	1.64451i	0.569117	−	0.822257i	$-0.307285\pi$
$314$		−	76176.5i		−	0.772612i
$315$	−20416.8			−0.205763
$316$			74171.4i			0.742784i
$317$	−109743.			−1.09209			−0.546044	−	0.837756i	$-0.683867\pi$
$317$	−109743.			−1.09209			−0.546044	+	0.837756i	$0.683867\pi$
$318$			82615.1i			0.816968i
$319$			929.744i			0.00913654i
$320$			69486.1i			0.678575i
$321$		−	92425.3i		−	0.896976i
$322$	−144316.			−1.39188
$323$	82703.8			0.792721
$324$	−11044.0			−0.105205
$325$			65158.5i			0.616885i
$326$		−	106920.i		−	1.00606i
$327$	−16975.4			−0.158754
$328$	1807.19			0.0167980
$329$			48452.8i			0.447638i
$330$	−14801.4			−0.135917
$331$		−	1932.01i		−	0.0176341i	−0.999961	−	0.00881706i	$-0.997193\pi$
$331$		−	1932.01i		−	0.0176341i	0.999961	−	0.00881706i	$-0.00280659\pi$
$332$	50487.9			0.458048
$333$	−66806.0			−0.602459
$334$			28981.0i			0.259789i
$335$	56046.3	+	64524.9i	0.499410	+	0.574960i
$336$	−55490.7			−0.491521
$337$		−	173606.i		−	1.52864i	−0.644837	−	0.764321i	$-0.723075\pi$
$337$		−	173606.i		−	1.52864i	0.644837	−	0.764321i	$-0.276925\pi$
$338$			184462.i			1.61463i
$339$	4744.82			0.0412877
$340$		−	81250.0i		−	0.702855i
$341$	34667.8			0.298138
$342$			44242.7i			0.378259i
$343$		−	128070.i		−	1.08858i
$344$	6362.32			0.0537649
$345$	−64408.8			−0.541137
$346$			21627.6i			0.180657i
$347$			155273.i			1.28955i	0.764374	+	0.644773i	$0.223048\pi$
$347$			155273.i			1.28955i	−0.764374	+	0.644773i	$0.776952\pi$
$348$		−	2730.24i		−	0.0225446i
$349$	−88217.5			−0.724276			−0.362138	−	0.932125i	$-0.617953\pi$
$349$	−88217.5			−0.724276			−0.362138	+	0.932125i	$0.617953\pi$
$350$	−58188.8			−0.475010
$351$	34823.9			0.282659
$352$	−38192.9			−0.308246
$353$		−	43776.8i		−	0.351313i	−0.984451	−	0.175657i	$-0.943795\pi$
$353$		−	43776.8i		−	0.351313i	0.984451	−	0.175657i	$-0.0562049\pi$
$354$	−151013.			−1.20506
$355$			160438.i			1.27306i
$356$	71858.1			0.566990
$357$	58133.8			0.456134
$358$	−121743.			−0.949898
$359$	184456.			1.43121			0.715607	−	0.698503i	$-0.246150\pi$
$359$	184456.			1.43121			0.715607	+	0.698503i	$0.246150\pi$
$360$	−2439.97			−0.0188269
$361$	−44121.6			−0.338561
$362$			224667.i			1.71444i
$363$			72342.9i			0.549013i
$364$	−149350.			−1.12720
$365$			158708.i			1.19128i
$366$		−	3264.29i		−	0.0243684i
$367$		−	167186.i		−	1.24127i	−0.784098	−	0.620637i	$-0.786874\pi$
$367$		−	167186.i		−	1.24127i	0.784098	−	0.620637i	$-0.213126\pi$
$368$	−175056.			−1.29265
$369$		−	10280.1i		−	0.0754997i
$370$	262923.			1.92055
$371$	113142.			0.822011
$372$	−101804.			−0.735660
$373$			199398.i			1.43319i	0.697490	+	0.716594i	$0.254300\pi$
$373$			199398.i			1.43319i	−0.697490	+	0.716594i	$0.745700\pi$
$374$	42144.8			0.301301
$375$	−87801.8			−0.624369
$376$			5790.48i			0.0409580i
$377$			8608.95i			0.0605714i
$378$			31098.9i			0.217652i
$379$		−	129947.i		−	0.904664i	−0.891850	−	0.452332i	$-0.850592\pi$
$379$		−	129947.i		−	0.904664i	0.891850	−	0.452332i	$-0.149408\pi$
$380$		−	84684.2i		−	0.586456i
$381$		−	21915.5i		−	0.150974i
$382$	13949.3			0.0955928
$383$			99376.2i			0.677462i	0.940883	+	0.338731i	$0.109998\pi$
$383$			99376.2i			0.677462i	−0.940883	+	0.338731i	$0.890002\pi$
$384$	−12609.8			−0.0855156
$385$			20270.7i			0.136756i
$386$			72413.8i			0.486012i
$387$		−	36191.7i		−	0.241650i
$388$			127656.i			0.847963i
$389$	126184.			0.833881			0.416941	−	0.908934i	$-0.363102\pi$
$389$	126184.			0.833881			0.416941	+	0.908934i	$0.363102\pi$
$390$	−137053.			−0.901074
$391$	183395.			1.19959
$392$		−	3909.08i		−	0.0254392i
$393$			35276.9i			0.228405i
$394$	−403981.			−2.60237
$395$	93215.3			0.597438
$396$			10965.0i			0.0699227i
$397$	4674.40			0.0296582			0.0148291	−	0.999890i	$-0.495280\pi$
$397$	4674.40			0.0296582			0.0148291	+	0.999890i	$0.495280\pi$
$398$		−	249658.i		−	1.57608i
$399$	60591.0			0.380594
$400$	−70583.7			−0.441148
$401$		−	68733.9i		−	0.427447i	−0.976894	−	0.213724i	$-0.931441\pi$
$401$		−	68733.9i		−	0.427447i	0.976894	−	0.213724i	$-0.0685592\pi$
$402$	98284.5	−	85369.9i	0.608181	−	0.528266i
$403$	321006.			1.97653
$404$		−	290547.i		−	1.78014i
$405$			13879.6i			0.0846190i
$406$	−7688.09			−0.0466408
$407$			66328.0i			0.400413i
$408$	6947.44			0.0417354
$409$		−	217262.i		−	1.29878i	−0.760454	−	0.649392i	$-0.775024\pi$
$409$		−	217262.i		−	1.29878i	0.760454	−	0.649392i	$-0.224976\pi$
$410$			40458.6i			0.240682i
$411$	−101901.			−0.603248
$412$	192196.			1.13227
$413$			206814.i			1.21250i
$414$			98107.7i			0.572404i
$415$		−	63450.9i		−	0.368419i
$416$	−353646.			−2.04354
$417$	−115525.			−0.664361
$418$	43926.1			0.251403
$419$	−244895.			−1.39493			−0.697464	−	0.716620i	$-0.745688\pi$
$419$	−244895.			−1.39493			−0.697464	+	0.716620i	$0.745688\pi$
$420$		−	59525.9i		−	0.337448i
$421$	258938.			1.46094			0.730468	−	0.682947i	$-0.239302\pi$
$421$	258938.			1.46094			0.730468	+	0.682947i	$0.239302\pi$
$422$		−	299185.i		−	1.68002i
$423$	32938.9			0.184089
$424$	13521.4			0.0752124
$425$	73945.7			0.409388
$426$	244379.			1.34662
$427$	−4470.49			−0.0245188
$428$	269469.			1.47103
$429$		−	34574.7i		−	0.187864i
$430$			142437.i			0.770345i
$431$	334720.			1.80188			0.900942	−	0.433940i	$-0.142877\pi$
$431$	334720.			1.80188			0.900942	+	0.433940i	$0.142877\pi$
$432$			37723.4i			0.202136i
$433$			243028.i			1.29623i	0.761544	+	0.648113i	$0.224441\pi$
$433$			243028.i			1.29623i	−0.761544	+	0.648113i	$0.775559\pi$
$434$			286669.i			1.52195i
$435$	−3431.24			−0.0181331
$436$		−	49492.3i		−	0.260354i
$437$	191146.			1.00093
$438$	241745.			1.26011
$439$	−72902.0			−0.378277			−0.189139	−	0.981950i	$-0.560570\pi$
$439$	−72902.0			−0.378277			−0.189139	+	0.981950i	$0.560570\pi$
$440$			2422.51i			0.0125130i
$441$	−22236.6			−0.114338
$442$	390239.			1.99750
$443$		−	68980.4i		−	0.351494i	−0.984435	−	0.175747i	$-0.943766\pi$
$443$		−	68980.4i		−	0.351494i	0.984435	−	0.175747i	$-0.0562341\pi$
$444$		−	194775.i		−	0.988025i
$445$		−	90308.0i		−	0.456043i
$446$			287697.i			1.44633i
$447$		−	61290.2i		−	0.306744i
$448$		−	144951.i		−	0.722213i
$449$	99464.3			0.493372			0.246686	−	0.969095i	$-0.420658\pi$
$449$	99464.3			0.493372			0.246686	+	0.969095i	$0.420658\pi$
$450$			39557.5i			0.195346i
$451$	−10206.6			−0.0501795
$452$			13833.7i			0.0677113i
$453$		−	150524.i		−	0.733515i
$454$		−	116768.i		−	0.566515i
$455$			187696.i			0.906636i
$456$	7241.09			0.0348237
$457$	−392362.			−1.87869			−0.939343	−	0.342980i	$-0.888564\pi$
$457$	−392362.			−1.87869			−0.939343	+	0.342980i	$0.888564\pi$
$458$	−27222.2			−0.129775
$459$		−	39520.2i		−	0.187583i
$460$		−	187786.i		−	0.887458i
$461$	86619.1			0.407579			0.203789	−	0.979015i	$-0.434674\pi$
$461$	86619.1			0.407579			0.203789	+	0.979015i	$0.434674\pi$
$462$	30876.4			0.144658
$463$			294020.i			1.37156i	0.727809	+	0.685780i	$0.240539\pi$
$463$			294020.i			1.37156i	−0.727809	+	0.685780i	$0.759461\pi$
$464$	−9325.74			−0.0433159
$465$			127942.i			0.591708i
$466$	−21385.7			−0.0984806
$467$	−211995.			−0.972056			−0.486028	−	0.873943i	$-0.661555\pi$
$467$	−211995.			−0.972056			−0.486028	+	0.873943i	$0.661555\pi$
$468$			101530.i			0.463558i
$469$	−116915.	−	134602.i	−0.531527	−	0.611935i
$470$	−129635.			−0.586848
$471$			70921.3i			0.319694i
$472$			24715.9i			0.110941i
$473$	−35932.8			−0.160608
$474$		−	141986.i		−	0.631957i
$475$	77071.1			0.341589
$476$			169491.i			0.748054i
$477$		−	76915.7i		−	0.338048i
$478$	−575937.			−2.52069
$479$	−76374.7			−0.332873			−0.166436	−	0.986052i	$-0.553226\pi$
$479$	−76374.7			−0.332873			−0.166436	+	0.986052i	$0.553226\pi$
$480$		−	140951.i		−	0.611768i
$481$			614163.i			2.65457i
$482$		−	84437.1i		−	0.363445i
$483$	134360.			0.575937
$484$	−210918.			−0.900375
$485$	160432.			0.682036
$486$	21141.5			0.0895082
$487$		−	280777.i		−	1.18387i	−0.805987	−	0.591934i	$-0.798365\pi$
$487$		−	280777.i		−	1.18387i	0.805987	−	0.591934i	$-0.201635\pi$
$488$	−534.258			−0.00224342
$489$			99543.6i			0.416289i
$490$	87514.8			0.364493
$491$	221040.			0.916870			0.458435	−	0.888728i	$-0.348410\pi$
$491$	221040.			0.916870			0.458435	+	0.888728i	$0.348410\pi$
$492$	29972.0			0.123819
$493$	9769.94			0.0401974
$494$	406733.			1.66669
$495$	13780.3			0.0562404
$496$			347733.i			1.41346i
$497$		−	334680.i		−	1.35493i
$498$	−96648.6			−0.389706
$499$		−	43504.7i		−	0.174717i	−0.996177	−	0.0873585i	$-0.972157\pi$
$499$		−	43504.7i		−	0.174717i	0.996177	−	0.0873585i	$-0.0278426\pi$
$500$		−	255989.i		−	1.02396i
$501$		−	26981.7i		−	0.107496i
$502$	264424.			1.04928
$503$		−	422574.i		−	1.67019i	−0.550104	−	0.835096i	$-0.685412\pi$
$503$		−	422574.i		−	1.67019i	0.550104	−	0.835096i	$-0.314588\pi$
$504$	5089.88			0.0200376
$505$	−365146.			−1.43181
$506$	97405.7			0.380437
$507$		−	171737.i		−	0.668108i
$508$	63895.5			0.247596
$509$	47216.0			0.182244			0.0911221	−	0.995840i	$-0.470955\pi$
$509$	47216.0			0.182244			0.0911221	+	0.995840i	$0.470955\pi$
$510$			155536.i			0.597986i
$511$		−	331072.i		−	1.26789i
$512$		−	362671.i		−	1.38348i
$513$		−	41190.6i		−	0.156518i
$514$			223351.i			0.845398i
$515$		−	241543.i		−	0.910711i
$516$	105518.			0.396304
$517$		−	32703.2i		−	0.122351i
$518$	−548469.			−2.04405
$519$		−	20135.6i		−	0.0747531i
$520$			22431.2i			0.0829555i
$521$		−	12790.3i		−	0.0471200i	−0.999722	−	0.0235600i	$-0.992500\pi$
$521$		−	12790.3i		−	0.0471200i	0.999722	−	0.0235600i	$-0.00750008\pi$
$522$			5226.47i			0.0191808i
$523$	352761.			1.28966			0.644832	−	0.764324i	$-0.276927\pi$
$523$	352761.			1.28966			0.644832	+	0.764324i	$0.276927\pi$
$524$	−102851.			−0.374581
$525$	54174.5			0.196552
$526$		−	193165.i		−	0.698161i
$527$		−	364296.i		−	1.31170i
$528$	37453.4			0.134346
$529$	144023.			0.514661
$530$			302711.i			1.07765i
$531$	140595.			0.498634
$532$			176655.i			0.624170i
$533$	−94507.5			−0.332668
$534$	−137557.			−0.482393
$535$		−	338656.i		−	1.18318i
$536$	−13972.3	−	16086.0i	−0.0486337	−	0.0559909i
$537$	113344.			0.393052
$538$			470559.i			1.62573i
$539$			22077.5i			0.0759928i
$540$	−40466.5			−0.138774
$541$			487513.i			1.66568i	0.553514	+	0.832840i	$0.313286\pi$
$541$			487513.i			1.66568i	−0.553514	+	0.832840i	$0.686714\pi$
$542$	−65694.3			−0.223630
$543$		−	209168.i		−	0.709408i
$544$			401338.i			1.35617i
$545$	−62199.7			−0.209409
$546$	285899.			0.959021
$547$		−	281370.i		−	0.940378i	−0.882566	−	0.470189i	$-0.844186\pi$
$547$		−	281370.i		−	0.940378i	0.882566	−	0.470189i	$-0.155814\pi$
$548$		−	297097.i		−	0.989319i
$549$			3039.10i			0.0100832i
$550$	39274.5			0.129833
$551$	10182.9			0.0335403
$552$	16057.0			0.0526971
$553$	−194451.			−0.635858
$554$		−	658564.i		−	2.14575i
$555$	−244785.			−0.794691
$556$		−	336818.i		−	1.08954i
$557$	−170162.			−0.548469			−0.274235	−	0.961663i	$-0.588425\pi$
$557$	−170162.			−0.548469			−0.274235	+	0.961663i	$0.588425\pi$
$558$	194882.			0.625897
$559$	−332719.			−1.06476
$560$	−203324.			−0.648355
$561$	−39237.4			−0.124674
$562$	−49206.1			−0.155792
$563$		−	278597.i		−	0.878942i	−0.898257	−	0.439471i	$-0.855166\pi$
$563$		−	278597.i		−	0.878942i	0.898257	−	0.439471i	$-0.144834\pi$
$564$			96034.4i			0.301904i
$565$	17385.6			0.0544617
$566$		−	373850.i		−	1.16698i
$567$		−	28953.5i		−	0.0900607i
$568$		−	39996.9i		−	0.123974i
$569$	187080.			0.577834			0.288917	−	0.957354i	$-0.406705\pi$
$569$	187080.			0.577834			0.288917	+	0.957354i	$0.406705\pi$
$570$			162110.i			0.498954i
$571$	−152795.			−0.468638			−0.234319	−	0.972160i	$-0.575286\pi$
$571$	−152795.			−0.468638			−0.234319	+	0.972160i	$0.575286\pi$
$572$	100804.			0.308095
$573$	−12987.0			−0.0395547
$574$		−	84398.4i		−	0.256159i
$575$	170904.			0.516913
$576$	−98539.7			−0.297007
$577$			213894.i			0.642460i	0.947001	+	0.321230i	$0.104096\pi$
$577$			213894.i			0.642460i	−0.947001	+	0.321230i	$0.895904\pi$
$578$			23279.5i			0.0696815i
$579$		−	67418.2i		−	0.201104i
$580$		−	10003.9i		−	0.0297381i
$581$			132361.i			0.392111i
$582$		−	244370.i		−	0.721443i
$583$	−76365.4			−0.224677
$584$		−	39565.7i		−	0.116009i
$585$	127599.			0.372850
$586$			518290.i			1.50931i
$587$			166217.i			0.482392i	0.970476	+	0.241196i	$0.0775397\pi$
$587$			166217.i			0.482392i	−0.970476	+	0.241196i	$0.922460\pi$
$588$		−	64831.6i		−	0.187513i
$589$		−	379694.i		−	1.09447i
$590$	−553329.			−1.58957
$591$	376112.			1.07682
$592$	−665299.			−1.89834
$593$		−	149059.i		−	0.423885i	−0.977282	−	0.211943i	$-0.932021\pi$
$593$		−	149059.i		−	0.423885i	0.977282	−	0.211943i	$-0.0679790\pi$
$594$		−	20990.2i		−	0.0594900i
$595$	213009.			0.601677
$596$	178694.			0.503057
$597$			232435.i			0.652157i
$598$	901926.			2.52214
$599$			694911.i			1.93676i	0.249481	+	0.968380i	$0.419740\pi$
$599$			694911.i			1.93676i	−0.249481	+	0.968380i	$0.580260\pi$
$600$	6474.28			0.0179841
$601$	83199.9			0.230342			0.115171	−	0.993346i	$-0.463258\pi$
$601$	83199.9			0.230342			0.115171	+	0.993346i	$0.463258\pi$
$602$		−	297129.i		−	0.819884i
$603$	−91504.2	+	79480.5i	−0.251655	+	0.218588i
$604$	438857.			1.20296
$605$			265072.i			0.724192i
$606$			556191.i			1.51453i
$607$	−127480.			−0.345990			−0.172995	−	0.984923i	$-0.555345\pi$
$607$	−127480.			−0.345990			−0.172995	+	0.984923i	$0.555345\pi$
$608$			418301.i			1.13157i
$609$	7157.71			0.0192992
$610$		−	11960.7i		−	0.0321438i
$611$		−	302814.i		−	0.811137i
$612$	115222.			0.307634
$613$	297930.			0.792853			0.396426	−	0.918066i	$-0.370250\pi$
$613$	297930.			0.792853			0.396426	+	0.918066i	$0.370250\pi$
$614$			598721.i			1.58814i
$615$		−	37667.5i		−	0.0995902i
$616$		−	5053.46i		−	0.0133176i
$617$	−23333.8			−0.0612936			−0.0306468	−	0.999530i	$-0.509757\pi$
$617$	−23333.8			−0.0612936			−0.0306468	+	0.999530i	$0.509757\pi$
$618$	−367919.			−0.963331
$619$	−379444.			−0.990300			−0.495150	−	0.868807i	$-0.664887\pi$
$619$	−379444.			−0.990300			−0.495150	+	0.868807i	$0.664887\pi$
$620$	−373020.			−0.970395
$621$		−	91339.6i		−	0.236851i
$622$	−150849.			−0.389906
$623$			188386.i			0.485371i
$624$	346799.			0.890654
$625$	−157649.			−0.403582
$626$	−899191.			−2.29458
$627$	−40895.8			−0.104026
$628$	−206773.			−0.524295
$629$	696988.			1.76167
$630$			113950.i			0.287100i
$631$		−	326686.i		−	0.820486i	−0.911976	−	0.410243i	$-0.865444\pi$
$631$		−	326686.i		−	0.820486i	0.911976	−	0.410243i	$-0.134556\pi$
$632$	−23238.4			−0.0581798
$633$			278545.i			0.695166i
$634$			612494.i			1.52378i
$635$		−	80301.0i		−	0.199147i
$636$	224250.			0.554395
$637$			204426.i			0.503800i
$638$	5189.07			0.0127482
$639$	−227520.			−0.557209
$640$	−46203.7			−0.112802
$641$			665309.i			1.61922i	0.586965	+	0.809612i	$0.300323\pi$
$641$			665309.i			1.61922i	−0.586965	+	0.809612i	$0.699677\pi$
$642$	−515842.			−1.25155
$643$	122385.			0.296009			0.148005	−	0.988987i	$-0.452715\pi$
$643$	122385.			0.296009			0.148005	+	0.988987i	$0.452715\pi$
$644$			391730.i			0.944529i
$645$		−	132610.i		−	0.318756i
$646$		−	461585.i		−	1.10608i
$647$			270270.i			0.645639i	0.946460	+	0.322820i	$0.104631\pi$
$647$			270270.i			0.645639i	−0.946460	+	0.322820i	$0.895369\pi$
$648$		−	3460.17i		−	0.00824038i
$649$		−	139589.i		−	0.331408i
$650$	363661.			0.860737
$651$		−	266893.i		−	0.629760i
$652$	−290223.			−0.682710
$653$		−	309993.i		−	0.726985i	−0.931597	−	0.363492i	$-0.881584\pi$
$653$		−	309993.i		−	0.726985i	0.931597	−	0.363492i	$-0.118416\pi$
$654$			94742.7i			0.221508i
$655$			129258.i			0.301284i
$656$		−	102376.i		−	0.237898i
$657$	−225068.			−0.521413
$658$	270424.			0.624587
$659$	−162248.			−0.373602			−0.186801	−	0.982398i	$-0.559812\pi$
$659$	−162248.			−0.373602			−0.186801	+	0.982398i	$0.559812\pi$
$660$			40177.0i			0.0922336i
$661$			663676.i			1.51898i	0.650517	+	0.759492i	$0.274552\pi$
$661$			663676.i			1.51898i	−0.650517	+	0.759492i	$0.725448\pi$
$662$	−10782.9			−0.0246048
$663$	−363318.			−0.826532
$664$			15818.2i			0.0358774i
$665$	222012.			0.502034
$666$			372857.i			0.840608i
$667$	22580.4			0.0507551
$668$	78666.1			0.176293
$669$		−	267850.i		−	0.598466i
$670$	360125.	−	312805.i	0.802239	−	0.696825i
$671$	3017.35			0.00670164
$672$			294031.i			0.651110i
$673$			80024.4i			0.176682i	0.996090	+	0.0883410i	$0.0281565\pi$
$673$			80024.4i			0.176682i	−0.996090	+	0.0883410i	$0.971843\pi$
$674$	−968927.			−2.13290
$675$		−	36828.6i		−	0.0808309i
$676$	500704.			1.09569
$677$			318422.i			0.694745i	0.937727	+	0.347373i	$0.112926\pi$
$677$			318422.i			0.694745i	−0.937727	+	0.347373i	$0.887074\pi$
$678$		−	26481.7i		−	0.0576085i
$679$	−334668.			−0.725897
$680$	25456.2			0.0550523
$681$			108712.i			0.234415i
$682$		−	193487.i		−	0.415991i
$683$		−	774006.i		−	1.65922i	−0.558346	−	0.829608i	$-0.688564\pi$
$683$		−	774006.i		−	1.65922i	0.558346	−	0.829608i	$-0.311436\pi$
$684$	120093.			0.256687
$685$	−373377.			−0.795732
$686$	−714781.			−1.51888
$687$	25344.2			0.0536989
$688$		−	360421.i		−	0.761436i
$689$	−707104.			−1.48951
$690$			359477.i			0.755046i
$691$	35730.5			0.0748313			0.0374156	−	0.999300i	$-0.488087\pi$
$691$	35730.5			0.0748313			0.0374156	+	0.999300i	$0.488087\pi$
$692$	58705.9			0.122594
$693$	−28746.3			−0.0598572
$694$	866606.			1.79930
$695$	−423297.			−0.876346
$696$	855.402			0.00176584
$697$			107253.i			0.220771i
$698$			492358.i			1.01058i
$699$	19910.3			0.0407497
$700$			157948.i			0.322342i
$701$			538944.i			1.09675i	0.836232	+	0.548375i	$0.184753\pi$
$701$			538944.i			1.09675i	−0.836232	+	0.548375i	$0.815247\pi$
$702$		−	194358.i		−	0.394393i
$703$	726447.			1.46992
$704$			97834.6i			0.197400i
$705$	120692.			0.242828
$706$	−244326.			−0.490186
$707$	761711.			1.52388
$708$			409910.i			0.817753i
$709$	−586365.			−1.16648			−0.583238	−	0.812301i	$-0.698214\pi$
$709$	−586365.			−1.16648			−0.583238	+	0.812301i	$0.698214\pi$
$710$	895431.			1.77630
$711$			132191.i			0.261494i
$712$			22513.6i			0.0444105i
$713$		−	841966.i		−	1.65621i
$714$		−	324455.i		−	0.636442i
$715$		−	126685.i		−	0.247808i
$716$			330459.i			0.644601i
$717$	536205.			1.04302
$718$		−	1.02948e6i		−	1.99697i
$719$	−261335.			−0.505521			−0.252760	−	0.967529i	$-0.581338\pi$
$719$	−261335.			−0.505521			−0.252760	+	0.967529i	$0.581338\pi$
$720$			138222.i			0.266633i
$721$			503870.i			0.969278i
$722$			246250.i			0.472392i
$723$			78612.1i			0.150388i
$724$	609837.			1.16342
$725$	9104.54			0.0173214
$726$	403759.			0.766035
$727$			673278.i			1.27387i	0.770917	+	0.636936i	$0.219798\pi$
$727$			673278.i			1.27387i	−0.770917	+	0.636936i	$0.780202\pi$
$728$		−	46792.4i		−	0.0882902i
$729$	−19683.0			−0.0370370
$730$	885779.			1.66219
$731$			377589.i			0.706617i
$732$	−8860.59			−0.0165364
$733$		−	66317.1i		−	0.123429i	−0.998094	−	0.0617146i	$-0.980343\pi$
$733$		−	66317.1i		−	0.123429i	0.998094	−	0.0617146i	$-0.0196568\pi$
$734$	−933095.			−1.73194
$735$	−81477.4			−0.150821
$736$			927578.i			1.71236i
$737$	78911.8	+	90849.4i	0.145280	+	0.167258i
$738$	−57375.2			−0.105344
$739$			583781.i			1.06896i	0.845181	+	0.534479i	$0.179492\pi$
$739$			583781.i			1.06896i	−0.845181	+	0.534479i	$0.820508\pi$
$740$		−	713678.i		−	1.30328i
$741$	−378674.			−0.689651
$742$		−	631468.i		−	1.14695i
$743$	66950.3			0.121276			0.0606380	−	0.998160i	$-0.480686\pi$
$743$	66950.3			0.121276			0.0606380	+	0.998160i	$0.480686\pi$
$744$		−	31895.8i		−	0.0576219i
$745$		−	224574.i		−	0.404620i
$746$	1.11288e6			1.99972
$747$	89981.1			0.161254
$748$		−	114398.i		−	0.204463i
$749$			706452.i			1.25927i
$750$			490038.i			0.871178i
$751$	131525.			0.233200			0.116600	−	0.993179i	$-0.462800\pi$
$751$	131525.			0.233200			0.116600	+	0.993179i	$0.462800\pi$
$752$	328027.			0.580061
$753$	−246182.			−0.434177
$754$	48048.1			0.0845149
$755$		−	551536.i		−	0.967564i
$756$	84415.0			0.147698
$757$		−	69360.5i		−	0.121038i	−0.998167	−	0.0605189i	$-0.980724\pi$
$757$		−	69360.5i		−	0.121038i	0.998167	−	0.0605189i	$-0.0192755\pi$
$758$	−725256.			−1.26227
$759$	−90686.0			−0.157419
$760$	26532.1			0.0459352
$761$	−826452.			−1.42708			−0.713540	−	0.700615i	$-0.752909\pi$
$761$	−826452.			−1.42708			−0.713540	+	0.700615i	$0.752909\pi$
$762$	−122315.			−0.210653
$763$	129751.			0.222876
$764$		−	37863.9i		−	0.0648693i
$765$		−	144806.i		−	0.247437i
$766$	554636.			0.945259
$767$		−	1.29252e6i		−	2.19709i
$768$			373801.i			0.633750i
$769$		−	968362.i		−	1.63751i	−0.574141	−	0.818757i	$-0.694664\pi$
$769$		−	968362.i		−	1.63751i	0.574141	−	0.818757i	$-0.305336\pi$
$770$	113134.			0.190815
$771$		−	207942.i		−	0.349812i
$772$	196560.			0.329808
$773$	−82487.3			−0.138047			−0.0690237	−	0.997615i	$-0.521988\pi$
$773$	−82487.3			−0.138047			−0.0690237	+	0.997615i	$0.521988\pi$
$774$	−201993.			−0.337173
$775$		−	339485.i		−	0.565220i
$776$	−39995.4			−0.0664182
$777$	510632.			0.845796
$778$		−	704254.i		−	1.16351i
$779$			111786.i			0.184209i
$780$			372018.i			0.611469i
$781$			225892.i			0.370339i
$782$		−	1.02356e6i		−	1.67378i
$783$		−	4865.91i		−	0.00793671i
$784$	−221447.			−0.360278
$785$			259863.i			0.421702i
$786$	196887.			0.318692
$787$		−	516718.i		−	0.834266i	−0.908846	−	0.417133i	$-0.863035\pi$
$787$		−	516718.i		−	0.834266i	0.908846	−	0.417133i	$-0.136965\pi$
$788$			1.09657e6i			1.76597i
$789$			179839.i			0.288888i
$790$		−	520251.i		−	0.833602i
$791$	−36267.0			−0.0579641
$792$	−3435.41			−0.00547682
$793$	27939.1			0.0444290
$794$		−	26088.6i		−	0.0413819i
$795$		−	281828.i		−	0.445912i
$796$	−677671.			−1.06953
$797$	−838052.			−1.31933			−0.659666	−	0.751559i	$-0.729302\pi$
$797$	−838052.			−1.31933			−0.659666	+	0.751559i	$0.729302\pi$
$798$		−	338169.i		−	0.531041i
$799$	−343651.			−0.538300
$800$			374004.i			0.584382i
$801$	128068.			0.199606
$802$	−383616.			−0.596415
$803$			223457.i			0.346548i
$804$	−231728.	−	266784.i	−0.358481	−	0.412712i
$805$	492309.			0.759706
$806$		−	1.79159e6i		−	2.75784i
$807$		−	438097.i		−	0.672702i
$808$	91030.4			0.139432
$809$			570570.i			0.871790i	0.899998	+	0.435895i	$0.143568\pi$
$809$			570570.i			0.871790i	−0.899998	+	0.435895i	$0.856432\pi$
$810$	77464.7			0.118068
$811$			36569.1i			0.0555997i	0.999614	+	0.0277998i	$0.00885010\pi$
$811$			36569.1i			0.0555997i	−0.999614	+	0.0277998i	$0.991150\pi$
$812$			20868.6i			0.0316505i
$813$	61162.3			0.0925343
$814$	370188.			0.558694
$815$			364738.i			0.549119i
$816$		−	393568.i		−	0.591071i
$817$			393548.i			0.589595i
$818$	−1.21258e6			−1.81219
$819$	−266176.			−0.396827
$820$	109821.			0.163327
$821$	−1.32600e6			−1.96724			−0.983622	−	0.180242i	$-0.942312\pi$
$821$	−1.32600e6			−1.96724			−0.983622	+	0.180242i	$0.942312\pi$
$822$			568729.i			0.841709i
$823$	−942640.			−1.39170			−0.695851	−	0.718186i	$-0.744973\pi$
$823$	−942640.			−1.39170			−0.695851	+	0.718186i	$0.744973\pi$
$824$			60216.4i			0.0886871i
$825$	−36565.1			−0.0537228
$826$	1.15427e6			1.69179
$827$	−545161.			−0.797102			−0.398551	−	0.917146i	$-0.630487\pi$
$827$	−545161.			−0.797102			−0.398551	+	0.917146i	$0.630487\pi$
$828$	266304.			0.388433
$829$	−982390.			−1.42947			−0.714735	−	0.699395i	$-0.753453\pi$
$829$	−982390.			−1.42947			−0.714735	+	0.699395i	$0.753453\pi$
$830$	−354131.			−0.514053
$831$			613132.i			0.887875i
$832$			905897.i			1.30868i
$833$	231995.			0.334340
$834$			644767.i			0.926980i
$835$		−	98863.9i		−	0.141796i
$836$		−	119233.i		−	0.170602i
$837$	−181437.			−0.258986
$838$			1.36680e6i			1.94633i
$839$	1.17991e6			1.67619			0.838096	−	0.545522i	$-0.183669\pi$
$839$	1.17991e6			1.67619			0.838096	+	0.545522i	$0.183669\pi$
$840$	18649.9			0.0264312
$841$	−706078.			−0.998299
$842$		−	1.44518e6i		−	2.03844i
$843$	45811.5			0.0644643
$844$	−812108.			−1.14006
$845$		−	629262.i		−	0.881288i
$846$		−	183838.i		−	0.256858i
$847$		−	552952.i		−	0.770763i
$848$		−	765978.i		−	1.06518i
$849$			348060.i			0.482879i
$850$		−	412704.i		−	0.571217i
$851$	1.61089e6			2.22437
$852$		−	663343.i		−	0.913816i
$853$	−858893.			−1.18043			−0.590216	−	0.807245i	$-0.700957\pi$
$853$	−858893.			−1.18043			−0.590216	+	0.807245i	$0.700957\pi$
$854$			24950.6i			0.0342109i
$855$		−	150927.i		−	0.206459i
$856$			84426.5i			0.115221i
$857$		−	736523.i		−	1.00282i	−0.865209	−	0.501412i	$-0.832814\pi$
$857$		−	736523.i		−	1.00282i	0.865209	−	0.501412i	$-0.167186\pi$
$858$	−192968.			−0.262126
$859$	−444498.			−0.602397			−0.301199	−	0.953561i	$-0.597387\pi$
$859$	−444498.			−0.602397			−0.301199	+	0.953561i	$0.597387\pi$
$860$	386630.			0.522756
$861$			78576.0i			0.105995i
$862$		−	1.86813e6i		−	2.51416i
$863$	571082.			0.766791			0.383396	−	0.923584i	$-0.374755\pi$
$863$	571082.			0.766791			0.383396	+	0.923584i	$0.374755\pi$
$864$	199886.			0.267766
$865$		−	73778.9i		−	0.0986053i
$866$	1.35638e6			1.80862
$867$		−	21673.5i		−	0.0288331i
$868$	778136.			1.03280
$869$	131245.			0.173797
$870$			19150.3i			0.0253010i
$871$	730682.	+	841219.i	0.963146	+	1.10885i
$872$	15506.3			0.0203927
$873$			227512.i			0.298522i
$874$		−	1.06682e6i		−	1.39659i
$875$	671113.			0.876556
$876$		−	656192.i		−	0.855111i
$877$	−97939.8			−0.127339			−0.0636693	−	0.997971i	$-0.520280\pi$
$877$	−97939.8			−0.127339			−0.0636693	+	0.997971i	$0.520280\pi$
$878$			406879.i			0.527809i
$879$		−	482535.i		−	0.624526i
$880$	137233.			0.177213
$881$	859048.			1.10679			0.553396	−	0.832919i	$-0.313332\pi$
$881$	859048.			1.10679			0.553396	+	0.832919i	$0.313332\pi$
$882$			124107.i			0.159536i
$883$		−	298183.i		−	0.382438i	−0.981547	−	0.191219i	$-0.938756\pi$
$883$		−	298183.i		−	0.382438i	0.981547	−	0.191219i	$-0.0612441\pi$
$884$		−	1.05927e6i		−	1.35550i
$885$	515156.			0.657737
$886$	−384992.			−0.490438
$887$	370543.			0.470968			0.235484	−	0.971878i	$-0.424332\pi$
$887$	370543.			0.470968			0.235484	+	0.971878i	$0.424332\pi$
$888$	61024.4			0.0773888
$889$			167511.i			0.211954i
$890$	−504025.			−0.636315
$891$			19542.2i			0.0246160i
$892$	780926.			0.981477
$893$	−358176.			−0.449153
$894$	−342072.			−0.427998
$895$	415305.			0.518467
$896$	96382.9			0.120056
$897$	−839705.			−1.04362
$898$		−	555128.i		−	0.688400i
$899$		−	44853.9i		−	0.0554984i
$900$	107375.			0.132562
$901$			802463.i			0.988497i
$902$			56964.6i			0.0700152i
$903$			276631.i			0.339255i
$904$	−4334.19			−0.00530361
$905$		−	766415.i		−	0.935765i
$906$	−840100.			−1.02347
$907$	−278151.			−0.338117			−0.169058	−	0.985606i	$-0.554073\pi$
$907$	−278151.			−0.338117			−0.169058	+	0.985606i	$0.554073\pi$
$908$	−316955.			−0.384437
$909$		−	517822.i		−	0.626690i
$910$	1.04757e6			1.26502
$911$	−1.13407e6			−1.36648			−0.683238	−	0.730195i	$-0.739429\pi$
$911$	−1.13407e6			−1.36648			−0.683238	+	0.730195i	$0.739429\pi$
$912$		−	410203.i		−	0.493184i
$913$		−	89337.2i		−	0.107174i
$914$			2.18984e6i			2.62132i
$915$			11135.6i			0.0133006i
$916$			73891.9i			0.0880656i
$917$		−	269639.i		−	0.320659i
$918$	−220569.			−0.261734
$919$		−	130892.i		−	0.154983i	−0.996993	−	0.0774914i	$-0.975309\pi$
$919$		−	130892.i		−	0.154983i	0.996993	−	0.0774914i	$-0.0246910\pi$
$920$	58834.7			0.0695117
$921$		−	557417.i		−	0.657145i
$922$		−	483437.i		−	0.568693i
$923$			2.09164e6i			2.45519i
$924$		−	83810.9i		−	0.0981650i
$925$	649518.			0.759116
$926$	1.64098e6			1.91373
$927$	342538.			0.398611
$928$			49414.6i			0.0573799i
$929$			726513.i			0.841805i	0.907106	+	0.420903i	$0.138287\pi$
$929$			726513.i			0.841805i	−0.907106	+	0.420903i	$0.861713\pi$
$930$	714068.			0.825608
$931$	241801.			0.278970
$932$			58049.3i			0.0668290i
$933$	140442.			0.161337
$934$			1.18318e6i			1.35630i
$935$	−143770.			−0.164454
$936$	−31810.1			−0.0363089
$937$		−	1956.96i		−	0.00222896i	−0.999999	−	0.00111448i	$-0.999645\pi$
$937$		−	1956.96i		−	0.00222896i	0.999999	−	0.00111448i	$-0.000354751\pi$
$938$	−751237.	+	652524.i	−0.853830	+	0.741636i
$939$	837159.			0.949460
$940$			351880.i			0.398235i
$941$			824102.i			0.930683i	0.885131	+	0.465341i	$0.154068\pi$
$941$			824102.i			0.930683i	−0.885131	+	0.465341i	$0.845932\pi$
$942$	395825.			0.446068
$943$			247884.i			0.278756i
$944$	1.40014e6			1.57119
$945$		−	106089.i		−	0.118797i
$946$			200547.i			0.224096i
$947$	117874.			0.131437			0.0657187	−	0.997838i	$-0.479066\pi$
$947$	117874.			0.131437			0.0657187	+	0.997838i	$0.479066\pi$
$948$	−385406.			−0.428846
$949$			2.06910e6i			2.29746i
$950$		−	430148.i		−	0.476618i
$951$		−	570241.i		−	0.630517i
$952$	−53102.8			−0.0585927
$953$	−207588.			−0.228569			−0.114284	−	0.993448i	$-0.536457\pi$
$953$	−207588.			−0.228569			−0.114284	+	0.993448i	$0.536457\pi$
$954$	−429281.			−0.471677
$955$	−47585.7			−0.0521758
$956$			1.56332e6i			1.71054i
$957$	−4831.09			−0.00527499
$958$			426261.i			0.464456i
$959$	778882.			0.846904
$960$	−361060.			−0.391775
$961$	−748966.			−0.810990
$962$	3.42775e6			3.70390
$963$	480256.			0.517869
$964$	−229196.			−0.246634
$965$		−	247028.i		−	0.265272i
$966$		−	749886.i		−	0.803602i
$967$	−1.59379e6			−1.70443			−0.852213	−	0.523195i	$-0.824740\pi$
$967$	−1.59379e6			−1.70443			−0.852213	+	0.523195i	$0.824740\pi$
$968$		−	66082.1i		−	0.0705234i
$969$			429742.i			0.457678i
$970$		−	895399.i		−	0.951641i
$971$	−304145.			−0.322584			−0.161292	−	0.986907i	$-0.551566\pi$
$971$	−304145.			−0.322584			−0.161292	+	0.986907i	$0.551566\pi$
$972$		−	57386.5i		−	0.0607403i
$973$	883016.			0.932702
$974$	−1.56707e6			−1.65184
$975$	−338574.			−0.356159
$976$			30265.3i			0.0317721i
$977$	815943.			0.854812			0.427406	−	0.904060i	$-0.359427\pi$
$977$	815943.			0.854812			0.427406	+	0.904060i	$0.359427\pi$
$978$	555570.			0.580847
$979$		−	127151.i		−	0.132665i
$980$		−	237550.i		−	0.247345i
$981$		−	88206.7i		−	0.0916566i
$982$		−	1.23366e6i		−	1.27930i
$983$		−	979165.i		−	1.01333i	−0.862144	−	0.506663i	$-0.830879\pi$
$983$		−	979165.i		−	1.01333i	0.862144	−	0.506663i	$-0.169121\pi$
$984$			9390.45i			0.00969831i
$985$	1.37811e6			1.42041
$986$		−	54527.8i		−	0.0560872i
$987$	−251768.			−0.258444
$988$		−	1.10404e6i		−	1.13102i
$989$			872688.i			0.892209i
$990$		−	76910.4i		−	0.0784720i
$991$			19258.7i			0.0196101i	0.999952	+	0.00980504i	$0.00312109\pi$
$991$			19258.7i			0.0196101i	−0.999952	+	0.00980504i	$0.996879\pi$
$992$	1.84255e6			1.87239
$993$	10039.0			0.0101811
$994$	−1.86791e6			−1.89053
$995$			851666.i			0.860247i
$996$			262343.i			0.264454i
$997$	1.45865e6			1.46744			0.733720	−	0.679451i	$-0.237782\pi$
$997$	1.45865e6			1.46744			0.733720	+	0.679451i	$0.237782\pi$
$998$	−242808.			−0.243782
$999$		−	347134.i		−	0.347830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.8	✓	46
67.66	odd	2	inner	201.5.b.a.133.39	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.8	✓	46	1.1	even	1	trivial
201.5.b.a.133.39	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)

\(f(q)\)	\(=\)	\(q-5.58118i q^{2} +5.19615i q^{3} -15.1496 q^{4} +19.0393i q^{5} +29.0007 q^{6} -39.7168i q^{7} -4.74646i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-5.58118i q^{2} +5.19615i q^{3} -15.1496 q^{4} +19.0393i q^{5} +29.0007 q^{6} -39.7168i q^{7} -4.74646i q^{8} -27.0000 q^{9} +106.262 q^{10} +26.8068i q^{11} -78.7194i q^{12} +248.217i q^{13} -221.666 q^{14} -98.9310 q^{15} -268.884 q^{16} +281.691 q^{17} +150.692i q^{18} +293.597 q^{19} -288.437i q^{20} +206.374 q^{21} +149.614 q^{22} +651.048 q^{23} +24.6633 q^{24} +262.506 q^{25} +1385.34 q^{26} -140.296i q^{27} +601.691i q^{28} +34.6831 q^{29} +552.151i q^{30} -1293.25i q^{31} +1424.75i q^{32} -139.292 q^{33} -1572.17i q^{34} +756.178 q^{35} +409.038 q^{36} +2474.30 q^{37} -1638.62i q^{38} -1289.77 q^{39} +90.3692 q^{40} +380.745i q^{41} -1151.81i q^{42} +1340.43i q^{43} -406.111i q^{44} -514.060i q^{45} -3633.62i q^{46} -1219.96 q^{47} -1397.16i q^{48} +823.579 q^{49} -1465.09i q^{50} +1463.71i q^{51} -3760.38i q^{52} +2848.73i q^{53} -783.018 q^{54} -510.382 q^{55} -188.514 q^{56} +1525.58i q^{57} -193.573i q^{58} -5207.23 q^{59} +1498.76 q^{60} -112.559i q^{61} -7217.84 q^{62} +1072.35i q^{63} +3649.62 q^{64} -4725.87 q^{65} +777.415i q^{66} +(3389.04 - 2943.72i) q^{67} -4267.50 q^{68} +3382.95i q^{69} -4220.37i q^{70} +8426.67 q^{71} +128.154i q^{72} +8335.83 q^{73} -13809.5i q^{74} +1364.02i q^{75} -4447.87 q^{76} +1064.68 q^{77} +7198.46i q^{78} -4895.95i q^{79} -5119.35i q^{80} +729.000 q^{81} +2125.01 q^{82} -3332.63 q^{83} -3126.48 q^{84} +5363.20i q^{85} +7481.21 q^{86} +180.219i q^{87} +127.237 q^{88} -4743.25 q^{89} -2869.06 q^{90} +9858.38 q^{91} -9863.10 q^{92} +6719.91 q^{93} +6808.80i q^{94} +5589.88i q^{95} -7403.19 q^{96} -8426.37i q^{97} -4596.54i q^{98} -723.784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 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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