LMFDB - Embedded newform 201.5.b.a.133.4

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			133.4
Character	$\chi$	$=$	201.133
Dual form			201.5.b.a.133.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.50857i q^{2} -5.19615i q^{3} -40.3787 q^{4} +11.1565i q^{5} -39.0157 q^{6} +57.6520i q^{7} +183.049i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q-7.50857i q^{2} -5.19615i q^{3} -40.3787 q^{4} +11.1565i q^{5} -39.0157 q^{6} +57.6520i q^{7} +183.049i q^{8} -27.0000 q^{9} +83.7695 q^{10} -61.5038i q^{11} +209.814i q^{12} -14.9937i q^{13} +432.884 q^{14} +57.9709 q^{15} +728.379 q^{16} -231.762 q^{17} +202.731i q^{18} +627.264 q^{19} -450.485i q^{20} +299.569 q^{21} -461.806 q^{22} -308.744 q^{23} +951.151 q^{24} +500.532 q^{25} -112.581 q^{26} +140.296i q^{27} -2327.91i q^{28} -73.3391 q^{29} -435.279i q^{30} +368.308i q^{31} -2540.30i q^{32} -319.583 q^{33} +1740.20i q^{34} -643.195 q^{35} +1090.22 q^{36} +1527.90 q^{37} -4709.86i q^{38} -77.9096 q^{39} -2042.19 q^{40} +2574.47i q^{41} -2249.33i q^{42} +3633.51i q^{43} +2483.44i q^{44} -301.226i q^{45} +2318.23i q^{46} +2225.17 q^{47} -3784.77i q^{48} -922.754 q^{49} -3758.28i q^{50} +1204.27i q^{51} +605.426i q^{52} -1139.07i q^{53} +1053.42 q^{54} +686.168 q^{55} -10553.2 q^{56} -3259.36i q^{57} +550.672i q^{58} -4029.98 q^{59} -2340.79 q^{60} -1749.78i q^{61} +2765.47 q^{62} -1556.60i q^{63} -7419.98 q^{64} +167.277 q^{65} +2399.61i q^{66} +(-4304.57 + 1273.50i) q^{67} +9358.24 q^{68} +1604.28i q^{69} +4829.48i q^{70} +4699.38 q^{71} -4942.33i q^{72} -697.889 q^{73} -11472.4i q^{74} -2600.84i q^{75} -25328.1 q^{76} +3545.82 q^{77} +584.990i q^{78} +1718.64i q^{79} +8126.17i q^{80} +729.000 q^{81} +19330.6 q^{82} +10072.4 q^{83} -12096.2 q^{84} -2585.66i q^{85} +27282.5 q^{86} +381.081i q^{87} +11258.2 q^{88} -193.110 q^{89} -2261.78 q^{90} +864.417 q^{91} +12466.7 q^{92} +1913.79 q^{93} -16707.8i q^{94} +6998.08i q^{95} -13199.8 q^{96} -3606.17i q^{97} +6928.57i q^{98} +1660.60i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	7.50857i		−	1.87714i	−0.345084	−	0.938572i	$-0.612150\pi$
$2$		−	7.50857i		−	1.87714i	0.345084	−	0.938572i	$-0.387850\pi$
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−40.3787			−2.52367
$5$			11.1565i			0.446260i	0.974789	+	0.223130i	$0.0716275\pi$
$5$			11.1565i			0.446260i	−0.974789	+	0.223130i	$0.928372\pi$
$6$	−39.0157			−1.08377
$7$			57.6520i			1.17657i	0.808653	+	0.588286i	$0.200197\pi$
$7$			57.6520i			1.17657i	−0.808653	+	0.588286i	$0.799803\pi$
$8$			183.049i			2.86014i
$9$	−27.0000			−0.333333
$10$	83.7695			0.837695
$11$		−	61.5038i		−	0.508296i	−0.967165	−	0.254148i	$-0.918205\pi$
$11$		−	61.5038i		−	0.508296i	0.967165	−	0.254148i	$-0.0817950\pi$
$12$			209.814i			1.45704i
$13$		−	14.9937i		−	0.0887202i	−0.999016	−	0.0443601i	$-0.985875\pi$
$13$		−	14.9937i		−	0.0887202i	0.999016	−	0.0443601i	$-0.0141249\pi$
$14$	432.884			2.20859
$15$	57.9709			0.257649
$16$	728.379			2.84523
$17$	−231.762			−0.801945			−0.400972	−	0.916090i	$-0.631328\pi$
$17$	−231.762			−0.801945			−0.400972	+	0.916090i	$0.631328\pi$
$18$			202.731i			0.625715i
$19$	627.264			1.73757			0.868786	−	0.495187i	$-0.164901\pi$
$19$	627.264			1.73757			0.868786	+	0.495187i	$0.164901\pi$
$20$		−	450.485i		−	1.12621i
$21$	299.569			0.679294
$22$	−461.806			−0.954144
$23$	−308.744			−0.583638			−0.291819	−	0.956474i	$-0.594260\pi$
$23$	−308.744			−0.583638			−0.291819	+	0.956474i	$0.594260\pi$
$24$	951.151			1.65130
$25$	500.532			0.800852
$26$	−112.581			−0.166540
$27$			140.296i			0.192450i
$28$		−	2327.91i		−	2.96928i
$29$	−73.3391			−0.0872047			−0.0436023	−	0.999049i	$-0.513883\pi$
$29$	−73.3391			−0.0872047			−0.0436023	+	0.999049i	$0.513883\pi$
$30$		−	435.279i		−	0.483643i
$31$			368.308i			0.383255i	0.981468	+	0.191628i	$0.0613766\pi$
$31$			368.308i			0.383255i	−0.981468	+	0.191628i	$0.938623\pi$
$32$		−	2540.30i		−	2.48076i
$33$	−319.583			−0.293465
$34$			1740.20i			1.50537i
$35$	−643.195			−0.525057
$36$	1090.22			0.841223
$37$	1527.90			1.11607			0.558035	−	0.829817i	$-0.311555\pi$
$37$	1527.90			1.11607			0.558035	+	0.829817i	$0.311555\pi$
$38$		−	4709.86i		−	3.26167i
$39$	−77.9096			−0.0512226
$40$	−2042.19			−1.27637
$41$			2574.47i			1.53151i	0.643131	+	0.765756i	$0.277635\pi$
$41$			2574.47i			1.53151i	−0.643131	+	0.765756i	$0.722365\pi$
$42$		−	2249.33i		−	1.27513i
$43$			3633.51i			1.96512i	0.185938	+	0.982561i	$0.440468\pi$
$43$			3633.51i			1.96512i	−0.185938	+	0.982561i	$0.559532\pi$
$44$			2483.44i			1.28277i
$45$		−	301.226i		−	0.148753i
$46$			2318.23i			1.09557i
$47$	2225.17			1.00732			0.503660	−	0.863902i	$-0.331987\pi$
$47$	2225.17			1.00732			0.503660	+	0.863902i	$0.331987\pi$
$48$		−	3784.77i		−	1.64269i
$49$	−922.754			−0.384321
$50$		−	3758.28i		−	1.50331i
$51$			1204.27i			0.463003i
$52$			605.426i			0.223900i
$53$		−	1139.07i		−	0.405507i	−0.979230	−	0.202754i	$-0.935011\pi$
$53$		−	1139.07i		−	0.405507i	0.979230	−	0.202754i	$-0.0649890\pi$
$54$	1053.42			0.361256
$55$	686.168			0.226832
$56$	−10553.2			−3.36516
$57$		−	3259.36i		−	1.00319i
$58$			550.672i			0.163696i
$59$	−4029.98			−1.15771			−0.578854	−	0.815431i	$-0.696500\pi$
$59$	−4029.98			−1.15771			−0.578854	+	0.815431i	$0.696500\pi$
$60$	−2340.79			−0.650219
$61$		−	1749.78i		−	0.470246i	−0.971966	−	0.235123i	$-0.924451\pi$
$61$		−	1749.78i		−	0.470246i	0.971966	−	0.235123i	$-0.0755493\pi$
$62$	2765.47			0.719425
$63$		−	1556.60i		−	0.392191i
$64$	−7419.98			−1.81152
$65$	167.277			0.0395923
$66$			2399.61i			0.550875i
$67$	−4304.57	+	1273.50i	−0.958915	+	0.283694i
$67$	−4304.57	+	1273.50i	−0.958915	+	0.283694i
$68$	9358.24			2.02384
$69$			1604.28i			0.336964i
$70$			4829.48i			0.985608i
$71$	4699.38			0.932231			0.466116	−	0.884724i	$-0.345653\pi$
$71$	4699.38			0.932231			0.466116	+	0.884724i	$0.345653\pi$
$72$		−	4942.33i		−	0.953381i
$73$	−697.889			−0.130961			−0.0654803	−	0.997854i	$-0.520858\pi$
$73$	−697.889			−0.130961			−0.0654803	+	0.997854i	$0.520858\pi$
$74$		−	11472.4i		−	2.09503i
$75$		−	2600.84i		−	0.462372i
$76$	−25328.1			−4.38506
$77$	3545.82			0.598046
$78$			584.990i			0.0961522i
$79$			1718.64i			0.275378i	0.990475	+	0.137689i	$0.0439675\pi$
$79$			1718.64i			0.275378i	−0.990475	+	0.137689i	$0.956032\pi$
$80$			8126.17i			1.26971i
$81$	729.000			0.111111
$82$	19330.6			2.87487
$83$	10072.4			1.46210			0.731048	−	0.682326i	$-0.239031\pi$
$83$	10072.4			1.46210			0.731048	+	0.682326i	$0.239031\pi$
$84$	−12096.2			−1.71431
$85$		−	2585.66i		−	0.357876i
$86$	27282.5			3.68882
$87$			381.081i			0.0503476i
$88$	11258.2			1.45380
$89$	−193.110			−0.0243795			−0.0121897	−	0.999926i	$-0.503880\pi$
$89$	−193.110			−0.0243795			−0.0121897	+	0.999926i	$0.503880\pi$
$90$	−2261.78			−0.279232
$91$	864.417			0.104386
$92$	12466.7			1.47291
$93$	1913.79			0.221273
$94$		−	16707.8i		−	1.89088i
$95$			6998.08i			0.775410i
$96$	−13199.8			−1.43227
$97$		−	3606.17i		−	0.383268i	−0.981466	−	0.191634i	$-0.938621\pi$
$97$		−	3606.17i		−	0.383268i	0.981466	−	0.191634i	$-0.0613787\pi$
$98$			6928.57i			0.721425i
$99$			1660.60i			0.169432i
$100$	−20210.8			−2.02108
$101$			5715.47i			0.560285i	0.959958	+	0.280143i	$0.0903818\pi$
$101$			5715.47i			0.560285i	−0.959958	+	0.280143i	$0.909618\pi$
$102$	9042.35			0.869123
$103$	3857.79			0.363633			0.181817	−	0.983332i	$-0.441802\pi$
$103$	3857.79			0.363633			0.181817	+	0.983332i	$0.441802\pi$
$104$	2744.59			0.253752
$105$			3342.14i			0.303142i
$106$	−8552.79			−0.761195
$107$	−8645.03			−0.755091			−0.377545	−	0.925991i	$-0.623232\pi$
$107$	−8645.03			−0.755091			−0.377545	+	0.925991i	$0.623232\pi$
$108$		−	5664.97i		−	0.485680i
$109$			18990.8i			1.59842i	0.601052	+	0.799210i	$0.294748\pi$
$109$			18990.8i			1.59842i	−0.601052	+	0.799210i	$0.705252\pi$
$110$		−	5152.14i		−	0.425797i
$111$		−	7939.21i		−	0.644364i
$112$			41992.5i			3.34762i
$113$			3696.37i			0.289480i	0.989470	+	0.144740i	$0.0462346\pi$
$113$			3696.37i			0.289480i	−0.989470	+	0.144740i	$0.953765\pi$
$114$	−24473.1			−1.88313
$115$		−	3444.51i		−	0.260455i
$116$	2961.34			0.220076
$117$			404.830i			0.0295734i
$118$			30259.4i			2.17318i
$119$		−	13361.5i		−	0.943545i
$120$			10611.5i			0.736912i
$121$	10858.3			0.741635
$122$	−13138.4			−0.882719
$123$	13377.3			0.884219
$124$		−	14871.8i		−	0.967209i
$125$			12557.0i			0.803649i
$126$	−11687.9			−0.736198
$127$	952.274			0.0590411			0.0295206	−	0.999564i	$-0.490602\pi$
$127$	952.274			0.0590411			0.0295206	+	0.999564i	$0.490602\pi$
$128$			15068.6i			0.919717i
$129$	18880.3			1.13456
$130$		−	1256.02i		−	0.0743204i
$131$	22651.6			1.31995			0.659973	−	0.751290i	$-0.270568\pi$
$131$	22651.6			1.31995			0.659973	+	0.751290i	$0.270568\pi$
$132$	12904.3			0.740607
$133$			36163.0i			2.04438i
$134$	9562.18	+	32321.2i	0.532534	+	1.80002i
$135$	−1565.22			−0.0858829
$136$		−	42423.8i		−	2.29368i
$137$		−	11551.2i		−	0.615439i	−0.951477	−	0.307720i	$-0.900434\pi$
$137$		−	11551.2i		−	0.615439i	0.951477	−	0.307720i	$-0.0995659\pi$
$138$	12045.9			0.632529
$139$			31916.1i			1.65189i	0.563753	+	0.825943i	$0.309357\pi$
$139$			31916.1i			1.65189i	−0.563753	+	0.825943i	$0.690643\pi$
$140$	25971.4			1.32507
$141$		−	11562.3i		−	0.581576i
$142$		−	35285.6i		−	1.74993i
$143$	−922.170			−0.0450961
$144$	−19666.2			−0.948410
$145$		−	818.209i		−	0.0389160i
$146$			5240.15i			0.245832i
$147$			4794.77i			0.221888i
$148$	−61694.6			−2.81659
$149$	−35773.3			−1.61134			−0.805668	−	0.592367i	$-0.798194\pi$
$149$	−35773.3			−1.61134			−0.805668	+	0.592367i	$0.798194\pi$
$150$	−19528.6			−0.867938
$151$	35565.0			1.55980			0.779900	−	0.625904i	$-0.215270\pi$
$151$	35565.0			1.55980			0.779900	+	0.625904i	$0.215270\pi$
$152$			114820.i			4.96971i
$153$	6257.57			0.267315
$154$		−	26624.0i		−	1.12262i
$155$	−4109.04			−0.171032
$156$	3145.89			0.129269
$157$	−27904.1			−1.13206			−0.566029	−	0.824385i	$-0.691521\pi$
$157$	−27904.1			−1.13206			−0.566029	+	0.824385i	$0.691521\pi$
$158$	12904.5			0.516925
$159$	−5918.78			−0.234120
$160$	28340.9			1.10707
$161$		−	17799.7i		−	0.686692i
$162$		−	5473.75i		−	0.208572i
$163$	−30419.7			−1.14493			−0.572467	−	0.819928i	$-0.694013\pi$
$163$	−30419.7			−1.14493			−0.572467	+	0.819928i	$0.694013\pi$
$164$		−	103954.i		−	3.86503i
$165$		−	3565.43i		−	0.130962i
$166$		−	75629.3i		−	2.74457i
$167$	−41347.0			−1.48256			−0.741279	−	0.671197i	$-0.765780\pi$
$167$	−41347.0			−1.48256			−0.741279	+	0.671197i	$0.765780\pi$
$168$			54835.8i			1.94288i
$169$	28336.2			0.992129
$170$	−19414.6			−0.671785
$171$	−16936.1			−0.579191
$172$		−	146716.i		−	4.95932i
$173$	−6480.80			−0.216539			−0.108270	−	0.994122i	$-0.534531\pi$
$173$	−6480.80			−0.216539			−0.108270	+	0.994122i	$0.534531\pi$
$174$	2861.38			0.0945097
$175$			28856.7i			0.942259i
$176$		−	44798.1i		−	1.44622i
$177$			20940.4i			0.668403i
$178$			1449.98i			0.0457638i
$179$		−	8650.61i		−	0.269986i	−0.990847	−	0.134993i	$-0.956899\pi$
$179$		−	8650.61i		−	0.269986i	0.990847	−	0.134993i	$-0.0431011\pi$
$180$			12163.1i			0.375404i
$181$	5580.75			0.170347			0.0851736	−	0.996366i	$-0.472856\pi$
$181$	5580.75			0.170347			0.0851736	+	0.996366i	$0.472856\pi$
$182$		−	6490.54i		−	0.195947i
$183$	−9092.15			−0.271497
$184$		−	56515.4i		−	1.66929i
$185$			17046.0i			0.498058i
$186$		−	14369.8i		−	0.415360i
$187$			14254.2i			0.407625i
$188$	−89849.4			−2.54214
$189$	−8088.35			−0.226431
$190$	52545.6			1.45556
$191$		−	9606.79i		−	0.263337i	−0.991294	−	0.131668i	$-0.957967\pi$
$191$		−	9606.79i		−	0.263337i	0.991294	−	0.131668i	$-0.0420334\pi$
$192$			38555.4i			1.04588i
$193$	52588.8			1.41182			0.705909	−	0.708303i	$-0.250539\pi$
$193$	52588.8			1.41182			0.705909	+	0.708303i	$0.250539\pi$
$194$	−27077.2			−0.719449
$195$		−	869.199i		−	0.0228586i
$196$	37259.6			0.969898
$197$			25358.0i			0.653404i	0.945127	+	0.326702i	$0.105937\pi$
$197$			25358.0i			0.653404i	−0.945127	+	0.326702i	$0.894063\pi$
$198$	12468.8			0.318048
$199$	−16949.2			−0.427998			−0.213999	−	0.976834i	$-0.568649\pi$
$199$	−16949.2			−0.427998			−0.213999	+	0.976834i	$0.568649\pi$
$200$			91622.0i			2.29055i
$201$	6617.31	+	22367.2i	0.163791	+	0.553630i
$202$	42915.0			1.05174
$203$		−	4228.15i		−	0.102603i
$204$		−	48626.9i		−	1.16847i
$205$	−28722.1			−0.683453
$206$		−	28966.5i		−	0.682592i
$207$	8336.10			0.194546
$208$		−	10921.1i		−	0.252429i
$209$		−	38579.1i		−	0.883201i
$210$	25094.7			0.569041
$211$	−30267.2			−0.679841			−0.339921	−	0.940454i	$-0.610400\pi$
$211$	−30267.2			−0.679841			−0.339921	+	0.940454i	$0.610400\pi$
$212$			45994.1i			1.02336i
$213$		−	24418.7i		−	0.538224i
$214$			64911.9i			1.41741i
$215$	−40537.3			−0.876957
$216$	−25681.1			−0.550435
$217$	−21233.7			−0.450927
$218$	142594.			3.00046
$219$			3626.34i			0.0756102i
$220$	−27706.6			−0.572449
$221$			3474.97i			0.0711486i
$222$	−59612.1			−1.20956
$223$	−65127.5			−1.30965			−0.654824	−	0.755782i	$-0.727257\pi$
$223$	−65127.5			−1.30965			−0.654824	+	0.755782i	$0.727257\pi$
$224$	146454.			2.91880
$225$	−13514.4			−0.266951
$226$	27754.5			0.543396
$227$	13405.9			0.260162			0.130081	−	0.991503i	$-0.458476\pi$
$227$	13405.9			0.260162			0.130081	+	0.991503i	$0.458476\pi$
$228$			131609.i			2.53171i
$229$		−	10184.3i		−	0.194204i	−0.995274	−	0.0971021i	$-0.969043\pi$
$229$		−	10184.3i		−	0.194204i	0.995274	−	0.0971021i	$-0.0309574\pi$
$230$	−25863.4			−0.488911
$231$		−	18424.6i		−	0.345282i
$232$		−	13424.7i		−	0.249418i
$233$			91902.6i			1.69284i	0.532516	+	0.846420i	$0.321247\pi$
$233$			91902.6i			1.69284i	−0.532516	+	0.846420i	$0.678753\pi$
$234$	3039.70			0.0555135
$235$			24825.1i			0.449527i
$236$	162725.			2.92167
$237$	8930.30			0.158990
$238$	−100326.			−1.77117
$239$		−	63660.6i		−	1.11449i	−0.830349	−	0.557244i	$-0.811859\pi$
$239$		−	63660.6i		−	1.11449i	0.830349	−	0.557244i	$-0.188141\pi$
$240$	42224.8			0.733070
$241$	−58851.5			−1.01327			−0.506633	−	0.862162i	$-0.669110\pi$
$241$	−58851.5			−1.01327			−0.506633	+	0.862162i	$0.669110\pi$
$242$		−	81530.2i		−	1.39216i
$243$		−	3788.00i		−	0.0641500i
$244$			70654.0i			1.18674i
$245$		−	10294.7i		−	0.171507i
$246$		−	100445.i		−	1.65981i
$247$		−	9405.01i		−	0.154158i
$248$	−67418.5			−1.09616
$249$		−	52337.7i		−	0.844142i
$250$	94285.3			1.50856
$251$		−	89457.5i		−	1.41994i	−0.704233	−	0.709969i	$-0.748709\pi$
$251$		−	89457.5i		−	1.41994i	0.704233	−	0.709969i	$-0.251291\pi$
$252$			62853.6i			0.989759i
$253$			18989.0i			0.296661i
$254$		−	7150.22i		−	0.110829i
$255$	−13435.5			−0.206620
$256$	−5575.67			−0.0850779
$257$	63363.1			0.959335			0.479668	−	0.877450i	$-0.340757\pi$
$257$	63363.1			0.959335			0.479668	+	0.877450i	$0.340757\pi$
$258$		−	141764.i		−	2.12974i
$259$			88086.6i			1.31314i
$260$	−6754.44			−0.0999178
$261$	1980.16			0.0290682
$262$		−	170081.i		−	2.47773i
$263$	46527.5			0.672664			0.336332	−	0.941743i	$-0.390814\pi$
$263$	46527.5			0.672664			0.336332	+	0.941743i	$0.390814\pi$
$264$		−	58499.4i		−	0.839351i
$265$	12708.0			0.180962
$266$	271533.			3.83759
$267$			1003.43i			0.0140755i
$268$	173813.	−	51422.3i	2.41998	−	0.715949i
$269$	6652.57			0.0919359			0.0459680	−	0.998943i	$-0.485363\pi$
$269$	6652.57			0.0919359			0.0459680	+	0.998943i	$0.485363\pi$
$270$			11752.5i			0.161214i
$271$			94746.3i			1.29010i	0.764140	+	0.645050i	$0.223164\pi$
$271$			94746.3i			1.29010i	−0.764140	+	0.645050i	$0.776836\pi$
$272$	−168811.			−2.28172
$273$		−	4491.64i		−	0.0602671i
$274$	−86732.9			−1.15527
$275$		−	30784.6i		−	0.407069i
$276$		−	64778.9i		−	0.850384i
$277$	116806.			1.52231			0.761157	−	0.648568i	$-0.224632\pi$
$277$	116806.			1.52231			0.761157	+	0.648568i	$0.224632\pi$
$278$	239644.			3.10083
$279$		−	9944.32i		−	0.127752i
$280$		−	117736.i		−	1.50174i
$281$			62919.1i			0.796838i	0.917203	+	0.398419i	$0.130441\pi$
$281$			62919.1i			0.796838i	−0.917203	+	0.398419i	$0.869559\pi$
$282$	−86816.5			−1.09170
$283$	−110460.			−1.37922			−0.689609	−	0.724182i	$-0.742217\pi$
$283$	−110460.			−1.37922			−0.689609	+	0.724182i	$0.742217\pi$
$284$	−189755.			−2.35264
$285$	36363.1			0.447683
$286$			6924.18i			0.0846518i
$287$	−148423.			−1.80193
$288$			68588.2i			0.826921i
$289$	−29807.4			−0.356885
$290$	−6143.58			−0.0730509
$291$	−18738.2			−0.221280
$292$	28179.8			0.330501
$293$	−139463.			−1.62452			−0.812258	−	0.583299i	$-0.801762\pi$
$293$	−139463.			−1.62452			−0.812258	+	0.583299i	$0.801762\pi$
$294$	36001.9			0.416515
$295$		−	44960.5i		−	0.516639i
$296$			279681.i			3.19212i
$297$	8628.74			0.0978216
$298$			268606.i			3.02471i
$299$			4629.22i			0.0517805i
$300$			105019.i			1.16687i
$301$	−209479.			−2.31211
$302$		−	267043.i		−	2.92797i
$303$	29698.5			0.323481
$304$	456886.			4.94380
$305$	19521.5			0.209852
$306$		−	46985.5i		−	0.501788i
$307$	51595.5			0.547438			0.273719	−	0.961810i	$-0.411746\pi$
$307$	51595.5			0.547438			0.273719	+	0.961810i	$0.411746\pi$
$308$	−143175.			−1.50927
$309$		−	20045.6i		−	0.209944i
$310$			30853.0i			0.321051i
$311$		−	178911.i		−	1.84976i	−0.380256	−	0.924881i	$-0.624164\pi$
$311$		−	178911.i		−	1.84976i	0.380256	−	0.924881i	$-0.375836\pi$
$312$		−	14261.3i		−	0.146504i
$313$			176853.i			1.80520i	0.430483	+	0.902599i	$0.358343\pi$
$313$			176853.i			1.80520i	−0.430483	+	0.902599i	$0.641657\pi$
$314$			209520.i			2.12504i
$315$	17366.3			0.175019
$316$		−	69396.3i		−	0.694964i
$317$	132925.			1.32279			0.661393	−	0.750040i	$-0.269966\pi$
$317$	132925.			1.32279			0.661393	+	0.750040i	$0.269966\pi$
$318$			44441.6i			0.439476i
$319$			4510.63i			0.0443258i
$320$		−	82781.1i		−	0.808409i
$321$			44920.9i			0.435952i
$322$	−133651.			−1.28902
$323$	−145376.			−1.39344
$324$	−29436.1			−0.280408
$325$		−	7504.83i		−	0.0710517i
$326$			228409.i			2.14920i
$327$	98679.2			0.922848
$328$	−471255.			−4.38034
$329$			128285.i			1.18518i
$330$	−26771.3			−0.245834
$331$		−	105420.i		−	0.962202i	−0.876665	−	0.481101i	$-0.840237\pi$
$331$		−	105420.i		−	0.962202i	0.876665	−	0.481101i	$-0.159763\pi$
$332$	−406710.			−3.68985
$333$	−41253.3			−0.372024
$334$			310457.i			2.78297i
$335$	−14207.8	−	48024.0i	−0.126601	−	0.427926i
$336$	218200.			1.93275
$337$		−	113274.i		−	0.997406i	−0.866773	−	0.498703i	$-0.833810\pi$
$337$		−	113274.i		−	0.997406i	0.866773	−	0.498703i	$-0.166190\pi$
$338$		−	212764.i		−	1.86237i
$339$	19206.9			0.167132
$340$			104405.i			0.903161i
$341$	22652.4			0.194807
$342$			127166.i			1.08722i
$343$			85223.8i			0.724391i
$344$	−665111.			−5.62053
$345$	−17898.2			−0.150374
$346$			48661.6i			0.406475i
$347$		−	75711.8i		−	0.628789i	−0.949292	−	0.314394i	$-0.898199\pi$
$347$		−	75711.8i		−	0.628789i	0.949292	−	0.314394i	$-0.101801\pi$
$348$		−	15387.6i		−	0.127061i
$349$	7779.19			0.0638680			0.0319340	−	0.999490i	$-0.489833\pi$
$349$	7779.19			0.0638680			0.0319340	+	0.999490i	$0.489833\pi$
$350$	216673.			1.76876
$351$	2103.56			0.0170742
$352$	−156238.			−1.26096
$353$			183672.i			1.47398i	0.675902	+	0.736992i	$0.263754\pi$
$353$			183672.i			1.47398i	−0.675902	+	0.736992i	$0.736246\pi$
$354$	157233.			1.25469
$355$			52428.7i			0.416018i
$356$	7797.52			0.0615257
$357$	−69428.6			−0.544756
$358$	−64953.7			−0.506802
$359$	36678.2			0.284590			0.142295	−	0.989824i	$-0.454552\pi$
$359$	36678.2			0.284590			0.142295	+	0.989824i	$0.454552\pi$
$360$	55139.1			0.425456
$361$	263139.			2.01916
$362$		−	41903.5i		−	0.319766i
$363$		−	56421.3i		−	0.428183i
$364$	−34904.0			−0.263435
$365$		−	7786.01i		−	0.0584426i
$366$			68269.1i			0.509638i
$367$		−	215345.i		−	1.59883i	−0.600780	−	0.799414i	$-0.705143\pi$
$367$		−	215345.i		−	1.59883i	0.600780	−	0.799414i	$-0.294857\pi$
$368$	−224883.			−1.66058
$369$		−	69510.7i		−	0.510504i
$370$	127992.			0.934927
$371$	65669.6			0.477108
$372$	−77276.2			−0.558418
$373$			63209.3i			0.454322i	0.973857	+	0.227161i	$0.0729443\pi$
$373$			63209.3i			0.454322i	−0.973857	+	0.227161i	$0.927056\pi$
$374$	107029.			0.765171
$375$	65248.2			0.463987
$376$			407315.i			2.88108i
$377$			1099.63i			0.00773681i
$378$			60732.0i			0.425044i
$379$			17250.8i			0.120097i	0.998195	+	0.0600484i	$0.0191255\pi$
$379$			17250.8i			0.120097i	−0.998195	+	0.0600484i	$0.980874\pi$
$380$		−	282573.i		−	1.95688i
$381$		−	4948.16i		−	0.0340874i
$382$	−72133.3			−0.494321
$383$			34221.9i			0.233295i	0.993173	+	0.116648i	$0.0372149\pi$
$383$			34221.9i			0.233295i	−0.993173	+	0.116648i	$0.962785\pi$
$384$	78299.0			0.530999
$385$			39559.0i			0.266884i
$386$		−	394867.i		−	2.65018i
$387$		−	98104.8i		−	0.655041i
$388$			145612.i			0.967242i
$389$	−124299.			−0.821425			−0.410712	−	0.911765i	$-0.634720\pi$
$389$	−124299.			−0.821425			−0.410712	+	0.911765i	$0.634720\pi$
$390$	−6526.45			−0.0429089
$391$	71555.2			0.468045
$392$		−	168909.i		−	1.09921i
$393$		−	117701.i		−	0.762071i
$394$	190402.			1.22653
$395$	−19174.0			−0.122891
$396$		−	67052.9i		−	0.427590i
$397$	66666.2			0.422985			0.211492	−	0.977380i	$-0.432168\pi$
$397$	66666.2			0.422985			0.211492	+	0.977380i	$0.432168\pi$
$398$			127264.i			0.803415i
$399$	187909.			1.18032
$400$	364577.			2.27861
$401$		−	264915.i		−	1.64747i	−0.566974	−	0.823736i	$-0.691886\pi$
$401$		−	264915.i		−	1.64747i	0.566974	−	0.823736i	$-0.308114\pi$
$402$	167946.	−	49686.5i	1.03924	−	0.307459i
$403$	5522.31			0.0340025
$404$		−	230783.i		−	1.41397i
$405$			8133.10i			0.0495845i
$406$	−31747.4			−0.192600
$407$		−	93971.7i		−	0.567294i
$408$	−220441.			−1.32425
$409$			317151.i			1.89592i	0.318390	+	0.947960i	$0.396858\pi$
$409$			317151.i			1.89592i	−0.318390	+	0.947960i	$0.603142\pi$
$410$			215662.i			1.28294i
$411$	−60021.7			−0.355324
$412$	−155772.			−0.917690
$413$		−	232337.i		−	1.36213i
$414$		−	62592.2i		−	0.365191i
$415$			112373.i			0.652476i
$416$	−38088.5			−0.220094
$417$	165841.			0.953717
$418$	−289674.			−1.65789
$419$	309971.			1.76560			0.882802	−	0.469745i	$-0.155654\pi$
$419$	309971.			1.76560			0.882802	+	0.469745i	$0.155654\pi$
$420$		−	134951.i		−	0.765030i
$421$	203585.			1.14863			0.574316	−	0.818634i	$-0.305268\pi$
$421$	203585.			1.14863			0.574316	+	0.818634i	$0.305268\pi$
$422$			227264.i			1.27616i
$423$	−60079.6			−0.335773
$424$	208506.			1.15981
$425$	−116004.			−0.642239
$426$	−183349.			−1.01032
$427$	100879.			0.553278
$428$	349075.			1.90560
$429$			4791.73i			0.0260362i
$430$			304377.i			1.64617i
$431$	−227353.			−1.22390			−0.611949	−	0.790897i	$-0.709614\pi$
$431$	−227353.			−1.22390			−0.611949	+	0.790897i	$0.709614\pi$
$432$			102189.i			0.547565i
$433$		−	140437.i		−	0.749042i	−0.927218	−	0.374521i	$-0.877807\pi$
$433$		−	140437.i		−	0.749042i	0.927218	−	0.374521i	$-0.122193\pi$
$434$			159435.i			0.846455i
$435$	−4251.54			−0.0224682
$436$		−	766825.i		−	4.03388i
$437$	−193664.			−1.01411
$438$	27228.6			0.141931
$439$	100763.			0.522846			0.261423	−	0.965224i	$-0.415808\pi$
$439$	100763.			0.522846			0.261423	+	0.965224i	$0.415808\pi$
$440$			125602.i			0.648773i
$441$	24914.4			0.128107
$442$	26092.1			0.133556
$443$			200373.i			1.02102i	0.859873	+	0.510508i	$0.170543\pi$
$443$			200373.i			1.02102i	−0.859873	+	0.510508i	$0.829457\pi$
$444$			320575.i			1.62616i
$445$		−	2154.43i		−	0.0108796i
$446$			489014.i			2.45840i
$447$			185883.i			0.930306i
$448$		−	427777.i		−	2.13138i
$449$	331295.			1.64332			0.821660	−	0.569978i	$-0.193048\pi$
$449$	331295.			1.64332			0.821660	+	0.569978i	$0.193048\pi$
$450$			101474.i			0.501104i
$451$	158340.			0.778461
$452$		−	149255.i		−	0.730552i
$453$		−	184801.i		−	0.900551i
$454$		−	100659.i		−	0.488361i
$455$			9643.88i			0.0465832i
$456$	596623.			2.86926
$457$	−73776.6			−0.353253			−0.176627	−	0.984278i	$-0.556519\pi$
$457$	−73776.6			−0.353253			−0.176627	+	0.984278i	$0.556519\pi$
$458$	−76469.3			−0.364549
$459$		−	32515.3i		−	0.154334i
$460$			139085.i			0.657301i
$461$	−253710.			−1.19381			−0.596905	−	0.802312i	$-0.703603\pi$
$461$	−253710.			−1.19381			−0.596905	+	0.802312i	$0.703603\pi$
$462$	−138343.			−0.648144
$463$			219039.i			1.02178i	0.859645	+	0.510892i	$0.170685\pi$
$463$			219039.i			1.02178i	−0.859645	+	0.510892i	$0.829315\pi$
$464$	−53418.7			−0.248117
$465$			21351.2i			0.0987452i
$466$	690057.			3.17770
$467$	271969.			1.24706			0.623528	−	0.781801i	$-0.285699\pi$
$467$	271969.			1.24706			0.623528	+	0.781801i	$0.285699\pi$
$468$		−	16346.5i		−	0.0746334i
$469$	−73419.9	−	248167.i	−0.333786	−	1.12823i
$470$	186401.			0.843827
$471$			144994.i			0.653594i
$472$		−	737685.i		−	3.31121i
$473$	223475.			0.998864
$474$		−	67053.8i		−	0.298447i
$475$	313966.			1.39154
$476$			539522.i			2.38119i
$477$			30754.9i			0.135169i
$478$	−478001.			−2.09205
$479$	265206.			1.15588			0.577938	−	0.816080i	$-0.303857\pi$
$479$	265206.			1.15588			0.577938	+	0.816080i	$0.303857\pi$
$480$		−	147264.i		−	0.639165i
$481$		−	22908.9i		−	0.0990180i
$482$			441891.i			1.90205i
$483$	−92490.2			−0.396462
$484$	−438443.			−1.87164
$485$	40232.3			0.171037
$486$	−28442.4			−0.120419
$487$		−	121656.i		−	0.512950i	−0.966551	−	0.256475i	$-0.917439\pi$
$487$		−	121656.i		−	0.512950i	0.966551	−	0.256475i	$-0.0825611\pi$
$488$	320297.			1.34497
$489$			158066.i			0.661028i
$490$	−77298.7			−0.321944
$491$	17225.3			0.0714502			0.0357251	−	0.999362i	$-0.488626\pi$
$491$	17225.3			0.0714502			0.0357251	+	0.999362i	$0.488626\pi$
$492$	−540160.			−2.23147
$493$	16997.2			0.0699333
$494$	−70618.2			−0.289376
$495$	−18526.5			−0.0756108
$496$			268268.i			1.09045i
$497$			270929.i			1.09684i
$498$	−392981.			−1.58458
$499$		−	98755.1i		−	0.396605i	−0.980141	−	0.198303i	$-0.936457\pi$
$499$		−	98755.1i		−	0.396605i	0.980141	−	0.198303i	$-0.0635429\pi$
$500$		−	507036.i		−	2.02814i
$501$			214846.i			0.855955i
$502$	−671699.			−2.66543
$503$		−	311903.i		−	1.23278i	−0.787443	−	0.616388i	$-0.788595\pi$
$503$		−	311903.i		−	1.23278i	0.787443	−	0.616388i	$-0.211405\pi$
$504$	284935.			1.12172
$505$	−63764.7			−0.250033
$506$	142580.			0.556875
$507$		−	147239.i		−	0.572806i
$508$	−38451.6			−0.149000
$509$	−336269.			−1.29793			−0.648964	−	0.760819i	$-0.724797\pi$
$509$	−336269.			−1.29793			−0.648964	+	0.760819i	$0.724797\pi$
$510$			100881.i			0.387855i
$511$		−	40234.7i		−	0.154085i
$512$			282964.i			1.07942i
$513$			88002.7i			0.334396i
$514$		−	475767.i		−	1.80081i
$515$			43039.4i			0.162275i
$516$	−762361.			−2.86326
$517$		−	136856.i		−	0.512016i
$518$	661405.			2.46495
$519$			33675.2i			0.125019i
$520$			30620.0i			0.113240i
$521$			168314.i			0.620075i	0.950724	+	0.310037i	$0.100342\pi$
$521$			168314.i			0.620075i	−0.950724	+	0.310037i	$0.899658\pi$
$522$		−	14868.1i		−	0.0545652i
$523$	61745.5			0.225737			0.112868	−	0.993610i	$-0.463996\pi$
$523$	61745.5			0.225737			0.112868	+	0.993610i	$0.463996\pi$
$524$	−914641.			−3.33110
$525$	149944.			0.544014
$526$		−	349355.i		−	1.26269i
$527$		−	85359.9i		−	0.307349i
$528$	−232778.			−0.834975
$529$	−184518.			−0.659367
$530$		−	95419.3i		−	0.339691i
$531$	108809.			0.385903
$532$		−	1.46021e6i		−	5.15933i
$533$	38600.9			0.135876
$534$	7534.31			0.0264217
$535$		−	96448.4i		−	0.336967i
$536$	−233113.	−	787948.i	−0.811405	−	2.74263i
$537$	−44949.9			−0.155876
$538$		−	49951.4i		−	0.172577i
$539$			56752.9i			0.195349i
$540$	63201.3			0.216740
$541$		−	245482.i		−	0.838736i	−0.907816	−	0.419368i	$-0.862252\pi$
$541$		−	245482.i		−	0.838736i	0.907816	−	0.419368i	$-0.137748\pi$
$542$	711409.			2.42170
$543$		−	28998.4i		−	0.0983500i
$544$			588746.i			1.98944i
$545$	−211871.			−0.713312
$546$	−33725.8			−0.113130
$547$		−	543462.i		−	1.81633i	−0.418615	−	0.908164i	$-0.637484\pi$
$547$		−	543462.i		−	1.81633i	0.418615	−	0.908164i	$-0.362516\pi$
$548$			466421.i			1.55316i
$549$			47244.2i			0.156749i
$550$	−231149.			−0.764128
$551$	−46003.0			−0.151524
$552$	−293663.			−0.963764
$553$	−99082.9			−0.324002
$554$		−	877044.i		−	2.85760i
$555$	88573.9			0.287554
$556$		−	1.28873e6i		−	4.16881i
$557$	−484104.			−1.56037			−0.780187	−	0.625546i	$-0.784876\pi$
$557$	−484104.			−1.56037			−0.780187	+	0.625546i	$0.784876\pi$
$558$	−74667.7			−0.239808
$559$	54479.8			0.174346
$560$	−468490.			−1.49391
$561$	74067.2			0.235342
$562$	472433.			1.49578
$563$		−	259682.i		−	0.819266i	−0.912250	−	0.409633i	$-0.865657\pi$
$563$		−	259682.i		−	0.819266i	0.912250	−	0.409633i	$-0.134343\pi$
$564$			466871.i			1.46771i
$565$	−41238.6			−0.129184
$566$			829398.i			2.58899i
$567$			42028.3i			0.130730i
$568$			860217.i			2.66631i
$569$	229640.			0.709288			0.354644	−	0.935001i	$-0.384602\pi$
$569$	229640.			0.709288			0.354644	+	0.935001i	$0.384602\pi$
$570$		−	273035.i		−	0.840366i
$571$	425625.			1.30543			0.652717	−	0.757602i	$-0.273629\pi$
$571$	425625.			1.30543			0.652717	+	0.757602i	$0.273629\pi$
$572$	37236.0			0.113808
$573$	−49918.4			−0.152038
$574$			1.11445e6i			3.38249i
$575$	−154537.			−0.467407
$576$	200340.			0.603840
$577$			420185.i			1.26209i	0.775748	+	0.631043i	$0.217373\pi$
$577$			420185.i			1.26209i	−0.775748	+	0.631043i	$0.782627\pi$
$578$			223811.i			0.669924i
$579$		−	273259.i		−	0.815113i
$580$			33038.2i			0.0982110i
$581$			580693.i			1.72026i
$582$			140697.i			0.415374i
$583$	−70057.1			−0.206117
$584$		−	127748.i		−	0.374566i
$585$	−4516.49			−0.0131974
$586$			1.04717e6i			3.04945i
$587$		−	409684.i		−	1.18897i	−0.804105	−	0.594487i	$-0.797355\pi$
$587$		−	409684.i		−	1.18897i	0.804105	−	0.594487i	$-0.202645\pi$
$588$		−	193607.i		−	0.559971i
$589$			231026.i			0.665934i
$590$	−337589.			−0.969806
$591$	131764.			0.377243
$592$	1.11289e6			3.17548
$593$		−	358737.i		−	1.02016i	−0.860128	−	0.510078i	$-0.829617\pi$
$593$		−	358737.i		−	1.02016i	0.860128	−	0.510078i	$-0.170383\pi$
$594$		−	64789.6i		−	0.183625i
$595$	149068.			0.421067
$596$	1.44448e6			4.06648
$597$			88070.5i			0.247105i
$598$	34758.9			0.0971993
$599$		−	549094.i		−	1.53036i	−0.643818	−	0.765179i	$-0.722651\pi$
$599$		−	549094.i		−	1.53036i	0.643818	−	0.765179i	$-0.277349\pi$
$600$	476082.			1.32245
$601$	−29996.9			−0.0830475			−0.0415238	−	0.999138i	$-0.513221\pi$
$601$	−29996.9			−0.0830475			−0.0415238	+	0.999138i	$0.513221\pi$
$602$			1.57289e6i			4.34016i
$603$	116223.	−	34384.5i	0.319638	−	0.0945646i
$604$	−1.43607e6			−3.93642
$605$			121141.i			0.330963i
$606$		−	222993.i		−	0.607220i
$607$	−578491.			−1.57007			−0.785035	−	0.619451i	$-0.787355\pi$
$607$	−578491.			−1.57007			−0.785035	+	0.619451i	$0.787355\pi$
$608$		−	1.59344e6i		−	4.31051i
$609$	−21970.1			−0.0592376
$610$		−	146579.i		−	0.393923i
$611$		−	33363.5i		−	0.0893695i
$612$	−252673.			−0.674614
$613$	−476900.			−1.26913			−0.634565	−	0.772869i	$-0.718821\pi$
$613$	−476900.			−1.26913			−0.634565	+	0.772869i	$0.718821\pi$
$614$		−	387409.i		−	1.02762i
$615$			149245.i			0.394592i
$616$			649059.i			1.71050i
$617$	−207971.			−0.546303			−0.273151	−	0.961971i	$-0.588066\pi$
$617$	−207971.			−0.546303			−0.273151	+	0.961971i	$0.588066\pi$
$618$	−150514.			−0.394095
$619$	−121089.			−0.316027			−0.158014	−	0.987437i	$-0.550509\pi$
$619$	−121089.			−0.316027			−0.158014	+	0.987437i	$0.550509\pi$
$620$	165917.			0.431627
$621$		−	43315.7i		−	0.112321i
$622$	−1.34337e6			−3.47227
$623$		−	11133.2i		−	0.0286842i
$624$	−56747.7			−0.145740
$625$	172740.			0.442215
$626$	1.32792e6			3.38861
$627$	−200463.			−0.509916
$628$	1.12673e6			2.85694
$629$	−354109.			−0.895027
$630$		−	130396.i		−	0.328536i
$631$		−	663202.i		−	1.66566i	−0.553527	−	0.832831i	$-0.686718\pi$
$631$		−	663202.i		−	1.66566i	0.553527	−	0.832831i	$-0.313282\pi$
$632$	−314595.			−0.787622
$633$			157273.i			0.392506i
$634$		−	998080.i		−	2.48306i
$635$			10624.1i			0.0263477i
$636$	238992.			0.590840
$637$			13835.5i			0.0340970i
$638$	33868.4			0.0832058
$639$	−126883.			−0.310744
$640$	−168114.			−0.410433
$641$		−	425703.i		−	1.03607i	−0.855358	−	0.518037i	$-0.826663\pi$
$641$		−	425703.i		−	1.03607i	0.855358	−	0.518037i	$-0.173337\pi$
$642$	337292.			0.818344
$643$	−204200.			−0.493893			−0.246946	−	0.969029i	$-0.579427\pi$
$643$	−204200.			−0.493893			−0.246946	+	0.969029i	$0.579427\pi$
$644$			718730.i			1.73298i
$645$			210638.i			0.506311i
$646$			1.09157e6i			2.61568i
$647$			387455.i			0.925576i	0.886469	+	0.462788i	$0.153151\pi$
$647$			387455.i			0.925576i	−0.886469	+	0.462788i	$0.846849\pi$
$648$			133443.i			0.317794i
$649$			247859.i			0.588458i
$650$	−56350.6			−0.133374
$651$			110334.i			0.260343i
$652$	1.22831e6			2.88943
$653$			429994.i			1.00841i	0.863585	+	0.504204i	$0.168214\pi$
$653$			429994.i			1.00841i	−0.863585	+	0.504204i	$0.831786\pi$
$654$		−	740940.i		−	1.73232i
$655$			252713.i			0.589039i
$656$			1.87519e6i			4.35751i
$657$	18843.0			0.0436535
$658$	963241.			2.22476
$659$	−611849.			−1.40888			−0.704439	−	0.709765i	$-0.748801\pi$
$659$	−611849.			−1.40888			−0.704439	+	0.709765i	$0.748801\pi$
$660$			143967.i			0.330504i
$661$			487198.i			1.11507i	0.830153	+	0.557536i	$0.188253\pi$
$661$			487198.i			1.11507i	−0.830153	+	0.557536i	$0.811747\pi$
$662$	−791552.			−1.80619
$663$	18056.5			0.0410777
$664$			1.84374e6i			4.18181i
$665$	−403453.			−0.912325
$666$			309754.i			0.698342i
$667$	22643.0			0.0508959
$668$	1.66954e6			3.74148
$669$			338412.i			0.756125i
$670$	−360592.	+	106681.i	−0.803278	+	0.237649i
$671$	−107618.			−0.239024
$672$		−	760995.i		−	1.68517i
$673$		−	561568.i		−	1.23986i	−0.784657	−	0.619930i	$-0.787161\pi$
$673$		−	561568.i		−	1.23986i	0.784657	−	0.619930i	$-0.212839\pi$
$674$	−850529.			−1.87227
$675$			70222.7i			0.154124i
$676$	−1.14418e6			−2.50380
$677$		−	165348.i		−	0.360763i	−0.983597	−	0.180381i	$-0.942267\pi$
$677$		−	165348.i		−	0.360763i	0.983597	−	0.180381i	$-0.0577332\pi$
$678$		−	144217.i		−	0.313730i
$679$	207903.			0.450943
$680$	473302.			1.02358
$681$		−	69658.9i		−	0.150204i
$682$		−	170087.i		−	0.365681i
$683$			226173.i			0.484840i	0.970171	+	0.242420i	$0.0779412\pi$
$683$			226173.i			0.484840i	−0.970171	+	0.242420i	$0.922059\pi$
$684$	683858.			1.46169
$685$	128871.			0.274646
$686$	639910.			1.35979
$687$	−52919.0			−0.112124
$688$			2.64657e6i			5.59123i
$689$	−17078.9			−0.0359766
$690$			134390.i			0.282273i
$691$	120638.			0.252655			0.126327	−	0.991989i	$-0.459681\pi$
$691$	120638.			0.252655			0.126327	+	0.991989i	$0.459681\pi$
$692$	261686.			0.546473
$693$	−95737.1			−0.199349
$694$	−568488.			−1.18033
$695$	−356072.			−0.737172
$696$	−69756.6			−0.144001
$697$		−	596665.i		−	1.22819i
$698$		−	58410.6i		−	0.119889i
$699$	477540.			0.977362
$700$		−	1.16520e6i		−	2.37795i
$701$			202005.i			0.411080i	0.978649	+	0.205540i	$0.0658950\pi$
$701$			202005.i			0.411080i	−0.978649	+	0.205540i	$0.934105\pi$
$702$		−	15794.7i		−	0.0320507i
$703$	958397.			1.93925
$704$			456357.i			0.920787i
$705$	128995.			0.259534
$706$	1.37911e6			2.76688
$707$	−329508.			−0.659216
$708$		−	845546.i		−	1.68683i
$709$	341403.			0.679164			0.339582	−	0.940576i	$-0.389714\pi$
$709$	341403.			0.679164			0.339582	+	0.940576i	$0.389714\pi$
$710$	393664.			0.780925
$711$		−	46403.2i		−	0.0917928i
$712$		−	35348.6i		−	0.0697288i
$713$		−	113713.i		−	0.223682i
$714$			521310.i			1.02259i
$715$		−	10288.2i		−	0.0201246i
$716$			349300.i			0.681354i
$717$	−330790.			−0.643450
$718$		−	275401.i		−	0.534216i
$719$	31060.3			0.0600826			0.0300413	−	0.999549i	$-0.490436\pi$
$719$	31060.3			0.0600826			0.0300413	+	0.999549i	$0.490436\pi$
$720$		−	219407.i		−	0.423238i
$721$			222409.i			0.427841i
$722$		−	1.97580e6i		−	3.79025i
$723$			305801.i			0.585009i
$724$	−225343.			−0.429900
$725$	−36708.6			−0.0698380
$726$	−423644.			−0.803762
$727$		−	786229.i		−	1.48758i	−0.668413	−	0.743790i	$-0.733026\pi$
$727$		−	786229.i		−	1.48758i	0.668413	−	0.743790i	$-0.266974\pi$
$728$			158231.i			0.298558i
$729$	−19683.0			−0.0370370
$730$	−58461.8			−0.109705
$731$		−	842110.i		−	1.57592i
$732$	367129.			0.685167
$733$			259902.i			0.483728i	0.970310	+	0.241864i	$0.0777588\pi$
$733$			259902.i			0.483728i	−0.970310	+	0.241864i	$0.922241\pi$
$734$	−1.61693e6			−3.00123
$735$	−53492.9			−0.0990197
$736$			784304.i			1.44787i
$737$	78325.1	+	264747.i	0.144200	+	0.487412i
$738$	−521927.			−0.958289
$739$		−	1.00091e6i		−	1.83276i	−0.400306	−	0.916382i	$-0.631096\pi$
$739$		−	1.00091e6i		−	1.83276i	0.400306	−	0.916382i	$-0.368904\pi$
$740$		−	688297.i		−	1.25693i
$741$	−48869.9			−0.0890030
$742$		−	493085.i		−	0.895600i
$743$	−883707.			−1.60078			−0.800388	−	0.599482i	$-0.795373\pi$
$743$	−883707.			−1.60078			−0.800388	+	0.599482i	$0.795373\pi$
$744$			350317.i			0.632871i
$745$		−	399105.i		−	0.719076i
$746$	474612.			0.852827
$747$	−271954.			−0.487366
$748$		−	575567.i		−	1.02871i
$749$		−	498404.i		−	0.888418i
$750$		−	489921.i		−	0.870970i
$751$	346086.			0.613626			0.306813	−	0.951770i	$-0.400737\pi$
$751$	346086.			0.613626			0.306813	+	0.951770i	$0.400737\pi$
$752$	1.62077e6			2.86606
$753$	−464835.			−0.819802
$754$	8256.62			0.0145231
$755$			396782.i			0.696077i
$756$	326597.			0.571437
$757$			227362.i			0.396759i	0.980125	+	0.198380i	$0.0635679\pi$
$757$			227362.i			0.396759i	−0.980125	+	0.198380i	$0.936432\pi$
$758$	129529.			0.225439
$759$	98669.5			0.171277
$760$	−1.28099e6			−2.21778
$761$	366600.			0.633027			0.316514	−	0.948588i	$-0.397488\pi$
$761$	366600.			0.633027			0.316514	+	0.948588i	$0.397488\pi$
$762$	−37153.6			−0.0639870
$763$	−1.09486e6			−1.88066
$764$			387910.i			0.664575i
$765$			69812.7i			0.119292i
$766$	256958.			0.437929
$767$			60424.4i			0.102712i
$768$			28972.0i			0.0491198i
$769$		−	282891.i		−	0.478373i	−0.970974	−	0.239187i	$-0.923119\pi$
$769$		−	282891.i		−	0.478373i	0.970974	−	0.239187i	$-0.0768808\pi$
$770$	297031.			0.500980
$771$		−	329245.i		−	0.553872i
$772$	−2.12347e6			−3.56296
$773$	497931.			0.833317			0.416658	−	0.909063i	$-0.363201\pi$
$773$	497931.			0.833317			0.416658	+	0.909063i	$0.363201\pi$
$774$	−736627.			−1.22961
$775$			184350.i			0.306931i
$776$	660107.			1.09620
$777$	457711.			0.758140
$778$			933307.i			1.54193i
$779$			1.61487e6i			2.66111i
$780$			35097.1i			0.0576876i
$781$		−	289029.i		−	0.473849i
$782$		−	537278.i		−	0.878588i
$783$		−	10289.2i		−	0.0167825i
$784$	−672115.			−1.09348
$785$		−	311313.i		−	0.505193i
$786$	−883767.			−1.43052
$787$		−	566094.i		−	0.913985i	−0.889471	−	0.456992i	$-0.848927\pi$
$787$		−	566094.i		−	0.913985i	0.889471	−	0.456992i	$-0.151073\pi$
$788$		−	1.02392e6i		−	1.64897i
$789$		−	241764.i		−	0.388363i
$790$			143969.i			0.230683i
$791$	−213103.			−0.340594
$792$	−303972.			−0.484600
$793$	−26235.8			−0.0417203
$794$		−	500568.i		−	0.794003i
$795$		−	66032.9i		−	0.104478i
$796$	684385.			1.08013
$797$	842210.			1.32588			0.662939	−	0.748673i	$-0.269309\pi$
$797$	842210.			1.32588			0.662939	+	0.748673i	$0.269309\pi$
$798$		−	1.41093e6i		−	2.21563i
$799$	−515710.			−0.807814
$800$		−	1.27150e6i		−	1.98672i
$801$	5213.96			0.00812649
$802$	−1.98913e6			−3.09254
$803$			42922.8i			0.0665667i
$804$	−267198.	−	903158.i	−0.413353	−	1.39718i
$805$	198583.			0.306443
$806$		−	41464.6i		−	0.0638275i
$807$		−	34567.8i		−	0.0530792i
$808$	−1.04621e6			−1.60250
$809$			640563.i			0.978734i	0.872078	+	0.489367i	$0.162772\pi$
$809$			640563.i			0.978734i	−0.872078	+	0.489367i	$0.837228\pi$
$810$	61068.0			0.0930772
$811$			996462.i			1.51502i	0.652822	+	0.757511i	$0.273585\pi$
$811$			996462.i			1.51502i	−0.652822	+	0.757511i	$0.726415\pi$
$812$			170727.i			0.258935i
$813$	492316.			0.744840
$814$	−705594.			−1.06489
$815$		−	339378.i		−	0.510939i
$816$			877166.i			1.31735i
$817$			2.27917e6i			3.41454i
$818$	2.38135e6			3.55891
$819$	−23339.3			−0.0347952
$820$	1.15976e6			1.72481
$821$	−1.19101e6			−1.76696			−0.883482	−	0.468465i	$-0.844807\pi$
$821$	−1.19101e6			−1.76696			−0.883482	+	0.468465i	$0.844807\pi$
$822$			450677.i			0.666994i
$823$	545714.			0.805685			0.402842	−	0.915269i	$-0.368022\pi$
$823$	545714.			0.805685			0.402842	+	0.915269i	$0.368022\pi$
$824$			706164.i			1.04004i
$825$	−159962.			−0.235022
$826$	−1.74452e6			−2.55691
$827$	450314.			0.658422			0.329211	−	0.944256i	$-0.393217\pi$
$827$	450314.			0.658422			0.329211	+	0.944256i	$0.393217\pi$
$828$	−336601.			−0.490969
$829$	641264.			0.933099			0.466550	−	0.884495i	$-0.345497\pi$
$829$	641264.			0.933099			0.466550	+	0.884495i	$0.345497\pi$
$830$	843759.			1.22479
$831$		−	606940.i		−	0.878908i
$832$			111253.i			0.160718i
$833$	213859.			0.308204
$834$		−	1.24523e6i		−	1.79026i
$835$		−	461289.i		−	0.661607i
$836$			1.55777e6i			2.22891i
$837$	−51672.2			−0.0737575
$838$		−	2.32744e6i		−	3.31429i
$839$	−79910.1			−0.113521			−0.0567607	−	0.998388i	$-0.518077\pi$
$839$	−79910.1			−0.113521			−0.0567607	+	0.998388i	$0.518077\pi$
$840$	−611776.			−0.867030
$841$	−701902.			−0.992395
$842$		−	1.52863e6i		−	2.15615i
$843$	326937.			0.460055
$844$	1.22215e6			1.71569
$845$			316133.i			0.442748i
$846$			451112.i			0.630294i
$847$			626002.i			0.872587i
$848$		−	829674.i		−	1.15376i
$849$			573968.i			0.796291i
$850$			871027.i			1.20557i
$851$	−471731.			−0.651381
$852$			985994.i			1.35830i
$853$	−709915.			−0.975682			−0.487841	−	0.872932i	$-0.662215\pi$
$853$	−709915.			−0.975682			−0.487841	+	0.872932i	$0.662215\pi$
$854$		−	757454.i		−	1.03858i
$855$		−	188948.i		−	0.258470i
$856$		−	1.58247e6i		−	2.15967i
$857$			1.10812e6i			1.50877i	0.656430	+	0.754387i	$0.272066\pi$
$857$			1.10812e6i			1.50877i	−0.656430	+	0.754387i	$0.727934\pi$
$858$	35979.1			0.0488737
$859$	901393.			1.22160			0.610798	−	0.791786i	$-0.290849\pi$
$859$	901393.			1.22160			0.610798	+	0.791786i	$0.290849\pi$
$860$	1.63684e6			2.21315
$861$			771231.i			1.04035i
$862$			1.70709e6i			2.29743i
$863$	−757815.			−1.01752			−0.508758	−	0.860910i	$-0.669895\pi$
$863$	−757815.			−1.01752			−0.508758	+	0.860910i	$0.669895\pi$
$864$	356395.			0.477423
$865$		−	72303.2i		−	0.0966329i
$866$	−1.05448e6			−1.40606
$867$			154884.i			0.206048i
$868$	857389.			1.13799
$869$	105703.			0.139974
$870$			31923.0i			0.0421760i
$871$	19094.5	+	64541.4i	0.0251694	+	0.0850751i
$872$	−3.47625e6			−4.57171
$873$			97366.6i			0.127756i
$874$			1.45414e6i			1.90364i
$875$	−723937.			−0.945551
$876$		−	146427.i		−	0.190815i
$877$	−657571.			−0.854955			−0.427478	−	0.904026i	$-0.640598\pi$
$877$	−657571.			−0.854955			−0.427478	+	0.904026i	$0.640598\pi$
$878$		−	756589.i		−	0.981457i
$879$			724671.i			0.937914i
$880$	499790.			0.645390
$881$	−568325.			−0.732226			−0.366113	−	0.930570i	$-0.619312\pi$
$881$	−568325.			−0.732226			−0.366113	+	0.930570i	$0.619312\pi$
$882$		−	187071.i		−	0.240475i
$883$		−	71147.1i		−	0.0912506i	−0.998959	−	0.0456253i	$-0.985472\pi$
$883$		−	71147.1i		−	0.0912506i	0.998959	−	0.0456253i	$-0.0145280\pi$
$884$		−	140315.i		−	0.179556i
$885$	−233622.			−0.298282
$886$	1.50452e6			1.91659
$887$	785316.			0.998154			0.499077	−	0.866558i	$-0.333673\pi$
$887$	785316.			0.998154			0.499077	+	0.866558i	$0.333673\pi$
$888$	1.45327e6			1.84297
$889$			54900.5i			0.0694661i
$890$	−16176.7			−0.0204226
$891$		−	44836.3i		−	0.0564773i
$892$	2.62976e6			3.30512
$893$	1.39577e6			1.75029
$894$	1.39572e6			1.74632
$895$	96510.6			0.120484
$896$	−868738.			−1.08211
$897$	24054.2			0.0298955
$898$		−	2.48755e6i		−	3.08475i
$899$		−	27011.4i		−	0.0334216i
$900$	545692.			0.673694
$901$			263993.i			0.325194i
$902$		−	1.18891e6i		−	1.46128i
$903$			1.08849e6i			1.33490i
$904$	−676618.			−0.827955
$905$			62261.7i			0.0760193i
$906$	−1.38759e6			−1.69046
$907$	558772.			0.679235			0.339618	−	0.940564i	$-0.389702\pi$
$907$	558772.			0.679235			0.339618	+	0.940564i	$0.389702\pi$
$908$	−541311.			−0.656562
$909$		−	154318.i		−	0.186762i
$910$	72411.8			0.0874433
$911$	−171153.			−0.206229			−0.103114	−	0.994670i	$-0.532881\pi$
$911$	−171153.			−0.206229			−0.103114	+	0.994670i	$0.532881\pi$
$912$		−	2.37405e6i		−	2.85430i
$913$		−	619490.i		−	0.743178i
$914$			553957.i			0.663107i
$915$		−	101437.i		−	0.121158i
$916$			411227.i			0.490107i
$917$			1.30591e6i			1.55301i
$918$	−244144.			−0.289708
$919$		−	1.29218e6i		−	1.53000i	−0.644030	−	0.765000i	$-0.722739\pi$
$919$		−	1.29218e6i		−	1.53000i	0.644030	−	0.765000i	$-0.277261\pi$
$920$	630515.			0.744937
$921$		−	268098.i		−	0.316064i
$922$			1.90500e6i			2.24095i
$923$		−	70461.1i		−	0.0827077i
$924$			743961.i			0.871378i
$925$	764764.			0.893807
$926$	1.64467e6			1.91804
$927$	−104160.			−0.121211
$928$			186304.i			0.216334i
$929$			266209.i			0.308454i	0.988035	+	0.154227i	$0.0492887\pi$
$929$			266209.i			0.308454i	−0.988035	+	0.154227i	$0.950711\pi$
$930$	160317.			0.185359
$931$	−578810.			−0.667785
$932$		−	3.71091e6i		−	4.27217i
$933$	−929648.			−1.06796
$934$		−	2.04210e6i		−	2.34090i
$935$	−159028.			−0.181907
$936$	−74103.8			−0.0845841
$937$		−	489987.i		−	0.558091i	−0.960278	−	0.279046i	$-0.909982\pi$
$937$		−	489987.i		−	0.558091i	0.960278	−	0.279046i	$-0.0900180\pi$
$938$	−1.86338e6	+	551279.i	−2.11785	+	0.626564i
$939$	918957.			1.04223
$940$		−	1.00241e6i		−	1.13446i
$941$			845521.i			0.954872i	0.878667	+	0.477436i	$0.158434\pi$
$941$			845521.i			0.954872i	−0.878667	+	0.477436i	$0.841566\pi$
$942$	1.08870e6			1.22689
$943$		−	794854.i		−	0.893849i
$944$	−2.93535e6			−3.29395
$945$		−	90237.8i		−	0.101047i
$946$		−	1.67798e6i		−	1.87501i
$947$	−174479.			−0.194556			−0.0972778	−	0.995257i	$-0.531014\pi$
$947$	−174479.			−0.194556			−0.0972778	+	0.995257i	$0.531014\pi$
$948$	−360594.			−0.401237
$949$			10463.9i			0.0116188i
$950$		−	2.35743e6i		−	2.61212i
$951$		−	690701.i		−	0.763711i
$952$	2.44582e6			2.69867
$953$	1.01732e6			1.12013			0.560067	−	0.828447i	$-0.310775\pi$
$953$	1.01732e6			1.12013			0.560067	+	0.828447i	$0.310775\pi$
$954$	230925.			0.253732
$955$	107178.			0.117517
$956$			2.57053e6i			2.81260i
$957$	23437.9			0.0255915
$958$		−	1.99132e6i		−	2.16975i
$959$	665949.			0.724108
$960$	−430143.			−0.466735
$961$	787870.			0.853115
$962$	−172013.			−0.185871
$963$	233416.			0.251697
$964$	2.37635e6			2.55715
$965$			586707.i			0.630038i
$966$			694469.i			0.744216i
$967$	1.01234e6			1.08261			0.541305	−	0.840827i	$-0.317931\pi$
$967$	1.01234e6			1.08261			0.541305	+	0.840827i	$0.317931\pi$
$968$			1.98760e6i			2.12118i
$969$			755395.i			0.804501i
$970$		−	302087.i		−	0.321062i
$971$	825377.			0.875415			0.437707	−	0.899117i	$-0.355791\pi$
$971$	825377.			0.875415			0.437707	+	0.899117i	$0.355791\pi$
$972$			152954.i			0.161893i
$973$	−1.84003e6			−1.94356
$974$	−913462.			−0.962881
$975$	−38996.3			−0.0410217
$976$		−	1.27451e6i		−	1.33796i
$977$	276465.			0.289635			0.144818	−	0.989458i	$-0.453740\pi$
$977$	276465.			0.289635			0.144818	+	0.989458i	$0.453740\pi$
$978$	1.18685e6			1.24084
$979$			11877.0i			0.0123920i
$980$			415687.i			0.432827i
$981$		−	512752.i		−	0.532807i
$982$		−	129337.i		−	0.134122i
$983$			1.17938e6i			1.22052i	0.792201	+	0.610261i	$0.208935\pi$
$983$			1.17938e6i			1.22052i	−0.792201	+	0.610261i	$0.791065\pi$
$984$			2.44871e6i			2.52899i
$985$	−282906.			−0.291588
$986$		−	127625.i		−	0.131275i
$987$	666591.			0.684266
$988$			379762.i			0.389043i
$989$		−	1.12183e6i		−	1.14692i
$990$			139108.i			0.141932i
$991$			367542.i			0.374249i	0.982336	+	0.187124i	$0.0599167\pi$
$991$			367542.i			0.374249i	−0.982336	+	0.187124i	$0.940083\pi$
$992$	935614.			0.950766
$993$	−547777.			−0.555527
$994$	2.03429e6			2.05892
$995$		−	189094.i		−	0.190999i
$996$			2.11333e6i			2.13033i
$997$	−916832.			−0.922358			−0.461179	−	0.887307i	$-0.652573\pi$
$997$	−916832.			−0.922358			−0.461179	+	0.887307i	$0.652573\pi$
$998$	−741510.			−0.744485
$999$			214359.i			0.214788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.5.b.a.133.4	✓	46
67.66	odd	2	inner	201.5.b.a.133.43	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.5.b.a.133.4	✓	46	1.1	even	1	trivial
201.5.b.a.133.43	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)

\(f(q)\)	\(=\)	\(q-7.50857i q^{2} -5.19615i q^{3} -40.3787 q^{4} +11.1565i q^{5} -39.0157 q^{6} +57.6520i q^{7} +183.049i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q-7.50857i q^{2} -5.19615i q^{3} -40.3787 q^{4} +11.1565i q^{5} -39.0157 q^{6} +57.6520i q^{7} +183.049i q^{8} -27.0000 q^{9} +83.7695 q^{10} -61.5038i q^{11} +209.814i q^{12} -14.9937i q^{13} +432.884 q^{14} +57.9709 q^{15} +728.379 q^{16} -231.762 q^{17} +202.731i q^{18} +627.264 q^{19} -450.485i q^{20} +299.569 q^{21} -461.806 q^{22} -308.744 q^{23} +951.151 q^{24} +500.532 q^{25} -112.581 q^{26} +140.296i q^{27} -2327.91i q^{28} -73.3391 q^{29} -435.279i q^{30} +368.308i q^{31} -2540.30i q^{32} -319.583 q^{33} +1740.20i q^{34} -643.195 q^{35} +1090.22 q^{36} +1527.90 q^{37} -4709.86i q^{38} -77.9096 q^{39} -2042.19 q^{40} +2574.47i q^{41} -2249.33i q^{42} +3633.51i q^{43} +2483.44i q^{44} -301.226i q^{45} +2318.23i q^{46} +2225.17 q^{47} -3784.77i q^{48} -922.754 q^{49} -3758.28i q^{50} +1204.27i q^{51} +605.426i q^{52} -1139.07i q^{53} +1053.42 q^{54} +686.168 q^{55} -10553.2 q^{56} -3259.36i q^{57} +550.672i q^{58} -4029.98 q^{59} -2340.79 q^{60} -1749.78i q^{61} +2765.47 q^{62} -1556.60i q^{63} -7419.98 q^{64} +167.277 q^{65} +2399.61i q^{66} +(-4304.57 + 1273.50i) q^{67} +9358.24 q^{68} +1604.28i q^{69} +4829.48i q^{70} +4699.38 q^{71} -4942.33i q^{72} -697.889 q^{73} -11472.4i q^{74} -2600.84i q^{75} -25328.1 q^{76} +3545.82 q^{77} +584.990i q^{78} +1718.64i q^{79} +8126.17i q^{80} +729.000 q^{81} +19330.6 q^{82} +10072.4 q^{83} -12096.2 q^{84} -2585.66i q^{85} +27282.5 q^{86} +381.081i q^{87} +11258.2 q^{88} -193.110 q^{89} -2261.78 q^{90} +864.417 q^{91} +12466.7 q^{92} +1913.79 q^{93} -16707.8i q^{94} +6998.08i q^{95} -13199.8 q^{96} -3606.17i q^{97} +6928.57i q^{98} +1660.60i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 396 q^{4} - 1242 q^{9}+O(q^{10}) \) 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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