LMFDB - Embedded newform 33.7.b.a.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(23,33)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.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:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 1026 x^{18} + 441321 x^{16} + 103808124 x^{14} + 14594358456 x^{12} + 1256133373152 x^{10} + \cdots + 32\!\cdots\!64 $ x^20 + 1026x^18 + 441321x^16 + 103808124x^14 + 14594358456x^12 + 1256133373152x^10 + 64843235559312x^8 + 1864534894961472x^6 + 25120735435348224x^4 + 103653954147713024*x^2 + 32367107232497664
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{17}\cdot 11^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.5
Root			$-9.36068i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.36068i q^{2} +(26.7168 + 3.90029i) q^{3} -23.6224 q^{4} -36.7722i q^{5} +(36.5094 - 250.088i) q^{6} +305.058 q^{7} -377.962i q^{8} +(698.575 + 208.407i) q^{9} +O(q^{10})$	\(q-9.36068i q^{2} +(26.7168 + 3.90029i) q^{3} -23.6224 q^{4} -36.7722i q^{5} +(36.5094 - 250.088i) q^{6} +305.058 q^{7} -377.962i q^{8} +(698.575 + 208.407i) q^{9} -344.213 q^{10} -401.312i q^{11} +(-631.115 - 92.1342i) q^{12} -1885.23 q^{13} -2855.55i q^{14} +(143.422 - 982.437i) q^{15} -5049.82 q^{16} -2577.08i q^{17} +(1950.83 - 6539.14i) q^{18} -2652.80 q^{19} +868.648i q^{20} +(8150.17 + 1189.82i) q^{21} -3756.55 q^{22} +17760.0i q^{23} +(1474.16 - 10097.9i) q^{24} +14272.8 q^{25} +17647.0i q^{26} +(17850.9 + 8292.61i) q^{27} -7206.20 q^{28} +12903.9i q^{29} +(-9196.28 - 1342.53i) q^{30} +24344.0 q^{31} +23080.2i q^{32} +(1565.23 - 10721.8i) q^{33} -24123.3 q^{34} -11217.7i q^{35} +(-16502.0 - 4923.06i) q^{36} -48101.2 q^{37} +24832.0i q^{38} +(-50367.3 - 7352.95i) q^{39} -13898.5 q^{40} +46161.2i q^{41} +(11137.5 - 76291.2i) q^{42} +63933.0 q^{43} +9479.94i q^{44} +(7663.58 - 25688.2i) q^{45} +166246. q^{46} +152492. i q^{47} +(-134915. - 19695.8i) q^{48} -24588.7 q^{49} -133603. i q^{50} +(10051.4 - 68851.5i) q^{51} +44533.7 q^{52} -206148. i q^{53} +(77624.5 - 167096. i) q^{54} -14757.1 q^{55} -115300. i q^{56} +(-70874.3 - 10346.7i) q^{57} +120790. q^{58} +331908. i q^{59} +(-3387.98 + 23207.5i) q^{60} -69809.8 q^{61} -227877. i q^{62} +(213106. + 63576.1i) q^{63} -107142. q^{64} +69324.1i q^{65} +(-100363. - 14651.6i) q^{66} -488926. q^{67} +60876.9i q^{68} +(-69269.3 + 474491. i) q^{69} -105005. q^{70} +338285. i q^{71} +(78769.8 - 264035. i) q^{72} -50624.3 q^{73} +450260. i q^{74} +(381324. + 55668.1i) q^{75} +62665.4 q^{76} -122423. i q^{77} +(-68828.6 + 471473. i) q^{78} +121132. q^{79} +185693. i q^{80} +(444574. + 291176. i) q^{81} +432100. q^{82} -1.02009e6i q^{83} +(-192527. - 28106.3i) q^{84} -94765.2 q^{85} -598457. i q^{86} +(-50329.1 + 344752. i) q^{87} -151681. q^{88} -71967.7i q^{89} +(-240459. - 71736.3i) q^{90} -575105. q^{91} -419534. i q^{92} +(650395. + 94948.8i) q^{93} +1.42743e6 q^{94} +97549.3i q^{95} +(-90019.4 + 616628. i) q^{96} -693911. q^{97} +230167. i q^{98} +(83636.0 - 280346. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	9.36068i		−	1.17009i	−0.811002	−	0.585043i	$-0.801078\pi$
$2$		−	9.36068i		−	1.17009i	0.811002	−	0.585043i	$-0.198922\pi$
$3$	26.7168	+	3.90029i	0.989511	+	0.144455i
$3$	26.7168	+	3.90029i	0.989511	+	0.144455i
$4$	−23.6224			−0.369100
$5$		−	36.7722i		−	0.294178i	−0.989123	−	0.147089i	$-0.953010\pi$
$5$		−	36.7722i		−	0.294178i	0.989123	−	0.147089i	$-0.0469904\pi$
$6$	36.5094	−	250.088i	0.169025	−	1.15781i
$7$	305.058			0.889382			0.444691	−	0.895684i	$-0.353314\pi$
$7$	305.058			0.889382			0.444691	+	0.895684i	$0.353314\pi$
$8$		−	377.962i		−	0.738207i
$9$	698.575	+	208.407i	0.958265	+	0.285880i
$10$	−344.213			−0.344213
$11$		−	401.312i		−	0.301511i
$11$		−	401.312i		−	0.301511i
$12$	−631.115	−	92.1342i	−0.365229	−	0.0533184i
$13$	−1885.23			−0.858093			−0.429047	−	0.903282i	$-0.641150\pi$
$13$	−1885.23			−0.858093			−0.429047	+	0.903282i	$0.641150\pi$
$14$		−	2855.55i		−	1.04065i
$15$	143.422	−	982.437i	0.0424955	−	0.291092i
$16$	−5049.82			−1.23287
$17$		−	2577.08i		−	0.524544i	−0.964994	−	0.262272i	$-0.915528\pi$
$17$		−	2577.08i		−	0.524544i	0.964994	−	0.262272i	$-0.0844718\pi$
$18$	1950.83	−	6539.14i	0.334504	−	1.12125i
$19$	−2652.80			−0.386761			−0.193381	−	0.981124i	$-0.561945\pi$
$19$	−2652.80			−0.386761			−0.193381	+	0.981124i	$0.561945\pi$
$20$			868.648i			0.108581i
$21$	8150.17	+	1189.82i	0.880053	+	0.128476i
$22$	−3756.55			−0.352794
$23$			17760.0i			1.45969i	0.683614	+	0.729844i	$0.260407\pi$
$23$			17760.0i			1.45969i	−0.683614	+	0.729844i	$0.739593\pi$
$24$	1474.16	−	10097.9i	0.106638	−	0.730464i
$25$	14272.8			0.913459
$26$			17647.0i			1.00404i
$27$	17850.9	+	8292.61i	0.906918	+	0.421308i
$28$	−7206.20			−0.328271
$29$			12903.9i			0.529089i	0.964374	+	0.264544i	$0.0852215\pi$
$29$			12903.9i			0.529089i	−0.964374	+	0.264544i	$0.914778\pi$
$30$	−9196.28	−	1342.53i	−0.340603	−	0.0497234i
$31$	24344.0			0.817160			0.408580	−	0.912722i	$-0.366024\pi$
$31$	24344.0			0.817160			0.408580	+	0.912722i	$0.366024\pi$
$32$			23080.2i			0.704351i
$33$	1565.23	−	10721.8i	0.0435549	−	0.298349i
$34$	−24123.3			−0.613761
$35$		−	11217.7i		−	0.261636i
$36$	−16502.0	−	4923.06i	−0.353696	−	0.105518i
$37$	−48101.2			−0.949622			−0.474811	−	0.880088i	$-0.657484\pi$
$37$	−48101.2			−0.949622			−0.474811	+	0.880088i	$0.657484\pi$
$38$			24832.0i			0.452544i
$39$	−50367.3	−	7352.95i	−0.849093	−	0.123956i
$40$	−13898.5			−0.217164
$41$			46161.2i			0.669770i	0.942259	+	0.334885i	$0.108697\pi$
$41$			46161.2i			0.669770i	−0.942259	+	0.334885i	$0.891303\pi$
$42$	11137.5	−	76291.2i	0.150328	−	1.02974i
$43$	63933.0			0.804118			0.402059	−	0.915614i	$-0.368295\pi$
$43$	63933.0			0.804118			0.402059	+	0.915614i	$0.368295\pi$
$44$			9479.94i			0.111288i
$45$	7663.58	−	25688.2i	0.0840996	−	0.281900i
$46$	166246.			1.70796
$47$			152492.i			1.46877i	0.678732	+	0.734386i	$0.262530\pi$
$47$			152492.i			1.46877i	−0.678732	+	0.734386i	$0.737470\pi$
$48$	−134915.	−	19695.8i	−1.21993	−	0.178094i
$49$	−24588.7			−0.209000
$50$		−	133603.i		−	1.06883i
$51$	10051.4	−	68851.5i	0.0757731	−	0.519042i
$52$	44533.7			0.316722
$53$		−	206148.i		−	1.38469i	−0.721568	−	0.692343i	$-0.756578\pi$
$53$		−	206148.i		−	1.38469i	0.721568	−	0.692343i	$-0.243422\pi$
$54$	77624.5	−	167096.i	0.492967	−	1.06117i
$55$	−14757.1			−0.0886980
$56$		−	115300.i		−	0.656548i
$57$	−70874.3	−	10346.7i	−0.382705	−	0.0558697i
$58$	120790.			0.619079
$59$			331908.i			1.61608i	0.589129	+	0.808039i	$0.299471\pi$
$59$			331908.i			1.61608i	−0.589129	+	0.808039i	$0.700529\pi$
$60$	−3387.98	+	23207.5i	−0.0156851	+	0.107442i
$61$	−69809.8			−0.307558			−0.153779	−	0.988105i	$-0.549144\pi$
$61$	−69809.8			−0.307558			−0.153779	+	0.988105i	$0.549144\pi$
$62$		−	227877.i		−	0.956147i
$63$	213106.	+	63576.1i	0.852264	+	0.254257i
$64$	−107142.			−0.408715
$65$			69324.1i			0.252432i
$66$	−100363.	−	14651.6i	−0.349094	−	0.0509630i
$67$	−488926.			−1.62562			−0.812810	−	0.582529i	$-0.802063\pi$
$67$	−488926.			−1.62562			−0.812810	+	0.582529i	$0.802063\pi$
$68$			60876.9i			0.193609i
$69$	−69269.3	+	474491.i	−0.210860	+	1.44438i
$70$	−105005.			−0.306137
$71$			338285.i			0.945166i	0.881286	+	0.472583i	$0.156678\pi$
$71$			338285.i			0.945166i	−0.881286	+	0.472583i	$0.843322\pi$
$72$	78769.8	−	264035.i	0.211039	−	0.707398i
$73$	−50624.3			−0.130134			−0.0650670	−	0.997881i	$-0.520726\pi$
$73$	−50624.3			−0.130134			−0.0650670	+	0.997881i	$0.520726\pi$
$74$			450260.i			1.11114i
$75$	381324.	+	55668.1i	0.903878	+	0.131954i
$76$	62665.4			0.142754
$77$		−	122423.i		−	0.268159i
$78$	−68828.6	+	471473.i	−0.145039	+	0.993511i
$79$	121132.			0.245684			0.122842	−	0.992426i	$-0.460799\pi$
$79$	121132.			0.245684			0.122842	+	0.992426i	$0.460799\pi$
$80$			185693.i			0.362682i
$81$	444574.	+	291176.i	0.836545	+	0.547898i
$82$	432100.			0.783688
$83$		−	1.02009e6i		−	1.78405i	−0.451991	−	0.892023i	$-0.649286\pi$
$83$		−	1.02009e6i		−	1.78405i	0.451991	−	0.892023i	$-0.350714\pi$
$84$	−192527.	−	28106.3i	−0.324828	−	0.0474204i
$85$	−94765.2			−0.154309
$86$		−	598457.i		−	0.940887i
$87$	−50329.1	+	344752.i	−0.0764296	+	0.523539i
$88$	−151681.			−0.222578
$89$		−	71967.7i		−	0.102086i	−0.998696	−	0.0510431i	$-0.983745\pi$
$89$		−	71967.7i		−	0.102086i	0.998696	−	0.0510431i	$-0.0162546\pi$
$90$	−240459.	−	71736.3i	−0.329848	−	0.0984038i
$91$	−575105.			−0.763172
$92$		−	419534.i		−	0.538771i
$93$	650395.	+	94948.8i	0.808589	+	0.118043i
$94$	1.42743e6			1.71859
$95$			97549.3i			0.113777i
$96$	−90019.4	+	616628.i	−0.101747	+	0.696963i
$97$	−693911.			−0.760306			−0.380153	−	0.924924i	$-0.624129\pi$
$97$	−693911.			−0.760306			−0.380153	+	0.924924i	$0.624129\pi$
$98$			230167.i			0.244548i
$99$	83636.0	−	280346.i	0.0861961	−	0.288928i
$100$	−337158.			−0.337158
$101$		−	1.41503e6i		−	1.37341i	−0.726935	−	0.686706i	$-0.759056\pi$
$101$		−	1.41503e6i		−	1.37341i	0.726935	−	0.686706i	$-0.240944\pi$
$102$	−644497.	−	94087.8i	−0.607324	−	0.0886611i
$103$	798529.			0.730767			0.365383	−	0.930857i	$-0.380938\pi$
$103$	798529.			0.730767			0.365383	+	0.930857i	$0.380938\pi$
$104$			712546.i			0.633450i
$105$	43752.2	−	299700.i	0.0377948	−	0.258892i
$106$	−1.92969e6			−1.62020
$107$		−	1.53532e6i		−	1.25327i	−0.779311	−	0.626637i	$-0.784431\pi$
$107$		−	1.53532e6i		−	1.25327i	0.779311	−	0.626637i	$-0.215569\pi$
$108$	−421680.	−	195891.i	−0.334743	−	0.155505i
$109$	1.14124e6			0.881249			0.440624	−	0.897692i	$-0.354757\pi$
$109$	1.14124e6			0.881249			0.440624	+	0.897692i	$0.354757\pi$
$110$			138137.i			0.103784i
$111$	−1.28511e6	−	187609.i	−0.939661	−	0.137178i
$112$	−1.54049e6			−1.09649
$113$			434523.i			0.301146i	0.988599	+	0.150573i	$0.0481119\pi$
$113$			434523.i			0.301146i	−0.988599	+	0.150573i	$0.951888\pi$
$114$	−96852.0	+	663431.i	−0.0653724	+	0.447797i
$115$	653076.			0.429408
$116$		−	304822.i		−	0.195287i
$117$	−1.31698e6	−	392895.i	−0.822281	−	0.245312i
$118$	3.10689e6			1.89095
$119$		−	786160.i		−	0.466520i
$120$	−371324.	−	54208.2i	−0.214886	−	0.0313705i
$121$	−161051.			−0.0909091
$122$			653467.i			0.359869i
$123$	−180042.	+	1.23328e6i	−0.0967517	+	0.662745i
$124$	−575064.			−0.301614
$125$		−	1.09941e6i		−	0.562897i
$126$	595116.	−	1.99482e6i	0.297502	−	0.997221i
$127$	3.18701e6			1.55586			0.777932	−	0.628348i	$-0.216269\pi$
$127$	3.18701e6			1.55586			0.777932	+	0.628348i	$0.216269\pi$
$128$			2.48005e6i			1.18258i
$129$	1.70809e6	+	249357.i	0.795684	+	0.116159i
$130$	648921.			0.295367
$131$		−	746504.i		−	0.332061i	−0.986121	−	0.166031i	$-0.946905\pi$
$131$		−	746504.i		−	0.332061i	0.986121	−	0.166031i	$-0.0530951\pi$
$132$	−36974.5	+	253274.i	−0.0160761	+	0.110121i
$133$	−809257.			−0.343979
$134$			4.57668e6i			1.90211i
$135$	304938.	−	656416.i	0.123940	−	0.266795i
$136$	−974040.			−0.387222
$137$		−	73100.9i		−	0.0284290i	−0.999899	−	0.0142145i	$-0.995475\pi$
$137$		−	73100.9i		−	0.0284290i	0.999899	−	0.0142145i	$-0.00452476\pi$
$138$	4.44156e6	+	648408.i	1.69005	+	0.246724i
$139$	−4.23704e6			−1.57768			−0.788838	−	0.614602i	$-0.789317\pi$
$139$	−4.23704e6			−1.57768			−0.788838	+	0.614602i	$0.789317\pi$
$140$			264988.i			0.0965700i
$141$	−594765.	+	4.07411e6i	−0.212172	+	1.45337i
$142$	3.16658e6			1.10592
$143$			756565.i			0.258725i
$144$	−3.52768e6	−	1.05242e6i	−1.18141	−	0.352452i
$145$	474507.			0.155646
$146$			473878.i			0.152268i
$147$	−656930.	−	95902.9i	−0.206808	−	0.0301912i
$148$	1.13626e6			0.350505
$149$			4.99811e6i			1.51094i	0.655184	+	0.755469i	$0.272591\pi$
$149$			4.99811e6i			1.51094i	−0.655184	+	0.755469i	$0.727409\pi$
$150$	521091.	−	3.56945e6i	0.154397	−	1.05761i
$151$	−5.94916e6			−1.72793			−0.863963	−	0.503555i	$-0.832025\pi$
$151$	−5.94916e6			−1.72793			−0.863963	+	0.503555i	$0.832025\pi$
$152$			1.00266e6i			0.285510i
$153$	537082.	−	1.80029e6i	0.149957	−	0.502652i
$154$	−1.14597e6			−0.313769
$155$		−	895184.i		−	0.240391i
$156$	1.18980e6	+	173694.i	0.313400	+	0.0457522i
$157$	−3.24841e6			−0.839406			−0.419703	−	0.907662i	$-0.637866\pi$
$157$	−3.24841e6			−0.839406			−0.419703	+	0.907662i	$0.637866\pi$
$158$		−	1.13388e6i		−	0.287472i
$159$	804037.	−	5.50761e6i	0.200025	−	1.37016i
$160$	848709.			0.207204
$161$			5.41784e6i			1.29822i
$162$	2.72560e6	−	4.16152e6i	0.641088	−	0.978829i
$163$	4.59105e6			1.06011			0.530053	−	0.847965i	$-0.322172\pi$
$163$	4.59105e6			1.06011			0.530053	+	0.847965i	$0.322172\pi$
$164$		−	1.09044e6i		−	0.247212i
$165$	−394263.	−	57557.1i	−0.0877676	−	0.0128129i
$166$	−9.54878e6			−2.08749
$167$		−	8.44272e6i		−	1.81273i	−0.422496	−	0.906365i	$-0.638846\pi$
$167$		−	8.44272e6i		−	1.81273i	0.422496	−	0.906365i	$-0.361154\pi$
$168$	449705.	−	3.08046e6i	0.0948418	−	0.649662i
$169$	−1.27271e6			−0.263676
$170$			887067.i			0.180555i
$171$	−1.85318e6	−	552861.i	−0.370620	−	0.110567i
$172$	−1.51025e6			−0.296800
$173$		−	1.24673e6i		−	0.240787i	−0.992726	−	0.120393i	$-0.961584\pi$
$173$		−	1.24673e6i		−	0.240787i	0.992726	−	0.120393i	$-0.0384156\pi$
$174$	3.22711e6	+	471115.i	0.612585	+	0.0894292i
$175$	4.35403e6			0.812414
$176$			2.02655e6i			0.371723i
$177$	−1.29454e6	+	8.86753e6i	−0.233451	+	1.59913i
$178$	−673667.			−0.119450
$179$		−	9.79453e6i		−	1.70775i	−0.520477	−	0.853876i	$-0.674246\pi$
$179$		−	9.79453e6i		−	1.70775i	0.520477	−	0.853876i	$-0.325754\pi$
$180$	−181032.	+	606816.i	−0.0310412	+	0.104049i
$181$	9.68302e6			1.63296			0.816479	−	0.577374i	$-0.195923\pi$
$181$	9.68302e6			1.63296			0.816479	+	0.577374i	$0.195923\pi$
$182$			5.38337e6i			0.892977i
$183$	−1.86509e6	−	272279.i	−0.304332	−	0.0444284i
$184$	6.71261e6			1.07755
$185$			1.76879e6i			0.279358i
$186$	888786.	−	6.08814e6i	0.138121	−	0.946119i
$187$	−1.03421e6			−0.158156
$188$		−	3.60223e6i		−	0.542124i
$189$	5.44555e6	+	2.52973e6i	0.806596	+	0.374704i
$190$	913128.			0.133128
$191$		−	9.37570e6i		−	1.34556i	−0.739842	−	0.672781i	$-0.765100\pi$
$191$		−	9.37570e6i		−	1.34556i	0.739842	−	0.672781i	$-0.234900\pi$
$192$	−2.86250e6	−	417886.i	−0.404428	−	0.0590410i
$193$	3.78854e6			0.526988			0.263494	−	0.964661i	$-0.415125\pi$
$193$	3.78854e6			0.526988			0.263494	+	0.964661i	$0.415125\pi$
$194$			6.49548e6i			0.889624i
$195$	−270384.	+	1.85212e6i	−0.0364651	+	0.249784i
$196$	580843.			0.0771419
$197$			1.20376e7i			1.57450i	0.616636	+	0.787248i	$0.288495\pi$
$197$			1.20376e7i			1.57450i	−0.616636	+	0.787248i	$0.711505\pi$
$198$	−2.62423e6	−	782890.i	−0.338070	−	0.100857i
$199$	−2.99708e6			−0.380312			−0.190156	−	0.981754i	$-0.560899\pi$
$199$	−2.99708e6			−0.380312			−0.190156	+	0.981754i	$0.560899\pi$
$200$		−	5.39458e6i		−	0.674322i
$201$	−1.30625e7	−	1.90695e6i	−1.60857	−	0.234829i
$202$	−1.32456e7			−1.60701
$203$			3.93645e6i			0.470562i
$204$	−237438.	+	1.62644e6i	−0.0279679	+	0.191578i
$205$	1.69745e6			0.197031
$206$		−	7.47477e6i		−	0.855060i
$207$	−3.70131e6	+	1.24067e7i	−0.417296	+	1.39877i
$208$	9.52007e6			1.05791
$209$			1.06460e6i			0.116613i
$210$	−2.80540e6	−	409550.i	−0.302926	−	0.0442231i
$211$	2.46073e6			0.261949			0.130974	−	0.991386i	$-0.458189\pi$
$211$	2.46073e6			0.261949			0.130974	+	0.991386i	$0.458189\pi$
$212$			4.86971e6i			0.511088i
$213$	−1.31941e6	+	9.03790e6i	−0.136534	+	0.935252i
$214$	−1.43716e7			−1.46644
$215$		−	2.35096e6i		−	0.236554i
$216$	3.13429e6	−	6.74695e6i	0.311013	−	0.669493i
$217$	7.42634e6			0.726768
$218$		−	1.06828e7i		−	1.03114i
$219$	−1.35252e6	−	197450.i	−0.128769	−	0.0187985i
$220$	348599.			0.0327384
$221$			4.85840e6i			0.450108i
$222$	−1.75615e6	+	1.20295e7i	−0.160510	+	1.09948i
$223$	6.75130e6			0.608797			0.304399	−	0.952545i	$-0.401545\pi$
$223$	6.75130e6			0.608797			0.304399	+	0.952545i	$0.401545\pi$
$224$			7.04079e6i			0.626437i
$225$	9.97063e6	+	2.97455e6i	0.875336	+	0.261140i
$226$	4.06743e6			0.352367
$227$			7.66381e6i			0.655190i	0.944818	+	0.327595i	$0.106238\pi$
$227$			7.66381e6i			0.655190i	−0.944818	+	0.327595i	$0.893762\pi$
$228$	1.67422e6	+	244413.i	0.141256	+	0.0206215i
$229$	1.57426e6			0.131090			0.0655449	−	0.997850i	$-0.479121\pi$
$229$	1.57426e6			0.131090			0.0655449	+	0.997850i	$0.479121\pi$
$230$		−	6.11324e6i		−	0.502444i
$231$	477487.	−	3.27076e6i	0.0387369	−	0.265346i
$232$	4.87720e6			0.390577
$233$		−	2.05950e6i		−	0.162815i	−0.996681	−	0.0814073i	$-0.974059\pi$
$233$		−	2.05950e6i		−	0.162815i	0.996681	−	0.0814073i	$-0.0259415\pi$
$234$	−3.67776e6	+	1.23278e7i	−0.287036	+	0.962139i
$235$	5.60748e6			0.432080
$236$		−	7.84047e6i		−	0.596494i
$237$	3.23626e6	+	472450.i	0.243108	+	0.0354904i
$238$	−7.35900e6			−0.545868
$239$			7.02074e6i			0.514268i	0.966376	+	0.257134i	$0.0827782\pi$
$239$			7.02074e6i			0.514268i	−0.966376	+	0.257134i	$0.917222\pi$
$240$	−724257.	+	4.96112e6i	−0.0523913	+	0.358878i
$241$	−1.73973e7			−1.24288			−0.621442	−	0.783460i	$-0.713453\pi$
$241$	−1.73973e7			−1.24288			−0.621442	+	0.783460i	$0.713453\pi$
$242$			1.50755e6i			0.106371i
$243$	1.07419e7	+	9.51325e6i	0.748624	+	0.662995i
$244$	1.64907e6			0.113520
$245$			904180.i			0.0614832i
$246$	1.15443e7	+	1.68532e6i	0.775468	+	0.113208i
$247$	5.00113e6			0.331877
$248$		−	9.20112e6i		−	0.603234i
$249$	3.97866e6	−	2.72537e7i	0.257715	−	1.76533i
$250$	−1.02912e7			−0.658638
$251$		−	3.11159e7i		−	1.96771i	−0.178961	−	0.983856i	$-0.557274\pi$
$251$		−	3.11159e7i		−	1.96771i	0.178961	−	0.983856i	$-0.442726\pi$
$252$	−5.03407e6	−	1.50182e6i	−0.314570	−	0.0938461i
$253$	7.12730e6			0.440113
$254$		−	2.98325e7i		−	1.82049i
$255$	−2.53182e6	−	369612.i	−0.152691	−	0.0222908i
$256$	1.63579e7			0.975007
$257$		−	8.20791e6i		−	0.483541i	−0.970333	−	0.241770i	$-0.922272\pi$
$257$		−	8.20791e6i		−	0.483541i	0.970333	−	0.241770i	$-0.0777281\pi$
$258$	2.33416e6	−	1.59888e7i	0.135916	−	0.931018i
$259$	−1.46736e7			−0.844576
$260$		−	1.63760e6i		−	0.0931726i
$261$	−2.68927e6	+	9.01438e6i	−0.151256	+	0.507007i
$262$	−6.98779e6			−0.388540
$263$		−	1.28328e6i		−	0.0705433i	−0.999378	−	0.0352716i	$-0.988770\pi$
$263$		−	1.28328e6i		−	0.0705433i	0.999378	−	0.0352716i	$-0.0112296\pi$
$264$	−4.05242e6	−	591598.i	−0.220243	−	0.0321525i
$265$	−7.58052e6			−0.407344
$266$			7.57520e6i			0.402484i
$267$	280695.	−	1.92275e6i	0.0147469	−	0.101016i
$268$	1.15496e7			0.600016
$269$			2.56455e7i			1.31751i	0.752357	+	0.658756i	$0.228917\pi$
$269$			2.56455e7i			1.31751i	−0.752357	+	0.658756i	$0.771083\pi$
$270$	−6.14450e6	−	2.85443e6i	−0.312173	−	0.145020i
$271$	−2.96795e7			−1.49124			−0.745622	−	0.666369i	$-0.767848\pi$
$271$	−2.96795e7			−1.49124			−0.745622	+	0.666369i	$0.767848\pi$
$272$			1.30138e7i			0.646692i
$273$	−1.53650e7	−	2.24308e6i	−0.755168	−	0.110244i
$274$	−684274.			−0.0332643
$275$		−	5.72784e6i		−	0.275418i
$276$	1.63631e6	−	1.12086e7i	0.0778283	−	0.533120i
$277$	−2.35905e7			−1.10993			−0.554967	−	0.831872i	$-0.687269\pi$
$277$	−2.35905e7			−1.10993			−0.554967	+	0.831872i	$0.687269\pi$
$278$			3.96615e7i			1.84602i
$279$	1.70061e7	+	5.07346e6i	0.783056	+	0.233610i
$280$	−4.23985e6			−0.193142
$281$		−	3.53612e7i		−	1.59371i	−0.604174	−	0.796853i	$-0.706497\pi$
$281$		−	3.53612e7i		−	1.59371i	0.604174	−	0.796853i	$-0.293503\pi$
$282$	3.81364e7	+	5.56740e6i	1.70056	+	0.248259i
$283$	−2.92368e7			−1.28994			−0.644970	−	0.764208i	$-0.723130\pi$
$283$	−2.92368e7			−1.28994			−0.644970	+	0.764208i	$0.723130\pi$
$284$		−	7.99110e6i		−	0.348860i
$285$	−380471.	+	2.60620e6i	−0.0164356	+	0.112583i
$286$	7.08197e6			0.302730
$287$			1.40818e7i			0.595681i
$288$	−4.81006e6	+	1.61232e7i	−0.201360	+	0.674955i
$289$	1.74962e7			0.724854
$290$		−	4.44171e6i		−	0.182119i
$291$	−1.85391e7	−	2.70646e6i	−0.752332	−	0.109830i
$292$	1.19587e6			0.0480324
$293$			2.50824e7i			0.997163i	0.866843	+	0.498582i	$0.166146\pi$
$293$			2.50824e7i			0.997163i	−0.866843	+	0.498582i	$0.833854\pi$
$294$	−897717.	+	6.14932e6i	−0.0353262	+	0.241983i
$295$	1.22050e7			0.475414
$296$			1.81804e7i			0.701017i
$297$	3.32792e6	−	7.16376e6i	0.127029	−	0.273446i
$298$	4.67857e7			1.76793
$299$		−	3.34817e7i		−	1.25255i
$300$	−9.00778e6	−	1.31501e6i	−0.333621	−	0.0487042i
$301$	1.95033e7			0.715168
$302$			5.56882e7i			2.02182i
$303$	5.51902e6	−	3.78050e7i	0.198397	−	1.35901i
$304$	1.33961e7			0.476825
$305$			2.56706e6i			0.0904767i
$306$	−1.68519e7	−	5.02745e6i	−0.588146	−	0.175462i
$307$	1.08562e7			0.375199			0.187599	−	0.982246i	$-0.439929\pi$
$307$	1.08562e7			0.375199			0.187599	+	0.982246i	$0.439929\pi$
$308$			2.89193e6i			0.0989773i
$309$	2.13341e7	+	3.11450e6i	0.723102	+	0.105563i
$310$	−8.37954e6			−0.281277
$311$		−	8.33423e6i		−	0.277067i	−0.990358	−	0.138533i	$-0.955761\pi$
$311$		−	8.33423e6i		−	0.277067i	0.990358	−	0.138533i	$-0.0442388\pi$
$312$	−2.77914e6	+	1.90369e7i	−0.0915053	+	0.626806i
$313$	−1.57961e7			−0.515130			−0.257565	−	0.966261i	$-0.582920\pi$
$313$	−1.57961e7			−0.515130			−0.257565	+	0.966261i	$0.582920\pi$
$314$			3.04073e7i			0.982176i
$315$	2.33784e6	−	7.83638e6i	0.0747967	−	0.250717i
$316$	−2.86143e6			−0.0906821
$317$			2.39503e7i			0.751853i	0.926649	+	0.375927i	$0.122675\pi$
$317$			2.39503e7i			0.751853i	−0.926649	+	0.375927i	$0.877325\pi$
$318$	−5.15550e7	−	7.52634e6i	−1.60321	−	0.234047i
$319$	5.17850e6			0.159526
$320$			3.93986e6i			0.120235i
$321$	5.98818e6	−	4.10187e7i	0.181042	−	1.24013i
$322$	5.07147e7			1.51903
$323$			6.83648e6i			0.202873i
$324$	−1.05019e7	−	6.87826e6i	−0.308769	−	0.202229i
$325$	−2.69075e7			−0.783833
$326$		−	4.29754e7i		−	1.24041i
$327$	3.04904e7	+	4.45118e6i	0.872006	+	0.127301i
$328$	1.74472e7			0.494429
$329$			4.65190e7i			1.30630i
$330$	−538774.	+	3.69057e6i	−0.0149922	+	0.102696i
$331$	6.08158e7			1.67700			0.838498	−	0.544904i	$-0.183434\pi$
$331$	6.08158e7			1.67700			0.838498	+	0.544904i	$0.183434\pi$
$332$			2.40971e7i			0.658491i
$333$	−3.36023e7	−	1.00246e7i	−0.909989	−	0.271478i
$334$	−7.90296e7			−2.12105
$335$			1.79789e7i			0.478221i
$336$	−4.11569e7	−	6.00835e6i	−1.08499	−	0.158393i
$337$	4.49215e7			1.17372			0.586860	−	0.809689i	$-0.300364\pi$
$337$	4.49215e7			1.17372			0.586860	+	0.809689i	$0.300364\pi$
$338$			1.19135e7i			0.308523i
$339$	−1.69477e6	+	1.16091e7i	−0.0435022	+	0.297988i
$340$	2.23858e6			0.0569555
$341$		−	9.76954e6i		−	0.246383i
$342$	−5.17515e6	+	1.73470e7i	−0.129373	+	0.433657i
$343$	−4.33907e7			−1.07526
$344$		−	2.41642e7i		−	0.593605i
$345$	1.74481e7	+	2.54719e6i	0.424904	+	0.0620302i
$346$	−1.16702e7			−0.281741
$347$			2.03637e7i			0.487382i	0.969853	+	0.243691i	$0.0783582\pi$
$347$			2.03637e7i			0.487382i	−0.969853	+	0.243691i	$0.921642\pi$
$348$	1.18889e6	−	8.14387e6i	0.0282102	−	0.193238i
$349$	−1.65717e7			−0.389844			−0.194922	−	0.980819i	$-0.562445\pi$
$349$	−1.65717e7			−0.389844			−0.194922	+	0.980819i	$0.562445\pi$
$350$		−	4.07567e7i		−	0.950594i
$351$	−3.36530e7	−	1.56335e7i	−0.778220	−	0.361522i
$352$	9.26234e6			0.212370
$353$		−	9.15516e6i		−	0.208133i	−0.994570	−	0.104067i	$-0.966814\pi$
$353$		−	9.15516e6i		−	0.208133i	0.994570	−	0.104067i	$-0.0331855\pi$
$354$	8.30062e7	+	1.21178e7i	1.87112	+	0.273158i
$355$	1.24395e7			0.278047
$356$			1.70005e6i			0.0376800i
$357$	3.06625e6	−	2.10037e7i	0.0673913	−	0.461627i
$358$	−9.16835e7			−1.99821
$359$			1.00397e7i			0.216990i	0.994097	+	0.108495i	$0.0346031\pi$
$359$			1.00397e7i			0.216990i	−0.994097	+	0.108495i	$0.965397\pi$
$360$	−9.70916e6	−	2.89654e6i	−0.208101	−	0.0620829i
$361$	−4.00086e7			−0.850416
$362$		−	9.06397e7i		−	1.91070i
$363$	−4.30277e6	−	628146.i	−0.0899556	−	0.0131323i
$364$	1.35853e7			0.281687
$365$			1.86157e6i			0.0382825i
$366$	−2.54871e6	+	1.74586e7i	−0.0519850	+	0.356094i
$367$	2.18107e7			0.441237			0.220618	−	0.975360i	$-0.429192\pi$
$367$	2.18107e7			0.441237			0.220618	+	0.975360i	$0.429192\pi$
$368$		−	8.96849e7i		−	1.79960i
$369$	−9.62030e6	+	3.22471e7i	−0.191474	+	0.641817i
$370$	1.65571e7			0.326872
$371$		−	6.28871e7i		−	1.23151i
$372$	−1.53639e7	−	2.24292e6i	−0.298450	−	0.0435697i
$373$	3.77267e7			0.726980			0.363490	−	0.931598i	$-0.381585\pi$
$373$	3.77267e7			0.726980			0.363490	+	0.931598i	$0.381585\pi$
$374$			9.68095e6i			0.185056i
$375$	4.28802e6	−	2.93727e7i	0.0813135	−	0.556993i
$376$	5.76363e7			1.08426
$377$		−	2.43269e7i		−	0.454007i
$378$	2.36800e7	−	5.09740e7i	0.438436	−	0.943786i
$379$	−4.88163e7			−0.896701			−0.448350	−	0.893858i	$-0.647988\pi$
$379$	−4.88163e7			−0.896701			−0.448350	+	0.893858i	$0.647988\pi$
$380$		−	2.30435e6i		−	0.0419950i
$381$	8.51466e7	+	1.24303e7i	1.53955	+	0.224753i
$382$	−8.77630e7			−1.57442
$383$			9.00171e7i			1.60224i	0.598501	+	0.801122i	$0.295763\pi$
$383$			9.00171e7i			1.60224i	−0.598501	+	0.801122i	$0.704237\pi$
$384$	−9.67293e6	+	6.62591e7i	−0.170830	+	1.17018i
$385$	−4.50178e6			−0.0788864
$386$		−	3.54634e7i		−	0.616620i
$387$	4.46620e7	+	1.33241e7i	0.770558	+	0.229881i
$388$	1.63918e7			0.280629
$389$			3.19559e6i			0.0542879i	0.999632	+	0.0271439i	$0.00864125\pi$
$389$			3.19559e6i			0.0542879i	−0.999632	+	0.0271439i	$0.991359\pi$
$390$	1.73371e7	+	2.53098e6i	0.292269	+	0.0426673i
$391$	4.57691e7			0.765671
$392$			9.29358e6i			0.154285i
$393$	2.91158e6	−	1.99442e7i	0.0479680	−	0.328578i
$394$	1.12680e8			1.84230
$395$		−	4.45430e6i		−	0.0722749i
$396$	−1.97568e6	+	6.62245e6i	−0.0318150	+	0.106643i
$397$	−5.79273e6			−0.0925789			−0.0462894	−	0.998928i	$-0.514740\pi$
$397$	−5.79273e6			−0.0925789			−0.0462894	+	0.998928i	$0.514740\pi$
$398$			2.80548e7i			0.444997i
$399$	−2.16208e7	−	3.15634e6i	−0.340371	−	0.0496895i
$400$	−7.20750e7			−1.12617
$401$		−	2.76743e7i		−	0.429183i	−0.976704	−	0.214592i	$-0.931158\pi$
$401$		−	2.76743e7i		−	0.429183i	0.976704	−	0.214592i	$-0.0688421\pi$
$402$	−1.78504e7	+	1.22274e8i	−0.274770	+	1.88216i
$403$	−4.58941e7			−0.701200
$404$			3.34263e7i			0.506926i
$405$	1.07072e7	−	1.63480e7i	0.161180	−	0.246093i
$406$	3.68479e7			0.550597
$407$			1.93036e7i			0.286322i
$408$	−2.60232e7	−	3.79904e6i	−0.383161	−	0.0559363i
$409$	−5.58799e7			−0.816743			−0.408371	−	0.912816i	$-0.633903\pi$
$409$	−5.58799e7			−0.816743			−0.408371	+	0.912816i	$0.633903\pi$
$410$		−	1.58893e7i		−	0.230544i
$411$	285115.	−	1.95302e6i	0.00410671	−	0.0281308i
$412$	−1.88632e7			−0.269726
$413$			1.01251e8i			1.43731i
$414$	1.16135e8	+	3.46468e7i	1.63668	+	0.488272i
$415$	−3.75111e7			−0.524827
$416$		−	4.35114e7i		−	0.604398i
$417$	−1.13200e8	−	1.65257e7i	−1.56113	−	0.227904i
$418$	9.96537e6			0.136447
$419$			6.73673e7i			0.915814i	0.889000	+	0.457907i	$0.151401\pi$
$419$			6.73673e7i			0.915814i	−0.889000	+	0.457907i	$0.848599\pi$
$420$	−1.03353e6	+	7.07963e6i	−0.0139500	+	0.0955571i
$421$	8.35973e7			1.12033			0.560165	−	0.828381i	$-0.310738\pi$
$421$	8.35973e7			1.12033			0.560165	+	0.828381i	$0.310738\pi$
$422$		−	2.30341e7i		−	0.306502i
$423$	−3.17804e7	+	1.06527e8i	−0.419893	+	1.40747i
$424$	−7.79161e7			−1.02219
$425$		−	3.67822e7i		−	0.479150i
$426$	8.46009e7	+	1.23506e7i	1.09432	+	0.159757i
$427$	−2.12960e7			−0.273536
$428$			3.62678e7i			0.462584i
$429$	−2.95082e6	+	2.02130e7i	−0.0373742	+	0.256011i
$430$	−2.20066e7			−0.276788
$431$			1.88964e7i			0.236019i	0.993012	+	0.118009i	$0.0376513\pi$
$431$			1.88964e7i			0.236019i	−0.993012	+	0.118009i	$0.962349\pi$
$432$	−9.01435e7	−	4.18762e7i	−1.11811	−	0.519416i
$433$	−235358.			−0.00289912			−0.00144956	−	0.999999i	$-0.500461\pi$
$433$	−235358.			−0.00289912			−0.00144956	+	0.999999i	$0.500461\pi$
$434$		−	6.95156e7i		−	0.850380i
$435$	1.26773e7	+	1.85071e6i	0.154014	+	0.0224839i
$436$	−2.69589e7			−0.325269
$437$		−	4.71137e7i		−	0.564551i
$438$	−1.84826e6	+	1.26605e7i	−0.0219959	+	0.150671i
$439$	2.07474e7			0.245227			0.122614	−	0.992454i	$-0.460872\pi$
$439$	2.07474e7			0.245227			0.122614	+	0.992454i	$0.460872\pi$
$440$			5.57763e6i			0.0654775i
$441$	−1.71770e7	−	5.12444e6i	−0.200278	−	0.0597490i
$442$	4.54779e7			0.526664
$443$		−	8.83807e7i		−	1.01659i	−0.861183	−	0.508296i	$-0.830276\pi$
$443$		−	8.83807e7i		−	1.01659i	0.861183	−	0.508296i	$-0.169724\pi$
$444$	3.03574e7	+	4.43177e6i	0.346829	+	0.0506323i
$445$	−2.64641e6			−0.0300315
$446$		−	6.31967e7i		−	0.712345i
$447$	−1.94941e7	+	1.33533e8i	−0.218263	+	1.49509i
$448$	−3.26846e7			−0.363504
$449$			1.25246e8i			1.38365i	0.722067	+	0.691823i	$0.243192\pi$
$449$			1.25246e8i			1.38365i	−0.722067	+	0.691823i	$0.756808\pi$
$450$	2.78438e7	−	9.33319e7i	0.305556	−	1.02422i
$451$	1.85250e7			0.201943
$452$		−	1.02645e7i		−	0.111153i
$453$	−1.58943e8	−	2.32035e7i	−1.70980	−	0.249608i
$454$	7.17385e7			0.766628
$455$			2.11479e7i			0.224508i
$456$	−3.91065e6	+	2.67878e7i	−0.0412434	+	0.282515i
$457$	1.67043e8			1.75017			0.875084	−	0.483971i	$-0.160806\pi$
$457$	1.67043e8			1.75017			0.875084	+	0.483971i	$0.160806\pi$
$458$		−	1.47361e7i		−	0.153386i
$459$	2.13708e7	−	4.60032e7i	0.220995	−	0.475718i
$460$	−1.54272e7			−0.158494
$461$		−	4.82411e6i		−	0.0492396i	−0.999697	−	0.0246198i	$-0.992162\pi$
$461$		−	4.82411e6i		−	0.0492396i	0.999697	−	0.0246198i	$-0.00783751\pi$
$462$	−3.06165e7	−	4.46960e6i	−0.310478	−	0.0453255i
$463$	1.36085e8			1.37110			0.685550	−	0.728026i	$-0.259562\pi$
$463$	1.36085e8			1.37110			0.685550	+	0.728026i	$0.259562\pi$
$464$		−	6.51625e7i		−	0.652295i
$465$	3.49148e6	−	2.39165e7i	0.0347257	−	0.237869i
$466$	−1.92783e7			−0.190507
$467$		−	8.41293e7i		−	0.826031i	−0.910724	−	0.413016i	$-0.864475\pi$
$467$		−	8.41293e7i		−	0.826031i	0.910724	−	0.413016i	$-0.135525\pi$
$468$	3.11101e7	+	9.28111e6i	0.303504	+	0.0905446i
$469$	−1.49151e8			−1.44580
$470$		−	5.24899e7i		−	0.505571i
$471$	−8.67871e7	−	1.26697e7i	−0.830601	−	0.121257i
$472$	1.25449e8			1.19300
$473$		−	2.56571e7i		−	0.242451i
$474$	4.42246e6	−	3.02936e7i	0.0415268	−	0.284457i
$475$	−3.78628e7			−0.353291
$476$			1.85710e7i			0.172192i
$477$	4.29626e7	−	1.44010e8i	0.395854	−	1.32690i
$478$	6.57190e7			0.601737
$479$		−	1.94263e7i		−	0.176759i	−0.996087	−	0.0883797i	$-0.971831\pi$
$479$		−	1.94263e7i		−	0.176759i	0.996087	−	0.0883797i	$-0.0281689\pi$
$480$	2.26748e7	+	3.31021e6i	0.205031	+	0.0299318i
$481$	9.06818e7			0.814864
$482$			1.62851e8i			1.45428i
$483$	−2.11311e7	+	1.44747e8i	−0.187535	+	1.28460i
$484$	3.80441e6			0.0335545
$485$			2.55167e7i			0.223665i
$486$	8.90505e7	−	1.00552e8i	0.775761	−	0.875954i
$487$	1.68322e7			0.145732			0.0728658	−	0.997342i	$-0.476786\pi$
$487$	1.68322e7			0.145732			0.0728658	+	0.997342i	$0.476786\pi$
$488$			2.63855e7i			0.227041i
$489$	1.22658e8	+	1.79064e7i	1.04899	+	0.153138i
$490$	8.46374e6			0.0719406
$491$		−	9.38793e7i		−	0.793095i	−0.918014	−	0.396548i	$-0.870208\pi$
$491$		−	9.38793e7i		−	0.793095i	0.918014	−	0.396548i	$-0.129792\pi$
$492$	4.25303e6	−	2.91330e7i	0.0357111	−	0.244619i
$493$	3.32545e7			0.277530
$494$		−	4.68140e7i		−	0.388325i
$495$	−1.03090e7	−	3.07548e6i	−0.0849962	−	0.0253570i
$496$	−1.22933e8			−1.00745
$497$			1.03197e8i			0.840613i
$498$	−2.55113e8	−	3.72430e7i	−2.06559	−	0.301548i
$499$	−2.51357e7			−0.202297			−0.101148	−	0.994871i	$-0.532252\pi$
$499$	−2.51357e7			−0.202297			−0.101148	+	0.994871i	$0.532252\pi$
$500$			2.59707e7i			0.207765i
$501$	3.29291e7	−	2.25562e8i	0.261858	−	1.79372i
$502$	−2.91266e8			−2.30239
$503$			1.37148e8i			1.07767i	0.842411	+	0.538836i	$0.181136\pi$
$503$			1.37148e8i			1.07767i	−0.842411	+	0.538836i	$0.818864\pi$
$504$	2.40294e7	−	8.05460e7i	0.187694	−	0.629147i
$505$	−5.20337e7			−0.404027
$506$		−	6.67164e7i		−	0.514969i
$507$	−3.40028e7	−	4.96396e6i	−0.260910	−	0.0380894i
$508$	−7.52847e7			−0.574269
$509$		−	4.02455e7i		−	0.305185i	−0.988289	−	0.152593i	$-0.951238\pi$
$509$		−	4.02455e7i		−	0.305185i	0.988289	−	0.152593i	$-0.0487623\pi$
$510$	−3.45982e6	+	2.36996e7i	−0.0260821	+	0.178661i
$511$	−1.54434e7			−0.115739
$512$			5.60231e6i			0.0417405i
$513$	−4.73547e7	−	2.19986e7i	−0.350761	−	0.162946i
$514$	−7.68316e7			−0.565784
$515$		−	2.93637e7i		−	0.214975i
$516$	−4.03491e7	−	5.89042e6i	−0.293687	−	0.0428743i
$517$	6.11969e7			0.442852
$518$			1.37355e8i			0.988226i
$519$	4.86259e6	−	3.33085e7i	0.0347829	−	0.238261i
$520$	2.62019e7			0.186347
$521$			4.51010e7i			0.318913i	0.987205	+	0.159457i	$0.0509742\pi$
$521$			4.51010e7i			0.318913i	−0.987205	+	0.159457i	$0.949026\pi$
$522$	8.43807e7	+	2.51734e7i	0.593242	+	0.176982i
$523$	2.35772e8			1.64811			0.824057	−	0.566507i	$-0.191706\pi$
$523$	2.35772e8			1.64811			0.824057	+	0.566507i	$0.191706\pi$
$524$			1.76342e7i			0.122564i
$525$	1.16326e8	+	1.69820e7i	0.803893	+	0.117357i
$526$	−1.20124e7			−0.0825417
$527$		−	6.27366e7i		−	0.428637i
$528$	−7.90414e6	+	5.41429e7i	−0.0536973	+	0.367824i
$529$	−1.67383e8			−1.13069
$530$			7.09589e7i			0.476627i
$531$	−6.91719e7	+	2.31863e8i	−0.462005	+	1.54863i
$532$	1.91166e7			0.126962
$533$		−	8.70245e7i		−	0.574725i
$534$	−1.79982e7	−	2.62750e6i	−0.118197	−	0.0172551i
$535$	−5.64570e7			−0.368686
$536$			1.84795e8i			1.20004i
$537$	3.82015e7	−	2.61679e8i	0.246694	−	1.68984i
$538$	2.40060e8			1.54160
$539$			9.86771e6i			0.0630159i
$540$	−7.20336e6	+	1.55061e7i	−0.0457461	+	0.0984740i
$541$	−2.51573e8			−1.58881			−0.794407	−	0.607386i	$-0.792218\pi$
$541$	−2.51573e8			−1.58881			−0.794407	+	0.607386i	$0.792218\pi$
$542$			2.77821e8i			1.74488i
$543$	2.58699e8	+	3.77666e7i	1.61583	+	0.235890i
$544$	5.94795e7			0.369463
$545$		−	4.19660e7i		−	0.259244i
$546$	−2.09967e7	+	1.43827e8i	−0.128995	+	0.883611i
$547$	9.08807e7			0.555277			0.277639	−	0.960686i	$-0.410448\pi$
$547$	9.08807e7			0.555277			0.277639	+	0.960686i	$0.410448\pi$
$548$			1.72682e6i			0.0104931i
$549$	−4.87674e7	−	1.45488e7i	−0.294722	−	0.0879247i
$550$	−5.36165e7			−0.322263
$551$		−	3.42315e7i		−	0.204631i
$552$	1.79340e8	+	2.61812e7i	1.06625	+	0.155658i
$553$	3.69523e7			0.218507
$554$			2.20823e8i			1.29872i
$555$	−6.89879e6	+	4.72564e7i	−0.0403547	+	0.276428i
$556$	1.00089e8			0.582320
$557$		−	1.46509e8i		−	0.847809i	−0.905707	−	0.423904i	$-0.860659\pi$
$557$		−	1.46509e8i		−	0.847809i	0.905707	−	0.423904i	$-0.139341\pi$
$558$	4.74910e7	−	1.59189e8i	0.273344	−	0.916243i
$559$	−1.20528e8			−0.690008
$560$			5.66471e7i			0.322562i
$561$	−2.76309e7	−	4.03374e6i	−0.156497	−	0.0228465i
$562$	−3.31005e8			−1.86477
$563$			1.28874e8i			0.722174i	0.932532	+	0.361087i	$0.117594\pi$
$563$			1.28874e8i			0.722174i	−0.932532	+	0.361087i	$0.882406\pi$
$564$	1.40498e7	−	9.62402e7i	0.0783126	−	0.536438i
$565$	1.59784e7			0.0885906
$566$			2.73676e8i			1.50934i
$567$	1.35621e8	+	8.88254e7i	0.744008	+	0.487291i
$568$	1.27859e8			0.697728
$569$		−	2.21698e7i		−	0.120344i	−0.998188	−	0.0601721i	$-0.980835\pi$
$569$		−	2.21698e7i		−	0.120344i	0.998188	−	0.0601721i	$-0.0191649\pi$
$570$	2.43959e7	+	3.56147e6i	0.131732	+	0.0192311i
$571$	2.43886e7			0.131002			0.0655011	−	0.997852i	$-0.479135\pi$
$571$	2.43886e7			0.131002			0.0655011	+	0.997852i	$0.479135\pi$
$572$		−	1.78719e7i		−	0.0954953i
$573$	3.65680e7	−	2.50489e8i	0.194374	−	1.33145i
$574$	1.31816e8			0.696997
$575$			2.53485e8i			1.33337i
$576$	−7.48469e7	−	2.23291e7i	−0.391657	−	0.116844i
$577$	1.05895e8			0.551251			0.275625	−	0.961265i	$-0.411115\pi$
$577$	1.05895e8			0.551251			0.275625	+	0.961265i	$0.411115\pi$
$578$		−	1.63776e8i		−	0.848141i
$579$	1.01218e8	+	1.47764e7i	0.521460	+	0.0761261i
$580$	−1.12090e7			−0.0574490
$581$		−	3.11188e8i		−	1.58670i
$582$	−2.53343e7	+	1.73539e8i	−0.128511	+	0.880293i
$583$	−8.27296e7			−0.417499
$584$			1.91341e7i			0.0960658i
$585$	−1.44476e7	+	4.84281e7i	−0.0721653	+	0.241897i
$586$	2.34788e8			1.16677
$587$		−	1.12136e8i		−	0.554409i	−0.960811	−	0.277204i	$-0.910592\pi$
$587$		−	1.12136e8i		−	0.554409i	0.960811	−	0.277204i	$-0.0894079\pi$
$588$	1.55183e7	+	2.26546e6i	0.0763328	+	0.0111436i
$589$	−6.45798e7			−0.316046
$590$		−	1.14247e8i		−	0.556275i
$591$	−4.69502e7	+	3.21607e8i	−0.227444	+	1.55798i
$592$	2.42902e8			1.17076
$593$		−	2.17826e8i		−	1.04459i	−0.852765	−	0.522295i	$-0.825076\pi$
$593$		−	2.17826e8i		−	1.04459i	0.852765	−	0.522295i	$-0.174924\pi$
$594$	−6.70577e7	−	3.11516e7i	−0.319955	−	0.148635i
$595$	−2.89089e7			−0.137240
$596$		−	1.18067e8i		−	0.557687i
$597$	−8.00725e7	−	1.16895e7i	−0.376323	−	0.0549380i
$598$	−3.13412e8			−1.46559
$599$		−	2.22688e8i		−	1.03613i	−0.855340	−	0.518067i	$-0.826652\pi$
$599$		−	2.22688e8i		−	1.03613i	0.855340	−	0.518067i	$-0.173348\pi$
$600$	2.10404e7	−	1.44126e8i	0.0974094	−	0.667249i
$601$	−4.04878e8			−1.86510			−0.932548	−	0.361047i	$-0.882419\pi$
$601$	−4.04878e8			−1.86510			−0.932548	+	0.361047i	$0.882419\pi$
$602$		−	1.82564e8i		−	0.836807i
$603$	−3.41552e8	−	1.01895e8i	−1.55777	−	0.464732i
$604$	1.40533e8			0.637777
$605$			5.92221e6i			0.0267434i
$606$	−3.53881e8	−	5.16618e7i	−1.59015	−	0.232141i
$607$	−1.36375e7			−0.0609775			−0.0304887	−	0.999535i	$-0.509706\pi$
$607$	−1.36375e7			−0.0609775			−0.0304887	+	0.999535i	$0.509706\pi$
$608$		−	6.12270e7i		−	0.272416i
$609$	−1.53533e7	+	1.05169e8i	−0.0679751	+	0.465626i
$610$	2.40295e7			0.105866
$611$		−	2.87483e8i		−	1.26034i
$612$	−1.26872e7	+	4.25271e7i	−0.0553490	+	0.185529i
$613$	1.09382e8			0.474860			0.237430	−	0.971405i	$-0.423695\pi$
$613$	1.09382e8			0.474860			0.237430	+	0.971405i	$0.423695\pi$
$614$		−	1.01621e8i		−	0.439015i
$615$	4.53504e7	+	6.62055e6i	0.194965	+	0.0284622i
$616$	−4.62714e7			−0.197957
$617$			1.08907e8i			0.463659i	0.972756	+	0.231830i	$0.0744712\pi$
$617$			1.08907e8i			0.463659i	−0.972756	+	0.231830i	$0.925529\pi$
$618$	2.91538e7	−	1.99702e8i	0.123518	−	0.846091i
$619$	−2.86793e8			−1.20920			−0.604599	−	0.796530i	$-0.706666\pi$
$619$	−2.86793e8			−1.20920			−0.604599	+	0.796530i	$0.706666\pi$
$620$			2.11464e7i			0.0887281i
$621$	−1.47277e8	+	3.17032e8i	−0.614979	+	1.32382i
$622$	−7.80141e7			−0.324192
$623$		−	2.19543e7i		−	0.0907937i
$624$	2.54346e8	+	3.71310e7i	1.04682	+	0.152821i
$625$	1.82585e8			0.747867
$626$			1.47862e8i			0.602746i
$627$	−4.15224e6	+	2.84427e7i	−0.0168454	+	0.115390i
$628$	7.67352e7			0.309825
$629$			1.23961e8i			0.498118i
$630$	−7.33539e7	−	2.18837e7i	−0.293360	−	0.0875185i
$631$	1.59510e8			0.634890			0.317445	−	0.948277i	$-0.397175\pi$
$631$	1.59510e8			0.634890			0.317445	+	0.948277i	$0.397175\pi$
$632$		−	4.57833e7i		−	0.181366i
$633$	6.57428e7	+	9.59755e6i	0.259201	+	0.0378399i
$634$	2.24191e8			0.879732
$635$		−	1.17193e8i		−	0.457701i
$636$	−1.89933e7	+	1.30103e8i	−0.0738293	+	0.505727i
$637$	4.63553e7			0.179342
$638$		−	4.84743e7i		−	0.186659i
$639$	−7.05009e7	+	2.36318e8i	−0.270204	+	0.905719i
$640$	9.11971e7			0.347889
$641$			5.46194e7i			0.207383i	0.994610	+	0.103691i	$0.0330654\pi$
$641$			5.46194e7i			0.207383i	−0.994610	+	0.103691i	$0.966935\pi$
$642$	−3.83963e8	−	5.60534e7i	−1.45106	−	0.211835i
$643$	2.80950e8			1.05681			0.528405	−	0.848992i	$-0.322790\pi$
$643$	2.80950e8			1.05681			0.528405	+	0.848992i	$0.322790\pi$
$644$		−	1.27982e8i		−	0.479173i
$645$	9.16943e6	−	6.28101e7i	0.0341714	−	0.234073i
$646$	6.39941e7			0.237379
$647$			2.49482e8i			0.921141i	0.887623	+	0.460570i	$0.152355\pi$
$647$			2.49482e8i			0.921141i	−0.887623	+	0.460570i	$0.847645\pi$
$648$	1.10053e8	−	1.68032e8i	0.404462	−	0.617543i
$649$	1.33199e8			0.487266
$650$			2.51873e8i			0.917152i
$651$	1.98408e8	+	2.89649e7i	0.719145	+	0.104985i
$652$	−1.08452e8			−0.391285
$653$			2.86755e7i			0.102984i	0.998673	+	0.0514921i	$0.0163977\pi$
$653$			2.86755e7i			0.102984i	−0.998673	+	0.0514921i	$0.983602\pi$
$654$	4.16661e7	−	2.85411e8i	0.148953	−	1.02032i
$655$	−2.74506e7			−0.0976851
$656$		−	2.33105e8i		−	0.825736i
$657$	−3.53649e7	−	1.05504e7i	−0.124703	−	0.0372027i
$658$	4.35450e8			1.52848
$659$		−	1.73934e8i		−	0.607755i	−0.952711	−	0.303878i	$-0.901719\pi$
$659$		−	1.73934e8i		−	0.607755i	0.952711	−	0.303878i	$-0.0982814\pi$
$660$	9.31344e6	+	1.35964e6i	0.0323950	+	0.00472924i
$661$	2.74123e7			0.0949165			0.0474582	−	0.998873i	$-0.484888\pi$
$661$	2.74123e7			0.0949165			0.0474582	+	0.998873i	$0.484888\pi$
$662$		−	5.69277e8i		−	1.96223i
$663$	−1.89492e7	+	1.29801e8i	−0.0650204	+	0.445387i
$664$	−3.85557e8			−1.31699
$665$			2.97582e7i			0.101191i
$666$	−9.38372e7	+	3.14541e8i	−0.317653	+	1.06477i
$667$	−2.29174e8			−0.772304
$668$			1.99437e8i			0.669078i
$669$	1.80373e8	+	2.63320e7i	0.602412	+	0.0879439i
$670$	1.68295e8			0.559560
$671$			2.80155e7i			0.0927322i
$672$	−2.74611e7	+	1.88107e8i	−0.0904921	+	0.619866i
$673$	9.36537e7			0.307241			0.153621	−	0.988130i	$-0.450907\pi$
$673$	9.36537e7			0.307241			0.153621	+	0.988130i	$0.450907\pi$
$674$		−	4.20496e8i		−	1.37335i
$675$	2.54782e8	+	1.18359e8i	0.828432	+	0.384848i
$676$	3.00645e7			0.0973228
$677$			4.99954e8i			1.61125i	0.592423	+	0.805627i	$0.298171\pi$
$677$			4.99954e8i			1.61125i	−0.592423	+	0.805627i	$0.701829\pi$
$678$	1.08669e8	+	1.58642e7i	0.348671	+	0.0509013i
$679$	−2.11683e8			−0.676203
$680$			3.58176e7i			0.113912i
$681$	−2.98911e7	+	2.04753e8i	−0.0946456	+	0.648318i
$682$	−9.14496e7			−0.288289
$683$		−	5.09802e8i		−	1.60007i	−0.599951	−	0.800036i	$-0.704813\pi$
$683$		−	5.09802e8i		−	1.60007i	0.599951	−	0.800036i	$-0.295187\pi$
$684$	4.37765e7	+	1.30599e7i	0.136796	+	0.0408104i
$685$	−2.68808e6			−0.00836317
$686$			4.06167e8i			1.25815i
$687$	4.20591e7	+	6.14006e6i	0.129715	+	0.0189366i
$688$	−3.22850e8			−0.991369
$689$			3.88636e8i			1.18819i
$690$	2.38434e7	−	1.63326e8i	0.0725807	−	0.497174i
$691$	−3.05932e8			−0.927238			−0.463619	−	0.886035i	$-0.653449\pi$
$691$	−3.05932e8			−0.927238			−0.463619	+	0.886035i	$0.653449\pi$
$692$			2.94506e7i			0.0888743i
$693$	2.55138e7	−	8.55219e7i	0.0766613	−	0.256967i
$694$	1.90619e8			0.570278
$695$			1.55805e8i			0.464117i
$696$	1.30303e8	+	1.90225e7i	0.386480	+	0.0564209i
$697$	1.18961e8			0.351324
$698$			1.55123e8i			0.456151i
$699$	8.03264e6	−	5.50232e7i	0.0235194	−	0.161107i
$700$	−1.02853e8			−0.299862
$701$			1.00619e8i			0.292097i	0.989277	+	0.146048i	$0.0466555\pi$
$701$			1.00619e8i			0.292097i	−0.989277	+	0.146048i	$0.953344\pi$
$702$	−1.46340e8	+	3.15015e8i	−0.423011	+	0.910584i
$703$	1.27603e8			0.367277
$704$			4.29974e7i			0.123232i
$705$	1.49814e8	+	2.18708e7i	0.427548	+	0.0624163i
$706$	−8.56985e7			−0.243534
$707$		−	4.31666e8i		−	1.22149i
$708$	3.05801e7	−	2.09472e8i	0.0861667	−	0.590238i
$709$	−3.07875e8			−0.863846			−0.431923	−	0.901911i	$-0.642165\pi$
$709$	−3.07875e8			−0.863846			−0.431923	+	0.901911i	$0.642165\pi$
$710$		−	1.16442e8i		−	0.325338i
$711$	8.46199e7	+	2.52447e7i	0.235431	+	0.0702363i
$712$	−2.72010e7			−0.0753608
$713$			4.32350e8i			1.19280i
$714$	−1.96609e8	−	2.87022e7i	−0.540143	−	0.0788535i
$715$	2.78206e7			0.0761111
$716$			2.31370e8i			0.630331i
$717$	−2.73830e7	+	1.87572e8i	−0.0742887	+	0.508874i
$718$	9.39789e7			0.253897
$719$		−	4.80615e8i		−	1.29304i	−0.762899	−	0.646518i	$-0.776225\pi$
$719$		−	4.80615e8i		−	1.29304i	0.762899	−	0.646518i	$-0.223775\pi$
$720$	−3.86997e7	+	1.29721e8i	−0.103684	+	0.347545i
$721$	2.43598e8			0.649931
$722$			3.74507e8i			0.995059i
$723$	−4.64800e8	−	6.78546e7i	−1.22985	−	0.179541i
$724$	−2.28736e8			−0.602725
$725$			1.84175e8i			0.483301i
$726$	−5.87988e6	+	4.02769e7i	−0.0153659	+	0.105256i
$727$	4.87349e7			0.126834			0.0634171	−	0.997987i	$-0.479800\pi$
$727$	4.87349e7			0.126834			0.0634171	+	0.997987i	$0.479800\pi$
$728$			2.17368e8i			0.563379i
$729$	2.49886e8	+	2.96060e8i	0.644999	+	0.764184i
$730$	1.74256e7			0.0447938
$731$		−	1.64761e8i		−	0.421795i
$732$	4.40580e7	+	6.43187e6i	0.112329	+	0.0163985i
$733$	1.29791e8			0.329558			0.164779	−	0.986330i	$-0.447309\pi$
$733$	1.29791e8			0.329558			0.164779	+	0.986330i	$0.447309\pi$
$734$		−	2.04163e8i		−	0.516285i
$735$	−3.52656e6	+	2.41568e7i	−0.00888157	+	0.0608383i
$736$	−4.09904e8			−1.02813
$737$			1.96212e8i			0.490143i
$738$	3.01855e8	+	9.00526e7i	0.750981	+	0.224041i
$739$	−4.06663e8			−1.00763			−0.503815	−	0.863811i	$-0.668071\pi$
$739$	−4.06663e8			−1.00763			−0.503815	+	0.863811i	$0.668071\pi$
$740$		−	4.17830e7i		−	0.103111i
$741$	1.33614e8	+	1.95059e7i	0.328396	+	0.0479414i
$742$	−5.88666e8			−1.44098
$743$			5.64696e8i			1.37673i	0.725366	+	0.688364i	$0.241671\pi$
$743$			5.64696e8i			1.37673i	−0.725366	+	0.688364i	$0.758329\pi$
$744$	3.58870e7	−	2.45824e8i	0.0871403	−	0.596906i
$745$	1.83792e8			0.444485
$746$		−	3.53148e8i		−	0.850628i
$747$	2.12594e8	−	7.12613e8i	0.510023	−	1.70959i
$748$	2.44306e7			0.0583754
$749$		−	4.68360e8i		−	1.11464i
$750$	−2.74949e8	−	4.01388e7i	−0.651730	−	0.0951437i
$751$	2.75502e8			0.650438			0.325219	−	0.945639i	$-0.394562\pi$
$751$	2.75502e8			0.650438			0.325219	+	0.945639i	$0.394562\pi$
$752$		−	7.70058e8i		−	1.81080i
$753$	1.21361e8	−	8.31318e8i	0.284246	−	1.94707i
$754$	−2.27716e8			−0.531227
$755$			2.18764e8i			0.508318i
$756$	−1.28637e8	−	5.97582e7i	−0.297714	−	0.138303i
$757$	−4.58300e7			−0.105648			−0.0528241	−	0.998604i	$-0.516822\pi$
$757$	−4.58300e7			−0.105648			−0.0528241	+	0.998604i	$0.516822\pi$
$758$			4.56954e8i			1.04922i
$759$	1.90419e8	+	2.77986e7i	0.435496	+	0.0635766i
$760$	3.68699e7			0.0839907
$761$			3.14684e8i			0.714036i	0.934097	+	0.357018i	$0.116207\pi$
$761$			3.14684e8i			0.714036i	−0.934097	+	0.357018i	$0.883793\pi$
$762$	1.16356e8	−	7.97030e8i	0.262980	−	1.80140i
$763$	3.48145e8			0.783766
$764$			2.21477e8i			0.496647i
$765$	−6.62006e7	−	1.97497e7i	−0.147869	−	0.0441140i
$766$	8.42622e8			1.87476
$767$		−	6.25724e8i		−	1.38675i
$768$	4.37031e8	+	6.38006e7i	0.964780	+	0.140845i
$769$	−6.55679e8			−1.44182			−0.720912	−	0.693026i	$-0.756277\pi$
$769$	−6.55679e8			−1.44182			−0.720912	+	0.693026i	$0.756277\pi$
$770$			4.21397e7i			0.0923038i
$771$	3.20132e7	−	2.19289e8i	0.0698500	−	0.478469i
$772$	−8.94945e7			−0.194511
$773$			1.76850e7i			0.0382883i	0.999817	+	0.0191442i	$0.00609415\pi$
$773$			1.76850e7i			0.0382883i	−0.999817	+	0.0191442i	$0.993906\pi$
$774$	1.24722e8	−	4.18067e8i	0.268981	−	0.901619i
$775$	3.47457e8			0.746443
$776$			2.62272e8i			0.561264i
$777$	−3.92033e8	−	5.72315e7i	−0.835718	−	0.122003i
$778$	2.99129e7			0.0635215
$779$		−	1.22456e8i		−	0.259041i
$780$	6.38713e6	−	4.37515e7i	0.0134593	−	0.0921954i
$781$	1.35758e8			0.284978
$782$		−	4.28430e8i		−	0.895900i
$783$	−1.07007e8	+	2.30346e8i	−0.222909	+	0.479840i
$784$	1.24168e8			0.257669
$785$			1.19451e8i			0.246935i
$786$	−1.86691e8	−	2.72544e7i	−0.384465	−	0.0561266i
$787$	5.94805e8			1.22025			0.610127	−	0.792304i	$-0.291118\pi$
$787$	5.94805e8			1.22025			0.610127	+	0.792304i	$0.291118\pi$
$788$		−	2.84357e8i		−	0.581146i
$789$	5.00518e6	−	3.42853e7i	0.0101904	−	0.0698034i
$790$	−4.16952e7			−0.0845678
$791$			1.32555e8i			0.267834i
$792$	−1.05960e8	−	3.16112e7i	−0.213289	−	0.0636306i
$793$	1.31608e8			0.263913
$794$			5.42239e7i			0.108325i
$795$	−2.02527e8	−	2.95662e7i	−0.403072	−	0.0588430i
$796$	7.07983e7			0.140373
$797$		−	2.09616e8i		−	0.414046i	−0.978336	−	0.207023i	$-0.933622\pi$
$797$		−	2.09616e8i		−	0.414046i	0.978336	−	0.207023i	$-0.0663775\pi$
$798$	−2.95455e7	+	2.02385e8i	−0.0581410	+	0.398263i
$799$	3.92986e8			0.770436
$800$			3.29419e8i			0.643396i
$801$	1.49985e7	−	5.02748e7i	0.0291845	−	0.0978258i
$802$	−2.59050e8			−0.502181
$803$			2.03161e7i			0.0392369i
$804$	3.08569e8	+	4.50468e7i	0.593722	+	0.0866755i
$805$	1.99226e8			0.381908
$806$			4.29600e8i			0.820464i
$807$	−1.00025e8	+	6.85166e8i	−0.190322	+	1.30369i
$808$	−5.34827e8			−1.01386
$809$			7.15976e8i			1.35224i	0.736793	+	0.676118i	$0.236339\pi$
$809$			7.15976e8i			1.35224i	−0.736793	+	0.676118i	$0.763661\pi$
$810$	−1.53028e8	−	1.00226e8i	−0.287950	−	0.188594i
$811$	−8.74555e8			−1.63955			−0.819775	−	0.572686i	$-0.805901\pi$
$811$	−8.74555e8			−1.63955			−0.819775	+	0.572686i	$0.805901\pi$
$812$		−	9.29884e7i		−	0.173684i
$813$	−7.92942e8	−	1.15759e8i	−1.47560	−	0.215418i
$814$	1.80695e8			0.335021
$815$		−	1.68823e8i		−	0.311860i
$816$	−5.07576e7	+	3.47687e8i	−0.0934181	+	0.639909i
$817$	−1.69601e8			−0.311002
$818$			5.23074e8i			0.955659i
$819$	−4.01754e8	−	1.19856e8i	−0.731322	−	0.218176i
$820$	−4.00978e7			−0.0727243
$821$			9.31144e8i			1.68262i	0.540550	+	0.841312i	$0.318216\pi$
$821$			9.31144e8i			1.68262i	−0.540550	+	0.841312i	$0.681784\pi$
$822$	−1.82816e7	−	2.66887e6i	−0.0329154	−	0.00480520i
$823$	−9.36645e8			−1.68026			−0.840128	−	0.542389i	$-0.817520\pi$
$823$	−9.36645e8			−1.68026			−0.840128	+	0.542389i	$0.817520\pi$
$824$		−	3.01814e8i		−	0.539457i
$825$	2.23403e7	−	1.53030e8i	0.0397856	−	0.272530i
$826$	9.47781e8			1.68178
$827$		−	6.66445e8i		−	1.17828i	−0.808032	−	0.589139i	$-0.799467\pi$
$827$		−	6.66445e8i		−	1.17828i	0.808032	−	0.589139i	$-0.200533\pi$
$828$	8.74338e7	−	2.93076e8i	0.154024	−	0.516285i
$829$	9.54093e8			1.67466			0.837331	−	0.546696i	$-0.184115\pi$
$829$	9.54093e8			1.67466			0.837331	+	0.546696i	$0.184115\pi$
$830$			3.51130e8i			0.614092i
$831$	−6.30262e8	−	9.20097e7i	−1.09829	−	0.160336i
$832$	2.01988e8			0.350715
$833$			6.33670e7i			0.109630i
$834$	−1.54692e8	+	1.05963e9i	−0.266667	+	1.82665i
$835$	−3.10458e8			−0.533265
$836$		−	2.51484e7i		−	0.0430418i
$837$	4.34562e8	+	2.01876e8i	0.741097	+	0.344276i
$838$	6.30604e8			1.07158
$839$			9.73449e7i			0.164827i	0.996598	+	0.0824133i	$0.0262627\pi$
$839$			9.73449e7i			0.164827i	−0.996598	+	0.0824133i	$0.973737\pi$
$840$	−1.13275e8	−	1.65367e7i	−0.191116	−	0.0279004i
$841$	4.28312e8			0.720065
$842$		−	7.82528e8i		−	1.31088i
$843$	1.37919e8	−	9.44738e8i	0.230219	−	1.57699i
$844$	−5.81283e7			−0.0966852
$845$			4.68005e7i			0.0775677i
$846$	9.97169e8	+	2.97487e8i	1.64686	+	0.491311i
$847$	−4.91299e7			−0.0808529
$848$			1.04101e9i			1.70713i
$849$	−7.81113e8	−	1.14032e8i	−1.27641	−	0.186339i
$850$	−3.44307e8			−0.560646
$851$		−	8.54278e8i		−	1.38615i
$852$	3.11676e7	−	2.13497e8i	0.0503947	−	0.345201i
$853$	−1.07587e9			−1.73345			−0.866727	−	0.498783i	$-0.833780\pi$
$853$	−1.07587e9			−1.73345			−0.866727	+	0.498783i	$0.833780\pi$
$854$			1.99345e8i			0.320061i
$855$	−2.03299e7	+	6.81455e7i	−0.0325265	+	0.109028i
$856$	−5.80291e8			−0.925176
$857$			3.17854e8i			0.504993i	0.967598	+	0.252496i	$0.0812516\pi$
$857$			3.17854e8i			0.504993i	−0.967598	+	0.252496i	$0.918748\pi$
$858$	1.89207e8	+	2.76217e7i	0.299555	+	0.0437310i
$859$	6.47990e8			1.02232			0.511162	−	0.859484i	$-0.329215\pi$
$859$	6.47990e8			1.02232			0.511162	+	0.859484i	$0.329215\pi$
$860$			5.55353e7i			0.0873119i
$861$	−5.49233e7	+	3.76222e8i	−0.0860492	+	0.589433i
$862$	1.76883e8			0.276162
$863$			2.10868e8i			0.328079i	0.986454	+	0.164040i	$0.0524525\pi$
$863$			2.10868e8i			0.328079i	−0.986454	+	0.164040i	$0.947548\pi$
$864$	−1.91395e8	+	4.12001e8i	−0.296749	+	0.638788i
$865$	−4.58449e7			−0.0708341
$866$			2.20311e6i			0.00339221i
$867$	4.67443e8	+	6.82403e7i	0.717251	+	0.104709i
$868$	−1.75428e8			−0.268250
$869$		−	4.86117e7i		−	0.0740767i
$870$	1.73240e7	−	1.18668e8i	0.0263081	−	0.180209i
$871$	9.21739e8			1.39493
$872$		−	4.31346e8i		−	0.650544i
$873$	−4.84749e8	−	1.44616e8i	−0.728575	−	0.217357i
$874$	−4.41017e8			−0.660573
$875$		−	3.35383e8i		−	0.500631i
$876$	3.19498e7	+	4.66423e6i	0.0475286	+	0.00693854i
$877$	7.26048e8			1.07638			0.538191	−	0.842823i	$-0.319108\pi$
$877$	7.26048e8			1.07638			0.538191	+	0.842823i	$0.319108\pi$
$878$		−	1.94209e8i		−	0.286937i
$879$	−9.78287e7	+	6.70122e8i	−0.144046	+	0.986704i
$880$	7.45208e7			0.109353
$881$			4.19910e8i			0.614084i	0.951696	+	0.307042i	$0.0993393\pi$
$881$			4.19910e8i			0.614084i	−0.951696	+	0.307042i	$0.900661\pi$
$882$	−4.79683e7	+	1.60789e8i	−0.0699114	+	0.234342i
$883$	−4.54761e8			−0.660543			−0.330271	−	0.943886i	$-0.607140\pi$
$883$	−4.54761e8			−0.660543			−0.330271	+	0.943886i	$0.607140\pi$
$884$		−	1.14767e8i		−	0.166135i
$885$	3.26079e8	+	4.76031e7i	0.470428	+	0.0686761i
$886$	−8.27304e8			−1.18950
$887$			1.56829e8i			0.224727i	0.993667	+	0.112363i	$0.0358421\pi$
$887$			1.56829e8i			0.224727i	−0.993667	+	0.112363i	$0.964158\pi$
$888$	−7.09089e7	+	4.85723e8i	−0.101266	+	0.693665i
$889$	9.72221e8			1.38376
$890$			2.47722e7i			0.0351395i
$891$	1.16852e8	−	1.78413e8i	0.165198	−	0.252228i
$892$	−1.59482e8			−0.224707
$893$		−	4.04531e8i		−	0.568064i
$894$	1.24996e9	+	1.82478e8i	1.74938	+	0.255386i
$895$	−3.60167e8			−0.502383
$896$			7.56560e8i			1.05177i
$897$	1.30589e8	−	8.94525e8i	0.180937	−	1.23941i
$898$	1.17239e9			1.61898
$899$			3.14134e8i			0.432350i
$900$	−2.35530e8	−	7.02659e7i	−0.323087	−	0.0963867i
$901$	−5.31261e8			−0.726329
$902$		−	1.73407e8i		−	0.236291i
$903$	5.21065e8	+	7.60684e7i	0.707667	+	0.103310i
$904$	1.64233e8			0.222308
$905$		−	3.56066e8i		−	0.480380i
$906$	−2.17200e8	+	1.48781e9i	−0.292063	+	2.00061i
$907$	9.54647e7			0.127944			0.0639721	−	0.997952i	$-0.479623\pi$
$907$	9.54647e7			0.127944			0.0639721	+	0.997952i	$0.479623\pi$
$908$		−	1.81038e8i		−	0.241830i
$909$	2.94901e8	−	9.88504e8i	0.392631	−	1.31609i
$910$	1.97959e8			0.262694
$911$		−	3.68267e8i		−	0.487089i	−0.969890	−	0.243544i	$-0.921690\pi$
$911$		−	3.68267e8i		−	0.487089i	0.969890	−	0.243544i	$-0.0783101\pi$
$912$	3.57902e8	+	5.22488e7i	0.471823	+	0.0688798i
$913$	−4.09376e8			−0.537910
$914$		−	1.56364e9i		−	2.04785i
$915$	−1.00123e7	+	6.85837e7i	−0.0130698	+	0.0895277i
$916$	−3.71877e7			−0.0483852
$917$		−	2.27727e8i		−	0.295329i
$918$	−4.30621e8	−	2.00045e8i	−0.556631	−	0.258583i
$919$	6.16278e7			0.0794018			0.0397009	−	0.999212i	$-0.487359\pi$
$919$	6.16278e7			0.0794018			0.0397009	+	0.999212i	$0.487359\pi$
$920$		−	2.46838e8i		−	0.316992i
$921$	2.90042e8	+	4.23422e7i	0.371263	+	0.0541994i
$922$	−4.51569e7			−0.0576145
$923$		−	6.37746e8i		−	0.811040i
$924$	−1.12794e7	+	7.72632e7i	−0.0142978	+	0.0979392i
$925$	−6.86539e8			−0.867441
$926$		−	1.27385e9i		−	1.60430i
$927$	5.57833e8	+	1.66419e8i	0.700269	+	0.208912i
$928$	−2.97825e8			−0.372664
$929$			1.10253e9i			1.37513i	0.726121	+	0.687567i	$0.241321\pi$
$929$			1.10253e9i			1.37513i	−0.726121	+	0.687567i	$0.758679\pi$
$930$	−2.23874e8	−	3.26826e7i	−0.278327	−	0.0406320i
$931$	6.52287e7			0.0808332
$932$			4.86503e7i			0.0600949i
$933$	3.25059e7	−	2.22664e8i	0.0400238	−	0.274161i
$934$	−7.87508e8			−0.966527
$935$			3.80304e7i			0.0465260i
$936$	−1.48499e8	+	4.97767e8i	−0.181091	+	0.607014i
$937$	−8.37765e8			−1.01837			−0.509183	−	0.860658i	$-0.670052\pi$
$937$	−8.37765e8			−1.01837			−0.509183	+	0.860658i	$0.670052\pi$
$938$			1.39615e9i			1.69170i
$939$	−4.22021e8	−	6.16094e7i	−0.509727	−	0.0744133i
$940$	−1.32462e8			−0.159481
$941$		−	4.31743e8i		−	0.518151i	−0.965857	−	0.259076i	$-0.916582\pi$
$941$		−	4.31743e8i		−	0.518151i	0.965857	−	0.259076i	$-0.0834179\pi$
$942$	−1.18598e8	+	8.12387e8i	−0.141881	+	0.971875i
$943$	−8.19824e8			−0.977655
$944$		−	1.67608e9i		−	1.99241i
$945$	9.30237e7	−	2.00245e8i	0.110230	−	0.237283i
$946$	−2.40168e8			−0.283688
$947$		−	4.93903e8i		−	0.581556i	−0.956791	−	0.290778i	$-0.906086\pi$
$947$		−	4.93903e8i		−	0.581556i	0.956791	−	0.290778i	$-0.0939141\pi$
$948$	−7.64482e7	−	1.11604e7i	−0.0897310	−	0.0130995i
$949$	9.54385e7			0.111667
$950$			3.54422e8i			0.413380i
$951$	−9.34131e7	+	6.39875e8i	−0.108609	+	0.743967i
$952$	−2.97139e8			−0.344388
$953$		−	6.00534e8i		−	0.693839i	−0.937895	−	0.346920i	$-0.887228\pi$
$953$		−	6.00534e8i		−	0.693839i	0.937895	−	0.346920i	$-0.112772\pi$
$954$	−1.34803e9	−	4.02159e8i	−1.55258	−	0.463184i
$955$	−3.44766e8			−0.395835
$956$		−	1.65847e8i		−	0.189816i
$957$	1.38353e8	+	2.01977e7i	0.157853	+	0.0230444i
$958$	−1.81843e8			−0.206824
$959$		−	2.23000e7i		−	0.0252842i
$960$	−1.53666e7	+	1.05260e8i	−0.0173686	+	0.118974i
$961$	−2.94872e8			−0.332249
$962$		−	8.48844e8i		−	0.953460i
$963$	3.19970e8	−	1.07253e9i	0.358286	−	1.20097i
$964$	4.10966e8			0.458749
$965$		−	1.39313e8i		−	0.155028i
$966$	1.35493e9	+	1.97802e8i	1.50310	+	0.219432i
$967$	1.26092e9			1.39446			0.697231	−	0.716847i	$-0.254415\pi$
$967$	1.26092e9			1.39446			0.697231	+	0.716847i	$0.254415\pi$
$968$			6.08712e7i			0.0671097i
$969$	−2.66643e7	+	1.82649e8i	−0.0293061	+	0.200746i
$970$	2.38853e8			0.261708
$971$			5.45286e7i			0.0595617i	0.999556	+	0.0297808i	$0.00948094\pi$
$971$			5.45286e7i			0.0595617i	−0.999556	+	0.0297808i	$0.990519\pi$
$972$	−2.53750e8	−	2.24726e8i	−0.276317	−	0.244711i
$973$	−1.29254e9			−1.40316
$974$		−	1.57561e8i		−	0.170518i
$975$	−7.18883e8	−	1.04947e8i	−0.775612	−	0.113229i
$976$	3.52527e8			0.379177
$977$		−	1.11457e9i		−	1.19515i	−0.801812	−	0.597577i	$-0.796130\pi$
$977$		−	1.11457e9i		−	1.19515i	0.801812	−	0.597577i	$-0.203870\pi$
$978$	1.67617e8	−	1.14816e9i	0.179184	−	1.22740i
$979$	−2.88815e7			−0.0307802
$980$		−	2.13589e7i		−	0.0226934i
$981$	7.97244e8	+	2.37843e8i	0.844470	+	0.251932i
$982$	−8.78774e8			−0.927989
$983$			1.25423e9i			1.32044i	0.751074	+	0.660218i	$0.229536\pi$
$983$			1.25423e9i			1.32044i	−0.751074	+	0.660218i	$0.770464\pi$
$984$	4.66133e8	+	6.80491e7i	0.489243	+	0.0714228i
$985$	4.42650e8			0.463182
$986$		−	3.11285e8i		−	0.324734i
$987$	−1.81438e8	+	1.24284e9i	−0.188702	+	1.29260i
$988$	−1.18139e8			−0.122496
$989$			1.13545e9i			1.17376i
$990$	−2.87886e7	+	9.64990e7i	−0.0296699	+	0.0994528i
$991$	3.84253e7			0.0394817			0.0197409	−	0.999805i	$-0.493716\pi$
$991$	3.84253e7			0.0394817			0.0197409	+	0.999805i	$0.493716\pi$
$992$			5.61864e8i			0.575567i
$993$	1.62480e9	+	2.37199e8i	1.65941	+	0.242251i
$994$	9.65990e8			0.983589
$995$			1.10209e8i			0.111879i
$996$	−9.39856e7	+	6.43796e8i	−0.0951225	+	0.651584i
$997$	1.13090e9			1.14114			0.570571	−	0.821248i	$-0.306722\pi$
$997$	1.13090e9			1.14114			0.570571	+	0.821248i	$0.306722\pi$
$998$			2.35287e8i			0.236705i
$999$	−8.58647e8	−	3.98884e8i	−0.861228	−	0.400083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.5	✓	20
3.2	odd	2	inner	33.7.b.a.23.16	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.5	✓	20	1.1	even	1	trivial
33.7.b.a.23.16	yes	20	3.2	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-9.36068i q^{2} +(26.7168 + 3.90029i) q^{3} -23.6224 q^{4} -36.7722i q^{5} +(36.5094 - 250.088i) q^{6} +305.058 q^{7} -377.962i q^{8} +(698.575 + 208.407i) q^{9} +O(q^{10})\)	\(q-9.36068i q^{2} +(26.7168 + 3.90029i) q^{3} -23.6224 q^{4} -36.7722i q^{5} +(36.5094 - 250.088i) q^{6} +305.058 q^{7} -377.962i q^{8} +(698.575 + 208.407i) q^{9} -344.213 q^{10} -401.312i q^{11} +(-631.115 - 92.1342i) q^{12} -1885.23 q^{13} -2855.55i q^{14} +(143.422 - 982.437i) q^{15} -5049.82 q^{16} -2577.08i q^{17} +(1950.83 - 6539.14i) q^{18} -2652.80 q^{19} +868.648i q^{20} +(8150.17 + 1189.82i) q^{21} -3756.55 q^{22} +17760.0i q^{23} +(1474.16 - 10097.9i) q^{24} +14272.8 q^{25} +17647.0i q^{26} +(17850.9 + 8292.61i) q^{27} -7206.20 q^{28} +12903.9i q^{29} +(-9196.28 - 1342.53i) q^{30} +24344.0 q^{31} +23080.2i q^{32} +(1565.23 - 10721.8i) q^{33} -24123.3 q^{34} -11217.7i q^{35} +(-16502.0 - 4923.06i) q^{36} -48101.2 q^{37} +24832.0i q^{38} +(-50367.3 - 7352.95i) q^{39} -13898.5 q^{40} +46161.2i q^{41} +(11137.5 - 76291.2i) q^{42} +63933.0 q^{43} +9479.94i q^{44} +(7663.58 - 25688.2i) q^{45} +166246. q^{46} +152492. i q^{47} +(-134915. - 19695.8i) q^{48} -24588.7 q^{49} -133603. i q^{50} +(10051.4 - 68851.5i) q^{51} +44533.7 q^{52} -206148. i q^{53} +(77624.5 - 167096. i) q^{54} -14757.1 q^{55} -115300. i q^{56} +(-70874.3 - 10346.7i) q^{57} +120790. q^{58} +331908. i q^{59} +(-3387.98 + 23207.5i) q^{60} -69809.8 q^{61} -227877. i q^{62} +(213106. + 63576.1i) q^{63} -107142. q^{64} +69324.1i q^{65} +(-100363. - 14651.6i) q^{66} -488926. q^{67} +60876.9i q^{68} +(-69269.3 + 474491. i) q^{69} -105005. q^{70} +338285. i q^{71} +(78769.8 - 264035. i) q^{72} -50624.3 q^{73} +450260. i q^{74} +(381324. + 55668.1i) q^{75} +62665.4 q^{76} -122423. i q^{77} +(-68828.6 + 471473. i) q^{78} +121132. q^{79} +185693. i q^{80} +(444574. + 291176. i) q^{81} +432100. q^{82} -1.02009e6i q^{83} +(-192527. - 28106.3i) q^{84} -94765.2 q^{85} -598457. i q^{86} +(-50329.1 + 344752. i) q^{87} -151681. q^{88} -71967.7i q^{89} +(-240459. - 71736.3i) q^{90} -575105. q^{91} -419534. i q^{92} +(650395. + 94948.8i) q^{93} +1.42743e6 q^{94} +97549.3i q^{95} +(-90019.4 + 616628. i) q^{96} -693911. q^{97} +230167. i q^{98} +(83636.0 - 280346. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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