LMFDB - Embedded newform 33.7.b.a.23.15

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			23.15
Root			$9.18066i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.18066i q^{2} +(-4.20063 - 26.6712i) q^{3} -20.2844 q^{4} +92.7007i q^{5} +(244.859 - 38.5645i) q^{6} -527.539 q^{7} +401.338i q^{8} +(-693.709 + 224.072i) q^{9} +O(q^{10})$	\(q+9.18066i q^{2} +(-4.20063 - 26.6712i) q^{3} -20.2844 q^{4} +92.7007i q^{5} +(244.859 - 38.5645i) q^{6} -527.539 q^{7} +401.338i q^{8} +(-693.709 + 224.072i) q^{9} -851.053 q^{10} +401.312i q^{11} +(85.2074 + 541.011i) q^{12} -1318.71 q^{13} -4843.16i q^{14} +(2472.44 - 389.401i) q^{15} -4982.75 q^{16} -3885.27i q^{17} +(-2057.13 - 6368.71i) q^{18} -2931.39 q^{19} -1880.38i q^{20} +(2216.00 + 14070.1i) q^{21} -3684.30 q^{22} +20992.8i q^{23} +(10704.2 - 1685.87i) q^{24} +7031.59 q^{25} -12106.6i q^{26} +(8890.29 + 17560.8i) q^{27} +10700.8 q^{28} -4509.96i q^{29} +(3574.96 + 22698.6i) q^{30} -29792.3 q^{31} -20059.3i q^{32} +(10703.5 - 1685.76i) q^{33} +35669.3 q^{34} -48903.2i q^{35} +(14071.5 - 4545.17i) q^{36} +96389.8 q^{37} -26912.1i q^{38} +(5539.40 + 35171.5i) q^{39} -37204.3 q^{40} -65052.9i q^{41} +(-129173. + 20344.3i) q^{42} +26395.5 q^{43} -8140.38i q^{44} +(-20771.6 - 64307.3i) q^{45} -192728. q^{46} +121272. i q^{47} +(20930.7 + 132896. i) q^{48} +160649. q^{49} +64554.6i q^{50} +(-103625. + 16320.6i) q^{51} +26749.2 q^{52} -77720.0i q^{53} +(-161220. + 81618.7i) q^{54} -37201.9 q^{55} -211721. i q^{56} +(12313.7 + 78183.8i) q^{57} +41404.4 q^{58} +27953.1i q^{59} +(-50152.1 + 7898.78i) q^{60} -381430. q^{61} -273513. i q^{62} +(365959. - 118207. i) q^{63} -134738. q^{64} -122245. i q^{65} +(15476.4 + 98264.9i) q^{66} +283312. q^{67} +78810.4i q^{68} +(559905. - 88183.1i) q^{69} +448964. q^{70} +302771. i q^{71} +(-89928.5 - 278412. i) q^{72} -291126. q^{73} +884922. i q^{74} +(-29537.1 - 187541. i) q^{75} +59461.6 q^{76} -211708. i q^{77} +(-322898. + 50855.3i) q^{78} -463355. q^{79} -461904. i q^{80} +(431025. - 310882. i) q^{81} +597228. q^{82} +869836. i q^{83} +(-44950.3 - 285405. i) q^{84} +360167. q^{85} +242328. i q^{86} +(-120286. + 18944.7i) q^{87} -161061. q^{88} +162920. i q^{89} +(590383. - 190697. i) q^{90} +695669. q^{91} -425828. i q^{92} +(125147. + 794598. i) q^{93} -1.11336e6 q^{94} -271742. i q^{95} +(-535005. + 84261.6i) q^{96} -1.08608e6 q^{97} +1.47486e6i q^{98} +(-89922.7 - 278394. 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 $

$2$			9.18066i			1.14758i	0.819002	+	0.573791i	$0.194528\pi$
$2$			9.18066i			1.14758i	−0.819002	+	0.573791i	$0.805472\pi$
$3$	−4.20063	−	26.6712i	−0.155579	−	0.987823i
$3$	−4.20063	−	26.6712i	−0.155579	−	0.987823i
$4$	−20.2844			−0.316944
$5$			92.7007i			0.741605i	0.928712	+	0.370803i	$0.120917\pi$
$5$			92.7007i			0.741605i	−0.928712	+	0.370803i	$0.879083\pi$
$6$	244.859	−	38.5645i	1.13361	−	0.178540i
$7$	−527.539			−1.53802			−0.769008	−	0.639240i	$-0.779249\pi$
$7$	−527.539			−1.53802			−0.769008	+	0.639240i	$0.779249\pi$
$8$			401.338i			0.783862i
$9$	−693.709	+	224.072i	−0.951590	+	0.307369i
$10$	−851.053			−0.851053
$11$			401.312i			0.301511i
$11$			401.312i			0.301511i
$12$	85.2074	+	541.011i	0.0493098	+	0.313085i
$13$	−1318.71			−0.600230			−0.300115	−	0.953903i	$-0.597025\pi$
$13$	−1318.71			−0.600230			−0.300115	+	0.953903i	$0.597025\pi$
$14$		−	4843.16i		−	1.76500i
$15$	2472.44	−	389.401i	0.732575	−	0.115378i
$16$	−4982.75			−1.21649
$17$		−	3885.27i		−	0.790813i	−0.918506	−	0.395407i	$-0.870604\pi$
$17$		−	3885.27i		−	0.790813i	0.918506	−	0.395407i	$-0.129396\pi$
$18$	−2057.13	−	6368.71i	−0.352731	−	1.09203i
$19$	−2931.39			−0.427379			−0.213689	−	0.976902i	$-0.568548\pi$
$19$	−2931.39			−0.427379			−0.213689	+	0.976902i	$0.568548\pi$
$20$		−	1880.38i		−	0.235048i
$21$	2216.00	+	14070.1i	0.239283	+	1.51929i
$22$	−3684.30			−0.346009
$23$			20992.8i			1.72539i	0.505723	+	0.862696i	$0.331226\pi$
$23$			20992.8i			1.72539i	−0.505723	+	0.862696i	$0.668774\pi$
$24$	10704.2	−	1685.87i	0.774318	−	0.121952i
$25$	7031.59			0.450021
$26$		−	12106.6i		−	0.688813i
$27$	8890.29	+	17560.8i	0.451674	+	0.892183i
$28$	10700.8			0.487465
$29$		−	4509.96i		−	0.184918i	−0.995717	−	0.0924588i	$-0.970527\pi$
$29$		−	4509.96i		−	0.184918i	0.995717	−	0.0924588i	$-0.0294726\pi$
$30$	3574.96	+	22698.6i	0.132406	+	0.840690i
$31$	−29792.3			−1.00004			−0.500022	−	0.866012i	$-0.666675\pi$
$31$	−29792.3			−1.00004			−0.500022	+	0.866012i	$0.666675\pi$
$32$		−	20059.3i		−	0.612160i
$33$	10703.5	−	1685.76i	0.297840	−	0.0469088i
$34$	35669.3			0.907523
$35$		−	48903.2i		−	1.14060i
$36$	14071.5	−	4545.17i	0.301601	−	0.0974188i
$37$	96389.8			1.90294			0.951472	−	0.307736i	$-0.0995714\pi$
$37$	96389.8			1.90294			0.951472	+	0.307736i	$0.0995714\pi$
$38$		−	26912.1i		−	0.490452i
$39$	5539.40	+	35171.5i	0.0933832	+	0.592922i
$40$	−37204.3			−0.581317
$41$		−	65052.9i		−	0.943876i	−0.881632	−	0.471938i	$-0.843555\pi$
$41$		−	65052.9i		−	0.943876i	0.881632	−	0.471938i	$-0.156445\pi$
$42$	−129173.	+	20344.3i	−1.74351	+	0.274596i
$43$	26395.5			0.331990			0.165995	−	0.986127i	$-0.446916\pi$
$43$	26395.5			0.331990			0.165995	+	0.986127i	$0.446916\pi$
$44$		−	8140.38i		−	0.0955623i
$45$	−20771.6	−	64307.3i	−0.227946	−	0.705705i
$46$	−192728.			−1.98003
$47$			121272.i			1.16807i	0.811729	+	0.584034i	$0.198527\pi$
$47$			121272.i			1.16807i	−0.811729	+	0.584034i	$0.801473\pi$
$48$	20930.7	+	132896.i	0.189260	+	1.20168i
$49$	160649.			1.36549
$50$			64554.6i			0.516437i
$51$	−103625.	+	16320.6i	−0.781184	+	0.123034i
$52$	26749.2			0.190240
$53$		−	77720.0i		−	0.522042i	−0.965333	−	0.261021i	$-0.915941\pi$
$53$		−	77720.0i		−	0.522042i	0.965333	−	0.261021i	$-0.0840591\pi$
$54$	−161220.	+	81618.7i	−1.02385	+	0.518332i
$55$	−37201.9			−0.223602
$56$		−	211721.i		−	1.20559i
$57$	12313.7	+	78183.8i	0.0664911	+	0.422175i
$58$	41404.4			0.212208
$59$			27953.1i			0.136105i	0.997682	+	0.0680525i	$0.0216785\pi$
$59$			27953.1i			0.136105i	−0.997682	+	0.0680525i	$0.978321\pi$
$60$	−50152.1	+	7898.78i	−0.232186	+	0.0365684i
$61$	−381430.			−1.68045			−0.840224	−	0.542239i	$-0.817577\pi$
$61$	−381430.			−1.68045			−0.840224	+	0.542239i	$0.817577\pi$
$62$		−	273513.i		−	1.14763i
$63$	365959.	−	118207.i	1.46356	−	0.472738i
$64$	−134738.			−0.513986
$65$		−	122245.i		−	0.445134i
$66$	15476.4	+	98264.9i	0.0538317	+	0.341796i
$67$	283312.			0.941976			0.470988	−	0.882140i	$-0.343897\pi$
$67$	283312.			0.941976			0.470988	+	0.882140i	$0.343897\pi$
$68$			78810.4i			0.250644i
$69$	559905.	−	88183.1i	1.70438	−	0.268434i
$70$	448964.			1.30893
$71$			302771.i			0.845940i	0.906144	+	0.422970i	$0.139012\pi$
$71$			302771.i			0.845940i	−0.906144	+	0.422970i	$0.860988\pi$
$72$	−89928.5	−	278412.i	−0.240935	−	0.745916i
$73$	−291126.			−0.748364			−0.374182	−	0.927355i	$-0.622076\pi$
$73$	−291126.			−0.748364			−0.374182	+	0.927355i	$0.622076\pi$
$74$			884922.i			2.18378i
$75$	−29537.1	−	187541.i	−0.0700138	−	0.444542i
$76$	59461.6			0.135455
$77$		−	211708.i		−	0.463729i
$78$	−322898.	+	50855.3i	−0.680426	+	0.107165i
$79$	−463355.			−0.939794			−0.469897	−	0.882721i	$-0.655709\pi$
$79$	−463355.			−0.939794			−0.469897	+	0.882721i	$0.655709\pi$
$80$		−	461904.i		−	0.902156i
$81$	431025.	−	310882.i	0.811049	−	0.584979i
$82$	597228.			1.08318
$83$			869836.i			1.52126i	0.649186	+	0.760630i	$0.275110\pi$
$83$			869836.i			1.52126i	−0.649186	+	0.760630i	$0.724890\pi$
$84$	−44950.3	−	285405.i	−0.0758393	−	0.481530i
$85$	360167.			0.586471
$86$			242328.i			0.380985i
$87$	−120286.	+	18944.7i	−0.182666	+	0.0287693i
$88$	−161061.			−0.236343
$89$			162920.i			0.231102i	0.993302	+	0.115551i	$0.0368634\pi$
$89$			162920.i			0.231102i	−0.993302	+	0.115551i	$0.963137\pi$
$90$	590383.	−	190697.i	0.809854	−	0.261587i
$91$	695669.			0.923163
$92$		−	425828.i		−	0.546853i
$93$	125147.	+	794598.i	0.155586	+	0.987868i
$94$	−1.11336e6			−1.34045
$95$		−	271742.i		−	0.316946i
$96$	−535005.	+	84261.6i	−0.604706	+	0.0952392i
$97$	−1.08608e6			−1.19000			−0.595001	−	0.803725i	$-0.702848\pi$
$97$	−1.08608e6			−1.19000			−0.595001	+	0.803725i	$0.702848\pi$
$98$			1.47486e6i			1.56701i
$99$	−89922.7	−	278394.i	−0.0926752	−	0.286915i
$100$	−142632.			−0.142632
$101$		−	597957.i		−	0.580371i	−0.956970	−	0.290185i	$-0.906283\pi$
$101$		−	597957.i		−	0.580371i	0.956970	−	0.290185i	$-0.0937170\pi$
$102$	−149833.	−	951344.i	−0.141191	−	0.896472i
$103$	−1.82566e6			−1.67073			−0.835367	−	0.549693i	$-0.814745\pi$
$103$	−1.82566e6			−1.67073			−0.835367	+	0.549693i	$0.814745\pi$
$104$		−	529246.i		−	0.470498i
$105$	−1.30431e6	+	205424.i	−1.12671	+	0.177453i
$106$	713520.			0.599085
$107$			230579.i			0.188222i	0.995562	+	0.0941108i	$0.0300008\pi$
$107$			230579.i			0.188222i	−0.995562	+	0.0941108i	$0.969999\pi$
$108$	−180335.	−	356212.i	−0.143155	−	0.282772i
$109$	1.59071e6			1.22832			0.614161	−	0.789180i	$-0.289494\pi$
$109$	1.59071e6			1.22832			0.614161	+	0.789180i	$0.289494\pi$
$110$		−	341537.i		−	0.256602i
$111$	−404898.	−	2.57083e6i	−0.296058	−	1.87977i
$112$	2.62859e6			1.87098
$113$			636982.i			0.441460i	0.975335	+	0.220730i	$0.0708440\pi$
$113$			636982.i			0.441460i	−0.975335	+	0.220730i	$0.929156\pi$
$114$	−717779.	+	113048.i	−0.484480	+	0.0763040i
$115$	−1.94605e6			−1.27956
$116$			91481.9i			0.0586086i
$117$	914799.	−	295485.i	0.571173	−	0.184492i
$118$	−256628.			−0.156192
$119$			2.04963e6i			1.21628i
$120$	156281.	+	992283.i	0.0904406	+	0.574238i
$121$	−161051.			−0.0909091
$122$		−	3.50178e6i		−	1.92845i
$123$	−1.73504e6	+	273263.i	−0.932383	+	0.146847i
$124$	604321.			0.316959
$125$			2.10028e6i			1.07534i
$126$	1.08522e6	+	3.35974e6i	0.542506	+	1.67956i
$127$	1.50887e6			0.736615			0.368307	−	0.929704i	$-0.379937\pi$
$127$	1.50887e6			0.736615			0.368307	+	0.929704i	$0.379937\pi$
$128$		−	2.52078e6i		−	1.20200i
$129$	−110878.	−	704001.i	−0.0516506	−	0.327947i
$130$	1.12229e6			0.510828
$131$		−	135648.i		−	0.0603391i	−0.999545	−	0.0301695i	$-0.990395\pi$
$131$		−	135648.i		−	0.0603391i	0.999545	−	0.0301695i	$-0.00960472\pi$
$132$	−217114.	+	34194.7i	−0.0943987	+	0.0148675i
$133$	1.54642e6			0.657315
$134$			2.60099e6i			1.08099i
$135$	−1.62790e6	+	824136.i	−0.661648	+	0.334964i
$136$	1.55930e6			0.619889
$137$		−	1.16046e6i		−	0.451304i	−0.974208	−	0.225652i	$-0.927549\pi$
$137$		−	1.16046e6i		−	0.451304i	0.974208	−	0.225652i	$-0.0724512\pi$
$138$	809579.	+	5.14029e6i	0.308051	+	1.95592i
$139$	−34562.9			−0.0128696			−0.00643481	−	0.999979i	$-0.502048\pi$
$139$	−34562.9			−0.0128696			−0.00643481	+	0.999979i	$0.502048\pi$
$140$			991975.i			0.361507i
$141$	3.23448e6	−	509420.i	1.15385	−	0.181727i
$142$	−2.77964e6			−0.970785
$143$		−	529212.i		−	0.180976i
$144$	3.45658e6	−	1.11649e6i	1.15760	−	0.373911i
$145$	418076.			0.137136
$146$		−	2.67273e6i		−	0.858808i
$147$	−674825.	−	4.28470e6i	−0.212441	−	1.34886i
$148$	−1.95521e6			−0.603127
$149$			3.73756e6i			1.12987i	0.825135	+	0.564936i	$0.191099\pi$
$149$			3.73756e6i			1.12987i	−0.825135	+	0.564936i	$0.808901\pi$
$150$	1.72175e6	−	271170.i	0.510148	−	0.0803466i
$151$	−3.21860e6			−0.934838			−0.467419	−	0.884036i	$-0.654816\pi$
$151$	−3.21860e6			−0.934838			−0.467419	+	0.884036i	$0.654816\pi$
$152$		−	1.17648e6i		−	0.335006i
$153$	870579.	+	2.69525e6i	0.243071	+	0.752530i
$154$	1.94361e6			0.532167
$155$		−	2.76177e6i		−	0.741639i
$156$	−112364.	−	713434.i	−0.0295973	−	0.187923i
$157$	−2.10390e6			−0.543657			−0.271829	−	0.962346i	$-0.587628\pi$
$157$	−2.10390e6			−0.543657			−0.271829	+	0.962346i	$0.587628\pi$
$158$		−	4.25390e6i		−	1.07849i
$159$	−2.07289e6	+	326473.i	−0.515685	+	0.0812186i
$160$	1.85951e6			0.453981
$161$		−	1.10745e7i		−	2.65368i
$162$	2.85410e6	+	3.95709e6i	0.671311	+	0.930745i
$163$	4.24042e6			0.979142			0.489571	−	0.871963i	$-0.337153\pi$
$163$	4.24042e6			0.979142			0.489571	+	0.871963i	$0.337153\pi$
$164$			1.31956e6i			0.299156i
$165$	156271.	+	992219.i	0.0347878	+	0.220880i
$166$	−7.98567e6			−1.74577
$167$		−	1.13602e6i		−	0.243914i	−0.992535	−	0.121957i	$-0.961083\pi$
$167$		−	1.13602e6i		−	0.243914i	0.992535	−	0.121957i	$-0.0389169\pi$
$168$	−5.64687e6	+	889363.i	−1.19091	+	0.187565i
$169$	−3.08782e6			−0.639724
$170$			3.30657e6i			0.673024i
$171$	2.03353e6	−	656843.i	0.406690	−	0.131363i
$172$	−535418.			−0.105222
$173$			8.64216e6i			1.66911i	0.550928	+	0.834553i	$0.314274\pi$
$173$			8.64216e6i			1.66911i	−0.550928	+	0.834553i	$0.685726\pi$
$174$	−173924.	−	1.10431e6i	−0.0330151	−	0.209624i
$175$	−3.70944e6			−0.692140
$176$		−	1.99963e6i		−	0.366786i
$177$	745544.	−	117421.i	0.134448	−	0.0211751i
$178$	−1.49571e6			−0.265209
$179$		−	8.59955e6i		−	1.49940i	−0.661779	−	0.749699i	$-0.730198\pi$
$179$		−	8.59955e6i		−	1.49940i	0.661779	−	0.749699i	$-0.269802\pi$
$180$	421341.	+	1.30444e6i	0.0722463	+	0.223669i
$181$	−233395.			−0.0393600			−0.0196800	−	0.999806i	$-0.506265\pi$
$181$	−233395.			−0.0393600			−0.0196800	+	0.999806i	$0.506265\pi$
$182$			6.38670e6i			1.05941i
$183$	1.60225e6	+	1.01732e7i	0.261442	+	1.65999i
$184$	−8.42521e6			−1.35247
$185$			8.93540e6i			1.41123i
$186$	−7.29493e6	+	1.14893e6i	−1.13366	+	0.178548i
$187$	1.55920e6			0.238439
$188$		−	2.45994e6i		−	0.370213i
$189$	−4.68998e6	−	9.26403e6i	−0.694681	−	1.37219i
$190$	2.49477e6			0.363722
$191$			8.00179e6i			1.14838i	0.818721	+	0.574192i	$0.194684\pi$
$191$			8.00179e6i			1.14838i	−0.818721	+	0.574192i	$0.805316\pi$
$192$	565986.	+	3.59364e6i	0.0799654	+	0.507728i
$193$	1.32758e7			1.84667			0.923336	−	0.383994i	$-0.125452\pi$
$193$	1.32758e7			1.84667			0.923336	+	0.383994i	$0.125452\pi$
$194$		−	9.97095e6i		−	1.36563i
$195$	−3.26042e6	+	513506.i	−0.439714	+	0.0692534i
$196$	−3.25867e6			−0.432785
$197$			4.02813e6i			0.526872i	0.964677	+	0.263436i	$0.0848558\pi$
$197$			4.02813e6i			0.526872i	−0.964677	+	0.263436i	$0.915144\pi$
$198$	2.55584e6	−	825549.i	0.329259	−	0.106352i
$199$	1.48110e7			1.87943			0.939713	−	0.341963i	$-0.111092\pi$
$199$	1.48110e7			1.87943			0.939713	+	0.341963i	$0.111092\pi$
$200$			2.82204e6i			0.352755i
$201$	−1.19009e6	−	7.55627e6i	−0.146552	−	0.930506i
$202$	5.48964e6			0.666023
$203$			2.37918e6i			0.284406i
$204$	2.10197e6	−	331053.i	0.247592	−	0.0389949i
$205$	6.03045e6			0.699984
$206$		−	1.67607e7i		−	1.91730i
$207$	−4.70391e6	−	1.45629e7i	−0.530332	−	1.64187i
$208$	6.57078e6			0.730174
$209$		−	1.17640e6i		−	0.128860i
$210$	−1.88593e6	−	1.19744e7i	−0.203642	−	1.29299i
$211$	−1.50497e7			−1.60206			−0.801031	−	0.598623i	$-0.795715\pi$
$211$	−1.50497e7			−1.60206			−0.801031	+	0.598623i	$0.795715\pi$
$212$			1.57651e6i			0.165458i
$213$	8.07528e6	−	1.27183e6i	0.835639	−	0.131610i
$214$	−2.11687e6			−0.216000
$215$			2.44688e6i			0.246205i
$216$	−7.04783e6	+	3.56801e6i	−0.699349	+	0.354050i
$217$	1.57166e7			1.53808
$218$			1.46038e7i			1.40960i
$219$	1.22291e6	+	7.76469e6i	0.116430	+	0.739251i
$220$	754619.			0.0708695
$221$			5.12352e6i			0.474670i
$222$	2.36019e7	−	3.71723e6i	2.15719	−	0.339751i
$223$	−2.35455e6			−0.212321			−0.106161	−	0.994349i	$-0.533856\pi$
$223$	−2.35455e6			−0.212321			−0.106161	+	0.994349i	$0.533856\pi$
$224$			1.05821e7i			0.941512i
$225$	−4.87788e6	+	1.57558e6i	−0.428236	+	0.138323i
$226$	−5.84791e6			−0.506612
$227$			710451.i			0.0607375i	0.999539	+	0.0303687i	$0.00966816\pi$
$227$			710451.i			0.0607375i	−0.999539	+	0.0303687i	$0.990332\pi$
$228$	−249776.	−	1.58591e6i	−0.0210740	−	0.133806i
$229$	7.83568e6			0.652484			0.326242	−	0.945286i	$-0.394218\pi$
$229$	7.83568e6			0.652484			0.326242	+	0.945286i	$0.394218\pi$
$230$		−	1.78660e7i		−	1.46840i
$231$	−5.64650e6	+	889305.i	−0.458082	+	0.0721464i
$232$	1.81001e6			0.144950
$233$			1.74190e7i			1.37707i	0.725205	+	0.688533i	$0.241745\pi$
$233$			1.74190e7i			1.37707i	−0.725205	+	0.688533i	$0.758255\pi$
$234$	2.71275e6	+	8.39845e6i	0.211720	+	0.655468i
$235$	−1.12420e7			−0.866246
$236$		−	567013.i		−	0.0431377i
$237$	1.94638e6	+	1.23582e7i	0.146212	+	0.928350i
$238$	−1.88169e7			−1.39578
$239$			8.93719e6i			0.654647i	0.944912	+	0.327324i	$0.106147\pi$
$239$			8.93719e6i			0.654647i	−0.944912	+	0.327324i	$0.893853\pi$
$240$	−1.23195e7	+	1.94029e6i	−0.891171	+	0.140356i
$241$	1.39851e7			0.999110			0.499555	−	0.866282i	$-0.333497\pi$
$241$	1.39851e7			0.999110			0.499555	+	0.866282i	$0.333497\pi$
$242$		−	1.47855e6i		−	0.104326i
$243$	−1.01022e7	−	1.01901e7i	−0.704038	−	0.710163i
$244$	7.73709e6			0.532609
$245$			1.48922e7i			1.01266i
$246$	−2.50873e6	−	1.59288e7i	−0.168519	−	1.06999i
$247$	3.86564e6			0.256526
$248$		−	1.19568e7i		−	0.783897i
$249$	2.31996e7	−	3.65386e6i	1.50274	−	0.236676i
$250$	−1.92820e7			−1.23405
$251$		−	1.05603e7i		−	0.667811i	−0.942606	−	0.333906i	$-0.891633\pi$
$251$		−	1.05603e7i		−	0.667811i	0.942606	−	0.333906i	$-0.108367\pi$
$252$	−7.42327e6	+	2.39776e6i	−0.463867	+	0.149832i
$253$	−8.42467e6			−0.520225
$254$			1.38524e7i			0.845326i
$255$	−1.51293e6	−	9.60609e6i	−0.0912425	−	0.579330i
$256$	1.45192e7			0.865409
$257$		−	5.63179e6i		−	0.331778i	−0.986144	−	0.165889i	$-0.946951\pi$
$257$		−	5.63179e6i		−	0.331778i	0.986144	−	0.165889i	$-0.0530493\pi$
$258$	6.46319e6	−	1.01793e6i	0.376346	−	0.0592733i
$259$	−5.08494e7			−2.92676
$260$			2.47967e6i			0.141083i
$261$	1.01055e6	+	3.12860e6i	0.0568379	+	0.175966i
$262$	1.24534e6			0.0692440
$263$		−	1.28255e7i		−	0.705027i	−0.935807	−	0.352514i	$-0.885327\pi$
$263$		−	1.28255e7i		−	0.705027i	0.935807	−	0.352514i	$-0.114673\pi$
$264$	676559.	+	4.29571e6i	0.0367700	+	0.233466i
$265$	7.20469e6			0.387149
$266$			1.41972e7i			0.754323i
$267$	4.34527e6	−	684366.i	0.228288	−	0.0359546i
$268$	−5.74682e6			−0.298554
$269$		−	3.54865e7i		−	1.82308i	−0.411210	−	0.911540i	$-0.634894\pi$
$269$		−	3.54865e7i		−	1.82308i	0.411210	−	0.911540i	$-0.365106\pi$
$270$	−7.56611e6	−	1.49452e7i	−0.384398	−	0.759295i
$271$	−2.14662e7			−1.07857			−0.539283	−	0.842125i	$-0.681305\pi$
$271$	−2.14662e7			−1.07857			−0.539283	+	0.842125i	$0.681305\pi$
$272$			1.93593e7i			0.962017i
$273$	−2.92225e6	−	1.85544e7i	−0.143625	−	0.911922i
$274$	1.06538e7			0.517908
$275$			2.82186e6i			0.135687i
$276$	−1.13574e7	+	1.78875e6i	−0.540194	+	0.0850788i
$277$	−1.97973e7			−0.931466			−0.465733	−	0.884925i	$-0.654209\pi$
$277$	−1.97973e7			−0.931466			−0.465733	+	0.884925i	$0.654209\pi$
$278$		−	317310.i		−	0.0147689i
$279$	2.06672e7	−	6.67563e6i	0.951633	−	0.307383i
$280$	1.96267e7			0.894074
$281$		−	3.15186e7i		−	1.42052i	−0.703939	−	0.710261i	$-0.748577\pi$
$281$		−	3.15186e7i		−	1.42052i	0.703939	−	0.710261i	$-0.251423\pi$
$282$	4.67681e6	+	2.96947e7i	0.208546	+	1.32413i
$283$	2.12607e7			0.938032			0.469016	−	0.883190i	$-0.344609\pi$
$283$	2.12607e7			0.938032			0.469016	+	0.883190i	$0.344609\pi$
$284$		−	6.14154e6i		−	0.268116i
$285$	−7.24769e6	+	1.14149e6i	−0.313087	+	0.0493102i
$286$	4.85851e6			0.207685
$287$			3.43179e7i			1.45170i
$288$	4.49472e6	+	1.39153e7i	0.188159	+	0.582526i
$289$	9.04228e6			0.374614
$290$			3.83821e6i			0.157375i
$291$	4.56223e6	+	2.89672e7i	0.185139	+	1.17551i
$292$	5.90533e6			0.237190
$293$		−	2.61042e7i		−	1.03779i	−0.854839	−	0.518893i	$-0.826344\pi$
$293$		−	2.61042e7i		−	1.03779i	0.854839	−	0.518893i	$-0.173656\pi$
$294$	3.93363e7	−	6.19534e6i	1.54793	−	0.243794i
$295$	−2.59127e6			−0.100936
$296$			3.86848e7i			1.49165i
$297$	−7.04737e6	+	3.56778e6i	−0.269003	+	0.136185i
$298$	−3.43132e7			−1.29662
$299$		−	2.76834e7i		−	1.03563i
$300$	599143.	+	3.80417e6i	0.0221905	+	0.140895i
$301$	−1.39247e7			−0.510605
$302$		−	2.95489e7i		−	1.07280i
$303$	−1.59482e7	+	2.51180e6i	−0.573304	+	0.0902935i
$304$	1.46064e7			0.519902
$305$		−	3.53588e7i		−	1.24623i
$306$	−2.47441e7	+	7.99249e6i	−0.863590	+	0.278944i
$307$	1.22355e7			0.422871			0.211436	−	0.977392i	$-0.432186\pi$
$307$	1.22355e7			0.422871			0.211436	+	0.977392i	$0.432186\pi$
$308$			4.29437e6i			0.146976i
$309$	7.66891e6	+	4.86925e7i	0.259931	+	1.65039i
$310$	2.53549e7			0.851091
$311$			5.55486e6i			0.184668i	0.995728	+	0.0923341i	$0.0294328\pi$
$311$			5.55486e6i			0.184668i	−0.995728	+	0.0923341i	$0.970567\pi$
$312$	−1.41156e7	+	2.22317e6i	−0.464769	+	0.0731995i
$313$	3.37402e7			1.10031			0.550154	−	0.835063i	$-0.314569\pi$
$313$	3.37402e7			1.10031			0.550154	+	0.835063i	$0.314569\pi$
$314$		−	1.93151e7i		−	0.623892i
$315$	1.09578e7	+	3.39246e7i	0.350585	+	1.08538i
$316$	9.39890e6			0.297862
$317$			5.46343e7i			1.71509i	0.514408	+	0.857546i	$0.328012\pi$
$317$			5.46343e7i			1.71509i	−0.514408	+	0.857546i	$0.671988\pi$
$318$	−2.99724e6	−	1.90305e7i	−0.0932050	−	0.591791i
$319$	1.80990e6			0.0557548
$320$		−	1.24903e7i		−	0.381175i
$321$	6.14984e6	−	968579.i	0.185930	−	0.0292833i
$322$	1.01672e8			3.04531
$323$			1.13892e7i			0.337977i
$324$	−8.74309e6	+	6.30606e6i	−0.257057	+	0.185406i
$325$	−9.27259e6			−0.270117
$326$			3.89298e7i			1.12365i
$327$	−6.68200e6	−	4.24263e7i	−0.191101	−	1.21337i
$328$	2.61082e7			0.739869
$329$		−	6.39759e7i		−	1.79651i
$330$	−9.10922e6	+	1.43467e6i	−0.253478	+	0.0399219i
$331$	−4.35383e6			−0.120057			−0.0600286	−	0.998197i	$-0.519119\pi$
$331$	−4.35383e6			−0.120057			−0.0600286	+	0.998197i	$0.519119\pi$
$332$		−	1.76441e7i		−	0.482154i
$333$	−6.68665e7	+	2.15983e7i	−1.81082	+	0.584906i
$334$	1.04294e7			0.279911
$335$			2.62632e7i			0.698575i
$336$	−1.10417e7	−	7.01078e7i	−0.291085	−	1.84820i
$337$	−3.70595e7			−0.968300			−0.484150	−	0.874985i	$-0.660871\pi$
$337$	−3.70595e7			−0.968300			−0.484150	+	0.874985i	$0.660871\pi$
$338$		−	2.83482e7i		−	0.734135i
$339$	1.69891e7	−	2.67573e6i	0.436085	−	0.0686819i
$340$	−7.30578e6			−0.185879
$341$		−	1.19560e7i		−	0.301525i
$342$	6.03025e6	+	1.86692e7i	0.150750	+	0.466710i
$343$	−2.26840e7			−0.562130
$344$			1.05935e7i			0.260234i
$345$	8.17464e6	+	5.19036e7i	0.199072	+	1.26398i
$346$	−7.93407e7			−1.91544
$347$		−	5.80336e6i		−	0.138896i	−0.997586	−	0.0694482i	$-0.977876\pi$
$347$		−	5.80336e6i		−	0.138896i	0.997586	−	0.0694482i	$-0.0221239\pi$
$348$	2.43994e6	−	384282.i	0.0578949	−	0.00911826i
$349$	−3.26877e7			−0.768968			−0.384484	−	0.923132i	$-0.625621\pi$
$349$	−3.26877e7			−0.768968			−0.384484	+	0.923132i	$0.625621\pi$
$350$		−	3.40551e7i		−	0.794287i
$351$	−1.17237e7	−	2.31576e7i	−0.271108	−	0.535515i
$352$	8.05002e6			0.184573
$353$			1.58584e7i			0.360526i	0.983618	+	0.180263i	$0.0576948\pi$
$353$			1.58584e7i			0.360526i	−0.983618	+	0.180263i	$0.942305\pi$
$354$	1.07800e6	+	6.84458e6i	0.0243001	+	0.154290i
$355$	−2.80671e7			−0.627353
$356$		−	3.30474e6i		−	0.0732465i
$357$	5.46662e7	−	8.60974e6i	1.20147	−	0.189228i
$358$	7.89496e7			1.72068
$359$			5.82010e7i			1.25790i	0.777444	+	0.628952i	$0.216516\pi$
$359$			5.82010e7i			1.25790i	−0.777444	+	0.628952i	$0.783484\pi$
$360$	2.58089e7	−	8.33643e6i	0.553175	−	0.178679i
$361$	−3.84528e7			−0.817347
$362$		−	2.14272e6i		−	0.0451689i
$363$	676516.	+	4.29543e6i	0.0141435	+	0.0898021i
$364$	−1.41113e7			−0.292591
$365$		−	2.69876e7i		−	0.554990i
$366$	−9.33967e7	+	1.47097e7i	−1.90497	+	0.300026i
$367$	−1.35672e6			−0.0274468			−0.0137234	−	0.999906i	$-0.504368\pi$
$367$	−1.35672e6			−0.0274468			−0.0137234	+	0.999906i	$0.504368\pi$
$368$		−	1.04602e8i		−	2.09892i
$369$	1.45765e7	+	4.51278e7i	0.290118	+	0.898183i
$370$	−8.20328e7			−1.61951
$371$			4.10003e7i			0.802908i
$372$	−2.53853e6	−	1.61180e7i	−0.0493121	−	0.313099i
$373$	5.56756e7			1.07285			0.536425	−	0.843948i	$-0.319775\pi$
$373$	5.56756e7			1.07285			0.536425	+	0.843948i	$0.319775\pi$
$374$			1.43145e7i			0.273628i
$375$	5.60171e7	−	8.82250e6i	1.06225	−	0.167301i
$376$	−4.86712e7			−0.915605
$377$			5.94731e6i			0.110993i
$378$	8.50499e7	−	4.30571e7i	1.57470	−	0.797203i
$379$	−3.90740e7			−0.717746			−0.358873	−	0.933386i	$-0.616839\pi$
$379$	−3.90740e7			−0.717746			−0.358873	+	0.933386i	$0.616839\pi$
$380$			5.51213e6i			0.100454i
$381$	−6.33820e6	−	4.02434e7i	−0.114602	−	0.727645i
$382$	−7.34617e7			−1.31787
$383$		−	8.13148e7i		−	1.44735i	−0.690141	−	0.723675i	$-0.742452\pi$
$383$		−	8.13148e7i		−	1.44735i	0.690141	−	0.723675i	$-0.257548\pi$
$384$	−6.72323e7	+	1.05889e7i	−1.18737	+	0.187006i
$385$	1.96254e7			0.343904
$386$			1.21881e8i			2.11921i
$387$	−1.83108e7	+	5.91449e6i	−0.315918	+	0.102043i
$388$	2.20306e7			0.377165
$389$			5.69242e7i			0.967048i	0.875331	+	0.483524i	$0.160643\pi$
$389$			5.69242e7i			0.967048i	−0.875331	+	0.483524i	$0.839357\pi$
$390$	−4.71432e6	−	2.99328e7i	−0.0794740	−	0.504608i
$391$	8.15627e7			1.36446
$392$			6.44743e7i			1.07036i
$393$	−3.61789e6	+	569806.i	−0.0596044	+	0.00938749i
$394$	−3.69809e7			−0.604629
$395$		−	4.29533e7i		−	0.696956i
$396$	1.82403e6	+	5.64706e6i	0.0293729	+	0.0909362i
$397$	4.97215e7			0.794645			0.397322	−	0.917679i	$-0.369939\pi$
$397$	4.97215e7			0.794645			0.397322	+	0.917679i	$0.369939\pi$
$398$			1.35975e8i			2.15680i
$399$	−6.49595e6	−	4.12450e7i	−0.102264	−	0.649311i
$400$	−3.50366e7			−0.547447
$401$			6.17789e6i			0.0958091i	0.998852	+	0.0479046i	$0.0152543\pi$
$401$			6.17789e6i			0.0958091i	−0.998852	+	0.0479046i	$0.984746\pi$
$402$	6.93715e7	−	1.09258e7i	1.06783	−	0.168180i
$403$	3.92873e7			0.600257
$404$			1.21292e7i			0.183945i
$405$	2.88189e7	+	3.99563e7i	0.433823	+	0.601478i
$406$	−2.18424e7			−0.326379
$407$			3.86823e7i			0.573759i
$408$	−6.55005e6	−	4.15885e7i	−0.0964416	−	0.612341i
$409$	3.56529e7			0.521105			0.260553	−	0.965460i	$-0.416095\pi$
$409$	3.56529e7			0.521105			0.260553	+	0.965460i	$0.416095\pi$
$410$			5.53634e7i			0.803289i
$411$	−3.09509e7	+	4.87467e6i	−0.445809	+	0.0702134i
$412$	3.70324e7			0.529530
$413$		−	1.47464e7i		−	0.209332i
$414$	1.33697e8	−	4.31849e7i	1.88418	−	0.608599i
$415$	−8.06344e7			−1.12817
$416$			2.64523e7i			0.367437i
$417$	145186.	+	921835.i	0.00200224	+	0.0127129i
$418$	1.08001e7			0.147877
$419$		−	3.35085e7i		−	0.455526i	−0.973717	−	0.227763i	$-0.926859\pi$
$419$		−	3.35085e7i		−	0.455526i	0.973717	−	0.227763i	$-0.0731412\pi$
$420$	2.64572e7	−	4.16692e6i	0.357105	−	0.0562428i
$421$	−2.57230e7			−0.344727			−0.172364	−	0.985033i	$-0.555140\pi$
$421$	−2.57230e7			−0.344727			−0.172364	+	0.985033i	$0.555140\pi$
$422$		−	1.38166e8i		−	1.83850i
$423$	−2.71737e7	−	8.41278e7i	−0.359028	−	1.11152i
$424$	3.11919e7			0.409209
$425$		−	2.73196e7i		−	0.355883i
$426$	1.16762e7	+	7.41364e7i	0.151034	+	0.958964i
$427$	2.01219e8			2.58455
$428$		−	4.67717e6i		−	0.0596557i
$429$	−1.41147e7	+	2.22302e6i	−0.178773	+	0.0281561i
$430$	−2.24640e7			−0.282541
$431$		−	1.36459e8i		−	1.70439i	−0.523225	−	0.852195i	$-0.675271\pi$
$431$		−	1.36459e8i		−	1.70439i	0.523225	−	0.852195i	$-0.324729\pi$
$432$	−4.42981e7	−	8.75012e7i	−0.549457	−	1.08533i
$433$	−3.59879e7			−0.443296			−0.221648	−	0.975127i	$-0.571144\pi$
$433$	−3.59879e7			−0.443296			−0.221648	+	0.975127i	$0.571144\pi$
$434$			1.44289e8i			1.76508i
$435$	−1.75618e6	−	1.11506e7i	−0.0213355	−	0.135466i
$436$	−3.22667e7			−0.389310
$437$		−	6.15382e7i		−	0.737396i
$438$	−7.12850e7	+	1.12271e7i	−0.848351	+	0.133612i
$439$	1.31429e8			1.55345			0.776724	−	0.629841i	$-0.216880\pi$
$439$	1.31429e8			1.55345			0.776724	+	0.629841i	$0.216880\pi$
$440$		−	1.49305e7i		−	0.175274i
$441$	−1.11443e8	+	3.59968e7i	−1.29939	+	0.419709i
$442$	−4.70373e7			−0.544723
$443$		−	902738.i		−	0.0103837i	−0.999987	−	0.00519183i	$-0.998347\pi$
$443$		−	902738.i		−	0.0103837i	0.999987	−	0.00519183i	$-0.00165262\pi$
$444$	8.21313e6	+	5.21479e7i	0.0938339	+	0.595783i
$445$	−1.51028e7			−0.171387
$446$		−	2.16163e7i		−	0.243656i
$447$	9.96853e7	−	1.57001e7i	1.11611	−	0.175784i
$448$	7.10798e7			0.790519
$449$		−	4.91803e7i		−	0.543315i	−0.962394	−	0.271658i	$-0.912428\pi$
$449$		−	4.91803e7i		−	0.543315i	0.962394	−	0.271658i	$-0.0875719\pi$
$450$	−1.44649e7	−	4.47821e7i	−0.158737	−	0.491436i
$451$	2.61065e7			0.284589
$452$		−	1.29208e7i		−	0.139918i
$453$	1.35201e7	+	8.58440e7i	0.145441	+	0.923455i
$454$	−6.52241e6			−0.0697012
$455$			6.44890e7i			0.684623i
$456$	−3.13781e7	+	4.94195e6i	−0.330927	+	0.0521199i
$457$	1.02021e7			0.106891			0.0534453	−	0.998571i	$-0.482980\pi$
$457$	1.02021e7			0.106891			0.0534453	+	0.998571i	$0.482980\pi$
$458$			7.19367e7i			0.748779i
$459$	6.82285e7	−	3.45411e7i	0.705550	−	0.357189i
$460$	3.94745e7			0.405549
$461$			1.20844e8i			1.23345i	0.787180	+	0.616724i	$0.211540\pi$
$461$			1.20844e8i			1.23345i	−0.787180	+	0.616724i	$0.788460\pi$
$462$	−8.16441e6	−	5.18386e7i	−0.0827940	−	0.525687i
$463$	8.57239e7			0.863692			0.431846	−	0.901947i	$-0.357862\pi$
$463$	8.57239e7			0.863692			0.431846	+	0.901947i	$0.357862\pi$
$464$			2.24720e7i			0.224951i
$465$	−7.36598e7	+	1.16012e7i	−0.732608	+	0.115383i
$466$	−1.59918e8			−1.58030
$467$			1.69170e8i			1.66102i	0.557007	+	0.830508i	$0.311950\pi$
$467$			1.69170e8i			1.66102i	−0.557007	+	0.830508i	$0.688050\pi$
$468$	−1.85562e7	+	5.99375e6i	−0.181030	+	0.0584737i
$469$	−1.49458e8			−1.44877
$470$		−	1.03209e8i		−	0.994088i
$471$	8.83769e6	+	5.61135e7i	0.0845816	+	0.537038i
$472$	−1.12186e7			−0.106688
$473$			1.05928e7i			0.100099i
$474$	−1.13457e8	+	1.78691e7i	−1.06536	+	0.167790i
$475$	−2.06123e7			−0.192330
$476$		−	4.15756e7i		−	0.385494i
$477$	1.74149e7	+	5.39151e7i	0.160459	+	0.496770i
$478$	−8.20492e7			−0.751261
$479$			1.40743e8i			1.28062i	0.768117	+	0.640309i	$0.221194\pi$
$479$			1.40743e8i			1.28062i	−0.768117	+	0.640309i	$0.778806\pi$
$480$	−7.81110e6	−	4.95954e7i	−0.0706299	−	0.448453i
$481$	−1.27110e8			−1.14220
$482$			1.28392e8i			1.14656i
$483$	−2.95372e8	+	4.65201e7i	−2.62137	+	0.412856i
$484$	3.26683e6			0.0288131
$485$		−	1.00681e8i		−	0.882512i
$486$	9.35514e7	−	9.27446e7i	0.814970	−	0.807941i
$487$	1.08499e8			0.939377			0.469688	−	0.882832i	$-0.344366\pi$
$487$	1.08499e8			0.939377			0.469688	+	0.882832i	$0.344366\pi$
$488$		−	1.53082e8i		−	1.31724i
$489$	−1.78124e7	−	1.13097e8i	−0.152334	−	0.967220i
$490$	−1.36720e8			−1.16210
$491$		−	7.17611e7i		−	0.606240i	−0.952952	−	0.303120i	$-0.901972\pi$
$491$		−	7.17611e7i		−	0.606240i	0.952952	−	0.303120i	$-0.0980283\pi$
$492$	3.51943e7	−	5.54299e6i	0.295514	−	0.0465424i
$493$	−1.75224e7			−0.146235
$494$			3.54891e7i			0.294384i
$495$	2.58073e7	−	8.33589e6i	0.212778	−	0.0687284i
$496$	1.48448e8			1.21655
$497$		−	1.59724e8i		−	1.30107i
$498$	3.35448e7	+	2.12988e8i	0.271605	+	1.72451i
$499$	−9.86768e6			−0.0794170			−0.0397085	−	0.999211i	$-0.512643\pi$
$499$	−9.86768e6			−0.0794170			−0.0397085	+	0.999211i	$0.512643\pi$
$500$		−	4.26030e7i		−	0.340824i
$501$	−3.02990e7	+	4.77199e6i	−0.240944	+	0.0379478i
$502$	9.69502e7			0.766368
$503$			5.29675e7i			0.416203i	0.978107	+	0.208101i	$0.0667284\pi$
$503$			5.29675e7i			0.416203i	−0.978107	+	0.208101i	$0.933272\pi$
$504$	4.74408e7	+	1.46873e8i	0.370562	+	1.14723i
$505$	5.54310e7			0.430406
$506$		−	7.73440e7i		−	0.597001i
$507$	1.29708e7	+	8.23561e7i	0.0995275	+	0.631934i
$508$	−3.06066e7			−0.233466
$509$		−	1.30233e8i		−	0.987568i	−0.869585	−	0.493784i	$-0.835613\pi$
$509$		−	1.30233e8i		−	0.987568i	0.869585	−	0.493784i	$-0.164387\pi$
$510$	8.81902e7	−	1.38897e7i	0.664829	−	0.104708i
$511$	1.53580e8			1.15099
$512$		−	2.80346e7i		−	0.208874i
$513$	−2.60609e7	−	5.14777e7i	−0.193036	−	0.381300i
$514$	5.17036e7			0.380742
$515$		−	1.69240e8i		−	1.23903i
$516$	2.24909e6	+	1.42803e7i	0.0163704	+	0.103941i
$517$	−4.86680e7			−0.352186
$518$		−	4.66831e8i		−	3.35869i
$519$	2.30497e8	−	3.63025e7i	1.64878	−	0.259678i
$520$	4.90615e7			0.348924
$521$			8.34952e7i			0.590402i	0.955435	+	0.295201i	$0.0953867\pi$
$521$			8.34952e7i			0.590402i	−0.955435	+	0.295201i	$0.904613\pi$
$522$	−2.87226e7	+	9.27755e6i	−0.201935	+	0.0652262i
$523$	−2.47513e8			−1.73019			−0.865094	−	0.501610i	$-0.832741\pi$
$523$	−2.47513e8			−1.73019			−0.865094	+	0.501610i	$0.832741\pi$
$524$			2.75154e6i			0.0191241i
$525$	1.55820e7	+	9.89353e7i	0.107682	+	0.683712i
$526$	1.17746e8			0.809076
$527$			1.15751e8i			0.790849i
$528$	−5.33327e7	+	8.39972e6i	−0.362320	+	0.0570641i
$529$	−2.92663e8			−1.97698
$530$			6.61438e7i			0.444285i
$531$	−6.26351e6	−	1.93913e7i	−0.0418345	−	0.129516i
$532$	−3.13683e7			−0.208332
$533$			8.57856e7i			0.566543i
$534$	6.28293e6	+	3.98925e7i	0.0412609	+	0.261979i
$535$	−2.13749e7			−0.139586
$536$			1.13704e8i			0.738380i
$537$	−2.29361e8	+	3.61235e7i	−1.48114	+	0.233275i
$538$	3.25789e8			2.09213
$539$			6.44701e7i			0.411711i
$540$	3.30211e7	−	1.67171e7i	0.209706	−	0.106165i
$541$	−1.82232e7			−0.115089			−0.0575444	−	0.998343i	$-0.518327\pi$
$541$	−1.82232e7			−0.115089			−0.0575444	+	0.998343i	$0.518327\pi$
$542$		−	1.97074e8i		−	1.23774i
$543$	980406.	+	6.22493e6i	0.00612359	+	0.0388808i
$544$	−7.79356e7			−0.484104
$545$			1.47460e8i			0.910931i
$546$	1.70341e8	−	2.68282e7i	1.04651	−	0.164821i
$547$	−3.10803e7			−0.189899			−0.0949497	−	0.995482i	$-0.530269\pi$
$547$	−3.10803e7			−0.189899			−0.0949497	+	0.995482i	$0.530269\pi$
$548$			2.35393e7i			0.143038i
$549$	2.64601e8	−	8.54677e7i	1.59910	−	0.516518i
$550$	−2.59065e7			−0.155711
$551$			1.32204e7i			0.0790299i
$552$	3.53912e7	+	2.24711e8i	0.210416	+	1.33600i
$553$	2.44438e8			1.44542
$554$		−	1.81752e8i		−	1.06893i
$555$	2.38318e8	−	3.75343e7i	1.39405	−	0.219558i
$556$	701089.			0.00407895
$557$		−	1.18250e8i		−	0.684281i	−0.939649	−	0.342141i	$-0.888848\pi$
$557$		−	1.18250e8i		−	0.684281i	0.939649	−	0.342141i	$-0.111152\pi$
$558$	6.12866e7	+	1.89739e8i	0.352747	+	1.09208i
$559$	−3.48079e7			−0.199270
$560$			2.43672e8i			1.38753i
$561$	−6.54963e6	−	4.15858e7i	−0.0370961	−	0.235536i
$562$	2.89361e8			1.63016
$563$			2.01387e8i			1.12851i	0.825600	+	0.564255i	$0.190837\pi$
$563$			2.01387e8i			1.12851i	−0.825600	+	0.564255i	$0.809163\pi$
$564$	−6.56097e7	+	1.03333e7i	−0.365705	+	0.0575973i
$565$	−5.90487e7			−0.327389
$566$			1.95187e8i			1.07647i
$567$	−2.27382e8	+	1.64002e8i	−1.24741	+	0.899706i
$568$	−1.21513e8			−0.663100
$569$			2.10616e8i			1.14329i	0.820502	+	0.571643i	$0.193694\pi$
$569$			2.10616e8i			1.14329i	−0.820502	+	0.571643i	$0.806306\pi$
$570$	−1.04796e7	−	6.65386e7i	−0.0565875	−	0.359293i
$571$	−1.65602e8			−0.889523			−0.444762	−	0.895649i	$-0.646712\pi$
$571$	−1.65602e8			−0.889523			−0.444762	+	0.895649i	$0.646712\pi$
$572$			1.07348e7i			0.0573594i
$573$	2.13418e8	−	3.36126e7i	1.13440	−	0.178664i
$574$	−3.15061e8			−1.66594
$575$			1.47613e8i			0.776463i
$576$	9.34693e7	−	3.01911e7i	0.489105	−	0.157983i
$577$	−2.48350e7			−0.129282			−0.0646409	−	0.997909i	$-0.520590\pi$
$577$	−2.48350e7			−0.129282			−0.0646409	+	0.997909i	$0.520590\pi$
$578$			8.30141e7i			0.429901i
$579$	−5.57668e7	−	3.54083e8i	−0.287303	−	1.82418i
$580$	−8.48044e6			−0.0434645
$581$		−	4.58873e8i		−	2.33972i
$582$	−2.65938e8	+	4.18843e7i	−1.34900	+	0.212462i
$583$	3.11899e7			0.157401
$584$		−	1.16840e8i		−	0.586614i
$585$	2.73917e7	+	8.48025e7i	0.136820	+	0.423585i
$586$	2.39654e8			1.19094
$587$			5.26785e7i			0.260447i	0.991485	+	0.130223i	$0.0415695\pi$
$587$			5.26785e7i			0.260447i	−0.991485	+	0.130223i	$0.958431\pi$
$588$	1.36885e7	+	8.69127e7i	0.0673321	+	0.427515i
$589$	8.73330e7			0.427398
$590$		−	2.37896e7i		−	0.115833i
$591$	1.07435e8	−	1.69207e7i	0.520457	−	0.0819702i
$592$	−4.80286e8			−2.31491
$593$		−	2.58808e8i		−	1.24112i	−0.784160	−	0.620559i	$-0.786906\pi$
$593$		−	2.58808e8i		−	1.24112i	0.784160	−	0.620559i	$-0.213094\pi$
$594$	−3.27545e7	−	6.46995e7i	−0.156283	−	0.308703i
$595$	−1.90002e8			−0.902002
$596$		−	7.58143e7i		−	0.358107i
$597$	−6.22156e7	−	3.95028e8i	−0.292399	−	1.85654i
$598$	2.54152e8			1.18847
$599$			1.47913e8i			0.688217i	0.938930	+	0.344108i	$0.111819\pi$
$599$			1.47913e8i			0.688217i	−0.938930	+	0.344108i	$0.888181\pi$
$600$	7.52673e7	−	1.18543e7i	0.348460	−	0.0548812i
$601$	3.08523e7			0.142123			0.0710615	−	0.997472i	$-0.477361\pi$
$601$	3.08523e7			0.142123			0.0710615	+	0.997472i	$0.477361\pi$
$602$		−	1.27838e8i		−	0.585961i
$603$	−1.96536e8	+	6.34822e7i	−0.896376	+	0.289534i
$604$	6.52875e7			0.296291
$605$		−	1.49295e7i		−	0.0674187i
$606$	−2.30599e7	−	1.46415e8i	−0.103619	−	0.657913i
$607$	1.59735e7			0.0714223			0.0357111	−	0.999362i	$-0.488630\pi$
$607$	1.59735e7			0.0714223			0.0357111	+	0.999362i	$0.488630\pi$
$608$			5.88016e7i			0.261624i
$609$	6.34556e7	−	9.99405e6i	0.280943	−	0.0442476i
$610$	3.24617e8			1.43015
$611$		−	1.59923e8i		−	0.701110i
$612$	−1.76592e7	−	5.46715e7i	−0.0770401	−	0.238510i
$613$	−8.53450e7			−0.370507			−0.185254	−	0.982691i	$-0.559311\pi$
$613$	−8.53450e7			−0.370507			−0.185254	+	0.982691i	$0.559311\pi$
$614$			1.12330e8i			0.485279i
$615$	−2.53317e7	−	1.60839e8i	−0.108903	−	0.691460i
$616$	8.49662e7			0.363500
$617$			9.16191e7i			0.390059i	0.980797	+	0.195030i	$0.0624803\pi$
$617$			9.16191e7i			0.390059i	−0.980797	+	0.195030i	$0.937520\pi$
$618$	−4.47029e8	+	7.04056e7i	−1.89396	+	0.298292i
$619$	2.10435e8			0.887248			0.443624	−	0.896213i	$-0.353693\pi$
$619$	2.10435e8			0.887248			0.443624	+	0.896213i	$0.353693\pi$
$620$			5.60209e7i			0.235058i
$621$	−3.68652e8	+	1.86632e8i	−1.53937	+	0.779314i
$622$	−5.09973e7			−0.211922
$623$		−	8.59466e7i		−	0.355439i
$624$	−2.76014e7	−	1.75251e8i	−0.113600	−	0.721283i
$625$	−8.48289e7			−0.347459
$626$			3.09757e8i			1.26269i
$627$	−3.13761e7	+	4.94163e6i	−0.127290	+	0.0200478i
$628$	4.26764e7			0.172309
$629$		−	3.74500e8i		−	1.50487i
$630$	−3.11450e8	+	1.00600e8i	−1.24557	+	0.402325i
$631$	3.98246e8			1.58512			0.792562	−	0.609791i	$-0.208747\pi$
$631$	3.98246e8			1.58512			0.792562	+	0.609791i	$0.208747\pi$
$632$		−	1.85962e8i		−	0.736669i
$633$	6.32180e7	+	4.01393e8i	0.249247	+	1.58255i
$634$	−5.01578e8			−1.96821
$635$			1.39873e8i			0.546277i
$636$	4.20474e7	−	6.62232e6i	0.163443	−	0.0257418i
$637$	−2.11848e8			−0.819609
$638$			1.66160e7i			0.0639832i
$639$	−6.78425e7	−	2.10035e8i	−0.260016	−	0.804988i
$640$	2.33678e8			0.891411
$641$			1.32899e8i			0.504600i	0.967649	+	0.252300i	$0.0811870\pi$
$641$			1.32899e8i			0.504600i	−0.967649	+	0.252300i	$0.918813\pi$
$642$	8.89219e6	+	5.64595e7i	0.0336050	+	0.213369i
$643$	−3.27585e8			−1.23223			−0.616114	−	0.787657i	$-0.711294\pi$
$643$	−3.27585e8			−1.23223			−0.616114	+	0.787657i	$0.711294\pi$
$644$			2.24641e8i			0.841068i
$645$	6.52614e7	−	1.02784e7i	0.243207	−	0.0383044i
$646$	−1.04561e8			−0.387856
$647$			5.02023e8i			1.85358i	0.375582	+	0.926789i	$0.377443\pi$
$647$			5.02023e8i			1.85358i	−0.375582	+	0.926789i	$0.622557\pi$
$648$	1.24768e8	+	1.72986e8i	0.458543	+	0.635751i
$649$	−1.12179e7			−0.0410372
$650$		−	8.51285e7i		−	0.309981i
$651$	−6.60197e7	−	4.19182e8i	−0.239293	−	1.51936i
$652$	−8.60145e7			−0.310334
$653$			2.62090e8i			0.941264i	0.882330	+	0.470632i	$0.155974\pi$
$653$			2.62090e8i			0.941264i	−0.882330	+	0.470632i	$0.844026\pi$
$654$	3.89501e8	−	6.13451e7i	1.39244	−	0.219304i
$655$	1.25746e7			0.0447478
$656$			3.24142e8i			1.14822i
$657$	2.01957e8	−	6.52332e7i	0.712136	−	0.230024i
$658$	5.87341e8			2.06164
$659$		−	3.43070e7i		−	0.119874i	−0.998202	−	0.0599372i	$-0.980910\pi$
$659$		−	3.43070e7i		−	0.119874i	0.998202	−	0.0599372i	$-0.0190900\pi$
$660$	−3.16987e6	−	2.01266e7i	−0.0110258	−	0.0700066i
$661$	−1.98059e7			−0.0685787			−0.0342894	−	0.999412i	$-0.510917\pi$
$661$	−1.98059e7			−0.0685787			−0.0342894	+	0.999412i	$0.510917\pi$
$662$		−	3.99711e7i		−	0.137775i
$663$	1.36651e8	−	2.15220e7i	0.468890	−	0.0738486i
$664$	−3.49098e8			−1.19246
$665$			1.43355e8i			0.487468i
$666$	−1.98286e8	−	6.13878e8i	−0.671227	−	2.07807i
$667$	9.46768e7			0.319055
$668$			2.30435e7i			0.0773070i
$669$	9.89061e6	+	6.27988e7i	0.0330327	+	0.209736i
$670$	−2.41113e8			−0.801672
$671$		−	1.53072e8i		−	0.506674i
$672$	2.82236e8	−	4.44513e7i	0.930048	−	0.146479i
$673$	3.14596e8			1.03207			0.516034	−	0.856568i	$-0.327408\pi$
$673$	3.14596e8			1.03207			0.516034	+	0.856568i	$0.327408\pi$
$674$		−	3.40230e8i		−	1.11120i
$675$	6.25128e7	+	1.23481e8i	0.203263	+	0.401502i
$676$	6.26348e7			0.202757
$677$			3.96301e8i			1.27720i	0.769538	+	0.638601i	$0.220487\pi$
$677$			3.96301e8i			1.27720i	−0.769538	+	0.638601i	$0.779513\pi$
$678$	2.45649e7	+	1.55971e8i	0.0788181	+	0.500443i
$679$	5.72951e8			1.83024
$680$			1.44548e8i			0.459713i
$681$	1.89486e7	−	2.98434e6i	0.0599979	−	0.00944947i
$682$	1.09764e8			0.346024
$683$			1.58416e8i			0.497208i	0.968605	+	0.248604i	$0.0799718\pi$
$683$			1.58416e8i			0.497208i	−0.968605	+	0.248604i	$0.920028\pi$
$684$	−4.12491e7	+	1.33237e7i	−0.128898	+	0.0416347i
$685$	1.07576e8			0.334689
$686$		−	2.08254e8i		−	0.645090i
$687$	−3.29148e7	−	2.08987e8i	−0.101513	−	0.644539i
$688$	−1.31522e8			−0.403862
$689$			1.02490e8i			0.313345i
$690$	−4.76509e8	+	7.50485e7i	−1.45052	+	0.228452i
$691$	−4.72199e6			−0.0143117			−0.00715585	−	0.999974i	$-0.502278\pi$
$691$	−4.72199e6			−0.0143117			−0.00715585	+	0.999974i	$0.502278\pi$
$692$		−	1.75301e8i		−	0.529014i
$693$	4.74377e7	+	1.46864e8i	0.142536	+	0.441280i
$694$	5.32787e7			0.159395
$695$		−	3.20400e6i		−	0.00954418i
$696$	−7.60320e6	−	4.82753e7i	−0.0225512	−	0.143185i
$697$	−2.52748e8			−0.746430
$698$		−	3.00095e8i		−	0.882454i
$699$	4.64586e8	−	7.31707e7i	1.36030	−	0.214242i
$700$	7.52438e7			0.219370
$701$		−	5.18927e7i		−	0.150644i	−0.997159	−	0.0753221i	$-0.976001\pi$
$701$		−	5.18927e7i		−	0.150644i	0.997159	−	0.0753221i	$-0.0239985\pi$
$702$	2.12602e8	−	1.07631e8i	0.614548	−	0.311119i
$703$	−2.82556e8			−0.813278
$704$		−	5.40721e7i		−	0.154973i
$705$	4.72236e7	+	2.99839e8i	0.134770	+	0.855698i
$706$	−1.45591e8			−0.413733
$707$			3.15446e8i			0.892619i
$708$	−1.51229e7	+	2.38181e6i	−0.0426124	+	0.00671132i
$709$	−3.60623e7			−0.101185			−0.0505923	−	0.998719i	$-0.516111\pi$
$709$	−3.60623e7			−0.101185			−0.0505923	+	0.998719i	$0.516111\pi$
$710$		−	2.57674e8i		−	0.719939i
$711$	3.21434e8	−	1.03825e8i	0.894299	−	0.288863i
$712$	−6.53858e7			−0.181152
$713$		−	6.25426e8i		−	1.72547i
$714$	7.90430e7	+	5.01871e8i	0.217155	+	1.37879i
$715$	4.90583e7			0.134213
$716$			1.74437e8i			0.475226i
$717$	2.38366e8	−	3.75418e7i	0.646676	−	0.101849i
$718$	−5.34323e8			−1.44355
$719$			1.03757e8i			0.279145i	0.990212	+	0.139573i	$0.0445729\pi$
$719$			1.03757e8i			0.279145i	−0.990212	+	0.139573i	$0.955427\pi$
$720$	1.03500e8	+	3.20427e8i	0.277295	+	0.858483i
$721$	9.63105e8			2.56961
$722$		−	3.53022e8i		−	0.937973i
$723$	−5.87461e7	−	3.72999e8i	−0.155440	−	0.986944i
$724$	4.73428e6			0.0124749
$725$		−	3.17121e7i		−	0.0832169i
$726$	−3.94349e7	+	6.21086e6i	−0.103055	+	0.0162309i
$727$	−3.88322e8			−1.01062			−0.505311	−	0.862937i	$-0.668622\pi$
$727$	−3.88322e8			−1.01062			−0.505311	+	0.862937i	$0.668622\pi$
$728$			2.79198e8i			0.723633i
$729$	−2.29346e8	+	3.12242e8i	−0.591982	+	0.805951i
$730$	2.47764e8			0.636897
$731$		−	1.02554e8i		−	0.262542i
$732$	−3.25006e7	−	2.06358e8i	−0.0828626	−	0.526123i
$733$	4.38504e7			0.111343			0.0556713	−	0.998449i	$-0.482270\pi$
$733$	4.38504e7			0.111343			0.0556713	+	0.998449i	$0.482270\pi$
$734$		−	1.24556e7i		−	0.0314974i
$735$	3.97194e8	−	6.25568e7i	1.00032	−	0.157548i
$736$	4.21101e8			1.05622
$737$			1.13696e8i			0.284017i
$738$	−4.14303e8	+	1.33822e8i	−1.03074	+	0.332934i
$739$	−3.49447e8			−0.865861			−0.432930	−	0.901427i	$-0.642520\pi$
$739$	−3.49447e8			−0.865861			−0.432930	+	0.901427i	$0.642520\pi$
$740$		−	1.81250e8i		−	0.447282i
$741$	−1.62381e7	−	1.03101e8i	−0.0399100	−	0.253402i
$742$	−3.76410e8			−0.921403
$743$			1.35356e8i			0.329997i	0.986294	+	0.164999i	$0.0527619\pi$
$743$			1.35356e8i			0.329997i	−0.986294	+	0.164999i	$0.947238\pi$
$744$	−3.18902e8	+	5.02260e7i	−0.774352	+	0.121958i
$745$	−3.46474e8			−0.837919
$746$			5.11139e8i			1.23118i
$747$	−1.94906e8	−	6.03414e8i	−0.467588	−	1.44762i
$748$	−3.16275e7			−0.0755719
$749$		−	1.21640e8i		−	0.289488i
$750$	8.09963e7	+	5.14273e8i	0.191991	+	1.21902i
$751$	−2.43586e8			−0.575085			−0.287542	−	0.957768i	$-0.592838\pi$
$751$	−2.43586e8			−0.575085			−0.287542	+	0.957768i	$0.592838\pi$
$752$		−	6.04269e8i		−	1.42094i
$753$	−2.81655e8	+	4.43598e7i	−0.659680	+	0.103897i
$754$	−5.46002e7			−0.127374
$755$		−	2.98366e8i		−	0.693281i
$756$	9.51336e7	+	1.87916e8i	0.220175	+	0.434908i
$757$	−1.73804e8			−0.400656			−0.200328	−	0.979729i	$-0.564201\pi$
$757$	−1.73804e8			−0.400656			−0.200328	+	0.979729i	$0.564201\pi$
$758$		−	3.58725e8i		−	0.823672i
$759$	3.53889e7	+	2.24696e8i	0.0809360	+	0.513891i
$760$	1.09060e8			0.248442
$761$			1.45446e8i			0.330027i	0.986291	+	0.165013i	$0.0527667\pi$
$761$			1.45446e8i			0.330027i	−0.986291	+	0.165013i	$0.947233\pi$
$762$	3.69461e8	−	5.81888e7i	0.835033	−	0.131515i
$763$	−8.39164e8			−1.88918
$764$		−	1.62312e8i		−	0.363974i
$765$	−2.49851e8	+	8.07033e7i	−0.558080	+	0.180263i
$766$	7.46523e8			1.66095
$767$		−	3.68619e7i		−	0.0816943i
$768$	−6.09896e7	−	3.87244e8i	−0.134639	−	0.854872i
$769$	4.90480e8			1.07856			0.539278	−	0.842128i	$-0.318697\pi$
$769$	4.90480e8			1.07856			0.539278	+	0.842128i	$0.318697\pi$
$770$			1.80174e8i			0.394658i
$771$	−1.50207e8	+	2.36571e7i	−0.327738	+	0.0516176i
$772$	−2.69293e8			−0.585292
$773$			3.68902e8i			0.798680i	0.916803	+	0.399340i	$0.130761\pi$
$773$			3.68902e8i			0.798680i	−0.916803	+	0.399340i	$0.869239\pi$
$774$	−5.42989e7	−	1.68105e8i	−0.117103	−	0.362542i
$775$	−2.09487e8			−0.450042
$776$		−	4.35886e8i		−	0.932798i
$777$	2.13599e8	+	1.35622e9i	0.455341	+	2.89112i
$778$	−5.22601e8			−1.10977
$779$			1.90695e8i			0.403393i
$780$	6.61358e7	−	1.04162e7i	0.139365	−	0.0219495i
$781$	−1.21506e8			−0.255060
$782$			7.48799e8i			1.56583i
$783$	7.91986e7	−	4.00948e7i	0.164980	−	0.0835224i
$784$	−8.00471e8			−1.66111
$785$		−	1.95033e8i		−	0.403179i
$786$	−5.23119e6	−	3.32146e7i	−0.0107729	−	0.0684009i
$787$	−3.59319e8			−0.737150			−0.368575	−	0.929598i	$-0.620154\pi$
$787$	−3.59319e8			−0.737150			−0.368575	+	0.929598i	$0.620154\pi$
$788$		−	8.17084e7i		−	0.166989i
$789$	−3.42071e8	+	5.38750e7i	−0.696442	+	0.109687i
$790$	3.94340e8			0.799814
$791$		−	3.36033e8i		−	0.678973i
$792$	1.11730e8	−	3.60893e7i	0.224902	−	0.0726446i
$793$	5.02994e8			1.00866
$794$			4.56476e8i			0.911920i
$795$	−3.02643e7	−	1.92158e8i	−0.0602322	−	0.382435i
$796$	−3.00433e8			−0.595674
$797$		−	5.92225e8i		−	1.16980i	−0.811105	−	0.584900i	$-0.801134\pi$
$797$		−	5.92225e8i		−	1.16980i	0.811105	−	0.584900i	$-0.198866\pi$
$798$	3.78656e8	−	5.96371e7i	0.745138	−	0.117357i
$799$	4.71175e8			0.923724
$800$		−	1.41048e8i		−	0.275485i
$801$	−3.65058e7	−	1.13019e8i	−0.0710336	−	0.219915i
$802$	−5.67171e7			−0.109949
$803$		−	1.16832e8i		−	0.225640i
$804$	2.41402e7	+	1.53275e8i	0.0464487	+	0.294919i
$805$	1.02662e9			1.96798
$806$			3.60683e8i			0.688844i
$807$	−9.46468e8	+	1.49066e8i	−1.80088	+	0.283633i
$808$	2.39982e8			0.454931
$809$		−	8.75547e8i		−	1.65361i	−0.562487	−	0.826806i	$-0.690155\pi$
$809$		−	8.75547e8i		−	1.65361i	0.562487	−	0.826806i	$-0.309845\pi$
$810$	−3.66825e8	+	2.64577e8i	−0.690245	+	0.497848i
$811$	2.30112e8			0.431397			0.215699	−	0.976460i	$-0.430797\pi$
$811$	2.30112e8			0.431397			0.215699	+	0.976460i	$0.430797\pi$
$812$		−	4.82603e7i		−	0.0901409i
$813$	9.01714e7	+	5.72529e8i	0.167802	+	1.06543i
$814$	−3.55129e8			−0.658436
$815$			3.93090e8i			0.726137i
$816$	5.16336e8	−	8.13212e7i	0.950303	−	0.149670i
$817$	−7.73756e7			−0.141885
$818$			3.27317e8i			0.598011i
$819$	−4.82592e8	+	1.55880e8i	−0.878473	+	0.283752i
$820$	−1.22324e8			−0.221856
$821$		−	2.27265e8i		−	0.410680i	−0.978691	−	0.205340i	$-0.934170\pi$
$821$		−	2.27265e8i		−	0.410680i	0.978691	−	0.205340i	$-0.0658300\pi$
$822$	−4.47527e7	−	2.84150e8i	−0.0805756	−	0.511602i
$823$	6.08667e8			1.09189			0.545947	−	0.837820i	$-0.316170\pi$
$823$	6.08667e8			1.09189			0.545947	+	0.837820i	$0.316170\pi$
$824$		−	7.32704e8i		−	1.30963i
$825$	7.52624e7	−	1.18536e7i	0.134034	−	0.0211100i
$826$	1.35381e8			0.240225
$827$			4.43026e6i			0.00783272i	0.999992	+	0.00391636i	$0.00124662\pi$
$827$			4.43026e6i			0.00783272i	−0.999992	+	0.00391636i	$0.998753\pi$
$828$	9.54161e7	+	2.95401e8i	0.168086	+	0.520380i
$829$	1.59052e8			0.279174			0.139587	−	0.990210i	$-0.455422\pi$
$829$	1.59052e8			0.279174			0.139587	+	0.990210i	$0.455422\pi$
$830$		−	7.40277e8i		−	1.29467i
$831$	8.31612e7	+	5.28019e8i	0.144916	+	0.920124i
$832$	1.77680e8			0.308510
$833$		−	6.24162e8i		−	1.07985i
$834$	−8.46305e6	+	1.33290e6i	−0.0145891	+	0.00229773i
$835$	1.05310e8			0.180888
$836$			2.38626e7i			0.0408413i
$837$	−2.64863e8	−	5.23179e8i	−0.451694	−	0.892223i
$838$	3.07630e8			0.522754
$839$		−	5.88477e8i		−	0.996423i	−0.867056	−	0.498211i	$-0.833990\pi$
$839$		−	5.88477e8i		−	0.996423i	0.867056	−	0.498211i	$-0.166010\pi$
$840$	−8.24445e7	−	5.23468e8i	−0.139099	−	0.883187i
$841$	5.74484e8			0.965805
$842$		−	2.36154e8i		−	0.395603i
$843$	−8.40640e8	+	1.32398e8i	−1.40322	+	0.221003i
$844$	3.05274e8			0.507764
$845$		−	2.86243e8i		−	0.474422i
$846$	7.72348e8	−	2.49473e8i	1.27556	−	0.412014i
$847$	8.49607e7			0.139820
$848$			3.87259e8i			0.635059i
$849$	−8.93083e7	−	5.67049e8i	−0.145938	−	0.926610i
$850$	2.50812e8			0.408405
$851$			2.02350e9i			3.28332i
$852$	−1.63802e8	+	2.57983e7i	−0.264851	+	0.0417132i
$853$	2.59527e8			0.418154			0.209077	−	0.977899i	$-0.432954\pi$
$853$	2.59527e8			0.418154			0.209077	+	0.977899i	$0.432954\pi$
$854$			1.84732e9i			2.96599i
$855$	6.08897e7	+	1.88510e8i	0.0974195	+	0.301603i
$856$	−9.25402e7			−0.147540
$857$			4.57389e8i			0.726681i	0.931657	+	0.363340i	$0.118364\pi$
$857$			4.57389e8i			0.726681i	−0.931657	+	0.363340i	$0.881636\pi$
$858$	−2.04088e7	−	1.29583e8i	−0.0323114	−	0.205156i
$859$	−6.92273e8			−1.09219			−0.546094	−	0.837724i	$-0.683886\pi$
$859$	−6.92273e8			−1.09219			−0.546094	+	0.837724i	$0.683886\pi$
$860$		−	4.96336e7i		−	0.0780334i
$861$	9.15302e8	−	1.44157e8i	1.43402	−	0.225853i
$862$	1.25278e9			1.95593
$863$		−	1.04509e9i		−	1.62601i	−0.582257	−	0.813005i	$-0.697830\pi$
$863$		−	1.04509e9i		−	1.62601i	0.582257	−	0.813005i	$-0.302170\pi$
$864$	3.52258e8	−	1.78333e8i	0.546159	−	0.276497i
$865$	−8.01134e8			−1.23782
$866$		−	3.30393e8i		−	0.508718i
$867$	−3.79833e7	−	2.41169e8i	−0.0582821	−	0.370053i
$868$	−3.18803e8			−0.487487
$869$		−	1.85950e8i		−	0.283358i
$870$	1.02370e8	−	1.61229e7i	0.155458	−	0.0244842i
$871$	−3.73605e8			−0.565403
$872$			6.38413e8i			0.962836i
$873$	7.53426e8	−	2.43361e8i	1.13239	−	0.365770i
$874$	5.64961e8			0.846222
$875$		−	1.10798e9i		−	1.65389i
$876$	−2.48061e7	−	1.57502e8i	−0.0369017	−	0.234301i
$877$	1.37913e8			0.204458			0.102229	−	0.994761i	$-0.467402\pi$
$877$	1.37913e8			0.204458			0.102229	+	0.994761i	$0.467402\pi$
$878$			1.20660e9i			1.78271i
$879$	−6.96232e8	+	1.09654e8i	−1.02515	+	0.161458i
$880$	1.85367e8			0.272010
$881$			8.68687e8i			1.27039i	0.772353	+	0.635193i	$0.219080\pi$
$881$			8.68687e8i			1.27039i	−0.772353	+	0.635193i	$0.780920\pi$
$882$	−3.30475e8	−	1.02312e9i	−0.481651	−	1.49115i
$883$	−6.90449e8			−1.00288			−0.501441	−	0.865192i	$-0.667196\pi$
$883$	−6.90449e8			−1.00288			−0.501441	+	0.865192i	$0.667196\pi$
$884$		−	1.03928e8i		−	0.150444i
$885$	1.08850e7	+	6.91124e7i	0.0157035	+	0.0997071i
$886$	8.28772e6			0.0119161
$887$		−	1.49225e7i		−	0.0213832i	−0.999943	−	0.0106916i	$-0.996597\pi$
$887$		−	1.49225e7i		−	0.0213832i	0.999943	−	0.0106916i	$-0.00340330\pi$
$888$	1.03177e9	−	1.62501e8i	1.47348	−	0.232069i
$889$	−7.95988e8			−1.13292
$890$		−	1.38653e8i		−	0.196680i
$891$	1.24760e8	+	1.72975e8i	0.176378	+	0.244540i
$892$	4.77608e7			0.0672941
$893$		−	3.55497e8i		−	0.499208i
$894$	1.44137e8	+	9.15177e8i	0.201727	+	1.28083i
$895$	7.97185e8			1.11196
$896$			1.32981e9i			1.84870i
$897$	−7.38350e8	+	1.16288e8i	−1.02302	+	0.161122i
$898$	4.51507e8			0.623499
$899$			1.34362e8i			0.184926i
$900$	9.89450e7	−	3.19598e7i	0.135727	−	0.0438406i
$901$	−3.01963e8			−0.412837
$902$			2.39675e8i			0.326590i
$903$	5.84924e7	+	3.71388e8i	0.0794394	+	0.504388i
$904$	−2.55645e8			−0.346044
$905$		−	2.16359e7i		−	0.0291896i
$906$	−7.88105e8	+	1.24124e8i	−1.05974	+	0.166905i
$907$	−4.75454e8			−0.637216			−0.318608	−	0.947887i	$-0.603215\pi$
$907$	−4.75454e8			−0.637216			−0.318608	+	0.947887i	$0.603215\pi$
$908$		−	1.44111e7i		−	0.0192504i
$909$	1.33985e8	+	4.14808e8i	0.178388	+	0.552275i
$910$	−5.92051e8			−0.785661
$911$			6.97055e7i			0.0921960i	0.998937	+	0.0460980i	$0.0146787\pi$
$911$			6.97055e7i			0.0921960i	−0.998937	+	0.0460980i	$0.985321\pi$
$912$	−6.13560e7	−	3.89570e8i	−0.0808858	−	0.513572i
$913$	−3.49075e8			−0.458677
$914$			9.36616e7i			0.122666i
$915$	−9.43063e8	+	1.48529e8i	−1.23105	+	0.193887i
$916$	−1.58942e8			−0.206801
$917$			7.15595e7i			0.0928024i
$918$	3.17110e8	+	6.26383e8i	0.409904	+	0.809677i
$919$	−3.36828e8			−0.433972			−0.216986	−	0.976175i	$-0.569623\pi$
$919$	−3.36828e8			−0.433972			−0.216986	+	0.976175i	$0.569623\pi$
$920$		−	7.81023e8i		−	1.00300i
$921$	−5.13970e7	−	3.26337e8i	−0.0657898	−	0.417722i
$922$	−1.10942e9			−1.41548
$923$		−	3.99266e8i		−	0.507759i
$924$	1.14536e8	−	1.80391e7i	0.145187	−	0.0228664i
$925$	6.77773e8			0.856365
$926$			7.87001e8i			0.991157i
$927$	1.26647e9	−	4.09078e8i	1.58985	−	0.513532i
$928$	−9.04664e7			−0.113199
$929$			3.04843e8i			0.380215i	0.981763	+	0.190108i	$0.0608837\pi$
$929$			3.04843e8i			0.380215i	−0.981763	+	0.190108i	$0.939116\pi$
$930$	−1.06506e8	−	6.76245e8i	−0.132412	−	0.840728i
$931$	−4.70924e8			−0.583582
$932$		−	3.53334e8i		−	0.436453i
$933$	1.48155e8	−	2.33339e7i	0.182420	−	0.0287305i
$934$	−1.55310e9			−1.90615
$935$			1.44539e8i			0.176828i
$936$	1.18589e8	+	3.67143e8i	0.144616	+	0.447721i
$937$	−8.46326e8			−1.02877			−0.514386	−	0.857559i	$-0.671980\pi$
$937$	−8.46326e8			−1.02877			−0.514386	+	0.857559i	$0.671980\pi$
$938$		−	1.37212e9i		−	1.66259i
$939$	−1.41730e8	−	8.99892e8i	−0.171185	−	1.08691i
$940$	2.28038e8			0.274552
$941$			2.13556e8i			0.256296i	0.991755	+	0.128148i	$0.0409033\pi$
$941$			2.13556e8i			0.256296i	−0.991755	+	0.128148i	$0.959097\pi$
$942$	−5.15159e8	+	8.11358e7i	−0.616295	+	0.0970643i
$943$	1.36564e9			1.62856
$944$		−	1.39283e8i		−	0.165570i
$945$	8.58782e8	−	4.34764e8i	1.01762	−	0.515179i
$946$	−9.72491e7			−0.114871
$947$			3.89333e8i			0.458428i	0.973376	+	0.229214i	$0.0736156\pi$
$947$			3.89333e8i			0.458428i	−0.973376	+	0.229214i	$0.926384\pi$
$948$	−3.94813e7	−	2.50680e8i	−0.0463411	−	0.294235i
$949$	3.83910e8			0.449190
$950$		−	1.89235e8i		−	0.220714i
$951$	1.45716e9	−	2.29498e8i	1.69421	−	0.266832i
$952$	−8.22593e8			−0.953398
$953$		−	1.40967e9i		−	1.62869i	−0.580380	−	0.814346i	$-0.697096\pi$
$953$		−	1.40967e9i		−	1.62869i	0.580380	−	0.814346i	$-0.302904\pi$
$954$	−4.94976e8	+	1.59880e8i	−0.570084	+	0.184140i
$955$	−7.41772e8			−0.851648
$956$		−	1.81286e8i		−	0.207487i
$957$	−7.60271e6	−	4.82722e7i	−0.00867426	−	0.0550759i
$958$	−1.29211e9			−1.46961
$959$			6.12189e8i			0.694112i
$960$	−3.33133e8	+	5.24673e7i	−0.376534	+	0.0593028i
$961$	79584.4			8.96722e−5
$962$		−	1.16695e9i		−	1.31077i
$963$	−5.16664e7	−	1.59955e8i	−0.0578534	−	0.179110i
$964$	−2.83679e8			−0.316662
$965$			1.23068e9i			1.36950i
$966$	−4.27085e8	−	2.71171e9i	−0.473786	−	3.00823i
$967$	5.83081e8			0.644836			0.322418	−	0.946597i	$-0.395504\pi$
$967$	5.83081e8			0.644836			0.322418	+	0.946597i	$0.395504\pi$
$968$		−	6.46358e7i		−	0.0712602i
$969$	3.03765e8	−	4.78419e7i	0.333861	−	0.0525821i
$970$	9.24314e8			1.01276
$971$			8.49665e8i			0.928090i	0.885812	+	0.464045i	$0.153602\pi$
$971$			8.49665e8i			0.928090i	−0.885812	+	0.464045i	$0.846398\pi$
$972$	2.04917e8	+	2.06700e8i	0.223141	+	0.225082i
$973$	1.82333e7			0.0197937
$974$			9.96094e8i			1.07801i
$975$	3.89507e7	+	2.47312e8i	0.0420244	+	0.266827i
$976$	1.90057e9			2.04425
$977$		−	1.10581e8i		−	0.118577i	−0.998241	−	0.0592883i	$-0.981117\pi$
$977$		−	1.10581e8i		−	0.118577i	0.998241	−	0.0592883i	$-0.0188831\pi$
$978$	1.03831e9	−	1.63530e8i	1.10996	−	0.174816i
$979$	−6.53816e7			−0.0696799
$980$		−	3.02081e8i		−	0.320955i
$981$	−1.10349e9	+	3.56434e8i	−1.16886	+	0.377548i
$982$	6.58814e8			0.695710
$983$		−	6.40274e8i		−	0.674071i	−0.941492	−	0.337035i	$-0.890576\pi$
$983$		−	6.40274e8i		−	0.674071i	0.941492	−	0.337035i	$-0.109424\pi$
$984$	−1.09671e8	−	6.96337e8i	−0.115108	−	0.730860i
$985$	−3.73411e8			−0.390731
$986$		−	1.60867e8i		−	0.167817i
$987$	−1.70632e9	+	2.68739e8i	−1.77463	+	0.279499i
$988$	−7.84124e7			−0.0813044
$989$			5.54117e8i			0.572812i
$990$	7.65290e7	+	2.36928e8i	0.0788715	+	0.244180i
$991$	−7.57573e8			−0.778401			−0.389201	−	0.921153i	$-0.627249\pi$
$991$	−7.57573e8			−0.778401			−0.389201	+	0.921153i	$0.627249\pi$
$992$			5.97613e8i			0.612188i
$993$	1.82888e7	+	1.16122e8i	0.0186784	+	0.118595i
$994$	1.46637e9			1.49308
$995$			1.37299e9i			1.39379i
$996$	−4.70591e8	+	7.41165e7i	−0.476284	+	0.0750131i
$997$	1.10877e9			1.11881			0.559405	−	0.828894i	$-0.311030\pi$
$997$	1.10877e9			1.11881			0.559405	+	0.828894i	$0.311030\pi$
$998$		−	9.05918e7i		−	0.0911375i
$999$	8.56933e8	+	1.69269e9i	0.859509	+	1.69777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.15	yes	20
3.2	odd	2	inner	33.7.b.a.23.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.6	✓	20	3.2	odd	2	inner
33.7.b.a.23.15	yes	20	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+9.18066i q^{2} +(-4.20063 - 26.6712i) q^{3} -20.2844 q^{4} +92.7007i q^{5} +(244.859 - 38.5645i) q^{6} -527.539 q^{7} +401.338i q^{8} +(-693.709 + 224.072i) q^{9} +O(q^{10})\)	\(q+9.18066i q^{2} +(-4.20063 - 26.6712i) q^{3} -20.2844 q^{4} +92.7007i q^{5} +(244.859 - 38.5645i) q^{6} -527.539 q^{7} +401.338i q^{8} +(-693.709 + 224.072i) q^{9} -851.053 q^{10} +401.312i q^{11} +(85.2074 + 541.011i) q^{12} -1318.71 q^{13} -4843.16i q^{14} +(2472.44 - 389.401i) q^{15} -4982.75 q^{16} -3885.27i q^{17} +(-2057.13 - 6368.71i) q^{18} -2931.39 q^{19} -1880.38i q^{20} +(2216.00 + 14070.1i) q^{21} -3684.30 q^{22} +20992.8i q^{23} +(10704.2 - 1685.87i) q^{24} +7031.59 q^{25} -12106.6i q^{26} +(8890.29 + 17560.8i) q^{27} +10700.8 q^{28} -4509.96i q^{29} +(3574.96 + 22698.6i) q^{30} -29792.3 q^{31} -20059.3i q^{32} +(10703.5 - 1685.76i) q^{33} +35669.3 q^{34} -48903.2i q^{35} +(14071.5 - 4545.17i) q^{36} +96389.8 q^{37} -26912.1i q^{38} +(5539.40 + 35171.5i) q^{39} -37204.3 q^{40} -65052.9i q^{41} +(-129173. + 20344.3i) q^{42} +26395.5 q^{43} -8140.38i q^{44} +(-20771.6 - 64307.3i) q^{45} -192728. q^{46} +121272. i q^{47} +(20930.7 + 132896. i) q^{48} +160649. q^{49} +64554.6i q^{50} +(-103625. + 16320.6i) q^{51} +26749.2 q^{52} -77720.0i q^{53} +(-161220. + 81618.7i) q^{54} -37201.9 q^{55} -211721. i q^{56} +(12313.7 + 78183.8i) q^{57} +41404.4 q^{58} +27953.1i q^{59} +(-50152.1 + 7898.78i) q^{60} -381430. q^{61} -273513. i q^{62} +(365959. - 118207. i) q^{63} -134738. q^{64} -122245. i q^{65} +(15476.4 + 98264.9i) q^{66} +283312. q^{67} +78810.4i q^{68} +(559905. - 88183.1i) q^{69} +448964. q^{70} +302771. i q^{71} +(-89928.5 - 278412. i) q^{72} -291126. q^{73} +884922. i q^{74} +(-29537.1 - 187541. i) q^{75} +59461.6 q^{76} -211708. i q^{77} +(-322898. + 50855.3i) q^{78} -463355. q^{79} -461904. i q^{80} +(431025. - 310882. i) q^{81} +597228. q^{82} +869836. i q^{83} +(-44950.3 - 285405. i) q^{84} +360167. q^{85} +242328. i q^{86} +(-120286. + 18944.7i) q^{87} -161061. q^{88} +162920. i q^{89} +(590383. - 190697. i) q^{90} +695669. q^{91} -425828. i q^{92} +(125147. + 794598. i) q^{93} -1.11336e6 q^{94} -271742. i q^{95} +(-535005. + 84261.6i) q^{96} -1.08608e6 q^{97} +1.47486e6i q^{98} +(-89922.7 - 278394. 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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