LMFDB - Embedded newform 33.7.b.a.23.14

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			23.14
Root			$8.58590i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.58590i q^{2} +(-21.1258 - 16.8137i) q^{3} -9.71763 q^{4} -61.7994i q^{5} +(144.360 - 181.384i) q^{6} +427.595 q^{7} +466.063i q^{8} +(163.602 + 710.405i) q^{9} +O(q^{10})$	\(q+8.58590i q^{2} +(-21.1258 - 16.8137i) q^{3} -9.71763 q^{4} -61.7994i q^{5} +(144.360 - 181.384i) q^{6} +427.595 q^{7} +466.063i q^{8} +(163.602 + 710.405i) q^{9} +530.603 q^{10} -401.312i q^{11} +(205.293 + 163.389i) q^{12} +2365.10 q^{13} +3671.29i q^{14} +(-1039.07 + 1305.56i) q^{15} -4623.50 q^{16} +4070.95i q^{17} +(-6099.47 + 1404.67i) q^{18} +12625.2 q^{19} +600.543i q^{20} +(-9033.31 - 7189.44i) q^{21} +3445.62 q^{22} -4647.31i q^{23} +(7836.22 - 9845.97i) q^{24} +11805.8 q^{25} +20306.5i q^{26} +(8488.29 - 17758.6i) q^{27} -4155.21 q^{28} -26007.8i q^{29} +(-11209.4 - 8921.38i) q^{30} -33212.1 q^{31} -9868.84i q^{32} +(-6747.52 + 8478.04i) q^{33} -34952.7 q^{34} -26425.1i q^{35} +(-1589.82 - 6903.45i) q^{36} -24798.6 q^{37} +108399. i q^{38} +(-49964.7 - 39766.0i) q^{39} +28802.4 q^{40} +63549.2i q^{41} +(61727.8 - 77559.0i) q^{42} -27569.2 q^{43} +3899.80i q^{44} +(43902.6 - 10110.5i) q^{45} +39901.3 q^{46} +67479.0i q^{47} +(97675.2 + 77737.9i) q^{48} +65188.7 q^{49} +101364. i q^{50} +(68447.5 - 86002.1i) q^{51} -22983.1 q^{52} -167698. i q^{53} +(152474. + 72879.6i) q^{54} -24800.8 q^{55} +199286. i q^{56} +(-266719. - 212277. i) q^{57} +223300. q^{58} +225514. i q^{59} +(10097.3 - 12687.0i) q^{60} -289474. q^{61} -285156. i q^{62} +(69955.3 + 303766. i) q^{63} -211171. q^{64} -146162. i q^{65} +(-72791.6 - 57933.5i) q^{66} +235553. q^{67} -39559.9i q^{68} +(-78138.2 + 98178.2i) q^{69} +226883. q^{70} +153861. i q^{71} +(-331093. + 76248.7i) q^{72} -306148. q^{73} -212918. i q^{74} +(-249408. - 198499. i) q^{75} -122687. q^{76} -171599. i q^{77} +(341426. - 428992. i) q^{78} +637841. q^{79} +285729. i q^{80} +(-477910. + 232447. i) q^{81} -545627. q^{82} -934055. i q^{83} +(87782.3 + 69864.3i) q^{84} +251582. q^{85} -236707. i q^{86} +(-437286. + 549436. i) q^{87} +187036. q^{88} -953248. i q^{89} +(86807.6 + 376943. i) q^{90} +1.01130e6 q^{91} +45160.8i q^{92} +(701634. + 558418. i) q^{93} -579368. q^{94} -780232. i q^{95} +(-165931. + 208487. i) q^{96} -723082. q^{97} +559703. i q^{98} +(285094. - 65655.3i) 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 $

$2$			8.58590i			1.07324i	0.843825	+	0.536619i	$0.180299\pi$
$2$			8.58590i			1.07324i	−0.843825	+	0.536619i	$0.819701\pi$
$3$	−21.1258	−	16.8137i	−0.782438	−	0.622728i
$3$	−21.1258	−	16.8137i	−0.782438	−	0.622728i
$4$	−9.71763			−0.151838
$5$		−	61.7994i		−	0.494395i	−0.968965	−	0.247198i	$-0.920490\pi$
$5$		−	61.7994i		−	0.494395i	0.968965	−	0.247198i	$-0.0795097\pi$
$6$	144.360	−	181.384i	0.668335	−	0.839742i
$7$	427.595			1.24663			0.623317	−	0.781970i	$-0.285785\pi$
$7$	427.595			1.24663			0.623317	+	0.781970i	$0.285785\pi$
$8$			466.063i			0.910279i
$9$	163.602	+	710.405i	0.224419	+	0.974493i
$10$	530.603			0.530603
$11$		−	401.312i		−	0.301511i
$11$		−	401.312i		−	0.301511i
$12$	205.293	+	163.389i	0.118804	+	0.0945537i
$13$	2365.10			1.07651			0.538256	−	0.842781i	$-0.319083\pi$
$13$	2365.10			1.07651			0.538256	+	0.842781i	$0.319083\pi$
$14$			3671.29i			1.33793i
$15$	−1039.07	+	1305.56i	−0.307874	+	0.386834i
$16$	−4623.50			−1.12878
$17$			4070.95i			0.828607i	0.910139	+	0.414304i	$0.135975\pi$
$17$			4070.95i			0.828607i	−0.910139	+	0.414304i	$0.864025\pi$
$18$	−6099.47	+	1404.67i	−1.04586	+	0.240855i
$19$	12625.2			1.84068			0.920341	−	0.391116i	$-0.127911\pi$
$19$	12625.2			1.84068			0.920341	+	0.391116i	$0.127911\pi$
$20$			600.543i			0.0750679i
$21$	−9033.31	−	7189.44i	−0.975414	−	0.776314i
$22$	3445.62			0.323593
$23$		−	4647.31i		−	0.381960i	−0.981594	−	0.190980i	$-0.938833\pi$
$23$		−	4647.31i		−	0.381960i	0.981594	−	0.190980i	$-0.0611666\pi$
$24$	7836.22	−	9845.97i	0.566856	−	0.712237i
$25$	11805.8			0.755573
$26$			20306.5i			1.15535i
$27$	8488.29	−	17758.6i	0.431250	−	0.902233i
$28$	−4155.21			−0.189286
$29$		−	26007.8i		−	1.06637i	−0.845998	−	0.533187i	$-0.820994\pi$
$29$		−	26007.8i		−	1.06637i	0.845998	−	0.533187i	$-0.179006\pi$
$30$	−11209.4	−	8921.38i	−0.415164	−	0.330422i
$31$	−33212.1			−1.11484			−0.557419	−	0.830231i	$-0.688208\pi$
$31$	−33212.1			−1.11484			−0.557419	+	0.830231i	$0.688208\pi$
$32$		−	9868.84i		−	0.301173i
$33$	−6747.52	+	8478.04i	−0.187760	+	0.235914i
$34$	−34952.7			−0.889292
$35$		−	26425.1i		−	0.616329i
$36$	−1589.82	−	6903.45i	−0.0340754	−	0.147965i
$37$	−24798.6			−0.489578			−0.244789	−	0.969576i	$-0.578719\pi$
$37$	−24798.6			−0.489578			−0.244789	+	0.969576i	$0.578719\pi$
$38$			108399.i			1.97549i
$39$	−49964.7	−	39766.0i	−0.842305	−	0.670375i
$40$	28802.4			0.450037
$41$			63549.2i			0.922059i	0.887385	+	0.461029i	$0.152520\pi$
$41$			63549.2i			0.922059i	−0.887385	+	0.461029i	$0.847480\pi$
$42$	61727.8	−	77559.0i	0.833169	−	1.04685i
$43$	−27569.2			−0.346752			−0.173376	−	0.984856i	$-0.555468\pi$
$43$	−27569.2			−0.346752			−0.173376	+	0.984856i	$0.555468\pi$
$44$			3899.80i			0.0457809i
$45$	43902.6	−	10110.5i	0.481784	−	0.110952i
$46$	39901.3			0.409934
$47$			67479.0i			0.649943i	0.945724	+	0.324972i	$0.105355\pi$
$47$			67479.0i			0.649943i	−0.945724	+	0.324972i	$0.894645\pi$
$48$	97675.2	+	77737.9i	0.883203	+	0.702925i
$49$	65188.7			0.554095
$50$			101364.i			0.810910i
$51$	68447.5	−	86002.1i	0.515997	−	0.648334i
$52$	−22983.1			−0.163455
$53$		−	167698.i		−	1.12642i	−0.826315	−	0.563208i	$-0.809567\pi$
$53$		−	167698.i		−	1.12642i	0.826315	−	0.563208i	$-0.190433\pi$
$54$	152474.	+	72879.6i	0.968310	+	0.462833i
$55$	−24800.8			−0.149066
$56$			199286.i			1.13478i
$57$	−266719.	−	212277.i	−1.44022	−	1.14624i
$58$	223300.			1.14447
$59$			225514.i			1.09804i	0.835810	+	0.549019i	$0.184998\pi$
$59$			225514.i			1.09804i	−0.835810	+	0.549019i	$0.815002\pi$
$60$	10097.3	−	12687.0i	0.0467469	−	0.0587360i
$61$	−289474.			−1.27532			−0.637662	−	0.770316i	$-0.720098\pi$
$61$	−289474.			−1.27532			−0.637662	+	0.770316i	$0.720098\pi$
$62$		−	285156.i		−	1.19649i
$63$	69955.3	+	303766.i	0.279769	+	1.21484i
$64$	−211171.			−0.805553
$65$		−	146162.i		−	0.532223i
$66$	−72791.6	−	57933.5i	−0.253192	−	0.201511i
$67$	235553.			0.783185			0.391592	−	0.920139i	$-0.371924\pi$
$67$	235553.			0.783185			0.391592	+	0.920139i	$0.371924\pi$
$68$		−	39559.9i		−	0.125814i
$69$	−78138.2	+	98178.2i	−0.237857	+	0.298860i
$70$	226883.			0.661468
$71$			153861.i			0.429887i	0.976626	+	0.214943i	$0.0689567\pi$
$71$			153861.i			0.429887i	−0.976626	+	0.214943i	$0.931043\pi$
$72$	−331093.	+	76248.7i	−0.887060	+	0.204284i
$73$	−306148.			−0.786979			−0.393490	−	0.919329i	$-0.628732\pi$
$73$	−306148.			−0.786979			−0.393490	+	0.919329i	$0.628732\pi$
$74$		−	212918.i		−	0.525433i
$75$	−249408.	−	198499.i	−0.591190	−	0.470517i
$76$	−122687.			−0.279485
$77$		−	171599.i		−	0.375874i
$78$	341426.	−	428992.i	0.719471	−	0.903993i
$79$	637841.			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$79$	637841.			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$80$			285729.i			0.558065i
$81$	−477910.	+	232447.i	−0.899272	+	0.437390i
$82$	−545627.			−0.989588
$83$		−	934055.i		−	1.63357i	−0.576941	−	0.816786i	$-0.695754\pi$
$83$		−	934055.i		−	1.63357i	0.576941	−	0.816786i	$-0.304246\pi$
$84$	87782.3	+	69864.3i	0.148105	+	0.117874i
$85$	251582.			0.409659
$86$		−	236707.i		−	0.372147i
$87$	−437286.	+	549436.i	−0.664061	+	0.834371i
$88$	187036.			0.274459
$89$		−	953248.i		−	1.35218i	−0.736817	−	0.676092i	$-0.763672\pi$
$89$		−	953248.i		−	1.35218i	0.736817	−	0.676092i	$-0.236328\pi$
$90$	86807.6	+	376943.i	0.119078	+	0.517069i
$91$	1.01130e6			1.34202
$92$			45160.8i			0.0579960i
$93$	701634.	+	558418.i	0.872292	+	0.694241i
$94$	−579368.			−0.697543
$95$		−	780232.i		−	0.910025i
$96$	−165931.	+	208487.i	−0.187549	+	0.235649i
$97$	−723082.			−0.792269			−0.396134	−	0.918193i	$-0.629649\pi$
$97$	−723082.			−0.792269			−0.396134	+	0.918193i	$0.629649\pi$
$98$			559703.i			0.594675i
$99$	285094.	−	65655.3i	0.293821	−	0.0676650i
$100$	−114725.			−0.114725
$101$			754847.i			0.732647i	0.930488	+	0.366323i	$0.119384\pi$
$101$			754847.i			0.732647i	−0.930488	+	0.366323i	$0.880616\pi$
$102$	738406.	+	587683.i	0.695816	+	0.553787i
$103$	732883.			0.670691			0.335346	−	0.942095i	$-0.391147\pi$
$103$	732883.			0.670691			0.335346	+	0.942095i	$0.391147\pi$
$104$			1.10228e6i			0.979927i
$105$	−444303.	+	558253.i	−0.383806	+	0.482240i
$106$	1.43983e6			1.20891
$107$			1.57887e6i			1.28883i	0.764676	+	0.644415i	$0.222899\pi$
$107$			1.57887e6i			1.28883i	−0.764676	+	0.644415i	$0.777101\pi$
$108$	−82486.0	+	172572.i	−0.0654801	+	0.136993i
$109$	−564799.			−0.436129			−0.218064	−	0.975934i	$-0.569974\pi$
$109$	−564799.			−0.436129			−0.218064	+	0.975934i	$0.569974\pi$
$110$		−	212937.i		−	0.159983i
$111$	523891.	+	416955.i	0.383065	+	0.304874i
$112$	−1.97698e6			−1.40718
$113$		−	1.15918e6i		−	0.803366i	−0.915779	−	0.401683i	$-0.868425\pi$
$113$		−	1.15918e6i		−	0.803366i	0.915779	−	0.401683i	$-0.131575\pi$
$114$	1.82258e6	−	2.29002e6i	1.23019	−	1.54570i
$115$	−287201.			−0.188839
$116$			252734.i			0.161916i
$117$	386934.	+	1.68018e6i	0.241590	+	1.04905i
$118$	−1.93624e6			−1.17845
$119$			1.74072e6i			1.03297i
$120$	−608475.	−	484274.i	−0.352127	−	0.280251i
$121$	−161051.			−0.0909091
$122$		−	2.48540e6i		−	1.36872i
$123$	1.06849e6	−	1.34253e6i	0.574192	−	0.721454i
$124$	322743.			0.169275
$125$		−	1.69521e6i		−	0.867947i
$126$	−2.60810e6	+	600629.i	−1.30381	+	0.300258i
$127$	−1.80832e6			−0.882803			−0.441402	−	0.897310i	$-0.645519\pi$
$127$	−1.80832e6			−0.882803			−0.441402	+	0.897310i	$0.645519\pi$
$128$		−	2.44470e6i		−	1.16572i
$129$	582423.	+	463540.i	0.271312	+	0.215932i
$130$	1.25493e6			0.571201
$131$			2.57704e6i			1.14633i	0.819441	+	0.573163i	$0.194284\pi$
$131$			2.57704e6i			1.14633i	−0.819441	+	0.573163i	$0.805716\pi$
$132$	65569.9	−	82386.5i	0.0285090	−	0.0358207i
$133$	5.39849e6			2.29466
$134$			2.02243e6i			0.840543i
$135$	−1.09747e6	−	524571.i	−0.446059	−	0.213208i
$136$	−1.89732e6			−0.754264
$137$		−	3.68029e6i		−	1.43126i	−0.698477	−	0.715632i	$-0.746139\pi$
$137$		−	3.68029e6i		−	1.43126i	0.698477	−	0.715632i	$-0.253861\pi$
$138$	−842948.	−	670887.i	−0.320748	−	0.255277i
$139$	2.76794e6			1.03065			0.515327	−	0.856994i	$-0.327671\pi$
$139$	2.76794e6			1.03065			0.515327	+	0.856994i	$0.327671\pi$
$140$			256790.i			0.0935822i
$141$	1.13457e6	−	1.42555e6i	0.404738	−	0.508540i
$142$	−1.32104e6			−0.461371
$143$		−	949142.i		−	0.324581i
$144$	−756412.	−	3.28456e6i	−0.253321	−	1.09999i
$145$	−1.60726e6			−0.527210
$146$		−	2.62856e6i		−	0.844616i
$147$	−1.37717e6	−	1.09606e6i	−0.433545	−	0.345050i
$148$	240983.			0.0743365
$149$			5.91362e6i			1.78770i	0.448366	+	0.893850i	$0.352006\pi$
$149$			5.91362e6i			1.78770i	−0.448366	+	0.893850i	$0.647994\pi$
$150$	1.70429e6	−	2.14139e6i	0.504976	−	0.634487i
$151$	−3.76456e6			−1.09341			−0.546705	−	0.837325i	$-0.684118\pi$
$151$	−3.76456e6			−1.09341			−0.546705	+	0.837325i	$0.684118\pi$
$152$			5.88416e6i			1.67554i
$153$	−2.89202e6	+	666014.i	−0.807472	+	0.185956i
$154$	1.47333e6			0.403402
$155$			2.05249e6i			0.551171i
$156$	485538.	+	386431.i	0.127894	+	0.101788i
$157$	−4.75014e6			−1.22746			−0.613730	−	0.789516i	$-0.710332\pi$
$157$	−4.75014e6			−1.22746			−0.613730	+	0.789516i	$0.710332\pi$
$158$			5.47644e6i			1.38844i
$159$	−2.81961e6	+	3.54275e6i	−0.701451	+	0.881352i
$160$	−609888.			−0.148898
$161$		−	1.98717e6i		−	0.476164i
$162$	−1.99577e6	−	4.10329e6i	−0.469423	−	0.965132i
$163$	2.22277e6			0.513253			0.256626	−	0.966511i	$-0.417389\pi$
$163$	2.22277e6			0.513253			0.256626	+	0.966511i	$0.417389\pi$
$164$		−	617548.i		−	0.140004i
$165$	523938.	+	416992.i	0.116635	+	0.0928274i
$166$	8.01970e6			1.75321
$167$		−	2.25235e6i		−	0.483600i	−0.970326	−	0.241800i	$-0.922262\pi$
$167$		−	2.25235e6i		−	0.483600i	0.970326	−	0.241800i	$-0.0777378\pi$
$168$	3.35073e6	−	4.21009e6i	0.706662	−	0.887899i
$169$	766883.			0.158880
$170$			2.16006e6i			0.439662i
$171$	2.06551e6	+	8.96904e6i	0.413085	+	1.79373i
$172$	267908.			0.0526501
$173$		−	2.10302e6i		−	0.406167i	−0.979161	−	0.203084i	$-0.934904\pi$
$173$		−	2.10302e6i		−	0.406167i	0.979161	−	0.203084i	$-0.0650963\pi$
$174$	−4.71740e6	−	3.75449e6i	−0.895478	−	0.712694i
$175$	5.04812e6			0.941923
$176$			1.85546e6i			0.340341i
$177$	3.79171e6	−	4.76417e6i	0.683779	−	0.859146i
$178$	8.18449e6			1.45121
$179$		−	2.28274e6i		−	0.398014i	−0.979998	−	0.199007i	$-0.936228\pi$
$179$		−	2.28274e6i		−	0.398014i	0.979998	−	0.199007i	$-0.0637716\pi$
$180$	−426629.	+	98250.0i	−0.0731531	+	0.0168467i
$181$	−7.63145e6			−1.28698			−0.643490	−	0.765455i	$-0.722514\pi$
$181$	−7.63145e6			−1.28698			−0.643490	+	0.765455i	$0.722514\pi$
$182$			8.68296e6i			1.44030i
$183$	6.11538e6	+	4.86712e6i	0.997862	+	0.794180i
$184$	2.16594e6			0.347690
$185$			1.53254e6i			0.242045i
$186$	−4.79452e6	+	6.02416e6i	−0.745085	+	0.936176i
$187$	1.63372e6			0.249834
$188$		−	655736.i		−	0.0986860i
$189$	3.62955e6	−	7.59351e6i	0.537610	−	1.12475i
$190$	6.69899e6			0.976672
$191$		−	255455.i		−	0.0366618i	−0.999832	−	0.0183309i	$-0.994165\pi$
$191$		−	255455.i		−	0.0366618i	0.999832	−	0.0183309i	$-0.00583524\pi$
$192$	4.46116e6	+	3.55056e6i	0.630296	+	0.501641i
$193$	−4.93418e6			−0.686346			−0.343173	−	0.939272i	$-0.611502\pi$
$193$	−4.93418e6			−0.686346			−0.343173	+	0.939272i	$0.611502\pi$
$194$		−	6.20831e6i		−	0.850292i
$195$	−2.45751e6	+	3.08779e6i	−0.331430	+	0.416431i
$196$	−633479.			−0.0841326
$197$		−	1.11023e7i		−	1.45216i	−0.687611	−	0.726079i	$-0.741341\pi$
$197$		−	1.11023e7i		−	1.45216i	0.687611	−	0.726079i	$-0.258659\pi$
$198$	563709.	+	2.44779e6i	0.0726206	+	0.315339i
$199$	−1.19979e7			−1.52246			−0.761230	−	0.648482i	$-0.775404\pi$
$199$	−1.19979e7			−1.52246			−0.761230	+	0.648482i	$0.775404\pi$
$200$			5.50226e6i			0.687783i
$201$	−4.97625e6	−	3.96051e6i	−0.612794	−	0.487711i
$202$	−6.48104e6			−0.786304
$203$		−	1.11208e7i		−	1.32938i
$204$	−665147.	+	835737.i	−0.0783479	+	0.0984417i
$205$	3.92730e6			0.455861
$206$			6.29245e6i			0.719811i
$207$	3.30147e6	−	760308.i	0.372217	−	0.0857192i
$208$	−1.09350e7			−1.21515
$209$		−	5.06666e6i		−	0.554987i
$210$	−4.79310e6	−	3.81474e6i	−0.517558	−	0.411914i
$211$	−1.08238e7			−1.15221			−0.576107	−	0.817374i	$-0.695429\pi$
$211$	−1.08238e7			−1.15221			−0.576107	+	0.817374i	$0.695429\pi$
$212$			1.62962e6i			0.171033i
$213$	2.58697e6	−	3.25045e6i	0.267703	−	0.336360i
$214$	−1.35560e7			−1.38322
$215$			1.70376e6i			0.171433i
$216$	8.27664e6	+	3.95608e6i	0.821283	+	0.392557i
$217$	−1.42014e7			−1.38979
$218$		−	4.84931e6i		−	0.468069i
$219$	6.46764e6	+	5.14747e6i	0.615763	+	0.490074i
$220$	241005.			0.0226338
$221$			9.62819e6i			0.892006i
$222$	−3.57993e6	+	4.49807e6i	−0.327202	+	0.411119i
$223$	1.55801e7			1.40493			0.702467	−	0.711717i	$-0.252082\pi$
$223$	1.55801e7			1.40493			0.702467	+	0.711717i	$0.252082\pi$
$224$		−	4.21987e6i		−	0.375452i
$225$	1.93146e6	+	8.38693e6i	0.169565	+	0.736301i
$226$	9.95256e6			0.862203
$227$		−	2.08889e7i		−	1.78582i	−0.450236	−	0.892909i	$-0.648660\pi$
$227$		−	2.08889e7i		−	1.78582i	0.450236	−	0.892909i	$-0.351340\pi$
$228$	2.59187e6	+	2.06282e6i	0.218680	+	0.174043i
$229$	1.03530e7			0.862103			0.431052	−	0.902327i	$-0.358143\pi$
$229$	1.03530e7			0.862103			0.431052	+	0.902327i	$0.358143\pi$
$230$		−	2.46588e6i		−	0.202669i
$231$	−2.88521e6	+	3.62517e6i	−0.234067	+	0.294098i
$232$	1.21213e7			0.970697
$233$		−	1.66227e7i		−	1.31411i	−0.753842	−	0.657056i	$-0.771801\pi$
$233$		−	1.66227e7i		−	1.31411i	0.753842	−	0.657056i	$-0.228199\pi$
$234$	−1.44258e7	+	3.32218e6i	−1.12588	+	0.259284i
$235$	4.17016e6			0.321329
$236$		−	2.19146e6i		−	0.166724i
$237$	−1.34749e7	−	1.07244e7i	−1.01223	−	0.805619i
$238$	−1.49456e7			−1.10862
$239$			8.00954e6i			0.586697i	0.956006	+	0.293349i	$0.0947697\pi$
$239$			8.00954e6i			0.586697i	−0.956006	+	0.293349i	$0.905230\pi$
$240$	4.80415e6	−	6.03627e6i	0.347523	−	0.436651i
$241$	635159.			0.0453765			0.0226883	−	0.999743i	$-0.492777\pi$
$241$	635159.			0.0453765			0.0226883	+	0.999743i	$0.492777\pi$
$242$		−	1.38277e6i		−	0.0975670i
$243$	1.40045e7	+	3.12478e6i	0.976000	+	0.217771i
$244$	2.81300e6			0.193642
$245$		−	4.02862e6i		−	0.273942i
$246$	1.15268e7	+	9.17399e6i	0.774291	+	0.616244i
$247$	2.98599e7			1.98152
$248$		−	1.54789e7i		−	1.01481i
$249$	−1.57049e7	+	1.97327e7i	−1.01727	+	1.27817i
$250$	1.45549e7			0.931513
$251$			2.75782e7i			1.74399i	0.489511	+	0.871997i	$0.337175\pi$
$251$			2.75782e7i			1.74399i	−0.489511	+	0.871997i	$0.662825\pi$
$252$	−679800.	−	2.95188e6i	−0.0424795	−	0.184458i
$253$	−1.86502e6			−0.115165
$254$		−	1.55260e7i		−	0.947457i
$255$	−5.31488e6	−	4.23001e6i	−0.320533	−	0.255106i
$256$	7.47498e6			0.445544
$257$			1.56614e7i			0.922636i	0.887235	+	0.461318i	$0.152623\pi$
$257$			1.56614e7i			0.922636i	−0.887235	+	0.461318i	$0.847377\pi$
$258$	−3.97990e6	+	5.00062e6i	−0.231747	+	0.291182i
$259$	−1.06038e7			−0.610324
$260$			1.42034e6i			0.0808116i
$261$	1.84761e7	−	4.25492e6i	1.03917	−	0.239315i
$262$	−2.21262e7			−1.23028
$263$			9.54165e6i			0.524513i	0.964998	+	0.262257i	$0.0844667\pi$
$263$			9.54165e6i			0.524513i	−0.964998	+	0.262257i	$0.915533\pi$
$264$	−3.95130e6	−	3.14477e6i	−0.214748	−	0.170914i
$265$	−1.03636e7			−0.556895
$266$			4.63509e7i			2.46271i
$267$	−1.60276e7	+	2.01382e7i	−0.842043	+	1.05800i
$268$	−2.28902e6			−0.118917
$269$			6.94559e6i			0.356822i	0.983956	+	0.178411i	$0.0570957\pi$
$269$			6.94559e6i			0.356822i	−0.983956	+	0.178411i	$0.942904\pi$
$270$	4.50391e6	−	9.42279e6i	0.228822	−	0.478728i
$271$	−2.55822e6			−0.128537			−0.0642687	−	0.997933i	$-0.520471\pi$
$271$	−2.55822e6			−0.128537			−0.0642687	+	0.997933i	$0.520471\pi$
$272$		−	1.88220e7i		−	0.935318i
$273$	−2.13647e7	−	1.70037e7i	−1.05005	−	0.835712i
$274$	3.15986e7			1.53609
$275$		−	4.73782e6i		−	0.227814i
$276$	759318.	−	954060.i	0.0361157	−	0.0453783i
$277$	−1.78029e6			−0.0837630			−0.0418815	−	0.999123i	$-0.513335\pi$
$277$	−1.78029e6			−0.0837630			−0.0418815	+	0.999123i	$0.513335\pi$
$278$			2.37653e7i			1.10614i
$279$	−5.43356e6	−	2.35941e7i	−0.250191	−	1.08640i
$280$	1.23158e7			0.561032
$281$		−	3.36915e7i		−	1.51845i	−0.650826	−	0.759227i	$-0.725577\pi$
$281$		−	3.36915e7i		−	1.51845i	0.650826	−	0.759227i	$-0.274423\pi$
$282$	1.22396e7	+	9.74130e6i	0.545784	+	0.434380i
$283$	4.57062e6			0.201658			0.100829	−	0.994904i	$-0.467850\pi$
$283$	4.57062e6			0.201658			0.100829	+	0.994904i	$0.467850\pi$
$284$		−	1.49517e6i		−	0.0652732i
$285$	−1.31186e7	+	1.64831e7i	−0.566698	+	0.712038i
$286$	8.14923e6			0.348352
$287$			2.71733e7i			1.14947i
$288$	7.01087e6	−	1.61456e6i	0.293491	−	0.0675891i
$289$	7.56496e6			0.313410
$290$		−	1.37998e7i		−	0.565821i
$291$	1.52757e7	+	1.21577e7i	0.619901	+	0.493368i
$292$	2.97504e6			0.119493
$293$			1.49535e7i			0.594485i	0.954802	+	0.297243i	$0.0960670\pi$
$293$			1.49535e7i			0.594485i	−0.954802	+	0.297243i	$0.903933\pi$
$294$	9.41066e6	−	1.18242e7i	0.370321	−	0.465296i
$295$	1.39366e7			0.542864
$296$		−	1.15577e7i		−	0.445653i
$297$	−7.12675e6	−	3.40645e6i	−0.272033	−	0.130027i
$298$	−5.07737e7			−1.91863
$299$		−	1.09913e7i		−	0.411185i
$300$	2.42366e6	+	1.92894e6i	0.0897650	+	0.0714423i
$301$	−1.17885e7			−0.432273
$302$		−	3.23221e7i		−	1.17349i
$303$	1.26917e7	−	1.59468e7i	0.456240	−	0.573251i
$304$	−5.83728e7			−2.07773
$305$			1.78893e7i			0.630514i
$306$	−5.71833e6	−	2.48306e7i	−0.199574	−	0.866608i
$307$	3.20285e7			1.10693			0.553467	−	0.832871i	$-0.313305\pi$
$307$	3.20285e7			1.10693			0.553467	+	0.832871i	$0.313305\pi$
$308$			1.66753e6i			0.0570719i
$309$	−1.54828e7	−	1.23224e7i	−0.524775	−	0.417658i
$310$	−1.76225e7			−0.591537
$311$			2.90897e7i			0.967071i	0.875325	+	0.483535i	$0.160648\pi$
$311$			2.90897e7i			0.967071i	−0.875325	+	0.483535i	$0.839352\pi$
$312$	1.85334e7	−	2.32867e7i	0.610228	−	0.766732i
$313$	−2.25247e7			−0.734559			−0.367280	−	0.930111i	$-0.619711\pi$
$313$	−2.25247e7			−0.734559			−0.367280	+	0.930111i	$0.619711\pi$
$314$		−	4.07842e7i		−	1.31736i
$315$	1.87725e7	−	4.32320e6i	0.600608	−	0.138316i
$316$	−6.19830e6			−0.196432
$317$		−	4.68720e7i		−	1.47142i	−0.677298	−	0.735709i	$-0.736849\pi$
$317$		−	4.68720e7i		−	1.47142i	0.677298	−	0.735709i	$-0.263151\pi$
$318$	−3.04177e7	−	2.42089e7i	−0.945899	−	0.752824i
$319$	−1.04372e7			−0.321524
$320$			1.30502e7i			0.398262i
$321$	2.65466e7	−	3.33550e7i	0.802591	−	1.00843i
$322$	1.70616e7			0.511037
$323$			5.13967e7i			1.52520i
$324$	4.64415e6	−	2.25883e6i	0.136544	−	0.0664124i
$325$	2.79220e7			0.813385
$326$			1.90844e7i			0.550842i
$327$	1.19319e7	+	9.49634e6i	0.341244	+	0.271590i
$328$	−2.96179e7			−0.839331
$329$			2.88537e7i			0.810241i
$330$	−3.58025e6	+	4.49848e6i	−0.0996258	+	0.125177i
$331$	2.43741e7			0.672116			0.336058	−	0.941841i	$-0.390906\pi$
$331$	2.43741e7			0.672116			0.336058	+	0.941841i	$0.390906\pi$
$332$			9.07680e6i			0.248038i
$333$	−4.05709e6	−	1.76170e7i	−0.109871	−	0.477090i
$334$	1.93384e7			0.519018
$335$		−	1.45570e7i		−	0.387203i
$336$	4.17655e7	+	3.32403e7i	1.10103	+	0.876290i
$337$	−4.01005e7			−1.04776			−0.523878	−	0.851793i	$-0.675515\pi$
$337$	−4.01005e7			−1.04776			−0.523878	+	0.851793i	$0.675515\pi$
$338$			6.58437e6i			0.170516i
$339$	−1.94900e7	+	2.44885e7i	−0.500279	+	0.628585i
$340$	−2.44478e6			−0.0622018
$341$			1.33284e7i			0.336136i
$342$	−7.70072e7	+	1.77343e7i	−1.92510	+	0.443338i
$343$	−2.24318e7			−0.555880
$344$		−	1.28490e7i		−	0.315641i
$345$	6.06736e6	+	4.82890e6i	0.147755	+	0.117595i
$346$	1.80563e7			0.435914
$347$			6.13151e6i			0.146750i	0.997304	+	0.0733752i	$0.0233771\pi$
$347$			6.13151e6i			0.146750i	−0.997304	+	0.0733752i	$0.976623\pi$
$348$	4.24938e6	−	5.33921e6i	0.100830	−	0.126689i
$349$	−1.40998e6			−0.0331694			−0.0165847	−	0.999862i	$-0.505279\pi$
$349$	−1.40998e6			−0.0331694			−0.0165847	+	0.999862i	$0.505279\pi$
$350$			4.33426e7i			1.01091i
$351$	2.00756e7	−	4.20009e7i	0.464246	−	0.971265i
$352$	−3.96048e6			−0.0908071
$353$			8.24893e7i			1.87531i	0.347566	+	0.937655i	$0.387008\pi$
$353$			8.24893e7i			1.87531i	−0.347566	+	0.937655i	$0.612992\pi$
$354$	4.09046e7	+	3.25552e7i	0.922068	+	0.733857i
$355$	9.50853e6			0.212534
$356$			9.26331e6i			0.205313i
$357$	2.92678e7	−	3.67741e7i	0.643259	−	0.808235i
$358$	1.95994e7			0.427163
$359$		−	2.62249e7i		−	0.566801i	−0.959002	−	0.283400i	$-0.908537\pi$
$359$		−	2.62249e7i		−	0.566801i	0.959002	−	0.283400i	$-0.0914625\pi$
$360$	4.71212e6	+	2.04614e7i	0.100997	+	0.438558i
$361$	1.12351e8			2.38811
$362$		−	6.55229e7i		−	1.38123i
$363$	3.40234e6	+	2.70786e6i	0.0711308	+	0.0566116i
$364$	−9.82748e6			−0.203769
$365$			1.89198e7i			0.389079i
$366$	−4.17886e7	+	5.25061e7i	−0.852343	+	1.07094i
$367$	−8.60190e7			−1.74019			−0.870094	−	0.492886i	$-0.835942\pi$
$367$	−8.60190e7			−1.74019			−0.870094	+	0.492886i	$0.835942\pi$
$368$			2.14868e7i			0.431150i
$369$	−4.51457e7	+	1.03968e7i	−0.898540	+	0.206928i
$370$	−1.31582e7			−0.259772
$371$		−	7.17067e7i		−	1.40423i
$372$	−6.81822e6	−	5.42650e6i	−0.132447	−	0.105412i
$373$	6.51372e7			1.25517			0.627585	−	0.778548i	$-0.284044\pi$
$373$	6.51372e7			1.25517			0.627585	+	0.778548i	$0.284044\pi$
$374$			1.40269e7i			0.268132i
$375$	−2.85027e7	+	3.58127e7i	−0.540495	+	0.679115i
$376$	−3.14495e7			−0.591630
$377$		−	6.15110e7i		−	1.14796i
$378$	6.51971e7	+	3.11629e7i	1.20713	+	0.576983i
$379$	3.82484e7			0.702580			0.351290	−	0.936267i	$-0.385743\pi$
$379$	3.82484e7			0.702580			0.351290	+	0.936267i	$0.385743\pi$
$380$			7.58201e6i			0.138176i
$381$	3.82022e7	+	3.04045e7i	0.690739	+	0.549746i
$382$	2.19331e6			0.0393468
$383$			2.01915e6i			0.0359395i	0.999839	+	0.0179698i	$0.00572026\pi$
$383$			2.01915e6i			0.0359395i	−0.999839	+	0.0179698i	$0.994280\pi$
$384$	−4.11043e7	+	5.16463e7i	−0.725928	+	0.912106i
$385$	−1.06047e7			−0.185830
$386$		−	4.23644e7i		−	0.736612i
$387$	−4.51037e6	−	1.95853e7i	−0.0778179	−	0.337908i
$388$	7.02664e6			0.120296
$389$			1.28575e6i			0.0218429i	0.999940	+	0.0109214i	$0.00347647\pi$
$389$			1.28575e6i			0.0218429i	−0.999940	+	0.0109214i	$0.996524\pi$
$390$	−2.65114e7	−	2.10999e7i	−0.446930	−	0.355703i
$391$	1.89189e7			0.316495
$392$			3.03820e7i			0.504381i
$393$	4.33295e7	−	5.44422e7i	0.713849	−	0.896929i
$394$	9.53231e7			1.55851
$395$		−	3.94182e7i		−	0.639595i
$396$	−2.77044e6	+	638014.i	−0.0446131	+	0.0102741i
$397$	3.91765e7			0.626116			0.313058	−	0.949734i	$-0.398647\pi$
$397$	3.91765e7			0.626116			0.313058	+	0.949734i	$0.398647\pi$
$398$		−	1.03013e8i		−	1.63396i
$399$	−1.14048e8	−	9.07684e7i	−1.79543	−	1.42895i
$400$	−5.45842e7			−0.852879
$401$			4.98966e7i			0.773817i	0.922118	+	0.386908i	$0.126457\pi$
$401$			4.98966e7i			0.773817i	−0.922118	+	0.386908i	$0.873543\pi$
$402$	3.40045e7	−	4.27256e7i	0.523430	−	0.657673i
$403$	−7.85500e7			−1.20014
$404$		−	7.33532e6i		−	0.111244i
$405$	1.43651e7	+	2.95345e7i	0.216244	+	0.444596i
$406$	9.54821e7			1.42674
$407$			9.95196e6i			0.147613i
$408$	4.00824e7	+	3.19008e7i	0.590165	+	0.469701i
$409$	−9.10442e6			−0.133071			−0.0665353	−	0.997784i	$-0.521195\pi$
$409$	−9.10442e6			−0.133071			−0.0665353	+	0.997784i	$0.521195\pi$
$410$			3.37194e7i			0.489247i
$411$	−6.18791e7	+	7.77491e7i	−0.891289	+	1.11988i
$412$	−7.12188e6			−0.101836
$413$			9.64286e7i			1.36885i
$414$	6.52792e6	+	2.83461e7i	0.0919971	+	0.399477i
$415$	−5.77240e7			−0.807630
$416$		−	2.33408e7i		−	0.324217i
$417$	−5.84751e7	−	4.65393e7i	−0.806423	−	0.641817i
$418$	4.35018e7			0.595632
$419$		−	7.33984e7i		−	0.997802i	−0.866659	−	0.498901i	$-0.833737\pi$
$419$		−	7.33984e7i		−	0.997802i	0.866659	−	0.498901i	$-0.166263\pi$
$420$	4.31757e6	−	5.42489e6i	0.0582763	−	0.0732223i
$421$	−8.18943e7			−1.09751			−0.548754	−	0.835984i	$-0.684898\pi$
$421$	−8.18943e7			−1.09751			−0.548754	+	0.835984i	$0.684898\pi$
$422$		−	9.29323e7i		−	1.23660i
$423$	−4.79375e7	+	1.10397e7i	−0.633365	+	0.145860i
$424$	7.81576e7			1.02535
$425$			4.80609e7i			0.626074i
$426$	2.79080e7	+	2.22115e7i	0.360994	+	0.287308i
$427$	−1.23778e8			−1.58986
$428$		−	1.53429e7i		−	0.195693i
$429$	−1.59585e7	+	2.00514e7i	−0.202126	+	0.253964i
$430$	−1.46283e7			−0.183988
$431$		−	6.34091e7i		−	0.791990i	−0.918253	−	0.395995i	$-0.870400\pi$
$431$		−	6.34091e7i		−	0.791990i	0.918253	−	0.395995i	$-0.129600\pi$
$432$	−3.92456e7	+	8.21070e7i	−0.486787	+	1.01843i
$433$	−5.92822e7			−0.730232			−0.365116	−	0.930962i	$-0.618971\pi$
$433$	−5.92822e7			−0.730232			−0.365116	+	0.930962i	$0.618971\pi$
$434$		−	1.21931e8i		−	1.49158i
$435$	3.39548e7	+	2.70240e7i	0.412509	+	0.328308i
$436$	5.48851e6			0.0662209
$437$		−	5.86734e7i		−	0.703067i
$438$	−4.41957e7	+	5.55305e7i	−0.525966	+	0.660860i
$439$	4.05820e7			0.479668			0.239834	−	0.970814i	$-0.422907\pi$
$439$	4.05820e7			0.479668			0.239834	+	0.970814i	$0.422907\pi$
$440$		−	1.15587e7i		−	0.135691i
$441$	1.06650e7	+	4.63104e7i	0.124350	+	0.539961i
$442$	−8.26667e7			−0.957334
$443$		−	7.91832e7i		−	0.910798i	−0.890288	−	0.455399i	$-0.849497\pi$
$443$		−	7.91832e7i		−	0.910798i	0.890288	−	0.455399i	$-0.150503\pi$
$444$	−5.09098e6	−	4.05181e6i	−0.0581637	−	0.0462914i
$445$	−5.89101e7			−0.668513
$446$			1.33769e8i			1.50783i
$447$	9.94296e7	−	1.24930e8i	1.11325	−	1.39877i
$448$	−9.02957e7			−1.00423
$449$		−	4.94668e7i		−	0.546480i	−0.961946	−	0.273240i	$-0.911905\pi$
$449$		−	4.94668e7i		−	0.546480i	0.961946	−	0.273240i	$-0.0880954\pi$
$450$	−7.20093e7	+	1.65833e7i	−0.790225	+	0.181984i
$451$	2.55030e7			0.278011
$452$			1.12644e7i			0.121982i
$453$	7.95295e7	+	6.32960e7i	0.855527	+	0.680898i
$454$	1.79350e8			1.91661
$455$		−	6.24980e7i		−	0.663487i
$456$	9.89342e7	−	1.24308e8i	1.04340	−	1.31100i
$457$	−5.36689e7			−0.562308			−0.281154	−	0.959663i	$-0.590717\pi$
$457$	−5.36689e7			−0.562308			−0.281154	+	0.959663i	$0.590717\pi$
$458$			8.88897e7i			0.925241i
$459$	7.22945e7	+	3.45554e7i	0.747596	+	0.357337i
$460$	2.79091e6			0.0286729
$461$			5.43448e7i			0.554696i	0.960770	+	0.277348i	$0.0894555\pi$
$461$			5.43448e7i			0.554696i	−0.960770	+	0.277348i	$0.910545\pi$
$462$	−3.11253e7	−	2.47721e7i	−0.315637	−	0.251210i
$463$	−1.67649e8			−1.68911			−0.844553	−	0.535472i	$-0.820134\pi$
$463$	−1.67649e8			−1.68911			−0.844553	+	0.535472i	$0.820134\pi$
$464$			1.20247e8i			1.20370i
$465$	3.45099e7	−	4.33606e7i	0.343229	−	0.431257i
$466$	1.42720e8			1.41035
$467$			1.42546e8i			1.39960i	0.714337	+	0.699801i	$0.246728\pi$
$467$			1.42546e8i			1.39960i	−0.714337	+	0.699801i	$0.753272\pi$
$468$	−3.76008e6	−	1.63273e7i	−0.0366826	−	0.159286i
$469$	1.00721e8			0.976344
$470$			3.58046e7i			0.344862i
$471$	1.00351e8	+	7.98672e7i	0.960412	+	0.764374i
$472$	−1.05104e8			−0.999520
$473$			1.10639e7i			0.104550i
$474$	9.20789e7	−	1.15694e8i	0.864620	−	1.08637i
$475$	1.49052e8			1.39077
$476$		−	1.69156e7i		−	0.156844i
$477$	1.19133e8	−	2.74356e7i	1.09768	−	0.252790i
$478$	−6.87691e7			−0.629665
$479$		−	1.30914e8i		−	1.19118i	−0.803287	−	0.595591i	$-0.796918\pi$
$479$		−	1.30914e8i		−	1.19118i	0.803287	−	0.595591i	$-0.203082\pi$
$480$	1.28844e7	+	1.02545e7i	0.116504	+	0.0927233i
$481$	−5.86511e7			−0.527037
$482$			5.45341e6i			0.0486997i
$483$	−3.34115e7	+	4.19805e7i	−0.296521	+	0.372569i
$484$	1.56503e6			0.0138034
$485$			4.46860e7i			0.391694i
$486$	−2.68290e7	+	1.20241e8i	−0.233720	+	1.04748i
$487$	1.96605e8			1.70219			0.851093	−	0.525015i	$-0.175940\pi$
$487$	1.96605e8			1.70219			0.851093	+	0.525015i	$0.175940\pi$
$488$		−	1.34913e8i		−	1.16090i
$489$	−4.69578e7	−	3.73728e7i	−0.401588	−	0.319617i
$490$	3.45893e7			0.294004
$491$			4.48770e7i			0.379123i	0.981869	+	0.189561i	$0.0607066\pi$
$491$			4.48770e7i			0.379123i	−0.981869	+	0.189561i	$0.939293\pi$
$492$	−1.03832e7	+	1.30462e7i	−0.0871841	+	0.109544i
$493$	1.05876e8			0.883604
$494$			2.56374e8i			2.12664i
$495$	−4.05746e6	−	1.76186e7i	−0.0334532	−	0.145263i
$496$	1.53556e8			1.25841
$497$			6.57903e7i			0.535911i
$498$	−1.69423e8	−	1.34840e8i	−1.37178	−	1.09177i
$499$	−7.28271e7			−0.586127			−0.293063	−	0.956093i	$-0.594675\pi$
$499$	−7.28271e7			−0.586127			−0.293063	+	0.956093i	$0.594675\pi$
$500$			1.64734e7i			0.131787i
$501$	−3.78702e7	+	4.75828e7i	−0.301151	+	0.378387i
$502$	−2.36784e8			−1.87172
$503$			7.83377e7i			0.615555i	0.951458	+	0.307777i	$0.0995852\pi$
$503$			7.83377e7i			0.615555i	−0.951458	+	0.307777i	$0.900415\pi$
$504$	−1.41574e8	+	3.26036e7i	−1.10584	+	0.254668i
$505$	4.66491e7			0.362217
$506$		−	1.60129e7i		−	0.123600i
$507$	−1.62010e7	−	1.28941e7i	−0.124314	−	0.0989389i
$508$	1.75726e7			0.134043
$509$			2.24352e8i			1.70128i	0.525746	+	0.850641i	$0.323786\pi$
$509$			2.24352e8i			1.70128i	−0.525746	+	0.850641i	$0.676214\pi$
$510$	3.63185e7	−	4.56330e7i	0.273790	−	0.344008i
$511$	−1.30908e8			−0.981075
$512$		−	9.22812e7i		−	0.687549i
$513$	1.07167e8	−	2.24207e8i	0.793794	−	1.66072i
$514$	−1.34467e8			−0.990207
$515$		−	4.52917e7i		−	0.331587i
$516$	−5.65977e6	−	4.50451e6i	−0.0411955	−	0.0327867i
$517$	2.70801e7			0.195965
$518$		−	9.10428e7i		−	0.655023i
$519$	−3.53594e7	+	4.44280e7i	−0.252932	+	0.317801i
$520$	6.81205e7			0.484471
$521$			7.44722e7i			0.526600i	0.964714	+	0.263300i	$0.0848109\pi$
$521$			7.44722e7i			0.526600i	−0.964714	+	0.263300i	$0.915189\pi$
$522$	3.65323e7	+	1.58634e8i	0.256842	+	1.11528i
$523$	−1.27965e8			−0.894509			−0.447254	−	0.894407i	$-0.647598\pi$
$523$	−1.27965e8			−0.894509			−0.447254	+	0.894407i	$0.647598\pi$
$524$		−	2.50428e7i		−	0.174056i
$525$	−1.06646e8	−	8.48774e7i	−0.736997	−	0.586562i
$526$	−8.19236e7			−0.562927
$527$		−	1.35205e8i		−	0.923763i
$528$	3.11971e7	−	3.91982e7i	0.211940	−	0.266296i
$529$	1.26438e8			0.854107
$530$		−	8.89809e7i		−	0.597680i
$531$	−1.60206e8	+	3.68944e7i	−1.07003	+	0.246421i
$532$	−5.24606e7			−0.348416
$533$			1.50300e8i			0.992608i
$534$	−1.72904e8	−	1.37611e8i	−1.13549	−	0.903712i
$535$	9.75734e7			0.637191
$536$			1.09783e8i			0.712917i
$537$	−3.83813e7	+	4.82248e7i	−0.247854	+	0.311421i
$538$	−5.96341e7			−0.382955
$539$		−	2.61610e7i		−	0.167066i
$540$	1.06648e7	+	5.09758e6i	0.0677287	+	0.0323730i
$541$	−1.24047e8			−0.783421			−0.391711	−	0.920088i	$-0.628117\pi$
$541$	−1.24047e8			−0.783421			−0.391711	+	0.920088i	$0.628117\pi$
$542$		−	2.19646e7i		−	0.137951i
$543$	1.61221e8	+	1.28313e8i	1.00698	+	0.801438i
$544$	4.01755e7			0.249554
$545$			3.49042e7i			0.215620i
$546$	1.45992e8	−	1.83435e8i	0.896917	−	1.12695i
$547$	1.73340e8			1.05910			0.529549	−	0.848279i	$-0.322361\pi$
$547$	1.73340e8			1.05910			0.529549	+	0.848279i	$0.322361\pi$
$548$			3.57636e7i			0.217320i
$549$	−4.73585e7	−	2.05644e8i	−0.286207	−	1.24279i
$550$	4.06784e7			0.244498
$551$		−	3.28355e8i		−	1.96285i
$552$	−4.57572e7	−	3.64173e7i	−0.272046	−	0.216516i
$553$	2.72738e8			1.61276
$554$		−	1.52854e7i		−	0.0898976i
$555$	2.57676e7	−	3.23761e7i	0.150728	−	0.189385i
$556$	−2.68978e7			−0.156492
$557$			3.76312e7i			0.217762i	0.994055	+	0.108881i	$0.0347268\pi$
$557$			3.76312e7i			0.217762i	−0.994055	+	0.108881i	$0.965273\pi$
$558$	2.02576e8	−	4.66520e7i	1.16597	−	0.268515i
$559$	−6.52040e7			−0.373283
$560$			1.22176e8i			0.695702i
$561$	−3.45137e7	−	2.74688e7i	−0.195480	−	0.155579i
$562$	2.89272e8			1.62966
$563$		−	2.07977e8i		−	1.16544i	−0.812673	−	0.582720i	$-0.801989\pi$
$563$		−	2.07977e8i		−	1.16544i	0.812673	−	0.582720i	$-0.198011\pi$
$564$	−1.10253e7	+	1.38530e7i	−0.0614546	+	0.0772157i
$565$	−7.16363e7			−0.397180
$566$			3.92429e7i			0.216427i
$567$	−2.04352e8	+	9.93932e7i	−1.12106	+	0.545265i
$568$	−7.17090e7			−0.391317
$569$			1.59764e8i			0.867244i	0.901095	+	0.433622i	$0.142765\pi$
$569$			1.59764e8i			0.867244i	−0.901095	+	0.433622i	$0.857235\pi$
$570$	−1.41522e8	−	1.12635e8i	−0.764186	−	0.608201i
$571$	6.00513e7			0.322563			0.161281	−	0.986908i	$-0.448437\pi$
$571$	6.00513e7			0.322563			0.161281	+	0.986908i	$0.448437\pi$
$572$			9.22340e6i			0.0492837i
$573$	−4.29513e6	+	5.39670e6i	−0.0228304	+	0.0286856i
$574$	−2.33308e8			−1.23365
$575$		−	5.48653e7i		−	0.288599i
$576$	−3.45479e7	−	1.50017e8i	−0.180782	−	0.785006i
$577$	1.58727e8			0.826270			0.413135	−	0.910670i	$-0.364434\pi$
$577$	1.58727e8			0.826270			0.413135	+	0.910670i	$0.364434\pi$
$578$			6.49520e7i			0.336364i
$579$	1.04239e8	+	8.29616e7i	0.537023	+	0.427407i
$580$	1.56188e7			0.0800504
$581$		−	3.99397e8i		−	2.03646i
$582$	−1.04384e8	+	1.31156e8i	−0.529501	+	0.665301i
$583$	−6.72990e7			−0.339627
$584$		−	1.42684e8i		−	0.716371i
$585$	1.03834e8	−	2.39123e7i	0.518647	−	0.119441i
$586$	−1.28389e8			−0.638023
$587$			1.31689e8i			0.651079i	0.945528	+	0.325539i	$0.105546\pi$
$587$			1.31689e8i			0.651079i	−0.945528	+	0.325539i	$0.894454\pi$
$588$	1.33828e7	+	1.06511e7i	0.0658286	+	0.0523917i
$589$	−4.19311e8			−2.05206
$590$			1.19658e8i			0.582622i
$591$	−1.86670e8	+	2.34545e8i	−0.904299	+	1.13622i
$592$	1.14656e8			0.552627
$593$			3.77910e8i			1.81227i	0.422984	+	0.906137i	$0.360983\pi$
$593$			3.77910e8i			1.81227i	−0.422984	+	0.906137i	$0.639017\pi$
$594$	2.92474e7	−	6.11895e7i	0.139549	−	0.291956i
$595$	1.07575e8			0.510695
$596$		−	5.74664e7i		−	0.271441i
$597$	2.53466e8	+	2.01729e8i	1.19123	+	0.948079i
$598$	9.43705e7			0.441299
$599$			1.23920e8i			0.576581i	0.957543	+	0.288291i	$0.0930869\pi$
$599$			1.23920e8i			0.576581i	−0.957543	+	0.288291i	$0.906913\pi$
$600$	9.25131e7	−	1.16240e8i	0.428302	−	0.538148i
$601$	−1.29691e8			−0.597430			−0.298715	−	0.954342i	$-0.596558\pi$
$601$	−1.29691e8			−0.597430			−0.298715	+	0.954342i	$0.596558\pi$
$602$		−	1.01215e8i		−	0.463931i
$603$	3.85369e7	+	1.67338e8i	0.175762	+	0.763208i
$604$	3.65826e7			0.166021
$605$			9.95285e6i			0.0449450i
$606$	1.36917e8	+	1.08970e8i	0.615234	+	0.489653i
$607$	6.95280e7			0.310881			0.155440	−	0.987845i	$-0.450320\pi$
$607$	6.95280e7			0.310881			0.155440	+	0.987845i	$0.450320\pi$
$608$		−	1.24596e8i		−	0.554364i
$609$	−1.86981e8	+	2.34936e8i	−0.827840	+	1.04016i
$610$	−1.53596e8			−0.676691
$611$			1.59595e8i			0.699672i
$612$	2.81036e7	−	6.47208e6i	0.122605	−	0.0282351i
$613$	2.15222e7			0.0934343			0.0467171	−	0.998908i	$-0.485124\pi$
$613$	2.15222e7			0.0934343			0.0467171	+	0.998908i	$0.485124\pi$
$614$			2.74993e8i			1.18800i
$615$	−8.29676e7	−	6.60323e7i	−0.356683	−	0.283878i
$616$	7.99759e7			0.342150
$617$		−	4.63719e7i		−	0.197424i	−0.995116	−	0.0987119i	$-0.968528\pi$
$617$		−	4.63719e7i		−	0.197424i	0.995116	−	0.0987119i	$-0.0314722\pi$
$618$	1.05799e8	−	1.32933e8i	0.448246	−	0.563208i
$619$	2.00493e8			0.845333			0.422666	−	0.906285i	$-0.361094\pi$
$619$	2.00493e8			0.845333			0.422666	+	0.906285i	$0.361094\pi$
$620$		−	1.99453e7i		−	0.0836886i
$621$	−8.25299e7	−	3.94477e7i	−0.344617	−	0.164720i
$622$	−2.49761e8			−1.03790
$623$		−	4.07604e8i		−	1.68568i
$624$	2.31011e8	+	1.83858e8i	0.950780	+	0.756708i
$625$	7.97033e7			0.326465
$626$		−	1.93395e8i		−	0.788356i
$627$	−8.51890e7	+	1.07037e8i	−0.345606	+	0.434243i
$628$	4.61601e7			0.186375
$629$		−	1.00954e8i		−	0.405668i
$630$	3.71185e7	+	1.61179e8i	0.148446	+	0.644595i
$631$	−2.28777e8			−0.910593			−0.455296	−	0.890340i	$-0.650467\pi$
$631$	−2.28777e8			−0.910593			−0.455296	+	0.890340i	$0.650467\pi$
$632$			2.97274e8i			1.17762i
$633$	2.28662e8	+	1.81988e8i	0.901537	+	0.717517i
$634$	4.02438e8			1.57918
$635$			1.11753e8i			0.436454i
$636$	2.73999e7	−	3.44271e7i	0.106507	−	0.133823i
$637$	1.54178e8			0.596490
$638$		−	8.96129e7i		−	0.345071i
$639$	−1.09304e8	+	2.51720e7i	−0.418922	+	0.0964750i
$640$	−1.51081e8			−0.576328
$641$			4.68559e7i			0.177906i	0.996036	+	0.0889528i	$0.0283520\pi$
$641$			4.68559e7i			0.177906i	−0.996036	+	0.0889528i	$0.971648\pi$
$642$	2.86383e8	+	2.27927e8i	1.08228	+	0.861370i
$643$	−4.42973e6			−0.0166627			−0.00833133	−	0.999965i	$-0.502652\pi$
$643$	−4.42973e6			−0.0166627			−0.00833133	+	0.999965i	$0.502652\pi$
$644$			1.93105e7i			0.0722998i
$645$	2.86465e7	−	3.59934e7i	0.106756	−	0.134135i
$646$	−4.41287e8			−1.63690
$647$		−	4.29638e8i		−	1.58632i	−0.609015	−	0.793158i	$-0.708435\pi$
$647$		−	4.29638e8i		−	1.58632i	0.609015	−	0.793158i	$-0.291565\pi$
$648$	−1.08335e8	−	2.22736e8i	−0.398147	−	0.818588i
$649$	9.05013e7			0.331071
$650$			2.39735e8i			0.872954i
$651$	3.00015e8	+	2.38777e8i	1.08743	+	0.865464i
$652$	−2.16000e7			−0.0779312
$653$			2.50420e8i			0.899352i	0.893192	+	0.449676i	$0.148461\pi$
$653$			2.50420e8i			0.899352i	−0.893192	+	0.449676i	$0.851539\pi$
$654$	−8.15346e7	+	1.02446e8i	−0.291480	+	0.366235i
$655$	1.59260e8			0.566738
$656$		−	2.93820e8i		−	1.04080i
$657$	−5.00864e7	−	2.17489e8i	−0.176613	−	0.766906i
$658$	−2.47735e8			−0.869580
$659$		−	3.48197e8i		−	1.21666i	−0.793684	−	0.608330i	$-0.791840\pi$
$659$		−	3.48197e8i		−	1.21666i	0.793684	−	0.608330i	$-0.208160\pi$
$660$	−5.09143e6	−	4.05218e6i	−0.0177096	−	0.0140947i
$661$	−3.12380e8			−1.08163			−0.540816	−	0.841141i	$-0.681884\pi$
$661$	−3.12380e8			−1.08163			−0.540816	+	0.841141i	$0.681884\pi$
$662$			2.09273e8i			0.721340i
$663$	1.61885e8	−	2.03404e8i	0.555477	−	0.697940i
$664$	4.35328e8			1.48701
$665$		−	3.33624e8i		−	1.13447i
$666$	1.51258e8	−	3.48338e7i	0.512031	−	0.117917i
$667$	−1.20866e8			−0.407312
$668$			2.18875e7i			0.0734288i
$669$	−3.29143e8	−	2.61959e8i	−1.09927	−	0.874891i
$670$	1.24985e8			0.415560
$671$			1.16169e8i			0.384525i
$672$	−7.09514e7	+	8.91482e7i	−0.233805	+	0.293768i
$673$	4.53025e8			1.48620			0.743099	−	0.669181i	$-0.233355\pi$
$673$	4.53025e8			1.48620			0.743099	+	0.669181i	$0.233355\pi$
$674$		−	3.44299e8i		−	1.12449i
$675$	1.00211e8	−	2.09656e8i	0.325841	−	0.681703i
$676$	−7.45228e6			−0.0241240
$677$			1.75815e7i			0.0566616i	0.999599	+	0.0283308i	$0.00901918\pi$
$677$			1.75815e7i			0.0566616i	−0.999599	+	0.0283308i	$0.990981\pi$
$678$	−2.10256e8	−	1.67339e8i	−0.674620	−	0.536918i
$679$	−3.09187e8			−0.987669
$680$			1.17253e8i			0.372904i
$681$	−3.51218e8	+	4.41295e8i	−1.11208	+	1.39729i
$682$	−1.14436e8			−0.360754
$683$		−	2.10343e7i		−	0.0660185i	−0.999455	−	0.0330093i	$-0.989491\pi$
$683$		−	2.10343e7i		−	0.0660185i	0.999455	−	0.0330093i	$-0.0105091\pi$
$684$	−2.00719e7	−	8.71578e7i	−0.0627220	−	0.272357i
$685$	−2.27439e8			−0.707610
$686$		−	1.92597e8i		−	0.596592i
$687$	−2.18716e8	−	1.74072e8i	−0.674543	−	0.536856i
$688$	1.27466e8			0.391408
$689$		−	3.96621e8i		−	1.21260i
$690$	−4.14604e7	+	5.20937e7i	−0.126208	+	0.158576i
$691$	3.85193e8			1.16747			0.583734	−	0.811945i	$-0.301591\pi$
$691$	3.85193e8			1.16747			0.583734	+	0.811945i	$0.301591\pi$
$692$			2.04364e7i			0.0616716i
$693$	1.21905e8	−	2.80739e7i	0.366287	−	0.0843534i
$694$	−5.26445e7			−0.157498
$695$		−	1.71057e8i		−	0.509550i
$696$	−2.56072e8	−	2.03803e8i	−0.759511	−	0.604480i
$697$	−2.58705e8			−0.764025
$698$		−	1.21060e7i		−	0.0355987i
$699$	−2.79488e8	+	3.51167e8i	−0.818335	+	1.02821i
$700$	−4.90557e7			−0.143020
$701$		−	3.42899e8i		−	0.995434i	−0.867339	−	0.497717i	$-0.834172\pi$
$701$		−	3.42899e8i		−	0.995434i	0.867339	−	0.497717i	$-0.165828\pi$
$702$	3.60616e8	+	1.72367e8i	1.04240	+	0.498246i
$703$	−3.13088e8			−0.901158
$704$			8.47453e7i			0.242883i
$705$	−8.80982e7	−	7.01157e7i	−0.251420	−	0.200100i
$706$	−7.08244e8			−2.01265
$707$			3.22769e8i			0.913342i
$708$	−3.68464e7	+	4.62964e7i	−0.103824	+	0.130451i
$709$	−8.67298e7			−0.243349			−0.121675	−	0.992570i	$-0.538826\pi$
$709$	−8.67298e7			−0.243349			−0.121675	+	0.992570i	$0.538826\pi$
$710$			8.16393e7i			0.228099i
$711$	1.04352e8	+	4.53125e8i	0.290330	+	1.26069i
$712$	4.44273e8			1.23086
$713$			1.54347e8i			0.425824i
$714$	3.15739e8	+	2.51291e8i	0.867427	+	0.690369i
$715$	−5.86564e7			−0.160471
$716$			2.21828e7i			0.0604336i
$717$	1.34670e8	−	1.69208e8i	0.365353	−	0.459054i
$718$	2.25164e8			0.608312
$719$		−	7.72888e7i		−	0.207936i	−0.994581	−	0.103968i	$-0.966846\pi$
$719$		−	7.72888e7i		−	0.207936i	0.994581	−	0.103968i	$-0.0331540\pi$
$720$	−2.02984e8	+	4.67458e7i	−0.543830	+	0.125241i
$721$	3.13377e8			0.836106
$722$			9.64633e8i			2.56301i
$723$	−1.34183e7	−	1.06793e7i	−0.0355043	−	0.0282572i
$724$	7.41596e7			0.195412
$725$		−	3.07044e8i		−	0.805723i
$726$	−2.32494e7	+	2.92121e7i	−0.0607577	+	0.0763402i
$727$	9.65172e7			0.251190			0.125595	−	0.992082i	$-0.459916\pi$
$727$	9.65172e7			0.251190			0.125595	+	0.992082i	$0.459916\pi$
$728$			4.71332e8i			1.22161i
$729$	−2.43318e8	−	3.01481e8i	−0.628047	−	0.778175i
$730$	−1.62443e8			−0.417574
$731$		−	1.12233e8i		−	0.287321i
$732$	−5.94270e7	−	4.72969e7i	−0.151513	−	0.120587i
$733$	1.31671e8			0.334332			0.167166	−	0.985929i	$-0.446538\pi$
$733$	1.31671e8			0.334332			0.167166	+	0.985929i	$0.446538\pi$
$734$		−	7.38550e8i		−	1.86763i
$735$	−6.77359e7	+	8.51080e7i	−0.170591	+	0.214342i
$736$	−4.58635e7			−0.115036
$737$		−	9.45302e7i		−	0.236139i
$738$	−8.92655e7	−	3.87616e8i	−0.222083	−	0.964346i
$739$	4.28137e8			1.06084			0.530419	−	0.847735i	$-0.322034\pi$
$739$	4.28137e8			1.06084			0.530419	+	0.847735i	$0.322034\pi$
$740$		−	1.48926e7i		−	0.0367516i
$741$	−6.30816e8	−	5.02055e8i	−1.55042	−	1.23395i
$742$	6.15666e8			1.50707
$743$		−	1.62861e8i		−	0.397054i	−0.980095	−	0.198527i	$-0.936384\pi$
$743$		−	1.62861e8i		−	0.397054i	0.980095	−	0.198527i	$-0.0636158\pi$
$744$	−2.60258e8	+	3.27006e8i	−0.631953	+	0.794029i
$745$	3.65458e8			0.883830
$746$			5.59261e8i			1.34709i
$747$	6.63557e8	−	1.52813e8i	1.59190	−	0.366605i
$748$	−1.58759e7			−0.0379343
$749$			6.75118e8i			1.60670i
$750$	−3.07484e8	−	2.44721e8i	−0.728851	−	0.580079i
$751$	−5.91156e8			−1.39567			−0.697834	−	0.716259i	$-0.745853\pi$
$751$	−5.91156e8			−1.39567			−0.697834	+	0.716259i	$0.745853\pi$
$752$		−	3.11989e8i		−	0.733645i
$753$	4.63691e8	−	5.82613e8i	1.08603	−	1.36457i
$754$	5.28127e8			1.23204
$755$			2.32648e8i			0.540577i
$756$	−3.52706e7	+	7.37909e7i	−0.0816296	+	0.170780i
$757$	−2.53338e8			−0.583999			−0.292000	−	0.956418i	$-0.594321\pi$
$757$	−2.53338e8			−0.583999			−0.292000	+	0.956418i	$0.594321\pi$
$758$			3.28397e8i			0.754035i
$759$	3.94001e7	+	3.13578e7i	0.0901097	+	0.0717167i
$760$	3.63637e8			0.828376
$761$			1.25680e8i			0.285175i	0.989782	+	0.142587i	$0.0455422\pi$
$761$			1.25680e8i			0.285175i	−0.989782	+	0.142587i	$0.954458\pi$
$762$	−2.61050e8	+	3.28001e8i	−0.590008	+	0.741327i
$763$	−2.41505e8			−0.543693
$764$			2.48242e6i			0.00556666i
$765$	4.11593e7	+	1.78725e8i	0.0919355	+	0.399210i
$766$	−1.73362e7			−0.0385716
$767$			5.33362e8i			1.18205i
$768$	−1.57915e8	−	1.25682e8i	−0.348610	−	0.277453i
$769$	3.39405e8			0.746344			0.373172	−	0.927762i	$-0.378270\pi$
$769$	3.39405e8			0.746344			0.373172	+	0.927762i	$0.378270\pi$
$770$		−	9.10509e7i		−	0.199440i
$771$	2.63325e8	−	3.30859e8i	0.574551	−	0.721905i
$772$	4.79485e7			0.104213
$773$			2.76288e8i			0.598169i	0.954227	+	0.299085i	$0.0966813\pi$
$773$			2.76288e8i			0.598169i	−0.954227	+	0.299085i	$0.903319\pi$
$774$	1.68158e8	−	3.87256e7i	0.362655	−	0.0835171i
$775$	−3.92097e8			−0.842342
$776$		−	3.37002e8i		−	0.721186i
$777$	2.24013e8	+	1.78288e8i	0.477541	+	0.380066i
$778$	−1.10394e7			−0.0234426
$779$			8.02324e8i			1.69722i
$780$	2.38812e7	−	3.00060e7i	0.0503236	−	0.0632301i
$781$	6.17463e7			0.129616
$782$			1.62436e8i			0.339674i
$783$	−4.61863e8	−	2.20761e8i	−0.962117	−	0.459873i
$784$	−3.01400e8			−0.625453
$785$			2.93556e8i			0.606850i
$786$	4.67435e8	+	3.72023e8i	0.962618	+	0.766129i
$787$	6.46616e8			1.32655			0.663273	−	0.748377i	$-0.269167\pi$
$787$	6.46616e8			1.32655			0.663273	+	0.748377i	$0.269167\pi$
$788$			1.07888e8i			0.220493i
$789$	1.60430e8	−	2.01575e8i	0.326629	−	0.410399i
$790$	3.38440e8			0.686437
$791$		−	4.95658e8i		−	1.00150i
$792$	3.05995e7	+	1.32872e8i	0.0615940	+	0.267459i
$793$	−6.84635e8			−1.37290
$794$			3.36366e8i			0.671971i
$795$	2.18940e8	+	1.74250e8i	0.435736	+	0.346794i
$796$	1.16591e8			0.231167
$797$		−	8.60041e8i		−	1.69881i	−0.527744	−	0.849403i	$-0.676962\pi$
$797$		−	8.60041e8i		−	1.69881i	0.527744	−	0.849403i	$-0.323038\pi$
$798$	7.79328e8	−	9.79202e8i	1.53360	−	1.92692i
$799$	−2.74704e8			−0.538547
$800$		−	1.16510e8i		−	0.227558i
$801$	6.77192e8	−	1.55953e8i	1.31769	−	0.303456i
$802$	−4.28407e8			−0.830489
$803$			1.22861e8i			0.237283i
$804$	4.83574e7	+	3.84867e7i	0.0930454	+	0.0740531i
$805$	−1.22806e8			−0.235413
$806$		−	6.74422e8i		−	1.28803i
$807$	1.16781e8	−	1.46731e8i	0.222203	−	0.279191i
$808$	−3.51806e8			−0.666913
$809$			5.70895e8i			1.07823i	0.842233	+	0.539114i	$0.181241\pi$
$809$			5.70895e8i			1.07823i	−0.842233	+	0.539114i	$0.818759\pi$
$810$	−2.53581e8	+	1.23337e8i	−0.477157	+	0.232081i
$811$	1.41408e8			0.265101			0.132551	−	0.991176i	$-0.457683\pi$
$811$	1.41408e8			0.265101			0.132551	+	0.991176i	$0.457683\pi$
$812$			1.08068e8i			0.201850i
$813$	5.40445e7	+	4.30130e7i	0.100573	+	0.0800439i
$814$	−8.54465e7			−0.158424
$815$		−	1.37366e8i		−	0.253750i
$816$	−3.16467e8	+	3.97631e8i	−0.582449	+	0.731828i
$817$	−3.48068e8			−0.638261
$818$		−	7.81696e7i		−	0.142816i
$819$	1.65451e8	+	7.18436e8i	0.301175	+	1.30779i
$820$	−3.81641e7			−0.0692171
$821$			1.08328e8i			0.195755i	0.995198	+	0.0978773i	$0.0312053\pi$
$821$			1.08328e8i			0.195755i	−0.995198	+	0.0978773i	$0.968795\pi$
$822$	−6.67546e8	−	5.31287e8i	−1.20189	−	0.956564i
$823$	3.21242e8			0.576278			0.288139	−	0.957589i	$-0.406963\pi$
$823$	3.21242e8			0.576278			0.288139	+	0.957589i	$0.406963\pi$
$824$			3.41569e8i			0.610516i
$825$	−7.96601e7	+	1.00090e8i	−0.141866	+	0.178250i
$826$	−8.27926e8			−1.46910
$827$			1.87711e8i			0.331874i	0.986136	+	0.165937i	$0.0530648\pi$
$827$			1.87711e8i			0.331874i	−0.986136	+	0.165937i	$0.946935\pi$
$828$	−3.20825e7	+	7.38839e6i	−0.0565167	+	0.0130154i
$829$	5.12600e8			0.899736			0.449868	−	0.893095i	$-0.351471\pi$
$829$	5.12600e8			0.899736			0.449868	+	0.893095i	$0.351471\pi$
$830$		−	4.95612e8i		−	0.866778i
$831$	3.76102e7	+	2.99333e7i	0.0655394	+	0.0521616i
$832$	−4.99440e8			−0.867188
$833$			2.65380e8i			0.459127i
$834$	3.99581e8	−	5.02061e8i	0.688822	−	0.865483i
$835$	−1.39194e8			−0.239090
$836$			4.92359e7i			0.0842680i
$837$	−2.81914e8	+	5.89803e8i	−0.480774	+	1.00584i
$838$	6.30191e8			1.07088
$839$			3.52199e8i			0.596352i	0.954511	+	0.298176i	$0.0963783\pi$
$839$			3.52199e8i			0.596352i	−0.954511	+	0.298176i	$0.903622\pi$
$840$	−2.60181e8	−	2.07073e8i	−0.438973	−	0.349370i
$841$	−8.15811e7			−0.137152
$842$		−	7.03136e8i		−	1.17789i
$843$	−5.66478e8	+	7.11762e8i	−0.945584	+	1.18810i
$844$	1.05182e8			0.174950
$845$		−	4.73929e7i		−	0.0785494i
$846$	−9.47856e7	−	4.11586e8i	−0.156542	−	0.679751i
$847$	−6.88646e7			−0.113330
$848$			7.75349e8i			1.27148i
$849$	−9.65581e7	−	7.68488e7i	−0.157785	−	0.125578i
$850$	−4.12646e8			−0.671925
$851$			1.15247e8i			0.186999i
$852$	−2.51392e7	+	3.15866e7i	−0.0406474	+	0.0510722i
$853$	−8.76921e8			−1.41291			−0.706453	−	0.707760i	$-0.749706\pi$
$853$	−8.76921e8			−1.41291			−0.706453	+	0.707760i	$0.749706\pi$
$854$		−	1.06274e9i		−	1.70630i
$855$	5.54281e8	−	1.27647e8i	0.886812	−	0.204227i
$856$	−7.35854e8			−1.17320
$857$		−	4.20740e8i		−	0.668453i	−0.942493	−	0.334227i	$-0.891525\pi$
$857$		−	4.20740e8i		−	0.668453i	0.942493	−	0.334227i	$-0.108475\pi$
$858$	−1.72159e8	−	1.37018e8i	−0.272564	−	0.216929i
$859$	−7.70655e8			−1.21585			−0.607925	−	0.793994i	$-0.707998\pi$
$859$	−7.70655e8			−1.21585			−0.607925	+	0.793994i	$0.707998\pi$
$860$		−	1.65565e7i		−	0.0260300i
$861$	4.56883e8	−	5.74060e8i	0.715807	−	0.899389i
$862$	5.44424e8			0.849993
$863$			2.91517e8i			0.453556i	0.973946	+	0.226778i	$0.0728193\pi$
$863$			2.91517e8i			0.453556i	−0.973946	+	0.226778i	$0.927181\pi$
$864$	−1.75257e8	−	8.37695e7i	−0.271728	−	0.129881i
$865$	−1.29965e8			−0.200807
$866$		−	5.08991e8i		−	0.783712i
$867$	−1.59816e8	−	1.27195e8i	−0.245224	−	0.195169i
$868$	1.38003e8			0.211024
$869$		−	2.55973e8i		−	0.390063i
$870$	−2.32025e8	+	2.91532e8i	−0.352353	+	0.442720i
$871$	5.57106e8			0.843109
$872$		−	2.63232e8i		−	0.396999i
$873$	−1.18298e8	−	5.13681e8i	−0.177800	−	0.772060i
$874$	5.03764e8			0.754558
$875$		−	7.24863e8i		−	1.08201i
$876$	−6.28501e7	−	5.00212e7i	−0.0934962	−	0.0744119i
$877$	2.08570e8			0.309210			0.154605	−	0.987976i	$-0.450590\pi$
$877$	2.08570e8			0.309210			0.154605	+	0.987976i	$0.450590\pi$
$878$			3.48433e8i			0.514797i
$879$	2.51424e8	−	3.15906e8i	0.370203	−	0.465148i
$880$	1.14666e8			0.168263
$881$		−	3.31715e8i		−	0.485106i	−0.970138	−	0.242553i	$-0.922015\pi$
$881$		−	3.31715e8i		−	0.485106i	0.970138	−	0.242553i	$-0.0779849\pi$
$882$	−3.97616e8	+	9.15684e7i	−0.579506	+	0.133457i
$883$	5.25935e8			0.763924			0.381962	−	0.924178i	$-0.375249\pi$
$883$	5.25935e8			0.763924			0.381962	+	0.924178i	$0.375249\pi$
$884$		−	9.35632e7i		−	0.135440i
$885$	−2.94423e8	−	2.34325e8i	−0.424758	−	0.338057i
$886$	6.79859e8			0.977502
$887$		−	1.61908e8i		−	0.232005i	−0.993249	−	0.116003i	$-0.962992\pi$
$887$		−	1.61908e8i		−	0.232005i	0.993249	−	0.116003i	$-0.0370081\pi$
$888$	−1.94327e8	+	2.44166e8i	−0.277520	+	0.348696i
$889$	−7.73228e8			−1.10053
$890$		−	5.05796e8i		−	0.717473i
$891$	9.32837e7	+	1.91791e8i	0.131878	+	0.271141i
$892$	−1.51402e8			−0.213322
$893$			8.51939e8i			1.19634i
$894$	1.07264e9	+	8.53692e8i	1.50121	+	1.19478i
$895$	−1.41072e8			−0.196776
$896$		−	1.04534e9i		−	1.45323i
$897$	−1.84805e8	+	2.32201e8i	−0.256056	+	0.321727i
$898$	4.24717e8			0.586503
$899$			8.63774e8i			1.18883i
$900$	−1.87692e7	−	8.15010e7i	−0.0257465	−	0.111798i
$901$	6.82688e8			0.933357
$902$			2.18966e8i			0.298372i
$903$	2.49041e8	+	1.98207e8i	0.338227	+	0.269189i
$904$	5.40248e8			0.731288
$905$			4.71619e8i			0.636276i
$906$	−5.43453e8	+	6.82832e8i	−0.730765	+	0.918183i
$907$	1.04292e9			1.39775			0.698877	−	0.715242i	$-0.253683\pi$
$907$	1.04292e9			1.39775			0.698877	+	0.715242i	$0.253683\pi$
$908$			2.02990e8i			0.271155i
$909$	−5.36247e8	+	1.23494e8i	−0.713959	+	0.164420i
$910$	5.36602e8			0.712078
$911$		−	7.73283e8i		−	1.02278i	−0.859348	−	0.511391i	$-0.829130\pi$
$911$		−	7.73283e8i		−	1.02278i	0.859348	−	0.511391i	$-0.170870\pi$
$912$	1.23317e9	+	9.81460e8i	1.62570	+	1.29386i
$913$	−3.74847e8			−0.492540
$914$		−	4.60796e8i		−	0.603490i
$915$	3.00785e8	−	3.77927e8i	0.392639	−	0.493338i
$916$	−1.00606e8			−0.130900
$917$			1.10193e9i			1.42905i
$918$	−2.96689e8	+	6.20713e8i	−0.383507	+	0.802348i
$919$	1.17870e9			1.51865			0.759323	−	0.650714i	$-0.225530\pi$
$919$	1.17870e9			1.51865			0.759323	+	0.650714i	$0.225530\pi$
$920$		−	1.33854e8i		−	0.171896i
$921$	−6.76629e8	−	5.38516e8i	−0.866107	−	0.689319i
$922$	−4.66599e8			−0.595320
$923$			3.63897e8i			0.462779i
$924$	2.80374e7	−	3.52281e7i	0.0355403	−	0.0446553i
$925$	−2.92768e8			−0.369912
$926$		−	1.43941e9i		−	1.81281i
$927$	1.19901e8	+	5.20644e8i	0.150516	+	0.653584i
$928$	−2.56666e8			−0.321163
$929$			2.44846e8i			0.305384i	0.988274	+	0.152692i	$0.0487942\pi$
$929$			2.44846e8i			0.305384i	−0.988274	+	0.152692i	$0.951206\pi$
$930$	3.72289e8	+	2.96298e8i	0.462841	+	0.368367i
$931$	8.23023e8			1.01991
$932$			1.61533e8i			0.199532i
$933$	4.89105e8	−	6.14545e8i	0.602222	−	0.756673i
$934$	−1.22389e9			−1.50211
$935$		−	1.00963e8i		−	0.123517i
$936$	−7.83069e8	+	1.80336e8i	−0.954932	+	0.219915i
$937$	−3.75897e8			−0.456930			−0.228465	−	0.973552i	$-0.573371\pi$
$937$	−3.75897e8			−0.456930			−0.228465	+	0.973552i	$0.573371\pi$
$938$			8.64783e8i			1.04785i
$939$	4.75854e8	+	3.78723e8i	0.574747	+	0.457431i
$940$	−4.05241e7			−0.0487899
$941$		−	9.68016e8i		−	1.16175i	−0.813992	−	0.580876i	$-0.802710\pi$
$941$		−	9.68016e8i		−	1.16175i	0.813992	−	0.580876i	$-0.197290\pi$
$942$	−6.85732e8	+	8.61600e8i	−0.820355	+	1.03075i
$943$	2.95333e8			0.352190
$944$		−	1.04266e9i		−	1.23945i
$945$	−4.69274e8	−	2.24304e8i	−0.556073	−	0.265792i
$946$	−9.49931e7			−0.112207
$947$			1.49923e9i			1.76530i	0.470027	+	0.882652i	$0.344244\pi$
$947$			1.49923e9i			1.76530i	−0.470027	+	0.882652i	$0.655756\pi$
$948$	1.30944e8	+	1.04216e8i	0.153696	+	0.122323i
$949$	−7.24071e8			−0.847193
$950$			1.27974e9i			1.49263i
$951$	−7.88090e8	+	9.90211e8i	−0.916293	+	1.15129i
$952$	−8.11284e8			−0.940290
$953$		−	3.09825e8i		−	0.357962i	−0.983853	−	0.178981i	$-0.942720\pi$
$953$		−	3.09825e8i		−	0.357962i	0.983853	−	0.178981i	$-0.0572801\pi$
$954$	2.35559e8	+	1.02287e9i	0.271303	+	1.17808i
$955$	−1.57870e7			−0.0181254
$956$		−	7.78338e7i		−	0.0890829i
$957$	2.20495e8	+	1.75488e8i	0.251572	+	0.200222i
$958$	1.12401e9			1.27842
$959$		−	1.57367e9i		−	1.78426i
$960$	2.19422e8	−	2.75697e8i	0.248009	−	0.311615i
$961$	2.15543e8			0.242864
$962$		−	5.03572e8i		−	0.565636i
$963$	−1.12164e9	+	2.58306e8i	−1.25596	+	0.289239i
$964$	−6.17223e6			−0.00688987
$965$			3.04929e8i			0.339326i
$966$	−3.60441e8	−	2.86868e8i	−0.399855	−	0.318237i
$967$	−2.99980e8			−0.331752			−0.165876	−	0.986147i	$-0.553045\pi$
$967$	−2.99980e8			−0.331752			−0.165876	+	0.986147i	$0.553045\pi$
$968$		−	7.50599e7i		−	0.0827526i
$969$	8.64167e8	−	1.08580e9i	0.949787	−	1.19338i
$970$	−3.83670e8			−0.420380
$971$			5.47979e8i			0.598558i	0.954166	+	0.299279i	$0.0967462\pi$
$971$			5.47979e8i			0.598558i	−0.954166	+	0.299279i	$0.903254\pi$
$972$	−1.36091e8	−	3.03654e7i	−0.148194	−	0.0330659i
$973$	1.18356e9			1.28485
$974$			1.68803e9i			1.82685i
$975$	−5.89875e8	−	4.69470e8i	−0.636423	−	0.506517i
$976$	1.33838e9			1.43956
$977$		−	1.09258e9i		−	1.17157i	−0.810466	−	0.585786i	$-0.800786\pi$
$977$		−	1.09258e9i		−	1.17157i	0.810466	−	0.585786i	$-0.199214\pi$
$978$	3.20879e8	−	4.03175e8i	0.343025	−	0.431000i
$979$	−3.82549e8			−0.407699
$980$			3.91486e7i			0.0415947i
$981$	−9.24021e7	−	4.01236e8i	−0.0978757	−	0.425004i
$982$	−3.85310e8			−0.406889
$983$			3.36671e8i			0.354442i	0.984171	+	0.177221i	$0.0567107\pi$
$983$			3.36671e8i			0.354442i	−0.984171	+	0.177221i	$0.943289\pi$
$984$	6.25703e8	+	4.97986e8i	0.656725	+	0.522675i
$985$	−6.86115e8			−0.717940
$986$			9.09043e8i			0.948317i
$987$	4.85137e8	−	6.09559e8i	0.504560	−	0.633963i
$988$	−2.90168e8			−0.300870
$989$			1.28123e8i			0.132445i
$990$	1.51272e8	−	3.48369e7i	0.155902	−	0.0359033i
$991$	6.84835e8			0.703663			0.351832	−	0.936063i	$-0.385559\pi$
$991$	6.84835e8			0.703663			0.351832	+	0.936063i	$0.385559\pi$
$992$			3.27765e8i			0.335759i
$993$	−5.14923e8	−	4.09817e8i	−0.525889	−	0.418545i
$994$	−5.64869e8			−0.575160
$995$			7.41463e8i			0.752697i
$996$	1.52614e8	−	1.91755e8i	0.154460	−	0.194074i
$997$	1.00327e9			1.01235			0.506177	−	0.862430i	$-0.331058\pi$
$997$	1.00327e9			1.01235			0.506177	+	0.862430i	$0.331058\pi$
$998$		−	6.25286e8i		−	0.629053i
$999$	−2.10498e8	+	4.40389e8i	−0.211130	+	0.441713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.14	yes	20
3.2	odd	2	inner	33.7.b.a.23.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.7	✓	20	3.2	odd	2	inner
33.7.b.a.23.14	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)

\(f(q)\)	\(=\)	\(q+8.58590i q^{2} +(-21.1258 - 16.8137i) q^{3} -9.71763 q^{4} -61.7994i q^{5} +(144.360 - 181.384i) q^{6} +427.595 q^{7} +466.063i q^{8} +(163.602 + 710.405i) q^{9} +O(q^{10})\)	\(q+8.58590i q^{2} +(-21.1258 - 16.8137i) q^{3} -9.71763 q^{4} -61.7994i q^{5} +(144.360 - 181.384i) q^{6} +427.595 q^{7} +466.063i q^{8} +(163.602 + 710.405i) q^{9} +530.603 q^{10} -401.312i q^{11} +(205.293 + 163.389i) q^{12} +2365.10 q^{13} +3671.29i q^{14} +(-1039.07 + 1305.56i) q^{15} -4623.50 q^{16} +4070.95i q^{17} +(-6099.47 + 1404.67i) q^{18} +12625.2 q^{19} +600.543i q^{20} +(-9033.31 - 7189.44i) q^{21} +3445.62 q^{22} -4647.31i q^{23} +(7836.22 - 9845.97i) q^{24} +11805.8 q^{25} +20306.5i q^{26} +(8488.29 - 17758.6i) q^{27} -4155.21 q^{28} -26007.8i q^{29} +(-11209.4 - 8921.38i) q^{30} -33212.1 q^{31} -9868.84i q^{32} +(-6747.52 + 8478.04i) q^{33} -34952.7 q^{34} -26425.1i q^{35} +(-1589.82 - 6903.45i) q^{36} -24798.6 q^{37} +108399. i q^{38} +(-49964.7 - 39766.0i) q^{39} +28802.4 q^{40} +63549.2i q^{41} +(61727.8 - 77559.0i) q^{42} -27569.2 q^{43} +3899.80i q^{44} +(43902.6 - 10110.5i) q^{45} +39901.3 q^{46} +67479.0i q^{47} +(97675.2 + 77737.9i) q^{48} +65188.7 q^{49} +101364. i q^{50} +(68447.5 - 86002.1i) q^{51} -22983.1 q^{52} -167698. i q^{53} +(152474. + 72879.6i) q^{54} -24800.8 q^{55} +199286. i q^{56} +(-266719. - 212277. i) q^{57} +223300. q^{58} +225514. i q^{59} +(10097.3 - 12687.0i) q^{60} -289474. q^{61} -285156. i q^{62} +(69955.3 + 303766. i) q^{63} -211171. q^{64} -146162. i q^{65} +(-72791.6 - 57933.5i) q^{66} +235553. q^{67} -39559.9i q^{68} +(-78138.2 + 98178.2i) q^{69} +226883. q^{70} +153861. i q^{71} +(-331093. + 76248.7i) q^{72} -306148. q^{73} -212918. i q^{74} +(-249408. - 198499. i) q^{75} -122687. q^{76} -171599. i q^{77} +(341426. - 428992. i) q^{78} +637841. q^{79} +285729. i q^{80} +(-477910. + 232447. i) q^{81} -545627. q^{82} -934055. i q^{83} +(87782.3 + 69864.3i) q^{84} +251582. q^{85} -236707. i q^{86} +(-437286. + 549436. i) q^{87} +187036. q^{88} -953248. i q^{89} +(86807.6 + 376943. i) q^{90} +1.01130e6 q^{91} +45160.8i q^{92} +(701634. + 558418. i) q^{93} -579368. q^{94} -780232. i q^{95} +(-165931. + 208487. i) q^{96} -723082. q^{97} +559703. i q^{98} +(285094. - 65655.3i) 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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