LMFDB - Embedded newform 33.9.b.a.23.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,9,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, 9, names="a")

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
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:	$13.4434941320$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.8320i q^{2} +(18.7312 - 78.8045i) q^{3} -61.9787 q^{4} -794.590i q^{5} +(-1405.24 - 334.014i) q^{6} +2438.07 q^{7} -3459.78i q^{8} +(-5859.29 - 2952.20i) q^{9} +O(q^{10})$	\(q-17.8320i q^{2} +(18.7312 - 78.8045i) q^{3} -61.9787 q^{4} -794.590i q^{5} +(-1405.24 - 334.014i) q^{6} +2438.07 q^{7} -3459.78i q^{8} +(-5859.29 - 2952.20i) q^{9} -14169.1 q^{10} -4414.43i q^{11} +(-1160.94 + 4884.20i) q^{12} +43779.7 q^{13} -43475.6i q^{14} +(-62617.2 - 14883.6i) q^{15} -77561.2 q^{16} +149669. i q^{17} +(-52643.6 + 104483. i) q^{18} -17473.1 q^{19} +49247.7i q^{20} +(45668.0 - 192131. i) q^{21} -78717.9 q^{22} +463124. i q^{23} +(-272646. - 64805.8i) q^{24} -240748. q^{25} -780678. i q^{26} +(-342398. + 406440. i) q^{27} -151109. q^{28} -499557. i q^{29} +(-265404. + 1.11659e6i) q^{30} +137455. q^{31} +497364. i q^{32} +(-347877. - 82687.5i) q^{33} +2.66889e6 q^{34} -1.93727e6i q^{35} +(363151. + 182974. i) q^{36} +564033. q^{37} +311580. i q^{38} +(820046. - 3.45004e6i) q^{39} -2.74911e6 q^{40} +376771. i q^{41} +(-3.42607e6 - 814351. i) q^{42} +5.67728e6 q^{43} +273601. i q^{44} +(-2.34579e6 + 4.65573e6i) q^{45} +8.25840e6 q^{46} -9.56433e6i q^{47} +(-1.45281e6 + 6.11217e6i) q^{48} +179407. q^{49} +4.29301e6i q^{50} +(1.17946e7 + 2.80347e6i) q^{51} -2.71341e6 q^{52} +4.43429e6i q^{53} +(7.24761e6 + 6.10563e6i) q^{54} -3.50766e6 q^{55} -8.43520e6i q^{56} +(-327293. + 1.37696e6i) q^{57} -8.90809e6 q^{58} +2.31520e6i q^{59} +(3.88094e6 + 922467. i) q^{60} -2.29915e7 q^{61} -2.45109e6i q^{62} +(-1.42854e7 - 7.19769e6i) q^{63} -1.09867e7 q^{64} -3.47869e7i q^{65} +(-1.47448e6 + 6.20332e6i) q^{66} +7.17358e6 q^{67} -9.27627e6i q^{68} +(3.64962e7 + 8.67486e6i) q^{69} -3.45453e7 q^{70} -3.78446e6i q^{71} +(-1.02140e7 + 2.02718e7i) q^{72} -9.80584e6 q^{73} -1.00578e7i q^{74} +(-4.50950e6 + 1.89720e7i) q^{75} +1.08296e6 q^{76} -1.07627e7i q^{77} +(-6.15209e7 - 1.46230e7i) q^{78} +1.13989e6 q^{79} +6.16293e7i q^{80} +(2.56157e7 + 3.45956e7i) q^{81} +6.71856e6 q^{82} +2.95242e7i q^{83} +(-2.83045e6 + 1.19080e7i) q^{84} +1.18925e8 q^{85} -1.01237e8i q^{86} +(-3.93673e7 - 9.35730e6i) q^{87} -1.52729e7 q^{88} +5.92978e7i q^{89} +(8.30208e7 + 4.18300e7i) q^{90} +1.06738e8 q^{91} -2.87038e7i q^{92} +(2.57469e6 - 1.08321e7i) q^{93} -1.70551e8 q^{94} +1.38840e7i q^{95} +(3.91945e7 + 9.31623e6i) q^{96} +7.89069e7 q^{97} -3.19918e6i q^{98} +(-1.30323e7 + 2.58654e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) $ 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * 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 $

$2$		−	17.8320i		−	1.11450i	−0.830346	−	0.557249i	$-0.811857\pi$
$2$		−	17.8320i		−	1.11450i	0.830346	−	0.557249i	$-0.188143\pi$
$3$	18.7312	−	78.8045i	0.231249	−	0.972895i
$3$	18.7312	−	78.8045i	0.231249	−	0.972895i
$4$	−61.9787			−0.242104
$5$		−	794.590i		−	1.27134i	−0.771959	−	0.635672i	$-0.780723\pi$
$5$		−	794.590i		−	1.27134i	0.771959	−	0.635672i	$-0.219277\pi$
$6$	−1405.24	−	334.014i	−1.08429	−	0.257727i
$7$	2438.07			1.01544			0.507721	−	0.861522i	$-0.330488\pi$
$7$	2438.07			1.01544			0.507721	+	0.861522i	$0.330488\pi$
$8$		−	3459.78i		−	0.844673i
$9$	−5859.29	−	2952.20i	−0.893048	−	0.449962i
$10$	−14169.1			−1.41691
$11$		−	4414.43i		−	0.301511i
$11$		−	4414.43i		−	0.301511i
$12$	−1160.94	+	4884.20i	−0.0559865	+	0.235542i
$13$	43779.7			1.53285			0.766425	−	0.642334i	$-0.222034\pi$
$13$	43779.7			1.53285			0.766425	+	0.642334i	$0.222034\pi$
$14$		−	43475.6i		−	1.13171i
$15$	−62617.2	−	14883.6i	−1.23688	−	0.293997i
$16$	−77561.2			−1.18349
$17$			149669.i			1.79199i	0.444066	+	0.895994i	$0.353536\pi$
$17$			149669.i			1.79199i	−0.444066	+	0.895994i	$0.646464\pi$
$18$	−52643.6	+	104483.i	−0.501482	+	0.995299i
$19$	−17473.1			−0.134078			−0.0670389	−	0.997750i	$-0.521355\pi$
$19$	−17473.1			−0.134078			−0.0670389	+	0.997750i	$0.521355\pi$
$20$			49247.7i			0.307798i
$21$	45668.0	−	192131.i	0.234820	−	0.987917i
$22$	−78717.9			−0.336034
$23$			463124.i			1.65495i	0.561500	+	0.827477i	$0.310224\pi$
$23$			463124.i			1.65495i	−0.561500	+	0.827477i	$0.689776\pi$
$24$	−272646.	−	64805.8i	−0.821777	−	0.195330i
$25$	−240748.			−0.616315
$26$		−	780678.i		−	1.70836i
$27$	−342398.	+	406440.i	−0.644282	+	0.764788i
$28$	−151109.			−0.245843
$29$		−	499557.i		−	0.706307i	−0.935565	−	0.353153i	$-0.885109\pi$
$29$		−	499557.i		−	0.706307i	0.935565	−	0.353153i	$-0.114891\pi$
$30$	−265404.	+	1.11659e6i	−0.327659	+	1.37850i
$31$	137455.			0.148838			0.0744189	−	0.997227i	$-0.476290\pi$
$31$	137455.			0.148838			0.0744189	+	0.997227i	$0.476290\pi$
$32$			497364.i			0.474324i
$33$	−347877.	−	82687.5i	−0.293339	−	0.0697243i
$34$	2.66889e6			1.99717
$35$		−	1.93727e6i		−	1.29098i
$36$	363151.	+	182974.i	0.216211	+	0.108938i
$37$	564033.			0.300952			0.150476	−	0.988614i	$-0.451919\pi$
$37$	564033.			0.300952			0.150476	+	0.988614i	$0.451919\pi$
$38$			311580.i			0.149429i
$39$	820046.	−	3.45004e6i	0.354470	−	1.49130i
$40$	−2.74911e6			−1.07387
$41$			376771.i			0.133334i	0.997775	+	0.0666672i	$0.0212366\pi$
$41$			376771.i			0.133334i	−0.997775	+	0.0666672i	$0.978763\pi$
$42$	−3.42607e6	−	814351.i	−1.10103	−	0.261706i
$43$	5.67728e6			1.66061			0.830303	−	0.557312i	$-0.188167\pi$
$43$	5.67728e6			1.66061			0.830303	+	0.557312i	$0.188167\pi$
$44$			273601.i			0.0729972i
$45$	−2.34579e6	+	4.65573e6i	−0.572057	+	1.13537i
$46$	8.25840e6			1.84444
$47$		−	9.56433e6i		−	1.96003i	−0.198919	−	0.980016i	$-0.563743\pi$
$47$		−	9.56433e6i		−	1.96003i	0.198919	−	0.980016i	$-0.436257\pi$
$48$	−1.45281e6	+	6.11217e6i	−0.273681	+	1.15141i
$49$	179407.			0.0311211
$50$			4.29301e6i			0.686882i
$51$	1.17946e7	+	2.80347e6i	1.74342	+	0.414396i
$52$	−2.71341e6			−0.371109
$53$			4.43429e6i			0.561980i	0.959711	+	0.280990i	$0.0906628\pi$
$53$			4.43429e6i			0.561980i	−0.959711	+	0.280990i	$0.909337\pi$
$54$	7.24761e6	+	6.10563e6i	0.852354	+	0.718051i
$55$	−3.50766e6			−0.383325
$56$		−	8.43520e6i		−	0.857716i
$57$	−327293.	+	1.37696e6i	−0.0310054	+	0.130443i
$58$	−8.90809e6			−0.787177
$59$			2.31520e6i			0.191065i	0.995426	+	0.0955323i	$0.0304553\pi$
$59$			2.31520e6i			0.191065i	−0.995426	+	0.0955323i	$0.969545\pi$
$60$	3.88094e6	+	922467.i	0.299455	+	0.0711780i
$61$	−2.29915e7			−1.66054			−0.830268	−	0.557365i	$-0.811813\pi$
$61$	−2.29915e7			−1.66054			−0.830268	+	0.557365i	$0.811813\pi$
$62$		−	2.45109e6i		−	0.165879i
$63$	−1.42854e7	−	7.19769e6i	−0.906837	−	0.456910i
$64$	−1.09867e7			−0.654857
$65$		−	3.47869e7i		−	1.94878i
$66$	−1.47448e6	+	6.20332e6i	−0.0777075	+	0.326925i
$67$	7.17358e6			0.355989			0.177995	−	0.984031i	$-0.443039\pi$
$67$	7.17358e6			0.355989			0.177995	+	0.984031i	$0.443039\pi$
$68$		−	9.27627e6i		−	0.433848i
$69$	3.64962e7	+	8.67486e6i	1.61010	+	0.382707i
$70$	−3.45453e7			−1.43879
$71$		−	3.78446e6i		−	0.148926i	−0.997224	−	0.0744630i	$-0.976276\pi$
$71$		−	3.78446e6i		−	0.148926i	0.997224	−	0.0744630i	$-0.0237243\pi$
$72$	−1.02140e7	+	2.02718e7i	−0.380071	+	0.754333i
$73$	−9.80584e6			−0.345297			−0.172649	−	0.984983i	$-0.555233\pi$
$73$	−9.80584e6			−0.345297			−0.172649	+	0.984983i	$0.555233\pi$
$74$		−	1.00578e7i		−	0.335410i
$75$	−4.50950e6	+	1.89720e7i	−0.142522	+	0.599610i
$76$	1.08296e6			0.0324608
$77$		−	1.07627e7i		−	0.306167i
$78$	−6.15209e7	−	1.46230e7i	−1.66205	−	0.395056i
$79$	1.13989e6			0.0292653			0.0146327	−	0.999893i	$-0.495342\pi$
$79$	1.13989e6			0.0292653			0.0146327	+	0.999893i	$0.495342\pi$
$80$			6.16293e7i			1.50462i
$81$	2.56157e7	+	3.45956e7i	0.595068	+	0.803675i
$82$	6.71856e6			0.148601
$83$			2.95242e7i			0.622109i	0.950392	+	0.311054i	$0.100682\pi$
$83$			2.95242e7i			0.622109i	−0.950392	+	0.311054i	$0.899318\pi$
$84$	−2.83045e6	+	1.19080e7i	−0.0568510	+	0.239179i
$85$	1.18925e8			2.27823
$86$		−	1.01237e8i		−	1.85074i
$87$	−3.93673e7	−	9.35730e6i	−0.687162	−	0.163333i
$88$	−1.52729e7			−0.254678
$89$			5.92978e7i			0.945101i	0.881303	+	0.472551i	$0.156667\pi$
$89$			5.92978e7i			0.945101i	−0.881303	+	0.472551i	$0.843333\pi$
$90$	8.30208e7	+	4.18300e7i	1.26537	+	0.637556i
$91$	1.06738e8			1.55652
$92$		−	2.87038e7i		−	0.400671i
$93$	2.57469e6	−	1.08321e7i	0.0344186	−	0.144804i
$94$	−1.70551e8			−2.18445
$95$			1.38840e7i			0.170459i
$96$	3.91945e7	+	9.31623e6i	0.461467	+	0.109687i
$97$	7.89069e7			0.891309			0.445654	−	0.895205i	$-0.352971\pi$
$97$	7.89069e7			0.891309			0.445654	+	0.895205i	$0.352971\pi$
$98$		−	3.19918e6i		−	0.0346844i
$99$	−1.30323e7	+	2.58654e7i	−0.135669	+	0.269264i
$100$	1.49213e7			0.149213
$101$		−	5.31378e7i		−	0.510644i	−0.966856	−	0.255322i	$-0.917819\pi$
$101$		−	5.31378e7i		−	0.510644i	0.966856	−	0.255322i	$-0.0821815\pi$
$102$	4.99914e7	−	2.10320e8i	0.461843	−	1.94303i
$103$	−7.34994e6			−0.0653032			−0.0326516	−	0.999467i	$-0.510395\pi$
$103$	−7.34994e6			−0.0653032			−0.0326516	+	0.999467i	$0.510395\pi$
$104$		−	1.51468e8i		−	1.29476i
$105$	−1.52665e8	−	3.62874e7i	−1.25598	−	0.298537i
$106$	7.90721e7			0.626325
$107$			2.06587e7i			0.157604i	0.996890	+	0.0788022i	$0.0251096\pi$
$107$			2.06587e7i			0.157604i	−0.996890	+	0.0788022i	$0.974890\pi$
$108$	2.12214e7	−	2.51906e7i	0.155984	−	0.185158i
$109$	9.90700e7			0.701837			0.350918	−	0.936406i	$-0.385869\pi$
$109$	9.90700e7			0.701837			0.350918	+	0.936406i	$0.385869\pi$
$110$			6.25484e7i			0.427214i
$111$	1.05650e7	−	4.44483e7i	0.0695950	−	0.292795i
$112$	−1.89100e8			−1.20176
$113$		−	6.46222e6i		−	0.0396340i	−0.999804	−	0.0198170i	$-0.993692\pi$
$113$		−	6.46222e6i		−	0.0396340i	0.999804	−	0.0198170i	$-0.00630836\pi$
$114$	2.45539e7	+	5.83627e6i	0.145379	+	0.0345554i
$115$	3.67993e8			2.10401
$116$			3.09619e7i			0.171000i
$117$	−2.56518e8	−	1.29247e8i	−1.36891	−	0.689724i
$118$	4.12845e7			0.212941
$119$			3.64903e8i			1.81966i
$120$	−5.14940e7	+	2.16642e8i	−0.248331	+	1.04476i
$121$	−1.94872e7			−0.0909091
$122$			4.09984e8i			1.85066i
$123$	2.96912e7	+	7.05737e6i	0.129720	+	0.0308335i
$124$	−8.51928e6			−0.0360343
$125$		−	1.19091e8i		−	0.487795i
$126$	−1.28349e8	+	2.54736e8i	−0.509225	+	1.01067i
$127$	−3.58839e8			−1.37938			−0.689692	−	0.724103i	$-0.742254\pi$
$127$	−3.58839e8			−1.37938			−0.689692	+	0.724103i	$0.742254\pi$
$128$			3.23239e8i			1.20416i
$129$	1.06342e8	−	4.47395e8i	0.384014	−	1.61560i
$130$	−6.20319e8			−2.17191
$131$		−	1.61346e8i		−	0.547865i	−0.961749	−	0.273933i	$-0.911675\pi$
$131$		−	1.61346e8i		−	0.547865i	0.961749	−	0.273933i	$-0.0883245\pi$
$132$	2.15609e7	+	5.12486e6i	0.0710186	+	0.0168806i
$133$	−4.26008e7			−0.136148
$134$		−	1.27919e8i		−	0.396749i
$135$	3.22953e8	+	2.72066e8i	0.972308	+	0.819104i
$136$	5.17821e8			1.51364
$137$		−	1.61874e8i		−	0.459511i	−0.973248	−	0.229756i	$-0.926207\pi$
$137$		−	1.61874e8i		−	0.459511i	0.973248	−	0.229756i	$-0.0737927\pi$
$138$	1.54690e8	−	6.50799e8i	0.426526	−	1.79445i
$139$	−2.22110e8			−0.594988			−0.297494	−	0.954724i	$-0.596151\pi$
$139$	−2.22110e8			−0.594988			−0.297494	+	0.954724i	$0.596151\pi$
$140$			1.20069e8i			0.312551i
$141$	−7.53712e8	−	1.79151e8i	−1.90690	−	0.453256i
$142$	−6.74844e7			−0.165978
$143$		−	1.93262e8i		−	0.462171i
$144$	4.54453e8	+	2.28976e8i	1.05691	+	0.532526i
$145$	−3.96943e8			−0.897959
$146$			1.74857e8i			0.384833i
$147$	3.36050e6	−	1.41381e7i	0.00719673	−	0.0302775i
$148$	−3.49580e7			−0.0728618
$149$			1.98969e8i			0.403683i	0.979418	+	0.201842i	$0.0646926\pi$
$149$			1.98969e8i			0.403683i	−0.979418	+	0.201842i	$0.935307\pi$
$150$	3.38308e8	+	8.04132e7i	0.668263	+	0.158841i
$151$	−8.07910e8			−1.55401			−0.777007	−	0.629492i	$-0.783263\pi$
$151$	−8.07910e8			−1.55401			−0.777007	+	0.629492i	$0.783263\pi$
$152$			6.04532e7i			0.113252i
$153$	4.41852e8	−	8.76951e8i	0.806327	−	1.60033i
$154$	−1.91920e8			−0.341222
$155$		−	1.09220e8i		−	0.189224i
$156$	−5.08254e7	+	2.13829e8i	−0.0858188	+	0.361050i
$157$	7.01708e8			1.15494			0.577468	−	0.816413i	$-0.304041\pi$
$157$	7.01708e8			1.15494			0.577468	+	0.816413i	$0.304041\pi$
$158$		−	2.03264e7i		−	0.0326162i
$159$	3.49442e8	+	8.30596e7i	0.546747	+	0.129957i
$160$	3.95201e8			0.603028
$161$			1.12913e9i			1.68051i
$162$	6.16907e8	−	4.56778e8i	0.895694	−	0.663202i
$163$	2.75803e8			0.390705			0.195353	−	0.980733i	$-0.437415\pi$
$163$	2.75803e8			0.390705			0.195353	+	0.980733i	$0.437415\pi$
$164$		−	2.33518e7i		−	0.0322808i
$165$	−6.57026e7	+	2.76419e8i	−0.0886435	+	0.372934i
$166$	5.26475e8			0.693338
$167$			7.99618e7i			0.102806i	0.998678	+	0.0514028i	$0.0163692\pi$
$167$			7.99618e7i			0.102806i	−0.998678	+	0.0514028i	$0.983631\pi$
$168$	−6.64731e8	−	1.58001e8i	−0.834467	−	0.198346i
$169$	1.10093e9			1.34963
$170$		−	2.12067e9i		−	2.53909i
$171$	1.02380e8	+	5.15843e7i	0.119738	+	0.0603299i
$172$	−3.51871e8			−0.402040
$173$			3.23146e7i			0.0360756i	0.999837	+	0.0180378i	$0.00574192\pi$
$173$			3.23146e7i			0.0360756i	−0.999837	+	0.0180378i	$0.994258\pi$
$174$	−1.66859e8	+	7.01997e8i	−0.182034	+	0.765840i
$175$	−5.86962e8			−0.625832
$176$			3.42388e8i			0.356836i
$177$	1.82448e8	+	4.33664e7i	0.185886	+	0.0441835i
$178$	1.05740e9			1.05331
$179$			1.32151e9i			1.28723i	0.765348	+	0.643617i	$0.222567\pi$
$179$			1.32151e9i			1.28723i	−0.765348	+	0.643617i	$0.777433\pi$
$180$	1.45389e8	−	2.88556e8i	0.138497	−	0.274878i
$181$	−1.43857e9			−1.34035			−0.670173	−	0.742205i	$-0.733780\pi$
$181$	−1.43857e9			−1.34035			−0.670173	+	0.742205i	$0.733780\pi$
$182$		−	1.90335e9i		−	1.73474i
$183$	−4.30658e8	+	1.81183e9i	−0.383998	+	1.61553i
$184$	1.60231e9			1.39789
$185$		−	4.48175e8i		−	0.382614i
$186$	−1.93157e8	−	4.59118e7i	−0.161383	−	0.0383595i
$187$	6.60701e8			0.540305
$188$			5.92785e8i			0.474532i
$189$	−8.34792e8	+	9.90930e8i	−0.654231	+	0.776597i
$190$	2.47579e8			0.189976
$191$			6.10916e8i			0.459038i	0.973304	+	0.229519i	$0.0737152\pi$
$191$			6.10916e8i			0.459038i	−0.973304	+	0.229519i	$0.926285\pi$
$192$	−2.05794e8	+	8.65800e8i	−0.151435	+	0.637107i
$193$	3.86706e8			0.278709			0.139355	−	0.990243i	$-0.455497\pi$
$193$	3.86706e8			0.278709			0.139355	+	0.990243i	$0.455497\pi$
$194$		−	1.40706e9i		−	0.993361i
$195$	−2.74136e9	−	6.51600e8i	−1.89596	−	0.450654i
$196$	−1.11194e7			−0.00753455
$197$		−	3.67511e8i		−	0.244009i	−0.992530	−	0.122004i	$-0.961068\pi$
$197$		−	3.67511e8i		−	0.244009i	0.992530	−	0.122004i	$-0.0389322\pi$
$198$	4.61231e8	+	2.32391e8i	0.300094	+	0.151202i
$199$	−1.34145e8			−0.0855387			−0.0427693	−	0.999085i	$-0.513618\pi$
$199$	−1.34145e8			−0.0855387			−0.0427693	+	0.999085i	$0.513618\pi$
$200$			8.32935e8i			0.520585i
$201$	1.34370e8	−	5.65310e8i	0.0823222	−	0.346340i
$202$	−9.47552e8			−0.569111
$203$		−	1.21796e9i		−	0.717213i
$204$	−7.31012e8	−	1.73756e8i	−0.422089	−	0.100327i
$205$	2.99378e8			0.169514
$206$			1.31064e8i			0.0727803i
$207$	1.36724e9	−	2.71357e9i	0.744667	−	1.47795i
$208$	−3.39561e9			−1.81411
$209$			7.71339e7i			0.0404260i
$210$	−6.47075e8	+	2.72232e9i	−0.332719	+	1.39979i
$211$	−3.26060e8			−0.164501			−0.0822504	−	0.996612i	$-0.526211\pi$
$211$	−3.26060e8			−0.164501			−0.0822504	+	0.996612i	$0.526211\pi$
$212$		−	2.74832e8i		−	0.136058i
$213$	−2.98232e8	−	7.08875e7i	−0.144889	−	0.0344390i
$214$	3.68386e8			0.175650
$215$		−	4.51111e9i		−	2.11120i
$216$	1.40619e9	+	1.18462e9i	0.645995	+	0.544208i
$217$	3.35125e8			0.151136
$218$		−	1.76661e9i		−	0.782195i
$219$	−1.83675e8	+	7.72744e8i	−0.0798497	+	0.335938i
$220$	2.17400e8			0.0928046
$221$			6.55245e9i			2.74685i
$222$	−7.92600e8	−	1.88395e8i	−0.326319	−	0.0775634i
$223$	−3.88094e9			−1.56934			−0.784671	−	0.619912i	$-0.787168\pi$
$223$	−3.88094e9			−1.56934			−0.784671	+	0.619912i	$0.787168\pi$
$224$			1.21261e9i			0.481648i
$225$	1.41061e9	+	7.10737e8i	0.550399	+	0.277319i
$226$	−1.15234e8			−0.0441720
$227$			2.76866e9i			1.04272i	0.853338	+	0.521358i	$0.174574\pi$
$227$			2.76866e9i			1.04272i	−0.853338	+	0.521358i	$0.825426\pi$
$228$	2.02852e7	−	8.53423e7i	0.00750654	−	0.0315809i
$229$	4.15714e9			1.51165			0.755827	−	0.654771i	$-0.227235\pi$
$229$	4.15714e9			1.51165			0.755827	+	0.654771i	$0.227235\pi$
$230$		−	6.56204e9i		−	2.34492i
$231$	−8.48149e8	−	2.01598e8i	−0.297868	−	0.0708009i
$232$	−1.72836e9			−0.596598
$233$		−	1.25649e9i		−	0.426321i	−0.977017	−	0.213161i	$-0.931624\pi$
$233$		−	1.25649e9i		−	0.426321i	0.977017	−	0.213161i	$-0.0683758\pi$
$234$	−2.30472e9	+	4.57421e9i	−0.768696	+	1.52564i
$235$	−7.59972e9			−2.49187
$236$		−	1.43493e8i		−	0.0462576i
$237$	2.13515e7	−	8.98282e7i	0.00676759	−	0.0284721i
$238$	6.50694e9			2.02801
$239$		−	4.11430e9i		−	1.26097i	−0.776202	−	0.630484i	$-0.782856\pi$
$239$		−	4.11430e9i		−	1.26097i	0.776202	−	0.630484i	$-0.217144\pi$
$240$	4.85667e9	+	1.15439e9i	1.46384	+	0.347943i
$241$	4.78117e9			1.41731			0.708656	−	0.705554i	$-0.249302\pi$
$241$	4.78117e9			1.41731			0.708656	+	0.705554i	$0.249302\pi$
$242$			3.47494e8i			0.101318i
$243$	3.20610e9	−	1.37062e9i	0.919500	−	0.393089i
$244$	1.42498e9			0.402023
$245$		−	1.42555e8i		−	0.0395656i
$246$	1.25847e8	−	5.29453e8i	0.0343638	−	0.144573i
$247$	−7.64969e8			−0.205521
$248$		−	4.75564e8i		−	0.125719i
$249$	2.32664e9	+	5.53024e8i	0.605246	+	0.143862i
$250$	−2.12362e9			−0.543647
$251$			6.21023e9i			1.56463i	0.622880	+	0.782317i	$0.285962\pi$
$251$			6.21023e9i			1.56463i	−0.622880	+	0.782317i	$0.714038\pi$
$252$	8.85389e8	+	4.46104e8i	0.219549	+	0.110620i
$253$	2.04443e9			0.498987
$254$			6.39881e9i			1.53732i
$255$	2.22761e9	−	9.37184e9i	0.526840	−	2.21648i
$256$	2.95140e9			0.687176
$257$			4.23582e9i			0.970967i	0.874246	+	0.485484i	$0.161356\pi$
$257$			4.23582e9i			0.970967i	−0.874246	+	0.485484i	$0.838644\pi$
$258$	−7.97793e9	−	1.89629e9i	−1.80058	−	0.427983i
$259$	1.37515e9			0.305599
$260$			2.15605e9i			0.471808i
$261$	−1.47479e9	+	2.92705e9i	−0.317811	+	0.630766i
$262$	−2.87712e9			−0.610594
$263$			3.17671e8i			0.0663978i	0.999449	+	0.0331989i	$0.0105695\pi$
$263$			3.17671e8i			0.0663978i	−0.999449	+	0.0331989i	$0.989431\pi$
$264$	−2.86080e8	+	1.20358e9i	−0.0588942	+	0.247775i
$265$	3.52344e9			0.714470
$266$			7.59656e8i			0.151737i
$267$	4.67293e9	+	1.11072e9i	0.919484	+	0.218554i
$268$	−4.44609e8			−0.0861866
$269$		−	8.66604e9i		−	1.65505i	−0.561427	−	0.827526i	$-0.689748\pi$
$269$		−	8.66604e9i		−	1.65505i	0.561427	−	0.827526i	$-0.310252\pi$
$270$	4.85147e9	−	5.75888e9i	0.912890	−	1.08363i
$271$	2.09615e8			0.0388637			0.0194319	−	0.999811i	$-0.493814\pi$
$271$	2.09615e8			0.0388637			0.0194319	+	0.999811i	$0.493814\pi$
$272$		−	1.16085e10i		−	2.12080i
$273$	1.99933e9	−	8.41144e9i	0.359944	−	1.51433i
$274$	−2.88654e9			−0.512124
$275$			1.06277e9i			0.185826i
$276$	−2.26199e9	−	5.37657e8i	−0.389811	−	0.0926550i
$277$	6.26791e9			1.06464			0.532321	−	0.846542i	$-0.321320\pi$
$277$	6.26791e9			1.06464			0.532321	+	0.846542i	$0.321320\pi$
$278$			3.96065e9i			0.663113i
$279$	−8.05387e8	−	4.05795e8i	−0.132919	−	0.0669714i
$280$	−6.70252e9			−1.09045
$281$		−	3.55296e9i		−	0.569856i	−0.958549	−	0.284928i	$-0.908030\pi$
$281$		−	3.55296e9i		−	0.569856i	0.958549	−	0.284928i	$-0.0919698\pi$
$282$	−3.19462e9	+	1.34402e10i	−0.505153	+	2.12524i
$283$	−9.44681e9			−1.47278			−0.736392	−	0.676555i	$-0.763472\pi$
$283$	−9.44681e9			−1.47278			−0.736392	+	0.676555i	$0.763472\pi$
$284$			2.34556e8i			0.0360557i
$285$	1.09412e9	+	2.60064e8i	0.165839	+	0.0394185i
$286$	−3.44625e9			−0.515089
$287$			9.18596e8i			0.135393i
$288$	1.46832e9	−	2.91420e9i	0.213428	−	0.423594i
$289$	−1.54250e10			−2.21122
$290$			7.07827e9i			1.00077i
$291$	1.47802e9	−	6.21822e9i	0.206114	−	0.867149i
$292$	6.07753e8			0.0835980
$293$		−	1.26871e10i		−	1.72144i	−0.509080	−	0.860719i	$-0.670014\pi$
$293$		−	1.26871e10i		−	1.72144i	0.509080	−	0.860719i	$-0.329986\pi$
$294$	−2.52109e8	−	5.99244e7i	−0.0337442	−	0.00802074i
$295$	1.83963e9			0.242909
$296$		−	1.95143e9i		−	0.254206i
$297$	1.79420e9	+	1.51149e9i	0.230592	+	0.194258i
$298$	3.54801e9			0.449904
$299$			2.02754e10i			2.53679i
$300$	2.79493e8	−	1.17586e9i	0.0345053	−	0.145168i
$301$	1.38416e10			1.68625
$302$			1.44066e10i			1.73195i
$303$	−4.18750e9	−	9.95335e8i	−0.496803	−	0.118086i
$304$	1.35524e9			0.158680
$305$			1.82688e10i			2.11111i
$306$	−1.56378e10	−	7.87909e9i	−1.78356	−	0.898650i
$307$	2.82965e9			0.318551			0.159276	−	0.987234i	$-0.449084\pi$
$307$	2.82965e9			0.318551			0.159276	+	0.987234i	$0.449084\pi$
$308$			6.67059e8i			0.0741244i
$309$	−1.37673e8	+	5.79208e8i	−0.0151013	+	0.0635331i
$310$	−1.94761e9			−0.210890
$311$			1.23649e10i			1.32175i	0.750498	+	0.660873i	$0.229814\pi$
$311$			1.23649e10i			1.32175i	−0.750498	+	0.660873i	$0.770186\pi$
$312$	−1.19364e10	−	2.83718e9i	−1.25966	−	0.299411i
$313$	6.60686e9			0.688363			0.344182	−	0.938903i	$-0.388156\pi$
$313$	6.60686e9			0.688363			0.344182	+	0.938903i	$0.388156\pi$
$314$		−	1.25128e10i		−	1.28717i
$315$	−5.71921e9	+	1.13510e10i	−0.580890	+	1.15290i
$316$	−7.06488e7			−0.00708527
$317$			5.87200e9i			0.581499i	0.956799	+	0.290750i	$0.0939047\pi$
$317$			5.87200e9i			0.581499i	−0.956799	+	0.290750i	$0.906095\pi$
$318$	1.48111e9	−	6.23123e9i	0.144837	−	0.609348i
$319$	−2.20526e9			−0.212960
$320$			8.72991e9i			0.832549i
$321$	1.62800e9	+	3.86963e8i	0.153332	+	0.0364459i
$322$	2.01346e10			1.87292
$323$		−	2.61518e9i		−	0.240266i
$324$	−1.58763e9	−	2.14419e9i	−0.144069	−	0.194573i
$325$	−1.05399e10			−0.944718
$326$		−	4.91812e9i		−	0.435440i
$327$	1.85570e9	−	7.80716e9i	0.162299	−	0.682813i
$328$	1.30354e9			0.112624
$329$		−	2.33186e10i		−	1.99030i
$330$	4.92910e9	+	1.17161e9i	0.415634	+	0.0987930i
$331$	1.45085e9			0.120868			0.0604338	−	0.998172i	$-0.480752\pi$
$331$	1.45085e9			0.120868			0.0604338	+	0.998172i	$0.480752\pi$
$332$		−	1.82987e9i		−	0.150615i
$333$	−3.30483e9	−	1.66514e9i	−0.268765	−	0.135417i
$334$	1.42588e9			0.114577
$335$		−	5.70006e9i		−	0.452585i
$336$	−3.54207e9	+	1.49019e10i	−0.277907	+	1.16919i
$337$	−1.91392e9			−0.148390			−0.0741948	−	0.997244i	$-0.523639\pi$
$337$	−1.91392e9			−0.148390			−0.0741948	+	0.997244i	$0.523639\pi$
$338$		−	1.96318e10i		−	1.50415i
$339$	−5.09252e8	−	1.21045e8i	−0.0385597	−	0.00916534i
$340$	−7.37083e9			−0.551570
$341$		−	6.06785e8i		−	0.0448763i
$342$	9.19848e8	−	1.82564e9i	0.0672375	−	0.133447i
$343$	−1.36176e10			−0.983840
$344$		−	1.96421e10i		−	1.40267i
$345$	6.89296e9	−	2.89995e10i	0.486552	−	2.04698i
$346$	5.76232e8			0.0402062
$347$			4.93870e9i			0.340639i	0.985389	+	0.170320i	$0.0544800\pi$
$347$			4.93870e9i			0.340639i	−0.985389	+	0.170320i	$0.945520\pi$
$348$	2.43994e9	+	5.79954e8i	0.166365	+	0.0395436i
$349$	2.16559e10			1.45973			0.729867	−	0.683589i	$-0.239582\pi$
$349$	2.16559e10			1.45973			0.729867	+	0.683589i	$0.239582\pi$
$350$			1.04667e10i			0.697488i
$351$	−1.49901e10	+	1.77938e10i	−0.987588	+	1.17230i
$352$	2.19558e9			0.143014
$353$			7.37136e9i			0.474732i	0.971420	+	0.237366i	$0.0762841\pi$
$353$			7.37136e9i			0.474732i	−0.971420	+	0.237366i	$0.923716\pi$
$354$	7.73308e8	−	3.25340e9i	0.0492424	−	0.207169i
$355$	−3.00709e9			−0.189336
$356$		−	3.67520e9i		−	0.228813i
$357$	2.87560e10	+	6.83507e9i	1.77034	+	0.420795i
$358$	2.35651e10			1.43462
$359$		−	3.13260e9i		−	0.188594i	−0.995544	−	0.0942969i	$-0.969940\pi$
$359$		−	3.13260e9i		−	0.188594i	0.995544	−	0.0942969i	$-0.0300603\pi$
$360$	1.61078e10	+	8.11592e9i	0.959016	+	0.483201i
$361$	−1.66783e10			−0.982023
$362$			2.56525e10i			1.49381i
$363$	−3.65018e8	+	1.53568e9i	−0.0210227	+	0.0884450i
$364$	−6.61550e9			−0.376840
$365$			7.79162e9i			0.438992i
$366$	3.23085e10	+	7.67948e9i	1.80050	+	0.427964i
$367$	2.33114e10			1.28500			0.642500	−	0.766285i	$-0.277897\pi$
$367$	2.33114e10			1.28500			0.642500	+	0.766285i	$0.277897\pi$
$368$		−	3.59204e10i		−	1.95862i
$369$	1.11230e9	−	2.20761e9i	0.0599954	−	0.119074i
$370$	−7.99183e9			−0.426422
$371$			1.08111e10i			0.570658i
$372$	−1.59576e8	+	6.71357e8i	−0.00833291	+	0.0350576i
$373$	−8.44159e9			−0.436103			−0.218051	−	0.975937i	$-0.569970\pi$
$373$	−8.44159e9			−0.436103			−0.218051	+	0.975937i	$0.569970\pi$
$374$		−	1.17816e10i		−	0.602168i
$375$	−9.38488e9	−	2.23071e9i	−0.474573	−	0.112802i
$376$	−3.30905e10			−1.65559
$377$		−	2.18705e10i		−	1.08266i
$378$	1.76702e10	+	1.48860e10i	0.865515	+	0.729139i
$379$	1.94801e10			0.944136			0.472068	−	0.881562i	$-0.343508\pi$
$379$	1.94801e10			0.944136			0.472068	+	0.881562i	$0.343508\pi$
$380$		−	8.60512e8i		−	0.0412688i
$381$	−6.72149e9	+	2.82781e10i	−0.318982	+	1.34200i
$382$	1.08938e10			0.511596
$383$			1.04727e10i			0.486701i	0.969938	+	0.243351i	$0.0782466\pi$
$383$			1.04727e10i			0.486701i	−0.969938	+	0.243351i	$0.921753\pi$
$384$	2.54727e10	+	6.05466e9i	1.17152	+	0.278461i
$385$	−8.55194e9			−0.389244
$386$		−	6.89572e9i		−	0.310621i
$387$	−3.32648e10	−	1.67605e10i	−1.48300	−	0.747210i
$388$	−4.89055e9			−0.215790
$389$			2.50214e10i			1.09273i	0.837546	+	0.546366i	$0.183989\pi$
$389$			2.50214e10i			1.09273i	−0.837546	+	0.546366i	$0.816011\pi$
$390$	−1.16193e10	+	4.88839e10i	−0.502252	+	2.11304i
$391$	−6.93151e10			−2.96566
$392$		−	6.20708e8i		−	0.0262871i
$393$	−1.27148e10	−	3.02221e9i	−0.533015	−	0.126693i
$394$	−6.55343e9			−0.271947
$395$		−	9.05743e8i		−	0.0372063i
$396$	8.07724e8	−	1.60310e9i	0.0328460	−	0.0651900i
$397$	3.10148e10			1.24855			0.624276	−	0.781204i	$-0.285394\pi$
$397$	3.10148e10			1.24855			0.624276	+	0.781204i	$0.285394\pi$
$398$			2.39207e9i			0.0953326i
$399$	−7.97964e8	+	3.35714e9i	−0.0314841	+	0.132458i
$400$	1.86727e10			0.729403
$401$		−	2.65629e10i		−	1.02730i	−0.858000	−	0.513650i	$-0.828293\pi$
$401$		−	2.65629e10i		−	1.02730i	0.858000	−	0.513650i	$-0.171707\pi$
$402$	−1.00806e10	−	2.39608e9i	−0.385995	−	0.0917479i
$403$	6.01773e9			0.228146
$404$			3.29341e9i			0.123629i
$405$	2.74893e10	−	2.03540e10i	1.02175	−	0.756536i
$406$	−2.17186e10			−0.799332
$407$		−	2.48988e9i		−	0.0907405i
$408$	9.69939e9	−	4.08066e10i	0.350029	−	1.47262i
$409$	2.09301e10			0.747959			0.373979	−	0.927437i	$-0.377993\pi$
$409$	2.09301e10			0.747959			0.373979	+	0.927437i	$0.377993\pi$
$410$		−	5.33850e9i		−	0.188923i
$411$	−1.27564e10	−	3.03210e9i	−0.447056	−	0.106262i
$412$	4.55540e8			0.0158102
$413$			5.64462e9i			0.194015i
$414$	−4.83883e10	−	2.43805e10i	−1.64717	−	0.829929i
$415$	2.34597e10			0.790914
$416$			2.17745e10i			0.727067i
$417$	−4.16038e9	+	1.75032e10i	−0.137591	+	0.578861i
$418$	1.37545e9			0.0450546
$419$		−	3.60119e10i		−	1.16839i	−0.811612	−	0.584197i	$-0.801409\pi$
$419$		−	3.60119e10i		−	1.16839i	0.811612	−	0.584197i	$-0.198591\pi$
$420$	9.46201e9	+	2.24904e9i	0.304079	+	0.0722771i
$421$	−3.14094e10			−0.999843			−0.499922	−	0.866071i	$-0.666638\pi$
$421$	−3.14094e10			−0.999843			−0.499922	+	0.866071i	$0.666638\pi$
$422$			5.81430e9i			0.183336i
$423$	−2.82358e10	+	5.60401e10i	−0.881940	+	1.75040i
$424$	1.53417e10			0.474689
$425$		−	3.60324e10i		−	1.10443i
$426$	−1.26406e9	+	5.31807e9i	−0.0383822	+	0.161479i
$427$	−5.60550e10			−1.68618
$428$		−	1.28040e9i		−	0.0381567i
$429$	−1.52299e10	−	3.62003e9i	−0.449644	−	0.106877i
$430$	−8.04420e10			−2.35293
$431$		−	4.33885e10i		−	1.25738i	−0.777657	−	0.628689i	$-0.783592\pi$
$431$		−	4.33885e10i		−	1.25738i	0.777657	−	0.628689i	$-0.216408\pi$
$432$	2.65568e10	−	3.15239e10i	0.762502	−	0.905118i
$433$	−4.18298e10			−1.18996			−0.594982	−	0.803739i	$-0.702841\pi$
$433$	−4.18298e10			−1.18996			−0.594982	+	0.803739i	$0.702841\pi$
$434$		−	5.97594e9i		−	0.168441i
$435$	−7.43522e9	+	3.12809e10i	−0.207652	+	0.873619i
$436$	−6.14023e9			−0.169918
$437$		−	8.09223e9i		−	0.221892i
$438$	1.37795e10	+	3.27528e9i	0.374402	+	0.0889923i
$439$	4.51585e10			1.21585			0.607927	−	0.793993i	$-0.292002\pi$
$439$	4.51585e10			1.21585			0.607927	+	0.793993i	$0.292002\pi$
$440$			1.21357e10i			0.323784i
$441$	−1.05120e9	−	5.29645e8i	−0.0277926	−	0.0140033i
$442$	1.16843e11			3.06135
$443$			3.75532e10i			0.975061i	0.873106	+	0.487531i	$0.162102\pi$
$443$			3.75532e10i			0.975061i	−0.873106	+	0.487531i	$0.837898\pi$
$444$	−6.54805e8	+	2.75485e9i	−0.0168492	+	0.0708869i
$445$	4.71174e10			1.20155
$446$			6.92048e10i			1.74903i
$447$	1.56797e10	+	3.72693e9i	0.392741	+	0.0933514i
$448$	−2.67864e10			−0.664969
$449$			5.20394e10i			1.28040i	0.768206	+	0.640202i	$0.221149\pi$
$449$			5.20394e10i			1.28040i	−0.768206	+	0.640202i	$0.778851\pi$
$450$	1.26738e10	−	2.51540e10i	0.309071	−	0.613418i
$451$	1.66323e9			0.0402018
$452$			4.00520e8i			0.00959557i
$453$	−1.51331e10	+	6.36669e10i	−0.359365	+	1.51189i
$454$	4.93706e10			1.16210
$455$		−	8.48131e10i		−	1.97887i
$456$	4.76398e9	+	1.13236e9i	0.110182	+	0.0261894i
$457$	6.83028e10			1.56594			0.782968	−	0.622062i	$-0.213705\pi$
$457$	6.83028e10			1.56594			0.782968	+	0.622062i	$0.213705\pi$
$458$		−	7.41299e10i		−	1.68474i
$459$	−6.08313e10	−	5.12463e10i	−1.37049	−	1.15455i
$460$	−2.28078e10			−0.509391
$461$			1.04289e10i			0.230906i	0.993313	+	0.115453i	$0.0368320\pi$
$461$			1.04289e10i			0.230906i	−0.993313	+	0.115453i	$0.963168\pi$
$462$	−3.59489e9	+	1.51242e10i	−0.0789074	+	0.331973i
$463$	4.32260e10			0.940636			0.470318	−	0.882497i	$-0.344139\pi$
$463$	4.32260e10			0.940636			0.470318	+	0.882497i	$0.344139\pi$
$464$			3.87463e10i			0.835907i
$465$	−8.60705e9	−	2.04583e9i	−0.184095	−	0.0437579i
$466$	−2.24058e10			−0.475134
$467$			4.19215e10i			0.881392i	0.897656	+	0.440696i	$0.145268\pi$
$467$			4.19215e10i			0.881392i	−0.897656	+	0.440696i	$0.854732\pi$
$468$	1.58986e10	+	8.01054e9i	0.331418	+	0.166985i
$469$	1.74897e10			0.361486
$470$			1.35518e11i			2.77719i
$471$	1.31438e10	−	5.52977e10i	0.267078	−	1.12363i
$472$	8.01007e9			0.161387
$473$		−	2.50620e10i		−	0.500692i
$474$	−1.60181e9	−	3.80738e8i	−0.0317321	−	0.00754246i
$475$	4.20663e9			0.0826341
$476$		−	2.26162e10i		−	0.440547i
$477$	1.30909e10	−	2.59818e10i	0.252870	−	0.501875i
$478$	−7.33660e10			−1.40535
$479$			6.93538e10i			1.31743i	0.752392	+	0.658716i	$0.228900\pi$
$479$			6.93538e10i			1.31743i	−0.752392	+	0.658716i	$0.771100\pi$
$480$	7.40258e9	−	3.11436e10i	0.139450	−	0.586683i
$481$	2.46932e10			0.461314
$482$		−	8.52576e10i		−	1.57959i
$483$	8.89805e10	+	2.11500e10i	1.63496	+	0.388616i
$484$	1.20779e9			0.0220095
$485$		−	6.26986e10i		−	1.13316i
$486$	−2.44408e10	−	5.71710e10i	−0.438097	−	1.02478i
$487$	−8.34846e10			−1.48419			−0.742096	−	0.670293i	$-0.766168\pi$
$487$	−8.34846e10			−1.48419			−0.742096	+	0.670293i	$0.766168\pi$
$488$			7.95456e10i			1.40261i
$489$	5.16613e9	−	2.17345e10i	0.0903503	−	0.380115i
$490$	−2.54203e9			−0.0440958
$491$		−	6.29706e10i		−	1.08346i	−0.840554	−	0.541728i	$-0.817770\pi$
$491$		−	6.29706e10i		−	1.08346i	0.840554	−	0.541728i	$-0.182230\pi$
$492$	−1.84022e9	−	4.37407e8i	−0.0314058	−	0.00746492i
$493$	7.47681e10			1.26569
$494$			1.36409e10i			0.229053i
$495$	2.05524e10	+	1.03553e10i	0.342327	+	0.172482i
$496$	−1.06612e10			−0.176148
$497$		−	9.22680e9i		−	0.151226i
$498$	9.86150e9	−	4.14886e10i	0.160334	−	0.674545i
$499$	1.47251e10			0.237497			0.118748	−	0.992924i	$-0.462112\pi$
$499$	1.47251e10			0.237497			0.118748	+	0.992924i	$0.462112\pi$
$500$			7.38109e9i			0.118097i
$501$	6.30135e9	+	1.49778e9i	0.100019	+	0.0237737i
$502$	1.10741e11			1.74378
$503$			7.62579e10i			1.19128i	0.803253	+	0.595638i	$0.203101\pi$
$503$			7.62579e10i			1.19128i	−0.803253	+	0.595638i	$0.796899\pi$
$504$	−2.49024e10	+	4.94242e10i	−0.385940	+	0.765981i
$505$	−4.22228e10			−0.649204
$506$		−	3.64561e10i		−	0.556120i
$507$	2.06218e10	−	8.67583e10i	0.312100	−	1.31304i
$508$	2.22404e10			0.333955
$509$			2.49715e10i			0.372025i	0.982547	+	0.186013i	$0.0595566\pi$
$509$			2.49715e10i			0.372025i	−0.982547	+	0.186013i	$0.940443\pi$
$510$	−1.67118e11	−	3.97227e10i	−2.47026	−	0.587162i
$511$	−2.39074e10			−0.350629
$512$			3.01200e10i			0.438304i
$513$	5.98277e9	−	7.10178e9i	0.0863839	−	0.102541i
$514$	7.55329e10			1.08214
$515$			5.84018e9i			0.0830228i
$516$	−6.59096e9	+	2.77290e10i	−0.0929715	+	0.391143i
$517$	−4.22210e10			−0.590972
$518$		−	2.45217e10i		−	0.340590i
$519$	2.54653e9	+	6.05290e8i	0.0350978	+	0.00834246i
$520$	−1.20355e11			−1.64608
$521$			1.00175e11i			1.35959i	0.733403	+	0.679794i	$0.237931\pi$
$521$			1.00175e11i			1.35959i	−0.733403	+	0.679794i	$0.762069\pi$
$522$	5.21950e10	+	2.62985e10i	0.702987	+	0.354200i
$523$	3.81458e10			0.509847			0.254924	−	0.966961i	$-0.417950\pi$
$523$	3.81458e10			0.509847			0.254924	+	0.966961i	$0.417950\pi$
$524$			1.00000e10i			0.132641i
$525$	−1.09945e10	+	4.62552e10i	−0.144723	+	0.608868i
$526$	5.66469e9			0.0740002
$527$			2.05727e10i			0.266716i
$528$	2.69817e10	+	6.41334e9i	0.347163	+	0.0825180i
$529$	−1.36173e11			−1.73887
$530$		−	6.28299e10i		−	0.796275i
$531$	6.83493e9	−	1.35654e10i	0.0859718	−	0.170630i
$532$	2.64034e9			0.0329620
$533$			1.64949e10i			0.204381i
$534$	1.98063e10	−	8.33275e10i	0.243578	−	1.02476i
$535$	1.64152e10			0.200369
$536$		−	2.48190e10i		−	0.300694i
$537$	1.04141e11	+	2.47534e10i	1.25234	+	0.297672i
$538$	−1.54532e11			−1.84455
$539$		−	7.91979e8i		−	0.00938336i
$540$	−2.00162e10	−	1.68623e10i	−0.235400	−	0.198309i
$541$	−6.93777e10			−0.809899			−0.404950	−	0.914339i	$-0.632711\pi$
$541$	−6.93777e10			−0.809899			−0.404950	+	0.914339i	$0.632711\pi$
$542$		−	3.73784e9i		−	0.0433135i
$543$	−2.69461e10	+	1.13366e11i	−0.309954	+	1.30402i
$544$	−7.44399e10			−0.849983
$545$		−	7.87200e10i		−	0.892276i
$546$	−1.49993e11	−	3.56520e10i	−1.68771	−	0.401156i
$547$	−1.12694e11			−1.25878			−0.629392	−	0.777088i	$-0.716696\pi$
$547$	−1.12694e11			−1.25878			−0.629392	+	0.777088i	$0.716696\pi$
$548$			1.00328e10i			0.111250i
$549$	1.34714e11	+	6.78756e10i	1.48294	+	0.747178i
$550$	1.89512e10			0.207103
$551$			8.72884e9i			0.0947000i
$552$	3.00131e10	−	1.26269e11i	0.323262	−	1.36000i
$553$	2.77913e9			0.0297172
$554$		−	1.11769e11i		−	1.18654i
$555$	−3.53182e10	−	8.39485e9i	−0.372243	−	0.0884791i
$556$	1.37661e10			0.144049
$557$			5.32134e10i			0.552841i	0.961037	+	0.276421i	$0.0891483\pi$
$557$			5.32134e10i			0.552841i	−0.961037	+	0.276421i	$0.910852\pi$
$558$	−7.23611e9	+	1.43616e10i	−0.0746395	+	0.148138i
$559$	2.48550e11			2.54546
$560$			1.50257e11i			1.52786i
$561$	1.23757e10	−	5.20662e10i	0.124945	−	0.525660i
$562$	−6.33563e10			−0.635103
$563$			5.66387e10i			0.563741i	0.959453	+	0.281870i	$0.0909548\pi$
$563$			5.66387e10i			0.563741i	−0.959453	+	0.281870i	$0.909045\pi$
$564$	4.67141e10	+	1.11036e10i	0.461670	+	0.109735i
$565$	−5.13482e9			−0.0503885
$566$			1.68455e11i			1.64141i
$567$	6.24530e10	+	8.43466e10i	0.604257	+	0.816085i
$568$	−1.30934e10			−0.125794
$569$		−	1.44297e11i		−	1.37660i	−0.725426	−	0.688301i	$-0.758357\pi$
$569$		−	1.44297e11i		−	1.37660i	0.725426	−	0.688301i	$-0.241643\pi$
$570$	4.63744e9	−	1.95103e10i	0.0439318	−	0.184827i
$571$	−1.10870e11			−1.04297			−0.521484	−	0.853261i	$-0.674621\pi$
$571$	−1.10870e11			−1.04297			−0.521484	+	0.853261i	$0.674621\pi$
$572$			1.19782e10i			0.111894i
$573$	4.81429e10	+	1.14432e10i	0.446595	+	0.106152i
$574$	1.63804e10			0.150895
$575$		−	1.11496e11i		−	1.01997i
$576$	6.43741e10	+	3.24349e10i	0.584819	+	0.294661i
$577$	2.43968e10			0.220105			0.110053	−	0.993926i	$-0.464898\pi$
$577$	2.43968e10			0.220105			0.110053	+	0.993926i	$0.464898\pi$
$578$			2.75057e11i			2.46440i
$579$	7.24345e9	−	3.04741e10i	0.0644513	−	0.271155i
$580$	2.46020e10			0.217400
$581$			7.19823e10i			0.631715i
$582$	−1.10883e11	−	2.63560e10i	−0.966436	−	0.229714i
$583$	1.95749e10			0.169443
$584$			3.39260e10i			0.291663i
$585$	−1.02698e11	+	2.03826e11i	−0.876877	+	1.74035i
$586$	−2.26236e11			−1.91854
$587$		−	1.61206e11i		−	1.35778i	−0.734241	−	0.678889i	$-0.762462\pi$
$587$		−	1.61206e11i		−	1.35778i	0.734241	−	0.678889i	$-0.237538\pi$
$588$	−2.08280e8	+	8.76259e8i	−0.00174236	+	0.00733032i
$589$	−2.40177e9			−0.0199558
$590$		−	3.28043e10i		−	0.270721i
$591$	−2.89615e10	−	6.88391e9i	−0.237395	−	0.0564268i
$592$	−4.37471e10			−0.356174
$593$		−	1.80683e11i		−	1.46116i	−0.682825	−	0.730582i	$-0.739249\pi$
$593$		−	1.80683e11i		−	1.46116i	0.682825	−	0.730582i	$-0.260751\pi$
$594$	2.69529e10	−	3.19941e10i	0.216501	−	0.256994i
$595$	2.89949e11			2.31341
$596$		−	1.23319e10i		−	0.0977335i
$597$	−2.51270e9	+	1.05712e10i	−0.0197808	+	0.0832201i
$598$	3.61550e11			2.82725
$599$			7.23626e9i			0.0562091i	0.999605	+	0.0281046i	$0.00894714\pi$
$599$			7.23626e9i			0.0562091i	−0.999605	+	0.0281046i	$0.991053\pi$
$600$	6.56390e10	+	1.56019e10i	0.506474	+	0.120385i
$601$	8.49524e10			0.651145			0.325572	−	0.945517i	$-0.394443\pi$
$601$	8.49524e10			0.651145			0.325572	+	0.945517i	$0.394443\pi$
$602$		−	2.46824e11i		−	1.87932i
$603$	−4.20321e10	−	2.11779e10i	−0.317915	−	0.160182i
$604$	5.00732e10			0.376234
$605$			1.54843e10i			0.115577i
$606$	−1.77488e10	+	7.46713e10i	−0.131607	+	0.553685i
$607$	−1.64821e11			−1.21411			−0.607056	−	0.794659i	$-0.707650\pi$
$607$	−1.64821e11			−1.21411			−0.607056	+	0.794659i	$0.707650\pi$
$608$		−	8.69052e9i		−	0.0635962i
$609$	−9.59805e10	−	2.28138e10i	−0.697773	−	0.165855i
$610$	3.25769e11			2.35283
$611$		−	4.18724e11i		−	3.00443i
$612$	−2.73854e10	+	5.43523e10i	−0.195215	+	0.387447i
$613$	1.48468e11			1.05145			0.525726	−	0.850654i	$-0.323794\pi$
$613$	1.48468e11			1.05145			0.525726	+	0.850654i	$0.323794\pi$
$614$		−	5.04582e10i		−	0.355024i
$615$	5.60771e9	−	2.35924e10i	0.0391999	−	0.164919i
$616$	−3.72366e10			−0.258611
$617$		−	2.48259e11i		−	1.71303i	−0.516126	−	0.856513i	$-0.672626\pi$
$617$		−	2.48259e11i		−	1.71303i	0.516126	−	0.856513i	$-0.327374\pi$
$618$	1.03284e10	+	2.45498e9i	0.0708075	+	0.0168304i
$619$	−7.36993e10			−0.501997			−0.250998	−	0.967988i	$-0.580759\pi$
$619$	−7.36993e10			−0.501997			−0.250998	+	0.967988i	$0.580759\pi$
$620$			6.76933e9i			0.0458120i
$621$	−1.88232e11	−	1.58573e11i	−1.26569	−	1.06626i
$622$	2.20490e11			1.47308
$623$			1.44572e11i			0.959695i
$624$	−6.36037e10	+	2.67589e11i	−0.419512	+	1.76494i
$625$	−1.88670e11			−1.23647
$626$		−	1.17813e11i		−	0.767179i
$627$	6.07850e9	+	1.44481e9i	0.0393302	+	0.00934847i
$628$	−4.34910e10			−0.279615
$629$			8.44180e10i			0.539303i
$630$	2.02411e11	+	1.01985e11i	1.28491	+	0.647400i
$631$	−1.48945e11			−0.939522			−0.469761	−	0.882794i	$-0.655660\pi$
$631$	−1.48945e11			−0.939522			−0.469761	+	0.882794i	$0.655660\pi$
$632$		−	3.94376e9i		−	0.0247196i
$633$	−6.10750e9	+	2.56950e10i	−0.0380407	+	0.160042i
$634$	1.04709e11			0.648079
$635$			2.85130e11i			1.75367i
$636$	−2.16580e10	−	5.14792e9i	−0.132370	−	0.0314633i
$637$	7.85438e9			0.0477039
$638$			3.93241e10i			0.237343i
$639$	−1.11725e10	+	2.21742e10i	−0.0670111	+	0.132998i
$640$	2.56843e11			1.53090
$641$			6.16541e10i			0.365199i	0.983187	+	0.182600i	$0.0584512\pi$
$641$			6.16541e10i			0.365199i	−0.983187	+	0.182600i	$0.941549\pi$
$642$	6.90030e9	−	2.90304e10i	0.0406189	−	0.170889i
$643$	−1.57651e10			−0.0922260			−0.0461130	−	0.998936i	$-0.514683\pi$
$643$	−1.57651e10			−0.0922260			−0.0461130	+	0.998936i	$0.514683\pi$
$644$		−	6.99821e10i		−	0.406858i
$645$	−3.55496e11	−	8.44985e10i	−2.05398	−	0.488214i
$646$	−4.66338e10			−0.267776
$647$		−	8.01644e10i		−	0.457472i	−0.973489	−	0.228736i	$-0.926541\pi$
$647$		−	8.01644e10i		−	0.457472i	0.973489	−	0.228736i	$-0.0734592\pi$
$648$	1.19693e11	−	8.86247e10i	0.678843	−	0.502638i
$649$	1.02203e10			0.0576081
$650$			1.87947e11i			1.05289i
$651$	6.27730e9	−	2.64094e10i	0.0349501	−	0.147040i
$652$	−1.70939e10			−0.0945915
$653$			2.16243e10i			0.118929i	0.998230	+	0.0594647i	$0.0189394\pi$
$653$			2.16243e10i			0.118929i	−0.998230	+	0.0594647i	$0.981061\pi$
$654$	−1.39217e11	−	3.30907e10i	−0.760993	−	0.180882i
$655$	−1.28204e11			−0.696525
$656$		−	2.92228e10i		−	0.157800i
$657$	5.74552e10	+	2.89488e10i	0.308367	+	0.155371i
$658$	−4.15815e11			−2.21818
$659$			2.62619e11i			1.39246i	0.717817	+	0.696232i	$0.245142\pi$
$659$			2.62619e11i			1.39246i	−0.717817	+	0.696232i	$0.754858\pi$
$660$	4.07217e9	−	1.71321e10i	0.0214610	−	0.0902891i
$661$	−1.30141e11			−0.681726			−0.340863	−	0.940113i	$-0.610719\pi$
$661$	−1.30141e11			−0.681726			−0.340863	+	0.940113i	$0.610719\pi$
$662$		−	2.58715e10i		−	0.134707i
$663$	5.16362e11	+	1.22735e11i	2.67239	+	0.635207i
$664$	1.02147e11			0.525478
$665$			3.38502e10i			0.173091i
$666$	−2.96927e10	+	5.89316e10i	−0.150922	+	0.299537i
$667$	2.31357e11			1.16890
$668$		−	4.95593e9i		−	0.0248897i
$669$	−7.26947e10	+	3.05836e11i	−0.362909	+	1.52680i
$670$	−1.01643e11			−0.504404
$671$			1.01494e11i			0.500670i
$672$	9.55592e10	+	2.27137e10i	0.468593	+	0.111381i
$673$	−8.82678e10			−0.430271			−0.215135	−	0.976584i	$-0.569019\pi$
$673$	−8.82678e10			−0.430271			−0.215135	+	0.976584i	$0.569019\pi$
$674$			3.41289e10i			0.165380i
$675$	8.24317e10	−	9.78495e10i	0.397081	−	0.471350i
$676$	−6.82343e10			−0.326750
$677$		−	1.16064e11i		−	0.552512i	−0.961084	−	0.276256i	$-0.910906\pi$
$677$		−	1.16064e11i		−	0.552512i	0.961084	−	0.276256i	$-0.0890938\pi$
$678$	−2.15847e9	+	9.08096e9i	−0.0102147	+	0.0429747i
$679$	1.92381e11			0.905072
$680$		−	4.11455e11i		−	1.92436i
$681$	2.18183e11	+	5.18603e10i	1.01445	+	0.241127i
$682$	−1.08202e10			−0.0500145
$683$			8.64283e9i			0.0397167i	0.999803	+	0.0198584i	$0.00632153\pi$
$683$			8.64283e9i			0.0397167i	−0.999803	+	0.0198584i	$0.993678\pi$
$684$	−6.34539e9	−	3.19713e9i	−0.0289890	−	0.0146061i
$685$	−1.28624e11			−0.584197
$686$			2.42829e11i			1.09649i
$687$	7.78682e10	−	3.27601e11i	0.349569	−	1.47068i
$688$	−4.40337e11			−1.96531
$689$			1.94132e11i			0.861430i
$690$	−5.17118e11	−	1.22915e11i	−2.28136	−	0.542261i
$691$	−4.32510e11			−1.89707			−0.948537	−	0.316666i	$-0.897437\pi$
$691$	−4.32510e11			−1.89707			−0.948537	+	0.316666i	$0.897437\pi$
$692$		−	2.00281e9i		−	0.00873406i
$693$	−3.17737e10	+	6.30618e10i	−0.137764	+	0.273422i
$694$	8.80667e10			0.379641
$695$			1.76486e11i			0.756435i
$696$	−3.23742e10	+	1.36202e11i	−0.137963	+	0.580427i
$697$	−5.63908e10			−0.238934
$698$		−	3.86166e11i		−	1.62687i
$699$	−9.90174e10	−	2.35356e10i	−0.414766	−	0.0985865i
$700$	3.63791e10			0.151517
$701$		−	2.44947e11i		−	1.01438i	−0.861834	−	0.507190i	$-0.830684\pi$
$701$		−	2.44947e11i		−	1.01438i	0.861834	−	0.507190i	$-0.169316\pi$
$702$	3.17298e11	+	2.67303e11i	1.30653	+	1.10066i
$703$	−9.85543e9			−0.0403510
$704$			4.84999e10i			0.197447i
$705$	−1.42352e11	+	5.98892e11i	−0.576244	+	2.42433i
$706$	1.31446e11			0.529088
$707$		−	1.29554e11i		−	0.518529i
$708$	−1.13079e10	−	2.68779e9i	−0.0450037	−	0.0106970i
$709$	−1.67637e11			−0.663416			−0.331708	−	0.943382i	$-0.607625\pi$
$709$	−1.67637e11			−0.663416			−0.331708	+	0.943382i	$0.607625\pi$
$710$			5.36224e10i			0.211015i
$711$	−6.67893e9	−	3.36518e9i	−0.0261353	−	0.0131683i
$712$	2.05157e11			0.798301
$713$			6.36586e10i			0.246320i
$714$	1.21883e11	−	5.12776e11i	0.468975	−	1.97304i
$715$	−1.53564e11			−0.587579
$716$		−	8.19053e10i		−	0.311645i
$717$	−3.24225e11	−	7.70657e10i	−1.22679	−	0.291598i
$718$	−5.58604e10			−0.210187
$719$		−	4.47281e11i		−	1.67365i	−0.547469	−	0.836826i	$-0.684408\pi$
$719$		−	4.47281e11i		−	1.67365i	0.547469	−	0.836826i	$-0.315592\pi$
$720$	1.81942e11	−	3.61104e11i	0.677023	−	1.34370i
$721$	−1.79197e10			−0.0663116
$722$			2.97406e11i			1.09446i
$723$	8.95569e10	−	3.76777e11i	0.327753	−	1.37890i
$724$	8.91608e10			0.324504
$725$			1.20267e11i			0.435308i
$726$	2.73841e10	+	6.50898e9i	0.0985717	+	0.0234297i
$727$	3.23809e11			1.15918			0.579590	−	0.814908i	$-0.303213\pi$
$727$	3.23809e11			1.15918			0.579590	+	0.814908i	$0.303213\pi$
$728$		−	3.69291e11i		−	1.31475i
$729$	−4.79566e10	−	2.78328e11i	−0.169800	−	0.985478i
$730$	1.38940e11			0.489255
$731$			8.49711e11i			2.97579i
$732$	2.66917e10	−	1.12295e11i	0.0929675	−	0.391126i
$733$	−4.15223e11			−1.43835			−0.719177	−	0.694827i	$-0.755481\pi$
$733$	−4.15223e11			−1.43835			−0.719177	+	0.694827i	$0.755481\pi$
$734$		−	4.15687e11i		−	1.43213i
$735$	−1.12340e10	−	2.67022e9i	−0.0384932	−	0.00914952i
$736$	−2.30341e11			−0.784984
$737$		−	3.16673e10i		−	0.107335i
$738$	−3.93660e10	−	1.98346e10i	−0.132708	−	0.0668647i
$739$	3.26651e11			1.09523			0.547617	−	0.836729i	$-0.315535\pi$
$739$	3.26651e11			1.09523			0.547617	+	0.836729i	$0.315535\pi$
$740$			2.77773e10i			0.0926324i
$741$	−1.43288e10	+	6.02830e10i	−0.0475266	+	0.199950i
$742$	1.92784e11			0.635996
$743$			4.93833e10i			0.162041i	0.996712	+	0.0810205i	$0.0258179\pi$
$743$			4.93833e10i			0.162041i	−0.996712	+	0.0810205i	$0.974182\pi$
$744$	−3.74765e10	−	8.90787e9i	−0.122312	−	0.0290725i
$745$	1.58099e11			0.513220
$746$			1.50530e11i			0.486035i
$747$	8.71615e10	−	1.72991e11i	0.279925	−	0.555573i
$748$	−4.09494e10			−0.130810
$749$			5.03675e10i			0.160038i
$750$	−3.97779e10	+	1.67351e11i	−0.125718	+	0.528911i
$751$	2.95780e11			0.929841			0.464921	−	0.885352i	$-0.346083\pi$
$751$	2.95780e11			0.929841			0.464921	+	0.885352i	$0.346083\pi$
$752$			7.41821e11i			2.31968i
$753$	4.89394e11	+	1.16325e11i	1.52222	+	0.361821i
$754$	−3.89993e11			−1.20662
$755$			6.41957e11i			1.97569i
$756$	5.17393e10	−	6.14166e10i	0.158392	−	0.188018i
$757$	5.65447e11			1.72190			0.860951	−	0.508688i	$-0.169869\pi$
$757$	5.65447e11			1.72190			0.860951	+	0.508688i	$0.169869\pi$
$758$		−	3.47369e11i		−	1.05224i
$759$	3.82945e10	−	1.61110e11i	0.115390	−	0.485462i
$760$	4.80355e10			0.143982
$761$		−	1.88062e11i		−	0.560742i	−0.959892	−	0.280371i	$-0.909543\pi$
$761$		−	1.88062e11i		−	0.560742i	0.959892	−	0.280371i	$-0.0904574\pi$
$762$	5.04255e11	+	1.19857e11i	1.49565	+	0.355504i
$763$	2.41540e11			0.712674
$764$		−	3.78638e10i		−	0.111135i
$765$	−6.96817e11	−	3.51091e11i	−2.03457	−	1.02512i
$766$	1.86748e11			0.542427
$767$			1.01359e11i			0.292873i
$768$	5.52832e10	−	2.32583e11i	0.158909	−	0.668550i
$769$	−2.59993e11			−0.743457			−0.371728	−	0.928342i	$-0.621235\pi$
$769$	−2.59993e11			−0.743457			−0.371728	+	0.928342i	$0.621235\pi$
$770$			1.52498e11i			0.433811i
$771$	3.33801e11	+	7.93419e10i	0.944649	+	0.224535i
$772$	−2.39675e10			−0.0674767
$773$			5.17513e11i			1.44945i	0.689038	+	0.724725i	$0.258033\pi$
$773$			5.17513e11i			1.44945i	−0.689038	+	0.724725i	$0.741967\pi$
$774$	−2.98872e11	+	5.93177e11i	−0.832764	+	1.65280i
$775$	−3.30920e10			−0.0917310
$776$		−	2.73001e11i		−	0.752864i
$777$	2.57583e10	−	1.08368e11i	0.0706696	−	0.297316i
$778$	4.46181e11			1.21785
$779$		−	6.58337e9i		−	0.0178772i
$780$	1.69906e11	+	4.03853e10i	0.459019	+	0.109105i
$781$	−1.67062e10			−0.0449029
$782$			1.23602e12i			3.30522i
$783$	2.03040e11	+	1.71047e11i	0.540175	+	0.455061i
$784$	−1.39150e10			−0.0368315
$785$		−	5.57570e11i		−	1.46832i
$786$	−5.38919e10	+	2.26730e11i	−0.141199	+	0.594044i
$787$	−2.70083e11			−0.704043			−0.352021	−	0.935992i	$-0.614506\pi$
$787$	−2.70083e11			−0.704043			−0.352021	+	0.935992i	$0.614506\pi$
$788$			2.27778e10i			0.0590755i
$789$	2.50339e10	+	5.95035e9i	0.0645981	+	0.0153544i
$790$	−1.61512e10			−0.0414663
$791$		−	1.57554e10i		−	0.0402460i
$792$	8.94885e10	+	4.50888e10i	0.227440	+	0.114596i
$793$	−1.00656e12			−2.54535
$794$		−	5.53055e11i		−	1.39151i
$795$	6.59983e10	−	2.77663e11i	0.165221	−	0.695104i
$796$	8.31414e9			0.0207093
$797$		−	5.71162e11i		−	1.41555i	−0.706437	−	0.707776i	$-0.749699\pi$
$797$		−	5.71162e11i		−	1.41555i	0.706437	−	0.707776i	$-0.250301\pi$
$798$	5.98643e10	+	1.42293e10i	0.147624	+	0.0350890i
$799$	1.43148e12			3.51235
$800$		−	1.19740e11i		−	0.292333i
$801$	1.75059e11	−	3.47443e11i	0.425260	−	0.844021i
$802$	−4.73668e11			−1.14492
$803$			4.32872e10i			0.104111i
$804$	−8.32806e9	+	3.50372e10i	−0.0199306	+	0.0838504i
$805$	8.97196e11			2.13650
$806$		−	1.07308e11i		−	0.254268i
$807$	−6.82923e11	−	1.62325e11i	−1.61019	−	0.382730i
$808$	−1.83845e11			−0.431327
$809$		−	7.77063e10i		−	0.181410i	−0.995878	−	0.0907051i	$-0.971088\pi$
$809$		−	7.77063e10i		−	0.181410i	0.995878	−	0.0907051i	$-0.0289121\pi$
$810$	−3.62952e11	−	4.90188e11i	−0.843157	−	1.13874i
$811$	−4.20722e11			−0.972550			−0.486275	−	0.873806i	$-0.661645\pi$
$811$	−4.20722e11			−0.972550			−0.486275	+	0.873806i	$0.661645\pi$
$812$			7.54875e10i			0.173640i
$813$	3.92633e9	−	1.65186e10i	0.00898721	−	0.0378103i
$814$	−4.43995e10			−0.101130
$815$		−	2.19151e11i		−	0.496721i
$816$	−9.14800e11	−	2.17441e11i	−2.06331	−	0.490433i
$817$	−9.92000e10			−0.222650
$818$		−	3.73224e11i		−	0.833598i
$819$	−6.25409e11	−	3.15113e11i	−1.39004	−	0.700375i
$820$	−1.85551e10			−0.0410400
$821$			1.94681e11i			0.428501i	0.976779	+	0.214250i	$0.0687309\pi$
$821$			1.94681e11i			0.428501i	−0.976779	+	0.214250i	$0.931269\pi$
$822$	−5.40683e10	+	2.27472e11i	−0.118428	+	0.498243i
$823$	−3.96058e11			−0.863294			−0.431647	−	0.902043i	$-0.642067\pi$
$823$	−3.96058e11			−0.863294			−0.431647	+	0.902043i	$0.642067\pi$
$824$			2.54292e10i			0.0551598i
$825$	8.37506e10	+	1.99069e10i	0.180789	+	0.0429721i
$826$	1.00655e11			0.216229
$827$			3.83915e11i			0.820753i	0.911916	+	0.410377i	$0.134603\pi$
$827$			3.83915e11i			0.820753i	−0.911916	+	0.410377i	$0.865397\pi$
$828$	−8.47395e10	+	1.68184e11i	−0.180287	+	0.357819i
$829$	4.77482e11			1.01097			0.505486	−	0.862835i	$-0.331313\pi$
$829$	4.77482e11			1.01097			0.505486	+	0.862835i	$0.331313\pi$
$830$		−	4.18332e11i		−	0.881471i
$831$	1.17405e11	−	4.93939e11i	0.246198	−	1.03578i
$832$	−4.80994e11			−1.00380
$833$			2.68516e10i			0.0557686i
$834$	3.12117e11	+	7.41877e10i	0.645139	+	0.153344i
$835$	6.35369e10			0.130701
$836$		−	4.78066e9i		−	0.00978730i
$837$	−4.70643e10	+	5.58671e10i	−0.0958936	+	0.113829i
$838$	−6.42162e11			−1.30217
$839$			2.03578e11i			0.410850i	0.978673	+	0.205425i	$0.0658577\pi$
$839$			2.03578e11i			0.410850i	−0.978673	+	0.205425i	$0.934142\pi$
$840$	−1.25546e11	+	5.28189e11i	−0.252166	+	1.06089i
$841$	2.50689e11			0.501131
$842$			5.60092e11i			1.11432i
$843$	−2.79989e11	−	6.65512e10i	−0.554410	−	0.131779i
$844$	2.02088e10			0.0398264
$845$		−	8.74789e11i		−	1.71584i
$846$	9.99305e11	+	5.03500e11i	1.95082	+	0.982920i
$847$	−4.75112e10			−0.0923128
$848$		−	3.43929e11i		−	0.665097i
$849$	−1.76950e11	+	7.44450e11i	−0.340580	+	1.43286i
$850$	−6.42529e11			−1.23088
$851$			2.61217e11i			0.498062i
$852$	1.84841e10	+	4.39351e9i	0.0350783	+	0.00833784i
$853$	9.38595e11			1.77289			0.886445	−	0.462833i	$-0.153167\pi$
$853$	9.38595e11			1.77289			0.886445	+	0.462833i	$0.153167\pi$
$854$			9.99571e11i			1.87924i
$855$	4.09883e10	−	8.13502e10i	0.0767001	−	0.152228i
$856$	7.14746e10			0.133124
$857$		−	1.35992e11i		−	0.252110i	−0.992023	−	0.126055i	$-0.959768\pi$
$857$		−	1.35992e11i		−	0.252110i	0.992023	−	0.126055i	$-0.0402316\pi$
$858$	−6.45523e10	+	2.71580e11i	−0.119114	+	0.501127i
$859$	1.34551e11			0.247123			0.123562	−	0.992337i	$-0.460568\pi$
$859$	1.34551e11			0.247123			0.123562	+	0.992337i	$0.460568\pi$
$860$			2.79593e11i			0.511131i
$861$	7.23894e10	+	1.72064e10i	0.131723	+	0.0313096i
$862$	−7.73702e11			−1.40134
$863$		−	8.12673e11i		−	1.46512i	−0.680703	−	0.732560i	$-0.738326\pi$
$863$		−	8.12673e11i		−	1.46512i	0.680703	−	0.732560i	$-0.261674\pi$
$864$	−2.02149e11	−	1.70297e11i	−0.362757	−	0.305598i
$865$	2.56768e10			0.0458645
$866$			7.45907e11i			1.32621i
$867$	−2.88928e11	+	1.21556e12i	−0.511344	+	2.15129i
$868$	−2.07706e10			−0.0365907
$869$		−	5.03195e9i		−	0.00882383i
$870$	5.57800e11	+	1.32585e11i	0.973646	+	0.231428i
$871$	3.14057e11			0.545678
$872$		−	3.42760e11i		−	0.592822i
$873$	−4.62338e11	−	2.32949e11i	−0.795981	−	0.401055i
$874$	−1.44300e11			−0.247298
$875$		−	2.90352e11i		−	0.495328i
$876$	1.13839e10	−	4.78937e10i	0.0193320	−	0.0813320i
$877$	−3.79776e10			−0.0641991			−0.0320996	−	0.999485i	$-0.510219\pi$
$877$	−3.79776e10			−0.0641991			−0.0320996	+	0.999485i	$0.510219\pi$
$878$		−	8.05264e11i		−	1.35507i
$879$	−9.99799e11	−	2.37644e11i	−1.67478	−	0.398081i
$880$	2.72058e11			0.453661
$881$			8.59369e11i			1.42651i	0.700903	+	0.713257i	$0.252781\pi$
$881$			8.59369e11i			1.42651i	−0.700903	+	0.713257i	$0.747219\pi$
$882$	−9.44462e9	+	1.87449e10i	−0.0156067	+	0.0309748i
$883$	−7.29170e11			−1.19946			−0.599731	−	0.800202i	$-0.704726\pi$
$883$	−7.29170e11			−1.19946			−0.599731	+	0.800202i	$0.704726\pi$
$884$		−	4.06112e11i		−	0.665024i
$885$	3.44585e10	−	1.44971e11i	0.0561725	−	0.236325i
$886$	6.69647e11			1.08670
$887$			4.01669e10i			0.0648894i	0.999474	+	0.0324447i	$0.0103293\pi$
$887$			4.01669e10i			0.0648894i	−0.999474	+	0.0324447i	$0.989671\pi$
$888$	−1.53781e11	−	3.65526e10i	−0.247316	−	0.0587850i
$889$	−8.74877e11			−1.40068
$890$		−	8.40196e11i		−	1.33912i
$891$	1.52720e11	−	1.13079e11i	0.242317	−	0.179420i
$892$	2.40536e11			0.379945
$893$			1.67119e11i			0.262797i
$894$	6.64584e10	−	2.79599e11i	0.104040	−	0.437709i
$895$	1.05006e12			1.63652
$896$			7.88082e11i			1.22275i
$897$	1.59779e12	+	3.79783e11i	2.46803	+	0.586632i
$898$	9.27965e11			1.42701
$899$		−	6.86666e10i		−	0.105125i
$900$	−8.74279e10	−	4.40506e10i	−0.133254	−	0.0671400i
$901$	−6.63674e11			−1.00706
$902$		−	2.96586e10i		−	0.0448048i
$903$	2.59270e11	−	1.09078e12i	0.389944	−	1.64054i
$904$	−2.23579e10			−0.0334778
$905$			1.14307e12i			1.70404i
$906$	1.13531e12	+	2.69853e11i	1.68500	+	0.400511i
$907$	−5.89931e11			−0.871710			−0.435855	−	0.900017i	$-0.643554\pi$
$907$	−5.89931e11			−0.871710			−0.435855	+	0.900017i	$0.643554\pi$
$908$		−	1.71598e11i		−	0.252446i
$909$	−1.56874e11	+	3.11350e11i	−0.229771	+	0.456029i
$910$	−1.51238e12			−2.20545
$911$			6.83544e11i			0.992414i	0.868204	+	0.496207i	$0.165274\pi$
$911$			6.83544e11i			0.992414i	−0.868204	+	0.496207i	$0.834726\pi$
$912$	2.53852e10	−	1.06799e11i	0.0366945	−	0.154379i
$913$	1.30333e11			0.187573
$914$		−	1.21797e12i		−	1.74523i
$915$	1.43966e12	+	3.42197e11i	2.05389	+	0.488193i
$916$	−2.57654e11			−0.365978
$917$		−	3.93374e11i		−	0.556325i
$918$	−9.13821e11	+	1.08474e12i	−1.28674	+	1.52741i
$919$	−1.13461e11			−0.159068			−0.0795341	−	0.996832i	$-0.525343\pi$
$919$	−1.13461e11			−0.159068			−0.0795341	+	0.996832i	$0.525343\pi$
$920$		−	1.27318e12i		−	1.77720i
$921$	5.30027e10	−	2.22989e11i	0.0736647	−	0.309917i
$922$	1.85968e11			0.257345
$923$		−	1.65683e11i		−	0.228281i
$924$	5.25672e10	+	1.24948e10i	0.0721152	+	0.0171412i
$925$	−1.35790e11			−0.185481
$926$		−	7.70805e11i		−	1.04834i
$927$	4.30654e10	+	2.16985e10i	0.0583189	+	0.0293840i
$928$	2.48462e11			0.335018
$929$			1.07038e12i			1.43706i	0.695497	+	0.718529i	$0.255184\pi$
$929$			1.07038e12i			1.43706i	−0.695497	+	0.718529i	$0.744816\pi$
$930$	−3.64811e10	+	1.53480e11i	−0.0487681	+	0.205174i
$931$	−3.13480e9			−0.00417264
$932$			7.78759e10i			0.103214i
$933$	9.74407e11	+	2.31609e11i	1.28592	+	0.305653i
$934$	7.47542e11			0.982309
$935$		−	5.24987e11i		−	0.686913i
$936$	−4.47165e11	+	8.87495e11i	−0.582591	+	1.15628i
$937$	1.71227e11			0.222133			0.111067	−	0.993813i	$-0.464573\pi$
$937$	1.71227e11			0.222133			0.111067	+	0.993813i	$0.464573\pi$
$938$		−	3.11876e11i		−	0.402875i
$939$	1.23754e11	−	5.20650e11i	0.159183	−	0.669705i
$940$	4.71021e11			0.603294
$941$		−	1.43674e12i		−	1.83240i	−0.400721	−	0.916200i	$-0.631240\pi$
$941$		−	1.43674e12i		−	1.83240i	0.400721	−	0.916200i	$-0.368760\pi$
$942$	−9.86067e11	−	2.34380e11i	−1.25228	−	0.297658i
$943$	−1.74492e11			−0.220662
$944$		−	1.79569e11i		−	0.226123i
$945$	7.87383e11	+	6.63317e11i	0.987322	+	0.831753i
$946$	−4.46904e11			−0.558020
$947$		−	5.25277e11i		−	0.653113i	−0.945178	−	0.326557i	$-0.894112\pi$
$947$		−	5.25277e11i		−	0.653113i	0.945178	−	0.326557i	$-0.105888\pi$
$948$	−1.32334e9	+	5.56744e9i	−0.00163846	+	0.00689322i
$949$	−4.29297e11			−0.529289
$950$		−	7.50124e10i		−	0.0920955i
$951$	4.62740e11	+	1.09990e11i	0.565737	+	0.134471i
$952$	1.26249e12			1.53702
$953$		−	2.67354e11i		−	0.324127i	−0.986780	−	0.162064i	$-0.948185\pi$
$953$		−	2.67354e11i		−	0.324127i	0.986780	−	0.162064i	$-0.0518150\pi$
$954$	−4.63306e11	−	2.33437e11i	−0.559338	−	0.281823i
$955$	4.85428e11			0.583595
$956$			2.54999e11i			0.305286i
$957$	−4.13071e10	+	1.73784e11i	−0.0492467	+	0.207187i
$958$	1.23671e12			1.46827
$959$		−	3.94662e11i		−	0.466607i
$960$	6.87956e11	+	1.63522e11i	0.809982	+	0.192526i
$961$	−8.33997e11			−0.977847
$962$		−	4.40328e11i		−	0.514133i
$963$	6.09887e10	−	1.21045e11i	0.0709160	−	0.140748i
$964$	−2.96331e11			−0.343138
$965$		−	3.07272e11i		−	0.354335i
$966$	3.77145e11	−	1.58670e12i	0.433112	−	1.82216i
$967$	9.71724e10			0.111131			0.0555657	−	0.998455i	$-0.482304\pi$
$967$	9.71724e10			0.111131			0.0555657	+	0.998455i	$0.482304\pi$
$968$			6.74213e10i			0.0767884i
$969$	−2.06088e11	−	4.89855e10i	−0.233753	−	0.0555613i
$970$	−1.11804e12			−1.26290
$971$			5.20921e11i			0.585997i	0.956113	+	0.292998i	$0.0946531\pi$
$971$			5.20921e11i			0.585997i	−0.956113	+	0.292998i	$0.905347\pi$
$972$	−1.98710e11	+	8.49491e10i	−0.222615	+	0.0951686i
$973$	−5.41520e11			−0.604176
$974$			1.48869e12i			1.65413i
$975$	−1.97424e11	+	8.30590e11i	−0.218465	+	0.919111i
$976$	1.78325e12			1.96523
$977$			1.52575e12i			1.67458i	0.546758	+	0.837290i	$0.315862\pi$
$977$			1.52575e12i			1.67458i	−0.546758	+	0.837290i	$0.684138\pi$
$978$	−3.87569e11	−	9.21222e10i	−0.423637	−	0.100695i
$979$	2.61766e11			0.284959
$980$			8.83537e9i			0.00957901i
$981$	−5.80479e11	−	2.92475e11i	−0.626774	−	0.315800i
$982$	−1.12289e12			−1.20751
$983$			6.63916e11i			0.711048i	0.934667	+	0.355524i	$0.115698\pi$
$983$			6.63916e11i			0.711048i	−0.934667	+	0.355524i	$0.884302\pi$
$984$	2.44169e10	−	1.02725e11i	0.0260442	−	0.109571i
$985$	−2.92020e11			−0.310219
$986$		−	1.33326e12i		−	1.41061i
$987$	−1.83761e12	−	4.36784e11i	−1.93635	−	0.460255i
$988$	4.74118e10			0.0497575
$989$			2.62929e12i			2.74823i
$990$	1.84656e11	−	3.66489e11i	0.192230	−	0.381523i
$991$	−4.78852e11			−0.496485			−0.248243	−	0.968698i	$-0.579853\pi$
$991$	−4.78852e11			−0.496485			−0.248243	+	0.968698i	$0.579853\pi$
$992$			6.83652e10i			0.0705973i
$993$	2.71761e10	−	1.14333e11i	0.0279505	−	0.117591i
$994$	−1.64532e11			−0.168541
$995$			1.06590e11i			0.108749i
$996$	−1.44202e11	−	3.42757e10i	−0.146533	−	0.0348297i
$997$	−2.53062e11			−0.256122			−0.128061	−	0.991766i	$-0.540875\pi$
$997$	−2.53062e11			−0.256122			−0.128061	+	0.991766i	$0.540875\pi$
$998$		−	2.62578e11i		−	0.264689i
$999$	−1.93124e11	+	2.29245e11i	−0.193898	+	0.230164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.6	✓	26
3.2	odd	2	inner	33.9.b.a.23.21	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.6	✓	26	1.1	even	1	trivial
33.9.b.a.23.21	yes	26	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-17.8320i q^{2} +(18.7312 - 78.8045i) q^{3} -61.9787 q^{4} -794.590i q^{5} +(-1405.24 - 334.014i) q^{6} +2438.07 q^{7} -3459.78i q^{8} +(-5859.29 - 2952.20i) q^{9} +O(q^{10})\)	\(q-17.8320i q^{2} +(18.7312 - 78.8045i) q^{3} -61.9787 q^{4} -794.590i q^{5} +(-1405.24 - 334.014i) q^{6} +2438.07 q^{7} -3459.78i q^{8} +(-5859.29 - 2952.20i) q^{9} -14169.1 q^{10} -4414.43i q^{11} +(-1160.94 + 4884.20i) q^{12} +43779.7 q^{13} -43475.6i q^{14} +(-62617.2 - 14883.6i) q^{15} -77561.2 q^{16} +149669. i q^{17} +(-52643.6 + 104483. i) q^{18} -17473.1 q^{19} +49247.7i q^{20} +(45668.0 - 192131. i) q^{21} -78717.9 q^{22} +463124. i q^{23} +(-272646. - 64805.8i) q^{24} -240748. q^{25} -780678. i q^{26} +(-342398. + 406440. i) q^{27} -151109. q^{28} -499557. i q^{29} +(-265404. + 1.11659e6i) q^{30} +137455. q^{31} +497364. i q^{32} +(-347877. - 82687.5i) q^{33} +2.66889e6 q^{34} -1.93727e6i q^{35} +(363151. + 182974. i) q^{36} +564033. q^{37} +311580. i q^{38} +(820046. - 3.45004e6i) q^{39} -2.74911e6 q^{40} +376771. i q^{41} +(-3.42607e6 - 814351. i) q^{42} +5.67728e6 q^{43} +273601. i q^{44} +(-2.34579e6 + 4.65573e6i) q^{45} +8.25840e6 q^{46} -9.56433e6i q^{47} +(-1.45281e6 + 6.11217e6i) q^{48} +179407. q^{49} +4.29301e6i q^{50} +(1.17946e7 + 2.80347e6i) q^{51} -2.71341e6 q^{52} +4.43429e6i q^{53} +(7.24761e6 + 6.10563e6i) q^{54} -3.50766e6 q^{55} -8.43520e6i q^{56} +(-327293. + 1.37696e6i) q^{57} -8.90809e6 q^{58} +2.31520e6i q^{59} +(3.88094e6 + 922467. i) q^{60} -2.29915e7 q^{61} -2.45109e6i q^{62} +(-1.42854e7 - 7.19769e6i) q^{63} -1.09867e7 q^{64} -3.47869e7i q^{65} +(-1.47448e6 + 6.20332e6i) q^{66} +7.17358e6 q^{67} -9.27627e6i q^{68} +(3.64962e7 + 8.67486e6i) q^{69} -3.45453e7 q^{70} -3.78446e6i q^{71} +(-1.02140e7 + 2.02718e7i) q^{72} -9.80584e6 q^{73} -1.00578e7i q^{74} +(-4.50950e6 + 1.89720e7i) q^{75} +1.08296e6 q^{76} -1.07627e7i q^{77} +(-6.15209e7 - 1.46230e7i) q^{78} +1.13989e6 q^{79} +6.16293e7i q^{80} +(2.56157e7 + 3.45956e7i) q^{81} +6.71856e6 q^{82} +2.95242e7i q^{83} +(-2.83045e6 + 1.19080e7i) q^{84} +1.18925e8 q^{85} -1.01237e8i q^{86} +(-3.93673e7 - 9.35730e6i) q^{87} -1.52729e7 q^{88} +5.92978e7i q^{89} +(8.30208e7 + 4.18300e7i) q^{90} +1.06738e8 q^{91} -2.87038e7i q^{92} +(2.57469e6 - 1.08321e7i) q^{93} -1.70551e8 q^{94} +1.38840e7i q^{95} +(3.91945e7 + 9.31623e6i) q^{96} +7.89069e7 q^{97} -3.19918e6i q^{98} +(-1.30323e7 + 2.58654e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9}+O(q^{10}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9	\( 26 q - 35 q^{3} - 2596 q^{4} - 3746 q^{6} + 7156 q^{7} + 9011 q^{9} - 31836 q^{10} - 28900 q^{12} - 131624 q^{13} + 71041 q^{15} + 311972 q^{16} - 675394 q^{18} + 134608 q^{19} + 490306 q^{21} - 59088 q^{24} - 2324740 q^{25} + 2011426 q^{27} - 1996688 q^{28} - 324146 q^{30} + 964738 q^{31} - 512435 q^{33} + 9219648 q^{34} - 6887660 q^{36} - 5721542 q^{37} - 5782712 q^{39} + 8363496 q^{40} + 10350076 q^{42} + 4260820 q^{43} + 6595181 q^{45} - 39680292 q^{46} + 22674164 q^{48} + 20017254 q^{49} - 7985018 q^{51} + 48711952 q^{52} - 18774176 q^{54} - 4304454 q^{55} + 15476796 q^{57} - 16060008 q^{58} - 26730016 q^{60} + 58840 q^{61} - 42877282 q^{63} - 57365836 q^{64} - 10395110 q^{66} - 63186734 q^{67} + 100738079 q^{69} + 50969160 q^{70} + 48890880 q^{72} - 21879656 q^{73} - 122009926 q^{75} - 119289368 q^{76} - 123440744 q^{78} + 117211444 q^{79} + 138667019 q^{81} + 121755480 q^{82} - 28504816 q^{84} + 28880604 q^{85} + 14774868 q^{87} + 90481380 q^{88} + 189044834 q^{90} + 192183008 q^{91} - 113622071 q^{93} - 453996696 q^{94} + 11988416 q^{96} + 24314206 q^{97} - 57905155 q^{99}+O(q^{100}) \) 26 * q - 35 * q^3 - 2596 * q^4 - 3746 * q^6 + 7156 * q^7 + 9011 * q^9 - 31836 * q^10 - 28900 * q^12 - 131624 * q^13 + 71041 * q^15 + 311972 * q^16 - 675394 * q^18 + 134608 * q^19 + 490306 * q^21 - 59088 * q^24 - 2324740 * q^25 + 2011426 * q^27 - 1996688 * q^28 - 324146 * q^30 + 964738 * q^31 - 512435 * q^33 + 9219648 * q^34 - 6887660 * q^36 - 5721542 * q^37 - 5782712 * q^39 + 8363496 * q^40 + 10350076 * q^42 + 4260820 * q^43 + 6595181 * q^45 - 39680292 * q^46 + 22674164 * q^48 + 20017254 * q^49 - 7985018 * q^51 + 48711952 * q^52 - 18774176 * q^54 - 4304454 * q^55 + 15476796 * q^57 - 16060008 * q^58 - 26730016 * q^60 + 58840 * q^61 - 42877282 * q^63 - 57365836 * q^64 - 10395110 * q^66 - 63186734 * q^67 + 100738079 * q^69 + 50969160 * q^70 + 48890880 * q^72 - 21879656 * q^73 - 122009926 * q^75 - 119289368 * q^76 - 123440744 * q^78 + 117211444 * q^79 + 138667019 * q^81 + 121755480 * q^82 - 28504816 * q^84 + 28880604 * q^85 + 14774868 * q^87 + 90481380 * q^88 + 189044834 * q^90 + 192183008 * q^91 - 113622071 * q^93 - 453996696 * q^94 + 11988416 * q^96 + 24314206 * q^97 - 57905155 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more