LMFDB - Embedded newform 33.9.b.a.23.3

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			23.3
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-27.3024i q^{2} +(-36.6798 - 72.2191i) q^{3} -489.423 q^{4} +131.340i q^{5} +(-1971.76 + 1001.45i) q^{6} -44.0163 q^{7} +6373.03i q^{8} +(-3870.19 + 5297.96i) q^{9} +O(q^{10})$	\(q-27.3024i q^{2} +(-36.6798 - 72.2191i) q^{3} -489.423 q^{4} +131.340i q^{5} +(-1971.76 + 1001.45i) q^{6} -44.0163 q^{7} +6373.03i q^{8} +(-3870.19 + 5297.96i) q^{9} +3585.90 q^{10} +4414.43i q^{11} +(17951.9 + 35345.7i) q^{12} -6563.79 q^{13} +1201.75i q^{14} +(9485.24 - 4817.52i) q^{15} +48706.9 q^{16} -105271. i q^{17} +(144647. + 105666. i) q^{18} -82626.7 q^{19} -64280.8i q^{20} +(1614.51 + 3178.82i) q^{21} +120525. q^{22} +20607.9i q^{23} +(460254. - 233761. i) q^{24} +373375. q^{25} +179207. i q^{26} +(524571. + 85173.1i) q^{27} +21542.6 q^{28} +1.04815e6i q^{29} +(-131530. - 258970. i) q^{30} -1.11820e6 q^{31} +301679. i q^{32} +(318806. - 161920. i) q^{33} -2.87414e6 q^{34} -5781.10i q^{35} +(1.89416e6 - 2.59295e6i) q^{36} -1.77509e6 q^{37} +2.25591e6i q^{38} +(240758. + 474030. i) q^{39} -837032. q^{40} +4.15439e6i q^{41} +(86789.5 - 44080.1i) q^{42} +606228. q^{43} -2.16052e6i q^{44} +(-695833. - 508309. i) q^{45} +562645. q^{46} -7.81050e6i q^{47} +(-1.78656e6 - 3.51756e6i) q^{48} -5.76286e6 q^{49} -1.01940e7i q^{50} +(-7.60254e6 + 3.86130e6i) q^{51} +3.21247e6 q^{52} -490682. i q^{53} +(2.32543e6 - 1.43221e7i) q^{54} -579790. q^{55} -280517. i q^{56} +(3.03073e6 + 5.96722e6i) q^{57} +2.86172e7 q^{58} +1.98365e7i q^{59} +(-4.64230e6 + 2.35780e6i) q^{60} -1.67301e7 q^{61} +3.05295e7i q^{62} +(170351. - 233197. i) q^{63} +2.07055e7 q^{64} -862086. i q^{65} +(-4.42082e6 - 8.70418e6i) q^{66} +1.41991e7 q^{67} +5.15219e7i q^{68} +(1.48828e6 - 755893. i) q^{69} -157838. q^{70} -1.70553e7i q^{71} +(-3.37641e7 - 2.46648e7i) q^{72} -1.82226e7 q^{73} +4.84643e7i q^{74} +(-1.36953e7 - 2.69648e7i) q^{75} +4.04394e7 q^{76} -194307. i q^{77} +(1.29422e7 - 6.57329e6i) q^{78} -2.20505e7 q^{79} +6.39715e6i q^{80} +(-1.30900e7 - 4.10082e7i) q^{81} +1.13425e8 q^{82} -4.39847e7i q^{83} +(-790179. - 1.55579e6i) q^{84} +1.38262e7 q^{85} -1.65515e7i q^{86} +(7.56967e7 - 3.84461e7i) q^{87} -2.81333e7 q^{88} -9.75343e7i q^{89} +(-1.38781e7 + 1.89979e7i) q^{90} +288914. q^{91} -1.00860e7i q^{92} +(4.10152e7 + 8.07551e7i) q^{93} -2.13246e8 q^{94} -1.08522e7i q^{95} +(2.17870e7 - 1.10655e7i) q^{96} -1.33932e8 q^{97} +1.57340e8i q^{98} +(-2.33875e7 - 1.70847e7i) 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 $

$2$		−	27.3024i		−	1.70640i	−0.521582	−	0.853201i	$-0.674658\pi$
$2$		−	27.3024i		−	1.70640i	0.521582	−	0.853201i	$-0.325342\pi$
$3$	−36.6798	−	72.2191i	−0.452837	−	0.891593i
$3$	−36.6798	−	72.2191i	−0.452837	−	0.891593i
$4$	−489.423			−1.91181
$5$			131.340i			0.210144i	0.994465	+	0.105072i	$0.0335072\pi$
$5$			131.340i			0.210144i	−0.994465	+	0.105072i	$0.966493\pi$
$6$	−1971.76	+	1001.45i	−1.52142	+	0.772722i
$7$	−44.0163			−0.0183325			−0.00916625	−	0.999958i	$-0.502918\pi$
$7$	−44.0163			−0.0183325			−0.00916625	+	0.999958i	$0.502918\pi$
$8$			6373.03i			1.55592i
$9$	−3870.19	+	5297.96i	−0.589877	+	0.807493i
$10$	3585.90			0.358590
$11$			4414.43i			0.301511i
$11$			4414.43i			0.301511i
$12$	17951.9	+	35345.7i	0.865738	+	1.70456i
$13$	−6563.79			−0.229816			−0.114908	−	0.993376i	$-0.536657\pi$
$13$	−6563.79			−0.229816			−0.114908	+	0.993376i	$0.536657\pi$
$14$			1201.75i			0.0312826i
$15$	9485.24	−	4817.52i	0.187363	−	0.0951608i
$16$	48706.9			0.743208
$17$		−	105271.i		−	1.26041i	−0.776429	−	0.630204i	$-0.782971\pi$
$17$		−	105271.i		−	1.26041i	0.776429	−	0.630204i	$-0.217029\pi$
$18$	144647.	+	105666.i	1.37791	+	1.00657i
$19$	−82626.7			−0.634024			−0.317012	−	0.948421i	$-0.602680\pi$
$19$	−82626.7			−0.634024			−0.317012	+	0.948421i	$0.602680\pi$
$20$		−	64280.8i		−	0.401755i
$21$	1614.51	+	3178.82i	0.00830164	+	0.0163451i
$22$	120525.			0.514500
$23$			20607.9i			0.0736414i	0.999322	+	0.0368207i	$0.0117230\pi$
$23$			20607.9i			0.0736414i	−0.999322	+	0.0368207i	$0.988277\pi$
$24$	460254.	−	233761.i	1.38724	−	0.704576i
$25$	373375.			0.955840
$26$			179207.i			0.392159i
$27$	524571.	+	85173.1i	0.987074	+	0.160268i
$28$	21542.6			0.0350483
$29$			1.04815e6i			1.48195i	0.671533	+	0.740975i	$0.265636\pi$
$29$			1.04815e6i			1.48195i	−0.671533	+	0.740975i	$0.734364\pi$
$30$	−131530.	−	258970.i	−0.162383	−	0.319716i
$31$	−1.11820e6			−1.21080			−0.605399	−	0.795922i	$-0.706986\pi$
$31$	−1.11820e6			−1.21080			−0.605399	+	0.795922i	$0.706986\pi$
$32$			301679.i			0.287704i
$33$	318806.	−	161920.i	0.268826	−	0.136535i
$34$	−2.87414e6			−2.15076
$35$		−	5781.10i		−	0.00385246i
$36$	1.89416e6	−	2.59295e6i	1.12773	−	1.54377i
$37$	−1.77509e6			−0.947138			−0.473569	−	0.880757i	$-0.657035\pi$
$37$	−1.77509e6			−0.947138			−0.473569	+	0.880757i	$0.657035\pi$
$38$			2.25591e6i			1.08190i
$39$	240758.	+	474030.i	0.104069	+	0.204903i
$40$	−837032.			−0.326966
$41$			4.15439e6i			1.47019i	0.677967	+	0.735093i	$0.262861\pi$
$41$			4.15439e6i			1.47019i	−0.677967	+	0.735093i	$0.737139\pi$
$42$	86789.5	−	44080.1i	0.0278914	−	0.0141659i
$43$	606228.			0.177322			0.0886609	−	0.996062i	$-0.471741\pi$
$43$	606228.			0.177322			0.0886609	+	0.996062i	$0.471741\pi$
$44$		−	2.16052e6i		−	0.576432i
$45$	−695833.	−	508309.i	−0.169689	−	0.123959i
$46$	562645.			0.125662
$47$		−	7.81050e6i		−	1.60062i	−0.599589	−	0.800308i	$-0.704669\pi$
$47$		−	7.81050e6i		−	1.60062i	0.599589	−	0.800308i	$-0.295331\pi$
$48$	−1.78656e6	−	3.51756e6i	−0.336552	−	0.662639i
$49$	−5.76286e6			−0.999664
$50$		−	1.01940e7i		−	1.63105i
$51$	−7.60254e6	+	3.86130e6i	−1.12377	+	0.570760i
$52$	3.21247e6			0.439365
$53$		−	490682.i		−	0.0621866i	−0.999516	−	0.0310933i	$-0.990101\pi$
$53$		−	490682.i		−	0.0621866i	0.999516	−	0.0310933i	$-0.00989890\pi$
$54$	2.32543e6	−	1.43221e7i	0.273482	−	1.68434i
$55$	−579790.			−0.0633607
$56$		−	280517.i		−	0.0285238i
$57$	3.03073e6	+	5.96722e6i	0.287110	+	0.565292i
$58$	2.86172e7			2.52880
$59$			1.98365e7i			1.63703i	0.574484	+	0.818516i	$0.305203\pi$
$59$			1.98365e7i			1.63703i	−0.574484	+	0.818516i	$0.694797\pi$
$60$	−4.64230e6	+	2.35780e6i	−0.358202	+	0.181929i
$61$	−1.67301e7			−1.20831			−0.604155	−	0.796867i	$-0.706489\pi$
$61$	−1.67301e7			−1.20831			−0.604155	+	0.796867i	$0.706489\pi$
$62$			3.05295e7i			2.06611i
$63$	170351.	−	233197.i	0.0108139	−	0.0148034i
$64$	2.07055e7			1.23415
$65$		−	862086.i		−	0.0482945i
$66$	−4.42082e6	−	8.70418e6i	−0.232985	−	0.458725i
$67$	1.41991e7			0.704630			0.352315	−	0.935881i	$-0.385395\pi$
$67$	1.41991e7			0.704630			0.352315	+	0.935881i	$0.385395\pi$
$68$			5.15219e7i			2.40966i
$69$	1.48828e6	−	755893.i	0.0656582	−	0.0333475i
$70$	−157838.			−0.00657385
$71$		−	1.70553e7i		−	0.671160i	−0.942012	−	0.335580i	$-0.891068\pi$
$71$		−	1.70553e7i		−	0.671160i	0.942012	−	0.335580i	$-0.108932\pi$
$72$	−3.37641e7	−	2.46648e7i	−1.25639	−	0.917799i
$73$	−1.82226e7			−0.641680			−0.320840	−	0.947133i	$-0.603965\pi$
$73$	−1.82226e7			−0.641680			−0.320840	+	0.947133i	$0.603965\pi$
$74$			4.84643e7i			1.61620i
$75$	−1.36953e7	−	2.69648e7i	−0.432840	−	0.852220i
$76$	4.04394e7			1.21213
$77$		−	194307.i		−	0.00552746i
$78$	1.29422e7	−	6.57329e6i	0.349647	−	0.177584i
$79$	−2.20505e7			−0.566123			−0.283062	−	0.959102i	$-0.591350\pi$
$79$	−2.20505e7			−0.566123			−0.283062	+	0.959102i	$0.591350\pi$
$80$			6.39715e6i			0.156180i
$81$	−1.30900e7	−	4.10082e7i	−0.304089	−	0.952644i
$82$	1.13425e8			2.50873
$83$		−	4.39847e7i		−	0.926807i	−0.886147	−	0.463404i	$-0.846628\pi$
$83$		−	4.39847e7i		−	0.926807i	0.886147	−	0.463404i	$-0.153372\pi$
$84$	−790179.	−	1.55579e6i	−0.0158711	−	0.0312488i
$85$	1.38262e7			0.264867
$86$		−	1.65515e7i		−	0.302582i
$87$	7.56967e7	−	3.84461e7i	1.32130	−	0.671081i
$88$	−2.81333e7			−0.469126
$89$		−	9.75343e7i		−	1.55452i	−0.629177	−	0.777262i	$-0.716608\pi$
$89$		−	9.75343e7i		−	1.55452i	0.629177	−	0.777262i	$-0.283392\pi$
$90$	−1.38781e7	+	1.89979e7i	−0.211524	+	0.289559i
$91$	288914.			0.00421311
$92$		−	1.00860e7i		−	0.140788i
$93$	4.10152e7	+	8.07551e7i	0.548294	+	1.07954i
$94$	−2.13246e8			−2.73130
$95$		−	1.08522e7i		−	0.133236i
$96$	2.17870e7	−	1.10655e7i	0.256515	−	0.130283i
$97$	−1.33932e8			−1.51286			−0.756430	−	0.654074i	$-0.773058\pi$
$97$	−1.33932e8			−1.51286			−0.756430	+	0.654074i	$0.773058\pi$
$98$			1.57340e8i			1.70583i
$99$	−2.33875e7	−	1.70847e7i	−0.243468	−	0.177855i
$100$	−1.82738e8			−1.82738
$101$		−	5.67481e7i		−	0.545338i	−0.962108	−	0.272669i	$-0.912094\pi$
$101$		−	5.67481e7i		−	0.545338i	0.962108	−	0.272669i	$-0.0879064\pi$
$102$	1.05423e8	+	2.07568e8i	0.973946	+	1.91761i
$103$	2.31177e7			0.205398			0.102699	−	0.994712i	$-0.467252\pi$
$103$	2.31177e7			0.205398			0.102699	+	0.994712i	$0.467252\pi$
$104$		−	4.18312e7i		−	0.357575i
$105$	−417505.	+	212049.i	−0.00343483	+	0.00174454i
$106$	−1.33968e7			−0.106115
$107$		−	1.15379e8i		−	0.880224i	−0.897943	−	0.440112i	$-0.854939\pi$
$107$		−	1.15379e8i		−	0.880224i	0.897943	−	0.440112i	$-0.145061\pi$
$108$	−2.56737e8	−	4.16857e7i	−1.88710	−	0.306402i
$109$	−1.63794e8			−1.16036			−0.580180	−	0.814488i	$-0.697018\pi$
$109$	−1.63794e8			−1.16036			−0.580180	+	0.814488i	$0.697018\pi$
$110$			1.58297e7i			0.108119i
$111$	6.51099e7	+	1.28195e8i	0.428899	+	0.844462i
$112$	−2.14390e6			−0.0136249
$113$			2.60072e8i			1.59507i	0.603273	+	0.797535i	$0.293863\pi$
$113$			2.60072e8i			1.59507i	−0.603273	+	0.797535i	$0.706137\pi$
$114$	1.62920e8	−	8.27463e7i	0.964615	−	0.489925i
$115$	−2.70663e6			−0.0154753
$116$		−	5.12991e8i		−	2.83321i
$117$	2.54031e7	−	3.47747e7i	0.135563	−	0.185575i
$118$	5.41585e8			2.79343
$119$			4.63363e6i			0.0231064i
$120$	3.07022e7	+	6.04497e7i	0.148062	+	0.291520i
$121$	−1.94872e7			−0.0909091
$122$			4.56772e8i			2.06186i
$123$	3.00026e8	−	1.52382e8i	1.31081	−	0.665754i
$124$	5.47272e8			2.31481
$125$			1.00344e8i			0.411007i
$126$	−6.36684e6	−	4.65101e6i	−0.0252605	−	0.0184529i
$127$	−3.39607e8			−1.30545			−0.652727	−	0.757593i	$-0.726375\pi$
$127$	−3.39607e8			−1.30545			−0.652727	+	0.757593i	$0.726375\pi$
$128$		−	4.88082e8i		−	1.81825i
$129$	−2.22363e7	−	4.37812e7i	−0.0802979	−	0.158099i
$130$	−2.35371e7			−0.0824098
$131$			9.39738e7i			0.319096i	0.987190	+	0.159548i	$0.0510037\pi$
$131$			9.39738e7i			0.319096i	−0.987190	+	0.159548i	$0.948996\pi$
$132$	−1.56031e8	+	7.92476e7i	−0.513943	+	0.261030i
$133$	3.63692e6			0.0116233
$134$		−	3.87670e8i		−	1.20238i
$135$	−1.11866e7	+	6.88971e7i	−0.0336793	+	0.207427i
$136$	6.70892e8			1.96109
$137$			6.33508e7i			0.179833i	0.995949	+	0.0899166i	$0.0286601\pi$
$137$			6.33508e7i			0.179833i	−0.995949	+	0.0899166i	$0.971340\pi$
$138$	−2.06377e7	−	4.06337e7i	−0.0569043	−	0.112039i
$139$	−4.69989e8			−1.25901			−0.629505	−	0.776997i	$-0.716742\pi$
$139$	−4.69989e8			−1.25901			−0.629505	+	0.776997i	$0.716742\pi$
$140$			2.82940e6i			0.00736517i
$141$	−5.64067e8	+	2.86487e8i	−1.42710	+	0.724818i
$142$	−4.65652e8			−1.14527
$143$		−	2.89754e7i		−	0.0692923i
$144$	−1.88505e8	+	2.58047e8i	−0.438401	+	0.600135i
$145$	−1.37664e8			−0.311422
$146$			4.97521e8i			1.09496i
$147$	2.11381e8	+	4.16189e8i	0.452685	+	0.891294i
$148$	8.68770e8			1.81075
$149$		−	2.91586e7i		−	0.0591592i	−0.999562	−	0.0295796i	$-0.990583\pi$
$149$		−	2.91586e7i		−	0.0591592i	0.999562	−	0.0295796i	$-0.00941685\pi$
$150$	−7.36204e8	+	3.73915e8i	−1.45423	+	0.738599i
$151$	9.83817e8			1.89237			0.946186	−	0.323623i	$-0.104901\pi$
$151$	9.83817e8			1.89237			0.946186	+	0.323623i	$0.104901\pi$
$152$		−	5.26582e8i		−	0.986488i
$153$	5.57719e8	+	4.07417e8i	1.01777	+	0.743487i
$154$	−5.30505e6			−0.00943207
$155$		−	1.46864e8i		−	0.254441i
$156$	−1.17833e8	−	2.32002e8i	−0.198961	−	0.391735i
$157$	−2.39574e8			−0.394313			−0.197156	−	0.980372i	$-0.563171\pi$
$157$	−2.39574e8			−0.394313			−0.197156	+	0.980372i	$0.563171\pi$
$158$			6.02034e8i			0.966034i
$159$	−3.54366e7	+	1.79981e7i	−0.0554451	+	0.0281604i
$160$	−3.96225e7			−0.0604591
$161$		−	907084.i		−	0.00135003i
$162$	−1.11962e9	+	3.57390e8i	−1.62559	+	0.518899i
$163$	4.51535e8			0.639647			0.319824	−	0.947477i	$-0.396376\pi$
$163$	4.51535e8			0.639647			0.319824	+	0.947477i	$0.396376\pi$
$164$		−	2.03326e9i		−	2.81071i
$165$	2.12666e7	+	4.18719e7i	0.0286921	+	0.0564920i
$166$	−1.20089e9			−1.58151
$167$			5.15624e8i			0.662930i	0.943468	+	0.331465i	$0.107543\pi$
$167$			5.15624e8i			0.662930i	−0.943468	+	0.331465i	$0.892457\pi$
$168$	−2.02587e7	+	1.02893e7i	−0.0254316	+	0.0129166i
$169$	−7.72647e8			−0.947184
$170$		−	3.77489e8i		−	0.451970i
$171$	3.19781e8	−	4.37753e8i	0.373997	−	0.511970i
$172$	−2.96702e8			−0.339006
$173$		−	3.97074e8i		−	0.443289i	−0.975128	−	0.221645i	$-0.928858\pi$
$173$		−	3.97074e8i		−	0.443289i	0.975128	−	0.221645i	$-0.0711425\pi$
$174$	−1.04967e9	−	2.06671e9i	−1.14513	−	2.25466i
$175$	−1.64346e7			−0.0175229
$176$			2.15013e8i			0.224086i
$177$	1.43257e9	−	7.27599e8i	1.45957	−	0.741308i
$178$	−2.66293e9			−2.65264
$179$		−	7.85792e8i		−	0.765412i	−0.923870	−	0.382706i	$-0.874992\pi$
$179$		−	7.85792e8i		−	0.765412i	0.923870	−	0.382706i	$-0.125008\pi$
$180$	3.40557e8	+	2.48778e8i	0.324414	+	0.236986i
$181$	1.59130e9			1.48265			0.741325	−	0.671146i	$-0.234198\pi$
$181$	1.59130e9			1.48265			0.741325	+	0.671146i	$0.234198\pi$
$182$		−	7.88805e6i		−	0.00718926i
$183$	6.13655e8	+	1.20823e9i	0.547167	+	1.07732i
$184$	−1.31335e8			−0.114580
$185$		−	2.33140e8i		−	0.199035i
$186$	2.20481e9	−	1.11982e9i	1.84213	−	0.935610i
$187$	4.64709e8			0.380027
$188$			3.82264e9i			3.06007i
$189$	−2.30897e7	−	3.74901e6i	−0.0180955	−	0.00293812i
$190$	−2.96291e8			−0.227355
$191$			7.23571e8i			0.543685i	0.962342	+	0.271843i	$0.0876330\pi$
$191$			7.23571e8i			0.543685i	−0.962342	+	0.271843i	$0.912367\pi$
$192$	−7.59475e8	−	1.49533e9i	−0.558867	−	1.10036i
$193$	−4.55812e8			−0.328516			−0.164258	−	0.986417i	$-0.552523\pi$
$193$	−4.55812e8			−0.328516			−0.164258	+	0.986417i	$0.552523\pi$
$194$			3.65668e9i			2.58155i
$195$	−6.22591e7	+	3.16211e7i	−0.0430590	+	0.0218695i
$196$	2.82048e9			1.91117
$197$		−	2.55244e9i		−	1.69469i	−0.531040	−	0.847347i	$-0.678199\pi$
$197$		−	2.55244e9i		−	1.69469i	0.531040	−	0.847347i	$-0.321801\pi$
$198$	−4.66453e8	+	6.38535e8i	−0.303492	+	0.415455i
$199$	2.10450e8			0.134195			0.0670974	−	0.997746i	$-0.478626\pi$
$199$	2.10450e8			0.134195			0.0670974	+	0.997746i	$0.478626\pi$
$200$			2.37953e9i			1.48721i
$201$	−5.20820e8	−	1.02545e9i	−0.319083	−	0.628244i
$202$	−1.54936e9			−0.930567
$203$		−	4.61359e7i		−	0.0271678i
$204$	3.72086e9	−	1.88981e9i	2.14844	−	1.09118i
$205$	−5.45637e8			−0.308950
$206$		−	6.31170e8i		−	0.350491i
$207$	−1.09180e8	−	7.97563e7i	−0.0594649	−	0.0434394i
$208$	−3.19701e8			−0.170801
$209$		−	3.64749e8i		−	0.191165i
$210$	5.78947e6	+	1.13989e7i	0.00297688	+	0.00586120i
$211$	3.76856e8			0.190128			0.0950638	−	0.995471i	$-0.469694\pi$
$211$	3.76856e8			0.190128			0.0950638	+	0.995471i	$0.469694\pi$
$212$			2.40151e8i			0.118889i
$213$	−1.23172e9	+	6.25585e8i	−0.598402	+	0.303926i
$214$	−3.15014e9			−1.50202
$215$			7.96218e7i			0.0372630i
$216$	−5.42810e8	+	3.34311e9i	−0.249364	+	1.53580i
$217$	4.92189e7			0.0221969
$218$			4.47199e9i			1.98004i
$219$	6.68401e8	+	1.31602e9i	0.290577	+	0.572118i
$220$	2.83763e8			0.121134
$221$			6.90974e8i			0.289663i
$222$	3.50004e9	−	1.77766e9i	1.44099	−	0.731875i
$223$	−1.78266e9			−0.720856			−0.360428	−	0.932787i	$-0.617369\pi$
$223$	−1.78266e9			−0.720856			−0.360428	+	0.932787i	$0.617369\pi$
$224$		−	1.32788e7i		−	0.00527433i
$225$	−1.44503e9	+	1.97813e9i	−0.563828	+	0.771834i
$226$	7.10060e9			2.72183
$227$		−	2.32944e9i		−	0.877302i	−0.898658	−	0.438651i	$-0.855457\pi$
$227$		−	2.32944e9i		−	0.877302i	0.898658	−	0.438651i	$-0.144543\pi$
$228$	−1.48331e9	−	2.92050e9i	−0.548899	−	1.08073i
$229$	4.82444e9			1.75430			0.877152	−	0.480212i	$-0.159440\pi$
$229$	4.82444e9			1.75430			0.877152	+	0.480212i	$0.159440\pi$
$230$			7.38977e7i			0.0264070i
$231$	−1.40327e7	+	7.12714e6i	−0.00492824	+	0.00250304i
$232$	−6.67992e9			−2.30579
$233$			1.02242e9i			0.346899i	0.984843	+	0.173450i	$0.0554914\pi$
$233$			1.02242e9i			0.346899i	−0.984843	+	0.173450i	$0.944509\pi$
$234$	−9.49434e8	−	6.93566e8i	−0.316666	−	0.231326i
$235$	1.02583e9			0.336359
$236$		−	9.70845e9i		−	3.12969i
$237$	8.08809e8	+	1.59247e9i	0.256361	+	0.504752i
$238$	1.26509e8			0.0394289
$239$		−	2.32559e9i		−	0.712757i	−0.934342	−	0.356379i	$-0.884011\pi$
$239$		−	2.32559e9i		−	0.712757i	0.934342	−	0.356379i	$-0.115989\pi$
$240$	4.61996e8	−	2.34646e8i	0.139249	−	0.0707242i
$241$	−3.50877e9			−1.04013			−0.520063	−	0.854128i	$-0.674092\pi$
$241$	−3.50877e9			−1.04013			−0.520063	+	0.854128i	$0.674092\pi$
$242$			5.32047e8i			0.155128i
$243$	−2.48143e9	+	2.44952e9i	−0.711668	+	0.702516i
$244$	8.18808e9			2.31006
$245$		−	7.56893e8i		−	0.210073i
$246$	−4.16041e9	−	8.19145e9i	−1.13604	−	2.23677i
$247$	5.42344e8			0.145709
$248$		−	7.12630e9i		−	1.88390i
$249$	−3.17654e9	+	1.61335e9i	−0.826335	+	0.419693i
$250$	2.73962e9			0.701344
$251$			4.49017e9i			1.13127i	0.824655	+	0.565637i	$0.191370\pi$
$251$			4.49017e9i			1.13127i	−0.824655	+	0.565637i	$0.808630\pi$
$252$	−8.33740e7	+	1.14132e8i	−0.0206742	+	0.0283012i
$253$	−9.09720e7			−0.0222037
$254$			9.27210e9i			2.22763i
$255$	−5.07143e8	−	9.98516e8i	−0.119942	−	0.236154i
$256$	−8.02521e9			−1.86851
$257$		−	2.12580e9i		−	0.487293i	−0.969864	−	0.243646i	$-0.921656\pi$
$257$		−	2.12580e9i		−	0.487293i	0.969864	−	0.243646i	$-0.0783436\pi$
$258$	−1.19533e9	+	6.07106e8i	−0.269780	+	0.137020i
$259$	7.81329e7			0.0173634
$260$			4.21925e8i			0.0923298i
$261$	−5.55308e9	−	4.05655e9i	−1.19666	−	0.874168i
$262$	2.56571e9			0.544507
$263$			4.54665e9i			0.950317i	0.879900	+	0.475159i	$0.157609\pi$
$263$			4.54665e9i			0.950317i	−0.879900	+	0.475159i	$0.842391\pi$
$264$	1.03192e9	+	2.03176e9i	0.212438	+	0.418270i
$265$	6.44461e7			0.0130681
$266$		−	9.92969e7i		−	0.0198339i
$267$	−7.04384e9	+	3.57754e9i	−1.38600	+	0.703946i
$268$	−6.94937e9			−1.34712
$269$		−	2.48249e9i		−	0.474109i	−0.971496	−	0.237055i	$-0.923818\pi$
$269$		−	2.48249e9i		−	0.474109i	0.971496	−	0.237055i	$-0.0761820\pi$
$270$	1.88106e9	+	3.05422e8i	0.353954	+	0.0574705i
$271$	9.49043e9			1.75958			0.879790	−	0.475363i	$-0.157683\pi$
$271$	9.49043e9			1.75958			0.879790	+	0.475363i	$0.157683\pi$
$272$		−	5.12740e9i		−	0.936745i
$273$	−1.05973e7	−	2.08651e7i	−0.00190785	−	0.00375638i
$274$	1.72963e9			0.306868
$275$			1.64824e9i			0.288196i
$276$	−7.28400e8	+	3.69952e8i	−0.125526	+	0.0637542i
$277$	−4.51936e9			−0.767641			−0.383820	−	0.923408i	$-0.625392\pi$
$277$	−4.51936e9			−0.767641			−0.383820	+	0.923408i	$0.625392\pi$
$278$			1.28319e10i			2.14838i
$279$	4.32763e9	−	5.92416e9i	0.714222	−	0.977710i
$280$	3.68431e7			0.00599410
$281$		−	7.64027e9i		−	1.22542i	−0.790309	−	0.612708i	$-0.790080\pi$
$281$		−	7.64027e9i		−	1.22542i	0.790309	−	0.612708i	$-0.209920\pi$
$282$	7.82181e9	+	1.54004e10i	1.23683	+	2.43521i
$283$	−5.96187e9			−0.929474			−0.464737	−	0.885449i	$-0.653851\pi$
$283$	−5.96187e9			−0.929474			−0.464737	+	0.885449i	$0.653851\pi$
$284$			8.34727e9i			1.28313i
$285$	−7.83733e8	+	3.98055e8i	−0.118792	+	0.0603343i
$286$	−7.91098e8			−0.118240
$287$		−	1.82861e8i		−	0.0269522i
$288$	−1.59828e9	−	1.16755e9i	−0.232319	−	0.169710i
$289$	−4.10614e9			−0.588630
$290$			3.75857e9i			0.531412i
$291$	4.91262e9	+	9.67248e9i	0.685079	+	1.34886i
$292$	8.91856e9			1.22677
$293$		−	6.54569e9i		−	0.888147i	−0.895990	−	0.444074i	$-0.853533\pi$
$293$		−	6.54569e9i		−	0.888147i	0.895990	−	0.444074i	$-0.146467\pi$
$294$	1.13630e10	−	5.77121e9i	1.52091	−	0.772462i
$295$	−2.60532e9			−0.344012
$296$		−	1.13127e10i		−	1.47367i
$297$	−3.75990e8	+	2.31568e9i	−0.0483227	+	0.297614i
$298$	−7.96102e8			−0.100949
$299$		−	1.35266e8i		−	0.0169240i
$300$	6.70281e9	+	1.31972e10i	0.827507	+	1.62928i
$301$	−2.66839e7			−0.00325075
$302$		−	2.68606e10i		−	3.22915i
$303$	−4.09830e9	+	2.08151e9i	−0.486220	+	0.246949i
$304$	−4.02449e9			−0.471212
$305$		−	2.19732e9i		−	0.253919i
$306$	1.11235e10	−	1.52271e10i	1.26869	−	1.73673i
$307$	1.21591e10			1.36882			0.684412	−	0.729096i	$-0.260059\pi$
$307$	1.21591e10			1.36882			0.684412	+	0.729096i	$0.260059\pi$
$308$			9.50984e7i			0.0105674i
$309$	−8.47952e8	−	1.66954e9i	−0.0930117	−	0.183131i
$310$	−4.00974e9			−0.434179
$311$		−	1.56012e10i		−	1.66769i	−0.551997	−	0.833846i	$-0.686134\pi$
$311$		−	1.56012e10i		−	1.66769i	0.551997	−	0.833846i	$-0.313866\pi$
$312$	−3.02101e9	+	1.53436e9i	−0.318811	+	0.161923i
$313$	5.51545e9			0.574650			0.287325	−	0.957833i	$-0.407234\pi$
$313$	5.51545e9			0.574650			0.287325	+	0.957833i	$0.407234\pi$
$314$			6.54095e9i			0.672856i
$315$	3.06280e7	+	2.23739e7i	0.00311083	+	0.00227248i
$316$	1.07921e10			1.08232
$317$		−	1.20811e9i		−	0.119638i	−0.998209	−	0.0598192i	$-0.980948\pi$
$317$		−	1.20811e9i		−	0.119638i	0.998209	−	0.0598192i	$-0.0190524\pi$
$318$	4.91393e8	+	9.67506e8i	0.0480530	+	0.0946117i
$319$	−4.62700e9			−0.446824
$320$			2.71946e9i			0.259348i
$321$	−8.33260e9	+	4.23210e9i	−0.784802	+	0.398598i
$322$	−2.47656e7			−0.00230370
$323$			8.69816e9i			0.799130i
$324$	6.40658e9	+	2.00704e10i	0.581361	+	1.82127i
$325$	−2.45075e9			−0.219668
$326$		−	1.23280e10i		−	1.09150i
$327$	6.00794e9	+	1.18291e10i	0.525454	+	1.03457i
$328$	−2.64761e10			−2.28748
$329$			3.43790e8i			0.0293433i
$330$	1.14320e9	−	5.80629e8i	0.0963981	−	0.0489602i
$331$	1.60134e10			1.33405			0.667026	−	0.745034i	$-0.267567\pi$
$331$	1.60134e10			1.33405			0.667026	+	0.745034i	$0.267567\pi$
$332$			2.15272e10i			1.77188i
$333$	6.86992e9	−	9.40435e9i	0.558695	−	0.764807i
$334$	1.40778e10			1.13122
$335$			1.86491e9i			0.148074i
$336$	7.86377e7	+	1.54830e8i	0.00616984	+	0.0121478i
$337$	−2.02686e10			−1.57146			−0.785730	−	0.618569i	$-0.787713\pi$
$337$	−2.02686e10			−1.57146			−0.785730	+	0.618569i	$0.787713\pi$
$338$			2.10952e10i			1.61628i
$339$	1.87821e10	−	9.53938e9i	1.42215	−	0.722307i
$340$	−6.76687e9			−0.506375
$341$		−	4.93620e9i		−	0.365069i
$342$	−1.19517e10	−	8.73079e9i	−0.873627	−	0.638189i
$343$	5.07406e8			0.0366588
$344$			3.86351e9i			0.275898i
$345$	9.92788e7	+	1.95471e8i	0.00700777	+	0.0137976i
$346$	−1.08411e10			−0.756430
$347$		−	1.24843e10i		−	0.861085i	−0.902570	−	0.430542i	$-0.858322\pi$
$347$		−	1.24843e10i		−	0.861085i	0.902570	−	0.430542i	$-0.141678\pi$
$348$	−3.70477e10	+	1.88164e10i	−2.52607	+	1.28298i
$349$	−2.54367e10			−1.71458			−0.857292	−	0.514830i	$-0.827855\pi$
$349$	−2.54367e10			−1.71458			−0.857292	+	0.514830i	$0.827855\pi$
$350$			4.48705e8i			0.0299012i
$351$	−3.44317e9	−	5.59058e8i	−0.226846	−	0.0368322i
$352$	−1.33174e9			−0.0867459
$353$			1.97543e10i			1.27222i	0.771598	+	0.636110i	$0.219458\pi$
$353$			1.97543e10i			1.27222i	−0.771598	+	0.636110i	$0.780542\pi$
$354$	−1.98652e10	−	3.91127e10i	−1.26497	−	2.49061i
$355$	2.24004e9			0.141040
$356$			4.77356e10i			2.97196i
$357$	3.34636e8	−	1.69960e8i	0.0206016	−	0.0104635i
$358$	−2.14540e10			−1.30610
$359$		−	5.92821e9i		−	0.356899i	−0.983949	−	0.178450i	$-0.942892\pi$
$359$		−	5.92821e9i		−	0.356899i	0.983949	−	0.178450i	$-0.0571082\pi$
$360$	3.23947e9	−	4.43456e9i	0.192870	−	0.264022i
$361$	−1.01564e10			−0.598013
$362$		−	4.34465e10i		−	2.53000i
$363$	7.14785e8	+	1.40735e9i	0.0411670	+	0.0810539i
$364$	−1.41401e8			−0.00805467
$365$		−	2.39335e9i		−	0.134845i
$366$	3.29876e10	−	1.67543e10i	1.83834	−	0.933688i
$367$	2.46231e10			1.35731			0.678655	−	0.734457i	$-0.262563\pi$
$367$	2.46231e10			1.35731			0.678655	+	0.734457i	$0.262563\pi$
$368$			1.00375e9i			0.0547309i
$369$	−2.20098e10	−	1.60783e10i	−1.18716	−	0.867229i
$370$	−6.36529e9			−0.339634
$371$			2.15980e7i			0.00114004i
$372$	−2.00738e10	−	3.95234e10i	−1.04823	−	2.06387i
$373$	2.71718e10			1.40373			0.701863	−	0.712312i	$-0.252352\pi$
$373$	2.71718e10			1.40373			0.701863	+	0.712312i	$0.252352\pi$
$374$		−	1.26877e10i		−	0.648480i
$375$	7.24672e9	−	3.68058e9i	0.366451	−	0.186119i
$376$	4.97765e10			2.49042
$377$		−	6.87986e9i		−	0.340576i
$378$	−1.02357e8	+	6.30406e8i	−0.00501361	+	0.0308783i
$379$	1.99323e10			0.966051			0.483026	−	0.875606i	$-0.339538\pi$
$379$	1.99323e10			0.966051			0.483026	+	0.875606i	$0.339538\pi$
$380$			5.31130e9i			0.254722i
$381$	1.24567e10	+	2.45261e10i	0.591158	+	1.16393i
$382$	1.97552e10			0.927746
$383$			1.73119e10i			0.804545i	0.915520	+	0.402272i	$0.131780\pi$
$383$			1.73119e10i			0.804545i	−0.915520	+	0.402272i	$0.868220\pi$
$384$	−3.52488e10	+	1.79027e10i	−1.62114	+	0.823369i
$385$	2.55202e7			0.00116156
$386$			1.24448e10i			0.560580i
$387$	−2.34621e9	+	3.21177e9i	−0.104598	+	0.143186i
$388$	6.55497e10			2.89230
$389$		−	4.43612e9i		−	0.193734i	−0.995297	−	0.0968668i	$-0.969118\pi$
$389$		−	4.43612e9i		−	0.193734i	0.995297	−	0.0968668i	$-0.0308821\pi$
$390$	8.63335e8	+	1.69982e9i	0.0373182	+	0.0734760i
$391$	2.16940e9			0.0928182
$392$		−	3.67269e10i		−	1.55539i
$393$	6.78670e9	−	3.44694e9i	0.284504	−	0.144499i
$394$	−6.96879e10			−2.89183
$395$		−	2.89611e9i		−	0.118967i
$396$	1.14464e10	+	8.36163e9i	0.465465	+	0.340024i
$397$	4.61270e9			0.185692			0.0928460	−	0.995680i	$-0.470404\pi$
$397$	4.61270e9			0.185692			0.0928460	+	0.995680i	$0.470404\pi$
$398$		−	5.74579e9i		−	0.228991i
$399$	−1.33402e8	−	2.62655e8i	−0.00526344	−	0.0103632i
$400$	1.81859e10			0.710387
$401$			3.92776e10i			1.51903i	0.650487	+	0.759517i	$0.274565\pi$
$401$			3.92776e10i			1.51903i	−0.650487	+	0.759517i	$0.725435\pi$
$402$	−2.79972e10	+	1.42197e10i	−1.07204	+	0.544484i
$403$	7.33960e9			0.278261
$404$			2.77739e10i			1.04258i
$405$	5.38601e9	−	1.71924e9i	0.200192	−	0.0639024i
$406$	−1.25962e9			−0.0463593
$407$		−	7.83600e9i		−	0.285573i
$408$	−2.46082e10	−	4.84512e10i	−0.888053	−	1.74849i
$409$	−4.04898e10			−1.44695			−0.723474	−	0.690352i	$-0.757456\pi$
$409$	−4.04898e10			−1.44695			−0.723474	+	0.690352i	$0.757456\pi$
$410$			1.48972e10i			0.527193i
$411$	4.57514e9	−	2.32370e9i	0.160338	−	0.0814352i
$412$	−1.13143e10			−0.392681
$413$		−	8.73130e8i		−	0.0300109i
$414$	−2.17754e9	+	2.98087e9i	−0.0741251	+	0.101471i
$415$	5.77694e9			0.194763
$416$		−	1.98016e9i		−	0.0661190i
$417$	1.72391e10	+	3.39422e10i	0.570126	+	1.12252i
$418$	−9.95855e9			−0.326205
$419$			3.01067e10i			0.976805i	0.872619	+	0.488402i	$0.162420\pi$
$419$			3.01067e10i			0.976805i	−0.872619	+	0.488402i	$0.837580\pi$
$420$	2.04337e8	−	1.03782e8i	0.00656674	−	0.00333522i
$421$	−3.18581e10			−1.01413			−0.507063	−	0.861909i	$-0.669269\pi$
$421$	−3.18581e10			−1.01413			−0.507063	+	0.861909i	$0.669269\pi$
$422$		−	1.02891e10i		−	0.324434i
$423$	4.13797e10	+	3.02281e10i	1.29249	+	0.944167i
$424$	3.12713e9			0.0967571
$425$		−	3.93054e10i		−	1.20475i
$426$	1.70800e10	+	3.36289e10i	0.518621	+	1.02112i
$427$	7.36396e8			0.0221513
$428$			5.64694e10i			1.68282i
$429$	−2.09257e9	+	1.06281e9i	−0.0617805	+	0.0313781i
$430$	2.17387e9			0.0635858
$431$			2.29512e10i			0.665115i	0.943083	+	0.332558i	$0.107912\pi$
$431$			2.29512e10i			0.665115i	−0.943083	+	0.332558i	$0.892088\pi$
$432$	2.55502e10	+	4.14851e9i	0.733601	+	0.119113i
$433$	−1.91534e10			−0.544872			−0.272436	−	0.962174i	$-0.587829\pi$
$433$	−1.91534e10			−0.544872			−0.272436	+	0.962174i	$0.587829\pi$
$434$		−	1.34380e9i		−	0.0378769i
$435$	5.04950e9	+	9.94199e9i	0.141023	+	0.277662i
$436$	8.01648e10			2.21839
$437$		−	1.70276e9i		−	0.0466904i
$438$	3.59305e10	−	1.82490e10i	0.976263	−	0.495841i
$439$	−1.76811e10			−0.476048			−0.238024	−	0.971259i	$-0.576500\pi$
$439$	−1.76811e10			−0.476048			−0.238024	+	0.971259i	$0.576500\pi$
$440$		−	3.69502e9i		−	0.0985839i
$441$	2.23034e10	−	3.05314e10i	0.589679	−	0.807221i
$442$	1.88653e10			0.494281
$443$			4.22211e10i			1.09626i	0.836392	+	0.548131i	$0.184661\pi$
$443$			4.22211e10i			1.09626i	−0.836392	+	0.548131i	$0.815339\pi$
$444$	−3.18663e10	−	6.27418e10i	−0.819974	−	1.61445i
$445$	1.28101e10			0.326673
$446$			4.86709e10i			1.23007i
$447$	−2.10581e9	+	1.06953e9i	−0.0527459	+	0.0267895i
$448$	−9.11382e8			−0.0226250
$449$			4.43622e10i			1.09151i	0.837945	+	0.545754i	$0.183757\pi$
$449$			4.43622e10i			1.09151i	−0.837945	+	0.545754i	$0.816243\pi$
$450$	5.40077e10	+	3.94528e10i	1.31706	+	0.962118i
$451$	−1.83393e10			−0.443278
$452$		−	1.27285e11i		−	3.04947i
$453$	−3.60862e10	−	7.10503e10i	−0.856936	−	1.68723i
$454$	−6.35995e10			−1.49703
$455$			3.79459e7i			0.000885358i
$456$	−3.80293e10	+	1.93149e10i	−0.879546	+	0.446718i
$457$	−6.38635e10			−1.46416			−0.732079	−	0.681220i	$-0.761450\pi$
$457$	−6.38635e10			−1.46416			−0.732079	+	0.681220i	$0.761450\pi$
$458$		−	1.31719e11i		−	2.99355i
$459$	8.96622e9	−	5.52219e10i	0.202003	−	1.24412i
$460$	1.32469e9			0.0295858
$461$			7.38538e9i			0.163519i	0.996652	+	0.0817596i	$0.0260540\pi$
$461$			7.38538e9i			0.163519i	−0.996652	+	0.0817596i	$0.973946\pi$
$462$	1.94588e8	+	3.83126e8i	0.00427119	+	0.00840957i
$463$	5.59667e10			1.21788			0.608942	−	0.793215i	$-0.291594\pi$
$463$	5.59667e10			1.21788			0.608942	+	0.793215i	$0.291594\pi$
$464$			5.10523e10i			1.10140i
$465$	−1.06064e10	+	5.38693e9i	−0.226858	+	0.115220i
$466$	2.79144e10			0.591950
$467$		−	5.32082e10i		−	1.11869i	−0.828934	−	0.559347i	$-0.811052\pi$
$467$		−	5.32082e10i		−	1.11869i	0.828934	−	0.559347i	$-0.188948\pi$
$468$	−1.24329e10	+	1.70195e10i	−0.259172	+	0.354784i
$469$	−6.24992e8			−0.0129176
$470$		−	2.80076e10i		−	0.573965i
$471$	8.78752e9	+	1.73018e10i	0.178559	+	0.351567i
$472$	−1.26419e11			−2.54708
$473$			2.67615e9i			0.0534645i
$474$	4.34783e10	−	2.20825e10i	0.861309	−	0.437456i
$475$	−3.08507e10			−0.606025
$476$		−	2.26780e9i		−	0.0441751i
$477$	2.59961e9	+	1.89903e9i	0.0502152	+	0.0366825i
$478$	−6.34943e10			−1.21625
$479$		−	2.22266e10i		−	0.422213i	−0.977463	−	0.211106i	$-0.932293\pi$
$479$		−	2.22266e10i		−	0.422213i	0.977463	−	0.211106i	$-0.0677067\pi$
$480$	1.45334e9	+	2.86150e9i	0.0273781	+	0.0539049i
$481$	1.16513e10			0.217668
$482$			9.57979e10i			1.77487i
$483$	−6.55087e7	+	3.32716e7i	−0.00120368	+	0.000611344i
$484$	9.53748e9			0.173801
$485$		−	1.75907e10i		−	0.317918i
$486$	6.68780e10	+	6.77492e10i	1.19878	+	1.21439i
$487$	−1.07915e11			−1.91851			−0.959257	−	0.282534i	$-0.908825\pi$
$487$	−1.07915e11			−1.91851			−0.959257	+	0.282534i	$0.908825\pi$
$488$		−	1.06621e11i		−	1.88003i
$489$	−1.65622e10	−	3.26094e10i	−0.289656	−	0.570305i
$490$	−2.06650e10			−0.358469
$491$			3.87397e10i			0.666547i	0.942830	+	0.333274i	$0.108153\pi$
$491$			3.87397e10i			0.666547i	−0.942830	+	0.333274i	$0.891847\pi$
$492$	−1.46840e11	+	7.45794e10i	−2.50601	+	1.27280i
$493$	1.10340e11			1.86786
$494$		−	1.48073e10i		−	0.248638i
$495$	2.24389e9	−	3.07170e9i	0.0373750	−	0.0511633i
$496$	−5.44639e10			−0.899874
$497$			7.50713e8i			0.0123041i
$498$	4.40484e10	+	8.67272e10i	0.716165	+	1.41006i
$499$	−3.37873e10			−0.544943			−0.272471	−	0.962164i	$-0.587841\pi$
$499$	−3.37873e10			−0.544943			−0.272471	+	0.962164i	$0.587841\pi$
$500$		−	4.91105e10i		−	0.785768i
$501$	3.72379e10	−	1.89130e10i	0.591064	−	0.300199i
$502$	1.22593e11			1.93041
$503$		−	3.41165e10i		−	0.532957i	−0.963841	−	0.266479i	$-0.914140\pi$
$503$		−	3.41165e10i		−	0.532957i	0.963841	−	0.266479i	$-0.0858602\pi$
$504$	1.48617e9	+	1.08565e9i	0.0230328	+	0.0168256i
$505$	7.45329e9			0.114599
$506$			2.48376e9i			0.0378885i
$507$	2.83405e10	+	5.57999e10i	0.428920	+	0.844503i
$508$	1.66212e11			2.49578
$509$		−	8.29669e10i		−	1.23604i	−0.786161	−	0.618022i	$-0.787934\pi$
$509$		−	8.29669e10i		−	1.23604i	0.786161	−	0.618022i	$-0.212066\pi$
$510$	−2.72619e10	+	1.38462e10i	−0.402973	+	0.204669i
$511$	8.02092e8			0.0117636
$512$			9.41589e10i			1.37019i
$513$	−4.33436e10	−	7.03757e9i	−0.625828	−	0.101614i
$514$	−5.80395e10			−0.831518
$515$			3.03627e9i			0.0431630i
$516$	1.08830e10	+	2.14275e10i	0.153514	+	0.302255i
$517$	3.44789e10			0.482604
$518$		−	2.13322e9i		−	0.0296290i
$519$	−2.86763e10	+	1.45646e10i	−0.395234	+	0.200738i
$520$	5.49410e9			0.0751421
$521$			6.81143e9i			0.0924458i	0.998931	+	0.0462229i	$0.0147184\pi$
$521$			6.81143e9i			0.0924458i	−0.998931	+	0.0462229i	$0.985282\pi$
$522$	−1.10754e11	+	1.51613e11i	−1.49168	+	2.04199i
$523$	5.27677e9			0.0705280			0.0352640	−	0.999378i	$-0.488773\pi$
$523$	5.27677e9			0.0705280			0.0352640	+	0.999378i	$0.488773\pi$
$524$		−	4.59930e10i		−	0.610051i
$525$	6.02818e8	+	1.18689e9i	0.00793503	+	0.0156233i
$526$	1.24135e11			1.62162
$527$			1.17713e11i			1.52610i
$528$	1.55280e10	−	7.88663e9i	0.199793	−	0.101474i
$529$	7.78863e10			0.994577
$530$		−	1.75954e9i		−	0.0222995i
$531$	−1.05093e11	−	7.67709e10i	−1.32189	−	0.965648i
$532$	−1.78000e9			−0.0222214
$533$		−	2.72685e10i		−	0.337873i
$534$	9.76756e10	+	1.92314e11i	1.20122	+	2.36508i
$535$	1.51539e10			0.184974
$536$			9.04912e10i			1.09635i
$537$	−5.67492e10	+	2.88227e10i	−0.682437	+	0.346607i
$538$	−6.77780e10			−0.809021
$539$		−	2.54397e10i		−	0.301410i
$540$	5.47499e9	−	3.37198e10i	0.0643885	−	0.396561i
$541$	−6.44764e10			−0.752682			−0.376341	−	0.926481i	$-0.622818\pi$
$541$	−6.44764e10			−0.752682			−0.376341	+	0.926481i	$0.622818\pi$
$542$		−	2.59112e11i		−	3.00255i
$543$	−5.83687e10	−	1.14922e11i	−0.671399	−	1.32192i
$544$	3.17579e10			0.362624
$545$		−	2.15127e10i		−	0.243842i
$546$	−5.69668e8	+	2.89332e8i	−0.00640990	+	0.00325556i
$547$	1.11191e11			1.24199			0.620996	−	0.783814i	$-0.286728\pi$
$547$	1.11191e11			1.24199			0.620996	+	0.783814i	$0.286728\pi$
$548$		−	3.10054e10i		−	0.343807i
$549$	6.47484e10	−	8.86352e10i	0.712754	−	0.975701i
$550$	4.50009e10			0.491779
$551$		−	8.66055e10i		−	0.939592i
$552$	4.81733e9	+	9.48486e9i	0.0518859	+	0.102159i
$553$	9.70584e8			0.0103785
$554$			1.23390e11i			1.30990i
$555$	−1.68371e10	+	8.55152e9i	−0.177458	+	0.0901304i
$556$	2.30024e11			2.40699
$557$			1.69283e11i			1.75870i	0.476175	+	0.879351i	$0.342023\pi$
$557$			1.69283e11i			1.75870i	−0.476175	+	0.879351i	$0.657977\pi$
$558$	−1.61744e11	−	1.18155e11i	−1.66837	−	1.21875i
$559$	−3.97915e9			−0.0407515
$560$		−	2.81579e8i		−	0.00286318i
$561$	−1.70454e10	−	3.35609e10i	−0.172090	−	0.338830i
$562$	−2.08598e11			−2.09105
$563$		−	1.35792e11i		−	1.35157i	−0.737097	−	0.675787i	$-0.763804\pi$
$563$		−	1.35792e11i		−	1.35157i	0.737097	−	0.675787i	$-0.236196\pi$
$564$	2.76067e11	−	1.40214e11i	2.72834	−	1.38571i
$565$	−3.41578e10			−0.335194
$566$			1.62774e11i			1.58606i
$567$	5.76176e8	+	1.80503e9i	0.00557472	+	0.0174643i
$568$	1.08694e11			1.04427
$569$			8.05901e10i			0.768834i	0.923160	+	0.384417i	$0.125597\pi$
$569$			8.05901e10i			0.768834i	−0.923160	+	0.384417i	$0.874403\pi$
$570$	1.08679e10	+	2.13978e10i	0.102955	+	0.202708i
$571$	2.68487e9			0.0252569			0.0126284	−	0.999920i	$-0.495980\pi$
$571$	2.68487e9			0.0252569			0.0126284	+	0.999920i	$0.495980\pi$
$572$			1.41812e10i			0.132474i
$573$	5.22556e10	−	2.65404e10i	0.484746	−	0.246201i
$574$	−4.99256e9			−0.0459913
$575$			7.69446e9i			0.0703894i
$576$	−8.01342e10	+	1.09697e11i	−0.727995	+	0.996564i
$577$	−2.53602e10			−0.228796			−0.114398	−	0.993435i	$-0.536494\pi$
$577$	−2.53602e10			−0.228796			−0.114398	+	0.993435i	$0.536494\pi$
$578$			1.12108e11i			1.00444i
$579$	1.67191e10	+	3.29183e10i	0.148764	+	0.292903i
$580$	6.73762e10			0.595380
$581$			1.93605e9i			0.0169907i
$582$	2.64082e11	−	1.34126e11i	2.30169	−	1.16902i
$583$	2.16608e9			0.0187500
$584$		−	1.16133e11i		−	0.998400i
$585$	4.56730e9	+	3.33643e9i	0.0389974	+	0.0284878i
$586$	−1.78713e11			−1.51554
$587$			5.37419e10i			0.452648i	0.974052	+	0.226324i	$0.0726709\pi$
$587$			5.37419e10i			0.452648i	−0.974052	+	0.226324i	$0.927329\pi$
$588$	−1.03455e11	−	2.03692e11i	−0.865447	−	1.70398i
$589$	9.23929e10			0.767675
$590$			7.11316e10i			0.587023i
$591$	−1.84335e11	+	9.36231e10i	−1.51098	+	0.767420i
$592$	−8.64590e10			−0.703920
$593$		−	1.91782e10i		−	0.155092i	−0.996989	−	0.0775459i	$-0.975292\pi$
$593$		−	1.91782e10i		−	0.155092i	0.996989	−	0.0775459i	$-0.0247084\pi$
$594$	6.32238e10	+	1.02655e10i	0.507849	+	0.0824579i
$595$	−6.08579e8			−0.00485567
$596$			1.42709e10i			0.113101i
$597$	−7.71925e9	−	1.51985e10i	−0.0607684	−	0.119647i
$598$	−3.69308e9			−0.0288792
$599$			1.07951e11i			0.838530i	0.907864	+	0.419265i	$0.137712\pi$
$599$			1.07951e11i			0.838530i	−0.907864	+	0.419265i	$0.862288\pi$
$600$	1.71847e11	−	8.72806e10i	1.32598	−	0.673462i
$601$	3.28941e10			0.252128			0.126064	−	0.992022i	$-0.459766\pi$
$601$	3.28941e10			0.252128			0.126064	+	0.992022i	$0.459766\pi$
$602$			7.28537e8i			0.00554709i
$603$	−5.49531e10	+	7.52262e10i	−0.415646	+	0.568984i
$604$	−4.81503e11			−3.61786
$605$		−	2.55944e9i		−	0.0191040i
$606$	5.68303e10	+	1.11893e11i	0.421395	+	0.829687i
$607$	−1.99786e11			−1.47167			−0.735836	−	0.677159i	$-0.763211\pi$
$607$	−1.99786e11			−1.47167			−0.735836	+	0.677159i	$0.763211\pi$
$608$		−	2.49267e10i		−	0.182411i
$609$	−3.33189e9	+	1.69226e9i	−0.0242227	+	0.0123026i
$610$	−5.99923e10			−0.433287
$611$			5.12664e10i			0.367848i
$612$	−2.72961e11	−	1.99399e11i	−1.94578	−	1.42141i
$613$	−1.94014e10			−0.137402			−0.0687008	−	0.997637i	$-0.521885\pi$
$613$	−1.94014e10			−0.137402			−0.0687008	+	0.997637i	$0.521885\pi$
$614$		−	3.31973e11i		−	2.33576i
$615$	2.00139e10	+	3.94054e10i	0.139904	+	0.275458i
$616$	1.23832e9			0.00860026
$617$			2.03207e11i			1.40216i	0.713083	+	0.701080i	$0.247298\pi$
$617$			2.03207e11i			1.40216i	−0.713083	+	0.701080i	$0.752702\pi$
$618$	−4.55825e10	+	2.31512e10i	−0.312496	+	0.158715i
$619$	1.64997e10			0.112386			0.0561932	−	0.998420i	$-0.482104\pi$
$619$	1.64997e10			0.112386			0.0561932	+	0.998420i	$0.482104\pi$
$620$			7.18785e10i			0.486444i
$621$	−1.75524e9	+	1.08103e10i	−0.0118024	+	0.0726895i
$622$	−4.25950e11			−2.84576
$623$			4.29310e9i			0.0284983i
$624$	1.17266e10	+	2.30885e10i	0.0773451	+	0.152285i
$625$	1.32670e11			0.869469
$626$		−	1.50585e11i		−	0.980585i
$627$	−2.63419e10	+	1.33789e10i	−0.170442	+	0.0865668i
$628$	1.17253e11			0.753851
$629$			1.86865e11i			1.19378i
$630$	6.10863e8	−	8.36220e8i	0.00387776	−	0.00530833i
$631$	7.99871e10			0.504548			0.252274	−	0.967656i	$-0.418822\pi$
$631$	7.99871e10			0.504548			0.252274	+	0.967656i	$0.418822\pi$
$632$		−	1.40529e11i		−	0.880840i
$633$	−1.38230e10	−	2.72162e10i	−0.0860968	−	0.169517i
$634$	−3.29844e10			−0.204151
$635$		−	4.46039e10i		−	0.274333i
$636$	1.73435e10	−	8.80870e9i	0.106001	−	0.0538373i
$637$	3.78262e10			0.229739
$638$			1.26328e11i			0.762462i
$639$	9.03584e10	+	6.60072e10i	0.541957	+	0.395902i
$640$	6.41045e10			0.382093
$641$			2.36630e11i			1.40165i	0.713335	+	0.700823i	$0.247184\pi$
$641$			2.36630e11i			1.40165i	−0.713335	+	0.700823i	$0.752816\pi$
$642$	1.15547e11	+	2.27500e11i	0.680169	+	1.33919i
$643$	5.35545e10			0.313294			0.156647	−	0.987655i	$-0.449931\pi$
$643$	5.35545e10			0.313294			0.156647	+	0.987655i	$0.449931\pi$
$644$			4.43948e8i			0.00258100i
$645$	5.75021e9	−	2.92051e9i	0.0332235	−	0.0168741i
$646$	2.37481e11			1.36364
$647$		−	5.97099e10i		−	0.340745i	−0.985380	−	0.170372i	$-0.945503\pi$
$647$		−	5.97099e10i		−	0.340745i	0.985380	−	0.170372i	$-0.0544970\pi$
$648$	2.61346e11	−	8.34233e10i	1.48223	−	0.473137i
$649$	−8.75668e10			−0.493583
$650$			6.69115e10i			0.374841i
$651$	−1.80534e9	−	3.55455e9i	−0.0100516	−	0.0197907i
$652$	−2.20992e11			−1.22288
$653$		−	2.94711e11i		−	1.62085i	−0.585841	−	0.810426i	$-0.699236\pi$
$653$		−	2.94711e11i		−	1.62085i	0.585841	−	0.810426i	$-0.300764\pi$
$654$	3.22963e11	−	1.64032e11i	1.76539	−	0.896636i
$655$	−1.23425e10			−0.0670560
$656$			2.02347e11i			1.09265i
$657$	7.05248e10	−	9.65426e10i	0.378513	−	0.518152i
$658$	9.38629e9			0.0500715
$659$		−	3.57804e10i		−	0.189716i	−0.995491	−	0.0948579i	$-0.969760\pi$
$659$		−	3.57804e10i		−	0.189716i	0.995491	−	0.0948579i	$-0.0302397\pi$
$660$	−1.04084e10	−	2.04931e10i	−0.0548538	−	0.108002i
$661$	1.26426e11			0.662263			0.331132	−	0.943585i	$-0.392570\pi$
$661$	1.26426e11			0.662263			0.331132	+	0.943585i	$0.392570\pi$
$662$		−	4.37206e11i		−	2.27643i
$663$	4.99015e10	−	2.53448e10i	0.258261	−	0.131170i
$664$	2.80316e11			1.44203
$665$			4.77673e8i			0.00244255i
$666$	−2.56762e11	−	1.87566e11i	−1.30507	−	0.953359i
$667$	−2.16002e10			−0.109133
$668$		−	2.52359e11i		−	1.26740i
$669$	6.53876e10	+	1.28742e11i	0.326430	+	0.642711i
$670$	5.09165e10			0.252673
$671$		−	7.38536e10i		−	0.364319i
$672$	−9.58983e8	+	4.87064e8i	−0.00470255	+	0.00238841i
$673$	−7.02840e10			−0.342607			−0.171304	−	0.985218i	$-0.554798\pi$
$673$	−7.02840e10			−0.342607			−0.171304	+	0.985218i	$0.554798\pi$
$674$			5.53382e11i			2.68154i
$675$	1.95862e11	+	3.18015e10i	0.943484	+	0.153191i
$676$	3.78152e11			1.81084
$677$		−	9.16109e10i		−	0.436106i	−0.975937	−	0.218053i	$-0.930029\pi$
$677$		−	9.16109e10i		−	0.436106i	0.975937	−	0.218053i	$-0.0699706\pi$
$678$	−2.60448e11	−	5.12799e11i	−1.23255	−	2.42677i
$679$	5.89522e9			0.0277345
$680$			8.81149e10i			0.412110i
$681$	−1.68230e11	+	8.54435e10i	−0.782196	+	0.397275i
$682$	−1.34770e11			−0.622955
$683$		−	1.83141e11i		−	0.841596i	−0.907154	−	0.420798i	$-0.861750\pi$
$683$		−	1.83141e11i		−	0.841596i	0.907154	−	0.420798i	$-0.138250\pi$
$684$	−1.56508e11	+	2.14246e11i	−0.715010	+	0.978789i
$685$	−8.32049e9			−0.0377908
$686$		−	1.38534e10i		−	0.0625548i
$687$	−1.76959e11	−	3.48417e11i	−0.794414	−	1.56413i
$688$	2.95275e10			0.131787
$689$			3.22073e9i			0.0142915i
$690$	5.33683e9	−	2.71055e9i	0.0235443	−	0.0119581i
$691$	−1.70702e11			−0.748731			−0.374366	−	0.927281i	$-0.622140\pi$
$691$	−1.70702e11			−0.748731			−0.374366	+	0.927281i	$0.622140\pi$
$692$			1.94337e11i			0.847485i
$693$	1.02943e9	+	7.52004e8i	0.00446338	+	0.00326052i
$694$	−3.40852e11			−1.46936
$695$		−	6.17283e10i		−	0.264573i
$696$	2.45018e11	+	4.82417e11i	1.04415	+	2.05582i
$697$	4.37335e11			1.85303
$698$			6.94484e11i			2.92577i
$699$	7.38379e10	−	3.75020e10i	0.309293	−	0.157089i
$700$	8.04348e9			0.0335005
$701$			2.78433e11i			1.15305i	0.817079	+	0.576526i	$0.195592\pi$
$701$			2.78433e11i			1.15305i	−0.817079	+	0.576526i	$0.804408\pi$
$702$	−1.52636e10	+	9.40071e10i	−0.0628506	+	0.387090i
$703$	1.46670e11			0.600508
$704$			9.14031e10i			0.372109i
$705$	−3.76272e10	−	7.40844e10i	−0.152316	−	0.299896i
$706$	5.39340e11			2.17092
$707$			2.49784e9i			0.00999742i
$708$	−7.01135e11	+	3.56104e11i	−2.79041	+	1.41724i
$709$	2.55436e11			1.01088			0.505438	−	0.862863i	$-0.331331\pi$
$709$	2.55436e11			1.01088			0.505438	+	0.862863i	$0.331331\pi$
$710$		−	6.11586e10i		−	0.240671i
$711$	8.53397e10	−	1.16823e11i	0.333943	−	0.457140i
$712$	6.21589e11			2.41871
$713$		−	2.30437e10i		−	0.0891648i
$714$	−4.64034e9	−	9.13638e9i	−0.0178549	−	0.0351545i
$715$	3.80562e9			0.0145613
$716$			3.84585e11i			1.46332i
$717$	−1.67952e11	+	8.53022e10i	−0.635490	+	0.322763i
$718$	−1.61855e11			−0.609014
$719$		−	4.37975e11i		−	1.63883i	−0.573201	−	0.819415i	$-0.694299\pi$
$719$		−	4.37975e11i		−	1.63883i	0.573201	−	0.819415i	$-0.305701\pi$
$720$	−3.38918e10	−	2.47582e10i	−0.126115	−	0.0921273i
$721$	−1.01756e9			−0.00376545
$722$			2.77294e11i			1.02045i
$723$	1.28701e11	+	2.53400e11i	0.471008	+	0.927370i
$724$	−7.78821e11			−2.83455
$725$			3.91355e11i			1.41651i
$726$	3.84240e10	−	1.95154e10i	0.138311	−	0.0702475i
$727$	−3.88581e11			−1.39105			−0.695527	−	0.718500i	$-0.744829\pi$
$727$	−3.88581e11			−1.39105			−0.695527	+	0.718500i	$0.744829\pi$
$728$			1.84126e9i			0.00655524i
$729$	2.67921e11	+	8.93587e10i	0.948628	+	0.316393i
$730$	−6.53443e10			−0.230100
$731$		−	6.38180e10i		−	0.223498i
$732$	−3.00337e11	−	5.91336e11i	−1.04608	−	2.05963i
$733$	3.28148e11			1.13672			0.568360	−	0.822780i	$-0.307578\pi$
$733$	3.28148e11			1.13672			0.568360	+	0.822780i	$0.307578\pi$
$734$		−	6.72272e11i		−	2.31612i
$735$	−5.46621e10	+	2.77627e10i	−0.187300	+	0.0951288i
$736$	−6.21697e9			−0.0211869
$737$			6.26809e10i			0.212454i
$738$	−4.38976e11	+	6.00921e11i	−1.47984	+	2.02578i
$739$	1.11991e11			0.375497			0.187748	−	0.982217i	$-0.439881\pi$
$739$	1.11991e11			0.375497			0.187748	+	0.982217i	$0.439881\pi$
$740$			1.14104e11i			0.380517i
$741$	−1.98931e10	−	3.91676e10i	−0.0659825	−	0.129913i
$742$	5.89679e8			0.00194536
$743$		−	5.06571e11i		−	1.66221i	−0.556118	−	0.831103i	$-0.687710\pi$
$743$		−	5.06571e11i		−	1.66221i	0.556118	−	0.831103i	$-0.312290\pi$
$744$	−5.14655e11	+	2.61391e11i	−1.67967	+	0.853099i
$745$	3.82969e9			0.0124319
$746$		−	7.41855e11i		−	2.39532i
$747$	2.33029e11	+	1.70229e11i	0.748390	+	0.546703i
$748$	−2.27440e11			−0.726540
$749$			5.07858e9i			0.0161367i
$750$	−1.00489e11	−	1.97853e11i	−0.317594	−	0.625314i
$751$	2.89932e11			0.911458			0.455729	−	0.890119i	$-0.349379\pi$
$751$	2.89932e11			0.911458			0.455729	+	0.890119i	$0.349379\pi$
$752$		−	3.80425e11i		−	1.18959i
$753$	3.24276e11	−	1.64698e11i	1.00864	−	0.512282i
$754$	−1.87837e11			−0.581160
$755$			1.29214e11i			0.397670i
$756$	1.13006e10	+	1.83485e9i	0.0345952	+	0.00561712i
$757$	−5.49298e11			−1.67273			−0.836363	−	0.548176i	$-0.815322\pi$
$757$	−5.49298e11			−1.67273			−0.836363	+	0.548176i	$0.815322\pi$
$758$		−	5.44200e11i		−	1.64847i
$759$	3.33683e9	+	6.56991e9i	0.0100547	+	0.0197967i
$760$	6.91612e10			0.207304
$761$		−	3.35949e11i		−	1.00169i	−0.865536	−	0.500847i	$-0.833022\pi$
$761$		−	3.35949e11i		−	1.00169i	0.865536	−	0.500847i	$-0.166978\pi$
$762$	6.69622e11	−	3.40099e11i	1.98614	−	1.00875i
$763$	7.20963e9			0.0212723
$764$		−	3.54132e11i		−	1.03942i
$765$	−5.35100e10	+	7.32507e10i	−0.156239	+	0.213878i
$766$	4.72658e11			1.37288
$767$		−	1.30203e11i		−	0.376217i
$768$	2.94363e11	+	5.79573e11i	0.846132	+	1.66595i
$769$	−4.79303e11			−1.37058			−0.685290	−	0.728270i	$-0.740325\pi$
$769$	−4.79303e11			−1.37058			−0.685290	+	0.728270i	$0.740325\pi$
$770$		−	6.96765e8i		−	0.00198209i
$771$	−1.53523e11	+	7.79739e10i	−0.434467	+	0.220664i
$772$	2.23085e11			0.628060
$773$			5.74251e10i			0.160836i	0.996761	+	0.0804180i	$0.0256255\pi$
$773$			5.74251e10i			0.160836i	−0.996761	+	0.0804180i	$0.974374\pi$
$774$	8.76892e10	+	6.40574e10i	0.244333	+	0.178487i
$775$	−4.17507e11			−1.15733
$776$		−	8.53556e11i		−	2.35388i
$777$	−2.86590e9	−	5.64269e9i	−0.00786280	−	0.0154811i
$778$	−1.21117e11			−0.330588
$779$		−	3.43264e11i		−	0.932133i
$780$	3.04710e10	−	1.54761e10i	0.0823207	−	0.0418104i
$781$	7.52895e10			0.202362
$782$		−	5.92300e10i		−	0.158385i
$783$	−8.92745e10	+	5.49832e11i	−0.237509	+	1.46279i
$784$	−2.80691e11			−0.742958
$785$		−	3.14656e10i		−	0.0828623i
$786$	−9.41099e10	−	1.85293e11i	−0.246573	−	0.485478i
$787$	−3.28821e10			−0.0857158			−0.0428579	−	0.999081i	$-0.513646\pi$
$787$	−3.28821e10			−0.0857158			−0.0428579	+	0.999081i	$0.513646\pi$
$788$			1.24923e12i			3.23993i
$789$	3.28355e11	−	1.66770e11i	0.847297	−	0.430339i
$790$	−7.90710e10			−0.203006
$791$		−	1.14474e10i		−	0.0292416i
$792$	1.08881e11	−	1.49049e11i	0.276727	−	0.378816i
$793$	1.09813e11			0.277689
$794$		−	1.25938e11i		−	0.316865i
$795$	−2.36387e9	−	4.65424e9i	−0.00591773	−	0.0116514i
$796$	−1.02999e11			−0.256555
$797$			3.68934e11i			0.914357i	0.889375	+	0.457178i	$0.151140\pi$
$797$			3.68934e11i			0.914357i	−0.889375	+	0.457178i	$0.848860\pi$
$798$	−7.17113e9	+	3.64219e9i	−0.0176838	+	0.00898154i
$799$	−8.22216e11			−2.01743
$800$			1.12639e11i			0.274998i
$801$	5.16733e11	+	3.77476e11i	1.25527	+	0.916979i
$802$	1.07237e12			2.59208
$803$		−	8.04423e10i		−	0.193474i
$804$	2.54901e11	+	5.01877e11i	0.610025	+	1.20108i
$805$	1.19136e8			0.000283700
$806$		−	2.00389e11i		−	0.474825i
$807$	−1.79283e11	+	9.10572e10i	−0.422712	+	0.214694i
$808$	3.61657e11			0.848500
$809$		−	2.83299e11i		−	0.661380i	−0.943739	−	0.330690i	$-0.892719\pi$
$809$		−	2.83299e11i		−	0.661380i	0.943739	−	0.330690i	$-0.107281\pi$
$810$	−4.69396e10	−	1.47051e11i	−0.109043	−	0.341608i
$811$	−6.40995e11			−1.48174			−0.740868	−	0.671650i	$-0.765586\pi$
$811$	−6.40995e11			−1.48174			−0.740868	+	0.671650i	$0.765586\pi$
$812$			2.25800e10i			0.0519397i
$813$	−3.48107e11	−	6.85390e11i	−0.796803	−	1.56883i
$814$	−2.13942e11			−0.487302
$815$			5.93045e10i			0.134418i
$816$	−3.70296e11	+	1.88072e11i	−0.835196	+	0.424193i
$817$	−5.00906e10			−0.112426
$818$			1.10547e12i			2.46907i
$819$	−1.11815e9	+	1.53065e9i	−0.00248522	+	0.00340206i
$820$	2.67047e11			0.590654
$821$			2.09233e11i			0.460530i	0.973128	+	0.230265i	$0.0739593\pi$
$821$			2.09233e11i			0.460530i	−0.973128	+	0.230265i	$0.926041\pi$
$822$	−6.34426e10	−	1.24912e11i	−0.138961	−	0.273601i
$823$	−1.50852e11			−0.328815			−0.164408	−	0.986393i	$-0.552571\pi$
$823$	−1.50852e11			−0.328815			−0.164408	+	0.986393i	$0.552571\pi$
$824$			1.47330e11i			0.319581i
$825$	1.19034e11	−	6.04570e10i	0.256954	−	0.130506i
$826$	−2.38386e10			−0.0512106
$827$			7.27889e11i			1.55612i	0.628189	+	0.778060i	$0.283796\pi$
$827$			7.27889e11i			1.55612i	−0.628189	+	0.778060i	$0.716204\pi$
$828$	5.34351e10	+	3.90346e10i	0.113686	+	0.0830479i
$829$	−4.15800e11			−0.880372			−0.440186	−	0.897907i	$-0.645088\pi$
$829$	−4.15800e11			−0.880372			−0.440186	+	0.897907i	$0.645088\pi$
$830$		−	1.57725e11i		−	0.332344i
$831$	1.65769e11	+	3.26384e11i	0.347616	+	0.684423i
$832$	−1.35907e11			−0.283627
$833$			6.06660e11i			1.25998i
$834$	9.26705e11	−	4.70670e11i	1.91548	−	0.972864i
$835$	−6.77220e10			−0.139310
$836$			1.78517e11i			0.365472i
$837$	−5.86574e11	−	9.52402e10i	−1.19515	−	0.194052i
$838$	8.21988e11			1.66682
$839$		−	1.98754e11i		−	0.401114i	−0.979682	−	0.200557i	$-0.935725\pi$
$839$		−	1.98754e11i		−	0.401114i	0.979682	−	0.200557i	$-0.0642752\pi$
$840$	−1.35140e9	−	2.66077e9i	−0.00271435	−	0.00534430i
$841$	−5.98381e11			−1.19617
$842$			8.69805e11i			1.73051i
$843$	−5.51773e11	+	2.80244e11i	−1.09257	+	0.554914i
$844$	−1.84442e11			−0.363488
$845$		−	1.01479e11i		−	0.199045i
$846$	8.25300e11	−	1.12977e12i	1.61113	−	2.20550i
$847$	8.57754e8			0.00166659
$848$		−	2.38996e10i		−	0.0462176i
$849$	2.18680e11	+	4.30561e11i	0.420900	+	0.828713i
$850$	−1.07313e12			−2.05579
$851$		−	3.65808e10i		−	0.0697486i
$852$	6.02832e11	−	3.06176e11i	1.14403	−	0.581049i
$853$	5.03229e11			0.950538			0.475269	−	0.879841i	$-0.342351\pi$
$853$	5.03229e11			0.950538			0.475269	+	0.879841i	$0.342351\pi$
$854$		−	2.01054e10i		−	0.0377991i
$855$	5.74944e10	+	4.19999e10i	0.107587	+	0.0785930i
$856$	7.35317e11			1.36955
$857$		−	3.25995e10i		−	0.0604348i	−0.999543	−	0.0302174i	$-0.990380\pi$
$857$		−	3.25995e10i		−	0.0604348i	0.999543	−	0.0302174i	$-0.00961997\pi$
$858$	2.90173e10	+	5.71324e10i	0.0535437	+	0.105422i
$859$	4.46503e11			0.820071			0.410036	−	0.912070i	$-0.365516\pi$
$859$	4.46503e11			0.820071			0.410036	+	0.912070i	$0.365516\pi$
$860$		−	3.89688e10i		−	0.0712399i
$861$	−1.32061e10	+	6.70731e9i	−0.0240304	+	0.0122049i
$862$	6.26625e11			1.13495
$863$		−	3.19673e11i		−	0.576319i	−0.957582	−	0.288159i	$-0.906957\pi$
$863$		−	3.19673e11i		−	0.576319i	0.957582	−	0.288159i	$-0.0930433\pi$
$864$	−2.56949e10	+	1.58252e11i	−0.0461097	+	0.283985i
$865$	5.21516e10			0.0931544
$866$			5.22935e11i			0.929771i
$867$	1.50612e11	+	2.96541e11i	0.266553	+	0.524818i
$868$	−2.40889e10			−0.0424363
$869$		−	9.73405e10i		−	0.170693i
$870$	2.71441e11	−	1.37864e11i	0.473803	−	0.240643i
$871$	−9.31998e10			−0.161936
$872$		−	1.04387e12i		−	1.80542i
$873$	5.18344e11	−	7.09569e11i	0.892402	−	1.22162i
$874$	−4.64895e10			−0.0796727
$875$		−	4.41676e9i		−	0.00753479i
$876$	−3.27131e11	−	6.44090e11i	−0.555527	−	1.09378i
$877$	4.26579e11			0.721109			0.360555	−	0.932738i	$-0.382587\pi$
$877$	4.26579e11			0.721109			0.360555	+	0.932738i	$0.382587\pi$
$878$			4.82737e11i			0.812330i
$879$	−4.72723e11	+	2.40095e11i	−0.791866	+	0.402186i
$880$	−2.82397e10			−0.0470902
$881$		−	1.14290e12i		−	1.89717i	−0.316528	−	0.948583i	$-0.602517\pi$
$881$		−	1.14290e12i		−	1.89717i	0.316528	−	0.948583i	$-0.397483\pi$
$882$	−8.33582e11	−	6.08936e11i	−1.37744	−	1.00623i
$883$	1.50217e11			0.247102			0.123551	−	0.992338i	$-0.460572\pi$
$883$	1.50217e11			0.247102			0.123551	+	0.992338i	$0.460572\pi$
$884$		−	3.38179e11i		−	0.553780i
$885$	9.55626e10	+	1.88154e11i	0.155781	+	0.306719i
$886$	1.15274e12			1.87066
$887$			2.38490e11i			0.385280i	0.981270	+	0.192640i	$0.0617049\pi$
$887$			2.38490e11i			0.385280i	−0.981270	+	0.192640i	$0.938295\pi$
$888$	−8.16992e11	+	4.14947e11i	−1.31391	+	0.667331i
$889$	1.49483e10			0.0239322
$890$		−	3.49748e11i		−	0.557436i
$891$	1.81028e11	−	5.77851e10i	0.287233	−	0.0916864i
$892$	8.72475e11			1.37814
$893$			6.45355e11i			1.01483i
$894$	2.92009e10	+	5.74937e10i	0.0457136	+	0.0900058i
$895$	1.03206e11			0.160847
$896$			2.14836e10i			0.0333330i
$897$	−9.76876e9	+	4.96152e9i	−0.0150893	+	0.00766381i
$898$	1.21120e12			1.86255
$899$		−	1.17204e12i		−	1.79434i
$900$	7.07231e11	−	9.68141e11i	1.07793	−	1.47560i
$901$	−5.16544e10			−0.0783805
$902$			5.00707e11i			0.756410i
$903$	9.78761e8	+	1.92709e9i	0.00147206	+	0.00289835i
$904$	−1.65745e12			−2.48179
$905$			2.09002e11i			0.311570i
$906$	−1.93985e12	+	9.85242e11i	−2.87909	+	1.46228i
$907$	1.46391e11			0.216315			0.108157	−	0.994134i	$-0.465505\pi$
$907$	1.46391e11			0.216315			0.108157	+	0.994134i	$0.465505\pi$
$908$			1.14008e12i			1.67723i
$909$	3.00649e11	+	2.19626e11i	0.440357	+	0.321683i
$910$	1.03602e9			0.00151078
$911$		−	5.04419e11i		−	0.732349i	−0.930546	−	0.366175i	$-0.880667\pi$
$911$		−	5.04419e11i		−	0.732349i	0.930546	−	0.366175i	$-0.119333\pi$
$912$	1.47617e11	+	2.90645e11i	0.213382	+	0.420129i
$913$	1.94167e11			0.279443
$914$			1.74363e12i			2.49844i
$915$	−1.58689e11	+	8.05973e10i	−0.226392	+	0.114984i
$916$	−2.36119e12			−3.35390
$917$		−	4.13638e9i		−	0.00584983i
$918$	−1.50769e12	−	2.44800e11i	−2.12296	−	0.344699i
$919$	5.64585e11			0.791530			0.395765	−	0.918352i	$-0.370479\pi$
$919$	5.64585e11			0.791530			0.395765	+	0.918352i	$0.370479\pi$
$920$		−	1.72495e10i		−	0.0240782i
$921$	−4.45993e11	−	8.78118e11i	−0.619854	−	1.22043i
$922$	2.01639e11			0.279030
$923$			1.11947e11i			0.154244i
$924$	6.86791e9	−	3.48819e9i	0.00942187	−	0.00478533i
$925$	−6.62774e11			−0.905312
$926$		−	1.52803e12i		−	2.07820i
$927$	−8.94698e10	+	1.22477e11i	−0.121159	+	0.165857i
$928$	−3.16206e11			−0.426362
$929$		−	2.13830e11i		−	0.287081i	−0.989644	−	0.143541i	$-0.954151\pi$
$929$		−	2.13830e11i		−	0.287081i	0.989644	−	0.143541i	$-0.0458488\pi$
$930$	1.47076e11	+	2.89580e11i	0.196613	+	0.387112i
$931$	4.76166e11			0.633811
$932$		−	5.00394e11i		−	0.663206i
$933$	−1.12670e12	+	5.72248e11i	−1.48690	+	0.755193i
$934$	−1.45271e12			−1.90894
$935$			6.10348e10i			0.0798604i
$936$	2.21620e11	+	1.61894e11i	0.288739	+	0.210925i
$937$	1.29643e12			1.68187			0.840934	−	0.541138i	$-0.182006\pi$
$937$	1.29643e12			1.68187			0.840934	+	0.541138i	$0.182006\pi$
$938$			1.70638e10i			0.0220427i
$939$	−2.02306e11	−	3.98321e11i	−0.260223	−	0.512354i
$940$	−5.02065e11			−0.643055
$941$		−	1.08479e12i		−	1.38352i	−0.722126	−	0.691762i	$-0.756835\pi$
$941$		−	1.08479e12i		−	1.38352i	0.722126	−	0.691762i	$-0.243165\pi$
$942$	4.72381e11	−	2.39921e11i	0.599914	−	0.304694i
$943$	−8.56132e10			−0.108266
$944$			9.66174e11i			1.21665i
$945$	4.92394e8	−	3.03260e9i	0.000617426	−	0.00380266i
$946$	7.30654e10			0.0912320
$947$		−	8.10922e11i		−	1.00828i	−0.863623	−	0.504138i	$-0.831810\pi$
$947$		−	8.10922e11i		−	1.00828i	0.863623	−	0.504138i	$-0.168190\pi$
$948$	−3.95850e11	−	7.79392e11i	−0.490114	−	0.964989i
$949$	1.19609e11			0.147469
$950$			8.42300e11i			1.03412i
$951$	−8.72487e10	+	4.43133e10i	−0.106669	+	0.0541766i
$952$	−2.95302e10			−0.0359517
$953$		−	4.62488e10i		−	0.0560698i	−0.999607	−	0.0280349i	$-0.991075\pi$
$953$		−	4.62488e10i		−	0.0560698i	0.999607	−	0.0280349i	$-0.00892495\pi$
$954$	5.18482e10	−	7.09758e10i	0.0625950	−	0.0856874i
$955$	−9.50336e10			−0.114252
$956$			1.13820e12i			1.36266i
$957$	1.69717e11	+	3.34158e11i	0.202339	+	0.398386i
$958$	−6.06841e11			−0.720465
$959$		−	2.78847e9i		−	0.00329679i
$960$	1.96397e11	−	9.97492e10i	0.231233	−	0.117442i
$961$	3.97473e11			0.466030
$962$		−	3.18109e11i		−	0.371429i
$963$	6.11276e11	+	4.46540e11i	0.710775	+	0.519225i
$964$	1.71727e12			1.98852
$965$		−	5.98662e10i		−	0.0690355i
$966$	9.08397e8	+	1.78855e9i	0.00104320	+	0.00205396i
$967$	−2.00768e11			−0.229609			−0.114804	−	0.993388i	$-0.536624\pi$
$967$	−2.00768e11			−0.229609			−0.114804	+	0.993388i	$0.536624\pi$
$968$		−	1.24192e11i		−	0.141447i
$969$	6.28173e11	−	3.19047e11i	0.712499	−	0.361875i
$970$	−4.80268e11			−0.542496
$971$			1.55116e12i			1.74493i	0.488675	+	0.872466i	$0.337480\pi$
$971$			1.55116e12i			1.74493i	−0.488675	+	0.872466i	$0.662520\pi$
$972$	1.21447e12	−	1.19885e12i	1.36057	−	1.34308i
$973$	2.06872e10			0.0230808
$974$			2.94634e12i			3.27376i
$975$	8.98931e10	+	1.76991e11i	0.0994736	+	0.195854i
$976$	−8.14869e11			−0.898025
$977$			1.59766e12i			1.75350i	0.480947	+	0.876750i	$0.340293\pi$
$977$			1.59766e12i			1.75350i	−0.480947	+	0.876750i	$0.659707\pi$
$978$	−8.90316e11	+	4.52188e11i	−0.973171	+	0.494270i
$979$	4.30558e11			0.468707
$980$			3.70441e11i			0.401620i
$981$	6.33914e11	−	8.67776e11i	0.684470	−	0.936983i
$982$	1.05769e12			1.13740
$983$		−	4.00959e11i		−	0.429423i	−0.976677	−	0.214712i	$-0.931119\pi$
$983$		−	4.00959e11i		−	0.429423i	0.976677	−	0.214712i	$-0.0688812\pi$
$984$	9.71136e11	+	1.91208e12i	1.03586	+	2.03951i
$985$	3.35237e11			0.356129
$986$		−	3.01255e12i		−	3.18732i
$987$	2.48282e10	−	1.26101e10i	0.0261623	−	0.0132877i
$988$	−2.65436e11			−0.278568
$989$			1.24931e10i			0.0130582i
$990$	−8.38650e10	−	6.12638e10i	−0.0873052	−	0.0637769i
$991$	−4.91421e11			−0.509517			−0.254759	−	0.967005i	$-0.581996\pi$
$991$	−4.91421e11			−0.509517			−0.254759	+	0.967005i	$0.581996\pi$
$992$		−	3.37337e11i		−	0.348351i
$993$	−5.87370e11	−	1.15648e12i	−0.604108	−	1.18943i
$994$	2.04963e10			0.0209957
$995$			2.76404e10i			0.0282002i
$996$	1.55467e12	−	7.89611e11i	1.57980	−	0.802373i
$997$	−1.19748e12			−1.21195			−0.605977	−	0.795482i	$-0.707218\pi$
$997$	−1.19748e12			−1.21195			−0.605977	+	0.795482i	$0.707218\pi$
$998$			9.22475e11i			0.929892i
$999$	−9.31161e11	−	1.51190e11i	−0.934895	−	0.151796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.3	✓	26
3.2	odd	2	inner	33.9.b.a.23.24	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.3	✓	26	1.1	even	1	trivial
33.9.b.a.23.24	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)

\(f(q)\)	\(=\)	\(q-27.3024i q^{2} +(-36.6798 - 72.2191i) q^{3} -489.423 q^{4} +131.340i q^{5} +(-1971.76 + 1001.45i) q^{6} -44.0163 q^{7} +6373.03i q^{8} +(-3870.19 + 5297.96i) q^{9} +O(q^{10})\)	\(q-27.3024i q^{2} +(-36.6798 - 72.2191i) q^{3} -489.423 q^{4} +131.340i q^{5} +(-1971.76 + 1001.45i) q^{6} -44.0163 q^{7} +6373.03i q^{8} +(-3870.19 + 5297.96i) q^{9} +3585.90 q^{10} +4414.43i q^{11} +(17951.9 + 35345.7i) q^{12} -6563.79 q^{13} +1201.75i q^{14} +(9485.24 - 4817.52i) q^{15} +48706.9 q^{16} -105271. i q^{17} +(144647. + 105666. i) q^{18} -82626.7 q^{19} -64280.8i q^{20} +(1614.51 + 3178.82i) q^{21} +120525. q^{22} +20607.9i q^{23} +(460254. - 233761. i) q^{24} +373375. q^{25} +179207. i q^{26} +(524571. + 85173.1i) q^{27} +21542.6 q^{28} +1.04815e6i q^{29} +(-131530. - 258970. i) q^{30} -1.11820e6 q^{31} +301679. i q^{32} +(318806. - 161920. i) q^{33} -2.87414e6 q^{34} -5781.10i q^{35} +(1.89416e6 - 2.59295e6i) q^{36} -1.77509e6 q^{37} +2.25591e6i q^{38} +(240758. + 474030. i) q^{39} -837032. q^{40} +4.15439e6i q^{41} +(86789.5 - 44080.1i) q^{42} +606228. q^{43} -2.16052e6i q^{44} +(-695833. - 508309. i) q^{45} +562645. q^{46} -7.81050e6i q^{47} +(-1.78656e6 - 3.51756e6i) q^{48} -5.76286e6 q^{49} -1.01940e7i q^{50} +(-7.60254e6 + 3.86130e6i) q^{51} +3.21247e6 q^{52} -490682. i q^{53} +(2.32543e6 - 1.43221e7i) q^{54} -579790. q^{55} -280517. i q^{56} +(3.03073e6 + 5.96722e6i) q^{57} +2.86172e7 q^{58} +1.98365e7i q^{59} +(-4.64230e6 + 2.35780e6i) q^{60} -1.67301e7 q^{61} +3.05295e7i q^{62} +(170351. - 233197. i) q^{63} +2.07055e7 q^{64} -862086. i q^{65} +(-4.42082e6 - 8.70418e6i) q^{66} +1.41991e7 q^{67} +5.15219e7i q^{68} +(1.48828e6 - 755893. i) q^{69} -157838. q^{70} -1.70553e7i q^{71} +(-3.37641e7 - 2.46648e7i) q^{72} -1.82226e7 q^{73} +4.84643e7i q^{74} +(-1.36953e7 - 2.69648e7i) q^{75} +4.04394e7 q^{76} -194307. i q^{77} +(1.29422e7 - 6.57329e6i) q^{78} -2.20505e7 q^{79} +6.39715e6i q^{80} +(-1.30900e7 - 4.10082e7i) q^{81} +1.13425e8 q^{82} -4.39847e7i q^{83} +(-790179. - 1.55579e6i) q^{84} +1.38262e7 q^{85} -1.65515e7i q^{86} +(7.56967e7 - 3.84461e7i) q^{87} -2.81333e7 q^{88} -9.75343e7i q^{89} +(-1.38781e7 + 1.89979e7i) q^{90} +288914. q^{91} -1.00860e7i q^{92} +(4.10152e7 + 8.07551e7i) q^{93} -2.13246e8 q^{94} -1.08522e7i q^{95} +(2.17870e7 - 1.10655e7i) q^{96} -1.33932e8 q^{97} +1.57340e8i q^{98} +(-2.33875e7 - 1.70847e7i) 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

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