LMFDB - Embedded newform 33.9.b.a.23.15

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			23.15
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.28405i q^{2} +(49.1853 - 64.3569i) q^{3} +237.647 q^{4} -147.746i q^{5} +(275.708 + 210.712i) q^{6} +2560.99 q^{7} +2114.81i q^{8} +(-1722.62 - 6330.82i) q^{9} +O(q^{10})$	\(q+4.28405i q^{2} +(49.1853 - 64.3569i) q^{3} +237.647 q^{4} -147.746i q^{5} +(275.708 + 210.712i) q^{6} +2560.99 q^{7} +2114.81i q^{8} +(-1722.62 - 6330.82i) q^{9} +632.952 q^{10} +4414.43i q^{11} +(11688.7 - 15294.2i) q^{12} -27499.2 q^{13} +10971.4i q^{14} +(-9508.48 - 7266.94i) q^{15} +51777.7 q^{16} -121040. i q^{17} +(27121.5 - 7379.77i) q^{18} +195684. q^{19} -35111.4i q^{20} +(125963. - 164817. i) q^{21} -18911.6 q^{22} +319348. i q^{23} +(136102. + 104017. i) q^{24} +368796. q^{25} -117808. i q^{26} +(-492159. - 200521. i) q^{27} +608611. q^{28} -964775. i q^{29} +(31131.9 - 40734.8i) q^{30} -751405. q^{31} +763208. i q^{32} +(284099. + 217125. i) q^{33} +518539. q^{34} -378376. i q^{35} +(-409374. - 1.50450e6i) q^{36} -3.03725e6 q^{37} +838319. i q^{38} +(-1.35256e6 + 1.76976e6i) q^{39} +312455. q^{40} +2.07405e6i q^{41} +(706085. + 539631. i) q^{42} +1.45243e6 q^{43} +1.04908e6i q^{44} +(-935355. + 254510. i) q^{45} -1.36810e6 q^{46} +8.01496e6i q^{47} +(2.54670e6 - 3.33225e6i) q^{48} +793869. q^{49} +1.57994e6i q^{50} +(-7.78973e6 - 5.95337e6i) q^{51} -6.53510e6 q^{52} -1.56213e6i q^{53} +(859042. - 2.10843e6i) q^{54} +652215. q^{55} +5.41600e6i q^{56} +(9.62477e6 - 1.25936e7i) q^{57} +4.13314e6 q^{58} +1.83187e7i q^{59} +(-2.25966e6 - 1.72697e6i) q^{60} -4.66270e6 q^{61} -3.21906e6i q^{62} +(-4.41160e6 - 1.62132e7i) q^{63} +9.98547e6 q^{64} +4.06290e6i q^{65} +(-930173. + 1.21709e6i) q^{66} +2.39675e6 q^{67} -2.87647e7i q^{68} +(2.05522e7 + 1.57072e7i) q^{69} +1.62098e6 q^{70} +185635. i q^{71} +(1.33885e7 - 3.64300e6i) q^{72} +1.29315e7 q^{73} -1.30117e7i q^{74} +(1.81393e7 - 2.37346e7i) q^{75} +4.65037e7 q^{76} +1.13053e7i q^{77} +(-7.58175e6 - 5.79442e6i) q^{78} -3.28662e7 q^{79} -7.64996e6i q^{80} +(-3.71119e7 + 2.18111e7i) q^{81} -8.88534e6 q^{82} +6.20811e7i q^{83} +(2.99347e7 - 3.91683e7i) q^{84} -1.78831e7 q^{85} +6.22226e6i q^{86} +(-6.20899e7 - 4.74528e7i) q^{87} -9.33566e6 q^{88} +4.32410e7i q^{89} +(-1.09033e6 - 4.00710e6i) q^{90} -7.04252e7 q^{91} +7.58920e7i q^{92} +(-3.69581e7 + 4.83581e7i) q^{93} -3.43364e7 q^{94} -2.89116e7i q^{95} +(4.91177e7 + 3.75386e7i) q^{96} +3.04904e7 q^{97} +3.40097e6i q^{98} +(2.79470e7 - 7.60436e6i) 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 $

$2$			4.28405i			0.267753i	0.990998	+	0.133876i	$0.0427425\pi$
$2$			4.28405i			0.267753i	−0.990998	+	0.133876i	$0.957257\pi$
$3$	49.1853	−	64.3569i	0.607226	−	0.794529i
$3$	49.1853	−	64.3569i	0.607226	−	0.794529i
$4$	237.647			0.928308
$5$		−	147.746i		−	0.236394i	−0.992990	−	0.118197i	$-0.962289\pi$
$5$		−	147.746i		−	0.236394i	0.992990	−	0.118197i	$-0.0377114\pi$
$6$	275.708	+	210.712i	0.212738	+	0.162586i
$7$	2560.99			1.06663			0.533317	−	0.845915i	$-0.320945\pi$
$7$	2560.99			1.06663			0.533317	+	0.845915i	$0.320945\pi$
$8$			2114.81i			0.516310i
$9$	−1722.62	−	6330.82i	−0.262554	−	0.964917i
$10$	632.952			0.0632952
$11$			4414.43i			0.301511i
$11$			4414.43i			0.301511i
$12$	11688.7	−	15294.2i	0.563693	−	0.737568i
$13$	−27499.2			−0.962824			−0.481412	−	0.876494i	$-0.659876\pi$
$13$	−27499.2			−0.962824			−0.481412	+	0.876494i	$0.659876\pi$
$14$			10971.4i			0.285595i
$15$	−9508.48	−	7266.94i	−0.187822	−	0.143544i
$16$	51777.7			0.790065
$17$		−	121040.i		−	1.44921i	−0.689164	−	0.724606i	$-0.742022\pi$
$17$		−	121040.i		−	1.44921i	0.689164	−	0.724606i	$-0.257978\pi$
$18$	27121.5	−	7379.77i	0.258359	−	0.0702996i
$19$	195684.			1.50155			0.750777	−	0.660556i	$-0.229679\pi$
$19$	195684.			1.50155			0.750777	+	0.660556i	$0.229679\pi$
$20$		−	35111.4i		−	0.219446i
$21$	125963.	−	164817.i	0.647688	−	0.847473i
$22$	−18911.6			−0.0807305
$23$			319348.i			1.14118i	0.821237	+	0.570588i	$0.193285\pi$
$23$			319348.i			1.14118i	−0.821237	+	0.570588i	$0.806715\pi$
$24$	136102.	+	104017.i	0.410224	+	0.313517i
$25$	368796.			0.944118
$26$		−	117808.i		−	0.257799i
$27$	−492159.	−	200521.i	−0.926085	−	0.377316i
$28$	608611.			0.990166
$29$		−	964775.i		−	1.36406i	−0.731323	−	0.682031i	$-0.761097\pi$
$29$		−	964775.i		−	1.36406i	0.731323	−	0.682031i	$-0.238903\pi$
$30$	31131.9	−	40734.8i	0.0384344	−	0.0502899i
$31$	−751405.			−0.813631			−0.406815	−	0.913510i	$-0.633361\pi$
$31$	−751405.			−0.813631			−0.406815	+	0.913510i	$0.633361\pi$
$32$			763208.i			0.727852i
$33$	284099.	+	217125.i	0.239560	+	0.183085i
$34$	518539.			0.388031
$35$		−	378376.i		−	0.252146i
$36$	−409374.	−	1.50450e6i	−0.243731	−	0.895741i
$37$	−3.03725e6			−1.62059			−0.810295	−	0.586022i	$-0.800693\pi$
$37$	−3.03725e6			−1.62059			−0.810295	+	0.586022i	$0.800693\pi$
$38$			838319.i			0.402045i
$39$	−1.35256e6	+	1.76976e6i	−0.584651	+	0.764992i
$40$	312455.			0.122053
$41$			2.07405e6i			0.733981i	0.930225	+	0.366990i	$0.119612\pi$
$41$			2.07405e6i			0.733981i	−0.930225	+	0.366990i	$0.880388\pi$
$42$	706085.	+	539631.i	0.226913	+	0.173420i
$43$	1.45243e6			0.424835			0.212418	−	0.977179i	$-0.431866\pi$
$43$	1.45243e6			0.424835			0.212418	+	0.977179i	$0.431866\pi$
$44$			1.04908e6i			0.279896i
$45$	−935355.	+	254510.i	−0.228101	+	0.0620661i
$46$	−1.36810e6			−0.305553
$47$			8.01496e6i			1.64252i	0.570557	+	0.821258i	$0.306728\pi$
$47$			8.01496e6i			1.64252i	−0.570557	+	0.821258i	$0.693272\pi$
$48$	2.54670e6	−	3.33225e6i	0.479748	−	0.627730i
$49$	793869.			0.137710
$50$			1.57994e6i			0.252790i
$51$	−7.78973e6	−	5.95337e6i	−1.15144	−	0.879998i
$52$	−6.53510e6			−0.893797
$53$		−	1.56213e6i		−	0.197977i	−0.995089	−	0.0989886i	$-0.968439\pi$
$53$		−	1.56213e6i		−	0.197977i	0.995089	−	0.0989886i	$-0.0315607\pi$
$54$	859042.	−	2.10843e6i	0.101027	−	0.247962i
$55$	652215.			0.0712754
$56$			5.41600e6i			0.550714i
$57$	9.62477e6	−	1.25936e7i	0.911782	−	1.19303i
$58$	4.13314e6			0.365232
$59$			1.83187e7i			1.51177i	0.654704	+	0.755885i	$0.272793\pi$
$59$			1.83187e7i			1.51177i	−0.654704	+	0.755885i	$0.727207\pi$
$60$	−2.25966e6	−	1.72697e6i	−0.174357	−	0.133254i
$61$	−4.66270e6			−0.336758			−0.168379	−	0.985722i	$-0.553853\pi$
$61$	−4.66270e6			−0.336758			−0.168379	+	0.985722i	$0.553853\pi$
$62$		−	3.21906e6i		−	0.217852i
$63$	−4.41160e6	−	1.62132e7i	−0.280049	−	1.02921i
$64$	9.98547e6			0.595180
$65$			4.06290e6i			0.227606i
$66$	−930173.	+	1.21709e6i	−0.0490217	+	0.0641428i
$67$	2.39675e6			0.118939			0.0594693	−	0.998230i	$-0.481059\pi$
$67$	2.39675e6			0.118939			0.0594693	+	0.998230i	$0.481059\pi$
$68$		−	2.87647e7i		−	1.34532i
$69$	2.05522e7	+	1.57072e7i	0.906698	+	0.692951i
$70$	1.62098e6			0.0675128
$71$			185635.i			0.00730509i	0.999993	+	0.00365254i	$0.00116264\pi$
$71$			185635.i			0.00730509i	−0.999993	+	0.00365254i	$0.998837\pi$
$72$	1.33885e7	−	3.64300e6i	0.498197	−	0.135559i
$73$	1.29315e7			0.455363			0.227682	−	0.973736i	$-0.426885\pi$
$73$	1.29315e7			0.455363			0.227682	+	0.973736i	$0.426885\pi$
$74$		−	1.30117e7i		−	0.433918i
$75$	1.81393e7	−	2.37346e7i	0.573293	−	0.750129i
$76$	4.65037e7			1.39390
$77$			1.13053e7i			0.321602i
$78$	−7.58175e6	−	5.79442e6i	−0.204829	−	0.156542i
$79$	−3.28662e7			−0.843804			−0.421902	−	0.906642i	$-0.638637\pi$
$79$	−3.28662e7			−0.843804			−0.421902	+	0.906642i	$0.638637\pi$
$80$		−	7.64996e6i		−	0.186766i
$81$	−3.71119e7	+	2.18111e7i	−0.862131	+	0.506685i
$82$	−8.88534e6			−0.196525
$83$			6.20811e7i			1.30812i	0.756444	+	0.654059i	$0.226935\pi$
$83$			6.20811e7i			1.30812i	−0.756444	+	0.654059i	$0.773065\pi$
$84$	2.99347e7	−	3.91683e7i	0.601254	−	0.786716i
$85$	−1.78831e7			−0.342585
$86$			6.22226e6i			0.113751i
$87$	−6.20899e7	−	4.74528e7i	−1.08379	−	0.828294i
$88$	−9.33566e6			−0.155673
$89$			4.32410e7i			0.689185i	0.938752	+	0.344592i	$0.111983\pi$
$89$			4.32410e7i			0.689185i	−0.938752	+	0.344592i	$0.888017\pi$
$90$	−1.09033e6	−	4.00710e6i	−0.0166184	−	0.0610746i
$91$	−7.04252e7			−1.02698
$92$			7.58920e7i			1.05936i
$93$	−3.69581e7	+	4.83581e7i	−0.494058	+	0.646454i
$94$	−3.43364e7			−0.439789
$95$		−	2.89116e7i		−	0.354958i
$96$	4.91177e7	+	3.75386e7i	0.578300	+	0.441971i
$97$	3.04904e7			0.344410			0.172205	−	0.985061i	$-0.444911\pi$
$97$	3.04904e7			0.344410			0.172205	+	0.985061i	$0.444911\pi$
$98$			3.40097e6i			0.0368722i
$99$	2.79470e7	−	7.60436e6i	0.290934	−	0.0791630i
$100$	8.76433e7			0.876433
$101$		−	7.28299e6i		−	0.0699881i	−0.999388	−	0.0349941i	$-0.988859\pi$
$101$		−	7.28299e6i		−	0.0699881i	0.999388	−	0.0349941i	$-0.0111412\pi$
$102$	2.55045e7	−	3.33716e7i	0.235622	−	0.308302i
$103$	−5.23703e7			−0.465303			−0.232651	−	0.972560i	$-0.574740\pi$
$103$	−5.23703e7			−0.465303			−0.232651	+	0.972560i	$0.574740\pi$
$104$		−	5.81555e7i		−	0.497116i
$105$	−2.43511e7	−	1.86106e7i	−0.200337	−	0.153109i
$106$	6.69226e6			0.0530090
$107$			1.02373e8i			0.780998i	0.920603	+	0.390499i	$0.127697\pi$
$107$			1.02373e8i			0.780998i	−0.920603	+	0.390499i	$0.872303\pi$
$108$	−1.16960e8	−	4.76532e7i	−0.859692	−	0.350266i
$109$	−8.12446e7			−0.575558			−0.287779	−	0.957697i	$-0.592917\pi$
$109$	−8.12446e7			−0.575558			−0.287779	+	0.957697i	$0.592917\pi$
$110$			2.79412e6i			0.0190842i
$111$	−1.49388e8	+	1.95468e8i	−0.984064	+	1.28761i
$112$	1.32602e8			0.842711
$113$		−	1.89311e7i		−	0.116108i	−0.998313	−	0.0580540i	$-0.981510\pi$
$113$		−	1.89311e7i		−	0.116108i	0.998313	−	0.0580540i	$-0.0184896\pi$
$114$	5.39516e7	+	4.12330e7i	0.319437	+	0.244132i
$115$	4.71824e7			0.269767
$116$		−	2.29276e8i		−	1.26627i
$117$	4.73706e7	+	1.74093e8i	0.252793	+	0.929045i
$118$	−7.84780e7			−0.404781
$119$		−	3.09981e8i		−	1.54578i
$120$	1.53682e7	−	2.01086e7i	0.0741135	−	0.0969744i
$121$	−1.94872e7			−0.0909091
$122$		−	1.99752e7i		−	0.0901680i
$123$	1.33480e8	+	1.02013e8i	0.583169	+	0.445692i
$124$	−1.78569e8			−0.755300
$125$		−	1.12202e8i		−	0.459578i
$126$	6.94580e7	−	1.88995e7i	0.275575	−	0.0749839i
$127$	8.64758e7			0.332414			0.166207	−	0.986091i	$-0.446848\pi$
$127$	8.64758e7			0.332414			0.166207	+	0.986091i	$0.446848\pi$
$128$			2.38160e8i			0.887214i
$129$	7.14380e7	−	9.34736e7i	0.257971	−	0.337544i
$130$	−1.74057e7			−0.0609421
$131$		−	3.70977e8i		−	1.25968i	−0.776723	−	0.629842i	$-0.783120\pi$
$131$		−	3.70977e8i		−	1.25968i	0.776723	−	0.629842i	$-0.216880\pi$
$132$	6.75152e7	+	5.15991e7i	0.222385	+	0.169960i
$133$	5.01145e8			1.60161
$134$			1.02678e7i			0.0318462i
$135$	−2.96262e7	+	7.27147e7i	−0.0891952	+	0.218921i
$136$	2.55975e8			0.748243
$137$		−	1.34241e8i		−	0.381069i	−0.981681	−	0.190534i	$-0.938978\pi$
$137$		−	1.34241e8i		−	0.381069i	0.981681	−	0.190534i	$-0.0610221\pi$
$138$	−6.72904e7	+	8.80467e7i	−0.185540	+	0.242771i
$139$	3.02648e8			0.810735			0.405368	−	0.914154i	$-0.367144\pi$
$139$	3.02648e8			0.810735			0.405368	+	0.914154i	$0.367144\pi$
$140$		−	8.99200e7i		−	0.234069i
$141$	5.15818e8	+	3.94218e8i	1.30503	+	0.997378i
$142$	−795267.			−0.00195596
$143$		−	1.21393e8i		−	0.290302i
$144$	−8.91931e7	−	3.27795e8i	−0.207435	−	0.762347i
$145$	−1.42542e8			−0.322456
$146$			5.53992e7i			0.121925i
$147$	3.90467e7	−	5.10909e7i	0.0836208	−	0.109414i
$148$	−7.21793e8			−1.50441
$149$		−	7.22803e8i		−	1.46648i	−0.679972	−	0.733238i	$-0.738008\pi$
$149$		−	7.22803e8i		−	1.46648i	0.679972	−	0.733238i	$-0.261992\pi$
$150$	1.01680e8	+	7.77098e7i	0.200849	+	0.153501i
$151$	−4.54541e8			−0.874309			−0.437155	−	0.899386i	$-0.644014\pi$
$151$	−4.54541e8			−0.874309			−0.437155	+	0.899386i	$0.644014\pi$
$152$			4.13834e8i			0.775267i
$153$	−7.66280e8	+	2.08505e8i	−1.39837	+	0.380496i
$154$	−4.84325e7			−0.0861100
$155$			1.11017e8i			0.192337i
$156$	−3.21431e8	+	4.20579e8i	−0.542737	+	0.710148i
$157$	4.51818e8			0.743644			0.371822	−	0.928304i	$-0.378733\pi$
$157$	4.51818e8			0.743644			0.371822	+	0.928304i	$0.378733\pi$
$158$		−	1.40800e8i		−	0.225931i
$159$	−1.00534e8	−	7.68340e7i	−0.157299	−	0.120217i
$160$	1.12761e8			0.172060
$161$			8.17846e8i			1.21722i
$162$	−9.34400e7	−	1.58989e8i	−0.135667	−	0.230838i
$163$	−1.22159e9			−1.73051			−0.865257	−	0.501329i	$-0.832845\pi$
$163$	−1.22159e9			−1.73051			−0.865257	+	0.501329i	$0.832845\pi$
$164$			4.92893e8i			0.681360i
$165$	3.20794e7	−	4.19745e7i	0.0432803	−	0.0566304i
$166$	−2.65958e8			−0.350252
$167$			2.41230e8i			0.310145i	0.987903	+	0.155073i	$0.0495611\pi$
$167$			2.41230e8i			0.310145i	−0.987903	+	0.155073i	$0.950439\pi$
$168$	3.48557e8	+	2.66387e8i	0.437559	+	0.334408i
$169$	−5.95240e7			−0.0729702
$170$		−	7.66122e7i		−	0.0917281i
$171$	−3.37088e8	−	1.23884e9i	−0.394239	−	1.44887i
$172$	3.45165e8			0.394378
$173$		−	1.01187e9i		−	1.12965i	−0.825212	−	0.564823i	$-0.808945\pi$
$173$		−	1.01187e9i		−	1.12965i	0.825212	−	0.564823i	$-0.191055\pi$
$174$	2.03290e8	−	2.65996e8i	0.221778	−	0.290187i
$175$	9.44483e8			1.00703
$176$			2.28569e8i			0.238214i
$177$	1.17893e9	+	9.01009e8i	1.20115	+	0.917986i
$178$	−1.85246e8			−0.184531
$179$			1.78227e9i			1.73605i	0.496521	+	0.868025i	$0.334611\pi$
$179$			1.78227e9i			1.73605i	−0.496521	+	0.868025i	$0.665389\pi$
$180$	−2.22284e8	+	6.04835e7i	−0.211748	+	0.0576165i
$181$	−1.38880e7			−0.0129398			−0.00646988	−	0.999979i	$-0.502059\pi$
$181$	−1.38880e7			−0.0129398			−0.00646988	+	0.999979i	$0.502059\pi$
$182$		−	3.01705e8i		−	0.274977i
$183$	−2.29336e8	+	3.00077e8i	−0.204488	+	0.267564i
$184$	−6.75359e8			−0.589201
$185$			4.48742e8i			0.383098i
$186$	−2.07168e8	−	1.58330e8i	−0.173090	−	0.132285i
$187$	5.34320e8			0.436954
$188$			1.90473e9i			1.52476i
$189$	−1.26042e9	−	5.13533e8i	−0.987794	−	0.402458i
$190$	1.23858e8			0.0950410
$191$		−	1.77911e9i		−	1.33681i	−0.743798	−	0.668404i	$-0.766978\pi$
$191$		−	1.77911e9i		−	1.33681i	0.743798	−	0.668404i	$-0.233022\pi$
$192$	4.91138e8	−	6.42634e8i	0.361409	−	0.472888i
$193$	−1.01316e9			−0.730210			−0.365105	−	0.930966i	$-0.618967\pi$
$193$	−1.01316e9			−0.730210			−0.365105	+	0.930966i	$0.618967\pi$
$194$			1.30622e8i			0.0922169i
$195$	2.61476e8	+	1.99835e8i	0.180839	+	0.138208i
$196$	1.88660e8			0.127837
$197$		−	1.20325e9i		−	0.798900i	−0.916755	−	0.399450i	$-0.869201\pi$
$197$		−	1.20325e9i		−	0.798900i	0.916755	−	0.399450i	$-0.130799\pi$
$198$	3.25774e7	+	1.19726e8i	0.0211961	+	0.0778983i
$199$	2.15794e9			1.37603			0.688013	−	0.725698i	$-0.258483\pi$
$199$	2.15794e9			1.37603			0.688013	+	0.725698i	$0.258483\pi$
$200$			7.79932e8i			0.487458i
$201$	1.17885e8	−	1.54247e8i	0.0722226	−	0.0945002i
$202$	3.12007e7			0.0187395
$203$		−	2.47078e9i		−	1.45496i
$204$	−1.85121e9	−	1.41480e9i	−1.06889	−	0.816910i
$205$	3.06434e8			0.173509
$206$		−	2.24357e8i		−	0.124586i
$207$	2.02173e9	−	5.50113e8i	1.10114	−	0.299620i
$208$	−1.42385e9			−0.760693
$209$			8.63833e8i			0.452735i
$210$	7.97285e7	−	1.04321e8i	0.0409955	−	0.0536409i
$211$	3.88183e9			1.95842			0.979211	−	0.202844i	$-0.0650185\pi$
$211$	3.88183e9			1.95842			0.979211	+	0.202844i	$0.0650185\pi$
$212$		−	3.71237e8i		−	0.183784i
$213$	1.19469e7	+	9.13049e6i	0.00580411	+	0.00443584i
$214$	−4.38570e8			−0.209114
$215$		−	2.14590e8i		−	0.100428i
$216$	4.24063e8	−	1.04082e9i	0.194812	−	0.478147i
$217$	−1.92434e9			−0.867847
$218$		−	3.48056e8i		−	0.154107i
$219$	6.36040e8	−	8.32232e8i	0.276508	−	0.361800i
$220$	1.54997e8			0.0661656
$221$			3.32849e9i			1.39534i
$222$	−8.37393e8	−	6.39985e8i	−0.344760	−	0.263486i
$223$	2.82915e9			1.14403			0.572015	−	0.820243i	$-0.306162\pi$
$223$	2.82915e9			1.14403			0.572015	+	0.820243i	$0.306162\pi$
$224$			1.95457e9i			0.776353i
$225$	−6.35294e8	−	2.33478e9i	−0.247882	−	0.910996i
$226$	8.11017e7			0.0310882
$227$			3.77541e9i			1.42187i	0.703256	+	0.710937i	$0.251729\pi$
$227$			3.77541e9i			1.42187i	−0.703256	+	0.710937i	$0.748271\pi$
$228$	2.28730e9	−	2.99283e9i	0.846415	−	1.10750i
$229$	−3.41544e9			−1.24195			−0.620976	−	0.783830i	$-0.713263\pi$
$229$	−3.41544e9			−1.24195			−0.620976	+	0.783830i	$0.713263\pi$
$230$			2.02132e8i			0.0722309i
$231$	7.27574e8	+	5.56055e8i	0.255523	+	0.195285i
$232$	2.04031e9			0.704279
$233$		−	3.15053e9i		−	1.06896i	−0.845182	−	0.534479i	$-0.820508\pi$
$233$		−	3.15053e9i		−	1.06896i	0.845182	−	0.534479i	$-0.179492\pi$
$234$	−7.45821e8	+	2.02938e8i	−0.248755	+	0.0676861i
$235$	1.18418e9			0.388281
$236$			4.35338e9i			1.40339i
$237$	−1.61653e9	+	2.11517e9i	−0.512379	+	0.670427i
$238$	1.32797e9			0.413887
$239$		−	7.86944e7i		−	0.0241186i	−0.999927	−	0.0120593i	$-0.996161\pi$
$239$		−	7.86944e7i		−	0.0241186i	0.999927	−	0.0120593i	$-0.00383869\pi$
$240$	−4.92327e8	−	3.76265e8i	−0.148391	−	0.113409i
$241$	−3.78787e9			−1.12286			−0.561431	−	0.827523i	$-0.689749\pi$
$241$	−3.78787e9			−1.12286			−0.561431	+	0.827523i	$0.689749\pi$
$242$		−	8.34839e7i		−	0.0243412i
$243$	−4.21663e8	+	3.46119e9i	−0.120932	+	0.992661i
$244$	−1.10808e9			−0.312616
$245$		−	1.17291e8i		−	0.0325537i
$246$	−4.37028e8	+	5.71833e8i	−0.119335	+	0.156145i
$247$	−5.38115e9			−1.44573
$248$		−	1.58908e9i		−	0.420086i
$249$	3.99534e9	+	3.05348e9i	1.03934	+	0.794323i
$250$	4.80677e8			0.123053
$251$		−	5.21737e9i		−	1.31449i	−0.753678	−	0.657244i	$-0.771722\pi$
$251$		−	5.21737e9i		−	1.31449i	0.753678	−	0.657244i	$-0.228278\pi$
$252$	−1.04840e9	−	3.85301e9i	−0.259972	−	0.955428i
$253$	−1.40974e9			−0.344077
$254$			3.70466e8i			0.0890049i
$255$	−8.79587e8	+	1.15090e9i	−0.208026	+	0.272194i
$256$	1.53599e9			0.357626
$257$			8.53465e9i			1.95638i	0.207713	+	0.978190i	$0.433398\pi$
$257$			8.53465e9i			1.95638i	−0.207713	+	0.978190i	$0.566602\pi$
$258$	4.00445e8	+	3.06044e8i	0.0903784	+	0.0690724i
$259$	−7.77836e9			−1.72858
$260$			9.65537e8i			0.211288i
$261$	−6.10782e9	+	1.66194e9i	−1.31621	+	0.358140i
$262$	1.58928e9			0.337284
$263$		−	7.16055e9i		−	1.49666i	−0.663326	−	0.748330i	$-0.730856\pi$
$263$		−	7.16055e9i		−	1.49666i	0.663326	−	0.748330i	$-0.269144\pi$
$264$	−4.59177e8	+	6.00814e8i	−0.0945289	+	0.123687i
$265$	−2.30799e8			−0.0468006
$266$			2.14693e9i			0.428835i
$267$	2.78285e9	+	2.12682e9i	0.547577	+	0.418491i
$268$	5.69579e8			0.110412
$269$		−	7.67838e9i		−	1.46643i	−0.679999	−	0.733213i	$-0.738020\pi$
$269$		−	7.67838e9i		−	1.46643i	0.679999	−	0.733213i	$-0.261980\pi$
$270$	−3.11513e8	−	1.26920e8i	−0.0586167	−	0.0238823i
$271$	5.29927e9			0.982514			0.491257	−	0.871015i	$-0.336538\pi$
$271$	5.29927e9			0.982514			0.491257	+	0.871015i	$0.336538\pi$
$272$		−	6.26715e9i		−	1.14497i
$273$	−3.46388e9	+	4.53235e9i	−0.623610	+	0.815967i
$274$	5.75095e8			0.102032
$275$			1.62802e9i			0.284662i
$276$	4.88417e9	+	3.73277e9i	0.841695	+	0.643272i
$277$	−6.92362e8			−0.117602			−0.0588009	−	0.998270i	$-0.518728\pi$
$277$	−6.92362e8			−0.117602			−0.0588009	+	0.998270i	$0.518728\pi$
$278$			1.29656e9i			0.217077i
$279$	1.29438e9	+	4.75701e9i	0.213622	+	0.785087i
$280$	8.00193e8			0.130186
$281$		−	7.39132e9i		−	1.18549i	−0.805391	−	0.592744i	$-0.798045\pi$
$281$		−	7.39132e9i		−	1.18549i	0.805391	−	0.592744i	$-0.201955\pi$
$282$	−1.68885e9	+	2.20979e9i	−0.267051	+	0.349425i
$283$	4.01890e9			0.626558			0.313279	−	0.949661i	$-0.398572\pi$
$283$	4.01890e9			0.626558			0.313279	+	0.949661i	$0.398572\pi$
$284$			4.41155e7i			0.00678137i
$285$	−1.86066e9	−	1.42202e9i	−0.282025	−	0.215540i
$286$	5.20054e8			0.0777293
$287$			5.31163e9i			0.782889i
$288$	4.83174e9	−	1.31471e9i	0.702317	−	0.191100i
$289$	−7.67482e9			−1.10021
$290$		−	6.10656e8i		−	0.0863385i
$291$	1.49968e9	−	1.96227e9i	0.209135	−	0.273644i
$292$	3.07314e9			0.422718
$293$			7.16525e9i			0.972212i	0.873900	+	0.486106i	$0.161583\pi$
$293$			7.16525e9i			0.972212i	−0.873900	+	0.486106i	$0.838417\pi$
$294$	2.18876e8	+	1.67278e8i	0.0292960	+	0.0223897i
$295$	2.70651e9			0.357373
$296$		−	6.42319e9i		−	0.836727i
$297$	8.85186e8	−	2.17260e9i	0.113765	−	0.279225i
$298$	3.09652e9			0.392653
$299$		−	8.78181e9i		−	1.09875i
$300$	4.31076e9	−	5.64045e9i	0.532192	−	0.696351i
$301$	3.71965e9			0.453144
$302$		−	1.94727e9i		−	0.234099i
$303$	−4.68711e8	−	3.58216e8i	−0.0556076	−	0.0424986i
$304$	1.01321e10			1.18632
$305$			6.88896e8i			0.0796076i
$306$	−8.93244e8	−	3.28278e9i	−0.101879	−	0.374417i
$307$	−1.17418e8			−0.0132185			−0.00660925	−	0.999978i	$-0.502104\pi$
$307$	−1.17418e8			−0.0132185			−0.00660925	+	0.999978i	$0.502104\pi$
$308$			2.68667e9i			0.298546i
$309$	−2.57585e9	+	3.37039e9i	−0.282544	+	0.369697i
$310$	−4.75603e8			−0.0514989
$311$		−	5.66272e9i		−	0.605318i	−0.953099	−	0.302659i	$-0.902126\pi$
$311$		−	5.66272e9i		−	0.605318i	0.953099	−	0.302659i	$-0.0978743\pi$
$312$	−3.74271e9	−	2.86040e9i	−0.394973	−	0.301861i
$313$	6.58032e9			0.685598			0.342799	−	0.939409i	$-0.388625\pi$
$313$	6.58032e9			0.685598			0.342799	+	0.939409i	$0.388625\pi$
$314$			1.93561e9i			0.199113i
$315$	−2.39543e9	+	6.51797e8i	−0.243300	+	0.0662019i
$316$	−7.81056e9			−0.783310
$317$		−	1.24923e8i		−	0.0123710i	−0.999981	−	0.00618549i	$-0.998031\pi$
$317$		−	1.24923e8i		−	0.0123710i	0.999981	−	0.00618549i	$-0.00196891\pi$
$318$	3.29161e8	−	4.30693e8i	0.0321884	−	0.0421172i
$319$	4.25893e9			0.411280
$320$		−	1.47531e9i		−	0.140697i
$321$	6.58840e9	+	5.03524e9i	0.620525	+	0.474242i
$322$	−3.50369e9			−0.325914
$323$		−	2.36855e10i		−	2.17607i
$324$	−8.81953e9	+	5.18335e9i	−0.800323	+	0.470360i
$325$	−1.01416e10			−0.909019
$326$		−	5.23335e9i		−	0.463350i
$327$	−3.99604e9	+	5.22865e9i	−0.349493	+	0.457297i
$328$	−4.38622e9			−0.378962
$329$			2.05262e10i			1.75197i
$330$	1.79821e8	+	1.37430e8i	0.0151630	+	0.0115884i
$331$	1.61347e10			1.34416			0.672079	−	0.740480i	$-0.265402\pi$
$331$	1.61347e10			1.34416			0.672079	+	0.740480i	$0.265402\pi$
$332$			1.47534e10i			1.21434i
$333$	5.23201e9	+	1.92283e10i	0.425492	+	1.56374i
$334$	−1.03344e9			−0.0830422
$335$		−	3.54110e8i		−	0.0281164i
$336$	6.52207e9	−	8.53386e9i	0.511716	−	0.669558i
$337$	−9.77279e9			−0.757703			−0.378851	−	0.925458i	$-0.623681\pi$
$337$	−9.77279e9			−0.757703			−0.378851	+	0.925458i	$0.623681\pi$
$338$		−	2.55004e8i		−	0.0195380i
$339$	−1.21835e9	−	9.31131e8i	−0.0922512	−	0.0705037i
$340$	−4.24987e9			−0.318024
$341$		−	3.31702e9i		−	0.245319i
$342$	5.30725e9	−	1.44410e9i	0.387940	−	0.105559i
$343$	−1.27305e10			−0.919749
$344$			3.07160e9i			0.219347i
$345$	2.32068e9	−	3.03651e9i	0.163809	−	0.214338i
$346$	4.33492e9			0.302466
$347$		−	1.07473e10i		−	0.741278i	−0.928777	−	0.370639i	$-0.879139\pi$
$347$		−	1.07473e10i		−	0.741278i	0.928777	−	0.370639i	$-0.120861\pi$
$348$	−1.47555e10	−	1.12770e10i	−1.00609	−	0.768912i
$349$	1.18993e10			0.802081			0.401041	−	0.916060i	$-0.368649\pi$
$349$	1.18993e10			0.802081			0.401041	+	0.916060i	$0.368649\pi$
$350$			4.04621e9i			0.269635i
$351$	1.35340e10	+	5.51417e9i	0.891656	+	0.363289i
$352$	−3.36913e9			−0.219456
$353$		−	1.87082e9i		−	0.120485i	−0.998184	−	0.0602425i	$-0.980813\pi$
$353$		−	1.87082e9i		−	0.120485i	0.998184	−	0.0602425i	$-0.0191874\pi$
$354$	−3.85996e9	+	5.05060e9i	−0.245793	+	0.321610i
$355$	2.74268e7			0.00172688
$356$			1.02761e10i			0.639776i
$357$	−1.99494e10	−	1.52465e10i	−1.22817	−	0.938637i
$358$	−7.63534e9			−0.464832
$359$			1.53969e10i			0.926945i	0.886111	+	0.463473i	$0.153397\pi$
$359$			1.53969e10i			0.926945i	−0.886111	+	0.463473i	$0.846603\pi$
$360$	−5.38239e8	−	1.97809e9i	−0.0320454	−	0.117771i
$361$	2.13086e10			1.25466
$362$		−	5.94970e7i		−	0.00346466i
$363$	−9.58482e8	+	1.25413e9i	−0.0552023	+	0.0722299i
$364$	−1.67363e10			−0.953355
$365$		−	1.91058e9i		−	0.107645i
$366$	−1.28554e9	−	9.82487e8i	−0.0716411	−	0.0547523i
$367$	−1.56278e10			−0.861454			−0.430727	−	0.902482i	$-0.641743\pi$
$367$	−1.56278e10			−0.861454			−0.430727	+	0.902482i	$0.641743\pi$
$368$			1.65351e10i			0.901603i
$369$	1.31305e10	−	3.57280e9i	0.708231	−	0.192709i
$370$	−1.92243e9			−0.102576
$371$		−	4.00061e9i		−	0.211169i
$372$	−8.78298e9	+	1.14922e10i	−0.458638	+	0.600108i
$373$	−2.86221e10			−1.47865			−0.739326	−	0.673348i	$-0.764856\pi$
$373$	−2.86221e10			−1.47865			−0.739326	+	0.673348i	$0.764856\pi$
$374$			2.28905e9i			0.116996i
$375$	−7.22094e9	−	5.51867e9i	−0.365148	−	0.279067i
$376$	−1.69501e10			−0.848048
$377$			2.65306e10i			1.31335i
$378$	2.20000e9	−	5.39968e9i	0.107759	−	0.264485i
$379$	8.99780e9			0.436093			0.218047	−	0.975938i	$-0.430032\pi$
$379$	8.99780e9			0.436093			0.218047	+	0.975938i	$0.430032\pi$
$380$		−	6.87074e9i		−	0.329511i
$381$	4.25334e9	−	5.56531e9i	0.201851	−	0.264113i
$382$	7.62178e9			0.357934
$383$			8.97317e9i			0.417014i	0.978021	+	0.208507i	$0.0668604\pi$
$383$			8.97317e9i			0.417014i	−0.978021	+	0.208507i	$0.933140\pi$
$384$	1.53272e10	+	1.17139e10i	0.704917	+	0.538739i
$385$	1.67032e9			0.0760249
$386$		−	4.34041e9i		−	0.195516i
$387$	−2.50197e9	−	9.19505e9i	−0.111542	−	0.409931i
$388$	7.24595e9			0.319719
$389$		−	1.64728e10i		−	0.719396i	−0.933069	−	0.359698i	$-0.882880\pi$
$389$		−	1.64728e10i		−	0.719396i	0.933069	−	0.359698i	$-0.117120\pi$
$390$	−8.56103e8	+	1.12017e9i	−0.0370056	+	0.0484203i
$391$	3.86537e10			1.65380
$392$			1.67888e9i			0.0711009i
$393$	−2.38749e10	−	1.82466e10i	−1.00086	−	0.764912i
$394$	5.15480e9			0.213908
$395$			4.85586e9i			0.199470i
$396$	6.64151e9	−	1.80715e9i	0.270076	−	0.0734876i
$397$	−3.38226e10			−1.36158			−0.680792	−	0.732476i	$-0.738364\pi$
$397$	−3.38226e10			−1.36158			−0.680792	+	0.732476i	$0.738364\pi$
$398$			9.24471e9i			0.368435i
$399$	2.46489e10	−	3.22521e10i	0.972538	−	1.27253i
$400$	1.90954e10			0.745914
$401$			1.66389e10i			0.643497i	0.946825	+	0.321748i	$0.104271\pi$
$401$			1.66389e10i			0.643497i	−0.946825	+	0.321748i	$0.895729\pi$
$402$	6.60802e8	+	5.05023e8i	0.0253027	+	0.0193378i
$403$	2.06631e10			0.783383
$404$		−	1.73078e9i		−	0.0649706i
$405$	3.22251e9	+	5.48314e9i	0.119777	+	0.203802i
$406$	1.05849e10			0.389569
$407$		−	1.34077e10i		−	0.488626i
$408$	1.25902e10	−	1.64738e10i	0.454352	−	0.594501i
$409$	4.76040e10			1.70118			0.850589	−	0.525831i	$-0.176246\pi$
$409$	4.76040e10			1.70118			0.850589	+	0.525831i	$0.176246\pi$
$410$			1.31278e9i			0.0464574i
$411$	−8.63934e9	−	6.60269e9i	−0.302770	−	0.231395i
$412$	−1.24456e10			−0.431945
$413$			4.69139e10i			1.61251i
$414$	2.35671e9	+	8.66120e9i	0.0802241	+	0.294833i
$415$	9.17224e9			0.309231
$416$		−	2.09876e10i		−	0.700794i
$417$	1.48858e10	−	1.94775e10i	0.492299	−	0.644153i
$418$	−3.70070e9			−0.121221
$419$		−	4.04022e10i		−	1.31084i	−0.755265	−	0.655420i	$-0.772492\pi$
$419$		−	4.04022e10i		−	1.31084i	0.755265	−	0.655420i	$-0.227508\pi$
$420$	−5.78697e9	−	4.42274e9i	−0.185975	−	0.142133i
$421$	−4.85918e10			−1.54680			−0.773402	−	0.633916i	$-0.781446\pi$
$421$	−4.85918e10			−1.54680			−0.773402	+	0.633916i	$0.781446\pi$
$422$			1.66299e10i			0.524373i
$423$	5.07413e10	−	1.38067e10i	1.58489	−	0.431249i
$424$	3.30361e9			0.102218
$425$		−	4.46389e10i		−	1.36823i
$426$	−3.91154e7	+	5.11809e7i	−0.00118771	+	0.00155407i
$427$	−1.19411e10			−0.359198
$428$			2.43286e10i			0.725007i
$429$	−7.81249e9	−	5.97076e9i	−0.230654	−	0.176279i
$430$	9.19315e8			0.0268900
$431$		−	1.39888e10i		−	0.405388i	−0.979242	−	0.202694i	$-0.935030\pi$
$431$		−	1.39888e10i		−	0.405388i	0.979242	−	0.202694i	$-0.0649697\pi$
$432$	−2.54829e10	−	1.03825e10i	−0.731667	−	0.298104i
$433$	2.81047e10			0.799515			0.399757	−	0.916621i	$-0.369094\pi$
$433$	2.81047e10			0.799515			0.399757	+	0.916621i	$0.369094\pi$
$434$		−	8.24397e9i		−	0.232369i
$435$	−7.01096e9	+	9.17355e9i	−0.195804	+	0.256201i
$436$	−1.93075e10			−0.534295
$437$			6.24912e10i			1.71354i
$438$	3.56532e9	+	2.72483e9i	0.0968729	+	0.0740359i
$439$	3.32684e9			0.0895724			0.0447862	−	0.998997i	$-0.485739\pi$
$439$	3.32684e9			0.0895724			0.0447862	+	0.998997i	$0.485739\pi$
$440$			1.37931e9i			0.0368002i
$441$	−1.36753e9	−	5.02584e9i	−0.0361562	−	0.132878i
$442$	−1.42594e10			−0.373605
$443$		−	2.43654e10i		−	0.632643i	−0.948652	−	0.316321i	$-0.897552\pi$
$443$		−	2.43654e10i		−	0.632643i	0.948652	−	0.316321i	$-0.102448\pi$
$444$	−3.55016e10	+	4.64523e10i	−0.913515	+	1.19530i
$445$	6.38869e9			0.162919
$446$			1.21202e10i			0.306317i
$447$	−4.65174e10	−	3.55513e10i	−1.16516	−	0.890482i
$448$	2.55727e10			0.634840
$449$		−	3.97344e9i		−	0.0977645i	−0.998805	−	0.0488823i	$-0.984434\pi$
$449$		−	3.97344e9i		−	0.0977645i	0.998805	−	0.0488823i	$-0.0155659\pi$
$450$	1.00023e10	−	2.72163e9i	0.243922	−	0.0663711i
$451$	−9.15576e9			−0.221303
$452$		−	4.49892e9i		−	0.107784i
$453$	−2.23567e10	+	2.92528e10i	−0.530903	+	0.694664i
$454$	−1.61740e10			−0.380711
$455$			1.04051e10i			0.242772i
$456$	2.66330e10	+	2.03545e10i	0.615973	+	0.470762i
$457$	−4.17820e9			−0.0957909			−0.0478955	−	0.998852i	$-0.515251\pi$
$457$	−4.17820e9			−0.0957909			−0.0478955	+	0.998852i	$0.515251\pi$
$458$		−	1.46319e10i		−	0.332536i
$459$	−2.42710e10	+	5.95708e10i	−0.546811	+	1.34209i
$460$	1.12128e10			0.250427
$461$		−	3.33867e10i		−	0.739214i	−0.929188	−	0.369607i	$-0.879492\pi$
$461$		−	3.33867e10i		−	0.739214i	0.929188	−	0.369607i	$-0.120508\pi$
$462$	−2.38216e9	+	3.11696e9i	−0.0522882	+	0.0684169i
$463$	−4.52543e10			−0.984773			−0.492386	−	0.870377i	$-0.663875\pi$
$463$	−4.52543e10			−0.984773			−0.492386	+	0.870377i	$0.663875\pi$
$464$		−	4.99538e10i		−	1.07770i
$465$	7.14472e9	+	5.46042e9i	0.152818	+	0.116792i
$466$	1.34970e10			0.286216
$467$			6.41507e10i			1.34876i	0.738385	+	0.674379i	$0.235589\pi$
$467$			6.41507e10i			1.34876i	−0.738385	+	0.674379i	$0.764411\pi$
$468$	1.12575e10	+	4.13726e10i	0.234670	+	0.862441i
$469$	6.13804e9			0.126864
$470$			5.07308e9i			0.103963i
$471$	2.22228e10	−	2.90776e10i	0.451560	−	0.590847i
$472$	−3.87404e10			−0.780542
$473$			6.41163e9i			0.128093i
$474$	−9.06148e9	−	6.92531e9i	−0.179509	−	0.137191i
$475$	7.21675e10			1.41764
$476$		−	7.36661e10i		−	1.43496i
$477$	−9.88960e9	+	2.69096e9i	−0.191032	+	0.0519797i
$478$	3.37130e8			0.00645783
$479$			5.17111e10i			0.982294i	0.871077	+	0.491147i	$0.163422\pi$
$479$			5.17111e10i			0.982294i	−0.871077	+	0.491147i	$0.836578\pi$
$480$	5.54619e9	−	7.25695e9i	0.104479	−	0.136707i
$481$	8.35219e10			1.56034
$482$		−	1.62274e10i		−	0.300650i
$483$	5.26340e10	+	4.02260e10i	0.967115	+	0.739126i
$484$	−4.63107e9			−0.0843917
$485$		−	4.50484e9i		−	0.0814165i
$486$	−1.48279e10	−	1.80642e9i	−0.265788	−	0.0323798i
$487$	−3.57951e10			−0.636367			−0.318184	−	0.948029i	$-0.603073\pi$
$487$	−3.57951e10			−0.636367			−0.318184	+	0.948029i	$0.603073\pi$
$488$		−	9.86071e9i		−	0.173872i
$489$	−6.00843e10	+	7.86177e10i	−1.05081	+	1.37494i
$490$	5.02480e8			0.00871635
$491$			3.11400e10i			0.535788i	0.963448	+	0.267894i	$0.0863276\pi$
$491$			3.11400e10i			0.535788i	−0.963448	+	0.267894i	$0.913672\pi$
$492$	3.17210e10	+	2.42431e10i	0.541361	+	0.413740i
$493$	−1.16776e11			−1.97681
$494$		−	2.30531e10i		−	0.387099i
$495$	−1.12352e9	−	4.12906e9i	−0.0187136	−	0.0687749i
$496$	−3.89060e10			−0.642821
$497$			4.75408e8i			0.00779186i
$498$	−1.30812e10	+	1.71162e10i	−0.212682	+	0.278286i
$499$	−8.51820e10			−1.37387			−0.686935	−	0.726719i	$-0.741044\pi$
$499$	−8.51820e10			−1.37387			−0.686935	+	0.726719i	$0.741044\pi$
$500$		−	2.66644e10i		−	0.426630i
$501$	1.55248e10	+	1.18650e10i	0.246419	+	0.188328i
$502$	2.23514e10			0.351958
$503$		−	2.06352e10i		−	0.322357i	−0.986925	−	0.161179i	$-0.948470\pi$
$503$		−	2.06352e10i		−	0.322357i	0.986925	−	0.161179i	$-0.0515295\pi$
$504$	3.42877e10	−	9.32968e9i	0.531394	−	0.144592i
$505$	−1.07603e9			−0.0165448
$506$		−	6.03938e9i		−	0.0921277i
$507$	−2.92771e9	+	3.83078e9i	−0.0443094	+	0.0579769i
$508$	2.05507e10			0.308583
$509$		−	6.05655e10i		−	0.902307i	−0.892446	−	0.451153i	$-0.851013\pi$
$509$		−	6.05655e10i		−	0.902307i	0.892446	−	0.451153i	$-0.148987\pi$
$510$	−4.93052e9	−	3.76819e9i	−0.0728806	−	0.0556996i
$511$	3.31175e10			0.485706
$512$			6.75491e10i			0.982969i
$513$	−9.63077e10	−	3.92388e10i	−1.39057	−	0.566560i
$514$	−3.65628e10			−0.523826
$515$			7.73751e9i			0.109995i
$516$	1.69770e10	−	2.22137e10i	0.239476	−	0.313345i
$517$	−3.53814e10			−0.495237
$518$		−	3.33229e10i		−	0.462832i
$519$	−6.51210e10	−	4.97693e10i	−0.897536	−	0.685950i
$520$	−8.59225e9			−0.117515
$521$			1.54998e10i			0.210366i	0.994453	+	0.105183i	$0.0335428\pi$
$521$			1.54998e10i			0.210366i	−0.994453	+	0.105183i	$0.966457\pi$
$522$	−7.11982e9	−	2.61662e10i	−0.0958930	−	0.352418i
$523$	8.83139e10			1.18038			0.590191	−	0.807264i	$-0.299052\pi$
$523$	8.83139e10			1.18038			0.590191	+	0.807264i	$0.299052\pi$
$524$		−	8.81615e10i		−	1.16937i
$525$	4.64547e10	−	6.07840e10i	0.611494	−	0.800114i
$526$	3.06761e10			0.400735
$527$			9.09498e10i			1.17912i
$528$	1.47100e10	+	1.12422e10i	0.189268	+	0.144649i
$529$	−2.36720e10			−0.302282
$530$		−	9.88756e8i		−	0.0125310i
$531$	1.15972e11	−	3.15560e10i	1.45873	−	0.396921i
$532$	1.19095e11			1.48679
$533$		−	5.70349e10i		−	0.706694i
$534$	−9.11140e9	+	1.19219e10i	−0.112052	+	0.146615i
$535$	1.51252e10			0.184623
$536$			5.06865e9i			0.0614092i
$537$	1.14702e11	+	8.76616e10i	1.37934	+	1.05417i
$538$	3.28945e10			0.392640
$539$			3.50448e9i			0.0415210i
$540$	−7.04058e9	+	1.72804e10i	−0.0828006	+	0.203226i
$541$	2.03346e10			0.237381			0.118691	−	0.992931i	$-0.462130\pi$
$541$	2.03346e10			0.237381			0.118691	+	0.992931i	$0.462130\pi$
$542$			2.27023e10i			0.263071i
$543$	−6.83087e8	+	8.93790e8i	−0.00785736	+	0.0102810i
$544$	9.23784e10			1.05481
$545$			1.20036e10i			0.136058i
$546$	−1.94168e10	−	1.48394e10i	−0.218478	−	0.166973i
$547$	−2.04113e10			−0.227993			−0.113996	−	0.993481i	$-0.536365\pi$
$547$	−2.04113e10			−0.227993			−0.113996	+	0.993481i	$0.536365\pi$
$548$		−	3.19020e10i		−	0.353749i
$549$	8.03204e9	+	2.95187e10i	0.0884172	+	0.324944i
$550$	−6.97453e9			−0.0762192
$551$		−	1.88791e11i		−	2.04821i
$552$	−3.32177e10	+	4.34640e10i	−0.357778	+	0.468137i
$553$	−8.41701e10			−0.900030
$554$		−	2.96611e9i		−	0.0314882i
$555$	2.88796e10	+	2.20715e10i	0.304382	+	0.232627i
$556$	7.19234e10			0.752612
$557$		−	7.84661e10i		−	0.815195i	−0.913162	−	0.407598i	$-0.866367\pi$
$557$		−	7.84661e10i		−	0.815195i	0.913162	−	0.407598i	$-0.133633\pi$
$558$	−2.03793e10	+	5.54519e9i	−0.210209	+	0.0571979i
$559$	−3.99406e10			−0.409041
$560$		−	1.95915e10i		−	0.199212i
$561$	2.62807e10	−	3.43872e10i	0.265330	−	0.347173i
$562$	3.16648e10			0.317418
$563$			6.43548e10i			0.640542i	0.947326	+	0.320271i	$0.103774\pi$
$563$			6.43548e10i			0.640542i	−0.947326	+	0.320271i	$0.896226\pi$
$564$	1.22582e11	+	9.36847e10i	1.21147	+	0.925875i
$565$	−2.79700e9			−0.0274472
$566$			1.72172e10i			0.167763i
$567$	−9.50432e10	+	5.58581e10i	−0.919579	+	0.540448i
$568$	−3.92581e8			−0.00377169
$569$		−	4.22079e9i		−	0.0402666i	−0.999797	−	0.0201333i	$-0.993591\pi$
$569$		−	4.22079e9i		−	0.0402666i	0.999797	−	0.0201333i	$-0.00640906\pi$
$570$	6.09201e9	−	7.97114e9i	0.0577114	−	0.0755129i
$571$	5.68903e10			0.535173			0.267586	−	0.963534i	$-0.413774\pi$
$571$	5.68903e10			0.535173			0.267586	+	0.963534i	$0.413774\pi$
$572$		−	2.88487e10i		−	0.269490i
$573$	−1.14498e11	−	8.75060e10i	−1.06213	−	0.811744i
$574$	−2.27553e10			−0.209621
$575$			1.17774e11i			1.07740i
$576$	−1.72011e10	−	6.32162e10i	−0.156267	−	0.574300i
$577$	−1.76519e9			−0.0159253			−0.00796266	−	0.999968i	$-0.502535\pi$
$577$	−1.76519e9			−0.0159253			−0.00796266	+	0.999968i	$0.502535\pi$
$578$		−	3.28793e10i		−	0.294585i
$579$	−4.98324e10	+	6.52037e10i	−0.443402	+	0.580173i
$580$	−3.38746e10			−0.299339
$581$			1.58989e11i			1.39528i
$582$	8.40644e9	+	6.42469e9i	0.0732690	+	0.0559964i
$583$	6.89593e9			0.0596924
$584$			2.73477e10i			0.235109i
$585$	2.57215e10	−	6.99882e9i	0.219621	−	0.0597587i
$586$	−3.06963e10			−0.260313
$587$		−	8.84870e10i		−	0.745293i	−0.927973	−	0.372646i	$-0.878450\pi$
$587$		−	8.84870e10i		−	0.745293i	0.927973	−	0.372646i	$-0.121550\pi$
$588$	9.27932e9	−	1.21416e10i	0.0776259	−	0.101570i
$589$	−1.47038e11			−1.22171
$590$			1.15948e10i			0.0956877i
$591$	−7.74377e10	−	5.91824e10i	−0.634750	−	0.485113i
$592$	−1.57262e11			−1.28037
$593$			1.90377e11i			1.53956i	0.638310	+	0.769780i	$0.279634\pi$
$593$			1.90377e11i			1.53956i	−0.638310	+	0.769780i	$0.720366\pi$
$594$	9.30753e9	+	3.79218e9i	0.0747633	+	0.0304609i
$595$	−4.57985e10			−0.365413
$596$		−	1.71772e11i		−	1.36134i
$597$	1.06139e11	−	1.38878e11i	0.835559	−	1.09329i
$598$	3.76217e10			0.294194
$599$			1.27321e11i			0.988988i	0.869181	+	0.494494i	$0.164647\pi$
$599$			1.27321e11i			0.988988i	−0.869181	+	0.494494i	$0.835353\pi$
$600$	5.01940e10	+	3.83612e10i	0.387299	+	0.295997i
$601$	7.29170e10			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$601$	7.29170e10			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$602$			1.59352e10i			0.121331i
$603$	−4.12867e9	−	1.51734e10i	−0.0312278	−	0.114766i
$604$	−1.08020e11			−0.811629
$605$			2.87916e9i			0.0214904i
$606$	1.53461e9	−	2.00798e9i	0.0113791	−	0.0148891i
$607$	−3.23926e10			−0.238611			−0.119306	−	0.992858i	$-0.538067\pi$
$607$	−3.23926e10			−0.238611			−0.119306	+	0.992858i	$0.538067\pi$
$608$			1.49348e11i			1.09291i
$609$	−1.59012e11	−	1.21526e11i	−1.15601	−	0.883487i
$610$	−2.95126e9			−0.0213152
$611$		−	2.20405e11i		−	1.58145i
$612$	−1.82104e11	+	4.95505e10i	−1.29812	+	0.353218i
$613$	1.06951e11			0.757432			0.378716	−	0.925513i	$-0.376366\pi$
$613$	1.06951e11			0.757432			0.378716	+	0.925513i	$0.376366\pi$
$614$		−	5.03026e8i		−	0.00353929i
$615$	1.50720e10	−	1.97211e10i	0.105359	−	0.137858i
$616$	−2.39085e10			−0.166047
$617$			2.71614e11i			1.87418i	0.349084	+	0.937092i	$0.386493\pi$
$617$			2.71614e11i			1.87418i	−0.349084	+	0.937092i	$0.613507\pi$
$618$	−1.44389e10	−	1.10350e10i	−0.0989874	−	0.0756520i
$619$	−1.34883e11			−0.918741			−0.459371	−	0.888245i	$-0.651925\pi$
$619$	−1.34883e11			−0.918741			−0.459371	+	0.888245i	$0.651925\pi$
$620$			2.63829e10i			0.178548i
$621$	6.40360e10	−	1.57170e11i	0.430584	−	1.05683i
$622$	2.42594e10			0.162076
$623$			1.10740e11i			0.735108i
$624$	−7.00323e10	+	9.16343e10i	−0.461913	+	0.604393i
$625$	1.27484e11			0.835477
$626$			2.81904e10i			0.183571i
$627$	5.55936e10	+	4.24878e10i	0.359712	+	0.274913i
$628$	1.07373e11			0.690331
$629$			3.67627e11i			2.34858i
$630$	−2.79233e9	−	1.02622e10i	−0.0177257	−	0.0651443i
$631$	2.31338e11			1.45925			0.729624	−	0.683848i	$-0.239695\pi$
$631$	2.31338e11			1.45925			0.729624	+	0.683848i	$0.239695\pi$
$632$		−	6.95057e10i		−	0.435664i
$633$	1.90929e11	−	2.49822e11i	1.18920	−	1.55602i
$634$	5.35174e8			0.00331236
$635$		−	1.27765e10i		−	0.0785807i
$636$	−2.38916e10	−	1.82594e10i	−0.146022	−	0.111598i
$637$	−2.18308e10			−0.132590
$638$			1.82455e10i			0.110122i
$639$	1.17522e9	−	3.19777e8i	0.00704881	−	0.00191798i
$640$	3.51872e10			0.209732
$641$		−	2.14020e11i		−	1.26771i	−0.773450	−	0.633857i	$-0.781471\pi$
$641$		−	2.14020e11i		−	1.26771i	0.773450	−	0.633857i	$-0.218529\pi$
$642$	−2.15712e10	+	2.82250e10i	−0.126980	+	0.166148i
$643$	−2.73869e11			−1.60213			−0.801066	−	0.598576i	$-0.795734\pi$
$643$	−2.73869e11			−1.60213			−0.801066	+	0.598576i	$0.795734\pi$
$644$			1.94359e11i			1.12995i
$645$	−1.38104e10	−	1.05547e10i	−0.0797933	−	0.0609827i
$646$	1.01470e11			0.582649
$647$			7.84848e10i			0.447887i	0.974602	+	0.223944i	$0.0718931\pi$
$647$			7.84848e10i			0.447887i	−0.974602	+	0.223944i	$0.928107\pi$
$648$	−4.61264e10	−	7.84845e10i	−0.261607	−	0.445127i
$649$	−8.08664e10			−0.455816
$650$		−	4.34471e10i		−	0.243393i
$651$	−9.46493e10	+	1.23845e11i	−0.526979	+	0.689530i
$652$	−2.90307e11			−1.60645
$653$		−	6.61757e10i		−	0.363954i	−0.983303	−	0.181977i	$-0.941750\pi$
$653$		−	6.61757e10i		−	0.363954i	0.983303	−	0.181977i	$-0.0582496\pi$
$654$	−2.23998e10	−	1.71192e10i	−0.122443	−	0.0935779i
$655$	−5.48104e10			−0.297781
$656$			1.07390e11i			0.579892i
$657$	−2.22760e10	−	8.18671e10i	−0.119557	−	0.439388i
$658$	−8.79353e10			−0.469094
$659$		−	2.09798e11i		−	1.11239i	−0.831050	−	0.556197i	$-0.812260\pi$
$659$		−	2.09798e11i		−	1.11239i	0.831050	−	0.556197i	$-0.187740\pi$
$660$	7.62356e9	−	9.97511e9i	0.0401774	−	0.0525705i
$661$	3.52015e11			1.84398			0.921988	−	0.387217i	$-0.126564\pi$
$661$	3.52015e11			1.84398			0.921988	+	0.387217i	$0.126564\pi$
$662$			6.91220e10i			0.359902i
$663$	2.14211e11	+	1.63713e11i	1.10863	+	0.847284i
$664$	−1.31289e11			−0.675395
$665$		−	7.40422e10i		−	0.378611i
$666$	−8.23748e10	+	2.24142e10i	−0.418695	+	0.113927i
$667$	3.08099e11			1.55663
$668$			5.73275e10i			0.287910i
$669$	1.39153e11	−	1.82076e11i	0.694684	−	0.908965i
$670$	1.51702e9			0.00752824
$671$		−	2.05832e10i		−	0.101536i
$672$	1.25790e11	+	9.61360e10i	0.616835	+	0.471421i
$673$	1.52184e11			0.741839			0.370920	−	0.928665i	$-0.379043\pi$
$673$	1.52184e11			0.741839			0.370920	+	0.928665i	$0.379043\pi$
$674$		−	4.18671e10i		−	0.202877i
$675$	−1.81506e11	−	7.39514e10i	−0.874333	−	0.356231i
$676$	−1.41457e10			−0.0677388
$677$		−	2.48469e11i		−	1.18282i	−0.806373	−	0.591408i	$-0.798572\pi$
$677$		−	2.48469e11i		−	1.18282i	0.806373	−	0.591408i	$-0.201428\pi$
$678$	3.98901e9	−	5.21945e9i	0.0188776	−	0.0247005i
$679$	7.80856e10			0.367360
$680$		−	3.78194e10i		−	0.176880i
$681$	2.42974e11	+	1.85695e11i	1.12972	+	0.863399i
$682$	1.42103e10			0.0656849
$683$		−	1.05623e11i		−	0.485374i	−0.970105	−	0.242687i	$-0.921971\pi$
$683$		−	1.05623e11i		−	0.485374i	0.970105	−	0.242687i	$-0.0780288\pi$
$684$	−8.01080e10	−	2.94407e11i	−0.365975	−	1.34500i
$685$	−1.98336e10			−0.0900823
$686$		−	5.45381e10i		−	0.246265i
$687$	−1.67989e11	+	2.19807e11i	−0.754145	+	0.986767i
$688$	7.52033e10			0.335647
$689$			4.29575e10i			0.190617i
$690$	1.30086e10	+	9.94190e9i	0.0573896	+	0.0438605i
$691$	−1.08847e11			−0.477426			−0.238713	−	0.971090i	$-0.576726\pi$
$691$	−1.08847e11			−0.477426			−0.238713	+	0.971090i	$0.576726\pi$
$692$		−	2.40469e11i		−	1.04866i
$693$	7.15719e10	−	1.94747e10i	0.310320	−	0.0844380i
$694$	4.60419e10			0.198479
$695$		−	4.47151e10i		−	0.191653i
$696$	1.00353e11	−	1.31308e11i	0.427657	−	0.559571i
$697$	2.51043e11			1.06369
$698$			5.09770e10i			0.214760i
$699$	−2.02758e11	−	1.54960e11i	−0.849318	−	0.649098i
$700$	2.24454e11			0.934833
$701$		−	1.13189e11i		−	0.468739i	−0.972148	−	0.234370i	$-0.924697\pi$
$701$		−	1.13189e11i		−	0.468739i	0.972148	−	0.234370i	$-0.0753026\pi$
$702$	−2.36230e10	+	5.79803e10i	−0.0972716	+	0.238744i
$703$	−5.94340e11			−2.43340
$704$			4.40801e10i			0.179454i
$705$	5.82442e10	−	7.62101e10i	0.235774	−	0.308501i
$706$	8.01468e9			0.0322602
$707$		−	1.86517e10i		−	0.0746518i
$708$	2.80170e11	+	2.14122e11i	1.11503	+	0.852174i
$709$	3.57983e11			1.41670			0.708349	−	0.705862i	$-0.249440\pi$
$709$	3.57983e11			1.41670			0.708349	+	0.705862i	$0.249440\pi$
$710$			1.17498e8i			0.000462377i
$711$	5.66159e10	+	2.08070e11i	0.221544	+	0.814201i
$712$	−9.14463e10			−0.355833
$713$		−	2.39960e11i		−	0.928496i
$714$	6.53168e10	−	8.54642e10i	0.251323	−	0.328845i
$715$	−1.79354e10			−0.0686257
$716$			4.23552e11i			1.61159i
$717$	−5.06452e9	−	3.87061e9i	−0.0191629	−	0.0146454i
$718$	−6.59608e10			−0.248192
$719$			2.84634e11i			1.06505i	0.846413	+	0.532527i	$0.178758\pi$
$719$			2.84634e11i			1.06505i	−0.846413	+	0.532527i	$0.821242\pi$
$720$	−4.84305e10	+	1.31779e10i	−0.180214	+	0.0490363i
$721$	−1.34120e11			−0.496308
$722$			9.12872e10i			0.335939i
$723$	−1.86307e11	+	2.43775e11i	−0.681831	+	0.892147i
$724$	−3.30045e9			−0.0120121
$725$		−	3.55805e11i		−	1.28784i
$726$	−5.37277e9	−	4.10618e9i	−0.0193398	−	0.0147806i
$727$	−5.31637e11			−1.90317			−0.951585	−	0.307385i	$-0.900546\pi$
$727$	−5.31637e11			−1.90317			−0.951585	+	0.307385i	$0.900546\pi$
$728$		−	1.48936e11i		−	0.530241i
$729$	2.02012e11	+	1.97377e11i	0.715265	+	0.698853i
$730$	8.18502e9			0.0288223
$731$		−	1.75801e11i		−	0.615676i
$732$	−5.45011e10	+	7.13124e10i	−0.189828	+	0.248382i
$733$	3.62492e11			1.25569			0.627846	−	0.778338i	$-0.283937\pi$
$733$	3.62492e11			1.25569			0.627846	+	0.778338i	$0.283937\pi$
$734$		−	6.69500e10i		−	0.230657i
$735$	−7.54849e9	−	5.76899e9i	−0.0258649	−	0.0197675i
$736$	−2.43729e11			−0.830607
$737$			1.05803e10i			0.0358613i
$738$	1.53060e10	+	5.62515e10i	0.0515985	+	0.189631i
$739$	4.77190e11			1.59998			0.799989	−	0.600015i	$-0.204839\pi$
$739$	4.77190e11			1.59998			0.799989	+	0.600015i	$0.204839\pi$
$740$			1.06642e11i			0.355633i
$741$	−2.64674e11	+	3.46314e11i	−0.877885	+	1.14868i
$742$	1.71388e10			0.0565412
$743$		−	1.77243e11i		−	0.581586i	−0.956786	−	0.290793i	$-0.906081\pi$
$743$		−	1.77243e11i		−	0.581586i	0.956786	−	0.290793i	$-0.0939191\pi$
$744$	−1.02268e11	−	7.81592e10i	−0.333771	−	0.255087i
$745$	−1.06791e11			−0.346666
$746$		−	1.22618e11i		−	0.395913i
$747$	3.93024e11	−	1.06942e11i	1.26223	−	0.343451i
$748$	1.26980e11			0.405628
$749$			2.62176e11i			0.833039i
$750$	2.36422e10	−	3.09349e10i	0.0747211	−	0.0977694i
$751$	−2.38698e11			−0.750393			−0.375196	−	0.926945i	$-0.622425\pi$
$751$	−2.38698e11			−0.750393			−0.375196	+	0.926945i	$0.622425\pi$
$752$			4.14996e11i			1.29769i
$753$	−3.35773e11	−	2.56618e11i	−1.04440	−	0.798191i
$754$	−1.13658e11			−0.351654
$755$			6.71567e10i			0.206681i
$756$	−2.99534e11	−	1.22039e11i	−0.916977	−	0.373605i
$757$	8.03201e9			0.0244591			0.0122295	−	0.999925i	$-0.496107\pi$
$757$	8.03201e9			0.0244591			0.0122295	+	0.999925i	$0.496107\pi$
$758$			3.85470e10i			0.116765i
$759$	−6.93383e10	+	9.07263e10i	−0.208933	+	0.273380i
$760$	6.11423e10			0.183268
$761$		−	2.31764e11i		−	0.691046i	−0.938410	−	0.345523i	$-0.887701\pi$
$761$		−	2.31764e11i		−	0.691046i	0.938410	−	0.345523i	$-0.112299\pi$
$762$	2.38421e10	+	1.82215e10i	0.0707170	+	0.0540461i
$763$	−2.08067e11			−0.613910
$764$		−	4.22800e11i		−	1.24097i
$765$	3.08058e10	+	1.13215e11i	0.0899469	+	0.330566i
$766$	−3.84415e10			−0.111657
$767$		−	5.03749e11i		−	1.45557i
$768$	7.55482e10	−	9.88517e10i	0.217160	−	0.284145i
$769$	−4.04627e11			−1.15704			−0.578522	−	0.815667i	$-0.696370\pi$
$769$	−4.04627e11			−1.15704			−0.578522	+	0.815667i	$0.696370\pi$
$770$			7.15571e9i			0.0203559i
$771$	5.49263e11	+	4.19779e11i	1.55440	+	1.18796i
$772$	−2.40774e11			−0.677860
$773$			4.03497e11i			1.13011i	0.825052	+	0.565056i	$0.191146\pi$
$773$			4.03497e11i			1.13011i	−0.825052	+	0.565056i	$0.808854\pi$
$774$	3.93920e10	−	1.07186e10i	0.109760	−	0.0298657i
$775$	−2.77115e11			−0.768164
$776$			6.44813e10i			0.177823i
$777$	−3.82581e11	+	5.00591e11i	−1.04964	+	1.37341i
$778$	7.05701e10			0.192620
$779$			4.05859e11i			1.10211i
$780$	6.21389e10	+	4.74902e10i	0.167875	+	0.128300i
$781$	−8.19470e8			−0.00220257
$782$			1.65594e11i			0.442811i
$783$	−1.93458e11	+	4.74823e11i	−0.514683	+	1.26324i
$784$	4.11047e10			0.108800
$785$		−	6.67544e10i		−	0.175793i
$786$	7.81693e10	−	1.02281e11i	0.204807	−	0.267982i
$787$	−5.01810e11			−1.30810			−0.654049	−	0.756452i	$-0.726931\pi$
$787$	−5.01810e11			−1.30810			−0.654049	+	0.756452i	$0.726931\pi$
$788$		−	2.85950e11i		−	0.741626i
$789$	−4.60831e11	−	3.52194e11i	−1.18914	−	0.908811i
$790$	−2.08027e10			−0.0534087
$791$		−	4.84824e10i		−	0.123845i
$792$	1.60818e10	+	5.91024e10i	0.0408726	+	0.150212i
$793$	1.28221e11			0.324239
$794$		−	1.44897e11i		−	0.364568i
$795$	−1.13519e10	+	1.48535e10i	−0.0284185	+	0.0371844i
$796$	5.12828e11			1.27738
$797$			1.67781e11i			0.415824i	0.978147	+	0.207912i	$0.0666668\pi$
$797$			1.67781e11i			0.415824i	−0.978147	+	0.207912i	$0.933333\pi$
$798$	1.38170e11	+	1.05597e11i	0.340722	+	0.260400i
$799$	9.70127e11			2.38035
$800$			2.81468e11i			0.687178i
$801$	2.73751e11	−	7.44876e10i	0.665006	−	0.180948i
$802$	−7.12817e10			−0.172298
$803$			5.70852e10i			0.137297i
$804$	2.80149e10	−	3.66563e10i	0.0670448	−	0.0877253i
$805$	1.20834e11			0.287743
$806$			8.85215e10i			0.209753i
$807$	−4.94156e11	−	3.77663e11i	−1.16512	−	0.890452i
$808$	1.54021e10			0.0361356
$809$		−	3.26697e11i		−	0.762695i	−0.924432	−	0.381348i	$-0.875460\pi$
$809$		−	3.26697e11i		−	0.762695i	0.924432	−	0.381348i	$-0.124540\pi$
$810$	−2.34900e10	+	1.38054e10i	−0.0545687	+	0.0320707i
$811$	3.02616e11			0.699534			0.349767	−	0.936837i	$-0.386261\pi$
$811$	3.02616e11			0.699534			0.349767	+	0.936837i	$0.386261\pi$
$812$		−	5.87173e11i		−	1.35065i
$813$	2.60646e11	−	3.41044e11i	0.596608	−	0.780636i
$814$	5.74392e10			0.130831
$815$			1.80485e11i			0.409083i
$816$	−4.03334e11	−	3.08252e11i	−0.909713	−	0.695256i
$817$	2.84217e11			0.637912
$818$			2.03938e11i			0.455495i
$819$	1.21316e11	+	4.45850e11i	0.269638	+	0.990952i
$820$	7.28230e10			0.161069
$821$		−	5.97917e10i		−	0.131604i	−0.997833	−	0.0658019i	$-0.979039\pi$
$821$		−	5.97917e10i		−	0.131604i	0.997833	−	0.0658019i	$-0.0209605\pi$
$822$	2.82862e10	−	3.70113e10i	0.0619566	−	0.0810677i
$823$	2.06175e10			0.0449404			0.0224702	−	0.999748i	$-0.492847\pi$
$823$	2.06175e10			0.0449404			0.0224702	+	0.999748i	$0.492847\pi$
$824$		−	1.10753e11i		−	0.240241i
$825$	1.04775e11	+	8.00748e10i	0.226173	+	0.172854i
$826$	−2.00981e11			−0.431753
$827$		−	2.05635e11i		−	0.439618i	−0.975543	−	0.219809i	$-0.929457\pi$
$827$		−	2.05635e11i		−	0.439618i	0.975543	−	0.219809i	$-0.0705435\pi$
$828$	4.80459e11	−	1.30733e11i	1.02220	−	0.278140i
$829$	−2.31065e11			−0.489233			−0.244616	−	0.969620i	$-0.578662\pi$
$829$	−2.31065e11			−0.489233			−0.244616	+	0.969620i	$0.578662\pi$
$830$			3.92943e10i			0.0827975i
$831$	−3.40540e10	+	4.45583e10i	−0.0714109	+	0.0934381i
$832$	−2.74592e11			−0.573054
$833$		−	9.60895e10i		−	0.199570i
$834$	8.34425e10	+	6.37716e10i	0.172474	+	0.131815i
$835$	3.56408e10			0.0733164
$836$			2.05287e11i			0.420278i
$837$	3.69811e11	+	1.50673e11i	0.753491	+	0.306996i
$838$	1.73085e11			0.350981
$839$		−	7.00858e9i		−	0.0141443i	−0.999975	−	0.00707216i	$-0.997749\pi$
$839$		−	7.00858e9i		−	0.0141443i	0.999975	−	0.00707216i	$-0.00225116\pi$
$840$	3.93577e10	−	5.14979e10i	0.0790520	−	0.103436i
$841$	−4.30545e11			−0.860667
$842$		−	2.08170e11i		−	0.414161i
$843$	−4.75682e11	−	3.63544e11i	−0.941904	−	0.719858i
$844$	9.22504e11			1.81802
$845$			8.79444e9i			0.0172497i
$846$	5.91485e10	+	2.17378e11i	0.115468	+	0.424360i
$847$	−4.99064e10			−0.0969668
$848$		−	8.08837e10i		−	0.156415i
$849$	1.97671e11	−	2.58644e11i	0.380462	−	0.497819i
$850$	1.91235e11			0.366347
$851$		−	9.69938e11i		−	1.84938i
$852$	2.83914e9	+	2.16983e9i	0.00538800	+	0.00411783i
$853$	−1.07903e11			−0.203815			−0.101908	−	0.994794i	$-0.532495\pi$
$853$	−1.07903e11			−0.203815			−0.101908	+	0.994794i	$0.532495\pi$
$854$		−	5.11564e10i		−	0.0961763i
$855$	−1.83034e11	+	4.98035e10i	−0.342505	+	0.0931956i
$856$	−2.16499e11			−0.403237
$857$			5.88295e11i			1.09062i	0.838236	+	0.545308i	$0.183587\pi$
$857$			5.88295e11i			1.09062i	−0.838236	+	0.545308i	$0.816413\pi$
$858$	2.55790e10	−	3.34691e10i	0.0471992	−	0.0617582i
$859$	3.42059e11			0.628244			0.314122	−	0.949383i	$-0.398290\pi$
$859$	3.42059e11			0.628244			0.314122	+	0.949383i	$0.398290\pi$
$860$		−	5.09968e10i		−	0.0932285i
$861$	3.41840e11	+	2.61254e11i	0.622028	+	0.475390i
$862$	5.99286e10			0.108544
$863$		−	6.78858e11i		−	1.22387i	−0.790907	−	0.611936i	$-0.790391\pi$
$863$		−	6.78858e11i		−	1.22387i	0.790907	−	0.611936i	$-0.209609\pi$
$864$	1.53039e11	−	3.75620e11i	0.274630	−	0.674053i
$865$	−1.49501e11			−0.267041
$866$			1.20402e11i			0.214072i
$867$	−3.77488e11	+	4.93928e11i	−0.668078	+	0.874152i
$868$	−4.57314e11			−0.805630
$869$		−	1.45086e11i		−	0.254416i
$870$	−3.92999e10	−	3.00353e10i	−0.0685985	−	0.0524270i
$871$	−6.59086e10			−0.114517
$872$		−	1.71817e11i		−	0.297166i
$873$	−5.25232e10	−	1.93029e11i	−0.0904262	−	0.332327i
$874$	−2.67715e11			−0.458804
$875$		−	2.87347e11i		−	0.490201i
$876$	1.51153e11	−	1.97777e11i	0.256685	−	0.335862i
$877$	−1.35277e11			−0.228679			−0.114339	−	0.993442i	$-0.536475\pi$
$877$	−1.35277e11			−0.228679			−0.114339	+	0.993442i	$0.536475\pi$
$878$			1.42523e10i			0.0239833i
$879$	4.61133e11	+	3.52425e11i	0.772451	+	0.590352i
$880$	3.37702e10			0.0563122
$881$			1.03254e11i			0.171397i	0.996321	+	0.0856985i	$0.0273122\pi$
$881$			1.03254e11i			0.171397i	−0.996321	+	0.0856985i	$0.972688\pi$
$882$	2.15309e10	−	5.85856e9i	0.0355786	−	0.00968092i
$883$	−5.86624e11			−0.964977			−0.482488	−	0.875902i	$-0.660267\pi$
$883$	−5.86624e11			−0.964977			−0.482488	+	0.875902i	$0.660267\pi$
$884$			7.91006e11i			1.29530i
$885$	1.33121e11	−	1.74183e11i	0.217006	−	0.283944i
$886$	1.04382e11			0.169392
$887$			5.50355e11i			0.889096i	0.895755	+	0.444548i	$0.146636\pi$
$887$			5.50355e11i			0.889096i	−0.895755	+	0.444548i	$0.853364\pi$
$888$	−4.13376e11	−	3.15926e11i	−0.664804	−	0.508082i
$889$	2.21464e11			0.354565
$890$			2.73694e10i			0.0436220i
$891$	−9.62837e10	−	1.63828e11i	−0.152771	−	0.259942i
$892$	6.72340e11			1.06201
$893$			1.56840e12i			2.46633i
$894$	1.52303e11	−	1.99283e11i	0.238429	−	0.311975i
$895$	2.63324e11			0.410392
$896$			6.09924e11i			0.946333i
$897$	−5.65170e11	−	4.31936e11i	−0.872990	−	0.667190i
$898$	1.70224e10			0.0261767
$899$			7.24937e11i			1.10984i
$900$	−1.50976e11	−	5.54854e11i	−0.230111	−	0.845685i
$901$	−1.89080e11			−0.286911
$902$		−	3.92237e10i		−	0.0592547i
$903$	1.82952e11	−	2.39385e11i	0.275161	−	0.360036i
$904$	4.00356e10			0.0599477
$905$			2.05190e9i			0.00305888i
$906$	−1.25320e11	−	9.57772e10i	−0.185998	−	0.142151i
$907$	9.64617e11			1.42536			0.712682	−	0.701487i	$-0.247480\pi$
$907$	9.64617e11			1.42536			0.712682	+	0.701487i	$0.247480\pi$
$908$			8.97216e11i			1.31994i
$909$	−4.61073e10	+	1.25458e10i	−0.0675328	+	0.0183756i
$910$	−4.45757e10			−0.0650029
$911$			1.12061e12i			1.62698i	0.581582	+	0.813488i	$0.302434\pi$
$911$			1.12061e12i			1.62698i	−0.581582	+	0.813488i	$0.697566\pi$
$912$	4.98348e11	−	6.52068e11i	0.720367	−	0.942570i
$913$	−2.74052e11			−0.394412
$914$		−	1.78996e10i		−	0.0256483i
$915$	4.43352e10	+	3.38836e10i	0.0632506	+	0.0483398i
$916$	−8.11669e11			−1.15291
$917$		−	9.50068e11i		−	1.34362i
$918$	−2.55204e11	−	1.03978e11i	−0.359349	−	0.146410i
$919$	−2.33654e11			−0.327576			−0.163788	−	0.986496i	$-0.552371\pi$
$919$	−2.33654e11			−0.327576			−0.163788	+	0.986496i	$0.552371\pi$
$920$			9.97817e10i			0.139283i
$921$	−5.77525e9	+	7.55668e9i	−0.00802662	+	0.0105025i
$922$	1.43030e11			0.197927
$923$		−	5.10480e9i		−	0.00703351i
$924$	1.72906e11	+	1.32145e11i	0.237204	+	0.181285i
$925$	−1.12012e12			−1.53003
$926$		−	1.93872e11i		−	0.263676i
$927$	9.02138e10	+	3.31547e11i	0.122167	+	0.448979i
$928$	7.36325e11			0.992836
$929$		−	5.29948e11i		−	0.711493i	−0.934583	−	0.355746i	$-0.884227\pi$
$929$		−	5.29948e11i		−	0.711493i	0.934583	−	0.355746i	$-0.115773\pi$
$930$	−2.33927e10	+	3.06083e10i	−0.0312715	+	0.0409174i
$931$	1.55347e11			0.206778
$932$		−	7.48714e11i		−	0.992322i
$933$	−3.64435e11	−	2.78522e11i	−0.480943	−	0.367565i
$934$	−2.74825e11			−0.361134
$935$		−	7.89438e10i		−	0.103293i
$936$	−3.68172e11	+	1.00180e11i	−0.479676	+	0.130520i
$937$	−6.30417e11			−0.817843			−0.408921	−	0.912570i	$-0.634095\pi$
$937$	−6.30417e11			−0.817843			−0.408921	+	0.912570i	$0.634095\pi$
$938$			2.62957e10i			0.0339682i
$939$	3.23655e11	−	4.23489e11i	0.416313	−	0.544728i
$940$	2.81417e11			0.360444
$941$			2.06673e11i			0.263587i	0.991277	+	0.131794i	$0.0420736\pi$
$941$			2.06673e11i			0.263587i	−0.991277	+	0.131794i	$0.957926\pi$
$942$	1.24570e11	+	9.52036e10i	0.158201	+	0.120907i
$943$	−6.62344e11			−0.837601
$944$			9.48498e11i			1.19440i
$945$	−7.58725e10	+	1.86222e11i	−0.0951387	+	0.233508i
$946$	−2.74677e10			−0.0342972
$947$		−	7.89234e11i		−	0.981310i	−0.871354	−	0.490655i	$-0.836758\pi$
$947$		−	7.89234e11i		−	0.981310i	0.871354	−	0.490655i	$-0.163242\pi$
$948$	−3.84164e11	+	5.02663e11i	−0.475646	+	0.622363i
$949$	−3.55607e11			−0.438435
$950$			3.09169e11i			0.379578i
$951$	−8.03963e9	−	6.14435e9i	−0.00982910	−	0.00751197i
$952$	6.55550e11			0.798102
$953$			1.54759e12i			1.87622i	0.346334	+	0.938111i	$0.387426\pi$
$953$			1.54759e12i			1.87622i	−0.346334	+	0.938111i	$0.612574\pi$
$954$	−1.15282e10	−	4.23675e10i	−0.0139177	−	0.0511493i
$955$	−2.62857e11			−0.316013
$956$		−	1.87015e10i		−	0.0223895i
$957$	2.09477e11	−	2.74092e11i	0.249740	−	0.326774i
$958$	−2.21533e11			−0.263012
$959$		−	3.43790e11i		−	0.406461i
$960$	−9.49466e10	−	7.25638e10i	−0.111788	−	0.0854348i
$961$	−2.88281e11			−0.338005
$962$			3.57812e11i			0.417786i
$963$	6.48104e11	−	1.76349e11i	0.753598	−	0.205054i
$964$	−9.00175e11			−1.04236
$965$			1.49690e11i			0.172617i
$966$	−1.72330e11	+	2.25487e11i	−0.197903	+	0.258948i
$967$	−1.40458e11			−0.160635			−0.0803173	−	0.996769i	$-0.525593\pi$
$967$	−1.40458e11			−0.160635			−0.0803173	+	0.996769i	$0.525593\pi$
$968$		−	4.12116e10i		−	0.0469373i
$969$	−1.52432e12	−	1.16498e12i	−1.72895	−	1.32136i
$970$	1.92989e10			0.0217995
$971$		−	1.53987e11i		−	0.173223i	−0.996242	−	0.0866116i	$-0.972396\pi$
$971$		−	1.53987e11i		−	0.173223i	0.996242	−	0.0866116i	$-0.0276039\pi$
$972$	−1.00207e11	+	8.22542e11i	−0.112262	+	0.921495i
$973$	7.75079e11			0.864758
$974$		−	1.53348e11i		−	0.170389i
$975$	−4.98818e11	+	6.52682e11i	−0.551980	+	0.722243i
$976$	−2.41424e11			−0.266061
$977$		−	7.07551e11i		−	0.776568i	−0.921540	−	0.388284i	$-0.873068\pi$
$977$		−	7.07551e11i		−	0.776568i	0.921540	−	0.388284i	$-0.126932\pi$
$978$	−3.36802e11	−	2.57404e11i	−0.368145	−	0.281358i
$979$	−1.90884e11			−0.207797
$980$		−	2.78739e10i		−	0.0302199i
$981$	1.39953e11	+	5.14345e11i	0.151115	+	0.555365i
$982$	−1.33405e11			−0.143459
$983$		−	2.55827e11i		−	0.273989i	−0.990572	−	0.136994i	$-0.956256\pi$
$983$		−	2.55827e11i		−	0.273989i	0.990572	−	0.136994i	$-0.0437442\pi$
$984$	−2.15738e11	+	2.82284e11i	−0.230115	+	0.301096i
$985$	−1.77776e11			−0.188855
$986$		−	5.00274e11i		−	0.529298i
$987$	1.32100e12	+	1.00959e12i	1.39199	+	1.06384i
$988$	−1.27881e12			−1.34208
$989$			4.63829e11i			0.484811i
$990$	1.76891e10	−	4.81319e9i	0.0184147	−	0.00501063i
$991$	6.90149e11			0.715564			0.357782	−	0.933805i	$-0.383533\pi$
$991$	6.90149e11			0.715564			0.357782	+	0.933805i	$0.383533\pi$
$992$		−	5.73479e11i		−	0.592203i
$993$	7.93592e11	−	1.03838e12i	0.816207	−	1.06797i
$994$	−2.03667e9			−0.00208629
$995$		−	3.18827e11i		−	0.325284i
$996$	9.49481e11	+	7.25649e11i	0.964826	+	0.737377i
$997$	1.74695e12			1.76808			0.884038	−	0.467415i	$-0.154815\pi$
$997$	1.74695e12			1.76808			0.884038	+	0.467415i	$0.154815\pi$
$998$		−	3.64924e11i		−	0.367858i
$999$	1.49481e12	+	6.09032e11i	1.50080	+	0.611475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.15	yes	26
3.2	odd	2	inner	33.9.b.a.23.12	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.12	✓	26	3.2	odd	2	inner
33.9.b.a.23.15	yes	26	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4.28405i q^{2} +(49.1853 - 64.3569i) q^{3} +237.647 q^{4} -147.746i q^{5} +(275.708 + 210.712i) q^{6} +2560.99 q^{7} +2114.81i q^{8} +(-1722.62 - 6330.82i) q^{9} +O(q^{10})\)	\(q+4.28405i q^{2} +(49.1853 - 64.3569i) q^{3} +237.647 q^{4} -147.746i q^{5} +(275.708 + 210.712i) q^{6} +2560.99 q^{7} +2114.81i q^{8} +(-1722.62 - 6330.82i) q^{9} +632.952 q^{10} +4414.43i q^{11} +(11688.7 - 15294.2i) q^{12} -27499.2 q^{13} +10971.4i q^{14} +(-9508.48 - 7266.94i) q^{15} +51777.7 q^{16} -121040. i q^{17} +(27121.5 - 7379.77i) q^{18} +195684. q^{19} -35111.4i q^{20} +(125963. - 164817. i) q^{21} -18911.6 q^{22} +319348. i q^{23} +(136102. + 104017. i) q^{24} +368796. q^{25} -117808. i q^{26} +(-492159. - 200521. i) q^{27} +608611. q^{28} -964775. i q^{29} +(31131.9 - 40734.8i) q^{30} -751405. q^{31} +763208. i q^{32} +(284099. + 217125. i) q^{33} +518539. q^{34} -378376. i q^{35} +(-409374. - 1.50450e6i) q^{36} -3.03725e6 q^{37} +838319. i q^{38} +(-1.35256e6 + 1.76976e6i) q^{39} +312455. q^{40} +2.07405e6i q^{41} +(706085. + 539631. i) q^{42} +1.45243e6 q^{43} +1.04908e6i q^{44} +(-935355. + 254510. i) q^{45} -1.36810e6 q^{46} +8.01496e6i q^{47} +(2.54670e6 - 3.33225e6i) q^{48} +793869. q^{49} +1.57994e6i q^{50} +(-7.78973e6 - 5.95337e6i) q^{51} -6.53510e6 q^{52} -1.56213e6i q^{53} +(859042. - 2.10843e6i) q^{54} +652215. q^{55} +5.41600e6i q^{56} +(9.62477e6 - 1.25936e7i) q^{57} +4.13314e6 q^{58} +1.83187e7i q^{59} +(-2.25966e6 - 1.72697e6i) q^{60} -4.66270e6 q^{61} -3.21906e6i q^{62} +(-4.41160e6 - 1.62132e7i) q^{63} +9.98547e6 q^{64} +4.06290e6i q^{65} +(-930173. + 1.21709e6i) q^{66} +2.39675e6 q^{67} -2.87647e7i q^{68} +(2.05522e7 + 1.57072e7i) q^{69} +1.62098e6 q^{70} +185635. i q^{71} +(1.33885e7 - 3.64300e6i) q^{72} +1.29315e7 q^{73} -1.30117e7i q^{74} +(1.81393e7 - 2.37346e7i) q^{75} +4.65037e7 q^{76} +1.13053e7i q^{77} +(-7.58175e6 - 5.79442e6i) q^{78} -3.28662e7 q^{79} -7.64996e6i q^{80} +(-3.71119e7 + 2.18111e7i) q^{81} -8.88534e6 q^{82} +6.20811e7i q^{83} +(2.99347e7 - 3.91683e7i) q^{84} -1.78831e7 q^{85} +6.22226e6i q^{86} +(-6.20899e7 - 4.74528e7i) q^{87} -9.33566e6 q^{88} +4.32410e7i q^{89} +(-1.09033e6 - 4.00710e6i) q^{90} -7.04252e7 q^{91} +7.58920e7i q^{92} +(-3.69581e7 + 4.83581e7i) q^{93} -3.43364e7 q^{94} -2.89116e7i q^{95} +(4.91177e7 + 3.75386e7i) q^{96} +3.04904e7 q^{97} +3.40097e6i q^{98} +(2.79470e7 - 7.60436e6i) 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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