LMFDB - Embedded newform 33.9.b.a.23.8

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			23.8
Character	$\chi$	$=$	33.23
Dual form			33.9.b.a.23.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.0184i q^{2} +(36.8732 - 72.1205i) q^{3} +59.4833 q^{4} +519.567i q^{5} +(-1011.02 - 516.905i) q^{6} -3946.73 q^{7} -4422.58i q^{8} +(-3841.73 - 5318.63i) q^{9} +O(q^{10})$	\(q-14.0184i q^{2} +(36.8732 - 72.1205i) q^{3} +59.4833 q^{4} +519.567i q^{5} +(-1011.02 - 516.905i) q^{6} -3946.73 q^{7} -4422.58i q^{8} +(-3841.73 - 5318.63i) q^{9} +7283.52 q^{10} -4414.43i q^{11} +(2193.34 - 4289.97i) q^{12} -41219.6 q^{13} +55327.0i q^{14} +(37471.4 + 19158.1i) q^{15} -46770.0 q^{16} -55821.2i q^{17} +(-74558.9 + 53855.1i) q^{18} +3935.59 q^{19} +30905.6i q^{20} +(-145529. + 284640. i) q^{21} -61883.4 q^{22} -152236. i q^{23} +(-318959. - 163075. i) q^{24} +120675. q^{25} +577835. i q^{26} +(-525239. + 80952.6i) q^{27} -234765. q^{28} +684379. i q^{29} +(268567. - 525291. i) q^{30} +1.38221e6 q^{31} -476539. i q^{32} +(-318371. - 162774. i) q^{33} -782526. q^{34} -2.05059e6i q^{35} +(-228519. - 316370. i) q^{36} +564324. q^{37} -55170.9i q^{38} +(-1.51990e6 + 2.97278e6i) q^{39} +2.29783e6 q^{40} -4.96736e6i q^{41} +(3.99021e6 + 2.04008e6i) q^{42} -12010.8 q^{43} -262585. i q^{44} +(2.76339e6 - 1.99604e6i) q^{45} -2.13411e6 q^{46} +711200. i q^{47} +(-1.72456e6 + 3.37308e6i) q^{48} +9.81186e6 q^{49} -1.69167e6i q^{50} +(-4.02585e6 - 2.05831e6i) q^{51} -2.45188e6 q^{52} -8.30602e6i q^{53} +(1.13483e6 + 7.36303e6i) q^{54} +2.29359e6 q^{55} +1.74547e7i q^{56} +(145118. - 283837. i) q^{57} +9.59392e6 q^{58} -2.73466e6i q^{59} +(2.22893e6 + 1.13959e6i) q^{60} -1.60852e7 q^{61} -1.93764e7i q^{62} +(1.51623e7 + 2.09912e7i) q^{63} -1.86535e7 q^{64} -2.14164e7i q^{65} +(-2.28184e6 + 4.46306e6i) q^{66} -3.77081e7 q^{67} -3.32043e6i q^{68} +(-1.09793e7 - 5.61343e6i) q^{69} -2.87461e7 q^{70} -8.44368e6i q^{71} +(-2.35221e7 + 1.69904e7i) q^{72} +1.44822e7 q^{73} -7.91095e6i q^{74} +(4.44967e6 - 8.70314e6i) q^{75} +234102. q^{76} +1.74225e7i q^{77} +(4.16738e7 + 2.13066e7i) q^{78} +6.67221e7 q^{79} -2.43002e7i q^{80} +(-1.35289e7 + 4.08655e7i) q^{81} -6.96346e7 q^{82} +6.89613e7i q^{83} +(-8.65652e6 + 1.69313e7i) q^{84} +2.90029e7 q^{85} +168373. i q^{86} +(4.93577e7 + 2.52353e7i) q^{87} -1.95232e7 q^{88} -3.31613e7i q^{89} +(-2.79813e7 - 3.87384e7i) q^{90} +1.62683e8 q^{91} -9.05550e6i q^{92} +(5.09665e7 - 9.96856e7i) q^{93} +9.96991e6 q^{94} +2.04480e6i q^{95} +(-3.43682e7 - 1.75715e7i) q^{96} -6.75853e7 q^{97} -1.37547e8i q^{98} +(-2.34787e7 + 1.69590e7i) 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 $

$2$		−	14.0184i		−	0.876153i	−0.898938	−	0.438076i	$-0.855660\pi$
$2$		−	14.0184i		−	0.876153i	0.898938	−	0.438076i	$-0.144340\pi$
$3$	36.8732	−	72.1205i	0.455225	−	0.890376i
$3$	36.8732	−	72.1205i	0.455225	−	0.890376i
$4$	59.4833			0.232357
$5$			519.567i			0.831307i	0.909523	+	0.415654i	$0.136447\pi$
$5$			519.567i			0.831307i	−0.909523	+	0.415654i	$0.863553\pi$
$6$	−1011.02	−	516.905i	−0.780106	−	0.398846i
$7$	−3946.73			−1.64379			−0.821893	−	0.569643i	$-0.807082\pi$
$7$	−3946.73			−1.64379			−0.821893	+	0.569643i	$0.807082\pi$
$8$		−	4422.58i		−	1.07973i
$9$	−3841.73	−	5318.63i	−0.585541	−	0.810643i
$10$	7283.52			0.728352
$11$		−	4414.43i		−	0.301511i
$11$		−	4414.43i		−	0.301511i
$12$	2193.34	−	4289.97i	0.105775	−	0.206885i
$13$	−41219.6			−1.44321			−0.721607	−	0.692303i	$-0.756596\pi$
$13$	−41219.6			−1.44321			−0.721607	+	0.692303i	$0.756596\pi$
$14$			55327.0i			1.44021i
$15$	37471.4	+	19158.1i	0.740177	+	0.378432i
$16$	−46770.0			−0.713654
$17$		−	55821.2i		−	0.668349i	−0.942511	−	0.334175i	$-0.891542\pi$
$17$		−	55821.2i		−	0.668349i	0.942511	−	0.334175i	$-0.108458\pi$
$18$	−74558.9	+	53855.1i	−0.710247	+	0.513023i
$19$	3935.59			0.0301992			0.0150996	−	0.999886i	$-0.495193\pi$
$19$	3935.59			0.0301992			0.0150996	+	0.999886i	$0.495193\pi$
$20$			30905.6i			0.193160i
$21$	−145529.	+	284640.i	−0.748292	+	1.46359i
$22$	−61883.4			−0.264170
$23$		−	152236.i		−	0.544009i	−0.962296	−	0.272004i	$-0.912314\pi$
$23$		−	152236.i		−	0.544009i	0.962296	−	0.272004i	$-0.0876865\pi$
$24$	−318959.	−	163075.i	−0.961368	−	0.491521i
$25$	120675.			0.308928
$26$			577835.i			1.26448i
$27$	−525239.	+	80952.6i	−0.988330	+	0.152327i
$28$	−234765.			−0.381945
$29$			684379.i			0.967619i	0.875173	+	0.483810i	$0.160747\pi$
$29$			684379.i			0.967619i	−0.875173	+	0.483810i	$0.839253\pi$
$30$	268567.	−	525291.i	0.331564	−	0.648508i
$31$	1.38221e6			1.49667			0.748336	−	0.663320i	$-0.230853\pi$
$31$	1.38221e6			1.49667			0.748336	+	0.663320i	$0.230853\pi$
$32$		−	476539.i		−	0.454463i
$33$	−318371.	−	162774.i	−0.268459	−	0.137255i
$34$	−782526.			−0.585576
$35$		−	2.05059e6i		−	1.36649i
$36$	−228519.	−	316370.i	−0.136054	−	0.188358i
$37$	564324.			0.301108			0.150554	−	0.988602i	$-0.451894\pi$
$37$	564324.			0.301108			0.150554	+	0.988602i	$0.451894\pi$
$38$		−	55170.9i		−	0.0264591i
$39$	−1.51990e6	+	2.97278e6i	−0.656987	+	1.28500i
$40$	2.29783e6			0.897590
$41$		−	4.96736e6i		−	1.75788i	−0.476929	−	0.878942i	$-0.658250\pi$
$41$		−	4.96736e6i		−	1.75788i	0.476929	−	0.878942i	$-0.341750\pi$
$42$	3.99021e6	+	2.04008e6i	1.28233	+	0.655618i
$43$	−12010.8			−0.00351316			−0.00175658	−	0.999998i	$-0.500559\pi$
$43$	−12010.8			−0.00351316			−0.00175658	+	0.999998i	$0.500559\pi$
$44$		−	262585.i		−	0.0700582i
$45$	2.76339e6	−	1.99604e6i	0.673894	−	0.486764i
$46$	−2.13411e6			−0.476635
$47$			711200.i			0.145747i	0.997341	+	0.0728736i	$0.0232170\pi$
$47$			711200.i			0.145747i	−0.997341	+	0.0728736i	$0.976783\pi$
$48$	−1.72456e6	+	3.37308e6i	−0.324873	+	0.635420i
$49$	9.81186e6			1.70203
$50$		−	1.69167e6i		−	0.270668i
$51$	−4.02585e6	−	2.05831e6i	−0.595083	−	0.304249i
$52$	−2.45188e6			−0.335341
$53$		−	8.30602e6i		−	1.05266i	−0.850279	−	0.526332i	$-0.823567\pi$
$53$		−	8.30602e6i		−	1.05266i	0.850279	−	0.526332i	$-0.176433\pi$
$54$	1.13483e6	+	7.36303e6i	0.133461	+	0.865928i
$55$	2.29359e6			0.250649
$56$			1.74547e7i			1.77485i
$57$	145118.	−	283837.i	0.0137474	−	0.0268887i
$58$	9.59392e6			0.847782
$59$		−	2.73466e6i		−	0.225681i	−0.993613	−	0.112841i	$-0.964005\pi$
$59$		−	2.73466e6i		−	0.225681i	0.993613	−	0.112841i	$-0.0359949\pi$
$60$	2.22893e6	+	1.13959e6i	0.171985	+	0.0879312i
$61$	−1.60852e7			−1.16173			−0.580866	−	0.813999i	$-0.697286\pi$
$61$	−1.60852e7			−1.16173			−0.580866	+	0.813999i	$0.697286\pi$
$62$		−	1.93764e7i		−	1.31131i
$63$	1.51623e7	+	2.09912e7i	0.962503	+	1.33252i
$64$	−1.86535e7			−1.11183
$65$		−	2.14164e7i		−	1.19975i
$66$	−2.28184e6	+	4.46306e6i	−0.120257	+	0.235211i
$67$	−3.77081e7			−1.87126			−0.935632	−	0.352978i	$-0.885169\pi$
$67$	−3.77081e7			−1.87126			−0.935632	+	0.352978i	$0.885169\pi$
$68$		−	3.32043e6i		−	0.155296i
$69$	−1.09793e7	−	5.61343e6i	−0.484372	−	0.247646i
$70$	−2.87461e7			−1.19725
$71$		−	8.44368e6i		−	0.332275i	−0.986103	−	0.166138i	$-0.946870\pi$
$71$		−	8.44368e6i		−	0.332275i	0.986103	−	0.166138i	$-0.0531296\pi$
$72$	−2.35221e7	+	1.69904e7i	−0.875278	+	0.632227i
$73$	1.44822e7			0.509968			0.254984	−	0.966945i	$-0.417930\pi$
$73$	1.44822e7			0.509968			0.254984	+	0.966945i	$0.417930\pi$
$74$		−	7.91095e6i		−	0.263816i
$75$	4.44967e6	−	8.70314e6i	0.140632	−	0.275062i
$76$	234102.			0.00701699
$77$			1.74225e7i			0.495620i
$78$	4.16738e7	+	2.13066e7i	1.12586	+	0.575621i
$79$	6.67221e7			1.71301			0.856507	−	0.516135i	$-0.172630\pi$
$79$	6.67221e7			1.71301			0.856507	+	0.516135i	$0.172630\pi$
$80$		−	2.43002e7i		−	0.593266i
$81$	−1.35289e7	+	4.08655e7i	−0.314285	+	0.949329i
$82$	−6.96346e7			−1.54017
$83$			6.89613e7i			1.45309i	0.687118	+	0.726546i	$0.258875\pi$
$83$			6.89613e7i			1.45309i	−0.687118	+	0.726546i	$0.741125\pi$
$84$	−8.65652e6	+	1.69313e7i	−0.173871	+	0.340074i
$85$	2.90029e7			0.555604
$86$			168373.i			0.00307806i
$87$	4.93577e7	+	2.52353e7i	0.861546	+	0.440485i
$88$	−1.95232e7			−0.325552
$89$		−	3.31613e7i		−	0.528533i	−0.964450	−	0.264266i	$-0.914870\pi$
$89$		−	3.31613e7i		−	0.528533i	0.964450	−	0.264266i	$-0.0851298\pi$
$90$	−2.79813e7	−	3.87384e7i	−0.426480	−	0.590434i
$91$	1.62683e8			2.37233
$92$		−	9.05550e6i		−	0.126404i
$93$	5.09665e7	−	9.96856e7i	0.681323	−	1.33260i
$94$	9.96991e6			0.127697
$95$			2.04480e6i			0.0251048i
$96$	−3.43682e7	−	1.75715e7i	−0.404643	−	0.206883i
$97$	−6.75853e7			−0.763423			−0.381711	−	0.924282i	$-0.624665\pi$
$97$	−6.75853e7			−0.763423			−0.381711	+	0.924282i	$0.624665\pi$
$98$		−	1.37547e8i		−	1.49124i
$99$	−2.34787e7	+	1.69590e7i	−0.244418	+	0.176547i
$100$	7.17815e6			0.0717815
$101$		−	5.08374e7i		−	0.488537i	−0.969708	−	0.244269i	$-0.921452\pi$
$101$		−	5.08374e7i		−	0.488537i	0.969708	−	0.244269i	$-0.0785479\pi$
$102$	−2.88543e7	+	5.64362e7i	−0.266569	+	0.521383i
$103$	2.07722e8			1.84558			0.922791	−	0.385301i	$-0.125902\pi$
$103$	2.07722e8			1.84558			0.922791	+	0.385301i	$0.125902\pi$
$104$			1.82297e8i			1.55829i
$105$	−1.47890e8	−	7.56119e7i	−1.21669	−	0.622061i
$106$	−1.16437e8			−0.922294
$107$		−	1.62479e8i		−	1.23955i	−0.784781	−	0.619773i	$-0.787224\pi$
$107$		−	1.62479e8i		−	1.23955i	0.784781	−	0.619773i	$-0.212776\pi$
$108$	−3.12430e7	+	4.81533e6i	−0.229645	+	0.0353941i
$109$	−4.92758e7			−0.349082			−0.174541	−	0.984650i	$-0.555844\pi$
$109$	−4.92758e7			−0.349082			−0.174541	+	0.984650i	$0.555844\pi$
$110$		−	3.21526e7i		−	0.219606i
$111$	2.08085e7	−	4.06994e7i	0.137072	−	0.268099i
$112$	1.84588e8			1.17309
$113$		−	1.82763e7i		−	0.112092i	−0.998428	−	0.0560461i	$-0.982151\pi$
$113$		−	1.82763e7i		−	0.112092i	0.998428	−	0.0560461i	$-0.0178494\pi$
$114$	−3.97895e6	−	2.03433e6i	−0.0235586	−	0.0120448i
$115$	7.90968e7			0.452238
$116$			4.07091e7i			0.224833i
$117$	1.58355e8	+	2.19232e8i	0.845061	+	1.16993i
$118$	−3.83357e7			−0.197731
$119$			2.20311e8i			1.09862i
$120$	8.47284e7	−	1.65721e8i	0.408605	−	0.799193i
$121$	−1.94872e7			−0.0909091
$122$			2.25489e8i			1.01785i
$123$	−3.58248e8	−	1.83163e8i	−1.56518	−	0.800232i
$124$	8.22184e7			0.347762
$125$			2.65655e8i			1.08812i
$126$	2.94264e8	−	2.12551e8i	1.16749	−	0.843299i
$127$	−4.80457e8			−1.84688			−0.923442	−	0.383739i	$-0.874636\pi$
$127$	−4.80457e8			−1.84688			−0.923442	+	0.383739i	$0.874636\pi$
$128$			1.39498e8i			0.519672i
$129$	−442877.	+	866225.i	−0.00159928	+	0.00312804i
$130$	−3.00224e8			−1.05117
$131$			2.46002e8i			0.835321i	0.908603	+	0.417661i	$0.137150\pi$
$131$			2.46002e8i			0.835321i	−0.908603	+	0.417661i	$0.862850\pi$
$132$	−1.89377e7	−	9.68235e6i	−0.0623782	−	0.0318922i
$133$	−1.55327e7			−0.0496410
$134$			5.28608e8i			1.63951i
$135$	−4.20603e7	−	2.72897e8i	−0.126630	−	0.821606i
$136$	−2.46874e8			−0.721639
$137$		−	3.42820e8i		−	0.973159i	−0.873636	−	0.486580i	$-0.838244\pi$
$137$		−	3.42820e8i		−	0.973159i	0.873636	−	0.486580i	$-0.161756\pi$
$138$	−7.86915e7	+	1.53913e8i	−0.216976	+	0.424384i
$139$	1.08652e7			0.0291058			0.0145529	−	0.999894i	$-0.495368\pi$
$139$	1.08652e7			0.0291058			0.0145529	+	0.999894i	$0.495368\pi$
$140$		−	1.21976e8i		−	0.317513i
$141$	5.12921e7	+	2.62242e7i	0.129770	+	0.0663478i
$142$	−1.18367e8			−0.291124
$143$			1.81961e8i			0.435146i
$144$	1.79678e8	+	2.48752e8i	0.417873	+	0.578518i
$145$	−3.55581e8			−0.804389
$146$		−	2.03018e8i		−	0.446810i
$147$	3.61795e8	−	7.07636e8i	0.774806	−	1.51545i
$148$	3.35679e7			0.0699644
$149$		−	7.87272e8i		−	1.59727i	−0.601812	−	0.798637i	$-0.705555\pi$
$149$		−	7.87272e8i		−	1.59727i	0.601812	−	0.798637i	$-0.294445\pi$
$150$	−1.22004e8	−	6.23775e7i	−0.240996	−	0.123215i
$151$	5.86177e8			1.12751			0.563756	−	0.825942i	$-0.309356\pi$
$151$	5.86177e8			1.12751			0.563756	+	0.825942i	$0.309356\pi$
$152$		−	1.74055e7i		−	0.0326071i
$153$	−2.96892e8	+	2.14450e8i	−0.541793	+	0.391346i
$154$	2.44237e8			0.434239
$155$			7.18150e8i			1.24419i
$156$	−9.04088e7	+	1.76831e8i	−0.152655	+	0.298579i
$157$	1.09527e8			0.180269			0.0901347	−	0.995930i	$-0.471270\pi$
$157$	1.09527e8			0.180269			0.0901347	+	0.995930i	$0.471270\pi$
$158$		−	9.35339e8i		−	1.50086i
$159$	−5.99034e8	−	3.06270e8i	−0.937267	−	0.479199i
$160$	2.47594e8			0.377799
$161$			6.00834e8i			0.894233i
$162$	5.72870e8	+	1.89654e8i	0.831757	+	0.275361i
$163$	−5.26046e8			−0.745201			−0.372601	−	0.927992i	$-0.621534\pi$
$163$	−5.26046e8			−0.745201			−0.372601	+	0.927992i	$0.621534\pi$
$164$		−	2.95475e8i		−	0.408456i
$165$	8.45721e7	−	1.65415e8i	0.114102	−	0.223172i
$166$	9.66729e8			1.27313
$167$			7.12216e8i			0.915685i	0.889033	+	0.457842i	$0.151378\pi$
$167$			7.12216e8i			0.915685i	−0.889033	+	0.457842i	$0.848622\pi$
$168$	1.25884e9	+	6.43612e8i	1.58028	+	0.807955i
$169$	8.83329e8			1.08287
$170$		−	4.06575e8i		−	0.486794i
$171$	−1.51195e7	−	2.09320e7i	−0.0176829	−	0.0244808i
$172$	−714442.			−0.000816307
$173$		−	4.19068e8i		−	0.467843i	−0.972256	−	0.233921i	$-0.924844\pi$
$173$		−	4.19068e8i		−	0.467843i	0.972256	−	0.233921i	$-0.0751558\pi$
$174$	3.53759e8	−	6.91919e8i	0.385932	−	0.754845i
$175$	−4.76271e8			−0.507811
$176$			2.06463e8i			0.215175i
$177$	−1.97225e8	−	1.00836e8i	−0.200941	−	0.102736i
$178$	−4.64870e8			−0.463075
$179$			8.39762e8i			0.817982i	0.912538	+	0.408991i	$0.134119\pi$
$179$			8.39762e8i			0.817982i	−0.912538	+	0.408991i	$0.865881\pi$
$180$	1.64375e8	−	1.18731e8i	0.156584	−	0.113103i
$181$	2.98819e8			0.278416			0.139208	−	0.990263i	$-0.455544\pi$
$181$	2.98819e8			0.278416			0.139208	+	0.990263i	$0.455544\pi$
$182$		−	2.28056e9i		−	2.07853i
$183$	−5.93112e8	+	1.16007e9i	−0.528849	+	1.03438i
$184$	−6.73276e8			−0.587384
$185$			2.93204e8i			0.250313i
$186$	−1.39744e9	−	7.14470e8i	−1.16756	−	0.596943i
$187$	−2.46419e8			−0.201515
$188$			4.23045e7i			0.0338654i
$189$	2.07298e9	−	3.19498e8i	1.62460	−	0.250392i
$190$	2.86650e7			0.0219957
$191$			1.95127e9i			1.46617i	0.680138	+	0.733084i	$0.261920\pi$
$191$			1.95127e9i			1.46617i	−0.680138	+	0.733084i	$0.738080\pi$
$192$	−6.87813e8	+	1.34530e9i	−0.506134	+	0.989950i
$193$	−3.98052e8			−0.286887			−0.143443	−	0.989659i	$-0.545817\pi$
$193$	−3.98052e8			−0.286887			−0.143443	+	0.989659i	$0.545817\pi$
$194$			9.47440e8i			0.668875i
$195$	−1.54456e9	−	7.89691e8i	−1.06823	−	0.546158i
$196$	5.83642e8			0.395478
$197$		−	9.80294e8i		−	0.650866i	−0.945565	−	0.325433i	$-0.894490\pi$
$197$		−	9.80294e8i		−	0.650866i	0.945565	−	0.325433i	$-0.105510\pi$
$198$	2.37739e8	+	3.29135e8i	0.154682	+	0.214148i
$199$	9.65223e8			0.615482			0.307741	−	0.951470i	$-0.400427\pi$
$199$	9.65223e8			0.615482			0.307741	+	0.951470i	$0.400427\pi$
$200$		−	5.33695e8i		−	0.333559i
$201$	−1.39042e9	+	2.71952e9i	−0.851846	+	1.66613i
$202$	−7.12661e8			−0.428033
$203$		−	2.70106e9i		−	1.59056i
$204$	−2.39471e8	−	1.22435e8i	−0.138271	−	0.0706944i
$205$	2.58088e9			1.46134
$206$		−	2.91194e9i		−	1.61701i
$207$	−8.09686e8	+	5.84849e8i	−0.440997	+	0.318539i
$208$	1.92784e9			1.02996
$209$		−	1.73734e7i		−	0.00910541i
$210$	−1.05996e9	+	2.07318e9i	−0.545020	+	1.06601i
$211$	−4.40130e8			−0.222050			−0.111025	−	0.993818i	$-0.535413\pi$
$211$	−4.40130e8			−0.222050			−0.111025	+	0.993818i	$0.535413\pi$
$212$		−	4.94070e8i		−	0.244593i
$213$	−6.08962e8	−	3.11346e8i	−0.295850	−	0.151260i
$214$	−2.27771e9			−1.08603
$215$		−	6.24042e6i		−	0.00292052i
$216$	3.58019e8	+	2.32291e9i	0.164472	+	1.06713i
$217$	−5.45520e9			−2.46021
$218$			6.90770e8i			0.305849i
$219$	5.34005e8	−	1.04446e9i	0.232150	−	0.454064i
$220$	1.36430e8			0.0582399
$221$			2.30093e9i			0.964572i
$222$	−5.70542e8	−	2.91702e8i	−0.234896	−	0.120096i
$223$	−2.74504e9			−1.11002			−0.555008	−	0.831845i	$-0.687285\pi$
$223$	−2.74504e9			−1.11002			−0.555008	+	0.831845i	$0.687285\pi$
$224$			1.88077e9i			0.747040i
$225$	−4.63601e8	−	6.41825e8i	−0.180890	−	0.250430i
$226$	−2.56206e8			−0.0982098
$227$		−	1.60354e9i		−	0.603917i	−0.953321	−	0.301959i	$-0.902360\pi$
$227$		−	1.60354e9i		−	0.603917i	0.953321	−	0.301959i	$-0.0976404\pi$
$228$	8.63210e6	−	1.68836e7i	0.00319431	−	0.00624776i
$229$	2.43869e9			0.886778			0.443389	−	0.896329i	$-0.353776\pi$
$229$	2.43869e9			0.886778			0.443389	+	0.896329i	$0.353776\pi$
$230$		−	1.10881e9i		−	0.396230i
$231$	1.25652e9	+	6.42425e8i	0.441288	+	0.225619i
$232$	3.02672e9			1.04477
$233$		−	2.13769e9i		−	0.725304i	−0.931925	−	0.362652i	$-0.881871\pi$
$233$		−	2.13769e9i		−	0.725304i	0.931925	−	0.362652i	$-0.118129\pi$
$234$	3.07329e9	−	2.21989e9i	1.02504	−	0.740402i
$235$	−3.69516e8			−0.121161
$236$		−	1.62667e8i		−	0.0524385i
$237$	2.46026e9	−	4.81203e9i	0.779807	−	1.52523i
$238$	3.08842e9			0.962561
$239$			3.80931e9i			1.16749i	0.811936	+	0.583747i	$0.198414\pi$
$239$			3.80931e9i			1.16749i	−0.811936	+	0.583747i	$0.801586\pi$
$240$	−1.75254e9	−	8.96025e8i	−0.528230	−	0.270069i
$241$	−1.42831e9			−0.423404			−0.211702	−	0.977334i	$-0.567901\pi$
$241$	−1.42831e9			−0.423404			−0.211702	+	0.977334i	$0.567901\pi$
$242$			2.73180e8i			0.0796502i
$243$	2.44838e9	+	2.48255e9i	0.702190	+	0.711990i
$244$	−9.56799e8			−0.269936
$245$			5.09792e9i			1.41491i
$246$	−2.56765e9	+	5.02208e9i	−0.701126	+	1.37133i
$247$	−1.62224e8			−0.0435839
$248$		−	6.11293e9i		−	1.61601i
$249$	4.97352e9	+	2.54282e9i	1.29380	+	0.661483i
$250$	3.72406e9			0.953360
$251$		−	3.96523e9i		−	0.999018i	−0.866309	−	0.499509i	$-0.833514\pi$
$251$		−	3.96523e9i		−	0.999018i	0.866309	−	0.499509i	$-0.166486\pi$
$252$	9.01902e8	+	1.24863e9i	0.223644	+	0.309621i
$253$	−6.72034e8			−0.164025
$254$			6.73525e9i			1.61815i
$255$	1.06943e9	−	2.09170e9i	0.252925	−	0.494697i
$256$	−2.81974e9			−0.656521
$257$		−	1.52950e8i		−	0.0350605i	−0.999846	−	0.0175302i	$-0.994420\pi$
$257$		−	1.52950e8i		−	0.0350605i	0.999846	−	0.0175302i	$-0.00558033\pi$
$258$	1.21431e7	+	6.20844e6i	0.00274064	+	0.00140121i
$259$	−2.22724e9			−0.494956
$260$		−	1.27392e9i		−	0.278771i
$261$	3.63996e9	−	2.62920e9i	0.784394	−	0.566580i
$262$	3.44857e9			0.731869
$263$		−	8.80263e9i		−	1.83988i	−0.392058	−	0.919940i	$-0.628237\pi$
$263$		−	8.80263e9i		−	1.83988i	0.392058	−	0.919940i	$-0.371763\pi$
$264$	−7.19882e8	+	1.40802e9i	−0.148199	+	0.289863i
$265$	4.31554e9			0.875087
$266$			2.17744e8i			0.0434931i
$267$	−2.39161e9	−	1.22276e9i	−0.470593	−	0.240601i
$268$	−2.24300e9			−0.434801
$269$		−	2.86682e9i		−	0.547508i	−0.961800	−	0.273754i	$-0.911735\pi$
$269$		−	2.86682e9i		−	0.547508i	0.961800	−	0.273754i	$-0.0882654\pi$
$270$	−3.82559e9	+	5.89620e8i	−0.719852	+	0.110947i
$271$	−1.53127e8			−0.0283907			−0.0141953	−	0.999899i	$-0.504519\pi$
$271$	−1.53127e8			−0.0283907			−0.0141953	+	0.999899i	$0.504519\pi$
$272$			2.61076e9i			0.476970i
$273$	5.99864e9	−	1.17328e10i	1.07995	−	2.11227i
$274$	−4.80580e9			−0.852636
$275$		−	5.32711e8i		−	0.0931453i
$276$	−6.53087e8	−	3.33905e8i	−0.112547	−	0.0575423i
$277$	7.21265e9			1.22511			0.612556	−	0.790428i	$-0.290142\pi$
$277$	7.21265e9			1.22511			0.612556	+	0.790428i	$0.290142\pi$
$278$		−	1.52314e8i		−	0.0255011i
$279$	−5.31007e9	−	7.35145e9i	−0.876362	−	1.21327i
$280$	−9.06891e9			−1.47544
$281$			3.77901e9i			0.606112i	0.952973	+	0.303056i	$0.0980070\pi$
$281$			3.77901e9i			0.606112i	−0.952973	+	0.303056i	$0.901993\pi$
$282$	3.67623e8	−	7.19035e8i	0.0581308	−	0.113698i
$283$	−2.31942e9			−0.361604			−0.180802	−	0.983520i	$-0.557869\pi$
$283$	−2.31942e9			−0.361604			−0.180802	+	0.983520i	$0.557869\pi$
$284$		−	5.02258e8i		−	0.0772065i
$285$	1.47472e8	+	7.53985e7i	0.0223528	+	0.0114283i
$286$	2.55081e9			0.381254
$287$			1.96048e10i			2.88958i
$288$	−2.53454e9	+	1.83074e9i	−0.368407	+	0.266107i
$289$	3.85975e9			0.553309
$290$			4.98469e9i			0.704768i
$291$	−2.49209e9	+	4.87428e9i	−0.347529	+	0.679734i
$292$	8.61449e8			0.118495
$293$			7.86939e9i			1.06775i	0.845563	+	0.533876i	$0.179265\pi$
$293$			7.86939e9i			1.06775i	−0.845563	+	0.533876i	$0.820735\pi$
$294$	−9.91996e9	−	5.07180e9i	−1.32776	−	0.678848i
$295$	1.42084e9			0.187610
$296$		−	2.49577e9i		−	0.325116i
$297$	3.57359e8	+	2.31863e9i	0.0459282	+	0.297993i
$298$	−1.10363e10			−1.39946
$299$			6.27511e9i			0.785121i
$300$	2.64681e8	−	5.17692e8i	0.0326767	−	0.0639125i
$301$	4.74034e7			0.00577488
$302$		−	8.21729e9i		−	0.987872i
$303$	−3.66642e9	−	1.87454e9i	−0.434982	−	0.222394i
$304$	−1.84068e8			−0.0215518
$305$		−	8.35732e9i		−	0.965757i
$306$	3.00626e9	+	4.16197e9i	0.342878	+	0.474693i
$307$	−1.01555e10			−1.14326			−0.571632	−	0.820510i	$-0.693689\pi$
$307$	−1.01555e10			−1.14326			−0.571632	+	0.820510i	$0.693689\pi$
$308$			1.03635e9i			0.115161i
$309$	7.65938e9	−	1.49810e10i	0.840155	−	1.64326i
$310$	1.00673e10			1.09010
$311$			1.30763e10i			1.39779i	0.715224	+	0.698896i	$0.246325\pi$
$311$			1.30763e10i			1.39779i	−0.715224	+	0.698896i	$0.753675\pi$
$312$	1.31474e10	+	6.72189e9i	1.38746	+	0.709370i
$313$	1.19622e10			1.24634			0.623168	−	0.782088i	$-0.285845\pi$
$313$	1.19622e10			1.24634			0.623168	+	0.782088i	$0.285845\pi$
$314$		−	1.53540e9i		−	0.157943i
$315$	−1.09063e10	+	7.87782e9i	−1.10774	+	0.800136i
$316$	3.96885e9			0.398031
$317$			1.49250e10i			1.47801i	0.673700	+	0.739005i	$0.264704\pi$
$317$			1.49250e10i			1.47801i	−0.673700	+	0.739005i	$0.735296\pi$
$318$	−4.29342e9	+	8.39753e9i	−0.419851	+	0.821189i
$319$	3.02114e9			0.291748
$320$		−	9.69172e9i		−	0.924275i
$321$	−1.17181e10	−	5.99114e9i	−1.10366	−	0.564273i
$322$	8.42275e9			0.783485
$323$		−	2.19689e8i		−	0.0201836i
$324$	−8.04745e8	+	2.43082e9i	−0.0730262	+	0.220583i
$325$	−4.97418e9			−0.445849
$326$			7.37435e9i			0.652910i
$327$	−1.81696e9	+	3.55380e9i	−0.158911	+	0.310815i
$328$	−2.19686e10			−1.89804
$329$		−	2.80691e9i		−	0.239577i
$330$	−2.31886e9	−	1.18557e9i	−0.195532	−	0.0999703i
$331$	−3.41926e9			−0.284852			−0.142426	−	0.989805i	$-0.545490\pi$
$331$	−3.41926e9			−0.284852			−0.142426	+	0.989805i	$0.545490\pi$
$332$			4.10205e9i			0.337636i
$333$	−2.16798e9	−	3.00143e9i	−0.176311	−	0.244091i
$334$	9.98416e9			0.802280
$335$		−	1.95919e10i		−	1.55560i
$336$	6.80637e9	−	1.33126e10i	0.534021	−	1.04449i
$337$	1.29398e10			1.00325			0.501623	−	0.865086i	$-0.332737\pi$
$337$	1.29398e10			1.00325			0.501623	+	0.865086i	$0.332737\pi$
$338$		−	1.23829e10i		−	0.948758i
$339$	−1.31810e9	−	6.73907e8i	−0.0998042	−	0.0510271i
$340$	1.72519e9			0.129098
$341$		−	6.10166e9i		−	0.451264i
$342$	−2.93433e8	+	2.11952e8i	−0.0214489	+	0.0154929i
$343$	−1.59726e10			−1.15399
$344$			5.31188e7i			0.00379327i
$345$	2.91655e9	−	5.70450e9i	0.205870	−	0.402662i
$346$	−5.87468e9			−0.409901
$347$		−	9.40896e9i		−	0.648969i	−0.945891	−	0.324484i	$-0.894809\pi$
$347$		−	9.40896e9i		−	0.648969i	0.945891	−	0.324484i	$-0.105191\pi$
$348$	2.93596e9	+	1.50108e9i	0.200186	+	0.102350i
$349$	6.54870e9			0.441421			0.220711	−	0.975339i	$-0.429162\pi$
$349$	6.54870e9			0.441421			0.220711	+	0.975339i	$0.429162\pi$
$350$			6.67658e9i			0.444920i
$351$	2.16502e10	−	3.33684e9i	1.42637	−	0.219840i
$352$	−2.10365e9			−0.137026
$353$		−	3.57815e9i		−	0.230441i	−0.993340	−	0.115220i	$-0.963243\pi$
$353$		−	3.57815e9i		−	0.230441i	0.993340	−	0.115220i	$-0.0367574\pi$
$354$	−1.41356e9	+	2.76479e9i	−0.0900121	+	0.176055i
$355$	4.38706e9			0.276223
$356$		−	1.97255e9i		−	0.122808i
$357$	1.58889e10	+	8.12358e9i	0.978188	+	0.500120i
$358$	1.17721e10			0.716677
$359$		−	1.98781e10i		−	1.19673i	−0.801222	−	0.598367i	$-0.795816\pi$
$359$		−	1.98781e10i		−	1.19673i	0.801222	−	0.598367i	$-0.204184\pi$
$360$	−8.82764e9	−	1.22213e10i	−0.525575	−	0.727625i
$361$	−1.69681e10			−0.999088
$362$		−	4.18898e9i		−	0.243935i
$363$	−7.18555e8	+	1.40542e9i	−0.0413841	+	0.0809433i
$364$	9.67691e9			0.551228
$365$			7.52447e9i			0.423940i
$366$	1.62624e10	+	8.31450e9i	0.906274	+	0.463353i
$367$	7.03860e9			0.387991			0.193996	−	0.981002i	$-0.437855\pi$
$367$	7.03860e9			0.387991			0.193996	+	0.981002i	$0.437855\pi$
$368$			7.12007e9i			0.388234i
$369$	−2.64195e10	+	1.90833e10i	−1.42502	+	1.02931i
$370$	4.11027e9			0.219313
$371$			3.27816e10i			1.73035i
$372$	3.03166e9	−	5.92963e9i	0.158310	−	0.309639i
$373$	1.14441e10			0.591216			0.295608	−	0.955309i	$-0.404478\pi$
$373$	1.14441e10			0.591216			0.295608	+	0.955309i	$0.404478\pi$
$374$			3.45441e9i			0.176558i
$375$	1.91591e10	+	9.79554e9i	0.968838	+	0.495340i
$376$	3.14534e9			0.157368
$377$		−	2.82099e10i		−	1.39648i
$378$	−4.47886e9	−	2.90599e10i	−0.219382	−	1.42340i
$379$	8.19870e9			0.397363			0.198682	−	0.980064i	$-0.436334\pi$
$379$	8.19870e9			0.397363			0.198682	+	0.980064i	$0.436334\pi$
$380$			1.21632e8i			0.00583328i
$381$	−1.77160e10	+	3.46508e10i	−0.840747	+	1.64442i
$382$	2.73538e10			1.28459
$383$			2.69297e10i			1.25152i	0.780017	+	0.625758i	$0.215210\pi$
$383$			2.69297e10i			1.25152i	−0.780017	+	0.625758i	$0.784790\pi$
$384$	1.00607e10	+	5.14375e9i	0.462704	+	0.236568i
$385$	−9.05218e9			−0.412012
$386$			5.58006e9i			0.251356i
$387$	4.61423e7	+	6.38810e7i	0.00205710	+	0.00284792i
$388$	−4.02020e9			−0.177386
$389$		−	2.09740e10i		−	0.915975i	−0.888959	−	0.457987i	$-0.848571\pi$
$389$		−	2.09740e10i		−	0.915975i	0.888959	−	0.457987i	$-0.151429\pi$
$390$	−1.10702e10	+	2.16523e10i	−0.478518	+	0.935936i
$391$	−8.49799e9			−0.363588
$392$		−	4.33938e10i		−	1.83774i
$393$	1.77418e10	+	9.07089e9i	0.743750	+	0.380259i
$394$	−1.37422e10			−0.570258
$395$			3.46666e10i			1.42404i
$396$	−1.39659e9	+	1.00878e9i	−0.0567922	+	0.0410219i
$397$	−4.06938e9			−0.163820			−0.0819098	−	0.996640i	$-0.526102\pi$
$397$	−4.06938e9			−0.163820			−0.0819098	+	0.996640i	$0.526102\pi$
$398$		−	1.35309e10i		−	0.539256i
$399$	−5.72741e8	+	1.12023e9i	−0.0225978	+	0.0441992i
$400$	−5.64397e9			−0.220467
$401$		−	3.01677e10i		−	1.16671i	−0.812216	−	0.583357i	$-0.801739\pi$
$401$		−	3.01677e10i		−	1.16671i	0.812216	−	0.583357i	$-0.198261\pi$
$402$	3.81235e10	+	1.94915e10i	1.45978	+	0.746347i
$403$	−5.69741e10			−2.16002
$404$		−	3.02398e9i		−	0.113515i
$405$	−2.12324e10	−	7.02918e9i	−0.789184	−	0.261267i
$406$	−3.78646e10			−1.39357
$407$		−	2.49117e9i		−	0.0907874i
$408$	−9.10304e9	+	1.78047e10i	−0.328508	+	0.642530i
$409$	−9.56003e9			−0.341638			−0.170819	−	0.985302i	$-0.554641\pi$
$409$	−9.56003e9			−0.341638			−0.170819	+	0.985302i	$0.554641\pi$
$410$		−	3.61799e10i		−	1.28036i
$411$	−2.47244e10	−	1.26409e10i	−0.866478	−	0.443006i
$412$	1.23560e10			0.428833
$413$			1.07930e10i			0.370971i
$414$	8.19868e9	+	1.13505e10i	0.279089	+	0.386381i
$415$	−3.58300e10			−1.20797
$416$			1.96428e10i			0.655888i
$417$	4.00636e8	−	7.83606e8i	0.0132497	−	0.0259151i
$418$	−2.43548e8			−0.00797772
$419$		−	5.31606e10i		−	1.72478i	−0.506244	−	0.862390i	$-0.668967\pi$
$419$		−	5.31606e10i		−	1.72478i	0.506244	−	0.862390i	$-0.331033\pi$
$420$	−8.79697e9	−	4.49765e9i	−0.282706	−	0.144540i
$421$	−4.20805e10			−1.33953			−0.669765	−	0.742573i	$-0.733605\pi$
$421$	−4.20805e10			−1.33953			−0.669765	+	0.742573i	$0.733605\pi$
$422$			6.16994e9i			0.194550i
$423$	3.78261e9	−	2.73224e9i	0.118149	−	0.0853409i
$424$	−3.67341e10			−1.13659
$425$		−	6.73622e9i		−	0.206472i
$426$	−4.36458e9	+	8.53670e9i	−0.132527	+	0.259210i
$427$	6.34837e10			1.90964
$428$		−	9.66481e9i		−	0.288017i
$429$	1.31231e10	+	6.70949e9i	0.387443	+	0.198089i
$430$	−8.74809e7			−0.00255882
$431$			5.43859e10i			1.57608i	0.615626	+	0.788039i	$0.288903\pi$
$431$			5.43859e10i			1.57608i	−0.615626	+	0.788039i	$0.711097\pi$
$432$	2.45654e10	−	3.78615e9i	0.705325	−	0.108708i
$433$	6.71925e10			1.91148			0.955738	−	0.294218i	$-0.0950592\pi$
$433$	6.71925e10			1.91148			0.955738	+	0.294218i	$0.0950592\pi$
$434$			7.64734e10i			2.15552i
$435$	−1.31114e10	+	2.56447e10i	−0.366178	+	0.716209i
$436$	−2.93109e9			−0.0811117
$437$		−	5.99138e8i		−	0.0164286i
$438$	−1.46417e10	−	7.48592e9i	−0.397829	−	0.203399i
$439$	2.69041e10			0.724371			0.362185	−	0.932106i	$-0.382031\pi$
$439$	2.69041e10			0.724371			0.362185	+	0.932106i	$0.382031\pi$
$440$		−	1.01436e10i		−	0.270633i
$441$	−3.76945e10	−	5.21857e10i	−0.996607	−	1.37974i
$442$	3.22555e10			0.845112
$443$		−	4.04313e9i		−	0.104979i	−0.998621	−	0.0524896i	$-0.983284\pi$
$443$		−	4.04313e9i		−	0.104979i	0.998621	−	0.0524896i	$-0.0167156\pi$
$444$	1.23776e9	−	2.42093e9i	0.0318496	−	0.0622947i
$445$	1.72295e10			0.439373
$446$			3.84812e10i			0.972543i
$447$	−5.67784e10	−	2.90293e10i	−1.42218	−	0.727119i
$448$	7.36201e10			1.82761
$449$		−	6.37499e10i		−	1.56853i	−0.620423	−	0.784267i	$-0.713039\pi$
$449$		−	6.37499e10i		−	1.56853i	0.620423	−	0.784267i	$-0.286961\pi$
$450$	−8.99739e9	+	6.49896e9i	−0.219415	+	0.158487i
$451$	−2.19280e10			−0.530022
$452$		−	1.08714e9i		−	0.0260454i
$453$	2.16142e10	−	4.22754e10i	0.513271	−	1.00391i
$454$	−2.24792e10			−0.529124
$455$			8.45246e10i			1.97214i
$456$	−1.25529e9	−	6.41796e8i	−0.0290326	−	0.0148436i
$457$	−1.86548e9			−0.0427686			−0.0213843	−	0.999771i	$-0.506807\pi$
$457$	−1.86548e9			−0.0427686			−0.0213843	+	0.999771i	$0.506807\pi$
$458$		−	3.41866e10i		−	0.776953i
$459$	4.51887e9	+	2.93195e10i	0.101807	+	0.660550i
$460$	4.70494e9			0.105081
$461$			1.45767e10i			0.322741i	0.986894	+	0.161371i	$0.0515914\pi$
$461$			1.45767e10i			0.322741i	−0.986894	+	0.161371i	$0.948409\pi$
$462$	9.00580e9	−	1.76145e10i	0.197676	−	0.386636i
$463$	−4.00653e10			−0.871854			−0.435927	−	0.899982i	$-0.643579\pi$
$463$	−4.00653e10			−0.871854			−0.435927	+	0.899982i	$0.643579\pi$
$464$		−	3.20084e10i		−	0.690545i
$465$	5.17933e10	+	2.64805e10i	1.10780	+	0.566389i
$466$	−2.99670e10			−0.635477
$467$		−	4.87127e10i		−	1.02418i	−0.858933	−	0.512088i	$-0.828872\pi$
$467$		−	4.87127e10i		−	1.02418i	0.858933	−	0.512088i	$-0.171128\pi$
$468$	9.41947e9	+	1.30407e10i	0.196356	+	0.271842i
$469$	1.48823e11			3.07595
$470$			5.18004e9i			0.106155i
$471$	4.03861e9	−	7.89913e9i	0.0820631	−	0.160508i
$472$	−1.20943e10			−0.243675
$473$			5.30208e7i			0.00105926i
$474$	−6.74571e10	−	3.44890e10i	−1.33633	−	0.683230i
$475$	4.74927e8			0.00932938
$476$			1.31048e10i			0.255272i
$477$	−4.41766e10	+	3.19095e10i	−0.853334	+	0.616377i
$478$	5.34006e10			1.02290
$479$			3.02656e10i			0.574920i	0.957793	+	0.287460i	$0.0928108\pi$
$479$			3.02656e10i			0.574920i	−0.957793	+	0.287460i	$0.907189\pi$
$480$	9.12959e9	−	1.78566e10i	0.171983	−	0.336383i
$481$	−2.32613e10			−0.434563
$482$			2.00227e10i			0.370966i
$483$	4.33324e10	+	2.21547e10i	0.796204	+	0.407077i
$484$	−1.15916e9			−0.0211233
$485$		−	3.51151e10i		−	0.634639i
$486$	3.48015e10	−	3.43225e10i	0.623812	−	0.615225i
$487$	−2.09765e10			−0.372922			−0.186461	−	0.982462i	$-0.559702\pi$
$487$	−2.09765e10			−0.372922			−0.186461	+	0.982462i	$0.559702\pi$
$488$			7.11380e10i			1.25436i
$489$	−1.93970e10	+	3.79387e10i	−0.339234	+	0.663510i
$490$	7.14649e10			1.23968
$491$		−	8.00971e10i		−	1.37813i	−0.724698	−	0.689066i	$-0.758021\pi$
$491$		−	8.00971e10i		−	1.37813i	0.724698	−	0.689066i	$-0.241979\pi$
$492$	−2.13098e10	−	1.08951e10i	−0.363680	−	0.185939i
$493$	3.82029e10			0.646708
$494$			2.27412e9i			0.0381862i
$495$	−8.81136e9	−	1.21988e10i	−0.146765	−	0.203187i
$496$	−6.46459e10			−1.06811
$497$			3.33249e10i			0.546189i
$498$	3.56464e10	−	6.97210e10i	0.579560	−	1.13356i
$499$	−7.16624e10			−1.15582			−0.577909	−	0.816101i	$-0.696131\pi$
$499$	−7.16624e10			−1.15582			−0.577909	+	0.816101i	$0.696131\pi$
$500$			1.58020e10i			0.252832i
$501$	5.13654e10	+	2.62617e10i	0.815304	+	0.416843i
$502$	−5.55863e10			−0.875292
$503$		−	6.52015e10i		−	1.01856i	−0.860602	−	0.509279i	$-0.829912\pi$
$503$		−	6.52015e10i		−	1.01856i	0.860602	−	0.509279i	$-0.170088\pi$
$504$	9.28353e10	−	6.70564e10i	1.43877	−	1.03925i
$505$	2.64134e10			0.406125
$506$			9.42087e9i			0.143711i
$507$	3.25712e10	−	6.37061e10i	0.492949	−	0.964160i
$508$	−2.85792e10			−0.429136
$509$			1.11289e10i			0.165799i	0.996558	+	0.0828996i	$0.0264181\pi$
$509$			1.11289e10i			0.165799i	−0.996558	+	0.0828996i	$0.973582\pi$
$510$	−2.93224e10	−	1.49917e10i	−0.433430	−	0.221601i
$511$	−5.71573e10			−0.838278
$512$			7.52399e10i			1.09488i
$513$	−2.06713e9	+	3.18596e8i	−0.0298468	+	0.00460014i
$514$	−2.14412e9			−0.0307183
$515$			1.07925e11i			1.53425i
$516$	−2.63438e7	+	5.15259e7i	−0.000371603	+	0.000726820i
$517$	3.13954e9			0.0439444
$518$			3.12224e10i			0.433657i
$519$	−3.02234e10	−	1.54524e10i	−0.416556	−	0.212974i
$520$	−9.47157e10			−1.29541
$521$		−	9.14474e10i		−	1.24114i	−0.784151	−	0.620570i	$-0.786901\pi$
$521$		−	9.14474e10i		−	1.24114i	0.784151	−	0.620570i	$-0.213099\pi$
$522$	−3.68573e10	−	5.10265e10i	−0.496411	−	0.687249i
$523$	8.83183e10			1.18044			0.590220	−	0.807242i	$-0.299041\pi$
$523$	8.83183e10			1.18044			0.590220	+	0.807242i	$0.299041\pi$
$524$			1.46330e10i			0.194093i
$525$	−1.75617e10	+	3.43489e10i	−0.231168	+	0.452143i
$526$	−1.23399e11			−1.61202
$527$		−	7.71565e10i		−	1.00030i
$528$	1.48902e10	+	7.61295e9i	0.191586	+	0.0979529i
$529$	5.51352e10			0.704055
$530$		−	6.04971e10i		−	0.766710i
$531$	−1.45446e10	+	1.05058e10i	−0.182947	+	0.132145i
$532$	−9.23937e8			−0.0115344
$533$			2.04753e11i			2.53700i
$534$	−1.71413e10	+	3.35267e10i	−0.210803	+	0.412311i
$535$	8.44189e10			1.03044
$536$			1.66767e11i			2.02046i
$537$	6.05640e10	+	3.09647e10i	0.728312	+	0.372366i
$538$	−4.01883e10			−0.479701
$539$		−	4.33138e10i		−	0.513181i
$540$	−2.50189e9	−	1.62328e10i	−0.0294234	−	0.190906i
$541$	−6.12903e10			−0.715488			−0.357744	−	0.933820i	$-0.616454\pi$
$541$	−6.12903e10			−0.715488			−0.357744	+	0.933820i	$0.616454\pi$
$542$			2.14661e9i			0.0248746i
$543$	1.10184e10	−	2.15510e10i	0.126742	−	0.247895i
$544$	−2.66010e10			−0.303740
$545$		−	2.56021e10i		−	0.290195i
$546$	−1.64475e11	−	8.40915e10i	−1.85067	−	0.946197i
$547$	6.34897e10			0.709175			0.354588	−	0.935023i	$-0.384621\pi$
$547$	6.34897e10			0.709175			0.354588	+	0.935023i	$0.384621\pi$
$548$		−	2.03921e10i		−	0.226120i
$549$	6.17949e10	+	8.55510e10i	0.680241	+	0.941750i
$550$	−7.46778e9			−0.0816095
$551$			2.69344e9i			0.0292213i
$552$	−2.48259e10	+	4.85570e10i	−0.267392	+	0.522993i
$553$	−2.63334e11			−2.81583
$554$		−	1.01110e11i		−	1.07338i
$555$	2.11461e10	+	1.08114e10i	0.222873	+	0.113949i
$556$	6.46300e8			0.00676294
$557$		−	5.10273e10i		−	0.530129i	−0.964231	−	0.265065i	$-0.914607\pi$
$557$		−	5.10273e10i		−	0.530129i	0.964231	−	0.265065i	$-0.0853933\pi$
$558$	−1.03056e11	+	7.44389e10i	−1.06301	+	0.767827i
$559$	4.95081e8			0.00507024
$560$			9.59061e10i			0.975201i
$561$	−9.08625e9	+	1.77718e10i	−0.0917346	+	0.179424i
$562$	5.29759e10			0.531047
$563$			3.28025e10i			0.326492i	0.986585	+	0.163246i	$0.0521965\pi$
$563$			3.28025e10i			0.326492i	−0.986585	+	0.163246i	$0.947804\pi$
$564$	3.05102e9	+	1.55990e9i	0.0301529	+	0.0154164i
$565$	9.49578e9			0.0931830
$566$			3.25146e10i			0.316820i
$567$	5.33950e10	−	1.61285e11i	0.516616	−	1.56049i
$568$	−3.73429e10			−0.358769
$569$			6.53450e10i			0.623395i	0.950181	+	0.311698i	$0.100898\pi$
$569$			6.53450e10i			0.623395i	−0.950181	+	0.311698i	$0.899102\pi$
$570$	1.05697e9	−	2.06733e9i	0.0100130	−	0.0195844i
$571$	−4.52576e10			−0.425742			−0.212871	−	0.977080i	$-0.568281\pi$
$571$	−4.52576e10			−0.425742			−0.212871	+	0.977080i	$0.568281\pi$
$572$			1.08237e10i			0.101109i
$573$	1.40727e11	+	7.19496e10i	1.30544	+	0.667436i
$574$	2.74829e11			2.53172
$575$		−	1.83711e10i		−	0.168059i
$576$	7.16616e10	+	9.92108e10i	0.651023	+	0.901299i
$577$	7.02381e10			0.633679			0.316839	−	0.948479i	$-0.397378\pi$
$577$	7.02381e10			0.633679			0.316839	+	0.948479i	$0.397378\pi$
$578$		−	5.41077e10i		−	0.484783i
$579$	−1.46774e10	+	2.87077e10i	−0.130598	+	0.255437i
$580$	−2.11511e10			−0.186905
$581$		−	2.72171e11i		−	2.38857i
$582$	6.83298e10	+	3.49352e10i	0.595550	+	0.304488i
$583$	−3.66663e10			−0.317390
$584$		−	6.40487e10i		−	0.550629i
$585$	−1.13906e11	+	8.22760e10i	−0.972573	+	0.702505i
$586$	1.10317e11			0.935514
$587$		−	6.91379e10i		−	0.582323i	−0.956674	−	0.291162i	$-0.905958\pi$
$587$		−	6.91379e10i		−	0.582323i	0.956674	−	0.291162i	$-0.0940417\pi$
$588$	2.15208e10	−	4.20926e10i	0.180031	−	0.352124i
$589$	5.43981e9			0.0451983
$590$		−	1.99180e10i		−	0.164375i
$591$	−7.06993e10	−	3.61466e10i	−0.579515	−	0.296290i
$592$	−2.63935e10			−0.214887
$593$			1.92692e11i			1.55828i	0.626852	+	0.779139i	$0.284343\pi$
$593$			1.92692e11i			1.55828i	−0.626852	+	0.779139i	$0.715657\pi$
$594$	3.25036e10	−	5.00962e9i	0.261087	−	0.0402401i
$595$	−1.14466e11			−0.913293
$596$		−	4.68296e10i		−	0.371138i
$597$	3.55909e10	−	6.96124e10i	0.280183	−	0.548011i
$598$	8.79673e10			0.687886
$599$		−	3.52194e10i		−	0.273574i	−0.990600	−	0.136787i	$-0.956322\pi$
$599$		−	3.52194e10i		−	0.273574i	0.990600	−	0.136787i	$-0.0436776\pi$
$600$	−3.84904e10	−	1.96791e10i	−0.296993	−	0.151845i
$601$	−2.87646e10			−0.220476			−0.110238	−	0.993905i	$-0.535161\pi$
$601$	−2.87646e10			−0.220476			−0.110238	+	0.993905i	$0.535161\pi$
$602$		−	6.64521e8i		−	0.00505968i
$603$	1.44864e11	+	2.00555e11i	1.09570	+	1.51693i
$604$	3.48678e10			0.261985
$605$		−	1.01249e10i		−	0.0755734i
$606$	−2.62781e10	+	5.13975e10i	−0.194851	+	0.381111i
$607$	1.60002e11			1.17861			0.589305	−	0.807910i	$-0.299402\pi$
$607$	1.60002e11			1.17861			0.589305	+	0.807910i	$0.299402\pi$
$608$		−	1.87546e9i		−	0.0137244i
$609$	−1.94802e11	−	9.95967e10i	−1.41620	−	0.724062i
$610$	−1.17157e11			−0.846150
$611$		−	2.93154e10i		−	0.210345i
$612$	−1.76601e10	+	1.27562e10i	−0.125889	+	0.0909318i
$613$	7.25734e10			0.513968			0.256984	−	0.966416i	$-0.417271\pi$
$613$	7.25734e10			0.513968			0.256984	+	0.966416i	$0.417271\pi$
$614$			1.42364e11i			1.00167i
$615$	9.51652e10	−	1.86134e11i	0.665239	−	1.30114i
$616$	7.70527e10			0.535137
$617$		−	2.78669e11i		−	1.92286i	−0.275051	−	0.961430i	$-0.588695\pi$
$617$		−	2.78669e11i		−	1.92286i	0.275051	−	0.961430i	$-0.411305\pi$
$618$	−2.10010e11	−	1.07372e11i	−1.43975	−	0.736104i
$619$	−8.02240e8			−0.00546439			−0.00273220	−	0.999996i	$-0.500870\pi$
$619$	−8.02240e8			−0.00546439			−0.00273220	+	0.999996i	$0.500870\pi$
$620$			4.27180e10i			0.289097i
$621$	1.23239e10	+	7.99603e10i	0.0828669	+	0.537660i
$622$	1.83309e11			1.22468
$623$			1.30879e11i			0.868794i
$624$	7.10858e10	−	1.39037e11i	0.468861	−	0.917048i
$625$	−9.08868e10			−0.595636
$626$		−	1.67692e11i		−	1.09198i
$627$	−1.25298e9	−	6.40613e8i	−0.00810724	−	0.00414501i
$628$	6.51502e9			0.0418868
$629$		−	3.15013e10i		−	0.201245i
$630$	1.10435e11	+	1.52890e11i	0.701041	+	0.970546i
$631$	2.42886e11			1.53209			0.766047	−	0.642785i	$-0.222221\pi$
$631$	2.42886e11			1.53209			0.766047	+	0.642785i	$0.222221\pi$
$632$		−	2.95084e11i		−	1.84960i
$633$	−1.62290e10	+	3.17424e10i	−0.101083	+	0.197708i
$634$	2.09225e11			1.29496
$635$		−	2.49630e11i		−	1.53533i
$636$	−3.56326e10	−	1.82179e10i	−0.217780	−	0.111345i
$637$	−4.04441e11			−2.45639
$638$		−	4.23517e10i		−	0.255616i
$639$	−4.49088e10	+	3.24383e10i	−0.269357	+	0.194561i
$640$	−7.24788e10			−0.432007
$641$			1.74837e11i			1.03562i	0.855496	+	0.517810i	$0.173253\pi$
$641$			1.74837e11i			1.03562i	−0.855496	+	0.517810i	$0.826747\pi$
$642$	−8.39864e10	+	1.64269e11i	−0.494389	+	0.966977i
$643$	2.47853e10			0.144994			0.0724969	−	0.997369i	$-0.476903\pi$
$643$	2.47853e10			0.144994			0.0724969	+	0.997369i	$0.476903\pi$
$644$			3.57396e10i			0.207781i
$645$	−4.50062e8	−	2.30104e8i	−0.00260036	−	0.00132949i
$646$	−3.07970e9			−0.0176839
$647$			8.78637e10i			0.501409i	0.968064	+	0.250705i	$0.0806623\pi$
$647$			8.78637e10i			0.501409i	−0.968064	+	0.250705i	$0.919338\pi$
$648$	1.80731e11	+	5.98328e10i	1.02502	+	0.339343i
$649$	−1.20720e10			−0.0680454
$650$			6.97302e10i			0.390632i
$651$	−2.01151e11	+	3.93432e11i	−1.11995	+	2.19051i
$652$	−3.12910e10			−0.173153
$653$		−	2.32111e11i		−	1.27657i	−0.769802	−	0.638283i	$-0.779645\pi$
$653$		−	2.32111e11i		−	1.27657i	0.769802	−	0.638283i	$-0.220355\pi$
$654$	4.98187e10	+	2.54709e10i	0.272321	+	0.139230i
$655$	−1.27815e11			−0.694409
$656$			2.32323e11i			1.25452i
$657$	−5.56367e10	−	7.70254e10i	−0.298607	−	0.413402i
$658$	−3.93485e10			−0.209906
$659$		−	1.98567e10i		−	0.105285i	−0.998613	−	0.0526423i	$-0.983236\pi$
$659$		−	1.98567e10i		−	0.105285i	0.998613	−	0.0526423i	$-0.0167643\pi$
$660$	5.03063e9	−	9.83943e9i	0.0265123	−	0.0518554i
$661$	−1.35925e11			−0.712022			−0.356011	−	0.934482i	$-0.615863\pi$
$661$	−1.35925e11			−0.712022			−0.356011	+	0.934482i	$0.615863\pi$
$662$			4.79327e10i			0.249574i
$663$	1.65944e11	+	8.48427e10i	0.858832	+	0.439097i
$664$	3.04987e11			1.56895
$665$		−	8.07029e9i		−	0.0412669i
$666$	−4.20754e10	+	3.03917e10i	−0.213861	+	0.154475i
$667$	1.04187e11			0.526393
$668$			4.23650e10i			0.212766i
$669$	−1.01218e11	+	1.97974e11i	−0.505307	+	0.988332i
$670$	−2.74647e11			−1.36294
$671$			7.10068e10i			0.350275i
$672$	1.35642e11	+	6.93501e10i	0.665147	+	0.340071i
$673$	−5.50037e10			−0.268122			−0.134061	−	0.990973i	$-0.542802\pi$
$673$	−5.50037e10			−0.268122			−0.134061	+	0.990973i	$0.542802\pi$
$674$		−	1.81396e11i		−	0.878996i
$675$	−6.33832e10	+	9.76895e9i	−0.305323	+	0.0470579i
$676$	5.25433e10			0.251612
$677$		−	3.65063e10i		−	0.173785i	−0.996218	−	0.0868926i	$-0.972306\pi$
$677$		−	3.65063e10i		−	0.173785i	0.996218	−	0.0868926i	$-0.0276937\pi$
$678$	−9.44712e9	+	1.84777e10i	−0.0447075	+	0.0874437i
$679$	2.66741e11			1.25490
$680$		−	1.28268e11i		−	0.599904i
$681$	−1.15648e11	−	5.91278e10i	−0.537714	−	0.274918i
$682$	−8.55357e10			−0.395376
$683$			2.83554e11i			1.30303i	0.758637	+	0.651513i	$0.225866\pi$
$683$			2.83554e11i			1.30303i	−0.758637	+	0.651513i	$0.774134\pi$
$684$	−8.99357e8	−	1.24510e9i	−0.00410873	−	0.00568828i
$685$	1.78118e11			0.808995
$686$			2.23912e11i			1.01107i
$687$	8.99224e10	−	1.75880e11i	0.403683	−	0.789566i
$688$	5.61745e8			0.00250718
$689$			3.42371e11i			1.51922i
$690$	−7.99682e10	−	4.08855e10i	−0.352794	−	0.180374i
$691$	−1.98471e11			−0.870530			−0.435265	−	0.900302i	$-0.643345\pi$
$691$	−1.98471e11			−0.870530			−0.435265	+	0.900302i	$0.643345\pi$
$692$		−	2.49275e10i		−	0.108706i
$693$	9.26641e10	−	6.69327e10i	0.401771	−	0.290206i
$694$	−1.31899e11			−0.568595
$695$			5.64522e9i			0.0241959i
$696$	1.11605e11	−	2.18289e11i	0.475605	−	0.930239i
$697$	−2.77284e11			−1.17488
$698$		−	9.18026e10i		−	0.386753i
$699$	−1.54171e11	−	7.88234e10i	−0.645794	−	0.330177i
$700$	−2.83302e10			−0.117993
$701$		−	2.79144e10i		−	0.115600i	−0.998328	−	0.0577999i	$-0.981591\pi$
$701$		−	2.79144e10i		−	0.115600i	0.998328	−	0.0577999i	$-0.0184085\pi$
$702$	−4.67772e10	−	3.03502e11i	−0.192613	−	1.24972i
$703$	2.22095e9			0.00909322
$704$			8.23443e10i			0.335230i
$705$	−1.36253e10	+	2.66497e10i	−0.0551554	+	0.107879i
$706$	−5.01600e10			−0.201901
$707$			2.00641e11i			0.803050i
$708$	−1.17316e10	−	5.99804e9i	−0.0466900	−	0.0238713i
$709$	−2.13247e11			−0.843913			−0.421956	−	0.906616i	$-0.638656\pi$
$709$	−2.13247e11			−0.843913			−0.421956	+	0.906616i	$0.638656\pi$
$710$		−	6.14997e10i		−	0.242014i
$711$	−2.56328e11	−	3.54870e11i	−1.00304	−	1.38864i
$712$	−1.46659e11			−0.570674
$713$		−	2.10422e11i		−	0.814203i
$714$	1.13880e11	−	2.22738e11i	0.438182	−	0.857042i
$715$	−9.45410e10			−0.361740
$716$			4.99518e10i			0.190064i
$717$	2.74729e11	+	1.40461e11i	1.03951	+	0.531472i
$718$	−2.78660e11			−1.04852
$719$			2.75685e10i			0.103157i	0.998669	+	0.0515785i	$0.0164252\pi$
$719$			2.75685e10i			0.103157i	−0.998669	+	0.0515785i	$0.983575\pi$
$720$	−1.29244e11	+	9.33547e10i	−0.480927	+	0.347381i
$721$	−8.19822e11			−3.03374
$722$			2.37866e11i			0.875353i
$723$	−5.26664e10	+	1.03011e11i	−0.192744	+	0.376989i
$724$	1.77748e10			0.0646918
$725$			8.25874e10i			0.298925i
$726$	1.97019e10	+	1.00730e10i	0.0709187	+	0.0362588i
$727$	4.35710e11			1.55977			0.779883	−	0.625925i	$-0.215279\pi$
$727$	4.35710e11			1.55977			0.779883	+	0.625925i	$0.215279\pi$
$728$		−	7.19478e11i		−	2.56149i
$729$	2.69323e11	−	8.50389e10i	0.953593	−	0.301098i
$730$	1.05481e11			0.371436
$731$			6.70457e8i			0.00234802i
$732$	−3.52803e10	+	6.90048e10i	−0.122882	+	0.240345i
$733$	4.32110e11			1.49685			0.748426	−	0.663219i	$-0.230810\pi$
$733$	4.32110e11			1.49685			0.748426	+	0.663219i	$0.230810\pi$
$734$		−	9.86702e10i		−	0.339939i
$735$	3.67665e11	+	1.87977e11i	1.25980	+	0.644102i
$736$	−7.25464e10			−0.247232
$737$			1.66459e11i			0.564207i
$738$	2.67517e11	+	3.70361e11i	0.901834	+	1.24853i
$739$	3.83614e11			1.28622			0.643111	−	0.765773i	$-0.277643\pi$
$739$	3.83614e11			1.28622			0.643111	+	0.765773i	$0.277643\pi$
$740$			1.74408e10i			0.0581620i
$741$	−5.98171e9	+	1.16997e10i	−0.0198405	+	0.0388061i
$742$	4.59547e11			1.51605
$743$		−	3.37129e11i		−	1.10622i	−0.833109	−	0.553109i	$-0.813441\pi$
$743$		−	3.37129e11i		−	1.10622i	0.833109	−	0.553109i	$-0.186559\pi$
$744$	−4.40868e11	−	2.25404e11i	−1.43885	−	0.735646i
$745$	4.09041e11			1.32783
$746$		−	1.60428e11i		−	0.517995i
$747$	3.66779e11	−	2.64931e11i	1.17794	−	0.850844i
$748$	−1.46578e10			−0.0468234
$749$			6.41262e11i			2.03755i
$750$	1.37318e11	−	2.68581e11i	0.433993	−	0.848850i
$751$	−2.24773e11			−0.706618			−0.353309	−	0.935507i	$-0.614944\pi$
$751$	−2.24773e11			−0.706618			−0.353309	+	0.935507i	$0.614944\pi$
$752$		−	3.32628e10i		−	0.104013i
$753$	−2.85974e11	−	1.46211e11i	−0.889502	−	0.454778i
$754$	−3.95458e11			−1.22353
$755$			3.04558e11i			0.937309i
$756$	1.23308e11	−	1.90048e10i	0.377487	−	0.0581803i
$757$	−2.91254e11			−0.886927			−0.443464	−	0.896292i	$-0.646250\pi$
$757$	−2.91254e11			−0.886927			−0.443464	+	0.896292i	$0.646250\pi$
$758$		−	1.14933e11i		−	0.348151i
$759$	−2.47801e10	+	4.84675e10i	−0.0746682	+	0.146044i
$760$	9.04332e9			0.0271065
$761$			5.05091e11i			1.50602i	0.658008	+	0.753011i	$0.271399\pi$
$761$			5.05091e11i			1.50602i	−0.658008	+	0.753011i	$0.728601\pi$
$762$	4.85750e11	+	2.48351e11i	1.44076	+	0.736623i
$763$	1.94478e11			0.573816
$764$			1.16068e11i			0.340674i
$765$	−1.11421e11	−	1.54256e11i	−0.325329	−	0.450396i
$766$	3.77512e11			1.09652
$767$			1.12722e11i			0.325706i
$768$	−1.03973e11	+	2.03361e11i	−0.298865	+	0.584551i
$769$	5.39233e11			1.54195			0.770977	−	0.636863i	$-0.219768\pi$
$769$	5.39233e11			1.54195			0.770977	+	0.636863i	$0.219768\pi$
$770$			1.26897e11i			0.360986i
$771$	−1.10308e10	−	5.63977e9i	−0.0312170	−	0.0159604i
$772$	−2.36774e10			−0.0666600
$773$		−	6.68064e11i		−	1.87111i	−0.353176	−	0.935557i	$-0.614898\pi$
$773$		−	6.68064e11i		−	1.87111i	0.353176	−	0.935557i	$-0.385102\pi$
$774$	8.95512e8	−	6.46842e8i	0.00249521	−	0.00180233i
$775$	1.66798e11			0.462364
$776$			2.98901e11i			0.824292i
$777$	−8.21253e10	+	1.60629e11i	−0.225317	+	0.440698i
$778$	−2.94023e11			−0.802533
$779$		−	1.95495e10i		−	0.0530867i
$780$	−9.18756e10	−	4.69734e10i	−0.248211	−	0.126904i
$781$	−3.72740e10			−0.100185
$782$			1.19129e11i			0.318558i
$783$	−5.54022e10	−	3.59463e11i	−0.147394	−	0.956328i
$784$	−4.58901e11			−1.21466
$785$			5.69065e10i			0.149859i
$786$	1.27160e11	−	2.48712e11i	0.333165	−	0.651639i
$787$	4.63331e11			1.20779			0.603897	−	0.797063i	$-0.293614\pi$
$787$	4.63331e11			1.20779			0.603897	+	0.797063i	$0.293614\pi$
$788$		−	5.83111e10i		−	0.151233i
$789$	−6.34850e11	−	3.24581e11i	−1.63819	−	0.837560i
$790$	4.85972e11			1.24768
$791$			7.21317e10i			0.184255i
$792$	7.50028e10	+	1.03837e11i	0.190624	+	0.263906i
$793$	6.63025e11			1.67663
$794$			5.70463e10i			0.143531i
$795$	1.59128e11	−	3.11239e11i	0.398361	−	0.779157i
$796$	5.74147e10			0.143011
$797$		−	1.44672e11i		−	0.358551i	−0.983799	−	0.179276i	$-0.942625\pi$
$797$		−	1.44672e11i		−	0.358551i	0.983799	−	0.179276i	$-0.0573754\pi$
$798$	1.57038e10	+	8.02894e9i	0.0387252	+	0.0197991i
$799$	3.97000e10			0.0974101
$800$		−	5.75063e10i		−	0.140396i
$801$	−1.76373e11	+	1.27397e11i	−0.428451	+	0.309477i
$802$	−4.22903e11			−1.02222
$803$		−	6.39306e10i		−	0.153761i
$804$	−8.27067e10	+	1.61766e11i	−0.197932	+	0.387136i
$805$	−3.12173e11			−0.743383
$806$			7.98689e11i			1.89251i
$807$	−2.06756e11	−	1.05709e11i	−0.487488	−	0.249239i
$808$	−2.24833e11			−0.527490
$809$		−	3.44070e11i		−	0.803253i	−0.915804	−	0.401627i	$-0.868445\pi$
$809$		−	3.44070e11i		−	0.803253i	0.915804	−	0.401627i	$-0.131555\pi$
$810$	−9.85382e10	+	2.97645e11i	−0.228910	+	0.691446i
$811$	2.79089e11			0.645149			0.322574	−	0.946544i	$-0.395452\pi$
$811$	2.79089e11			0.645149			0.322574	+	0.946544i	$0.395452\pi$
$812$		−	1.60668e11i		−	0.369577i
$813$	−5.64630e9	+	1.10436e10i	−0.0129242	+	0.0252784i
$814$	−3.49223e10			−0.0795436
$815$		−	2.73316e11i		−	0.619491i
$816$	1.88289e11	+	9.62671e10i	0.424683	+	0.217129i
$817$	−4.72696e7			−0.000106095
$818$			1.34017e11i			0.299327i
$819$	−6.24983e11	−	8.65249e11i	−1.38910	−	1.92312i
$820$	1.53519e11			0.339553
$821$			3.46373e11i			0.762379i	0.924497	+	0.381190i	$0.124486\pi$
$821$			3.46373e11i			0.762379i	−0.924497	+	0.381190i	$0.875514\pi$
$822$	−1.77205e11	+	3.46597e11i	−0.388141	+	0.759167i
$823$	−5.60299e11			−1.22129			−0.610647	−	0.791903i	$-0.709091\pi$
$823$	−5.60299e11			−1.22129			−0.610647	+	0.791903i	$0.709091\pi$
$824$		−	9.18668e11i		−	1.99273i
$825$	−3.84194e10	−	1.96428e10i	−0.0829343	−	0.0424020i
$826$	1.51300e11			0.325027
$827$		−	2.54796e11i		−	0.544717i	−0.962196	−	0.272359i	$-0.912196\pi$
$827$		−	2.54796e11i		−	0.544717i	0.962196	−	0.272359i	$-0.0878037\pi$
$828$	−4.81628e10	+	3.47888e10i	−0.102469	+	0.0740147i
$829$	−4.42641e11			−0.937202			−0.468601	−	0.883410i	$-0.655242\pi$
$829$	−4.42641e11			−0.937202			−0.468601	+	0.883410i	$0.655242\pi$
$830$			5.02281e11i			1.05836i
$831$	2.65953e11	−	5.20180e11i	0.557701	−	1.09081i
$832$	7.68889e11			1.60461
$833$		−	5.47710e11i		−	1.13755i
$834$	−1.09849e10	−	5.61629e9i	−0.0227056	−	0.0116088i
$835$	−3.70044e11			−0.761216
$836$		−	1.03343e9i		−	0.00211570i
$837$	−7.25990e11	+	1.11893e11i	−1.47921	+	0.227983i
$838$	−7.45229e11			−1.51117
$839$			3.82430e11i			0.771798i	0.922541	+	0.385899i	$0.126109\pi$
$839$			3.82430e11i			0.771798i	−0.922541	+	0.385899i	$0.873891\pi$
$840$	−3.34400e11	+	6.54054e11i	−0.671659	+	1.31370i
$841$	3.18720e10			0.0637126
$842$			5.89903e11i			1.17363i
$843$	2.72544e11	+	1.39344e11i	0.539668	+	0.275917i
$844$	−2.61804e10			−0.0515949
$845$			4.58949e11i			0.900196i
$846$	−3.83017e10	−	5.30263e10i	−0.0747716	−	0.103517i
$847$	7.69106e10			0.149435
$848$			3.88473e11i			0.751237i
$849$	−8.55243e10	+	1.67277e11i	−0.164611	+	0.321963i
$850$	−9.44313e10			−0.180901
$851$		−	8.59105e10i		−	0.163805i
$852$	−3.62231e10	−	1.85199e10i	−0.0687428	−	0.0351463i
$853$	−4.73895e11			−0.895131			−0.447565	−	0.894251i	$-0.647709\pi$
$853$	−4.73895e11			−0.895131			−0.447565	+	0.894251i	$0.647709\pi$
$854$		−	8.89943e11i		−	1.67313i
$855$	1.08756e10	−	7.85559e9i	0.0203511	−	0.0146999i
$856$	−7.18578e11			−1.33838
$857$			5.97480e11i			1.10764i	0.832635	+	0.553822i	$0.186831\pi$
$857$			5.97480e11i			1.10764i	−0.832635	+	0.553822i	$0.813169\pi$
$858$	9.40566e10	−	1.83966e11i	0.173556	−	0.339459i
$859$	−7.68905e11			−1.41221			−0.706107	−	0.708105i	$-0.749550\pi$
$859$	−7.68905e11			−1.41221			−0.706107	+	0.708105i	$0.749550\pi$
$860$		−	3.71201e8i		−	0.000678602i
$861$	1.41391e12	+	7.22893e11i	2.57282	+	1.31541i
$862$	7.62406e11			1.38088
$863$			1.00737e12i			1.81613i	0.418828	+	0.908066i	$0.362441\pi$
$863$			1.00737e12i			1.81613i	−0.418828	+	0.908066i	$0.637559\pi$
$864$	3.85771e10	+	2.50297e11i	0.0692268	+	0.449160i
$865$	2.17734e11			0.388921
$866$		−	9.41934e11i		−	1.67474i
$867$	1.42321e11	−	2.78367e11i	0.251880	−	0.492653i
$868$	−3.24494e11			−0.571646
$869$		−	2.94540e11i		−	0.516493i
$870$	3.59498e11	+	1.83802e11i	0.627509	+	0.320828i
$871$	1.55431e12			2.70063
$872$			2.17927e11i			0.376916i
$873$	2.59644e11	+	3.59461e11i	0.447015	+	0.618863i
$874$	−8.39899e9			−0.0143940
$875$		−	1.04847e12i		−	1.78864i
$876$	3.17644e10	−	6.21281e10i	0.0539417	−	0.105505i
$877$	−4.62619e11			−0.782033			−0.391016	−	0.920384i	$-0.627876\pi$
$877$	−4.62619e11			−0.782033			−0.391016	+	0.920384i	$0.627876\pi$
$878$		−	3.77154e11i		−	0.634659i
$879$	5.67544e11	+	2.90170e11i	0.950702	+	0.486068i
$880$	−1.07271e11			−0.178876
$881$		−	1.11487e12i		−	1.85064i	−0.379187	−	0.925320i	$-0.623796\pi$
$881$		−	1.11487e12i		−	1.85064i	0.379187	−	0.925320i	$-0.376204\pi$
$882$	−7.31562e11	+	5.28419e11i	−1.20886	+	0.873180i
$883$	−7.86791e11			−1.29425			−0.647123	−	0.762386i	$-0.724028\pi$
$883$	−7.86791e11			−1.29425			−0.647123	+	0.762386i	$0.724028\pi$
$884$			1.36867e11i			0.224125i
$885$	5.23909e10	−	1.02472e11i	0.0854049	−	0.167044i
$886$	−5.66784e10			−0.0919778
$887$			8.48282e11i			1.37039i	0.728358	+	0.685197i	$0.240284\pi$
$887$			8.48282e11i			1.37039i	−0.728358	+	0.685197i	$0.759716\pi$
$888$	−1.79996e11	−	9.20272e10i	−0.289476	−	0.148001i
$889$	1.89623e12			3.03588
$890$		−	2.41531e11i		−	0.384958i
$891$	1.80398e11	+	5.97225e10i	0.286233	+	0.0947604i
$892$	−1.63284e11			−0.257920
$893$			2.79899e9i			0.00440145i
$894$	−4.06945e11	+	7.95945e11i	−0.637067	+	1.24604i
$895$	−4.36313e11			−0.679995
$896$		−	5.50562e11i		−	0.854229i
$897$	4.52564e11	+	2.31384e11i	0.699053	+	0.357407i
$898$	−8.93674e11			−1.37428
$899$			9.45954e11i			1.44821i
$900$	−2.75765e10	−	3.81779e10i	−0.0420310	−	0.0581892i
$901$	−4.63652e11			−0.703547
$902$			3.07397e11i			0.464380i
$903$	1.74791e9	−	3.41875e9i	0.00262887	−	0.00514182i
$904$	−8.08286e10			−0.121029
$905$			1.55257e11i			0.231449i
$906$	−5.92635e11	−	3.02998e11i	−0.879578	−	0.449704i
$907$	−5.84653e11			−0.863911			−0.431956	−	0.901895i	$-0.642176\pi$
$907$	−5.84653e11			−0.863911			−0.431956	+	0.901895i	$0.642176\pi$
$908$		−	9.53841e10i		−	0.140324i
$909$	−2.70385e11	+	1.95304e11i	−0.396029	+	0.286058i
$910$	1.18490e12			1.72789
$911$		−	3.41329e11i		−	0.495564i	−0.968816	−	0.247782i	$-0.920298\pi$
$911$		−	3.41329e11i		−	0.495564i	0.968816	−	0.247782i	$-0.0797016\pi$
$912$	−6.78717e9	+	1.32750e10i	−0.00981091	+	0.0191892i
$913$	3.04424e11			0.438123
$914$			2.61511e10i			0.0374718i
$915$	−6.02734e11	−	3.08161e11i	−0.859887	−	0.439637i
$916$	1.45061e11			0.206049
$917$		−	9.70903e11i		−	1.37309i
$918$	4.11013e11	−	6.33475e10i	0.578742	−	0.0891987i
$919$	1.02519e12			1.43728			0.718642	−	0.695380i	$-0.244764\pi$
$919$	1.02519e12			1.43728			0.718642	+	0.695380i	$0.244764\pi$
$920$		−	3.49812e11i		−	0.488297i
$921$	−3.74465e11	+	7.32418e11i	−0.520442	+	1.01794i
$922$	2.04342e11			0.282770
$923$			3.48045e11i			0.479545i
$924$	7.47421e10	+	3.82136e10i	0.102536	+	0.0524240i
$925$	6.80998e10			0.0930206
$926$			5.61652e11i			0.763877i
$927$	−7.98012e11	−	1.10480e12i	−1.08066	−	1.49611i
$928$	3.26133e11			0.439747
$929$		−	8.52331e11i		−	1.14431i	−0.820144	−	0.572157i	$-0.806107\pi$
$929$		−	8.52331e11i		−	1.14431i	0.820144	−	0.572157i	$-0.193893\pi$
$930$	3.71215e11	−	7.26062e11i	0.496243	−	0.970603i
$931$	3.86155e10			0.0513999
$932$		−	1.27157e11i		−	0.168529i
$933$	9.43067e11	+	4.82164e11i	1.24456	+	0.636309i
$934$	−6.82876e11			−0.897334
$935$		−	1.28031e11i		−	0.167521i
$936$	9.69572e11	−	7.00338e11i	1.26321	−	0.912439i
$937$	6.13489e11			0.795881			0.397941	−	0.917411i	$-0.369725\pi$
$937$	6.13489e11			0.795881			0.397941	+	0.917411i	$0.369725\pi$
$938$		−	2.08627e12i		−	2.69501i
$939$	4.41087e11	−	8.62723e11i	0.567364	−	1.10971i
$940$	−2.19801e10			−0.0281525
$941$		−	4.18991e11i		−	0.534375i	−0.963645	−	0.267187i	$-0.913906\pi$
$941$		−	4.18991e11i		−	0.534375i	0.963645	−	0.267187i	$-0.0860942\pi$
$942$	−1.10733e11	−	5.66150e10i	−0.140629	−	0.0718998i
$943$	−7.56210e11			−0.956304
$944$			1.27900e11i			0.161058i
$945$	1.66001e11	+	1.07705e12i	0.208153	+	1.35054i
$946$	7.43269e8			0.000928071
$947$			4.33363e11i			0.538830i	0.963024	+	0.269415i	$0.0868303\pi$
$947$			4.33363e11i			0.538830i	−0.963024	+	0.269415i	$0.913170\pi$
$948$	1.46344e11	−	2.86235e11i	0.181193	−	0.354397i
$949$	−5.96951e11			−0.735993
$950$		−	6.65774e9i		−	0.00817396i
$951$	1.07640e12	+	5.50333e11i	1.31598	+	0.672827i
$952$	9.74345e11			1.18622
$953$		−	5.22908e11i		−	0.633948i	−0.948434	−	0.316974i	$-0.897333\pi$
$953$		−	5.22908e11i		−	0.633948i	0.948434	−	0.316974i	$-0.102667\pi$
$954$	4.47321e11	+	6.19288e11i	0.540040	+	0.747651i
$955$	−1.01382e12			−1.21884
$956$			2.26590e11i			0.271275i
$957$	1.11399e11	−	2.17886e11i	0.132811	−	0.259766i
$958$	4.24276e11			0.503717
$959$			1.35302e12i			1.59966i
$960$	−6.98972e11	−	3.57365e11i	−0.822952	−	0.420753i
$961$	1.05761e12			1.24003
$962$			3.26087e11i			0.380744i
$963$	−8.64167e11	+	6.24202e11i	−1.00483	+	0.725805i
$964$	−8.49607e10			−0.0983807
$965$		−	2.06815e11i		−	0.238491i
$966$	3.10574e11	−	6.07453e11i	0.356662	−	0.697596i
$967$	−7.07165e11			−0.808751			−0.404376	−	0.914593i	$-0.632511\pi$
$967$	−7.07165e11			−0.808751			−0.404376	+	0.914593i	$0.632511\pi$
$968$			8.61837e10i			0.0981575i
$969$	−1.58441e10	−	8.10066e9i	−0.0179710	−	0.00918809i
$970$	−4.92259e11			−0.556040
$971$			9.06578e11i			1.01983i	0.860224	+	0.509916i	$0.170323\pi$
$971$			9.06578e11i			1.01983i	−0.860224	+	0.509916i	$0.829677\pi$
$972$	1.45638e11	+	1.47671e11i	0.163159	+	0.165436i
$973$	−4.28821e10			−0.0478437
$974$			2.94058e11i			0.326736i
$975$	−1.83414e11	+	3.58740e11i	−0.202962	+	0.396974i
$976$	7.52303e11			0.829074
$977$		−	1.25294e11i		−	0.137516i	−0.997633	−	0.0687581i	$-0.978096\pi$
$977$		−	1.25294e11i		−	0.137516i	0.997633	−	0.0687581i	$-0.0219037\pi$
$978$	5.31842e11	+	2.71916e11i	0.581336	+	0.297221i
$979$	−1.46388e11			−0.159359
$980$			3.03241e11i			0.328764i
$981$	1.89305e11	+	2.62080e11i	0.204402	+	0.282981i
$982$	−1.12284e12			−1.20745
$983$		−	1.25573e12i		−	1.34487i	−0.740155	−	0.672436i	$-0.765248\pi$
$983$		−	1.25573e12i		−	1.34487i	0.740155	−	0.672436i	$-0.234752\pi$
$984$	−8.10052e11	+	1.58438e12i	−0.864037	+	1.68997i
$985$	5.09328e11			0.541069
$986$		−	5.35544e11i		−	0.566615i
$987$	−2.02436e11	−	1.03500e11i	−0.213314	−	0.109061i
$988$	−9.64961e9			−0.0101270
$989$			1.82847e9i			0.00191119i
$990$	−1.71008e11	+	1.23522e11i	−0.178022	+	0.128588i
$991$	−1.20264e12			−1.24693			−0.623463	−	0.781852i	$-0.714275\pi$
$991$	−1.20264e12			−1.24693			−0.623463	+	0.781852i	$0.714275\pi$
$992$		−	6.58676e11i		−	0.680182i
$993$	−1.26079e11	+	2.46599e11i	−0.129672	+	0.253626i
$994$	4.67163e11			0.478545
$995$			5.01498e11i			0.511655i
$996$	2.95842e11	+	1.51256e11i	0.300623	+	0.153700i
$997$	−1.38817e11			−0.140495			−0.0702475	−	0.997530i	$-0.522379\pi$
$997$	−1.38817e11			−0.140495			−0.0702475	+	0.997530i	$0.522379\pi$
$998$			1.00460e12i			1.01267i
$999$	−2.96405e11	+	4.56835e10i	−0.297594	+	0.0458667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.9.b.a.23.8	✓	26
3.2	odd	2	inner	33.9.b.a.23.19	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.9.b.a.23.8	✓	26	1.1	even	1	trivial
33.9.b.a.23.19	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)

\(f(q)\)	\(=\)	\(q-14.0184i q^{2} +(36.8732 - 72.1205i) q^{3} +59.4833 q^{4} +519.567i q^{5} +(-1011.02 - 516.905i) q^{6} -3946.73 q^{7} -4422.58i q^{8} +(-3841.73 - 5318.63i) q^{9} +O(q^{10})\)	\(q-14.0184i q^{2} +(36.8732 - 72.1205i) q^{3} +59.4833 q^{4} +519.567i q^{5} +(-1011.02 - 516.905i) q^{6} -3946.73 q^{7} -4422.58i q^{8} +(-3841.73 - 5318.63i) q^{9} +7283.52 q^{10} -4414.43i q^{11} +(2193.34 - 4289.97i) q^{12} -41219.6 q^{13} +55327.0i q^{14} +(37471.4 + 19158.1i) q^{15} -46770.0 q^{16} -55821.2i q^{17} +(-74558.9 + 53855.1i) q^{18} +3935.59 q^{19} +30905.6i q^{20} +(-145529. + 284640. i) q^{21} -61883.4 q^{22} -152236. i q^{23} +(-318959. - 163075. i) q^{24} +120675. q^{25} +577835. i q^{26} +(-525239. + 80952.6i) q^{27} -234765. q^{28} +684379. i q^{29} +(268567. - 525291. i) q^{30} +1.38221e6 q^{31} -476539. i q^{32} +(-318371. - 162774. i) q^{33} -782526. q^{34} -2.05059e6i q^{35} +(-228519. - 316370. i) q^{36} +564324. q^{37} -55170.9i q^{38} +(-1.51990e6 + 2.97278e6i) q^{39} +2.29783e6 q^{40} -4.96736e6i q^{41} +(3.99021e6 + 2.04008e6i) q^{42} -12010.8 q^{43} -262585. i q^{44} +(2.76339e6 - 1.99604e6i) q^{45} -2.13411e6 q^{46} +711200. i q^{47} +(-1.72456e6 + 3.37308e6i) q^{48} +9.81186e6 q^{49} -1.69167e6i q^{50} +(-4.02585e6 - 2.05831e6i) q^{51} -2.45188e6 q^{52} -8.30602e6i q^{53} +(1.13483e6 + 7.36303e6i) q^{54} +2.29359e6 q^{55} +1.74547e7i q^{56} +(145118. - 283837. i) q^{57} +9.59392e6 q^{58} -2.73466e6i q^{59} +(2.22893e6 + 1.13959e6i) q^{60} -1.60852e7 q^{61} -1.93764e7i q^{62} +(1.51623e7 + 2.09912e7i) q^{63} -1.86535e7 q^{64} -2.14164e7i q^{65} +(-2.28184e6 + 4.46306e6i) q^{66} -3.77081e7 q^{67} -3.32043e6i q^{68} +(-1.09793e7 - 5.61343e6i) q^{69} -2.87461e7 q^{70} -8.44368e6i q^{71} +(-2.35221e7 + 1.69904e7i) q^{72} +1.44822e7 q^{73} -7.91095e6i q^{74} +(4.44967e6 - 8.70314e6i) q^{75} +234102. q^{76} +1.74225e7i q^{77} +(4.16738e7 + 2.13066e7i) q^{78} +6.67221e7 q^{79} -2.43002e7i q^{80} +(-1.35289e7 + 4.08655e7i) q^{81} -6.96346e7 q^{82} +6.89613e7i q^{83} +(-8.65652e6 + 1.69313e7i) q^{84} +2.90029e7 q^{85} +168373. i q^{86} +(4.93577e7 + 2.52353e7i) q^{87} -1.95232e7 q^{88} -3.31613e7i q^{89} +(-2.79813e7 - 3.87384e7i) q^{90} +1.62683e8 q^{91} -9.05550e6i q^{92} +(5.09665e7 - 9.96856e7i) q^{93} +9.96991e6 q^{94} +2.04480e6i q^{95} +(-3.43682e7 - 1.75715e7i) q^{96} -6.75853e7 q^{97} -1.37547e8i q^{98} +(-2.34787e7 + 1.69590e7i) 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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