LMFDB - Embedded newform 81.11.d.d.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,11,Mod(26,81)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("81.26");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	81.d (of order $6$, degree $2$, not 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:	$51.4639374666$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.2
Root			$1.93649 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	81.26
Dual form			81.11.d.d.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(23.2379 + 13.4164i) q^{2} +(-152.000 - 263.272i) q^{4} +(2463.22 - 1422.14i) q^{5} +(-8617.00 + 14925.1i) q^{7} -35634.0i q^{8} +O(q^{10})$	\(q+(23.2379 + 13.4164i) q^{2} +(-152.000 - 263.272i) q^{4} +(2463.22 - 1422.14i) q^{5} +(-8617.00 + 14925.1i) q^{7} -35634.0i q^{8} +76320.0 q^{10} +(-161782. - 93405.0i) q^{11} +(84827.0 + 146925. i) q^{13} +(-400482. + 231218. i) q^{14} +(322432. - 558469. i) q^{16} +343245. i q^{17} -949462. q^{19} +(-748818. - 432330. i) q^{20} +(-2.50632e6 - 4.34107e6i) q^{22} +(-2.30157e6 + 1.32881e6i) q^{23} +(-837852. + 1.45120e6i) q^{25} +4.55229e6i q^{26} +5.23914e6 q^{28} +(2.75588e6 + 1.59111e6i) q^{29} +(1.48966e7 + 2.58016e7i) q^{31} +(-1.66153e7 + 9.59284e6i) q^{32} +(-4.60512e6 + 7.97630e6i) q^{34} +4.90183e7i q^{35} -6.08118e7 q^{37} +(-2.20635e7 - 1.27384e7i) q^{38} +(-5.06765e7 - 8.77742e7i) q^{40} +(-1.57329e8 + 9.08341e7i) q^{41} +(-5.37099e7 + 9.30282e7i) q^{43} +5.67903e7i q^{44} -7.13117e7 q^{46} +(-2.32091e8 - 1.33998e8i) q^{47} +(-7.26775e6 - 1.25881e7i) q^{49} +(-3.89399e7 + 2.24819e7i) q^{50} +(2.57874e7 - 4.46651e7i) q^{52} -1.92091e8i q^{53} -5.31340e8 q^{55} +(5.31840e8 + 3.07058e8i) q^{56} +(4.26938e7 + 7.39479e7i) q^{58} +(5.62187e8 - 3.24579e8i) q^{59} +(-5.15397e8 + 8.92693e8i) q^{61} +7.99433e8i q^{62} -1.17515e9 q^{64} +(4.17895e8 + 2.41272e8i) q^{65} +(-9.38371e8 - 1.62531e9i) q^{67} +(9.03668e7 - 5.21733e7i) q^{68} +(-6.57649e8 + 1.13908e9i) q^{70} -2.68338e9i q^{71} -2.84653e9 q^{73} +(-1.41314e9 - 8.15877e8i) q^{74} +(1.44318e8 + 2.49966e8i) q^{76} +(2.78816e9 - 1.60974e9i) q^{77} +(-7.44324e8 + 1.28921e9i) q^{79} -1.83417e9i q^{80} -4.87467e9 q^{82} +(1.09626e9 + 6.32927e8i) q^{83} +(4.88143e8 + 8.45488e8i) q^{85} +(-2.49621e9 + 1.44119e9i) q^{86} +(-3.32839e9 + 5.76495e9i) q^{88} +6.02052e9i q^{89} -2.92382e9 q^{91} +(6.99679e8 + 4.03960e8i) q^{92} +(-3.59554e9 - 6.22766e9i) q^{94} +(-2.33873e9 + 1.35027e9i) q^{95} +(7.96474e8 - 1.37953e9i) q^{97} -3.90029e8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 608 q^{4} - 34468 q^{7}+O(q^{10}) $ 4 * q - 608 * q^4 - 34468 * q^7	$ 4 q - 608 q^{4} - 34468 q^{7} + 305280 q^{10} + 339308 q^{13} + 1289728 q^{16} - 3797848 q^{19} - 10025280 q^{22} - 3351410 q^{25} + 20956544 q^{28} + 59586236 q^{31} - 18420480 q^{34} - 243247384 q^{37} - 202705920 q^{40} - 214839412 q^{43} - 285246720 q^{46} - 29071014 q^{49} + 103149632 q^{52} - 2125359360 q^{55} + 170775360 q^{58} - 2061587284 q^{61} - 4700585984 q^{64} - 3753484948 q^{67} - 2630597760 q^{70} - 11386113976 q^{73} + 577272896 q^{76} - 2977295236 q^{79} - 19498671360 q^{82} + 1952570880 q^{85} - 13313571840 q^{88} - 11695268144 q^{91} - 14382155520 q^{94} + 3185897852 q^{97}+O(q^{100}) $ 4 * q - 608 * q^4 - 34468 * q^7 + 305280 * q^10 + 339308 * q^13 + 1289728 * q^16 - 3797848 * q^19 - 10025280 * q^22 - 3351410 * q^25 + 20956544 * q^28 + 59586236 * q^31 - 18420480 * q^34 - 243247384 * q^37 - 202705920 * q^40 - 214839412 * q^43 - 285246720 * q^46 - 29071014 * q^49 + 103149632 * q^52 - 2125359360 * q^55 + 170775360 * q^58 - 2061587284 * q^61 - 4700585984 * q^64 - 3753484948 * q^67 - 2630597760 * q^70 - 11386113976 * q^73 + 577272896 * q^76 - 2977295236 * q^79 - 19498671360 * q^82 + 1952570880 * q^85 - 13313571840 * q^88 - 11695268144 * q^91 - 14382155520 * q^94 + 3185897852 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	23.2379	+	13.4164i	0.726184	+	0.419263i	0.817025	−	0.576603i	$-0.195622\pi$
$2$	23.2379	+	13.4164i	0.726184	+	0.419263i	−0.0908403	+	0.995865i	$0.528955\pi$
$3$		0			0
$3$		0			0
$4$	−152.000	−	263.272i	−0.148438	−	0.257101i
$5$	2463.22	−	1422.14i	0.788230	−	0.455085i	−0.0511093	−	0.998693i	$-0.516276\pi$
$5$	2463.22	−	1422.14i	0.788230	−	0.455085i	0.839339	+	0.543609i	$0.182942\pi$
$6$		0			0
$7$	−8617.00	+	14925.1i	−0.512703	+	0.888028i	0.487188	+	0.873297i	$0.338022\pi$
$7$	−8617.00	+	14925.1i	−0.512703	+	0.888028i	−0.999891	+	0.0147309i	$0.995311\pi$
$8$		−	35634.0i		−	1.08746i
$9$		0			0
$10$	76320.0			0.763200
$11$	−161782.	−	93405.0i	−1.00454	−	0.579972i	−0.0949520	−	0.995482i	$-0.530270\pi$
$11$	−161782.	−	93405.0i	−1.00454	−	0.579972i	−0.909589	+	0.415510i	$0.863603\pi$
$12$		0			0
$13$	84827.0	+	146925.i	0.228464	+	0.395711i	0.957353	−	0.288921i	$-0.0932964\pi$
$13$	84827.0	+	146925.i	0.228464	+	0.395711i	−0.728889	+	0.684632i	$0.759963\pi$
$14$	−400482.	+	231218.i	−0.744634	+	0.429915i
$15$		0			0
$16$	322432.	−	558469.i	0.307495	−	0.532597i
$17$			343245.i			0.241746i	0.992668	+	0.120873i	$0.0385695\pi$
$17$			343245.i			0.241746i	−0.992668	+	0.120873i	$0.961431\pi$
$18$		0			0
$19$	−949462.			−0.383451			−0.191725	−	0.981449i	$-0.561408\pi$
$19$	−949462.			−0.383451			−0.191725	+	0.981449i	$0.561408\pi$
$20$	−748818.	−	432330.i	−0.234006	−	0.135103i
$21$		0			0
$22$	−2.50632e6	−	4.34107e6i	−0.486321	−	0.842333i
$23$	−2.30157e6	+	1.32881e6i	−0.357590	+	0.206455i	−0.668023	−	0.744140i	$-0.732859\pi$
$23$	−2.30157e6	+	1.32881e6i	−0.357590	+	0.206455i	0.310433	+	0.950595i	$0.399526\pi$
$24$		0			0
$25$	−837852.	+	1.45120e6i	−0.0857961	+	0.148603i
$26$			4.55229e6i			0.383145i
$27$		0			0
$28$	5.23914e6			0.304417
$29$	2.75588e6	+	1.59111e6i	0.134360	+	0.0775727i	0.565673	−	0.824629i	$-0.308616\pi$
$29$	2.75588e6	+	1.59111e6i	0.134360	+	0.0775727i	−0.431313	+	0.902202i	$0.641950\pi$
$30$		0			0
$31$	1.48966e7	+	2.58016e7i	0.520328	+	0.901235i	0.999721	+	0.0236344i	$0.00752377\pi$
$31$	1.48966e7	+	2.58016e7i	0.520328	+	0.901235i	−0.479392	+	0.877601i	$0.659143\pi$
$32$	−1.66153e7	+	9.59284e6i	−0.495174	+	0.285889i
$33$		0			0
$34$	−4.60512e6	+	7.97630e6i	−0.101355	+	0.175552i
$35$			4.90183e7i			0.933293i
$36$		0			0
$37$	−6.08118e7			−0.876960			−0.438480	−	0.898741i	$-0.644483\pi$
$37$	−6.08118e7			−0.876960			−0.438480	+	0.898741i	$0.644483\pi$
$38$	−2.20635e7	−	1.27384e7i	−0.278456	−	0.160767i
$39$		0			0
$40$	−5.06765e7	−	8.77742e7i	−0.494887	−	0.857170i
$41$	−1.57329e8	+	9.08341e7i	−1.35797	+	0.784024i	−0.989350	−	0.145556i	$-0.953503\pi$
$41$	−1.57329e8	+	9.08341e7i	−1.35797	+	0.784024i	−0.368620	+	0.929580i	$0.620170\pi$
$42$		0			0
$43$	−5.37099e7	+	9.30282e7i	−0.365352	+	0.632809i	−0.988833	−	0.149030i	$-0.952385\pi$
$43$	−5.37099e7	+	9.30282e7i	−0.365352	+	0.632809i	0.623480	+	0.781839i	$0.285718\pi$
$44$			5.67903e7i			0.344358i
$45$		0			0
$46$	−7.13117e7			−0.346235
$47$	−2.32091e8	−	1.33998e8i	−1.01197	−	0.584263i	−0.100205	−	0.994967i	$-0.531950\pi$
$47$	−2.32091e8	−	1.33998e8i	−1.01197	−	0.584263i	−0.911769	+	0.410704i	$0.865283\pi$
$48$		0			0
$49$	−7.26775e6	−	1.25881e7i	−0.0257288	−	0.0445636i
$50$	−3.89399e7	+	2.24819e7i	−0.124608	+	0.0719422i
$51$		0			0
$52$	2.57874e7	−	4.46651e7i	0.0678252	−	0.117477i
$53$		−	1.92091e8i		−	0.459332i	−0.973269	−	0.229666i	$-0.926237\pi$
$53$		−	1.92091e8i		−	0.459332i	0.973269	−	0.229666i	$-0.0737634\pi$
$54$		0			0
$55$	−5.31340e8			−1.05574
$56$	5.31840e8	+	3.07058e8i	0.965697	+	0.557545i
$57$		0			0
$58$	4.26938e7	+	7.39479e7i	0.0650467	+	0.112664i
$59$	5.62187e8	−	3.24579e8i	0.786359	−	0.454005i	−0.0523202	−	0.998630i	$-0.516662\pi$
$59$	5.62187e8	−	3.24579e8i	0.786359	−	0.454005i	0.838679	+	0.544626i	$0.183328\pi$
$60$		0			0
$61$	−5.15397e8	+	8.92693e8i	−0.610229	+	1.05695i	0.380973	+	0.924586i	$0.375589\pi$
$61$	−5.15397e8	+	8.92693e8i	−0.610229	+	1.05695i	−0.991202	+	0.132361i	$0.957744\pi$
$62$			7.99433e8i			0.872617i
$63$		0			0
$64$	−1.17515e9			−1.09444
$65$	4.17895e8	+	2.41272e8i	0.360164	+	0.207941i
$66$		0			0
$67$	−9.38371e8	−	1.62531e9i	−0.695025	−	1.20382i	−0.970172	−	0.242417i	$-0.922060\pi$
$67$	−9.38371e8	−	1.62531e9i	−0.695025	−	1.20382i	0.275147	−	0.961402i	$-0.411274\pi$
$68$	9.03668e7	−	5.21733e7i	0.0621533	−	0.0358842i
$69$		0			0
$70$	−6.57649e8	+	1.13908e9i	−0.391295	+	0.677743i
$71$		−	2.68338e9i		−	1.48727i	−0.668585	−	0.743636i	$-0.733100\pi$
$71$		−	2.68338e9i		−	1.48727i	0.668585	−	0.743636i	$-0.266900\pi$
$72$		0			0
$73$	−2.84653e9			−1.37310			−0.686549	−	0.727084i	$-0.740875\pi$
$73$	−2.84653e9			−1.37310			−0.686549	+	0.727084i	$0.740875\pi$
$74$	−1.41314e9	−	8.15877e8i	−0.636834	−	0.367676i
$75$		0			0
$76$	1.44318e8	+	2.49966e8i	0.0569185	+	0.0985857i
$77$	2.78816e9	−	1.60974e9i	1.03006	−	0.594707i
$78$		0			0
$79$	−7.44324e8	+	1.28921e9i	−0.241895	+	0.418974i	−0.961254	−	0.275664i	$-0.911102\pi$
$79$	−7.44324e8	+	1.28921e9i	−0.241895	+	0.418974i	0.719359	+	0.694638i	$0.244436\pi$
$80$		−	1.83417e9i		−	0.559745i
$81$		0			0
$82$	−4.87467e9			−1.31485
$83$	1.09626e9	+	6.32927e8i	0.278307	+	0.160680i	0.632657	−	0.774433i	$-0.281964\pi$
$83$	1.09626e9	+	6.32927e8i	0.278307	+	0.160680i	−0.354350	+	0.935113i	$0.615298\pi$
$84$		0			0
$85$	4.88143e8	+	8.45488e8i	0.110015	+	0.190552i
$86$	−2.49621e9	+	1.44119e9i	−0.530626	+	0.306357i
$87$		0			0
$88$	−3.32839e9	+	5.76495e9i	−0.630698	+	1.09240i
$89$			6.02052e9i			1.07816i	0.842254	+	0.539081i	$0.181228\pi$
$89$			6.02052e9i			1.07816i	−0.842254	+	0.539081i	$0.818772\pi$
$90$		0			0
$91$	−2.92382e9			−0.468536
$92$	6.99679e8	+	4.03960e8i	0.106160	+	0.0612913i
$93$		0			0
$94$	−3.59554e9	−	6.22766e9i	−0.489919	−	0.848565i
$95$	−2.33873e9	+	1.35027e9i	−0.302247	+	0.174503i
$96$		0			0
$97$	7.96474e8	−	1.37953e9i	0.0927498	−	0.160647i	−0.815917	−	0.578168i	$-0.803768\pi$
$97$	7.96474e8	−	1.37953e9i	0.0927498	−	0.160647i	0.908667	+	0.417521i	$0.137101\pi$
$98$		−	3.90029e8i		−	0.0431485i
$99$		0			0
$100$	5.09414e8			0.0509414
$101$	3.66342e9	+	2.11508e9i	0.348562	+	0.201242i	0.664052	−	0.747687i	$-0.268836\pi$
$101$	3.66342e9	+	2.11508e9i	0.348562	+	0.201242i	−0.315490	+	0.948929i	$0.602169\pi$
$102$		0			0
$103$	−2.20880e9	−	3.82576e9i	−0.190533	−	0.330013i	0.754894	−	0.655847i	$-0.227688\pi$
$103$	−2.20880e9	−	3.82576e9i	−0.190533	−	0.330013i	−0.945427	+	0.325834i	$0.894355\pi$
$104$	5.23551e9	−	3.02272e9i	0.430321	−	0.248446i
$105$		0			0
$106$	2.57717e9	−	4.46378e9i	0.192581	−	0.333560i
$107$			3.19343e9i			0.227687i	0.993499	+	0.113844i	$0.0363163\pi$
$107$			3.19343e9i			0.227687i	−0.993499	+	0.113844i	$0.963684\pi$
$108$		0			0
$109$	−1.54650e10			−1.00512			−0.502561	−	0.864542i	$-0.667609\pi$
$109$	−1.54650e10			−1.00512			−0.502561	+	0.864542i	$0.667609\pi$
$110$	−1.23472e10	−	7.12867e9i	−0.766665	−	0.442634i
$111$		0			0
$112$	5.55679e9	+	9.62465e9i	0.315307	+	0.546128i
$113$	−2.19397e10	+	1.26669e10i	−1.19080	+	0.687507i	−0.958488	−	0.285135i	$-0.907962\pi$
$113$	−2.19397e10	+	1.26669e10i	−1.19080	+	0.687507i	−0.232310	+	0.972642i	$0.574628\pi$
$114$		0			0
$115$	−3.77952e9	+	6.54632e9i	−0.187909	+	0.325468i
$116$		−	9.67392e8i		−	0.0460588i
$117$		0			0
$118$	1.74187e10			0.761389
$119$	−5.12297e9	−	2.95775e9i	−0.214678	−	0.123944i
$120$		0			0
$121$	4.48029e9	+	7.76009e9i	0.172734	+	0.299185i
$122$	−2.39535e10	+	1.38295e10i	−0.886277	+	0.511692i
$123$		0			0
$124$	4.52855e9	−	7.84369e9i	0.154472	−	0.267554i
$125$			3.25423e10i			1.06635i
$126$		0			0
$127$	5.84098e10			1.76794			0.883970	−	0.467544i	$-0.154861\pi$
$127$	5.84098e10			1.76794			0.883970	+	0.467544i	$0.154861\pi$
$128$	−1.02939e10	−	5.94318e9i	−0.299592	−	0.172969i
$129$		0			0
$130$	6.47400e9	+	1.12133e10i	0.174364	+	0.302007i
$131$	4.91670e10	−	2.83866e10i	1.27443	−	0.735794i	0.298614	−	0.954374i	$-0.403476\pi$
$131$	4.91670e10	−	2.83866e10i	1.27443	−	0.735794i	0.975819	+	0.218580i	$0.0701424\pi$
$132$		0			0
$133$	8.18151e9	−	1.41708e10i	0.196596	−	0.340515i
$134$		−	5.03583e10i		−	1.16559i
$135$		0			0
$136$	1.22312e10			0.262890
$137$	6.83539e10	+	3.94641e10i	1.41632	+	0.817711i	0.995973	−	0.0896543i	$-0.0285762\pi$
$137$	6.83539e10	+	3.94641e10i	1.41632	+	0.817711i	0.420344	+	0.907365i	$0.361910\pi$
$138$		0			0
$139$	−4.44842e9	−	7.70488e9i	−0.0857297	−	0.148488i	0.819972	−	0.572403i	$-0.193989\pi$
$139$	−4.44842e9	−	7.70488e9i	−0.0857297	−	0.148488i	−0.905702	+	0.423915i	$0.860655\pi$
$140$	1.29051e10	−	7.45078e9i	0.239951	−	0.138536i
$141$		0			0
$142$	3.60013e10	−	6.23561e10i	0.623557	−	1.08003i
$143$		−	3.16931e10i		−	0.530010i
$144$		0			0
$145$	9.05109e9			0.141209
$146$	−6.61473e10	−	3.81902e10i	−0.997122	−	0.575688i
$147$		0			0
$148$	9.24340e9	+	1.60100e10i	0.130174	+	0.225467i
$149$	6.43683e10	−	3.71631e10i	0.876478	−	0.506035i	0.00698246	−	0.999976i	$-0.497777\pi$
$149$	6.43683e10	−	3.71631e10i	0.876478	−	0.506035i	0.869496	+	0.493941i	$0.164444\pi$
$150$		0			0
$151$	2.95475e10	−	5.11777e10i	0.376388	−	0.651923i	−0.614146	−	0.789193i	$-0.710499\pi$
$151$	2.95475e10	−	5.11777e10i	0.376388	−	0.651923i	0.990534	+	0.137270i	$0.0438327\pi$
$152$			3.38331e10i			0.416988i
$153$		0			0
$154$	8.63878e10			0.997353
$155$	7.33869e10	+	4.23700e10i	0.820276	+	0.473587i
$156$		0			0
$157$	1.90932e10	+	3.30703e10i	0.200161	+	0.346689i	0.948580	−	0.316537i	$-0.102520\pi$
$157$	1.90932e10	+	3.30703e10i	0.200161	+	0.346689i	−0.748419	+	0.663226i	$0.769187\pi$
$158$	−3.45930e10	+	1.99723e10i	−0.351320	+	0.202835i
$159$		0			0
$160$	−2.72847e10	+	4.72585e10i	−0.260207	+	0.450692i
$161$		−	4.58016e10i		−	0.423400i
$162$		0			0
$163$	1.61034e11			1.39952			0.699760	−	0.714378i	$-0.253290\pi$
$163$	1.61034e11			1.39952			0.699760	+	0.714378i	$0.253290\pi$
$164$	4.78281e10	+	2.76136e10i	0.403147	+	0.232757i
$165$		0			0
$166$	1.69832e10	+	2.94158e10i	0.134735	+	0.233367i
$167$	5.15933e10	−	2.97874e10i	0.397202	−	0.229325i	−0.288074	−	0.957608i	$-0.593015\pi$
$167$	5.15933e10	−	2.97874e10i	0.397202	−	0.229325i	0.685276	+	0.728284i	$0.259682\pi$
$168$		0			0
$169$	5.45380e10	−	9.44626e10i	0.395609	−	0.685214i
$170$			2.61965e10i			0.184501i
$171$		0			0
$172$	3.26556e10			0.216928
$173$	−1.79242e11	−	1.03486e11i	−1.15667	−	0.667805i	−0.206168	−	0.978517i	$-0.566099\pi$
$173$	−1.79242e11	−	1.03486e11i	−1.15667	−	0.667805i	−0.950504	+	0.310712i	$0.899433\pi$
$174$		0			0
$175$	−1.44395e10	−	2.50100e10i	−0.0879758	−	0.152379i
$176$	−1.04328e11	+	6.02335e10i	−0.617783	+	0.356677i
$177$		0			0
$178$	−8.07737e10	+	1.39904e11i	−0.452033	+	0.782944i
$179$		−	5.22122e10i		−	0.284123i	−0.989858	−	0.142062i	$-0.954627\pi$
$179$		−	5.22122e10i		−	0.284123i	0.989858	−	0.142062i	$-0.0453732\pi$
$180$		0			0
$181$	−3.38840e11			−1.74422			−0.872112	−	0.489306i	$-0.837250\pi$
$181$	−3.38840e11			−1.74422			−0.872112	+	0.489306i	$0.837250\pi$
$182$	−6.79434e10	−	3.92271e10i	−0.340244	−	0.196440i
$183$		0			0
$184$	4.73510e10	+	8.20143e10i	0.224512	+	0.388866i
$185$	−1.49793e11	+	8.64829e10i	−0.691245	+	0.399091i
$186$		0			0
$187$	3.20608e10	−	5.55310e10i	0.140206	−	0.242844i
$188$			8.14707e10i			0.346906i
$189$		0			0
$190$	−7.24629e10			−0.292650
$191$	1.34684e11	+	7.77597e10i	0.529844	+	0.305906i	0.740953	−	0.671557i	$-0.234374\pi$
$191$	1.34684e11	+	7.77597e10i	0.529844	+	0.305906i	−0.211109	+	0.977463i	$0.567707\pi$
$192$		0			0
$193$	−1.75177e11	−	3.03416e11i	−0.654172	−	1.13306i	−0.982101	−	0.188356i	$-0.939684\pi$
$193$	−1.75177e11	−	3.03416e11i	−0.654172	−	1.13306i	0.327929	−	0.944702i	$-0.393649\pi$
$194$	3.70168e10	−	2.13717e10i	0.134707	−	0.0777731i
$195$		0			0
$196$	−2.20940e9	+	3.82679e9i	−0.00763824	+	0.0132298i
$197$			3.11997e11i			1.05152i	0.850632	+	0.525762i	$0.176220\pi$
$197$			3.11997e11i			1.05152i	−0.850632	+	0.525762i	$0.823780\pi$
$198$		0			0
$199$	−1.51943e11			−0.486871			−0.243436	−	0.969917i	$-0.578274\pi$
$199$	−1.51943e11			−0.486871			−0.243436	+	0.969917i	$0.578274\pi$
$200$	5.17121e10	+	2.98560e10i	0.161600	+	0.0933001i
$201$		0			0
$202$	5.67534e10	+	9.82998e10i	0.168747	+	0.292278i
$203$	−4.74948e10	+	2.74211e10i	−0.137773	+	0.0795435i
$204$		0			0
$205$	−2.58357e11	+	4.47488e11i	−0.713595	+	1.23598i
$206$		−	1.18537e11i		−	0.319534i
$207$		0			0
$208$	1.09404e11			0.281006
$209$	1.53606e11	+	8.86845e10i	0.385192	+	0.222391i
$210$		0			0
$211$	−6.81143e10	−	1.17977e11i	−0.162864	−	0.282089i	0.773030	−	0.634369i	$-0.218740\pi$
$211$	−6.81143e10	−	1.17977e11i	−0.162864	−	0.282089i	−0.935895	+	0.352280i	$0.885407\pi$
$212$	−5.05721e10	+	2.91978e10i	−0.118095	+	0.0681821i
$213$		0			0
$214$	−4.28444e10	+	7.42086e10i	−0.0954608	+	0.165343i
$215$			3.05532e11i			0.665065i
$216$		0			0
$217$	−5.13455e11			−1.06710
$218$	−3.59375e11	−	2.07485e11i	−0.729903	−	0.421410i
$219$		0			0
$220$	8.07637e10	+	1.39887e11i	0.156712	+	0.271433i
$221$	−5.04312e10	+	2.91165e10i	−0.0956617	+	0.0552303i
$222$		0			0
$223$	−5.77865e10	+	1.00089e11i	−0.104786	+	0.181494i	−0.913651	−	0.406500i	$-0.866749\pi$
$223$	−5.77865e10	+	1.00089e11i	−0.104786	+	0.181494i	0.808865	+	0.587994i	$0.200082\pi$
$224$		−	3.30646e11i		−	0.586304i
$225$		0			0
$226$	−6.79776e11			−1.15298
$227$	−1.92618e10	−	1.11208e10i	−0.0319571	−	0.0184505i	0.483936	−	0.875103i	$-0.339207\pi$
$227$	−1.92618e10	−	1.11208e10i	−0.0319571	−	0.0184505i	−0.515893	+	0.856653i	$0.672540\pi$
$228$		0			0
$229$	−2.74102e11	−	4.74759e11i	−0.435246	−	0.753868i	0.562070	−	0.827090i	$-0.310005\pi$
$229$	−2.74102e11	−	4.74759e11i	−0.435246	−	0.753868i	−0.997316	+	0.0732215i	$0.976672\pi$
$230$	−1.75656e11	+	1.01415e11i	−0.272913	+	0.157566i
$231$		0			0
$232$	5.66974e10	−	9.82028e10i	0.0843574	−	0.146111i
$233$		−	8.58665e11i		−	1.25039i	−0.780470	−	0.625193i	$-0.785020\pi$
$233$		−	8.58665e11i		−	1.25039i	0.780470	−	0.625193i	$-0.214980\pi$
$234$		0			0
$235$	−7.62254e11			−1.06356
$236$	−1.70905e11	−	9.86720e10i	−0.233450	−	0.134783i
$237$		0			0
$238$	−7.93646e10	−	1.37464e11i	−0.103930	−	0.180013i
$239$	7.88997e11	−	4.55527e11i	1.01178	−	0.584151i	0.100067	−	0.994981i	$-0.468094\pi$
$239$	7.88997e11	−	4.55527e11i	1.01178	−	0.584151i	0.911712	+	0.410830i	$0.134761\pi$
$240$		0			0
$241$	−1.85625e11	+	3.21512e11i	−0.228324	+	0.395468i	−0.957311	−	0.289058i	$-0.906658\pi$
$241$	−1.85625e11	+	3.21512e11i	−0.228324	+	0.395468i	0.728988	+	0.684527i	$0.239991\pi$
$242$			2.40437e11i			0.289685i
$243$		0			0
$244$	3.13361e11			0.362323
$245$	−3.58041e10	−	2.06715e10i	−0.0405604	−	0.0234176i
$246$		0			0
$247$	−8.05400e10	−	1.39499e11i	−0.0876046	−	0.151736i
$248$	9.19414e11	−	5.30824e11i	0.980060	−	0.565838i
$249$		0			0
$250$	−4.36601e11	+	7.56215e11i	−0.447080	+	0.774365i
$251$		−	1.75865e11i		−	0.176527i	−0.996097	−	0.0882636i	$-0.971868\pi$
$251$		−	1.75865e11i		−	0.176527i	0.996097	−	0.0882636i	$-0.0281318\pi$
$252$		0			0
$253$	4.96472e11			0.478952
$254$	1.35732e12	+	7.83650e11i	1.28385	+	0.741231i
$255$		0			0
$256$	4.42203e11	+	7.65918e11i	0.402181	+	0.696598i
$257$	−6.58483e11	+	3.80175e11i	−0.587325	+	0.339093i	−0.764039	−	0.645170i	$-0.776787\pi$
$257$	−6.58483e11	+	3.80175e11i	−0.587325	+	0.339093i	0.176714	+	0.984262i	$0.443453\pi$
$258$		0			0
$259$	5.24016e11	−	9.07622e11i	0.449620	−	0.778764i
$260$		−	1.46693e11i		−	0.123465i
$261$		0			0
$262$	1.52338e12			1.23396
$263$	2.05990e11	+	1.18928e11i	0.163707	+	0.0945163i	0.579615	−	0.814890i	$-0.303203\pi$
$263$	2.05990e11	+	1.18928e11i	0.163707	+	0.0945163i	−0.415908	+	0.909407i	$0.636536\pi$
$264$		0			0
$265$	−2.73180e11	−	4.73161e11i	−0.209035	−	0.362059i
$266$	3.80242e11	−	2.19533e11i	0.285530	−	0.164851i
$267$		0			0
$268$	−2.85265e11	+	4.94093e11i	−0.206336	+	0.357384i
$269$			1.57259e12i			1.11649i	0.829678	+	0.558243i	$0.188524\pi$
$269$			1.57259e12i			1.11649i	−0.829678	+	0.558243i	$0.811476\pi$
$270$		0			0
$271$	−1.66619e12			−1.13993			−0.569965	−	0.821669i	$-0.693043\pi$
$271$	−1.66619e12			−1.13993			−0.569965	+	0.821669i	$0.693043\pi$
$272$	1.91692e11	+	1.10673e11i	0.128753	+	0.0743359i
$273$		0			0
$274$	1.05893e12	+	1.83413e12i	0.685671	+	1.18762i
$275$	2.71099e11	−	1.56519e11i	0.172371	−	0.0995186i
$276$		0			0
$277$	1.03260e12	−	1.78851e12i	0.633186	−	1.09671i	−0.353711	−	0.935355i	$-0.615080\pi$
$277$	1.03260e12	−	1.78851e12i	0.633186	−	1.09671i	0.986896	−	0.161355i	$-0.0515865\pi$
$278$		−	2.38727e11i		−	0.143773i
$279$		0			0
$280$	1.74672e12			1.01492
$281$	−2.32951e12	−	1.34495e12i	−1.32964	−	0.767667i	−0.344395	−	0.938825i	$-0.611916\pi$
$281$	−2.32951e12	−	1.34495e12i	−1.32964	−	0.767667i	−0.985244	+	0.171157i	$0.945249\pi$
$282$		0			0
$283$	−7.22667e11	−	1.25170e12i	−0.398113	−	0.689551i	0.595380	−	0.803444i	$-0.297001\pi$
$283$	−7.22667e11	−	1.25170e12i	−0.398113	−	0.689551i	−0.993493	+	0.113893i	$0.963668\pi$
$284$	−7.06458e11	+	4.07873e11i	−0.382379	+	0.220767i
$285$		0			0
$286$	4.25207e11	−	7.36480e11i	0.222214	−	0.384885i
$287$		−	3.13087e12i		−	1.60789i
$288$		0			0
$289$	1.89818e12			0.941559
$290$	2.10328e11	+	1.21433e11i	0.102543	+	0.0592035i
$291$		0			0
$292$	4.32672e11	+	7.49410e11i	0.203819	+	0.353025i
$293$	−2.93657e12	+	1.69543e12i	−1.35988	+	0.785129i	−0.989608	−	0.143793i	$-0.954070\pi$
$293$	−2.93657e12	+	1.69543e12i	−1.35988	+	0.785129i	−0.370275	+	0.928922i	$0.620737\pi$
$294$		0			0
$295$	9.23193e11	−	1.59902e12i	0.413221	−	0.715720i
$296$			2.16697e12i			0.953661i
$297$		0			0
$298$	1.99438e12			0.848646
$299$	−3.90471e11	−	2.25439e11i	−0.163393	−	0.0943349i
$300$		0			0
$301$	−9.25636e11	−	1.60325e12i	−0.374634	−	0.648886i
$302$	1.37324e12	−	7.92842e11i	0.546654	−	0.315611i
$303$		0			0
$304$	−3.06137e11	+	5.30245e11i	−0.117909	+	0.204225i
$305$			2.93186e12i			1.11082i
$306$		0			0
$307$	2.07104e12			0.759447			0.379723	−	0.925100i	$-0.376019\pi$
$307$	2.07104e12			0.759447			0.379723	+	0.925100i	$0.376019\pi$
$308$	−8.47599e11	−	4.89362e11i	−0.305800	−	0.176554i
$309$		0			0
$310$	1.13691e12	+	1.96918e12i	0.397115	+	0.687823i
$311$	−1.85665e12	+	1.07194e12i	−0.638159	+	0.368441i	−0.783905	−	0.620881i	$-0.786775\pi$
$311$	−1.85665e12	+	1.07194e12i	−0.638159	+	0.368441i	0.145746	+	0.989322i	$0.453442\pi$
$312$		0			0
$313$	4.07419e11	−	7.05670e11i	0.135619	−	0.234898i	−0.790215	−	0.612830i	$-0.790031\pi$
$313$	4.07419e11	−	7.05670e11i	0.135619	−	0.234898i	0.925834	+	0.377931i	$0.123364\pi$
$314$			1.02465e12i			0.335680i
$315$		0			0
$316$	4.52549e11			0.143625
$317$	7.11202e11	+	4.10612e11i	0.222176	+	0.128273i	0.606957	−	0.794734i	$-0.292390\pi$
$317$	7.11202e11	+	4.10612e11i	0.222176	+	0.128273i	−0.384782	+	0.923008i	$0.625723\pi$
$318$		0			0
$319$	−2.97235e11	−	5.14825e11i	−0.0899800	−	0.155850i
$320$	−2.89464e12	+	1.67122e12i	−0.862670	+	0.498063i
$321$		0			0
$322$	6.14493e11	−	1.06433e12i	0.177516	−	0.307467i
$323$		−	3.25898e11i		−	0.0926979i
$324$		0			0
$325$	−2.84290e11			−0.0784052
$326$	3.74209e12	+	2.16049e12i	1.01631	+	0.586766i
$327$		0			0
$328$	3.23678e12	+	5.60627e12i	0.852597	+	1.47674i
$329$	3.99986e12	−	2.30932e12i	1.03768	−	0.599107i
$330$		0			0
$331$	−8.83667e11	+	1.53056e12i	−0.222407	+	0.385220i	−0.955538	−	0.294867i	$-0.904725\pi$
$331$	−8.83667e11	+	1.53056e12i	−0.222407	+	0.385220i	0.733131	+	0.680087i	$0.238058\pi$
$332$		−	3.84819e11i		−	0.0954040i
$333$		0			0
$334$	1.59856e12			0.384589
$335$	−4.62282e12	−	2.66899e12i	−1.09568	−	0.632591i
$336$		0			0
$337$	2.67889e11	+	4.63997e11i	0.0616318	+	0.106749i	0.895195	−	0.445675i	$-0.147036\pi$
$337$	2.67889e11	+	4.63997e11i	0.0616318	+	0.106749i	−0.833563	+	0.552424i	$0.813703\pi$
$338$	2.53470e12	−	1.46341e12i	0.574570	−	0.331728i
$339$		0			0
$340$	1.48395e11	−	2.57028e11i	0.0326607	−	0.0565700i
$341$		−	5.56565e12i		−	1.20710i
$342$		0			0
$343$	−4.61767e12			−0.972641
$344$	3.31496e12	+	1.91390e12i	0.688156	+	0.397307i
$345$		0			0
$346$	−2.77681e12	−	4.80958e12i	−0.559971	−	0.969899i
$347$	4.22045e12	−	2.43668e12i	0.838902	−	0.484340i	−0.0179889	−	0.999838i	$-0.505726\pi$
$347$	4.22045e12	−	2.43668e12i	0.838902	−	0.484340i	0.856891	+	0.515498i	$0.172393\pi$
$348$		0			0
$349$	−3.91883e10	+	6.78761e10i	−0.00756884	+	0.0131096i	−0.869785	−	0.493431i	$-0.835743\pi$
$349$	−3.91883e10	+	6.78761e10i	−0.00756884	+	0.0131096i	0.862216	+	0.506540i	$0.169076\pi$
$350$		−	7.74908e11i		−	0.147540i
$351$		0			0
$352$	3.58408e12			0.663230
$353$	4.25049e12	+	2.45402e12i	0.775471	+	0.447718i	0.834823	−	0.550519i	$-0.185570\pi$
$353$	4.25049e12	+	2.45402e12i	0.775471	+	0.447718i	−0.0593519	+	0.998237i	$0.518903\pi$
$354$		0			0
$355$	−3.81614e12	−	6.60974e12i	−0.676834	−	1.17231i
$356$	1.58503e12	−	9.15119e11i	0.277197	−	0.160040i
$357$		0			0
$358$	7.00501e11	−	1.21330e12i	0.119122	−	0.206326i
$359$			8.23695e11i			0.138132i	0.997612	+	0.0690660i	$0.0220019\pi$
$359$			8.23695e11i			0.138132i	−0.997612	+	0.0690660i	$0.977998\pi$
$360$		0			0
$361$	−5.22959e12			−0.852966
$362$	−7.87394e12	−	4.54602e12i	−1.26663	−	0.731288i
$363$		0			0
$364$	4.44420e11	+	7.69758e11i	0.0695484	+	0.120461i
$365$	−7.01162e12	+	4.04816e12i	−1.08232	+	0.624875i
$366$		0			0
$367$	−2.77967e12	+	4.81452e12i	−0.417506	+	0.723141i	−0.995688	−	0.0927667i	$-0.970429\pi$
$367$	−2.77967e12	+	4.81452e12i	−0.417506	+	0.723141i	0.578182	+	0.815908i	$0.303762\pi$
$368$			1.71381e12i			0.253936i
$369$		0			0
$370$	−4.64116e12			−0.669296
$371$	2.86697e12	+	1.65525e12i	0.407900	+	0.235501i
$372$		0			0
$373$	2.10961e10	+	3.65394e10i	0.00292185	+	0.00506078i	0.867483	−	0.497467i	$-0.165737\pi$
$373$	2.10961e10	+	3.65394e10i	0.00292185	+	0.00506078i	−0.864561	+	0.502528i	$0.832403\pi$
$374$	1.49005e12	−	8.60283e11i	0.203631	−	0.117566i
$375$		0			0
$376$	−4.77488e12	+	8.27033e12i	−0.635364	+	1.10048i
$377$			5.39875e11i			0.0708902i
$378$		0			0
$379$	−9.51422e12			−1.21668			−0.608341	−	0.793676i	$-0.708165\pi$
$379$	−9.51422e12			−1.21668			−0.608341	+	0.793676i	$0.708165\pi$
$380$	7.10974e11	+	4.10481e11i	0.0897296	+	0.0518054i
$381$		0			0
$382$	2.08651e12	+	3.61394e12i	0.256510	+	0.444288i
$383$	2.44862e12	−	1.41371e12i	0.297117	−	0.171540i	−0.344030	−	0.938959i	$-0.611792\pi$
$383$	2.44862e12	−	1.41371e12i	0.297117	−	0.171540i	0.641147	+	0.767418i	$0.278459\pi$
$384$		0			0
$385$	4.57856e12	−	7.93029e12i	0.541284	−	0.937531i
$386$		−	9.40101e12i		−	1.09708i
$387$		0			0
$388$	−4.84256e11			−0.0550702
$389$	−9.70929e11	−	5.60566e11i	−0.109003	−	0.0629330i	0.444507	−	0.895775i	$-0.353379\pi$
$389$	−9.70929e11	−	5.60566e11i	−0.109003	−	0.0629330i	−0.553510	+	0.832842i	$0.686712\pi$
$390$		0			0
$391$	−4.56110e11	−	7.90005e11i	−0.0499097	−	0.0864462i
$392$	−4.48565e11	+	2.58979e11i	−0.0484613	+	0.0279791i
$393$		0			0
$394$	−4.18588e12	+	7.25016e12i	−0.440865	+	0.763601i
$395$			4.23413e12i			0.440330i
$396$		0			0
$397$	−7.46731e12			−0.757202			−0.378601	−	0.925560i	$-0.623595\pi$
$397$	−7.46731e12			−0.757202			−0.378601	+	0.925560i	$0.623595\pi$
$398$	−3.53083e12	−	2.03852e12i	−0.353558	−	0.204127i
$399$		0			0
$400$	5.40301e11	+	9.35829e11i	0.0527638	+	0.0913895i
$401$	1.41128e13	−	8.14803e12i	1.36110	−	0.785834i	0.371333	−	0.928500i	$-0.378901\pi$
$401$	1.41128e13	−	8.14803e12i	1.36110	−	0.785834i	0.989771	+	0.142666i	$0.0455674\pi$
$402$		0			0
$403$	−2.52726e12	+	4.37734e12i	−0.237752	+	0.411799i
$404$		−	1.28597e12i		−	0.119488i
$405$		0			0
$406$	−1.47157e12			−0.133399
$407$	9.83828e12	+	5.68013e12i	0.880941	+	0.508612i
$408$		0			0
$409$	−5.25671e12	−	9.10489e12i	−0.459301	−	0.795533i	0.539623	−	0.841907i	$-0.318567\pi$
$409$	−5.25671e12	−	9.10489e12i	−0.459301	−	0.795533i	−0.998924	+	0.0463738i	$0.985233\pi$
$410$	−1.20074e13	+	6.93246e12i	−1.03640	+	0.598367i
$411$		0			0
$412$	−6.71476e11	+	1.16303e12i	−0.0565646	+	0.0979727i
$413$			1.11876e13i			0.931078i
$414$		0			0
$415$	3.60044e12			0.292493
$416$	−2.81885e12	−	1.62746e12i	−0.226259	−	0.130631i
$417$		0			0
$418$	2.37966e12	+	4.12168e12i	0.186480	+	0.322993i
$419$	−1.89407e13	+	1.09354e13i	−1.46665	+	0.846769i	−0.999304	−	0.0373062i	$-0.988122\pi$
$419$	−1.89407e13	+	1.09354e13i	−1.46665	+	0.846769i	−0.467344	+	0.884076i	$0.654789\pi$
$420$		0			0
$421$	−3.37840e12	+	5.85155e12i	−0.255447	+	0.442446i	−0.965017	−	0.262188i	$-0.915556\pi$
$421$	−3.37840e12	+	5.85155e12i	−0.255447	+	0.442446i	0.709570	+	0.704635i	$0.248889\pi$
$422$		−	3.65540e12i		−	0.273132i
$423$		0			0
$424$	−6.84496e12			−0.499507
$425$	−4.98119e11	−	2.87589e11i	−0.0359243	−	0.0207409i
$426$		0			0
$427$	−8.88235e12	−	1.53847e13i	−0.625732	−	1.08380i
$428$	8.40740e11	−	4.85401e11i	0.0585387	−	0.0337973i
$429$		0			0
$430$	−4.09914e12	+	7.09991e12i	−0.278837	+	0.482959i
$431$			1.58220e13i			1.06383i	0.846797	+	0.531917i	$0.178528\pi$
$431$			1.58220e13i			1.06383i	−0.846797	+	0.531917i	$0.821472\pi$
$432$		0			0
$433$	−1.46123e13			−0.960020			−0.480010	−	0.877263i	$-0.659367\pi$
$433$	−1.46123e13			−0.960020			−0.480010	+	0.877263i	$0.659367\pi$
$434$	−1.19316e13	−	6.88872e12i	−0.774908	−	0.447393i
$435$		0			0
$436$	2.35069e12	+	4.07151e12i	0.149198	+	0.258418i
$437$	2.18526e12	−	1.26166e12i	0.137118	−	0.0791653i
$438$		0			0
$439$	6.34129e12	−	1.09834e13i	0.388915	−	0.673621i	−0.603389	−	0.797447i	$-0.706183\pi$
$439$	6.34129e12	−	1.09834e13i	0.388915	−	0.673621i	0.992304	+	0.123826i	$0.0395165\pi$
$440$			1.89338e13i			1.14808i
$441$		0			0
$442$	−1.56255e12			−0.0926240
$443$	4.05864e12	+	2.34326e12i	0.237882	+	0.137341i	0.614203	−	0.789148i	$-0.289478\pi$
$443$	4.05864e12	+	2.34326e12i	0.237882	+	0.137341i	−0.376321	+	0.926489i	$0.622811\pi$
$444$		0			0
$445$	8.56201e12	+	1.48298e13i	0.490655	+	0.849839i
$446$	−2.68567e12	+	1.55057e12i	−0.152187	+	0.0878655i
$447$		0			0
$448$	1.01262e13	−	1.75392e13i	0.561123	−	0.971893i
$449$		−	2.82413e13i		−	1.54758i	−0.633443	−	0.773789i	$-0.718359\pi$
$449$		−	2.82413e13i		−	1.54758i	0.633443	−	0.773789i	$-0.281641\pi$
$450$		0			0
$451$	3.39374e13			1.81885
$452$	6.66966e12	+	3.85073e12i	0.353518	+	0.204104i
$453$		0			0
$454$	−2.98403e11	−	5.16849e11i	−0.0154712	−	0.0267969i
$455$	−7.20200e12	+	4.15807e12i	−0.369314	+	0.213224i
$456$		0			0
$457$	−4.61427e12	+	7.99215e12i	−0.231484	+	0.400943i	−0.958245	−	0.285948i	$-0.907692\pi$
$457$	−4.61427e12	+	7.99215e12i	−0.231484	+	0.400943i	0.726761	+	0.686891i	$0.241025\pi$
$458$		−	1.47099e13i		−	0.729930i
$459$		0			0
$460$	2.29795e12			0.111571
$461$	−6.76345e12	−	3.90488e12i	−0.324835	−	0.187544i	0.328710	−	0.944431i	$-0.393386\pi$
$461$	−6.76345e12	−	3.90488e12i	−0.324835	−	0.187544i	−0.653546	+	0.756887i	$0.726719\pi$
$462$		0			0
$463$	1.65216e13	+	2.86162e13i	0.776510	+	1.34495i	0.933942	+	0.357425i	$0.116345\pi$
$463$	1.65216e13	+	2.86162e13i	0.776510	+	1.34495i	−0.157432	+	0.987530i	$0.550322\pi$
$464$	1.77716e12	−	1.02605e12i	0.0826300	−	0.0477065i
$465$		0			0
$466$	1.15202e13	−	1.99536e13i	0.524240	−	0.908011i
$467$			4.06927e12i			0.183203i	0.995796	+	0.0916014i	$0.0291986\pi$
$467$			4.06927e12i			0.183203i	−0.995796	+	0.0916014i	$0.970801\pi$
$468$		0			0
$469$	3.23438e13			1.42537
$470$	−1.77132e13	−	1.02267e13i	−0.772338	−	0.445910i
$471$		0			0
$472$	−1.15660e13	−	2.00330e13i	−0.493713	−	0.855136i
$473$	1.73786e13	−	1.00335e13i	0.734022	−	0.423788i
$474$		0			0
$475$	7.95509e11	−	1.37786e12i	0.0328986	−	0.0569820i
$476$			1.79831e12i			0.0735918i
$477$		0			0
$478$	2.44462e13			0.979651
$479$	−1.11906e13	−	6.46091e12i	−0.443789	−	0.256222i	0.261414	−	0.965227i	$-0.415811\pi$
$479$	−1.11906e13	−	6.46091e12i	−0.443789	−	0.256222i	−0.705204	+	0.709005i	$0.749144\pi$
$480$		0			0
$481$	−5.15849e12	−	8.93476e12i	−0.200353	−	0.347022i
$482$	−8.62707e12	+	4.98084e12i	−0.331610	+	0.191455i
$483$		0			0
$484$	1.36201e12	−	2.35907e12i	0.0512805	−	0.0888205i
$485$		−	4.53079e12i		−	0.168836i
$486$		0			0
$487$	−2.16371e13			−0.789867			−0.394933	−	0.918710i	$-0.629232\pi$
$487$	−2.16371e13			−0.789867			−0.394933	+	0.918710i	$0.629232\pi$
$488$	3.18102e13	+	1.83656e13i	1.14939	+	0.663601i
$489$		0			0
$490$	−5.54675e11	−	9.60725e11i	−0.0196362	−	0.0340110i
$491$	2.93877e13	−	1.69670e13i	1.02981	−	0.594563i	0.112882	−	0.993608i	$-0.463992\pi$
$491$	2.93877e13	−	1.69670e13i	1.02981	−	0.594563i	0.916931	+	0.399045i	$0.130658\pi$
$492$		0			0
$493$	−5.46140e11	+	9.45942e11i	−0.0187529	+	0.0324810i
$494$		−	4.32223e12i		−	0.146917i
$495$		0			0
$496$	1.92125e13			0.639994
$497$	4.00496e13	+	2.31227e13i	1.32074	+	0.762528i
$498$		0			0
$499$	9.16873e12	+	1.58807e13i	0.296351	+	0.513295i	0.975298	−	0.220892i	$-0.0708969\pi$
$499$	9.16873e12	+	1.58807e13i	0.296351	+	0.513295i	−0.678947	+	0.734187i	$0.737564\pi$
$500$	8.56747e12	−	4.94643e12i	0.274159	−	0.158286i
$501$		0			0
$502$	2.35948e12	−	4.08674e12i	0.0740112	−	0.128191i
$503$		−	9.29154e12i		−	0.288568i	−0.989536	−	0.144284i	$-0.953912\pi$
$503$		−	9.29154e12i		−	0.288568i	0.989536	−	0.144284i	$-0.0460879\pi$
$504$		0			0
$505$	1.20317e13			0.366329
$506$	1.15370e13	+	6.66087e12i	0.347808	+	0.200807i
$507$		0			0
$508$	−8.87830e12	−	1.53777e13i	−0.262429	−	0.454540i
$509$	1.32864e13	−	7.67092e12i	0.388883	−	0.224522i	−0.292793	−	0.956176i	$-0.594585\pi$
$509$	1.32864e13	−	7.67092e12i	0.388883	−	0.224522i	0.681676	+	0.731654i	$0.261251\pi$
$510$		0			0
$511$	2.45285e13	−	4.24847e13i	0.703991	−	1.21935i
$512$			3.59027e13i			1.02042i
$513$		0			0
$514$	−2.04023e13			−0.568675
$515$	−1.08815e13	−	6.28245e12i	−0.300368	−	0.173417i
$516$		0			0
$517$	2.50321e13	+	4.33569e13i	0.677712	+	1.17383i
$518$	2.43540e13	−	1.40608e13i	0.653014	−	0.377018i
$519$		0			0
$520$	8.59747e12	−	1.48913e13i	0.226128	−	0.391665i
$521$		−	3.59230e13i		−	0.935803i	−0.883781	−	0.467901i	$-0.845010\pi$
$521$		−	3.59230e13i		−	0.935803i	0.883781	−	0.467901i	$-0.154990\pi$
$522$		0			0
$523$	5.78871e13			1.47936			0.739679	−	0.672960i	$-0.234978\pi$
$523$	5.78871e13			1.47936			0.739679	+	0.672960i	$0.234978\pi$
$524$	−1.49468e13	−	8.62951e12i	−0.378347	−	0.218439i
$525$		0			0
$526$	3.19118e12	+	5.52729e12i	0.0792543	+	0.137272i
$527$	−8.85628e12	+	5.11318e12i	−0.217870	+	0.125788i
$528$		0			0
$529$	−1.71818e13	+	2.97597e13i	−0.414753	+	0.718373i
$530$		−	1.46604e13i		−	0.350562i
$531$		0			0
$532$	−4.97436e12			−0.116729
$533$	−2.66915e13	−	1.54104e13i	−0.620494	−	0.358242i
$534$		0			0
$535$	4.54150e12	+	7.86611e12i	0.103617	+	0.179470i
$536$	−5.79161e13	+	3.34379e13i	−1.30911	+	0.755814i
$537$		0			0
$538$	−2.10985e13	+	3.65436e13i	−0.468101	+	0.810774i
$539$			2.71538e12i			0.0596879i
$540$		0			0
$541$	−3.16844e12			−0.0683690			−0.0341845	−	0.999416i	$-0.510883\pi$
$541$	−3.16844e12			−0.0683690			−0.0341845	+	0.999416i	$0.510883\pi$
$542$	−3.87188e13	−	2.23543e13i	−0.827799	−	0.477930i
$543$		0			0
$544$	−3.29270e12	−	5.70312e12i	−0.0691126	−	0.119707i
$545$	−3.80937e13	+	2.19934e13i	−0.792266	+	0.457415i
$546$		0			0
$547$	1.14535e13	−	1.98381e13i	0.233885	−	0.405100i	−0.725063	−	0.688682i	$-0.758189\pi$
$547$	1.14535e13	−	1.98381e13i	0.233885	−	0.405100i	0.958948	+	0.283582i	$0.0915228\pi$
$548$		−	2.39942e13i		−	0.485516i
$549$		0			0
$550$	8.39971e12			0.166898
$551$	−2.61660e12	−	1.51069e12i	−0.0515204	−	0.0297453i
$552$		0			0
$553$	−1.28277e13	−	2.22182e13i	−0.248040	−	0.429618i
$554$	4.79907e13	−	2.77074e13i	0.919619	−	0.530942i
$555$		0			0
$556$	−1.35232e12	+	2.34228e12i	−0.0254510	+	0.0440824i
$557$			9.11885e13i			1.70084i	0.526103	+	0.850421i	$0.323653\pi$
$557$			9.11885e13i			1.70084i	−0.526103	+	0.850421i	$0.676347\pi$
$558$		0			0
$559$	−1.82242e13			−0.333879
$560$	2.73752e13	+	1.58051e13i	0.497069	+	0.286983i
$561$		0			0
$562$	−3.60887e13	−	6.25074e13i	−0.643709	−	1.11494i
$563$	−4.11249e13	+	2.37435e13i	−0.727048	+	0.419761i	−0.817341	−	0.576154i	$-0.804553\pi$
$563$	−4.11249e13	+	2.37435e13i	−0.727048	+	0.419761i	0.0902935	+	0.995915i	$0.471219\pi$
$564$		0			0
$565$	−3.60281e13	+	6.24025e13i	−0.625748	+	1.08383i
$566$		−	3.87824e13i		−	0.667655i
$567$		0			0
$568$	−9.56194e13			−1.61735
$569$	−9.85971e12	−	5.69251e12i	−0.165311	−	0.0954426i	0.415062	−	0.909793i	$-0.363760\pi$
$569$	−9.85971e12	−	5.69251e12i	−0.165311	−	0.0954426i	−0.580373	+	0.814351i	$0.697093\pi$
$570$		0			0
$571$	9.98538e12	+	1.72952e13i	0.164507	+	0.284934i	0.936480	−	0.350721i	$-0.114063\pi$
$571$	9.98538e12	+	1.72952e13i	0.164507	+	0.284934i	−0.771973	+	0.635655i	$0.780730\pi$
$572$	−8.34389e12	+	4.81735e12i	−0.136266	+	0.0786734i
$573$		0			0
$574$	4.20050e13	−	7.27548e13i	0.674127	−	1.16762i
$575$		−	4.45340e12i		−	0.0708521i
$576$		0			0
$577$	−8.52618e12			−0.133314			−0.0666569	−	0.997776i	$-0.521233\pi$
$577$	−8.52618e12			−0.133314			−0.0666569	+	0.997776i	$0.521233\pi$
$578$	4.41096e13	+	2.54667e13i	0.683745	+	0.394760i
$579$		0			0
$580$	−1.37577e12	−	2.38290e12i	−0.0209606	−	0.0363049i
$581$	−1.88930e13	+	1.09079e13i	−0.285377	+	0.164763i
$582$		0			0
$583$	−1.79422e13	+	3.10769e13i	−0.266400	+	0.461418i
$584$			1.01433e14i			1.49319i
$585$		0			0
$586$	−9.09862e13			−1.31670
$587$	−1.28947e13	−	7.44475e12i	−0.185021	−	0.106822i	0.404629	−	0.914481i	$-0.367401\pi$
$587$	−1.28947e13	−	7.44475e12i	−0.185021	−	0.106822i	−0.589649	+	0.807659i	$0.700734\pi$
$588$		0			0
$589$	−1.41437e13	−	2.44976e13i	−0.199520	−	0.345579i
$590$	4.29061e13	−	2.47719e13i	0.600149	−	0.346496i
$591$		0			0
$592$	−1.96077e13	+	3.39615e13i	−0.269661	+	0.467066i
$593$			3.80871e13i			0.519404i	0.965689	+	0.259702i	$0.0836243\pi$
$593$			3.80871e13i			0.519404i	−0.965689	+	0.259702i	$0.916376\pi$
$594$		0			0
$595$	−1.68253e13			−0.225620
$596$	−1.95680e13	−	1.12976e13i	−0.260204	−	0.150229i
$597$		0			0
$598$	−6.04916e12	−	1.04774e13i	−0.0791023	−	0.137009i
$599$	−7.41686e13	+	4.28213e13i	−0.961803	+	0.555297i	−0.896727	−	0.442583i	$-0.854062\pi$
$599$	−7.41686e13	+	4.28213e13i	−0.961803	+	0.555297i	−0.0650753	+	0.997880i	$0.520729\pi$
$600$		0			0
$601$	1.44866e13	−	2.50915e13i	0.184754	−	0.320004i	−0.758739	−	0.651394i	$-0.774184\pi$
$601$	1.44866e13	−	2.50915e13i	0.184754	−	0.320004i	0.943494	+	0.331391i	$0.107518\pi$
$602$		−	4.96748e13i		−	0.628281i
$603$		0			0
$604$	−1.79649e13			−0.223480
$605$	2.20718e13	+	1.27432e13i	0.272309	+	0.157218i
$606$		0			0
$607$	4.20704e13	+	7.28681e13i	0.510544	+	0.884289i	0.999925	+	0.0122187i	$0.00388942\pi$
$607$	4.20704e13	+	7.28681e13i	0.510544	+	0.884289i	−0.489381	+	0.872070i	$0.662777\pi$
$608$	1.57756e13	−	9.10804e12i	0.189875	−	0.109624i
$609$		0			0
$610$	−3.93351e13	+	6.81304e13i	−0.465726	+	0.806662i
$611$		−	4.54665e13i		−	0.533932i
$612$		0			0
$613$	2.27205e13			0.262492			0.131246	−	0.991350i	$-0.458102\pi$
$613$	2.27205e13			0.262492			0.131246	+	0.991350i	$0.458102\pi$
$614$	4.81267e13	+	2.77860e13i	0.551498	+	0.318408i
$615$		0			0
$616$	−5.73615e13	−	9.93531e13i	−0.646721	−	1.12015i
$617$	2.25944e13	−	1.30449e13i	0.252683	−	0.145887i	−0.368309	−	0.929703i	$-0.620063\pi$
$617$	2.25944e13	−	1.30449e13i	0.252683	−	0.145887i	0.620992	+	0.783817i	$0.286730\pi$
$618$		0			0
$619$	−8.59395e13	+	1.48852e14i	−0.945670	+	1.63795i	−0.191267	+	0.981538i	$0.561260\pi$
$619$	−8.59395e13	+	1.48852e14i	−0.945670	+	1.63795i	−0.754403	+	0.656411i	$0.772074\pi$
$620$		−	2.57609e13i		−	0.281192i
$621$		0			0
$622$	−5.75263e13			−0.617895
$623$	−8.98567e13	−	5.18788e13i	−0.957437	−	0.552777i
$624$		0			0
$625$	3.80976e13	+	6.59869e13i	0.399482	+	0.691923i
$626$	1.89351e13	−	1.09322e13i	0.196968	−	0.113720i
$627$		0			0
$628$	5.80432e12	−	1.00534e13i	0.0594228	−	0.102923i
$629$		−	2.08734e13i		−	0.212002i
$630$		0			0
$631$	−1.35624e12			−0.0135578			−0.00677891	−	0.999977i	$-0.502158\pi$
$631$	−1.35624e12			−0.0135578			−0.00677891	+	0.999977i	$0.502158\pi$
$632$	4.59396e13	+	2.65232e13i	0.455619	+	0.263052i
$633$		0			0
$634$	1.10179e13	+	1.90835e13i	0.107560	+	0.186300i
$635$	1.43876e14	−	8.30669e13i	1.39354	−	0.804562i
$636$		0			0
$637$	1.23300e12	−	2.13562e12i	0.0117562	−	0.0203623i
$638$		−	1.59513e13i		−	0.150901i
$639$		0			0
$640$	−3.38081e13			−0.314863
$641$	−1.01810e14	−	5.87803e13i	−0.940811	−	0.543177i	−0.0505962	−	0.998719i	$-0.516112\pi$
$641$	−1.01810e14	−	5.87803e13i	−0.940811	−	0.543177i	−0.890214	+	0.455542i	$0.849445\pi$
$642$		0			0
$643$	−6.80648e13	−	1.17892e14i	−0.619253	−	1.07258i	−0.989622	−	0.143693i	$-0.954102\pi$
$643$	−6.80648e13	−	1.17892e14i	−0.619253	−	1.07258i	0.370370	−	0.928884i	$-0.379231\pi$
$644$	−1.20583e13	+	6.96184e12i	−0.108857	+	0.0628485i
$645$		0			0
$646$	4.37239e12	−	7.57320e12i	0.0388648	−	0.0673157i
$647$		−	1.40299e14i		−	1.23747i	−0.785601	−	0.618734i	$-0.787646\pi$
$647$		−	1.40299e14i		−	1.23747i	0.785601	−	0.618734i	$-0.212354\pi$
$648$		0			0
$649$	−1.21269e14			−1.05324
$650$	−6.60630e12	−	3.81415e12i	−0.0569366	−	0.0328724i
$651$		0			0
$652$	−2.44771e13	−	4.23956e13i	−0.207741	−	0.359818i
$653$	−1.07018e14	+	6.17869e13i	−0.901346	+	0.520392i	−0.877636	−	0.479327i	$-0.840881\pi$
$653$	−1.07018e14	+	6.17869e13i	−0.901346	+	0.520392i	−0.0237091	+	0.999719i	$0.507548\pi$
$654$		0			0
$655$	8.07393e13	−	1.39845e14i	0.669697	−	1.15995i
$656$			1.17151e14i			0.964335i
$657$		0			0
$658$	1.23931e14			1.00473
$659$	1.68113e14	+	9.70601e13i	1.35262	+	0.780933i	0.988615	−	0.150466i	$-0.0480775\pi$
$659$	1.68113e14	+	9.70601e13i	1.35262	+	0.780933i	0.364000	+	0.931399i	$0.381411\pi$
$660$		0			0
$661$	1.12407e14	+	1.94694e14i	0.890810	+	1.54293i	0.838906	+	0.544276i	$0.183195\pi$
$661$	1.12407e14	+	1.94694e14i	0.890810	+	1.54293i	0.0519034	+	0.998652i	$0.483471\pi$
$662$	−4.10691e13	+	2.37113e13i	−0.323017	+	0.186494i
$663$		0			0
$664$	2.25537e13	−	3.90641e13i	0.174734	−	0.302648i
$665$		−	4.65410e13i		−	0.357872i
$666$		0			0
$667$	−8.45714e12			−0.0640611
$668$	−1.56844e13	−	9.05537e12i	−0.117919	−	0.0680807i
$669$		0			0
$670$	−7.16165e13	−	1.24043e14i	−0.530443	−	0.918755i
$671$	1.66764e14	−	9.62813e13i	1.22600	−	0.707831i
$672$		0			0
$673$	−3.19647e13	+	5.53644e13i	−0.231523	+	0.401010i	−0.958257	−	0.285910i	$-0.907704\pi$
$673$	−3.19647e13	+	5.53644e13i	−0.231523	+	0.401010i	0.726733	+	0.686920i	$0.241038\pi$
$674$			1.43764e13i			0.103360i
$675$		0			0
$676$	−3.31591e13			−0.234893
$677$	5.92439e13	+	3.42045e13i	0.416582	+	0.240514i	0.693614	−	0.720347i	$-0.256017\pi$
$677$	5.92439e13	+	3.42045e13i	0.416582	+	0.240514i	−0.277032	+	0.960861i	$0.589351\pi$
$678$		0			0
$679$	1.37264e13	+	2.37749e13i	0.0951063	+	0.164729i
$680$	3.01281e13	−	1.73945e13i	0.207218	−	0.119637i
$681$		0			0
$682$	7.46711e13	−	1.29334e14i	0.506093	−	0.876579i
$683$			1.17660e14i			0.791639i	0.918328	+	0.395819i	$0.129539\pi$
$683$			1.17660e14i			0.791639i	−0.918328	+	0.395819i	$0.870461\pi$
$684$		0			0
$685$	2.24494e14			1.48851
$686$	−1.07305e14	−	6.19526e13i	−0.706317	−	0.407792i
$687$		0			0
$688$	3.46356e13	+	5.99905e13i	0.224688	+	0.389171i
$689$	2.82229e13	−	1.62945e13i	0.181763	−	0.104941i
$690$		0			0
$691$	−2.70246e13	+	4.68080e13i	−0.171541	+	0.297119i	−0.938959	−	0.344029i	$-0.888208\pi$
$691$	−2.70246e13	+	4.68080e13i	−0.171541	+	0.297119i	0.767417	+	0.641148i	$0.221541\pi$
$692$			6.29193e13i			0.396509i
$693$		0			0
$694$	1.30766e14			0.812263
$695$	−2.19148e13	−	1.26525e13i	−0.135149	−	0.0780285i
$696$		0			0
$697$	−3.11784e13	−	5.40025e13i	−0.189535	−	0.328284i
$698$	−1.82131e12	+	1.05153e12i	−0.0109927	+	0.00634667i
$699$		0			0
$700$	−4.38962e12	+	7.60305e12i	−0.0261178	+	0.0452374i
$701$		−	2.61865e14i		−	1.54699i	−0.633804	−	0.773493i	$-0.718508\pi$
$701$		−	2.61865e14i		−	1.54699i	0.633804	−	0.773493i	$-0.281492\pi$
$702$		0			0
$703$	5.77385e13			0.336271
$704$	1.90118e14	+	1.09765e14i	1.09941	+	0.634745i
$705$		0			0
$706$	6.58483e13	+	1.14053e14i	0.375423	+	0.650252i
$707$	−6.31353e13	+	3.64512e13i	−0.357417	+	0.206355i
$708$		0			0
$709$	6.08017e13	−	1.05312e14i	0.339378	−	0.587821i	−0.644938	−	0.764235i	$-0.723117\pi$
$709$	6.08017e13	−	1.05312e14i	0.339378	−	0.587821i	0.984316	+	0.176415i	$0.0564499\pi$
$710$		−	2.04795e14i		−	1.13509i
$711$		0			0
$712$	2.14535e14			1.17246
$713$	−6.85711e13	−	3.95895e13i	−0.372129	−	0.214849i
$714$		0			0
$715$	−4.50720e13	−	7.80669e13i	−0.241199	−	0.417770i
$716$	−1.37460e13	+	7.93626e12i	−0.0730485	+	0.0421746i
$717$		0			0
$718$	−1.10510e13	+	1.91409e13i	−0.0579136	+	0.100309i
$719$			2.82360e14i			1.46946i	0.678359	+	0.734731i	$0.262692\pi$
$719$			2.82360e14i			1.46946i	−0.678359	+	0.734731i	$0.737308\pi$
$720$		0			0
$721$	7.61330e13			0.390748
$722$	−1.21525e14	−	7.01623e13i	−0.619410	−	0.357617i
$723$		0			0
$724$	5.15037e13	+	8.92071e13i	0.258908	+	0.448442i
$725$	−4.61803e12	+	2.66622e12i	−0.0230551	+	0.0133109i
$726$		0			0
$727$	3.49005e13	−	6.04494e13i	0.171854	−	0.297660i	−0.767214	−	0.641391i	$-0.778358\pi$
$727$	3.49005e13	−	6.04494e13i	0.171854	−	0.297660i	0.939068	+	0.343731i	$0.111691\pi$
$728$			1.04187e14i			0.509516i
$729$		0			0
$730$	−2.17247e14			−1.04795
$731$	−3.19315e13	−	1.84357e13i	−0.152979	−	0.0883226i
$732$		0			0
$733$	1.64199e14	+	2.84400e14i	0.775978	+	1.34403i	0.934243	+	0.356637i	$0.116077\pi$
$733$	1.64199e14	+	2.84400e14i	0.775978	+	1.34403i	−0.158265	+	0.987397i	$0.550590\pi$
$734$	−1.29187e14	+	7.45863e13i	−0.606372	+	0.350089i
$735$		0			0
$736$	2.54942e13	−	4.41573e13i	0.118046	−	0.204462i
$737$			3.50594e14i			1.61238i
$738$		0			0
$739$	3.04479e14			1.38145			0.690726	−	0.723117i	$-0.257291\pi$
$739$	3.04479e14			1.38145			0.690726	+	0.723117i	$0.257291\pi$
$740$	4.55370e13	+	2.62908e13i	0.205213	+	0.118480i
$741$		0			0
$742$	4.44149e13	+	7.69289e13i	0.197474	+	0.342034i
$743$	−2.44010e14	+	1.40879e14i	−1.07762	+	0.622162i	−0.930253	−	0.366920i	$-0.880412\pi$
$743$	−2.44010e14	+	1.40879e14i	−1.07762	+	0.622162i	−0.147364	+	0.989082i	$0.547079\pi$
$744$		0			0
$745$	1.05702e14	−	1.83082e14i	0.460577	−	0.797743i
$746$			1.13213e12i			0.00490008i
$747$		0			0
$748$	−1.94930e13			−0.0832474
$749$	−4.76622e13	−	2.75178e13i	−0.202193	−	0.116736i
$750$		0			0
$751$	−1.93318e14	−	3.34836e14i	−0.809230	−	1.40163i	−0.913398	−	0.407068i	$-0.866551\pi$
$751$	−1.93318e14	−	3.34836e14i	−0.809230	−	1.40163i	0.104168	−	0.994560i	$-0.466782\pi$
$752$	−1.49667e14	+	8.64104e13i	−0.622354	+	0.359316i
$753$		0			0
$754$	−7.24318e12	+	1.25456e13i	−0.0297216	+	0.0514794i
$755$		−	1.68083e14i		−	0.685153i
$756$		0			0
$757$	−1.76968e13			−0.0711893			−0.0355947	−	0.999366i	$-0.511333\pi$
$757$	−1.76968e13			−0.0711893			−0.0355947	+	0.999366i	$0.511333\pi$
$758$	−2.21091e14	−	1.27647e14i	−0.883536	−	0.510110i
$759$		0			0
$760$	4.81154e13	+	8.33383e13i	0.189765	+	0.328683i
$761$	−1.50970e14	+	8.71625e13i	−0.591517	+	0.341512i	−0.765697	−	0.643201i	$-0.777606\pi$
$761$	−1.50970e14	+	8.71625e13i	−0.591517	+	0.341512i	0.174180	+	0.984714i	$0.444272\pi$
$762$		0			0
$763$	1.33262e14	−	2.30817e14i	0.515329	−	0.892576i
$764$		−	4.72779e13i		−	0.181632i
$765$		0			0
$766$	7.58677e13			0.287682
$767$	9.53773e13	+	5.50661e13i	0.359309	+	0.207447i
$768$		0			0
$769$	−9.69869e13	−	1.67986e14i	−0.360646	−	0.624658i	0.627421	−	0.778680i	$-0.284111\pi$
$769$	−9.69869e13	−	1.67986e14i	−0.360646	−	0.624658i	−0.988067	+	0.154023i	$0.950777\pi$
$770$	2.12792e14	−	1.22856e14i	0.786143	−	0.453880i
$771$		0			0
$772$	−5.32539e13	+	9.22385e13i	−0.194207	+	0.336377i
$773$			5.25639e13i			0.190454i	0.995456	+	0.0952270i	$0.0303577\pi$
$773$			5.25639e13i			0.190454i	−0.995456	+	0.0952270i	$0.969642\pi$
$774$		0			0
$775$	−4.99245e13			−0.178569
$776$	−4.91583e13	−	2.83816e13i	−0.174698	−	0.100862i
$777$		0			0
$778$	−1.50416e13	−	2.60527e13i	−0.0527710	−	0.0914020i
$779$	1.49378e14	−	8.62435e13i	0.520715	−	0.300635i
$780$		0			0
$781$	−2.50641e14	+	4.34123e14i	−0.862575	+	1.49402i
$782$		−	2.44774e13i		−	0.0837012i
$783$		0			0
$784$	−9.37343e12			−0.0316459
$785$	9.40612e13	+	5.43063e13i	0.315546	+	0.182180i
$786$		0			0
$787$	7.63325e13	+	1.32212e14i	0.252834	+	0.437922i	0.964305	−	0.264794i	$-0.0853039\pi$
$787$	7.63325e13	+	1.32212e14i	0.252834	+	0.437922i	−0.711471	+	0.702716i	$0.751971\pi$
$788$	8.21400e13	−	4.74236e13i	0.270348	−	0.156086i
$789$		0			0
$790$	−5.68068e13	+	9.83923e13i	−0.184614	+	0.319761i
$791$		−	4.36602e14i		−	1.40995i
$792$		0			0
$793$	−1.74878e14			−0.557661
$794$	−1.73525e14	−	1.00185e14i	−0.549868	−	0.317467i
$795$		0			0
$796$	2.30953e13	+	4.00022e13i	0.0722700	+	0.125175i
$797$	2.78797e14	−	1.60963e14i	0.866954	−	0.500536i	0.000619207	−	1.00000i	$-0.499803\pi$
$797$	2.78797e14	−	1.60963e14i	0.866954	−	0.500536i	0.866335	+	0.499464i	$0.166470\pi$
$798$		0			0
$799$	4.59941e13	−	7.96642e13i	0.141244	−	0.244641i
$800$		−	3.21495e13i		−	0.0981126i
$801$		0			0
$802$	4.37269e14			1.31788
$803$	4.60518e14	+	2.65880e14i	1.37933	+	0.796358i
$804$		0			0
$805$	−6.51362e13	−	1.12819e14i	−0.192683	−	0.333737i
$806$	−1.17456e14	+	6.78135e13i	−0.345304	+	0.199361i
$807$		0			0
$808$	7.53685e13	−	1.30542e14i	0.218843	−	0.379048i
$809$			4.22482e14i			1.21917i	0.792719	+	0.609587i	$0.208665\pi$
$809$			4.22482e14i			1.21917i	−0.792719	+	0.609587i	$0.791335\pi$
$810$		0			0
$811$	−5.21066e14			−1.48521			−0.742607	−	0.669728i	$-0.766411\pi$
$811$	−5.21066e14			−1.48521			−0.742607	+	0.669728i	$0.766411\pi$
$812$	1.44384e13	+	8.33602e12i	0.0409015	+	0.0236145i
$813$		0			0
$814$	1.52414e14	+	2.63989e14i	0.426484	+	0.738692i
$815$	3.96661e14	−	2.29012e14i	1.10314	−	0.636900i
$816$		0			0
$817$	5.09955e13	−	8.83267e13i	0.140095	−	0.242651i
$818$		−	2.82105e14i		−	0.770272i
$819$		0			0
$820$	1.57081e14			0.423697
$821$	1.61767e14	+	9.33960e13i	0.433684	+	0.250387i	0.700915	−	0.713245i	$-0.252775\pi$
$821$	1.61767e14	+	9.33960e13i	0.433684	+	0.250387i	−0.267231	+	0.963632i	$0.586109\pi$
$822$		0			0
$823$	−3.11391e13	−	5.39345e13i	−0.0824721	−	0.142846i	0.821839	−	0.569720i	$-0.192948\pi$
$823$	−3.11391e13	−	5.39345e13i	−0.0824721	−	0.142846i	−0.904311	+	0.426874i	$0.859615\pi$
$824$	−1.36327e14	+	7.87084e13i	−0.358877	+	0.207198i
$825$		0			0
$826$	−1.50097e14	+	2.59976e14i	−0.390366	+	0.676134i
$827$			3.99626e14i			1.03306i	0.856269	+	0.516530i	$0.172777\pi$
$827$			3.99626e14i			1.03306i	−0.856269	+	0.516530i	$0.827223\pi$
$828$		0			0
$829$	−5.51493e14			−1.40853			−0.704267	−	0.709935i	$-0.748724\pi$
$829$	−5.51493e14			−1.40853			−0.704267	+	0.709935i	$0.748724\pi$
$830$	8.36666e13	+	4.83050e13i	0.212404	+	0.122631i
$831$		0			0
$832$	−9.96842e13	−	1.72658e14i	−0.250040	−	0.433082i
$833$	4.32081e12	−	2.49462e12i	0.0107731	−	0.00621985i
$834$		0			0
$835$	8.47237e13	−	1.46746e14i	0.208724	−	0.361521i
$836$		−	5.39202e13i		−	0.132044i
$837$		0			0
$838$	−5.86856e14			−1.42008
$839$	−1.71889e14	−	9.92403e13i	−0.413465	−	0.238714i	0.278812	−	0.960346i	$-0.410059\pi$
$839$	−1.71889e14	−	9.92403e13i	−0.413465	−	0.238714i	−0.692277	+	0.721631i	$0.743393\pi$
$840$		0			0
$841$	−2.05290e14	−	3.55573e14i	−0.487965	−	0.845180i
$842$	−1.57014e14	+	9.06519e13i	−0.371003	+	0.214198i
$843$		0			0
$844$	−2.07067e13	+	3.58651e13i	−0.0483503	+	0.0837453i
$845$		−	3.10243e14i		−	0.720141i
$846$		0			0
$847$	−1.54427e14			−0.354246
$848$	−1.07277e14	−	6.19362e13i	−0.244639	−	0.141242i
$849$		0			0
$850$	−7.71682e12	−	1.33659e13i	−0.0173918	−	0.0301234i
$851$	1.39963e14	−	8.08077e13i	0.313592	−	0.181053i
$852$		0			0
$853$	−3.59566e14	+	6.22786e14i	−0.796221	+	1.37909i	0.125841	+	0.992050i	$0.459837\pi$
$853$	−3.59566e14	+	6.22786e14i	−0.796221	+	1.37909i	−0.922061	+	0.387044i	$0.873496\pi$
$854$		−	4.76677e14i		−	1.04938i
$855$		0			0
$856$	1.13795e14			0.247601
$857$	2.22970e14	+	1.28732e14i	0.482327	+	0.278472i	0.721386	−	0.692533i	$-0.243505\pi$
$857$	2.22970e14	+	1.28732e14i	0.482327	+	0.278472i	−0.239059	+	0.971005i	$0.576839\pi$
$858$		0			0
$859$	−2.40682e14	−	4.16874e14i	−0.514610	−	0.891331i	−0.999856	−	0.0169533i	$-0.994603\pi$
$859$	−2.40682e14	−	4.16874e14i	−0.514610	−	0.891331i	0.485246	−	0.874378i	$-0.338730\pi$
$860$	8.04378e13	−	4.64408e13i	0.170989	−	0.0987205i
$861$		0			0
$862$	−2.12274e14	+	3.67669e14i	−0.446026	+	0.772539i
$863$		−	1.08169e13i		−	0.0225969i	−0.999936	−	0.0112985i	$-0.996404\pi$
$863$		−	1.08169e13i		−	0.0225969i	0.999936	−	0.0112985i	$-0.00359649\pi$
$864$		0			0
$865$	−5.88684e14			−1.21563
$866$	−3.39560e14	−	1.96045e14i	−0.697152	−	0.402501i
$867$		0			0
$868$	7.80451e13	+	1.35178e14i	0.158397	+	0.274352i
$869$	2.40837e14	−	1.39047e14i	0.485986	−	0.280584i
$870$		0			0
$871$	1.59198e14	−	2.75740e14i	0.317576	−	0.550058i
$872$			5.51081e14i			1.09303i
$873$		0			0
$874$	6.77077e13			0.132764
$875$	−4.85697e14	−	2.80417e14i	−0.946946	−	0.546719i
$876$		0			0
$877$	3.47221e13	+	6.01404e13i	0.0669280	+	0.115923i	0.897548	−	0.440918i	$-0.145347\pi$
$877$	3.47221e13	+	6.01404e13i	0.0669280	+	0.115923i	−0.830620	+	0.556840i	$0.812014\pi$
$878$	2.94717e14	−	1.70155e14i	0.564849	−	0.326116i
$879$		0			0
$880$	−1.71321e14	+	2.96737e14i	−0.324636	+	0.562287i
$881$		−	9.22199e14i		−	1.73758i	−0.495180	−	0.868791i	$-0.664898\pi$
$881$		−	9.22199e14i		−	1.73758i	0.495180	−	0.868791i	$-0.335102\pi$
$882$		0			0
$883$	−3.03213e13			−0.0564864			−0.0282432	−	0.999601i	$-0.508991\pi$
$883$	−3.03213e13			−0.0564864			−0.0282432	+	0.999601i	$0.508991\pi$
$884$	1.53311e13	+	8.85141e12i	0.0283996	+	0.0163965i
$885$		0			0
$886$	6.28763e13	+	1.08905e14i	0.115164	+	0.199470i
$887$	−8.12098e14	+	4.68865e14i	−1.47907	+	0.853944i	−0.999720	−	0.0236769i	$-0.992463\pi$
$887$	−8.12098e14	+	4.68865e14i	−1.47907	+	0.853944i	−0.479355	+	0.877621i	$0.659129\pi$
$888$		0			0
$889$	−5.03318e14	+	8.71772e14i	−0.906428	+	1.56998i
$890$			4.59486e14i			0.822853i
$891$		0			0
$892$	3.51342e13			0.0622165
$893$	2.20362e14	+	1.27226e14i	0.388042	+	0.224036i
$894$		0			0
$895$	−7.42531e13	−	1.28610e14i	−0.129300	−	0.223955i
$896$	1.77405e14	−	1.02425e14i	0.307203	−	0.177364i
$897$		0			0
$898$	3.78897e14	−	6.56268e14i	0.648842	−	1.12383i
$899$			9.48080e13i			0.161453i
$900$		0			0
$901$	6.59342e13			0.111042
$902$	7.88635e14	+	4.55319e14i	1.32082	+	0.762575i
$903$		0			0
$904$	4.51371e14	+	7.81798e14i	0.747639	+	1.29495i
$905$	−8.34638e14	+	4.81878e14i	−1.37485	+	0.793769i
$906$		0			0
$907$	4.57765e14	−	7.92873e14i	0.745773	−	1.29172i	−0.204060	−	0.978958i	$-0.565414\pi$
$907$	4.57765e14	−	7.92873e14i	0.745773	−	1.29172i	0.949833	−	0.312758i	$-0.101253\pi$
$908$			6.76145e12i			0.0109550i
$909$		0			0
$910$	−2.23146e14			−0.357587
$911$	−9.63748e14	−	5.56420e14i	−1.53593	−	0.886770i	−0.999071	−	0.0430993i	$-0.986277\pi$
$911$	−9.63748e14	−	5.56420e14i	−1.53593	−	0.886770i	−0.536860	−	0.843671i	$-0.680390\pi$
$912$		0			0
$913$	−1.18237e14	−	2.04793e14i	−0.186380	−	0.322820i
$914$	−2.14452e14	+	1.23814e14i	−0.336201	+	0.194106i
$915$		0			0
$916$	−8.33270e13	+	1.44327e14i	−0.129214	+	0.223805i
$917$			9.78428e14i			1.50898i
$918$		0			0
$919$	4.68203e14			0.714260			0.357130	−	0.934055i	$-0.383755\pi$
$919$	4.68203e14			0.714260			0.357130	+	0.934055i	$0.383755\pi$
$920$	2.33271e14	+	1.34679e14i	0.353934	+	0.204344i
$921$		0			0
$922$	−1.04779e14	−	1.81482e14i	−0.157260	−	0.272383i
$923$	3.94254e14	−	2.27623e14i	0.588529	−	0.339788i
$924$		0			0
$925$	5.09514e13	−	8.82503e13i	0.0752397	−	0.130319i
$926$			8.86642e14i			1.30225i
$927$		0			0
$928$	−6.10529e13			−0.0887087
$929$	−3.51235e14	−	2.02786e14i	−0.507597	−	0.293062i	0.224248	−	0.974532i	$-0.428007\pi$
$929$	−3.51235e14	−	2.02786e14i	−0.507597	−	0.293062i	−0.731846	+	0.681471i	$0.761341\pi$
$930$		0			0
$931$	6.90046e12	+	1.19519e13i	0.00986573	+	0.0170880i
$932$	−2.26062e14	+	1.30517e14i	−0.321476	+	0.185604i
$933$		0			0
$934$	−5.45950e13	+	9.45613e13i	−0.0768101	+	0.133039i
$935$		−	1.82380e14i		−	0.255223i
$936$		0			0
$937$	−1.63835e14			−0.226834			−0.113417	−	0.993547i	$-0.536180\pi$
$937$	−1.63835e14			−0.226834			−0.113417	+	0.993547i	$0.536180\pi$
$938$	7.51602e14	+	4.33937e14i	1.03508	+	0.597603i
$939$		0			0
$940$	1.15863e14	+	2.00680e14i	0.157872	+	0.273442i
$941$	6.60424e14	−	3.81296e14i	0.895106	−	0.516790i	0.0194969	−	0.999810i	$-0.493794\pi$
$941$	6.60424e14	−	3.81296e14i	0.895106	−	0.516790i	0.875609	+	0.483020i	$0.160460\pi$
$942$		0			0
$943$	2.41403e14	−	4.18123e14i	0.323731	−	0.560719i
$944$		−	4.18618e14i		−	0.558417i
$945$		0			0
$946$	5.38456e14			0.710714
$947$	8.73508e14	+	5.04320e14i	1.14688	+	0.662150i	0.948124	−	0.317900i	$-0.102978\pi$
$947$	8.73508e14	+	5.04320e14i	1.14688	+	0.662150i	0.198753	+	0.980050i	$0.436311\pi$
$948$		0			0
$949$	−2.41462e14	−	4.18225e14i	−0.313703	−	0.543349i
$950$	3.69719e13	−	2.13457e13i	0.0477809	−	0.0275863i
$951$		0			0
$952$	−1.05396e14	+	1.82552e14i	−0.134785	+	0.233454i
$953$		−	2.25382e14i		−	0.286718i	−0.989671	−	0.143359i	$-0.954210\pi$
$953$		−	2.25382e14i		−	0.286718i	0.989671	−	0.143359i	$-0.0457903\pi$
$954$		0			0
$955$	4.42340e14			0.556852
$956$	−2.39855e14	−	1.38480e14i	−0.300372	−	0.173420i
$957$		0			0
$958$	−1.73364e14	−	3.00276e14i	−0.214848	−	0.372128i
$959$	−1.17801e15	+	6.80125e14i	−1.45230	+	0.838486i
$960$		0			0
$961$	−3.40008e13	+	5.88911e13i	−0.0414832	+	0.0718510i
$962$		−	2.76833e14i		−	0.336003i
$963$		0			0
$964$	1.12860e14			0.135567
$965$	−8.63000e14	−	4.98253e14i	−1.03127	−	0.595407i
$966$		0			0
$967$	−3.94637e14	−	6.83532e14i	−0.466730	−	0.808400i	0.532548	−	0.846400i	$-0.321235\pi$
$967$	−3.94637e14	−	6.83532e14i	−0.466730	−	0.808400i	−0.999278	+	0.0379997i	$0.987901\pi$
$968$	2.76523e14	−	1.59650e14i	0.325352	−	0.187842i
$969$		0			0
$970$	6.07869e13	−	1.05286e14i	0.0707867	−	0.122606i
$971$		−	2.37876e14i		−	0.275584i	−0.990461	−	0.137792i	$-0.955999\pi$
$971$		−	2.37876e14i		−	0.275584i	0.990461	−	0.137792i	$-0.0440006\pi$
$972$		0			0
$973$	1.53328e14			0.175816
$974$	−5.02800e14	−	2.90292e14i	−0.573589	−	0.331162i
$975$		0			0
$976$	3.32361e14	+	5.75666e14i	0.375285	+	0.650012i
$977$	4.00876e14	−	2.31446e14i	0.450337	−	0.260002i	−0.257636	−	0.966242i	$-0.582943\pi$
$977$	4.00876e14	−	2.31446e14i	0.450337	−	0.260002i	0.707972	+	0.706240i	$0.249610\pi$
$978$		0			0
$979$	5.62347e14	−	9.74013e14i	0.625303	−	1.08306i
$980$			1.25683e13i			0.0139042i
$981$		0			0
$982$	9.10545e14			0.997112
$983$	−6.10331e14	−	3.52375e14i	−0.664964	−	0.383917i	0.129202	−	0.991618i	$-0.458758\pi$
$983$	−6.10331e14	−	3.52375e14i	−0.664964	−	0.383917i	−0.794166	+	0.607701i	$0.792092\pi$
$984$		0			0
$985$	4.43703e14	+	7.68517e14i	0.478533	+	0.828843i
$986$	−2.53823e13	+	1.46545e13i	−0.0272362	+	0.0157248i
$987$		0			0
$988$	−2.44842e13	+	4.24078e13i	−0.0260076	+	0.0450465i
$989$		−	2.85482e14i		−	0.301715i
$990$		0			0
$991$	9.64032e14			1.00861			0.504305	−	0.863526i	$-0.331749\pi$
$991$	9.64032e14			1.00861			0.504305	+	0.863526i	$0.331749\pi$
$992$	−4.95021e14	−	2.85801e14i	−0.515306	−	0.297512i
$993$		0			0
$994$	6.20446e14	+	1.07464e15i	0.639399	+	1.10747i
$995$	−3.74268e14	+	2.16084e14i	−0.383766	+	0.221568i
$996$		0			0
$997$	4.34836e14	−	7.53159e14i	0.441418	−	0.764558i	−0.556377	−	0.830930i	$-0.687809\pi$
$997$	4.34836e14	−	7.53159e14i	0.441418	−	0.764558i	0.997795	+	0.0663715i	$0.0211423\pi$
$998$			4.92045e14i			0.496996i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.11.d.d.26.2		4
3.2	odd	2	inner	81.11.d.d.26.1		4
9.2	odd	6		3.11.b.a.2.2	yes	2
9.4	even	3	inner	81.11.d.d.53.1		4
9.5	odd	6	inner	81.11.d.d.53.2		4
9.7	even	3		3.11.b.a.2.1	✓	2
36.7	odd	6		48.11.e.c.17.2		2
36.11	even	6		48.11.e.c.17.1		2
45.2	even	12		75.11.d.b.74.2		4
45.7	odd	12		75.11.d.b.74.4		4
45.29	odd	6		75.11.c.d.26.1		2
45.34	even	6		75.11.c.d.26.2		2
45.38	even	12		75.11.d.b.74.3		4
45.43	odd	12		75.11.d.b.74.1		4
72.11	even	6		192.11.e.d.65.2		2
72.29	odd	6		192.11.e.e.65.1		2
72.43	odd	6		192.11.e.d.65.1		2
72.61	even	6		192.11.e.e.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.11.b.a.2.1	✓	2	9.7	even	3
3.11.b.a.2.2	yes	2	9.2	odd	6
48.11.e.c.17.1		2	36.11	even	6
48.11.e.c.17.2		2	36.7	odd	6
75.11.c.d.26.1		2	45.29	odd	6
75.11.c.d.26.2		2	45.34	even	6
75.11.d.b.74.1		4	45.43	odd	12
75.11.d.b.74.2		4	45.2	even	12
75.11.d.b.74.3		4	45.38	even	12
75.11.d.b.74.4		4	45.7	odd	12
81.11.d.d.26.1		4	3.2	odd	2	inner
81.11.d.d.26.2		4	1.1	even	1	trivial
81.11.d.d.53.1		4	9.4	even	3	inner
81.11.d.d.53.2		4	9.5	odd	6	inner
192.11.e.d.65.1		2	72.43	odd	6
192.11.e.d.65.2		2	72.11	even	6
192.11.e.e.65.1		2	72.29	odd	6
192.11.e.e.65.2		2	72.61	even	6

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(23.2379 + 13.4164i) q^{2} +(-152.000 - 263.272i) q^{4} +(2463.22 - 1422.14i) q^{5} +(-8617.00 + 14925.1i) q^{7} -35634.0i q^{8} +O(q^{10})\)	\(q+(23.2379 + 13.4164i) q^{2} +(-152.000 - 263.272i) q^{4} +(2463.22 - 1422.14i) q^{5} +(-8617.00 + 14925.1i) q^{7} -35634.0i q^{8} +76320.0 q^{10} +(-161782. - 93405.0i) q^{11} +(84827.0 + 146925. i) q^{13} +(-400482. + 231218. i) q^{14} +(322432. - 558469. i) q^{16} +343245. i q^{17} -949462. q^{19} +(-748818. - 432330. i) q^{20} +(-2.50632e6 - 4.34107e6i) q^{22} +(-2.30157e6 + 1.32881e6i) q^{23} +(-837852. + 1.45120e6i) q^{25} +4.55229e6i q^{26} +5.23914e6 q^{28} +(2.75588e6 + 1.59111e6i) q^{29} +(1.48966e7 + 2.58016e7i) q^{31} +(-1.66153e7 + 9.59284e6i) q^{32} +(-4.60512e6 + 7.97630e6i) q^{34} +4.90183e7i q^{35} -6.08118e7 q^{37} +(-2.20635e7 - 1.27384e7i) q^{38} +(-5.06765e7 - 8.77742e7i) q^{40} +(-1.57329e8 + 9.08341e7i) q^{41} +(-5.37099e7 + 9.30282e7i) q^{43} +5.67903e7i q^{44} -7.13117e7 q^{46} +(-2.32091e8 - 1.33998e8i) q^{47} +(-7.26775e6 - 1.25881e7i) q^{49} +(-3.89399e7 + 2.24819e7i) q^{50} +(2.57874e7 - 4.46651e7i) q^{52} -1.92091e8i q^{53} -5.31340e8 q^{55} +(5.31840e8 + 3.07058e8i) q^{56} +(4.26938e7 + 7.39479e7i) q^{58} +(5.62187e8 - 3.24579e8i) q^{59} +(-5.15397e8 + 8.92693e8i) q^{61} +7.99433e8i q^{62} -1.17515e9 q^{64} +(4.17895e8 + 2.41272e8i) q^{65} +(-9.38371e8 - 1.62531e9i) q^{67} +(9.03668e7 - 5.21733e7i) q^{68} +(-6.57649e8 + 1.13908e9i) q^{70} -2.68338e9i q^{71} -2.84653e9 q^{73} +(-1.41314e9 - 8.15877e8i) q^{74} +(1.44318e8 + 2.49966e8i) q^{76} +(2.78816e9 - 1.60974e9i) q^{77} +(-7.44324e8 + 1.28921e9i) q^{79} -1.83417e9i q^{80} -4.87467e9 q^{82} +(1.09626e9 + 6.32927e8i) q^{83} +(4.88143e8 + 8.45488e8i) q^{85} +(-2.49621e9 + 1.44119e9i) q^{86} +(-3.32839e9 + 5.76495e9i) q^{88} +6.02052e9i q^{89} -2.92382e9 q^{91} +(6.99679e8 + 4.03960e8i) q^{92} +(-3.59554e9 - 6.22766e9i) q^{94} +(-2.33873e9 + 1.35027e9i) q^{95} +(7.96474e8 - 1.37953e9i) q^{97} -3.90029e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 608 q^{4} - 34468 q^{7}+O(q^{10}) \) 4 * q - 608 * q^4 - 34468 * q^7	\( 4 q - 608 q^{4} - 34468 q^{7} + 305280 q^{10} + 339308 q^{13} + 1289728 q^{16} - 3797848 q^{19} - 10025280 q^{22} - 3351410 q^{25} + 20956544 q^{28} + 59586236 q^{31} - 18420480 q^{34} - 243247384 q^{37} - 202705920 q^{40} - 214839412 q^{43} - 285246720 q^{46} - 29071014 q^{49} + 103149632 q^{52} - 2125359360 q^{55} + 170775360 q^{58} - 2061587284 q^{61} - 4700585984 q^{64} - 3753484948 q^{67} - 2630597760 q^{70} - 11386113976 q^{73} + 577272896 q^{76} - 2977295236 q^{79} - 19498671360 q^{82} + 1952570880 q^{85} - 13313571840 q^{88} - 11695268144 q^{91} - 14382155520 q^{94} + 3185897852 q^{97}+O(q^{100}) \) 4 * q - 608 * q^4 - 34468 * q^7 + 305280 * q^10 + 339308 * q^13 + 1289728 * q^16 - 3797848 * q^19 - 10025280 * q^22 - 3351410 * q^25 + 20956544 * q^28 + 59586236 * q^31 - 18420480 * q^34 - 243247384 * q^37 - 202705920 * q^40 - 214839412 * q^43 - 285246720 * q^46 - 29071014 * q^49 + 103149632 * q^52 - 2125359360 * q^55 + 170775360 * q^58 - 2061587284 * q^61 - 4700585984 * q^64 - 3753484948 * q^67 - 2630597760 * q^70 - 11386113976 * q^73 + 577272896 * q^76 - 2977295236 * q^79 - 19498671360 * q^82 + 1952570880 * q^85 - 13313571840 * q^88 - 11695268144 * q^91 - 14382155520 * q^94 + 3185897852 * q^97

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