LMFDB - Embedded newform 27.10.c.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, 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:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 $ x^16 - 8x^15 + 1984x^14 - 13748x^13 + 1552498x^12 - 9136628x^11 + 609566956x^10 - 2964409064x^9 + 126210674407x^8 - 487156186164x^7 + 13162328064828x^6 - 37794288146040x^5 + 578928267028062x^4 - 1095428523832956x^3 + 5807598664427172x^2 - 5266103139591300*x + 1336504689748125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{40}\cdot 17^{2} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.3
Root			$0.500000 + 9.36376i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.10.c.a.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.85925 + 15.3447i) q^{2} +(99.0272 + 171.520i) q^{4} +(-369.939 - 640.753i) q^{5} +(3013.67 - 5219.83i) q^{7} -12581.1 q^{8} +13109.5 q^{10} +(9215.52 - 15961.8i) q^{11} +(-58793.0 - 101832. i) q^{13} +(53397.7 + 92487.6i) q^{14} +(60757.3 - 105235. i) q^{16} +468308. q^{17} +834842. q^{19} +(73268.0 - 126904. i) q^{20} +(163285. + 282819. i) q^{22} +(660262. + 1.14361e6i) q^{23} +(702853. - 1.21738e6i) q^{25} +2.08345e6 q^{26} +1.19374e6 q^{28} +(32123.4 - 55639.3i) q^{29} +(-3.70875e6 - 6.42375e6i) q^{31} +(-2.14423e6 - 3.71392e6i) q^{32} +(-4.14886e6 + 7.18604e6i) q^{34} -4.45949e6 q^{35} +3.68044e6 q^{37} +(-7.39608e6 + 1.28104e7i) q^{38} +(4.65424e6 + 8.06138e6i) q^{40} +(-1.26806e7 - 2.19634e7i) q^{41} +(-1.21419e7 + 2.10304e7i) q^{43} +3.65035e6 q^{44} -2.33977e7 q^{46} +(3.51686e6 - 6.09137e6i) q^{47} +(2.01239e6 + 3.48557e6i) q^{49} +(1.24535e7 + 2.15701e7i) q^{50} +(1.16442e7 - 2.01684e7i) q^{52} +3.10597e7 q^{53} -1.36367e7 q^{55} +(-3.79153e7 + 6.56712e7i) q^{56} +(569179. + 985846. i) q^{58} +(-7.68270e7 - 1.33068e8i) q^{59} +(7.75804e7 - 1.34373e8i) q^{61} +1.31427e8 q^{62} +1.38201e8 q^{64} +(-4.34996e7 + 7.53435e7i) q^{65} +(6.98640e6 + 1.21008e7i) q^{67} +(4.63753e7 + 8.03244e7i) q^{68} +(3.95078e7 - 6.84295e7i) q^{70} +3.45182e8 q^{71} -3.01511e8 q^{73} +(-3.26059e7 + 5.64751e7i) q^{74} +(8.26721e7 + 1.43192e8i) q^{76} +(-5.55451e7 - 9.62069e7i) q^{77} +(-1.79834e8 + 3.11482e8i) q^{79} -8.99059e7 q^{80} +4.49361e8 q^{82} +(-5.25069e7 + 9.09446e7i) q^{83} +(-1.73245e8 - 3.00070e8i) q^{85} +(-2.15137e8 - 3.72628e8i) q^{86} +(-1.15941e8 + 2.00817e8i) q^{88} -8.60555e8 q^{89} -7.08730e8 q^{91} +(-1.30768e8 + 2.26497e8i) q^{92} +(6.23135e7 + 1.07930e8i) q^{94} +(-3.08840e8 - 5.34927e8i) q^{95} +(-4.74261e7 + 8.21444e7i) q^{97} -7.13133e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22}+ \cdots - 4827300318 q^{98}+O(q^{100}) $ 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−8.85925	+	15.3447i	−0.391527	+	0.678145i	−0.992651	−	0.121011i	$-0.961387\pi$
$2$	−8.85925	+	15.3447i	−0.391527	+	0.678145i	0.601124	+	0.799156i	$0.294720\pi$
$3$		0			0
$3$		0			0
$4$	99.0272	+	171.520i	0.193413	+	0.335000i
$5$	−369.939	−	640.753i	−0.264707	−	0.458485i	0.702780	−	0.711407i	$-0.251942\pi$
$5$	−369.939	−	640.753i	−0.264707	−	0.458485i	−0.967487	+	0.252922i	$0.918608\pi$
$6$		0			0
$7$	3013.67	−	5219.83i	0.474411	−	0.821703i	−0.525160	−	0.851004i	$-0.675995\pi$
$7$	3013.67	−	5219.83i	0.474411	−	0.821703i	0.999571	+	0.0293001i	$0.00932785\pi$
$8$	−12581.1			−1.08596
$9$		0			0
$10$	13109.5			0.414560
$11$	9215.52	−	15961.8i	0.189781	−	0.328711i	−0.755396	−	0.655268i	$-0.772555\pi$
$11$	9215.52	−	15961.8i	0.189781	−	0.328711i	0.945177	+	0.326558i	$0.105889\pi$
$12$		0			0
$13$	−58793.0	−	101832.i	−0.570927	−	0.988874i	−0.996471	−	0.0839366i	$-0.973251\pi$
$13$	−58793.0	−	101832.i	−0.570927	−	0.988874i	0.425544	−	0.904938i	$-0.360083\pi$
$14$	53397.7	+	92487.6i	0.371490	+	0.643439i
$15$		0			0
$16$	60757.3	−	105235.i	0.231771	−	0.401438i
$17$	468308.			1.35992			0.679958	−	0.733251i	$-0.261998\pi$
$17$	468308.			1.35992			0.679958	+	0.733251i	$0.261998\pi$
$18$		0			0
$19$	834842.			1.46965			0.734824	−	0.678258i	$-0.237265\pi$
$19$	834842.			1.46965			0.734824	+	0.678258i	$0.237265\pi$
$20$	73268.0	−	126904.i	0.102395	−	0.177354i
$21$		0			0
$22$	163285.	+	282819.i	0.148609	+	0.257398i
$23$	660262.	+	1.14361e6i	0.491973	+	0.852122i	0.999957	−	0.00924405i	$-0.00294251\pi$
$23$	660262.	+	1.14361e6i	0.491973	+	0.852122i	−0.507984	+	0.861366i	$0.669609\pi$
$24$		0			0
$25$	702853.	−	1.21738e6i	0.359861	−	0.623297i
$26$	2.08345e6			0.894134
$27$		0			0
$28$	1.19374e6			0.367028
$29$	32123.4	−	55639.3i	0.00843394	−	0.0146080i	−0.861778	−	0.507286i	$-0.830649\pi$
$29$	32123.4	−	55639.3i	0.00843394	−	0.0146080i	0.870212	+	0.492678i	$0.163982\pi$
$30$		0			0
$31$	−3.70875e6	−	6.42375e6i	−0.721274	−	1.24928i	−0.960489	−	0.278317i	$-0.910224\pi$
$31$	−3.70875e6	−	6.42375e6i	−0.721274	−	1.24928i	0.239215	−	0.970967i	$-0.423110\pi$
$32$	−2.14423e6	−	3.71392e6i	−0.361491	−	0.626121i
$33$		0			0
$34$	−4.14886e6	+	7.18604e6i	−0.532444	+	0.922220i
$35$	−4.45949e6			−0.502318
$36$		0			0
$37$	3.68044e6			0.322843			0.161422	−	0.986886i	$-0.448392\pi$
$37$	3.68044e6			0.322843			0.161422	+	0.986886i	$0.448392\pi$
$38$	−7.39608e6	+	1.28104e7i	−0.575407	+	0.996635i
$39$		0			0
$40$	4.65424e6	+	8.06138e6i	0.287461	+	0.497897i
$41$	−1.26806e7	−	2.19634e7i	−0.700827	−	1.21387i	−0.968176	−	0.250269i	$-0.919481\pi$
$41$	−1.26806e7	−	2.19634e7i	−0.700827	−	1.21387i	0.267349	−	0.963600i	$-0.413852\pi$
$42$		0			0
$43$	−1.21419e7	+	2.10304e7i	−0.541601	+	0.938081i	0.457211	+	0.889358i	$0.348848\pi$
$43$	−1.21419e7	+	2.10304e7i	−0.541601	+	0.938081i	−0.998812	+	0.0487226i	$0.984485\pi$
$44$	3.65035e6			0.146824
$45$		0			0
$46$	−2.33977e7			−0.770484
$47$	3.51686e6	−	6.09137e6i	0.105127	−	0.182085i	−0.808663	−	0.588272i	$-0.799808\pi$
$47$	3.51686e6	−	6.09137e6i	0.105127	−	0.182085i	0.913790	+	0.406187i	$0.133142\pi$
$48$		0			0
$49$	2.01239e6	+	3.48557e6i	0.0498690	+	0.0863757i
$50$	1.24535e7	+	2.15701e7i	0.281791	+	0.488076i
$51$		0			0
$52$	1.16442e7	−	2.01684e7i	0.220849	−	0.382521i
$53$	3.10597e7			0.540700			0.270350	−	0.962762i	$-0.412861\pi$
$53$	3.10597e7			0.540700			0.270350	+	0.962762i	$0.412861\pi$
$54$		0			0
$55$	−1.36367e7			−0.200945
$56$	−3.79153e7	+	6.56712e7i	−0.515191	+	0.892337i
$57$		0			0
$58$	569179.	+	985846.i	0.00660424	+	0.0114389i
$59$	−7.68270e7	−	1.33068e8i	−0.825429	−	1.42969i	−0.901591	−	0.432590i	$-0.857600\pi$
$59$	−7.68270e7	−	1.33068e8i	−0.825429	−	1.42969i	0.0761619	−	0.997095i	$-0.475733\pi$
$60$		0			0
$61$	7.75804e7	−	1.34373e8i	0.717410	−	1.24259i	−0.244612	−	0.969621i	$-0.578661\pi$
$61$	7.75804e7	−	1.34373e8i	0.717410	−	1.24259i	0.962023	−	0.272970i	$-0.0880060\pi$
$62$	1.31427e8			1.12959
$63$		0			0
$64$	1.38201e8			1.02968
$65$	−4.34996e7	+	7.53435e7i	−0.302256	+	0.523523i
$66$		0			0
$67$	6.98640e6	+	1.21008e7i	0.0423562	+	0.0733631i	0.886426	−	0.462870i	$-0.153180\pi$
$67$	6.98640e6	+	1.21008e7i	0.0423562	+	0.0733631i	−0.844070	+	0.536233i	$0.819847\pi$
$68$	4.63753e7	+	8.03244e7i	0.263025	+	0.455572i
$69$		0			0
$70$	3.95078e7	−	6.84295e7i	0.196671	−	0.340645i
$71$	3.45182e8			1.61207			0.806037	−	0.591865i	$-0.201608\pi$
$71$	3.45182e8			1.61207			0.806037	+	0.591865i	$0.201608\pi$
$72$		0			0
$73$	−3.01511e8			−1.24265			−0.621327	−	0.783551i	$-0.713406\pi$
$73$	−3.01511e8			−1.24265			−0.621327	+	0.783551i	$0.713406\pi$
$74$	−3.26059e7	+	5.64751e7i	−0.126402	+	0.218935i
$75$		0			0
$76$	8.26721e7	+	1.43192e8i	0.284248	+	0.492333i
$77$	−5.55451e7	−	9.62069e7i	−0.180068	−	0.311888i
$78$		0			0
$79$	−1.79834e8	+	3.11482e8i	−0.519458	+	0.899728i	0.480286	+	0.877112i	$0.340533\pi$
$79$	−1.79834e8	+	3.11482e8i	−0.519458	+	0.899728i	−0.999744	+	0.0226159i	$0.992801\pi$
$80$	−8.99059e7			−0.245405
$81$		0			0
$82$	4.49361e8			1.09757
$83$	−5.25069e7	+	9.09446e7i	−0.121441	+	0.210342i	−0.920336	−	0.391128i	$-0.872085\pi$
$83$	−5.25069e7	+	9.09446e7i	−0.121441	+	0.210342i	0.798895	+	0.601470i	$0.205418\pi$
$84$		0			0
$85$	−1.73245e8	−	3.00070e8i	−0.359978	−	0.623501i
$86$	−2.15137e8	−	3.72628e8i	−0.424103	−	0.734569i
$87$		0			0
$88$	−1.15941e8	+	2.00817e8i	−0.206095	+	0.356967i
$89$	−8.60555e8			−1.45386			−0.726932	−	0.686710i	$-0.759054\pi$
$89$	−8.60555e8			−1.45386			−0.726932	+	0.686710i	$0.759054\pi$
$90$		0			0
$91$	−7.08730e8			−1.08342
$92$	−1.30768e8	+	2.26497e8i	−0.190308	+	0.329622i
$93$		0			0
$94$	6.23135e7	+	1.07930e8i	0.0823202	+	0.142583i
$95$	−3.08840e8	−	5.34927e8i	−0.389025	−	0.673812i
$96$		0			0
$97$	−4.74261e7	+	8.21444e7i	−0.0543932	+	0.0942118i	−0.891940	−	0.452154i	$-0.850656\pi$
$97$	−4.74261e7	+	8.21444e7i	−0.0543932	+	0.0942118i	0.837547	+	0.546366i	$0.183989\pi$
$98$	−7.13133e7			−0.0781004
$99$		0			0
$100$	2.78406e8			0.278406
$101$	2.38579e8	−	4.13231e8i	0.228132	−	0.395137i	−0.729122	−	0.684383i	$-0.760071\pi$
$101$	2.38579e8	−	4.13231e8i	0.228132	−	0.395137i	0.957255	+	0.289247i	$0.0934048\pi$
$102$		0			0
$103$	−1.68556e8	−	2.91947e8i	−0.147563	−	0.255586i	0.782763	−	0.622319i	$-0.213809\pi$
$103$	−1.68556e8	−	2.91947e8i	−0.147563	−	0.255586i	−0.930326	+	0.366733i	$0.880476\pi$
$104$	7.39681e8	+	1.28116e9i	0.620004	+	1.07388i
$105$		0			0
$106$	−2.75166e8	+	4.76602e8i	−0.211699	+	0.366673i
$107$	1.05652e9			0.779203			0.389602	−	0.920983i	$-0.372613\pi$
$107$	1.05652e9			0.779203			0.389602	+	0.920983i	$0.372613\pi$
$108$		0			0
$109$	5.44814e8			0.369683			0.184841	−	0.982768i	$-0.440823\pi$
$109$	5.44814e8			0.369683			0.184841	+	0.982768i	$0.440823\pi$
$110$	1.20811e8	−	2.09251e8i	0.0786756	−	0.136270i
$111$		0			0
$112$	−3.66205e8	−	6.34285e8i	−0.219909	−	0.380893i
$113$	5.45264e8	+	9.44426e8i	0.314597	+	0.544897i	0.979352	−	0.202164i	$-0.0647974\pi$
$113$	5.45264e8	+	9.44426e8i	0.314597	+	0.544897i	−0.664755	+	0.747061i	$0.731464\pi$
$114$		0			0
$115$	4.88513e8	−	8.46130e8i	0.260457	−	0.451125i
$116$	1.27244e7			0.00652492
$117$		0			0
$118$	2.72252e9			1.29271
$119$	1.41133e9	−	2.44449e9i	0.645158	−	1.11745i
$120$		0			0
$121$	1.00912e9	+	1.74785e9i	0.427966	+	0.741259i
$122$	1.37461e9	+	2.38089e9i	0.561772	+	0.973017i
$123$		0			0
$124$	7.34535e8	−	1.27225e9i	0.279007	−	0.483254i
$125$	−2.48512e9			−0.910443
$126$		0			0
$127$	−1.90290e9			−0.649082			−0.324541	−	0.945872i	$-0.605210\pi$
$127$	−1.90290e9			−0.649082			−0.324541	+	0.945872i	$0.605210\pi$
$128$	−1.26507e8	+	2.19117e8i	−0.0416553	+	0.0721491i
$129$		0			0
$130$	−7.70748e8	−	1.33497e9i	−0.236683	−	0.409947i
$131$	−3.85457e8	−	6.67631e8i	−0.114355	−	0.198069i	0.803167	−	0.595754i	$-0.203147\pi$
$131$	−3.85457e8	−	6.67631e8i	−0.114355	−	0.198069i	−0.917522	+	0.397686i	$0.869813\pi$
$132$		0			0
$133$	2.51594e9	−	4.35773e9i	0.697217	−	1.20761i
$134$	−2.47577e8			−0.0663345
$135$		0			0
$136$	−5.89184e9			−1.47681
$137$	−2.11984e8	+	3.67166e8i	−0.0514114	+	0.0890472i	−0.890586	−	0.454815i	$-0.849705\pi$
$137$	−2.11984e8	+	3.67166e8i	−0.0514114	+	0.0890472i	0.839174	+	0.543862i	$0.183039\pi$
$138$		0			0
$139$	1.24855e9	+	2.16255e9i	0.283687	+	0.491359i	0.972290	−	0.233779i	$-0.0751092\pi$
$139$	1.24855e9	+	2.16255e9i	0.283687	+	0.491359i	−0.688603	+	0.725138i	$0.741776\pi$
$140$	−4.41611e8	−	7.64893e8i	−0.0971547	−	0.168277i
$141$		0			0
$142$	−3.05805e9	+	5.29670e9i	−0.631171	+	1.09322i
$143$	−2.16723e9			−0.433404
$144$		0			0
$145$	−4.75347e7			−0.00893007
$146$	2.67116e9	−	4.62659e9i	0.486533	−	0.842700i
$147$		0			0
$148$	3.64463e8	+	6.31269e8i	0.0624419	+	0.108153i
$149$	1.77396e9	+	3.07258e9i	0.294853	+	0.510700i	0.974951	−	0.222422i	$-0.0713961\pi$
$149$	1.77396e9	+	3.07258e9i	0.294853	+	0.510700i	−0.680098	+	0.733121i	$0.738063\pi$
$150$		0			0
$151$	−2.12395e9	+	3.67879e9i	−0.332466	+	0.575849i	−0.982995	−	0.183633i	$-0.941214\pi$
$151$	−2.12395e9	+	3.67879e9i	−0.332466	+	0.575849i	0.650529	+	0.759482i	$0.274547\pi$
$152$	−1.05032e10			−1.59598
$153$		0			0
$154$	1.96835e9			0.282007
$155$	−2.74402e9	+	4.75279e9i	−0.381852	+	0.661387i
$156$		0			0
$157$	9.15878e8	+	1.58635e9i	0.120307	+	0.208377i	0.919889	−	0.392180i	$-0.128279\pi$
$157$	9.15878e8	+	1.58635e9i	0.120307	+	0.208377i	−0.799582	+	0.600557i	$0.794946\pi$
$158$	−3.18639e9	−	5.51900e9i	−0.406764	−	0.704536i
$159$		0			0
$160$	−1.58647e9	+	2.74785e9i	−0.191378	+	0.331477i
$161$	7.95925e9			0.933589
$162$		0			0
$163$	4.81775e9			0.534564			0.267282	−	0.963618i	$-0.413874\pi$
$163$	4.81775e9			0.534564			0.267282	+	0.963618i	$0.413874\pi$
$164$	2.51144e9	−	4.34994e9i	0.271098	−	0.469555i
$165$		0			0
$166$	−9.30344e8	−	1.61140e9i	−0.0950949	−	0.164709i
$167$	−7.53553e8	−	1.30519e9i	−0.0749704	−	0.129853i	0.826103	−	0.563519i	$-0.190553\pi$
$167$	−7.53553e8	−	1.30519e9i	−0.0749704	−	0.129853i	−0.901073	+	0.433667i	$0.857220\pi$
$168$		0			0
$169$	−1.61098e9	+	2.79030e9i	−0.151915	+	0.263124i
$170$	6.13930e9			0.563766
$171$		0			0
$172$	−4.80953e9			−0.419010
$173$	−1.08021e10	+	1.87099e10i	−0.916859	+	1.58805i	−0.112703	+	0.993629i	$0.535951\pi$
$173$	−1.08021e10	+	1.87099e10i	−0.916859	+	1.58805i	−0.804156	+	0.594418i	$0.797382\pi$
$174$		0			0
$175$	−4.23634e9	−	7.33755e9i	−0.341444	−	0.591398i
$176$	−1.11982e9	−	1.93959e9i	−0.0879714	−	0.152371i
$177$		0			0
$178$	7.62388e9	−	1.32049e10i	0.569227	−	0.985931i
$179$	1.94882e10			1.41884			0.709418	−	0.704788i	$-0.248958\pi$
$179$	1.94882e10			1.41884			0.709418	+	0.704788i	$0.248958\pi$
$180$		0			0
$181$	7.45903e9			0.516569			0.258285	−	0.966069i	$-0.416843\pi$
$181$	7.45903e9			0.516569			0.258285	+	0.966069i	$0.416843\pi$
$182$	6.27882e9	−	1.08752e10i	0.424187	−	0.734713i
$183$		0			0
$184$	−8.30683e9	−	1.43879e10i	−0.534263	−	0.925371i
$185$	−1.36154e9	−	2.35825e9i	−0.0854587	−	0.148019i
$186$		0			0
$187$	4.31571e9	−	7.47503e9i	0.258086	−	0.447018i
$188$	1.39306e9			0.0813315
$189$		0			0
$190$	1.09444e10			0.609256
$191$	−3.28300e9	+	5.68633e9i	−0.178493	+	0.309159i	−0.941365	−	0.337391i	$-0.890456\pi$
$191$	−3.28300e9	+	5.68633e9i	−0.178493	+	0.309159i	0.762872	+	0.646550i	$0.223789\pi$
$192$		0			0
$193$	9.40057e9	+	1.62823e10i	0.487693	+	0.844709i	0.999900	−	0.0141532i	$-0.00450525\pi$
$193$	9.40057e9	+	1.62823e10i	0.487693	+	0.844709i	−0.512207	+	0.858862i	$0.671172\pi$
$194$	−8.40320e8	−	1.45548e9i	−0.0425929	−	0.0737730i
$195$		0			0
$196$	−3.98564e8	+	6.90333e8i	−0.0192906	+	0.0334123i
$197$	1.66201e9			0.0786206			0.0393103	−	0.999227i	$-0.487484\pi$
$197$	1.66201e9			0.0786206			0.0393103	+	0.999227i	$0.487484\pi$
$198$		0			0
$199$	1.45345e10			0.656996			0.328498	−	0.944505i	$-0.393458\pi$
$199$	1.45345e10			0.656996			0.328498	+	0.944505i	$0.393458\pi$
$200$	−8.84267e9	+	1.53160e10i	−0.390795	+	0.676876i
$201$		0			0
$202$	4.22727e9	+	7.32185e9i	0.178640	+	0.309414i
$203$	−1.93619e8	−	3.35357e8i	−0.00800230	−	0.0138604i
$204$		0			0
$205$	−9.38206e9	+	1.62502e10i	−0.371027	+	0.642638i
$206$	5.97312e9			0.231099
$207$		0			0
$208$	−1.42884e10			−0.529296
$209$	7.69351e9	−	1.33255e10i	0.278911	−	0.483089i
$210$		0			0
$211$	−6.96607e8	−	1.20656e9i	−0.0241945	−	0.0419061i	0.853675	−	0.520807i	$-0.174369\pi$
$211$	−6.96607e8	−	1.20656e9i	−0.0241945	−	0.0419061i	−0.877869	+	0.478901i	$0.841035\pi$
$212$	3.07576e9	+	5.32737e9i	0.104578	+	0.181135i
$213$		0			0
$214$	−9.35998e9	+	1.62120e10i	−0.305079	+	0.528413i
$215$	1.79671e10			0.573462
$216$		0			0
$217$	−4.47078e10			−1.36872
$218$	−4.82665e9	+	8.36000e9i	−0.144741	+	0.250699i
$219$		0			0
$220$	−1.35041e9	−	2.33897e9i	−0.0388653	−	0.0673167i
$221$	−2.75333e10	−	4.76890e10i	−0.776412	−	1.34479i
$222$		0			0
$223$	1.43684e10	−	2.48867e10i	0.389077	−	0.673900i	−0.603249	−	0.797553i	$-0.706127\pi$
$223$	1.43684e10	−	2.48867e10i	0.389077	−	0.673900i	0.992326	+	0.123653i	$0.0394608\pi$
$224$	−2.58481e10			−0.685981
$225$		0			0
$226$	−1.93225e10			−0.492693
$227$	−1.92088e10	+	3.32705e10i	−0.480157	+	0.831656i	−0.999741	−	0.0227637i	$-0.992753\pi$
$227$	−1.92088e10	+	3.32705e10i	−0.480157	+	0.831656i	0.519584	+	0.854419i	$0.326087\pi$
$228$		0			0
$229$	6.69528e9	+	1.15966e10i	0.160883	+	0.278657i	0.935185	−	0.354158i	$-0.115233\pi$
$229$	6.69528e9	+	1.15966e10i	0.160883	+	0.278657i	−0.774303	+	0.632815i	$0.781899\pi$
$230$	8.65573e9	+	1.49922e10i	0.203952	+	0.353255i
$231$		0			0
$232$	−4.04148e8	+	7.00004e8i	−0.00915892	+	0.0158637i
$233$	−4.50134e10			−1.00055			−0.500276	−	0.865866i	$-0.666768\pi$
$233$	−4.50134e10			−1.00055			−0.500276	+	0.865866i	$0.666768\pi$
$234$		0			0
$235$	−5.20409e9			−0.111311
$236$	1.52159e10	−	2.63548e10i	0.319297	−	0.553038i
$237$		0			0
$238$	2.50066e10	+	4.33127e10i	0.505194	+	0.875022i
$239$	−3.27972e10	−	5.68064e10i	−0.650199	−	1.12618i	−0.983074	−	0.183207i	$-0.941352\pi$
$239$	−3.27972e10	−	5.68064e10i	−0.650199	−	1.12618i	0.332876	−	0.942971i	$-0.391981\pi$
$240$		0			0
$241$	−1.34067e10	+	2.32210e10i	−0.256002	+	0.443409i	−0.965167	−	0.261634i	$-0.915739\pi$
$241$	−1.34067e10	+	2.32210e10i	−0.256002	+	0.443409i	0.709165	+	0.705043i	$0.249072\pi$
$242$	−3.57603e10			−0.670242
$243$		0			0
$244$	3.07303e10			0.555025
$245$	1.48893e9	−	2.57889e9i	0.0264013	−	0.0457284i
$246$		0			0
$247$	−4.90829e10	−	8.50140e10i	−0.839061	−	1.45330i
$248$	4.66602e10	+	8.08179e10i	0.783275	+	1.35667i
$249$		0			0
$250$	2.20163e10	−	3.81334e10i	0.356464	−	0.617413i
$251$	4.29625e10			0.683216			0.341608	−	0.939842i	$-0.389028\pi$
$251$	4.29625e10			0.683216			0.341608	+	0.939842i	$0.389028\pi$
$252$		0			0
$253$	2.43387e10			0.373469
$254$	1.68583e10	−	2.91994e10i	0.254133	−	0.440172i
$255$		0			0
$256$	3.31379e10	+	5.73965e10i	0.482219	+	0.835229i
$257$	4.72752e10	+	8.18831e10i	0.675981	+	1.17083i	0.976181	+	0.216958i	$0.0696134\pi$
$257$	4.72752e10	+	8.18831e10i	0.675981	+	1.17083i	−0.300200	+	0.953876i	$0.597053\pi$
$258$		0			0
$259$	1.10916e10	−	1.92113e10i	0.153160	−	0.265281i
$260$	−1.72306e10			−0.233841
$261$		0			0
$262$	1.36594e10			0.179092
$263$	5.62344e10	−	9.74008e10i	0.724771	−	1.25534i	−0.234297	−	0.972165i	$-0.575279\pi$
$263$	5.62344e10	−	9.74008e10i	0.724771	−	1.25534i	0.959068	−	0.283176i	$-0.0913879\pi$
$264$		0			0
$265$	−1.14902e10	−	1.99016e10i	−0.143127	−	0.247903i
$266$	4.45787e10	+	7.72125e10i	0.545959	+	0.945628i
$267$		0			0
$268$	−1.38369e9	+	2.39662e9i	−0.0163844	+	0.0283787i
$269$	1.11208e11			1.29494			0.647472	−	0.762089i	$-0.275826\pi$
$269$	1.11208e11			1.29494			0.647472	+	0.762089i	$0.275826\pi$
$270$		0			0
$271$	1.30075e10			0.146498			0.0732491	−	0.997314i	$-0.476663\pi$
$271$	1.30075e10			0.146498			0.0732491	+	0.997314i	$0.476663\pi$
$272$	2.84531e10	−	4.92823e10i	0.315188	−	0.545922i
$273$		0			0
$274$	−3.75603e9	−	6.50564e9i	−0.0402580	−	0.0697288i
$275$	−1.29543e10	−	2.24375e10i	−0.136590	−	0.236580i
$276$		0			0
$277$	−2.12715e10	+	3.68434e10i	−0.217090	+	0.376011i	−0.953917	−	0.300070i	$-0.902990\pi$
$277$	−2.12715e10	+	3.68434e10i	−0.217090	+	0.376011i	0.736827	+	0.676081i	$0.236323\pi$
$278$	−4.42448e10			−0.444284
$279$		0			0
$280$	5.61053e10			0.545498
$281$	−6.91828e10	+	1.19828e11i	−0.661941	+	1.14652i	0.318164	+	0.948036i	$0.396934\pi$
$281$	−6.91828e10	+	1.19828e11i	−0.661941	+	1.14652i	−0.980105	+	0.198480i	$0.936400\pi$
$282$		0			0
$283$	−4.40394e10	−	7.62785e10i	−0.408134	−	0.706909i	0.586547	−	0.809915i	$-0.300487\pi$
$283$	−4.40394e10	−	7.62785e10i	−0.408134	−	0.706909i	−0.994681	+	0.103007i	$0.967154\pi$
$284$	3.41824e10	+	5.92056e10i	0.311795	+	0.540046i
$285$		0			0
$286$	1.92001e10	−	3.32555e10i	0.169690	−	0.293911i
$287$	−1.52860e11			−1.32992
$288$		0			0
$289$	1.00725e11			0.849370
$290$	4.21122e8	−	7.29405e8i	0.00349637	−	0.00605589i
$291$		0			0
$292$	−2.98578e10	−	5.17152e10i	−0.240345	−	0.416289i
$293$	−7.58720e10	−	1.31414e11i	−0.601419	−	1.04169i	−0.992606	−	0.121377i	$-0.961269\pi$
$293$	−7.58720e10	−	1.31414e11i	−0.601419	−	1.04169i	0.391188	−	0.920311i	$-0.372064\pi$
$294$		0			0
$295$	−5.68425e10	+	9.84542e10i	−0.436993	+	0.756894i
$296$	−4.63040e10			−0.350595
$297$		0			0
$298$	−6.28638e10			−0.461772
$299$	7.76376e10	−	1.34472e11i	0.561761	−	0.972999i
$300$		0			0
$301$	7.31835e10	+	1.26758e11i	0.513883	+	0.890071i
$302$	−3.76332e10	−	6.51826e10i	−0.260339	−	0.450921i
$303$		0			0
$304$	5.07227e10	−	8.78544e10i	0.340621	−	0.589973i
$305$	−1.14800e11			−0.759613
$306$		0			0
$307$	−1.76213e11			−1.13218			−0.566089	−	0.824344i	$-0.691544\pi$
$307$	−1.76213e11			−1.13218			−0.566089	+	0.824344i	$0.691544\pi$
$308$	1.10010e10	−	1.90542e10i	0.0696550	−	0.120646i
$309$		0			0
$310$	−4.86200e10	−	8.42123e10i	−0.299011	−	0.517902i
$311$	4.99482e10	+	8.65128e10i	0.302760	+	0.524395i	0.976760	−	0.214336i	$-0.0687587\pi$
$311$	4.99482e10	+	8.65128e10i	0.302760	+	0.524395i	−0.674000	+	0.738731i	$0.735425\pi$
$312$		0			0
$313$	−9.17125e10	+	1.58851e11i	−0.540106	+	0.935491i	0.458791	+	0.888544i	$0.348283\pi$
$313$	−9.17125e10	+	1.58851e11i	−0.540106	+	0.935491i	−0.998897	+	0.0469470i	$0.985051\pi$
$314$	−3.24560e10			−0.188413
$315$		0			0
$316$	−7.12340e10			−0.401879
$317$	−1.29176e11	+	2.23739e11i	−0.718479	+	1.24444i	0.243123	+	0.969995i	$0.421828\pi$
$317$	−1.29176e11	+	2.23739e11i	−0.718479	+	1.24444i	−0.961602	+	0.274447i	$0.911505\pi$
$318$		0			0
$319$	−5.92068e8	−	1.02549e9i	−0.00320120	−	0.00554465i
$320$	−5.11258e10	−	8.85525e10i	−0.272562	−	0.472091i
$321$		0			0
$322$	−7.05130e10	+	1.22132e11i	−0.365526	+	0.633109i
$323$	3.90964e11			1.99860
$324$		0			0
$325$	−1.65291e11			−0.821817
$326$	−4.26816e10	+	7.39268e10i	−0.209296	+	0.362512i
$327$		0			0
$328$	1.59535e11	+	2.76324e11i	0.761071	+	1.31821i
$329$	−2.11973e10	−	3.67148e10i	−0.0997468	−	0.172766i
$330$		0			0
$331$	1.41624e11	−	2.45301e11i	0.648503	−	1.12324i	−0.334978	−	0.942226i	$-0.608729\pi$
$331$	1.41624e11	−	2.45301e11i	0.648503	−	1.12324i	0.983481	−	0.181014i	$-0.0579379\pi$
$332$	−2.07984e10			−0.0939528
$333$		0			0
$334$	2.67037e10			0.117412
$335$	5.16908e9	−	8.95311e9i	0.0224239	−	0.0388394i
$336$		0			0
$337$	1.49793e11	+	2.59450e11i	0.632642	+	1.09577i	0.987010	+	0.160662i	$0.0513628\pi$
$337$	1.49793e11	+	2.59450e11i	0.632642	+	1.09577i	−0.354368	+	0.935106i	$0.615304\pi$
$338$	−2.85442e10	−	4.94399e10i	−0.118958	−	0.206041i
$339$		0			0
$340$	3.43120e10	−	5.94302e10i	0.139249	−	0.241186i
$341$	−1.36712e11			−0.547537
$342$		0			0
$343$	2.67484e11			1.04345
$344$	1.52759e11	−	2.64586e11i	0.588157	−	1.01872i
$345$		0			0
$346$	−1.91398e11	−	3.31511e11i	−0.717951	−	1.24353i
$347$	−2.73670e10	−	4.74010e10i	−0.101332	−	0.175511i	0.810902	−	0.585182i	$-0.198977\pi$
$347$	−2.73670e10	−	4.74010e10i	−0.101332	−	0.175511i	−0.912233	+	0.409671i	$0.865644\pi$
$348$		0			0
$349$	1.52107e11	−	2.63458e11i	0.548828	−	0.950598i	−0.449527	−	0.893267i	$-0.648408\pi$
$349$	1.52107e11	−	2.63458e11i	0.548828	−	0.950598i	0.998355	−	0.0573311i	$-0.0182591\pi$
$350$	1.50123e11			0.534738
$351$		0			0
$352$	−7.90410e10			−0.274417
$353$	−2.65017e11	+	4.59022e11i	−0.908421	+	1.57343i	−0.0921629	+	0.995744i	$0.529378\pi$
$353$	−2.65017e11	+	4.59022e11i	−0.908421	+	1.57343i	−0.816258	+	0.577687i	$0.803955\pi$
$354$		0			0
$355$	−1.27696e11	−	2.21176e11i	−0.426727	−	0.739112i
$356$	−8.52184e10	−	1.47603e11i	−0.281195	−	0.487045i
$357$		0			0
$358$	−1.72651e11	+	2.99039e11i	−0.555513	+	0.962177i
$359$	4.60506e11			1.46322			0.731611	−	0.681722i	$-0.238769\pi$
$359$	4.60506e11			1.46322			0.731611	+	0.681722i	$0.238769\pi$
$360$		0			0
$361$	3.74274e11			1.15986
$362$	−6.60814e10	+	1.14456e11i	−0.202251	+	0.350309i
$363$		0			0
$364$	−7.01836e10	−	1.21562e11i	−0.209546	−	0.362944i
$365$	1.11541e11	+	1.93194e11i	0.328939	+	0.569738i
$366$		0			0
$367$	2.26386e11	−	3.92112e11i	0.651407	−	1.12827i	−0.331374	−	0.943499i	$-0.607512\pi$
$367$	2.26386e11	−	3.92112e11i	0.651407	−	1.12827i	0.982782	−	0.184771i	$-0.0591544\pi$
$368$	1.60463e11			0.456100
$369$		0			0
$370$	4.82488e10			0.133838
$371$	9.36038e10	−	1.62127e11i	0.256514	−	0.444295i
$372$		0			0
$373$	5.05651e10	+	8.75814e10i	0.135257	+	0.234273i	0.925696	−	0.378269i	$-0.123481\pi$
$373$	5.05651e10	+	8.75814e10i	0.135257	+	0.234273i	−0.790438	+	0.612542i	$0.790147\pi$
$374$	7.64679e10	+	1.32446e11i	0.202096	+	0.350040i
$375$		0			0
$376$	−4.42459e10	+	7.66362e10i	−0.114164	+	0.197737i
$377$	−7.55452e9			−0.0192606
$378$		0			0
$379$	−5.06871e11			−1.26189			−0.630944	−	0.775829i	$-0.717332\pi$
$379$	−5.06871e11			−1.26189			−0.630944	+	0.775829i	$0.717332\pi$
$380$	6.11672e10	−	1.05945e11i	0.150485	−	0.260647i
$381$		0			0
$382$	−5.81699e10	−	1.00753e11i	−0.139770	−	0.242088i
$383$	−1.48470e11	−	2.57157e11i	−0.352569	−	0.610667i	0.634130	−	0.773226i	$-0.281358\pi$
$383$	−1.48470e11	−	2.57157e11i	−0.352569	−	0.610667i	−0.986699	+	0.162560i	$0.948025\pi$
$384$		0			0
$385$	−4.10966e10	+	7.11813e10i	−0.0953306	+	0.165117i
$386$	−3.33128e11			−0.763781
$387$		0			0
$388$	−1.87859e10			−0.0420813
$389$	−2.64170e10	+	4.57556e10i	−0.0584939	+	0.101314i	−0.893790	−	0.448487i	$-0.851963\pi$
$389$	−2.64170e10	+	4.57556e10i	−0.0584939	+	0.101314i	0.835296	+	0.549801i	$0.185296\pi$
$390$		0			0
$391$	3.09206e11	+	5.35561e11i	0.669042	+	1.15881i
$392$	−2.53182e10	−	4.38523e10i	−0.0541558	−	0.0938005i
$393$		0			0
$394$	−1.47242e10	+	2.55030e10i	−0.0307821	+	0.0533162i
$395$	2.66111e11			0.550016
$396$		0			0
$397$	4.35046e11			0.878978			0.439489	−	0.898248i	$-0.355160\pi$
$397$	4.35046e11			0.878978			0.439489	+	0.898248i	$0.355160\pi$
$398$	−1.28765e11	+	2.23028e11i	−0.257232	+	0.445539i
$399$		0			0
$400$	−8.54069e10	−	1.47929e11i	−0.166810	−	0.288924i
$401$	2.02055e10	+	3.49970e10i	0.0390230	+	0.0675897i	0.884877	−	0.465824i	$-0.154242\pi$
$401$	2.02055e10	+	3.49970e10i	0.0390230	+	0.0675897i	−0.845854	+	0.533414i	$0.820909\pi$
$402$		0			0
$403$	−4.36097e11	+	7.55343e11i	−0.823589	+	1.42650i
$404$	9.45034e10			0.176495
$405$		0			0
$406$	6.86126e9			0.0125325
$407$	3.39172e10	−	5.87462e10i	0.0612695	−	0.106122i
$408$		0			0
$409$	−1.20679e11	−	2.09022e11i	−0.213244	−	0.369349i	0.739484	−	0.673174i	$-0.235069\pi$
$409$	−1.20679e11	−	2.09022e11i	−0.213244	−	0.369349i	−0.952728	+	0.303825i	$0.901736\pi$
$410$	−1.66236e11	−	2.87929e11i	−0.290535	−	0.503221i
$411$		0			0
$412$	3.33833e10	−	5.78215e10i	0.0570809	−	0.0988671i
$413$	−9.26125e11			−1.56637
$414$		0			0
$415$	7.76973e10			0.128585
$416$	−2.52132e11	+	4.36705e11i	−0.412770	+	0.714938i
$417$		0			0
$418$	1.36318e11	+	2.36109e11i	0.218403	+	0.378285i
$419$	−1.87685e11	−	3.25080e11i	−0.297486	−	0.515262i	0.678074	−	0.734994i	$-0.262815\pi$
$419$	−1.87685e11	−	3.25080e11i	−0.297486	−	0.515262i	−0.975560	+	0.219732i	$0.929482\pi$
$420$		0			0
$421$	−3.63197e11	+	6.29075e11i	−0.563472	+	0.975962i	0.433718	+	0.901049i	$0.357201\pi$
$421$	−3.63197e11	+	6.29075e11i	−0.563472	+	0.975962i	−0.997190	+	0.0749136i	$0.976132\pi$
$422$	2.46857e10			0.0378912
$423$		0			0
$424$	−3.90766e11			−0.587179
$425$	3.29152e11	−	5.70108e11i	0.489380	−	0.847632i
$426$		0			0
$427$	−4.67603e11	−	8.09913e11i	−0.680694	−	1.17900i
$428$	1.04624e11	+	1.81215e11i	0.150708	+	0.261033i
$429$		0			0
$430$	−1.59175e11	+	2.75699e11i	−0.224526	+	0.388890i
$431$	−8.99614e11			−1.25576			−0.627882	−	0.778308i	$-0.716078\pi$
$431$	−8.99614e11			−1.25576			−0.627882	+	0.778308i	$0.716078\pi$
$432$		0			0
$433$	−7.77024e11			−1.06228			−0.531140	−	0.847284i	$-0.678236\pi$
$433$	−7.77024e11			−1.06228			−0.531140	+	0.847284i	$0.678236\pi$
$434$	3.96078e11	−	6.86027e11i	0.535892	−	0.928191i
$435$		0			0
$436$	5.39515e10	+	9.34467e10i	0.0715013	+	0.123844i
$437$	5.51215e11	+	9.54732e11i	0.723027	+	1.25232i
$438$		0			0
$439$	7.63494e11	−	1.32241e12i	0.981104	−	1.69932i	0.322994	−	0.946401i	$-0.395311\pi$
$439$	7.63494e11	−	1.32241e12i	0.981104	−	1.69932i	0.658110	−	0.752921i	$-0.271356\pi$
$440$	1.71565e11			0.218218
$441$		0			0
$442$	9.75696e11			1.21595
$443$	1.39049e11	−	2.40841e11i	0.171535	−	0.297107i	−0.767422	−	0.641143i	$-0.778461\pi$
$443$	1.39049e11	−	2.40841e11i	0.171535	−	0.297107i	0.938957	+	0.344036i	$0.111794\pi$
$444$		0			0
$445$	3.18353e11	+	5.51403e11i	0.384847	+	0.666575i
$446$	2.54586e11	+	4.40956e11i	0.304668	+	0.527701i
$447$		0			0
$448$	4.16491e11	−	7.21384e11i	0.488489	−	0.846088i
$449$	−3.39438e11			−0.394141			−0.197071	−	0.980389i	$-0.563143\pi$
$449$	−3.39438e11			−0.394141			−0.197071	+	0.980389i	$0.563143\pi$
$450$		0			0
$451$	−4.67432e11			−0.532015
$452$	−1.07992e11	+	1.87048e11i	−0.121694	+	0.210780i
$453$		0			0
$454$	−3.40350e11	−	5.89504e11i	−0.375989	−	0.651232i
$455$	2.62187e11	+	4.54121e11i	0.286787	+	0.496730i
$456$		0			0
$457$	−4.10189e11	+	7.10468e11i	−0.439907	+	0.761942i	−0.997682	−	0.0680509i	$-0.978322\pi$
$457$	−4.10189e11	+	7.10468e11i	−0.439907	+	0.761942i	0.557775	+	0.829992i	$0.311655\pi$
$458$	−2.37261e11			−0.251960
$459$		0			0
$460$	1.93504e11			0.201503
$461$	4.95721e11	−	8.58613e11i	0.511190	−	0.885408i	−0.488725	−	0.872438i	$-0.662538\pi$
$461$	4.95721e11	−	8.58613e11i	0.511190	−	0.885408i	0.999916	−	0.0129702i	$-0.00412867\pi$
$462$		0			0
$463$	2.46462e11	+	4.26884e11i	0.249250	+	0.431713i	0.963318	−	0.268363i	$-0.0864827\pi$
$463$	2.46462e11	+	4.26884e11i	0.249250	+	0.431713i	−0.714068	+	0.700076i	$0.753149\pi$
$464$	−3.90346e9	−	6.76099e9i	−0.00390948	−	0.00677141i
$465$		0			0
$466$	3.98785e11	−	6.90716e11i	0.391744	−	0.678520i
$467$	9.59285e11			0.933301			0.466650	−	0.884442i	$-0.345461\pi$
$467$	9.59285e11			0.933301			0.466650	+	0.884442i	$0.345461\pi$
$468$		0			0
$469$	8.42188e10			0.0803769
$470$	4.61043e10	−	7.98550e10i	0.0435814	−	0.0754852i
$471$		0			0
$472$	9.66568e11	+	1.67415e12i	0.896383	+	1.55258i
$473$	2.23788e11	+	3.87613e11i	0.205571	+	0.356060i
$474$		0			0
$475$	5.86772e11	−	1.01632e12i	0.528869	−	0.916027i
$476$	5.59039e11			0.499127
$477$		0			0
$478$	1.16223e12			1.01828
$479$	−5.29978e10	+	9.17948e10i	−0.0459989	+	0.0796725i	−0.888108	−	0.459634i	$-0.847980\pi$
$479$	−5.29978e10	+	9.17948e10i	−0.0459989	+	0.0796725i	0.842109	+	0.539307i	$0.181314\pi$
$480$		0			0
$481$	−2.16384e11	−	3.74788e11i	−0.184320	−	0.319251i
$482$	−2.37546e11	−	4.11442e11i	−0.200464	−	0.347214i
$483$		0			0
$484$	−1.99861e11	+	3.46170e11i	−0.165548	+	0.286738i
$485$	7.01790e10			0.0575929
$486$		0			0
$487$	−4.79462e11			−0.386255			−0.193127	−	0.981174i	$-0.561863\pi$
$487$	−4.79462e11			−0.386255			−0.193127	+	0.981174i	$0.561863\pi$
$488$	−9.76047e11	+	1.69056e12i	−0.779079	+	1.34940i
$489$		0			0
$490$	2.63815e10	+	4.56942e10i	0.0206737	+	0.0358079i
$491$	6.09225e11	+	1.05521e12i	0.473054	+	0.819354i	0.999524	−	0.0308399i	$-0.00981819\pi$
$491$	6.09225e11	+	1.05521e12i	0.473054	+	0.819354i	−0.526470	+	0.850194i	$0.676485\pi$
$492$		0			0
$493$	1.50437e10	−	2.60564e10i	0.0114694	−	0.0198657i
$494$	1.73935e12			1.31406
$495$		0			0
$496$	−9.01335e11			−0.668680
$497$	1.04026e12	−	1.80179e12i	0.764785	−	1.32465i
$498$		0			0
$499$	−9.38654e11	−	1.62580e12i	−0.677724	−	1.17385i	−0.975665	−	0.219269i	$-0.929633\pi$
$499$	−9.38654e11	−	1.62580e12i	−0.677724	−	1.17385i	0.297940	−	0.954585i	$-0.403700\pi$
$500$	−2.46095e11	−	4.26249e11i	−0.176091	−	0.304999i
$501$		0			0
$502$	−3.80616e11	+	6.59246e11i	−0.267498	+	0.463320i
$503$	−1.91484e12			−1.33375			−0.666877	−	0.745168i	$-0.732370\pi$
$503$	−1.91484e12			−1.33375			−0.666877	+	0.745168i	$0.732370\pi$
$504$		0			0
$505$	−3.53039e11			−0.241552
$506$	−2.15622e11	+	3.73469e11i	−0.146223	+	0.253266i
$507$		0			0
$508$	−1.88439e11	−	3.26386e11i	−0.125541	−	0.217443i
$509$	−6.73207e11	−	1.16603e12i	−0.444548	−	0.769979i	0.553473	−	0.832867i	$-0.313302\pi$
$509$	−6.73207e11	−	1.16603e12i	−0.444548	−	0.769979i	−0.998021	+	0.0628880i	$0.979969\pi$
$510$		0			0
$511$	−9.08654e11	+	1.57384e12i	−0.589528	+	1.02109i
$512$	−1.30385e12			−0.838519
$513$		0			0
$514$	−1.67529e12			−1.05866
$515$	−1.24711e11	+	2.16005e11i	−0.0781216	+	0.135311i
$516$		0			0
$517$	−6.48194e10	−	1.12270e11i	−0.0399022	−	0.0691127i
$518$	1.96527e11	+	3.40395e11i	0.119933	+	0.207730i
$519$		0			0
$520$	5.47273e11	−	9.47905e11i	0.328238	−	0.568525i
$521$	−1.22696e12			−0.729557			−0.364778	−	0.931094i	$-0.618855\pi$
$521$	−1.22696e12			−0.729557			−0.364778	+	0.931094i	$0.618855\pi$
$522$		0			0
$523$	2.16646e12			1.26617			0.633087	−	0.774080i	$-0.281787\pi$
$523$	2.16646e12			1.26617			0.633087	+	0.774080i	$0.281787\pi$
$524$	7.63414e10	−	1.32227e11i	0.0442354	−	0.0766179i
$525$		0			0
$526$	9.96389e11	+	1.72580e12i	0.567536	+	0.983001i
$527$	−1.73684e12	−	3.00830e12i	−0.980872	−	1.69892i
$528$		0			0
$529$	2.86834e10	−	4.96811e10i	0.0159250	−	0.0275829i
$530$	4.07178e11			0.224152
$531$		0			0
$532$	9.96586e11			0.539402
$533$	−1.49106e12	+	2.58258e12i	−0.800242	+	1.38606i
$534$		0			0
$535$	−3.90848e11	−	6.76968e11i	−0.206260	−	0.357253i
$536$	−8.78967e10	−	1.52242e11i	−0.0459971	−	0.0796694i
$537$		0			0
$538$	−9.85221e11	+	1.70645e12i	−0.507006	+	0.878161i
$539$	7.41811e10			0.0378568
$540$		0			0
$541$	−1.66976e12			−0.838041			−0.419021	−	0.907977i	$-0.637626\pi$
$541$	−1.66976e12			−0.838041			−0.419021	+	0.907977i	$0.637626\pi$
$542$	−1.15237e11	+	1.99596e11i	−0.0573580	+	0.0993470i
$543$		0			0
$544$	−1.00416e12	−	1.73926e12i	−0.491597	−	0.851471i
$545$	−2.01548e11	−	3.49091e11i	−0.0978575	−	0.169494i
$546$		0			0
$547$	−8.71587e11	+	1.50963e12i	−0.416263	+	0.720988i	−0.995560	−	0.0941279i	$-0.969994\pi$
$547$	−8.71587e11	+	1.50963e12i	−0.416263	+	0.720988i	0.579297	+	0.815116i	$0.303327\pi$
$548$	−8.39686e10			−0.0397745
$549$		0			0
$550$	4.59063e11			0.213914
$551$	2.68180e10	−	4.64501e10i	0.0123949	−	0.0214686i
$552$		0			0
$553$	1.08392e12	+	1.87741e12i	0.492873	+	0.853681i
$554$	−3.76900e11	−	6.52809e11i	−0.169993	−	0.294437i
$555$		0			0
$556$	−2.47281e11	+	4.28302e11i	−0.109737	+	0.190070i
$557$	3.88681e12			1.71098			0.855490	−	0.517820i	$-0.173256\pi$
$557$	3.88681e12			1.71098			0.855490	+	0.517820i	$0.173256\pi$
$558$		0			0
$559$	2.85544e12			1.23686
$560$	−2.70947e11	+	4.69293e11i	−0.116423	+	0.201650i
$561$		0			0
$562$	−1.22582e12	−	2.12317e12i	−0.518336	−	0.897785i
$563$	1.40604e12	+	2.43533e12i	0.589806	+	1.02157i	0.994257	+	0.107015i	$0.0341292\pi$
$563$	1.40604e12	+	2.43533e12i	0.589806	+	1.02157i	−0.404451	+	0.914560i	$0.632537\pi$
$564$		0			0
$565$	4.03429e11	−	6.98759e11i	0.166552	−	0.288476i
$566$	1.56063e12			0.639183
$567$		0			0
$568$	−4.34277e12			−1.75065
$569$	9.10981e11	−	1.57787e12i	0.364338	−	0.631051i	−0.624332	−	0.781159i	$-0.714629\pi$
$569$	9.10981e11	−	1.57787e12i	0.364338	−	0.631051i	0.988670	+	0.150108i	$0.0479621\pi$
$570$		0			0
$571$	1.68248e12	+	2.91413e12i	0.662348	+	1.14722i	0.979997	+	0.199012i	$0.0637733\pi$
$571$	1.68248e12	+	2.91413e12i	0.662348	+	1.14722i	−0.317649	+	0.948208i	$0.602893\pi$
$572$	−2.14615e11	−	3.71724e11i	−0.0838259	−	0.145191i
$573$		0			0
$574$	1.35423e12	−	2.34559e12i	0.520700	−	0.901879i
$575$	1.85627e12			0.708167
$576$		0			0
$577$	2.47809e12			0.930737			0.465368	−	0.885117i	$-0.345922\pi$
$577$	2.47809e12			0.930737			0.465368	+	0.885117i	$0.345922\pi$
$578$	−8.92348e11	+	1.54559e12i	−0.332551	+	0.575996i
$579$		0			0
$580$	−4.70723e9	−	8.15317e9i	−0.00172719	−	0.00299158i
$581$	3.16477e11	+	5.48154e11i	0.115226	+	0.199577i
$582$		0			0
$583$	2.86232e11	−	4.95768e11i	0.102615	−	0.177734i
$584$	3.79334e12			1.34947
$585$		0			0
$586$	2.68868e12			0.941888
$587$	−5.73505e11	+	9.93340e11i	−0.199373	+	0.345324i	−0.948325	−	0.317300i	$-0.897224\pi$
$587$	−5.73505e11	+	9.93340e11i	−0.199373	+	0.345324i	0.748952	+	0.662624i	$0.230557\pi$
$588$		0			0
$589$	−3.09622e12	−	5.36282e12i	−1.06002	−	1.83601i
$590$	−1.00717e12	−	1.74446e12i	−0.342189	−	0.592690i
$591$		0			0
$592$	2.23613e11	−	3.87310e11i	0.0748256	−	0.129602i
$593$	−3.07354e12			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$593$	−3.07354e12			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$594$		0			0
$595$	−2.08842e12			−0.683111
$596$	−3.51340e11	+	6.08539e11i	−0.114056	+	0.197551i
$597$		0			0
$598$	1.37562e12	+	2.38265e12i	0.439890	+	0.761912i
$599$	6.51632e11	+	1.12866e12i	0.206815	+	0.358214i	0.950709	−	0.310083i	$-0.100357\pi$
$599$	6.51632e11	+	1.12866e12i	0.206815	+	0.358214i	−0.743895	+	0.668297i	$0.767024\pi$
$600$		0			0
$601$	3.02726e12	−	5.24336e12i	0.946486	−	1.63936i	0.193737	−	0.981053i	$-0.437939\pi$
$601$	3.02726e12	−	5.24336e12i	0.946486	−	1.63936i	0.752749	−	0.658308i	$-0.228728\pi$
$602$	−2.59341e12			−0.804797
$603$		0			0
$604$	−8.41315e11			−0.257213
$605$	7.46627e11	−	1.29320e12i	0.226571	−	0.392432i
$606$		0			0
$607$	2.03918e12	+	3.53196e12i	0.609685	+	1.05601i	0.991292	+	0.131681i	$0.0420376\pi$
$607$	2.03918e12	+	3.53196e12i	0.609685	+	1.05601i	−0.381607	+	0.924325i	$0.624629\pi$
$608$	−1.79010e12	−	3.10054e12i	−0.531264	−	0.920177i
$609$		0			0
$610$	1.01704e12	−	1.76157e12i	0.297409	−	0.515128i
$611$	−8.27066e11			−0.240079
$612$		0			0
$613$	2.84192e12			0.812904			0.406452	−	0.913672i	$-0.366766\pi$
$613$	2.84192e12			0.812904			0.406452	+	0.913672i	$0.366766\pi$
$614$	1.56111e12	−	2.70393e12i	0.443279	−	0.767781i
$615$		0			0
$616$	6.98819e11	+	1.21039e12i	0.195547	+	0.338697i
$617$	2.91123e12	+	5.04240e12i	0.808711	+	1.40073i	0.913757	+	0.406262i	$0.133168\pi$
$617$	2.91123e12	+	5.04240e12i	0.808711	+	1.40073i	−0.105045	+	0.994467i	$0.533499\pi$
$618$		0			0
$619$	−2.75415e12	+	4.77032e12i	−0.754014	+	1.30599i	0.191849	+	0.981424i	$0.438551\pi$
$619$	−2.75415e12	+	4.77032e12i	−0.754014	+	1.30599i	−0.945863	+	0.324566i	$0.894782\pi$
$620$	−1.08693e12			−0.295420
$621$		0			0
$622$	−1.77001e12			−0.474155
$623$	−2.59343e12	+	4.49195e12i	−0.689728	+	1.19464i
$624$		0			0
$625$	−4.53417e11	−	7.85341e11i	−0.118861	−	0.205873i
$626$	−1.62501e12	−	2.81460e12i	−0.422933	−	0.732541i
$627$		0			0
$628$	−1.81394e11	+	3.14183e11i	−0.0465376	+	0.0806055i
$629$	1.72358e12			0.439039
$630$		0			0
$631$	−3.74010e12			−0.939184			−0.469592	−	0.882884i	$-0.655599\pi$
$631$	−3.74010e12			−0.939184			−0.469592	+	0.882884i	$0.655599\pi$
$632$	2.26251e12	−	3.91879e12i	0.564111	−	0.977069i
$633$		0			0
$634$	−2.28880e12	−	3.96432e12i	−0.562609	−	0.974467i
$635$	7.03957e11	+	1.21929e12i	0.171816	+	0.297595i
$636$		0			0
$637$	2.36629e11	−	4.09854e11i	0.0569431	−	0.0986284i
$638$	2.09811e10			0.00501344
$639$		0			0
$640$	1.87200e11			0.0441058
$641$	−7.09241e11	+	1.22844e12i	−0.165933	+	0.287405i	−0.936986	−	0.349366i	$-0.886397\pi$
$641$	−7.09241e11	+	1.22844e12i	−0.165933	+	0.287405i	0.771053	+	0.636771i	$0.219730\pi$
$642$		0			0
$643$	3.55066e11	+	6.14992e11i	0.0819142	+	0.141880i	0.904072	−	0.427380i	$-0.140563\pi$
$643$	3.55066e11	+	6.14992e11i	0.0819142	+	0.141880i	−0.822158	+	0.569259i	$0.807230\pi$
$644$	7.88183e11	+	1.36517e12i	0.180568	+	0.312753i
$645$		0			0
$646$	−3.46365e12	+	5.99921e12i	−0.782505	+	1.35534i
$647$	−1.71001e12			−0.383645			−0.191823	−	0.981430i	$-0.561440\pi$
$647$	−1.71001e12			−0.383645			−0.191823	+	0.981430i	$0.561440\pi$
$648$		0			0
$649$	−2.83200e12			−0.626603
$650$	1.46436e12	−	2.53634e12i	0.321764	−	0.557311i
$651$		0			0
$652$	4.77088e11	+	8.26341e11i	0.103391	+	0.179079i
$653$	−9.38362e11	−	1.62529e12i	−0.201958	−	0.349801i	0.747201	−	0.664598i	$-0.231397\pi$
$653$	−9.38362e11	−	1.62529e12i	−0.201958	−	0.349801i	−0.949159	+	0.314796i	$0.898064\pi$
$654$		0			0
$655$	−2.85191e11	+	4.93965e11i	−0.0605410	+	0.104860i
$656$	−3.08175e12			−0.649725
$657$		0			0
$658$	7.51169e11			0.156214
$659$	1.05120e12	−	1.82073e12i	0.217121	−	0.376064i	−0.736806	−	0.676105i	$-0.763667\pi$
$659$	1.05120e12	−	1.82073e12i	0.217121	−	0.376064i	0.953927	+	0.300040i	$0.0970001\pi$
$660$		0			0
$661$	3.07493e12	+	5.32593e12i	0.626511	+	1.08515i	0.988247	+	0.152868i	$0.0488509\pi$
$661$	3.07493e12	+	5.32593e12i	0.626511	+	1.08515i	−0.361736	+	0.932281i	$0.617816\pi$
$662$	2.50937e12	+	4.34636e12i	0.507813	+	0.879558i
$663$		0			0
$664$	6.60595e11	−	1.14418e12i	0.131880	−	0.228423i
$665$	−3.72297e12			−0.738231
$666$		0			0
$667$	8.48395e10			0.0165971
$668$	1.49245e11	−	2.58499e11i	0.0290004	−	0.0502302i
$669$		0			0
$670$	9.15884e10	+	1.58636e11i	0.0175592	+	0.0304134i
$671$	−1.42989e12	−	2.47664e12i	−0.272302	−	0.471641i
$672$		0			0
$673$	−1.87092e12	+	3.24053e12i	−0.351551	+	0.608904i	−0.986521	−	0.163632i	$-0.947679\pi$
$673$	−1.87092e12	+	3.24053e12i	−0.351551	+	0.608904i	0.634971	+	0.772536i	$0.281012\pi$
$674$	−5.30823e12			−0.990787
$675$		0			0
$676$	−6.38124e11			−0.117529
$677$	1.97991e12	−	3.42930e12i	0.362240	−	0.627418i	−0.626089	−	0.779751i	$-0.715345\pi$
$677$	1.97991e12	−	3.42930e12i	0.362240	−	0.627418i	0.988329	+	0.152333i	$0.0486788\pi$
$678$		0			0
$679$	2.85853e11	+	4.95112e11i	0.0516094	+	0.0893902i
$680$	2.17962e12	+	3.77521e12i	0.390922	+	0.677097i
$681$		0			0
$682$	1.21117e12	−	2.09781e12i	0.214376	−	0.371309i
$683$	−3.62977e12			−0.638243			−0.319121	−	0.947714i	$-0.603388\pi$
$683$	−3.62977e12			−0.638243			−0.319121	+	0.947714i	$0.603388\pi$
$684$		0			0
$685$	3.13684e11			0.0544358
$686$	−2.36971e12	+	4.10445e12i	−0.408541	+	0.707614i
$687$		0			0
$688$	1.47542e12	+	2.55550e12i	0.251054	+	0.434839i
$689$	−1.82609e12	−	3.16289e12i	−0.308700	−	0.534684i
$690$		0			0
$691$	1.63408e12	−	2.83030e12i	0.272660	−	0.472260i	−0.696882	−	0.717185i	$-0.745430\pi$
$691$	1.63408e12	−	2.83030e12i	0.272660	−	0.472260i	0.969542	+	0.244925i	$0.0787634\pi$
$692$	−4.27883e12			−0.709328
$693$		0			0
$694$	9.69805e11			0.158696
$695$	9.23773e11	−	1.60002e12i	0.150187	−	0.260132i
$696$		0			0
$697$	−5.93841e12	−	1.02856e13i	−0.953066	−	1.65076i
$698$	2.69512e12	+	4.66808e12i	0.429762	+	0.744370i
$699$		0			0
$700$	8.39025e11	−	1.45323e12i	0.132079	−	0.228768i
$701$	5.82077e12			0.910435			0.455218	−	0.890380i	$-0.349561\pi$
$701$	5.82077e12			0.910435			0.455218	+	0.890380i	$0.349561\pi$
$702$		0			0
$703$	3.07258e12			0.474466
$704$	1.27359e12	−	2.20593e12i	0.195413	−	0.338465i
$705$		0			0
$706$	−4.69570e12	−	8.13319e12i	−0.711343	−	1.23208i
$707$	−1.43800e12	−	2.49069e12i	−0.216457	−	0.374914i
$708$		0			0
$709$	3.41640e12	−	5.91738e12i	0.507763	−	0.879471i	−0.492197	−	0.870484i	$-0.663806\pi$
$709$	3.41640e12	−	5.91738e12i	0.507763	−	0.879471i	0.999960	−	0.00898692i	$-0.00286067\pi$
$710$	4.52517e12			0.668301
$711$		0			0
$712$	1.08267e13			1.57884
$713$	4.89750e12	−	8.48272e12i	0.709695	−	1.22923i
$714$		0			0
$715$	8.01743e11	+	1.38866e12i	0.114725	+	0.198710i
$716$	1.92986e12	+	3.34261e12i	0.274421	+	0.475310i
$717$		0			0
$718$	−4.07974e12	+	7.06632e12i	−0.572892	+	0.992277i
$719$	5.93643e12			0.828411			0.414205	−	0.910183i	$-0.364060\pi$
$719$	5.93643e12			0.828411			0.414205	+	0.910183i	$0.364060\pi$
$720$		0			0
$721$	−2.03189e12			−0.280021
$722$	−3.31579e12	+	5.74311e12i	−0.454119	+	0.786557i
$723$		0			0
$724$	7.38647e11	+	1.27937e12i	0.0999110	+	0.173051i
$725$	−4.51561e10	−	7.82126e10i	−0.00607009	−	0.0105137i
$726$		0			0
$727$	−2.98924e12	+	5.17751e12i	−0.396877	+	0.687411i	−0.993339	−	0.115231i	$-0.963239\pi$
$727$	−2.98924e12	+	5.17751e12i	−0.396877	+	0.687411i	0.596462	+	0.802641i	$0.296573\pi$
$728$	8.91661e12			1.17655
$729$		0			0
$730$	−3.95266e12			−0.515154
$731$	−5.68617e12	+	9.84873e12i	−0.736532	+	1.27571i
$732$		0			0
$733$	−4.73505e11	−	8.20135e11i	−0.0605838	−	0.104934i	0.834143	−	0.551549i	$-0.185963\pi$
$733$	−4.73505e11	−	8.20135e11i	−0.0605838	−	0.104934i	−0.894727	+	0.446614i	$0.852630\pi$
$734$	4.01123e12	+	6.94765e12i	0.510088	+	0.883498i
$735$		0			0
$736$	2.83152e12	−	4.90433e12i	0.355688	−	0.616069i
$737$	2.57533e11			0.0321536
$738$		0			0
$739$	8.03141e12			0.990585			0.495293	−	0.868726i	$-0.335061\pi$
$739$	8.03141e12			0.990585			0.495293	+	0.868726i	$0.335061\pi$
$740$	2.69658e11	−	4.67062e11i	0.0330576	−	0.0572574i
$741$		0			0
$742$	1.65852e12	+	2.87264e12i	0.200864	+	0.347907i
$743$	−2.22290e12	−	3.85017e12i	−0.267590	−	0.463479i	0.700649	−	0.713506i	$-0.252894\pi$
$743$	−2.22290e12	−	3.85017e12i	−0.267590	−	0.463479i	−0.968239	+	0.250027i	$0.919560\pi$
$744$		0			0
$745$	1.31251e12	−	2.27334e12i	0.156099	−	0.270371i
$746$	−1.79188e12			−0.211828
$747$		0			0
$748$	1.70949e12			0.199668
$749$	3.18400e12	−	5.51485e12i	0.369662	−	0.640274i
$750$		0			0
$751$	1.10885e12	+	1.92058e12i	0.127202	+	0.220320i	0.922591	−	0.385779i	$-0.126067\pi$
$751$	1.10885e12	+	1.92058e12i	0.127202	+	0.220320i	−0.795390	+	0.606098i	$0.792734\pi$
$752$	−4.27349e11	−	7.40191e11i	−0.0487307	−	0.0844041i
$753$		0			0
$754$	6.69274e10	−	1.15922e11i	0.00754107	−	0.0130615i
$755$	3.14292e12			0.352024
$756$		0			0
$757$	−9.93039e12			−1.09909			−0.549547	−	0.835463i	$-0.685200\pi$
$757$	−9.93039e12			−1.09909			−0.549547	+	0.835463i	$0.685200\pi$
$758$	4.49050e12	−	7.77777e12i	0.494064	−	0.855743i
$759$		0			0
$760$	3.88555e12	+	6.72998e12i	0.422466	+	0.731733i
$761$	−4.26425e11	−	7.38590e11i	−0.0460906	−	0.0798312i	0.842060	−	0.539384i	$-0.181343\pi$
$761$	−4.26425e11	−	7.38590e11i	−0.0460906	−	0.0798312i	−0.888150	+	0.459553i	$0.848010\pi$
$762$		0			0
$763$	1.64189e12	−	2.84384e12i	0.175381	−	0.303770i
$764$	−1.30043e12			−0.138091
$765$		0			0
$766$	5.26133e12			0.552161
$767$	−9.03378e12	+	1.56470e13i	−0.942519	+	1.63249i
$768$		0			0
$769$	3.38623e12	+	5.86513e12i	0.349179	+	0.604796i	0.986104	−	0.166130i	$-0.0531271\pi$
$769$	3.38623e12	+	5.86513e12i	0.349179	+	0.604796i	−0.636925	+	0.770926i	$0.719794\pi$
$770$	−7.28170e11	−	1.26123e12i	−0.0746491	−	0.129296i
$771$		0			0
$772$	−1.86183e12	+	3.22478e12i	−0.188652	+	0.326755i
$773$	−3.60630e12			−0.363291			−0.181645	−	0.983364i	$-0.558142\pi$
$773$	−3.60630e12			−0.363291			−0.181645	+	0.983364i	$0.558142\pi$
$774$		0			0
$775$	−1.04268e13			−1.03823
$776$	5.96673e11	−	1.03347e12i	0.0590688	−	0.102310i
$777$		0			0
$778$	−4.68070e11	−	8.10721e11i	−0.0458039	−	0.0793348i
$779$	−1.05863e13	−	1.83360e13i	−1.02997	−	1.78396i
$780$		0			0
$781$	3.18103e12	−	5.50970e12i	0.305941	−	0.529906i
$782$	−1.09574e13			−1.04779
$783$		0			0
$784$	4.89071e11			0.0462327
$785$	6.77638e11	−	1.17370e12i	0.0636919	−	0.110318i
$786$		0			0
$787$	−1.79432e12	−	3.10785e12i	−0.166730	−	0.288785i	0.770538	−	0.637394i	$-0.219987\pi$
$787$	−1.79432e12	−	3.10785e12i	−0.166730	−	0.288785i	−0.937268	+	0.348609i	$0.886654\pi$
$788$	1.64584e11	+	2.85069e11i	0.0152062	+	0.0263379i
$789$		0			0
$790$	−2.35754e12	+	4.08338e12i	−0.215346	+	0.372991i
$791$	6.57299e12			0.596992
$792$		0			0
$793$	−1.82447e13			−1.63835
$794$	−3.85418e12	+	6.67564e12i	−0.344144	+	0.596075i
$795$		0			0
$796$	1.43932e12	+	2.49297e12i	0.127071	+	0.220094i
$797$	2.62673e12	+	4.54963e12i	0.230597	+	0.399405i	0.957984	−	0.286822i	$-0.0925988\pi$
$797$	2.62673e12	+	4.54963e12i	0.230597	+	0.399405i	−0.727387	+	0.686227i	$0.759266\pi$
$798$		0			0
$799$	1.64697e12	−	2.85264e12i	0.142964	−	0.247621i
$800$	−6.02833e12			−0.520346
$801$		0			0
$802$	−7.16023e11			−0.0611142
$803$	−2.77858e12	+	4.81264e12i	−0.235832	+	0.408473i
$804$		0			0
$805$	−2.94443e12	−	5.09991e12i	−0.247127	−	0.428037i
$806$	−7.72699e12	−	1.33835e13i	−0.644916	−	1.11703i
$807$		0			0
$808$	−3.00159e12	+	5.19891e12i	−0.247742	+	0.429103i
$809$	7.22017e12			0.592623			0.296312	−	0.955091i	$-0.404243\pi$
$809$	7.22017e12			0.592623			0.296312	+	0.955091i	$0.404243\pi$
$810$		0			0
$811$	−8.41322e12			−0.682918			−0.341459	−	0.939897i	$-0.610921\pi$
$811$	−8.41322e12			−0.682918			−0.341459	+	0.939897i	$0.610921\pi$
$812$	3.83470e10	−	6.64190e10i	0.00309549	−	0.00536155i
$813$		0			0
$814$	6.00961e11	+	1.04090e12i	0.0479774	+	0.0830993i
$815$	−1.78227e12	−	3.08698e12i	−0.141503	−	0.245090i
$816$		0			0
$817$	−1.01366e13	+	1.75571e13i	−0.795963	+	1.37865i
$818$	4.27650e12			0.333963
$819$		0			0
$820$	−3.71632e12			−0.287045
$821$	−1.73801e12	+	3.01032e12i	−0.133508	+	0.231243i	−0.925027	−	0.379902i	$-0.875958\pi$
$821$	−1.73801e12	+	3.01032e12i	−0.133508	+	0.231243i	0.791518	+	0.611145i	$0.209291\pi$
$822$		0			0
$823$	−6.61717e11	−	1.14613e12i	−0.0502774	−	0.0870831i	0.839791	−	0.542909i	$-0.182677\pi$
$823$	−6.61717e11	−	1.14613e12i	−0.0502774	−	0.0870831i	−0.890069	+	0.455826i	$0.849344\pi$
$824$	2.12062e12	+	3.67302e12i	0.160247	+	0.277556i
$825$		0			0
$826$	8.20477e12	−	1.42111e13i	0.613277	−	1.06223i
$827$	−3.65944e11			−0.0272044			−0.0136022	−	0.999907i	$-0.504330\pi$
$827$	−3.65944e11			−0.0272044			−0.0136022	+	0.999907i	$0.504330\pi$
$828$		0			0
$829$	2.59469e13			1.90805			0.954025	−	0.299728i	$-0.0968960\pi$
$829$	2.59469e13			1.90805			0.954025	+	0.299728i	$0.0968960\pi$
$830$	−6.88340e11	+	1.19224e12i	−0.0503445	+	0.0871992i
$831$		0			0
$832$	−8.12523e12	−	1.40733e13i	−0.587869	−	1.01822i
$833$	9.42421e11	+	1.63232e12i	0.0678176	+	0.117464i
$834$		0			0
$835$	−5.57537e11	+	9.65682e11i	−0.0396903	+	0.0687456i
$836$	3.04747e12			0.215780
$837$		0			0
$838$	6.65101e12			0.465896
$839$	−7.12846e12	+	1.23469e13i	−0.496669	+	0.860255i	−0.999993	−	0.00384244i	$-0.998777\pi$
$839$	−7.12846e12	+	1.23469e13i	−0.496669	+	0.860255i	0.503324	+	0.864098i	$0.332110\pi$
$840$		0			0
$841$	7.25151e12	+	1.25600e13i	0.499858	+	0.865779i
$842$	−6.43530e12	−	1.11463e13i	−0.441230	−	0.764232i
$843$		0			0
$844$	1.37966e11	−	2.38964e11i	0.00935904	−	0.0162103i
$845$	2.38386e12			0.160851
$846$		0			0
$847$	1.21646e13			0.812127
$848$	1.88710e12	−	3.26856e12i	0.125318	−	0.217058i
$849$		0			0
$850$	5.83208e12	+	1.01015e13i	0.383212	+	0.663742i
$851$	2.43005e12	+	4.20898e12i	0.158830	+	0.275102i
$852$		0			0
$853$	1.79052e10	−	3.10127e10i	0.00115800	−	0.00200571i	−0.865446	−	0.501003i	$-0.832965\pi$
$853$	1.79052e10	−	3.10127e10i	0.00115800	−	0.00200571i	0.866604	+	0.498997i	$0.166298\pi$
$854$	1.65705e13			1.06604
$855$		0			0
$856$	−1.32922e13			−0.846184
$857$	6.97342e12	−	1.20783e13i	0.441603	−	0.764880i	−0.556205	−	0.831045i	$-0.687743\pi$
$857$	6.97342e12	−	1.20783e13i	0.441603	−	0.764880i	0.997809	+	0.0661654i	$0.0210765\pi$
$858$		0			0
$859$	7.06018e12	+	1.22286e13i	0.442432	+	0.766314i	0.997869	−	0.0652438i	$-0.0207825\pi$
$859$	7.06018e12	+	1.22286e13i	0.442432	+	0.766314i	−0.555437	+	0.831558i	$0.687449\pi$
$860$	1.77923e12	+	3.08172e12i	0.110915	+	0.192110i
$861$		0			0
$862$	7.96991e12	−	1.38043e13i	0.491666	−	0.851591i
$863$	2.25669e13			1.38492			0.692458	−	0.721458i	$-0.256528\pi$
$863$	2.25669e13			1.38492			0.692458	+	0.721458i	$0.256528\pi$
$864$		0			0
$865$	1.59845e13			0.970795
$866$	6.88385e12	−	1.19232e13i	0.415911	−	0.720380i
$867$		0			0
$868$	−4.42729e12	−	7.66829e12i	−0.264728	−	0.458522i
$869$	3.31453e12	+	5.74094e12i	0.197167	+	0.341503i
$870$		0			0
$871$	8.21503e11	−	1.42288e12i	0.0483646	−	0.0837699i
$872$	−6.85437e12			−0.401461
$873$		0			0
$874$	−1.95334e13			−1.13234
$875$	−7.48934e12	+	1.29719e13i	−0.431924	+	0.748114i
$876$		0			0
$877$	−1.52634e13	−	2.64371e13i	−0.871273	−	1.50909i	−0.860681	−	0.509145i	$-0.829962\pi$
$877$	−1.52634e13	−	2.64371e13i	−0.871273	−	1.50909i	−0.0105925	−	0.999944i	$-0.503372\pi$
$878$	1.35280e13	+	2.34311e13i	0.768258	+	1.33066i
$879$		0			0
$880$	−8.28530e11	+	1.43506e12i	−0.0465732	+	0.0806671i
$881$	−2.00261e13			−1.11997			−0.559983	−	0.828504i	$-0.689192\pi$
$881$	−2.00261e13			−1.11997			−0.559983	+	0.828504i	$0.689192\pi$
$882$		0			0
$883$	1.87899e13			1.04016			0.520080	−	0.854117i	$-0.325902\pi$
$883$	1.87899e13			1.04016			0.520080	+	0.854117i	$0.325902\pi$
$884$	5.45308e12	−	9.44502e12i	0.300336	−	0.520197i
$885$		0			0
$886$	2.46375e12	+	4.26734e12i	0.134321	+	0.232651i
$887$	1.44494e13	+	2.50272e13i	0.783781	+	1.35755i	0.929724	+	0.368256i	$0.120045\pi$
$887$	1.44494e13	+	2.50272e13i	0.783781	+	1.35755i	−0.145943	+	0.989293i	$0.546622\pi$
$888$		0			0
$889$	−5.73472e12	+	9.93282e12i	−0.307931	+	0.533353i
$890$	−1.12815e13			−0.602713
$891$		0			0
$892$	5.69143e12			0.301009
$893$	2.93602e12	−	5.08534e12i	0.154500	−	0.267601i
$894$		0			0
$895$	−7.20942e12	−	1.24871e13i	−0.375575	−	0.650515i
$896$	7.62502e11	+	1.32069e12i	0.0395235	+	0.0684567i
$897$		0			0
$898$	3.00717e12	−	5.20856e12i	0.154317	−	0.267285i
$899$	−4.76551e11			−0.0243327
$900$		0			0
$901$	1.45455e13			0.735306
$902$	4.14110e12	−	7.17259e12i	0.208299	−	0.360784i
$903$		0			0
$904$	−6.86003e12	−	1.18819e13i	−0.341639	−	0.591737i
$905$	−2.75938e12	−	4.77939e12i	−0.136739	−	0.236839i
$906$		0			0
$907$	−1.38734e12	+	2.40294e12i	−0.0680691	+	0.117899i	−0.898051	−	0.439891i	$-0.855017\pi$
$907$	−1.38734e12	+	2.40294e12i	−0.0680691	+	0.117899i	0.829982	+	0.557790i	$0.188351\pi$
$908$	−7.60876e12			−0.371473
$909$		0			0
$910$	−9.29112e12			−0.449140
$911$	1.79009e13	−	3.10053e13i	0.861079	−	1.49143i	−0.00980917	−	0.999952i	$-0.503122\pi$
$911$	1.79009e13	−	3.10053e13i	0.861079	−	1.49143i	0.870888	−	0.491481i	$-0.163544\pi$
$912$		0			0
$913$	9.67757e11	+	1.67620e12i	0.0460944	+	0.0798378i
$914$	−7.26794e12	−	1.25884e13i	−0.344471	−	0.596642i
$915$		0			0
$916$	−1.32603e12	+	2.29675e12i	−0.0622334	+	0.107791i
$917$	−4.64656e12			−0.217005
$918$		0			0
$919$	−1.46068e13			−0.675516			−0.337758	−	0.941233i	$-0.609669\pi$
$919$	−1.46068e13			−0.675516			−0.337758	+	0.941233i	$0.609669\pi$
$920$	−6.14604e12	+	1.06452e13i	−0.282846	+	0.489903i
$921$		0			0
$922$	8.78343e12	+	1.52133e13i	0.400290	+	0.693323i
$923$	−2.02943e13	−	3.51507e13i	−0.920376	−	1.59414i
$924$		0			0
$925$	2.58681e12	−	4.48048e12i	0.116179	−	0.201227i
$926$	−8.73386e12			−0.390352
$927$		0			0
$928$	−2.75520e11			−0.0121952
$929$	−1.98224e13	+	3.43333e13i	−0.873142	+	1.51233i	−0.0144124	+	0.999896i	$0.504588\pi$
$929$	−1.98224e13	+	3.43333e13i	−0.873142	+	1.51233i	−0.858729	+	0.512430i	$0.828746\pi$
$930$		0			0
$931$	1.68003e12	+	2.90990e12i	0.0732899	+	0.126942i
$932$	−4.45755e12	−	7.72070e12i	−0.193519	−	0.335185i
$933$		0			0
$934$	−8.49855e12	+	1.47199e13i	−0.365413	+	0.632914i
$935$	−6.38619e12			−0.273268
$936$		0			0
$937$	−1.72240e13			−0.729973			−0.364987	−	0.931013i	$-0.618926\pi$
$937$	−1.72240e13			−0.729973			−0.364987	+	0.931013i	$0.618926\pi$
$938$	−7.46116e11	+	1.29231e12i	−0.0314698	+	0.0545073i
$939$		0			0
$940$	−5.15346e11	−	8.92606e11i	−0.0215290	−	0.0372893i
$941$	2.06449e13	+	3.57581e13i	0.858341	+	1.48669i	0.873510	+	0.486806i	$0.161838\pi$
$941$	2.06449e13	+	3.57581e13i	0.858341	+	1.48669i	−0.0151687	+	0.999885i	$0.504829\pi$
$942$		0			0
$943$	1.67450e13	−	2.90032e13i	0.689576	−	1.19438i
$944$	−1.86712e13			−0.765241
$945$		0			0
$946$	−7.93040e12			−0.321947
$947$	8.80925e12	−	1.52581e13i	0.355929	−	0.616488i	−0.631347	−	0.775500i	$-0.717498\pi$
$947$	8.80925e12	−	1.52581e13i	0.355929	−	0.616488i	0.987277	+	0.159013i	$0.0508310\pi$
$948$		0			0
$949$	1.77267e13	+	3.07036e13i	0.709464	+	1.22883i
$950$	1.03967e13	+	1.80076e13i	0.414133	+	0.717300i
$951$		0			0
$952$	−1.77561e13	+	3.07544e13i	−0.700616	+	1.21350i
$953$	−4.44553e13			−1.74584			−0.872922	−	0.487859i	$-0.837778\pi$
$953$	−4.44553e13			−1.74584			−0.872922	+	0.487859i	$0.837778\pi$
$954$		0			0
$955$	4.85804e12			0.188993
$956$	6.49563e12	−	1.12508e13i	0.251513	−	0.435634i
$957$		0			0
$958$	−9.39042e11	−	1.62647e12i	−0.0360197	−	0.0623879i
$959$	1.27770e12	+	2.21304e12i	0.0487803	+	0.0844899i
$960$		0			0
$961$	−1.42899e13	+	2.47508e13i	−0.540472	+	0.936126i
$962$	7.66800e12			0.288665
$963$		0			0
$964$	−5.31050e12			−0.198056
$965$	6.95527e12	−	1.20469e13i	0.258191	−	0.447200i
$966$		0			0
$967$	7.41879e12	+	1.28497e13i	0.272844	+	0.472579i	0.969589	−	0.244739i	$-0.0787024\pi$
$967$	7.41879e12	+	1.28497e13i	0.272844	+	0.472579i	−0.696745	+	0.717319i	$0.745369\pi$
$968$	−1.26959e13	−	2.19899e13i	−0.464754	−	0.804978i
$969$		0			0
$970$	−6.21734e11	+	1.07687e12i	−0.0225492	+	0.0390564i
$971$	3.34482e13			1.20750			0.603749	−	0.797174i	$-0.293673\pi$
$971$	3.34482e13			1.20750			0.603749	+	0.797174i	$0.293673\pi$
$972$		0			0
$973$	1.50508e13			0.538336
$974$	4.24768e12	−	7.35719e12i	0.151229	−	0.261937i
$975$		0			0
$976$	−9.42714e12	−	1.63283e13i	−0.332549	−	0.575992i
$977$	1.02021e13	+	1.76705e13i	0.358231	+	0.620475i	0.987665	−	0.156579i	$-0.0500465\pi$
$977$	1.02021e13	+	1.76705e13i	0.358231	+	0.620475i	−0.629434	+	0.777054i	$0.716713\pi$
$978$		0			0
$979$	−7.93047e12	+	1.37360e13i	−0.275916	+	0.477900i
$980$	5.89777e11			0.0204254
$981$		0			0
$982$	−2.15891e13			−0.740855
$983$	1.15500e13	−	2.00051e13i	0.394539	−	0.683361i	−0.598504	−	0.801120i	$-0.704238\pi$
$983$	1.15500e13	−	2.00051e13i	0.394539	−	0.683361i	0.993042	+	0.117759i	$0.0375711\pi$
$984$		0			0
$985$	−6.14842e11	−	1.06494e12i	−0.0208114	−	0.0360464i
$986$	2.66551e11	+	4.61680e11i	0.00898120	+	0.0155559i
$987$		0			0
$988$	9.72108e12	−	1.68374e13i	0.324570	−	0.562172i
$989$	−3.20674e13			−1.06581
$990$		0			0
$991$	−4.59514e13			−1.51345			−0.756724	−	0.653734i	$-0.773201\pi$
$991$	−4.59514e13			−1.51345			−0.756724	+	0.653734i	$0.773201\pi$
$992$	−1.59049e13	+	2.75480e13i	−0.521468	+	0.903209i
$993$		0			0
$994$	1.84319e13	+	3.19250e13i	0.598869	+	1.03727i
$995$	−5.37689e12	−	9.31305e12i	−0.173911	−	0.301223i
$996$		0			0
$997$	2.19764e13	−	3.80642e13i	0.704414	−	1.22008i	−0.262489	−	0.964935i	$-0.584543\pi$
$997$	2.19764e13	−	3.80642e13i	0.704414	−	1.22008i	0.966903	−	0.255146i	$-0.0821234\pi$
$998$	3.32631e13			1.06139
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.c.a.19.3		16
3.2	odd	2		9.10.c.a.7.6	yes	16
9.2	odd	6		81.10.a.c.1.3		8
9.4	even	3	inner	27.10.c.a.10.3		16
9.5	odd	6		9.10.c.a.4.6	✓	16
9.7	even	3		81.10.a.d.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.6	✓	16	9.5	odd	6
9.10.c.a.7.6	yes	16	3.2	odd	2
27.10.c.a.10.3		16	9.4	even	3	inner
27.10.c.a.19.3		16	1.1	even	1	trivial
81.10.a.c.1.3		8	9.2	odd	6
81.10.a.d.1.6		8	9.7	even	3

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.85925 + 15.3447i) q^{2} +(99.0272 + 171.520i) q^{4} +(-369.939 - 640.753i) q^{5} +(3013.67 - 5219.83i) q^{7} -12581.1 q^{8} +13109.5 q^{10} +(9215.52 - 15961.8i) q^{11} +(-58793.0 - 101832. i) q^{13} +(53397.7 + 92487.6i) q^{14} +(60757.3 - 105235. i) q^{16} +468308. q^{17} +834842. q^{19} +(73268.0 - 126904. i) q^{20} +(163285. + 282819. i) q^{22} +(660262. + 1.14361e6i) q^{23} +(702853. - 1.21738e6i) q^{25} +2.08345e6 q^{26} +1.19374e6 q^{28} +(32123.4 - 55639.3i) q^{29} +(-3.70875e6 - 6.42375e6i) q^{31} +(-2.14423e6 - 3.71392e6i) q^{32} +(-4.14886e6 + 7.18604e6i) q^{34} -4.45949e6 q^{35} +3.68044e6 q^{37} +(-7.39608e6 + 1.28104e7i) q^{38} +(4.65424e6 + 8.06138e6i) q^{40} +(-1.26806e7 - 2.19634e7i) q^{41} +(-1.21419e7 + 2.10304e7i) q^{43} +3.65035e6 q^{44} -2.33977e7 q^{46} +(3.51686e6 - 6.09137e6i) q^{47} +(2.01239e6 + 3.48557e6i) q^{49} +(1.24535e7 + 2.15701e7i) q^{50} +(1.16442e7 - 2.01684e7i) q^{52} +3.10597e7 q^{53} -1.36367e7 q^{55} +(-3.79153e7 + 6.56712e7i) q^{56} +(569179. + 985846. i) q^{58} +(-7.68270e7 - 1.33068e8i) q^{59} +(7.75804e7 - 1.34373e8i) q^{61} +1.31427e8 q^{62} +1.38201e8 q^{64} +(-4.34996e7 + 7.53435e7i) q^{65} +(6.98640e6 + 1.21008e7i) q^{67} +(4.63753e7 + 8.03244e7i) q^{68} +(3.95078e7 - 6.84295e7i) q^{70} +3.45182e8 q^{71} -3.01511e8 q^{73} +(-3.26059e7 + 5.64751e7i) q^{74} +(8.26721e7 + 1.43192e8i) q^{76} +(-5.55451e7 - 9.62069e7i) q^{77} +(-1.79834e8 + 3.11482e8i) q^{79} -8.99059e7 q^{80} +4.49361e8 q^{82} +(-5.25069e7 + 9.09446e7i) q^{83} +(-1.73245e8 - 3.00070e8i) q^{85} +(-2.15137e8 - 3.72628e8i) q^{86} +(-1.15941e8 + 2.00817e8i) q^{88} -8.60555e8 q^{89} -7.08730e8 q^{91} +(-1.30768e8 + 2.26497e8i) q^{92} +(6.23135e7 + 1.07930e8i) q^{94} +(-3.08840e8 - 5.34927e8i) q^{95} +(-4.74261e7 + 8.21444e7i) q^{97} -7.13133e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22}+ \cdots - 4827300318 q^{98}+O(q^{100}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

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