LMFDB - Embedded newform 45.9.g.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,9,Mod(28,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("45.28");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	45.g (of order $4$, degree $2$, 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:	$18.3320374528$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 $ x^6 - 2x^5 + 2x^4 - 30x^3 + 1089x^2 - 3168*x + 4608
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$1.52966 - 1.52966i$ of defining polynomial
Character	$\chi$	$=$	45.37
Dual form			45.9.g.a.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.2610 - 15.2610i) q^{2} +209.796i q^{4} +(-558.542 + 280.457i) q^{5} +(-2415.21 - 2415.21i) q^{7} +(-705.116 + 705.116i) q^{8} +O(q^{10})$	\(q+(-15.2610 - 15.2610i) q^{2} +209.796i q^{4} +(-558.542 + 280.457i) q^{5} +(-2415.21 - 2415.21i) q^{7} +(-705.116 + 705.116i) q^{8} +(12804.0 + 4243.86i) q^{10} +981.878 q^{11} +(-26582.1 + 26582.1i) q^{13} +73717.1i q^{14} +75229.4 q^{16} +(18503.9 + 18503.9i) q^{17} -50374.1i q^{19} +(-58838.8 - 117180. i) q^{20} +(-14984.4 - 14984.4i) q^{22} +(-13652.5 + 13652.5i) q^{23} +(233313. - 313294. i) q^{25} +811340. q^{26} +(506702. - 506702. i) q^{28} -1.05137e6i q^{29} +1.09477e6 q^{31} +(-967566. - 967566. i) q^{32} -564775. i q^{34} +(2.02636e6 + 671634. i) q^{35} +(77885.1 + 77885.1i) q^{37} +(-768759. + 768759. i) q^{38} +(196082. - 591591. i) q^{40} -554897. q^{41} +(-1.07414e6 + 1.07414e6i) q^{43} +205994. i q^{44} +416702. q^{46} +(4.06986e6 + 4.06986e6i) q^{47} +5.90168e6i q^{49} +(-8.34176e6 + 1.22058e6i) q^{50} +(-5.57683e6 - 5.57683e6i) q^{52} +(-1.88025e6 + 1.88025e6i) q^{53} +(-548420. + 275374. i) q^{55} +3.40601e6 q^{56} +(-1.60450e7 + 1.60450e7i) q^{58} +1.27248e7i q^{59} +1.40038e7 q^{61} +(-1.67073e7 - 1.67073e7i) q^{62} +1.02733e7i q^{64} +(7.39210e6 - 2.23024e7i) q^{65} +(-9.54151e6 - 9.54151e6i) q^{67} +(-3.88204e6 + 3.88204e6i) q^{68} +(-2.06744e7 - 4.11741e7i) q^{70} +2.82034e7 q^{71} +(1.11578e7 - 1.11578e7i) q^{73} -2.37721e6i q^{74} +1.05683e7 q^{76} +(-2.37144e6 - 2.37144e6i) q^{77} +6.87542e7i q^{79} +(-4.20188e7 + 2.10986e7i) q^{80} +(8.46828e6 + 8.46828e6i) q^{82} +(3.29194e6 - 3.29194e6i) q^{83} +(-1.55247e7 - 5.14565e6i) q^{85} +3.27850e7 q^{86} +(-692338. + 692338. i) q^{88} +7.97635e7i q^{89} +1.28403e8 q^{91} +(-2.86424e6 - 2.86424e6i) q^{92} -1.24220e8i q^{94} +(1.41278e7 + 2.81360e7i) q^{95} +(-1.96546e7 - 1.96546e7i) q^{97} +(9.00656e7 - 9.00656e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8	$ 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8} + 30870 q^{10} - 23192 q^{11} - 119142 q^{13} + 218616 q^{16} + 265502 q^{17} - 412260 q^{20} - 35664 q^{22} - 28888 q^{23} - 340350 q^{25} + 801388 q^{26} + 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} + 4971680 q^{35} - 454002 q^{37} - 1443720 q^{38} + 2683500 q^{40} - 2489432 q^{41} + 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} - 29537650 q^{50} - 735732 q^{52} + 13509122 q^{53} + 4448040 q^{55} + 18454800 q^{56} - 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} + 30943610 q^{65} - 32827752 q^{67} - 8118692 q^{68} - 44156280 q^{70} + 13992928 q^{71} + 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 23045920 q^{80} + 38023056 q^{82} + 14768432 q^{83} - 19713030 q^{85} + 135560008 q^{86} - 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} - 239661000 q^{95} - 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8 + 30870 * q^10 - 23192 * q^11 - 119142 * q^13 + 218616 * q^16 + 265502 * q^17 - 412260 * q^20 - 35664 * q^22 - 28888 * q^23 - 340350 * q^25 + 801388 * q^26 + 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 + 4971680 * q^35 - 454002 * q^37 - 1443720 * q^38 + 2683500 * q^40 - 2489432 * q^41 + 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 - 29537650 * q^50 - 735732 * q^52 + 13509122 * q^53 + 4448040 * q^55 + 18454800 * q^56 - 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 + 30943610 * q^65 - 32827752 * q^67 - 8118692 * q^68 - 44156280 * q^70 + 13992928 * q^71 + 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 23045920 * q^80 + 38023056 * q^82 + 14768432 * q^83 - 19713030 * q^85 + 135560008 * q^86 - 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 - 239661000 * q^95 - 186656202 * q^97 + 345959698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−15.2610	−	15.2610i	−0.953812	−	0.953812i	0.0451670	−	0.998979i	$-0.485618\pi$
$2$	−15.2610	−	15.2610i	−0.953812	−	0.953812i	−0.998979	+	0.0451670i	$0.985618\pi$
$3$		0			0
$3$		0			0
$4$			209.796i			0.819516i
$5$	−558.542	+	280.457i	−0.893667	+	0.448731i
$5$	−558.542	+	280.457i	−0.893667	+	0.448731i
$6$		0			0
$7$	−2415.21	−	2415.21i	−1.00592	−	1.00592i	−0.999982	−	0.00593626i	$-0.998110\pi$
$7$	−2415.21	−	2415.21i	−1.00592	−	1.00592i	−0.00593626	−	0.999982i	$-0.501890\pi$
$8$	−705.116	+	705.116i	−0.172147	+	0.172147i
$9$		0			0
$10$	12804.0	+	4243.86i	1.28040	+	0.424386i
$11$	981.878			0.0670636			0.0335318	−	0.999438i	$-0.489325\pi$
$11$	981.878			0.0670636			0.0335318	+	0.999438i	$0.489325\pi$
$12$		0			0
$13$	−26582.1	+	26582.1i	−0.930715	+	0.930715i	−0.997751	−	0.0670358i	$-0.978646\pi$
$13$	−26582.1	+	26582.1i	−0.930715	+	0.930715i	0.0670358	+	0.997751i	$0.478646\pi$
$14$			73717.1i			1.91892i
$15$		0			0
$16$	75229.4			1.14791
$17$	18503.9	+	18503.9i	0.221547	+	0.221547i	0.809150	−	0.587602i	$-0.199928\pi$
$17$	18503.9	+	18503.9i	0.221547	+	0.221547i	−0.587602	+	0.809150i	$0.699928\pi$
$18$		0			0
$19$		−	50374.1i		−	0.386539i	−0.981146	−	0.193269i	$-0.938091\pi$
$19$		−	50374.1i		−	0.386539i	0.981146	−	0.193269i	$-0.0619091\pi$
$20$	−58838.8	−	117180.i	−0.367742	−	0.732375i
$21$		0			0
$22$	−14984.4	−	14984.4i	−0.0639661	−	0.0639661i
$23$	−13652.5	+	13652.5i	−0.0487866	+	0.0487866i	−0.731079	−	0.682293i	$-0.760983\pi$
$23$	−13652.5	+	13652.5i	−0.0487866	+	0.0487866i	0.682293	+	0.731079i	$0.260983\pi$
$24$		0			0
$25$	233313.	−	313294.i	0.597281	−	0.802032i
$26$	811340.			1.77545
$27$		0			0
$28$	506702.	−	506702.i	0.824367	−	0.824367i
$29$		−	1.05137e6i		−	1.48650i	−0.669015	−	0.743249i	$-0.733284\pi$
$29$		−	1.05137e6i		−	1.48650i	0.669015	−	0.743249i	$-0.266716\pi$
$30$		0			0
$31$	1.09477e6			1.18543			0.592717	−	0.805411i	$-0.298055\pi$
$31$	1.09477e6			1.18543			0.592717	+	0.805411i	$0.298055\pi$
$32$	−967566.	−	967566.i	−0.922743	−	0.922743i
$33$		0			0
$34$		−	564775.i		−	0.422629i
$35$	2.02636e6	+	671634.i	1.35034	+	0.447570i
$36$		0			0
$37$	77885.1	+	77885.1i	0.0415573	+	0.0415573i	0.727580	−	0.686023i	$-0.240645\pi$
$37$	77885.1	+	77885.1i	0.0415573	+	0.0415573i	−0.686023	+	0.727580i	$0.740645\pi$
$38$	−768759.	+	768759.i	−0.368685	+	0.368685i
$39$		0			0
$40$	196082.	−	591591.i	0.0765947	−	0.231090i
$41$	−554897.			−0.196371			−0.0981854	−	0.995168i	$-0.531304\pi$
$41$	−554897.			−0.196371			−0.0981854	+	0.995168i	$0.531304\pi$
$42$		0			0
$43$	−1.07414e6	+	1.07414e6i	−0.314187	+	0.314187i	−0.846529	−	0.532342i	$-0.821312\pi$
$43$	−1.07414e6	+	1.07414e6i	−0.314187	+	0.314187i	0.532342	+	0.846529i	$0.321312\pi$
$44$			205994.i			0.0549597i
$45$		0			0
$46$	416702.			0.0930666
$47$	4.06986e6	+	4.06986e6i	0.834043	+	0.834043i	0.988067	−	0.154024i	$-0.0492235\pi$
$47$	4.06986e6	+	4.06986e6i	0.834043	+	0.834043i	−0.154024	+	0.988067i	$0.549223\pi$
$48$		0			0
$49$			5.90168e6i			1.02374i
$50$	−8.34176e6	+	1.22058e6i	−1.33468	+	0.195293i
$51$		0			0
$52$	−5.57683e6	−	5.57683e6i	−0.762736	−	0.762736i
$53$	−1.88025e6	+	1.88025e6i	−0.238294	+	0.238294i	−0.816143	−	0.577850i	$-0.803892\pi$
$53$	−1.88025e6	+	1.88025e6i	−0.238294	+	0.238294i	0.577850	+	0.816143i	$0.303892\pi$
$54$		0			0
$55$	−548420.	+	275374.i	−0.0599325	+	0.0300935i
$56$	3.40601e6			0.346333
$57$		0			0
$58$	−1.60450e7	+	1.60450e7i	−1.41784	+	1.41784i
$59$			1.27248e7i			1.05013i	0.851063	+	0.525063i	$0.175958\pi$
$59$			1.27248e7i			1.05013i	−0.851063	+	0.525063i	$0.824042\pi$
$60$		0			0
$61$	1.40038e7			1.01141			0.505705	−	0.862707i	$-0.331233\pi$
$61$	1.40038e7			1.01141			0.505705	+	0.862707i	$0.331233\pi$
$62$	−1.67073e7	−	1.67073e7i	−1.13068	−	1.13068i
$63$		0			0
$64$			1.02733e7i			0.612338i
$65$	7.39210e6	−	2.23024e7i	0.414109	−	1.24939i
$66$		0			0
$67$	−9.54151e6	−	9.54151e6i	−0.473498	−	0.473498i	0.429547	−	0.903045i	$-0.358673\pi$
$67$	−9.54151e6	−	9.54151e6i	−0.473498	−	0.473498i	−0.903045	+	0.429547i	$0.858673\pi$
$68$	−3.88204e6	+	3.88204e6i	−0.181562	+	0.181562i
$69$		0			0
$70$	−2.06744e7	−	4.11741e7i	−0.861076	−	1.71487i
$71$	2.82034e7			1.10986			0.554930	−	0.831897i	$-0.312745\pi$
$71$	2.82034e7			1.10986			0.554930	+	0.831897i	$0.312745\pi$
$72$		0			0
$73$	1.11578e7	−	1.11578e7i	0.392905	−	0.392905i	−0.482817	−	0.875721i	$-0.660386\pi$
$73$	1.11578e7	−	1.11578e7i	0.392905	−	0.392905i	0.875721	+	0.482817i	$0.160386\pi$
$74$		−	2.37721e6i		−	0.0792758i
$75$		0			0
$76$	1.05683e7			0.316775
$77$	−2.37144e6	−	2.37144e6i	−0.0674605	−	0.0674605i
$78$		0			0
$79$			6.87542e7i			1.76519i	0.470136	+	0.882594i	$0.344205\pi$
$79$			6.87542e7i			1.76519i	−0.470136	+	0.882594i	$0.655795\pi$
$80$	−4.20188e7	+	2.10986e7i	−1.02585	+	0.515102i
$81$		0			0
$82$	8.46828e6	+	8.46828e6i	0.187301	+	0.187301i
$83$	3.29194e6	−	3.29194e6i	0.0693649	−	0.0693649i	−0.671573	−	0.740938i	$-0.734381\pi$
$83$	3.29194e6	−	3.29194e6i	0.0693649	−	0.0693649i	0.740938	+	0.671573i	$0.234381\pi$
$84$		0			0
$85$	−1.55247e7	−	5.14565e6i	−0.297405	−	0.0985745i
$86$	3.27850e7			0.599351
$87$		0			0
$88$	−692338.	+	692338.i	−0.0115448	+	0.0115448i
$89$			7.97635e7i			1.27129i	0.771982	+	0.635645i	$0.219266\pi$
$89$			7.97635e7i			1.27129i	−0.771982	+	0.635645i	$0.780734\pi$
$90$		0			0
$91$	1.28403e8			1.87245
$92$	−2.86424e6	−	2.86424e6i	−0.0399814	−	0.0399814i
$93$		0			0
$94$		−	1.24220e8i		−	1.59104i
$95$	1.41278e7	+	2.81360e7i	0.173452	+	0.345437i
$96$		0			0
$97$	−1.96546e7	−	1.96546e7i	−0.222012	−	0.222012i	0.587333	−	0.809345i	$-0.300178\pi$
$97$	−1.96546e7	−	1.96546e7i	−0.222012	−	0.222012i	−0.809345	+	0.587333i	$0.800178\pi$
$98$	9.00656e7	−	9.00656e7i	0.976460	−	0.976460i
$99$		0			0
$100$	6.57278e7	+	4.89482e7i	0.657278	+	0.489482i
$101$	−3.02468e7			−0.290666			−0.145333	−	0.989383i	$-0.546425\pi$
$101$	−3.02468e7			−0.290666			−0.145333	+	0.989383i	$0.546425\pi$
$102$		0			0
$103$	−4.28162e7	+	4.28162e7i	−0.380416	+	0.380416i	−0.871252	−	0.490836i	$-0.836691\pi$
$103$	−4.28162e7	+	4.28162e7i	−0.380416	+	0.380416i	0.490836	+	0.871252i	$0.336691\pi$
$104$		−	3.74870e7i		−	0.320440i
$105$		0			0
$106$	5.73890e7			0.454575
$107$	−8.84746e7	−	8.84746e7i	−0.674969	−	0.674969i	0.283888	−	0.958857i	$-0.408375\pi$
$107$	−8.84746e7	−	8.84746e7i	−0.674969	−	0.674969i	−0.958857	+	0.283888i	$0.908375\pi$
$108$		0			0
$109$			4.49302e7i			0.318297i	0.987255	+	0.159148i	$0.0508749\pi$
$109$			4.49302e7i			0.318297i	−0.987255	+	0.159148i	$0.949125\pi$
$110$	1.25719e7	+	4.16695e6i	0.0858679	+	0.0284608i
$111$		0			0
$112$	−1.81695e8	−	1.81695e8i	−1.15470	−	1.15470i
$113$	−9.24017e6	+	9.24017e6i	−0.0566717	+	0.0566717i	−0.734875	−	0.678203i	$-0.762759\pi$
$113$	−9.24017e6	+	9.24017e6i	−0.0566717	+	0.0566717i	0.678203	+	0.734875i	$0.262759\pi$
$114$		0			0
$115$	3.79656e6	−	1.14544e7i	0.0217069	−	0.0654911i
$116$	2.20574e8			1.21821
$117$		0			0
$118$	1.94193e8	−	1.94193e8i	1.00162	−	1.00162i
$119$		−	8.93815e7i		−	0.445717i
$120$		0			0
$121$	−2.13395e8			−0.995502
$122$	−2.13712e8	−	2.13712e8i	−0.964695	−	0.964695i
$123$		0			0
$124$			2.29679e8i			0.971483i
$125$	−4.24498e7	+	2.40422e8i	−0.173874	+	0.984768i
$126$		0			0
$127$	2.89529e8	+	2.89529e8i	1.11295	+	1.11295i	0.992749	+	0.120204i	$0.0383548\pi$
$127$	2.89529e8	+	2.89529e8i	1.11295	+	1.11295i	0.120204	+	0.992749i	$0.461645\pi$
$128$	−9.09157e7	+	9.09157e7i	−0.338687	+	0.338687i
$129$		0			0
$130$	−4.53167e8	+	2.27546e8i	−1.58667	+	0.796701i
$131$	1.84509e8			0.626516			0.313258	−	0.949668i	$-0.398580\pi$
$131$	1.84509e8			0.626516			0.313258	+	0.949668i	$0.398580\pi$
$132$		0			0
$133$	−1.21664e8	+	1.21664e8i	−0.388826	+	0.388826i
$134$			2.91226e8i			0.903256i
$135$		0			0
$136$	−2.60947e7			−0.0762777
$137$	−1.60104e8	−	1.60104e8i	−0.454484	−	0.454484i	0.442356	−	0.896840i	$-0.354143\pi$
$137$	−1.60104e8	−	1.60104e8i	−0.454484	−	0.454484i	−0.896840	+	0.442356i	$0.854143\pi$
$138$		0			0
$139$		−	2.86303e8i		−	0.766949i	−0.923551	−	0.383475i	$-0.874727\pi$
$139$		−	2.86303e8i		−	0.766949i	0.923551	−	0.383475i	$-0.125273\pi$
$140$	−1.40906e8	+	4.25122e8i	−0.366791	+	1.10663i
$141$		0			0
$142$	−4.30412e8	−	4.30412e8i	−1.05860	−	1.05860i
$143$	−2.61004e7	+	2.61004e7i	−0.0624171	+	0.0624171i
$144$		0			0
$145$	2.94864e8	+	5.87235e8i	0.667037	+	1.32843i
$146$	−3.40558e8			−0.749515
$147$		0			0
$148$	−1.63400e7	+	1.63400e7i	−0.0340569	+	0.0340569i
$149$			1.84894e8i			0.375127i	0.982253	+	0.187563i	$0.0600590\pi$
$149$			1.84894e8i			0.375127i	−0.982253	+	0.187563i	$0.939941\pi$
$150$		0			0
$151$	−6.16679e8			−1.18618			−0.593091	−	0.805135i	$-0.702093\pi$
$151$	−6.16679e8			−1.18618			−0.593091	+	0.805135i	$0.702093\pi$
$152$	3.55196e7	+	3.55196e7i	0.0665416	+	0.0665416i
$153$		0			0
$154$			7.23811e7i			0.128689i
$155$	−6.11477e8	+	3.07037e8i	−1.05938	+	0.531941i
$156$		0			0
$157$	2.91004e8	+	2.91004e8i	0.478961	+	0.478961i	0.904799	−	0.425838i	$-0.140021\pi$
$157$	2.91004e8	+	2.91004e8i	0.478961	+	0.478961i	−0.425838	+	0.904799i	$0.640021\pi$
$158$	1.04926e9	−	1.04926e9i	1.68366	−	1.68366i
$159$		0			0
$160$	8.11786e8	+	2.69066e8i	1.23869	+	0.410562i
$161$	6.59473e7			0.0981508
$162$		0			0
$163$	7.65254e8	−	7.65254e8i	1.08406	−	1.08406i	0.0879389	−	0.996126i	$-0.471972\pi$
$163$	7.65254e8	−	7.65254e8i	1.08406	−	1.08406i	0.996126	−	0.0879389i	$-0.0280280\pi$
$164$		−	1.16415e8i		−	0.160929i
$165$		0			0
$166$	−1.00477e8			−0.132322
$167$	4.23551e8	+	4.23551e8i	0.544552	+	0.544552i	0.924860	−	0.380308i	$-0.124182\pi$
$167$	4.23551e8	+	4.23551e8i	0.544552	+	0.544552i	−0.380308	+	0.924860i	$0.624182\pi$
$168$		0			0
$169$		−	5.97490e8i		−	0.732460i
$170$	1.58395e8	+	3.15450e8i	0.189647	+	0.377690i
$171$		0			0
$172$	−2.25351e8	−	2.25351e8i	−0.257482	−	0.257482i
$173$	1.22912e9	−	1.22912e9i	1.37217	−	1.37217i	0.514955	−	0.857217i	$-0.327809\pi$
$173$	1.22912e9	−	1.22912e9i	1.37217	−	1.37217i	0.857217	−	0.514955i	$-0.172191\pi$
$174$		0			0
$175$	−1.32017e9	+	1.93170e8i	−1.40760	+	0.205962i
$176$	7.38661e7			0.0769829
$177$		0			0
$178$	1.21727e9	−	1.21727e9i	1.21257	−	1.21257i
$179$		−	4.39309e8i		−	0.427916i	−0.976843	−	0.213958i	$-0.931364\pi$
$179$		−	4.39309e8i		−	0.427916i	0.976843	−	0.213958i	$-0.0686355\pi$
$180$		0			0
$181$	1.68623e9			1.57110			0.785549	−	0.618799i	$-0.212380\pi$
$181$	1.68623e9			1.57110			0.785549	+	0.618799i	$0.212380\pi$
$182$	−1.95956e9	−	1.95956e9i	−1.78596	−	1.78596i
$183$		0			0
$184$		−	1.92532e7i		−	0.0167970i
$185$	−6.53455e7	−	2.16587e7i	−0.0557865	−	0.0184904i
$186$		0			0
$187$	1.81685e7	+	1.81685e7i	0.0148578	+	0.0148578i
$188$	−8.53842e8	+	8.53842e8i	−0.683512	+	0.683512i
$189$		0			0
$190$	2.13780e8	−	6.44988e8i	0.164041	−	0.494922i
$191$	1.52273e9			1.14416			0.572082	−	0.820196i	$-0.306136\pi$
$191$	1.52273e9			1.14416			0.572082	+	0.820196i	$0.306136\pi$
$192$		0			0
$193$	−1.96356e8	+	1.96356e8i	−0.141519	+	0.141519i	−0.774317	−	0.632798i	$-0.781906\pi$
$193$	−1.96356e8	+	1.96356e8i	−0.141519	+	0.141519i	0.632798	+	0.774317i	$0.281906\pi$
$194$			5.99897e8i			0.423516i
$195$		0			0
$196$	−1.23815e9			−0.838976
$197$	1.25390e9	+	1.25390e9i	0.832525	+	0.832525i	0.987862	−	0.155337i	$-0.0496463\pi$
$197$	1.25390e9	+	1.25390e9i	0.832525	+	0.832525i	−0.155337	+	0.987862i	$0.549646\pi$
$198$		0			0
$199$			1.10010e9i			0.701489i	0.936471	+	0.350745i	$0.114071\pi$
$199$			1.10010e9i			0.701489i	−0.936471	+	0.350745i	$0.885929\pi$
$200$	5.63956e7	+	3.85421e8i	0.0352473	+	0.240888i
$201$		0			0
$202$	4.61597e8	+	4.61597e8i	0.277241	+	0.277241i
$203$	−2.53928e9	+	2.53928e9i	−1.49530	+	1.49530i
$204$		0			0
$205$	3.09933e8	−	1.55625e8i	0.175490	−	0.0881176i
$206$	1.30684e9			0.725691
$207$		0			0
$208$	−1.99976e9	+	1.99976e9i	−1.06838	+	1.06838i
$209$		−	4.94612e7i		−	0.0259227i
$210$		0			0
$211$	2.62708e9			1.32539			0.662695	−	0.748889i	$-0.269412\pi$
$211$	2.62708e9			1.32539			0.662695	+	0.748889i	$0.269412\pi$
$212$	−3.94470e8	−	3.94470e8i	−0.195286	−	0.195286i
$213$		0			0
$214$			2.70042e9i			1.28759i
$215$	2.98703e8	−	9.01205e8i	0.139793	−	0.421764i
$216$		0			0
$217$	−2.64411e9	−	2.64411e9i	−1.19245	−	1.19245i
$218$	6.85680e8	−	6.85680e8i	0.303596	−	0.303596i
$219$		0			0
$220$	−5.77725e7	−	1.15056e8i	−0.0246621	−	0.0491157i
$221$	−9.83745e8			−0.412395
$222$		0			0
$223$	−2.23974e9	+	2.23974e9i	−0.905687	+	0.905687i	−0.995921	−	0.0902332i	$-0.971239\pi$
$223$	−2.23974e9	+	2.23974e9i	−0.905687	+	0.905687i	0.0902332	+	0.995921i	$0.471239\pi$
$224$			4.67375e9i			1.85641i
$225$		0			0
$226$	2.82028e8			0.108108
$227$	−2.86595e9	−	2.86595e9i	−1.07936	−	1.07936i	−0.996567	−	0.0827897i	$-0.973617\pi$
$227$	−2.86595e9	−	2.86595e9i	−1.07936	−	1.07936i	−0.0827897	−	0.996567i	$-0.526383\pi$
$228$		0			0
$229$		−	4.21694e9i		−	1.53340i	−0.642005	−	0.766701i	$-0.721897\pi$
$229$		−	4.21694e9i		−	1.53340i	0.642005	−	0.766701i	$-0.278103\pi$
$230$	−2.32745e8	+	1.16867e8i	−0.0831705	+	0.0417618i
$231$		0			0
$232$	7.41339e8	+	7.41339e8i	0.255897	+	0.255897i
$233$	1.39423e9	−	1.39423e9i	0.473052	−	0.473052i	−0.429849	−	0.902901i	$-0.641433\pi$
$233$	1.39423e9	−	1.39423e9i	0.473052	−	0.473052i	0.902901	+	0.429849i	$0.141433\pi$
$234$		0			0
$235$	−3.41461e9	−	1.13177e9i	−1.11962	−	0.371096i
$236$	−2.66961e9			−0.860596
$237$		0			0
$238$	−1.36405e9	+	1.36405e9i	−0.425131	+	0.425131i
$239$		−	2.78614e9i		−	0.853907i	−0.904274	−	0.426954i	$-0.859587\pi$
$239$		−	2.78614e9i		−	0.853907i	0.904274	−	0.426954i	$-0.140413\pi$
$240$		0			0
$241$	−1.82461e9			−0.540881			−0.270441	−	0.962737i	$-0.587169\pi$
$241$	−1.82461e9			−0.540881			−0.270441	+	0.962737i	$0.587169\pi$
$242$	3.25662e9	+	3.25662e9i	0.949523	+	0.949523i
$243$		0			0
$244$			2.93795e9i			0.828866i
$245$	−1.65517e9	−	3.29634e9i	−0.459386	−	0.914887i
$246$		0			0
$247$	1.33905e9	+	1.33905e9i	0.359757	+	0.359757i
$248$	−7.71943e8	+	7.71943e8i	−0.204070	+	0.204070i
$249$		0			0
$250$	4.31690e9	−	3.02125e9i	1.10513	−	0.773440i
$251$	1.08818e9			0.274162			0.137081	−	0.990560i	$-0.456228\pi$
$251$	1.08818e9			0.274162			0.137081	+	0.990560i	$0.456228\pi$
$252$		0			0
$253$	−1.34051e7	+	1.34051e7i	−0.00327181	+	0.00327181i
$254$		−	8.83700e9i		−	2.12310i
$255$		0			0
$256$	5.40490e9			1.25843
$257$	1.38793e9	+	1.38793e9i	0.318151	+	0.318151i	0.848057	−	0.529905i	$-0.177773\pi$
$257$	1.38793e9	+	1.38793e9i	0.318151	+	0.318151i	−0.529905	+	0.848057i	$0.677773\pi$
$258$		0			0
$259$		−	3.76218e8i		−	0.0836066i
$260$	4.67896e9	+	1.55083e9i	1.02390	+	0.339369i
$261$		0			0
$262$	−2.81579e9	−	2.81579e9i	−0.597578	−	0.597578i
$263$	−3.30796e9	+	3.30796e9i	−0.691412	+	0.691412i	−0.962543	−	0.271130i	$-0.912603\pi$
$263$	−3.30796e9	+	3.30796e9i	−0.691412	+	0.691412i	0.271130	+	0.962543i	$0.412603\pi$
$264$		0			0
$265$	5.22870e8	−	1.57753e9i	0.106025	−	0.319885i
$266$	3.71343e9			0.741735
$267$		0			0
$268$	2.00177e9	−	2.00177e9i	0.388039	−	0.388039i
$269$			4.82096e9i			0.920713i	0.887734	+	0.460356i	$0.152278\pi$
$269$			4.82096e9i			0.920713i	−0.887734	+	0.460356i	$0.847722\pi$
$270$		0			0
$271$	−5.54038e9			−1.02722			−0.513609	−	0.858025i	$-0.671692\pi$
$271$	−5.54038e9			−1.02722			−0.513609	+	0.858025i	$0.671692\pi$
$272$	1.39203e9	+	1.39203e9i	0.254316	+	0.254316i
$273$		0			0
$274$			4.88668e9i			0.866985i
$275$	2.29085e8	−	3.07616e8i	0.0400558	−	0.0537871i
$276$		0			0
$277$	6.27804e9	+	6.27804e9i	1.06636	+	1.06636i	0.997635	+	0.0687272i	$0.0218938\pi$
$277$	6.27804e9	+	6.27804e9i	1.06636	+	1.06636i	0.0687272	+	0.997635i	$0.478106\pi$
$278$	−4.36927e9	+	4.36927e9i	−0.731526	+	0.731526i
$279$		0			0
$280$	−1.90240e9	+	9.55238e8i	−0.309506	+	0.155410i
$281$	−9.60308e9			−1.54023			−0.770114	−	0.637906i	$-0.779801\pi$
$281$	−9.60308e9			−1.54023			−0.770114	+	0.637906i	$0.779801\pi$
$282$		0			0
$283$	2.69661e9	−	2.69661e9i	0.420409	−	0.420409i	−0.464936	−	0.885344i	$-0.653923\pi$
$283$	2.69661e9	−	2.69661e9i	0.420409	−	0.420409i	0.885344	+	0.464936i	$0.153923\pi$
$284$			5.91696e9i			0.909548i
$285$		0			0
$286$	7.96637e8			0.119068
$287$	1.34019e9	+	1.34019e9i	0.197533	+	0.197533i
$288$		0			0
$289$		−	6.29097e9i		−	0.901833i
$290$	4.46187e9	−	1.34617e10i	0.630849	−	1.90331i
$291$		0			0
$292$	2.34086e9	+	2.34086e9i	0.321992	+	0.321992i
$293$	6.28799e9	−	6.28799e9i	0.853182	−	0.853182i	−0.137342	−	0.990524i	$-0.543856\pi$
$293$	6.28799e9	−	6.28799e9i	0.853182	−	0.853182i	0.990524	+	0.137342i	$0.0438560\pi$
$294$		0			0
$295$	−3.56875e9	−	7.10731e9i	−0.471224	−	0.938464i
$296$	−1.09836e8			−0.0143080
$297$		0			0
$298$	2.82167e9	−	2.82167e9i	0.357800	−	0.357800i
$299$		−	7.25825e8i		−	0.0908129i
$300$		0			0
$301$	5.18856e9			0.632093
$302$	9.41114e9	+	9.41114e9i	1.13140	+	1.13140i
$303$		0			0
$304$		−	3.78961e9i		−	0.443711i
$305$	−7.82171e9	+	3.92746e9i	−0.903863	+	0.453850i
$306$		0			0
$307$	−4.34115e8	−	4.34115e8i	−0.0488710	−	0.0488710i	0.682249	−	0.731120i	$-0.261002\pi$
$307$	−4.34115e8	−	4.34115e8i	−0.0488710	−	0.0488710i	−0.731120	+	0.682249i	$0.761002\pi$
$308$	4.97519e8	−	4.97519e8i	0.0552850	−	0.0552850i
$309$		0			0
$310$	1.40174e10	+	4.64606e9i	1.51783	+	0.503082i
$311$	5.29907e9			0.566445			0.283223	−	0.959054i	$-0.408596\pi$
$311$	5.29907e9			0.566445			0.283223	+	0.959054i	$0.408596\pi$
$312$		0			0
$313$	−5.51999e9	+	5.51999e9i	−0.575123	+	0.575123i	−0.933556	−	0.358433i	$-0.883311\pi$
$313$	−5.51999e9	+	5.51999e9i	−0.575123	+	0.575123i	0.358433	+	0.933556i	$0.383311\pi$
$314$		−	8.88202e9i		−	0.913678i
$315$		0			0
$316$	−1.44244e10			−1.44660
$317$	3.86039e9	+	3.86039e9i	0.382291	+	0.382291i	0.871927	−	0.489636i	$-0.162870\pi$
$317$	3.86039e9	+	3.86039e9i	0.382291	+	0.382291i	−0.489636	+	0.871927i	$0.662870\pi$
$318$		0			0
$319$		−	1.03232e9i		−	0.0996899i
$320$	−2.88122e9	−	5.73808e9i	−0.274775	−	0.547226i
$321$		0			0
$322$	−1.00642e9	−	1.00642e9i	−0.0936174	−	0.0936174i
$323$	9.32115e8	−	9.32115e8i	0.0856366	−	0.0856366i
$324$		0			0
$325$	2.12606e9	+	1.45300e10i	0.190564	+	1.30236i
$326$	−2.33571e10			−2.06799
$327$		0			0
$328$	3.91267e8	−	3.91267e8i	0.0338047	−	0.0338047i
$329$		−	1.96591e10i		−	1.67796i
$330$		0			0
$331$	−4.43747e9			−0.369678			−0.184839	−	0.982769i	$-0.559176\pi$
$331$	−4.43747e9			−0.369678			−0.184839	+	0.982769i	$0.559176\pi$
$332$	6.90636e8	+	6.90636e8i	0.0568456	+	0.0568456i
$333$		0			0
$334$		−	1.29276e10i		−	1.03880i
$335$	8.00532e9	+	2.65335e9i	0.635622	+	0.210676i
$336$		0			0
$337$	5.03851e9	+	5.03851e9i	0.390645	+	0.390645i	0.874917	−	0.484272i	$-0.160916\pi$
$337$	5.03851e9	+	5.03851e9i	0.390645	+	0.390645i	−0.484272	+	0.874917i	$0.660916\pi$
$338$	−9.11830e9	+	9.11830e9i	−0.698630	+	0.698630i
$339$		0			0
$340$	1.07954e9	−	3.25703e9i	0.0807834	−	0.243728i
$341$	1.07493e9			0.0794995
$342$		0			0
$343$	3.30601e8	−	3.30601e8i	0.0238852	−	0.0238852i
$344$		−	1.51479e9i		−	0.108173i
$345$		0			0
$346$	−3.75151e10			−2.61759
$347$	2.80674e9	+	2.80674e9i	0.193590	+	0.193590i	0.797246	−	0.603655i	$-0.206290\pi$
$347$	2.80674e9	+	2.80674e9i	0.193590	+	0.193590i	−0.603655	+	0.797246i	$0.706290\pi$
$348$		0			0
$349$		−	1.32267e10i		−	0.891561i	−0.895142	−	0.445780i	$-0.852926\pi$
$349$		−	1.32267e10i		−	0.891561i	0.895142	−	0.445780i	$-0.147074\pi$
$350$	2.30951e10	+	1.71992e10i	1.53903	+	1.14613i
$351$		0			0
$352$	−9.50031e8	−	9.50031e8i	−0.0618824	−	0.0618824i
$353$	1.16376e9	−	1.16376e9i	0.0749489	−	0.0749489i	−0.668639	−	0.743587i	$-0.733123\pi$
$353$	1.16376e9	−	1.16376e9i	0.0749489	−	0.0749489i	0.743587	+	0.668639i	$0.233123\pi$
$354$		0			0
$355$	−1.57528e10	+	7.90983e9i	−0.991845	+	0.498028i
$356$	−1.67341e10			−1.04184
$357$		0			0
$358$	−6.70430e9	+	6.70430e9i	−0.408151	+	0.408151i
$359$			1.99414e10i			1.20054i	0.799797	+	0.600270i	$0.204940\pi$
$359$			1.99414e10i			1.20054i	−0.799797	+	0.600270i	$0.795060\pi$
$360$		0			0
$361$	1.44460e10			0.850588
$362$	−2.57336e10	−	2.57336e10i	−1.49853	−	1.49853i
$363$		0			0
$364$			2.69385e10i			1.53450i
$365$	−3.10282e9	+	9.36138e9i	−0.174817	+	0.527434i
$366$		0			0
$367$	2.26918e10	+	2.26918e10i	1.25085	+	1.25085i	0.955341	+	0.295506i	$0.0954881\pi$
$367$	2.26918e10	+	2.26918e10i	1.25085	+	1.25085i	0.295506	+	0.955341i	$0.404512\pi$
$368$	−1.02707e9	+	1.02707e9i	−0.0560026	+	0.0560026i
$369$		0			0
$370$	6.66704e8	+	1.32777e9i	0.0355735	+	0.0708461i
$371$	9.08241e9			0.479408
$372$		0			0
$373$	1.70421e10	−	1.70421e10i	0.880417	−	0.880417i	−0.113160	−	0.993577i	$-0.536097\pi$
$373$	1.70421e10	−	1.70421e10i	0.880417	−	0.880417i	0.993577	+	0.113160i	$0.0360971\pi$
$374$		−	5.54540e8i		−	0.0283430i
$375$		0			0
$376$	−5.73945e9			−0.287157
$377$	2.79477e10	+	2.79477e10i	1.38351	+	1.38351i
$378$		0			0
$379$			2.63026e10i			1.27480i	0.770534	+	0.637399i	$0.219990\pi$
$379$			2.63026e10i			1.27480i	−0.770534	+	0.637399i	$0.780010\pi$
$380$	−5.90283e9	+	2.96395e9i	−0.283091	+	0.142147i
$381$		0			0
$382$	−2.32383e10	−	2.32383e10i	−1.09132	−	1.09132i
$383$	−2.24947e10	+	2.24947e10i	−1.04541	+	1.04541i	−0.0464865	+	0.998919i	$0.514802\pi$
$383$	−2.24947e10	+	2.24947e10i	−1.04541	+	1.04541i	−0.998919	+	0.0464865i	$0.985198\pi$
$384$		0			0
$385$	1.98964e9	+	6.59463e8i	0.0905588	+	0.0300156i
$386$	5.99317e9			0.269965
$387$		0			0
$388$	4.12345e9	−	4.12345e9i	0.181943	−	0.181943i
$389$		−	5.72221e9i		−	0.249900i	−0.992163	−	0.124950i	$-0.960123\pi$
$389$		−	5.72221e9i		−	0.249900i	0.992163	−	0.124950i	$-0.0398770\pi$
$390$		0			0
$391$	−5.05248e8			−0.0216171
$392$	−4.16137e9	−	4.16137e9i	−0.176235	−	0.176235i
$393$		0			0
$394$		−	3.82715e10i		−	1.58814i
$395$	−1.92826e10	−	3.84021e10i	−0.792094	−	1.57749i
$396$		0			0
$397$	2.97350e9	+	2.97350e9i	0.119703	+	0.119703i	0.764421	−	0.644718i	$-0.223025\pi$
$397$	2.97350e9	+	2.97350e9i	0.119703	+	0.119703i	−0.644718	+	0.764421i	$0.723025\pi$
$398$	1.67887e10	−	1.67887e10i	0.669089	−	0.669089i
$399$		0			0
$400$	1.75520e10	−	2.35689e10i	0.685625	−	0.920660i
$401$	1.77762e10			0.687481			0.343741	−	0.939065i	$-0.388306\pi$
$401$	1.77762e10			0.687481			0.343741	+	0.939065i	$0.388306\pi$
$402$		0			0
$403$	−2.91014e10	+	2.91014e10i	−1.10330	+	1.10330i
$404$		−	6.34567e9i		−	0.238205i
$405$		0			0
$406$	7.75040e10			2.85246
$407$	7.64737e7	+	7.64737e7i	0.00278698	+	0.00278698i
$408$		0			0
$409$		−	2.57868e10i		−	0.921519i	−0.887525	−	0.460759i	$-0.847577\pi$
$409$		−	2.57868e10i		−	0.921519i	0.887525	−	0.460759i	$-0.152423\pi$
$410$	−7.10487e9	−	2.35490e9i	−0.251432	−	0.0833369i
$411$		0			0
$412$	−8.98267e9	−	8.98267e9i	−0.311757	−	0.311757i
$413$	3.07330e10	−	3.07330e10i	1.05634	−	1.05634i
$414$		0			0
$415$	−9.15439e8	+	2.76193e9i	−0.0308629	+	0.0931152i
$416$	5.14399e10			1.71762
$417$		0			0
$418$	−7.54827e8	+	7.54827e8i	−0.0247254	+	0.0247254i
$419$			2.80387e9i			0.0909707i	0.998965	+	0.0454853i	$0.0144834\pi$
$419$			2.80387e9i			0.0909707i	−0.998965	+	0.0454853i	$0.985517\pi$
$420$		0			0
$421$	3.39054e10			1.07929			0.539647	−	0.841891i	$-0.318558\pi$
$421$	3.39054e10			1.07929			0.539647	+	0.841891i	$0.318558\pi$
$422$	−4.00919e10	−	4.00919e10i	−1.26417	−	1.26417i
$423$		0			0
$424$		−	2.65159e9i		−	0.0820433i
$425$	1.01143e10	−	1.47995e9i	0.310014	−	0.0453619i
$426$		0			0
$427$	−3.38221e10	−	3.38221e10i	−1.01740	−	1.01740i
$428$	1.85616e10	−	1.85616e10i	0.553148	−	0.553148i
$429$		0			0
$430$	−1.83118e10	+	9.19477e9i	−0.535620	+	0.268947i
$431$	−4.74314e10			−1.37454			−0.687269	−	0.726403i	$-0.741190\pi$
$431$	−4.74314e10			−1.37454			−0.687269	+	0.726403i	$0.741190\pi$
$432$		0			0
$433$	2.85545e10	−	2.85545e10i	0.812313	−	0.812313i	−0.172667	−	0.984980i	$-0.555238\pi$
$433$	2.85545e10	−	2.85545e10i	0.812313	−	0.812313i	0.984980	+	0.172667i	$0.0552384\pi$
$434$			8.07035e10i			2.27475i
$435$		0			0
$436$	−9.42619e9			−0.260850
$437$	6.87732e8	+	6.87732e8i	0.0188579	+	0.0188579i
$438$		0			0
$439$			4.70888e10i			1.26783i	0.773404	+	0.633913i	$0.218552\pi$
$439$			4.70888e10i			1.26783i	−0.773404	+	0.633913i	$0.781448\pi$
$440$	1.92529e8	−	5.80870e8i	0.00513671	−	0.0154977i
$441$		0			0
$442$	1.50129e10	+	1.50129e10i	0.393347	+	0.393347i
$443$	2.13908e10	−	2.13908e10i	0.555407	−	0.555407i	−0.372589	−	0.927996i	$-0.621530\pi$
$443$	2.13908e10	−	2.13908e10i	0.555407	−	0.555407i	0.927996	+	0.372589i	$0.121530\pi$
$444$		0			0
$445$	−2.23702e10	−	4.45513e10i	−0.570467	−	1.13611i
$446$	6.83614e10			1.72771
$447$		0			0
$448$	2.48122e10	−	2.48122e10i	0.615962	−	0.615962i
$449$		−	1.99035e9i		−	0.0489717i	−0.999700	−	0.0244858i	$-0.992205\pi$
$449$		−	1.99035e9i		−	0.0489717i	0.999700	−	0.0244858i	$-0.00779487\pi$
$450$		0			0
$451$	−5.44841e8			−0.0131693
$452$	−1.93855e9	−	1.93855e9i	−0.0464434	−	0.0464434i
$453$		0			0
$454$			8.74745e10i			2.05901i
$455$	−7.17184e10	+	3.60115e10i	−1.67334	+	0.840224i
$456$		0			0
$457$	1.28799e10	+	1.28799e10i	0.295290	+	0.295290i	0.839166	−	0.543876i	$-0.183044\pi$
$457$	1.28799e10	+	1.28799e10i	0.295290	+	0.295290i	−0.543876	+	0.839166i	$0.683044\pi$
$458$	−6.43548e10	+	6.43548e10i	−1.46258	+	1.46258i
$459$		0			0
$460$	2.40310e9	+	7.96503e8i	0.0536710	+	0.0177892i
$461$	−2.95032e10			−0.653229			−0.326615	−	0.945158i	$-0.605908\pi$
$461$	−2.95032e10			−0.653229			−0.326615	+	0.945158i	$0.605908\pi$
$462$		0			0
$463$	−2.68794e10	+	2.68794e10i	−0.584919	+	0.584919i	−0.936251	−	0.351332i	$-0.885729\pi$
$463$	−2.68794e10	+	2.68794e10i	−0.584919	+	0.584919i	0.351332	+	0.936251i	$0.385729\pi$
$464$		−	7.90941e10i		−	1.70636i
$465$		0			0
$466$	−4.25545e10			−0.902407
$467$	−2.41860e10	−	2.41860e10i	−0.508507	−	0.508507i	0.405561	−	0.914068i	$-0.367076\pi$
$467$	−2.41860e10	−	2.41860e10i	−0.508507	−	0.508507i	−0.914068	+	0.405561i	$0.867076\pi$
$468$		0			0
$469$			4.60895e10i			0.952601i
$470$	3.48384e10	+	6.93822e10i	0.713949	+	1.42186i
$471$		0			0
$472$	−8.97244e9	−	8.97244e9i	−0.180777	−	0.180777i
$473$	−1.05468e9	+	1.05468e9i	−0.0210705	+	0.0210705i
$474$		0			0
$475$	−1.57819e10	−	1.17529e10i	−0.310016	−	0.230872i
$476$	1.87519e10			0.365273
$477$		0			0
$478$	−4.25192e10	+	4.25192e10i	−0.814467	+	0.814467i
$479$			1.00060e11i			1.90073i	0.311144	+	0.950363i	$0.399288\pi$
$479$			1.00060e11i			1.90073i	−0.311144	+	0.950363i	$0.600712\pi$
$480$		0			0
$481$	−4.14071e9			−0.0773560
$482$	2.78454e10	+	2.78454e10i	0.515899	+	0.515899i
$483$		0			0
$484$		−	4.47694e10i		−	0.815831i
$485$	1.64902e10	+	5.46564e9i	0.298029	+	0.0987812i
$486$		0			0
$487$	−4.35298e10	−	4.35298e10i	−0.773875	−	0.773875i	0.204907	−	0.978782i	$-0.434311\pi$
$487$	−4.35298e10	−	4.35298e10i	−0.773875	−	0.773875i	−0.978782	+	0.204907i	$0.934311\pi$
$488$	−9.87431e9	+	9.87431e9i	−0.174112	+	0.174112i
$489$		0			0
$490$	−2.50459e10	+	7.55649e10i	−0.434463	+	1.31080i
$491$	1.74821e10			0.300794			0.150397	−	0.988626i	$-0.451945\pi$
$491$	1.74821e10			0.300794			0.150397	+	0.988626i	$0.451945\pi$
$492$		0			0
$493$	1.94544e10	−	1.94544e10i	0.329330	−	0.329330i
$494$		−	4.08705e10i		−	0.686282i
$495$		0			0
$496$	8.23592e10			1.36077
$497$	−6.81171e10	−	6.81171e10i	−1.11643	−	1.11643i
$498$		0			0
$499$		−	6.18997e10i		−	0.998358i	−0.866499	−	0.499179i	$-0.833635\pi$
$499$		−	6.18997e10i		−	0.998358i	0.866499	−	0.499179i	$-0.166365\pi$
$500$	−5.04396e10	−	8.90581e9i	−0.807033	−	0.142493i
$501$		0			0
$502$	−1.66068e10	−	1.66068e10i	−0.261499	−	0.261499i
$503$	5.48962e10	−	5.48962e10i	0.857571	−	0.857571i	−0.133480	−	0.991051i	$-0.542615\pi$
$503$	5.48962e10	−	5.48962e10i	0.857571	−	0.857571i	0.991051	+	0.133480i	$0.0426152\pi$
$504$		0			0
$505$	1.68941e10	−	8.48292e9i	0.259759	−	0.130431i
$506$	4.09150e8			0.00624138
$507$		0			0
$508$	−6.07420e10	+	6.07420e10i	−0.912083	+	0.912083i
$509$			2.78975e9i			0.0415618i	0.999784	+	0.0207809i	$0.00661524\pi$
$509$			2.78975e9i			0.0415618i	−0.999784	+	0.0207809i	$0.993385\pi$
$510$		0			0
$511$	−5.38969e10			−0.790460
$512$	−5.92097e10	−	5.92097e10i	−0.861615	−	0.861615i
$513$		0			0
$514$		−	4.23623e10i		−	0.606914i
$515$	1.19065e10	−	3.59227e10i	0.169261	−	0.510670i
$516$		0			0
$517$	3.99611e9	+	3.99611e9i	0.0559339	+	0.0559339i
$518$	−5.74146e9	+	5.74146e9i	−0.0797450	+	0.0797450i
$519$		0			0
$520$	1.05135e10	+	2.09381e10i	0.143791	+	0.286367i
$521$	7.48087e10			1.01532			0.507658	−	0.861559i	$-0.330511\pi$
$521$	7.48087e10			1.01532			0.507658	+	0.861559i	$0.330511\pi$
$522$		0			0
$523$	−1.13284e10	+	1.13284e10i	−0.151412	+	0.151412i	−0.778748	−	0.627336i	$-0.784145\pi$
$523$	−1.13284e10	+	1.13284e10i	−0.151412	+	0.151412i	0.627336	+	0.778748i	$0.284145\pi$
$524$			3.87093e10i			0.513440i
$525$		0			0
$526$	1.00966e11			1.31896
$527$	2.02575e10	+	2.02575e10i	0.262630	+	0.262630i
$528$		0			0
$529$			7.79382e10i			0.995240i
$530$	−3.20542e10	+	1.60951e10i	−0.406239	+	0.203982i
$531$		0			0
$532$	−2.55247e10	−	2.55247e10i	−0.318650	−	0.318650i
$533$	1.47503e10	−	1.47503e10i	0.182765	−	0.182765i
$534$		0			0
$535$	7.42301e10	+	2.46035e10i	0.906077	+	0.300318i
$536$	1.34557e10			0.163023
$537$		0			0
$538$	7.35726e10	−	7.35726e10i	0.878187	−	0.878187i
$539$			5.79473e9i			0.0686560i
$540$		0			0
$541$	−1.41419e11			−1.65090			−0.825448	−	0.564479i	$-0.809077\pi$
$541$	−1.41419e11			−1.65090			−0.825448	+	0.564479i	$0.809077\pi$
$542$	8.45517e10	+	8.45517e10i	0.979773	+	0.979773i
$543$		0			0
$544$		−	3.58074e10i		−	0.408863i
$545$	−1.26010e10	−	2.50954e10i	−0.142830	−	0.284452i
$546$		0			0
$547$	−2.99290e10	−	2.99290e10i	−0.334305	−	0.334305i	0.519914	−	0.854219i	$-0.325964\pi$
$547$	−2.99290e10	−	2.99290e10i	−0.334305	−	0.334305i	−0.854219	+	0.519914i	$0.825964\pi$
$548$	3.35891e10	−	3.35891e10i	0.372457	−	0.372457i
$549$		0			0
$550$	−8.19059e9	+	1.19846e9i	−0.0895086	+	0.0130971i
$551$	−5.29619e10			−0.574589
$552$		0			0
$553$	1.66056e11	−	1.66056e11i	1.77564	−	1.77564i
$554$		−	1.91618e11i		−	2.03422i
$555$		0			0
$556$	6.00653e10			0.628527
$557$	−5.59400e10	−	5.59400e10i	−0.581168	−	0.581168i	0.354056	−	0.935224i	$-0.384802\pi$
$557$	−5.59400e10	−	5.59400e10i	−0.581168	−	0.581168i	−0.935224	+	0.354056i	$0.884802\pi$
$558$		0			0
$559$		−	5.71061e10i		−	0.584837i
$560$	1.52442e11	+	5.05266e10i	1.55007	+	0.513769i
$561$		0			0
$562$	1.46553e11	+	1.46553e11i	1.46909	+	1.46909i
$563$	−5.76816e9	+	5.76816e9i	−0.0574121	+	0.0574121i	−0.735230	−	0.677818i	$-0.762926\pi$
$563$	−5.76816e9	+	5.76816e9i	−0.0574121	+	0.0574121i	0.677818	+	0.735230i	$0.262926\pi$
$564$		0			0
$565$	2.56955e9	−	7.75249e9i	0.0252153	−	0.0760759i
$566$	−8.23058e10			−0.801982
$567$		0			0
$568$	−1.98867e10	+	1.98867e10i	−0.191059	+	0.191059i
$569$			1.53674e11i			1.46606i	0.680196	+	0.733031i	$0.261895\pi$
$569$			1.53674e11i			1.46606i	−0.680196	+	0.733031i	$0.738105\pi$
$570$		0			0
$571$	−3.33206e10			−0.313450			−0.156725	−	0.987642i	$-0.550094\pi$
$571$	−3.33206e10			−0.313450			−0.156725	+	0.987642i	$0.550094\pi$
$572$	−5.47577e9	−	5.47577e9i	−0.0511518	−	0.0511518i
$573$		0			0
$574$		−	4.09054e10i		−	0.376819i
$575$	1.09194e9	+	7.46255e9i	0.00998908	+	0.0682678i
$576$		0			0
$577$	6.01902e10	+	6.01902e10i	0.543029	+	0.543029i	0.924416	−	0.381387i	$-0.124553\pi$
$577$	6.01902e10	+	6.01902e10i	0.543029	+	0.543029i	−0.381387	+	0.924416i	$0.624553\pi$
$578$	−9.60065e10	+	9.60065e10i	−0.860180	+	0.860180i
$579$		0			0
$580$	−1.23200e11	+	6.18614e10i	−1.08867	+	0.546648i
$581$	−1.59015e10			−0.139551
$582$		0			0
$583$	−1.84618e9	+	1.84618e9i	−0.0159808	+	0.0159808i
$584$			1.57351e10i			0.135275i
$585$		0			0
$586$	−1.91922e11			−1.62755
$587$	1.49796e11	+	1.49796e11i	1.26168	+	1.26168i	0.950280	+	0.311397i	$0.100797\pi$
$587$	1.49796e11	+	1.49796e11i	1.26168	+	1.26168i	0.311397	+	0.950280i	$0.399203\pi$
$588$		0			0
$589$		−	5.51482e10i		−	0.458216i
$590$	−5.40021e10	+	1.62927e11i	−0.445659	+	1.34458i
$591$		0			0
$592$	5.85925e9	+	5.85925e9i	0.0477040	+	0.0477040i
$593$	9.15532e10	−	9.15532e10i	0.740381	−	0.740381i	−0.232271	−	0.972651i	$-0.574616\pi$
$593$	9.15532e10	−	9.15532e10i	0.740381	−	0.740381i	0.972651	+	0.232271i	$0.0746155\pi$
$594$		0			0
$595$	2.50676e10	+	4.99233e10i	0.200007	+	0.398323i
$596$	−3.87901e10			−0.307422
$597$		0			0
$598$	−1.10768e10	+	1.10768e10i	−0.0866185	+	0.0866185i
$599$		−	1.74821e11i		−	1.35796i	−0.734158	−	0.678979i	$-0.762423\pi$
$599$		−	1.74821e11i		−	1.35796i	0.734158	−	0.678979i	$-0.237577\pi$
$600$		0			0
$601$	6.55639e10			0.502536			0.251268	−	0.967918i	$-0.419153\pi$
$601$	6.55639e10			0.502536			0.251268	+	0.967918i	$0.419153\pi$
$602$	−7.91827e10	−	7.91827e10i	−0.602899	−	0.602899i
$603$		0			0
$604$		−	1.29377e11i		−	0.972096i
$605$	1.19190e11	−	5.98480e10i	0.889648	−	0.446713i
$606$		0			0
$607$	8.22746e10	+	8.22746e10i	0.606054	+	0.606054i	0.941912	−	0.335859i	$-0.109026\pi$
$607$	8.22746e10	+	8.22746e10i	0.606054	+	0.606054i	−0.335859	+	0.941912i	$0.609026\pi$
$608$	−4.87402e10	+	4.87402e10i	−0.356676	+	0.356676i
$609$		0			0
$610$	1.79304e11	+	5.94302e10i	1.29500	+	0.429228i
$611$	−2.16371e11			−1.55251
$612$		0			0
$613$	3.09061e10	−	3.09061e10i	0.218878	−	0.218878i	−0.589148	−	0.808026i	$-0.700536\pi$
$613$	3.09061e10	−	3.09061e10i	0.218878	−	0.218878i	0.808026	+	0.589148i	$0.200536\pi$
$614$			1.32501e10i			0.0932276i
$615$		0			0
$616$	3.34428e9			0.0232263
$617$	1.72051e11	+	1.72051e11i	1.18718	+	1.18718i	0.977844	+	0.209337i	$0.0671305\pi$
$617$	1.72051e11	+	1.72051e11i	1.18718	+	1.18718i	0.209337	+	0.977844i	$0.432870\pi$
$618$		0			0
$619$			2.58123e11i			1.75818i	0.476652	+	0.879092i	$0.341850\pi$
$619$			2.58123e11i			1.75818i	−0.476652	+	0.879092i	$0.658150\pi$
$620$	−6.44151e10	−	1.28286e11i	−0.435934	−	0.868182i
$621$		0			0
$622$	−8.08691e10	−	8.08691e10i	−0.540283	−	0.540283i
$623$	1.92646e11	−	1.92646e11i	1.27881	−	1.27881i
$624$		0			0
$625$	−4.37179e10	−	1.46191e11i	−0.286510	−	0.958077i
$626$	1.68481e11			1.09712
$627$		0			0
$628$	−6.10515e10	+	6.10515e10i	−0.392516	+	0.392516i
$629$			2.88235e9i			0.0184138i
$630$		0			0
$631$	−2.49622e11			−1.57458			−0.787292	−	0.616580i	$-0.788518\pi$
$631$	−2.49622e11			−1.57458			−0.787292	+	0.616580i	$0.788518\pi$
$632$	−4.84797e10	−	4.84797e10i	−0.303873	−	0.303873i
$633$		0			0
$634$		−	1.17827e11i		−	0.729267i
$635$	−2.42914e11	−	8.05136e10i	−1.49403	−	0.495193i
$636$		0			0
$637$	−1.56879e11	−	1.56879e11i	−0.952814	−	0.952814i
$638$	−1.57542e10	+	1.57542e10i	−0.0950854	+	0.0950854i
$639$		0			0
$640$	2.52823e10	−	7.62781e10i	0.150694	−	0.454653i
$641$	−1.95384e11			−1.15733			−0.578666	−	0.815565i	$-0.696427\pi$
$641$	−1.95384e11			−1.15733			−0.578666	+	0.815565i	$0.696427\pi$
$642$		0			0
$643$	4.31377e10	−	4.31377e10i	0.252355	−	0.252355i	−0.569580	−	0.821936i	$-0.692894\pi$
$643$	4.31377e10	−	4.31377e10i	0.252355	−	0.252355i	0.821936	+	0.569580i	$0.192894\pi$
$644$			1.38355e10i			0.0804362i
$645$		0			0
$646$	−2.84500e10			−0.163363
$647$	5.34194e10	+	5.34194e10i	0.304847	+	0.304847i	0.842907	−	0.538060i	$-0.180842\pi$
$647$	5.34194e10	+	5.34194e10i	0.304847	+	0.304847i	−0.538060	+	0.842907i	$0.680842\pi$
$648$		0			0
$649$			1.24942e10i			0.0704252i
$650$	1.89296e11	−	2.54188e11i	1.06045	−	1.42397i
$651$		0			0
$652$	1.60547e11	+	1.60547e11i	0.888409	+	0.888409i
$653$	−1.68747e11	+	1.68747e11i	−0.928074	+	0.928074i	−0.997581	−	0.0695077i	$-0.977857\pi$
$653$	−1.68747e11	+	1.68747e11i	−0.928074	+	0.928074i	0.0695077	+	0.997581i	$0.477857\pi$
$654$		0			0
$655$	−1.03056e11	+	5.17467e10i	−0.559896	+	0.281137i
$656$	−4.17445e10			−0.225416
$657$		0			0
$658$	−3.00018e11	+	3.00018e11i	−1.60046	+	1.60046i
$659$			2.23769e11i			1.18647i	0.805028	+	0.593237i	$0.202150\pi$
$659$			2.23769e11i			1.18647i	−0.805028	+	0.593237i	$0.797850\pi$
$660$		0			0
$661$	1.49226e11			0.781700			0.390850	−	0.920454i	$-0.372181\pi$
$661$	1.49226e11			0.781700			0.390850	+	0.920454i	$0.372181\pi$
$662$	6.77202e10	+	6.77202e10i	0.352603	+	0.352603i
$663$		0			0
$664$			4.64240e9i			0.0238820i
$665$	3.38330e10	−	1.02076e11i	0.173003	−	0.521960i
$666$		0			0
$667$	1.43539e10	+	1.43539e10i	0.0725212	+	0.0725212i
$668$	−8.88594e10	+	8.88594e10i	−0.446270	+	0.446270i
$669$		0			0
$670$	−8.16763e10	−	1.62662e11i	−0.405319	−	0.807210i
$671$	1.37500e10			0.0678287
$672$		0			0
$673$	−1.20787e11	+	1.20787e11i	−0.588791	+	0.588791i	−0.937304	−	0.348513i	$-0.886687\pi$
$673$	−1.20787e11	+	1.20787e11i	−0.588791	+	0.588791i	0.348513	+	0.937304i	$0.386687\pi$
$674$		−	1.53785e11i		−	0.745204i
$675$		0			0
$676$	1.25351e11			0.600263
$677$	−1.59570e11	−	1.59570e11i	−0.759621	−	0.759621i	0.216632	−	0.976253i	$-0.430493\pi$
$677$	−1.59570e11	−	1.59570e11i	−0.759621	−	0.759621i	−0.976253	+	0.216632i	$0.930493\pi$
$678$		0			0
$679$			9.49399e10i			0.446652i
$680$	1.45750e10	−	7.31845e9i	0.0681668	−	0.0342281i
$681$		0			0
$682$	−1.64046e10	−	1.64046e10i	−0.0758276	−	0.0758276i
$683$	−2.73157e11	+	2.73157e11i	−1.25525	+	1.25525i	−0.301913	+	0.953336i	$0.597625\pi$
$683$	−2.73157e11	+	2.73157e11i	−1.25525	+	1.25525i	−0.953336	+	0.301913i	$0.902375\pi$
$684$		0			0
$685$	1.34327e11	+	4.45224e10i	0.610098	+	0.202216i
$686$	−1.00906e10			−0.0455639
$687$		0			0
$688$	−8.08071e10	+	8.08071e10i	−0.360658	+	0.360658i
$689$		−	9.99622e10i		−	0.443567i
$690$		0			0
$691$	1.64854e11			0.723082			0.361541	−	0.932356i	$-0.382251\pi$
$691$	1.64854e11			0.723082			0.361541	+	0.932356i	$0.382251\pi$
$692$	2.57864e11	+	2.57864e11i	1.12452	+	1.12452i
$693$		0			0
$694$		−	8.56672e10i		−	0.369298i
$695$	8.02956e10	+	1.59912e11i	0.344154	+	0.685397i
$696$		0			0
$697$	−1.02677e10	−	1.02677e10i	−0.0435054	−	0.0435054i
$698$	−2.01853e11	+	2.01853e11i	−0.850382	+	0.850382i
$699$		0			0
$700$	−4.05263e10	−	2.76967e11i	−0.168789	−	1.15355i
$701$	4.11487e11			1.70406			0.852028	−	0.523496i	$-0.175373\pi$
$701$	4.11487e11			1.70406			0.852028	+	0.523496i	$0.175373\pi$
$702$		0			0
$703$	3.92339e9	−	3.92339e9i	0.0160635	−	0.0160635i
$704$			1.00871e10i			0.0410655i
$705$		0			0
$706$	−3.55203e10			−0.142974
$707$	7.30524e10	+	7.30524e10i	0.292386	+	0.292386i
$708$		0			0
$709$			3.55785e11i			1.40800i	0.710201	+	0.703999i	$0.248604\pi$
$709$			3.55785e11i			1.40800i	−0.710201	+	0.703999i	$0.751396\pi$
$710$	3.61115e11	+	1.19691e11i	1.42106	+	0.471008i
$711$		0			0
$712$	−5.62426e10	−	5.62426e10i	−0.218849	−	0.218849i
$713$	−1.49464e10	+	1.49464e10i	−0.0578334	+	0.0578334i
$714$		0			0
$715$	7.25814e9	−	2.18982e10i	0.0277716	−	0.0837885i
$716$	9.21654e10			0.350684
$717$		0			0
$718$	3.04325e11	−	3.04325e11i	1.14509	−	1.14509i
$719$		−	1.68430e10i		−	0.0630238i	−0.999503	−	0.0315119i	$-0.989968\pi$
$719$		−	1.68430e10i		−	0.0630238i	0.999503	−	0.0315119i	$-0.0100322\pi$
$720$		0			0
$721$	2.06820e11			0.765335
$722$	−2.20461e11	−	2.20461e11i	−0.811301	−	0.811301i
$723$		0			0
$724$			3.53765e11i			1.28754i
$725$	−3.29388e11	−	2.45299e11i	−1.19222	−	0.887858i
$726$		0			0
$727$	−7.96403e9	−	7.96403e9i	−0.0285099	−	0.0285099i	0.692708	−	0.721218i	$-0.256417\pi$
$727$	−7.96403e9	−	7.96403e9i	−0.0285099	−	0.0285099i	−0.721218	+	0.692708i	$0.756417\pi$
$728$	−9.05390e10	+	9.05390e10i	−0.322337	+	0.322337i
$729$		0			0
$730$	1.90216e11	−	9.55119e10i	0.669816	−	0.336330i
$731$	−3.97516e10			−0.139215
$732$		0			0
$733$	−3.27099e10	+	3.27099e10i	−0.113309	+	0.113309i	−0.761488	−	0.648179i	$-0.775531\pi$
$733$	−3.27099e10	+	3.27099e10i	−0.113309	+	0.113309i	0.648179	+	0.761488i	$0.275531\pi$
$734$		−	6.92598e11i		−	2.38615i
$735$		0			0
$736$	2.64194e10			0.0900350
$737$	−9.36860e9	−	9.36860e9i	−0.0317545	−	0.0317545i
$738$		0			0
$739$		−	2.49954e11i		−	0.838075i	−0.907969	−	0.419038i	$-0.862368\pi$
$739$		−	2.49954e11i		−	0.838075i	0.907969	−	0.419038i	$-0.137632\pi$
$740$	4.54391e9	−	1.37092e10i	0.0151532	−	0.0457179i
$741$		0			0
$742$	−1.38607e11	−	1.38607e11i	−0.457265	−	0.457265i
$743$	2.19494e11	−	2.19494e11i	0.720224	−	0.720224i	−0.248427	−	0.968651i	$-0.579914\pi$
$743$	2.19494e11	−	2.19494e11i	0.720224	−	0.720224i	0.968651	+	0.248427i	$0.0799135\pi$
$744$		0			0
$745$	−5.18548e10	−	1.03271e11i	−0.168331	−	0.335238i
$746$	−5.20160e11			−1.67951
$747$		0			0
$748$	−3.81169e9	+	3.81169e9i	−0.0121762	+	0.0121762i
$749$			4.27370e11i			1.35793i
$750$		0			0
$751$	−3.34163e11			−1.05051			−0.525253	−	0.850946i	$-0.676029\pi$
$751$	−3.34163e11			−1.05051			−0.525253	+	0.850946i	$0.676029\pi$
$752$	3.06173e11	+	3.06173e11i	0.957405	+	0.957405i
$753$		0			0
$754$		−	8.53020e11i		−	2.63921i
$755$	3.44441e11	−	1.72952e11i	1.06005	−	0.532276i
$756$		0			0
$757$	3.61172e11	+	3.61172e11i	1.09984	+	1.09984i	0.994428	+	0.105414i	$0.0336168\pi$
$757$	3.61172e11	+	3.61172e11i	1.09984	+	1.09984i	0.105414	+	0.994428i	$0.466383\pi$
$758$	4.01403e11	−	4.01403e11i	1.21592	−	1.21592i
$759$		0			0
$760$	−2.98009e10	−	9.87747e9i	−0.0893254	−	0.0296068i
$761$	−1.43773e10			−0.0428685			−0.0214342	−	0.999770i	$-0.506823\pi$
$761$	−1.43773e10			−0.0428685			−0.0214342	+	0.999770i	$0.506823\pi$
$762$		0			0
$763$	1.08516e11	−	1.08516e11i	0.320181	−	0.320181i
$764$			3.19462e11i			0.937661i
$765$		0			0
$766$	6.86583e11			1.99424
$767$	−3.38252e11	−	3.38252e11i	−0.977368	−	0.977368i
$768$		0			0
$769$		−	4.36097e10i		−	0.124703i	−0.998054	−	0.0623517i	$-0.980140\pi$
$769$		−	4.36097e10i		−	0.124703i	0.998054	−	0.0623517i	$-0.0198600\pi$
$770$	−2.02998e10	−	4.04279e10i	−0.0577469	−	0.115005i
$771$		0			0
$772$	−4.11947e10	−	4.11947e10i	−0.115977	−	0.115977i
$773$	4.23792e11	−	4.23792e11i	1.18696	−	1.18696i	0.209051	−	0.977905i	$-0.432963\pi$
$773$	4.23792e11	−	4.23792e11i	1.18696	−	1.18696i	0.977905	−	0.209051i	$-0.0670374\pi$
$774$		0			0
$775$	2.55425e11	−	3.42986e11i	0.708038	−	0.950756i
$776$	2.77175e10			0.0764377
$777$		0			0
$778$	−8.73267e10	+	8.73267e10i	−0.238357	+	0.238357i
$779$			2.79524e10i			0.0759049i
$780$		0			0
$781$	2.76923e10			0.0744311
$782$	7.71059e9	+	7.71059e9i	0.0206187	+	0.0206187i
$783$		0			0
$784$			4.43980e11i			1.17517i
$785$	−2.44152e11	−	8.09238e10i	−0.642956	−	0.213107i
$786$		0			0
$787$	−6.89291e10	−	6.89291e10i	−0.179682	−	0.179682i	0.611535	−	0.791217i	$-0.290552\pi$
$787$	−6.89291e10	−	6.89291e10i	−0.179682	−	0.179682i	−0.791217	+	0.611535i	$0.790552\pi$
$788$	−2.63063e11	+	2.63063e11i	−0.682268	+	0.682268i
$789$		0			0
$790$	−2.91783e11	+	8.80326e11i	−0.749120	+	2.26014i
$791$	4.46339e10			0.114014
$792$		0			0
$793$	−3.72251e11	+	3.72251e11i	−0.941333	+	0.941333i
$794$		−	9.07571e10i		−	0.228349i
$795$		0			0
$796$	−2.30797e11			−0.574882
$797$	4.21172e11	+	4.21172e11i	1.04382	+	1.04382i	0.998995	+	0.0448261i	$0.0142734\pi$
$797$	4.21172e11	+	4.21172e11i	1.04382	+	1.04382i	0.0448261	+	0.998995i	$0.485727\pi$
$798$		0			0
$799$			1.50616e11i			0.369560i
$800$	−5.28878e11	+	7.73865e10i	−1.29121	+	0.188932i
$801$		0			0
$802$	−2.71282e11	−	2.71282e11i	−0.655728	−	0.655728i
$803$	1.09556e10	−	1.09556e10i	0.0263496	−	0.0263496i
$804$		0			0
$805$	−3.68343e10	+	1.84954e10i	−0.0877141	+	0.0440433i
$806$	8.88234e11			2.10469
$807$		0			0
$808$	2.13275e10	−	2.13275e10i	0.0500374	−	0.0500374i
$809$			3.91293e11i			0.913499i	0.889595	+	0.456750i	$0.150986\pi$
$809$			3.91293e11i			0.913499i	−0.889595	+	0.456750i	$0.849014\pi$
$810$		0			0
$811$	1.43185e11			0.330989			0.165495	−	0.986211i	$-0.447078\pi$
$811$	1.43185e11			0.330989			0.165495	+	0.986211i	$0.447078\pi$
$812$	−5.32732e11	−	5.32732e11i	−1.22542	−	1.22542i
$813$		0			0
$814$		−	2.33413e9i		−	0.00531652i
$815$	−2.12806e11	+	6.42047e11i	−0.482340	+	1.45525i
$816$		0			0
$817$	5.41090e10	+	5.41090e10i	0.121445	+	0.121445i
$818$	−3.93532e11	+	3.93532e11i	−0.878956	+	0.878956i
$819$		0			0
$820$	3.26494e10	+	6.50228e10i	0.0722138	+	0.143817i
$821$	−5.36389e11			−1.18061			−0.590306	−	0.807180i	$-0.700993\pi$
$821$	−5.36389e11			−1.18061			−0.590306	+	0.807180i	$0.700993\pi$
$822$		0			0
$823$	2.70833e11	−	2.70833e11i	0.590339	−	0.590339i	−0.347384	−	0.937723i	$-0.612930\pi$
$823$	2.70833e11	−	2.70833e11i	0.590339	−	0.590339i	0.937723	+	0.347384i	$0.112930\pi$
$824$		−	6.03807e10i		−	0.130975i
$825$		0			0
$826$	−9.38032e11			−2.01510
$827$	2.55449e11	+	2.55449e11i	0.546113	+	0.546113i	0.925314	−	0.379201i	$-0.123801\pi$
$827$	2.55449e11	+	2.55449e11i	0.546113	+	0.546113i	−0.379201	+	0.925314i	$0.623801\pi$
$828$		0			0
$829$		−	3.10375e11i		−	0.657157i	−0.944477	−	0.328579i	$-0.893430\pi$
$829$		−	3.10375e11i		−	0.657157i	0.944477	−	0.328579i	$-0.106570\pi$
$830$	5.61204e10	−	2.81793e10i	0.118252	−	0.0593770i
$831$		0			0
$832$	−2.73087e11	−	2.73087e11i	−0.569912	−	0.569912i
$833$	−1.09204e11	+	1.09204e11i	−0.226808	+	0.226808i
$834$		0			0
$835$	−3.55359e11	−	1.17783e11i	−0.731006	−	0.242291i
$836$	1.03768e10			0.0212440
$837$		0			0
$838$	4.27898e10	−	4.27898e10i	0.0867690	−	0.0867690i
$839$		−	3.11103e11i		−	0.627851i	−0.949448	−	0.313925i	$-0.898356\pi$
$839$		−	3.11103e11i		−	0.627851i	0.949448	−	0.313925i	$-0.101644\pi$
$840$		0			0
$841$	−6.05136e11			−1.20968
$842$	−5.17430e11	−	5.17430e11i	−1.02944	−	1.02944i
$843$		0			0
$844$			5.51152e11i			1.08618i
$845$	1.67570e11	+	3.33723e11i	0.328677	+	0.654575i
$846$		0			0
$847$	5.15393e11	+	5.15393e11i	1.00139	+	1.00139i
$848$	−1.41450e11	+	1.41450e11i	−0.273539	+	0.273539i
$849$		0			0
$850$	−1.76940e11	−	1.31769e11i	−0.338962	−	0.252429i
$851$	−2.12665e9			−0.00405488
$852$		0			0
$853$	−7.97714e10	+	7.97714e10i	−0.150678	+	0.150678i	−0.778421	−	0.627743i	$-0.783979\pi$
$853$	−7.97714e10	+	7.97714e10i	−0.150678	+	0.150678i	0.627743	+	0.778421i	$0.283979\pi$
$854$			1.03232e12i			1.94081i
$855$		0			0
$856$	1.24770e11			0.232388
$857$	−4.72560e10	−	4.72560e10i	−0.0876060	−	0.0876060i	0.661946	−	0.749552i	$-0.269731\pi$
$857$	−4.72560e10	−	4.72560e10i	−0.0876060	−	0.0876060i	−0.749552	+	0.661946i	$0.769731\pi$
$858$		0			0
$859$			6.23299e11i			1.14478i	0.819980	+	0.572392i	$0.193984\pi$
$859$			6.23299e11i			1.14478i	−0.819980	+	0.572392i	$0.806016\pi$
$860$	1.89069e11	+	6.26668e10i	0.345643	+	0.114563i
$861$		0			0
$862$	7.23850e11	+	7.23850e11i	1.31105	+	1.31105i
$863$	3.76731e11	−	3.76731e11i	0.679185	−	0.679185i	−0.280631	−	0.959816i	$-0.590544\pi$
$863$	3.76731e11	−	3.76731e11i	0.679185	−	0.679185i	0.959816	+	0.280631i	$0.0905437\pi$
$864$		0			0
$865$	−3.41799e11	+	1.03123e12i	−0.610529	+	1.84200i
$866$	−8.71542e11			−1.54959
$867$		0			0
$868$	5.54724e11	−	5.54724e11i	0.977233	−	0.977233i
$869$			6.75082e10i			0.118380i
$870$		0			0
$871$	5.07268e11			0.881383
$872$	−3.16810e10	−	3.16810e10i	−0.0547940	−	0.0547940i
$873$		0			0
$874$		−	2.09910e10i		−	0.0359738i
$875$	6.83195e11	−	4.78144e11i	1.16550	−	0.815693i
$876$		0			0
$877$	−6.00059e11	−	6.00059e11i	−1.01437	−	1.01437i	−0.999895	−	0.0144728i	$-0.995393\pi$
$877$	−6.00059e11	−	6.00059e11i	−1.01437	−	1.01437i	−0.0144728	−	0.999895i	$-0.504607\pi$
$878$	7.18623e11	−	7.18623e11i	1.20927	−	1.20927i
$879$		0			0
$880$	−4.12573e10	+	2.07162e10i	−0.0687971	+	0.0345446i
$881$	5.01925e11			0.833174			0.416587	−	0.909096i	$-0.363226\pi$
$881$	5.01925e11			0.833174			0.416587	+	0.909096i	$0.363226\pi$
$882$		0			0
$883$	7.06343e11	−	7.06343e11i	1.16191	−	1.16191i	0.177854	−	0.984057i	$-0.443085\pi$
$883$	7.06343e11	−	7.06343e11i	1.16191	−	1.16191i	0.984057	−	0.177854i	$-0.0569153\pi$
$884$		−	2.06386e11i		−	0.337964i
$885$		0			0
$886$	−6.52889e11			−1.05951
$887$	−2.38573e11	−	2.38573e11i	−0.385414	−	0.385414i	0.487634	−	0.873048i	$-0.337860\pi$
$887$	−2.38573e11	−	2.38573e11i	−0.385414	−	0.385414i	−0.873048	+	0.487634i	$0.837860\pi$
$888$		0			0
$889$		−	1.39855e12i		−	2.23908i
$890$	−3.38505e11	+	1.02129e12i	−0.539517	+	1.62775i
$891$		0			0
$892$	−4.69889e11	−	4.69889e11i	−0.742226	−	0.742226i
$893$	2.05016e11	−	2.05016e11i	0.322390	−	0.322390i
$894$		0			0
$895$	1.23207e11	+	2.45373e11i	0.192019	+	0.382414i
$896$	4.39161e11			0.681384
$897$		0			0
$898$	−3.03748e10	+	3.03748e10i	−0.0467098	+	0.0467098i
$899$		−	1.15101e12i		−	1.76215i
$900$		0			0
$901$	−6.95838e10			−0.105587
$902$	8.31481e9	+	8.31481e9i	0.0125611	+	0.0125611i
$903$		0			0
$904$		−	1.30308e10i		−	0.0195118i
$905$	−9.41832e11	+	4.72916e11i	−1.40404	+	0.705000i
$906$		0			0
$907$	−4.12169e11	−	4.12169e11i	−0.609040	−	0.609040i	0.333655	−	0.942695i	$-0.391718\pi$
$907$	−4.12169e11	−	4.12169e11i	−0.609040	−	0.609040i	−0.942695	+	0.333655i	$0.891718\pi$
$908$	6.01265e11	−	6.01265e11i	0.884551	−	0.884551i
$909$		0			0
$910$	1.64407e12	+	5.44924e11i	2.39747	+	0.794640i
$911$	6.90488e10			0.100250			0.0501248	−	0.998743i	$-0.484038\pi$
$911$	6.90488e10			0.100250			0.0501248	+	0.998743i	$0.484038\pi$
$912$		0			0
$913$	3.23228e9	−	3.23228e9i	0.00465185	−	0.00465185i
$914$		−	3.93121e11i		−	0.563302i
$915$		0			0
$916$	8.84699e11			1.25665
$917$	−4.45628e11	−	4.45628e11i	−0.630224	−	0.630224i
$918$		0			0
$919$		−	1.35037e12i		−	1.89317i	−0.322447	−	0.946587i	$-0.604505\pi$
$919$		−	1.35037e12i		−	1.89317i	0.322447	−	0.946587i	$-0.395495\pi$
$920$	5.39969e9	+	1.07537e10i	0.00753733	+	0.0150109i
$921$		0			0
$922$	4.50248e11	+	4.50248e11i	0.623058	+	0.623058i
$923$	−7.49707e11	+	7.49707e11i	−1.03296	+	1.03296i
$924$		0			0
$925$	4.25725e10	−	6.22930e9i	0.0581517	−	0.00850888i
$926$	8.20414e11			1.11581
$927$		0			0
$928$	−1.01727e12	+	1.01727e12i	−1.37166	+	1.37166i
$929$		−	8.74727e11i		−	1.17438i	−0.809448	−	0.587191i	$-0.800234\pi$
$929$		−	8.74727e11i		−	1.17438i	0.809448	−	0.587191i	$-0.199766\pi$
$930$		0			0
$931$	2.97292e11			0.395717
$932$	2.92503e11	+	2.92503e11i	0.387674	+	0.387674i
$933$		0			0
$934$			7.38206e11i			0.970041i
$935$	−1.52434e10	−	5.05240e9i	−0.0199450	−	0.00661076i
$936$		0			0
$937$	−8.71252e11	−	8.71252e11i	−1.13028	−	1.13028i	−0.990131	−	0.140148i	$-0.955242\pi$
$937$	−8.71252e11	−	8.71252e11i	−1.13028	−	1.13028i	−0.140148	−	0.990131i	$-0.544758\pi$
$938$	7.03372e11	−	7.03372e11i	0.908602	−	0.908602i
$939$		0			0
$940$	2.37441e11	−	7.16372e11i	0.304119	−	0.917544i
$941$	−7.43237e11			−0.947914			−0.473957	−	0.880548i	$-0.657175\pi$
$941$	−7.43237e11			−0.947914			−0.473957	+	0.880548i	$0.657175\pi$
$942$		0			0
$943$	7.57573e9	−	7.57573e9i	0.00958027	−	0.00958027i
$944$			9.57276e11i			1.20545i
$945$		0			0
$946$	3.21909e10			0.0401946
$947$	2.14562e11	+	2.14562e11i	0.266780	+	0.266780i	0.827801	−	0.561022i	$-0.189592\pi$
$947$	2.14562e11	+	2.14562e11i	0.266780	+	0.266780i	−0.561022	+	0.827801i	$0.689592\pi$
$948$		0			0
$949$			5.93196e11i			0.731364i
$950$	6.14858e10	+	4.20209e11i	0.0754884	+	0.515906i
$951$		0			0
$952$	6.30243e10	+	6.30243e10i	0.0767291	+	0.0767291i
$953$	−3.76794e11	+	3.76794e11i	−0.456807	+	0.456807i	−0.897606	−	0.440799i	$-0.854695\pi$
$953$	−3.76794e11	+	3.76794e11i	−0.456807	+	0.456807i	0.440799	+	0.897606i	$0.354695\pi$
$954$		0			0
$955$	−8.50506e11	+	4.27059e11i	−1.02250	+	0.513422i
$956$	5.84521e11			0.699791
$957$		0			0
$958$	1.52702e12	−	1.52702e12i	1.81294	−	1.81294i
$959$			7.73367e11i			0.914348i
$960$		0			0
$961$	3.45639e11			0.405255
$962$	6.31913e10	+	6.31913e10i	0.0737831	+	0.0737831i
$963$		0			0
$964$		−	3.82796e11i		−	0.443261i
$965$	5.46036e10	−	1.64742e11i	0.0629669	−	0.189975i
$966$		0			0
$967$	1.15307e12	+	1.15307e12i	1.31871	+	1.31871i	0.914798	+	0.403911i	$0.132349\pi$
$967$	1.15307e12	+	1.15307e12i	1.31871	+	1.31871i	0.403911	+	0.914798i	$0.367651\pi$
$968$	1.50468e11	−	1.50468e11i	0.171373	−	0.171373i
$969$		0			0
$970$	−1.68245e11	−	3.35067e11i	−0.190045	−	0.378482i
$971$	1.14897e12			1.29250			0.646250	−	0.763126i	$-0.276336\pi$
$971$	1.14897e12			1.29250			0.646250	+	0.763126i	$0.276336\pi$
$972$		0			0
$973$	−6.91482e11	+	6.91482e11i	−0.771488	+	0.771488i
$974$			1.32862e12i			1.47626i
$975$		0			0
$976$	1.05350e12			1.16101
$977$	−4.00572e11	−	4.00572e11i	−0.439646	−	0.439646i	0.452247	−	0.891893i	$-0.350623\pi$
$977$	−4.00572e11	−	4.00572e11i	−0.439646	−	0.439646i	−0.891893	+	0.452247i	$0.850623\pi$
$978$		0			0
$979$			7.83180e10i			0.0852572i
$980$	6.91559e11	−	3.47248e11i	0.749765	−	0.376474i
$981$		0			0
$982$	−2.66795e11	−	2.66795e11i	−0.286901	−	0.286901i
$983$	−6.04096e11	+	6.04096e11i	−0.646982	+	0.646982i	−0.952262	−	0.305281i	$-0.901250\pi$
$983$	−6.04096e11	+	6.04096e11i	−0.646982	+	0.646982i	0.305281	+	0.952262i	$0.401250\pi$
$984$		0			0
$985$	−1.05202e12	−	3.48690e11i	−1.11758	−	0.370420i
$986$	−5.93788e11			−0.628238
$987$		0			0
$988$	−2.80928e11	+	2.80928e11i	−0.294827	+	0.294827i
$989$		−	2.93295e10i		−	0.0306563i
$990$		0			0
$991$	4.34203e10			0.0450193			0.0225096	−	0.999747i	$-0.492834\pi$
$991$	4.34203e10			0.0450193			0.0225096	+	0.999747i	$0.492834\pi$
$992$	−1.05927e12	−	1.05927e12i	−1.09385	−	1.09385i
$993$		0			0
$994$			2.07907e12i			2.12973i
$995$	−3.08531e11	−	6.14454e11i	−0.314780	−	0.626898i
$996$		0			0
$997$	5.58826e11	+	5.58826e11i	0.565582	+	0.565582i	0.930888	−	0.365305i	$-0.119035\pi$
$997$	5.58826e11	+	5.58826e11i	0.565582	+	0.565582i	−0.365305	+	0.930888i	$0.619035\pi$
$998$	−9.44651e11	+	9.44651e11i	−0.952246	+	0.952246i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.9.g.a.37.1		6
3.2	odd	2		5.9.c.a.2.3	✓	6
5.3	odd	4	inner	45.9.g.a.28.1		6
12.11	even	2		80.9.p.c.17.2		6
15.2	even	4		25.9.c.b.18.1		6
15.8	even	4		5.9.c.a.3.3	yes	6
15.14	odd	2		25.9.c.b.7.1		6
60.23	odd	4		80.9.p.c.33.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.9.c.a.2.3	✓	6	3.2	odd	2
5.9.c.a.3.3	yes	6	15.8	even	4
25.9.c.b.7.1		6	15.14	odd	2
25.9.c.b.18.1		6	15.2	even	4
45.9.g.a.28.1		6	5.3	odd	4	inner
45.9.g.a.37.1		6	1.1	even	1	trivial
80.9.p.c.17.2		6	12.11	even	2
80.9.p.c.33.2		6	60.23	odd	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.2610 - 15.2610i) q^{2} +209.796i q^{4} +(-558.542 + 280.457i) q^{5} +(-2415.21 - 2415.21i) q^{7} +(-705.116 + 705.116i) q^{8} +O(q^{10})\)	\(q+(-15.2610 - 15.2610i) q^{2} +209.796i q^{4} +(-558.542 + 280.457i) q^{5} +(-2415.21 - 2415.21i) q^{7} +(-705.116 + 705.116i) q^{8} +(12804.0 + 4243.86i) q^{10} +981.878 q^{11} +(-26582.1 + 26582.1i) q^{13} +73717.1i q^{14} +75229.4 q^{16} +(18503.9 + 18503.9i) q^{17} -50374.1i q^{19} +(-58838.8 - 117180. i) q^{20} +(-14984.4 - 14984.4i) q^{22} +(-13652.5 + 13652.5i) q^{23} +(233313. - 313294. i) q^{25} +811340. q^{26} +(506702. - 506702. i) q^{28} -1.05137e6i q^{29} +1.09477e6 q^{31} +(-967566. - 967566. i) q^{32} -564775. i q^{34} +(2.02636e6 + 671634. i) q^{35} +(77885.1 + 77885.1i) q^{37} +(-768759. + 768759. i) q^{38} +(196082. - 591591. i) q^{40} -554897. q^{41} +(-1.07414e6 + 1.07414e6i) q^{43} +205994. i q^{44} +416702. q^{46} +(4.06986e6 + 4.06986e6i) q^{47} +5.90168e6i q^{49} +(-8.34176e6 + 1.22058e6i) q^{50} +(-5.57683e6 - 5.57683e6i) q^{52} +(-1.88025e6 + 1.88025e6i) q^{53} +(-548420. + 275374. i) q^{55} +3.40601e6 q^{56} +(-1.60450e7 + 1.60450e7i) q^{58} +1.27248e7i q^{59} +1.40038e7 q^{61} +(-1.67073e7 - 1.67073e7i) q^{62} +1.02733e7i q^{64} +(7.39210e6 - 2.23024e7i) q^{65} +(-9.54151e6 - 9.54151e6i) q^{67} +(-3.88204e6 + 3.88204e6i) q^{68} +(-2.06744e7 - 4.11741e7i) q^{70} +2.82034e7 q^{71} +(1.11578e7 - 1.11578e7i) q^{73} -2.37721e6i q^{74} +1.05683e7 q^{76} +(-2.37144e6 - 2.37144e6i) q^{77} +6.87542e7i q^{79} +(-4.20188e7 + 2.10986e7i) q^{80} +(8.46828e6 + 8.46828e6i) q^{82} +(3.29194e6 - 3.29194e6i) q^{83} +(-1.55247e7 - 5.14565e6i) q^{85} +3.27850e7 q^{86} +(-692338. + 692338. i) q^{88} +7.97635e7i q^{89} +1.28403e8 q^{91} +(-2.86424e6 - 2.86424e6i) q^{92} -1.24220e8i q^{94} +(1.41278e7 + 2.81360e7i) q^{95} +(-1.96546e7 - 1.96546e7i) q^{97} +(9.00656e7 - 9.00656e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8	\( 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8} + 30870 q^{10} - 23192 q^{11} - 119142 q^{13} + 218616 q^{16} + 265502 q^{17} - 412260 q^{20} - 35664 q^{22} - 28888 q^{23} - 340350 q^{25} + 801388 q^{26} + 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} + 4971680 q^{35} - 454002 q^{37} - 1443720 q^{38} + 2683500 q^{40} - 2489432 q^{41} + 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} - 29537650 q^{50} - 735732 q^{52} + 13509122 q^{53} + 4448040 q^{55} + 18454800 q^{56} - 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} + 30943610 q^{65} - 32827752 q^{67} - 8118692 q^{68} - 44156280 q^{70} + 13992928 q^{71} + 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 23045920 q^{80} + 38023056 q^{82} + 14768432 q^{83} - 19713030 q^{85} + 135560008 q^{86} - 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} - 239661000 q^{95} - 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8 + 30870 * q^10 - 23192 * q^11 - 119142 * q^13 + 218616 * q^16 + 265502 * q^17 - 412260 * q^20 - 35664 * q^22 - 28888 * q^23 - 340350 * q^25 + 801388 * q^26 + 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 + 4971680 * q^35 - 454002 * q^37 - 1443720 * q^38 + 2683500 * q^40 - 2489432 * q^41 + 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 - 29537650 * q^50 - 735732 * q^52 + 13509122 * q^53 + 4448040 * q^55 + 18454800 * q^56 - 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 + 30943610 * q^65 - 32827752 * q^67 - 8118692 * q^68 - 44156280 * q^70 + 13992928 * q^71 + 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 23045920 * q^80 + 38023056 * q^82 + 14768432 * q^83 - 19713030 * q^85 + 135560008 * q^86 - 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 - 239661000 * q^95 - 186656202 * q^97 + 345959698 * q^98

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