LMFDB - Embedded newform 81.12.c.l.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,12,Mod(28,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 12, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.28"); S:= CuspForms(chi, 12); N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	81.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,9,0,-8709] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$62.2357976253$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 7011 x^{10} - 35000 x^{9} + 17884836 x^{8} - 71329410 x^{7} + 20475172451 x^{6} + \cdots + 14\!\cdots\!75 $ x^12 - 6x^11 + 7011x^10 - 35000x^9 + 17884836x^8 - 71329410x^7 + 20475172451x^6 - 61176011352x^5 + 10720227603096x^4 - 21338578334950x^3 + 2259611521703223x^2 - 2248952416659900*x + 141844474156177975
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 50.7537i$ of defining polynomial
Character	$\chi$	$=$	81.55
Dual form			81.12.c.l.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-43.2040 + 74.8315i) q^{2} +(-2709.16 - 4692.41i) q^{4} +(5654.31 + 9793.56i) q^{5} +(-3828.09 + 6630.45i) q^{7} +291223. q^{8} -977155. q^{10} +(72631.6 - 125802. i) q^{11} +(-1.08595e6 - 1.88092e6i) q^{13} +(-330778. - 572924. i) q^{14} +(-7.03363e6 + 1.21826e7i) q^{16} +1.52707e6 q^{17} +1.84377e7 q^{19} +(3.06369e7 - 5.30647e7i) q^{20} +(6.27595e6 + 1.08703e7i) q^{22} +(8.46452e6 + 1.46610e7i) q^{23} +(-3.95285e7 + 6.84653e7i) q^{25} +1.87670e8 q^{26} +4.14837e7 q^{28} +(-4.94752e7 + 8.56935e7i) q^{29} +(-4.55697e7 - 7.89290e7i) q^{31} +(-3.09549e8 - 5.36154e8i) q^{32} +(-6.59755e7 + 1.14273e8i) q^{34} -8.65810e7 q^{35} +3.51689e8 q^{37} +(-7.96582e8 + 1.37972e9i) q^{38} +(1.64667e9 + 2.85211e9i) q^{40} +(5.50954e8 + 9.54281e8i) q^{41} +(-2.21288e8 + 3.83281e8i) q^{43} -7.87084e8 q^{44} -1.46280e9 q^{46} +(-5.87011e8 + 1.01673e9i) q^{47} +(9.59355e8 + 1.66165e9i) q^{49} +(-3.41557e9 - 5.91595e9i) q^{50} +(-5.88404e9 + 1.01915e10i) q^{52} +2.40091e9 q^{53} +1.64273e9 q^{55} +(-1.11483e9 + 1.93094e9i) q^{56} +(-4.27505e9 - 7.40460e9i) q^{58} +(-7.40846e8 - 1.28318e9i) q^{59} +(2.25548e9 - 3.90660e9i) q^{61} +7.87516e9 q^{62} +2.46852e10 q^{64} +(1.22806e10 - 2.12706e10i) q^{65} +(6.64818e9 + 1.15150e10i) q^{67} +(-4.13708e9 - 7.16564e9i) q^{68} +(3.74064e9 - 6.47898e9i) q^{70} -1.89679e10 q^{71} +5.25732e9 q^{73} +(-1.51944e10 + 2.63174e10i) q^{74} +(-4.99508e10 - 8.65173e10i) q^{76} +(5.56081e8 + 9.63161e8i) q^{77} +(5.05595e9 - 8.75716e9i) q^{79} -1.59081e11 q^{80} -9.52136e10 q^{82} +(-1.72968e10 + 2.99589e10i) q^{83} +(8.63453e9 + 1.49554e10i) q^{85} +(-1.91210e10 - 3.31185e10i) q^{86} +(2.11520e10 - 3.66364e10i) q^{88} +2.76357e9 q^{89} +1.66285e10 q^{91} +(4.58635e10 - 7.94380e10i) q^{92} +(-5.07224e10 - 8.78537e10i) q^{94} +(1.04253e11 + 1.80571e11i) q^{95} +(-2.55150e10 + 4.41933e10i) q^{97} -1.65792e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{2} - 8709 q^{4} + 10278 q^{5} - 22944 q^{7} + 197010 q^{8} - 465462 q^{10} + 668448 q^{11} - 1861770 q^{13} + 455508 q^{14} - 15304209 q^{16} + 24634260 q^{17} + 35867472 q^{19} + 83336409 q^{20}+ \cdots - 1101686223906 q^{98}+O(q^{100}) $ 12 * q + 9 * q^2 - 8709 * q^4 + 10278 * q^5 - 22944 * q^7 + 197010 * q^8 - 465462 * q^10 + 668448 * q^11 - 1861770 * q^13 + 455508 * q^14 - 15304209 * q^16 + 24634260 * q^17 + 35867472 * q^19 + 83336409 * q^20 - 50304960 * q^22 - 13446360 * q^23 - 94232976 * q^25 + 343544994 * q^26 + 290261256 * q^28 + 105349014 * q^29 - 180650424 * q^31 - 267341121 * q^32 + 384127731 * q^34 - 1387830096 * q^35 - 314305788 * q^37 - 1912591260 * q^38 + 777367917 * q^40 + 625918284 * q^41 + 843299808 * q^43 - 10808909856 * q^44 - 2412142560 * q^46 - 544330872 * q^47 - 1603672110 * q^49 - 7200193860 * q^50 - 10297810587 * q^52 - 7976661624 * q^53 + 21041467056 * q^55 + 4513671900 * q^56 - 26453162025 * q^58 - 13877974224 * q^59 - 13543180554 * q^61 - 46131549768 * q^62 + 88547470338 * q^64 + 13506091074 * q^65 - 17368622760 * q^67 - 80563033863 * q^68 - 54376835508 * q^70 - 139458339360 * q^71 + 90107169684 * q^73 - 72968645457 * q^74 - 90059767140 * q^76 - 79651538712 * q^77 - 46910199000 * q^79 - 691221292074 * q^80 + 88254243756 * q^82 - 107141792328 * q^83 - 25423165494 * q^85 - 307626642216 * q^86 - 229083441120 * q^88 - 561148241724 * q^89 + 320631230928 * q^91 - 86149640592 * q^92 - 366645472236 * q^94 - 191492732304 * q^95 - 270295503060 * q^97 - 1101686223906 * q^98

Character values

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

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

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 $

$2$	−43.2040	+	74.8315i	−0.954682	+	1.65356i	−0.219587	+	0.975593i	$0.570471\pi$
$2$	−43.2040	+	74.8315i	−0.954682	+	1.65356i	−0.735095	+	0.677964i	$0.762862\pi$
$3$		0			0
$3$		0			0
$4$	−2709.16	−	4692.41i	−1.32283	−	2.29122i
$5$	5654.31	+	9793.56i	0.809180	+	1.40154i	0.913433	+	0.406989i	$0.133421\pi$
$5$	5654.31	+	9793.56i	0.809180	+	1.40154i	−0.104253	+	0.994551i	$0.533245\pi$
$6$		0			0
$7$	−3828.09	+	6630.45i	−0.0860881	+	0.149109i	−0.905854	−	0.423589i	$-0.860770\pi$
$7$	−3828.09	+	6630.45i	−0.0860881	+	0.149109i	0.819766	+	0.572698i	$0.194103\pi$
$8$	291223.			3.14218
$9$		0			0
$10$	−977155.			−3.09004
$11$	72631.6	−	125802.i	0.135977	−	0.235519i	−0.789993	−	0.613116i	$-0.789916\pi$
$11$	72631.6	−	125802.i	0.135977	−	0.235519i	0.925970	+	0.377596i	$0.123249\pi$
$12$		0			0
$13$	−1.08595e6	−	1.88092e6i	−0.811188	−	1.40502i	−0.912033	−	0.410117i	$-0.865488\pi$
$13$	−1.08595e6	−	1.88092e6i	−0.811188	−	1.40502i	0.100845	−	0.994902i	$-0.467846\pi$
$14$	−330778.	−	572924.i	−0.164374	−	0.284703i
$15$		0			0
$16$	−7.03363e6	+	1.21826e7i	−1.67695	+	2.90456i
$17$	1.52707e6			0.260849			0.130425	−	0.991458i	$-0.458366\pi$
$17$	1.52707e6			0.260849			0.130425	+	0.991458i	$0.458366\pi$
$18$		0			0
$19$	1.84377e7			1.70829			0.854146	−	0.520034i	$-0.174081\pi$
$19$	1.84377e7			1.70829			0.854146	+	0.520034i	$0.174081\pi$
$20$	3.06369e7	−	5.30647e7i	2.14082	−	3.70801i
$21$		0			0
$22$	6.27595e6	+	1.08703e7i	0.259630	+	0.449692i
$23$	8.46452e6	+	1.46610e7i	0.274220	+	0.474963i	0.969938	−	0.243352i	$-0.0782470\pi$
$23$	8.46452e6	+	1.46610e7i	0.274220	+	0.474963i	−0.695718	+	0.718315i	$0.744914\pi$
$24$		0			0
$25$	−3.95285e7	+	6.84653e7i	−0.809543	+	1.40217i
$26$	1.87670e8			3.09771
$27$		0			0
$28$	4.14837e7			0.455521
$29$	−4.94752e7	+	8.56935e7i	−0.447918	+	0.775816i	−0.998250	−	0.0591293i	$-0.981168\pi$
$29$	−4.94752e7	+	8.56935e7i	−0.447918	+	0.775816i	0.550333	+	0.834946i	$0.314501\pi$
$30$		0			0
$31$	−4.55697e7	−	7.89290e7i	−0.285882	−	0.495162i	0.686941	−	0.726713i	$-0.258953\pi$
$31$	−4.55697e7	−	7.89290e7i	−0.285882	−	0.495162i	−0.972823	+	0.231551i	$0.925620\pi$
$32$	−3.09549e8	−	5.36154e8i	−1.63081	−	2.82465i
$33$		0			0
$34$	−6.59755e7	+	1.14273e8i	−0.249028	+	0.431329i
$35$	−8.65810e7			−0.278643
$36$		0			0
$37$	3.51689e8			0.833775			0.416888	−	0.908958i	$-0.363121\pi$
$37$	3.51689e8			0.833775			0.416888	+	0.908958i	$0.363121\pi$
$38$	−7.96582e8	+	1.37972e9i	−1.63087	+	2.82476i
$39$		0			0
$40$	1.64667e9	+	2.85211e9i	2.54259	+	4.40389i
$41$	5.50954e8	+	9.54281e8i	0.742684	+	1.28637i	0.951269	+	0.308363i	$0.0997810\pi$
$41$	5.50954e8	+	9.54281e8i	0.742684	+	1.28637i	−0.208585	+	0.978004i	$0.566886\pi$
$42$		0			0
$43$	−2.21288e8	+	3.83281e8i	−0.229552	+	0.397595i	−0.957675	−	0.287851i	$-0.907059\pi$
$43$	−2.21288e8	+	3.83281e8i	−0.229552	+	0.397595i	0.728124	+	0.685446i	$0.240393\pi$
$44$	−7.87084e8			−0.719501
$45$		0			0
$46$	−1.46280e9			−1.04717
$47$	−5.87011e8	+	1.01673e9i	−0.373343	+	0.646649i	−0.990077	−	0.140522i	$-0.955122\pi$
$47$	−5.87011e8	+	1.01673e9i	−0.373343	+	0.646649i	0.616735	+	0.787171i	$0.288455\pi$
$48$		0			0
$49$	9.59355e8	+	1.66165e9i	0.485178	+	0.840352i
$50$	−3.41557e9	−	5.91595e9i	−1.54571	−	2.67725i
$51$		0			0
$52$	−5.88404e9	+	1.01915e10i	−2.14614	+	3.71722i
$53$	2.40091e9			0.788603			0.394302	−	0.918981i	$-0.370986\pi$
$53$	2.40091e9			0.788603			0.394302	+	0.918981i	$0.370986\pi$
$54$		0			0
$55$	1.64273e9			0.440120
$56$	−1.11483e9	+	1.93094e9i	−0.270504	+	0.468527i
$57$		0			0
$58$	−4.27505e9	−	7.40460e9i	−0.855238	−	1.48132i
$59$	−7.40846e8	−	1.28318e9i	−0.134909	−	0.233670i	0.790654	−	0.612264i	$-0.209741\pi$
$59$	−7.40846e8	−	1.28318e9i	−0.134909	−	0.233670i	−0.925563	+	0.378594i	$0.876408\pi$
$60$		0			0
$61$	2.25548e9	−	3.90660e9i	0.341920	−	0.592223i	−0.642869	−	0.765976i	$-0.722256\pi$
$61$	2.25548e9	−	3.90660e9i	0.341920	−	0.592223i	0.984789	+	0.173753i	$0.0555894\pi$
$62$	7.87516e9			1.09170
$63$		0			0
$64$	2.46852e10			2.87373
$65$	1.22806e10	−	2.12706e10i	1.31279	−	2.27383i
$66$		0			0
$67$	6.64818e9	+	1.15150e10i	0.601577	+	1.04196i	0.992582	+	0.121574i	$0.0387941\pi$
$67$	6.64818e9	+	1.15150e10i	0.601577	+	1.04196i	−0.391005	+	0.920388i	$0.627873\pi$
$68$	−4.13708e9	−	7.16564e9i	−0.345061	−	0.597662i
$69$		0			0
$70$	3.74064e9	−	6.47898e9i	0.266015	−	0.460752i
$71$	−1.89679e10			−1.24767			−0.623833	−	0.781558i	$-0.714425\pi$
$71$	−1.89679e10			−1.24767			−0.623833	+	0.781558i	$0.714425\pi$
$72$		0			0
$73$	5.25732e9			0.296817			0.148408	−	0.988926i	$-0.452585\pi$
$73$	5.25732e9			0.296817			0.148408	+	0.988926i	$0.452585\pi$
$74$	−1.51944e10	+	2.63174e10i	−0.795990	+	1.37870i
$75$		0			0
$76$	−4.99508e10	−	8.65173e10i	−2.25979	−	3.91407i
$77$	5.56081e8	+	9.63161e8i	0.0234120	+	0.0405509i
$78$		0			0
$79$	5.05595e9	−	8.75716e9i	0.184865	−	0.320195i	−0.758666	−	0.651479i	$-0.774149\pi$
$79$	5.05595e9	−	8.75716e9i	0.184865	−	0.320195i	0.943531	+	0.331285i	$0.107482\pi$
$80$	−1.59081e11			−5.42781
$81$		0			0
$82$	−9.52136e10			−2.83611
$83$	−1.72968e10	+	2.99589e10i	−0.481987	+	0.834826i	−0.999786	−	0.0206764i	$-0.993418\pi$
$83$	−1.72968e10	+	2.99589e10i	−0.481987	+	0.834826i	0.517799	+	0.855502i	$0.326751\pi$
$84$		0			0
$85$	8.63453e9	+	1.49554e10i	0.211074	+	0.365591i
$86$	−1.91210e10	−	3.31185e10i	−0.438298	−	0.759154i
$87$		0			0
$88$	2.11520e10	−	3.66364e10i	0.427265	−	0.740044i
$89$	2.76357e9			0.0524596			0.0262298	−	0.999656i	$-0.491650\pi$
$89$	2.76357e9			0.0524596			0.0262298	+	0.999656i	$0.491650\pi$
$90$		0			0
$91$	1.66285e10			0.279335
$92$	4.58635e10	−	7.94380e10i	0.725495	−	1.25659i
$93$		0			0
$94$	−5.07224e10	−	8.78537e10i	−0.712847	−	1.23469i
$95$	1.04253e11	+	1.80571e11i	1.38231	+	2.39424i
$96$		0			0
$97$	−2.55150e10	+	4.41933e10i	−0.301683	+	0.522531i	−0.976517	−	0.215439i	$-0.930882\pi$
$97$	−2.55150e10	+	4.41933e10i	−0.301683	+	0.522531i	0.674834	+	0.737969i	$0.264215\pi$
$98$	−1.65792e11			−1.85276
$99$		0			0
$100$	4.28357e11			4.28357
$101$	3.25776e10	−	5.64261e10i	0.308427	−	0.534211i	−0.669592	−	0.742729i	$-0.733531\pi$
$101$	3.25776e10	−	5.64261e10i	0.308427	−	0.534211i	0.978018	+	0.208519i	$0.0668642\pi$
$102$		0			0
$103$	−3.15541e10	−	5.46533e10i	−0.268195	−	0.464528i	0.700201	−	0.713946i	$-0.253094\pi$
$103$	−3.15541e10	−	5.46533e10i	−0.268195	−	0.464528i	−0.968396	+	0.249418i	$0.919761\pi$
$104$	−3.16254e11	−	5.47768e11i	−2.54890	−	4.41482i
$105$		0			0
$106$	−1.03729e11	+	1.79664e11i	−0.752865	+	1.30400i
$107$	1.48137e11			1.02106			0.510531	−	0.859859i	$-0.329449\pi$
$107$	1.48137e11			1.02106			0.510531	+	0.859859i	$0.329449\pi$
$108$		0			0
$109$	−1.46800e11			−0.913860			−0.456930	−	0.889503i	$-0.651051\pi$
$109$	−1.46800e11			−0.913860			−0.456930	+	0.889503i	$0.651051\pi$
$110$	−7.09724e10	+	1.22928e11i	−0.420174	+	0.727763i
$111$		0			0
$112$	−5.38508e10	−	9.32722e10i	−0.288731	−	0.500096i
$113$	−9.24963e10	−	1.60208e11i	−0.472273	−	0.818000i	0.527224	−	0.849726i	$-0.323233\pi$
$113$	−9.24963e10	−	1.60208e11i	−0.472273	−	0.818000i	−0.999497	+	0.0317262i	$0.989900\pi$
$114$		0			0
$115$	−9.57221e10	+	1.65796e11i	−0.443786	+	0.768661i
$116$	5.36145e11			2.37008
$117$		0			0
$118$	1.28030e11			0.515182
$119$	−5.84576e9	+	1.01252e10i	−0.0224560	+	0.0388950i
$120$		0			0
$121$	1.32105e11	+	2.28813e11i	0.463020	+	0.801975i
$122$	1.94891e11	+	3.37562e11i	0.652850	+	1.13077i
$123$		0			0
$124$	−2.46912e11	+	4.27663e11i	−0.756349	+	1.31003i
$125$	−3.41847e11			−1.00190
$126$		0			0
$127$	−4.84205e11			−1.30049			−0.650247	−	0.759723i	$-0.725335\pi$
$127$	−4.84205e11			−1.30049			−0.650247	+	0.759723i	$0.725335\pi$
$128$	−4.32541e11	+	7.49184e11i	−1.11269	+	1.92723i
$129$		0			0
$130$	1.06114e12	+	1.83795e12i	2.50660	+	4.34156i
$131$	−1.22114e11	−	2.11507e11i	−0.276549	−	0.478997i	0.693976	−	0.719999i	$-0.255858\pi$
$131$	−1.22114e11	−	2.11507e11i	−0.276549	−	0.478997i	−0.970525	+	0.241001i	$0.922524\pi$
$132$		0			0
$133$	−7.05812e10	+	1.22250e11i	−0.147064	+	0.254722i
$134$	−1.14891e12			−2.29726
$135$		0			0
$136$	4.44718e11			0.819636
$137$	7.83077e10	−	1.35633e11i	0.138625	−	0.240105i	−0.788351	−	0.615225i	$-0.789065\pi$
$137$	7.83077e10	−	1.35633e11i	0.138625	−	0.240105i	0.926976	+	0.375120i	$0.122398\pi$
$138$		0			0
$139$	−3.41479e11	−	5.91458e11i	−0.558190	−	0.966813i	−0.997648	−	0.0685500i	$-0.978163\pi$
$139$	−3.41479e11	−	5.91458e11i	−0.558190	−	0.966813i	0.439458	−	0.898263i	$-0.355171\pi$
$140$	2.34562e11	+	4.06273e11i	0.368599	+	0.638431i
$141$		0			0
$142$	8.19488e11	−	1.41939e12i	1.19112	−	2.06309i
$143$	−3.15498e11			−0.441212
$144$		0			0
$145$	−1.11899e12			−1.44978
$146$	−2.27137e11	+	3.93413e11i	−0.283366	+	0.490804i
$147$		0			0
$148$	−9.52783e11	−	1.65027e12i	−1.10295	−	1.91036i
$149$	1.60013e11	+	2.77151e11i	0.178497	+	0.309166i	0.941366	−	0.337387i	$-0.109543\pi$
$149$	1.60013e11	+	2.77151e11i	0.178497	+	0.309166i	−0.762869	+	0.646553i	$0.776210\pi$
$150$		0			0
$151$	−8.52081e11	+	1.47585e12i	−0.883299	+	1.52992i	−0.0356477	+	0.999364i	$0.511349\pi$
$151$	−8.52081e11	+	1.47585e12i	−0.883299	+	1.52992i	−0.847651	+	0.530554i	$0.821984\pi$
$152$	5.36949e12			5.36776
$153$		0			0
$154$	−9.60997e10			−0.0894042
$155$	5.15331e11	−	8.92579e11i	0.462660	−	0.801350i
$156$		0			0
$157$	1.83944e11	+	3.18601e11i	0.153900	+	0.266562i	0.932658	−	0.360762i	$-0.117483\pi$
$157$	1.83944e11	+	3.18601e11i	0.153900	+	0.266562i	−0.778758	+	0.627324i	$0.784150\pi$
$158$	4.36874e11	+	7.56688e11i	0.352974	+	0.611368i
$159$		0			0
$160$	3.50057e12	−	6.06316e12i	2.63924	−	4.57130i
$161$	−1.29612e11			−0.0944283
$162$		0			0
$163$	−4.79589e11			−0.326466			−0.163233	−	0.986588i	$-0.552192\pi$
$163$	−4.79589e11			−0.326466			−0.163233	+	0.986588i	$0.552192\pi$
$164$	2.98525e12	−	5.17061e12i	1.96490	−	3.40330i
$165$		0			0
$166$	−1.49458e12	−	2.58868e12i	−0.920288	−	1.59399i
$167$	1.41658e12	+	2.45359e12i	0.843920	+	1.46171i	0.886556	+	0.462621i	$0.153091\pi$
$167$	1.41658e12	+	2.45359e12i	0.843920	+	1.46171i	−0.0426362	+	0.999091i	$0.513576\pi$
$168$		0			0
$169$	−1.46250e12	+	2.53312e12i	−0.816053	+	1.41345i
$170$	−1.49218e12			−0.806034
$171$		0			0
$172$	2.39802e12			1.21464
$173$	−3.13677e11	+	5.43305e11i	−0.153897	+	0.266557i	−0.932657	−	0.360765i	$-0.882516\pi$
$173$	−3.13677e11	+	5.43305e11i	−0.153897	+	0.266557i	0.778760	+	0.627322i	$0.215849\pi$
$174$		0			0
$175$	−3.02637e11	−	5.24183e11i	−0.139384	−	0.241420i
$176$	1.02173e12	+	1.76968e12i	0.456053	+	0.789907i
$177$		0			0
$178$	−1.19397e11	+	2.06802e11i	−0.0500822	+	0.0867449i
$179$	−3.65808e12			−1.48786			−0.743929	−	0.668258i	$-0.767040\pi$
$179$	−3.65808e12			−1.48786			−0.743929	+	0.668258i	$0.767040\pi$
$180$		0			0
$181$	1.44728e12			0.553760			0.276880	−	0.960905i	$-0.410700\pi$
$181$	1.44728e12			0.553760			0.276880	+	0.960905i	$0.410700\pi$
$182$	−7.18416e11	+	1.24433e12i	−0.266676	+	0.461896i
$183$		0			0
$184$	2.46506e12	+	4.26962e12i	0.861649	+	1.49242i
$185$	1.98856e12	+	3.44429e12i	0.674674	+	1.16857i
$186$		0			0
$187$	1.10914e11	−	1.92108e11i	0.0354696	−	0.0614351i
$188$	6.36123e12			1.97548
$189$		0			0
$190$	−1.80165e13			−5.27868
$191$	1.18911e12	−	2.05960e12i	0.338484	−	0.586272i	−0.645664	−	0.763622i	$-0.723419\pi$
$191$	1.18911e12	−	2.05960e12i	0.338484	−	0.586272i	0.984148	+	0.177350i	$0.0567525\pi$
$192$		0			0
$193$	5.30499e11	+	9.18851e11i	0.142600	+	0.246990i	0.928475	−	0.371395i	$-0.121120\pi$
$193$	5.30499e11	+	9.18851e11i	0.142600	+	0.246990i	−0.785875	+	0.618385i	$0.787787\pi$
$194$	−2.20470e12	−	3.81865e12i	−0.576023	−	0.997701i
$195$		0			0
$196$	5.19810e12	−	9.00337e12i	1.28362	−	2.22329i
$197$	−3.65734e12			−0.878215			−0.439108	−	0.898434i	$-0.644705\pi$
$197$	−3.65734e12			−0.878215			−0.439108	+	0.898434i	$0.644705\pi$
$198$		0			0
$199$	−4.39205e12			−0.997643			−0.498822	−	0.866705i	$-0.666234\pi$
$199$	−4.39205e12			−0.997643			−0.498822	+	0.866705i	$0.666234\pi$
$200$	−1.15116e13	+	1.99387e13i	−2.54373	+	4.40587i
$201$		0			0
$202$	2.81497e12	+	4.87566e12i	0.588899	+	1.02000i
$203$	−3.78791e11	−	6.56085e11i	−0.0771208	−	0.133577i
$204$		0			0
$205$	−6.23054e12	+	1.07916e13i	−1.20193	+	2.08180i
$206$	5.45305e12			1.02416
$207$		0			0
$208$	3.05527e13			5.44128
$209$	1.33916e12	−	2.31949e12i	0.232289	−	0.402336i
$210$		0			0
$211$	4.70703e12	+	8.15282e12i	0.774807	+	1.34200i	0.934903	+	0.354904i	$0.115486\pi$
$211$	4.70703e12	+	8.15282e12i	0.774807	+	1.34200i	−0.160096	+	0.987101i	$0.551180\pi$
$212$	−6.50446e12	−	1.12661e13i	−1.04319	−	1.80686i
$213$		0			0
$214$	−6.40010e12	+	1.10853e13i	−0.974790	+	1.68839i
$215$	−5.00492e12			−0.742994
$216$		0			0
$217$	6.97780e11			0.0984442
$218$	6.34233e12	−	1.09852e13i	0.872445	−	1.51112i
$219$		0			0
$220$	−4.45042e12	−	7.70836e12i	−0.582206	−	1.00841i
$221$	−1.65832e12	−	2.87230e12i	−0.211598	−	0.366498i
$222$		0			0
$223$	4.35537e12	−	7.54372e12i	0.528869	−	0.916028i	−0.470564	−	0.882366i	$-0.655950\pi$
$223$	4.35537e12	−	7.54372e12i	0.528869	−	0.916028i	0.999433	−	0.0336621i	$-0.0107170\pi$
$224$	4.73992e12			0.561574
$225$		0			0
$226$	1.59848e13			1.80348
$227$	6.30681e12	−	1.09237e13i	0.694493	−	1.20290i	−0.275859	−	0.961198i	$-0.588962\pi$
$227$	6.30681e12	−	1.09237e13i	0.694493	−	1.20290i	0.970351	−	0.241699i	$-0.0777045\pi$
$228$		0			0
$229$	1.52094e12	+	2.63435e12i	0.159594	+	0.276426i	0.934723	−	0.355378i	$-0.115648\pi$
$229$	1.52094e12	+	2.63435e12i	0.159594	+	0.276426i	−0.775128	+	0.631804i	$0.782315\pi$
$230$	−8.27115e12	−	1.43260e13i	−0.847350	−	1.46765i
$231$		0			0
$232$	−1.44083e13	+	2.49559e13i	−1.40744	+	2.43775i
$233$	1.51645e13			1.44667			0.723336	−	0.690496i	$-0.242608\pi$
$233$	1.51645e13			1.44667			0.723336	+	0.690496i	$0.242608\pi$
$234$		0			0
$235$	−1.32766e13			−1.20841
$236$	−4.01415e12	+	6.95271e12i	−0.356925	+	0.618213i
$237$		0			0
$238$	−5.05120e11	−	8.74894e11i	−0.0428767	−	0.0742647i
$239$	1.15463e13	+	1.99987e13i	0.957751	+	1.65887i	0.727943	+	0.685638i	$0.240477\pi$
$239$	1.15463e13	+	1.99987e13i	0.957751	+	1.65887i	0.229809	+	0.973236i	$0.426190\pi$
$240$		0			0
$241$	−7.99086e12	+	1.38406e13i	−0.633140	+	1.09663i	0.353766	+	0.935334i	$0.384901\pi$
$241$	−7.99086e12	+	1.38406e13i	−0.633140	+	1.09663i	−0.986906	+	0.161297i	$0.948432\pi$
$242$	−2.28299e13			−1.76815
$243$		0			0
$244$	−2.44419e13			−1.80921
$245$	−1.08490e13	+	1.87910e13i	−0.785192	+	1.35999i
$246$		0			0
$247$	−2.00224e13	−	3.46799e13i	−1.38575	−	2.40018i
$248$	−1.32709e13	−	2.29860e13i	−0.898292	−	1.55589i
$249$		0			0
$250$	1.47691e13	−	2.55809e13i	0.956499	−	1.65671i
$251$	5.48461e12			0.347488			0.173744	−	0.984791i	$-0.444413\pi$
$251$	5.48461e12			0.347488			0.173744	+	0.984791i	$0.444413\pi$
$252$		0			0
$253$	2.45917e12			0.149151
$254$	2.09196e13	−	3.62337e13i	1.24156	−	2.15044i
$255$		0			0
$256$	−1.20974e13	−	2.09533e13i	−0.687657	−	1.19106i
$257$	7.81957e12	+	1.35439e13i	0.435061	+	0.753548i	0.997301	−	0.0734263i	$-0.0233934\pi$
$257$	7.81957e12	+	1.35439e13i	0.435061	+	0.753548i	−0.562239	+	0.826975i	$0.690060\pi$
$258$		0			0
$259$	−1.34630e12	+	2.33186e12i	−0.0717782	+	0.124323i
$260$	−1.33081e14			−6.94644
$261$		0			0
$262$	2.11032e13			1.05607
$263$	−1.37196e13	+	2.37630e13i	−0.672332	+	1.16451i	0.304909	+	0.952382i	$0.401374\pi$
$263$	−1.37196e13	+	2.37630e13i	−0.672332	+	1.16451i	−0.977241	+	0.212132i	$0.931959\pi$
$264$		0			0
$265$	1.35755e13	+	2.35135e13i	0.638122	+	1.10526i
$266$	−6.09878e12	−	1.05634e13i	−0.280798	−	0.486356i
$267$		0			0
$268$	3.60220e13	−	6.23920e13i	1.59157	−	2.75669i
$269$	4.06420e12			0.175929			0.0879646	−	0.996124i	$-0.471964\pi$
$269$	4.06420e12			0.175929			0.0879646	+	0.996124i	$0.471964\pi$
$270$		0			0
$271$	3.34423e13			1.38984			0.694921	−	0.719086i	$-0.255439\pi$
$271$	3.34423e13			1.38984			0.694921	+	0.719086i	$0.255439\pi$
$272$	−1.07408e13	+	1.86037e13i	−0.437431	+	0.757652i
$273$		0			0
$274$	6.76641e12	+	1.17198e13i	0.264685	+	0.458449i
$275$	5.74204e12	+	9.94550e12i	0.220159	+	0.381326i
$276$		0			0
$277$	4.32364e12	−	7.48877e12i	0.159298	−	0.275913i	−0.775318	−	0.631572i	$-0.782410\pi$
$277$	4.32364e12	−	7.48877e12i	0.159298	−	0.275913i	0.934616	+	0.355659i	$0.115744\pi$
$278$	5.90129e13			2.13157
$279$		0			0
$280$	−2.52144e13			−0.875546
$281$	−1.83130e13	+	3.17190e13i	−0.623555	+	1.08003i	0.365264	+	0.930904i	$0.380979\pi$
$281$	−1.83130e13	+	3.17190e13i	−0.623555	+	1.08003i	−0.988818	+	0.149124i	$0.952355\pi$
$282$		0			0
$283$	−2.95929e13	−	5.12565e13i	−0.969087	−	1.67851i	−0.698209	−	0.715894i	$-0.746019\pi$
$283$	−2.95929e13	−	5.12565e13i	−0.969087	−	1.67851i	−0.270878	−	0.962614i	$-0.587314\pi$
$284$	5.13871e13	+	8.90051e13i	1.65045	+	2.85867i
$285$		0			0
$286$	1.36307e13	−	2.36091e13i	0.421218	−	0.729570i
$287$	−8.43642e12			−0.255745
$288$		0			0
$289$	−3.19400e13			−0.931958
$290$	4.83449e13	−	8.37358e13i	1.38408	−	2.39730i
$291$		0			0
$292$	−1.42429e13	−	2.46695e13i	−0.392640	−	0.680072i
$293$	−3.47577e13	−	6.02021e13i	−0.940327	−	1.62869i	−0.764847	−	0.644211i	$-0.777186\pi$
$293$	−3.47577e13	−	6.02021e13i	−0.940327	−	1.62869i	−0.175480	−	0.984483i	$-0.556148\pi$
$294$		0			0
$295$	8.37795e12	−	1.45110e13i	0.218332	−	0.378161i
$296$	1.02420e14			2.61987
$297$		0			0
$298$	−2.76528e13			−0.681631
$299$	1.83841e13	−	3.18422e13i	0.444888	−	0.770569i
$300$		0			0
$301$	−1.69422e12	−	2.93447e12i	−0.0395234	−	0.0684565i
$302$	−7.36265e13	−	1.27525e14i	−1.68654	−	2.92117i
$303$		0			0
$304$	−1.29684e14	+	2.24619e14i	−2.86472	+	4.96183i
$305$	5.10127e13			1.10670
$306$		0			0
$307$	6.45270e13			1.35046			0.675228	−	0.737609i	$-0.264045\pi$
$307$	6.45270e13			1.35046			0.675228	+	0.737609i	$0.264045\pi$
$308$	3.01303e12	−	5.21873e12i	0.0619405	−	0.107284i
$309$		0			0
$310$	4.45286e13	+	7.71259e13i	0.883385	+	1.53007i
$311$	1.58404e13	+	2.74363e13i	0.308733	+	0.534741i	0.978085	−	0.208204i	$-0.0667618\pi$
$311$	1.58404e13	+	2.74363e13i	0.308733	+	0.534741i	−0.669353	+	0.742945i	$0.733428\pi$
$312$		0			0
$313$	1.48249e13	−	2.56774e13i	0.278931	−	0.483123i	−0.692188	−	0.721717i	$-0.743353\pi$
$313$	1.48249e13	−	2.56774e13i	0.278931	−	0.483123i	0.971119	+	0.238594i	$0.0766866\pi$
$314$	−3.17885e13			−0.587702
$315$		0			0
$316$	−5.47896e13			−0.978181
$317$	−1.35650e13	+	2.34952e13i	−0.238009	+	0.412243i	−0.960143	−	0.279510i	$-0.909828\pi$
$317$	−1.35650e13	+	2.34952e13i	−0.238009	+	0.412243i	0.722134	+	0.691753i	$0.243161\pi$
$318$		0			0
$319$	7.18692e12	+	1.24481e13i	0.121813	+	0.210987i
$320$	1.39578e14	+	2.41756e14i	2.32536	+	4.02765i
$321$		0			0
$322$	5.59975e12	−	9.69904e12i	0.0901490	−	0.156143i
$323$	2.81557e13			0.445607
$324$		0			0
$325$	1.71704e14			2.62677
$326$	2.07202e13	−	3.58884e13i	0.311671	−	0.539830i
$327$		0			0
$328$	1.60451e14	+	2.77909e14i	2.33365	+	4.04200i
$329$	−4.49426e12	−	7.78429e12i	−0.0642808	−	0.111338i
$330$		0			0
$331$	4.87551e13	−	8.44463e13i	0.674475	−	1.16823i	−0.302146	−	0.953262i	$-0.597703\pi$
$331$	4.87551e13	−	8.44463e13i	0.674475	−	1.16823i	0.976622	−	0.214964i	$-0.0689635\pi$
$332$	1.87439e14			2.55035
$333$		0			0
$334$	−2.44808e14			−3.22270
$335$	−7.51818e13	+	1.30219e14i	−0.973568	+	1.68627i
$336$		0			0
$337$	5.35413e13	+	9.27362e13i	0.671003	+	1.16221i	0.977620	+	0.210378i	$0.0674694\pi$
$337$	5.35413e13	+	9.27362e13i	0.671003	+	1.16221i	−0.306618	+	0.951833i	$0.599197\pi$
$338$	−1.26371e14	−	2.18882e14i	−1.55814	−	2.69878i
$339$		0			0
$340$	4.67847e13	−	8.10335e13i	0.558432	−	0.967232i
$341$	−1.32392e13			−0.155494
$342$		0			0
$343$	−2.98288e13			−0.339248
$344$	−6.44441e13	+	1.11620e14i	−0.721293	+	1.24932i
$345$		0			0
$346$	−2.71042e13	−	4.69458e13i	−0.293845	−	0.508954i
$347$	7.26926e13	+	1.25907e14i	0.775671	+	1.34350i	0.934416	+	0.356183i	$0.115922\pi$
$347$	7.26926e13	+	1.25907e14i	0.775671	+	1.34350i	−0.158745	+	0.987320i	$0.550745\pi$
$348$		0			0
$349$	−7.40820e13	+	1.28314e14i	−0.765901	+	1.32658i	0.173867	+	0.984769i	$0.444374\pi$
$349$	−7.40820e13	+	1.28314e14i	−0.765901	+	1.32658i	−0.939769	+	0.341811i	$0.888960\pi$
$350$	5.23005e13			0.532270
$351$		0			0
$352$	−8.99321e13			−0.887013
$353$	−4.11259e13	+	7.12321e13i	−0.399350	+	0.691695i	−0.993646	−	0.112552i	$-0.964098\pi$
$353$	−4.11259e13	+	7.12321e13i	−0.399350	+	0.691695i	0.594295	+	0.804247i	$0.297431\pi$
$354$		0			0
$355$	−1.07250e14	−	1.85763e14i	−1.00959	−	1.74865i
$356$	−7.48696e12	−	1.29678e13i	−0.0693953	−	0.120196i
$357$		0			0
$358$	1.58044e14	−	2.73740e14i	1.42043	−	2.46026i
$359$	−1.09985e14			−0.973454			−0.486727	−	0.873554i	$-0.661809\pi$
$359$	−1.09985e14			−0.973454			−0.486727	+	0.873554i	$0.661809\pi$
$360$		0			0
$361$	2.23459e14			1.91826
$362$	−6.25284e13	+	1.08302e14i	−0.528664	+	0.915674i
$363$		0			0
$364$	−4.50493e13	−	7.80277e13i	−0.369514	−	0.640016i
$365$	2.97265e13	+	5.14879e13i	0.240178	+	0.416001i
$366$		0			0
$367$	6.35463e13	−	1.10065e14i	0.498227	−	0.862954i	−0.501771	−	0.865001i	$-0.667318\pi$
$367$	6.35463e13	−	1.10065e14i	0.498227	−	0.862954i	0.999998	+	0.00204615i	$0.000651310\pi$
$368$	−2.38145e14			−1.83941
$369$		0			0
$370$	−3.43655e14			−2.57640
$371$	−9.19091e12	+	1.59191e13i	−0.0678894	+	0.117588i
$372$		0			0
$373$	−6.89595e13	−	1.19441e14i	−0.494533	−	0.856557i	0.505447	−	0.862858i	$-0.331328\pi$
$373$	−6.89595e13	−	1.19441e14i	−0.494533	−	0.856557i	−0.999980	+	0.00630102i	$0.997994\pi$
$374$	9.58381e12	+	1.65997e13i	0.0677243	+	0.117302i
$375$		0			0
$376$	−1.70951e14	+	2.96096e14i	−1.17311	+	2.03189i
$377$	2.14910e14			1.45338
$378$		0			0
$379$	2.38517e14			1.56676			0.783382	−	0.621540i	$-0.213493\pi$
$379$	2.38517e14			1.56676			0.783382	+	0.621540i	$0.213493\pi$
$380$	5.64875e14	−	9.78392e14i	3.65715	−	6.33436i
$381$		0			0
$382$	1.02748e14	+	1.77966e14i	0.646289	+	1.11941i
$383$	−3.39198e13	−	5.87509e13i	−0.210310	−	0.364268i	0.741501	−	0.670951i	$-0.234114\pi$
$383$	−3.39198e13	−	5.87509e13i	−0.210310	−	0.364268i	−0.951812	+	0.306683i	$0.900781\pi$
$384$		0			0
$385$	−6.28852e12	+	1.08920e13i	−0.0378891	+	0.0656258i
$386$	−9.16786e13			−0.544550
$387$		0			0
$388$	2.76498e14			1.59631
$389$	−8.36223e13	+	1.44838e14i	−0.475992	+	0.824442i	−0.999622	−	0.0275039i	$-0.991244\pi$
$389$	−8.36223e13	+	1.44838e14i	−0.475992	+	0.824442i	0.523630	+	0.851946i	$0.324577\pi$
$390$		0			0
$391$	1.29259e13	+	2.23883e13i	0.0715301	+	0.123894i
$392$	2.79386e14	+	4.83911e14i	1.52452	+	2.64054i
$393$		0			0
$394$	1.58012e14	−	2.73684e14i	0.838416	−	1.45218i
$395$	1.14352e14			0.598354
$396$		0			0
$397$	−1.32401e14			−0.673817			−0.336909	−	0.941537i	$-0.609381\pi$
$397$	−1.32401e14			−0.673817			−0.336909	+	0.941537i	$0.609381\pi$
$398$	1.89754e14	−	3.28663e14i	0.952432	−	1.64966i
$399$		0			0
$400$	−5.56057e14	−	9.63119e14i	−2.71512	−	4.70273i
$401$	1.46827e14	+	2.54312e14i	0.707151	+	1.22482i	0.965910	+	0.258880i	$0.0833534\pi$
$401$	1.46827e14	+	2.54312e14i	0.707151	+	1.22482i	−0.258758	+	0.965942i	$0.583313\pi$
$402$		0			0
$403$	−9.89729e13	+	1.71426e14i	−0.463808	+	0.803339i
$404$	−3.53033e14			−1.63199
$405$		0			0
$406$	6.54611e13			0.294503
$407$	2.55437e13	−	4.42431e13i	0.113374	−	0.196370i
$408$		0			0
$409$	−4.80699e13	−	8.32594e13i	−0.207680	−	0.359712i	0.743303	−	0.668955i	$-0.233258\pi$
$409$	−4.80699e13	−	8.32594e13i	−0.207680	−	0.359712i	−0.950983	+	0.309242i	$0.899925\pi$
$410$	−5.38368e14	−	9.32480e14i	−2.29492	−	3.97492i
$411$		0			0
$412$	−1.70970e14	+	2.96130e14i	−0.709556	+	1.22899i
$413$	1.13441e13			0.0464563
$414$		0			0
$415$	−3.91205e14			−1.56006
$416$	−6.72309e14	+	1.16447e15i	−2.64579	+	4.58264i
$417$		0			0
$418$	1.15714e14	+	2.00423e14i	0.443524	+	0.768205i
$419$	−9.45188e13	−	1.63711e14i	−0.357554	−	0.619301i	0.629998	−	0.776597i	$-0.283056\pi$
$419$	−9.45188e13	−	1.63711e14i	−0.357554	−	0.619301i	−0.987552	+	0.157296i	$0.949722\pi$
$420$		0			0
$421$	5.16879e13	−	8.95261e13i	0.190475	−	0.329912i	−0.754933	−	0.655802i	$-0.772331\pi$
$421$	5.16879e13	−	8.95261e13i	0.190475	−	0.329912i	0.945408	+	0.325890i	$0.105664\pi$
$422$	−8.13449e14			−2.95878
$423$		0			0
$424$	6.99201e14			2.47793
$425$	−6.03627e13	+	1.04551e14i	−0.211169	+	0.365755i
$426$		0			0
$427$	1.72684e13	+	2.99097e13i	0.0588705	+	0.101967i
$428$	−4.01327e14	−	6.95119e14i	−1.35070	−	2.33948i
$429$		0			0
$430$	2.16232e14	−	3.74525e14i	0.709323	−	1.22858i
$431$	−2.42262e13			−0.0784620			−0.0392310	−	0.999230i	$-0.512491\pi$
$431$	−2.42262e13			−0.0784620			−0.0392310	+	0.999230i	$0.512491\pi$
$432$		0			0
$433$	−4.82141e14			−1.52227			−0.761133	−	0.648596i	$-0.775356\pi$
$433$	−4.82141e14			−1.52227			−0.761133	+	0.648596i	$0.775356\pi$
$434$	−3.01469e13	+	5.22159e13i	−0.0939828	+	0.162783i
$435$		0			0
$436$	3.97705e14	+	6.88845e14i	1.20889	+	2.09385i
$437$	1.56066e14	+	2.70315e14i	0.468448	+	0.811375i
$438$		0			0
$439$	−2.62298e13	+	4.54314e13i	−0.0767786	+	0.132984i	−0.901858	−	0.432032i	$-0.857797\pi$
$439$	−2.62298e13	+	4.54314e13i	−0.0767786	+	0.132984i	0.825080	+	0.565016i	$0.191130\pi$
$440$	4.78401e14			1.38294
$441$		0			0
$442$	2.86584e14			0.808035
$443$	8.34812e13	−	1.44594e14i	0.232471	−	0.402651i	−0.726064	−	0.687627i	$-0.758652\pi$
$443$	8.34812e13	−	1.44594e14i	0.232471	−	0.402651i	0.958535	+	0.284976i	$0.0919857\pi$
$444$		0			0
$445$	1.56261e13	+	2.70651e13i	0.0424492	+	0.0735242i
$446$	3.76338e14	+	6.51837e14i	1.00980	+	1.74903i
$447$		0			0
$448$	−9.44971e13	+	1.63674e14i	−0.247394	+	0.428499i
$449$	−2.18915e14			−0.566136			−0.283068	−	0.959100i	$-0.591352\pi$
$449$	−2.18915e14			−0.566136			−0.283068	+	0.959100i	$0.591352\pi$
$450$		0			0
$451$	1.60067e14			0.403953
$452$	−5.01175e14	+	8.68061e14i	−1.24948	+	2.16416i
$453$		0			0
$454$	5.44959e14	+	9.43896e14i	1.32604	+	2.29677i
$455$	9.40227e13	+	1.62852e14i	0.226032	+	0.391499i
$456$		0			0
$457$	−1.80862e14	+	3.13263e14i	−0.424433	+	0.735139i	−0.996367	−	0.0851601i	$-0.972860\pi$
$457$	−1.80862e14	+	3.13263e14i	−0.424433	+	0.735139i	0.571934	+	0.820299i	$0.306193\pi$
$458$	−2.62843e14			−0.609448
$459$		0			0
$460$	1.03731e15			2.34822
$461$	3.84198e13	−	6.65450e13i	0.0859408	−	0.148854i	−0.819851	−	0.572577i	$-0.805944\pi$
$461$	3.84198e13	−	6.65450e13i	0.0859408	−	0.148854i	0.905792	+	0.423723i	$0.139277\pi$
$462$		0			0
$463$	1.91306e14	+	3.31352e14i	0.417863	+	0.723760i	0.995724	−	0.0923750i	$-0.0294459\pi$
$463$	1.91306e14	+	3.31352e14i	0.417863	+	0.723760i	−0.577861	+	0.816135i	$0.696113\pi$
$464$	−6.95980e14	−	1.20547e15i	−1.50227	−	2.60201i
$465$		0			0
$466$	−6.55166e14	+	1.13478e15i	−1.38111	+	2.39216i
$467$	3.74303e14			0.779795			0.389898	−	0.920858i	$-0.372510\pi$
$467$	3.74303e14			0.779795			0.389898	+	0.920858i	$0.372510\pi$
$468$		0			0
$469$	−1.01799e14			−0.207155
$470$	5.73600e14	−	9.93505e14i	1.15364	−	1.99817i
$471$		0			0
$472$	−2.15751e14	−	3.73693e14i	−0.423909	−	0.734232i
$473$	3.21450e13	+	5.56767e13i	0.0624276	+	0.108128i
$474$		0			0
$475$	−7.28814e14	+	1.26234e15i	−1.38294	+	2.39532i
$476$	6.33486e13			0.118822
$477$		0			0
$478$	−1.99538e15			−3.65739
$479$	−2.56237e14	+	4.43815e14i	−0.464297	+	0.804186i	−0.999170	−	0.0407465i	$-0.987026\pi$
$479$	−2.56237e14	+	4.43815e14i	−0.464297	+	0.804186i	0.534872	+	0.844933i	$0.320360\pi$
$480$		0			0
$481$	−3.81917e14	−	6.61499e14i	−0.676349	−	1.17147i
$482$	−6.90474e14	−	1.19594e15i	−1.20889	−	2.09387i
$483$		0			0
$484$	7.15789e14	−	1.23978e15i	1.22500	−	2.12176i
$485$	−5.77080e14			−0.976464
$486$		0			0
$487$	9.34798e13			0.154635			0.0773176	−	0.997007i	$-0.475364\pi$
$487$	9.34798e13			0.154635			0.0773176	+	0.997007i	$0.475364\pi$
$488$	6.56848e14	−	1.13769e15i	1.07437	−	1.86087i
$489$		0			0
$490$	−9.37438e14	−	1.62369e15i	−1.49922	−	2.59672i
$491$	4.76100e14	+	8.24630e14i	0.752922	+	1.30410i	0.946401	+	0.322995i	$0.104690\pi$
$491$	4.76100e14	+	8.24630e14i	0.752922	+	1.30410i	−0.193478	+	0.981105i	$0.561977\pi$
$492$		0			0
$493$	−7.55520e13	+	1.30860e14i	−0.116839	+	0.202371i
$494$	3.46019e15			5.29179
$495$		0			0
$496$	1.28208e15			1.91764
$497$	7.26109e13	−	1.25766e14i	0.107409	−	0.186038i
$498$		0			0
$499$	−2.24475e13	−	3.88802e13i	−0.0324799	−	0.0562569i	0.849329	−	0.527865i	$-0.177007\pi$
$499$	−2.24475e13	−	3.88802e13i	−0.0324799	−	0.0562569i	−0.881808	+	0.471608i	$0.843674\pi$
$500$	9.26119e14	+	1.60408e15i	1.32535	+	2.29558i
$501$		0			0
$502$	−2.36957e14	+	4.10421e14i	−0.331741	+	0.574592i
$503$	−2.98702e14			−0.413632			−0.206816	−	0.978380i	$-0.566310\pi$
$503$	−2.98702e14			−0.413632			−0.206816	+	0.978380i	$0.566310\pi$
$504$		0			0
$505$	7.36817e14			0.998291
$506$	−1.06246e14	+	1.84023e14i	−0.142391	+	0.246629i
$507$		0			0
$508$	1.31179e15	+	2.27209e15i	1.72034	+	2.97971i
$509$	4.13266e14	+	7.15798e14i	0.536144	+	0.928629i	0.999107	+	0.0422516i	$0.0134531\pi$
$509$	4.13266e14	+	7.15798e14i	0.536144	+	0.928629i	−0.462963	+	0.886378i	$0.653214\pi$
$510$		0			0
$511$	−2.01255e13	+	3.48584e13i	−0.0255524	+	0.0442581i
$512$	3.18932e14			0.400603
$513$		0			0
$514$	−1.35134e15			−1.66138
$515$	3.56834e14	−	6.18054e14i	0.434036	−	0.751773i
$516$		0			0
$517$	8.52711e13	+	1.47694e14i	0.101532	+	0.175859i
$518$	−1.16331e14	−	2.01491e14i	−0.137051	−	0.237379i
$519$		0			0
$520$	3.57640e15	−	6.19451e15i	4.12503	−	7.14477i
$521$	−1.51372e15			−1.72757			−0.863787	−	0.503857i	$-0.831914\pi$
$521$	−1.51372e15			−1.72757			−0.863787	+	0.503857i	$0.831914\pi$
$522$		0			0
$523$	−5.57360e14			−0.622840			−0.311420	−	0.950272i	$-0.600805\pi$
$523$	−5.57360e14			−0.622840			−0.311420	+	0.950272i	$0.600805\pi$
$524$	−6.61653e14	+	1.14602e15i	−0.731658	+	1.26727i
$525$		0			0
$526$	−1.18548e15	−	2.05331e15i	−1.28373	−	2.22348i
$527$	−6.95881e13	−	1.20530e14i	−0.0745721	−	0.129163i
$528$		0			0
$529$	3.33109e14	−	5.76961e14i	0.349607	−	0.605537i
$530$	−2.34606e15			−2.43681
$531$		0			0
$532$	7.64865e14			0.778163
$533$	1.19662e15	−	2.07260e15i	1.20491	−	2.08697i
$534$		0			0
$535$	8.37613e14	+	1.45079e15i	0.826223	+	1.43106i
$536$	1.93610e15	+	3.35343e15i	1.89026	+	3.27403i
$537$		0			0
$538$	−1.75590e14	+	3.04130e14i	−0.167956	+	0.290909i
$539$	2.78718e14			0.263892
$540$		0			0
$541$	−1.91740e15			−1.77880			−0.889399	−	0.457131i	$-0.848877\pi$
$541$	−1.91740e15			−1.77880			−0.889399	+	0.457131i	$0.848877\pi$
$542$	−1.44484e15	+	2.50254e15i	−1.32686	+	2.29818i
$543$		0			0
$544$	−4.72702e14	−	8.18744e14i	−0.425396	−	0.736808i
$545$	−8.30052e14	−	1.43769e15i	−0.739477	−	1.28081i
$546$		0			0
$547$	−4.86823e14	+	8.43203e14i	−0.425051	+	0.736210i	−0.996425	−	0.0844798i	$-0.973077\pi$
$547$	−4.86823e14	+	8.43203e14i	−0.425051	+	0.736210i	0.571374	+	0.820690i	$0.306410\pi$
$548$	−8.48594e14			−0.733512
$549$		0			0
$550$	−9.92315e14			−0.840726
$551$	−9.12208e14	+	1.57999e15i	−0.765174	+	1.32532i
$552$		0			0
$553$	3.87093e13	+	6.70464e13i	0.0318293	+	0.0551299i
$554$	3.73597e14	+	6.47089e14i	0.304158	+	0.526818i
$555$		0			0
$556$	−1.85024e15	+	3.20472e15i	−1.47679	+	2.55787i
$557$	7.26474e14			0.574139			0.287069	−	0.957910i	$-0.407319\pi$
$557$	7.26474e14			0.574139			0.287069	+	0.957910i	$0.407319\pi$
$558$		0			0
$559$	9.61230e14			0.744839
$560$	6.08978e14	−	1.05478e15i	0.467270	−	0.809335i
$561$		0			0
$562$	−1.58239e15	−	2.74078e15i	−1.19059	−	2.06217i
$563$	−6.50146e14	−	1.12609e15i	−0.484412	−	0.839026i	0.515428	−	0.856933i	$-0.327633\pi$
$563$	−6.50146e14	−	1.12609e15i	−0.484412	−	0.839026i	−0.999840	+	0.0179073i	$0.994300\pi$
$564$		0			0
$565$	1.04601e15	−	1.81174e15i	0.764307	−	1.32382i
$566$	5.11413e15			3.70068
$567$		0			0
$568$	−5.52389e15			−3.92039
$569$	8.03645e14	−	1.39195e15i	0.564868	−	0.978379i	−0.432194	−	0.901780i	$-0.642261\pi$
$569$	8.03645e14	−	1.39195e15i	0.564868	−	0.978379i	0.997062	−	0.0765989i	$-0.0244061\pi$
$570$		0			0
$571$	5.18353e14	+	8.97813e14i	0.357377	+	0.618995i	0.987522	−	0.157482i	$-0.0503378\pi$
$571$	5.18353e14	+	8.97813e14i	0.357377	+	0.618995i	−0.630145	+	0.776478i	$0.717004\pi$
$572$	8.54735e14	+	1.48044e15i	0.583651	+	1.01091i
$573$		0			0
$574$	3.64487e14	−	6.31309e14i	0.244155	−	0.422889i
$575$	−1.33836e15			−0.887972
$576$		0			0
$577$	4.84499e13			0.0315374			0.0157687	−	0.999876i	$-0.494980\pi$
$577$	4.84499e13			0.0315374			0.0157687	+	0.999876i	$0.494980\pi$
$578$	1.37993e15	−	2.39011e15i	0.889723	−	1.54105i
$579$		0			0
$580$	3.03153e15	+	5.25077e15i	1.91782	+	3.32177i
$581$	−1.32427e14	−	2.29371e14i	−0.0829867	−	0.143737i
$582$		0			0
$583$	1.74382e14	−	3.02039e14i	0.107232	−	0.185731i
$584$	1.53105e15			0.932652
$585$		0			0
$586$	6.00668e15			3.59085
$587$	3.66564e14	−	6.34908e14i	0.217090	−	0.376012i	−0.736827	−	0.676082i	$-0.763677\pi$
$587$	3.66564e14	−	6.34908e14i	0.217090	−	0.376012i	0.953917	+	0.300070i	$0.0970100\pi$
$588$		0			0
$589$	−8.40200e14	−	1.45527e15i	−0.488370	−	0.845881i
$590$	7.23921e14	+	1.25387e15i	0.416874	+	0.722048i
$591$		0			0
$592$	−2.47365e15	+	4.28448e15i	−1.39820	+	2.42175i
$593$	3.92847e14			0.220000			0.110000	−	0.993932i	$-0.464915\pi$
$593$	3.92847e14			0.220000			0.110000	+	0.993932i	$0.464915\pi$
$594$		0			0
$595$	−1.32215e14			−0.0726839
$596$	8.67003e14	−	1.50169e15i	0.472244	−	0.817950i
$597$		0			0
$598$	1.58853e15	+	2.75142e15i	0.849453	+	1.47130i
$599$	−5.29756e14	−	9.17565e14i	−0.280691	−	0.486171i	0.690864	−	0.722985i	$-0.257230\pi$
$599$	−5.29756e14	−	9.17565e14i	−0.280691	−	0.486171i	−0.971555	+	0.236813i	$0.923897\pi$
$600$		0			0
$601$	−9.98869e14	+	1.73009e15i	−0.519635	+	0.900035i	0.480104	+	0.877212i	$0.340599\pi$
$601$	−9.98869e14	+	1.73009e15i	−0.519635	+	0.900035i	−0.999740	+	0.0228235i	$0.992734\pi$
$602$	2.92788e14			0.150929
$603$		0			0
$604$	9.23371e15			4.67383
$605$	−1.49393e15	+	2.58756e15i	−0.749333	+	1.29788i
$606$		0			0
$607$	−1.28694e15	−	2.22904e15i	−0.633899	−	1.09795i	−0.986747	−	0.162265i	$-0.948120\pi$
$607$	−1.28694e15	−	2.22904e15i	−0.633899	−	1.09795i	0.352848	−	0.935681i	$-0.385213\pi$
$608$	−5.70736e15	−	9.88544e15i	−2.78590	−	4.82532i
$609$		0			0
$610$	−2.20395e15	+	3.81736e15i	−1.05655	+	1.82999i
$611$	2.54986e15			1.21141
$612$		0			0
$613$	8.73092e14			0.407406			0.203703	−	0.979033i	$-0.434702\pi$
$613$	8.73092e14			0.407406			0.203703	+	0.979033i	$0.434702\pi$
$614$	−2.78782e15	+	4.82865e15i	−1.28926	+	2.23306i
$615$		0			0
$616$	1.61944e14	+	2.80495e14i	0.0735649	+	0.127418i
$617$	6.51547e14	+	1.12851e15i	0.293344	+	0.508087i	0.974598	−	0.223960i	$-0.0718985\pi$
$617$	6.51547e14	+	1.12851e15i	0.293344	+	0.508087i	−0.681254	+	0.732047i	$0.738565\pi$
$618$		0			0
$619$	6.93567e14	−	1.20129e15i	0.306754	−	0.531313i	−0.670897	−	0.741551i	$-0.734091\pi$
$619$	6.93567e14	−	1.20129e15i	0.306754	−	0.531313i	0.977650	+	0.210238i	$0.0674239\pi$
$620$	−5.58446e15			−2.44809
$621$		0			0
$622$	−2.73746e15			−1.17897
$623$	−1.05792e13	+	1.83237e13i	−0.00451615	+	0.00782220i
$624$		0			0
$625$	−2.80641e12	−	4.86085e12i	−0.00117709	−	0.00203879i
$626$	1.28099e15	+	2.21873e15i	0.532581	+	0.922457i
$627$		0			0
$628$	9.96671e14	−	1.72628e15i	0.407168	−	0.705236i
$629$	5.37053e14			0.217490
$630$		0			0
$631$	−9.63116e14			−0.383281			−0.191640	−	0.981465i	$-0.561381\pi$
$631$	−9.63116e14			−0.383281			−0.191640	+	0.981465i	$0.561381\pi$
$632$	1.47241e15	−	2.55029e15i	0.580878	−	1.00611i
$633$		0			0
$634$	−1.17212e15	−	2.03017e15i	−0.454445	−	0.787122i
$635$	−2.73785e15	−	4.74209e15i	−1.05233	−	1.82270i
$636$		0			0
$637$	2.08362e15	−	3.60894e15i	0.787141	−	1.36337i
$638$	−1.24201e15			−0.465171
$639$		0			0
$640$	−9.78290e15			−3.60145
$641$	−2.02145e15	+	3.50125e15i	−0.737808	+	1.27792i	0.215672	+	0.976466i	$0.430806\pi$
$641$	−2.02145e15	+	3.50125e15i	−0.737808	+	1.27792i	−0.953480	+	0.301455i	$0.902528\pi$
$642$		0			0
$643$	1.51378e15	+	2.62194e15i	0.543127	+	0.940723i	0.998722	+	0.0505362i	$0.0160930\pi$
$643$	1.51378e15	+	2.62194e15i	0.543127	+	0.940723i	−0.455596	+	0.890187i	$0.650574\pi$
$644$	3.51140e14	+	6.08192e14i	0.124913	+	0.216356i
$645$		0			0
$646$	−1.21644e15	+	2.10693e15i	−0.425413	+	0.736836i
$647$	5.21900e15			1.80973			0.904866	−	0.425697i	$-0.139971\pi$
$647$	5.21900e15			1.80973			0.904866	+	0.425697i	$0.139971\pi$
$648$		0			0
$649$	−2.15235e14			−0.0733783
$650$	−7.41829e15	+	1.28489e16i	−2.50773	+	4.34351i
$651$		0			0
$652$	1.29929e15	+	2.25043e15i	0.431860	+	0.748004i
$653$	−1.85875e13	−	3.21945e13i	−0.00612630	−	0.0106111i	0.862946	−	0.505296i	$-0.168617\pi$
$653$	−1.85875e13	−	3.21945e13i	−0.00612630	−	0.0106111i	−0.869072	+	0.494685i	$0.835283\pi$
$654$		0			0
$655$	1.38094e15	−	2.39186e15i	0.447556	−	0.775190i
$656$	−1.55008e16			−4.98177
$657$		0			0
$658$	7.76680e14			0.245471
$659$	1.34217e15	−	2.32471e15i	0.420666	−	0.728615i	−0.575339	−	0.817915i	$-0.695130\pi$
$659$	1.34217e15	−	2.32471e15i	0.420666	−	0.728615i	0.996005	+	0.0893002i	$0.0284630\pi$
$660$		0			0
$661$	1.00239e15	+	1.73618e15i	0.308978	+	0.535165i	0.978139	−	0.207952i	$-0.0666799\pi$
$661$	1.00239e15	+	1.73618e15i	0.308978	+	0.535165i	−0.669161	+	0.743117i	$0.733347\pi$
$662$	4.21283e15	+	7.29683e15i	1.28782	+	2.23057i
$663$		0			0
$664$	−5.03722e15	+	8.72471e15i	−1.51449	+	2.62317i
$665$	−1.59635e15			−0.476004
$666$		0			0
$667$	−1.67513e15			−0.491312
$668$	7.67551e15	−	1.32944e16i	2.23273	−	3.86721i
$669$		0			0
$670$	−6.49630e15	−	1.12519e16i	−1.85889	−	3.21970i
$671$	−3.27638e14	−	5.67486e14i	−0.0929867	−	0.161058i
$672$		0			0
$673$	3.03717e15	−	5.26053e15i	0.847981	−	1.46875i	−0.0350255	−	0.999386i	$-0.511151\pi$
$673$	3.03717e15	−	5.26053e15i	0.847981	−	1.46875i	0.883007	−	0.469360i	$-0.155515\pi$
$674$	−9.25278e15			−2.56238
$675$		0			0
$676$	1.58486e16			4.31801
$677$	9.04998e14	−	1.56750e15i	0.244574	−	0.423614i	−0.717438	−	0.696622i	$-0.754685\pi$
$677$	9.04998e14	−	1.56750e15i	0.244574	−	0.423614i	0.962012	+	0.273008i	$0.0880187\pi$
$678$		0			0
$679$	−1.95348e14	−	3.38352e14i	−0.0519427	−	0.0899674i
$680$	2.51458e15	+	4.35537e15i	0.663232	+	1.14875i
$681$		0			0
$682$	5.71986e14	−	9.90709e14i	0.148447	−	0.257118i
$683$	−2.47421e15			−0.636976			−0.318488	−	0.947927i	$-0.603175\pi$
$683$	−2.47421e15			−0.636976			−0.318488	+	0.947927i	$0.603175\pi$
$684$		0			0
$685$	1.77111e15			0.448690
$686$	1.28872e15	−	2.23213e15i	0.323874	−	0.560967i
$687$		0			0
$688$	−3.11291e15	−	5.39172e15i	−0.769892	−	1.33349i
$689$	−2.60727e15	−	4.51592e15i	−0.639706	−	1.10800i
$690$		0			0
$691$	2.98889e15	−	5.17691e15i	0.721740	−	1.25009i	−0.238561	−	0.971127i	$-0.576676\pi$
$691$	2.98889e15	−	5.17691e15i	0.721740	−	1.25009i	0.960302	−	0.278964i	$-0.0899909\pi$
$692$	3.39921e15			0.814319
$693$		0			0
$694$	−1.25624e16			−2.96208
$695$	3.86165e15	−	6.68858e15i	0.903352	−	1.56465i
$696$		0			0
$697$	8.41345e14	+	1.45725e15i	0.193729	+	0.335548i
$698$	−6.40127e15	−	1.10873e16i	−1.46238	−	2.53292i
$699$		0			0
$700$	−1.63979e15	+	2.84020e15i	−0.368764	+	0.638718i
$701$	1.45232e14			0.0324051			0.0162026	−	0.999869i	$-0.494842\pi$
$701$	1.45232e14			0.0324051			0.0162026	+	0.999869i	$0.494842\pi$
$702$		0			0
$703$	6.48433e15			1.42433
$704$	1.79292e15	−	3.10544e15i	0.390762	−	0.676819i
$705$		0			0
$706$	−3.55360e15	−	6.15502e15i	−0.762505	−	1.32070i
$707$	2.49420e14	+	4.32009e14i	0.0531038	+	0.0919784i
$708$		0			0
$709$	−2.27704e15	+	3.94394e15i	−0.477327	+	0.826754i	−0.999662	−	0.0259858i	$-0.991728\pi$
$709$	−2.27704e15	+	3.94394e15i	−0.477327	+	0.826754i	0.522336	+	0.852740i	$0.325061\pi$
$710$	1.85346e16			3.85533
$711$		0			0
$712$	8.04815e14			0.164837
$713$	7.71451e14	−	1.33619e15i	0.156789	−	0.271567i
$714$		0			0
$715$	−1.78392e15	−	3.08984e15i	−0.357020	−	0.618377i
$716$	9.91034e15	+	1.71652e16i	1.96819	+	3.40901i
$717$		0			0
$718$	4.75180e15	−	8.23037e15i	0.929339	−	1.60966i
$719$	2.31846e15			0.449977			0.224988	−	0.974361i	$-0.427766\pi$
$719$	2.31846e15			0.449977			0.224988	+	0.974361i	$0.427766\pi$
$720$		0			0
$721$	4.83168e14			0.0923537
$722$	−9.65430e15	+	1.67217e16i	−1.83133	+	3.17195i
$723$		0			0
$724$	−3.92093e15	−	6.79125e15i	−0.732533	−	1.26878i
$725$	−3.91136e15	−	6.77467e15i	−0.725217	−	1.25611i
$726$		0			0
$727$	1.01125e15	−	1.75154e15i	0.184680	−	0.319875i	−0.758789	−	0.651337i	$-0.774209\pi$
$727$	1.01125e15	−	1.75154e15i	0.184680	−	0.319875i	0.943469	+	0.331462i	$0.107542\pi$
$728$	4.84260e15			0.877720
$729$		0			0
$730$	−5.13722e15			−0.917175
$731$	−3.37922e14	+	5.85297e14i	−0.0598784	+	0.103712i
$732$		0			0
$733$	3.34140e15	+	5.78747e15i	0.583252	+	1.01022i	0.995091	+	0.0989651i	$0.0315532\pi$
$733$	3.34140e15	+	5.78747e15i	0.583252	+	1.01022i	−0.411839	+	0.911257i	$0.635113\pi$
$734$	5.49091e15	+	9.51053e15i	0.951296	+	1.64769i
$735$		0			0
$736$	5.24036e15	−	9.07657e15i	0.894402	−	1.54915i
$737$	1.93147e15			0.327203
$738$		0			0
$739$	−5.14189e15			−0.858180			−0.429090	−	0.903262i	$-0.641166\pi$
$739$	−5.14189e15			−0.858180			−0.429090	+	0.903262i	$0.641166\pi$
$740$	1.07747e16	−	1.86623e16i	1.78496	−	3.09165i
$741$		0			0
$742$	−7.94167e14	−	1.37554e15i	−0.129626	−	0.224518i
$743$	−1.90712e15	−	3.30323e15i	−0.308986	−	0.535180i	0.669155	−	0.743123i	$-0.266656\pi$
$743$	−1.90712e15	−	3.30323e15i	−0.308986	−	0.535180i	−0.978141	+	0.207943i	$0.933323\pi$
$744$		0			0
$745$	−1.80953e15	+	3.13419e15i	−0.288872	+	0.500341i
$746$	1.19173e16			1.88849
$747$		0			0
$748$	−1.20193e15			−0.187681
$749$	−5.67082e14	+	9.82215e14i	−0.0879014	+	0.152250i
$750$		0			0
$751$	−2.90785e14	−	5.03655e14i	−0.0444174	−	0.0769331i	0.842962	−	0.537973i	$-0.180810\pi$
$751$	−2.90785e14	−	5.03655e14i	−0.0444174	−	0.0769331i	−0.887379	+	0.461040i	$0.847476\pi$
$752$	−8.25763e15	−	1.43026e16i	−1.25215	−	2.16879i
$753$		0			0
$754$	−9.28498e15	+	1.60821e16i	−1.38752	+	2.40325i
$755$	−1.92717e16			−2.85899
$756$		0			0
$757$	4.29778e15			0.628372			0.314186	−	0.949362i	$-0.398269\pi$
$757$	4.29778e15			0.628372			0.314186	+	0.949362i	$0.398269\pi$
$758$	−1.03049e16	+	1.78486e16i	−1.49576	+	2.59074i
$759$		0			0
$760$	3.03608e16	+	5.25864e16i	4.34348	+	7.52313i
$761$	3.03268e15	+	5.25275e15i	0.430735	+	0.746055i	0.996937	−	0.0782114i	$-0.0249209\pi$
$761$	3.03268e15	+	5.25275e15i	0.430735	+	0.746055i	−0.566201	+	0.824267i	$0.691588\pi$
$762$		0			0
$763$	5.61963e14	−	9.73349e14i	0.0786725	−	0.136265i
$764$	−1.28860e16			−1.79103
$765$		0			0
$766$	5.86188e15			0.803117
$767$	−1.60904e15	+	2.78695e15i	−0.218874	+	0.379100i
$768$		0			0
$769$	5.11903e15	+	8.86641e15i	0.686424	+	1.18892i	0.972987	+	0.230860i	$0.0741539\pi$
$769$	5.11903e15	+	8.86641e15i	0.686424	+	1.18892i	−0.286563	+	0.958061i	$0.592513\pi$
$770$	−5.43378e14	−	9.41158e14i	−0.0723441	−	0.125304i
$771$		0			0
$772$	2.87442e15	−	4.97864e15i	0.377272	−	0.653454i
$773$	4.29417e15			0.559619			0.279810	−	0.960056i	$-0.409729\pi$
$773$	4.29417e15			0.559619			0.279810	+	0.960056i	$0.409729\pi$
$774$		0			0
$775$	7.20520e15			0.925735
$776$	−7.43056e15	+	1.28701e16i	−0.947943	+	1.64189i
$777$		0			0
$778$	−7.22563e15	−	1.25152e16i	−0.908841	−	1.57416i
$779$	1.01583e16	+	1.75947e16i	1.26872	+	2.19749i
$780$		0			0
$781$	−1.37767e15	+	2.38619e15i	−0.169654	+	0.293849i
$782$	−2.23380e15			−0.273154
$783$		0			0
$784$	−2.69910e16			−3.25447
$785$	−2.08016e15	+	3.60294e15i	−0.249065	+	0.431394i
$786$		0			0
$787$	−5.88679e15	−	1.01962e16i	−0.695052	−	1.20387i	−0.970163	−	0.242453i	$-0.922048\pi$
$787$	−5.88679e15	−	1.01962e16i	−0.695052	−	1.20387i	0.275111	−	0.961413i	$-0.411285\pi$
$788$	9.90834e15	+	1.71617e16i	1.16173	+	2.01218i
$789$		0			0
$790$	−4.94044e15	+	8.55710e15i	−0.571238	+	0.989413i
$791$	1.41634e15			0.162628
$792$		0			0
$793$	−9.79736e15			−1.10945
$794$	5.72023e15	−	9.90773e15i	0.643281	−	1.11420i
$795$		0			0
$796$	1.18988e16	+	2.06093e16i	1.31972	+	2.28582i
$797$	−4.34099e15	−	7.51881e15i	−0.478154	−	0.828187i	0.521532	−	0.853232i	$-0.325361\pi$
$797$	−4.34099e15	−	7.51881e15i	−0.478154	−	0.828187i	−0.999686	+	0.0250444i	$0.992027\pi$
$798$		0			0
$799$	−8.96406e14	+	1.55262e15i	−0.0973862	+	0.168678i
$800$	4.89439e16			5.28085
$801$		0			0
$802$	−2.53741e16			−2.70042
$803$	3.81848e14	−	6.61380e14i	0.0403603	−	0.0699061i
$804$		0			0
$805$	−7.32866e14	−	1.26936e15i	−0.0764095	−	0.132345i
$806$	−8.55204e15	−	1.48126e16i	−0.885578	−	1.53387i
$807$		0			0
$808$	9.48736e15	−	1.64326e16i	0.969132	−	1.67859i
$809$	1.41762e16			1.43827			0.719137	−	0.694868i	$-0.244537\pi$
$809$	1.41762e16			1.43827			0.719137	+	0.694868i	$0.244537\pi$
$810$		0			0
$811$	−5.37994e15			−0.538472			−0.269236	−	0.963074i	$-0.586771\pi$
$811$	−5.37994e15			−0.538472			−0.269236	+	0.963074i	$0.586771\pi$
$812$	−2.05241e15	+	3.55489e15i	−0.204036	+	0.353401i
$813$		0			0
$814$	2.20718e15	+	3.82295e15i	0.216473	+	0.374942i
$815$	−2.71175e15	−	4.69689e15i	−0.264170	−	0.457555i
$816$		0			0
$817$	−4.08004e15	+	7.06683e15i	−0.392141	+	0.679209i
$818$	8.30723e15			0.793073
$819$		0			0
$820$	6.75182e16			6.35982
$821$	2.59589e14	−	4.49622e14i	0.0242884	−	0.0420688i	−0.853626	−	0.520887i	$-0.825601\pi$
$821$	2.59589e14	−	4.49622e14i	0.0242884	−	0.0420688i	0.877914	+	0.478818i	$0.158935\pi$
$822$		0			0
$823$	−3.00259e15	−	5.20064e15i	−0.277203	−	0.480129i	0.693486	−	0.720470i	$-0.256074\pi$
$823$	−3.00259e15	−	5.20064e15i	−0.277203	−	0.480129i	−0.970688	+	0.240341i	$0.922741\pi$
$824$	−9.18928e15	−	1.59163e16i	−0.842718	−	1.45963i
$825$		0			0
$826$	−4.90110e14	+	8.48896e14i	−0.0443510	+	0.0768182i
$827$	−1.03022e15			−0.0926085			−0.0463043	−	0.998927i	$-0.514744\pi$
$827$	−1.03022e15			−0.0926085			−0.0463043	+	0.998927i	$0.514744\pi$
$828$		0			0
$829$	−1.78974e16			−1.58759			−0.793796	−	0.608184i	$-0.791898\pi$
$829$	−1.78974e16			−1.58759			−0.793796	+	0.608184i	$0.791898\pi$
$830$	1.69016e16	−	2.92745e16i	1.48936	−	2.57964i
$831$		0			0
$832$	−2.68069e16	−	4.64309e16i	−2.33114	−	4.03765i
$833$	1.46500e15	+	2.53746e15i	0.126558	+	0.219205i
$834$		0			0
$835$	−1.60196e16	+	2.77468e16i	−1.36577	+	2.36557i
$836$	−1.45120e16			−1.22912
$837$		0			0
$838$	1.63344e16			1.36540
$839$	8.61564e15	−	1.49227e16i	0.715479	−	1.23925i	−0.247296	−	0.968940i	$-0.579542\pi$
$839$	8.61564e15	−	1.49227e16i	0.715479	−	1.23925i	0.962775	−	0.270306i	$-0.0871248\pi$
$840$		0			0
$841$	1.20467e15	+	2.08655e15i	0.0987394	+	0.171022i
$842$	4.46624e15	+	7.73576e15i	0.363686	+	0.629922i
$843$		0			0
$844$	2.55042e16	−	4.41746e16i	2.04988	−	3.55050i
$845$	−3.30777e16			−2.64133
$846$		0			0
$847$	−2.02284e15			−0.159442
$848$	−1.68871e16	+	2.92493e16i	−1.32245	+	2.29054i
$849$		0			0
$850$	−5.21582e15	−	9.03406e15i	−0.403198	−	0.698359i
$851$	2.97688e15	+	5.15610e15i	0.228638	+	0.396012i
$852$		0			0
$853$	−2.79547e15	+	4.84190e15i	−0.211951	+	0.367110i	−0.952325	−	0.305085i	$-0.901315\pi$
$853$	−2.79547e15	+	4.84190e15i	−0.211951	+	0.367110i	0.740374	+	0.672195i	$0.234648\pi$
$854$	−2.98425e15			−0.224810
$855$		0			0
$856$	4.31409e16			3.20836
$857$	3.56838e15	−	6.18062e15i	0.263680	−	0.456707i	−0.703537	−	0.710659i	$-0.748397\pi$
$857$	3.56838e15	−	6.18062e15i	0.263680	−	0.456707i	0.967217	+	0.253952i	$0.0817304\pi$
$858$		0			0
$859$	2.79683e15	+	4.84425e15i	0.204035	+	0.353398i	0.949825	−	0.312783i	$-0.101261\pi$
$859$	2.79683e15	+	4.84425e15i	0.204035	+	0.353398i	−0.745790	+	0.666181i	$0.767928\pi$
$860$	1.35591e16	+	2.34851e16i	0.982858	+	1.70236i
$861$		0			0
$862$	1.04667e15	−	1.81288e15i	0.0749063	−	0.129741i
$863$	2.08114e16			1.47993			0.739966	−	0.672645i	$-0.234842\pi$
$863$	2.08114e16			1.47993			0.739966	+	0.672645i	$0.234842\pi$
$864$		0			0
$865$	−7.09452e15			−0.498120
$866$	2.08304e16	−	3.60793e16i	1.45328	−	2.51715i
$867$		0			0
$868$	−1.89040e15	−	3.27427e15i	−0.130225	−	0.225557i
$869$	−7.34444e14	−	1.27209e15i	−0.0502747	−	0.0870784i
$870$		0			0
$871$	1.44392e16	−	2.50094e16i	0.975985	−	1.69046i
$872$	−4.27515e16			−2.87151
$873$		0			0
$874$	−2.69707e16			−1.78887
$875$	1.30862e15	−	2.26660e15i	0.0862520	−	0.149393i
$876$		0			0
$877$	4.48976e15	+	7.77650e15i	0.292231	+	0.506158i	0.974337	−	0.225095i	$-0.0722692\pi$
$877$	4.48976e15	+	7.77650e15i	0.292231	+	0.506158i	−0.682106	+	0.731253i	$0.738936\pi$
$878$	−2.26646e15	−	3.92563e15i	−0.146598	−	0.253916i
$879$		0			0
$880$	−1.15543e16	+	2.00127e16i	−0.738058	+	1.27835i
$881$	−1.86114e16			−1.18144			−0.590721	−	0.806876i	$-0.701157\pi$
$881$	−1.86114e16			−1.18144			−0.590721	+	0.806876i	$0.701157\pi$
$882$		0			0
$883$	−2.75230e16			−1.72549			−0.862743	−	0.505642i	$-0.831255\pi$
$883$	−2.75230e16			−1.72549			−0.862743	+	0.505642i	$0.831255\pi$
$884$	−8.98534e15	+	1.55631e16i	−0.559818	+	0.969633i
$885$		0			0
$886$	7.21344e15	+	1.24940e16i	0.443871	+	0.768807i
$887$	−4.56886e15	−	7.91350e15i	−0.279401	−	0.483937i	0.691835	−	0.722056i	$-0.256803\pi$
$887$	−4.56886e15	−	7.91350e15i	−0.279401	−	0.483937i	−0.971236	+	0.238119i	$0.923469\pi$
$888$		0			0
$889$	1.85358e15	−	3.21050e15i	0.111957	−	0.193915i
$890$	−2.70043e15			−0.162102
$891$		0			0
$892$	−4.71976e16			−2.79842
$893$	−1.08231e16	+	1.87462e16i	−0.637778	+	1.10466i
$894$		0			0
$895$	−2.06839e16	−	3.58256e16i	−1.20394	−	2.08529i
$896$	−3.31162e15	−	5.73589e15i	−0.191578	−	0.331823i
$897$		0			0
$898$	9.45800e15	−	1.63817e16i	0.540480	−	0.936138i
$899$	9.01827e15			0.512206
$900$		0			0
$901$	3.66636e15			0.205707
$902$	−6.91552e15	+	1.19780e16i	−0.385646	+	0.667959i
$903$		0			0
$904$	−2.69371e16	−	4.66564e16i	−1.48397	−	2.57030i
$905$	8.18340e15	+	1.41741e16i	0.448091	+	0.776117i
$906$		0			0
$907$	−1.20959e16	+	2.09507e16i	−0.654332	+	1.13334i	0.327729	+	0.944772i	$0.393717\pi$
$907$	−1.20959e16	+	2.09507e16i	−0.654332	+	1.13334i	−0.982061	+	0.188564i	$0.939617\pi$
$908$	−6.83448e16			−3.67480
$909$		0			0
$910$	−1.62486e16			−0.863154
$911$	6.72908e15	−	1.16551e16i	0.355308	−	0.615411i	−0.631863	−	0.775080i	$-0.717709\pi$
$911$	6.72908e15	−	1.16551e16i	0.355308	−	0.615411i	0.987171	+	0.159669i	$0.0510427\pi$
$912$		0			0
$913$	2.51258e15	+	4.35192e15i	0.131078	+	0.227035i
$914$	−1.56279e16	−	2.70684e16i	−0.810396	−	1.40365i
$915$		0			0
$916$	8.24097e15	−	1.42738e16i	0.422234	−	0.731331i
$917$	1.86985e15			0.0952305
$918$		0			0
$919$	2.13639e16			1.07509			0.537546	−	0.843234i	$-0.319351\pi$
$919$	2.13639e16			1.07509			0.537546	+	0.843234i	$0.319351\pi$
$920$	−2.78765e16	+	4.82835e16i	−1.39446	+	2.41527i
$921$		0			0
$922$	3.31977e15	+	5.75001e15i	0.164092	+	0.284216i
$923$	2.05982e16	+	3.56771e16i	1.01209	+	1.75299i
$924$		0			0
$925$	−1.39017e16	+	2.40785e16i	−0.674977	+	1.16909i
$926$	−3.30608e16			−1.59570
$927$		0			0
$928$	6.12599e16			2.92188
$929$	−1.76745e16	+	3.06131e16i	−0.838033	+	1.45151i	0.0535048	+	0.998568i	$0.482961\pi$
$929$	−1.76745e16	+	3.06131e16i	−0.838033	+	1.45151i	−0.891537	+	0.452947i	$0.850373\pi$
$930$		0			0
$931$	1.76883e16	+	3.06370e16i	0.828825	+	1.43557i
$932$	−4.10831e16	−	7.11580e16i	−1.91371	−	3.31464i
$933$		0			0
$934$	−1.61714e16	+	2.80096e16i	−0.744456	+	1.28944i
$935$	2.50856e15			0.114805
$936$		0			0
$937$	1.94562e16			0.880017			0.440008	−	0.897994i	$-0.354975\pi$
$937$	1.94562e16			0.880017			0.440008	+	0.897994i	$0.354975\pi$
$938$	4.39814e15	−	7.61780e15i	0.197767	−	0.342542i
$939$		0			0
$940$	3.59684e16	+	6.22991e16i	1.59852	+	2.76872i
$941$	2.21948e16	+	3.84425e16i	0.980636	+	1.69851i	0.659920	+	0.751336i	$0.270590\pi$
$941$	2.21948e16	+	3.84425e16i	0.980636	+	1.69851i	0.320717	+	0.947175i	$0.396076\pi$
$942$		0			0
$943$	−9.32712e15	+	1.61550e16i	−0.407318	+	0.705495i
$944$	2.08433e16			0.904943
$945$		0			0
$946$	−5.55516e15			−0.238394
$947$	3.38488e15	−	5.86279e15i	0.144417	−	0.250138i	−0.784738	−	0.619827i	$-0.787203\pi$
$947$	3.38488e15	−	5.86279e15i	0.144417	−	0.250138i	0.929155	+	0.369690i	$0.120536\pi$
$948$		0			0
$949$	−5.70919e15	−	9.88861e15i	−0.240774	−	0.417033i
$950$	−6.29753e16	−	1.09076e17i	−2.64053	−	4.57353i
$951$		0			0
$952$	−1.70242e15	+	2.94868e15i	−0.0705609	+	0.122215i
$953$	3.24089e16			1.33553			0.667764	−	0.744373i	$-0.267252\pi$
$953$	3.24089e16			1.33553			0.667764	+	0.744373i	$0.267252\pi$
$954$		0			0
$955$	2.68944e16			1.09558
$956$	6.25614e16	−	1.08360e17i	2.53389	−	4.38883i
$957$		0			0
$958$	−2.21409e16	−	3.83491e16i	−0.886512	−	1.53548i
$959$	5.99538e14	+	1.03843e15i	0.0238679	+	0.0413405i
$960$		0			0
$961$	8.55105e15	−	1.48108e16i	0.336543	−	0.582910i
$962$	6.60013e16			2.58279
$963$		0			0
$964$	8.65943e16			3.35016
$965$	−5.99921e15	+	1.03909e16i	−0.230778	+	0.399719i
$966$		0			0
$967$	7.89694e15	+	1.36779e16i	0.300340	+	0.520204i	0.976213	−	0.216814i	$-0.0695665\pi$
$967$	7.89694e15	+	1.36779e16i	0.300340	+	0.520204i	−0.675873	+	0.737018i	$0.736233\pi$
$968$	3.84721e16	+	6.66356e16i	1.45489	+	2.51995i
$969$		0			0
$970$	2.49321e16	−	4.31837e16i	0.932212	−	1.61464i
$971$	−1.26754e16			−0.471254			−0.235627	−	0.971844i	$-0.575714\pi$
$971$	−1.26754e16			−0.471254			−0.235627	+	0.971844i	$0.575714\pi$
$972$		0			0
$973$	5.22885e15			0.192214
$974$	−4.03870e15	+	6.99523e15i	−0.147627	+	0.255698i
$975$		0			0
$976$	3.17284e16	+	5.49552e16i	1.14676	+	1.98625i
$977$	1.57622e16	+	2.73009e16i	0.566496	+	0.981200i	0.996909	+	0.0785679i	$0.0250347\pi$
$977$	1.57622e16	+	2.73009e16i	0.566496	+	0.981200i	−0.430413	+	0.902632i	$0.641632\pi$
$978$		0			0
$979$	2.00722e14	−	3.47661e14i	0.00713331	−	0.0123553i
$980$	1.17567e17			4.15471
$981$		0			0
$982$	−8.22777e16			−2.87521
$983$	−8.78298e15	+	1.52126e16i	−0.305209	+	0.528638i	−0.977308	−	0.211824i	$-0.932060\pi$
$983$	−8.78298e15	+	1.52126e16i	−0.305209	+	0.528638i	0.672099	+	0.740462i	$0.265393\pi$
$984$		0			0
$985$	−2.06797e16	−	3.58184e16i	−0.710634	−	1.23085i
$986$	−6.52829e15	−	1.13073e16i	−0.223088	−	0.386400i
$987$		0			0
$988$	−1.08488e17	+	1.87907e17i	−3.66623	+	6.35009i
$989$	−7.49237e15			−0.251791
$990$		0			0
$991$	3.80581e16			1.26486			0.632430	−	0.774618i	$-0.282058\pi$
$991$	3.80581e16			1.26486			0.632430	+	0.774618i	$0.282058\pi$
$992$	−2.82121e16	+	4.88647e16i	−0.932439	+	1.61503i
$993$		0			0
$994$	6.27415e15	+	1.08672e16i	0.205083	+	0.355214i
$995$	−2.48340e16	−	4.30138e16i	−0.807272	−	1.39824i
$996$		0			0
$997$	2.11041e16	−	3.65534e16i	0.678491	−	1.17518i	−0.296944	−	0.954895i	$-0.595967\pi$
$997$	2.11041e16	−	3.65534e16i	0.678491	−	1.17518i	0.975435	−	0.220286i	$-0.0706992\pi$
$998$	3.87928e15			0.124032
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.12.c.l.55.1		12
3.2	odd	2		81.12.c.k.55.6		12
9.2	odd	6		81.12.a.b.1.1	yes	6
9.4	even	3	inner	81.12.c.l.28.1		12
9.5	odd	6		81.12.c.k.28.6		12
9.7	even	3		81.12.a.a.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.12.a.a.1.6	✓	6	9.7	even	3
81.12.a.b.1.1	yes	6	9.2	odd	6
81.12.c.k.28.6		12	9.5	odd	6
81.12.c.k.55.6		12	3.2	odd	2
81.12.c.l.28.1		12	9.4	even	3	inner
81.12.c.l.55.1		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-43.2040 + 74.8315i) q^{2} +(-2709.16 - 4692.41i) q^{4} +(5654.31 + 9793.56i) q^{5} +(-3828.09 + 6630.45i) q^{7} +291223. q^{8} -977155. q^{10} +(72631.6 - 125802. i) q^{11} +(-1.08595e6 - 1.88092e6i) q^{13} +(-330778. - 572924. i) q^{14} +(-7.03363e6 + 1.21826e7i) q^{16} +1.52707e6 q^{17} +1.84377e7 q^{19} +(3.06369e7 - 5.30647e7i) q^{20} +(6.27595e6 + 1.08703e7i) q^{22} +(8.46452e6 + 1.46610e7i) q^{23} +(-3.95285e7 + 6.84653e7i) q^{25} +1.87670e8 q^{26} +4.14837e7 q^{28} +(-4.94752e7 + 8.56935e7i) q^{29} +(-4.55697e7 - 7.89290e7i) q^{31} +(-3.09549e8 - 5.36154e8i) q^{32} +(-6.59755e7 + 1.14273e8i) q^{34} -8.65810e7 q^{35} +3.51689e8 q^{37} +(-7.96582e8 + 1.37972e9i) q^{38} +(1.64667e9 + 2.85211e9i) q^{40} +(5.50954e8 + 9.54281e8i) q^{41} +(-2.21288e8 + 3.83281e8i) q^{43} -7.87084e8 q^{44} -1.46280e9 q^{46} +(-5.87011e8 + 1.01673e9i) q^{47} +(9.59355e8 + 1.66165e9i) q^{49} +(-3.41557e9 - 5.91595e9i) q^{50} +(-5.88404e9 + 1.01915e10i) q^{52} +2.40091e9 q^{53} +1.64273e9 q^{55} +(-1.11483e9 + 1.93094e9i) q^{56} +(-4.27505e9 - 7.40460e9i) q^{58} +(-7.40846e8 - 1.28318e9i) q^{59} +(2.25548e9 - 3.90660e9i) q^{61} +7.87516e9 q^{62} +2.46852e10 q^{64} +(1.22806e10 - 2.12706e10i) q^{65} +(6.64818e9 + 1.15150e10i) q^{67} +(-4.13708e9 - 7.16564e9i) q^{68} +(3.74064e9 - 6.47898e9i) q^{70} -1.89679e10 q^{71} +5.25732e9 q^{73} +(-1.51944e10 + 2.63174e10i) q^{74} +(-4.99508e10 - 8.65173e10i) q^{76} +(5.56081e8 + 9.63161e8i) q^{77} +(5.05595e9 - 8.75716e9i) q^{79} -1.59081e11 q^{80} -9.52136e10 q^{82} +(-1.72968e10 + 2.99589e10i) q^{83} +(8.63453e9 + 1.49554e10i) q^{85} +(-1.91210e10 - 3.31185e10i) q^{86} +(2.11520e10 - 3.66364e10i) q^{88} +2.76357e9 q^{89} +1.66285e10 q^{91} +(4.58635e10 - 7.94380e10i) q^{92} +(-5.07224e10 - 8.78537e10i) q^{94} +(1.04253e11 + 1.80571e11i) q^{95} +(-2.55150e10 + 4.41933e10i) q^{97} -1.65792e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{2} - 8709 q^{4} + 10278 q^{5} - 22944 q^{7} + 197010 q^{8} - 465462 q^{10} + 668448 q^{11} - 1861770 q^{13} + 455508 q^{14} - 15304209 q^{16} + 24634260 q^{17} + 35867472 q^{19} + 83336409 q^{20}+ \cdots - 1101686223906 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 8709 * q^4 + 10278 * q^5 - 22944 * q^7 + 197010 * q^8 - 465462 * q^10 + 668448 * q^11 - 1861770 * q^13 + 455508 * q^14 - 15304209 * q^16 + 24634260 * q^17 + 35867472 * q^19 + 83336409 * q^20 - 50304960 * q^22 - 13446360 * q^23 - 94232976 * q^25 + 343544994 * q^26 + 290261256 * q^28 + 105349014 * q^29 - 180650424 * q^31 - 267341121 * q^32 + 384127731 * q^34 - 1387830096 * q^35 - 314305788 * q^37 - 1912591260 * q^38 + 777367917 * q^40 + 625918284 * q^41 + 843299808 * q^43 - 10808909856 * q^44 - 2412142560 * q^46 - 544330872 * q^47 - 1603672110 * q^49 - 7200193860 * q^50 - 10297810587 * q^52 - 7976661624 * q^53 + 21041467056 * q^55 + 4513671900 * q^56 - 26453162025 * q^58 - 13877974224 * q^59 - 13543180554 * q^61 - 46131549768 * q^62 + 88547470338 * q^64 + 13506091074 * q^65 - 17368622760 * q^67 - 80563033863 * q^68 - 54376835508 * q^70 - 139458339360 * q^71 + 90107169684 * q^73 - 72968645457 * q^74 - 90059767140 * q^76 - 79651538712 * q^77 - 46910199000 * q^79 - 691221292074 * q^80 + 88254243756 * q^82 - 107141792328 * q^83 - 25423165494 * q^85 - 307626642216 * q^86 - 229083441120 * q^88 - 561148241724 * q^89 + 320631230928 * q^91 - 86149640592 * q^92 - 366645472236 * q^94 - 191492732304 * q^95 - 270295503060 * q^97 - 1101686223906 * q^98

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