LMFDB - Embedded newform 81.11.d.e.53.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,11,Mod(26,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.26"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

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

Newform invariants

comment:select newform

sage:traces = [8,0,0,548] 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:	$51.4639374666$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 86x^{6} + 6052x^{4} + 115584x^{2} + 1806336 $ x^8 + 86x^6 + 6052x^4 + 115584*x^2 + 1806336
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{19} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.3
Root			$2.26538 - 3.92375i$ of defining polynomial
Character	$\chi$	$=$	81.53
Dual form			81.11.d.e.26.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(20.3884 - 11.7713i) q^{2} +(-234.875 + 406.815i) q^{4} +(3831.75 + 2212.26i) q^{5} +(10784.0 + 18678.4i) q^{7} +35166.6i q^{8} +104164. q^{10} +(210295. - 121414. i) q^{11} +(199052. - 344768. i) q^{13} +(439737. + 253882. i) q^{14} +(173444. + 300414. i) q^{16} +2.02619e6i q^{17} -2.77192e6 q^{19} +(-1.79996e6 + 1.03921e6i) q^{20} +(2.85839e6 - 4.95088e6i) q^{22} +(2.14688e6 + 1.23950e6i) q^{23} +(4.90538e6 + 8.49636e6i) q^{25} -9.37237e6i q^{26} -1.01315e7 q^{28} +(-7.90991e6 + 4.56679e6i) q^{29} +(9.07315e6 - 1.57152e7i) q^{31} +(-2.41136e7 - 1.39220e7i) q^{32} +(2.38509e7 + 4.13109e7i) q^{34} +9.54280e7i q^{35} +1.14330e7 q^{37} +(-5.65150e7 + 3.26290e7i) q^{38} +(-7.77977e7 + 1.34750e8i) q^{40} +(1.18731e8 + 6.85496e7i) q^{41} +(-4.93948e7 - 8.55544e7i) q^{43} +1.14068e8i q^{44} +5.83620e7 q^{46} +(1.22806e8 - 7.09022e7i) q^{47} +(-9.13512e7 + 1.58225e8i) q^{49} +(2.00026e8 + 1.15485e8i) q^{50} +(9.35045e7 + 1.61955e8i) q^{52} -1.39084e8i q^{53} +1.07440e9 q^{55} +(-6.56857e8 + 3.79237e8i) q^{56} +(-1.07514e8 + 1.86219e8i) q^{58} +(-9.24898e8 - 5.33990e8i) q^{59} +(7.24880e8 + 1.25553e9i) q^{61} -4.27210e8i q^{62} -1.01073e9 q^{64} +(1.52543e9 - 8.80709e8i) q^{65} +(-7.23067e8 + 1.25239e9i) q^{67} +(-8.24286e8 - 4.75902e8i) q^{68} +(1.12331e9 + 1.94563e9i) q^{70} -1.33807e9i q^{71} -1.46812e9 q^{73} +(2.33101e8 - 1.34581e8i) q^{74} +(6.51053e8 - 1.12766e9i) q^{76} +(4.53564e9 + 2.61865e9i) q^{77} +(2.47690e9 + 4.29012e9i) q^{79} +1.53481e9i q^{80} +3.22766e9 q^{82} +(4.85531e8 - 2.80322e8i) q^{83} +(-4.48247e9 + 7.76386e9i) q^{85} +(-2.01417e9 - 1.16288e9i) q^{86} +(4.26972e9 + 7.39537e9i) q^{88} -4.73263e9i q^{89} +8.58629e9 q^{91} +(-1.00850e9 + 5.82255e8i) q^{92} +(1.66922e9 - 2.89117e9i) q^{94} +(-1.06213e10 - 6.13220e9i) q^{95} +(-6.08507e9 - 1.05396e10i) q^{97} +4.30128e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 548 q^{4} - 20516 q^{7} - 399600 q^{10} + 262420 q^{13} + 3207800 q^{16} - 16467032 q^{19} + 21085704 q^{22} + 47203580 q^{25} - 135208424 q^{28} + 46994920 q^{31} + 78985368 q^{34} + 216172888 q^{37}+ \cdots - 12969797468 q^{97}+O(q^{100}) $ 8 * q + 548 * q^4 - 20516 * q^7 - 399600 * q^10 + 262420 * q^13 + 3207800 * q^16 - 16467032 * q^19 + 21085704 * q^22 + 47203580 * q^25 - 135208424 * q^28 + 46994920 * q^31 + 78985368 * q^34 + 216172888 * q^37 - 196812720 * q^40 - 78251000 * q^43 + 1765291536 * q^46 - 1826240448 * q^49 + 771022300 * q^52 + 2069150400 * q^55 - 1267544592 * q^58 + 3222389524 * q^61 - 2332527904 * q^64 - 1972286516 * q^67 + 17482328280 * q^70 + 8155197880 * q^73 + 603762388 * q^76 + 10402780252 * q^79 - 15891105312 * q^82 - 19825132320 * q^85 + 19783893168 * q^88 + 68321793560 * q^91 - 22345655544 * q^94 - 12969797468 * q^97

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	20.3884	−	11.7713i	0.637138	−	0.367852i	−0.146373	−	0.989229i	$-0.546760\pi$
$2$	20.3884	−	11.7713i	0.637138	−	0.367852i	0.783511	+	0.621378i	$0.213427\pi$
$3$		0			0
$3$		0			0
$4$	−234.875	+	406.815i	−0.229370	+	0.397280i
$5$	3831.75	+	2212.26i	1.22616	+	0.707923i	0.966224	−	0.257703i	$-0.0829656\pi$
$5$	3831.75	+	2212.26i	1.22616	+	0.707923i	0.259935	+	0.965626i	$0.416299\pi$
$6$		0			0
$7$	10784.0	+	18678.4i	0.641637	+	1.11135i	0.985067	+	0.172169i	$0.0550777\pi$
$7$	10784.0	+	18678.4i	0.641637	+	1.11135i	−0.343431	+	0.939178i	$0.611589\pi$
$8$			35166.6i			1.07320i
$9$		0			0
$10$	104164.			1.04164
$11$	210295.	−	121414.i	1.30577	−	0.753885i	0.324380	−	0.945927i	$-0.394844\pi$
$11$	210295.	−	121414.i	1.30577	−	0.753885i	0.981387	+	0.192042i	$0.0615110\pi$
$12$		0			0
$13$	199052.	−	344768.i	0.536105	−	0.928560i	−0.463004	−	0.886356i	$-0.653229\pi$
$13$	199052.	−	344768.i	0.536105	−	0.928560i	0.999109	−	0.0422044i	$-0.0134381\pi$
$14$	439737.	+	253882.i	0.817623	+	0.472055i
$15$		0			0
$16$	173444.	+	300414.i	0.165409	+	0.286497i
$17$			2.02619e6i			1.42704i	0.700634	+	0.713520i	$0.252900\pi$
$17$			2.02619e6i			1.42704i	−0.700634	+	0.713520i	$0.747100\pi$
$18$		0			0
$19$	−2.77192e6			−1.11947			−0.559735	−	0.828672i	$-0.689097\pi$
$19$	−2.77192e6			−1.11947			−0.559735	+	0.828672i	$0.689097\pi$
$20$	−1.79996e6	+	1.03921e6i	−0.562488	+	0.324753i
$21$		0			0
$22$	2.85839e6	−	4.95088e6i	0.554636	−	0.960658i
$23$	2.14688e6	+	1.23950e6i	0.333556	+	0.192579i	0.657419	−	0.753525i	$-0.271648\pi$
$23$	2.14688e6	+	1.23950e6i	0.333556	+	0.192579i	−0.323863	+	0.946104i	$0.604982\pi$
$24$		0			0
$25$	4.90538e6	+	8.49636e6i	0.502311	+	0.870028i
$26$		−	9.37237e6i		−	0.788828i
$27$		0			0
$28$	−1.01315e7			−0.588689
$29$	−7.90991e6	+	4.56679e6i	−0.385640	+	0.222649i	−0.680269	−	0.732962i	$-0.738137\pi$
$29$	−7.90991e6	+	4.56679e6i	−0.385640	+	0.222649i	0.294630	+	0.955612i	$0.404804\pi$
$30$		0			0
$31$	9.07315e6	−	1.57152e7i	0.316920	−	0.548921i	−0.662924	−	0.748687i	$-0.730685\pi$
$31$	9.07315e6	−	1.57152e7i	0.316920	−	0.548921i	0.979844	+	0.199765i	$0.0640180\pi$
$32$	−2.41136e7	−	1.39220e7i	−0.718642	−	0.414908i
$33$		0			0
$34$	2.38509e7	+	4.13109e7i	0.524940	+	0.909222i
$35$			9.54280e7i			1.81692i
$36$		0			0
$37$	1.14330e7			0.164874			0.0824369	−	0.996596i	$-0.473730\pi$
$37$	1.14330e7			0.164874			0.0824369	+	0.996596i	$0.473730\pi$
$38$	−5.65150e7	+	3.26290e7i	−0.713257	+	0.411799i
$39$		0			0
$40$	−7.77977e7	+	1.34750e8i	−0.759744	+	1.31591i
$41$	1.18731e8	+	6.85496e7i	1.02482	+	0.591678i	0.915495	−	0.402328i	$-0.131799\pi$
$41$	1.18731e8	+	6.85496e7i	1.02482	+	0.591678i	0.109321	+	0.994006i	$0.465132\pi$
$42$		0			0
$43$	−4.93948e7	−	8.55544e7i	−0.336000	−	0.581969i	0.647676	−	0.761916i	$-0.275741\pi$
$43$	−4.93948e7	−	8.55544e7i	−0.336000	−	0.581969i	−0.983676	+	0.179946i	$0.942408\pi$
$44$			1.14068e8i			0.691674i
$45$		0			0
$46$	5.83620e7			0.283362
$47$	1.22806e8	−	7.09022e7i	0.535465	−	0.309151i	−0.207774	−	0.978177i	$-0.566622\pi$
$47$	1.22806e8	−	7.09022e7i	0.535465	−	0.309151i	0.743239	+	0.669026i	$0.233289\pi$
$48$		0			0
$49$	−9.13512e7	+	1.58225e8i	−0.323396	+	0.560138i
$50$	2.00026e8	+	1.15485e8i	0.640083	+	0.369552i
$51$		0			0
$52$	9.35045e7	+	1.61955e8i	0.245932	+	0.425968i
$53$		−	1.39084e8i		−	0.332582i	−0.986077	−	0.166291i	$-0.946821\pi$
$53$		−	1.39084e8i		−	0.332582i	0.986077	−	0.166291i	$-0.0531792\pi$
$54$		0			0
$55$	1.07440e9			2.13477
$56$	−6.56857e8	+	3.79237e8i	−1.19270	+	0.688605i
$57$		0			0
$58$	−1.07514e8	+	1.86219e8i	−0.163804	+	0.283717i
$59$	−9.24898e8	−	5.33990e8i	−1.29370	−	0.746918i	−0.314393	−	0.949293i	$-0.601801\pi$
$59$	−9.24898e8	−	5.33990e8i	−1.29370	−	0.746918i	−0.979308	+	0.202375i	$0.935134\pi$
$60$		0			0
$61$	7.24880e8	+	1.25553e9i	0.858256	+	1.48654i	0.873591	+	0.486660i	$0.161785\pi$
$61$	7.24880e8	+	1.25553e9i	0.858256	+	1.48654i	−0.0153358	+	0.999882i	$0.504882\pi$
$62$		−	4.27210e8i		−	0.466318i
$63$		0			0
$64$	−1.01073e9			−0.941317
$65$	1.52543e9	−	8.80709e8i	1.31470	−	0.759042i
$66$		0			0
$67$	−7.23067e8	+	1.25239e9i	−0.535556	+	0.927610i	0.463581	+	0.886055i	$0.346564\pi$
$67$	−7.23067e8	+	1.25239e9i	−0.535556	+	0.927610i	−0.999136	+	0.0415549i	$0.986769\pi$
$68$	−8.24286e8	−	4.75902e8i	−0.566935	−	0.327320i
$69$		0			0
$70$	1.12331e9	+	1.94563e9i	0.668357	+	1.15763i
$71$		−	1.33807e9i		−	0.741630i	−0.928707	−	0.370815i	$-0.879078\pi$
$71$		−	1.33807e9i		−	0.741630i	0.928707	−	0.370815i	$-0.120922\pi$
$72$		0			0
$73$	−1.46812e9			−0.708187			−0.354094	−	0.935210i	$-0.615211\pi$
$73$	−1.46812e9			−0.708187			−0.354094	+	0.935210i	$0.615211\pi$
$74$	2.33101e8	−	1.34581e8i	0.105047	−	0.0606491i
$75$		0			0
$76$	6.51053e8	−	1.12766e9i	0.256773	−	0.444743i
$77$	4.53564e9	+	2.61865e9i	1.67566	+	0.967441i
$78$		0			0
$79$	2.47690e9	+	4.29012e9i	0.804959	+	1.39423i	0.916319	+	0.400450i	$0.131146\pi$
$79$	2.47690e9	+	4.29012e9i	0.804959	+	1.39423i	−0.111360	+	0.993780i	$0.535521\pi$
$80$			1.53481e9i			0.468388i
$81$		0			0
$82$	3.22766e9			0.870600
$83$	4.85531e8	−	2.80322e8i	0.123261	−	0.0711650i	−0.437102	−	0.899412i	$-0.643995\pi$
$83$	4.85531e8	−	2.80322e8i	0.123261	−	0.0711650i	0.560363	+	0.828247i	$0.310662\pi$
$84$		0			0
$85$	−4.48247e9	+	7.76386e9i	−1.01024	+	1.74978i
$86$	−2.01417e9	−	1.16288e9i	−0.428157	−	0.247197i
$87$		0			0
$88$	4.26972e9	+	7.39537e9i	0.809070	+	1.40135i
$89$		−	4.73263e9i		−	0.847524i	−0.905774	−	0.423762i	$-0.860709\pi$
$89$		−	4.73263e9i		−	0.847524i	0.905774	−	0.423762i	$-0.139291\pi$
$90$		0			0
$91$	8.58629e9			1.37594
$92$	−1.00850e9	+	5.82255e8i	−0.153015	+	0.0883435i
$93$		0			0
$94$	1.66922e9	−	2.89117e9i	0.227443	−	0.393944i
$95$	−1.06213e10	−	6.13220e9i	−1.37265	−	0.792498i
$96$		0			0
$97$	−6.08507e9	−	1.05396e10i	−0.708609	−	1.22735i	−0.965373	−	0.260873i	$-0.915990\pi$
$97$	−6.08507e9	−	1.05396e10i	−0.708609	−	1.22735i	0.256764	−	0.966474i	$-0.417344\pi$
$98$			4.30128e9i			0.475847i
$99$		0			0
$100$	−4.60860e9			−0.460860
$101$	−1.03897e10	+	5.99851e9i	−0.988547	+	0.570738i	−0.904840	−	0.425753i	$-0.860009\pi$
$101$	−1.03897e10	+	5.99851e9i	−0.988547	+	0.570738i	−0.0837072	+	0.996490i	$0.526676\pi$
$102$		0			0
$103$	−5.89242e9	+	1.02060e10i	−0.508286	+	0.880377i	0.491668	+	0.870783i	$0.336387\pi$
$103$	−5.89242e9	+	1.02060e10i	−0.508286	+	0.880377i	−0.999954	+	0.00959411i	$0.996946\pi$
$104$	1.21243e10	+	6.99998e9i	0.996531	+	0.575348i
$105$		0			0
$106$	−1.63720e9	−	2.83571e9i	−0.122341	−	0.211901i
$107$			1.67650e10i			1.19532i	0.801749	+	0.597661i	$0.203903\pi$
$107$			1.67650e10i			1.19532i	−0.801749	+	0.597661i	$0.796097\pi$
$108$		0			0
$109$	1.39867e10			0.909040			0.454520	−	0.890736i	$-0.349811\pi$
$109$	1.39867e10			0.909040			0.454520	+	0.890736i	$0.349811\pi$
$110$	2.19053e10	−	1.26470e10i	1.36014	−	0.785280i
$111$		0			0
$112$	−3.74084e9	+	6.47932e9i	−0.212265	+	0.367654i
$113$	−1.43914e9	−	8.30890e8i	−0.0781110	−	0.0450974i	0.460436	−	0.887693i	$-0.347693\pi$
$113$	−1.43914e9	−	8.30890e8i	−0.0781110	−	0.0450974i	−0.538547	+	0.842596i	$0.681026\pi$
$114$		0			0
$115$	5.48420e9	+	9.49892e9i	0.272662	+	0.472264i
$116$		−	4.29049e9i		−	0.204276i
$117$		0			0
$118$	−2.51430e10			−1.09902
$119$	−3.78461e10	+	2.18505e10i	−1.58594	+	0.915642i
$120$		0			0
$121$	1.65140e10	−	2.86030e10i	0.636685	−	1.10277i
$122$	2.95583e10	+	1.70655e10i	1.09366	+	0.631422i
$123$		0			0
$124$	4.26211e9	+	7.38219e9i	0.145384	+	0.251812i
$125$			1.99685e8i			0.00654329i
$126$		0			0
$127$	2.55071e9			0.0772045			0.0386022	−	0.999255i	$-0.487709\pi$
$127$	2.55071e9			0.0772045			0.0386022	+	0.999255i	$0.487709\pi$
$128$	4.08513e9	−	2.35855e9i	0.118893	−	0.0686428i
$129$		0			0
$130$	2.07341e10	−	3.59125e10i	0.558430	−	0.967229i
$131$	−1.40948e10	−	8.13764e9i	−0.365344	−	0.210932i	0.306078	−	0.952006i	$-0.400983\pi$
$131$	−1.40948e10	−	8.13764e9i	−0.365344	−	0.210932i	−0.671423	+	0.741075i	$0.734316\pi$
$132$		0			0
$133$	−2.98923e10	−	5.17750e10i	−0.718293	−	1.24412i
$134$			3.40457e10i			0.788021i
$135$		0			0
$136$	−7.12544e10			−1.53150
$137$	5.67115e10	−	3.27424e10i	1.17508	−	0.678434i	0.220211	−	0.975452i	$-0.429326\pi$
$137$	5.67115e10	−	3.27424e10i	1.17508	−	0.678434i	0.954872	+	0.297018i	$0.0959922\pi$
$138$		0			0
$139$	1.50595e10	−	2.60839e10i	0.290227	−	0.502688i	−0.683636	−	0.729823i	$-0.739603\pi$
$139$	1.50595e10	−	2.60839e10i	0.290227	−	0.502688i	0.973863	+	0.227135i	$0.0729359\pi$
$140$	−3.88215e10	−	2.24136e10i	−0.721826	−	0.416746i
$141$		0			0
$142$	−1.57508e10	−	2.72811e10i	−0.272810	−	0.472521i
$143$		−	9.66707e10i		−	1.61664i
$144$		0			0
$145$	−4.04117e10			−0.630474
$146$	−2.99327e10	+	1.72817e10i	−0.451213	+	0.260508i
$147$		0			0
$148$	−2.68532e9	+	4.65112e9i	−0.0378171	+	0.0655011i
$149$	−8.56031e10	−	4.94230e10i	−1.16562	−	0.672973i	−0.212978	−	0.977057i	$-0.568316\pi$
$149$	−8.56031e10	−	4.94230e10i	−1.16562	−	0.672973i	−0.952645	+	0.304084i	$0.901650\pi$
$150$		0			0
$151$	−4.16530e10	−	7.21452e10i	−0.530594	−	0.919015i	−0.999363	−	0.0356943i	$-0.988636\pi$
$151$	−4.16530e10	−	7.21452e10i	−0.530594	−	0.919015i	0.468769	−	0.883321i	$-0.344698\pi$
$152$		−	9.74790e10i		−	1.20141i
$153$		0			0
$154$	1.23299e11			1.42350
$155$	6.95320e10	−	4.01443e10i	0.777189	−	0.448710i
$156$		0			0
$157$	3.94580e10	−	6.83432e10i	0.413653	−	0.716469i	−0.581633	−	0.813452i	$-0.697586\pi$
$157$	3.94580e10	−	6.83432e10i	0.413653	−	0.716469i	0.995286	+	0.0969828i	$0.0309192\pi$
$158$	1.01000e11	+	5.83126e10i	1.02574	+	0.592211i
$159$		0			0
$160$	−6.15982e10	−	1.06691e11i	−0.587446	−	1.01749i
$161$			5.34671e10i			0.494262i
$162$		0			0
$163$	1.98358e10			0.172390			0.0861951	−	0.996278i	$-0.472529\pi$
$163$	1.98358e10			0.172390			0.0861951	+	0.996278i	$0.472529\pi$
$164$	−5.57740e10	+	3.22011e10i	−0.470124	+	0.271426i
$165$		0			0
$166$	6.59948e9	−	1.14306e10i	0.0523564	−	0.0906839i
$167$	3.73359e10	+	2.15559e10i	0.287438	+	0.165952i	0.636786	−	0.771041i	$-0.280264\pi$
$167$	3.73359e10	+	2.15559e10i	0.287438	+	0.165952i	−0.349348	+	0.936993i	$0.613597\pi$
$168$		0			0
$169$	−1.03141e10	−	1.78645e10i	−0.0748162	−	0.129585i
$170$			2.11057e11i			1.48647i
$171$		0			0
$172$	4.64064e10			0.308273
$173$	−1.09895e11	+	6.34480e10i	−0.709167	+	0.409438i	−0.810752	−	0.585389i	$-0.800942\pi$
$173$	−1.09895e11	+	6.34480e10i	−0.709167	+	0.409438i	0.101586	+	0.994827i	$0.467608\pi$
$174$		0			0
$175$	−1.05799e11	+	1.83249e11i	−0.644602	+	1.11648i
$176$	7.29488e10	+	4.21170e10i	0.431971	+	0.249399i
$177$		0			0
$178$	−5.57090e10	−	9.64908e10i	−0.311763	−	0.539990i
$179$		−	1.71735e11i		−	0.934531i	−0.884117	−	0.467265i	$-0.845239\pi$
$179$		−	1.71735e11i		−	0.934531i	0.884117	−	0.467265i	$-0.154761\pi$
$180$		0			0
$181$	−9.76637e10			−0.502737			−0.251368	−	0.967892i	$-0.580881\pi$
$181$	−9.76637e10			−0.502737			−0.251368	+	0.967892i	$0.580881\pi$
$182$	1.75061e11	−	1.01072e11i	0.876663	−	0.506141i
$183$		0			0
$184$	−4.35891e10	+	7.54986e10i	−0.206675	+	0.357972i
$185$	4.38084e10	+	2.52928e10i	0.202162	+	0.116718i
$186$		0			0
$187$	2.46008e11	+	4.26099e11i	1.07582	+	1.86338i
$188$			6.66126e10i			0.283640i
$189$		0			0
$190$	−2.88735e11			−1.16609
$191$	8.71784e10	−	5.03325e10i	0.342959	−	0.198007i	−0.318621	−	0.947882i	$-0.603220\pi$
$191$	8.71784e10	−	5.03325e10i	0.342959	−	0.198007i	0.661580	+	0.749875i	$0.269886\pi$
$192$		0			0
$193$	1.64225e11	−	2.84445e11i	0.613270	−	1.06221i	−0.377415	−	0.926044i	$-0.623187\pi$
$193$	1.64225e11	−	2.84445e11i	0.613270	−	1.06221i	0.990685	−	0.136171i	$-0.0434795\pi$
$194$	−2.48130e11	−	1.43258e11i	−0.902964	−	0.521327i
$195$		0			0
$196$	−4.29122e10	−	7.43261e10i	−0.148354	−	0.256957i
$197$			2.22370e11i			0.749453i	0.927135	+	0.374727i	$0.122263\pi$
$197$			2.22370e11i			0.749453i	−0.927135	+	0.374727i	$0.877737\pi$
$198$		0			0
$199$	1.76697e11			0.566191			0.283095	−	0.959092i	$-0.408639\pi$
$199$	1.76697e11			0.566191			0.283095	+	0.959092i	$0.408639\pi$
$200$	−2.98789e11	+	1.72506e11i	−0.933714	+	0.539080i
$201$		0			0
$202$	−1.41220e11	+	2.44600e11i	−0.419894	+	0.727278i
$203$	−1.70601e11	−	9.84964e10i	−0.494881	−	0.285720i
$204$		0			0
$205$	3.03299e11	+	5.25329e11i	0.837725	+	1.45098i
$206$			2.77445e11i			0.747896i
$207$		0			0
$208$	1.38097e11			0.354706
$209$	−5.82920e11	+	3.36549e11i	−1.46177	+	0.843951i
$210$		0			0
$211$	1.33629e11	−	2.31453e11i	0.319513	−	0.553414i	−0.660873	−	0.750498i	$-0.729814\pi$
$211$	1.33629e11	−	2.31453e11i	0.319513	−	0.553414i	0.980387	+	0.197084i	$0.0631472\pi$
$212$	5.65817e10	+	3.26674e10i	0.132128	+	0.0762844i
$213$		0			0
$214$	1.97345e11	+	3.41812e11i	0.439701	+	0.761585i
$215$		−	4.37097e11i		−	0.951449i
$216$		0			0
$217$	3.91379e11			0.813390
$218$	2.85167e11	−	1.64641e11i	0.579184	−	0.334392i
$219$		0			0
$220$	−2.52349e11	+	4.37081e11i	−0.489652	+	0.848102i
$221$	6.98567e11	+	4.03318e11i	1.32509	+	0.765043i
$222$		0			0
$223$	2.53690e11	+	4.39404e11i	0.460023	+	0.796783i	0.998962	−	0.0455621i	$-0.0145079\pi$
$223$	2.53690e11	+	4.39404e11i	0.460023	+	0.796783i	−0.538939	+	0.842345i	$0.681175\pi$
$224$		−	6.00539e11i		−	1.06488i
$225$		0			0
$226$	−3.91225e10			−0.0663566
$227$	8.32283e11	−	4.80519e11i	1.38083	−	0.797225i	0.388576	−	0.921417i	$-0.372967\pi$
$227$	8.32283e11	−	4.80519e11i	1.38083	−	0.797225i	0.992258	+	0.124192i	$0.0396338\pi$
$228$		0			0
$229$	−1.04136e11	+	1.80369e11i	−0.165357	+	0.286407i	−0.936782	−	0.349913i	$-0.886211\pi$
$229$	−1.04136e11	+	1.80369e11i	−0.165357	+	0.286407i	0.771425	+	0.636321i	$0.219544\pi$
$230$	2.23628e11	+	1.29112e11i	0.347446	+	0.200598i
$231$		0			0
$232$	−1.60599e11	−	2.78165e11i	−0.238947	−	0.413869i
$233$			1.26797e12i			1.84642i	0.384296	+	0.923210i	$0.374444\pi$
$233$			1.26797e12i			1.84642i	−0.384296	+	0.923210i	$0.625556\pi$
$234$		0			0
$235$	6.27417e11			0.875420
$236$	4.34470e11	−	2.50842e11i	0.593472	−	0.342641i
$237$		0			0
$238$	−5.14415e11	+	8.90993e11i	−0.673641	+	1.16678i
$239$	−8.64760e11	−	4.99270e11i	−1.10894	−	0.640244i	−0.170382	−	0.985378i	$-0.554500\pi$
$239$	−8.64760e11	−	4.99270e11i	−1.10894	−	0.640244i	−0.938553	+	0.345134i	$0.887834\pi$
$240$		0			0
$241$	−2.80502e11	−	4.85843e11i	−0.345025	−	0.597601i	0.640333	−	0.768097i	$-0.278796\pi$
$241$	−2.80502e11	−	4.85843e11i	−0.345025	−	0.597601i	−0.985358	+	0.170496i	$0.945463\pi$
$242$		−	7.77561e11i		−	0.936823i
$243$		0			0
$244$	−6.81024e11			−0.787432
$245$	−7.00070e11	+	4.04185e11i	−0.793069	+	0.457879i
$246$		0			0
$247$	−5.51755e11	+	9.55668e11i	−0.600153	+	1.03949i
$248$	5.52649e11	+	3.19072e11i	0.589103	+	0.340119i
$249$		0			0
$250$	2.35055e9	+	4.07127e9i	0.00240696	+	0.00416898i
$251$		−	1.09342e12i		−	1.09753i	−0.835975	−	0.548767i	$-0.815097\pi$
$251$		−	1.09342e12i		−	1.09753i	0.835975	−	0.548767i	$-0.184903\pi$
$252$		0			0
$253$	6.01971e11			0.580728
$254$	5.20050e10	−	3.00251e10i	0.0491899	−	0.0283998i
$255$		0			0
$256$	5.73021e11	−	9.92501e11i	0.521159	−	0.902675i
$257$	−1.51176e12	−	8.72816e11i	−1.34840	−	0.778497i	−0.360374	−	0.932808i	$-0.617351\pi$
$257$	−1.51176e12	−	8.72816e11i	−1.34840	−	0.778497i	−0.988022	+	0.154311i	$0.950684\pi$
$258$		0			0
$259$	1.23293e11	+	2.13550e11i	0.105789	+	0.183232i
$260$			8.27425e11i			0.696405i
$261$		0			0
$262$	−3.83161e11			−0.310367
$263$	3.30907e11	−	1.91049e11i	0.262983	−	0.151833i	−0.362712	−	0.931901i	$-0.618149\pi$
$263$	3.30907e11	−	1.91049e11i	0.262983	−	0.151833i	0.625695	+	0.780068i	$0.284816\pi$
$264$		0			0
$265$	3.07691e11	−	5.32937e11i	0.235443	−	0.407799i
$266$	−1.21891e12	−	7.03741e11i	−0.915303	−	0.528451i
$267$		0			0
$268$	−3.39660e11	−	5.88309e11i	−0.245681	−	0.425531i
$269$		−	1.54623e12i		−	1.09777i	−0.835896	−	0.548887i	$-0.815052\pi$
$269$		−	1.54623e12i		−	1.09777i	0.835896	−	0.548887i	$-0.184948\pi$
$270$		0			0
$271$	1.85954e12			1.27221			0.636104	−	0.771603i	$-0.280545\pi$
$271$	1.85954e12			1.27221			0.636104	+	0.771603i	$0.280545\pi$
$272$	−6.08696e11	+	3.51431e11i	−0.408843	+	0.236045i
$273$		0			0
$274$	7.70839e11	−	1.33513e12i	0.499127	−	0.864513i
$275$	2.06315e12	+	1.19116e12i	1.31180	+	0.757369i
$276$		0			0
$277$	9.83899e11	+	1.70416e12i	0.603326	+	1.04499i	0.992314	+	0.123748i	$0.0394914\pi$
$277$	9.83899e11	+	1.70416e12i	0.603326	+	1.04499i	−0.388988	+	0.921243i	$0.627175\pi$
$278$		−	7.09079e11i		−	0.427042i
$279$		0			0
$280$	−3.35588e12			−1.94992
$281$	3.06376e11	−	1.76886e11i	0.174873	−	0.100963i	−0.410008	−	0.912082i	$-0.634474\pi$
$281$	3.06376e11	−	1.76886e11i	0.174873	−	0.100963i	0.584882	+	0.811119i	$0.301141\pi$
$282$		0			0
$283$	7.77229e11	−	1.34620e12i	0.428170	−	0.741613i	−0.568540	−	0.822655i	$-0.692492\pi$
$283$	7.77229e11	−	1.34620e12i	0.428170	−	0.741613i	0.996711	+	0.0810425i	$0.0258250\pi$
$284$	5.44347e11	+	3.14279e11i	0.294635	+	0.170107i
$285$		0			0
$286$	−1.13794e12	−	1.97096e12i	−0.594686	−	1.03003i
$287$			2.95695e12i			1.51857i
$288$		0			0
$289$	−2.08947e12			−1.03645
$290$	−8.23931e11	+	4.75697e11i	−0.401699	+	0.231921i
$291$		0			0
$292$	3.44825e11	−	5.97254e11i	0.162437	−	0.281349i
$293$	3.16621e12	+	1.82801e12i	1.46623	+	0.846526i	0.999287	−	0.0377630i	$-0.0120232\pi$
$293$	3.16621e12	+	1.82801e12i	1.46623	+	0.846526i	0.466940	+	0.884289i	$0.345357\pi$
$294$		0			0
$295$	−2.36265e12	−	4.09223e12i	−1.05752	−	1.83168i
$296$			4.02060e11i			0.176943i
$297$		0			0
$298$	−2.32708e12			−0.990217
$299$	8.54681e11	−	4.93450e11i	0.357642	−	0.206485i
$300$		0			0
$301$	1.06535e12	−	1.84523e12i	0.431180	−	0.746826i
$302$	−1.69848e12	−	9.80618e11i	−0.676123	−	0.390360i
$303$		0			0
$304$	−4.80772e11	−	8.32722e11i	−0.185170	−	0.320724i
$305$			6.41449e12i			2.43032i
$306$		0			0
$307$	4.14571e12			1.52022			0.760111	−	0.649793i	$-0.225144\pi$
$307$	4.14571e12			1.52022			0.760111	+	0.649793i	$0.225144\pi$
$308$	−2.13061e12	+	1.23011e12i	−0.768690	+	0.443803i
$309$		0			0
$310$	9.45099e11	−	1.63696e12i	0.330118	−	0.571781i
$311$	−6.42068e11	−	3.70698e11i	−0.220688	−	0.127414i	0.385581	−	0.922674i	$-0.374001\pi$
$311$	−6.42068e11	−	3.70698e11i	−0.220688	−	0.127414i	−0.606269	+	0.795260i	$0.707334\pi$
$312$		0			0
$313$	5.99277e11	+	1.03798e12i	0.199483	+	0.345515i	0.948361	−	0.317193i	$-0.102740\pi$
$313$	5.99277e11	+	1.03798e12i	0.199483	+	0.345515i	−0.748878	+	0.662708i	$0.769407\pi$
$314$		−	1.85788e12i		−	0.608653i
$315$		0			0
$316$	−2.32705e12			−0.738533
$317$	1.80801e12	−	1.04386e12i	0.564814	−	0.326096i	−0.190261	−	0.981733i	$-0.560934\pi$
$317$	1.80801e12	−	1.04386e12i	0.564814	−	0.326096i	0.755076	+	0.655638i	$0.227600\pi$
$318$		0			0
$319$	−1.10894e12	+	1.92075e12i	−0.335704	+	0.581456i
$320$	−3.87287e12	−	2.23600e12i	−1.15420	−	0.666380i
$321$		0			0
$322$	6.29375e11	+	1.09011e12i	0.181815	+	0.314913i
$323$		−	5.61644e12i		−	1.59753i
$324$		0			0
$325$	3.90570e12			1.07716
$326$	4.04422e11	−	2.33493e11i	0.109836	−	0.0634141i
$327$		0			0
$328$	−2.41066e12	+	4.17538e12i	−0.634989	+	1.09983i
$329$	2.64868e12	+	1.52922e12i	0.687148	+	0.396725i
$330$		0			0
$331$	−2.86746e12	−	4.96659e12i	−0.721701	−	1.25002i	−0.960317	−	0.278910i	$-0.910027\pi$
$331$	−2.86746e12	−	4.96659e12i	−0.721701	−	1.25002i	0.238616	−	0.971114i	$-0.423306\pi$
$332$			2.63362e11i			0.0652924i
$333$		0			0
$334$	1.01496e12			0.244184
$335$	−5.54122e12	+	3.19923e12i	−1.31335	+	0.758265i
$336$		0			0
$337$	1.90495e11	−	3.29947e11i	0.0438262	−	0.0759092i	−0.843280	−	0.537474i	$-0.819379\pi$
$337$	1.90495e11	−	3.29947e11i	0.0438262	−	0.0759092i	0.887106	+	0.461565i	$0.152712\pi$
$338$	−4.20574e11	−	2.42819e11i	−0.0953365	−	0.0550426i
$339$		0			0
$340$	−2.10564e12	−	3.64707e12i	−0.463435	−	0.802693i
$341$		−	4.40643e12i		−	0.955685i
$342$		0			0
$343$	2.15190e12			0.453264
$344$	3.00866e12	−	1.73705e12i	0.624570	−	0.360595i
$345$		0			0
$346$	−1.49373e12	+	2.58721e12i	−0.301225	+	0.521737i
$347$	−3.07166e11	−	1.77342e11i	−0.0610556	−	0.0352505i	0.469161	−	0.883112i	$-0.344556\pi$
$347$	−3.07166e11	−	1.77342e11i	−0.0610556	−	0.0352505i	−0.530217	+	0.847862i	$0.677890\pi$
$348$		0			0
$349$	3.83987e12	+	6.65085e12i	0.741634	+	1.28455i	0.951751	+	0.306872i	$0.0992822\pi$
$349$	3.83987e12	+	6.65085e12i	0.741634	+	1.28455i	−0.210117	+	0.977676i	$0.567384\pi$
$350$			4.98156e12i			0.948473i
$351$		0			0
$352$	−6.76130e12			−1.25117
$353$	5.70032e12	−	3.29108e12i	1.03998	−	0.600434i	0.120154	−	0.992755i	$-0.461661\pi$
$353$	5.70032e12	−	3.29108e12i	1.03998	−	0.600434i	0.919828	+	0.392321i	$0.128328\pi$
$354$		0			0
$355$	2.96016e12	−	5.12715e12i	0.525017	−	0.909356i
$356$	1.92530e12	+	1.11157e12i	0.336705	+	0.194397i
$357$		0			0
$358$	−2.02154e12	−	3.50141e12i	−0.343769	−	0.595425i
$359$		−	6.68773e12i		−	1.12152i	−0.827979	−	0.560760i	$-0.810509\pi$
$359$		−	6.68773e12i		−	1.12152i	0.827979	−	0.560760i	$-0.189491\pi$
$360$		0			0
$361$	1.55245e12			0.253211
$362$	−1.99121e12	+	1.14963e12i	−0.320313	+	0.184933i
$363$		0			0
$364$	−2.01670e12	+	3.49303e12i	−0.315599	+	0.546633i
$365$	−5.62548e12	−	3.24787e12i	−0.868350	−	0.501342i
$366$		0			0
$367$	4.65590e12	+	8.06426e12i	0.699316	+	1.21125i	0.968704	+	0.248219i	$0.0798453\pi$
$367$	4.65590e12	+	8.06426e12i	0.699316	+	1.21125i	−0.269388	+	0.963032i	$0.586821\pi$
$368$			8.59936e11i			0.127417i
$369$		0			0
$370$	1.19091e12			0.171740
$371$	2.59788e12	−	1.49989e12i	0.369615	−	0.213397i
$372$		0			0
$373$	−3.09224e11	+	5.35591e11i	−0.0428281	+	0.0741804i	−0.886645	−	0.462451i	$-0.846970\pi$
$373$	−3.09224e11	+	5.35591e11i	−0.0428281	+	0.0741804i	0.843817	+	0.536631i	$0.180303\pi$
$374$	1.00314e13	+	5.79165e12i	1.37090	+	0.791488i
$375$		0			0
$376$	2.49339e12	+	4.31868e12i	0.331781	+	0.574661i
$377$			3.63611e12i			0.477453i
$378$		0			0
$379$	6.79881e11			0.0869435			0.0434717	−	0.999055i	$-0.486158\pi$
$379$	6.79881e11			0.0869435			0.0434717	+	0.999055i	$0.486158\pi$
$380$	4.98934e12	−	2.88060e12i	0.629688	−	0.363550i
$381$		0			0
$382$	1.18495e12	−	2.05240e12i	0.145675	−	0.252316i
$383$	−4.87000e12	−	2.81170e12i	−0.590929	−	0.341173i	0.174536	−	0.984651i	$-0.444158\pi$
$383$	−4.87000e12	−	2.81170e12i	−0.590929	−	0.341173i	−0.765465	+	0.643478i	$0.777491\pi$
$384$		0			0
$385$	1.15863e13	+	2.00680e13i	1.36975	+	2.37247i
$386$		−	7.73252e12i		−	0.902370i
$387$		0			0
$388$	5.71692e12			0.650135
$389$	−8.35189e12	+	4.82197e12i	−0.937642	+	0.541348i	−0.889220	−	0.457479i	$-0.848752\pi$
$389$	−8.35189e12	+	4.82197e12i	−0.937642	+	0.541348i	−0.0484214	+	0.998827i	$0.515419\pi$
$390$		0			0
$391$	−2.51147e12	+	4.35000e12i	−0.274818	+	0.475998i
$392$	−5.56424e12	−	3.21252e12i	−0.601140	−	0.347068i
$393$		0			0
$394$	2.61757e12	+	4.53377e12i	0.275688	+	0.477505i
$395$			2.19182e13i			2.27940i
$396$		0			0
$397$	−1.48431e11			−0.0150512			−0.00752561	−	0.999972i	$-0.502395\pi$
$397$	−1.48431e11			−0.0150512			−0.00752561	+	0.999972i	$0.502395\pi$
$398$	3.60256e12	−	2.07994e12i	0.360742	−	0.208274i
$399$		0			0
$400$	−1.70162e12	+	2.94729e12i	−0.166173	+	0.287821i
$401$	−1.86635e11	−	1.07754e11i	−0.0180000	−	0.0103923i	0.490973	−	0.871175i	$-0.336641\pi$
$401$	−1.86635e11	−	1.07754e11i	−0.0180000	−	0.0103923i	−0.508973	+	0.860782i	$0.669975\pi$
$402$		0			0
$403$	−3.61205e12	−	6.25626e12i	−0.339804	−	0.588559i
$404$		−	5.63560e12i		−	0.523640i
$405$		0			0
$406$	−4.63771e12			−0.420410
$407$	2.40430e12	−	1.38813e12i	0.215287	−	0.124296i
$408$		0			0
$409$	5.52925e12	−	9.57694e12i	0.483114	−	0.836778i	−0.516698	−	0.856168i	$-0.672839\pi$
$409$	5.52925e12	−	9.57694e12i	0.483114	−	0.836778i	0.999812	+	0.0193896i	$0.00617229\pi$
$410$	1.23676e13	+	7.14043e12i	1.06749	+	0.616318i
$411$		0			0
$412$	−2.76796e12	−	4.79425e12i	−0.233171	−	0.403864i
$413$		−	2.30342e13i		−	1.91700i
$414$		0			0
$415$	2.48058e12			0.201517
$416$	−9.59973e12	+	5.54240e12i	−0.770535	+	0.444868i
$417$		0			0
$418$	−7.92322e12	+	1.37234e13i	−0.620898	+	1.07543i
$419$	−6.71893e12	−	3.87918e12i	−0.520272	−	0.300379i	0.216774	−	0.976222i	$-0.430447\pi$
$419$	−6.71893e12	−	3.87918e12i	−0.520272	−	0.300379i	−0.737046	+	0.675843i	$0.763780\pi$
$420$		0			0
$421$	4.72007e12	+	8.17540e12i	0.356893	+	0.618156i	0.987440	−	0.157995i	$-0.0505028\pi$
$421$	4.72007e12	+	8.17540e12i	0.356893	+	0.618156i	−0.630547	+	0.776151i	$0.717170\pi$
$422$		−	6.29194e12i		−	0.470135i
$423$		0			0
$424$	4.89113e12			0.356928
$425$	−1.72153e13	+	9.93925e12i	−1.24157	+	0.716818i
$426$		0			0
$427$	−1.56342e13	+	2.70792e13i	−1.10138	+	1.90764i
$428$	−6.82026e12	−	3.93768e12i	−0.474878	−	0.274171i
$429$		0			0
$430$	−5.14518e12	−	8.91172e12i	−0.349992	−	0.606205i
$431$			1.56255e13i			1.05063i	0.850909	+	0.525313i	$0.176052\pi$
$431$			1.56255e13i			1.05063i	−0.850909	+	0.525313i	$0.823948\pi$
$432$		0			0
$433$	−1.68288e13			−1.10564			−0.552820	−	0.833301i	$-0.686448\pi$
$433$	−1.68288e13			−1.10564			−0.552820	+	0.833301i	$0.686448\pi$
$434$	7.97960e12	−	4.60702e12i	0.518242	−	0.299207i
$435$		0			0
$436$	−3.28513e12	+	5.69000e12i	−0.208506	+	0.361144i
$437$	−5.95097e12	−	3.43580e12i	−0.373406	−	0.215586i
$438$		0			0
$439$	3.07061e12	+	5.31844e12i	0.188322	+	0.326184i	0.944691	−	0.327962i	$-0.106362\pi$
$439$	3.07061e12	+	5.31844e12i	0.188322	+	0.326184i	−0.756369	+	0.654145i	$0.773028\pi$
$440$			3.77829e13i			2.29104i
$441$		0			0
$442$	1.89902e13			1.12569
$443$	−1.18984e12	+	6.86954e11i	−0.0697380	+	0.0402633i	−0.534464	−	0.845192i	$-0.679486\pi$
$443$	−1.18984e12	+	6.86954e11i	−0.0697380	+	0.0402633i	0.464726	+	0.885455i	$0.346153\pi$
$444$		0			0
$445$	1.04698e13	−	1.81342e13i	0.599982	−	1.03920i
$446$	1.03447e13	+	5.97251e12i	0.586196	+	0.338441i
$447$		0			0
$448$	−1.08997e13	−	1.88789e13i	−0.603984	−	1.04613i
$449$			1.04566e13i			0.573004i	0.958080	+	0.286502i	$0.0924925\pi$
$449$			1.04566e13i			0.573004i	−0.958080	+	0.286502i	$0.907508\pi$
$450$		0			0
$451$	3.32915e13			1.78423
$452$	6.76037e11	−	3.90310e11i	0.0358326	−	0.0206880i
$453$		0			0
$454$	1.13126e13	−	1.95940e13i	0.586521	−	1.01588i
$455$	3.29005e13	+	1.89951e13i	1.68712	+	0.974058i
$456$		0			0
$457$	−1.69623e13	−	2.93796e13i	−0.850951	−	1.47389i	−0.880351	−	0.474322i	$-0.842693\pi$
$457$	−1.69623e13	−	2.93796e13i	−0.850951	−	1.47389i	0.0294005	−	0.999568i	$-0.490640\pi$
$458$			4.90325e12i			0.243308i
$459$		0			0
$460$	−5.15240e12			−0.250162
$461$	1.98110e13	−	1.14379e13i	0.951485	−	0.549340i	0.0579434	−	0.998320i	$-0.481546\pi$
$461$	1.98110e13	−	1.14379e13i	0.951485	−	0.549340i	0.893542	+	0.448979i	$0.148212\pi$
$462$		0			0
$463$	1.83345e12	−	3.17563e12i	0.0861716	−	0.149254i	−0.819718	−	0.572767i	$-0.805870\pi$
$463$	1.83345e12	−	3.17563e12i	0.0861716	−	0.149254i	0.905890	+	0.423513i	$0.139203\pi$
$464$	−2.74385e12	−	1.58416e12i	−0.127577	−	0.0736563i
$465$		0			0
$466$	1.49256e13	+	2.58520e13i	0.679209	+	1.17642i
$467$		−	2.48699e13i		−	1.11967i	−0.828605	−	0.559834i	$-0.810865\pi$
$467$		−	2.48699e13i		−	1.11967i	0.828605	−	0.559834i	$-0.189135\pi$
$468$		0			0
$469$	−3.11902e13			−1.37453
$470$	1.27920e13	−	7.38548e12i	0.557764	−	0.322025i
$471$		0			0
$472$	1.87786e13	−	3.25256e13i	0.801593	−	1.38840i
$473$	−2.07750e13	−	1.19944e13i	−0.877475	−	0.506611i
$474$		0			0
$475$	−1.35973e13	−	2.35512e13i	−0.562321	−	0.973969i
$476$		−	2.05285e13i		−	0.840083i
$477$		0			0
$478$	−2.35081e13			−0.942060
$479$	3.81706e12	−	2.20378e12i	0.151374	−	0.0873959i	−0.422400	−	0.906410i	$-0.638812\pi$
$479$	3.81706e12	−	2.20378e12i	0.151374	−	0.0873959i	0.573774	+	0.819014i	$0.305479\pi$
$480$		0			0
$481$	2.27576e12	−	3.94173e12i	0.0883896	−	0.153095i
$482$	−1.14380e13	−	6.60372e12i	−0.439657	−	0.253836i
$483$		0			0
$484$	7.75743e12	+	1.34363e13i	0.292073	+	0.505885i
$485$		−	5.38470e13i		−	2.00656i
$486$		0			0
$487$	−9.42862e12			−0.344194			−0.172097	−	0.985080i	$-0.555054\pi$
$487$	−9.42862e12			−0.344194			−0.172097	+	0.985080i	$0.555054\pi$
$488$	−4.41527e13	+	2.54916e13i	−1.59536	+	0.921080i
$489$		0			0
$490$	−9.51555e12	+	1.64814e13i	−0.336863	+	0.583464i
$491$	−1.21887e13	−	7.03713e12i	−0.427119	−	0.246597i	0.271000	−	0.962579i	$-0.412646\pi$
$491$	−1.21887e13	−	7.03713e12i	−0.427119	−	0.246597i	−0.698119	+	0.715982i	$0.745979\pi$
$492$		0			0
$493$	−9.25320e12	−	1.60270e13i	−0.317729	−	0.550323i
$494$			2.59794e13i			0.883069i
$495$		0			0
$496$	6.29473e12			0.209686
$497$	2.49930e13	−	1.44297e13i	0.824208	−	0.475857i
$498$		0			0
$499$	1.68854e13	−	2.92464e13i	0.545769	−	0.945300i	−0.452789	−	0.891618i	$-0.649571\pi$
$499$	1.68854e13	−	2.92464e13i	0.545769	−	0.945300i	0.998558	−	0.0536824i	$-0.0170959\pi$
$500$	−8.12350e10	−	4.69010e10i	−0.00259952	−	0.00150083i
$501$		0			0
$502$	−1.28709e13	−	2.22931e13i	−0.403730	−	0.699281i
$503$			4.24460e12i			0.131825i	0.997825	+	0.0659124i	$0.0209958\pi$
$503$			4.24460e12i			0.131825i	−0.997825	+	0.0659124i	$0.979004\pi$
$504$		0			0
$505$	−5.30811e13			−1.61615
$506$	1.22732e13	−	7.08596e12i	0.370004	−	0.213622i
$507$		0			0
$508$	−5.99097e11	+	1.03767e12i	−0.0177084	+	0.0306718i
$509$	−1.74176e13	−	1.00560e13i	−0.509798	−	0.294332i	0.222952	−	0.974829i	$-0.428431\pi$
$509$	−1.74176e13	−	1.00560e13i	−0.509798	−	0.294332i	−0.732751	+	0.680497i	$0.761764\pi$
$510$		0			0
$511$	−1.58322e13	−	2.74222e13i	−0.454399	−	0.787042i
$512$		−	2.21504e13i		−	0.629552i
$513$		0			0
$514$	−4.10966e13			−1.14549
$515$	−4.51566e13	+	2.60712e13i	−1.24648	+	0.719655i
$516$		0			0
$517$	1.72170e13	−	2.98208e13i	0.466128	−	0.807358i
$518$	5.02752e12	+	2.90264e12i	0.134805	+	0.0778295i
$519$		0			0
$520$	3.09716e13	+	5.36443e13i	0.814604	+	1.41094i
$521$			1.35570e12i			0.0353163i	0.999844	+	0.0176581i	$0.00562105\pi$
$521$			1.35570e12i			0.0353163i	−0.999844	+	0.0176581i	$0.994379\pi$
$522$		0			0
$523$	5.72383e13			1.46278			0.731389	−	0.681961i	$-0.238872\pi$
$523$	5.72383e13			1.46278			0.731389	+	0.681961i	$0.238872\pi$
$524$	6.62103e12	−	3.82265e12i	0.167598	−	0.0967628i
$525$		0			0
$526$	4.49779e12	−	7.79040e12i	0.111704	−	0.193478i
$527$	3.18420e13	+	1.83840e13i	0.783333	+	0.452258i
$528$		0			0
$529$	−1.76405e13	−	3.05543e13i	−0.425827	−	0.737554i
$530$		−	1.44877e13i		−	0.346432i
$531$		0			0
$532$	2.80838e13			0.659019
$533$	4.72674e13	−	2.72898e13i	1.09882	−	0.634403i
$534$		0			0
$535$	−3.70886e13	+	6.42393e13i	−0.846196	+	1.46565i
$536$	−4.40423e13	−	2.54278e13i	−0.995511	−	0.574759i
$537$		0			0
$538$	−1.82011e13	−	3.15252e13i	−0.403818	−	0.699434i
$539$			4.43653e13i			0.975212i
$540$		0			0
$541$	2.34478e13			0.505961			0.252980	−	0.967471i	$-0.418589\pi$
$541$	2.34478e13			0.505961			0.252980	+	0.967471i	$0.418589\pi$
$542$	3.79130e13	−	2.18891e13i	0.810573	−	0.467985i
$543$		0			0
$544$	2.82087e13	−	4.88589e13i	0.592091	−	1.02553i
$545$	5.35935e13	+	3.09422e13i	1.11463	+	0.643531i
$546$		0			0
$547$	6.84180e12	+	1.18503e13i	0.139712	+	0.241988i	0.927388	−	0.374102i	$-0.122049\pi$
$547$	6.84180e12	+	1.18503e13i	0.139712	+	0.241988i	−0.787676	+	0.616090i	$0.788716\pi$
$548$			3.07615e13i			0.622449i
$549$		0			0
$550$	5.60859e13			1.11440
$551$	2.19256e13	−	1.26588e13i	0.431712	−	0.249249i
$552$		0			0
$553$	−5.34218e13	+	9.25293e13i	−1.03298	+	1.78918i
$554$	4.01203e13	+	2.31635e13i	0.768804	+	0.443869i
$555$		0			0
$556$	7.07421e12	+	1.22529e13i	0.133139	+	0.230603i
$557$			6.54044e13i			1.21992i	0.792432	+	0.609960i	$0.208814\pi$
$557$			6.54044e13i			1.21992i	−0.792432	+	0.609960i	$0.791186\pi$
$558$		0			0
$559$	−3.93285e13			−0.720525
$560$	−2.86679e13	+	1.65514e13i	−0.520541	+	0.300535i
$561$		0			0
$562$	4.16435e12	−	7.21287e12i	0.0742790	−	0.128655i
$563$	−2.72295e13	−	1.57209e13i	−0.481390	−	0.277931i	0.239605	−	0.970870i	$-0.422982\pi$
$563$	−2.72295e13	−	1.57209e13i	−0.481390	−	0.277931i	−0.720996	+	0.692940i	$0.756315\pi$
$564$		0			0
$565$	−3.67629e12	−	6.36752e12i	−0.0638510	−	0.110593i
$566$		−	3.65959e13i		−	0.630013i
$567$		0			0
$568$	4.70554e13			0.795917
$569$	−8.78437e13	+	5.07166e13i	−1.47282	+	0.850332i	−0.999532	−	0.0305771i	$-0.990265\pi$
$569$	−8.78437e13	+	5.07166e13i	−1.47282	+	0.850332i	−0.473286	+	0.880909i	$0.656932\pi$
$570$		0			0
$571$	−1.43078e13	+	2.47818e13i	−0.235718	+	0.408275i	−0.959481	−	0.281773i	$-0.909077\pi$
$571$	−1.43078e13	+	2.47818e13i	−0.235718	+	0.408275i	0.723763	+	0.690048i	$0.242411\pi$
$572$	3.93271e13	+	2.27055e13i	0.642261	+	0.370810i
$573$		0			0
$574$	3.48071e13	+	6.02876e13i	0.558609	+	0.967539i
$575$			2.43209e13i			0.386937i
$576$		0			0
$577$	−1.60161e13			−0.250425			−0.125212	−	0.992130i	$-0.539961\pi$
$577$	−1.60161e13			−0.250425			−0.125212	+	0.992130i	$0.539961\pi$
$578$	−4.26010e13	+	2.45957e13i	−0.660359	+	0.381259i
$579$		0			0
$580$	9.49169e12	−	1.64401e13i	0.144612	−	0.250475i
$581$	1.04719e13	+	6.04597e12i	0.158178	+	0.0913241i
$582$		0			0
$583$	−1.68868e13	−	2.92488e13i	−0.250729	−	0.434275i
$584$		−	5.16289e13i		−	0.760027i
$585$		0			0
$586$	8.60719e13			1.24559
$587$	−1.14113e14	+	6.58831e13i	−1.63736	+	0.945330i	−0.655623	+	0.755089i	$0.727594\pi$
$587$	−1.14113e14	+	6.58831e13i	−1.63736	+	0.945330i	−0.981737	+	0.190242i	$0.939073\pi$
$588$		0			0
$589$	−2.51500e13	+	4.35611e13i	−0.354782	+	0.614501i
$590$	−9.63414e13	−	5.56228e13i	−1.34758	−	0.778023i
$591$		0			0
$592$	1.98298e12	+	3.43463e12i	0.0272716	+	0.0472358i
$593$			4.28136e13i			0.583859i	0.956440	+	0.291930i	$0.0942973\pi$
$593$			4.28136e13i			0.583859i	−0.956440	+	0.291930i	$0.905703\pi$
$594$		0			0
$595$	−1.93356e14			−2.59282
$596$	4.02120e13	−	2.32164e13i	0.534718	−	0.308719i
$597$		0			0
$598$	1.16171e13	−	2.01214e13i	0.151911	−	0.263118i
$599$	−1.09823e14	−	6.34064e13i	−1.42416	−	0.822240i	−0.427511	−	0.904010i	$-0.640609\pi$
$599$	−1.09823e14	−	6.34064e13i	−1.42416	−	0.822240i	−0.996651	+	0.0817702i	$0.973943\pi$
$600$		0			0
$601$	6.29495e13	+	1.09032e14i	0.802823	+	1.39053i	0.917751	+	0.397157i	$0.130003\pi$
$601$	6.29495e13	+	1.09032e14i	0.802823	+	1.39053i	−0.114927	+	0.993374i	$0.536664\pi$
$602$		−	5.01619e13i		−	0.634442i
$603$		0			0
$604$	3.91330e13			0.486809
$605$	1.26555e14	−	7.30664e13i	1.56135	−	0.901448i
$606$		0			0
$607$	2.57876e13	−	4.46654e13i	0.312944	−	0.542035i	−0.666054	−	0.745903i	$-0.732018\pi$
$607$	2.57876e13	−	4.46654e13i	0.312944	−	0.542035i	0.978998	+	0.203868i	$0.0653514\pi$
$608$	6.68410e13	+	3.85906e13i	0.804498	+	0.464477i
$609$		0			0
$610$	7.55066e13	+	1.30781e14i	0.893997	+	1.54845i
$611$		−	5.64529e13i		−	0.662949i
$612$		0			0
$613$	6.86500e13			0.793119			0.396560	−	0.918009i	$-0.370204\pi$
$613$	6.86500e13			0.793119			0.396560	+	0.918009i	$0.370204\pi$
$614$	8.45245e13	−	4.88003e13i	0.968592	−	0.559217i
$615$		0			0
$616$	−9.20892e13	+	1.59503e14i	−1.03826	+	1.79832i
$617$	8.06745e13	+	4.65775e13i	0.902216	+	0.520895i	0.877919	−	0.478810i	$-0.158932\pi$
$617$	8.06745e13	+	4.65775e13i	0.902216	+	0.520895i	0.0242976	+	0.999705i	$0.492265\pi$
$618$		0			0
$619$	4.65318e13	+	8.05954e13i	0.512031	+	0.886864i	0.999903	+	0.0139483i	$0.00444002\pi$
$619$	4.65318e13	+	8.05954e13i	0.512031	+	0.886864i	−0.487872	+	0.872915i	$0.662227\pi$
$620$			3.77156e13i			0.411682i
$621$		0			0
$622$	−1.74543e13			−0.187478
$623$	8.83980e13	−	5.10366e13i	0.941894	−	0.543803i
$624$		0			0
$625$	4.74623e13	−	8.22072e13i	0.497679	−	0.862005i
$626$	2.44366e13	+	1.41085e13i	0.254197	+	0.146760i
$627$		0			0
$628$	1.85354e13	+	3.21042e13i	0.189759	+	0.328673i
$629$			2.31655e13i			0.235282i
$630$		0			0
$631$	8.95590e13			0.895288			0.447644	−	0.894212i	$-0.352263\pi$
$631$	8.95590e13			0.895288			0.447644	+	0.894212i	$0.352263\pi$
$632$	−1.50869e14	+	8.71044e13i	−1.49629	+	0.863882i
$633$		0			0
$634$	2.45750e13	−	4.25652e13i	0.239910	−	0.415536i
$635$	9.77368e12	+	5.64283e12i	0.0946650	+	0.0546548i
$636$		0			0
$637$	3.63673e13	+	6.29900e13i	0.346748	+	0.600585i
$638$			5.22147e13i			0.493957i
$639$		0			0
$640$	2.08709e13			0.194375
$641$	−9.32438e13	+	5.38344e13i	−0.861648	+	0.497473i	−0.864564	−	0.502523i	$-0.832405\pi$
$641$	−9.32438e13	+	5.38344e13i	−0.861648	+	0.497473i	0.00291565	+	0.999996i	$0.499072\pi$
$642$		0			0
$643$	−2.37874e13	+	4.12010e13i	−0.216417	+	0.374846i	−0.953710	−	0.300728i	$-0.902771\pi$
$643$	−2.37874e13	+	4.12010e13i	−0.216417	+	0.374846i	0.737293	+	0.675573i	$0.236104\pi$
$644$	−2.17512e13	−	1.25581e13i	−0.196361	−	0.113369i
$645$		0			0
$646$	−6.61126e13	−	1.14510e14i	−0.587654	−	1.01785i
$647$			1.19789e13i			0.105656i	0.998604	+	0.0528280i	$0.0168235\pi$
$647$			1.19789e13i			0.105656i	−0.998604	+	0.0528280i	$0.983176\pi$
$648$		0			0
$649$	−2.59335e14			−2.25236
$650$	7.96310e13	−	4.59750e13i	0.686303	−	0.396237i
$651$		0			0
$652$	−4.65894e12	+	8.06952e12i	−0.0395411	+	0.0684873i
$653$	−1.38814e13	−	8.01446e12i	−0.116915	−	0.0675007i	0.440402	−	0.897801i	$-0.354836\pi$
$653$	−1.38814e13	−	8.01446e12i	−0.116915	−	0.0675007i	−0.557317	+	0.830300i	$0.688169\pi$
$654$		0			0
$655$	−3.60051e13	−	6.23627e13i	−0.298647	−	0.517272i
$656$			4.75580e13i			0.391476i
$657$		0			0
$658$	7.20033e13			0.583744
$659$	1.93514e14	−	1.11726e14i	1.55699	−	0.898930i	0.559450	−	0.828864i	$-0.311012\pi$
$659$	1.93514e14	−	1.11726e14i	1.55699	−	0.898930i	0.997542	−	0.0700656i	$-0.0223208\pi$
$660$		0			0
$661$	−9.09783e12	+	1.57579e13i	−0.0720992	+	0.124880i	−0.899821	−	0.436259i	$-0.856303\pi$
$661$	−9.09783e12	+	1.57579e13i	−0.0720992	+	0.124880i	0.827722	+	0.561138i	$0.189636\pi$
$662$	−1.16926e14	−	6.75073e13i	−0.919647	−	0.530959i
$663$		0			0
$664$	9.85797e12	+	1.70745e13i	0.0763743	+	0.132284i
$665$		−	2.64518e14i		−	2.03398i
$666$		0			0
$667$	−2.26422e13			−0.171510
$668$	−1.75385e13	+	1.01259e13i	−0.131859	+	0.0761289i
$669$		0			0
$670$	−7.53178e13	+	1.30454e14i	−0.557858	+	0.966239i
$671$	3.04877e14	+	1.76021e14i	2.24136	+	1.29405i
$672$		0			0
$673$	−1.19622e14	−	2.07191e14i	−0.866432	−	1.50070i	−0.865618	−	0.500705i	$-0.833074\pi$
$673$	−1.19622e14	−	2.07191e14i	−0.866432	−	1.50070i	−0.000814545	−	1.00000i	$-0.500259\pi$
$674$		−	8.96946e12i		−	0.0644862i
$675$		0			0
$676$	9.69004e12			0.0686423
$677$	−2.00676e14	+	1.15860e14i	−1.41108	+	0.814686i	−0.995490	−	0.0948664i	$-0.969758\pi$
$677$	−2.00676e14	+	1.15860e14i	−1.41108	+	0.814686i	−0.415588	+	0.909553i	$0.636424\pi$
$678$		0			0
$679$	1.31243e14	−	2.27319e14i	0.909340	−	1.57502i
$680$	−2.73029e14	−	1.57633e14i	−1.87786	−	1.08419i
$681$		0			0
$682$	−5.18692e13	−	8.98401e13i	−0.351550	−	0.608903i
$683$		−	1.67561e14i		−	1.12738i	−0.825986	−	0.563690i	$-0.809381\pi$
$683$		−	1.67561e14i		−	1.12738i	0.825986	−	0.563690i	$-0.190619\pi$
$684$		0			0
$685$	2.89739e14			1.92112
$686$	4.38738e13	−	2.53305e13i	0.288792	−	0.166734i
$687$		0			0
$688$	1.71345e13	−	2.96778e13i	0.111155	−	0.192526i
$689$	−4.79519e13	−	2.76850e13i	−0.308823	−	0.178299i
$690$		0			0
$691$	−9.62134e13	−	1.66647e14i	−0.610725	−	1.05781i	−0.991119	−	0.132982i	$-0.957545\pi$
$691$	−9.62134e13	−	1.66647e14i	−0.610725	−	1.05781i	0.380394	−	0.924825i	$-0.375788\pi$
$692$		−	5.96094e13i		−	0.375651i
$693$		0			0
$694$	−8.35017e12			−0.0518678
$695$	1.15409e14	−	6.66312e13i	0.711729	−	0.410917i
$696$		0			0
$697$	−1.38895e14	+	2.40573e14i	−0.844349	+	1.46246i
$698$	1.56578e14	+	9.04003e13i	0.945047	+	0.545623i
$699$		0			0
$700$	−4.96991e13	−	8.60813e13i	−0.295705	−	0.512175i
$701$			3.26565e14i			1.92921i	0.263702	+	0.964604i	$0.415057\pi$
$701$			3.26565e14i			1.92921i	−0.263702	+	0.964604i	$0.584943\pi$
$702$		0			0
$703$	−3.16913e13			−0.184571
$704$	−2.12552e14	+	1.22717e14i	−1.22914	+	0.709645i
$705$		0			0
$706$	7.74804e13	−	1.34200e14i	0.441742	−	0.765119i
$707$	−2.24085e14	−	1.29376e14i	−1.26858	−	0.732413i
$708$		0			0
$709$	1.60811e14	+	2.78533e14i	0.897604	+	1.55470i	0.830549	+	0.556946i	$0.188027\pi$
$709$	1.60811e14	+	2.78533e14i	0.897604	+	1.55470i	0.0670547	+	0.997749i	$0.478640\pi$
$710$		−	1.39379e14i		−	0.772514i
$711$		0			0
$712$	1.66431e14			0.909563
$713$	3.89579e13	−	2.24924e13i	0.211421	−	0.122064i
$714$		0			0
$715$	2.13861e14	−	3.70418e14i	1.14446	−	1.98226i
$716$	6.98644e13	+	4.03362e13i	0.371271	+	0.214353i
$717$		0			0
$718$	−7.87231e13	−	1.36352e14i	−0.412553	−	0.714563i
$719$			2.74758e13i			0.142990i	0.997441	+	0.0714950i	$0.0227770\pi$
$719$			2.74758e13i			0.142990i	−0.997441	+	0.0714950i	$0.977223\pi$
$720$		0			0
$721$	−2.54175e14			−1.30454
$722$	3.16521e13	−	1.82743e13i	0.161331	−	0.0931442i
$723$		0			0
$724$	2.29387e13	−	3.97311e13i	0.115313	−	0.199727i
$725$	−7.76022e13	−	4.48037e13i	−0.387422	−	0.223678i
$726$		0			0
$727$	−4.21021e13	−	7.29230e13i	−0.207316	−	0.359081i	0.743552	−	0.668678i	$-0.233139\pi$
$727$	−4.21021e13	−	7.29230e13i	−0.207316	−	0.359081i	−0.950868	+	0.309597i	$0.899806\pi$
$728$			3.01951e14i			1.47666i
$729$		0			0
$730$	−1.52926e14			−0.737679
$731$	1.73350e14	−	1.00084e14i	0.830494	−	0.479486i
$732$		0			0
$733$	−1.81007e14	+	3.13513e14i	−0.855412	+	1.48162i	0.0208494	+	0.999783i	$0.493363\pi$
$733$	−1.81007e14	+	3.13513e14i	−0.855412	+	1.48162i	−0.876262	+	0.481835i	$0.839970\pi$
$734$	1.89853e14	+	1.09612e14i	0.891122	+	0.514489i
$735$		0			0
$736$	−3.45127e13	−	5.97778e13i	−0.159805	−	0.276790i
$737$			3.51162e14i			1.61499i
$738$		0			0
$739$	−2.44206e14			−1.10799			−0.553993	−	0.832522i	$-0.686896\pi$
$739$	−2.44206e14			−1.10799			−0.553993	+	0.832522i	$0.686896\pi$
$740$	−2.05790e13	+	1.18813e13i	−0.0927395	+	0.0535432i
$741$		0			0
$742$	3.53111e13	−	6.11606e13i	0.156997	−	0.271927i
$743$	5.96794e13	+	3.44559e13i	0.263560	+	0.152167i	0.625958	−	0.779857i	$-0.284708\pi$
$743$	5.96794e13	+	3.44559e13i	0.263560	+	0.152167i	−0.362397	+	0.932024i	$0.618042\pi$
$744$		0			0
$745$	−2.18673e14	−	3.78753e14i	−0.952826	−	1.65034i
$746$			1.45598e13i			0.0630176i
$747$		0			0
$748$	−2.31124e14			−0.987047
$749$	−3.13144e14	+	1.80794e14i	−1.32842	+	0.766962i
$750$		0			0
$751$	1.22270e14	−	2.11778e14i	0.511825	−	0.886506i	−0.488081	−	0.872798i	$-0.662303\pi$
$751$	1.22270e14	−	2.11778e14i	0.511825	−	0.886506i	0.999906	−	0.0137082i	$-0.00436360\pi$
$752$	4.26000e13	+	2.45951e13i	0.177141	+	0.102273i
$753$		0			0
$754$	4.28016e13	+	7.41346e13i	0.175632	+	0.304203i
$755$		−	3.68589e14i		−	1.50248i
$756$		0			0
$757$	−3.72001e13			−0.149646			−0.0748230	−	0.997197i	$-0.523839\pi$
$757$	−3.72001e13			−0.149646			−0.0748230	+	0.997197i	$0.523839\pi$
$758$	1.38617e13	−	8.00306e12i	0.0553950	−	0.0319823i
$759$		0			0
$760$	2.15649e14	−	3.73515e14i	0.850510	−	1.47313i
$761$	4.82702e13	+	2.78688e13i	0.189128	+	0.109193i	0.591574	−	0.806250i	$-0.298507\pi$
$761$	4.82702e13	+	2.78688e13i	0.189128	+	0.109193i	−0.402446	+	0.915444i	$0.631840\pi$
$762$		0			0
$763$	1.50833e14	+	2.61250e14i	0.583274	+	1.01026i
$764$			4.72873e13i			0.181668i
$765$		0			0
$766$	−1.32389e14			−0.502005
$767$	−3.68205e14	+	2.12583e14i	−1.38712	+	0.800853i
$768$		0			0
$769$	−2.09461e13	+	3.62798e13i	−0.0778883	+	0.134906i	−0.902339	−	0.431028i	$-0.858151\pi$
$769$	−2.09461e13	+	3.62798e13i	−0.0778883	+	0.134906i	0.824450	+	0.565934i	$0.191484\pi$
$770$	4.72452e14	+	2.72770e14i	1.74544	+	1.00773i
$771$		0			0
$772$	7.71444e13	+	1.33618e14i	0.281331	+	0.487280i
$773$			4.44998e13i			0.161236i	0.996745	+	0.0806178i	$0.0256893\pi$
$773$			4.44998e13i			0.161236i	−0.996745	+	0.0806178i	$0.974311\pi$
$774$		0			0
$775$	1.78029e14			0.636769
$776$	3.70644e14	−	2.13991e14i	1.31719	−	0.760480i
$777$		0			0
$778$	−1.13521e14	+	1.96625e14i	−0.398272	+	0.689827i
$779$	−3.29113e14	−	1.90014e14i	−1.14725	−	0.662365i
$780$		0			0
$781$	−1.62460e14	−	2.81389e14i	−0.559103	−	0.968395i
$782$			1.18253e14i			0.404369i
$783$		0			0
$784$	−6.33773e13			−0.213970
$785$	3.02386e14	−	1.74583e14i	1.01441	−	0.585670i
$786$		0			0
$787$	2.64586e12	−	4.58276e12i	0.00876381	−	0.0151794i	−0.861610	−	0.507570i	$-0.830544\pi$
$787$	2.64586e12	−	4.58276e12i	0.00876381	−	0.0151794i	0.870374	+	0.492391i	$0.163877\pi$
$788$	−9.04634e13	−	5.22291e13i	−0.297743	−	0.171902i
$789$		0			0
$790$	2.58005e14	+	4.46878e14i	0.838481	+	1.45229i
$791$		−	3.58412e13i		−	0.115745i
$792$		0			0
$793$	5.77155e14			1.84046
$794$	−3.02627e12	+	1.74722e12i	−0.00958971	+	0.00553662i
$795$		0			0
$796$	−4.15016e13	+	7.18828e13i	−0.129867	+	0.224936i
$797$	−1.98830e14	−	1.14794e14i	−0.618287	−	0.356968i	0.157915	−	0.987453i	$-0.449523\pi$
$797$	−1.98830e14	−	1.14794e14i	−0.618287	−	0.356968i	−0.776202	+	0.630485i	$0.782856\pi$
$798$		0			0
$799$	1.43662e14	+	2.48829e14i	0.441171	+	0.764130i
$800$		−	2.73171e14i		−	0.833651i
$801$		0			0
$802$	−5.07360e12			−0.0152913
$803$	−3.08739e14	+	1.78251e14i	−0.924728	+	0.533892i
$804$		0			0
$805$	−1.18283e14	+	2.04872e14i	−0.349900	+	0.606044i
$806$	−1.47288e14	−	8.50369e13i	−0.433005	−	0.249995i
$807$		0			0
$808$	−2.10947e14	−	3.65372e14i	−0.612516	−	1.06091i
$809$		−	2.21639e14i		−	0.639594i	−0.947486	−	0.319797i	$-0.896385\pi$
$809$		−	2.21639e14i		−	0.639594i	0.947486	−	0.319797i	$-0.103615\pi$
$810$		0			0
$811$	2.70111e14			0.769907			0.384953	−	0.922936i	$-0.374218\pi$
$811$	2.70111e14			0.769907			0.384953	+	0.922936i	$0.374218\pi$
$812$	8.01396e13	−	4.62686e13i	0.227022	−	0.131071i
$813$		0			0
$814$	3.26800e13	−	5.66034e13i	0.0914450	−	0.158387i
$815$	7.60059e13	+	4.38821e13i	0.211378	+	0.122039i
$816$		0			0
$817$	1.36918e14	+	2.37150e14i	0.376142	+	0.651496i
$818$		−	2.60345e14i		−	0.710858i
$819$		0			0
$820$	−2.84949e14			−0.768596
$821$	1.26495e14	−	7.30320e13i	0.339124	−	0.195793i	−0.320761	−	0.947160i	$-0.603939\pi$
$821$	1.26495e14	−	7.30320e13i	0.339124	−	0.195793i	0.659885	+	0.751367i	$0.270605\pi$
$822$		0			0
$823$	1.91213e13	−	3.31190e13i	0.0506428	−	0.0877159i	−0.839593	−	0.543216i	$-0.817206\pi$
$823$	1.91213e13	−	3.31190e13i	0.0506428	−	0.0877159i	0.890236	+	0.455500i	$0.150540\pi$
$824$	−3.58910e14	−	2.07217e14i	−0.944821	−	0.545493i
$825$		0			0
$826$	−2.71141e14	−	4.69631e14i	−0.705173	−	1.22140i
$827$			3.49746e13i			0.0904119i	0.998978	+	0.0452060i	$0.0143944\pi$
$827$			3.49746e13i			0.0904119i	−0.998978	+	0.0452060i	$0.985606\pi$
$828$		0			0
$829$	6.43554e14			1.64366			0.821831	−	0.569732i	$-0.192953\pi$
$829$	6.43554e14			1.64366			0.821831	+	0.569732i	$0.192953\pi$
$830$	5.05751e13	−	2.91995e13i	0.128394	−	0.0741286i
$831$		0			0
$832$	−2.01188e14	+	3.48468e14i	−0.504644	+	0.874070i
$833$	−3.20595e14	−	1.85095e14i	−0.799339	−	0.461499i
$834$		0			0
$835$	9.53744e13	+	1.65193e14i	0.234963	+	0.406968i
$836$		−	3.16188e14i		−	0.774308i
$837$		0			0
$838$	−1.82651e14			−0.441980
$839$	6.72646e13	−	3.88352e13i	0.161799	−	0.0934149i	−0.416914	−	0.908946i	$-0.636888\pi$
$839$	6.72646e13	−	3.88352e13i	0.161799	−	0.0934149i	0.578713	+	0.815531i	$0.303555\pi$
$840$		0			0
$841$	−1.68643e14	+	2.92097e14i	−0.400855	+	0.694301i
$842$	1.92469e14	+	1.11122e14i	0.454780	+	0.262567i
$843$		0			0
$844$	6.27723e13	+	1.08725e14i	0.146574	+	0.253873i
$845$		−	9.12695e13i		−	0.211857i
$846$		0			0
$847$	7.12346e14			1.63408
$848$	4.17829e13	−	2.41234e13i	0.0952838	−	0.0550121i
$849$		0			0
$850$	−2.33995e14	+	4.05291e14i	−0.527366	+	0.913424i
$851$	2.45453e13	+	1.41712e13i	0.0549946	+	0.0317512i
$852$		0			0
$853$	1.76843e14	+	3.06302e14i	0.391601	+	0.678272i	0.992661	−	0.120931i	$-0.0385881\pi$
$853$	1.76843e14	+	3.06302e14i	0.391601	+	0.678272i	−0.601060	+	0.799204i	$0.705255\pi$
$854$			7.36136e14i			1.62057i
$855$		0			0
$856$	−5.89569e14			−1.28282
$857$	4.79645e14	−	2.76923e14i	1.03757	−	0.599040i	0.118424	−	0.992963i	$-0.462216\pi$
$857$	4.79645e14	−	2.76923e14i	1.03757	−	0.599040i	0.919143	+	0.393924i	$0.128883\pi$
$858$		0			0
$859$	−2.41046e14	+	4.17503e14i	−0.515387	+	0.892676i	0.484454	+	0.874817i	$0.339018\pi$
$859$	−2.41046e14	+	4.17503e14i	−0.515387	+	0.892676i	−0.999841	+	0.0178594i	$0.994315\pi$
$860$	1.77818e14	+	1.02663e14i	0.377992	+	0.218234i
$861$		0			0
$862$	1.83932e14	+	3.18580e14i	0.386475	+	0.669394i
$863$			2.02122e14i			0.422240i	0.977460	+	0.211120i	$0.0677111\pi$
$863$			2.02122e14i			0.422240i	−0.977460	+	0.211120i	$0.932289\pi$
$864$		0			0
$865$	−5.61454e14			−1.15940
$866$	−3.43113e14	+	1.98096e14i	−0.704446	+	0.406712i
$867$		0			0
$868$	−9.19250e13	+	1.59219e14i	−0.186567	+	0.323144i
$869$	1.04176e15	+	6.01461e14i	2.10218	+	1.21369i
$870$		0			0
$871$	2.87856e14	+	4.98581e14i	0.574228	+	0.994592i
$872$			4.91866e14i			0.975583i
$873$		0			0
$874$	−1.61775e14			−0.317215
$875$	−3.72981e12	+	2.15340e12i	−0.00727187	+	0.00419842i
$876$		0			0
$877$	1.41832e14	−	2.45660e14i	0.273386	−	0.473518i	−0.696341	−	0.717711i	$-0.745190\pi$
$877$	1.41832e14	−	2.45660e14i	0.273386	−	0.473518i	0.969727	+	0.244193i	$0.0785232\pi$
$878$	1.25210e14	+	7.22898e13i	0.239975	+	0.138549i
$879$		0			0
$880$	1.86348e14	+	3.22763e14i	0.353110	+	0.611605i
$881$		−	7.92783e14i		−	1.49374i	−0.664970	−	0.746870i	$-0.731556\pi$
$881$		−	7.92783e14i		−	1.49374i	0.664970	−	0.746870i	$-0.268444\pi$
$882$		0			0
$883$	5.58732e14			1.04088			0.520439	−	0.853899i	$-0.325768\pi$
$883$	5.58732e14			1.04088			0.520439	+	0.853899i	$0.325768\pi$
$884$	−3.28151e14	+	1.89458e14i	−0.607873	+	0.350956i
$885$		0			0
$886$	−1.61726e13	+	2.80118e13i	−0.0296218	+	0.0513065i
$887$	−4.85660e13	−	2.80396e13i	−0.0884533	−	0.0510685i	0.455121	−	0.890430i	$-0.349596\pi$
$887$	−4.85660e13	−	2.80396e13i	−0.0884533	−	0.0510685i	−0.543574	+	0.839361i	$0.682929\pi$
$888$		0			0
$889$	2.75068e13	+	4.76432e13i	0.0495372	+	0.0858010i
$890$		−	4.92971e14i		−	0.882818i
$891$		0			0
$892$	−2.38342e14			−0.422062
$893$	−3.40409e14	+	1.96535e14i	−0.599437	+	0.346085i
$894$		0			0
$895$	3.79922e14	−	6.58045e14i	0.661576	−	1.14588i
$896$	8.81080e13	+	5.08692e13i	0.152572	+	0.0880876i
$897$		0			0
$898$	1.23087e14	+	2.13193e14i	0.210781	+	0.365083i
$899$			1.65741e14i			0.282248i
$900$		0			0
$901$	2.81812e14			0.474609
$902$	6.78761e14	−	3.91883e14i	1.13680	−	0.656332i
$903$		0			0
$904$	2.92196e13	−	5.06099e13i	0.0483985	−	0.0838287i
$905$	−3.74223e14	−	2.16058e14i	−0.616435	−	0.355899i
$906$		0			0
$907$	5.11795e13	+	8.86455e13i	0.0833795	+	0.144418i	0.904700	−	0.426050i	$-0.140095\pi$
$907$	5.11795e13	+	8.86455e13i	0.0833795	+	0.144418i	−0.821320	+	0.570468i	$0.806762\pi$
$908$			4.51447e14i			0.731438i
$909$		0			0
$910$	8.94386e14			1.43324
$911$	1.75865e14	−	1.01536e14i	0.280277	−	0.161818i	−0.353272	−	0.935521i	$-0.614931\pi$
$911$	1.75865e14	−	1.01536e14i	0.280277	−	0.161818i	0.633549	+	0.773703i	$0.281597\pi$
$912$		0			0
$913$	6.80699e13	−	1.17901e14i	0.107300	−	0.185850i
$914$	−6.91670e14	−	3.99336e14i	−1.08435	−	0.626048i
$915$		0			0
$916$	−4.89178e13	−	8.47282e13i	−0.0758560	−	0.131386i
$917$		−	3.51025e14i		−	0.541366i
$918$		0			0
$919$	−1.21378e15			−1.85167			−0.925835	−	0.377929i	$-0.876636\pi$
$919$	−1.21378e15			−1.85167			−0.925835	+	0.377929i	$0.876636\pi$
$920$	−3.34045e14	+	1.92861e14i	−0.506834	+	0.292621i
$921$		0			0
$922$	2.69277e14	−	4.66401e14i	0.404152	−	0.700012i
$923$	−4.61324e14	−	2.66345e14i	−0.688648	−	0.397591i
$924$		0			0
$925$	5.60832e13	+	9.71390e13i	0.0828179	+	0.143445i
$926$		−	8.63281e13i		−	0.126794i
$927$		0			0
$928$	2.54315e14			0.369516
$929$	−6.37295e14	+	3.67942e14i	−0.921005	+	0.531742i	−0.883955	−	0.467571i	$-0.845129\pi$
$929$	−6.37295e14	+	3.67942e14i	−0.921005	+	0.531742i	−0.0370493	+	0.999313i	$0.511796\pi$
$930$		0			0
$931$	2.53218e14	−	4.38586e14i	0.362031	−	0.627057i
$932$	−5.15831e14	−	2.97815e14i	−0.733546	−	0.423513i
$933$		0			0
$934$	−2.92750e14	−	5.07057e14i	−0.411872	−	0.713383i
$935$			2.17694e15i			3.04640i
$936$		0			0
$937$	−9.68431e14			−1.34082			−0.670410	−	0.741991i	$-0.733882\pi$
$937$	−9.68431e14			−1.34082			−0.670410	+	0.741991i	$0.733882\pi$
$938$	−6.35919e14	+	3.67148e14i	−0.875765	+	0.505623i
$939$		0			0
$940$	−1.47364e14	+	2.55242e14i	−0.200795	+	0.347787i
$941$	4.94676e14	+	2.85601e14i	0.670460	+	0.387090i	0.796251	−	0.604967i	$-0.206814\pi$
$941$	4.94676e14	+	2.85601e14i	0.670460	+	0.387090i	−0.125791	+	0.992057i	$0.540147\pi$
$942$		0			0
$943$	1.69935e14	+	2.94336e14i	0.227889	+	0.394716i
$944$		−	3.70469e14i		−	0.494188i
$945$		0			0
$946$	−5.64759e14			−0.745431
$947$	−4.38321e14	+	2.53065e14i	−0.575496	+	0.332263i	−0.759341	−	0.650693i	$-0.774479\pi$
$947$	−4.38321e14	+	2.53065e14i	−0.575496	+	0.332263i	0.183846	+	0.982955i	$0.441145\pi$
$948$		0			0
$949$	−2.92233e14	+	5.06162e14i	−0.379662	+	0.657595i
$950$	−5.54455e14	−	3.20115e14i	−0.716553	−	0.413702i
$951$		0			0
$952$	−7.68407e14	−	1.33092e15i	−0.982667	−	1.70203i
$953$		−	1.56038e14i		−	0.198503i	−0.995062	−	0.0992515i	$-0.968355\pi$
$953$		−	1.56038e14i		−	0.198503i	0.995062	−	0.0992515i	$-0.0316448\pi$
$954$		0			0
$955$	4.45394e14			0.560696
$956$	4.06221e14	−	2.34532e14i	0.508713	−	0.293705i
$957$		0			0
$958$	5.18826e13	−	8.98632e13i	0.0642975	−	0.111366i
$959$	1.22315e15	+	7.06187e14i	1.50795	+	0.870617i
$960$		0			0
$961$	2.45170e14	+	4.24647e14i	0.299124	+	0.518097i
$962$		−	1.07154e14i		−	0.130057i
$963$		0			0
$964$	2.63531e14			0.316553
$965$	1.25853e15	−	7.26615e14i	1.50393	−	0.868296i
$966$		0			0
$967$	4.10240e14	−	7.10557e14i	0.485183	−	0.840362i	−0.514672	−	0.857387i	$-0.672086\pi$
$967$	4.10240e14	−	7.10557e14i	0.485183	−	0.840362i	0.999855	+	0.0170254i	$0.00541962\pi$
$968$	1.00587e15	+	5.80741e14i	1.18349	+	0.683291i
$969$		0			0
$970$	−6.33847e14	−	1.09786e15i	−0.738118	−	1.27846i
$971$		−	3.49738e14i		−	0.405179i	−0.979264	−	0.202590i	$-0.935064\pi$
$971$		−	3.49738e14i		−	0.405179i	0.979264	−	0.202590i	$-0.0649357\pi$
$972$		0			0
$973$	6.49608e14			0.744881
$974$	−1.92235e14	+	1.10987e14i	−0.219299	+	0.126612i
$975$		0			0
$976$	−2.51452e14	+	4.35527e14i	−0.283926	+	0.491775i
$977$	−3.49868e13	−	2.01996e13i	−0.0393035	−	0.0226919i	0.480219	−	0.877148i	$-0.340557\pi$
$977$	−3.49868e13	−	2.01996e13i	−0.0393035	−	0.0226919i	−0.519523	+	0.854456i	$0.673890\pi$
$978$		0			0
$979$	−5.74607e14	−	9.95248e14i	−0.638936	−	1.10667i
$980$		−	3.79732e14i		−	0.420094i
$981$		0			0
$982$	−3.31344e14			−0.362845
$983$	2.67505e14	−	1.54444e14i	0.291450	−	0.168269i	−0.347146	−	0.937811i	$-0.612849\pi$
$983$	2.67505e14	−	1.54444e14i	0.291450	−	0.168269i	0.638595	+	0.769543i	$0.279516\pi$
$984$		0			0
$985$	−4.91940e14	+	8.52065e14i	−0.530556	+	0.918949i
$986$	−3.77316e14	−	2.17844e14i	−0.404875	−	0.233755i
$987$		0			0
$988$	−2.59187e14	−	4.48925e14i	−0.275314	−	0.476858i
$989$		−	2.44900e14i		−	0.258826i
$990$		0			0
$991$	1.06886e15			1.11828			0.559140	−	0.829073i	$-0.311131\pi$
$991$	1.06886e15			1.11828			0.559140	+	0.829073i	$0.311131\pi$
$992$	−4.37573e14	+	2.52633e14i	−0.455504	+	0.262985i
$993$		0			0
$994$	3.39712e14	−	5.88399e14i	0.350090	−	0.606373i
$995$	6.77057e14	+	3.90899e14i	0.694240	+	0.400820i
$996$		0			0
$997$	−4.62631e14	−	8.01300e14i	−0.469633	−	0.813429i	0.529764	−	0.848145i	$-0.322281\pi$
$997$	−4.62631e14	−	8.01300e14i	−0.469633	−	0.813429i	−0.999397	+	0.0347164i	$0.988947\pi$
$998$		−	7.95051e14i		−	0.803049i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.11.d.e.53.3		8
3.2	odd	2	inner	81.11.d.e.53.2		8
9.2	odd	6	inner	81.11.d.e.26.3		8
9.4	even	3		27.11.b.c.26.3	yes	4
9.5	odd	6		27.11.b.c.26.2	✓	4
9.7	even	3	inner	81.11.d.e.26.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.b.c.26.2	✓	4	9.5	odd	6
27.11.b.c.26.3	yes	4	9.4	even	3
81.11.d.e.26.2		8	9.7	even	3	inner
81.11.d.e.26.3		8	9.2	odd	6	inner
81.11.d.e.53.2		8	3.2	odd	2	inner
81.11.d.e.53.3		8	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(20.3884 - 11.7713i) q^{2} +(-234.875 + 406.815i) q^{4} +(3831.75 + 2212.26i) q^{5} +(10784.0 + 18678.4i) q^{7} +35166.6i q^{8} +104164. q^{10} +(210295. - 121414. i) q^{11} +(199052. - 344768. i) q^{13} +(439737. + 253882. i) q^{14} +(173444. + 300414. i) q^{16} +2.02619e6i q^{17} -2.77192e6 q^{19} +(-1.79996e6 + 1.03921e6i) q^{20} +(2.85839e6 - 4.95088e6i) q^{22} +(2.14688e6 + 1.23950e6i) q^{23} +(4.90538e6 + 8.49636e6i) q^{25} -9.37237e6i q^{26} -1.01315e7 q^{28} +(-7.90991e6 + 4.56679e6i) q^{29} +(9.07315e6 - 1.57152e7i) q^{31} +(-2.41136e7 - 1.39220e7i) q^{32} +(2.38509e7 + 4.13109e7i) q^{34} +9.54280e7i q^{35} +1.14330e7 q^{37} +(-5.65150e7 + 3.26290e7i) q^{38} +(-7.77977e7 + 1.34750e8i) q^{40} +(1.18731e8 + 6.85496e7i) q^{41} +(-4.93948e7 - 8.55544e7i) q^{43} +1.14068e8i q^{44} +5.83620e7 q^{46} +(1.22806e8 - 7.09022e7i) q^{47} +(-9.13512e7 + 1.58225e8i) q^{49} +(2.00026e8 + 1.15485e8i) q^{50} +(9.35045e7 + 1.61955e8i) q^{52} -1.39084e8i q^{53} +1.07440e9 q^{55} +(-6.56857e8 + 3.79237e8i) q^{56} +(-1.07514e8 + 1.86219e8i) q^{58} +(-9.24898e8 - 5.33990e8i) q^{59} +(7.24880e8 + 1.25553e9i) q^{61} -4.27210e8i q^{62} -1.01073e9 q^{64} +(1.52543e9 - 8.80709e8i) q^{65} +(-7.23067e8 + 1.25239e9i) q^{67} +(-8.24286e8 - 4.75902e8i) q^{68} +(1.12331e9 + 1.94563e9i) q^{70} -1.33807e9i q^{71} -1.46812e9 q^{73} +(2.33101e8 - 1.34581e8i) q^{74} +(6.51053e8 - 1.12766e9i) q^{76} +(4.53564e9 + 2.61865e9i) q^{77} +(2.47690e9 + 4.29012e9i) q^{79} +1.53481e9i q^{80} +3.22766e9 q^{82} +(4.85531e8 - 2.80322e8i) q^{83} +(-4.48247e9 + 7.76386e9i) q^{85} +(-2.01417e9 - 1.16288e9i) q^{86} +(4.26972e9 + 7.39537e9i) q^{88} -4.73263e9i q^{89} +8.58629e9 q^{91} +(-1.00850e9 + 5.82255e8i) q^{92} +(1.66922e9 - 2.89117e9i) q^{94} +(-1.06213e10 - 6.13220e9i) q^{95} +(-6.08507e9 - 1.05396e10i) q^{97} +4.30128e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 548 q^{4} - 20516 q^{7} - 399600 q^{10} + 262420 q^{13} + 3207800 q^{16} - 16467032 q^{19} + 21085704 q^{22} + 47203580 q^{25} - 135208424 q^{28} + 46994920 q^{31} + 78985368 q^{34} + 216172888 q^{37}+ \cdots - 12969797468 q^{97}+O(q^{100}) \) 8 * q + 548 * q^4 - 20516 * q^7 - 399600 * q^10 + 262420 * q^13 + 3207800 * q^16 - 16467032 * q^19 + 21085704 * q^22 + 47203580 * q^25 - 135208424 * q^28 + 46994920 * q^31 + 78985368 * q^34 + 216172888 * q^37 - 196812720 * q^40 - 78251000 * q^43 + 1765291536 * q^46 - 1826240448 * q^49 + 771022300 * q^52 + 2069150400 * q^55 - 1267544592 * q^58 + 3222389524 * q^61 - 2332527904 * q^64 - 1972286516 * q^67 + 17482328280 * q^70 + 8155197880 * q^73 + 603762388 * q^76 + 10402780252 * q^79 - 15891105312 * q^82 - 19825132320 * q^85 + 19783893168 * q^88 + 68321793560 * q^91 - 22345655544 * q^94 - 12969797468 * q^97

Introduction

L-functions

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