LMFDB - Embedded newform 81.9.d.c.53.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,9,Mod(26,81)] 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([1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.26"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,28] 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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.2
Root			$1.58114 - 2.73861i$ of defining polynomial
Character	$\chi$	$=$	81.53
Dual form			81.9.d.c.26.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(14.2302 - 8.21584i) q^{2} +(7.00000 - 12.1244i) q^{4} +(-369.986 - 213.612i) q^{5} +(339.500 + 588.031i) q^{7} +3976.47i q^{8} -7020.00 q^{10} +(11583.4 - 6687.69i) q^{11} +(15408.5 - 26688.3i) q^{13} +(9662.34 + 5578.55i) q^{14} +(34462.0 + 59689.9i) q^{16} -128266. i q^{17} -138391. q^{19} +(-5179.81 + 2990.57i) q^{20} +(109890. - 190335. i) q^{22} +(-263003. - 151845. i) q^{23} +(-104052. - 180224. i) q^{25} -506375. i q^{26} +9506.00 q^{28} +(1.14895e6 - 663347. i) q^{29} +(-176107. + 305026. i) q^{31} +(99213.3 + 57280.8i) q^{32} +(-1.05381e6 - 1.82525e6i) q^{34} -290085. i q^{35} +1.18999e6 q^{37} +(-1.96934e6 + 1.13700e6i) q^{38} +(849420. - 1.47124e6i) q^{40} +(947450. + 547011. i) q^{41} +(-3.12304e6 - 5.40927e6i) q^{43} -187255. i q^{44} -4.99014e6 q^{46} +(-2077.62 + 1199.51i) q^{47} +(2.65188e6 - 4.59319e6i) q^{49} +(-2.96139e6 - 1.70976e6i) q^{50} +(-215719. - 373636. i) q^{52} +1.25779e7i q^{53} -5.71428e6 q^{55} +(-2.33829e6 + 1.35001e6i) q^{56} +(1.08999e7 - 1.88792e7i) q^{58} +(9.12452e6 + 5.26804e6i) q^{59} +(-8.29020e6 - 1.43590e7i) q^{61} +5.78747e6i q^{62} -1.57621e7 q^{64} +(-1.14019e7 + 6.58287e6i) q^{65} +(-3.83358e6 + 6.63995e6i) q^{67} +(-1.55514e6 - 897860. i) q^{68} +(-2.38329e6 - 4.12798e6i) q^{70} -2.32211e7i q^{71} +2.49496e7 q^{73} +(1.69339e7 - 9.77677e6i) q^{74} +(-968737. + 1.67790e6i) q^{76} +(7.86514e6 + 4.54094e6i) q^{77} +(-2.08425e7 - 3.61003e7i) q^{79} -2.94460e7i q^{80} +1.79766e7 q^{82} +(3.87356e7 - 2.23640e7i) q^{83} +(-2.73991e7 + 4.74566e7i) q^{85} +(-8.88834e7 - 5.13168e7i) q^{86} +(2.65934e7 + 4.60611e7i) q^{88} -740707. i q^{89} +2.09247e7 q^{91} +(-3.68205e6 + 2.12583e6i) q^{92} +(-19710.0 + 34138.7i) q^{94} +(5.12028e7 + 2.95620e7i) q^{95} +(5.29630e7 + 9.17347e7i) q^{97} -8.71497e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 28 q^{4} + 1358 q^{7} - 28080 q^{10} + 61634 q^{13} + 137848 q^{16} - 553564 q^{19} + 439560 q^{22} - 416210 q^{25} + 38024 q^{28} - 704428 q^{31} - 4215240 q^{34} + 4759964 q^{37} + 3397680 q^{40}+ \cdots + 211852178 q^{97}+O(q^{100}) $ 4 * q + 28 * q^4 + 1358 * q^7 - 28080 * q^10 + 61634 * q^13 + 137848 * q^16 - 553564 * q^19 + 439560 * q^22 - 416210 * q^25 + 38024 * q^28 - 704428 * q^31 - 4215240 * q^34 + 4759964 * q^37 + 3397680 * q^40 - 12492172 * q^43 - 19960560 * q^46 + 10607520 * q^49 - 862876 * q^52 - 22857120 * q^55 + 43599600 * q^58 - 33160798 * q^61 - 63048416 * q^64 - 15334306 * q^67 - 9533160 * q^70 + 99798524 * q^73 - 3874948 * q^76 - 83370178 * q^79 + 71906400 * q^82 - 109596240 * q^85 + 106373520 * q^88 + 83698972 * q^91 - 78840 * q^94 + 211852178 * 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 $

$2$	14.2302	−	8.21584i	0.889391	−	0.513490i	0.0156475	−	0.999878i	$-0.495019\pi$
$2$	14.2302	−	8.21584i	0.889391	−	0.513490i	0.873743	+	0.486388i	$0.161686\pi$
$3$		0			0
$3$		0			0
$4$	7.00000	−	12.1244i	0.0273438	−	0.0473608i
$5$	−369.986	−	213.612i	−0.591978	−	0.341779i	0.173901	−	0.984763i	$-0.444363\pi$
$5$	−369.986	−	213.612i	−0.591978	−	0.341779i	−0.765879	+	0.642984i	$0.777696\pi$
$6$		0			0
$7$	339.500	+	588.031i	0.141399	+	0.244911i	0.928024	−	0.372521i	$-0.121506\pi$
$7$	339.500	+	588.031i	0.141399	+	0.244911i	−0.786624	+	0.617432i	$0.788173\pi$
$8$			3976.47i			0.970817i
$9$		0			0
$10$	−7020.00			−0.702000
$11$	11583.4	−	6687.69i	0.791163	−	0.456778i	−0.0492086	−	0.998789i	$-0.515670\pi$
$11$	11583.4	−	6687.69i	0.791163	−	0.456778i	0.840372	+	0.542010i	$0.182337\pi$
$12$		0			0
$13$	15408.5	−	26688.3i	0.539494	−	0.934432i	−0.459437	−	0.888210i	$-0.651949\pi$
$13$	15408.5	−	26688.3i	0.539494	−	0.934432i	0.998931	−	0.0462213i	$-0.0147179\pi$
$14$	9662.34	+	5578.55i	0.251519	+	0.145214i
$15$		0			0
$16$	34462.0	+	59689.9i	0.525848	+	0.910796i
$17$		−	128266.i		−	1.53573i	−0.640612	−	0.767865i	$-0.721319\pi$
$17$		−	128266.i		−	1.53573i	0.640612	−	0.767865i	$-0.278681\pi$
$18$		0			0
$19$	−138391.			−1.06192			−0.530962	−	0.847396i	$-0.678169\pi$
$19$	−138391.			−1.06192			−0.530962	+	0.847396i	$0.678169\pi$
$20$	−5179.81	+	2990.57i	−0.0323738	+	0.0186910i
$21$		0			0
$22$	109890.	−	190335.i	0.469102	−	0.812509i
$23$	−263003.	−	151845.i	−0.939832	−	0.542612i	−0.0499242	−	0.998753i	$-0.515898\pi$
$23$	−263003.	−	151845.i	−0.939832	−	0.542612i	−0.889908	+	0.456141i	$0.849231\pi$
$24$		0			0
$25$	−104052.	−	180224.i	−0.266374	−	0.461374i
$26$		−	506375.i		−	1.10810i
$27$		0			0
$28$	9506.00			0.0154656
$29$	1.14895e6	−	663347.i	1.62446	−	0.937883i	0.638755	−	0.769411i	$-0.279450\pi$
$29$	1.14895e6	−	663347.i	1.62446	−	0.937883i	0.985706	−	0.168472i	$-0.0538834\pi$
$30$		0			0
$31$	−176107.	+	305026.i	−0.190691	+	0.330286i	−0.945479	−	0.325682i	$-0.894406\pi$
$31$	−176107.	+	305026.i	−0.190691	+	0.330286i	0.754789	+	0.655968i	$0.227739\pi$
$32$	99213.3	+	57280.8i	0.0946172	+	0.0546273i
$33$		0			0
$34$	−1.05381e6	−	1.82525e6i	−0.788582	−	1.36586i
$35$		−	290085.i		−	0.193309i
$36$		0			0
$37$	1.18999e6			0.634946			0.317473	−	0.948267i	$-0.397166\pi$
$37$	1.18999e6			0.634946			0.317473	+	0.948267i	$0.397166\pi$
$38$	−1.96934e6	+	1.13700e6i	−0.944465	+	0.545287i
$39$		0			0
$40$	849420.	−	1.47124e6i	0.331805	−	0.574703i
$41$	947450.	+	547011.i	0.335290	+	0.193580i	0.658187	−	0.752854i	$-0.271323\pi$
$41$	947450.	+	547011.i	0.335290	+	0.193580i	−0.322897	+	0.946434i	$0.604657\pi$
$42$		0			0
$43$	−3.12304e6	−	5.40927e6i	−0.913491	−	1.58221i	−0.809096	−	0.587676i	$-0.800043\pi$
$43$	−3.12304e6	−	5.40927e6i	−0.913491	−	1.58221i	−0.104395	−	0.994536i	$-0.533291\pi$
$44$		−	187255.i		−	0.0499601i
$45$		0			0
$46$	−4.99014e6			−1.11450
$47$	−2077.62	+	1199.51i	−0.000425769	+	0.000245818i	−0.500213	−	0.865902i	$-0.666745\pi$
$47$	−2077.62	+	1199.51i	−0.000425769	+	0.000245818i	0.499787	+	0.866148i	$0.333412\pi$
$48$		0			0
$49$	2.65188e6	−	4.59319e6i	0.460012	−	0.796765i
$50$	−2.96139e6	−	1.70976e6i	−0.473822	−	0.273561i
$51$		0			0
$52$	−215719.	−	373636.i	−0.0295036	−	0.0511017i
$53$			1.25779e7i			1.59406i	0.603938	+	0.797031i	$0.293598\pi$
$53$			1.25779e7i			1.59406i	−0.603938	+	0.797031i	$0.706402\pi$
$54$		0			0
$55$	−5.71428e6			−0.624469
$56$	−2.33829e6	+	1.35001e6i	−0.237764	+	0.137273i
$57$		0			0
$58$	1.08999e7	−	1.88792e7i	0.963187	−	1.66829i
$59$	9.12452e6	+	5.26804e6i	0.753012	+	0.434752i	0.826781	−	0.562524i	$-0.190169\pi$
$59$	9.12452e6	+	5.26804e6i	0.753012	+	0.434752i	−0.0737690	+	0.997275i	$0.523503\pi$
$60$		0			0
$61$	−8.29020e6	−	1.43590e7i	−0.598750	−	1.03707i	−0.993006	−	0.118065i	$-0.962331\pi$
$61$	−8.29020e6	−	1.43590e7i	−0.598750	−	1.03707i	0.394256	−	0.919001i	$-0.371002\pi$
$62$			5.78747e6i			0.391671i
$63$		0			0
$64$	−1.57621e7			−0.939495
$65$	−1.14019e7	+	6.58287e6i	−0.638738	+	0.368776i
$66$		0			0
$67$	−3.83358e6	+	6.63995e6i	−0.190241	+	0.329508i	−0.945330	−	0.326115i	$-0.894260\pi$
$67$	−3.83358e6	+	6.63995e6i	−0.190241	+	0.329508i	0.755089	+	0.655623i	$0.227594\pi$
$68$	−1.55514e6	−	897860.i	−0.0727333	−	0.0419926i
$69$		0			0
$70$	−2.38329e6	−	4.12798e6i	−0.0992624	−	0.171928i
$71$		−	2.32211e7i		−	0.913797i	−0.889519	−	0.456898i	$-0.848960\pi$
$71$		−	2.32211e7i		−	0.913797i	0.889519	−	0.456898i	$-0.151040\pi$
$72$		0			0
$73$	2.49496e7			0.878563			0.439281	−	0.898350i	$-0.355233\pi$
$73$	2.49496e7			0.878563			0.439281	+	0.898350i	$0.355233\pi$
$74$	1.69339e7	−	9.77677e6i	0.564715	−	0.326038i
$75$		0			0
$76$	−968737.	+	1.67790e6i	−0.0290370	+	0.0502935i
$77$	7.86514e6	+	4.54094e6i	0.223740	+	0.129176i
$78$		0			0
$79$	−2.08425e7	−	3.61003e7i	−0.535109	−	0.926836i	−0.999158	−	0.0410266i	$-0.986937\pi$
$79$	−2.08425e7	−	3.61003e7i	−0.535109	−	0.926836i	0.464049	−	0.885810i	$-0.346396\pi$
$80$		−	2.94460e7i		−	0.718895i
$81$		0			0
$82$	1.79766e7			0.397605
$83$	3.87356e7	−	2.23640e7i	0.816202	−	0.471235i	−0.0329028	−	0.999459i	$-0.510475\pi$
$83$	3.87356e7	−	2.23640e7i	0.816202	−	0.471235i	0.849105	+	0.528224i	$0.177142\pi$
$84$		0			0
$85$	−2.73991e7	+	4.74566e7i	−0.524880	+	0.909119i
$86$	−8.88834e7	−	5.13168e7i	−1.62490	−	0.938137i
$87$		0			0
$88$	2.65934e7	+	4.60611e7i	0.443448	+	0.768075i
$89$		−	740707.i		−	0.0118056i	−0.999983	−	0.00590278i	$-0.998121\pi$
$89$		−	740707.i		−	0.0118056i	0.999983	−	0.00590278i	$-0.00187892\pi$
$90$		0			0
$91$	2.09247e7			0.305137
$92$	−3.68205e6	+	2.12583e6i	−0.0513971	+	0.0296741i
$93$		0			0
$94$	−19710.0	+	34138.7i	−0.000252450	+	0.000437256i
$95$	5.12028e7	+	2.95620e7i	0.628636	+	0.362943i
$96$		0			0
$97$	5.29630e7	+	9.17347e7i	0.598255	+	1.03621i	0.993079	+	0.117451i	$0.0374722\pi$
$97$	5.29630e7	+	9.17347e7i	0.598255	+	1.03621i	−0.394824	+	0.918757i	$0.629194\pi$
$98$		−	8.71497e7i		−	0.944847i
$99$		0			0
$100$	−2.91347e6			−0.0291347
$101$	−1.81799e7	+	1.04962e7i	−0.174705	+	0.100866i	−0.584803	−	0.811176i	$-0.698828\pi$
$101$	−1.81799e7	+	1.04962e7i	−0.174705	+	0.100866i	0.410097	+	0.912042i	$0.365495\pi$
$102$		0			0
$103$	−1.29268e7	+	2.23898e7i	−0.114853	+	0.198931i	−0.917721	−	0.397226i	$-0.869973\pi$
$103$	−1.29268e7	+	2.23898e7i	−0.114853	+	0.198931i	0.802868	+	0.596157i	$0.203306\pi$
$104$	1.06125e8	+	6.12714e7i	0.907162	+	0.523750i
$105$		0			0
$106$	1.03338e8	+	1.78987e8i	0.818535	+	1.41774i
$107$			1.92732e8i			1.47035i	0.677879	+	0.735173i	$0.262899\pi$
$107$			1.92732e8i			1.47035i	−0.677879	+	0.735173i	$0.737101\pi$
$108$		0			0
$109$	−1.09904e8			−0.778585			−0.389292	−	0.921114i	$-0.627280\pi$
$109$	−1.09904e8			−0.778585			−0.389292	+	0.921114i	$0.627280\pi$
$110$	−8.13156e7	+	4.69476e7i	−0.555397	+	0.320658i
$111$		0			0
$112$	−2.33997e7	+	4.05295e7i	−0.148709	+	0.257572i
$113$	2.32811e7	+	1.34414e7i	0.142787	+	0.0824384i	0.569692	−	0.821858i	$-0.307063\pi$
$113$	2.32811e7	+	1.34414e7i	0.142787	+	0.0824384i	−0.426904	+	0.904297i	$0.640396\pi$
$114$		0			0
$115$	6.48718e7	+	1.12361e8i	0.370907	+	0.642429i
$116$		−	1.85737e7i		−	0.102581i
$117$		0			0
$118$	1.73126e8			0.892963
$119$	7.54242e7	−	4.35462e7i	0.376117	−	0.217151i
$120$		0			0
$121$	−1.77290e7	+	3.07075e7i	−0.0827070	+	0.143253i
$122$	−2.35943e8	−	1.36222e8i	−1.06505	−	0.614904i
$123$		0			0
$124$	2.46550e6	+	4.27037e6i	0.0104284	+	0.0180625i
$125$			2.55792e8i			1.04772i
$126$		0			0
$127$	−2.16766e7			−0.0833253			−0.0416627	−	0.999132i	$-0.513265\pi$
$127$	−2.16766e7			−0.0833253			−0.0416627	+	0.999132i	$0.513265\pi$
$128$	−2.49697e8	+	1.44163e8i	−0.930195	+	0.537048i
$129$		0			0
$130$	−1.08168e8	+	1.87352e8i	−0.378725	+	0.655971i
$131$	1.17598e8	+	6.78953e7i	0.399314	+	0.230544i	0.686188	−	0.727424i	$-0.259283\pi$
$131$	1.17598e8	+	6.78953e7i	0.399314	+	0.230544i	−0.286874	+	0.957968i	$0.592616\pi$
$132$		0			0
$133$	−4.69837e7	−	8.13782e7i	−0.150155	−	0.260077i
$134$			1.25984e8i			0.390748i
$135$		0			0
$136$	5.10044e8			1.49091
$137$	−2.85177e6	+	1.64647e6i	−0.00809529	+	0.00467382i	−0.504042	−	0.863679i	$-0.668154\pi$
$137$	−2.85177e6	+	1.64647e6i	−0.00809529	+	0.00467382i	0.495947	+	0.868353i	$0.334821\pi$
$138$		0			0
$139$	−4.10480e7	+	7.10972e7i	−0.109959	+	0.190455i	−0.915754	−	0.401740i	$-0.868405\pi$
$139$	−4.10480e7	+	7.10972e7i	−0.109959	+	0.190455i	0.805794	+	0.592196i	$0.201739\pi$
$140$	−3.51709e6	−	2.03059e6i	−0.00915528	−	0.00528580i
$141$		0			0
$142$	−1.90781e8	−	3.30442e8i	−0.469225	−	0.812722i
$143$		−	4.12189e8i		−	0.985718i
$144$		0			0
$145$	−5.66795e8			−1.28219
$146$	3.55039e8	−	2.04982e8i	0.781385	−	0.451133i
$147$		0			0
$148$	8.32994e6	−	1.44279e7i	0.0173618	−	0.0300715i
$149$	6.21930e8	+	3.59072e8i	1.26182	+	0.728511i	0.973426	−	0.229002i	$-0.0735461\pi$
$149$	6.21930e8	+	3.59072e8i	1.26182	+	0.728511i	0.288392	+	0.957512i	$0.406879\pi$
$150$		0			0
$151$	−2.49967e8	−	4.32956e8i	−0.480812	−	0.832791i	0.518945	−	0.854807i	$-0.326325\pi$
$151$	−2.49967e8	−	4.32956e8i	−0.480812	−	0.832791i	−0.999758	+	0.0220160i	$0.992992\pi$
$152$		−	5.50307e8i		−	1.03093i
$153$		0			0
$154$	1.49231e8			0.265323
$155$	1.30314e8	−	7.52371e7i	0.225770	−	0.130348i
$156$		0			0
$157$	4.18020e8	−	7.24031e8i	0.688015	−	1.19168i	−0.284463	−	0.958687i	$-0.591815\pi$
$157$	4.18020e8	−	7.24031e8i	0.688015	−	1.19168i	0.972479	−	0.232991i	$-0.0748512\pi$
$158$	−5.93189e8	−	3.42478e8i	−0.951842	−	0.549546i
$159$		0			0
$160$	−2.44717e7	−	4.23863e7i	−0.0373409	−	0.0646763i
$161$		−	2.06206e8i		−	0.306900i
$162$		0			0
$163$	−7.36451e8			−1.04326			−0.521631	−	0.853171i	$-0.674676\pi$
$163$	−7.36451e8			−1.04326			−0.521631	+	0.853171i	$0.674676\pi$
$164$	1.32643e7	−	7.65815e6i	0.0183362	−	0.0105864i
$165$		0			0
$166$	3.67478e8	−	6.36491e8i	0.483948	−	0.838223i
$167$	−1.10515e9	−	6.38060e8i	−1.42088	−	0.820343i	−0.424502	−	0.905427i	$-0.639551\pi$
$167$	−1.10515e9	−	6.38060e8i	−1.42088	−	0.820343i	−0.996374	+	0.0850837i	$0.972884\pi$
$168$		0			0
$169$	−6.69784e7	−	1.16010e8i	−0.0821084	−	0.142216i
$170$			9.00425e8i			1.07808i
$171$		0			0
$172$	−8.74452e7			−0.0999130
$173$	3.48663e8	−	2.01301e8i	0.389243	−	0.224730i	−0.292589	−	0.956238i	$-0.594517\pi$
$173$	3.48663e8	−	2.01301e8i	0.389243	−	0.224730i	0.681832	+	0.731509i	$0.261183\pi$
$174$		0			0
$175$	7.06516e7	−	1.22372e8i	0.0753304	−	0.130476i
$176$	7.98376e8	+	4.60943e8i	0.832064	+	0.480392i
$177$		0			0
$178$	−6.08553e6	−	1.05404e7i	−0.00606203	−	0.0104998i
$179$		−	1.44429e9i		−	1.40683i	−0.710780	−	0.703414i	$-0.751658\pi$
$179$		−	1.44429e9i		−	1.40683i	0.710780	−	0.703414i	$-0.248342\pi$
$180$		0			0
$181$	−1.32830e9			−1.23760			−0.618800	−	0.785548i	$-0.712381\pi$
$181$	−1.32830e9			−1.23760			−0.618800	+	0.785548i	$0.712381\pi$
$182$	2.97764e8	−	1.71914e8i	0.271386	−	0.156685i
$183$		0			0
$184$	6.03807e8	−	1.04582e9i	0.526777	−	0.912405i
$185$	−4.40281e8	−	2.54196e8i	−0.375874	−	0.217011i
$186$		0			0
$187$	−8.57801e8	−	1.48576e9i	−0.701488	−	1.21501i
$188$			33586.3i			2.68863e-5i
$189$		0			0
$190$	9.71505e8			0.745471
$191$	−1.64673e9	+	9.50741e8i	−1.23734	+	0.714379i	−0.968550	−	0.248820i	$-0.919957\pi$
$191$	−1.64673e9	+	9.50741e8i	−1.23734	+	0.714379i	−0.268791	+	0.963199i	$0.586624\pi$
$192$		0			0
$193$	−3.90686e8	+	6.76689e8i	−0.281578	+	0.487708i	−0.971774	−	0.235915i	$-0.924191\pi$
$193$	−3.90686e8	+	6.76689e8i	−0.281578	+	0.487708i	0.690195	+	0.723623i	$0.257525\pi$
$194$	1.50735e9	+	8.70272e8i	1.06416	+	0.614395i
$195$		0			0
$196$	−3.71263e7	−	6.43047e7i	−0.0251569	−	0.0435731i
$197$			2.18762e9i			1.45247i	0.687448	+	0.726234i	$0.258731\pi$
$197$			2.18762e9i			1.45247i	−0.687448	+	0.726234i	$0.741269\pi$
$198$		0			0
$199$	2.94513e8			0.187798			0.0938991	−	0.995582i	$-0.470067\pi$
$199$	2.94513e8			0.187798			0.0938991	+	0.995582i	$0.470067\pi$
$200$	7.16655e8	−	4.13761e8i	0.447910	−	0.258601i
$201$		0			0
$202$	−1.72470e8	+	2.98726e8i	−0.103587	+	0.179419i
$203$	7.80137e8	+	4.50412e8i	0.459396	+	0.265232i
$204$		0			0
$205$	−2.33696e8	−	4.04773e8i	−0.132323	−	0.229190i
$206$			4.24817e8i			0.235903i
$207$		0			0
$208$	2.12403e9			1.13477
$209$	−1.60304e9	+	9.25516e8i	−0.840155	+	0.485064i
$210$		0			0
$211$	−1.67025e9	+	2.89296e9i	−0.842659	+	1.45953i	0.0449795	+	0.998988i	$0.485678\pi$
$211$	−1.67025e9	+	2.89296e9i	−0.842659	+	1.45953i	−0.887639	+	0.460541i	$0.847656\pi$
$212$	1.52499e8	+	8.80455e7i	0.0754960	+	0.0435877i
$213$		0			0
$214$	1.58346e9	+	2.74263e9i	0.755008	+	1.30771i
$215$			2.66848e9i			1.24885i
$216$		0			0
$217$	−2.39153e8			−0.107854
$218$	−1.56396e9	+	9.02950e8i	−0.692466	+	0.399795i
$219$		0			0
$220$	−4.00000e7	+	6.92820e7i	−0.0170753	+	0.0295753i
$221$	−3.42319e9	−	1.97638e9i	−1.43503	−	0.828518i
$222$		0			0
$223$	−1.35372e9	−	2.34471e9i	−0.547405	−	0.948133i	−0.998451	−	0.0556326i	$-0.982282\pi$
$223$	−1.35372e9	−	2.34471e9i	−0.547405	−	0.948133i	0.451046	−	0.892500i	$-0.351051\pi$
$224$			7.77874e7i			0.0308970i
$225$		0			0
$226$	4.41728e8			0.169325
$227$	4.52451e9	−	2.61222e9i	1.70399	−	0.983800i	0.762363	−	0.647150i	$-0.224039\pi$
$227$	4.52451e9	−	2.61222e9i	1.70399	−	0.983800i	0.941630	−	0.336651i	$-0.109294\pi$
$228$		0			0
$229$	1.09309e8	−	1.89329e8i	0.0397480	−	0.0688456i	−0.845467	−	0.534028i	$-0.820678\pi$
$229$	1.09309e8	−	1.89329e8i	0.0397480	−	0.0688456i	0.885215	+	0.465182i	$0.154011\pi$
$230$	1.84628e9	+	1.06595e9i	0.659762	+	0.380914i
$231$		0			0
$232$	2.63778e9	+	4.56876e9i	0.910513	+	1.57705i
$233$		−	4.81293e9i		−	1.63300i	−0.577346	−	0.816499i	$-0.695912\pi$
$233$		−	4.81293e9i		−	1.63300i	0.577346	−	0.816499i	$-0.304088\pi$
$234$		0			0
$235$	1.02492e6			0.000336061
$236$	1.27743e8	−	7.37526e7i	0.0411804	−	0.0237755i
$237$		0			0
$238$	7.15537e8	−	1.23935e9i	0.223010	−	0.386265i
$239$	−9.93958e7	−	5.73862e7i	−0.0304633	−	0.0175880i	0.484691	−	0.874685i	$-0.338932\pi$
$239$	−9.93958e7	−	5.73862e7i	−0.0304633	−	0.0175880i	−0.515154	+	0.857097i	$0.672265\pi$
$240$		0			0
$241$	2.05726e9	+	3.56328e9i	0.609848	+	1.05629i	0.991265	+	0.131885i	$0.0421028\pi$
$241$	2.05726e9	+	3.56328e9i	0.609848	+	1.05629i	−0.381417	+	0.924403i	$0.624564\pi$
$242$			5.82634e8i			0.169877i
$243$		0			0
$244$	−2.32126e8			−0.0654883
$245$	−1.96232e9	+	1.13295e9i	−0.544635	+	0.314445i
$246$		0			0
$247$	−2.13240e9	+	3.69342e9i	−0.572902	+	0.992296i
$248$	−1.21293e9	−	7.00283e8i	−0.320647	−	0.185126i
$249$		0			0
$250$	2.10154e9	+	3.63998e9i	0.537995	+	0.931834i
$251$		−	5.13492e9i		−	1.29371i	−0.762611	−	0.646857i	$-0.776083\pi$
$251$		−	5.13492e9i		−	1.29371i	0.762611	−	0.646857i	$-0.223917\pi$
$252$		0			0
$253$	−4.06197e9			−0.991414
$254$	−3.08464e8	+	1.78092e8i	−0.0741088	+	0.0427867i
$255$		0			0
$256$	−3.51287e8	+	6.08447e8i	−0.0817904	+	0.141665i
$257$	2.24752e9	+	1.29761e9i	0.515194	+	0.297448i	0.734966	−	0.678104i	$-0.237198\pi$
$257$	2.24752e9	+	1.29761e9i	0.515194	+	0.297448i	−0.219772	+	0.975551i	$0.570531\pi$
$258$		0			0
$259$	4.04002e8	+	6.99752e8i	0.0897810	+	0.155505i
$260$			1.84320e8i			0.0403348i
$261$		0			0
$262$	2.23127e9			0.473529
$263$	−4.20627e8	+	2.42849e8i	−0.0879172	+	0.0507590i	−0.543314	−	0.839530i	$-0.682831\pi$
$263$	−4.20627e8	+	2.42849e8i	−0.0879172	+	0.0507590i	0.455397	+	0.890289i	$0.349497\pi$
$264$		0			0
$265$	2.68679e9	−	4.65366e9i	0.544817	−	0.943651i
$266$	−1.33718e9	−	7.72022e8i	−0.267094	−	0.154207i
$267$		0			0
$268$	5.36701e7	+	9.29593e7i	0.0104038	+	0.0180200i
$269$			2.94120e8i			0.0561714i	0.999606	+	0.0280857i	$0.00894114\pi$
$269$			2.94120e8i			0.0561714i	−0.999606	+	0.0280857i	$0.991059\pi$
$270$		0			0
$271$	5.47200e9			1.01454			0.507270	−	0.861787i	$-0.330655\pi$
$271$	5.47200e9			1.01454			0.507270	+	0.861787i	$0.330655\pi$
$272$	7.65617e9	−	4.42029e9i	1.39874	−	0.807561i
$273$		0			0
$274$	−2.70543e7	+	4.68594e7i	−0.00479992	+	0.00831370i
$275$	−2.41057e9	−	1.39174e9i	−0.421491	−	0.243348i
$276$		0			0
$277$	−1.83725e9	−	3.18221e9i	−0.312068	−	0.540518i	0.666742	−	0.745289i	$-0.267688\pi$
$277$	−1.83725e9	−	3.18221e9i	−0.312068	−	0.540518i	−0.978810	+	0.204771i	$0.934355\pi$
$278$			1.34897e9i			0.225852i
$279$		0			0
$280$	1.15351e9			0.187668
$281$	4.17095e9	−	2.40810e9i	0.668974	−	0.386233i	−0.126713	−	0.991939i	$-0.540443\pi$
$281$	4.17095e9	−	2.40810e9i	0.668974	−	0.386233i	0.795688	+	0.605707i	$0.207110\pi$
$282$		0			0
$283$	−4.62093e9	+	8.00369e9i	−0.720417	+	1.24780i	0.240416	+	0.970670i	$0.422716\pi$
$283$	−4.62093e9	+	8.00369e9i	−0.720417	+	1.24780i	−0.960833	+	0.277129i	$0.910617\pi$
$284$	−2.81541e8	−	1.62548e8i	−0.0432781	−	0.0249866i
$285$		0			0
$286$	−3.38648e9	−	5.86556e9i	−0.506156	−	0.876688i
$287$			7.42840e8i			0.109488i
$288$		0			0
$289$	−9.47632e9			−1.35847
$290$	−8.06563e9	+	4.65669e9i	−1.14037	+	0.658394i
$291$		0			0
$292$	1.74647e8	−	3.02498e8i	0.0240232	−	0.0416094i
$293$	5.49756e9	+	3.17402e9i	0.745932	+	0.430664i	0.824222	−	0.566267i	$-0.191613\pi$
$293$	5.49756e9	+	3.17402e9i	0.745932	+	0.430664i	−0.0782902	+	0.996931i	$0.524946\pi$
$294$		0			0
$295$	−2.25063e9	−	3.89821e9i	−0.297178	−	0.514727i
$296$			4.73196e9i			0.616416i
$297$		0			0
$298$	1.18003e10			1.49633
$299$	−8.10498e9	+	4.67941e9i	−1.01407	+	0.585472i
$300$		0			0
$301$	2.12055e9	−	3.67289e9i	0.258334	−	0.447448i
$302$	−7.11420e9	−	4.10738e9i	−0.855260	−	0.493785i
$303$		0			0
$304$	−4.76923e9	−	8.26055e9i	−0.558411	−	0.967196i
$305$			7.08354e9i			0.818561i
$306$		0			0
$307$	−5.37906e9			−0.605554			−0.302777	−	0.953061i	$-0.597914\pi$
$307$	−5.37906e9			−0.605554			−0.302777	+	0.953061i	$0.597914\pi$
$308$	1.10112e8	−	6.35732e7i	0.0122358	−	0.00706433i
$309$		0			0
$310$	1.23627e9	−	2.14128e9i	0.133865	−	0.231861i
$311$	5.50494e9	+	3.17828e9i	0.588452	+	0.339743i	0.764485	−	0.644641i	$-0.222993\pi$
$311$	5.50494e9	+	3.17828e9i	0.588452	+	0.339743i	−0.176033	+	0.984384i	$0.556327\pi$
$312$		0			0
$313$	−5.57421e8	−	9.65481e8i	−0.0580772	−	0.100593i	0.835525	−	0.549452i	$-0.185164\pi$
$313$	−5.57421e8	−	9.65481e8i	−0.0580772	−	0.100593i	−0.893602	+	0.448860i	$0.851830\pi$
$314$		−	1.37375e10i		−	1.41316i
$315$		0			0
$316$	−5.83591e8			−0.0585276
$317$	−1.19931e9	+	6.92425e8i	−0.118767	+	0.0685702i	−0.558207	−	0.829702i	$-0.688510\pi$
$317$	−1.19931e9	+	6.92425e8i	−0.118767	+	0.0685702i	0.439440	+	0.898272i	$0.355177\pi$
$318$		0			0
$319$	8.87252e9	−	1.53677e10i	0.856809	−	1.48404i
$320$	5.83177e9	+	3.36697e9i	0.556160	+	0.321099i
$321$		0			0
$322$	−1.69415e9	−	2.93436e9i	−0.157590	−	0.272954i
$323$			1.77508e10i			1.63083i
$324$		0			0
$325$	−6.41317e9			−0.574830
$326$	−1.04799e10	+	6.05056e9i	−0.927867	+	0.535704i
$327$		0			0
$328$	−2.17517e9	+	3.76750e9i	−0.187931	+	0.325505i
$329$	−1.41070e6	−	814469.i	−0.000120407	−	6.95170e-5i
$330$		0			0
$331$	−4.68265e9	−	8.11058e9i	−0.390103	−	0.675678i	0.602360	−	0.798225i	$-0.294227\pi$
$331$	−4.68265e9	−	8.11058e9i	−0.390103	−	0.675678i	−0.992463	+	0.122546i	$0.960894\pi$
$332$		−	6.26192e8i		−	0.0515413i
$333$		0			0
$334$	−2.09688e10			−1.68495
$335$	2.83674e9	−	1.63779e9i	0.225238	−	0.130041i
$336$		0			0
$337$	7.72518e9	−	1.33804e10i	0.598948	−	1.03741i	−0.394029	−	0.919098i	$-0.628919\pi$
$337$	7.72518e9	−	1.33804e10i	0.598948	−	1.03741i	0.992977	−	0.118310i	$-0.0377476\pi$
$338$	−1.90624e9	−	1.10057e9i	−0.146053	−	0.0843237i
$339$		0			0
$340$	3.83587e8	+	6.64392e8i	0.0287044	+	0.0497174i
$341$			4.71100e9i			0.348414i
$342$		0			0
$343$	7.51555e9			0.542981
$344$	2.15098e10	−	1.24187e10i	1.53604	−	0.886832i
$345$		0			0
$346$	3.30771e9	−	5.72912e9i	0.230793	−	0.399745i
$347$	−1.27197e8	−	7.34370e7i	−0.00877320	−	0.00506521i	0.495607	−	0.868547i	$-0.334946\pi$
$347$	−1.27197e8	−	7.34370e7i	−0.00877320	−	0.00506521i	−0.504380	+	0.863482i	$0.668279\pi$
$348$		0			0
$349$	1.37452e10	+	2.38074e10i	0.926508	+	1.60476i	0.789118	+	0.614241i	$0.210538\pi$
$349$	1.37452e10	+	2.38074e10i	0.926508	+	1.60476i	0.137389	+	0.990517i	$0.456129\pi$
$350$		−	2.32185e9i		−	0.154726i
$351$		0			0
$352$	1.53231e9			0.0998102
$353$	1.65208e10	−	9.53828e9i	1.06398	−	0.614287i	0.137447	−	0.990509i	$-0.456110\pi$
$353$	1.65208e10	−	9.53828e9i	1.06398	−	0.614287i	0.926529	+	0.376222i	$0.122777\pi$
$354$		0			0
$355$	−4.96030e9	+	8.59150e9i	−0.312316	+	0.540948i
$356$	−8.98060e6	−	5.18495e6i	−0.000559120	−	0.000322808i
$357$		0			0
$358$	−1.18660e10	−	2.05525e10i	−0.722392	−	1.25122i
$359$		−	6.80030e9i		−	0.409402i	−0.978825	−	0.204701i	$-0.934378\pi$
$359$		−	6.80030e9i		−	0.409402i	0.978825	−	0.204701i	$-0.0656222\pi$
$360$		0			0
$361$	2.16851e9			0.127683
$362$	−1.89020e10	+	1.09131e10i	−1.10071	+	0.635495i
$363$		0			0
$364$	1.46473e8	−	2.53699e8i	0.00834358	−	0.0144515i
$365$	−9.23103e9	−	5.32954e9i	−0.520090	−	0.300274i
$366$		0			0
$367$	7.78861e8	+	1.34903e9i	0.0429334	+	0.0743629i	0.886694	−	0.462358i	$-0.152996\pi$
$367$	7.78861e8	+	1.34903e9i	0.0429334	+	0.0743629i	−0.843760	+	0.536720i	$0.819663\pi$
$368$		−	2.09315e10i		−	1.14133i
$369$		0			0
$370$	−8.35374e9			−0.445732
$371$	−7.39621e9	+	4.27020e9i	−0.390403	+	0.225400i
$372$		0			0
$373$	1.02627e9	−	1.77755e9i	0.0530184	−	0.0918306i	−0.838298	−	0.545212i	$-0.816449\pi$
$373$	1.02627e9	−	1.77755e9i	0.0530184	−	0.0918306i	0.891317	+	0.453381i	$0.149782\pi$
$374$	−2.44135e10	−	1.40951e10i	−1.24779	−	0.720414i
$375$		0			0
$376$	−4.76982e6	−	8.26157e6i	−0.000238644	−	0.000413344i
$377$		−	4.08847e10i		−	2.02393i
$378$		0			0
$379$	2.21941e10			1.07567			0.537837	−	0.843049i	$-0.319241\pi$
$379$	2.21941e10			1.07567			0.537837	+	0.843049i	$0.319241\pi$
$380$	7.16839e8	−	4.13867e8i	0.0343785	−	0.0198485i
$381$		0			0
$382$	−1.56223e10	+	2.70586e10i	−0.733653	+	1.27072i
$383$	1.58171e10	+	9.13201e9i	0.735075	+	0.424396i	0.820276	−	0.571968i	$-0.193820\pi$
$383$	1.58171e10	+	9.13201e9i	0.735075	+	0.424396i	−0.0852009	+	0.996364i	$0.527153\pi$
$384$		0			0
$385$	−1.94000e9	−	3.36018e9i	−0.0882995	−	0.152939i
$386$			1.28393e10i			0.578350i
$387$		0			0
$388$	1.48297e9			0.0654341
$389$	6.57693e9	−	3.79719e9i	0.287227	−	0.165830i	−0.349464	−	0.936950i	$-0.613636\pi$
$389$	6.57693e9	−	3.79719e9i	0.287227	−	0.165830i	0.636690	+	0.771119i	$0.280303\pi$
$390$		0			0
$391$	−1.94765e10	+	3.37343e10i	−0.833306	+	1.44333i
$392$	1.82647e10	+	1.05451e10i	0.773513	+	0.446588i
$393$		0			0
$394$	1.79731e10	+	3.11303e10i	0.745828	+	1.29181i
$395$			1.78089e10i			0.731556i
$396$		0			0
$397$	3.83153e10			1.54245			0.771223	−	0.636564i	$-0.219645\pi$
$397$	3.83153e10			1.54245			0.771223	+	0.636564i	$0.219645\pi$
$398$	4.19099e9	−	2.41967e9i	0.167026	−	0.0964325i
$399$		0			0
$400$	7.17171e9	−	1.24218e10i	0.280145	−	0.485226i
$401$	7.41009e8	+	4.27822e8i	0.0286580	+	0.0165457i	0.514261	−	0.857634i	$-0.328066\pi$
$401$	7.41009e8	+	4.27822e8i	0.0286580	+	0.0165457i	−0.485603	+	0.874180i	$0.661400\pi$
$402$		0			0
$403$	5.42709e9	+	9.39999e9i	0.205753	+	0.356375i
$404$			2.93893e8i			0.0110322i
$405$		0			0
$406$	1.48021e10			0.544776
$407$	1.37842e10	−	7.95829e9i	0.502346	−	0.290030i
$408$		0			0
$409$	1.57822e9	−	2.73355e9i	0.0563992	−	0.0976863i	−0.836447	−	0.548047i	$-0.815371\pi$
$409$	1.57822e9	−	2.73355e9i	0.0563992	−	0.0976863i	0.892847	+	0.450361i	$0.148705\pi$
$410$	−6.65110e9	−	3.84001e9i	−0.235374	−	0.135893i
$411$		0			0
$412$	1.80975e8	+	3.13458e8i	0.00628101	+	0.0108790i
$413$			7.15400e9i			0.245895i
$414$		0			0
$415$	−1.91089e10			−0.644232
$416$	3.05746e9	−	1.76522e9i	0.102091	−	0.0589422i
$417$		0			0
$418$	−1.52078e10	+	2.63407e10i	−0.498151	+	0.862823i
$419$	−5.95341e9	−	3.43720e9i	−0.193157	−	0.111519i	0.400303	−	0.916383i	$-0.368905\pi$
$419$	−5.95341e9	−	3.43720e9i	−0.193157	−	0.111519i	−0.593459	+	0.804864i	$0.702238\pi$
$420$		0			0
$421$	7.65029e9	+	1.32507e10i	0.243528	+	0.421804i	0.961717	−	0.274045i	$-0.0883618\pi$
$421$	7.65029e9	+	1.32507e10i	0.243528	+	0.421804i	−0.718188	+	0.695849i	$0.755028\pi$
$422$			5.48901e10i			1.73079i
$423$		0			0
$424$	−5.00157e10			−1.54754
$425$	−2.31166e10	+	1.33464e10i	−0.708546	+	0.409079i
$426$		0			0
$427$	5.62905e9	−	9.74979e9i	0.169326	−	0.293281i
$428$	2.33676e9	+	1.34913e9i	0.0696367	+	0.0402048i
$429$		0			0
$430$	2.19238e10	+	3.79731e10i	0.641270	+	1.11071i
$431$			3.16429e9i			0.0916996i	0.998948	+	0.0458498i	$0.0145996\pi$
$431$			3.16429e9i			0.0916996i	−0.998948	+	0.0458498i	$0.985400\pi$
$432$		0			0
$433$	6.22045e10			1.76958			0.884791	−	0.465989i	$-0.154301\pi$
$433$	6.22045e10			1.76958			0.884791	+	0.465989i	$0.154301\pi$
$434$	−3.40321e9	+	1.96484e9i	−0.0959246	+	0.0553821i
$435$		0			0
$436$	−7.69325e8	+	1.33251e9i	−0.0212894	+	0.0368744i
$437$	3.63973e10	+	2.10140e10i	0.998030	+	0.576213i
$438$		0			0
$439$	1.15143e10	+	1.99433e10i	0.310012	+	0.536957i	0.978365	−	0.206888i	$-0.0663335\pi$
$439$	1.15143e10	+	1.99433e10i	0.310012	+	0.536957i	−0.668352	+	0.743845i	$0.733000\pi$
$440$		−	2.27226e10i		−	0.606245i
$441$		0			0
$442$	−6.49505e10			−1.70174
$443$	−3.41001e10	+	1.96877e10i	−0.885402	+	0.511187i	−0.872436	−	0.488729i	$-0.837461\pi$
$443$	−3.41001e10	+	1.96877e10i	−0.885402	+	0.511187i	−0.0129661	+	0.999916i	$0.504127\pi$
$444$		0			0
$445$	−1.58224e8	+	2.74052e8i	−0.00403489	+	0.00698863i
$446$	−3.85275e10	−	2.22439e10i	−0.973714	−	0.562174i
$447$		0			0
$448$	−5.35123e9	−	9.26861e9i	−0.132844	−	0.230093i
$449$			5.66523e10i			1.39390i	0.717119	+	0.696951i	$0.245461\pi$
$449$			5.66523e10i			1.39390i	−0.717119	+	0.696951i	$0.754539\pi$
$450$		0			0
$451$	1.46330e10			0.353692
$452$	3.25936e8	−	1.88179e8i	0.00780869	−	0.00450835i
$453$		0			0
$454$	4.29232e10	−	7.43452e10i	1.01034	−	1.74997i
$455$	−7.74187e9	−	4.46977e9i	−0.180634	−	0.104289i
$456$		0			0
$457$	1.67428e10	+	2.89993e10i	0.383851	+	0.664849i	0.991609	−	0.129273i	$-0.0412643\pi$
$457$	1.67428e10	+	2.89993e10i	0.383851	+	0.664849i	−0.607758	+	0.794122i	$0.707931\pi$
$458$		−	3.59227e9i		−	0.0816408i
$459$		0			0
$460$	1.81641e9			0.0405679
$461$	−4.23738e10	+	2.44645e10i	−0.938196	+	0.541668i	−0.889395	−	0.457140i	$-0.848874\pi$
$461$	−4.23738e10	+	2.44645e10i	−0.938196	+	0.541668i	−0.0488020	+	0.998808i	$0.515540\pi$
$462$		0			0
$463$	−1.70190e10	+	2.94777e10i	−0.370347	+	0.641461i	−0.989619	−	0.143716i	$-0.954095\pi$
$463$	−1.70190e10	+	2.94777e10i	−0.370347	+	0.641461i	0.619271	+	0.785177i	$0.287428\pi$
$464$	7.91903e10	+	4.57205e10i	1.70844	+	0.986368i
$465$		0			0
$466$	−3.95423e10	−	6.84892e10i	−0.838528	−	1.45237i
$467$		−	7.93796e10i		−	1.66894i	−0.551052	−	0.834471i	$-0.685773\pi$
$467$		−	7.93796e10i		−	1.66894i	0.551052	−	0.834471i	$-0.314227\pi$
$468$		0			0
$469$	−5.20600e9			−0.107600
$470$	1.45849e7	−	8.42058e6i	0.000298890	−	0.000172564i
$471$		0			0
$472$	−2.09482e10	+	3.62833e10i	−0.422064	+	0.731037i
$473$	−7.23511e10	−	4.17719e10i	−1.44544	−	0.834526i
$474$		0			0
$475$	1.43999e10	+	2.49414e10i	0.282869	+	0.489944i
$476$		−	1.21929e9i		−	0.0237509i
$477$		0			0
$478$	−1.88590e9			−0.0361250
$479$	7.86093e10	−	4.53851e10i	1.49325	−	0.862127i	0.493278	−	0.869872i	$-0.335799\pi$
$479$	7.86093e10	−	4.53851e10i	1.49325	−	0.862127i	0.999970	+	0.00774485i	$0.00246529\pi$
$480$		0			0
$481$	1.83360e10	−	3.17588e10i	0.342550	−	0.593314i
$482$	5.85507e10	+	3.38043e10i	1.08479	+	0.626302i
$483$		0			0
$484$	2.48206e8	+	4.29905e8i	0.00452304	+	0.00783413i
$485$		−	4.52541e10i		−	0.817883i
$486$		0			0
$487$	2.51505e10			0.447127			0.223563	−	0.974689i	$-0.428231\pi$
$487$	2.51505e10			0.447127			0.223563	+	0.974689i	$0.428231\pi$
$488$	5.70983e10	−	3.29657e10i	1.00680	−	0.581277i
$489$		0			0
$490$	−1.86162e10	+	3.22442e10i	−0.322929	+	0.559329i
$491$	−8.44100e10	−	4.87341e10i	−1.45234	−	0.838508i	−0.453724	−	0.891142i	$-0.649905\pi$
$491$	−8.44100e10	−	4.87341e10i	−1.45234	−	0.838508i	−0.998614	+	0.0526344i	$0.983238\pi$
$492$		0			0
$493$	−8.50846e10	−	1.47371e11i	−1.44033	−	2.49473i
$494$			7.00777e10i			1.17672i
$495$		0			0
$496$	−2.42760e10			−0.401098
$497$	1.36547e10	−	7.88357e9i	0.223799	−	0.129210i
$498$		0			0
$499$	3.47648e10	−	6.02144e10i	0.560709	−	0.971177i	−0.436725	−	0.899595i	$-0.643862\pi$
$499$	3.47648e10	−	6.02144e10i	0.560709	−	0.971177i	0.997435	−	0.0715823i	$-0.0228049\pi$
$500$	3.10131e9	+	1.79054e9i	0.0496209	+	0.0286487i
$501$		0			0
$502$	−4.21876e10	−	7.30711e10i	−0.664309	−	1.15062i
$503$			2.66836e10i			0.416842i	0.978039	+	0.208421i	$0.0668325\pi$
$503$			2.66836e10i			0.416842i	−0.978039	+	0.208421i	$0.933168\pi$
$504$		0			0
$505$	8.96842e9			0.137896
$506$	−5.78029e10	+	3.33725e10i	−0.881754	+	0.509081i
$507$		0			0
$508$	−1.51736e8	+	2.62815e8i	−0.00227843	+	0.00394635i
$509$	−1.33777e10	−	7.72363e9i	−0.199302	−	0.115067i	0.397028	−	0.917806i	$-0.370042\pi$
$509$	−1.33777e10	−	7.72363e9i	−0.199302	−	0.115067i	−0.596330	+	0.802740i	$0.703375\pi$
$510$		0			0
$511$	8.47040e9	+	1.46712e10i	0.124228	+	0.215170i
$512$		−	6.22669e10i		−	0.906102i
$513$		0			0
$514$	4.26437e10			0.610945
$515$	9.56547e9	−	5.52263e9i	0.135981	−	0.0785085i
$516$		0			0
$517$	−1.60439e7	+	2.77889e7i	−0.000224569	+	0.000388964i
$518$	1.14981e10	+	6.63843e9i	0.159701	+	0.0922033i
$519$		0			0
$520$	−2.61766e10	−	4.53392e10i	−0.358014	−	0.620098i
$521$		−	7.64491e9i		−	0.103758i	−0.998653	−	0.0518790i	$-0.983479\pi$
$521$		−	7.64491e9i		−	0.103758i	0.998653	−	0.0518790i	$-0.0165210\pi$
$522$		0			0
$523$	−7.26324e10			−0.970787			−0.485393	−	0.874296i	$-0.661324\pi$
$523$	−7.26324e10			−0.970787			−0.485393	+	0.874296i	$0.661324\pi$
$524$	1.64637e9	−	9.50534e8i	0.0218375	−	0.0126079i
$525$		0			0
$526$	−3.99042e9	+	6.91161e9i	−0.0521285	+	0.0902892i
$527$	3.91244e10	+	2.25885e10i	0.507230	+	0.292850i
$528$		0			0
$529$	6.95839e9	+	1.20523e10i	0.0888559	+	0.153903i
$530$		−	8.82970e10i		−	1.11903i
$531$		0			0
$532$	−1.31554e9			−0.0164233
$533$	2.91976e10	−	1.68572e10i	0.361774	−	0.208871i
$534$		0			0
$535$	4.11699e10	−	7.13084e10i	0.502533	−	0.870413i
$536$	−2.64035e10	−	1.52441e10i	−0.319892	−	0.184690i
$537$		0			0
$538$	2.41644e9	+	4.18540e9i	0.0288435	+	0.0499583i
$539$		−	7.09398e10i		−	0.840495i
$540$		0			0
$541$	3.77715e10			0.440935			0.220468	−	0.975394i	$-0.429242\pi$
$541$	3.77715e10			0.440935			0.220468	+	0.975394i	$0.429242\pi$
$542$	7.78679e10	−	4.49571e10i	0.902322	−	0.520956i
$543$		0			0
$544$	7.34716e9	−	1.27257e10i	0.0838927	−	0.145306i
$545$	4.06628e10	+	2.34767e10i	0.460905	+	0.266104i
$546$		0			0
$547$	3.12038e10	+	5.40466e10i	0.348544	+	0.603697i	0.985991	−	0.166798i	$-0.0533427\pi$
$547$	3.12038e10	+	5.40466e10i	0.348544	+	0.603697i	−0.637447	+	0.770494i	$0.720009\pi$
$548$			4.61012e7i			0.000511199i
$549$		0			0
$550$	−4.57373e10			−0.499827
$551$	−1.59004e11	+	9.18012e10i	−1.72505	+	0.995960i
$552$		0			0
$553$	1.41521e10	−	2.45121e10i	0.151328	−	0.262108i
$554$	−5.22891e10	−	3.01891e10i	−0.555101	−	0.320488i
$555$		0			0
$556$	5.74672e8	+	9.95360e8i	0.00601341	+	0.0104155i
$557$			6.15741e10i			0.639702i	0.947468	+	0.319851i	$0.103633\pi$
$557$			6.15741e10i			0.639702i	−0.947468	+	0.319851i	$0.896367\pi$
$558$		0			0
$559$	−1.92486e11			−1.97129
$560$	1.73151e10	−	9.99690e9i	0.176065	−	0.101651i
$561$		0			0
$562$	3.95691e10	−	6.85357e10i	0.396653	−	0.687023i
$563$	2.54611e10	+	1.47000e10i	0.253422	+	0.146313i	0.621330	−	0.783549i	$-0.286593\pi$
$563$	2.54611e10	+	1.47000e10i	0.253422	+	0.146313i	−0.367908	+	0.929862i	$0.619926\pi$
$564$		0			0
$565$	−5.74247e9	−	9.94624e9i	−0.0563514	−	0.0976035i
$566$			1.51859e11i			1.47971i
$567$		0			0
$568$	9.23380e10			0.887129
$569$	−3.70418e9	+	2.13861e9i	−0.0353380	+	0.0204024i	−0.517565	−	0.855644i	$-0.673161\pi$
$569$	−3.70418e9	+	2.13861e9i	−0.0353380	+	0.0204024i	0.482227	+	0.876046i	$0.339828\pi$
$570$		0			0
$571$	−3.57366e10	+	6.18976e10i	−0.336178	+	0.582277i	−0.983710	−	0.179761i	$-0.942468\pi$
$571$	−3.57366e10	+	6.18976e10i	−0.336178	+	0.582277i	0.647533	+	0.762038i	$0.275801\pi$
$572$	−4.99753e9	−	2.88532e9i	−0.0466843	−	0.0269532i
$573$		0			0
$574$	6.10306e9	+	1.05708e10i	0.0562212	+	0.0973779i
$575$			6.31995e10i			0.578152i
$576$		0			0
$577$	−1.09889e10			−0.0991404			−0.0495702	−	0.998771i	$-0.515785\pi$
$577$	−1.09889e10			−0.0991404			−0.0495702	+	0.998771i	$0.515785\pi$
$578$	−1.34850e11	+	7.78559e10i	−1.20821	+	0.697558i
$579$		0			0
$580$	−3.96756e9	+	6.87202e9i	−0.0350600	+	0.0607257i
$581$	2.63015e10	+	1.51852e10i	0.230821	+	0.133265i
$582$		0			0
$583$	8.41173e10	+	1.45695e11i	0.728133	+	1.26116i
$584$			9.92114e10i			0.852923i
$585$		0			0
$586$	1.04309e11			0.884567
$587$	1.06206e11	−	6.13180e10i	0.894533	−	0.516459i	0.0191105	−	0.999817i	$-0.493917\pi$
$587$	1.06206e11	−	6.13180e10i	0.894533	−	0.516459i	0.875423	+	0.483358i	$0.160583\pi$
$588$		0			0
$589$	2.43716e10	−	4.22129e10i	0.202499	−	0.350739i
$590$	−6.40541e10	−	3.69817e10i	−0.528615	−	0.305196i
$591$		0			0
$592$	4.10095e10	+	7.10305e10i	0.333885	+	0.578306i
$593$			1.00435e11i			0.812206i	0.913827	+	0.406103i	$0.133113\pi$
$593$			1.00435e11i			0.812206i	−0.913827	+	0.406103i	$0.866887\pi$
$594$		0			0
$595$	−3.72079e10			−0.296871
$596$	8.70702e9	−	5.02700e9i	0.0690057	−	0.0398404i
$597$		0			0
$598$	−7.68906e10	+	1.33178e11i	−0.601268	+	1.04143i
$599$	9.87946e10	+	5.70391e10i	0.767407	+	0.443063i	0.831949	−	0.554852i	$-0.187225\pi$
$599$	9.87946e10	+	5.70391e10i	0.767407	+	0.443063i	−0.0645417	+	0.997915i	$0.520559\pi$
$600$		0			0
$601$	−3.16891e10	−	5.48871e10i	−0.242891	−	0.420700i	0.718646	−	0.695377i	$-0.244762\pi$
$601$	−3.16891e10	−	5.48871e10i	−0.242891	−	0.420700i	−0.961537	+	0.274677i	$0.911429\pi$
$602$		−	6.96883e10i		−	0.530608i
$603$		0			0
$604$	−6.99909e9			−0.0525889
$605$	1.31190e10	−	7.57424e9i	0.0979215	−	0.0565350i
$606$		0			0
$607$	−1.33154e11	+	2.30630e11i	−0.980846	+	1.69887i	−0.321734	+	0.946830i	$0.604266\pi$
$607$	−1.33154e11	+	2.30630e11i	−0.980846	+	1.69887i	−0.659112	+	0.752045i	$0.729068\pi$
$608$	−1.37302e10	−	7.92715e9i	−0.100476	−	0.0580100i
$609$		0			0
$610$	5.81972e10	+	1.00801e11i	0.420323	+	0.728020i
$611$			7.39307e7i			0.000530469i
$612$		0			0
$613$	2.39412e11			1.69552			0.847761	−	0.530378i	$-0.177950\pi$
$613$	2.39412e11			1.69552			0.847761	+	0.530378i	$0.177950\pi$
$614$	−7.65454e10	+	4.41935e10i	−0.538574	+	0.310946i
$615$		0			0
$616$	−1.80569e10	+	3.12755e10i	−0.125407	+	0.217211i
$617$	9.17604e10	+	5.29779e10i	0.633162	+	0.365556i	0.781976	−	0.623309i	$-0.214212\pi$
$617$	9.17604e10	+	5.29779e10i	0.633162	+	0.365556i	−0.148814	+	0.988865i	$0.547545\pi$
$618$		0			0
$619$	1.06934e10	+	1.85215e10i	0.0728372	+	0.126158i	0.900144	−	0.435593i	$-0.143461\pi$
$619$	1.06934e10	+	1.85215e10i	0.0728372	+	0.126158i	−0.827306	+	0.561751i	$0.810128\pi$
$620$		−	2.10664e9i		−	0.0142568i
$621$		0			0
$622$	1.04449e11			0.697818
$623$	4.35559e8	−	2.51470e8i	0.00289131	−	0.00166930i
$624$		0			0
$625$	1.39946e10	−	2.42393e10i	0.0917150	−	0.158855i
$626$	−1.58645e10	−	9.15936e9i	−0.103307	−	0.0596441i
$627$		0			0
$628$	−5.85228e9	−	1.01364e10i	−0.0376258	−	0.0651699i
$629$		−	1.52635e11i		−	0.975105i
$630$		0			0
$631$	−1.12422e11			−0.709145			−0.354573	−	0.935028i	$-0.615374\pi$
$631$	−1.12422e11			−0.709145			−0.354573	+	0.935028i	$0.615374\pi$
$632$	1.43552e11	−	8.28797e10i	0.899788	−	0.519493i
$633$		0			0
$634$	−1.13777e10	+	1.97068e10i	−0.0704202	+	0.121971i
$635$	8.02006e9	+	4.63039e9i	0.0493268	+	0.0284788i
$636$		0			0
$637$	−8.17230e10	−	1.41548e11i	−0.496348	−	0.859700i
$638$		−	2.91581e11i		−	1.75985i
$639$		0			0
$640$	1.23179e11			0.734207
$641$	−1.25164e11	+	7.22636e10i	−0.741392	+	0.428043i	−0.822575	−	0.568656i	$-0.807463\pi$
$641$	−1.25164e11	+	7.22636e10i	−0.741392	+	0.428043i	0.0811832	+	0.996699i	$0.474130\pi$
$642$		0			0
$643$	−2.78752e10	+	4.82813e10i	−0.163070	+	0.282446i	−0.935968	−	0.352084i	$-0.885473\pi$
$643$	−2.78752e10	+	4.82813e10i	−0.163070	+	0.282446i	0.772898	+	0.634530i	$0.218806\pi$
$644$	−2.50011e9	−	1.44344e9i	−0.0145350	−	0.00839180i
$645$		0			0
$646$	1.45838e11	+	2.52599e11i	0.837414	+	1.45044i
$647$			5.47913e10i			0.312676i	0.987704	+	0.156338i	$0.0499689\pi$
$647$			5.47913e10i			0.312676i	−0.987704	+	0.156338i	$0.950031\pi$
$648$		0			0
$649$	1.40924e11			0.794341
$650$	−9.12610e10	+	5.26896e10i	−0.511248	+	0.295169i
$651$		0			0
$652$	−5.15515e9	+	8.92899e9i	−0.0285267	+	0.0494097i
$653$	−1.18927e11	−	6.86628e10i	−0.654078	−	0.377632i	0.135939	−	0.990717i	$-0.456595\pi$
$653$	−1.18927e11	−	6.86628e10i	−0.654078	−	0.377632i	−0.790017	+	0.613085i	$0.789928\pi$
$654$		0			0
$655$	−2.90065e10	−	5.02407e10i	−0.157590	−	0.272954i
$656$			7.54043e10i			0.407175i
$657$		0			0
$658$	−2.67662e7			−0.000142785
$659$	2.01218e11	−	1.16173e11i	1.06691	−	0.615978i	0.139571	−	0.990212i	$-0.455428\pi$
$659$	2.01218e11	−	1.16173e11i	1.06691	−	0.615978i	0.927334	+	0.374234i	$0.122094\pi$
$660$		0			0
$661$	−6.37522e10	+	1.10422e11i	−0.333956	+	0.578429i	−0.983284	−	0.182080i	$-0.941717\pi$
$661$	−6.37522e10	+	1.10422e11i	−0.333956	+	0.578429i	0.649328	+	0.760509i	$0.275050\pi$
$662$	−1.33270e11	−	7.69437e10i	−0.693908	−	0.400628i
$663$		0			0
$664$	8.89297e10	+	1.54031e11i	0.457483	+	0.792383i
$665$			4.01451e10i			0.205280i
$666$		0			0
$667$	−4.02904e11			−2.03563
$668$	−1.54721e10	+	8.93284e9i	−0.0777042	+	0.0448625i
$669$		0			0
$670$	2.69117e10	−	4.66124e10i	0.133549	−	0.231314i
$671$	−1.92058e11	−	1.10885e11i	−0.947418	−	0.546992i
$672$		0			0
$673$	3.27191e9	+	5.66712e9i	0.0159493	+	0.0276250i	0.873890	−	0.486124i	$-0.161590\pi$
$673$	3.27191e9	+	5.66712e9i	0.0159493	+	0.0276250i	−0.857941	+	0.513749i	$0.828256\pi$
$674$		−	2.53875e11i		−	1.23021i
$675$		0			0
$676$	−1.87539e9			−0.00898061
$677$	2.01079e11	−	1.16093e11i	0.957221	−	0.552652i	0.0619041	−	0.998082i	$-0.480283\pi$
$677$	2.01079e11	−	1.16093e11i	0.957221	−	0.552652i	0.895316	+	0.445431i	$0.146949\pi$
$678$		0			0
$679$	−3.59619e10	+	6.22879e10i	−0.169186	+	0.293038i
$680$	−1.88709e11	−	1.08951e11i	−0.882588	−	0.509562i
$681$		0			0
$682$	3.87048e10	+	6.70387e10i	0.178907	+	0.309876i
$683$			4.94502e10i			0.227240i	0.993524	+	0.113620i	$0.0362446\pi$
$683$			4.94502e10i			0.227240i	−0.993524	+	0.113620i	$0.963755\pi$
$684$		0			0
$685$	1.40682e9			0.00638965
$686$	1.06948e11	−	6.17466e10i	0.482922	−	0.278815i
$687$		0			0
$688$	2.15253e11	−	3.72828e11i	0.960715	−	1.66401i
$689$	3.35683e11	+	1.93807e11i	1.48954	+	0.859988i
$690$		0			0
$691$	−5.76414e10	−	9.98378e10i	−0.252826	−	0.437908i	0.711477	−	0.702710i	$-0.248027\pi$
$691$	−5.76414e10	−	9.98378e10i	−0.252826	−	0.437908i	−0.964303	+	0.264802i	$0.914693\pi$
$692$		−	5.63642e9i		−	0.0245798i
$693$		0			0
$694$	−2.41339e9			−0.0104037
$695$	3.03744e10	−	1.75367e10i	0.130187	−	0.0751636i
$696$		0			0
$697$	7.01627e10	−	1.21525e11i	0.297286	−	0.514915i
$698$	3.91195e11	+	2.25856e11i	1.64805	+	0.951505i
$699$		0			0
$700$	−9.89123e8	−	1.71321e9i	−0.00411963	−	0.00713541i
$701$			2.53572e10i			0.105009i	0.998621	+	0.0525047i	$0.0167205\pi$
$701$			2.53572e10i			0.105009i	−0.998621	+	0.0525047i	$0.983280\pi$
$702$		0			0
$703$	−1.64684e11			−0.674264
$704$	−1.82579e11	+	1.05412e11i	−0.743294	+	0.429141i
$705$		0			0
$706$	1.56730e11	−	2.71464e11i	0.630860	−	1.09268i
$707$	−1.23441e10	−	7.12689e9i	−0.0494064	−	0.0285248i
$708$		0			0
$709$	−1.23635e11	−	2.14142e11i	−0.489279	−	0.847456i	0.510645	−	0.859792i	$-0.329407\pi$
$709$	−1.23635e11	−	2.14142e11i	−0.489279	−	0.847456i	−0.999924	+	0.0123356i	$0.996073\pi$
$710$			1.63012e11i			0.641485i
$711$		0			0
$712$	2.94540e9			0.0114610
$713$	9.26335e10	−	5.34820e10i	0.358435	−	0.206942i
$714$		0			0
$715$	−8.80485e10	+	1.52504e11i	−0.336897	+	0.583523i
$716$	−1.75110e10	−	1.01100e10i	−0.0666284	−	0.0384679i
$717$		0			0
$718$	−5.58701e10	−	9.67699e10i	−0.210224	−	0.364118i
$719$		−	1.96339e10i		−	0.0734668i	−0.999325	−	0.0367334i	$-0.988305\pi$
$719$		−	1.96339e10i		−	0.0734668i	0.999325	−	0.0367334i	$-0.0116952\pi$
$720$		0			0
$721$	−1.75546e10			−0.0649605
$722$	3.08584e10	−	1.78161e10i	0.113560	−	0.0655637i
$723$		0			0
$724$	−9.29807e9	+	1.61047e10i	−0.0338406	+	0.0586137i
$725$	−2.39102e11	−	1.38046e11i	−0.865430	−	0.499656i
$726$		0			0
$727$	−3.08655e10	−	5.34606e10i	−0.110493	−	0.191380i	0.805476	−	0.592628i	$-0.201910\pi$
$727$	−3.08655e10	−	5.34606e10i	−0.110493	−	0.191380i	−0.915969	+	0.401249i	$0.868576\pi$
$728$			8.32065e10i			0.296232i
$729$		0			0
$730$	−1.75146e11			−0.616751
$731$	−6.93824e11	+	4.00579e11i	−2.42985	+	1.40287i
$732$		0			0
$733$	8.93673e10	−	1.54789e11i	0.309573	−	0.536196i	−0.668696	−	0.743536i	$-0.733147\pi$
$733$	8.93673e10	−	1.54789e11i	0.309573	−	0.536196i	0.978269	+	0.207340i	$0.0664807\pi$
$734$	2.21668e10	+	1.27980e10i	0.0763692	+	0.0440918i
$735$		0			0
$736$	−1.73956e10	−	3.01301e10i	−0.0592828	−	0.102681i
$737$			1.02551e11i			0.347593i
$738$		0			0
$739$	2.19706e11			0.736655			0.368328	−	0.929696i	$-0.379931\pi$
$739$	2.19706e11			0.736655			0.368328	+	0.929696i	$0.379931\pi$
$740$	−6.16393e9	+	3.55875e9i	−0.0205556	+	0.0118678i
$741$		0			0
$742$	−7.01666e10	+	1.21532e11i	−0.231481	+	0.400936i
$743$	3.07763e11	+	1.77687e11i	1.00986	+	0.583042i	0.911150	−	0.412074i	$-0.135196\pi$
$743$	3.07763e11	+	1.77687e11i	1.00986	+	0.583042i	0.0987084	+	0.995116i	$0.468529\pi$
$744$		0			0
$745$	−1.53404e11	−	2.65703e11i	−0.497979	−	0.862525i
$746$		−	3.37267e10i		−	0.108898i
$747$		0			0
$748$	−2.40184e10			−0.0767253
$749$	−1.13333e11	+	6.54327e10i	−0.360104	+	0.207906i
$750$		0			0
$751$	−4.15260e10	+	7.19252e10i	−0.130545	+	0.226111i	−0.923887	−	0.382666i	$-0.875006\pi$
$751$	−4.15260e10	+	7.19252e10i	−0.130545	+	0.226111i	0.793342	+	0.608777i	$0.208339\pi$
$752$	−1.43198e8	−	8.26752e7i	−0.000447780	−	0.000258526i
$753$		0			0
$754$	−3.35902e11	−	5.81800e11i	−1.03927	−	1.80006i
$755$			2.13584e11i			0.657326i
$756$		0			0
$757$	−1.47694e11			−0.449759			−0.224879	−	0.974387i	$-0.572199\pi$
$757$	−1.47694e11			−0.449759			−0.224879	+	0.974387i	$0.572199\pi$
$758$	3.15828e11	−	1.82343e11i	0.956695	−	0.552348i
$759$		0			0
$760$	−1.17552e11	+	2.03606e11i	−0.352351	+	0.610290i
$761$	−3.42783e11	−	1.97906e11i	−1.02207	−	0.590093i	−0.107367	−	0.994219i	$-0.534242\pi$
$761$	−3.42783e11	−	1.97906e11i	−1.02207	−	0.590093i	−0.914703	+	0.404127i	$0.867575\pi$
$762$		0			0
$763$	−3.73123e10	−	6.46268e10i	−0.110091	−	0.190684i
$764$			2.66207e10i			0.0781352i
$765$		0			0
$766$	3.00108e11			0.871692
$767$	2.81190e11	−	1.62345e11i	0.812492	−	0.469092i
$768$		0			0
$769$	3.09706e11	−	5.36427e11i	0.885615	−	1.53393i	0.0406078	−	0.999175i	$-0.487071\pi$
$769$	3.09706e11	−	5.36427e11i	0.885615	−	1.53393i	0.845007	−	0.534755i	$-0.179596\pi$
$770$	−5.52133e10	−	3.18774e10i	−0.157066	−	0.0906818i
$771$		0			0
$772$	5.46961e9	+	9.47364e9i	0.0153988	+	0.0266715i
$773$		−	8.71283e10i		−	0.244029i	−0.992528	−	0.122014i	$-0.961065\pi$
$773$		−	8.71283e10i		−	0.244029i	0.992528	−	0.122014i	$-0.0389354\pi$
$774$		0			0
$775$	7.32975e10			0.203181
$776$	−3.64780e11	+	2.10606e11i	−1.00597	+	0.580796i
$777$		0			0
$778$	6.23942e10	−	1.08070e11i	0.170304	−	0.294976i
$779$	−1.31119e11	−	7.57013e10i	−0.356053	−	0.205567i
$780$		0			0
$781$	−1.55296e11	−	2.68980e11i	−0.417403	−	0.722963i
$782$			6.40064e11i			1.71158i
$783$		0			0
$784$	3.65556e11			0.967587
$785$	−3.09323e11	+	1.78588e11i	−0.814581	+	0.470298i
$786$		0			0
$787$	−2.43548e11	+	4.21837e11i	−0.634870	+	1.09963i	0.351673	+	0.936123i	$0.385613\pi$
$787$	−2.43548e11	+	4.21837e11i	−0.634870	+	1.09963i	−0.986543	+	0.163504i	$0.947720\pi$
$788$	2.65235e10	+	1.53133e10i	0.0687900	+	0.0397159i
$789$		0			0
$790$	1.46315e11	+	2.53424e11i	0.375647	+	0.650639i
$791$			1.82534e10i			0.0466269i
$792$		0			0
$793$	−5.10958e11			−1.29209
$794$	5.45236e11	−	3.14792e11i	1.37184	−	0.792031i
$795$		0			0
$796$	2.06159e9	−	3.57077e9i	0.00513511	−	0.00889427i
$797$	3.39906e11	+	1.96245e11i	0.842415	+	0.486368i	0.858084	−	0.513509i	$-0.171655\pi$
$797$	3.39906e11	+	1.96245e11i	0.842415	+	0.486368i	−0.0156696	+	0.999877i	$0.504988\pi$
$798$		0			0
$799$	1.53856e8	+	2.66487e8i	0.000377510	+	0.000653866i
$800$		−	2.38409e10i		−	0.0582052i
$801$		0			0
$802$	1.40597e10			0.0339842
$803$	2.89002e11	−	1.66855e11i	0.695087	−	0.401308i
$804$		0			0
$805$	−4.40480e10	+	7.62933e10i	−0.104892	+	0.181678i
$806$	1.54458e11	+	8.91762e10i	0.365990	+	0.211304i
$807$		0			0
$808$	−4.17376e10	−	7.22917e10i	−0.0979225	−	0.169607i
$809$		−	6.95054e11i		−	1.62265i	−0.584597	−	0.811324i	$-0.698747\pi$
$809$		−	6.95054e11i		−	1.62265i	0.584597	−	0.811324i	$-0.301253\pi$
$810$		0			0
$811$	−5.75064e11			−1.32933			−0.664665	−	0.747142i	$-0.731426\pi$
$811$	−5.75064e11			−1.32933			−0.664665	+	0.747142i	$0.731426\pi$
$812$	1.09219e10	−	6.30577e9i	0.0251232	−	0.0145049i
$813$		0			0
$814$	1.30768e11	−	2.26497e11i	0.297855	−	0.515899i
$815$	2.72477e11	+	1.57315e11i	0.617588	+	0.356565i
$816$		0			0
$817$	4.32201e11	+	7.48594e11i	0.970058	+	1.68019i
$818$		−	5.18655e10i		−	0.115842i
$819$		0			0
$820$	−6.54348e9			−0.0144728
$821$	−8.10334e8	+	4.67846e8i	−0.00178357	+	0.00102975i	−0.500892	−	0.865510i	$-0.666994\pi$
$821$	−8.10334e8	+	4.67846e8i	−0.00178357	+	0.00102975i	0.499108	+	0.866540i	$0.333661\pi$
$822$		0			0
$823$	3.29715e9	−	5.71082e9i	0.00718685	−	0.0124480i	−0.862410	−	0.506211i	$-0.831046\pi$
$823$	3.29715e9	−	5.71082e9i	0.00718685	−	0.0124480i	0.869596	+	0.493763i	$0.164379\pi$
$824$	−8.90324e10	−	5.14029e10i	−0.193125	−	0.111501i
$825$		0			0
$826$	5.87761e10	+	1.01803e11i	0.126264	+	0.218696i
$827$		−	8.55938e11i		−	1.82987i	−0.403601	−	0.914935i	$-0.632242\pi$
$827$		−	8.55938e11i		−	1.82987i	0.403601	−	0.914935i	$-0.367758\pi$
$828$		0			0
$829$	8.38807e11			1.77600			0.888002	−	0.459839i	$-0.152093\pi$
$829$	8.38807e11			1.77600			0.888002	+	0.459839i	$0.152093\pi$
$830$	−2.71924e11	+	1.56995e11i	−0.572974	+	0.330807i
$831$		0			0
$832$	−2.42870e11	+	4.20664e11i	−0.506852	+	0.877894i
$833$	−5.89149e11	−	3.40145e11i	−1.22362	−	0.706455i
$834$		0			0
$835$	2.72594e11	+	4.72147e11i	0.560752	+	0.971251i
$836$			2.59145e10i			0.0530539i
$837$		0			0
$838$	−1.12958e11			−0.229056
$839$	9.33975e10	−	5.39231e10i	0.188490	−	0.108825i	−0.402786	−	0.915294i	$-0.631958\pi$
$839$	9.33975e10	−	5.39231e10i	0.188490	−	0.108825i	0.591275	+	0.806470i	$0.298625\pi$
$840$		0			0
$841$	6.29935e11	−	1.09108e12i	1.25925	−	2.18108i
$842$	2.17731e11	+	1.25707e11i	0.433184	+	0.250099i
$843$		0			0
$844$	2.33835e10	+	4.05014e10i	0.0460829	+	0.0798180i
$845$			5.72295e10i			0.112252i
$846$		0			0
$847$	−2.40760e10			−0.0467789
$848$	−7.50775e11	+	4.33460e11i	−1.45187	+	0.838235i
$849$		0			0
$850$	−2.19303e11	+	3.79844e11i	−0.420116	+	0.727662i
$851$	−3.12972e11	−	1.80694e11i	−0.596742	−	0.344529i
$852$		0			0
$853$	3.17218e11	+	5.49438e11i	0.599187	+	1.03782i	0.992941	+	0.118606i	$0.0378427\pi$
$853$	3.17218e11	+	5.49438e11i	0.599187	+	1.03782i	−0.393754	+	0.919216i	$0.628824\pi$
$854$		−	1.84989e11i		−	0.347788i
$855$		0			0
$856$	−7.66394e11			−1.42744
$857$	6.55178e11	−	3.78267e11i	1.21461	−	0.701254i	0.250848	−	0.968026i	$-0.419290\pi$
$857$	6.55178e11	−	3.78267e11i	1.21461	−	0.701254i	0.963760	+	0.266772i	$0.0859571\pi$
$858$		0			0
$859$	−5.28165e11	+	9.14808e11i	−0.970055	+	1.68019i	−0.274685	+	0.961534i	$0.588573\pi$
$859$	−5.28165e11	+	9.14808e11i	−0.970055	+	1.68019i	−0.695371	+	0.718651i	$0.744760\pi$
$860$	3.23535e10	+	1.86793e10i	0.0591464	+	0.0341482i
$861$		0			0
$862$	2.59973e10	+	4.50287e10i	0.0470868	+	0.0815567i
$863$			4.06826e11i			0.733441i	0.930331	+	0.366720i	$0.119519\pi$
$863$			4.06826e11i			0.733441i	−0.930331	+	0.366720i	$0.880481\pi$
$864$		0			0
$865$	−1.72001e11			−0.307232
$866$	8.85186e11	−	5.11062e11i	1.57385	−	0.908662i
$867$		0			0
$868$	−1.67407e9	+	2.89958e9i	−0.00294914	+	0.00510806i
$869$	−4.82856e11	−	2.78777e11i	−0.846718	−	0.488853i
$870$		0			0
$871$	1.18139e11	+	2.04623e11i	0.205268	+	0.355535i
$872$		−	4.37028e11i		−	0.755863i
$873$		0			0
$874$	6.90590e11			1.18352
$875$	−1.50413e11	+	8.68412e10i	−0.256599	+	0.148147i
$876$		0			0
$877$	1.55974e11	−	2.70155e11i	0.263666	−	0.456683i	−0.703547	−	0.710649i	$-0.748402\pi$
$877$	1.55974e11	−	2.70155e11i	0.263666	−	0.456683i	0.967213	+	0.253965i	$0.0817350\pi$
$878$	3.27702e11	+	1.89199e11i	0.551444	+	0.318376i
$879$		0			0
$880$	−1.96926e11	−	3.41085e11i	−0.328376	−	0.568764i
$881$			1.97724e11i			0.328213i	0.986443	+	0.164107i	$0.0524741\pi$
$881$			1.97724e11i			0.328213i	−0.986443	+	0.164107i	$0.947526\pi$
$882$		0			0
$883$	1.84908e11			0.304168			0.152084	−	0.988368i	$-0.451402\pi$
$883$	1.84908e11			0.304168			0.152084	+	0.988368i	$0.451402\pi$
$884$	−4.79247e10	+	2.76693e10i	−0.0784784	+	0.0453096i
$885$		0			0
$886$	−3.23502e11	+	5.60321e11i	−0.524979	+	0.909290i
$887$	−1.19803e11	−	6.91683e10i	−0.193541	−	0.111741i	0.400098	−	0.916472i	$-0.368976\pi$
$887$	−1.19803e11	−	6.91683e10i	−0.193541	−	0.111741i	−0.593639	+	0.804731i	$0.702309\pi$
$888$		0			0
$889$	−7.35922e9	−	1.27465e10i	−0.0117822	−	0.0204073i
$890$			5.19976e9i			0.00828750i
$891$		0			0
$892$	−3.79041e10			−0.0598724
$893$	2.87523e8	−	1.66002e8i	0.000452134	−	0.000261040i
$894$		0			0
$895$	−3.08516e11	+	5.34366e11i	−0.480824	+	0.832812i
$896$	−1.69544e11	−	9.78865e10i	−0.263058	−	0.151877i
$897$		0			0
$898$	4.65446e11	+	8.06177e11i	0.715755	+	1.23972i
$899$			4.67280e11i			0.715383i
$900$		0			0
$901$	1.61332e12			2.44805
$902$	2.08231e11	−	1.20222e11i	0.314571	−	0.181618i
$903$		0			0
$904$	−5.34491e10	+	9.25766e10i	−0.0800326	+	0.138620i
$905$	4.91451e11	+	2.83740e11i	0.732633	+	0.422986i
$906$		0			0
$907$	3.20510e10	+	5.55140e10i	0.0473601	+	0.0820302i	0.888734	−	0.458424i	$-0.151586\pi$
$907$	3.20510e10	+	5.55140e10i	0.0473601	+	0.0820302i	−0.841374	+	0.540454i	$0.818252\pi$
$908$		−	7.31423e10i		−	0.107603i
$909$		0			0
$910$	−1.46892e11			−0.214206
$911$	−5.92130e11	+	3.41866e11i	−0.859693	+	0.496344i	−0.863910	−	0.503647i	$-0.831991\pi$
$911$	−5.92130e11	+	3.41866e11i	−0.859693	+	0.496344i	0.00421617	+	0.999991i	$0.498658\pi$
$912$		0			0
$913$	2.99127e11	−	5.18103e11i	0.430500	−	0.745647i
$914$	4.76508e11	+	2.75112e11i	0.682787	+	0.394207i
$915$		0			0
$916$	−1.53033e9	−	2.65061e9i	−0.00217372	−	0.00376499i
$917$			9.22018e10i			0.130395i
$918$		0			0
$919$	1.30518e11			0.182982			0.0914908	−	0.995806i	$-0.470837\pi$
$919$	1.30518e11			0.182982			0.0914908	+	0.995806i	$0.470837\pi$
$920$	−4.46801e11	+	2.57961e11i	−0.623681	+	0.360083i
$921$		0			0
$922$	−4.01993e11	+	6.96273e11i	−0.556282	+	0.963509i
$923$	−6.19732e11	−	3.57803e11i	−0.853881	−	0.492988i
$924$		0			0
$925$	−1.23822e11	−	2.14465e11i	−0.169133	−	0.292948i
$926$			5.59300e11i			0.760679i
$927$		0			0
$928$	1.51988e11			0.204936
$929$	−4.93543e11	+	2.84947e11i	−0.662616	+	0.382562i	−0.793273	−	0.608866i	$-0.791625\pi$
$929$	−4.93543e11	+	2.84947e11i	−0.662616	+	0.382562i	0.130657	+	0.991428i	$0.458291\pi$
$930$		0			0
$931$	−3.66996e11	+	6.35656e11i	−0.488498	+	0.846104i
$932$	−5.83537e10	−	3.36905e10i	−0.0773401	−	0.0446523i
$933$		0			0
$934$	−6.52170e11	−	1.12959e12i	−0.856985	−	1.48434i
$935$			7.32946e11i			0.959015i
$936$		0			0
$937$	−4.64545e11			−0.602656			−0.301328	−	0.953521i	$-0.597430\pi$
$937$	−4.64545e11			−0.602656			−0.301328	+	0.953521i	$0.597430\pi$
$938$	−7.40826e10	+	4.27716e10i	−0.0956985	+	0.0552515i
$939$		0			0
$940$	7.17444e6	−	1.24265e7i	9.18918e−6	−	1.59161e-5i
$941$	1.25303e12	+	7.23435e11i	1.59809	+	0.922659i	0.991855	+	0.127375i	$0.0406553\pi$
$941$	1.25303e12	+	7.23435e11i	1.59809	+	0.922659i	0.606238	+	0.795284i	$0.292678\pi$
$942$		0			0
$943$	−1.66122e11	−	2.87731e11i	−0.210078	−	0.363865i
$944$			7.26189e11i			0.914454i
$945$		0			0
$946$	−1.37276e12			−1.71408
$947$	−6.26905e11	+	3.61944e11i	−0.779474	+	0.450030i	−0.836244	−	0.548358i	$-0.815253\pi$
$947$	−6.26905e11	+	3.61944e11i	−0.779474	+	0.450030i	0.0567698	+	0.998387i	$0.481920\pi$
$948$		0			0
$949$	3.84436e11	−	6.65863e11i	0.473980	−	0.820957i
$950$	4.09829e11	+	2.36615e11i	0.503163	+	0.290501i
$951$		0			0
$952$	1.73160e11	+	2.99922e11i	0.210814	+	0.365141i
$953$		−	3.62461e11i		−	0.439430i	−0.975564	−	0.219715i	$-0.929487\pi$
$953$		−	3.62461e11i		−	0.439430i	0.975564	−	0.219715i	$-0.0705127\pi$
$954$		0			0
$955$	8.12358e11			0.976639
$956$	−1.39154e9	+	8.03407e8i	−0.00166596	+	0.000961842i
$957$		0			0
$958$	7.45753e11	−	1.29168e12i	0.885387	−	1.53354i
$959$	−1.93635e9	−	1.11795e9i	−0.00228934	−	0.00132175i
$960$		0			0
$961$	3.64418e11	+	6.31191e11i	0.427274	+	0.740060i
$962$		−	6.02582e11i		−	0.703583i
$963$		0			0
$964$	5.76034e10			0.0667021
$965$	2.89097e11	−	1.66910e11i	0.333376	−	0.192475i
$966$		0			0
$967$	−6.86133e11	+	1.18842e12i	−0.784697	+	1.35914i	0.144482	+	0.989507i	$0.453848\pi$
$967$	−6.86133e11	+	1.18842e12i	−0.784697	+	1.35914i	−0.929180	+	0.369628i	$0.879485\pi$
$968$	−1.22107e11	−	7.04987e10i	−0.139072	−	0.0802934i
$969$		0			0
$970$	−3.71801e11	−	6.43977e11i	−0.419975	−	0.727417i
$971$		−	4.29812e11i		−	0.483505i	−0.970338	−	0.241753i	$-0.922278\pi$
$971$		−	4.29812e11i		−	0.483505i	0.970338	−	0.241753i	$-0.0777223\pi$
$972$		0			0
$973$	−5.57431e10			−0.0621928
$974$	3.57898e11	−	2.06632e11i	0.397670	−	0.229595i
$975$		0			0
$976$	5.71394e11	−	9.89683e11i	0.629704	−	1.09068i
$977$	3.59273e11	+	2.07426e11i	0.394318	+	0.227659i	0.684029	−	0.729455i	$-0.260226\pi$
$977$	3.59273e11	+	2.07426e11i	0.394318	+	0.227659i	−0.289712	+	0.957114i	$0.593559\pi$
$978$		0			0
$979$	−4.95362e9	−	8.57992e9i	−0.00539252	−	0.00934012i
$980$			3.17225e10i			0.0343924i
$981$		0			0
$982$	−1.60157e12			−1.72226
$983$	6.95470e11	−	4.01530e11i	0.744842	−	0.430035i	−0.0789852	−	0.996876i	$-0.525168\pi$
$983$	6.95470e11	−	4.01530e11i	0.744842	−	0.430035i	0.823827	+	0.566841i	$0.191835\pi$
$984$		0			0
$985$	4.67301e11	−	8.09389e11i	0.496423	−	0.859830i
$986$	−2.42155e12	−	1.39808e12i	−2.56204	−	1.47919i
$987$		0			0
$988$	2.98536e10	+	5.17079e10i	0.0313306	+	0.0542662i
$989$			1.89688e12i			1.98268i
$990$		0			0
$991$	6.15925e11			0.638606			0.319303	−	0.947653i	$-0.396551\pi$
$991$	6.15925e11			0.638606			0.319303	+	0.947653i	$0.396551\pi$
$992$	−3.49443e10	+	2.01751e10i	−0.0360853	+	0.0208338i
$993$		0			0
$994$	1.29540e11	−	2.24370e11i	0.132696	−	0.229837i
$995$	−1.08966e11	−	6.29114e10i	−0.111172	−	0.0641855i
$996$		0			0
$997$	−4.36615e11	−	7.56240e11i	−0.441894	−	0.765383i	0.555936	−	0.831225i	$-0.312360\pi$
$997$	−4.36615e11	−	7.56240e11i	−0.441894	−	0.765383i	−0.997830	+	0.0658422i	$0.979027\pi$
$998$		−	1.14249e12i		−	1.15167i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.d.c.53.2		4
3.2	odd	2	inner	81.9.d.c.53.1		4
9.2	odd	6	inner	81.9.d.c.26.2		4
9.4	even	3		27.9.b.c.26.2	yes	2
9.5	odd	6		27.9.b.c.26.1	✓	2
9.7	even	3	inner	81.9.d.c.26.1		4
36.23	even	6		432.9.e.f.161.1		2
36.31	odd	6		432.9.e.f.161.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.b.c.26.1	✓	2	9.5	odd	6
27.9.b.c.26.2	yes	2	9.4	even	3
81.9.d.c.26.1		4	9.7	even	3	inner
81.9.d.c.26.2		4	9.2	odd	6	inner
81.9.d.c.53.1		4	3.2	odd	2	inner
81.9.d.c.53.2		4	1.1	even	1	trivial
432.9.e.f.161.1		2	36.23	even	6
432.9.e.f.161.2		2	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(14.2302 - 8.21584i) q^{2} +(7.00000 - 12.1244i) q^{4} +(-369.986 - 213.612i) q^{5} +(339.500 + 588.031i) q^{7} +3976.47i q^{8} -7020.00 q^{10} +(11583.4 - 6687.69i) q^{11} +(15408.5 - 26688.3i) q^{13} +(9662.34 + 5578.55i) q^{14} +(34462.0 + 59689.9i) q^{16} -128266. i q^{17} -138391. q^{19} +(-5179.81 + 2990.57i) q^{20} +(109890. - 190335. i) q^{22} +(-263003. - 151845. i) q^{23} +(-104052. - 180224. i) q^{25} -506375. i q^{26} +9506.00 q^{28} +(1.14895e6 - 663347. i) q^{29} +(-176107. + 305026. i) q^{31} +(99213.3 + 57280.8i) q^{32} +(-1.05381e6 - 1.82525e6i) q^{34} -290085. i q^{35} +1.18999e6 q^{37} +(-1.96934e6 + 1.13700e6i) q^{38} +(849420. - 1.47124e6i) q^{40} +(947450. + 547011. i) q^{41} +(-3.12304e6 - 5.40927e6i) q^{43} -187255. i q^{44} -4.99014e6 q^{46} +(-2077.62 + 1199.51i) q^{47} +(2.65188e6 - 4.59319e6i) q^{49} +(-2.96139e6 - 1.70976e6i) q^{50} +(-215719. - 373636. i) q^{52} +1.25779e7i q^{53} -5.71428e6 q^{55} +(-2.33829e6 + 1.35001e6i) q^{56} +(1.08999e7 - 1.88792e7i) q^{58} +(9.12452e6 + 5.26804e6i) q^{59} +(-8.29020e6 - 1.43590e7i) q^{61} +5.78747e6i q^{62} -1.57621e7 q^{64} +(-1.14019e7 + 6.58287e6i) q^{65} +(-3.83358e6 + 6.63995e6i) q^{67} +(-1.55514e6 - 897860. i) q^{68} +(-2.38329e6 - 4.12798e6i) q^{70} -2.32211e7i q^{71} +2.49496e7 q^{73} +(1.69339e7 - 9.77677e6i) q^{74} +(-968737. + 1.67790e6i) q^{76} +(7.86514e6 + 4.54094e6i) q^{77} +(-2.08425e7 - 3.61003e7i) q^{79} -2.94460e7i q^{80} +1.79766e7 q^{82} +(3.87356e7 - 2.23640e7i) q^{83} +(-2.73991e7 + 4.74566e7i) q^{85} +(-8.88834e7 - 5.13168e7i) q^{86} +(2.65934e7 + 4.60611e7i) q^{88} -740707. i q^{89} +2.09247e7 q^{91} +(-3.68205e6 + 2.12583e6i) q^{92} +(-19710.0 + 34138.7i) q^{94} +(5.12028e7 + 2.95620e7i) q^{95} +(5.29630e7 + 9.17347e7i) q^{97} -8.71497e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 28 q^{4} + 1358 q^{7} - 28080 q^{10} + 61634 q^{13} + 137848 q^{16} - 553564 q^{19} + 439560 q^{22} - 416210 q^{25} + 38024 q^{28} - 704428 q^{31} - 4215240 q^{34} + 4759964 q^{37} + 3397680 q^{40}+ \cdots + 211852178 q^{97}+O(q^{100}) \) 4 * q + 28 * q^4 + 1358 * q^7 - 28080 * q^10 + 61634 * q^13 + 137848 * q^16 - 553564 * q^19 + 439560 * q^22 - 416210 * q^25 + 38024 * q^28 - 704428 * q^31 - 4215240 * q^34 + 4759964 * q^37 + 3397680 * q^40 - 12492172 * q^43 - 19960560 * q^46 + 10607520 * q^49 - 862876 * q^52 - 22857120 * q^55 + 43599600 * q^58 - 33160798 * q^61 - 63048416 * q^64 - 15334306 * q^67 - 9533160 * q^70 + 99798524 * q^73 - 3874948 * q^76 - 83370178 * q^79 + 71906400 * q^82 - 109596240 * q^85 + 106373520 * q^88 + 83698972 * q^91 - 78840 * q^94 + 211852178 * q^97

Introduction

L-functions

Modular forms

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